Class 10th Mathematics CBSE Solution
Exercise 3.1- Aftab tells his daughter, Seven years ago, I was seven times as old as you were…
- The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys…
- The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160.…
Exercise 3.2- Form the pair of linear equations in the following problems, and find their…
- On comparing the ratios a_1/a_2 , b_1/b_2 and c_1/c_2 find out whether the lines…
- On comparing the ratios a_1/a_2 , b_1/b_2 and c_1/c_2 find out whether the…
- Which of the following pairs of linear equations are consistent/inconsistent? If…
- Half the perimeter of a rectangular garden, whose length is 4 m more than its…
- Given the linear equation 2x+3y-8 = 0 write another linear equation in two…
- Draw the graphs of the equations and Determine the coordinates of the vertices…
Exercise 3.3- Solve the following pair of linear equations by the substitution method. (i)…
- Solve 2x+3y = 11 and 2x-4y = - 24 and hence find the value of m for which y =…
- Form the pair of linear equations for the following problems and find their…
Exercise 3.4- Solve the following pair of linear equations by the elimination method and the…
- Form the pair of linear equations in the following problems, and find their…
Exercise 3.5- Which of the following pairs of linear equations has unique solution, no…
- For which values of a and b does the following pair of linear equations have an…
- For which value of k will the following pair of linear equations have no…
- Solve the following pair of linear equations by the substitution and…
- Form the pair of linear equations in the following problems and find their…
Exercise 3.6- Solve the following pairs of equations by reducing them to a pair of linear…
- Formulate the following problems as a pair of equations, and hence find their…
Exercise 3.7- The ages of two friends Ani and Biju differ by 3 years. Anis father Dharam is…
- One says, Give me a hundred, friend! I shall then become twice as rich as you.…
- A train covered a certain distance at a uniform speed. If the train would have…
- The students of a class are made to stand in rows. If 3 students are extra in a…
- In a deltaabc , angle c = 3 angle b = 2 (angle a + angle b) Find the three…
- Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the…
- Solve the following pair of linear equations. (i) px + qy = p - q qx - py = p +…
- ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic…
- Aftab tells his daughter, Seven years ago, I was seven times as old as you were…
- The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys…
- The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160.…
- Form the pair of linear equations in the following problems, and find their…
- On comparing the ratios a_1/a_2 , b_1/b_2 and c_1/c_2 find out whether the lines…
- On comparing the ratios a_1/a_2 , b_1/b_2 and c_1/c_2 find out whether the…
- Which of the following pairs of linear equations are consistent/inconsistent? If…
- Half the perimeter of a rectangular garden, whose length is 4 m more than its…
- Given the linear equation 2x+3y-8 = 0 write another linear equation in two…
- Draw the graphs of the equations and Determine the coordinates of the vertices…
- Solve the following pair of linear equations by the substitution method. (i)…
- Solve 2x+3y = 11 and 2x-4y = - 24 and hence find the value of m for which y =…
- Form the pair of linear equations for the following problems and find their…
- Solve the following pair of linear equations by the elimination method and the…
- Form the pair of linear equations in the following problems, and find their…
- Which of the following pairs of linear equations has unique solution, no…
- For which values of a and b does the following pair of linear equations have an…
- For which value of k will the following pair of linear equations have no…
- Solve the following pair of linear equations by the substitution and…
- Form the pair of linear equations in the following problems and find their…
- Solve the following pairs of equations by reducing them to a pair of linear…
- Formulate the following problems as a pair of equations, and hence find their…
- The ages of two friends Ani and Biju differ by 3 years. Anis father Dharam is…
- One says, Give me a hundred, friend! I shall then become twice as rich as you.…
- A train covered a certain distance at a uniform speed. If the train would have…
- The students of a class are made to stand in rows. If 3 students are extra in a…
- In a deltaabc , angle c = 3 angle b = 2 (angle a + angle b) Find the three…
- Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the…
- Solve the following pair of linear equations. (i) px + qy = p - q qx - py = p +…
- ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic…
Exercise 3.1
Question 1.Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.
Answer:Given: Seven years ago, Aftab was seven times as old as his daughter and after 3 years Aftab will be 3 times as old as his daughter.
To Represent the situations algebraically and graphically we need to find the linear equations for these situations.
Let present age of Aftab = x
Let present age of his daughter = y
Then, seven years ago the age of Aftab and his daughter must have been seven less than their present ages,
Age of Aftab seven years ago = x – 7
Age of Daughter seven years ago = y – 7
According to the question,
Seven years ago, Aftab was seven times as old as his daughter, So
x - 7 = 7(y - 7)
⇒ x - 7 = 7y - 49
⇒ x = 7y - 42
Now for finding different points of this equation, we can either take different values of x and put them in the equation to obtain values of y or vice versa
Putting y = 5, 6 and 7 in equation (¡),
we get,
For y = 5,
x = 7 × 5 – 42
= 35 – 42
= -7
For x =6,
x = 7 × 6 – 42
= 42 – 42
= 0
For y = 7,
x = 7 × 7 – 42
= 49 – 42
= 7
![](data:image/png;base64,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)
Thus we got 3 points to plot on graph for this equation.
Three years from now,
Age of Aftab = x+3
Age of Daughter = y+3
According to the question,
⇒ x + 3 = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x = 3y + 6
Now for finding different points of this equation, we can either take different values of x and put them in equation to obtain values of y or vice versa
Putting x = 0, 3 and 6
![](data:image/png;base64,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)
Thus we got 3 points to plot on graph for this equation.
Algebraic representation
x - 7y = -42 (i)
x - 3y = 6 (ii)
Graphical representation:
![](data:image/jpeg;base64,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Question 2.The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
Answer:We need to form linear equations for the situations.
Let cost of one bat = Rs. x
Let cost of one ball = Rs. y
In first case, three bats and 6 balls cost him 3900 rupees. therefore our equation becomes
⇒ 3x + 6y = 3900 ........(i)
Dividing equation by 3 both side
⇒ x + 2y = 1300
⇒ x = 1300 - 2y
For plotting the equation of graph, take different values of y and obtain the value of x from equation or you can do vice versa
At y = 0
⇒ x = 1300 - 2(0)
⇒ x = 1300
Now finding the value at x = 0
⇒ 0 = 1300 - 2y
⇒ 2y = 1300
⇒ y = 650
![](data:image/png;base64,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)
From above points, we make the graph as follows [Graphic representation]
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHSCAAAAADgHKPWAAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAABIAAAASABGyWs+AACAAElEQVR42u29DagT17rw7/9933vvOfee+5733t7j3tba2tPaU9tjT3u039/WahU/qmgVq2hppS1aWqpYWpSWlopUKqKUimwRUUTcyCaEkBBCCCGEzWaz2YQQQgghBIZhGIaBYRiGQJh/Zj3P7Fkrs1ayP3VvncDJc2bvn5NZvzzdWbOy1rMWObbmuA8IrbhFgtpyg0EOMCCnpEgAAINhOl5oDb3zwF/WXjOcJuBakwrA6QnyIx5gGuSgMEYBPK484vh4S3WooNkkpBT32YLzWQbVKB2AjER+ozt+QABDtu74uM3hmnHyKx0k6bQkwBtnSiKLnm2Tb3Gi1WpSZLGLTLQIwUi0etgujQotQqgMBy0yMms5oUW0AzLRos3h8lWRxQnblkgmtAZlLqpXi3X3AaE2WCFHhZr7XIIDCMiND1GAx5XrfsgcWbtk6RtnRstBrkx+VrxNvWC9WKUCAPVMilxLoU4FhsslyUG5JOSGxt3nCgEweAA0KjLGAWpUiI1QeAUuFgIC1cGqSJIbGsOv/cc/kg0x4NqmJTEWkStwbKMksUzQgkBpUGgRuWyyh+18ImiR4YZjQotoOzoisoghPiyShK3GzOTJ9ADS3kVNS226D5MEO2aQI8V2nzU4gICclKQADDpwENS0eeu9B/vfOK86rU5OJ6eLkx9ZCvzGooJBgOb4KLkWADCoFhWKw00f53JJiQBa0w8eYJKQbpBWA4ABAAyZGoWbtCRsjRUjL6XB+bROrv7Wy8teX1PkW8QQ10UWEVB4tuEfQVATQZkGDehxoUW0UxzpYbucD1pkZFazQotoB2TyLCKXq/AtTnB2zPQtsjLxRCBzUcfnAPxhd7Rgl6PJdDkA4HFa+1PSuL1r+ZLXzzU6OLNnlwM+TYvj5FoAaPG6HKP0hyDD6cDxuhwa1YfALgfblWBOxOtyYNDoLgf7IehzuU9Kfx87PMS32AQOuxwa0+WgOa/LEbTYRSYDGAmhRYvpcvAsAsd2OViO0+XgAE62IbKIIV8D3BJxLY5tr9UIQJdjVhKafiu0JLzb7z/c99KvKpz8Pkhol2sZtqm0z2tX26doOdZT9fYzP6EhhAm9YBLaceTkhyuWPP9tOfBW3JMJHdvUvpG9/EYjv+GV28ax1Ydd0HyqJrIYJvTcJXQLmoUhARcApzJtKiCgpikAg2VTQU9NnG/408cXP/t9zefgRjVJ/1vmRDZcbqkQ/JUBzddJqIzSOI9Lk7t1G95aDAjAe5WRiRL4TdMMnijXoPAmNB4DAK045JcLjG1/Ju803nmsevjkxd3xTZltEfdln66LLHq26QYwFlv4ZqY4ti2K48lELRCsBMcOBNRSHhNahFAbCVpkuEZeaBFt5ySRRQzD8OfDbAYlIZdoimR6APnZotHh3Kj7wHBtmIQsec4NU2EEfpa5CcAIFfL5UT9kb4x6+PjI5fXLHlh5eHAsR3G566PU+XgnikYogMfFh6gX5HI3MlSjMDCNupkWARhupSicx41cG5kAyvldWfvMwTdKeweS687vknf8Wm3/5rGoyCKG63mRRa81N3rY5slkgHxP2yCTvbAczSVuCyVBo5KDPQCU2cX2YLKn7WGRTGwUyFxUKoyW3AeE4s1xcjRCnsfGqVAEbngQgCIVGG7kVsnHy6OxwyseeHj3tVJ5AhilgdJokQrjY+QgmSAAXAQGhkvFSj7ewRVIGBymzoeBAW7n/VaXCjSAYShL4YwkBIo3ya/G3Ge1sSuXffvTlbEPB5LvXtgp7zgrtX/zeFJkEU/k2S6KOJQpts2TybR67KbQInIgk2sRQiYatMjIzEaEFvFEQzmRRQyRTGlCZlfbdOM9oEjJnOhyNGfe5TCZLsfEh2D56D/6Vnw54gi6HK3gp2mR0+XQeV0O4Yfgne5yOPUd7YR++v+e+er4mX3pzUNb4850uxzmZLsctEzPdisAsF0OxuJkuxzVLl0OaPwsdzm4XO8uB2nvnN0U0h32ys/P9D9+MNu07t2bQuXr9jUXDihjm95MWieeP+42JLwpvJdGOZgXcwo//HPxYwdiuug9WPAJ7djtn7WaTcv9j7YF/8hLaCdoMUzoBZ7QmlO/8OqSZe/H7Hs1oY0gZz5dvXlWd6QzV20nTGjnTiU0fmkFoVtCA6ekOYqBM5mEDly1euHl/oe3xw0zySimT2SJExoV60xCm0KOk9AOL6HhNzYNYMh1SWhoYRzmCsH5IDRpznq69vEff3Z++eNuKqFp206CTmjGovdecf58sAnNkWnRgMkkNGMRtZTFCQ2hSie0w8nXek5osVtC0xwmNMdit4Rmcgz70IYmGe4Dgh5VyVFDd59lOICgNchBLWH6gMcphh8aMYPCKc60iufeWrJ0/YVByz2FHgAMQ5HdZ3N0mAI8TvODOZ4zfZzlJMKZ8ZobVAJgYIFkhfwGGo8BAAhmqkxeQ1JFnBbRfAADI1NZWSosW5b465KxgEUMUUVkEYF6nCOJ5qQYI4myiEGOiix6tsdyQdsSbbuQNSmZQc4spU2BRdSCMrvYzhQp24xFbJQeUX2LrEy0AzIXWbpsuQ8IZlQjQTLdoJADDMjVEwAYNKdSnBQnB4ZEAnAYVF258s7S/tWX67YAgBONjVBn4HGFPDlQFeoiMMg6+VWi7j5rBMDAAska+Y0cBDCkK5aPs5IAMKK6SBIEdWXJOvunh//jexFgRlWRRWx1Iy6UBEGOBSUxgBIzRRbRznheaBFCMSuUBEA50wNAmTyLGDIloSTPtiaw7eUiyLyDXQ74ELSub1784JsXdO+zxuvVTbLLoU2/y9GaWpcjOxtdDsd68//7hxK0eJe7HNr0uxyt+dvluKM3hdRbofyw/eElr/4uGZTbhX9TyLmdIaMcv/7hq2bQYnhTuNBHOai3wkg1I/se7X/5ZCOg+B5M6N/+eCxM6AWX0J3zoZ1uCe2+B83cgb8uXv1TdZ4ktM25gZ/5sJ3b5XAu/OEoL6GBY7ocPNszT2hzJgk9gy7H9BLaENru3eXAhGaXB8xoxQpwSqIZXE1Ar7VQ3TUULTu59/H+1d+V1Ca11kK/qytW2BNNYsUKs4YiyOlPVZrNwvGUGbTYZcUKcrgEJSGySMvsWLGi39UVKzyg64oVEma+YsWOwYoVTalr7gOCGpHJUU11nxtwAAG5Slz3AY+TND/UotT5WE4iQB0AvZr99Im//O2TnG50APpw3n0NtUY4DHUFTuQGfTRLLkJqaAJOj1XcIBMAAwskyuQ3dQrQAICgJ4vkNeoyzdUpThlSRJIgSE+Ot89jy0JAi0giiwq8Ri0mssjKxLYh0KCARkRkETmUybVNgj6e1gMWaU4vpCiAsYj6UKbCsYi2UwVdJAkahZnJs412QOYUuhzAzU6XA4HRL1f2PfX1SGtedTkmMcqBXY4m3XhBl4Nv8d7vckxilKNFcbPX5bjzN4XMe1A7tqrvsU+GcV7XPXhTGE5OIjIX2E3h9BPa0Usnn12y4lDUot6KMKHDhHYWakK3nxu/vNj/8AepZpjQAS5M6AUybNfxHsi/rul/ZE/MtMOEDhN6hgnddZSDc99d4dx3c0c5aiKuzgLkPlkfPv1637INF8vuiIc+nAved9fo+/OeoxwaM8rBcHDfrbGjHPXgiZJFCu8Y5SCtwVEOPF+dvu+WcZRjTGQRQ89Rjmov2xyZE6McJLCjHLXgKIfWZZQDOBzlENsupIQW0Q7I5FmEoKfGgxbZUY4hmW68HMgxFUc52JFRHO3DcjY6PcTqjUOnOCOjdM0fdhxatakAgAaAzQIt7fLbS5asv2E4rVZhrEUNaKqBkdFWaaRFRkbF49Ap2R8Z9UoJ0UCrV+WkFo5D48goh7M5lZMYmcZTFdoibxyaHvXvUjmJY7GLTGyuwYxDBy0i0CqO0LaD49Ctch5scwojAVDNtgQWUQvK7GI7V2kJLE7YDo76d1ROIr+aH10OCNqNTQ8te3tAuQtdDs6JplFoZjLDdsw3hfG5H7abUZdDn1yXo363uhwsME9uCmnF2vUtD/W/eSlfCJoJ+9BhH9pZEKMczFwOyxza9ejSZ7+pO2FCu48woaee0Hd4PvTEe9ChmABkJm/yw6UPvPCL3DnLZcZLsKY4H3pWlmCJLC7cJVjzeD40LMEydcl0HxCMqEqOGob7rMCBrPqAWU+QIBlUQA5CI06dj8fJMQbQqaAq7Sdbv/zOY/2rT4zJFrkkDjeeNydwD2C5RJ0AMs01oDUaCcmq+6wBgAEA5NJlCu/gSGv0qE6dDwI2SiNBXVkUWcQQVUQWEUCZYts8mdBcDEqUY4fhQCbXIoRi1vRlGowkibS6nBZaRDupisgihkxJZBEBI6r5FlmZaAdSd5H3zzROQvP+dS0RvJouCd3QaU4RvQcYALDGhrOHHl+88si41U5pvRHkxnPUW9ahmJfQ9FshCRPaQHUQUkxCS0FOZxUzHAkKJLQsTGgDE7rRK6E5FjFIHJkM4CU0xyLawYRuCLmeCV2iE5q16CV0WWTR4CS0NrWE9gDS3nnY5SBfrLRGP39q8apvxsIuh8BiuOpb0OWYXzeF9DeFha/+3vfk4VHvquf5TaHdpAAHZqaEN4X3/SgHndCOXjm+qu+JT6GE3DxPaPVi3f5ly3lbOf5JzRnadd0lwoS+m6Mck54PLe5yzHJCu0oqp9csWb4v05yzhJ6lVd/yxyuGR7/+5d3I6T0Hvyps+2qre4HT63KwCT3JLseCnA9Nc7M3H7proRklWNWjlgiWPplcoZlutVHYEimjwx5gmeWTf//LI3tSmqxTJVLGc1QpFW5Bml6FZoxehWaMVJmqlNKr0Mz4qc1Zs2Vu+/3AxeTGge3KzouWW2imKLI4k0Iz8uwWmjHGckKLEArZoEVGZikttIhleEBmF9uZIoXPqNBMIh5JuI8YCfGBGDmKxN3nKBxAQG7oMgXwuAgAiHO46IAQiEXJwY0bFJC8/OVz/9P34tFI0uduXk/4OHLs+S4PUedjOLzYK7dFAIargxTOcPga8QG/URXpg9i4+uO+2p6B+Nqzu6Ttp8fjicgjV0UWMQzQ5+NxkV62eTKZi+1tG2RyLUK4dU1sm1zE4FXGDg3gxV4N2mZfg7HNpOSE7ZhQEpwIgFntQ5Ogcj4Emc/C3htvsnM5dEf9/bUlD22JGE5Hl8PkfAh22XiT0+XgbrwJjRJ3OVpMHxq6fY1duebpgw3n4Pno1hvbGjuuOV370OzGmxyLXTbe7N2HNijAENvu0uXosvFmzz40Y9HrcnA23tRojt14k+YmuhxWQKbN7UPP25tCWp0+sG7pQxuumB3DdvPnprCxKz+07K0DI1feXXu68cG7O933J7wpDEc5xBP8G9feW7p07TX4D3n+JbQ9rFdOnTxdNm9d1p3COVIUP0zoMKG71LZzrBtuCbGzbqbOv4TGcWi873aYgudhQofDdkEzLmAndi3rf/mcNP+G7WajjEE4bDcrw3aCJVjUQhemqoferdAM4WoxAqi9Cs2oNREgLDSjG+qV7cv7nj8ZzRvdFwXpsap7CqbQjNZRaEYEdBSaUTiLguAFJ1VophvQZQkW6NNR5hQLzdAAt9BMXfVbPcVCMx11ZAhQ7F1opkQVmlGmWGhGozKzd6GZyZcCg6UwvFJgmk5xCmc7daZGlRrvAWApMARYTjPyBx/vW/FZudXqVpxqEqXA6uQ30HgINtaUgpCpUjgriVcKTDUCnL6yIrLo2aZLgTEWkZMTQkmTLAWmiW13KwVmUqGjFJgd4LAUGM+iuBQYy2EpMI7FiUpfRkCmySsFdlcrJzlT63JgyH3y2APPfVu8+8Uaw8pJ87BY40K5KaS5VmL3U31PflWAnfjmx01huGJlvtwULsCEdspjha+fXrLycKblhAkdkHmfJ/TsjXKYU0ro7vOhuyt2RznqPzy3+NGP8i3HmUlCz/WWFM6URznM6YxyTHE+9D25JQUmNHfTIIuzaZBBbxqEAAYVOJXZNEjmcJx9bmThpkEmACbDyf6mQXbp21X9f/0ohXvfsBx30yBqIxwrRTYN0gHQZ2HToCDnbhoksAjBjKkii54+dtMgyuJkNw1SY0KLHZsGCbliLmiRkYmbBvEsKpPcNChbElnEVpucLZqYHEOZi9j5X3qk1/yvWq/5X/Wes+2iDMCZ/+XPthPM/4IJYqY6eualxcu3XFUtgz/bTpGoeWfeBDGYr8WZbce+YLfZdqQ13G3dGhSnrCyILHqz7eQetic7246ROeuz7TJBi4xMZrYdD+DPtqMblWZm2zWCnDfbDhov0ZIQwNl2d30JFg1MfeNN5cIr/ct2urVLwyVYk+9yhEuwnHl2U0h9U6j8/ubShzfc1J1pJTQ0PrwpvIduChd6Qrf/QFxb9+CDG65J9FsRJnSY0PDThZfQbUC7se3hpW/8LjthQjv3e0K3bK3lPiwSmnGTHKlN91mHAwjIySkKwGDQnJpsUTjLGe6zlgBAhd/YVADArT7qXgsAGDSaK42QA9NAoN34oW0P9r12QWsbJL9KyQTQW37wTmSRkG6QVgOAAQAM2TqFW7QkbI0dIy+lw/n0IGc+VRVZxBA3RBbRjpIUWewikwGMuNAi2gGZXNsQKvmgRUZmLSe0iLZBJs8icrmqyCJyzbglkoknApmLNBkmf0BQh2BqDDNdpj6l+tBVTsViDA0ye6UeEQJYsXg4R82T4XGjGc3HgdMbl7YtX/L8ySxcGNSHlmD2ilSnGoUVi+Ml0mq2PrRKBXF9aNWrDy1T50OuRnENpj50PVgfWo00RBa9+tBRkcXJ14dWe9geyVK2eXWkx9JBi4zMQlJoUVwfmuWY+tCMRZWpD13nyGTrQ3vrWLxFQfBtshrscti9uxy9lmAZk1yCVRgPfjqzXY4Rx8dbKnzG6a30/uV9//iJfLrxuhzQqN5LsCB0WYKl0l0OnelyaBTH63J02J7BEiyxTG8JFglGotXDNnY5VLqn0GUJFiOpyxIsBKDxvCVYDMcuwdKCXPPeWoLVow/tBTt7cEXf6h+LYR/auW/70PdUQrvqDj/R9/fjpbRKvWVhQocJvWAT2mgWjjzV9/edaeotCxP6fkrohTo5aQIPcsWTzzzw+KcjrXBy0n04OUlX67r7UBrusxaRyVFdc58lOGiQgFw1TgEsB6EW0ymcwzWiDKBSQZbIwUieXAsAGocby+o+HuQMY3zvE3957OMkXDnLNRQSEmW/1V7j4SoxJEsUzuPUiEqdDzlapvTkeMAOthqCFpFEFpFDmWLbPJloEYIUEVpEbjTXw/Z4RmgbWl1MCS2iHZDZxXa6ILKIrdYiiiglPYD8bJFtKrb7MEiwYjo5ki33WYUDCMg1khSAQQMOgpywKZzlNHK6OA0oJhV0Atjjo+RaZJsKDFcctn2cxzVT+V+e71++fdBsupxKAwYJqTpptWpTgTlRpgqNN3w7ExxpjRkzfaCDI0FfWRZZxBDTRBY9fQmRReQUjky0CJwWE1pErjDcw3YpB7ZVDkdaXckILaKddFVkEUO2LLKIgBUzRDLxRJC6C2rVtzOJPrT3TaHqyGee73tkd8q6M12Oye6CBUC46tuZq1Xf99pNIf3Vt3z+taUPb7ll2XRfew7rcrScJv4HEtaHDkc5qLdi1vYpbNYH3lqybNNNKah4lhO6+EWpdeW1Y0Z594Z88+xrP7m/ChP67oxyQLMwJPArIlBiU6EFp1ehywEHGNhRDsh4xPUWxcGiViPJA4KjHOxrMBwzytHBwVsB49DtP83G1U3Llq4d0CcaZQCQkQnQZT50g8JZSfiWUV2O8o4n8rXNF7ff+ubwyY9ymy5tcS1ZT9dFFr0uhyWyiBzK5FjsIhO1AIBdDp5F3Fm9PCa0CBx2ORDXaA7s1PNCi2gbZPIsckc5GA4vDBKaJxMBnA9drxbr7gNCbbBCjgo197kEBxCQGx+iAI8r1/1QuE2dr16sUaFMgBIANQSqAaCeSVNAB0dCLkkOyiUCFOpUQG5o3H2utIFG6bfXFve9dqHYYE4UGfOAiVCD1uCJYiNU4ytFisNWVwerE0Dp5vZ8drP08bf7LiXX/75D3nlebV/eipzIIobBMnW+Mm0RgcKQyCKGIiszCJQHhRaxNdmk0CKEfIKRFORGYkKL2PjoiMgihviwUBKeDzKTJ7OIAGnvolwmlXMfELJX0iQks25IkQMMmSQ5SFwjAQAMaZpLAoA4h0tdzcFrCE90e5ACPC5DhcgtcpBOCblrCR8YTpza+OADT310M593Xx6A63G/1V7j4SIw3IhBozJC7kpmAqhLu/LpLdJHX++9nHjn3C55x5lSNpd69JbIIoTs1bTIotcasW2xTAZIX82KLIKd3NCtoMUUzUVvMrZpScDFbggt4olAZhfbN6OTtM2RiQDIXOS04A97i+ly6E7w7zsAvC6HRXM62+VgOPpTsuNDkP40LRU4H4L0h2UFuhy2FeQM4Ca6HCTYdmrPo/2rz0pOR5ejCUCT03fp0uUAoAWbv5gEaOzMFTeOfPjb56eu7YxsGXt/0H1ZXpeDtU03wOJ8mnpdjqBFvkxaCwDWtLocaBFCFaaC2RxJTJejKQScnCSyiGEY7lhAZovHJZoimR5wjyzBmmRdjlZi36P9L3xf9YbZZvmmUDowYn295oN6fO3LV7VDaw66Lx/eFIajHHOX0O0Wpg6t6Ft1YhT/Qs9uQrckyzGGpZZVGm86Wp68epjQYULPZUK3P8Xzn65Y8vRxcvbZHoc2aa4F32mECb2wJydNLaFbs5DQgslJjnA+dKt0fOXiJ46Mh/WhnXk8OWlG3xSyX5zjXA6LM5fDgC/nYS6HJZs0B5MCIHhzOQAHDgPMLvCmH/AA+JZ/bIQCeFwhb/s4XoQJAadqJBv+9IOJWQgwa+CLp/ufOJJPkLkcOjQeAgIYYPoBno+VhC8YJb9SQBIEhtM4cznQIgQrpoksYqulhMhiF5loEWfOxCyRRbTjzeWgG48WZRI65nIEOZzLwbOIdti5HBwO53JwLE7Y1gUyvVwEmYt0FeY0qQ1qTpMO05gkhQoAGNW40X3+Vz1mBGZCYZDpCWKaEDBG8kZwXhc1/8sYyxrC+V+EM+JVl1BgPhkGAhiyVvj+ub88+vZNzTQm5n9RgMelSoZ/PpWeJ4acBrPtOJIwyCsL3QGdN7cRgubNtgvalnEKoVAmA0gM0AjOtnMrJ4lsk+BWThJIQqCYEgOk1UaSyORZRNvpoiGS5NlWRDLRDs62u+uVk6Y2H3p2Nq+vn179wPIDSTusnOTMxy7H/V05aXrldBtfrFmyfFsU13CGK1buoZvC+zOhnVzh99f6l225aYveijChw4ReSAmdkR3lyvqlyzZc08KEdu6phIafcutymPSrACenAGhSgVeXA8/H4SZRl4N8GdvEggwQmEoRJbouB5fDhAYlpk41CoG0O2xnXl374JJ1V4wmp+SEl9AWdSKm8kS3uhwkeAmNFs0AgO8BzyKT0F1saz3rcsSFFpm6HF1sY0IzFhmZk63L0aUKCrcuh8bYtnyLDOfZ8bZ161I5qd6rcpI6l5WTlElXTlKDNX8mWTlJKV7a+PCDr/w0SnY2q8KJqjOvnETCnaicVJu9ykmMRZniulROqnEqJzEW0U5CXDmpKq6cVKO53pWTSHMWsdXWsIIYFhybYm07o2dtOwLoUI6tCYDWpILZs7adxq1tF+Sgtp1F17ZrMUBaIoDh2LGdyxa/cF4lfwsoDmvbYbU1Tg289l9oH8DAyJxebTuDKdvGq21HcxpHJlo0xbXtICBXGu1huzIctMjI7FLbTmdq24krCebp2nasJM82U9uO5rzaduRX928f2v/q24rvfnTJy6crU97WLexDz8s+NP2v78uEdudYfvzXvud+GKNPFCZ0mNALN6HN5vDBJ/tWnSg4YUJTFhdkQt+P3xQ6vMlJY18/0ff0V8Xwm8JObmF9U2ioDfdbdAw6PZfD3WvID8hx5nIYkuxzBs7l0BpBTnY5oxE1BHM5AODO5TAamh9w+oG7yRX1ZT9y1FwOBBiuDZCfJSodgGHqyUN/W/y3I5maaUzM5QC8QxI9l4ORxHLyyoLBt+iFKDWXg7HY1kcuth4zRJKEMlmAmcvBWsTGg8xOi8aETJzLwdqmZeJcDjGAczm4Fpm5HDyLzFwOrkx2LodlwG51EHA3OAs2gFN1KsCmcO5sOwLA/oMyZ5/ChE3tIcfhFNh7z+QAGtlqzp1t5wMeR+2c586283Ee5862c3e6gx37MACgAJCq2VbHPoVtYPz7Z/of25Nyp2+lKza1c14HB64Maic+CIxMbWVZYNELMU1kEVuDMllJNMeTCVowePsUBi16tgvDPWyXcnbAIi3TnW0XsOMBpNXubDvfDodzZ9sJLE7Y1kUy0Q7IvM/mQztOr8pJ9e//sfixj/LN6XU55vt86IVRrDGsnBR8K2ZQ8Lz280tLln+QSDcoPLwpXDg3hWFCd7wVji6ffbl/+Rs3TR8PE/oeTGjgeAk9H4s1TimhAx+Wyu/v/GXp5htm94Ru0pLmpsvRM6EXcLHGFsXN4hIspsArFi1lC7wytUulqZXTVSwqAIDldC0OwJbTVRiOLafb9HFuIdikRNbo4BIsrFoLrQFAXE7XDc2WeuLFJQ9tuKHohojjldNlZGI5XW3m5XQ5FrvIxObqTDldcfHiApE52XK6NoerZPkWfTtQm1hku/3IVkQW2XK6nkwjAHjldCeqS2MJblgAVINq1T0Lntd6Fjyn1/xIZI3OFAue8zi24HmNGnDyuHiVALBGBwI2qi4ueA4ABCM9cmnj0iVv/FQxDD6nwhCnJ4kp1U0CFjznWWQLntd6FjwPWsRQFxc8l7DgudbD9miWtlgLcl7B86AklMkWPGeALgXPGY5b8LxOc6xtXsFz0pwFM8oxlS0pnNnYvL79KWlGtj3c99ol5Y6OckxrSwqmy3F/b0kR3hQ6XSb420PbH+l//Yzk1X2mDXa5KXTCuhwL4Kbwfkxo92/kh3/tX/1TMag4kNAjP6Sa+tXzmjP2E3mHw4QOE3r+JXT7fKn9j/U/933F6Z7QdmPL5o3jlzdt+Kn2wZbtLh0m9N1I6Hti8/ogN5ub1zv26KeP9T39TamtmAI6Nq+3R9+Kbb750fnYlutbGzuutGY4wR/tTGfzerPn5vXaPbx5fTwWibsPDANREobIcyRKBQSGLlMAhmiUCgggDs8YAIgMMECMCniiG9eD/5bhbl6jX5e5FuQuk6Movm4kCFy5TV1ELBI80ZVBH0/ETm985IHHdp8dSvhA7FKMvrB0Y8+TGwt7B+Jrz+6Stp8ea2OPXBFZ5NlmLLK2ORa7yGSA6IDQInIok2cRwq1rQYsMN3hVaNGzPdjD9tVbFM7lBmIimR5AfrbI0mGGBwQzCjNfJDLfQ4EDCDgTpJ6gAAwqzUlxevqNZFBBJdNbZJguY0giwBobIdci0RwzraaQh+k3CsVhkGH2SqLuAxOcSQHJGjVPhgEwpCvU+XTVKn/z9/95dH/WanqAAdNlPEnG7Y35D84cuJjceHm7svOS3W7NypLIIgQzpoosenbiQklimQygMgA7OQkaP54XWgSumOVJorhyRmgRTwQy2VRjuEyJajzDoR2TtU3L9ADS3tnpQy/0bwq5m4YHJieVT6zqe+KzbFPQh06/8936y2d27TlW3PbpVnfxC3fYDvvQ8LpsH3pa3xT26kPPwjeFPfvQvGG76fWhjan1oZkThTeFzqRuCunx5fKJF/r+uietQAM6Erp1c+95Uz3xRcOJHBh02xveFIajHPM8oW2zceb5Jct3Jt0f8sahcbzagdaECX0/LsGigTldguXwEnrqxRql39/sX751yGS2dbt/lmDxehTz45tCbwmWJhnuA4IeVclRQ3efZTiAoDXIQS1BAR6nGH5oxAwKZziFABIAOg+Q3WdzdNj0AY/T/GCO50wfZzkJuHjNfVYJgIEBzGSF/AYajwEACGaqDLjawZl24/TLfUs3XZdjug9gYGQqK4u0HdoihqgisohAPS6yiBxPJmjBIEdFFj3bY7mgbYm2XciaAYs0Z5bSpsAiakGZXWxniqbAIjZKj6i+RVYm2gGZ/FEOkzPKoXNGOTxOpThvlEM4iDHZUQ6DN8oh8UY5OLfVkxzl0GThidhRDua+W2lcWv/Qsre+rNsCSRB4oxwdtlWRRWx1Y8ajHErMFFnsGOXgWITAH+WguDkd5ZgYU9JEMjtGOe52l2Nqq77v4OSkrkuwrFublv7325eNhdnluCcnJyXCm8IZbRpk3Hrl4aVvnmvgznnhipX5clMYJvQ0y+k60fjuh/te/ImuUspNaDtosYk1Uh2RxTCh7+YSrAX/xQrvK4FJVE5q2ak9j/e9cKrsdJ0PPVxz4t8MamixePKM7EgnDn+RcfQvj425u+LO8y9WptXlmOYXKzNfgtU01ab7gGDHDHKk2O6zBgcQLOCkJAVg0GlOSTQpnOV091mNA6DAbywqANAcHyXXAgAGleaKw+TA0IRcUvIBllNNEtJ10moATM6JMjUKZyRha6yY2Ww1swceXfzMd9WWHuT0pypuGN07fOudPW+dJYCdeu+DtR9oV/+250Dc+vqf29aNp/dV1KBFz05CZLGLTAbQ4xw7ENBOcURoEUI5L7ZNGlXNCi2ibZDJs4ghV4HGC23bMVOUkh5A2rtIU6BoLwQ1ItMVi+EAAnKVuO4DvMrGXsXiuhbgJALUAVBrIkAfzus+gKFOVTZ2Vw35BY55nA71oWWogCw3gkCiTFcsxjrNmh/0ZFH3KxYrdGVj5NQh90xGPX5wxeKnv4orhs9BkJ50ix7rX3wi7/jCOvVa2T2f8uGHau5I4Zs9um1lXzyp7PhK++S7urA+dI2uxs1I6iKTARoRjsU6VR8aZXJtk6CPp/WARZrTCykKYCyiPpTJs4i2UwU9kGpMCmFm8lIS7URIe8MuR+DDchKjHNjl8L5YGTv+VP+Kw+MOt8uhbLhivHvViT1LGqW9sX3jO7eb21Y+v6cYefly88tNrSvvlKGLcE91Oe7aqu/wptCZhT1WykdXLv7bkZFWi+bgpjC/JqttuO3EnxlxfyavXF869dLYD6eK+3dcf/Oa/cU7zeFXQWl4UxiOcsybhHac0e9XL3nsYEqjOEjoxD9G9PXXnNhzpFHKS2ec2rPXHNMZfO63Vy/bX25uFd+KOgGLYUKHCX13E9psNn76Z9+je3K20/kXOtPa841z4Q2ZvNLOb5yxf978JuFceDP92k/Nvced/KvwXVWY0PMnoRd6H3qWtnWrn3ulf/muiIWdO0hoZf1F58baj9f+YiZK7ZPf2vzpex+qR9Z++s4F+4vVe9aNOZc2VMNx6NlL6I5RjiFmlINz313h3HdzRzlqIq4u3iZrYhes4H03uwtWr1EOjRnlYDhvFyxmlKMePJF4FyzN2wVLoc7nBl0v/fDi4mVbblZJQyWyC5b+1UeKevXj32vS8d9dzYlDJyta7YeDVxSt+snBhC7vP9llF6xetuu9d8ESWkSuyyiHtwuW2DbsgpUSWkQ7yeAuWEyjdGYXLO4oB2Sm13g5kGMqjnJ4g3mWSo32NWEQ0RsZNalBPynVCo6MGhTOjkPDEGuTHmnVALA5gEGGEt1Fsj7gcdTIqLuu08d5I6itlEwNMwOHjdIASDdazY5xaAQgtDK1FjUyyuHsmOUDniRD+e2dpcve/d1wWi3r6Xr7FK3xPVn3T4iu/5J0tbh/TJruX7tW+ypbTjO5r6YGLWKrlaTIYheZ2FyDGYcOWvRsF4lM8Th0q5wnJkzaYpPiWtVsS2ARtaDMLrZzFco2k5ITtk1RSmIuxsmvwi6H6ERT7XJMcPr19UuXvHtdb0WWDrjtMUbJ561hVk3eEqxaYU6/KZxRl2NqS7DufJeDBcKbwtnuQ0/cDV7b+PCSdW/957/8+2ZqOl44OWnh3BSGCc2+FS05vmPx//nTn//077+Es+2IzPtoCdbU5kPP4S5YzuSWYE0A3XbBap9v77/++c9//sOWeTkf+l7eBcvUJdN9aCQYUZUcNQz3WYEDmQTk6gkSJCPIQWjETQpHTqI4OcYAOhVUhRyMDpNrAcDgcON508eNBodL1Akgm35ATtZISFZJqwHQaABDukzhDIet1qM6dT4Ivkzr1B//88//91+W/FhStaBFDFElYAcDAiiTYxGDxJGJFiEoUaFF5EAm1yKEYjZoEYNE2lZOCy2inVRFZBFDpsS16ANGVPMtsjLRDqTuIu+f8RKa969rieDVdEnohk5zxGCXhFaYhGbVMQmdo94yLidOaKlLQhtUYBNaCnI6q5jh2gldXfPHP/7xfx7te+brvGmZ3IQ2MKEbvRKaYxFDl4RWmITmWOQmNIfrmdAlNqFpi15Cl0UWDU5Ca1NLaA8gzQm7HKIPyxlvvNk49Odd46UvVv5l5dGic890Oeb9qu/wptCZ/ZtCCM2/u2/j+JG/9T99dKxlhjeF4SiH6K2YnwndUsymYbT/dVMmL4hLsMzxk//oW/FJOkzoOzrKcce3pJgfCT3dVd9OsMth//ryruLoptdj5ndrvnJP6C3Bsp3K98/2//XjXPOub7w5r+ZD09zszYeeKH0iUeU8upQ+qXFKnzBcXVxohlsbRQuWSBkdDpY0YUqkjOeoUipcjik0w3BYGKZXoRlDVGhmAtAiGnU+SR/feetS4cg35/YmN8W2Ri230EwBW92+8/rh2b8s3xXXvX/boGqjTLHQjDy7hWbcvb672y5khLahIE0pLbSIdriFZnSKyxQpvFuhGYXm6FZ7hWYS8UjCfUCID8TIUSTuPkfhAAJyQ5cpgMdFLlPn43HRASEQi5KDGzcogMfdvJ7wcS53eYg6H8PhxV65HQASAGC4OkjhHVwcXNGNj+Rvr35z8+iHA8l1F3bKO34djycij1ydAJKpq5+t+u/+107cTlLX0tN2pJdtnkzmYnvbBpldbN+6JrQdJcDgVaFFvNirPNtxkW3vNVjbMaGkOCVzVvvQJKicD8FJdzngQ4vpcjTFXQ6T8yGoYYGAyXU5oNs30ftrUUHc5WgxfWgd+9DNW29UPjj54ZX0ugu79B3nnM66HGZTvrD2wYc3DLoXY2tgm9eHNqlWe31oTr+sSx/aoABDbLtLlwMtQphqH5q26HU56iKLGPJVx5fJ73JYgZS0w5tCZ+5uCu381tyOM198d35vcnNia8zhFZoxLr/dv3TjTct7jfCmMBzlmL8Jbf388r7G8IbXouax1V+6r8irnKRc2LRs2bpLElxYmNBhQs/bhHaH7ayWpZNhO/Izbikwwx7aurT/9XPkRcKEnqcJvXCH7XThWzGTL1ag7rloSwozsv3R/jfO1TuG7cL50LOS0C0L9tWC0IyR/bKaSnBbN+RgW7cmbCCGQYd9xCAoSep87K5tes9t3WBjMNjWzYbtujzOojjc1g1wW2lSOHK8bd2AY7Z1M2FjMAgIYMjWYF8yk9phjOHsmOUDHkfLNDjbupHfOHZ8xyOL15ySEqbIIrYaZXIsdpGJFiHocaFF5IojdKMYixDKzLZujCSQWc0KLaKdTE1kEUOuwrHI2jYFKenlIm7r1rmmUBKtXrujawqDi9M61hQG1wqyHKwplKa4plCluGmsKeyoDdQgawq5FrVK5IPH+p7dm9H1rrar0R62Z2VNYQ/bY2mhbVxTmORZVCk74jWFyPHWFMrTWlMY9qGduZrL0a2cru60hj9f8V9//7bizMs+tE1x0xy2o080G12O4LBdeFNIKb7LCe2G1tiWFX1/Pz7u6PMvoe/zm8IwoadZ8Dz3zar+vx1OhQkdJrRQ8UJK6ITtVL5Ztfixz8ZaYUILLM5dQgPHS+gFPNsOGz+T6qPYeHHB8x5rCiu/PNf/+IeppjWtYbsFPNuuRXGzN9tOUB+aupecan3omE7hs10fuj79+tBaR31oXQB01IdWOPfd8IIwysGTRNeH7gJASWNDHz7x3F+Wf3CrZuoTFlV8pVjQ9qzVh5anUx9a49SHLk6tPrQyp/WhZ6OCv8ar4M8W6J9xBX9lshX8oZDRZCv4qwxgU0Fcwd/2K/h3Np5XwZ9n0atTBe1VW/Wzry1ZtvmW2eqo4C8nRBanV8Gfsditgj9ImloFf55FcQV/lvMq+ActThToN0Qy2Qr+YcHzzg/Lyfehp9PlmBi2cx/UN4Xqxdf6l22JGOyawoVb8Hx6feiw4LmzoG8Kmbkcjd/eW/rQpsuSTQHhTWE4yrFgE9q0jVvvPbT0jQHNCRM6wN2rlZPmy06yTu8yBtPZSda+uW3ZkrfOqd7FTnZN4RTLGNyTO8liQk96r2+Ds9c3BpXmvL2+ZdEu1ZPd69vk7fUt8/b6tqgwtb2+dQ7Qc6/vid2n9e5befP2+kYtEMyY2mmxqd7a8nD/C79W4MKkGe/1rTIAY7Fjr2+OReD4e31T3Jzu9T2xlXdwr2+Dt9c3uyJxviySNY0ei2RN0bLNO7JIllxsxyLZ4PJOf5FswKJ4kaypSkO7H+1b/W3BNCe/SJaxPeVFsj1sFzJC27O1SNZMT22RrCxeJHvXuxw0MKeVk5ypdTlmXDlp+pvX2yOfPL742e8rTlg5yZl8lyOsnOTMr5tCxmJ2/4r+Z0+WVN6fj/CmMBzlCCqe5wntaMWvn+p78pMBkcUwocOEXkgJ7QKFY08vfuTL0WaY0M6UlmBp9HqXOCxxUYNLsGzgYAkWAhgMmlOTzKIghuu5BAtWF8ESrCYATQ6HS7BwURDDacDxlmAhQC/BsgDAwJzIW4JlUYuHMODasJhNSwpyJmcJFlrEAKuGeBZdO06r/M1jfY8dyDX1oMUuMhnAiAstoh2QybUIocIswWI50upaVmgRbWfrIosYclWRRQSacUskE0/kLcGSYZIIBFyCpTKTjupTWoJV5a6wAo7MXqlHeIBwCZYykyVYMHtFotcGeUuwStRsI97iIfESLNVbgiVT50OuRnHsEizGIgQ10hBZBECvD3z3j77le29Iut82sDj5JVhqD9sjk12CJVxhNa0lWKp4CRZjUWWWYNU5MjuXYGnU33fscrT/Kwv8fbd7dzm6VE6iPgt7V04qjAc/ndkux4jj45OunASN6lI5CQAMXSonqXSXQ59Sl8OzrVGfkt0qJ6Wc+plX+pdvJ+8L06MwelZOIsHoaXuKlZMYSbwuBwtA43mVkxiOrZykcbiwcpJz9/rQLbqc7ow3DVLOv9C/bGe0Gfahw5vCO5vQVsUyxnK2oySgMPQsJXS7vb+te/CRjdfhTQ8TOkzoO5TQp1fVY++8ckn95MV97k71s5fQumNcf3fJg29fM50woQOSOicnQbMwJGw0SJTYVGjBz3CoHw54nA4ZjzjDwSIjI8kALSrgKiRIaPbfMlwFEto2g5wBXFqlAIYz4L3KyFSr8Tsu5kS5BoWzkgBowTeF5sQ3hcW3n6weOn1zx9CW4vZb7lmfrossYkhYPWzjN4XugXFzy7KH1l2UPUlimQyA3xTyLKKW8pjQInDVEbFtoqCeD9phbYNMnkUMw7Ueth3GNiMJAfymMJNKZNwHhPSVFAnxtBuS5CCTSPlAJnaVBAAwJJMZP8QBSCdEXOIKDSTSVMATDd6Ci8hQgeFu36ResIODa74ao64Z2wYXgcC1qAjAcD0SbDzLXU5R50sMGz9++XZ57+XE2rO75O2/FNOZxPIbVKN4J7qSFFn09FG2c8kTLyz+79XHb6ez3WUyJ0peEVpEDmRyLUIYusGTRAGR60KLeKLrvWzfENrOcG2nggDIXCTVy5L7gNC4XSNHpYb7XIEDCMgVoxSAoVqluFKEOp9UblABuMoQ+VFDCEi5DAV4XJ0K+RQ5qBG8UZKogFykSICK5AcWiBUCgAQAhvgYNKpOtaZOc43bdVqSHPvnlmXX911Kbri4U9l5QWu35olhkUUMt6tBi9Ua1WqUiZIqtcFtyxc/811elj28zJHpnYiE6m2hRWx1Pi20CGEkGbTIcKNxoUVsPMjkWcSQGBVKAjuYmTyZmIsgs2NykhPH8Zrgh2DH5CSH5pjJSWyXg/7sMnt2OXh9aA7HTE7qmA0Dn3HY5TDoD0uN/hCELke3yUmcLge7yIidnNQcO/jW/wx8++nxQ8Obz23JuJfH6XJ0TE6yRBY7uhytic/WzMHli1f/LHWTiVosZnKS2DbK5FlkJifZQttdJicZdB+a7UowHG9ykjf3CG3blEyGwxOFk5Oc2b4prB3Tqnu3jDbPv3nG/dXs3RTSFpupPSv6//lDEbrI4U1hOMoxl+PQTWiAA82dk4Rutyb/xd/6n/5yTCTzPk/ou7WtW2sWEnreLcGaTqEZrsUe27oVjqz8y8pjhVkpNDP/lmDNaNW3bSi2+4BgxXQSZMsNKjnAYMjkoJEEwKSCqtl+kBPkwAQcAAwaAZS4GFDJwdgIAJaIK+RtH7c8jgTFIL9KNtxnHc6n0xwCqRr5DTQeAgIY0hXbx1lJ+IJR8isFJEFgOG1lWWQRghXTRBax1VJCYNEaPbay74lPcjzbaBFsqzGhReQKw0KLMgmlXNAiI7OSEVpEO+mqyCKGbFlkccK2LpDp5SLIXKSrDd19QNAiCjmqk2dJoQIARjVuEEDT/SDJuh/qMcPHWU4mQCNKfqTVRYAxkjd8AEND9Tl3az2CS7qAM+JVl1AI4AUGSFQI0AgCEIxUyfBxRhJyWkQVSMIgryx0B/SILLLo2YkFbRNJhqmMfLPqfx774KxqGR0ywSIGibHtWVT9VqNMrm0S3H0KBZIQKKbEAGm1kSQyeRbRdrpoiCR5thWRTLQDMu/+EqyprfpeQJvXT38JluP3IboswbKcyukX+5fsTjbv5BKs+bvqOxzlcGb/pnBWJ/g7vetyyKf+1r/8g5TlhDeF4SgH5WzBJrRj3vjtrQcffv+GFLQYJrQTJjQVFkZC60lHu/zWg0vfJRvUhgntLGIXBeFCF1xGY9CriwBw5JQTWD+DnIFLsJzg8hia02HVUBMArUkFk6yicQpjTtdFQU5pxPFxHucmtL8oyKTXBiGQliiAWTwEwU1oalEQb6lW3PYBRhIGXIJldFmCRS94YyyiHZQptq0l2u+mMbD+waXvDegObREDuwSLWVqFttsJ3d12O6EDFmmZbkILLKIWlNnFdr5K2WYlebaZJVg05y3BIr/qugSr3msJljrpJVjU4qHJLsFSuizBylCLjNjNq2ayBKuqUmFGS7BImPkSrIldsIIWmT3H9NpvG5b2v3pulNIy5SVYjEWZ4roswapxlmAxFtFOQrwEqypeglWjud5LsEhzuv6FnuIiWYNZJKuJuJ5/obmLZJm/Ld4iWeFfaFwkK/4L3UpLFMD72wLrOmfhL/QUF8kazPrPZA/buEi2aViD2x7uf/nXdkdqin+hW6XRHrYrw0GLjMxaTmhRZxbJim3n6UWyM/oLHfahnQXdh/Zlmum9D/c//0udHba77/rQYUI790hCt698aM9j/S+cKloUECY0rThM6AWV0O1/O/rpE31PHS/7wP2X0OE3hQv0m0JBscbhz1f0PfNtqXW/flOoqw2ce0ECPZfDkBTDD+K5HIYk+5yB0w+04FwOQ3Y5QzyXAwDBXA7NDzj9wJAl0SwEmMthKATAgI2i53LwAHYuh+HN5aAl0XM5OiVRnLyyYPAt8uZyMBZRn8GZy+FJ8mQarEzD1DOfrfzLik9zMjlRx1wO2iI2njOXw+DM5eBKoudyiAF/LkfQIjOXg2eRmcvBlcnO5bAMKHsNwYxhpWsoma1TAapLu7PtCAAFz2W64DkJ7gQxqhg1w2lQsxqKeJs8gNSsdmfb+YDHGT7nzrbzcR7nzrZzS2ZD6W8MACgApGoEgMZjAACCO9uO4Lpvh+XMqOEDLAdBW1kWWPRCTBNYxNZ4MjkWkePItHV9/PjT/Ss+Spi27RU877BoULYLw2LbbnBn2wUs0jLd2XYCi6jFnW0nsIi2s+WgbYO1rYtkoh2QGc6HFn1Yzuv50E5HlyMwH7ry4+q+x/ZnWwtyS4pwF6zgW3F/3hTSFhs/Pdf/6P60wXay74ObwjCh782EduzS2Tf6/7r1B/pjLExo6l8DF+717Sf0HehyTGJyUkCmP2Fau/h63+JtQ9Z0E3oh7vVtm7DexcQlWLj2hix70ej1LshJSQpgOQjeoiDAFYsKAKiwBMviADqsQhofpQCPM6lQHLZ93ILVRRiQS0pkjQ67BItaU2Wn6hSAAQAMmSo03hBxZsz0AQyMTB2WYPEsYoBVQzyLCKBMjkUMCkcmWmyHZks694+lyzZcVZoci8h5S7A4FiF0LMEKcrgEi2cR7YDMLrazFZFFtIOZ6S3BMgKADasHF+kKDItA0GDsQ6uRkZAGjCpBUIGrxgOjbezioVpMp/A6veZHImt0cNiOB8CaKn0kT4008bixrO7j7LAdcvEqAWBcBwI2qg4Dk4kyaTUuwaIBDMkiNF4RcSoMcQLgcbRM6clxkUUVbUsii8ihTI5FDHWOTJkCDOXW5XeX9L1xvmQYAtujWWgUxyKE8UzQIiOzmBJaRDvJUg/b6YLIosehbY7MukbJnDejHPSn6cLdeHMWuhzmjEc5Opdg6Te3LF/65kXJWSijHDPaeDO8KXTu0ZtC6qvvVmznQ30vn1W9slHhTaETJnRAMbfQDLxgCwp/zpuEbrdwcOdfl7z0y1iL4sKEdh9hQgsS2ta+fuVbo7Z/y1jz97fmsBTYNOtD6630x4/1rfq+5nP3aELfkWKNdC/xni3WeDqy4caJT4/NXbFGTl970sUa26/RGv54Rd+zPxTv7WKNgnK6kqh2KZbTZavg1qhCsFgBtjHb5XRpji2nyyu7yymnK82knG4lWAi2o5xuTXOULVf2u+V0d0yxnC7HIrecLqdabmUK5XRluTH40aN/WXkkV6H0eeV0xcWLmXK6niSa61ZOt07J5FnsXU4XL0xcTrfMlNPtVvA8gaW6k1R1aSh4zlar5hU8T/UseB4XAfyC53Sl646C55wK20zB8+SdKHieLEhffK7sCRY851lkCp6nJ1fwnFsYnSezo+A5XaA8mb62/7H/Wrbxols0vaPgOcciU/A8KaxnPqcFzztsB6vHp9mC5+GWFP6HJXOiqW5J0TSPfqE7n/xyc8fQ1rnYkqLD4vS3pCj+8Fz/Ex8Pz68tKdgux0y2pAhvCp3ZuSls3uh/9t105O1XLqkHX5jlTYNm4aaQBurf/KPvsYPDeGH32k1hmNCzNMqhxG5FZGs0aztygrx/8zahHb1y+uUlf90xSBoQJnTgasKEnhiHBsCBAYZ5m9DtEynnX+57eIf7dt9zCa1R/zrcGtmZla2RybXMxtbISZHFmW+NrJ59fenD265bleltjUzZmfWtkWnOmeLWyB07hd+bm9fTFZYW0ub1nZWTKIuzsHm9UrzwVv+D635KmNo9tHl9y4LyMxCaTLW1KVZO0pnKSSqHM6hiPx5gU8EQV05iOK9yki6s+QOVk0w9yGlQyyfdCNTyYU+UrVE4IwlbY8fsQC0fhpte5STk4CIUXuUk+EdimQzAVk5iLLb/hBtXNy77y6u/t//cdquclBfbJq2uZYUWNaZyEscihhxdOYnHdVROYspLNSmZYR+a+rCceR96nk5O6jLB34iu71vy+u+yw7PYuw9Nf1OI/be73oem/3WY0PdbQrdt/7Jz+ZLXzxQ5FjkJbbTFWu2GS2VXYKPg9qXzN5ueRa2ka2T8OExo6q0IE/pOJnRp3Mrse6z/H6fqTu+Ezh0rO5W1tx153+o3rzjVXf98N9O6+PyTRw2wOLJ59bas/OXIvJmcdBcqJ9HAnFZOcngJfe9VTpreHivp/cv7V/9U6TY5ycWtT87pmRf//YpzZaN0bp367Rb52+0jb5+7+s5NYrG594i675Bz+gvbuWuVkwxNMtwHBD2ikqOG7j7LCjmQyc+0BjmoxSmggyOhHjMonMNJAOgIaBSgyO6zOTps+kAHR8J4zvRxLhevuc8qAVhOghYmKwSAxmMAAIKZKlM4j9MiGnU+CIxMZWUhYAe1YIgqIosI1HvZ7pBJWcQgR4UWkRtzZVpa/OPHF688OipZAa6Q8WybibdGa9/sX3HRbBS0k+tKm741Y2u+ey2T2fMRsV164bp14bVG9s20aTC2QWYX25miyCI2CjOTl5JoB2QusnQoPwPBjELdHokUo1GgRg8ELFNTT5AAAAaV5qQ4XRtIMqigkto7MtTyMSQRYI2NUAAGpuZPIU8ONKj2BAAGGUrrJOo+MMGZFJCsUUV8GABDukKdj5UEgAG1fBhJDKeuLIks4oliqsiipy8ulCSWyQAqA7CVk6Dx40SmKVv5wyv6Vn4+bNoTkoArZickfb9FlfTKM5css/HDk4fq7/1qpZ77/N2R7J73XUAtvBy3B/5ZUd4622EbZPIsYsiURBY9DjKTJ9MDVKZy0gIp1jjP1xTOdpdjsmsKp9jlEK0pLBxftfiJT0fFXY5Pd7UvrPHs1favjPhLNzafc3Krv1w/nt//gdtqs/pKyrn2vNTa/cNd6HKEN4VOeFPoPpivvstHn+lf8VlebVEcdVN4ZGf7lerPXnEKaUd/5czuY0781fNv5nIfHiWA8tZ158J6o7n953CUI0zoeZHQjl79+YW+FbsSTZ+jEvq397R2Qq+67Fx4KX7h5ZFf34of+Li64cjJN1O22rKM1pFdyU3HHOXN6wshoYHjJvQ9VTlp8gndpBs/yTIGmNDAMV0OHjfzhO69eX1gcpL06wuLH9njblAb6HKU3s3qjro/5RjHn98w1NK/fn5f1Um9/czFZvGw3LbY+OTFI2Untqk2zYSehcpJTVNtug8IdswgR4rtPmtwAMECTkpSAI9TEuTAUgCwKE7X3Wc1zgMsH2iOj5JrAcDmcMVhcmBoQU4FLin5AMupJgnput/qCcCmQqZG4YwkbI0VMwONZzj9qYrIIgQ7rgttw8XKCZHFLjIZQI8LLaKd4kiHxVar/uOrS5Zvua3rhCvnJyTZJ462xbba/0e13aCZ7edWNdtqVo9Lpns+u6kYX/5kexbRNsjkWUQuVxFZ9DiObYsFSHsXaQrMGIGgRmR6GgwcQECuEtd9gDetphajzsdyEj2fRq2JAH04rwemy9QVP7jFfuhJR0FOh8lJMkzTwcAAibIuACC4lZN8XKGn1SCnDikiSRCkJ8e7AxrMp+FZVPGVYkHbIKmLTAZoREQWsdUok7GoS+Xzr/cvWX+hYeiaPp7WPVwvnBnTO89HKieN3VY9i+VTJX3CtkzJ5FlE26mCLpLkzT2SRTLRDk5OCos1OjMs1ji1LgcAd6RY43S7HGBRvbxh2dL3rqodlZN4UzXmVbHG8KbQCW8K+RbtWxuW9r91yaiNiG3Pxwn+9L8OEzpMaMqidGvz8qVvfxcT2w4TOkxoKsz3hNZbzcSeRx5Y9avshAkdJvTCT2iXs1Pblva/8EsFu8jzPqE7RjmGhPfdk12CVWMXBQW5unh3e94SLHUGS7DkRpDzlmCVqRvujkVB5GfiJViatwRLoc5Xp++7eUuwGrwlWL1sV3vZnsQSLKFF5Eaz3W0bY+cO/nXxqmM5iTP21GUJFm2bswSLbRSzBEvhcLgEy2u8HMgxfwkWrJWB0IyRtS1NJbgECzlYgtWERTxNBVYhwZofCLhqyKLX/CCu91yCBSuiYAmWjSudIKgWxeESLMBtuFgMyOESLI1ePAQAswTLAzQKwOAtwTJFnB2zfACDJ5NwBi7BMoIW0TasGuJZ7FiCFbTYRSZahKDHeRYtiiuOCC1CKI80Rw+tWPz00ULL6ZAEMqtZoUW0k6lRa6p4XK4isjhh26RSkua8XJzNJVgLfdhubrocvb8pjM/9N4Uz60P7X32PHH+q76kj492G7e58l4MFvAn+9Nhf2IcO+9CURWYuR+GLpxc/cWRcbb+Yzg4zz5c+dKtJEvqHo00nTGgnTOigRSahbbP44+olj+8deO2/+j9S52FC28W9w86i1pkVN8AJvM8OnMuhHvDCCJh5GmA4/FGOxjlcK0sDTfoAH7VK8N8yXKPEvCKHy5v0pbeCwIghAjCMakGA5TIcgLnMVYrIYhfbDqMv18N2kyeTeWSFFvGBMsW25cIEq599se+Pf/jTv//bURpQx4QWsdU8mQw3rggl9bTtAwfX5Bddf+CZQ+7j4wPu8yfvfUTC/k/ccJAcHDrwkQ8c2reZAlgOwv5NcL79JACA4eBBcrqNDPAxFQA4tHMHnPwQFRhu1/vk4KODwWs5ANzmfQQ4EOQQ2PIhDRwInmjrHqrxPO7j9z72AVYShI/+e4/IItreSF8YY9Gzs0lksYtMBji48RORRdByaNd2oUUIu7f5Fj/dtez//Oef//zHxfsoYM9WoUW0s2VvD9vbdgslIQeZyZHpAW2ZB5c8FiZ0mNBTSehDhzb8x5/aCf2vz+//bH4mdNjlEHwIhl2Ozi4HtEBe/Yc//ce//PnhHYPO/OtyrM7Py5vCQs+bwi7TZSZ5U5ie+U1hTFyskYT5cVMYF1qc9E1hnraoj77+X/37Lq9dunTdNc2c7E1hsFgj26icuFgj3vPFgsUauTeF1LBdU9acrKG0G6HK7ctTWpx/3dRGNLcSWr39M13jvBVNLW0oLacl6xRAvxUttf0e2C3HrLcpxdQDCd1q1kruv3YBRzGDb0UbKLojR5bUfkHV4L0V2ojpuLsBmy7HS2hjRAdA1wRvRVVtX57l2OR+nqPYboy2G6G0TEsxO96KpmT0Smjd0eWmU3RBUzEECW03zYLilrgguw0EE7ot2iKArprchNZVxy4oVifgJ3Q7WsW6a7H98u23LTAO7S5bKdYI0NQQIMN2jRubH35w3RnZPYVWbqJtjZPQTde25gJNsN05fdRtwJiGttWAbUOT3ZRs27YmbHcbtpv419bPL72ZbBxZc8Iaen3juPzRmjN651thfHGyFXn7ldvW92sO69l330rpHX/JzaPHm/kPXj5t/rzmkDb83htxvTOhK7uvpJ3RN/PSvufP2xdf2F1xOt6K+t7r+rHn14+4F2BfeWlHWe94K6T9A83bb64fUT9d87N945VtRT2Q0NE3X4+b36z+ykiufSfHS+jx7a+eM9xGZNqN4Ca0+f4p22sEL6H1o2s2jjfajbB+f2F3nUlo87s1X5JKQt2+WMm8t/qEdeOVrSX3HPzPQ3XDRbcRZoo0IpDQ1vj2V84ZJ/Gd4CS0lVn30g3rp4lGdCa0bV7Yb6LFreXah89faHUktH1pr57fvPob8/ZrmwrywTW/NilJZnzH8v4XN51on27TOevkmiN6et3b6Y6ENvWj3zjFXa/8Yvy05lM1v4GSiQmtf/O1k1//4lX7lzUfKWObXot02s5tXn184gKsgZd2Vrt+seJ/z2gMVr/78Pa2+ObUrovHjl7aHdlcsNkvbe1Tqz5xDn79897sxvj7tz756dQBo8l8Gdv89Zl9rZNfD10f2Rjbee3zk2c/1Jvsl7bSoZXnMuanfakL+25vyW8e/OiXFvulrXJ45Xn9Vv3w4YH2BeS23vj0B5v6FrbNaV+uPN3cff67I9d2RDdl3r965FsAqC9tm3u+PXkgtSmxNbL/zA+HmuxX3wQ4fvz2jZzbiI/bjbA5X8Y61/q+KniNsDhffSu3Gp98TTVi4svYZivbfuVoO3b76lvLpTJvp7df+eK78/sGN9d5X3075/9yKus3ovOrb8PwG/HzqYN28Ktv87PDv+4a9hvR+ZV2a/DVN83rO2LE4olz+we31Du++o6+8YoynMy/ndh56eixi3uGNldoSY4d2fHAvyw927jUd2KkfR2D5DrYr7SbZ1btb534+vb14Y3xndc/+/7XCZkItM4/u9v58pPz20c3Rndf/uqbC7tN9qvv1nBy+O3ELryA3Jabh37q+tW3NytJkWzH/uyb3/arm85uGT6/48QX0juw/gcmhKhKQ7OrP3zp/PrOuu+H3ld2f7/z9tB6qlSxqkqyXTt12Nr96os/xbaqB77dcy2xrqb780dUWdbNwke/1QY/eil94mj1nUub6sc+tfxpMKos6Wbx0IV2Cu47/dOR+rrfN1VOHjAoQG1oVvnwr/qW9MDWHw8p6y9sKpzao9PTZSRFVa2f1607dWOXtuPn9+PXN6rs5CQXULe//uIvt7dre0gjZJ2dVtNQVaP02dsnkl4jGjo7raYNtP/G6XvOfXes7jXCn1Zj3typ7Thrdp+c1O7BD27NbCqc3nP8eG1txghy5uih187e9BvROTlJkrAR7jtxu92IwOQk/bd33v02Thpx3W1E5+QkU7q+Wz/jWTz2TW1t1mAmJ1nyrV3tC41sTm8eObfzuy8b7yQMZnKSocVf+nP/ytX/PB1pX8cPO4dub5A1ZnKSWfv5sPXBay/+HN2q7v9u9/W4LxM4u37mkDOwdv3R1Gblk6P7BjJrazozOandH4tOXEA7I6onDprdJieRP+zN755ZteoH64e9jd/3a+2EHrlAEho+psjfd+n9Vateijtnvmx+u2v3lze3q7u/3+XmguP1/pRdq1a9MORc+Nze/kN87eVtGmr0e3+pV1et2lxrHRqQNn/994HvjtXaudA49qnf5ci9sWrVhrJz+IJVP/qx+uMRcvknD9gTwMjbq1atKzhfndG3ZC5v/fFT960ontpjUZ9xrVPPrlr15dcf7Dp2dZe+4+ftiesbdbbLcfa5VasOvffL0LpLXkKrbJfj99WrVn3y+YE390W2YiPkjpu9Q6tWPXdJP/KZDglNGkF1OW7u1Hecc3r1oZPbbtY2koSur815Fn1Otz469OIX17xGGMEuh7KZbUSgy6H/sHPP4dt+Izq7HJad8hK6eGrvsW/c6+jocmR2yU5m27XGplE3n6R3Uh09CsM5s/3gf/7xT++e26FDQmvsZA+jdf6w9f6P8XfaGdFO6BtxXyZ2OayLh1o/b9/zaXSLShL6nUZHl6OZeb99ASPnd574Ulp3sZ3QH7V6z4eWxsbG6t9/MNYc2hbbnPrg4tFjA+2/78XWhOJmZWy0YDi/fGFuPXtrbXRT+wOm3eU46O+O4ALjunPus9ZXJ66vT2yK7bx++OSvHxp+QpuF0dGybX88UN3wzH8eONv+hMtvGTx4xk9oszg6WrKbn523vtpfbl5yP2C23Tj0Y2sCsIpjbaD1xS/NPe0ux/Wd0U3Z7VcPf9ekDcrtlhTeu3j13aHN8a3RA2e+P9RiE1ppA9XPfhrYGCONaH9KNtmEVttA+fDqB56Ke42wO2Zw1dpE7fBH1eZ5vxFUQmfbrxzrkdBGZuNlU9t+5ciJC+5HPSeh9QP//K8Xbm+ZaEQgofXP/Ub8fJCqo4GApew4FXkr5jcikNBWYpeBFo+cPH/gVvs62IQ2UjuU/KbfDWPnpa+PX9p7e3Ol856vdfor48Mn/vAvSx+/tn2ofR0fNTsLTZ/7rPnFyWsb2hmx4/rn35/ZZ3f2oX//xNr9feKN+CbS5Ti/2+pIaO8CjrkZkd9685OfJjXBv2U1Vj+66oRyePVJa/DVTQVp/5pfmZvClstf/rl18+2XfjO+W33EyLzzdpq5P3fLBl//wRnZ+cqA9ePqT7X8+jcSBn1TaLcB+8T1cvvTeqSx9/kL9m/P76n5Cd3+ZfuVWj/crDz92DO/Ng6s+dUeeHFnxaAAx2zft5y63Bp6Y8Oo8vGaU/a1l7eVdPZPQvv/XnvzlQHj2OqvzcRb6/IdN4Wme6Lh91+7ZrYboafbjei4KXTgBY+ds71GBO672/8be3LFs7/V3UZceH5Px03h8fbtaI+ENo8ueeq96o2Xt5Xb5/hNMMrx+VXLb0Qgoa2R91+9Zp5ovxPQCCcwyjH0zotnTb8RwYTOf2kon4DFcn2Pex0dCT38hXZiyVPvlgdf3VyU9j9/thkY3rt8qh0Ovr3yP/9zdTb5ztpMALj2gzO285XL1g+rP9Ny776ZCNwU3jzpxN594bR5as3H6uh7r0U7bVMXsOasfenFXRM3hQ49xhxcsdLS213Ygqm64zDtn7V73MG3otk0yro7bEcGi/TgsF3TNgqmO3jjjq4YOmfYztbabbLIGIzTvvkw/T/AuM+N3TQlSTIJ4KicYbtmU6pqbdJ2Rxg1s2O8Gv4S1ZtOU202LZ0MNwSH7cyGC9htwG0+O8oB++FoVvv/2e6fSoc3ytHUpLLpSrJs1fXDDNsp5KBrl8NSJKWluJYsFQHOsF1Tdt8OHf9L6xy2a4tuA+47ofn9so5huxYBDAaYGLZruX9h3KFDrX0ySw0O27X/BFlKrS2z7btlUMCETHdgz5KbpROrFv/towRn2K5pu7ZtsG1QMr3UcAGjbhPbLXpcz/vz0TbVvgDJQdsTw3b6oQ8168h+ZTJLsDqH45zOMga87dTZL1bYqw5+seLtlcr5YqVcooBuX6yIizXmVMfp+sVKXqGc8Rbgj0jQKPHC+rSwjAHsgdq7jEGK/hPDK2OgZTi2me9N4E9zlzIGKaFFtFMtCC3ijhNjYtuk1Q13Ol71x38sfvzjbJNbxmCEKRrBpgZ5Hm0IbetoOzDbzt79byfO/eE9ky1jMC8LzeTmvtBMfLKFZniLguAF70ShmehdKTTD2qYKzfiNpwvNFFJtQNdHjq7ue3TH7YpB2561QjNDgUIz+ujS//v/Fmd1ttAMvxSYe0D2JApLgd1/pcB8SWpnKTA+V81Cqw3p7Et9y7ZE3bS5E6XA7FP/+r+/7ywFxu1y2MlCyymMNGAWfFis8f4q1ug4wvrQ/C4HVTlJvvD2kkfev2U4k6+cRMK0Kie1Lv3r/7kwcaJufWhl1f/ksw+8ePnPhwOKwxUr9+uKlUnW5TB+W7tk6Xs3TJ22PTcrVuSV//ZvjzYmVZfj3L+/tOY/bmT+62hAcZjQYUI73RLa0bWr65ct23BeoWzPSUK3vvnXg1/+26HWZHbBkjf9n/+9oyl9m6MUAxduSeHcu1tSzLzLAXbsoW3L+t64qM/tlhRjSx6paSv/K6MzXQ7+pkHKrX/7Q8RS3P1jwk2D7o9Ng3gWA5sGdUoCrpzpBGzl5vqHl7x2vqzO4aZB0o10++pv1tlNg/jbulW3/q//tSvc1s24b7Z162bb39YtwEkEKKXNTjumWY3ufXjxc98UTPd3c7Ktm2m2r8iyTXZbN36XY+A/Vq38z6jF+2Il3HjzXtx4c9JdjinUh25mP3y8b/WpsnNHN97k3hQ2VvwpEf3T05WwLkd4UzjVm0IaaOUOrehfdbzi5O5y9dHh10+2Wt+8lbWD/zpM6DChnckmdBsY/vyJxU9/e/Vul9P1JnQF/3WY0GFCO1NI6KYz9u2qJQ8fHGndoYT2Frpgqcc4VHdUg9VHbeCg+igCGAyaU5NMPUyG61l9FFYXQfXRJgBNDofVR3FpFcNpwGH1UT3IMdVHLQAszom86qMWtRoIA5ZFjdm0pCBn4hIsjkUMsGqIZ7Gj+mjQYheZDGDEhRbRDsjkWoRQyYttk1bXskKLbaD9X8Q3jz2w4tPRZpNjEUOuKrKIQDNuiWTiibwlWHKNmjGC9aFVZrpMfUr1oavc8s/Akekt9QgPENaHVmZQH1qqM5zqT5fR4iVqnkxHZWMSxPWhVa8+tEydDzlaJrsEq86rD90QWfTqQ0dFFidfH1rtYbtXfWhtLK35MllJ3epDU4B+5cjq/sd23azqIo6pD82mJDM5qc6R2bkES6P+vmOXo6UGZxfYvbscJvUpKe5RdOtywIcg1OVgP51500dNzocgTvzldTmgUUyXA7/cwg9LADCIuxwIYJdjanU5PNsa9SnJs9jR5eD0ywxxl8Og7Bg9bfO6HN70aRLYLocnibLDdjkYi2gnJ0mnn+97ZGfG7rSIIS+uy4FcPFiXw558HzqsPhr2oZ1Z6UP73xRKv77Wv/yD29ZduSkME3pGCe30XLFyHya048jn3lyybMuQRrc6TGj3eT4mtG1f+GDAVr//ouHEDwy6RJjQHQndNPWBtQ899N5v1Br2+ZnQC30+NO9EU07okcMn3o3/umvPseL7n251Vy3Niy0pZmE+dM+E9r4p1EUA9U2hfmvjQ/1vX1EF86GnltA00HVyEk6X4U2rmebkJLP7fBre5KSO6TK8yUmqkONOTqLn3aToyUn6DCcntY26++nY23478Hty4+X3lZ2X7K6Tk4zpTU6iLE5xcpI5xclJNNcxOYnh6MlJunD2EjU5yW5ql9c91P/WBUmxKM6bnBS0bXlzj4JTwQwWgMlJ8Vgk7j4wDERJGCLPkSgVEBi6TAEYolEqIIB4JAaBAiIDPCBGnejGdfo1ONzNa/TrMteC3GVyFMXXjQSBK7epi4hFgie6MkjhPC52KeYBo+eOHf1+XP9lb2XvQHzt2V3S9tNjbeyRKyKLPNuMRdY2x2IXmQwQHRBaRA5l8ixCuHU1aJHhBq8KLXq2BykgfvOntUseWLn/ajIxwV291cN2fCAmkukB5GcL5osVbe6/WGmxX6zUKbzbFyttQDn+we5PRs/tqzoHLsS2XH9f2nGlNS+/WNHm5ouVXNBii7ENMj2LersDsfvhvhdOV8mwnfuYvS9WwptCZ1ZuCh0n+siGw+OX3tvwU23nlu1uUdXwprDLBH87v39F3zMnqw78bJ7dFIYJ3eaK3375XdG8fE5zRn4klY7ChO66YkV1p+L94/vh+TjKESY0vhVYHAd2SQgTuscSrFbh66cX/+0L992exYRmZlN3S2jgukzwn1pC89YUdknohbGmsHcZAwBme00hk9B3f02hH3qtKSwef7Jv5RejzvDMJ/hjQutKXXcfELSITEJNc0ODHGBQgavGSahrVJCAg1CL6RReV6kgSeR0USEgE0AfyZOLqAu5sazu48hpDBevEqCh+wEbVVfIzxJl0moAFBrAkCxC4xURp0YUH/A4Wqb05LjIooq2JZFF5FAmxyKGOkemTANSROthezQLjeJYhDCeCVpkZBZTQotoJ1kSWDT05FfPLF5x4FzBFFj0zoe2OTLrGiVzkW0qtvuAYMUMciRb7rOmkwNV9wFbSlIAy0GQE9T5bMWiAgBqnPzI4gC6Rg7GRynA40wqFIdtH7dkmwrIJSX32VCBU2kAWpiqUwAGADBkqtB4Q8SZMdMHMDAy9ZVlkUUMMU1kEQGUybGIQeHIRIsQtJjQInKFYaFFCKVc0CLDVTJCi2gHZHJtK83KT8/1LdmVsptNnkW0g5mp6kHbmIsx8qsp9KGB4/Whp9XlmE996Kl2ObAPPSddjin2oTldjrtZOcmZQpejNcHVTz37l8c+iFlTrJzE7XKEN4VOONvOuSs3hXSjEidf61+2I6I2RVw4ykG9ZWFCz/uEzteV395e+sh713XnHhnlmFZC34ujHMaMRznMBTTK4VBlDMzr65csWX/NnNkoh2XAJBEIZgxL5sD0Fp0KMBPEbiRJNSUZJifJ9LQaEmwpYVMTRxhOg+I3MOHG5AFkfok9NmL7gMcZPmcX8jY1OYnD2cmGS+gwTQcDAAoAqZrdOTkJAQh2umL702UMDmdGDR9gOQjayrLAohdimsAitsaTybGIHE8maMHgTU5iLRqU7fZNodC2G9ybwoBFWqZ7UyiwiFrsdNUWWETb2bJt2U3597eXLX3nUlW1KZmebV0kE+2AzEW62jDIEAgEGBzRyXiIISmGH1Qy2GJU44Y/VALBkGSfcysnkVGUhh7gZJczcNhOqwsA3RjJG4HhuIbmB2MsRzhZ4nBkpMmIV92XUgiAARuFQKIiADwuVTJ8nJWELxhROZIoTl5ZMPgWvQCDpByLqM+TyZPkyTQ6ZTKALjG2GYvYeJDJWMRWg0yjkBFKAqCY6g7oRrIUsMNy6SJcc2Nw29LFa36smWbAtiJISc8OyBRUTppWl+NOFGucQeWkKXY5wspJd7rLARat+PZH+187VwtsFDuTyknhTWF4U+hzd+SmkPrqu5nc+9f+1T82WgYFhKMc1FsWJvSCSminpeYOPN733PejFBAmNPWWhQm9sBK6DbRyXz7Zt/Jo0ZlyQrNTznEaNc66nuIEf4OZ4K+JOB3mpGMZHa1JBbPnBH+NmeBvCDmY4G/RE/xbDJCWKIA3NR0n+OOUc95CgLjtAxgYmdOb4G8wc9d5E/xpTuPIRIumeII/BORKoz1sV4aDFhmZXSb468wEf7HtPD3B33ZTtFU4/PjilV8XWzraZib407a9Cf7kV37lJKjlw1ROqveqnKROunKS4tf8mWzlJKVL5aRMsCJSt8pJdAmeLpWTqioVZlQ5iYTZr5xEWfQ20Zt55aSRLMeiTHFdKifVOJWTGItoJ1EUWUSOVzlJiX25qu/xA4OTrZxEmtP1L7QR/M/BkVNO978Z7U/J4H89U/oL7RTGnK5/M5zSiOPjPM7tcrS6/YV20hIFcP5muF0Ov/Ez+QttdPkLTS94YyyiHZQ5l3+h3S5Hd9vtLkfAIi3T7XIILKIWlNnFdr5K2fYkGU71xDOLH/14pOl28Cb5FzrsQzthH9qZd33oiVD5eXX/4/vaqsObQidMaGfhJ3T7+n59qe+RDxIRYUqGCe0+woReKAmtOfK51x98+JXrljOphA6/KQy/Kexu+85+U9hpkTRKu/L2A0s3DhqT+KaQnV2g0XM5dEmhgnguB7t4CKcfqMG5HLpMAPFcDgT4czlUarYCTD/gLsGi53LoCiwywsAAZC7HxKIgGmDmcujeXA56CgY9l4MnCYO8stAdYOZysBY9O8G5HCipi0wG6JjLQS+tglbz5nLonLkcPEk6PZeDD5BWT8zlCFpk5nJwJbmAYda/eHPpkg2/l7Qgx87lsA1Yx2LgEiwdFthY9HoXEgxYMtNIAmBSQYW1PBC8JViAA4BB06hVQ1wAFueMjQBgibhC3vZxy+NIwBVWyYa/amhi8RANpGrkN9B4CAhgSFdsH2cl4QtGya8UkASB4TRYgsWzCMGKaSKL2GopIbLYRSZaBECNCS0i5y3B4liUSehYgkVLAg6XYPEsop10VWQRQ7Yssuhxcen25mVLXjzXaHbI9HIRZIbzoUUflvfkfGheH3r+dTlEE/ybg9uW9b95Xg6XYN2xm8ImvGArrA89izeF1FffZvSDR/vX/NIw7UCOhaMclLNZSujsIaW2f8to8/e3zhD7YULP+ub1ppH68NH+538sB3KMP8qBw9f4OQD/HWDo6HI4NMeMckDGYw0h3Fhcpz5UjaQQ4I5ycDimy9HxGQdvRZrsAeL1KGjOACAj0wBvlKNB4U0O12K6HO23wtj6cO3bT48fym8+tyXjXt7TdZFFr8thiSxiq1Emx2IXmajFYrocYtsok2eR6XLYQttduhwGU/AcgCaH441yeD0KtG2jxebY539bvOrbsi/JoWQukuplyX1AaNyukaNSw32uwAEE5IpRCsBQrVJcKUKdTyo3qABcZYj8qCEEpFyGAjyuToV8ihzUCN4oSVRALlIkQEXyAwvECgFAAgBDfAwaVadaU6e5xu2612p4q69sfam071Jyw8Udys4LWrs1TwyLLGK4XQ1arNaoVqNMniQIZY5MBqjeFlrEVufTQosQRpJBiww3GhdaxMaDTJ5FDIlRoSSwg5npArIU3fPw/zx1dLhRoXMRZC7KpBIZ9wEhfSVFQjzthiQ5yCRSPpCJXSUBAAzJZMYPcQDSCRGXuEIDiTQV8ESDt+AiMlRguNs3qRfs4OCar8aoa8a2wUUgcC0qAjBcjwQbz3KXUwikhz9Z9872a/tPvTy693Ji7dld8vZfiulMYvkNqlG8E11Jiix6+nrZ5slkgOQVoUXkQCbXIoShGzxJFBC5LrSIJ7rey/YNoe1Mp+32I5scOLjivx9efz6T8wGQuajjcyCBH6DUpyQG/PuupimAx+lsl4PmrJ5dDvg0hS4H+28ZrjJKfwgynAEcdjnMIMd0OdiuBHMiXpejSXPY5XBbbd44e/bS7yse+Y8fDv1yc8fQ1uL2W+5ZOV0ObDUG7HKIbXtdjqDFLjIZALscPIuopTwmtAhcdURsG7oc+aAd1naO0+VgOK+2ndC249t2Q9Mpfbuqb8WRMR8Il2A5s3lT6P6/2FuVyNuvXFIPvrDP/c8lvCmc/ZtCWmb5xD/6V+zPNI1wlMOZm1EOq2KZoznbkRPk/QsTem4Tup0op9f0Ld831AQgTOi526cQBhjChJ7bhG7qTuPMa0uW74yYdEJr1L8Ot0Z2ZmVrZHIt9/bWyJTM3lsjg0yeRe7WyBqHE22NrP7+Sv9D227b+LVr1yVY98zm9ZNcgjXvN68PLsGahc3rR+Z+83qU2cX2DDav10fPvLHkoQ2/XSMXu2B2wVLv+C5YNQrvtgsWvSiI4ebhLljq3OyClRVa5O6CRVvEMJNdsDTHuPXeg/3/uNj+ix4uwaI/LGetDx1O8L8zfWg/x4xbG/sefOdSI7wpFL4VYUIvpIRu0z9vf7jv5Z/DhBa9FWFCL6yEdpJaYtdf++/+EiwamNMlWA4vocMlWFOcD+1w8nXul2A5kyvW2Ep/scjQJMN9QNAjKjlq6O6zrBh+0BrkoBanAB5XjxkUzuEkAHQENApQZHIwOmz6QAdHwnjO9HEuF6+5zyqcj+EkaGGyQgBoPAYAMKTKFN7BkYvVIhp1PgiMTGVlQWQRQ1TpYbvey7bEsa3QrZajQovIjeV62C5khLYlApTSQotoB2TyLAJnposii8hhZnqNVwOtJjItY5G35z0EMwrltmGDe9jzHgNWl64nSAAAg0pzUpwu6S0ZVFBJyWwZSnAbkgiwxkbgImiOKdVdyENJb4XiMMhQETtR94EJzqSAZI2qvc0AGNIV6nysJAAMKMHNSGI4dWVJZBGCGVNFFj19caEksUwGUBmALXgOjR/PCy0CV8zyJFFcOSO0iCcCmTyLGDIlkUW0g5nJk+kBpL13v8sxtVXf83wJ1mx3OSa7BGuKXY55vgRrRltShDeFTnhT6NwDN4XhXA7KWZjQ92NCA8dN6Oms+p5PCW1zbuAnvfEmNn6Sq74xoYFjuhw8buYJfbc23pxeQs/CxptNU226Dwh2zCBHiu0+a3AAwQJOSlIAj1MS5MBSALAoTtfdZzXOAywfaI6PkmsBwOZwxWFyYGhBTjVJSEo+wHIIpOt+qycAmwqZGoWzkgCwYmag8QynP1URWbTQti60DRcrJ0QWu8hkAD0utIh2iiNCiyrhyvketqtZoUU8EcjkWcSQq4gsYqsxM3kyPYC0d5GmwIwRCGoECwPD/BeZCshV4ro/n4Y3raYW0ymc4SR6Po1aEwH6cF4PTJepK35w91v3Z9fwOB0mJ8kw/QYDAyTKugCA4G5e7+MKPa0GOXVIEUmCID053h3QIpLIooqvFAvaBkldZDJAIyKyiK1GmV1sj6f1gCSaczevF1jE2UYok208YztV0EWSvPLPskgm2gGZ4V7fgQ/Lqe71PbUuBwDhXt9+o8jz7HU5wptCJ7wpdO7Lm8IwocOEDhM6TOgwoZ0wocOEvtsJbVPcVBO6FTzRbCR0cAkWN6E7RjmGhPfdk12C1bEvU5Cri7fJ4i3BUmeyBKsR5LwlWGVyY85dFER+Jl6CpXlLsBTqfHX6vpu3BKvBW4LVy7a3BEtoexJLsIQWkRud7BIs3pjS9JdgaeIlWAqPgyVYXuPlQI6hzEUtC9bKQGjGYA8mJbgECzlYgtWERTwYdFjzAwFXDVmcNT96zyVYsIgHlmDZuNIJOYvicAkW4LbSpHDkeEuwgGOWYJmwiAcCAhi8JVgmtRqI4eyY5QMep1KLhwzOEizWdtwQWexYghW02EUmWoSgx4UWkSuO0I1iLEIoM0uwGEkgs5oVWkQ7mZrIIoZcRWRxwrYpkOnlIsicnS7HQh+2m5suR+9vCuNz/03hjPrQ+uS6HPWwD+3c2wkd1uUIE/oeSOj6+bilD142nNI5cn1hQocJvYAT2tY+37Erc23D2l8ae9/d6dZNCRN6oSd0l8pJk0xoUMwkdFOc0FOsnMRJaLZykjfgREKXyklMQmNtILOV3fLdb/LBc9GtN7bWd1xzuib0LFRO6pLQBgV0qZzUJaG7VE6a9LBdi7LNq5zEcGzlJJrrMmxn8xI6EY8k3AeE+ECMHEXi7nMUDiAgN3SZAnhc5DJ1Ph4XHRACsSg5uHGDAnjczesJH+dyl4eo8zEcXuyV2wEgAQCGq4MU3sHFwZXXqHgxG7kdv7Tq47du7B2Irz27S9p+ejyeiDxyVWQRQ0/bkV62eTKZi+1tG2R2sX3rmtB2lACDV4UW8WKv8mzHRba912Btx4SS4pTMRRPLNufVItngcsyORbLUMtC7sEgWWugvkq3uWrNm7ckt1sFv9l9KvjewQ9l50bqji2S9xk9vkWwP24WM0PZsLZI1MlNbJCsJFskaxt3b1m1+9KFnbU2h41S3f7fh5qk9B78qbP1qq3uBC2Rbt7s2247mwtl2QsV36aaw/VYk956zla8/rjm3dl53ifCmcKHfFN7PCc3sU+hAc8OEvhsJvbDKGISb14eVkxx+lwP3WDE1yXQfEIyoSo4ahvsswwEEHbhaggIwKMBBaMRNCm/oNKeQ08VoQNKpAIA5OkyupWFSgeHGc+RAVYRcok4A2fSDB2gkJKuk1QBoCBhUSJeh8Zpvh+X0qEZLYjgSlJVFkUUdbSsii56+uMgiBokjU6UBJSq0iNx4voftYjZokZFZSgstghYzVRZZxJApiSxiqw3WNiPJoGQu8n7KS2iF86/rkNDSJBMaOYniuiS0yiQ0AAaHg/egI6EZTpzQcpeEpt8rNqFpzvQSWqfOB4GRqUJCK8KENjGhpV4JzbGIoUtCq0xCi22zCc3heiZ0mU1oGvASuiKyaHISWp9aQqMdSN2wyyH6sAy7HAusclK4rZsz+zeF98wE/wV8UxgmdJjQTpjQ99h8aM6Jpjw5KcCF86HnOqFZACsnddTygUo3UBdHxzI1JlWmRkq1/Go1Xi0fg8K9ykmAqzYVANAAsDmAQYrfuCtWfMDjLD+4K1Z8vKOWD+FaKZnU3sHKSTrVKA2AdKPlAxgAgOAusvAbz+PsmOUDrCQIxlNV2k4QaMbpOlWMRWy1khRZ7CITm2swlZOCFj3bRSKTZxFtl/PEhElbbFKcu2JFYBG1oMwutnMVyjYrybNtilIScxFkBtYUyj1Wud2ZNYXBWj4dawp7VE7SmMpJk15TSJ9o5msKpV5rCrXeawp72Z6VNYXCyknemkKxbVhTmBJa7LmmEILOW1OoTGtNYdjlcMI+tBP2ocObwjChnTChw4QOEzpM6DChw4Sek4QG7p7sQy/g6qPzteD5Xas+KqgPrfr3klOtDx0N3qLOXn3o2vTrQ6sd9aHp++4u9aF5tXzgBeeyPrR3A88Z5Zi1+tDSdOpDczi9MLX60PKc1oeejQr+Oq+Cv8rhZlDBX51sBX/gJlvBnx4ZZU8kruDf5FbwD3I9K/g343QFf51TwR9lcixOr4I/Ow7dpYI/zU22gr8p3lCBU8GfbZRXwV9o2+bsl8Ct4B92OTo/LCffh55Ol4P5pjDcY6WjDx0uwXLCm8KAzPCm0P/XYUKHCU1ZXJAJvbDmQ99nO8nO0Xzoe3InWZA5+b2+dc5e3x6nUpy317dwK+/J7vVt8Pb6lnh7fXM2l57kXt+aLDzR3Oz13WFbFVnEVjdmvNe3EjNFFjv2+uZYhMDf65vi5nSv7wnbwb2+dd5e32xVDz3KFJqBA5mu6lFL9Ch90hAXmlGEtVGYEinuEqyupU/cNYXdS5+whWZUOQCYvQrNmFMpNMMvkaKsLNJ2aIszKTSjzG6hGXMsF7Qt0bYLWTNgkebcNYUCi6jF5BaaoW1niqbAYkehGU5K8gvN3LUuBw3M6RIsZ2pdjnAJ1sJc9R3eFDpzUB+aHIQ3heEox4JO6MiHV5rq9180nPiBQZcIE3rBJvRC/2JlVpZgVdZ/+l7u1117jhXf/3TrmDNPlmDNwhcrk12CNRtfrEx/CZb3xQp3lMPijHIYnFEODCrNeaMcsuj+fLKjHCZvlEPmjXJYVJjaKIfOAaYxytE22nKKay9vvn3g9+TGy+8rOy/Z/FEO1ALBjKkii56dGY9yqAzAWOwY5eBYBI4/ykFxczrKMTGIERxTMnijHPFYJO4+MAxESRgiz5EoFRAYukwBGKJRKiCAODxjACAywAAxKuCJblwP/luGu3mNfl3mWpC7TI6i+LqRIHDlNnURsUjwRFcGKZzHxS7FPGD07NGvv8/teWrT2ER96LE29sgVkUWebcYia5tjsYtMBogOCC0ihzJ5FiHcuha0yHCDV4UWPduDPWxfvdXDdnwgJpLpAeRni1q2Ru+hFYdts9Tgtm7IwbZuCGAwaE6FncgQZ7me27rBjmWwrVsTAAwazeG2bqYh5HjbuiFAb+tmAYABAAzZOoVbtCQE7BjsstYGlOO7dx/6aWN9908fXYhtuf6+tOOK+7Kcbd1QCwbYiYy1CMGzkxRZ7CLTpAEjzrEDAe2ATK5FCBVmWzeWI3ZqOaFFtA0yOyw2KS5XbXky+Vwzbolk4olmc1u38Kaw/Rhbv2fd7YH3NvxU27l5e8UJbwop2wvtpjBMaPetyJ2M2Mbl85oz8lOetCZM6DChycECTWgfcMhvwoS+m5OT7viWFK2pJfTCmJw0C0uwmG8Kp7UlxX06OQkTWlfquvuAoEVkEmqaGxrkAIMKXDVOQp0AOnAScBBqMZ3C6yoVJImcLioEZALoI3lyEXUhN5bVfVyr6RSOXLxKgIbuB2xUXSE/S5RJqwFQaABDsgiNV0ScGlFoSYpvEYP05LjIooq2JZFF5FAmxyKGOkemTANSROthezRLW6wFufFM0CIjs5gSWgQterLUw3a6ILLocaxtWlJdo2Qusk3Fdh8QrJhBjmTLfdZ0cqDqPmBLSQpgOQhygjqfrVhUAECNkx9ZHEDXyMH4KAV4nEmF4nDTxy3ZpgJyScl9NlSbOi0AKgCpOgVgAABDpgq4IeLMmOkDGBiZ+sqyyCKGmCayiADK5FjsIhObC0GLCS0iVyAyuRYhlHJwPrrxDFfJCi2iHZDZxXa2IrKIdjAzPZlGALBj5FezsgRrAe+CpQs/LBfIqm9Ol2NeLMG6a6u+w5tCJ1yx4txLN4VhQocJ7dxLCb1ARjm0+2WUY0433lwYoxwzm5xkwBQVCDgFxIJZH6pOBZgJYjeSNgFgcpJMT6uBICVsauIIh1Ngwo3JATQyv8QeG7F9wOOoaTV2IW/7OI+zkw2X0GGaDgYAFABSNQJA4zEAAMFOV8hrKLol4Myo4QMYGJnayrLAohdimsgitgZlspJojicTtGDAyUkci57twnAP2+2bwoBFWqZdydgCi6jFTldt3w7PdrZM2WYsTtjWRTLRDshcZKgNQ9d1DDoMjuhkPMSQFMMPyFXjhj9UAsGQZJ9z9/omoyiNICe7nNGIGvQwWwDQjZG84QMQjIbmB3d7ajcokjFxsRMcGWky4lVjAmC4NkB+lqgIAI9LlYwJvEMSvmBE7ZTEcvLKgsG36IWoLLDY1kcuAmXyJAllsoAUFVrExoPMTovGhEx3r2+RJLBTTHUHdCNZEllELl0UWZywrQhS0rMDI853fwnW1FZ9h7tghbtgOfwuR7gEywlvCt3HvXZTGCZ0mNBOmNBhQocJ7czLhGannOM0apx1PcUJ/kbPCf4E0GFOehMArUkFs+cEf21KE/wteoJ/iwHSEgV0meCPU845XDuhfQADI3NGE/xRH2+CP81pHJlo0ew5wR+40mgP25XhoEVGZpcJ/jozwV9sO09P8GclebaZCf40503wJ79apMlQpxeCOiRB9V9ScrcOhYbrwl2wVE5l46p4k6sGKSBcjwiBiV2wKIDHjWY0H1e9a6E5qA8tQQFhqU43CnfBKlGlinH/pqpKBfEuWKq3C5ZMnQ85WmaD2QWrHtwFS400KJncXbCiIov8Pcd4u2CpPWyPZDkWZYobSwctYgCukBRaRDuJ4C5Y3omAY3bBYlOS2QWLl5JeAWnSnHaXA/5uQ8AuR/u/CupDED8HgJNTADSp4H1YmtSnJJ6Pw3XrcsCHYGGMAHARGDT47IJQGnF8nMthlwM+tEydahQCaYkCLBrA4HU5LBGHXQ6d6XLQMr0uB1o0AwB+SvIsMl2OLrY1XpfDoOy0/0KLLJp0l6OLbexyMBYZmWyXgwHQDsjsYjtfFVmcsG35FhnOsxP2oZ2wD+0+7rE+dJjQTpjQTpjQYUKHCe3Mz4QOvykMvynsbnthfVOoq7AuBoJGz+XQJYUKAPDmcrCLh3D6gRqcqqHLBGjQswt4AG8uh96gFgUZY1nyGrgEi8PBXA5dgUVGGBiAzOWYWBREA8xcDsRVevEQM5eDJwmDvLLQHcDpBzyLmrcEK2gbJHWRyQDMXA7GIurDuRxc2/RcDp4kBGAuBx8grYa5HFyLzFwOriR6LgdXJjuXwzZgHYuBS7B0WGBj+auGMBiwVqaRBMCkOVjLA8FbggU4cBg0AihxMQCLc8ZGKIDHFfK2j+NFmBAUWPOTbFCrhnSaQyBVI7+BxkNAAEMalmABzkrCF4ySXykgCQLDabAEi2cRghXTRBax1VJCZLGLTLQIgBqzRBbRTmE42HiUJJPALMHicZWM0CLaAZk8ixiyZZHFCdu6QKaXiyAznA8t+rC8J+dD8/rQ86/LES7BCr4Vd/ymkHkrwHR4UxiOcizchJYtxxiWmkZ5vOloeXLyMKHDhF6oCd26/vqodfz5D+rJdS9f1T5fc9B9+TCh70pCt6BZGBJwAXAq06YCAmqaAjBYNKdDxrd0Dkcuw0jSP9NbAcApFYL/1uNIqEBC21aQM4BLqwSAtxYDAvBeZWSiBH7TNIMnyjUovAmNxwBAK+7/Vz+6a3W++N7Ih7999vO1nZHNY+8Pui/7dF1k0bNNN4CxiPpw2I5jkS+T1gKAlRBaRC3lMaFFCNWRoEVGZj0vtIi2c5LIIoZh+PNhNik7LJdoimR6AAzb5TKpnPuAkL2SJiGZdUOKHGDIJMlB4hoJAGBI01wSAMQ5XOpqDl5DeKLbgxTgcRkqRG6Rg3RKyF1L+MAEB40C4Hrcb7XXeAAw3IjlfJzLXWn/KjsiSbKsyoVd+fQW6aOv915OvHNul7zjTCmbSz16S2QRQvZqWmTRa43YtlgmA6SvZkUW0c7QraDFFM1FbwYtMjJjN4QW8UQgs4vtm9HJ2ObLRABkLqpXi3X3AaE2WCFHhZr7XIIDCMiND1GAx5Xrfijcps5XL9aoUCZACYAaAtUAUM+kKaCDIyGXJAflEgEKdSogNzTuPlcIgIEFImMcoEZxsRGq8ZUixWGrq4PumaTfnn3qqQNaY1c+u0X6+Nt9A8n1v+9Udp5X25e3IieyiGGwTJ2vTFtEoDAksoihyMoMAuVBoUVsTTYptAghnwhaZLiRmNAiNj46IrKIIT4slITng8zkySwiQNq7qONzALscmhP8+w5/2XldDvabQrbLEexR4KdkBxD8prBLl4MZtuvg4DOO1+XQ6A9B6HJ0+6ZQ3OXAXiIM29marptOfXuutvni9lvfHDn5UW7TwBbXksXrcsBVesN2dJeDsdjR5eD0y8QyUQsA5rS6HN6wHXQ5hoMWeV0OnkWvy9EQWeR+U8jrckAfmicTgXBNoTM7N4XkWf2+1Lr46nGzvHNDvvnLqz+5PwxvCsNRjgWY0Djjt9n+WWviJhNaEyb0/VQ5aX4kdPhN4d0r1khzs/dNoVeTlJnLYXPmciDXmFo5XZaD2QVxGuAVeMVyuuICr8Vh28e7lNPtmMtBTc7oUk7X4pXTVRgOZhdwyukysxB0zlyO6ZXT5VhETuHI1OnJHl45XY7FiXK6PWx3zOVgOHouB88i2mHnctAWbWYuB8ciW06XJ5Mtp+tNi8Mq1Lz5X10Kntd7FjwPclMseK71LHjO49iC5zTXEBc8x8rZEKBGN7fgeR0LnqvU+dhS3YTDgue8QuZswfN6z4LnQtsNccFzGQueCy16Bc9zPWx7Bc95cxs5Bc8Zi10KnjMct+A5PZnOm23XpeA5WzlpFroc5pS6HNObDz3PJyfN9nzoyXY5pjgfep5PTprRlhThTaETrlhx7qWbwjChw4R2woQOEzpMaGeeJjT8lFuXg/7Xdu+Eputy8PJ10nU5xoPvPZvQdF2Olsq8ZUxdDiahsVIEndCTqMsRTOhJ1OUgHC+heXU5eBY7EprzX71YJluXI9HqYRsTmmeRqcvBWGRkTrYuB89it7ocrG1LJJNN6G6Vkxq9Kidpc1k5SZ105SSNrvkzg8pJTFGgGVVOItydqJxUn73KSRyLPSsn1TmVkzgAyuxim1s5ieF6V04iPws3rxdVW+u2eT1pDbV5fYu77fr0atvp9Ob1ynQ2rzd6bl6vhpvXh31oKoR96Hndh6b/dZjQYUJTFsOEdsKE9kOY0Pdl5SQaCCsnzfvKSQ4nX+fHN4U4H9rQGob7gKBHFHLU0N1nGQ4gIFeLUwCPq8eo8/E4KcoAGhUUmRyMDpNrAUDncGM5w8e5XLxGACnISSoJyYr7rAIAgT1RqkzhDIet0SIadT4I2CjglJUFkUUMUbmH7Xov2xJrm7YIQY4KLSIHMrvYLmSEtqHVpbTQItoBmTyLGNJFkUUE9IhKNV6iJSEQJT9bZOmw2RsEMwqb4Elk6zcFDiDgpnD1BAVgYPcpjNM78bEc2elOhp3zDIneEU8yfMAaGyHXAoDJcBAKeWonPi6XqBMAdrqD4AGw012qRm2ZpyNgUiFdoXBWEgAG7JznSQpy6sqSyCIEM6aKLHr64pQdxiJXJmNRZfYp5FhEO+P5HraLuaBFRmY5I7SIuziCTJ5FDNmSyCK22mRtM5JMSmY4OUn0YRlOTgonJ4U3heFN4d2/KQwTOkxo575MaOC4Cb1wl2Bh4zk38JNI6Cbd+BkvweK9VzNP6Lu1BGt6CT0LS7Captp0HxDsmEGOFNt91uAAgqWQAylJAR6nU5ySaFK4YlFBJ5wa7wE0x0cpgMcVh8mBoZFrBgCDapKQlHyA5RBI18lvoPEQbGgNhkyVwllJAFgxk5KkGgFOX1kRWfRs6yKLyMkJoSSxTAbQxLbRTnFEaBFCOc9YtANcNSu0iCfK1EQWMeQqIotoBzOTkdkBkPYu0hSYMQJBjeB+XjD/RaYCAHolrvsTQjqm1RCuFiOAWtcCnETPp1FrIkAfzuuB6TJ1mC5Tdzl9NKv7s2t4nB6ruoQM028wMECiLAIg6Mmi7uOMJOTUIUUgCYP05Hh3QIP5NLzJSaBPR5kcSV1kMkAjIrKIrUaZfNtu0MfTukASAsWUGJBBZkkXWETbqYIukoQXBpnJk4l2cHJSuOrbmcVRjnDV92yMcoT1oYNvxR2/KbRozoFcCm8K5/VNYZjQXRK6Oaw5qdPZpj54WXeK58j1hQkdJvRCTWjrp78Pj+15f/3wtQ1rTzf2vLvTXYARJvRCT+heS7B6JzQoZhK6KU5ok6O4yxIsTkJzl2BBo7oswWIT2r2i0UNv5g2l+f75j89Ft97YWt9xzema0LOwBKtLQhsUYIhtd0noLkuweiY0Y9FLaM4SLI3m2CVYNDeRr5NcgpWIRxLuI0ZCfCBGjiJx9zkKBxCQG7pMATwuAgDiHC46IARiUXJw4wYF8Lib1xM+zuUuD1HnYzi82Cu3RQCGq4MUznD4GvGBdohnCpGhobxS+yA2bt7cNrp3IL727C5p++nxeCLyyFWRRQwD9Pl4XM7YVSkAAAoOSURBVKSXbZ5M5mJ72waZXWzfuia2TS5i8CpjhwbwYq8GbbOvwdhmUnLCdkwoCU4EwCJDgzlNEPSoypnXRU+BqiV6zP9q9JxtF2PmddHAZGfbjU9ytp0K51OZ2XYAcGbbGQBg6DbbDlpIZtuZV15ds+Zzo7Era9/cnmrtu5TcOLBD2XnRcmfbFUUWvdl2veY2Tna2HSNz1mfbZYMWGZnMbDvWYrfZdjSXYWbb0SnZMdtODcpEOzjbLhy2c2Y2bAeP+o5c7h+fXGn8vOfgV4WtX211LzActguH7RbqTaGjX25k1r+9Nase/aTm3Np13SXCm8KFflN4Hye00wKr8IIONDdM6PtxCdbU5kOHS7DCJVgOv8uBS7BMTTLdBwQjqpKjhuE+y3AAQQeulqAADApwEBpxk8IbOs0p5HQxGpB0KgBgjg6Ta2kA1why4zlyoCoUZzBcok4A2fSDB2gkJKuk1QBoCBhUSJWh8Zpvh+X0qEZLYjgS2jeFIos62lZEFj19cZFFDBJHJgMoUY4dCGhnPC+0CKGYDVpkZJbSQougBWXyLGLIlEQWsdUGa5uRZFAyF3UqphNa4fzrOiS0ZFChS0JzuC4JrTIJDYDB4eA98BKax7EJTSe+LExok3mv0kxCsxwmtE6dD4JOvxUqJLQiTGgTE1rqldBi2zyZaFFlElpsGxNabLtnQpfphGYtegldEVk0OQmtTy2h0Q6kbtjlEH1Yhl2OBbYEK9wFy5nNm8Jwxcp8uSkMEzpMaCdM6HtrCRbvRFNN6EnOh8aEBo5N6DlZgjWjhNYnl9D1u5XQLIBLsCxYx2LhoiBYMgMLbHRc72L6QFNKUcteMCCnM0uwAFdtKgCgAWBzAIOsonGrj1KLgpCz/OAWzPTxjsVDwKVkskYHl2DpVKMAaKUbFIABAAgtWDWEjedxdszyAVYSBOOpCm3RCADNOL3gjbGIgJIUWewiE5sLQY+LLHq2iyO0bSXAtcp5sB2UhEA12xJYRC0os4vtXKUlsDhhm17wxnCYiyBTtARLWLG4Z33oGluxOMjVxQWkYU2VPpwLLgpi60P3WoKF9aFlulKySi8K0hJlArAVi+kTietDa159aIU6X51eFCTjEiy6PnQjWB+6yxIsrz50L9uTqA8ttIhclyVYwOESLLHtQkpoUVwfmmmUztSH7liCRdeHZlb7cetDh10OJ+xDO2EfOrwpDBPaCRM6TOgwocOEDhM6TOg5SWjg7sk+9FTnQ2NCh5WTZvRNYYviZm8+dNdRDk5Vj26FZphRjrkpNEPuuydTaIYe5ZAbQYAd5ehSaIY3ygEtnMtCM94NPGeUo3ehmQYFcAvNMGNKUys0w+H0Qu9CM0Wq0Iw8xUIzKpWZvQvNTL4UGI5DJ+mxP2YEVeOMQ7PclEqBiUdGJ0qBicehe5cCC45DsyfCcWhOKbAmrxSYFuR0GIfWuoxD06XAdE7JMJTJsTjZUmDeODTHYrdSYDTXUQqM4ehSYKa4MhunFBjbKCwFpgltd4xDM4P1TCmwcNiu88Nyen3oyXY5mG8K7+Eux10r1hjeFDrhTaFzX94UhgkdJvRCSOiFNR96IW5JIbvbaOs11a3AMj/mQ9+TW1KATP6mQSZn0yCd3jTIhO1pPE6lOG/TIHobG2Y3G94+N7xNgxDgcbhpkMrZpQb3BOJuGkQDSbJpkCYHgWluGqQFOG/ToAOLr9r55a98sDTTeaKoKrKIrW6wmwYF9wTquWmQEjNFFjs2DeJYhFDMCiUxmwaJgd6bBmVKIosTtjWBbS8XQWb3QjOcqh61hNm99EmXQjPK5ArNuEuwupY+cdcU+jiv9InZq9CM2avQjLsMzi99Ii4007GtGy0TC80okf96uv7+v5/+8P+mzNkoNKPMbqEZcywXtC3RtgtZk5IZ5Nw1hQKLqAVldrGdKVK2Z6XQzL2/8aYztS7HrC3BMq2v/mPXf7+t3donz5cux7286ju8KXTm/KZQfup//08WCkiHN4XhKMfCSGjLfd2Wbbh/HltaR8HzX/9lZzjKESb0Qkro/IcFxxncLI1vfTNp/fD8cbchfkLf+uPnYULfqYTG6lVNCAm4ADiVaVMBOTVNARgsmtMh41s6h4MSv0n6Z3orADjFQvDfehwJFUho2wxyBnBplQIYzoD3KiOTVsNvmpwT5RoU3mQkAdCK+//VF95fmXeU9ctrXx47sy+1aWhr3H3Zp+uo5dYfPmMtYkhYIouoD/vQHIusTM92KwBYCaFF1FIeE1qEUB0R2yZ26nmhRbSdk0QWMQzDnw9TaNtJNH07rEwPgD50qTBach8QijfHydEIeR4bp0IRuOFBAIpUYLiRWyUK53CjDDBapML4GDlIJggAF4GB4VKxko93cAUSBoep82FggNt5v9WlAg1gGMpSOCMJgeJN91cVkhyNxM5s8/zu10ofDiTfvbBT3nFWajf38SS2+vJDX7IW8USe7aBFT9+tHrZ5MplWj90UWkQOZHItQshEgxYZmdmI0CKeaCgnsoghkoFG9bDNNr7A5BjIXDQ6nBt1HxiuDZOQJc+5YSqMwM8yNwEYoUI+P+qH7I1RCudwues9gNFohAJ4XHyIekEudyNDNQoD06ibaRGA4VaKwnncyDX3pQq/v/jcc5+ojV25kc3Hn818eDm57vwuecev1fY/fSwqsojhel5k0WvNjR62eTIZIN/TNshkLyxHc4nbQknQqORgDwBldrE9mOxpe1gkExsFMhd1fgjOoMthMV0OzucKt8tBH9jwYVnidDkMXpfDEnJ3rsshZVKpYquxM5/852N/+vnw9xd3xzdntkUcussRsNily2FNtsthi2SiFpvT5WC6EpPtctS6dDkI0JjlLgcrCbneXQ7ys/CmkAB68ESTvSm0yIH8WfuShrdL2XdfuW18ufqwC4ZzOcJRjgWY0PAetNzXbeq2pbTPa9XIC1phQi/UhF7o86FnYRyamcnrfqiqFevpek0KE5rIvHMJ3bK0lvuA0Iyb5Ehtus86HECwVXIgpyjA4wyKU5MtCldtijMIpyV4gO0DbuUk91oAaHK40gg5MPUgp1kkpGQfYDkE0g2/1S0TGg9XiSFbo3BGErbGjlmUJM3s4DIvXPn7tRdv8i3aaNsQWUROSYosdpHJAHpcaBHtgEyuRY1wlXwP27Ws0CKeKFMXWUQuV+Vb9DnITFYmC5D2LuooHjTUa5Vbz8pJ1Z6VkyIMwKnlM5wLrl7rqJyk+TiXgzWFUj3IYS2feIla3ubV/FGpIK6cpIorJ1GccvSx/7f8QKNb5SQ10uhhG2XOceWkHrbH0kLb0OpCUmhRXDmJ5ZjKSbwKS2zlpDqz8HJ6lZPs3n1ok/qUnMnGm4Xx4Kcz2+WA++452ngTQpeNN9VgH5rzYdn6+oG9luBTchY23jTEXY55sfEmhC4bbzLcrG28+f8Dar3N7MKIc8oAAAAldEVYdGRhdGU6Y3JlYXRlADIwMTgtMDYtMTFUMDk6NTg6NTYrMDA6MDC5DfUOAAAAJXRFWHRkYXRlOm1vZGlmeQAyMDE4LTA2LTExVDA5OjU4OjU2KzAwOjAwyFBNsgAAAABJRU5ErkJggg==)
In second case he buys one bat and 3 balls for 1300, therefore,
⇒ x + 3y = 1300 ......(ii) [Algebraic representation]
⇒ x = 1300 - 3y
At y = 400
⇒ x = 1300 - 3(400)
⇒ x = 100
At y = 300
⇒ x = 1300 - 3(300)
⇒ x = 400
![](data:image/png;base64,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)
From above points, we make the graph as follows, [Graphical representation]
Question 3.The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Answer:Let the cost of each kg of apples = Rs. X
Let the cost of each kg of grapes = Rs. Y
According to the question,
Cost of 2 kg of Apples = 2 x
Cost of 1 kg of grapes = y
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMoAAAAVCAMAAAAw04FgAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZjqQZmZmZpDbZrb/kDoAkDpmkLaQkNv/tmYAtmY6tmZmttuQtv//25A627Zm2////7Zm/9uQ//+2///bkxKCAgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACFElEQVRYR+1Xa1ODMBCEFlGLD7TxERvg//9L7xlCygTQdEZneh+0Yshl73b30qK4xrUC1wrMVcDuP+WxqU7/uURDe6DjE4yufqY/XFmWu2MmWN2t38mWVLahLflD1lAkQ3uD+3JaAzD6Zj7Z0DLatdE3vihdTTkASXUa2uxYXLSjxeYYbJQtZ8+8EQrsb6W/Xc39Lxw+cPPbr63Q+TppxviPkQ2UC6gA+bFLGlMoxBhYlBKZQBlTGSxf33CLsoWKQ0iMZ5fSFZTw7QimYMP2TKC4A23QN/rS3MEEim8D8gvfyewx1GsMb15GiuUdYPd6Hx4wIhjVursTDRuwC46gjwLF7D/qEtvHUPhnxlAoQfcrkaYUOpT/3EmxBi7VlIKhMAtR+ReCojNlpIghKCO0kXFcwVj2sMPwkjRWhUJdANoqwTJrRbsyqp2hKM3QaaZEiKGARXVPypMEwYRQiEtkn2zlduYplGDiY7HIkok2/cPX1K5jKFCE9/S081rBZQiDbD67Gau4veqJTzIo4RNwB5aEWoih9M3jwswUKDQgHXo7mpdXPc1KBKdjJ36wtEBdXTQBv4TwhEJ4ciDFgl5DVsdQzibTlBp4R4HAHTowMJ6LcAPwtF06KeRPY/UDSqa9Vfckam2JBc1v2eqXayODCq5+KzeezM+V71xo2QSLSmdtLrgMZPahtZnn1/38+wrf0P5wfAP+ySeJP4BmiQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Putting y = 20, 40 and 60 we get,
x = (160 - 20)/2 = 70
x = (160 - 40))/2 = 60
x = (160 - 60)/2 = 50
![](data:image/png;base64,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)
Algebraic Representation:
2 x + y = 160
Graphical Representation:
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5MMCTrGfiQQ7Zcuc2XgfolvU/kmwMLt2p6UjDsqArsROw0a8r6ora92ST+cA0BABBaaZik7VNHR3fUBvSOx0a8wqy1yrTIHw7bH2QYO1KexeRL+kX50dP4pCQH2p70vu1b/AKHFNY/0wJDLeFG8eX3kBGgJ0/70jWadqe9PjZJGBkZrkwwJOsZ+JAbAzFP30n+LXvpm1B27U9KRh2VAV2InYaNeV9UVte7JJ/OAaAgAgtNMr3bLlzmy8D9Et6n8k2oMXkS/pF+dHT+KQkB9qe9L7tW/6HFNY/0wJDLYS8dhTMvwHXItPp2eXV4aMbGPbRk2gNVo1xprp8FTRlp/zFP30n+LXvpm2k58n5CikGBdswE6stMzzd5FAPrtbwYXgu8KTW2/Dl1g0qBmnjxZAZDAq+dsuXObLwP0S3qfyTYGCEdqeyVbvtPrpFitU15zWk/jjXyk44jAUZz5HO1PrDnvuA4RT/a15Wuk3fKs8vGC01rIZLRaDCfC3kS/slUOjrwMYwfanvS40xJH3kEcR4jXEUNCHeY68hAbcO9zrwN9p5p2p70xqUXZxrI1RhTEgADE0BDTYP8AmKfvpP8AFr30zYfAu1PrD7vuA4RUPa15Wuk3nIs8vGSy1qJZDQZDa/2y5c5svA/RLep/JNqEDeQgMOHm514G+1A07U96Z1qLw4UkapwriAQRiKgFpgL82y1DTWjREpzK4SFiW5ocqSAvI0QmvGIJaQVqXVhLV0loFZJDt+kvHoeEVGYTmAstHrXjJ1MSYpsyW77r/wDqXd4a42/bukVlG9vJhWlmFZZM4XCTmpaWfJCVRaett9i62rh4y6YGc8iFSeWGm2XcrtND2LiryJf2SlnR14GEYftT3pcSYrD7yAOMcQpgKCoDzxx6rDAqMlO7lOqFXKIc6xF8OR1NTStOUF2vLz0MTjcQstPGZylhbVWZbc0RUMqrb98xmts9ja5M9GzjUPY+7hhTEvx/W4tPp2eXqYaMbOPbRnKoFFoUxrqr8NDVllweO1PSkGdlQFdiKOGjXlfVEnVuyCPzAmhAIADLTXM+TvlBXb3n3PSzeTJ5mxVlGf1GcZ3QlJPu7n2PYaTZun1dWE109KVLz4MKjbCq6zgwC0KPGiSSS1uhu8iX9IuDo6fzWEj/ALU96X3aT/0Oa6j/AKYkFlgH/MU/fSf4te+mbUE12qaOge+oDekDjo15jRlnkWmgfg22HsQ2dqF7tly5zZeB+iW9T+SbD068eX3cBBAp0/70gmadqe9PiZBOAkZnlxwBGs5mBIOLx2p6UgzsqArsRRw0a8r6ok6t2QR+YE0IBAAZaav5in76T/Fr30zZAbvIl/SLg6On81hI/wC1Pel92k/9Dmuo/wCmJBZYv9suXObLwP0S3qfyTYGFNdqmjoHvqA3pA46NeY0ZZ5FpoH4Nth7ENnahQT3ambz5v77T/WJd37WN/fNeecaLVTx1qyMca5+0PynXjy+7gIIFOn/ekEzTtT3p8TIJwEjM8uOAI1nMwJUoKf0Nm8Oao0wE6Zr6RbuobN7Wt4OzM52tXlts1T+xrrlAVNnO7nSoLJZIAIDbyk7VNHR3fUBvSOx0a8wqy1yrTIHw7bH2QYO1N/MU/fSf4te+mba/Ubx5feQEaAnT/vSNZp2p70+NkkYGRmuTDAk6xn4kEO2XLnNl4H6Jb1P5JsDC7dqelIw7KgK7ETsNGvK+qK2vdkk/nANAQAQWmmcRztT6w577gOEU/wBrXla6Td8qzy8YLTWshktFoMKDF5Ev6RfnR0/ikJAfanvS+7Vv+hxTWP8ATAkMtyOvIQG3Dvc68Dfaeadqe9MalF2cayNUYUxIAAxNAQ02D/mKfvpP8WvfTNh8I7U9kq3fafXSLFaprzmtJ/HGvlJxxGAoznr/AGy5c5svA/RLep/JNh8LeRL+yVQ6OvAxjB9qe9LjTEkfeQRxHiNcRQ0Idhm8dhTMvwHXItPp2eXV4aMbGPbRk2gNVo1xprp8FTRlp/zFP30n+LXvpm2k58n5CikGBdswE6stMzzd5FAPrtbwYXgu8KTW2/Dl1g0qBmnjxZAZDAq+dsuXObLwP0S3qfyTYGCEdqeyVbvtPrpFitU15zWk/jjXyk44jAUZz5Fu1PZKT32n10i3Sia85rVvxxr5CMcDgatZifC3kS/slUOjrwMYwfanvS40xJH3kEcR4jXEUNCHciryJf2SlnR14GEYftT3pcSYrD7yAOMcQpgKCoDwNgZin76T/Fr30zYfAu1PrD7vuA4RUPa15Wuk3nIs8vGSy1qJZDQZDa/2y5c5svA/RLep/JNqEDeQgMOHm514G+1A07U96Z1qLw4UkapwriAQRiKgFpgG+LdqeyUnvtPrpFulE15zWrfjjXyEY4HA1azCGYp++k/xa99M21/FXkS/slLOjrwMIw/anvS4kxWH3kAcY4hTAUFQHhDtly5zZeB+iW9T+SbAPuqdqnawu661FwPrEk7HRjz72UniC0Bqpy0wAqAy204vHanpSDOyoCuxFHDRryvqiTq3ZBH5gTQgEABlprT93E/IsFd3d9BPYKdQ9cSLJ0O/bhbtbwFCFDzQqSzRhQSJbad1AaOAehksnOaAALJcG7yJf0i4Ojp/NYSP+1Pel92k/wDQ5rqP+mJBZYB/zFP30n+LXvpm1BNdqmjoHvqA3pA46NeY0ZZ5FpoH4Nth7ENnahe7Zcuc2XgfolvU/kmw9OvHl93AQQKdP+9IJmnanvT4mQTgJGZ5ccARrOZgSDi7dqelIw7KgK7ETsNGvK+qK2vdkk/nANAQAQWmmYpO1TR0d31Ab0jsdGvMKstcq0yB8O2x9kGDtSnsXkS/pF+dHT+KQkB9qe9L7tW/6HFNY/0wJDLeFG8eX3kBGgJ0/wC9I1mnanvT42SRgZGa5MMCTrGfiQGwMxT99J/i176Zsgp7tTN58399p/rEu79rG/vmvPONFqp461ZGONc/aG92y5c5svA/RLep/JNkKCn9DZvDmqNMBOma+kW7qGze1reDszOdrV5bbNU/sa65QFTZzu50qCyWSACA28pO1TR0d31Ab0jsdGvMKstcq0yB8O2x9kGDtTfzFP30n+LXvpm2v1G8eX3kBGgJ0/70jWadqe9PjZJGBkZrkwwJOsZ+JBDtly5zZeB+iW9T+SbAwQjtT2Srd9p9dIsVqmvOa0n8ca+UnHEYCjOfI52p9Yc99wHCKf7WvK10m75Vnl4wWmtZDJaLQYT4W8iX9kqh0deBjGD7U96XGmJI+8gjiPEa4ihoQ7zHXkIDbh3udeBvtPNO1PemNSi7ONZGqMKYkAAYmgIabB/zFP30n+LXvpm0sn9suXObLwP0S3qfyTaWDYlhiTwYm9HJ/kWbY2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsQINcJQfRql5ZHtlW4MUujlDyLVhzyEidKQY0nHBrYijqYTKeGlcqP8AvFOMmuazFKEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgDJYWzwlGdGpvlli02JGc6R3yU30PYe7hInSkYNJxxa2Ina2EynhqvIj/vNeIima0C9ex9bC8j4iTl+rStbYttV3qQ77tX3i1j4599Qk4j2u45YVx7myK41xOsDUzVpnYGxIznSO+Sm+h7BmD30r9IuvNaTbCh6i46STvOTqw+EhYnZKrRUjq6RYqcxM5rSqU3IOGrj145xwDEj4WJ6w53TjuEk/2KZr0k7HM5qK8QoaAbYYtNgyWGQe+lfpF15rSbY2JGc6R3yU30PYfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BgCMZvpI6Re+a1axOy3FwsTslKqqR1dIt0OYmc1qta7kDDXx68c4YhshsSM50jvkpvoewKV2frdUfj7er+1Kc7N0ZvpI6Re+a1ayBdzDv8Asfj6R8f6/L1ObcT20pyOPcsaVp+QDUashui4WJ2SlVVI6ukW6HMTOa1WtdyBhr49eOcMQ2DJYWn+ov8ApJR85PbTYkZzpHfJTfQ9h8BCxPWH26cdwkoexTNekng5nFBXiNTQnbHBpgCDXCUH0apeWR7cISh1P27qT71kOfxebfJMkiSXN94N4V1GTjMShdf2jroJ9vbS11KvHmiUCiXVy3e6svJlE4Tsy7QLzr07y5PlVqeF7sLlGWOtSuzLPb7yEidKQY0nHBrYijqYTKeGlcqP+8U4ya5rJDYkZzpHfJTfQ9g4zyccjuRsnJceTgkzteveK8hZETbqLrYC8tWlJRgLibl0ZW0yk3OXeNyhIsoLitLjCoEt5EzHec/vKvYmQoMvO5tnWMeIDliy9eN/xTMjf/sC6pZ/9G9Sdt26mwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdseErw3D7+tIyPKRsZX+gP1S2hGwKgf0jupV1FCwBTEa3ZIDDG2dkNsWDv5W4MUujlDyLVidltShInRsdunHb1jq0CWMKNY1KQRr/Bw4887YENiRnOkd8lN9D2CM8JRnRqb5ZYtlW4MUujlDyLVhzuEidKRg0nHFrYidrYTKeGq8iP8AvNeIima1FKEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgDJYWzwlGdGpvlli02JGc6R3yU30PYe7hInSkYNJxxa2Ina2EynhqvIj/vNeIima0AK8z1up3x9uq/alJltg21beNDv+x+ArHx/r8ur5twPbSk04dywrSn5CdZoyX7YkZzpHfJTfQ9gzB76V+kXXmtJthQ9RcdJJ3nJ1YfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWmwZLC0/1F/wBJKPnJ7abEjOdI75Kb6HsPgIWJ6w+3TjuElD2KZr0k8HM4oK8RqaE7Y4NMARjN9JHSL3zWrWHLyAkTWhLktTBAwyogTCmKCEupsQA1BKaYrJ7xKVExtktBoO3zppty34LVGiwy0CWiJFwsTslKqqR1dIt0OYmc1qta7kDDXx68c4YhshsSM50jvkpvoeweC/UoJ1UsmK+jKR6mJP0e/fJ92M+3h3q5LCkqRLstzDc0tz+tBXSAeuDukurrTSy7Ydh628fv57ZADuWGyfehrhKD6NUvLI9vCPql91E6yZJV1/VCLlRGvb4ci6+C9eY12EhWiyZvuHVr1ZwZvGlRTYzM1t2znENtZzPWpVWp6Gaeugs+v9095MuX3SDdve9IkwqSpKF4kjupqQYzNSgzo5Ydoz9mEbokhoqDDbRdFlosAPXL5lnOZIaAbxsMSeDE3o5P8izbGxIznSO+Sm+h7D02EidGwO6cdvWBpUJZwozjUJAGv8HHizDtiBBrhKD6NUvLI9illt5CROlIMaTjg1sRR1MJlPDSuVH/AHinGTXNZIbEjOdI75Kb6HsGUngxN6OT/Is2T0/66E2/ES7z9Z7z7H02EidGwO6cdvWBpUJZwozjUJAGv8HHizDtiowEM/7Z83kR8fXsEu7FNzMPqmvPOHcwfwcWRQGlc49bsD+rcGKXRyh5FqxOy2pQkTo2O3Tjt6x1aBLGFGsalII1/g4ceedsCGxIznSO+Sm+h7BGeEozo1N8ssWih6i46STvOTqw93CROlIwaTji1sRO1sJlPDVeRH/ea8RFM1qR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWmwZLDIPfSv0i681pNsbEjOdI75Kb6HsPhIWJ2Sq0VI6ukWKnMTOa0qlNyDhq49eOccAwAK8z1up3x9uq/alJltg21beNDv+x+ArHx/r8ur5twPbSk04dywrSn5CdZoyX7YkZzpHfJTfQ9gzB76V+kXXmtJtIzfSR0i981q1h0JCxOyVWipHV0ixU5iZzWlUpuQcNXHrxzjgGJFwsTslKqqR1dIt0OYmc1qta7kDDXx68c4YhsGSwtP9Rf9JKPnJ7abEjOdI75Kb6HsPgIWJ6w+3TjuElD2KZr0k8HM4oK8RqaE7Y4NMARjN9JHSL3zWrWJ2W4uFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDENkNiRnOkd8lN9D2BOun+thdv8RJN/VpJs4tcJQfRql5ZHtr+6uHfdq+7qkfHOfqEk4e13FLCQPc2hXCuB1k62aNNODyEidKQY0nHBrYijqYTKeGlcqP+8U4ya5rIMlhiTwYm9HJ/kWbY2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsQIM8JRnRqb5ZYtlW4MUujlDyLVhzuEidKRg0nHFrYidrYTKeGq8iP8AvNeIima1FKEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgDJbXif9dCbfiJd5+s959m/YkZzpHfJTfQ9kGAhn/bPm8iPj69gl3YpuZh9U155w7mD+DiyKA0rnHrdgf1bgxS6OUPItWJ2W1KEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgQ2JGc6R3yU30PYMwe+lfpF15rSbYUPUXHSSd5ydWHwkLE7JVaKkdXSLFTmJnNaVSm5Bw1cevHOOAYkfCxPWHO6cdwkn+xTNeknY5nNRXiFDQDbDFpsGS0sL2JGc6R3yU30PaWDOkHfuUf4rUv4VqCbHudGwPc47ekD7WKYPgs8rto4ceOGs5wIZZYrDEngxN6OT/Is2Cg8jnOlIPuUdvRQx0ap/dpBx7mKclSCKgjAhppqKUe50bHdzjt6R3tYpk+C1yO2TjxY46xmgFlq81wlB9GqXlke2VbgxS6OUPItWCaQd+5R/itS/hWoO45zpSM7lHb0T8dGqf3aucO5mvJUACpAxJZaZYrC2eEozo1N8ssWBAvWjnTd2F4tXUePqEnLApikDjLCuK062PyDGpJAFGiy0zsDSDv3KP8VqX8Kybex9bC8j4iTl+rStbYtgXISOdbJVu5R53RZHBqlzWlf5YwxwOo0NAKEtZjo9z1hz3OO4SgPaxS5zYr/dfkxNRQg5pBDLF+D30r9IuvNaTbCh6i46STvOTqwZ0g79yj/Fal/CsPhI51slW7lHndFkcGqXNaV/ljDHA6jQ0AoS0x2GQe+lfpF15rSbAPi451slJ7lHjdFocGqXNar/AJZwwxOoVFQagskNIO/co/xWpfwrSM30kdIvfNatYnYNW3cxzp3L0eA6j6dnt6mpMUz9tKcsPA/KRrqCDgCAG+LjnWyUnuUeN0Whwapc1qv+WcMMTqFRUGoLIG7P1uqPx9vV/alOdm6M30kdIvfNatYJpB37lH+K1L+FahAx7nrD7ucdwlH+1ilzm3T+6/LiKCgJzQAWW2KwtP8AUX/SSj5ye2Ci8jnOlIPuUdvRQx0ap/dpBx7mKclSCKgjAhppq/pB37lH+K1L+FbDXCUH0apeWR7FLAupse50bA9zjt6QPtYpg+Czyu2jhx44aznAhlnhG8KNdf1pGR411uNoMgfqljJonKNanKO6lXSjIYqRtDVoMEeBVpjrjtm3fqTwYm9HJ/kWbcI3jf8AFMyN/wDsC6pZ/wDRvUnbB2+pR7nRsd3OO3pHe1imT4LXI7ZOPFjjrGaAWWr+kHfuUf4rUv4VorcGKXRyh5FqxOwLruOc6UjO5R29E/HRqn92rnDuZryVAAqQMSWWmYpR7nRsd3OO3pHe1imT4LXI7ZOPFjjrGaAWWrzPCUZ0am+WWLZVuDFLo5Q8i1YJpB37lH+K1L+Fag7jnOlIzuUdvRPx0ap/dq5w7ma8lQAKkDEllplisLZ4SjOjU3yyxYEG8aOdPJegAXUfTs9ur1pimPtpSbh4H5CdVACcQCC/6Qd+5R/itS/hWUbzPW6nfH26r9qUmW2DYFyEjnWyVbuUed0WRwapc1pX+WMMcDqNDQChLWY6Pc9Yc9zjuEoD2sUuc2K/3X5MTUUIOaQQyxfg99K/SLrzWk2woeouOkk7zk6sGdIO/co/xWpfwrUIGPc9YfdzjuEo/wBrFLnNun91+XEUFATmgAstsVhaf6i/6SUfOT2wUIuOdbJSe5R43RaHBqlzWq/5ZwwxOoVFQagskNIO/co/xWpfwrSM30kdIvfNatYnYNJyrBIExyLM0trybpdEXJpvhS11NiExRjYFUgFe8CdWFdLpmULL1hp67bH3NWXTLLTWcz499TSmdVySMpe/3qYU/Rii+RJKipgvryTVRQcKlZguYnBUaWVaWnbLYLppuWG2mSass500i8AnrhYYdNe192frdUfj7er+1Kc7eRHVfbq5sldLuYy/bl4Np5fTkVLzU5qUPCFtgTncwrKyY7vGlRVfAhvRLLmPq8DLYadSosz8RSoJD2l0g79yj/Fal/CtQTY9zo2B7nHb0gfaxTB8FnldtHDjxw1nOBDLKDczetKF+l1F3178gRjKhJ940qpk3IcSwy7ZeMwKzBBvYLQdss0V0Ztko0QMGWXjl4A099js1J4MTejk/wAizYKDyOc6Ug+5R29FDHRqn92kHHuYpyVIIqCMCGmmr+kHfuUf4rUv4VsNcJQY/Fqj5ZI//wCGxSwLqbHudGwPc47ekD7WKYPgs8rto4ceOGs5wIZZT4CPc9s+b6uo/wBYd3ftYp4/VNefq2lMNeAGGPg7Qv6TwYm9HJ/kWbJ6f9dCbfiJd5+s959gYVKPc6Nju5x29I72sUyfBa5HbJx4scdYzQCy1f0g79yj/Fal/CtFbgxS6OUPItWJ2BddxznSkZ3KO3on46NU/u1c4dzNeSoAFSBiSy0zI6Pc9Yc9zjuEoD2sUuc2K/3X5MTUUIOaQQyxeZ4SjOjU3yyxaKHqLjpJO85OrBnSDv3KP8VqX8Kw+EjnWyVbuUed0WRwapc1pX+WMMcDqNDQChLTHYZB76V+kXXmtJsCBeNHOnkvQALqPp2e3V60xTH20pNw8D8hOqgBOIBBf9IO/co/xWpfwrKN5nrdTvj7dV+1KTLbBsC5CRzrZKt3KPO6LI4NUua0r/LGGOB1GhoBQlqRcc62Sk9yjxui0ODVLmtV/wAs4YYnUKioNQWSEHvpX6Rdea0m0jN9JHSL3zWrWCaQd+5R/itS/hWoQMe56w+7nHcJR/tYpc5t0/uvy4igoCc0AFltisLT/UX/AEko+cntgoRcc62Sk9yjxui0ODVLmtV/yzhhidQqKg1BZIaQd+5R/itS/hWkZvpI6Re+a1axOwasupjnTF2F3VHUefqEk3AJikThLCQK062fyHGoIINWg0004vI5zpSD7lHb0UMdGqf3aQce5inJUgioIwIaaaXLp/rYXb/ESTf1aSbOLXCUH0apeWR7BnSDv3KP8VqX8K1BNj3OjYHucdvSB9rFMHwWeV20cOPHDWc4EMssVhiTwYm9HJ/kWbBQdxznSkZ3KO3on46NU/u1c4dzNeSoAFSBiSy0zFKPc6Nju5x29I72sUyfBa5HbJx4scdYzQCy1eZ4SjOjU3yyxbKtwYpdHKHkWrBNIO/co/xWpfwrIEBHue2fN9XUf6w7u/axTx+qa8/VtKYa8AMMfB2h2lbXif8AXQm34iXefrPefYGFSj3OjY7ucdvSO9rFMnwWuR2yceLHHWM0AstX9IO/co/xWpfwrRW4MUujlDyLVidgXISOdbJVu5R53RZHBqlzWlf5YwxwOo0NAKEtZjo9z1hz3OO4SgPaxS5zYr/dfkxNRQg5pBDLF+D30r9IuvNaTbCh6i46STvOTqwZ0g79yj/Fal/CtLE7SwDNHu/dY/xopfxbUE2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01e2XGc1x3yk30xYemxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqA+nkC50pB91jt6KGGklP7tIGPdDXloSBUk4ktMsxSgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM/LyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzUUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1IEdHu/dY/xopfxbUHcC50pGd1jt6J+GklP7tXGHdBTloCRUA4EMstXtlxnNcd8pN9MWHu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMgoXrQLpi7C8Wr2PP1CTliVNSJwlhXNK9cP5RhUEAirQZZa2Bo937rH+NFL+LbX16kQ+7V94tYCOc/UJOJ9ruKWFc+6NCuFMRrI1s1Za2BsuM5rjvlJvpiwUISBdbJVu6x43RZPCSlzWlf5hwwwGoVNCakM5joBz1hz3SO4SgPbNS5zYr/e/kwNBQAZwADTfzCRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuR8VE9Yc7mR3CSf7JM16SdnngUFeMVNCNqcWWAI6Pd+6x/jRS/i2HwkC62Srd1jxuiyeElLmtK/zDhhgNQqaE1IZv7LjOa475Sb6YsPhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC2GYuBdbJSe6x53RaPCSlzWq/5gwxxGo0FSKANENHu/dY/xopfxbDouKidkpVUuOrpFugz0zmtVrXdc4a+LXhmnEsENlxnNcd8pN9MWBBu5gXTyXo8h7H07Pb1NSmpj7aU5Y+H+UDVQADEAEt8XAutkpPdY87otHhJS5rVf8wYY4jUaCpFAGlC7mIf9j8fSAj/X5epzbge2lOQx7rhWlfyEazVot0XFROyUqqXHV0i3QZ6ZzWq1ruucNfFrwzTiWAI6Pd+6x/jRS/i2oQMA56w+7pHcJR/tmpc5t0/vfy4CooSM4glpi9suM5rjvlJvpiw+AionrD7cyO4SUPZJmvSTw88GorxmhoDtRgy2H08gXOlIPusdvRQw0kp/dpAx7oa8tCQKknElplm/o937rH+NFL+LYc8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc0Q2XGc1x3yk30xYKKbAOdGwPdI7ekD7ZqZPgs8rxk48eGOo5oAaa4RvCgnX9aRkeM9cjaHIH6pY0aKKjWoyjupV0o0G6gbc1ZDYHgVZb627at3YmxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqOErw377+tIyPKQUZX+gP1S2gGwKkf0jupV1NS2RTAa3gJDbG1eEtt2Du9SgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM39Hu/dY/xopfxbDlKLidGx25kdvWOrQpZwo1hQq4Gv8ACx48w7UkNlxnNcd8pN9MWCi7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhllqKUA50bHd0jt6R3tmpg+C1yPGjhxYYahnAlpn5dxcTpSMOjI4NbETtbaZTw1XkWP3CnEDXOZilFxOjY7cyO3rHVoUs4UawoVcDX+Fjx5h2pAjo937rH+NFL+Lag7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhllq9suM5rjvlJvpiw93FxOlIw6Mjg1sRO1tplPDVeRY/cKcQNc5kFG8aBdO5egCXsfTs9ur1qamftpSbj4f5AddQSMASQ/6Pd+6x/jRS/i2QLxoh/wBj8BWAj/X5dXzbie2lJow7rjStfyA6jRoP2y4zmuO+Um+mLBQhIF1slW7rHjdFk8JKXNaV/mHDDAahU0JqQzmOgHPWHPdI7hKA9s1LnNiv97+TA0FABnAANN/MJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5HxUT1hzuZHcJJ/skzXpJ2eeBQV4xU0I2pxZYAjo937rH+NFL+LahAwDnrD7ukdwlH+2alzm3T+9/LgKihIziCWmL2y4zmuO+Um+mLD4CKiesPtzI7hJQ9kma9JPDzwaivGaGgO1GDLYZi4F1slJ7rHndFo8JKXNar/mDDHEajQVIoA0Q0e791j/Gil/FsOi4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwQ2XGc1x3yk30xYEG7mBdPJejyHsfTs9vU1KamPtpTlj4f5QNVAAMQASWXpZRpgYikJYhXqmkLqDMCMqp8SpKDcDFJitopKVE1ujZPW3rstMgDMaGc8zS7zi0wJu5iH/Y/H0gI/1+Xqc24HtpTkMe64VpX8hGs1aLc8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc0Hhv1NiMUMkLKYygupfzuoKzUuy+qqd/GSYoqKkqtNK9zM5KjSsrys7LRYFJYeZrRziGWpmF4JB1V9yk2Ac6MgavI7ekD7ZqZ9izxl4zhy4Y6jmgBo+OXVeLqZzSZWuoy77lUSN7d+RFNDyfIhl2Ex2ZuuXbLIvMlVWaZaIeIpSWnjx62w2w06lV9PecwC8Zbb9N7hb4JWv3uauvvhkR1ERcoXiyQgTghvy0lBqCdrac03ox5iyQqoDbJQX4zWGG3jDQbaeDONkc7f7ttt+PLE8VmftPP7f+OZctHKJn2413J6Rc/LUDOc+RcvXg3mzOkrryY41lzc5dKnoyleI0iu0hcRG+ziYSrIyHJRabahzMcWWnzpthhos9py0uIc4S3Ls2oMVER6JM6ImzAmRTpRjwzFJytAOlRMeZweggNuX7LQzqEMGhBJLFvPBLuUvLv0yhb+76VKf7+Li4BJjk/J8uzSEOUbnA7m+7ST81Um2aXiPf7dXeW08RZnnteXG3S5LTiW4aaJUl6XWgJhadQrVtq5DkuzndRd1NeT3NSLNj2BuBvCX5DkObVpDZgIG8C6tVZE33bq6UraGllAWXstoK05u/mhqXoZ45dzTLkQHjTHX2Sep6hpumU6Tp6aecP4vQVw21l63tN9RbX92TJE922OI0O+HDFaRNt/qWtM8uO6dquoZesT9et40PUJtEccY50E1rWYjz/jOZ38bbbeku102Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA00nwEA57Z831ex/rDu79s1PD6prz9W3pjqwJww8HbhJWr+7s5JiJtQZmWIiAjrtbqu3BP4hIBZV+xO7o6VdszIsxiRDtunbl7opfMty86LM1zSEFeeyjKbx1L0QHOlcnrK/uqyjLy51f3cy7lCwMI7utu7W3ane3knZUeTugxkAFa8d43HIU1ZQd092CEuMtsKYaZbl4vGmmWXjQePHbttljlv33+/v8Ad2XHpG0eztBSgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM39Hu/dY/xopfxbccXc5ceTdfZOSndrdxMk2K0xxUtzJMUrKytdTetJkj3ny9K75wkLsy3F3rznIUvXfX+oCE/VEh4+XbkZovKYdQ6zDxJYLhtl4z2NsuM5rjvlJvpiwUXcC50pGd1jt6J+GklP7tXGHdBTloCRUA4EMstSOgHPWHPdI7hKA9s1LnNiv97+TA0FABnAANN8XTb1QDJcka+pUuUmKepgcTgkTFKcjTaup9116sxXQ3bT/OLkqklyDe7lFIEkr9wN1E+TMVpCeSpIN5V6csTU+7NJHZcyox2VSo1MJK/rLoycsnmZ4CSb0ppmxHmFiDRJqmhiV7qb07yEK7CTVuaiiI09X4zldvIc0SNk+yNML0K713eDfXMt20oGFQpmieyRpzKkytwgdnaPd+6x/jRS/i2HwkC62Srd1jxuiyeElLmtK/zDhhgNQqaE1IZQ4K9KVYm8R5dm6UIjs1MkwV4EGimGfO9MSm9XHqK0ro6lhL62HSx1l1NDcuv3xlZlXl0TUIJiZZYainuEionZKrRLjq6RYqM9M5rSqU3XGGri14ZowLYKN40C6dy9AEvY+nZ7dXrU1M/bSk3Hw/yA66gkYAkh/wBHu/dY/wAaKX8WyBeNEP8AsfgKwEf6/Lq+bcT20pNGHdcaVr+QHUaNB+2XGc1x3yk30xYKEJAutkq3dY8bosnhJS5rSv8AMOGGA1CpoTUhmRcC62Sk91jzui0eElLmtV/zBhjiNRoKkUAaxCRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuRcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYAjo937rH+NFL+LahAwDnrD7ukdwlH+2alzm3T+9/LgKihIziCWmL2y4zmuO+Um+mLD4CKiesPtzI7hJQ9kma9JPDzwaivGaGgO1GDLYZi4F1slJ7rHndFo8JKXNar/mDDHEajQVIoA0Q0e791j/ABopfxbDouKidkpVUuOrpFugz0zmtVrXdc4a+LXhmnEsENlxnNcd8pN9MWBAupgXTd2F3VHsePqEk3EKakDjLCQaV64PynCpJJNGi0yy4vIFzpSD7rHb0UMNJKf3aQMe6GvLQkCpJxJaZZTbq4h92r7uqQEc++oSTj7XccsJB90ZFcaYDWDqZoyy4PIuJ0pBnRkcWtiKOptMp4aVyrH7jXjApnNAR0e791j/ABopfxbUE2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01e2XGc1x3yk30xYemxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqA+ncC50pGd1jt6J+GklP7tXGHdBTloCRUA4EMstRSgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM/LuLidKRh0ZHBrYidrbTKeGq8ix+4U4ga5zMUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1IEdHu/dY/xopfxbIEBAOe2fN9Xsf6w7u/bNTw+qa8/Vt6Y6sCcMPB24ftlxnNcd8pN9MWQYCJf9s+bwICPr2CXdmu5mP1TXnjDuhP4WLRqBWmcOuWBwUoBzo2O7pHb0jvbNTB8FrkeNHDiww1DOBLTN/R7v3WP8aKX8Ww5Si4nRsduZHb1jq0KWcKNYUKuBr/Cx48w7UkNlxnNcd8pN9MWChCQLrZKt3WPG6LJ4SUua0r/ADDhhgNQqaE1IZzHQDnrDnukdwlAe2alzmxX+9/JgaCgAzgAGm/mEionZKrRLjq6RYqM9M5rSqU3XGGri14ZowLcj4qJ6w53MjuEk/2SZr0k7PPAoK8YqaEbU4ssAR0e791j/Gil/FtLY2XGc1x3yk30xaWApYYk8GJvRyf5Fmyd2tJc5zvA/S1ep/O1h6ddxL7yAgiVGf8AekE1XtsXp8bIBxE8tcmOJJ1HPwADYDXCUH0apeWR7ZVuDFLo5Q8i1bX7d28v6RcDSM/ikJH/AG2L0vu0n/rgU1n/AFwJLTeFG7iX3cBGkKM/70jWq9ti9PiZIGJnlnlwxBGoZmIIbUsLZ4SjOjU3yyxZP7Wkuc53gfpavU/na1Bi7eX9IvxpGfzWEgPtsXpfdq3/AFwa6h/riQGmAvXsfWwvI+Ik5fq0rW2Lbny8eQUWCu7vBjXUbOoeuJFnGIcMRV5V4ChCh5oVWaq2nq8yNO6gNDEugyWTmskABov/AGtJc5zvA/S1ep/O1gcYPfSv0i681pNsKHqLjpJO85Ora/hbt5f2SqDSN4GEYPtsXpcSYkn79wOM8YpiaipLzMddugMOHe6N4G+08V7bF6Z1qLsY1nmpwpgSQRgagBlgNp2GQe+lfpF15rSbJ3a0lznO8D9LV6n87WHwt28v7JVBpG8DCMH22L0uJMST9+4HGeMUxNRUl4GwYzfSR0i981q1idtVxV28v7JSxpG8DGMP22L0uNMVj9+5HEOM1wNTQF2Q7Wkuc53gfpavU/nawfd2frdUfj7er+1Kc7N0ZvpI6Re+a1a2kpDkFCikGOeNR86stMzzeHCkubyrwYXgu8KcmGPAmJg0qDnDjwaJZDBq2RV28v7JSxpG8DGMP22L0uNMVj9+5HEOM1wNTQF2G1LC0/1F/wBJKPnJ7ZP7Wkuc53gfpavU/na1CBu3QG3DzdG8DfagK9ti9MalF4MKTzUYVwBAAwFASy2D+1wlB9GqXlke3J8oZVSbO16a5JqNcvfy5u3S1ub5dhMpOKlqWG7hplnG7d0pu50lZJaTp+e3roTqWllFW5bany8G6mU7rprmdEiZXkmdZqfxMtiI3zCyMiQa2nRjqKm5t66g1CIYZi7xJ9UGCS0lMNZ6arr8QwWTQChYoxqbFXlB4uXX5B04yblCIkBLNwTm7uPQZ5yq5ivay3zM8iRkflCXL35t3pK93lwSQUifJlygFhqVl68SUZgey7ebK8p3VXSNXYumLn25pz3Ng9DsnHLDkjKMWXknpMk3r3dPYqRE29a65QvMSZRToC/e5dYVijJN8V3jEnz3N64ky62qtJTETLl5zm7W9iWyvS69myTINtectlevG/4pmRv/ANgXVLP/AKN6k7bQ2SFcPfs8vAuhXL6Lr1a55KyY8jp7kgwSmLw5TXu3RMaqsXYKa/endwrXYz5NEwI11QSbo0pmU27zHd2F6jDxcHXJLlkMNMtbAvDkNHY6pzkfpzMdOBcxGQT1R+MaeG8WfCoh7D5QPUtXQDtVMxGKdu913ue6dxDLp60y5evA8acOeth6Tq3Bil0coeRasTtqtRu4l93ARpCjP+9I1qvbYvT4mSBiZ5Z5cMQRqGZiCQ7Wkuc53gfpavU/nawODPCUZ0am+WWLZVuDFLo5Q8i1bX7F28v6RfjSM/msJAfbYvS+7Vv+uDXUP9cSA0xhRu4l93ARpCjP+9I1qvbYvT4mSBiZ5Z5cMQRqGZiCG1LC2eEozo1N8ssWT+1pLnOd4H6Wr1P52tQYu3l/SL8aRn81hID7bF6X3at/1wa6h/riQGmAJXmet1O+Pt1X7UpMtsG3P8+SChQqDAvGY+dWmmp5u8hQX15V4MVwpeFJrDfhzE2aVIzRxYtAtBsUfO1pLnOd4H6Wr1P52sDjB76V+kXXmtJthQ9RcdJJ3nJ1bX8LdvL+yVQaRvAwjB9ti9LiTEk/fuBxnjFMTUVJeZjrt0Bhw73RvA32nivbYvTOtRdjGs81OFMCSCMDUAMsBtOwtP8AUX/SSj5ye2T+1pLnOd4H6Wr1P52tQgbt0Btw83RvA32oCvbYvTGpReDCk81GFcAQAMBQEsthsCM30kdIvfNatYnbVcVdvL+yUsaRvAxjD9ti9LjTFY/fuRxDjNcDU0BdkO1pLnOd4H6Wr1P52sH3dn63VH4+3q/tSnOza1wlB9GqXlke2k5DkFCikGOeNR86stMzzeHCkubyrwYXgu8KcmGPAmJg0qDnDjwaJZDBq2PLt5f0g4GkZ/3pH49ti9LVnJJ1dnAHGeXlwqS2/XkMkyupfiJaXIaZmIBuV3qQpQ8wsKnW9ENoLxOfaXZUy9bYcBNaSy9ZiC20y5Dsth6WWM+34Tckbq0N7ORimz7djcBc/J97+SND3wzhNlxTi9idpmu2vOi7qlhYYepCIklKl2aUCTWJmo0uSsJkZmQgLjwzY8lV4HMuO/21TrcnJE9yhNEkrqjeEUecZaXpYU2HF6t54bbTVpNfI6mGWjNDIZeFxHvWWXhDVGqNZoZZbYZ/z8b9upkZf2SIkTVBzLk1zze5I916EpxSXfFc9ESstyBOF3aKmF2lTWsMNL3ZFJTARQ0JrQZkGbK7OnXjHZVJjQmy1vfKDpPy86vrOqU+YHUbdO0tdPv0rbekXv2zERFoisxM2iN9r7xvHneFY/MfX/HHT9JoI+DunV6j35KVzWmfzUr3RvO2+39O+8zH8v3dZGWVdIOWtcRdplH3dOFlOQJ2Sl+DWJXmGBYT5nkOcpQmNuVJukeaGIJt7CMLUrzGmrKK08dl5DzCwyxMMpvH0rLDD9vsTMZIoDSpqP8A+ceTkpyV128V+owZNKDdh1PfJ9iH06xs0THetBzlfXOMZJc63gIkpwE3XizS+WH8spadDzAiMf2eQ7KTIcxhp06amyaklamV+yw/iSwz60draWwK6RvA2poP7Wb1By/9aD4dVbVZ1PHpsPVdfXpt7X6fXPljBe+/dalcs1xzMc8zSKzM+vmY9I7/AKd+InQ6C2trWmvtirbJWNtq3mte6PWeJ8+Z9p8vG6TJVhcoTJH6pzDTbfPLuTjMt/mUtfvcYvX1Temoy0n3by7KXYhk/Xcpmh51XpbQ6mSEpHMrS/MUyMETPOzxp22+eEQzxavVjcorJwvGvYyYFC/y8/KnRr5Opx38T1L043nydcJKF4F1c53Dpi0kI6WhN5PV01xUhmQJlN43WWjM0rzLNEuzOwgfVUIR6HR7kRciKTH01ZRkuzbBvJ9ya8qNDT5kny62bJ5vBUIc3grcrp8jXhJjyWNMmXF6Q7yJLREN5FOlp4IqDmtHWW4nsmcTWyJbLXM5EuT1cnepP8XJUBexGrqjdfdahP5tvIylspG+iemJehpovMeuZJSbwb571rxJ9RJIYeo7l69kOX5qcSs+f58Q+lxqJaL97qN9y3eVobtZdRe7VWwNg9tm6jsY7Gs3N7Xn9C2+rTGh6Y6E0Dm51fY9b/Ct7UW4Hu/6njkr3LzE+nq7eTp+QVxFRZwSpRcRuUHlIThJ13idN8Q5WJvTbpLu5wvamK7+5lImlVYa7JkS7KWJWYmAMMbJZeMuGGBte6a5GIleWVNNnCZ7xF5SjZ8vHV4dtq/C/mYHSVLqvPyusymkMrM7zzp5sS+glHcEsBmFdvA+h5UzJVDhw0HhPKsLlAyLkD5TGVLNV9Ccrwl11/eV1eNeHkkKNzdzU2XJ3zy8h5VN52mbvb9m50keZb4Vm9R8hJQl2VZgu3vMuvlWWGXV3zvtSTQ7ll47m/0AusikOOm3qt6nNrpPgYuPnm7+LX4aY9HAwl1v9EO63QhWc3ufY/mdmud1z2RXOt41Ft5TZ1OXJGvCvGiZ6muQZxX46IXpXvBXJXjL/cpCAuqmu8iUFOH0FeZOdxTF7DFzc7z1LwRkd7LN4E0XdTFNLttAl8u5nYYl2W3sJYvk6nZkqX3TZET7ebI94CzMyxLsuSVN0YjZROUdIcFejd8izK9VUq7++VFke9aXJfvrkOX21NXeuZDvllubpXaZmCYXRcuncyTO8iA4puujJ2lrJ06hfPS4yrub0hFXN3SzQ4i81pbWpNvIyVp1E5JKxQnwW5QlK8J6ycQ1JRrjb3Cg99K/SLrzWk24wmfJVZni/u6WfFtRWIO6642WZkWrvpbdXnXpxq9F3xzglMSh2Tqztpaco6CkXdyAFxClR3L8wvnsxRF58y9dZltzKrpmb+joW7eX9kqg0jeBhGD7bF6XEmJJ+/cDjPGKYmoqS8AneZ63U74+3VftSky2wbc/z5IKFCoMC8Zj51aaanm7yFBfXlXgxXCl4UmsN+HMTZpUjNHFi0C0GxR87Wkuc53gfpavU/nawOMHvpX6Rdea0m0jN9JHSL3zWrW19C3by/slUGkbwMIwfbYvS4kxJP37gcZ4xTE1FSXkirt5f2SljSN4GMYftsXpcaYrH79yOIcZrgamgLsNqWFp/qL/AKSUfOT2yf2tJc5zvA/S1ep/O1qEDdugNuHm6N4G+1AV7bF6Y1KLwYUnmowrgCABgKAllsNgRm+kjpF75rVrE7arirt5f2SljSN4GMYftsXpcaYrH79yOIcZrgamgLsh2tJc5zvA/S1ep/O1gxdP9bC7f4iSb+rSTZxa4Sg+jVLyyPbSF3Egosbd3d9GvY2dS9fyLJ0Q/YhbyrwE+FLzQqS1VhPSJkZd1IZOIdFkMjNaJBLQcG7t5f0i4GkZ/FISP+2xel92k/8AXAprP+uBJabDadhiTwYm9HJ/kWbJ3a0lznO8D9LV6n87WHp13EvvICCJUZ/3pBNV7bF6fGyAcRPLXJjiSdRz8AA2AzwlGdGpvlli2VbgxS6OUPItW1+xdvL+kX40jP5rCQH22L0vu1b/AK4NdQ/1xIDTGFG7iX3cBGkKM/70jWq9ti9PiZIGJnlnlwxBGoZmIIbUtrxP+uhNvxEu8/We8+2O1pLnOd4H6Wr1P52shQUgIbV4c1QRj50zXMi3dROd2yrwdmZzxavLYZqodkvXKEpjOd3SlSWi0AQCG7lbgxS6OUPItWJ21Wo3cS+7gI0hRn/eka1XtsXp8TJAxM8s8uGII1DMxBIdrSXOc7wP0tXqfztYHGD30r9IuvNaTbCh6i46STvOTq2v4W7eX9kqg0jeBhGD7bF6XEmJJ+/cDjPGKYmoqS8zHXboDDh3ujeBvtPFe2xemdai7GNZ5qcKYEkEYGoAZYDadpbXfa0lznO8D9LV6n87WlgcNlxnNcd8pN9MWHpsXE6NgdzI7esDSpSxhRnCgVyNf4WHFnnahksMSeDE3o5P8izYBzyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzUUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1JBrhKD6NUvLI9sq3Bil0coeRasGNlxnNcd8pN9MWHu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMslhbPCUZ0am+WWLBr+9SIfdq+8WsBHOfqEnE+13FLCufdGhXCmI1ka2astbA2XGc1x3yk30xZOvY+theR8RJy/VpWtsWwLcJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5HxUT1hzuZHcJJ/skzXpJ2eeBQV4xU0I2pxZYIwe+lfpF15rSbYUPUXHSSd5ydWCbLjOa475Sb6YsPhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC2yWGQe+lfpF15rSbAOi4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwQ2XGc1x3yk30xbMZvpI6Re+a1axOwatu5iH/Y/H0gI/wBfl6nNuB7aU5DHuuFaV/IRrNWi3RcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYBXZ+t1R+Pt6v7Upzs3Rm+kjpF75rVrBjZcZzXHfKTfTFh8BFRPWH25kdwkoeyTNeknh54NRXjNDQHajBltksLT/AFF/0ko+cntgHvIuJ0pBnRkcWtiKOptMp4aVyrH7jXjApnNENlxnNcd8pN9MWjXCUH0apeWR7FLAtpsXE6NgdzI7esDSpSxhRnCgVyNf4WHFnnajhK8N++/rSMjykFGV/oD9UtoBsCpH9I7qVdTUtkUwGt4CQ2xtXhLbdu/kngxN6OT/ACLNuEbxv+KZkb/9gXVLP/o3qTtg7dUouJ0bHbmR29Y6tClnCjWFCrga/wALHjzDtSQ2XGc1x3yk30xbKtwYpdHKHkWrE7Atu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMxSi4nRsduZHb1jq0KWcKNYUKuBr/Cx48w7UkGeEozo1N8ssWyrcGKXRyh5FqwY2XGc1x3yk30xYe7i4nSkYdGRwa2Ina20ynhqvIsfuFOIGucyyWFs8JRnRqb5ZYsCDeNEP+x+ArAR/r8ur5txPbSk0Yd1xpWv5AdRo0H7ZcZzXHfKTfTFlK8z1up3x9uq/alJltg2BbhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC3I+KiesOdzI7hJP9kma9JOzzwKCvGKmhG1OLLBGD30r9IuvNaTbCh6i46STvOTqwTZcZzXHfKTfTFh8BFRPWH25kdwkoeyTNeknh54NRXjNDQHajBltksLT/UX/AEko+cntgHxcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYIbLjOa475Sb6YtmM30kdIvfNatYnYNW3cxD/sfj6QEf6/L1ObcD20pyGPdcK0r+QjWatFueRcTpSDOjI4tbEUdTaZTw0rlWP3GvGBTOaBXZ+t1R+Pt6v7Upzs2tcJQfRql5ZHsGNkxfNUb/wDqZ6XsutQ8Oty9odTQXqglKCJo9TTn5SoqDjYFSTgw/Tmg0sbZlt20GGi0SHjtoZjQYeMvQ72GJPBib0cn+RZsHhD1O9SVci/K7v26mhNrmO7BokruUNkgxak/Zb2dd1NqxnzZKoJBq1LDZz3JGLLxFn9oBrFlr3d2XGc1x3yk30xbx36rpc/Nzcl3X5a9yMM12+Mh6YI+9NKDiGd1ma612oowvLlZXaYAaeIzKEy0vPyS0GJacTK6ZAMwttH0xuCvhlLKDudu7vrkSI2RKt50sJ02JQabaaewQU2XAVEhTJdOmNMy+sO1NBiGGGWmGYhLesMttAVsGx02LidGwO5kdvWBpUpYwozhQK5Gv8LDizztQowES/7Z83gQEfXsEu7NdzMfqmvPGHdCfwsWjUCtM4dcs/pPBib0cn+RZsnp/wBdCbfiJd5+s959gPqUXE6NjtzI7esdWhSzhRrChVwNf4WPHmHakhsuM5rjvlJvpi2VbgxS6OUPItWJ2BbdxcTpSMOjI4NbETtbaZTw1XkWP3CnEDXOZkfFRPWHO5kdwkn+yTNeknZ54FBXjFTQjanFlggzwlGdGpvlli0UPUXHSSd5ydWCbLjOa475Sb6YsPhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC2yWGQe+lfpF15rSbAgXjRD/ALH4CsBH+vy6vm3E9tKTRh3XGla/kB1GjQftlxnNcd8pN9MWUrzPW6nfH26r9qUmW2DYFuEionZKrRLjq6RYqM9M5rSqU3XGGri14ZowLci4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwRg99K/SLrzWk2kZvpI6Re+a1awY2XGc1x3yk30xYfARUT1h9uZHcJKHskzXpJ4eeDUV4zQ0B2owZbZLC0/1F/0ko+cntgHxcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYIbLjOa475Sb6YtmM30kdIvfNatYnYNV3VxD7tX3dUgI599QknH2u45YSD7oyK40wGsHUzRllweRcTpSDOjI4tbEUdTaZTw0rlWP3GvGBTOaXrp/rYXb/ABEk39Wkmzi1wlB9GqXlkewTZcZzXHfKTfTFh6bFxOjYHcyO3rA0qUsYUZwoFcjX+FhxZ52oZLDEngxN6OT/ACLNgHO4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMxSi4nRsduZHb1jq0KWcKNYUKuBr/AAsePMO1JBnhKM6NTfLLFsq3Bil0coeRasGNlxnNcd8pN9MWQYCJf9s+bwICPr2CXdmu5mP1TXnjDuhP4WLRqBWmcOuW2lbXif8AXQm34iXefrPefYD6lFxOjY7cyO3rHVoUs4UawoVcDX+Fjx5h2pIbLjOa475Sb6YtlW4MUujlDyLVidgW4SKidkqtEuOrpFioz0zmtKpTdcYauLXhmjAtyPionrDncyO4ST/ZJmvSTs88CgrxipoRtTiywRg99K/SLrzWk2woeouOkk7zk6sE2XGc1x3yk30xaWKWlgGaKTub4L5qx9C1FNTE7RsBufA70gcBCsUwDPKCcK1GOvwqs0Fruep+9U/xk99DWoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7Yhl4mJxVIQaPgcIRQ+xWK4NpGI2oHEBjhgNTWcbZUkxO0bH7nwO9I7AwrFMQ1yAHGlTjr8GjNRb5ePFPSkGNiwFdiKOOknlfVEnVuMSfzEGgBJILLLMUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wAhopO5vgvmrH0LUHaYnBUixo+BxhE/7FYri2r4nakcZGGGJ1tZptez1P3qn+Mnvoa1B28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtAn3qpae5uvvF62nwPrDnHDYrvilhX+Dj8EitKE8ZBtsDRSdzfBfNWPoW19eq8VO1heL12EgfWJOOGk3n3sq3GUUDVXlpiTUBphrYGep+9U/xk99DWCjCJadspVGj4EjSLBxhHZxKWk4+DSuAxwAoNVDWRyYndYc7nwJ3SgNUKxrCm7NQANYJJFasgk4UzafMI8U9kq3eifXSLFaqTzmtJ/E+vlBxwGJqzmSOeKfWHPekBwin+2TytdJu+VG5eIBlrWA0Gg0WwI6KTub4L5qx9C1CES07ZSqNHwJGkWDjCOziUtJx8GlcBjgBQaqGt7PU/eqf4ye+hrD4R4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMD6i0tO2UlDR8CBpFs4QjsYhLVsfBpXE44g1Ouopf0Unc3wXzVj6Fh0W8U9kpPeifXSLdKKTzmtW/E+vkAxxOIo1nkM9T96p/jJ76GsCFdylpz2X1DrifAmk+3qV71YphenOfHminKa8ZPFQWb4tLTtlJQ0fAgaRbOEI7GIS1bHwaVxOOINTrqKJ13DamZfj+twifTs8vUx0m2Me2jOVSKIprjXVT4amrTTfFvFPZKT3on10i3Sik85rVvxPr5AMcTiKNZ4EdFJ3N8F81Y+hahApid1h9ufAjdKP1wrGsqbw1II1kgE0oySBhTOrez1P3qn+Mnvoaw+BeKfWH3ekBwioe2TytdJvORG5eIhprUC0WiyWA+niYnFUhBo+BwhFD7FYrg2kYjagcQGOGA1NZxtf0Unc3wXzVj6Fh7x4p6UgxsWArsRRx0k8r6ok6txiT+Yg0AJJBZZZv56n71T/GT30NYKSamJ2jYDc+B3pA4CFYpgGeUE4VqMdfhVZoLcIXhJ0Aeqj5HjOwYPNayB+qWNEbGZoWmco7qVeaSKZpI642a0qM9vNoGqW7tTXipo6B71gN6QOGknmFWWeRFZA+Da4+xLB2x4QvBeKJ6qNke0hoEN/0COqWZo0g1mlj+kd1KzPJa0QWwQet0ZAaZOc3nnOYBeh3ipJido2P3Pgd6R2BhWKYhrkAONKnHX4NGai17RSdzfBfNWPoWHqTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YX89T96p/jJ76GsFF2mJwVIsaPgcYRP+xWK4tq+J2pHGRhhidbWabZUkxO0bH7nwO9I7AwrFMQ1yAHGlTjr8GjNRb5dvFPSkYNiwFdiJ2OknlfVFbXuMCPzkmhJBADTLUUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wAhopO5vgvmrH0LUHaYnBUixo+BxhE/7FYri2r4nakcZGGGJ1tZptez1P3qn+Mnvoa1B28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtAo3jJac6l9P62nwIrPt1dO9WKY3pyZx5pryinGBxVFn7RSdzfBfNWPoW1/eO2piX4DrkIn07PLq8dJtnHtoybQmqKKY011+Cho0y/56n71T/GT30NYKMIlp2ylUaPgSNIsHGEdnEpaTj4NK4DHACg1UNZHJid1hzufAndKA1QrGsKbs1AA1gkkVqyCThTNp8wjxT2Srd6J9dIsVqpPOa0n8T6+UHHAYmrOZI54p9Yc96QHCKf7ZPK10m75Ubl4gGWtYDQaDRbAjopO5vgvmrH0LUIFMTusPtz4EbpR+uFY1lTeGpBGskAmlGSQMKZ1b2ep+9U/xk99DWHwLxT6w+70gOEVD2yeVrpN5yI3LxENNagWi0WSwH1FpadspKGj4EDSLZwhHYxCWrY+DSuJxxBqddRS/opO5vgvmrH0LDot4p7JSe9E+ukW6UUnnNat+J9fIBjicRRrPIZ6n71T/GT30NYEK7lLTnsvqHXE+BNJ9vUr3qxTC9Oc+PNFOU14yeKgs3vExOKpCDR8DhCKH2KxXBtIxG1A4gMcMBqazjZOu4bUzL8f1uET6dnl6mOk2xj20ZyqRRFNca6qfDU1aacHjxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyyBDRSdzfBfNWPoWopqYnaNgNz4HekDgIVimAZ5QThWox1+FVmgtdz1P3qn+Mnvoa1BNeKmjoHvWA3pA4aSeYVZZ5EVkD4Nrj7EsHbEKalLiCqvtHKCKlRqeoJqhDR6fFpsBFQcbBltLZadvGG2QCwM5hlgNstD2WYM121bxK6n0wci3K9v86mtNjksSCvxShlH5HCipwwpFXerW1nC79KOhnQaEsklkANmrxHn1sVDNbe4Lx4p6UgxsWArsRRx0k8r6ok6txiT+Yg0AJJBZZZ8kuq1XNz/H3ZSBlk3LJ0H2/MiKaBevL7cK9aiYqY7vQwy7vLlFUZ0G02pojCKBMLbt71ssy2jzE7YznsyvWWQ9b01MTtGwG58DvSBwEKxTAM8oJwrUY6/CqzQWToFMThefN+50DjIl3VTsVivrnvP14U4q4CtfwMLJuTpfKg5Q1xt1990hGBipVvJk6X5iSw2ottGBLTl07WEiPa0KwGFaWlx2qoD5hllphqISC2W2Gw1muMA9U+2dOHekB6xLvPbJs6plvPGrQudhjraOOAGftw/TmfZiZiImZ8QblFOTymxw0dA70jsNjMU8FrkZrjSppTGlKM1FrjSbADUnQZrx7GdavkVr/wDz8NuO5ly4Lk0tQn2XWmr0lOJkGPXpanVclPJ2ym54k2V19DgOvLyapT7JNyExyL1xEZestv2hMTTIZLPXAw2cw9RIE0Q83IqXMkvRqGry+uJ8GpoywkrRj01TTlN2y9TlJPUHaUXb5h86aDbssFtkh6w0C1x+8uj1OnwfXy6edJETX88xPbzWltt5iN+6sxaI5/LMW5jlq4dbo9ZO2DVxaY4mu/O8TETtE+Of5jzxsMu0xO0pF7nwNTBp/wBiu64tK2va/CRhyn2VCJHJid1hzufAndKA1QrGsKbs1AA1gkkVqyCThTNp8uninpOM71T87YadU6Tefdq2vcbOHHrLRpUggBplqRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi3HHiOd+I59/u2xHRSdzfBfNWPoWoQiWnbKVRo+BI0iwcYR2cSlpOPg0rgMcAKDVQ1vZ6n71T/GT30NYfCPFPZKt3on10ixWqk85rSfxPr5QccBias5mQpXjJac6l9P62nwIrPt1dO9WKY3pyZx5pryinGBxVFn7RSdzfBfNWPoW1/eO2piX4DrkIn07PLq8dJtnHtoybQmqKKY011+Cho0y/56n71T/GT30NYKMIlp2ylUaPgSNIsHGEdnEpaTj4NK4DHACg1UNZFpadspKGj4EDSLZwhHYxCWrY+DSuJxxBqddRT5hHinslW70T66RYrVSec1pP4n18oOOAxNWcyRbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWeBHRSdzfBfNWPoWoQKYndYfbnwI3Sj9cKxrKm8NSCNZIBNKMkgYUzq3s9T96p/jJ76GsPgXin1h93pAcIqHtk8rXSbzkRuXiIaa1AtFoslgPqLS07ZSUNHwIGkWzhCOxiEtWx8GlcTjiDU66il/RSdzfBfNWPoWHRbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWeQz1P3qn+MnvoawIF1SWnvrr7uuuJ8D6w5Ow2K745YSPg4vBArSgHGCbOLxMTiqQg0fA4Qih9isVwbSMRtQOIDHDAams42Tbqnip2sLuutQkD6xJOw0m8+9lJ4wikaqclcCKAssMuLx4p6UgxsWArsRRx0k8r6ok6txiT+Yg0AJJBZZZAhopO5vgvmrH0LUU1MTtGwG58DvSBwEKxTAM8oJwrUY6/CqzQWu56n71T/GT30NagmvFTR0D3rAb0gcNJPMKss8iKyB8G1x9iWDtiGXaYnBUixo+BxhE/7FYri2r4nakcZGGGJ1tZptlSTE7RsfufA70jsDCsUxDXIAcaVOOvwaM1Fvl28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtRSeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbACGik7m+C+asfQsgQKYnds+b9zoHGQ7uvsVivrnvP10FOIHAVr+DhZ+z1P3qn+MnvoayCnvFMXnzf3on+sS7v2zb++a88Y0RajjrVo44Uz9uAcVJMTtGx+58DvSOwMKxTENcgBxpU46/BozUWvaKTub4L5qx9Cw9SeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbC/nqfvVP8ZPfQ1gowiWnbKVRo+BI0iwcYR2cSlpOPg0rgMcAKDVQ1kcmJ3WHO58Cd0oDVCsawpuzUADWCSRWrIJOFM2nzCPFPZKt3on10ixWqk85rSfxPr5QccBias5kjnin1hz3pAcIp/tk8rXSbvlRuXiAZa1gNBoNFsCOik7m+C+asfQtLYz1P3qn+Mnvoa0sBSwxJ4MTejk/yLNpopO5vgvmrH0LUU1MTtGwG58DvSBwEKxTAM8oJwrUY6/CqzQWC61wlB9GqXlke2VbgxS6OUPItWoPExOKpCDR8DhCKH2KxXBtIxG1A4gMcMBqazjbKkmJ2jY/c+B3pHYGFYpiGuQA40qcdfg0ZqLAw2Fs8JRnRqb5ZYtnRSdzfBfNWPoWoO0xOCpFjR8DjCJ/2KxXFtXxO1I4yMMMTrazTYFy9j62F5HxEnL9Wla2xbasvVS09zdfeL1tPgfWHOOGxXfFLCv8HH4JFaUJ4yDbYGik7m+C+asfQsEg99K/SLrzWk2woeouOkk7zk6tRhEtO2UqjR8CRpFg4wjs4lLScfBpXAY4AUGqhrI5MTusOdz4E7pQGqFY1hTdmoAGsEkitWQScKZtAYrDIPfSv0i681pNpopO5vgvmrH0LUIRLTtlKo0fAkaRYOMI7OJS0nHwaVwGOAFBqoahfjN9JHSL3zWrWJ2XYtLTtlJQ0fAgaRbOEI7GIS1bHwaVxOOINTrqKX9FJ3N8F81Y+hYFG7P1uqPx9vV/alOdm6M30kdIvfNatZBu5S057L6h1xPgTSfb1K96sUwvTnPjzRTlNeMnioLN8Wlp2ykoaPgQNItnCEdjEJatj4NK4nHEGp11FAYrC0/1F/0ko+cnts6KTub4L5qx9C1CBTE7rD7c+BG6UfrhWNZU3hqQRrJAJpRkkDCmdULzXCUH0apeWR7FLLrxMTiqQg0fA4Qih9isVwbSMRtQOIDHDAams42XYxZkpPmlEkuLVZRgJtmdHmFXluV4yLSYNemRPQm0Vlfj0hGainayrpaDpZFE0PHcM8cuCpo5iGmevOmCDik8GJvRyf5Fm3CN43/FMyN/+wLqln/0b1J23Rd2d6txN6zybEC7K826S81ausXzI95iTd/OMqTsoXbzi06JMpzimIa9Mj6SV5ijbYl2YG3cQwGSc1oM5zXMt4SdAHqo+R4zsGDzWsgfqljRGxmaFpnKO6lXmkimaSOuNmtKjPbzaBqlg79VuDFLo5Q8i1YnZeUkxO0bH7nwO9I7AwrFMQ1yAHGlTjr8GjNRa9opO5vgvmrH0LBhnhKM6NTfLLFsq3Bil0coeRatQdpicFSLGj4HGET/ALFYri2r4nakcZGGGJ1tZptlSTE7RsfufA70jsDCsUxDXIAcaVOOvwaM1FgYbC2eEozo1N8ssWzopO5vgvmrH0LUHaYnBUixo+BxhE/7FYri2r4nakcZGGGJ1tZpsAC8z1up3x9uq/alJltg21deMlpzqX0/rafAis+3V071YpjenJnHmmvKKcYHFUWftFJ3N8F81Y+hYJB76V+kXXmtJthQ9RcdJJ3nJ1ajCJadspVGj4EjSLBxhHZxKWk4+DSuAxwAoNVDWRyYndYc7nwJ3SgNUKxrCm7NQANYJJFasgk4UzaAxWFp/qL/AKSUfOT22dFJ3N8F81Y+hahApid1h9ufAjdKP1wrGsqbw1II1kgE0oySBhTOqF+M30kdIvfNatYnZdi0tO2UlDR8CBpFs4QjsYhLVsfBpXE44g1Ouopf0Unc3wXzVj6FgUbs/W6o/H29X9qU52bWuEoPo1S8sj2QruUtOey+odcT4E0n29SverFML05z480U5TXjJ4qCze8TE4qkINHwOEIofYrFcG0jEbUDiAxwwGprONgYrDEngxN6OT/Is2mik7m+C+asfQtRTUxO0bAbnwO9IHAQrFMAzygnCtRjr8KrNBYLrXCUH0apeWR7fUZBwSlCP4ONhYeMgY2H2PEwz9yIyDioRoNbRtgslhtlplsnbAjGtDtWrD3iYnFUhBo+BwhFD7FYrg2kYjagcQGOGA1NZxtf0Unc3wXzVj6Fg8LOp5v47Ipyu77OpuTM+fOLt5v0nlMZHihGUDEbJK0KzhIaQA7LbbUsNMlhgF4w6diUpjiHjL1qYXbNvaGCNLzpu+Id3v6zXoG3lR1Vu4OYle5m7jK9uTSnAyg8iWYEy+GVusJwai5ju/TGmWryJSWW2jnrCS2iQDqYGXLZzGnaOsswrJEyvQzduC6rh1OO+28KWk1FylrnUicLz7ubp3CLKi8tMocQ6nt4pTg2rSC3NKwxDyy1PSEsraQhmXXMwGaG5j7k4cPW3jto+8Wj1uq3vjw5clcUxbJ9LHfJ2Vjbm/bE7Rt5mdvdFlyY6R23yUx2vE1rF7RTumY4iO6Y3+2339n87oZWylpnjctR1c/erc3IKPH5Tt9ybCpk63HzZPK8JhfS9LrsKLM1JN+MooaW7MQ8cEl/dfMLLt2z11+xMTRzXnZ+REvwUw5J1wcUnoLEsQkLdvLiCxLzKhHqTKa3Kzh1L8c5T1ZU74VUtl4mEuHxZGdDtMgvWmjRmotZF1w8UrzxMrUNe4kxM9rUwTVOSNKmUxlHXfyjMC8uhplZUVKTpMvZl6Rs9dZYdiIpLztg1aLTNAAx00hypLkvoqZLyEgJKWiIibBpKOkpqfAwCelJiUHbCanpkA6dsuodNdMMEOHLBYZdZoYZzQQXf2+rdZ0mu0mXTUrf/N0Vt50cUrX6WijHaNqzNtV3TMTE3iZp2771nJesc50fout0Wp/E55jtmZ/1bzta0T/98Rzv5mI3VxM8su5wjJTbmFDdTSzLMDNHYs+U00L3Y8yqK6QJj0PnMrAQQrMtOml8smEESGnPXXTwNBrW912Unk6ZQ8JMTeT/AH93NX4sSVMSfL84NXO3nyPeexKEwFQZASJpMlLkxBBWgHRaLhd6w0et9dDpkFpq3hlf5Ns1zXkvdUSvilyVoScZ3vfy2LvcjpNlVZXWZUSzczJl/wBI2TP2vnk4JCFNL2SZImcrV5EyzVMXY1NJlXtlzJN7cpGm22nffF3mZPt4s5QF6ss5PqzekuZCmU5E5MV7GTTddP8AcSzdnJlzzMlLKncNeJd+vX5Xky7ei7l10tyZMt1F4cMxKzmU4lDmBhzdNK7uZHzUT8GP742/j0/T0dQ9hJEylMnm9C8Cf7qbsr9Lmbxr0rrolmGvOu2kG82R5uvBu4LKg0lN9n0nIS2/mOTaK4eOixMMI5bbeMvGGAXjeYzuiD30r9IuvNaTbxfX5FlK6eUuotvbsJcRUp4l3oXdXTQionOGVBUirrLycli9FbnNGbU2WM1Zl+YlmU0GZppbz2m25oSZfm54ww07z3vsjCJadspVGj4EjSLBxhHZxKWk4+DSuAxwAoNVDUNZ30TfKcsy7LDMzTCgy72QXrXNSsh6ZV01DeLMwLF6cpsI8vIzKoQFVdiGme4obhhuIiAXmY7GY007D3p5TGTpcfM0hSPfRf7cndJO166kUi62T7zb15FkKbryVRpQS0V6lXeIk3ryCuzorNLasjIbh3L7l+0H60isZrT6IcsPPzM5cGWXkZ5QWU1k8XjTLlfZNKKi5KHVHsne7a6m5OPygbvUGdEdSlOf1mVMo7KQvNu8dz6FkIhzhd5JzN40sBxKcpoMwzg5o7vLZp60SLIMhXsTv1Xh5P8ALEvzixMS9LdzUdDK0GlR6ZHXNo2SxJE5ynKrOcw3RBK/eNOEwllpphoTGtv3oIachpgPUSBmiXHs2L8mQ68iRM3JMGmzEqyu4UkxuYEdEWXjxJQ1VSSs96su0hfepCwy5W4iHDp89SlR05etGHLsNsZvpI6Re+a1a3hxc7OMym5/qNmUhMZafXi3kJF1Nw17ETEpbvZ83Sdfvk2trSu0rZzJOf217upNmTbhpgUXc0eHX24i0tO2UlDR8CBpFs4QjsYhLVsfBpXE44g1OuooDFYWn+ov+klHzk9tnRSdzfBfNWPoWoQKYndYfbnwI3Sj9cKxrKm8NSCNZIBNKMkgYUzqhfjN9JHSL3zWrWJ2XYtLTtlJQ0fAgaRbOEI7GIS1bHwaVxOOINTrqKX9FJ3N8F81Y+hYE26f62F2/wARJN/VpJs4tcJQfRql5ZHsgXVJae+uvu664nwPrDk7DYrvjlhI+Di8ECtKAcYJs4vExOKpCDR8DhCKH2KxXBtIxG1A4gMcMBqazjYGKwxJ4MTejk/yLNpopO5vgvmrH0LUU1MTtGwG58DvSBwEKxTAM8oJwrUY6/CqzQWC6zwlGdGpvlli2VbgxS6OUPItWoO0xOCpFjR8DjCJ/wBisVxbV8TtSOMjDDE62s02ypJido2P3Pgd6R2BhWKYhrkAONKnHX4NGaiwMNteJ/10Jt+Il3n6z3n2cNFJ3N8F81Y+hZAgUxO7Z837nQOMh3dfYrFfXPefroKcQOArX8HCwP6twYpdHKHkWrE7LykmJ2jY/c+B3pHYGFYpiGuQA40qcdfg0ZqLXtFJ3N8F81Y+hYJB76V+kXXmtJthQ9RcdJJ3nJ1ajCJadspVGj4EjSLBxhHZxKWk4+DSuAxwAoNVDWRyYndYc7nwJ3SgNUKxrCm7NQANYJJFasgk4UzaAxWlhmik7m+C+asfQtLAnaMvT+/KQf0bTP8A7sWopqdedsCC63OMg02JA/a4mY4EDlvYrTXTi152czhZ/wBKp3OEF86Y+naimqado2A3Qgd6QOIimKYhnlIONKDDX4VGaGwJzxOvP0i5+rGQR3qoY9riZsRnJHEL2By4/BSlDnZ0Uk687YEb1ycZBpsSO+1xMwwAPJexWmqvFqzc1nCzg8U04KkIdIQOMIofZTFcW0jAbYjjBxwxGtrOFsqSmnaNj90IHekdiYpimAa5CThWhw1+DVmpsC5oy9P78pB/RtM/+7FqLtOvP0i++rGQT3qn49riZsBnK/Eb2DyYfBWtTm5r/pVO5wgvnTH07UHamnFUizpCBwhE/wCymK4Nq+B2wHEThhgdTWaLBp+8lOvGYu7vBbUJpkmJghI04CLhYa71ag46IgtDKpzWVFq9jMdjMOdngMnbFprMabOa/aMvT+/KQf0bTP8A7sWo3rKae8uvvF63GwR+oOcvshj72Fc6hq1Gp5K8dAX/AEqnc4QXzpj6dg1/Cp15+yVQdmMg12XX63My8SWkE1/tX1Yj4aUpiWy1mOT7zusu+uTjIIpFp/2uZn16RdgHC9cHAAUrXEGu1zQHCEVE7ZSqdIQIGkWBjFuxiEtJw8KlcRhiDUa6mkjlNO6w53QgRulAaopjWVN2KAg6yQQK0ZJBxpm1Bd0Zen9+Ug/o2mf/AHYtQhU68/ZKoOzGQa7Lr9bmZeJLSCa/2r6sR8NKUxLZa2BpVO5wgvnTH07UIRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaAnRSdefslLHZjINdl1+tzMvGlq5FP7V9WB+Gla4hgs39GXp/flIP6Npn/3YsxRaonbKSjpCBI0i2MIt2cSlq2HhUrgcMAKHVQVv6VTucIL50x9OwaRkGAvGeocczCTTI0O67N7xBSIu8WYs7P7YM5aUBzL18AWs4DbAgFqjLQaaAbopOvP2SljsxkGuy6/W5mXjS1cin9q+rA/DStcQwWfq7lTTnUvqHXI2BZJny9X7KZIxvSnIfCDjX89eKlm+LVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCoLujL0/vykH9G0z/AO7FqMCn3ndZedbnGQTWLUPtczPr0i8BON65OIJrSmJFNrnAv+lU7nCC+dMfTtQgVNO6w+3QgTulH64pjWFN4KEk6wSAaVZBIxpnUBQdp94zlWTRGTTJcQ7EKp9ecQ8jq0GdhmPSPAabn1+GWmWMCWmGmSfYt4g+CkQr5Qy/1VS7+Z7wMk/KAki8ic7iMuq7u7yfpjm/JMV7r5autRVS5Z5duqSa1JuUnMt4D6XtOJDuZJwamC7WXb0GprvRl9w3KrcoSrFO5R/Q08U04KkIdIQOMIofZTFcW0jAbYjjBxwxGtrOFr+lU7nCC+dMfTsHhN1P2YJZnq9jJyh7kVhBY7RHU4Uu4nKSh0twI1q66/V1Nl1rUoXNXwpCIvBpDvSlh4j3wr7+7uZOxiapSdLLWftZpaA6yvBT7wj1TjJAdtzNJhUzkG9Ud2JGsyEshLYThlAdS22U7bS+2m0/ePWnzSOXT1iIdsu2Xb1lt08L9huG9GIBYTnkBBPHihAddahYItUimKEtBk8oOOPFrrWgtwjeEoQP9aRkeHZcHms5A/VLQWtks0Bayj+pVgMk4sgtdbbwrUllvNBDINg6+Uk687YEb1ycZBpsSO+1xMwwAPJexWmqvFqzc1nC17Rl6f35SD+jaZ/92LMakpp2jY/dCB3pHYmKYpgGuQk4VocNfg1ZqbXtKp3OEF86Y+nYEB2nXn6RffVjIJ71T8e1xM2AzlfiN7B5MPgrWpzc2KSdedsCN65OMg02JHfa4mYYAHkvYrTVXi1ZuazhZwdqacVSLOkIHCET/spiuDavgdsBxE4YYHU1mi2VJTTtGx+6EDvSOxMUxTANchJwrQ4a/BqzU2Bc0Zen9+Ug/o2mf/di1F2nXn6RffVjIJ71T8e1xM2AzlfiN7B5MPgrWpzc1/0qnc4QXzpj6dqDtTTiqRZ0hA4Qif8AZTFcG1fA7YDiJwwwOprNFg1BP0BeM6Q4FmLmmRoh12b3dikPd4swh2f2wZN0WBn3r4gNZoO2JIDNWWQyyC+6MvT+/KQf0bTP/uxaleMppz2X0/rcbAtET5dV9lMgYXpSaPgAxp+enFWz9pVO5wgvnTH07Br+FTrz9kqg7MZBrsuv1uZl4ktIJr/avqxHw0pTEtlrMcn3ndZd9cnGQRSLT/tczPr0i7AOF64OAApWuINdrmgOEIqJ2ylU6QgQNIsDGLdjEJaTh4VK4jDEGo11NJHKad1hzuhAjdKA1RTGsqbsUBB1kggVoySDjTNqC7oy9P78pB/RtM/+7FqMCn3ndZedbnGQTWLUPtczPr0i8BON65OIJrSmJFNrnAv+lU7nCC+dMfTtQgVNO6w+3QgTulH64pjWFN4KEk6wSAaVZBIxpnUBOik68/ZKWOzGQa7Lr9bmZeNLVyKf2r6sD8NK1xDBZv6MvT+/KQf0bTP/ALsWYotUTtlJR0hAkaRbGEW7OJS1bDwqVwOGAFDqoK39Kp3OEF86Y+nYNIyDAXjPUOOZhJpkaHddm94gpEXeLMWdn9sGctKA5l6+ALWcBtgQC1RloNNAN7xOvP0i5+rGQR3qoY9riZsRnJHEL2By4/BSlDnZ2buVNOdS+odcjYFkmfL1fspkjG9Kch8IONfz14qWb3imnBUhDpCBxhFD7KYri2kYDbEcYOOGI1tZwsC7oy9P78pB/RtM/wDuxaimp152wILrc4yDTYkD9riZjgQOW9itNdOLXnZzOFn/AEqnc4QXzpj6dqKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobAnPE68/SLn6sZBHeqhj2uJmxGckcQvYHLj8FKUOdnXtGXp/flIP6Npn/wB2LMTxTTgqQh0hA4wih9lMVxbSMBtiOMHHDEa2s4Wv6VTucIL50x9OweUnVUkbKQiupr5XDi6xfg1WZ4249ectockSFMSdOijKLejBeWmSa+dTvMTzsgirsxN7uWXSPLr6sdscOWGGyyWv8/aOe3fRF3r4xJQHt2b9CEICMECKl8GoI5CKYHi11Fv9VJPUE5pNgSVCBI2JBA99OyDVlkaia40oK/DWgt+dnqlHU5ri0FRX8tTJYuHugkfKYyX1C7DKZgIyT5HlpNYn5pEmy8RavA00lpaMyhrK+9dJSVMzS8HERNDLxDbdtxLLa/WJuP5XfNjH8uNH8QaLL0DD1ivWMM46ZMlKzbHa1IpxvWeI33id+N5j7xVnzC+XeX441vQdXj69m6THSMtbzXHa1Yy7Wrba0Vmu+8xtz3e8by9P8htCynobIWyV4W/KYkyCvdh8m26qEvHT51kdai58hZjdSCjsLCfOSi1P7vrk8s5rAm1tty001NJWSM5llgsdkaMvT1dmMg05O1tM/wDuxbV9wmULIOUlk/SJflJKhCNS3eVJDuY4SHEW6ajkVRbTA7WpXVDR2WFuXFp2rIcS7DGD1JeNMFobY9A6VTucIL50x9O1QZsn1suXL29v1cl8nbHivfabdvG3jfZaGKn08WPHvv2UpTf37axXf99nmShZIc8vpzyv7mZ0dSZMOTdlOxqffK/iYOWVNDMvXhTWQi3lSqGkW9qXZ7SVx+uSmjXwyleNLjYeCaZgmPMeShEytKxmZhu7yHpok+ela9G83KMnDKrvDiZRibq5amDKIkiS2mbvLq5tVkpUm+RJTle55zcjIbDE2PEZFezXMUxyxM15s0BFl5zME4PIGHduLegztTTiqRZ0hA4Qif8AZTFcG1fA7YDiJwwwOprNFpHKad1hzuhAjdKA1RTGsqbsUBB1kggVoySDjTNrG9vOO5bqfSvc3O8kzG1lFT/eTJdy6auI2TVc/edLMrrt2WThALic0hFzd12OCXLypxeQ8k5l30szHfhebehMMoyY8XpXkuJllxMsT1vpG5tDykoCX5kN40+S8oTFE3jXiRCQFyQYCNjE6TG5yXW7vYBsSVO8vS+XbMjNIbLlltmImR27DLqb5pmGZBEvD01pVO5wgvnTH07UIRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaBx9lKXFzBfJL90rM6TyjuGLrsoa4y+SXexuRVeBexM5yXeIkBCZVWFec5iz5aqsP3cyIeY6fP2HbLbM0y5Vt471Lff1PlZvlvInC8NJynr1LjO29LCDd7lDSdcvL8tJcn5R8mSo2+cpCTeOZ3F4kwygtsoKktyGzeJcdNNx16TcnKjuXHk3vGZaktuW+7LxlNOey+n9bjYFoifLqvspkDC9KTR8AGNPz04q2ftKp3OEF86Y+nYPPqarg72Jwv6uCcOhIUuXJZL0Opz1Kj+Ak15DpatewpyDEXOybK6ZKbu9V4uwyHdrIqvOUwxD56zKrh2+WrvXMnvZuImbsZ7Fik68/ZKWOzGQa7Lr9bmZeNLVyKf2r6sD8NK1xDBZcYRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaSLVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCoLujL0/vykH9G0z/7sWowKfed1l51ucZBNYtQ+1zM+vSLwE43rk4gmtKYkU2ucC/6VTucIL50x9O1CBU07rD7dCBO6UfrimNYU3goSTrBIBpVkEjGmdQE6KTrz9kpY7MZBrsuv1uZl40tXIp/avqwPw0rXEMFm/oy9P78pB/RtM/+7FmKLVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCt/SqdzhBfOmPp2DSF2ydeM3d3d82nzTJMNBGRpPEJCxN3q1GR0PBaGSjmtKLN7GY8GYM7PIaO1DTOe0wM5weJ15+kXP1YyCO9VDHtcTNiM5I4hewOXH4KUoc7Ol1Kmnu7r7uuuRsEPqDk37IY+9hIOo69YoeSnHUBweKacFSEOkIHGEUPspiuLaRgNsRxg44YjW1nCwLujL0/vykH9G0z/7sWopqdedsCC63OMg02JA/a4mY4EDlvYrTXTi152czhZ/0qnc4QXzpj6dqKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobAnO068/SL76sZBPeqfj2uJmwGcr8RvYPJh8Fa1ObmxSTrztgRvXJxkGmxI77XEzDAA8l7Faaq8WrNzWcLODtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WypKado2P3Qgd6R2JimKYBrkJOFaHDX4NWamwLmjL0/vykH9G0z/wC7FkGCT7xBeHNbDM0yPs/sFu7EREm71a2AYHTV5ZdDR/bZDwZzekqGppqq2yxW279Kp3OEF86Y+nZBgFNO7Z839+QJpIl3f2Sz98954x4tZ+HbcWbWwYUk687YEb1ycZBpsSO+1xMwwAPJexWmqvFqzc1nC17Rl6f35SD+jaZ/92LMakpp2jY/dCB3pHYmKYpgGuQk4VocNfg1ZqbXtKp3OEF86Y+nYNfwqdefslUHZjINdl1+tzMvElpBNf7V9WI+GlKYlstZjk+87rLvrk4yCKRaf9rmZ9ekXYBwvXBwAFK1xBrtc0BwhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppI5TTusOd0IEbpQGqKY1lTdigIOskECtGSQcaZtQXdGXp/flIP6Npn/3YtLOOlU7nCC+dMfTtLATsMSeDE3o5P8AIs2xmKfvpP8AFr30zagmu1TR0D31Ab0gcdGvMaMs8i00D8G2w9iGztQF9rhKD6NUvLI9sq3Bil0coeRasPeO1PSkGdlQFdiKOGjXlfVEnVuyCPzAmhAIADLTUUnapo6O76gN6R2OjXmFWWuVaZA+HbY+yDB2pBjsLZ4SjOjU3yyxaZin76T/ABa99M2oO3anpSMOyoCuxE7DRryvqitr3ZJP5wDQEAEFppkF29j62F5HxEnL9Wla2xbarvVdqnawvF67FwPrEnHHRjz72VbiK0RqryVxBoC02zsDMU/fSf4te+mbBmD30r9IuvNaTbCh6i46STvOTqw+EdqeyVbvtPrpFitU15zWk/jjXyk44jAUZz5HO1PrDnvuA4RT/a15Wuk3fKs8vGC01rIZLRaDAMlhkHvpX6Rdea0m2MxT99J/i176ZsPhHanslW77T66RYrVNec1pP4418pOOIwFGc8CMZvpI6Re+a1axOy3Fu1PZKT32n10i3Sia85rVvxxr5CMcDgatZhDMU/fSf4te+mbApXZ+t1R+Pt6v7Upzs3Rm+kjpF75rVra/u4YUxL8f1uLT6dnl6mGjGzj20ZyqBRaFMa6q/DQ1ZZb4t2p7JSe+0+ukW6UTXnNat+ONfIRjgcDVrMBksLT/AFF/0ko+cntpmKfvpP8AFr30zYfAu1PrD7vuA4RUPa15Wuk3nIs8vGSy1qJZDQZDYEGuEoPo1S8sj2KWXHjtT0pBnZUBXYijho15X1RJ1bsgj8wJoQCAAy01fzFP30n+LXvpmwZSeDE3o5P8izbhG8b/AIpmRv8A9gXVLP8A6N6k7bt5NdqmjoHvqA3pA46NeY0ZZ5FpoH4Nth7ENnajhC8F2ojqo2R7SJgS3/QI6pZmnR7WaGP6R3UrM8FnS4bJJ63RoFlkZreeM5sB0Hf6twYpdHKHkWrE7Lik7VNHR3fUBvSOx0a8wqy1yrTIHw7bH2QYO1N/MU/fSf4te+mbBGeEozo1N8ssWyrcGKXRyh5Fqw927U9KRh2VAV2InYaNeV9UVte7JJ/OAaAgAgtNMxSdqmjo7vqA3pHY6NeYVZa5VpkD4dtj7IMHakGOwtnhKM6NTfLLFpmKfvpP8WvfTNqDt2p6UjDsqArsROw0a8r6ora92ST+cA0BABBaaZADeZ63U74+3VftSky2wbasvHYUzL8B1yLT6dnl1eGjGxj20ZNoDVaNcaa6fBU0Zaf8xT99J/i176ZsGYPfSv0i681pNsKHqLjpJO85OrD4R2p7JVu+0+ukWK1TXnNaT+ONfKTjiMBRnPkc7U+sOe+4DhFP9rXla6Td8qzy8YLTWshktFoMAyWFp/qL/pJR85PbTMU/fSf4te+mbD4F2p9Yfd9wHCKh7WvK10m85Fnl4yWWtRLIaDIbAjGb6SOkXvmtWsTstxbtT2Sk99p9dIt0omvOa1b8ca+QjHA4GrWYQzFP30n+LXvpmwKV2frdUfj7er+1Kc7NrXCUH0apeWR7IF3DCmJfj+txafTs8vUw0Y2ce2jOVQKLQpjXVX4aGrLLg8dqelIM7KgK7EUcNGvK+qJOrdkEfmBNCAQAGWmgY7DEngxN6OT/ACLNsZin76T/ABa99M2oJrtU0dA99QG9IHHRrzGjLPItNA/BtsPYhs7UBfa4Sg+jVLyyPYpZceO1PSkGdlQFdiKOGjXlfVEnVuyCPzAmhAIADLTV/MU/fSf4te+mbBlJ4MTejk/yLNkSGhHEXePO0JFOnEQ4f3fXeQ0U4fOARFgrF59a1NCM0kZtDTGlCA1ZrTXapo6B76gN6QOOjXmNGWeRaaB+DbYexDZ2oUE92pm8+b++0/1iXd+1jf3zXnnGi1U8dasjHGuftCHjLkVPH+QxlnZQPU51p89gbp71Xcw5R2R5ExTTbMAymKzDYnG6pHYYp10y4ymVdOnpZdsiUV6IzS3MjDDXvZbxx6rxcFO033Jy9lQXNh2xlCZGC67vskWJgU16Y5Xk9KIavGlNrOJYWUZ6iQDMwMoIOc+bQy5zi1MLLNu/cme/ZBym7irs7+JKUU9tDvLlhOmNlwYcvHiIotBh0tSqqsMq4DKzLi6wqIT7HND1KbLRpmZwb9Z4SjOjU3yyxaKHqLjpJO85OrUHbtT0pGHZUBXYidho15X1RW17skn84BoCACC00ziOdqfWHXfifgpJ5O5rzXpN3hwwKY8dWmhiQyWi0GHjz9v58f8Afp7hksMg99K/SLrzWk2xmKfvpP8AFr30zYfCO1PZKt32n10ixWqa85rSfxxr5SccRgKM54ArzPW6nfH26r9qUmW2DbVl47CmZfgOuRafTs8urw0Y2Me2jJtAarRrjTXT4KmjLT/mKfvpP8WvfTNgzB76V+kXXmtJtIzfSR0i981q1h0I7U9kq3fafXSLFaprzmtJ/HGvlJxxGAoznyLdqeyUnvtPrpFulE15zWrfjjXyEY4HA1azAZLC0/1F/wBJKPnJ7aZin76T/Fr30zYfAu1PrD7vuA4RUPa15Wuk3nIs8vGSy1qJZDQZDYEYzfSR0i981q1idluLdqeyUnvtPrpFulE15zWrfjjXyEY4HA1azCGYp++k/wAWvfTNgTrp/rYXb/ESTf1aSbOLXCUH0apeWR7a/uqdqnawu661FwPrEk7HRjz72UniC0Bqpy0wAqAy204vHanpSDOyoCuxFHDRryvqiTq3ZBH5gTQgEABlpoGOwxJ4MTejk/yLNsZin76T/Fr30zagmu1TR0D31Ab0gcdGvMaMs8i00D8G2w9iGztQF9nhKM6NTfLLFsq3Bil0coeRasPdu1PSkYdlQFdiJ2GjXlfVFbXuySfzgGgIAILTTMUnapo6O76gN6R2OjXmFWWuVaZA+HbY+yDB2pBjtrxP+uhNvxEu8/We8+zfmKfvpP8AFr30zZBT3ambz5v77T/WJd37WN/fNeecaLVTx1qyMca5+0IP6twYpdHKHkWrE7Lik7VNHR3fUBvSOx0a8wqy1yrTIHw7bH2QYO1N/MU/fSf4te+mbBmD30r9IuvNaTbCh6i46STvOTqw+EdqeyVbvtPrpFitU15zWk/jjXyk44jAUZz5HO1PrDnvuA4RT/a15Wuk3fKs8vGC01rIZLRaDAMlpYXmKfvpP8WvfTNpYM6VTucIL50x9O1FNU07RsBuhA70gcRFMUxDPKQcaUGGvwqM0NmGwxJ4MTejk/yLNgoPFNOCpCHSEDjCKH2UxXFtIwG2I4wccMRrazhbKkpp2jY/dCB3pHYmKYpgGuQk4VocNfg1ZqbXWuEoPo1S8sj2yrcGKXRyh5FqwTSqdzhBfOmPp2oO1NOKpFnSEDhCJ/2UxXBtXwO2A4icMMDqazRZisLZ4SjOjU3yyxYEG9ZTT3l194vW42CP1Bzl9kMfewrnUNWo1PJXjoC/6VTucIL50x9Oybex9bC8j4iTl+rStbYtgXYRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaSOU07rDndCBG6UBqimNZU3YoCDrJBArRkkHGmbW/B76V+kXXmtJthQ9RcdJJ3nJ1YM6VTucIL50x9O1CEVE7ZSqdIQIGkWBjFuxiEtJw8KlcRhiDUa6mjFYZB76V+kXXmtJsFCLVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCt/SqdzhBfOmPp2kZvpI6Re+a1axOwauu5U051L6h1yNgWSZ8vV+ymSMb0pyHwg41/PXipZvi1RO2UlHSECRpFsYRbs4lLVsPCpXA4YAUOqgqAuz9bqj8fb1f2pTnZujN9JHSL3zWrWCaVTucIL50x9O1CBU07rD7dCBO6UfrimNYU3goSTrBIBpVkEjGmdRisLT/UX/AEko+cntgovFNOCpCHSEDjCKH2UxXFtIwG2I4wccMRrazha/pVO5wgvnTH07Ya4Sg+jVLyyPYpYF5NU07RsBuhA70gcRFMUxDPKQcaUGGvwqM0NuELwlCB/rSMjw7Lg81nIH6paC1slmgLWUf1KsBknFkFrrbeFakst5oIZBt36k8GJvRyf5Fm3CN43/ABTMjf8A7AuqWf8A0b1J2wdwKSmnaNj90IHekdiYpimAa5CThWhw1+DVmpte0qnc4QXzpj6dorcGKXRyh5FqxOwLrtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WypKado2P3Qgd6R2JimKYBrkJOFaHDX4NWam11nhKM6NTfLLFsq3Bil0coeRasE0qnc4QXzpj6dqDtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WYrC2eEozo1N8ssWBCvGU057L6f1uNgWiJ8uq+ymQML0pNHwAY0/PTirZ+0qnc4QXzpj6dlG8z1up3x9uq/alJltg2BdhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppI5TTusOd0IEbpQGqKY1lTdigIOskECtGSQcaZtb8HvpX6Rdea0m2FD1Fx0knecnVgzpVO5wgvnTH07UIFTTusPt0IE7pR+uKY1hTeChJOsEgGlWQSMaZ1GKwtP9Rf8ASSj5ye2CjFqidspKOkIEjSLYwi3ZxKWrYeFSuBwwAodVBW/pVO5wgvnTH07SM30kdIvfNatYnYNXXcqac6l9Q65GwLJM+Xq/ZTJGN6U5D4Qca/nrxUs3vFNOCpCHSEDjCKH2UxXFtIwG2I4wccMRrazhYBdn63VH4+3q/tSnOza1wlB9GqXlkewZ0qnc4QXzpj6dqKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobMNhiTwYm9HJ/kWbBQeKacFSEOkIHGEUPspiuLaRgNsRxg44YjW1nC1/SqdzhBfOmPp2w1wlB9GqXlkexSwLyapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobJ8App3bPm/vyBNJEu7+yWfvnvPGPFrPw7biza2fkngxN6OT/Is2T0/66E2/ES7z9Z7z7AZWY1IikhTcvoqAfw75OUIZ9Dv4pgCIZ62WKGpJNQWhUMnwwAaCrPh3kRqLvITy57+Op9LkfDwFzV80WpZRuSDERcSyzBQzKm232xrq0ZsAtsmXAkvGXKAG2etsSk0+zc+ZgwPdtW4MUujlDyLVvJ7qs1wM1z7cfLuUvclDsQuUVkZzQb8Lt1CEhqKCtLyG2FO8qUWmSAVtIX0NJdrj6WwAJkaRGIJmpX6kPU9hSTypRnf8FhCpuAindcG1XXtqDBk8oNDjWlkC8a82Qru5SiplnKb06V0eDjoKFdRj8NxD6LUX8aywlS8hJMC6fK69MEwviyjy3L0vOIiY5kiHjlzLEI/i3zoNo+S9f8AShlTXM3cX9Sa0zoS8WSJfVn6f18Nty7MPXFNMmuVVLNaLTCzLK+6VUCJZOaWnrhpplksdbeW1TlCB1/SxyLOyPrPYkVC/HQezqBN7b3YKliUCeu9yK/2DdtDsbzO6da0/m0edZrsdM02HV6m2PL3flpktMRtEz+AxWydtd+O63ZtzE+d9rcVfO6prM+i08Z9PtMd1a88/wBU1rvPtEesce0THruS7bKKuyvUVFeWJdVpmTZqRU4rsdJt5F3F5tzc8OZdLexjNDuUL4ZKlCZ1eWysOmkvsjREF7LbLx+IdmJL5hzD23RCKadslVzY6CA0g7BrFOwahMSsDVulcQfyEa8balmBWueTL4LqU2anEutX0zCgT7D3ZPIhE0hMjqX0p2hqd4TKSuBMelISWGQgsxLUQ+SHUYOtMOy+LZYY3TBYxCqK+2DvA9Fpf78afBWzU4sNZjJTDO81iY7pjeYi0VmYntjeu8cbxHtM28zJoM+e9O7PzE8/l5jmIn08Ttv5giXjKac8l5PDuNgWiJ8uqrWKYGq9KTRiBgMfhONNYJNn/SqdzhBfOmPp2UbzPW6nfH26r9qUmW2DbXbpdhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppItUTtlJR0hAkaRbGEW7OJS1bDwqVwOGAFDqoK34PfSv0i681pNpGb6SOkXvmtWsE0qnc4QXzpj6dqECpp3WH26ECd0o/XFMawpvBQknWCQDSrIJGNM6jFYWn+ov+klHzk9sFGLVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCt/SqdzhBfOmPp2kZvpI6Re+a1axOwatupU093dfd11yNgh9Qcm/ZDH3sJB1HXrFDyU46gODxTTgqQh0hA4wih9lMVxbSMBtiOMHHDEa2s4WXLp/rYXb/ESTf1aSbOLXCUH0apeWR7BnSqdzhBfOmPp2opqmnaNgN0IHekDiIpimIZ5SDjSgw1+FRmhsw2GJPBib0cn+RZsFB2ppxVIs6QgcIRP+ymK4Nq+B2wHEThhgdTWaLZUlNO0bH7oQO9I7ExTFMA1yEnCtDhr8GrNTa6zwlGdGpvlli2VbgxS6OUPItWCaVTucIL50x9OyDAKad2z5v78gTSRLu/sln757zxjxaz8O24s2tto214n/XQm34iXefrPefYGJSU07RsfuhA70jsTFMUwDXIScK0OGvwas1Nr2lU7nCC+dMfTtFbgxS6OUPItWJ2BdhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppI5TTusOd0IEbpQGqKY1lTdigIOskECtGSQcaZtb8HvpX6Rdea0m2FD1Fx0knecnVgzpVO5wgvnTH07SxO0sAvYkZzpHfJTfQ9h6bCROjYHdOO3rA0qEs4UZxqEgDX+DjxZh2xX+2XLnNl4H6Jb1P5JsPTrx5fdwEECnT/AL0gmadqe9PiZBOAkZnlxwBGs5mBIODyEidKQY0nHBrYijqYTKeGlcqP+8U4ya5rMUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2Cg3eRL+kXB0dP5rCR/wBqe9L7tJ/6HNdR/wBMSCyxhRvHl95ARoCdP+9I1mnanvT42SRgZGa5MMCTrGfiQGwNiRnOkd8lN9D2Hu4SJ0pGDSccWtiJ2thMp4aryI/7zXiIpmtL/bLlzmy8D9Et6n8k2oMXkS/pF+dHT+KQkB9qe9L7tW/6HFNY/wBMCQy2GL1Id92r7xax8c++oScR7XccsK49zZFca4nWBqZq0zsDYkZzpHfJTfQ9tIXjz8ixt3d4ME6gp1L1/Is4w7huKu1vAT4UvNCqzNG1BXltl3UhkYF6WQyM5kEEMh/7Zcuc2XgfolvU/kmwMEJCxOyVWipHV0ixU5iZzWlUpuQcNXHrxzjgGJHwsT1hzunHcJJ/sUzXpJ2OZzUV4hQ0A2wxabT4W8iX9kqh0deBjGD7U96XGmJI+8gjiPEa4ihoQ7zHXkIDbh3udeBvtPNO1PemNSi7ONZGqMKYkAAYmgIabB/2JGc6R3yU30PYfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44Bhf7Zcuc2XgfolvU/kmw+FvIl/ZKodHXgYxg+1PelxpiSPvII4jxGuIoaEOwcIuFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDENkNiRnOkd8lN9D21/FXkS/slLOjrwMIw/anvS4kxWH3kAcY4hTAUFQHhDtly5zZeB+iW9T+SbBRu5h3/Y/H0j4/1+Xqc24ntpTkce5Y0rT8gGo1ZDdFwsTslKqqR1dIt0OYmc1qta7kDDXx68c4YhvUchz8hQqDHO2oCdWmmp5vDiiHN2t4MVwpeFOTbHgS62aVJzjxYMkNBs0bIq8iX9kpZ0deBhGH7U96XEmKw+8gDjHEKYCgqA8DYGxIznSO+Sm+h7D4CFiesPt047hJQ9ima9JPBzOKCvEamhO2ODTC/2y5c5svA/RLep/JNqEDeQgMOHm514G+1A07U96Z1qLw4UkapwriAQRiKgFpgG95CROlIMaTjg1sRR1MJlPDSuVH/eKcZNc1khsSM50jvkpvoeyA3eRL+kXB0dP5rCR/2p70vu0n/oc11H/TEgssee6tPt+V0uVcmI0HlITplAoswyTfFexfNcKq3c3OSvI+TldSkJS0q3STbKD6Srr5cvkSF+a5zRu13Cot9V6l5xvUdvJ9myU4eVmpReMy2HpumwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdseErw3D7+tIyPKRsZX+gP1S2hGwKgf0jupV1FCwBTEa3ZIDDG2dkNsW0vkf39X5ObwLoEO+W89WvcS8pzI7byvoJLZu8lNB7S8xJCxdcmLt1l26RdjIUrTAs3V6IvaSTKTu8t5edem28QWeuTrMzLRaZf7w58R2+qc5H6izAzgHMPkE9Ufg2nZu6nwKJexGUD1LV6C7SjLoinjvch7nvXcO06dNNOXTwu2n7nrgeiylCROjY7dOO3rHVoEsYUaxqUgjX+Dhx552wIbEjOdI75Kb6Htr9RvHl95ARoCdP+9I1mnanvT42SRgZGa5MMCTrGfiQQ7Zcuc2XgfolvU/kmwMDuEidKRg0nHFrYidrYTKeGq8iP+814iKZrUUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2CgxeRL+kX50dP4pCQH2p70vu1b/ocU1j/AEwJDLeFG8eX3kBGgJ0/70jWadqe9PjZJGBkZrkwwJOsZ+JAbA2JGc6R3yU30PYe7hInSkYNJxxa2Ina2EynhqvIj/vNeIima0v9suXObLwP0S3qfyTagxeRL+kX50dP4pCQH2p70vu1b/ocU1j/AEwJDLYZvGh3/Y/AVj4/1+XV824HtpSacO5YVpT8hOs0ZL9sSM50jvkpvoe2k58n5CikGBdswE6stMzzd5FAPrtbwYXgu8KTW2/Dl1g0qBmnjxZAZDAq+dsuXObLwP0S3qfyTYGCEhYnZKrRUjq6RYqcxM5rSqU3IOGrj145xwDEj4WJ6w53TjuEk/2KZr0k7HM5qK8QoaAbYYtNp8LeRL+yVQ6OvAxjB9qe9LjTEkfeQRxHiNcRQ0Id5jryEBtw73OvA32nmnanvTGpRdnGsjVGFMSAAMTQENNg/wCxIznSO+Sm+h7D4CFiesPt047hJQ9ima9JPBzOKCvEamhO2ODTC/2y5c5svA/RLep/JNqEDeQgMOHm514G+1A07U96Z1qLw4UkapwriAQRiKgFpgG+LhYnZKVVUjq6RbocxM5rVa13IGGvj145wxDZDYkZzpHfJTfQ9tfxV5Ev7JSzo68DCMP2p70uJMVh95AHGOIUwFBUB4Q7Zcuc2XgfolvU/kmwUbuYd/2Px9I+P9fl6nNuJ7aU5HHuWNK0/IBqNWQ3PISJ0pBjSccGtiKOphMp4aVyo/7xTjJrms6jkOfkKFQY521ATq001PN4cUQ5u1vBiuFLwpybY8CXWzSpOceLBkhoNmja3eRL+kXB0dP5rCR/2p70vu0n/oc11H/TEgssA/7EjOdI75Kb6HsPTYSJ0bA7px29YGlQlnCjONQkAa/wceLMO2K/2y5c5svA/RLep/JNh6dePL7uAggU6f8AekEzTtT3p8TIJwEjM8uOAI1nMwJBweQkTpSDGk44NbEUdTCZTw0rlR/3inGTXNZIbEjOdI75Kb6HsgN3kS/pFwdHT+awkf8AanvS+7Sf+hzXUf8ATEgssX+2XLnNl4H6Jb1P5JsDAmwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsVGAhn/bPm8iPj69gl3YpuZh9U155w7mD+DiyKA0rnHrdvlOvHl93AQQKdP+9IJmnanvT4mQTgJGZ5ccARrOZgSpQU/obN4c1RpgJ0zX0i3dQ2b2tbwdmZztavLbZqn9jXXKAqbOd3OlQWSyQAQG3VKEidGx26cdvWOrQJYwo1jUpBGv8ABw4887YW3ie2+dvXb1Rjn7l6KPXL+GS8wgga2dEVa1Dwq0pWuFkRRvHl95ARoCdP+9I1mnanvT42SRgZGa5MMCTrGfiQQ7ZUuc23gfolvU/kmz99vv7ff9h+d66DKBuc6j/lmZQWSHlD3sJd02TVfRCMZR2SwtzDGtaLRW1tU0NOt37Ca7Q2swtLYb62Q0SGkRgkZ0y4e2ycqZN+WZc9ALcsThId/wBdBNMfCso00yVNCcupkNMqOptMBZRZuk14VeTZ/lVWZYacrCIty9NMnTS572bl2aYbOZ/CX1UlRnRU6pvlfR15rpaczc+XpN7AuyVPVkWN/o+dr5B7Xhk5LW2WA1JLRE2l41LTDBavV7PWmmWZx7KAPS//APpwpgmlEvVyy2U13Nr25WKR7kGJkbRJYmlcl9m/9pSmENlhpDRphRXc59rIoxm9uCeMPOxwXfdmbTAEtPHd19X+VWLoXy26F8w8HxBgvm6lMd+lrkrbJSbWrtMRE98TX1naN9t4iOVU6L4/zdV+ONf8DanoGeMWPH3fiLY7dm35ee7+iKzExMTE88eN+P1TXaZON2t1quoTVLEHNUROCtA6KiJ6ny8K8C+SfWEFrPiexpLnK+WZbxJjRpZZV3mlmJZRlp3Lgi3bEW3CtEM13PBwkTshVopx43Qd1OYmc2JRHtUaU/8A4ia45xBAYXu2XLZ1pt4H6Jr0/wCTMOPl/JahC3kIAiFMhOn+mzGaUunvSodzEnDGSSMSDx40IoaFl3Sd82bUZa5cmoiaxFYj1ma1isViZtvxER+kem3paGHBi0+H6GGNo9p5mJ7q/wB+8zHhyT1Qy8KY5KufkKRJMm+Ply8PKGyiLibhpDmVw0k7NlpRnG8BIVl2aEkFFbYK9K8iIk3zDKZaG1mlHQc1o57wW5b6ozcDLKBIae3IV6OV9BZTN/C/d3k25OkJLmXpl6yHJ0BeEupRRezldu5uwynbu5cX0i7KSkWYL652fly5mSbjJy0xN02Pnkwvnw2x1ReKT1u7O5W9lHQp+VlLJdypbjsoyNRnN3E+wL9XlCUJvYk68d05dq0tstPFZzIM6TcuykiF477JZnQ4J27Zfl68eOtmTwmwd8uUhkn39orx+vXM3QSdfJNCdGwsj3wR64uTne9K0lId3MzyhoiRHsvK0vO5EN44iF4zDtCvoZcO3jxupymc8t3Grk3X73cZCsw5QeU7H3SXFZJqHeFOE2oWUPfPdnf1fLeOtTSmXayfNt5GUNdlPkq3wrDMuIcpzivFBdTK6lmb5qXmWpyEy9i7Ad9FZBl4s6XhXLqCNPM4rk2zHcvf5fnk+xU7rjpNC9PaVc5eHOkmSpNa03od2w8XJil9IReyqYGQG5hmsTE2SWX7DBSL8ke+RHv/AEHKeyX0KX50nyEu2UrmLybo75k+/q6OUJxkt6rJU3ybNCTevJWTffkvo08XdLrS2HMtPrsprczXK84TAWn0rvHQfW/lclGP8k+T7jLsldNjZ8vBvyv2vYna+CZkiQr6JUT2J+vHT7yr5LxJku7lNu6maG1pFRFxh5L8uS8vr0pUlFpmaGIgvIN1Lr4OpMoS5aab8kSW5Egb6LyLp5Tbm5KWbzmrrVJYkaf57klFT1hrsCle9+S16Vp7uper0yv0N7M09XdvmJvak9FiJUgG5bbmN/Mrvx9Tb3by7rbucuW7vJ6v3vgmS6eUcqnJ3yXLiL372JlWL95turvEvum2SJMyjUuVL276H01TtfQk3ZLk8Mr0pTFeLMt6Ilu9VVXLpi08lCUDLMr92ZeUVlQXm3RpN3eSDDQSPGzROMFB3yqk7KuUdcRN4uYZgnzyapZujvFknJWv5fSdPs1tFKQxNDcqNvZXld7Mb2UOsTu3LkzyrplKulvNvJyQZiyX1y5i6PI+YkGJkpVyZX9wCvlG5UEnSdON2s9wV5koKs5pM7ZJuSK1ouW52lRLezQgw8wTBMc3O36+zETPK05sw796BeVbvDcDlep2RrL98WU5Nd0eUvkw3qXkMs3n5Rl8t8t4t20+Xcq0kXbLk03fX43oXgzTfLJrU1Id5CZEdjsvTOxLcpTLKDqapPhpXezHNfXet8iy8ybr1LjIB7eCsx8XeTdjPV49xF4ymXCYOyCdLm59WbtlWZwyUZmjMzsIydMm0DLDLKsAQAwS1y7IT69CHviUctDLeQbs7oo26W5eYbt5Pl65sX/XuSfJ0jqrxxePfHelNt7F5eTvcXMEM+mxUk6UZfcXew12pcybLsmNRbybZtezS26lvaeQg9fyRccoTNOstT+gznfte1fBlGLyJE3U3pMKMvO75LwlqcJRldZLMjhorstSG3KcszIGs0iJRmzQgst2Dsq6uHfdq+7qkfHOfqEk4e13FLCQPc2hXCuB1k62aNNODyEidKQY0nHBrYijqYTKeGlcqP8AvFOMmuazqC7ifkWCu7u+gnsFOoeuJFk6Hftwt2t4ChCh5oVJZowoJEttO6gNHAPQyWTnNAAFkuDd5Ev6RcHR0/msJH/anvS+7Sf+hzXUf9MSCywD/sSM50jvkpvoew9NhInRsDunHb1gaVCWcKM41CQBr/Bx4sw7Yr/bLlzmy8D9Et6n8k2Hp148vu4CCBTp/wB6QTNO1PenxMgnASMzy44AjWczAkHB3CROlIwaTji1sRO1sJlPDVeRH/ea8RFM1qKUJE6Njt047esdWgSxhRrGpSCNf4OHHnnbBQYvIl/SL86On8UhID7U96X3at/0OKax/pgSGW8KN48vvICNATp/3pGs07U96fGySMDIzXJhgSdYz8SA2BsSM50jvkpvoeyDAQz/ALZ83kR8fXsEu7FNzMPqmvPOHcwfwcWRQGlc49bte7Zcuc2XgfolvU/kmyFBT+hs3hzVGmAnTNfSLd1DZva1vB2ZnO1q8ttmqf2NdcoCps53c6VBZLJABAbdUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2BDYkZzpHfJTfQ9tfqN48vvICNATp/3pGs07U96fGySMDIzXJhgSdYz8SCHbLlzmy8D9Et6n8k2BghIWJ2Sq0VI6ukWKnMTOa0qlNyDhq49eOccAxI+FiesOd047hJP9ima9JOxzOaivEKGgG2GLTafC3kS/slUOjrwMYwfanvS40xJH3kEcR4jXEUNCHeY68hAbcO9zrwN9p5p2p70xqUXZxrI1RhTEgADE0BDTYP+xIznSO+Sm+h7Syf2y5c5svA/RLep/JNpYNiWGJPBib0cn+RZtjYkZzpHfJTfQ9h6bCROjYHdOO3rA0qEs4UZxqEgDX+DjxZh2xAg1wlB9GqXlke2VbgxS6OUPItWHPISJ0pBjSccGtiKOphMp4aVyo/7xTjJrmsxShInRsdunHb1jq0CWMKNY1KQRr/Bw4887YAyWFs8JRnRqb5ZYtNiRnOkd8lN9D2Hu4SJ0pGDSccWtiJ2thMp4aryI/7zXiIpmtAvXsfWwvI+Ik5fq0rW2LbVd6kO+7V94tY+OffUJOI9ruOWFce5siuNcTrA1M1aZ2BsSM50jvkpvoewZg99K/SLrzWk2woeouOkk7zk6sPhIWJ2Sq0VI6ukWKnMTOa0qlNyDhq49eOccAxI+FiesOd047hJP9ima9JOxzOaivEKGgG2GLTYMlhkHvpX6Rdea0m2NiRnOkd8lN9D2HwkLE7JVaKkdXSLFTmJnNaVSm5Bw1cevHOOAYAjGb6SOkXvmtWsTstxcLE7JSqqkdXSLdDmJnNarWu5Aw18evHOGIbIbEjOdI75Kb6HsCldn63VH4+3q/tSnOzdGb6SOkXvmtWsgXcw7/sfj6R8f6/L1ObcT20pyOPcsaVp+QDUashui4WJ2SlVVI6ukW6HMTOa1WtdyBhr49eOcMQ2DJYWn+ov+klHzk9tNiRnOkd8lN9D2HwELE9Yfbpx3CSh7FM16SeDmcUFeI1NCdscGmAINcJQfRql5ZHtwfcdkRKVw1494E6JuVnlOT9K958+TjP883TXhoWSGoSpN8yTs06dNNLs5SlkmyllArTmV0hlMl6S2JgvuetyxKKAgyoG30oy/DwjHcDyEidKQY0nHBrYijqYTKeGlcqP+8U4ya5rJDYkZzpHfJTfQ9g4zyccjuRsnJceTgkzteveK8hZETbqLrYC8tWlJRgLibl0ZW0yk3OXeNyhIsoLitLjCoEt5EzHec/vKvYmQoMvO5tnWMeIDliy9eN/xTMjf/sC6pZ/9G9Sdt26mwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdseErw3D7+tIyPKRsZX+gP1S2hGwKgf0jupV1FCwBTEa3ZIDDG2dkNsWDv5W4MUujlDyLVidltShInRsdunHb1jq0CWMKNY1KQRr/Bw4887YENiRnOkd8lN9D2CM8JRnRqb5ZYtlW4MUujlDyLVhzuEidKRg0nHFrYidrYTKeGq8iP8AvNeIima1FKEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgDJYWzwlGdGpvlli02JGc6R3yU30PYe7hInSkYNJxxa2Ina2EynhqvIj/vNeIima0AK8z1up3x9uq/alJltg21beNDv+x+ArHx/r8ur5twPbSk04dywrSn5CdZoyX7YkZzpHfJTfQ9gzB76V+kXXmtJthQ9RcdJJ3nJ1YfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWmwZLC0/1F/wBJKPnJ7abEjOdI75Kb6HsPgIWJ6w+3TjuElD2KZr0k8HM4oK8RqaE7Y4NMARjN9JHSL3zWrWJ2W4uFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDENkNiRnOkd8lN9D2BSuz9bqj8fb1f2pTnZta4Sg+jVLyyPZBu5h3/AGPx9I+P9fl6nNuJ7aU5HHuWNK0/IBqNWQ3PISJ0pBjSccGtiKOphMp4aVyo/wC8U4ya5rIMlhiTwYm9HJ/kWbY2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsQINcJQfRql5ZHsUstvISJ0pBjSccGtiKOphMp4aVyo/7xTjJrmskNiRnOkd8lN9D2DKTwYm9HJ/kWbJ6f9dCbfiJd5+s959j6bCROjYHdOO3rA0qEs4UZxqEgDX+DjxZh2xUYCGf9s+byI+Pr2CXdim5mH1TXnnDuYP4OLIoDSucet2B/VuDFLo5Q8i1YnZbUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2BDYkZzpHfJTfQ9g5XygMi7JVysopPc5SNwV118r6WICB7HFybZSTYyYEDOUVcqycjTYwwxMCQkPXrQevkOFX2HBLb8Fzns548q8iuXULqb+XJex1POBgE6VcnXKIUTlG5IsPAOGYFOR5kaUh2x7sHZZ641iwkhtwy02CHUoMtts58zMhn3sdwkTpSMGk44tbETtbCZTw1XkR/3mvERTNa8sOqz5O833pXAJV9tz0XFuMovI/nOCv1ubUYGHS2lKKeICqiLE6ysCWGA9cTChJLK28QmQOyWJRJfhm2S2T1uadRntijBObJOCvjDN7Tjj/jTftj3naOUcYsUXnLGPHGSfOSKVi8/rbbf+XrnQcn/8/wD8k/8A7YZB76V+kXXmtJtzlkpX+SxlWZO91V/UoqTzR94MtQEeoJwCc2ZemV0QmTbK7ZDn1WW190roJ27xrOdhrbNEW35CQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiFIBXmet1O+Pt1X7UpMtsG2rbxod/2PwFY+P8AX5dXzbge2lJpw7lhWlPyE6zRkv2xIznSO+Sm+h7BmD30r9IuvNaTaRm+kjpF75rVrDoSFidkqtFSOrpFipzEzmtKpTcg4auPXjnHAMSLhYnZKVVUjq6RbocxM5rVa13IGGvj145wxDYMlhaf6i/6SUfOT202JGc6R3yU30PYfAQsT1h9unHcJKHsUzXpJ4OZxQV4jU0J2xwaYAjGb6SOkXvmtWsTstxcLE7JSqqkdXSLdDmJnNarWu5Aw18evHOGIbIbEjOdI75Kb6HsCddP9bC7f4iSb+rSTZxa4Sg+jVLyyPbX91cO+7V93VI+Oc/UJJw9ruKWEge5tCuFcDrJ1s0aacHkJE6UgxpOODWxFHUwmU8NK5Uf94pxk1zWQZLDEngxN6OT/Is2xsSM50jvkpvoew9NhInRsDunHb1gaVCWcKM41CQBr/Bx4sw7YgQZ4SjOjU3yyxbKtwYpdHKHkWrDncJE6UjBpOOLWxE7WwmU8NV5Ef8Aea8RFM1qKUJE6Njt047esdWgSxhRrGpSCNf4OHHnnbAGS2vE/wCuhNvxEu8/We8+zfsSM50jvkpvoeyDAQz/ALZ83kR8fXsEu7FNzMPqmvPOHcwfwcWRQGlc49bsD+rcGKXRyh5FqxOy2pQkTo2O3Tjt6x1aBLGFGsalII1/g4ceedsCGxIznSO+Sm+h7BmD30r9IuvNaTbCh6i46STvOTqw+EhYnZKrRUjq6RYqcxM5rSqU3IOGrj145xwDEj4WJ6w53TjuEk/2KZr0k7HM5qK8QoaAbYYtNgyWlhexIznSO+Sm+h7SwTZcZzXHfKTfTFh6bFxOjYHcyO3rA0qUsYUZwoFcjX+FhxZ52oZLDEngxN6OT/Is2Ac8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc1FKLidGx25kdvWOrQpZwo1hQq4Gv8LHjzDtSQa4Sg+jVLyyPbKtwYpdHKHkWrBjZcZzXHfKTfTFh7uLidKRh0ZHBrYidrbTKeGq8ix+4U4ga5zLJYWzwlGdGpvlliwa/vUiH3avvFrARzn6hJxPtdxSwrn3RoVwpiNZGtmrLWwNlxnNcd8pN9MWTr2PrYXkfEScv1aVrbFsC3CRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuR8VE9Yc7mR3CSf7JM16SdnngUFeMVNCNqcWWCMHvpX6Rdea0m2FD1Fx0knecnVgmy4zmuO+Um+mLD4SKidkqtEuOrpFioz0zmtKpTdcYauLXhmjAtslhkHvpX6Rdea0mwDouKidkpVUuOrpFugz0zmtVrXdc4a+LXhmnEsENlxnNcd8pN9MWzGb6SOkXvmtWsTsGrbuYh/2Px9ICP8AX5epzbge2lOQx7rhWlfyEazVot0XFROyUqqXHV0i3QZ6ZzWq1ruucNfFrwzTiWAV2frdUfj7er+1Kc7N0ZvpI6Re+a1awY2XGc1x3yk30xYfARUT1h9uZHcJKHskzXpJ4eeDUV4zQ0B2owZbZLC0/wBRf9JKPnJ7YB7yLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzRDZcZzXHfKTfTFo1wlB9GqXlkexSwLabFxOjYHcyO3rA0qUsYUZwoFcjX+FhxZ52o4SvDfvv60jI8pBRlf6A/VLaAbAqR/SO6lXU1LZFMBreAkNsbV4S23bv5J4MTejk/wAizbhG8b/imZG//YF1Sz/6N6k7YO3VKLidGx25kdvWOrQpZwo1hQq4Gv8ACx48w7UkNlxnNcd8pN9MWyrcGKXRyh5FqxOwLbuLidKRh0ZHBrYidrbTKeGq8ix+4U4ga5zMUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1JBnhKM6NTfLLFsq3Bil0coeRasGNlxnNcd8pN9MWHu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMslhbPCUZ0am+WWLAg3jRD/sfgKwEf6/Lq+bcT20pNGHdcaVr+QHUaNB+2XGc1x3yk30xZSvM9bqd8fbqv2pSZbYNgW4SKidkqtEuOrpFioz0zmtKpTdcYauLXhmjAtyPionrDncyO4ST/ZJmvSTs88CgrxipoRtTiywRg99K/SLrzWk2woeouOkk7zk6sE2XGc1x3yk30xYfARUT1h9uZHcJKHskzXpJ4eeDUV4zQ0B2owZbZLC0/1F/wBJKPnJ7YB8XFROyUqqXHV0i3QZ6ZzWq1ruucNfFrwzTiWCGy4zmuO+Um+mLZjN9JHSL3zWrWJ2DVt3MQ/7H4+kBH+vy9Tm3A9tKchj3XCtK/kI1mrRbnkXE6UgzoyOLWxFHU2mU8NK5Vj9xrxgUzmgV2frdUfj7er+1Kc7NrXCUH0apeWR7BNlxnNcd8pN9MWHpsXE6NgdzI7esDSpSxhRnCgVyNf4WHFnnahksMSeDE3o5P8AIs2Ac8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc0Q2XGc1x3yk30xaNcJQfRql5ZHsUsC2mxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqFGAiX/bPm8CAj69gl3ZruZj9U154w7oT+Fi0agVpnDrln9J4MTejk/wAizZPT/roTb8RLvP1nvPsB9Si4nRsduZHb1jq0KWcKNYUKuBr/AAsePMO1JDZcZzXHfKTfTFsq3Bil0coeRasTsC27i4nSkYdGRwa2Ina20ynhqvIsfuFOIGuczlQi4jrHBkdvpOrtks+2TFPbhj8hxFNYBxYYvs8JRnRqb5ZYtFD1Fx0knecnVg8Lsk+Je5BPVBr4siVThY5KuHypgp5R+SrsqLTGU2XpyoWbyLrEZsLuexQpFWERmuawjILTOcJpBPuDCRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFvzX6q5k7TVe9k8p97t0RiYLKJyS5ohL+7nFNPFY6Mbk9t0sTdKIaJoGZoQUolyxQtNzOiS+WaMsENdR5HuUXKuVhcFd/f1KTbgQk/JMBFqyW4f1MsTYmpiclTZKhJJLZl1ecqsOatNFouw2QGm7Bte8aIf9j8BWAj/X5dXzbie2lJow7rjStfyA6jRoP2y4zmuO+Um+mLKV5nrdTvj7dV+1KTLbBsC3CRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuRcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYIwe+lfpF15rSbSM30kdIvfNatYMbLjOa475Sb6YsPgIqJ6w+3MjuElD2SZr0k8PPBqK8ZoaA7UYMtslhaf6i/6SUfOT2wD4uKidkpVUuOrpFugz0zmtVrXdc4a+LXhmnEsENlxnNcd8pN9MWzGb6SOkXvmtWsTsGq7q4h92r7uqQEc++oSTj7XccsJB90ZFcaYDWDqZoyy4PIuJ0pBnRkcWtiKOptMp4aVyrH7jXjApnNL10/1sLt/iJJv6tJNnFrhKD6NUvLI9gmy4zmuO+Um+mLD02LidGwO5kdvWBpUpYwozhQK5Gv8LDizztQyWGJPBib0cn+RZsA53FxOlIw6Mjg1sRO1tplPDVeRY/cKcQNc5mKUXE6NjtzI7esdWhSzhRrChVwNf4WPHmHakgzwlGdGpvlli2VbgxS6OUPItWDGy4zmuO+Um+mLIMBEv+2fN4EBH17BLuzXczH6przxh3Qn8LFo1ArTOHXLbStrxP8AroTb8RLvP1nvPsB9Si4nRsduZHb1jq0KWcKNYUKuBr/Cx48w7UkNlxnNcd8pN9MWyrcGKXRyh5FqxOwLcJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5HxUT1hzuZHcJJ/skzXpJ2eeBQV4xU0I2pxZYIwe+lfpF15rSbYUPUXHSSd5ydWCbLjOa475Sb6YtLFLSwDNHu/dY/xopfxbUE2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01e2XGc1x3yk30xYemxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqA+nkC50pB91jt6KGGklP7tIGPdDXloSBUk4ktMsxSgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM/LyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzUUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1IEdHu/dY/xopfxbUHcC50pGd1jt6J+GklP7tXGHdBTloCRUA4EMstXtlxnNcd8pN9MWHu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMgoXrQLpi7C8Wr2PP1CTliVNSJwlhXNK9cP5RhUEAirQZZa2Bo937rH+NFL+LbX16kQ+7V94tYCOc/UJOJ9ruKWFc+6NCuFMRrI1s1Za2BsuM5rjvlJvpiwUISBdbJVu6x43RZPCSlzWlf5hwwwGoVNCakM5joBz1hz3SO4SgPbNS5zYr/e/kwNBQAZwADTfzCRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuR8VE9Yc7mR3CSf7JM16SdnngUFeMVNCNqcWWAI6Pd+6x/jRS/i2HwkC62Srd1jxuiyeElLmtK/zDhhgNQqaE1IZv7LjOa475Sb6YsPhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC2GYuBdbJSe6x53RaPCSlzWq/5gwxxGo0FSKANENHu/dY/xopfxbDouKidkpVUuOrpFugz0zmtVrXdc4a+LXhmnEsENlxnNcd8pN9MWBBu5gXTyXo8h7H07Pb1NSmpj7aU5Y+H+UDVQADEAEt8XAutkpPdY87otHhJS5rVf8wYY4jUaCpFAGlC7mIf9j8fSAj/X5epzbge2lOQx7rhWlfyEazVot0XFROyUqqXHV0i3QZ6ZzWq1ruucNfFrwzTiWAI6Pd+6x/jRS/i2oQMA56w+7pHcJR/tmpc5t0/vfy4CooSM4glpi9suM5rjvlJvpiw+AionrD7cyO4SUPZJmvSTw88GorxmhoDtRgy2H08gXOlIPusdvRQw0kp/dpAx7oa8tCQKknElplm/o937rH+NFL+LYc8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc0Q2XGc1x3yk30xYKKbAOdGwPdI7ekD7ZqZPgs8rxk48eGOo5oAaa4RvCgnX9aRkeM9cjaHIH6pY0aKKjWoyjupV0o0G6gbc1ZDYHgVZb627at3YmxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqOErw377+tIyPKQUZX+gP1S2gGwKkf0jupV1NS2RTAa3gJDbG1eEtt2Du9SgHOjY7ukdvSO9s1MHwWuR40cOLDDUM4EtM39Hu/dY/xopfxbDlKLidGx25kdvWOrQpZwo1hQq4Gv8ACx48w7UkNlxnNcd8pN9MWCi7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhllqKUA50bHd0jt6R3tmpg+C1yPGjhxYYahnAlpn5dxcTpSMOjI4NbETtbaZTw1XkWP3CnEDXOZilFxOjY7cyO3rHVoUs4UawoVcDX+Fjx5h2pAjo937rH+NFL+Lag7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhllq9suM5rjvlJvpiw93FxOlIw6Mjg1sRO1tplPDVeRY/cKcQNc5kFG8aBdO5egCXsfTs9ur1qamftpSbj4f5AddQSMASQ/6Pd+6x/jRS/i2QLxoh/wBj8BWAj/X5dXzbie2lJow7rjStfyA6jRoP2y4zmuO+Um+mLBQhIF1slW7rHjdFk8JKXNaV/mHDDAahU0JqQzmOgHPWHPdI7hKA9s1LnNiv97+TA0FABnAANN/MJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5HxUT1hzuZHcJJ/skzXpJ2eeBQV4xU0I2pxZYAjo937rH+NFL+LahAwDnrD7ukdwlH+2alzm3T+9/LgKihIziCWmL2y4zmuO+Um+mLD4CKiesPtzI7hJQ9kma9JPDzwaivGaGgO1GDLYZi4F1slJ7rHndFo8JKXNar/mDDHEajQVIoA0Q0e791j/Gil/FsOi4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwQ2XGc1x3yk30xYEG7mBdPJejyHsfTs9vU1KamPtpTlj4f5QNVAAMQAS4PIFzpSD7rHb0UMNJKf3aQMe6GvLQkCpJxJaZZT7uYh/wBj8fSAj/X5epzbge2lOQx7rhWlfyEazVotzyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzQEdHu/dY/xopfxbUE2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01e2XGc1x3yk30xYemxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqA+nkC50pB91jt6KGGklP7tIGPdDXloSBUk4ktMs39Hu/dY/xopfxbDnkXE6UgzoyOLWxFHU2mU8NK5Vj9xrxgUzmiGy4zmuO+Um+mLBRTYBzo2B7pHb0gfbNTJ8FnleMnHjwx1HNADTSfAQDntnzfV7H+sO7v2zU8PqmvP1bemOrAnDDwduG5Ni4nRsDuZHb1gaVKWMKM4UCuRr/Cw4s87UKMBEv+2fN4EBH17BLuzXczH6przxh3Qn8LFo1ArTOHXLA4KUA50bHd0jt6R3tmpg+C1yPGjhxYYahnAlpm/o937rH+NFL+LYcpRcTo2O3Mjt6x1aFLOFGsKFXA1/hY8eYdqSGy4zmuO+Um+mLBRdwLnSkZ3WO3on4aSU/u1cYd0FOWgJFQDgQyy1I6Ac9Yc90juEoD2zUuc2K/3v5MDQUAGcAA038u4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMyPionrDncyO4ST/AGSZr0k7PPAoK8YqaEbU4ssAR0e791j/ABopfxbeEuSy6dZB3VFL6MipVex6VcBlXxahlCZK4bUlCBTZdn8QDtq8u69Hzl55tS7YLx2A2Gs1Hl4tMh7MzOZ7s7LjOa475Sb6Yt5adVMyfpvvoyf31510qcrwGUVkszkn383JLafozSGkZRT0ZYm2U2WiuMM5kyoaVmOhTbzSjy8WCWWath6G3jQLp3L0AS9j6dnt1etTUz9tKTcfD/IDrqCRgCSH/R7v3WP8aKX8W3E1xeUzLeVrksXP39SlBF04nhbupiFxMh4pNb7G5wSL0ZOSJxlltsLBaLcuL7pWckNtvO5unbZa662GG+2NlxnNcd8pN9MWChCQLrZKt3WPG6LJ4SUua0r/ADDhhgNQqaE1IZkXAutkpPdY87otHhJS5rVf8wYY4jUaCpFAGsQkVE7JVaJcdXSLFRnpnNaVSm64w1cWvDNGBbkXFROyUqqXHV0i3QZ6ZzWq1ruucNfFrwzTiWAI6Pd+6x/jRS/i2oQMA56w+7pHcJR/tmpc5t0/vfy4CooSM4glpi9suM5rjvlJvpiw+AionrD7cyO4SUPZJmvSTw88GorxmhoDtRgy2GYuBdbJSe6x53RaPCSlzWq/5gwxxGo0FSKANENHu/dY/wAaKX8Ww6LionZKVVLjq6RboM9M5rVa13XOGvi14ZpxLBDZcZzXHfKTfTFgQLqYF03dhd1R7Hj6hJNxCmpA4ywkGleuD8pwqSSTRotMsuLyBc6Ug+6x29FDDSSn92kDHuhry0JAqScSWmWU26uIfdq+7qkBHPvqEk4+13HLCQfdGRXGmA1g6maMsuDyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzQEdHu/dY/wAaKX8W1BNgHOjYHukdvSB9s1MnwWeV4ycePDHUc0ANNXtlxnNcd8pN9MWHpsXE6NgdzI7esDSpSxhRnCgVyNf4WHFnnagPp3AudKRndY7eifhpJT+7Vxh3QU5aAkVAOBDLLUUoBzo2O7pHb0jvbNTB8FrkeNHDiww1DOBLTPy7i4nSkYdGRwa2Ina20ynhqvIsfuFOIGuczFKLidGx25kdvWOrQpZwo1hQq4Gv8LHjzDtSBHR7v3WP8aKX8WyBAQDntnzfV7H+sO7v2zU8PqmvP1bemOrAnDDwduH7ZcZzXHfKTfTFkGAiX/bPm8CAj69gl3ZruZj9U154w7oT+Fi0agVpnDrlgcFKAc6Nju6R29I72zUwfBa5HjRw4sMNQzgS0zf0e791j/Gil/FsOUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1JDZcZzXHfKTfTFgoQkC62Srd1jxuiyeElLmtK/wAw4YYDUKmhNSGcx0A56w57pHcJQHtmpc5sV/vfyYGgoAM4ABpv5hIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC3I+KiesOdzI7hJP9kma9JOzzwKCvGKmhG1OLLAEdHu/dY/xopfxbS2NlxnNcd8pN9MWlgKWGJPBib0cn+RZt5ZTBkI9RRli8aRbopjyNupbS5e1eSlqSxd3dcu5O2SUnz9P6WlFlhXU5QlBVkiGmWbEpBzmG38RLsM9duXbDYfEMOxTaMB1KTqXD6Cg2nvU1cgNppqFgmmmmsjnJxNWmmQWiSLv2yc6vKaknNziSyA77a4Sg+jVLyyPbKtwYpdHKHkWrcBN9Sk6luI5yx/Vq5AZYMLGtNMf0OcnLNLTLSYGWiz2vwCWQ22AaYBpoYAgt5j+pSdS4cwUY066mrkBstMwsa0y0zkc5OIo0yySyQTd+wRm05RQgZ2aQGSHofYWzwlGdGpvlli3B/wDVP9S2/wCWjkA/+muTl/t/amx1KTqW5jnzH9WrkBhgQsE0yx/Q5ycs0NNNKYaaDPa/IBaDDAJpiGWRiASwHZd7H1sLyPiJOX6tK1ti28w7xOpU9TGg7v58fpXU3shOGVISTZjfpsSl5HeT8I9xHlJVGmCnDtfstMvWXjLJdsOiyK0axGaGVuZshLqKcoS7eRNU35GvUtpSlW56Jbgb3JomXJ0yS5el66yNaSUlYAvCXFaSnSLJm4y0jLWbMz2GznKwjvG6OXzjrgepsHvpX6Rdea0m2FD1Fx0knecnVvN6TupndSVn5AT5yk7qfvU75xk6Z4NPXJQmqXck3JtW5dmJAVE1LeJiqjKyPIbSUrozzObbdNuXjx22yyy8YazSw8eMsb1KXqXLtywXXU1MgMNGKgGcMjnJxFGW492y0PWCxg0yWgQCagkUJLTLIeiFhkHvpX6Rdea0m3B39U/1Lb/lo5AP/prk5f7f2pw3UpepctRCky11NXIFaZYigywycjnJyLLLJTkxsssg3f7VkttttlnAVaLRpUNNh37Gb6SOkXvmtWsTt53xPUpepcsxCayz1NXIFZZbiiy2yMjnJyDLTITlNsMtAXf7ZkNsMNhnEVZDQrQtMXP6p/qW3/LRyAf/AE1ycv8Ab+wdh3Z+t1R+Pt6v7Upzs3Rm+kjpF75rVrePFzeRb1EufpvvAudlzJV6lJPl9l2MyTfE3i3YytchkiTbeZdwnmd1l0hidpOSJfXplk5llHKQ6YZmF3DtZwDrrbohpgOl22Qr1Fe++FUFy5HI06l7eymSxNalJU0KF2eTtkmT4ny9N6PA56pKq2oylI8wukeZZfYYDT9AfPXUS4eF0H4GczQPWawtP9Rf9JKPnJ7bg/8Aqn+pbf8ALRyAf/TXJy/2/tTgupS9S5eOWy96mpkBloRUezjkc5OJqyxHvGWR6wW8GWQyACRQACgIZZaDvxrhKD6NUvLI9ilvO9vqUnUtxHOWP6tXIDLBhY1ppj+hzk5ZpaZaTAy0We1+ASyG2wDTANNDAEFu5/VP9S2/5aOQD/6a5OX+39g7xSeDE3o5P8izbhG8b/imZG//AGBdUs/+jepO209dvkFdRbvOUp4li77Iv6l5eLNV1Kz2JXqS7I+TrkjzXMl3c4h3ntyteEjy7JT99JkyAh4dAzC7h3/c84MFl0HjXOk+dTR6nBB9UdyVpFgep+5EziSpkyK8vqbFuUHOSXcOxKaxMcmX79TQSpSmVUQWZFdIqyty0iXhTkiSmutu38VLMPOs1u3FHMxzE7bD3aVuDFLo5Q8i1Ynbzwj+pSdS4cwUY066mrkBstMwsa0y0zkc5OIo0yySyQTd+wRm05RQgZ2aQGTb/qn+pbf8tHIB/wDTXJy/2/sHeDPCUZ0am+WWLZVuDFLo5Q8i1bgJjqUnUtzHPmP6tXIDDAhYJplj+hzk5ZoaaaUw00Ge1+QC0GGATTEMsjEAljMf1KTqXDmCjGnXU1cgNlpmFjWmWmcjnJxFGmWSWSCbv2CM2nKKEDOzSAyQ9D7C2eEozo1N8ssW4P8A6p/qW3/LRyAf/TXJy/2/tTY6lJ1Lcxz5j+rVyAwwIWCaZY/oc5OWaGmmlMNNBntfkAtBhgE0xDLIxAJYDs+8z1up3x9uq/alJltg28Y50yLeokC9BMycYDJX6lTB5SEaoyXMELcS9uSyQU+/CLkxmZkZcWFFzdy3LbM9tS83JCesPmnzqXi6alzPZZazGHjIfpeyDuoqzZeZOdzcrZGXUtpiveu8TU5WvBuqQsnfJKV7yZCTVZoukZSm6QUeSn8yoCSvjukLETA5hHL8PHIhztwWQ9S4PfSv0i681pNsKHqLjpJO85OrcBw3UpepctRCky11NXIFaZYigywycjnJyLLLJTkxsssg3f7VkttttlnAVaLRpUNNyN6lL1Ll25YLrqamQGGjFQDOGRzk4ijLce7ZaHrBYwaZLQIBNQSKElplkPRCwtP9Rf8ASSj5ye24P/qn+pbf8tHIB/8ATXJy/wBv7U4LqUvUuXjlsvepqZAZaEVHs45HOTiassR7xlkesFvBlkMgAkUAAoCGWWg79jN9JHSL3zWrWJ2874nqUvUuWYhNZZ6mrkCsstxRZbZGRzk5BlpkJym2GWgLv9syG2GGwziKshoVoWmP7vepSdSxdsF486mv1P8AcutZLWRxk4AHjG3N32b+Slg7Iuz9bqj8fb1f2pTnZta4Sg+jVLyyPbxvhsjDqI1313ksXiXoZLHUo5RkW9Cel1Juynucrk8kNGlCe+y2el03eJMmTWroDtAm57MKC8RXsqIMuPIhp45dssuHZbaZDPSjfUpOpbiOcsf1auQGWDCxrTTH9DnJyzS0y0mBlos9r8AlkNtgGmAaaGAILYeiFhiTwYm9HJ/kWbcHf1T/AFLb/lo5AP8A6a5OX+39qkB1KTqXD6Cg2nvU1cgNppqFgmmmmsjnJxNWmmQWiSLv2yc6vKaknNziSyA77a4Sg+jVLyyPYpbzvb6lJ1LcRzlj+rVyAywYWNaaY/oc5OWaWmWkwMtFntfgEshtsA0wDTQwBBbuf1T/AFLb/lo5AP8A6a5OX+39g7xSeDE3o5P8izZPT/roTb8RLvP1nvPtxfA9Sm6loynQj6J6mzkAnvF2/fxD/I4ycRiWGWi02Rd8QKVJJxZoKFsNYW5rkfI96iBeBC3n3wSTkwdScni4679FTkec7xpTucyMpsuzkRflCPnFSvAE3TSiIcVL8mK8voimhRE1tTHEQexoRiG66Qw4egh7KK3Bil0coeRasTt5ayb1OjqPt6V3yTeJdbkJdTSvIkOaUVlVlGfZAyXclubpQmJNeMPGWFhFmpAkR+grEO9bdvCHqK/aYZbYaZZbqGAxsb+qf6lt/wAtHIB/9NcnL/b+wd4M8JRnRqb5ZYtFD1Fx0knecnVuA2OpSdS3Mc+Y/q1cgMMCFgmmWP6HOTlmhpppTDTQZ7X5ALQYYBNMQyyMQCWJG9Sl6ly7csF11NTIDDRioBnDI5ycRRluPdstD1gsYNMloEAmoJFCS0yyHohYZB76V+kXXmtJtwd/VP8AUtv+WjkA/wDprk5f7f2pw3UpepctRCky11NXIFaZYigywycjnJyLLLJTkxsssg3f7VkttttlnAVaLRpUNNh583XNf0Ccvm8bI6UiIDJ9ywZ+u9yg8mMZwdpsuXjC9CTReRICYwy8e5jt47TGX7Dp6002wwkS028GfMoA/Qtb8yHVTOpqdTJX7qYy6rJ2yd+p93aZcUg6CygLrblZLunybpVvgvTk2TFVlmbk1WukQ0VBmKdpBfIIXWnpipdmaWeuorIad57bynQWRPcn1D3LSu2llZu8yKOpeqt63YLLk03q3LIuTtktR94F1yo9ePUdadzbd+6liImZCQDMKcpOJYX5jcsiYIYsxDt7QNMAPdqD30r9IuvNaTaRm+kjpF75rVrcBQ3UpepctRCky11NXIFaZYigywycjnJyLLLJTkxsssg3f7VkttttlnAVaLRpUNNyJ6lL1LlmITWWepq5ArLLcUWW2Rkc5OQZaZCcpthloC7/AGzIbYYbDOIqyGhWhaYD0QsLT/UX/SSj5ye24P8A6p/qW3/LRyAf/TXJy/2/tTgupS9S5eOWy96mpkBloRUezjkc5OJqyxHvGWR6wW8GWQyACRQACgIZZaDv2M30kdIvfNatYnbzviepS9S5ZiE1lnqauQKyy3FFltkZHOTkGWmQnKbYZaAu/wBsyG2GGwziKshoVoWmA56mR1JXsjMmnqevU7zOTaGZgMqf0TsmzT/Y7s8o/ZPogSAF3QYV29Ead6xsXZZzeu5wJsHcd0/1sLt/iJJv6tJNnFrhKD6NUvLI9vH253Ii6izOEkrUOjZI3Us53XbkUmGlu/yIl+4jJCm+OuqnJBl1p5NyNe4qoSHMLqS15C0WrPZodzQ9ctsZj16023mPWi/XbdT86jRffLCHeNczkN9THvau7X3CjoKfLssmvJanqR1fRqgymvmkuapSkdel5VLDxpp2WXUQ8zG3ZZqy27eMOw9WLDEngxN6OT/Is24O/qn+pbf8tHIB/wDTXJy/2/tUgOpSdS4fQUG096mrkBtNNQsE0001kc5OJq00yC0SRd+2TnV5TUk5ucSWQHfbPCUZ0am+WWLZVuDFLo5Q8i1bgJjqUnUtzHPmP6tXIDDAhYJplj+hzk5ZoaaaUw00Ge1+QC0GGATTEMsjEAljMf1KTqXDmCjGnXU1cgNlpmFjWmWmcjnJxFGmWSWSCbv2CM2nKKEDOzSAyQ9D7a8T/roTb8RLvP1nvPtw5MfUyOpKSaiR0wzZ1PTqdMsy6lO2otRXJjyTsmpDRE12GfDVFZWkN25dMktgMvWiyC0WWSBVkW0bM2RX1Ee7i/hGukvJyVOpSSLeBejLcow10l0873J5JMsz/PqmyrTi7Wmru7vlxCdTBMLZLSM7e9jsuNNNPmc148evXbRZD2FVuDFLo5Q8i1YnbyYfZCfUUn94y5cen5HPUu4i/ZCk93OyrdBD5POSSL2kmUHweaMmxTu9MjPZmSJffFpl27Xn8t7GIadMu23jQYYa3H/VP9S2/wCWjkA/+muTl/t/YO8YPfSv0i681pNsKHqLjpJO85OrcBw3UpepctRCky11NXIFaZYigywycjnJyLLLJTkxsssg3f7VkttttlnAVaLRpUNNyN6lL1Ll25YLrqamQGGjFQDOGRzk4ijLce7ZaHrBYwaZLQIBNQSKElplkPRC0t59/wBU/wBS2/5aOQD/AOmuTl/t/aWDyZmibYqISpxuyvIleVLqMsDKEmbqYV4VwdwCYl6Am+BQbujcm9nBLu6lIPGV9ZkfJtnlJvieTgZddNtXUyo2W5yeOw0Q+/SqG1DDMhU7reBcUUXgB/8A4WQkHN/M03rw+ArYYk8GJvRyf5FmwD3jxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyzFJ4qaOju9YDekdhpJ5jRlrlRWgfh2uHsi2dsL7XCUH0apeWR7ZVuDFLo5Q8i1YMZ6n71T/GT30NZPXn83uoRdblVIQVSYnUsPItBTFua1SX0VRX85YKUkq6ykyPNUQhIbxpkOnkwu5YmV86YLTTErL79y7B2JYWzwlGdGpvlliweey1en1S5Ik28JaWMjvJfiFJIkOaIySUu5XLem29WfpkvBYTWWZSS2ZUvsyOskG7p4itRTQfTFETJflKQZhUrrbkNF608Z8brhFmMu1UL6F29y669a4m6m5nqolxl7GURPmVDMNwkWzD6YyV0HTF4V482XL35XmSEiMs3srEl3hzbMra+LrZPC9L4bmllqWprlCVf003sfWwvI+Ik5fq0rW2LYPObqdAeRNxc8zKiungu2n7KcypZ+ubfMvnkCmrd1c533TotynNMpZoLl9I82BRVZ9k5eZddcmeVF1Dmx3vthk96xzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi2Qhd9qv/8Aef8A+rSLRQ9RcdJJ3nJ1YJnqfvVP8ZPfQ1h8I8U9kq3eifXSLFaqTzmtJ/E+vlBxwGJqzmMlhkHvpX6Rdea0mwDottT2SlZ8LAV0i3TdN4fatV1gozP5gKGtaNCjQb5LXJ46oQ5n1STJayZsj1UuvYmbYidOa5ly30S9eBFylpCrSwoXcpXU85pltJXtENMtMy8xepHOA8zHfZa00evM9ixm+kjpF75rVrE7B+dWZ8oHJ1y052vQk/JYvyya0aaMnG5PLKutyf7lZFvTuze3/Xs3wTXKK/KF4aubjpKXYi8CS7j5YXkVjsbRoiXWJsvbm1ozo9lmVpMlaTJlvV6PyGZyu3vSykpgnjJzWEKYLpZayKMmi6GcVOUIjrkpI98Umzbeg+eXVrDSWXrEv3pXZyMrssTjIDYE0SgwuS85mvrL15DBn1gkZUj1VHjYuOfMvHzmcLwksAkbwRZ+X0VJ1YHNRkxxSgxJwFmiM30kdIvfNatYMZ6n71T/ABk99DWHwLxT6w+70gOEVD2yeVrpN5yI3LxENNagWi0WSwyWFp/qL/pJR85PbBQePFPSkGNiwFdiKOOknlfVEnVuMSfzEGgBJILLLNVaC1FIizDp7uDh49+lqjhLf9fMVsZRaTjotppksMV7q3ntCoOLLQBDdWzLXCUH0apeWR7FLB4GdT4XUObr4ckdFuzjkdTXMnHIBnC5zK2TUGJaYUrt75RPdyTSNdVfCksvm2pQvYExI18kyNS7MzLmaS6EwTU9dNOpkbeve4bwXiieqjZHtIaBDf8AQI6pZmjSDWaWP6R3UrM8lrRBbBB63RkBpk5zeec5gF739ANl5AQL14AHrcNAlr8pp/rVq3CV43/FMyN/+wLqln/0b1J2wdvKTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YX89T96p/jJ76GtlW4MUujlDyLVidgXHbxT0pGDYsBXYidjpJ5X1RW17jAj85JoSQQA0y1FJ4qaOju9YDekdhpJ5jRlrlRWgfh2uHsi2dsL7PCUZ0am+WWLZVuDFLo5Q8i1YMZ6n71T/GT30Nag7eKelIwbFgK7ETsdJPK+qK2vcYEfnJNCSCAGmWmOwtnhKM6NTfLLFg8Wr1sp7JIvfyyZYyNYK/XJluima5zKMu3vUvag1y+G6yQr7b0codHSkVcu5utuiu8C7L14U5L0wMdibN7V4rcugPJUDFzknNThFTTNL26/WOTwrpKjf8A5Ll0krx6dEZRlxeU5l9z7lTSqmVhJrka668dXvrCNM14iEXmnkOSb7F9eucmO6p5M7DlibnaS5m6Uns1upTq69zJ5VI9KR4KLgXzLt8+nC71LIBG8FqfkBFVteAzkZTf1qMCMRZ7sC3CPFPZKt3on10ixWqk85rSfxPr5QccBias5kjnin1hz3pAcIp/tk8rXSbvlRuXiAZa1gNBoNFsjB76V+kXXmtJthQ9RcdJJ3nJ1YJnqfvVP8ZPfQ1h8C8U+sPu9IDhFQ9snla6TeciNy8RDTWoFotFksMlhaf6i/6SUfOT2wD4t4p7JSe9E+ukW6UUnnNat+J9fIBjicRRrP4iy9Yi+iLulRZLuvuLvkvpQp8mh6g3zJVxM63CS9P6bdOwlrSqsJqecoS9u4yX4pm8VqASrv5nMvzX2USxK0xLr+UnL2LhnEWz3dGb6SOkXvmtWsTsH5YMnS8i7u7/ACT8gedso+VYS5C6VS6mJfnk+yCh3niQkuBVrwFZUuSRUuQZTWZInybJeezBfdIiK9buiu8Eyu71JuYRV1wZQYnJlqW7e+OSci3iSvk0ZMUs3lwcUbxZfyebukie4Zbjqx8NOiRKMmuV1lUDKMCFplbD1ltkhjNeMPWw7aeM5x3jIcZFR6RGxMW9bexDE43hQFX2B2AlXgTckpjBoyKjY8O5DOFSyAKAMgWaWuEoPo1S8sj2CZ6n71T/ABk99DWoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7YsdhiTwYm9HJ/kWbAPePFPSkGNiwFdiKOOknlfVEnVuMSfzEGgBJILLLN/PU/eqf4ye+hrRrhKD6NUvLI9ilg4ly10W8WZ8iTKQQLvUxlRndWuBnRxKKdDpSnNzagqvJUeu2k1qVUqIltpdD3rhcw8vOJiYMzMtNQ1Qw20wPIR1eIgzNLV8anLF8sr5VWTBdVfL1PWeJ8ynIWSbgoRMl6W5Nvu0xePcOrzbk9yHdjd8sSPkkIKTJ15DxmYBM80XSyvMMxMTvN7wsu27fpCSeDE3o5P8izZVTlCPe3izQmPWnmjoeTJBjYVzWuxVBUV7yXama01tuUlKBOOLLNKM0Fg4IyEFOFmpAytbz5BVEuYrl71Mqi8KerippQFJqPk2cJMVbv7r0hYny75WSm38urUjzReyk3lL7qY5fabl2adkPJscPgX79p56QZ6n71T/GT30NbKtwYpdHKHkWrE7AuO3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBplrEc8U+sOe9IDhFP9snla6Td8qNy8QDLWsBoNBotkGeEozo1N8ssWih6i46STvOTqwTPU/eqf4ye+hrD4R4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMZLDIPfSv0i681pNg/O/exPUnJeXZNkhRk2IaXN6/l05Nd4MJkixCikvMqa+BUSJXurk1AyqbpVlttp+jZK8sy+jrZvXlxi7eaGX7F2E1NvMo66xpmZLq2PMnITWlHJp6rnd3kkPJhl+Bh17KVyu76H8nsRbtDmG69qbUm+eUVSVVSUnjbC4iIt97SPc7eJJrU0PGGJqldEu+ak1uaAM8fstnxTiktFgXya861FNzld5AN9ZNDo5Wn+VEZWBoCM3Q6o9B4hnAjajHgHqqGTXMl/eTiZ1uqMRAZQuTTMEHfvcUtprICmZik0ulhVldNeEHbTKipZEO6FA3MiXLrTLJDBAD0WhHinslW70T66RYrVSec1pP4n18oOOAxNWcyRbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWfzFkVZS8u5XuTjd3fzLYcOuzNOgBNKLCO/WxOaQmJaZNctPWqtkbGW2HnWW2w2HiC8cNtZjRJt1dGb6SOkXvmtWsGM9T96p/jJ76GsPgXin1h93pAcIqHtk8rXSbzkRuXiIaa1AtFoslhksLT/UX/AEko+cntgHxbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWf5lxN0KJJ2X7ejMEhpGwL0r3Mh68NamCbVVbmubl1WmVNvUQU2Vk5tUWF54usSPLD1YPYlIMsxEvSpKZVFx5Kkuy49mV40fUWM30kdIvfNatYnYPymO41EvKupu4dXJswUxS3k49T/uZupy2Zdl1MK/HSNMEn5R2TxOE4XL3hygivnswId6ksyPKF/S/N93UyMuJqlSWVd411omauvPvXvIemqV7y708ty+O55bl+dbiL0L8LvVe7C8CUlqBXrvbx1ZCyf7s5TvFmy7ucJefTHL84S4F9DSZcfL6C9Zcv5ok2YYN401oABvvu7yOi1SQpHVFR/suNU5Ol2MU4h6MYqPU0hLfPGzhQltttoNYbYtAnEk2aWuEoPo1S8sj2CZ6n71T/GT30NagmvFTR0D3rAb0gcNJPMKss8iKyB8G1x9iWDtix2GJPBib0cn+RZsA928U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtRSeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbC+zwlGdGpvlli2VbgxS6OUPItWDzc6p/dVKV4eSRP67PyG5mJ7de8RZyk2GiZkmZmXU+b2ZvlR2kzKqypDAywtLkqNgLMnL8zyxM76UZiYYmuWexuLZaeHQeXdlPZKKle4qZCM134ZNFwU+3k9p6d7959vdvYunuom5zJbqaNK3cSrdujzYsIEy3n33zU+lNhDlFtljseuqll6JueTX2XCUJNmv2yshwCpHNz/NCM08GjoCT5JVYZzVlow6isLF4ztVaqPCznaQkg4amQNRFg8NZeWkOLyirsrkIOPSIvKmlHqot+eUHPUnwG58/omTzN0g32I6TfKtI7LxteZuqmK6hYk27qVbxGXYlSa5rEvyf1x7OIDLv3yz1P3qn+Mnvoa2VbgxS6OUPItWJ2BbhHinslW70T66RYrVSec1pP4n18oOOAxNWcyRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi2Rg99K/SLrzWk2woeouOkk7zk6sEz1P3qn+Mnvoa0sUtLAM0Unc3wXzVj6FqKamJ2jYDc+B3pA4CFYpgGeUE4VqMdfhVZoLXc9T96p/jJ76GtQTXipo6B71gN6QOGknmFWWeRFZA+Da4+xLB2xDLxMTiqQg0fA4Qih9isVwbSMRtQOIDHDAams42ypJido2P3Pgd6R2BhWKYhrkAONKnHX4NGai3y8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWYpPFTR0d3rAb0jsNJPMaMtcqK0D8O1w9kWztgBDRSdzfBfNWPoWoO0xOCpFjR8DjCJ/2KxXFtXxO1I4yMMMTrazTa9nqfvVP8ZPfQ1qDt4p6UjBsWArsROx0k8r6ora9xgR+ck0JIIAaZaBPvVS09zdfeL1tPgfWHOOGxXfFLCv8HH4JFaUJ4yDbYGik7m+C+asfQtr69V4qdrC8XrsJA+sSccNJvPvZVuMooGqvLTEmoDTDWwM9T96p/jJ76GsFGES07ZSqNHwJGkWDjCOziUtJx8GlcBjgBQaqGsjkxO6w53PgTulAaoVjWFN2agAawSSK1ZBJwpm0+YR4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMkc8U+sOe9IDhFP9snla6Td8qNy8QDLWsBoNBotgR0Unc3wXzVj6FqEIlp2ylUaPgSNIsHGEdnEpaTj4NK4DHACg1UNb2ep+9U/xk99DWHwjxT2Srd6J9dIsVqpPOa0n8T6+UHHAYmrOYH1FpadspKGj4EDSLZwhHYxCWrY+DSuJxxBqddRS/opO5vgvmrH0LDot4p7JSe9E+ukW6UUnnNat+J9fIBjicRRrPIZ6n71T/GT30NYEK7lLTnsvqHXE+BNJ9vUr3qxTC9Oc+PNFOU14yeKgs3xaWnbKSho+BA0i2cIR2MQlq2Pg0riccQanXUUTruG1My/H9bhE+nZ5epjpNsY9tGcqkURTXGuqnw1NWmm+LeKeyUnvRPrpFulFJ5zWrfifXyAY4nEUazwI6KTub4L5qx9C1CBTE7rD7c+BG6UfrhWNZU3hqQRrJAJpRkkDCmdW9nqfvVP8ZPfQ1h8C8U+sPu9IDhFQ9snla6TeciNy8RDTWoFotFksB9PExOKpCDR8DhCKH2KxXBtIxG1A4gMcMBqazja/opO5vgvmrH0LD3jxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyzfz1P3qn+MnvoawUk1MTtGwG58DvSBwEKxTAM8oJwrUY6/CqzQW4QvCToA9VHyPGdgwea1kD9UsaI2MzQtM5R3Uq80kUzSR1xs1pUZ7ebQNUt3amvFTR0D3rAb0gcNJPMKss8iKyB8G1x9iWDtjwheC8UT1UbI9pDQIb/AKBHVLM0aQazSx/SO6lZnktaILYIPW6MgNMnObzznMAvQ7xUkxO0bH7nwO9I7AwrFMQ1yAHGlTjr8GjNRa9opO5vgvmrH0LD1J4qaOju9YDekdhpJ5jRlrlRWgfh2uHsi2dsL+ep+9U/xk99DWCi7TE4KkWNHwOMIn/YrFcW1fE7UjjIwwxOtrNNsqSYnaNj9z4HekdgYVimIa5ADjSpx1+DRmot8u3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBplqKTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YAQ0Unc3wXzVj6FqDtMTgqRY0fA4wif8AYrFcW1fE7UjjIwwxOtrNNr2ep+9U/wAZPfQ1qDt4p6UjBsWArsROx0k8r6ora9xgR+ck0JIIAaZaBRvGS051L6f1tPgRWfbq6d6sUxvTkzjzTXlFOMDiqLP2ik7m+C+asfQtr+8dtTEvwHXIRPp2eXV46TbOPbRk2hNUUUxprr8FDRpl/wA9T96p/jJ76GsFGES07ZSqNHwJGkWDjCOziUtJx8GlcBjgBQaqGsjkxO6w53PgTulAaoVjWFN2agAawSSK1ZBJwpm0+YR4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMkc8U+sOe9IDhFP8AbJ5Wuk3fKjcvEAy1rAaDQaLYEdFJ3N8F81Y+hahApid1h9ufAjdKP1wrGsqbw1II1kgE0oySBhTOrez1P3qn+Mnvoaw+BeKfWH3ekBwioe2TytdJvORG5eIhprUC0WiyWA+otLTtlJQ0fAgaRbOEI7GIS1bHwaVxOOINTrqKX9FJ3N8F81Y+hYdFvFPZKT3on10i3Sik85rVvxPr5AMcTiKNZ5DPU/eqf4ye+hrAhXcpac9l9Q64nwJpPt6le9WKYXpznx5opymvGTxUFm94mJxVIQaPgcIRQ+xWK4NpGI2oHEBjhgNTWcbJ13DamZfj+twifTs8vUx0m2Me2jOVSKIprjXVT4amrTTg8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWQIaKTub4L5qx9C1FNTE7RsBufA70gcBCsUwDPKCcK1GOvwqs0Fruep+9U/xk99DWoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7Yhl4mJxVIQaPgcIRQ+xWK4NpGI2oHEBjhgNTWcbX9FJ3N8F81Y+hYe8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWb+ep+9U/xk99DWCkmpido2A3Pgd6QOAhWKYBnlBOFajHX4VWaCydApid2z5v3OgcZDu6+xWK+ue8/XQU4gcBWv4OFm9NeKmjoHvWA3pA4aSeYVZZ5EVkD4Nrj7EsHbFQT3imLz5v70T/WJd37Zt/fNeeMaItRx1q0ccKZ+3AOKkmJ2jY/c+B3pHYGFYpiGuQA40qcdfg0ZqLXtFJ3N8F81Y+hYepPFTR0d3rAb0jsNJPMaMtcqK0D8O1w9kWzthfz1P3qn+MnvoawUXaYnBUixo+BxhE/7FYri2r4nakcZGGGJ1tZptI5MTusOdz4E7pQGqFY1hTdmoAGsEkitWQScKZtMO3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBplrEc8U+sOe9IDhFP9snla6Td8qNy8QDLWsBoNBotgR0Unc3wXzVj6FqEIlp2ylUaPgSNIsHGEdnEpaTj4NK4DHACg1UNb2ep+9U/wAZPfQ1h8I8U9kq3eifXSLFaqTzmtJ/E+vlBxwGJqzmApXjJac6l9P62nwIrPt1dO9WKY3pyZx5pryinGBxVFn7RSdzfBfNWPoW1/eO2piX4DrkIn07PLq8dJtnHtoybQmqKKY011+Cho0y/wCep+9U/wAZPfQ1g8H7gYeAyA+qY3o5LkdAuYLJ2y34qOvsydhEOMxNlm+JLTHYvNkVJZabDuq8yOvHPz2s1iQ3TBznrWd7pRaWnbKSho+BA0i2cIR2MQlq2Pg0riccQanXUU81Oqe5NE1ZQ2TsuL92LtqBygcnaboC/e4dZTH2auwU4yZAJCqqo6Q0GGQyZjRWHzLllkgNTQyhtEN5oaG+cjHKZgsr/J0uhv7QYVJcxU0wYhJzRXCk28ZlyfUNMVEebEjgdpsNu1plsOWm2s7seeJUSyxmvGmGg7B0Unc3wXzVj6FqECmJ3WH258CN0o/XCsaypvDUgjWSATSjJIGFM6t7PU/eqf4ye+hrD4F4p9Yfd6QHCKh7ZPK10m85Ebl4iGmtQLRaLJYD6i0tO2UlDR8CBpFs4QjsYhLVsfBpXE44g1Ouopf0Unc3wXzVj6Fh0W8U9kpPeifXSLdKKTzmtW/E+vkAxxOIo1nkM9T96p/jJ76GsCBdUlp766+7rrifA+sOTsNiu+OWEj4OLwQK0oBxgmzi8TE4qkINHwOEIofYrFcG0jEbUDiAxwwGprONk26p4qdrC7rrUJA+sSTsNJvPvZSeMIpGqnJXAigLLDLi8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWQIaKTub4L5qx9C1FNTE7RsBufA70gcBCsUwDPKCcK1GOvwqs0Fruep+9U/xk99DWoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7Yhl2mJwVIsaPgcYRP+xWK4tq+J2pHGRhhidbWabZUkxO0bH7nwO9I7AwrFMQ1yAHGlTjr8GjNRb5dvFPSkYNiwFdiJ2OknlfVFbXuMCPzkmhJBADTLUUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wAhopO5vgvmrH0LIECmJ3bPm/c6BxkO7r7FYr657z9dBTiBwFa/g4Wfs9T96p/jJ76Gsgp7xTF58396J/rEu79s2/vmvPGNEWo461aOOFM/bgHFSTE7RsfufA70jsDCsUxDXIAcaVOOvwaM1Fr2ik7m+C+asfQsPUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wv56n71T/ABk99DWCjCJadspVGj4EjSLBxhHZxKWk4+DSuAxwAoNVDWRyYndYc7nwJ3SgNUKxrCm7NQANYJJFasgk4UzafMI8U9kq3eifXSLFaqTzmtJ/E+vlBxwGJqzmSOeKfWHPekBwin+2TytdJu+VG5eIBlrWA0Gg0WwI6KTub4L5qx9C0tjPU/eqf4ye+hrSwZ0qnc4QXzpj6dqKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobMNhiTwYm9HJ/kWbBQeKacFSEOkIHGEUPspiuLaRgNsRxg44YjW1nC2VJTTtGx+6EDvSOxMUxTANchJwrQ4a/BqzU2utcJQfRql5ZHtlW4MUujlDyLVgmlU7nCC+dMfTtQdqacVSLOkIHCET/spiuDavgdsBxE4YYHU1mizFYWzwlGdGpvlliwIN6ymnvLr7xetxsEfqDnL7IY+9hXOoatRqeSvHQF/0qnc4QXzpj6dk29j62F5HxEnL9Wla2xbAuwionbKVTpCBA0iwMYt2MQlpOHhUriMMQajXU0kcpp3WHO6ECN0oDVFMaypuxQEHWSCBWjJIONM2t+D30r9IuvNaTbCh6i46STvOTqwZ0qnc4QXzpj6dqEIqJ2ylU6QgQNIsDGLdjEJaTh4VK4jDEGo11NGKwyD30r9IuvNaTYKEWqJ2yko6QgSNItjCLdnEpath4VK4HDACh1UFb+lU7nCC+dMfTtIzfSR0i981q1idg1ddyppzqX1DrkbAskz5er9lMkY3pTkPhBxr+evFSzfFqidspKOkIEjSLYwi3ZxKWrYeFSuBwwAodVBUBdn63VH4+3q/tSnOzdGb6SOkXvmtWsE0qnc4QXzpj6dqECpp3WH26ECd0o/XFMawpvBQknWCQDSrIJGNM6jFYWn+ov+klHzk9sFF4ppwVIQ6QgcYRQ+ymK4tpGA2xHGDjhiNbWcLX9Kp3OEF86Y+nbDXCUH0apeWR7ablHKPyerxLx54ufkC/i5mfr3rsgz2xLrZMvQkOaLy7vGWz1osTlJyMuv5ik1tp7RlnsihYcttbWpJoQ2umqado2A3Qgd6QOIimKYhnlIONKDDX4VGaG3CF4ShA/1pGR4dlweazkD9UtBa2SzQFrKP6lWAyTiyC11tvCtSWW80EMg26kuhvpufvqQVFVuYvZuzvbSZUWY6TZqjrsJ6leeE6XJxSG2NMSkrR8nrcxOkaYEBnPYiJffPGYhwS7YaDLDbBHNV43/ABTMjf8A7AuqWf8A0b1J2wdwKSmnaNj90IHekdiYpimAa5CThWhw1+DVmpte0qnc4QXzpj6dorcGKXRyh5FqxOwLrtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WypKado2P3Qgd6R2JimKYBrkJOFaHDX4NWam11nhKM6NTfLLFsq3Bil0coeRasE0qnc4QXzpj6dqDtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WYrC2eEozo1N8ssWBCvGU057L6f1uNgWiJ8uq+ymQML0pNHwAY0/PTirZ+0qnc4QXzpj6dlG8z1up3x9uq/alJltg2BdhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppI5TTusOd0IEbpQGqKY1lTdigIOskECtGSQcaZtb8HvpX6Rdea0m2FD1Fx0knecnVgzpVO5wgvnTH07UIFTTusPt0IE7pR+uKY1hTeChJOsEgGlWQSMaZ1GKwtP9Rf8ASSj5ye2CjFqidspKOkIEjSLYwi3ZxKWrYeFSuBwwAodVBW/pVO5wgvnTH07SM30kdIvfNatYnYNXXcqac6l9Q65GwLJM+Xq/ZTJGN6U5D4Qca/nrxUs3vFNOCpCHSEDjCKH2UxXFtIwG2I4wccMRrazhYBdn63VH4+3q/tSnOza1wlB9GqXlkewZ0qnc4QXzpj6dqKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobMNhiTwYm9HJ/kWbBQeKacFSEOkIHGEUPspiuLaRgNsRxg44YjW1nC1/SqdzhBfOmPp2w1wlB9GqXlkexSwLyapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobJ8App3bPm/vyBNJEu7+yWfvnvPGPFrPw7biza2fkngxN6OT/Is2T0/66E2/ES7z9Z7z7AxKSmnaNj90IHekdiYpimAa5CThWhw1+DVmpte0qnc4QXzpj6dorcGKXRyh5FqxOwLrtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0Wkcpp3WHO6ECN0oDVFMaypuxQEHWSCBWjJIONM2t5nhKM6NTfLLFooeouOkk7zk6sGdKp3OEF86Y+nahCKidspVOkIEDSLAxi3YxCWk4eFSuIwxBqNdTRisMg99K/SLrzWk2BBvGU057L6f1uNgWiJ8uq+ymQML0pNHwAY0/PTirZ+0qnc4QXzpj6dlG8z1up3x9uq/alJltg2BdhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1Gupp4Y3MxMHkCdU0nLJ0exbuAybcvGLUr67kaRQZQ5Ov3Rk1aZvIkRirQA7Iwz11hobagu+lJllpoBk+7sHvpX6Rdea0m3mv1UzJkX8o/JxCjdtsyCv9uKmiFvvuGXkpnOWoSdZMT1FVKOmPCwCw9mNITXjuHdghlqZHaG00Gi6BZD0o0qnc4QXzpj6dqECpp3WH26ECd0o/XFMawpvBQknWCQDSrIJGNM6nMOQ9lOIWV/k03YX9JWxXKrMqK5S56RXO37Grw0OiROSOGQyWmA7WmG30OWmznIL5IellkNgnqxP9Rf9JKPnJ7YKMWqJ2yko6QgSNItjCLdnEpath4VK4HDACh1UFb+lU7nCC+dMfTtIzfSR0i981q1idg1bdSpp7u6+7rrkbBD6g5N+yGPvYSDqOvWKHkpx1AcHimnBUhDpCBxhFD7KYri2kYDbEcYOOGI1tZwsuXT/AFsLt/iJJv6tJNnFrhKD6NUvLI9gzpVO5wgvnTH07UU1TTtGwG6EDvSBxEUxTEM8pBxpQYa/CozQ2YbDEngxN6OT/Is2Cg7U04qkWdIQOEIn/ZTFcG1fA7YDiJwwwOprNFsqSmnaNj90IHekdiYpimAa5CThWhw1+DVmptdZ4SjOjU3yyxbKtwYpdHKHkWrBNKp3OEF86Y+nZBgFNO7Z839+QJpIl3f2Sz98954x4tZ+HbcWbW20ba8T/roTb8RLvP1nvPsDEpKado2P3Qgd6R2JimKYBrkJOFaHDX4NWam17SqdzhBfOmPp2itwYpdHKHkWrE7AuwionbKVTpCBA0iwMYt2MQlpOHhUriMMQajXU0kcpp3WHO6ECN0oDVFMaypuxQEHWSCBWjJIONM2t+D30r9IuvNaTbCh6i46STvOTqwZ0qnc4QXzpj6dpYnaWDXejL0/vykH9G0z/wC7FqKanXnbAgutzjINNiQP2uJmOBA5b2K0104tednM4Wf9Kp3OEF86Y+naimqado2A3Qgd6QOIimKYhnlIONKDDX4VGaGwJzxOvP0i5+rGQR3qoY9riZsRnJHEL2By4/BSlDnZ0Uk687YEb1ycZBpsSO+1xMwwAPJexWmqvFqzc1nCzg8U04KkIdIQOMIofZTFcW0jAbYjjBxwxGtrOFsqSmnaNj90IHekdiYpimAa5CThWhw1+DVmpsC5oy9P78pB/RtM/wDuxai7Trz9IvvqxkE96p+Pa4mbAZyvxG9g8mHwVrU5ua/6VTucIL50x9O1B2ppxVIs6QgcIRP+ymK4Nq+B2wHEThhgdTWaLBp+8lOvGYu7vBbUJpkmJghI04CLhYa71ag46IgtDKpzWVFq9jMdjMOdngMnbFprMabOa/aMvT+/KQf0bTP/ALsWo3rKae8uvvF63GwR+oOcvshj72Fc6hq1Gp5K8dAX/SqdzhBfOmPp2DX8KnXn7JVB2YyDXZdfrczLxJaQTX+1fViPhpSmJbLWY5PvO6y765OMgikWn/a5mfXpF2AcL1wcABStcQa7XNAcIRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaSOU07rDndCBG6UBqimNZU3YoCDrJBArRkkHGmbUF3Rl6f35SD+jaZ/92LUIVOvP2SqDsxkGuy6/W5mXiS0gmv8AavqxHw0pTEtlrYGlU7nCC+dMfTtQhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GupoCdFJ15+yUsdmMg12XX63My8aWrkU/tX1YH4aVriGCzf0Zen9+Ug/o2mf/dizFFqidspKOkIEjSLYwi3ZxKWrYeFSuBwwAodVBW/pVO5wgvnTH07BpGQYC8Z6hxzMJNMjQ7rs3vEFIi7xZizs/tgzlpQHMvXwBazgNsCAWqMtBpoBuik68/ZKWOzGQa7Lr9bmZeNLVyKf2r6sD8NK1xDBZ+ruVNOdS+odcjYFkmfL1fspkjG9Kch8IONfz14qWb4tUTtlJR0hAkaRbGEW7OJS1bDwqVwOGAFDqoKgu6MvT+/KQf0bTP/ALsWowKfed1l51ucZBNYtQ+1zM+vSLwE43rk4gmtKYkU2ucC/wClU7nCC+dMfTtQgVNO6w+3QgTulH64pjWFN4KEk6wSAaVZBIxpnUDkBdnPL7d3kRMBL2TPkgqV2jhc2EmzUvZdN9CFP8dJ5UEtrske3VJXU95nlpKW2WOuHsfYvRi3TD1l27M1ssNdfZ8uJiv/AMnXLWnq8yU8l2/HJsRpqybLkcsi664G5WQ71bsnl/V7t8c1SsvSdeCsC4aSl9ue5FuRlteS2TLKDMDt1NV7U1gTm/lWVpLlOTppvU/QM8U04KkIdIQOMIofZTFcW0jAbYjjBxwxGtrOFr+lU7nCC+dMfTsHjjkRThI96uULN865McxSiq3ZSzkU5K9zs0TGhuHkxSfLV8knTdei9N2C4mo6+yHN6N2MhqwQZyl1uahM0nsrMuws2htppw6ebnvBT7wj1TjJAdtzNJhUzkG9Ud2JGsyEshLYThlAdS22U7bS+2m0/ePWnzSOXT1iIdsu2Xb1lt08L9huG9GIBYT3kBBvXihA9eMLAF+RFMUBIB4zrLRa18prQUJ4RvCUIH+tIyPDsuDzWcgfqloLWyWaAtZR/UqwGScWQWutt4VqSy3mghkGwdfKSdedsCN65OMg02JHfa4mYYAHkvYrTVXi1Zuazha9oy9P78pB/RtM/wDuxZjUlNO0bH7oQO9I7ExTFMA1yEnCtDhr8GrNTa9pVO5wgvnTH07AgO068/SL76sZBPeqfj2uJmwGcr8RvYPJh8Fa1ObmxSTrztgRvXJxkGmxI77XEzDAA8l7Faaq8WrNzWcLODtTTiqRZ0hA4Qif9lMVwbV8DtgOInDDA6ms0WypKado2P3Qgd6R2JimKYBrkJOFaHDX4NWamwLmjL0/vykH9G0z/wC7FqLtOvP0i++rGQT3qn49riZsBnK/Eb2DyYfBWtTm5r/pVO5wgvnTH07UHamnFUizpCBwhE/7KYrg2r4HbAcROGGB1NZosGoJ+gLxnSHAsxc0yNEOuze7sUh7vFmEOz+2DJuiwM+9fEBrNB2xJAZqyyGWQX3Rl6f35SD+jaZ/92LUrxlNOey+n9bjYFoifLqvspkDC9KTR8AGNPz04q2ftKp3OEF86Y+nYNfwqdefslUHZjINdl1+tzMvElpBNf7V9WI+GlKYlstZjk+87rLvrk4yCKRaf9rmZ9ekXYBwvXBwAFK1xBrtc0BwhFRO2UqnSECBpFgYxbsYhLScPCpXEYYg1GuppI5TTusOd0IEbpQGqKY1lTdigIOskECtGSQcaZtQXdGXp/flIP6Npn/3YtRgU+87rLzrc4yCaxah9rmZ9ekXgJxvXJxBNaUxIptc4F/0qnc4QXzpj6dqECpp3WH26ECd0o/XFMawpvBQknWCQDSrIJGNM6gJ0UnXn7JSx2YyDXZdfrczLxpauRT+1fVgfhpWuIYLN/Rl6f35SD+jaZ/92LMUWqJ2yko6QgSNItjCLdnEpath4VK4HDACh1UFb+lU7nCC+dMfTsGkZBgLxnqHHMwk0yNDuuze8QUiLvFmLOz+2DOWlAcy9fAFrOA2wIBaoy0GmgG94nXn6Rc/VjII71UMe1xM2IzkjiF7A5cfgpShzs7N3KmnOpfUOuRsCyTPl6v2UyRjelOQ+EHGv568VLN7xTTgqQh0hA4wih9lMVxbSMBtiOMHHDEa2s4WBd0Zen9+Ug/o2mf/AHYtRTU687YEF1ucZBpsSB+1xMxwIHLexWmunFrzs5nCz/pVO5wgvnTH07UU1TTtGwG6EDvSBxEUxTEM8pBxpQYa/CozQ2BOeJ15+kXP1YyCO9VDHtcTNiM5I4hewOXH4KUoc7OvaMvT+/KQf0bTP/uxZieKacFSEOkIHGEUPspiuLaRgNsRxg44YjW1nC1/SqdzhBfOmPp2BATU687YEF1ucZBpsSB+1xMxwIHLexWmunFrzs5nCyfBJ94gvDmthmaZH2f2C3diIiTd6tbAMDpq8suho/tsh4M5vSVDU01VbZYrbcKapp2jYDdCB3pA4iKYpiGeUg40oMNfhUZobJ8App3bPm/vyBNJEu7+yWfvnvPGPFrPw7biza2DCknXnbAjeuTjINNiR32uJmGAB5L2K01V4tWbms4WvaMvT+/KQf0bTP8A7sWY1JTTtGx+6EDvSOxMUxTANchJwrQ4a/BqzU2vaVTucIL50x9OwIDtOvP0i++rGQT3qn49riZsBnK/Eb2DyYfBWtTm5sjk+87rLvrk4yCKRaf9rmZ9ekXYBwvXBwAFK1xBrtc0BwdqacVSLOkIHCET/spiuDavgdsBxE4YYHU1mi0jlNO6w53QgRulAaopjWVN2KAg6yQQK0ZJBxpm1Bd0Zen9+Ug/o2mf/di1CFTrz9kqg7MZBrsuv1uZl4ktIJr/AGr6sR8NKUxLZa2BpVO5wgvnTH07UIRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaBqCfoC8Z0hwLMXNMjRDrs3u7FIe7xZhDs/tgybosDPvXxAazQdsSQGasshlkF90Zen9+Ug/o2mf/di1K8ZTTnsvp/W42BaIny6r7KZAwvSk0fABjT89OKtn7SqdzhBfOmPp2DX8KnXn7JVB2YyDXZdfrczLxJaQTX+1fViPhpSmJbLUik68/ZKWOzGQa7Lr9bmZeNLVyKf2r6sD8NK1xDBZcYRUTtlKp0hAgaRYGMW7GIS0nDwqVxGGINRrqaSLVE7ZSUdIQJGkWxhFuziUtWw8KlcDhgBQ6qCoeCl00BeH1P/AKpVN9wzyZJQS8n3L7iFK9i6aKfSQsmXJcyhUnNM4yKjI4nZ27S2pldUbzeyBpnP7AnDODTdfbuBT7zusvOtzjIJrFqH2uZn16ReAnG9cnEE1pTEim1zgeHeqe5OETlPZMysbv493A37XJq0DfZcMuJr6A09Az/JTTtUZS0posvCW5mS23qA5AaduzMLxCetEhyCdrZCOVVLuVzkwXaX2wsSnwMwTBCxiZPSIIlktS7eMgqjaLOCOQQ13JldaZewzLIZLMuq6G0WmQ2xnh0XFJ15+yUsdmMg12XX63My8aWrkU/tX1YH4aVriGCzf0Zen9+Ug/o2mf8A3YsxRaonbKSjpCBI0i2MIt2cSlq2HhUrgcMAKHVQVv6VTucIL50x9OwaQu2Trxm7u7vm0+aZJhoIyNJ4hIWJu9WoyOh4LQyUc1pRZvYzHgzBnZ5DR2oaZz2mBnODxOvP0i5+rGQR3qoY9riZsRnJHEL2By4/BSlDnZ0upU093dfd11yNgh9Qcm/ZDH3sJB1HXrFDyU46gODxTTgqQh0hA4wih9lMVxbSMBtiOMHHDEa2s4WBd0Zen9+Ug/o2mf8A3YtRTU687YEF1ucZBpsSB+1xMxwIHLexWmunFrzs5nCz/pVO5wgvnTH07UU1TTtGwG6EDvSBxEUxTEM8pBxpQYa/CozQ2BOdp15+kX31YyCe9U/HtcTNgM5X4jeweTD4K1qc3NiknXnbAjeuTjINNiR32uJmGAB5L2K01V4tWbms4WcHamnFUizpCBwhE/7KYrg2r4HbAcROGGB1NZotlSU07RsfuhA70jsTFMUwDXIScK0OGvwas1NgXNGXp/flIP6Npn/3YsgwSfeILw5rYZmmR9n9gt3YiIk3erWwDA6avLLoaP7bIeDOb0lQ1NNVW2WK23fpVO5wgvnTH07IMApp3bPm/vyBNJEu7+yWfvnvPGPFrPw7biza2DCknXnbAjeuTjINNiR32uJmGAB5L2K01V4tWbms4WvaMvT+/KQf0bTP/uxZjUlNO0bH7oQO9I7ExTFMA1yEnCtDhr8GrNTa9pVO5wgvnTH07Br+FTrz9kqg7MZBrsuv1uZl4ktIJr/avqxHw0pTEtlrMcn3ndZd9cnGQRSLT/tczPr0i7AOF64OAApWuINdrmgOEIqJ2ylU6QgQNIsDGLdjEJaTh4VK4jDEGo11NJHKad1hzuhAjdKA1RTGsqbsUBB1kggVoySDjTNqC7oy9P78pB/RtM/+7FpZx0qnc4QXzpj6dpYCdhiTwYm9HJ/kWbY2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsQINcJQfRql5ZHtlW4MUujlDyLVhzyEidKQY0nHBrYijqYTKeGlcqP+8U4ya5rMUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2AMlhbPCUZ0am+WWLTYkZzpHfJTfQ9h7uEidKRg0nHFrYidrYTKeGq8iP+814iKZrQL17H1sLyPiJOX6tK1ti21XepDvu1feLWPjn31CTiPa7jlhXHubIrjXE6wNTNWmdgbEjOdI75Kb6HsGYPfSv0i681pNsKHqLjpJO85OrD4SFidkqtFSOrpFipzEzmtKpTcg4auPXjnHAMSPhYnrDndOO4ST/YpmvSTsczmorxChoBthi02DJYZB76V+kXXmtJtjYkZzpHfJTfQ9h8JCxOyVWipHV0ixU5iZzWlUpuQcNXHrxzjgGAIxm+kjpF75rVrE7LcXCxOyUqqpHV0i3Q5iZzWq1ruQMNfHrxzhiGyGxIznSO+Sm+h7ApXZ+t1R+Pt6v7Upzs3Rm+kjpF75rVrIF3MO/7H4+kfH+vy9Tm3E9tKcjj3LGlafkA1GrIbouFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDENgyWFp/qL/pJR85PbTYkZzpHfJTfQ9h8BCxPWH26cdwkoexTNekng5nFBXiNTQnbHBpgCDXCUH0apeWR7FLLbyEidKQY0nHBrYijqYTKeGlcqP8AvFOMmuayQ2JGc6R3yU30PYMpPBib0cn+RZtwjeN/xTMjf/sC6pZ/9G9Sdt26mwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdseErw3D7+tIyPKRsZX+gP1S2hGwKgf0jupV1FCwBTEa3ZIDDG2dkNsWDv5W4MUujlDyLVidltShInRsdunHb1jq0CWMKNY1KQRr/Bw4887YENiRnOkd8lN9D2CM8JRnRqb5ZYtlW4MUujlDyLVhzuEidKRg0nHFrYidrYTKeGq8iP8AvNeIima1FKEidGx26cdvWOrQJYwo1jUpBGv8HDjzztgDJYWzwlGdGpvlli02JGc6R3yU30PYe7hInSkYNJxxa2Ina2EynhqvIj/vNeIima0AK8z1up3x9uq/alJltg21beNDv+x+ArHx/r8ur5twPbSk04dywrSn5CdZoyX7YkZzpHfJTfQ9gzB76V+kXXmtJthQ9RcdJJ3nJ1YfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWmwZLC0/1F/wBJKPnJ7abEjOdI75Kb6HsPgIWJ6w+3TjuElD2KZr0k8HM4oK8RqaE7Y4NMARjN9JHSL3zWrWJ2W4uFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDENkNiRnOkd8lN9D2BSuz9bqj8fb1f2pTnZta4Sg+jVLyyPZBu5h3/AGPx9I+P9fl6nNuJ7aU5HHuWNK0/IBqNWQ3PISJ0pBjSccGtiKOphMp4aVyo/wC8U4ya5rIMlhiTwYm9HJ/kWbY2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsQINcJQfRql5ZHsUstvISJ0pBjSccGtiKOphMp4aVyo/7xTjJrmskNiRnOkd8lN9D2DKTwYm9HJ/kWbJ6f9dCbfiJd5+s959j6bCROjYHdOO3rA0qEs4UZxqEgDX+DjxZh2xUYCGf9s+byI+Pr2CXdim5mH1TXnnDuYP4OLIoDSucet2B/VuDFLo5Q8i1YnZbUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2BDYkZzpHfJTfQ9gjPCUZ0am+WWLcEzx1SbI8kyOWoRYvJnFQleUZmeS9PN9En3B5Q8+ZM13qoiTOEObk68nKsku6qacmeRGZCXk56hXpv5yvPlxzde8dxbudX0qvYV67Y3LlTO7wITJzykn12KioPLx4W4O8V/IexoZLi4xqczKc4aCDLGhWmTVZ60ywKYNBshhjOaFuZpGfzk5yCsmhxkf3aXF3xSQp3K3YJDuVb0b6ZsuLkVq7s3fo4YCIsSTk3ZTKytqj965cS+9l2YJelt47dPlp7ETM7iHLtw+D0lTlCBWICDUUqLhVNNjoaEioCPgYtiNgIuDegFiNgVB0Wnb4NO2w2y2y2euBkNMk55aP9oPfSv0i681pNvAG4aOf5WE99TgSUuYL6MnK4RdyDb070IrJpuTyjLw5ZQoOYbt7z8nmS7ukhUvUkhu7G8Ga0S7d0sLTt26dNy0xNTLTMtTxKb2UH0RKjfK+UPevlCaKvIyt7oo3Kifwki5Uaajp2VPeflizVk8ZOavLSLlLyXc2j3U3EZBF2E8343f5Q7DKHpq7yaZkyjrsLhTepntXuybN0z9flgSqH6eLzPW6nfH26r9qUmWFId6sir94k6XSJi8Yu8K72WZHmycpdCWrOylIN4rU3sSgo6SeJDKEqmYn0mTbmhEfv3rLxGiXUQ7YzWQ34a3n3aTLfBPHVNJxmXLAynZJjMnfKEutg7i0yQL959lKT7hY9q5PJ/nQz8s3dIcwsXfXoIDcwqzMwt3fX1yvNl1mcjL1JNHZTNj+ZAt012S9lqXz3wXn3vXpZRN1q3MPU38gC8pVlvJ/vpvMyYYxFvVnOVcpxWE1q01XOLN28/LT6V2lhY2PIExTLM92UNEdbiZplaYolxJ790H6J4PfSv0i681pNpGb6SOkXvmtWtwPkLXvXj3pdT7uGv1nhcipivFmbJzkye5mU2XKUx2TTG1ICSsPFVkMorBLUw7VtotMtU64yWAW6lnzOlmJvMlbJXyHeqGwWUXlBXg5ReUJelksPb0JVmW++fI+4Se5fyqZrl2T5tuqlDJlXFj+j/dm6uzRJpZeSUv3b3ayvek5fSQ9amua5pezTOTc0h7cSZlE3V3lXn3iXRSQqTXMU33RxASp6UIG7W9Bm7JJmXcSIiJQd35PZHZucXZ9l8KiYJtkCW7xF+b5UdvmhNctw7Tp4XHgtLWVTcJ1L7qoN+dxM5XiOJfycMq9+m3qxiimyzNMwSZk/ZRC6ohlale8yaZKQZhlm7NiZEP6pWzNEwSv2JSisyFNs3OWJReMzVbuDqXNzErXcTn1QRTl6Z72o+IjMuu+CXH0PP1+V9F6yexBJMBJ6uyUhLvNnubJeR19ttbVGJqmJAZdzbNDsIDM4P3zEqyq6h+XOrI3VynlF3XTNkXZLN28DO2XLOS2zlLsREnoksoMJdCnIoak9Wvov5mp6g53XLy5flFq5y6aXmz2Y3szWhy+JRZ7D7r5rmuUg/Qm8fOYppFiYd86fOH0VsiHfuCzmxWckqrVQRUEZpDevjINDhY7b8fMTluTc4lDIxl+4bKJnW79Fyx7t7vMnHKfZWVO8Camup9qF0DaJc8sX9ygWUKZ5buVbvKbWnlzzLU0GU5SZvVXbo73Qc6XJs65+qLsYmaSbuWUO7mKjZwmGU5UZS5QhL0LyFzNmZQQ0t5DITm8O9ZXku8+d2BMAYdGap9alybZnZettxZhpiiWaPAP3T/AFsLt/iJJv6tJNnFrhKD6NUvLI9vD3qeF6GX7NV8+UNLd5N29xrF16DePcykrT5My0L1J6U7pJe/op3NriYjXO3frmQxKcuzmizGFdKmCZi1Nl1bPZWtTA9rMhdszRNfX2XQvTzdazk95RUuT/NyDJVyV8aZFX6y9BLLyAl6ZriryGGrsZzU5qSWmXKEsM3Zrk2SheO5ezAyy7llxJ65FOT3VogPRiwxJ4MTejk/yLNvPjIAmOer25RvlyjJnnOd1eWb87/7wlW5uW15YaUEGULiLvVZq7C7pqU0vrjSEju7yHMmvryX+g2WmX7yc3TYeF66abY5dvavPaRrx5zTRl1dWhkQp6u1CiUbjepSm9m6KXc1hiiXd3eH/U0X4dm0vsEFt3MAvRvJL05zHZXEZ1Gw9qGeEozo1N8ssW0/AXyXZTRPV7FzsrzwlLl490iNKilebKCS6KmoyZB3kwy48lEq7DhzDpOlZjdoykshBD99MIhmGHr+Edwa/LzyIKSXDFUlFIZeTLPq05UJFQmitzYgtSLeAqBXglglUXEcSRdu3KU0NB400/QmJalrsYimWw1KcrNlkNeOmTnk93d5L2U51UGQsm6TDI8On5NOTlNkFBuIltdX5wvEWpayg1ZRm2dZsmErl4V50+TGuNMPZtvAmyZpsmuZ4hlhma5rfxTMMWg9B5Yy/wDJTna9t3cui3iLUdM0RO00Xco8zRV1t76XcpN95kmtRDE1XW3d5RSrIbrJ9vLvTlVtMW0KYruLur1JlnJxMEvzugREssxsqzW4l4PE5a+TdLOVNM9zCtPa52av4W6q7N8qQt296CndQkXnKyveKqJF2E235JcjG4STL1JjdLCQ0gSBM15iFOsyNL6G4h5YevXsGYnytuLhL67jciTqZF+k235Or5pPmZcyMrv5kyY1K524g3OpMbe8qoUnJN6N0Cv2AzLf2iX73azAtpN4jUxTNfvNksTXM6HPpcSpKhmmX3coD4t0+/qzcvrRcXW8Xtn31bKMMEszEL5/6fmUAZPAoCOzgrvYh2J1oA0JdAqaWD9JatwYpdHKHkWrE7J7cLGdj52Qpx3XNCNGKGalg10eeubbQpGuuNAAT4JG1JzYkZzpHfJTfQ9gzB76V+kXXmtJthQ9RcdJJ3nJ1YfCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWmwZLSwvYkZzpHfJTfQ9pYM6Qd+5R/itS/hWoJse50bA9zjt6QPtYpg+Czyu2jhx44aznAhllisMSeDE3o5P8izYKDyOc6Ug+5R29FDHRqn92kHHuYpyVIIqCMCGmmopR7nRsd3OO3pHe1imT4LXI7ZOPFjjrGaAWWrzXCUH0apeWR7ZVuDFLo5Q8i1YJpB37lH+K1L+Fag7jnOlIzuUdvRPx0ap/dq5w7ma8lQAKkDEllplisLZ4SjOjU3yyxYEC9aOdN3YXi1dR4+oScsCmKQOMsK4rTrY/IMakkAUaLLTOwNIO/co/xWpfwrJt7H1sLyPiJOX6tK1ti2BchI51slW7lHndFkcGqXNaV/ljDHA6jQ0AoS1mOj3PWHPc47hKA9rFLnNiv91+TE1FCDmkEMsX4PfSv0i681pNsKHqLjpJO85OrBnSDv3KP8VqX8Kw+EjnWyVbuUed0WRwapc1pX+WMMcDqNDQChLTHYZB76V+kXXmtJsA+LjnWyUnuUeN0Whwapc1qv+WcMMTqFRUGoLJDSDv3KP8VqX8K0jN9JHSL3zWrWJ2DVt3Mc6dy9HgOo+nZ7epqTFM/bSnLDwPyka6gg4AgBvi451slJ7lHjdFocGqXNar/lnDDE6hUVBqCyBuz9bqj8fb1f2pTnZujN9JHSL3zWrWCaQd+5R/itS/hWoQMe56w+7nHcJR/tYpc5t0/uvy4igoCc0AFltisLT/UX/SSj5ye2Ci8jnOlIPuUdvRQx0ap/dpBx7mKclSCKgjAhppq/pB37lH+K1L+FbDXCUH0apeWR7FLAupse50bA9zjt6QPtYpg+Czyu2jhx44aznAhlnhG8KNdf1pGR411uNoMgfqljJonKNanKO6lXSjIYqRtDVoMEeBVpjrjtm3fqTwYm9HJ/kWbcI3jf8UzI3/7AuqWf/RvUnbB2+pR7nRsd3OO3pHe1imT4LXI7ZOPFjjrGaAWWr+kHfuUf4rUv4VorcGKXRyh5FqxOwLruOc6UjO5R29E/HRqn92rnDuZryVAAqQMSWWmYpR7nRsd3OO3pHe1imT4LXI7ZOPFjjrGaAWWrzPCUZ0am+WWLZVuDFLo5Q8i1YJpB37lH+K1L+Fag7jnOlIzuUdvRPx0ap/dq5w7ma8lQAKkDEllplisLZ4SjOjU3yyxYEG8aOdPJegAXUfTs9ur1pimPtpSbh4H5CdVACcQCC/6Qd+5R/itS/hWUbzPW6nfH26r9qUmW2DYFyEjnWyVbuUed0WRwapc1pX+WMMcDqNDQChLWY6Pc9Yc9zjuEoD2sUuc2K/3X5MTUUIOaQQyxfg99K/SLrzWk2woeouOkk7zk6sGdIO/co/xWpfwrUIGPc9YfdzjuEo/2sUuc26f3X5cRQUBOaACy2xWFp/qL/pJR85PbBQi451slJ7lHjdFocGqXNar/AJZwwxOoVFQagskNIO/co/xWpfwrSM30kdIvfNatYnYNW3cxzp3L0eA6j6dnt6mpMUz9tKcsPA/KRrqCDgCAHB5HOdKQfco7eihjo1T+7SDj3MU5KkEVBGBDTTQC7P1uqPx9vV/alOdm1rhKD6NUvLI9gzpB37lH+K1L+Fagmx7nRsD3OO3pA+1imD4LPK7aOHHjhrOcCGWWKwxJ4MTejk/yLNgoPI5zpSD7lHb0UMdGqf3aQce5inJUgioIwIaaav6Qd+5R/itS/hWw1wlB9GqXlkexSwLqbHudGwPc47ekD7WKYPgs8rto4ceOGs5wIZZT4CPc9s+b6uo/1h3d+1inj9U15+raUw14AYY+DtC/pPBib0cn+RZsnp/10Jt+Il3n6z3n2BhUo9zo2O7nHb0jvaxTJ8FrkdsnHixx1jNALLV/SDv3KP8AFal/CtFbgxS6OUPItWJ2BddxznSkZ3KO3on46NU/u1c4dzNeSoAFSBiSy0zwJeF1NjIznaLmqNVruLx0iXJ4mdqYrw7n7vb9cp+7PJ2vIXViYmVqb1K8nJjuzvWlbJ6vRavGiC8bvXE13YTQ6vVz3nZqzNDD1sN+hLPCUZ0am+WWLRQ9RcdJJ3nJ1YNMp9zlz8uzpJM+S7JEHLC/dddipXOyAJdT1VFRJXuwXlOS1ZTlBIlFHah5ddIOyJSk9l27Yl09jJRWHbDyGdM9aPHkydS8yFZ5j7wuyy52cFSV55nuOn9Suuc31ZT8Fcqk3irK6kzgs3oyZk8JV6ri5u7K9J7OL3sle3kXcXcSzOLUxK0wzU7mgP5mmhtr09sMg99K/SLrzWk2DxoV+pt3brN8uVTfLfklNTdCX/ZSFxcwy8iSrepf5KUvTndehypctdk3IOUfICAtSrd7fYhO5jRpwXpXu8vKhLz5SAXc4MO2pkmly16gpV1l2KRPU93jJ8qxEDN95MmyTd7OKpDmZMxVlG7oTiZRRmExltlCSWJdbnObmHOgIZ0+Olnrbx40XrmrReZ63U74+3VftSky2wbBo+6C7iQLjLuZaufutlpQle7m7hKTJSk1AZeTSuNIcvpKQmMpyayqLb2YpgU2XLtugerr9uJLJLLWd1sNvOeJSyE8ky7u9dGvblC7qZU9dgZwWpwliUYq8a/RbuRkGcprT1lmYp7u3yZFue4rJ9uunpfYK2y3P92t1srzOXswTCBFgzVMza93JB76V+kXXmtJtIzfSR0i981q1g1Vdzdnd3ddEz+/kaXFJBeXlXjTFerO+e9mdRKzeBNoQwsLQKy9iGktmKYSE120jITTiXHYdnNh3bbx603yMqdTkyVly8W8y913/Sqkye75Jxamm8qNuiy4+qBXLy/OMxJMO7QUtVV5TubyjpUkJkuUBITUNjYstuGWHLo5rtlp40w16Q2Fp/qL/pJR85PbB+bBCya7iMjLqjN7WT7ON3DMx5JfVZ7vHcumFn97NE2CLvDk6V1VJXLqVlZnNl8v6EmR1NyzMOb2TnOmudJfZDTE4N9dH6GZNl5Cu+lSXZHlqHmUy/KCFAICC1MqxPc2rYgEqDYS01wrTfOL2Y5pXXzLl07bbW5jmFfmB8W2m4p8/baapxT1TfJYU8qfJoVEOR3jUFfXdctQd79xS3DMsNx6XeRJkAqqqMnJr0Ow07amLNeS+GGSGGnkQlNvGSXbLQ2dkF5UkDlgZMV218zphmDmqNS2ZWvOQatFqW70ZSbKPOaSXbLQAZKu703C4M50tq6I8azi2bBv+6mOdMXYXdUdR5+oSTcAmKROEsJArTrZ/Icaggg1aDTTXPmWTd7edfhcdNtyV2aTIMS8vpkubbqp/mC86LmeATpDkGcUZ4hL8/o0nJN1k3s3mzvLhaMTKl3UxRV2cuTY964y3PcvMZrLXSN0/wBbC7f4iSb+rSTZxa4Sg+jVLyyPYNd3TyJJ1zF193l0UkJ8ZASddhJstyLLcFo9RrBoEopTCMlMtjrbRqHSWwcTiG2BQMtMmzsmx7nRsD3OO3pA+1imD4LPK7aOHHjhrOcCGWWKwxJ4MTejk/yLNgoO45zpSM7lHb0T8dGqf3aucO5mvJUACpAxJZaZ1Un3aXZyzP8AehfAkS7Gp94l5srSTLs9TCW5rUG1mX7uXa8ZSTSmtPW0NNEvmblwsdj7p08aaVIh89aeN5htuNnhKM6NTfLLFsq3Bil0coeRasHF0vZDeSnK17SNfMmXZTG+m+XF+YJmkeX1i8K/aZLkrs55mll4wt3gXPZPK/O6/k/3LTwvtLC+Iu8K7O7GVZsb7LJ6aamMtzVNomBTiMjDJpXcqmbb8I6QF7s3curqLy4yBSZ6viRLsJkvUSVa8dKQ70pwuISplYuani9OWHSYiiXrx5quzX5zllhARW4OZ3DSBCtOfRC2vE/66E2/ES7z9Z7z7AwqUe50bHdzjt6R3tYpk+C1yO2TjxY46xmgFlq/pB37lH+K1L+FaK3Bil0coeRasTsC5CRzrZKt3KPO6LI4NUua0r/LGGOB1GhoBQlrMdHuesOe5x3CUB7WKXObFf7r8mJqKEHNIIZYvwe+lfpF15rSbYUPUXHSSd5ydWDOkHfuUf4rUv4VpYnaWAXsSM50jvkpvoew9NhInRsDunHb1gaVCWcKM41CQBr/AAceLMO2K/2YTN/hZP3jK67+f7UU6cJh0fA0utn573pAa1K66oBZoDheAziKA1oK6wWSKkG55CROlIMaTjg1sRR1MJlPDSuVH/eKcZNc1mKUJE6Njt047esdWgSxhRrGpSCNf4OHHnnbBQeThMIUHP8AZbPxa2IoV3SutxGckE/bApjUAY8RJqCyGcqM4TDo+OrdbPzrvSP1KV11SAzQnG8BrE1JrQ01ktE1AP2xIznSO+Sm+h7D3cJE6UjBpOOLWxE7WwmU8NV5Ef8Aea8RFM1pf7MJm/wsn7xldd/P9qDucJhKg+/stn4NbET6bpXW4DOVyPtgUwoQceMEUAaDQYvUh33avvFrHxz76hJxHtdxywrj3NkVxridYGpmrTOwNiRnOkd8lN9D20heTNa7FXcz84e3cTwnuIiSJyh3yhEql32xIR2EVWDUe80XPjxsgkdcbLAdvACzizti0/8AZhM3+Fk/eMrrv5/sDBCQsTslVoqR1dIsVOYmc1pVKbkHDVx68c44BiR8LE9Yc7px3CSf7FM16Sdjmc1FeIUNANsMWm1CGnCYBEqn9ls+5wix7ZXXa9FpGr+0GnsgMajWaGrIZzGzjMHWHZ7Vs+kbLTtSjddrKkwBrvAPGBWlKggChziQftiRnOkd8lN9D2HwkLE7JVaKkdXSLFTmJnNaVSm5Bw1cevHOOAYX+zCZv8LJ+8ZXXfz/AGoQ04TAIlU/stn3OEWPbK67XotI1f2g09kBjUazQ1ZDIN8XCxOyUqqpHV0i3Q5iZzWq1ruQMNfHrxzhiGyGxIznSO+Sm+h7IETOEwGJS/7LZ9zjFn2yuu16LV9f9oNPYkYUGo0FGg1f7MJm/wALJ+8ZXXfz/YKN3MO/7H4+kfH+vy9Tm3E9tKcjj3LGlafkA1GrIbouFidkpVVSOrpFuhzEzmtVrXcgYa+PXjnDEN6jkKa192hxpdXbzvFs9m15MV1xwp3ekZ3bBnAiA20+Zx63QCmLG3FaGlW2JnCYDEpf9ls+5xiz7ZXXa9Fq+v8AtBp7EjCg1Ggo0Ggf9iRnOkd8lN9D2HwELE9Yfbpx3CSh7FM16SeDmcUFeI1NCdscGmF/swmb/CyfvGV138/2owU4zB1h4e1bPoGy1HWo3XawpNg6rwBxk0rWgBBqc0gG55CROlIMaTjg1sRR1MJlPDSuVH/eKcZNc1khsSM50jvkpvoe3GcxZcFziBeU/u9UpLyxIiYU5b7F4hRQup65fM3yBs/Sacw02n3rydk3TJdCtoTTZaInhAmuLlQOWWIhmZ2Yd3sgeQs49VCl6d8s68aNuZysbp5jRJHyRcutLuwycpDvtkGY5gWL1bh3t2j5Fn28e71tfJZnmY15LvN7CpamQhhxdRJnZc5ZZYmWaWAH6Nk2EidGwO6cdvWBpUJZwozjUJAGv8HHizDtjwleG4ff1pGR5SNjK/0B+qW0I2BUD+kd1KuooWAKYjW7JAYY2zshti2oMlCMmu6m/uabp0+fr4L7ZQX8kG4/KIinN4t6izevOMFepOc2zpKU4q6HMd6E7RDqVZSvGSkJFmSFu6l5flq62UWkeIEjSlKjMQ+cxDteFNC3/Wc5IMV2upzafwuQd1R6EZTWlGQSoxbs5QHUtTpNnNnjY4dwwdO3LfXHzD/OWXRdMNsiI62HospQkTo2O3Tjt6x1aBLGFGsalII1/g4ceedsCGxIznSO+Sm+h7IKjOEw6Pjq3Wz8670j9SlddUgM0JxvAaxNSa0NNZLRNRe7MJm/wsn7xldd/P8AYGB3CROlIwaTji1sRO1sJlPDVeRH/ea8RFM1qKUJE6Njt047esdWgSxhRrGpSCNf4OHHnnbBQdzhMJUH39ls/BrYifTdK63AZyuR9sCmFCDjxgigDQayozhMOj46t1s/Ou9I/UpXXVIDNCcbwGsTUmtDTWS0TUA/bEjOdI75Kb6HsPdwkTpSMGk44tbETtbCZTw1XkR/3mvERTNaX+zCZv8ACyfvGV138/2oO5wmEqD7+y2fg1sRPpuldbgM5XI+2BTChBx4wRQBoNBm8aHf9j8BWPj/AF+XV824HtpSacO5YVpT8hOs0ZL9sSM50jvkpvoe2k59mtfeIcEXt287wjPZtdtFdcfqd3oGd2wZPJgNrPmcOuVIpgxtDSprR87MJm/wsn7xldd/P9gYISFidkqtFSOrpFipzEzmtKpTcg4auPXjnHAMSPhYnrDndOO4ST/YpmvSTsczmorxChoBthi02oQ04TAIlU/stn3OEWPbK67XotI1f2g09kBjUazQ1ZDOY2cZg6w7Patn0jZadqUbrtZUmANd4B4wK0pUEAUOcSD9sSM50jvkpvoew+AhYnrD7dOO4SUPYpmvSTwczigrxGpoTtjg0wv9mEzf4WT94yuu/n+1GCnGYOsPD2rZ9A2Wo61G67WFJsHVeAOMmla0AINTmkA3RcLE7JSqqkdXSLdDmJnNarWu5Aw18evHOGIbIbEjOdI75Kb6HsgRM4TAYlL/ALLZ9zjFn2yuu16LV9f9oNPYkYUGo0FGg1f7MJm/wsn7xldd/P8AYKN3MO/7H4+kfH+vy9Tm3E9tKcjj3LGlafkA1GrIbnkJE6UgxpOODWxFHUwmU8NK5Uf94pxk1zWdRyFNa+7Q40urt53i2eza8mK644U7vSM7tgzgRAbafM49boBTFjbitDSra8nCYQoOf7LZ+LWxFCu6V1uIzkgn7YFMagDHiJNQWQyD/sSM50jvkpvoew9NhInRsDunHb1gaVCWcKM41CQBr/Bx4sw7Yr/ZhM3+Fk/eMrrv5/tRTpwmHR8DS62fnvekBrUrrqgFmgOF4DOIoDWgrrBZIqQbnkJE6UgxpOODWxFHUwmU8NK5Uf8AeKcZNc1khsSM50jvkpvoeyA8nCYQoOf7LZ+LWxFCu6V1uIzkgn7YFMagDHiJNQWQzf7MJm/wsn7xldd/P9gYE2EidGwO6cdvWBpUJZwozjUJAGv8HHizDtiowEM/7Z83kR8fXsEu7FNzMPqmvPOHcwfwcWRQGlc49btE6cJh0fA0utn573pAa1K66oBZoDheAziKA1oK6wWSKlQgZrXu2LNT7tcTsy9iZIu5hynhSu82ZCMtLV5ZaUDWe8Q+BLuudnkpJIq1miwbdUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2BDYkZzpHfJTfQ9kFRnCYdHx1brZ+dd6R+pSuuqQGaE43gNYmpNaGmslomovdmEzf4WT94yuu/n+wMDuEidKRg0nHFrYidrYTKeGq8iP8AvNeIima1I+FiesOd047hJP8AYpmvSTsczmorxChoBthi02oO5wmEqD7+y2fg1sRPpuldbgM5XI+2BTChBx4wRQBoNZjZxmDrDs9q2fSNlp2pRuu1lSYA13gHjArSlQQBQ5xIP2xIznSO+Sm+h7D4SFidkqtFSOrpFipzEzmtKpTcg4auPXjnHAML/ZhM3+Fk/eMrrv5/tQhpwmARKp/ZbPucIse2V12vRaRq/tBp7IDGo1mhqyGQzeNDv+x+ArHx/r8ur5twPbSk04dywrSn5CdZoyX7YkZzpHfJTfQ9tJz7Na+8Q4Ivbt53hGeza7aK64/U7vQM7tgyeTAbWfM4dcqRTBjaGlTWj52YTN/hZP3jK67+f7AwQkLE7JVaKkdXSLFTmJnNaVSm5Bw1cevHOOAYkXCxOyUqqpHV0i3Q5iZzWq1ruQMNfHrxzhiG1CGnCYBEqn9ls+5wix7ZXXa9FpGr+0GnsgMajWaGrIZkTOEwGJS/7LZ9zjFn2yuu16LV9f8AaDT2JGFBqNBRoNA/7EjOdI75Kb6HsPgIWJ6w+3TjuElD2KZr0k8HM4oK8RqaE7Y4NML/AGYTN/hZP3jK67+f7UYKcZg6w8Patn0DZajrUbrtYUmwdV4A4yaVrQAg1OaQDdFwsTslKqqR1dIt0OYmc1qta7kDDXx68c4YhvxGk1OfZAHVQFu7bZMcmZM/VHnkZPMhhzDpjEvSZlNobxlub5Y7mgtNFq8fSvXGHdQHpWJddtPGGZbLxn2KiZwmAxKX/ZbPucYs+2V12vRavr/tBp7EjCg1Ggo0GuDuqS3BzTlZZMMySrKd2E+pV8F36kn3r3FTHCql1rMcjXqya00sIuZW8BphnsiZYey49ABLWmGWjmBmjQd4XVw77tX3dUj45z9QknD2u4pYSB7m0K4VwOsnWzRppweQkTpSDGk44NbEUdTCZTw0rlR/3inGTXNZ88+p1ZXz3KfyPLl7xUu7qbo5ehJNSJBvDg0+IkSB0FeTJiWkIs2pzxOXp5QVpyw28ZczFCsNuHX1OKyK27afPnhZY7deThMIUHP9ls/FrYihXdK63EZyQT9sCmNQBjxEmoLIZB/2JGc6R3yU30PYemwkTo2B3Tjt6wNKhLOFGcahIA1/g48WYdsV/swmb/CyfvGV138/2op04TDo+BpdbPz3vSA1qV11QCzQHC8BnEUBrQV1gskVINzuEidKRg0nHFrYidrYTKeGq8iP+814iKZrUUoSJ0bHbpx29Y6tAljCjWNSkEa/wcOPPO2Cg7nCYSoPv7LZ+DWxE+m6V1uAzlcj7YFMKEHHjBFAGg1lRnCYdHx1brZ+dd6R+pSuuqQGaE43gNYmpNaGmslomoB+2JGc6R3yU30PZBgIZ/2z5vIj4+vYJd2KbmYfVNeecO5g/g4sigNK5x63a92YTN/hZP3jK67+f7IUDNa92xZqfdridmXsTJF3MOU8KV3mzIRlpavLLSgaz3iHwJd1zs8lJJFWs0WDbqlCROjY7dOO3rHVoEsYUaxqUgjX+Dhx552wIbEjOdI75Kb6HsgqM4TDo+OrdbPzrvSP1KV11SAzQnG8BrE1JrQ01ktE1F7swmb/AAsn7xldd/P9gYISFidkqtFSOrpFipzEzmtKpTcg4auPXjnHAMSPhYnrDndOO4ST/YpmvSTsczmorxChoBthi02oQ04TAIlU/stn3OEWPbK67XotI1f2g09kBjUazQ1ZDOY2cZg6w7Patn0jZadqUbrtZUmANd4B4wK0pUEAUOcSD9sSM50jvkpvoe0sn9mEzf4WT94yuu/n+0sGxLDEngxN6OT/ACLNpo937rH+NFL+LagmwDnRsD3SO3pA+2amT4LPK8ZOPHhjqOaAGmgvNcJQfRql5ZHtlW4MUujlDyLVqDyBc6Ug+6x29FDDSSn92kDHuhry0JAqScSWmWYpQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmQYrC2eEozo1N8ssWzo937rH+NFL+Lag7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhlloFy9j62F5HxEnL9Wla2xbasvWgXTF2F4tXsefqEnLEqakThLCuaV64fyjCoIBFWgyy1sDR7v3WP8aKX8WwSD30r9IuvNaTbCh6i46STvOTq1CEgXWyVbuseN0WTwkpc1pX+YcMMBqFTQmpDOY6Ac9Yc90juEoD2zUuc2K/3v5MDQUAGcAA02DFYZB76V+kXXmtJtNHu/dY/xopfxbD4SBdbJVu6x43RZPCSlzWlf5hwwwGoVNCakMgQjN9JHSL3zWrWJ2XIuBdbJSe6x53RaPCSlzWq/wCYMMcRqNBUigDRDR7v3WP8aKX8WwKN2frdUfj7er+1Kc7N0ZvpI6Re+a1ayBdzAunkvR5D2Pp2e3qalNTH20pyx8P8oGqgAGIAJb4uBdbJSe6x53RaPCSlzWq/5gwxxGo0FSKANAx2Fp/qL/pJR85PbZ0e791j/Gil/FtQgYBz1h93SO4Sj/bNS5zbp/e/lwFRQkZxBLTAEGuE4T/+zj//APNKtq+YbnruJtn9AvNmKWnK1OqFIc6XbJsepRilo/sGvHj0BVnKWlWVWohmXViFXnkporx6F2XolsNJLDIeM5xYtsB5AudKQfdY7eihhpJT+7SBj3Q15aEgVJOJLTLN/R7v3WP8aKX8Wwc3ZP2S/ctk7QK03dJLy2kRk2Q6BpFVmm8K8+9hag0BJYiBKchoy1epOc2r0vXWSo0rrjMmXayu9l27OTnamsmVJUlkP4gPdRXjf8UzI3/7AuqWf/RvUnbdvpsA50bA90jt6QPtmpk+CzyvGTjx4Y6jmgBprhG8KCdf1pGR4z1yNocgfqljRooqNajKO6lXSjQbqBtzVkNgeBVlvrbtqwd+q3Bil0coeRasTsuqUA50bHd0jt6R3tmpg+C1yPGjhxYYahnAlpm/o937rH+NFL+LYMM8JRnRqb5ZYtlW4MUujlDyLVqDuBc6UjO6x29E/DSSn92rjDugpy0BIqAcCGWWopQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmQYrC2eEozo1N8ssWzo937rH+NFL+Lag7gXOlIzusdvRPw0kp/dq4w7oKctASKgHAhlloAF5nrdTvj7dV+1KTLbBtq28aBdO5egCXsfTs9ur1qamftpSbj4f5AddQSMASQ/6Pd+6x/jRS/i2CQe+lfpF15rSbYUPUXHSSd5ydWoQkC62Srd1jxuiyeElLmtK/zDhhgNQqaE1IZzHQDnrDnukdwlAe2alzmxX+9/JgaCgAzgAGmwYrC0/1F/0ko+cnts6Pd+6x/jRS/i2oQMA56w+7pHcJR/tmpc5t0/vfy4CooSM4glpgL8ZvpI6Re+a1axOy5FwLrZKT3WPO6LR4SUua1X/MGGOI1GgqRQBoho937rH+NFL+LYFG7P1uqPx9vV/alOdm1rhKD6NUvLI9kG7mBdPJejyHsfTs9vU1KamPtpTlj4f5QNVAAMQAS4PIFzpSD7rHb0UMNJKf3aQMe6GvLQkCpJxJaZZBisMSeDE3o5P8izaaPd+6x/jRS/i2oJsA50bA90jt6QPtmpk+CzyvGTjx4Y6jmgBpoLzXCUH0apeWR7FLLryBc6Ug+6x29FDDSSn92kDHuhry0JAqScSWmWb+j3fusf40Uv4tgiTwYm9HJ/kWbJ6f9dCbfiJd5+s959mFNgHOjYHukdvSB9s1MnwWeV4ycePDHUc0ANNJ8BAOe2fN9Xsf6w7u/bNTw+qa8/Vt6Y6sCcMPB24B/VuDFLo5Q8i1YnZdUoBzo2O7pHb0jvbNTB8FrkeNHDiww1DOBLTN/R7v3WP8aKX8WwYZ4SjOjU3yyxaKHqLjpJO85OrUXcC50pGd1jt6J+GklP7tXGHdBTloCRUA4EMstSOgHPWHPdI7hKA9s1LnNiv97+TA0FABnAANNgxWGQe+lfpF15rSbTR7v3WP8aKX8Ww+EgXWyVbuseN0WTwkpc1pX+YcMMBqFTQmpDIAbzPW6nfH26r9qUmW2DbVt40C6dy9AEvY+nZ7dXrU1M/bSk3Hw/yA66gkYAkh/wBHu/dY/wAaKX8WwSD30r9IuvNaTaRm+kjpF75rVrD4SBdbJVu6x43RZPCSlzWlf5hwwwGoVNCakMyLgXWyUnused0Wjwkpc1qv+YMMcRqNBUigDQMdhaf6i/6SUfOT22dHu/dY/wAaKX8W1CBgHPWH3dI7hKP9s1LnNun97+XAVFCRnEEtMBfjN9JHSL3zWrWJ2XIuBdbJSe6x53RaPCSlzWq/5gwxxGo0FSKANENHu/dY/wAaKX8WweAdwWdkBZecoSS1ROybeqTyNLk2ycyw6bdIMoZVCHLaJptIZbdomdn3kMqrQDJaYYevFhAdPC7YltvN9+2uEoPo1S8sj28xcsrJMf5WeQgjSrLBiIK92RpNkG9m4tehI147j0W9eTZYcqqIykvGiQkNTH3aXG22SGAysVaDDLFTtbIEylU3K+ycLs73IgRSfOztMjZGvalwvlNPUZZvZlBtKSZwTHiUXzsJIevW3a+5dsBltmW11Bbz2+udzDviwxJ4MTejk/yLNpo937rH+NFL+LagmwDnRsD3SO3pA+2amT4LPK8ZOPHhjqOaAGmgvM8JRnRqb5ZYtlW4MUujlDyLVqDuBc6UjO6x29E/DSSn92rjDugpy0BIqAcCGWWopQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmQYra8T/roTb8RLvP1nvPs4aPd+6x/jRS/i2QICAc9s+b6vY/1h3d+2anh9U15+rb0x1YE4YeDtwD+rcGKXRyh5FqxOy6pQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmb+j3fusf40Uv4tgkHvpX6Rdea0m2FD1Fx0knecnVqEJAutkq3dY8bosnhJS5rSv8w4YYDUKmhNSGcx0A56w57pHcJQHtmpc5sV/vfyYGgoAM4ABpsGK0sM0e791j/Gil/FtLBjZcZzXHfKTfTFh6bFxOjYHcyO3rA0qUsYUZwoFcjX+FhxZ52oZLDEngxN6OT/ACLNgHPIuJ0pBnRkcWtiKOptMp4aVyrH7jXjApnNRSi4nRsduZHb1jq0KWcKNYUKuBr/AAsePMO1JBrhKD6NUvLI9sq3Bil0coeRasGNlxnNcd8pN9MWHu4uJ0pGHRkcGtiJ2ttMp4aryLH7hTiBrnMslhbPCUZ0am+WWLBr+9SIfdq+8WsBHOfqEnE+13FLCufdGhXCmI1ka2astbA2XGc1x3yk30xZOvY+theR8RJy/VpWtsWwLcJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5HxUT1hzuZHcJJ/skzXpJ2eeBQV4xU0I2pxZYIwe+lfpF15rSbYUPUXHSSd5ydWCbLjOa475Sb6YsPhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC2yWGQe+lfpF15rSbAOi4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwQ2XGc1x3yk30xbMZvpI6Re+a1axOwatu5iH/AGPx9ICP9fl6nNuB7aU5DHuuFaV/IRrNWi3RcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYBXZ+t1R+Pt6v7Upzs3Rm+kjpF75rVrBjZcZzXHfKTfTFh8BFRPWH25kdwkoeyTNeknh54NRXjNDQHajBltksLT/UX/SSj5ye2Ae8i4nSkGdGRxa2Io6m0ynhpXKsfuNeMCmc0Q2XGc1x3yk30xaNcJQfRql5ZHsUsC2mxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqOErw377+tIyPKQUZX+gP1S2gGwKkf0jupV1NS2RTAa3gJDbG1eEtt27+SeDE3o5P8izbhG8b/imZG/8A2BdUs/8Ao3qTtg7dUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1JDZcZzXHfKTfTFsq3Bil0coeRasTsC27i4nSkYdGRwa2Ina20ynhqvIsfuFOIGuczFKLidGx25kdvWOrQpZwo1hQq4Gv8ACx48w7UkGeEozo1N8ssWyrcGKXRyh5FqwY2XGc1x3yk30xYe7i4nSkYdGRwa2Ina20ynhqvIsfuFOIGucyyWFs8JRnRqb5ZYsCDeNEP+x+ArAR/r8ur5txPbSk0Yd1xpWv5AdRo0H7ZcZzXHfKTfTFlK8z1up3x9uq/alJltg2BbhIqJ2Sq0S46ukWKjPTOa0qlN1xhq4teGaMC3I+KiesOdzI7hJP8AZJmvSTs88CgrxipoRtTiywRg99K/SLrzWk2woeouOkk7zk6sE2XGc1x3yk30xYfARUT1h9uZHcJKHskzXpJ4eeDUV4zQ0B2owZbZLC0/1F/0ko+cntgHxcVE7JSqpcdXSLdBnpnNarWu65w18WvDNOJYIbLjOa475Sb6YtmM30kdIvfNatYnYNW3cxD/ALH4+kBH+vy9Tm3A9tKchj3XCtK/kI1mrRbnkXE6UgzoyOLWxFHU2mU8NK5Vj9xrxgUzmgV2frdUfj7er+1Kc7NrXCUH0apeWR7BNlxnNcd8pN9MWHpsXE6NgdzI7esDSpSxhRnCgVyNf4WHFnnahksMSeDE3o5P8izYBzyLidKQZ0ZHFrYijqbTKeGlcqx+414wKZzRDZcZzXHfKTfTFo1wlB9GqXlkexSwLabFxOjYHcyO3rA0qUsYUZwoFcjX+FhxZ52oUYCJf9s+bwICPr2CXdmu5mP1TXnjDuhP4WLRqBWmcOuWf0ngxN6OT/Is2T0/66E2/ES7z9Z7z7AfUouJ0bHbmR29Y6tClnCjWFCrga/wsePMO1JDZcZzXHfKTfTFsq3Bil0coeRasTsC27i4nSkYdGRwa2Ina20ynhqvIsfuFOIGuczI+KiesOdzI7hJP9kma9JOzzwKCvGKmhG1OLLBBnhKM6NTfLLFooeouOkk7zk6sE2XGc1x3yk30xYfCRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFtksMg99K/SLrzWk2BAvGiH/Y/AVgI/wBfl1fNuJ7aUmjDuuNK1/IDqNGg/bLjOa475Sb6YspXmet1O+Pt1X7UpMtsGwLcJFROyVWiXHV0ixUZ6ZzWlUpuuMNXFrwzRgW5FxUTslKqlx1dIt0Gemc1qta7rnDXxa8M04lgjB76V+kXXmtJtIzfSR0i981q1gxsuM5rjvlJvpiw+AionrD7cyO4SUPZJmvSTw88GorxmhoDtRgy2yWFp/qL/pJR85PbAPi4qJ2SlVS46ukW6DPTOa1Wtd1zhr4teGacSwQ2XGc1x3yk30xbMZvpI6Re+a1axOwaruriH3avu6pARz76hJOPtdxywkH3RkVxpgNYOpmjLPjckvXuQH1UqOQmE6JS8mzqkDiOWZfcZye6l+T8qpCfMtq6aMyjSQxeUVTODHqMVM86BholxLxJ9oLp/rYXb/ESTf1aSbcedUdyVojK0ybZqkWXhsK9qUHRvKuTmSGLUEpIt6cnPUpVRCkqzLLZRm5hZCjLL1401TMWGnrbea7NQ702XGc1x3yk30xYemxcTo2B3Mjt6wNKlLGFGcKBXI1/hYcWedqOOOp7ZUjnK+yXZFvTUWdg3ip5fyNfFLz2G2HHS1erKLTCXN6e+SNrocrDxlhdcO85kO4ZadMhpou6s9sJPBib0cn+RZsA53FxOlIw6Mjg1sRO1tplPDVeRY/cKcQNc5mKUXE6NjtzI7esdWhSzhRrChVwNf4WPHmHakgzwlGdGpvlli2VbgxS6OUPItWDGy4zmuO+Um+mLIMBEv8AtnzeBAR9ewS7s13Mx+qa88Yd0J/CxaNQK0zh1y20ra8T/roTb8RLvP1nvPsB9Si4nRsduZHb1jq0KWcKNYUKuBr/AAsePMO1JDZcZzXHfKTfTFsq3Bil0coeRasTsC3CRUTslVolx1dIsVGemc1pVKbrjDVxa8M0YFuR8VE9Yc7mR3CSf7JM16SdnngUFeMVNCNqcWWCMHvpX6Rdea0m2FD1Fx0knecnVgmy4zmuO+Um+mLSxS0sAzR7v3WP8aKX8W1BNgHOjYHukdvSB9s1MnwWeV4ycePDHUc0ANNXs9T96p/jJ76GtQTXipo6B71gN6QOGknmFWWeRFZA+Da4+xLB2xDLyBc6Ug+6x29FDDSSn92kDHuhry0JAqScSWmWYpQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmcPHinpSDGxYCuxFHHSTyvqiTq3GJP5iDQAkkFllmKTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YAQ0e791j/Gil/FtQdwLnSkZ3WO3on4aSU/u1cYd0FOWgJFQDgQyy1ez1P3qn+Mnvoa1B28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtAn3rQLpi7C8Wr2PP1CTliVNSJwlhXNK9cP5RhUEAirQZZa2Bo937rH+NFL+LbX16rxU7WF4vXYSB9Yk44aTefeyrcZRQNVeWmJNQGmGtgZ6n71T/GT30NYKEJAutkq3dY8bosnhJS5rSv8w4YYDUKmhNSGcx0A56w57pHcJQHtmpc5sV/vfyYGgoAM4ABpv5hHinslW70T66RYrVSec1pP4n18oOOAxNWcyRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi2BHR7v3WP8aKX8Ww+EgXWyVbuseN0WTwkpc1pX+YcMMBqFTQmpDN/PU/eqf4ye+hrD4R4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMDMXAutkpPdY87otHhJS5rVf8AMGGOI1GgqRQBoho937rH+NFL+LYdFvFPZKT3on10i3Sik85rVvxPr5AMcTiKNZ5DPU/eqf4ye+hrAg3cwLp5L0eQ9j6dnt6mpTUx9tKcsfD/ACgaqAAYgAlvi4F1slJ7rHndFo8JKXNar/mDDHEajQVIoA0n3cNqZl+P63CJ9Ozy9THSbYx7aM5VIoimuNdVPhqatNN8W8U9kpPeifXSLdKKTzmtW/E+vkAxxOIo1ngR0e791j/Gil/FtQgYBz1h93SO4Sj/AGzUuc26f3v5cBUUJGcQS0xez1P3qn+Mnvoaw+BeKfWH3ekBwioe2TytdJvORG5eIhprUC0WiyWA+nkC50pB91jt6KGGklP7tIGPdDXloSBUk4ktMs39Hu/dY/xopfxbD3jxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyzfz1P3qn+MnvoawUU2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01wjeFBOv60jI8Z65G0OQP1Sxo0UVGtRlHdSrpRoN1A25qyGwPAqy31t21bu1NeKmjoHvWA3pA4aSeYVZZ5EVkD4Nrj7EsHbHhC8F4onqo2R7SGgQ3/AECOqWZo0g1mlj+kd1KzPJa0QWwQet0ZAaZOc3nnOYBeh3gpQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmb+j3fusf40Uv4th6k8VNHR3esBvSOw0k8xoy1yorQPw7XD2RbO2F/PU/eqf4ye+hrBRdwLnSkZ3WO3on4aSU/u1cYd0FOWgJFQDgQyy1FKAc6Nju6R29I72zUwfBa5HjRw4sMNQzgS0zh28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtRSeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbACGj3fusf40Uv4tqDuBc6UjO6x29E/DSSn92rjDugpy0BIqAcCGWWr2ep+9U/xk99DWoO3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBploFC8aBdO5egCXsfTs9ur1qamftpSbj4f5AddQSMASQ/6Pd+6x/jRS/i21/eO2piX4DrkIn07PLq8dJtnHtoybQmqKKY011+Cho0y/56n71T/GT30NYKEJAutkq3dY8bosnhJS5rSv8w4YYDUKmhNSGcx0A56w57pHcJQHtmpc5sV/vfyYGgoAM4ABpv5hHinslW70T66RYrVSec1pP4n18oOOAxNWcyRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi2BHR7v3WP8aKX8W1CBgHPWH3dI7hKP9s1LnNun97+XAVFCRnEEtMXs9T96p/jJ76GsPgXin1h93pAcIqHtk8rXSbzkRuXiIaa1AtFoslgMxcC62Sk91jzui0eElLmtV/zBhjiNRoKkUAaIaPd+6x/jRS/i2HRbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWeQz1P3qn+MnvoawIN3MC6eS9HkPY+nZ7epqU1MfbSnLHw/ygaqAAYgAlweQLnSkH3WO3ooYaSU/u0gY90NeWhIFSTiS0yynXcNqZl+P63CJ9Ozy9THSbYx7aM5VIoimuNdVPhqatNODx4p6UgxsWArsRRx0k8r6ok6txiT+Yg0AJJBZZZAho937rH+NFL+LagmwDnRsD3SO3pA+2amT4LPK8ZOPHhjqOaAGmr2ep+9U/wAZPfQ1qCa8VNHQPesBvSBw0k8wqyzyIrIHwbXH2JYO2IZeQLnSkH3WO3ooYaSU/u0gY90NeWhIFSTiS0yzf0e791j/ABopfxbD3jxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyzfz1P3qn+MnvoawUU2Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA00nwEA57Z831ex/rDu79s1PD6prz9W3pjqwJww8HbhvTXipo6B71gN6QOGknmFWWeRFZA+Da4+xLB2xUE94pi8+b+9E/1iXd+2bf3zXnjGiLUcdatHHCmftwDgpQDnRsd3SO3pHe2amD4LXI8aOHFhhqGcCWmb+j3fusf40Uv4th6k8VNHR3esBvSOw0k8xoy1yorQPw7XD2RbO2F/PU/eqf4ye+hrBRdwLnSkZ3WO3on4aSU/u1cYd0FOWgJFQDgQyy1I6Ac9Yc90juEoD2zUuc2K/3v5MDQUAGcAA03h28U9KRg2LAV2InY6SeV9UVte4wI/OSaEkEANMtYjnin1hz3pAcIp/tk8rXSbvlRuXiAZa1gNBoNFsCOj3fusf40Uv4th8JAutkq3dY8bosnhJS5rSv8w4YYDUKmhNSGb+ep+9U/wAZPfQ1h8I8U9kq3eifXSLFaqTzmtJ/E+vlBxwGJqzmAo3jQLp3L0AS9j6dnt1etTUz9tKTcfD/ACA66gkYAkh/0e791j/Gil/Ftr+8dtTEvwHXIRPp2eXV46TbOPbRk2hNUUUxprr8FDRpl/z1P3qn+MnvoawUISBdbJVu6x43RZPCSlzWlf5hwwwGoVNCakMyLgXWyUnused0Wjwkpc1qv+YMMcRqNBUigDWIR4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMkW8U9kpPeifXSLdKKTzmtW/E+vkAxxOIo1ngR0e791j/Gil/FtQgYBz1h93SO4Sj/bNS5zbp/e/lwFRQkZxBLTF7PU/eqf4ye+hrD4F4p9Yfd6QHCKh7ZPK10m85Ebl4iGmtQLRaLJYDMXAutkpPdY87otHhJS5rVf8wYY4jUaCpFAGiGj3fusf40Uv4th0W8U9kpPeifXSLdKKTzmtW/E+vkAxxOIo1nkM9T96p/jJ76GsCBdTAum7sLuqPY8fUJJuIU1IHGWEg0r1wflOFSSSaNFpllxeQLnSkH3WO3ooYaSU/u0gY90NeWhIFSTiS0yym3VPFTtYXddahIH1iSdhpN597KTxhFI1U5K4EUBZYZcXjxT0pBjYsBXYijjpJ5X1RJ1bjEn8xBoASSCyyyHiLBwTjqf/VR38CyIlKyZ+qStNxEMNlKUAhSJlVo1Q0wCagC8xpWDQoWM+a5yYazg6lmp9u02Ac6Nge6R29IH2zUyfBZ5XjJx48MdRzQA01xB1RHJejsrnJaneQEV3AwV5iA0nXj3ITFCqxglGXL1pNeMqkptpau2itNI7S8WWpffPq4OllsnODINvjqcuVNE5W2SjIN4CjCwMJeLL7h7d3fGgxMS3BKiBevJxCVNzCsksozJSG15tkTG6YaYIDlaYdMM7RpuwdxO4FzpSM7rHb0T8NJKf3auMO6CnLQEioBwIZZailAOdGx3dI7ekd7ZqYPgtcjxo4cWGGoZwJaZw7eKelIwbFgK7ETsdJPK+qK2vcYEfnJNCSCAGmWopPFTR0d3rAb0jsNJPMaMtcqK0D8O1w9kWztgBDR7v3WP8aKX8WyBAQDntnzfV7H+sO7v2zU8PqmvP1bemOrAnDDwduH7PU/eqf4ye+hrIKe8UxefN/eif6xLu/bNv75rzxjRFqOOtWjjhTP24BwUoBzo2O7pHb0jvbNTB8FrkeNHDiww1DOBLTN/R7v3WP8AGil/FsPUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wv56n71T/GT30NYKEJAutkq3dY8bosnhJS5rSv8w4YYDUKmhNSGcx0A56w57pHcJQHtmpc5sV/vfyYGgoAM4ABpv5hHinslW70T66RYrVSec1pP4n18oOOAxNWcyRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi2BHR7v3WP8aKX8W0tjPU/eqf4ye+hrSwFLDEngxN6OT/Is2Te1Ndb/hxIH/h0seibUE66m7J5AQReXbyDjBwRI7D5YaxzRxaGZAFcQAKD2JYO2IbAa4Sg+jVLyyPbKtwYpdHKHkWra+eXT3YlQcs9riQcIWPPrOlniaSOVGPKf/wVqAyyxFG6m7J3ARpd3byDhBxpA7D5YZxzTxaGaBFcSCKH2RbO2AbUsLZ4SjOjU3yyxZO7U11v+HEgf+HSx6JtQd3T3YhQfM9riQcYWAPrOlnjaV+RGHIP/wBNKAtMthfvY+theR8RJy/VpWtsW3Pt412t3cDd1P8AHwMgSTBRcBI04xcHEQssI0HFw8cUVXPXGWmHDJFWiSKtUaaziDmllll97U11v+HEgf8Ah0seibA5Qe+lfpF15rSbYUPUXHSSd5ydW19C3UXY7JVGe1xII77GqT5Z5sSa+03+ta4VBGaGMxt1N2LDh31u7iQcItOGEnyyAKqLsGm4pHGdQBBxFDVpsNqWGQe+lfpF15rSbJvamut/w4kD/wAOlj0TYfC3UXY7JVGe1xII77GqT5Z5sSa+03+ta4VBGaGA2FGb6SOkXvmtWsTtqqKuoux2Sls9riQT32dcnyzzYrU9pv8ASlMaADODZDtTXW/4cSB/4dLHomwf0uz9bqj8fb1f2pTnZujN9JHSL3zWrW0hIF2l3aghRr+LkGSIl8J3vDg+uvpYR2jsNIvAnJKSsGnLWdmO2c1kg7Zl43tGWs1pltirqLsdkpbPa4kE99nXJ8s82K1Pab/SlMaADODYbVsLT/UX/SSj5ye2Tu1Ndb/hxIH/AIdLHom1CCupuxbcPOuXcSDjFqIxk+WSDRReAV3FA4hrBJOJqaNMBsBrhKD6NUvLI9vMCSeqSIU4XpXyorxEuaF1d0kmXpTqpP5XyoZBm/KcRpVu1bVGGLx7yMklmXJfmCSrrbySkqIulmVDvNnKaJicqksvZwkyT3cwxDct70mLIhuXXrxom8aLnLLDczAoLgmttMQeqE5fUrSBCqRUkxtlMTbqEHKSl+6JIl8t5hEjQ0rQ0sl0yIUS09hnjcO3xg31Oq8iY4hJuYmxq5uUMme7eMyulKSJ1ktTmtTvrvEOV8mXmo6rKl413TMiytIEmokgG8pUXJkmBxeXerF3uTfKcszY1CXVPHb5y7DsHJiyoJ8vanFXuuveudT7mp/gLsrvr75SREe81i9eAmG5q8pUXUOUVNaWXkjXYvEG9GW1mUFWHvWu+g5ZmWWJTfrMuvpSvYnN1FPTDC7xv+KZkb/9gXVLP/o3qTtl7Jvyc74E+8OZr2MqSBucjluIuPuuydZYlS6tZm28CUlqTbsponCcnl6E2Kk53fXaspUwXjrC4mP+1qzLkzIF1zEuNMwd6059k74uAd4l293jrqnmSBAMyJJQg4vIM6o9GRUKJZSNhxUcmZQXUtWHDZdbHLsl2ysKrIL1lppnrr0GoBqHpWrcGKXRyh5FqxO2q1G6m7J3ARpd3byDhBxpA7D5YZxzTxaGaBFcSCKH2RbO2F/tTXW/4cSB/wCHSx6JsDizwlGdGpvlli2VbgxS6OUPItW187unuxCg+Z7XEg4wsAfWdLPG0r8iMOQf/ppQFpluKN1N2TuAjS7u3kHCDjSB2Hywzjmni0M0CK4kEUPsi2dsA2pYWzwlGdGpvlliyd2prrf8OJA/8Olj0Tag7unuxCg+Z7XEg4wsAfWdLPG0r8iMOQf/AKaUBaZbAneZ63U74+3VftSky2wbc+z/AHaXdp6FBP4SQZIhnxne7yD665lhHZOw1e8CTUpVwZcs5ue7azWiTtWXbG0aazmmn3tTXW/4cSB/4dLHomwOUHvpX6Rdea0m2FD1Fx0knecnVtfQt1F2OyVRntcSCO+xqk+WebEmvtN/rWuFQRmhjMbdTdiw4d9bu4kHCLThhJ8sgCqi7BpuKRxnUAQcRQ1abDalhaf6i/6SUfOT2yd2prrf8OJA/wDDpY9E2oQV1N2Lbh51y7iQcYtRGMnyyQaKLwCu4oHENYJJxNTRpgNgxm+kjpF75rVrE7aqirqLsdkpbPa4kE99nXJ8s82K1Pab/SlMaADODZDtTXW/4cSB/wCHSx6JsH9Ls/W6o/H29X9qU52bWuEoPo1S8sj20jIF2l3aghRr+LkGSIl8J3vDg+uvpYR2jsNIvAnJKSsGnLWdmO2c1kg7Zl43tGWs1plueXT3YlQcs9riQcIWPPrOlniaSOVGPKf/AMFagMssBtSwxJ4MTejk/wAizZN7U11v+HEgf+HSx6JtQTrqbsnkBBF5dvIOMHBEjsPlhrHNHFoZkAVxAAoPYlg7YhsBrhKD6NUvLI9iltVvLp7sSoOWe1xIOELHn1nSzxNJHKjHlP8A+CtQGWWL/amut/w4kD/w6WPRNgckngxN6OT/ACLNk9P+uhNvxEu8/We8+w5OupuyeQEEXl28g4wcESOw+WGsc0cWhmQBXEACg9iWDtinwF293j68aaYBuQJI2HCyNd5Fwrkywj7Eh41SW7ymHxLAchgkhJSxRhkGodljF5VgN4q3Bil0coeRasTtqtRupuydwEaXd28g4QcaQOw+WGcc08WhmgRXEgih9kWzthf7U11v+HEgf+HSx6JsDizwlGdGpvlli0UPUXHSSd5ydW1+7unuxCg+Z7XEg4wsAfWdLPG0r8iMOQf/AKaUBaZbkbdTdiw4d9bu4kHCLThhJ8sgCqi7BpuKRxnUAQcRQ1abDalhkHvpX6Rdea0myb2prrf8OJA/8Olj0TYfC3UXY7JVGe1xII77GqT5Z5sSa+03+ta4VBGaGAKXmet1O+Pt1X7UpMtsG3Ps/wB2l3aehQT+EkGSIZ8Z3u8g+uuZYR2TsNXvAk1KVcGXLObnu2s1ok7Vl2xtGms5pp97U11v+HEgf+HSx6JsDlB76V+kXXmtJtIzfSR0i981q1tewt1F2OyVRntcSCO+xqk+WebEmvtN/rWuFQRmhiRV1F2OyUtntcSCe+zrk+WebFantN/pSmNABnBsNq2Fp/qL/pJR85PbJ3amut/w4kD/AMOlj0TahBXU3YtuHnXLuJBxi1EYyfLJBoovAK7igcQ1gknE1NGmA2DGb6SOkXvmtWsTtqqKuoux2Sls9riQT32dcnyzzYrU9pv9KUxoAM4NkO1Ndb/hxIH/AIdLHomwS6f62F2/xEk39Wkmzi1wlB9GqXlke2kbubtbu467qQI+OkCSY2Lj5Gk6LjIiKlhGjIuIjgipB640024aJo0ATRqjLWaSc0NMtNzy6e7EqDlntcSDhCx59Z0s8TSRyox5T/8AgrUBllgNqW8JoIHqfnVNk1+GdFZM3VJoVOhX4OaJfkXKsRaNM0x3D7ZTSsBts3ssmydMaCWK29lO1Ndb/hxIH/h0seibcO5d+Q3d/lU5KM53dS/Jcnod48Knps7XTTInIaNAqCNehKJCtKTwKzLDtphhbeVl5808baZZcLL140TRnND0TZ4SjOjU3yyxbKtwYpdHKHkWreafU5b1LssrXJrlOepju7kOCvVlF09u0vrlqKk6WYJQly9WUapc4sNJLLttpFZmHcuYnbsFlnMWGHdDm5w7rUbqbsncBGl3dvIOEHGkDsPlhnHNPFoZoEVxIIofZFs7YBtS2vE/66E2/ES7z9Z7z7fPamut/wAOJA/8Olj0TZAgLt7vH1400wDcgSRsOFka7yLhXJlhH2JDxqkt3lMPiWA5DBJCSlijDINQ7LGLyrAbxVuDFLo5Q8i1YnbVajdTdk7gI0u7t5Bwg40gdh8sM45p4tDNAiuJBFD7ItnbC/2prrf8OJA/8Olj0TYHKD30r9IuvNaTbCh6i46STvOTq2voW6i7HZKoz2uJBHfY1SfLPNiTX2m/1rXCoIzQxmNupuxYcO+t3cSDhFpwwk+WQBVRdg03FI4zqAIOIoatNhtS0trrtTXW/wCHEgf+HSx6JtLA456n71T/ABk99DWoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7Yy0sEePFPSkGNiwFdiKOOknlfVEnVuMSfzEGgBJILLLMUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wlpYL+ep+9U/xk99DWoO3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBplqWlgTr1Xip2sLxeuwkD6xJxw0m8+9lW4yigaq8tMSagNMNbAz1P3qn+Mnvoa0tLAPhHinslW70T66RYrVSec1pP4n18oOOAxNWcyRzxT6w570gOEU/wBsnla6Td8qNy8QDLWsBoNBoty0sBDPU/eqf4ye+hrD4R4p7JVu9E+ukWK1UnnNaT+J9fKDjgMTVnMlpYJFvFPZKT3on10i3Sik85rVvxPr5AMcTiKNZ5DPU/eqf4ye+hrS0sCBdw2pmX4/rcIn07PL1MdJtjHtozlUiiKa411U+Gpq003xbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWfLSwEM9T96p/jJ76GsPgXin1h93pAcIqHtk8rXSbzkRuXiIaa1AtFosliWlgy8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWb+ep+9U/xk99DWlpYKCa8VNHQPesBvSBw0k8wqyzyIrIHwbXH2JYO2PCF4LxRPVRsj2kNAhv+gR1SzNGkGs0sf0jupWZ5LWiC2CD1ujIDTJzm885zAL2Wlg7vUnipo6O71gN6R2GknmNGWuVFaB+Ha4eyLZ2wv56n71T/GT30NaWlgoO3inpSMGxYCuxE7HSTyvqitr3GBH5yTQkggBplqKTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YS0sF/PU/eqf4ye+hrUHbxT0pGDYsBXYidjpJ5X1RW17jAj85JoSQQA0y1LSwJ947amJfgOuQifTs8urx0m2ce2jJtCaoopjTXX4KGjTL/nqfvVP8ZPfQ1paWAfCPFPZKt3on10ixWqk85rSfxPr5QccBias5kjnin1hz3pAcIp/tk8rXSbvlRuXiAZa1gNBoNFuWlgIZ6n71T/ABk99DWHwLxT6w+70gOEVD2yeVrpN5yI3LxENNagWi0WSxLSwSLeKeyUnvRPrpFulFJ5zWrfifXyAY4nEUazyGep+9U/xk99DWlpYEC7htTMvx/W4RPp2eXqY6TbGPbRnKpFEU1xrqp8NTVppwePFPSkGNiwFdiKOOknlfVEnVuMSfzEGgBJILLLMtLBfz1P3qn+Mnvoa1BNeKmjoHvWA3pA4aSeYVZZ5EVkD4Nrj7EsHbGWlgjx4p6UgxsWArsRRx0k8r6ok6txiT+Yg0AJJBZZZv56n71T/GT30NaWlgoJrxU0dA96wG9IHDSTzCrLPIisgfBtcfYlg7YqCe8UxefN/eif6xLu/bNv75rzxjRFqOOtWjjhTP24lpYG9SeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbC/nqfvVP8ZPfQ1paWCg7eKelIwbFgK7ETsdJPK+qK2vcYEfnJNCSCAGmWsRzxT6w570gOEU/2yeVrpN3yo3LxAMtawGg0Gi3LSwEM9T96p/jJ76GsPhHinslW70T66RYrVSec1pP4n18oOOAxNWcyWlgULx21MS/AdchE+nZ5dXjpNs49tGTaE1RRTGmuvwUNGmX/PU/eqf4ye+hrS0sA+EeKeyVbvRPrpFitVJ5zWk/ifXyg44DE1ZzJFvFPZKT3on10i3Sik85rVvxPr5AMcTiKNZ8tLAQz1P3qn+Mnvoaw+BeKfWH3ekBwioe2TytdJvORG5eIhprUC0WiyWJaWCRbxT2Sk96J9dIt0opPOa1b8T6+QDHE4ijWeQz1P3qn+Mnvoa0tLBr+6p4qdrC7rrUJA+sSTsNJvPvZSeMIpGqnJXAigLLDLi8eKelIMbFgK7EUcdJPK+qJOrcYk/mINACSQWWWZaWC/nqfvVP8ZPfQ1qCa8VNHQPesBvSBw0k8wqyzyIrIHwbXH2JYO2MtLB4eqkRE5AfVTIdYacwSVk2dUldJ6SuHSDx0hSflVoD5phIVKPRnozF5zKo07beCrEVMi6207Jcy+yT7hKTxU0dHd6wG9I7DSTzGjLXKitA/DtcPZFs7YS0sF/PU/eqf4ye+hrIKe8UxefN/eif6xLu/bNv75rzxjRFqOOtWjjhTP24lpYG9SeKmjo7vWA3pHYaSeY0Za5UVoH4drh7ItnbC/nqfvVP8ZPfQ1paWAfCPFPZKt3on10ixWqk85rSfxPr5QccBias5kjnin1hz3pAcIp/tk8rXSbvlRuXiAZa1gNBoNFuWlgIZ6n71T/GT30NaWlpYP/Z)
Now taking another case
Cost of 4 kg of apples and 2 kg of grapes is Rs. 300……………………………(Given)
So,
![](data:image/png;base64,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)
Dividing the equation by 2 , we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Putting x = 70, 75 and 80 we get,
y = 150 – 2×70 = 10
y = 150 – 2(75) = 0
y = 150 – 2(80) = 150 – 160 = -10
![](data:image/png;base64,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)
Algebraic representation :
4 x + 2 y = 300
Graphical representation :
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)
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.
Answer:
Given: Seven years ago, Aftab was seven times as old as his daughter and after 3 years Aftab will be 3 times as old as his daughter.
To Represent the situations algebraically and graphically we need to find the linear equations for these situations.
Let present age of Aftab = x
Let present age of his daughter = y
Then, seven years ago the age of Aftab and his daughter must have been seven less than their present ages,
Age of Aftab seven years ago = x – 7
Age of Daughter seven years ago = y – 7
According to the question,
Seven years ago, Aftab was seven times as old as his daughter, Sox - 7 = 7(y - 7)
⇒ x - 7 = 7y - 49
⇒ x = 7y - 42
Putting y = 5, 6 and 7 in equation (¡),
we get,For y = 5,
x = 7 × 5 – 42
= 35 – 42
= -7
For x =6,
x = 7 × 6 – 42
= 42 – 42
= 0
For y = 7,
x = 7 × 7 – 42
= 49 – 42
= 7
Thus we got 3 points to plot on graph for this equation.
Three years from now,
Age of Aftab = x+3
Age of Daughter = y+3
According to the question,
⇒ x + 3 = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x = 3y + 6
Putting x = 0, 3 and 6
Thus we got 3 points to plot on graph for this equation.
Algebraic representation
x - 7y = -42 (i)
x - 3y = 6 (ii)
Graphical representation:
Question 2.
The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
Answer:
We need to form linear equations for the situations.
Let cost of one bat = Rs. x
Let cost of one ball = Rs. y
In first case, three bats and 6 balls cost him 3900 rupees. therefore our equation becomes
⇒ 3x + 6y = 3900 ........(i)
Dividing equation by 3 both side
⇒ x + 2y = 1300
⇒ x = 1300 - 2y
For plotting the equation of graph, take different values of y and obtain the value of x from equation or you can do vice versa
At y = 0
⇒ x = 1300 - 2(0)
⇒ x = 1300
Now finding the value at x = 0
⇒ 0 = 1300 - 2y
⇒ 2y = 1300
⇒ y = 650
From above points, we make the graph as follows [Graphic representation]
In second case he buys one bat and 3 balls for 1300, therefore,
⇒ x + 3y = 1300 ......(ii) [Algebraic representation]
⇒ x = 1300 - 3y
At y = 400
⇒ x = 1300 - 3(400)
⇒ x = 100
At y = 300
⇒ x = 1300 - 3(300)
⇒ x = 400
From above points, we make the graph as follows, [Graphical representation]
Question 3.
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Answer:
Let the cost of each kg of apples = Rs. X
Let the cost of each kg of grapes = Rs. Y
According to the question,
Cost of 2 kg of Apples = 2 xCost of 1 kg of grapes = y
Putting y = 20, 40 and 60 we get,
x = (160 - 20)/2 = 70
x = (160 - 40))/2 = 60
x = (160 - 60)/2 = 50
Algebraic Representation:
2 x + y = 160
Graphical Representation:
Now taking another case
Cost of 4 kg of apples and 2 kg of grapes is Rs. 300……………………………(Given)
So,
Dividing the equation by 2 , we get,
Putting x = 70, 75 and 80 we get,
y = 150 – 2×70 = 10
y = 150 – 2(75) = 0
y = 150 – 2(80) = 150 – 160 = -10
Algebraic representation :
4 x + 2 y = 300
Graphical representation :
Exercise 3.2
Question 1.Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
Answer:For representing the situation graphically and algebraically, we need to form linear equations
(i) Let number of girls = x
Let number of boys = y
According to the question, Total no of students is equal to 10,
![](data:image/png;base64,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)
⇒
................................eq(i)
Now we will find different points to plot the equation. We can take any value of y and put in eq (i) to obtain the value of x at that point
Putting y = 4, 5 and 6. we get,
at x = 4
X = 10 – 4 = 6
at x = 5
X = 10 – 5 = 5
at x = 6
X = 10 – 6 = 4
![](data:image/png;base64,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)
Number of girls is 4 more than number of boys …………Given
So,
x = y + 4
⇒ y = x - 4 ................................(ii)
Now for plotting the points on graph, take any values of x and put them in eq (ii) to obtain values of y
Putting x = 3 ,5 and 7 we get
at x = 3
y = 3 - 4 = -1
at x = 4
y = 5 - 4 = 1
at x = 7
y = 7 - 4 = 3
![](data:image/png;base64,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)
Graphical representation :
Plotting the points obtain on graph we get,
![](data:image/png;base64,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)
As, both lines intersect each other at (7, 3)
Solution of this pair of equation is (7, 3)
i.e.
No of girls, x = 7
No of boys, y = 3
(ii)
Let cost of one pencil = Rs. X
Let cost of one pen = Rs. Y
According to the question, 5 pencils and 7 pens together cost Rs 50
5x + 7y = 50
⇒5x = 50 - 7y
⇒![](data:image/png;base64,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)
Putting value of y = 0 , 5 , 10 we get,
x = 10 - 0 = 10
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now,
7 pencils and 5 pens together cost Rs. 46
7x + 5y = 46
⇒ 5y = 46 – 7x
![](data:image/png;base64,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)
Putting x = -2 , 3 , 8 we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO0AAAB/CAYAAAAD40XHAAAACXBIWXMAAAsTAAALEwEAmpwYAAAK/ElEQVR4Xu2abagtZRXH78230jJNfKnES7dSSa1EywoJQiwhCrN3tBetL5GFhdmHkqDwixSZhX6Q7GKJfQgtpVJSu5YEvWi+5SVNPZqZaFqRloZ2+v9hNgzD2mfW7LPPnHXO+T3wZ/as/cxa6/k9e+2ZeWY2baJBAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgMCYBDaPGYxYoxJYHDUawSAAgWUTGKNox4gxBMRY+YwVJxr74nMiKzYIQKAuAYq27tyQGQRCAhRtiAUjBOoSoGjrzg2ZQSAkQNGGWDBCoC4Birbu3JAZBEICFG2IBSME6hKgaOvODZlBICRA0YZYMEKgLgGKtu7ckBkEQgIUbYgFIwTqEqBo684NmUEgJEDRhlgwQqAuAYq27tyQGQRCAhRtiAUjBOoSoGjrzg2ZQSAkQNGGWDBCoC4Birbu3JAZBEICFG2IBSME6hKgaOvODZlBICRA0YZYMEKgLgGKtu7ckBkEQgIUbYgFIwTqEqBo684NmUEgJEDRhlgwQqAuAYq27tyQGQRCAhRtiAUjBOoSoGjrzg2ZQSAkQNGGWDBCoC4Birbu3JAZBEICFG2IBSME6hKgaOvODZlBICRA0YZYMEKgLgGKtu7ckBkEQgIUbYgFIwTqEqBo684NmUEgJEDRhlgwQqAuAYq27tys58z21+DOlm6R7pB2SFdKR44w6Jcrxtekmxvdpe310ltWIPYb5PMa6U7pduk30ntXIA4u1wmBxRHGMWuM85Tb/dLWJsddtL1Yeko6ahl5Z/I5Xf4fkl7RxNlJ2683sY9Ixs7EeaV8PSFdIE1Ojh/TZx/7zmScqFsmdnQctjVAYIzJnTWGi/aMDsN9tG9/Fy2DbSafd8n/JzoxDmxin5WMnYnz2cbnyzo+H9H+pck4UbdFLo8jLBvD5stRn9n8A7ytGfI2bZ+UHpP8o1updqYcn99x7phPS3uvVNDG7xXaXtiJsWez/7c5xn6m8bVzx6fP7M/OMQ6u1hGBzNngFI3X/d7fjNtnu1slbzMtEyPjx322SPbny9dZ2yz5+Ex4rXSDtFsycCbOi+Trbsln1edJPkF+XvqHtJx790zs5DDoVo1AdnJ/pMQflfaVvi+dNGAg2RgZl+eokxeFds90ntJnSD6+53xQ8jGXS14cy7ZsnIPkcLv0H8lXEi7iN2WDTOmXjT3lcMyVCWQn9wAN4nHpD9JlAwfUF8OXhnu1tMcU/8fI7h/1cs5Adt2XTxTeZ0RfLvte8+ioQ2DLxDlcx/1V8kq1z+A+035Y+rd0YuAza8rEzvqiXzECQyb3U8rd/U8bOIa+GCc0ft3Pujrwf6hsD0jHBd8NNfXlM82f7zP/JP1qWoeOPRPHawYuWvtut59q5+GObchuJvYQf/QtRCA7uT4D+H7u15IXYuZ5meiz7LEtHdbhc4j275WO79hn3c2M2feXm4MAXqDywlymZeLcJ0c3Bs6+IZuPH8K57SYTOwiLaS0QyE6uV4nPbX5EvkT1/V22ZWNE/lyw90jtgt1V+z5Dzdoy+biQ/EfSbb+Twc9vMy0Tx3+CvoLo/kH8UDb/OWQXvbr5ZGJ3j2F/jRDITO7BGstN0nObMZ2srY/7YHKMmRiRK8d1gXxH8gr2RKfq80J0QNKWycdF+wtpv5bPye3BPJ/Tfkj+nY9XjCftbfrgR0Hdx12tLr0fM2PsdUKHmgT6JverSvvvjSY/LN/X+Tivdl6XGFZfjGkuLmni+PiuFqYdlLBn8vFZdpvkhTc/3vIrhi7iIa8XZuI43Xc0vndo69c1fy99Uuo+u3XfbMvGzvqjXyECY0zuGDGGIB0rn7HiRGPnjaiICjYIVCbglUMaBCCwhghQtGtoskgVAibQXY6GyvohsJr3XeuHIiOBwIgExijaMWIMQTZWPmPFicbOQlREBRsEKhPgnrby7JAbBAICFG0ABRMEKhOgaCvPDrlBICBA0QZQMEGgMgGKtvLskBsEAgIUbQAFEwQqE6BoK88OuUEgIEDRBlAwQaAyAYq28uyQGwQCAhRtAAUTBCoToGgrzw65QSAgQNEGUDBBoDIBirby7JAbBAICFG0ABRMEKhOgaCvPDrlBICBA0QZQMEGgMgGKtvLskBsEAgIUbQAFEwQqE6BoK88OuUEgIEDRBlAwQaAyAYq28uyQGwQCAhRtAAUTBCoToGgrzw65QSAgQNEGUDBBoDIBirby7JAbBAICFG0ABRMEKhOgaCvPDrlBICBA0QZQMEGgMgGKtvLskBsEAgIUbQAFEwQqE6BoK88OuUEgIEDRBlAwQaAyAYq28uyQGwQCAhRtAAUTBCoToGgrzw65QSAgQNEGUDCtCIEt8vpL6cEV8b6BnFK0G2iyV3GoH1DsG6SXLJHD4fruQmmHdLt0p3SBdMASx8zy1YE6aHGK9prF4YBj9lffs6VbpDskj/VK6cgBPui6jgn4h7nSLRNjNyWxXTpI+oE07UzrH/JPpD2bpPfV9ibpPun5ja1vk8nHRXurdEqgXfoCNN9n4kSuzpPxfmlr86XjXSw9JR0VHRDYZo0duMJUjcAYk5uJsVlgJld0fUX72g7Ed2vfMU5Ows3k46K9OulvWrdMnOhYF+0ZnS/20b79XRQdENgWuTwOqGwAk89+f2l+LP/U9sfNmH0p6jPhM833O82BhX+Q/0v4eb36+Gzbbg81O3snjl8LXc5Ukud3En1M+09L6TFStGthquefo38kL5XulrZLb29CPKzt66Q/Nt8/29jH2Pw3CHJwY/P98Dybx36Z9FvJY/2u9Kp5Bpjiy3+G3T+wLbJNbiGmHIZ5oxDIXMJ9UTBcLL5/nLTP6cMXkpAyMdqulro87ob0ZfWN0ve6Xyyxn8nnxTreC12Te0jfQ18iPSG9Zgnf7a8ycZKuNp2jjndJuycPmGfsZEi6jUUgM7n+l/c//6dbSd2mz140yrRMjLafIUX7GR3oFdYXZhJp+gzNZ+LaBePL1KuSsfri7Cw/XomeaI8pfo9p4g5ZPe6LPSUU5rVAIDu52zUYr9K6HS1d13zObLIxJr6yRfs+HeBLdy8aDWlD82n79iX4o8lgfXFOkB/3mSha+DpU3z8gHZeMOenWF3ugO7pXIpCd3FObH9dh2n5T+siAQWRjTFxmitYrxr7PzJ7t2+lm8vGZe9dgjNfL9nhgj0x9cXyGPbYls223Q7Rzr3R8x57Z7Yud8UGfogSyk/sC5f+kNHmGmH0m6mFnY0wQ9RXtSerYLdg3yvalJONMPtvk6+Mdf14IekS6do5xprlywd4jtQvWfyJ+ySLTFn3tTdvYBP6l4V8hnS5dKnlBZjWaC9bxvyK9uZXAq/V5vzkndJb8/Uzyiw5+rHWu5EcuX55znK47r4b/XLpG8ttRfsHDzS9ZeJy0DU4gc9aZIHqrPrj/St1ffVu+FySf0f3Yw59vltrN93fOIdK2Tt9pu5kxH6GDvyV5BdmLbn+WXES+nM22TJzIl1epo/HZthAdENhmjR24wlSNwJDJ9b++i2boc/shMcbgM1Y+Y8WJmPFGVERlA9reozH7BYPug/8NiIIhQ2D1CPSdDfxK3WmSF2F8qbh1hlT7YszgclmHjJXPWHEiGKsZO8oH2xwJ9E3uRxXLLxQsSH6RYZbWF2MWn8s5Zqx8xooTsVj0q2K09UlgNX9Y65Moo4IABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAgQ1J4P+R6aeS4xbWQAAAAABJRU5ErkJggg==)
Graphical Representation:
Plotting the points obtain on graph we get,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAY8AAAFBCAAAAACqE3z/AAAAAXNSR0ICQMB9xQAAx9pJREFUeNrsvXm4ZVdVL/obY8w511p7n0pVpZJUGtKQhEAIgSQCQUloRQVFbAFRnw1e9T3FZ/PuVbmK3qs8L159j+/aoKJiw73KE0RpnoB0SisiEiJIkxCICQlpKlU5Z6812zHuH2ufU+cUzX1frO9d8HN/X3111p5rzTXmmHO08zfmJsO/fr6APvzFSLQarKrpv87HF8jHUO4yqoC19i9LwOmLbjhH71B/6imit64O7gsluQWryb/Kx/+sT/u7H7z0S14xgX/m2W+4adMfWJqW6V+O5nJfbJoqPXHj7veljekTX/qsLwcAi6Hr/lVf/c/8fOIH8bzTXvrYxwKV/uVoqi+G+SiOPtvXN/2bG3/icecNWlPnTO66sbv0X4yEfGHaj6IAkO5NhlY+w9vV+z/ptpcsBlhZSCr5T5/7WyOg5V+Eo/UFaD9qsyrsGbGeWk2zhr1CUuryEdcEQtMlIvXlL998ZwRaZtH22eXpX+Xjn+VBZVtKvuGPP7r/EEpjV2LdMxviyqf/6ZNHUItm3+e/vwvH3rQFv5QSyxe9fMjPfuGJrCex4b3fcv0oZ3mpumx2XIotk3f1+q0rHnG688gk9/yHN7StO688RwtXGsoXaYD7Be3vaqnqzv+yN73pih99RgiWwy4e01Bz6L7924FMnhbA7R9OaB/9FKy2IPpF73B9wcmHZZChS4sLr/v07a8/cv7punIoctwuVHOI1aGAC9HRP/5DAFsXPmzDNxLy8q/66iQ74JVRWUp3zstvRvmbd5/6EKqNd4mxgsk5wLmy8jKuLl50X/K1Dz93yN2/hFjk/zd9Zen42q0tnOgHaXYOAFrpCC5ax/mSD98JDBO6VEmLUAlcW6DjaV0ZGKc+7Wm///avfwpQzQgASusIABK6z0eM+M8roxS+2Pwr3eP1/I8jilGR4/oiRwOAXKHTapdPNK0KQHWcesfcPfGUA492z/721REO26FFmgyh355L6QUA7o2rqWY3cE0aK4hQVpN9LsdXp89Dd4r2xSgfFiXMnqn///o8uQ7K+k/LQynwmlfmQMTUcl9b30MnIoiAFwCOrM59zE/0D3vZK/jbmgWgAwTo/fxoRH+cjoN8Vw0MRPUAPGLvG03BAcja7Z2XiEAMUA8AkToAtYQdwaVZsOgkhPu59QRYdJ9dEGvp+OTpKxFwD4BoHRP0e4c980HTTEzNPTsZg7cjd3siJBsYt73lLZ867Su+tc8qFMF6bOsVt/zkIRx782s+ffDa7+Fjq8Nnfw9w0XOff+R/p00/szVyANDSzlCYAJxy0JHEIx/5w2u/jXq85iVHD37Xk++dJ44IQK3HHTQG92lbGc3fEvPO5AQAea+ia2nbLlmiDsja7xG3tLMkI3og2bqZ5t7nzufJ2V4Bn08x3Sd7TjWZA8COt7U/7+5/arOtUJm/bRViYH7vL19+Se5ppD66G28688w/e8OFZwRycjcv0fCy1z791DLdsnHmzb930/3P/cT/edp52rpHfOIX64MOOUKsDkoCpOzECYCcvZPS+MMf3P8lodldL6JrBnvfhw9deP3b6bJlqQ4QR0BJx+dDBDZq2LkAwC6ZAMpikwlQTrAdWpLN7p2x2NQ8TdjlOWiNOmcFlARAzfOgxREAcqU5wCAUi4fVKqnNrKOTp680zm5+TZ2rqRe19cSU0jNaIlYjYL0YIvpN8oC87YVHF6LAokxCF168gUe+/k4NgAqBNjYu2GDwvsfux/UvcLxY3vLb/pE8Hnre8jf++vxLvu+QYF6+ELV5FdbcEwTV7R+mja676KzTBtCpTz8V1/7Iq76dBbDI3Y6xOr6Y6LjChUUJGjsPBICcAIAB09ysMTju79V5cVMA4EtzTtBi52CT99Rt1rVODIAlHgoBNnkPIOkw+xXOAQJA4UgIGF04mfaDuDWHiYMXsCfoFBxgk3PGALkwxQCUMlBqA0nbah1aDv/vB3/9gfANzhVfNlj5b+NXnBpz6E8lAGggCFMO/1C+74F6v2/9z6+7qore+snxrdiQZ5+WWnYeFp3fErEWuz4QksW/e+n7H/TE04E8tmDx/sDmq695ZmJfx95RLaHYkoGWQ9UBkVzyDpbDrMDJ5dYvGRpb6BBSCUk84LJ2kTtyqXVYkADRhlnUIRQiOs8AXG49ehYgWk8oNWSRJih5Fj1pq34BIGbfk69TJ1qdR00iJ9eeGwvgsvaR+gDYLH0+aTd6z2GyDQKYV51jgrfaezjGUXca7D2vdvumdO7DLwt3vvf0a86Dq8eOHdIcck9kiL1P752++SK2Axe3TXYO7/sTkG299KtOc0hc8uAylo6gPjUv5LTje44c2o/Y8z5Kg9uS4ejwhKvrVF0gjxRd3wuAFsUpkJnzwgGglgLQYtcrecBmd7uoz52DVcJKHCik0sGhTuY8MOUQUvCAlNhH6ink3MOjTeo8ATWHBZEjtNJn9DbJUJgAy+oIqMk3DbNPX/Ow1i8nRT4WQoCXBo+SewnOASDPhnndlNwTRAoLVp1z+xygVYbxE5fQ+U9hV3V5Tmeb6Un3U3Ibvow+kIcZwQF65P6PB8ifLmAGvvQ7X74FnDFgxYvaAnmeTVfgxgQR/6hvO+uqBRyQG8GTu/XPnnKVSuVeAPh9a8Pm9zELsARvCEBLhjDAgXk2IhtCAAbwMk0DOeZZ/y9m29vBE+BZeEnYHjmAWWY4mGcAnWcCGAiOHUCeZlNECxIAwQmcAPAiswXiwCfHv8ouzL6DgwYGYxU8AMFMphclAPAABZ59DHbQ4QF9PO1MoHjg9o+VBx986d/8+P3QdTXlQYCygtNP/V2+9J1/9rRHH/lQGgDgsuc//m/3f+K6T1/Ss8vwgNRVL5h1MgAM+wc1OJDsc9PgXv3OR97/j45+/8bsVDNjwgCA5rsFcCMN5GYHhzxQ0iC7m8kAvx4IBLBJuoAJA5zb5hfz/IcAGLkPiDoQmIGoi51mD9jow56H2tT57afBfJLsR2Do5MO6z5H6E5zpotsJJ2YAOvlAgi8/9hf7z0xpMKuu/N3vfbg/cOk3n/LDH/qhr3KsNrW6fxO4/nfeuTrjwgcfQLnjyx+NsRM6+395Wrj+3/3gz3wDMMx+TLWoizm2cx1AbECZPu7uvf0svPG/fOi6/3TwW9NGtAGIOlDIq2EXdW06ISKQnidb7FprJ/KkTm3Y5XOVPPDeAFMH8tvxpy9b/a7nqeNcdt2fc/j8WZ37sl9b8pB1aDuz24AY/K4RdwzB8UGWGHypA+c//b9++doUNwRtCpu3bVY+ePYp17+u/27lxRT4lqMX7cO9t47FTr3fwG/59z/61K7xxCEh4H3f/IAXXNZF+Bi8Kess76bEwCted/l37bO6uiucPuCmO0XvOvv+WAICNAjiRKfsYqA1yXWx7Wza6CT12HZgJ11Qw16O2RYWstuX72WPq7q5pzm2bldzyUOuu+9X44n7kzwfpmx7IE85B0+7m5MO1CBY8QBATaCl9Hz7dfWy+xtRLP3a/c7u5mOHzlISlel4rN8E//Dh8y/dgE7cUQMzPv5v06+db5N2jkoa9nDs1a974Heeglp7SzsjVYpr5Q7VPTn4NvW8i/hGpEzATGqDYMKAlezima6jXht5AFppJ8jHdmg3YjGPdS+n9kR+uQxGfJLnAza6DkaosfPAiUTsorERA5MuAaBGGfBpPTBgtDnxBCNglM5G163vjdpFb3FD7i5nYtKFMrWpdwDe/jPlNy81FcB0O+Gio+vX8hFrLwY2MhUAOvFnz0fsevqEXcltNjXI8Yu9t0C2O/hs6TE1JqDGQXIeZIc5s86LvYPRmlNGJzefSL2HrjJkcGYA+AQJ3zFUwgZ0w5ysWnTA4cO01bpBgLiC3X0XbMEr9HVqm43bZgkdDx6EaXEm0PUQggxxAvDo59z2zDdSVoBolQBbTeBFACx0ZAiDI2ZdZRIAZeV6BhBXdqKnTjKO64txAmAGm0mdL5DS+uKEB2EpAzASQlqdgMCbVgZuKwVkwfALBmRw2+wAZBDkVZs5Vbbayc0n6uR6GggkiG1BgIG2Z92gU9+2NXSsC2YYKJUFzwY48ISeLEDHRWhT58Qm6cwMvKTUFgwAXVoNzGVciIHNANDXHPqel5z/ABiV2VgN69W0uhcLQW4L/RSds6BY9NYDZw2RAmABBOS0reCNJizQGDPFPQCk1iXXwchAiLqEGrYHBAJgKxmACYt1ElIXhOCPT9gWLzCnvLxjGHidNiMBoKuO0iAGWTfXafBueZLlA81gc769GwjIxzYr6lYFDFPkhfPb+cVuyUDdPJbDggHwIhCjs1HHxLxcOB4cMRpY9gUQUTe7UOBhYMAtBXlUgplN7drX3vG8I4iTW5RsbautSV8eqHc3dN140w/8RLPWXffs//xJcgsP2JgZMDWYYV6XfQ8jMrM4rn2/zk/eo61KXql1AwCCWRrXewQAVAEMA4wZsE62GohhNovT3My61QwM5KPH6vp12+7DQpBWOs9UWSlAfLLngwBeeDMYWAFFL5ANZ2nUoSe2lLaFfPYoocSA6bz2Igbozm6EzcuQyOpW2qbHjKFGrBYWbNTGNnQ47zkfe8onB9riRZtkw5sqYEa2OAiQGy6gO0gcLQ67CjDBaNGZIeopMk0GU1kKM4ilja1fQA0wwC1KhSx9t6RVYYClja0bFHA9wxTMpiC0rWKmY509OxsTbJW3m8FLmSYAYUGEsqq2Hv4+jQz0S0YcAYT9+z2gwOcqlrgv+V3TKmJMMboImwRaixMijW1gIrQtdCDTtuIWnaGO6MQMecyZpW1xr1tdD9uEQ5CYXGUPRUpDUQdFqyFVp6OKjRCjTEFEjemB8dWfvuSMKQcvbJpX1XGd7n7tm+oDDiOpf2V9FlfiI/WS86CaJk8oK/IO5DRRHBFgCnWOhUA6kdQVtxREYDADe1aYOBaiNjHXRJySdL5GirkPEqdORBxjisE5mHclUh/ahJh7OGdqJB4klEhMR9PogjOFweCcKYzItETmEoWxXor/XPtRY+dKHsSUOuIljbQRAejoXRwIbTRdySIngELA6Fg6gY5955UZRNkxs6mxpbKEKWwOWogXBB0DCwJa7Nu0WFIuPVHL3TE7MPbPueTHbvu5K1fI1o017GNTt/WR99zk76WWwpiJcc+++LGPXQ2MzRwmdhTJZMF9id0CQEoE6/2oCMOSALTgLQZaNYFbUo4EdH5qfcdT62Wyzk2dd4i1A4HYkqM85OQticSBg0wa3GLKwYzaZBhkagvk4NBi18pyZgcRL6RORuYWMXaLaMET0KbBnQx/d46LEVuf1sFN49mgG81hGozp+OS36AOMUFLvdvzGSX3FQIhtiNLt+IxiZEYjD7N7oCa2JYMyaYtd0Nf/4LUvOAyFMXLrJ+nNXv7+qx5zBgA8fes1bHTzb3/yWV/ZGFgrSZjxjrcBQxPCDmk2So9G3KbgoUwGKPEcZ26TtOV96oRmP3d3y9zlJi8BozZ5bwyyxow2hQAjKFiNbaJh3TmZEtGOP/2Zju998q+4J6BRDyxgyqQ1dx4gNUGDIImkdVRqygTpCSDAewCmUfjoTe28w/AEoAc63g4sclsQclougdlZj1gQqKWecltyCo//rl+4/f/ZqJQH9o6XAJHedOArzNiItDEhnCkHkTqBTh0DhJyWAtBMC7XoPc99NwgtYTWFIBtzjEDAhA1Ku2JocuQcAJ06D4suKNMcRtBugyobyGVBWkrPkI25uaVQsaAlYJE6AaykwUHjnGsCnRx7rqsEjW2d3VHUdVYmRSBlUOfcUqDVgDY1aJ4qgNaAprDIXj/wzEf+wKve94m43V2NCuhU+yVVhR1HFywWMFO3lFQ7ao76n3re3X9wJPglo0QDtNnhcwdoTC2Px+4BEO+5c0QnUF36Ha9Cq82kQpZ5smprUgFNcZiZ4zZca4DBat/vDrbmZtnwWnnpYjSUqLsjk/UnLAlTWjpotfmNfjHRnDWiJUUAcVpSAy/DycX7mIHW8a/3gLNEDLSOrfWokphUqJaB4DYAzQtW48RikTpZTqV/5Nf/zitegSc/49zuAWc0gnkPqG2gGScvntBMaFjv/zgGMJTUZwywH7/gp9N3nIbKXQegtVBjgnCTex+SFcDWPYmRxNeyAFSFxBNKHQjeo0Fg1FI3AFhoFcq6D4DN2biiCzjWtDsPbluy3E5HVaFiS2CuAJof8gSgmZvVsCMArfRU2pxWlu2+BwAQj8SCmTB8tgIWuw8fXSVrq7xznbaa1VKPrqytSt5qZnmz7rTWoqWNR5tZyzaNZjUVsxedAQC48DU2tWOruRe1aaVmrajFrWa1mI2jZt396mPtzp/HT8a2mee+zf76J194zKxsVrOiVqvlYrqVzMysbBVrRc3MSjWzcTRbTWbzS9JWMzMt1dpW2r6l1nVzLWalmq4m07IezvqPuctdD42rue/jzbVsk1038/bDbQ/LzHQrnsDa+4ZPFCGwkNU51SaBUKqHEwi7QNVcYGDdnJtkZrhmmloIQI7kcXF4MwgbP/UtrG2GeYqv5D0BtThygZCrI+81sbXjq0j1lMvvfo97WC+wRrl6vPUDFz7UqwuMlj3V4oWqBJlfz0K1OAIsmZulec5b1uxIAgGwSEJBAItwQFY3wxJK80jqyDvYGjCwvgUlO6rNBQGQdLtfv34JanZUdmqJeDvFbnFOLGnl9aspuJOBL7FN85ZINLFoIYIV8p48zDbZwXIlnmF+MuPViZzHlvahwFn1HTH1h45+uB16WNg8eLDBsVWwJmEtRESzL+A8AeCgSXfQGOSd9k+77mWHHwzUles88Ofvu+xKV7gx2NfqOoytA1pDYmlZmJgJIO9gFQxU4/Ua2t7NEQDFeM0dmZvZreeugHffolXWC3AminYhRcg7WzPbzXNdiYBivH5Ra0w7EJSTh98lJ+QFHAQtO4YWZgBj7U0hxKkEAsgLtBBpKiwAHJXOwTJblWqHn7A64/ue9bbnffiCs49xoMTCoZllx7UK1TonFYqKbfGSUFSA2rgCmR5y3S+e9YCgJUgzfOzgl58eXF2tXn/DxbkM45vv/PCd59UVhSDgwMiTazov0UQCW6krs1y3ygRYIQLyXNRgJRfsvHr+ppAArVIxB5TclBgovIaVbMU1OmGmMJe1S6xztxVi2ZwVYyvQKtX82jxtj/Gfb8/d8fl1DhUSpJprTG2ICqzqwsqMgdYq0CYzJrBWMfMLNEeOsPxlAR599e98x9cP/aOesABgVYIDhAhaPaoGNHjqCUCDB7RJy12fzn+u/butZw9BYCrdB/1ZA3z/qf+0/OoFbnjrB7/prjfXBxwYtOzgd9bb3du+jtY5Ad2qR1VXS/AYAGR2Vnskv06vzw9Jq47QqhtmTFmYVGB1G+Pd5eqoWFhTSMu17zWvUZebpwFAdbDG7GjnQWj1n81Vug/2/NjRbGYlWS5mdmyzHk1pqsfs06+8y2psMZuNycYbb8tmqbS0yrVs/tUHrOpWTa/9bx81/fsP5biqpsVeEgA8+C3JWlYrycziPc3MLG+Ns0nMa2OampnZ6qjZZPf8+NUvNstjNnv39//0ZDlZ/fonN7P/eM0n1F7xmL83a2Mxs1zKOJvRksxyMYvJzMq2N5InsziZ5WK6ymaWs5lZi2o23z+mXUOfaWlppqyU9ddxtD2kzv+XpOPsdsz3F80rNdPccvocrL0v8qGpkWoRLc2sBeo0KgJM3vbBg62ZQqjVnuw9f/CoZ3pTqludNFv98v1/oQ3L694wLu668do733PuU0/hlsR9IjtrH/rplx+u4ymkqqVRSN5pGheDJYcMhXdFKGt1wTL8hIADP/GhXzz1G1D56Pve+Ml7/urhG42VYMCRoyDc8cl7UEQIGuMwOGSSrMZArD1BYHkUKeI0GwnQ6YQpbNCiToCKZAO0Bao+0qJ03IpBAnKDxX4B5Mn2NeLqYxk6qgXokDzXYrFbWhaKaSGwXKE9tQxkO4XQYnKLBVCnuk/tJOZ3TftTOijCgD4Y0AV0AtDy117xjNOjDbSKMMOnXvvqT1EBkwxkPuy795NbQe5+920/8m9veO7qSY+48a23mlGHKy+vDYt7/v1vfPQAgxmqbs569x5Qg+qyVxiMFs4ACwPUAP3RM37gdbqvq/dc/4Gbj9ZusGbzvkMFSAxmzWDWe6y76Qag77SpAebnFLNqawaoat8BUFUdeqgqLxhm1nU236bzXdYHACYDqUGtCwqYqqqpAWp9mDNQvQdg3WAKqKobCDD0ogCMeu76kxgPyjI35gHgAewByBIoTTdPG7Y2nIEGJuEbb3/gg87vjMzckA2Yzjo8ePy3j37fKTiz3XLGEzf/8Pzz2AFPOfjyFB561htf8Pvf952IjocCGlAKLwEagCUS9+gBhwBQj8YDgFMf98Kfeu6LrsZp37jv9Q/7JgF572Mj8nIqNOceAcNMWauh30ZSeQ/kNb59wAylR5TtrfsQgGzdAnMex0GAIZOfH16n6kroOqAHBohf9wkMawSS5sBYzoE9MCBjedzSApa89ye9/kMJ88bmNoBEAWz91vQ0QReA4JimIxc9ST6NEL2ftyxtNZnhH95bABtvgdz1dx9ONo7NP+a//Oav/JuveeGvn/v8//UfNvqklhMA0+3KkBOTbtTmlof/rH/e2wC0jT7NEQWY8JjHvXfrtn0/fv89eJ0Tkwt7stWj0m5ocv6M4oo936TpRLTNajdAOE97ureY7cQymJNe/1FLX2IPECxxAMBK8P7e1+h3DeW9728H77j76gtfdM43v+u2d1zzSAJaIg8MNXrGoQeeo7xx9mFgGe4FCMjWFabcPfmxL3vVDz/yG6+igM3Se4+0BmPT3gnJusjzF1f93Hf+0K9cU++44wJDtu7oMYw9f9UFr3n3OVdeuYuBbbkHX5JPADoQdyWu1UeygOF/AJAKJ+Seprrc3exPaF7wiWUwJ70+isRYgC6sd4pjDbECtM/unmh5+JxDZ198qDtt8+NT+8hN3JkCUwZw6kEAX3bwVcdQVocByfs7GgYhwpygW3zX73zL25/xYzdDl54AdH6Np6MT8Om6tobhK/6w/HxzpQiBGYsfeo5jcg9+6sUPvOhYQ5kMKRoIe47IIhrTCXg42uECEfdSJ9sL3ui213oCEOSE04T6U9aBSIwAzPZIGPUl7ln+Yayo4+fGM9yXeFCbrEvCZ4S+MpnUFrob2mO6w5deevFDrjj31Mdefs7yrx77LQfuvhGneOcY5dfvfPxBnHvbX176Fzc987JAb33H0y9Gi+QpBs2DAzBcdU169SsXVzmAdRICINLi3qSCOOg2fuXCK9//1iu7m/Y/JFRje8iluQrTGZffD0EIEDISEtHdtRbkaAfIV9LcsgM3FwfE7PYC3oRhEwSkc7rD3InNQCyOlARQiDEDyGl3VUiL65eaCRuETuZ8GNhIEKvbyWY5BodL/uq2b8V25Fn2L/qzv+4Cvf534xUQLlM9/SFndy5ccOGqPfEJHdF7P/qMs0EzeRA3UUuODj326kOv/a8fe1TXIpc1UHCdFNrN0h2pPnff777rtHTLly6URAnGro7NKQVCa45EaG9CI1aHinXlzYzdwfpim4Hm9habWlQHcE1zFVA8sRYM61KdeVZFaE6GGAmhRl5XsZpQSUIgx5+zFue+zgcLicw0IG2nzWr1bgjuVMrOIsuE3PZdOjS3+Z4zr5r17uWXce/S8oL9jzhz8vTKf/zfLutz7hkkkTzARBxzOPdR9//Yi984XXTAU24eU/O7FjQApCoRAovNATjnjF95Oz/y4UGEhEhDbpSdl3pEA4RScYSSjy9HY7FRA81rmIWQiltjr0goFoknVt4SmEkY66QahI/P3YwxdYBgmqchFb/DJMDIzV+QI4CEdj94EvGJkws6q5GmHhOFGGAe4+3p8AY7u9cNzal6VJJ82/I0m1xYwxireWCKfOTm/VcATR0Burl2KDHnuVZvue6Vi+d8nW9Ze800EKDzlm5qPdfSXOMBZcak53c95+ivPdlhevdN77nwew9UkpKb72a0dzUPxLQxr9GaegFsS8Jcqz5RD9SiC4JG7+ezBmp2LgV3vDTDEgeNLgDIdaCceOC2SwXeyxs2ia+Oc+255TZIKT2n1jOAEYFj0NqvAZul9m6m4yTmE20iD2KGTQgA1eKcCOA2NrpmjlxgIRaAGXJgUSbneF3iOCcWPZeLz91eoFnq9poUho5E93/CQz/8S3/5qDM8izi2j64OgIR1JGEhdtwJM4TrxAy5YOuNx742vOOF1z3yQTe86ooDDJmol1CKX7+t1cBoE8m8ZpEoEKc8jwDsLE5zGZmNHEhS60gI7KhERwAmCyBHsKkGAdgJsRBQovC6O4gIgZiptOCISGi+B2hwJMRCMXugVe9oTcdJnI/iLHacsmNhgG2a63CIXWBhcM4zg8fqATBVkjZxzTKpm8sM9zmyyaSNLMJZPDA1Xk3kwK5u4sLHX7n52+8/93RGKS44eOESgxPB1DyP5GGTUvS1+GL/+JebV779vf/HtRff8OJrLgTge9m2s3ViFs+UUnCp9IQcnXciRMJgbhPXPPCMAAKRMOA8y9Q8j+aEY3Mo7Eli9UTerUuHc5LYPAuV6LxnSM4eKMUTOU8gIbBgMpuCY1nPn2ZHJIHQsvA81zaemLC6L/FHSV2wDmjVCotOHhIYNfW1LSBlBajqoiSQ9zX1LaI5cCe59oGgozaxnGFtAe6i62eVWanrjYFc/CG1g1//hBf/7mu++QfOC0LqAmFSX4hBIY1Dx7n0gWkfK/7pN19/U3vxVR+/8f3nnEGHgla3sgWtsMS9WOoWdXlyCzjL7A0Yza+sp5UusRoYHCIHONRNG2nfwqcVgB5RbBy6pANCWg0LqiM6Ww0ub/HCl3sBFyjE1E/O+bF3bdSOV720qjmHfqoABg8KWTvieu+cWnYtW0xBYvIdT3MBNHV0EuyHttQhDzyVDYNYYyq589bEkg6sagRArIGErK3/AKC5DgJUI+amZJRogQbRLT8ACoudg27KgiYvROXGN72k/cjTxWfyQCOeUTJqFJ1TiSksAIyffN0dV/gXXf6A33z41a/52MsvNWrm0MyhklhjtkZCsJpcDzTiakLNBCqU6mLerFC1Bi/QRgBTE6hAjaYgKhN3zRyakDYSsmYQm3o2VmK0SfrtZmNVlqZk6wGbANaMYCRkum5mwYlFJv8sfUUiLMIkfsZfEokIEY3ohIlYONeOSCiSEBMJRwgAEscEsHAbnWdhJwwuMz4RRCRCIN+1yfuSnDvtkV+a/uCl7dJhbI6Y1ttExMTCTOw9A1kO3/6ew0/9yB+d+h+e8MC6esxh0pjZUYQTnrRjIs2OQCJu5nX0QhThmcCOOWUZzbM4x7ZCYE7N86QBIIYwMyIFFiLGqB3TVDoRIifMxARwso6FCJN5G53X0TsWnpVRsNEcC7PQaA4Tr2+R9QahrU7UV/fJfmiEY0LO215GjcIgEWYCYJTnA2OECbZSB5FtViJPwjHN9TjEMGJHebbnM86Y08oGZkThdujRT9r6xT+834PWKGuk5ChmThCAxUZmYtx8+8GrHj29dnjcb3/ol85xIMnsIY5gc01mqZ63z3IASGLza4KIAdap89tNQkDUbjtCICaA3PFmxryrvBsSnTlsR2HkJOVeCG2EzEcCiOQovO5bJMfeETmOxR9/4z/fnkfyOsI7mXH5OXeC7fWLtuIQGAbisXkSV0cvgI3qALDnOElPgK7MtRU71iJ+2/YD4DwNpfZOYhE689GPP/biD1x0iHPyRuwEYjH4HIVBTmLp6B8+csYV+y667cV/9aTvOtsBxEUweTZduRkHuWCK0VFMAWMJnJgmX1MwStERaelknbRkmn3u0cmeeHCNaOQSPaU2MKV43N/NFAADMYGYGFkY7ITq6KSuCgfHAIEpx8BCmYWYZP38Z2zY3rf5qM5BhHnm8aQLNza/XTZBXnJxFIuHcwQm5mgO5ISMQCDpOoKBnSPyQnUaAgHiyAgwojA4ccTEzjHcuU+89m+e/7fnnNPbiiw5QLwj4YmlRfGe7JbbT78s7L/2fi97yFcBiFEqe89TDZ4JRoLsSDyDPUEcwTv2LE7HuYyDg2Be0LZSBxSsH1yPh6SUgKl6QDybeCGIZxjmWQqegJg9AbDResdkYDIKTOSDI8bMHPYEuDkZs10CRyfn/BLvyCIJyDkCJDCcB0AlCoOIxDGco/VrSZwjGFMZHecowgSk7JlARCDPRDCmtmIpo+NaHNMc6xJyWp7z5ef9+UtWD94IQo7HlQWAyAuRZyas/v4jhy6XsjzwwXcOD4MVDd4RkfNEhDKKOM8gwvY/i80TEbETWhc6gNgJrUfjtx9ktJHEwG49kSDSEX7NzpQ9zWqHAOcYBiLniAglCqcU5ohkR+MR0dQ8baOHDVTHzwCa3Df7sTJHfnbZzWgeaBuFOTDM6HiREMxAZkxoKxb2AvFsIF2DeaAgwmRORwh7IQkMEl7jfXSkzpn1l3+d++O3bBxYUHSuC6Soq8JMRAD8zbed/RBRf/Ab3v+2K88ouoEt89vgWPZMOwni+cSyHV1B21WIkzkQQFhLxfpBgL1QG5kxrywFkRcYwYwgnuA8zYufCJiqn7uBeN7BE9nxfgHnSEF1dPNckz9J+iqz3x5OnRwDClAnIAJylqhia2Fso3CdHBvWzWY0VcTt6HVkAYkAXgg0j7QmR2YEmHg2rBK5jUd/h/7U78uFByg1h0l9H1LzUBDo1o+EKwZH9daHffwFFz2g03aUesNUPRREhDQ5NqNtUrGqAXsnSAgzW2MJWBVvICKKxROBA8XiCWaYmodRicQ5OYLNs+QEBJjBexhSEoLx8dlelTD7IWoEojKxSFjPNdHJ0VeWjyfdJDCsRKl57YY4z+xadLn4GZxn1AE5rddLiRK0Lty6mCAIrEWyuK7Iq5NjFqaUPMXqaapegqujG674xs3fec/pB07hSVxpwYJDG80BH/ib/lGd3fMnv/zue971Z+dfkrIsMTnvyOZsQKuBU3IECTwXE20Tn5MjtRl8GByUnCdU5mmd1ZkpXtGCgJxccKQjOonUeUZaD3hcmSfUyTHpyB2vR67reolCAXCBEEuAxrJwa3klOnn5kkyOADUyI4LmEpwLBJiSGSM2P8P71IgwVreyPsyLiCQwichaUDwBLXrvPO80o0THLhBEGN7blDiEtKLTvvwZn/yld7lzTqmr0LctEY19B+BTxy65yvEf//Tzfmr/O/SdG4/uC3eBVyWQ95jLrdgFghpDzSbXzUUqDBcIKQcRghK1SYQAEfEy1yZAQcA8f84zESiwiXcgwHlSEFD8kqDUMcCdGAV2zmg91xj9sBZEH4CIJQPQtWTOZxqdBHxizuwUJWFUD6xqKExKqiW73JxKyYFgTbc0AKWxikNV1C1HRk1j8oSyRb1TUjAnctQUusWk3LS0wNpUU2GyZi4wmHtM7pQnPO5NL7rhtH6/Z6tm5Byh3PJn76Sz9/s73n7v/W7q/+Ot//CIQ0qiXE2YtNUtZvUGappKwFbtXDFpqiWDCFVdqBFStlSkm9+qnpqWBKa2RawcuKkqGE1VNdZA2lSJSDchSsFb01i9EppqKp40Th7cU0tZOmdN5wFbUxFjaJxcmeMPG3Ey4kFrfW+ROokaHKCFFi5nlyZZsvc2ZfOOUKeM4ACrtvDQMTsxXzJSMucJVquz7JIhDx46RcB8LRKTuUB5KqX3SepUS8mQhCBR5fA3XfCuX3vdeec5DpsjVBj3vv9Pr7t5etD+8x/3sufW5195/mtedNUFoU7oKDvKUyUfAkflKYUBaMxRvE25uC6T6JgFefA1QtkBeSrVBbY48ZDhoE7nXkqGR4y15DAAMZYmDFNnyRF0ymGwSDbmEgZCSt6n5m1yIQm3MVd1gVCnXLN6ylG6NcbkM/HU9+33JnadX6D6WZLHnz0902b864J2ntmugph3OMvy8xyhMBdL9QD+8idv+u5nPwhQakJq8pevv+jb+zre8I9vf/vBFz301b8gL3z4zmk3x89N2B3Mfr4DRNbnAX2+xbh3wCec5XAiPz5npuok5tt1y/w2Trwmx9p2GyerXE784Y6mDOTqCOIb1e1ESymOmiJVYkB8I9LKlCa/5wAYskYtqqvkGJge+C13vv6NRw+cKi0x1yr/9Pd29eD/5Dt+5PvPfO2BB1/xiLfc8sBTddfCy+Pu7tZZ9T14GdtVE9i8a3tNbdvdjhbr3rGtWliPD0A1S7yH+Gh+TyqWm/HJng+ok3XhAyQwSvZ7IEwadm9BV6Uaze84LLH67TQzCVMpQaq6StQ22bUsbOSotZ1DSpK06pLvEQs7QMvyyU878vuviWedGrhRoLfdfvWDmO/80FA/cuQpl7gzr/m5t155Gm1zCKjteLlTVUbck8OrjdJOkVJtSKJ5D8NtM8quLzKGvfOVKayX2rzVv2ezyWLYI4wla/m8GN37hi/pqAmOn8cjoe4ikUMt6xEWYyA3l4OvTNBC1Fpf83Y6Lo6BXbBNt5hrRbxaz/M+Wz1eztLE156UuOfKVQLqgcd/2c2/97YzLpA2dnjnLZddHHDOg95188aXPLlT3qgve+83LJL6HfjF8dWSVGrHu8p7kJsn4R1SQ1A6AbBgXU879QOAUN5TZJYoAM6jgkHetT3FHdslH8fBMbkLJ1tfteJqc7t+2qGlskcHeFtzM5kDnNROSg2AJU+tSEDd5hA7AsjmchLyXJojpDHwLEtWwLAEVE9MBQYR1lRIzn7aldf/+UenwwdRbv9Q/JIe7vwnP/FRV3QRotec/Y83PHyflPUKkF3C671m0bU2LcaA80gk26R6WtdH7UkOzaswOwaQa9h7aL/OB9Wti4+q9Sdqw+rWK7EygQKfdPvBvrhgmQVArQJUXew1Wtuh1DyUloXFVy3Wqzk/pxrmqvVA2VCDu/v6ezc/esv+jkiOH05bGhUSkHcsL3vL9Tfcf+D8zvcuDmZxVvnCZ573+l+64fQL5EOfPP8KrR6Z0NhTbO6Kg79590UHk5+3Rk8kvm3vyq1LcOZquePSzoy8W8evLzg0FeAzzpteP0heamUqbQdvM9f6wHuaWdCqm8uMWuGTvH9ed37aoag7zt8TRgCgFqH52Mabf/WP3jFdWJvfKd8CNnOPAh0D/cUv3Hzdb33w2gOtOgKIqRahosELNDONH3/TjTfecdWBd7/8zhv/fvUQJVRHuPhZp7zvtfd2dx45/9KmHciYkQovCGef+vzbHnWQsvrA2KMwACsQy+A1J4vKcXJLE6xqh90aySoEyE0sm5tv2bt7bbz+tlU/pw5bEaqzDqjVZH1ypXhCUw9o/dz1avfxvHCGFnGafQcgk8vO1r9ZkBGs5eCKuPVRDWilo9vf53t46eqcZZ4Dl3fgqzRwG2o+4xmHy/s+xvAeqePV4EzW5yHBmg4fffFVP3wIubz2ra9bPuf5Dz/FB5ecAM959h//0Z88iu+kffTRX7/nrH05fPVlpKNsfNPqV5//gkWTVgLXuCE7eR4HcjV5pZlUQGsFbZsB1TmZMdQUCLV53obT6Qy2B6yY59oCoZXAACbeWB/y4z1QC3tWtW2YrzTVssMccItenDu5eGrY6BekApqx3FYL7aDGDaCh6HydpE9OzAhv+LUnPfFJi5pulAfh+ulyrwDw6coMkI107bWAf0Oor2pfr28+8vDzIDdfPy3rannOBactNrH1zve++anPDH9z62UNG3e//GsP16JSWkeL737ar/7Wke+Ly3hrdP5D1z9p6RNW3TB8f/vdX3reUGBc0/EQS7k2P5blzFqdUcKR5vQ3LLluxuKvs0+2PlJjCfTQ7GWGD6+X2e5PB0tzPUFu+3hXRcGq73VmRrYOsEbYnsiT6O8mx6XnWnsu1UGVmJ1DAk2l85qF4JzMpxM2YfbZ0rEjL33TvvPs9ne8559u8udvhPz+t9xw3VjfdvRg39zCGj40fuW59utv/ObF7133xFNy3rrHFtL27du/QJbFAx+/9drbLrnxAxdf4979F/LkQ2oLVnOU677HXfjxv76OTrv8qU97Qvj0z58HR9Y74BH/9PPpwfu020w+OILFUtR5UXXSBwJaZu80cat9Y0bqHNBIABYBhJOQmUepnIWztMqVtQoa9QTxkRgq1DKzQ2at3MiKgwTnCYhgIAFJPJNncYQKB3AwZjShmnkuwpZ//nzU5EOJjmP2JYtDRYtegFYqINxWJVWfUs21c+S4xDzJBV/1tWe/5APP2jj8hhdc8tWPGKZc7767/tX40GP7T5/PEMZv3Pl15pzsu9+nTn1C2eq23n/09luH889A1pr3P+gBT/jIC594yw1XP4TfeeQrr/DUxeQCoWHz7W+8NeIN7xgfyvi7dzzx0JZxLiSpXhxfGK4O0739QplKnNF3CSE2wZRLZSGg5cbOtZhjreq8xlrUIWaiWgi1EEzEo+XRes9xZSW4KddcSGqCy5mlgVsZ2+Akja0w1VJyJeGWtBXupcZca6niKeZCunIW2UNnVHY74ajD+6SviFT92uJ1Hug0LhxAfdEOgCyUHBERKKrrCESLAOBpb3hngpx5v6+52FZEGw9/OO7AVwAa53OpjzgC3OodHz90FTB0qlVbyVWYFuZQ3TWfOk1e/7qnuk+Frz4EapOUyH1AdDd98Et/9uZX//Jff+/Nn/j5MwszD4VBetH/fcF/Xf6kPzUYCDhed8G6c7ZNaV1mDxjxwmzeVptxDiSLBCcZHqjqh0QeQKB5W4cgHZrrQD6ASIZEDkAg3TnqzwDqtHUAsVKuA81vlg1R0jHMW1Sfmbm5T/VqQyYRoPPcoeZOeA2/XSfJOpQ2n6BUynrkSRzwNZcfwBgPv3/fab5DLp17TAPAC2Tgro889BIIzjvzY6dfeco9+z0u/F4cR8i+553fsLr9+x/gr3vdDecfvvJ+3hCHXhMj2f7Hb8olD3zUN73+HT/1vqc/F8qxDFzRofQ/kf6k/zGg7lAGdFBT42F7YaFDzf1se3XsvEdU4z4p0K1/oMGieHRAS/Ox6NvprbD9gwsAuvnHTmSnOc2/keIwOcYCofnoGAvA2qzZt8N3CSclvzsXNTRHMAhBI7fsKBWP2Bxga+kR7wjQsbg//4WbNx72kBt+7VNXH37xgS8JI5OpnHnWXDm/In/HK698nI35rP9O25uG23aVZaLv14wx11p7ny7JOen7PoG0EAjSN/bcUmwK9do8WnXLpureH1JqqVXqU1r6UGKVqFgiRLkoSo+giDRBBET6LiZAgNAkJCSkO3uvOedov/tjzLX32ic094mnzo9zzlpjzTnHmKP/xtsMr/+R87fSIve5BRXHrCj8wOdnOHy1xxmPsfGCJx1ZmpAP5gsjG3/xvnOv9vWip37hg5+9/YwjVjkVUcByefRnX5jOPpBGx402YCMElcRG5hyEeFJ/oUmDTwhWR/O7BJMG8nY2QmDCAOJwTDxxOdmJTNc0poeuTtdYYUIsjSRDKZASoNweTfXYle/Dq4+eMSoZGu4YMYiAFEYCI4y8ioEOpRFc2Ac+9+xDPsZLrrn0pKs3HvSuVEqijTYQxc1OOXWm3n/ijidevJj5CJ5iXMZilk9/3MZ552qPA6fsX5x9qBcvQpXJRJX4PTefcaWvFsvjLvvbV9572UHt1Q/MLLZ45H1/cuEVlD0BZCxkzKQFYhKia+j/kOeTPC0pjclpgYx+PYYVyMOYSTkGJUux43XawIS/mpJDdI3p0Y50rbJOxizMSohpEYt+VWGFf0G8vW55n4p3k+MJSiprxgk1q1WH0eZIcEB6SAwhpA3K5hILkOAmvkG+9feve+zGGQDQQhOjtUhSbid0lhqPqRaHuALwJ9PX3HjNs2cmW/efxTe///89+rRfmaNmDZgDuPeGN/6HZx3FQss4kxzmDNhR3oeWs1IcZXPAim+Q4JCJWgEwURJ2NZFy9UAtSqW4db7BlNVSHOVknZTiVj+JO9yr0eZArZIJx5tvAHWixAyavAukMbDG6ACQtKjBDmVIj4V9qW+pMTmIAOpy4ATkCx95sOG1J/MlwZAdQhtkSThEIZTEvAvZJ/7iFw89sgu528846eqrwt+8PlzcCZHYSLy46MV/deq1FKuSEhpMXT03itpQO8JkU0TMeWAnADM1ssSYHCBscScgy2JDdRN4vWodTBqYpDEbWDCggxALDbXDUBXCMUxZZcFQ/UTtSUEIeeDjgvdBhEwyOJMn1u4jV2cMa6LVLdWGVUfd+c/q8ghhQZpfc0YbOJgpBCUWgISxy49qwP32voai1ptj+tg/yvVztcxKw20XP/3C97z2b8oVnAyjaHaPf8dbv+n0mjsZiuMBK/sL7Dp5gYRJGA+hZQhD+JjzktUHgnD7sGqRE5dqBxrLU2NdqRWxrJ5IQtPDHkoEefh8nNVsN0zAsdyzCjBk11g6K3Y3M2oPmco1ZAdKya3cOWzIDj11PLAn7oui6V+t6CzMZXB1NVxP1dFux0wsDNx+z5lXd7HM3O88/4QLvJz31Kd85A/e86iTVZwS6SlPue+PzrtQqdWsF6BfNYfd6gDQZy8E1J7LBAZdMTCn/lF6EtCKuQFJ0bULd5pZdhCeOB3MU2sbSkcIYc8td0tyvPCJjmrfDiJJZMhOhNBQbCxMJGVsFJUJ28aSRpXWkBisFji1GZNI69B1VEd2WDbDmPamCUNy6JPn0TxNxJXcM6fBOWplYwbwmdtOeoTG+f3/rvzI5YcF2H/2U6+4+UV3XbpZKEWPQ2d/6k/PvmiQaEpCKINYmnhBKwBSjA6kbL0pOJRuGl7jxI+CB/rkW8sf0oyH7NBQY00gQAlpEBa2oWLQteNI69ExdhB+faGBczjOfE7YaLrqa8TEJfmQ/Y4jjQU4Fp44ajRkidAp98zAUGciLCuDPhJPIOcI4lNwhDydT7AyWJnFrZamIBFi8Q2nmXtmAB/9wL7rOv30q856wrmHBSHS3Qeuesr5r33+rY/ZKDwKnXjmO1/ZPZZ4WkVxQtdGlYbgJh6pYzCDWIk4YkZAGpint5jYAazcOASYaeuWq7au3jX8ujCIhdt8MnUJ4lwdwNxaFwvzTsmPZ32M5JjGIGNRgEt0IgwM0aPPjpiZibn0lIMS11EdMzAGR6tcETHQN/gr9aija0wSG5Vz9AzYklyr3rFOK4I+OybkIKIMjGEuBNinv3DCRfvpvb9Un/6Pz6ELfPAztvnlj+eX/uWd5x72PNbTn/aGL3z7nNtQQq16p64MjGkmjhtBgGnn7IZEiJj67Mjp1Bsxjk7alJ+XLKhL06n7DJPpHYfUNU4FKxPS4JwwMI5KrAzOoSMqwzR4fBW+2sM6H1yWeUfozQWt0WMcLTnNvWSTXrraxzRm4Ri6VGeCNBYTKT2XogM6LGMak3LeHp23nstW8k6Exz6GkTsZlzwbKQdJozn0hZZRnfVDHKPzdTkGuEiu9EPiOYWtez/8h2/80D2XHnrnW//vJ5538Hkbj0pfXMwJfPDy777uFb979+XzQN2Bx73vTx5xogkk9SE6gfVDyCpclgN3xJSWOZMC4zKGCEXfxyIcB8ngXiUvx2AOSCFlltJTXVYvafR1mVW0LgftsCTbHgN3jLGHD8WjN4pO6vYYI3XEdXsMNGOEpXVt8P4q/I+Ho0dWc65mVqoVq8Ws5Jyr1Vxrrbm2z7laLVaKrSeXWtaSV9/mtDVOP8vFrKRxO9ZarORiVkrNqaxflIvlMv3HagoP/tfznvam0V524d+b3XT2860MTTLMzO54zr7r3rI0M3v1mWe/3dLRXFLKddyqOadcbdyKaXjgaK4l51xq3VqmnHKpVnJOW0PNtZS681Rr/9aaa82lWi1WmxhpztUs19qyaCW3kpdaS7to5+pq1WouX/vdPiy+GvOYHIgm3DcxNzIKUWMUcfti4husJ9Na8upbJieg1dcgFlEiTPci4rHq2kVMZSShnR939wxP+K5Fdfs+5E/+3G1Pvpi0rwoQjPY98Um3vejNs3NduOTCvylXHtSeKThmh4E4yFg3ZMTChx6eOY7e5arBYVRmZlViGorjZXHMTNaePkbPRNwKR8zNfoaangEzxUGEp/dCRDBM5Wp5zz3L17GbeHh+XmOn4DURdNC6UH9Z82P5qsmdxV3VG0MZ53mPRk5Mcx5z+0mPxbGIszR2qzCDAaC3v+msH1nEbuvNd+KkJx7xsG2dw5AGLMjil3/nFRf+3hWKj/zU1c+bb2sHLGnDttzM0EuXROPRTd+A9wwzrg9YlzbrtttHDZ5cl7wgIKQm/FNN9roSLEO3VtihLNagNinMU13siUzMmY43nkE0wAFDcas8cL8Wx2flldGwgYAxybA2bbEK7/LBrC/ekeyRDCFlkukITR01AZE1RIKGKSxde1iij9x05Iq5Vrv46qsecYIApEqlh+9cMO8PPeWsv3x5d97GKe6Fb3vGARNQDMV3jqyfh5tv3a///HcfoxMad6gyYXjxqx/48uHunmFuiXvSvJxRdARxrR7Gwv0evE/UBe2QpaBuHZzF7pjVlDgGmR3f9a7BiRFUJwC4SiPn7J6PhGnD1xcHqMLtUdihGJUm8wtyShj2hv1T1BWDpRKBjtFfIV5hQcgJK3/6yyeftwlSm3cKI9gAbZEPJ2mQ7oofOevPX9af+bjtV93y+BPiqB1VT2bs7n7f1mP2f+j++X+/85rOVSPrk9oX34WL68mH+JM3zQ/DCUp2nWvMo6G4Cf6+nh/nCRjjRGmjss55Ippa7crpg+qSZeKhHLf6yKOmNn80hgXF4PZiWFft3TkAlIeHJPMOO4boIasMcavlexmgwDH9w4yrERq/hQi3fmLfdV2IXf3Mp+6hmbTbEcXRUSgLEG1e9f2zX3/e2c++4OVnXDh3bOoJY3R4/hd+cH84fPGpn7/6yc766sht1wdeEJ90+WPm2Lz3v+H6UXmMGzoNTzStj/1eOGlzIvWT+3hFJ3t8VtpZeumFzUBgL5Cvg8F6OOdRTknMKhNoA1aZuu6YcIrMGsamGTMcKxgYMCtMTmmCOtdxr2qaldHPmjncJmB1vrd7p2Ej1wWG1anS+MAS8Bxe/Zd3nPOLp8DK6DoAna/sDYN44o0fveqXf/utFz3h5z/8KydgWxbAPKZ7bzyyiQXCF04/m633HqAT6nb/kTds/sZTPU6595Y4MyOmCgYq2Eae46Fg61UyAhZArAsgxUlkzqqYMQDdJKQ4l2YE+HVmkIfnd1eNbMywYs3EAcVgkwxbLdjw46QTmIYKWFlLBuB9GTJALbkWmrmdVCuG2M89CAijlYraxzVzh2IgLn4BbKzezL5TDhEiPveCs172imuBMjhnxWqpQ8kjbdLR7TKkq//mbzbfec7GC/57wr4OALzettxANXz+d573so/XTQ+g1LLxO2//vY3/9C7AHb79YzSm2SYtxyb+RhtzADXnvKc0ywFAGAyLBQDvssFvNl0G5CGOwYrVQoDfFOQ+7bn4OOLbWag2MlxB3WYpo7BVRoxKsW7wTmQdpR9Z68BiDYkcqptGKPWMGKUHgpIVBvKoXCYAtPM2QtkP1QENFl5GYfE7AOgMM3z61kNXdWqfveV97zp4AYN9bxQk5s6zeIJS9l6B/d9+7Yc/fffnaX77nbOFGQ03vuPyb0ngQ992+ks/8Z0eVmiA75guuOTPrrkK4e9vOfXaTmptgGnnpszHIWWROsgK1R/IA85PVKc0VOVaecqqC+gwco5KxRggBJYcjjMerkG5nWITteoER9RNlFi8dh0aRtKKFggyy6w3yCZqLB1B0GFy2CgQZNdVM+dQorHRamwrkELMG6iT9HoqnRboZq5MM65VrBAHx9D4QPaouO5lD/76L+27flZEWXVtXBFHgFXBpb/4rBve9JyDD5z/Mz90wLrwpbSAT9ubswOPu3aziMVZx6j3lcPdt54DpC9e+8yoyHnmqFathrETk8n6QzZzreOCalUlK4KK4NQE3lVGiU5ZN3OlshjjfAPaAbHMmUrZJCjxikXyEP+Ph7W+ikmldjqOroxViS1UL7ASeB5ILJdhFK4hWawOI2xbOgbyWDsNWfMyqailUkN1GBM3vYzROloWbwW1eM7BQiFGDlUSO4BqslidhcS2DSTpe3GeSrrvn7f3HdyftmfoDqe7zjphgChynf6U2naOeasq+dO+Y/9fjbj/ltMv7e5bPP11D/yA3f7xL9zxzm/54fjg2+46R0aSL77kK37xvRdV3PPHFz+7S4G76l0JNuSZl6GXWkGlFKOQtKvIwTpfQ232az1VykulyokEGEtJ4qXlhZ31zqpKyTmqhay0Y1/xL+wfNaorcU4GS9oBkfYFBiyoywuCBSOJkmgxeFfLnJJ3DFhUHWmOGohH4jqC1AGLmDwMwCLGmWNY8ARkmY/zHBWpzkgtKxLNR+9Ai5Bmnp0zmTlCHpa3vebGg1/5mZOMYIefUfdjPtQ5hRWA0GhGcUZgV7IHMADAA//07Rvp3o3rtm87Re/52AU/fcoY5EWzR564UWI48VP7nr6BurztUU9UxK25RPLsonkAWgKs86FAFouQOKrXQVAXQ/UEaA6YS8d50A1CLbNUNoAyGsFYiB3H0UkKfhPDJJm8cTz25yuOVkMVNcRoGxEnb/BMnJVqcUAOncLGvajwSZ20UcNKlbAX9RLCRsJsZzMyt4D1JVad9qExtX3xX7z63O+7Yvbgh+876+R4ZJMsm8jXZJC993lvfhA47Uf/zXm498A/fez7DrcVUrr7gweu9+2MO6VFtrtuvvgMoqJkKXmKM0bNbddgx7gS5GgLAixP6qMrsHQreV5tlBMLkjCScC07G6rEcrzm82lgbn4ssZ0GiCeUzBFIwrvY9nYQloyBXGSiRKzW5ik7Ekvc+BFonlBeMf1WPLZ5FZBocP3YRKtWm5xb7778m2c4+s6/p4tPWxAsZKG0tkeIg+OcmXIR4IxnnnT++OWDn70l7T+VN07dP0ujpULjp668rDKpZt4uixRjPem0HFyC1CiqjoDaqAs5mOxmFcA2bdAu/6OELAxLYPYMUCQ04kGAWiDELFyi1IaSt3DsAPXw8CXbbr5Ce+Qwk5JYGZPlR8yzvSjIBN7q5hMWZbRZElQllOwYNamgHvU+zjjmWfPGCKEpSo/WZVbgqGxMgJCY54SasuPqKFcPFJO/ffslz95YdTlkc5kszCpcc/jgMWxKzHMKdSI+3fibX/6P991w4Ce+dwNIRJGrMfmcFkgJXSEOXcz7UpQus0wGgzv4kjF3Srsjw95kR8t8AEAdvdbkuCZo2dGyLB4xtdPD0ebHcf8BM1huuwLdEFjOBqB94xeUh3XJ81Jo7gCadwBmc8tW07SVaH/xTHXB8Asqu8LNNdTZHNlQmwJrKe3eQC1zb3nysKvFeHlfHrcygBqBmmuuuiHtVlYM6gl+Qc36GLXfeuoLr/nr73zNST/3b/8ByIVpyR18onmshRdCkIWIr9nPLNU9cu81G2bzZC0fJVTskYO3DLiuhgxeWLJisJTMr2KnNVf4Ra0AMJsfx/hu0y/Z80XaO2THMqOvk3zMZJT3ChA3gdY6djKR4Wb8NfMhCvzV6y75d84WyWelRApE1q8NjPEAcPR7429e/yevG574pCegrzxDdkG4KbsHdA8pbHvQ+h0A5KYaG8jveR8NAzpSd+zvp0oROe58Z1TmGsE1rCLhaS+Q6FjCVNq7zE55Dwe1HINCIlJKZc477Lj6tYqQkin++fazr9r0JZfupr89simY2E05fRVifDaOxHAXvvLVT/6WH9DXvfKTR87yiNnESF002cW67rZY4rV5N++isVpUzpj3lK8Rx3Y4N810aqfANQkf//ooJJaFbfJhynlPE7ZoAiBHppSEUOIaHi9Hpmp7XlXdG7+N1hHWFYfXFiElEpdGnYhVyMEUn7v79EslO8c3/9KfPvsUlNiwkmVaxcRdgpkF9WXpBHTmxTf93Ted8MjvXL75jVtnHiKaUYa013osgd+W1ZMTTI3vIeSmZZmS0dacupbV1e9rUWop7L7+DPHw4lcAeK7glT3xMZYaFkb7Rtdjx0HESp/2NuJln/2cxvZtHT3t3s4AEEKYyEt+BsSvfKUYo98e6yEGQBZHA9xqys1hLf4FmW8vYeNTf/nBX7oJJ/znV33/W3/8V27zGJ2MmPsmqmbHdNf1QqblWGP8KsktQwQbE4AQm2P9WMpYgzV/HCDHGiKAGI5jfeS+EOqQd0ndXSyY/GsB0GxG1Ozc3YwQ8izmHV8TnfGOkcskiL7QPfYufsaTrtx6BbZkmQvQmBozDxsigFCEdRzzaw99NxcAtisrFUcDpd6AFsGcOdAsBxDhsb/w2p96H3Duc/7gmt/6nldgloONBahD/FpvqjU++hpvjGcOsBFu5f4icwWIxpFWxQKQ+m8wXz8s/w+GraQY42hgKq1ymOuQAAstV3XMK4hhmrCSQ2xtaArLd6XPKKO3sSFqWpVVmUscbFZHYBx5FmvXsJerKut5miy5qdx6rXLXP5x9qtN9CEQDOgLSYGgSSQsGaPUeS7//QBkc/DP/7Naf+wyQz/2tVzzphh994XJRBgNIZhszQvPoqEOaFpNjWjWoyjP2vvYZsCGvJWMMIILJwqGZowC59851PH0YK/yCO5/74rvjOH/UDGXSVCgQSJFB0UsJbFWrMLCEq0KovWibAZueD9EAZUDEFCGpxaomnHtHEGRgNBEbUQfHBhmLCiphhDKQQWNRsRHc2GBcoqrU+MAb/jqddwr95S/e84HXf/L2C45wJuE6QsAjdRi4U0LMXawChCKWuQ6uFn/5o/7p3U+fF8El337au2541wmPcGkkzlKihCqQmNUkRxFlLNmBamqSdCOVIEqgmqqCHdM2OaDmKiqsFIaqsWjDjakA42AKxOCZBWNVSMyKoerxOq+d56QwYogKYNxIDkIkGrOS5jIjgDRWBSxnn7JSTVnnDGCEG4hIElSVQZLEA8bcLMJVVYiVzDtABFZJAMtR5gKylHXGLfKmQErDG26sjz6L+exzT/vK7d/2mE2tlQWWIilopSwPYsTi0JeZEovTIfly3qGXv/vSU4IQzv3my2/+kzufNM/JQwiCEqBgSkwkwnn0VhQiObITGFM15jx2kpMo51GRlaSOXXO4AEVTIbBlpRgEQGTOxcWsBEIWsDS/juNRH6x9cTSoIxmrAqk6IZBQqgpjDE6p6VETCyACAQmExTWUvjJYBeYVNhanPTWVgEQMkpg7QoiqnAdhkA7mARHqQlYIWxUCyWgdAFL7zPZTnnWwO+Mxj776rvf9j3NNdEmOhElExahLQ1HKRUWoqWkma/jTiLM3nn/SFaojZH7ZM8758IvvuPQkiqN4ilAWFRirYKxCnkkAVkhITpgVzEYsAhmrohMSgJwQmAaaKbzCkgmEwCJOIcSqEPROrTXjr7oReXjrXXidsPPMgAn6CRwrEAGJWLMnaY8kHthNiHthwJc44ymoRRBuEE1jnnx8WuCLCY2wgWYaRhNjjNUCZJqtqmO9L136uFlIOtqRbzqjc4C6MkgTumVpvH2jHQMMDEQjqQDsL7nkZfc8nRCLQ3flY/R/veL+axbbR8Uh04xWyPcBnRBLGZipvXAISaOgkNBgXbs3WAipKk0FIWOVAcjtdyAhKaNr5hPJHb/5oyzzypan/VXGBiDhCfE+lpXqUAiOxqi8Bu0nITDvcECE0d6v8IooUdtA25trvhArNZSJLlKS6oTmJ2HwJz5x4pUaPROfeMGCGBYha8QKtuJ5nWiR2LXXw7G7/LOvuOv6mTCj2oFrr918y0vuu+xkGtWtbfBS23wTtSmRBhVeY7NMfLUJ708lNOmtEJwwjIT2sArUN1+fr7UrfFj4RHJCdUIhpUEYtHfXSSI8ZY8FkDWFqSlMq3tgSbx3g86eKQRdocj3+EfZUJRXjnWtTXzqS6eet08QfF3mjgH05GUvCGrvfhNdY3qQgq+5/fduu/hkbmpeZz7+Ud2fvFyuc7I+tEd2tYfQJPnO4nld1SySt94U1Hy/OuZdQg4QsMcdLCfZA44/PvXBYY1vIEKsDQnJ2CW6tGQWgGvv3LHMo1VpbMiT4NH6iYISrQHJ1ug9oCZOGkelEBwhJr7tjpMfOWNQlJkMEKCp0cZRqdEGVrHxNAgDtPLr4mAO7rHu5U++cHsM6oYvuu7IYx/7gf/1wQtPw6i76DzXHG1syI6EibGHWqOOiCeGFdFOz+RJF3waglcDOvP/hniJDeRWpZyg+8eiqIhpL19wTwfYTSQWtmFveDJHz+s/0fXaXE1UTCzUm2P+2E0nXqVH59v/7efevHFuRyDVPEhjb+zJVPuwgjsSS4mKjSvii+aPci6Zn81D9Kc+4/rbfv+tJ1+wI+9lo+kESz7mVbYhaqyKPS1xd/Bad1XYdXjAca+PFT+qtDFronGsHlV28ZTL4h6ypd3N66oE5I5x9HONP4jp3sfg4dIgPLkJiDDTZ29ePGrutu+89JvveukzTgJsgGvsjcnhYmVGMOVwNN+6j6jwWPZfccfvf/HbWFQ8s9pw8KInnvuRP/jnpy5S0sZmkYkMxozGcVmVUdqSoc1qDRM7BtdsE6lRuVY0sb2Uq+NcH3WEQpSojY2sdR3SShIMvXAcpHGv08hhbT0hEka38pvoSVDvLbu6EXVJ4wOdsHJv6EUd2bg3ZM3c8KVhbPLnn/nckWtnLPtPP/P+z37riSFIYMfU7zyx0XvW6lOpZ2ZhIiZWWjzujjc8eOWCcs/KLH3Zd+nTr3j/C9IFmwQWWwZWEqGpmUWTHkIqNL3ksTpgiBOdjRXL1p9IhZhH6tj6FdIZhJElDasj3f748GttZDe1UADgHLyjJthu1MwClIndNOgwAs+aUYsRiIe6IGq4Z1IhWHJ+92qVio6JSXW6Q2oaIxM8Gzl0nmAkDsuqwGduO+lqf3/YvOVnb/2v5wm7Zg/W7CtSr1yq45W3g4EQ0enUfQCmvHRPvf9VjzkrqgrBONYOG5dcd+iPf3d8tKbiNAZzPESvTIApQudWV8OozW7imAmGHjRMYp7EBBJNxTXfhCF6IKWZErvJBJb0OPFrkzgA4zhpkRNFFtS+ivUQWGNtEVGDfefou2YqKoMpTF3pWWBMRkzjqFUVGJKirwoi6QRN0p4IYdTCrjlsDMVh8n8oS9LmL2C3fOLQVZ3rZN8p7371VacSIYqDEZeehB2RKJMBfVWjITtE8kx98BMTQlS6y47+1qErqBdKoxTyMDp41bc/8II3XHz6jPpuoYyAjvus6OGdEKwVbcgOibyBCda827glT3VvrErWjvsdyJgDS9PqN/pqs8nDrQ8BIRY3VoUhx04JpCk6J5SX5ISBOHAozpbmuZ0QsbAIlaVYmCu1sZWQyswLCFKjqlJdWg1KIQiQe+WUO6cEE2uCLb3ZoAx2Y7VBJY93/eGfxQtPKKR69u2vfsaFBiTR2vfkVABq2McQnGruVdX6bkawZJ4QA49FaaiHTn3jG0642vGQ5+IV6A3jSU9+wmde/KUj3M1zoqUuyLTxJK2nEnSsWnvu2Jyv2yPEengeWAhL1EEIdXskG0SoLAcIgdIgsXTKyL06bVOSHYvlfVjnH7zRpWUBE8071GV03ZAA8Nz1aKTSAMDNRpmBFl2eHIFjaIHQKnMl6EI6WbajibEHuJvRGMGLkmaErlsejbohYLEhoC7TbAFKS1t4WDWAFhYWChg6F79Mm+GT99zPF56FsLSNDrzY5+tYYo+F8oLRLWiMuiEh8FwJdSndssD70VGPRe0v+bsr/+Q9lGlDrMalLVwpqXvCH7/5rm/7D7dEP+uzUN0u3czGBCzUzTHrwAuLZZkgm/trT4uO3EYMhoXThQyjbO6vYU4G2disywoYaDYDD0E3CCwLB9gyHI/z87p03YqAAhiQh7lbjafTwQ3Rrh1PGZ3fJUoZhR36lBHGPG9+UiHPabKjWqw1HcO2LGCg2nsHAiyPviv9TEGVyOz1N17yAwdx43+5at8Fz54zgG03A3os2qAy1AXtcIMM1qfZHLYaU1p+U50f/Y8fev6jHGqfuxlhLHOuROj/4rn+e77/Ao9qBA55AUt5zij9bPJnsm1ZTGOTNf2fhdt9GpbaEfqGHzOCVQKRLV2HXcLSccH7oDbLGAYQY7e+jLNedZhLY9M0/NuedUSdqquuLHS2/Hw9byFsSAVXIlQitBLvui2lMNP2ofY6A970hnN+anMMJbtNt3QetuVmtuaKE+IeQ/q6LQvbhWdZtdH5Kvjwb33oN75HYJW4ZWywuTEefOfzvvR9P3QpHpQFwMCQF7LH+ekob06nMligUh7naqv7m6HHZitZBQNxoI2vNkz9C+ePIK4MJLC26CaE9QADeUbHaJ6xQI1DXDcsw1B5YEHtoVaJyKro+sFnKZ5DlLFq7aFAmLaLOxrKMhW4oa8/eceZj/AqdHCO3isBSWjQnamSat17Zh2Fh92dXVyWDZeihDMv+MAHzzwX1BceiYzgtA6Q2UXPXL70LZsnneSpz4qqHMnWzVSyOKBWhjqyoXoVSuNK/2p0Zr79ekwekJk30NfwYnn49VFF2cuOX0JMiz07thKyo8m5DBjL5l59IRZZXVwnv6JjBOw9q2ev0/3rXvxODpJSewcEAJ+6ed9VHWruwNykprmbdhy1cqMj7undNCUXEKAzb1DPDqde/VdfuH4TGZ20lQa1Aiye8sy7f/+tctqGr1FGeBqbPN8q1O2abBoRgbzmUVg8t0eLM+2sdTfnAdRKw3HXb582prtC/bp3w2WDrOaHWoncMdGSSYi/VU0nsHwMyttsFSCxiofyB6V57yBOKv4f/9jBR8+q+ttu7g/OBbv9CQhZmx3VnmCnTiPlOG3TVvTFI5e88hXXH+okjtyt5bnSCU++6pY/fdcJJ2969hzzwq/fsBivuGqVaIeMNpllDiQ2MV9qJYpRO7VyvPvH2Gh9bsdoIa8PiORpVVVTrvYkY08cKFsNM6m8N50a2aVZO+0xJMjGE/VlFRW77a4zrnKxv/kl//Xtp57WAaii02si5Xa79cxvV26eELumKLUQ1cJn+te++sknh7Knt9t2pXLR91/71r+488DmHEOZc5/XAgaj6VTxacW6qYWmqCV5AXlBGYVT1PZtDseXzwnyVLkVJ2Yl1Lguk26ZVoDp9s4s7sXDhSI7fggWauc5lPWAYhgcx3bu6QVWPJddunowta0dfUrUSrfeduQRrJ9/x3f84OdfUi9cTCJZobgpd8f4f8DYr/XnUqkiR6WYlK644gP3nX2yp7zH8oO9A875safd+PyP+DMXsq0w3m3hAuNGQBJPSJGI0q7aXyYUarBy8QRYJvp6fM6Hh2egVBW5clNfyaGsRwTryHvOD3JM6/F2y87XNv/nyuRczeSPOS3zO0HxXBF2DAma20BN5qVZeSTULLd9bHbtvBy56pRTLhiHc05Gqy4nmZtfWlmz78iVj/FjSZW3MfME9YRy/lW//d6rDiMErF0zHawe+e5z3vDy4cDJc1asyStu96wEWG5UzZqEd+j0NYWa8/rjEY5/vD1HYWbsHBMFma8L0LOXlXtHM9WgRVoL6Vpg1DbBN4+OXfj9ihToMxhIYCBU7wvvsQnPaYHKFkxthFf67OeOXDNDdcG9592/eMHO/LHy6InV85r/h0MwbnSEXBkgZnNNLZUp6qFT/vA9377PzXYbkB1NjnKGDXLps/e97W+/tHkq1vULasNpWzvEidhYH4zz3GxNvSGY+yoaZP/S+hDPqWqzByhF4LjsXUAlmV5gav4fabZnNSwlO6Bmdg5Ipp7TOsclGUeWiVAx/WTv4ykWR25aftmH3rV4skvZu/e97exrNwCCUiIST8hFoLzWmJ0DiK0Nr7EqkItz1kgpHqj+8pPee9PTfF7j9C+kaErsPMM/+v+Mf/TicMk6rckpkEHUFpN7iUfiSB3ahNJ+a/8b+keNhYSBEnNOppRDKYWQqMZSMhBzLUWopEzKiDGXSpY5p1ykFE4JVJjiUi0YJeNYnAdSyoVr4QTYTHIWqrlyNkqkbAmIuWTjnEou3gM5VkEJwxdf+pq7+JwDDrf+7YU/uVGDMdiSlpgL5+JSlI6SUcwlFymFYiLvucRcvLOYQZVzlZjVJ8pj1GuPvPHBi/ZtoTBZ7KskUomkqEzjMtt1z7jtVR/LG4dQEEvJVYAatrO1AmdGohpzEYs5M2IWspSPDgtKlVMfZcYllpJBiWqRZMdBf7eGMbMCJdXadYRt28iZKUlJtVamRJRNqcZaWSwlFmMrknOF5iqxWK3KYK0RzmkNIzkg5WpaqqRcoZSLpFxNs3EYyCEyhVoracq1mjCwPapSGcPWzV+ZH7rihC+8+Fc2z33XPy4OkGQ4l2Ktpk5CzqxIxqnUCi3GiZURU6lV2FKp1RyIUmZKQil1ywsP/PuvXKkJZhJ78UnYYinVHA1lf+lP/75H/PMNfxcvndE4VLKSiaJyRStwzbW9htJ0mmyosizGzBka+yw15wIrLCnXWh/CV3t4/I+j3brweIBPe1ZwY9kzQdeBne5dEOyuFyM5HHV76Clr/LoWkZBjaI9RBBbYN1rGm/76sp9G+dgNd23weNJPXAlE1hrawJHjjGvenQwSHAL5vYTGmGS2KkkXt/ff9/zn/fjv15JkBtTsU96hN1r0VKrDG2748JN+4FsRC1GOPPc7JUGajtYCO6Qos7RFcziKZSYld0B5kDc0mkf2o9W477j4D1osOhmupOoJJZCvdW2OS9WlNQaLi4JduxbEKPPd2Z26uuUWdff3GMOmpLr2e+K069mUqgtT9Tbqy2tef+lP7qtSBSXNpmjOHnrPuLl7a8zae1ubrWRrNpto/aihap3jD17+fzynFgfEqH47L2Y7gQcYGXeMV77y9mt+6Hpsy6yP824yy5pZFG3knBzVB9JY53m5nyM5oMQuk4aOysgzG3huA/vjo79bKkvjkRZTQqksdUXYyFGoghuxNCWhbFLZpjafocjqd4g8pAqw8kRLjVkIuXhe8T8yFJVQJv5uEirmXM5rzk933nfqI2dci4Cam0bdUWptRJ419q7qOqOmba+b8maGAig2H2qH6774P9O1s0ghdx3RzFto5CN2pfpZpTBe/X373njDzWee5Wh0CwJQg3pgYpHUkGbuwc4R+5Q6Jdm6Y1PyjHKyWSrO25bO6z3YxPHx20ZxntomS5QA0cw7W4xiSqU6N6l3KalaoVWyKqBSdyhRFqpQIZ5uV0wJJLpjiqYKW9bZtKOrpiQKlPby2jb7Qx894UqXKCsRBzCwc/M8wQbDdMxjwaSOna77oIiSTrwZC1AlFkE8f/mb9194kEuHyBXSCEhckjhPA7Tkji7/1vKZt3zy0CkdITA3lhepgJzAyuJDbz9FcMtf3HFof4fP3nnHTX4/JKqYFOpvvu3oUTswvuO9Z/six6U+2najjlMzp+YgYFJHckrYGXtkEpOXaZymUBShOMcxKUJRVJK6bPvt6eJmNACMhia1vUIATsmwUf0U1mQAt95y4NquOhc//cDBytzYWyMEpDUJhcKF2wZcirCVaLrHB8XG1e6oROOgrg718HXyRyc+hZSrSSVp75krFCGyqSBJ3vfkZ9W/fsmnLzqJi6TsNDXEoo0mpB949+Kyju56yyfOPB/ll2/+lvnzth6FbfYSOn3H8y695MYXXHv61k3xxDkfh/PBKV4cexBgw4rdxJPTTSNKhBEYw/SfME5XNQHF3Q/U+d1I+/RvGiriUInAGEfQavieAnWhrRHHIDNBjnV2wkFlnxO95I94ps1TZQcdBhDxTImn/4DnnkEzN0GTMjBpzwfQrCPmMUBmOOE//9gb/gwYa7f2hpzrC/v5QgwMSvA/dsN33vCvX24zoZUDfRzBBMT/8bkf2j/vTr50XwXu+bydceUZn/kUFg5GY/+l/qxTLznxg/c++rG/+1H9unwcG8JEOvoGE7qhDon9XJo53XZfAOocuFOAOA62qx/NbENmAK4jeA94GgyuA/w6jmcMPBPAhsQEMFOn0jEzrCkajdx4gXHkTtNQmMtQ4si4I52lKTL7W96zBOJQgTI4TYO1J+pY4TqC64BxBCqVocRQhwQSCmM7z2wRRhnUEqwCs/904q/8bRKqy+0EG7YCMAQImdmQdD5j7QCc/dxXHfn5f/WS6G0qjdTBOzz47k8O0BEPfi4I7n3ZWU8Dri8fMC/gTj/4iSefhLOf+sW7kT7x3gebltOe+ih9QenrDt75G/YZGxNIWD2A3DtlHgtKX5D6itibn2vzX/eu9MXJkuYeNoSdN9/ECfq4F1bVfiJsAHTa4XsPS6Wh2fuE0pf5bOvunoW9IyXulNPddxSKUeA3qSQWjKnhpac17NHBVj2hwYEDCTGTMLgTrstKq2MMQABqs+wZz330c97pdGww9obg5o659Hsa8TNueO6ZP/ed7+rS9nYExh7UR9Tbxg2Asf/w3fcjfvnBivzJ24kwhhJcPgrG/R+9M2Fx+DN3Yiwitd+KKPcuyzY3I5Iw0hBRe3GwUv//xXglDnUIpEDBhoK0mbOIAqU0Ht4wNjuYUlZ65+MACFUbAqASe0McDdZeCEmLThuAvMzIy4LW7wDnSRmkVIrOm36ZZVMK9az99xad1wQqlVk9m7EfonoMMfdZ5vtk5SII70Fk7FndFOBwMz9T2EQpFc+o7CUMwOW/+cT/8k5yc66AnzvAu9yXWt18zxx88vc/739u/MzP3705L72pc3PPmHcaIzxKPwhO+oEjd6Hec+QRBJU61kdd+d678eVPnHc6RO97AEKlknoBd04cYxjZs3RzL7FnwtfgiTwEX9JXiCOn4hniO94JKYunIWuTEHXKniGzThpnpK2v3ExZBeRFHJADbczQuI5eAYx5gwHxAvaM1Nu8W7UAsGdxcz8GZcDGAlI+5/wTFigLBjFXQ1l2HeAaP4adqKa6c1YJ1KWbr7pm7A1gT0j9qtDWywKAYlnDuc/pfubPXHSzvCxIfR1GcSydn2iZrbUgj7MfuOHXjj7r//n8fEZZHJxiqRszAdDbt1wOd9lnPg7+B1wGcHGLcd/JdxTcfvNlJyKOZ54Cx5JHh1rGzfG+Tn6V6xhV6tBxC3LTSlz86/E/tEYfB9I0Gg9DziFAgTFzT1KXoZbc5WWMWakfY4wlmgIhyUC+9mNOqavLEAXJUTafeiiG7HkoWnviIqFPJTJF4ZhdhtSeLHDMWr9is+Wgc3xFw9YBDf7B5//2je9++6UH7z74wJ/rj9I4VKmMZXZ1GbJQCFzGdhzfm8PYhzS3yCPTKATmsQcPJsiSR0ehz1rB/ZhJo7lDj/izjz/5sGOwjMkL5dG0VO4HcOQcvFIaVdS2lpc9wb3oFV+6aB5HcxhTd+S1/llpOHrTB+699PRlPvf+F7/1O7+LX/wb9Ii+KDZOffsr9v/bK8196hU//PgyijpmSUmCLFh+tbjOj8V5gsU0+YXwN+J/qDhmViZWZhFVVbYeFJwSuPOiTKKqwqSqTkXZBuMgyiBVUSHWhtrMxbMIg6woC4O9ErOoqBIJleqCeZDk4GL1YGdhwWPpoDL6krqN+aFrv+OR+8Xzq8oPojrnmZnaA1ouPBPZyE4ZJG6mxOo0B89MPTsnxKLMxAISbVerc+KIDj/tltc/ZV9UXtkaaJt5OsdMqj2U+b4wJ+ZD1z7p8nf86cbl+62P7Py+L80v3RR3wpVXnOydO++SI1c+43SiB688jyTXw5cfPv+Jj5zRJ997+TNPIJH44PbwwDibxw9+/iT5hZf8wotuOuO05St/ledv2Zpv1EFK+vr9gyT28DRVB7EIBacgdiqeQBIbw0tEmEREOIiuahEkUnJHJNKoQ+IosANYmAMUgSyqyCqZHUd2JMRe1DG5suRFqvvqa1/3pr866XzQmQ988pIfXkTlo7eHjdPmyjZCRVYPEMpRiUV8O7sV7sGDCnsmQLzWwQvAjc4mglCciLCNVAd32oXvv+HEywBuXqkixGXslMDEDBYWEsvzGUY+44rH4rl/oY/2wfMyXfPlN1+zaQcOn36AeeR955/jK7pzT5t7Ea3pzPPmX5nrx+/94ZMLDdHZ+5772/6JcC+/+Rnya4dvfdWd/+rMm9/6zdd/+cZ4/kH6BgYVU4Bwhl2+AULwQrl3ssNVKWuIGqTeKZVeZYX+pxW7IwQl4nqvzWsPZWJmsEx+E71p7aFsD9h8MhrhBvIZ3eLv//3Z3/HIC37vo4/cj5s+d/IlnkpwVz/hjP0MYCTa8/joGcQ08XFsNM9rdIQc3e4AnUaJkAZlIieKk/e98L4LT15jowxpxjSZ5TR7EOoYUC106DGPvvWF/3j4fM+iG2efu6mCQmNxzDEoM9yJ+7T2qmAaw4a7d/Paw0Is6rpDR15z5zed+OB9Z18mv3bwCee/Lb3/cz/++AObF150QJUn6nzpSdIgHEcds9vjVGHJe4gQTSehTJFlB7VTelVeh/AwJdpJJmWKSWkMjsDKBNBsxhOXgkFMNeYVCkiEQH52DBlO9DU/jX9z9SnnzV76T0/cfP+XLr9EWaRbHNhkhCCZvfCQHPplcYSVXGnzdiq97+oovMPEYCfSas96c8LOMUsI3ikzgDOe9pd3Pt1h3C46ZAew4wFCoo2eNerkCAKmWM572tPv/O23nXl2cZgf9sJEPTpmYhUMeeGE6qhCTNw50kOLbW5U0MX5B9/+prledoXCzG7/vhN+7vZcLA61FDOzsJXNaqpW49ZYcs3ZbI9JQln7ULaCWa7rdhTVrG6PlreCWd0aj7nYrOS6vWxODVvR0lZeT9saa85bY27fLpfHeF1s92bDV37mjLeHwcx+5OS/Gn79GX/er9+75S73WyWnXLbGuufhNVWrufZbubbHr/6MWyUXK9vB8lYsa1l63XU/dNSGlGsuaSvZqjQlt5LYuFWt365mJddkR19/9Rk/++VslrbTsMwPDrsZy1vBrFSLqwLXXC1u535pln4WT7vJRpNfBRZXv/vGr3yrNuunVRtGHVlIRHLQWNyeSKQxxUE4BKUxeBXak0pMRiRC5ISM5Jjk9gt1bNQYECTrgB4SJWYVdjxG13rgEHdOMEhz9OLe/9FHXdKVpG/9xBMu7erhi9zavY0p9Sqqwswkx9g71JGFmJoIe+vGNiTXdP4JECFSYd4FhF4cX/p3jz6NrVchFTJM/lE82eKwcjO9S1EJ3cXPvO79v/mPh88UCSwTVWUclYgtihpPo0LpwcQEFpYcPNVbPnn5Iz3kV1Hf8tc/md/9xJNB1Jg8fZzRBPGykZG8U7LlmgPWwMROwCoQZR4S9Xteeb+sjglENAbHlJZC6wCsfqs6pjgogXiZ/Z7BDUxH7+2UiEgcEZGhx1rUjQSjC2+8+bsugAq9+vP/+sKb3jhev3uegtKzsBKIYWN0TKHXNXcL0jE7GOdB2MA0Bh6lm6JqBuIhegZyv5NnuuLwyx54xKFGWadxO+tOLFuUsKx+UrAhFaIUTjj/8Ze/83fvfELnRSWa1CV7xwZiL2kZRMooRKxjdVgagvIYw4sWP3H3n8+uEvmVB1/6D//X1Zfd8rsXnp4cqYIQrTMANC7Ne5novWuIHlYZszek6ACGaU2zuIagMjXz+P9oe+8oy67qTPzbe59zbnhVXZ27pe6WWqkltbJaSAIkkZMZkY1xAMOwwB5jYwbsGcZ5xnjh7J8jGGOPjTHYIIkMRiShTJIEAiWUszp3Vb2bTti/P+59Va+aYFvWaK3W6tfn3nNPjl8AxQrOghCjm+araWdKQuNH3HNrHVa6KDWdCSxhLBIqw20rnt0UVptMdWj1w5/cs+tI5S99cMcvubvGp5669EAVnanVUgWDVFHBimahXNrh1sFRRw7j5Byjaw2Jtlk2weo3ndMWDlVyliec/SruOvd99ZPJUNsa6mgkS1BiIqBlrsi3luA76YUHRie84OD7r95BlLGLwVkmTpUagES8YZIGBrCG4IQsgW77vbOfv+Xsz/xd83R5+1s/evGzeM38R76w7dTBFcC6VHFsnS0sFnd3JfX8t2UUUWOsTRU5o5UaHVNmZaq64lhyqxUJW6FYM4ujKcG4WNmCoOJ6eJSzFFfK/0lReBFyArYCsdTS8ttkWYoRn3r05bPHdg/+znl/MKOXX7VpV7aM9iDu2JIVilWWcay0nF0+cDA2jYMzyRqAwEZAxpp+8aIKY7XyzqoxRBNarzrHx5z07iuel5FwLVlGqKNNE64FecpMQwUlMLWcqmAIMM98bfytz2xcv2ffWHKuoiVrKFYQybntcisUK9ZDYyHiOtz1qQfO2knF7ofWn0xpPs0IkV+MAlvyYCyiBGD+ULjzj7/5hl/v5damT1EW21kHAJNWfxCrp8fouh6t0BM6sLhxxe/989unAaKLB+ZWTQfve+xEmf7e3emY6Y9X3oyAxXfefQI//ekArr3iqFetOLZ+aGZu+W7c4eCe41fMII/Y9cH0GYoCYDHN9IlpMwB4DJtW5LWZn8uAP//dXe/ZDAB+PpsBMJGBi/Iobxz+hihA50c9EQQ3v/OKseK4n/qpTVNJ233mclrmv3j9+guPyrIROm+dqvfsDM0hVbnhMoOiHzKbNNL9+w7d/oGrY2r1m/cnZdZECGSgzCk03zp4/IkISaAcm1Hac3tz+qZEzBohCHrno5t3UA3bmiyOS3fg5sWd2zgpU1IwJf34Pa9f471m6ELGku67d/MOSayJWBNA//iZd5yYOqlNposW4GuLpEKJJEXmhdENH37hBazNK5U5vzty/aU71n/XEiVO4KSh2XfL0TubEk0qCV09Yz5yxS8eSz6y4ZRqynF5d8FGD0QCQREP7NU1a3MTvc2aBZpNX5o/d1Ne1yULJ60433v5lqc48/xvfvwLT6uaVem2ezbvKEkjASRJef7L5YVGwRxVybT375vdOGeUx5iZ+c38/wI32S27hBAXJVctPvr5N50Um1bLLEW+6V1XqeUzfuVkGmU5YjPKBjyD0jTBBKrafPB9dx5oAJTtUWfuWSjKWNt4KJ/19czq8Z6u3j978tyDB9fMViHLZx99YDHsmDvIozXdY9ike9KBR1adGA01eSRus+KR23jrFlRaoCa1rk53LZy3aXe1Pi1wUUXR/Xcfe/L8OONaC9TqRnfet/P0vQ9vIHA7xmhU3+S2+1VUUZa8mJDtuXXmxPV1NdJYLHq4Nbc9tHVrp6YpoppaR/TIfes368a2zpjRtDPu9vtOPN7v9pmz3BIp3d6dsKplqSMVtoqjQ3e6jZnbUN+34fybHt6Q1TdXR286strNYV2xQER+94PZUWvLerz/rnLb5tG+hx/Bjs3NISdIyD2bR+7cevq+xGTaZEjcA3fnp65Z6IpWsm7tvd8GgNXHrYtBas+dP/WBa7c8eeGh1bVZ1RycO3BbLyW36viXv+KEgbD1ffElvsvjvq9dcdOj+3crXveXutcTAFNwM9/QyOd82Q2n/8jmdh9t9I+GTavo8kvmXnfavpRmZKwjDdUnP3fa62dBNeUx5bW76QP0miftR5kqKUNDTH954zu25829s4Xkwvc/svvD57xWk2a2iiV1a92ff/YdJ+4u3P7c7Unr5vjR373tda9cDMWhem5u8eCa7KMffPKPbTmUSG3eiPjw/o+c+7bV86RU0JiK0eK173nxT9wxN5caGqVKRnjv537r1L1und63sHHVQVr7wHvXPPvQyau6rHIZFHLDZYsvPXu+mNs93haUhf/X3v9z1IPtEWYfcVsaGV/z3h9528H9xbZb3v7Z//4bi+MvfXTD209+6OFtFmlhwc0tXvMPT3oLr+Ld88Xs6uau2a9csvlnj90PqC3o0DUfvS6stvTyp20qZ6EMad915c9eWDbztV1VUP6B33wYsnnd6gtfeOoM/TC8T0rSigXqqy65If3Ez+eH+0/5++0RFghhuEht9vIGC9QTUFMIGaHRAi1bNGzbauV8krq852z5dgZI7Qr0VZN11Ro0UwCvB9qt+SGanSwoDjx04orztc9ecvQvzk5H8KVw5rYp3du93z1iO8ZUwvsSAG5tjpuertKhZm5igdZQhv0ke9dPPVDFWb93fUpF+IXb33IxPbC73OjNerTIUC/BypolF7XOTcogB+qr95+z9VN/ffA1r9zgtZ9xD5q5yd7m+r/4pr3whWdswpIi/g+oj84XnFR0oPdVMc+ARrPG2AgDHaOQyAqKQtDWCqC1jnqXDdQPVSPqttiYSyQGUn0A66aL/N4H6nrnlsAl+9YZht5w8LjtU8f599ya71o7LilCYm3M3Vd8c9XTzp8Zy0wkRs1Z3Hfz6EnSExUz4DOfOOaNSxN4BDcH3lxdlkcIMI6rcPDayx99+vOOQWypALqUbvvKoZMvWlOngjtfKDTk37h1xxmKXCvjgi9vf+++pz9jfRGJgQWawf6H7lh83ua6AN7x+f+JLzy2pbjzSW/M++j23o/7t58JNCEX6mJx4MFD5mzbFAC0WdxbbG/m57KvvPmrz//Fp84izt++aieQDs2bddI6EzvJJ7NFLdkPxpeII3gvbTJAF63LDRDEkRVfR0PRZexbqYO0hIRFOXS/zzLXMzdo97X/+qmvfvJTO7dzZ7qOGY/ccM2e9XNT0X/wXVdfufGEUU6RbMuCu19+xYXbljHhe79+6d/effRWRRelddneT96XvvpPR5wycqENTMx88DO/8dALbFDu6Wy3P7ztNLfMjrF29jO7X23aaAKBLa7/2urRe2580lyHjCLE71+19crfPPeEUFLgjBp1ZuFP/jieP2dAzvjW3XHZg092q7aiBidKwvs+dvkRr5ol01TZWft/5oGnPOv08aX5i7lRxwiX/O799x1YN8cijUk23XvJ17726flN6xGI0r6bf/WKi4vRI9ddvq644rPzUs6G11//Y23A1e/ee/Qa05JzpiewCcgOHJfvz2XTIM6hiMFAdIAuGYqGnIsPtWnvqm1zFgYyQhOdueY7bvWGY4/plWD0gYePXb/uxk9EUBFc6MzCB/e9efOK1e+tJ7z5ZLReQivFDDD/xePWjJeGRPX03Jfd+9Z/Pi1GKyhDyM/98TW3/dkjDx2rbaZd0ZGsOeW41QU8UY+Sk268fMNcRm/BaPMCsc1tAra98ngcfc1VW4rxeOQNhdVu849XG1EAnjjkDNy2+sLNPcuLiNsP3fCcbc/MghmhaWYL3P/exXPOiCa1ntOqF9914OynhBOy3EvZehMfvPeU35v95V9678bgZtCYO3/trP925J4L7/ojtGzNEau27VHgHz74qe3X/dXdX/7EjrdetNFH6vKtfMv52wYV/jY6YwCEtici/ID66CVYfBLyauDJ0AjBs5I88g9rn/bAB17xavgM3lCOQ1995zm/f8tbzvvtHs5PO49fjfl1m7fC2y4zrvnHfWff9cApUyaVe/IvXfnrz1074Yvd93V+xV33L0mCk9vUfuuet5+oPWjLpFW7CE27eUZpBFgUAM2N9wIWqRdc9yvUlKO3oOgRYGZCTRyPJIB3PS+DYTbCq9BdcdWTdgBAgdg5PnT77MvmDkXEJJ1hk/2YXrL7dS86SgYq4K0f+tXRX+984Sasgtedf/5zf7rq2L8++oU5YEOX9MAntu9od2ZB+jveu85eB11jgFETjO7h9QRPrsP593/0N/e+/U0/sXubiEW5dXeYyG4XsdJCk3SDxZz5ARfkAIB8+NNja9lyI/6WOy485aiPfnvPBh+gBjHNbjC7777p5POWWmgJ/O1Nv7cZOUYAHnvPU4657LqX/NimMFYLH2x+9O//3K+/4e/O+u5qzXy7btMdxUv/7BvHClIXvBpRP0vfeNPLfmV28e6xdLMyWpeX93ztuGdtXHikPijFvB6znWZXWaDjfHB1qabWG14ctHMjbcWgM5l6J7tveOyMI4AM8J2zkPmPf2fvT24JnGBG2P2v9796/lszLWIwJWCw5Td+6zuvuONvAFjrWbo6vXjr7970M2d4E8gUf/6aV7/mkz8328LFhkfHvO7ev9j9zv+ORSeAN0f99Cfufe2WwgAwBD20UDIOHTrSIR6469Gnf+Gyf7qlvObJDMZCAyBEZwkyC3TBTNqr+TeVShBtGb1VYkaBcP+jBrNv+PAH3lwOTFuc+ZIP/fjCnz5nz8MHF/zMlo2ltXjkMdnz0CIRd7PVzBG7zvjTf1z8lfYBzLSVzm6YW9z+J2de++3Z1X6mWTjmS/X291x677kVNdWhWjMrG5if/dZ3j/6a73hsFWdYV65dvGnDG4C4/6H73MbxvD2629+sBkoMjiO2nKJPRc+GlRRkgBKgErr/6y/Y1fPaizZY+Bef/us3XbAl2ACDeO03Tr7hb698wf4jxPXQ+hFw0o4RAA/xVgKtxq4/esXxZ4SYp87NvOnXf+2luxCQ7CrgQPfTr7/s6uOePqOdQ4HNb1v9sa+e0mTwxqfMHJM9lpCb+QjMHJkj+/FXve4frv6VN66NZi6H+ixOWEhTOLR/yz8qMEWL2C3u6x68e/PJ+w+cePKV7sTrsQXtbbeaow8cWn3s9pPOuP3Al7fMLN7zYLueSmFcecxzzYEH9rKsOThz1MIY5jXX3At3pEizNjdMMyjPWzz/ef0HPvLFu7s0alrm2UxJk2SMbe+4fh7uVZPl2N9vecH14Zh1p50/IUGb2RLoophBot4MzisxWtPBIB3wpTTOwasLu6+8+wL5THlWCQSTY+9VZx7TlBfvQg4BkI7Ps/3bznCcIOg4NcXt9sSHXrQdQIQtgdmdXznb/f2Lnoa80RSBZz3wVuSwPSrqlsuPev2LfuqNX1u1KEpAiq9//cO/9YyXIpqirmdnSgFm6K4Cl3/+JTsAdO3p57/vmz+7Zn5mFghE5nutMf6N+qDSa94ZZ/am+t6bjt/0yN5XXfjRb5V/+LOv8GH3bXkxfqA64sZPnv0Hf/yO6o+Peurw0sLfnPnsuObY4ZDmRXd/5sz3n/xc2LXADID2izdt37H7zWtiByfJv/SlwD/fdNEaQHv86+LHvrVx59O3wQ6nSPsu/dTMDWnXZrJKSN4R6YFDs51DgC0R1Vj1AmgCUrRJdl83c9TRTeakjU4V6Y7Pf/vrs3LOzpys8YrF22+fwfqtGbQziNaeeirw1JvzExxSFzNTmOv2XSz/ZWPyNod6w0/Vz71f6jdtBRWe885hx85rfu1NT+mlJ7bU7z64eu1PzyGzgAdXuPO6ta85EVlnCNXtN6Iu8czF9+f3b3le3uRo7pn9tYf//l35QxsOgEp0yXwP1O3f9FdTTUl92rgRuwYGxUsu/PTrLkIaPec5/X7qir373Ns/fN8yvyaceQwiImxjjaff/tDNtrn4fGgn7C2Hxb335Bec6qN20onRyji/Y+0xQOdZCFDae0dz9K9SxRlisBH29J2Pzp9+/BHiB2kaE5rzt6culgIgxPjQzfTQNssCWNum4p4/XPu2i9qkRhplwB35WveQ2XjkBgBpnLntb7/k+mf8PDq1SUMrMRgHs2VkAGgZgutOfgQnpSaRAdJYiuI5z/lU+zIEA62sHfv81Pcc+vGvfPyUuimCOfrFMj//nGfFziF57wjp0Ik/jyiqsNIuPHeztOFZT/2T+170NByEyPinDuw977zP/8kX5SlPQydO2+/hf/wbfBxtzRLrBtpGZ/WbC/P3vy7vbGs0Os8W9bvvfd7mL297xUQSQeJisQpog2SE5JEtPriDAW0jUcYhZv2GNnY5sw2hx6qnLlqHlq22eW9hy2Ths3EoswF6Thn75BbiyHqHcWNzp61B8+gvf/TsX71gDQfLCAs8d+dfymtOPxhnMgDjpsw6sYAumDwm6w2CI6CxEQ6ou5ngneuS4040Zp0nAuXoQrIZOnVtdBbBoFGIQ8dS12UB/9E/LN91ktfxjDoAvmtnKLnWUIeMofNpZL2go4yANthhchinGe+AztLCpVc+dvTzL6YK5OQ/yP/ouS2qBp2XmFKiR9pTn/HoYilRjCGjdSyefMoj5St2DmwMw6mcyUIr1kRplWPydvW4IyFDlBNS6nxIYklm1bi4WLCnhWQ1ZhYafLLGt8F7LuxYc0vE2u1LOXy0OSElYTbYpzZmIwESC8L+9oznbM5ZDcA2p25/vfkojVa9kBBZCsGzgqwma0LLEhKigQ9CLMZIaGtrY8WUODoX0EWqssIAkYxxGmixUQWEWquhMNp17a6zrr9x5wawMwD2VuVs8Cll0rYz7Dtv2HAkxBQ6lQShxvskHTg637ZVjOVZL46X/+Ptm7Zb/Q/rJ/bclpikCWKN42SP3F6mhbLoshCpIY0kYWbnFkCT+GAANnoo2CRdyikSx4zV+WQFPSskpQJ1cJ4cDHvvrCoHsWS4B9kKxTaMCKJsGRBrXcO5Bse1Z2tIqI2jTGxoIRRJzGzXnPKcstm/2B5a7KKR+MANG05zhdEkLeW2FYzFirUtZUAwGe0LI9t6sFBKQilSZlk7yQyZEPLkxbEJXihCgLp1hrmwCo4M5ZhgZtqjNvzGLWduMi1Sx7Wd0WizxEQilCLnDl0mbJ11RheTNVaTBiUlMayOnQBnvFBu/OQd67cyHld9iKHkHAA2BB/tKFflRKxinKXkQ8fMhlM/HZGXzFAigREyxKhNaZcvexEpM4kEgCInNlMCMGII4owYARlGaiBA5pgMa+qJTDFBmVOEiEYS4JvfWXeana/q8WK1uL8s9nzm0fNOBFrNKZJoIrYFY3BJMAKtpdBkc0NIKsTWBhLiPm4YsxhGhhOG+mBjQmSDCGOYDaLNDZKs3vIvt562MQonUWvJcIpCbAgpgbm3Ee8zRIw2ZlZz5ozAJmYSGubRhS+kS9//4CmzsWVOfvn5H14ftAQFWMYEiEEkY0hkCBVntD+56G8S25JbQ8uwbEV2mNuXDKHcu2AcZqoUE1MvRKPKHJvesontwJCzNjGTsTLwrm69c8OZzsyUs2tWz45GMv/wnpNORB1F0NfqoCo/keCiPOMh4b1wkKaefDBkICt4aBeDRn6ybglkToZ9JwbFOdsuveMlLoScHLWGoCrkO0NikkwJEpEQWDMhQz4ZNFGSkJIQUJ771IOXfnLzSZbRLGQ8KO88Pr6aP9yDbKVgDetEIKprBxbCyvPjKQUkZaFez2o5uOkNCYZ4Vab0WVa0Da1VgDvuWn9WbkyWZVk+MnTb+285/TSPzAJovSH4Vlaa7+kPTbxXNCsUnPuq6pZjEULszjjyquvOmVOqm97qwxCUDLqYtaqN0CSPXq2hrrNQEqhPeZd4UBPZ+Pxzq098ojrzY7/xwDlZ0xMuH6ffhHCqpzRJ0rSw72DtMEjsfV+5jin8pUiohVbUL/eeDABSrUKmicumZtoko8ufZgZueWA43228BTq/8Vnnz9TFpD0va6j3+BJL4zR9GdN+D1iZeIXc/ZK++FDGg0C7nOx/41s7twKSGTSqDTPLuCW0ZAmTTtDbaEBjKwZV62xqyLJy6y3qaI963pabP/zZ913/8AVb0bvsPr766CAgZmjvueObFYrfWic0fZZYCAiNTOU61YSwsr237FYeCfYotWQGqL2dgruBUyPDSUMf+s3bN53hBkAogPU7T1rD1qBr+3bRNlNaPWCBtameKvDYDd0z9P/q1a40ayAfhmpQMkBohEBS44Qd7x0/dRR8Fy2EITReWCUJpU0+o0nOOSVqyBgxYIgws/M+p94LRauw46QrP3sQizeesl0ff//Qimyv598bnAQTp7NAEJlqk403HdzK/tP3jzpYVNGawwgOXeu4bQ31pgGxtrJy9KDAlpcNOL59/7bTXNMZYgFql+5JJVXtchKiX/64CLRNZtoexJDQVONBHQ/351QnAGJNVoCmc0KIFZvirGM//uBzhY0RYRKqiz3vG22tvvBJPXYqr3XMmCnO773q0WMNfeyDT3EQVGJTZQwxyw1/VcPGB+mkjf8JPTJrB/8P6RHnjleAMsV3OcE3S6JkbKfl3cl7S01vKgFixmEMILFCxCKMVEFoWt9v6BVWQL1fm7e45/61p2WT5YN86s3v+af5E0fSpWyCl17p/9ETEYaJyhCIK7KTube3BwGa5RmLyBqtsOSrYiwBxM539tQr/iE/eUYYVaUW/On3PWXHnqv2nnr1xzavn/jPkLHaCh+44upPv/eqEzZnh963ceuBQiQ01lD01hcXnLf7IcV311/4n9Lrk8k46msxHA9TEaLBvIba1hJzag/zvOxNjSYUXK2mu88Aih28cnoeB6+EL/bK9TxI/91y2/qz3ESS4bv+3Oec85Gv/YgTYaDp7Pd4PGjXV2+qyMjgGTP9gLE8ITsuz1G8VB0cG0MgqVPG2OV+/9Pv/1JxjBiD2n3tvtev+Yu/eemzb/rOOUfw1FTJHA80pzx9w5fv2n6y+b9Hn86mhRFHADOvOeG8Z7zirIN3f709z/57zq++P5eT0Q+lmZWcAc4YSLXJhst3meSjb5rkGNCa86ngCV+vpoIy5iEEQI9DaEPB/XQMbUWAWocrAjuNrhBg/OBt5sGTBgEROvIYB3zqm51VbQq2fnG4JAlNZpFq60DDXEXZxJZnZRkIllO3PIQaB6ANJWHQ9nLMwPZTFm/A1Q8fcxKg2d9f93SDlz/8B3ZfcYzUKLQ23JbkfQnetDFDWW/fgi2v+hf/OjheMt8CsGPHRRc/dOsqxuOsjzhGGbuia0wuTcprD1NSG8q8SVltDcaJVErfgAqrC4lUSu58kTVVXhtL40TKZaxBuUtjT52UPmW1NVrlqQaVOESjFLUSUyWCsrOhKVw3zjtyVRjxvI5QKXI7ThwX7/j0Vx84FnN2LQlCQ/PWfWrHa9zeOJcTfMykaWzRkkRtQ5m3dY+Cg7rC1B1BC6kSQWmUquklicsaT4DmtopwLrDvirZyqTGmTqSmNF1NbB4DgNuv2TILaj9x58ubePIb3/LTT/3pGXKItT9o1mildj4WORr97BV/vHGs5/7V1a/7nlKnY445t3aPtz54pExMzpDAKWUORLCGpADlxE6095gCBFwqQAQjjDJRTsysADEzwKASUCILypkywzwCpEPOeUY5qNS+3WcFU544AxUqGKmgBJhKJS1mXrbtlBdvGN/0rUfajWvDs3fQ/kvOeQ5WqyXA+ZZd8pqBZkkNSe6miPeZBSlTMYwro5Ur8syBFEyFgmmGwJRZ5pyoAJAWczMC0YbNjwJHPnN0ICuzbsPZM7TnxuNf/6X3nbw9aJanVdnDf7bv9LmD+8947mq6avZPj0WOBxdn0JrvpTAPd1KPpz6IGpMJiKGV5BB0Pm+pALjv6DJZxg/m1aEuOi2hJFPBMECFXnt7bHIIlKR/yfX+GDR5lJtq1Icux28mo4rJNhXlqpGcttMna2i1ufXS/3pemF9loQTODJMJmMS30ker/+HbYa9yWFEsCc5UnPdfJobK8JzpWWQvPPq2r19GJc8BYur5Dfi7L/3RKRe88xf+v+N8m80Qbf6FhXI2haI8ePDIMzbuT3OjbXnEtLonCGh9yf/e+4/vtztvMgugooIKQqocInIAqNMIQKzzGEqqtcSYC60MJ821rzsAsc60K7mJJeWAVlwgaR/dkMLQFdzEvDFZqmwWq7xQoOnnD62MNIVPJQbkNzRfN2ORTUDL//r54+j2B/ZfvKkNJSsJYFfuv/vpZ0hqlVtzGFtyWVu964oOBbJmPEKFEkBoCq+udg6MJmWNWXvRBT9x8R8//Z0vAbDhodu2y8mf++23zx29pby1OgXcxNGAK5v/7CX2hD173/BstSMHv9w/mlQSnGU0sXy8+0G2hhQDh4DIiGQMhpIxBAVZEsswvV8KGSNOQETGAKRgI+IYYhhESv0jAIklJYVWMIZJLBsBG9MzTwjG9AY5xrBjMaRVtDpWg/G3bszOztt+gar7Pn3pDVdf5n5mbZNKRtMaAg2I/d5eIY6Z++h0GFR5qWaXNkWDU4tlI0DNOUGG59kYNkJxzM6IFQK5E3dc/bG50wknbglHjLY/ZeZz8hMXzf3Vr93z1Jx7W0wF3fvl+7a79rXnu+/845N/at3U7sCYQYlG+lbzuPThoPBdIVhq88BYTJOboZmPJT/shb55+bbwqZxyB2h9IUCqLbWFDB1LyfuCJ04RvQ1Nr5maqA0lL9tc9PYH6Qtf2vKyI5L2ezaJHcHnq3rFfe26QpSoYlvnIWWNyZC49SMCYu0cgCZljXWxdi7UhVFl1aHxSw6g9SNMaKq5Xe4+CURQ6rqi5fyBV8//n/8CvPvSP91hEBZdCTz6T/f+5vomudrmaZwb3yaraRb+6t952wtCM624kRjLThD/Of8P5T51qgCRLhWT6iC50n+mD142AEltHPXlC1CiXsF58Jca4qM29FyUCiUqyglArHv/D98WNC3pctnHT3rj2iaWpMpKaA/UR+RDYQNKTS0ztNw/AFWaTjtIdegjBN/k4n05yU4arMEZ0MHUoI79WF9xrmPjiBZ4hId/7tG/3Un1g7edflTsSu/L9EV6Sk4KjK1TUBtHQOrydMt9Z26001wC+KaUSV3/p/w/gCYM05CvaIXkeWq0t9gYcwEgjNNo+oCqokyZkCqbQSsudGGlnqXGpi/5vrgOcw+BJq5RAqqcCMqfuHLHizZBCbWW0P2f/qs7fvZtheUl/8C2nZkSH1Na5NFk/lAlKC/vbYBYd3lBY8mRlFBbl8YBWUH9nKtK6HxmCIhEigYlDvEs8OFf0kvOBbzUYRUlFXTDhjKS9+Wk6qlKFoevrZZ9YR7//rwTq4ms5aSECOOMkCYiTaRK2nDRn8E6Q4gQG8UsB4NNaoRB1gBkDWlYCiZNRL4rbN+fEhHFqmODCFIFaSIKjckMAW0njWrg++/fcKYFEhmTqB2f+sr7rpvbRfWE0EhJh+sVTURdJ4lNImORiFItobNqLKHPCbGNmsGKUl3DioG65AqKsJaTpkrESEMCrYHaOkm0kAqlncff9NCO9VVOVZOjTXbiT5sayiwPQmsEkxli0jTtb0CY5gI+7vpINQmhTibVMKlhiY2wb00XLbFhkr6GoBUMZwapZomN8d6iTc72C9CUiHq9xFSTpJolNIbJMKXEQGgMg50VSjXM5BGxCtZE1rEzYtI9dxRnGk+t4eQtr5JH73vRq6kyxZSc9tD2G8PGMZvUiFCqiZCJMbEhA1TJagUDSmxBbUsmd6g5NS6zlBoS0iZmGackTlJix5Qliq2ZKcOiyInPfO8d56yFFnndZW55OnBA78cQQQAhNiSh+cH+Bo9P73UYYDR9f/vPSjKtrEu1dd93uAMP+Po2FJyUarPiSNX7nDtfKDEQIag4P+x42bpUZ0ajEND+0yd3vWk1UtQYAsnso3/5d6/9HyMDTUxJJRIlQdL+zzDyo//RhpKwYnbVNMhX6lhLDhZg9DMcDxyNJpW9QVMbXcc5pYQYM2Jc/183/eMR/dDqu4KhiVUFNQpUnGtlnSYmhCdev129N0ZjpLgoAo3QxEiJEjRSUorCUTMOaowmSkAcgtEHj70hQUqJrKPYBicyvEiaKEUSjWRpUS3QeiEj/YsJmijFlAxFNUqpEYRu8YvX1xs2tffvXtj7yCN7Szu38+6PV7ty33mTmoCW0IJ8C+46Jg0pGU4pdtFEWEcKcRRSSqyJEkJlQjKhiabIsTieIQLq1mCROHLjKSWRmBJxyxmqDE3XBB8pS/v98eOPXnXhhpapjSbrPTiCN5ElJtOr1ekicdcuLXaeOP32OlqDphVRI0BDaIm9Ny20ky5JXfsYrW9CMNGbFtSCgjetohUfpfFKpm2jj0wRLZdYBDrpErccvWm7tonRw8AIwDGaKlErPnJLyZuujSGEEIIn59hX83d++o52y0a/B6tm1xx5BCibwdX0o7TgSmqM7XJL6CiTVhx1EpoYog/Bi6OGpb3vrr3VYqfRxz6pkpwImpw6pNasfuyam+7ekzkYNdrCUTP5NkYCDd3sN/5lyxYne649ZB5b/bTjvnj3rrW1XZwXB3RxJCTUdiGE4NV0DYsajUWo9Ye4Cj++8aoRp4PKbYqGtGmmF1C6sELgO8bU5NMjTp2yyQWEz5UkLdhy5XhVEIBAAtQoDtMLj5Aw+bQwkL5w5QmvzBMjcuyKhVsPrLvt0bOerkuWLcHrCj2akMww7KT2G5fFo+7e88tPWhZHNqHZk46yiBVyU1176XfrU954Tr/jqDMztX0PJPDV/77sXc/CwrffffZbbBC66uee/0vyrXNn6mKy+S6WtIAR1QApGawcIf+jeNHv+58lTLCOsWP1YSVAxPK0BHtoyaz4TNG1xUStUmuWw1F61nphaGsEKAA9zA5Y826CacwYaPY9tqGzIdPWOIM9n7l9l3vOmRpkufxXuIekNsH1NIp44MCqzcc/+I0W/XwSyat4c9ttr1mbZDYQ9t16we+sw+L8HDQJj0KU4OuQGWIjXkSrhxbnrMjX3vqHPwIEtSf9j//10Il/+oZf2Dq0lhyptTIobftkgBAMYGZ+cMk+vvrwIpPjUGtRY3ZlnysQOpYY+3OzLDv8bR4BSMEwQOUKLNFwwRoyBo0mxqwrL9vz5ItlrWugLDJLIn1MOO63BoIXeGC85L7Lp+VRRnHotdZufP7FaEdHbcXND1544OrsotVWUGBVMUNRpRPprv36ZW98Xl7d9PDpm27+zgtKTvvG8F3Obs2MjSnedvIzbzbp3i/GQ9/4xlEX5n7Dq7/8t8Dvu18pJq2FR70E+kCkgbOd+aHiYo9PD9kItItIXQSAojj89iaYkSAFRei+z3gYIwAkr/2QBfJx5XCYZnprKmiIAHxYOX35tLTuDhON8WnybpqI4YSmA2DLldvJxQoAUujNUy75ws9sx9Vve/89V11lTDp0zce/teeOj1/7YOWLrJn74GWrf/sDh1Z96Q3325s+Pu9EEwWeTZFJQ/fINV2pcZ/90N/95JZb/vnnv4Uw/4mvIbP4ynUegBn1bd2V3BdD7LRPfOzSE90/rGgg0cFGJiS7AuEUJz0HKdiemrFiDUHLrVsjyaS9TyJH0YlAgwGXQPIr0HQdWYOBPIxggE4p6gruo0NqoxNQ0UUlj8MAPX1vsbbfQt/4zV+Ef2V45+/9FdBx3Pcd893rizpfHw1Zxel/8w+/veZHtm4gvODiuYotq49ttClRnl/386f8t3vu/MuTRie9cBfW/M8bTx8t3LZ+3T7ghssvWmp5NiY3FEMKhiAjYGowfWLqg0rfuRKQyTSc1E+ZOFARJoJVzgGgNMUGB5D8siUhFYhRg04HQyNpdOWALIpmqr41CtT74YqlBBDD9IDWkS0XJdNy6epXw0p/TmJK3jJSJEF6+MxdgF23dXEMIGLti14Eu+7VNnWZF84JsuuiEWZm7z6eM3asZnbUccacUUdHPjvs7Ubb/EWP/clbzsFsGbDxl3/6U1++7o59H3vmhYW3ADQEyKQYrEVHEgwb88Sud2MnMRl0E9kV78X45ZpNLaU07QflxUx5PKTOyNJs35s4dN204aXhkEuYzILqbGhpyl9NA41dDsD3mi72rtvnzsyWO5c59IFvrNtECL7vh0mxvAXromggCsIgKwH1u9b8pP/Otw/sHT9cHK3OQLvIq9cbMrpox1d+9Nu6+dnbjHPX5TsySbDlKCtXz5SFtJGPeOHFp+07+L9P2bz5xiP8Y0e+Yh2A4uwXHnHscd/58gvWRwHANqbp8ypPOpYf2gUeT//QVGUO0OXfPk6PKaouNcuLIo0pZNMHzDqFb9MeVb0iGV3TS5EPs6BqtsJtR6lfLmpKPbdjerTKgf0fu9MdA9U0EZsw09dxICbp51uj0LpG/sjeTT/61EvnfSgsFHZ7l6FTV1qOe7p2tlRZ3LfjmJHXRABsmp8x0EQSu4x3rc4rPuEv79571stD1OA821e+Epd8dw7cZITosy6lbgntlCMVP7zEH9/9RzM40OiALNRmpSERgs84BMc+ZvS9jjU+ZoTQzwstObQr20yI/QDTpRwtssMMbVawhcQCH/niaT8xtYKsPvehfT/2aqgF0KWMVuDhAOg8zw791CDdlx+BJkfngNRZQeoMBUddcr4H3Wt1KN3z3ZfPhegIsXMyEIrm42gAwjiLxEBjEFwYkhqgS3lMrTWxc/LvWyk9rvk8R1+SvQ2sMdQLRPT6Jdo4MWa4se6F7PLlSgwhIyJausomGhpFbxgUfE7G9Iwsoun1X+wyxsp89fGW+Whm+ez6lm+vWb8vCSF2eS/qKgIgtZMX+3Vxp1mOEPJjEHyBmJTAOQDOAQEcVCn6jEDZrd35Fw5nsMyAMa0YIA/Uq5RkAyE87wuzr4JgrJ2sWbjoMWDDsqZh9wTXR2xVnekSOio4dOhqU6CLGbfJdgYd2uhc67OssVarRMo5+5BRG13HrJXmrnbaCBBaEDpQFnxGPrmOBZUSkPvOeMm0SdSBXOxc9AYNGWomVwXqnLapO/DgJVdf8Z0XbfnGV+ZO3b7nq2bzGadeY9ZRt0AjgLqQB9jWoKXGcZvgTKNZ7FwXMzSRx+oE45RljdXougDJQgfOUszzzlPtEGST2DEypLEShDqVOofPnTQdMmPQMncpBtcFGKdg1MllOUIDUuvaAOM6FoUfQzxJp6njnJ/I+qAeuevQEkDiosc4Y+VMFEwwLngGCylT7/TKBGbKJIHZmFZJmdDre+pw/M9wEsEkRZsIoMxyb+/S39EzkbNgEunipD4YYJh81drVa7fMZht2uLVztPXW2z6f7tj/1w/8aGEzrRMzyAcmWOeJmMAkCcSUK8DGtIml6AIpExgs/f+IiAFyxhNYTkikRGLaRErEKjOsDOhwrdFKwXlM/ctEUnSBU2tYQMoQKBMzESgTUZDY1NH/q/ljabaAE2g9maeXghvkAFLnOkwdYLXIpoOnDbL7/hf65XCb+q1CSz+sh+Mznz7z9UN8Vhauve3A1XTBU588AgZ2d1uv+j7NMXRDI136y2FjwGQJogum/H4c18l/CyuBW6ErqD9X+L4T69Tk/oT1j9D0LPYuFARobWO7inuNCABdyLkL+SBcDW0EjchS+XqfM8UmM6HNBdCG8lQ7Ox1dqo0gNhkToUaBxjig0QJAaKdfnJyAYHGmn0QDzz7veXjX7Rc8C40WcAhtZuz0aWoXCupi1ooYAmKTGTIAUmMt+o/UKFCzERr+lQoCKuOgDeVaG26FulAQQpeFVPTLu0bz3tmKDY+dI9f/yCCE2GRmEjdzQ9Jn4ImrD3b99mzQFpiIgw+tWEBO0rAd7LWVR31NCRPAhmzXGQZbsj2Fk0fTmFnDwozW93LdBsCIAJgeWGAZ3OOMDIU2MwAOPbopJi9dNmm2L314Lrb9DpPtSnJNj6cjGuh0ZLmf7geOlNG+VRkSQaO5YQAWoZHB0oWMLJlRc8+TKPvUEdCF3JCIn9wNGgK5wexsEreMZMjAE1kf/RWY6Y+UHcCoRNrMINXOCiA6zsV3RYccFmDUZJs+HyKAZBZghxoFLADbqutfnEQHwxbwXW4B9aJ9ydeUu6kXU79kEoogQ5YaLVCJrddsBnpOTaMF4H3m0bfsXES04hy2v8NjB4Q291o4tKHPkfXjwvZFQw5tzDuymaHhvL1PXR+LA09keoIaghBZoD+eqSmHBVJtXf+RzPRBfc6f2PWu1mIdoQ0FT9DmjsgxlgjuvWvO8q7bEjtZgsBPwPy2x7drhWziHqTU17XI0s032T7uIafwbV9eYKolA0ZzjkjAMAAc8QhIddFpAVgFkLwzAA0pBPWT05JlNju2CsBwz5CzxhGaVPSJN4JOMga6rm/mgzIfLZ342F62alhYN6k/jJuAKZx0vujNg/rT05Ke+P2HemQMGOF+kPE1ldLbsVssJZp5iD3UWgosgMHIvCcTAH0xgTJm2Cmwv6l69BQzahTwnE0TA8TVw4a9L5Qw2mj6AvTjwmD/lxfssWeR1WUkMQ2I397FoCejMvcMh0bz2tK4YBEdm4yyJhZTpAaB9tgEM4zOVntYgBnKt4iNLchgAAtY7UUEzeR4p4758mYLhr8HDfBE7Af7JMoygqOekhCOTaahz0+PyZUcK+DClWa0lCqD0Kw0RaxRCE+qzAHqJVs5XDIj1pkFDDq1zf75BKtaWZNRnd3/wbvOO8rhB8yYXcgCDcKLMEywgGNk1DNCQAYBgEy68uSG2joG2pg3hitnhs8DhqnrWwVljNhkKRQZT5gs8G3hQOP+2c7nHblK7BO/Px+SGOvMItUmyy0jNLnpfN4h76nvAJD1mpOmVhfrzIamkM4XGfGw4m1DwZCc6zRCxbbJYijJdeOCrWHUqSQBaERItaUu7/pZKLXWcdF/0YD00N6YfJ4COzTuI5ec+5Zta8Z5t4Rxc4aB0OTGt4UYIRAop84XzAxIqPIulRhz0RdG2Rc2TS6xaNSMy5wQ68wayogKAXhYITFjRKSVybS1jnNmIQMzOcA0qJ3ToXKMsCPKmZYQ9U/Q+S60E9sbMzBhYihBRoiFxTDXyWqF3qaERIhYiEz/PIu0yWhvMcGGCUQVcgYbFmHDYCM98UBMj4prkiExLCzC0rsBEg1fJKL7Hty8KxOi3IIsH7zx8s+ms0bck9x8zdw74RghNkzEZG2srPBkEiNhMTQ4uwJoojVCUyw3MsJMIMPMNLjVEBN8JYPRKA3OSNOhCBUJSZ/UtjWV2v7tiQvNE1gfsJZSTQKqkwH3yHBiAjERQcUAIkh9nRDQB2n/iHJvfKNjtYwqGohjKPfZUYBY0TYGnGqhrrFiaAglYlKASeOYhJgUGm+4fc32WarnmZpF5iOf9rwjr37gKVJHC218Lo23WgfbJwEK1MkJ90yTMCYhxpA0pao1YCGm3nEkjSnWhojTWA1xFQyArhHqiaDSqhDG0WqtQlx7A8BXQl0j3Juo9EllY4bq7xozGMs+gfvzOEZu0zininLDqbbUlj1hg9uiI1sNu4+kI9cTNnLThrxrsqyxvKR2qKnMgNhqUUse60x93rKtUo+5VkbulGoteCymKby6xqnPu44AqGQdF1qlZvd33/2VmWe87Kibv33kCeP7V110nOHF1+3957WLWYkxi88YWluNeSvSFL62RSVZlZDZxmmXdWKrRCpFR7YuumbiLGxmUautM6dUdbmrHLcl2o56EGDiWWpimRoqMW+y2ibNmv5sTRNTolluYt5yruNICTNa8SjUS1huLuUJPS9JqaVSSRMxgEjUtYXp0c2kRLGi4QaWCKoE32ROOSlxoh7tvgxdrZHTvC2RCH0MSl1XSO/Co5RAGEuufdRQTjqcoSkIEQjdxz939E8eYdvWWO2k7NJc9f72DXnqaR+J4LvcDNhrQiJa5FIVTImgrD2InTgRJVadAHqIkLzPhaCLVLICPUh1OVgVtTjGApfKqpwYaQLQB0N96yaXRKyJOCUeIlfiJ/Y+ShvJQYrBdNtyoyBaYoXJTNNOJtNQFxKaSH1w/0iFYpn/UYBSzyXEEAOyyX2Fb0rpurLsD+V7ACw3mg1+20iNySRbv3rTUXkP4MmyePPCzrtPPDlXnuA16ljIUuogmJAfJsn1bW6WfhEwxnAexdmwx2AGAanK7TTPlwjFgJOmIX6eEg4nZxi+KQy0Rye2Wv4/2n+EJrcAaioAVS6hM7TienBqhW1mqE4ztCIRRTseIB/OEQA+LI1dV4oqA2aGYC2qFfSeTJFTT3TjEgAOLSSfTw4OePXdVx532kxazLKBLZR3h62nmXqyzsBOMVzbbGg6BkA6DHre116CzCxf/UyDcwaKy/CJbEWoKWtHw2oqBwBrFJPPP2H1YQ2pMkoAaGNJ6MI04ictkUv6POU47OvqsuUBK4G1WYmnJgLaUPJAgEKp0+4tFNpiAtzqo8kngB4C6LijYsZQSomp1MSgzNFh6LDYl3xDBQCaoB/NzMpd1eT5mf4oemg0PStClxM0s0QDVOVJ8FDgJCOCmcwbAEjHuQ1N+cTiEynVVCKBgVzpcMSbzKSl8ksqoCk6Vr+ipGLq6IXztLLAYYWHZhhrm2mSNi73oARro1JfF5EYKGi8jN9KZHxiyGzVlKA2lpQO93gf86gv+YE/uiyNvdwBpl9KRMOzSaVHs3bLhNg+OAcBnS8ZoS2kJ/MNRdVbmvctAKozBGue2PNEaG2ypebVF9wKw7uWs4GJ4H3J0NCucJ7PaJmoQCOEpvRhdNgVQk8OkBkgVXbq/ltryWIzRJdqmwFdk2hqcz8aLSwWM1xoFOT9Kf/K9WU/HSwnvSloWhGrwgzQLbcAHVMhGHIzIlihFQ2wQSYgaKIsA2CIl/WNNUmTCiaY2UllltPsmycKX1JqFCzd0qSYuinYhMacJ5DhLAPgqxmatmRqeXLYC41CZpTsdAeLPAL8cF4SITNVtzxo0whdNcNRgKT9kO6mIRsjnf9us2/VmTZLE/kN3yzj7SKk75xxMi4lGqWaygHBC4FA44oJSzsuCNAoWQbELq2E72VtUzDQD7qRYpeZqZnW5WH4fJtGiMYmpid8Pu8KH3vkdoQA3f/f3rfGXJeeZV33fT+ntfb+vplOp7TTM+20UAuBYqDSBBsECRANSEAwiBqa1MSQEE30n8bEaIqa8AtJ1Kjwo6YgECmxNA5IbThJCAmRQjn1NJ1CjzPzvXut9Rxvfzxr7cP7jYOZvDPw1dk/vsN+1l7P+XTf13Vfi93pqcHb4pX2QGur2YAcnawXAMbWRurJbfEWuNw/UvNC3qMwAxEj7dqFwBZZSm0EculjOOo5PvePHvnJb/82J1sclBVjcnJNjrjiPZDarpcwtRCtQ39daiP5tVCnJnJhrZYFkHR32RoH3mMLea+LuHNok5WZtsv4cDkSb3I/t8X4Fq2DRhYgBOjZniD7bnUueaCqQhDiS4RvLiNQ4yB9QWqXNRw6AFqj8egs/EjnQ9JaHOdeVYOR57Nf/5uf+aH28Yd7ZxYSYMjx9OsRUEOt9QKVPFDAOtG97212wK39JRgT0Mq8nq+Gdo3hZLaM+uxdj8/rN7xD2pqhZ797NvA+acW30wigCPVCl2Okg7BhRUsZgXbWIGjV9lVsdbZXaCxWTnXqfsTWzG5bV7oWQ59P9XIvzGrwmU+9+gS4/vgTr/3UT+y/5ysLm2qScBG2Hbm5/ZBG1GU4oVnvGm1PVeE+hSoEaBdw+d6b0cq23a/VOkWYdA6oZVgroFVU5WbxoprZauGaa+PW9JChglopFqZCmkurSqW0WsnaXCqHQq1yzaCCllpttXLLrYI1X6mnQqicMnFVyoXzbFvMWom1XGVqnisV5Nm0pqm2VmshKoWosOjy4R/9+fmF4c5nHnvsE4997GPv+tDXf/e3/coPv/RlIVbjKBZpyplazI0pl0pUaqXQMnoJC1EureiatRZmVa4ZVPOWUSvqqVGhdMXSqpGalXsyGLWUFnrygaTlVmtRtpxqK+jFJBIuKLNprR0kH1hu9P7REhhZagJJad6VRM2WanaxcCZEAJZzBcDcksJxIc1SouMs3kwNIGkJGKDZuJaMqVmGnCWzSSoAijFTY0EWSmRq4WyNUkYwc+qjOFVClrpMnzP3HT77ETt95kpz1D1+I4avyx944ygeKNVJbFK8YrdUJAVsrjCSU+glBCM3QKSQTU2QuSy2F7X0u1BSKEtRymRLtjUaUxcrJferGOZsSErjTDYX2xJ6GLWaAFgpGSZTq5z7KmackMn2ZvlqZ2vLOmOmICeQyzl1wAIF5vrz58kAnrjkq5XSD7hF17nP8n9fN6E/9wuv/xunReYHf/xfv+ynPve2l/YcSwwS51tPB7G5vgTebT69bm7KFxForuF9ri0lpzUcufg/mW3zjPCJueOjNxpALrLLzaJsZ8jEXAwDKGSBUnu48ONqJ6iWsjpUWCTm1IEh/XWahYVQmqWihjIkFxx50y1brtVUWCSyWiCYn4gt2SNg6i+NH3l897pXtKrNEozBFtANR6pKaW5lkLRspGU+G0tnpUPPSK/MTjMbTUagmSmv+vZrOVY4d9eG6TVfmWGJbM+nA5CtRYYU09oN4xm0jTW5vjWvVKNWaQXGdj7Oet8YACDUeG6g0spaLVpTCgAqaHWgaX9dJa5C2laOH3EbWjna6KuBVmlqUXs0M4y2VEVeD9Tpy77sTn4AyUmuFlltvqRbaLXQqtTNxFqlY2y18pFfotX2CFCtSgMQGKiMfqKvBF1rs5bDE4CsUulY8z7ldCshKkOTmLVuWvVm/R/9zL9OwrZZh2q2gpaNVrfG6XTH5Gi02kJcbD1n3pyQ7DBZzAZUrLWP4aTru0tzSHCXrJ5+U7PAT/y3L33brdQCUKpN7FChkbwASM0ldkCC0yTUAc1rJitpK2vPOsH11/VMznCEiQ2uZV2q3ZDsffAf2+O4kvbnj7nqIu7Zw7fDbzDOM/KFruyXBiR1vaM7CaMpoFCg9edLWZcQbT0+LhRNANXjj1pV2t4ds9Gus7t2vCvq18s1gN1tA2yMk9AtgibN1qMTaWtx2mPHtF7Ms5KdKtBofd3l11uhFNBEDkjqAdUz9gtt7QHfu5ftGTnmZMXEec1vtj9idg5ATX1hr0m9yLBi6w1ADfBonZec1IkaAw8M6GE6zcbesNiY3cORPwBjuoPDd66IQzD9P/5oANazSs6fu9O2zmL88k/BOvnCbz5tsmUW3989bGjwlQqQqycHgEpxYXtdn9za2y+SI87NkT9anbI6tnYtSylO0sr06D9ot67b3UGd8LKuR/HG+QYlEQPwqKvZNk/hGuA4XHPw+qfMhwCN5Md0zf3RQy/2GU7XzW9JfeyBZZtLQs34B18kawMqDo8+Ouqv5+9pvPkxYjmPBZWrm4VXFgn12pzxrUv2Sz/VtbguMDp3g1WLTqCLGTMBLZ6ka7uJkHoX+LxcnqLoOFVWAtKRiXRzfAOClxaNFek0HHPLra2TXYEHLcZT57YAcNCTdTpqgDflyKYhImgjtGhsTa5VTyTsO0ijJC/G6Cx7XcS1aLUE2uLqdbccEY2hAaQtGmvwxFd8037+V5/42y8sJ3OXnY2t0UtJXjo/SAjozwPEPmvAQl4XEcaAGp1Dl/DwAOC8LsZujtimSiA6UuCb8zqLk47WtybqhpB3BtBmj5f2HpTco96wfVfCkzqCaYVwM5lj6zARQN6UTpaa2eOEtN58TQt57Sm5eI8zCAqIAMu5carBr1Z82tHxEQYs4IEaXf+HzH/82H0dFktoy+5Bh2H55K1esdgCObT+bhATjEGgflRa7Xwi2IhcTCLI3T9Bx8VxWLMOSDV4FALymQNu2OL6M20HnX7TWNFAuYSOqHcGMDw5I/Is4BPZI9UgtBV8bR04AIv4vgYIQRfDaWPRRe9WmOgavbE3eCOwB3jFWZIwhDogdkFAYaGzZGARy4Y7PwFh/tRLP7fXYj3AI0qSj7/89T6K5oFM09la9isPTbb5Ktxft46YdbPqNRHFGi++JJ87IJw80BbHRH3jEVVCTb60ALudK1xZAkwDIEqAyEKePBo61YdL8XRdbORm7oNTddCpGpqCQGdLaUSqPgonn8nOkU0PrxgEJMw0O1ujpGxogVuUFhBUKRijC3NkzjnkaH0UWRqBIghRvQNMmgahknxRm6wWnzK1sisLEhvMtU0ffc8vfuS1f3n+jU+80H30Q/f/zdfxnXe87m3mjreqS7HGxGaj1dJLV2N3myZ1NlrMMFJig7OLa9XHQgC5Nkc2A5bi2AAaC5QCFkMtxm2JsIhFZrJATMZFy7MOdUrczUVskUoQKimURFGDmUI9tEwAJSgPN7t/2KqAFcuZYg1GiK8CExkmQwZk7Xr2XUQAF9XdYWt2omRhQGbe1oJFBooy2tLYkDghQ2T1uAUKgKKOKllDAjKshgyBYNUCRmBY8eI3ty94eD98ycs9P/iq4QUG8wcf8tBp9DAk5CRNltX00rED9aOYkGE4OFKrEDJM1Mfuort9AwPGyOww+aweYPhOFuiFI4KIKcxAaoZ3RBYstJW981wKW+lwXYYBD6fkm74PliPHpahFXMxlzOF5PZr0x0qu7iL5itbDaIFBIdEnr9mvcrdoL22gAp75kitc46WD7r2PvOE7z0xIH38P3vy6UNq2Si/14nCnc/XnB85FwyUb+0pvnVmftMmhh6FYWVyxDadXWQvckfHCmXY6WmYyZy212rCGZ+M+aDZiFwwAEzRfZGvp/OVGUr643Q7nmRsAe7p2nu4dYEAwUGfSRQ+QHC4cF/HqzhlGJ5qvefmuwix1zcZouizcZYBPq9fCCw3bUOjsCdnAYitDRWTtGACWcS0cAaReHYMbWECTrTnEY5XZnEcov6H+yDFYPbU6RFDOqlSXcDmEa74kNcoJEdVx+/GSUOAsH9lKE0Z7wouv0JrNZto5AblcyHe84AELWd1KSxvIyMX5kuy8AUomGgCBruG0Sg/onCGXohadI4FVss9At9tDt5jsAGDWtcISykXvOgaRpSMTia68Fc83fN49SdmvfKDz17DnEzi8LMFwuC5izLSOEg68yoNc2I8DbV3gO6Tk2oDe2tZzd8CdhujEoU7G6VTC1qxkrnvT0GGGfkMS8lat7gQI10BYSxv6jhfL2N93JHhseC2ntAqYkMVZMpm+eYDWCzqFa4TGG+gPpsn4dXj1a9JGT9nKcPIYSJC78u9cHAkMkJlo6J7ys/4mOqkLANisVes35WqQM7mWQz1f/T232bh2cI7XX886PgW+zR2Rbzmut9W133aXtYHOGtbyWOlBl3FOGJhoAHITgmHqYfEvkrt7njY+1Z+AF31m8ciC3bA8IgDidL7j1quSDnrsHEK+qvN03mb9tmrW6HHlylz4rOfIUwL0KgKYJmB/uQeyn6INBKBdRSBciFYL3v/2b30XxkLtqn/v6HAR/kuXeEZhBOTydIBl4cuYLydnGhvA0VW9UFT0etXgfD9SwcmhnCW3qwtLFkx4Fuy7OQ6pjZAtzPWkPp/50Hg46g+uId3rueJfnYOeELUqoFHmc4iJBwVeythve6hzMHqxfwQoA0rgEYDMbX82qv7lL/3T4Z/99H8YgKE/lFq4GK1U+RieWwlLC528dsLvXhe7xBrmfeIBSPXa5WHB0GOTTxgB9t2M33PI0dU0nBQuJrYHf+N4H0OzBEBR52ChFMAXcndyMHIYBMDEAwDLy9mBSEZaA34qqE7BklyOIU5ppBXjrgwdaTnDi8KBdyueGgxAB55P+8fyO3/48heNv9t4wggsdSSfzvBwAcBua3lNeWQH3rbivm6NuBAB6eYazBi7+ddfX1IaS3++D/3S8T4zDZ2iplqnYKHkAQTQs4BvJ9OLSMOO+rbcV9xjJUbQyID2sD9EZjxKH0DBSGXgziyUHaPM4XLIqG5varN1ROpAp8DzHdffEUYH6zE/MZ2tR+G7fv8rv/tvvWLAoErwCnBofBywDGChsCMFYcZuowlspAAAEcMKEz9b0jUc7YHApXtvxVPv1n7qYQwQCEorE2FH2wjo9t2ncQ8+M75aIwWpMUoENqQgI6RtaoYUUCUFK/IkQqhXTcAANSzRAnlhsBFV7cdYVbKTivZw+aCmECu6RAEIwtA2q1XStDAhz0TdQUQA1IrW+u5H/CtfUNMS4zJHftl9H3jv8HUDNC8GVA4sACnKgbiH5G9sGTQnBzb9iytInVWoqaqqCJTYsKqqKqipQg9keyqp1lkZtCWDoKrGKvXkvKx8hjwT9RxBSo5UVYEyI8cbxlPXg8K5xWGindS5IZjF2br4urjFYVZS5xZL9TDaeqiazBDJzoGoLeJlarAhJlIKrk4NxjOVOKTFhcj2oKOmIVE4tMHrXEnJ27IMSX10moY0k9KoKUQ2y1APV7//vz5cXvdpd/XJOy3f8d/8cx/4sd/7h7/97x+c3I4OLERIy5hhiWLzSxrsVAczD9QdLVAf0LSkkOKRZ6e0K9XHrq9mpoLgCGVSgvJYZhPyE27o3DU34JD7mjrkCNqVMsQC3nHKQzwEP6fBzqHWsGRSGlsOUfw03CxfTRuYlLYFqBHXTursnLJtUq7JUGVV6cmbBUdPzpqyOMtKCqySKSkNnXnZn9WDjF1Npaef5rySQst/fd8bvusWWu1l+Ue/9lMP/b3f+tHXNAF0aSO1VAZe896Uidag/isjYLJ+LdxZq2xGNGqTDNDjfzdlo+2/6IG21p8f/26rTFJdW+qi3De8f2hdrAehgdHAiDDJWxw5ZY3QmNZUQst5SDpuyaBGdBJkaLAyw69J6xfcGS+q3IgaaCOrEbrd+PhuAjlHbnBoS79mvOl//+evfcVDD9XGrUPZYx366wigpkwNUKKShk7CAg/UZXrWPWtltjXqdCAeOjtii8AJ7vWDKmvj1XG11q0RGqsyFhrQiNpipXNAtkFQwXgaftQzmR+589WwlC6TtspAnR1oN321iQZgbtfOFBPb2dteS514uECctclRGnp8hrIMiex87YS4qlAdODQmVXrvL77hW3ZtbRa0z/7BrZftDGqqI0MbU8oDb1I+E0ZMIt0ysurM6WT8Ud9oPbY2pcmsqkdTcgMd+Qkz3OI0j7SVY6IBm5aFTmKWVSPrJK51quPEdi4jLze8XgFNuW3yHCuIjxrr+i3O6BZ9fWNVptaH+9pwOQ7SW7HdcYOe/bo1odbMGUdj/eHZrzdbTFL7rp9509+9tdSRKgQ1IyBW3yWNNrT5EVtFx0IdO3D99vSPpnx2wl51A9ZekstXHes4t/HUZYAem6GuRW7XNE5u9n6OlNpSAF3yEXFSl5aTLqVjMNdv03olrmVRpKhLKYuiFQB2LyhLqxWwjJ7Sn68JyFGRo6JWoC79h63n2ur6frM3cJ4ffPkeCDtCikBEALyf2zgCgN0b6Ba+uiwNgMbcrZ7HbzeH91IBLVoXRdhRD6WMujQAGEcAedEt2PlSTlgbAMOOEOMxFrpuyW2pPSPe+fOGuWH/xzVIa6t0gdguCWdGiKpyOWu25MIMnWm4/jqtKrx6TyaM1zwMKNHUlbNRSICffM8b33arqlnhi0985GOvfiMq8aaIEeNOzs0etZHp6g9bAdsJINxmNsfkHrOnNjKnibKUa9bRVsmcyEexq31dXyK25JTt0ztsn9F+nmbf+Y2rDH2b6v5c/yOpp83ZBCTQlRsuSBt9rEQrKiM0Tf5S/+PKDAyNxlYzQnO9XG3ZJueAAtOiIeW6e1BQqkFVTuY3H7nzgfGbv8ELt8Wf6V5oYumDY0qDQer9V0SVr+owoPSm4N3VFIRyE9o4T4c89uB9nqHFymIv4o8f0iDU2UVAMbLUE1i5VTPhFoC2BNOqIaOZVc3N9keLW0CM5BlAwa35IkL6GJNQUdNZKQOau67/MZ64Q9B8LYR2k510rlFi2aJSnpvjRwY0seEdspJ5/NE0GJdN1mH82H+5eod7xztf9+VxCXugJpbuMFrRxbUEY32WYatAq94Ze5aL7MIly9x6r5lF9gA0GS/zhcHauBO7SBOH3XSyf9UkrvWlFajJoGTHqcnN3gfl9sK1SYMxuRigIOwAaGHpY6IY36tkO1ugO6aPtIEibv2Pc0Bt+xMwv6gFjFIms1ay6v7o2wVasWQtUJsZ0YphCzz44sFq5UYBivf9zlc7fPn8x4fSwvoGo3SkLsA5DKiZt7Y/egTHbUkbjmXpjUMDQMVIK5bAu3XW9KIWtbDbDzMZGgE6JcPabGTjHFib2Zn5acORPcN4S8QtS1WDBCpEjAwGxUKCnCAFohlaJKrRWIgjCZAyM9AKz8VpysQFWrkkNVlZcyHKqNUmMHOCQQYyUZoclSrImZjQUmFkolJsaejaJo/8z/tffx9f5UxXj7tbv/kIlV/4afmKBwcgKwqTklBJjakWbqlxUWFpjYFaJSsDWTllsF5BChdtVxZVkBKoNEFRymyopcKUiWphqoWpNM5JLSIMnoQFciIuypqBwpQTqFZKJO1KUAU1l8JCjmuqcrPxlvRKg2VlZGd7xxTmlgKaQW5WIIzESM1bkEXCIGjZl8UT4mwaObJokglFSrOcSYDaahUnMUudraNChShLrcZSqZItJselhUqUDYlJiZwrudz5wLt+9er2w/oHn5jLk59rX/iqJz/+0Ps/+j1f3Ig1UTsYaUUKuyLcUi0ZplI9mLQEoORaiLKU3EoVQRJMpkGoVRUynE1tRg+EqybCrpTShFuREtWSEmfnAW6lkBXNxlQpaihRnRwbmkSrs1KyuFYMzZPZSSmCkmBulK+2hfQgqszGQDQRQ2sjAUIu0pJ1IyBLZSDKEGdrtIplACb0mNQOHQ4RSjaGoSVo3gGtjRwJqNUwyYgiHlmcVpJAaNUOpY2JTauDQGvTZfIPveRB47+geA73a/5z78CPD9//LXRgQwNKYLChSiyAMbMdAQGHHu3RmSVIqYuT7rZzwkEIMizVEWBMNAKQ8ugJwJDLAJBQNR6orYe5nYqlgaGNmCmg1kAlEMCeDTQbYMg0AGbvo9HSrDPlxvkG/eqy7oqIh2Ag47ZmoquPdry4NhJuChkga4h5W6IjdIqKJh7aZEfesCpm83Jo3czbs+yoJ3dOUybqUjA0APuH7M+//K27/NBKcT489sH3/LW/WugWWnJsDJDnfUAtvO4UOvFe0CNi8wgQ19bxFhQAwQG3EFI1BLTWBNAm0qkq1mpiap3r4aGVBFC3W6GWrZrEetg5Y4DeODphN3T4okdrjagatJvWx+kYl5PXYQuo7bdUdy6Wg1IvYxJ4yasn54yHcfcc7Efqu6JLOImgjY0BAH/0u4Sm0GwYQJ3kB++rlTtiirMrNfCZlM8ZGq3HIVd9Cv6fWz2dwDGQYltdDUx0UcKNylLJWqjKRawYGnM7ntZ4QKbdaczdWH9QkK31kzqCkUXv8nAeaZkwEi+S40q02CgfdM0DqoojY8ID6i+Hk4zLiZwDYHYPGnZr69T9m95UMjVKcCuPQfxTDKZOq1nZJmJxyjGcaVMcaUa9zLmGAUUvbbS+M1l6hIEjNGWLOa8dtLLpZFj7LPjPQT5HfwqLf2T/PIXpsXo68myu9dd6JzTXIWWwZ+f7CE8+L2esotRCWDuy67EM4XyONUBZJLY07QERuLvmHeFyOj8VL+XuJWFzuG9EnqOHmK4F+6C7Ov/slS1ac9P8D+hS3ZqF6yjIy5AFeiagBqDkS8CnL/Px+WPkt2t13wYSoSZ3kU58RobpfXbmP/fdbGspDCDkkgPN821zVwu5a917ynHG7WvyxUciiN2YguflYT4fbz20aN4CAFGI1V/AWZieDr77DOcHOzmrElin84j9RHHrIGs7O345v/Eu5Qht5ADU5Ot8YU+JRjZ+lEOj2fmL9mReOm6mt8Nl9a7e/2tveTOzx4fePX/7aytmez18/XyhbkFt8uWcjTnedZZc1Rp0YQ9wnv0FZZfiBjdGAGydvByttCV5zvNpNixk9bxzbsa+W2ZbF2BZju07mnk5oyOsAMZtBB4qXTDoJdipbM8WkNDd4QLSpMxoUwaHS/gi1ckFhs4LgGUGit2dPWA++2MfZKD8ux955Yvf/UsypGLPVodlAe3GOp3MrHawxNxzxDIDrV3fblZjaa/E0U5/7N4kxzCLOkcyBLPlyIYunmcGPwv4Eum6TFgZSHKJSSK5fCtbnS4A0JVYCCUGAQmB3WTc5QmKwYb8RttxaT5bD62kg3edcwZRwFA5rVfz8NoHHFP94K8+/K34Kx99C3aSz+IzCKB1A6POnQC/CnexIYgCC9xJCgZAlx+ZVy4q+Hq8pIGl6384gIQvYkO1KuvzOhsHONTCN27fFZmMWxHLwgQr9VwBjT1iHQglBY51IGOQ+TJP9ugh/ztJ6VK+c9mksTrRrS4r6+/4/pB52wEsAG56yt3isNsPePQH3vC9mPnRj73Cxno2fSyARdb1z9AZThKrHgR2qIs37Rr+yurZGy5PH9j0PwA4XBgLWXrDxBpWMzvbm+dHAZbRFocZo+ksiIM3wJR9wExursYSluIZq7R1l8RgSV5yDhVGZyOFJZUQ2czw0uYymMXanAaTp8Cxhk630mCjdcACG62tcwsOFjmHSAGTMenJX37voy/+uvtQDIBogc98NvrDr98OoAc+/YcP7LKOQF4wSs6+aKA91qJatKl579Z3l+RqHZHhHWeVxSKHhADTmR5tcZh4kJxDXmyILCnkNmASO7XB6uwwYzDsEKMMjJJ8rUO/BhkmhzIj2FY4zzze6Pkqp4FBluGJAdhYgmOUxQQBLMipYZ0oyMFZ0QO5HntfDFmGtEkcyObkGMJkie0kllzX6BMzeZk9DJNlWDZpHmJ2bYZnK2CnpYyYm0xiyiLSypO/9/v3l8OHfvNRwhe8kl/7at3tDG5/08NA+/hDX6p1yFPgUkaGgBMCkmiUYICZvFMDneHYCtgyCZC5ZRKQFbRJLHQRjl3PUz31CgQmS2QmdoBjcspdJaFHB4ZnAsTM5NrsaDHCAizFQ8BmZk83bG+3k/VkZ3ILGZBlbcmzdMeYAexyxwXPrJ4B8jEHz2BvOhjQS7qyg2U1gEAzBR8Bsl2rnb1wJkBEk3iGkYrxJBFCDjVdDZakCDVvSIeXf1P90r/4gN9NDcMtvoVxd3V13wu+5t389jTffqARlezhXY/uPwKa2+AlpQGWyCEml72BBZixqAF1QQtYwAszkDV4A5DtuPxanOFuvWFmoEQ7ds+Ic4DNk3HcuQlMoj5u4qPWmK5C+bSCXs8s/pWxANzGnEgInnHaQjSRI7Nh7A23low7JRsyvAL4Uw6WVoGojZZwJHc4WtH8UfwZh0NCnp2D6T8gkZe/4bX3u/vu32pZP/rh6ba89b9/6IOPfP9XleRz3Z8OoNLF9birOa2b2YmeZRWAnjLrZq2tZI4AzDVcJq92m7UtpK5RlUw/1aQj2a5XODl74/Es2UfyPUzIuomRWbkqK8OCqOMpDjwAzOo2eZJgeg1WLIwRJqBd50cZRiwd9O8BXfkfqwLN0oazLTOpvfr4fSlQnjvO5upFP2Dn6O//J586vOWNTuVT/jYd7F0hKiQf+plQoIt1qxbJU43c1b+0Fcjh2ut2xMDctiAQ9hYfiwrACZ0JAsEIP71D6kbwDCkN0lT6P84fqb2su5WVsobdrZCLN2ijks4gSTkN3M6CDK7PriCaI9SJh84OeOSXXv2NL+6YIgEKTK2aB8ESZpZFXIudTrpiePSKd9s9ouPA6/l7cYX93QSLYE73CG3XA5Tpgb1scK7jI3qKc/4UtbnR85V00lHpfANY0xkQq6qZThJwkrDzx6jn67UvYTjCtuYe79WdXxgl0Aojr7P10NgBbOuvNyZY2Eh5dz62cwD1mMUH45YgahiF4YgGwSoH3TllG+FvBasPvGpEXbsZnzEcdBKPxXoAS9kR9O7LK3VAqjW8rgEkm2FYKZahr3frYJWbP++2Vf1JdoS8jEKkdAbZp7DBVBUEMLRj9jezj994OrQ2SFgv6Otb+mTRg/U90r4nOiMsLC1Mti+XHAhA7lCE/uMBisfb4CfDeR4tBMsiOz51ZJ1qCEdVCQFyDFmvG0ncyYZLgcgKAUrOEea2u7TvHmgg6aHNAaiMdNICgx7sMTq4NQzUKdibx8NVYkCVGGp2jPzEnYJyVY77+Z25kwKmBQDKk08kQKe4GvMoHZoq2iGhzQX1zpPdH1KvMvJVhVaogkarxNB6dSet/NB5AeCDti1m1ZIB3B5Sg6arijQ15t/54R/9hOfBvfP7fq/vQL7phbWeKhTLtJoWVcLcVdbP7czp5EDQJQJMqFeZGeqHcriIR6TzpAC4i/DF5VRPABhtXnStNiu0NVW98fVqNTcMOkkgwOxVIMdrMDnH3UQyAlCY3aTdzt0mEzrXaJLAI1RGqIxTj2AnO4LZMUBYMIDntsOMcXdnszZ1t0lZBtPhzn1++AcfYMSy45UXvTz5JIPxyQ+tZqcLi5GChUv0QTu7kmMLYAYmHvRgwgql9mdzYM1d9iu6+JraKYWhWxuNB+DT5C02OHCOY6oDd7UG1Nlr2vM51+cm/bXDCmpqRDR7S5s2DDSKp92qWaCTcV0AnjeoTEAXq+AJIx94MLfmaQftMXgIIEaAKgVtNKCT4Rpt2PauC1FnbxSL8dDHP/EAwzvq8aZxv/v0EwBwm6auy9Hn8vpHKmEHhO7k847gV8LtuAq5UefXUl/SGhGEV3mJjpAjc7YWAwjEaERdi2RVt5Bdd38agSMCvCcoZEewdL4W3hh+dw2q14+hWbGz0HJI2hTaKJgGigswLaBgSye6tNpApE3nBVBowzAAO18bDSNwmAC0hqZ2ZKBOleqhETXsB7RpUW2KeohK1BQ8mDTR6BWHz1Z3VYgi4HadW+bQANQG1ENSOzDSVBTlkNQFJiqHqg1oSq1LGK0OLa1xak15MNqAZWpYFlDwdcqKehUVjUi1Vz4eav87ap0ioFBFU1WFNiJNh9iIptKdycB0QKdIpbnqzc+PNntEnyRQoJy8oTo7W+IgMY9LDAM5aBsIurDfqZLWmN1ALZUBCp2NLM4S0NIio0AbUAWpuuiQhoQQoNZQi3UEEe8OU5idod2hjm22rs3WOmpI6fDr7/zgg1/7wOc+OYzlEF4yLHfUYvG8zAqlcQalQQVzsFamRmVQELXcdljYzsGUZaRUfKZB5+QGntlMQ817GtLkA0EjWR/VyW5unIPJeUCsI3ueXcGIgDKNFnX2LY2RTQyUyiCx+KyB9q21aWhlJEJOTvMAJ9MN67H05bTCL8FCF2OxBGt2U/V7gBg0BiDBzc6BdvPsknVtDgGEqHs0Bu2AcVIPXeg+qFKbvc4jh7wMJjYMqHMdfH/+jowgUdljqYP0bUN2Uxt0dnr4nLl9/+tf+Kn3/w95meTXfN2wmPsCxtnRDprzuIcyLdHuCaq7GTvc4d3+YIce3b41a+vMYXEOtBvLPIQuvQc0GWbnQD5dcTAA75ZV/2OmPUDOTNYDB2OlNZY9ItEI9bzoHgg5egu0mR3De2BMcZAmNJHf3/T+odpd/LbDcJe4F4D387IDvO+Qi2GlnmLIizOQW1hq5wzLGp9tD4A8qN2xo+y7Bb0HvwcgtzagRz+QbHCBEVqi9aAdQDvYl7zkG93DL7Mv/evfsfoKb+HJGXBiHn+8OQcgLfuhyxnEYVzZu/u6uikW8SVavxaVrMUd3NrDeCDquO90ufvbrF5bN1+lNqyn4y40oXXYHeC7HkulGsNwco22O97pjjaoKlK8tVuW8ab9tUYuHJu0cmdWp6vGS5OAlZncmRTWGM/iAUQayFwj4JsLwY7rIdXKtfA4ZnpiOHltW9VlrhLD7VfvO5HgGC1h9ZAbwqr/sQpEXL5OcH6a677vrhnd9T+uqWPAEGi/nq90kWvXC8M1nXEvyFxitW/EXtL5SxcYVJ3/rxATVD2jOt3opwPS3v2zX/R3bp9668mJ/TggHqoYmIHQng5P/mft84z4znGQi17HKVb4U3ySGiQMz0Z/RCNATmcHyEL39fuA9zr1QGTXivr51x/W/j8Auy7uKc9Kb9RmdwBgwpm5NXEYzwyzra56LPfKh3HPfkrua23GmUthDNdcNe3eqpS5d/vDrwoitpwFVMqwQIbp3KCnhco+Pz+ehTWrbJTWbdK0fsYqtXtS7rUKPaP9vFwHrbRs5DkveqmuAxT9GTprKMkWI+uG1Zp2aZXP6/7Qau765rnvjiOQ0DpDXRqmVkut6WxdsQWuL2lNP9/nx92Lsox/CkV30MVQEzl8uqhCoynL3jhotzjq2Tbz/H7+nKxXlpQtHnzwRfdDACJHJpJDKHl4WhGBP8Mf0nu2Pw75dnFXv/KrH37Uv/6L3vowYrE2FueA3C7YKc/Pj+fmvOsYSp/4FxOAf/D1LTWQ0qBX7G29pCg8f959ToaSTIZ2b3kpAPcNr6qz31n2AjGb9sbz/fEcr7VCQHgFgb/4fsh9ArQpm0EAMZTiPVmnZxQP4M/GJ2W/qPiHf/djr/rnf8HTH/zj//jYlxv50A/924de+djP/if/hfz8/Hhui25gGP6tr8Htt95C8X/+1348O40PfdWLUZ4Mt+/NnfFe3j8sWQPgNa97swD8iu992we+7zPmo/PbH8Zv/9Z3vukerdQ9vH+sAhHf8dWv2c9spvHtn/6J9z2+fK0DvuQFt5fd8/eP59pgUiXqFiiOc9o/8SPv/JK//0ZgNjaRvSfrdC+fr9jyxhM1ZbZhuu9rHnvtGyeFqwdT5+fXqz+F4yE6F84bQ4YBV+EmX6u/R6fHve3/aFcRFAw4xCztquLT6T3vM2FuwVBK92SV7uH9Yym7RtwpbQ01uoL2x3prt2tcl4HuzaF2D/dHW1u8/626wp4bH4lYz/fH85//n/ePz8PP/wG4ZiEKWo1EMwAAAABJRU5ErkJggg==)
As, both lines intersect each other at (3, 5)
Solution of this pair of equation is (3, 5)
i.e.
cost of pencil, x = 3
cost of pen, y = 5
Question 2.On comparing the ratios
and
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) ![](data:image/png;base64,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)
![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAAaCAYAAAAwnlc+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMwSURBVHja7Vk9btswFOYBcoAGCLPlAA7lsVuhKEHmwrHgrcgUEAgyF7I3D80Bmi0H6NwlJ8gNPPgGukNrWiBFyXykSP1Yad/wTZKoj4/f+94jSVarFUEgjgUMAgIFiEABIhAoQAQKUGG9vj9JzsgbYfNX6J2M311csfMXQsgfiXN29XLHs4sxTlbMiafTGaVkozifJW/36/XJuDgmNxGlv8u40pyy+XNTnnNGXsV3LF3eDsl7zugzJST34QwOliY02w8ECDDLFqeMkK0uPj1gCc8mYxPfPqHqXEcmwGXKbs0xbcb1IaZP8v2hBAjGtgFn90CAAOVEdZUXWVBkn805jwHFi16+j9WhpQCLKsInZaVJJtJZbKKSaxJF0c8hBaiSZic2GVtRHS8peXfxCBZgsaCHTqeCVftOOaYhI8Szgmw/zqkHqInbyfehwEFz7xNSXBAnyZnGD08u/n0ld/1/Ku4WMwIHVYIBPlYTTtJMX1Tb5PUgtRWfGEsfp8ueSCaRaXzTHLrkahegOUb1pB9SgKVpse0iy06bmk5rAQrwmH0rSgPNRdlYLOKv0MKZyLZxvqaLWv6T5nHMvlc2ILtynKT8Bpx7LXBqLM++sa0AXdWj/uw/EyDdiJ6jXFiaT1M+c7kLiZJfbcquvwCBxt6wUFBQbS7UlwDLvvrwv1BC+AhQ9cYW2LgfTYCmxVhy/klsxV2ky0mzbeiGIMQBv3D+uZJA6XQG9Yb1+dnKcl8CtInPuWO2JNiHd0DbwDZCcnekjm88SlmTTDVxtfGxPdNdxLf0hnKFEgdyXBSgpwCV+Ha91/U1/dEmOP6bEEsJM3ItHS+09IY6oGpTAo+MhizBR9kF633V4TlgUYLr4tTFJzcgruzoalFVILQFrRy225p7SjehpTeU6158LQ7Ihz6Ggc4BpUbanQMCVq4fjrpuQvSM1p0m5Egj1FXgTDc7WyUWLW9LfLjqNxmhtyFDC7DfmxBLLyFUXr2zPLwLhsTXpF/sUoCF400f9aRx3Vt3daf6rwtQr36d3AUj4BsdRLfAIHju7BAowN7hundFoACx9KIAEQgUIAIFiECgABEfFH8Boye1mIX4YxwAAAAASUVORK5CYII=)
(iii) ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:i) Comparing these equation with
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAVCAMAAACXDjebAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OgBmOjqQOma2OpCQOpDbZgAAZgA6ZjqQZmZmZpDbZrb/kDoAkDpmkLaQkNv/tmYAtmY6tmZmtv//25A627Zm2////7Zm/9uQ//+2///bzcGnuQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB6klEQVRIS+1Vy3LCMAzEhJaWlvSBC2ljsJP//8hKlu3ICuDkwAwHfMjAjFeP3ZW8WDzOg4E7YKBRVXsHZYgSmueb1NRrNaPdXu94Fb3eFooSgGkt9Hp16vVkEUSO7uNwi6LsEsJaRf1bpZb7zWnIAzQCFQ3eoSOKslWb28og64BaxSCSKbeeIEyDJHW1t4aB2qziLvk9mKo1TDGRwzzpXQBTV1u3httdnVSVAEhhUsUXWEb1MAh+3RpC+aDs2OX+jf0VOZBDCjFQCU251zSTOcCnsGI4GhVPUIQi0teT5l5yl3R18tsITIzkRS0aCGWJqDHApygeVlSvsQOQKwOJ+RKNYwdcPgrQ/wwxMgClKJ4oH1wObSOsq1W0lh08Oza67wCnhAOq1n1zOZkdktfY/YuE+sv+Y3DacND9VMLPz2NGXc4USoV6MQDq/8fIzgCxKH7/HG84cbQSkFv7Xm+d3wnkLRACnB8sMmLK7zcT3BnN2NVffFTG8sEawUjSvLw4HLxgVdhSz2BOmiWDXsWEsHSYEbIcbnMclo4HYB+5b+T0JV/E+2cdhvKOF4cc26I5E4C7/ApqdgKgaNKUsJwDgK/ay0XNTkDrzeZL9DpVEQAvQOmF9oFmJ6CNoMJzWNTNz2gA0FNZPpMT/ANZgSe+wsGxVgAAAABJRU5ErkJggg==)
We get,
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALkAAAAVCAMAAAAtrb/7AAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6Ojo6OjqQOpCQOpDbZgAAZgA6ZmZmZrb/kDoAkLaQkNv/tmYAtv//25A625Bm27Zm29vb2////7Zm/9uQ//+2///bSuLbQQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB10lEQVRYR+2W0VrDIAyFqZurzlWHMtRB+/6PaRJopYQBxRsvlot9s2uSv4eTVCHucVfgrgBT4PNjfUl1u8t/l8n2HcRDRC7UoQlcs0KVZQhjW0/bnxPFJ3mqbLm6zfaN5LoDCrMNPU0+vsaHUPMg4/DWRj7J/RUaKGdRAx54P+KFbKTJze7SYHV1MpwcfVAampmc+FH/GvnT5PpRnsdhm++E2V85OXJoIsqF6cCdBi0jbA9fOZXCcaSYxbH9c2pA4WcvxG9DnryCQYcxcuIwkQSJQuMwnwxZxj6V3YqzOMnokMcB+jFyLlqIQEMN5Ho18d66Zc9CskbhJ4mPqUv+mguSMkHQI290C8yVi5DccRTDiTRJ4PWiubRgN9848BiSHtnZrpwccsVuIQ4XuUK+Px4QZZD68JldkwrviTVXKAF+FJKZmDfJ84VmzaEjnpJ5GU72eP0WOndiimbR28pbm/6m12EhmZEv79ClEvSGFVsqRCLTgsFtfhCqcwsyR45D7W6D8P3s8WvZwdnkmBzfIW4pzOON29y1zxfCKeHvgvrm44DWXkV98iqNV2opVJ0zSQZekIrZxV9IVKqmCGo2/t/HVsItzLrr2ylgqjuyfkv8KTlsWFvoB2LEG+22C/fPAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
We find that, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAhCAMAAAC7gZh/AAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOpDbZgAAZgA6ZgBmZpDbZrb/kDoAkDo6kJC2kNu2kNv/tmYAtv/btv//25A62////7Zm/9uQ//+2///b3a47dgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA/klEQVRIS+2U2xaCIBBFIS0rLCkllcv//2YoAQkiyFMP8eRy7TMXmDkA/PKhsBzz6iPXPJ3AzUJIIYRFnxCL1y2CNik9dGA4JegAq4qemhRz/rTiB3k3VsjOHeB1JzPaf4H0U3gia1OgFApcvJ4CH2/bjXLUANmXBgWGhxbJPgGPCFkF4cR5YExoGnBBX0iW76aVDkjkcy5fhV1Wm/ZB9zKH/RM2BVVnvo3VYxD18cW447Qkw6OmpmLnSSk1FDIr4RSMJi2Mn1Y8MjoMVf/3nI1RWfccjqImqTxHg9pz5HYKvLlHH8/RoPWcmOkYz3HBwML7TTsgLUd2T9kiBb4BJ7MRs8EBK1QAAAAASUVORK5CYII=)
Therefore, both lines intersect at one point.
Graph of the lines look like below:
![](data:image/png;base64,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)
ii) Comparing these equations with ,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
We get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASwAAAAhCAMAAABUSmYtAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjqQOpCQOpDbZgAAZgA6ZgBmZpCQZpDbZrbbZrb/kDoAkDo6kGaQkJA6kJC2kLaQkNu2kNvbkNv/tmYAtmZmtv/btv//25A629vb2////7Zm/9uQ//+2///b1dJUxQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADz0lEQVRoQ+1Za3fTMAxN2tIAYxmwpQzGMhry+v+/EEl2Xse2pDb1enZYvrQnke+1r2XZuUmS9+tdgTeqQJPu6jfa9RXdbrM0vRXal3s3oJQaYZMq5cF9wCvGMmtqkLs8TT19H+NO5O/yh6TNHrgewohdwr5g2xi8/vCcNJvnELgX+CJaWeTuTsffwJxujzJzg0F8lvxNKles7u4pFzMS6duPQbG8wFKX+0IxsBmygh/n0zNEtyeI1RdcquJqcp+32fZIQgsXn4GqLi4YsK/tJ5l3RK64ckFR1EVVVaGyIqWIZ0wV1HeFWGWacsv1dLGYRFmIOiA3bB5QFELigk00A7KRTIp4xoQzgeVRFIwtiCvEEogtskAwiNUX2z8/++LDVzFlu1za2NxNA/cFWOoCPs4XK5ZuN4I9bcyPLoe/L0dxYAYZ86phUpuioApunnLchzpJLAgV9jXfQsUDB21zPD5/dNBUAMr3+XQiM3aYJbbIeHJg6oDDL4olVWjheWx8ovdlZwziGJhz/WLjE5evPkUght2IPcKuzKvksvhwONz8uqkBdVfDfyoP8Lt9dF+tLku8VoYrtK9Anibdw7mn2T7CD0pUQWWEe6/eG5wMc4XfQOA8oIrydV5oKQK3GezKpjxVePLDrWp2L6iXCEwtw1HjgM2fAM9JUUuMZdPQOGwUTz8+LfGFwBw68W9foGB4b/56uSAWeIdYJf+rZ+8KQvPSVaE6pBPm2OzeCuRzmq5NV4lz5TKkw5RRh9YiboGze2H22OOSxn2N5yQMFSuz7kqo77N71+jSak6zSUW4MKmaL/lte1PTWiz3/eH3dC8CY3zIaGLhiWpPRyxbqXDTHu/FH1gMBnyFxpXyH3rwk1UdXlwLI3s083RuGYgadgglh/z8uZ6QOdPjNH5rVeNOHfZp/Ea2yoPnPVjBIT9fKjLozOGsP3wOeipTlMqDt1Y1rSzWWnL9SZ0HL5p7WuNzUk7lwePxg0631T3/YYWitB68NaExs1j717EHVR58X3zL+NrGOuS+3NJ68AkhN/iiyaUoRqk9eDP1OFucW+oxslUefJsNW1ugw7xD7mukTUVCBhunL+5/hI86FDV48FjC2E8wJBZmFfeFx7eYjAcv4NNnAJQ1cImr1G1nxZIGZpDJCmVS20QBJHnwJC2XM1SpaMcI1yyfkW09eAEfuZlZkBxyn8TWgxeIJ2RuGdqoyYNnverBhMbf4Px7jezRg+e9cGx7GrC4Bw4ePEc863IVXlnuwDQfJMUOMgGx8YPUEYibXd1+XyOG0DY2fpD+csT/AB7PVP2Pw5PMAAAAAElFTkSuQmCC)
We find that,
=![](data:image/png;base64,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)
Therefore , both lines are coincident.
![](data:image/png;base64,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)
iii) Comparing these equations with,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
We get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
We find that,
=![](data:image/png;base64,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)
Therefore, both lines are parallel.
Question 3.On comparing the ratios
and
find out whether the following pair of linearequations are consistent, or inconsistent.
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) ![](data:image/png;base64,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)
(iv) ![](data:image/png;base64,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)
(v) ![](data:image/png;base64,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)
Answer:(i) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
Therefore , these linear equations will intersect at one point only and have only one possible solution and pair of linear equations is inconsistent.
(ii) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACwAAAAhCAMAAACVxLntAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOpDbZgAAZgA6ZgBmZpDbZrb/kDoAkNv/tmYAtmZmtv//25A62////7Zm/9uQ//+2///b29ceIwAAAAF0Uk5TAEDm2GYAAADFSURBVDjL3ZTbDoMgEERnqkWFWpBSBf7/Q/tgrL1EwKRNk84rh80suwPwYwVF1mMZG41EUBKIhqxcrrAGrEA0Ar5zJZU1fDsU+SAlVnhKeAlKIxqBoARwcdEc+23YN7Nn+IbUAEICxpXPT5eE33ztgC1J8e1FsFx0eJkBH7V1PXP8ARv/K9+Qsjivel7TkgxOlQOsLMugb4cZLMrglSTlAgeVMxNOw5LB0LtoZLJHiTWDyahEMzP3JrryWE316M87vsnsjG5DGgrNLZiLNwAAAABJRU5ErkJggg==)
Hence,
=![](data:image/png;base64,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)
Therefore, these linear equations are parallel to each other and have no possible solution.
And pair of linear equations is inconsistent.
(iii) ![](data:image/png;base64,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)
9x – 10y = 14
We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
Therefore, these linear equations will intersect each other at one point and have only one possible solution.
And, the pair of linear equations is consistent.
(iv) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAAjCAMAAADIbFY6AAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOpDbZgAAZgA6ZgBmZpDbZrb/kDoAkDo6kJC2kNu2kNv/tmYAtv/btv//25A62////7Zm/9uQ//+2///b3a47dgAAAAF0Uk5TAEDm2GYAAAEGSURBVEjH7ZXbDoIwDEDbgXhBZcoQ2OX/f9MMBwqJ7SRqjKGvnLZb13AA/jc0pu2HSle7DxV2sphzUcSkZiC7L3Pkj23WiMMRtFDQZHxKUmu2vxbKndTjNfkhNmkLbOXxyMxGgd37PmSi711lDGS24WNHmY1yMrmcnVwdnifZvOiuSkLdKZsMAuUkijIXCsASSf5lPENCABXeXnlC0UmvQF+rXCEiu3xRUCT17p8E9iHUbAjH8aRKFARR0E9PY4nFg4sHX/GgzcmZ3DzIQMGDgeo9aA+1kzvGgzTUezBQdw9Svhg8SEul9+CEGpxOvmQMNKF02poju6Ex0ITyY2cXNgqKpObHFefAF2xGaIHyAAAAAElFTkSuQmCC)
Therefore these pair of lines has the infinite number of solutions. and pair of linear equations is inconsistent
v) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
Therefore these pair of lines have infinite number of solutions and pair of linear equation is consistent.
Question 4.Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) ![](data:image/png;base64,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)
(iv) ![](data:image/png;base64,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)
Answer:(i) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
Therefore these pair of lines have infinite number of solutions and pair of linear equations is consistent.
x + y = 5
x = 5 - y
putting y = 1,2,3 we get,
x = 5 -1 = 4
x = 5 - 2 = 3
x = 5 - 3 = 2
![](data:image/png;base64,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)
And, 2x + 2y = 10
x = ![](data:image/png;base64,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)
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)
(ii) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence,
![](data:image/png;base64,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)
Therefore, these linear equations are parallel to each other and have no possible solution,
Hence, the pair of linear equations is inconsistent.
(iii) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence,
= ![](data:image/png;base64,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)
Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution.
Hence, pair of linear equations is consistent.
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
And, ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAB/CAYAAAAzQ5ajAAAACXBIWXMAAAsTAAALEwEAmpwYAAAH60lEQVR4Xu1de6hmUxy9HnkOiQxNgxnvx2AUf3hkGqL85S0hhJJXTU0hCSXlmfKHN91CEVGEDGkewuRNRobMGEPIMwx5rzWdMx2n8927znd/52z7tnat7vn29zu/9dtrne98+3y39h4ZcbMCVsAKWAErYAWsgBWwAlbAClgBK6ArsJ4Q+o8Q45AMFOjTyL64Jh3P+hlcSC5RUMBGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEGIjc3BJqNFGCiLlEJKzkTtB4CXA6hyE7rrGCCMXosifAK6U8QPwZFH0BvhLkfke+58u+iP+nIoki4BpEckG5JiF/juAD4D3gGXA7cD2A+KH7d4FJ94CvFlgOf6+CMwdNuGg85SlTA7CyX8CSwEaWLYpOHgXmFHpG+tQ4doYCRYCOwKPAcN8IhWet5H7GWDLouBt8fcNYAXAcSlN4bkYib4Adi0SUr9bgd+AfRUSxCg8WhCS3VQknF8hvwvH54vFMEwpiIs8lXeSro2cXav9xKLG08UxKeM5HrkuqOWbXvBcGsgjiUu+TYGPgDUAbxdHAQvEQsowZeDVlF0auVFD7QejjzXyU6S0tuMpc+5d8JyjkBSx44a2KWYOsv0NLAb4vcLbX5vWhot5uzSyqe6z0MkaQ295NaKZeP0CwDkAv0aUJukmBVXYOCHgObcpFdRi2nL1aSRv6S8BD7YYV5vx7Ia8/L7nOY8D27XhiZi11vlWoOMv4Gxgh/qbGb+eh9q3Ai7qaAz8WuJ34zbAVwDvaAdGcrW5qvYAMWd7xwI8j7O+Nq0NF/P29Yk8BVyl0F2Op8zNmevHwMsimaSbFARCfrp56zmkIL8ff3numWIxDFO5ypR9GMmZ6odA2+97dTycJDYtt/oE+vkIojRJNykIbJwq88G2bLwN8fnoW0C936tcJUfXRp4AorqJnLlevW6UYx8o4+HFf1hDmtfRR/2UpvBIn5K9wPYOwKur2o7DC5I8Wusf9FIqqHJyl0bSxF+BK4AzKrgRx6ODBlDrV8ZDIznLn1o59xIc89xenyNfASF/giN49ZbtCBysBPg4wqI+BY5Z927zgTJwnnkfsBL4BeAvSjzmT1xqU3hWIRnjmjAqEik8/DQy3/sAPwzLABp7ssjBMIVHC2pBOlaoVNBYCcT3Jh1PF48fopYOi1TARkaqmTCXjUwofiR10/NLPX9f3yd1Xr8OVqBPI/vimnQ8vrUGX/Wp0tnIVMoH89rIYEFTpbORqZQP5rWRwYKmSmcjUykfzGsjgwVNlc5GplI+mNdGBguaKp2NTKV8MK+NDBY0VTobmUr5YF4bGSxoqnQ2MpXywbw2MljQVOlsZCrlg3ltZLCgqdLZyFTKB/PayGBBU6WzkamUD+a1kcGCpkpnI1MpH8xrI4MFTZXORqZSPpjXRgYLmiqdjUylfDCvjQwWNFU6G5lK+WBeGxksaKp0NjKV8sG8NjJY0FTpbGQq5YN5bWSwoKnS2chUygfz2shgQVOls5GplA/mtZHBggakexg5uFjFrIBc/0kx1goYXJ+1XPX3j+KYfWXj4vTfAT8DD1T6Bx2OxVU9hytP3gNw7Ttu58CtKLgCsdoUHgo50e0iFJ5qzVwilee0NVLiUYK41wcX95vdoORz6Jvb0N/UpXBxbaDFABf15ZrffH0D8DnALR2UpvBwAWFydL1dRFkvx/Eq8BSQzMgZIF8DcMXf6iJMJ+H1Q4DaFIG5vUJ9oJug70eAhipN4aGR9Quzi+0iynpPwwE3bjkPqI9vvDEp45FXh7yyKODcgnVz/OW63G12rlEK4uLwXzeM7Fn0cflopSk8fW4XwQtxBXAAMJSRkZMdbuDCdb+vB7YGrgLuBr4EItt+SMZB1xv7dgZ4AUW03xuS7F70LWp4byJd83Eyc741kSTjnatcvWWOo3HAeE4+lgLV7ZXG4+H7CheXh36+IRkvIJ6v7Gyg8NQp+JXB1Y55R1CbwsM7Fi/2aUXSoT6RG6oViXHceYd7VnAZ6TkAt42YLG0eBsLZcvR2Edch552Aun55o57RRpLkNYBGftLIOPHOb5Bii4Y0nF3yE8DHnejG7SIuBDj75qQqqu2PRNx6as+JJuzCyInWNN753P2Ot/B6m4kOXjxc5zyycaZ6LXAksDoyMXLRRE50uI552aYUB3xs47P5ZcAjlfeHPlTu89Xkl+MFz5k+BKPCxU874/ap5OfzJBfHj3z8YPo+touoy/S/+I6sF9XFa25ssgTgtg18puTs8hqAz7E3A1GNJvIZmJ/GwytJOWueGkXSZx7lU1LWwy0Pvgd4zmcAZ5JtmsrFSce9wHKAP9HxF5jy0UDhU3hWIRHjmjCqkBTniqEjhyJwJcA5ADn5SxVfbwaM15TxrE3aV+uLa9LxRP4g0JfZ5mlQwEY2iJJjl43M0bWGmqv/qWh4e21XX98ng/jdbwWsgBWwAlbAClgBK2AFrIAVsAJWwAoEK/AvweJxAIhGKlIAAAAASUVORK5CYII=)
Graphical representation
![](data:image/png;base64,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)
(iv) We get,
= ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
=
s
Hence,
= ![](data:image/png;base64,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)
Therefore, these linear equations are parallel to each other and have no possible solution,
Hence, the pair of linear equations is inconsistent.
Question 5.Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Answer:Let the length and breadth of garden be 'x' and 'y' respectively.
Given,
Half the perimeter is 36 m
We know perimeter of Rectangle = 2(length + breadth)
Half the perimeter = x + y
⇒ x + y = 36
⇒ x = 36 - y [1]
Also, Length is 4 m more than width
⇒ x = y + 4 [2]
From [1] and [2], we have
36 - y = y + 4
⇒ 2y = 32
⇒ y = 16
Putting in [1], we have
⇒ x = 36 - 16 = 20
Hence, Length and Breadth of garden are 20 m and 16 m respectively.
Question 6.Given the linear equation
write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines
Answer:(i)Intersecting lines: For this condition,
![](data:image/png;base64,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)
The second line such that it is intersecting the given line is
2x + 4y - 6 = 0
As
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(ii)Parallel lines:
For this condition,
![](data:image/png;base64,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)
Hence, the second line can be 4x + 6y - 8 = 0
As ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAjCAMAAAA0eX3wAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgA6OgBmOjoAOpDbZgAAZgA6ZgBmZpDbZrbbZrb/kDoAkDo6kGaQkJC2kNu2kNv/tmYAtv/btv//25A629vb2////7Zm/9uQ//+2///b+uLxcAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABQUlEQVRIS92W4VLCMBCEc1BQsSpGhUokbd7/Jc2lklbsbQKEGcb8KpPLl91ryFap/zK6mmiJzDRw9s/K7mmr7GwrEs14O0tE8126le29DPxSJirkjYdfgGse0aYR4fSrUg2s7TkWNykC2Qh3yK+AvlMmxkCn558fTi+eQSNZn/VexBHfstM029T8AjsA5FNDJAP9WyY67hsCps/AREVpYONFn3baz5JdaBGr7cfk3w1Ox6X9g6Dop0rSm5guZHOMucTyFeQURDpdFaR5VHFgV6P740h8eweK+8gJd2vucG8rufp35ORlilknto+Rk5cpdpnyc4icvEzxV5vT6/e93KAYOYdM4bbKoRJuZKpk4BA5HhgyJWhA4QctjyJnyBQYKkoZYGA6ctqHjM+H3FPGsVzt25cT6lOlQXXGB0SKc/vz3ymSEmZQYv58AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
So,
![](data:image/png;base64,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)
(iii)Coincident lines: For coincident lines,
![](data:image/png;base64,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)
Hence,
the second line can be 6x + 9y - 24 = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
So,
![](data:image/png;base64,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)
Question 7.Draw the graphs of the equations
and
Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Answer:Equation: 1
x - y + 1 = 0
x = y – 1
Let us find the coordinates satisfying the above equation,
![](data:image/png;base64,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)
Equation 2:
3x + 2y - 12 = 0
![](data:image/png;base64,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)
Coordinates for equation 2 are:
![](data:image/png;base64,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)
By taking, coordinates we can plot the both equations in graph.
Hence, the graphic representation is as follows.
![](data:image/jpeg;base64,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)
Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
Answer:
For representing the situation graphically and algebraically, we need to form linear equations
(i) Let number of girls = x
Let number of boys = y
According to the question, Total no of students is equal to 10,
⇒ ................................eq(i)
Putting y = 4, 5 and 6. we get,
at x = 4X = 10 – 4 = 6
at x = 5X = 10 – 5 = 5
at x = 6X = 10 – 6 = 4
Number of girls is 4 more than number of boys …………Given
So,
x = y + 4
⇒ y = x - 4 ................................(ii)
Putting x = 3 ,5 and 7 we get
at x = 3
y = 3 - 4 = -1
at x = 4
y = 5 - 4 = 1
at x = 7
y = 7 - 4 = 3
Graphical representation :
Plotting the points obtain on graph we get,
Solution of this pair of equation is (7, 3)
i.e.
No of girls, x = 7
No of boys, y = 3
(ii)
Let cost of one pencil = Rs. X
Let cost of one pen = Rs. Y
According to the question, 5 pencils and 7 pens together cost Rs 50
5x + 7y = 50
⇒5x = 50 - 7y
⇒
Putting value of y = 0 , 5 , 10 we get,
x = 10 - 0 = 10
Now,
7 pencils and 5 pens together cost Rs. 46
7x + 5y = 46
⇒ 5y = 46 – 7x
Putting x = -2 , 3 , 8 we get,
Graphical Representation:
Plotting the points obtain on graph we get,Solution of this pair of equation is (3, 5)
i.e.
cost of pencil, x = 3
cost of pen, y = 5
Question 2.
On comparing the ratios and
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i)
(ii)
(iii)
Answer:
i) Comparing these equation with
=
=
We get,
=
=
Hence,
=
We find that,
Therefore, both lines intersect at one point.
Graph of the lines look like below:
ii) Comparing these equations with ,
=
=
We get,
=
=
Hence,
=
We find that,
=
Therefore , both lines are coincident.
iii) Comparing these equations with,
=
=
We get,
=
=
Hence,
=
We find that,
=
Therefore, both lines are parallel.
Question 3.
On comparing the ratios and
find out whether the following pair of linearequations are consistent, or inconsistent.
(i)
(ii)
(iii)
(iv)
(v)
Answer:
(i) We get,
=
=
Hence,
=
Therefore , these linear equations will intersect at one point only and have only one possible solution and pair of linear equations is inconsistent.
(ii) We get,
=
=
=
Hence,
=
Therefore, these linear equations are parallel to each other and have no possible solution.
And pair of linear equations is inconsistent.
(iii)
9x – 10y = 14
We get,
=
=
=
Hence,
=
Therefore, these linear equations will intersect each other at one point and have only one possible solution.
And, the pair of linear equations is consistent.
(iv) We get,
=
=
=
Hence,
=
Therefore these pair of lines has the infinite number of solutions. and pair of linear equations is inconsistent
v) We get,
=
=
=
Hence,
=
Therefore these pair of lines have infinite number of solutions and pair of linear equation is consistent.
Question 4.
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i)
(ii)
(iii)
(iv)
Answer:
(i) We get,
=
=
=
Hence,
=
Therefore these pair of lines have infinite number of solutions and pair of linear equations is consistent.
x + y = 5
x = 5 - y
putting y = 1,2,3 we get,
x = 5 -1 = 4
x = 5 - 2 = 3
x = 5 - 3 = 2
And, 2x + 2y = 10
x =
(ii) We get,
=
=
Hence,
Therefore, these linear equations are parallel to each other and have no possible solution,
Hence, the pair of linear equations is inconsistent.
(iii) We get,
=
=
=
Hence,
=
Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution.
Hence, pair of linear equations is consistent.
=
=
And,
=
Graphical representation
(iv) We get,
=
=
= s
Hence,
=
Therefore, these linear equations are parallel to each other and have no possible solution,
Hence, the pair of linear equations is inconsistent.
Question 5.
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Answer:
Let the length and breadth of garden be 'x' and 'y' respectively.
Given,
Half the perimeter is 36 m
We know perimeter of Rectangle = 2(length + breadth)
Half the perimeter = x + y
⇒ x + y = 36
⇒ x = 36 - y [1]
Also, Length is 4 m more than width
⇒ x = y + 4 [2]
From [1] and [2], we have
36 - y = y + 4
⇒ 2y = 32
⇒ y = 16
Putting in [1], we have
⇒ x = 36 - 16 = 20
Hence, Length and Breadth of garden are 20 m and 16 m respectively.
Question 6.
Given the linear equation write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines
Answer:
(i)Intersecting lines: For this condition,
The second line such that it is intersecting the given line is
2x + 4y - 6 = 0
As
(ii)Parallel lines:
For this condition,
Hence, the second line can be 4x + 6y - 8 = 0
As
So,
(iii)Coincident lines: For coincident lines,
Hence,
the second line can be 6x + 9y - 24 = 0
So,
Question 7.
Draw the graphs of the equations and
Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Answer:
Equation: 1
x - y + 1 = 0
x = y – 1
Let us find the coordinates satisfying the above equation,
Equation 2:
3x + 2y - 12 = 0
Coordinates for equation 2 are:
By taking, coordinates we can plot the both equations in graph.
Hence, the graphic representation is as follows.
Exercise 3.3
Question 1.Solve the following pair of linear equations by the substitution method.
![](data:image/png;base64,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)
Answer:i) x + y = 14...............(i)
x - y = 4....................(ii)
From equation (i)
take x on one side and when we take y to the other side its sign changes and we get,
x = 14 - y .........(iii)
Putting value of x in equation (ii) we get,
(14 - y) - y = 4
14 - 2y = 4
2y = 10
![](data:image/png;base64,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)
Putting value of y in equation (iii) we get,
x = 14 - 5 = 9
Hence, x = 9 and y = 5
ii) s - t = 3......................(i)
and,
![](data:image/png;base64,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)
From equation (i) we get,
taking t to the other side, the sign of t changes to positive
s = t + 3...............(iii)
Putting value of x from (iii) to (ii)
⇒ ![](data:image/png;base64,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)
⇒ 2t + 6 + 3t = 36
⇒ 5t = 30
⇒ t = ![](data:image/png;base64,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)
Putting value of t in equation (iii) , we get,
s = 6 + 3 = 9
Hence, s = 9, t = 6
iii) 3x - y = 3..................(i)
9x - 3y = 9......................(ii)
Comparing with general pair of equations i.e.
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0, we jhave
a1 = 3, b1 = -1, c1 = -3
a2 = 9, b2 = -2 and c2 = -9
Here,
![](data:image/png;base64,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)
and In this case, the system of linear equation is consistent and has infinite solutions.
iv) 0.2 x + 0.3 y = 1.3 .....................(i)
0.4 x + 0.5 y = 2.3 ........................(ii)
From equation (i) . we get,
![](data:image/png;base64,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)
Putting value of x in equation (ii) we get,
(6.5 - 1.5 y) × 0.4 + 0.5 y = 2.3
6.5 x 0.4 - 1.5 y x 0.4 + 0.5 y = 2.3
2.6 - 0.6 y + 0.5 y = 2.3
- 0.1 y = -0.3
y = ![](data:image/png;base64,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)
Putting value of y in equation (iii) we get,
x = 6.5 - 1.5 × 3 = 6.5 - 4.5 = 2
Hence, x = 2 and y = 3
v) ![](data:image/png;base64,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)
![](data:image/png;base64,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)
From equation (i) , we get,
![](data:image/png;base64,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)
x = ![](data:image/png;base64,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)
Putting value of x in equation (ii). we get,
⇒ ![](data:image/png;base64,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)
⇒
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
so, y = 0
Putting value of y in equation (iii) we get.
x = 0
Hence, x = 0 and y = 0
vi)
................(i)
and
![](data:image/png;base64,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)
From equation (i) we get,
By taking L.C.M and solving we get,
![](data:image/png;base64,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)
9 x - 10 y = -12
![](data:image/png;base64,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)
Putting this value of x in equation (ii), we get,
⇒ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 47y = 117 + 24
⇒ 47y = 141
⇒ y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAAgCAMAAACB1hBXAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjoAOpDbZgAAZgBmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtv//25A629vb2////7Zm/9uQ//+2///bRZNGxQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA+klEQVQ4T71U7RKCIBCUSvswVKTUe/8X7T4QbTTxaqb7Ywwse7sXm2X/L5cLZ1/c+TuutzvxxggOqjPh4joh4JF5wfnSEi6uk8IF1+XAOLwg9J0C8rnh1oIt66cWh7KwThrc6N/Y524/jbmwLnNs2c+wXtPX4eahSSlf7DvEgNUDHTXmjfiuLUdy1AWWTd8qx7OhioqGaxhW3Hr7sXVbX3zVJ/4jZWyfa6VPOtwXCdziRrCE6NRzAIvSdhi6ICQ7wzNXD3AO4GgBS7PY+WgZLdEC+GqhahQNhGghrzR0U7So6GbRoqKbokVFx8ZIBKroCCDRoqZTWP/j0RfK3wp8JCVuIgAAAABJRU5ErkJggg==)
Putting value of y in (iii)
⇒ x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANcAAAAgCAMAAAC2NB0mAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OpDbZgAAZgA6ZgBmZjqQZra2Zrb/kDoAkDo6kDpmkNv/tmYAtmY6tmZmtv//25A629vb2////7Zm/9uQ//+2///bwg6hswAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACVUlEQVRYR+2Y6VLDIBCAibW1Vdtqo4mmyfu/pnsAOSGQJdOx0/2hnQDfniwhSj3k30Yg36Lp9SHL6EcrNNCcs2wf5ZuLx8+HvDLz81va82+MGcBFffXrRVVPF9Z8wn96oNyq6ws9D5MRr49TmpejjvqtaD6s3im+pjXnPQQ+Krw/qIlF268N4YH6cAJHgZhD1q67+ZiNeD2c5SEXY9nRO+WXpuFsxZkLF+tXyQHRhkDG0C/UDcTyVIJPeoafPeD1cJYHDh7R2K6+SSzROF883Su4m1BwqrGjonocDBi/lKo2RfNZOKgu3uh5yzN25myFS9i6+F1u/bJh7ufL1CFGugqqcA0yvEG+DK/NF5S3xzHC8G6IrEOuW8xWRXxrCA3AH953zfn4HtSRBrw+zvAwb2aPef0iGs2I21/YZ6ElcMF0/eoMcDhzbpczMuK1/ZAaOioC3heyoB9i2/WcI5pGszw9q4LhIOumjC8D9u2c1+uMY8Trw8a1+X1Kv4ugXriO3XPUHPd96W0/DgT0o6CeMWfBiuPVEr9WtCcVOl9Uhz3tcORoWbxZJ70J407P4qZqDYv84QpuJGY03cEdzPOklt717k+iD21BvcRHb3kdxp3Z8ZbdaAW+k6uwt7wbWbhILb/o0Sl2V6Lr9+78CkjSdRf7OWMeKmQKl5N9eHXwXhvmvRjNEDKFy9kcuBQn34BCpnA5+4WdJc0Z16ZNyBQu13aYi9yCenMuETKFy61Z5vNXSteETOFy3TrSnwOR3zSHERUuRxxcIJNf94VM4fKUZfdgpY3AHzEXJF0E/zvqAAAAAElFTkSuQmCC)
Hence, x = 2 and y = 3
Question 2.Solve 2x + 3y = 11 and 2x - 4y = -24and hence find the value of ‘m’ for which y = mx + x.
Answer:To Solve: 2x + 3y = 11.........(i)
2x - 4y = - 24..........(ii)
Solving by substitution method,
From equation (i)
2x = 11 - 3y..........(iii)
putting value of 2x from equation (iii) to equation (ii)
(11 - 3y) - 4y = - 24
⇒ 11 - 7y = - 24
⇒ - 7y = -35
![](data:image/png;base64,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)
Putting value of y in equation (iii) we get,
2x = 11 - 3 × 5 = 11 - 15 = - 4
x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAgCAMAAABto3VBAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOpDbZgAAZgA6ZgBmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtv//25A62////7Zm/9uQ//+2///bn/mqZgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAxklEQVRIS9WUyxbCIAxEE7U+qhUtxRT+/0MllJWeIpzOxqzhJjNMIPqfmo931LDhcYax3GBQLOkCiuVvUzDD84VwzLHWAcKK88A0Rpbj/dQiUaKQ3dhyY/WsjRzft7Vfg9lL0oLKEZEAWfa3RpsSolU2N6/wx/F8tfgqXx2CUc8gFUxXwanTaGtQFd00D7pxAlE5nzTzKWWbK/sAYRWG8T0zyEt/HUlAW68TL25iyuF8FJBdGj0cSqcSzMemkWDgx4Z5wU2UNxn4BvvfxkWjAAAAAElFTkSuQmCC)
Now , putting values of x and y in equation
y = mx + 3
5 = -2 m + 3
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Value of m is -1
Question 3.Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of25 km?
(v) A fraction becomes
if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes
Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Answer:i) Let larger number = x
Let smaller number = y
According to the question,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
And,
= ![](data:image/png;base64,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)
Comparing values of x from both equation, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
So, x = 3y = 3 × 13 = 39
Hence, the numbers are 13 and 39.
ii) Let the first angle = x
Let second angle = y
According to the question,
= ![](data:image/png;base64,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)
x = ![](data:image/png;base64,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)
And,
= ![](data:image/png;base64,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)
Putting value of x from equation (i) to (ii). we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
so, ![](data:image/png;base64,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)
Hence the angles are 99ᵒ and 81ᵒ
iii) Let cost of each bat = Rs. X
Let cost of each ball = Rs. Y
According to the question,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
And,
= ![](data:image/png;base64,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)
Putting value of y from Equation (i) to equation (ii)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAgCAMAAAAIToc+AAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6Ojo6Oma2OpDbZgAAZgA6ZjqQZrb/kDoAkDo6kDpmkGaQkLaQkNv/tmYAtmY6tv//25A625Bm27Zm29vb2////7Zm/9uQ//+2///bBRjGbgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABt0lEQVRYR+1W7VaDMAxt94EKOvwAQR207/+Uy00o3TzA2LDlj/lhsyPNbW5umir1b7MYMJnWu6NStdZ6Uyiba53SRrfOinH3RzZPlckIrz5wjHqv2ofCr3cHnrXRZIRa7h06fsqBZA1sDoqZ3yvzTHnTYdwaBh3VhiFDKTRZmxzioPc5CcXEPCstjcw85ctU29cCucNl1bl1ivov+m6hod7UcSgAKoCSQP1uHY7eJigbNai05rYS6py38EjXtjNjXbV2R5sD3ubOu7Z76f89egMCGtDlPSKBWCyZmhDm0UukbTKSrfc+i3pbdbdXUHTQDXSQ3nnAazYfTz1uKc3thHLjeQZ2t8mjiE4wpeSdh+gmEyGOWH+caWdsO25Im/NQGkSPcEm3CY4gfNOF0XtgnsdmZ3/OPMc91xo0LvrDrW1evieZv7H0vz8vgYHcaTih2fDHe/atoqZogk1I9LLcMRdyF+nV8kiR2RHCeERKad3b6NwLARk0Jh44MmwCkjaSAY06Rn+ncUfDNrL94D0p1oTTy3hSDj1e6v55x2/o9VJ36PFSvygDa36tqqPT6G5cKfXIPRYK7gTDJx+p8znDJwAAAABJRU5ErkJggg==)
Putting value of x in equation (i) , we get
= ![](data:image/png;base64,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)
Hence,
Cost of each bat = Rs.500 and Cost of each ball = Rs. 50
iv) Let the fixed charge for taxi = Rs. X
Let variable cost per km = Rs. y
We know that,
Total cost = Fixed charge + Variable Charge
According to the question,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
And, For a journey of 15 km charge paid = Rs.155
so, ![](data:image/png;base64,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)
Putting value of x from equation (i) to equation (ii). we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Putting value of y in equation (i) . we get,
= ![](data:image/png;base64,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)
So, People have to pay for travelling a distance of 25 km
= ![](data:image/png;base64,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)
v) Let numerator = x
Let denominator = y
Fraction will be = ![](data:image/png;base64,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)
According to the question,
Fraction become ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAiCAMAAADfyfGoAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZgA6ZgBmZjqQZma2Zra2Zrb/kDoAkDpmkGaQkNv/tmYAtmZmtrZmttuQtv+2tv//25A625CQ29vb2//b2////7Zm/9uQ//+2///bkPqnKQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABNUlEQVRIS+WV2XLCMAxFnUJTIHSJW1wgBurl/78RybYSxhTpiU471Yszia62sU6U+nUWuqZ55KvybdOsrlyi7uFdWG+Ue9hwAULXK9+iM5iDZC5Fy3o0/8Tq3WxQyuQCwqtf7JYOlZPeXhd3WQ+Gj5p6jHr+BXGgazQM5IT2lUVPyhG68kT5rSRPdcOY0A775+389AEVUP2YPfXDj7AkNbMhdHncZf6pEV4fteAgZP8/n02+FWA3rvT4vX64MaPK7d6TFOu/dwF/ML4EQFP2m05qsey/AEBgR9LTaQAkvkUETfziAHhUmS/ltL0FbQLehZ4FIPGpnEDT+A4QmfgnALDSQ78uwWjMLwCw0kf99oL4G/USAOv5m7KaNH8egMTuieFWgi13hz8H4WcjLID+5kf6gztzBrjuEyHc/TJuAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
And, if 3 is added to both numerator and denominator it become ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgCAMAAADpJZJvAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZgA6ZpCQZrb/kDoAkDo6kNv/tv//25A62////7Zm/9uQ//+2///bak8bvgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYUlEQVQYV42PbQ+AIAiEoUx7IcOS//9Xg9hqs7V1X5j3nHgCtGJE7DIAL07uqf7g1hGdCSWQNV9nIeXpte3T0LTp/4UnuWO/2ePehn0IzRFD0S6hGKqT/SF4R4vWEY03OgFMcgL/fRJMyQAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Putting value of x from equation (i) to equation (ii)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALgAAAAgCAMAAACW2ELbAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OpDbZgAAZgA6ZgBmZjoAZjqQZmZmZpDbZra2ZrbbZrb/kDoAkDo6kDpmkGaQkNv/tmYAtmY6tmZmttuQtv//25A625Bm29vb29v/2/+22////7Zm/9uQ/9u2//+2///bKE6mjAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACiUlEQVRYR+1YbVMbIRAGrTmtOW2t5mxz2tDWQo////+6LHAsCXAvc+3cOOFDiA777MOzb0wYO6/1KKAqzrdJOqrarYfmCZOu3rE0Q/38cc3E5eWBsXbLWpBdVR9+h5uJp2bNxNX1nulmI3YCSAuSM3KjV02cCQ4LCIP0+uuhq82fnO+6+4Nunr6RCKww37u7PWPwIYngeB9OU2d9xLvaENbN4+dY30VT5QdoM3H1JoKbQjxeuuG2BtuLI+z0eW9visMs0075psAJD/Bj8LSBA41MVFVCBxxR7iGx/lALloow15Yl5qVxkAGlJqpyCQxVh7f1u73664F2lJQckQ+oZIHEdYNl0KZi6VBGE+9B6WCBjudw/nxCJ1199Svwg3xJT096JI5ITLxQxYE45h64CoePy8iCUuLSJbIXqasHEudE9IwPia00oJ8Gqycut/jV9gK7hom3l9+hRuxVIbxvk3nnfAAPToq+tWOAVqOqbn1tYtzVjc3VInFvYuPj65NGq3eU+YL4CTqsjyroJ0qJppst3NrmQAss/LQogAaTuIaiNDuNbfo/6ahaYN0UihPhXG8QOJ6Dg0yqBBNHvC+ot3ryTEz7cLXSd5WUjIaGOweNQ30hwpSIWxOLjJ94iaWK0yte0AGenr3iMGBeieC5wiEmmN7YAZz4k5lnxMH0RuDcMhPZ51JXP0RNNQNKTXCKGiPpxPEje1aOQ5WYZWIph+Y5Pjid0zBOEl0lgFKTsfz+7bmoMhdz1bqZ5PfFgAPQwHtolkd4gCNxv88CKRq97IfeQ7N8/mQCift9FkjJaMR7aKZPSxw0n/qMmelvMbMz8cWkHAn0H7rKSCaTjvmfKfw+yfh8+L0o8BfBCTxhkSt3pQAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= y = 9
Putting value of y in equation (i)
=![](data:image/png;base64,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)
Hence , the fraction is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAgCAMAAADzGXLhAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAABmAGa2OgAAOgA6OpDbZgAAZgA6Zrb/kDoAkDo6kGaQkNv/tmYAtv//25A62////7Zm/9uQ//+2///buqSjWgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaElEQVQoU51QWxKAIAjEXqZlD5X7XzUEs/pwxmm/YHeBHQAqQKsIPau4noCLK04vNEu/6drhBj4lIzQ4v5aon+Dvml1hUGoSf9SGWsO173aATYQwOkCbdxwpQh5IM3P5T9Q3TU+ULVVcM3EC/Wqu2IUAAAAASUVORK5CYII=)
vi) Let present age of Jacob = X years
Let present age of his son = Y years
Five year hence,
Age of Jacob = X + 5
Age of son = Y + 5
And, age of Jacob is 3 times of his son Given
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Five years ago,
Age of Jacob = X - 5
Age of son = Y - 5
And, Jacob's age was 7 times of his son Given
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAXCAMAAAD9aBd4AAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOjo6Oma2OpDbZgAAZjqQZmZmZpDbZrb/kDoAkDpmkLaQkNv/tmYAtmY6tmZmtv//25A625Bm27Zm2////7Zm/9uQ//+2///bdJIdYAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABfUlEQVRIS+1WyVbDMAysC4RCw5JSAwa8/P9XIsXy9lI5CkdefY08HY1m5O521/OfFTA3n+L29O2PuBYLv86i8jAdRXWE6IZXWbkbFJw9T8Lgd6WwKxmHCtHdy5pbZauxm1hlRbOoEY1sIqskZkFnK4TpTqJujUhShEnBHDWrt4iEH9ELqdQooAS4TJc1Ig3w/QxdGN4gIhJm7sHGTuxxvhOJXTgNoibx7P7tkZfRDQ+1L3W0YetVmgORoLm4AxPWBjHF1I/FT8vfQMHC1EkH9q5mJcuOQGhLQiwgG8REQhAsN3TzT0hZCaQTTt2tlRATCcs5qMzIj8n3l8aRAAsJyKp76SYlIZIn/NN3L946+r6nhKb7xXGQvA9WiBqRpgCyweU0wCV7DG+YejRzDMqe8OMzn7caMe4JDBdEmt8yfqSdzKrbTCFWdddWjSjcmJIdmGqyxVdcmTGlb8cWEvkF6yy/Gk+0CDcRiMUQTtjBsgd96/+JDXTiY3Q9f1HgF1myGWvvmxPmAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAAAXCAMAAAA2s/OGAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZjqQZmZmZpDbZrb/kDoAkDpmkLaQkNv/tmYAtmY6tmZmtv//25A627Zm2////7Zm/9uQ//+2///biD26ygAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACB0lEQVRYR+1XyXbCMAxMKKUt6ZKWtHVx4v//zEojKxshsQG/xyE+mM2RNaPxyGTZOlYGVgbugwHz8DtIpNoe7yOx22bhyj0CCjzM9e4jZA+TY1xIi6VHNwfex5V5PuI6ZPvINYrTlY/Yk+esfkIGC6NiOgJJOQlVEUhXMlJXbo+uTI7UTu5ggss01v0SO/p7xToyOXFlGa3ldymHL+F4C5SUJEXZMPXnR1NIwkQXLQ+mxwesmGVMTQEppRuqPKQqCcuxofy/D1QuM8+0QTn2CCOgwwdrVpTLz8aSFL4PVkI3PHpehI8g2G6+XmYDqiDwWj97967EpVq3mQzRFOJjfbiRyccsV6ADLwJujtIU3QmezL49WsyTnS/oaYB6B8V3cGMyj1yrXiKy68QnQNWSzwZtWy7FcZ/DdhyQiSUTUOkmPqNaUWkoXVsRoHbBXuqdFpHMu35XaEHS5cV43ptR3PkOYHG4RIFKZbtegTPavP7NtzfkiEEU/cQUVLQC5UuPSd1e1HVHXoQ8SIv088zJ69lsU7xFNULcEDrDlXc4LPQ9Q/diGX+OXqB9y9smvRAsmX2BMu4c1Btnzk5r2e2VKlxRbLo+tvpvUqCZvxkZ3DtlZg3HdrULnCiclJusnDTWsLtuf/+Fe8VNUr0yyATS2Is6XaESe+aVGP3j1/4flTvxOlYG7oSBfzyBJTKimAhiAAAAAElFTkSuQmCC)
Putting value of X from equation (i) to equation (ii)
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= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAXCAMAAABamWPGAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOpDbZgAAZgA6ZmZmZpDbZrb/kDoAkDpmkNv/tmYAtmY6tmZmtv//25A62////7Zm/9uQ//+2///bU++xggAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABEklEQVRIS+1UyxKCMAxsBVHwgaCUlv7/f5qYBtCWgco4HrQHLs1uNpstQvzPjzmgNtWKiR3allImTYjHZGv4HdqWaWvLUIOuOK7gZ7RGDi3P/gB1/rgTCseDKdM2xixG1yi9K7YeVqct9c5NBt27Io+hZzTag2BPXHeoBOkH7dDd7HlHteQzbV+PJn76joG2BLnAr9C4Gm71jPynrgN6zD+eX7NG5FdJYy/BiE1YNqDZH99/gDp/hE4ac+qplviDxYR2+w1Oz/xmV91i5JMUTh84EMwn+OIWCFkO5HcuToTG6JBJfkKlHAVoju71HnbgGsi5pxO33Fgh4NMb7izucq1U1MtdTEyF8OP5JH2kmi+W3wG0iQ+erirLaAAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
Putting value of Y in (i)
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Hence, ![](data:image/png;base64,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)
Solve the following pair of linear equations by the substitution method.
Answer:
i) x + y = 14...............(i)
x - y = 4....................(ii)
From equation (i)
take x on one side and when we take y to the other side its sign changes and we get,
x = 14 - y .........(iii)
Putting value of x in equation (ii) we get,
(14 - y) - y = 4
14 - 2y = 4
2y = 10
Putting value of y in equation (iii) we get,
x = 14 - 5 = 9
Hence, x = 9 and y = 5
ii) s - t = 3......................(i)
and,
From equation (i) we get,
taking t to the other side, the sign of t changes to positives = t + 3...............(iii)
Putting value of x from (iii) to (ii)
⇒
⇒ 2t + 6 + 3t = 36
⇒ 5t = 30
⇒ t =
Putting value of t in equation (iii) , we get,
s = 6 + 3 = 9
Hence, s = 9, t = 6
iii) 3x - y = 3..................(i)
9x - 3y = 9......................(ii)
Comparing with general pair of equations i.e.a1x + b1y + c1 = 0
a2x + b2y + c2 = 0, we jhave
a1 = 3, b1 = -1, c1 = -3
a2 = 9, b2 = -2 and c2 = -9
Here,
and In this case, the system of linear equation is consistent and has infinite solutions.
iv) 0.2 x + 0.3 y = 1.3 .....................(i)
0.4 x + 0.5 y = 2.3 ........................(ii)
From equation (i) . we get,
Putting value of x in equation (ii) we get,
(6.5 - 1.5 y) × 0.4 + 0.5 y = 2.3
6.5 x 0.4 - 1.5 y x 0.4 + 0.5 y = 2.3
2.6 - 0.6 y + 0.5 y = 2.3
y =
Putting value of y in equation (iii) we get,
x = 6.5 - 1.5 × 3 = 6.5 - 4.5 = 2
Hence, x = 2 and y = 3
v)
From equation (i) , we get,
x =
Putting value of x in equation (ii). we get,
⇒
⇒
⇒
so, y = 0
Putting value of y in equation (iii) we get.
x = 0
Hence, x = 0 and y = 0
vi) ................(i)
and
From equation (i) we get,
By taking L.C.M and solving we get,9 x - 10 y = -12
Putting this value of x in equation (ii), we get,
⇒
⇒
⇒ 47y = 117 + 24
⇒ 47y = 141
⇒ y =
Putting value of y in (iii)
⇒ x =
Hence, x = 2 and y = 3
Question 2.
Solve 2x + 3y = 11 and 2x - 4y = -24and hence find the value of ‘m’ for which y = mx + x.
Answer:
To Solve: 2x + 3y = 11.........(i)
2x - 4y = - 24..........(ii)
Solving by substitution method,
From equation (i)
2x = 11 - 3y..........(iii)
putting value of 2x from equation (iii) to equation (ii)
(11 - 3y) - 4y = - 24
⇒ 11 - 7y = - 24
⇒ - 7y = -35
Putting value of y in equation (iii) we get,
2x = 11 - 3 × 5 = 11 - 15 = - 4
x =
Now , putting values of x and y in equation
y = mx + 3
5 = -2 m + 3
Value of m is -1
Question 3.
Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of25 km?
(v) A fraction becomes if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes
Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Answer:
i) Let larger number = x
Let smaller number = y
According to the question,
=
=
And,
=
Comparing values of x from both equation, we get,
So, x = 3y = 3 × 13 = 39
Hence, the numbers are 13 and 39.
ii) Let the first angle = x
Let second angle = y
According to the question,
=
x =
And,
=
Putting value of x from equation (i) to (ii). we get,
=
=
=
so,
Hence the angles are 99ᵒ and 81ᵒ
iii) Let cost of each bat = Rs. X
Let cost of each ball = Rs. Y
According to the question,
=
=
=
And,
=
Putting value of y from Equation (i) to equation (ii)
=
=
=
=
Putting value of x in equation (i) , we get
=
Hence,
Cost of each bat = Rs.500 and Cost of each ball = Rs. 50
iv) Let the fixed charge for taxi = Rs. X
Let variable cost per km = Rs. y
We know that,
Total cost = Fixed charge + Variable Charge
According to the question,
=
=
And, For a journey of 15 km charge paid = Rs.155
so,
Putting value of x from equation (i) to equation (ii). we get,
=
=
=
Putting value of y in equation (i) . we get,
=
So, People have to pay for travelling a distance of 25 km
=
v) Let numerator = x
Let denominator = y
Fraction will be =
According to the question,
Fraction become
=
=
=
=
And, if 3 is added to both numerator and denominator it become
=
=
Putting value of x from equation (i) to equation (ii)
=
=
=
= y = 9
Putting value of y in equation (i)
=
Hence , the fraction is
vi) Let present age of Jacob = X years
Let present age of his son = Y years
Five year hence,
Age of Jacob = X + 5
Age of son = Y + 5
And, age of Jacob is 3 times of his son Given
=
=
=
Five years ago,
Age of Jacob = X - 5
Age of son = Y - 5
And, Jacob's age was 7 times of his son Given
=
=
=
Putting value of X from equation (i) to equation (ii)
=
=
=
Putting value of Y in (i)
=
Hence,
Exercise 3.4
Question 1.Solve the following pair of linear equations by the elimination method and the substitution method :
(i) x + y = 5 and 2x - 3y = 4
(ii) 3x + 4y = 10 and 2x - 2y = 2
(iii) 3x - 5y - 4 = 0 and 9x = 2y + 7
(iv)
and ![](data:image/png;base64,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)
Answer:i) By elimination method
x + y = 5.............(i)
2x - 3y = 4..........(ii)
Multiplying equation (i) by 2 we get,
2x + 2y = 10 ..............(iii)
Subtracting equation (ii) from equation (iii) we get,
5y = 6
y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgCAMAAADpJZJvAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZgA6ZpCQZrb/kDoAkDo6kNv/tv//25A62////7Zm/9uQ//+2///bak8bvgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAXElEQVQYV42OSw6AIAxEW63gBxGU3v+q9pPogg2zaTpvmg5ArxvnC4DTYqj44LQHpApPoKqobVkYiR892lZUPip0jcb/XJGrSX8f7n1TfK8qHZ1ZtzPbzkl47N69m9IC/7S8dRQAAAAASUVORK5CYII=)
Putting value of y in equation (i). we get,
x = ![](data:image/png;base64,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)
By substitution method
x + y = 5 ...........(i)
2x - 3y = 4 ......................(ii)
from equation (i)
x = 5 - y................(iii)
Putting value of x from equation (iii) to equation (ii) we get,
2(5 - y) - 3y = 4
= 10 - 2y - 3y = 4
= -5y = -6
= y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgCAMAAADpJZJvAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZgA6ZpCQZrb/kDoAkDo6kNv/tv//25A62////7Zm/9uQ//+2///bak8bvgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAXElEQVQYV42OSw6AIAxEW63gBxGU3v+q9pPogg2zaTpvmg5ArxvnC4DTYqj44LQHpApPoKqobVkYiR892lZUPip0jcb/XJGrSX8f7n1TfK8qHZ1ZtzPbzkl47N69m9IC/7S8dRQAAAAASUVORK5CYII=)
Putting value of y in equation (iii) we get,
x =
.
ii) By elimination method
3x + 4y = 10 ..............(i)
2x - 2y = 2.................(ii)
Multiplying equation (ii) by 2 we get,
4x - 4y = 4 ...............(iii)
Adding equations (i) and (iii) we get,
7x = 14
= x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAgCAMAAABjCgsuAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAA///b//+22///tv///9uQ29vbkNv//7ZmZrb/Zrbb25A6OpDbkGaQtmYAkDo6AGa2kDoAOjoAADqQZgBmZgAAOgA6OgAAAABmAAA6AAAAMCal+gAAAAF0Uk5TAEDm2GYAAACvSURBVHja5ZPdDoMgDEap6ABBBPdr3/9BF2xMXKakXbLd7LvRC049LVWpXyQmenZ3xznuEQmAcWIBJ+UJ8H12PCUCbAIR0FxayP2g2YDHkrOWTImptJQO9PZoD49ZRJyN4K5mo5prpeAbEBYFJ1sJKwXioVLENds+adfwNZX6kIPIB3KqyO4oxSRr2JetsXyp7mbW22BOlAzDhz815EILmoJBKxiNcE+EU/vDD3wzT1mzC4fqcwxYAAAAAElFTkSuQmCC)
Putting value of x in equation (i) we get,
3 (2) + 4y = 10
4y = 10 - 6 = 4
y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACkAAAAgCAMAAAC4saEMAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAZgAAZgBmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtv//25A62////7Zm/9uQ//+2///bzJcH6AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAg0lEQVQ4T+2TyQ6AIAxERcQNcaEu/P+XCoQDBwMTDTfn2peZdpJWVRmd7YQZm7kHSZIKIw9hMPIatVFy2fObEnNqANJ6gemWJMZ1Kvzs1vxulrgGVkPkwTVhpNvuE7n5ypxim+AZJqnjCqYDnX5Lfwgwyt8sgOwY+f8IKSz3R4jHO+YGKSsGTmFfytMAAAAASUVORK5CYII=)
By substitution method
3x + 4y = 10 ..............(i)
2x - 2y = 2.................(ii)
From equation (ii)
2x = 2 + 2y
Dividing both side by 2, we get
x = 1 + y
putting value of x in equation (i) we get,
3(1 + y) + 4y = 10
3 + 3y + 4y = 10
7y = 7
y = 1
and
x = 1 + y = 1 + 1 = 2
(iii) By elimination method
3x - 5y = 4................(i)
9x - 2y = 7..........(ii)
Multiplying equation (i) by 3 we get,
9x - 15y = 12.................(iii)
Subtracting equation (ii) from (iii) we get,
- 13y = 5
= y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAgCAMAAADdXFNzAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OpDbZgA6Zrb/kDoAkDo6kNv/tmYA25A629vb/7Zm/9uQ//+2///b7SmRKwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAhUlEQVQ4T82SSQ6AIAxFizMiir3/YW1BXNEaSUhkBfz0d3oALY43xnROdvaLnvVVJ/9etwiDngPtJBrg6kCLR0v55fAWE6333KjWdOJGnle61Pv+N3KLaDCDpR3RP+u846PE6A4+oxXGIsNZR1tG7NZp8KoOEmOx/nMWGOS+uDGpv297uQDEbgLoQs0ZGwAAAABJRU5ErkJggg==)
Putting value of y in equation (i) we get,
3x - ![](data:image/png;base64,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)
3x + ![](data:image/png;base64,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)
Taking LCM,
![](data:image/png;base64,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)
By substitution method
3x - 5y = 4................(i)
9x - 2y = 7..........(ii)
From equation (i)
x = ![](data:image/png;base64,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)
Putting value of x in equation (ii) we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 13y = -5
y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAgCAMAAADdXFNzAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OpDbZgA6Zrb/kDoAkDo6kNv/tmYA25A629vb/7Zm/9uQ//+2///b7SmRKwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAhUlEQVQ4T82SSQ6AIAxFizMiir3/YW1BXNEaSUhkBfz0d3oALY43xnROdvaLnvVVJ/9etwiDngPtJBrg6kCLR0v55fAWE6333KjWdOJGnle61Pv+N3KLaDCDpR3RP+u846PE6A4+oxXGIsNZR1tG7NZp8KoOEmOx/nMWGOS+uDGpv297uQDEbgLoQs0ZGwAAAABJRU5ErkJggg==)
Putting value of y in equation (i) we get
3x - ![](data:image/png;base64,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)
3x = 4 - ![](data:image/png;base64,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)
= x = ![](data:image/png;base64,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)
iv) By elimination method
=
.....(i)
= ![](data:image/png;base64,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)
Multiplying equation (i) by 2, we get,
x + ![](data:image/png;base64,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)
Subtracting equation (ii) from equation (iii) we get,
= ![](data:image/png;base64,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)
= y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFIAAAAgCAMAAAC2GN9jAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZrb/kDoAkDo6kNv/tmYAtv//25A629vb2////7Zm/9uQ//+2///b4vdsRQAAAAF0Uk5TAEDm2GYAAAC2SURBVHja1ZXNDsIgEIR3Wu0K0qLWff9XNYCY2EMDyfTQOZRL8zH7w67IWTVf0zcCGAIFGIGCdDSPD4lspFQkvnZ5SBFZJ8dGmldmxe0eaC5TDqFiPh8devG6rsY2BDFPZc6aQ3T0hzcuXKD5y7P5clTt5Op9Awpy8zv+1XfTOrEDT42kzMCLTWWWRrNLx0SOS1fJG5QKzpuGraODOwG4S+I45CGZ5u2dTevycMS983PYu3fOpw//ZAXrys0UjAAAAABJRU5ErkJggg==)
Putting value of y in equation (ii) we get,
x + ![](data:image/png;base64,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)
= x - 4 = - 2
= x = 2
By substitution method
=
.....(i)
= ![](data:image/png;base64,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)
From equation (ii) we get,
x = 3 +
(iii)
Putting value of x in equation (i) we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGQAAAAgCAMAAADT9S0cAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOpDbZgAAZgA6ZgBmZjqQZpCQZra2ZrbbZrb/kDoAkDo6kDpmkGaQkNv/tmYAtmZmtv//25A62////7Zm/9uQ//+2///bFi/9wQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABRUlEQVRIS91W7XaDIAyFdnXTbl2lXa2Zwvu/5RKgltOCg3myr/tHJZzc3EsQhPg/GCsp60/kjFW7SLBuWuFyGHWb6TJiDk/LSIZ1L0RHUnzKDnWN1cN7QAt7yx9ECnWNjydMv5lSQgtIANZATzts7EsYKSQRIBG1bughJSZDbebYi2lEP/dG7d9Qmo+UMrj5ensKzMGvwXWCU2KrkOTfNVLOo5vQHEz9+kIrErSC9+0aKSUxijwKU3YrEhaOgKT2wKW/RHJJaMXjgGS/piPRTLis8arOveuse6QjiWKxTyBKguYlONKRGe/iJLlmZ85bRtK5bYWY7QVPMk3OfZnVcMu9TMkvtCuzpC9O+wN25SjDnUWgY+QnMfh/ImMN7qxkBnwDh1G7yp6FnKDbCrtj9tCnWwsnjKr9PYmThe5DzEI4y2fL/QGCBRTZBlwr2wAAAABJRU5ErkJggg==)
= 5y = - 6 - 9 = - 15
= y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFIAAAAgCAMAAAC2GN9jAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZrb/kDoAkDo6kNv/tmYAtv//25A629vb2////7Zm/9uQ//+2///b4vdsRQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA2UlEQVRIS9VVXQ/CMAgEPzatq9VN/v9fFcrsgyZNm9yWyMv6QI87uA6if414NuaJmQ8TRINCOeQVAmcgD0poSOVXhOcDIhxSYxlQ4gukhBFBUTHyxOU2wViaeXgkCfnTETPOdWvVqCaWAHKyY0aTlBg10NKeeLx3tKohVcLp2ZDmomxkOSq9el2YHfIrvVz2Q7XoT6VlQAsnmpt91yTcn3CXleuN98c7I00kQdvYM/IGa9jA/ee9VwD3zocycO9sCblJp3F7pxgAt3cyJHLvrBz7985e7sbVeQP/ZAXr4ALvGQAAAABJRU5ErkJggg==)
Putting this value in (iii), we get
x = 3 - 1 = 2
Question 2.Form the pair of linear equations in the following problems, and find their solutions(if they exist) by the elimination method :
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes
if we only add 1 to the denominator. What is the fraction?
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice a sold as Sonu. How old are Nuri and Sonu?
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
(iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.
(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer:i) Let the fraction is = ![](data:image/png;base64,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)
According condition (i)
= ![](data:image/png;base64,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)
= x + 1 = y - 1
= x - y = -2..................(i)
According condition (ii)
= ![](data:image/png;base64,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)
= 2x = y + 1
= 2x - y = 1..................(ii)
Subtracting equation (i) from equation (ii) we get,
x = 3
Putting value of x in equation (i) we get,
3 - y = -2
= - y = - 5 and y = 5
Hence, the required fraction is ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAgCAMAAAD68tKbAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OpDbZgAAZgA6Zrb/kDoAkDo6kNv/tmYA25A6/7Zm/9uQ//+2///b3Fh/VQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQoU5VRSRLAIAiD7rXUhf8/ttKLxnbGkVsgoEmIeuWZeSskvYTCJLAVV8Dqznp8MwMmiktppEMAU/Ne73uj86zGanTtl5/2Gfotfoemp/bLN2Z8cObjWfQnn1RXArE8aj/VYV4doQ+FAAJ6SF/HqgAAAABJRU5ErkJggg==)
ii) Let present age of Nuri = x
Let present age of Sonu = y
According to condition (i)
five years before Nuri's age is 3 times that of Sonu's age
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAAAXCAMAAAAx8S2TAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOjo6Oma2OpDbZgAAZjqQZmZmZpDbZrb/kDoAkDpmkLaQkNv/tmYAtmY6tmZmtv//25A625Bm27Zm2////7Zm/9uQ//+2///bdJIdYAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABrUlEQVRIS+1W2U7EMAxsOMqxhaWwAQLk+P+vxM7Z0BwmEi9o87DSKs7EHo+nmabz+j8MiMt3cjH86osc6wJH0c16oN70cZomNT9RwzFuGJ12UM0M1gXkNakb/G0uGWKJaZXQJamJW5ZEr5Uc8jerLWIY3azXvepxf5tXlzCOwhAM+j2OHi40KwM0rLS4tnnROs+xD+GYYPAPrqgwXUCXPpPXE8yNqEo6UzvvU2xWm4JHlwd7Xi+VCSugh7wQ4+W+2lI133nZQ0j0Co7DYFfOs16Yoyai24aq24ofFdCTu+glTcDuQuydl/Imr4Yy1YxoCR1rkZ4uCnriqy8bNTtgkrdK1GtChwzNc9O+c/RNH2uqjKzoxQkr6qvWRzfBWV5gGOrYnPwcPUpOP3w2nMyOvq+oR6zbl+gTSdBgLm9VugrowWGAZAAJCtgV5qzSJd7zLxvnBjL5l14eq8Nu7eknunNkYXdY1QBwwkKfu35vgx1U9Pumw5bQe13ZUdejKzsQ0Tuij4cS+i8TG3xP1C07qyNDH30hNccrbgI6fExobymSA9GuJUS5b+95/R0D30JfIXl2AuPOAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
According to condition (ii)
x + 10 = 2(y + 10)
= ![](data:image/png;base64,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)
Subtracting equation (i) from equation (ii) we get,
y = 20
Putting value of y in equation (i) we get,
x - 60 = -10
x = 50
Hence,
Present age of Nuri = 50 years
Present age of Sonu = 20 years
iii) Let the unit digit of number = x
Let tens digit = y
so number = 10y + x
Number formed after reversing the digits = 10x + y
According to the question,
x + y = 9 ...................(i)
9(10y + x) = 2(10x + y)
= 90y + 9x = 20x + 2y
= 88y -11x = 0
= - x + 8y = 0..................(ii)
Adding equations (i) and (ii). we get,
9y = 9
= y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAgCAMAAABXc8oyAAAAAXNSR0IArs4c6QAAADxQTFRFAAAAAAAAAAA6AABmAGa2OgAAOgA6OpDbZgAAZgA6Zrb/kDoAkNv/tmYAtv//25A6/7Zm/9uQ//+2///b/ILEngAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAg0lEQVQ4T+2TSw6AIAxEWxXFLwL3v6vFEGNiQid+ds6W6Zu0pUTvyxvmDsAGO5A3g+5c64VoBpC+nSiOjU4kxyKAmFChnwCi+CwEjCOXe05dAAqWK8Qo03OQUTIfGec0012nuEzMD4W2PovWR/ko+oqXBSch3/Ao/m+muCb1ZvQl33NsrUkEuYh8/XEAAAAASUVORK5CYII=)
Putting value of y in equation (i), we get,
x = 8
Hence,
The required number is = 10y + x = 10×1+8 = 18
iv) Let the number of Rs, 50 notes = x
Let the number of Rs, 100 notes = y
According to the question,
x + y = 25 ......................(i)
50x + 100y = 2000...............(ii)
Multiplying equation (i) by 50 we get,
50x + 50y = 1250.................(iii)
Subtracting equation (iii) from equation (ii) . we get,
50 y = 750
= y = ![](data:image/png;base64,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)
Putting value of y in equation (i) we get,
x = 10
Hence,
Meena has 10 notes of Rs, 50 and 15 notes of Rs, 100.
v) Let the fixed charge for first three days = Rs. x
Let each day charge there after = Rs. y
According to the question,
x + 4y = 27.................(i)
x + 2y = 21 ................(ii)
Subtracting equation (ii) from equation (i) we get,
2y = 6
= y = ![](data:image/png;base64,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)
Putting value of y in equation (i). we get,
x + 12 = 27
= x = 27 - 12 = 15
Hence,
Fixed charge = Rs. 15
Charge per day = Rs. 3
Solve the following pair of linear equations by the elimination method and the substitution method :
(i) x + y = 5 and 2x - 3y = 4
(ii) 3x + 4y = 10 and 2x - 2y = 2
(iii) 3x - 5y - 4 = 0 and 9x = 2y + 7
(iv) and
Answer:
i) By elimination method
x + y = 5.............(i)
2x - 3y = 4..........(ii)
Multiplying equation (i) by 2 we get,
2x + 2y = 10 ..............(iii)
Subtracting equation (ii) from equation (iii) we get,
5y = 6
y =
Putting value of y in equation (i). we get,
x =
By substitution method
x + y = 5 ...........(i)
2x - 3y = 4 ......................(ii)
from equation (i)
x = 5 - y................(iii)
Putting value of x from equation (iii) to equation (ii) we get,
2(5 - y) - 3y = 4
= 10 - 2y - 3y = 4
= -5y = -6
= y =
Putting value of y in equation (iii) we get,
x = .
ii) By elimination method
3x + 4y = 10 ..............(i)
2x - 2y = 2.................(ii)
Multiplying equation (ii) by 2 we get,
4x - 4y = 4 ...............(iii)
Adding equations (i) and (iii) we get,
7x = 14
= x =
Putting value of x in equation (i) we get,
3 (2) + 4y = 10
4y = 10 - 6 = 4
y =
By substitution method
3x + 4y = 10 ..............(i)
2x - 2y = 2.................(ii)
From equation (ii)
2x = 2 + 2y
Dividing both side by 2, we get
x = 1 + y
putting value of x in equation (i) we get,
3(1 + y) + 4y = 103 + 3y + 4y = 10
7y = 7
y = 1
and
x = 1 + y = 1 + 1 = 2
(iii) By elimination method
3x - 5y = 4................(i)
9x - 2y = 7..........(ii)
Multiplying equation (i) by 3 we get,
9x - 15y = 12.................(iii)
Subtracting equation (ii) from (iii) we get,
- 13y = 5
= y =
Putting value of y in equation (i) we get,
3x -
3x +
By substitution method
3x - 5y = 4................(i)
9x - 2y = 7..........(ii)
From equation (i)
x =
Putting value of x in equation (ii) we get,
=
=
= 13y = -5
y =
Putting value of y in equation (i) we get
3x -
3x = 4 -
= x =
iv) By elimination method
= .....(i)
=
Multiplying equation (i) by 2, we get,
x +
Subtracting equation (ii) from equation (iii) we get,
=
= y =
Putting value of y in equation (ii) we get,
x +
= x - 4 = - 2
= x = 2
By substitution method
= .....(i)
=
From equation (ii) we get,
x = 3 + (iii)
Putting value of x in equation (i) we get,
=
=
= 5y = - 6 - 9 = - 15
= y =
Putting this value in (iii), we get
x = 3 - 1 = 2
Question 2.
Form the pair of linear equations in the following problems, and find their solutions(if they exist) by the elimination method :
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomesif we only add 1 to the denominator. What is the fraction?
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice a sold as Sonu. How old are Nuri and Sonu?
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
(iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.
(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer:
i) Let the fraction is =
According condition (i)
=
= x + 1 = y - 1
= x - y = -2..................(i)
According condition (ii)
=
= 2x = y + 1
= 2x - y = 1..................(ii)
Subtracting equation (i) from equation (ii) we get,
x = 3
Putting value of x in equation (i) we get,
3 - y = -2
= - y = - 5 and y = 5
Hence, the required fraction is
ii) Let present age of Nuri = x
Let present age of Sonu = y
According to condition (i)
five years before Nuri's age is 3 times that of Sonu's ageAccording to condition (ii)
x + 10 = 2(y + 10)
=
Subtracting equation (i) from equation (ii) we get,
y = 20
Putting value of y in equation (i) we get,
x - 60 = -10
x = 50
Hence,
Present age of Nuri = 50 years
Present age of Sonu = 20 years
iii) Let the unit digit of number = x
Let tens digit = y
so number = 10y + x
Number formed after reversing the digits = 10x + y
According to the question,
x + y = 9 ...................(i)
9(10y + x) = 2(10x + y)
= 90y + 9x = 20x + 2y
= 88y -11x = 0
= - x + 8y = 0..................(ii)
Adding equations (i) and (ii). we get,
9y = 9
= y =
Putting value of y in equation (i), we get,
x = 8
Hence,
The required number is = 10y + x = 10×1+8 = 18
iv) Let the number of Rs, 50 notes = x
Let the number of Rs, 100 notes = y
According to the question,
x + y = 25 ......................(i)
50x + 100y = 2000...............(ii)
Multiplying equation (i) by 50 we get,
50x + 50y = 1250.................(iii)
Subtracting equation (iii) from equation (ii) . we get,
50 y = 750
= y =
Putting value of y in equation (i) we get,
x = 10
Hence,
Meena has 10 notes of Rs, 50 and 15 notes of Rs, 100.
v) Let the fixed charge for first three days = Rs. x
Let each day charge there after = Rs. y
According to the question,
x + 4y = 27.................(i)
x + 2y = 21 ................(ii)
Subtracting equation (ii) from equation (i) we get,
2y = 6
= y =
Putting value of y in equation (i). we get,
x + 12 = 27
= x = 27 - 12 = 15
Hence,
Fixed charge = Rs. 15
Charge per day = Rs. 3
Exercise 3.5
Question 1.Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(i) x – 3y – 3 = 0
3x – 9y – 2 = 0
(ii) 2x + y = 5
3x + 2y = 8
(iii) 3x – 5y = 20
6x – 10y = 40
(iv) x – 3y – 7 = 0
3x – 3y – 15 = 0
Answer:For two linear equations: a1 x + b1 y = c1 and a2 x + b2 y = c2
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igfqV9OUVfjVVfvBDYVEHp4dsXZY6NnHcHb6Uoc7SdPnl5CGFggzeWUibxvq7x3tffPKNEZlFqhsxfbASxyZd6KLGoZnMretv0jTF+r5mjS/nmsDt12NRAsURZL5GpnHaWPI9xSpgToSGx3D0owSigWGDhTIgZ3yq+a6VMorxg8SZ5JrKAhZcCC0Ig+PahmEWvnL7vEffmzlUo6dFTivtQ1Ph2klCU0z1yyr7kvaTvcurNNTnjp6R9MU9OH//SuYy6LmleyuXv6zZKoEvhLYnfTfGxAGaHPN0dLMW7b+Uprd+U72b39g3BsvU3pVAKrp+yDbuqse938jHGIrNL6cC9i4Uqixjcv9JyTHCJRUZxg46FmFysOeyc407GRwf3sl8KFh0+0iyIcDOi8L+x4qJ0E7uL+1kscTGHxfN2BX0XLz1k+3Kre0RYbBGnC9PfC0oiLnex4KqM6y+bAii0Vw0WdJKIoSinBWsPi680o3bKGkstizSOocK6Rmn2xY1DX8QFXG5b0uviJsZdJT2i5QH3D94ruxZoY8yBvBb5Y/OAGGSSYMVSyqREPnPHAHUZ0peMmzH6aqz6Mt5xacVyiVzH8U0dkdOjEusfv5Echnfz93TclzLJGe99/c0zSmQ2xhzXzl/MkWzY8l+8JviWEb5QWmrm6FK+beyafck66P9JYlyzCV0iUzltLnkeCjrx0OkGLYk2Ubzo45ifIn1vKRPuZUMHTyY8b1CU+krf96h2ruK9D5ZEKAzzevQM6qvPvuS9pO/66hx/zxk/Je1jkyCHf+lcRn27+n1u81Iuf1+3UQJdCm9J/G6KDwvYb4bdui9slOuuZmMVICszMTFzPopoCd2GssvCBWttaiWMdcfDgNhNlNp0MYZ1A/dOFhTsLKcLCNzF2GHHgsj5yLgnx912lLpm4VnssqM088FOC+8ldp164JJaWubQvtw6M4+wKMM6gLKXMo3zCIojCiQJn4hPa2Z979sggDUbaRT6rekd0dUXue2I17FBwoJ+V2Z62sqCEQWpLencWHPguZL4XeKR2+Svlsku+SwZA0P6cte4Ke2rkvriPcCmSbNf2YjEA4HYcSyVsSDXWLtQNlAqosxFWcPahiynpZZJ33jnHV1joEZma+cvNhnx0sAaTmEuxa2b8V2Se6Jmjq7lG/uSzQzCIdJ6snAnbIvYfEqJTOXI65DnER6FtZdNFzaJ2koNE7yP2IDMPX2jTz775qpd/KMMkjiO+uSWfcn7kL7b1Zac8VPavlz+JXMZ9e/r9znNS7my4+s2SqBL4a2J3wUjCwRcbq40ICvqGruDHTh2VFl0pfGka2zr1G0iIRQLVBbNxJC2lTZrIdeRfALLLwtbrDqx0D9YK0iCxU5z04217R0x9oVYVN6XFuKR+IdigfJcUubSvtw6E2vELjMJVIh9TgvJnu4TrBPwfWtQHHDJSzMtd1l7eB7KJdlKibVkgdcsXX2R2w6ugz11ZCGGu1/zzG7aivx8JMQFt222jDUHkuCJZ+06f3cIkzb5LBkDkRNKYGlfjtVXNfVlMwb38FT2CFdAfpubUz8cwnPwXknjdGP9+UbGGMpUdkqZ5Iz3rjFQK7ND5i/WDsxthH4Q6oEMoEgSP59bSufoITK3qy+pK21gc55xXyJTOe0c+rwYKkL4B/kEmqWGSZ+8tL2j73vbN1dF/uR1ScdMlMGS+N2++u+ao0vlfWjfdclH1/ipaV8u/9y5LM5nff0+t3kpZ0z6mo0S2KXwpvG7BOzHRA59mOJRLCgiJMXYWmFhyo4gE2WzsID+sWA17EoKxM4zVoOYLGJrDHPayzE2JEjCWoNCQGGTBYsDsZrRWkhMKQk+0kKiFVyT6SsycmIhZgedBTDJbFiscjRJm+tYs24s8HDn+9lGzBUxVScFt1tiA5EHLJ1tC5a29s6lfTl9wTUxJvrSIWlVvA+LLy659AdeDcwrxOCiMDYt4rjdYsWI8bvwwv0/WtVYKOFqzu9Y1IkVJk43jqXYFygzLFxrCzHHyANzHpbkZiEenDGOe1jTVZ5rx5wDyRSOZZE2EUtHm1MZymWSK5/0Ve4YiLHZNX05Vl8xp5bWl3O7sd6nBXdxlC8UuNRiH70Tmsntorth5Mp1zDXIe4189433WNdd/c17a2S2dP7CtZ4cFFh9+N+xMPcy5vBeavNEaBuLNXM0z6nhy33MTcwnKOZkPI6FOYlwDLx62LwqkamcOWbo83aF39B3rwrzTSkT5ijkhTwJeJ31lRz57JuryIXAN5FNRDYuY4kyWBK/WztHl8p7yXzYx5DfWf/ljJ+a9vXxL53L+K7m9DvtOvS8lLuuyukjX7NiArsU3hi/i5tJc/e+CwduFcTWoWTgTrq1sutYIjhj/cKKwHEYXWXNxxKRNIF4HWI6cXEtcX9LmaEsYSnHNSguUHFJY/FLfFpMtEDW35gZmPvpH7IDI9fE5tAvMcswihVJa3CT3pVkCndnNiKiizRtwQ2L+N00ZpT/z84o1+M+jSWOf7muzXNpX+74xZWRWDA2x2AbCx9Z2o+CweKMjQAUA1y9ieGNhX5gvkCZZb5BLlBuWYRSuI9YaBZKJIxigc+GGtmS48YEfcEGSDOmMrcN8ToWqMQbo2Cya54WForID0lCsGq1bVyNNQfGhTJu9SjXzMnIBcpGCZNS+cwdA4yzmr6k7mP1Fc8aWl84455LAjY2ZVKLPXLLuc4sVFNFGMWO/scdlPhdYvSxWiGXNUz6xntffzN+amS2dP5iPmP8UV+4xILyinLAmGYDJKfUzNHM3zV8qQ95GJiLmn2JosWYJQFZLLkylRu3nPs8vEbwPMK7iA2YGH6DGyqbXXHzj7mAOQGZq5lTeS7eZmzy0qdtJf3W9cln31zF83eNJWLhSeKJIpzjVcWzaufoUnnne53bdzmywNovZ/yUtm8I/11zGd/Vvn6fy7yUu67KmZd8zYoJ7FJ4cUdmgUqcR5ospQ8FljGsu81dvL77Sn+vPVy99D1jXR+PUWBBlR5bM9bzc55DX2Oxwl2XY1PY4Y1Hv+TcP8Y1LBKjOzdKZckxMen7UWw4G5MFJx9JdiKxwiCvFKyFvKcZv0usHhlVuZffsZwRv4WsU1CWmDxR1NIFLvLGOMC9NR5l0hXHB2cUExQ44vw4LxjrZW5Cjjm0L7e/kSsWiySawjMh7rbiGo71G4tPVFx5Jm6guOcR6xsXcCTGwJKB8oD1jH7DxZlslpToMs3mBBm5cUFEIY2ZmGNfkCyL80WHFtrBhgzKd0xqhgyQpZeNCzZXdh29MtYcGBcxsMUjgQXj+5JkXblM2uJMu+SzZAzU9OXYfVVaX75tKD/IHrKLskpfH9+I30WG2MDBGsgGFuwpKGrMHdFrgwzgKCPx2L4aJn3jPWcMlMpszfxFUieyM3N0TLpZycKYbxtuqTmeMUPm6Bq+vI9vBN88vjvRwsgYQkln4yxtT4lM5cw1uc/j24ylnLh8lEDkjrHPd4s5D7bIHXMl35OYV6KGCQot7WaOS/NTtH3r+uSzb65KxxJeETHhIN9HNhBZMxJOUFL2Ie98r3P7LqfuJAfLHT8l7SvhXzKX9fX7XOal3HVVTh/5mhUTSBVedg1Z0JElkDhHJlkmP1xHcZkhDq8tXi3Fg9WFFPooImmm1jER1hyuPub7a54FV5JPYLU6VGFSZLHHR5X6sNBrxp1OXTdi5fiYM0GxO137fpTU5welEutCtBDGRQvn4+LChuLaTA5GQiEszVgkcMVj8Zou0li8xWzA3IsFAMsNxybEDzWcqAMWe2JimtmGGUu0k3hWLEdYnhlDuWUO7cuta4yXoi+xcrPTzdyBBR22MalSfB7WCtyvYMkClE0H4v6wNjwpzDP0HTIaj8Sgf1kscA33IMtxc6OvL3LbkV7H+24T5AeFnbGLtRerPXXsCkkYcw7EOss50owV5j3iSKOsDmHSJ5+5Y6CmL7vGTU1fcU9JfZkbsELyXWOTDLdO5DQNj4j1gDHKBN8z5BtllzkG10zkAusI7vycmRozNdcy6ZrPqE9ff5fKbM38dbbgkslmIC7/bJzSfjZV4NO3Pkj7t3aOruEb30syTcYUih5zFGOK8Zxm2Y7X5spUrszmPI9xiRyQiZ65j+8UGynUFw8XvCr4fpPDIB7bxvtrmCAveOKxUYEs933r+uSza66K8nvvEHbEhgljCcs64ytuCOeyjM8rmaNr5H1sWSgZP6XjOYd/6VzWtw6Zy7xUIje+dsMEupJW1WBhEYoSwe5k7k5vyXtKDpwvee6U18ajiDgep0TpmapO0QLFTl96fuRU72t7Lkf9sGPNh722sBmDte1TjaOFeB5KGEoRC7Fd78fCE4/naF6DEs2zUbC4JipezetiTHabazburyj4KIC5rlrp8+fQvpy+ibFxMX6XvoUf7e5yWWdjjbkCxTdex8KNRSh/ayqVzFUsktgs4diOkr7IaUfbNYxd4sJR5IlZzHHBH3sOZNFLwheYNOfUIUz65DN3DMCttC+7xk1tX5XUl/cja1hb8AbBupuGRzTrwHzCedq4nEbLPnF2WA0Jz0gTYMV7S5l0jff4zL7+5roSma2dv5BJeKAoMi5KFN3YlqFzdCnf+N7Yb3wb+rytSmQqR25znocccI4334z4faLfMUKw8QrvXWurGiZRXuL7dn3rcuSza65K+511HN8HvHnwMsPqW5uzZB/yTt1z+i5HBrimZPyUtC+Xf8lcltPvc5mXcvn7uo0SGEPhZReIRQCTMbuQxKrmJq4owV5zuHrJ86e8lokoPe91ynf1PRsLJ5luh8Y69r2n63fcqfAAqHVpHvJu3zsuAdwYcTWe0qtj3BqP/7R9zYHj19xPJFM7LvQk1alR3EzQBEygmwDjCzdsvHZirCsb0iScRMEmHrl5zJyZmoAJmMCoBIYqvLgI4cpEDB6xTiSFwEWm9BiWnEbVHK6e89wtXUN/4z6KlWyMWMcaduwYcp4gx9Xs2k2uea7v2T+BmM2dxUrz/N391+Ywb9znHHiYFq73rfH8XeIIdx1vtt7Wu2UmsB8C5F3A64+QKsJ7KFh3yXNBPoc04/d+auS3mIAJbI7AUIWXWAySHnBUBzFQWDH52xSl5nD1Keqx5GeeNSRfQdlMEwnts02k5cc1kIRGLsslgMcF7svEM5LIC0svGxhb26nf5xy4XGmZV8357uHaSlgFViasTyy+kd8pQnHm1XrXxgT2S4ANbvIfxCMECafCE5AjAucQ5rVfGn6bCZjAQQgMVXiJBSAZA4tcMv2RYGGKBW/N4eoHATrzl7LAOzFsUhCTwmYFBRf0NFPjVM04QtKVkw/fVO/xc6cnQMZtstjGgosa3h45xzNMX7v9vWFfc+D+WrT+NxGvS06FtOB58qCOuP/1U3ELTWAaAoR8EEbFKQesAciFQCjBPtYc07TITzUBE1gcgaEK774azG586eHqUyje+2rvVO/Bskt2ZnZXceOLB8GTtIW42k9O9WI/1wRMwARMwARMwARMwARMwAT2TWApCm/N4eopS84EZVcflzWOo2jLqrlv9vt+HxY44nfJHMxZhDFuBhnA6vtmSffYd6X8PhMwARMwARMwARMwARMwAROYisBSFF7aX3O4Om5qnNWGhZgD3UmodQtJjwhHUWwpXivG73J2JGcgpoUzZjkDkHNrc45emUoe/VwTMAETMAETMAETMAETMAETGI3AkhTemsPVidPCkvnahBgHdHOIOjGITx+N5PwflMbvklE7lmg9R/m/VMv5p/NvmWtoAiZgAiZgAiZgAiZgAiZgAi0ElqTwxurnHq6OdZesgG+S9OBEkUNxxtrLQetbUvA4fxdrd/O81LNLen9gwlEBqdXbruCeNkzABEzABEzABEzABEzABBZLYIkKby5sMju/LRydcj5Jn0huJGHTBYLyx1FKWygvk0Qcb/O81KtJermku0t6aABhV/AtSITbaAImYAImYAImYAImYAIrJ7BmhZeuw5pJSvzXJ/1IPC8uvZ9RiwgAACAASURBVN8Kx/J8Y+V9HJsXE1Pds9HeJ4SjpY6S9PHwm13BNyIUbqYJmIAJmIAJmIAJmIAJrJnA2hXetr67ZDiOB8XvYWvu3EbbXhzcu49L/n4uSSdLur+kx4S/2xV8Q0LhppqACZiACZiACZiACZjAmglsTeElQdMLJX0pJK3ainUXGb6JpOtIumkQ6NNKOkHSpyUdk2Rntiv4mke822YCJmACJmACJmACJmACGyKwNYX3LuFoIjI0f3lD/UxTUXBJ3vUxSe+RdOPg2n18y1FEdgXfmHC4uSZgAiZgAiZgAiZgAiawRgJbUnhvJOlyku4m6Wtr7MzMNuHGzJm7ZGYusXBv1RU8E6svMwETMAETMAETMAETMAETmBuBrSi8l5XEv4ck1syLS3pnodI3t/7bV3227Aq+L8Z+jwmYgAmYgAmYgAmYgAmYwMgEtqDwHhksu4+T9J2E350kPTZkax4Z6+oet2VX8NV1phtkAiZgAiZgAiZgAiZgAlshsHaF9zySnizpdY0OPULS6SXdYSsdPaCddgUfAM+3moAJmIAJmIAJmIAJmIAJHI7AmhVe3HBfGay7bYSPlZQe0XO4Xpjvm+0KPt++cc1MwARMwARMwARMwARMwAR6CKxZ4XXnDyNgV/Bh/Hy3CZiACZiACZiACZiACZjAgQlY4T1wB8z09XYFn2nHuFomYAImYAImYAImYAImYAL5BKzw5rPaypV2Bd9KT7udJmACJmACJmACJmACJrByAlZ4V97Bbp4JmIAJmIAJmIAJmIAJmIAJbJWAFd6t9rzbbQImYAImYAImYAImYAImYAIrJ2CFd+Ud7OaZgAmYgAmYgAmYgAmYgAmYwFYJWOHdas+73SZgAiZgAiZgAiZgAiZgAiawcgJWeFfewW6eCZiACZiACZiACZiACZiACWyVgBXerfa8220CJmACJmACJmACJmACJmACKydghXflHezmmYAJmIAJmIAJmIAJmIAJmMBWCVjh3WrPu90mYAImYAImYAImYAImYAImsHICVnhX3sFungmYgAmYgAmYgAmYgAmYgAlslYAV3q32vNttAiZgAiZgAiZgAiZgAiZgAisnYIV35R3s5pmACZiACZiACZiACZiACZjAVglY4d1qz7vdJmACJmACJmACJmACJmACJrByAlZ4V97Bbp4JmIAJmIAJmIAJmIAJmIAJbJWAFd6t9rzbbQImYAImYAImYAImYAImYAIrJ2CFd+Ud7OaZgAmYgAmYgAmYgAmYgAmYwFYJWOHdas+73SZgAiZgAiZgAiZgAiZgAiawcgJWeFfewW6eCZiACZiACZiACZiACZiACWyVgBXerfa8220CJmACJmACJmACJmACJmACKydghXflHezmmYAJmIAJmIAJmIAJmIAJmMBWCVjh3WrPu90mYAImYAImYAImYAImYAImsHICVnhX3sGN5tHf15B0tKQzSnqHpGdtC4FbawImYAImYAImYAImYAImsBUCVni30tP/3c5TSbpSUHgfIul2kh6/LQRurQmYgAmYgAmYgAmYgAmYwFYIWOHdSk+fsp2Xl/QaSReVdPI2EbjVJmACJmACJmACJmACJmACayewZIX3eyVdU9L5JH1G0jMlfUfSf0n69to7bmD7jpV0K0lHSfriwGdt8fbzS7q+pK9I+lqQvS9tEYTbbAImYAImYAImYAImYAJzJrBUhfe8kp4Y/j1X0jkk3VzStSSdKOm+c4Z+4LrR56+U9GVJ1z5wXZb2+jNJwhUc5fZBkj4r6ayS7izpuKAAL61Nrq8JmIAJmIAJmIAJmIAJrJbAEhXe80h6taR7Snp20jO3kPQ0STdzIqZOeUVBe5+k+0l6zGole/yGnVnSSyS9VhIWcjwJiIl+iiRk70KS3jv+a/1EEzABEzABEzABEzABEzCBWgJLU3hPI+kFks4i6QqSvpU0/AaSni7pwpI+VAtkA/ddMVjBLyHptJL4L+UESZ/bQPtrmoj7/FMlXUzSJYOFl+ecWtKLJH1D0k2De3PN832PCZiACZiACZiACZiACZjABASWpvBeVdIrJN06WNZSJGQbRhnhHwqISzsBLLtkZ350sJSfFBS540NM9CcN7v8QuHKQu3tIerj5mIAJmIAJmIAJmIAJmIAJLIPA0hTe50i6rqSLSPpAghhL5ZskvTEoc8ugv/9a4oJL/C5Jly4r6cOhCsgBsc9vloRS53JKAiREw4OgKXfmZAImYAImYAImYAImYAImMGMCS1J4TyfprSETM264X0+4ksTq3ZJuKYkkVi7tBGL87gMkPapxyUsl/aCkyzjL9SnIRLljswCX5q9auEzABEzABEzABEzABEzABJZBYEkK7xkkvTMottdr4L1JcHGO8bsobW8IyvEyemI/tUzjd9+SvJLYaCzkJGK6lKRv7qc6i3gLcveOEBd+tUXU2JU0ARMwARMwARMwARMwARP4LoElKbxRKXt7iOGNXUgbnhGSVWH55Qze2+/IQPyTQXFBsdtiIbvwbYJr7ucTAGeX9P5gQb9KUHxTPlvmhmWXuHE8Cjj3ua3wdzI0f7Dx45a5bXF8uc0mYAImYAImYAImYAIzI7AkhRd09wrZma+eWG/JjnuMpC9KQlnjeBhcnDlChnJ6SRcMih6ZnY/esFvqy8JROvBLlX4sly+XdHdJDzW3/zNKUWgfGTJap5msyd7M+c+4OT/P3GY2u7k6JmACJmACJmACJmACmyewNIX3+yT9cbBG4mZ68ZCECevbkyTdR9KlJT0kHBFzTkl3lPQuSUdKumH471bjMGNiKs4wTssTJOEmfpSkj0syt1PyYZzcVtIvhOObyAKOPHEsEbHPWMcp5rb5KdUATMAETMAETMAETMAE5kRgaQpvZHduST8QFA1cmCkow1h2UT7aYlDvHZJaoahsVeF9cYjVPS4RwnNJOlnS/Xe4gZvb/8KK3gJfkfTRnnN3zW1OM53rYgImYAImYAImYAImsEkCS1V4azrLCohEcq/rSMINnMJxTidI+nRwC4+bBylfc6uRNsnc6rj5LhMwARMwARMwARMwARMYjYAV3tFQLuJBKLgPlvQxSe+RdGNJZGs+vuMoIitudV1rbnXcfJcJmIAJmIAJmIAJmIAJjEbACu9oKBf1INyYOXMX92/iUbuKFbe6rjW3Om6+ywRMwARMwARMwARMwARGI2CFdzSUq32QFbe6rjW3Om6+ywRMwARMwARMwARMwARGI9Cl8JIU6lrhrN5/DYmgSAzFma3/GY796TvP9nKSOPKG+zn39VktZ7yO1pieB1kBqSNtbuvixpj8eUlnDq7tjzvgmKwj233X2ts3BbN9P3Pod4Hzra8t6azhmDWy8qfniu+7PX6fCYxJwHNYP82hc0j/Gw5/hee5w/fBVDVw305FtuO5fQrvLwbX1wcERZcjgd4Wjq55dc9C+aKSnirp8pJuJ+muki4l6YMHaCevtOJWB97c1sWNo5U4fuoPJT1D0u/UNW+2d629fW3gv18SR4u9M/TrbDtH0hjfhR8N35W7SeIsbI6n+1qj0UtiMuf+Wkrd1tTfS57D9tEPuXPIVHWZ6rnNsZYzzy1lfLqepyRw6L7dlwzPqt9zXJqJ9STB0X/sWFi0NYjnPjNkAf4VSa8PFqVLSvrCgQhYcasDb27L43YVSY8M5wbjjdEsPy7pvZJ+TdJf1DXvoHetvX2lcLHYnyTpYZJQAudaxvwuoOi+VtJHJP1qS4OXwmSufTWnevWNd+q6tv5e6hw9dT+UzCFT1aXvuTnymju++ua53Of4uvkRmKpvc+SvT4bnR2uEGuUovJeR9HeS/nzHwqKtGrhDv0sSFmEW3pxfivvz10eoc+0jrLjVkTO35XF7sqSjJbHB1JaU7HphPP+MpA/XNe+gd629faVwTyXp/JL+qSPbeukzp7h+zO/COcOmzR0lPb2lskthMgXntT2zb7zT3rX191Ln6Kn7oWQOmaoufc/NkdfcMdo3z+U+x9fNj8BUfZsjf30yPD9aI9QoR+G9l6QHSfr1HQuLtmpcJLjXsdPwqhHqOcYj7ivp5pKOlPTVMR64kWeYW11HH4obR0/9g6S/l3TbHVX/0xBesEshrmvxfu5ae/v2Q/Ewbxnzu0BuiJdIurCk9x2mOX7rHgjkjPc9VGPvr1jyHD0lrDHnkCnqOba8ep6bopfm8cwp+nZs+ZsHqZFq0afw8vsrQrwUE80HMt+LYvlEST8t6V8y75nisjNKuktIvIVw/ZCkvwqW5hdLetMUL13BM82trhPnwI1kCIQg3GyHu/Jpgty/XdKt65p50LvW3r6Dwp345WN+F/5I0jUKwmwmbpofPxGBvvE+0WsP+tilz9FTwhtzDpminmPLq+e5KXppHs+com/Hlr95kBqpFn0KL/G7/xjidy/RkhgkrQYmcpKHMFljWSKL3q3CPf8WYq1GqrYfYwImkBA4m6SfCv+fhCdkrb1pyMJMMh8SzcWM6ucJY5qxyWYWMfbsCjJ+/ywj2y0WtauHcf3vQan+Vng388kNJfGOF4VznvmJJCNXlHQ6SW+R9MrCzNBzaV+u0MHhlyVdILT1HSG50jUl/YSkz4WM9d9seSBxPVx3PkmfCbkQvhN4fbtx/bklXT/0BX2XhoykffGXYbMS/jcK+RRwZX9ZYT+kr8eF+jrBZR6PmeeE7P3NJk3xXeiKfcplMkQ+u8ZA2v7cvpy6r2rq++kge8wbJJ48MTQMvjcIXlJNmeMS3PRYA3x0x2DJYVIy3rv6u1mFPpkdY/76ubD2YSx+IsyDbeO8ay4ZMkfn8G2+e4w6TznuSueQqeqy67kl8pqy7xuXffPckHHYlIG2OSj9drNGeGvw2OR7xBhnw5Hv2RkkPa8nIW2uXA4Zg0Pnpq4xWTJG+uYZ3jNm35bI3xrny9x1mfoU3hi/y4ftlj1PZQCwAEL4f1/Sl0P8LrdhTUJxXntBiBGoPq5dHFhgcIxTc3G7ZnbmNqx3WSCh6FLuIOksko6TxIcJpemvE8WGjyQJ5W4TFN3nBiX3NyT9tqQrS/pKS3XIKkhMPuP44SH5HC7RhC3wLgpHxXw8KD4otVcIih/Zg8kDgMKFks3H8U8KmjyX9uVWGYYscj8U2k08Hkosx7KRpZ5NBhKGoXym2YXPGzxj8I6hX84RwjA4Hg6FAzf5WGBCFn3iddjg4H2En8SCwv2p0Bd/GxRjNh1OCHMUGbpvHxI/5baL684UkmMhI/eT9NngHv/YsMnS9AKa4rvwI8GNmQzjafxuH5Oh8pkzBiLLkr6cqq9K60um7ycF2YPxdYMCy3GEdw4bWWx2IZ9keW/KHIoJ4x65Y8OtWXKZ5I73vv6O78+V2SHygULAPMiG3vPD9xtrCxtSzJfMxbmldo7O5RvrMVad+/phCFfqWjKHTFWXrufmymvknjsua+c51lOvCevItnHYJofNOQiDFf3W9u1+gaSbhM1uPDjJF0LyS757fPNqx/2QNURfv9cwoT4lYyR3nuG5XX1bOsfmyl8fo6XOl7nzaq9iFuN3yYJJ0qqcglvnyZKeLekPcm5Y0TXs2DHwGVy1BYWXjyRJv7ZSzG2cno7xG2RF33Xc0OMlReWWjaxYLhSUWXYyiQFOC8mtUFQfKulRyQ9s7LCYu0dY0JFAiN+ZzEmghKLN3/DwiOWBwdp72cJFYPz4ULdDtC/XSsOi/3clPTqEULBB8MagALAJSImJV+DGPEnhY8RRb/dM/sbfbyHpacFFHYWZAncUEM5QRmFmA4FzlVGAKcw/zb5AEWGRgqLKhgdKNxsSsMwtvIO4WbIjH9uwDpOc8IJhg6Nts27M7wKWBUJS0vjdGiYl8pkzBqKMlPTlVH1VWt/XhfAfZCkWvEDYUGGzBm+AO0kithTrZVPmuOfswasD2WhuaJUwie/vms/6+js+I1dmuX7I/IVigYEgnXfZQGScchxjW7b8XeOuZo6u4TtGnfv6oU2+S8ZdyqhvDpmqLn3PzZHXeE3JuKyZ53hPTIZExn42p/pKbh+xoYMHFxtjfOejZxdGLhRjxny6Pij9ruXWo7mGyOmfUiaRWe4YyZ1n4rdxV98OmWO3Ol/2yff//N5liayN38W1kiNPsF68MLsmp7wwtWRUPqL6tkO+u7rSjRsP0YZDvHMsXvE5h2jDmO+M8RsoNm1jjwmRuHXcDdlUSRUTFmUkusJq++YELNYddotZzGMhTLM+47pDMjsWuCy4uBcFDqsvVkUWyi9tdBLKFkdu1Ci8h2xfrqzxYWWH9imS2DyAN7vlWLhjiQsElHdirbFgsGuOZR4lNC4kuB5rD1ZMlLu4e44XCbvpbFgQdsJi4zHB0hsXGc2+4BgC+pfC/WxKpP3c1z4WI7yPevCsphfAb4XFzq68DWN8F2Id2WQhJwMhNDEBYQ2TXPnMHQPUr7Qv28bN0L4aq754IbCpwkYG64Eoc+TCeHfw4MK7IBb65OUhhIFN71hKmcT7usZ7X3/zjBKZZaNqyPzFRhCbfCi4sbB4ZXMretv0jTF+r5mja/mOUee+fhjzu9A3h0xVl77n5sgr15SMS67PnefYhIpeVtyHMsV3lwStOYaTkj7iW/azIcwxtpvvFvPBg8N3qHbcl9QjXUO09c9QJrENOWOkZJ6JOY36+rZ0jqW+W5wvc+bU/7mmS+Etid9NX8pij91gLEYovjVlTCWg9P2HfHdpXXddf4g2HOKdY/GKzzlEG8Z8J7uRWGR2KR24vPFhIjwBl9m0HBNcYhm3uEHHwo4u1hzcX7E0MrkTt/NLwaLDhxbrBe48FP43O7Ao3cTufjF5VlzMYfG8XUXnHbJ9udU9Iig9xOnC9PeCkvj55AG4KuP6y6YACu1VgwWdJGIoymnB2sNCPM2onbLGUvvU4Fb2/nBjsy9uHPriS7mNaLkubmLcVdIjWn6/f/Do2bXIGuO7wGuRPzYPiEEmgU0spUxK5DN3DFCXIX3JuBmjr8aqL+OdOHQsl8h1HN/UETk9StI/J31AEhbezd/TcV/KJD6ya7z39TfPKJHZGHNcO38xRxLSxX/xmvibnpjGXUOxZo6u5TtGnfv6YczvQt8cMlVd+p6bI69cUzIua+c53oPiSRgNrsbRq6hr6s/pI8KR2KDlXzPZZdzYZbMW759YSuUypx5ta4ic/illEtuQM0ZK5hk2IHL6tnSOpb5bnC+LljRdCm9J/G76Uqw9vxl2l75QVBtfbAImMIQAyi6LTay1qZUwPhOvC2I3UWqJJY0F6wZuZlh82R2OCa74HRd9LGFYEP8juCd/TBKJmFDqmoVnYRFGaeajmxbeSzw/9cAltbTMoX25dWZuJSP8qYPFN2Ua51YURxRIEj4RL9nMhN+3QQBrNhcp9FszTrCrL3LbEa9jg4QF/a5s/bQVCyAKEvLRLGN9F86VxO8Sj9wmf7VMdslnyRgY0pe7xk1pX5XUF+8BNk2a/Xr6sLgldhxLZSzINQm/sFaxoI0yF2WNmG5kOS21TPrGO+/oGgM1Mls7f7HJiJcG1nAKcykunozvknwcNXN0Ld+x6tzXD/H3od+F3DlkyLzY9Y3qe26fvJaMy755Lo5DNqIIZYkyFuWXpHNsppaULtmP1kM2y2NoTXz2fUL+D7x/0o3dWrmsHYNTMMkZI6XzTG7flsyx9EWf/PWN09J2DBnXOVxLZDfr2i6FtyZ+l5fyMcSN50oDMoBmVd4XmYAJ/A+BuAPLooIY0rbSZi3kOpJoYPllYYtVJxZ2IrFW4LLEbnFbMqvme2IcH7GovC8txBTxj0UFynNJmUv7cutMTA+7ucTyEvucFpI9sUhgZxi+ZL9EcSATfpppucvaw/NQLsnATawli4uSvshtB9fBnjqyELlYyznmtBX5+UiLS3Z8z1jfBZKr8Kxd5+8OYdImnyVjIHKq6cuucVPSVzX1ZTMG9/BU9ghXQH6bm1M/HDy38ExJ43Rj/Vk34E4YSy2TnPHeNQZqZXbI/MV6irmN0A9CPRjPKCPEz+eW0jm6lm+szxh1HjoX5X4XcueQseeAyKrruX3yWjIueV/fPBfHIXly0vEW5Tc3fjeVyy7Zj4nUiEFOvTpwpydUBm9OQiCGjnvurx2DUzChPl1jpGaeye3b3Dk2fqOxvnet/9Y4X+bOq9+9bpfCm8bvNgW86wXx2BGgkwBiawVWLGBZANYWrOLESWBB20oxt+E9zTE2JEjCWsPCgMLGExYHYjWjtZCYUo4NSwuJVnBNRokgQzgWYuSPBTDJbFjAczRJaqXcVWMWeLjzEeeTyjAfxpNCUhs+jCwAsHSmLlBdFObSvtyeijHRlw5Jq+J9WHxxyaU/yKzNXEsMLgpj0yKO2y2uozF+F15vSKxqLHZwNed3LOrMGyw+YvKk2BcoMyistYWYY/qShQ6W5GYhHhzrBW5YTVd5rh3zu0CmcCyLtImEXbQ5laFcJrnySV/ljoEYm13Tl2P1FZsSpfXl3G6s92nBXRzlCwUutdhH74Rmcrvo1he5ch1zDfJeI9994z3WdVd/894amS2dv3CtJzkV1hX+dyzMvYy5B4TM6Dljr2aO5rmlfIl5HKvOff3QnItyx13zu1Ayh4w9B8S6dD23T15LxiVM++Y54vz5nrIByaZnLFF+c+N3U7ncJftcg1LNO9nESfN48H7GOV5geIkR7sTYI1FlqVxGb5HSMRj7Z0wmP5Y5Rmq+jX19WzrHMsb65K9vnC5xvsyZU09xzS6FN8bv4hbRtDp0vQRTPXFkLKhxndxaYVKDwZAszbimMFmUHGOwdM5b5kZyAuJLiOnExbXE/S3td5Ql3BNxFYkLVLKrs/glPi26JJH1N2YG5n5klezAjHVijJgTYpZhZJCkNbhJ70oyxYeO3d3oIk1b2A0mfjeNGeX/swMZP4zslvMv17V5Lu3LHWu4MpKFmc0c2MbCx4yFAQrGq0K8LwsGXL3T2Cj6gTkUZZY5GLlAucW1nMIGArHQLHZIGMUHi01GsiXHjQn6gg2QZkxlbhvidYxP4o1RMNmdTgsLUeSHZBxYtdqyWY/1XYiLRuZHlGu+U8gFykYJk1L5zB0DjLOavqTuY/UVzxpaXzjjnksCNjZl0vAI5JZznVkQpoowih39j2s08bvE6LNIRi5rmPSN977+ZvzUyGzp/MV8xvijvnCJBeWVzRLGNBsgOaVmjmb+LuVLlt2x6tzXD+lcVDruUma5c0juvFhal77n5shr7rhk44Tv9q55Di67xiFx9BxjhyKa45GVMt4l+3Ejhm9NM36X98GSjQzGPb8zDjDclMplrEvpGIxriDGZ5I6R0m9j3zesq293zbGMsRz565LhJc6XOXPqKa7ZpfDijsxijIyqaWKQvhdgBcK629x16ruv9PfcQ6xLn7vm6+lrrDO4ppLen93vZizGmts/Vttw9cOixccEBYAxMiQZEIvEeDwQSmXJMTFpm1BsOBuTBSd1Y8cPKwz1o2At5D3N+F1i9cioyr38juWMJBCMfwrKEh8UFLV0gcsYZG4gS248yqQrjg/ZQzFBgSPOj/OCsV7mJNWgHnNoX64MMdbIVkuiKeIZ4w40ruFYv4k9jYorz8QNlIQfJGWJG10koCDpFYsIrGf0Gy7OZI2kRJdpNifIyI0bJfIYMzHHviCmivMUhxbawYYMyndMaoYMkKWXjQs2V3YdvTLWdyEuFmCLRwILnPeFTdYSJm1xpl3yWTIGavpy7L4qrS/fe5LQIXvILsoqfX18I34XxmzgcNYsG1iwp6CoMXdErw0ygGN5j0cZ1jDpG+85/V0qszXzF8nayM7M8S/pZiULUDYLcC3N8YwZMkeX8iVD7Fh1zumHGq7N70LuHJI7L5bOAX3PzZHX3HHZN8+l4xBFMyYr5NvK5iNrcEIRSkpXH/HdYVO7uVnO8/HoYd5gfcEGJO9l3qj9rg2RlTg3jcGkZIyUzDMlfVsyx+bIX58Ml7SD/q3pqzHnyxL5/u61qcKLsLJ4wd2FmD4WwnzAcJPENYGYs7ZEOOlLsTDcPSy60+D14op13FB6uPqY717ysxBOFjYovPQzi5pmjOWS2zd13VEC4YZy+6CgtJ01HEPB4rt0NzXWFwWaJDt84LGI1PYJ9Xt+UCrZkY0WwrgI43w83GtRXFOXJOpBMhAszVgkcMVj8Zou0li8xWzA3Iu7FJYbjj6IH1ueQx2I+yP2pJltmPmFdhLPiuWIHWzmldwyh/bl1jXGtNKXyAvWb+ZTLOiwjUmV4vNIToGbEyzZiGLTgbg/XMqfFOZe+g75Q6mNczcfZa7hHsZ33Nzo64vcdqTXIU+3CfKDwv79wdqL1Z46dp1TPOZ3AWsC50gzVvgWEEcaZZU61jLpk8/cMVDTl13jpqavuKekvswNWCH51rNJxvFXyGkaHhHrAWMULDbWkG+UXeYY3CuRC6wQuPM/LMnUXMukaz7LGQOlMlszf50tuD6yGYjLP5vJtB+FCj59a6a0f2vn6FK+Y9Y5px9quDblPncOmWoOyHlun7yWjMuueS4yv3cIWWKzhXGIFZyxGTeTS+aOrj5iIxbjCAp7PFYnPpvNWI7i4vvFd4ucFXEtVCqXfd+tvjmaPhqLSckYKZ1ncvq2dI7tWx/ljNPSdtSM6xKuJfKbdW1X0qqsBzQuYsHFghmXitxdzZL31ByuXvL8LVwbd0rZPUrPStxC22vb2HaoOAoGSh27nkOO4Ip1IvYFKx1HzNQWNqiwtn2qcbQQz6MN1JmFWFvh/ezUxuM5mtegRPNsFCyuiYpX8zpcHXHFanPNxv0VBR8FsGaDYA7ty+kblFNibWP8LmzhR7u7XNbZbGT+RPGN17FoQLHjb02lkvmbhQ6bJZ9oqVhXX+S0o+0aFHfiwlHkcb3LccEf+7vA5gwJSmDS/M4MYdInn7ljAG6lfTlFX5XUl/cja1j+sNZgpUnDI5qywHzCWZgkKouWfeLZJIh0ogAAIABJREFU8CwhPCNNgBXvLWXSNd7jM/v6m+tKZLZ2/kIm4YFHBuOiRNGNbRk6R5fyHaPOuf1QyzU+v2QO6ZOJ2rr0PTdHXmlP7rjsmudSmWFdzLcF5RPFFAtnzZGgu7hQX5TpNEY9nQ+oJ4oM83FbKF6pXNb2zxRMSsZIyTyT27clc2yO/PXJ8JLmy+I1zBgKL1o+HzwsPsSUscPTdlxEceUaN9Qerj70vWu7H2seWV2HxvWtjcuu9jCJoITipo+LanRfRt5JDoXFE/fTXQpgLidiwfCKqHVpzn2Pr5ueAG6MuBpjBZvK02X6Vgx7w76+C8Nq6bvbCJCpnU08ksDUKG6magJjEPAc0k6RsUm4Cx4/MXcGm9msR1iHkN9gSzlgoGQmY4y4lT9jqMLLebu47bDgJ66HZCzErZQeOZKDufQQ65xnbu0a+htXSSxCY8T1bYEfZ4u+IiQgwl1yioJS/UBJHFczVHGeon5+Zj6BmOGeBQeuYFN4uuTX5jBX7vO7cJgWrvet8fxdYgF3HW+23ta7ZXMh4Dlkd0+QswEvSkLUCA2iYN0lRwa5IHZZYufSt1PUw0ymoLqyZw5VeIkdIIkJSXyI9yGZCX+botQeYj1FXZb6TGJOSTSCYpUmzVlqe/ZRb1ypiLnAWoer3hSFIyJwDSShkctyCeCFgvsy8Ywk8sLSywbG1nbb9/ldWK60zKvmrAVwSSasAksRFiQW0MjvFjdt5tU726uN55Ddfc7mOLkT4vGDhKfhWcnxgiV5MdYkVWaypt6cqC1DFV78y0mOwYLucyEr4xSLu6GHq0+Eb3GPZTFzYtikIC6DzQoKLuj0n8spCfQdKj4GryMkYUWOH68xnulnHIYAGbfJFBkLbmZ4wES3s8PUav9v3dd3Yf8tW+8bide9ZaN5eJ7EBH3rbblbNkcCnkN29wqu3oSlcUIC6wfyKBCGsOU1nJnMcRTPrE5DFd59NYed59pDrPdVxyW8B8su2ZnZDcRlLR5cToISYkg/uYRG7LGO8VBxspZebY/v9atMwARMwARMwARMwARMwARGILAUhRdXwdpDrMHE+ZfsYOOexdELbRkkR8A560dgbSJ+lyy5nPca4zyQAay+bw5xqrNuxJ4rBzPid5EXNgTaCn8nI2JqxbO87bmj/DoTMAETMAETMAETMAETaCOwFIWXupcers49uGRxdiSWureGhFocI/OIcOzClmKTYvwu5yRy3l9aOE+VM844ozXnmJEtjSYU2kcG9+/UZQjZunlwKyJe0/K2JalwW03ABEzABEzABEzABBZBYEkKb80h1sQkYcl8bdIbJCDigHDi7Z6+iF4ap5Jp/C4ZtWOJ1nOU/0u1nPU5ztuX+xTGyG3DZgmxzhxDdGQ4houNAs6ei8Xyttx+ds1NwARMwARMwARMwARWSGBJCm/En3uINRY4EgHhCv3gRJFDccba+5WNKXicv4u1u3k26NmD0gYTUtunVm+75v7voI+HiiM3H205PsjytsIJ0k0yARMwARMwARMwARNYNoElKry5xMmw+7ZwTMj5JH0iuZGETRcIyh9HKW2hvEwSManNs0FJxvRySXeX9NAAwq7g5RJheStn5jtMwARMwARMwARMwARMYFICa1Z4AYc1k3Tlr08oEs+LS++3QlwmLqpbKDEx1T0bjX1COFrqKEkfD7/ZNbdOIixvddx8lwmYgAmYgAmYgAmYgAlMQmDtCm8btEuG43hQ/B42CdV5PvTFwb37uKR655J0sqT7S3pM+Ltdc8ftv63K27gU/TQTMAETMAETMAETMAETqCCwNYWXBE0vlPSlkLRqK9ZdROMmkq4j6aZBTk4riSRMn5Z0TJKd2a65FQNpxy1blrfxKPpJJmACJmACJmACJmACJlBJYGsK711Ctl0yNH+5ktlSb0PBJXnXxyS9R9KNg2v38S1HEdk1d5xe3rK8jUPQTzEBEzABEzABEzABEzCBAQS2pPDeSNLlJN2tJcPuAISLuxU3Zs7c5TidEgu3XXPLutryVsbLV5uACZiACZiACZiACZjA6AS2ovBeVhL/HpJYMy8u6Z2FSt/oHbCQB9o1t6yjLG9lvHy1CZiACZiACZiACZiACUxCYAsK75HBsvs4Sd9JKN5J0mNDtuZJ4K7ooXbNze9My1s+K19pAiZgAiZgAiZgAiZgApMSWLvCex5JT5b0ugbFIySdXtIdJqW7jofbNTe/Hy1v+ax8pQmYgAmYgAmYgAmYgAlMTmDNCi9uuK8M1t02kMdKSo/omRz2Al9g19z8TrO85bPylSZgAiZgAiZgAiZgAiawFwJrVnj3AnDFL7Fr7oo7100zARMwARMwARMwARMwgS0QsMK7hV4ub6Ndc8uZ+Q4TMAETMAETMAETMAETMIGZEbDCO7MOmUF17Jo7g05wFUzABEzABEzABEzABEzABIYTsMI7nKGfYAImYAImYAImYAImYAImYAImMEMCVnhn2CmukgmYgAmYgAmYgAmYgAmYgAmYwHACVniHM/QTTMAETMAETMAETMAETMAETMAEZkjACu8MO8VVMgETMAETMAETMAETMAETMAETGE7ACu9whn6CCZiACZiACZiACZiACZiACZjADAlY4Z1hp7hKJmACJmACJmACJmACJmACJmACwwlY4R3O0E8wARMwARMwARMwARMwARMwAROYIQErvDPsFFfJBEzABEzABEzABEzABEzABExgOAErvMMZ+gkmYAImYAImYAImYAImYAImYAIzJGCFd4ad4iqZgAmYgAmYgAmYgAmYgAmYgAkMJ2CFdzhDP8EETMAETMAETMAETMAETMAETGCGBKzwzrBTXCUTMAETMAETMAETMAETMAETMIHhBKzwDmfoJ5iACZiACZiACZiACZiACZiACcyQgBXeGXaKq2QCJmACJmACJmACJmACJmACJjCcgBXe4Qz9BBMwARMwARMwARMwARMwARMwgRkSsMI7w05xlUzABEzABEzABEzABEzABEzABIYTsMI7nKGfYAImYAImYAImYAImYAImYAImMEMCVnhn2CmukgmYgAmYgAmYgAmYgAmYgAmYwHACVniHM/QTTMAETMAETMAETMAETMAETMAEZkjACu8MO8VVMgETMAETMAETMAETMAETMAETGE7ACu9whkt6Av19DUlHSzqjpHdIetaSGuC6moAJmIAJmIAJmIAJmIAJmEAuASu8uaTWcd2pJF0pKLwPkXQ7SY9fR9PcChMwARMwARMwARMwARMwARM4JQErvNuUiMtLeo2ki0o6eZsI3GoTMAETMAETMAETMAETMIG1E1iywvu9kq4p6XySPiPpmZK+I+m/JH177R03sH3HSrqVpKMkfXHgs7Z4+/klXV/SVyR9Lcjel7YIwm02ARMwARMwARMwARMwgTkTWKrCe15JTwz/nivpHJJuLulakk6UdN85Qz9w3ejzV0r6sqRrH7guS3v9mSThCo5y+yBJn5V0Vkl3lnRcUICX1ibX1wRMwARMwARMwARMwARWS2CJCu95JL1a0j0lPTvpmVtIepqkmzkRU6e8oqC9T9L9JD1mtZI9fsPOLOklkl4rCQs5ngTERD9FErJ3IUnvHf+1fqIJmIAJmIAJmIAJmIAJmEAtgaUpvKeR9AJJZ5F0BUnfShp+A0lPl3RhSR+qBbKB+64YrOCXkHRaSfyXcoKkz22g/TVNxH3+qZIuJumSwcLLc04t6UWSviHppsG9ueb5vscETMAETMAETMAETMAETGACAktTeK8q6RWSbh0saykSsg2jjPAPBcSlnQCWXbIzPzpYyk8KitzxISb6kwb3fwhcOcjdPSQ93HxMwARMwARMwARMwARMwASWQWBpCu9zJF1X0kUkfSBBjKXyTZLeGJS5ZdDffy1xwSV+l6RLl5X04VAF5IDY5zdLQqlzOSUBEqLhQdCUO3MyARMwARMwARMwARMwAROYMYElKbynk/TWkIkZN9yvJ1xJYvVuSbeURBIrl3YCMX73AZIe1bjkpZJ+UNJlnOX6FGSi3LFZgEvzVy1cJmACJmACJmACJmACJmACyyCwJIX3DJLeGRTb6zXw3iS4OMf4XZS2NwTleBk9sZ9apvG7b0leSWw0FnISMV1K0jf3U51FvAW5e0eIC7/aImrsSpqACZiACZiACZiACZiACXyXwJIU3qiUvT3E8MYupA3PCMmqsPxyBu/td2Qg/smguKDYbbGQXfg2wTX38wmAs0t6f7CgXyUovimfLXPDskvcOB4FnPvcVvg7GZo/2Phxy9y2OL7cZhMwARMwARMwARMwgZkRWJLCC7p7hezMV0+st2THPUbSFyWhrHE8DC7OHCFDOb2kCwZFj8zOR2/YLfVl4Sgd+KVKP5bLl0u6u6SHmtv/GaUotI8MGa3TTNZkb+b8Z9ycn2duM5vdXB0TMAETMAETMAETMIHNE1iawvt9kv44WCNxM714SMKE9e1Jku4j6dKSHhKOiDmnpDtKepekIyXdMPx3q3GYMTEVZxin5QmScBM/StLHJZnbKfkwTm4r6RfC8U1kAUeeOJaI2Ges4xRz2/yUagAmYAImYAImYAImYAJzIrA0hTeyO7ekHwiKBi7MFJRhLLsoH20xqPcOSa1QVLaq8L44xOoelwjhuSSdLOn+O9zAze1/YUVvga9I+mjPubvmNqeZznUxARMwARMwARMwARPYJIGlKrw1nWUFRCK513Uk4QZO4TinEyR9OriFx82DlK+51UibZG513HyXCZiACZiACZiACZiACYxGwArvaCgX8SAU3AdL+pik90i6sSSyNR/fcRSRFbe6rjW3Om6+ywRMwARMwARMwARMwARGI2CFdzSUi3oQbsycuYv7N/GoXcWKW13XmlsdN99lAiZgAiZgAiZgAiZgAqMRsMI7GsrVPsiKW13XmlsdN99lAiZgAiZgAiZgAiZgAqMR6FJ4SQp1rXBW77+GRFAkhuLM1v8Mx/70nWd7OUkcecP9nPv6rJYzXkdrTM+DrIDUkTa3dXFjTP68pDMH1/bHHXBM1pHtvmvt7ZuC2b6fOfS7wPnW15Z01nDMGln503PF990ev88ExiTgOWxMmuM9y/POeCz9JBPYO4E+hfcXg+vrA4Kiy5FAbwtH17y6Z6F8UUlPlXR5SbeTdFdJl5L0wb238r9faMWtDry5rYsbRytx/NQfSnqGpN+pa95s71p7+9rAf78kjhZ7Z+jX2XaOpDG+Cz8avit3k8RZ2BxP97VGo5fEZM79tZS6ram/tziHLUHOcuadKduxJhmfkpOfbQKtBHJcmon1JMHRf+xYWLQ9mOc+M2QB/hVJrw8WpUtK+sKB+sKKWx14c1set6tIemQ4NxhvjGb5cUnvlfRrkv6irnkHvWvt7SuFi8X+JEkPk4QSONcy5ncBRfe1kj4i6VdbGrwUJnPtqznVq2+8U9e19ffS5+g5yc+Ydembd2rftUUZr2Xl+0ygikCOwnsZSX8n6c93LCzaXow79LskYRFm4c35pbg/f72qluPcZMWtjuMcueHKyAbMnMshuT1Z0tGS2GBqS0p2vTCef0bSh+cMcUfd1t6+0i45laTzS/qnjmzrpc+c4voxvwvnDJs2d5T09JbKLoXJFJzX9sy+8U5719bfS5+j1yaDsT19805tu7co47WsfJ8JVBHIUXjvJelBkn59x8Ki7cUXCe517Fq9qqpm4990X0k3l3SkpK+O//jVPnFu3C4m6U8lsRHTl2H6kJ1yKG4cPfUPkv5e0m13AIAf4QW7FOJDcut799rb19f+Jf8+5neB3BAvkXRhSe9bMhTXvZNAznhfI8Ilz9Fr7I/Ypinmna3K+JrlxG2bIYE+hZffXxHipVisfCCzDSiWT5T005L+JfOeKS47o6S7hMRbTFQ/JOmvgqX5xZLeNMVLV/DMOXN7UpAp4srnVubAjcQahCDcbIe78mmC3L9d0q3nBjCjPmtvXwaCxV4y5nfhjyRdoyDMZrHQNl7xvvG+RjxLn6PX2CexTVPMO1uU8TXLiNs2UwJ9Ci/xu/8Y3Ecv0ZIYJG0WLkUkD2GyxrJEpsFbhXv+LcRazRSDq7UQAueRdGKQrY8tpM77qObZJP1UeBEJT8hae9OQhZlkPiSaixnVYciYZmyymUWMPTvMjN8/y8h2i0Xt6mFc/3tQqr8V3s18ckNJvONF4ZxnfiJR0RUlnU7SWyS9sjAz9Fzal9uXcPhlSRcIbX1HSK50TUk/IelzIWP9N1seSIwY151P0mdCLoTvBF7fblx/bknXD31B36UhI2lf/GXYrIT/jUI+BVzZX1bYD+nrcaG+TvCywGPmOSF7f7NJU3wXuuLocpkMkc+uMZC2P7cvp+6rmvp+Osge8waJJ5l3KfC9QfCSasocv+PyyRrgozsGSw6TkvHe1d/NKvTJ7Bjz18+F7xNj8RNhHmwb511zyZA5Oodv891D6zwGN+rU1z+582+8rqRdOe/um3dKxsWSZby0H3y9CcyCQJ/CG+N3+bDdsqfGfORYAJ1B0u9L+nKI3+U2rEksstdemBD5APdx7eLAAoNjnJqL2zWzy+XGRgpKxJ1bYGyRW8TAAglFl3IHSWeRdJwkFCWUpr9OFBs+yiSUu01QdJ8blNzfkPTbkq4s6SstfMlQSUw+4/jhIfkcLtGELfAuCkfFfDwoPii1VwiKH9mDyQOAwoWS/TxJf1Ig0HNpX26VYcgi90Oh3cTjocRyLBtZ6tlkIGEYymeaXfi8wTMG7xj65RwhDIPj4VA4cJNP+5ws+sR+scHB+wg/iQWF+1OhL/42KMZsOpwQ5igydN8+JH7KbRfXnSkkx0JG7ifps8E9/rFhk6XpBTTFd+FHghszGcbT+F3kpIvJUPnMGQORZUlfTtVXpfUl0zceNMgejK8bFFiOI2TOhS+bXcgnWd6bMsfmBuMeuWPDrVlymeSO977+ju/Pldkh8sGmIfMgG3rPD99vLHdsSDFfMhfnlto5OpdvrMdYdR7CrWZO6eNY0q5c2eCdXfNO6bhYooz3cffvJjBrAn2KWYzfJQsmSatyCm6dJ0t6tqQ/yLlhRdewk07WWxS42oLixkeSpF9bKbi+415O2v3awgYLCtgWNlZ2MYqxQGRF33Xc0OMlReWWjaxYLhTYsStODHBaSG6FovpQSY9KfmD+YDF3j7CgI4EQv7MwIIESijZ/w8MjlgcGa+9lCxeB3H/I9uVaaVj0/66kR4cQCuTxjUEBQEYpMXkT3JgnKSyAOOrtnsnf+PstJD0tuKijMFPgjgLCGcoozGwgcK4yyh6F+afZFygiNwmbGWx4oHSzIYGs5BbeQdws2ZGPbViHSU54wbDB0bZZN+Z3AVdmQlLS+N0aJiXymTMGooyU9OVUfVVa39eF8B9kKRa8QNhQYbMGb4A7hfwJWC+bMsc9Zw9eHchGc0OrhEl8f9d47+vv+IxcmeX6IfMXCj4GgnTeZQORcUq+hLZs+bvGXc0cXcN3jDq3yW/JuMrtnxIDQG67St+9a94ZMi6WJOO53wlfZwKzJNCl8NbG7+JayZEnWC9eWNnq1JJR+Yjq2w757upKN248RBumfieLByxdeBGU7JaXMJ26DW11GfOdMRYIxaZt7PFxZWMBd0M2VdJFBIsyEl2xafDmpKJYd14TrDlYCNNEYbiBkcyOBS4LLu5FgcPqi1WRhfJLG41G2eLIjRqF95Dty5UjXDrZ7X+KJDYP4E14BxbuWPCCwerNxgKx1lhBXxAs8yih0UWc67H2YMVEucNiTMGLBCsyGxaEnfCsxwRLL7+39QXHttC/8X42JdJ+7msfC1veRz14VtML4LfCZseuvA1jfBdiHdlkIScDITQxAWENk1z5zB0D1K+0L6foq7HqixcCmypsZLAeiDJHLox3Bw8uvAtioU9eHkIY2PSOpZRJvK9rvPf1N88okVk2qobMX2wEscmXeh+hCLG5Fb1t+sYYv9fM0bV8x6jzkHm/pH9KcsHktKvm3X3zTum4oL+XJOM58utrTGC2BLoU3pL43bSBLPbYDcZihOJbU8ZUAkrff8h3l9Z11/WHaMOU7+RYqzcE69ffjAWp5TlTtmEffcXONhaZXUoHLm8sVAlPwG0xLccEl1jGLW7QsRCTizUH91csjSwUiEP9pWDRYTGH9QLXMAr/GysuSjexu19MnhUXc1g8b1fRj4dsX251jwhKD3G6MP29oCR+PnkArsq4/rIpgEJ71WBBJ4kYinJasPawEE8zaqessdQ+NRxD9f5wY7Mvbhz64ku5jWi5Lm5i3FXSI1p+v3/w6CELfpt3yhjfBV6L/LF5QAwySbBiKWVSIp+5Y4C6DOlLxs0YfTVWfRnvhJBguUSu4/imjsjpUZL+OekDEvrwbv6ejvtSJvGRXeO9r795RonMxpjj2vmLOZLNWP6L1wTfKcIXSkvNHF3Ld4w6D5n3S/qnxOMtp12l786Zd0rHBbKxJBkvlWVfbwKzItCl8JbE76aNwtrzm+H4ny/MqrWuzFIJYDkgKzNxqnM+iujQfFF2WWxirU2thLFeeF0Qu4lSmy7GsG7ghobFF7etmOCK+3DRxxKGBZGzj3FPJmEYiZhQ6pqFZ2ERRmkmdjUtvJd4fuqBS2ppmUP7cuvM3EpG+FMHi2/KNM6tKI4okCR8Il6ymQm/b4MA1mwuUui3pudDV1/ktiNexwYJC/pd2fppKxZAFKS2hHJjfRfOlcTvEo/cJn+1THbJZ8kYGNKXu8ZNaV+V1BfvATZNmv3KJiMeCMSOY6mMBbkm4RdWZBStKHNR1ojpRpbTUsukb7zzjq4xUCOztfMXm4x4aWANpzCX4tbN+C5xx62Zo2v5jlXn2A+l835N/+SMhZx2lb67b96pGRe0ZUkynsPe15jAbAl0Kbw18bs0lI8hbjxXGpABdLbAXLG9E2BnlfhRFmZpzOneKzLzF5IQigUqiw5iSNtKm7WQ60hug+WXhS1WnVhgj7WCJFhH70hm1XxPjOMjFpX3peVukviHYoHyXFLm0r7cOhMfhlWCWF5in9NCsqf7BAsUfN8aFAcy4aeZlrusPTwP5ZIM3MRasugt6YvcdnAd7KkjygDnYDfPMaetyM9HQlxw22bLWN8FEjzxrF3n7w5h0iafJWMgckIJLO3LrnFT0lc19WUzBvfwVPYIV0B+m5tTPxw8t/CGSeN0Y/1ZN3CGbCy1THLGe9cYqJXZIfMX6ynmNkI/CPVABoirJ34+t5TO0bV8Y33GqDPPKuVW2z+5HLvaVfPuvnmndFzEebXvmz03Gc/l7+tMYHYEdim8afwuyS9St6WuRsRjR1h0kwBiawVWLGBZANYWrOLE/GFB20rpSvbFIvvHgmWxK3EQu+hYFmrd6JfOmmNsSJCEtQaFgMLGExYHYjWjtZCYUrJdp4VEK7gm0w9kCMdCjPyxACaZDQt4jiZJrZS7eLHAw53vZxsyTJzZSSGpDbGBLMyxdJIAKafMpX05deWaGBN96ZC0Kt6HxReXXPoDjwXmWmJwURibFnHcbnEdjfG78MK1P1rVSAqIqzm/Y1Fn3iBON46T2BcoMyistYWYY+SB7wCW5GYhHhyrIi59TVd5rh3zu0CmcCyLtImEXbQ5laFcJrnySV/ljoEYm13Tl2P1FfNlaX05txvrfVpwF0f5QoFLLfbRO6GZ3C66iEauXMdcg7zXyHffeI913dXfvLdGZkvnL1zryS+BpY7/HQtzL2MOz6Q2T4S2sVgzR/OcUr7EP49V59iOUm58k2r6p2sOY52Q066a+axv3ikdF8zRS5Hx3G907ffF95nAXgjsUnhj/C5n8TV3qrsqhtsHcWQsqHGd3FphsQGDIVmaUdxwG50qMdMc+2TXsUTIJxYyLA0cmdFVlnosEYkuHhxiOnFxLXF/S3mgLGEFx50rLlDJrs7il/i0mByDrL8xMzD3w57swIx14u9gHrMMI4MkrcFNeleSKdyd2WSILtK0hbhU4nfTmFH+P7vZXI/7NJY4/uW6Ns+lfbnjB1dGsjCzCQbbWFgY0X4UjFeFeF8UA1y9ieGNhX5gDkWZZQ5GLlBucS2nsIFALDQWXhJGscBnk5FsyXFjgr5gA6QZU5nbhngd8xrxxiiYWDrSgjKL/JBUBqtW26bUWN+FqMwxP6Jc851CLlA2SpiUymfuGGCc1fQldR+rr3jW0PrCGfdcErCxKZNa7JFbznVGuUgVYRQ7+h/XaOJ3idHH0otc1jDpG+99/c34qZHZ0vmL+YzxR33hEgvKK5sljGk2QHJKzRzN/F3Kl2/pWHWO7SrlRmKpmv7p4pjbrtL5rG/eoU6l44I5eikynvuNzpFxX2MCByOwS+HFHZnFGBlV08QgfRXFCoR1F7c3FmJTlZrD1aeqy1KeS19jncE1lSNC2F2Nx5zMtQ3xqAUWXenRNoesL65+WLTIUosCwBgZkgyIRWJ01UapLDkmJuWAYsPZmCw4qRu7x1hhqB8FayHvacbvEqtHRlXu5XcsZyQiYfxTUJb44KGopQtcxiBzA+6t8SiTrjg+ZA/FBAWOOD/OC8Z6GY/q6evTObSvr47xd8Ya2WpJNIXXQdwhxzUc6zcWn6i4cg9uoGRnJrFT3OgimQlJr1AesJ7Rb7g4s1CkRJdpNifIyI0bJfIYMzHHviBZFudkDi20gw0ZlO+Y1AwZIEsvGxdsruw6emWs70JceMIWjwQWme8Lm6wlTNriTLvks2QM1PTl2H1VWl++9yShQ/aQXZRV+vr4RvwujNnA4axZNrBgT0FRY+6IXhtkAMfyHo8yrGHSN95z+rtUZmvmL5K1kZ2Zs4nTzUqUGb5buMnneMYMmaNL+ZJteKw6U+8absz7pf3TN4eVtKvk3X3zTu24WIqM536j+/rHv5vAQQmkCi+75SxecHchpo+FMB8w3CRxmSHmrC02K20AFoa7h0V3mpV0zEaWHq4+5ruX/CzsCIarAAAJjUlEQVQmbRY2KLz0M4uaZozl3NpHPTmbF8vWoQtKIPVBuX1QUNrOGo6hYPHdPKYlt74o0CTZ4aOCRaS2T6jf84NSiXUhWgjjIozzcXGvRXFtJv4ioRCWZiwSuOKxeE0XaSzeYjZg7iUTL5YbjhyKmYFpL3XAGk98XzPbMPML7SSeFcsRlmfmldwyh/bl1jXGtNKXyAvWb+ZTLOiwjUmV4vNIAITLHCzZiGLTgbg/XMqfFOZe+g75Q6mlxDOQuYZ7GN9xc6OvL3LbkV7H+24T5AeFnXGJtRerPXXsCjcY87uAdZZzpBkrfAuII42yOoRJn3zmjoGavuwaNzV9xT0l9WVuwArJt55NMo6/Qk7T8IhYDxijYLGxhnyj7DLHEK6AXGDpxZ3/YUmm5lomXfNZzhgoldma+etswY2WzUBc/tlMpv1sqsCnb82U9m/tHF3Kd8w69801XeOqtH/6xkJJu0rf3TXvRFksHRd937S5yHgfd/9uAosg0JW0qqYBLLhYMHNeau6uZsl7ag5XL3n+Fq6N1hZ26NOzEufW9ngUEUfolChGU7Sj7YB6FAyUOlyEhxzBFevLUT9Y6ThiprawQYW17VONo4V4Hm2gzizE2grvx8ITj+doXoMSzbNRsLgmKl7N62K8dZtrNu6vKPgogDUbBHNoX07foJwSaxvjd2ELP9rd5bLOZiPzJ4pvvI7FLIodf2sqlczfKBxslnyipWJdfZHTjrZrGJfEhaPIE7OY44I/9neBzRmSxMCk+Z0ZwqRPPnPHANxK+3KKviqpL+9H1rD84Q2CdTcNj2jKAvMJ52mTqCxa9omNxLOEI7fSBFjx3lImXeM9PrOvv7muRGZr5y9kEh54ZDAuShTd2Jahc3Qp3zHqHOtey620f3LmrZJ2lchG17yT9mHJuFiSjOew9zUmMFsCYyi87FLxwcPiQ0wZMZe5SRpKwNQerl7yji1cizWPrK5D4/r2wYoPTHom7D7e2XwHHySUUNz0cVGN7svIO8mhsHjifrpLAcytM7FgeEXUujTnvsfXTU8AN0ZcjbGCTeXpMn0rhr1hX9+FYbX03W0EyNTOJt7PVypupmoCJmACJmACsyIwVOHlvF3cdljwE9dDMhbiVkqPHMmBUnu4es6zt3IN/Y2rJBahMeL6tsCNs0U5FokERMQITVFQqh8oieNqhirOU9TPz8wnEDPcYy0nJncKT5f82hzmyn1+Fw7TwvW+NZ6/SyKyXcebrbf1bpkJmIAJmMAqCQxVeEnUQBITkvgQ74M1jr9NUWoPV5+iLkt9JjGnJBpBsUqT5iy1PfuoN+6YxO9grcNVb4rCUQq4BpLQyGW5BPBCwX2ZeEYSeWHpZQNjSxnX6b19fheWKy3zqjlrAVySCavAc4WEaSSZQ363uGkzr95xbUzABEzABAYRGKrwEqtAcgwWdJ8LWRmnWNwNPVx9EKQV3cxi5sSwSUF8F5sVFFzQ6T+XUxLoO6B+DF5HSMKKHM/OHeOZfsZhCJBxmyy2sRAzjQdMPLLpMLXa/1v39V3Yf8vW+0bidcmXkBY8T2KCvvW23C0zARMwARNYPYGhCu++ALHzXHq4+hSK977aO9V7sOySnZk4a1zWsEQRm0qCEmJIPznVixf63HhAPVlLr7bQNrjaJmACJmACJmACJmACJrBZAktReHEVLD1cPe1Uzr9kBxv3LI5eaMsguXYhwNpE/C5ZcjnvlUySFGQAq++bQ5zq2jmUtA9mxO8iL2wItBX+/t6GFc/yVkLZ15qACZiACZiACZiACZjARASWovDS/NLD1bkHlyzOjsRS99aQUItjZB4RrJpbik2K8buck8h5f2nhPFXOy+OM1pxjRiYSx1k+FoX2kcH9O3X7RrZuLumrIV7T8jbL7nOlTMAETMAETMAETMAEtkxgSQpv6eHq9CsxSVgyX5t0MgmIONCeeLunb6jz0/hdMmrHEq3nKP+Xajnrc0OIWpvKGLlt2Cwh1pljiI4Mx3CxUcBZoLFY3rYuLW6/CZiACZiACZiACZjArAgsSeGN4HIPV8cCRyIgXKEfnChyKM5Ye7+yMQWP83exdjfPBj17UNpgcpVGRk675v7vcI0H1CM3H205PsjyNqupzZUxARMwARMwARMwARMwgf+O31xrIcPu28IxIeeT9ImkoSRsukBQ/jhKaQvlZZKISW2eDUoyppdLurukhwYQdgUvlwjLWzkz32ECJmACJmACJmACJmACkxJYs8ILOKyZZ5L0+oQi8by49H4rxGXiorqFEhNT3bPR2CeEo6WOkvTx8Jtdc+skwvJWx813mYAJmIAJmIAJmIAJmMAkBNau8LZBu2Q4jgfF72GTUJ3nQ18c3LuPS6p3LkknS7q/pMeEv9s1d9z+26q8jUvRTzMBEzABEzABEzABEzCBCgJbU3hJ0PRCSV8KSau2Yt1FNG4i6TqSbhrk5LSSSML0aUnHJNmZ7ZpbMZB23LJleRuPop9kAiZgAiZgAiZgAiZgApUEtqbw3iVk2yVD85crmS31NhRcknd9TNJ7JN04uHYf33IUkV1zx+nlLcvbOAT9FBMwARMwARMwARMwARMYQGBLCu+NJF1O0t1aMuwOQLi4W3Fj5sxdjtMpsXDbNbesqy1vZbx8tQmYgAmYgAmYgAmYgAmMTmArCu9lJfHvIYk18+KS3lmo9I3eAQt5oF1zyzrK8lbGy1ebgAmYgAmYgAmYgAmYwCQEtqDwHhksu4+T9J2E4p0kPTZka54E7ooeatfc/M60vOWz8pUmYAImYAImYAImYAImMCmBtSu855H0ZEmva1A8QtLpJd1hUrrreLhdc/P70fKWz8pXmoAJmIAJmIAJmIAJmMDkBNas8OKG+8pg3W0Deayk9IieyWEv8AV2zc3vNMtbPitfaQImYAImYAImYAImYAJ7IbBmhXcvAFf8Ervmrrhz3TQTMAETMAETMAETMAET2AIBK7xb6OXyNto1t5yZ7zABEzABEzABEzABEzABE5gZASu8M+uQGVTHrrkz6ARXwQRMwARMwARMwARMwARMYDgBK7zDGfoJJmACJmACJmACJmACJmACJmACMyRghXeGneIqmYAJmIAJmIAJmIAJmIAJmIAJDCdghXc4Qz/BBEzABEzABEzABEzABEzABExghgSs8M6wU1wlEzABEzABEzABEzABEzABEzCB4QSs8A5n6CeYgAmYgAmYgAmYgAmYgAmYgAnMkIAV3hl2iqtkAiZgAiZgAiZgAiZgAiZgAiYwnMD/B/Q26P5TPwD8AAAAAElFTkSuQmCC)
(i) Linear equations:
x – 3y – 3 = 0
3x – 9y – 2 = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the given sets of lines are parallel to each other. Therefore, they will not intersect each other and thus, there will not be any solution for these equations.
(ii) Linear Equations:
2x + y = 5
3x + 2y = 8
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD4AAAA2CAYAAACfkiopAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJfSURBVGje7Zk9bsIwFIDfAbgAEh57AHBnxsiqEGMliFA3JpSFqUNl2HINRoaeoFyEgRtwB1onpJAIxzZ27Px48IBB+H3v336w3W6hi6uT0B7cg3vweq85hh0AXADwaUFpv1MWXwVoDQNyWMZxrzPgcbzskQEcULBad8rVKV30McAJh5tJ5eD3cRVG5A0BnHU0rrM2IZ4wOWY0emGWT+WCi4oipLULeL7LPhOE9qoHGY9vhI4I0JFEdJi5vkqyU4LOW//5jGoivovnp16AzkwR2uCPAP8PLijDWnxHZMjCrOhtxsAzaxfjmLdvO76L3pYYSaG8KR+QxJeCZitpXgre9owxyhNIATxzs2w//Q1cbFmfV78za38E6EtWHgH4zbKJB/z9OXmFb6ZxOiNj9h3btwWeKj7N5Lw8JCuPRPZMaySDze1d3c0m+M0gV5keWFcbXCXZuEp0OvJ4cNfgiQsb6A0aBc7K0QhGPyY6QSvguUSjYS2WmU30/SryOOi6bhmZt2xcfmrxjOTilpf/IGEN2SXtARIhUoVM3tWd3LIcXW2dgSetL0J7Vzc8Z+Cs7Lju9mrRZnpwDy56B9QbHzXW4rrjo0aCmxgfNRLcxPhIGrxt4yMheFvHR6XgbR4flYK3eXzEBW/7+IgL3vbxERdcZnyUz/bVK0M0PmLWVpGnBFwwPprizyzWTHRScvHNHx8xGVXkEWTP8vHRvbuZeh4WlrKS8ZGKPOa6KRzSWnV3AnmMHBQFwbuLuq4jj5ES07nZ2f2DIUs+ZEbHrqFl5TGWaFy1sc/K45+ePLgHb/f6BcWaRMlOzl90AAAAAElFTkSuQmCC)
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication method,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAA4CAYAAAACaT/nAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAS1SURBVHja7Z0xTtxAFIZ9AC4QiaFKDgCzbaiixYq4ALuiSkSB0DbUkaHbhgOEjpITpOEE3ICCG3CHBNuM117ssb3MG8/GX/FJAaL1zvP8b957nnmOrq+vIwAIB4wAgCgBAFECIEoAQJQAiBJgnFzN9XEURX/V9OISUQIMyHJ5thPvRg+pIBElQEAki3hfRdHL6EVpDKHnV8fln6Pd+OFsudxhskiFaeolXiT75nczHd2N3eaIshTDZ+jZXfYzYhQlE19NmJb/Xj+fJsknREn4Gl1M1aURJsIZZvKledVUT3+xUiLK2hAWPBU2Sk4wvQfxSXKIs0KUlUkiZQywi5JVElG+N8ZJfKhU9EQ+6Tm3fLN3av9y0QdRjlyUmdeO5z/yos+4Cw1DiHKRnHzRep5gE0SZF3dew6fFVP9MvXRuEPWU/num1Q2e24P9X53gZDL5jSNElKVJsSrLl3dVUPDxZ39sXYoczOO5DPdRGxMPWvN4ohG/YASwh2l6doMtECUMiNkttVh8+6pUfE+VG1FCIDkkj50QJQAgSv+8r9zVwL7e0duTmwuAKAGgsyhbQwHojMtwC3u6s+c2jA3PBED4CgCIEgBRyhLCYVsO/AKifCNJTj8dROoxhE3S+RGeg0eONMFoRZkd21LqPqRTC5kw2SMKoYmy2C8pvIsi2yzt6LO7tJ5PV2UdRc9t5+bS0nyI5w27ttdff7Tg+vBunzb/1S7kfjtMZHYQmrtVjdjH5ehiq4uYiez6xpqb9dHJ37X1vBmHuZ6tDUloLUr6tNcvmlqXROnKwfRt8z9kC9Git7DAtdPPNmMvHL1lw7+IdzEtPNwbzd3Eb2vpsN4JvK7dYpOAgwqtW9pWpOOU7g7Y5XsM2eEgvX8Tpf5kzsnxvDW9pWwLmdBKuTKmVCHGdbt820RpWu2bjGkTbMiirKySPW1b9v4f/R5mlRrKqeW9nubfsxXMwz1sc4TOQxSJMK64hi9RNjR9rnu3hpTT8CHKd7WAHsJwJcryvZ3HKim+iydbmnEUYaWwKLvkrQKJrHtRShjMNlGaPLfNo+fFknrBhirK8/Pzz30KWhKiLK/W5u+S+d26QzDPmqVFWc3d7fPE6XK8ehGPW2EWA0KUznO5uvF1+f+uRNlkUx/2TBeSctrlY6VcibNnTtln9322QpZCDZuANj0lYbupEp/ZFL7m0UD9RJEuVGwyzk36kzblO52u3zDRNhGltD3Xm4K1idLlgeq2HNpNrldXfRWolPpaKfsWeoauHrpaKbsUIaTC1/W/2fJ3t+lWHbIrdFu1XqQAI/X4wpco6wo3bRVW2yq6TaKca534zCmtjt1j4cxX+LqyR97lXySnbOpg7vLZl+9CT10I27b6b1tOWbdlsZxj+RJlXS47xCsPpUS5PvYu+hAJBaR287jynF1bz1crZvaVP7RHIm1jrFZc+9+3rqLsauvK27oHSAPERPnOzu2OOwiP3n2Shfm2rVA3D8B2sjVfVDrxl0zcAf5LUbrakC7nMHhnJoxMlMXkDzBE9LGpGxBlwLllWC+K5ZAzjF6UWf62d3QbggjSkPpoT98StsKoRRnK6hRiaxJAlACAKAEQJQAgSoBx8w9n0FtKkTokeAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ x = 2, y = 1
(iii) Linear Equations:
3x – 5y = 20
6x – 10y = 40
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAA2CAYAAACoXOUdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALMSURBVHja7Zs9bsIwFIB9AC6AhEcO0LozY2RVqGMliJiomKosnToZNq7RkaEnKBfpwA24Q1snOCQhDqH2ewnhDW+gHfz8+fn9+YWtVitGgiMEgWATbBKCTbBJugD7NeBvjLGfRMRuplQfcr1lKMZ6LR68vt0UbL1xs2mlZn3B2I4N5HaxXvd8r7VeL3pywLbmYG8Kdrx5Gc5PrRzWulUk7zhje1TYU8E+zNUNI/noSwEX0TpB64AKO72uYvphfkvONxq8CJfjJkEbnToBuwg6b+Xwwalq88kt43sZqbtOwC6DmgYOBKuqB70DPttYdXER29+byk6g3RkK7GQjp1aTZADw17cWiMPBXz3ssrSqeHVNgdGUlSf68G/Ig0eEfbTg2NL/Cgj5wD61v1YTOdL/yxYamIHKxI5OpH7FCkoDzv3tECDRYJvMKC3V4V3Zsbbw0x7wWkKTEGyCTbAJdnth53rLDVeUN2HZ7hG+RDwdHOZarYRNlm1+nLOCC8SrkojrQu6T3Ai5EQqQJBWSbWXYupAECgC27cWfQAFIKOWcYCOIbsnKiRqRG8FwIxVDQ93wkQCPvif9fA/986sEnfZkgHLkGDTnGwP3+HDhBvxqQcM+8k6Gk0gNi77Y9Xnswkqs2dEzjNEF6wF4GOGotUAbRs+yASiUXKW+FGiKtSzLcH3Jrw06b+X4o2fZsTNjXcbSMfobPoY4z7iO9oye2VxIoifsS3t80FxuXG/QRf6pydEzG2zogFnMTLzDbuPomS0bSHSF00nfHF8HWZFeVY+e5bMU+AOwubBYV6AgWQY6CsTLf/daAfvM6NmTeDeKQG64zJWk39UcDADChVgfHhz2Wa9UtYyeZX35Pbv/wshQ0gzkIKigHYdI/SX8IlTUkEKAHQXBcxOffNwcbJqIQoId+09Tylc0zUkcYec/a8b5tJl8NgnBJtgEmyBgyS9Yjm0lMcXDTgAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAA2CAYAAAAf4R06AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALxSURBVHja7Vw9btswGP0OkAsECLf6AAn3jIKGzAUcIeiQIoMRaMlcMN58jYw5Q3ORDL5B7tBCUlRJDEWpIk3xI97wJsMm+b3vl3ww7fd7AvgCRgCBAAgEQCAINOBW0gsR/SGSxzulzmEwhhH4mIknusjfHg6HM+6H7Ryygcgen9bYx3Mhb3ytb/3wcHg4yy/oba2D+oQq80tB9NEnUBbPNyH30NrTpwPZD63uziXRMfRBTxV9sThi60wnJ7AJdXncqnLT9xxuhA6iL4JyEIzAuv4J8S5IvOeluuxSAK+mpj5HL3Wu7YRBCBwjq4lK8VERyoXA3W73rV8S1u6sgxDYLqJ7KkcCT9kFRktgW/90L61b8QjqiD4SGCFvX2JsaoIQWBtIM0CbglIYK5ImcGz+a6PvRyZ+rZmCfKCQUiVbA5sFms5zmLK6lFqlWA4E1s4oxGv/LFVXmnwXqrfe+mJcCBx2nuteoZlrt1s37NTJpVALuQMEgkAYEQQCYQkcNDiWYRmIOAJD35zEdAEQ0zngxSlF4KRnzYS3zXnaD7dzIIUihQJoYgAv6AuhTPe3MBIjAk3vsDASIxR5fg8CmaJ6gsq36np2CoWsPrIUOiJjsX6Zs6x+jnBpDZWars52FYhNLsTtwnqufF1XnY+JuLzvracO6BxoOYk05Z1cZfVTsgVdXfeP+BMO4arcbral2vzPPhcTyF1WbzPMmLqueWUJW/NdlX72+sdYVm8lMCLRsklA5kxgCrJ6G4Ftg2MmMGyWcdWnWg/PWVbPgcB6jyJ/denyrfUvFln9kheAJSm0qYFhHNSkV/VGYAqy+tibmMrGPiJ99vynR18XFXGm1BjHCBt5ZSZ/LrHjrK7IJKtvNxDrbc0UgXoaDRV9o+VgoQ3HR4iZUvQqHV3R1e+YRou58vXhHx+sSJ6D3N/PICoLxfG2JgU4/0CZZd/xWsGUQKizGRNYz4qfHdvYYyMQKYFf/7YDj75sayAAAgEQCAIBpvgLplv7lpLAt6AAAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGoAAAA2CAYAAAAvbQwbAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALxSURBVHja7ZsxTuQwFIZ9AC6ANC45AHjrLaNoRb3STES1KyqUhnplppuGQ1Bygi2Yi1BwA+4AcgaT2LETBzLOc/IXfzEzUeblffbzc/KHbbdbBtEXkgBQEEABFARQEEA1tdtdn+QrtmeMvR3EX/NSnruOlfLqVDD2cjhOvFxJeRorzrtCXKr/5dnN7eJAVZA4f9RgahBtWPo3Udxd1ok7Pix7IC0SlCzXZ+tSnpnf5eecsVc7IRvBHtgq31/vdidGAsXmIU6s7ri+DEqfsK+MkIX3MXOaCXF9p3ST8dtYJXBUUIfAazjqc+iJ6cwylRD+3BxgOkm67JnrRpzBOBooO2jfxVGXKnF2MvRC7gbV/p4sqNj1+qjJ4PmjXodmBypmwKGzom63PbIGld0BupJkX59d6smDirmoHhOub6DNpplwBVyN0Lz4U/8evgegAKnMxN/mTJlFe27vml1lRB1DEZS3TDaguMpf7CoyWtenZ41v/0QRVNda5orV3CPGg9SOs/+/v3WvKrU9VcoCKICCAAqgwmQ0GonfvZj9jIpxd4HqHm2K68BoTXFG9Y6UQI0W3EjxTH0dQ68FpQ+lD5pNMwEBFEBBAAUBFEAlqaqd9rTLU1iah1iuFwNKP6l2gZrC0jzEcr0YUCoJPzj/Xz3BdYCawjMxxHI9CFTKduaN4Pd5WfyqRqyVfAoupL5YgkGlbGfWz8o+S4sNioCl2YzFtFwHg0rZzqxKWCayf6qk+UBRcMo2S3DIBPB3JYk+EFQzXyeaOiif5ToIFDU78+fCH3DHurpwsblvtd+BpS+mpbnLch0EKmU7s+lFtNUo5QSaiS7L9ZdBNe3M7VFOtxv0zaip2vMuSLblOrj09dmZDSuwZRdOAdRUluZQy3VQ19dnZ7aTccEuniiWyi5Q7X3ihJACXrgYJxmikHO+FUVB3z5BmWW/U36PahGg4JZNAFTVdHzUflXr87X8iYQSA9Xer6T9Guki1igIoCCAAijoSHoH1gUQEYxj3rAAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.
(iv) Linear Equations:
x – 3y – 7 = 0
3x – 3y – 15 = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = 4 and y = -1
∴ x = 4, y = -1
Question 2.For which values of a and b does the following pair of linear equations have an infinite number of solutions?
2x + 3y = 7
(a – b)x + (a + b)y = 3a + b - 2
Answer:(i) 2x + 3y - 7 =0
(a - b)x + (a + b)y - (3a + b - 2) = 0
we know, a pair of linear equations (say a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0) have infinite solution,
if
![](data:image/png;base64,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)
therefore from the given equations,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
For infinitely many solutions,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
6a + 2b - 4 = 7a – 7b
a – 9b = -4.............. (i)
![](data:image/png;base64,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)
2a + 2b = 3a – 3b
a – 5b = 0...............(ii)
Subtracting (i) from (ii), we obtain
4b = 4
b = 1
Substituting this in equation (ii), we obtain
a - 5 × 1 = 0
a = 5
Hence, a = 5 and b = 1 are the values for which the given equations give infinitely many solutions.
Question 3.For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k – 1)x + (k – 1)y = 2k + 1
Answer:3x + y - 1 = 0
(2k - 1)x + (k - 1)y - 2k - 1 = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
For no solution,
![](data:image/png;base64,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)
(This means that the coefficients of variables bear the same ratio, due to which they will eliminate together leaving no value for a variable)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ 3k - 3 = 2k - 1
⇒ k = 2
Therefore, for k = 2, the given equation has no solution.
Also, k - 1 ≠ 2k + 1
2k - k ≠ -1 - 1
k ≠ -2
Hence, for k = 2 and k ≠ -2 the equation has no solution.
Question 4.Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4
Answer:8x + 5y = 9........(i)
3x + 2y = 4........(ii)
From equation (ii), we get
....... (iii)
Substituting this value in equation (i), we obtain
![](data:image/png;base64,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)
32 - 16y + 15y = 27
-y = -5
y = 5............. (iv)
Substituting this value in equation (ii), we obtain
3x + 10 = 4
x = -2
Hence, x = -2, y =5
Again, by cross-multiplication method, we obtain
8 x + 5 y - 9 =0
3 x + 2 y - 4 = 0
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARoAAAA4CAYAAAAioDczAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWISURBVHja7Z0xctQwFIZ9AA5AZjAVOQA4LVTMxkUusNmhgqHIMG6oGSddmhyAdClzB07ADSi4AXcA7B05Xq0kS7tPtrz7Ff9MspvJ6L3/+X9PT5aU3dzcZAAAEBM4AQCA0AAAEBoAAEBoAAAIDQAAoQEAHAKuV8VFlmV/88WXrwgNAEAUt7efn5Uvsh+NyCA0AICoqKvydZ5lfxCaPZxXrK4v+r9nL8ofn29vnxFgqZfy+Z+yql+rzy6L7AHuEJok55wtisuH9neCdBZoBcVQyq8/L35/qOsT/ITQJIUvi/yrEhsCat6B3/QTFsXiG8kCoUl++gTmga5J2UsQDZflsn6HfxCaZAN2KgcCGaGhmkFo0nbgsnyX59kv+jPzQ7/52/DYbwwDhCatrFiuPq4bwzQR5yo0Vb08LYpVjU8QmqTQNoD/l9zVovjUZMG1E/Nfzc+XRX5HZpwRj/8TxNnZ2XeSBEKTaIA+LY32336kKTw/HuFshMpRvQrSYvzqHyLAdFmWvszRACeA6Ur54vIOXyA0AIhCvb1dVe/f5nn5yCohQgOAOLq3uHkVAaEBAACE5giwvUpgAHu74A+hAQAAhAYAMJXQDJZ7QBxSpTe+TIM7+DP7B7UFADB1AgAgNAAAcNxCk8JhShzoBHfggIWmrj+cvMnynyls2ltv0X/zk6MQ4A6hObBsWOb5Y0o7g9uAZX8P3CE0ewRG7yY8/a4ePVMVWfY79pkY7eY9oTcvfa4S7fbwDLz12Sx7pnT2ii93G1fbaJC2R4q7TU7MsRYSu2NxF3J17eb4ZZ8nn3Hoy/iuvxXNPk9Csk2Y+k6RFev4TeX8fYPC9ypRdUqcskPZafr7lI4cDeHO/l6IrC1S3DV+Vv7v7NI2cobYPwZ3oVfXxrpmyHcc3WWNnklnz5Jyebqs6lPTAPQB6rcQmq7bkFNiuYAYOgKxtUuzQR01aqvoUqhqfLlrx/zy/F6fNkhWjZLcqXOkXckgNHbH5M7nyM0xTib0ifuQY0GjNPL0jG7L8qYA2BfS16oOOVwn3dXIjCWuMbm7rqrnJl/GOJs51pW4vg+Fqxodi7uheFNTmikFb6Oa8eQr0gDXB4XrA9OdY7p/WaTsG1Fotuf5buFM+X5pE3fWB9JQ5aTGna3i3NX+MbhzxVvfR6syr7uYizAm1zi2epIewifuKFP2sKmwtDp382zBrON7evyT8z2ERlBcp8j8ja3Sp+lLc7fZQ/Dz95D9Y3DnW0mo77tGvXCl5RrH1dXVq82+1nDcyzvJsAw4mtAoIkYWGhWgT6szdqenKjS+S7ixlp9jcLf5cLofBB/7pxYa2/MSY1wh17P4rFA5HBq2+9QVgLap07oKCFnlcC8hu5wT4392NvRK16EHJmYjb1cbQ8TD/4EMG4dX033Hw6SGEpqv/VM3YW122Ma1j89C74EaqgZFg9xGwFjN4LErGluD0GVXincZhbwjEmPaFLOi6cefzUZf+6cWGtt30r3OZIXGRJS6RdLWSIvRxZ9MaLRmnGuZ1lbFpSQyOnexp03RhcbR5A2xfwzudk5swg3hUKFZFUUdtUdjLc80w/XpU4yl7SmawbZbM91TgDSExpe70D7OlNzpfLn4CLV/6h6NqR9ia0vEGocp2TTPQNRVJ9cccHD9PeJbwVLq7nuVqL7cN7hykcDydih3MadNktxtroTYV5x2sT82d77xpm8JkRYZ1zi2/eu3XSKJHoG8k9J4zd+39AVwd+g4OINiNMakpwdcag93CM3MIbUxL96DlGbGhju4Q2h2CYoES9zQjWhHW9XAHUIzn/m+/Ka/vUpvDk+CO4Tm8BBj498+U4Lzl8U9ZTfcITSHGLAJZKIUj6aEO7hDaAAACA0AACA0AACEBgBwfPgHS/N8vlgYeToAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = -2 and y = 5
Question 5.Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.
(ii) A fraction becomes
when 1 is subtracted from the numerator and it becomes
when 8 is added to its denominator. Find the fraction.
(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Answer:(i) Let x be the fixed charge of the food and y be the charge for food per day. According to the given information,
x + 20y = 1000 .......... (1)
x + 26y = 1180 ........... (2)
Subtracting equation (1) from equation (2), we obtain
6y = 180
y = 30
Substituting this value in equation (1), we obtain
X + 20 × 30 = 1000
x = 1000 - 600 = 400
x = 400
Hence, fixed charge = Rs 400 And charge per day = Rs 30
(ii) Let the fraction be
.
According to the given information,
.......(i)
.......(ii)
Subtracting equation (i) from equation (ii), we obtain
x = 5 ............. (iii)
Putting this value in equation (i), we obtain
15 – y = 3
y = 12
Hence, the fraction is
.
(iii) Let the number of right answers and wrong answers be x and y respectively.
According to the given information,
Case I
3x –y = 40......(i)
Case II
4x – 2y = 50
2x – y = 25 .........(ii)
Subtracting equation (ii) from equation (i),
we obtain x = 15 (iii)
Substituting this in equation (ii), we obtain
30 – y = 25
y = 5
Therefore,
number of right answers = 15
And number of wrong answers = 5
Total number of questions = 20
(iv)
Let the speed of car from A be ‘a’ and of car from B be ‘b’
Speed = distance/time
Relative speed of cars when moving in same direction = a + b
Relative speed of cars when moving in opposite direction = a – b
Given, places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour
⇒ a – b = 100/5 = 20 (1)
Also, a + b = 100/1 = 100 (2)
Adding (1) and (2)
a - b + a + b = 20 + 100
⇒ 2a = 120
⇒ a = 60 km/hr
Putting value of a in (1) we get,
Thus, b = 60 – 20 = 40 km/hr
Speed of two cars are 60 km/h and 40 km/h
(v) Let length and breadth of rectangle be x unit and y unit respectively.
Area = xy
According to the question,
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.
(x - 5) (y + 3) = xy - 9
3x – 5y – 6 = 0 ..........(i)
and if we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units
(x + 3) (y + 2) = xy + 67
2x + 3y – 61 = 0 ........(ii)
By cross-multiplication method, we obtain
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x = 17, y = 9
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(i) x – 3y – 3 = 0
3x – 9y – 2 = 0
(ii) 2x + y = 5
3x + 2y = 8
(iii) 3x – 5y = 20
6x – 10y = 40
(iv) x – 3y – 7 = 0
3x – 3y – 15 = 0
Answer:
For two linear equations: a1 x + b1 y = c1 and a2 x + b2 y = c2
(i) Linear equations:
x – 3y – 3 = 0
3x – 9y – 2 = 0
Therefore, the given sets of lines are parallel to each other. Therefore, they will not intersect each other and thus, there will not be any solution for these equations.
(ii) Linear Equations:
2x + y = 5
3x + 2y = 8
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication method,
∴ x = 2, y = 1
(iii) Linear Equations:
3x – 5y = 20
6x – 10y = 40
Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.
(iv) Linear Equations:
x – 3y – 7 = 0
3x – 3y – 15 = 0
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication,
x = 4 and y = -1
∴ x = 4, y = -1
Question 2.
For which values of a and b does the following pair of linear equations have an infinite number of solutions?
2x + 3y = 7
(a – b)x + (a + b)y = 3a + b - 2
Answer:
(i) 2x + 3y - 7 =0
(a - b)x + (a + b)y - (3a + b - 2) = 0
if
therefore from the given equations,
For infinitely many solutions,
6a + 2b - 4 = 7a – 7b
a – 9b = -4.............. (i)
2a + 2b = 3a – 3b
a – 5b = 0...............(ii)
Subtracting (i) from (ii), we obtain
4b = 4
b = 1
Substituting this in equation (ii), we obtain
a - 5 × 1 = 0
a = 5
Hence, a = 5 and b = 1 are the values for which the given equations give infinitely many solutions.
Question 3.
For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k – 1)x + (k – 1)y = 2k + 1
Answer:
3x + y - 1 = 0
(2k - 1)x + (k - 1)y - 2k - 1 = 0
For no solution,
(This means that the coefficients of variables bear the same ratio, due to which they will eliminate together leaving no value for a variable)
⇒ 3k - 3 = 2k - 1
⇒ k = 2
Therefore, for k = 2, the given equation has no solution.
Also, k - 1 ≠ 2k + 1
2k - k ≠ -1 - 1
k ≠ -2
Hence, for k = 2 and k ≠ -2 the equation has no solution.
Question 4.
Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4
Answer:
8x + 5y = 9........(i)
3x + 2y = 4........(ii)
From equation (ii), we get
....... (iii)
Substituting this value in equation (i), we obtain
32 - 16y + 15y = 27
-y = -5
y = 5............. (iv)
Substituting this value in equation (ii), we obtain
3x + 10 = 4
x = -2
Hence, x = -2, y =5
Again, by cross-multiplication method, we obtain
8 x + 5 y - 9 =0
3 x + 2 y - 4 = 0
x = -2 and y = 5
Question 5.
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.
(ii) A fraction becomes when 1 is subtracted from the numerator and it becomes
when 8 is added to its denominator. Find the fraction.
(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Answer:
(i) Let x be the fixed charge of the food and y be the charge for food per day. According to the given information,
x + 20y = 1000 .......... (1)
x + 26y = 1180 ........... (2)
Subtracting equation (1) from equation (2), we obtain
6y = 180
y = 30
Substituting this value in equation (1), we obtain
X + 20 × 30 = 1000
x = 1000 - 600 = 400
x = 400
Hence, fixed charge = Rs 400 And charge per day = Rs 30
(ii) Let the fraction be .
According to the given information,
.......(i)
.......(ii)
Subtracting equation (i) from equation (ii), we obtain
x = 5 ............. (iii)
Putting this value in equation (i), we obtain
15 – y = 3
y = 12
Hence, the fraction is .
(iii) Let the number of right answers and wrong answers be x and y respectively.
According to the given information,
Case I3x –y = 40......(i)
Case II
4x – 2y = 50
2x – y = 25 .........(ii)
Subtracting equation (ii) from equation (i),
we obtain x = 15 (iii)
Substituting this in equation (ii), we obtain
30 – y = 25
y = 5
Therefore,
number of right answers = 15
And number of wrong answers = 5
Total number of questions = 20
(iv)
Let the speed of car from A be ‘a’ and of car from B be ‘b’
Speed = distance/time
Relative speed of cars when moving in same direction = a + b
Relative speed of cars when moving in opposite direction = a – b
Given, places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour
⇒ a – b = 100/5 = 20 (1)
Also, a + b = 100/1 = 100 (2)
Adding (1) and (2)
a - b + a + b = 20 + 100
⇒ 2a = 120
⇒ a = 60 km/hr
Putting value of a in (1) we get,
Thus, b = 60 – 20 = 40 km/hr
Speed of two cars are 60 km/h and 40 km/h
(v) Let length and breadth of rectangle be x unit and y unit respectively.
Area = xy
According to the question,
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.(x - 5) (y + 3) = xy - 9
3x – 5y – 6 = 0 ..........(i)
and if we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units
(x + 3) (y + 2) = xy + 67
2x + 3y – 61 = 0 ........(ii)
By cross-multiplication method, we obtain
x = 17, y = 9
Exercise 3.6
Question 1.Solve the following pairs of equations by reducing them to a pair of linear equations:
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)
Answer:(i)
Let
and
, then the equations becomes.
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUIAAAAqCAMAAADxo6ItAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOjqQOpCQOpDbZgAAZrb/kDoAkDpmkJA6kLaQkNv/tmYAttuQtv//25A62////7Zm/9uQ//+2///buKNhrwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAD80lEQVRoQ+1a23KcMAxdsl3apoS0paFc/v8/K8k2tvFFMg2TIcADuzMYIx0s6ejg2+06LgQ+DwLj19/kzFBV1ZP6ex0lCEyNxq0D+Ob2wrAEPLX07m+9gq37Aae+eime4sA3dNUDgy/jM1x9+vX9L+OjhpBGdfe3AyNSanr7Mtx/PnJOIzYD4CyGcG6/cHhzkx3sel9B7LlryLd/rOHyWLORaWaArFidDcIOHU5DSEE58PXBmWGsTxXIUD6xACSz19xiCPc8Ju5LGHBhn+egGJ2aVK6bGkBDkt1cCCn4z3NQjKYDlSCkdCkqJ2pND+ciNcjhMqsGA3l4bthqorPp3ELISxYt90aOdL17hhKaZ4UP07wl/ZpbaOsqZD5YkHkGdCSAWFsnwQK79WdjKSxs7gB2gVG3wRLromcedbDiJUQC8az+iBgfBCdfTYphkSs68pE3uVyEqYdnaq5XqlJCosf1RGfdcHRhKzG3q9Q41u9fYVHRmZq4E74Bcu2nQC7CikelT3xoBL3xyRAOIBQ/pmBgTtFZQSjVfkrkIkXlSlYGzB66lyoSe0E4flsbQT6EUlHEAN09caKRWC6i+dINRQiWil+kyHinOkMoa515PX4vCEMCD47AwwKpKDDAEE1WNLIQ5rmpujo1cqaxCC1LNVGJMV4lshB2RADx4JUH9W6IKUbv0WYFUtHKgEX74UWjuFwU2qwgLGkBTP/mVBN0DrmKdY/8DZ62uh7PdnYQM9yTs80r9KSi+CtS2o8vGsVGSuWi7RAqdrJwFENsVrjsFsj+FwGTXUKpKGIAaj8C0UgqF5lAlvNdo1Wp7LfkwC0Qvl8gG74eSkURCDGGBaJRXC6K2KzLiZzvmkBWUC7i3xYIC3hLMNTTg4gPDOBDKBV5EFrtRyAaKQgFchFllBJSY2z3qkmyb9srkD1So0IB2WEoFa0gNNqPQDQyELJyERbjpZoQx7ZmaK6jfgzx0aUPbJhfgUbgeWtF/p9V6N6rgwsgDKUi/x1a7QdYYU40KpKL3E88EggtL8SF3ms+onMi14Jy1z1QDeeUIy2Siux0HyYaZboTrgXNNbNroMZaXuLMvSKpyD7ow0SjTI/MbT/grjswbvpkIvg46DxiF9FIFjIhht6nYW77gah2mXQhs8iMikhFmQn2EI3E9q6+Y7qEhm90OIjJChHOYnuPNFCw/UCwmQEZyv1Pfb6dDPpVM9sPUnqEv1CAUwBb3lJRjrTgkrZmtx8Ic5xOB6KY/xSg+U5ka6mQR2gI07tzPiFu5BLfTy7NLAeBWn/nW4Xs9gPbzHIQUho82Y4kwoTbfmCbWQ5CKCWguPJbR9h5rgEXAhcCZQj8Az9EQTnAcJbbAAAAAElFTkSuQmCC)
Using cross-multiplication method, we obtain,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
p = 2 and q = 3
Note: These questions can also be solved by elimination method and the substitution method.
In the elimination method, the coefficient of one variable in both equations is made the same by multiplying the equation and the variable is eliminated.
In the substitution method, the value of one variable is calculated in terms of another variable by equation one and then that value is put into another equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(ii) Putting
in the given equations, we obtain
2p +3q = 2........(i)
4p - 9q = -1 .......(ii)
Multiplying equation (1) by 3,
we obtain 6p + 9q = 6....... (iii)
Adding equation (ii) and (iii), we obtain
10p = 5
![](data:image/png;base64,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)
Putting in equation (i), we obtain
= ![](data:image/png;base64,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)
= 3q = 1
= ![](data:image/png;base64,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)
p = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
q = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Hence, x = 4 and y = 9.
(iii) Putting ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQkAAAAgCAMAAAA2Yn0cAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOjqQOmZmOmaQOma2OpCQOpDbZgAAZgA6ZgBmZjqQZma2Zra2Zrb/kDoAkDo6kDpmkGYAkGaQkJA6kJBmkLaQkNu2kNvbkNv/tmYAtmY6trZmttuQtv+2tv/btv//25A625Bm25CQ29uQ29vb2/+22//b2////7Zm/9uQ//+2///bnKRLSQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAD3UlEQVRoQ+1XDXObMAyFJmHr1oala7LvLWzdwj4D5P//t0lPsmygCYS2WXeH73IB2ZKeniXZRNE4RgbaDGSzkRVmII/jkQmkwq8oH5nQohiZcN1hZGJkonlSHHd2ZNPtoaOmY3rYKfUgRltQ6OyI43lvhLvVwf7aMd3bTW3hgxgdBuVfae1W/bdoGMaH9zAMV1OriJf3Y2ivlSM8ZHTvKmJDlMeTTRRl8XQbCCNecfZxsaFrGk+XCa2vUijRM9/cmhoqFs0P51ssoLezNemobLfiwp2pUYhRxoEtclK/GCo+smVQgoujg+lgOQ896N6tlsXk3SzKOEAMal4q3K2sd+YUdJlwA+HeVkx/JvNqsckINnOeT76JGa8hYrKZU+hFTDO0gClmk2yNZGrN/mTpMvRepfOo0UQYKfxAbn6A3cM0+d5enPEuYGBzRJ0CYhQY6hdCO3PKhN4YlZsuE0oHgkz00IOEHGqYGJp4wypY9zJ1Jn/qhB/Nltip9RI2UyZs69U6cM/YPUzzH9LoIt+bILJNjgnESyQAtoOAUGFdp5HklBWSIpLSoYaJkWtSEswr1CErn7AFcSZ/EFcpUsXZktfaYGP5M9IuLzRD7WD0MM2/etgbfDgh8Vp1AKGQIFuJN5S4BeCygDOXiEZh1TRMLFsChMDE1gOZUCSsBIkR2CoTy10FTTrV4oY0PrMp574O08vVwy1MtKtDt9pxD9RCAkKXPbOalmmkQnVFP9nUpoaJtaKYSITLhAdVptY8U5I+oXcKqn680GQ+r9Jl4VLMovQwPSz1cAsTbRF8e+qkw+Ddmg1c1FvcLNq9dhsdfXcWnIYgITEeUPXgtUyYQS/T9fgLSDPvXADNW1eZXF9tq/SaSlM3gt3bhgGm+fcx9OBC+q3bWvLLIYLKbMZNiQZXR/mcC0an6a96wVOAiQ+8moaJ+aG4TNEwKauv3pDJTyKbl+dbShFqNmqU+chQC2brvUshBSHxEmDNFO++BVNhiQet7w42sks6sn0C5nyoaCnb+UKXg+lviUdkcpYLLux4Q8OJ+Yowk9ZDoskG6iyT6wXZlWMHDZhMacuR8+NszRcM1w/dCQ1PLlHMD8B4mCZXD8GFYC8dVHFdiSPbb12ja3lrPj/8SdfTXifQQzA7lZlHbNjBgWvFHT6SjvsU3gOFLy+DYXYr81Y3T6m2OzQ0qeAh45gjfYh9p9MNk7upXH5uG/I5cHDgdO5ctdcEPlJOMDphVi/LpzcXxUnAnCDeO7no0zjv5OC/UT5VoT52Qn58XXyZ/nnb1Qweexj3gI9vWengxn8PAEYTIwOPlYG/TxOAMqbBLZgAAAAASUVORK5CYII=)
= 4p + 3y = 14
= 4p + 3y - 14 = 0.....................(i)
And, 3p - 4y = 23
= 3p - 4y -23 = 0.......................(ii)
By cross- multiplication , we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Now,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Also, p = ![](data:image/png;base64,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)
Hence, x = ![](data:image/png;base64,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)
(iv) Putting ![](data:image/png;base64,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)
= 5p + q = 2....................(i)
= 6p - 3q = 1 .....................(ii)
Now, multiplying equation (i) by 3 we get,
= 15p + 3q = 6..............(iii)
Adding equations (ii) and (iii)
21 p = 7
= p = ![](data:image/png;base64,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)
Putting value of p in equation (iii) we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgCAMAAADpJZJvAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAAA6AGa2OgAAOgA6OpDbZgA6Zrb/kDoAkDo6kNv/tmYA25A629vb/7Zm/9uQ//+2///b7SmRKwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAU0lEQVQYV42PSQ6AMAwDY9ZCWgr9/2NJjNQLQcKXkUZWFpF38uiuAOQhhTTzwd4HlmBcrPDkd78X7S5f03aVOij1OZNtS44MkOanJNeqpP8TnHcDtOwBwHcoEFwAAAAASUVORK5CYII=)
We know that,
p = ![](data:image/png;base64,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)
= 3 = x - 1
= x = 4
And, q = ![](data:image/png;base64,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)
= y - 2 = 3
= y = 5
Hence, x = 4 and y = 5
(v)![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Putting
in (i) and (ii) to get,
7q - 2p = 5 ................(iii)
8q + 7p = 15 .................(iv)
multiplying equation (iii) by 7 and equation (iv) by 2 . we get,
49q - 14p = 35.................(v)
16q + 14p = 30..................(vi)
After adding equations (v) and (vi) . we get,
65q = 65
= q = 1
Putting value of q in equation (iv) , we get,
8 + 7p = 15
= 7p = 15 - 8 = 7
= p = 1
Now,
p = ![](data:image/png;base64,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)
q = ![](data:image/png;base64,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)
Hence , x = 1 and y = 1
(vi) 6x + 3y = 6xy
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAicAAAAuCAMAAADEHkkOAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADqQAGaQAGa2OgAAOgA6OgBmOjqQOmaQOma2OpCQOpDbZgAAZgA6ZgBmZjqQZmZmZpDbZrb/kDoAkDo6kDpmkGYAkJA6kLaQkNu2kNvbkNv/tmYAtmY6tmZmttuQtv//25A625Bm27Zm29uQ2/+22//b2////7Zm/9uQ//+2///bFOZ8RQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAHOUlEQVR4Xu1cC3PbNgyO48zusi1es9nb2i3qZrfbItn//+cNDz4lPkBZ0mUufdecJAIgBEIgiI/s3V39VQtUC1QLVAsILHBarY95sna1Wt2/5OkUhUxoX1yKq1ABsaaVUGSBbruR0DXgI5eD1FGEQnsdJ7nKFJC8UqUpsEC3fRJRN0h2Wu1FxFKhvrA0V5ECIi0rkdwCl4OOJpfDClwBv9r4r8EJiuYGoH54jRGGhJZwZRSQv12lnMoCrYkQn15O6+MpFS8uB3SN9qnbAtV5F49DAaFFXHH/i/vmVAapcoIWaNZ/bVcqNLT3H7+Pm+m803QULrpv47lvUGgRV0gNq0Ady6UtwNOHyh/Pu8y6p9syQQM8bTycRISWcEXsoBVY2kxffX88ldxR3gE5Ry6lbTGFgQxlfbz8Gg8nEaElXLGBUQp89eO2tAHUkJ4oe20TqSkrplYk7frY/RxXNSK0hCsmfNxCammr3mB/HEno7/n5S3ze4VijEtTu3cufqcpcWGgBV8DQngI3OBBv/JUoNaFoDjMJLGRiacflQIthXm+cdz8l6yhhoXKukM08Bd64UW9RvQ6WO7g2xqkHEtBobRZXG7rV1kei+WZAqJgrLNRV4BYH4gbfKZXEJtKWROr7/zQSZOZKcVzLmR94NH5u3jP3PtJ+lQ36nXnCGhGAd1X/QeZkNS7a3Tiu6bWfSqJeHtIQUe1R/6gG2Q+fzn2w/Sq1MrG6EUF4V2kwYIa6bW75HOhwHFe55uNg6vJ+bBVBDRFk6UaK5zQB2bn2AnXytQwQJiIq6LRHejkEslWGgUp/Y7lksKMzQMt9OLDM96xwslNPv6lvrVx7gXUtRJJgOv8o3w9S0LcmDfrJCDmjWUoVWLK6Moj0KqDALpn1B3AZDmywStjD8hD+6EDntzdQsoIn/DnAxf3v77X34QKDvB4ff3x8vUNauFOlLnoGnx+tLhzh9BV7YoFnfeQUxQdjLfKbB2lTY1g6TKP9IcZYqEB2QTWlgnruMBMdB3dcNrYmjW0f/t4+nd8fcU8EZ5peO7xfu/6w0XVJcBe7AwcDBeXJioNo4ZbE4P4O2ws6hiN874vFTr857M+7TR/CNcivAKS9JT8RxeCpfIW/azNEeIHoKO7mIRfSaQtf79X9oP1EmzkwblCTQeFJBvqJ5aBbRlP7vXBnSgJeWrGkItU80JV6YKxBfv3nDUYp+on2pQk/50KpyroSVVIKBHp1Yeqp3CEqR/uJDWLNgypsU5Macb6GyYTvqVLttuMDFYl4nlIZGYGm5EOGg9yJxNAzmudUL45wjBtMYbJXtbxiJM+DcC3ymwFpzWg5F/yV9MYxShgwZIjWPotZvkcRVyA+SznY9+x+omsndh8O+Ak7DTWpdIWnDgwyOKyDdhpLFX8o+1DJMSUeeO1wUE8oxnmmvNURTkHFikU7KI+iZMcHY+1CKAPSJs0pjCfzDUmZAh5MPZ9SSrKOJ3Y9DH7iFEaUH+F3en7GlIIgNFtY4XZyEXIOFQfUosl4nxMLqCcMFMNerHAOVlas8g0DzflgrEV+veeFM4RwmAqlzjbveDD1Yn7i1GQ3PIKUG+hqLMwVXL2mTHPQTqOqmghoU+t69pPPLy4HulO3Rb8b9mKEqz2HRizNDdiqCrYeGOsgvzmQNmVPoZ/MNySFCjgw9Xw6ack6kzAFc4zhOCO0P+yeusd/Dxv0D3jAxQu4gPtBO3lZs7n88oID3H2ndwDR1HKCf4oDsxZY+JyffwPaP0wvr/DKkPywcHIF3t9sxVLX0AnvHPEhXBf5zYG0t+QnFqY21qGlJtUF2Vr2fvAgS8AzA/816xk1RDiF4LQAtY4NFzpOvFYwy2a+77WrTIOaoF7y8M9OFxYR9SS9kYPnNngEG5iR1koBJq6LcOrMOY1OYNRqpXv8op5btVGyh/xeU1Mo/Jyn/4ZLFdDYd8gvsm6QJfD9RKecyh/A7Fft8eaoEynUXifaG5cYhDsO2p1+yG9PYg80cfGdES9LJZTYRz0hjBcDY28NpB0xBHOxeI5yLbTHuWa4rJU6AlP0cjEwdimQtkjZGyKO7D8Z84ZUMInMXAQSTfCLgbESkFaMBYkJ9QsVM2TAKMl5xQmMWUUELSDGgsSEuptShhwYlT+vWId4TgtEsKBhl2JCzVrKkDsxmD6vOKeNqmxcdesNNxksSEyorVrMIFagjtvyFhBjQWJCm6FQpQh+QpQpe2JQy1veSrXHCBYUmHdMPp452WfmnWKG9DnD/HnFOpqzWUCMBYkJzbRjzxcKUaY0WfK84mz2qYLJAmIsSExoZh3nfKEQZUqSpc8r1uGc1QJiLEhMqNUtZkCnNf+50/Clc+cVZzVTFe5aQIwFiQmd2CIxdbFcidBKM7UFxFiQmNAEF1nduVju1Bao8rIWEGNBYkLdpZBBSJZ9kUowpwUkWBAnvqXnAYUMQrI5bVBlVwtUC1QLvBkL/Ac6pe0XX5amiwAAAABJRU5ErkJggg==)
2x + 4y = 5xy
![](data:image/png;base64,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)
Putting ![](data:image/png;base64,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)
6q + 3p - 6 = 0
2q + 4p - 5 = 0
By cross multiplication method , we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAAgCAMAAAArFdbrAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OgBmOpDbZgAAZgA6ZgBmZrb/kDoAkNvbkNv/tmYAtmY6trZmtv//25A629vb2////7Zm/9uQ//+2///b0nEqDQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABR0lEQVRIS+1WyxLCIAwMvq2KRa1S+P//NKG1ow6RdRz1oLnoId1dksCG6B8vVsBNXwR46vPGmCxftKPamfEBAvPGoKlHarJ8u601m1BtED4/qhWU3Nd5PgqrmjC+aFmVg5QJv8LnJydqF0g92zkrY3VgKHzN5BSqJYLBfKFidWDk5zNangGIjjh1vEeHnOczixvWSCmHI+HtU6rgDV4h4sECbw5Y819Jc9LtFHzFHwSaRzQA3v1RwO/TNQ1Pwn6rf2id0LxvnePP+44KdC95qAz0trUz8IFXYPtNI9olU5adQry5nZVdV4XtN43k8cBO5eXFdmVdD2CTE3fnK+sWl48WscEbWOmWhBB0zi/Oq8q+StecNE0WBJv45GyYbs6FthgVNnUtzQDQvySt3D5OU2Av9ZFfxOu57uUuc5P6BQaFfcdF/xzmGRaVD7f5FcR6AAAAAElFTkSuQmCC)
After comparing we get,
p = 1 and q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgBAMAAAAs1X9uAAAAAXNSR0IArs4c6QAAADBQTFRFAAAAAAAAAAA6AGa2OgA6OpDbZgAAZgA6Zrb/kNv/tmYA25A629vb/7Zm/9uQ//+2Yg8ohgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAASUlEQVQYV2NgQAAuAwYGbkEgwcMNJBjQCIisYACSBjSmoKCgAG5ZsAx/ojADw/cJlyYA2U9AxFYg5gXZthnM4G1g+CYo2IAwBQBKDQtgu3qkcwAAAABJRU5ErkJggg==)
Now ,
p = ![](data:image/png;base64,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)
Hence, x = 1 and y = 2
(vii) Putting ![](data:image/png;base64,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)
10p + 2q - 4 = 0....................(i)
15p - 5q +2 = 0 ..................,,(ii)
By applying cross multiplication method , we get,
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
After comparing we get,
p = ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Adding equations (iii) and (iv) we get,
2x = 6
= x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACkAAAAgCAMAAAC4saEMAAAAAXNSR0IArs4c6QAAAEVQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OpDbZgAAZgA6ZpCQZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///bkYOaVAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAvElEQVQ4T7WT2RbCMAhEQWusC8aWNP//qULjdkxPM32Q1wzDZQnRf0J5f0ecsxwQmWkGVJjlErgbAdsUuhEDmM43I0BMs/SEedJ04lVOZead1W1GNFUWRBp7nyRfm5ZFELElWvF6NNHoS3zA3h0/X1YxUgCrEyl7X9+xVN3fU/hV1gy+QvdsTymLIS41X5t664ye8Cvdk6Acv09FDmB2Tkfkqlw5tKdVWBXC3PKN3VHbK6D5GzGwLPDmt8keK+UGEFdh6PgAAAAASUVORK5CYII=)
Putting value of equation (iii) we get,
y = 2
Hence, x = 3 and y = 2
(viii) Putting ![](data:image/png;base64,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)
p + q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAgCAMAAABD5lTTAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOpDbZgAAZgA6ZgBmZrbbZrb/kDoAkDo6kDpmkGaQkNv/tmYAtv//25A62////7Zm/9uQ//+2///beDhntwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABCUlEQVRIS9VVywKCMAxbVVBRHApMWP//P+3eMo+2B3rhcUjbLEuU2nsZALjKLYHDqJbDKNeAkNezKD7qh+T4E4AoPvHTcjUwxzlSMZ3e/s3eRjZ81EGIHjsNzafPBI+6cV3YVbNkcgJHJlLEJJ44dkFjXqAQHvdIfDHNn10gSUdN/hy4KuEXnlwjcjdXDE2S9m2X7DIvwoCuskuWY5XB/7rDrPwn/eSpa/2gJmEZMru1DQzWP+pv2/kB4yOeKz3w6V2o1v+f+CreXwMxrpjvL627ydk8Pps9bxpkVBwuXPavfv2fbK4XzcelEc1fe59R968QZgLl4guANwmqMUX5cTkGVbAJ0LRXyA+4oBCCx7gRfAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
p - q = ![](data:image/png;base64,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)
Adding (i) and (ii) we get,
2p = ![](data:image/png;base64,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)
= p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAgCAMAAADpJZJvAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAABmADqQAGa2OgAAOjoAOpDbZgBmZrbbZrb/kDoAkDo6kGaQtmYAtv//25A629vb/7Zm/9uQ//+2///bBw3ATwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAVUlEQVQYV2NgwAR8LCAxAUZGMC3IIACmgSI4aLh6RkZ2LMZhF2KEAKLVIykUZuUC8UR52MC0ACc3iBZiEQXRIhz8otycvCDnAwEzWCFYHuQjJn50+wDixQJEljShvwAAAABJRU5ErkJggg==)
Putting value of p in (ii) we get,
= ![](data:image/png;base64,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)
= q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAgCAMAAAB+dDW1AAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOpDbZgAAZgA6ZgBmZrbbZrb/kDoAkDo6kGaQkNv/tmYAtv//25A629vb2////7Zm/9uQ//+2///bYSsilAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA3UlEQVRIS+WU6w6CMAyFWxXviALTAe//nm4VM8H1hAgkJO7nvu2sPe1KtJxVJCAWCIle2DDrGhCGu3cyugaERAEDDfcUSjTgpWhMUhfmg1JdVxcdSl1iuMkuozv3PzQKb6CsVd61rN2Wza9TnzDitIbn9VTPpR/ivHEMb70p4hj+WudktQVfBML62A7S5rrXNSCsTzlZaTiTgq8Koc+m2jkNmwAbIRRDjBs99blssvT2iHoJodywfmTLKOJNXANCieI99WFLQOijsFIQw+tSbQsEfWmZx8/OH3uyf+0JV9sLkhAFJQ0AAAAASUVORK5CYII=)
Now,
p = ![](data:image/png;base64,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)
q = ![](data:image/png;base64,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)
Adding equations (iii) and (iv) we get,
6x = 6
= x = 1
Putting value of x in equation (iii) we get,
3(1) + y = 4
= y = 1
Hence, x = 1 and y = 1
Question 2.Formulate the following problems as a pair of equations, and hence find their solutions:
(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Answer:(i) Let the speed of Ritu in still water and the speed of stream be x km/h and y km/h respectively.
While rowing upstream, Ritu's speed slows down and the speed will be her speed minus speed of stream and while rowing downstream her speed will increase and will be equal to sum of her speed and speed of stream. Therefore,
The speed of Ritu while rowing
Upstream = (x - y) km/h
Downstream = (x + y) km/h
According to the question:
Ritu can row downstream 20 km in 2 hours, and
distance = speed x time
⇒ 2 (x+y) = 20
⇒ x+y = 10............(1)
also,
Ritu can row upstream 4 km in 2 hours
⇒ 2 (x - y) = 4
⇒ x-y = 2 ............(2)
Adding equation (1) and (2),
we obtain
⇒ x + y + x - y = 10 + 2
⇒ 2 x = 12
⇒ x = 6
Putting this in equation (1),
6 + y = 10
we obtain y = 4
Hence, Ritu's speed in still water is 6 km/h and the speed of the current is 4 km/h.
(ii)Let the number of days taken by a woman and a man be x and y respectively.
Therefore, work done by a woman in 1 day = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAgCAMAAAAYLsniAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAA///b//+22///2//btv//tv+2/9uQ29vbkNv/ttuQ/7ZmtrZm25CQZrb/25A6OpDbkGaQtmYAZma2Oma2AGa2kDoAADqQZgBmZgAAOgBmAABmAAA6AAAADTZ+4AAAAAF0Uk5TAEDm2GYAAABXSURBVHjarY7bCoAgAEOX3bPSLDOr/f9vBib0IkHQedlgbAxIYWwQRd6mgbIxejFPi9T4BiP4DUkLSQ0x13u3yBFAtro8ZMKHf0O19a6YcpijFP5sEysXjUME1tn1sr4AAAAASUVORK5CYII=)
and work done by a man in 1 day = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAiCAMAAABV5mjpAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgA6ZjqQZra2Zrb/kDoAkDpmkNv/tmYAtmZmtv//25A629vb2////7Zm/9uQ//+2///bupJSrQAAAAF0Uk5TAEDm2GYAAABcSURBVHjarY9LCoAwFAPnabV+W/ts1fuf1EULgoggOKtAksXAE74BQEVyWNGmVC/heolYviEFfsOLZWsNOqqJqAVSHY45AHvnkgU4pqGPeV65ojMCLEGzwnRXOQFHSgLqIJ91kgAAAABJRU5ErkJggg==)
According to the question,
2 women and 5 men take 4 days to complete the work
i.e. they take 4 days to complete one work
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Also,
3 women and 6 men take 3 days to complete the work i.e.
they take 3 days to complete one work
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Putting
in these equations,
we obtain
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAAAqCAMAAACQshUDAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAA///b//+22///tv///9uQkNv//7ZmZrb/kLaQ25Bm25A6kJA6OpDbOpCQtmYAZmZmAGa2kDoAOjqQOjo6ADqQZgA6ZgAAOgA6OgAAAABmAAA6AAAANF/sXgAAAAF0Uk5TAEDm2GYAAAFeSURBVHja7ZZ/c4MgDIYjqGFjlOHmWDXf/3PuQLqJqxW8w9vtzF/tmfRp3vwwAKdtW/PZFiYwS2NhBg61LM0AgJNxMk7GilUdOTN/dM8970kfidJ2V3OlVNeF6bEFZof6vqQiYoiduWvlGoBESUbQSwBoMk44kcJAovHpjWclM9RVJ3B4Me7jNsM1Pua1ZYiWpOK5WTLeQ8mbq5ojNd1svSGqTk2+Pf9h/A50blXnvvlc8XGHfYfTFGtmqHWtQjIqBMj7vbhSDDNTjFkDjxjuObPKPet5slbS+aIKyUcKxAzf5S4Pz/DFy7qBtJqGxFdzjTG2UHVD7bXCi02flpCoAtAXS/EsxgxmicgLhERm133GbNYYyz5hApcvkMw/pk3K3C0YmLVRfd03fV4Xv6mp5zmrgcT2usXiB2/PSzPYRwuFGX4z4dhKUVCp234RULgkBxxx+D+OUSQ6IJGj7AtixxtG3Oo2BgAAAABJRU5ErkJggg==)
⇒ 8p + 20q = 1
and
![](data:image/png;base64,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)
⇒ 9p + 18q = 1
By cross-multiplication, we obtain
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = 18, y = 36
Hence, number of days taken by a woman, x = 18
Number of days taken by a man, y = 36
(iii) Let the speed of train and bus be u km/h and v km/h respectively.
According to the given information,
It takes her 4 hours if she travels 60 km by bus and rest ( i.e. 240 km) by train
As
![](data:image/png;base64,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)
we have,
![](data:image/png;base64,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)
and also, If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer i.e. 4 hours and 10 minutes
Also,
1 hour = 60 minutes
![](data:image/png;base64,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)
and
![](data:image/png;base64,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)
we have,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMgAAAArCAMAAAAKVjeAAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAA///b//+22///tv///9uQ29uQkNv/ttuQ/7ZmZrb/25Bm25A6OpDbtmYAkGYAkDpmkDo6ZjqQAGa2kDoAOjo6ADqQZgBmZgA6ZgAAOgA6OgAAAABmAAA6AAAA8cybRAAAAAF0Uk5TAEDm2GYAAAJwSURBVHja7VjbcqQgEG0Q14UFkg2siRH7/z8zD3iB2XiBSI1TNf3UVnmoPvQdgKc85Ub+NKcdVX/6s4hFdCzWVoUj4tAkw0Jk3eN8yAlCu9mgtiLWsVBbFT00QLv45wOwCFn34kTPcsekJ8KHBoCjCLV1cxQAyPjnA7AIeS4RABiJaMcAaGdCbS9IRA5sQhYiQmxbAdCurRZtB6gdy4FNl1aUiI/zSdspEr3IgU1IqPt/J+Z6PhFiFeQR8UggVgGxJzKJQ8sE2rY1BjJgC3JyjiqU7CrUtsLcBOF+HBYgx+pvzibiiymKUNsAtRUAV6mwEKlVGY/ElWcn1v00oFUiLELqoYH9BnpUiEVERON7PHozFm01PBAREVUiLELSDg/8/5TriwyjUT+sS8cmFMzQIgktrsVjmaHnLeTBiHAfV8sMPdbzRyMSTQVjz0pxyWWIRBmhp8VUFSUyNgw8dcLlwVkzKW0AcFNWDToAW5HU/9eJLI5IKMGXCa2lhwTZUphI4dAKZuhH9MhMZJ6hb/eCexMh1jGQKKa5/vZ73FumBF9m6PJVqwiRKTOC6TuttZfIW8xZRfj/IHnXubHuTabn1Leb2v14qOwYVOu93kddW8Wd86hJKIB2KNKs+cGTw+Y+QqzgjmXsKbz91Sv6znTSDXMsWDykY1k3NT44Jlmm3e++2L6uzaFXqe97FH1nSZGFbZWd7ztCO5VXAaRjAFKlpUhbLWP42XXks8k7WrcV0Lcqg4gcShRO7hjUfUbYagPkNZG/v7AyHpFDQ99eDPmbeEvEGvqRXrMNAEdVJkfQMZkxcmeNGnWPiFd50HhKAfkCiz9E3rFLXhoAAAAASUVORK5CYII=)
Putting
in these equations, we obtain
60p+240q = 4 ......(3)
100p+200q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAgCAMAAAD68tKbAAAAAXNSR0IArs4c6QAAAEVQTFRFAAAA///b//+22///tv///9uQkNv//7ZmZrb/25A6ZpCQOpDbkDo6AGa2kDoAADqQZgA6ZgAAOgA6OgAAAABmAAA6AAAAa4WsuwAAAAF0Uk5TAEDm2GYAAAB7SURBVHjavZHBDsIwDEOdDdqG0g7Wzf//qSiD0eUCF8S7WXYSyQG+MdzJAkBJrgHDLSCuAdD0jpxnrzW/8mWTsey5ZhndJaTmpxsT5Bo2386RCVJJZvwcevAnIpdTV1KLc9VLqZfGaez9tmk8jtgPoD1gPbqVVuJh/gMP+ysGJimZh+YAAAAASUVORK5CYII=)
600p+1200q = 25 ....(4)
Multiplying equation (3) by 10, we obtain
600p+2400q = 40 ....(5)
Subtracting equation (4) from (5), we obtain
1200q = 15
..... (6)
Substituting in equation (3), we obtain
60p+3 = 4
60p = 1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
u = 60km/h and v = 80km/h
Hence, speed of train = 60 km/h
Speed of bus = 80 km/h
Solve the following pairs of equations by reducing them to a pair of linear equations:
Answer:
(i)
Let and
, then the equations becomes.
Using cross-multiplication method, we obtain,
p = 2 and q = 3
Note: These questions can also be solved by elimination method and the substitution method.In the elimination method, the coefficient of one variable in both equations is made the same by multiplying the equation and the variable is eliminated.
In the substitution method, the value of one variable is calculated in terms of another variable by equation one and then that value is put into another equation.
(ii) Putting in the given equations, we obtain
2p +3q = 2........(i)
4p - 9q = -1 .......(ii)
Multiplying equation (1) by 3,
we obtain 6p + 9q = 6....... (iii)
Adding equation (ii) and (iii), we obtain
10p = 5
Putting in equation (i), we obtain
=
= 3q = 1
=
p =
=
q =
=
Hence, x = 4 and y = 9.
(iii) Putting
= 4p + 3y = 14
= 4p + 3y - 14 = 0.....................(i)
And, 3p - 4y = 23
= 3p - 4y -23 = 0.......................(ii)
By cross- multiplication , we get,
=
=
Now,
=
=
Also, p =
Hence, x =
(iv) Putting
= 5p + q = 2....................(i)
= 6p - 3q = 1 .....................(ii)
Now, multiplying equation (i) by 3 we get,
= 15p + 3q = 6..............(iii)
Adding equations (ii) and (iii)
21 p = 7
= p =
Putting value of p in equation (iii) we get,
=
=
= q =
We know that,
p =
= 3 = x - 1
= x = 4
And, q =
= y - 2 = 3
= y = 5
Hence, x = 4 and y = 5
(v)
=
=
=
Putting in (i) and (ii) to get,
7q - 2p = 5 ................(iii)
8q + 7p = 15 .................(iv)
multiplying equation (iii) by 7 and equation (iv) by 2 . we get,
49q - 14p = 35.................(v)
16q + 14p = 30..................(vi)
After adding equations (v) and (vi) . we get,
65q = 65
= q = 1
Putting value of q in equation (iv) , we get,
8 + 7p = 15
= 7p = 15 - 8 = 7
= p = 1
Now,
p =
q =
Hence , x = 1 and y = 1
(vi) 6x + 3y = 6xy
2x + 4y = 5xy
Putting
6q + 3p - 6 = 0
2q + 4p - 5 = 0
By cross multiplication method , we get,
=
=
After comparing we get,
p = 1 and q =
Now ,
p =
Hence, x = 1 and y = 2
(vii) Putting
10p + 2q - 4 = 0....................(i)
15p - 5q +2 = 0 ..................,,(ii)
By applying cross multiplication method , we get,
=
=
After comparing we get,
p =
Now,
Adding equations (iii) and (iv) we get,
2x = 6
= x =
Putting value of equation (iii) we get,
y = 2
Hence, x = 3 and y = 2
(viii) Putting
p + q =
p - q =
Adding (i) and (ii) we get,
2p =
= p =
Putting value of p in (ii) we get,
=
= q =
Now,
p =
q =
Adding equations (iii) and (iv) we get,
6x = 6
= x = 1
Putting value of x in equation (iii) we get,
3(1) + y = 4
= y = 1
Hence, x = 1 and y = 1
Question 2.
Formulate the following problems as a pair of equations, and hence find their solutions:
(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Answer:
(i) Let the speed of Ritu in still water and the speed of stream be x km/h and y km/h respectively.
While rowing upstream, Ritu's speed slows down and the speed will be her speed minus speed of stream and while rowing downstream her speed will increase and will be equal to sum of her speed and speed of stream. Therefore,
The speed of Ritu while rowing
Upstream = (x - y) km/h
Downstream = (x + y) km/h
According to the question:
Ritu can row downstream 20 km in 2 hours, anddistance = speed x time
⇒ 2 (x+y) = 20
⇒ x+y = 10............(1)
also,
Ritu can row upstream 4 km in 2 hours
⇒ 2 (x - y) = 4
⇒ x-y = 2 ............(2)
Adding equation (1) and (2),
we obtain
⇒ x + y + x - y = 10 + 2⇒ 2 x = 12
⇒ x = 6
Putting this in equation (1),
6 + y = 10we obtain y = 4
Hence, Ritu's speed in still water is 6 km/h and the speed of the current is 4 km/h.
(ii)Let the number of days taken by a woman and a man be x and y respectively.
Therefore, work done by a woman in 1 day =
and work done by a man in 1 day =
According to the question,
2 women and 5 men take 4 days to complete the worki.e. they take 4 days to complete one work
⇒
⇒
Also,
3 women and 6 men take 3 days to complete the work i.e.
they take 3 days to complete one work
⇒
⇒
Putting in these equations,
we obtain
⇒ 8p + 20q = 1
and
⇒ 9p + 18q = 1
By cross-multiplication, we obtain
x = 18, y = 36
Hence, number of days taken by a woman, x = 18
Number of days taken by a man, y = 36
(iii) Let the speed of train and bus be u km/h and v km/h respectively.
According to the given information,
It takes her 4 hours if she travels 60 km by bus and rest ( i.e. 240 km) by trainAs
we have,
and also, If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer i.e. 4 hours and 10 minutes
Also,
1 hour = 60 minutes
and
we have,
Putting in these equations, we obtain
60p+240q = 4 ......(3)
100p+200q =
600p+1200q = 25 ....(4)
Multiplying equation (3) by 10, we obtain
600p+2400q = 40 ....(5)
Subtracting equation (4) from (5), we obtain
1200q = 15
..... (6)
Substituting in equation (3), we obtain
60p+3 = 4
60p = 1
u = 60km/h and v = 80km/h
Hence, speed of train = 60 km/h
Speed of bus = 80 km/h
Exercise 3.7
Question 1.The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.
Answer:The difference between the ages of Biju and Ani is 3 years. Either Biju is 3 years older than Ani or Ani is 3 years older than Biju. However, it is obvious that in both cases, Ani's father's age will be 30 years more than that of Cathy's age.
Let the age of Ani and Biju be x and y years respectively.
Therefore, age of Ani's father, Dharam = 2 × x = 2x years
And age of Biju's sister Cathy =
years
By using the information given in the question,
Case (I) When Ani is older than Biju by 3 years, x - y = 3 (i)
![](data:image/png;base64,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)
4x - y = 60 (ii)
Subtracting (i) from (ii), we obtain 3x = 60 - 3 = 57
x = 57/3 = 19
Therefore, age of Ani = 19 years
And age of Biju = 19 - 3 = 16 years
Case (II) When Biju is older than Ani, y - x = 3 (i)
![](data:image/png;base64,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)
4x - y = 60 (ii)
Adding (i) and (ii), we obtain 3x = 63
x = 21
Therefore, age of Ani = 21 years
And age of Biju = 21 + 3 = 24 years
Question 2.One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, "If you give me ten, I shall be six times as rich as you". Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II)
[Hint: x + 100 = 2 (y - 100), y + 10 = 6(x - 10)]
Answer:Let those friends were having Rs x and y with them. Using the information given in the question,
we obtain
From the first condition,
x + 100 = 2(y - 100)
x + 100 = 2y - 200
x - 2y = -300 (i)
And,
From the second condition
6(x - 10) = (y + 10)
6x - 60 = y + 10
6x - y = 70 (ii)
Multiplying equation (ii) by 2, we obtain
12x - 2y = 140 (iii)
Subtracting equation (i) from equation (iii),
we obtain
11x = 140 + 300
11x = 440
x = 40
Using this in equation (i), we obtain
40 - 2y = -300
40 + 300 = 2y
2y = 340
y = 170
Therefore, those friends had Rs 40 and Rs 170 with them respectively.
Question 3.A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Answer:Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel was d km.
We know that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Or, d = xt (i)
If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time
⇒ (x + 10) = ![](data:image/png;base64,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)
⇒ (x + 10)(t - 2) = d
⇒ xt + 10t - 2x - 20 = d
From (i), we have
⇒ d + 10t - 2x - 20 = d
⇒ - 2x + 10t = 20
⇒ x - 5t = -10
⇒ x = 5t - 10 (ii)
Also,
if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time
⇒ (x - 10) = ![](data:image/png;base64,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)
⇒ (x - 10)(t + 3) = d
⇒ xt - 10t + 3x - 30 = d
By using equation (i),
⇒ d - 10t + 3x - 30 = d
⇒ 3x - 10t = 30 (iii)
Substituting the value of x from eq (ii) into eq (iii), we get
⇒ 3(5t - 10) - 10t = 30
⇒ 15t - 30 - 10t = 30
⇒ 5t = 60
⇒ t = 12 hours
Putting this in eq(ii)
⇒ x = 5t - 10
= 5(12) - 10
= 50 km/h
From equation (i), we obtain
Distance to travel = d = xt
= 50 × 12
= 600 km
Hence, the distance covered by the train is 600 km.
Question 4.The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Answer:Let the number of rows be x and number of students in a row be y.
Total students of the class = Number of rows x Number of students in a row = xy
Using the information given in the question,
Condition 1
Total number of students = (x - 1) (y + 3)
= (x - 1) (y + 3)
= xy - y + 3x - 3
3x - y - 3 = 0
3x - y = 3 ....(i)
Condition 2
Total number of students = (x + 2) (y - 3)
= xy + 2y - 3x - 6
⇒3x - 2y = -6 ... (ii)
Subtracting equation (ii) from (i),
(3x - y) - (3x - 2y) = 3 - (-6)
⇒- y + 2y = 9
⇒3 + 6 y = 9
By using equation (i), we obtain 3x - 9 = 3,
⇒3x = 9 + 3
⇒3x = 12
⇒ x = 4
From (i),
⇒ 3(4) - y = 3
⇒ 12 - y = 3
⇒ 9 = y
Number of rows = x = 4
Number of students in a row = y = 9
Number of total students in a class = Number of students in 1 row × Number of rows
= xy
= 4 x 9
= 36
Question 5.In a
Find the three angles.
Answer:Given that,
∠ C = 3∠ B = 2(∠ A + ∠ B)
Let's take
3∠ B = 2(∠ A + ∠ B)
3∠ B = 2∠ A + 2∠ B
∠ B = 2∠ A
2 ∠ A - ∠ B = 0 … (i)
We know that the sum of the measures of all angles of a triangle is 180°. Therefore,
∠ A + ∠ B + ∠ C = 180°
∠ A + ∠ B + 3 ∠ B = 180°
∠ A + 4 ∠ B = 180° … (ii)
Multiplying equation (i) by 4, we obtain
8 ∠ A - 4 ∠ B = 0 … (iii)
Adding equations (ii) and (iii), we obtain
9 ∠ A = 180°
∠ A = 20°
From equation (ii), we obtain
20° + 4 ∠ B = 180°
4 ∠ B = 160°
∠ B = 40°
and
∠ C = 3 ∠ B
= 3 x 40° = 120°
Therefore, ∠ A, ∠ B, ∠ C are 20°, 40°, and 120° respectively.
Question 6.Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
Answer:5x - y = 5 Or,
y = 5x - 5
The solution table will be as follows.
![](data:image/png;base64,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)
The graphical representation of these lines will be as follows.
![](data:image/jpeg;base64,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)
It can be observed that the required triangle is ΔABC formed by these lines and y-axis. The coordinates of vertices are A (1, 0), B (0, - 3), C (0, - 5).
Question 7.Solve the following pair of linear equations.
(i) px + qy = p - q
qx - py = p + q
(ii) ax + by = c
bx + ay = 1 + c
(iii) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAAAxCAAAAADrFki1AAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAA7DAAAOwwHHb6hkAAACiElEQVRYw2P4T3vAMGrHqB20tOOc+RwQNd98LV71Mzy+gKgd5nvIsOObANf7//+XMGn/wKu+kvEQkPwiyP+JnLCazpj6fxUzASv+b2doBpIxjKvICav/f+XYFrNoEbDi/3NWz///jzHZkGAFcpxvZ2QgaMX//4KS/3/JcT0n044dzExnCGvQ5fxWzziZFCuQ7NjBIs5sRFhDKtMONh2SrEDYsYdF/pMD43aCGlYw8LPdIc+OPSyy7//fY1H+S0jDPWaGetKsgNmxj03sJZCKYJxPSMMjVkWC7sAVVsQCM+YLpGoh1Y4ZjBmkWkGqHc85JQlnIQrtWG1+hGQraFW2vzZnYWD3/0FLO37JMiqYiTNY0NKOhQx+wEJWnekC3A5zDJCATSOmMvOnOOxwZLoEJBczlNDQDkkOUBV2hcmJWmH1koUBCji/QIX4eH6BJeSpZccXD5i3An9BhXh5/xNnxwGY8xiYrpBoLR+xdtyDB7vTSxL9IckBCrVLTPbUCiss8QFJV3MZ8qllBxYAzR+MZ2hoxy8Z2ufz/y8pK6/UuUgt3Um24weXOqlaSLbjHOkVIcKOZWIsDIwCXYQ0NDN0aTIxar8myw5fMQNzHSamGwQ02DAwK5gJMniSH1bJDJvxq/8rwH0KWM2xCZJnx5fVOZ7izLfwq3/AEgSihHnJseOcOiOoOOD7hV/9fAZQd+svrxgZdlxiZXZY+Og1uzEB9UHMD/6DGqRuZNjhx7geSO5jrCSgXkoA1BJNZdxIhh3yLMB685MF4zH8yt+zgcqgzcyapLR5YXZ4MYiaabIwcHzBr3w7A7Cw02ASeknQYCx2vFRlZBTJ55UnoDyHUYSJgdWGlBw4fMYZAKvygXmKANGuAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDE3LTExLTAyVDA1OjA5OjQ2KzAwOjAwLCVc6wAAACV0RVh0ZGF0ZTptb2RpZnkAMjAxNy0xMS0wMlQwNTowOTo0NiswMDowMF145FcAAAAASUVORK5CYII=)
ax + by = a2 + b2
(iv) (a - b) x + (a + b) y = a2 - 2ab - b2
(a + b) (x + y) = a2 + b2
(v) 152 x - 378 y = - 74
-378 x + 152 y = - 604
Answer:(i)p x + q y = p - q … (1)
q x - p y = p + q … (2)
Multiplying equation (1) by p and equation (2) by q,
we obtain p2 x + pq y = p2 - pq … (3)
q2 x - pq y = pq + q2 … (4)
Adding equations (3) and (4),
we obtain p2x + q2x = p2 + q2
(p2 + q2) x = p2 + q2
![](data:image/png;base64,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)
From equation putting the value of x (1),
we obtain p (1) + qy = p - q
qy = - q
y = - 1
(ii)ax + by = c … (1)
bx + ay = 1 + c … (2)
Multiplying equation (1) by a and equation (2) by b,
we obtain a2 x + ab y = ac … (3)
b2 x + ab y = b + bc … (4)
Subtracting equation (4) from equation (3),
(a2 - b2) x = ac - bc – b
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From equation (1), we obtain ax + by = c, now putting the value of x in the equation
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(iii)![](data:image/png;base64,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)
Or, bx - ay = 0 … (1)
ax + by = a2 + b2 … (2)
Multiplying equation (1) and (2) by b and a respectively, we obtain b2 x - ab y = 0 … (3)
a2 x + ab y = a3 + ab2 … (4)
Adding equations (3) and (4), we obtain b2x + a2x = a3 + ab2
x (b2 + a2) = a (a2 + b2) x
Thus, x = a
By using (1), and putting the value of x in the equation we obtain b (a) - ay = 0
ab - ay = 0
ay = ab
y = b
(iv) (a - b) x + (a + b) y = a2 - 2ab - b2 … (1)
(a + b) (x + y) = a2 + b2
(a + b) x + (a + b) y = a2 + b2 … (2)
Subtracting equation (2) from (1),
we obtain
(a - b) x - (a + b) x = (a2 - 2ab - b2) - (a2 + b2) (a - b - a - b) x = - 2ab - 2b2
- 2bx = - 2b (a + b)
x = a + b
Using equation (1), and putting the value of x in the equation we obtain
(a - b) (a + b) + (a + b) y = a2 - 2ab - b2a2 - b2 + (a + b) y = a2 - 2ab - b2
(a + b) y = - 2ab
![](data:image/png;base64,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)
(v) 152 x - 378 y = - 74 ------------(1)
-378 x + 152 y = - 604 -------- (2)
Multiply eq (2) by 152 and equation (1) by 378
378 × 152x – 3782y = -74 × 378
-378 × 152x + 1522y = -604 × 152
Adding both the questions we get
(1522 – 3782)y = -119780
-119780 y = -119780
y = 1
put the value in eq 1,
152 x - 378 x 1 = - 74
152 x = 378 - 74
152 x = 304
x = 2
we get x = 2.
Question 8.ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.
![](data:image/png;base64,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)
Answer:We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°. Therefore, ∠ A + ∠ C = 180
⇒4y + 20 - 4x = 180
⇒- 4x + 4y = 160
⇒x - y = - 40 ....(i)
Also, ∠ B + ∠ D = 180
⇒3y - 5 - 7x + 5 = 180
⇒- 7x+ 3y = 180 .... (ii)
Multiplying equation (i) by 3, we obtain 3x - 3y = - 120.... (iii)
Adding equations (ii) and (iii), we obtain
- 7x + 3x = 180 - 120
- 4x = 60
x = -15
By using equation (i), we obtain x - y = - 40
-15 - y = - 40
y = -15 + 40
= 25
∠ A = 4y + 20
= 4(25) + 20
∠A= 120°
∠ B = 3y - 5
= 3(25) - 5
∠B= 70°
∠C = - 4x
= - 4(- 15)
∠C = 60°
∠D = - 7x + 5
= - 7(-15) + 5
= 105 + 5
∠D = 110°
The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.
Answer:
The difference between the ages of Biju and Ani is 3 years. Either Biju is 3 years older than Ani or Ani is 3 years older than Biju. However, it is obvious that in both cases, Ani's father's age will be 30 years more than that of Cathy's age.
Let the age of Ani and Biju be x and y years respectively.
Therefore, age of Ani's father, Dharam = 2 × x = 2x years
And age of Biju's sister Cathy = years
By using the information given in the question,
Case (I) When Ani is older than Biju by 3 years, x - y = 3 (i)
4x - y = 60 (ii)
Subtracting (i) from (ii), we obtain 3x = 60 - 3 = 57
x = 57/3 = 19
Therefore, age of Ani = 19 years
And age of Biju = 19 - 3 = 16 years
Case (II) When Biju is older than Ani, y - x = 3 (i)
4x - y = 60 (ii)
Adding (i) and (ii), we obtain 3x = 63
x = 21
Therefore, age of Ani = 21 years
And age of Biju = 21 + 3 = 24 years
Question 2.
One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, "If you give me ten, I shall be six times as rich as you". Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II)
[Hint: x + 100 = 2 (y - 100), y + 10 = 6(x - 10)]
Answer:
Let those friends were having Rs x and y with them. Using the information given in the question,
we obtain
From the first condition,
x + 100 = 2(y - 100)
x + 100 = 2y - 200
x - 2y = -300 (i)
And,
From the second condition
6(x - 10) = (y + 10)
6x - 60 = y + 10
6x - y = 70 (ii)
Multiplying equation (ii) by 2, we obtain
12x - 2y = 140 (iii)
Subtracting equation (i) from equation (iii),
we obtain
11x = 140 + 300
11x = 440
x = 40
Using this in equation (i), we obtain
40 - 2y = -300
40 + 300 = 2y
2y = 340
y = 170
Therefore, those friends had Rs 40 and Rs 170 with them respectively.
Question 3.
A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Answer:
Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel was d km.
We know that,
Or, d = xt (i)
If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time⇒ (x + 10) =
⇒ (x + 10)(t - 2) = d
⇒ xt + 10t - 2x - 20 = d
From (i), we have
⇒ d + 10t - 2x - 20 = d
⇒ - 2x + 10t = 20
⇒ x - 5t = -10
⇒ x = 5t - 10 (ii)
Also,
if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time
⇒ (x - 10) =
⇒ (x - 10)(t + 3) = d
⇒ xt - 10t + 3x - 30 = d
By using equation (i),
⇒ d - 10t + 3x - 30 = d
⇒ 3x - 10t = 30 (iii)
Substituting the value of x from eq (ii) into eq (iii), we get
⇒ 3(5t - 10) - 10t = 30
⇒ 5t = 60
⇒ t = 12 hours
Putting this in eq(ii)
⇒ x = 5t - 10
= 5(12) - 10
= 50 km/h
From equation (i), we obtain
Distance to travel = d = xt
= 50 × 12
= 600 km
Hence, the distance covered by the train is 600 km.
Question 4.
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Answer:
Let the number of rows be x and number of students in a row be y.
Total students of the class = Number of rows x Number of students in a row = xy
Using the information given in the question,
Condition 1
Total number of students = (x - 1) (y + 3)
= (x - 1) (y + 3)
= xy - y + 3x - 3
3x - y - 3 = 0
3x - y = 3 ....(i)
Condition 2
Total number of students = (x + 2) (y - 3)
= xy + 2y - 3x - 6
⇒3x - 2y = -6 ... (ii)
Subtracting equation (ii) from (i),
(3x - y) - (3x - 2y) = 3 - (-6)
⇒- y + 2y = 9
⇒3 + 6 y = 9
By using equation (i), we obtain 3x - 9 = 3,
⇒3x = 9 + 3
⇒3x = 12
⇒ x = 4
⇒ 3(4) - y = 3
⇒ 12 - y = 3
⇒ 9 = y
Number of rows = x = 4
Number of students in a row = y = 9
Number of total students in a class = Number of students in 1 row × Number of rows
= xy
= 4 x 9
= 36
Question 5.
In a Find the three angles.
Answer:
Given that,
∠ C = 3∠ B = 2(∠ A + ∠ B)
Let's take
3∠ B = 2(∠ A + ∠ B)
3∠ B = 2∠ A + 2∠ B
∠ B = 2∠ A
2 ∠ A - ∠ B = 0 … (i)
We know that the sum of the measures of all angles of a triangle is 180°. Therefore,
∠ A + ∠ B + ∠ C = 180°
∠ A + ∠ B + 3 ∠ B = 180°
∠ A + 4 ∠ B = 180° … (ii)
Multiplying equation (i) by 4, we obtain
8 ∠ A - 4 ∠ B = 0 … (iii)
Adding equations (ii) and (iii), we obtain
9 ∠ A = 180°
∠ A = 20°
From equation (ii), we obtain
20° + 4 ∠ B = 180°
4 ∠ B = 160°
∠ B = 40°
and∠ C = 3 ∠ B
= 3 x 40° = 120°
Therefore, ∠ A, ∠ B, ∠ C are 20°, 40°, and 120° respectively.
Question 6.
Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
Answer:
5x - y = 5 Or,
y = 5x - 5
The solution table will be as follows.
The graphical representation of these lines will be as follows.
It can be observed that the required triangle is ΔABC formed by these lines and y-axis. The coordinates of vertices are A (1, 0), B (0, - 3), C (0, - 5).
Question 7.
Solve the following pair of linear equations.
(i) px + qy = p - q
qx - py = p + q
(ii) ax + by = c
bx + ay = 1 + c
(iii)
ax + by = a2 + b2
(iv) (a - b) x + (a + b) y = a2 - 2ab - b2
(a + b) (x + y) = a2 + b2
(v) 152 x - 378 y = - 74
-378 x + 152 y = - 604
Answer:
(i)p x + q y = p - q … (1)
q x - p y = p + q … (2)
Multiplying equation (1) by p and equation (2) by q,
we obtain p2 x + pq y = p2 - pq … (3)
q2 x - pq y = pq + q2 … (4)
Adding equations (3) and (4),
we obtain p2x + q2x = p2 + q2
(p2 + q2) x = p2 + q2
From equation putting the value of x (1),
we obtain p (1) + qy = p - q
qy = - q
y = - 1
(ii)ax + by = c … (1)
bx + ay = 1 + c … (2)
Multiplying equation (1) by a and equation (2) by b,
we obtain a2 x + ab y = ac … (3)
b2 x + ab y = b + bc … (4)
Subtracting equation (4) from equation (3),
(a2 - b2) x = ac - bc – b
From equation (1), we obtain ax + by = c, now putting the value of x in the equation
(iii)
Or, bx - ay = 0 … (1)
ax + by = a2 + b2 … (2)
Multiplying equation (1) and (2) by b and a respectively, we obtain b2 x - ab y = 0 … (3)
a2 x + ab y = a3 + ab2 … (4)
Adding equations (3) and (4), we obtain b2x + a2x = a3 + ab2
x (b2 + a2) = a (a2 + b2) x
Thus, x = a
By using (1), and putting the value of x in the equation we obtain b (a) - ay = 0
ab - ay = 0
ay = ab
y = b
(iv) (a - b) x + (a + b) y = a2 - 2ab - b2 … (1)
(a + b) (x + y) = a2 + b2
(a + b) x + (a + b) y = a2 + b2 … (2)
Subtracting equation (2) from (1),
we obtain
(a - b) x - (a + b) x = (a2 - 2ab - b2) - (a2 + b2) (a - b - a - b) x = - 2ab - 2b2
- 2bx = - 2b (a + b)
x = a + b
Using equation (1), and putting the value of x in the equation we obtain
(a - b) (a + b) + (a + b) y = a2 - 2ab - b2a2 - b2 + (a + b) y = a2 - 2ab - b2
(a + b) y = - 2ab
(v) 152 x - 378 y = - 74 ------------(1)
-378 x + 152 y = - 604 -------- (2)
Multiply eq (2) by 152 and equation (1) by 378
378 × 152x – 3782y = -74 × 378
-378 × 152x + 1522y = -604 × 152
Adding both the questions we get
(1522 – 3782)y = -119780
-119780 y = -119780
y = 1
put the value in eq 1,
152 x - 378 x 1 = - 74
152 x = 378 - 74
152 x = 304
x = 2
we get x = 2.
Question 8.
ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.
Answer:
We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°. Therefore, ∠ A + ∠ C = 180
⇒4y + 20 - 4x = 180
⇒- 4x + 4y = 160
⇒x - y = - 40 ....(i)
Also, ∠ B + ∠ D = 180
⇒3y - 5 - 7x + 5 = 180
⇒- 7x+ 3y = 180 .... (ii)
Multiplying equation (i) by 3, we obtain 3x - 3y = - 120.... (iii)
Adding equations (ii) and (iii), we obtain
- 7x + 3x = 180 - 120
- 4x = 60
x = -15
By using equation (i), we obtain x - y = - 40
-15 - y = - 40
y = -15 + 40
= 25
∠ A = 4y + 20
= 4(25) + 20
∠A= 120°
∠ B = 3y - 5
= 3(25) - 5
∠B= 70°
∠C = - 4x
= - 4(- 15)
∠C = 60°
∠D = - 7x + 5
= - 7(-15) + 5
= 105 + 5
∠D = 110°