5240 Particle Slides on Rotating Circular Track.ipynb

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"
    }
   },
   "cell_type": "markdown",
   "id": "04a5d40f",
   "metadata": {},
   "source": [
    "![dedic.png](attachment:c9fff4c9-2c42-4f2f-9214-9bfc1d497739.png)"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "259455f1-add4-4217-91cd-c476d4ea741b",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5036e200-da97-4f27-8a2e-dfce5548ee46",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mu=0"
   ]
  },
  {
   "attachments": {
    "d7fc5c1e-36d4-45c9-b137-70e519bfcb17.png": {
     "image/png": 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sKNWv34AyZsyILyu40kAABExDQG3xxk/dfv31V5mFsn379ijkbZorARMFARAAAXUIQLypwxG9REDAHfHGWSV/+GGduLv8Nz179lT2XLhwYapevQY4gwAIgICpCKgt3njxW7ZspiZNmtCAAQOoTZu2puKByYIACIAACHhGAOLNM3442wEBV8UbWyXZEjR06BCZDnvQoMFgDAIgAAKmJQDxZtrQYeIgAAIgYEgCEG+GDIt1JuWqeGOrZFBQkLyrXLRoUUqTJq11YGAlIAACPkcA4s3nQo4FgwAIgICmBCDeNMWLzj8l3hR75NWr12ygXrx4QX5+ftSoUUMU4MblAwIgYHoCEG+mDyEWAAIgAAKGIgDxZqhwWG8y9uKNbZBK9khe6d2796Q98sSJE7aF169fH1ZJ610GWBEI+CwBtcXbvXt3aceOHTRs2DDq0aMHNWjQ0GfZYuEgAAIg4IsEIN58Meo6rtlevF27dpWmTJlqGz127FjSHpkhQ0bba198kRRWSR3jg6FAAAS0JaC2eBsxYgSdPn2KmjZtSl999RUlSZJU2wWgdxAAARAAAUMRgHgzVDjMN5mnT5/Sjz/+QNeuXQ938vv27aU9e/ZQ7dq1KXHiJPT06RNbu1ixYlPjxo1gjzRf2DFjEAABJwmoLd5QpNtJ8GgGAiAAAhYlAPFm0cB6uqwnT57Qgwf3HXZz585dGjx4EJ08eTLctryvjTNIJkyYkJo1awZLpEOiaAACIGAlAmqJt5cvXwqr+R0aPXq0eG9+QNOnz6C4ceNaCRXWAgIgAAIg4AQBiDcnIPlik2XLgmnatGkOlx4nThzx9KxxhE/PVq5cQStXrqT+/ftTpUqVYIl0SBQNQAAErERALfF28OBB8T76HVWsWIkqV65MmTJlosiRI1sJFdYCAiAAAiDgBAGINycg+WKTnTt30P/+9z+HS48dO47Yt9aY0qZNF25bV0sFOBwQDUAABEDARAQ8EW+XLl2U78MvX76i169fSzdEjRo1qXDhwiYigKmCAAiAAAioSQDiTU2a6CsMAYg3XBQgAAK+TMBd8caZebdt2yaySg6nZ8+eUsGCBWGV9OULCWsHARAAgX8IQLzhUtCUAMSbpnjROQiAgMEJuCveRo4cKbNKsi09evQYcn/bl19+CaukweON6YEACICA1gQg3rQm7OP9Q7z5+AWA5YOAjxNwVbwpVsnbt29T8uTJhS29qRBv0X2cIpYPAiAAAiCgEIB4w7WgKQGIN03xonMQAAGDE3Ak3ngfG5dcUQ5OTDJkyBDq1asXCnAbPLaYHgiAAAh4gwDEmzeo+9CYEG8+FGwsFQRAIAwBR+KNi25v2LDedl7GjBmlVTJ79uwowI3rCQRAAARAIAwBiDdcFJoSgHjTFC86BwEQMDgBe/FWoUIFmT3y1avXtlk/evRQJCR5Zvs3lwCAVdLgQcX0QAAEQMCLBCDevAjfF4aGePOFKGONIODbBDgzpL0As6exY8cO6t69O/Xo0ZPSp08nLZHPnz+3NeF/16/fwLcBYvUgAAIgAAJOE4B4cxoVGrpDAOLNHWo4BwRAwEwEhg8fTvyELbzj8ePHdO7cOUqVKhUVKlSIGjVqRNGi/ZuAJGPGDLBHminYmCsIgAAIeJkAxJuXA2D14SHerB5hrA8ErEng4sUL9NNPP4ni2G8cLpCTjkT05O3SpcuiXttWWaetWrVq1LRpMyHeojnsEw1AAARAAARAIDwCEG+4LjQlAPGmKV50DgIgoBEBFlydO3cOYXGMaKhhw4ZRQED9cH/tKGGJRtNHtyAAAiAAAhYlAPFm0cAaZVkQb0aJBOYBAiDgCoGHDx/QqVOn6d27dw5Py5QpY4TWR4g3h/jQAARAAARAwAUCEG8uwEJT1wlAvLnODGeAAAhYhwDEm3ViiZWAAAiAgBEIQLwZIQoWngPEm4WDi6WBAAg4JADx5hARGoAACIAACLhAAOLNBVho6joBiDfXmeEMEAAB6xCAeLNOLLESEAABEDACAYg3I0TBwnOAeLNwcLE0EAABhwQg3hwiQgMQAAEQAAEXCEC8uQALTV0nAPHmOjOcAQIgYB0CEG/WiSVWAgIgAAJGIADxZoQoWHgOEG8WDi6WBgIg4JAAxJtDRGgAAiAAAiDgAgGINxdgoanrBCDeXGeGM0AABKxDAOLNOrHESkAABEDACAQg3owQBYPP4dmzZ/To0UO3ZjlvXiAFBs6jSZMmUcGCBZ3q47PPPqP48RNQlChRnGqPRiAAAiBgVAIQb0aNDOYFAiAAAuYkAPFmzrjpOusVK5bTzJkz3Rrz5s1bdPPmDcqQIQPFjh3bqT7ix49PAwcOoly5cjnVHo1AAARAwKgEIN6MGhnMCwRAAATMSQDizZxx82jWhw8fpl9/3eV0H7/+upvWrv3e6faeNkycODHVq1eP0qVL51JXOXPmpNKly7h0DhqDAAiAgJYEIN60pIu+QQAEQMD3CEC8WTzm7969o4cPH9Dr169tK509ezYNGTLEpZXHiBGD4saN67KV8fnz58S2S3fPvXPnjtPzbNasGQ0bNszWPlKkSLBfOk0PDUEABLQgAPGmBVX0CQIgAAK+SwDizeKxv3XrJg0YMJBOnz5lW+nNmzfpzJkzLq08RYoU1K9fP8qe3d+l89asWU2rV6+mvn37Uo4cOV069/vv19DkyZOdPidNmjTE/ylHvHjx5Nrz5MnjdB9oCAIgAAJqEoB4U5Mm+gIBEAABEIB4s9g1wJbI3bt/ta3qwYOHtGxZMJ09ezbEShMmTEhly5alpEmTOkWAn5zxk6106dI71V5p5Em2yZ07d9D33zu2az5//oK2bv2FLl68GGaNAQEBcr+dcuTIkQPWSpciiMYgAAKeEIB484QezgUBEAABEAhNAOLNxNcEWyIfPLhPb968sa1i1qxZNHTo0DCrSpAgoUgYEsv2Oou26dNnUN68eTUl4Il4c3Zid+7cprZt29Hhw7/ZTmG7ZniWy6ZNm9Lw4cNt7WCtdJYy2oEACLhDAOLNHWo4BwRAAARAICICEG8mvjY4iyNnZTxz5rRtFTdu3AjXElm3bl0pcJQjatSolC1bNqczQLqLSQ/xxuL1xIkTopzBI9s0161bK8sThD7YVpk2bVrby/xEEdZKd6OL80AABBwRgHhzRAi/BwEQAAEQcIUAxJsrtLzU9vHjx7Rx4waRcv9miBmwJTI4eCn9/fffIV5PlCgRlSlTJoQlslSpUlS9eg3dV6CHeAtvUbt27SLeb6ccrlgr+Zzo0aNTlSpVKGXKVLozw4AgAALWIQDxZp1YYiUgAAIgYAQCEG9GiEI4c1CyRPJTpcuXr1CHDu3pt9/+tQXan8KWyFixYtpe+uKLL3SxRDqDzlviLfTc7t69Q23atBUMD9l+9eLFi3CtldwgWbJkMllKsWLFiK2V8eLFdznTpjN80AYEQMDaBCDerB1frA4EQAAE9CYA8aY3cSfHUyyRZ8+eoZcvX4mna2fp7t274Z7NNdFat25t+13UqNHoq6++0twS6cxSjCLeFGsll01Qjh9++CFcayX/nguKZ8yYUZY4iBMnDvXvP0Dz/YHO8EQbEAABcxGAeDNXvDBbEAABEDA6AYg3A0VIsUfeunWL7t9/QEuXLqFz587ZZpg/f34qWLBgmBmXLl3aK5ZIZ9AZRbyFN1e2Vq5evSrMr3j/3LZt22yv85PN+vUDpJiLFi0a7JTOBB5tQMBCBC5duiis6xtD1Mt0dnmnT5+m5cuXU6VKlcJ9/46onzJlyorSLNmdHQbtQAAEQAAEfIQAxJuXA832yEePHsqMkWyPbNeurciaeNhOOCSgmDE/WiKbN/9GJCgZ6OUZuza8kcVbRCtZsGC+jfPLly9DWCvZkjplyhQqXry4tFPGjRsPdkrXLgm0BgGvE3j16pV83/3w4YNTc9m6dSt17tyZ7t2751R7NRqNGTOWGjVq6FJXUaJEke9J/N6EAwRAAARAwJoEIN68HNcbN67ToEGDRR228O2R9pbIVKlSUfr0/9Ys8/LUnRrejOKNY6IUMf/xxx9p4sSJtrXa2yn5Z7ZT5suXzykWaAQCIGAMAvv27aMhQwYTizhnjgcPHshamVyCRK8ja9asTtfhVOaUM2dOGjx4iLR64wABEAABELAmAYg3L8aVn7D973//C5Mxku2RBQoUkDPjrJHeyBKpFhYzijf7tf/666+0cuUK+RLbKbdv3277tWKnrF69Ogp/q3XBoB8Q0IDAL79soZMnT9p65p+Dg4OJrequHGXLlqMsWTK7cgpdvXpVvm/kz1/A5XOvXbsmz7Uvg/KpwXmvc8OGjShGjOi2ZqVKlSZ/f3+X5ozGIAACIAACxiUA8aZzbJ49e0ZPnz6Ro06fPp2GDRsmf2YhEDNmDPnzN9+0ELXHBug8M22GM7t4s6cSkZ2ycePGNHr0aNk0evQYuOutzaWEXkHAKQLhWSK7dOlCK1Z8vAljfyROnFjuY3X2GDlypNj/2sDZ5rKdJwlLduzYLjINd6AnTz5+ZnzqePr0KfETwtDHqFGjqUmTxraXYa10RBK/BwEQAAFjE4B40zk+XJctMDBQjnrtGtvzPhbYDggIoJYtW8qfU6dObTp7ZEQYrSTerl+/ZrNT8hNTxU7Jhb/Tp08vEVSpUpW6d++u81WF4UAABBQCiiXy9evXNiic+Ony5cthIPXq1UsmEnH2yJIlC33xRTJnm8t2noi3Bw/u0/HjJ+jt2zcOx5w0aRKxzTv0wfZL3qurHDly5IC10iFNNAABEAAB4xKAeNMhNmyP3Lt3jxyJLTDr1q2zjcp3frmANou3atWq6zAbfYewknizJ8d2ykWLFomslFvpwoULtl+VKFGCatasKf/NmeJKly6jL3CMBgI+RmDLls106tQp26rZ3rxs2bIwlkjOFssZHD//PLKtLT9FK1y4sKbEPBFvrkxs2bJg8Tmz13YKWy537NhBDx8+DNFNtmzZpLVScXrwL2GtdIU02oIACICAdwlAvGnEnze2K/bIadOm2eyRPFyMGB+tdZEjR6YUKVLQjBkzKXfu3BrNxLvdWlW8MVW+K96qVSs6cOAAvX//XsT7aYgvjGynHDNmjAwA2yk5wQkOEAAB9wjw/rSXL1+EOblTp05iX+rKMK/zjbGoUaPaXucMsXPnzpPvv3oeeom30GviUijt27cLsV+ObfvhWStHjhxFzZo1DYMlduw44r3r3/1zenLDWCAAAiAAAuETgHjT6Mpge2RQUJDs/epVttt9tEfywTa73r17U+bMmcV+i+jyCY1Vv9hbWbxxeYfjx49LEcdfLEeMGEGHDh0KEecMGT5mB61cuQrslBr9raFb3yDAf1/8pDv08ffff4drieT32AoVKtiaJ0yYiDihx2effaYrMG+JN8Vy+ebNv/ZRLnPyww8/hFk/P42zt1YqDXi/nRUdIbpeABgMBEAABFQmAPGmMlD+Es8f1lyUNTx7JN8NTpgwoUhK8o3Y25ZG5dGN152VxZs9bb6jPW/eXJlO/OXLV8Ieuy2MnbJBgwZCxFWmlClTGS9QmBEIGJAAZ4lULJHBwcto//594c4yU6ZM0vpnb4ls0KCh5pZIZ5B5S7yFNze2Vu7Z89HCz8f169fDtVYqv69bty4VLVpU/rNkyVLIWulMwNEGBEAABDQmAPGmAmAutP348SOxqfwtXbx4idq2bUNHjhyx2SP5Tm/KlCktbY+MCKOviDf79T98+IBatGgp7JT7pZ2ShR2L+qRJk9LUqVPFl6CS5OfnJ6yzcVHgW4W/P3RhLQKcWVGxR3bs2DGEJZLt5rFixZJ/P/YH/02xJdKIFj8jibfQVwrv3W3Xrm2YfXH8WcblCV6+fGk7ha2VzZs3k/+OFSu2IVlb6y8BqwEBEACB8AlAvKlwZXAWQi6Meu7c3/TixQv59OXu3bvSHtmnTx/68ssv5Z4ntuxY1R4J8fYvAf7i89dff0k7JX8RZWh/yfgAACAASURBVLvXwYMH5ZdOvhbixYsnkgXERIFvFf720IX1CAwfPlw+ueaD30uvXLliWyQ/Bfruu+/C3PRgSyTbzyNFimQ4IEYWb3yj6a+/jpO9tZIBHjt2TJY/uX37to0nZ61Mluxjps327dubuv6o4S4STAgEQAAEXCAA8eYCrPCa8hM2Thu/ZMliId7O2Zrky5dPpqBu0aKFT9gjId7CJ6DYKTmFd8gC3wmIbZTVqlVDRkoP/wZxuvkJsD3y9OmP+4KXLg0OYY9ULJGRI38mb4C1bNlK2CM/N82ijSzeIoLIsQgMnCddAzdu3KCdO3eGSHTCdspixYrJ00uUKAk7pWmuRkwUBEDACgQg3tyMomKVnDBhAvGdYj4SJEhgs5LwFwyrFNp2E5E8zRdtk+HxWrhwgXxiwAcXEeYns3w0atSIxo8fDwulJxcZzjUtAa7FxpZzfpKzatUq2zrs7ZFcSoUtka4U0zYSEDOKN3t+u3fvltZKzlIZnp1yxIiR1KZNa/keZsQnn0a6FjAXEAABEFCDAMSbmxQVqyTfkbQvtM2JSPjgZCRcV8jXD4i3j1cAXy9K4oX169eHKPCdM2dOIez6Ez+txQECvkSAk2cMHz6MuDabfRFttkd+++230h6ZKFFiw1oinYmV2cWbYq18/foV/f7777L8ya1bt2xL50yV5cuXp4EDBwpLeHxnkKANCIAACICABwQg3tyAx0W3f/rpJ1q8eBGdP3+erF5o2w1EtlMg3sLS4yQBCxcutGWk5Ce29evXF3tIqsNC6cnFhnNNQeDixQsiI+/PxO4F3hsaHBws94ba2yN5/xon/TGTPTIi+GYXb/brOnPmjLRTck1Lezsl74dr3LiJ2Ncbk5InTy62DFRGQhNT/DVikiAAAmYkAPHmZNQ4EcmzZ09l68mTJ9uskvHjx5dJKGbOnEW5cuVysjffaQbxFn6slYyUO3fuoHv37slGXNR73Lhx8meu/8cJTnCAgBUIsD3yyZPH9OHDB9q4cSNxFknOwKociRIlknuE2R5pX1jbCmu3knizj4dip7x69WqIbJW8F2727DnipmYiIb6jyCRdsFNa4UrGGkAABIxCAOLNyUgsXbqE5s9fIFvzh5W9VbJDh46WLrTtJKJwm0G8hU+P9478+eefMtHNxIkTZSPOTpohw0erLX+R7dGjhyfocS4IGIYAf9Fne+SbN2/p/v170kJsn4aes/LWqxdgantkRLCtKt4UOyXv+163bq1t+VwShW9osnDz988u937Hj5/AMNciJgICIAACZicA8eYgglzrZvPmTbRs2bIwRbe5tlBAQABSJn+CIcTbpy+wjxbKBTIT5YULF2yNixcvLp/EVahQgVKlSm329xnM3wcJsD1y06ZN0h7JNyqWLl0q7XbKUa5cOdu+YLbcFSpUyJKUrCrelGBx4W9+H+Nj3759cl+ccih2ytixY0k7ZcWKlWCntORVjkWBAAjoSQDi7RO02SrJezI4k9bRo0dl0W22snHR7VSpUklrCCebwBExAYg3x1cH38Fu2bIl7d27VzbmL7i8ByhJkiQ0bdo0qly5iqwLhwMEzEKAr+G1a78PY49MmDChrUYbP7GpW7eeWZbk9jytLt7swfTu3Uu4CZbIl/jz8+HDh7ZfcxKaOXPmUrp06UybOdTtiwAnggAIgICKBCDePgEzOHgpzZgxQ1gkz8jU7mnTpqVevXrJjfVcdNvf39/nim67eu1BvDkmplgo2U7GX3pHjhxpK+qdOXNm+QUXFkrHHNHCOAS4MP3q1avCtUeWLVtWTpRrtn3xxceiz1Y+fEm8cX24q1c/FlWfPn1GGDslv5916tSJatSoaeWQY20gAAIgoCkBiLdw8P5rlVxu+/BB0W33rkOIN9e48d3q2bNnycLvSlHvEiVKyHpwFStWpJQpU7nWIVqDgE4EuND22bNn5WiLFy+xFdouW5btkRnk602bNqOCBQvqNCNjDONL4s2eONspd+3aJV/av3+/zU7JBb75PY2PYsWKo8C3MS5TzAIEQMBEBCDeQgVLsUq2bt2Kjh07ZrNKtm/fgfr372+i0BpjqhBv7sVh0aKF1LdvX5uFkstRTJ8+HRZK93DiLA0JcCbJp0+fCHt5G/G0bbVtJC60zXZfTshTp05dDWdg7K59VbzZR6VPn94i4dd8aQe3T1TDBb7btWsntyMgI6Wxr2PMDgRAwDgEIN5CxYKzSs6aNYvY/sFWSc4AyFbJ8uUroOi2G9ctxJsb0MQpXNT74MGDNGrUqBAWSs7I1717d/c6xVkgoAEBziQ5YsTwMIW2OWV8v379ZAkVX7BHRoQW4o2kfXbjxg00duxYunnzpg2VUuCbb4wmSJBQg6sTXYIACICA9QhAvP0T0/CySsIq6fkFD/HmPkN+Cjxnzmz68ccfYaF0HyPO1JAAWyXXrFljyyTJ+4FLliwlkjpFkna4Vq1aU+TIkTWcgfG7hnj7GCPeOz5v3lz59O3WrVu0c+dOevDgASkZKatUqQILpfEvZ8wQBEDAAAQg3kQQwrNKst2HrZJcowaH+wQg3txnp5zJpQTYQvns2TP5xQcWSs+ZogfPCIRnleRMklyfMDAwyJZR0rNRrHE2xFvYOHJmXd6acO3aNVtGSlgorXG9YxUgAALaE4B4E4zDs0r27t2bypUrD6ukh9cgxJuHAMXpbKE8dOgQslB6jhI9qERAKbp98uRJunz5suyVC21zZlR+4ob9S/+ChngLe9FxeZQ//viTJk2aZEsKBgulSn+c6AYEQMDyBHxavLFVcsuWzRQczAW418pgs1WSs/q1atUKxZFVuPwh3lSAKLpQslCyhXLHjh2yU87YphTyRhZKdTijl4gJcNHtzZs30/v378UX7z9o0aJF9Pz5c1k6pUSJktSiRQufyyTpzPUC8RYxJc5IuXLlSlnk+/79+5QlSxaZkTROnNiULFkyudec66viAAEQAAEQ+JeAz4o3znjFBbhbtWops0pGixZN1myDVVLdPw+IN3V5soWSn3Dwl2Z7C2WVKlXxJUdd1OjNjgBbdr//fg116NBBXnfKwUkmKleGVfJTFwvE26f/lPbs2SMylbYW9eGuEt9QVQ6lqHf69OkpatSo+HsEARAAARD4h4DPije2Ss6ePVtmwVIKcPfs2RNZJVX+04B4UxfotWtXpYXSPgsl361muxqyUKrLGr39S4CLbq9Zs5qOHz9OvN9NOfhGApcByJEjB6ySEVwwEG+f/ksKz0LJZyRNmlQ+ieOi3tWr18CfIwiAAAiAgK+Kt/Csknnz5pUb7WGVVP/vAuJNfaYRWSibNGkibj6URyFv9ZH7bI9sldyyZYuo0bUgRNFtfhrCR7NmzahQoUI+y8eZhUO8OUOJiC2UO3bslI0PHjwQoqh3vXr1YKF0DiNagQAI+AABn3vyxumKGzSoT4cPH4ZVUocLHOJNO8hcyJsT69hbKBcuXChuRFTWblD07DMEQlsl2VbOWXgnT55MtWvX8RkOni4U4s11glzUOygoSBR/fyqLehcpUoTmzp1HsFC6zhJngAAIWI+AT4u3tGnTElslOaskb7rHoT4BiDf1mSo9soWSC3mPGTOGDhw4IEsIQLxpx9vXemarJO9z473BbJUsXry43G+ZO3duny667ep1APHmKrGPRb03bNhA48ePoxs3bkgLJdeD69ixIyyUruPEGSAAAhYj4FPi7ciRI7R+/XrxBXcBJUiQAFkldbiYId60hWxvoeTEO5x9snr16rJQMg4QcIdARFbJ6tWridpcbUQB7s/c6dZnz4F4cy/0SlFvtu3+/vvvspO6desSLJTu8cRZIAAC1iHgE+KNU1uzBWjMmNE0fPhwGb1+/frRsGEff8ahHQGIN+3Y2vc8d+4c8cW6tXypYcOGNHXqNGlxixw5sj4TwCiWIMAWXE5M0r59e2lZY6skp2qfMmUKrJJuRhjizU1w/5zGFsrAwED5Ga5YKOfNC6R06dIhC6VnaHE2CICASQn4hHi7evWKFG07d+6UdgyIN/2uVog3fVjbize2A+fKlYv69u1H+fPn12cCGMUSBPh9cu3a72GVVDGaEG+eweTP7I0bN9C4cSEtlFy2okaNmp51jrNBAARAwIQELC/ejh49Sj/99JO0Sp4/f56SJElCxYoVl0lLkH5Y+ysW4k17xjwCF7kNCgqkXbt20YULFyhevHjE2SerVasGC6U+ITD1KGyV/OWXX8Q1NN+WVbJMmbLiPbKaqMHVFlZJD6IL8eYBvH9OPXv2LM2ZM1tkPv1FFIj/10IZEBAg96yjkLfnjNEDCICAeQhYVryFZ5XkL7ScmISzVnFdIhzaE4B4056xMgIXT+bU7Tt2bKf79+/Ll2Gh1I+/WUdiq+Tq1atkAW5YJdWPIsSbekzDs1AiC6V6fNETCICAOQhYVryFZ5Xku3R8F5ktZbyXA4f2BCDetGesjPD27Vu5sT84eClNnDhRvvzRQplbWCj7wkKpXyhMNVJ4WSW5BAVnlUyWLLmp1mLEyUK8qReVkydPCgvlxhBZKLNlyyZvPMBJox5n9AQCIGBsApYUb2yV5KySCxbMt1klixYtJq2S8Mjre0FCvOnLm0djC2Vg4Dz5f3sLJX+5KVGihP4TwoiGJMBWya1bt4prJSiMVbJt23YUKVIkQ87bbJOCeFM3YmyhnD17lrD5brVZKDkDJf8HC6W6rNEbCICAMQlYUrwNHTqUBg4cIInHjRuXMmfOLPzyc2GV9MI1CPHmBehiSMVCuX37Nnrw4IGcRPPm39C8efO8MyGMaigCSlbJtm3byiLv7ESIHj06TZs2jWrVqm2ouZp9MhBv2kSQLZScdfL5849ZKAsXLixvRCALpTa80SsIgIBxCFhevMEq6d2LDeLNO/zZQsl139hCOWnSJIg374TBsKOOHDlSFuD+888/bQW4e/XqRXny5IFVUuWoQbypDPSf7thCyYW8J0wYbyvk/dVXX1G7du3gsNEGOXoFARAwCAFLibdHjx4JG9AvtGTJUtq7dw/BKun9qwzizbsxsLdQpkqVipo2bSqsReUoZcpU3p0YRvcqAbaQL1u2TM5BySoJq6Q2IYF404Yr9xqehXL8+PHUtWs37QZFzyAAAiDgZQKWEm9cD6ZhwwZ05MgR4k3MLOI4OQkO7xGAePMee2Xkx48fU0BAPbnRP1GiRKJsxkKqXLmK9yeGGehOgJ/Isk2yRYtv6Oeff7ZZJWvXrqP7XHxlQIg37SPdu3cvaZl8+vQJDRo0mDp27CjLB/j5+Wk/OEYAARAAAZ0JQLzpDNzXhoN4837EId68HwOjzGD37t00atRIOn78OKVOnZqQVVL7yEC8ac/YPgtlwoQJpbvg22+/pYQJE2k/OEYAARAAAZ0JWEa8cYZJ9r/Pnx9E8ePHpwoVKoiyAG0oVarUOiPFcPYEIN68fz28ePGCZs2aST/88IPIzvaHLN6NzJPej4veM9i2bSutWbNGvEfOlwkeOPPuihUrUIBb40BAvGkM+J/u+cZEo0YN6dKlS5QlSxb65psWVLFiRcqePbs+E8AoIAACIKATAdOLNy7GzV9O+W7y8OHDJTa+4zZ06DCdEGKYTxGAeDPO9TFv3lxq1aqVnBAX754+fYa0zUWOHNk4k8RMVCfw5s0b+R75zTfNpXjjg29wValSRZRTWQjxpjrxkB1CvGkM+J/u9+3bRy1btqCrV68Suw34GDFiJCyU+uDHKCAAAjoSML1442LcXGR2586dxNYJiDcdrx4nhoJ4cwKSTk3sxRsX786dOw/16dMHxbt14u+tYfiJxOjRo+ivv/6STyX4YLsk73PjQtzYF6RtZCDetOWr9P7gwX2ZYXfq1Gm0bt1a+TI/dStfvjz169cPFkp9woBRQAAEdCBgevFmn6QkSZIkyDCpw0XjyhAQb67Q0rZt6OLdnLxkwYIF4glMVW0HRu9eIxDaKpkpUyYqVqyYeALbmgoWLOi1efnSwBBv+kZ72bJgWr58Oe3Zs4fu378vLZRc47JSpUqwUOobCowGAiCgEQFTi7fXr1/LOkWcOe3ChQuyGDcX7fT399cIF7p1lQDEm6vEtG3/9OlTueeNi3d/9tlnYi/cLKpa9WuKFi2atgOjd10JcFZJtko2b97MZpWMFy+etEouXLgIVkkdowHxpiPsf4aKyELZqVMnaRXH02b9Y4IRQQAE1CNgavHGd9jmzp0r7UCcXap169aiyGxeih07tnqE0JNHBCDePMKn+sn8pZ6T+/Dfzrx584iL2rJ9rls31EVSHbYXO4RV0ovwQw0N8aZ/LNhCye9z06ZNt1ko+aYuf0+AhVL/eGBEEAABdQmYWrwNHTqUBg4cIIkgSYm6F4ZavUG8qUVS3X4CA+eJzf0tZafNmzeXT6xxWIfA6tWrqHHjxjKrJFslixYtKm5utYFV0gshhnjzAvR/hgwOXiotlHv37pUWSrYMc3H6FClSem9SGBkEQAAEPCRgSvHGGSb5SwlnmBw3bpwsxtmpU2caMOCjkMNhHAIQb8aJhf1MFi1aKJ62dRd/Ry+oZs2aNGPGTGmdZCslDnMT4PdGFm+cWZRjWrVqVWSV9GJIId68CF8MrVgor1y5Ive8BQXNp/Tp09Pnn3/u3YlhdBAAARBwk4ApxZt9hkn+osKWr/LlK9CXX37pJgacphUBiDetyHrWL/8NHThwQN78uH37NuXKlRuZJz1DapizR44cSWvXfi9r+nXt2hVZJb0cGYg37wbA3kK5b99eYRXPTu3bt5O1LnGAAAiAgBkJmFK8cYbJBg3qS08779lZvHiJ+PKZy4z8LT9niDfjhvjJkycUEFBPFrdPmDChSGSxEJknjRsup2fGMeXi23wsXbpUxLi+0+eiofoEIN7UZ+pOj127dqHJkyfLU8eNG499vu5AxDkgAAKGIGA68cYZJjlBCRec5QyT/LSN9+vkyJHDEEAxiZAEIN6Me0UomSc5nfxnn0WmOXNmy8yTUaNGNe6kMbMICXAyGnYiNGvWlDZt2iTjOGPGDPnkDYf3CEC8eY+9/ci9e/eSSZqePXtGgwYNps6dO0tbMTJPGiM+mAUIgIDzBEwn3ngDMr8B22eY5GLDceLEcX7VaKkbAYg33VC7PBB/2T9y5IjMPMlZW/39c1CdOrWF1Q6ZJ12GaYATOMPkmDGjZfmU1KlTU8+ePSlv3ryULFlyA8zOd6cA8WaM2J84cUK6DCZOnEBc45KLd/fp00f8nNgYE8QsQAAEQMBJAqYTb0OGDBF3zQbK5SHDpJNR9mIziDcvwndyaGSedBKUgZtx3b7Vq1dTYGAgsTuBk9CsWLGSIkWKZOBZ+8bUIN6ME2cu3N2oUUO6ePGiLN79zTctqGLFiijebZwQYSYgAAJOEDCNeOMMk69evaKRI0fIJAtcaJMzTA4c+FHI4TAmAYg3Y8bFflYfM092k5Y7/tI/c+YsablD5knjx06Zof0+t7hx48oMk4sWLYZ4M0AIId4MEIR/prB//3655eLq1avEe375wP4348QHMwEBEHCOgGnEG2fHGzVqFO3YsYOeP38uv2yWK1de3j3DYVwCEG/GjY0ysytXLtsyT969e5dy585NvXv3oXz58hl/8pihJGAv3nr16iX3ueXJkwf7eQxwfUC8GSAI/0yBM08ePnxYlkZZt24txJtxQoOZgAAIuEDANOLt5MmT1LBhA1uGySVLllLOnDldWCqaeoMAxJs3qLs+JicvqVevLjJPuo7Oq2dcunSRtm/fLpLNzKW7d+/IYtxt2rRFMW6vRiXk4BBvBgrGP1PhvfNcrJtrwLFtsn79+lS6dBlZMxYHCIAACBidgCnE25s3b2SCkubNm9H58+cpU6ZMNH/+ApFgwd/ofH1+fhBv5rgEOANbo0aNiDNPRo78uUhgMkdmnowSJYo5FuCjs1y1aiU1adJEWl5r1apFy5evgFXSYNcCxJvBAvLPdHj/W+PGjWTWar7pwWIuZcpUxpwsZgUCIAACdgRMId44Gx5nmOQsauXKlaNWrVqJLGr5KHbs2AimwQlAvBk8QP9MT8k8yXekg4KCZCFbZJ40fuwg3owfI4g3Y8YI4s2YccGsQAAEHBMwhXizzzD53Xff0ZAhQx2vDC0MQQDizRBhcHoS9pknmzVrJrIXBjl9LhrqS2Dnzh0ywySXeShSpAhVr16dOnToiH1u+obB4WgQbw4ReaXB2bNnxd636dJ2zBlaW7ZsSRUqVBQ3rr7yynwwKAiAAAg4S8DQ4o0zTPKb6ogRw2WGSS6o2aVLVxowYICz60M7LxOAePNyAFwcfuHCBTIZEGd25cyTs2bNltZJZJ50EaQOze2TlAQHB4s9iwE6jIohXCUA8eYqMX3bd+vWlSZNmiQHReZJfdljNBAAAfcIGFq8KRkmd+7cKTNMdunSRRTWrIAMk+7F2itnQbx5Bbvbg3LmSU6nPX78eJEA467MWNizZy/Knz+/233iRG0IQLxpw1XtXiHe1Caqbn8Qb+ryRG8gAALaEzC0eOMMkw0a1Kdjx47JIpqLFy9BhkntrwlVR4B4UxWnLp2Fzjy5YMECmbwEhzEIcIZJLpkyZ84cunPnjrRMcobJQoUKGWOCmEUIAhBvxr4gli5dIhL9LJeZJytVqiTKbgQg86SxQ4bZgYDPE4B48/lLQFsAEG/a8tWid4g3Laiq1ycnKeHMoGwpR4ZJ9bhq1RPEm1Zk1et379694m+qITJPqocUPYEACGhIAOJNQ7jomsRegok0efJkWrRoMRUvXhxITEAA4s3YQYJ4M3Z8Qs8O4s348YJ4M36MMEMQAIF/CRhWvP3++++0ceNGWW8qXrx4Yq9beWrfvj2lSpUa8TMRAYg3EwXrn6lyzbBp06bRjz/+8E99xeYik2ENWQsJh3cJIMOkd/m7MzrEmzvU9D2HM09Onz5NZp7kurJcjoj31yPzpL5xwGggAALOETCseBs8eDANHjxIrgLlAZwLphFbQbwZMSrOzSkoKJBatGghG6NsgHPMtG5Vr15dWrlypRwGGSa1pq1O/xBv6nDUoxf75CVjx46j7t276zEsxgABEAABlwhAvLmEC41dJQDx5iox47SHeDNOLJSZQLwZLyaOZgTx5oiQcX4P8WacWGAmIAACEROAeMPVoSkBiDdN8WraOcSbpnhd6pwzTO7atUvU3ZtFt2/fpsKFC1O7du2RYdIlit5pDPHmHe7ujLpkyWJatmwZHThwQGaebNCgAZUsWYpixIjhTnc4BwRAAAQ0IWA48fbhwweZRW348GE0ZswYih49uizMPXDgQE0AoFNtCUC8actXy965YHfXrl2J98DVqVPHVrA7UqRIWg6LvsMhsHLlCmrcuLEtw+SKFSvJz88PrExAAOLNBEGym2Lo5CVsT8Zee3PFELMFAasTMJx448LcLNp44zAX5u7cubPcOJw1a1arx8KS64N4M29YuWA3f5GZOHGiLNidN29eWbA7X7585l2USWcO8WbSwIlpQ7yZK3YQb+aKF2YLAr5IwHDiLXRh7iVLllKOHDl8MTaWWDPEm7nDyGUDAgLq0fr16ylBgoTET+NQsFvfmIbOMFmtWjXq2LETnrzpGwa3R4N4cxudV07kzJPTpk2lHTt22DJPVqhQkbJly+aV+WBQEAABEAhNAOIN14SmBCDeNMWreecQb5ojdjiAfZIS3o9Tt249h+eggXEIQLwZJxauzKR7927SdcAHMk+6Qg5tQQAEtCYA8aY1YR/vH+LN3BcAxJv34wfx5v0YeDIDiDdP6HnvXIg377HHyCAAAp8mAPGGK0RTAhBvmuLVvHOIN80ROxwA4s0hIkM3gHgzdHginBzEmznjhlmDgC8QMJR4e/fuHR0/fpyaNGlM7Dv/8ssvxR6bReTv7+8LsbDkGiHezB1WFm+NGjWkrVu3UpQoUSkwcJ7c8xY5cmRzL8wEs3///j29ffuWGjZsQD/99JPgH4Xmzp1LtWvXMcHsMUWFAMSbOa+FXr160uzZs+nVq1c0ZMhQmXmX3/eQ5dWc8cSsQcBKBAwl3pYvXya+HAbRH3/8TmXKlKEWLVpQ/vwFKE6cOFZi7lNrgXgzd7hZPBw6dIg+/m0GUq5cuYR4qC2ywHYx98JMMPvdu3fThAnj6ejRo5Q6dWr55bFAgQKUPHkKE8weU4R4M/c18Oeff9KGDRto6tQplDhxYpH1ujz16tWLEiVKbO6FYfYgAAKmJ2Ao8TZ48GAaPHiQhNq/f3/x8xDTA/b1BUC8WeMKsC/Y3bRpUwoKmm+NhRl4FVweoF69j8lJWDAvX74Cd/0NHK+IpoYnbyYM2j9T5rIBjRs3ovPnz1ORIkVkAW/UfDNvPDFzELAKAYg3q0TSoOuAeDNoYFycFsSbi8BUaA7xpgJEA3QB8WaAILg5BYg3N8HhNBAAAU0JQLxpihedQ7xZ4xqAeNM/jhBv+jPXYkSINy2o6tMnxJs+nDEKCICAawQMId4ePXpEv/66SyQnWUi7du2iggULCqtCY6pVq7Zrq0FrwxGAeDNcSNyaEBeKnjVrFu3fv5/SpUtHrVq1ouLFi1OKFCnd6g8nfZoAvw+uWbNa7LeZSiVKlKDq1atTp06dYZs04YUD8WbCoP0z5TNnztgKdvP+3zZt2lC5cuVRsNu8IcXMQcASBAwh3k6cOCEzqh07doyyZ89OS5YspRw5clgCsK8vAuLNOlfAs2fPxB6surR+/XpKkCAhLVgwn77++j/WWaCBVlK3bh1atWqVnBEKcxsoMG5MBeLNDWgGO8W+bMCYMWOpR48eBpshpgMCIOBLBCDefCnaXlgrxJsXoGs0JMSbRmDD6RbiTT/WWo8E8aY1Ye37h3jTnjFGAAEQcJ4AxJvzrNDSDQIQb25AM+gpEG/6BQbiTT/WWo8E8aY1Ye37h3jTnjFGAAEQcJ4AxJvzrNDSDQIQb25AM+gpKKKF8wAAIABJREFUEG/6BQbiTT/WWo8E8aY1Ye37h3jTnjFGAAEQcJ4AxJvzrNDSDQIQb25AM+gpEG/6BQbiTT/WWo8E8aY1Ye37h3jTnjFGAAEQcJ4AxJvzrNDSDQIQb25AM+gpEG/aB+bKlcsi8+6vNH36dLp165bMvNuhQ0cqXLiw9oNjBE0IQLxpglXXThcvXkRLly6l3377japUqSISrDWkYsWKU4wYMXSdBwYDARAAASYA8YbrQFMCEG+a4tW1c4g37XGHru22YsVK7QfFCJoSgHjTFK9une/bt48aNWpI58+fpyJFisgssKlSpdZtfAwEAiAAAgoBiDdcC5oSgHjTFK+unUO8aY8b4k17xnqPAPGmN3FtxoN404YregUBEHCdAMSb68xwhgsEIN5cgGXwphBv2gcI4k17xnqPAPGmN3FtxoN404YregUBEHCdgNfF24cPH+j48ePSjnDy5EnKkiULLV68hPz9/V1fDc4wHAGIN8OFxO0JsXirXz+AtmzZIvZ6xKSgoEBZpDtSpEhu94kT/yXw/v17YvFWv359ihYtGv33v/8V1qzlQGRyAhBvJg/gP9Pfv38/NWnSmC5dukR58+aVe+DSpElLfn5+1lggVgECIGAaAl4Xb/xlJSgoiI4ePUqlSpWib775hgoVKkxx4sQxDURMNGICEG/WuTrevn1LBw4coOXLl9HChQspV65cVLt2berYsZN1FunFlYwdO5bWrVtLfIe/e/fuVLNmLfFeWMiLM8LQahCAeFODovf7uH//nnz/mzNnDh08eFC+/7Vq1UrcZKnm/clhBiAAAj5FwOvibfDgwTR48CAJvX///uLnIT4VAKsvFuLNehGePz9I3mTho2nTpuLmy3zrLdILK7IvD7B8+XKqU6euF2aBIdUmAPGmNlHv9tejR3eaMGGCnMSYMWOpR48e3p0QRgcBEPA5AhBvPhdyfRcM8aYvbz1Gg3jThjLEmzZcvd0rxJu3I6Du+BBv6vJEbyAAAq4TgHhznRnOcIEAxJsLsEzSFOJNm0BBvGnD1du9Qrx5OwLqjg/xpi5P9AYCIOA6AYg315nhDBcIQLy5AMskTSHetAkUxJs2XL3dK8SbtyOg7vgQb+ryRG8gAAKuE4B4c50ZznCBAMSbC7BM0hTiTZtAQbxpw9XbvUK8eTsC6o4P8aYuT/QGAiDgOgGIN9eZ4QwXCEC8uQDLJE0h3rQJFMSbNly93SvEm7cjoO74EG/q8kRvIAACrhOAeHOdGc5wgQDEmwuwTNIU4k2bQEG8acPV271CvHk7AuqOD/GmLk/0BgIg4DoBiDfXmeEMFwhAvLkAyyRNId60CRTEmzZcvd0rxJu3I6Du+BBv6vJEbyAAAq4TgHhznRnOcIEAxJsLsEzSFOJNm0BBvGnD1du9Qrx5OwLqjg/xpi5P9AYCIOA6AYg315nhDBcIQLy5AMskTSHe1A3UlSuXae/evTR16lS6ceMG5c+fnzp37kKFCxdWdyD05hUCEG9ewa7ZoIsWLaQlS5bQkSNHqGrVqtSoUSMqUqQoxYgRQ7Mx0TEIgAAI2BOAeMP1oCkBiDdN8Xqlc4g3dbGvWLGcAgICZKe1a9emFStWqjsAevMqAYg3r+LXZPB9+/YJ0daQzp8/L4RbEQoODqbUqdNoMhY6BQEQAIHQBCDecE1oSgDiTVO8Xukc4k1d7BBv6vI0Wm8Qb0aLiOfzgXjznCF6AAEQcJ8AxJv77HCmEwQg3pyAZLImEG/qBgziTV2eRusN4s1oEfF8PhBvnjNEDyAAAu4TgHhznx3OdIIAxJsTkEzWBOJN3YBBvKnL02i9QbwZLSKezwfizXOG6AEEQMB9AhBv7rPDmU4QgHhzApLJmkC8qRswiDd1eRqtN4g3o0XE8/lAvHnOED2AAAi4TwDizX12ONMJAhBvTkAyWROIN3UDBvGmLk+j9QbxZrSIeD4fiDfPGaIHEAAB9wlAvLnPDmc6QQDizQlIJmsC8aZuwCDe1OVptN4g3owWEc/nA/HmOUP0AAIg4D4BiDf32eFMJwiweBs6dCjlyZOX6tcPoGbNmjtxFpoYmQDEm7rRgXhTl6fReoN4M1pEPJ8PxJvnDNEDCICA+wQg3txnhzOdIMDibciQIUK85aGCBQtSrly55FkZM2ai3LlzO9EDmhiNAMSbuhGBeFOXp9F6g3gzWkQ8nw/Em+cM0QMIgID7BCDe3GeHM50goNgmFy5cREeOHKY+ffrIs1q3bk2TJ09xogc0MRoBiDd1IwLxpi5Po/UG8Wa0iHg+H4g3zxmiBxAAAfcJQLy5zw5nOkHAfs9bkiRJ6OjRI/Ksc+fO05UrV6hz586UNWtWJ3pCE6MQgHhTNxIQb+ryNFpvEG9Gi4jn84F485whegABEHCfAMSb++xwphMEIkpYsn79T7RixQoqVKgQFS5cBBZKJ1gapQnEm7qRgHhTl6fReoN4M1pEPJ8PxJvnDNEDCICA+wQg3txnhzOdIBCRePvw4QNdv36NGjVqRDly5KBJkyY70RuaGIEAxJu6UYB4U5en0XqDeDNaRDyfD8Sb5wzRAwiAgPsEIN7cZ4cznSDwqVIBL1++pD17dtP+/QdgoXSCpVGaQLypGwmIN3V5Gq03iDejRcTz+UC8ec4QPYAACLhPAOLNfXY40wkCztR5Ywvl8uXLqUiRIpQ4cWKKFi2atFMmSpTYiRHQRG8CEG/qEod4U5en0XqDeDNaRDyfD8Sb5wzRAwiAgPsEIN7cZ4cznSDgjHizt1AePHiQOLEJZ6csXry4EyOgid4EIN7UJQ7xpi5Po/UG8Wa0iHg+H4g3zxmiBxAAAfcJQLy5zw5nOkHAGfHG3bx48UJaKO/cuUOvXr2i3377jfLmzYui3k4w1rsJxJu6xCHe1OVptN4g3owWEc/nA/HmOUP0AAIg4D4BiDf32eFMJwg4K97su3r48AGNGzeO3r9/T0WLFpXFvWGhdAK2Tk0g3tQFDfGmLk+j9aaIt5o1a1JAQH35fvb5558bbZqYjwsEIN5cgIWmIAACqhOAeFMdKTq0J+COeOPzWbhNmzZVZKGcRAsWLKQSJUoArEEIQLypGwiIN3V5Gq03Rbw9fvyYSpcuTcHByyhu3LhGmybm4wIBiDcXYKEpCICA6gS8Lt7+/PNP2rRpE82aNZNix45NZcuWlYWbU6VKrfpi0aH+BNwVbzzT06dP0969e+jw4cNetVA+efKEJk+eTCdPnrAB5C9hLVq0DAN0y5bNQmwuCBd0jBgxqVOnTuTv769/IFQYke2sLKZ//PEHOnHiBLVq1YqqV68hk8vgcJ8AxJv77MxwpiLe/u///ktffZWNjhw5Qm/fvhU/Z6cuXbpQjBgxzLAMzNGOAMQbLgcQAAFvEvC6eOPF8xfBhg0b0LFjxyh79uy0ZMlSWfsLh/kJeCLeePVsoRw/fjy9e/fOaxZKvmM+fvw4On78BL1581p++fr6669p5sxZYQK0adPPNHfuPPn65cuX6MyZM5QrVy5p+4wZMwZ169adcubMacrAPnv2jOrVq0vr16+nBAkSCpE6X3D4jynXYqRJQ7wZKRrqz8V+z1v+/AVowoTx9Pz5C/rii6RUrFgxefMjbdp06g+MHjUjAPGmGVp0DAIg4AQBiDcnIKGJ+wQ8FW88Mgu36dOnedVCyXPgrJj37t2lBg0aUqZMGcMVb2z35P/4mDNnNg0fPpwCAwOpXLny8rXPPvuM/Pz83AfqxTMh3rSBD/GmDVej9Gov3vhpPb+X8MFP6Vu0aEGDBw8O9ym+UeaPeYQlAPGGqwIEQMCbBCDevEnfB8ZWQ7wxJnsL5YMHDyhOnDjCgtiZsmbNqitFFm/16gXQtWtXxV3z4tSxY8cIbZBsBR46dKi0UZYvX0HXeWoxGMSbFlSJIN604WqUXiPKNnnz5g3avXu3zKwbJ05cWCiNEjAn5gHx5gQkNAEBENCMAMSbZmjRMRNQS7xxX0oWypMnT4lC3lFlHbhChQpLW6JehyLerly5THny5JG2p8KFi1Du3LnDTAHiTa+omHsciDdzx8/R7B2VCmBXAW8d+Ph+BgulI55G+D3EmxGigDmAgO8SgHjz3djrsnI1xRtPmDf6s33x9u1b1KRJE7Hp/yuRTGSKLmvhQRTxlj59ehoyZLCcQ8aMGUVmzOkQb7pFwVoDQbxZK56hV+NIvLGNcvPmTdSyZUsaNGgQLJQmuBwg3kwQJEwRBCxMAOLNwsE1wtLUFm/Kml6+fEm//rqLDh48JC2MHTp0pGzZsmm+ZEW8ZcyYQTxVnCxsT7/KOVy8eFFaKDnhjnLgyZvm4bDEABBvlghjhItwJN74xBs3rksLJSdDunLliuyrWbNmIvtyOWvDMenqIN5MGjhMGwQsQgDizSKBNOoytBJvnLb+4MGD8gvPn3/+IevAsX1R60yO9uJNyTbJX84WLlwobU9FihS12Tgh3ox6VRprXhBvxoqH2rNxRrwpY7KFcuvWbfKfXMybbdkFChRAUW+1g+JhfxBvHgLE6SAAAh4RgHjzCB9OdkRAK/HGtknO+pglS2bq06ePsC82lTWUtLZQhifeOLvknTu3w1goId4cXR34PROAeLP2deCKeGMLpZKtlp/k897aJUuWUPz4CawNyWSrg3gzWcAwXRCwGAGIN4sF1GjL0Uq83bp1kwICAuSet7Fjx9kslKdOnZQIypQpI2xHzVXHEZ5440H4dZ5PhgwZbCUEIN5Ux2/JDiHeLBlW26JcEW/2JPbv30/79++jP/74Q9RBbSje08paG5SJVgfxZqJgYaogYEEChhBvV69eoXHjxtG2bdvo6dOnIgV8J6pYsZLuaeAtGF+vL0kL8Xb+/Dk6cOAA7dy5S2R8zE2tWrWW61y//idRUy1I/pw585fSxsiWIy6QrdYRkXh78uSJuIbHEts5lXHXrFljmVIBXHB87969stbevXv3KF++fNS9ew/5fxyeEWDr74QJE+jo0SOUKlUq6tq1q7TMJU+ewrOOcbYhCLgr3njyx44do/Hjx4m9tP5UtGhReV18/vnnXlkXz+XChfOfHJsz/6ZLl94r89Nr0D///JM2bNhAU6dOocSJE1OFChWoR48e4uckek0B44AACPg4AUOIN84eyFkEhw0bSqNHj6aoUaNSt27daeDAgT4eHvMvXwvxxvtC+Mvu3LlzqWTJUrLwNR9sOVIK4M6ePYsmTpxI8+fPl23UOiISb9w/X8NcmJuvYR73zJkzlhFvCxcuoM6dO9Pr16+pdu3agv08ihw5MkWKFEkttD7bD9vk+Npp0KC+uAGxnqJEiULz5s2jWrVq+ywTKy3cE/GmXBt8Q9PbFspOnTrSokWLPhmakSNHUtu27awUvjBr6d27F82aNUveqBs8eIj4rtJNvhf6+flZet1YHAiAgHEIGEK8KTgGDx4s3gwHyX/2799fvjHiMDcBNcXbo0ePxJ62yeJD86Wsq8ZJSpIkSRouIC7qvWfPbnnnmtuqZaH8lHjjibBgU8Y9dOg3unTpoiWKdAcFBYoU5i0k66ZNm1JQ0HxzX5gGnH3dunVo1apVcmbLly+nOnXqGnCWmJKrBDwRb8pYbKE8cGA//f77716zUHKCqDNnTssp8T68GzduUOvWrUWB8Tg2JFyvLnr0GPJGj/3rrjIzcvsePbrLm4d8jBkzVj51wwECIAACehKAeNOTtg+OpaZ4U/a5cTr+KVOmOqTJYm/s2DHyqUbJkiUpf/78HlsoHYk3nhRbf8eMGS2tNfwFZ8GCBVS+fAWH8zVyA4g37aMD8aY9Y2+MoIZ443nzjSi2Zvv755C2cD7Yppg2bTrdl9WhQ3s6deoUBQcHh7iBxvt8jx37nUqVKiktnla0UEK86X65YUAQAIFQBCDecEloSsCb4o3tuGyjnDlzhmoWSmfEGwNlwcjWzREjRkC8aXqFWadziDfrxNJ+JWqJN3sL5fLly+QQY8eOFcW9W+kOLiLxxu+3O3ZslwXH+YlUu3btdZ+b1gNCvGlNGP2DAAg4ImAo8cZZtX7++We5b4gtF+XKlZOFj1OlSu1oHfi9QQl4Kt746dmUKVPo7Nkzci9Qjhw5qFChwjIRibMHWyi5mDZfXw8ePKBYsWK5VNSbk5FMnTpV3Gk+Kfc5cLKUmDFjUt68eeUUSpUqRc2bfxNmOlbINsnF0HntP/74A/3111/SOlm9eg1Rz66Is/jRzkkCEG9OgjJZM7XEm7JstlDy+yEfbFOMEyeuTPLF70l6HRGJNx6fxVvjxo2pZ8+e4vO7k15T0m0crcTbufMfaNKM91ShtB/9p+q/e4k5Qde0adPo7t27Tq0xTZo08ntTRFsKnOoEjUAABAxNwFDijUmdPHlSbtxniwjb45YsWSq/sOMwJwFPxBtnNmOhtH37DuK6bnHjxhV3c3vK68LVg0UgWxn5yw4nxGHB5WxR78ePH8tzjx8/Hu6w5cuXD/cOM39p470hPGe2N5nxYAtoQEA9mUgjQYKEohj5Aqpa9WszLsXwc4Z4M3yI3Jqg2uLNfhKcvIlvqpQuXVraFNOkSevWHF09KSLxxjfI9u3bK96zt8u9eV9//R9XuzZ8ezXF28OHRAd/e0/PnhP9LRJ59g76QMMbE/Xt8TEJFx+8j5qzcXMtUf4cY8YpU6YUltSwdlm+Uck3vtnOmj59BsOzdDRB/uz97bdDxDdQeV358xeQN19xgICvE4B48/UrQOP1eyLe+IsJp6afPXu2SJNdTGbzcjfDoZLRlK1Hd+/eEQlMmslSFM4U9bY/NzxcnO2S5xX6ULJfujtnjUPjVPcQb05hUqURxJsqGA3XiZbije3Zv/yyhdq0aUPffvutbhbKiMRbly6dxU2uEyLbbhAlS5bclgnYcEHxYEJqireDv32g/2v/nm4/+mdC74mGCxesvXjjz583b94Q///w4cPis6upeLLZJNxEKd99962oefqrZcQbl2Xg9Z47d46+/PJLsQVhIUpIeXDt4lTrEIB4s04sDbkSV8Xbpk0/yw8ePvjuIj+x4mQjalpA2Aq4a9dO4myQ169fo/btO1C2bNkMyc/bk4J40y8CEG/6sdZzJC3FGycS4icx/v7+8gtu7NhxdLFQsnj73//+JyzshShatGg2nF9+mVnUfswry7PYv64nb63HUku8LV3xnhas+EBbT4kZvyWKHVdk2W7oR5XK+VH2r8IvO3Do0CFq1KihyPjbjPr06RNmqUeOHBFJsq5L/mZ/QrVmzWraunWrvLbZEsyfRSzm2OlSo0ZNrcOM/kHA0AQg3gwdHvNPjsUbb6rnvQ9Zs2ZxuKATJ07SwYMHZLtKlSqJVNRtHJ7jboMNG9bLukVsoUyWLJmtG87eljNnTne7tdR5EG/6hRPiTT/Weo6kpXjjJ25sL1+2bJn8T7FQsjWci0bny5dP7hVW+2DxtnbtWvk+yWPdu3dPfrEeOnSo3E9s5cNT8aZYJacGfqD1h/8llT0l0Q9BkShd2ojrxTkSb+5wZyvmoUMH6dmzZ7bTs2bNJp90hXdwe7Yy8mcDb2XIly9/hEKRt8Eo5SW4L2esj2yV5PnwE8T79+9Tr169xI3cVPL6atiwgdxzPWjQIHeWinNAwDIEIN4sE0pjLoTFG98h5LuwzhR05o3uo0aNlothO+Lnn3+u2cLY1sh3KTkJB9cwUg7eq+FMKQLNJmagjiHe9AsGxJt+rPUcSS/xxk/dtm79RRTJbiv3RnFSIb45xXtV1T5YvPH+4YULF0qRuHPnDvk+2rt3b4g3B7BtVkmx340+eF+8HT16VG4juHz5km0yvXv3kbEM7+Bag02bNhE1TC9RlixZZTbliIQei6wpUybbusmcObO0PvL/Izr4BgT3/5///J/87sA3H3jLBMSb2n/F6M/MBAwn3viuC38QLFy4SNx52SVtGY0aNaJatWqbmbPPzp3F2+jRo+UHe6ZMmRxy4A+D8DJJbt68iZYuXSrPL1u2rPT8q3HwJvCAgPq0bdtWW3dsoVQySfKLbNlga+VXX32lxpCm6YP/Dnm/IWe3S5s2rYwhW1hTpBC3iHGoToB5r169mqZPny6fBlevXt2S2fpUB2fwDrUQb/wFlzMQpk6dWiRxyEclSpSUT8Bu3rwhPj93yqy4/NSC2wUEBIj3zHKqUgq9541rcPK4/MU+RoyYMtuh1Yp0nz17VvxtThPZNHfQ69evqVWrVrJ+pzOfC0omyXsPxNOn2KI+X3Y/+n7jBzpw+aNVcvOuD3RT/M7dJ28XL16QWYH5fYNFj7PHihXLxRaCXTIpXPTo0W2nsQWX94d36NCBkib9wvb6qlUr5frZyhgjRgyZSOTPP/+iypUr0X//W83WjoUgX58xY8YSiVXSytfXrVsnBd/SpcFC9EXswmEbMD9hq1mzFg0cONDWJ8Sbs1FFO18gYDjxpkAfPHgwDR48SP7zu+++oyFDhvpCPCy3Rlf3vIUGwF9CfvvtN/kBc+DAfvlrTjTCH1JsCUqYMJFHzJQslBs3bqTz58/LDyW2jyg/J0yYUH4p4mxuyZMnl3cBedxEiRJ7NK4ZTrYvzM13ZgMDg8wwbVPPceXKFVSvXj25htq1a9OKFStNvR5MnkT5m43iSUJTaSlUoyYbC6S9e/eIG07bRImS5uKLc5VwMdsX9S5evLiqFsqIEpbw62yVYwunmvuUjXAd7du3T+43488GfqrJa3SmjNHxEx9o74EPtHnnB3oqnIlJxIPQ8qX86K+TH+jGrX9/fvGCqF+PSJQ0iWPbZOHCheXNHeVgsTV58mS5zaBv375O4+rXr6/cV8ZZve1vri5atJB4/xxbFpMnT0GKlZE/hx8K3yc/lePX2bI7evQYue2gZMkSMhsk3+zka49Z1alTl/r37y/ns3jxImGHPCTP/dQNQEW8sSWX3wOV4/LlyzKBWcOGjWCbdDrCaGhVAhBvVo2sQdblqXjjO7pspeQ7dfwhwQcXv+a7ekFB84m/lHhyKJm8uJD3mDFjhEAJlKmZ+Wkh/1yqVGmxn+OufOrEZQvY4x8UFCTEXBlPhjXFuRBv+ocJ4k1/5lqPqLZ4a9++nfjSfEG+D7Flke3l4R385ISzFHbt2kVY4i6raqGEeHNevPX87h1tF6784OmRKHUqP/rtyAeq2fU9da3jR8UK+1Et8XMX8XO3jpHENgESFsGIr0hlz9v169dDZDjmWHMiroEDB6ki3jiLKffJ2xbYsqhYJflpGAs65XX+/OSnkEOHDhEicJu00bKFMjzxxn3yVgXFBhnRKhXxdvHixRBr5LFeCIXbp09fiDet37TQv+EJQLwZPkTmnqAn4o2tkqtWrRZ13b6Shbm5jhEf7KEfP368/DLCWbXUONgOM3LkSNkn3xVkyy5bjjjbJdsq2dJ248YN+WWIX+e7j8rBVsJmzZqrMQ1D9QHxpn84IN70Z671iGqLt9atWxPb5JYvX07x4ydwOH1+YsSuhb/+Oi5rNqphoYxIvPENrv3790krHe/hZFuhVQ5Xn7z9fe4DTZn1nhLEJ8qXy49Kl4xE6356T7v3f6Ac2fyoeBE/+SSuSLv3NCLAj/p0/7cwd0TMFPHGn0uVK1e2Nbt48RLNmzdX1htV48lb6PF5XxxbGfmzkJ1QoQ8uUfDzzz9LSyTvZ3vw4L600fJ5bJXkg58U2lsrw1sjZ5jkJ8pcy5VtmfbHtWvXae7cOdSkSVOIN6v8UWEdbhMwrHhbtixYPvnguzDlypUTdpOWYh9SPsv56N2OnElO9ES8sUibMGGCvJtnL9K0EG/r1/8kx+H9dFy8m/d4jRo1Ut4pLFOmjNwDx1ZJ9vjz6yzglIOfChYrVkz+k4vkmr2oPN8h5XpC/DfId/ezZ/cX9pfa1KVLV5NcdeadJmdYGzdurHzfS5MmDXXv3l3a3bhmFg5zElBDvPGTDyWhBF8j/PSCn0A4mw6en4SMHTtGvDflFGVRskqQ/D7lSlFv3nPEopGPuXPn0tWrV6lbt27SjcD2dX6PZIs5txszZrTYC5Zd/PexBAvb0TmLr1mP48ePE1vr+fMsUaJE8jsJJ9P4lH3+1OkPNGLCe/q/Sn5UrnQkOnT4PW0Ve9vs7ZH7D35wS7yFLhXA+/HYOVKhQnlhNazjNOaIbJOhO3BVvCnns1WS9/HykSdPXuFkKSm/x0V03Q4cOECWoGARyNsjlIOLj/NNAbZ4chbq+vUbOL1GNAQBKxIwrHjjL5Afsw41FR7zjwUa589fID8EcJiHgFnEG19vbNH85ptv5J3DSZMmSzsI381kAalYKBWbCFtKlIML0iq+/gYNGpg+UyVnmGzcuJG8A8r2mDlz5lDVql9rknLcPFeyPjPlmwV83XGSJv7Sz1+GOWkMEjbpw1+LUdQQb/yki/dY8TF8+HD5pN+R/cx+Lfx+xddVt25dxT7KFfJX7DRo1aq100vmAtyLFy+W7dmBwO+ZnEWYbXWcZIpdC2zjVMbq1aunLcnUsGHDRBbMdk6PZbSGffr0ln+HbNsbNGiwsKJ2dcifPyIEcmH9Izpy7ANV6/CeOgt7ZJf2kcS5H+2Raok3hXlkMRj/5+yhtXhTrhOez4gRw0VB+a02a2V4c4xIvA0ZMoT4Buvs2XPkUzlX1ugsC7QDATMRMKx4Y4i88blBg/rSP81/sIsXL0H9LTNdXWKunoo3TlzDGUeTJEliW/np02fo2rWrqtomuXNOjrJ9+zbx1OljoVO2oHB5A7ZQclps3kDNdzxDH3xXcN++vfLlzJmziCd3hU0WpZDTZfFWr15d2rBhg7ijnlCmgmbxhkM/AvZlA/hLe926H5OY4DAfAU/EG9/AnDFjuqxzlTz5x1qU7Az4VKr1TxFi69/p01wVmoif1nB5gfbt24v/ixSIDg7OOnvq1MlwW33xxRdyf7B9YW779gULFgrxJMXRWEb7fffu3WjixIlyWmPGjKUePXq4NEXb1jLfAAAgAElEQVQp0tq+p5EN/Kh3t4/2yOCV7+nXfR/IP6sflSgacWFu+4HUrvMWkXjjrJL8BJWvDc42ef/+PZllkp8A8w1M5XV+GszZcTnDaO7cueQ1wFlGr1y5LF/nz0LFKtm//3fyM+VT2SYjEm/8+o8//ijP5WzQOEDA1wlAvPn6FaDx+t0Rb/YZJtkqEfq4dOmy9NSruefNfgz+sjRixAjZf5kyZWWmrdGjR8k7zVayR0YUeog3jf8onOge4s0JSCZp4qp4u3v3jsywy08t2JrIT8DZEVCp0r97nNRYOu/z/eOPP4UFsKx8cuaKhVKN8c3Uhyfi7YTIKrlH7HPbtOMD1asmEpRU/yjeuvV9R1tFIpN1gZ8uzK2leFuwYL7M5MzbBexLO7BI5EzMSlZJZQ6chXL79u2yPdtluTg7Wxm//vrrEDeYlIQluXPntmWM5Guay1ew3TSibJMQb2b6q8BcvUkA4s2b9H1gbHfEm32GyZEjR4WhNHPmTJm0RC/xplgl2UKp1J1he+TkyVMsGUGIN++HFeLN+zFQawauijcutM3ZbXl/LbsO2LbMaffVtoqxjZLrW/JTFP6S7oqFUi02ZunHE/HWq/872iFE2uKpkSh9Oj+ZUdIo4o1vELCo4sLuV69esYWja9ducr8t27bZFqsc3J5LCLRp01o8XbsitrNkplmzZsmnqmyxVw5FvHGWU+X1zp27UM+ePaXdlB0t4R0Qb2b5i8A8vU3A0OKN7/zs2LFd2iV37/5VPoJv2LChLN6IwxwE3BFvXGiWC8vy/sYpU6baFspPwLgQ6YsXz+XvuNabfQFRtYicOnVKWiV5kzpn9VKskvy68iTw+vUbdP36NbmPw5kirWrNTet++C7snDmzRR2pvTJhBn+JZM4ozK01+ZD9Q7zpy1vL0RTxxvu2M2TI4HCoePHiyfcUFmtcW5KtaPyFV4uD32vZDscWOU4/zwd/xqqRkVKL+XqrT3fEGxfm5myT8eMR5c3pR2VKRRI10P5dwaHDojD3zQ8yC2WsWBGvjGupsQWRn3Lxf2x95etISehRs2ZN8eTrP7YOOKkMt797967ttdBt7EdTLJH8+aocnFwkosRb9u0TJEhgs0ra98nOGL6u+DuccuTOncfhtpfQ4o0FJa8latRoNlsmP/HDAQK+TsDQ4k0JDm9WHTRooPwnCnab65JVU7zxEzkWdbz/0V7UaUGEP8hGjhwhN9+zRYQzqdkXBN+wYb1IoDNfZh0rUqSoZRLpBAbOk5ld+UBhbi2uLOf65GQS69attRW15YQlfA3iMB8BRbylSJFC3ARJ4XAB/KW5b99+stix/cF2Ss4Cy08/OMshXw/2TzscdvyJBmyh3LRpk2xRtGgxKlGihOxfK9HoyVz1PJdFCD9pmj59htzXzJl327ZtQzVq1PzkNNgqyYW5N277aJWsXcNxGYCIOuS6o5y98/bt2+E24eRGSoZJzhPANxh/+eUX+eSWP8d432T37j1cKiGgJ2P7sTg7Jc+9fPnyxDcx2GbJ/0aGSW9FBOMalQDEm1EjY5F5mVW82VsleaP6vHnz5B1G5VCyU7LQyZQpk2UslBBvxvjD432fnDSAC9TznWbeU7Jo0eIQFiZjzBSzcERAEW+ckdaZepBcdDu8TJJsceS9b/ylvEiRItI2Hi+eKCKmwsEWSn5P44OzRHIRcO7f/oaVCsOYrgtOutKixTeyyDkLN75hx0+9HFlYI7JKugOAbyDy+wF/JoV3sIBXRPyAAf3lnjTOysjlblh4snuiSZMmphBvfGOCk6KwLZOLdGfMmJFmzpwlb9iqdaPCnRjgHBAwGgFTiDf2T3OWIi4azHdj+K5Mu3btKFWq1EbjifmEImBW8aYsQ0le8rEGXLkQqwudndLMFkpey7Rp00RGrx9kjbHmzZuLoqo1bAlacGHrTyB0we7ly1dAvOkfBo9HdHXPW3gDcjkStjayVY6Fw4MHD2U25vr1A6h06TIez9G+A7bl8dObkydPyULbvmyhZPs4l005f/68FMyc+fVT3zsUq2Q84exTCnN/yhKpauBEZ3379pHiLTg4mNKnzyBslnflv3lvmlnqj/LTTp4zWy7jx48vr29YJdW+UtCf2QmYQrwxZP6gatiwAXGxSN4PsGTJUof+abMHxwrzV0u8sY+fM2Bt3rxFFPvMrVvNIK4tw6nyP2WPtLdQsi2K75rnyZPnkwVcjRbb0ElKWKxWqVLVaNP0qflAvFkj3J6IN8UqyRn97Atzb9myWT5NGTBggHhK0VZ1UPz0g616XNTbly2Uroq3fcIqWZRLAjT8tySA6sH5RIehxZueY2MsEAAB/QhAvOnH2idHUku8zZw5Q9SMmyQ3L5coUVK3vRhsJeKab61bt5aF4rl4d+iD2/DGf25z4MBBcZcwjrRZqn1HXMsLCOJNS7ru9Q3x5h43o53liXjjzJNszeYsfWy5VLL/aS3euFg8P41nCyXb1/gGFu+z87UD4s3XIo71goA5CJhGvPEjdC6gzJkn9+zZLS0MnK4dmSeNfaG5I95evHghU1gfPXpM7L04LxeYLFky+cS1TJkymmSY/BTFly9fymsvbtx48roL71AslJyxjcUcZ6Zkm0p4Rb2NFjHOMMllEPbs2UOpU6eWlsnSpUvLwsA4vEeAnzZzja+5c+fJIrlFixaVT1m4JhcO8xDwRLxt3rxJvIc0lSVKWrduY1u01uJNGYjFy4EDXJz7NNWpU9unLJTLlgVLm+TevfuoQoXywqJaX96QC51IRmHFRbf3iCdv2b78WHTbP/u/Kfb1ulpDP3nj9xAurcNPT6tW/VqvaWAcEAABjQmYRrwpHOwzT3777bc0dOgwjRGhe08IuCPelPF4/9XcuXPlP6tUqaKbVdKT9fK5nFCAM1WyiGO7pdEtlPZJSli4zZsX6CkCnK8igXr16tLKlStlj/xlsm7deir2jq60JqCGeKtVqxZVrFjRNtVjx34XLoCJ4vNvqCa2SXsm9hbKkiVLyvczX8hCaV8eYOzYcbLuWXjHw4dEh4++p83bP4gyNkT9e0WixIn1F248N94byTfjKlSoIItu37lzR2w12EzVqlUT4ruu1pc6+gcBENCJAMSbTqB9dRhPxBtnnuInWnxwpim2DJnh4Kxg/LSOP0gnTJggi+yWKVPWsFOHeDNsaOTEIN6MHR9Hs1NDvLEbwT7DIWcgfPbsmbSSa7HnzX5NbKHk97M+fXrLLJS+YqF0VrwdOPSBanZ6Tx1r+1GntpEoWjQSiYUcXRXa/J6zhvLecC68fu3aVZnghsscZM6c2ScEtzZU0SsIGI+A6cSbknmSv3ByJiK+w9S2bVtknjTetSVn5Il4M+iSnJ4WWyd37dppWAslfyGbMWOGzDDJd9e5rhtnmCxevLjTa0RD7QlAvGnPWMsR3BVvCxbMl5lfs2TJEiY1PSfwmj9/AQ0bpv2TN4WNvYXy7ds3okTKlzLrMz/hseLhjHizt0qWLOZH2b/ykmqzCwBnmGS7NTtAEiVKJK2esWPHtmKIsCYQ8FkCphNvHCn+UtygQX1b5kneB5crVy6fDaKRF+7L4o3jYm+hLFWqlAwVp5r29/f3eth4bgEB9WQZjoT/3955gEdRvH/8TaHXhF6C9CooSFERUZpUETChBgRC7+UvNRQJVWwQQEpoUgIIovID6R3pHZEqKr2DBERS/vPOsccluSPXb3fvO89zD8lmdnb2M3PHfXe+877ZshEiTHp8SMx2YNy4cTJh98GDB8Xqx2DihN1sXUPRBgF7xRsHQPrzz0vSKhsQEGi8WU4ZsGfPbpFUe4PMQebOqLD8kGfixAky+XOePHlF8uQPqFKlSmKv7CvaGAwrenn//j1jYm7mzHutWaSaJuZmq+Tho/G0XiTh9rRV0opbQhUQAAGdEYB409mAqu12vF28mVooOegAl5YtW9KUKVM9PlQQbx4fAqs6wCukHHmyc+fOlD59epmwe8GChcj5ZhU9z1dytnjr3buXzDs2c+ZMypkzl1uTFysWSv5c48BhvXv3pv79+ycKpuJ54o71YN++fcbE3GXKvCryy86ViblNk0SzVbJJr3jqE+J5q6Rjd4uzQQAEtEhAk+KNI09yNELO9WaIPFlV5oAzfTKmxcHQY5+9XbwpY8qrxTxXudy4cVOmH+C9KvxU1xNl586dMsLkrl27xEpgkIwwyZE8EWHSE6OR8jVZvLVt25Z4TwsHr1i2bDnEW8rYVFHD2eKNV+Q4imB0dHSiFTl33yynR2F73m+//SZseZnl9gU9WCjZHhoa2kbu7+MIr5zwOmli7j17E+id7vE0IdSHPu3n6270uB4IgICXE9CkeFPGjCNtjRw5Qv6KyJPqnMkQb8nHhZN6c0THDz6oIx88eMJCiSAl6ny/WOoVR5DjpMknT56kggULivxbn1L58uWldQ1F3QT0Kt4U6tOmRRJHv9SDhZKF6C+//CICTX1BgYGBMlrwkCFDRPTInMZJdvp3seooxNv/NiVQq6Y+FNwU4k3d70D0DgT0RwDiTX9jqqo7gnhLPhwcRfPGjevySXWhQoU8YqGEeFPV2yTFznDaCY44yDm/OMdXWhHSjvM3Ic9liug8XkHv4o1tvdu3b6M+ffpIC2Xnzl08ztzeDnCeNE5P8+jRIxoxYiT17duX0qVLl2iVe9CIONp5kGjuV75UuJCPiOJo79VwHgiAAAjYR0DT4u3IkSMy2AKHZFciT3bt2hWRJ+2bCy45C+LNPFZOgcDW38OHj0ghxwl43WGh5C9aM2ZwhMmfZITJdu3ayQiTnMQVRf0ETCNPsp2rRYuW6u+0l/fQWeLt1KlTYp/bt5QrV24RsKa8TD+ilvQpbANnCyVHwbx+/YYccQ6GVLNmLU2Nfv/+/WT6BS5Jc7tduJhAkbPiKbMI3FihnA/VquErEnZr6vbQWRAAAZ0Q0LR44zHgvUS83+3w4cNyFYMTadaqVZuKFy+ukyHS9m1AvL18/AwWyjkyAW/Vqu/Qq6++6rIBv3z5b9q/f7/4UvI58aZ8DiPNOZvcGa3OZTfnJQ2PHTtWRp48dOiQjDwZHBwiI+36eCqxlJdwd+Q27RVv33zztdhPdprq1asrRdrff/8tLX1hYWGqfc9GRk6ldevWSVzVqr0rwtS/L+29ak/qzREm+WFwZOQ0GcmTH6SxM0JZ2War5J59CfTzhgRq3QxWSUfeDzgXBEDAcQK6Em9sJUqfPoO0b4SHhztOBy04TADi7eUIOQAFr7xxUlV++PDNN1McZm6pgYULF9DAgQNlwl22BUG8uQy1yxpm6+SKFctl5MkM4rE/R57kfF++vth34zLoDjZsr3jj9+mmTRuldY8jw1auXFnmZeSVN7WKIe4zf6ZxCQ8fThcuXJDRGjkqppoLP8zq1CmM/vrrLypdugxFRUXJCJMK50/D42j3YaI5X/hSkcKwSqp5LNE3EPAGApoXbxx5cvPmTbR48RL64YdVcswQvEQ9UxfiLeWxMLVQcoQzLu+8U1Xsb2qf8sk21ODokvylnwvbJDkpd82aNRFh0gaGaqjK4i00NNQYeTI6ehnEmxoGxkIf7BVv3NyVK5elHZE/I/Lly6cqq2RKyDlq4969e+ncubMyQqqaLZRJI0xybj3TyLt9PhX73IR4Wz3PlwoEeT4Rd0rs8XcQAAF9E9C8eFOGZ8mSxTRr1iwZtrh27doyDDvbiTJlEgZ1FI8RgHizHj1bKCMjI+UJbNupW7eunMPZsmW3vhEzNTnYxdGjR0XI68XSolm6dGlpt2OLMYr2CHCah/Hjx8nPOo48OWjQIGlNy507j/Zuxgt67Ih40zqe48ePy7n62muvq9ZCyfv0eIy++MIQYZIfaPED4OzZcxAn4z5yLJ7WiciSj58QjRzkKyJPQrxpfV6i/yCgdQK6EW/8ZPLEiRPS+nDp0iW5543DsXsiDLvWJ4Uz+w/xZj1Nthux7YjL4sWL5JcJTsTr6BNrtlzxKtvWrVvkCs23334r98xwFDUU7RHgaKVsn+TcfErkSbbTIfKkOsfSm8UbJ/V+/PgxDR8+jM6fPy8svvNUZ6E0RJicI/oZI6yeI2Ticf5s5M/KvfsTKKRPPPUUybh7dPYVx0kcV+c8Q69AAAS8h4BuxBsPmWnwEl5d4CTevHKB4jkCEG/2see5vG3bVvmFhx9AtGv3yYuGxBf32MjplHDyN+JvE349upJvWcuBTh4+fCgjv3EgAd7ntmDBAhEEob59HcNZqiHAY7ps2TLZH0SeVM2wJOuIN4s3Bcbu3btlkKTz58/Rs2exVLRoUdUk9TaNMDl58hcy3QGXpSviZZCS4kV86L1qPlT2Vay4qfddhp6BgHcR0JV442h648aNE196t8kVDA7OgMiTnp3QEG/28+egIuPGjRVfdp7RB8LKUy6BKJt4UUwMxQ0dS3ThqGzcZ+Rn5FupIpG/P/mWF5EHc+QwXpT3zPCXJo4weePGDfEwo7xMOlupUiX7O+ahM69cTaDjJxgAUb68PlSurHd/mVIiT7LjgC2wH38cjMiTHpqbL7ssxJuBjmKh5H3qefPmFav/9alixYpUoMArHhk1jjDJdvKpUyNlhEl+4MuBo2rUaGa0SornZDQCVkmPjA8uCgIgYJmArsRbfHy8tGhMnDhBWs44GluvXr1Fss0RmAMeIgDxZj/4hASxz0LMZ44SOXn0aJp281+qQQ9f0mBu8vtlIfnVqW2sw+f+3//9n7TZNWnSRH5RSZ8+vdB5/vZ3zENnLlkeT21GG8TbJ9VFktzpfh7qiTouy3ODg5dwSHMeU448OXfuPAQvUcfwGHsB8WZAwXtvec7y59q+fXtlVGiOpMk5Lj1R+KFW586dZITJkiVLGSNMHj2emoJ7G6yS3Tv5ivcWrJKeGB9cEwRAwEvEm3KbY8aMoZEjDYLtjTfekDm0unTpguTdHngnQLw5Dl1aKDespzOzo+jhqROUVjTZSbxKm2nab81a8qtfT648K8m4t2/fLmt26NBRBizRajl3PoG2bDeIt1t3EujCJcOdvPmGD3Xp6J0bUVi8caJ1Hm+O6IfIk+qb3RBvycfk+vVrIg3CJrnVIVOmzCLAWFfKkiWLWwePrZxt24YSR/itWrUqcYTJHXvy0a9inxuskm4dClwMBEDARgK6WnlT7p2DPXDkSY4idfv2bZk/S7FQFitWzEZEqO4IAYg3R+gZzk0QyXn/2befIiZOpGOHDlBqcayeeL0tXkkFnM+oMXStckU69IRXoCfKpNwZM2akUqVKUUhIc91EmNy4OZ7GTTUIuTJFiRrWMVgo8+axzk7JT//ZMnXz5g2rBoiTYPP+WbXlq9qxYwdNmDBeRp7kzzmOPMn9RORJq4bVLZUg3ixjnjYtUibHdreFkkXjunVrpUMnICBARpgcPnw4fTYxkHYLNzqnBAjK7922bLe8OXAREAABuwjoUrzxU+iTJ0/KyJPHjh0jTt7NX2DZQonk3XbNE7tPgnizG53xxNi58ykurD3FiCOx4vWPePUTryDx+spM84spkIbk9JcWJSUZN0cj5AiTbK/TQ+E8wOL2ZFn5Yzx1mmQQcu3fI4qalrKdkvcRduzI0Ro3WoWDI8/NmDGDPvywsVX13VWJ7yMm5pG4lzCZ0JnHd9q0adS0aTN3dQHXSYEAxJtlQGzn3rFjuwwSwlEe3WWhHDp0iIgwOVu8d2KEaAuX1+b3Tt9BCRBveEeDAAionoAuxRtT503R/GWGk3evXv2DHAhYKN0/HyHeHGceO2MmxYuIkkoRuoU2i9cx8bopXh3Fq4zJZeaKn7s//52TcX/yyScicE8t3SbjZjvl5m0G8Xb7bgJdvGS4+SovsVPy/lj+fOC0IhzOnEOY+/unEqzaJRuwgwcPyRx5HKVTreH4TSNPcmqJpk2byFyXvGKI4lkCEG8v569YKM+cOSMesmZyaRRKjt47a9ZM+dCGH+xy4QiTjT/qR9Nmx1NmkRb2NRFVsk5NX7Fn3rPzBlcHARAAAUsEdCvelBtOaqHkpLYcwIGjUMJC6fo3BsSb44zj1vyP4iI+J+GBFI2J8GfPyzrx7zzx+lS8RKxJuSp3XLyixWuuDq2S1pBkO+XYKQYh96pwSDf64IWd0lKob169atGihci6kFamF0latmzZLL7gTRZROodStWrVrOmG2+tERETQDz+solOnThHnC2zWrJlII7AcwUvcPhLJLwjxZt0gREZOlRZKDrzDwcYCAgKpXLlylCZNGusasKIW73MLDW0jH9rkypVLBCopSbXr9KDc+ZrR6l8SKPRjHwpu6p37Z63AhyogAAIqIaB78aZYKDmqFO9xgYXSvTMP4s0JvMWX8YRr1+hZc7EqtN8QfIQLr8CxlOMHxBw7ku2UHMiEa/iJfG5s8+N8bnqxSlpD0tROueqneAqbmHJ0ypTEG4shTuCbIUNGSpUqlTXdcHsdtn99//0KuWrBn3kQb24fAosXhHizbizYQrlz5w7q168f3b17VzploqKihMjKbV0DVtQyFW9vvvmWtE7OWlCIDv+WhmZN9qXChXyEWLSiIVQBARAAAQ8S0L14Y7Zsody4cYOwPi01WiiHDh1KEREiVxaKSwlAvDkJ74P79F+jYKJdm8w2uIuq0rwsrWiLiGZyjWv4p6ZalWtRUF7eGeed5cwloj3nDPce/A7Rsrnm98KlJN60Qu+PPy5KOxhbQO/du0fvvludwsLCqHLlylq5BV32E+LN+mFlCyXPYcN+3RgRCfKiTHHCVmBHy7Jl0TKp/Y4dO4XzpiZVrtKczl6qRblzZaByZXzog1qwSjrKGOeDAAi4h4BXiDcFpamFsnbt2uIpdXd67bXXRKhiYXRHcQkBiDcnYRUrK89EMu6EfYeIngmD5HML5QurZD2akrcXlRULTYFZ81FCUdNdcE7qgwaa+es20aVbzzuajujdgoafa1UlGv6pbeKNI1LyvhgOVsL2La0U0/1vixcvppYtW2ml67rsJ8SbfcPKyefHjRsr/o9+XSTOriH/rza1UMaLiJEJl/6UjfuWKkk+r7w82Xe/fn3pm2++kfW7dJ1Mld7sB6ukfUODs0AABDxMwKvEm6mFkj3vxYsXF5uXZ2vqi5mH54vNl4d4sxmZ+ROEkBCh0YRwExbKBw/pWYtPpIWSU3Z3Ea9tlIV8RQa4KfSMaoS0oNQzpjnpwtpqJvr7eOrxucEq2VgsOM2dahBsqcWKpKUABJZW3jipMEekTJ06jbRXaaVAvKlrpCDe7BsPfv+xHXjUqJF07ty5ZBbKZwMHUcKXkwzibep08u/R7aUXMhVvlOdzeqdCP/p2ki8VKQyrpH0jhLNAAAQ8RcCrxBtDPnv2LLVu3YoOHTokcjbllAEIWrVqJawZTT01Brq+LsSbC4ZX7MGKW7+BdkQvo/lLF9FOcYlL4pVDvDgFd9027SnVQo456R3l130JNGdhvLzZwACiwq8YgpQUF/nfar6fcvABRbydPv2b+Dx41wiNI1LyHhzee8NRa7VSOIrmypUrpX2So42y7YxDsPMKIor7CUC8Ocac96nt3btXWigbPRUPp2IND2cS1u8huv6bofFyb5JP+Vflj74tQ8ivTm3jRTnC5OzZs2jDhg1yP+gnn7Sn9Tvq0MNn5eiHucjn5tjo4GwQAAFPEPA68XblymUaMyaCtm/fRhyamEvLli2pe/cecgUOFkrnTkOIN+fy5Nb4ifTx48eFoFhEX31lyPT2irAMvVa4CH269ShVatNY9+Lt2vUEOnHS8CXupPj+9uMmw8+1xd42S/ZISyOhiLdDhw5SiRIljNXYNsnJfPkBj5bEG98ABy9p27at/LJavXp1Gjx4sEze7czgD86f2fpsEeLN8XFlC+XYsRFUdvd+Kn/lkmyQ36nmdvT6TppM/gMHyDr8fzwn4+ZosVevXqWy5d6hwUOW0OETeemxiPY0eogvZc+OdBqOjxBaAAEQcCcBrxNvnNOJExd//vkk4acfJ1kHBARIC+XMmbNgoXTy7IN4czJQ0dzDhw+lnW/r1m0iKtsdeYHQ0FD6avRnlKZVe0pdtJDuxdvSFfHUerRBsLV+m+ibCQZ7JEeKszU/kyLefH19xGfATNkO50fj4506dRK5pzJqWrxlzpxZhl6fMmWKavPUOf9dop4WId4cHwt+YPXo0T80atBgWiZW0VhuDRWvzmaaNhVvnIybI1b+888/8kFG2sxV6d/ci2lClyDqFmYIUIIFacfHBy2AAAi4l4DXiTcF7+HDh2nNmjW0cOECunjxIiyULpp3EG/OBbtz506aP38ebdu2TdiI/pAPHtq0aSOtce9VqCAjUvq8kl+X4o3tkVHfGeyRAVmJChV4YY+sVcN+S6ClPW9sm+QotX5+fjIvpJYKW8zYJjZ//nzat2+f7DonaoeF0v2jCPHmOPMEsectdvpM2rV2A506d0I2eEW8MotXmHhlMb2EsFBerFiW5vr70CYR2IlTBMmSMZgKFmpOYW1qU8O6mahcWay4OT4yaAEEQMATBLxWvMkPf2Gh/OyzMSJ08HajhZL3v7GFsmzZsrBQOmFGQrw5AaJogp88s3Vo0aLvElkl2Qo3dOgwqlSpkliSe6A78cb2yJOnDCtsJ04Rrd74wh4ZPsh89EhbieslVYC5+x4zZoxM3v3bb7/J5N28B47TpHDkPlgobZ0p9tWHeLOPm+lZcTt2UNx7zcQhEU72eZku/j0sXo3Eq4J4mVood4vfO4iXjEXpn1O8SlDREj2p1vvN6LOhsEo6PiJoAQRAwJMEvFq8KRbKyZM/F356Q843XskoVqwYolA6aVZCvDkHpCWr5Ndffy1sfZkMyaN1KN5M7ZGhYj/bV+Pst0daGgk9ize2iPP+t549e8rcWbBQOuf9aEsrEG+20DJf15x4eyyqskgbLF4ccdfUQplIvKV5iyjnDBrdrSj16Z5BfCOB64oAACAASURBVF7CKun4iKAFEAABTxLwavGmgDdnoeQn1BzIBFEoHZueEG+O8eOz2Sq5YMF8scdta3Kr5Hvvv7iADsXbmbMJtGmrYbWtRDFh/XPAHumN4o3v+eLFCzLxsamFkvNcsoWyc+cuiELp+Fv0pS1AvDkOOOHaNYr7ZQPFz5wnU6Qo5br4YZN4vSZeZZ8f/F78u1y8dolXzeBgKlCwOX3xcy36vGsmGtDbfnu143eBFkAABEDAOQQg3p5ztBSFskePnrBQOjDXIN7sh/cyq+SwYcOpYsWKiRvXoXizn97Lz+RIkhyx89atm8Qr8OPHjxerl6lp0KBP5YlsKWTrtFK4PttWb968YTyWtI6r+uqsdpNaKJs2bUbLli2Te/pQXEcA4s15bJ9170UJ30aabfCBOHqCqlKkyHe5Op1hP1vX9p2pYuVmtGptArUL8aHgphBvzhsNtAQCIOApAhBvz8lbslByFMpvv50p94ig2E4A4s12ZsoZDx48oLCwjsmjSor0AJkyZTZYJU0LxJvVsA2RJMPkihQXTgbMESbTp08vf2/QoKGwTs8ytsefDzwWHAREKfXrN9BU8u6kFkqIN6uni0MVId4cwpfo5JeJt/1UidoHzaYL/rlfnJMqA71bIh1NG29Ixp02rfP6gpZAAARAwFMEIN6SkEcUSudORYg3+3i+NKqkqVUS4s0uwBxJcsOG9dKGaq4ULVqUateuI/+0X0SsmzdvrsilV5CyZMlMvArHCbB5b+ySJUvtur6nTnoRhXIB3bt3V+SAe0+knehIlStX9lSXdH9diDfnDXGcsJAnHDNEm4xfvIJo3zb5s/hJvIJoa6bqVPtJeioQW5C+LtSZGr+Vldp87EN1axvSAqCAAAiAgB4IQLyZGUVzUSh5/1vPnr3o1VdfRRRKG2Y+xJsNsERVxSrJCbi//PJLebJMwC1WftkqKaNKWipYebMNtpW1lyxZLPaGdRb7DhfIPGks/EaPHkX+/qkoPDzcylbUVa1161a0dKlBeHL0yZCQ5tImyquPKM4lAPHmXJ5Ka7HfTKV7M+bRybNHaKo4uPr5HzhwSSVhn1xZcwl90jU/hTSDVdI1I4BWQQAEPEUA4s0MeVgonTcdId5sY2mzVdK0eYg322BbWTupeOPTOOkvCx1O4K3FYiresmXLRg0bNhQW0DlCkPpr8XZU3WeINxcNj7A6/7ptK3Xr3p3++vtvuv/8MoHi3zferEZfzV5KhYvkg1XSRfjRLAiAgOcIQLy9hD1bKH/++Wf67ruFxkTeHIUye/bs8tWpUycKCirgudHTwJUh3lIeJA7hPnv2LJlrkHNxmUaVbN26NTVt2pTes2SVhHhLGbCDNcyJNweb9PjpnHz8++9Xys+2f//9l4oXLyHmmMFC+dLVXY/3XHsdgHhzzZgtX76MoqOXiTytO+ju3TtUXFymjXhlaRZM+Vu1oDp1PhBWSXglXUMfrYIACHiSAMRbCvQVC+X27dvp7NkzxtpsZRs8eLDYF1ObChcu4skxVPW1Id5ePjxXr16hgwcP0rhx4+TeKqVYbZWEeHP5/E8q3njP28mTJ2WI/TJlyrj8+q66AH/pjYgYIx8a/C1WLrgMGzZMWijZHg4LpXPIQ7w5h6PSCrsT+P33lQjctGrVSnm4pHi9nzk7DS9cjHIO7kd+IcHOvShaAwEQAAEVEYB4S2Ew2EL5zz8P6YsvvjAm8uZTOCpdpkyZqFu37jRixAgVDam6ugLx9vLx4PxtvOeIIwGyFU8poaGhcs9b5sxZkkeVtNQkbJMumfxJxZsSeZJTC5hGpHTJxV3YKK/yPhRzpmvXbsYvwewoqF+/Ps2ZEwULpZPYQ7w5CeTzZvbu3SvmbFfxwOEvEXTnnjw6Sry6lalEAYuF9VcEEqJ06Zx7UbQGAiAAAioiAPFm5WAcOnSI9u79VdbevHkzrV5t2B7Nubbq1asn7UYFCrxiZWveUw3izfxYK1ZJtuVu2bJFVmJLbrBIKsuldOnS9P77NWybKBBvtvGysvbZs2dFSoENdPnyZSF2Hsqz8ucPojfeqCCtWVovHHVz5cpVJhbK4mLuvU/t23dAFEonDC7EmxMgPm+CrZLLli2n7du3CavkXWmVbC1e9T/6mF4XVkm/enUJYSWdxxstgQAIqJMAxJsd48KRAGfMmCFslGfp9u3bMhrgoEGDxBe5OrBQJuEJ8ZZ8giW1SnLQC84n2LJlKxowYIAdM/L5KRBv9rNL4UwlwuTu3XuEXdKHhg8Pl2JbL4UtlGPHRtDvv/9utFDyinDz5i1goXRwkCHeHAQoTk/RKjmkP/kFf+z4hdACCIAACGiAAMSbHYPEqybsue/WrSsdOXJEWigzZ84sLZRaDR1uBwarToF4S45p4cIFRqskr+TkypWLpkyZQnXr1nMsDQXEm1Vz0t5KPFZPn/4rT2c7a5o0aextSnXnPX361Gih/OGHVbJ/OXLkkBbKWbNmW2/dVd2deb5DEG+OjwFbJfn/27/+SmyV7PpqZQr8bhb5i4dfsEo6zhktgAAIaIMAxJud48Rf5Pg/5ejo6EQWSiVSW61atahJk6Z2tq6f0yDeDGPJSbejow15tThAhKlVsk2bNkK41ZVWPIcKxJtD+HAyycTlsFA6dyZAvDnGM6lVskSJEtS2bTuqvXYjlYt5Sql+Xk4++fI5dhGcDQIgAAIaIgDx5uBgsYVy+vTpdO7cOWmhVAon9e7Vq7eMRseBTby1eLt446TbvErLIdk5OppSFKtkixYtaeDAgc6ZHhBvzuHo5a0oUSjZQsn7/LggCqX9kwLizT52Zq2SJUtSzUqVKbxZMwrYvoso5jH5R4wiHxFoBwUEQAAEvIUAxJuDI61YKLt370acF04pgYGBVExEvZox41t6/fXXHbyKdk/3dvF2//49mQ+QU02Yinu2Sk6dOpU++KCu88Q9xJt23ygq6rlioWQbuBKKHRZK+wcI4s0+dr/++ivx/6umVskxYyKoa4UKlOGT/uQ/MIz8O3UQHuYsJDai2ncRnAUCIAACGiQA8eaEQeMnhOvX/0I3b96kO3fu0qJF39GFCxfknhFOfMv/ZsuWzSsjUnqjeFMiSfJq7L//PhVJt7fQH3/8QSzoW7VqJYOT8H4pjlLqsFXSdP5CvDnh3YwmFAJsoeRE3pwqgec0J/KuUcMQhRKJvK2fJxBv1rNSapqzSoaGtqW6YqWtbMwT8gnKR741a5CvFz8YtZ0qzgABENALAYg3J4/ktWtXadSo0XKlJWlSb45IyX79tGnTyQhu3mCn9Bbx9uzZMzp16pTIO3RX5msbO3YsHThwwDi7OCJpuXLlRECbETK9hEsKxJtLsHpzo5YslDVqGNJYcEqLXLlyezOiFO8d4i1FRLICR2++csVg0502bfqLBNywSloHELVAAAS8hgDEm5OHmhP4Pnhwn77++muKiIgwtq5EpPT396d8YnO1t9gpvUW8sWjr3Lkz7du3jzisPCfdVnKC8SRo27YtTZ48WUYpTJ06tZNn3fPmIN5cw9WLW7VkoVQibXIi+Y8/NuQmRDFPAOLNupkxdOgQ4VpZJCvHxMQYE3CzVbKLsEpm7DCA/Pt3JP+w9kRZssIqaR1W1AIBENAhAYg3Fw0qJ/Xes2e3bH3r1q3GiJT8O9soOQmuYqds3769yBVX0EU98WyzehZv/AUjKmqODFbD9sgtWzZLe6RSqlWrJr7YGnIP8UqrzUm3bR06iDdbiaG+lQTYFs5RKBULpXIa57Zs2rSpsISHkZ+fn5WteVc1iLeXjzd/fs6bN1dsPVgvU+8ohV0qbdqEUr3HT6js43/JJ39eWCW9662DuwUBELBAAOLNDVODv/BERUXJK125ctWsnVKvCb71Kt7YHsu2SHP2yMKFC8uxrlevvvMiSVozTyHerKGEOnYSUCyU7C7gvb2//36a/vvvP5msfPjw4dIWnDNnLjtb1+9pEG+Wx5aF27p1a2nixIl07do1MX9yykBf7E4oLVKnhIuHXwFbdxiiSo4djaiS+n2b4M5AAARsIADxZgMse6vyCs2jR//I0yMjI+UXfqWwnTJLlizUpUtXGjFihL2XUO15ehVvCxbMl19YeX9bUnskfxHhki6dIXm72wrEm9tQe+OF2ELJlvCEhATxhXsd9enTR85//vzi/buwUJqfFRBvlt8tw4YNFatu8+j+/fvCvfAvvfXWW3JLQa5cOcnv4CHKGPZ/0irp1/ET8skaAKukN37w4J5BAASSEYB4c/OksGSn5OhtlStXlr2pWbMmffRREzf3zDWX05N440TbHAWNy+nTpxMl2m4m8g5xcYs90tJQQby5ZhKj1WQELl68QL/88ovIX/id3OfJhd0DTZo0obCwTrBQmhCDeEv+BjJnlQwODqaQkBDpWEj98xpK2LsfVkl89oAACICAGQIQbx6cFmynjIycRufPJ0/wzcEvuAQFBVHhwkU82EvHLq118cb2SI6CxuWnn35KlGibVxuKFi1KLVu2cq89EuLNsUmJs51G4LPPPpNRATmht2KhDA8PJw7MlC1bdipTpgz5+Pg47XpabAjizTBqnFLnt99+E/PkKR07dowmTJhA169fl1ZJ/hzt168fNWtm2CP8rHsvSth3hFL9vJx88ubV4rCjzyAAAiDgMgIQby5Dm3LDbKfk8PI9enQnXpFTSmBgNsqQIb38tUOHjjRy5MiUG1NpDa2Lt/nz5xn5s63n1q1bRtK5c+emb775Ribadqs9EuJNpbPd+7rFX8h/+GFVMgslCzZOJzBr1mxKlSqV94ExuWOINwMMJen23bt3iVOrKFbJt99+m6ZPnyEFHG8jgHjz6rcLbh4EQMAKAhBvVkByZRXeL8Ubtm/cuEF3796jxYsXyQTfSmE7ZZUqVeSvHKGySZOmruyO09vWonhje+SKFcslC35SvGXLFiMXFtatWrWUXzTSpk1L9evXd26ibUdGALZJR+jhXDsJsIWS98BxmHfFQslNcVLvmiKRcrt2nxgt4XZeQtOnQbyRtJsvX76Ctm3bKv6fu2scT47G27x5c2mVZOGWcP48xc4Swb3EZ6vvq6XJr0F9Ek8yNT3+6DwIgAAIOJsAxJuziTrQ3vXr18QqzygRev6sDD2f1E7ZokULEdikS7IrqNlaqWbxdvXqFRnmP2mxZI9UAjOMGDGS3njjDQdG2kWnQry5CCyatYYAWyj5yzmX8+JL+OXLhoTLw4YNo1q1asmfS5Uq5XURKb1VvPFnK3/Gcpk6NdKYdJtTAOTJk0ce79Gjh9EqycItbuduil8UTX5dOpBfCPIHWvO+Qx0QAAHvIwDxpqIx5xDc9+/fk5aSv/7626ydMmPG5E8h27fvoFprpZrFG+cWGj16dLIZ8OTJk0T2SP6iwfbId955h3x9fSmriHrmskTbjsxHiDdH6OFcBwmwhfLJk8eylV69eom8cCvlz7yniVepuXCiem9L6u2t4o2Tbi9ZskSO+6NHj4wrbpx0u2PHDvJ45sxZXlglPx1CCQePkP83k8m3iEi38txC6eC0xOkgAAIgoDsCEG8qHVK2U65d+z9pp7x37578T5CfZpsrbK188803jX8KCAggtST+Vot44y8Pc+dGJbKk8n5DU0ukKVvFHlmkSBER8j+duuyRluYsxJtK383e1y1LSb0/+OADYacsLoG0bt3GK+yU3iTe2B65e/duOb67du1KlnSbx7xhw4b0+uuvG98U0io5ey5RmjQGq2TDBhBu3veRgTsGARCwgQDEmw2wPFVVsVOePXsmURfYWnnhwnm6fft2ouNsoxw6dKiwKJU2Hg8Kyk+FChmSR7uzeEq8cZTIc+deiF1e0YyIiKCDBw8mun2OGMkCjS2RpoUDkLCFtUKFCu7E5di1IN4c44eznUqA947yynZcXKx8AMVRWznoj1LYTlm7dh35a8mSJXRrp9S7eOOHilevXpXjyA4FDmCjFF515c9XdipwGhW21gYEBBr/brRKfreU/LqKfG6wSjr1PYjGQAAE9EkA4k0D48p2ynv3DBG6TMvff1+mnj17JBMkvPE7a9asiaK8cdCAUaNGuf1uPSXe2BLJXxSUEh8fL0NVmybU5r8plsiqVasmYsP2SP6SoUp7pKVRhHhz+/zGBS0TYKHGD004qTfnhONQ8Kbvv1y5chntlJMmTaLg4BBd4tS7eGN75NKlS+XYcdJ204Ak/LnK6XBy5swhP0v5M5U/W5XybNBQSjh0lPy/nCCskiIlDoKT6PI9gJsCARBwLgGIN+fydGtr/B8lWys5V45Stm/fQatX/5CsHxUrVqS33nrLeJzFHVsrCxYs5NI+u0O8MQe2RF68eNF4L5YskdWrVxcJ0D8y1tOMJdKaUYJ4s4YS6niAAEekXLt2rViFixPpUX6j6Oilch+UUthOyQm+ef+u3lIL6FW8cUASTqXCwvzIkSPGsSxZsqS0xPL+7Hz58gnLeQPjvjalEqySHngT4pIgAAK6IQDxppuhNNzI0qVLaObMmca7evr0P7PWyvz588socKVLl7GKQBqxH4H/U7Y1n5kj4o2tj+fPv0ibYKmjvCo5ZsyYRLnyuK5iiTTtc6NGH9KAAQOsumfNVYJ409yQeWOHeS8UuwBiYw25vhQ7ZbVq1WjEiBFihSYNBQYGysiUpqs0WmWlJ/HG7oXTp09LF8iRI4cTJdpmeyQL77JlyyazR5qOXYJIhRO3YxfFL1xCft3CYJXU6sRGv0EABDxGAOLNY+hdc2FO/P1QfIlXyuXLV6S18sCBA4kuyNZK3udlrS2Q9y6w/YWDo9hSHBFvUVFz5D61lIolS2TevHnlHgxOAquUDBky2ixAU7q+av4O8aaaoUBHLBMwtVOuX79e2ilZFLAbgB+0cIJvXiGfOXOWiGGRRvMo9STeOBgJ/3/Covu///6Texl5PDkSL///kCNHdrP2SNNBNFolv5pEvoWF8wNWSc3PcdwACICAewlAvLmXt9uvplgrr127Zrz2jh07zVorX9a5bNmyiYS7NSl37tw23cOJEyfo2LHjMlmvktvH2gb43K1bDXmjrCn8ha9x48bGqixQVZVE25qbsKaO+LIUO1sksg0MIP/WrV6cAfFmDT3UUREBxU65ePHiJAm+i8vccP7+/sIdUFrTdkqtizdeGV2wYD7xg8ErV67ICL0s2pTCibZDQkLM2iNNp5q0Ss6ZR0LdkU+ZUuTfqCGiSqrovYiugAAIaIcAxJt2xsppPU1qrUypYd5Tx/+Bu6vw03e24LDt0Zby4YeNqX///racos26D8RT70bB5FOoAKVaIEScUlIQbwliHNmy5Fu6FJFJxDdtQkCv9USAbc+bN2+St8R7V5UE3/w72ynDw8PFKlxaTdoptSjektojx48fL9PWKIUTbXPAGS6c069Zs49TnI5x27ZRXI2m5PvFSPLv1yfF+qgAAiAAAiBgngDEmxfODA4UYGqtTAnBrFmzxR6G5MmsUzrP3r/zJvcpU6ZQlSpVbGqCLZFJQ/7b1IBWKtsp3mIXLab4tqPIb+NM8hMroSggoBYCHJXy8WNDgu8+ffoYE3zz72ynVN7XvLr+7bczjVEq1dL/l/VDi+LNkj1SuU9OtN2+/Sfy1yxZsgrnY4YUhwLiLUVEqAACIAACVhGAeLMKk3dXOnz4MO3Ysd0uCLt27RbJWndSixYtRGTLgla1wV8EGjRoQHnz5rOqvtdVEntN4n5eQ/HHT5II2Ud+HdsbVtNSWHmLnTmb4rt1Jr+f/0d+Dep7HTbcsDYIcIJvDorBZdmy5cJOudfYcU7wrdgpTe+Gg5twpEpr9/C6k4SaxZupJdKUCe+V3ro1sT0yODjYGLH4/fdr0GuvvWY1xlgxjgn7D5JPrpzkW7sm+ZYvb/W5qAgCIAACIJCYAMQbZoRLCTgSsMSlHdNB47HfzqL47l3Ib81a8qtfz7J4E+HZ40//TvEipHf8j+vIf9IY8jVJG6EDFLgFnRJgO+WmTRvl3f3xxx+J7JSmt8wBM0aOHCmtlUopXryYKhJ/q0m8cUJt09Qyhw8fonHjxtHNmzfNzqDixdkemVP+jVdEmzZtZttMEw+U+LMnLnqFeNAUQ/4TI8gnMJttbaA2CIAACIBAIgIQb5gQLiUA8eY6vFaLN7E691/7zuSTJTP5jw4nHxF8RvjOXNcxtAwCTiLAaUAUOyVHpfz+++/NtqxYKzlSpVJ4n1bz5i2c1BP7m1GTeBsyZLBYzVxmvBmOGMlJtTlipLkSETGW2rVrK/+UNWuAVfZI03bi9+yh2FZdybdnO/IT7cjPHpMk3fZTxZkgAAIg4L0EIN68d+zdcucQb67DbLV4Yztl4xDyCcpHqRbOdV2H0DIIuJAAiyDFTml6meXLVySyVip/48TfnJtSKfyzJ6yVnhJvZ86coYULFxjFL3PYvn07HT16NNkosSXyzTffTHa8Ro2aFu2RCSJJd2zUfPKt/wH5vftusnPjxLjE7zsAq6QL3xNoGgRAwDsJQLx557i77a4h3lyH2hrxliAixMWfOEnx878jKl6UUo0Y7roOoWUQ8AABtlZu3LjBeGWOlHhOCIukq0lVq1aVycHTpk1nrFusWFGXWyvdJd7YEmkaEfLQoYNmLZGcs7NQocIioba/kUPfvn1ttkTGbd5CcbWbke9Xn5F/n14vRh5WSQ+8C3BJEAABbyIA8eZNo+2Be4V4cx10a8Rb7OIlFB86kvyix5FfnVrC+xTgug6hZRDwAAFTayVfftOmTTJliGkuMj7uKWulu8Tb4MGDaPny5cYRsGSJ5NQLnFA7UOSJVIo9lkhL4k1aJVt0Id/en8Aq6YH3Ay4JAiCgfwIQb/ofY4/eIcSb6/DHHz8ugpBsoIRbt8mn/Gvk37C+If/bK/mN9khEmHQdf7SsTgJ//HGR1qxZQ8+exRo7uGKFZWslR6q0toSENDdrL3zZ+Y6IN8X6+OTJkxS7uE3kUbNkiaxS5YUlMigoPzVq9KFD6RakJZKjR+bITr7ioZASPdLS8RQ7jwogAAIgAAJWE4B4sxoVKtpDAOLNHmo2nMM53z4U+9kKBlGqqV++EG/zRFoARJi0ASSq6plAREQEbdiw3niLlqyVKTEYMmQI1a/fIKVqif6+f/8+aV8MCwujhg0b2XTugQP75bm3b9+26jy2RBYuXIT8/f2M9TnQS5MmTa0639pKzzp3p4RjpyjVT8vFnjaRrFuxSi4VK38xjynVpLFEAYHWNod6IAACIAACNhCAeLMBFqraTgDizXZmNp1hSbxNn4IIkzaBRGU9E2BrZUxMjPEWN2/eTAMGDJCRFm0puXPnpnTpXuyZs+bcp0+fyuuwbdPecy1Fg0x6fcUSGRCQ1finACGirEmibc29KHWSirf43bsptnU38u0lrJKhbcgne3ZElbQFKOqCAAiAgA0EIN5sgIWqthOAeLOdmU1nWBJvkV8ls1Da1C4qg4COCZizVr7sdtm+uHz5MuIVO3eVkJAQqly5ik2XK1AgSK7upXVRKhAlwqTIhk4+ZUqRf6OGROnTk6X9bwkiiIqMSFmvjtmIlDbdHCqDAAiAAAhIAhBvmAguJQDx5lK8IvHtI3o2eJi8iG+jBhQ3QESTzJuT/D7tR/HzFhoiTI4Md3En0DwI6JvAHhGEY9SokWTN3rOkJB4+fEgXLlygoKAgys4rUlYWXhn86KMmVtZ2TzWDSGsiIkxGGCNMJly8SHE7dlF81ELy69WF/OrWofjfz5DYdEjx5y7I4749O5N/8xD3dBJXAQEQAAGdE4B40/kAe/r2IN5cPALx8ZQg9sPERS+j+L5inwndMFwwc3HynTmG/GrXJJ9AkRgXBQRAwG4CbFu8c+c2xYv3m62FA4mwEBs48P+oZUvrk4az3TFjxoy2Xs6l9c2Jt2eDhlLC0RPkP3EM+RYtShxIiS2U9OctoloVDMeLFSNxMy7tGxoHARAAAW8hAPHmLSPtofuEeHMPeCVtgOnV/NasJb/69dzTAVwFBEDALAFHok2qDampePNrUI9i5y4gER1FvESAlLv3SKhbYkslZQ8kH19xTES29G/8obRWooAACIAACDiHAMSbcziiFQsEIN7cMzXiflhNcUMjiM4cEhcUwQreKk/+k8eS71tvuacDuAoIgICuxZvRHjlnAfk0rEM+ufNQfJKf6cEj8qlSnlJ9Pg7RJvF+AAEQAAEXEYB4cxFYNGsgAPHmppkgIunFX/qTYtt3JcqXW6YNkBHfXBS4wE13hcuAgOYJ6GXlzWiPnBRBcbOiKOH8H9ISGTd7rvFnn0CRHiBNGpH/LQeiTWp+5uIGQAAE1EoA4k2tI6OTfkG8uXEgRa6lpEm63Xh1XAoEQMAMAd2It07dKCHqR/Lp8CElbP5V7mnjnylvHvIpVQL2SMx+EAABEHATAYg3N4H21stAvLlx5MXq27NPhxDlzIEIk27EjkuBwMsIaF68cQLuM2cpdrSwQq5d/fxWg4jK5JE/+4UPJL+QYEwCEAABEAABNxGAeHMTaG+9DMSbG0eeI0/eEhHeUvkjwqQbseNSIKBn8SYTcLfpLlbajhtv0yd8NPl3aCd/98kmotkikiTeBCAAAiDgNgIQb25D7Z0XgnjzznHHXYMACBgIaH3lLW7TZoqr05Sofg3yrfa2vCdfkYLEt0IFDDEIgAAIgIAHCEC8eQC6N10S4s2bRhv3CgIgkJSA1sVb/IEDFDtwGPn16KRJe+Q///xD586do7xib15uESETBQRAAAS0TgDiTesjqPL+Q7ypfIDQPRAAAZcS0Lp4I5GgPOH2bfLJKlKQaNAeeUCIzz59+lDHjh3EK8ylY43GQQAEQMAdBCDe3EHZi68B8eacwf9XfIFauHABBQQEUKNGH8qf+WlyWpEKoHXrNlSyZEnxHctQh4+nEeG627QJlcdNy9OnT2Wds2fPmu1YxYoVqXnzFs7p/rjmRQAADq1JREFUNFoBARDQvG1S60N45cpl+vnnn6lixUriVVHrt4P+gwAIgABBvGESuJQAxJvjeG/duknHjx+nESNGUK5cueRT5Hnz5gkBxuItDbVt25ZKlSotxNsTmj9/Pp0RkeGU49WrV6dChQrLTnA7p0//Ls6dK+so5e7dO3T58mUqWLCgFG7h4eGOdxotgAAISAKaX3nDOFok8Ndff9K1a9fl3195pQBsmZgrIAACbiEA8eYWzN57EYg3x8d+6dIlUlDdvXuX/Pz8KF++fDRs2DCqXLkyPXoUQ6NHj6KjR49SunTpaPjw4fJ4TMxjGjVqpBBuhWjixEmyE9HRS2n8+PHy3CpVqhg7tmzZcpo0aRJNnvy5WNVrRNmyieTeKCAAAk4hAPHmFIyqbCQiIkI6GbgMHDiQOnfuosp+olMgAAL6IgDxpq/xVN3dQLw5PiTHjh2jH3/8kZYvX0ZZsmShkJAQaty4sVgpK0QPHjygli1b0P37D8Sq2YvjDx8+pBYtmotN+vlozpw5shNz5symoUOH0oIFC6hevfrGjkVFzaHBgwfL4/XrN3C8w2gBBEDASADiTX+TgVfcFi78juLi4uRDMy4xMY/Eg69s0gmRNWuA/m4adwQCIKAaAhBvqhkKfXYE4s0548oijcVYUFABmjVrlrFRRbzly5efZs+ebTwO8eYc7mgFBBwl4A3iTYnomD9/PiFm0st9t8+ePaNMmTJRsWLFKFWqVKTUSXrclK9pHXPcCxZ8RVjHcyf7k6l9kf9oet1Hjx7J/uTJkzuRrdH0eMaMmWSd//77T8RkySj7nDp1arNDz9f69ddfpUW9TZs2cs8xl4EDB8jjS5cupQIFXnF02uB8EAABELBIAOINk8OlBCDenIMX4s05HNEKCLibgDeINxYt/fr1pe7du1Px4iWob98+dO/ePaogcsFNnTqVsmfPQfv27ZPH2f5dvnx5ioyMlMdNy/79++WeXt6Ha66wQ6B9+w7J/jR69GhasmSx8Xi5cuVk+yz0Dh48KNrsTR06JI42yce5P+3bt6fXXy8v69y6dYvKluVzp1rcv8ZWyX379gqLerjYa1yKMmfODPHm7jcVrgcCXk4A4s3LJ4Crbx/izTmEnSHeOOjJunXrxBPwh/IJs1I4YmVgYKC0YirBTZzTa7QCAiCgd/G2atVKWrFiBW3cuJHeeOMNGdExc+Ys5OPjI1ff+PMmPj5err5lypSZfH19jccbNmxE77zzjpwkP/ywSgotpY4yc/73vzV0/fp1YQtvLj6jPpLXUMqlS3/Qd98tku0r9sV169bK33kFjNMEcN/Wr18vLeP9+vWXp/70E9vQl9OGDRuoXLnXxD7hSrLP3LfY2Fh6+PCBsJbXo+rV30s2gXmFbe/evbJ9dkIoBStveK+DAAi4iwDEm7tIe+l1IN6cM/DOEG+3b9+S0Sbnzo2i338/Y+wYf0nhSJYoIAACziegd/E2ceJEWrx4Ef35558yGm6NGjVFYKRxIq1JIG3btpXatWsnU5e8/34NeTwwMBtt375N7g0bMGAA9e7dR0Lv3bsXnThxQooi02TavCLG+375eJ48eRMN0M6dO0U7oXK1rm/ffvJvX3zxhficOy2vxfvSOKAI923kyJFG8fbll1+KPb7z5fHs2bPTe++9R+PGjaOcOXPRnj17KDS0jVhF7CH7l7SwSNu8eTN99tlniSycU6dOoYsXL8I26fy3EFoEARBIQgDiDVPCpQQg3pyD1xnibdmyaBltcsiQIYmiTfIej6T2Jef0Gq2AAAjoXbzduXNbrmBxtMUuXbqKiIudKEeOnDIyriLeOnToKP7W2XjcleKNLZecz5KF2IMH92nLli2ybyzwlJU3rrN161YpzlhEduvWTdbnPlsj3qKioqRbwd/f3zjB79+/T0WLFoV4w1seBEDA5QQg3lyO2LsvAPHm+PjzXhFOF8CWRxZaDRs2pFatWosIk/fl8V9++YUyZMhADRo0kJvnWejx/g8+nj59emP9Xbt2yi8xderUkSkETAtvzleSfTveY7QAAiCgENC7eOP73Lp1i1xh+/TTT6lnz17GwVfEG3/u9OrV23jcWeLt8uW/ZSTemzdvijyX/8r22YpZrVo147V27dolV+d69eplFG/8x927d8vjPXr0pP79DXZKLpbEGwcqYYsm2yrZap60rF//ixSNCFiC9z4IgICrCUC8uZqwl7cP8eb4BOC9IJyHTSks1MaMiaAbN66LHG4TjcdZqEVEjE12nC1LvCmfxV50dLTZDrF44zpsH+IUBCggAALOIQDx1k4+NEpJvPFn3NGjR6hjx45y/5lSVqxYLgKY3KMJE8ZbdAhMnjyZVq78Xp7y0UdN6MMPP5SrYLzPzlnijYOysJ2ya9du8n6UEhMTQ+fPn5d5NHlvHrsbTG2fzplFaAUEQAAEXhCAeMNscCkBiDfH8XL4bN6vphTeVM8WH34CbM1xTtgdETFG5iAy/dJh2rPHj5/IOgUKFDAm9Xa852gBBEAA4s068cb2SxZaLH74QZNSOnXqLJwGLY22RnMzis/l9Chcpk+fLveycZRLjjbpavF2+PBhGWmTc2SyuOPPZlM7Jd4BIAACIOBsAhBvziaK9hIRgHjz/ITgLzWcyJs3+ysJu5P2inMecR653LlzizpRnu80egACOiEA8WadePvxx9UyOmSGDBllpEql1KpVS0awNFc42uSiRYulY0CJWslCigUV2xfz5s3ncvHGK3Jsv+T9fpYejulkKuM2QAAEVEIA4k0lA6HXbkC8eX5k2dYzZMhg+YWoTZtQsx3ivRpRUXNkqgBEnvT8mKEH+iGgd/HGe8HWrl0roy+GhobKPGxsWbx69Yrcp8vHW7duLfKsdaQiRYrQtWtX5X5czs1menzAgP4yyfWYMewSyJ5oAvBeX8UGafoHJdpks2bNRCqBFvJP33+/gu7cuSujTfI+OE4TwNcKCQmhsLBOsp3r16/JICt8PDg4WB7nvrEVnVMejBo1ij7++GPiVT8+zrZyS7ZJiDf9vFdxJyCgFQIQb1oZKY32E+LN8wPHOY9u3rwh9oSsFFaiSLMd4g34gwcPopo1a8qIcCggAALOIaB38TZy5AgRjn+hTHCdNWtWevfdd6VlkV8LFiwwHucgInwsMnKaDNPP9bNkySLrT5kyRYq2RYsWydD9vr5+ieC//vprsg5bEs2JN85byfnhuPCeudatW0nLJIf/59Qod+7cEX/PRFWrVpV9mDVrdqLjb7/9tjw+e/acZMf5uuxagHhzzvsBrYAACDhOAOLNcYZo4SUEIN7UMz04VxI/CTdX+MnyRx81psKFi6inw+gJCOiAgN7F24YN64VN8YhxpAoUCJJBQzi6renxoKD88viePbvp0KHDxvq8dzcm5pGI4JhO5oMzV5Q6DRo0NNojuZ4SbfKffx4ZT+MHUJUqVZK/b9q0UST+PmT8W758eWUf9u/fJyyaB60+zsLPnHhbs+ZneZytnmzvrFy5sg5mLG4BBEBA7QQg3tQ+QhrvH8SbxgcQ3QcBEHCIgN7Fm0NwxMmcNoDTDHC4fiVhd9I2FXtk3759Rb62vo5e0q7zjx8/TsOGDaW3365KtWvXlm1whEtEmLQLJ04CARBwgADEmwPwcGrKBCDeUmaEGiAAAvolAPH28rHVinjjfcG8J27atGkit9xP8qY4vQoiTOr3vYs7AwG1EoB4U+vI6KRfEG86GUjcBgiAgF0EIN5eju3vv/+i1atXi7Qnt4n3rpkrfn5+lD59BqpTp47FyJN2DY4dJ23evEnYLg/IM2vUqEFVqlSxoxWcAgIgAAL2E4B4s58dzrSCAMSbFZBQBQRAQLcEIN6sG1pO0r1q1UqzlV99texLk3RbdwXUAgEQAAF9EIB408c4qvYuIN5UOzToGAiAgBsIQLxZB/n27VsiOfcDs5XTpUsrclDmIV6BQwEBEAABbycA8ebtM8DF9w/x5mLAaB4EQEDVBCDeVD086BwIgAAIaI4AxJvmhkxbHYZ409Z4obcgAALOJQDx5lyeaA0EQAAEvJ0AxJu3zwAX3z/Em4sBo3kQAAFVE4B4U/XwoHMgAAIgoDkCEG+aGzJtdRjiTVvjhd6CAAg4lwDEm3N5ojUQAAEQ8HYCEG/ePgNcfP8Qby4GjOZBAARUTQDiTdXDg86BAAiAgOYIQLxpbsi01WGIN22NF3oLAiDgXAIQb87lidZAAARAwNsJQLx5+wxw8f1DvLkYMJoHARBQNQGIN1UPDzoHAiAAApojAPGmuSHTVoch3rQ1XugtCICAcwlAvDmXJ1oDARAAAW8nAPHm7TPAxfcP8eZiwGgeBEBA1QQg3lQ9POgcCIAACGiOAMSb5oZMWx2GeNPWeKG3IAACziUA8eZcnmgNBEAABLydAMSbt88AF98/xJuLAaN5EAABVROAeFP18KBzIAACIKA5AhBvmhsybXUY4k1b44XeggAIOJcAxJtzeaI1EAABEPB2AhBv3j4DXHz/EG8uBozmQQAEVE0A4k3Vw4POgQAIgIDmCEC8aW7ItNXhxYsX0cKFC2n8+AlUoUIFbXUevQUBEAABBwlAvDkIEKeDAAiAAAgkIgDxhgnhUgL379+ju3fvUp48eSldunQuvRYaBwEQAAG1EYB4U9uIoD8gAAIgoG0CEG/aHj/0HgRAAARAQMUEIN5UPDjoGgiAAAhokADEmwYHDV0GARAAARDQBgGIN22ME3oJAiAAAlohAPGmlZFCP0EABEAABDRHAOJNc0OGDoMACICAqglAvKl6eNA5EAABEAABLROAeNPy6KHvIAACIKA+AhBv6hsT9AgEQAAEQEAnBCDedDKQuA0QAAEQUAkBiDeVDAS6AQIgAAIgoD8CEG/6G1PcEQiAAAh4kgDEmyfp49ogAAIgAAK6JgDxpuvhxc2BAAiAgNsJQLy5HTkuCAIgAAIg4C0EIN68ZaRxnyAAAiDgHgIQb+7hjKuAAAiAAAh4IQGINy8cdNwyCIAACLiQwP8DU08s5Q7+MI0AAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "b4407ccb-19ae-40ce-898d-7fdcaec3909a",
   "metadata": {},
   "source": [
    "![image.png](attachment:d7fc5c1e-36d4-45c9-b137-70e519bfcb17.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3bbf5a54-9ebf-44aa-961d-7d135ae2d74c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2d71baca-a357-46d3-b469-8489256228fa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody()\n",
    "x1=x*cos(alpha)\n",
    "y1=x*sin(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08cdc0d7-0653-4a11-9784-ff11a5a2831d",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.add_forza(m*g,-pi/2)\n",
    "P.add_forza(N1,alpha+pi/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9417b3de-e14e-4f63-9fa3-d331198cf652",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fy =N_{1} \\cos{\\left(\\alpha \\right)} - g m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fy=P.Fy('Fy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "78b011fd-e80c-4933-b4d3-ca18b88a39a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F_{c} = N_{1} \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(Fc,-1*P.Fx())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "87c4c1f7-3b3f-42f6-a0d0-bfc36784aa32",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.add_forza(Fc,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "33ecd5ef-f412-4f5f-b368-62388eb96900",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - F_{c} \\sin{\\left(\\alpha \\right)} + N_{1} - g m \\cos{\\left(\\alpha \\right)} = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MQ(P.fyrelative(alpha),0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "084b1172-0db7-4c4e-aa2f-6ba6a5e36b28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N_{1} - R m w^{2} \\sin^{2}{\\left(\\alpha \\right)} - g m \\cos{\\left(\\alpha \\right)} = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2.subs(Fc,m*w*w*R*sin(alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2d9aa548-df66-4af3-9cec-e9f20e2afa42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N_{1} = m \\left(R w^{2} \\sin^{2}{\\left(\\alpha \\right)} + g \\cos{\\left(\\alpha \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2.alone(N1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f0104e51-8095-4312-86a7-85e046c4c38c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F = F_{c} \\cos{\\left(\\alpha \\right)} - g m \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q3=MQ(F,-m*g*sin(alpha)+Fc*cos(alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1659d00f-44e8-4dfd-bd28-61df40906988",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F = R m w^{2} \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} - g m \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q3.subs(Fc,m*w*w*R*sin(alpha))"
   ]
  },
  {
   "attachments": {
    "53dc594e-0b6e-483f-99d8-77c520d39daa.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "65b4f5d8-fe2c-4604-a26b-aaa3c0cace35",
   "metadata": {},
   "source": [
    "![image.png](attachment:53dc594e-0b6e-483f-99d8-77c520d39daa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ccc4a4c2-3842-474b-a1bf-07f8620e3afa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a1f96adc-c20e-465e-8a9b-17fe1aa8a6bb",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody(w1=0,y1=0,y2=R-R*cos(alpha),Io=m*(R*sin(alpha))**2)\n",
    "x1=x*cos(alpha)\n",
    "y1=x*sin(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b5777bc9-2bfd-406c-ac42-add080318585",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.add_forza(m*g,-pi/2)\n",
    "P.add_forza(N1,alpha+pi/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c0b18c36-a76e-4b93-94f2-81b2659d7b23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle En =\\frac{R^{2} m w_{2}^{2} \\sin^{2}{\\left(\\alpha \\right)}}{2} + g m \\left(- R \\cos{\\left(\\alpha \\right)} + R\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "En=P.energia('pr','En')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b60bf5c-1b90-4fd1-bbb0-01c19b51b7bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle En =\\frac{R m \\left(R w_{2}^{2} \\sin^{2}{\\left(\\alpha \\right)} - 2 g \\cos{\\left(\\alpha \\right)} + 2 g\\right)}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "En.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0172bbca-1cd2-4286-9143-97adccb9832a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle En =R w_{2}^{2} \\sin^{2}{\\left(\\alpha \\right)} - 2 g \\cos{\\left(\\alpha \\right)} + 2 g$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "En.reducecero()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "acef9128-0a6e-4717-a341-0c118582a838",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle En =R w_{2}^{2} \\cdot \\left(1 - \\cos^{2}{\\left(\\alpha \\right)}\\right) - 2 g \\cos{\\left(\\alpha \\right)} + 2 g$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "En.sin2cos(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0e32f43e-7d98-4a09-b0d1-dc47c64bb683",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle En =- R w_{2}^{2} \\cos^{2}{\\left(\\alpha \\right)} + R w_{2}^{2} - 2 g \\cos{\\left(\\alpha \\right)} + 2 g$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "En.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9c4ea065-3549-453b-a464-b6ca99d4329d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 1, \\  -1 - \\frac{2 g}{R w_{2}^{2}}\\right]$"
      ],
      "text/plain": [
       "⎡         2⋅g ⎤\n",
       "⎢1, -1 - ─────⎥\n",
       "⎢            2⎥\n",
       "⎣        R⋅w₂ ⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "En.solve(cos(alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "299c266a-31d6-41a5-8462-93cfc84809c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle aM =2 R w_{2}^{2} \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} + 2 g \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aM=MyEq(En.diff(alpha),'aM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8927f099-98a7-4a38-8c0c-5cab67e98cb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle aM =R w_{2}^{2} \\cos{\\left(\\alpha \\right)} + g$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aM.reducecero()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "36057070-84b5-4e29-ab15-e8de2a1e9ace",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle cos(alpha) =- \\frac{g}{R w_{2}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "calpha=aM.solve('cos(alpha)')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}