IM 7.6.7 Lesson: Reasoning about Solving Equations (Part 1)

In this diagram, all the triangles weigh the same and all the squares weigh the same.
[left][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQIAAAC9CAYAAABYpHNEAAAUz0lEQVR4Ae2dCXBUVbrHm3owDxWfyyDLY1VcUHAbkAFFUVlEnGJHGIdFkOXxCmQYMOibJ8UWxMECCoKM1Mi+OQ4RErZEIIKArGpAKghCMCSQjSyddPbO9+o7j26STtL73c75d1VXuvsu55zfd+4v5957zrk2wktpAs899xzt379faQYoPJENENQmABGoHX9X6SECFwlF/0IEigbeo9gQgQcQ1b5CBKpFvPbyQgS1c1HmV4hAmVB7LShE4BWP/AshAvlj7E8JIQJ/KEm8DkQgcXADKBpEEAAsGVeFCGSMauBlgggCZybVFhCBVOEMujAQQdDo5NgQIpAjjqGWAiIIlaDFt4cILB7AMGUfIggTSKvuBiKwauTCm2+IILw8Lbc3iMByIdMkwxCBJlits1OIwDqx0jKnEIGWdC2wb4jAAkHSIYsQgQ6QzZwERGDm6OiXN4hAP9amTAkiMGVYdM8URKA7cnMlCBGYKx5G5QYiMIq8SdKFCEwSCIOzAREYHACjk4cIjI6AOdKHCMwRB8NyAREYht5UCUMEpgqH/pmBCPRnbsYUIQIzRkXHPEEEOsI2cVIQgYmDo0fWIAI9KJs/DYjA/DHSNIcQgaZ4LbNziMAyodImoxCBNlyttleIwGoRC3N+IYIwA7Xo7iACiwYuXNmGCMJF0tr7gQisHb+Qcw8RhIxQih1ABFKEMfhCQATBs5NpS4hApmgGURaIIAhoEm4CEUgY1ECKBBEEQkvedSECeWPrV8kgAr8wSb8SRCB9iL0XECLwzkeVpRCBKpGuo5wQQR1gFPsZIlAs4J7FhQg8iaj5HSJQM+7uUkMEbhRKf4AIlA4/EUSgeAW4VXyIQPF6ABEoXgEgAlQAJgARoB4wAbQIFK8HEIHiFeBW8SECxesBRKB4BYAIUAGYAESAesAE0CJQvB5ABIpXgFvFhwgUrwcQgeIVACJABWACEAHqARNAi0DxegARKF4BbhUfIlC8HkAEilcAiAAVgAlABKgHTAAtAsXrAUSgeAW4VXyIQPF6ABEoXgEgAlQAJgARoB4wAbQIFK8HEIHiFeBW8SECxesBRKB4BYAIUAGYAESAesAE0CJQvB5ABIpXgFvFhwgUrwcQgeIVACJABWACEIH+9cDpdOqfqI8U0SLwAUj2xRCBfhF2OBy0ZMkSGjp0KM2cOZMyMzP1S9xHShCBD0CyL4YI9Ivw3LlzyWaziXe9evWod+/eVFpaql8GvKQEEXiBo8IiiEC/KD/xxBNuEbiEcOrUKf0y4CUliMALHBUWQQTaRpn/4ycmJtLy5cupUaNGNURw+vRpbTPg594hAj9ByboaRKBNZCsrK2ndunXErYD77ruPhg0bRpMnT3aLgE8NBg0aRBUVFdpkIMC9QgQBApNtdYggfBHNysqi6Ohoeuedd4QA3njjDYqKiqLk5GSRCLcONmzYQE2bNqU5c+ZQTk5O+BIPcU8QQYgArb45RBBaBPlWYHp6Or377rvUoEEDcZBHRkZSbm5urTvmFsCzzz5LaWlptS436keIwCjyJkkXIgguEGfPnqV58+ZR9+7dqWPHjvT+++/TwYMHyW63e90hROAVDxYaRQAi8I88H8AZGRm0a9cu6tmzJzVu3Jj69OkjvpeXl/u3EyJxTQAtAr9xYUW9CEAEvknzeT+f77dr14769u1LW7dupcuXL1MgAnClghaBiwT+mooARFAzHNy859t6s2fPpvbt29PTTz8tmv4XL16suXKAv0AEAQLD6voQgAhuc+YLfNz778EHH6TWrVuLbsDnzp3zed5/ew++P0EEvhlhDQMIqC4CbuJv3ryZBg8eLAQwYsQI2rJlC+Xl5WkSDYhAE6zYaagEVBXBmTNnqF+/fuKWH1/1/+KLL6i4uJi4I5CWL4hAS7rYd9AEVBJBQkICTZs2jTp16kTdunWjhQsX0smTJ4O66BcscIggWHLYTlMCMougrKyMsrOzadWqVaLZz119R40aRUlJSZoy9bZziMAbHSwzjICMIsjPzxcHf69evejRRx+lt99+m2JjY03Rmw8iMKyqI2FvBGQRAU/ywbf8JkyYQPfffz916dKFli1bptlFP29MvS2DCLzRwTLDCFhdBDzEd+LEiaKzD1/0W7p0KfH9/qKiIsOYeksYIvBGB8sMI2BFEXA//5UrV1KPHj1Eh5/x48dTfHy8LkN61ySm04DNiSG9uy2MoT+s/z6kffz33otU5gzfHQ4MOjLsEDRHwlYSwbZt26hDhw505513ii6/J06coMLCQs1v+VWN1KyDV6jHyhPGvqNOUv9NiWQvDd9cBhBB1Sgr+NnMIuCLfjt27BDn/TzBx+uvv04rVqygS5cuGRYpiMAw9EhYSwJmEwHf8uP/8hEREVS/fn2699576cMPP6SCggItMfi9b4jAb1RY0UoEzCICvre/YMECevHFF+nxxx+nGTNm0IEDB8Lazz8ccYEIwkER+zAdAaNEwF15eWafuLg40eR/4IEH6JVXXqHt27ebjlHVDEEEVWngszQEjBABT+4xcOBAatOmDb366quin/8vv/xCZnwCkGegIQJPIvguBQE9RMDn/Dx/P0/txVf9n3nmGfcQX6tBhAisFjHk1yuB4l+TKSs2mhZ07UTHI+dQzpFD5AzzU3dKSkrEwJ5WrVqJi348wSf/5/c1r5/XjBu8ECIwOABIPnQC5QV2yti+jW58OpgccU1qvK//7feUu3sGFZz7nijI4bhXr14V4/t5Hv9HHnlEPOdv48aNxLcCZXhBBDJEUeEylOXl0rWPhpBjX9MaAqgphWZ0ffPagGjxVX8+7+cHd3ALgOfvt8I5f0CFJCKIIFBiWN80BIpTU+j6kn5+COB2K+Hm2kcoZXFknacLfNX/8OHD4n4/z8rLg3x4Pv/jx4/r2tNPb8gQgd7EkV5YCPB5/7VFf6wmgcJ9D9LFyeMoa08MDezSmfavXkXXopZS7j+fJ/uOFu51C2LbUO7Rr9354M4+PKX3559/Lp7kw1N6Dx8+nH744Qf3OrJ/gAhkj7Ck5UvfusF9YPMpwNWZnanw7B53aaveNSjNTKe0qA+pcE9z9zYpc/pQflYWrV69Wszn36JFCxo5cqS4/3/t2jX3flT5ABGoEmmJyuksK6XcHQPdB3Xhnoep4IdvqpWwqgh4QbndTkkjh9GlqNb09YKmNLxZY2rZ+Ldieq/FixdLc9GvGoQAvkAEAcDCquYgUJ6TQ+lLOrhF4Dg6kio9nsrjKYKff/6ZJr71R2rR8DfUquG/01/atKSzW3pRYb42s/qag5T/uYAI/GeFNU1CwH7m8G0JxDWhjC+31shZ586dxdj+zz77THTx5X7+o0ePpvVjX3ZvWxD/MpXn1f5Qzxo7lPwHiEDyAMtYvMydm9wHM18fyD/5XbVi8hDfu+66S0zpzfP7ffvtt2JmH74jYE/4s3tb+66uVJqRXm1bVb9ABKpG3sLlzkmIdR/MLIKU2B20c+dOMbXXww8/TK+99hp98skntV71z9s7yb2tfU93KsvOsjCJ8GUdIggfS+xJJwJFl89Rzlf/SReiWtLEVs3ot3fcQffcc4+498/9/+t8OZ2UsbpXFRH0pnKTzAdQZ551WmAKEaw8gRmKdIq35ZPhR3ktnD+fOt33H9T2joY0snkTip7VmbKupfgsW8a/trklwC2J5Hl/DbrLsc/ELLYCRGCxgKmWXZ4d9/r16+L+/oABA6hZs2b0+y5daOkbvasd1Jlb3qOKwrpn+yk8f5wccW3c2+RHt6P870+phrPO8kIEdaLBAiMJsAB4Bt8333xTjO/nmX03bdpE3CLgZQXnEt0HNf9353fmxjFUeOF8tWw7i4roxsY1VLD3mWrrZ0dHVFtP9S8Qgeo1wETldzgcYnw/P7vvqaeeEuP7p0+fTvxgz9peN/etp4LdD1U7wHnwUeqiIZS56c+U/o9JlPZxt+rL45pQ9saeVJLq+1SitjRl/Q0ikDWyFioXD+VdsmSJeIwXT+k9adIk8TAPnxN7VlTQjU0rahzorhZCbX8zVvehkvQbFqKjT1YhAn04IxUPAtyfn5v6I0aMEJN6Dh06lNavX09ZWYHfzss/sZ2y1v/BqxDytj9B9kNTqTjlV4+c4CsTgAhQD3QjwOf2Fy5cEAd/gwYNiEf58aCfcL2y9+2mC28PJ0d8K3LEtSRHfAu6ue5p+vXjBVR09Uq4kpFyPxCBlGE1T6HKy8vp2LFj4h4/d/vt2rUrzZ07V/zGw3+1ePHdA27+l93MrnPeAS3StfI+IQIrR8+keS8tLRW3/Hgqr06dOlGTJk1o8ODB4uA3aZaVzxZEoHwVCB+AvLw8Wrt2LfXt21dM68Xn/7GxsZSSgiv04aOszZ4gAm24KrPX7OxsMbXXtGnTxFV/Hv770UcfiRaBMhAkKChEIEEQjSgCT9/N03i3bduWWrZsKab3Tk5OJu4LgJf1CEAE1ouZITnmi34//fQTffrpp9SnTx968sknacyYMRQTE0M8zz9e1iYAEVg7fprnnsfw83P8unXrJsb3v/DCC+IhnnxBkJfhJQcBIYKok9TDyDdGH5qrMvETe/gi3+TJk6ljx46iBcA9/7hFgJecBE5ct9PSk2mGv79IyqKKMP6DsckZLu1Kxc17vrrPj/Bu3bo18VN8+QIgrvhrxxx71p4AROAnY77At2jRInrppZfEo7z4AuDBgweJ7wbgBQJWJwAR1BFB1/j+vXv3iiG+/N+fJbBu3Toxr18dm+FnELAkAYjAI2x8Ye/QoUPiCT5t2rSh559/ntasWUNXrlzBVX8PVvgqDwGIgEjc0z916pTo4MMdffhZflOnThXP8ZMn1CgJCNRNQGkR8ASeK1eupMcee0xM6sn3+xMTE4UYcMuv7kqDJfIRUE4EaWlptHnzZnrrrbeoffv2xOP7ud9/amqqfNFFiUDATwLSi4D/s/MwXh7fP27cOGrUqJG47bd8+XJ08/WzkmA1+QlIKwIWAJ/3R0REUJcuXYjP/efMmUNHjx4lr3P6yx9zlBAEahCQSgTcnZeb+Nz056v9zZs3p/79+1NCQkKNguMHEACB2wSkEAGP5ON5/fgRXg899BANGTKEvvrqK9Hbj/sD4AUCIOCdgGVFcPPmTTpy5AjNmDFD9PTjqb3mz58v7vd7LzKWggAIeBKwnAi4T//MmTPFBT8e48/n/ZcuXcKFP8/I4jsIBEDANCJwOp3i6Tx8js+fq76SkpJo1apV1K9fP+rQoQONHTuWoqOjief5xwsEQCB0AqYQAR/4w4YNo3r16lH9+vVp9uzZomTc1ZfH9fPvPLkn9/tHR5/Qg449gIAnAVOIIDIykmw2W7U39/br2bOneLIP9/bjmX/wAgEQ0IaAKUQwaNCgahJgKUyZMkWbEmOvIAACNQiYQgQffPCBaP67WgV8KsDdfvECARDQh4ApRMB3Arj3X8OGDenuu+8Wk33qU3ykAgIgwARMIQLOCHcK4g5Bs2bNwvUA1E0Q0JmAaUTAdwMGDBgg5v3XmQGSAwHlCUAEylcBAAABE50aoEWA6ggCxhFAi8A49kgZBExDACIwTSiQERAwjgBEYBx7pAwCpiEAEZgmFMgICBhHACIwjj1SBgHTEIAITBMKZAQEjCMAERjHHimDgGkIQASmCQUyAgLGEYAIjGOPlEHANARMJYI3R/enhYvnmAYOMgICqhAwjQiKywto5tet6K/xv6MyZ4kq/FFOEDAFAdOIIO5qFI2MsdE7u22UlPOtKeAgEyCgCgFTiCCt4AKN22WjkTv//x3xTVNV+KOcIGAKAqYQwT/OjqdRtyTAMhgVY6OYy3+jSqo0BSRkAgRkJ2C4CPJK0mlsldaAq1Uw/cC/UUlFkez8UT4QMAUBQ0VQXG6nDw61rdYacImA/244P9UUkJAJEJCdgKEiOJK2qU4JuIRwMfeY7DFA+UDAcAKGiuC9hAfcFwhdB77n32VnBhgOCRkAAdkJGCICZ6WTtiS957M1wFIYHWOj8zcTZI8DygcChhIwRASpBUk0YY9N9BvwbAHU9n1qvI3ySzMMBYXEQUBmAoaI4O8/jvarNeCSAt9a3Je8XOY4oGwgYCgB3UWQmBUvmvuug9yfv3/aaaOJe21UUuEwFBYSBwFZCegqguLyQpp9pIPoMOSPAKquw62CqO+HUbmzTNZYoFwgYBgBXUVw/MaXAbcGqspg/G4bXbX/aBgsJAwCshLQTQTZRSk0Jf72eIKqB3ggnyO/e0HWWKBcIGAYAV1EwGMGNpyf5rPPgD9C4FOEhGtrDAOGhEFARgK6iMBemk3/tS/01gCLggckRSQ0p6Jyu4zxQJlAwBACmouAJxlZdPxlv/sM+NsqiLn8sSHAkCgIyEhAcxGcSt8RllMCT0HwiMWUgnMyxgRlAgHdCWgugtlHntREBNz1mDsm4QUCIBA6AU1FsDd5mSYScLUOWAZZjquhU8AeQEBxApqJIN1xWYwnqDrzkOsADudfHsHoKMtTPIwoPgiERkAzEWw8P41Gx4bnToEvcXxzbW1oFLA1CChOQBMRXM4/LWYj9nUAh2v5Xw78hpyV5YqHEsUHgeAJhF0EfLtw3rFOAY0uDFUI3Ldg/U9TyFlZETwJbAkCChMIuwjOZOyqdTLSUA92X9uP34PbiQrXYxQ9RAJhFUFhWQ5FJDTV9E6BNyGsODM0RBzYHATUJBBWEXx58X8NkwALgm8nns6IVTOSKDUIhEAgbCLIL82kqV/rc5egrlYBXyv4n0PtMA4hhAqBTdUkEBYRVJKT/v7jKENbAy45cKvgcOp6NaOJUoNAkATCIoJz2fuFBLTuPOQ62H39nbzPRplFyUEiwWYgoB6BsIhg4XfdiecV9HWA6rWcTxHWnpuMZyeqV59R4iAJhCyC767/k8bEmEcCLtnwZKc3i1ODxILNQEAtAiGJoLLSSdP31xczDPNzCsz2/vzsBLWiidKCQJAEQhIBp8l3C3JLbpjy7SjLDxILNgMBtQiELAK1cKG0ICAnAYhAzriiVCAQEAGIICBcWBkE5CQAEcgZV5QKBAIiABEEhAsrg4CcBCACOeOKUoFAQAQggoBwYWUQkJMARCBnXFEqEAiIAEQQEC6sDAJyEvg/YHIvx9frHp0AAAAASUVORK5CYII=[/img][/left]For this diagram, come up with one thing that [b][i]must[/i][/b] be true
For the same diagram, come up with one thing that [b][i]could[/i][/b] be true
For the same diagram, come up with one thing that [b][i]cannot possibly[/i][/b] be true
In this diagram, all the triangles weigh the same and all the squares weigh the same.
[left][img]data:image/png;base64,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[/img][/left]For this diagram, come up with one thing that [b][i]must[/i][/b] be true
For the same diagram, come up with one thing that [b][i]could[/i][/b] be true
For the same diagram, come up with one thing that [b][i]cannot possibly[/i][/b] be true
On each balanced hanger, figures with the same letter have the same weight.
Match one hanger to the equation.[br][img]data:image/png;base64,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[/img][br][br][math]2 \boxed{\phantom{3}} + 3 = 5[/math]
Complete the equation by writing [math]w[/math], [math]x[/math], [math]y[/math], or [math]z[/math] in the empty box. Find the solution to the equation. Use the hanger to explain what the solution means.
Match one hanger to the equation.[br][img]data:image/png;base64,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[/img][br][br]3 __ + 2 = 3
Complete the equation by writing [math]w[/math], [math]x[/math], [math]y[/math], or [math]z[/math] in the empty box. Find the solution to the equation. Use the hanger to explain what the solution means.
Match one hanger to the equation.[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAEMCAYAAAAYkcigAAAgAElEQVR4AeydB7glNfn/WUF6kbYsLG1hAZfeV0GaKCLShHVpilSBpffeFhClw4rSQRfp0qWXBQSBpfyAxZXei4Igiortn//zyfqefU9uZiZz7tx7z2SS55mTTJLJmXwnyXznzZs305jkEgI1ROD//b//ZziSSwhUiUBqU1WimcrSCIS0rZA8uswU7m4Epilze+nhl0Er5U0IJARiQCCNezE8xe6og25LOtwdd5fuomoEShEs+XNpGOJLfPITAmUR0G1IwuIXlRWar6iclJ4QcNuSe54QSggkBBICZREIJlj/+te/zF/+8hfz3//+t+x/pPwJgUIE5IX297//3Xz66adtx9/+9jfz2Wefmf/85z+F5aQMCYHeIsAYRzv885//bD766CN7MPb985//TONfb8FN11sEGMv++te/2kOPd7Q72pmMh2TOCicoux+BIILFA3744YfN8ccfb5577rnur1W6w1oiwIvt0ksvNWeccYY588wz7XH22WebCy64wFxzzTVm4sSJ5k9/+lMiWrV8uvW4aYjU888/by6++GJzyCGHmB133NHsvvvuZuzYsbYNvvrqq20vvHrUKt1ltyHw2muv2fHtrLPOsj5jHmPdRRddZO644w7z8ssvW4KvyVW31SHdTzECQQQLtr3RRhuZQYMGmb322isNMMW4phwdIICUdNFFFzWf+9znzODBg82QIUPM/PPPb8NzzTWXmXvuuc2oUaPMU089ldpgB/imS/IR+OCDD+xH5MILL2y+8IUv2La3yCKLmAUWWMC2wVlnndV897vfTVKsfBhTagACt99+u5lmmmnMzDPPbMc5xjoOxr3ZZpvNLLnkkuawww6zROvf//53QIkpSzciEESwnn32WfvQedkttNBC5o9//GM31iXdU80RgGANHz7cvtwmTJhgHn30UfPb3/7WPPDAA+ayyy4zm266qZl++unNl770JfPJJ5/UvLbp9rsJgY8//thst912tn2tuOKK5qc//amV1r/11lsGqRVt8PDDDzfXXnttN912upeaISASKaRUEKytttrKPPbYY62x7tZbbzU/+tGPzBprrGHfuauttpp55plnalbLdLuCQBDBOvroo80MM8xgTj75ZCtduOSSS+T65CcEKkMAgrX44oub+eabz+pcuQWjn/CVr3zFDkwPPvigm5zOEwIdIcDUNGMbEvr111/fvP76695y5OXoTUyRCYESCAjB2m+//bxXof+HBGvGGWc0a621llWN8GZMkV2NQCHBQlLAS2/NNdc0f/jDH8yCCy5o1llnHauI19U1SzdXOwQQhdPWEJOjC+NzDEh8+d1yyy2+5BSXECiNwLvvvmunA5mGRlqQiFRpCNMFJREQgrXPPvtkXsl4uPnmm9vx7sILL2zlS+2zBUXXBwoJ1g033GAfMAp4uL333tt8/vOfN0888UTXVy7dYL0QYPUMU4Q+gsWgggRrk002sXoL6GEllxCoAoFf/vKXdoxDvyq5hEB/IBBCsLiPe++9184abbDBBon498eDqfg/vASLlxkHyu0w6Nlnn92KzYn7zW9+YwnWQQcd1HrgxIvTYYlLfkKgCAHaDVOEiy22mJl33nkNq2zef/99e7z33ntW2ZPVhCi677rrrjZvUZkpPSEQggAfjUwPipQgjWEhqKU8vUFAE6y89saq6XnmmccMHTrUrirszX+ma/sfgTaCpR804cmTJ1tpAYp4kvaPf/zDrLrqqoaVNjz85BICVSEAwVpqqaUsgV977bXNV7/6VXugg4Bki+npY445JnP6sKr7SOU0C4EtttjCSrDuvPPOZlU81XbAENAEK+8msP+37LLL2sUXb7zxRl7WlNaFCLQRLH1/EKqTTjrJDjzXXXedfamheIduzCmnnGLjr7zySn1JCicEeoUAOgcsT2al4IYbbmhNg2Ae5Jvf/KZdObj00kub0aNHWzsxTCcmlxCoAgExQcPK1eQSAv2BQCjBYgHGSiutZD86IVgi6OiPe0z/0XsEMgkWRArmjL4VBvdOOOGE1oHhPRSNv/Wtb5lko6P3DyGVMAUBSJNPyZ1BBWvHvABXWGEFM+ecc5p77rknwZYQqAQBzDMwnt14442VlJcKSQgUIaAJVh5pYpEZs0WoRiTzSEWodl96D4IlD/u2226zynXow4jBR+xgcWB4j5ccBtEmTZrUfbVKd1RLBEJWEYqBPgyOJpcQqAKBY4891hIsTDUklxDoDwQ0wcr7P2xQItFHLSdJ7fOQ6s60aYRQ6dtDuR29K2xwsBweEsWDloNztjLB4jY6McklBKpAQOxg+VYRSvkvvviimXbaac0qq6ySLGoLKMnvGAHGPz4maVPo/bHvZXIJgb5GIIRg8cEp5B+bWK7zvbvdPOl8YBHoIcHidl555RW7cpCloVnuww8/tCsb0JlJVrWzUErxZRDQBIuNUH0OCRYrvtDRSi4hUAUC6Jai3zfddNOZ8ePHGxbypJdXFcimMrIQEIK17777erNA9FGJYAYJw8vsj5lc/RDwEqxTTz3VSqcuv/zy3BrROJLuQi5EKbEEAloHixWq6AFyQOA/+ugj87vf/c5A+tlVgE1Sk0sIVIUAxApzNEhPr7rqKqvvQtuDbPGyow2iA4MuYHIJgd4gAHkXgsXevhB82hc+ggt2Ejj//PPtqmn2xGS2KLl6ItCDYDGAoEiMnhWbn+Y59opjfhh9GFY7JJcQ6A0CSLAwxzDTTDOZI4880owdO9YebNW0ww47WAX4OeaYw7CsHsKVXEKgKgRQizjuuOOszSFUIzbeeGO7fc7FF19sxo0bZ4466igbl/YirArxZpeDSRBUbFgheMABB9hj//33t6ukkaaysTgb32PgO71b69tWLMHS4nAsZGPs8dBDD7W10mm6msQjcWAgWn755Q3bTSSXEOgEAWljtKevf/3rtv1hWA+7V/gcw4YNM1/72tfMGWeckQzudQJyuiYIgeuvv95uKk6bY2oGiRYHi3v48LzrrruCykmZEgJZCDDesXk471lWCOqxDjuAjHN8XD733HNtRcg42RaZTroagZYESx4eYkrsbSAeD3FM5WB1G1G6dlKejkvhhEAeArQZiDoicjloW4SJ120sta88JFNabxBAmvXSSy/ZlyCE6r777rMvuyQ17Q2q6VoQkHGLbb9kjBOf9y6zRrQ/yYcv4YRg/RBoEaz63Xq64xgRkMFE/BjrmOpUDwRSG6zHc6rbXdKuUtuq21Pr7H5bBEseuOtLsRIv58lPCCQEEgJNRSCNh0198qneCYFwBFoEK/yS7Jxp0MnGJqUkBBIC3YlA2XGrbP7urHW6q7ohkNpd3Z6YMZUSrPpVv/2OUwNuxyOdJQQSAs1AII19zXjOA13LprWzRLAGusWl/08IKAT0AKTDKksKJgT6BIHU3voE1lRogxFIBCvj4WN7JA04GeCk6D5BgPam25wO98kfpkITAsZYO0vS1sRPwCQEqkCA9pTVporse2VdV8V99VcZiWB5kMb0BFsThJqq8BSRohICQQjoQeTNN980kydPtsu0gy5OmRICvUQA4760OUwEJJcQ6AsE9Bgn5WO5nncs79qYXSJYnqd7wQUXWCODN910kyc1RSUE+gaBrbfe2lpvfv/99/vmD1KpCQEHgffee88avBw9erSTkk4TAn2HwA033GCGDBliLrroor77ky4oufEEy8euTz/9dLvH4tVXX90FjyjdQlMQ+OpXv2q3z0i7IjTliQ98Pd955x273dm666478DeT7iBqBPS7lv0+2cc49n0WG0+wfC2ah87DTwTLh06K6ysE2CaIffASweorhFO5LgJvvfWWbXPrr7++m5TOEwKVIaDJFYUKwWKvxZhdIliep5sIlgeUFNXnCECwZphhhkSw+hzp9AeCwNtvv203V0d6mlxCoL8QSASrv5Duwv9JBKsLH0oDbikRrAY85C6rohCsJMHqsgcT+e0IwTrrrLOirmmSYHkebyJYHlBSVJ8jkAhWn0Oc/sBBIBEsB5B02i8IJILVLzB3558kgtWdzyX2u0oEK/Yn3H31SwSr+55JE+4oEawmPOWMOiaClQFMiu5TBBLB6lN4U+EeBBLB8oCSovocgUSw+hzi7v2DRLC699nEfGeJYMX8dLuzbolgdedzif2uEsGK/Qnn1C8RrBxwUlKfIZAIVp9BmwrOQCARrAxgUnSfIpAIVp/C292FJ4LV3c8n1rtLBCvWJ9u99UoEq3ufTcx3lghWzE+3oG6JYBUAlJL7BIFEsPoE1lRoDgKJYOWAk5L6DIFEsPoIWteiax/9Ta+KxTZHN1py19jpcK8q2+CLuw3DDTbYIBkajbA9dls70xAngqXRqGe4m9tXFqI+glXHemTVT+K7zg5WN4B8xhlnJIIlLSRSvxvamQttt0qwuhErF7s6nXcTnhCsmWee2Yih0W66t7xnWpf7zKtDX6dpjCTs+n19D1K+/l/CPoIleQfKl3us8v+7jmBVWblOy0pThJ0il67rDQJf+9rXaiXB6osBqTf4pWvLIwDBYv/LtFVOeey65Yo69sNuJFh98Ty7gmDRQAbq+O9//9v234AsBItGMFD35f4v96nvtS8aQxPKBFec9l2sB+ocgqU3ex6o+8j73ya0kb6qo8ZV92Ud399hLcHS/y19RMcNRLivnkVTyh2IZxbyn5pgheQfiDxVtJGuIFhVVKTKMtjhGx2sa665pspiKy2LBpdcXAjIFOF7773XtRVL7a5rH01HN/bOO+/UQoKV2l1Hj7drL9IEq2tvUt2YEDwVFRQcMIL173//28jxr3/9y7gHaW5cX5zLPcj/4YsOFo2gL/6zbJlyj3Id53wBJ1ceAf2cBc+B9uWeRILFS0/iBvre5P+5Hw6RvJRHvrlXMDjL8xQcxRd8B8p/6623rA4Wbc+9J7nngbo3/b9u60mEy0VkqlReUv7zn/+0nql+ljqsMe7PsBAsZot890OcL77qe8z6H+LBT7tO2tyAECxu9KmnnjK/+c1vBvx4+OGHDQf3gv/QQw+Zfffd10qwxo4dO+D3l4XRc889p599Cgcg8Omnn7aecRauAxm/2mqrmemnn97ceOONXdPu3P7BCzm5cgiAmR5fZLwZyLYm/33DDTdYvb9VVlmla9qc3Jv44PXXv/61HOgpt5k0aVLbu03wHGif53n88cfbdyzv2m7qD3Iv+HCUTkiVbnoDQrBgoSuttJLt2F/4whdMtx1zzDGHkaPb7m3OOee0uDGdlFw5BJ5++mkz00wz2S92cOyWZyv30q1tDpxmm2022+5OP/10C3pvB55yT67euU877TSLHRhKm+NZS3igfbfdddO9scIRvcRnn3223o2gj+4+rx9+4xvf6PGOZazphucrbW722Wf39gNJ74++ASYyBos/wwwzWI7SW4n9gBGsZZZZxsw666xmr732Mvvss0/bsffee7edu+mcw3x98bHH7bLLLubzn/+8WXvttXvNrvuoz3dtsXyRDBo0yND2Ym8nUr+sfpLVx7Liv/Wtb9kvzh//+Mdd+3y79cZ+9KMfWew23njjxo1bbvvLal/SXl1/2WWXtdj93//9X7c+3gG7LyFX4rs3ss4665hpp53W7Lbbbna8c5+Fe+5iX/ZZudf357muiw53cg977rmn/aD84he/2JomzMLYxdw97zXB6uSPmd8cMWKEWXjhha2Ok74pX3lunHuur489/Mc//tE+/K985SuZVW0yPlmggAkEi8ULkNSEkR8pcPFhw1QS2J1yyin+C1NsJgKQUrC76aabMvM0IcHXrorq/YMf/CARrCKQMtIhWLPMMov505/+ZHMI/uJnXNbYaMHln//8p1lkkUXMUkst1SJYAorkEZ/4rDBpvSZY7h/LedYfczNUAHa40EILmX/84x/6Em9YV8CbIfJIXf/333/fEqy11lqrrdY6jyT44iStif6TTz5pB+udd965idXvVZ1/9atfWexOPfXUVjm0L7eNueetzA0JSP3Fp9pCsCCpOJ3WEFjaqlmm/nwMQU6Z3s9zlFmm3Lyy6pjmq7sQLD7KQ5yvjJDrBjpP1n1nxRfd79/+9jcvwZLyxC8qh/TKCBaFhf4xEqyll166B8HyXU+cLz6kcjHlEQxYws+8dZ4EK6Z6V1kXkWAJwRJMq/yPbi9L6iy+e786Xoevu+46+6JDgqXj3eubfC64iC9YCMFi8UJTV/+CicZFhwUnny8EK00R+tDJj1t33XWtBCuLYHX6TPL/tbtSi9qZiwF3//e//91LsMrUTMqtlGDpG5A/IE7C4udJsMjjc1nxvrwxx0Gw0F1DBwsnuIgfc917WzeXYPW2vCZdf/3117dJsKS94UtY8HDPJb4JvtRdfOosOlgQLHE6XeKa4pepu0uwuFaul7Ccu/hlxbv56niu6yY4UA8J40OweFf4CJa+Xtc/K17nqUu407pAsBZddFE7y+aaasiru+//ek2wdKE67LsRSdcSLMiWxPuuSXHtCGRNEbbnSmc+BBLB8qESFucSrLCrUq4///nPZr/99jPTTTed+clPfmKYfhCXxj1BIttH2swU4TPPPJOdqUEptJnQdiMSrA8++CAIodBygwob4ExliJF7qx9++KEZMmSIGTZsWFt/dfPJueCmnw1hrCX0mmDpP2Hw+OSTTwqPjz/+2CqQLbjgguajjz5q5Wcw4nrxdVmUrSsg/9s0/91337ViX6YIaUTycJuGQ2h9NT7ocTBY81WM02mh5cWUj+kq3cd8/U7irrzySovdSSed1HaNvt7tuwwwsbusNkT8m2++ac4991zzpS99yW6mjNT5l7/8pelmS/398bz4qJZ25bYf93zHHXe07e7RRx9tezdkXY+9rKxn0h916+v/QGeZuruH4Ca44KOni5L766+/nttnpd/GYmuMcQ1CjiSqrPvss8/Mz3/+cztFCMG6+uqrWwvxyrQrntOdd95ZHcGiIrfeeqv52c9+Zs4///zc46c//aldQTjffPPZrzryX3DBBZnXkJ8v6KY6OsArr7xiJk6caHjRYRsGUwP33nuvVf584403OmpMTcFTOsYDDzxgPve5z5mtt966sbow+pnzZTtu3Dhz3nnn2b4nvtt/6Zt77LGHNYL6ne98p0df1X1XwkhraLNNdAzSkHlM0IwcOdKSLMgWxhVXXXVVc9RRR5nf//731lJ1E/FhsQntw21nvnMUtTG+e8wxx/TIL21NruPdc9FFF0U7FjKO3X///bY9SZ3zfDGFhO26vHykgR3W1WPQEQSn7bff3tx8882ldp5AYAEpwjQIu7n88Ic/NMstt5zFvAgXecfQn5mh47+xklCZBIuCv/nNb5oll1zSbLbZZmaTTTYxm266qfUJd3pQFgrx6623XuPGor/85S/WwB6Nf8yYMQZbROx6v+aaa1odLLa3wLbOQQcdZK644grz0ksv2RWajQMqQBqFNOXggw82w4cPt+T05ZdfbiJMbXVGcZiXF0Zry/ZP3bclLP5GG21kPwJk1Vzbn0Z+AmnlY3DDDTe0fROr2XrwRQ8L0gBRvfvuu61kQadHDo+tHgsl5plnHu/7gfFM2lGZNsk1SPXnnXdegxpFrI4pU17c8o4FrzI4+fJS1oorrmjHxbpLnaUv8Y6EYD7xxBNBTYHryMsHEfa/IFR8KO2+++5mjTXWCJ6ippxHHnnEkjRmSyolWLzwedmL+FLEliKCFF/SQ32+/L785S9boATAINRqnImpwIsvvtgONpAqcL322mvtg0bk+9prrxnE5uTBVgyNANZ+2223GYhZ01xRu3j88cet2PcXv/iFVf5EL8Y3mBSVExOuEKy55prLTJ48udVndZ/U/dUNc+7GMfVP3B/+8AerJIpph6Y4BmRI+8knn2wHaci8ftHrdvXiiy8aXpT0WT6emrb9EBhRd91+dLtzw7QrN07OpQzy3HPPPYZZEY17bO3ve9/7ntluu+3sGC8Y4AsO+D68dDphOeda8iMNxO6Tb0ysI4a8M1FB4mOP/lbkyLPBBhuYbbfd1rY1yY8NsS233NK+h/Mk8tK/GUvXX399+yFfOcGiUoi/xcmf4sshaeJLfJZPPlbh0CGb4pjyO+SQQwz7g0EuX3311dyqI9pk+hC2zX52TKmKcbncCyNMpB25jj0I6SSjRo2ySZBQOh9fGk12ECy++Jm+wkkfdMM+jLLyEs+X32KLLdaYaX30Q2lL3//+961kefz48T0MFLoYoh/CRrf0VyxP8yzALVan+yVTL2LHT+Jd34eDzkNYDsnLB+fgwYOjI1hSb+r53e9+16CXJk7SXF/SxXfTOZeDPJdffrmdfYqFYCHNxIo7kmRIKQKLLPfOO+9Y0grBevvtt3tkQ5jBgoEddtihpT8peOrMXLvNNtuYzTff3E5pV0Kw9EOCuWmCpf9ch/U1Oj4rDMESCVZWnrrHywPj65+tDagv88HaSR7xdRphOgdKtcwhn3322dHqIrj1lvMsXLDhxLJbdD/IAyGlI3z7299u9CayvNSZqhGCJTj21kfBM2aCpdsZ0hKkoiiwo9uH7pWk4+swuMq5YDxhwgT7lc30P1Oq+sPIzSvX1N2HYPECDKlfSB7B9be//a1d/RWzBAvplSZYRW0hFD8Uu1Hv4R0Sek3Rf/d3ur5v3p/onv3ud7+z058HHnigXVAn9yR56W8HHHCA1Y3MW6mKAGPllVc2hx9+uJX4STnioxrA1CJTkwhELrnkErs4o9IpQvSkjjzySPlP61MRfbQlqq9mnUeHyd8EgkU9WV2DxArFuscee8yFqsc5OOEEL8nAw11iiSXsgC1xTfWxAUNnO/TQQ9sgoDOxk8A111zTFt+kE02wdFsCA2lT4vtwkWskv/hIZ2IlWFJnXkQM3kcccYSdEmR1JSui85xcK3nknC9opqxXX311uxURUxFFSrVSRh19LcFy71/XW/CRPJzLIXH4kg8pYowSLF1XpDFISsVJ3bN8yYcveXSchJG6CsGSuDr6Ukd0qeiTuDvuuMNuzYfiOrMZ4lClYSN2dLzRhyxyv/71r23ec845p818A+Uw7S0K8ZTD4qFKJFj6ppgidAmWTnfDujO5afq8CQSLhsEXGAqM6Fr11h122GF2+oGvOWl0vS2zbtfTvviKQaLn03Ph5ciqrpi/ePOeGQRr7rnnNkxJhzjaka8tuXExSbDcuoETOisMyEw5I7Vn4M1yvut9cbRVpAiYdEBCwXSXfhlklV+HeLe+ECy+9F3n5iOdOLDxpbnXgxn2i2Luz0iwmKoKwQN8Qt+xSGHrTLBcPOhHtDNx9C2252MVPh9HCDOoM3pnkMtQh84z5bDiktWClHPZZZfZcogTxyrZASNYTNGwTBnDjyGuCQSLh8XKotGjRwd3Co2dNDDxGWTYUBu2LU7S5Dx2H8VFJHkoEvvqjuQA8sVWJrTJpjktwSqqO6QCqSpT2EUuJoLl1pUXFgrB6E6xuMS3GtXX1nQ5eemMiVtttZWdQot1c2iZItSYZIXRa+HDM0Q/jXxNkGBBsFwnbUr7SELpsyEkq+4ES+MBBhAskWBJGu1OpEwsiGDsdzev5z0AadIOQsb7WdwJJ5xgy8Hsj5h1QJ9SHP/fJxIsvuaQYOmHLH8qPtMHdARWvLFkNMRBsGJXcmegRuH4oYce6gEJgwurE+QhM+hAUMVBJPR2CII/DQwJTcjgJGXF4lNn7BCxJF4M6Akuuo7YzcF0g8ZTp8ccDiVYEFG+AJnCyloZqLGFYC2++OJRKrkz+NKnkF7pfqXrr9sMfVWkp7zo6MdFlrVZ2QWBQ08wRse45JNg6bqCFX0S+1cs9qENFjneK7GvIkTJ3UewNDYQAoj6nnvuace/EIObMREssNBThIINuKAnRRr9C70s4rRDJwv7kkJK8dGTpB+Lo9+DLW2YMZEV/u4H+oBJsFAA22mnnewNyn56cuNZfhMkWBdeeKGd3+Xl5DpWQKCQjRSBBsEKQzoajhVMkFUYueueffZZS9oY1JvkeNlBVNGxchcKuDiAH3agWIGpX5huvhjPQwkWbROyimIy4vAiF7MEi7rT/1idJB88xGURLOzTMV3PAIzeH+YZwD3P0Sb50gb3GJ2WYGXhxvQoL0DMXTB1hWkaXFZ+0hLBmoIPsxcslEJ5e/nll2/TF8pqT7ERLHeKUOoNgWKVH1JiTFW47rnnnrPSL5meR3iB6hPx2qFvucUWW9iFLfIBr9MHjGDxJYJNIsRrRV8xcsNNIFjoXaDA6HN0GBTxeKgo1rKYAGkhDmKFErdefSRlQBiYY2aQb5JD6RDpKDZN8gZkwQQMhw4dai32kj/kGrm2zn4IwQKLhx9+2NqGYfqaBRRFLnaChfFQJCW+6UGw0e2HPIxzjHl8WDJ1IF/HgqPOTxxj4/zzz29t3UmemHxNsLLqRRvCajnSPkiCEKys/MQngjUFHd4TDz74oJk0aZJd+QZhL3JNIVjggM6pSJVdXGhvTB2yspoPKEg+Eiqfo01qyZbux6zmHzRoULWGRn1K7vKn4suN8lJLBEvQMAYjrccdd9zUCBViygBLu+xhhhkMVixguRiWjfSK1REuvnI5ZAyC2iSHIiNmGdyvDjDi5cZBWDDD5+X3jW98w37V6PiYcQshWFJ/MOGLDSXPIhc7weKFxQcPW4zkOTDjwB4PdnTo3+5Ugu96VhQiIXOJmC9vHeOyCJb0O10nyAIEC1tERa7JBMuHHePfSiutFLRYokkEK68dQapQR8IsAwSVsM8OpYu3nIvfbxIs+UO3UolgtSPCAHzWWWe1R/7vDBEk0zN80fGSQ3mRbYnuu+8+a7Avz4ga9nWyiFvWs/HeRE0iwQJ7JT57bEgT0E3AHhYSBRERg8Pzzz9vTQsw0DTFhRIsaSeI1i+99NJCeGIlWIIDPsZBIeSaBEm6Boi+e/TRR1vDtkw3+PJIftLQl2GLDxZmxOqyCBAooT8AACAASURBVJavvh9++GEiWAqYEB0sstOWhGA1WYLl62++OAWxnUJkJT/6Wq6ivM6XFab8fiNYchNSKfFZ5pwkWIKOsVNa6Bv4HJIqpgTZcBcSBoZ84TKtOHbsWHuJ4CrXyzlz0RgdbYJDOnDiiSfaAdm3VBvpC/owTMUyrQqp0g4bZCussEJL7CsY6jwxhUMJFnUGC/QAmz5FKG2Cjx2m8fKmriBLv/zlL63dIpbXh/RDpDCYGsiafoyh/eURLMFX6gnBQh/NlWC5+cjfZAmW4KV9dP6SBKt9yl7jQ9jXjrCZiE4uwglmjXxOrhPfzdMnqwh9U4S6EvpmkGCFrgxsgg4Wc73sm+SbQkCXiqk+DnTYwBGz/qxmyhuIEa9jV+v22293n3+U5xAmVq/5pFBgBlFlbp0pG1aBIGkRRzrz70i/IK1agVnyxOaXIVjUHQkWJFX3Yx8msUqwpK7UHz0/9BuzpkzJw0ILBmkkCUhMWUzBdXmODwCk2YwDRTjnldPNaS7Byqon8ayO5qPHJVi++jWdYLk4ssiJ8ayJqwizlNx97UbHgaEY6mZBj4upzpsX7ncJlnszLIVkCX2IawLBuvXWWy0Z8tkZ4iGzXFlPGyCpwQotjnRfQ0BKiPK2XuLsyxfyDLo9Dy91VmjxEssaUIhHbwbl96yl8kgcFllkkcKVXt2OR8j9lSVYmCZIqwinIEs/QqKMLqTvo4g4pM033nijvYBzJKR5G8bShnkhipQ65BnWMY9LsPLqgAQLMw0+guWOZU0nWC6OEHvMCGSNhxq/pIM1FT328sXCAR/kYCQ4uf7UK3qGBpxgoUCWpRvk3m4TCBYvfKQvWS8webiCjXsu8eJjzmGXXXaxLwCtJyLpsfmQSTZwxmaJzyGRwuI2qwsZeLIc0kKmX1k8kDUwZV1bt/iyBAur+Fn46rrHLsGSuvo+YCSN/una2CFOFlhIPu0/8cQT1lBm7DbZyhAsJH5M2WR9EGn8EsHSaExZLcfeeSHmZ2ImWEXvSlDjA4g29sILL5jNNtss095fO8L+KUbyDDjBYqBxByD35uU8doIlDUD2NfNJsQSLUJ/BmulBJGM4+Y/Q6+uSj3qxyhLJ1a677uq9bfKAB9M1TJdCtvLwYGoHyR97WPlc3rW+/N0aV5Zg0V9DyDrENNa9CPWzpN1hpLbMVhv6eglLe0JKjV5q6Lgo19fNZxU0i3aKnOCCcVcJ510jBKuK8TPvfwYqDQxCldy5R/L72pIPy5gJVsjzYsxiAc/+++9vTTOEqoi4WMo5ZhoGbKuckArrPBAs5lRjd9jUYEkyUwmywq2TOothUrbecc3+d1Jet1/DnDkv9Kwvf1ZysfoSAgbRQh8G8W+eY/oHnUKMu8bqIFjsHoBeWpUuVgmWDJ4aK6TETJ2GEE+5zlcOUgbZ7FnyxeqXkWCVwYDNnrFPJgTLh3OZ8rohr1uHMgSrzP3HSLDKrACEYGHY9/LLL2/t/FEGPzdv5RIsGgIvJKQw4nTj0GFJD/UhWCjE96aM0P8ayHzUj+WhbCbJ1iTaeKjUXfys+8SAGqsR0VvwTYUVXZ9VbjfGUxfqyyojvorFuXWEQLCsnj2kOGhP7ipDuUb8l156yUon0NmSOCk/Fl8kWBjekzq6fid1jZVg+bBg2pkdA+Sl7svjxgnGOp5nwT56vj6r88UQ1gTLh4XUkTQ3Xc7Fl7z4bPYMhmWehb6+DmEfwfLhRF18GGXVkfcNFvNj+SBnOxzaWSdO46bDZcqqnGDx55gS8NkfyruxogqQzma8IsEqyp/3X3VJQ8lVlF1Rig1p9EhkWEXH9gisLrzrrrvqUt2O7xMxLu0NMokybIiT9iN+3jVsBIpNIk1A8vLXLU0IVpZVY12fELwkf4wES+rv+rQ7FkXwYZTn5Do3j8Tztc1LwTel415T9/PQKcKy9USChYkL9+OpbDndnN9HsELuV9pZVl6muSFYoVNjWeV0SzxmeIRgUfesg/sVbMR365B1rY7nGi3F7hOCJRIs/ceE+WPt67BU0L1Gn9MhQ006uODU4Zy6Cg74KNyx/JsBlz2l0KNi+ovBHFEmnQDSBanCTgdfvSjHMw0GyUURWcqsQ/1D7lHqIz7XYDQUi+1XX311qwhJx5dwK1F1JuIkj/gSJz5mLmh3KNnGMvBI3fCFYCHhEwzoq7q/yjn5dbzkd33yQbBi3eyZ+roOu2pszMx0MkrZTO+XOVCuRfdKXghu+TGdg59IsAhL+3LbkXsubc+N1+ePPfaYlWA1hWBJ3QVDjRFthnSJk3MdJ9eTJlOEIR/z3doeqY84BDIIZgbK9YkdLLZ7YadvviTYv8w9dDxhlBLdPO45+caMGdPDKKkGc6BA7Mv/pX5ggTFRzFngsyXONddcY1fD3XbbbXa+mJWYbFy51lprGVaMYNZfY6PDfXm/fVm2rw5YJ8Z4I20OZWNebOLnvdwkX1Ye9wXJl90CCyxgdbf6so79UbaL49NPP23mnHNOc/311xv213P7nj6X/qr7sKRLnJQBwWdFJ+U2wV133XWW6J933nnWDAjTyhxF55KP1ZnoDrHDQBMcH8xs/VU0/kubI5+0MfGl7eETx3HBBRdYgpW3s0Xd8WV188Ybb1yIHX0RTMBO+qXEyblgSL5jjz22thIsd1zjGfNhjL1DPiL1wZjHQZzrE4dxVnxsiHFwLvn0NYTlXNLFJ/7II4+sXskdJWKYI8vcMYTpHqz0kjiM9C2xxBJ29ZfE4es8nLMlDOI+vRGyD9C6dxzu31cvvijYEocOsOWWW1pjoygms0IQnCEZEC8ebp7zlZ2Xv9vT7rzzTjPbbLOZH/zgB+aiiy5qe7HJi8vn89LDnpgvjQFax3OOTRRefrQ/pIcxucmTJ9uNTelzbPui+6EOk8aAhVQKRey8vNL3MQ6ZtQozJgypCzo/9E3GKowFu8eIESPMjDPOaKeyWclKuviSl7ETyV8THMrEqEDktSPaH+kQMdodxlfz8pOG7SLaZ4hJh7rhLOM3L27qKP1M91N5d4qPegOrXJnVkHySxrmEKQsJKm2yrlPUgo88V/ojXIRZnaKDvDoPO1aABwdhneaG9bUSxudaFl5NIzdUhQ9zw0I79mHQAcJ3D+J5OaIYClFg2Txxcp2bn3PS5OvOBbKK+65LGUhtwHjmmWe2gzXTgz6RbhFGRendjgf3f+qpp9oXFdbFMfaIfSt83yFpSAKnn356qzNTdI2Ug00UwqzIrHq1XX/gnPesWV2JwV9fn9Nx5IHgs+wYIgDh1+m+MH0WK9xNcUg+mSL0HawKBrsrrriiLR2Jq+SXVa15zysWLOlHeeO9tCfyQEDBDlKWdw1pHA8++KB3TIwFOz6KNA46LLjhE8+KdMY7JMlZ+eQa0plilfYnfl1xY8xCcR/VmbIHbW2OOeaw/KTstZh64BqmXDFaXSnBCn0YPDx2o0cKwxxxqKv7Qw+tZ14+Xlqzzz67/VrLyxd7mryYQn1eZgy+DNaI2fXLragMphNZ0RlisC9W3G+++WaLHdLSUJf66xSk+Big3YlV91D8Uj5jdVDB7ne/+12CoyQCSP1mmWUWS+JLXhpl9tDxCE7CwhVW85dxvvL7lWDJDSCGRGyOFIuXlsS7lcmKd/M16RypFVNj6Fxpl7DSaPjDSP8YrNlSp4wD2ybh66vrr371K4sdZCG5cgigbEu7u+GGG8pdGFluaVfih1QPO2NgR9/FZV2bFR/yH3XNU1RnJPbMdogkWfK7vq6/pOm4poVRBYFgocbEgjMcuLjYuOc+nPqEYBX9sSZYWu8g67qseF+FYo9DgROCFWIJOXYsytaPVYdlCZZuexIWv+z/d2N+XRcdlnuVOCFYmK7Ic5I/L0/T0iBYgwYNajTBCmkXvjxMSWuC1bS2k1VfH1ZuXgjWrLPO2iJYpMt14utrfHE6vQ7hKuqAKo5IsIRgdVr3SglWaOXQG0KCxRRhk6ddyjw0wVZLsCROl+OL0+lNDrsEqxOsOrkmBsxDCVYMda26DpDSJMGa+nIPxZe+5kqwQq+NMR94lBl/IFhMEYoESzApU4Zc082+1Ef8Tu5VX4sEC/M/WoIVWqYuh2sqJVhZN+H+aZYES64nv3uNpOHnpel8MYax8YIOlk+C1WRcQp61S7BCrtF5RF8wZpx13XQYUwSQhIG0LaOfRbeGNWaEOU488USLHRgml42Axk5yCcFiuXxZ5yuvbBl1ye+rq49g6Xw6TD3d87rU3XefMlb70iTOrS/nHEiwEP5geFXyiC/XhvhcUznBCrkRjDaKDhZkK+SakArFmMfFhq8RpghZkuxzbn5fnqbGCcFi0O7UxYhvSJ1YiQTBOu200zqFLurrwNDFkekFDASPHj3a2mdiu6bXXnvN6nW4eaMG53+V66TOQrBEBysUJ9/zCL02lnyi5I6B6qY5FjGVcbptvvDCC3ZHAKYJ2cUjy+lrfHlQ56mUYLHlBqs9Jk2aZK2L43OwhYv4Eh42bJi1LyTxktf1yU+ZYm3aV5EmxDFYs9oNLBD7YguF6UKWh7tsvejBNwEvXx0x9QFJwGhr05zvhcP0PMu+pU+6fU/OST/nnHMsdgcddFBQftopZiCa6lh5ytJ3zHtgcwgpFrZxIAwsh+cruamOF768J6SNZfngR59lFavbTtnBQl9H+osvvthSTI4RX8b8LOw0PoTZMm2mmWayezTqNI2ZYEg6RqpjcLwPMZfQicFZZoiwrQg5ZZZozz33bJtiDX23vvPOO4axslKCxUbP2Bxi2wg5tt1221Z46623tmEsj2OEC4bI153kzfKxRcTNNtHxkqJDYSuM/Y32339/a58D8SVW3DGyifmB0D0Lm4ghdaZjYAUfg48YhOQFF9pZBLOy+eW6bvVpMxho1H1Q91fpj8RhMZ9Vv5AEzqUv6zwSJg2MsRjdJCftg69ejNlinJUVq2wcjps4caI1XMiWYldeeWXUmxLnPXe2tqJ9SHvJ81daaSW7KwDvFV/b1NdCxjAMiUmVWB1mUrDkrutNWGMj/RMdIvrsqFGjeuR3r8eAJuQ/li3BIEhwBoQS0i/Fz2ob5MWQK0aS+RjH0v2yyy5rP45CJWL8B+3vwAMPtB8GlRIsBg6sw/K1y4bFeQcWsjny8pBGWViYxZp7kxwSK77G2JOQFxbYQjR33313c8wxx9iGsNNOO1mLvljqZbUNdnY6Ye11x7Wo45BO50GSgNFQrBvfcsstda92r+9fjNaOHTvWnH322bYviu/2S/bWgjRA8t00fc71bP0yzzzzmKbpHCERBFOmApEwM3a51v/Z35L+u9pqq1njrUxHxPJSC22QbGyNEjH4nHnmmW3tSbc/0s4991zb7nx5dbsjfb/99rMGImPei5AdJWg71FdjpbGQMNiFvmPZRJqdVVDZqbtjvIdgoasMBj5psfvOIA9jG/Y59buBMQxhBoIMty/7cEIgwvjHfyN5rZRg8aLH4rPPuRXy5cmKw/ZOkwgWqyz5+udLBDElAzJsmulA7cCUbTrYlxCxJhgdcsghlpj1Bm/9H7GE2SKHjoLUhhcgdsR42eW52DGEDLCbAi+kKuoqZSCiR0LdlL0IaUNMe910002tbXLuv//+vKZlWJWJHiXSfPK6fTv34ponstkzCtghTtqU+HnXIHVgW6uYCRZEqKwdP40ZOPqwRKKKxCsGgkV9IVhIkJFAQZJ0vdz6k8bsBoZFIVKu4+OSNPp33scQ722st7NFEYKmygkWUhZEbG4F3Bsue87moLETLMGMB8j2QQy+dCb2GJS0PNyQeP3617+2ki5E5cyzh1yXV2Ysaa+//rpt9GIkk3O+1vhi0fprTcMLgoWkCd3J3jgXN2zbsX9cEwgW7QfS/qMf/chKrZgayJIiuzih//b973/fTruy72Vvn0NvnmF/XgvB8q2C1vfgYhWSxsbGTSBYO+ywg4aj12GwZmuXmAgWfIE+ycGU3wMPPNA21gMa9ea9yQcO2wqdcMIJPbAkD3388MMPt/tnIujwtU3yoMYDoUOCiLS/EoLFn8kfCsGSm9d3q/NJfp2eF2ZpuBCsstfmlduNaY8//rhB7wBdq9B5X10PphXZv4t5d99AHzt+GgvCfJ3QOdj4U0usEK/zVZKl2NkEnCBYc889d2uPReos9dZhjambLvl0PASLRSwxEyzqy7QCL3Wm6vlaZu8zPpAEC41bVpg9CJlSYErxgAMOMM8++2zUe+mBA1OEmmCF4CV58CXsYvroo482hmBpDPIw8eXTcYIhBAsJP+OlL13ydasv9yw+4z3kiv6IxI/2hkK/OMlHfyMvM0B5Njnp6xBbJGMsCHAdghA4CrMjlH3++edXQ7D0HwnBkpvXaRLOS5M82id/UyRYKMehTMy0gazAov5lMCMvJIsBm+lCLRrVuMYU9uEjcSgWY9PE1QeCvPJSRBHSt2F2TPhk1UWmCKvexBqCFfsUIdNQl19+uZUY01+ZnpI2J3i75xIvvk5nc9oNN9zQLhJCB0R/DEj+OvvUVerLeM4LT86z6lWU7l6XJFhTECmLG1fFJsEaOXKkQVKK++CDD6z+MgsgmL0Qx8f15ptv3mNhhMZPhzGRxAIDZoj0mIkEW4QaIhRhWrESCZbcLL4QLML6xnQeCaMwFmqfAyYqEiy5PkYfhUSmrrKkKmXqzCA9dOhQu3JJX1f0XHTeuoeRDrBAgBUyPqLJnPqCCy5ol81LXTU+OizpMfmuBEvqJvUWX+L5AKDfuvGSLj5fgkwRomcUm2MqAMX0o48+2iobs5KXBRRZrggrfR1ThPvss4/9OEKqlWeDR19XpzB4+KYIs3BCAsELkqkcHPl0Xh0WCRamDGJ1qI3kTREKHvj0Q0gBbVaw07iQR/LXXYIl9ZL6IJWinck5K3lRu2GRGHrLHEi21ltvPTvF714v5/hSBmHs2lE25hvgL1IOki1s3El+1E/6jGDpG7L/6Pzw0JEoQChCnE+CVfQfIeV2Ux6UXJdbbjkr1nTviw5COnXmoONopVjEl3pPR67nGlg10xdynVtu7OcQKJYpM+3qay+QLkwUMJ0KGWuaC5VggROkgiXiXFPkYpZggcV2221ndTZoX0UOQqqnHpBMS1/1tUkIBSuHkQCizxqj8xEsXz3B6qGHHjLoTuaRWLn2kUcesQYim0ywBAskoCx+os/SpoqcJlhFebstXfqR+NyfECx9r0g4eceia8VivBVXXLH1cS3X0jdd1Rrak34/sACNcuAlLEBjtggJtnZ9SrD0H7lhiAFLJ1lxCAghrgkSLGxZoaCpRY+CDUYLWZ0gy0Tvu+8+gy0ZHA0DXRc9vyzXQWIhGDHbhZG6uj5fF0wBotfic9KhsO6OPTZ3CtF3TWxxkCWU3H1tTuoKTmCEbgE6GgzERS5mgoUkhRVCeiWXtCUXF+JRiqW/4pg+uOqqq1p2sdz8cs5/8EXMV3KMDh0s7KnlOUgBElBWUqPPFyLN4wU6ZMiQylbF5t3fQKUVSbC4Lz64L7nkEjudhZ6pJgdZ911nguWrk49gke+GG26wZnoYy1gU5rqXX37ZkiaZ8QA7zNjwftX9nPcFZXBAZF03YAQLBbFDDz3UKoRmbffi3mwTCBaMmqXLIs7VGPACXHnlla1eBgQVu2AyQMGusYuCeNx16InMP//8ZsKECW5SlOfSAXhBsZKDVTEhA/Nhhx1mv0KQrDbJhRAs8ADL8ePHW10FLCQXuZgJFnW/8MIL7arUvBeXtEVs0yFJ5iMHJXj0tdADkXQflvR3pq6FmPny1DnOlWD5sICMHnzwwebWW2+1q8Bk+iWv3k3UwfJhR/vhwxKCusoqq3jtQLk4NoVgUW9mzujDrgNLCBbvDRFKIKVmGtH3bkBQ5CuHcgeMYKFQzNcJL30hCW5F3fMmECwU8DCU53OIe1lGykPngTOthWVjiAQG5xi0fR2NODqYnor15fP9Z53jpJPQAXBFdUb3BQNz7LPnI7h1xiLv3kMJFl/EuC233NJ+GeeVSVrsBAsdST5cmL4qcmBHX6Wfgl/IFKu87LQaQNH/1CndJVi+e6fPIrFHes/YJwQrry83kWBp7AQb3gu8Z9kBhBXpMvOh87phaXMiuXHT63aeJcEqqgfT0ggzUImg7SHMwEZYWQfBGjRoULWGRrWSe9ENsU+XXqqbl78JBAtpHroG0knEBxceNFIqVitgN0e+iiEGsGvsb2Q5tqQ4/vjjs5KjiAcrORhYmM4CT3lBCZZ8FfMlgmIipFWvHmRZLQsMWIEp+aMAJ6cSoQRLiuAjgKmHIhc7wYKEM02IlCCkrTAlhkQK+3Z5jrIomx0b9thjj7ystU4LIVhSQab6NcEiPgvzphMswUx8TBBAsOQDSeJ9fpMIVlb7ARfS4DGihsPOH1qH0sUuq6wBk2DJDUKwkgRL0DBWJw17Xzh5aOLDqnnovNxQWuccZo1kipceXyz6Onvyvx9eBGw0K07KlPPYfHRe0Dvzza/ffffdFkPIFNNeonsEJgxC6L3stddeuR0qJrwSwer8abIMmxd/kXQAaRf6WijFyjS+2wf1OdP6rP694447Or+5Lr+ytwQrq3qJYLUj4yNYuq3p3E0iWLrevvCOO+5o9cQhV0UfRb7riUsEKwuZAYpHmVMrzurb4OXPogA25oUk4LCXhc4W8+y60+gw4l4sy4ZIHfT/1S0sdYZ4QjjZyFRIp64LpIs5c/bzwuyHaw4DZUUkDSFTP7rcuoYTwSr/5KStseybRSm81LPcO++8Y/bee28rmWZfPfYL1VJT33VXXHGFVcINWTXnu74OcWUIFmoRIsES7LPqmAhWOzJCsIo+ArgqVoJFm3HbTZEaCIIO9q3FpIN7rUbYV7akDzjBgiiE2rZqwhQhdm+YBvTNgaOzhqIsulcM0DxYiARxeYq2TCmiK/LEE0/Ic4/aZz8pVgQ+88wzmfVEPwsCdu2117blkc4C+UI6yHRiXudqu7imJ2UJFl90vr263OrHOkWo2wMEnmnoI444wttOyAuZx0I0LzgkU0zXv/322y5crXMGfuy25dk5amWucaAMwWJKn61ORAcrr9qJYLWjwziIKQJNsHQb1rljJVjUMavOuv46LFi4phd0Hl9Y/8+AEyykBAzYIa4JBIuX3eDBg+3egy4mDLzMCfNFIg6zDkUNgP2QWKaLZCd2xwsMhX62xdENXepNHBIFpISnnHKKRPfw2cORKUbMYsTuQgmW4LnLLrtYMwNFuMRKsNx6I5VCx4X6uo4+y0ckbU4c9nNcGzuSho9uIG0PI8GCuU6PJVyGYKErCTGV6fw8DBLBmoKOtB32ukQSowlWFn5CKnwf+FnXdHN8npK74OO7f7DiHTJmzBhfcmYcZepyWWDVZ4ZGM+9CJTCYyHSXivYGm0CwUKRDBwjF2RDDcF6gVCQSGBYR0Fhid0gTaCPouWQZGWTKBavbrNTMU1oEK4zH8eLMexnGgGkowZK6smEqUtEi1xSCxQuMj6KiDx3BSw/AEqd9pvuRwGK5PGYXSrDAi77K1L0rqfdhmQhWe6thzEOHKOR90iSC1Y7SlDOIJSak+LhBFQeL7WWc2x4HXIJV5uazCJZbqTJldmNejKAtuuiiBovEoc7FgHMaC4rcw4cPLzRqGPo/3ZyPzoDl66zpK174SPNQ+Ccv0q48XRhIGtMSLA7w6XJ1MxYh9yZtxkewJC2knKw84M1WOTFu9qzxoZ+xUAfi3luHxAsjkliJj92VIVhlsEgEqwxa7XnrTLB0n5Ra5UmwJI/2WamPMAIF95AdGvS1vnDlBItKljHT4LuprDiUztDX0kDqcNZ1dYtnwMaM/6qrrmpYZVnkfBjwcjvvvPPsdBmELXaHpI4phLzd0CFU6LXwIkQvBqV/3z6YGk8234UkyGounRYLpj6CVUXdRIIVY/vT7YAwbYmFJLTD3jh0jBZYYAFz//3396aYWlwbSrDKVqYJBAsCnqejp9tnGfzqTLB89SxLsMANfb/e9mO5l8oIln6goQRLXyM3lOdnSbDyrqljmjxk5n8hDUgAQmyYSF0hEmeffbadGkQ/JE9KI9fUzXfbDi84jIT6FNslL/aw2OqALV+YzsFnrl3SfRhAdnfbbTcrLkYPRFzeNZKnLn4RwZK6ih9aLyFYMUqwXAwgRp3sluBiioX8ESNGVDbAu/fZTecQrLXWWqvyW3IJlotx5X84AAXmbZWj66vDvtt00+tOsNz6CMFy431YlInLKs+Nr4xg6ZuDYB111FHeF5e+AR3W12eFUUoGsLLXZZXX7fEM2gcddJDZcMMN7TQV9nPyFNXR2cAEAfpbzB9jNRqRZ+wOxVcU25H64fLah5vmnmusJA2F92WWWaY19SjxOm+dwxCseeed1+qaFdVNp+uwW3/S0PmIdYpQ6isYQMTpc/RXcZIm59rPSsO4KDbYtMvKq/PUMYzh1VAj01I/wUJ8iRefeDZ1x3RGlh6m5K2jL/VGgoUtRNdJuo5349xznZdFPRhapj3H4EaOHGn1csvWxcXIPQ8tD5WUPlFyR/qC8idm+vXhxqELgzl6nUfC5JX85GPwYuPe2B0PUx4o4koMidKhMCuA4jV7md155512IOFr7eabb7bTgeAzatQowyovFGVDVo3UFUvBCN0o9m9EB4al74JbUb0kn/hufjee3ejZOoH943Buunt9t55z3+69Q7DmnHNOw4pU6XtZvvRXfF8e6a+kIS3EnhhtsQmOfspqXTZyxlQIB2ZAJAwO7L7ABrESp/NcfvnlVgpG326CQ4LFh5FuM742RZxudyghcw2+5NdlgCmblyPJj9HRfzEjg4kecNE4gIfgQxhceL/qd6zGSuNHPGo4bFwcC8FCpQgTKqziZbFSyEFeyLn4hDlCrnXz8BFROcHCThOiXwx0Mb2CXgwHYfdA1Mmh03VY8lMWBjU33njjHi+IGDuRrhONna8ypvswWIgCCrjBmQAAIABJREFUnthpwlYT52ydA8FCwZvOJM59mRbFS3o3+7pO4MKCAPZh5GVWdPBy40CBkamrrPzk0Wl8icwxxxx2g/LYplyR0KH3s/3227f6rPQ7fOm/9EHaGv2V9qbzSD6JIy8GNVkNx0a9TXD0O1YA0zfBEoz0gYQLe0Sbb755K17nw8gw/Vk2mI0dM9QYeJnTVqSNSftxfXlPILUhv07X7wvS+MhECsMK9dicjH1IOfngy8JCYyLY0R91fp0HPElDJQUhRiwEC0Pc9MkDDzzQzuwwu5N37L///q28XAPOHMTr63R5Oqzz8D7GPMZMM81U7V6EfKWxn17ewYa66FQxNcHX88knn2w32c26hulBruHFF6uTziO+W08a/RtvvGFQvEZJe/rpp7crBMGErWFiFIm7GLjn2BlBeoVhRl7+KH7qgxcc59rnAwDzC+zfqPPqsOSXOAZ2CD5fjbF9GSMlhbxn9T2Jp/9BCKaddlpr3JZz0sQnTD/V+TGci1HXJjj6J32TJd4cSJY5JEz7ZOPXo48+uhUnefAhovRj+n/WGBATjhg+pu3o9iNtR/ukY3yZdseLTqf5wrQ5FviU0VutG67sO0s9Q7AbNmyYmXHGGa2kX/LrfioYyjsWPaxYVk2jm4u6En2O2Z+Qg7zMirCaEG4CRyEurwxfuuTHn6bKBsbDYbBxD3QydBxKsIjUmUZAt0inZYVDbHlUWZf+KksG1dCBlZfibLPN1isl0dD/6i8MQv5H3zPhxx57zK7ww0YOL6iiAx01Mf6GuQbOs67hxShp5GMlIf+jld1D7rmb84AhR1Z/k3ikdoSR6iHy5uPI7c+S1/UxPdB0B8a83MCOdhXiuCYW56sL7cJtK75z2hkfOGAHKQttd7Fg56sH71hwkH4puLnnxLPTwCyzzGI/DCUffhaOxON8z8x3L90cB8lmcVMnB+/YhRde2EpZ0WXm6KQcrqmUYIUCzoNkxQxWi4uMPoaW2ZR8SKvyCJZ0DvGbgktRPcED3SAGa0TmvXFNxBY9IrDjaze5cghASpFgZZmtaGJ7CkWQ6SzanW+VcGgZTc2H5B2CVdZwbWztsWx90GFGxWGppZZqI5tlypG8lRIsKVT8rIYNi4ZgIcFCmpXnisrKuzbGNCFYfJ0kbMo9YcwzMFj7VuFISaGYhuaTcrvVD61HIlhhTxA8XUxRIKbdZRGssJKbmYuFO2DHgoxQ53sGodfGlE8IFhKZUOe23dDr6pSvqI5Iv4RgFUnhi8rqNcEq+gMf8EiwsF2EGK6IYPmub3IcekB5Eiyw6eSZ1BXT0LqS7+mnn7aDNYN2qAstP7S8bsiXVScdr8PccyjBcq/rhvoO1D0IFkKw0FGVOPG5Nx0eqHvtz/8tU1+kzWUJVn/Wpa//y4dVSBx5OiFYfV2fbi1fY4oEiwVUqDH1RieNMntNsMoAJpWAYHHzTBFqgiXp+HKUKT+GvIKBry6kaQmWL0+T4wQ71xdMIFhM1fgkWHKN5G2C79bZPdcYsPIS7FCMdZ1cJ76b3vRzplXBDoV2XJNxkrqLX9Q2+BgCOz1FGHptUdl1Su+kzhCsWWed1Voor1NdB/JewVkkWKx0LSJYRc+lXwmWAAfBwoAjEqzYlr5LHcv68qBc3y0nRILlXhPzueAVUkemGfga7q0OVsh/xZYHggV2PoLlq2uZ5+K7PpY49F9YkTrddNPZFUpiADgPn7y0GHApUz+RYD377LMxVL3f6gDGmCnAVIBvW7B+u5Eu+aMybQ6hDyswEQIVTREWVa9SgsWKQGy5FB0MOtgrGTp0qF3hUJSfBoJGftMdjQSDZnyVlLWEHDN27BpPG6KdsNIPn0Pi8MnzwAMP2K9h7BWRz9fu5Fq5PuZFGHzoSD19WEgcWI0fP94SrOOPP74NN9/1EoeuZZMdUpeDDz7YbjKOsja2edh14KWXXmoyLHZhk7StIp++CrF/6KGHWn1W2pe+VuLo52VepnV7EJ9++mlm/xMMwIU+i10rlNxpb+54p/MSJj32dyz1kzZDnTUGghlxvGPRDx8+fHiPPHK99sEua6eVSgnWxRdfbA0yHnLIIdY/9NBDW/5hhx3WCjPoQK4GDx5sjWTqfL4w5WHfJHaXNTDwAFmmzHYGJ554orVtwhwxRjDRjcEqr9h+oYyscmLEjwEHeyO+NidtSdoeU4MzzDCDNdSHrRNJz/IxGDdhwoQYYbN1YiChjtRfMPJhAVZbbLGFbXeQBM7z8KYMymXVZhMdX8AYtGUXhu985zvWxAV27DAGjMFkpr3Y1Llo+iFW7OhTvAN8bc2Nw+I7tpzou6QVtTvsHcVMFLBWD3bgkNdnSWe7KvR199lnn0KsKRNzIjG3SXZcyGo/GkuMhsJN2GPUbY++c8rE7pa8d8Wn/1ZKsLBGjGRFOoI0BG7APUjjYCCWNLlOzvGJwzDk+uuvH+t4k1kvdvbGHhMYMMBgBJPBmTDGC/H5wiOOL2OMFTZNaoA0dMiQIdbKeF57oy352lzeNZDY0CmxzIfYxQlMu8w+++zWkrPuc9LvdBz9VPDT8b4wA9Tcc89tt4fp4ur3ya2xbRPbKzEW7rvvvtZem/wRL6+7777b9t1NN93U8EHKl3DTHH2KvuUb7932RLuTtuemuedYLmdnghgtuUsbYcqUXQEEu6zxi3RJE1/HaeyI32STTcwKK6zQUtnRJEH+u+4+PIL9kgU7jYEOyzgnuOk0N0xZcB76M87FrVKCBQlicOWlx9JQ3yFp+BL25ZM48mBdtQl7EeoGzPYbWKJFcsB2BuPGjbMGL5l2YDPoV1991Uq10I1hlRJfy2wbQz7EnE1xtBP2H8MYKPWWdoPva2PkyWt3ksaLjw3G2WkgVodO2lxzzWUlTVJvjZ8OC5b4vMAkzb2Oc/byQr+SthmTcwdPt27sD8r2GpAr+iE44NzrXnzxRftBxGbufDm7kj43v/s/dT+nT7FXHH1M2lGWL+1O2pz4bn7yMQYgeYhtxwX9vPmgZm9ad6wTPHR/FOwkLcsnH7Mh2H2K+QOdNgeX0BjlYRKSj+fABwCSfZ+rlGDBECEFruvtgIGhPsBpinvyySettIq9y/jKfeWVV3KV7VgowDUQLayUM4XD9E8THB0EgvXoo49WXl321YydYIHdW2+9VSl2tEemJ2IjWIDkG8uYkrriiivsxxAvQKTORbp7XMPm0GzBhOSFa8BNyhe/0gfTJYWx2TN9K8RpHHTYdy27O8w333zREizqT/ti0UTVDh3LmDZ79uHDBzNcomqHiopLsKStVkKwpDDEb0ceeaS9f+Lk6G2FhGDJ//S2vG6+HjK15ZZbWmnUgw8+WOpW0cNiSxNWjyC6lBVLpQqpWWYhWLKXW6e372tbiH6bSLB8WITiyrXoIC222GLRESwfLigQo/iPNOqII47oIY3SuLnXc47Ua88997RSr7POOqsl9dLXxRaGYLmLdAQbfDl89ZZ8vrRHHnkkaoJFnSHjWQRLsNG+hH146Tj2IYRgxbyqv69mJBAquQRLsK2EYElhmmBJXJ4f+vBFpJxXVgxpGDhjigGChM0mHBgJTuJLvK/O5MGgIZsaX3DBBa0ydF5djo6vY1gIFi+qUBdSf/I0hWC9+eabodC12mLeBUKwYrZczgpMNnhGF3KzzTbroU9V1MZIlzyit7XRRhuZvffe2zz++OOttDyc65oGwWKj9lAnOBXlR4odswSL+gvBCsWkCDNJF4IV8xRhX0mw+o1gMUWIBCvr4WfFy0PO8pn6in2KEGzYWJgv/zvvvDMLisJ4ysF2BytCUFpEV0u7Tp+BLqObwkKw+Hrt1GVh0gSChTK6j2CBSRYuRTiLHRlWuMbo0M3g4wXFYJSOWRGYZS9HY6jDLi5IDjBEin7NqFGjrCQ6Vgn0SSed1EOCJXgIRuJLvOv70oVgxajkLvWFYLHYyXWSLj7pOqzPJV580iBYmE6KnWC5MxJgoHFwcQ051wTLLasyCRYFh0qwyMvXn1g2LqpEEyRYDLB8we6+++52t3ONifvQ3HPyunEQj5EjR5qxY8fqomzYzdsjQ40iyhAs9F6uu+46q68WUsUmECx0sHwEy8UHnK+88sogG04iwYpRB4t+etxxx9lVzRAFpvRxoX1K8onv4swiFhTfscJ9/vnnu8lRnPumCLMqxkpXzNNgjqXIIcVmRXGsSu60GQgWUtMQB+FkvAshTa4EK6t9hvxvt+YJmSKk3nwssdr39ttvD6qKECwfZpURLO4ki2Dxx/LnotyJsh6i9RDXBAkWAwl2N5gecB26VXfddZftKODIIAxBFUwxwsfKJNexXHz55ZdvG5zkGjdvXc+RJkASfBIsqSs+Ky/PPfdc+2I8/fTTW9WVPK0IFWgawcrCYtKkSXYBBdM6eaRJro+RYEndmBpEUo+eZNZLX/LSlFipSX/FiZkGbGLlOVYmrbbaatb8Sl6+uqa5BEvjRZ04ByvGPJbKgwXTqJLmqzfXQLCaMkXoYiAY4tP/UBPhY513MufaSV7iJOwSLJ0/lnARwQILpMaXX365lSRvvfXWQVUXguXL3C8ES/8xX3wog6J5zwssxDWBYP3kJz+xBjDdzgA+rAiEjLKsma+RMWPGmG233dZCh60szDOIDpJ0GHxMPUDaRJ8rBOu65QmVYN122212aTzTL6yyDHFNI1hZmDDgMOWMVOXSSy9tDcpZ+WMkWLquKLWDRYhCMFJ69CrpjxCGPfbYw7z88su6uB5hDAuzZB7JTYzOJVi+OkJekb6j+M+WJa+//rovW1ucS7BkLGzLVPMT0cHKqwYSPFR1WByGmogYoc67JhGsKehMnjzZ8hOkyKG2N7uKYPFC5IV/3333BSs6yirCvAZS1zQZBLbffnvv3Dr1Qqdg6aWXttu9IPZlKhFzDDhEwDQE12Ah5fIC4Do6T6wulGBh7Z6pMAzF0XlCXCJYU1DCBAiSQqySY7G4yMVOsNhVgamo559/vggKg7SKvorC/84772ynWZGC5Tk+BrAjJna08vLWMS2EYGHmgrGOze2RwiOBLnIuwSrKX8f0EILFRzczIcyKrLzyyolg/e9BF0mwyEZ7Q+KM2RSkfyGuqwiW3DBfc6ErSWImWIIHJAmdDp+jw9BRePgYcmWqC5LFly4vPbbg8DlIFuUyoMXqQgiWkFh8jMIlgjWlNTB9FaqDxRXYbEoEy9gXFlu4INULcZhMwVAyW3WIPoy0Sd/1TO1gYDjWbUtCCBa4gBFjXCJYU1tJCMGS3BiwZTW5lmBltbskwRLUpvhsdVU7giUPFx8dokSwpj5UphyyBmw2klx77bXNLbfcYg3NIYmBYDHPztdx3qoZ7PP4FN2n/nO9Q0UES9qc1BKCygsvxCUJVjtKvPQxfFvkYpdgUX/UHNDFEsKUhQn6VNi5GjZsWNBUPZsVMyV22WWXZRVZ+/gQgiX9FvwSwZr6yMsQLCRYECzRFRRMp5Y2NZQI1lQswIl3be0I1tQqGHPPPfcE62A1QYKF1XZe/j7HFwiGzJhG5AVHA9hggw2s9Oqcc87pcYl0JPxVV13VSrx6ZIokoohgudU88MADrQRLMHLT9XkiWBqNKRKsRLCmYML0FfqNvsUlghp27VhQgcSUDXdDPnQYFxdccMGglZ3yP3XzfQQrqz8KwXLNzfjqnKYI21FhqitritDFOxGsduzQnaylDpZUg4EkdH/BJhAsmcf12dNBlwoJF9IoWYL8jW98w0q18pbYQz4WWmghq+8muMfmlyVYkNg0RTilFaQpwvK9QV5MSJVRINYfOJImpWIHjI8iFpuANX2W/uvm0+cQMfYyLNLTkv+oo+8jWFn1gGAtt9xybTpYgpf4cm2TCZaLBZggwaKNigRLcPLlbTLB8uGBBAuD3yFO3t2+vP2+ilBuAiX30Ao0gWBhdyPry5UGcOGFF9ol8tIYmEKQVUYSJ9iKj2LtIossYqcQs/JI3rr6ZQkW04OynVNRnZMEawpC0nbQ96PdyXkWfrFPEUr9MSGAJNlHhtCfYgEK4xz5yYOupKu4LmWBJSZslllmmcwdGLLwrlt8WYKFmQbfKkKNHRgkgtXeEtDBWn311Q2SVHEuZhLfZIIlGGgfgsUHUYjrSoKFuQbZyqWoEk0gWChz8rWB7SqfQ4qlOwe6H76BXa4lPy9E7I3p6yQ9Fr8swbrjjjuCLeUngtXeSiD0rKATl9WuYidYUn/szy2wwAItY6MSjw82+sVGXFGfzStPl133cBmCBYbjxo2zK6iL6t1kguXDBmkp5n98eoJu300EayqCYIO5hhB1CK7qSoLFF547AE2tYnuoCQSLGqOvAckqspPTjo7/jO12UKydMGGCP0MksWUJFsSTI8QlgjUFJRmMIU5C6iXOh2NMBCuvnkicMINy3nnn+WAoHccK1yyJWOnCuviCEIIluOPznvCpTrhVTASrHREwAzvBsj21/SwRrHY84Cd69WV7avtZVxKs9lvMP2sKwcIMAysXMEbIaqKyTjoS7JvVhaxe0mRC0suW2835yxKsMnWJkWDpNlBWB0tfm4djTAQrr56k7bffflZnipdZKD6+MkWnC4lD7C6EYHWCQRMJVm/anMY4ESyNRrlwvxOsrIeeFV9UnaYQLHBAF4t58xNPPNHavcrCBix9eDLvvsMOO5iNN97YKtfq6335dXodw0KwHn74YS8eUidf3d04fU4YgsXLQMdLeTH4GPwVO1hSR+37wm69JY+ObxLBwtzM0KFDvTpCYOLDR2MlYbZ6YlUiCvGh18i1dfP7imCBYcx7EfKctZkG2klv24pc30SCJXUHVx329Sc3XZ+zKw2r/H2uciV32Fye0zeWl0+nNYlg8SWMrgsPjBVvWOSVaRmNiRvmCxj9IjogJh98e/O518Rwjg0wSAIEq8hJ2xPfl1+nxSjB0nUWCZYoEOu663xlwpSBFW6mp/P2LSxTZjfnZe+yJZdc0vz85z/v6DYFc8bNELtaHf1Jl13UVwQL0xmDBw/OtQvYZVCUvh1NsEIvljaWl3/8+PG2Hfv0tfKuq1MaltzhElU7LcFysa6cYB1zzDGt++fP5GhFZgTy8p1yyinmy1/+csaV8UXTyFkBOHr0aMOGk+zH9cADD1iJlugjMEfM8lsWC7C1BrhjafsHP/hB24bR7gOPDS0I1rzzzmtXEGXVNStesJB0fDlIW2uttczJJ58s2aLzsZMDOWWvS8GASmoMfJX2pes4pqUXX3xxg5mCJjgsr8teoSxWYXof33e4aZyjGoBByDPPPLMJcNk+heHkqpy0XQgWmz2DZ6wOgrXTTju1qid1J6JIT036qL5Gwuw3yodCUwiWYAFugoH4LXDVWOimyTl+v0qwmJpiQ1iWc3NIGJ+vPDmHMXNwrg99jYTZoDdWgsUDkoelHyzhiRMn2g2K2dj5+9//vpVosZ0Otnc4jj32WKuvRTqrBdmKA4N8WeVlxbv/W6dzpgjnmGMO28ilben2pMO0J6SDiMOlbWmfsJxzHQMOX9uxOqYIZ511VrtyVXCS+vt8BmHBTmPl5sUcAaS3KQTr9ttvtyZWZJ9L7KyxoTgHYQ7Mg0hY+8Rj+woTLeyXGavTYw99ir5Fm5N21Btf2i4vujnnnLNlKzBGLBnnkawLdlJ3Fz/ieb/SZ3VeySdxnBPeddddzRJLLBE1wYJDsLLerbtgID7pjHNgJ3iJT5q+nng4D4tTfK5SCRYDB1IUGPaOO+7Y40A3iDT8ZZdd1owYMcISB19eiWODVLbo8Fk5153WV7k6xlEnXS+kVEx/8dLCftMuu+xiv9LYTgMF2+OOO842BIzKFX3B1BGPontGAoD0YLvttrPtLavt0Y6QCA4fPtwauM3KR7sjjfybbLKJueqqqzJvQT+nzExdnMBqVWy9MGhLf/P54AEWSKWYus7Cjn7N9XwMYCzzwQcf7OLaV3drbLSOTSx2CfAd2PubYYYZ7NS9m87KQca2E044wU6tVndX3VvSlVdeaV9KWe3I1waL4iiLD03UI9yN77sXifJ3xmwO4x3jUxEmSEUZ75B65eWlLIgHGDIzEqvbf//9LZcoaneMh6wOxiYdY1kRdnAePqZ874NKCRZfYL/5zW8M9lw4CLvnxDPdhQFMvnIxIyD5te9eN2nSpFife3C92PQZqcNMM81kML739ttv97DSK4X5HjZpWfFyXd189NMee+wxbxvS7YmXPV8b00wzjR3cdfsin3suca5hyLrhk3e/Qt6lrhovN4zUAez22muvHli52HHOEfOLzsWV6cAPPvjAeyBpBjskCll56NtNcfQpt31VdY7OaszTXHwU8cEdgteKK65oiT0S1pD86GTG9n7Qfer555+3H31FWMBJ0OVjFxTeG+SXMU2udcc8Vu77XKUES/7A95B0HCwZhrjwwgt7Fbh1Xikz+VMQYEps9tlnt9vkJEzCEaBNIeUbNGiQFYeHXJna4VSU2F0ekoCttuTKIXDqqada7MAwuf5DIIb+25s6sGhi5pln7sjkT/89pe74J40zBH3RRRe1m6731vxKnxCsPMioCBVgehCGyJLu5MIQADsUOGebbTargB12VcolCDz11FP2RYdIPLlyCKBPBcGCLGinByYdn8JTEfjxj39ssWPhSnIJgf5CgIUEs8wyi+GjPLlwBFhIxgzbUkstVThl6hv/dFy/Eiz+mCMRrJ4PWz+UnqlTY6oiWKH/N/Wf6x+CYCHByiNYRbgUpdcfJf80MvvqgR1kIbkpCNAWQtpDGYIVUl7CPyGQhYBuP5pg6fisayW+TF65ps6+W18suIcSLOrtXq+xqJRg5f2RTitDsPR1+saz4nWeGMNCsFhJUuSahlFefUkrK8HKK68I+25J13UgrM/L3CM2rZBgoWTbRCe4iV8Gg1CCJWWLX+Y/Ut5mIFCmbayzzjpBEiy3TPe8GchOrWUZglWEVaUEa+otZoe4IRSTWQWXpgizcdIp+iFis4gpwirtyOj/ijEs+LFAoEiCVVR/KasoX7emd3r/SYI19UtVY6jDWc8cgkW7CzG8KuWJn1Vmik8IFCEAwcIMC7YCQ1xqc1NQgmChg8UUYacr8wXLygkWBcuR9VC5aZZAQrCKrJTLjeqyfHE6PeYwK7NCdbCKnkPMOPnqhpI7UhhMXYS4prUzX30l7uabb7bYnXHGGSHQRZ9HcAmp6GmnnWaxu+WWW2x291o5d/2QslOeZiIgbSWv9pgHCVFyDykr739iS2OGTaYIiwhWEXaVEiwx08DSxqIDcoUVaUw2sPQxLz9LImM208BDYomsDwc37tZbbzUzzjijWX755XMxk+WlXM/S3lgdnUGbadDtiLalzzF0iyQBG01ums4nYZZDYwojVsf2Smyp5LYxqb/2sWgPdmPGjGnDVOfRYcqN2UwDZhmoo65zVphN1yH2bNOh87i4yzmbFmNCI7mEgIsAYznvQ92OdFjaEHGYaZh++ukNZhp0Hl+Y65DwFxEG937qdA6H0Pj4cCDu/vvvt2YaMP5b9J6gPA5tpkFjWCnBwtAoBssYhPfYY4/MY7fddjOrrLKKWWGFFezWLnl5KWurrbbyGhqt08PNu1dYMkYaMQjHYJyHBwrayy23nLVsn5dP0jDS6q78yruXuqVhPwjjguCX1e7YygQ8wBcDt1/96ldzMaYcDgz6YRQxVsc2SxtuuKE1WwE+gpO0He3Tr8EOq8U63hemHEgsA0+sjoGYOgpmbtvT5xtttJHFDgxdvHQ+0rCozTN56aWXon7Zxdou+rpejOUYtqTdSNsT321bWC6nzyKxl3Ymvs5LHIaaMcBZNKPU1/WrunxNdvbdd1/LJbIwEEzYbg5yCkfJwlbyUhb9Gu6D0//HeaUEa/3117cvO15KV1xxRY9Dx1977bWGw81HHrYzkXjOIVixbpXDQ8AuGFayeVgaI8HA9cHtmmuuaWHkputzdLWwTBurE7tgWMIW7MQHB7ctoUt09dVXB2GHnmDMW+UgNcWmGlss6TbjC2PRHuzwfenECe5sMTFkyBCbP9Z2h9kK6ojxUNqY1N2HTQh2ch3Pgmfy5JNPxgpdqldJBPRLm49ExvS89iZtiXdEyDuW/Lx7eAexj2iMDgxHjhxpttlmm8zxS3DDF+z0+0OnS5jnwIf417/+dS9slRIsJANs51K1g7WzE3asDoLFPlA8rKodpv633377qovtmvIgWEw1M02Y5fQAlZXHF89KzZg3e4ZgsZtCJ9bq8zDlK5jBOma7TxCsYcOG5X7x52GUlcYiFp4JK16TSwi4CMi2Nzpe2pL4Oi00zIdCEzZ7dsdzH2a+uDwcjznmGINwyef6lWCVvXG5YVbhxC7BgmDRyItcWQybQrDQW6naNYVgvfXWW5VAJ20T48EQrJBVc5X88QAUIgSLFUdVOnT+EsGqEtF4yqJ/MRuBOkSnTvqoez2bG7NqLlYJFvVFSOMSLBeHTs7ZZJw9Wn2uXwkWN5D1gH03J3EohwrB6uR6KadbfZFg0cjzXCd1TwSrszbHc2gCwUL6VxXBkrYLwUK60wSChdXnUBfSf3kWiWCFItq8fD4Jlg+FkLamr2uqBEtjUBYzufaoo47qHoIlN1XGj51goeTOrudZBKvTBw/GTSBYvJBYWeO6LNyy4t3rm0Kw3njjjVbVQ7FpXeAJQDqaIsEqQ7A8UPWIevPNNxPB6oFKihAEIFi9kWBJOa7Pu6eJU4QuDjL+ie+m+841wXKv6xcJlvun3CRLxEN1PzTB8lWw7nEiwXKnCDVuhOX8448/Dt5fqgkEa+6557ZL5vPagWCHzhZL7ENcUwhWngRLcMNnFwH6bZH77LPPzGKLLdYICVboXqqMdT4yJvgKpkmCJUgk34dAGYLFdB9Tzm4b85WbCFY7Koxz77//fntkxhl65wM2Reh7uHylnX766YaVXyGuKQQLO01FDnsbKNWx2ijENYFgMc2FzaoiN3F+vDJaAAAgAElEQVTiRHPooYcGK183hWDRH/McHwATJkwwBx54YCGRpRyIRFMIlo80aSwhYBgYBTtMLxS5RLCKEGp2eijBwnr7ueeeaw455BC796+g5nsfk5YIliBkzKuvvmp1teAdIU5LsNz8/SLB0n/Kl9zxxx9vTS/wAgtxTSFYRVOEGHKFLWNXZ9tttw2BrhFThBAsjD5mOQYV0rFVwvYRKCWGuKYQrDwJFjhh3BZiil2YrDaq8YRUJII1xfwKJisOOuggM2LEiKCPgESwdEtKYReBPIIl5AkDv7wzxWZi0UcA/5EI1hSkX3/9dXPsscdafpJlesF9JhCsrlhFyI1RAaQv2JcI3U8PzX9RcqcMaUhuRet6LlOERS8vbONccsklhlWV2AYLcU2RYOURLHC6++67rU2YvfbayxxxxBEh0DVGyT1PgoV+IPavbrvtNmvv5dJLL7XY5fVBCFbSwTJ2H7OLLrrIWoZm/MIqdJFLBKsIoWan5xEsQYaprXHjxlnJ6aqrrmpCVro2mWDpsezFF1805513nqHfhhIsd4pQl9fvEiz0MxiAmXJYc801pU3k+k2XYAk44MbWMDx8rMeGuESwpqDEnDoN/+CDD7bSmBDsmiLByiNY4PTJJ59YuNgVAIJf5JIEaypC7DRAu0sEayomKdQ5AiEECzt0bLX0/PPPm5VWWqlFsPSLX4e5myYTLP00GLs4+KDErmeI64opQnmg4iNRSARryuMLlWCRG/zOP/98M2rUqJBnn6YIHYkn0zVMd4W4RLDaUWKLDiRY0ofbU6eeJYI1FQtC9O9EsNoxSWedIRBCsKRkNreHYMm+lnn9NhEsQW2Kz+b26623XntkxllXECz33u65555EsP4HShHBcjsGIswkwZoCnlhyL5oilPZ3wAEHmMMPP1xOc/1EsNrhSRKsqXiIodEQ/Rb6byJYU7FLoc4R6IRgpSnCKXiXMTSaCFbnbbTrriwiWHLDQrSQYCWCNQWVMgQL/JIES1qTMWyVwwKBoilCaXdsqp2mCKfgV4ZgMWWTCNbUdpdCnSNQlmCxaXEiWFPwziJYMr7ppwLBqtUUob55wnfddZdBAS/EJR2sdsV+lt8yXRPikg5WO0r77LOPXTLfHus/SxKsdlw22WQTc+GFF7YifQMTiWmKsAWRDYATLzr0TotcUnIvQqjZ6WUJ1jLLLNOaIsxDLk0RtqPDPqqhKkxdOUXIZqbY6AhxiWBNQUleaHfccUfwnkqJYLW3MBYIhNgb46pEsNqxw27dvffe2x7pOUsEqx0UVmIy1j333HPtCZ6zRLA8oKSoFgJlCNZrr71m9ttvP8PCsiKXCFY7Qo899pg1idQe6z/rSoKF7oLeosN/61Nim0ywhFRpfFiZhFXtEJcIVjtKH3zwgfnwww/bIzPOEsFqB+bdd981tL0ilwhWO0L0YaZhQ/S1EsFqxy6dtSNQhmBhyR2zSBD8IpcI1lSE6K8sDMAKfojrSoIVcuOSp8kESzDo1G86wfIR1FAsE8EKRao9XyJY7XiUOUsEqwxazctbhmCVQScRrJ5ohb47uoJghd4s1XTzxk6w+MJYYoklgqxk92wG+TFNJ1j56OSnugTLbZf5V3d/6tNPPx2k5F62JjETLGkDZZTcwU+uK8IyEawihJqdrgmWr0354kIQSwQrBCV/nn4jWNiNwKpplpOHL35WPjc+doIVuorQxSXkvAkEK2Sz5xCs3DwuwXLT63bu9jtWEYId01eSJn5v6gbBGjZsWCM2ew6Z9gvFEuwhWKzsREc1uYSAiwAEizG9agfB4iMfQ9ZVjAFV318V5bGKEC5R5Ki/HEV5SXctuetrKrXkzn48Rfu8dfLwTj31VLvMWd94TGEkWMOHD7fbB1Vdrx133LFHh+zkGVR9X1WVJ2YaHn/88cIii+rtpq+11lrmhz/8obdcN683UxdF+u5XzDSwP2iVDrMEbJXDSpyYnGCIf/3111sSyQtJnKTLeSc+upWDBw82bIuVXELARQCCtdNOO7nRmeehbfKKK64wSy65pKHvxuowlSIEKxSXECyOOeYY87Wvfc2btXKCNWbMGPP73/++dUyePNnIwWbFpIlPWNLkGjkXn3h2okeaEKtDgrXUUkuZU045xeIjdQ/1NXYaU/ZV2myzzXoQrJhwhGAhhbnqqqtabU7wECzwpc298MILrXwaX8krceRjc2P2wYzJ6YEFgvWFL3zB7pUn9cYXLMSXODCRsKThS5g0cGa13NChQw3TaLE66rbgggtaW2LUWXDB14dgA3bSBiVOfMnPOaYceCZJghVry+ldvbbffntrokf6orQdfNqPblPk0XE6Ta6TdPa35R2EYnysbuTIkdYOog8riXNxyYsnjXfsHnvsYTbYYAMvbJUSLIxf8pBgc+uuu641Nc+0IWE5OOfAxgTHOuus08onadpHKrb00kubb33rW94KxBCJBAubYCussII1bqbr30lYsOc5LLbYYmbvvfeOASZvHVgRuOiii5rVV1+9hZ3UH+x0GImUtDs3zW2fGJmDJJx11lne/61jpCZX3P+kSZPMXHPNZcCFfiZtTWNGHFiwMfsaa6xh8eM8Ly/XzzfffObWW2+tI0xt9+xiJonUbd5557XYCB4uboIdH4chYx3l8CzAjm1OkksIuAiwWT1juttffW2P/srhS5P+i897AjttTKHFLMH65je/abALpvkJ2Lj4cC59VuPky0ufhfOMHj3afVT2vBKCJYMQtiNuuukmgxVU8Qm7B1MHiyyyiBWFI2rPyytlyVYo8l/e2tQ4ki/XG2+80e6A7uLVyblgio+kQnATv8ZQtd06X1y33367bWO33HJLZlsi7eyzzzbTTjut/drIyyt4g90rr7zS9n91PnGf/V/+8pcefVPqrn2wOuyww8x0001nmHIuwg7caMuhpkTqiCl1AyPdz/S54AdWYEa7O+KIIwr7N+VxTYg5jDrilu65dwgwlkubkzYmvo6nDfHBPssss5jx48fbjx2dT+clnnPeQSEmHXpXg4G5mrHv4YcfDsLu2muvNUOGDDELLbSQHcc0bhLWPthlqahUQrAEMtgvLzw50E+QsPZRDB0xYoQVsf/1r3/15tH5CcfMrMFPY4VhOLf+nZ5TlmDnvmDludXd19jl4TRx4kQzzTTT2Bce14BNHtakxTrg8MxpD3l46bRrrrnGYseUqWCn0yWs8YwZO+rmq7OLDefofdDurrvuusL2JmXybGLtr3Ufbwby/lEnoY3ofiZtxvWROkOwsF/nprnntFOOmJ3LT1wMBNNPPvnEzoqgk8aCHTef71zesS5+lRIsKbxoYOBmIFgwRCpV1sU6+BThVhYnnd8t2z3XeWMLS10xSzBo0CCzyy67xFbFzPpI3TMzBCagcwRJYMGJuKrKlvJi8H2YoN9Cu0Oql+V812XlTfEJgRAEmNKCYGFcOc+ltjcVHbBAAMQM2xe/+EUDoe2Nq4xglXlIMGUhWDDE5BIC/YEAisOQhJ133rk//q62/+HryxAsSAILMXC+PLWtcAU3Dh5ZmECwaHeoRmTlSZhW8BAaUkRWG3Lj0W+GYLEQyE3LgkryiZ+VL7Z4qS8+m2NDsNCt6pRgSXmVEaxQwPljTbCy7MjIDYaWm/IlBKTN4EtYoyIEy5Vg+fLq63zhTq7xlVOXuDyCJViIX5c69dd9aoKV9Z+CnfhZ+VJ8QgAEpJ2I70NFJFhlCJavnNjjXAyzCJabLwSXfidY3JQmWEVThJ1UKqTiKU9cCIS0E2wLIUkoY0cmLpSya1OEn0wRigQrqyQpR/ysfDHG6zrrcAjBihGPVKeBRUB0sCBYOGmT4hfdXWi+onLqli5ThEiwQvVIBSvXr5xgyR/kgap1sMpOEYaUn/ffKa25CLACp+wUYRPaW0gdWe0LdloHq2ktSXASP7T+kFKmV8saXi37P6H3k/LVG4HQdiFThKGb24NKaNn1RjD/7rUEK5RgZZVYGcHiwYiWvmjju9r2Ek8FUCBDyZ1dq7PyEc81HFla+lkVS/HNQECv5pJ2JO3MPceMCCRhhx12aK3C0XmRrMo5Ya7XHSy2wYf6UE+pN3WX+gt24ssqQlbE+fJInPgudnVvje6z1+1O11nw0nHsBkC7Qwqo43WY6+Sc5+H+X93xS/ffOQK6LcgqQumzut24bQ9bTuhgsVOD5KONSTuTsJzH/o4FO6mzYOX6pGO+Bm5SZhUhzwMnz0r8yggWhfOlts0229hj6623NltttZXBdw/isVY8++yzG4yTuun6nPK23Xbb1pYlcuOdN9d0ZUwIYOZjt912a2t30n7c9rfhhhuaGWaYwRrqkzza1/ml3cVgLDPreb/xxhu2b4EB9dX117gQxlDmjDPOaJZffvnMfFwv/R//iSeeyPrrWsczBlE3xiXqqbHyYYg9ItodRkR1XsJufspjO5TXX3+91hilm+8bBC644AKz3Xbb9Wh3brviHIO19Nlvf/vbtt25bU2ukT576KGHWkFGrO/YE0880dtnBQfxt9xyS8tN4ChZmElesGMcOO2007wPvFKCtfHGG5tNN93U/OxnPzPnnnuuPX7605+2whKHf84555hx48Z503Q+yqLCWExNLiHgIoB+wQILLGAYHGg3We2NtJ/85Ce23WFwVM59+Yk777zz7A4Cp59+uvuX0ZxjLZxthpCw6D6r+5+E6avSZ32YkU/iwZdtZPLMEtQVRHn5UDfanbQlwcnnC3bgJxj58pHGs2AvQqazk0sIuAiwQAeizvik+5yvPdHeOBj3fOnSFun76KVizR2JTqwODjFq1Cg71mVhIpgKdj7cdNz5559vNtlkE8t7NG4yTlRKsKjAwQcfbD7++OPCA0vFHOT96KOPcvOPHTs26s2e9YNJ4XIIQLAgCffdd19uG5I2KW1OzrUvaeKzOSiGNaWzlLuz7s/NSxzs2FNL45AVFlyy0iUenY9hw4bZDZG7H4XO7pDpPpZyY2NI6p3lM76FYsfecGzBk/Yi7Oy5xH4V0s3vfe97hW1O2qKv3fnetxdeeKEZPnx4dKo4euxmKyC4BNj4MBDM8MGNoygfeeE8bL/jc5UTrCOPPNL3P604Kqwr3UrICaD3wcsuuYSAiwAEa5555jGylZKb3ptzdBhi2+xZ4wHBAjt0NMr2SV2OG0aPYfHFF4+eYEEiy3zxh2D81ltvJYLlNqh03kIAgoUOadXuF7/4hdU5El2iqsvvhvIgWH0xnh911FHdQ7A6AToRrE5Qa8Y1iWB1/pyFYPFSr9I1iWBpO35FBErSxfdhngiWD5UUJwiEEizdxnRYynH9RLBcRMLPu4pghTxst2qJYLmIpHNBIBEsQaK8LwTrzTffLH9xzhWYXllsscUaIcHSBCsHkmAJYSJYeSimtFCC5UMq792bCNbUFYA+7PLiuopg5d1oVloiWFnIpPhQgiWDi/ghyDVlilATrDL4ZGGYCJYfmRBsE8HyY5dipyDQG4KVh2EiWHno5Kd1JcG6+eabDYp1IS4RrBCUmpknlGCBDtIGVt/cf//9QWA1kWBlAfOnP/3JnHnmmeaZZ57JytKKTwSrBYWVXL366qt2GbcmslNztIcSwWrHI521I5BFsHzkfcKECXYVoehV+fJI6U0nWC421113nbn00ksFnly/awgWlcCw6FlnnWWwScQR4hLBCkGpmXmKCJZ0nFdeecUcdNBBZtVVVw22qZYI1pQ29fTTT5sxY8aY5ZZbzlx99dU2UnD1tbomESzqmuXA6N5777VL4MHu0Ucfzcraik8EqwVFCngQyCJYOis6kNjL2nzzze3iMN80ttt/m06wBD9WDmLP8+tf/7q1HybxeX7XECxukiXhxxxzjLXLgfHCEJcIVghKzcxTRLAEFb5IsF+y8847m8MPP1yic/1EsKbAg72c8ePH2w8i31edO1gzoCcdLGOXvLNqiba32mqrmQceeCC3vZGYCFYhRI3OEEKwaEOs5oc0rbTSSlZyXwRaIlhTEOJj8thjj7VCoCzTCy6WXUWwkGBhpfiee+4xvMBCXCJYISg1M08owXr33XcNeZFiHXbYYUFgNYVgYdFdO5cwMbXFl90WW2xhLrnkEp21R5hrIVhNsINFHYskWEwPMubxMZkIVo/mkiJKIhBCsGiTtDsMCa+88sqGremKXCJYUxD65JNPDOMdKkzrr79+EWw2vasIltwxovMkwRI0kt8pAqEES8o/8MADE8H6HxhlVxGGECyKbtIUoW/6Rdqa+JBO7PglgiWIJL9TBEIIlpQNwUKCBcFyP5okj/iJYAkSU/xbbrklePeYRLDasUtnESGQCFbnD7MswWJPsyIJFneTCFb7M+HlhpHDBx98sD3Bc5amCD2gpKgWAmUJFtvfiAQrj2QlgjUFYsGoNhIsueFWC/lfgCnCJMFyUUnnZRFIBKssYlPzJ4I1FYuyIbbKYYowRIL13//+10qwWNWFyxoTSUsEq+yTaFb+sgRLJFhFKCWCNQUh6ZsQrND9j7tWgrXGGmsUPXebnnSwgmBqZKayBGv//fe3G0OHgNUUHawQ8wHgxaqkiy++uBC6JMFqhwiClSRY7Ziks84QKEuwkGCFfAQ0mWAJqdJPBIK13nrr6ajMcFcSrLvvvjspuWc+spQQikBZgqWV3H0dS/9vIlgaDWN3or/sssvaIz1niWC1gwLB4mMy6WC145LOyiNQhmBNmjTJrLLKKq0pwrx/azLB8uFSmylC380Tx6quW2+9NSu5LT5JsNrgSCcKgbIEa+LEiebJJ59UJWQHE8Fqx4aFKS+88EJ7pOcsEax2UCDyjHXvvfdee4LnLE0RekBJUS0EyhCsjz76yNx0003WXEirgIxAIljtwLCy+vbbb2+PzDjrSgkWX3WifJdx363oRLBaUKSAg0AIwdKSqn/+85+GI8QlgtWOErj9+9//bo/0nCWC1RMUMGHMK3KJYBUh1Oz0MgSL9sb0IOOfHgN9CCaC1Y7Kf/7zn1wTLDp3VxCsogesb9gNJ4LlIpLOBYEQgiV5tR/SHhPB0oiFhxPBCsfKzZkIlotIOtcIhBCskLFNl0k4ESwXkfDzriBY4bfbc5WNEKxOGk6Z/01564eAEKyHH3648puHYNH2YnWsIpx33nmtYb0q6xgbwfKNO9dff33mKkJf/lB8E8EKRaqZ+UIIFsiUbYOJYHXenvqNYKF1j4n+Mg83JK8QrM4hSFfGioAQrEceeaTyKsZAsPL6V1kzDaEAx0awfPUuY6bBd31WnBCsUD3BrHJSfJwIQLB23HHHyiv385//3Cy11FJGNoau/A+6oEBW8rJ1VdUOgpVl9X2aKv8MuxHsM1i1O/XUU60dmbyXRdX/mcqrBwJCsJ544onKb3jttdduk2DF1v5EgvX++++3sKuijuh+NGUvQtGrqgI3HgLtefDgweapp55qPZMUSAgIAhCsnXbaSU57+CHt0M3D+ZVXXmmWWGKJ6AkWXKJqx96FWfsWVkqwkGCts8465sQTTzQnnHBC69DnY8eOtensWE1lySdx+hrCXMfBztZsNZFcQsBFgBfSbLPNZnbddVdz0kkn2fYk7U18t1255zofYTkWWWQRG3b/M5ZzCNbMM89sDj74YFtPjYvGRMf7wm7e4447zsw111x2k+NYsHLrwQbO1JG6uvWX9uPDyo1z8x5yyCFmlllmMX3xweDWIZ3XD4Hvfe97BttWbpvzvUN//OMfm9NOO601LtL23Os4Z9xkG6wll1wyaoI1cuRIyyV8OLj9MvQc7OA8cBTthMRWSrC4qdGjR1uGvcMOO1hRJuJMfey8886GNKwgDx061IZh5DoPYbmetG222cYghksuIeAiwOac2223nWHgkTYkbUfOQ325TvzvfOc75oYbbnD/Mprz1157zQ6s1FfqLFj54iTN58v14m+55Zbmt7/9bTRYuRV59NFHDXUEC6mzD5eiOPdazimXZ5NcQsBFYNy4cYZxyffO1G2NdKb85p9/frPtttsaee9mtVckY3vvvXfUBOuII44wW2+9davPun1P41cmvNVWW1ni6j4rzislWO+884556aWXzO9//3trL+fFF1+0PrZzdJh0phB4+JMnT27lIZ/kJb9cg//222/77j/FNRwBltO+/PLLts1Ju5N2VNZ3r6fdffzxx9EgLF9VUiHMLkgfK4uVL78ui/Cnn34qfxWFr/HDxAxjncbBrb9OKwrra2nPn332WRSYpUpUi8Af/vCHVp/VbUaHaWuMZauvvrqVUKPPx7nkEV+3SeKw/RSzg0P46q5x6CTMOIBdT5+rlGDxB3oQ0n+o47GlM2LECLPgggu22SSSPPgS1mWkcEIgFIHetp/eXh96n92Sz9fnmoZBJ8/Ch1uZchLGZdBKecsgsO6661qC9cEHH9jLdFuTsPhlyo0hb5X1ziurUoKV90f6ofDlDMFaaKGFrDEv9zr3XF+bwgmBhEDfIJD6XTlc+wqvviq3XO1S7rojwCId9PnQU8UVtaui9Lrj0Vf3n4dbZQTL/RP3XFfOJVg6LYUTAgmBhEBCICGQEJiKQN77dGqu9hDK15pgtadmn3XyX9mlNTulMoJVBkYhWEwRYjOnyPHAfQ/dF1dUVkpPCCQEEgIJgYRA7Ah0SrBix6U/61cZwSpDdjBm9sUvfrE1RehWuExZ7rXpPCGQEEgIJAQSAjEjEPKOFIIlOlgx49GtdauEYMnDFr+osuRbZpllLMESQ31F16T0hEBCICGQEEgINB2BvPesTkPJnSlCTNmEOn196DUpXzYClRAsKf7ZZ5819913n7n77rvNPffcYw8dlrg777zT2sCaZ555zG233Wbz3Xvvva1rJJ/4pGEUURyNIDUEQSP5CYGEQEIgIdAEBDC3kPWulHet+Msvv7yZbrrpDPtmyrvU55OfMh9//HH7Xk3v1upaUqUEC+Nma665pvn2t79tNt9889bBuY7bbLPNzCqrrGJWXnnlVh6dX4e5jtUQGJPEpYdf3cNPJSUEEgIJgYRAfRA4/PDD7a4m+n2q35e8W+V8tdVWMyussILZdNNNW3GSpn3KQtq10UYbGUwoJVcdApUSLPbjwWIs2zz4jokTJ7bin376acPhy6fjuAYLs2ussUZ1tU4lJQQSAgmBhEBCoGYIYHEdEqXfkW5Y3rPsZ6nfsRgcdfNy/v/bu5uXKqIwjuO7clm0iMhqFRRU1CbwJcoS7M3SNrYK2ihB2bqsoI3pIijdRy/0H0SWVBtx4UYEsV0rS91YUGaSyhPPwLmM4zRz5t5zZ8bxe2GYtzPjOZ87MD/mjudoeR1qp+iDPWfxVTsNWDrYc09PT6kd/qdN/uVSAcsFHVOJsQgtsSiGAAIIIFBIgbjBnstt9KtXr7yxCPU//Pm4E6hqwHJVzb6+PgKWK0zOgwACCCCwIQU0YOkYeq4/L1++LPxgz67NbM6XesAq50kWAcvmq6QMAggggECRBSoJWFH3XgJWda6aVAJW1Bdr0ywClo0SZRBAAAEEiiwQF7Ci7rVR+whY1blqUglY/qqbL1lHi5+dnfXv+u8yAeu/NOxAAAEEENgkAnEBy8+gfUzqPdbcc/37gssErKCIm/XUA5ZWe3p6Wm7evCldXV1WrSBgWTFRCAEEEECgwAK2AUt7b797965cvXpVwl5cD4YuAlZ1LprUA9bnz5+9fzO9ceOGaFf+Nh8Clo0SZRBAAAEEiixgE7C+fv0qV65cke7ubq+vyd+/f8eSELBiicoqkHrAmpubk7GxMRkeHpbGxkarShOwrJgohAACCCBQYAGbgPXjxw8ZGRkR7fdKO/NeXFyMFXnx4gX/RRirlLxA6gFrZWXF6y1Wu+bXXt9tPgQsGyXKIIAAAggUWSAYsII/9Wnb9R779+9fmZyclGPHjglPsLK7IlIPWKapOiYSActoMEcAAQQQQCBaIBiwokrr2MD6BCsYsMJCGT8RRkmWv4+AVb4dRyKAAAIIIJCagIuAFVZZAlaYSuXbMgtYOoI3T7Aq/wI5AwIIIIDA5hBIGrD0J0Kbd7AIWNW5fjILWPqSu472bfPhHSwbJcoggAACCBRZIEnAmpiYkIMHD8rCwkIsCQErlqisApkELP0NWEfxvnXrllWlCVhWTBRCAAEEECiwQJKA9eXLF+ns7JQ/f/6URMLev9KdBKwSkdOFTAKWtkA7P/v+/btVYwhYVkwUQgABBBAosECSgLW8vGx9jyVgVeeiSTVg/S89xzWNgBUnxH4EEEAAgaILJAlYxsLmvkvAMlpu56kGrHKrTsAqV47jEEAAAQSKIlBOwLJpOwHLRil5mVwFrLCkrdsePXokdXV1yVvHEQgggAACCBRAQO+F1QxY+/fvDx23sAB0mTXBecC6f/++88b09/cTsJyrckIEEEAAgY0koAHr+vXrzqv8+vVrb6gcfW+LjzsBpwGrublZbt++Ld++fZPp6WnRQSf9c10261omWM7sN2V0rmV0VPD6+np3reZMCCCAAAIIbCABfYJ17do16ejokNnZ2dK9VO+zlUx6j3369KkcOHDAG2JnA5HkvqoVByz/z3qXL1+WXbt2yZEjR+Tw4cNr5ocOHSqt6z4zmbL+8maf2bZ7925paWkR/9/KvSwVRAABBBBAwKGAdruwY8eO0Hup/76ZZFnvwXv37pWjR4/yE6HD70pPVXHA8tdnfHxc3r17503v378XnXTdLJv527dvZd++fbJz50558+bNuv3BY3R9bGzM/6dYRgABBBBAYFMJTE1NydDQ0Lp7prm3ljvXe+zo6CgPMRxfTU4Dlv5+q6N4Byfdrv1eme26rD3M7tmzx+sEzWwPm5tz6gjhfBBAAAEEENisAqurq6X7aNj9spJtvH/l/qpyGrBsq2cCVm1t7ZpeZsOOD/4sGFwPO4ZtCCCAAAIIIFC+APfa8u3MkZkELE3Z/idYpjLMEUAAAQQQQCBagPAT7SFckFwAAAOmSURBVJOXvU4CVvDLDq4HG+sPWEtLS8HdoevBcwbXQw9iIwIIIIAAAgggkIGAk4CVtN7+gOUfiDLpeSiPAAIIIIAAAgjkUcBpwLJ9qmTewTIvuRsYPd5MZhtzBBBAAAEEEEBgowk4DVhJGm/ewdKnWVEfAleUDvsQQAABBBBAII8CTgOWDsrc1tYmly5dkosXL5am1tZWb9nMdV9NTY1s2bJFLly4ILrdTP7jdFnP1d7eLg8fPsyjH3VCAAEEEEAAAQTWCTgNWGfPnpVz587J4OCgDAwMeN3vaxf8Opl1nev05MkTbzL7zdzsN+X1XBraTp06ta7ybEAAAQQQQAABBPIo4DRgNTU1yZ07d+TXr1/e9PPnz9Bl3b+wsOBNpqyZ+48x23p7exnsOY9XD3VCAAEEEEAAgVABpwHr9OnTcu/evdA/lHSj/92r/v7+NQFL9/FBAAEEEEAAAQTyKuA8YPX09MS2NWlA0ne76urqYs9LAQQQQAABBBBAIA8CmQSspA0nYCUVozwCCCCAAAIIZCmQScAyT7DMPA6AgBUnxH4EEEAAAQQQyJNAqgHLH6g+ffokz58/t7IgYFkxUQgBBBBAAAEEciKQasDSNi8uLnrdNBw/fty66wUCVk6uFqqBAAIIIIAAAlYCqQYsfYI1Pj4u3d3d8uzZMzlx4oRVJQlYVkwUQgABBBBAAIGcCKQasLTNS0tLMj8/Lx8/fpTGxkYrBgKWFROFEEAAAQQQQCAnAqkHLNPuDx8+SENDg1mNnBOwInnYiQACCCCAAAI5E8gsYOkTLAJWzq4GqoMAAggggAACTgRSCVjmvwfNXGvOEywn3x8nQQABBBBAAIEcCqQSsMLarQGLd7DCZNiGAAIIIIAAAhtdINWA5X+CNTw8LNpVg82Hd7BslCiDAAIIIIAAAnkRSDVgaaNNyJqZmZGhoSErBwKWFROFEEAAAQQQQCAnAqkHLG23hqzV1VWvywYbBwKWjRJlEEAAAQQQQCAvApkErKSNJ2AlFaM8AggggAACCGQpkEnAMj8T2jacgGUrRTkEEEAAAQQQyINAJgEracMJWEnFKI8AAggggAACWQo4D1gPHjxw3p7Hjx9LfX298/NyQgQQQAABBBBAoBoCTgNWS0uLnD9/XgYHB2VgYMDJpOdqa2uTkydPVqP9nBMBBBBAAAEEEHAu4DRgtba2ytatW2Xbtm3Opu3bt0tNTY2cOXPGeeM5IQIIIIAAAgggUA2Bf4p3JIym186nAAAAAElFTkSuQmCC[/img][br][br]6 = 2 __ + 3
Complete the equation by writing [math]w[/math], [math]x[/math], [math]y[/math], or [math]z[/math] in the empty box. Find the solution to the equation. Use the hanger to explain what the solution means.
Match one hanger to the equation.[br][img]data:image/png;base64,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[/img][br][br]7 = 3 __ + 1
Complete the equation by writing [math]w[/math], [math]x[/math], [math]y[/math], or [math]z[/math] in the empty box. Find the solution to the equation. Use the hanger to explain what the solution means.
Here is a balanced hanger where each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Write an equation.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger where each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Write an equation.[br]
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.[br]
Here is a balanced hanger where each piece is labeled with its weight.
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[/img][br]Write an equation.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger where each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Write an equation.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
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Information: IM 7.6.7 Lesson: Reasoning about Solving Equations (Part 1)