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h8AJIUC1atlDR4sXsNQCBIiwszPqiy5ddxIdELjd7GQAShOcDLzg42Lp3ovPnz+vQoUOO/jcCUTETzPR8800VDgnRqpUrrUlnDDPF+MMPP2wt39q+d88ede3WzZqkJm3atFY7cC8IvPBrQdmy20uAf9i1b6+9BDibmUWxW9eu1nKjxo2VLXt2Zc6cOdoA6/liuH//fu0K3aWPBg3SO/3fU9Nmzew9gNgh8MKvmcBLgIA/ML3Y1SpV5vcVAWPmjBk6cuSo2rVvZ7fEnCl7KBbyFH83uGfU8AIAgDiRIUN6eyl2KGeAtxB4AQAA4GgEXgAAADgagRcAAACORuAFAACAoxF4AQAA4GgMSwa/xrBk8GU/LlmiH3/80Vo+e/astmzeopKlSlrrgNMd+fOIdZ/h8QzWvUeePHn0RI4cypIlizJmzGi33h7HeXgDgRd+jQMhfNmnQ4eqWo0a9toNZjxeADdEdxznOA9vIPDCr3EghC8zgbdT58722g383gI33Onvgb8XeAM1vAAAAHA0Ai8AAAAcjcALAAAARyPwAkAc2rRpk70EAEgoXLQGv8bFDPBlx44d0y+//KLfN2/WAw8+qNOnzyh16lQa9vEn6tT5NXsvILB9OnQYF60hzhF44dc4EMJfhIaGWsORmd/Xw4cPKzw83N4CONOSxYut+2crVrTub+eRRx5R2rRp7bV/4zgPbyDwwq9xIIS/iBx4gUAwc8YM6752nTrWfWxxnIc3UMMLAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAIgTO3fu1Pnz5+21mDPjVwPewMQT8GsMSA5/wcQTCDQRERFa/vPP2rp1q9avXaeazz2nRIkT6crly/rr2DF7rxvM9NtpHnrIetzvm7coKDhIV69eVZWqVZU5c2Z7LyB2CLzwawRe+AsCLwJZTI/VHNvhbZQ0AAAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHC0RC43exnwO0HZsmvXvr32GuC7QkNDVa1SZX5fEVAOHjyotWvW6M03umvgh4Mld+RInjy5TPCIiIi4tpNbksSJlSRJEmv5woULGvbJUDVq3EilSpdRvifzKUWKFNY2ILYIvPBrBF74CwIvAs3ixYv1/fTperltWxUsWNBuvXthYWFa/vPPGjZ0qH5ctsxuBWKHkgYAAOB1586eVeXKlWMVdo20adOqdp06OrBvv90CxB6BFwAAAI5G4AUAAICjEXgBAADgaAReAAAAOBqBFwAAAI5G4AUAAICjEXgBAADgaEw8Ab/GxBPwZZ8OHeq+DbPXAHg0atpEefLkUdFixZQzZ067NWoc5+EN9PACQBwyH9S33syHPRDIJk+cpH69+6h65SqaOWOG3QrEHXp44df45g9fZnp4O3XubK/d0LtXL7Vo2VLBwcF2CxCYduzYoT/cNzOj2u1wnIc30MMLAAAARyPwAgAAwNEIvAAQh0aNHKXVq1crLCzMbgEAxDdqeOHXqO2CLzt9+rTWrVun3zZs0OgRI1W+4rMqV66ctm/frnLlyytr1qz2nkBg2rNnjy6cP08NL+IcgRd+jQMh/EVoaKiqVaqsd/q/Z62b0AtAqlGzpkqWLGmv/RvHeXgDgRd+jQMh/IUn8PL7ikDhGW4sut7bu8FxHt5ADS8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0LlqDX/OlixnOnz+v8PBwew1O9NBDDylJkiT2Wsxw0RoCDRetwZcQeOHXfOlA2LtXL02eOMlegxMt/HGJnnjiCXstZgi8CDQEXvgSAi/8mq8F3qJFi97zwR2+yfz/NmveXLlz57ZbYobAi0BD4IUvoYYXAAB4Xbbs2TVs6FAr+B4+fNhuvTumRMxMyW2+aFapXs1uBWKPHl74NXp4EV/o4QVizvzeL1m8RGPHjNGpsDA1atrEas+TJ49SpkxpLXvs3LlT//zzj3bv2qX1a9dZ+5opuEuXLq0UKVLYewGxQw8vAACIE8HBwWrXvp0Vdrds36YWLVtat8fSp7f3uKFylSrWto8+/tha7z9ggCpWrEjYhVcQeAEAQJwzwdUEYHMzQdacDYt8K1iwoLUtY8aM9iMA7yHwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAARyPwAgAAwNEIvAAAAHA0Ai8AAAAcjcALAAAAR0vkcrOXAb8TlC27du3ba68lrN69eqlo0aKqXaeO3YI7CQ0N1Vdjx2ra5Cl2i+9I8/BDatS4id7o/oa1bv5/mzVvrty5c1vrMWX+rdUqVfaZ31cgPsX0WO1Lx3Y4A4EXfo3A6588QXfVipX6b+vWKluunO6//357a8L5+++/9fmnn2r5zz9br+eVTh314osvWtsIvEDsEXiR0Ai88GsEXv+zcOFCDXj3PZ8KuhcuXNC4r7/W/HnzlNMdaCtXrqr9+/cpxxPZ1LhJE2sfXw28hw8f1prVq+0133Hp0iUdPHhQHTt1UooUKexWBCoCLxIaNbwA4kVYWJiGf/655s2Zq28mTFCVqlV9IuxOmzpVzdyhdsXy5Wre4iW1fKmVHs+Y0d7q276fPl1lS5fRsWN/6ezZcz5z+3DQYPf/9XB9MXKUDh06ZL9aAEg49PDCr9HD6/tM0P120iRNnTzF6tV9tmJFJU2a1N6asAa+/75WrVypFu6QmydvXrv1mtWrVvp0D+8od5jc+ccferFFC6XPkMFuTVg7duzQJ0OG6NjRo+r25pv6aelSdXqtk4KDg+09EKjo4UVCo4cXgFedP39e69at06CBAzX0k0809suxKliosCZOnmz16iZk2D179qxmz5ql9/v319v93lbGTJk14INB/wq7vuqoO0hOmjhRgwYNUtq0adXdHSp9IeyeOHFCnw4dqmlTp6legwYa8cUY5cyZy94KAAmPwAvAKzwlC/nz5NVPy35S7efrWqMcNH/xRQUFBSVo0DUXo73dt5/q162r7Tv+UIVKVfRCw0Z6qkhRJUniG73N0TFfIga6v0A0rP+CO+A+rhYtWuqZsmXtrQnH1D5/MWqU2r38sjJmzqK27durkPvLja/04AOAB4EXwD0xYWzEiBEqFvKUwsPPa84PP1gh96GHHrL3SDgmkJmex4b16yvc/Trf6t1XNWrWUqpUqew9fN+mjRtVrXIVnXe/t6b2Oa+P9Eab8oXXOnXSvLlz1eKl/+rpZ56xtwCA7yHwAog106v7cuvWOnf2nE8FXePbiRPVuEFDHTx0SN16vGWFsnTp0tlbfZ95b9968029+8676vvOO+rwyis+M6KF6dXt3bOnVU7x0SdDVbxECXsrAPgmAi+AGDNhzNOrW98dKn0p6C5fvly1a9bUnDlz1fTFFmr539Z+M+qCx6JFi/R87TrKnDmLhnzyiU/16nZo205z586xvkC88mpHpU6Txt4KAL6LwAvgrpnyBTMUlgm6nl7d4sWL21sT3meffqrBH3yg5i3/q559+vrNxWgep0+ftnp1Rw4foQ8GD1bdevV8qle3p/u1Zc5qQvgwenUB+BUCL4A78gTdqpWraNeu3T5XvrB//3691rGT9u3bp3cHvO93QdejxxtvKHfuPBrhDpfZs2e3WxPWjV7duXqpVWu94n6f6dUF4G8IvABu69agO3rMGJ8Kuma8V9Mj2rRhQwXnzGmdZk+e/D57q/8ws6W1e7mtChUOsYZu8wWXL1/WgP79r/XqZsuqIdTqAvBjTDwBv8bEE3Fn5YoV6vlWT2v63yZNm/pMyPWYOGGCJvzf/6l8xUp6pmw5r4+8EF8TTwz64AONGTXa6jUtV7683ZrwTAg3Peat3UE8tkF3zOhRTDwBCxNPIKEReOHXCLxxp1fPXtZEB2l89PT1rl27VKt2HT3xRA67xbviK/C2ad1aGR7PqHTpHrVbfMPa1avU/pVX76l8gcALDwIvEhqBF36NwBt3unbpqgoVKylLlix2i2/p3fMtvdCgUZyNwBBfgddX3+cpkyapof1vjy0CLzwIvEho1PACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACQCSXLl3U3DmzNX/uHOWK5QVqUTlx4oS9BACIbwReALCZkRne69dXWTJn1Gx34A0JCbG3xJ6ZvOPDwYPVvHETte3Q3m4FAMQnAi+AgLdnz259OGigwk4c1zcTxqtzly5KmzatvTX2Dh48qBrVqmnDr7/qu5kz9Eb37vYWAEB8IvACCFjh4eEa/804zZ01U7379NbHQz/x2pixYWFh6tjhFbVq3VpfjRunggUL2lsAAPGNwAsgIJla3bGjR6lGrRr6dspklSlTxt5y72bOmKFiIU+p3gv11bRZM6VIkcLeAgBICAReAAHntw0b9G7fPmr3Snu9UL++1wKpmU3tlQ4dNGzoUA0Z+omav/iivQUAkJAIvAACxp+HD2vwwPe1fesW/d/ECapataq95d6YC9MmTphgTR388MMP63/TpztmimkAcAICLwDHO3PmjL75+iuNHjlcffr10Vj3srdqdTdt2qT/tmypsV9+qfHfTlL/AQO8csEbAMB7CLwAHOn48eNauGC+Frlvf2zboh5v9dDSn5Z5pVZ3z549GjVypLp27qzp//tOr3bqpAWLFqlkyZL2HgAAX0LgBeAopmxh5PDPNWXSBLVu3UofDPrAHXbfUr68eZUsWTJ7r9g5c/q0evfqpcoVnlWGDBk0YOBAvfPeuypduvQ9/2wAQNwh8AJwDHMx2ugRn6vNy631/cwZXitb8DBh99SpU/pp5QqrRpfRFwDAPxB4Afg9M8SYmSVt2++btOjHJapSpYq9xbtKlCyp4SNGKGPGjHYLAMAfEHgB+LXt27bpnb599M/fYRo+cmSc9bq279BBb771lr0GAPAnBF4Afmv8/43T4oU/aPSYL/ThRx/FaYmB6dWlhAEA/FMil5u9DPidoGzZtWvfXnstYZn6zqJFizpm/NWuXbqqQsVKypIli93iHW91f0N/bN9ur8Xe4+4A2uK/L6lVq1Z2i38y7/PRo0eVKnVquyV2KlWurJw5c9lr927KpElq2KSJvRY7Y0aPUqfXOnm9lhr+J6bHal86tsMZCLzwawTeuBNXgXf2rFkqUbKUvXZnZvzcPn17OzY0HT58WOHh4fZa7CxZvESXIi6rXPnydsu9I/DCmwi8SGiUNABAAjKlEiYQ3sstQ4b09k8DAESFwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/ACAADA0Qi8AAAAcDQCLwAAAByNwAsAAABHI/Aixs6fP695c+faawAAAL6NwIu7tmnTJn04eLDy58mrFctX2K0AAAC+jcCLO4qIiNDq1avVvVs3ff/ddKutafNm1j0AAICvI/Dijv766y99OnSonq9bT11e76puPXooX7589lYAAADfRuBFtEJDQ9W8aVM1atxY7dq3U6bMmdWgYQN7KwAAgO8j8OK2TBlD2zZtNGDgQNWuU8dqK1mypNKmTWstAwAA+AMCL6I0auQo9XrrLY2fONEKuQAAAP6KwIubmCHHevfqpS1bNmvu/PnKmDGjvQUAAMA/EXhx3enTp9Xt9deVJk0afTRkiFKkSGFvAQAA8F8EXgczAdaMm2tuhw8ftltv75tx41SqVCm90b37HcPunj17rJ7giRMmWL3CAAAAvorA62BTp0zRvn37rJsZaSG6YGouUDuw/4CaNru78XVHDh9h3ffr3ccdlL+xlgEAAHxRIpebvRyQgrJlt5ecad2GX637YiFPaf6ihQoODrbWIzO9tGO//FIzZs1S6tSp7dbovffuu+rTt69mzpihr8aO1dYtv9tb4t+ufXvtpYRleryLFi16fUQLf9e1S1dVqFhJWbJksVu8Y7b796xEyVL22p198/VX7t+13lH+7uIa83e4/8AhlStf3m65d1MmTVLDJk3stdgZM3qUOr3Wif87WJ+1MTlWx3R/4E4IvA7+oxo0cKAOHDxoLW/fts26CC1yqYLp8f38s8+sHuD3+veP0XBjnTt1UvkKFTRs6FBVq17dKoMIdATeu0Pg9T4CL3wdgRcJjZIGB3ulY0fVq1fPuk2aPPl62DW1vaNGjtTgQYNVqnRpDR02LMZj677lDnepUqXS4A8/UucuXexWAAAA30PgdbCUKVOqwrPPWrf06dNbbaZWN6RAQRUsVEj93u6n0u7AmyxZMmtbTDz22GPWzy1StEisHg8AABBfCLwBxJz2NJNJmFpeJpMAAACBgsAbIMyFaQsXLrRmTqOeDgAABBICb4AwF5aZySSYOQ0AAAQaAm+AMBelMXMaAAAIRAReAAAAOBqBFwAAAI5G4AUAAICjEXgBAADgaAReAAAAOBqBFwAAAI5G4AUAAICjEXgBAADgaAReAAAAOBqBFwAAAI5G4AUAAICjEXgBAADgaAReAAAAOBqBFwAAAI5G4AUAAICjEXgBAADgaAEZeMPCwhQaGqrFixdb6zNnzNCmTZt0+PBhax0AAADOEVCB1wTdfn36qFjIU6pWqbLGjhmjRk2baOHChapXu47Kli6jCuXKadTIUVYgBgAAgP9zfOA9evSovnQH2zd79NDAAe/r2YoVtWHzJu3at1ffTpmi/gMGaPiIEdb6lu3b9M348cqZM1gT/m+8+vTurc2bN9s/CUB8u3r1qs6eOWOvAQAQO4lcbvay46xevVrNGzdRN3fYbdGyhVKkSGFvuTt79uxR5QrPWo9v176d3QpErXevXipatKhq16ljt/i3rl26qkLFSsqSJYvd4h2zZ81SiZKl7LXoLfvxRy38YZ5Onjhht+B2OnV9XeXKl7fX7t2USZPUsEkTey12Pv7wQ6VM9aAeeughu+WGIu6/lToO+VvBnQVly251LN2tmO4P3IljA68n7I76cowqVqxot8acqett3rSpGjRsROhFtPwl8J4/f14LFyyw125vxvczVK9BwwQLvHv27NYi9+us+0IDuwW3s+HXX5QpY0afC7wjhn+m+vXrK2vWrHbLDVOnTNGTTz6pHEFB1j2cjcCLhObIkgZTf2vC7jv937unsGtkdH+IjJ84UR8NGmRd3Ab4O3OxZv9337PXfNPqVSv1xcgRerZyZbsF/ihZ0mRW2A0ODv7XzZxx27x5i9q9/LK9NwDEHUcG3r69e1sXozVt1sxuuTcm9Jqe4tc7d2EkB/i9tWvWqGz5clZPdHS3h9OmtR8Rfy5duqj/TZ2i9evW6r9t2ipNmn+fCoczRFy6pFc7vqqjfx6xzjoAQFxyXOA1vbDHjh1T19dft1u8w/QUmxA9csQIuwXwT1s2b1bOXLnsNd9x4sQJfTl6tC5cvKB6DRolSOBG/DGlDOb/PP3jGbTEHiISAOKK4wLv5G+/1WudOyvtnT4sXX9qfqeSVp1QnjcW6ZTdHJ0WLVtq8sRJ9PLCr23d8rtCQkLsNd9g6nWHDP5Awblzq0q1GkqePLm9BU6VzX3s3bZ1q0qULKkf5s+3WwEgbjgq8JrJI9avXaenn3nGbonG31u1dP5RazFi7gptOn3VWo6OqTurUr2aZs+abbcA/sXzZS1fvnzWvS/w1OvWrltPhQr7VhBH3Hks/WPauXOnqlStqrVr1tqtABA3HBV4V69abQXSO/bu6qpOb1qhHyKSKPXDaZQkfJmWbAizt0Xv+bp19dOypfYa4F/WrVunB1OmjPEQfXHB1OvOnTNbS5cstup1cwQF21sQCNKlS6f58+apTJkyOhUWxpkzAHHKUYF3y5bNqnxXV3WHacPiZQrXU2rbs5Xy6oBm//yHe/3OzBXHphfZzNoG+Jvft/yugoUL2WsJ58yZM1a9rgk5LVq1oV43AJkvXY899ph1LH0iKAd1vADilKMC74J585Ute3Z7LRqnf9eS6QekVPn1ZMUSKpsxic7OX6Xfw+88JLEpazBOnjxp3QP+xEzkUKhQwgbec2fP6v333lGWbNn0fL361OsGsLLlymv79u0qU+Zp/bRsmd0KAN7nqIknzAVo8xctvB5Ko+ZS+NqPVKnhCIW98IVWfVhE296trxZfPahXp09U55BU9n63d3fPg0Dj6xNPmKGf8ufJe9eTscTVTGuDPxioy5ev6L777rNbcK+O/Pmnaj73nM9NPDFm9Ch1eq3TbY+VZkzo3zZssC5ce6n5i0w04GBMPIGEFniB90qYpraupp4rUqpYhWA9lMi0ndT2JRt0tsZQzRxaU48nMY23R+BFVHw98JoetK6du2jegh+sU8l3EleB1/TwXr5yxV6Dtzz44INKmjSpvXbv4iPwnj59WnXcQX3GrFmqVOFZvdmrp55//nl7K5yEwIuE5qiShizZsmr//v32WtSunNilsUv/0gMN+2iU+2A8YpT79sUwda/5H52a/a3m7ox+AHRqd+GvZs+ebfWq3k3YjUvmork0adJw8/LNm2E3vqROnVrVqlfX1q1b1bBxI4376it7CwB4l6MCb6nSpbUrdJe9FrUkjxXTAve3xs39yym13aZEj6vap6vd3yYnqU2eB+zGqB08eNC6p3cX/mbNqtUqVaa0vQb4hsIhIdq0cZOerVjRGiOaTgUAccFRgdfUr8X1kGFm6DMz4xrgT8xoCKZ3t3DhwnYL4Bvy5MljHbdz5sxprW/evNm6BwBvclTgNbNHmSHDzAQUccFc9DN1ymSvXhgCxIcDBw4o3aPp9Fj69HYL4BsyZsxoHbfN8bVA4UKaPWuWvQUAvMdRgddMOGF6X6dNnWq3eNfCBQus+9KlOS0M/2JOGd93//3WONKArzHH7T/++ENVq1bVsh+Z2AeA9zkq8BotWrbU5ImTtHr1arvFO0xd2bChQ/Va584+MUsVEBNmUpZVy1coU6ZMdgvgO8zoJuZLWfESJXT16lVmXQPgdY4LvOZisnf6v6deb73l1YNmn969lSdvXlWuUsVuAfxDRESENSmLGcWEL2vwRXnz5bO+lJk63jOnT2vVypX2FgDwDscFXqNuvXpWOH1/wACrLuxejRo5Stu3bVPPXr0IDPA7ZqxTMzqDGcUEiE+nT/9jL0XPdFSYL2VGsZIl9P3331vLAOAtjgy8JpR+NGSItdzt9ddj3dNresZM2P1o0CB9MmyYdXEF4G+OHz+u/zz2mHU1PBAfLl68qG/Gfa3kye+76zIaU8e7c+dOVa5cWetWr/FKZwUAeDgy8BqRQ2/zpk2tKSxjavK331qjMphZ1QoWLGi3Av7FDPNkJiVghAbEh7/++kvv9OurRx5Jq08/+/Suz4qZOt7ft2yxxuVN/3gGK/wCgLc4NvAa5kA7fMQIDf30U/26fr3e7NFDHw4arJUrV2rHjh06evSoTp48ad3M+i/rf9H/pk1Tvz599c7b71i9FHPnz2eSCfi1+fPm6ffNW5Q/f367BfA+cxz96ssv9duv6/XhRx+qZ8+eMSoBK1GypP7vm2+sOt7kyZPrq7Fj7S0AcO8cHXg9ChQooB5vvaUPBg1S/QYvaIv7w3/C+PEqU6Kkij9VxLq906+fZsz4XsmSJdPL7dqq39v91LpNmxgdsAFfY04L/x12SuHnwxN8SmE4l+kc+HbiBPXt10dvdO8eq/IZ8/sZFBysQ4cOqVXr1lrx83JGawDgNQEReCPLnj272rVvp/4DBmjXvr1Wm7n/dsoUq612nTrU6sIxNm7cqBzBQVywhjhjShjefbufWrRsYY2Ffi9KlSqlbVu36sn8+fVIuke0fft2ewsA3JuAC7xAIFmxfLkSJUrEBWuIE5s3bdLbfXqrY6eOXpmQxwTd9evXW2UNe3bt1rq1a+0tAHBvCLyAg40eMVIH9u/ngjV43by5c/XFyBH6+ptx1sgK3mCCrpk4yJSS1alXV1+N+dLeAgD3hsALONSmTZtUqkwZpXv0UaYUhteYet3BAwdq965QzZg9y6sX9ZqgW6V6NYWGhurpp59Wzty5rd9jALhXBF7AoVavWq0sWbPo4oULTCkMrzD1up07vqoSJYtbQ47da81uVDx1vGb2NcMMVQYA94rACziUGUPa1O+aSScYbQT3ytTrtmv1X/V752292rFjnP1OPZEjh1XHa3qOd+7YoZkzZtpbACD2CLyAA5nhnMwwTytXrFBwzpx2KxA7/5s21arX/WnlCq/V695Orly5rDpew8y+dujgQYWFhVnrABBbBF7AgZYtXaryFSpYyykffNC6B2LKU6979MgRLVi8KF6GbDRlEkWLF7O+tJnZ13IE5dAff/xhbwWA2EnkcrOXA1JQtuzXx+NF3Dl9+rQm2b02ZhxkJ+rdq5f1AW3Gck5ojRs2VPWaNfXHjh3KlTu3mjdvbm+5e127dFWevPmU4fHH7RYEkh/mztXG3zaoUZPGVglDfBo1cpSCgoOsiy17dO+ukiVLWhNawH/F9LOWz2Z4G4GXP6o4Z664fqPr69bFJ+s2/BonF7r4Al8JvOb0b/26da3ZqlKmTGl92Wj+4ov21rs3ZcpUrV2zxl5DIKpXr65Klyljr8Wf1atXW2NIm5BrjtGZsmTRsp9/srfCHxF4kdAIvPxRxamVK1daY8FucAfdgYMGqdZzz9lbnMdXAu9nn31mzSj42bBhGj5ypJb/9LNeavVfeyvg+8yU2DWqVdOMWbOsaeBXrVylgR8MVGZ38IV/IvAioVHDizi1ZfMWpUqTWr379nV02PUVJigMG/KxsmXLpqDgYJ07d05ZszEGL/yLGQGiWvXqWrdunSpVrqyrrqvazPBkAO4BgRdxxtThbdmyWR8NGaIyTz9ttyIubdy4UW07tNfuXbuUP38B7du7V4/Hw4VGgLcVDgnRrtBd1vBk61av0Y5t2+0tABBzBF7Eichh1/TWMPFB/DB1j+bLxc6dO1WwUEHr/kFGaYAfypMnj35attRaNsOTPfDgA9YyAMQGgRded2vYRfwx9dJmHNP58+YpS5Ys2rdvnx54gKAA/2OGQDt27Jh1EaapjT99+oy9BQBijsALryLsJpxNmzapSvVq9tq1wLBg3nw98sgjdgvgX0wdrxmD10wz/Lv7uAIAsUXghdcQdhPW6lWr9Xzdujp48KBKlS59beD+4sXsrYD/MXW8mzZusup4t/6+1fqdBoDYIPDCKwi7CW/qlMlW3aMZ79icAj5x4oRyBAXZWwH/Yyae8NTx1qhVU9u3c+EagNgh8OKeEXYTnpnc47HHHrPKGEwoMKeAzQgNJvgC/sr07K5fu86q4zUXvpopswEgNph4IsAGtzb/3oTm1Pc7ISeemDhhgnXftFkz6/94y/Zt+vyzz6wRG8y0rIC/Mn9XLzRoYA25916/t5mMwE8x8QQSGj28AcgcRLxx69ajh3WRlAlXUW2P6oa4MWf2bBUrXtzq6TX/J6an3YzQkC5dOnsPwD+ZL5GmTOefU6dUsUpl6+JMAIgpAi9i5Zf1v1DG4CPMhTxm+CZz+nf//v3WhBOGGaHBtAH+zJTnrFq1Sk/mz2/NIGjCLwDEFIEXMWbC7q+//qKhw4YRdn3A9OnT1bVbN2t53pw5KlGyhNXTW7laVasN8GfmS9vhg4esGvXjx49r8rffWlNoA0BMJKKGN7s1i0+gmDxx0j2VFnguUDNhN1myZHbr3fOFGuK4NGToJ/Faw2su5ikW8pRVVmJCgFk2/78zZ8ywtidEPTHgbaZGPX+BAqr7XG01b9lSlatUpjbdz1DDi4QW8IF39erV+uvYMXvN+V7v3CXWBxFvjMZgDmLzFy2015zHXEken73e5vfXTCf8RvfuVm3jtKlT1X/AAH04eDAXrMExzO/2yRMn9OOPP+qx9Ol1wf3lzvzOw38QeJHQAj7wBprYHkS8NfQYBzHvihxsTS9YypQprV7dVzp0UOcuXajhhSOYsxdjRo9W1mzZtHv3Hs2ZPUs/Lltmb4U/IPAioVHDiztinF3fZELA6BEjlStXLmvdjL+bLfu1khEuWIOTmOPOw2nTWhewrV+31qrnNXXqAHC3CLyIFmHXd+3cudMagiytOwgYpj47Z86cTCkMR7r//vutL3FmIoryFSpo29at9hYAuDNKGgKMOU2U0DhN5R3my0hQcJAqVqxo9Xb17d1b306ZclMtL+AUkyZNUpMmTayJKHLlzq01q1dr+IgR9tb4NW/ePEVcumSvBYYHU6ZU6dKlY93xQUkDEhqBF1GiZ9f3VShXTuMnTrSmE168eLF2he5Su/btGKEBjjTkw4/0+hvdrN/vAwcOatjHH1ujkyTE8alOrees8YDN5DsZMqS3W51t/fr1WrVypVq1bq1q1atfP7N0twi8SGgEXvwLYdf3Re7RNSL39jJCA5zof9OmqWChQtay+d3PERSkGjVrJsjv+TfffKOH0qTRsKFD1aBhI9V6rpb1xdPpzDCIU6dM1UeDBllhv0HDBncdfAm8SGjU8OImhF3/sG7tWtWsVctek35atlR58uSxljf8+itTCsNxsrkDkKnb9dTxPlWkiDZtTJhphh944AHrDMrc+fOtHt7mTZtapRZOv5DOhFtzFmndhl+VKlVK1a9bNyD+3XAGenhxnZlB7euvvyLs+oHGDRvq3f79rQ9/M1pD/jx5rd4Qz3JCjXXMyBCIKwcPHrRmWTPj75qQVax4cX07ceL1sxzxadq0aXrhhRfstWsjpixcsMDq8S1VurRatGwZEH8Lt/67X2jQQAULFrS33oweXiQ0Ai+ue+ftd9S9R3fCro87ffq06jz33PVxSCNfpPbLL7+oUf0bH8SA05gQZOp4jxw5qqlTJl+vY49PtwZej0AOvhs3btSn7n938RIlrDHAb0XgRUIj8MLq2Z07d6772/kLyps3r90KX7V27VodP35cNWvWtNZHDB+ufPnyqWy5ctapxWqVKvNBAUfyhKCTJ0+q5Ysvqmnz5jp75oxat2lj7xE/hn7yiQoUKGDVFD/yyCN26w0RERFWj7QpLzoXHq7EiRKpXPnyypw5s72Hc5kv3ebfffnyZSVPnty6niBr1qzXz0LdLQIvvI3AG+Co2fU/gwYOVKfOna//f5kPBlNTZ+rrCLxwssghyFycWbRYMbVu+VK8/76bQDtv7lyrxMJcPHennlwTfrt362Ytm7/dQLmg1IwJPnvWbOsiN4PAi4TERWsBjLDrn8xsap7/L88kEzEdIgjwd4VDQrRj+w5r8hVT1hOfkiVLZl20ZuqHzUgRZtQIU1e/evVqe4+bmZ5ds68Ju+a0f3T7OokpNfFc5AYkNAJvgCLsOoOZTjjkqafsNSBwmFFJzOgkpUqVssbETSimt/Zuw2zkfSeMHx8wwZcv5PAFBN4ARNj1X+bikH17b5zmM5NNmJ4uINCY3sNjx45Zs67NmT3bbk04MQ2+ZpY4M9LK3DlzrH3NhXjm7xtA3EhEDW9gIez6N3Pq9tChQ6pRo4a1bj4oPcOTGZ4aXsCpItd1eiZZ6fXWW/rf9Ok+1ZNowq4Jvsbgjz6K9oI183f7zbhx1kxmr7kDc3X337cpm3CSmNbkUsMLbyPwBhjTi1C5ShXCrp8yX1gqV6msJ554wuoNiumVz4CTeKbUPnPmtM/OLmi+pI4eNUp169VT6dKloz32eoLvlStX1LdfP0cdpwm8SGiUNAQYc6EFYdd/mXFHPbOo7dy5U42aNrGWgUDkqeM1ZT1m1ARfZCZieK9/fy1bulQ1qlWLtnTBnKkx42mbuvw77RsIAqG+GfGHwAv4CTMiw2OPPabUqVNb66aW1zOdMBCIPHW89913n6Z8+63d6nvMWL0myI4eM0br16+/Y5g1k1qYEg0zuYbZd+KECQoLC7O3Bg5PLbTpyae+GfeKwAv4iQMHDtw0IoP54Hwyf357DQhM1apXV9KkSd2h936tWLHCbvVNnh7cuwm+ph7ZDOllgu+ZM2dVLOQpq6QpkIKvuQjQXKPg6R03wZ/gi9gi8AJ+YtPGTTeNyGAucAmEmZuA6Ji/CfO3UaJkSf0wf77d6tsiB19TmnQ3wdczlm2gBV/Pe+UJ/m1bt7FqnYGYIvACfsKMrmGm6DQ85Q2Mb4lA56njrVy1ihYtWGi3+gcT5t7o3v16+YK5CNWEWYLvv3n+/d3f7KG2bdrolQ4dqPFFjDBKA+AHTJ3ii82aacGiRdb6kI+G6OiRI8qcOZO1DgSyX9b/og4dX9Ur7drr0+GfW6Mh+CMTdLf+vlUrVizXxQsX9GzFSsr3ZL4oLzQ2++7fv18rli+31s3ILQULFbLqhX2Rt0dpMNM1r12zxgr8ly9fVvLkyVWoUOHbvl8AgRfwA+Z059mzZ9XUHXrNB53pCdqyfRsHdsDNDP31xejR1rTbWzZt1v9NGG9v8V8myE2dMlUfDRqkbj16qEHDBrc9oxMREWGNUjFs6FCVcof9Fi1bWr3HviSuhyXzvF9mJBtT113n+ed97j1AwiLwAn7AM8C+GWfU9GxM/vZb61SovzAfXnAOXxwftUK5cnqrVy/17PGm1tun/Z3ABLnlP/9shdkGDRup1nO1rNEpomK+DC9csMAng29cB14Pz3tgjpFpH3lEb771Ftc6wELgBfyA+TAfP3Gi9UG3cuVKJU6c2CcH2b+d2H54wff46v+lqWcNCg7S2DFj9NHHH982FPqrmIRZs685Tpj3IkdQkE8E3/gKvJGZGt9P3L8LTZs2ZcIlcNEa4Os8F6V4PsDXrFqtQoUKWcsArilZqqS+nz5dZcuV1/bt2+1W5zBhzUwcNHf+fBUtWtS6cKt3r15Rjlhg9q1YsaI1rFeNmjXVt3dvazzbQLvIy3QKjBw1yhoJw3NBoOd4isBD4AV8nClhMD06HpkyZ6KnAriFmdFs+7ZtypAhvTVuq1NFFXynTZtmb/03E/pM8O3UufP1iRzMMSVQmIv4TPmXZ3SL+nXr3vaLApyNwAv4uN+3bLE+2ABEz9S4GpMnTrIu5HKyyMF3544ddwxxkYNv927dAq631zOsmXm/ypUvH7C93oGMGl7Ax5kPshcaNLB6sExt3ojPh+v1N7rZW/1DQtd9mg+1uXPm2Gs3VKpUSWXLlbPGNR45YoTderP2HTpY5STmvf/oww918eJFe8s15pRxVPXUZlaoW0+tmzFjzUgbRlSvyUyR2+2NN3y6B9+X67E9ozUYffr2Vfr06a3lQGB+n0wPrrlQq1nz5tHW+Jse3g8GDlTYyZNWAI5uX29JiBreO/H8DZpJfF5zvw/U+TobgRfwcebA7xmCzBygz4eHq8Kzz9pb/UNChiQTZps3baoD+/bbLTeYyQpGjBplXRRo3LpPlmxZrXISM9OTGSlj8qRJ+ufvf+ytN9z6bzM9beZUc1TPOerLMVZ9pXnOqLa37dDep0fg8OXAa5jXZ4bxKlKkiIoULWK3Bg5P8DXuFGbN7+k348Zp965datS4cZwGvpj+3sTn75l5H5YsXmINAffFV2NVoUIFewuchJIGwIeZsFa0eLHrH0JmkHkz1ijuXrj7C4IJlkOGfmJ9gHpu8xfdmJXLbDfBNvJ2c4scSP/55x/ravfI2xs1bWJv/Tfz2Dk/zL++r+f5zp09a92b7ebxkX9ep86vWc+D2DNfGIx97vczEEUuXfDU7JoQHBUzcoP5Mvdu//5av359tFMce4M5nt0N01Mfn8z74JnFzvT4mrNq8f0aEPcIvIAPM6fEQ556ylo2H0KjR4xUhgwZrHUA/2bGqzbTcB85csRuCUyxCb6jx4yJs+A7/ttJ1pkWc6bE/GzTq2puptbas2zazZTBXV57zdo/vpk63w8GDbJqfD94//3r71lcfQFA/CLwAj5s5YqV1sHXmDVzpl57vSs1ZrGULHlye+maZMmS2UvXmPrZW6V5KI29dM19999vL10T1WMiS5Ikib307+czbn38rT8fMWdKGU4cP66z587ZLYHNE3w/GTbMKocyNc5ff/WVduzY8a8L+zzBd9p33ylVqlRWucO4r7/W5s2b7zn0mddhpkY3pRMZM2bSwQMHrNtXY8deX87+xBPWRBFmv+hKMeKS+Tv1DOk2+KOPrPfsS/cXgQnjJ2jQwIHWNNanT5+294ZfMTW8AHxPeHi4K0fWbDctnzx50lr3N55/R0Iw79mE8ePttZutX7/euh85YqT1Ht/q0KFDrhnff28tm/t//vnHWvYwjzGPvdXtnnPVqlWujRs3WstRPaf5+Z7n81UJ+X95t8z7/HSp0lH+n8LlOnHihKtXz56u8mXLWr9v0b1Pnt9x8/9u7v31GOQN5t9u3i/zvpn378CBA/YW+AN6eAEf5Q5bqlK9mrVsBk43y7ebSx+3Z3qmxn75ZZT1gzu277Duf1q2NMoB6d0faNYpXsP8H9xaX2seYx57K/cHo9yh66YeNPM63CFYx48ft9bNnP+3PufOP3Zaz3Pd5cNaMbyDKuTIrlzl2qhbq3IqO3yzrtibETUzMcu5c2dvfi9xnRmb9m5LGMwZJU99q1Es5KmAncDBHH89Q8GZ0VnM8G6LFy+m5MFPEHgBH7Vt61aVKlXKWl69arWer1vXWkbMhNsXrf1iB1cPUzO4auUKa3n92nVRDkvWvPGNi9JM2P3+u+/stWvMY8xjo7Jg3nzt3r3bXrv2Bca0Rb5o7dbnNK/nRqi+rONLR6rbTwU1dNMubf32BT2w+0+du3RZDK0TPRPSnipa1BrDGrcXuXbXfDmILvh6xrEl+F77/TIlF6ZMxExyYt43MwxhIL4X/oTAC/go8wH0RI4c1rLpDQwJCbGWESj+1taf1it7nYrKnzKJkmYopTq1g+xtuJM0qdNozuzZ9hqiY4KvGQrvf9On68iRo1aAu12YjRx8zax2ZuYys+/djsDgJGacZ/OFYfzEiTpz5uz1LwHmyzR8D4EX8FHz581Trly5rOFx8uTNSzlDwLmqiIuX7WXElAkjpvedXre75wmzJvgaJsAt/3m5tXyryKf3TfA1IzCY4bxMOU+gMRPTRP4SYMbgNu/F7UbFQMIg8AI+yPMhbT5UKGfwDtNz5Rn+yNz277950odTp07dtN3cbnXyZNhN281jPMxA+Z6bx9EjR67ve+vzeUT+eebn3/CwniydX9sX/KztZ6/IdXa7li+O+mfg30qUunaV/4YNG6x73L3IvbhjRo+OtnTBnN73BF8zBXrXzp2t3+VA5PkS8OOyZVaNr2c4OOp8fUMic+WavQzAR5ieATMAujldZmbkMj0u5mDqr+Jz1qRbmQ9qc9o18iQSHjWfq6Whn35qjf1p6muj8k7/96zpgE2NXr/efezWG8zFhMNHjLgp6P60coXKli5jr93su5kzrGmibzfTmuf5LJcPa9nAjmo79jddeTivCqc/rL2Vv9KaLiFKem2PeJeQ/5cxYabPLf/0Mz4/c52vM0Htm3HfWLOQmRnsGjRsEO2xyNRNd+rY0ZrIxUzUYsolApkJ/2Z4NzN98Tvvvqenn3na3oL4RuAFfJAJVylTprRmVTPjZppA5c8SOiSZ0BvVqVbzwW2uWDcf6uaisqhE/sCOqucqU6ZMVi9X5MBr/q2mptFcMBfZAw88YJ3+NG73mm48X4SOrpymhSqrJqUzKqnrT81/rbmmPP2Vvn4hqxLZe8U3fwm8ZoSMPME5rWV/eL2+zvy+Lv/5Zw0bOtQdehuplvvLoud3+Vbm72mlO+CNHTNGOYKC9EKDBtaXvEBm3r/OHTspf8ECqvP88wH/RSAhEHgBH2Tqv0zviJnf3dSEmdNk/sxfQpJvcen85lFq9NJS5WpQXOlOrNX/thXRx+O6qsyjCdW/61//l2ZWLzM7oadXHffOhNmFCxZYwfduenHN2Spzat8ws74l1IQSvsB8CZs3d6713pnrMpo1bx7Q70d8I/ACPsiEii3bt1lXS5srgG/Xk+IvCLyxdUVnD27U6t8O6nyKzCpcspAyp7wxe1tC8Kf/SxO2zNByN5WJwCsIvvfGvB9mXO6wkyet2ecqV6linSlC3CHwAj7GnDbv27u33uzZ05rP3Uxx6e8IvM7hT/+XJpTlz5NXRYsXc8TfkS+6Nfh26drVKhO6HYLvzczxfsb331uj8phSkTvVSCP2CLyAj5k6Zap1b+rlGjVupNJlor74yZ94PuDgDCao+Ispkyer15tvaebcOcqXL5/dCm8zp+vNRCu/bdigM2fOKGOmTCpQoIAyZ85s73Ezc1Hh5s2bdfToUSVNkkTFS5RQjhw5lCxZMnuPwGK+OGz9fas2bvxNly5dUtKkSa33rwQlD15D4AV8jBnGplWbNtYFH/RKAffG08vLaA3xKyY9uZFHMnjNvS+n968ZPWqU9YWN98Q7CLyAD/F8OJuaQ4O6Q+DemWHntm/bZo2PivhF8L03npIHc/Hl3QwLh9sj8AI+xHPA371rlz76+GO/v1gN8AVm4P92rdto/qKFDAeVQAi+98YMa2bqfMd++SVjHMcSgRfwITNnzNDBg4e0csVyyhkALzFhwUyTy2gNCc9MlT5t6lTrS70JvkWKFLlt3a75fzPXNEydMpkLumzmLKBnjGPDvIeFChWi3OEuEHgBH2LG302eLLlyBOXggxnwIlPWYPj7JC5O4enFvXLlivr26xdtYPMEXzPb29f/93/MVmYzveZmRk56wu8OgRfwIWa6WdODMeyzzyhnALzIU9awbsOv1ED6kGnTpmnk8OF3Fdg8s5WVKlOG3t5IzJcHM0nRqhUrNHDwID47biOxfQ8ggZmDuRnax5ze44AFeFdISIh1/8cff1j38A0vvPCCRo8Zo/Xr11sT7ZiyLnPaPiom4I7+8tqpfFOiMmrkKOu4GehMLW+79u30SqeOat60qXWm0JSO4GYEXsBHmA/ixx5Lr5q1atktALzFhKUq1atpxfLldgt8hQls/QcMsILvzp07ow2+pgfYhDvTU2+mXa9ft64VfE0vZ6ArXry45s6frxo1a1qTFuFmBF7AR+zZvVunwsL0ZP78dgvgn3y1d+l5dzgyV7rDN5nga8ZK/t/06Tpy5KgVfG/Xi2u+wNSuU8cKeCb4tm3TxurZDPTga74QmBEwuOj53wi8gI8wp/QuXryoggUL2i2Af9q3d69Vj27CyuHDh+3WhGfKGg7s209voI8zYdb04prga0RXvmACnif4Fi1alOCL2yLwAj5izsxZati4sb0G+C8TQMwwUuaq+rKly1izB06cMCHBw6+nrGHd2rV2C3yZJ/ia8gXDBN/lP0ddknK74Hvy5El7DwQ6RmkAfMDPP/2kjq+8qgWLFyl9+vR2K+DfTB3miOHDtTt0l90iPZ4xo3Lmyqleffooe/bsdmv82bp1q7p27qw58+bddvxX+CZT0zt71iydPXtOly5dVJEiRa3fpdSpU9t73GAuAD548KBGjxyljBkft1sDixmjFzcQeAEf0Oqll5TmoYf08Sef2C2AM5jT0ObCIlNK4JE+QwYt/fmnBAucZkzeZs2bRzvbF3ybCb8LFyzQsKFDo515zHzpMj2/AIEX8AGFCxRUzedqWbMOAU5jQu+Iz4dbF2V6mCGUnnjiCXstfpl6+UyZMluny+Hf7hR8CbzwIPACPmDUyJHKkCGDvXbNlMlcZQvnOHP6tLZv26ZHH/uPUqdKrUMHDyooZ049+OCD9h5xr2GjhvaS9GDKlKpYsaK9Bn93u+BL4IUHgRfwUUHZsmvXvr32GuD/zHBlOd0h11xgZKZEfe3Vjnqn/3vxMo02f0+B4dbga84i/LdVK3srAhmBF/BRfEDD6cx0v+/37688efOqZ69ecTrDIH9PgWf16tXq0e0N/elDQ+PFJ37fb0bgBXwUH9AIBKa+9+MhQzR54iQNGfpJnJ1+5u8pMJkeX3NGAWAcXgBAgjFjrZppZUd9OcY6DW1GUPClySrg3wi78CDwAgASnLmAzMys9fDDD1uTVZiLjQDAWyhpAHyUOQULwHsoaQACF4EXAOBzTFnD+wMGaMG8+XFa2wsgMBB4AQA+y5Q2vN65iz746EPVr1/fbgWAmCHwAgB82unTpzVxwgT9sWOHnqtdWyVLleJiJAAxQuAFAPgFT5mDmbGtZ+/ezJQG4K4ReAEAfsVT5tCoaRN1ff11a2gzAIgOw5IBAPyKuYDtp5UrdOrUKdWvW9easQ0AokMPLwDAL5lZtKZ/95369e5Dby+AaNHDCwDwS+bCtabNmmn+ooXavWuX1du7evVqeysA3EAPLwDA70Xu7W3bob06d+miZMmS2VsBBDoCLwDAMUJDQ9W3d28VKlxYPd58024FEOgIvAAARzG9vR1feUW5cufWqx07MmYvAGp4AQDOYgLuoA8/1IZff1WNatW0adMmewuAQEXgBQA4ziOPPKKvxo1Tg4aNVK92HX04eLDV8wsgMFHSAABwtKNHj2rO7Nlat26d0j2STjVq1VSxYsW4qA0IIAReAEDAMOUNXV57Ta917mxNYAEgMBB4AQABxVPawMVsQOAg8AIAAMDRuGgNAAAAjkbgBQAAgKMReAEAvutKqP7Xta2GT1tjN9wD+2e93HWaQq/YbQACAoEXAOC7XGd0aOlCbf3jpN1wD+yf9ePSQzrD1StAQCHwAgAAwNEIvAAA/+A6q0NbtunQ2ejrEVxnD2n77sP22t0xj9myYZNCT1y0W24v/OSfd7GfS5dP7NJvG3Yp/GrU3cnWc245pLP0NgNxjsALAPB5f275XjWC8qtcrRoq92QBVWg7UiuORAqdl49o7ZfdVatwkIKffFq1ni2jXOU6aMSKw7ps7xIl9+M+fLmW9Zjn69ZRtSK5o3jcIc1sHaKggj007rsBqlK6jL1fZ41Ze+SWn39RR1aMVLtyTyp3kUp6oW4lVan3hkKvh/SLOrr2G3Wvlv/ac9Z6WoWyF9MLfb7T9jsEeQCxR+AFAPi839f9psyvvKePhg7Ru52ekRYPVqvWw7X2lAmJZ7Xt6zf1Yv+5Olesnd4d+okGvttJQQfn6+OXPtTcIxHXfsi/XHvclN2prccMMT+7W53bP+6fqerffZlqdntXvf/7jNLsm6lBr47RCus1GJd1fMUwvdxisJbqGb0yYIj7Zw5S3itr1fy9JTruuqJTa4erTZO3NfN8GXu7+znb59P+8T3U4vWpCr1Ady8QJ8zEEwAA+KSIX12fFMrmatjta9dlu8nluug6tvgdV9msuVzPvPOz6+/ze11LPhvkem/Yj65Dl65ae1y9fNa16uN6rhxZn3K1n3XIavP8rByFPnb9GuFev3DtcbNX7rm23e3qxWP/fpzroGtGq8Luthqu91f85bKe4epp16bPzH7FXZ3nH7H2unpsvqtr4SdcQZU+dK08eclqM/78bb7rzd7jXb/8PsPVyb09uOZnrl/+Ni/A45LrxI/vuv89eV1Vhqx3/+sAeBs9vAAAn5c9ey4lsZel5PpPyWf1bKqLOvz9L9qdNJsqvNJezZ4K07wPuqtds+rKn+NJNR/2q3vfq7p85Ta9pvdde1yKPbOsxxTJll3BOYtH87gnlDfHw0pkFhOl0H8yPe5euKRzF64VNVw5tF0/hV1VmmoVVCxtMqvNyFCoqga+10TBxzdoqXv71S1D1LBgsILcz3ftllPFX/pKhxSuXeOX6+RV+4EAvIbACwDwb65jWjGghao07aZBY+dpx/mMatbtHQ3pVNLe4Tbsx7XrPdx6TIX/dlKPgZ/f+XGx4tKViEsyRRLJnqqvDq910qtR3doW1oNWogbgTQReAIDPu3jhvL10jevYfm07IyUpll2PbP9O7335m1TsTU3/fbOWfTdGb77aWE/cd/NjbubSpS3XHtdwwETrMYP7dlGbxuXv8LjbS5zqYWV235/786TcL+268wfWq++gkfphXxL9x72eLE8Nte7SRZ0j3zo2V41ytdSsdVmlJvACXkfgBQD4vF17t7sjqsdZbV+8QBv0sEpVzKfke3Zot7v1wacKKVfKa4UPrkt/6cd5O63lqF1RmP24DFkzXGtyc53deofH3V7iTPlVNkcyRcxdpDV/3Ri74c8dazRp5FKdevIZ1ciQROFTpmvhgQv2ViNCR+b013PPV1KFnot1nuvWAK8j8AIAfN62RZPVf9ISrft1heYO76VXP/hZKtZWXao9occKllAxd849PfVrjV24Rhs2/Kppw4fos63h7kde1aWIK5HCskdS/cd+3JpZc6zHrFs6RR++0vkOj4tGioJq+mZDpQufrj7t39E3i9yvZe0SffbF90pb+796vkRZNe/j3h4xW73a9tWYeSvcz7tGi8a9q07vzFFEsip6s10ZpaCHF/A6Ai8AwOeFFMmt2T1bq0m95nrtw8VSxe4aO6ylCqRMosTZn9f7nzZXrr8X6OOXG6tB3fr6dGmExo97Q/n1jzas36lTUSRXz+N2ThtkPabJS0O0PnP7Oz7u9pLqUffr+nbky8qx51u918b9Whq21i+XCuqbAVWVIdF9ylDtTff29ip0dLoGdWjuft7Gav/2BG1O31AfzBqkxk+ksH8WAG9KZIZqsJcBAPBRZuay3dpy4IyS/idYT2ZKeW20hMgun1Do5gM6o/sV9GRupU5+d306Jw/v1v5jF/WfnLmUyS6JuGdmVrjfQ/VXRGJlzZ1PjzyQ1N5gu77dpUSpsih/cDp3XAYQVwi8AAAAcDRKGgAAAOBoBF4AAAA4GoEXAAAAjkbgBQAAgKMReAEAAOBoBF4AAAA4GoEXAAAAjkbgBQAAgKMReAEAAOBoBF4AAAA4GoEXAAAAjkbgBQAAgINJ/w/58R0hK9iDbgAAAABJRU5ErkJggg==" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# INVESTIGATION OF THE FORCE ON A CURRENT IN A MAGNETIC FIELD\n", "\n", "## Theory:\n", "The force on a current carrying wire in a magnetic field is described by the relationship: $F=BIl \\sin{\\theta}$. In this practical arrangement, the value of 𝜃=90 so the equation can be simplified to $F=BIl$. \n", "\n", "The value of $F$ is determined by the weight of the magnet placed on a balance. In effect $𝐹= \\Delta mg $ where $\\Delta m$ is the apparent change in mass as F varies due to the magnitude of the current. \n", "\n", "The current can be varied and a graph of $F against $I can be plotted which should be linear. The length of the wire can be measured and the magnetic flux density of the magnet can be determined from the gradient of the graph and the value of length of wire within the pole pieces of the magnet.\n", "\n", "## Apparatus:\n", "* Electronic scales with resolution ± 0.001 g\n", "* Ammeter\n", "* Rheostat – value can be chosen so that the current can be varied in the range 0 to 3.00A or 5.00A\n", "* 20 SWG copper wire\n", "* Ammeter or mutlimeter set to A range - ± 0.01A\n", "* Variable d.c. power supply\n", "* U shaped soft iron section with ceramic pole pieces\n", "* Stand and clamp\n", "* Metre rule\n", "\n", "## Method:\n", "\n", "Set up the apparatus as shown in the diagram. Measure the length, l of the wire which is between the poles of the magnet. Use the rheostat to increase the current in steps from zero. For each chosen current value, record Δm, the apparent change in mass of the magnet (this can be an increase or decrease, depending upon the orientation of the current and the magnetic field). The force, F on the wire is calculated from F = Δmg for each value of current I. A graph of F (y-axis) against I (x-axis) should be a straight line through the origin. The magnetic flux density, B of the magnet can be determined from: B= gradient\n", "length of wire\n", "\n", "![image.png](attachment:image.png)" ] }, { "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 }