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,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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
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.

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

There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. If the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below.[br][img]data:image/png;base64,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[/img][br][br]What is the constant of proportionality in this relationship?
In this situation, what is the meaning of the constant of proportionality in this relationship?
Add at least three more points to the graph, and label with their coordinates.
Write an equation that shows the relationship between the mass of a sample of helium and its volume. Use [math]m[/math] for mass and [math]v[/math] for volume.
Explain how the parts of the balanced hanger compare to the parts of the equation.
[math]7=2x+3[/math][br][img]data:image/png;base64,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[/img]
For the hanger below:
Write an equation to represent the hanger.[br][img]data:image/png;base64,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[/img]
Draw more hangers to show each step you would take to find x. Explain your reasoning.
Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.

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