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@tkphd
Created September 13, 2021 15:38
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Moiré Patterns with the Sine Function
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{
"cells": [
{
"cell_type": "markdown",
"id": "107a8bc7",
"metadata": {},
"source": [
"# Moiré Patterns with the Sine Function\n",
"\n",
"Inspired by [@AlgebraFact](https://twitter.com/AlgebraFact/status/1437426209944637443):\n",
"\n",
"> Mysterious hexagonal pattern appears when plotting sin(1), sin(2), sin(3), ...\n",
">\n",
"> ![hexagonal moiré](https://pbs.twimg.com/media/E_LDhWrWEAM3PZS?format=png&name=small)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "57b1e79c",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"from math import pi\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "476e2692",
"metadata": {},
"source": [
"Let's parameterize the graph. Let:\n",
"* `X` list the minimum & maximum values for the *x*-axis\n",
"* `N` list the minimum & maximum values for *n*, the frequency of the sine curves\n",
"* `C` list the colors used to plot\n",
"\n",
"Then we can play with these values, and let Python figure out all the fiddly bits!"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6d998230",
"metadata": {},
"outputs": [],
"source": [
"def plot_moire(X, N, C):\n",
" x = np.linspace(X[0], X[1], 1001)\n",
" Y = [np.sin(n * x) for n in np.arange(N[0], N[1]+1)]\n",
" \n",
" fig, ax = plt.subplots(1, figsize=(8,4))\n",
" ax.set_xlim([X[0], X[1]])\n",
" ax.set_ylim([-1, 1])\n",
" ax.set_xlabel(\"$x$\")\n",
" ax.set_ylabel(\"$\\mathrm{sin}\\,nx\\ \\mathrm{for}\\ n\\in[%d,\\,%d]$\" % (N[0], N[1]))\n",
" for i, y in enumerate(Y):\n",
" plt.scatter(x, y, s=1, c=C[i % len(C)])"
]
},
{
"cell_type": "markdown",
"id": "4f1ab03a",
"metadata": {},
"source": [
"## Reproduce the \"mysterious hexagonal pattern\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "26eef562",
"metadata": {},
"outputs": [
{
"data": {
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bTdUlZFepMkqjF85bsoggb2cA+N8AfjiQ1+sAvHqqzKmDlS6V7wpX554UH1Fjcuwl1FyDFFLLcOXvW6ly9f1U+S5Q6kdJI6FmGrjbKXXLoOQYpnAep4gQzqOB0zeWLCJ2AbgLwPnGwcqLHOkeN2xlnGy8dzKAU43/PwzgkqkyY76dMRXO5lgRchM0ZTJshRq2uVZmXAORGokoCUr9QlstI2LIjZOQuX2gtE+lthM1ckCNatYaw1S7Y+9PyYsK4bxpTlisiFjVDfsBfGL4lsZrh/euBHClkebHALzTuu+CQXTcAuCO8d6pq9TDpmxwh6ip4FbgqZMyFaVXDKFoUsl61YKvflPtGiOISvtnjg9w52cjNRIRs9ouEdlqgSVwXo1JvwXnLVpE1L5qiQjXCsPnjJzhPe5BYIcxc8KanLbFrIxcq/Jewp25yF05cm99pNi7ubkaJ5ub8fm57i0pCDlX5Clpe8YSOM/Fb0vgPBERMxQRrg6nrop9SJ34ciZMThHBOWHlhuPnSNwlbKbkabdfTyszTjFIETO1xOdS/HNunMctInrhPBERMxQRLuSuYlLvzyEkrrx8EQEbMSuU1IfzzBU5ExinD+RMDNyRMkp+1PzHUPz+/dPllT4Xs/RIGTVdbc7jjhz0wnkiIiqIiNyJhnOiyiUQzlAhF0rYxEm0PfV/iTI4V0Q5IWpXyJsbth1UP4nZVim9DdS7P/UUjYq5f6dynoiICiKilhNTkDu4U34jIhW1Vho5ZVPQU/9rzU92KdsWJcrY2uI7SEj1qV62gWqUGYNetpG0Fs7jLtuGiAhmEWE7XYwT+tAiZO4qM2aQTNlMaZcSk28vbRl7P6dPtQhn12p3it9Rtgx6D/n3NOlz+2dPY1Q4bxoiIphFxNiJY0f2TkY+lHZGu51coBK+D7lCqCeYdlPaLoQaq+lUW0rD3PIo6XsU9NTuHNtZc+Y8n83CedMQEcEsIlyqvHbouGU5MeG4mmHCWPt6K8fMjyO6ZaIl6aeWnToJxpI0xb7Uvp5ju7uwBM6rsQ2wVM4TEcEsIkqDM7xGTROTrgQxctuYem9M/r2uxlx14CSZ2Lyo2w9TYeZS7U2pjxndiGlD7raKQWk/4IRwXn661HspaUREzExEcE9k1AFATVeCnLgHc2rIj5vMWqC0uOHO3/c9+t62ZFzbI9w2zq3vuCCcV8ZGrrYSEdG5iCitNKlfPctRrbnk5Ls/laRd+XFHIjjv5URpO2Lyp6Tl/HGmkqCQdO446KnvSkI4b16cJyKicxGR6owtQnFTjh97WGjqvtJtw0mqva7yYsEptihtwj2xbW0duy+d6p+UslIIP7XOvYiAXAjnzYvzRER0LiJSiSEnzJWKqbxiB8BU+tKkydmGSyX41DCp795YxOYx2uaKEMQ+Y6JUn1Lbz15R7ySh6oJwXj5ShL2IiM5EBNeE1IKgufObS/kp5D1HUeFaxaeGSbkQ2/ackYhSkza1/exHac/Rp7Setrtm5HAunNOyfNvvRUR0JiIoxFRrxVE6dJaK0iuVEvbYaea4auQQDK1JkhOt68K5t98SU2Oh5lgRzou3RURERyLCtUrypfM5VOpnseWEUHrQ1xronG1J2QZIyXcKuVEr8zMO2+YonmqBu23G/hoPp8aG+WuIDwrn5UQqhPPKc56IiAoigtoxHI4YyqMWgfeqymPB2ZZUIqQSPrVMyj5/TZ9J7bveV9Mmeqnj2HcHDqRty+X0vXDevPIfkdKWIiIqiAhqx5Te05sTEfeAmm0ZS/gU20ZBMvUQpJ58xlfenCIYPlt7aUtqelcUiuNJn8J5/UIiEZ2KCHFywRRi/cB+foJrdbe+zvdo7FroZQLOwRKEkAkzorW+vv13LsJUUBbcIuI4CKJw1lnA5ZcD73gH8MAD7ex44AHgjW+MsyHlnpKYax0eeGDV/5dfvnqdYs873gG85jXb+ezfD1x//fZnOfWr2UaXXw4cPLjdFiPOOgvY2Fj97R0+W311K4HYPgulf8c7gPe9b+VTz3rW6r3rr1+9n4IeOC/Vp3vgCxNz5bwgOBVJ7gXgEgBHANwJ4GrH5y8C8LcAbh6un6fe67qo2xm2Eo8NZU8hRemnrJJ6W1nVqkOprYyDB7f/j92C8L1OPVTns08wD8T2WSi9va1BOfzdO+el+nRvY6EHzsNStzMAHA/gUwAuAPAYALcAuNBK8yIA70m513VRtzN8A4zrUF2tibG3sGStOnC3r03SsQ89Si3XBHUS4Si3N7/pAdztFXuGgbtPeue81Pr25rs9cN6SRcTzAVxnvL4GwDVWGp+ImLzXdVG/4unrRGrnTqXjdPTeBk0qWrdJDMm1aHNKmTF2UQ/WlUTpQ3ucKNVevaychfPqo1abLFlEvATA24zXLwfwa1aaFwH44hBpeD+Ai6j3Gp9dAeAwgMN79+6N7Zsk1CSGXkgoF6XqwUWCvcFlL5cQKr3qTbHXB18eteoQ+owq/CjbD71DOC8etThvySLiMocQeLOV5jQApwz/7wfwSeq9rqvGT4FrTSeGHldidujezDv0GWe5nOmn9n7nChcB9SqYqBN9SrSlpECh2uAD1YYlTIrCeXnlcqa3/WnJIiJ6SwLAPQDOKr2dwQGzI3OJrubAM22y7Qt9VtL2KTunyjfJbQmErXVeu9buO85Jt7XflbBhicJ2p3JeL35nct6SRcQuAHcBON84HHmRleaJANTw/3MBfBqAotzrumqKCNOZckOuJcO+Ibs5VHms7SWIl0Juc0Bvk3qLlVnNVWgtG2rlXRrCeWl2l+a8xYoIrR/dovjE8E2L1w7vXQngyuH/VwC4YxAJfwXgO0L3Tl01RYSJVGIY76Oc4J4qoxU5xZYbGoS57ThHYjZRO4oy1W6jPTFfA+xtAk6JrpVEDzZwYKdyXq4PcuRn37doEVH7aiUiUhFDKHMgn9yV5hzqWBKlQry5RBXzNcCSfZiy+k2JRPjyrBmCXyqE844GRx1FRFQSET0SQC6p1bAxBrkDomX71rKpNFx9UKtftrbKfhPBZ0eJyaZEO9ZGj/4vnHc0OGwXEVFYRKSspnyoRSLUlVWOjaUHc04duMC578r1ZD8bNUi6t/bmnhxK1K9GO5bqF+G8+DJS0/bAeSIiGK9nPnPtmA41fyipN1XuQ2hQTA0Yqo1jPlOPd6aUGXtPD8QUm4fLjzjyn9vqNgRqe9g/XubDktrGBY76uSYx4bxwGUvjvOoiAsCZhOt0TqNqXeeeu3bMIapSK8iSqKFot7Zoj3dODVH3EInghGt1l0MMY37UxyKXQou+oIiIVlsjNcHhA6YPCudNl7FEzmshIr42fH3y7sD1aU6jal2uSARHp/VAODHgDAMvYTVYyhdy8u2lXVPsyCXLEn4X2xe9tH+uLVz+GMp3DtjJnNdCRHyMI02PV6lvZ8zNqTjtbbkvzYVe+q8U4dt5l76vRtg21u9i9/9z2r9k3/UyjnoZM1TsZM5rISJO4EjT41VKRHATTmnCb+HcpQdxT6SfipLEXJr0qRNd7bZuEcKfcz9SIZw3jV44r8nByuHpkN82/H8hgJ8BsJ/TkBZXj8+JcDlaqvNxh55jMJVP6XBiL+Sag5JEVzqU3Wv7U+u9ubnaD9/crFdmb3nXgnBefLqcNmsRiTgwPB3yMID/DOCDAH4ewIeoT4bs9eIWERzOSFWYOXvJoXu5yD+UT0w7UexxEX6pvpgjWgiG2pEg7r4aD9Tt38+T31JRi/NyJ+Clcd6sIhEAbgNwPICTADwE4LTh/RMB3MppTO2LW0RwOCPVEXLKSnF2rvdjbU9V5RzodTUdi1RSoubFPYFPlVEj8kGNRJQOu/eOWpyXW87SOC/Hf5oerLQPUAK4mdOY2lePkQiqs9Ve6fnsahk+jM0vttylEP1Yj9BXA2v4HTWfKZEQK2RK9mNsu419wPFgpx5Qi/Nyy1ka5+WM1xYi4iMAThr+P854/3EAbuI0pvbFJSI4lWMNkubMr5UgSEHqambOYsK0nSvcyoHYvpiKRHCWFYPYCM64TTLHZzOM4OYy4bz4/HIihy1ExGM9758F4BmcxtS+uEQEhaRqh8ZzSJoTcyR8O92ctzVM21us5mrkVbOs3O2LUDRoLmKVOh6E82jpa3OePPa6MxGxtUV7WtmUY9mf1yb8Uo5ce2BztKNtc6/kzhkBo2DOYooLJdtgLu3LdV5EOG+F2pwnIqIzEcHliHY+tQmlF1WeC452rB2GTc13qm49hF2XhpJtmuN3NftGOK9Nvj7EtqOIiEoigrrK43peP7cq36ko2Y61tjmoPzg1VbfWK9s5+HBrG1P6yHUPR18L580TEonoVET0eM5B0Bap2xyx6TY2aCJiCqVJuXcRQ0HtaA5H/qFIhHnmokR4fw59KgijGxEBYLfv0OVcLo5IhCjnnYPU/h6JdzyRPxK9fcjOTte7X7WegDmwBCFkwrR3/H99fSVMc89tUdMI+kZPIuL64Rc838RmDHAJgCMA7gRwtePzfwfg1uH6MIBnGp/dMzwY62ZqI7lEhG+Q9DZ4erOnFnqrdwzxjtsU5tMQzW9OlPwp6xLorS9KYG51tM9YjD42Xi4xJJzXN7jr3Y2IWNkCBeAiFkNWT8X8FIALADwGwC0ALrTSfAeAM4b/vw/AR4zP7gFwVkyZLhHhC1nbD4fJ7djc+2NXSL0OwBIhV87yqPasr9NXeq5IBLVeIft77WMBHbF9OJV+FKehSITP91K371JtnYJwHk95vYmIy9kMAZ4P4Drj9TUArgmkPwPAZ43XLCLCd3jODjHndmztybDXsGxtYogpjxplMFd7pfszZD+nT/VKwD2Cs91it7Q4xrXvYJ5vu004Lw+tOa83EfFpNkOAlwB4m/H65QB+LZD+1Vb6uwHcBOBGAFcE7rti+DGxw3v37p3sgNxQX61QIWVF0uOkUNvumPxiogO1tiKokYiUdnPtp9ciYM5+ru3rnO3mi3xOpeesq68OPXFezDaicF7jSIRxBsG+bgPwdTZDgMscIuLNnrT/EsDHATzeeG/P8PfsYSvk4qkya/wUeC0y7lV156JEvXLJsDe47Expt5KRiKn8OPt5Kq+SdeOaIDh/ijwWtbcdei2jFUpzXgsR8XkA/xzAk63rKQA+x2YIcTsDwD8bzk58cyCv1wF49VSZNUQEhWA4SK2nlVxPtrgQGzLuHS7S6U0o1ZzYawqWWFDLnvMkWYPzWkYoS9tTmvOAPffqyiLi7QBe4Pns99gMAXYBuAvA+cbByousNHux+ubGd1jvnwzgVOP/DwO4ZKrMGiLChI8YeiOMkD2+/VLq/aURE+aUX1Ks11c5Nvr27Hsg/Ng8exN3pSGcVx7xnLemdU0RUfMCsB/AJ4ZIw2uH964EcOXw/9sAfBmrr3HePIZlsPpGxy3Ddcd479RVW0T49s5bE0sMSY+Dxfx6Yk5+3KAOZl9f7DS09j0K7D7tbQLSuk+beoBwHq/dLsRyHvCkR7+QwHE1Fw4tr9oiQus8silFVDH5UlR5Tv5T5XKRzhJIv0eiGlEyvFszlN3bZDdHCOeloRTntdjOuIkjTY9XCxHBFdblID4Om2rlb+7pcdi608k5FrGEFrNV1HJ7QetwO7YWm63L5wAH501N4MJ5dJuAXTfryiLiq4FvaIzf0mD7qmfNq4WI4ELPxBeDkpPT0lFitR+z2nIhhfhK+OtUniUEOVcbppa/ZEz1p3AeHS2+nWF/K8N1PYnTqFrXlIgoGZItmV/rEGwMWobJufProT1TQdn3pYDSBjX2j6fyLClcctuwJXodD1N5CefRUV1ELPmaEhGcRNNSKfucsKRNMYO65QHHOfdxj5EICkq3U4qQ4Sx3zpGIOY8HE8J5foiIqCQiuDu65cEr38Apqd5jBislbcv2i8mrJjnMKYRrovSqca7t4kLtcy/CeXHpKGWmpi3VfiIiGK/du9eif5SmN9RwRrOMEoMwhxR6Q8jOuZB0L7Dbck4hay7UFLlLGGMjhPP8aCIiAPwf4//3uN6f4wWskb/32ytq2GmWMTVJlrJlCf0xtl3Lby1woJZddjm5q0tOW3pBjF1T/tdrHW0I5+WhlYj4a+P/j7nen+MVikSkYC6D0IfcveS5rGSo4O7P2EhEr+0ZYxfn+QTufe6UCXjufcG93TZnzuOIMPTqFyG0EhEfNf6/yfX+HC/ur3jO0aFM5NrPOWH0gNb9yf0jTFxtzz351vA7VzpuMcRpKxUtf6hL6/ZjJAccts+R80REdCwiOImmxd55DWcvTTqcbdd68HO3VW3Cp/ZFrXZOPWNR0obe8ovFnDmvRP+78uyN85qJCAAnDf9/bPh7ioiIbXA6JHXvnFrmmN/+/XUHlSs/+z1fmam2xJ47mEJLIVGjP3LymfoqY+sJzkaKmO61D0rl16rspXCey+d747xWIuInAFwLQAG4afh7LYCf4DSm9sUpIjgJk6osqWVubdEegNNileRLE1M3e4Byrmh6mwhTUYLwp3wqpkxO+3LzMvs81P+p5bSOcHFBOM9d7lTftua8Zl/xBPAzAA4DeHAQEq/iNKTF1WskosT2A1d4j7oKzS0zdsVRMlS4kwif2wc47eOeaELlUCIRqeWIME3Pq3fOo6A15zV9TgSA4wCcA+A4TiNaXb3+dkbPJENdhdZCCfJZIqgH8Fr4Xqw44BIbuUidpFofhuwRwnl05HKePGyqQxHBPZH1vG9aYhVaY4LPIaklCJDxR3wOHAina1HXmCgJVRz0Mim57OjFthwI5/Vjnw8+PxMR0aGIoJJCK/LgDGXHoJctiRhbXOmWQPpUEUFBz4RfKk/O8w/U93qGcF5efi05r+WZiBcDeDuAXwZwOYA1AI/lNKb2xSUiqOFJqoO1ej4At2O3Gsg57eeyuWeCb7HSW4KoikXpOs+tTYXz8vLjjpTM5WDl5wD8IIDLALwewB8BuJPTmNpX7UgEFePe2/79PPlR0cvqLRc57dfLGQtuEmxxCG5JKN1+OX7X8xYUFcJ56aCeFRrRUkR8iLNgTxmXADgC4E4AVzs+VwB+dfj8VgDPpt7ruigiguIU3CpaDl7locaqpvTKkfsMQ6uVbs+Co5VtOX1R44yFcN68MKdIxOsBvAqA4jTAyP94AJ8CcAGAxwC4BcCFVpr9AN4/iInnAfgI9V7XRRERlAE6t1CkIA6pWxw5k9TGxqrMjY34e7ltycmv57HR+7459V7XBJxThnDestFSRLwLwCcA3A/gvQB+CcBlbIYAzwdwnfH6GgDXWGl+A8DLjNdHAOym3Ou6TjhhTR86FG7w0pOFoH+k9q+LaA8d0nrfPj3pd5wHIUug1QTMiSUIIa3p0Qmq7wnnLRvNv50B4EQAzwHwYwDexGYI8BIAbzNevxzAr1lp3gPgBcbrGwZbJu81PrtieGjWYWCv3rdvu3F72W+komfbSqDn+lJ9Z9++1aibs99p3b99nOi9rjvJ93q2rQRK1Le5iCh1DQc2bSHwZivNex0iYo1yr+uyIxE19hs5sYTVoNbLWBFSIweu1WBOvXrvW0E6uA/5Un2v53EmnJePJYuI6tsZ9pkIyn4j935mDpYw+Wo9z71pGzlnGHImi977VpAOat9yi1DhvPJoyXnAnnt1bRExHGQ8j7NgRxm7ANwF4HzjcORFVprvtw5WfpR6r+tKOVjJfbK6BpaiyrnBOZBrnGFIPeAZAzkln45W31jg9gHhvPJoy3lrWtcWEXo1Ud/IWbCnjP3D4c1PAXjt8N6VAK7U22Lm14fPbwPwnNC9U1fKVzxzVo09r6TngJ5XNTX6gju87UKL7+uXaLsWY4O77XqZgIXz2mExkQi9mqR/HcC3cRbe+ir5A1w1CKD3kB03uOtbY1IuDe4tDs7VdMvQc4twce9PcSwN4Tx+lOC8liLibwA8Mqz0bx0iAbdyGlP7KikifESRqvJjykjFTspva6ufX+XLQc4WR2lx1PIQXM975zXOOrTA3DhvDhGwMpzXbjvjya6L05jaV4ufAufcb+QG1Zaef1Zaa9rAG23bv7/PCAMVOSRTun9KECr3T3y3mJR6EXm10CvnxdixJM4DvvlB3UJELPGqLSJcJNgToVBJmrL3W4LwqaCeYWhlXy+g+FRPE9k2CbafgFzoZXLsCT1z3pg/5Se+l8R5wJM+q1uJCADPBPCK4XompyEtrtoiYg6nnCnlUFR5CXu5yWcJpN/LloQP3Ct9LpKOtauF4OpJwKVCOC8PZTiv3XbGKwHcDuAXhus2AD/JaUztq0UkgnsvkHO/keN+7nzM/LjPMOx0kqYgl8RanIuICe1S263nsxM9QzgvL78SnNfyYOWtAE42Xp8sByvbo9f9xhjspDMM3Ojl3IHP71pEhaihXWoo20zvS9f7eY0lQTgvD82eWDlEHk4wXp8A4DZOY2pfXD8FHouSq65e9htjEEP6NQ/Atc6zBVLPHeT6Xav+5ZqAej+vEYPexweV87gjFim2+dCS81qKiFcNT4J83XDdDOCnOY2pfcU8sZJTDXIRV4yT2WlrODF1H5m6guMaVNwrlxJhx9jyezx34EKt7Y3aYpq73VqK0qVwXkrEIrfdqWW05LzqIgLA7wx/Xwng2QB+avj/WZyGtLiokYhe9+JjBqadNnffmGvfOacOqeAm6FjS5Z5w5hTOzV2ptdgeaQFO+2P9bSmclxKJyOU8Ll5MSRtC00jE8JCpJw9RiDMAnGlenMbUvqhnInoNVedEInLzN507J0Rdug41EGvXVOg7Nr8W7VK6TF/+VDHc+/YXd5mUsRozGS1lrHHmT+G83DJy0lLRQkT8FICPA/j68CNX43U3gLs4jal9cRys7HWwpSIlDDz3VR8FNbcM5tCe3KHh1O2H3LbiXjm2wtQKeilbLSWw0ziv5ZmIt3AW3MPFISLm7EwupNSn9v5zC9TsZ07SL9XmvYRtc32vxj556Xy5RcIUhPPmzXnNRMQSrx4jEWN+1K+exebb0ulrkE/r9uMCV1u1JPyYya10++aesahpU6t8qBDOo6NHzhMR0ZmI4MbodNwHm1qsuOz8agzqUu1XG5yr1JZiqpdVK8XuqTSt27J0Pq3QivNKtNscOE9ERIcignu/PEZVhso2P2ux9xub32jj6vnuaXaUWNXMnaQ5YfYpx8TcE6b8tRdB1AOWwHkl+nMOnNfyTMSvAFCchbe+uERES3IJlZ3q0K1XrQcOtA9Duuya++TB0V7ch8tK9mFs3tRIRI5AnZOoCmEJnFcjEjGFFpzXUkT8IoA/Hh99DeB7APwlpzG1rx4jEbF5UlV5CZt6ER2liWynEX/NveRY0o85QFjKP3LyFUGan6dwXp7/NN3OAPDDAP4awF8AuA7Av+A0pvbV45mIET2SjW1TaxtrTnZzRuwKuma/xpD0aBf1+Rql+j3H70psty0FrfnEhTly3lSalpGI7wLwZwD+HMARAE9nM2L14KoPAPjk8PcMR5rzhvI/DuAOAK80PnsdgM8Oj+K+GcB+SrmcIiKGsFrtJefmyU3Sc9iOWIIA6XWbyIVQX01FIloTvA3OrcYeIZxX3x4KpnyrpYj4IIAXDP8/Y5isX8xiBHAQwNXD/1cDeIMjzW4Azx7+PxXAJwBcqLdFxKtjy+UUETGk0IpAKOVyOTkln562I3xplkT2OYe3pvJuFd7t1Zap+83P5ipUhfPi86nRDt1GIo65cTWpf5jFiFVkY7eR7xHCPX8E4Lt1JyIiZr92qpNLEUxNJ685eO28UvL12TsHgm+5rbMEkeVDrbrNtQ2F8+Lz6YHzuhERK1twIosRwIPW6y9PpH8KgE8DOE1vi4h7ANwK4FrXdohx7xUADgM4vHfv3ukWj0AJZ6xNMDVVOSdy26zlRJxbVkx9e1ut94xabZXje63bXziPPx8qUtus5XbGiwG8HcAvA7gcwBqAx0bcfz2A2x3XpTEiAsApAG4E8EPGe+cAOB7AcQB+CcC1FJu4f4ArRplTy2tNEnMBd5v1sL0xbj8cOBBOF1PfuRI0N1rYldv2rvtL9adwXv+YXSQCwOcA/CCAywC8fthOuJPFCOJ2BoBvwupbIT8TyOspAG6nlHvRRWt6fV3rjQ2+cNdcQ5OCo5G7vWGns8mWks8oIjY26oZ3OfPodTzE2lW73abuH/+3v+UxVcbmphbO2+FoKSI+xFmwlfcbrYOVBx1pFIDfBvArjs92G/+/CsA7KeWedtrao18Z27/fPxBjBn9tFb1TVPuc2nVr69hH0I5Ea4cfQ9+YGG0ocSAyBy23T7gQa1dvE6XPnik7R78UzusfperZUkS8fpig2Z9aCeDxAG7A6iueNwA4c3h/D4D3Df+/AIAezj3cDOOrnAB+B8Btw2fvNkVF6BojERdf7Cb8XggjhClb5zLgpuycS5+YAsImaVckgiIQcgi+BFqX3wKt6zzlA77IhI0xEiGc1x6tOK+liHgXVl+rvB/Ae4ezB5dxGlP7Gs9EUAdkqnOWdOqlTL4tiYErb5+A4CjbTDeXPhXwYarPc7dnODmv9CQunJeHZiLi0RuAEwE8B8CPAXgTpzG1r6mDlXYnpzpnS6deiiovCUr/UOwb86EKiFQbuduqt0jHHFGqDakRBq7yODiv9SQ+F/9tZWdzEbGka0pEpBJDSVKeywApjdptyiU0StqYWj6XWE5FiXarPU5KtWHrvkjhvNIid6eCqx1ERFQUEakoOfBbq/xewNUOqcKwB9g2pbYJp+hNubeET+eG92OR0oaUNJubq8jW5maaXbUgnFceXO3Q8kzEY7H6Aa6fA/Dz48VpTO2rlIiYIgdqiDIlb25budCT3Us5X2Db3oMgSmnPHiIRLfyAUuZc/FM4r3w5XJzXUkT8CYD/CeA1AH52vDiNqX21+hVPc++8NUGkrthiyaB1WNZnS48RBiq4ti96sCklv163CTnF3Jz904RwXnlQOa+liCA9wGlOV00R4dozpDplq71212chMqhF+BSEBnDJ/ds5oIeIBRWhfux1ld6rXbUxN87zvb80zmspIt4K4Bmchbe+aoqIHGKh3Lu1xfP42alyQ2TATZ6uQcg9AS6B8EuRFbVtuPoktr9T/IMrJMyRrnQerTE3zvOVuTTOayki/gbAPw6PqL51fLgTpzG1r1aRiBL3js5c2qE500/d7xqgNQbt3MDVJnZbUEmaWv5UOo56pJSRKjhzCD+3HnPA3Dgvxd45cl5LEbEXwJOHv49enMbUvrh/gCsW3PuwFMLvedIsTdJz6MeW5acSGLX8qW8a1FjBh7boYiMuJQl/KT5VMl/hvGm47q0uIgD8xfD3YQAPGdfDAB7iNKb2RRURpVYFNVcbozO1+B0Gaki69GBfQj9OgZtwOPukdjuV3n6Yi8hNwRLGSo+c54r21eY8eU5EAxFRaqKrSTijM4V+8InLNl/ZrkEcSyq9kHRN8RODngSNjdKTuo2e28KFnuwVzsuDry9T+nj2kYhHE65+AvzU4f//NPyWxrM4jal9pZyJ6GWgl558OcPY1EgEl101kGvHWO+U781T8u1B0KRiqm1ri5Fa4LaXy8fmOuZ65LyUPuZu/5Yi4tbh7wsA/D8AlwL4CKcxta8UEdELMZW2g5L/6Nwlfisix6452GG2XcxqqSe02jev6Xe9+FsM7DB+7rMZemkD4Tye/FqKiI8Nf/8zgB8235vrlfrtjF4GVSnEqO0eHh5TGxz9b68SW+zb5iK0QuI8Z+BKw+l3oTJrrMI5/Wn8awpTjmiXcN52urlzXksR8R4AvwHgUwBOHx6DfQunMbWvVBHBTSycoa+UcmzE1K+n0HKtdiwxsXDvQbdsb62PbSNu3+P0uxJiKAYc/mTmUcJm4bz4PHvlvJYi4iQAPwTgacPr3QC+h9OY2lcvkQjOQzgp5WjNP4nZ+VJX2jll12rH0uTAPankIqW+9j3c4oAK6j537EOLSoyRnkWjcB4dMZzHtS0a047y7YwORISJkgQQkzdlQLQI29qhVeqKIGXPseTqpmY4tzd7OVbqrcLhJVaiKemXhB44z043V86L5Ucbs4pELPHiEBG9kIlpR4pNpUg+Nt+trek9xxYTUi/9nIPUduMm4hb9N1Vm7OTVw69RtkIPY8G2oSc/TFn8TUUtOG1dpIgAcCaADwD45PD3DE+6e4bHbd9sNgT1fvvqJRLBkX/p0FzNleZUXi1IbAkTQEy7lez3XMKvVSZ3Pj1MvhzogfOokYhS5dcuk9N3lioiDgK4evj/agBv8KS7B8BZqffbF/dvZ6RuP4RQini4y6emqxmqzy1rCcLBnnype/8lJ7yUSSIUaUvJr6TtvnQlJ75WEM6bH+ctVUQcAbB7+H83gCOedD4RQbrfvrhFRIzz13TA2PJTVn3Ue2quxnLbeAkrx9Swb4rfcfpqSCiEBEYuuOpAsWkMYR84kFdWSwjnzY/zlioiHrRef9mT7m4ANwG4EcAVsfcPn10B4DCAw3v37p3slBjErPR8Thf7fo6tpZyeOlg5EGqv3FX33FaKrVe/rSbzkuIlFRSbliAihPOm7++N82YrIgBcD+B2x3VphIjYM/w9G8AtAC7WkSLCvEr8FHgpZ6ypZue0DcDRXrW2R1IQU2asj9Qk6bmgZpvk+l0v7S2cNy/Om62ICBqRsB0B4HUAXp16v44UEdwhrthyeiGM3sDZXlP3tNjeGMukfOU1ts616tOj79ayiaONW02ywnl9Ire9lioi3mgdjDzoSHMytn8A7GQAHwZwCfV+17W2tqY3N1cEvbnJH+5qMekI0jHVX7Gkan4NkLLV4Mur1O9rlBBaLvQ4DlJsqtVeoTxCEzbVn8yQt3DezsNSRcTjAdwwfEXzBgBnDu/vAfC+4f8Lhi2MWwDcAeC1U/dPXWtra3p9fdUKL3xh+PkErQikp3JaYW7taEYPxr/298BNcTBFuKNdPfy+Rq3JtzTmKoZCNlDsG9MAWm9sCOf1ipL1W6SIaHWtra3pjY1VK1x88Tbhz80xfeQxt4Hms7cH8o7BGN06dMgfRYjZprDz3dwsZvok5uZTnOih7iEfsKMMLmxt6UcXTuNf4bx2aMF5IiKYRYQr9Kx1WqjQRE1nXsrk2wMxcBywMld3ufuXZrq59aeAH1M+QPER4bx+0ILzREQwiwgf7M6lOmep0HPPoUUu9FDHUD9TykqJMFDtCZXPTfhLCEv3UgfOcxFTj9vOKasnzkuth3DeNEREVBIRqap8HHjch+DmprBrgaNdzL7NPWjGTWLUSEZsO3CsaCl25tqRg9S8Y+uS05aUsmLOz+SgJ84TvvMjt21ERFQSEamgDLyUvW3Oyam1Wm9dl9QJuHW7mbBtjt0e4V7R1pqwa+TNLaByhSl3dIsbJTivlhivhZacZ6cXEdG5iKDAPLXfAlyE3+Pq04bLxtQJuCf01vY9kWTt8nPyoEYi5uafNoTz2nGeXbaIiBmKCLtTqaq8FHmkkrS955kaxqxJ0q7By0UMPYFz0opJl4rc1XlM+hYCJ2fSWKI/Cue14zyJRCxARKQSSk6YnXMw+gaOb6DlgJukKfktYf+Vuw6lt3h8+W9t0X+LwbbBt0XD2TY1tr52sj8K503blOt7IiJmKCJSnTvHuTiJKGfPNxbUHyVqGT7vEbl1mIrO+PLnChPn5he6l3PLgCJyuPtijhDOo6M254mIaCQiWoZ3U+51vdfyYUVUG7l/2bDnfiuNGNumCLjGBB2blnovdzQqta1ibO4BPY8d4by4ck2IiGgkIqb2mXJRg3ioh5tKkAd15cA9KXGHhu2yew49c/pUjfB8qUmLUj6n0Gnpn5wQzstDr5wnIqKRiCg9edQgHqoqLzG4qaqcgpYrPS5i5WyPmDK4wUmAsX6d43u9oHSfc672hfNWmDvniYhoJCK0PrpzWhJTrTAj5VkCNR6C47OvddtzrM7N7/73vCr1IXVl5UKM3x08WP5wW8/iwwe7P3JD5TuJ8ygHepfAeSIiGoqIOZJ8Dqbq65oIbcyRiKnI8QcXGVGJLJRn7bZ2lZk7Tqh+N/U1u9yVbovxnhs5sP0nV0TsJM6j1HUJnCcioqGI4HSOlqFYasiTY++XMuioeYXQoj1L2JxD2i3DzZT7uPqIe3vEJ944t2qo4O7/WuOKM69WnMfV371znoiIhiLCBkc4e4oscomQkmfJ1QY1/OezgXvCyI0elF5h5K5EW0xo3H3EhRp29SLccu+tUYZwXtgm8/6SnCcioiMRUWNCog6U0ZYU0k9V5ZS8qXn50thtXHqVG8ISQrsx9Y/1vVC7xBA+xWbOyTbHP2Pbs+cwNwXCedN5U/NqxXkiIjoSEbVIoTRJp5bJeZ8Pdhtzr45zbOkdLntj+4fqe9QQb4pfuPb1c/b6U2zh8Dvq5NAzhPP47vOhNOeJiOhIRLhQYmVSeuC68k99SIvrPk77uUN9HCvMXuFqg7FeU9+AsNPHtAN35IBbRKTYx+F3Zh7UkPccIJw3L85bpIgAcCaADwD45PD3DEeapwO42bgeAvDTw2evA/BZ47P9lHJLiIixIyk/25u6MuEeYC7n41TlpZW6L01OKH6uWxf2REVdFXOiRn/XGAMpiCX8Xn/eOwbCefPivKWKiIMArh7+vxrAGybSHw/gfgBP1tsi4tWx5aaICMqKxfXVPcpql+p4PZN0T4SfExKlTsY1EBO2TY3AlF45tW5DE6XtoxJ+zuRZsz2F8+rl5QNnOy1VRBwBsHv4fzeAIxPpvwfAXxqvq4kI6sRUck+rJ0JuAe52muof7v6LxVg+52ErXxkxfs2dfy3k2EJpA866+lb5qSv6HBuE89qBs52WKiIetF5/eSL9tQBeYbx+HYB7ANw6fHbMdojreuYz1/TGhtbr61ofOkRbmaU4c40BsNRB1kPbcYSozX3T2CiHKxLRIlxaevKthdJiiDuq4To7kTppb26u+G5j49hzMcJ5faB0vWYrIgBcD+B2x3VpjIgA8BgADwA4x3jvnGGL4zgAvwTg2sD9VwA4DODw6afvfXSFt2/f0YOwp5UTBTVXJiWRSo49wCR8+2mK5g8BmXWaql8P4eyWZfaGntrdJ0ZDNo5+OPqicF5buGwu3Q+zFRFBIyK2MwbR8aeBz58C4HZKub5IhLnyo55i17qtE8958jXREzGkTOCj76yvH12PlEiEbxXKXR+u9DsRMW2U257UMR4a+75IhHBeG7hslkhEmoh4o3Ww8mAg7TsBXG69t9v4/1UA3kkp13cmImalOIKb8Mc8U51prhNAyzpzkLT5ee7Je18+tp2x2y1U/0yNklAxh5D31P0xbepLS93SSj28SIFwXhu0GENLFRGPB3DD8BXPGwCcOby/B8D7jHQnAfgigMdZ9/8OgNuGMxHvNkVF6PKJCOpK0QR14hjzo6h9TmXd6wDjtIvSXqHyqFGQKZu56uTLx7aT6iex34PnnEBL3F+jDE4hRe3PkB2lvhIqnFcH3DalcN4iRUSri/M5EVNh6fEzc+BNkVMPT2Mz7TGJwP6bamMN0nC1vyt8mFuXWigZiWgZnucgWO48a6yMqZGI3nyTKrKF8/hs8tkYw3kiIjoVESGYnUidsGJCipRVMddkbx4QpBDDFHLsS5k8XffUWBHXAEeEhMvvYjDmZT6FMtUXcvJIsZl7Vd2jWIiFL6InnJcW8fHdT7HdxXkiIhqKiNQBHntfjCKfGnjj57mkWioSYdvpm+in7nHZSl2N1urX0kgVQ7HEtrVFJ9KYyXb00VEIxNSDI4+Qvb7VNfequjdBW3Kis+8RzqvDeSIiGoqIWgM8phzqBFlrhTYF3yohFH6bysuuS4/9VAPUCdBGbD3MFVou4bvs45i4UvP02etbXae2aWpf1UaPY2lOnBcS6LGcFxJaMe0nIqKhiKg18EP55a6aQyu0nHrEknRoJUtdDXO3UWxZueXUqkPqhOZDTHpq2tLRoFxhyt1GnJNzST8SzkuzeYTZz6E+j80rpx4iIiqLiNzO5UZuWaH6uPJ2pXe9F0vSPR3I5CgrZWINkVutSYYDodUWFdSVvv1+rjjwfV6zzXIRaoPxs5jVuHAeH+dxjA1KPWIgIqKyiCg1gcQ4AqcjhuygDpScgceF3Dbh7rMYovMRe0qdSk92FFBXWyMovuLLJ1VsxNQhVH5NpPiATwzFnBERzuuT80zktCmw62YtIqKeiOAO56WQk++eHCemrlA4yhjT+u7JnTA523QKHP7QQz1ibaPcs7mZ9/PrFDtSfI9SBkckgnsCKc0VPgjnLZvzgD33ahER9USED9yT0NQ9LnKmKuaQHeYKhZsEzYcbheyi2mwelHLVJWYCqEmIVHBPXCmTAXXF5UKJ1Zo90ZvjIJekff6UktdUfil90YOQMSGcN40WnBcrSCQS0YmI4Bz8lPQlCNpObztsbj3M/Djai0r6OSvdnM96g68dQisyV/1iSdq8l9pnlDpsr6SOfp0q6DY2VvdvbNBtCCFUV98KtaQo5cbSOY9DtLXgvNjxKSKiExERAjVsZqcPfWUuZSUTC9thYwnOTp87gZjwrUx8aadUOnWV0ItoSFm9+w6vulZkoXJy2iDXB1IjEZy2UcsJPVbcJxxSJppefNLEEjgvRdD1wHl2e0xxnmxndCAippw4haRTn4LGuZKhOmOp+0NIrafvvhTCD6E0sYdI1y47x2bfvan1owi6muCwJ0WYUu630/g4oYXI3QmcxxGJmAPnASfepkVE8IqI0MothmhttCTpHgg7Bdz1qUH4Wof3Lu3Vs2t1MVVX6qQSY3NMfTmIm5P8W9rAPYZDZUyJRl8EwLbFFs3Cef2gNudJJKKAiDAHrDlwfcQ9NUBDoCr6lIFgDtYeCDsFXHXgbGffpG6+5ztPMr7v29cP1Zv6E+BTz9zgEBUcj/ptRfjc5XK0Sap/+nzAjgDYY8fkNvPzFM7zCWHuulIgnLcNajvLmYgCIsIkBXMAhVYDJuwB6oOPAFIU/1T+nORfAy57ucjFLiOUH7VPplb/5goxJRLhizq4VqFTvpKzT8sZ5QjlWxIcZXGP1RT/pPqF63UoEhHLeT4h7LNZOM+NVpwnD5sqICJMpKxaUvfXfZ3e08/hjja5BifnoE21M2bFRnnUNtdhw9zJ1ne/2U5Uu3IOEPrEUe7kz02gLntL+yc1AsnVT9RFTSxiOW+Ko4TzytqZy3kiIgqLiCnEEl2I9KcmitBJ5xSBkzoATPJyEULsAanRpkOHwuRFqePUpOqqQ+hz6ulyrhV5LKbKnVqNhHyQQmo24Yfsie2/2D5wlePKb6wPtc+oAmeqvWxhOlWvKRHRq8/ZEM7z29QD54mIYBYROQPEBeqgCcG3Ko4lfNve0ACgTAb2EwntAUodqGP5+/aF60Bpa9OeUPqpfojtt9hVBHX1EGt3bPrQypBaFnXijxUlo/9Qo0EjfN/Nt++h9tmY3/p63Fi3YbfN1KOnufs61ed89RDOWwbniYhgFhGuTshZXcXmF4JNiOZAiF1VuQbAoUO0p6tRB/LUhDS+N5Z76BA9LOqCrbQ52tlVF+o9KfmFJuHQfVx1tUkpNg+b/M16UNvIrmMof1d/pDzgJ+Sf5kOoUtp4zMtuV07/1HraN3xtNgfOcwnKJXDe+98f3gKrwXkiIphFRKkJxFSoFAVNdZ719RW5xT6AxAVTHfv2/mz7p+puHiS0JwbXaiClbcw2ThFWNlz1C60wOEl1ivBjJxCqjb429IGa3zgBr6+H+4HiU6bPrK+7J2R7pUjxJ7t8uyyqEAq1D3XMuO6dsnXqvilhOgfOM+tw4MByOI/qnyU5b5EiAsBlAO4A8A0AzwmkuwTAEQB3ArjaeP9MAB8A8Mnh7xmUcs0zET5SMmETPuUEs30635UfhcjtsqcmKYqzbm76w2um4qWG7HxEbOfnUuohgg0NRMqKwSa5XPKwSTqUHxUmGVEm/qlvePja266D/RU/X3nUPWCff9p1pPjUaKPLR237TeKmEL5dvq+9qD5FCcNPRZso/uT732UbVfj0yHmu9lsC51H6pjTnLVVEfAuApwP4c5+IAHA8gE8BuADAYwDcAuDC4bODo6gAcDWAN1DKNUWETVihPd4DB7b3S30hz5GwxnSuwTfm99Snrv6+8IU0te0aoKZtGxurvDY24ldQ5vu+VaDPplBdYybWzc2jIy7Ugeh7f8xjbGcfiYz1GMv17c2bq6Oxfaby862kXKTqI2p7rz404ZlkOSUQXBOXmd+Yz7h6CyEkhszJgJqXz7bQZy6Y7RGzqne9b46NEF/YbeLzk7HvR38K7ZuPPrCxQX+eg8/3hPOOfX8JnOfyT9OnFikiHjUmLCKeD+A64/U1AK4Z/j8CYPfw/24ARyjl2ZGI0SFGB8qdQKYO05hpQnlp7T5x7CJVcyW4vu534qn8XPZNraQog891StmGWeZIlr4Jh5Kf2SahiZWbVM1yfZOXa6L2+cDoc1ddFZ5ATEESym/qFwdjJsvQKt9OM04guf5pp6X41FOfGg6NT028WseJK1sghPxufT08KWm9nc/FF7vTmf5pjiMf/wjnhe2biuT1yHk+Thnrwi0ilF5NvF1AKfXnAF6ttT7s+OwlAC7RWv/E8PrlAL5da/0KpdSDWuvTjbRf1lqf4SnjCgBXDC+/FcDt258+aTdwzh7g858D7t8Czn488IUvAo88sp1mzznA7iet0nzjG8CXHwTOON2f7uG/Be69150GAHbtAp74hNX/X/ySP903PxU49XGr/P7u4VXe930G+Nznj81vzznAiScBX/174AlPdKeLyW+0D1i1j50umOYsAA8cW+7XvwY89gR3mSc+Fti7d2X/N77hLjMmP2ob79oFXPCU7Xa56x53mrMfDxx33MouXzpg25++8jDw919Z1eX+raPT2mWGfMXrn6cf3cZU3zN94K573P4+1nf087HedjuPZQKr/E59nL/PTnwscN55wNe+mu+fZtopnzrvvO328OVn1gOw0gy+bLbJeeeF6zra9ncPAQ8/NO13I6+40gHbPrB1/+pzX3+N/fR3D22PI9v3zPy64TyDL1pz3smnAKecls6Ldrm1OM8es8f019O11qcem28adnFlNAWl1PUAnuj46LVa6z+iZOF4L1oBaa3fCuCtg02HtdbPic1DQIe0cXlIG9eBtHN5SBuXh1LqmEV6DqqJCK31emYWnwFwnvH6SQA+N/z/eaXUbq31fUqp3QC+kFmWQCAQCASCCRzX2oAI/DWApymlzldKPQbASwG8e/js3QB+dPj/RwFQIhsCgUAgEAgy0IWIUEr9oFLqM1gdnnyvUuq64f09Sqn3AYDW+hEArwBwHYCPA/gDrfUdQxb/BcB3K6U+CeC7h9cUvJWxGgI3pI3LQ9q4DqSdy0PauDxY27irg5UCgUAgEAjmgy4iEQKBQCAQCOYHERECgUAgEAiSsCNFhFLqEqXUEaXUnUqpq1vbM1copc5TSv2ZUurjSqk7lFKvHN4/Uyn1AaXUJ4e/Zxj3XDO0+xGl1Pe2s35eUEodr5T6mFLqPcNraWNmKKVOV0r9oVJqc/Dp50s780Ip9aqBK25XSv2+UuoEaeN8KKWuVUp9QSl1u/FedLsqpdaUUrcNn/2qUsr1aIWjsONEhFLqeAC/DuD7AFwI4GVKqQvbWjVbPALgZ7XW3wLgeQCuGtryagA3aK2fBuCG4TWGz14K4CKsfgflvw/9IZjGK7E6UDxC2pgf/w3An2it9wF4JlbtLe3MBKXUuQB+CqunEn8rVj9l8FJIG3PgN7FqIxMp7foWrB7G+LThsvM8BjtORAB4LoA7tdZ3aa3/AcA7AVza2KZZQmt9n9b6puH/h7Ei3XOxas/fGpL9FoB/M/x/KYB3aq2/rrW+G6sfUntuVaNnCKXUkwB8P4C3GW9LGzNCKXUagIsBvB0AtNb/oLV+ENLO3NgF4ESl1C4AJ2H1rB9p40xorT8E4EvW21HtOjxj6TSt9SG9+sbFbxv3eLETRcS5AO41Xn9meE+QAaXUUwA8C8BHAJyjtb4PWAkNAGcPyaTt0/ArAF6D1a/cjpA25sUFALYAvGPYNnqbUupkSDuzQWv9WQBvAvBpAPcB+Fut9Z9C2rgUYtv13OF/+/0gdqKIYHl8tmAbSqlTAPwvAD+ttX4olNTxnrR9AEqpfwXgC1rrG6m3ON6TNp7GLgDPBvAWrfWzAHwFQ/jXA2nnSAx78pcCOB/AHgAnK6V+JHSL4z1p43z42jWpvXeiiAg9PlsQCaXUN2ElIH5Xa/2u4e3PD6ExWI8hl7aPx3cC+AGl1D1Ybb29WCn1PyBtzI3PAPiM1vojw+s/xEpUSDvzYR3A3VrrLa31PwJ4F4DvgLRxKcS262eG/+33g9iJIiL0+GxBBIaTu28H8HGt9X81PvI9hvzdAF6qlHqsUup8rA7ufLSWvXOE1voarfWTtNZPwcpXP6i1/hFIG7NCa30/gHuVUk8f3vouAH8DaWdOfBrA85RSJw3c8V1YnaOSNi6DqHYdtjweVko9b+iffw/CT0hU+wGuXqC1fkQpNT4++3gA1xqPzxbE4TsBvBzAbUqpm4f3fg6rx47/gVLqx7EijssAQGt9h1LqD7Ai50cAXKW1/qfqVi8D0sb8+EkAvzssLu4CcDlWCy1pZwZorT+ilPpDADdh1WYfw+oRzKdA2jgLSqnfB/AiAGep1U9IHEAaR/xHrL7pcSKA9w9XuGx57LVAIBAIBIIU7MTtDIFAIBAIBAwQESEQCAQCgSAJIiIEAoFAIBAkQUSEQCAQCASCJIiIEAgEAoFAkAQREQKBQCAQCJIgIkIgEAgEAkESREQIBIJqUEr9mVLqu4f/f1Ep9autbRIIBOnYcU+sFAgETXEAwC8opc7G6ldff6CxPQKBIAPyxEqBQFAVSqn/i9Wjjl+ktX64tT0CgSAdsp0hEAiqQSn1DAC7AXxdBIRAMH+IiBAIBFUw/Bzx7wK4FMBXlFLf29gkgUCQCRERAoGgOJRSJwF4F4Cf1Vp/HMDrAbyuqVECgSAbciZCIBAIBAJBEiQSIRAIBAKBIAkiIgQCgUAgECRBRIRAIBAIBIIkiIgQCAQCgUCQBBERAoFAIBAIkiAiQiAQCAQCQRJERAgEAoFAIEjC/weqxS5L5eGjugAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = [0, 1000]\n",
"N = [1, 3]\n",
"C = [\"blue\"]\n",
"\n",
"plot_moire(X, N, C)"
]
},
{
"cell_type": "markdown",
"id": "db162f55",
"metadata": {},
"source": [
"## Plot with Gaps"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "47ad5ae9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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T6Q7pOWrREwuMEkkAzWWJ5yHTygiFbBetrJxs8rUm1I9cP0qdyQE954F0D60P88YHjzLJyMyhQ6vbnssLN6jLy11UaedOfY0G9RXxz0GOdN5kpFTKK09DEVIO0Ln+JdniToEVzZb8Sp2pyQK9e1JFGtb7uuKKue92IilFEjAeWSChyBlYLqD0vhdGJ7S7bdussdW8GK406H/uCcoBwI0l8asNYglWuKCSktQE0ULCWuicK38OyiQg4kaa8vK8Oh4C5Om5EaF3pYelGXOuhC2PjINCnp6DCY1/aWAjRO1IBpg8E/pL/UiRCDkVxWWGyx2/Jw0gpSFjsGfPrKEjhbt//2wdJQjhIX9avKa1OfHBQSM3bLwOfCxqRl1OLfB3pFFaWekiD1S+JoNtO2vorEgCJ16/nTtndYs0KJpXr9VBAiYttK8BGf5bRnjk8yhxACT1I19gSDxyb5/zwI06LbbmxlPTKRwwHDjQ5asRAWc5BXf0aCffBE55WxBfFHnl0WDZjzINX3wb1ZmyjhG9afWbJwttS/mNkYbqS+6eIEVCxpgGJ1ds3HPgHjcHCBwpkoDJMDoZgu3bO+NGwhUJSVHeCwuzK3Kltyznvfi83eHDswOal2XNp1rePxG9KwcP/ZVGgRt/S/lqHpkXhpMet0XcM5HtIAc65cVRPe8X7j0SeYYoQtwrOnSo8+BIWcoV+doUg1yVzpWuBpAWF7uwM1+pTjJ59OgsIOP9zZUwKWwegpVhaD5NJNubA1YNFGh9QobBGj/cUPOxqQEAq581Q87bm+sCvoZCrg2SckXEZd6TcSIZPbDAKTegvE6lQFYSz0PzsrW+4uBAGvWlpdXOG3cOaJ3PwsKssbfAIudTrkugS0YJSM54ucQLj3Twce3pTLnmRmtrHiHToqxSb8oooszHimKNoKHnRaCBhI4v5Nq3b/W2ID4oLGMhBZgLH3U6gZILLuiUL0/LvVnLI+BCdfjwbNSB58FBBB9UmpHjpIW8pCerkWwXTTlqikarq4bWaQDzRW/yXW4spVfKSRpEzRBxL9EL4Wr9Y4GhKFk88blw3o6aJ655qBrA1ZQpeeE5ACuVGJc/CmWTrPO2lEaWg3HKS+sDq209ACdJGi9uPCeT2ciC5dXJNQM8wsCNhVwnwQ2E5FOOO887bdvV0QPJg5Ql7V6urbw2PHQoLdwG0lZdisRyeZB18HQmPdO2l5Is0XZFrR7a+jJLZxKg5U6ijJZxMCqBXMTLlxE4ry25PGj9xWWDg3RePpdjTUek6YmLPtP2sJsbbrg38iLQwIWOhJKvVZBAweoQGYqyFhtJA8/Ty3AUCY2FIOk+5clX4XqetjeguNLnQssBgEfk1XgLD62oikTs2uDjPEgPlcrgXoM1YCUIjEZXNKAiKRrtyLWjZbDJ4z961AaE0kPVDBefilteXr0XXMonr5um0OQiMh7a1cCwZriIV/k+bwsvimMZef5cG7NyrPE1DJoMSd49z90yKLm29ZwTDchLHizZpWd9Ig00XvguL9nXmoNl6UwOfiW4lWdpyDqSw0c7wbR+5X3AwTKQAIQ2NWL1nfa/jOTw/szpAWk3qB0s2dCcOukEkWzwtkt54M62h93ccMO9kZeMNPAQtTUotVCTVMDeYkjq2L17Z+eKqbO5h3z4cApF0/Y3LlCasaOLL/aSZCkKaWS5oMu28MJsbbsahHFgoEURtLSyLYlnOY2QU55y7ldTqBZwsgatDHNKY6KV3ZcoT1q/IRfsSuWoAS++i0d6QNx75+sduHxKw8jzswwCV+ikmKVC1pRt265WjJ4xLGljzdhr4F6TE86HXOCW62s55cF50QybVq6MEOUiBBYgyqWL0MpKkserruq2O0pjr/HOdSafnpDRSd4m/JAlTSa53qTF37ffrkdtuFzLnUpWu2h9p0UqJciNOBhURxltkRGanM6kNubTYlyn09ThCBp6XHxNAxcq3kkyvK5529Jw06IeaVy5cJOHxEOcPDQnPWt+DoM2d720NHvSofTAJBqVA4Q8RBr82vx+VPFIJcEHjqYQZBtx8ERtnVOSGk8W3zmlaUV7pCKwpms0cNE32iBPzKTV1HxNjWxrSwlJYyk9Ly47MgTPFaU2fScNJ5d5km1L6Xl9YvWdZ3S9NvW8Qh6J8aILpCestuPlycgJfyYjRRpI5YbWAmey/a17VpSjhqSMc7nQ+Jb9xA0aX5TO24GPRwIA2lozuX6LrweydjfJ6Jocy17fcb7oFFM68bIGrFkRFxkttXQmb3seJZNyNYKGHhcHDdzDlZECPkWhhYX4oJWKlD+XiI+XS3ly4MIjDWQ0eB5S0UwmHXBYXPQF0oo0RBBuRDHz96TR0sLTvK1ktIG8Wm89haZ8remhnKKUbZGLqHBFIPmIzGd6RGWQDPIIFe8PLfrBvTkCGNZiOIpgSKUqgSwHDaSI9+5drShl+vn52SkPTl4ESDNyXog9Amg5X17faTLPowscvPNDgqw+5DtseB0lyOTGQc6xa2soeF9HDVUUQOdIc3q4vPLoKI/OUH9p01qW3uRyIyNbXD8fOJBkUjuIjOteIll2ru+IJpPVC9w5CNfAWg7Mas5qic60ZIzTCBp6XDLSwJWJtu1SChQXViI+iHg6PqD4QjWpGCylJr1cyxBTKPiCC+x5TllnqXyjiyU9siI3sjwt3BpRqBpZ7+aMu1Z/y4hZ6SUPJZ6vR6RAjh5drZxJQfDtZNo5F7xtJX9cLhcWVoOdpaXViwItUKQpPe41kWxqilszgEtL+kJAOe40sJIDehro9vKyPEdqE2s1e9vqPPE6yLFtjVHJgzZ9Y23FlPzId/sQ7y8+TaCNWQuscJ64Z831MW8frf20NvJkktJy0CBl0xr7dM+bru7rKMg1SbydPJ1J72ljczJpR9DQ5+JrGrgx4/NCssH5QNVAAxcYrtzpJDX6IJEHCLwBT6QNhiNHZgcAzf9Zxj/ildUgZp635alz5SEHvsYDV3DyHAatTTQvUTPunqfmtZOnnPqABEmWMT1yZNZ70hRWRK6shYq877jMy1XenkEkBczblj6+dv31s/WUY1ACYy7D0kBbAE4SvWdt9ZTtI9vSA5KaLvDGiva+1R7WvYhcavn2jX5JflZW9KkFy7h6OkUaTNKbtMDRk22r3SS/HCjz3xQJkwBFUq6N5fqHEsfBk+XJRF9g6vGogdoRNPS45O4J6gBSivzAJOoga0W3JsQkPFIxW53tCWNOmCTokTs0tDlcbXGPJMvDsgxGhF96Ht2SKHngIcHScrX3SOlpR0W3rd5OEQVuvVtCnE85RUPg6ehRXVFrwEZGk0gp790bW+hKBsc7IEgaRF4uLTzbts2fArDGkrYQmCt+zxBK0EXtZXlk3nSA5tl5oEe+l5tu03jNyYPWF/JeDsyXEG8PfqaBJovWWjDZd9xJ4Fvg5+d98F+iMy0AqB3iRNNynHJ6s1Zn8ne1/pGOlkeyjrPntYygoRdo4ELKvXJaRCOF3prb0sKo1Mk033n++WmgW0LnCaMUmJwRImRJi3v43J4W3rLIU47agC15HjWm8j3vWwC8naKeVC6NFQr1eNTyr1XUlF4eKsPz1ZSSNMLcwyIlwtfA5Dyoti3fASCJH50u99R7u1IsxWsZ1yjvUrnycqRc5GSbSE4fRevIyQJDnCcvD4vXKKj2iMsV5UUGlx+dLddjWHIjpwt4HemS2yw5L1Z9SnUmtTV9mM2alsvpzT46U4LYtvWjNB7xsnj7j6ChxzU3N7dK8ZJwcS8np/R5OFZDzfxc9iNHVqPuiLdkCa00DNLbozppC474HLnlNUoerMFAlEPVVljWAhNRZM4NVnRKRVN+Xv+SbJQAEuLHOy8ikgff+UB8yqiBZUTp3sGDsx8T4rIpAVHOY5X8aTJoEcmgtqdersuIlh2RX69ttOkJzyB55fBQMFfWvCyrrbT6SK9Y63cLPGtAoVSGrXbkwErqTS3KwikXxSG5vOaaWZ1XAuByOlNre/7xJ63vNJCj9RvPs0RnUttw+deiNLm8PdkdQUNP0EBe6+23zwox74Cch8IXPMrOImGlT6Rq+XHPJKJ8tQGjrbzWVnRLIyYXB1knqmkIWONLCqpVVwkaNEUk/9fK43Op1iCJlCnb1lLIOWNqKe+IpyNJW+jGAaAGlrSFpXwdAueDg13Jl9Y2ub6IzpVTubt3JxmVfVfrGed40MA5T1PaR5ahsEBmDgC3rQ6CSxYB83QeiCiVRU5k8Pm5DBqIsQwrl0cyhFLWrW3lUq9qOlcjTWdq/U0Rk2uuWT3GtfEl9SYHGdHdU1ZfaWuKOMk+j+jNyaRtxxMhe4IGPnfFkayHprngacLH34/M20uj5nk/kjwvj8AMoXXN0FmhawmGJE88D/qtGSErqqIh8ogHxYn3gXYoldW+sg001B8N/cr8c8q7hOT6AWn0uIKKeGKy77xFVVw+tH6RpJVhEffo+NjT2kyOs4g85HiQRkYDE1qanIco39V24eSMmzQQvE5edKLEaJY804j3CR8r1q4lvv6Lv8fXC/Bn/DRea92ApTO5LvZ0jdXffBzxXW6UTgJM/r7cfikXFGttre2+iAJFCWQiejO10/jtieprbm5uptM0r5UPfIkutS1LvCP5J2KjA5rS87nBiMHWiAt0Lj1XPNz4Ew/aimAp2Lw8DSXneLaMu0Xc8FFfcJ4jwEOSHMSaopbGQno91gmHpcQ/WMXBK319j38K2guZagsO5b51y+ByA+EpsMiiWk5kGM4/f3YhpyQJbjyP2QM+EYPvGV9NNnNyZXmCXlt6oJOeycV5FniJUgngI55Ix/FIg1xIa21z1PqD6xPuAFh10nSmtV2TRys8eaF78rspljPH20JGAK1pNsmTdFqlo5iLOkfHJ6/fGGnocV1xxZwaFrU+HBLxSOh9LvjefLYUXJmeeLNQvDeoOPig8+G99FJQtblyy4vgZVr1zfFM7SoRvkWaks/1UcnKZwvx55SPNQcZJdmOBBC0UGipYWzbWXDHFapVV80r1z0Y2+uW76+s6F8LtNpDA4A5ACE9YG5sS+tRAmijkQat73IRARnWp/teH+Xy9MasRtpc/9KSHnGI6EzZXnQUdBR4c13Ex4UVjYh473wdmgU6tHs5+ZRn/nAnJbcA2OO35MyNcU1Dj+vss+dmDLtEitYg9gSF/udzY97Z9JZnYW1HiyiCtp1dbJYLk5UMbE35WflphsIy2DxPHn73BoHnIVn85Ay6NuhpuiYyIHP1jBA36vwoXOqb6A4Gy2sm2eCfF5Z1jxhV7/2cTHEPie+Ljy6mlPxaYI8Al2Zsc3lG7mvtxvvKU/qag5CjyPy2BfA9HnhkLlc+OSB0GJgcs6ULWXl7ySinZyyl7PXVmbw9qHxvisQC2hqPVjvnxlyEZ853BPSNoKFP5dGBhmjIUyPNeEnht4QrqoxKSX58KOJdRxWHVNDyMKxIOlk/S+nnvILSRWLaNEut4ZPphyICnPTpXm8+W+PDa5fJJHZATA7MckOcM4gacJEenTZOcgbcWm9BZfM5Zv7BN6vdaom3FR/3HvjiZcvvIpSQZjBlmSUynyMeQaW+k30VMWBybBF/crrRAutWGX36k+/o4LxYYM5zWqz68jbPjSGrPh5gioDukwo0ALgWwD0A7gXwEuX5YQAfml53A/hbABdMn90P4CPTZ6FGAea+e6BPqXBykkqae3laZ64FepRkbfXyjGN0oGkKAvC/rqmVY3mtHk81CtDLW/PQPG9AkgeESokA2AUXtN/15Gry8pSZNGqajHH51fqqbTt55wegybpYOzx4GJ0UMz/COmd8eP044Odlk1Imr9g6VK1mjHnyVLoup21ndxOUjnWrPM+Il9aZ5JK+aEmAwTJQkUibNtZyshkZ633AhIxCaieP9tGbkkdytHbsiE2XavcifSv5PGlAA4BTAXwSwF4ApwO4C8CTnfd/CsD/ZL/vB3BhSZkXXzyX7XDPSHGKKI6I58rfteYpS4VXepd9wIjGIx0QRMbO8xJl+tJB500vRAy4BvBku2r9EwUkXttqxph7CtwIWsY4QpZ8LC/Pfi2Vys0BBC3PyJoEq22kwtPykfv4ZVtZvPOyeXvyaTre7x6Yt8ZgaeQpJ+c5UO+RpWu4UfamEjXy+i3iWUfkR/utbbPkfRTRm9bC66hMc11fsyYiRyRT9DFCatPSxZoltkDK18kEGg4AeDv7/VIAL3Xe/y8A/g/2uxg08A9WWZRDclonWR+vsTzZ0nKtZ9pplZIn/unWGm9Y4/HgwU7x0/ZAzmMtIm/b/MD23tXaWw6gSJk8r5zC8OrKlS//dC0Pzx84EFsAVtKmVAYP1/OwsFTG0by5Uo2CRM0I03QMHy8aOIz0gTTs/ARU3u85D47Xr08kSoJUjaxtltwJkcBIAz1eOxDPufe1tplM/GPWtTrnxo98R0YZONXqzZx88nHhrbPStjTWkhyL1imvffSmBiS4DJ5MoOHnALyG/f5FALca724D8GWampje+xSADwD4KwAvipQZAQ0570MbDNZncnMD3SpXlmlFP7RvvhNxBVgSOs3xRcLIP78s69hnIPRB95pnGEHmkXpH68D7nBQQ/2wwPS+d1y5RpFQGHY1Lx2/LPeeRulnt0KefpEdHRkqCp0i7Rw17blxzvqhPoofsaM+8dSmeQeVA0wM4VvvIMWABGG2M8vUrMupTShagJz5I/ukbEzKtt77BKkeTK9nnuQWyEjjW1NfSmVwmcjvWapwESzZOJtDwXAU0/I7x7t8H8Efi3kXTv4+bTm3MG2lfBOBOAHfu3r073wOZTrEQs2ecpbfrDXZNIcv0RNbXHym/6BfSeBordG15LjmBLR0IOcAUIc/g1xg7q/+01dvaNjQt9F46r60BIv5MU7I5JRppD+u51ZecF8/L9YB4jiKAzlPiFrCMyjb3Rr1yLdmX/0t51wx2ZAeNxoc1HaO1G7UJP4hrSIfD0pse+OILayNAMNd/VvtqbZA7a4b3HZcn2e/a2PT0Jp+6jOoGT2eeTKAhPD0B4A8BPN/J6yYAv5ErMxJpsDrFEhwvzMbT59YYeMaVG6Oc98FJWxzprW7XFpp5xirXNpZxKJkj7XsGgmwjaw7UI6v/rLM0NC9T9q+2LTZCnuGX4C6ytc8ymF55Hk+cF0/xlU51cMoBVfmO9r82heUZd1l2dLeP5QjI/DReS+tcwwN/Tn2yuBg/U8MjD3B6wIvekfpI5pfTfyUGm6fRxroW4bPGXQQQe30ndXXuC6myTlJnnkygYQuA+wDsYQshL1feO3c6NbGd3dsO4Gz2/3sBXJsrsxY0SOKKVpuz5YJA9+T3KjwvwCuTC1DOYMuwGB+E0lhxQY2eLW/xaBnKpaXZqRyr7fj/0UhDzrPMGROv77hClf0XmUaS7TfEljvJp/R45AmQUa+sdDtZ265um1ykgacZYtuh5plZ4DDXzzkAUXO+BJVhrVWIjIOofpC8eotBJbAsKS9aZy2/HGDM6VerDzyQ50UsZLlcV1Mb0jocDqI0WZfOVY3epN+UF59Sicj1SRtpSHXBIQAfn+6ieNn03osBvJi9848A3C7S7Z2CjLsAfJTS5q6hQAMXRC5IGqqMIFUL8WqCHfW8KW/uMZAAawepaIrT8qQt1KwNGJnn7Hfeu/dlKN1qA6tdePpou1rGQrahZUBkupwnZMlNCUW8K6n4PF54X0VDojKtZQQ85by01K0ml2uBvHpp40eL2uTaKVKO17c1VJpHyfsar1Y0Sz7vG1GIENeDOU8+V2/ruXafy7WlmzQeLRCem4Iu0fOW3pTP+dok3qeaztTqdlKBhvW+ShdCel4d30Ij9/XmogESMWsI1BI0iTQtFCuNB/focsbY4s8yAt6Aseq8sjK7+E37vDDdixjySLjba3ctopHzlPjJhpq8WL/7rMqOeICaXOR4s9JFeOBtFwFvEtAePJivowcqtfbMyUBOpuWzmrU1Xn597mukeaC5cxXo+zvz88mTJo85IgNe3bQ2lkaYdjBoILdm/HrtJeXaAsjaGPe+RBwByB5fEb3J3yM+qJ+5ztTamOo2goY1Bg0aYtdQMPeUJdIjgaTtiF4ZFkUEkvLJeZ6lpyhqPHhUotysMrlRIH4PHvQHqgUgcuVF1ofI/DRetfejgKC2zSJkeSARKm1TmaYEvFmr9DVZ7LMGwuLVKiuXrrb83DiO6gN5r2ThnNQHXIdoEcAoaXpTa2NrAXBEZqN9FeXVm4qLTJ/10Zkl71pAV/sqsQZCRtDQ46qNNHDkJjtME6rcyvgSr8VDxZHFRKScc0fqagLMQVONB5obFFb50cWKpYPOm4+W5Xufb5aeC2+r3Emh9H4fw+7VfzKJ75rxPMJSQ+R5mV4f5SIIWvvVGA8L1JV4p5oX6o0LD3ha5VjpNQdGhs6l967VURpMyoc+dJerU659eVtp2wutKROvHSLPJVk6NlJODoh5DoLWTznK6WFJWhmerhlBwxqDBo085RoxiPJ+yXYabZBLIGOVJw2ZHKg5wyXLKo1W5BB9yQDp4+FFjQzlz5VwdNB7xk2LbgwBGrS2oXy9Q40sGdK8xdzCyFyf5PLxPDrefrXenMzLyscy8JrcSGNt9aMs0xujmmzyttMW2nHwokUPtH719FLN2PJI8pHz3r22KB0v1tqvXJ/w59aUpae/rXHoUem4i4454m8EDT2uUtBgdc4Q4V8uFCXeoJxr8+5zRKwt5IkupClB5zKdN8AixtxC/lGeJhM/sqN5Yd5Jm1r6SCTo6NH0rY4DB8q2e+bKlrwvLs4e6KS1EfdULG86x58FPLz20bwvGdWRAMxbm1HShtq73voL2XYaMPR2H0R59d7RZIvzYa2dyo3ftQAIkfpEnRQPXFLaXB2stV9yDZLWvnJMaQtstUhJie6z2qkknUUyP+Ciz7QjaFgf0GAZtT6godTbkGSVLb2fCM+WAJbwk3u/BBBFypAetBU+9Dwvi3eNnyiqt1aoU5l8BXc0glFCpBj56ZOWV9U31N+2Nni1eJMAQ96Tx2xbfaJ5ZSWhYKsOucihJW+akaHn2jkpXjtr9fH0RYlxGbLdPLLqmQP5OfLqE+VJvs/b0ZqytL6PEdGZnu6wxmYO1NXp5rm2HUHD+oAGq/NKDgiKGM0+q7/5fe7ZyjxzJ6HJfLQ8vDQlHpWXPlJGjk9pyC0PMLJS3FOCVt9pbb2yklap791bZ6QjbUJG0DrNzjJKNVNtJaCB58OjG8SL9NY5Px7wkXlF21T2HU/fZy5cPtfOSbGiV1rbWPWJyK/sa22XT0kIPUrWWOb93Udneu/kdKNsJ96OuSnc3HkiUaNv8RoFHTXljJGGdQQNGk0muhdrofaol1vyzCLNm6D0HG17ERIvj1IeovWp9Xat9LntkxFPjdLklLKW1jtLIzLQc6R57m1bvkZFyobVDp5CKzXYlBefArI++MbL8dq/tE09L6/2BFLKkx8i5EUaLMBXalRzoNbrH6nL1pJ4H+f6zpPHIb1wmU5bvJ5b1K7xVMNHaTuUlDOuaVgn0GAhOok8c6hdRgAiyDj3rIRna/5VK0Mayb48aPetqEppdMMrUwNymqLKlSXTeJEcTl5UZwjQoBleKrf09MyS37m+i8iMZsyi3pws09s5VFJfTrXnMXAD7BlxaiM6GZU+2FQy5WkZXQ8sexExOqMhclxxLVlTQTkPu8Qjrz3/REsv5ZR/GVPy562L6EOcLytSEtGbI2hYJ9BgedyWR+AJD6WJoMK+AmcNMjrMhSsFOQBrkXoJcX40VF3j+VhGgQM5OfAi7ax5dF4/RjzAIdpYM7y1XmOJhxO5H62fHDveiXueTEfKkjxpdR5C0UsAZb3DwYU3p+6Vo73rnQ+jAQ2+Swho2507O35qyXJcrKkXbzpIyrhV975jSsuTgxzvZFxLnw1JXPdYY8/bHjpOT6wTaMgJv2YYPI83Om+sLRYrEUaNJx5y5QLueWB9lKiX1jJuEW/B8jAtz0uWxQFfqaLhhk3ziGVZVhsM5YW0rR7+LjVAOU8vwnvE2+UekRwLuba1xlm0npInb4xY8jBUv1HZBw6k9S10quwQXqoXStcALf+8PdV/5079q7ml9eMG1dthYvWtNNqRtSA53Wo918YA1xVSfqw1bWuhMy2dJ9NZUaJUt3Eh5LqABo1kCDEnJJ5RlsQBhuWtRr1j6VFzhV26GlhbSJUjzxDRHDYdwWzVweNJom4+HSCBAee7ZN5Y48mLVGgeR86Y9iXezpGV+hYQLm2HUgXM+00L4dPznMGrDT9Hwb3nLfbxZrV2l3KqgdzSvLXf8l3NANF9a+dVn7ouLXUHR5VEkahd5DdUJEVAb67vpHwRsKV2kgf5WfnV6GuvHlp7lMrnZNKOkYY+Vx/QwL2hyLyjRt68pSZgUpiji840tE8KUS46sxSmVG4lykxTHNR23ryvxr/M14s08MGlRWy0OcvcgJbtIA2dpyC4MSTF2Sf0a/GmnWGh1VOTCw9YaL+jCljKUi7S4HlLRBEDEeUp8ryPF2m1u1cmH4tRgOT1hxVhsUBdzjDVUM16Fc5DdHGv1o60KLW0LWVkVh7iJR0IjZdSAGiNOxovOUDnyee4pmGDQEOp8Ht5REEHCYJceRw1dJrwags5PeEmxbO8XKdQ+HoObW1Bjv/ob8sQWUqb3/MGHA+TRj06zhOdmzA/v3aLzDzgFwETWl4l4ChHlpK16sEXncl8LAPRxzu2yomCdI2vmqgWf8/SFbmxwEnuBIkYu6HJ2xnjkQb05TONX+mklEZttMXOWoTWA4LeFs4oH9qXQGvXTYygYZ1AgxRM+UWxqHfjebc5ZcoRcw40eMpE/h+ZopCDrwbhtu0wYEsOmlJvV3q6sl+8/EqUt7bepeR0yVqypj5KlU0OfNWS5eFq5dMURTQiU2OQc+ksoGiR5qmXOggWDxJ0lPTpWkyJRSgCfnLpasZk2872Rc1aBy8CpwEKLS2X4Zpxw8dLzVSq5Bm45HPtCBrWHjRIRaB9UcwzWjLEpb2bU6YSeHieT85D5BRRipy3PnO9EY88p8w9jznKkww9ah4CgSpt7YJ1gJRsb4tHDbj09exywK4E3EbAmJc2dy8SaWjbFNHat69tX/jCYT3imvHBjZJXV2189gVgVr/wxY7adIJVhuRVOjM5gxglPla54Y7kGY3O1E7zyrykDOTklEdNLX0djTB49cvxEa1jp5PGhZDrAhqoE7inrC2C8zorNzdZokw5T5pCkIYuJ3S5KEKUt76eqKfMo4Y2Cjw042/xI5WypmC8SIOXb+2BOrLMKLDzSLZ3SV964KwmP55eq1cpqOEUkRHr3UhdtXTyeSRqlTMIXLdoToTVRhI0awfU9ZVPWY7laFltH41KDCGnbZvfVSMpEjWN8tZHliPjjkBg6oMx0rAuoIFoMvEXQGod2NeQlvB25MjqFcYRgeSDewg+uVGOAiHN0Gq7AKJ1sd7J9YdU2txDqjGAFqDgnlwJWLTqOZnM7kSJ1NPzfktArPWu5SFbeWgGksYb/46GBdb7Rm2isiFX1mtANgdMLKPI28lqM62+GqiWi0kt/vliYk0+a9uU19ma0qU6ykhJyTgt4YXXh6/RKj2UKTd+SqiPLEuwI/mSenNc07DOoKFtfYRZ2uG1yk4TTuKLTpfz1ihIWl7uvoYYTeO9Iz2ZCIqOIuZotMNq06gHUeoBRuulTQfVeBqaUdI8RitPrky00HYEpBEP3lSZxa/Fj+UBaopdpu17DDLlwyOJVjmaQo7Uh8hqj4icWXnLdpDbVrV0fddbRMhztkpkiFPpmNHel+1U4jTJ8RbhyRsDsh1qDyvTnAmuN0fQsM6ggTogtyAwKtAcgPQdAKULtjjJ0+OkcozyQFQbadC8p1ovJ+elWXlG5lJl+3gGQNZf9nlkkVZJfUt2pWhRFI93q0wNdFAeUfCpza/zMjjAynnYORDu9Vfu+Ge5nkZ66pEy+nrQ1jsawLLOCiFaD9AwZCjfa/NcOpk/OUtHj5brGZJLvrsnt9jU05lyLJU4nnI62kt3UoEGANcCuAfAvQBeojx/FoCvAfjQ9Prn0bTaVbOmIbrdMeoV1xp6TdH2MTzy9DgNRVtl9zF0Mk8OWCxDVJNnyTsaLznjYfHsoX65YK7v1JB1oFPfqJH3ntV+HhiRlPOUNEXM21uT0xxo1/pFAyFaPXMRnhyV8kYU6SOr3yMertenfWlIYEJ17BNRknnV5KNFT3J9V7IWyypT9ql3LotGJw1oAHAqgE8C2AvgdAB3AXiyeOdZAN5ck1a7anZPlBzo5CkmolplLcuoPTlOm9+z5j8tQ1jCr/UONwI0L08ALVKnWkUX9ZRz+8PpfwkApAHS2q7U6Fh1tiIkJYrRAruyfhEQEPWaLKPlgSqrva085T353OqXCPjhuqEkolbqcUf6MbfdNmdUpCxGnR+LqKzox6+iemMIniJeeY43CYasvKNjMMcPz0fq/ugW9JMJNBwA8Hb2+6UAXiresUBDNq121UQaSr78ZimmGg/aQ7A1oToNbEQWZvF6eYYgMkg0I0f3SsN0td5Z1BiWDHqpdD0vINKW0TpbIeASsGp5cVHZnUySLC4szH7V0/M0c7xY0QRKG13n4gEzjQcN/GhtWHJCq2eworJaM+6iBkzKkCUPUaL0uc9Je/zXgoSIXJWMOQ14eRFe6/0oKNBI+86FnJLLTdGdTKDh5wC8hv3+RQC3ineeBeChaSThKIDLo2nZsxcBuBPAnbt379Z7xqESr01Sibdmpa010FZ+1rcYImV75UYQvFaepiAi9cvx2GefdLQ+2rte+TlAUVIOtVt0bUwOhEbn5618Zd4eaIgYOm+u2AK1GgAokYOcsYqU66WR6S2DadVF62OtnWQenuFZXEx504mNBAK9b8N4xGW8NBok61uq43JyVaqHLeBVojdzuqwk0pB7Zr17MoGG5yqG/3fEO+cAOGv6/yEAn4im1a5cpEHzBDSv3lNomhDkFsuUGrAaJG4N2MjiOctTipYr5/Rz6fuUqXmYGmCK5uspuugUhgRD0bCiR9J7sto26vHUkgc6LONTYmy1KQCrXbkn6fFlTR8NCSS1NNo4jgD5UgfCMyZcBq3pV+Jh3766CKt29Lw2Lr38NNmx2k/7HQUoUeJprWlB7f2acRfVmZZdWFycbbuTCTQUTzEAuB/AhWs1PSEHGw/d8fvyTHcvD+uehWKjaLXU4Fjv5waAV05kYNZ6DZSP9ZU7TwF4xtry+izS+obPq0enOKSxqgF+nKIH00Tq2dcYWs/4R8pK8+NGJsc/tYVcE+ONG2289fUKI5QbY6ULCCNjUDOm1nkNfMxF+84CKdp4syJwNTrP66+czo2S1b65tS+l+lmTwxr+eVrqu5MJNGwBcB+APWwx4+XinScAaKb/PxXApwE0kbTaVRppsHY6lEYacoOCD+TcMcfevZr3uZKKeDkW4tbqRe/XGEvKx1qISs8j85Qa6o8qEG0w0/ckch/x8gxSn9XlmteW83i8+1FeogZWtlPEW9XyW1npFshGZEXKgmcsNfnLyUSpIYjkoY2PEhAQpYgO4sc/l0xRyHbWvGSP56iBtzxrzSMvdYAsstJYtiHXJtYaOc/BKOF/MlnddycNaEh1wSEAH5/uhHjZ9N6LAbx4+v8NAD46BQV/AeAaL23uKl0IGV1wVWLQvXc4Gq8J5ct8IoOD1zO3vZQrFu7Z8fejijfq/ebC7jXrRTyKgDFZZml/TyYdGJqfj0cbZPl9tmyWeLdavUtBa476yHFOVkry8vhaC+Md4Uu+M5Tx00Bg323AEQDqGf/SsjnfOf5r+tKSrcgUBRFf7C0PlYrozYh8e7TmoAHABYHrvD5MbNRVEmmIel/aYKwdgNogtjxpz2hGFbrMg8rKhdxI8Gm+uYQHS0HUKOBIulLjFum7GsXPSbZjNOLgefCl7RdVWLly+1Kuf0qMifTW+hp4mWfu2VBgKffOWpQj5UFbyxWhiN70dGYtqLOitPwdD5Dm+lJ7LqcoLF3Np7mPHu1O4o3WOWcLcrQeoOEb09D/p5zr032Y2KirZE1DTciW3+t7vG3Oq80JqsUfr6NlDHKom05V87zO3ICIDMpaI8jvRb4yKsFO7RkYVnt53svCQiprYSFfV6/vowqoj8HJRXVK26Ft8yCtZBpnZaVtDxxo2z17ul0BfcdfbiGatagyl3ftDoVa8FNCVA8+Nx4BNdED56yxWjttpL2Xc8BkeTl9pO1AiTpbFrCJgsESB1FrA2DLh9o1Bg0fHOKdE/HatWvOFeic8JcM2NqBkZubs1CnxZuHkEtPKJTC6x1uE/VeI8g+0u6awuZ8lvAYMRg5ioIPHrqMnBKqeTiyjTw5q/XoqOySPo2UmWunEtDAjd2ePf2Ma6kXyPsgujefxtwQfA0JJkh+Dh/uvmvjHQfNgV9J1NPKR9bNkwGrzbV+kUY3J5dDOFv8HpVv7UopdbS0NBqfwEWfadcYNJw5xDsn4gXMfXcA1Mx/1ipcKbSR0H+pN6fxZhkPzWBHDBylo8Vppd/PiNRDex5pdw1hWzsvolTS35aSyZ0aOJms/qpjBGR4c6ncKEXkYSiqiTTknud4lv1+4ECq9+JinNecsvfIO/LaG8OlkYYcIOGGW9sZUUt8J4Ulc3RPW+RnOTleHeU7HmjgjkEuUinvWQvac2mlPo98r4evASsFQB6dEJGGk/ki0GChYqLc8cqlHigfOF6kIbKYxyJtpXmJVxIZQJxHGqRDfJAmR6X5eIqqxED08ZIs70Yj/h0Q/jEczWBGF5p5YLFEga/V+Q4l5PFttbsFBrR0fbx3jbeo3OTe074t4q1x4vqDTy/UgHoi7uhQ2VZbaTt6tKhYhKL9SPnWfLTPatOos2A5W5bOXFqKfZag1jm1aF12TwDYD+CfAfj3AP7d9P8f6FPwiXDt2jWnfjOeK0jesdYhPJbiLjU+HkqUlFMwmndZa/R4OnmfFACh5kjYcijhj1LUWMh7JYsfo89LDI+2spr3ac7rtkgCgIgC521SMk00BMlyaA0NrVOIGmhP/nJGyTIIVj7W2iNvbOfGh/aNAa/vpB4bItIgZc5qN20MWTolQiWGu2Zc8me5vvNIO8jKA7K5g/5Ky4+8vx4LIf8Z0hclXwLgF6bXS+hen8I3+rIWQkoFKacJZKdYoKHUSJa8n3u31qBo6a25cqkEcgZlaOH39u1HPZNaA7GWAIgre+vjQd7q8Bx5SszjhRsgLhc1kTBp0Dw5leOLQPyePbrX2gewWZRbD2PVz/JWNfkpiTQMUadaonG3uKivhSKAcvDg6lMgc2Oypu9qnSGL+rRpBFx7OnSIvsyB4/VY0/BxAKcp90+nY5w363XFFXPfXdxz+LD+wY/FxTS37H1vfSglVfL+WiuLyaRTzpEDS+TvGqOaU7SSOKjzAFuNgi59vhb94QE/qhPfrrUWcqYBYip7aan8I1AyX5Ixz+hLHvhcsKZsI6CotL9KFmBqtB7ysl4kpzt4uJ2DB96/Uj6ssV2jN0rSrGW7TyY6WPL47aszqdyobKUy5tp2jUHDCoBLlfuXArinT+EbfV188Zwq/LzT5BHRawkE1osiPJEAl0y7RN+JevcRz4sWC3o8aoMq56V7BlujtYg8aMaPRxr4OhJvfptTX2Mp2yUCbLQ24XPPMr1MJ0O+HMwvL+t15HlykFOroIcYx33zGBro1pIVaaB8+bjU+lfjhX7XfpvhRNCxXGd6H+caysmU5UZB03pEGq4FcC/SVyVfPb3eNr33E30K3+jLijTwTqP5U1JOpeGtnNezXtGFCKKVgm2t6K5RuJoS5+l5WK/PauEI8bKsdFwBREDMWkUaeH/Iby/IRV98uiC3qr7WWHp9Jz0nD1CUtCXvLyrH+96LxhNfm8Tv9Znjj/Y5vbfWu3dKn/cx1B7JqZyIzJXqyY3Qm5azI+Vdi670HXce0Chdr7JeCyFPAfA0AD+L9BnqpwE4tU/BJ8LlHe5kCUBEiLz5LCk8JcJU481S+dq6BGsvc+6ri6WDUBrg3OCr9dpLlXjOI895wOtFXKZoy6a2FoC/V/I54pL7pX3Xt814P3B5lWDeSkN8amsS+vIWTU/vaSvlhzR+pc81MNaXJpPV9azxsnNyRL8j0bWh9GbO2SEehlh7EtXFNX24od+eAPCCPuk3+vJAAzd0lkcaFSJOnhLuqxS8enjb04hXOeCH8MaI75J8ao3/EAbKKzfyYbIhvTYJXLWV6BYo4NMXke1n0jOvBXAlHpLFU6R8TXa9NNqaBNlnuU+b5+oqn5EHqO3QondyRx3ntnXX6ASrjGgeWjppZPlWYU5a3+SAqPfbWqTdp35tq2/d5Pl5C5KtsRQhXkZkp1JNHTcaNGzK46PpmpubW9XodCDJ8vJseF4z7tY2zYgXq73jGfha5SANtqyHFHipXLXBEy13KONpkVRAfUFOzkB6zyXij3hAUX40cOCt5yCSiw09w28Z3Vqll3vfMx6eIeDvWp82jxghjRfNgHt9HslTTnFZ5Vq6QEaOuKzLtirhr+Y9izfe/iWLYyN1yPHogcU+ToS2lkeWY0118d+RunHS5Hjo6aP12HL5YeP6CIBv9il8o6+5ublVA4AU8cGD9kDQhJHfy+29tYRZepZa/jXb23h5mqH1ED0JPX0TITof69VxqAGggYQ+iiI3SKOeZY2y0EjbUiplxOsT4nd5OfZJaZluLYAXr4MEslxRR8rXzv+v9biteWEPgOQMdm6uOSdP0onh73oOBlF0LJSOGc3RIvmSXrjlsMg65MB+VK48XVZCFq8aSND4o9+5E2Bz5Wp596X1AA1fBPDD090S/HoSgAf6FL7RlxZpoANjaGUwNwBaKJSI38st0op4KDK8p0UFooNCU64lH5NZWurOnC/9HoLlQZXWwSItv9Jog6cgankZAhx54JSAXKSemmdkyW9fryZSb0vBlu7+GFKZlvDgvZurf61XHwXfmic/dKRBEtd3moMScVi06aMoj0O3uZaO65XINBY/1TWqDyJ9ar1XUsf1AA2vBfAM49l/6VP4Rl/amgbNiygVuj4ekAYOJG8R45ZTrnJAe0TvHjoU86CjfGnvlg6uIZD5UEBmSE/HSj+ZdFGfw4f9d/mzkt0rfcPdkXp5HqhHOY+vhAetr/qEyjl/JeugvPxLDeLQXmmEuL6Tui/az950QI5ygK8WzFvgtuS7POT8RXRiNDrpjd+IXI3fnlgj0FAS0o0okZI57iiy9BQmH4Q16XkaK1JhoeKoItfejQh/zvuKRlFK+dXKinikNVNKXnmaV1ZSFt95IPuz5sNtNeQBtahX6QHsaPk1++k9yvFUIjdrBbqHJD5++OK96BdyLR1XIs85o5sbO0TWN4Ykj7kvD9O96JHrVNfoVEbt7ozOUVzjcxpO5kuCBt7RFFqSglvq2ZKgaivgoxRFllyoIx9C0XjlAh5dw6HxGjlvwauD51lpRl4O0qjSKfX8StMNtZ2NyqPFufJckZKyrHByjvoaJMsg9+07a6V+jpe1Oip8yHbK8RQta63ARGeIVq8L03aqRJ2DyaRs949WhlZnL6LBD0uraQMJDqLGvVRPRNrOcxLHSMOAoIErIRIeuSixxtDJfIdQQt6AqAUoUvitBU1W+XRfW/EdrYPMKxqJkIYmOhBzkQYrn/VW1pQP79tab52fsBjt1xxfkcWja9F3Uc/W493iWfu0c2leQ1C0Xz2qBUAR3kiGqL34h8Ss8iP1iOz+KQFY2vscRNDhW3zaL0I8T7mYN+psaeMoJ58lzhi/t6FbLoe+pqdP3jM9bXLVx7AA/AO2e+O9AK5gz+6f7uj4ULRRtEjD0lISernVsuYz2F7aCCqOkCawEpnXGjg+AHILlXL1rlnEyb0YGoQlOxtygECWo00hWV7vWhoJTrIcObUQibpYFFVqnqzy9tHSlew1t9rXa2vpIZaCHc/Y9PX+IqA40h59DH4f/VVK3jiK9nFuG7uUeenoRPSeZeRLdLL1jAMPbXyWGHxN50Z4zE0nnzSgAcCpAD4JYO/0Y1h3AXiyeOcaAOdP//8JAO9jz+4HcGFJmQQaeOdSR0njG0WIvHO8wc4VU61R5fl4SjmndKx0taDBq6ulCD2jTyF5SyFFys55rHyQ8net7bMlirwPwJD96x0kI9OUzivLe1a7aDLnHfRTejS41wYayQ9Y9c1Tq1OONAOR49t6HhkbHh8e4OgDQLSyaHwuLqYdVrTrzDNqmlxFgZp0JHILfL08PJ0p34s+k3qytL0tQGOV643/pSW9PTcMNADYBeCMPoWL/A4AeDv7/VIAL3XePx/A59jvatDABfHw4W5OjrYZShTqeVrRxS/cAGgh1ohSy3lh2vva7xwg0hB+CWnllyhY3sbRFcZW2da9Ur5KFHkfRa0BWj6HX1K/Wr6lco7KNQd4tW0g+0Qrm4exo7JZCuQi7+eMfY0nHOFH00c5HoaIOHC9SRdNwWrHH0uwwOUjypc2HiLgqlRnluTn3c+d2RMt32qfCCiTCyw3EjTcAeBTAP51HwZYfj8H4DXs9y8CuNV5/zfE+58C8AEAfwXgRU66FwG4E8Cdu3fv/m4jS0E8dGj1B2Y0hCw7s8/0hWZUtfz6GqEhohp9SMtn6AHv5eF5Gn28vEjZNUQ8LS627c6ddaCJ5KgEdHnGyHqXj58okPGIA0aLjz6KOcqfJbN9wVQtryWnYWr1LAXfVl4UaXjhC5OzdfToLG+8bzgIjfBYYtRzgKyvzqwFWn0itJxq+Lf6eqOPkW4AXN4nD5bXcxXQ8DvGu/8rgI8B2MHuXTT9+7jp1MZ8rkxty6V3xkJE6KPehEdcQLQyS71LLe+ShWOUd8nCMI+nqGLrY6glWYp1LUDC0EQ80RTN/v1xAMX7u4/Byp09EjUIpSQNpGYohjCAUVCklVsSEq+Jlnl5lQLptegnr48igGYIAy/TRNqoRmeWAvaaXWxWXjleo+270aBhsA9WRacnAPyd6dqH73fyugnAb+TK1ECDJ7ARYyenGiIDwAMapKwp6mHlk0O0EbRs1a920JQoYqu8PuArUlZfkLceIIPKOHp09suO3vYxmbb0Y0ySNCC7b1+34KuPUovW35IT8vYjnwfm0YHISnWNZLlemVr79zFgJe9a5dROM1rkOSI1OrNGliSoW1rKf3MlGgXI6c6cfJYcJR3R0xZF9eZGg4bBPlgFYAuA+wDsYQshLxfv7J7urLhG3N8O4Gz2/3sBXJsrMxdpKCXqtNLjQzXjKr2ZnGeQGwAR8GINfuKlJtLgKSiLJ+m5RPkfgkpBo9d3a6GUuSzI6TNLBnJKLQJo+fTb0lK37qckatW3D6U88XpFvX7ioWT9UY4Pj6J1jqyUt+6Vlj30WBpaZ5ak83SH1Jmy7aKOVq6tc+OuJLJkOWgSFFngJaI31xw0YB0/WAXgEICPTyMJL5veezGAF0//fw2AryBtq/wQVR5px8Vd0+ujlDZ3aVsu5aehI56IplhrvFVt50V0sVAE0Uf496IJNcpGpilt05IIQDSa4JFnEKJIfmilTDzRZ5atnSSW8tJkyeJdkqwL/SY+aLFwrq6TyexXY0vrz5WvVl50MST/CFh0p5Pkw3q/j5GPrJS37kX4jdyvpRp5H0pnSj0ix6jXZ7l2yNWL0kvwLqkEVFk6nvMScWwkyF/XhZA4yT9YxYl7IaRgIx01lJHg+XjGaKhTBqPlEnHjVRpu04Q/9668l+PN8jBK+yfixUSMy1B74jmYJQ+/JBQsjW7JehbtWwK8/73+0RS21a6Rhb9U9sGDq7/6GPX+vb7NASo+/tZigXIEcAyx6HNoOno0LdC9/XbfYNWArghp+ktb+FuafxRU5Na4DbEANjrOJG+a7VoP0PA988Gq5eWklBcXVwu8dy55Hw8jkg9XqNzjHGpeMmLkJKru61loZeQ8qwhw0xaaRQZZlNcSxTM0mCyZDtDqHJnntcrm7W8BJ6m8Zfg/F8Gx8rY8yRovPNp/llHTpjSsz1f35SHK10YTTS3Qzh65lVwbvzlDl6Oc3qS8+HqCPu1u8ZADqpyP0rEXpRwAk/Xe0DUNm/2SoEE7k5/QoTREOQGPDoBoPp7i7jMYcuhf8lFy+l40b+197V4u0hB5j9elb9/k6jCUklpZSdMABw7MfkDNy1/yLuU5BxC9xYIlR0ZHAY4XadDK0N4bygv3+NHqyM8miFDEQ+W88Pp63rtMM5Rx9GgySU4WbbeUICq6JbWU79zY1Dz8nDNRWm8tz9x7NbvWhgahI2gYADSQklhcTJ8d5vOd2kLECMIsNXDRr0Zq78sBVDv4PI+cl1uzCGwoRTZEPmsxGD0l0pdnDhy5HHqKM/fFPs9wSaBaQ2sBnnI0BDCV+Xh5ykhD6VZky+BY4EvjSRv7JVNofftEA4dWmw3l3PDfkeiotZi8j36yxo+VTxTQcn3fd2suz5PztB7TEx8Y4p0T8dJOhIwcfBQx0p7S1AZVjQBrAyeqNDQ+JVmDP6KcKe8+4EqjaNlDUoTHiBGu5Zkv3rPmaCMyptWpFhSX0Hr1WYTv3NijfGoAT6ksW+9rusDasmn1u+fRluoIj3f6FkrEaSmRg6g8R/Sm1V78/+j2S4u/XB0j/cLf8yJRfXXmeoCGrzs7KGgXxWBbL9fzItCwspIiDPPzs/OSESHUOkXekwKj5audnBYVMK3cvifyaQq4xrPKKYpSg2J5HFYfle6truXRU+R9vTqu0HLKypKxXDsN5dVoVOol1rRXtB5aP9We1yBJG3t96hLJo0bWovrFI2pnbWFuVG9q78l+zJ3dwO9Hxqn1zlBbXq2IQhSo1QJfmYfXzusBGi4NXJf0YWKjLgINfHGfFf71hEUTFN75ua2Mbbu6rNIQY04BaoLm1SkHSIaIZLStH7brM4ByvNJzHgr0PLM+yL4PTSb6qXKaYijdLstlpk9kodRwRfum5INblObw4X6Ato9B1fqgdNxF+Yw88/jsA2Lbdnb7q2yrKMj2FrMuLeX1jKxHZAogAj48AFrqBPF8S6YoanVm2+bPjQC2fKhdS9BwMl8EGvh2Niv8WzNwLdARQbBDKJZc+d7CII/HqJHp6x3QsxpjF/Vmvb3/Xh08GkIpE1lGjCtXr88kT9pamL6hatmHOcVKSk8ulOO8RnjS5LtkwZkl433aIzKOSw19pF+HkLUS0qKz2pkL1ji05Dp3XDmnUrnTyOsfbXqg1KBznqL8lQITSRZo6PTp93+1HUFDP9BA83LLy7Z36xlU69laKCWLckBEM9S58wxKIxHy/ZzwSjCj1Uk7F2IoY8fLsPrbW9g41DkMHsnDiOT22z5bKEvrYcmYXKhbEh2yFGAtsObjq+ZY4+g7NcTB0nob+giALyEO6OUWS81xiZ5waIEJTa76OlqcP2s85BwUWaaUZ+2ck1JnSxtjOYfI4jXpi7m2HUFDP9BQilgj3rFlEK1BMTRZwuyF470BIJ9pITLZLtY8oTf4I56ZBSb6kges1sJDj5CmnKXBzclSifdmkQV2JQ8Rb6oEZGttkWvvlRX7WOISkOLdj5BMy41rbR61ZNU72qaStJM1vXNNouez5OSsZLoiQtqY90BPbroip0Nz55B4+s+bysnpTKKkk9cBNAD47+z/N2v3N+M1NzfXTiazx9tyoxZdqJVDzZaAWDSEorCE2dp+lOPDEn5usHLb/DS+5L1om2kDJqKgIm2mAaucR7IWRLK4uNidgliy752oxFhZeVoARSrCEtmV4yYHwqJzwh6YytUvZ1RL6ifTlp4jEWmTaD5RRyFKnkNRquMsT1qO6T4LBEt4siIN2jHouXw1Hbp/v+1sWfqvNhqq9Tdw0WfadQANf8n+/6B2fzNec3Nzq1CcNKqWt8lJDiALdEQHlyf8pYtpLB6stRu5/KTwRyM0nqEt8TZlGt5fWpi0RClS22pfFC1VrkMAP6pb6RSEVDIlYXGrD736DGF4pKHXFGXUKHhG0koXdRA8HjyeasgDaiX5lvAcJT6lK/nU+jLnPESmMok8g2jdLwFfEQBZ07cWH1YksFQXRnlZl8OdALyf/f8B7f5mvObm5mYW9BCaJeGVhsk6Q1wzqBGvpUZBl4Y4I2WUKhVKI7deenyvheLiZfI+8g6+8kiCxD4Gv29ek0kHFg4fLlMklgxG2mIIsBMlT0HyOuRAO3+/dGzVyn5Nf9YYmYhTkQPkQ+8OatvVJ8NKoK4dRuUt2s2t+PcAR4408FUDgvvoTKLItG7ufl8aQUNP0CAVrCYwclDmFsdFQ4E1qDIyBcDLi0Q9avhoW1t5eQMxcoJbjcGq8T5knYecbpBgpnTgU7p9+2YjBJ4ikTIo13zk2teT/VLZ6Etcdr02tPrOishJb7HPVtMh6jCEZ0l10tZxRAxPDXCir5sePqzzpNUr0o+Rfigdr7XAIwosanRmzbkWpTxatG6gAcC26f8fnP4962QADTLSUGJk+qBfSVKZ1Rpu61nEE5MegkXEn4w09FVQQyHrSPt5bdOXhjC0/OyQ6HRLtI+j6S2PcUjPp1QxWgZT8hTxXEvbJ8o/gQXyxr2IU6kcWuVZO0bWAqxzQJtbXOv1XV8QWuK0eHxZ9yPyEdWZ9K6246kGzBPVjMn1Ag3/GMDrADQAPjD9+zoA/7hP4Rt9aZEGqxOs+0N5qdqJkBFBGHLAShRs5c3f84Q/57lq/A7h+ZUq36E96CGMK4EGArOWYSrdgubxZhnkklP5Sg1DaVtFDQW1H3nCGpWEiiVRuZr3zHUK/8qil09UDnN6aKh29kiebVLjCJQYW4vkGBiijjyPyPjhYyS3WJPelQeQlZbptUGE1u2DVQBuBHAngK9OgcOv9Sn4RLiuuGJuZnW6txAlZ0D7DkZPcGqNWh+vyRvUHCh5q/lr2qY0TSkwqc2z5J0hQAg3ep4iKfW0SmQrWg/eZ5ZSLVF4URDiLQrmi0hLDGkEGPG0WgSBb0csBfMeyfYqTTsUMPais1EeJSCtJUtv1rZxbqG5zEtz9nKgnK+/knJcIpNaG0RoXb9yCeAUAI8HcEqfQk+Ua9euuRZIA4AUADeIfb8WN9Sg9hSURyXCVOtlartNSoxYjo8c1QyyaJ6eQpPKaujFZouLKf/FRV0xyoOeLK83WlfLy4nUIWrkZZrcMdI5L9ZbFMzParAW4JX0SXQ8SP69vGT9So3DUA5LKXnGMWc4idZab0ZlyKpbVIfl9IDl1PCj4UtkoKQNLBo/jT0AaKBFPbwDvVPlLLIMb60wEHlbASPpanY3eHXhxD3i0n3oQ5A2UIcYhCXn3kcUZamCP3AgvX/gQN4TqQWVVj0iMrCWwCxq2L1Dqyj//fs7AKYB2wiRjEW3vpaAL6/9c/kOGT2IErWFF53tO8U4BBiqBYdRvWe9LymiN2vBei2dVKABwLUA7gFwL4CXKM8bAP9++vzDAJ4STatdu3al6Qm+oI97cqUd5SndkoFgCW7fSIPHQ62i48Lfd4DV0lDtbvEaaZshIw2TSdvu3t2BhpyxLvXaIhGDtvXb1VpoGKVoe0Tf03gl4MdX+tfIYOn4K+2jknei75c8KymX2sLylGvI46fW4G9E25TwxCOJJcBjCB26nmsa/i6A1wL4NwBeAGAOwBl9Chf5nwrgkwD2AjgdwF0AnizeOQTg6BQ8PA3A+6Jp9TLTQsghkG3b1guqpJzHF81zrTwTzh+BhoWFPNCK1quUou1eGwkZSj6ixBeaaUqljyzJe7UyGwUNffs42vZaG9G206uu6tqyhkrlJtfmHt8Wae95bVPyrES+qS149KbWsPeth/fuUG0zJPG8+TkXJc5WH8ePaD1BwwMAfhrAcwG8EsD/AHBvn8JF/gcAvJ39fimAl4p3/iOA57Hf9wDYFUmrlznXvvCFdYptLbxmyjMa5VgPY5bzmuRnxUvyqh0A8gNj0X7gA7WEhvQSI+9x0KC1aUm/5/qvVoZKj3Sm/L102rPacUbl8m8GzM+X5WHVIUclkYZo3hpIKwV81smg0TY+erRtt2/v+OjTL7y+QzlbaxFpGJJ43svLacvq4mJZVNvjL6pP1xM0vLtPQYH8fw7Aa9jvXwRwq3jnzQCewX6/E8BVkbTs2Yumu0DuBHanFijoJPpNxrLPII4a0dpIwxCUU2ocNPCTCyNU68nSArf9+8sUOg8JllBEGUX5yA1s8o69j3ENCVBqZag20uABN29hYymf9P7ycjfVY/V7Lu8hxlnpGJb3+04HtW3dB7M4bduW0p92WrnseQ5Rid7M/Y7kudZU4xgMwatXLp9GXk/Q8EoAvwag6VOgk/9zFcP/O+KdtyigYS6SVi9zrr3hBr8jrFAen9Oz3vXyadvViqCvQaqhvgqThPGaa8q/keCRpyRrIw2Rvfsa5cKeZOxLvnXgAaWh2nAt5aa2Lb10XhRC1iXa75TOW9OwHhG7SBleBGgII1gzPcfL3bIl8bRlSz6dpTc1A1miN3O/I3n2pVxfRMqmcbB3b/kC9xK+6B6t60k6ev1AwxsBfBzAF6bG+18BeG6fwkX+6z49QZ/GLumIoRBz2/afF45EL3LUd3DxNQ3kxZSGPaP16Ks4S7w1K7owtNHh+XFFMsQOlPWKNPTxFKMUjcrJ91dWZhdCWqCvlKfSekX0COetb98NUae2neXp3/ybtj3llPS3NC/67R3Br/Eqd8jIL00OEWkobaucHonkxyO0/ACw2kjKZOJ/UpwfKLVuoOG7CYCt0ymBfwTgX/cpXOS7BcB9APawxYyXi3d+UiyEfH80rXZFQMNQpHVyX+9UU4BRA0bl861TNUTCf/31qw+0iSrBmvdqyDP+nlHqE40p8Uq4IonUsQ9fWvm1itbLY608vpp2lZGGPu0X9Xgtovdrv8gqyxyi3SkNjwbwdRBDfaa7to70f1S/RcdkSVtNJnqUuZQHfhQ3d7aicmW9F/ki6rqDhrW8kHZHfBxpJ8TLpvdeDODF0/8bAL87ff4RAFd5aXPXeoKGEiUTNWCaQEQHJR+ApYNQ847Jm7NCqh46twxQrl36UK4/ojxZFPWs+P+05uLAgVgdc3xJRZKTl1oD7+UxZJ/V8mRNieR4LZHF0nrS+32Onx+63TWZleCm7wmOpSTHiudo1QLZqDfP0+7fX74ImOdHYOzo0dkPjUXr20f+TirQsN7XRkcaol5MiWKPAgkSSG/BncUT/58UDC3es6IWUdBQMoAtirxb0h81Cljz2jSlzPOmKZ6FhVgZEU+55INTOaVcy9NGAAcNsMojpaXc5b6lEi2vls8+hqCv/Fp8cOO23ge3lRKXb+9ANNkekS+iEmlywp95/afpTYpaaCCkFsRT2dZYXhfQMPXwn9inoBPxWk/QwCmi7C3hyykHb15rqMNprP9rgUHEmHmhUS+/tTBYtaCE6sD7gfNau7sjV25Edoj6KCqt/Jo8a/osJwNa23PiHnWNrJREJax0Mo++fZHjLeKMyEhDX16iVAM+rfrkdCZ5+nJXiWV4rfxKHDrSlYuL+ifN5fulgJJ40fJdz4WQf9WnoBPx6gsaIkKsCV2pMoh6iBZq1Tzc0vIiijy6oj6H/K33LYXu5Rdp61IPO5qnZsRkHbiXU7sjobS+0bxqqFZ2tDxKDHjUm7RWqksFXRpxiQIDL12pYYhSxMh5kYaDB5Nxi7ZHlG8PGGi6qkS2ozxQntZ0w1qUyd+VH6/K8RkFlJ4Mrydo+F0AV/cp7ES7anZPcKKO07wX7t2UKtGo8pCCR8Lfd01Azlu08rEiDX2939L2ijzTDG0UyES8IM+IaWUvLc2u8i+hqFdVQ5G+Ku3PSJklkSXtntUfkWib5aXVynFtm/RN5+3wog+eadOTfBx7HqtFUZCkvUf3tE+KDyVbvG1yn7Neiz6Q7/HyrXQaqI1OLUtaT9Dw1wC+PV1o+OHpQsQP9yl8o68IaIgMAA8VS+GPCGEU3XJFSFefhVUWScG2+LM+kOVFOEqU+ZAkDa1UHBEkrxkl6m+vHzQjLw/JKqGhgQLPU1sUJ9vEut+Hr1qwbvFUckYBlwdrS6TkoyR8X3OaZokjwRctWnrJe4eDBtqySsfERyjSdxbAzQHG2nJl+SVrfWpIK8fij5evpcvlXao71xM0XKpdfQrf6KtvpMF7JyIgfcoseS+XLpeP5zVr78ntQ55QS+NknfOwlh609iwXntbaxIoseWVroKH21L8h24gvcM31QU75Dw0II2C0T6SBE+/nHCiOTqdYJzN649ICLBaAIz6lHGuetvRstUWEQxnVGn0aleuIbtWO0l6LSJAWMbD40w6rs5wODdBaC6stGndPrDFoaFtfWQ4x9zlEPiWCH1VAOQGWtLJibx/S3pUKWKLyobyBElDXtmXATn4htfTsDW6c5TkXpVTaRpoMEf/aMek1vBw6tDrcXVI/r+88ubTqxk8tLTVgFvCoGSfR1fpefSI8RGVC83Ypv9JIg8Vz7n6EN5kHr28kX55XCR/aux5fEZkkKjneO1dm5NC1dQUNAK4AcMP0uqJPwSfCFQUNOVTfF4XX5BM1/BpFAUepEaL3I3uYtYGiKWjvjIEISfAhedW8w5KyogM+5/lGF6mWlJF7ZslQn+iAp8yjdfQ8bI1vrX5eOu0gnRIAYYGgPsBWq0PJe1ZdomOd9xsHvny9VGm9cnozGpnx6ls6lZGTrZK6RIFEjmixac5hiDgl2noUyct6Tk/8CoC7AfyL6fURAL/cp/CNvjYi0mDlX5qPFSrtw4fGV4mnYBnoCP9e2Z4SzKW1FFQJr17+kflpWRbvb29B2pCkeclepKGWD0tRUd6yniUG0ONRLsLV+sUbM1Flz8uXIGgtxqBWvia30brk6imf8/MEagFkHz2Ry7vPFyL7RhpK3/OeedvViSIyqukm+VXT9QQNHwawnf3e/r2wEPJEo1KvbS3IE15LqfdRqLy83MCRCskz6qUAROOnhH9aJKktLlzrvvTkJtcOJc+tdy3PUAN1nnK32l4q3WiEwqqj9duaP14PwMDr4B0XHI00aDzL8cvn22vJKmc92ouXtZE6s219+YusISptM2vMrSdo+AiAM9nvMwF8pE/hG33VgIYaYR9ygGge45Dl1RrSHI+lKNm6n/PspVKtCRfm6lLavlJpyby8kzSHJk0R5bY35rzCkr7VtpLljij2Ig+Uh7XgL/eeRbJOuXGntcFaGMYcKJN9UBN14Pf7fk47x4NHQ7VfRGe2bd1XQEv4zEUh5JqbvrqLjzku9+sJGn5t+iGom6bXhwD8ap/CN/qqAQ01HVni4eQogtotb6SE18iHTyzSDtKJpPf4jnoLfdG5zMsKRefyLjFkfUK1Q3ojnsHmq+mtvsk9t3iKAJcISI20n+bRaeVE2jXn3Zd6trKMyBRebqt1TkY9/ldW0qFO+/YNH2mIvGP161rozLatB0jaGMqNiUg+0XaLAGHelmsOGgD83vTvrwB4CoB/Ov3/yj4FnwjXWkUaShS5HBg1Rk7Lo898vba3uGRbTxTZ58qO5LkW3pxWpjYwvb6jZ57SowVQtXPGGg85r1xSxKDLOlkyFfV2o0q8hscc8Tn6vmNGqy/PpzQ6JY1GdLFwLgoTAT/eYuH1COlbbam1WY1xjZTXJ9Igv3zJeYy2X035ET0j22g9QMNfT89kuAvA+QAu4Fefwjf6KgUNUSUc/fANoUS+OKwGXZcqYS+9RK6asc4Zjyj6zfESuV/iZUbK5nxLwCQBixzk0mBrefH24+c6lB7oxHm2jEJJ2wwNMLz7pX22Fn0sF2R6hqhEJq18rKiDLCe3HseTMa2dPFCZ43l5uX67ZSmV6qvoduxSfVL7XK6p4Y5BFDjWyLmma3Mytx6g4Z8C+BiAbwK4j12fAnBfn8I3+ioFDZFOlQNQpuOdTJ1aempYCWnCa/G8tBQDPJEB7q0GLhmQQ76b48FC7RZ4kIPS8xQ0GTh8uPuyZe15CFp9In3u8RctJ8pHqcKOllnT99zgeJEA3h59wBcfW160yvOao/XU5M9zCKScyMOC6MyVvoCtBpB67SDn6L38a/VmLp10piJjrY+zVTLuJG+yTYEtH2rXEjR890XgP/Qp6ES81irS4A16bphKBK7UEND7tK5AhmO1dzmIiSp0izTQkEPARBGFrSnACPjSyrCUkSQLPGiGxkor39XO2K+hWiNn8Rcppw8fOUMY4aemzvTe/v32x6si/EUpp8yl3ObqGalbNB/rN1+QNz/fXz4j/Hu8afppyAia9n6pLhiKF6utJLj00lnldLbnos+06wEaTsZrI7ZcemgyQqUKhAZ/7XHAtaTVk3g6fHj2FMWoR6HVTxqN3K4JDXyVGlmrD0vajxuLIUBaiZEbygh6v3NKN2fwI4Cj9DRASrtWx1vniOSGxuQQ0QWZf0k+PDLBZZpOgewzbZbjK/eOB7Zqvq9TCor5SaaeXujTNxpZZ4nQfQsYlLTxukUaTsZrSNBQajCGUAKRtN7JfLXGquaDO5wn7ZwCbWDmDIcXorSUpYbY+yxAshSKB8yIb9oDP9R8vVdulPdSQJHzjCLtUyrnllyVeJMRL7LEYEeJeM/1eymQzZWXG1/a/0NMm+UoauyijlbOy861pwYq6bP1Cwt1x7zzPKPOXu7U0pxT5PE4fnviBAENJYNce1fr7KEUh8zv4EF/usLjaTLpFF5ua5JljKVXYwn5UAqbeypyLzR/XtLOGijTyrQAEw+zDhFpsMq1eM9FcEqiLhY4WisvXuZd0381xnRI3jUwXxM54XlqoCs6vvj/0WONh6Bo+0aNpKVbS6K7Vp6R9R2eHo9MRUrQUrrGIdKe63lOw78F0PQpzMn7AgB/DOAT07/nK+88EcCfTBdlfhTAr7BnNwH43PTsiA8BOBQpd8gtl30HudbZuYVNpWVrKDrqkUqjl/u+hETXQyh6mX9Jey8tdSFXOU8b9XZKBqm1s4KUwOHD3TXEmgaPzxJAqinYtQIAWnSoZiFYDX+5k0I9UBsxyLkyOHHvMuJMWOm1cVozvtYKKNX2XQnI1d7V2ifXdxJQRSMNMlLA+Yn2iXbOTUlbnTCRBgD/EsAf0VHSAH4cwHv6FM7yPgLgJdP/XwLgVco7uwA8Zfr/2QA+DuDJbQcafqO03D6HO9V4h6VKURu8NQoi6tlL0j6RG50HpvcJXFied838JM8/ivo1b6HE2JQYWe19aUCozyIRn75keV9W3eX7US+vL1+8j2RZuf4u5YXaXzvkKVeeZ+Q55Q4LkmNAWwdSK+c5r9Zrr9rzCqxy+nxUqm39NojoTa19hlp8qvFjbQfNyajU59ZC675rO9Z1ISSA5wP4SwB/DuDtAJ7Zp3CW7z0AdrUdOLgnkOZ/APixdh1BAxmIEkVvGa7StPIeXxiTM+RaubUeTFRAvUiDNYhLhT/nvXAwRX3HPXtvW6hXnlT2GmjzFN9k0kU9Fhf7Gd4Ilfad92Enre9qAU9NpCE6HZSjHGiLyFdNpEFrPz5+PYMXoZyRthwNS6/0WbTdtnEQo6XhvPWZXtCeRSMN2rHnuf6wxkuOqN58obiWb80uktky5tp2PUADgB+dTg/86dTIX9anYJH3V8Xvr2TefxKATwM4p+1Aw/1IH9V6nTa9wdK+CMCdAO7cvXt3vLVbfZBrZCnWUuGP8BI5FU0rt9SD0X7nyJoblW0yxNcmo2CKpykBDZyktxKRB97+HMQtLg4nEzmK9p8H5PoASY2f6IJE+m3JSo1xlSDSes8bA6Xlau3H5dCaGqqJENLXDbWdQlJmJYjiW1KHAIaUVylAJ6oBqEP0nSx3CD689zynVMrCCR9pAPA/ATxj+v8PTdcO/N2C9HcgfVpbXs8pAQ0AzgLwVwB+ht17PIBTAZwC4F8BeF2Ep9pIQ07BD6lYedmewJd6KDV8lQ4Ybhy5suireDV+pCG3vpVg9U0JD54ijyi8yWT2+Og+irnGk8kZ3CGNs8czXxSq1d1S2N4XMUsoMk5zRqMUfGvlyPbgcsLl2YvIaY6KTOvJPJ+uGTLSQBQB6DnHp6++ivTd0CDRKif3rhaZqQEsktYVNKxKmKYR3tuncJZXaHoCwGnTaZEbnbyeBODuSLl9P1hlGY8aA5RLmxMYC0REw/4RnksHzMpK+tiNpyz6KH3e/tqajRKlIKcyaniyjK1WJue3j2IuUSRWvTSF3keGozzzRaGRdT4l4CZCfPrAMmq1RkQz4jkevTEs9+lL8vRSZEqHp1mLr65GeKptp+i9SN+V6M2o3JeOJb5ou3ZMWpTqt07TE2piYGuf9Cyfm8VCyCPKOw2A/wTg3yrPdrH/fw3A7ZFy++6ekIi+RnFFPZdSgSlVqFyR9xVMmac3n5nz9iL1zrVZ9AjtErDh8ZFTOLXTIhr1VSSTyeqP7ZTmb9U7YlC99DnS0nFAlsuL97Psk77tyvPrA0ItI1frAWt58PHBoz9DbgUm8nRmtA7a+BzCCyceSs9UGFJn8nyjY7JEFiaTdl2nJ/4ugNcC+DcAXgBgDsAZfQpnee8A8E6kLZfvxPRDWAAuAvDW6f/PANBO1y18CGxrJYDfA/CR6bM3cRDhXX3PaYgYpWgepYO/Ju/Iu322atXkmfPIIiAqV09PoUQ9lMj6hdxgpWc0v7seiyBzlDPYEWVsKdooAJbpazxJKWtRj9XaVVRrhIgPbQ5/yLFda7ByY4zajyKEQ+gBTmuhM9t2+B0fJQBsSJ1J+XoRuJyjmRt36/ntiQcA/DSA5wJ4JdLuhXv7FL7R13odI12KBPt6jn28Gmswl3hwkqKHxcgytN8ewMjVrTSCQcQNa3RBl+RdU8xDbbes8TKjaaP9LhVd5Ahwy8us8STpOYXWNVnT6mpFBGrAfA5c5updQtTe8khq7b1cPXjfrdX5IRHqoxeHijSUUAQA9QEzXO94B3+V7nZaz0jDu/sUdCJeawUaZKdGkWDumZV/aXqNeDotfx4yq807smaA8+G1W19wFYk+aPOvBBpyZ/JbdV5e7oxa7QmAVlm5cHKNbFlRhFydvYWUORCi8RBN43l9Wv05aIiMS28KhoPBqOHrY+worXckdTR/3nfedNVakje+c/WIgroaUGI9i+ij3FkdHq2szJ6+W7KeRWu3jYg0vHK6XmBNToXciGutQIMU8Bza9zycSP6cLAUbiSRIRMq9pT6RBjK2tLgqYrCtSEPU6+2jQLiB8IyMl4/FK981oZVZYzy4YY9+BMkiC6hFF4Zp4f5cFCFHufEkecg9k4cp8eiIlzY3BeOtVbHG/BCLqD3wmcuP50FjdHFxY0CDp4P6tBNRBBTyZzkgqvErx8laRBokeXxo5WMdT4R8I9IpjF8A8Jbp1sbn9il8o6/1ijTk7pcujMsZBG0AeIZQy9/bL1xDpQvDtAEb9Xr7GGBedm5L5WQS98ooHSnkhYVZBdh3xTpvm6WlYc6+0H7X5BFVfqX5eUrcI0ovt73m2kqTC/mlyBwQzYGxmmgFp9w4k/KrnV5I2y61cx7Wi3IGu2YxsSfbmnHVnCcv76G/JVPjqPHoBO9TztO6gYbvJgC2ArgKwD8C8K/7FL7RVwQ0RBVRjRdHxPdI1wxOOfg9ZRFVAFyxrtc+bc6nDBt7aN7KY62VHPEDJDDgeRS8Pa0PZvUFaLLtvL5byzbSIgN9dhhJsniPgkVKzxekWnPCGvFySsvkBsuLZFlynisvN92i8c63nVLkhYOpIftOUjQSYjlatTqT52G1VekYiQCH0jxr9SaPOMr+W3fQcDJdEdAQVQree7lQpHccsczD82JqDbwHMmp5ks+jqNlD92tl6CSf0TJ4nbiC1Yh7ANq0z5ALzyJ9l5PrPm2d83DXimqUvNZO2hSUtSB3LdrJi/LlyuOLjku+pMmBJl+3UxNpKGmTqH6V+VN/5HYueLxw4FHq0Vv55gByBARo/ZIDDSV6cwQNawwahog0WAND88hKBbFkAFkUATzeoOMCzd+X+Vrl9FXCfQ2S5TmW5JsLU1O+/OugQ3vgkjz+c3Otkb6qLXvIdEOAEQkK5BSBFQmynIEh+PaeR3SNF2HQiEc4IuF4j0qAgKfzIvo0105rpTdrdOZkYk9nWnrTcrY8IJuj9VzTcAbSB6v+TwD/nK4+hW/0VQIaShfi5Axh1PNu206IeMhL+3xqraKJCJx8hw8AUq5ykMo0mmGVJ93VGIEo+PLqovVVqeGk+zJESM9kPXNHXq8laXWLyGzpToohAaykGtBl9Z1cCyD7ShurfFwOaXRyPOcMlrcQWutbSjNUtGsIIFfryGh5aIuDI8Cjr86U71GZuSOivf6WOqZGb64naHgbgP8K4DcB/DpdfQrf6KtkekIqhtyg7/uckyYQxM/Bg2UDyDISOZIDkHvO2hyplqeca+ftKvMt8eikoswpBFmG5XVb7WP1Hd3nCxH56m++syBS775UovQiBjjXv1r+pR/X4elyxq+EH1kHWUcZXYgYkpxcRupZMvYsUFxqpGV+XsSQdlXMz+fPWZH1k/1XAuYt0FpST/k+7+NIn5U6DRppC1Pl4u6cDHH9xHWMpfMknzLv9QQNoe85bKZrvSINNc9zFD0wySuvj1entUuuTvyreWRMl5f9RWi8XG+nggUUNMMiyyjdS11iULii0gBTreKPUEn/RgxwjUxTXbWz9L20xI8XZq8xntY7ctW5RWsB7nKUq1cpTzI/7ewR6SxpfeGR1n9DOVq1uxOkd56jUqfBKzM6havxsLDQ9Y8GxjReud7csIWQAF4N4If6FHaiXet1IqRGQxiJvgqsdA9xH6Xctt0A2revKzO30IcrCu80Rs+Q56YBhjyC1uJLA0xrCRhK87WUUUkZmjxS/5Liy/Uz96YjytHKIwooJLjrszNnyH4cqu882aYy+DZgGRkaMtLgfbI7UmfpuJSS107R9i4dJ5E6eTxx0EZnu0TAE39HOmbrCRr+GsC3pl+k/DB966FP4Rt99QEN0tOOHr5BlDOWWpqcIrSiIhb1AR1RFM55Wlpa7XGWtEOtUrZQdw0IquVBRoasaMharm2o9VhrDTVPm6tXabvmxgfxRQtPrbrRfRnuLaWIQSupY+nYtN73omiUhn+evc9JnlEeLQ9Ylqf1r8dDRGdqVAJG+jpqGj+WzuSA+8CBDtSVyprMfz1Bw24Al07/fvfqU/hGX31AA1dKuQHAFRN1ZNTD5vmVhO9ygl3jyeX40/KVPPFQW0l5fUmCl+iqadl32nxkqRGQg57/joTIayknP5ZMeOnWMkrjUaQu1JY0JaStNOf/R7e3efxEvL8IKCsFy9Y7nndPdebfmrC2aXKPt6/BjDhaffRfSRr+TiTKNBRw4vxYOpPbCwn+SnSPfHfNQQOAP5/+fQTAw+x6BMDDfQrf6KtvpCG6+l0ix4jB0QQ0qlxkOEqjnOeV49FTaloe1D784Jhaj64vyNAGZa48blC0CEGJstHS8Tn1nTtTH+Z4kmVGZCpXX0uplSh3j4YCiZG68o9X8fa2eM7NP3vlRwyKlRf3+LX0XF5qI1GWQ+H1n0yzZ0/n7fahEhBUsmaqJo2VTqMS0FdaVk7vLi8n/eDphUi5k8k6gIaT+Rrq09ieUffez1Gt9xJR5BFlGDUIpJTn5/MDVXrZpVRqpDSqMVwWYIvURRojLS+q186d7XcjDrk+l6CnpG1qgQeR9GBLZboPj6XlyH7y6i4NvwWitH6vNSo8Pyt9JKTvkWWsImsehoo0EEUdE/lulCIRI28MWmXlQF+kPjINOQjRdqhdBMp5XM/piecCOHv6//81/RbFlX0K3+hr1665QU/iGwKJcoqs6M5FHywa6p227aYcooM7oqhKgdfQgC2aNsJPiRJbXk4LRb33KU95amBJHS3gEalz2+pz5aUylQPdfQAitdHiYmqnKLiR7aJt/bQUuFUfOQ1mjdnIfP1QX0alPOXWYG/8UHsuLJQtirTqEnFMauoY+RKtBQZLx3lpfYhWVtp227b07r59+Tr1dbY2JNJAix4BPAPAnwF4DoD39Sl8oy9gbjD03LYxJFpCJegyp4Dlu0OcREhl0OrrPXtioUuvPWoRda6Nc0ayT95EmvKoWWBHSo+vZrdkqtbzkAZN5uPVeTLRP7BVKufyffk7akgtw035Uei/JILCD03T+IoAVG1Ky2qnGuM4lPd56FBsfU/bDhtxaNt6Q+1RFKSXrOmK6o9S2QCS/oxQ7jyZ6NTVeoKGD07//t8Ans/vbdZLRhrWwlvNKT6vnJL5y5wC1t4tVTaWJ7i0VAZCvDapBTS5vtGMQS6f0n7gbU5p5Tn+kfbmCsWKNEUiHPy3dzCW1t5ee1qyJcsq3TGhlRmRY/5MgjXyjGnXTq4dKT1fX1A67nMGRuuTGseipu84Rb/QKdNYu4CGIitCE0lTMm49+bHkpIQnjTfLmYi0o8Ub8ZT7WmtX/pYPtesEGt4M4D8C+CSA86bHSt/Vp/CNvi6/fG7m4y65ec+agV3jpUhFEBGonALWBlUEYfNnXpi1dI7bW3QWMdKR8qzBGlUkpf2teQLRAS355ttTc6cUWvxHy48CkNx9yYMF/kpkJQcwpbxIsEb9bYFkesY/B10KgEvGkla2pW9qxr3MN1p+lKg/aMcFl6s+baHxFY0KWuApV78Iv6W/tXy8fi4BI9ZYoLQ5x4T4AL7/q+06gYZtAH4GwPdNf+8C8ON9Cmd5XwDgjwF8Yvr3fOO9+6fnQ3yIh1ii6eV1zjnd9ETJccYlA8DyZKx8NQVXM7gl5fLwEHZk3jNnKCRpoKGknpEtijmlrFGN92Xxzwd5zap32UaR+khDWhPp0OpT0hY58Fe6vbRGdnnbRQA0/0qpBv6s+nu8RRwEC/RYOihCOQeB3qnZPtgZnnZGd1r81gKTEmNugcIafW3Vt1RvevKnpY8CpJIdPpI6XT7XtusBGtbyAnAEwEum/78EwKuM9+4HcGFtenldfvncd0OX3OvhaNrau5xDml7HyfdzAjaE8EcVmKW4oou+Its9ZfvWtGVppCFKESUXNdg1oUyelwxfats2c8pMU0YlSkbKgcyvpo1Lo1JSNku3Ilt14W2nne8fAe4Rg5BzPPh7OaBWAmja1t65I09XLZEJOiFycdHuhxxwLCHuuFBb1gLamrKjepNT1LiXgLfJxD9KP8LzZNK2wEWfaU8C0HAPgF3T/3cBuMd4zwINofTympubc9Gxts1Jvh9VDN6zyMKdXB5DpokMSEuJlqQdYgAMDbC8QUx558AA1Y9C3jX72mU7elNWpe3Qx/uTdbdAZWm+UeDA13uU8F9iZKz2rlmbFN3C6fUlJ23XitefVrRKjr0SmdDC4RIIelOZpWNUk7Ga/iilUj5zdYzoTK9c3ndevXN9eVKc0wDgq+L3V4z3PgXgAwD+CsCLStNPn70IwJ0A7ty9e7f64Sc6SOPo0dVoWSL9UhAQBRmlnlKOvDSaV5sbLNYHsyJ8at5OKTixnvE5/BIPlt+zpliovOj2tNx8b5Q3zzBLfiPlRL3AqFx6Rw/neImOB26ocqAuCjC9+5pHP8S462M8Lb5K6k2y2SfKp62TkVNOcozInSRan5f2a2l/1IIVL/8SvRyVwZze5IBMa7ecPGyaSAOAOwDcrVzPKQANF03/Pg7AXQDm20LQwC8eaeCdwI+GlhTxWDzQEBVcKTglnhIvp+TI1pIBGEkT8ej4KuLS8LcG4Pg5+jm+tIhBzkBHlY7Mp8bgWMbdAxQl5eTeLQFJtUpdk1NtDU0kGleq5L002ngrDbVbBrqE32g9aox+zToXXpb8qNXCwuopC1kmTfdaC4b7gIAcyC1pbw/E8HylAY/o5ZyDlstHm0orG/Mnx5qG4ukFADcB+I3a9O0UNMhOpE6gD91Iighh5Dz+HOq0DEXp9j9vsRnPUxsg3qAsQbge79IwlawDsNJGw3d95vtz70ciUtH6eWcoWJ5kZPFlBNSV9klJ/pyoTtonxEuBclTJe2k0xVxaf95/tZGYXN6aU5EjLVLQh3L1bNu83oxGCL020/LlYz0ynZGTefm8dApSGnmv3yzgItfAlUzTbKpIg8sEcLNYyHhEeWc7uhMptwN4L4Bro+m1SztGugTBSyNagmgjHk5JOo1vHjLUjJfMK+eFlXqmckGg5kFaxrXk66FWlMKiKLqPKHVLKZWuU9GInwjK2zQH1jQlHpXjXPg7BwxrDCBPH5my8vi3yAOKlIflPJQelS3zi55bYdVLS+eBRQ8E8sjHEIsUNT5LwGrpolgLMFv190CAJjeU/759s2dRWBHRHAjN9ZPWx5LnkqhbZCycLGsadgB453TL5DsBXDC9fxGAt07/3zudkrgLwEcBvCyXPndFvj0RRfBcUUd3EGiKOKeUcycEykFhrTrWPn7DvT1NqZR6puTJUBhU21VgDYCI96K1Zc1zq/0sBeXVOVevEuJtIIEXV1LWIknt8CDvrIIjR/SFdrl28u5HKCL/HuUAgSzDy4P3tzdNmSOt/0vbiI/HiCxFQX1fucxRpJ7UH3yra6TvLafHKtPTm5bOlP0u283SiZ6+jdoPrjv4+p3cOgaZj7cw+aQADRt1RUBDJMxMiwLpMJ7ScGTEOOWEzzNqEtl6/A1xTKzmNVo8ee/UeGdaHrnwes5LkQd/5fKwpntq+efGVALSiJKgvKzIg+b5WYC3FtR6ZCnvSD6aF1gLXGSfRb4saHmWmlyXAqLcOMrxoj2PApAob5qsRxZrUp8vLHTHkecMvyVzntx6etPKVzv1smR9g9zlEZVjDgg02YlEMj39TjSChp6gQQq/PFaae16W8aB7dL695aHn5skkerbe0X5L8vL0PLvcACkhj0fuRdV8NCznnfK+y01b5Axv1DATWYO+BvxYylbry5K8It55DUW9TC5jGjCPHhIWAdw1JMd+TnaIT+4lDslLSQTFe9/a9VRKfEyQk2HpSK0/rXvamI7IVCng0ChapjUmhxpLFs9aNKJkiqKr1zodI30yXnz3BBd+GfLi4SpNieSQNReqyLxjDlW3bX4gaco0GqLL8VJDGjih9sx91VEjzrdWhxJDLxVYKUCTpC3qiig+r548MpPzeCy+NaWseUe5fEvK1N6VUzmybUr7rsRoRuslx741PmQUL+fJR3jLAXc+nnPHJ8s+HyKSKHlYWpqdZiDZl+tDSk5s5HWoXVheKhtRAJoD7kPqTU6yzUudLeL7pFgIuVFXJNLAjW1J6NUCCrWekSao2oIaT3A1w+UNyD5ebS4vyo8rMe9TtpIsr0R7Xppf1Fu2wB1Xon3bzjK0Mk/Nc7OMMfeIcoDJSiefRQyQNSZKlW7ueY4nq4+0MuR0kCcnHtiR/eh5pZ1y13mTjo5njDVwba1Z6kNSV8o5+Gg5WrsPpTP5PWqznB7hPNH9HIip5Teqxyj/HTt8gGrlP0YaeoKGWorO/UpPjgtByWI5TXikAsopI22AePPAssyogSgx4tw7i2y3GnqtQOS3lt4Kn69FeJrKpA8EHT2aytc+3+zNp9Jv7whhC9xpshxtKy5zQ/RfbtzklD8HYDnvl9qDdiB5BsFrCzk+c+NOtpM2diNGn6eTazRKAF8pWW0RNbg8YjOkzuT6Jqo3LXDogdISB8Qqx7o3mXQRsFxbaLI0rmkYCDSUeje5VeY8Xc7AyIER5UlLHwUBkcGipY8ofc/wWGAmskDL8sBK+y6qBCwvxPMo1wo08LxpOmffPttb1+ptgYZInelZbi++lI9cW0f6Ti4wXViIGw5OVDaBL21eX/NE+fRkKcAkklsLS738EmOpkaxHCe9eniXjrm3zejMno311ppWHpzf79F0JUNZ4t0AWrU2xDtOSdeV1G0HDQKDBM6KasvQQc1SxcI8hNzep5V06aDwvKZLe4ilX/0g6y9jyQbe8rCv7XN45Q2XVmaeLth0PvQ/txVGei4uxL0RaBjsKFHl6bT+99Hg1BZVTuNG+4+F4C7DlKAqs5ViUHnqNJ8nBSI1c9AUNVL51aF2fPOVhap7ht/Rmqc602r7UAbDK1+pZ0ne10Qar7Jze1KK03Bnjz0fQMBBoIIWvzUXnVlHnPNkcad7NkSPdvB5X1H0EMOIZeCuaI3lYZebWhVjtrxmNkgVVQ/BsKRqZd84L6ku5KIAV0q5dOMUVvGx7bnz5LhXy4uWWUAvk5NqJr/aPHGwVIa1/PZ74+JQAP+pJeuMgx09NPeX7kcWEpcT1hTZmSxaFluo1S965nGvnlPTRm94hWx4Y7tN3Ofny1jpxQDFOT6wBaGjb1cpBKsao9913gEtkyxXuWhgjWQ9e1z6DTUvv5aehZj5oIucllFJNVIQTf7evN1jCo8WHxjd/VsKbFmng8/ragjptLES2LkZ4qHkezdtrY1kH6bHX8MDTlHiylpHyHBfOf8l0ZISkUZPj1SvLa/+czGttvhF60+q7PuWV6MzJxAbq1vqZETQMBBrkHBGF1ni43PM2ZcfxZzWe0NJS215/fbdCNrclbi0WCGr3ovWJKjdOfM5+ZSXGj7xntYVVrjYgPY/eq6dUnjnvMUqW0pAK2pKBySS+2FSrmxa5sIxQtM+0cqxIgmeEapWzlJMc8OfTLJqBKB1/moxFjl+W4EUaFm3BNX/GDUhfQyr75vDhbr2NHE9a+3Ag6oGeXPvJ/I4eXb0OxatD3zaI9l1Ub5ZG06SzlTuQcAQNA4EGiU61swMkguOdqIVvNWXkkebNEU+eAfO8zL5UOpglTyX8TCazg72mLOlVy36IGLmaesgoAx/Iffultt+lYcptrcyR5hlKL6ZPvtYZAjlPfIi65BZwalNPQ4W/NdLqRGVoB6LJ/uVkGee+PHP5431H+kp7z+rXWjnS6iMBg+fADB25tHhfS71JDi7JZ65OI2jocclIg/Qk5KIhqSi5AdIMfkQ58+cSeFhhJ+7tkSKombOWdY8g/j6IWauzJL7oTFt8Z5XFjaO2GNEycjm+o56EBRqG2kVhefBWhKtt7b6LHost6y15yMload2saEmuD0rGm5an1hYyH1LMCwv62KiRd49XrR1zMmz1mVW/vtFJLdJgRVu1aBHnjY/Zkr6TWzO1qTAJOrljx6fZtHK9vrNkNSJPFnkndlrjQK5dyNVpBA0DgQbZOV7HaweYyPSl83raIjKNLw1geDxb6TnxvIgf+uRr6Rf+IobJU7YSkGmDPUqWoY30h+UVaeBJM5413q9XDw3IRuXUMrLewl4rDK7lYwGTIRYtRqiP95xrCyJvwVlOH1g8ecCgz6JInq+2TsjjqS9pwDLqhHBdGKkfj24QWPfGvNRJ9Jvv8pBpc33HDbS2YLiULP2j1Zv45WNNyqJWpxE0rAFoaFt98JZ43bKDLdQZ9YBlOjlvxcuz5n5z4cvl5U74+LGwJaQZem9dgxwkXMnxleY1C7lqjJQEMZYS1xTzWihhXtb27bN9ohm8WvCo9Umu7zxvVfZrhK8cjxEqTRd9XwOGRBJoa3vqtTlmbZyW6JhInazFuWsF4KRMltTH04WaztSMZQ5keSBFK9frO64nPecm0tYyXy1q7IFU2c+yLbneHEHDGoEGIi70mpK0kDU3eLn5UpmPpdQ9paspCu3bB9pCKa2u2hatUuGPeH+akda2aslBkFsYGgFitQpMpiVP5Zpr+oV7LeJ9v3NnAneWwdaAhEfS2+J95oHhnOGX/OVAbUk5HljJ8RQ1lJr8W3XIyYqsS65uGjit9VzXYqulJKm7IltSLb1pAfWc3FnPPb0py9RAYa7veP0i02cWyXcssGfxT+N3fl5vZ643x2OkBwQNFijQlJ8mRFxAudchEa230l3mKe95Rp+Ie77WNIMmlDmlGjUYnCJtKonvXNHyy3mssr0j9bGUtZaHfJeDtIjhjZKljOViJ83zipQ7mXSLxugLrTkgJr/FUFOXiBxFgEtpW5cYYDn9RzzxXSge8Oe/JcAo7SPP6HnrKGTE0DLIfWVVM6SWR6yl4XW0PnSVk22rDlGwymWKr6+QaUpAmNbWuXc1/RwZ37loJ2/j8YNVA4IGqYzkfU1Bacrw0KHVg1UOHg8ZR5B51BPT+KDnOSQry67ZPqi1HRdwzShb87BWW5Q+p3e4YijZZy3rpCmYGoAlKRdylCHg3FZAS4ZonUSkztEpBi8vzavUjJ6X3gPyHk/eNBcv0zIO1PbeAldpsKO6xOI5MgUkxzF/xrdBav3YR1Yj/OXamsuhBIMRPqOyFtWZnn4qaau+7arZFYuvySS/Jq7Tc1s/0vawmxtuuDfyoq9ckqDQMcX8PO8Sz4Armlx4P4eM+yhli6eowioBKDnSgArN1/EBKj226Gly0vONegK8TiUeqFUnb8641pOLzkdboE4aFQvseP0s847OHedkht7hi9D4zpmSPilpaw3AE3n1520dDUdr/Je0UY4nuXtA1pOeaWfN9I00SGA0P592ltCqf20XgFUO9fvRo/70b6nOtMZJRJ4s/VQCcqP3csT7zNObuTHTyeUYaegFGuQA56FHEnpPcfPBV+O9Rz2sWsNj5eHlJwdhrTcon5VMiVC7Ly76ikJ+hEfbVZLj3QKGOaUTATec11LQVdK+loKyvhYYMZAR3i0AZQEZmS/nj/qSIh/0m0/r5foy2tbRNTtaftp0lOTHi/B45UnK8eTlXTINUkpcb/IIAfGlTe9YfGvvalTajn2cHSvvvmV57/UFJCsrXVRJi4R14+MkWNMA4AIAfwzgE9O/5yvvXAbgQ+x6GMCvTp/dBOBz7NmhSLky0kBKaXGxGwDWojxtS1oJaCgV6KEHgKd4ogBFAxe5CEIU+FB67YQ5nhed/kYfE7J2lUQHs7a/m9LK38TjwoJvIPoAPuusCo83CxzmQKP2vGT9jSb/FjjRvHUr0sCnY7Q6Ro2o1n48zGu1iaw/8TM/HzPKJXrB4pffs3ZH8XuRaZQ+JPvw8OG2PXAgtYkWaZXtyPssFx2k9zWdor1Xqse8vLxdU7nxFMkvUr9SHeYB2rZt25Ni9wSAIwBeMv3/JQBelXn/VABfAHBp24GG3ygt19o9wT0Jb1uUtYo6Jzg5BR5VXlHShLJU6Wp1sAx0xDuM8Bw5+lgDLjWKgwPBaF6axzkEuOPEz2fweNOmoWSYMrdWhPNu/S/LLgEiWjkWSTmT04YlMquVKccEByeW0uaLCSMRJqIaA661kddusj28BZtrRVH+2rbMoEcBngVQo/pZK9PTCSUyqNWB8tPOXajVYUtLSc68g/5OFtBwD4Bd0/93Abgn8/6PA3gP+10FGq64Yq5Y+UVXqJcoSyl80UORcoNBKkZr0HFAogELa4Gfpggi8+Qecb48I2f1R6lBsvLMDVLpaXmyUevxTCbd4iY6Q4MrA86v9MK1BX98gZfWPpZM1UZvLOL5lRh8Xj9vDOZAtwT62sp9mZ/cg5+LHmhtyQGKZhC0/zmv2joBWZ48YKgWtHtkjRMPZEfXGtUCT0smLH3lyZ0lK5Jy68Ui23IlINXqliNZF082J5O2PSnWNAD4qvj9lcz7rwNwA/t9E4D7AXx4+mzV9IZ27do1990QOE1JWPPtGvL0BE/reGvgRLxEix/NeEseNGUo02hIOFfnnPEtRfeSr8nE9ugiysAqOzcoLY+FK6VoKN5q2xxpdefGk7bS8v7RjJEEgTXRKk1B1/avzM+Td94WFjCsAeea9xg5ECty/gCRtiZHKyc3jrXnEdmVJ4f26S/ZDgsLqQz6a4Egr261Y5PzETGUVt29cqxnskxLDi050/LwAEaNzmxbf8t6eneubTcDaABwB4C7les5JaABwOkAHgTweHbv8dMpi1MA/CsAr3PSvwjAnQDuPPfc3d8dhNoCkhx69IyB52lIIeLCZZ1AVmOYPWUoy/HmIK2V89YAyM09WvXSFHGpMuBUCia8vKWXTiBzcdGvU2m7SN754OdAguQ1503mPKqIcrL6OTcGIvlFDLaX3hujtLOG1kh4O0AibSH59qYoZD9R3WSUJbdgUpbJI08av3wBqQZMtPFUYqS4XM7PrwaskTHn9bnsw8ji17ZdXa+SMS7Jcu4kwLUW03K9mYs8luoGjW/Jh7fmZjJpT5pIQ3h6Ygoy3uE8fxKAuyPl7tw5115ySdteemlaUCc7Lyp4uQ73FKsURIkac8i7dHBoPGuDWCtXKgQrjTZvZ9Wb568pNG0hoAYucnWPLkazvAk+fcNXKc/P1xnL3HtLS50nJ7fMaZGFmnK0PojIkxZ5kmOgRCmXGC2NHwtAkPHcudNvr5ryOIjUPLrIAlbZ/pF24PpC0wvalF5uHOR0DKfl5bbdvbttL7kkAWZtaqykDtZ7Xj013WON2xq9afWLrKunI0kHavaE3/NsgwRQmn2w2oIfby3rcbLsnrhZLIQ84rx7O4AXiHu72P+/BuD2WLlzZsOWIFStczl583meF8c9C2susHRwaEKqDWINDWvCS4pRLlSzeLTayvLcKC33nri3EzV4NFD37fPnVbVBaUU/9u2bPX45x0OEeDuQp1BikK06aO97YM6KHFgKv0RpR7fY5Xj13qHyL7gg/T3//Lhh9Ii3T2Shrsej/D8SccnpGh6a9nSV56l6ZWvbK2sdF9kGMo1cw0OUAx3Ly92Uc3SMaGV702G5KIK2jkw6IIuLs2dbWDx6oMxqCw08dkD3ks+1JwFo2AHgndMtl+8EcMH0/kUA3sre2wbgIQDnivS/B+Aj0zUNb+Igwrse//i5dn7e7jSNPIVsCWIJktfSeR5yTglEDEipEZJpOKq19gdrCy21MiRwWVpKxpMPADmo6be3UnxlZdbjLGkLWX+uEDxjWQIg6F2+3bcmH60OOQWpKXQr4uYZACtf+Y5lpLR+9TysnKFaWmrbPXu6tiyJNETrxYFu1PhqlDOEHo88lM/5ieYZNaAcLFsOQjR/Tc4iz/hzq2weYbLeKdkSGtEJknK6hUeq9uyxF+BawEnjmZehgZqTCjRs1JX7YJWG6qUwSAOiKb0+2w4pRG0dcsT5pGfaPGNp2V7+8j43dHwOV1P6lgerGRmOlj2PjoOr3Glo/ByAqAcvebOmRjzFk2tXepfab+/e8gWLFnkyYPVL1GBHAHEUNPN+PHLEV9yR6SbepuQYRMdDTl6JuIzWfhm2bX2+rGfSE5XjZDLJh/HlPQtwUuTLi3ryvDydyfmi9o2uFYvQ8nLnIOQiZtQuUvYioLRWpx850kWEpIMg8/bGjjYuvXODuvxOgumJjbpyoIEbGqvjZMfwjrQ6vMQjkYZTE2ipXHNTGjmKDgjijfYF88V5UuBL6iyVBvegrO2X0QVHnlLKeRdta69MjipoLQpEvB8+3LbXX5/akQ6rKqVSb5fazovS5ICyZRxkGZE1KLlFZEQWaPD4kX0UMdTeGifZdouLsweN5dpR/o4e5CXbi8bfgQMdHzkQYAE4DkQo/eHDsxGbCED0dKYsQ/JlARvP65aU6z+t7a3trBEqBaNUljZFEdWbVt/KbcFySvakOKdho65IpKF00VnEK+UH9uTy1JC7NrBz4X+tDEspe0pKMx60pVObXtAQc87QaPd4OM/zLkvrkQMWsj4EjA4e1MvKbZXVokAERCjvSP9ZJNcL5AyVxntOAVoG2wJjGqDKUc64WTxGePBArTTYntdHv+fnu28vRAyyTE+/owd5aXnyKcISACjvee3kRft4XjULdXM6gfMQ0U3afcvz1vrWotzOilybTyb6FBJPl9ObJbvZNH01goYeVw40aB1RSppQaNuicmkkT9bOBf5Jbq8efBBGB6Dki/Phhbflb56PtmBHo5WVztvRVqtbaXJet2XstTb2FlNq9dWAHP84j1RmZID6TEtY26+0SJjFey70nwNdEkB6gCpaj+i71J60DkbW2wK10mBrYW2tjyldxKh6MjKZ2DuFPP0j60teqxd147/ljgBZLy6jUblcC51JPFiRhojRt8YCH6c5nq1FvBFgJ/VIJFJnOTK5aA6l5WdqUL4jaFhj0OBRdEBb8980aK3FLDlEz4UtF2nQDL43UCSqjQg1v+d5lhr690LA3Bsnw5ob3FEeuNL0gI/0ELQ21Aa4zFcOfLpPSj8KiKz2tNpX866sfLSPtFnpNIDB257vrrFCvxHg4dVXKnLZ9lYbeQabl+9NlVA+NDWg9V+JQZHvlhhDHvGzxr8G5Hg9qWwerpdfku1DEd2WA4ya7loLnanlG+FN6vVcRIDu5aJxms6S/cbfo3rRziGSzRE0bCBoGGLAax5/6QDg5Xgr00vQv6ZUuFL3FneWeJZSAfC68IHEw6+eFxzlQZbDB5nWX1wxU93llIn0XKRXxOsqFXHOu7faTuNbq5sF9DQ50rxsS5a9tQVa32lty/PmPOTOIqAycyvhNdLGHeedr1Xg0QTLKyWgxT06rX8swyV1BvWB9+l3Ss+jKhaAtM5TsBYg8jrLL8n2oZzO1N6R71l9V6I3eZ94QMDT4R7vvP04gLdkskRnWu1BdeHRMs7HwkJKO4KGHlcNaPAGvTcgLGM7maxeuGgJqiUonmcZrZP0mDlK1g40iUYStN/We/yeRNPkrV59dRvyyHMKpMSYTib659IXFnSFrYEP6UnIaZlSUNe2XV/IY8JzeXHZsUKllI/lLUXakdJQe1mhe6/dtTJLpk+se54Sl4Z7ZaUbozzixcGVBJBaPpZh1gwfj3Twd/iY4MZTO8xJbsHMtYEESwsL6f/bb/cXeJZQTmfKvrKAlwbKS/Sm1neaPHljSRp6OV60eq6lzuQ6ho4RX1pq22uuSfcoQjuChnUGDVIwc16dTKctEtKUlJYPf88Ki9cMACnQsk5aWSXbSK028hSGDE9zAwm07bZtaV1Aro4RA5LjmQzF3r2zPFh95ik9ubK5xLvQ6loC3rT7nrzkFF2UJ14e//y1x6NXl1wfa3LljdOIzGhjj0/j8DU3FG3wZM+bfmlbe2Em94p5mXzHhNQ1sn8lD7xduH6ygEsNWeM+CnC1tVqa0fb0myyP/tem4yze5X3NodIidR5I9epNbU79Lg+TkzzyyBTnh5yt669vR9DQ56oBDXJrTtQocSVgKVUvPM7zkILDB0/JmRL8PR7t0AZ4yfSEbAf+LudBhlr5AJaHRPG8tm1L7+zY4ddRtg3x730zQA4+OjYXSAOPeLDCylIxET/XXz9rLEmOKFLRBzjkgKpmvIm86azDh9uZw88iBl5GUCRR6HT/fp3HmnzpGcmMJpseWI3woLUT54kbYK/+Gj8aWTzxdHKdjxxX9GVUGSni7cXlmO7TQl+6F93m6FHNSZVt6xvLHGiWeUgAJuXGknHtPZk312FSj3uAVyMJMCaTbtwcPKjrxdw6pB072u86W+M5DesMGiLelzbgc2HgiCG2hNcaPNKA8t+e4pRCrqHp3Mpdnic3iBIUED9y/ltrJ6KEltv2iitWn1+hLVbU+LfAE/e0ZFThwIHZ/ooYJa6I+aDnfTGEJ6eR5DPngXOScm7JmAXaNAXbtrORhpxR0sCXxis33pF21MZfzgvU2om3CaWn1ercQOameDweZRrOB5W1d293wBofV5YusHSRFv2KgrpcHaytykRWOZ48RfpNG9OWrpDtJO9p8qXpTbklkoMIrz0tAMB1rtxZo+lNjY4e7Zwt4LKvtT3s5haMFKIHHwRuvRU4fhw4fBjYtg14wQtmn992W7r3ghcAx44Bkwlw003ADTfM5nXhhekdev+224Df/M307PDh2fyuuw5405tmy9q2bfV7t9wCPOtZs+9J/gFgaanj59ixdD34YJdO4+f1r+94BYA//VPgrW8FDh3Sy+O807u33da1G9WB0h471uV3yy1dfbV2AYBXvQr49KeBO+5Iv4mP225L9w4dAp73PODmm9P9178+9d2xY+n+ZAJ88IPp/1tvBV7xCuAd7wCe/vRZPq6+GviTP+nKfcYz0l/OF5V73XXde1Tv664DduwAtm8HnvlM4JWvBC6/PKVdWkp1es97gF//9S7dEMRlkbcb72PtHsk4kNrm2LHZOmp9LvvohhtSfY8d0/vuaU8DPvax9P/NN6e2P3Qo5b19++y7lDfxwccdlzEgtefznrd6rGh04YWz5Vx4YSqb+N2+vcuDj2nZdkCSkauvTvW+8MLE11OfCnzqU8D73pfSv+IV6d2//MtUz2PHUhl8bFNaOeZl+1L5110HvPnN6f+f/dluXAFJvufn098HH0x5c6I+esELOvmfTFIei4vA29+e+CRZWFrKt6lGxPuf/ilw773A/v1dnoCuM0kfSZ5J5z34YDeuqW2PHJltP2pP4oGPadKRXFdw/Xz8ePeX8nve87r+esMbZnn09ObNN3djfWmp0z/0vtVeBw/O3rfKAHS9qbXDtdcmnpIsnnVOvvcc6oM4NvtVEmnIRRgszz3ivWueK/fSrTy0UBgn/uEW6Wlwj8MLgWr3cx6TRN/W+otcfl4oj3i/4IIUeZCenOSBI3HN6+IRGOk1y7MTNO+MeyE8gmJFJLj3JT+fXEqebEXakp5bc+Ba+j59R5QLo3vhXs17rCFZj0gEKDf2yOu/5prVW++WllbvyqBoCz9Rlf5a2z3ldI3kSUYMrBC5jIRpaxqGalspC5bO5OOmRG96Xn9UbqnOtAiU86OdaaHVV4tg5dZNRHiTeUbbladNdZpr2x52c8MN90ZeJaAhFworCXnycBPfJmYJt6c0rDBw2642AlKpSKNmKRZZZul8bS606yklD8BoX9zjzyU4ovaS6yq0MwQk0JBtI5WBNi8q57xpncTRo7O8e98ViRAHmFSmXCMhw65WH5Hx8ECD1ndaP+WAAzcSlB8PY2tyKesrQUYkXO3JJuVBfb9z5+yuAV53DRTytgbSlBbnh8sEyQP/dguFoPn0n+w7Djhlf/IvznJwwttSGl5tz793NsVQZOk8C6xYQEmTEy4jVt0tnrje1BaEyjw9UEL6QR42VtM+0Tp4W0gnk7YFLvpM28Nubrjh3sir75ZL756XVm4n5EKeQ9BE2tybJDKIi4udsZTKwBpocv0D90pKvQ8NQctBbQm6B1T46nHaTqSBBW4E5OIvzQDxrWpUrtY2GliQbavtd6eP6ezbN4xS5gDHOlFSgkzNeycQpHkxXAZl30nDoxlIbbyQ0STF6oFAnk6LRvAx5ckn8U6r8eUcsQQMVCeZ3lq4SnnwbzXw9+W4ovYBUhr6jgTd57JIfUOAgR9Dz/nSAIEGECittlDQirLVUone1MYRN8CeDHvANtd3vHy+CFiuUdAcA+mUybUGnnNnkRZ5kfqqxqHEuHti7UGDZlj5by68mrdjvScXUUlDZg2GXAjL4llTprwseTBIpG4lxAeYzIsPMl4vDajwtLQo8sCB1YaDb9OyvBipSLm3S3lIYyL/l3nz9uMDmyIMt9++GiBFgWeubS2DaSk5a0pHyqC2SlwaLOn9WjzJkLhsK+1QLMsDpbJJbnOfbaa8tC9S8nHCdzrxOken5hYXu5P46K90CKSxttpFA6u7d+sGTXMKJIiWERpZrvxAVamT4LWLpTel06DJotRJ8nySnN4siUJ5OpOXRXlqUxkRefFIgiUZ8ZTyqoF1bQwDWz/S9rCbG264N/KKggbNG+WdpiFBPkAstCkHj+d1W8BDKiBScNLDsL58yfPQwn80KKLhSk+5yugIb1fpdXIkTd6XBFXkndH/PDpA6WS7a8aZK2958iQBD64gJD8c2fN3LFAhlaTmFZWSB1Y9707rA77dzgKyWp/LQ5xyHiOXec/rtMC1fM5PLsy1peZdW1NVbbsa8GoGmqfnBp7axIveyLqQDPM0Kyvd1jn6y7fi0fuWh831FK8P5/XgwVnQvLBQ5yRYfW/pTQ7cZXptXYKMmOTkXytTypzn1Gj14+NYk2UvQmGNSe251JtyLZAHWDTHDPj+r7Y97OaGG+6NvEoiDdocriZUlrLlnS4FQ+avKWi6x5UDFxbuJWtzmZEBIYVTeqW8HlYe3AhxoysNkVwUxtGwpvx5/bnR5vPBe/fOninAQYSGuKWHt7Q0u2WOQrO8LWU7aMaStx0HHXyumb5VsLDQPZfz5yWkKRtNUcp3pQLm7UR1sD6CpPFgrXXgylUz/hYokUBWA/BSSUa2cMo2ssZd286uIeD9yadTlpZm5ZZkneRpz57VX8GMOgeSB9o6x8+84CBMjhNqDw4KucxrYIf41ebFI6Q5T5oh423M28KTJSm3OZ3J68x1I5ctmo6QetqK2mig2xpP3voUnofUcxyMch0qj/WWZ1lo4JCvoRkjDT2u0oWQXGAj5wlQOstQauFza1BZg4TyWV7u5mAlYGhbGwBoPGhAQy6+0sAQry8pIBkG5oOCyudREG2gS5CkgTfibedOPR9eL8qH12dpqVMavG007+Xw4dVHSMt90nIgU9/QgKcDowg8bN8+204l8sjblStNyYMEAxLEStmT3rKmvCVJ5U95UFtFjpLmpPGqgUHL2HLKeZvceHIDy5U/5U/9OD8/e7w0X9xM/HKjzhdGagaEp6NxxKc6+PjWPEqpY/j78ih0Oea4oeHjNvfBMY0s5yk6x+8ZY2rjWp2pAUBNb0rgw39bETIZuZNAki+MzIF4Wa50DvlBWVyuuaPDnSoaE33XNIznNARI7nu9+ebujABg9f5c/j7Q7Ynme7YPHkxnBVA+b3lLt7eX7z0muvDC1ecNvOMdKf22bcDb3pb2Wi8spL3ItG+ciO/NBrq97+95zywP/PyI5z0v7S2n/e/33tudgfCGNwDXXAO8973d3maqN5DqsbQEXHll+n3LLen5sWPp/vHjHe9/+Zfp/xtvTHWkcxSIqM2e/vT03r593f78Cy9MdTt+HHjd61LauTngD/4gtSGv7623pnevvDLlMz8PfP/3pz3MN94ILC+nd6kNjx9PZS8tpfs33ZT+btsGvOtd6X/a5031of3dN96Y9lBffXV3DsGhQ8Av/zLwa7+W6vLa1wJf+EIq713vSmc6POEJ3dkecq86J74H/vWvX73Pnfr8jjvS2RC8LYiOH+/2vPNzC6i9af/68eOz5yP80i915w3w5zfckOSC6k3tBQCf/Wz6+9hjXT/IswmI7rkntd/LX55+87NFLrywk4PLLkv3JpPuvAHaEz+ZpDT33JPOx3jb2xKfJHuveEXi/4YbOtkAUr533AH80R8BKyuJ3yuv7PimczfoLIVjx7r2onMkduyYbeef+ingi18EvvIV4K67Ojl7z3tm35PnZNC5DpwOHAB+/Me79qN+u+mm2fF3xx1Jx1x2WXfuwuHDwOmnJ3m4+eb0HrXzoUPpLJFbb+10wv79Kd373gc89FC69/73p7HlySb10w03dPyQ7E0mKR+u+6TOvPDC7qyTl798lqedO1O/3Hhjp69IHi2dSfL1hjd0/U/1v/xy4NFHge/7PuBv/ibpKcqDxhTn/9ix7uyZW29N7c7Pj7juui7N296WeKVzFKgtAODd7549p+e667rft9zSyR3nG+j0CPUhjbvJJLURyc9//a/pXTrzYc+e7tyO3tQHcWz26+KL58yFKhwpSy99ZWX1scsWcpceL/dI5el4Wqh1cbELD0vvhCPUmvm4yWT1twA471ZZErFfdVXynMl7ptCa9Pos71/ywMN7kgft5DPK9/DhzmPfvn31oioZPeDhd3pOR1O37Wxoj3vdlJaHfvn6CW9emnsFfD6a8wAkz3Jx0fbEtPCt5pFo/Se9ch4KpXpY20C5xyi9WZ4nbxd6j3vcmkzQfS2sq8mv7BPZxnSddtrqvuNpNNmgRavkqWkRHBr7MvKheasLC120YMeO1Wt3+DkNvD1oTAHp3Ac59cKn2vj0j2wL3scymsB33vDyuafMr+g6By36pek5LUIk5cKKemiRSZoC5OtVZDRFyo9cl6CNNy3kL/uZjz2tH2gaZGGhbV/96k5fyXUJlv2weOD8yzQycoGTIdLQNM1zAdwE4AcAPLVt2zuN964F8O8AnArgNW3b/tb0/gUA/iuAJwG4H8D/3rbtV3Llfu5zyVv+8pcTCvvN3+yQGkejhw8ndEceCpAQ7x13dKdwkWdy440JKb7jHSnPF76wQ6ZXX9153uS9r6wAf/Zn6eKeI49KAMkT/ehHE8KU9NBD6S95ZDwtoc83vCH9vuGGziujk+lWVhKif/rTu5MAjx3rIgj/+T+n+xwVU5127ADuZL21ZUtql6c/vWs7furkO96R0l1+eWpDINV9ZSUh87e9LaHigwdTO0qvjbzM48c7T/baa1P//MzPpPuvfW0q84d/OLX/L/xCik7ce2/n4Rw6lOr8J3/SRTW2bgV+93eBn/u5NMRe9arO27vyysTTlVd2Xh6d+MZlBOi8gauv7vph+/bUTxRpueGG1KYkL+RJn39+8ki/8pXEy5vfDFx0UTqN8oUvnD1B8OUvBz7+8eQhPfhg1y/HjyceFhaA005L5WiRiVtvTe+Qd719e3ey4D33pPInkyR3t9yS7r/jHenUwHvu6aI+z352dzreQw+lNgO6ui8tJe+YvKbjx7vTUumEvGc+M/297rr0/333Ab/928BHPpJ+/+RPJh4ougCktA8+mDzpa69NvNCprfPzyZsDgG99CzjzTOAb30j833bbbNTtLW/pIkckUzffnGTy7//95MH+0A8BP/ADKe0rX9lFAN7ylk4mr7wyefJvfWvyfl/+8lQeRZLo70MPAb//++k3neRHumbHDuDnfz79f+AA8Nd/nf7ftw/4sR+bPV3ylluAv/f3Ep/33Zf+kmcpPfY9e1La48fTuLvhhk5XkPffNCntwYOdDqI8jx9PUUUg1eFd70pj57/9t1Qfili88Y1pPN16a1f2M5/ZeeFcfq+7ruOfR4huuqkb0y9/eeL97W9P/z/taUmWfvM3Uz2oDGpHrjPvvz+NeTrtcmlp1qO/996k25797BQBpLH7vOd1epo8eT5+brml0wu/9EupreTY27mzk0keSZtMOrl873uTbDYN8LjHpXukc0lvUkRZ6swbbpjl4R/+w/T7l38ZuOqqWRmgCDWNO+CSXehDfRDHUBcSWLgMwJ8CuMp451QAnwSwF8DpAO4C8OTpsyMAXjL9/yUAXhUp98wz576LwB73uNmV+DTXfPHFHQInhEhbnQjVkoewY0d3JgL3XsjbkqvG+cItng+9Tzzs3avzwNEm974nk1nPla91OHhw9lOpEonSXBnlxw/b4V6onDc988zu/x07ZuewKd/l5Y4vviiMIjCcZ14XuRPkyJHZuTrqN1pRzr0zoG3PPnu2vtSu55wz+97i4mxbkHe2uNiVweditQVkUka4R+N9r4N7jNQ/8qJ67d69eo3H4uLqeXZqI/K6Lr10tv94P9AiUn44kPRGuZzz+vA24JEGui+jeXwc7NuXts1y2af/yaPl5yYcPTq7FkVbb8D74fnPT+9fcYU+JvmiQNqXT+OR7zbiZ2xQFIJ/P4MvWqN3acEi1eP5z2/brVtn+3Tr1rQFl9dbrl8488z0sbTFxVk9IbeZ8qgOtTefA6c6cjmW6yF4P8no1NLS6ojYpZd2/PJICZ05we9LeaH727entpRyofUxRWV4X/E+pS/RUpuQbNM7WkSL79iQ0TNKNz/f5UO6m9qC6w0eQdy/f3YNA49I0tU03ZjmkS0+BqgceXIsX8fG105Yu4C68XESnQiZAQ0HALyd/X4pgJdO/78HwK7p/7sA3BMp7/LL51YNYqBtzzprtUGRA5mElhtK+p8+Q8oHKQkXHyxaiHd+vjMO11yTBIQUpTQmtBiPr8SnwUPlEl979qzee83rQXlQufv3p3IpH66sJJAghSNDrHv2zObLn5FS5ifXcX5pIPJBdPRoV6ZUXjz9VVel/085ZXW/XnJJ255xhp6WlPLu3SkPam+5BU0qIFK6si/5CnYtdG0RKWhquzPOaNtdu2bzvuCCBGjpN//ypyZ7/P/du7t6HDgw25a8Dhww8X6kdHv22DJJeXIZJ4UmdwHwvtNk9Prr9frJ8UTl8rqSguVjldf3wAF9eoi3B01XUNl8ukUCM3mAFy+Dfp955izIBhKoueyy1TIrL6ortRM3jpwvPl2hTYPxMUx9HaHJpDOe/Dr11OR48XtcZ15wQfor0/J+JVDL5WJ+vjsOX8onz4/nu7Cg60ySYXJgSKcdPdoZdLkYWupNKofrQ6rnnj2rgR3XHVIn8Gkw4m3HjtVjjcsTd0okmNbkn+ufztHqBxqaqaE9Iahpmj8F8ButMj3RNM3PAbi2bdt/PP39iwB+pG3bG5qm+Wrbtuexd7/Stu35RhkvAvCi6c8fBM7+FPCkPcDxR4GzzwVOZVM2f/tt4DvfAU47Pf1+9GHg9DPSRb/p4x8PfSmlP/0M4LFvdu9MvgCce376/ejDwCMPA7suAb75DeCMM9M7/H2e57FHgJWPAz94eXr3sW+m66xzujQTADsxmx/RI18DPv95YNcu4BtfB3Y+ocsXALaf3b1L5T72TeBbj6VnlOcjXwOOHwMef1G69zf3pzzPPhf4/GeBB77Y5bNlC/C/7Jn9KMqxR5KwfvMbwI7HpbKOPZryI/rsN4DzHkvpHvlaCtrxekLUcfIFYOu2dO873wFOOaVrf/7u3357tk8lHX808bb97Nm2f+RrKT/q2zPOBL4+DR7ufEL3Lm+bLz4APLodOOfriTfeBl98IPH5pYeAb3/b5ofTli3A/stW92v7HaA5Jf3/2DfT39PPSHX96pdTG1MbkewdeyS16bazUp23ndXlR3V59OFpHZ8AbFX6iPqCjwNZPm9r3l9cls4+N/3+7GeAxz8+Lfs66+yu7x77ZnrvzK2r++XLD3bv0v0vPgBs29711xcfmNZrO/Do/am9t2wBnjAN7p5ySjcWeJ2AlN+xR1Kf8j78/GdTusdflNr1nPO6MSlljsbIRRelNqdxdvzR9Jza6G//Fjj11NX93rbAt7+V9M5nv5H64syt6RnldeyR7n9qh8kX0ntnn9u18yNfAz7zGeD88zr+eV+QXvjiA8BnP7+aF422ngHs3p367exzOv1IxOWAdNbXz0l6inQB15vnXcDaZJqWt6tse+oX/g5P++jDiSepM3mb8fHN/6f2/Prx2f5/7JvA174CfPM84BLW75Z+4TIp85M6k9r0sv2zdZdyyPUiMCuHn/9sGhdnn5vSnXb67Biheh17FPjShW37zTNQSeu2pqFpmjsAPEF59LK2bf9HJAvlXjHiadv21QBePeXpzrZ9+KrSPE4kSnX4m01dB4Dq8YWTpB5f2dT1SHVoN3UdgJOjHidDHYBRT51I1DSNumYwSusGGtq2PZh/y6XPAngi+30JgKlHgS82TbOrbdvPN02zC8CXepY10kgjjTTSSCMJOmWjGSigvwTwfU3T7Gma5nQAPw/gTdNnbwLwS9P/fwlAJHIx0kgjjTTSSCMV0AkBGpqm+emmaT6LtNjxLU3TvH16/6Kmad4KAG3bfhvADQDeDuBjAH6/bduPTrP4LQA/1jTNJwD82PR3hF49YDU2ik6GOgBjPU4kOhnqAJwc9TgZ6gCM9TiRqFcdTqiFkCONNNJII4000olLJ0SkYaSRRhpppJFGOvFpBA0jjTTSSCONNFKIvidBQ9M01zZNc0/TNPc2TfOSjebHo6ZpXtc0zZeaprmb3bugaZo/bprmE9O/57NnL53W656maZ69MVzPUtM0T2ya5k+apvlY0zQfbZrmV6b3N1s9zmya5v1N09w1rccrpvc3VT0AoGmaU5um+WDTNG+e/t6Mdbi/aZqPNE3zIdpGtknrcV7TNH/QNM3KdIwc2Ez1aJrmsmkf0PVw0zS/upnqQNQ0za9Nx/bdTdO8YTrmN1U9mqb5lSn/H22a5len94arQ5+ToTbjBec46hPxAjAP4CkA7mb31GOzATx5Wp8zAOyZ1vPUE6AOuwA8Zfr/2QA+PuV1s9WjAXDW9P/TALwPwNM2Wz2mvN0I4L8AePNmlKkpb/cDuFDc24z1eD2Afzz9/3QA523Gekz5OxXAFwBcutnqAOBiAJ8CsHX6+/cB/KPNVA8APwjgbgDbkI5UuAPA9w1Zh+/FSMNTAdzbtu19bds+BuB2AM/ZYJ5Matv23QC+LG4/B0nRYPr377H7t7dt+822bT8F4F6k+m4otW37+bZtPzD9/xGk3S8XY/PVo23b9tHpz9OmV4tNVo+maS4B8JMAXsNub6o6OLSp6tE0zTlIjsFrAaBt28fatv0qNlk9GP0ogE+2bfs32Jx12AJga9M0W5AM7wPYXPX4AQB/0bbt8TbtOHwXgJ/GgHX4XgQNFwP4DPv92em9zUSPb9v280AyyACmxwaf+HVrmuZJAK5E8tI3XT2mYf0PIR0g9sdt227GevxbAL8J4Dvs3marA5AA2zuapvmrJh0PD2y+euxFOgv+tul00WuaptmOzVcPop8HMP2m7uaqQ9u2nwPwrwF8GsDnAXytbdt3YHPV424A803T7GiaZhuAQ0iHIg5Wh+9F0DDIcdQnKJ3QdWua5iwA/w3Ar7Zt+7D3qnLvhKhH27Z/27btDyOdSPrUpml+0Hn9hKtH0zT/G4AvtW37V9Ekyr0Toi8APL1t26cA+AkAi03TzDvvnqj12II0/fgf2ra9EsAxpPCxRSdqPdCkQ/euA/D/5V5V7m14Habz/M9BCtNfBGB70zS/4CVR7m1oPdq2/RiAVwH4YwBvQ5p68L51U1yH70XQ4B1HvVnoi006LhvN7LHZJ2zdmqY5DQkw/Oe2bd84vb3p6kE0DSH/KYBrsbnq8XQA1zVNcz/S1NzfbZrm/8XmqgMAoG3bB6Z/vwTgD5HCqputHp8F8NlpxAoA/gAJRGy2egAJvH2gbVv6GNNmq8NBAJ9q23bStu23ALwRwDXYZPVo2/a1bds+pW3beaSp7U9gwDp8L4IG7zjqzULWsdlvAvDzTdOc0TTNHqQFMO/fAP5mqGmaBmnO9mNt297CHm22euxsmua86f9bkZTMCjZRPdq2fWnbtpe0bfskJNn/n23b/gI2UR0AoGma7U3TnE3/A/hxpNDspqpH27ZfAPCZpmkum976UQB/jU1Wjyk9D93UBLD56vBpAE9rmmbbVGf9KNL6q01Vj6ZpHjf9uxvAzyD1yXB12MiVnht1Ic3zfBxppejLNpqfDK9vQJpf+xYSKnwhgB0A3omEIN8J4AL2/sum9boHwE9sNP9Tnp6BFPL6MIAPTa9Dm7AefwfAB6f1uBvAP5/e31T1YLw9C93uiU1VB6S1AHdNr4/SON5s9Zjy9cMA7pzK1X8HcP5mqwfSosGHAJzL7m2qOkz5egWSI3A3gN9D2lWwqeoB4M+QgOddAH506L4Yj5EeaaSRRhpppJFC9L04PTHSSCONNNJII1XQCBpGGmmkkUYaaaQQjaBhpJFGGmmkkUYK0QgaRhpppJFGGmmkEI2gYaSRRhpppJFGCtEIGkYaaaSRRhpppBCNoGGkkUYaaaSRRgrRCBpGGmmkdaOmaf6kaZofm/7/L5um+fcbzdNII40Upy0bzcBII430PUVLAP7F9KjbK5E+cDTSSCNtEhpPhBxppJHWlZqmeReAswA8q23bRzaan5FGGilO4/TESCONtG7UNM0PAdgF4JsjYBhppM1HI2gYaaSR1oWmn+T9zwCeA+BY0zTP3mCWRhpppEIaQcNII4205tQ0zTYAbwTw623bfgzAKwHctKFMjTTSSMU0rmkYaaSRRhpppJFCNEYaRhpppJFGGmmkEI2gYaSRRhpppJFGCtEIGkYaaaSRRhpppBCNoGGkkUYaaaSRRgrRCBpGGmmkkUYaaaQQjaBhpJFGGmmkkUYK0QgaRhpppJFGGmmkEP3/V2bzKlYU+ycAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = [0, 900]\n",
"N = [1, 10]\n",
"C = [\"b\", \"b\", \"b\"]\n",
"\n",
"plot_moire(X, N, C)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc1be835",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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