IM 8.4.2 Practice: Keeping the Equation Balanced

Which of the changes would keep the hanger in balance?
[size=150]Select all that 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[/img]
Here is a balanced hanger diagram.
[img]data:image/png;base64,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[/img][br][br]Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and [math]x[/math] represents the weight of each square. Select [i]all[/i] equations that represent the hanger.
What is the weight of a square if a triangle weighs 4 grams?
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[/img]
Explain your reasoning.
Andre came up with the following puzzle. “I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages?”
[size=150]Try to solve the puzzle.[/size]
[size=150]Jada writes this equation for the sum of the ages:[br][math]\text{(x)+(x+ 3)+ (x- 2)+ 3(x+3)-1=87.}[/math][br][br][size=100]Explain the meaning of the variable and each term of the equation.[/size][/size]
[size=150][size=100]Write the equation with fewer terms.[/size][/size]
[size=150][size=100]Solve the puzzle if you haven’t already.[/size][/size]
These two lines are parallel. Write an equation for each.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdIAAAGHCAYAAAAEI9NyAAAgAElEQVR4Aeydh3cUSZbu9z9569/bt7uzO7PjZ9rSTTfeew9N472HxtN4jzACISHvvUMOKwHy3nsvJCRACNfT3d8734XkFWqpVKXKTCSIPKdOZVVlZWTciBu/MDfu/TuoQ0lASUBJQElASUBJoN8S+Lt+/1P9UUlASUBJQElASUBJAAqkqhIoCSgJKAkoCSgJOCABqyD94Ycf8C5eL1++xP9/mf8MWtpm5/3lyx8s8v3SdNlr+X71/u7k/vKHH8CXWfJXch+c+sZ6+uLFC3nx3N76osr9dbkPMn3T2qnnz59L2dtb7tr1DnDzF3+1CtKioiIUFhahuLjE1Fd+fgEyMjKRm5uHoqJiq2nz97y8fKSnpSM1NU2et6i4BHwVFhXLffh9Tk6ufLaWF/lfUTEyM7PkXn2lbe1e/fmN6eUXFCI9IxN5+QVW892f+/f1n4KCQmRl5yA7J8f0cqfsWd4ZmVlSTvzc1/Pq9TvlzrxT7rm5+aalqz0/dSw7O0dkX/AO9I15Zt4pg3dR5zMyskQ/i4psL3M+K9uIq7FXkZiQKPLT5GnrO/Oak5sn+s772fo/va6jjlPu1Hnz5V4i+c7OzpW0zdY3abPTM8C23h55FhYWIzsrG4mJiYgIj0BGeqbdsqO+kW16HlZBevHiZcTGxuH6jZumvqKiY+B09hx8/QKQmHTNatr8PSQ0DGtWrcGsmbMQGRmFa9dv4Nq1G0hISMKRw0cxbcpUXDh/AQkJiVbvxf8lJl6Ds/MlfLdtO+LiEuReZuWfacfExsHJ6TzCwiOsPqsRz3Q1Lh4eHt7w8PBCfB+y0jX96zelvAICguDs7CLlxrLQNQ0rdTgp6TquXo3H6TNnERwSalq6Wv7i4hNwxd0Drm7uUue07816Z56Zd8qAsjArXU3fzp13hre3r6Rta7mHhUVg3Zp1+N1vfotZM2bCzz/gla5et72tor75BwThXbVz1HHqOnWez2KW3K9fvymyvnjRBT4+fkhMum5qO8c6FhgYjJOnziAqKsb2fF+/ifj4ROzdsw+fffwphg75AhcuOIvsbK03lDGZxjLX87AK0tDQcDQ3t+DZs2emvhobmxAUHILMrGx0dnZaTfvJkydoamrCoYMHMWnCBJSVlYHfdXQ8REVFBdatWYM1K1ehtqYGT550Wb0X07p//z6czpzB4oXforysvM/09ZTN48dMvxVBQSGorKyy+qx6pqvdq63tAe7cuYuUlDt4+PChaek/ffoMXV1d0juNio7Fo0eP8PTpU9PS73zyBG1tbSDIS0pKTUtXk3t7eztu3UoGG7gHD9pNT595Zt4pA8pCey6j31nGjx49Rnh4JNLSMkRv+yp31g3qxp5du6UhnTd7Du7euQPK8Kmd7RT1jbMgbFip90bnt/v9mQ/qOnWez9L9d6M+U986O58gJuYqOBvA877kruezsI5xJOrj64eGhkab8s1nJItOnzqFEV9/jUnjJ+BaUpK0/Xx2e8qe9yHb9DysgjQ6OhYPHz7SMz2b7vXgwQNEREbJ9OLf/vY3q//58ccfBXauLi6YMHYsCvILZJ2xo6MDIcHBmDxhIvz9/GT95Oeff7Z6L1aW8rIy+c+woV8hPi4OnIc36+Dc/ePHjxEREYWGxkazkn2TDjsgVCxON5mZbz7ATz/9hNLSMulxvnjxEn2V1ZuH1uGEdYx5Dw0LR3V1jQ53tO8WbAju3UtDSspd6VDY92/Hr2aemXfKoC99czy1/38HljHXu9ig5+TkgbrcW7nzez5fbm4uvtuyFWNGjsLmDRuRn5cnMmP9sfegvpWUlsnojIA2+6COU9ep83wWMw+WM0fBnGLleW9yN+KZmF55eTkCg0Kk89ZXGlwHr6qsxPFjx6TcV61YgZs3buBhR0e/6iuZRrbpeQx6kFKBnj97joiwcIwdNRp3UlJEsVhQS75dhI3r16O+rs4mmXEU5uvjg9/++jfy2rp5i4zMbPqzDhcpkCqQcmRu9jHQQUodJ3CvX7uGhfMX4E+//wOcTp9GbW2tQwBQIB3YICXcCd2c7BxsWr8BH//lr9i7ew/ycnMdgr8CaQ8tDIVNhbh18yYmjhuHqIhINNTXIzY6RsCafPu2KGEPf33rKxZYTXU1li9din//P/8mryGffiYL2/zNjEOBVIFUgfTtWSOOUtnBDfD3x+gRI0WnY6KjwVkrwtWRQ4F04IKU7Tp1gdO3UydPxshhw+B2+TIaGhpkKtiREbQCaS9awx5rdlYW5sycBY8r7shIT8fWTZuwe8cOdLS329Rr5bTR7Vu38NnHn+Bf/+mf5fXrX/0Kp0+elDW7XpLW9WsFUgVSBdJXIGVDSVBWVlTg9Emuiw3DimXLkJSYiM7Hj/s1pdddWRVIBx5IWe4//fgjGhsa4OnugSkTJ8osRHBQMFpaWmS7S/dytPezAmkvEqPwaWS0fOkynDx+HBcvXMDsGTNw7+5dmwXf0tyMs05O+N///C/4p7//B3nxnHAuLCjoJWV9v1YgVSBVIP1Z1su5Rk97hQ1r1+GLzz6XqT2uh3K9TK9DgXRggZTtOMuksaERh/YfAO1UFsydh5TkZFlH1qvcFUitSJLrJXt27cKqFSulB8O5dI4y+zJCkB7QTz+J0cLUSZMFoP/4v/4efP3LP/6TjFD9fX3FEMJK8rr8pECqQKpA+jOedD7BrZu3MGXiJIwaPgJnTp1Ga2urQJT6qtehQDqwQMrOU2FBIZYuWiwQ3b51K6oqq2SKl1P8eh0KpFYk2dzUhAvnzuHLz4dg1vQZSL13z6YpXRYQGy9vT08xMNIgyneOTP/rP/4TmzZslHWavqBs5fFs+kmBVIH0wwVprkzlNjc3w9vLCzOmTsPsGTMRGBCApsZGm6zubVIyi4sUSAcGSNmucuthVGSkjEAnjhuPyy4uqK6qks6T3u2uAqmFEnQ/5T6w4KAg/OWPf8I5p7PoemKb9SPXYerq6mTfKKdyLUHKc66XsleclZmJH14aa6KuQKpA+iGClFsRUlPTxZDk2JEjsh46Z9Ys6QxzW4qeo1DLdkOB9F2DNBhNTc0ySPHx8pLti9x5ER0VJeuheo5CLctdgdRSGt3OuTh9+ZILvpk3H0WFhX1O6Wp/73ryBLExMTKFyxFod5Dy8x9/93scOXQIvNbIQ4FUgfRDBCn3Uvp4+2Dd6jWgpTy3nZWWlBoyGrHUXwXSdwfSsvJyBAQGIS01DYcPHpStLSuWLpPOE3XAKIiy/BVILbXg9TmH/dzQzm0u9HLi6e6Ox48e93DlL79iYd1vaREvKb/+1X+JodF//+ev8Kt//w/85//9d/CcI1J+5gZwGjQZuRVGgVSB9EMCKXWJI85TJ09h3Jixsr3F5eIl2YZGoyKjRqJaS6BA+u5ASv+6339/QAY+I4cNB2ciaEzGKV69p3K18tbeFUg1SQDSY+H+stqaWuRkZ2Pnd9vBHg33kNoKO3oyKi4uxqTx4/GH3/4OX33xJXbt2Ik1q1aDhcutLxPGjsOf//AH/PVPf4aPl7esp1o8hq6nCqQKpB8KSLmk0nq/VRypcH/oyOHD4efrJ55ubNVfR5VPgdR8kHLwQq9zoSEhGDFsuEzjO5+/gMbGRtO8qSmQvtYc9lTZ4HBxmqNQLk5v2bgJuTk5dvVmuKmbBTp0yBDs3L4dd+/clUI+dOAA5s+ZK756uY+NRkzjx4wRE/yaGuNcyCmQKpB+KCCtq63DyeMn8Lvf/A+GffU1AgMCxdjI6NGIJXwVSM0HKSHq6eEhgxYOVoICA2UUauRUrmWZ81yB1EIiFDwdVZeWlKCkuBjcB2rvdBB9Nbq7XRG/jdzsy0aMUwuHDhzE/LnzxGqM3xG4TIPQLSwsNGzKSYFUgfR9Bik7wJwFKi0txfo1a2WLw5ZNm+HkdFbCFnIkavR0rkUTIpbAyteuOb52f6BRZ20tdm7fgeFffY1pk6fg0MHDqKmusepj2bK89DpXINVLkq/v8/wZoyB0vvHbSEXWQMqNwNXV1W/9xn2pbAiMUnYFUgXS9xWkHGnSy9iN69cxd9ZsmUXi0gl1jGEQGS+YnWOjdKunpkONSI0fkbI8aaTJ5bdNGzZg3Ogx2L51G8JCwyR04P3W1p6KxtDvFEgNFS8Emj2B1OBk39xegVSB9H0DKRtSApJ65e3phfFjxspINCQo+I2/XFuiv7xREh1PFEiNBSk7Txys0Dfy3Fmz8Pknn8rOCvo0Ly0rQ2BQsE3RX3QscrmVAqneEu12v95GpN0uM+yjAqkC6fsGUhoV0dE4PY3RmO/bb75BQUEBHj96JFOr/F2B9P0Lo8bO06OHD+Hqcln24XMkmpSQKODkLgtuf7E1jJreDa4Cqd4S7XY/BVIVj1TFI9Un0pFM6XV1iSOTbVu2YvSIEWIRn52VLcsjHK3wGgXS9yseqVamxUVFYmtCZzYb1q2T4OuMu8o2li974pF2a6Yd/qhA6rAIrd9AgVSBVIHUcZByNMKRNSO1cD2UbjudL1yQ+KGWVrlao6tGpO/HiJRlS4NPOsRZvWKlONfYtWOHGGhaBhtQILXOId1+pZVsRGQUCguLpPei2437uJECqQKpAqljIGVjSgfzfj6+shd78oSJYu3ObQ9curA8FEgbQa9OHKl1l42lnIw4Z1uXmKjvGinzkRAfjzEjR4pR0RVXN7Tevy/7Q1nW2qFAqknC4HcF0ig0NDYaLOVf3p5WyRkZWUjPyDRtc7T2FGyAS0vVGulgXSNlQ8kGkq796KWGnsDWrFqFWzdvii9VjlK7Hwqk7wdIWbbcPnj50iWw48Q9+BFh4WAgEXYQLCHKOqBA2l0TDPqsQKpA2l35DKpqclsqNjsRoWHhUCNS+0ek7ATRgITOS7geRqMi+s0tKSmR9dDeyk6BdHCDlOXHKdv6+nrs2r5DZiAWL/wWOdk50nnqTYcVSHvTCJ2/VyBVIO1NCXWuanI7BdIa6USwM0FZ2Htwa8u1xCRMGj9BjIrOOjmJdWZPoxHLeyuQDm6QsnwzMzLFNSuDr+/bvQcV5RUym8XOVW+HAmlvktH5ewVSBVIFUp2VysrtOArnaNxekLIhpXcxjytXMHXSZHlFhofLNB8by77KUIF0cIJUjMk4gxMcLMZk7ED5evuIlyIG57YGUVZDBVIryqjnT0aAlIX/oK1N3P5xCqqyshLVVdVg+DXNtSALWDlkUGuketZlW+7FadF799KQknLX0KAIvT2LvSAlAOnhq7a2FiePH5cpvYXzF0hIrM7Hj/tsSLXnUCAdfCBl56mttfWNc43pU6YiIjxcnGuw/bTlUCC1RUo6XKM3SDXFt7QkpK/HOTNnic/PstJS6SUpkCpjI7VG2ndjyBEHXb5tXLcev/31b7B7xw7xRc3vqWu2Hgqkgw+klRWVOLj/AP70+z/IFpd7d+/1aFBkrQ4okFqTjo6/6Q1SKvjTri54eXriu61bUVhQIIYRdFXV1NioRqSvy05Z7SpjI2ujCurRk85OJMTFY/aMmWKZ6+Xhgfq6un5ZeSuQDg6Qspw4ZZuVmYXlS5bi6y+H4sihwxJ8gG2GPZ0nNjUKpDrC0tqt9AYpp3VZ4K4uLjIV9ezp0x4LX41I1YhUjUh/OSJlQ8kpvebmZvj7+YnDeYI0KCBQrDP5W38OBdKBD1J2ntgex8fFSedp6qRJ4i/XkfihHxxIo6JiJD4nhWnmq7WtDeERkSgoKHwTo9CR9BnCh0HAuZ7jdPoMnnQ+kVEoGwAWqnZvuit7/OixTF1wL1RVZZUu6Wv37+uda7V0XxUWHon6+oY3z9XX//T6/XFnJ9LTM5CWlvHGjZte9+7rPiyHkpJSxMUlSO+XnZ++/qPX76wH3EzOKCRVVVWmpas9Pzt5d++mIjk5BZ2dT0xPn3kOCQl74xhAey7tnfLhFofDBw6C1plcD+X+UK7tatf0551lzJFOdHQssrNzBNZmljv1rbi4RBwTdDx86FBe+pN/6jh1nTrPZ+nPPfr7n5cvf0BCQiJyc/PA857kTp189OgRXC5exKjhwzF21GhEhkc4zATWJ+4ZDwgMAqO/9DcP/f0fnYOQbXoef2ftZt4+fiivqEBLy31TX+XlFfDy9sGt28lobGxyOG32nioqKsDYh5yWYGMwdMgXWLJoEcLDwqSRaG5ukbTYqDBm3tTJU5CRniGR283KP50wVFVVw9PLB3n5BQ7n297nrqmplUaFCsaG097/9//6FhntpKWlIygoRDoRLI/+38+++trY1CT7Rz08vZCVnWNaulr+amvrEBcXL87ba2prTU+fefbw8BIZUBbac/Gd9SA9LQ0LF3yDT/76EVYuX4HU1FRUVlWhqalZLHQtr7fnnGVMmPj5B+LWrdtoampCc4t55U59u3P3HkJCw0Xv7Hl2Pa6ljlPXqfN8Fj3uads9XrV1wcGhuJ2cIu1ed31jWRQXFYsNyacffYzZM2fhxo2bMp3b0ODYs7KO3b17D65u7uK83rZntk+nrd2TTCPb9DysgvTc+YtSycPCImDmi5XrxMnTcHPzQHBIqMNpU1H8A4Jw7OhxbN28Fdu2bJP3VStWSoDZHdt3wNfXH6xYPj5+WDBvAcaMGo1Lly7Ld2blPYjp+/rj5Kkz8PT0djjf9j63n18AnJ1dcPGSCwIDg01NPzQ0HC6X3XD6zFlQDtyOYe/z9/f64JAwMO/HT5yC2xUP09LVnpd188KFizh33hn+/oGmp888M++UAWURGhYho3NX1yvYsnmrhD7jaGT92nU4f95Z6gbLS3v+/r4zHercyVNOcHa+JKNiftff+9n7P9Yz5v2M0znRO3v/7+j11HHqOnWez+Lo/ez5P9tEp7Pn4XzRBcHBLPNX5clyJWT27NmHKRMnS8i75UuX4dSp0/B9XT/sSaena1nH3N09cez4yXfTzvkHgmzT87AKUip4RUUl7t9vNfVVVlYOXz9/2Q7AXq8x6d9Hbk4ujh46jFXLVyAvN0962OwdckQ6Y+o0ZGRkSi/ZmPR/KVOOvjkipmLl5xcYlO9fpqvlr6amBknXriMx6ZqMFLTvjX9nb7MFqWnp0pgy7BZ7lMan+0oWrGNcG+UsSFZ2tmnpavnjiDQ+PhGxsXHgrID2vVnvzDPzThmwDjY2NKKsrAzHjh4TL0Ujhw1HSHCwbBnT85lYxhzdBAQG49atZHBUdP++eeXOvN67lyrTq5WVVabLnTpOXafO81n0lK31e92Xto7wvH075fXMwqvv2P5dcbuC0SNGidN5dzc3cTqvpz5S31LT0gSmnOK1/qy9t1f9/R+ZRrbpeVgFaWRkNNrbO2T+nHPoZr3o9DosPEJgwrUDo9Ll9EVwUJBMXxAiL1+8lDUBmnfPmzMXNPV+8eKlYel3z9fz51wjfSh5r6uvNy1d7Tm4TpiWniFA4/qX9r0Z71yP4XrV1bgEPHv2XNauzUiXaXBt/NGjxwgJCQUbVLPS1dLhuiinGNmocR+z9r1Z78wzZ34oA/r65TLI/n37ZAnkm3nzkZmRIda6XNvS85lY5pZrpCwHPe/f172ob0XFJUhITJJ1v76u1/t36jjbOeo8n0Xv+1u7H2XNzltOTp60cSxbLoE5n78gAbhnTZ+O+Lh4POzokPVba/ey9zemXVJaioCAIOk42ft/R68n08g2PQ+rIKURABfCzT6MsNplA1FXV4cHbQ8k4CydM2RlZsp2mNMnT4qHFiq2csigHDKYXd8HgkMGTrGyA5ucnIzNGzZi+FdfY/++71GQX/DG8ExvuSir3XdvtUtjI3ZmGGx9/959GD1iJDZv3IQ7KSkCeEJL74PtrIpHqrdUe7if3iBlb4vhfHbv3IlD+w/Ax8sbl5wvYumixVgwd57sK2UvSYFUbX/5ELe/0MuXl5cPEhMSMX3qNDHIO3vGSUYo1B2jDgXSdwtSjkhTU9PEX+7ibxdJ52nv7j2yx55bBI06FEiNkmy3++oNUppJ06UZTfbPnDqFndu3S287wD8AXI9jr4tKrUCqQPohgjQvLx9rVq/FH3/3ezG+oyU7R8nUB+qFUYcC6bsFaVRUNE6fOi2jUBqTubpclj2jHFQYWe4KpEZpVLf76g1SVgrCktO73EPU1tYmU7n8zELVDgVSBdIPBaTUCdofVFVWykwNt4MtW7IEybdvi44Y2ZBq+sY02GjHxFyVtTqtQ6v9bvQ7R9slpWVISrouthFGp9f9/tzy8i4CezPftA/ZvWu3bAPknnk6XKChl9GdJ8pAgbR7TTDos94gtfUxFUgVSD8EkHKGhk5J8nJzwS1gQz79DN/MW4CK8nJTneYrkJoLUsqb66EMNsD1b3ae5s+Zg4z0dHHGwXphxqFAaoaUAZleiIiMQmFh0VsjRqOTVyBVIH3fQao1pnFXr2L2jBkC0e+2boOLy2VpTKkDZh0KpOaClCN+OplfsXSZTOPPmjET15KuiUcpsyDKuqVAapKGqRGpikfKRtasg4pNN33cV/c+g1SM7lpbccnZWZwszJo+AwnxCUhPTxd3bdyGo0BqVq2DeDMyY2qXkORuBIY74/54rof6envD08NL9sqzzM3WN2W1a0I9UyBVIDVbsd9nkFKWNLbj/tBTJ06KccmyxUtw6+at1/tGK/sV2NvRpoDPpdZIo974OHZUnt3/T/my81RfV4/LLi4YNXwEuC84NiZG7ERiY6+ChmYKpN0lZ//nD2Ifqa1iYYVS+0jVPlJb64te1xm5j1RrTDMzM7FuzRp8/Je/glscSktLxVk488BROEfj7EyoEalepdr3fYw0NmK5syzpaGbPzl3iZGHlsuW4d++edKr4W2LiNQXSvovJpisUSC3EpECq1kjfp6ldTukxege3fU2dNBnDv/pKQgnSHSMtdtnY8lAgff+sdtk5o0eq6VOmyP7QE8eOobGhQWYgWC8USGMtWn7HTxVILWSoQKpA+j6AVBuN1NXWwtPdQ+KHLpg7F2GhoWLIx3pueSiQvj8gJSTpvY3roXNnzcaUiZPgdtlVLHUt94cqkCqQWrYBup4rkCqQDnaQEqIcbXLUeeD77yV6x9xZs5B6L7XXrS0KpIMfpFrnifYl55ycMG70aIFoYnyCdJ602QetwVQgVSDV6oLu7wqkCqSDHaSc0svOysK82XPE1d+eXbvEexeNjTha6elQIB38IGXbVV1VhR3bvpP9oatWMKJVrgQb4G/dDwVSBdLudUK3zwqkCqSDFaSsu4wiEhUZiYULFohl7uVLLqiprhbLze4jEkulUSAdvCBl54idp5vXb0g4SG5toWV2SXEx6C+3t86TAqkCqWUboOu5AqkC6aAD6estJIzc4nHFXQA6cfx4JMTHo6O9vdeG1FJxFEgHJ0i19orhzqZPmSozEFdc3dDc1CydJ8sy7n6uQKpA2r1O6PZZq5iHDhyUqDDV1dWmbgfgni/GBOUmbZrGm31w+0NGhtr+YrbcHdn+whEHXfsxhu5Hf/4LVixbhtR792SdtLfRSPf8KZAOTpAyfihnHT796CPQX+71pGs2BxtQIFUg7d4O6PZZgVSBdLCMSGVKr6tL4kauXrkSY0aOwpFDh1BUWChGRdamcrsrjALp4AEpy5XGZGWlpdi1Y6c4Wdi6aTPS09IlzrKt5a5AqkDavR3Q7bMCqQLpYAAp6ymjGF2/dg2zpk+X6dyzTk4SvYNbHOw9FEgHB0jZeaLDmKzMTPFQRE9Fhw8eRG1NjYxE7Sl3BVIFUnvqi13XKpAqkA50kHLE0dbaiiuurvjqiy8lfigNjBgS0Nap3O5KoUA68EHKcqfldWhICCZPmChlzz3CD9ra+lXuCqQKpN3bAd0+K5AqkA5kkD5/9lyscLmlZfSIEVi9YqV4r+G6en8hSuVRIB3YIKXtBPcFHz18BONGj5HRaMrtZOlQ8bf+HAqkCqT9qTc2/UeBVIF0IIKUoxHCki7fNqxbL1O5u7bvQHlZGV48f/7G1Z9NlbyHixRIByZItVFoUVER9u7ZgxFfD8OGdeuQlvrKuQbDovX3UCBVIO1v3fnF/1hR+dIOBVIF0oEGUo40X754gZioaMyeMVOcztPlG0coeh0KpAMPpGyXuN6dkpwMRur59KOPcezwEek8OQJQrc4okCqQanWh3++spKxI3LBsubakQKpAOpBAyvrI/aFurq4yGqHfVDqgf9jxsM99gvYohwLpwAIpO08MNhAeFiau/uhkIdDfH/dbWvBchxkI1g0FUgVSe9qIX1yr9fToToubl8+fPSvTZhpcVRg1tY/0F5XG4C+67yNlQ8op2+KiYlkXo1ERQ6DdvXNHrDP1GJFYZkmBdGCAVGuDuH/9kvNFCb6+eOFCXI2J6THYgGUZ2nuuQKpAam+deet6NkKPHj6Eu9sVCS01e8YM2TbAxkuNSNWI9F2PSB8/7hRYFuTnY+Xy5eI3dffOXSgvL9d1FGqpFAqk7x6kL168lP2hhOiO7175y12+ZKn4TX7a1WVZXLqcK5AqkDpUkR4/eiRGG6uWr8DWzVuwYN48tN6/L1aPCqQKpO8SpMkpd1BfX4/YmBjZaD9+zBi4u7lJx88yBJZDCtDDnxVI3z1I6Sc5Iz0d7NjTqOjo4cMSP9RasIEeitLmrxRIFUhtriyWF3LahB5BSktK8N2WrXC5eBGuLpfFwTfXodSIFFAuAsNlK4hlvTHjvKvrKZKTUxAYGIzTJ09h6qRJEr0lMjxC1khZN2FhFKf3MymQviOQNjQiJDQMHIX6eHmLMRkDsPv6+IDu/7i1he2WEYcCqYkgDQ0NR3Nzi2wEZs/IrFdjYxOCgkOQmZUtnjwcTffp02foetIlvX3nCxewbs1alJaWwsfbG/PmzAEDINPoiOujhOr3e/dh9sxZKC4u0SV9W5+f03r377dK3isrq0yTt/Z8bW0PcOfOXaSk3JFIItr3Rr9L+XR1IT+/AFHRsWJowXVDo9PV7t/55Ana2toQEBCEkpJS0yCe+IsAACAASURBVNJl+swnyzwiIhLTpkzDX//0Z8yZNRv37t5Fa2sbKBvtOY16Z56Zd8qAsjAqne73Zd4fPXqM8PBIpKVnSEfOzHKnvuXm5iE2Nk6Wd7o/n5Gfnz57hvLyCri6XhHXjkOHDMGEseNkNqKxoVHaI6PSZ51iWxcTc1V8a3d2PpF6aFR63e/LOkZd9/HxQ0NDo2n1TXsOMo1s0/P4O2s3O37iFDw8veHnH2jqy93dCwcPHcX5Cxfh6+vveNp+AfDy8sHePfswY9p0HDp0BG5u7ti8cTNGDhsOFxdX+PoFwMfHH+7unpg3Zy6GffU1zp49L9+ZlX8fX394enrj0OGjomBmpaulQxmdcTqPM07n4O3j57jcba03foHw8wuA88VLOHrshCiYH7+z9f8OXsc65unlgwMHj+CSi6tp6TKP3t6+OH78BKZOnoLf/vo3GDtmLI4ePQ5PTx/4+gaY8izMM/NOGeiib7aWh1+g6NfhI8dx9tyFV/k1sdypb87OLjh2/KS57ZxfoLQ3x46dwLgx4/DrX/0XRg4fif37D8LDw+tVm2OkHJi+r7/k+9x551dlbmR63eoD03a+6IL9Bw7hirunKXXcsi0h08g2PQ+rIGWC6ekZKCoqNvV1714aXN3ccfVqvPRcHE2feQgKDJZR5pnTp3Hjxk1cv34DRw4fwfixY8EwRNnZOcjLy0dGRiY2rt/wKrp8YpIu6dv6/Hl5BZI+8377doqpMuczZmZmIzwiUkYIObl5pqZfWFiEhIREeHn7Ijc3H/xsq9wcvS4/vxCZmVlwueyG69dvmpIu6xpH/wf2H8DQL76UfYJ7d+/BzRs3ZZRUaKLOMc/MO2VAWTgqT1v/zzKmHAiPqOgYFBQUwsx8U9/iExJBoKanZ5qSb+aRbYzzBWeMHjEKn338CY4dOYprSdeQlZ1tWv7zC16NCKNjrkobZ7a+JSYm4eLFy7h7L9UUuVvWSfKAbNPzsArS6OhYPHz4SM/0bLrXgwcPEBEZJY0p5/IdPdrb23H65EnMmTkLJ44dg+tlVzifv4A1q1Zj9MiR4HRvcXGxbIBW21/U9hdH61tf/+dafXNzM/x8fcWoiLMie3fvBRsXrlObfag1UnPWSNmWtbNtCw+XrS3Dhn6FdWvXoaG+XqY3zSx3tUZq4hrp+wJSuleLiojE8aPHcPjgIYmYsH/fPiycPx9ffj4Ehw4cQE52thgjKZAqkBrZoNF4pKy0DPv27MUff/d78Zd7+9YtJCffkRfX6s0+FEiNBynLnd6ozjk54YvPPhfDoituV2RJg4OV/vrM7W9dUSBVILW77vzthx+kp08T8472DtncTKs4Lw9PzJoxA5UVFeIxhJVZgVSB1O4KZsMf2JA+6exEbk6OuHxjCKwjhw6Ly7e21jbcvZsqRl4KpMZYqfZURNT3ktIyJCUZC1IGGyguKsL6NWtlBmL71m3gPmFON4aGhYvBlQJpTyVkzHfsuHCQqOfxQUztdhcYGzV6jrmWmCSbnxnbkd+xl6ZAqkDavb448pn1ik5AGPosLvaqhMCaNH4CXC9fBgHKBpSWqrQLSEm5K9aajqTXn/+qEakxIGXZ09UfLbDpXIHB1xk/lM416OqvvqEBERFR4llNgbQ/Nbd//1Eg7Z/cevzXTz/+CK6dVlVWgiNWHgqkyiEDoaLXoXXO2JhecqZxyUh5xV29Kh02LR0F0qvIycmTDgdlZtZh5IiUe39ZrgH+/mDHiW4euT+Uzl+0o6GxUYG0rU0Th2nvCqQ6ilobKXC0oCmvAqkCqZ4g5aijqrIKm9ZvwLChQ7F29WoZjdCgyNJfrgLp+wVStiPcj37y+HHQoGj6lKm4k5ICznxZjjwVSENk77KOzbpNt1IgtUlM/b9IgVSBVA+QEpJcIuCU3qb162Wv8sH9+2WdjA2peCqyqKYKpO8HSFmu7DzlZOdg146dGPH119i2ZQuys7Nlyt6y88TiVyBVILVoBvQ/1Xv7i61PqECqQOooSNlY0ko8OioK0yZPEb+pNGpraW7+BUC1eqlAOvhBSojScw795TJiC3cD0JiMS0eWo1CtzPmuQKpAalkfdD9XII0SJdNdsH3cUPnadczXLhvTpsZGXHF1lTWxWdNnICE+Xkan7KT1diiQDn6Qtj9oR2hIiETrYdzY8NDQPoMNKJAqkPbWJujyvQKpAqm2bq1LherjJoQcOxHcitCfEalM6T17hrzcXBz4/nswEPOmDRuQmpoqEO0rLwqkgxOkLNcfXv6Auro6OJ0+g4njxmHJokVIjE/Ag7a2VzMQVoynFEgVSPtomhz7WYFUgbQv+DhWw97+tyMg5VQu94fm5eZh6aLFMiLh+lhNTY04+Hg7pZ4/KZAOPpCyfj6n4/myMmxYuw7Dv/oaG9etR0lxiQTI6Lmk3/5WgVSB9O0aofMnBVIF0kEB0p+Bhx0PERkRIXsEx40ejStubmKdSTjbmgcF0sEFUpYr3TzSI9U38155R6OFLmPJMm4sZyhsORRIFUhtqSf9vkaBVIHUVgj1u5JZ/LE/I1LNX+75s+fEycLcWbNxNTZWvGZxlGrP8yuQDh6Qsq7QX66nhwe4Bj5z+nSEBAeDoc/sDb6uQKpAatEM6X+qQKpAag+IHK2B9oCUz0XwVVZWYs+uXWJUxCnd/Lx8PHv61C6Aas+tQDo4QKp1ni6cOydbW2bPmIlrSUnofPz4rX3BWrn29a5AqkDaVx1x6HcFUgXSgQhSPhNHm9xcv2zJEvzuN/8jQRCqqqpkOq+/z6xAOvBByrKlf9wtmzbjL3/8E7Zs2oT8vDzxitbfclcgVSB1CJR9/VmBVIG0v41TX3Wrp99tGZHKlF57O0KCgsVTzaTx48X9G4MfcKTiyKFAOnBBynpIi+5bN25gwdx5si+YEVzYeWK5OVJPFUgVSB1pN/r8rwKpAqkjDVSfFazbBdZAyufg2he3ONCQiLFD582eg+jIKGlgOUJ19FAgHXggZbmzbO+3tCA8NAwTx43H1EmTJYYs3f/15mTBnrqgQKpAak99sftaBVIF0oEAUg2i9E6z87vtEkdy9YqVyMrMFLjaXbF7+YMC6cADKTtXbIdojUuH83SycOP6dV2j8yiQKpD20iTo87UCqQLpQAAp/eWmp6Vh3uzZGDlsGI4dOYKG+gZxBafn8ymQDiyQ0l8u94fSiOzrL4eKv9yKigrZL6zHDITWSiqQKpBqdcGQdwVSBVI9QdVXJbWc2q2qqpZwevfv30dUZCQWzJ2LKRMnws3VFVwPZUOq97MpkA4MkLJs2XmiJe6yxYsl5J3T6dNiod1TsIG+6lVfvyuQKpD2VUcc+l2BVIFUb1hZq5AaSENCw1BaWiYBty+cOy8NKdfF2LDSEb1RhwLpuwVpYtI1iU3MuLGB/v6yL5huHrk/9H7LfZsdLNhbPxRIFUjtrTN2Xa9AqkBqNkg5EvEPCER8XDx2bd+BoUOGYNXyFSgoKJCpXD2n9LorgwLpOwRpSSkSEpJQkF8g66GfffwJFi/8Fnfv3BVjMnayjDoUSBVIjapbcl+jQMrGmRaYXV1dYrre3RMJlYYN6qEDB8XUvbr61TSfoZm1uDmnjzjyiYhQIDUTpKwHtMQ8cOAgZs+cJSPRY0eOoqK8XLa2GP0sCqTvBqQs9/z8Qpx1Ood1a9aCLh537diBrKwsm4INWKhuv04VSBVI+1VxbP2T3iBlQ0hIceqGRgSMFRkWGoaMjAwBl7bupUD64cUjZb1ob29HXOxV2SM4dMgX8HB3R1tbW7+81dhaxy2vUyA1H6TUebYHsTGxGD1ilFhknzx+Ao0NDQ7vC7YsW2vnCqQKpNbqh8O/6Q1S9jybm5txcP9+zJ8zF2tXrQK3MdBX5ppVq1BbUysGJgqkHxZI2cHi/tALZ8/hj7/7PcaMGo2I8AjDp3K7K4gCqckg/Rlg/NCggECJ2jJqxEj4+frhYUeHtANGz0Bo5a9AqkCq1QVD3vUGqWaNd/3aNWRmZKKhvl5e8VfjZAqX3mrYmCmQfhggZUP5tKsLRYWF2Ll9h0zlrli2HIcPH0FxcYnuVrl9KYkCqXkgpReqmupqHDl0GKOGjxDDIqczZ9HQ0GCIRba1slcgVSC1Vj8c/k1vkPKB2Hhavn54+RKlJSVYs3IVPN09ZE1EgfT9BinL/6cff8LjR4+RnpYusxPDhn6FfXv2oLy8HH7+Af0K7O1ohVcgNR6k0nl6+lTKedOGjeJkgZ2nsLBwREXF4OHDR44Wo93/VyBVILW70tjzByNAapk+gck9gd6eXpgzcxZS790TIyQF0vcbpIwTSUOz4MAg2RvK9VBPD0+0tLRIRyo0NFyB1EArVUsd5DnhxmWXmBhjQcp0qNuJCQlguLuP/vxnnD3jhJqaWhQVFYPbX7heavahQKpAamidMwKkVKYnnZ0IDQ6RbQ1cK6XnkrDQUFEiTv8qkL6/IOWUHgMvnzh2HONGj8HC+Qtw88YNdLR3gJ5s6Jg8NEyBlDpg1mEGSJkfrody1olu/viKCAsTmwmWeUlJKZKSriuQ/vyzWcUu7SxngAKDPhCQ+voFSI+trq4eZr7y8wvg5e2DGzdvyQhBj7Rra+tQXFSMwIBA7N65GxvWrRdjo4ULvpEN95WVVZIW18i+27pNInxwL1l1dY1peadXHabPvGdmZpmWribfktIyxMUnIC4uARUVlaamz/JJTk5BYGAwWBb8rD2XI+81tbUoKytDamoq9u/bhyGffoZpU6YiJCQE5RUV4O8sYzaoHh5euJeapku69jxzWVm5jMoio2JQWlZmevrMM/NOGZhZ31nGlVVVYDuTlHRNRoi1dfqUu9y7skpsIo4fOyZWuZMmTISvr6+0acwn9e12cgqCg0NRVFxsutyp49R16jyfxZ464+i1zH9QUAiuXbshZa6XvtnyXEw7JeUO3NzckZeXb2q++XychWCd0/P4O2s3O3HiFHx8/BAUHGrqy8vbF4ePHMPFiy4ICAw2IO0QqUQXL17C8qXLMGPaDFy+7IaAgCCp2AvmzRdrvgsXLsI/IMiA9HuWJ9P38fXD4SPH4e7uaVq6Wvmycp0754yz55zh7x9oXvpBIdI7veTihuMnTr2SeVCIg+mHCJS9vX2xdcs2fPbJp/jT7/+AjevXiwKzNxwU/CoN1jFfX38cOnwUrm7uDqbbc9lqMu7p3c8vAE5O53HmzDlR8J6uMfI75pl5pwyM0bdeZBIUIjp39NgJUNfYiWLj7mheWbasyzQeGzb0a4kbu+TbRXB2vijpafenvl1yccWJk6ffSTtHHaeuU+f5LNpzGf5OuQcG48SJ03B2ft3G6iB3W5+babu4uOLAwSPw8vIxL9+vOUamkW16HlZByp5aY2OTTHtxGsSsV319AwKDgpGekSlGAEalW1FeAY8r7lizarWMWmhw0NLcgn179mLW9JkoLCg0NP3u+Xr48CGam1ukkpeXV5gmb+057t9vRXLyHdy+nYIHD9pNS7/zyRM8ftyJ3Nw8REZGo729Q9YstefqzzsdW9RU18Df1w80KBr+1dfw8/GRKT2uh1nek59b7t8XYyP2Vi1/M+O8tbUNN27ckilGOoYwI03LNJhnGlpRBt1lY3md3ud0ftLR0QGuTXNU/OjRY3R2Ot7OsM2in2Q6nGe5X7zgLFa5TMvy/tS37OwcRMfEoqm52XS5U8cJFeo8n0Vv+fZ2P+rbw0ePxMgqLS1D2jiWRW/X6/0961hubi44YOIIUe/793U/1g+yTc/DKkijo2PfiTWb3mukso+0qQmZGRmorKhES3Mz6uvqcPP6DWxYu04MD7hWptZIB/8aKQ2KWN4MfXb50iVZD/12wQIxNKEC8/fuB8udyqfWSJ+IDnSXj1Gf9Vwj1QyK2BEO8PPHzGnTZHkmwN9fOk+a0xXLvNAZB5cz1Brp30zd8kV9+6DWSN8XkLKRvHvnjuwZXbZkCTZt2CAOGWbPmIm1q1eLtyMqlQLp4AYpIfn82XPU19Vj+9ZtssVh5bLlyM/LE4Miy0bU8lyBtEY6EdQTysKsQy+Q8j7UX1riHzl0SIKvL5g3D/fu3kWnlWADCqTXZI2SZU4ZmnUwPQVSE6St94iUvdHnz56hrrYOSYmJCA4Kkqmfgvz8N/tHtR6t8rWbJVPqtGQ18yAEGXklPj4RL1687Jdi0yqbBmIzpk4Td38njh0Dw6HRYrenkaiWPwXSwQ1SzkAUFxVh3eo1+PLzIWIsWFZa2qeHKgVSBVKtDXD0/YOY2qWQtF7rs6dPZRqPm+CpSJY9MTaoCqSDD6RsSB+0tSEkKEicLEwcN172CDfZGD9UgXRwgpTlxrXwq7GxoDERy/3CuXOorqqyKdiAAqkCqaMA1f7/wYBUy7C1dwXSwTW1y04QR5tNTU3iL3fE18PA6frk28nSIbLsJPVV7mqNNFw6mNQBsw6WDztB/XHIQAjSeCgoMBDjx4wVN4/0ncsABJyBsuVQIFUgtaWe2HKNAqmFlBRIBw9I2QizwWQcScYP/csf/4TNGzciLy9PGmdrU7kWRS6nLHcF0sEDUpY9jcmOHzkqXoqWLl6M1Hup4i+7J6Oi7uWtfVYgVSDV6oKj7wqkFhJUIB0cIGVjSQtcrncvX7IUE8aOw+mTpyR+6LNnzyxK1LZTBdLBMbVLgD7teorsrCzZDzx6xAjs2bULebm5ds1AaLVCgVSBVKsLjr4rkFpIUIF0YIOUDSkbP66HxkTHvJnSo/s3gpXl159DgXRgg5TlzhkGBhtIvn0bUydNFmOy82fPytYWTu/351AgVSDtT73p6T8KpBZSUSAd2CDlSJRbHJzOnBHrTAYcuJaUJNaZbGz7eyiQDmyQEqJdT7ok4ProESNle0tIcIg4MXCk3BVIFUj722Z0/58CqYVEFEgHLki5hsn4oVwHZRzJLRs3yZQev7dnPdSiuN+cKpAOXJBytMn4obt37sLYUaMl4AT9JtPQiOXmyKFAqkDqSP2x/K8CqYU0FEgHHkg5CmWjSYcay5cskSm9g/sPSOPK8nJkRKIVvQLpwAOpjEK7upCbk4NtmzeLu7/t27aJc42+9gVr5drXuwKpAmlfdcTW3xVILSSlQDpwQPrTT6+schk/lG7eJo2fIJ6K/P38BKwWxebwqQLpwAIpO0c0GkuMj8e82bPBuLHO589LGDxHZx8sK4sCqQKpZX1w5FyB1EJ6CqQDB6QcdTTU14s1Lh2PMyAzR6XcgM9y0vNQIB04IOUMRFtbG7w8PGUKf/qUKYiNiZH9odxzqscMhFZ3FEgVSLW64Oi7AqmFBBVI3z1IY2PjxIgkOzsbe3fvkSk9rodmZ2bJKEXPEYlW9Aqk7x6kjMLCUWhpaSnOnDwl66Hc2nT71m2xyDai3BVIFUi1NsDRdwVSCwkqkL5bkDLAMUNqpdxOBp2OMwzW8aPHJFIPy8aoQ4H03YKUwTFS76WhoKAAa1etliDc2zZvEai+eN6/rS221BUFUgVSW+qJLdcokFpISYH03YCU03UccWRkZGDjhk0ShHvyhIkIDgx6NZX7gz5GRRZF/dapAum7BSljQ144f0Eca4wcNhyXnC+i1YZgA28VYj8+KJAqkPaj2vT4FwVSC7EokJoPUkKUkXkqKytx5OAhCcK9cP4CJMTFi1GRnmtiFkX91qkC6bsBKdfBGxsasGfXbpl9mDltOkJDQgSiXCs1uuwVSBVI32oIHPigQGohPAVSc0HKUSij8HBdjOugn3/yiUTxKCkusRo/1KLIdDlVIDUXpASkZkx24Pv9MpU7f86cV/FDOzsNB6hWaRRIFUi1uuDouwKphQQVSM0DKSFK45Lbt27h2wXfSGO6euUq+Pr64+nTZw47WbAo1j5PFUjNAykhytFmRno6Vq1YgT/+7veYPnU6EhMT8ezZc/z44099lpdeFyiQKpDqVZcUSC0kqUBqDki5jYEBt328vTFr+gwJxO3v64fk2ykSUqu/gb0titKuUwVSc0BKgD58+BDRUdFYuGCBxA89f/YcLl68hPT0DAGs0dO5lhVDgVSB1LI+OHKuQGohPQVSY0HKRvL58+dgwO3Lly7JutiUiZNw4/p1meKl1W58fCIUSC0qpQmn1dXGgpTlTmi1trbC19tH1sFZ7hFh4Xjw4AEiIqKQk5OnQGpCWWtJsK1LTFQg1eTh6LsCqYUEFUiNBSkbU4a82rJpE/76pz9j66bNKCkulkaWU72lpWUKpF1dFjXSnFOjQcqRaF1tLQ4fPIghn34mU/l3UlKk88S10v4E9tZDMmpEqkCqRz3iPRRILSSpQGoMSAlJ+stNSU7GN/PmY8zIUThz6rT4y+UIlSMWBdI0pKTcBV0imn0YCVIGFeB66PKly6TcaVxUWlIqgdQJWE7zK5A+ls6kmeWuRqSxuor7gwIpG2xWIPaC+eI5v9MOBVJ9QarJu7m5GWEhoRg3eoz4zPXz8RGwsiHVDgXS9wukLFt2nm7euCGdJ4Y/Y/zQ+rq6N3rH+qFAGiV7pTk6NvNQIFUg7Vd9o9JSubkmk5WZhfS0NNTX1b+1LqNAqi9I2TjQb+rxo0dlPXTa5Cm4dfOmTOl1L0QF0vcHpCzLRw8fwc3VVfzlsgMVExUtrv4sy12BtFHWh+k/WoHUsmYYe/7w4SPQm5aexwcxIhVAPu5EVGQkli5a/NpSdCpmTp+Oc05OeNLZKVOLCqT6gfRpVxcKCwqwbPESDP/qK3y3ZSuqKqsEomxoux8KpO8HSAmE+vp67NuzVzpPixd+i+ysLHT2EGxAgVSBlB1tsw8F0n5KnCPRR48ewfnCBXh6eCA/Nw+FhYVwuXQJM6ZORfLt23j5eqq3s7MThw4cxIK581BdXa17pBFrWWAjxN4prRgbGhutXWrIb7KelZGF9IzMfjtEYGeEWxw4pbdq+QqJH8oRaWVF5ZspvZ4eXoF0cIOUOkbnGmmpqdi0fgNGDR8uQQfobEPWwXvoPCmQKpB+ECCNioqRdQ42cma+WtvaEB4RiYKCQllD0SNtKjoVmrDi/fiZFqMcofp4eb1ap3j5Ax4/egwGjp4/Z66MoLiGo0f6ttyD67bsLYWFR6K+vsG0dLVne9zZKfv50tIy3kRa0X6z5Z2y5dQ5Y4aOHzNWIngwliiVhfK2dg8pj5JSxMUlSDn1db21e9n7m9aBCQkNQ1VVtdXntPfetlz/5EkX7t5NRXLyHXR2PjE9feaZedemGG15ZstrWFbshLHzxH3BjB967uxZcf+n6Zvl9do5//f8+QuZZmP0F177o4ltDfWNW664DYSdP+25zHqnjlPXqfN8FrPSZTqUdUJCEnJz8/Dy5Q996qeez8a0aaEfEBgsW6L0vLct9+LaPdmm52F1apcZra2tRUfHQ1NftCL0DwjEvdQ0aYT1Sb9DOgUUIl8P2tuRmpoqgYM5Sm1sbJK0OC1F35/0+5mbm6tj+n3LsLW1TabF/PwCRMH1yXff6WrpcBR88+Yt3LhxEy0tLXaUeYfEi5QQWKdO4aM//wWTJ05CVGQUGhoa0Nb24LXse3uWV//PysqWhoXOGtrbWU69Xa/v93y+hoZG+Pj6IS+/wLR0tfw1NTUjKem6bP1hPdS+N+udefbx8RMZvCore+Tbgeqqari6uODjv/xVOk8hwcGoqamRRrLDSjmyjFnWdFqfcueudMJe6ac96ff/WuobZ18iI6NRV1dvutwJceo62xw+i1nlTRmzc8uZL3bgeG62vmVmZsHD01s6rubl+1VdIdPINj0PqyC9eMkVEZHRSExMMvXF3rHT2fPw9fOXEYre6cfFxSMwMAh7du/B1MlTcOWKO65ejcfVuHgZCS9ZtBjjx46Dt4+vfKd3+r3dj8/AkfjZcxcQFBxqqsz5TJFR0XB394S7hxdiYq/alD5HkOHhkTjrdA4rl68Ao3fMmT0HZ844ISIiEgk21B1eE5+QCG8fPzg7X5KyYG+5Nznp/X1cfILk/cyZc/D3DzQtXS0fUdExcLvijsuuV6SnrH1v1jvzzLyz/CkLW9JNSEgEn9vV1Q1rV6+RqdzpU6bi8OEjCAoOkfLsq+xZxtS5c+edpc4x7b7+Y8uz2XoN9Y0gc77oInpn6//0uo46Tl2nzvNZ9LpvX/cRfYtPwMVLl+Hh4S1trNn6xoHSqdNOCAkJMy3fmlzINLJNz8MqSL29/VBUXCI9JvaazHoVFhbB08tbRkY1NbW6psuecnFxMfz9/CXmpbeXl6yFMm/8jaOq77Zuw9RJk3H37l35zqx8cyTOKQ/21Dg6MytdLZ2y8nJpSNm4VVZWWU2fPXjKi2vNoaGhGDNyND77+BNZXy4qKpKZDO2+fb3X1dejtq4OKSl3EBAQJL1U3r+v/+n1O+tYWVmZdCLS0tJNS1d7/vKKCtlLyZFReXmF6ekzz+xAUQa26FttbZ3oSXR0tGxp+vSjj7Hju+3Iy8tDVXW1zc/PMua0Mv0rX7t2HTW1tTIy1ORi9Dv17fbtFOm0lpSU2vzcej0XdZy6Tp3ns+h1377uQ32j7gYGBuP69ZtS5mbrW3JyinQc2db39bx6/06mkW16HlZBSsVub2+X+XOuZ5j1ut/airDwCJlm49qBnulyDY+OATh6cr9yRTbA00CGaTAtmu1zjXTe7DliIKN3+tbywjVcTnOEhUVIg2LtWiN+e/ToMdiopqamo6vrqVW5c52D07/+vr7i8m3C2PESP5RGXbLWZUd9ofz5H051sWdOZ/ZamRiRz+73lHJ/9AjBIaHSgej+u9GfaeB25849adQfP+60KncjnoWdJuadZddXfWc58XlpAU83f1989jkuOTujpblZytCecuO1LGuObLOycsQewp7/OyoL6ltRUbGsFbZ3dJgud8KLuk6d57M4mh9b/08Zs5zpjjMnJ1fOzZQ702bHxT8gSKb2bX1uva4j08g2PQ+rIOVeGy6Em32I/83IKLC3wgLWPghjDgAAIABJREFU4+AiNNcGbt28hbWrV4v17v2W+7LAr92faSmr3b6tdmmdyXWGk8ePi+PxJd8uEn+5bIgp5/4c/J9yETiwPRvR8I5+kp3Pn5cZG1q2R0dGSfxQAtbeQ1ntKqvdD8Jq930BKXsydL12984dLF28WDysNDc1Sw+c1oZab1CB1Po+UsKu68kTlJWWYvPGjeI3df3adaioqJDRBBvG/h4KpAN3+wvLlTpCw7Ejhw7LKJTB11Pv3ZPv+9t5UiBVIFUg7W+LacP/9B6REqL5+fnSi54+ZQounDsHt8uuuOLmBq6RJiYkCFQVSHsHKRtLTslQVvSX+8lfP8I5p7MyQulvQ2pZFRRIBy5IORKlJzDuC+Z66L7de1BRXmF1X7Bl2fZ2rkCqQKpA2pt26PC93iB9+eKl7Ak9fvQYjh4+Ig7TnU6fAV8Xzp1HaEiI7KFTIO0ZpJy2o79cD3d3WRebMXUaIsMj+j2l11MVUSAdeCBlmTzs6EBMdDRmz5iBcWPGwOPKFRmZcoTqyAwE64ACqQKpAmlPraFO3+kN0p9+/Akvnr+QUafsa+PettcvbsTmmh8hqkD6NkjZkFJuVVVVMh3+9ZdDZTTK+KE0EuHveh0KpAMHpAQcdYHroYwfOnbUaAm+HhsdI44LuFSix6FAqkCqQKqHJvVyD71B2ksyv/hagfRtkHLUUVxUjHVr1sh6KF2/FRfpZwBmWQAKpAMHpJyBaGpqwt7du/H5J59K/NDMjAxZD7UsM0fPFUgVSBVIHdUiK/9XIH2XvnYzxU0gG1KOPBmxhfFDuR7a3NQk66RsAPU+FEgHBkjpJjA3J0e2f434ehiOHDok+6w5a6PnDATrjwKpAqkCqd4tqcX9FEjfDUjp5/XO3XuIjIyCj5e3+E2dPHGiTO+1trY6vCZmUcS/OFUgfZcgrRZPX3V1dbL2/c28eTKd63LxEhrqGxw2KvpFYb/+QoFUgVSBtDft0OF7BVLzQcpG7WHHQ8TGXsW33yyUKT06peCWIY5GjD4USN8dSCsqKnH5sitOnTgp0Xro1etqDPeQPzS086RAqkCqQGpgy6pAai5I2aBxPZRTevT4xK0tG9auRXl5uUzl6j2l11PVUSA1H6QsdxoOpaWmYe6sOfjT7/+A1StWSj149vSVZ6ueykqv7xRIFUgVSPXSph7uo0BqHkhpWEKPT3FX48AgzAyBxaDMNdXV4mShh+Ix5CsFUnNBSoDSixfdZa5asVKCcDPqEYOxmzEDwUqkQKpAqkBqSHP66qYKpMaDlI0YIcqKHB4ahrGjRkljum/vPtChNLe3mHkokJoHUkKU7hzjr8bJvmA6WVizag0aGxtlBsKsclcgVSBVIDVQ2xRIjQcpG9PKykqcOHZc4kguW7wESYlJEoGFgb051WvmoUBqDkgpZwYboFevYUO/Eqts5wvO8PLyeeOUxKxyVyBVIFUgNVDbFEiNAykbUm5xyMnOxtZNmzF+zFjs3rETebl5aGm5j/T0TAl2rEBqYAXvdmtOpd67ZyxICS2mU1JcLPtDuaVpw9p14i83NydXgmvT7zT3Upt1KJAqkCqQGqhtCqT6g5SNFkehtMTkuhiDMNNT0dkzZ0B5swFlQ5qR0Xf0FyOKXo1IjQMpZctgA0WFRVi5bLk419i5fQeqKitlHZwxQUPDwqX8FUiNqN0937OhUYFUgbTnuqHLtwqk+oOUEOVI1NvTExPGjhMnC6GvY1ASsjwUSMMlwLIuldiOmxg5IiVEud4dHhaGyRMm4qsvvoSXh6d0nvgbDwaVViA1P1ykAmmI2GjYoSq6XMrQoIxspufxwcQjtUVo76uLQDakDHW2f9/3MpXLKB7cH9r5+LGMUjXZKJC+XyDVgg0w2tHEceMxf85cxMfFC0T5m3YokF4X4ytNHma9K5AqkBpa19SIVJ8RKUeh3OLAEHI7vtuOLz8fAvrL5RYHdhq0kahWmAqk7wdIOdJksIHS0lIc3H9AtjRxfyjXxXsKNqBAqkDavS3Q2gQj3tn2cI96YJACqRHyfXNPBVLHQUrFIEQT4uMxc/p0aUw5MmlpbvkFQDXBK5C+HyCloRiNxxjEfsinn2Hfnj2yHtrb+qcCqQKpAqnWCvbvXU3tWsjtfZjapUJwJMr4oX4+vhg9YqRM60WEh4uhkeWUnkXW5VSBdHCDlGXf3t6OyIgIjBo+ApPGT4C/rx/u379vNdiAAqkCqQJp99bQvs8KpBbyGuwgFcOSp09RWlKCM6dPi0ERvRXRSpeQ7OtQIB2cIGUj+OLFC9TX1cHN1RVTJk6U+KFRkZGyHtpXI6lAqkDaVx3pq+2w53c1tWuPtBy41sipXVYYAoejNs1qUXvUwQxS5uXVPsESrFm5StZDN2/cKGsR1kahWt75rkA6+ECqQbSivBzbt30nVrkrly9Hfl6ezd6pFEgVSBVILVtC+88/uBHpy5cvxbdsdVWVvFtWoMEKUkKU+0PpmYjWmSOHDcfFCxfEtJwQtcyjtSqiQDq4QMpyff7sGRh0e9HChfjis8/FuKimpsauYAMKpAqktrYR1toPW39TI1JbJeXgdUaMSAkb7qMsyM+H0+kzWDh/AeKuXn1rVDoYQUrDEgbc9vL0lPihdLQQ6B8Axg/96ccf7SoJBdLBA1J2kLiZPTQ4BPNmzwZDn7lddhV/uews2nMokCqQKpDaozG/vPaDGJGykhCSOTk52Lh+g7hG+3bBN7JJnVO82jGYQCqjkefPwdHHkUOHZEpv0TcLkZ6WJlN6/VEMBdKBD1KWKyHKjhLXQ4d/9bU4WoiNiZGp+e7LFVrdtvauQKpA2p/2wlqdsvabGpFak46OvxkxIiUwKysqZDsI3zetX4/I8PC3HBIMFpBqjWlGegY2rFuPTz/6CHt27UJ5WZk0sv1VCgXSgQ9S1tHi4mLs2rEDjNqybs0amWXpaX+orSqpQKpA2t82w9Y6ZnmdAqmlNAw8NwKkrCicBuXeSm4N2bJpk2wTGGwjUlbCB21tiI6KkvihUyZOwsULzqirrXM4BJYC6cAFqbY0kZKcIvFDx44ajaOHj4iFNo3MHGkIFUgVSB2pP/ai4IMDaUhImECHimrmi66zgoJDkJmZhcePO3VNm0Y5tbW1WL92HYICA9HZ+eTN/ZlW6/1WfL93H2bPmIniomLd07cmx0ePH8ueP3r8qKisevNc/E9X11OZumtuakZgQACGDhkiTue9vbxlmq/zyf/Ph7U0rP3W2taGlJS7SE6+g46Oh2+lb+1/jv7W9ZR560JeXj6iomJAX5hdXV2mpc/OVWtrG/wDAlFSUmpauprcHjxox81bt3Ht2g20tT34RfqUBddDOX07asRIMSriemh9Xb0u9ZN5Zt4pA8pCey6j35kvxkUNC4tAWlq66CLrudHpavenvuXk5iEmNk4iH2nfm/VOHaeuc58vn8WsdKlvjzs7xd9sRkam1CGz9Y267u3jh4aGBtPyrcmXAymyTc/D6hrpyVNnEBAQhPDwSFNffv6BOHrsBC5fdkNoaLiuaQcFh8LT0wvTp07Dzp275P5hr/MXEhoOf/9ALFzwDUZ8PRwuLq4ICQ3TNX1rsmT6AYHBkncvb9+30mXBe3v7YNOGjfjoz3/BJx99gt2790gDyIZIy4O1+/f1G5Xa2dkFF5xdEBxiXr757MyD2xUPnDzlJJU8LDzirfz39eyO/M46FhgYjCNHj8PD09u0dLVnDgoKwfnzzjh77gJ4rn3P99CwCAQGBsnWls8+/gR//sOfsGXzVnh7+4qjeT3KnXlm3ikDvfXNMi/dz1nGrNfHT5zCJZfLklc98tM9nd4+U99c3dxx6vRZ0bverjPqe+o42znqPJ/FqHS635cyZjmfOu0El9dtrNn65ubmjkOHj8LPP8C0fGtyINPINj0PqyBlj4E9torKSlNfmVnZ8PDwQmLSNZSWlumaNteXUlPTsGzJUrhcckFZWTkqKl7lj2nl5eZjy6bNEvD41s1buqdvTZYlpaXIzc2Hu4eXxKeU56qoRFZWNoKDgjF18hQZhTIE1u3bySgsLEJ5eYVu8snPL0B0zFXpqRYVF+t2X2t5lt8qKiUf12/chJ9fAIpLSlFeoV+++kq/tKwMzPuVKx5ITk4xL9+v9aqgsBCRkdHSmSgoKHyTvpRHVDSmvQ55t3nDRty4fkN8J0u91UkvmWd2YpgeZdGXvPT6nWXM0TA7BVfj4t/SRb3SsHYf6tv16zcREBiE3HfQzjEGLXWdOs9nsfasuv5WUSnl7B8QhPj4RGnjzNa3mzdvyUCJs4665s0GnSDTyDY9D6sgZagZTrOZfRixRqrlgR5g7re0DPw10oYGMRyiLG7duoWFCxaIheaZU6fR1NTk0JqYJovu72qNdGCskXLdnlOsaWlpWL1y1av9od/vF2M5ri/pvZ6l1kjVGqnedap722L5+YNbI1UgrZZtM5aVwMhzbmvgXtfwiCjU1tWJwwiuhdFf7rjRYxATFS0Bmo16BgXSdw9SlgHrQERYmLj6o3MNxg/lGqlRjZ0CqQKpUXWrp7ZKgbQnqRjw3Yc8IqXxBdeqOK3M+KHDhn6FpYuXIDMzUwxwLK2M9Ra9Aum7BGkqbt26jbLSMpxzcpJyZ/zQ69euCVjZyTLqUCBVIFUgdUy7PripXfaG2OP38fJCRnr6gPJsJF6Kmptx5PBRLFr4rUzl7vjuO9k3yClpoyu7Aum7ASktJglRN7crYHmPGTlKtrjQ9R/LxOhDgVSB1Oi2xbIOqxGppTQMPDdyRGrtsVnAXJs6dOAgFsydh+pq86Z2OdLs6OhAfFycAHTokC/gfP68mMYbOQq1lIcCqfkgFT/JHR0IDAzEiGHD8clf/4r933+P+vp6WSO3LB+jzhVIFUgVSB3Trg9uRGpNXO8KpGxMGxsb4X7linir4YgkNCREoE6ImlXJFUjNBSnLnZ2nqIhIjPh6mHSgfLy9JfQZp3LNKncFUgVSs+oa2181IrVGIR1/+1BGpGxIOa1XUlyC40ePiUHR/LnzcOjgYdmSY2blZvEpkJoHUk7j0zHIhXPnxZhs9IhRuOh8ES0tLW+5rdRRrXq9lQKpAqmZbY0Caa+qqO8P7ztIWWkFok+6kJuTg1XLl0v8UO5fpWP94OBQ0LuT2YcCqfEgZdkTovT3zPihDH3GYAOXXVzFsxE7VmYfCqQKpAqkjmmdmtq1kJ9ZU7ucriW0EuLiMWfmLHGywJEJ18Xa2zvE04cC6c8WJWPsKcud5REaZixI2Vhxyvb2rVtg9KHPP/kUJ44dF0tdOtigYwQFUvPKnWVRUlqGpCQFUgVSx9oYBVIL+ZkBUo5GCMzLLi4SQ5JbHMLDwtHe3i7hz2QPYUSUGpH+bF6DagZI//Y69FlgQCDmzpqNGVOnwcfLW9bGuU5KLzf0c6xAal65K5BeE//WrP8KpBYg6MepAqmF0IwEKadyGeqqrq4Op0+elNEIHeOnp6XL4rs2WlEgTcSLFy9NV2yjRqQ///QTGGibwdcZpWfIp59JAPabN26Is27WCzrTViDNk7VhMxt0BVIFUovm36FTBVIL8RkFUjYOhGhaaipWr1wpEN23Zy/qamvf8pxExVYgfb9ASogyTuyObd/JOjjLPy83V0LeadBQIL2KnBwFUoumyPBTtnWJiQqkeglagdRCkkaAlOuhba2tsh7KKb0JY8fB1cVFpvTYyFoeCqRl4kT7fRiREpL0UnXz5k0snL8A48eMBf0k11TXSKdKgyjLX4FUgZS6b+ahQBqrq7gVSC3EqSdIOWVHb0SNDY3w9/WTLQ6TJ0xETFQUOh8/7nHqUoF08IOUgGQ50jdu3NWrMo3LPaKe7u4SLMESoFrVUyBVIFUg1bTB+HcGYqEfeT0PBVILaeoJUo42GbR2767doJeibxcsQFZmpsDVIsm3ThVIBz9IOQPR0tyMUydOSrnPnDZdrHQJy94OBVIFUgXS3rRD/+8VSPWX6Vt31AOkHHFwxEk/vosXfgtG7zj4/X7U1NQIRDlS7e1QIB28IGW5v3j+XNZDN2/chK+++BIb1q5DQX6+TN0SsL0dCqQKpAqkvWmH/t8rkOov07fu6ChIOQrVpvQWL1wozsfPO52Vkam1hlR7CAXSwQlS1huuh966eRNLFy+Wafwjhw6htqZGLHZ7ms7VypzvCqQKpAqklhph7LkCqbHyFQva/jqtZ2PKLQ6uLpdlFDpt8hTEREfLRv++GlItWwqkgw+k7CA9fPgQEWHhYlCkxQ/taO94K7KQVsY9vSuQKpAqkPakGcZ8p0BqjFzf3LU/I1JCkv+rKC+XqDGfffwJli5ajMyMTLHOtDaV+ybh1ycKpIMLpCzb+ro6nDl1SoINzJ87V7Y4PenstGtPpAKpAqkCaffW0LjPCqTGyVbubC9IeT1HI3dSUrBpwwZxOr97506UlpSIP1V7H1eBdHCAlADtevIEhQUF2LNzF8aNHo2N69fLujghausMhFY/FEgVSBVINW0w/l2B1GAZ2wpSbRRK127XkpIwddIksdC8cP68uPqzZT20p6wokA5skLLcCVF6QWLnSfOTfPL4CYfihyqQKpAqkPbUIhrznQKpMXJ9c1dbQcpKz/VQxg8d/tXX4Hro1dhYaWDZ0No7ItEeQIF0YIOUHSRaZAcHBmHS+PGyFh7g74/2Bw/euHnUytKedwVSBVIFUns0xrFrFUgdk1+f/+4LpAQkp+7KSktx4PvvMX7MGKxesVJGJ11Pumw2LuntQRRIBy5IGWyguqoKHH1OGj8By5cuxbWka3jY0YEf//a33orUpu8VSBVIFUhtUhVdLlIg1UWMvd+kN5ASoDIa6exEfl4eVixdBhoVcX2MWxw4CtXjUCAdeCBl2dJPclVlJXbt2IlPP/oIa1etlnrA+tLf2QfL+qJAqkCqQGqpEbads02mbnJwQy9yti6pKZDaJt9+X9UbSNmYcltMRHg4Zk6bhmFDh8q07oO2Nt0gyodWIB1YICUkCTnuD/1m/nxxsnDy+HE0NjS8FWyg3xXu9R8VSBVIFUjt0yK2ybSYv3DuHDyuuEsgCLbRtnRsFUjtk7XdV/8CpFXVeNr1FHW1dXC5eFGm9BbMnYf4uDjQ0IjX63kokA4ckLJ329raikB/fzEmmzppMgL9A3D//n1xsqBnuSuQKpAqkNqnUQQmPYl5e3pJIJDJEyZg25YtiI2JkVlCRtHqrX1WILVP1nZfbQlSRmopKixEcVERjh89KqMR7g9NT0uTaQRbej72PoAC6bsHaWVllZRvbW0taIU9avgIcTx/+9YtmZUwotwVSBVIFUjtbS0ho8/S0lJxxfqrf/8P/Pv/+Tf8/n9+i0ULv0VYaBhKSkqkM9zV1fUWVBVI7Ze1Xf+wBOm0yZMRGhyMbxd8I1tb9u7eLT0dW+fh7Ur49cUKpO8epKWlZSgrK8P6tWvxyV8/wtrVa2Rf8A/dQt71p3x7+48CqQKpAmlv2mH9exoBxkRF4+O//BX/9q//G//4v/5eXv/7n/9FrOoZ9/nWzVuy31/rBJsOUj+/AImf2N7eLvsjzXqvrKyEt7cv7ty5i9b7raalzam8+rp67PhuO/7w29/hs48/xheffY6TJ06guLgYLS0tePDggWHPc7/lPjgS8vLyQWFhkWHp9FaO9fX1uHbtOpKSrqG5qdm89B+040HbA6SnZyA4OATNzcbKuXv+We51dXVwcXGFh7u7bGeiMdmB/fuRk5ODpqYmcD28+//0+sxQe/HxiYiNjRO/zHrd19b75OTkwsPDS+o+ZWHr/xy9jrpEnfL3D8Tt28kSt5dbiRy9r63/p76lpqYhNDRc9M7W/+l1HXWcuk6d57Podd8+7/OgXdrVkJAwpCTfkXMj27Xuz8M6lp6eDle3K6ioqHQo3/RtXllRieVLluLXv/qvNyD9p7//BxCm//2fvxIDwflz5sLX20eura6qRnh4pHVC2/mr1TBqmzZuws7tO/D93n2mvrZt2Ypv5i/A+jVrsXf3HlPSZs+FVpmM3MG9oezdcKpg2NCvsGHdevB3o+WwZ9dubN/2neR9y6bNhqfXPT87v9uOVctXYNXyldi9c5ep6VO+69asxaKFi0A5mCFvyf+evZJXynvKxMnSs/3Nf/03vvx8CNasWi3P8r3BZU8dW7FsOZYvXfZO9G3j+g2YP2++dCDN0jfKnmXMsv72m4VYvXLVK103WNaWdZ5pr1+7Dku+XSR6Z/mbGeesc2znqPN8FjPS1NJgOS/5dvEruZupb3v3STlvWL8B8+bOw9bNWxzO9+4dO8GlOEJTG5F2f/8///Kv+J///jVmTZ8Op9NncPbseTtRaf1yqyCdMW06pkycJD10Oh0w6zVx3HiZTh0zchRo5GF0ukxjwthxkiYF/i//+E9SKONGjzElfS1/fA7uUWT80vFjxhqeby1d7Z2Bx0cOGyFTIu+i3MeOGo2vvxxqap2jvNlZYrmz88RZCDPqnCZzvlPWdHbPAOAsA8vfzDhnPf9yyBeSttl5Z3pffTEUo0aMBJdTzMivlgbTZhvD8mc90L436506Tl1n2u9C7sz36BEj30na1PUvPh8CtvWOypv6QzlaTu1agpSjU7bp1HHONLHjtHHDJutktPNXqyD18fFDVVWVhAbjENqsV0VFBby8vJGcnIKW5hZD09WmU2mJywLlaOSPv/udNCrZWVky9WRWvpubm2Uq3dPTGwX5BYbmu6c81dbWITHxGhISEtHY2Ghq+pzuSUtNQ2BgMJoam8RIoKdn1Os7psfp65s3buCbefPxn//33zF18hTcvn3b1HwzP5xSj4uLR0x0rEwx65VHW++TnZ0Dd3cPmWLkVKut/3P0OpYBp839/Pxx8+YtsYhua201LX3q27279xASEorq6mrT0tXkRh2nrtdU14DPon1vxjvLmcsonFLnOcvCjHSZBtNLTU3F5ctuKC8vdyhdPjcdpaxasaLHEek//8M/ykiUHVRPdw+5llPBXE7Q87AK0ujoWHBh1uyD8/URkVGyTtibCbMez8RNvNzOEB4WLo3phLFjxXPNpvUbMHf2HFEuI9PvngdlbGSOsRHLVPOTvHLZcpmN2LdnD5zOnkNZeXn3YjH8szI2UsZGytiof2pGY6OE+HixZfmPf/u/4OjzX//pn2VAxNmGrZs2IygwULzRUecZM7qj4yHINj2PAQdSWlZJbykkFPn5BeKkwJEMc+MuG05Ck0Lnu7yeP5feMDfzatOJkRER0jM7uP8AuF+UvVQzQcrn4sJ8cHAoauvqHMm2Xf+lzGmNzLQ5C3DrVrJYuVG5NUs3u25ox8VMl/mmI/jcnFxERkbLNhMj5M688L4i46AgmdZi58nH21vqgn9AIGi1y3rCemP0wedh3tlxvH79BhITk6T+aekbLXvmj2lwBog9dM7OcFM7GxujD9YtdiDYuAWHhOLu3XsSHJ1eaph/lpPR+afs2cZEx8TKiPDZ06fS3hhd9rw/06ahTUBAkJQ5PfQYlV/el3pGubJseU75cvYpLy8fL1/+IL+xPLhVRJO/XnWA+WV5M49Ml+cciQYGhcholOnwmfhsTJvntsiC13DGdM3KVWJoRJuW//qP/5Tp+vNnz8lWReo607Q8TLfaNXtESoFTkNyruf277YiKjBJlsxSCPee8n7h3q6pCVGQkrri5ieXWjes3cPfOHTDkGdfEWBB5ubmgv1xu5D104KDpIGWlYEg2WrNt27oNfEY+vxkHKy47L4kJCbL4v+ibb3Hh3Hnk5uRI5balUvfnOXlfWmnevXMX55zOYuXyFfKKjoqSmQI+l54HFZjTqDQ2YOeJsw4pySnSgD969AgXL17CkUNH4OJ8ER3t7fjZQPkz79xQzrzSyGvBvPmYN2cutmzcBJeLlyR9vfPfXZbyDC9eyPYAGn9sXLdefEhT/1j3jCp3PgetoY8ePgIaOs2cNkMMjjZt2CjGfhJNp67+Fw1g9+d35DPzxtkoH28fLFm0RNJ1dbks+8YJE6MOlin9M1PXaNxIYyN/Pz/ptLN+GnHwvg319bh8yUUcFrDzwu8IUk7r02Ke9ZCGSPv37UP81TjpWOrV/lC3Um7fhtPp0+Jqk8C2BCnTkcFTUBD8fHykDe4Ov+5yYfkRvHTIQMNA7q7g7FJMdLTcix1CdlYo7+71+L0GKQuWFYxrlQQb1ysZXYUCseeg0PifyooKichCpwq+Pj5ScVPvpeJqTCy+37tXvNVwoZ0Vp6S4GM9f95b4X7NBqlUkbiKm1SyND4KDgqQS2JP3/lxLebHzEhoSgs0bNoIW0we+3y/Wo2tXr0ZWZqb83p97W/sP02UlT713D7S6O3vmjEyrr1qxUizwLjo7o/X+fWu3sPk3rU5kZ2VLR4FTPrSUlc5TV5coHHuu7LyNHzsOi75ZiKbGRkM7MixzjsKPHj4s9X3vblqFfw8vD09cv3YdT7scD4JgTUBMnzFV2YAuWbQYCxd8A4IkMCBA9IG/G3nQW1hURCS8vbxE7uzAuLtdEUMQPg+3I/XVmDryfGzcCZZpU6aCuxOcz1+QOsG2h/60jYIaZx/YoaduHT54COvWrpOtG6dOnkSNjn67KRtNt+/dvYud27dj5rTpYDpcj2X+EhKSZPvLOScn2Td9+dIluFy6hGWLl8DHy1v0z5Ey4H/ZcaWc6Z981owZyMnOlnqvgZTlnJWZhf1792He7NnYvm2bzND0JX/mjeut9DjHFwce3EbEgVBP8LSsK+81SNmYFxUVicDpUYZbIdxcXSVslaUQrJ1T+Xmf8tIyHDtyRGKFXnF1E3jye1biq7FXJQD3n//wR2zZtOmtnhcLno0bQcp9R9xv5EhFsvas2m8aUOjPlc7QOZ+/cP4CBAUE9FkhtHs48s70OTLiPlnKn0Yfd+7elRHDd1u3gkrGyqn3wXQpWxqT0ViAHZiCgkLZP3zxgjMWf7sINPY5tdpXAAAgAElEQVRy5NBky3tnZGSIXD//5FPZF0wFZ33hNRyBMP80OmJHZv7cubKf00iY8N5szPfs2iWN140bN3H7doo8iyN5tvW/7M0X5Odj9oyZ2LtnLy5ecpEZEX5vZL4tn4+yZ3oxMVeRkZElje661WtAnWWZsUE04mC6nM5mOXMkHhTEvcvN0oGgUQr3G3Kal9fpefB+udk5WLJokRi55WTnwM8/AMm3k7Fsyf9r70y8q66yfN//yXuvu6vW66rq6tWvu6urytJSywEHFGdkUmZBRRQBFUVRmWcCZGAmgcwjGcgcSEICJAyBQMIUQMI8T6JV1futz8YfXmJyc4ff7wfCPmvdde/9DWfce3/P3meffUZIYX6+qxYgxhFwgY+XL1smn3z0kcydPUdpm34vLikVYgX0ea23lBaXKHAiJ5ngcKoVAIxsiDShES5bulQnDFkZmTKgXz9pbGzUsXWAFL786otJCrZTvp6sYf5wIKJ+wRJ9ifIDD0Er4dDsPQ2kdMT3332v6wWtLa26t0oZKgwhDhEwm1y+dKl+nzp5UgkHgYHpgFkn2gjMgrYbu3ixNO/efWsQYFzMDlxn9sZxad3NjIINdjj3KBcPxmPfHFMTBYDa3cwqnPyDPQtRUhaASVAEPgTFWDBvnkyfOlUFbLD3o7nHuFM2n5bWVvXaTUlO1lk6GmQ0iTwxYyEYsT6w3SAnO1uZz2E8vg+3temMHE0I89awwYPVa9l5Jpo6dPUudWNiN+GjjyU1OUXXpWtqNvkGpAggymXyVlVVJRmZWSqQvJ44BvYHdOcAKcFXSopLdD8tPOxl31Mua2tvDR2mJt3srBw5c+asgmvf3q8rjXgBpIx5WWmZTtYAONZIs3Py1EsdPouZv0An8m6OAUf8OcFEUC6w/Bw7dkz7naW7r778Wt7s31/D6QF89DvWmPFjx0pSYqLWh/6KJJEXdMaHMR06aJBs3779NiDVYCdnz6p1ZNWKFfLFxIkamKM7IKU+1Mv5hFO/expInQ7h+9DBQ7o5HBMIBymHkiBS1hhTk5OlYetWJQD+sw6TsjZZzTbsl/to3Dhdg+VgbtZNszIz1UTg2NOvX7uugAuQAuh+ASlEx3ougI9WlOkjkDr9iza+taFRo700NTWpxk6YRC/XjGg3kwgmEJg0P5/4uQwbMkSWxMerAHDqFs43NMR44izG+L/w3HMy8q23ZGPVBmXqQEHFdgsczt59+22ZNWuOzJo5S8tn+w918ypRB7Qgxnra5CmqFU6bOk23YwCw0DPt8CpBZzjVsbQxf+48GfTmIBk7Zoya9I4eOeJ5+bSL9iEwEehsufrskwnKe6xdep2gaSZsr7/2mnz91de6dkjgDbQjr5wMGdPysjLVPpmo7tu3X7JzclUTZ7kJjRGZ5abMoY/5wGNzZ89WC5MDpOyMGPnWCLUCHjn845gzoSZgA2ua/I6GD3gXWmf5jAkqpl00SEcjPX365glatBngDgdII6WRewJIGVQ6FqHNTIWBckDM6Rhmi4TpCwdI0UYhEMzBMCL/ERYrli3TzboP/vEBBQZMeBDVTTNvkSyYN1/XhRzhdaeAlLbTD2jRdxJI61hHXl+s5kYEK9qam4ztjLHzjXDBtItmxtowmuOXn39+0+njyhXnsZC/yY/1xV27dqnr+5OPPaaza6wL9C/0R4LBv7txQ2qqq/U+3+xrmztnri9ASj1Z42F9mM34rM32eu559Q3A45D1YS/7nbUptnmxhMH+WQJ9E10HMx/lw5/U0cvEWACkObl5kpCQIH1ff13NifCn14m+he4AzqeefFJ6PP64RlLD0QpZ4NCJm/UgT+iSwy8y0tJlQ9UGdXBbv3690gDxnR1HIDfLJS8m6R2BlDB5g94YqO1mIgtPUEfGftqUKTJn1mwF9mjpgHxbW1o6BVJ4gAQmrDEgDX3Y6TCcijAr4T2JGRUHI2YpTooESHkfx6LMjEwF5/PnzkteTq6a8x74/R/0BI/1RUWyf98+dUSqqqhUpyOIl7VBGAuCuZ+BlD4k1u6HH3yoXssV5eWeC1OY7PKly7oempqSKh9/9LE6+6CdwHzhJhxoAEUcG5587HE17WM+6igMEOAcyo7nduLq1bolJmnNWt+AlHYhtOhzJn61tZskP79AkhKT1NkKS8mli6FZY8LtI57HsYUQiHgJE1sZ0+4FzL0pKerwAy8xGfUy0X7GgcAveCyPef/923wWvCybSTyT7tdeeVUmfDxBZRETWOqA1uTVJAbFIScrWycsLDMRzQrnnjcHDNBQldTrr9/fvl3DjX7oCkiHDBys5n28egOBdOrkyco7aMgdeSfc+hiQehCQgUFhxpOdmSV4iaExsqE20HwYCZBCoDin5OXkqBlhxbLlSqR9er+uJlw8NDHlUl58bKwkrlolHNKMp6yjqdzPQAqxY85cvmy5CjUcIBgnhJ2nKWCPG3va2FfX2NCga6QcpE69Qkk8d/LECXWHRzj17d1b2BfMjBeh2LEdFy9cUIc0zjHE+oETxvBhw6Vfnz5qwZg/d67satolrDGJh31Ava9cuSp1dZtl48ZqndRhcp05bbpuDQql7ZE8g+Cc+OmnuoeWLVdZ2TkK6hwXh+ML28O81gwZkxs3vpNFCxdrUIyCdfm+0BzlVlZUyKA3B0rs4jjJyMgUonoxyR49apQsWhCjvhodaSaSfu74jiP/MB8z3pRP/7P1CO9WAO/vfwuN5jvmHex/Z0DKxG3smLFqjUDmouRAj/DGxAmfqpyM1rRLncjTb42UCUDx+mLBidNpA32PiZmJ88yZs4N1V9j3fA/IAHH+9fvvlWEYsEsXL7pi2iUfwk4hEDHXMNvD5ZrZJSCNMOUZzDZ4iu7ft1892fY077klrO9HINXx+OtfVSvKTM+QN/u/oetkmJi8ECQOhZI3/Y15Fc0HJt7b0qICnUkPjj94+sGEwRJ7PRESmOnYi0rMZGb3aNPM7rtqA5oggostP2ghaGdoJ8S8JR4nByawNYc6epGcfkcjQ/MkIEFV1UYFb9anFsUsVDOfF2WTJw4oWINmTp+uQTjS0jO0PKw2ACl7iPGK9DLRt1gjMCnjrdv+gxOMl2WSN32flpKiXtxYQQgCwvYn6IUtKRyZ6Hh1e1EXyudDGXjNFhcXa4g7JjHwAffcTp0BKacNLVq0WK11jQ03vWmRk5if3x81SnKzs3WZJNr63AkgJbAHpmksjixPoRQwWeBwBPYuz5kzz9Uu9h1IQ6k9QpF9T7pGGmDy7epdBgpGYJMzG3M5RxLHARhTNYoOL3534zvdQ8ievUDAuDuA9JSwlxJQoz7REnGHpv/kL3135fIV3b/ItpsZ02fqTBmggamcWepPXozyAuXC3FWVleochil+586dEh+XoGP31rBhCmTBiqFvcM/HI3DM6NE69pyowXmiAFSoiTbS3rXJKbo1ZvjQoZ577VIm66CANfUFRNGMFi1cqAK+ttbbrTD0PSbwAX37qkPWUoIR7N2rQQLYLsEWBMbfy8QYEfcU71kcf7AMQRdeJ+iGMyrx0GUPaWpqmoIaWjjbgfDu92qd1KF72rp3b4tMnTJVy0QB+OboUc/4nfHGArd40aJbExb2kZaUlOouAZbZcIDCKsU2FCaY8FU4fNTVuNFmNNLhQ4botjp4zXE2um2NNClJl1q4Fm25yH2CQLBDAyfDvXv2yszpM9QnYF3eOt3y1FV9I7l+VwIpruHMyh3362ANQyBB9Ox94jQD1kPj4+LUpNcZECEc0ITRdghYHigs7gYgRYBxbFtudo5n2lBgf9J+vEcHDnhDNTEOyGVtsefTz+jJDEMGDpQD+/e7LuBgLkyHcYtj1cEGj2rK5Qg79nMyOw809wfWmd+MFfeJTMQRSkyg2POK6z5MGM4ExAFSgqcvXrRYN8vj9OWlUKdMzHtsP3HaDv2+0a+/BklgBk0bvUq0jTIwn7/2ys3TM3D0oj5EHYIuwunDSOrJ+KelpMrANwZKRXmlZ9pYZ3Wj7bk5OXryDnTnnLzDBJwziQPlQmfvR3oNRzii9+DUhfWDPnciOQGuXiXyZn8+WwOhbdpHSEq2uhG4nyP8cPZjixjhUbkGf7nBA+RBgBwsP6y9k29nQMqWv5kzZqgPTbT9D+3ibMouDYI94DxFkB+slmimWCHcTHclkOIcsnLlKj2ZoCuHBzoKRsRVn8gWHMHUv09fVedZA21ublZBgcBiIFXwXrmizgxorkQ7wskjUFjcaSAFANCsCVWHdhZYNzcHPTAv+oc1BNaMMtIzZP68+TJv7jydaBD1pqKsXOvkdl3Ij7IJT8Ym7YL8Ag2NF7NgoWopjG1XTIxQADDZH4pWAfhgqmMmS57hJt5BsKZnZCrN4bnpxT7CwHrRNmibwABFhYXq5ASIs9TAjL2rtgfmEe1v6B0TGGt17CdkTRlrULAJTLRlBr7POBLVJi4uXurrNyuPuk1ngeUF/qZ/WUdjXydbnqD9+vr6mx7/171zsoLH6ePi9etlTdIaWbBgoRw9+o3nfQ6NoxUCYIwvy2uECNyxo0ktQwf2H1CLHoEZAD2WwdyiQcYUGbNlyxaVJYx7RyClLBzgMCvDF25MImknTnu9evbUCQIWSLa7seXmng9aD7GjYQY7/YVOx1QBYRCv8i8PP6Jh1rZt26YxSjfV1qqrN95xeGYiJAEoZiOsoxGfEbNax8G600DKLAyCy8vLl2Pt7YF878tv+okIM+wl7WoC41VFGFMCxpeUlKkDSmcClWvff/edgih73Bh3NGnMdOFqoYHtcICUPX1tbYcDb/nym0lDff0Wqa2t81ygdtYg2kzbGf9IJiKd5RnKNcaTcSOyEQId/uts3EPJK5Jn4LeW1n1SXl6p66OR5BHNO/A4vA7PR6uBhVsPxtkJWs9vP/ud8joCabj17+552gNGoDQRV/udkSPV0Yh1/3tiH2l3HcD9YECKwMU8UltdI++OHKkBi2dMm6aACVPCjIAAQInjBM4UxG/8ctIkWb1q1c3O/OF0j47EY0B69wIpY8W44gSDIxCmXIK9E7yDddKOYxkKnTnPwNiAiAGpAalDE358G5D+ePqL2/2NLGfNH38H5+B0gmHA5/c9kAKUmH2zMjJ00ZgtDoSV4oDmwBkdQpX/REXC3IetnLVHTGbk0VUyIL07gZRxcZzJRgwbpmYaLAtYG9zQnA1ITSPFY9fvZEDqDZAi//HrIEoSQUeIU4DzIs5W4ADhIO9L0y5aqK6LHT+uJ0TgkII3FusMqO/RaCOBzGNAencBqTMhYqsGjghsaeLDeirrW9CFG8mA1IDUgNT9LTdd8aaXpl1n0o3nMU5TOJTiXEVcAZwSWf8lAt59CaSAZYuuh05Uz062h+CMA7i6BaIMugHp3QWkWA/YwkSAAjwr8ebFmzCYI1JXzBvsugGpAakB6b0BpDjPcdgJoMnRkMgKrJPsk+UaEfVa9rZIfkFRMJEQ9r270mtX10jz1umxWho+raZWw2jhKs75jSxUuw2i9JwB6d0DpDhgcPgAG6jRQjmVhVN8mFS5pYk63GJAakBqQHpvACmTb+QEUe7w0EVWoGyxrMfZykQ2am8/fn9opKxrEvuTszE5iJtN0phzCdAAyLqphTrC1IBUdCH+znrttiqBnz51Wk0yHDb9xF8e09NJiALDRMeLsTcgNSA1IL03gDRQnnf1+75xNjp16rQsW75Cw7bhncmRZkSncMOxpKvONSC980Da0tKqAcyXL12mG+TxtmMLE9qpFwDq0IIBqQGpAakBqSMPIvm+q0y7qOGY7oiPy7FO7BMc+8EYDVX17fVvXTfpdewwM+3eGdMuIIlJhihFnIvJuHPUFCHbcFdnXLxMBqQGpAakBqTRyJi7BkhZECbuLcJ01Nvv3NonSBi1wK0t0TQWoEYwcxYj628c7h2o6RiQ+g+k9DkaJ+sXTJpwKvpQQ4nt0UlVNOMd6rsGpAakBqQGpKHKi86euyuAFIBj7ZOQdC/16qUg+v7oD2TbNvfOBQQwMQ1zRBd7i3BgwasrUNsxIPUXSJ2JDeEJiYPJ4euffPyJhmkD3PxKBqQGpAakBqTRyJs7CqSOSY94uQlx8RqliJBvBGxPTUtXr103BCrloNXWbarT8wZnzZypxxYRsNuA9EfyQVv3y9mIccWpjKDlBO8mWHZsbJxGF7rugxn/x1aLhsWj7RbZyCIbBdKF178tIIM3ARm6G7d7ytkIbYTAyJw9yT7Bl194Uca8/4EQMJxDdnPz1klz8x5XYn8CpAhuAoRzbFdra6uM+/BDDdJtQPoj2fkBpIwFIR7ZwsTRUVgGODeWA3gbGhqluLi0y1i7P9bU3V+mkZpGahqpaaTRSJWgGml+fqGuWwJ6bn4QXITvI7j8sMFD1Llk+tSpunbJvdNnziiQ7t7drE4obpaNeZdjwzheJy8nVzVVJ3+0Vk4M4GgvThVhzxFnlzr3vf5mbyyzpZzcdfLNN8d8K9dp16XLl/VYpS1bGm7t13TuufGtpvPr13WfF/FyOTf2swmf6okntJ2gGwApY8SzbpQZSh6MO+u0Wdk5esRSKO+4+QwTmLq6zXrA9uXLV3xrt9MGjpWi7fQBfeFc9/qbMWasiTKzffvNo9v8HHdojjNBCd5+/odIWV63OTB/eBxeh+epS+A9r38zzqWlZbJzJ2eOfu87v3FARVp6pobs87qtHfPHFwdsczMFBdKMzGwFNwbarc/Zs+f0EN2c7GwN8/f4o3/RE1k4VJZ7hH7jNIq0tAzZvHmrrp26VTb5sLWGI4PGjH5fo1wQw5UyucdvQHb+3Hl6TmFDQ4PGZXSz/GB5EQOS8FWpaRnCVpBgz3pxj43KHKnF/l0CYbhZBsRLzOOigkLp0/t1efTPD+uRd2imxL88d/68roljieD/+fM3x8TNOnSVF3THgcbJKamya9duV9vdVZmB16G5iooqKS0rl+PHT/hePm2m7fTBTR50j98D29nxN2PMWGdl5cimTfXKfw4vdnzWi//wW2PjNhWq7FP2ooxgecLj8Do8T12CPevuvQs6zpzJyfF1+Kf4zW/4vyQlrZVDh9p8bPdNusbZFGxzMwUF0ti4BElNTZfc3HVRf5h5waxxcQkyfuw4Nen1eu55GTd2nKxZs1aZySknaU2yzJsXIytWrr7tunM/2HdObp6sXp0ks2fPkclfTZYZ02dIQvwSyc7OFe5lZGTpWaf9+vSVSV9M0pk4dSPPrOxcXZt95+13dN2OcxIzM7Ojbnuw+gbey8zKluSUNJk/f6EkJq31rVynDox1fMJSSViyTPvJuR7NN32bnp4py5Ytl88+/UxPYiBC1XvvjZblK1ZqOYxLTk6eLFu+UmIWLtYx53805YbzLtoYbZ87d4GsXLnat3KdOjJpjI9fIspvaRm+l0+baTt9QF849fL6mzGG5ucvWKg05/Co1+U6+VP2ylWJsnBRrCQnp/rWbqd8eBxeh+epi3Pd62/4DX8A2g2vM+Z+89uq1UkyZ878Oybn4DU3U1AgBZB2NzfL4cNHovgcFrTNPXv2SmVlpRAn9w+/+289vaV6Y7WwvYUDXQPLwKS7alWinhN48OCh2+4FPtfZ77bDh3ULTd/X+8gjD/1Znnqih3w16Us965J7+/cfUDMS59MtX7ZMTXlO+cyOMDnMmDZdevV8Tiorq+TAwYNhld9ZnUK9RlsxNSHYWC8M9T23nmtpbZWiomIpKCzSfoo235v92apaLuvfv/+v3+n5oRXl5UJbGY+bZRxWK0RNTa2kpKRp2Vgloi0/1PcPHjqkFgCAvX7zFt/KderXum+frMsvVEEK/TnX/fqmzbQdDYm+8Ktcxnj/gQOyZk2ylJdXqHbyI01EI3NCexcarNqwUdLSMpXv/Gq3Uw48Dq/D8+HKOSePyL6RyYckJTVdLSGMud/8tmFDtYL4rt27faM3p6/ANLDNzRQUSFH9MXeybhHphzVPzHpscRj05kAN+TZ7xkzdw4mdvrN8T50+rdojJifWDjp7Jtg18uU9DnFlDYbN/s7z165d16PYWCPNzcm57R7PsV7FGmmf13rL3j17bq3XOe97+U1dMbEwOzx69GZIPC/L65j3RT3FvkE2b9mqwZ473g/3v8a33LZNnYkw4X/y0ceyf9/NOMkd82LMECjri0t0fRa66fiMV/9vfPedHuyMVoCA8aqcrvKlnzBtVlfXyqVLl30vnzbTdhxu6Iuu6un2dcaYACz5BYWybdsO5UU/xx1+Y4JfWlquMsrt9nWXHzwOr8Pz1KW75928j3wsKSnTA9Vv3PhOnTHdzD9YXtAYkzYsMSwhBXvWi3tgGtjmZgoKpDgBYJuPJDmespwfSpg3nHc4+mxt0hpdK0NwdpU0aP26fNe8dgPLgYA4Vufj8ePNazewY8S9EIGMPVtbCgsKpH+fvuqRvTRhia4FMVnhfseEQwDaGMwNY3f2TMd33PqP8LbtL7naB/SFX4kxhh4KC9erQEdo+jnuyKCW1n1q+TKv3Z/ypFd0AI3hG5GeYdtfgvYxQvH6tWvC/tDlS5dq3NTer7wqVZVV6hUb9GURXfzO8whIYVyAetLnn8v6oiL1lHPqAyNfv3Zd4mPjNL5va0ura1GVnDKCfcPYeE7m5eULe8z8TtFuf0EIOhOVrIxMBdBnn3pKJ1Lnz50LKiQNSLdIbW1dSPzhNl1g1mPNjPE3IHW7d7vOz/aRGpB2TR0iaqbY19qqEYQw6X0w+n3Zu2dvyKDkpUYKWLLFhUPB9+7de5twNyCNLiADQrjt0CH5+ssvdX16+JChsm3bNgXXoAQjohMa00gNSE0j7Y5T3LkPr7Ltp6lpl06e/Ox300i7GUOA6ML587q5nkOY2WwfM3+BbndB2wp1sLwEUurAQLI209G8bEAaGZCiTXKALsE13h/1nsbL/fKLL3Rf6I1vQztswDRS00jhv1BlRDeiKKTbZto1IA2JUEJ4yJU1UoifxfKTJ07Iurx16pH7Uq8XZOXy5bc23IZQl1uPeAmktwrp5IcBafhA6pjKy0pL9QR6Qv0tionR/bgdJyqddPmtSwakBqQGpLfYwfMfppEWudrHUQMpIIrAPHLkiCyOWaheuYPfHKih+FgviyQZkP481kgBP5yK1iQmSY/Hn9A9onhCsz4ermZhQGpAakAaibSM7B0D0rsISBF+aKKE0ps08XMNOv/B6NG3to2EK0wdkjAgvbuBlHFFE2V/8OSvvtYQj8TLZbsQ68/QRbjJgNSA1IA0XK6J/HkD0rsESNFC0UbwxP3gvdHqoanxco8cUSEb+RB767UbrF5m2u3etAvgsVWgYWuDfDL+I3nhuefli4mfa7xc1p0jTQakBqQGpJFyT/jvGZDeYSBFG2EQ0Brz8/KEtdCnn+wha5KSdOtGJNpIRzIwjfTu00gZdwQd23NKiks0YMVTTzwpy5cu003V0Y67AakBqQFpR0no3X8D0jsMpJhyWQ9dFLNQ94e+OWCA1NbUqNdmtMLUIRsD0rsPSNUCcfqMrFy+QsMnvvziSxpwAe0UARhtMiA1IDUgjZaLQn/fgPQOASkaycULF3SLw8RPP9OtLUQH2tbYqOuk3HcrGZDeXUDKuuee5maZOnmKHsDNEWi1tbW6gd8NEIVuDEgNSA1I3ZKg3edjQOo3kJ6/oF65HMK9pX6zsD+UcyRnz5wp7ceOhe2d2f0Q2xrp3RLZCMHG/tDdu3cL4PnQA3+SiRM+FYJtuC30DEgNSN2mqe5kDVYWCxFoARm6o5NQ7ne7/QXt8OyZs5K8dq06FOFckp6Wpg4nbplyO1bUNNI7r5HiOMRhA0UFBfL6q68JR58tiU9QBzNms24nA1IDUgNSt7mq6/xMI/VRI03PyFTvzJh589WkN2LYcOEILE6rgOi9Sgakdw5It25tlLr6zXLwwEFZsWy5jvsb/fprgH/i5XoBotCRAakBqQGpVxL1p/kakPoIpHPmzJWxYz7UIAuj3nlHTXzsH/Q6GZDeGSBlglRTs0mysrJl8ldfqTf2wAEDZPv27Wri9XLcDUgNSA1IveSw2/M2IPURSB99+JFb54cS/s8rU+7tQ2xrpHdqjfTChQuSmZEpzzz1tDz4xwfk888mytGjRz3TQgPH3YDUgNSANJAjvP1tQOojkH40/iNJT0vXPaN+ErlppP5qpIwth93mr1snL7/wgjz71NOSlJgo7e3tCqJuemR3JR4MSA1I/ZQx0KE5G1nQ+q7kUbjXgzobpadnyunTZ8LNM+rnDUj9AVIAEqei9mPtCpw4kgGiBFk4e+aMbxYICMaA1IDUgDRq0RlyBqaR+qiRFhQUyYULF0MeHLceNCD1HkgBUWbkB/bvlylffS2P/vlh3dq0JGGJOhsReMPPZEBqQGpA6h/HGZAakHpGbTDy9WvXJT42Tvq93kdaW1oVbDwrsEPGABsh+LxeIwW0AEri5b47cqQ89sijMm3KFGlubpba2k2yZWuD3u9QPU//GpAakBqQespit2VuQGpAehtBuPnnfgBSwPrUqVOyvrBIhg8ZontE4xYvluPtx+XcufPS0LBNtjbcjFblZt92l5cBqQGpAWl3XOLefQNSA1L3qKlDTvcykGLKhXlOnTyp8XIJON/7lVelYF2+rpP+z9//R0P+GZAe7kAV3v8lelR9vQGpAan3tOaUYEBqQOrQguvf9zKQ4lR08MAB3R/KIdxvDR0mO7bv0EO40QZJV650f4ya653+Q4amkRqQGpB6xV0/zdeA1ID0p1Th0pV7EUgBqAvnL0htTa2MHjVKevXsqeuhrP+yThq4tcWANFfa2kwjdYmdus0G2iPAS2Hhetmxo8n1+M3dVcC2v9j2l+5oJNT7Qbe/3CteuzAsIIkJjeD7F86f1ziyOPagqWHWJN1LQEqbERQcc1ZZUSn9+/SVRx56SFYsWyYE1wgEUIdYDEgNSNFU/EoGpO3qWJIO32wAACAASURBVIgcglf9TKaRmkYaNr0BkJcvXVIHm4/GjZNXX3pZXurVS0YMGyYZaenCMWEO2N4rXrswyvHjx9UD+cnHHlcv5PKyMrl65UqX+0MNSA1IDUjDFi8Rv3Cs3YD0zBn/4xSwpRMl0c10X2ikAClguTYpSVLWJkvdpk36WZqQIG/2HyB1m+rUxHQvaKSYctGyW/bu1fXQ5555RsaMfl/q6+pVI6eNXSUDUgNSA9KuuMP96wakWXqalPs9GzxH34E0KztXTpw4qYIZ4ezXp739uGRkZknjtu160ky05QKimE+Y/RBPFhMvoLFjxw4ZOmiwrFq5Uu9xjVB5i2IWqkfrzp075dKly761m7JOnTotGRlZcvDgobDLpZ3Uv7GhQUa+9ZY8/OBDMn7sWN0P65ixg/XlmTNnpXZTne4lpZ+CPevmvWvXrutEZ9eu3ZJfUKTmaMbIzTKC5XX5yhUd/9S0DGlpafWtXKdOjNnGjTVSWblBzp4953v5tJm2wx/0hVMvr78ZY5YecnPX6d5l+M/PcYffdu5skqKiYt0S5nV7O+YPj8Pr8LyfcgZ+44AK1qbx0r982d9+h8bg9bVrU+TYsXbf6M3pfzANbHMzBdVIF8fGqwpcXl4pfn7WrSuQBTGLZM3aFCkpLXOp7AopK7/5Kee7rEJWr06UV158WSZ9MUkKCgqltLRciWvch2P15BPuF5eUulR+931YUlKm/U3bGehw+7ywsEiITPR8z57ywO//IMOGDJXMzKwf+rCi2/wKi9bLylWJ+llf7F+7dVzKKiQlNV1i4xKkpKRUxyrc9kf6vDPu8+bHSHpGVrf9FGk5Xb1XtL5Ylq9YJUuXrVCh3tVzXl2nzbQdwUpfeFVOx3wZd/hr0aI4SUpaK6Vl5b6OO/yWkpIm8fFL74icg8fhdcyM1KVj/3j1n35nnOPilkjSmmT9zTWvyuuYL2WnpKbJnLnzJW9dvm/lOvWgv8E2N1NQIF2xYpUS9qZN9eLnp7i4ROLjl0hWVo5UV9e4XnZ1Ta2sX18sUyZP0cPKOfGEcmpqaqWioko+Hv+xPP9sT0lLTVdNwa+2UwcAPj5hqRQUFoXUbjTIjRurJS0tXd5/b7T85eFHpH/fvrJ82XIpKS7RNm3aVBdSXhUVlZKckibJKamyYcPGkN5xp29uasGM9/LlK2VjdY1qxu7k3T3tQg/lFZUSG5ugzh9+leuUU1lZpZNGwKSissrHfr/ZN0TSou30AX3h1Mvr79paaLdGlixZphoxR/iFSqtu1A1+y8nJFeQcIO5GnuHkAY/D6/C8F3Ku67rUqVxg8paWlqG/kSNdP989D4XzLjSGFYIJ1Pr1Jb6V69SRSQNj7mYKCqTZObly8uQp3SbBVgm/PjjJZGZly7btO9QEG2q5169/q2aC06dPy549e2Tbtm2yq2mXHDly5AeT0beaH/fxZB37wRg9vPrixZveu5hGz58/f8u029TUpGaPUMuP9jlMLBwSkJGZLYcOtXXb31evXpMzp89I086dMvmrr6Xn08/o/lDWQ2lHuPXBrAixwVSY3MJ9P9LnGTdMert379bZuWOGjjS/cN+7cuWqnnCUlp4hra37fGu3U0/GCkFaVbVBTfPOdb++aTNtJ8Y1feFXuZjaGOvcvHXCgfLwH9f8Kh9+a2rapcL81OnTvpXrtA8eh9fheeriXPf6G37DjI4FqrFxm/72s9+hMXg9OTlVWMbzur0d8wfTwDY3U1Ag/Tluf8H7dl/rPj2QnMg9QwYNkpUrVsiNGzfUW/XqlavStLNJRr87SpbEJygjO1tBfk7ORtQZ4q+vq5ORw99STXTq5CnyzTff6DaeSIgE5rLIRraPNBLaieQdaNj2kearDLLtL5FQUGTv+O5s9HMEUroWgGGWT0zZc2fP6kwXb1aAYlvjNl07jFscK2dOn74NdH4uQIpnJTP5kuJi6fNabyFSUeLq1YKmzT1nYhAumRmQmteuee2GyzWRP29eu/eJ1+7PFUg7kjYACUigvU34+BOZPWOmHD58+JZ3qKOt/hyAlElCW1ubnhn6yosvqcadn7dO20L9o0kGpAakBqTRcFB47xqQGpCGRzFhPu32eaTYyPfv2yeDBw7UNUT2kuavy5fCgkIpXl8sWzZv1jW6uxlI0agxg7UdatP10D/94Q/y7si3ZeuWrapVR6qFBg6NAakBqQFpIEd4+9uA1IDUUwrzAkibdzfLiOHD9fDqEcOGy8i3Rsjbb42Q994dJfPmzNE9dHcrkAKS7PtCox4ycJCacqdNmSrt7e3y3Y3vIjbldhxEA1IDUgPSjlzh3X8DUgNS76hLRL0H2V/U3LxH1/yiLQzhgEcga6bH29tv+5w8eVLNomh7dxuQAqDUnaPPcnNy5M3+/QVz7oply+XE8RPy/XffRds1t71vQGpAakB6G0t4+seA1IDUUwJzWyMNtbJ3E5DifcvaLUC/dMkSefapp3XP64aqKtVOQ21TOM8ZkBqQGpCGwzHRPWtAakAaHQV187YBab4cOHhQ13U/+2SCEHR+1DvvyK6mJt1z5cZ6aGdDYEBqQGpA2hlneHPNgNSA1BvK+iHX+xlIiXFLhJvUlFR1Jnrhuedk7uzZGi8X8zNOR14lA1IDUgNSr7jrp/kakBqQ/pQqXLxyPwIpWibRfY4ePSoTP/tcTblPP9lDVi5frvtdvQRQZ+gMSA1IDUgdbvD+24DUgNRTKrsfgRSgBETjY2PlkYf+LG/06y9lpaUaXMIrU27HQTQgNSA1IO3IFd79NyA1IPWOujzw2g21snfC2QgAxamI2MBfTJyoof44I3Xjho2qofqhiTr9Y0BqQGpA6nCD998GpAaknlLZ/aKRIrQIZUhAiA9Gv6/m3LFjxkhCwhINtO9pJ3eSuQGpAakBaSeM4dElA1IDUo9I62a29wOQYq69dPGirMvL0yPb2N6yNGGJHDt2THJy8wQm8zsZkBqQGpD6x3UGpAaknlLbvQ6kmHJPHD8uCXHxqoX2ee01qa2p0UAUeO1yrJQB6f94SmOBmQMeTCI4WqmtzU5/CewbL38zmbTTX+z0Fy9prLO87fSXznrFxWter5EiOC5fuiS7du2Sr7/8Sp7p8ZR8+MEYaWxokOvXrqlQ4VQXDlo2IDUgdZG0g2bF5IFJBJMJ00iDdpWrN00jNY3UVYLqmNm9ppECoIA021s219fr+aEPPfAnmTV9hrQdOnQrVi5nEhqQlskNF+MHd6Stzv6bRmpAykH2ficDUgNST2nuXgNSBPW5c+ckMz1DXur1gvTq+ZykpqQIZtxADcCAdJ+UlBiQespcnWRuGmmlxtvupGs8vWRAakDqKYHdK0CKJsoRbocOHpT42DgNOD98yFApWHdzXQQtNTAZkBqQcriC38mA1IAUWeVXQnnYv3+/pGcYkHra5/cCkDqmXAjmi88mymOPPCKj3r4ZLxcHi86SAakBqQGpfwIdfmtp3Sfl5QakBqSdSeTQr/1DsEcLCooEDye/070ApKx1cn7o0EGD1TN36tdf69YWmLcrojUgNSA1IDUg9UPeohWWlVVIU9MuXV7qSiZ5URfTSL3o1U7y/LkCKcSIJnrixAnJTE+Xfq/3kT6v9Za1a9bomaIQUDCCNSA1IDUgNSDtRCS6fsmAtMjVPr2vNFIH6DCt8gH0AoGN/9evXdf1TECwtaVVALdQEqH8rl+/rvtDE1etkl49e8qLzz8vlRWVIZ8fakBqQGpAakAairyJ9hkDUgPSiGkIoDx39pw0794tu5p2yfHjxxVMnQyjAVKAmXw/Gf+RBp0n1F9rS4sCcSBYO2V19m1AakBqQGpA2plscPuaAakBadg0BUBdOH9e0lJTZczo92XEsOEybPAQ/V68cKFcvHBRATUSIIUgr1y+rPtD3x4xQjj6bP7cueqpC7iGCqI0yoDUgNSA1IA0bAEXwQsGpAakYZMNAHXq1CmZMW2aJK1eLU07d8ruXbtkSXy8vP7qa1JaUiI3vr2hYBqOaZdQfydPnNDtLK++9LLwWbVypQaiB5TDTQakBqQGpAak4cqNSJ43IDUgjYRuVDOEeBwNkW+2prz37ihZuXyFRhQKVSPlXdZE29vbJXbxYvnznx6UAX37KSB/H6YWGtgYA1IDUgNSA9JAmeDVbwNSA9KoaQvAZHvKptpaeaP/ACksKNTACaEAKSBKqL/du3fL+A/HSo/HH5fxY8fJgQMH9LoD1JFU0oDUgNSA1IA0EtkR7jsGpD4C6Zq1KbJ7d7McPnzE1w97m1YnrpGKyio5ePCQS2UfVrDbtGmT5Gbn6Mkrw4cOk1HvvCubN2+WAwcPyqFDh6SlpVWmT52mofwqK6vkwIGDP5R/WA4dapPm5j1SWlIq74wYKY898qi8PWKkVFVVSeu+fVHXk7Ka9+zRtm9taIw6v3DHbe/eFilaXyxFRcWyb99+H8s/LG1tbbKxukZS0zJk//4DegpLuPWP9PmDhw4JbV+5KlHq6jb72O6bfNXS2ir5BUV6WAH0F2k7In2PNtN2+oC+iDSfcN8jotL+AwdkbXKKlJWVK3+1HT7sW/nw24aN1RphB74Ot/7RPg+PI+fg+R/ljB+y9rCOc1p6pgajQMYyFtG2J9T3obHq6hpZtnyl7NzZ5Fu5Tv3ANLDNzRR0+8ucuQuUwZJTUsXPz/IVq2T6jFkSG5sga9Ymh112YtIaWblqtSxfsVJWrFwtiYlrZO3aFP3/2aefSf++/eTlF1+Sp57sIW/0f0NiYhZJ0pq1WtaqVYkyYvhb8sRjj8u8eQv0OoxOnvEJS2TMBx9Kj8efkIcffEg+eP8DiY9PkLXJ7vTPmjXJ2t/TZ8yWpcuWh93uaMdo1eok7YuYmMWSmLTW1/Lp49i4BJk1e64krUl2rU9D6RNojLZPmz5T4hOW+tpu6rc6MUnmL1go8+bH6O9Q6uzmM7SZttMHkfBbpHWBbxjrmbPmyMJFsQqoyS7xUih1gt/i4pfI7DnzVF6E8o6bz8Dj8DqTGOriZt7d5YU8pN30O2PulgzrrlzuUx40N3XaDJXJobzj5jP0N9jmZgoKpNk5eXLy1Ck1exIz1q/P8eMnJDMrW7Zv3yFXrlwNq1z2cu5p3iNom3jQvvLiSxIzf74GpcYke/nyZfXgJYj8tsZGGT3qPZkza7Zuhbl69ZqcP39BFscslN6vvCq7mpr0aClOhsB0O2vGTAXRvr1fl6rKSnUqIk+3+uXylSty+swZyczM1tm5W/mGms/Zc+dkU129bNpUp/0V6ntuPMe4MVMkmtalS5d1T64b+YaSB+ZUgoCkpWdIa+s+18YzlLJ55vz581JdXStVVRvl3LnzvpdPm2k7fUBfhFrvaJ9jzOHH3Lx82bq1UeA/rkWbb6jvw29Nu3bJ+vUlcvr0ad/KdeqHhQteh+epi3Pdj2/GubCoWBobt6mM9bPfKRteZ9LU3n7c13bTt2Aa2OZmCgqkP8cQgaxRsle0flOdOv9sqNog+1pbb9svSgfy3DfffCNJqxNlwkcfy/H2dn3m2tVrErc4ViMS7dmzR4XLtsZt8uUXk+T5Z3vqs5wfyoDgcORmsjVSWyNFyPidLGi9xdqNxrcjXHplfdaC1ofbaxE873aIQJyI2KrCwcV8rl29qt9omayHcsg2Yf3QLo8dO6b/Ac3Kigqpqa7W80Mx5c6YNl2OHD7sOoA6XWRAakBqQGrORo488PLbnI18dDb6OWqknREf4ImHLl62aJvZWVmyJjFRPh4/Xvr37Ssbqqr0bFD2lr41dJj85l9+Jf/3F7+U//p//6Froa++/LKkpaTIpYs3Azd0VoYb1wxIDUgNSA1I3ZAl3eVhQGpA2h2N/OQ+EYZOHD8ueTm5sigmRmZOn6HroomrV2tEIoQXgRXiY2Plt7/+jfziH/9J/ul//x/9fuD3f5ClS5bc2mf6k8xdvGBAakBqQGpA6qJI6TIrA1ID0i6JI9gN1gBY12T/KI5GfGPuddYGMNkSnOEf/9f/vvX55//zj/KXhx+RjLT0W88FKyPaewakBqQGpAak0cqRUN43IDUgDYVOunwG4HQ+gQ8dPnxYxn049haIAqhopmx1KSwoMCAN7CwPfuO4hfdoSUmZ3LgRXoziaKuDUMH8n52Tq/vpos0v3PdZm6+v3yK1tXXqNRvu+9E+b85G5mzkKBTR0lIo78Nv5mwUSk9F+YzbzkbBqoPZlzi8SYmJ8sRfHpN//dWv5Zf/9M8/rJH+P11X/ebo0WBZuHbPNFIDUtNITSN1TaAEycg0UtNIg5BH6LeYgSG02g4dkoS4OOnV8zkNYD9tylTp+fQz8qc//FEmfvqZHG5r07NLQ8858icNSA1IDUgNSCOXIKG/aUBqQBo6tXTxJCAKaHEKDOeHApqffPSR7Ni+Xa5euRrRwd5dFBXWZQNSA1IDUgPSsIRGhA8bkBqQRkg6N1/TgPUXL0llRaUMGThQox/FzF8g7ceOaVQV1qviY+Ok3+t9pLWlVQE3qgLDeNmA1IDUgNSANAyREfGjBqQGpBERD1ooXrrHvjkmOVnZ0r9PX+n7+uuyasUK9eKFsEI5/aWrwvECbm5ulrKyMvUIxnmG9VeiJ1VXV0tmZqZ+ampq5OTJk50GdQgXSMn/zJkz0tjYKOvXr9f8MzIypKCgQFpaWro8jYa+oL2sRTc1NUlRUZG+m5S0RuLi4qWkpFRDtzltqKurEz4IefrIi2TORuZsBG1Bm34l+K2ldZ8GbicMqN/pWHu7HlSA7KAufiYDUgPSsOnNAQSiFqF94lT0Zv8BGrkocAtMpEB6EwRa5Z133tEPQEm+gNxXX30ljzzyiDz//PPy3HPPyZNPPqnX2ILTEZTCBVLyWLJkieb58MMPy4svviivvvqq/OlPf5I+ffrIhg0bFDA7dhj1JbbmypUr5YUXXhDeffnll7V+//W738m7774rR44cVeYGPBcvXqzPbdmyRbcQdczPjf8GpAakBqRucFJoeRiQGpCGRik/PMUMl60Ne5qb5eNx49SU+8F7o9Vsy77SwBlwJEDKO+QfFxengFZbW6tgA4iuXbtW/vKXv0hiYqIGxcY7GI0RMOUe7wWmcIEUkCspKZGUlBQ9ZBwNkzKow0svvSSvvfaaBuPvCNiAFkBPHVasWKHhEXmXY+SWLl0m//Iv/yLz58+/pYFy9uqwYcNkyJAh2o7APgusfzS/DUgNSA1Io+Gg8N41IDUgDYliEPYIZwCtvKxMzw998fnnZf7cuRovF9DqCAiRACmaHWZUtM2RI0eqmZi89+3bJ71795bhw4frnimnPsT3/eSTT2TQoEEKYIF1CBdIYQYmA4EmV66hEU+YMEEeeughPYCca4GJMmnrhQsXFMzpJxL/c3Jy5be//Tfp27evgjLPcjJGbGys/Nu//ZuUl5crCAfm58ZvA1IDUgNSNzgptDwMSA1Iu6UUhD/rhxfOn5d1eXny2suvSI/HH5fszCw9GaarDCIBUtZWkpOT5b//+7/VBAogAIhohf/5n/8ps2fP1iPJnDIBpTVr1siDDz4ou3btum2tNFwgdfJ0vmk3mmZ7e7uMHTtWHn30UeEEm45A6jzf8Zu25ObmKZBi6sUU7uSJmfjXv/61TJ06VY/96vhutP8NSA1IDUij5aLQ3zcgNSDtllq+/+573R86e8ZMeeyRR2X4kKEaUxft0dG+OsskXCAFZND+PvroIwXGyspKBR7KweHnX//1X9Wsiyewk9D68vPz5d///d+F5wNBLlog5X3AD3Ntjx49ZPz48Qri1DOUxJprSkqq/PM//7OMGzdOHY54jz5D63788cdl6NChcvDgwVCyC+sZA1IDUgPSsFgmqocNSA1IuyQgGBEzJ/tBP//sMw2s8Pmnn+n/UM4PDRdIEf6EFuzXr5/07NlTwQbQAjizsrJUg2NNFGB1Eh56mEd/+9vfKtgCfk6KBEh5B/P1rFmzZMyYMfLmm28qiE6ePFk9cgOB2imn4zd15jnCdpHH73//e3VUcurGfQCaNVIcmhoaGjpmEfV/A1IDUgPSqNko5AwMSA1IOyUWhP758+elvq5OBr3xhjoVzZk1S0EGBg0lhQukDvg8++yzuh569OhR1Ug7Aikg7iSAtKKiQrXV3Nzc29zeOwNSQIzJAU5Ex48f13VVNEee5R4mbLRinINYFx0xYoR6CT/99NMK5tQFkOoqkQd5kf+8efO0XpMmTdL/ge9Qxueff64gXVVVFXjLld8GpAakBqSusFJImRiQGpD+hFAAA4AgPTVNnunRQ9dEU5KTFYCCgUjHjCIB0tbWVnniiSfkjTfeuOU8hAaal5cnv/nNb3T9NFAjZR2SfZs47rDnFIJ2UkcgpV3cZx8qHrgANk5NbE/Bw5bnSTxH3XkW0Mb0+uGHH8oDDzwg7FsNBHKnLOeb/sHcDIhibu7R4ykpKyu/TYvmWdZ2Z8yYoW1Fo3Y7GZAakBqQus1VXednQGpAeos6ABBAYv++fTJn5iyNl/v2WyOktqZGgyJwP5wUCZDinfvUU0+plyvmTxJaIuD3H//xHxITE3NrrZF7mGHZroJz0tatW2/bS9oRSHkegDly5IgC8urVq3XNFZBG++5sksA1tFDAGiDlnY7bbLSSIlr2iRMnZNWqVerhizablpYu9fWbfwK+TFS+/vpr3brD2q7byYDUgNSA1G2u6jo/A1IDUqUOmA7trnl3s3wxcaI898yzMvrdUbpfNJgG1jVp3QSW69euhxwikDqgGRIEoVevXrrlhfwBhb179+p64gcffCCOyRdgZ0112rRpqlkS9QjwvHz5soIdgIfpNy8vX4h64iRH00Sz5QNQUwbldxQ+DpDi7PTHP/5RkpKSNH/eob/w6nXeA0TZ4wqoE0yCCEn1m7fI1q0NtwEp9cYT+O2339bAEvX19U7VXPs2IDUg7UjLrhFXFxnBexbZaJdassJVOrro0pAuI8/sGLWQuiq6h7o7Rg2hy7phaUmpvNGvv3rmErEIrSkagoCRwwFSymLdElPrn//8ZzWjOi2nLgRpYK2S8H0wLSBWWloqzzzzjJpJMakCnOnp6bJw4ULZsWNHp0Dq5NnxG+BFWw0ERwCzra1NnYYAUkL78RyAj/kWTRkwRmuNj49Xb+OBAwfqJODcufOyZctW2bxlqz7j9CX97WjeAwYMUKeqjnWJ9r8BqQGpAWm0XBT6+6aR3ucaKUBx5vRpSUtNlVdfelnNudlZWbfi5YZOSj99MlwgJQdMrAkJCfK73/1Oli5desvcilaMFscWFEIEvv/++zJ69Gh57LHHBDBiRsYzgB5ev6+88op6w3amkf60pjevAG6DBw9WByA0ys8++0z3jwLeRFTCrMuEgzzT0tLkF7/4hTojsYa6c+dONT3/8pe/VG/cjz/+WPgMHTpMPzNnzhQ0T8AUoGZfLNt5Pv30U10v7apOkV43IDUgNSCNlHvCf8+A9D4FUgQ6R5xxIsvihYvk+Wd7yojhwzVebneeqZ2RGYIbLRFgdjSvSICUsrdt26bA9d5776n5lLwdAMIZafny5YKJFyAlbi17MiFkyt6+fbuuT+IchKk3HCBF6y0sLNS1S4B61KhRCthz5sxRECQv6kEdN27cqPFy8e7FA5cIS2x1IfQfIMy7b731lrz+eh+N08sEAO9c3sdLeNmyZfKrX/1K8DQOdJ7qrG8juWZAakBqQBoJ50T2jgHpfQak33//V/n73/6m2tvePXv1/NAH//iAfDx+vOxquj0yUKgkhdAGlHc1Nel2GTQuACMSIIUgWXskOD1OR6wzkl8oCUDCcQcTLM5BXa2RhpJXsGdom6P9Aq60v7NE+Q0N22RrQ6M+zzO8C/ADtqwDs97b1fud5RnqNQNSA1ID0lC5JfrnDEjvMyBFa0MjqqyokNdffU2dihbFxKj3K/fCTQADGlr1ho0ybPAQGTZkiJqKEeSRAKkDwAR2ZwsMpk/qy/XuEkDKnlKiCPEOAByORtpd/oH3qQ/MEwwEOwKp9sf16+qwhLmYbS/0nRfJgNSA1IDUC87qPE8D0vsESHNy82THjp1yuO2wpKakSt/evaVv79clNTlFz9GEECJJgNfRI0fk6y+/lOFDhsjAAQPk9KlTCjCRAKlTB9ZKN23apEeT4SwVCpDSBoCJdzEz8/EKSJ16BvvuCKSAG+COOZdITWje9JEXyYDUgNSA1AvO6jxPA9L7AEhPnzkjaekZUlpaJjOmTZdnejylB3E3NjTI9Sg0IoQ164qrVq6Uj8aOk3lz5sjQwYPVeYZ70QBp5+Qa3tW7DUjDq310TxuQGpAakEbHQ+G8bUB6HwApW0oWLIiRl194UQ/hnvDRx3LwwMHbHIPCIRqeRUNkv2ZFebkMHTRYNtXWqnZrQPpjT3bUSH+84/0vA1IDUgNS7/nMKcGA1EcgjYtfIlnZuVJUVOz5p7CoWNblF+jpIzOmz5AXn+8ljzz0Zxk0cLDExSVIfn6hFBauj6gevEeQgyVLlsqod96VcePGy9q1KfL5Z58rWKempklBYZEUFBTpeZyjR42WZ59+RpYtW6F18qP9lLEuv1Ays3IkZuFiSU1Nj6it0dQ1OztXli1fKctXrNL+iiavcN5l7AsK18vqxDWyeHG89nmkYx1Ouc6z+QWFQtvnL1goa9am+N7vOTl5snTpCklYskyyc/J8L58203b6gL5w+sXr78Ki9ZKfXyALFy5WmoP/uOZ1uU7+8FvSmmSJjUuQzKxs38p1yofH4XV4nro4173+Vn4rKNJ2r1ixKirZGkldoTHk77x5CyQtLcO3djt1BdPANjfTPwTLbOnS5bJpU51s37HTu8/2nbJt+w6pq9ssJSWlMm3qNHn4wYfkz396UObNnSd1dfWyffuO0MrfvlOf5Z3KyirNr7y8Qn8TP3b8uPEydsyHUlVZJRs2bJTZM2fLC8/1kpLiUmloaJTGxm2y03b/5QAAEsNJREFUefMWmfT5F/LsU8/o2Zxc97T9AX3b0LhN6uo3S1z8UqmoqPKtXKd9RDXKyMyW9Iws2brVv3Zvhwa27VCGWrFy9c2yQx3zgP5z2hHud2Pjdg2LiEAtLS33vd8JgoFQTU5Ok82bt/pePm2m7YSGpC/C7b+In9++Q/mOCSs+EY3btofO6y6MO/yWX1Akq1YnqfyJuB0R1gUeh9fheeriW/nbd6qsW7kqUfLyCvR3yDI2wrYGtg0aY9K0cFGs1NRu8q/dP9QdTAPb3ExBgZRZEtFuMLt59cGcw9pgy94WmT1zpgLo66/2lslfT5GdO5vkxo2b4fBCLZ/8yGvM6Pc1YMOgN96UmTNmSNLqRBnQt5+sSUqSrVu2aoCBubPnyKsvvywbqqrk1MmT8t2N73RbTNziWHVsIswfzjahlh3tc5R14cJFycldJ998c8y3cp16X7p0WbZsbdDoRteu3Ty71bnn5fff/vZ39Shmm01xcaluvWEcvSwzMG+8v3HyysrKkYMHD/lWrlMHTOpM/qprauXy5Su+l0+baTt9QF849fL6mzFmWxZCFUGOHPBz3OG3vXtbpLSsXM5fuOBbu51+hcfhdXjeTzkDvzHOJaVlKmP57We/Ux776/GDOXXqtO/9DqaBbW6moEAKgTPIXiUGT9fltjbIR+PGqVPRpIkTpXpjtaSnZ0pz8x4VsOGWz1ooIfH27NmjAe1bW1oE0GT7DOujb48YqdteevV8TsMLvjNypG6HgZHDCREYbr26e96cjfZJSUmZTp5C8Xrurj9Dvc96EXSYnZMrbW2HQ33Ntefw3K6vtzVS5IGf464T+NZ9Ul5eqR7prg1oiBkRT5slJyYw1MXPZGukPq6Regmk33/3nXrLAppDBw3SUH8zp8/QrSgEU89blx8xkHYkSLa8nDxxQsPxHTxwQMPz7WluloS4OHn1pZf04G+HmA1Ibw/I0LEvvfrPLL211YCUkI5+JyYPTCKYTCBg/UqAJtoJ6+E7djSpVmRA6k/vG5DeA0CK0GSv5ZrEROnx+BPqWJSZkSHfXv9WZ6TdBa2PltQoHy2AGL0EZOCsTa4xIzYgNSCNlr7Cfd80UgNS00jD5ZrIn8fKipLoZvLdtIvQONzWJjOnT5dnn3paBr85UBobGuXKD2tDNM5rIGXWC+Hu3bNHcrKz5drVqwrgBqQ/DRHoJrEFy8s0UjPtmmk3GIe4e8800p8pkCIoOTaMoAqffvKJPP1kD/1ubm7WhfZAk47XQApJ/s/fby644+zglG1AakBqa6Rm2nUXsrrOzdZIszTUa9c95M2dn6VGCkgx+2Htp7ysTDVQ9ofGx8bJsWPHOu0pP4C0s4INSA1IDUgNSDuTDV5cMyA1IA2ZrjChEqlo9cpV0vPpZ9RztqigQKMMdeXYYECaLzCZ30k9qDuc/uJXHcy0a6ZdM+36xW2iyk1ZWYU0Ne3S345Vzo8aIPc5j5n96mfOnPGjyNvK+FlppAhG1kNb9u6VmPnz5YXnnpf33nlXT3HBi5b7XSUDUgNSvxnbtr+Y125X8sir66aRGpAGpS1mHOzl3L1rt4z9YMyteLkH9h8Iyb3egNSA1IA0KIu5etO2v9g+Ur/5zTTSbliYAQEIKysqNToQmmjM/AVy9szZkE0IBqQGpH4ztmmkppF2I9pcv20aqWmkPyEqBB9hrjjrM2n1aunzWm8Z0K+/7tXk0OpgptyOmRmQGpAakHbkCu/+m0ZqGqnf/GYaaSf8DEhevXJFvjl6VLVPtrb0fuVVadi6VVgPDTcZkBqQ+s3YppGaRhqunIr2edNITSO9RUMIPPZibt68Wd579109+mzSxM/lyOHDIZtyb2X2ww8DUgNSA9KOXOHdf9NITSP1m99MIw3gZ+JkYrYtLSmRYYMHy/PP9pQl8Qly9OhRjRwU6eAYkBqQRko7AeQZ8k+c40wjNY00ZIJx6UHTSE0jVZMtptz01DR57plndU00KyNTTbzhrId2RpMGpAakBqSdcYY310wjNY3Ub3677zVSOvzvf/u7HDxwUDit5U9/+KOMGDZcamtqQtraEoooMCA1IPWbsU0jNY00FNnk5jOmkd6nGima5sWLF9WJ6J0RIzXo/FeTJul6aGDM2miJzYDUgNSANFouCv1900hNI/Wb3+5LjZROZh3p5MmTUlZaKsOHDJWXX3hRFsybL8fb213TRB3WNyA1IPWbsU0jNY3UkT9+fZtGeh9ppOfPX9DDd4mJuHLFCg319+LzvaSosFCjF3lBdAakBqQGpF5wVud5mkZqGqnf/HbfaaTt7cfl0MFDMm3yFDXlDh8yRLZv2ybXr10LK8hC5yzc+VUDUgNSvxnbNFLTSDuXRt5dNY30PtFIV69OkvVF6+WzTybo1pavv/xS9jTvkb/99a+3zvD0gswMSA1IDUi94KzO8zSN1DRSv/ntvtJIP/lkgrz28ivy2COPSkJcvJw4ccJTAHXY3AsghVA40o0whkRb4oODFHthne06dh6pnUcKqPidOCWpvt6OUbNj1PyjPHxe7Bg19/r7H4Jl1ePxJ2RA335SWFCgR6JB6H4kL4AUwjnc1iYbqqpUy0bTLi0plbpNm9QTGTA1IDUgNSC1g739kHGUYabd+8S0O23qNNm4YaOCqJ+qv9tASt3RRPPX5eue168mfalrvjOnT5fYRYvkm2++Ua3UgNSA1IDUgNSA1NseQKm5r0y76/IL5cKFC972aie5uw2kaJvXrl7VU2luxgE+IqdPndbj3i5dunRrzdeA1IDUgNSAtBOR5Mkl00jvE420oKBILly46AkRBcvUbSAFIPHKXJqwRObNmXPLTA3ABmraBqQGpAakBqTBZJOb9wxIDUjdpKef5OU2kGJKICLTrBkzZOrkybJ/3z6NxnT2zBn59vq3t8DUgNSA1IDUgPQnAsmjCwak9wmQZufkyalTp9S7FQ9Xvz7Hj5+QzKxs2b59h1y5cjXscvHIxRPy6tWr+n358mU5ffq0zJg2Xfr16SNv9Osvb/YfIOPGfCi5OTl6j+evXb0mBKBYHLNQz1Pd1dSkmqxf7UZrPn36jGRmZsuhQ21htzvaep49d07q6upl06Y6uXjxkq/lM2a7dzcLVpBLly7f8qqOtk2hvA+dMHlLS8+Q1tZ9vrab+p0/f16qq2ulqmqjnDt33vfyaTNtpw/oi1D6zI1nGHN4MzcvX7ZubZSrV6/J9ev+yRn4ralpt6xfX6IywI02hZMHPA6vw/PUJZx3o32WcS4qKpbGxu0qY51dDNHmG8r7lA2vJyenCnEKQnnHzWfANLDNzRTUa3fpspVSWbVBNm/Z6uunvLxC4uKXSHZOrmyqqw+77NraTVK8vlgKCwqlqLBIyK+mplZWrVotM6bPkPnzFsi0qdNlyKAh8tgjf5F5c+bJhg0bFUQ2bqyWTz+ZoCfaZGRkKqj41X4ADGFK29cXl4Td7mjruWFjtaSmZUhqarrU1G7yr/zNW6S+frPk5q6T5ctXSW1tndRv3uJb+UweGP/Y2HgF8mj7Mdz3q6trZG1yqiStSZaNG2t8a7dTTyYvtN3hAee619+MMby6ZOlySc/IUv7b7OO4w2/Q3IqVq6XqDsg5eBxeh+epi9f9fSv/zVu0r1esWKVAjoz1m9/y8vJl4aJYKSuv8K/dP+AYmAa2uZmCAumy5SulpKRMQQgg8utTWLheYuMSJCMzW6o2bAy53OqaWuGTn58vo0eNUq1zyKBBMm3KVKmoqNRBKy0rl9LScikuLpWUlFSZMGGCDB08RHJycgUg4f74ceM1AEVySooymF/thpmLS0qVudblF4TcbrfqR9vXrk2RtckpUlFZ5Vv5jNnG6hrJyMiSpctW6OQNcHGrXd3lA4CUlJbJ4sVxOnnr7nm37yNMkpLWCgFQysrKfWu30w4mrLSdPqAvnOtefzPGCLWEhKWSnJKq/ActeF2ukz/8huULOYc8cK779Q2PA6TwPHXxq1z6GFm3fMUqSUlJUxnrN79lZ+cqkDKJ86vdTjlgGmPuZgoKpFlZOXL8xAk1j6rpE/OnDx/WDjIys6SxcZua+cIp8+q1a2qiaj92TA63HdatLZh1MZ1gJsZ8RH6YFw4ePChJiYkyZvT7cmD/ATUzYd5auCBGA1Hs3LFDLl285EubqRPm1JMnT0l6RqYcOHDQt3Kd/j195oxqgxAcJm7nutffjAlj07Rrl+T/4CnO+HhdrpP/TdP/GUlNS5eWllbfynXKP3v2nGzYUC0VFVVy5sxZ38unzbQdEyN94dTL62/GGGfGnJw82bJlq1y+fOXWcozXZZM//LZj504pLFqvfOdHmYFlwOPwOjxPXQLvefkbfmP5pKCwSBoaGvW33/zW1LRL1qxNkWPHjvnWbqdPwTSwzc0UFEjvFa9dvHPZR0rgfdYCbnx7M7pR086dMv7DD2Xh/AVy7tw5C8hwxZyNzNnInI3cFLDB8jJno/vE2eheAVLCABLecPS7o+Ttt0bIl19Mkgkff6JOR1zjkHLCB5rXrgGpAakBaTDwc/OeAakBqZv09JO8vNj+gsmqprpaj4JbFLNQIxrlZGdLW1ubnqfKflIDUgNSA1ID0p8IJI8uGJAakHpEWjezdRtIQ62sAakBqQGpAWmo8iLa5wxIDUijpaGg7xuQ2jFqgRGnghKLCzcJ2IEzGt6rBqQGpC6QVEhZGJAakIZEKJE+ZEBqQGpAGin3hP8ekwcmEUwmmFT4lRhj/BfY7rZjR5Murfg57vhFtLTuk/JyO4/Uz36/74LW3yvORqEKBjPtmmnXNFID0lDlRbTPmUZqGmm0NBT0fdNITSP1e4Zspl3TSIMKJQ9uGpAakHpAVj9maUBqQGpA+iM/eP3LTLtm2vWb3+6r80jNtNuq+0u9FmRO/qzZcD4qcSiZrfqd0MoaGrbJ1oZGDSTtZ/kEzSB4OuG7btz47taJPH7UwZyNbI2U06H8TqaRmkbqKc2ZRmpA6vcM2Uy7Ztr1VKh1krkBqQFpJ2Th3iUDUgNSA1L3+Km7nMy0a6Zdv/nNTLvdcaUL9w1IDUj9ZmzTSE0jdUF0hZWFaaSmkYZFMOE+bEBqQGpAGi7XRP68aaSmkfrNb6aRRs6vIb9pQGpA6jdjm0ZqGmnIAsqlB00jNY3UJVLqPBsDUgNSA9LOecOLq6aRmkbqN7+ZRuoFJ3fI04DUgNRvxjaN1DTSDmLI87+mkZpG6imRGZAakBqQespit2VuGqlppH7zm2mkt7GgN38MSA1I/WZs00hNI/VGmnWdq2mkppF2TR0u3DEgNSA1IHWBkULMwjRS00j95jfTSENkzmgeMyA1IPWbsU0jNY00GpkVybumkZpGGgndhPyOAakBqQFpyOwS9YOmkZpG6je/mUYaNdt2n4EBqQGp34xtGqlppN1LJnefMI3UNFJ3KapDbgakBqQGpB2YwsO/ppGaRuo3v5lG6iFDO1kbkBqQ+s3YppGaRurIH7++TSM1jdRTWjMgNSA1IPWUxW7L3DRS00j95jfTSG9jQW/+GJAakPrN2KaRmkbqjTTrOlfTSE0j7Zo6XLhjQGpAakDqAiOFmIVppKaR+s1v95VGmpKaJgcOHpRTp077+tm//4CsTU6RmtpNcvz4Cd/KPnHihBw9elTmz50nr770stTV1Uv78eO+lU9Zh9raZM3aFNm1a7dv5Trje/jIESmvqJSy8gr55tgxH8s/JSdPnpQtW7ZKZlaOHDvWLidPnvKt/OMnTsjhw0ckMWmtbN++w7dynX4/cvSolJSUSVFRsRw5ctT38mkzbacP6AunXl5/M8aMdVpahmysrhH47+Qp/8Ydfquv3yw5OXly6FCbb+12+hUeh9fheT/lzKlTp1SuZmXnSk1Nrf72m982b94iK1clyr59+33vdzANbHMz/UOwzGbPmS8xCxdLXPwSXz9z5y2Qr76eKrPnzJPFsfG+lU1ZMTGL5e2Rb0vvV3vLtGkzZNHiOB/Lj5MFMQvl68lThT7wu98Z6+kzZsuMmbNl0aJYH8tPkNi4BJk5a65MnjJdFsfG6X+/2q/jvnDxLZrzq1ynnJv9PkumTpt5R/gNPoPfqIef/MaYw19fT54m02fMktg4eD3BN7qDzubMnSdTpk6X+QsW+lauM+7wOLwOz1MX57r33/BbvEyZOkP5nTFnLLwv9yaOUB5t//KrKXdMzoFtbqagQOpmQZaX9YD1gPWA9YD1wL3YAwak9+KoWpusB6wHrAesB3zrAQNS37raCrIesB6wHrAeuBd7wID0XhxVa5P1gPWA9YD1gG89YEDqW1dbQdYD1gPWA9YD92IPGJDei6NqbbIesB6wHrAe8K0HDEh962oryHrAesB6wHrgXuwBA9J7cVStTdYD1gPWA9YDvvWAAalvXW0FWQ9YD1gPWA/ciz3w/wG4Rz7/BD2nzwAAAABJRU5ErkJggg==[/img]
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Information: IM 8.4.2 Practice: Keeping the Equation Balanced