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FJP1kB86ol3V9q92h0ydizfUl8LGaFXTs6N+6GOn98FCO3PlUoEAB65I/d9abf/SZizfSmMmT9OHNyyi9WDzyR4PJo1BlNaqZze68G6B9p4PV6Il8rkdOAkEBCozUqN9wfZAFKMD1RSRThNqfOx1jnZ4sZG8FAM4S02dwmnQZkywH3E36Mg3umAGy29shcRH43ZDh/6/27/6f/nfoojLfX1i1m7ym/lOX6ruJLyp9yO86cS2znkgfIp9DJ+Ub6UQQLN8jB/Wn0uuBB+5zfZeOQfA1XQ249SNbdDxy5FH1B9Iq6NBxnYk4qorhrXWjuqlb/3k6kzaHHssiBew9rau5898MnQUK5FeuwFP664SXTl+k9jVhZFChei31yNG9+vpQbMY/9lD6QlX0YpMmanzz8qKqFIqmE65HQVVtVDWs8+7+AzrvkUWV8yRwLUxMx1zQUR3zjniMuI7ho4d1UnlVJH9Opclf9K7H2JVAfkMC4CxpCpa+42fw3K3/JnoOiA3zHH2f75Uo5+cCypMxhAyQxAj87ijolNZ/0EevvzVSm/b9LW9vL5087Klfdh5VSJbHVKRoKXUf3VLFfv1YA95fom0Hj+r0v0f1y9LxenfMZhWu21sjWpRWWldILFG1ivJ6HNDSz5ZZ2x0/vEfzR0/V8nP2c8UkfQG1ef81Vbi0QMOGL9KBoyflffKgNs/9SJOWHJR/oVLKmaOQXp/wumub+Rr07mdau/dvnfY6ob0/Tlffbm9qwLjVOmXw811C8bivpvq810BzO76izgMmaM6367Vjr+vEfvB3bflhkaaN6qeuvWbpVMmaerxkXvteseH6MvFsO3V4+C/N7jtAHvkrKVccqvfTZc6qbArS+QOe+uP4hbgdcx6HNG/0BGs775N/uI7hceoz9n96+OW+qlIkm5T9iUjH2J4jJ+T979+RjjE/TnMAnCZL+Tt+BmcpWinxc0A00qTLcPN873nwD/1zvZyer5nmZgbw8va2ztHzJ79PBkhqdudduJugf42tn/Yyqv7nYaNYkaKuSyXjhb5zjB3e1+wNQo0g7x3GF4NbGpWs9Q8blZ7vZXz609/GlZs95U3XjNNbpxldny5jPU7x8g2Mz3fsNdaavfYj9c6P0oPfcus5HrWeo5hRqekwY/Hus8atvvX2NiM6GE8/Ym7julRoaQyZt8PwtkZeQcIKNQJP7zaWT+prtKwZ9p7ePD7enmx8t+NElPc/OhFG6dlz3i67YZz+rqdRyvUeT996yi4zjJC7jtLj4jpWN41vYx2H1Tu8b44jccdjLtIoPaUHGd/t+s5o9mTYtiWf7una9nSE48t06xh7vCjHGIDUIubPYHscnUTOAdGM8BNy+eb53vwMMUfrCb5yKnIGcF0ad5sU5fxsjtLzQjQ5AwnFw/yfnf3hhgL8Lsgv4IY8MuVSvlyZomlXbSjY/4J8/A3lyp8n8uyrEQX7y8fHX2my5FDuHHHtzmPI78J5BYRmUZ482WL4iTB8P0KULU9eZbNGXUGiMq7p8rlLCjQ8lDlXXuXMlJw13WHvv7+yKlc2u9lQHI65a/6XdMk6dnLf4dixj8Mbae+yHQA4yd0+g5MiB0RkP9/VtMqVL5f9fOH7YDYTSq/c+XIrQxrO0UmJwA8AAAA4GI1bAQAAAAcj8AMAAAAORuAHAAAAHIzADwAAADgYgR9AggkMDLSXAADuyM/Pz16CkxD4EWtmmBs+dJh6vfOOAgIC7FIg7AOi1lM19ErLVvL19bVLAQDuwvyMHz9unPr16WOXwEkI/Ii1zJkz64EHH9Tqlau0Y/t2uxSQcuTIoT79+urA/v16q0cPuxQA4C7GjB6tmTM+00tNmtglcBICP+KkZauWeqhoEa35YY1dAoR5tkED69j4decurVi+3C4FAKR05jl7yZeLrHN43bp17VI4CYEfcZI7d2717NVLO3fsoL02IjF/ARozdqy1PGXyZAUFmTMqAgBSMi8vL/Xp1dtaNs/h5rkczkPgR5w1tn/u+2ntWusaCFe9enW1bttGJ4+f0L69++xSAEBKZFbM9H33XWu5a4/u1jkczkTgR7y82rGDVSOwfv16uwQI09v14fHkU09p5uef2yUAgJRoyeLFVjPM/u8NVK/eYbX8cCYPw8VeBmLNbM5TtnQZa3nNup9UokQJaxkwXbhwQfXr1tUn06dTYwQAKVD4eXrYiBE3f7mHc1HDj3gx2/i9P3qUtTxsyBDrGghn9vWoWq2aPp48mb4eAJACffThh8qTNy9hP5Ug8CPemjZrdnNUlqNHj9qlQJi6zzxjHRv09QCAlCV8VJ6Xmza1S+B0BH7Em1nLP8iu3d+4YYN1DYSrUbOmdW329TB/OgYAJL+Io/I0euEF6xrOR+DHPalXr56Gj3xfSxYtYjpuRFKgQAFN+WSqtdy9a1dm4AWAZLZ9+3ZrRvScuXJq9ry5Kly4sL0GTkenXSSIVi1aqETJkho9ZoxdAoT5cuFCDR8yVE9UraLFS5fapQCApHTmzBnVqBY2iAKDbaQ+1PAjQdSpW9dqD7hvH2OvIzL6egBA8lv+3XfWtTngBmE/9SHwI0HUrlPHuh73wQeMyoJIIs7AS18PAEgeP/6wRg2eb6i27drZJUhNCPxIEMWKFbOabDAqC6JjjsVvftBs+XmzXQIASCrmJJmnTp3UoMGD7RKkNgR+JIj06dNr0pQpeqxsWY0cMYIZeHGbkaNG6dixY1q+fLldAgBITEFBQdZsut06dVbX7t1VsGBBew1SGzrtIkGZw309/VQNa3nn7t90//33W8uAacb06frv+An6ZsVylS9f3i4FACSG8EETzH5Ua9etsyrnkDpRw48EZdYe9B0wwFresWOHdQ2Eo68HACQNcxANM+ybPps5k7CfyhH4keA6dOxg1Sb8vHGTXQKEoa8HACQ+sylP7549rWVG5YGJwI8EFz4D78YN66nFRSRmDdPAQYOs5SmTJzMDLwAkgq1btujk8ROMyoObaMOPRNOhXXulz5BeUz/91PoSAIQzO+727dVblZ6orLlffKEsWbLYawAA98Kc9b51ixZ6ompV9enbVzly5LDXIDVLO8LFXgYSVL78+TX5w4908dJF1X3mGbsUkEqVKqUMGTPpm2VfqVSZMipZsqS9BgAQX+av6gP691dISIg+nT5dGTNmtNcgtaNJDxJNxYoVrWtm4EV06OsBAAnr22++0dof1qj+s8/aJUAYAj8SjdmM58PJk6xlc1QWICL6egBAwok4Ks/LTZta10A4Aj8S1bMNGli1uOaoLCuYcAlR1KtXT1mzZrNqpQAA8RN1VB7mwEFUBH4kKrMW94sFC27OwHvq1Cl7DRCmU5fOVq3U96tX2yUAgLiY9flMXb50SaPHfsCoPIgWo/QgSRw5ckQN6z+rtu3b6/1RI+1SIKyTWdnSZaxlZuAFgLgJn+F+xqyZ1q+mQHSo4UeSMCf9MGfg3bd3r10ChKGvBwDEj1lh8sGYMdYQx4R93AmBH0nGHJXl1KmT2r59u10ChInY1+PPP/+0SwEAd8KoPIgtAj+SjFmTW7VaNQ1+7z1GZUEk5rExZuxYa3nb1q3WNQAgZozKg7gg8CNJvdGpkzXdd5/evQn9iKR69eoaO3GCvpy/QL6+vnYpACCqtWvX6vUOHVSsRHF9u3IFo/Lgrgj8SFKVKldW67Zt9NOPazVm9Gi7FAjTokULFX7oIU366CO7BAAQ0dGjR/Vm127KmSuX5sybp3LlytlrgJgR+JHk3u3Tx7o2Z+A1R+8BIqpV+2nr2KCvBwDcbtHCL61rc+LCggULWsvA3RD4keRy585tTQxiGuY6YQER1ahZ07qmrwcARGaeE7du3WL9Us6oPIgLAj+SRdNmzW6OymL+PAmEK1WqlJ6oWsXq6/HT2rV2KQDAHJXH5/x5DaayDHFE4EeyCJ+B1+xwNHf2HLsUCPPJtGnW7Mx9evVmBl4AqV5QUJDGjxtnjcrTp18/6zMUiAtm2kWyCp+Bd/Mv22iLiEguXLigKhUrWcs7d//GKBQAUq0hgwdbfZsaPN9Qk6dMUfr06e01QOxQw49kZc7A++RTT2n6tGl2CRAmYl+PTRs3WtcAkBp4eXlpxfLl1vL69eutsG8a5Ar+hH3EB4Efye7JGk8xKguiFd7Xg8m4AKQmP2/aZDVpXLJkiT6wh7CeMWsmv4Qj3gj8SHa169Sxrj+ePJlRWRBJ+Ay8W7ds4dgAkGqsXrXKuh4+eIg1gAGj8uBepR3hYi8DyeK+++5T+gzp9c1XX8vH10dPPfUUP1nipsKFC2vXzp1a8d1yPVO/njJmzGivAQDnWb16tebMnGUth3ezND8TQ0ND9VCRIpwDES8EfiS7NGnSqEqVKjp3/ryWLV6iUCPUCv1AuIIFC2nShx/qsp+f6j7zjF0KAM5i/pLZuNEL9q1bznh7q8R/Sqp69epUiCFeaNKDFKN7jx7W9WfTpsvX19daBkyPPvao1Zafvh4AnGzv3r32UmTmAAb9+vdnOE7EG4EfKYbZGSl8VJYdO3ZY14DJ/JDr2auXtUxfDwBOtXDBAnspTM5cObVg8SK1bdfOLgHih8CPFCV8VJZ1zLCKKJ5t0MCagdecnZkZeAE4jVmRsfaHNfatMB1ff91qxgPcKwI/UhSzJnfWnDna/dtuee7ebZcCYcfGpClTrBl4R44YoaNHj9prAMD97YjQXNGcn+bDyZPU48037RLg3hD4keI88sgjVsfMls2aW5OPAOEKFCigT2dM1+VLl/XF3Hl2KQC4v3U/rbOuzfH253+5UI2bNFHatGmtMuBeEfiRIj37XAPrmhl4EVV4X48dO+i8C8A5rly5om9WLGe8fSQKAj9SpIoVK1rX5qgs+/bts5aBcGZfD5/z560p5wHA3Znt9ytWqqjy5cvbJUDC8jDCZ3UAUpgD+/erR7fu1vLns2epVKlS1jJg+njKFH0xd65mzp7t+qCsZJcinDm0bVBQkC5dumSXOFuePHmsCxBXP3z/vZYsWqzjx4/rNM1I3U727NlVtlw5a/jmNu3aWZM14nYEfqRo5pjr7V9pY43c8/2aNYxBjJvMQFu1UmVrefMv25Q7d27t8fS0OrulRmYN4batW7V8+fLbRvpIDd7p1dN1CRu6FYit8M+YBs83VLv27fnS6IYCAgL0+Wef3TzvmcOYMrLR7Qj8SPGGDB5sNe1Z8tVXqvxEWMADTBMnTLAmanu6Th3XSf+qsmbNao3ylJqYgcUM+ua/Q1St27axl5zr4sWL1gc9gR9xZX5JbtSwoQoVLGR1koV7mzF9hv47frxVQbh23TpmJI6CwI8Uzxyp5+mnaqht+/Z6f9RIuxSQDh48GGka+mIlilsn+tRg48aNGj1ypE4eP2GXSHXr11PLVq1UunRpq3NzanDkyBE1rP8sgR9xZvYB6tapswYOHqROnTvbpXBX4V/gzHPiTxs3WCP+4RYCP9yC+c39u2+/STVhDncX/lN8VLs8d1vNe5zKfN3mbJzhP1+btVktW7VW9Serp8oOf+GB35yf4bFyZe3S2zV64QV+5kck4TXC365coXLlytmlcGdfLlyo4UOG0iIgGozSA7fwRqc3lDFjRo0eNcrqiBgu4jJSF69//7WXItu8ebO95AzmMW7OLNyjWzdVqlBBb3XvriuX/TR85PvatHWL9SW4W/duqX50D7OTv/+VK0qbJm2ky6+7dllNAs+dPWtvCYT5999T1nWGDBmsa7i/bNmyWdd+fpeta9xC4IdbMNvivdqhg+bNnmONqGDW6r3Zo4cOHTpkb4HUpnmLFlbnrKimTpliL7k38+fpFcuXq0H9+urRtZv+/PNPDRsxQtu2b7faG7d/9VVrNAraqd7y5ttvW83+Il6eqFLFXgsAqReBH26jTt261nWfXr2tn/DNJg2nToXV0CB1MptoRA39ZvtNd56h2azRN4O+2RbVPNbN19OlezdrlCpz5k1GqgIAxBWBH27D+/RpZc4SOewc+P13ewmpVXSh351/+Rk2dOjNoP9E1SrWa+s/YABBHwAQbwR+uAWzCY85CVdgQKBdEsbHx9deQmoWNfT/vGmTveQ+zBmlX2nVSl8tWWp1xP1w8iTNmTePjqYAgHtG4IdbKFq0qGo9/bR965b91PDDZgbjcRMnWMtmJ80zZ85YyymZ+avV6JGj1OTFl9SscROFhobqv5M+sjri0nwHAJBQCPxwC2bHxOHvj7BmQ4zo7yNH3Lq9NhJWxI68G9avt65TKrNG/4Xnn9e8OXNUsHAhrVn3k5Z+9ZWavPwyHXEBAAmKwA+3YYag/3744W2hn5F6EFF4857//e9/dknKcuHCBWv2aLNG3zRj1kx9Om2aSpQoYd0GACChMfEW3I45XGHfPn1uTjzUum0bjR4zxlpG6la86MP20u3+Pn7MXko+5syeH4wefXN23Nnz5urp2rWtZcRP+MRbJvNXkqhfnMwvV2YTL7NPhNlMCggXfmys/nGNSpUqZZfeG7Mp4c4dO+xbuJuiDz+coHOImCOcmYMefD57luo+84xdChM1/HA7ZrvmiDX95gkbSOm+X73amsY/fPQdM5wS9gHnMCujBg0caN9CbIz74ANrTh3z3w6Jixp+uC1zvPL3h4/QkkWLNP3zz1T/2bBaPqRc/v7+un79un3rlhw5ciRIu/WUVsNvHqNbt2zRyhUrtGP7DjV47jk1a9FcpUuXpp1+AqGGH/GVkDX85pwww4cO1egxH+jBgg/apYiN3379TdM+/USTpkxRzpw57dL4oYY/ZtTww21F7Mi73PVHjpRv4vgJqlqp8m2X48eP21s4h9kp15wlt8sbnbR65SpNmzHdmvm1XLlyhH3AYZYsXqzOXbsS9uOh8hOVrX+73b/9ZpcgMRD44dbCO/Ka+EnQPZhjzJv9LsIvOXPdW41OSuS5e7fVKddsvmO+XrPmuWKlSvZaAE6z5ocf9J///Me+hbgy/+2YOT9x0aQHKd6dmmnEV0rowJkaDR86TCGhIZE6WZtj0Bd6qLBy5cpll8TfnfpzmF8uksqWnzfrtJeXuvborrfefpvx9BMRTXoQXwnZpMf8nOJz5d58PHmy3unVy74VPzTpiRmBHyleQp9IOTEnn5gC/4H9++1bzmEOt1mvXj37FhILgR/xReBPWQj8iYvAjxSPwO8cMQX+xk1ftsbPv1cvPBd5joaIzA/1pJI9e3YVLFjQvoXEROBHfBH4UxYCf+KiDT+AZFe4cGHrA/deL3cS3faJdSHsAwBSEgI/AAAA4GAEfrg1s1e/+bOs+XOqeXmlVStt3bLVXgsAAOLCa9dy9ZjpqQD79i3Xdf73VZo+tKe6dOqsYR8u1L/XQu11EcV2OyQlAj/cljkMZ99337XaYIb7decu9XrnbW3fvt0uAQAAsXNNi+fM1LYTfgq2S8Lc0JFF/dTopd6a/Uc6FX+0tE5s+ExNey7SH/4h9jam2G6HpEbgh1vy9fVVx1df1e5fb5+o4/Kly2r/Shsm4wIA4K6CdfXsX9qxYroGdWyl5dtvHw//ypFNemPwbyo77CutW/pf9e/9rmbM/VhPHJigN/os1/GgsPFfYrsdkh6BH27pxzVrog37EfXt1VsXLlywbwEAgNuE/qOvuzRVh0n7VbDtR+r8UkV7xS3//LpTpzPXV/vm5XVfOg+rLHP+R9WtTQmdX7tIPxy6apXFdjskPYblRIoX3XBn4cOp3U10w/QxfFryiWlYzrd6vpMgY9ab721MeM+dKbbDcgIxSfXDchpntWfjaRV4qrweyJRGi4d21Fijo7aNrq0c9iYbP+qlLpsraM13HVXiZlVxiE599Zbq9durhtO+0aTnH9SmWG4X9lUgMoblTFzU8AMAAKRWHvn1+DOPW2E/Jn5XA5T2vqzKFCmpp1HOvPmUUX46ce6KzNrj2G6HpEfgh1sqXbq0vXRn999/v70EAADiI/DGDWUslFc5o6uajyC22yEZmE16gJSsWJGi9tItPj4+Rsvmza11MV2WLVtmbx2ZuQ7JY9iQocbgQYPsW2Eav/CisW7dOvvWvYl6DES8wJkOHz588z02l6Myjzdz3fLvvrNLgDDhx8ahQ4fskvhz0jlm0ZAORtnBm4zL9m3TytFdjRLtlxknQ+wCS4jh+9N7RpkiZY3WC4+4bsV+u+hMmTTJXoo/8+/cfC82rF9vlyAcNfxwS2bN/bz58/VY2bJ2SWQLFi9SixYt7FsAACC+Cjx4v0K9z+tScMQGOaHy9Tqp6yqkx4vnsZqMxHY7JD3+3eG2MmfOrKnTPlWD5xvaJdJDRYtoruuLQPXq1e0SAABwL/IWKSQd3a+/zgbZJS5GoP72/EdK/6jKPpLNKortdkh6BH64tcKFC+vTadOs0RHMy8aff1bNWjXttQAA4F7lf6SU8oRs11erDsrfrrwPufCP5n9/Xrlfrq/KedJZZbHdDkmPwA8AAIAYZS5cXn2fy67dHw7U4Jk/atfvv+vLTz/Vr7leUP/uNZXX7qQb2+2Q9Aj8AAAAsDxWp4m61y2qjPZtS9rcavbxd1qz8G1VuLxH61eulE+e2lr54zg1ezizvZFLbLdDkmPiLaR4CT2hCRNvJZ+YJt46sH+/fcsZateto6mffmr1M0Hiiu3EWx9OnqTGTZrYpcCtYyPVT7yVQjDxVuKihh9uwTyZJtQFSGw/b9ykvn36yMvLyy4BACD5UMMPIMmYNfw+vj7q1bu3XSK91aOH+g0YoCJFitgl8Rde0xsds/Y3qXw6dapWr1xlLVOznLio4Ud8UcOfslDDn7gI/ACSjBn4v1ywwL51S3RBLT7u9AtOUn4Y+/n56b2BA7X2hzXWbXPo2LHjxilHjhzWbSQcAj/ii8CfshD4ExdNegAkmdp16rhO6D1vu+TOndvewhnMYG8OF/vtyhXq+Prr+tsVSls0baolixfL19fX3goAgKRB4AeQZOrUNQN/r9su5szJTlSuXDkNGTZUa9etU8XKlTXkvUGqWqmyJk6YoAsXLthbAXB35qSP9NmJP/N8mDNXLvsWEgOBHwCSwLDhw9W6bRtr+bNp01WlYiXHjU4EpFYNn39ehw4dsm8hrv766y8VT4BmnYgZgR8AkoA5RKc5HKnZzvyJqlWssg7t22v9+vXWMgD3VaNmTc2eOVNBQUF2CWIrMDDQar//0EMP2SVIDAR+AEhCZqfSxUuXWp1ITd06ddYrrVpp+/bt1m0A7qd69eoqVry4fvj+e7sEsWGGfXMIY/PfrnDhwnYpEgOj9ABwjJQySk9snTt7VnPnzNHBAwf1v19+0YMFC6pZ82Zq2rw5H36xxCg9iK+EHKXHZNbum6PEhIYaypgxg12KmFy54q+LFy+oYqVKqlKlitKnT2+viT9G6YkZgR+AY7hb4I/I7LS2bOky/Xf8eOu22ezH7NBs1hwiZgR+xFdCB34kPwJ/zGjSAwApgDk0abfu3TR3/nzr9q87d6n9K22s5j5mhzYAAOKLwA8AKUjNWjW1y3O3+g4YYN02g38bV+j/cuFChvIEAMQLgR8AUpjw2n4z+Id37h0+ZKg1lOeM6TOsZiwAAMQWgR8AUigz+JvtzteuX69xEyeoZevW+vGHH6w2621atdasmTP126+/MXuvbcf27dq4YUOky6mTJ+21AJB6EfgBIIXLkyePmrdooQ/GjdXyVSutmv8HCj6ocWM+UGtXuTl7r9nWf8+ePfY9Uqf3hw1Xlzc6Rbr8snWbvRYAUi9G6QHgGO48Sk98mGP3f796tTXSSLgGzzfUy02bqmLFitYvBE4XPkrPs881UIPnnrNLb1fm0UdvG8EHqRuj9DgPo/TEjMAPwDFSW+APZ3bm9fT01MjhI3Tay8suDQv/LVq0UO06deyS5GXuZ0I3Pzpx4oQ1edk7vXpaw5gCsUXgdx4Cf8wI/AAcI7UG/nDXr1+3hvA87Lr8eehP+fic164dO3Xu3Dl7C+ci8COuJowfr8+nz9C3K1aoXPlydinc2cIFCzVi6FB9sXCBnqpRwy6FicAPwDFSe+AHEHtmkzhzrouBgwepU+fOdincVWBgoBo1bKiTx09o09YtzFYeBZ12AQBAqlOhQgU9VLSIvlq2zAqLcF/m+9e3Tx8r7JvvaYECBew1CEcNPwDHoIYfQFzs27dPzRo3sUJiz169rM7dcC/nz53T1I8/tiYpNH2zYrnKly9vLeMWAj8AxyDwA4ir0aNGad7sOfYtuCvzS9uYsWNVvXp1uwQREfgBOAaBH0BchYSEWKM9HT/GOcJdPViwoIoVK6b06dPbJYiKwA/AMQj8AADcjk67AAAAgIMR+AEAAAAHI/ADAAAADkbgBwAAAByMwA8AAAA4GIEfAAAAcDACPwAAAOBgBH4AAADAwQj8AAAAgIMR+AEAAAAHI/ADAAAADuZhuNjLAJAsihd92F5K+f4+fsxeAgDAPVDDDwAAADgYgR8AAABwMAI/AAAA4GAEfgAAAMDBCPwAAACAgxH4AQAAAAdjWE4AAADAwajhBwAAAByMwA8AAAA4GIEfAAAAcDACPwAAAOBgBH4AAADAwQj8AAAAgIMR+AEAAAAHI/ADAAAADkbgBwAAAByMwA8AAAA4GIEfAAAAcDACPwAAAOBgBH4AAADAwQj8AAAAgIMR+AEAAAAHI/ADAAAADkbgBwAAAByMwA8AAAA4GIEfAAAAcDACPwAAAOBgBH4AAADAwTwMF3s5xSte9GF7CQCAu/v7+DF7CQBSMTPwu4tiRYraS7e70zrTlEmT7KXbxfdx7/acMa2/076YEmN/7uU54/tvlxzPaYrpvvG9n+lO943vOlNM6+/l3y45njMx3i9TUj/n3e53p/Up7TnvtO5O/3ammO4b3/uZEuu+9/KcAJBa0KQHAAAAcDACPwAAAOBgBH4AAADAwdyu025K6oDF/tzZx5Mn651evexbyS+l/fuYUtI+pbT3y8Tf2J2xP3eWEo9pAEgO1PADAAAADkbgvwfv9OppL6UMKW1/qlarZi+lDCnt38eUkvYppb1fJv7G7oz9AQDEhgdNegAATkSTHgAIQw0/AAAA4GAEfgAAAMDBCPwAAACAgxH4AQAAAAcj8AMAAAAORuAHAAAAHIzADwAAADgYgR8AAABwMLebeIuZHAEAsbFzxw59uWSJfQsAUi+3CvwAAAAA4oYmPQAAAICDEfgBAAAAByPwAwAAAA5G4AcAAAAcjMAPAAAAOBiBHwAAAHAwAj8AAADgYAR+AAAAwMEI/ICbuHbtmlLqLHlXTv+lVSu36IhfiF0CAABSCgI/kOIZCjq1Qf3HfpJiA7/vn+vV+53P9b+zQXYJAABIKQj8QIpnKPCfLdp3IsC+DQAAEHsEfgAAAMDBCPxAAvDevVJdus+Wp5+Xdn0xWl0aVlbNF7przWE/Gbqu857faGKfV1S7RhNN+eEv+UdsmxMaqD9+mKXR5vpixVW5YWctWLfPbr5zWZ4z+6nP1J914cAGdevURzM9L9vlffTZl6u1YEgrVX68kbqMXKaz10Kl4AuRHq/1W+O1yzvgLs2BLuvzkeO0++SvkR5v7y/L1aXTGK3594a9nYtxWWuGdQ97vQExP+r5v36J9JqGTv5G/16J2OTnDq8BAAAkGAI/kACuXz6ljWtna2CPsVp5vazaDpuqd+rn0DuNW6rjG/01drWfHnvpbQ15p66+ebOlmn+wVRetrByk5VOGqfeyU8pfq4cmr1yl+WNf1bFvJ6nzx9t0JiiTCtdspdbPlFSWgqVdj9VaNQtnsu7nd+I3fT5jlv7IWlNdutZT8YeKKK3vXvVp8Uqkx3uzfm5NaN3SfryYAnqQ/ty9Sv36z4n0eOkDvbRx/SGdC4wYwoN0bt8Wbdx8Un7B0T1ekHw9F+jdEXMivabKabdrYL8PI+xD9K8hWwYPez0AAEgQBoB7dmzDJ0axItWMnt97GaF22bVjG4yyRYoapd7+3jgXXhjsbXxar4RRrNoEY+dVV+H1vUa7Wq3CliPw2bPMKFmknjF001nX44UYlzcNM2p1eN+1FO68sWlwLaNhj49uPp9p15xBtx77phvG4bkdIzxedM4bvV98KtL+m8JeV1tj3uFAu8Ql9Lwx76UyRrHSw4xNl8P2KNJ2rtdkvsb+07ZZ6265aozo0DTCPkT/GgAAQMKihh9IMA+qZKEcilw/nV4P/aegcoYXpkmnrFnSS5f9FRBsyDh7WN7XQ3T+0B55enrevBz596LS6IR2HvTWnca9uT9HnkjP5/XveaXNGxrl8X7XmaCMsXi87NHsf9yZr+nXo0EKDDgdYR/MyyFdDfG/bR+ivgYAAJCwCPxAgsmsrJnT2cvh0itL1kyKWhrOuHZVAWd+U89mzdSy6a1Lu7fGukJxkLy9L+qavW100qfLaC+FCbxxQyG/z4jyeM312pi1sXg815eR2/Y/7szXdClE+mFq/wj7ELYf3251fcGJsg9RXwMAAEhYBH4gmaUv00A/7diubdFc1vWtpuz2drGVpcWkBH28+Hr9o6+SfR8AAACBH0hWaQo/oUeue2v7pUzKV6CACtiXNOd+14T/fqENx67aW8ZOqdLFFbBhfeTHy59TPhtnx+vx0mUwa98v64zvrVF+gi6f116vmH8nMF/Ti5Vy6+ihk5FeU4F8GbXuy7lx3gcAAHBvCPxAcsr0qF5rXUrDG72qgfPWapfZ1n3nWr03cJSO5KysOmVzy8P1X6bc+XXtwE7NXvaN1h26Yt/5dhUat9NrD2yO9Hhr5v1XzQYtifB4sZe/RHk9mvaAZr7ZRxOXbdCu3ds0ccBo7clkjhQUA/M1zfhIl1ZOivSa5g3ooOnbLsR5HwAAwL0h8APJrMYrb2vYq7m1a1Q3tTHburfqJt8izTTzvbp6IJ0ZjT2UoUxjPfPwFY3vP0zTdp5WTCPVe2QtogGzZ0V6vLfHr1XL92dFeLzYS5//cc34or/qZd+lz/t3Uptm7XWkcH0Nqp3H3iJ6HnlrafDQVpFe0+j1mTVwaM847wMAALg3HuZQPfYygGRjKNj/gnz8zfFr0it3vtzKkCZyMA69EaBzF28oV75cynTXzHzr8TJkyaHcObLY5fEU7C8fH38Fx7Bv0Yv8mrLlya1shH0AAJIcgR8AAABwMJr0AAAAAA5G4AcAAAAcjMAPAAAAOBiBHwAAAHAwAj8AAADgYAR+AAAAwMEI/AAAAICDEfgBAAAAByPwAwAAAA5G4AcAAAAcjMAPAAAAOBiBHwAAAHAwAj8AAADgYAR+AAAAwMEI/AAAAICDEfgBAAAAByPwAwAAAA5G4AcAAAAcS/o/NASpq6+/mT4AAAAASUVORK5CYII=" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Investigation of the variation of intensity of gamma radiation\n", "\n", "## Theory:\n", "The relationship between count rate, C, and distance, d, follows an inverse square relationship and students can investigate this relationship or use a power relationship to determine the values. \n", "\n", "The equation can be rearranged using logs and values for n and k determined. \n", "\n", "Similarly students can determine a value for k and investigate the effect of background radiation on the equation.\n", "\n", "## Apparatus:\n", "\n", "* Gamma emitter e.g. 241 Americium\n", "* Metre rule\n", "* Geiger Muller tube and counter\n", "\n", "## Experimental Method:\n", "The apparatus can be set up as follows and the candidates measure the count rate at various distances.\n", "\n", "![image.png](attachment:image.png)\n", "\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The parameters of the line: [[ 0.13452381]\n", " [-0.01035714]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Importing the necessary libraries\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "#from prettytable import PrettyTable\n", "\n", "# Preparing the data to be computed and plotted\n", "dt = np.array([\n", " \n", " [1.0, 0.15],\n", " [2.0, 0.29],\n", " [3.0, 0.38],\n", " [4.0, 0.50],\n", " [5.0, 0.60],\n", " [6.0, 0.81],\n", " [7.0, 0.90],\n", " [8.0, 1.13]\n", "])\n", "\n", "# Preparing X and y data from the given data\n", "x = dt[:, 0].reshape(dt.shape[0], 1)\n", "X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)\n", "y = dt[:, 1].reshape(dt.shape[0], 1)\n", "\n", "# Calculating the parameters using the least square method\n", "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n", "\n", "print(f'The parameters of the line: {theta}')\n", "\n", "# Now, calculating the y-axis values against x-values according to\n", "# the parameters theta0 and theta1\n", "y_line = X.dot(theta)\n", "\n", "# Plotting the data points and the best fit line\n", "plt.scatter(x, y)\n", "plt.plot(x, y_line, 'r')\n", "plt.title('Best fit line using regression method')\n", "plt.xlabel('Length in cm')\n", "plt.ylabel('Resistance')\n", "\n", "plt.show()\n", "\n", "\n", "\n", "#def makePrettyTable(table_col1, table_col2):\n", " # table = PrettyTable()\n", " # table.add_column(\"Column-1\", x)\n", " # table.add_column(\"Column-2\", Y)\n", " #return table" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "In comparison, our calculated resistivity is 0.13 Ohm/m vs a databook value of 0.105 Ohm/m This is well within the expected variance of an A-level practical.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }