From c0feabd06aa84f18278f93b9ce1a368c7897141b Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Fri, 18 Mar 2022 12:52:17 +0100 Subject: [PATCH] Final: Do tasks 1, 2.1 and add comment to 2.2 --- ...l - Tight-binding propagation method.ipynb | 78 +++++++++++++++---- 1 file changed, 63 insertions(+), 15 deletions(-) diff --git a/Final/Final - Tight-binding propagation method.ipynb b/Final/Final - Tight-binding propagation method.ipynb index aa41e20..d0c4b14 100644 --- a/Final/Final - Tight-binding propagation method.ipynb +++ b/Final/Final - Tight-binding propagation method.ipynb @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "deletable": false, "nbgrader": { @@ -103,10 +103,8 @@ }, "outputs": [], "source": [ - "# Import packages here ...\n", - "\n", - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "import numpy as np\n", + "from matplotlib import pyplot as plt" ] }, { @@ -137,7 +135,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "deletable": false, "nbgrader": { @@ -154,9 +152,20 @@ }, "outputs": [], "source": [ - "def atomic_positions(n):\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()" + "def atomic_positions(n, a=1):\n", + " \"\"\"\n", + " Creates an array of atomic position in a 1D crystal lattice\n", + " for lattice constant a having default value a = 1.\n", + " \n", + " Args:\n", + " n: number of atoms in the 1D lattice string\n", + " a: numerical value for the lattice constant\n", + "\n", + " Returns:\n", + " A 1D array of atomic positions.\n", + " \"\"\"\n", + " \n", + " return np.arange(n)*a" ] }, { @@ -193,7 +202,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "deletable": false, "nbgrader": { @@ -208,13 +217,51 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAACKt0lEQVR4nO39eZgkV3Xmj39u5L5n7d1d3a3uVmvrFlpbEptlZEAIewCz2WDwYBvMeAwzthn/BgbmCwbPGMbbgMfMjLGN7bENMgZsCSyQAbGvam1oabXU+1Z7VWZW7hkR9/dHxM3asqpyiYisluLzPKKqMyMzD1mZceI999z3CCklPj4+Pj4+Ww2t3wH4+Pj4+Pi0wk9QPj4+Pj5bEj9B+fj4+PhsSfwE5ePj4+OzJfETlI+Pj4/PliTY7wDcYnh4WO7Zs6ffYfj4+Pj4bMIDDzwwK6UcWX37MzZB7dmzh8OHD/c7DB8fHx+fTRBCnG51u1/i8/Hx8fHZkvgJysfHx8dnS+InKB8fHx+fLckzdg3Kx8fHZyvSaDQ4d+4c1Wq136F4TjQaZefOnYRCobaO9xOUj4+Pj4ecO3eOVCrFnj17EEL0OxzPkFIyNzfHuXPn2Lt3b1uP8Ut8Pj4+Ph5SrVYZGhp6ViUnACEEQ0NDHSlHP0H5+Pj4eMyzLTkpOv3/7ScoHx8fH58tiZ+g1uGP/vUof/mdk/RtXpZpwnf/BH7059CnGKSU/M3jf8Onjnyqb++DlJK5v/5r5v/f3/Y1hke+dpZHvna2rzE89OUvcPgLn0eaZt9iKP7gAovfPIc0+zdH7vDhw3znO9/B7NP7AHD+/J2cOvV/kNLoWwxzdZ2pWqN/56hVfPnLX+aKK65g//79fOQjH3HkOf0miRZIKXnsfJ6vH51h33CC264c9T6Ixz8PX/n/rN8zO+GKl3sewr2n7+UPD/8hAGPxMV58yYs9j2Hxq19l+iP/A4Dg6CjpO17meQynH53jO//4NADxdJjLbhrzPoZHHuS+v/ozK4bsAAd+4jbPY6gdz5H75+MAaMkQiRu9fx9OnTrFF7/4RQDi8Tg33HCD5zHMz3+XJ4++D4BQaIDx8Td4HkNRNzhXrQMQEDAcbq8rzi0Mw+Ad73gHX/nKV9i5cyc33XQTr3zlKzlw4EBPz+srqBYIIfjEvz3EaCrCP9x/tj9BPHInpHdCagc8+P/6EsIXj3+R0dgoY/ExPvf05/oSQ/6f7yIwPExwdJT8F7/QlxiOfG+CWCpEciDC0R9N9iWGH993L9FUmvTIKE98676+xFD64SRaPEhgMEr5wam+xHD//fcTjUYZGBjg4Ycf7ksM5y/8A6HQIInEZVyY+GxfYlho6GgCogHBfKMzFXfq1CmuuuoqfvVXf5WDBw9y++23U6lUeornRz/6Efv372ffvn2Ew2He8IY3cNddd/X0nOArqHUJBTR+8vIRvnJkCtOUaJqHi5rVApz4Ojz316FWgMf+CUwDtIBnIZQbZb574bu86co3UTWq3H38bnRTJ6h595ExazVK3/oWA7/wRsx6nfxdd2PW62jhsGcxGLrJ6cfnOPDCHSDhyHcvoDcMgiHv/hamYXDy4Qc4eOuLCYRC/PgrX6JRrxEKRzyLQZqS6lMLxK8dQUQCFL93AbNuoIU9fB9Mk+PHj3PVVVcRj8f5/ve/T61WIxLx8H2QkoWF7zM09JNEI9s5febP0PVFgsFUV8/3wS88zhMXCh0/rmyYBIR1Md0wJfGAhjpDHdiR5gOvOLjh459++mk+/elP8+d//uf83M/9HJ/73Od485vfvOKYv//7v+cP/uAP1jx2//79fPazKxPz+fPn2bVrV/PfO3fu5Ic//GHH/79W4yuoDbhl3xC5coOnp4vevvDEI2DqsPdW2P18qOVh+glPQzi6cBTd1Dm07RA3jN5ARa/w1MJTnsZQO3IE2WgQu/FGki98IbJcpvrYY57GMHe+iNEw2bE/y+4Dg+gNk6mTnZ9QemH27Gn0Wo3xKw+w55rr0Rt1Jp560tMY9OkysmYQviRN9LIBMCT1U96+D3Nzc1SrVXbv3s2+ffswTZMzZ854GkOlcopGY55s9iYGBp6HlAa5nLem1NL+LyAE6vLA7HAdau/evVx33XUA3HjjjZw6dWrNMW9605t4+OGH1/y3Ojm5ia+gNuCmPQMAPHhmgSu2dXeF1BUTD1s/t18HjbL1+9kfwrbneBbCY7NWIjg4dBDd1AF4ePphDgz1VlPuhMqjVgyxa65pNopUn3ySuIfrDioZje5JEQha13Oz54qMXz7gWQwTT1vJaPtlVxKOxQCYOX2S3Vdf61kMtdPW+xC+JE0gbp02GhNFoh6+D2fPWuX2Xbt2kUpZ38eJiQkuu+wyz2LI5R8AIJu5kWh0HBAUFh9leLi7NcHNlE4rFho6Zyp1LktEiGoajxYrjIaDbI+0X1lYrjoDgUDLEl8nCmp8fLz59wFrM/L4+Hjb8ayHn6A2YNdAnFgowNNTHiuoCw9b60/JEevEHE7BzFFPQ3hi7glGY6OMxEeQUpIOpzmeO+5pDNXHHycwMkxwzFqMD2Qy1I54qxxmziwSS4VIDUYBiKVCzJ3z9vMwffIE0USSzOgYQggSA4PMnD7laQyNyRIiEiA4FEUIQSAdpjFZ9jSGqakpQqEQg4ODaJpGJpNhenra0xhKxafQtDDx+F6ECBCL7aJUetrTGCqGiRAQ1TQ0IYgIQc1wvpPvTW96E29605vaOvamm27i6aef5uTJk4yPj3PnnXfyqU99qucY/AS1AZom2D+a5OnpRW9fePYojF5l/S4EjFwBM96emE/kT3DZwGV2CIJ9mX2cyJ/wNIbayRNE9u9vbu6LXHkl1aPeJurcVJmBbYlmDEPjSWY9TlDzE+cYHN/VjGFk9x5mzpz0NAZ9pkJwNN6MIbgtQWOy5GkMs7OzDA8Po2mWkh0bG/M+QZWPE4/vQwiruJZIXE6x6G3pu2qaRDSBZv8togGNqtG/lnuAYDDIn/7pn/Kyl70MwzD4lV/5FQ4e7FwdrsZfg9qEy0aT3iooKWH+FAwu86oauQJmvPsSSCk5XTjN7vTu5m37st4mKCkl9ZOnCC+bihy5dB/1FrVyN1mYKpMdizf/Pbg9QW6q7Onek4UL5xnYsVQuGdq5m/lz3u7J0qfLhEZizX+HtiVoTJc93Q+lEpRidHSU2dlZDMO7vUil0nHi8Uub/04mLqdSOYlp1jyLoWZKItrSqTuiCWqmbHsdas+ePTy2bC33t3/7t/md3/mdnuP66Z/+aZ566imOHz/O+973vp6fD/wEtSmXjiaZLFQp1XRvXrA8B/VFGFiWoIYvh+IkVHKehDBXnaPUKHFJ+pLmbfsy+5ivzpOrehODkcthFgpEliWo0K7dmIUCRs6bGKqlBtViY0WCSo/EaNQMKosNT2KolUuUcgsM7tjZvC07th29UaeUW/AkBrOmYxTqBEeW3ofgUBQMiVGoexJDvV4nn8+vSFCDg4OYpkk+n/ckBsOoUa2eI5HY37wtHt+LlAbV6gVPYpBSUpeSyDLLoKidrOp93DztFn6C2oRdg9aX8txCb/sE2mbeLt0sV1Dq95w3HUunC9b05eUJalfKaiE9XzzvSQz1k6cAViio8G4rhvpZb/am5aatNZblCSpjq4jCrDefh4UJ68S3XEFlxrZZ8U1NeBKDPmeZewaHo83bgvaanDHvzfuQsy9KBgcHm7cNDAysuM9tqtXzgCQWW6osRGPWZ7JS8eYzWZcSJISXKaiwnazqfXTWcAs/QW3CrgHrhHRuwaMF4QU7QS1XUFn7C+FRgjq7aHdLpZb2NexI7gC8S1CN8+cASzUpQvY+i7pHrcWL9ok5PbR0Yk4PW5+H/Iw3J+bF2RkAMiNLrg1ZO0Hlp7zZNGzkrPJVMLs2Qenz3sw0Uiopm802b1MJamHBGyVZrVkXC9HIjuZtMZWgquc8iUGppMiyfZlh+/faFrE8chJPE5QQ4g4hxFEhxDEhxHta3P9rQohHhRAPCyG+I4Q4YN++RwhRsW9/WAjxf72KWSmos/NeJahT1s+BJfVC1v7dowQ1VbJcArYltjVvUwlqouTNVXtjwjr5hrYtnZjDdoJqeKSgivPWiTk5uDxBRUF4p6AW56wElRpaKm2lR0YRQiPnVYLKW+9DILusNTkbAc37BJXJZJq3pdNpNE3zLEHV7DJeNLqUoCLhUTQtTKXizXdTqaTwsgQVFAIhnpklPs+6+ITV9vJx4KXAOeB+IcTdUsrlO1A/JaX8v/bxrwT+GLjDvu+4lPI6r+JVDCXCxEIBb0t8qR0QWlqQJjYA4aRnCWqyPMlgdJBIYOmElA6nSYVSnikofXICLZNBiy+V17RYjEA2S2PSmxNzcaFKKBogElv6mgRDAeKpMEWPTsyF2RmC4QjR5NI+vEAwRGJwkMVZbzrY9FwNAgItseT3JgIagUwEw8MEpWkayWSyeZtqNfdMQVUvABqRyNJFkxAa0eg41YpHCspWSaFla1BCCMK2o8QzDS8V1M3AMSnlCSllHbgTeNXyA6SUy7emJ7A2TPcVIQTjAzHvElTuzEr1ZAVhlflypz0JYao0xVh8rRHo9uR2LhS9WQxuTEwS2rZtze3BsTH0KW9OzMWFGsmB6JrbE9kIxZw3zQGLc7OkhobXzNFJDQyxOD/nSQxGrkYgG0GssvsKZCKeNUnk83lSqVSzxVyRyWRYXPRmG0i1eoFIZBRNW2nMGo2MU615c9HUMCUhTaz5PIQ10UxezyS8TFDjwPLazDn7thUIId4hhDgO/D7wH5fdtVcI8ZAQ4ptCiJ9wN9SVbEtHmVr05kqRxQlIbV97e3oHFLxJDpPlScYSLRJUYjuTJY++iFPrJKhtYzQ8Km0VF6qkBtb6vCWyEUo5b9qKF+dmSA2PrLk9OThEaWHekxiMXI1gZu37EEiHPU1Qy8t7ilQq5WGCOr+ivKeIREap17wxz21ISbDF0L+QEDT6nKB+5Vd+hdHRUa6++mrHnnPLNUlIKT8upbwUeDfwX+2bJ4DdUsrrgXcBnxJCpFc/VgjxdiHEYSHE4ZmZGcdiGk1HmC54cEKSEhYnWyeo5DYoevMlWE9BjcRHmKk4975uhD4xSbBFggqNeqegFhdqJFskqKSXCWp2ZsX6UzOGwSGKHiuo1QTSEYxCzZP9WBslqEKh4EkM1dqFFQ0SinBkjFp9Bind76JrmHLF+pMiqAl0U/Z1NtQv/dIv8eUvf9nR5/QyQZ0Hdi379077tvW4E/hZACllTUo5Z//+AHAcuHz1A6SUn5BSHpJSHhoZWXvV2S1j6SjTi1X3//i1RWiUILX2xEzKTlCmu5sSy40yhXphRYOEYiQ2wnx1nobp7h4gs1rFWFggtL11ic+Ym0PW3b1yNxomlUJ9RYOEIpENUy010Dscc9BxDLpOMbdAamjtZzkxMEitXKJRdVfZS0NiLNYIrKOgZN1E1tx9H0zTpFAorJugDMPoeVzEZkhpUq1OrqugpGzQaLivaBtSrlh/Uqjb9DbOUW6M2wC49dZbV2wDcAIvrY7uBy4TQuzFSkxvAH5h+QFCiMuklMrY6meAp+3bR4B5KaUhhNgHXAZ4ZmswmorQMCQL5QaDCRdHPSzapatWCiq1DaQJpVlIuTcobqpsqbRWCmo4Zl3Jz1XmWiYwp9DtJohWCio4Zg2P1GdmCDlgRrkeRVshtVJQCVtNlHL15r4oNygtzIOULRVUanDIinNhjoHt7r0PxmIdTNZRUNZ3wSjU0aLunUqKxSKmaa6boAAWFxeJL2uocZpGYx4p60Qiaz+TkbD1XanVpgmH1/6tNuRL74HJR9s6VCLZa5iWghIrtUVWSqKmiRbQYNs18PKNJ9o6PW7DLTxLUFJKXQjxTuBeIAB8Ukr5uBDiQ8BhKeXdwDuFEC8BGsAC8Bb74bcCHxJCNAAT+DUppTcFeCwFBTBVqLqcoOwW7vUUFFiOEi4mKLXG1CoBjcat5DBbmXU1QTUmrSTZag0qZBvHNqamXE1QpZylTJLZVgpKJaiaqwlKNUGsV+IDKM67m6DMRXtqa3rt534pQdUIjbqXHEoly/NveQefIp22Kv2Li4uMjbn3vajXrb9FqwQUiVjfi1ptilTKPbd/pY0EaxWUElXtFnnaHbfRrlmsW3hqFiulvAe4Z9Vt71/2+2+s87jPAf0Z6QqMpa0T0vRijataiBvHaCqoVglq+9Ix290bs6DWmFquQcWsUtN02d01IN1ePwyOjq65L2hvUtWn3F2PK+WtE3M8s/bEvDxBuUnZtjKKZ7JrYxiwSilur0MZRTtBJVslKOt9MPLulluLRcsLM5FIrLlvuYJyk3p9FlgvQdkKqt7F92ITpbOckm5wolzj0niEUHDloEjDNDlerDIeDbU1/t3pcRtu4buZt8FoaklBucpGCippJwyVxFxirmKd8IZiQ2vuUyW+2cqsqzHoc9bzB4fWxhCyS3xKZblFxVYOsdTaE3PSTlBFlxNUKZ8DINEiQakSn9ut5mbRWm/UkmtPeppSUIvuJiiloFolKKWq+pmg1G21mrsXbo0We6AUnaxBtctWUFBbrotvKzKSshWU6wlq0tqQG2kxHNHDBBUJRIgH15ZshmJDCITrnXzG3ByEQmjpNY2aaJkMIhTCmHM3SZYLdWvmTosTczgWJBjSKOVdVlB5S0HF0mvXXsKxOOFYzPVWc8NOUIFWCSocQESDTacJt9ioxBcKhYjFYh4kqPVLfJoWJhQadL3VXLc34gZbdPEJIQhq/d2s+8Y3vpHnPe95HD16lJ07d/KXf/mXPT+nr6DaIBoKkI2HmHK71XxxorV6AgiGIT5krUG5yHx1nqHo0JqNgABBLchgdJCZsrsJSp+bJzg42DIGIQSBoSH0OXdPzJVCnWgqjLbOySCWDlN12dG8nM8RTaUJBFt/TeOZLOWCu07eZrGOiAQQoUDL+wOpUFNluUWxWCQYDBIOt17/9WIvVL0+ixBhgsG1F01glfm6KvF1gC4lQqyvKtrdC9Vq3IYTfPrTn3bkeZbjK6g2GU1FmHZ7s25pZkkptSK13X0FVZ1rWd5TjMZHXVdQ+txsy/KeIjg4iO5yaau82CDeoryniKXCzTKgW5RyuZblPUU8naVslwHdwig2Wpb3FFoy1FRZblEqlUgmky0vWMAq/SmV5Rb1+izhcOuLJoBwaKipstxCtzfprhdDUAj0Z5iZhJ+g2mQwEWah5PIMoNKspZLWIzFsJTEXmavMMRhdfy/DUGyouU7lFsbsHIHh9d+HwNAQhssKqlyoE0+vf2KOp0KUXU5Q5XyOxDL37jUxZDKeKKhWDRKKQCKEWXK/SaLV+pMiHo+7n6Aasxu2kIfCgzTq7n4m9XVcJBRB4ewa1FbAT1BtMpSIMFdyucRX3iRBxYetgYYuMl+d31BBDUQGyNVyrsagz80RHOyvgqoU6sRatFYrLAXlfokvnhlYP4Z0ZgsoqDCmyxdupVJpwwSVSCQol92dNmApqPU/k+HQIHWXN+rqkk0SlPAT1LOVgUSIeTevFE0DyvOWSlqP+BCU3Dsxm9JsrkGtx0B0gPmqe19EKSXG3BzBNhSUW84eUkoqi/W2SnxuuouU8rmWLeaKeDpLZbGAdHFQnVlstGyQUGiJEGZZRxouvg92iW89EokE1WoVXXdv6nW9Pkc4tLGCMoyiq6PfLQW1/v0BIZASjGdQkvITVJsMJiLkKg0Mt7pkKjlAWippPRLDUMuD4c4Va6FWwJDGhiW+gegAFb1CVXdnPc5cXEQ2GgRabE5VBIcGkbUaZsmdq+ZGzUBvmJsoqBCmIalX3DkpNmpVGtXKxgkqk0GaJtVS0ZUYpCExyw20jUp8yRBIMMvufCZN02xLQQGuqSgppZWgNijxhUPWd6buUplPStlGic/5VvN+4yeoNhlKhJEScmWXVFTZbpveTEGBa2W+uer6e6AUAxF7zLZLZT591ophQwVll/8Ml8p8ZduhO75JiQ9wrcxX3mAPlCJut5+X8+6sQ5nlBsjWLeYKNSPKrTJfpVJBStlWgnJrHUrXC0jZ2HQNCnDNj8+QlktEqEVXqUKpK19BPQsZsC2OXCvzlewEFd/AbFElqJI7e4Cam3Q3KPFlo1kAFqruDIkzNtikqwgOWe+RPudOglJJp9UmXUUsZZ2Y3WqUUM0PrfZANWNQCaqQcyUGY4NNugqVvNzq5NtoD5RCefC5paA22qSrCIesz2u94c73Qqmi9hSUKyFsyNmzZ7nttts4cOAABw8e5GMf+5gjz+vvg2qTITtBzZXqXObGCyhVtFmJb/mxDjNfs67+BqLrL8wrBeVWgtLt6aiBgfVjWFJQ7lytVm01EE2sf2JeUlDuJKiqbe+zfJLualT5zzUFpWyONvCfdFtBbWRzpHBbQS0lqPUvmkIh6/PqVidfZwnK+wwVDAb5oz/6I2644QYWFxe58cYbeelLX8qBA715E/oKqk2USeyCWwqqoxKfOwqqULMGGmci61+1q+S1UHMnQZkFK4ZACxcJhdsKqmavp0Ti61+/xV0u8al1pWhiA+XgsoJq2hylNu7is45153uxkc2RwrsEtYGCskt89YY7n8mlBLX+McphQt9kndyNcRvbt2/nhhtuAKyN01dddRXnz280Tak9fAXVJoPLFJQrqO68zdrMwer2c4FC3UoO6fD6ycFtBWXkrRi0FqMVFAF75oxbCqpWshofovH1T8xR+6TtloKqNRXU+gkqlkqDEK4pqKZR7AZKUosFQYDhkoJqJ0FFo1E0TXMtQTXssl0otH75PRjMIESgYwX1P370P3hy/snNY5CSmilJBLQWXuZLlAyTKweu4EPPf++Gz+fmuI1Tp07x0EMPccstt2wYQzv4CapNBuIur0GVZyGcguDauTtNYnbZy6U1qEKtQFgLEw2uHTGhSEfSaEJzTUEZhQIEAmgbnJC0SAQRj2Ms5FyJQSmo8AYKKhDQCMeCVFxae1EKKrKBgtICAaLJFBWXNuuaZR00ELH13wehCavV3KX3QV3Zx2LrjzURQhCPx11bg2ro1vsbCq1/4SaERjCYdW8vVAdVu3Y2Hbg1bqNYLPLa176Wj370o81RKL3gJ6g2CQc1UpGgiwlqDhIbqCeAQNBKUm6V+OqFDct7AJrQyEay7imoQp5AOr2unYsikMlguKQcamWdcCzY0odvOdFEkJpLyqFaKhKMRAiGNh6dEEumqBbd8aEzKzpaNLjp30KLh1xrM69Wq0QiETRt49UIN+2O9EYeTYuiaRtcPGKV+Trt4nv3ze9u67iJap3phs41ydiGf4+jpQphsfnKjRvjNhqNBq997Wt505vexGte85pNY2gHP0F1wGAy7G4X30YNEor4kGtNEvlafsPynsJNNwkzn99w/UkRyGYxcu7EUC03Nlx/UkQToWZDheMxFBc3XH9qxpBMUnEzQW2gnhRaPGipLReoVCpEo+srekUsFnNt7HtDLxAKbnzhBlYJ0K19UAYQZH0fPoWTbhKdKCgpJW9961u56qqreNe73uXI64PfJNERgwkXE1R5duMGCUV82L0SX71AOrJ5cshGs665SRj5wobrT4pANuNagqqV9fYTlEulrVqp2FaCiqXSVF1y8jYr+oblPYWloNxJUNVqdcPynsLNBKXreYIblPcU4fCQa/ugdCkJbJybgP7ZHX33u9/lb//2b7nvvvu47rrruO6667jnnns2f+Am+AqqAwbjYSbyLjmal+Zg2zWbH5cYhvmTroRQqBdaTtJdzWB0kBO5E67EYBQKBNpKUFlqE5svLndDraQT2aBBQhFJhMjNuHNSrJaKG64/KaKJJLNnT7sSQ9sKKhakUXFvDarvCqqRJxTMbnpcKDTgnoKSksAm6gksu6PNNuq6MW7jhS98oSu2X76C6gDXFJSUVtluow4+RXzQ1Tbzdkp82UjWxSaJNkt8rq5BNYgm2lNQbq1B1YrFDfdANWNIpam4pKBkuwkq4V6Jr10FpZok3DhJWgpq84umcGgQXc9hms6/F4akbQVlSDCfIW4SfoLqALUG5fiXoF4Co9ZmgrIdzV34ALbTJAHWXqhcLYcpnTcpNfMFAtn2FJSRz7tilFott6egookgtbKOaTgfQ6XdEl8yRaNawdCdT5RmpdHmGlQI2TCRDcPxGCqVStslPtM0qdedv4C0FNTmF01qs66uFxyPoV0F9UyzO/I0QQkh7hBCHBVCHBNCvKfF/b8mhHhUCPGwEOI7QogDy+77L/bjjgohXuZl3IqBeJi6YVJx+otYzVk/Y9nNj40PgalD1Vn1oJs6xUax7SYJU5rNjb1OIU0To1BoOep9NYFsFkwT02H1IKWk1m6ThG3zU3PBMNZSUOu32i/FYKks5TzhFFJKu8S3eaJWScwNFdVJiU8d7zS6XmhLQaljdN15Zd9Jic863vEQ+oJnCUoIEQA+DrwcOAC8cXkCsvmUlPI5UsrrgN8H/th+7AHgDcBB4A7gf9vP5ykZ+8uac7qltpKzfto+dxuikphKag6xWLdO9O00SSiVla87+0U0SyUwTQIb+M8pAvYgP6cbJfSGianLthKUUllON0oYuk6jVm1vDSplJajKosMXC3UDTNpWUACGwwmq0WhgGEbbCgqcT1Cm2cAwSgTb6eKzj2k0nP1eSCk7KvGBr6C64WbgmJTyhJSyDtwJvGr5AVLK5d+yBEvb014F3CmlrEkpTwLH7OfzlKydoPJOLwh3oqDUZl2V1ByiHRcJhUpQTiso5SIRyLS3BmU9xtmTgXKRaKvEZyuoasnZE3NN2Ry1sQYVS1rvldN7oUxbFWptJGp1jNN7oVSyaUdBuWUYq8p17ZX4sgA09JyjMSg1tJEPn0IlsWfKyA0vu/jGgbPL/n0OWOOFIYR4B/AuIAz81LLH/mDVY8dbPPbtwNsBdu/e7UjQy9kSCkodU3G2SUElm3YSlDrGcQVlOyK028UHziso5SKxkVGsQh3jdKOE2tfU7j6o5Y9xClWu60RBOV3iq1atjtl+KiiVoNop8akEpTusoAz7Oj2wocmRhV/icxkp5cellJcC7wb+a4eP/YSU8pCU8tDIyIjjsWXiW0hBOVziayqoNkp86hjnFZT1xW57DQr3ElR7+6CsY5zerFtrwyhWEUvZCsrhtTiloNrbB9V/BeVWglLlunY26gZtldVo5ByNQZXr2inxqSRmdOKN5ADVapWbb76Za6+9loMHD/KBD3zAkef1UkGdB3Yt+/dO+7b1uBP4P10+1hWyth9fvuJwp1BHa1CqxOewgrITVCa8+RfRLQW1VOLrREE5G0O1WeJrr83ceoyzJ+Z2fPiaMdgKyukSn6y0r6ACKkE53CzSjYJyusSnynXtbNRV61QNh7v4lBpqr0nC+ul1iS8SiXDfffeRTCZpNBq88IUv5OUvfznPfe5ze3peLxXU/cBlQoi9QogwVtPD3csPEEIsH7X0M8DT9u93A28QQkSEEHuBy4AfeRDzClwr8VVzgIA21EtTZTm8BpWvWSf6tpokwi6tQakSXzsKKm05eTuvoNpfgwrHgghNOK+g2pgFpQhFY2iBoPMlvg4SlAgFECGtrwoqGAwSDoedL/E11BpUdtNjNS1IIJBEd01BbZ6ghBAExMYlPjfGbQghmkMlG40GjUZjU1umdvBMQUkpdSHEO4F7gQDwSSnl40KIDwGHpZR3A+8UQrwEaAALwFvsxz4uhPgM8ASgA++QUjq/6WITEuEAQU24UOLLQzQDmxhiAhCKQTDqmoJqZw0qFAgRD8ZdWIPafBaUQgQCaOm0i2tQbZyYhSASDzreJFFpY9TG8hhiKecNYztJUOq4fq5BqeMcL/HZLePtrEEBhEKZjpokJn/v96gd2dgRpSElQVMyGdDaUhSB/fsx/vPGJrRujNswDIMbb7yRY8eO8Y53vOPiG7chpbwHuGfVbe9f9vtvbPDY/w78d/ei2xwhBJlYiJzTCaqSa2/9SRHNutIkEQ1ECQfWn566nHQk7U4XXyiEsDuyNsMNP75aWQcB4Wh7Xw03/PjUGlQkvvk+KLCUlitrUBqISHu7Odzw4+tEQYE7CUpvrkG1NzoiFMw2VZdTKDHUrh4RbG535Ma4jUAgwMMPP0wul+PVr341jz32GFdffXXbj2+F78XXIZl4yJ0miXbWnxSxAVeaJNpRT4pMOOPCGlR7ozYUyk3CSWqlBhG7dNcObjiaV0tFQtEYgWCbSTKZolJ09qTY7qgNheVo7nyJr51RG4pYLOZKm7mmxdC09i7cgh0qqG3v3XiwIMCFap1KQ+eSTUZtKI6Xq+ibLEG5MW5Dkc1mue222/jyl7/sJyivycZC5N1oM4+2V0IALLXlwj6odtafFK4oqEKhrfKeIpDJYMw5a85ZbdPJXBFNhlicd9ZAuFYqtlXeU8RSKXJTk47G0K5RrEKLB2lMO6te2vXhU8TjcSYnnX0fGnqeUJvlPbC6/YqlKUdjsDbpbj5qQxEUgroDFmCdKKiZmRlCoRDZbJZKpcJXvvIV3v3u9mZdbcSWazPf6lglPoe7+Kq5zkp8sQFXmiQ6VVBq3copzDaNYhWBdMaawOsgtbLe1h4oRSQebK5bOUWlzVlQCqvE57yCaqfFXOHG0MJ2bY4UbpX4gm2W98BSUE5bHRlIOrHNacfR3GkmJia47bbbuOaaa7jpppt46Utfyr/5N/+m5+f1FVSHZONhjs0463tmKahs+8fHBmDix46GUKgX2JHc0fbxbq1BBYYG2z4+kE43Gyucol0fPkUkHqTu8NpLu7OgmjEkklTLzk6T7VhBxYKYFR0ppSPdW9C5glIJyskY2h1WqAiFsjQaeUdjaNeHT6G6+NaLwY1xG9dccw0PPfRQz8+zGl9BdUgmFnK2zVzKzhVUNPvMXIMqFAhksm0fr2XSGIuLjjqa19p0MldE4iHqVQPTdO6KtVpsbxaUIppIotdqjjqatztqQyFiQTAksuHc36JTBRWNRi2z31rNsRj0Rq7tDj6wSnxSNjAM59bCVImvXdRmXec99r3HT1AdkomFWKzqGE6dkBoVMOqdK6h6EXTnSo3tzoJSpCNpakaNqu7c+ovR5rh3RSCVthzNS86ph44VlH0Sd1JFWWtQm++BasaQSNiPc+59MCuNpoVRO6hkJqvOvQ/dKCj1OKdo6PmOFJQbjuZGm9N0mzHYyeyZ4MfnJ6gOydpf2oJTnXyd2BwpHHY0b5gNynq5rVlQCpXMnFqHkvbojHaMYhXqWKfKfFLKtqfpKiL2fqmag52d1WJnTRKqHKgcKHpladRGZyU+cNZNohsFBc4mqHZHbSjUhl4nHc0NKdsyilWoZPZMcDT3E1SHNN0kHEtQ9ge5UwUFjjVKdGIUq1Adf8qBolfMxUWQsi0fPoU61qlGiUbNKtVF2tikq1DJrOaQgtLrdfRGvcM1KEtBOTUTStbaH7Wh0KLOJqhORm0onE5Q1qiNctt7oIBmx59TjuadjNpQPJMMY/0E1SFZpw1jVZLpdA0KHNus24lRrKJpd+SQgjKaLhLtX60GbKNU5eHXKyrJRDtRUPZJvOaQm0QnPnwKlcxqDjVKdOoisfxYpxJUp5t0wXnDWL1DFwlY8uNzytG8Ex8+ReAZNBPKT1AdkolZG/ZyZYfWf1SZrhsF5VCJrxObI4XTCqppFNvGuHeFKvEZDrVYd+JkrlDHOjVVd2kWVGddfOBciW8rJah+KqhG04evky4+paAc+l50MGpDoca++2tQz0IyTg8tbDqZd7hRF5xTUF2U+BxXUPkc0J4Pn0Id69QaVK0DJ3NFM0E51NnZySwoRVNBOVTi62TUhkIdKx1KUJ368IHzCaqpoDoq8WWtxzpkGNvJqA1FP0t8hmFw/fXXO7IHCvwE1TGOl/iaTRID7T/G6TUoNWqjkyYJp9eg7CTT1RqUwyW+SEcbdZ1dg+pkFlQzBodLfJ2M2lA4vQbVTYlP2fc4VeJTKqgTJwlNiyFE2LEmiW5KfJoQCNGfEt/HPvYxrrrqKseez09QHeL4yI1uFJQ61uk1qA4UVDKURBOagwqq/VlQCi2RAE1zrMRX7aLEFwxraAHhWIJSjQ6RDkp8wVCIYDjS1xKfCAhEOOBYgupGQWmaRjQadU5BNZSCav8zKYQgFEo7V+LrYNTGcjZyk3Bj3AbAuXPn+Jd/+Rfe9ra39fxcCt9JokNCAY1EOOCsgoqkQevAzEQLQCTj2BpUJ7OgmiEIjVQ45dwaVAejNhRC0wikUphOKahS500SauSGUyW+pTWo9vdBgdXJ51QXXzcJSh1vVp2ZgtONglLHO7YG1UWTBEAwmG17qu63P/MUs2fX/7s1pKRmmhwPaIg216GGdyUZ/ZldG5b43Bi38Zu/+Zv8/u//PosOOuv7CaoLsvGwswqqkwYJRSzrqIKKBWOEtPZPzOCsH59ZyCPCYUSHJyQtnXaszbxWbiA0QSjaifOZVeZzqklCzYKKtDlyRBFNJKmVHUxQHYzaUCi7IydQSaafCarTURuKUCjt2EbdpVEbHSooBPoGY9+dHrfxxS9+kdHRUW688Ua+8Y1vdBTrRvgJqgvSMQdHblRzEOvsCg1wNkF16CKhSIed8+Mz8nm0TPujNhSBdNrBLj7dGrXRYQyWgnJuDSoST6B1oqix1qFqDpb4Ohm1oRCxAKZD34tOR20onDSMbegFAoF426M2FMFghnptuq1jf+LnLt/w/gvVOrMNnWtSnV2wnCzXqMv1zY6cHrfx3e9+l7vvvpt77rmHarVKoVDgzW9+M3/3d3/XUdyr8RNUF6SjQeecJLpVUNGso00SnZT3FOlI2tE1qE72QCkCmbRzJb5yo6NNuopILOjYTKhqqTMfPkU0kaC44MzokU5dJBRaLITh0OiRTm2OFNFolNnZWUdi6NTJXBEKZiiVnnYkhk6NYhUBAUaPZnydKKgPf/jDfPjDHwbgG9/4Bn/4h3/Yc3ICv0miKzKOKqh8Z5t0FbHskgtFjxTqhWbbeCekww4mqA5nQSm0lHMlvmqHRrGKSDzo6D6oTvZANWNwWEGJLt4HJ0t8ndocKZxeg+pkD5Qi6GCJz4CORm0o+jFyww18BdUFziaoXPcKysEmid2p3R0/ztESXyFPaGS048c5WuIrNTqaBaWIxEOOdvF10mK+FEPC0S6+rhRUNIDpkFlspVLpWkE55yTRmQ+fIhTMoOuLSGkgRDfpZYnuFZTAlGBKibbq8W6M21jOi170Il70ohc58lyeKighxB1CiKNCiGNCiPe0uP9dQognhBA/FkJ8TQhxybL7DCHEw/Z/d3sZ92ocTVCVXPcKaouU+KQDV2pmvtCRi4TC2RJfZ9N0FWF7DcqJ96Ha4bBCRTSZpFYuOzJ6RJYbXZb4gsiagXRgh2i1Wu1KQcViMXRdR9d7T5TdlviWHM17v2DodNSGYskwtucQ+opnCUpYlxIfB14OHADeKIQ4sOqwh4BDUsprgM8Cv7/svoqU8jr7v1d6EvQ6ZGIhKg2Dut7jyUCvgV7pbA+UIpoFo2aN6+iRxfpi100ShjQo673PvjHyebQu1qC0VBpZr2M6UNaplfWONukqIvEg0pQ0ar23WFdLxY72QCmiiSRISa3S+9+iWwWl3CScUFG9KChwxk2i2xKf6vpzosynS9m0LuqEZ4ofn5cK6mbgmJTyhJSyDtwJvGr5AVLKr0sp1TfsB8BOD+Nrm4xTbhLNTbrZzh/b3Kyb6ymEhtGgole6TlBAz2U+aRiYxWJXa1BNP74e16GkKTueBaWIOuQmYY376GwWlCISVzOhertql1JiVrttknDG7khK2VOTBDiUoBr5rkp8amOvE24S3Zb41F/PT1DtMw6cXfbvc/Zt6/FW4EvL/h0VQhwWQvxACPGzLsTXNspNolDtMUF1Y3OkcGgmlJqK24nNkUKVBXttlGhu0u1gFpTCKT++es1ASrpqkggrR/MeE5Rer2HoendrUEllGNub3VE3ozYUThnGqlEb3Zb4oHe7I9OsY5qVLpskVImvx4smKTE7HLWhaCqoniLoP1uySUII8WbgEPCTy26+REp5XgixD7hPCPGolPL4qse9HXg7wO7dnS/6t0vaKcPYnhRUduVzdEk3NkcKp4YWmoXObY4UWsoZBVUrdW5zpFCt6fUePw/KCaKrNSjlx9ejgurWRWL5Y3pNUN3YHCmcUlANO7l01ySRtp+jNwXVjQ+fwi/xdc55YNeyf++0b1uBEOIlwPuAV0opa+p2KeV5++cJ4BvA9asfK6X8hJTykJTy0MjIiLPRL8MxR/NupukqHFJQTSfzbpokHEpQRhdGsQqnSnzNWVBdrEGpEl+1x5lQ3cyCUqgSX6+dfI4kqB7XoLq1OVr+mF4T1JKLRA8KqscSX7c+fNZjVj7HxYqXCup+4DIhxF6sxPQG4BeWHyCEuB74M+AOKeX0stsHgLKUsiaEGAZewMoGCk9JRx0a+36xK6iIM2tQRs76InejoJwq8XUzC0rhVIlPjcvoZh+UekytxxJfN6M2FE45mveioJwq8S0NK+xuoy4sqbBuWZoF1Tn9GLmxZ88eUqkUgUCAYDDI4cOHe35OzxKUlFIXQrwTuBfrPf+klPJxIcSHgMNSyruBPwCSwD/aNitn7I69q4A/E0KYWKrvI1LKJ7yKfTXOKSj7CqsrBeXM0MKmUWwfS3xGwU5Q3WzUdWjkRrU5C6q7Lj6Aeq8n5i5GbSiiDg0t7GbUhkI4VOLbCgqq0YOC0rQoQoQdUFDWz2AXCqpfIze+/vWvMzw87NjzeboGJaW8B7hn1W3vX/b7S9Z53PeA57gbXfs0E1SvhrHNabrdtJnbj+nRTaKbWVCKRCiBQDi2BtVViS9ldbz1ulm3FwUViQVBLI3r6JaqGlbYhYIKRWMITXNMQXWVoEIaBETPXXzdTNNVBINBgsFg7yU+tQbVRYJyauSG3kOJTz2uVYI6deoUL3/5y3nhC1/I9773PcbHx7nrrru6er/dZks2SWx1wkGNWMiBkRuVHISTEOj8qt0auZF2rMSXCnfe2qxGbvRc4utiFpRChEJo8XjPm3Wbwwq7SFBCE4SjvRvG9rIGJYQgkkj2dQ1KCOGI3VG3TuYKJ+yO1LiMUBclPrASWztdfF//608wffpE6xhMSc2UHAlodJKjRi/Zx22/9HbLj28dAeXGuA0hBLfffjtCCP7dv/t3vP3tb28/6HXwE1SXOOImUc11p54UDtgdFWoFEqEEQa27j4ITfnxGoYCIRtGWOSx3ghMjN2plHS0gCHU4YkIRiQep97oGVSoihEYk1plztSIaTzjTxdfFqA2FNROqfyU+cMbRvNGDggKrk6/XEt/SqI3uCG4wcsPpcRsA3/nOdxgfH2d6epqXvvSlXHnlldx6663dhN7ET1Bd4kiC6tbJXBHLOKKgull/UjjhaG7kc12tPymc8OOr2pt0Ox0xoXBiaKHlZJ5AdDhiohmDA4axykWi2/fBKQUVjUY7HrWhcEJB6XreHrXRRXUDq5OvXt/cVf22X1pfZXQ7akMREGLdkRtOj9sAGB+3trWOjo7y6le/mh/96Ed+guoXmVjImY263TRIKBxSUD0lKAcUlFkodLVJVxFI9+7HVyt152SucGImVLdGsYpo0pkSnxbr/n0Q0SBmj4m6WydzRTQapdjjdGHLh6/76kYomKFcal26a5duXSQUvY7c6ERBlUolTNMklUpRKpX413/9V97//vdv/sBN8MdtdIk1tLBHz7FeFVTUIQXVxR4ohROO5ka+0JUPn8KZEl93NkcKJ6bqdjsLaimGRM9OEma50VWLuUKLBXtukujW5kjhVIkv1MUmXUXQgSaJbkdtKLwcuTE1NcULX/hCrr32Wm6++WZ+5md+hjvuuKPn5/UVVJdkYiGOTPToot2rgople1dQ9QJ70nu6frwjJb5CgdCOHV0/PpBOU33ySE8x1Mo68XRnk1OXE4kHm24UXcdQ7G4WlCLqVImvByXpRInPCQXlxEbdXhSUapKQ0kSI7nSAZRTbi4KyRm5IKVeUbN0Yt7Fv3z4eeeSRnp9nNb6C6pJ0LNj/NSgHpurma/meFdRifbGnURNGId/bGpQDIzd6VlAxZ7r4einxRZJWgurlbyG7dDJXqCaJXmLoVUGpBGX2MHrEcjLv/jNp7Z+SPY3c6HbUhuKZMHLDT1BdkomFKNZ09G6LvEYDGqXeFZRescZ2dEnPTRLhNA2zQdXo/orVzOV7WoPS0mnMUgnZwwygWpfTdBWReAi9YWI0uj8pVouLPSmoSDyBoevo9e4/D92O2lBosSCYIOvd25Q6oaAAarXu3we9SydzhXKg6GXkhrUG1fXDnxF+fH6C6pIlR/MuT4pqg22vCgq6VlE1o0bNqPXcxQfd2x3JRgOzXO5qk64ioAxjFxe7i8GU1CrdDStUqMd2uw4lpex5DWrJMLa7daheRm0oerU7klJ2PQtKoR7bS5mv21lQiiW7o14TVA8Kyv65Xqv5xYCfoLqkZ7sjlVR6UlDK7qi7L0HTKLZHBQXd2x2ppBLooUlCqa9u/fhqFR1kd5t0Fc0E1WUHW6NaQZpmV7OgFNHmyI3uykq9jNpQLNkddaegGo0Gpmk6oqC6TVCmWcM0q11N01Wo9atu90ItjdroPkEF++DH5zR+guqSnhNU0+Yo230Q6rFdNkr0YnOkUA4UXSeovO3D18W4d0XTj6/bBNWDk7ki0uPQwl58+JZi6M3RvBcXCcXS0MLuvhe92Bwpek1QjUb3ozYUqgOwW8PYpVEbXYfgl/iezTRLfL0qqF6cJJT66rLE14uTuSITtuLvtsRnqgTVU5OEFUO3hrG9+PAplhRUlwmqh1lQil5nQjmZoLot8fVqcwS9O5qrdaNeSnxKfXWroHoZtaF4Jozc8BNUlzimoHrdqLv8uTqk6WTeYxcf9KCgejCKVSjDWLPQ3cmg1oOTuaLXEp9KUD3tg1Ilvi43qfYyakPRa4LaEgpKJSgHFFS3TRJq3aiXfUBej9zI5XK87nWv48orr+Sqq67i+9//fs/P6e+D6pLe16AWrJ+9btSFviqoXse+92IUq1CbfLst8VUdUVC9lfiU6ul1H5QVQ5dNEltIQfUzQemqxNeDgtK0GEKEHCjxda+gvB658Ru/8RvccccdfPazn6Ver1Mul3t+Tl9BdUnPY9+dUFA9TtV1okkiGbJOit0rKCdKfL3NhHJmDapHBeVAgook7DWoHhWU1kOiFpEAiN4VVC8lvnA4jBCi6xKfEwpKCEGwB8NYJ0p86vGrE9SpU6e46qqr+NVf/VUOHjzI7bff3rPzRj6f51vf+hZvfetbAetvkM1me3pO8BVU10RDAcJBrbc1qGAMgt05eAPWmI5QomcF1c2ojWYIWoBUqPuRG6rzrpcEpUWjiHC4mew6xYk1qEBQIxjWqHa9BmXPguqhxKdpAcKxeF/XoIQmLD++PiooTdN6cpPQ7VEbvXTxgZXgNmszz33hOPULaxVvQ5qkTUk+oFHo0M88vCNB9hWXAlareat+SqfHbZw8eZKRkRF++Zd/mUceeYQbb7yRj33sYyTsi6Zu8RVUD/TkaN6rzZGiB7ujQr1AKpQioPXi+NWb3ZGRyyPicUS4e5shAC2Txix0tw+qVtLtBNPb+xCJh3rq4hOaRija29C4XgxjzbI9aqPH96EXuyN1JR/pcvSKopcEtTRqo7cEFQxmmuXCbulNP1kKSm9R4mt33MbDDz+85r9WTua6rvPggw/y7//9v+ehhx4ikUjwkY98pMfofQXVE70lqHxv60+KHuyOerU5UvTiaG4UCj2pJ0Ugnemhzbw3myNFL358NdvmqNsxF80YehhaaFYaPY3aUPRiGKtcJLodtaGIRqPdd/E18gQCia5HbShCoTT1+vyGxyils5oL1TqLDZ29XY7aUASEoNEiQTk9bmPnzp3s3LmTW265BYDXve51foLqNz0lqEpuSyioXtafFMqPrxucS1DpHkp8vblIKHoZuVEtFnvapKvoZWhhr6M2FL0oKDULqldisVhPXXy9qiewFFi5fLKrx/bqItGMQUDV7K5JopNxG9u2bWPXrl0cPXqUK664gq997WscOHCgq9ddjp+geiATCzFV6NJOpZqD9M7eg4hmIXe6q4f2OgtKkY6kOZHrbvaNme/NKFYRSKfRZ2a6emy1rPfUIKGIxEMsznX3eejVKLYZQyLJwsT5rh5rVvSeWswVWixII9+dD16vNkeKWCxGPt9li7deIBTK9hxDMJhpbvrtFENayaVXvBy58b/+1//iTW96E/V6nX379vFXf/VXPT+npwlKCHEH8DGstbu/kFJ+ZNX97wLeBujADPArUsrT9n1vAf6rfeh/k1L+jWeBr0MmFuLp6e6UA5U8jB7sPYhYFia6s7kv1Atcmm1dYuiEXkt8od27eo5BS6cxjh/v6rG1coNktrc1D4BoPMjsue73QcUcSNTRZPcjN3odtaHYCgqqpzWohjMKKhRMdz1yQ0cS6HkFytqsu3rkhhvjNgCuu+46Dh8+7MhzKTxrkhBCBICPAy8HDgBvFEKs1oAPAYeklNcAnwV+337sIPAB4BbgZuADQogBr2Jfj0wsRL7b6aFONUn0MFXXyRJfL1ZHvfjwKQI9DC3sdZquopcmiZqDCqrboYW9jtpQqATVzcgNJxVUpVLpKgZdz/fUYq6wrJJMDKPzv4dTJT6vN+s6jZddfDcDx6SUJ6SUdeBO4FXLD5BSfl1KqXZ3/QBQNbCXAV+RUs5LKReArwC9j2vskXQsxGJNx+y0xmsaUCs40yQRy0K9aI3v6AAppWNNEqlwqumM3imOrUFl0piLi8guZgA51iSRCNKoGphdjGCplnobVqiIJpLo9Rp6o/MLp15HbShELAiGRHYxeqTXWVCKaDSKaZo0ungf9Eahp026iqajeRd7oaxZUD2HcNH78XmZoMaBs8v+fc6+bT3eCnypk8cKId4uhDgshDg80+V6RCeko0GkhMVOR24o9/GYAyJQuUl06GheNao0zIZjCgo69+OT9TqyUulpFpRCS6dBSswOR26YpqReNYg4sgbV3cgNaZrUSiVHFFS3fnxOjNpQLBnGdvg+2KM2nGqSgO78+Bp6rqdhhYpeZkI5pqDU812kIze25D4oIcSbgUPA2h7HDZBSfkJKeUhKeWhkZMSd4JbRtd2RsjlyqsQHHbeaO+EioejW7qjpw9eDzZFClQk7nQlVLysfPgcUlH1iVt5+7VKrlJHS7MmHrxlDl358TozaUHRrd6RGbTiloKBzuyPDqGGatZ6czBXdKijTgVEbCr/E1z7ngeWr4Tvt21YghHgJ8D7glVLKWieP9ZruE1TO+ulUiQ86Xodq+vA5tA9q+XO2i9F0kXAgQTXtjjpUkva+pagjbebd+fHVHBi1oVjy4+ssQTnhIqHoNkE5YXOk6FZBOeFkrmjOhOrQj8+JURsKlaBabda9GPAyQd0PXCaE2CuECANvAO5efoAQ4nrgz7CS0/Syu+4FbhdCDNjNEbfbt/WVrhNUdQsoKDULKtz7F7HbEp+Rs334HCjxqXWsTocW1poKysESX4eNM81RG07sg0p0N7RwKyWofiooZU3kSBdfcyZUZxdNar0o6NA+qOXPebHhWYKSUurAO7ESyxHgM1LKx4UQHxJCvNI+7A+AJPCPQoiHhRB324+dB34XK8ndD3zIvq2vZOIXsYKqOaigui7x9W4Uq2gOLezQMLbpw+fQPijrOTs7MTsxrLAZg1JQHZb4nBi1oeg2QTkxC0rRtYJq9G4Uq+h2JpRTRrHLn8PtEt/Ro0e57rrrmv+l02k++tGP9vy8HX0abeUTkFJ25SEipbwHuGfVbe9f9vtLNnjsJ4FPdvO6btG9gspZPx1pkshaP9W6Vpvk6/YsKCebJDpMUKYDs6AUgeZU3c5OBjUn16ASvSmoiBNdfF2OfXdi1IZiKymozkt8apputucYAoEEQgQ6HrmhzF17c0S08GrkxhVXXMHDDz8MgGEYjI+P8+pXv7rn521bQQkhfgOYAI4JIY4IId7Z86tf5DSn6la7VFBOWR1Bx118TjZJNMe+d1riU7OgHLDl77bEp9agnLI6gs67+Jxcg+p27LtZ7n3UhkJE+6+glNdcxyU+paAcKPFZIzcyHXfxOamg1PMsT1BujNtYzte+9jUuvfRSLrnkkp6fa9NPoxDiY8CDwG8AV0kpp4UQI8AHhRC/K6X8/3qO4iIlFgoQCojuuvh6HbWhCEas5+qiSUIgehq10QxBC5IIJbov8aV6j0HE4xAMdlHis2dBObAGFQwFCIS0jrv4nJgFpQgEg4Qi0Y7bzJ1cg7JGbgQ6bjN3UkGpkRvdNkk4sQ/Kep70hl18X/rSl5icnFxxW0NK6qbkgYDWlZfEtm3bePnLX978d6uRG06P21jOnXfeyRvf+MYuIl9LO5/GrwM3AMPA94QQBeDHwKPArwkh/tjePPusQwjRnWGsUy4Sili2qyaJVDiF1qEFy3p04yZh5PNoiQQi6MBJUYiu3CRq5QbBkEYg5Mz7YBnGdljiKxUJBIMEww5csGCVCqvFztwLzIozozYU3dgdKbXT66gNRTeGsSqZONEkAdZaVqddfApn9FNrP752x220axarqNfr3H333Xz4wx/uNtwVbHpmkFL+M/DPQojnAr+FVea7BrgWGATuE0KkpZS9m7pdhKSjXSSoSs6Z9SdFNNOVgnKivKfoJkGZ+QKaAx18ikA6jbnYuYJyokFC0Y3dUbW4SMSBURuKaBcjN5wataHoJkE5NWpD0Y2Cauh5AoEkmuaMTelmU3WXKx3F+Wqd+YbOc3octaFoNRPK6XEbii996UvccMMNjI2N9Ri1RSd/hXcAnwEexlJPVwGPSilfZDdPPCtJx0KdT9V1ahaUoouZUE7ZHClS4c6n6lo2R86UUsAaWthNic+J9SdFJBbseKpureiMD58imujcMNapURuKbhWUE+U9RTcKStfzjqw/KULBDJXKmY4e45SLhKLbkRvdKKhPf/rTjpX3oIMmCSnl01hmrZ8Folhlvlfb99Udi+gio6sSX2XB+RLfRaigjEKBgAMuEopuhhZWS8748Ckiie5KfE7sgVqKoRsF5cyoDUUvCsopulqDahQccZFQBLso8Tnlw6fwauRGqVTiK1/5Cq95zWsce86OPpF2IvoX+z8frAR1aq5Dt+JKDrZd41wQ0SxMPdHRQwq1Atvi2xwLIR1JU5jrtM08T3jPXsdiCKRS1M90NhurVtZJDTl3UozEg8xf6OzzUC0VSQ4MOhZDNJFkqhsF5UCjiEKLhTArndlOOeVkruhqDUrPOTILSrE0ckO2XT51WkGtHrnh1riNRCLB3NycI8+l2JJefBcT3TdJOLgG1aWCykScu1LsZqqukcs7ugalZdKYXWzUdcLmSNHdGpTDJb5kglqHIzesBOXc+yC6VFBOJiiloDoZudFo5AkFs47FEAxlkNLAMNq/YDCQBB1rkbi4/fj8BNUjGXsNqu2RG0bDGo/hZIkvmrXGd5irm0lbI6V0pcRX0Ss0Ohj74UqJb3GxoxNStawTSTrZJBGkXulsBEu1uOh4ia9RrWDo7ScIs+yMk7lCiwVBNzsaueHGGlSnIzd0Pd90IXeCJcPY9i+cdKdLfHayuxgdzf0E1SOZWAhTQqne5snASZsjRYebdSt6Bd3UyUaci0E1XCiHis0wq1VkrUYg41wMgXQaDAOzTfVgNEz0muHIHiiFeq56m+rB0HXqlbKjCWrJMLa990GaEll1usTX2WZd0zRdUVDQvpuElNJ5BdU0jG1/s64bJT71vBcbfoLqkY7tjpo2R1nngujQ7ihfs74sTpf4oH27I+U67qiCynTmJlG1mxmiCSdLfMruqL0Ts0oiTmzSVTQNY9v045NVHaQzm3QVWszaT2W2+b2o1+tIKR1XUNC+m4RhlJGy4YgPn0KpsXYNY00pkQ6N2lD4Jb5nMelOE9QWUFC5mhWDk23mnTqaLzmZO9hm3vTjay8G5fjg7D6ozvz4qkVr3c7pEh+0P7TQSRcJhWpZb1dBOekioehUQTVdJBxtkrAVVJslviWbI8dCuKin6voJqkfS9pe6cwXl5Ebd7Mrn3gRVhnNi1IZCJbt2GyWMfA6AQNbZNSjruTtUUA6Wtjp1NHczQbXbau6kD5+i0xKfGwmqUwXVaOQA+lri0+0c4sSojWYMQj23n6CedTQNYztVUI6W+DIrn3sTnrElvrR1km/X0bymjGL7WOJbmgXlQomvUwXlYKIWWyBBdaqgVBnOyRJfqMMSn9NGscufy+0S3//8n/+TgwcPcvXVV/PGN76x4xb/VvgJqkc6XoNS60SulPhybR2+FRKU6UKC0mwF1fYalF3ii/azxNc0inWwSSLZ2Uwo047V8S4+Li4FpSyJnCzxBQJJhAi0PRPKjRKfFyM3zp8/z5/8yZ9w+PBhHnvsMQzD4M477+z5ef0E1SNbq0ki19bhzXHvDreZQwdrUC42SbRb4nNyWKGi6xKfg/ugOi7xVVwo8dkjN9p1NHcjQSm/ubYVVLPE59z3whq5kW57JpQq8TmpoNTzKQXl1rgNXdepVCrouk65XGbHjh09P6dzn8hnKclIkIDWwciNSg7CSQg4d1IkFINAuCMFFQ1EiQadc1AIBULEgrH2S3y5PIRC1pgMh9ASCdC0tkt81VIDoQnCUWccvAGCYQ0tIDpukogkEs7FEAoRDEc6X4NyUEGJgEBEAh0rKCetjtTIjbbXoJolvqxjMcDGhrFPPfW7LBaPLMVgmtRMyaNBDdHlZt1U8iouv3zlFCRr5MaSgnJ63Mb4+Di//du/ze7du4nFYtx+++3cfvvtXcW/HD9B9YgQgnQ02JmCcrK8ZwXRkWGs00axilQ41dEaVCCTccw9G0BoGoFUqu0SX61kGcU6GoMQROLtG8ZWi0UiiQSa5lySBIgmEu138ZUbiEgAEXC2oNKJH1+lUiEUChEKOXjhhqXI2u7ia+QQIoymOafiwOrka3cNSgII50ZtKFb78Tk9bmNhYYG77rqLkydPks1mef3rX8/f/d3frUl6neInKAew3CTa3ajrsFGsogO7o3wt7+j6kyIdTndU4nOyvKfQMhmMQnudhNVyw9H1J0UkHmp7aKHTLhLNGBLJtvdBWU7mzp8KOk1QTpb3FJ0qqFDI2Ysm2NgwdrXSOVetk2sYXJ1y9r1YPXLD6XEbX/3qV9m7dy8jIyMAvOY1r+F73/vexZWghBB3AB/DUpx/IaX8yKr7bwU+ijVv6g1Sys8uu8/AGvMBcEZK+UpPgm6Djvz4KjnnFRR0pqDqeUdbzBWdOJq7laCsoYXtd/E56WSusOyO2i/xRRPOJ6hoMtm2k4RZdtaHT9FJgqpWq46W9xSdKKhGI+94eQ+sEl+lcratY3Upm23hjsYgoNbhyI1OFNTu3bv5wQ9+QLlcJhaL8bWvfY1Dhw51E+oKPGuSEEIEgI8DLwcOAG8UQhxYddgZ4JeAT7V4ioqU8jr7vy2TnMDarNtRie+ZqqAiWyRB5dtdg9JdU1DVthVU0dEW82YMHYzccEtBdWIYuxUUlN7IOTbqfTmdTNV12uZI4fbIjVtuuYXXve513HDDDTznOc/BNE3e/va39/y8Xiqom4FjUsoTAEKIO4FXAc05EVLKU/Z97TtMbgHSsRDnF9rsgqnk3ElQ0SzMPtXWoYWas07minQ4zZP1J9s61sjniF5xheMxBAYGqJ8/19axtXKDge3ONWkooskguan21Eu1tEh61Jnpo8uJJVPMnDrZ1rFmpUFozLkmDUWnJb7BQedGjig6UlB6nmi0986z1QSDGXQ939bIDUM6u0lXERDWc0spXRu38cEPfpAPfvCDjjyXwss283Fguc49Z9/WLlEhxGEhxA+EED/raGQ90lmJb8GdEl8suzVKfG2uQZk5lxRUNouxkGvr2GpJd9RFQhFNhKgU2/s8VIrODitsxpBMUSm2+bdw2MlcocVDmOVGW+7ybikolaDaiaHRyDWtiZwkFEzbIzc2v2gxXCrxXax+fBfTPqhLpJSHgF8APiqEuHT1AUKIt9tJ7PDMzIxngakEtemXoFEBvQJx568UiWYsLz5zY/FZ1avUjJorXXzpSJqyXqZhbnxylvU6ZrnsqM2RIpDNYhYKyE1GTZiGSb2iO7oHShFNhGhUDQx947+FNE1qxSIxF0p8sVQavVajUa9tHIOUjs+CUgQSQdBlWyM33EpQ8Xgc0zSp1TZ+H0CN2sg6HoOa0NtOmU93q8R3kY7c8DJBnQd2Lfv3Tvu2tpBSnrd/ngC+AVzf4phPSCkPSSkPqW4SL8jEQuimpFzfZB5Ted76GXMjQWUBac2F2gA3XCQUarNusb7x2ocyc9VcUlDLX2M9ahXlIuH8iTlmz5eqljZO1LVKGSlNVxRULGX9LaqLG3c0yroJhmyauzqJsk4yN3kfGo0Guq67pqAAyuXyhseZZh3DKLukoNRMqI3XRqWUmA7PglJcrCM3vExQ9wOXCSH2CiHCwBuAu9t5oBBiQAgRsX8fBl7AsrWrftO2m0TFTlDxIeeDaNPuyA2jWEW7dkduuEgoAgOWCa+xsPHokaaTuQslPqXKqpuU+ZZ8+Fwo8aWs56wsbvy3UOMwXOnis5/T3GRPmBsuEoq4vRF8s3Uo5fTgVhcfbG4Yq8pvbjVJLH+NiwXPEpSUUgfeCdwLHAE+I6V8XAjxISHEKwGEEDcJIc4Brwf+TAjxuP3wq4DDQohHgK8DH5FSXnwJqjxn/XSlxJe1fm6yDuWmglLPudk61FKCyjoeQ1NB5XIbHqfUjRtdfNE2FdSSk7k7Jb7lr7EebrhIKLREewrKiwS1mYLSbZujoINGsQplPrvZZl03jGIVF+vIDU/3QUkp7wHuWXXb+5f9fj9W6W/1474HPMf1ALuk8wTVPwWlkocbCSoVtq7aN1VQLsyCUrSboJRXnpNO5op2S3xLPnwulPiSbSooF0ZtKJolvk1sn7ZCgnJj1IYi2OZMKLWR1q0uPrj4EtTF1CSxZcnaX8TcZv5rZTdLfPZ8qU2m6m6pEp8LTRLBgaz1Gu0qKJe6+KCdEp97CipqK6jKJmtQqsQnXFmD6n+Jr901KDdGbSjaVlD2T2dNr+zntJOe7mJ++tjHPsbVV1/NwYMH+ehHP+rIc/oJygEGE2EAFsr1jQ9sNkk4OKxQoZKeeo11cLPEl41kgaWJvevRHFbopoLabA2q6WTuvHJoJqjNFFRJjXt3o0lCKaiNT4quKig76Rl9LPFFo1GEEJuvQTWsz0so5Px3MxBIANqmIzfcVFAauDpy47HHHuPP//zP+dGPfsQjjzzCF7/4RY4dO9bz8/oJygEG4laCmi9tlqDmIJJx1slcoToDVRlxHXK1HEEtSCzo/MlAJb2F6sbJwcjnQdPQXFAOIh5HhEKbKyhb3URcWHsJhgMEw9rmCsouv7mhoALBEOFYbNMuPpWgAi4kKBEQlpvEJpUFpW7iDjrbKzRNIxaLtVHicy9BCaG1NXLDzTUoIYTlJoE74zaOHDnCLbfcQjweJxgM8pM/+ZN8/vOf7zlu3yzWAaKhAIlwYPMEVZl3p0ECIBi2kt8mCSpfszbpOm2ICRDUgmQimc0T1MKC5WSuOX99JIQgkM2it5GgIvEgmsMO3opoIrRpgiov5gnH4gSCLlywYDVKVDZrkig1EGENEXKjsGQlvs1KfOVymWAwSDgcdiWGeDy+eYKqLyBE2FY7zhMKZZqNGMv5/54+x2NFKznUTUnDlCQCWk925lcnY/zuZWuW8q2RG3YSdHrcxtVXX8373vc+5ubmiMVi3HPPPY548fkJyiEGEmEW2lFQbiUosJ67NLvhIblajoGoCyVGm4HIAAu1zRJUjoALtjaKwMDApm4SlVKDWMqdEyJYnXyblfgqhQKxtPMbppdiSG/eJFFqODrqfTVaItSWgnJDPSnaVVDh0IArF24AodBgU6Wth8Qqwzk+a8NGOZoHcX7cxlVXXcW73/1ubr/9dhKJBNdddx2BQO8XPX6CcojBRJi5TRPUPCRH3QsiMbypglqoLriboKID5DbpJDTm5wnYzQxuEMhmNy3xVRbdGbWhiCbaSFCLBeIp59fhFLFUqllGXA+z3EBLupig4iGMwsYuDm4nqHg8Tm6Tz0O9MU8o7N73IhwepFq9sOb25UrnVKVG1TS5MuF8+R2sta26NAni/LgNgLe+9a289a1vBeC9730vO3euVXEdx9zzM/gAVoLafA1qHkaudC+I+BAU1n4JlrNQW+Cy7GWuhZCNZDlX3Nis1cgtEN6z17UYAtkstePHNzymWmyQGnJ+vIMimgwxc2ZjF+1KoUDSRSUZS6VZmNz482C4raDiQRqTG3vQeZGgLlzY+H1oNBZcWX9ShEKDLBYe2/AY3ZSuNEgogkJQNiGy+aFAZwoKYHp6mtHRUc6cOcPnP/95fvCDH3QX6DL8JgmHGIy3k6Dm3GkxV8SH+q6gBqODmyoofX6h6fjgBm0pqGKdWKr/CirmooKKplJUNrF8MksNAi4qSS0e2nSjbrlcJuHgyPvVqDWojbwyG415VxNUODRAvTG/YQzWLCgXE5RmvUY7xrnd8NrXvpYDBw7wile8go9//ONk7Y7aXvAVlEMMbKagGlVolFxeg7ITlJR2MXslhmmQr+VdTVDZSJaF2sK6owWkaWLkcgQGXUxQAwMYudz6MUhJtdhobqh1g2gyRK2sY5oSTWsdQ6WQd3UNKpZMU6+UMXSdQLD1V90suWMUq9ASQWTDRDaMdRsxSqWS62tQhmFQr9dXlLaWU68vEAq5990MhQeRsoFhrO9T6daoDUVQCJCw6xJ3xm18+9vfduR5luMrKIcYTIQp1w2qjXUMY5s+fC4nKL0K9dYllXw9j0Q29yu5wUB0AN3UKTZafxHNQgEMg6DLCgrDwFynxbpRNTANSTTpYpNEImR5967TIKDXauiNetOSyA02szuSDRNZN1xfgwIw1unkMwyDWq3meokP1vfjM00dXc8TdlVBWd/7er31PkUpJTrSFaNYxdJm3YvHTcJPUA6x6WZdN22OFInhla+1CtX+PRh1L0kqdbZeq7lub6B1tYtvE7ujStH6G7mqoDZxk1Ddda528W1iGGuUlVGs+wlqvTKfm3ugFJvZHVkmrtL1NSiwSomtMCTghYLCT1DPSlSCmiuul6BcHLWhaLpJtG41V0nDVQUVsRPUOq3mqv07kHVTQWXs12odgxomGHUxQS358bVWDuWC5Srg5hrUZiM3VNJwcw0qkNjY7mgrJCg3N+kqwmHru1m3E9TqdSA3N+kq1CDEfvrxdbr+5Scoh9gSCiquFFTrqzSVNPqpoIwFKzY3myRU+XA9BVVdtE7MMTdLfCpBrXPB0lRQHpT41lNQKkFpLjdJwPqGsV4kqM38+Op2glJJxA2aCqo+TzQaZW5ubsXJ2k2bI0W/FZSUkrm5OaLR9rtn/SYJh9jU7sjNWVAKtb61SYnP7X1Qy19rNUrVBN1skti0xOe+gtrMj08ljbirG3XtEt86o9+fLQlqszUoVXZzV0HZa1CNeXbu3Mm5c+dYPvW7YpjMNnQIBwm74LACVoKYqjWoBgNMB91xDtmMaDTa0f4oP0E5xFBikwTlplGsQiW/ddwktkKJT5+316DcbJKw17fUa62muQblZpu5nfwq661BeVHis5Pfeq3mzQTlZhefcjRfr9S5BRRUo+5+iS8QiKNpURr1OUKhEHv3rtwH+OmJOX7rybP86Ln72R1rd6dS57ziWz/mF7ZnW1ohbUX8Ep9DpGMhNMH6dkflOYikLc88t4hmQAuuq6BytRzJUJJwwL0YYsEYkUBk3b1QxsICIhZDc8G5WqGlUpZh7Hzr96FabKAFBaGIe1eRoUiAQEijsri+ghKaRsTFE3MoHCEUia7raG6UdRDuNkmIoIaIBPraJLGZYawXa1Dq+evrNEnM292/QyF3NcNQKMjcep3GWxA/QTlEQBNk4xvYHZXn3FVPYO19ig+t2yQxX513VT1ZIYjmXqhWuG1zpGIIDA2hz7ZOUJVig1gy7JrvmoohngpTKbT+PJQLeWKptCuGucuJZ7OU1il1mqUGWiyIaLFPy0kCqTDGOmtxpVKJSCTiiG/bRsTjcUql1tsvGo0FAoE4gYB7ziJglfnW6+Kbb+hENEHcJfNixVAoyFx9Y/PerYSfoBxkMBFev0miOO2uD58iPrxuk0SulnO1QUIxGB1cv808t0BwwP0YgoOD6BsoKDfXnxSxVIjK4jpNEoWCqw0Sing6Q9mev7Uas9Rwdf1JoSVCmOuUOt22OVIkk0mKxdZ78+qNOVcm6a4mFBpcdx/UbF1nMBR09aIJYCgcZK7hJ6hnJRvaHZVmIOFFghrcsEkiG826HsKGCmoh5+r6kyIwPISxjoKqFuuu7oFSxNNhyuslqEV3ncybMWQGmi3tq3HbyVwRSIY2VFBu2hwpEonEugqqXp8jHB52PYZwaGhdBTVTbzDicnkPVInPT1DPSjY0jC1OQ3LE/SASw+s3SdQWmk0MbjIQHVi/i29+3pMEFRwcQp9vfTIoL7prc6SIpcKU1yvx5XPEM+6/D4lMdl0FZRTrBFxsFFFoqfC6CqpUKpF0YWDjajZUUPVZwhH3v5uh8MYKaiTs/t9Clfjc8uNzGk8TlBDiDiHEUSHEMSHEe1rcf6sQ4kEhhC6EeN2q+94ihHja/u8t3kXdPuv68Rm6pWo8UVCtDWOllMxX5j0p8a03ckNKiT47S3DY/avV4PAQxuxsyy9iuVAnnnavU0oRS4epLjaQ5toYSrkFEpms6zHEMxkqhQKmuXZh3FhsoLm4F0wRSIYwyzrSMNfcVywWPVNQtVqNRmNtoqzXZwiHXNz+YRMODWKaFQxjbbv7TENnJOyBggoHqUtJscXfYiviWYISQgSAjwMvBw4AbxRCHFh12Bngl4BPrXrsIPAB4BbgZuADQgj3Lz87ZCRpJShj9QmpPAdIb9agEiPWnitj5RdxsbFI3awzHHM/OQxEBqzXM1Yma7NURlarniSowOAQstHAXHXVXK/q6DWDeMb9E3M8FcY0JbVVLgqNeo16pUzCRTeNZgyZLFKaa9wkpG4iKzoBF4c2KlQSXN3JZxgG5XLZMwUFa1vNpTSo1+c9KfGFwsruaGV1wZTSKvF5kaBsw975i6TM56WCuhk4JqU8IaWsA3cCr1p+gJTylJTyx8Dq9P4y4CtSynkp5QLwFeAOL4LuhJFUBFO22AtVmrZ+epGg1GusKvPNVqx/e5Gg1GvMV1eWM4xZa2NicMQbBQWgz658H1TTQjzt/ok5lrZKNqvXocp2V13cgXEEm6HKiKVVZT7DLrm5aRSrCNivYaxquVfJwosEpVTa6jKflSxMT0p8S4axKyscOd1Al3iUoKzXuFg6+bxMUOPA2WX/Pmff5thjhRBvF0IcFkIcXr5L2ytGUlbZaGZx1QTRop2gvCjxJcfs15xccfNcxfpSeJmgZsor/wYqWXiloMBa81pOOe9dgorb6mR1q3kpZ11BJzxag4KlpKgw7aYFbxRUa8NYlSy8VFCrGyVqdesz6a2CWvmZnLGTxagXa1B2Epz1FZT3SCk/IaU8JKU8NDLiQUPCKlSCml5cNUm1ZJ+oPVFQKkFNr7i5HwpKvaZCJaiAR2tQ1muuvFpVTQsxTxSU9RprFJStZrwo8cUyllNFuZBbcbthx+SNggqveE2FSlBerUEtf01FvZmgvFBQ1ue+Vl954TZTtxL3sAcKathWULO+glrDeWDXsn/vtG9z+7GeMZK0Nvqtr6A8SJoqCRanVtysksVQzP3F4GaCqq5KUDO2gvLg4kHZHa12k1AJylMFtdhaQXlR4lMqbXUnn+qq80RB2Z2Cqzv5vFRQKkGtVlAqQUU8UFCRiPXdrNdWJygrWXjRxadU2lR94ynHWwUvE9T9wGVCiL1CiDDwBuDuNh97L3C7EGLAbo643b5tSzFsf9lniqsSVGkaglGIpNwPoqmg1iaokBYiHXZ/782gPVJkttxCQQUCBDLu+c8pgsqPr4WCEsJqAXebaCKEEKxpNVfJIp7Ouh5DJJFACwTXrkHZSTPgQRefCAcQIW3NXiiVLLxQUOFwmHA43EJBzdj3e1B2DsQIBJLU6iurG0pBebEGFQ1oZIMBpnwFtRIppQ68EyuxHAE+I6V8XAjxISHEKwGEEDcJIc4Brwf+TAjxuP3YeeB3sZLc/cCH7Nu2FPFwkGQk2EJB2Zt0Xd4lDkAwAtEsLK5NUMOxYdd3qgOEtBADkYEWJb4ZgkNDrtv7AIhgkEA2u8ZNolyoE02FW45hdzwGTRBNhdf48ZVyC0RT6XXHsDsagxDEM2vdJMxiAxG1EocXMbRykygWi4RCoXXHsDtNq8269fosmhYhEHBfxYGlolopqJAQZD1yGB8Nh5iqXRwKylM3cynlPcA9q257/7Lf78cq37V67CeBT7oaoAOMpiJrE1TJo026iuTYGgU1V5nzZP1JMRwfbrkG5UWDhKKVm0S5UG+W3rwg3mKzrld7oJoxtNisayzWPSnvKbQWfnzFYtGT8p4imUy2TFDhsDcXbmCtda1VUDrD4SCaRzFsiwT9Et+zleFWCao47U0HnyI52rJJwov1J8VwdG2CMmZmCXjQYq4IDo+gr+rmLBfqnuyBUsTToZYlvoQH60+KVm4SRrHuSYOEIpBsraC8TFCJRGJtia8260l5T9FKQU17ZHOkuJgUlJ+gHGYkFVm7BuWVzZEita3lGpSnCirWfwUVGhtFn16ZqMuFmicNEopEJkI5v/LzUMoveGJz1IxhYJDiwsqKuLnY8FRBBVLhNV18XtkcKVrZHdUbs5508Cki4VFq9akVDide2RwpxiIhZi4SuyM/QTnMSDLCTGHZCcnQrfEXqnnBC1SJz/4AGqbBQm3B8xLfTGWm+SWQpok+P09w2LuTQXB0lMbMDNK09n1LKW2bIw8TVDZCKV/HXOYuUsoteNJirkgODlHO5TCNJbsjY7HuSYOEIpC2/PikvrQH3yubI0UqlaJSqaywO7JKfN5VFsKREUyzhq4vOXt4ZXOkGLPtjhb0rT8Xyk9QDjOSirBY06nU7T9+cQqkCekd3gWRHIVGGerW1eJCbQFTmgxHPUxQ0WEaZoNC3ZrmauTzoOueKqjg6Bg0Gs0x8/WKjqlLzxOUNGWz1bxeraDXasQ9XINKDgwhpdlsb5cNA1kzvC3x2d6HSkXpuk6lUvFUQaVt9/hF2/bJNHXb5shbBQVQt9ehDCmZrjfYFvHub9FsNb8Iynx+gnIYtVl3VpX5Chesn+l2TTMcYNVmXS836SrUaykHC7UWpDbQekFwzDoZ6FNWubPkoYuEIpG1Pg+lnPV5KNrOFkkPZmIpUkPD9mtbfwvDXhMLeGCYqwjY637qtVWSSHswckSxOkFZScIkGtnuWQwqGdZq1ndzpq5jSNjuYYIas19r+iJoNfcTlMOscZNYVAnKYwUFzXWo6bL1ZRiOe5egRuLWF3GmYiUmlSSCY96VOkP2azVUglqwkkRywLsTs3qt4oJKUNbFgkoansRg2z41E5S9JhbIeljiy0RWvHahYClrLxNUKpVa8dq1mmUHFolu8yyGSMT6TKr9VxdqVsL2MkFtsxXUpK+gnn1sS1tuEhN5O0EpBZXyMEGltq947cmS9UXcFvfui6gUlEqOjYkJAELbvItBJUN92joZLC5Yf5PkgLujvZezWkEtzlkJKtmHBLVoJ0fdVpIqaXhBwFathv3a/UhQ6rXUa1ftBOWlglJuEqrVfMJOEju8LPFFrPWu6Yug1dxPUA6zIxsDYCK3LEEFItakW69Q5cT8OcBKUAER8LTENxa3ksNU2VIv+uQkCOGJzZEiODwMQjTVm1IxCQ9PzLFUGKGJtQlq0LtSZ8zeFLxGQXn4PohYEIIaRqF/CioajRIOh5cUVNVWUBHvLpoCgSSaFm22mqsEtT3iYdk5ECAZ0C6KvVB+gnKYdDRIIhzgQt4eSla4YJX3PNqEB0A0DZEMFCy7wsnSJCPxEQKaNzvVAeKhOJlIpqneGhOTBEdGECHvrhRFMEhgeIjGtCrxVYmlwwQ8cE9QaJogkQkvS1AzxFJpQmEPk4MQJAaGViQoEQuihb37PAghCGbCzTWoQqFAJBIhGvVOzYJV5lNrULXaJJoWIxj0LkkKIYhERpvq7UK1QUQTDIa8+1sAbIuE/BLfsxEhBNuzsZUKysv1J0VmHPJWgpoqT3la3lNsi29jomSV9vSpSYLbvY8hNDqGPmWVU4oLNVIerj8pEtkIxWaTxJyn5T1FcnBZgsrVCHq4WVmhpSMr1qC8VE+KdDq9rMQ3QTS6zTMXCUU0soNa1Sq/T9TqbI+EPI9hRyTEBT9BPTvZnokuKajFfiWonZC3RmhNlibZlvA+OWxPbF+hoELbvKv1K4JjY80S3+JCrbkm5CWJbGRJQc3OeNogoUgODlFcWOri87K8pwisUlD9TlC16oSn5T1FNDpOtWZduE3UGp42SCjGo2HOVeubH9hn/ATlAjsyMS7kqtZG2X4pqPQ4FM4jpbQUVB8S1FhijInSBFJKGpOThLZ5uFnZJjg2utRmvlAlOehtSQlWJaj5OVKD3ieo1OAgi/NzSCkx8rX+JKh0BKNQQ0pJPp/vW4IqFouYpkm1NtmnBLWDWm0K06xzodZgh4frT4qdkTDTdZ2qsXp4+dbCT1AusCMbY7ZYo1aYBqPubQefIjMO5TkWFi9QM2p9U1CL9UUW5yaQlQrBPiio0NgYRj5PNVekXjVI9kFBJbMR6lWDUr5EtbjYHwU1MIReq1EtLGIWG31TUOiSxmKNYrHYlwSVSqUwTZNisUC9Pu1pB58iGh0HJJXqJJN9UlA7o1ZSnNjiZT4/QbnA9qx1lT4/cdq6oS8lPmu+4+TMY8BSV52XbE9YX/6pk08AEOrHGtQO673PPWV1NCYH+5Cg7NecPmmtO/QjQaVsi6nFM9Z6XL8UFEB+wtqs3C8FBTC/cBopDSLRfiQo6zM5UZygLqWnLhKK8aj1mlu9zOcnKBfYkbFazfNTp6wbvHSRUNivOTl/FKAvCkq95sKZpwFvN+kqQjut6S35E9ZaWDLrfYkvPWR9HmZOW+sOyT6U+DIj1nu/eM5qbw70oUkiaJdXcxPWWlg/ElTWdpFfWDgBQLRPJT6AMyXrb+HlHijFLltBna35CepZh1JQtRnrS8DAJd4HkbES1FTuFNCfBKUU1OK5kwCEtvehxDduJajCecuHzksXCUV62EpQ8xNWkkx56EfYjGHUSlDVyRzQHwUVtN/73Ez/FJRKUIXCKQAifSjxRSJWgjpdstrdx6PeXyxsj4QQwHlfQT37UAqKhVMQSkDcu02ZTZSCKl4gqAUZjHq4UdhmJD6CJjRqExcgEPDUKFYRHBlGhMMszpQQgr508cVSIYJhjdzUFAjRlyaJWCpNOBajMVcGlpKFl2jxECIaZGHeulgYGPDO0V0RjUaJxWJUymcAiMVazkd1lUAgQjg8zJmq1ThzSR8SVFjTGAuHOFf116CedcTCAQYTYUKLZy315PEeB8Aa/Z4c41xlivHkOJrw/k8d1IKMxEYQ56cI7diB8GDE+WqEphEaH2exYJAciBIIev8+CCFID8cozk2THBwiGPb+hCSEIDMyhizoaOkwwuONoYrgUJTcYp5EIkG4D+8DWImx3jhPKDRAMJjqSwzRyA7O1gWZYICsh8MKl7MzGvLXoJ6tXDIUJ1k+D9k+lPcUA3s4W8+zM+X9VaJiPDlOZHKB8K5dfYshtGsnxVqI9EisbzGkh6JUFmfJjnpfalVkxrYRrAaaa0H9IDgQIV8p9EU9KQYGBpByhli0f5/JSHQHFxrhvqgnxc5omPP+GtQSQog7hBBHhRDHhBDvaXF/RAjxD/b9PxRC7LFv3yOEqAghHrb/+79ext0NewfjDOkTMLCnbzHIgX2ck3V2Jfv3RbwkfQnp2TKh3f2LIbxzJyWSZIb7d2JODcdoVOfJjPUxQY2OEZFxAh6a5a4mMBgjr5f6nqACgQWifUxQseg4k2am2azQD3ZGw5yvNjC28GRdzxKUECIAfBx4OXAAeKMQ4sCqw94KLEgp9wP/E/gfy+47LqW8zv7v1zwJugeuzDRIUKWR7t+XIDcwzqIm2NWHFnPFXm2UREUit/cvBrbtohFKkkr3r2CQzAaQZolE1juz3NVkhrYR05JI74bYrkFkQ5Soko173yChyGYzRCJFNG20bzFEYnuYkcPsDPdvDWhPLEJDyi3dKOHlN/Zm4JiU8oSUsg7cCbxq1TGvAv7G/v2zwIuF1yZVDnFF1GqlnQ7074r5bDwDwC76U+MG2Fuyymq5Ye8X5RXVrNUwkqDUtxg0zerYCsX60DBjk0mMIoSgppX7FkM50kAKSAf7lyVTaR1Nk+hG/1RcKbSXhggzJhb6FsO+mPWdPFGp9S2GzfAyQY0DZ5f9+5x9W8tjpJQ6kAfUN3qvEOIhIcQ3hRA/4XawvbIHq6X4pNm/q7SzdlPCrnr/PoDb7O/fRLZ/ZYRKxPoIRauzfYvBNHIAaIFM32JIhrIAFPV832IoCMujMiX7tx4Yi1oXC9WKd+PmVzMtrPb2Efs80Q/2xe0EVfYTVK9MALullNcD7wI+JYRYUyMQQrxdCHFYCHF4xh4x3i/G6mfRpcaTde9bihVnsUY67yz174SUmbVc3U8m+njVrlkflcjc2U2OdI9G1TZqbfSnawwgotsbZUtTfYshV7OMWlP1/ilqhG0evBjvWwinG5aC3GYc71sMY+Eg8YDmKyib88DyBZmd9m0tjxFCBIEMMCelrEkp5wCklA8Ax4HLV7+AlPITUspDUspDIx4OxmtFNH+M82KM4/N632I4Vb7AmCGJ5k73LQZ56iwLaY2Tev+uFHMLOuHGIpx+um8x5KfOI7Q4xVz/KtbmfJ26rDEz1b/Pw+z8HGGCRHJ9C4FK5QSGEWJuzuhbDMfLdSLUSdaf7FsMQgj2xSK+grK5H7hMCLFXCBEG3gDcveqYu4G32L+/DrhPSimFECN2kwVCiH3AZcAJj+LujtljTIV3c2q2f+seJ3In2K9FYa5/b1Xt+HHy21OcLvTvpLgwUSIVKFE70b/3Ye7cWaLJURYm+6ckG9NlasEK8xf6pyRnZmYYiKTRZyp9i6FcOoFpjjIz07+S71PlKrsCBaqVU32LAawyn6+gaK4pvRO4FzgCfEZK+bgQ4kNCiFfah/0lMCSEOIZVylOt6LcCPxZCPIzVPPFrUsp5r2LvGNOAuWMUk3s52acEZZgGJ/InuDQyDHPH+hKDlJLaiRPUd432LUFJKVmYKJFJSeonTiD70FIrpWT+/FmSQ9tZmCghzf6sx+nTZcyUYP7COUyzP+phdnaWodQA+mwFafTnfSiVjxEK7mJ+fh5d70+F41i5xp6ITqVyGtPsXxfdpbEIZ6v1LTt2w9M1KCnlPVLKy6WUl0op/7t92/ullHfbv1ellK+XUu6XUt4spTxh3/45KeVBu8X8BinlF7yMu2NyZ8CoIUYvZ7JQJV/2vpX0Qskas3Fpdh+UpqE053kM+sQEslwmfOml5Go5ZiveX7GWcnXqVYPB7XHMUqk5G8pLyvkc1VKRofHd6A2Txfmq5zEYpQZmSSc0GsdoNChMT3seQ6VSoVgsMjwyAoZEn/deRel6kVptknjiUkzTZH7e++vcsmFyrlrn8ngUKXXK5ZOex6C4IhHFkHCs7P1nsh0uliaJi4sZy0E8vfMgAEenFj0P4UTOKmftG7vBumH6cc9jqB23FoCHD1wPwNML3q8BLUxYCnbo0tEVMXnJ3DmrpLZtv+Uq0o8ynz5tvWb8Equjce6892W+2VnrAmVs57YVMXlJuWx9LwYHrC2Y/WimOlGuIoErM9Znslg86nkMigNJq5vySMlPUM8eJn8MCHZecQiAJycLnodwPG+diPddcpt1w9QTnsdQO2bFsPdaa1fAUwtPeR7DvJ2gRq/fZ8X0lPdJcu6cVd7cffVl1r8vFD2PoTFlvQ8DV+6yYzrjeQxTtnrddum4HZP3CapYtJoStm2zLtz6kaAeK1rK8drBXQgRpFjqX4LaF4sQ0QRHin6CevYw8QgM7mN0eIhsPMSRCe8V1JPzT7ItsY304D6ID8PUY57HUD3yBMHRUYa37WUkNtKXBDVzdpF4Okx6z3aCo6NUj3ifqKdOHieWzjC8cxvJgQizZ7z/PDTOl9DiQeI7BkiPjDF10nslOTk5SSQSYXBsmMBQlEYfEvXi4hMEAknS6f0MDQ0xOel9d+ljxQrxgMb+RJJ4fF9fFVRQE1wWj3Kk1L+mlY3wE5QbTD4K269BCMEVYymO9kFBPTH3BAeHDlpO6mMHYcr7El/18SeIXn01AJcPXN6XEt/MmUVGLrH2HkUPHKD6hPcJavrkccb2XooQgpHdKWbOen9irl8oEtqRRAjB2L5LmT7hfePMxMQE27dvRwhBeDxJ/Xw/EtRjpJJXIYTG9u3buXDhgucxPLZY4WAiRkAIkskrmqquX1yZiPoK6llDJQe507DtOQAc2JHmiYkCuoddMov1RU4XTlsJCqxYpp8A3btuIaNYon7iBNGDVq3/8sHLOZY7Rt3wLoZGzWBhosTILjtBHTxI/cRJzLJ3pSW9Xmfu3BnG9u0HYGR3itxUmXrFu+4xqZs0JkuExy3nhLG9+8lNTVAteZcgDMNgcnKS7fbQyvB4EmOhhlHyroFISoPF4pOkUtb3YseOHRQKBYpF794HU0oeK1a4OmWt/aRSV1OrTVCr96/l/ZpUjMl6g8na1psN5Scop5n8sfVz27UAXL97gGrD5MlJ78o6R+aOAHBgyPbi3XkI9CpMPepZDLUnj4CURA9aJ4Nrhq+hYTY4Mn/EsxhmzxWR0koKgJUsTZPqUe9KKjNnTmIaBqN7LwWWYpk9591JsTFVBkMSaiYoK5bpk97tC5udncUwjGaCUrE0PFRR5fJJTLOyIkGBpey84nSlTtEweY7dnJBJXwdAIf+wZzGs5sa05WrxYKF/ezbXw09QTnPmh9bPnTcCcMPuLAAPnfHOFPLxOauct5SgbrZ+njvsWQyVR601r5idoK4dsRL2I9OPeBbD9GmrtDqqSnwHrXJj5RHvYpg8bpU1x/but2OxbJemTnpX9q2fsy6OlIIatdXc5HHv1gTPnTsHLCWF8I7kiti8IG8ngVTaqm5s22Z1E54/v9rQxj3ut5PA9WnLZimVOogQQQqFhz2LYTVXp2KEheCBQv82ka+Hn6Cc5sz3YfQAxCyn5PFsjJFUhIfO5DwL4cGpB9mV2sVA1HZrzoxDagec/ZFnMVQefIDQzp0EbcupkfgIOxI7eGTGu+Qw8XSO5GCEpD3/KDQ2SmjXLioPPOBZDOeOPE5ycIj0iNVSHE+HyYzGuHAs51kMtZN5tFSYgD2oMJ7OMLBjJ+eOeNc4c/r0aRKJBENDVpu7Fg8RHI1TO+Vdos7lfkQoNEgibiXoaDTK6OgoZ85419H4g1yRbDDAFQnrbxEIxEgmryDfxwQV0TQOJmM8kPcV1DMb07CSwO7nNm8SQnD9riyHT3ujoAzT4IGpB7h5280r79h1kxWbB04K0jQp/+h+4jevjOHakWt5eOZhT9wcpJRcOJZj/PKVIxXihw5RPvyAZzGce+JRdl51Ncunxuy4LMvEsZwnjhJSSuon8kT2plfEsOuqqzn/5BOeOUqcPn2aSy65ZEUMkX0Z6qcKnjlK5PL3k83cuCKGPXv2cPbsWc8cJX6YK3FTJoG2LIZM+gYKhUf66ihxKBPnkcUyNXNrOUr4CcpJph6D+iLsfv6Km5936RBn5sucmXNfQh9dOMpiY5Gbtt208o49PwH5MzDv/rpD7emnMfJ54jevjOHQtkNMl6c5VTjlegwLE2Uqiw12XJZdcXv80CGMhQXqHvjyLUxcoJzPsevAc1bcPn5ZllpZZ+6C+1esxnwVo1Ansm/lmI+dB66mXikzc8p9F4NcLkc+n+eSSy5ZcXtkXwZZNzxpN6/WJqlUzpDNrrxo2rNnD41Gw5Nuvpl6g+OVGrdkVs7CGhh8HoZRbpYg+8FPDKSomJL7t5iK8hOUkxz7qvVz78pxVbdebpW5vvW0+5sC75+8H4BDY4dW3nHpT1k/j33N9RjKP/gBAImbViao5++wEvd3z3/X9RjOHbUU6/jl2RW3x2+xTlCl737P9RjOPm6VM3ceuHrF7TtsVXfuSfdtdqrHcwBE9q5NUABnHnO/5HrCvhhYk6DsmFSMbjI//x0ABgZuWXG7iunkSfcT9TfmrfW2FwysHLkykH0eQgSYn/+26zGsx/OzSYICvjnv/R69jfATlJM8dS/suB5SK6fo7htOMJ6N8a2n3E9Q3zj7DfZn9zOWWDVifehSGNgDx91PUIv3fZ3wpZcSGl85j3Jnaid70nv47gX3E9SpH8+QHYuTHl45GC+8cyfh/Zey+PX7XI/h2OEfkt22nYHtK9+H1GCUwR0JTj7ifmtx9Yl5AgMRgqMrZx+lBocZ2bOP4w/80PUYjh49SiaTYWxs5WcykAoTGk9SfcJ9n8jZ2fuIRLaRTB5YcXsikWDHjh089ZT7DSP/OltgNBzk2tTKz2QolCadvraZRPtBMhjgUDrRTKJbBT9BOUVpzlrjufyONXcJIXjRFSN8++lZynX3at3z1XkenH6QF+9+cesD9r8UTnwTau6VVPSFBcqHD5N6yUta3v/C8Rdy/+T9FOvuxVArNzh/NMe+64ZXrDcoUrf9FOX7D2MU3Fugr5XLnHn0ES499NyWMey7boSJYzmqRff2npg1g+qxBWIHhlrGsP/QLZw/eoRyPudaDPV6nePHj3PFFVe0jCF2YIj62UWMgnvrL4ZRY37+2wwPv7hlDFdddRXnz5+n4OLnoW6afH2+wO1DmRXrT4qhoRdRWPwx1ar3G4cVLx5K82ixwpktNH7DT1BO8cQ/ARKueHnLu19x7Q4qDYOvPOGem/bXz3wdU5q85JLWyYGrXwt6BZ78F9diKN73dTCMdRPUy/a8jJpR42tn3FNyp348i2lK9l7bemhl6sU/BbrO4n3uqagTD92Paejsv+m5Le/fe+0wUsKJR9xT1dWj86BLogeGWt6//6bngZQcu/8HrsVw7NgxdF3niiuuaHl/7OAQSKg84Z6anJ//JoZRZmS49YXblVdeCcCRI+7t0fvG/CJFw+T24TWDwAEYG/0ZAKam3ftubsYrR7MA3DWd61sMq/ETlFM89Hcw9hzYdk3Lu2/eM8i2dJS7HnbvCumfjv0Te9J7uGKg9cmAXbdAZjc8+hnXYsh9/vOELtlN9OqDLe+/duRadiZ38oUT7k1MeeK7E6SHo4ztaX0yiF57LeFLLiH32c+6FsNj991LemSUHZdf2fL+kd0pBrbFOfJd9zaJlu6fJJCNrFl/asZwyV6Gdu7m0a//q2sxPPjgg6RSKfbs2dPy/uBYnOBYnNL97l24Xbjwj4TDowwMvKDl/SMjI2zbto2HHnrIte7OT03MMRIOcttg689kPL6HdOoaJifv7svMMoBLYhEOpeN8bmqhbzGsxk9QTjDxY7jwEFz/Jsv7rgWaJnjtjeN8/eg0p+ec75Q5On+UR2Ye4eeu+LmWZQw7CLj2DVajxKzzXmzVo09ReeABBn7+DevGIITglZe+kh9N/IgTeec76RYmS1x4OsfBnxhHaOvHkH3966gcfsCV8RsLE+c589iPec5PvQxNC6wbw1Uv2MHkiTxzLrgp6HMVak/nSBwa2/B9uObFL2Py2FNMn3L+b5HL5Th27BjXX389gcD670PyudtpnC+6smm3Wptkdu4bbN/+WjQtuO5xhw4dYnJysrmh2Ekmaw2+Mlfg9WODhNb5WwBs3/F6isUnyOW921C/mjdsH+LJUpXv57ZGN5+foJzgW38AkbR18t+AtzxvDyFN4y++7XzH0Ccf+yTRQJRXXvrKjQ+8+VchEIbv/YnjMcx/8i8RkQiZV//shsf9/JU/TyQQ4a8f+2vHY3jw3tMEghpXPm/7hsdlXv1qRDTK3Cc+4XgMP7rrcwSCQa6+7aUbHnfl87YRDGs88GXnpw0vfvMcBATxm7ZteNxVt/4UoUiUH/3zPzoew3e+8x00TeOGG27Y8Lj49aOIcMCK2WFOn/4zhNAY3/HzGx73nOc8h0gkwne/63wDz8fPWOrw3463LrUqtm97NaHQAGfO/IXjMbTLa8cGGAoF+d9nvR9o2Qo/QfXK+QfhyN1wy79rukesx2g6ymtv3Mmd95/h2LRzV81PzD3BPSfv4c0H3kwm0rqc0yQ5Cte/GR7+e5h2zkW5evQo+bu/wOAvvpngwMbvw2B0kNdc9hq+cPwLjjqcz10ocvQHkzznRePE0+ENjw0ODTHwpl8gf/cXqDrYwTV3/iyPf/OrXHv7z5AcGNzw2FgyzDW37eTpw1PMOqgeGjNlSocnSdy8jWAmskkMKW746Vdx9PvfZspBh/P5+XkefPBBbrjhBrLZ7IbHatEgyZ8Yp/LoLPWzzr0Plco5zp+/k+3bX0sstmvDYyORCM9//vN58sknOXvWuWGOZ6t1/vbCHK8fG2RPbOO/RSAQY+fOtzA7+1UWFrxzfVlOLKDx9p0jfHWuwHcW+t/R5yeoXtBrcPd/gOQ2eN4723rIf7r9cqKhAO/7p0cdcTivG3U+8L0PMBAZ4Jev/uX2HnTbeyGchC/+Jhi9dxXKep2J976PQDrN0Nve1tZjfu3aXyMRTvDB73+Qhtl7J5thmNz3N0cIx4PccMclmz8AGHrb2whkMky8933IRu8xmIbBvf/7o4RjMW752de39Zjrb7+EWDLE1/7mCIbe++dBmpKFzz6NCAdI37a7rcccesWriWey3Pt/PoruxPtgmtx1112EQiFuvfXWth6T+olxtFSI+c8+hWw48D5IkyNH3o2mhdm7p73v5nOf+1ySySR33303DQfeByklv/3kWTQh+E97N1ayikt2v41oZAdHn3o/htEfb7y37xphdzTMe546R0n3xmlkPfwE1S2mCXe9w3KPeMVHIZZt62HDyQgfeMVBfnhynt/94hM9LUaa0uSD3/8gT84/yQef/0HS4dYLsGtIDMPLf9/yDfzSf+7J/kiaJhO/80Gqjz/Otv/2uwQ2uVpWDEQHeO/N7+WRmUf4vR/+Hqbs/qQkpeRbnzrK9OlFXvQLVxJLbqyeFMGBAbb9zu9QfewxJn7nd3r6W0gp+don/w8Tx47ykrf+OvFMtq3HRRMhXvSmK5k9W+Qbf/9kT/ZHUkpyXzhO/XSB7Kv2E9hERS7FkOT2f/cfmTlzin/9sz9B9mB3I6Xk3nvv5fTp09xxxx2k0+19JrVokIHXXY4+VbaSVI/vw9PHPsxC7gdcdtl7iUZ3tPW4SCTCz/7szzIzM8M///M/Y/b4Pvzu8Qm+ubDIBy7dwa5oe3+LQCDGlVf+HqXSMZ544j9jmt6NZVHEAhp/dMUuTpRr/IcjZ2h4YMm1Hp4mKCHEHUKIo0KIY0KI97S4PyKE+Af7/h8KIfYsu++/2LcfFUK8zMu417A4Bf/wJnj0H+HF71+3tXw9XnfjTt76wr38zfdP867PPEKh2vnVWq6a413feBd3H7+bX7/u17lt922dPcG1Pw/P/49w+C/hc2+z5lh1iJHLcf43f4v85z/P8K//OumXbrzmspqf3vfTvO05b+OzT32Wd3/r3eRr+Y5jqJYa3Pvnj/PEdye48Y5L2H/jaEePT9/xMoZ//d+T/9znOf+bv4W+0LlnYrVY5F/+5A/48Ve/zM2veh1XvuAnO3r8vutGuPkVe3ny+5N8+c8fo7LY+Z4gs6Kz8A9HKX1/guStO4lf17rFfj0uvfFmXvDzv8iRb3+du/7o9ygXuvhbVKv80z/9Ez/84Q957nOfy3XXXdfR42NXDJK+Yw+VR2aY+39PYBQ7fx90fZEjR97N2bOfZOfOt7Bj+8919Pj9+/fz0pe+lMcff5xPf/rTXc2KKugG7zp6lv99dppfGh/m3+7YeO1pNUNDP8Fl+/8L0zNf4sc//lVqNe/H0v/EYIoP7h/nntk8v/jjE0z1aVaU8KqdUAgRAJ4CXgqcA+4H3iilfGLZMb8OXCOl/DUhxBuAV0spf14IcQD4NHAzsAP4KnC5lHJd/Xno0CF5+LCD3TCVnDXK/eg9Vku5XoWX/R7c/PZ1O/c2QkrJ/7rvGB/96lOkoiHecNMubrtylGt3ZomFW3c8lRolHp99nPvO3sddx+6iqlf5rRt/i1888Ivrd+5tHAR8+w/h6x+GSBKu/0Vro/H4jRCOt3yIWSpRefxxil+7j9w//RNmqcTou97F4K/8clcxSCn5y8f+kj996E+Jh+K8ev+r+cmdP8nVw1cTD7WOoV7VmTmzyMlHZnny+xPUqwbPfdU+rr99d9cxzH/yr5j+4z9Gi8XIvva1pF7yYiJXHSCQTLR8TKNaZerEMY498EMe/8ZXqZVKvODn38zNP/v6rmN45Gtn+d7njxMMaRx4wQ72XjfMyO4U4Wjr7jOzbtA4V6Ty5Bzlw1OYFZ30Sy4h9VO7uo7hoS/dzTf/7pMEQmGec9tL2X/Tcxndu59IfJ2/Rb3OxMQER48e5aGHHqJSqfCiF72IW2+9FU3r7vq3+L0L5P7lBCIgSBzaRvTgEOHxJNo674NhVFlcfIzZ2fu4MPGPNBoL7N3zTvbu/Y8I0V0M999/P1/+8pfRNI3rr7+eK6+8kh07dhCNRlseXzZMHi9W+NfZPH8/Mcd8w+C3Lhnj/7d3W8uNue1w7vynePrp3wUCbN/+WkaGX0wmcz3BYGrTxzrF31+Y431Pn0Mg+LltA9wxnOFQJkEq2Poc1S1CiAeklIfW3O5hgnoe8DtSypfZ//4vAFLKDy875l77mO8LIYLAJDACvGf5scuPW+/1ek1Qb/ncnzIXS3b9+FZIxIp/tX/sBnTw2W/7OTugk0+PXPZFbRVJL5/E1Y9d/fyd/H9vKw6x6pc1Aay8obP3vtNjJbL5v70/p1z2vxse1/x7WjEIiXXR0+qc0sFJWgICQUAEEEJD2LFb56ql/5dSmKAZ1n8qjnocrZQFPbzmOdvGjtXApBLQqQuj+fYJKdAQ1v9XIagEQ5TDYcrhMFIIhGmyf26O244dY8diu00G6783oXiOwb0Pktx2DE2zSo56PYpRS2AaQUw9hJQBkOpzKKzPmlz+vL1976cCQ9ybvI0fxa5HF9ZFQtIokjELxMwqo7Ucn3/Vr/T0GuslqPU3BjjPOLC8PeYccMt6x0gpdSFEHhiyb//BqseOr3osQoi3A28H2L27vQXi9ZiOp7kQbq9cJDr4+Hdy7KZIF54T956zk+dt5yulnqmz979dZNtntU6es91LlM5OKes909o0veFDxfJf2/n/L1ceJ5sfyLai2ey57ayLBrYiXEpW1iEaWiOAMAMIPYLQowhpK6ZVF/itXnuzeDQgJMNICQ1hoGNgCIlEYlrZmIFqmfFCjkStykhxkfH8AnG7waLUPLtu8EZuEIQEaCRZeOpWtGPPI5GdJJ6cJxwtEAxX0bQGgVAdTTNAqM+WbF4cCeHMd3gnM7xVPsmby2GeDlzGGW03s2KYvMhSCUZxc0iIlwnKdaSUnwA+AZaC6uW5vvTyf+tITD4+Pj4+3eFlk8R5YPlmhJ32bS2PsUt8GWCuzcf6+Pj4+DyD8DJB3Q9cJoTYK4QIA28A7l51zN3AW+zfXwfcJ63C893AG+wuv73AZUB/drL5+Pj4+HiCZyU+e03pncC9WBXiT0opHxdCfAg4LKW8G/hL4G+FEMeAeawkhn3cZ4AnAB14x0YdfD4+Pj4+Fz+edfF5jeNt5j4+Pj4+rrBeF5/vJOHj4+PjsyXxE5SPj4+Pz5bET1A+Pj4+PlsSP0H5+Pj4+GxJ/ATl4+Pj47MlecZ28QkhZoBeR5UOA7MOhHOx478PFv77YOG/Dxb++2DhxPtwiZRyjQX/MzZBOYEQ4nCr1sdnG/77YOG/Dxb++2Dhvw8Wbr4PfonPx8fHx2dL4icoHx8fH58tiZ+gNuYT/Q5gi+C/Dxb++2Dhvw8W/vtg4dr74K9B+fj4+PhsSXwF5ePj4+OzJfETlI+Pj4/PlsRPUC0QQtwhhDgqhDgmhHhPv+PpF0KIXUKIrwshnhBCPC6E+I1+x9QvhBABIcRDQogv9juWfiKEyAohPiuEeFIIcUQI8bx+x9QPhBC/ZX8nHhNCfFoIEe13TF4ghPikEGJaCPHYstsGhRBfEUI8bf8ccOr1/AS1CiFEAPg48HLgAPBGIcSB/kbVN3TgP0kpDwDPBd7xLH4vfgM40u8gtgAfA74spbwSuJZn4XsihBgH/iNwSEp5NdZ8uzf0NyrP+GvgjlW3vQf4mpTyMuBr9r8dwU9Qa7kZOCalPCGlrAN3Aq/qc0x9QUo5IaV80P59EetkNN7fqLxHCLET+BngL/odSz8RQmSAW7EGiyKlrEspc30Nqn8EgZgQIgjEgQt9jscTpJTfwhomu5xXAX9j//43wM869Xp+glrLOHB22b/P8Sw8Ka9GCLEHuB74YZ9D6QcfBf4zYPY5jn6zF5gB/soud/6FECLR76C8Rkp5HvhD4AwwAeSllP/a36j6ypiUcsL+fRIYc+qJ/QTlsylCiCTwOeA3pZSFfsfjJUKIfwNMSykf6HcsW4AgcAPwf6SU1wMlHCznXCzYayyvwkrYO4CEEOLN/Y1qayCtfUuO7V3yE9RazgO7lv17p33bsxIhRAgrOf29lPLz/Y6nD7wAeKUQ4hRWufenhBB/19+Q+sY54JyUUqnoz2IlrGcbLwFOSilnpJQN4PPA8/scUz+ZEkJsB7B/Tjv1xH6CWsv9wGVCiL1CiDDW4ufdfY6pLwghBNZ6wxEp5R/3O55+IKX8L1LKnVLKPVifhfuklM/Kq2Up5SRwVghxhX3Ti4En+hhSvzgDPFcIEbe/Iy/mWdgssoy7gbfYv78FuMupJw469UTPFKSUuhDincC9WN05n5RSPt7nsPrFC4BfBB4VQjxs3/ZeKeU9/QvJp8/8B+Dv7Yu3E8Av9zkez5FS/lAI8VngQaxO14d4ltgeCSE+DbwIGBZCnAM+AHwE+IwQ4q1YI45+zrHX862OfHx8fHy2In6Jz8fHx8dnS+InKB8fHx+fLYmfoHx8fHx8tiR+gvLx8fHx2ZL4CcrHx8fHZ0viJygfHx8fny2Jn6B8fHx8fLYkfoLy8bkIsOdyvdT+/b8JIf5Xv2Py8XEb30nCx+fi4APAh4QQo1iu8q/sczw+Pq7jO0n4+FwkCCG+CSSBF9nzuXx8ntH4JT4fn4sAIcRzgO1A3U9OPs8W/ATl47PFsUcY/D3WDKKiEGL1yG0fn2ckfoLy8dnCCCHiWPOG/pOU8gjwu1jrUT4+z3j8NSgfHx8fny2Jr6B8fHx8fLYkfoLy8fHx8dmS+AnKx8fHx2dL4icoHx8fH58tiZ+gfHx8fHy2JH6C8vHx8fHZkvgJysfHx8dnS/L/B3AJq2ztVNc3AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "def atomic_basis(x, mu, sigma):\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()\n", + " \"\"\"\n", + " Calculates the atomic basis functions for the 1D chain of atoms.\n", " \n", - "# Yann had result: plot of 10 peaks/gaussians at different centers x integers." + " Args:\n", + " x: array of positions to calculate the wavefunction at\n", + " mu: atomic position to center Gaussian wavefunction at\n", + " sigma: broadening constant for Gaussian function\n", + "\n", + " Returns:\n", + " A 1D array of values for the wavefunction over the positions\n", + " as given by x.\n", + " \"\"\"\n", + " \n", + " return np.pi**(-1/4)*sigma**(1/2)*np.exp(-1/2*((x - mu)/sigma)**2)\n", + "\n", + "n = 10\n", + "sigma = .25\n", + "x = np.linspace(0, 10, 1000)\n", + "\n", + "plt.figure()\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$\\phi$\")\n", + "\n", + "for mu in atomic_positions(n):\n", + " plt.plot(x, atomic_basis(x, mu, sigma), label=\"n = \" + str(mu))\n", + "\n", + "plt.legend()\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { @@ -262,7 +309,8 @@ "def integrate(yk, x):\n", " # YOUR CODE HERE\n", " raise NotImplementedError()\n", - "\n", + "#https://en.wikipedia.org/wiki/Numerical_integration#Quadrature_rules_based_on_interpolating_functions\n", + "#https://www.researchgate.net/post/Is_there_any_method_better_than_Gauss_Quadrature_for_numerical_integration\n", "# \"Make sure to add all the docstrings and comments as to not lose points.\"" ] },