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@bryan-lunt
Last active December 8, 2021 09:36
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Simple Picard Iteration Example
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{
"cells": [
{
"cell_type": "code",
"execution_count": 76,
"id": "d901765a-fdde-435e-9c1a-8389f17d3fda",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The autoreload extension is already loaded. To reload it, use:\n",
" %reload_ext autoreload\n"
]
}
],
"source": [
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"import scipy\n",
"import scipy.integrate\n",
"import scipy.sparse as spsp\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 77,
"id": "a4f4ca2b-206f-448e-829b-3da3adea96dd",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 78,
"id": "20ffd402-22fc-4da3-b6ab-e98ed68fe912",
"metadata": {},
"outputs": [],
"source": [
"t = np.linspace(0, 4, 100)"
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "a2f42f52-2a25-46cb-ad41-7374a6d27a57",
"metadata": {},
"outputs": [],
"source": [
"#forward ODE solution using whatever scipy has under the hood.\n",
"\n",
"\n",
"def yprime(t,y):\n",
" #sin, cos\n",
" return np.array([y[1],-y[0]])\n",
"\n",
"results = scipy.integrate.solve_ivp(yprime,t_span=(0.0,4.0),t_eval=t,y0=np.array([0,1]))"
]
},
{
"cell_type": "code",
"execution_count": 80,
"id": "32eb307d-aafc-46ad-a895-d0debaa51d28",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f1bc091ddc0>"
]
},
"execution_count": 80,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"results.y\n",
"\n",
"import pylab\n",
"pylab.plot(t,results.y[0],label=\"sin?\")\n",
"pylab.plot(t,results.y[1],label=\"cos?\")\n",
"pylab.legend()"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "b8ee4014-08bc-43b4-bc91-068c7053dfe1",
"metadata": {},
"outputs": [],
"source": [
"#\n",
"#My own Picard itteration. Maybe.\n",
"#\n",
"NT = 100\n",
"\n",
"\n",
"ts = np.linspace(0.0,4.0,NT)\n",
"ys = np.zeros((2,NT))\n",
"y_initial = np.array([0,1.0])\n",
"\n",
"ys[:,:] = y_initial.reshape(-1,1)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"id": "6d8628b8-663c-4be7-bc3b-b29cdbe6922c",
"metadata": {},
"outputs": [],
"source": [
"intermediates = list()\n",
"\n",
"#ys[1] = np.cos(ts)\n",
"\n",
"n_odes = 2\n",
"N_iterations = 15\n",
"\n",
"for k in range(N_iterations):\n",
" #better and better approximations, we hope\n",
" \n",
" for i in range(n_odes):\n",
" #looping over individual ODEs in our system of ODEs\n",
" #this loops could potentialy be parallel.\n",
" \n",
" \n",
" for j,t in enumerate(ts):\n",
" #Forward iteration of our integrator, looping over time with finite steps.\n",
" if j == 0:\n",
" continue\n",
" #skip initial value\n",
" dt = t - ts[j-1]\n",
" \n",
" #Super simple Euler integration.\n",
" vals_prev = ys[:,j-1]\n",
" grad_prev = yprime(t,vals_prev)\n",
" ys[i,j] = vals_prev[i] + dt*grad_prev[i]"
]
},
{
"cell_type": "code",
"execution_count": 94,
"id": "83ae8422-2370-4698-a1ae-caa7a38a0d14",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f1bc076ab20>"
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7il2WvFC7p+fj0mHYPc/zseB5z2iD8o9BYGdPwxm9ySUiIulYUo0f+BpoBOQ2DOMMMAJwAJim+TGwBM/ogSN4xg90TYrvm9457A5KZC9Biexx78OJjInk4NWD7Lu8L/bj872f4zJdGBiUy1mOGvlrUDNfTarlq6YtmSL/dG4vbJsFu7+FqFDIVRoefhcqPQVZ88W59HZFx5ilB+KtUEXHuPl59zmK586c6ArW7e41+7uY+vt7JPa9/+38vTz2387f7h654oMXJ3jv3sWwKCq9uYwAfz9OXblBjNtz1a2NVO5Y7tLw4BvQ6HU4vQl2ffPXat08TyOamt08K3X/cTusiIhIWpJkWyuTQ3rfWpmUImMi2XNpD1vPbWXL+S3surCLaHd0nMKuXsF61MxfE2+7t9VxRVJWdLjnnrdtsyBoK9h9oMKTUL0LFK2b4MpNQve4eXvZaFg6NxfDotl5OiTBb2UAx0c/mug9cn8XPclyL1kKuP120oS3ZebM5KBlYCG+2HQCpyv+3zl5svqweUgTftwVfO+/J84Iz0rrlk89Wy8dmT0jD2p29zRLERGRZKOtlffOknvkkoMKubsX5Ypiz8U9bDm/ha3ntrLzwk6i3dH4eflRt2BdGhZqSP1C9cntl9vqqCLJJzQI/pgOW2d5Vt9yl4UaXT1NMjLlvO1DEytKAKoV8efw+TCuR8XEO5fsjT9SsX8rXhNbsQPI7G0n0unG9Y+/k+75/rqg7bD1M8+9jzGRULi2p6Cr0BK89IaWiEhSUyF371TISTyRMZH8ce4P1p5ey9ozazl/4zwAlXJXokGhBjQu3JgyOcqocYqkD8E74fdpnpUZ0+1pV1/7BShSJ97q263F1v/uL0KM27O1MCH/dcUto7qbFbscmRxEOt0JbkXNl82Hza83/dfnvq0bV2DX17DlM7hyFLIWhPtf8qzI+mS9p9crIiI3pfVCbsGCBYwYMYLo6Gjq16/PJ598kuL/NlYhJ7dlmiYHrx5k7em1rDuzjj2X9mBiUixbMZoXb06L4i3i3Zcnkuq53Z6B3b9/ACfXg3dWqPY/qP18ooOkbx2s/U8Ou5HgNsCMvOJ2r25X/PabtzPR1boqhf0pmsOPZfvOxw46/+dj//PvudsNR1fChslw4jfwye65j67Oi54mKiIick/SeiG3bt06AgMDyZw5M/Xr12fMmDE88MADKZpBhZzckUsRl1h9ejVLjy9ly7ktmJiUy1mOFsVb0KJYCwpk0YwmScViomHXV7Bhime1JVshqPOCp4jzzZ5osXXycjiPTV3P9cj42yPzZ/NhcIvyWnFLBon990hstS6brxfFcmdm95nQBJ/vn4X1HTmzDTZMgv0/ecZNVH0a6r4CuUre+XOJiAiQOgq5OXPmMH78eAzDoHLlyrz77rs899xzXLx4kTx58jBz5kyKFCnCd999x1tvvYXdbid79uysW7cu9jlM06RGjRpMnz6dGjXi1U/JSoWc3LULNy6w7MQyfjn+C3suebrJBeYN5NHij/JIiUfI6q1tSJJKxETBjrmwfiKEnoYCVaFub08TE7sDSHgFyGE3CPD348TlG4k+9T+3T2rFLWXcy/11B95pjq/Dfnf/vS4fhY1TYOfX4IqGCk9Aw8GQr0LSvTgRkQzC6kLuzz//pHXr1mzYsIHcuXNz5coVnn32Wdq2bcuzzz7L559/zo8//sjChQupVKkSS5cuJSAggJCQEPz9/WOfZ9iwYRw4cIDvvvsuxV+DCjlJEqevnWbpiaUsOb6EIyFH8LX70qxYM9qWaUuVPFV0P51YwxkJ2+d4CrjrwVCopucf3qWaxLv/LbFVHi+bwasPl2H2xhOcvxYV7/xdr/LIPbmb++sAsvp6UbFgNrafCrn7rZfXz8Pmj+GPGRAdBhVbQ6MhnhEHIiLyn/yzCBnzxxgOXDmQpM9fLmc5BtUalOj5qVOncu7cOUaOHBl7LHfu3Jw9exaHw4HT6aRAgQJcunSJF154gaNHj/LUU0/RunVrcuXKBcCuXbvo2LEjW7duxdfXN0nz/xepcSC4pEGFsxWmR+UedK/UnX2X9/Hdoe/45fgvLDq6iFL+pWhTug2Pl3xcc+okZTgjPOMD1k+CsHNQuA60/ABKNE5wfMCFa5GJ/sPf5TZ5qVEpCmb3u+08N0lZLQMDEi26Ep69Z6PrA8U5FxrJgu1B8VbsIpwuxi07+N8Kuaz5oOkIz6ruxqmwebqnWU7l9tBwIOTUfcMiIqmdaZr/utDw9/mPP/6YzZs3s3jxYqpWrcrOnTvJlSsXe/bsoWHDhpYUcXdKK3JyR8Kd4Sw9vpTvD33P3st78bZ581Cxh+hQtgNV81a1Op6kRy6np4BbOxbCL0DRB6DRIChWHwzjllUcX54MDODkpRss+/Nc7ODpW6lhSdp0u/9WiW29/Hub7L89Pp6wi5576LZ86vkzWPUZT0HnXyRZXpuISHqQGrZWtmrVit9//51cuXJx5coVunTpQrt27ejcuTOzZs1i0aJFLFiwgKNHj1KypOe+6MDAQGbOnEnVqlU5fvw4V69epVq1apa8Bm2tlBRx8MpBvj/0PYuPLea68zqVc1emc4XONC3aFC+bFnvlHpmmZ0Vk1Ttw5RgUrQeNX4diN7tHJXRfFXhWajrWLkrebD5MXH5YDUsygNttvaxZLAflC2Tj262niXTe4dbL6+fgtwmwbabnz2SNrp6tvJlzJfVLEBFJ86wu5ABmz57NuHHjsNvtBAYG8uabb/Lcc89x6dKlOM1OWrduzeHDhzFNkyZNmjBp0iQMw+DHH39k3759DB482JL8KuQkRd1w3mDR0UXM3TeXU9dPUSBzAZ4p9wyty7Qmm3c2q+NJWnR8HSwfDsE7IG8FaPoWlH4o3hbKOu+t4FwC97gVzO7LxiFNAK24ZRQJFfW+DhvN78vP9lMhnLqScHOb/3w/ZGgQrBvnuT/TOws0eA1qPQ+O1L/1RkQkpaSGQi6tUyEnlnCbbtaeXssX+79gy7ktZPLKRKvSrehYviOFsxa2Op6kBef2wIo34cgKzxiBB4dC5fYs3HUuTjHWqU4RjlwI54ftZxJ8mn9up5OMI7Gi3e02KfH6kgQfc8d/Vi4c8LzJcHiZZ5tl0zfhvtYJ3qcpIpLRqJC7dyrkxHL7Lu9j7r65/HL8F9y4aV6sOT0r96Skv2Y0SQKunYWVb8Gub8A3OzToDzV7gMM30e2TDpuBt8NGeJQr3tOp66TcKrGtl34OO4terse+4Gt3tnJ7dDX8+gac3+vpnNrsPShcKxlfgYhI6qdC7t6pkJNU48KNC8zdN5dvDn5DZEwkDxV9iJ6Ve1I2p7oCCp5ZcJs+hLXjwB0DdV6EB/qBn3/sJfVGryQoJDLeQwtk92VQ83Ia2i3/SUJvCNhtBjYDnC4TmwH/7I3zn/4cuV2w8ytY9a6nk+p9reCht9UQRUQyLBVy9+5OCjlbiqWSDClvpry8WuNVlrVZRvdK3dkQvIG2P7Wl7+q+7L+83+p4YhXThINL4cM6nq2UJRtDr83w0FuxRZxpmqzcfz7BIg7gXGgkLQMDGNW6EgH+fhh4VuJUxElCEvqz8n67KvzxelOy+npxa4PTv0cX3JbNDtU6Q+9tngYoh5bBtFrw2/sQE51sr0VEJDVLzYtEqd2d/t5pRU5SVGhUKF/t/4ov9n/B9ejrNCzUkBeqvEDF3BWtjiYp5dJhWDoEjiyH3GWg+WgWXi8XZ4TAo5UKsPn4FXadCcVuM3AlMEZA2yclqfyX0QX/SchpWDoYDvwMuUrDo+OhRKMkSikikvodP36crFmzkitXrn+d5yZxmabJ5cuXuX79OsWLF49zTlsrJVW5Hn2drw98zZx9cwiNCuWhog/RO7A3xbMX//cHS9oUeQ3WjYVNH4EjEzQaDLV6snD3hQTvgcuRycHgFuXwshm8sfBPbZ+UZHO70QVNy+el30NlOHw+7L/fQ3d4OSwZAFePQ8U28PBIyFYgGV+BiEjq4HQ6OXPmDJGRCe+mkdvz9fWlUKFCOByOOMdVyEmqFO4MZ86+OczaO4soVxQtS7XkxSovki9zPqujSVLa/5PnH7bXz0FgJ2gyHLLkBRL/R7RGCEhKSWx0QZNyefnt8CWuRcZgN8B1J/fQOSM9A8V/mwB2b2g8xDOuwK4ZmyIicmdUyEmqdjniMjP2zGDewXl4GV50LN+R5yo9pzl0aV3oGVgyEA4uhnyV4PFJUOjmz6FjF8N48P21CT5UIwQkJSX2ZkFohJMHRq/ielRMvMf8p+29V455/h84shzyVYQnpkBA9WR6FSIikh6pkJM04fT103yw8wMWH1tMNu9sdK/UnafLPY2vl4bupiluF/wxA1a9A24Xe8u8xEtH63A61ElBfz9ebFSCQ+fD+GrzKVxuM8H7k3QPnKQW93wPnWl67ptbMtDT3fL+l6Hx6+DwS+qoIiKSDqmQkzRl/+X9TN4+mQ3BGwjIEkD/Gv1pUqSJbpxNC87uhp/6QPB2KNWUX4sNpM+yq/HugTOAjnWKUCZfVkYtOaB74CTVSmz7r82AUa0r0bZ6YX7aFfzv238jQ+HXYbB9NuQsAU9Mg2L1UuhViIhIWqVCTtKkTWc3MeaPMRwJOULt/LUZVGsQpXOUtjqWJCT6BqwZBb9/AJlyQvPRULEN9casTvAfwXmz+vDH0KaA7oGT1C2he+h8vGzkz+bDySsRFMjmw+VwJ9Eud+z5274ZcWwt/NgbQk5Cze7Q9E3wyZoCr0RERNIiFXKSZsW4Y/j24Ld8sPMDwp3hPFX2KXpV7UV2n+xWR5O/ndoMC1+EK0eh2v+g6VueYo4kbO0uYqGE3mx4smpBFu85S59vdt75iIzocM8g8U0fQbYAeHwylG6azK9CRETSIhVykuaFRIYwbec0vjv0Hdm8s9E7sDdtSrfBbrNbHS3jckbA6pGwcRpkLwxPToMSDQEIuRHN+F8PMnfTqQQfqnvgJL24pzcrTv8Bi16GSwehakfPSravmjyJiMhNKuQk3Th45SBjtoxhy7ktlM1RljfqvEHVvFWtjpXxnNnqWYW7dIjjxZ6i59mWHAmFAv6+1CuVmxX7znMtMoZ6JXPxx4krRDr/47YzkTQmsXvocmb2ZtsbTf/93l5npGfG4vqJkK0QtJ4OResmU1oREUlrVMhJumKaJstPLmfc1nGcDz9PuzLt6FO9j8YVpISYKFgz2jMjK2tBNtw3gu7rs8VrZlIyd2Y+6FSNcvmz6R44SdcSuofOAEzgwXJ5qVcyF59vOPHvf/5P/wHze8LVE1Cvj6ezpZdPSr0MERFJpVTISbp0w3mDaTun8eX+L8npm5NBtQbRrGgzdbdMLsE7YMGLcHG/Z7B3s/eoN2lbgqsRAf6+bBjcxIKQIinv1jcrXn2oNFfCnYxbdoBoV9y/Z2+7Ih0VBsuGwPY5ntmLrT+BfBVS6FWIiEhqpEJO0rU/L//JWxvfYv+V/dQPqM/QOkMJyKIVnyTjdnm2fa0ZBZnzwONToMzDABQbvDjBh6iZiQjUeW8l565Fxjv+r/eIHlji6WwZdR2ajoDaL4LNloxJRUQktUqskNPfCpIu3JfrPr569CsG1hzI1vNbabWoFbP2ziLGHWN1tLQv9AzMfsIz3Lv84/DS71DmYc6FRtJzTuJvtBT017BjkfMJFHEAwQmsYsdR7hF4aROUfBCWvQ5fPAmhQcmQUERE0ioVcpJueNm86FyhMz+2/JHaBWrz/rb3eXrx0xy8ctDqaGnXnwvho3oQvIPtgSOpd6Qzxd/aSJW3fqXh2FWsPXSRxysXwNcR90eJn8POgGZlrckskook9oaGYcDyfedv/+AseeDprz0r4Ge2wccPwKFlyZBSRETSIm2tlHTJNE1WnlrJu5veJTQqlOerPE+3St1w2BxWR0sbosJg6SDYMRcKVmN5+ZG88uu1OM0cbAa8/kh5utcvoWYmIolIbJh4zkwOzl6L4tHKBahdPCfT1x67/f8/lw7Dd13h/B64/2VoMgK8vFP41YiIiBV0j5xkSCGRIYz6YxRLji+hfM7yjHxgJKVzlLY6VuoWtB1+6A5XjkH9V6HREOqOW0dwyF3c5yMiCb7R8WjlAkxfe5SJyw9xSy+UxJuhOCPh16Gw5VMIqA5tP4ccxVLsdYiIiDVUyEmGtuLkCt7Z9A7Xoq/Rq2ovutzXBS+bl9WxUhe3G36fCivfhiz5PbOsij3A8UvhNB6/JsGHqKGJyL2pNXIFF65HxTt+2zdJ9i2CRb09Xz85FSo8mYwJRUTEamp2Ihla06JNWfDkApoUacLk7ZPpvKQzR0OOWh0r9bhxBb7uAMuHQ7lH4cX1uIvUY/bGE7SYvI7EhjmooYnIvbmYQBEH/9IMpcKT8MI6yF0Kvv0fLO7vWa0TEZEMRYWcZBg5fXMyvuF4xjccT1BYEO1+asesvbNwm26ro1nr9BaY3gDX0VW879WD4tufovbEbTSbtJYRP/5JnRK5GPFEBfwc9jgPU0MTkXuX2Jshvg47oTeciT8wRzHoutRzv9yWGfBZU892aBERyTC0tVIypMsRl3l307usOLWC2gVqM7LeSPJlzmd1rJRlmrDpQ1g+nHDf/Dx7/SW2OovFuaR9jUKMblMZwzDU0EQkGSTUDMXLZuBym+TL5su4dpW5HBZ9+//3Di2D+T0BE1p/GjvjUURE0gfdIydyC9M0WXBkAaP/GI233Zu37n+LJkWbWB0rZUSEwKJecOBnKPcYzY534GBo/AV6NTMRSX4JvUlSIk9m+s3bydGL4dj/Kuz+lmAzlKsnYF4nOLcXGg7yfGiAuIhIuqBCTiQRJ0JPMPi3wfx5+U/alG7DwJoDyeTIZHWs5BO0Hb7rAteC4KG3oc5LFBuyJMFL1cxExDqRThfV311OeJQr3rkE32RxRsDPr8Kur6D0w9D6E/DLkUJpRUQkuajZiUgiimUvxhctvqBbxW7MPzyf9j+358/Lf1odK+mZJmz9HD5vBm4XdF1KdM0XGfXLgUQfomYmItbxddi5kUARB4k0Q3H4QcsP4dEJcHQ1fNIIzu5O3pAiImIZFXIigMPuoG/1vnz68KfciLlBpyWd+Hzv5+mnEYozkhMzu8HP/VgTXZ4WUSOZcTwXbT7ayPR1x7i/ZE58HXF/HKiZiYj1EnszJV9234QfYBhQsxt0/QViouGzh2DXN8mYUERErKJCTuQfahWoxfwn5tO4cGMmbpvIiyte5ErkFatj3ZvQIK580JRip35gakxLnnMOYH+og5FL9nPkwnU+7lSNr3vcz+jWlQnw98PAs20rwYHEIpKiBjQrG69jLEB4pJMNRy4l/sDCNeH5tVCoJix4HpYMANdtumCKiEiao3vkRBJgmibfH/6e0ZtH4+/rz7gG46iWr5rVse7ciQ3w3bPcCL9Ov+gXWeauGed0/mw+bHq9qUXhROS/uLUZyjO1i7BgRxBHL4bRpFxe9p29xtmQyIQ7WrpiYMUI+H0aFG8A7WZDppzWvRgREbljanYichcOXDnAa2teIygsiN6BvelasSs2Iw0sZJsmbJ4Ovw6FHMVpGtyTI2b81TU1MxFJm25Ex/DczC1sOh53x0CCHS0Bdn4FP/WBbAHwzDzIo23TIiJphZqdiNyFcjnLMe+xeTQp0oRJ2yfRe1VvQiJDrI51e84IWPACLB0EpR/G7L6CS77FErxUzUxE0qZM3l6cvhq/4UmE08W4ZQfjP6DqM9BlMUSHw6dN4dCvKZBSRESSkwo5kX+RxTsL4xuOZ0itIWwM3ki7n9ux6+Iuq2MlLPSMpyvl7nnQeCg3Ws/mtR9PEBLhxGbEvVTNTETStgQ7V97mOIVrQc/VkKMYfPUUbJjiWb0XEZE0SYWcyH9gGAbPlH+GuS3mYjfsdPmlC3P+nEOq2pp8ZiuRHzYk/OwhukW/Rq311Xjw/XUs2BlE36alGd+2ipqZiKQjia2oO+w2LlyPTPhB2QvBc0uhwhOwfBgsfAliopIxpYiIJBfdIydyh0KjQhm2YRirT6+mRbEWvFn3TesHiO/+DtfClwh2+fNcdH8Om4ViT73QsASDW5S3MJyIJIeFO4IYMn8PEc6bs+YcdgPTNMmR2YcPnqlGreKJNDZxu2HdWFgzCgrVgg5fQpa8KZRcRETuhJqdiCQh0zT5bO9nTNk+hVI5SjG50WQKZyuc8kHcblg9En4bzw6jAs9FvMJVssW5JMDfjw2DH0z5bCKS7G7taDmgWVnKFcjKi3O3c+rKDR6tlJ9tJ68SnFhXyz8XwsIXIXNueOY7yFvOstciIiIJUyEnkgzWB61n4LqBGBiMbTCWegH1Uu6bR4d75kPt/wkCO1Pm94eIxiveZepMKZLxXI900vHTTew+cy3O8QS7WgZth6/ae7ZYdpjrGVMgIiKphrpWiiSDBwIeYN6j88iXOR8vrniRT/d8mjL3zYWegc+bw4HF0Ow9tlV5ixgjfhEH6kwpkhFl9XVwOSw63vEEu1oGVIMeKyFbQfiiNez8OoVSiojIvVAhJ3KPCmcrzNwWc2lerDmTt0/mtbWvEe4MT75veGYbzHgQrhyHZ77lK9vjdJixmRyZHPh4xf1fWp0pRTKu4JCEG54k2NXSv4inCUrRurDwBVg9Sh0tRURSORVyIkkgkyMTYxqMoX+N/qw8tZKOizty8trJJP8+mxfPJurT5py65qaj+Q5Pr87C6wv2ULdkbla91pgxbSqrM6WIAImvxmfx9Up454CfP3T8Hqp2hLWjPfMoY+Kv6omISOqge+REktims5sYsHYALtPF+w3f5/6C9yfJ8+75fhT37RnDTrMk3aP7c+WvpiZNy+dleuca2G8dFCciGVpCXS3thoHLNGlRMT/j21Uhs08CW7JNE9aNh9XvQrH60P4L8MuRgslFROSf1OxEJAWduX6G3qt6czz0OENqDaF9ufZ3/2RuFyx7HTZ/zC+umvR19iIK79jT6kopIom5tatl/4fLcDk8mveW7KdMvqy0q16IzzeciNP1MnYVf/e3sKgX5CgOnb73bL8UEZEUp0JOJIWFRYcx6LdBrDuzjg5lOzCo1iC8bAk3JElUdDj80B0OLuHTmEcYGfMM5i07otWVUkTu1G+HL9JzzlYinO44x+N1tTyxHr55BhyZoNN8yFfBgrQiIhmbulaKpLAs3lmY0ngKz1Z4lm8OfsNLK17iWvS1f3/g38IuwKzH4NBS3M3HMsneJV4RB+pKKSJ3rn7pPGTzc8Q7Hq+rZbEHoOtSz9czm8PJjSmUUERE/o0KOZFkZLfZ6V+zP2/XfZst57f89yYoFw/Cp03g4gEi28zhhUPVCYuKiXcfnLpSisjdunAtKsHj8bpa5qsA3X6FzHnhi1aesSciImI5FXIiKaBV6VbMeGgGIVEhPLP4Gf44+0fiF5/cCJ89BM5ILradT+uV/qzYf57hj1VgfFt1pRSRpJHYan7+7L7xD/oXgeeWQb6KMK8TbJuVvOFERORf6R45kRR0+vppeq/szclrJxl2/zBal24d5/zmxbOpuuU1Trvz8KpjGMdjcmJiMPWZQBqXzWtRahFJjxLqagmQL6sP379Yl8I5M8V/UHQ4fPssHFkOjYdCgwFgqGOuiEhyUrMTkVQiLDqM/mv7syF4Az0q9aB3YG8Mw2DngglU2vk2u8ySPBc9gBCyYgADm5flxUalrI4tIunQrV0tnwwsyJebTuFlM+hUpwjfbwuK39HS5YQfe8Our6Fmd2gxFmx2q1+KiEi6pUJOJBVxup2M3DSSHw7/wGMlHuPtmKw41o5hlasqvZyvEMHNrU0aLyAiKenYxTCe+ngjl8KdcY7H6WhpmrBiBGyYDBWehNYzwMvHosQiIulbYoXcHfZCF5Gk4LA5GHH/CApmzs/UnR9wPiKSxmY93nI+T8wt/1vGazwgIpKMSuTJgsPLDsQt5P7uaNkyMMCznfKhtz0NUH4dClFh0H4ueCewHVNERJKFmp2IWMSIiaLngQ2MunCJHX5+jAmIwuV1Pd51Gi8gIintXGhkgsfjvbFU92V4fAocXQVz20BkaAqkExERUCEnYo3IUPiyLez/kfo1BuN//RXwukbm4h9i8z0Te5nGC4iIFe6oo2X1Z6HtZ3DmD5j9BIRfTuZ0IiICKuREUtwvv+/i8JgGRB/fyDB7X+qvLcfFi4V5o9oH+Pv5kbnoJ3hlOaDxAiJimQHNyuLnSKCBiWkmvFpXsQ10+AouHoBZj8C1s8kfUkQkg1MhJ5KClm34gwpLnyLAfZZuzgF8EV6La5ExvNioJB2q1mJBy28on7skmYvMoX+bUBVxImKJloEBjGpdKc7cyhcaluBaZAytPtzAwXPxt4FTphl0/B5Cz8DnzeDK8RTPLSKSkahrpUhKuXSYc9Oa42feoGv0QLabZWJP/bMz5Q3nDfqt6cfG4I30qdaHbhW7YWhOk4ikAn8Gh9J15hYinC4631+URTuC448nOLMN5rYGhx90Xgh5y1kdW0QkTUusa6VW5ERSwtld8HlzvMxoOkQPi1PEQdwGApkcmZj24DRaFG/B5O2TGbtlLG7TndKJRUTiua9gdhb0qkcmh50PVx8lKCQCEwgKiWDI/D0s3BEEhapD11/AdMPMFhC80+rYIiLpkgo5keR2ahPMehzTy5f/8Rb7zaLxLrm1sYDD7mB0/dF0Kt+JufvnMuS3IThdzniPExFJaQH+fths8XcJ/D2eAIB8FTzFnHcWmPOEZ5VORESSlAo5keR0ZAXMaYk7cx6G5xrPvqh82G/5B1BinSltho2BNQfSp1oflhxfwsurXuaG80ZKJRcRSdR/Gk+QqyR0XQx+OeCLlnD6j5QJJyKSQaiQE0ku+xbBVx1w5SzJyz4j+WK/myEtyvF+uypxGgjcrjOlYRh0r9Sdt+q+xaazm+i2rBtXIq+k7OsQEblFYuMJCvjfMp7Avwh0WQKZ88AXreDkxhRIJyKSMajZiUgSW7gjiD8Xf8Rg5zT+tJVhoPcbHL7uxZg2lWlbvdBdP+/qU6sZsG4ABTIXYPpD0ymYpWASphYR+e8W7ghiyPw9RDhdcY5XKJCVH16sh5/3LaMLrp31bLEMPQPPzIPiDVIwrYhI2qZmJyIpYOGOIHYumMDQmKlscFekfcQgDoTaea5esXsq4gAaF2nM9IemczniMp1/6cyx0GNJlFpE5M4kNJ6gbfVC7D93nf99vpnQiFvu6c1WALosBv+i8GU7OLrKktwiIumJVuREktCkd/vRN+ZzVrgC6eXsQxTeQNzxAvfq4JWDPL/8eUxMPm76MeVzlU+S5xURuVeLd5+l77wdlMyThWdqFWb6uuNxxxOU8YE5T8Klw9DhSyj9kNWRRURSPa3IiSS39ZPoG/M5v7hq8qKzX2wRB7c0ALhHZXOWZVbzWXjbvem2rBs7L+xMsucWEbkXj1YuwMwutTh6MYwRP+6LP57gUBQ8+xPkKQvfPAMHf7E6sohImqVCTiQprB0LK0aw1KhHb2dvnHjFOZ1YY4C7VSx7MeY0n0NOv5z0XN6T34N/T9LnFxG5Ww+Uzo2/nze37veJHU+QKSc8+yPkqwjzOsGBxZbkFBFJ61TIidwL04SV78DqkQQVbUnvyBdx3VLEJTZe4F4VyFKAWc1nUShrIXqt7MWqU7rnRERSh0thUQkej92d4JcD/rcQClSFb5/VypyIyF1QISdyt0wTfn0DfhvP8SJtaHi4HRUL52Rkq4r/ebzAvcrtl5uZzWZSPmd5Xl3zKouP6Z1tEbFeYrsQ4hz3zQ6dfoD8FeHb/8GhX1MonYhI+uD175eISDxuNywdBH98woHC7Wlx6HHqlsrNJ51rkNnHi2dqF02xKNl9svPJw5/wyqpXGPLbEG7E3KBdmXYp9v1FRG41oFnZBMcTtKiUP+6Ffv7QeYGnAcq8TvD0V1CqacoFFRFJw7QiJ3KHFm4/zYKRHeCPT5jNYzQ//ARNKxTgs2drktnHmvdGMjsy80GTD6hfqD5v//42s/+cbUkOERGIP56gQHZfCufwY9aGE/y0KzjuxX45oPNCyFMGvn5GowlERP4jrciJ3IGF208TubAfHWzL+SjmccbEdMBu2Gh+Xz58HfZ/f4Jk5Ovly6TGkxi8bjDjt47H6XbSvVJ3SzOJSMbVMjAgzrby65FOus3ayivf7CAi2sVTNQvfvDhTTvjfjzD7cfj6aXjmWyjR0ILUIiJph+bIifxXbjcLRnaglWtZbBEHBpC0c+LuVYw7hqHrh7Lk+BJ6Ve3FC1VesDqSiAgAEdEunp+7jXWHLpLdz4trETE3Z8wFBkD4JU8xd+U4dPwOite3OrKIiOU0R07kXrjdsKQ/rVzL+PiWIg6Sdk7cvfKyefHeA+/xRMkn+GDnB0zdMZXU/IaNiGQcft52nqhcAJsBoRExcWfM7QiCzLk9K3M5isJXT8GJDVZHFhFJtVTIifwb04Ql/WHrZ3zqfoLRtxRxkPRz4u6V3WbnnXrv0KZ0Gz7Z/QmTtk9SMSciqcLEFYdx3/LjKHbGHECWPJ5iLnsh+LIdnN6S8iFFRNIAFXIit2OasPg12PoZy3N04N3o9njZ4v5vk1xz4u6VzbAx/P7htC/bns/3fs74reNVzImI5RLbwRDneNZ8nmIuS174sg2c3Z1C6URE0g4VciKJ+cdK3DL/p+hx9nGGtCjP+HZVUmxO3L2yGTaG1h5Kx/IdmbNvDqP+GKViTkQsldgOhkw+9rg/n7IVgGd/BO+s8EVLuHAgZQKKiKQRanYikoCF28/gWtyfNq5f+NT9OO9Gd2D4Y/fx3APFrY52V0zT5P2t7zN732zalWnHG3XewGbofRwRSXkLdwTFmzFntxm43CZd6hZjxOMVMIx/bF+/fBQ+bw6GDZ77BXKWsCC1iIh11OxE5D9auP0M1xZ6irjpMY/ybnQHHHYbOTN7Wx3trhmGwWs1XqN7pe58d+g73t30Lm7TbXUsEcmAbp0xF+Dvx/i2lelRvzizNp7gjYV7cf/zJrpcJeF/i8AVDbOfhJDTlmUXEUlNNEdO5J9Mk7DFb/A/2y98FtOCUTHPAAZOl8m4ZQdT7RbK/8IwDF4JfAWAT/d8GrvtMs473yIiKeDWGXMALU0TL7uNj9Yc5eiFME5dvcHZkMib4wk6z4fZT8CcJ6HrL5776EREMjCtyIn805pRdHIt4IuYprwT04nUOmLgbv1dzHWt2JV5B+fx3ub3dM+ciKQKhmEwsFlZmlXIy6bjVwgOiYw7nuB8Xuj4PVw/5ynmblyxOrKIiKVUyIn8bd14WDuG79yNGB7ThdQ+YuBuGYZBv2r9eLbCs3xz8BvGbBmjYk5EUgXDMNgbfD3e8djxBEVqw9Nfw5Vj8EUriAy1IKWISOqgQk4EYOM0WPUOv/k1YVB0d7zs9jinU+uIgbv19z1znSt05sv9XzJ2y1gVcyKSKvzreIISDaH9XDj/J3z5FETfSMF0IiKphwo5kT9mwK9D2eRXn64hXXi/fSDj2qadEQN3yzAMBtQYQKfynZi7f67mzIlIqpDY7ocC/r43f1HmYWj9CZzeDN89Cy5nCqUTEUk91OxEMrZts2FJf7b63k/nkB6Me6oarQILAaS7wi0hhmEwsOZAXKaLOfvmYDfs9KveTw1QRMQyA5qVjTeeAKCQvx9ut4nN9tfPp4qtPVsrf+4LC16A1jPApvenRSTjUCEnGdLCHUHsXjKdN6Kn8JtZlR4hLzDmqeqxRVxGYhgGQ2oNwW26mfnnTGyGjT7V+qiYExFL/P0m2rhlBwkOiaCgvx8VC2Zj2b7zDJm/h1GtK90s5mp0hYirsPIt8POHR8aDfnaJSAahQk4ynIU7glg1/1Mm2qaw0V2Bns6+mHZvbBn4L3/DMHi99uu4TTef7f0MXy9fXqjygtWxRCSDunU8gWmaTFh+iKmrjmCzwciW/yjmHujnKeY2TgG/nPDgUItSi4ikLBVykuGsW/I1422T2WGWpofzNaLwhnQwJ+5e2Qwbb9R5gyhXFB/s/ABfuy9dKnaxOpaICIZh8OpDZXC5TT5cc5STl8M5efkGwX/PmXv4eVoGXoV1Y8EvB9z/ktWRRUSSnQo5yVhObGBk9BgOm4V4LnoAEdy8eT49zIm7VzbDxtt13ybaFc37297H18uXDuU6WB1LRMTToKlZWQ6cu8aqAxdjjweFRDBkwV5oNZCWkaGwbIinmKv6tIVpRUSSn+4KlowjaDvmV+0JJjedo4dwjcxxTqeXOXH3ym6z817992hUuBEjN49kweEFVkcSEQE8xdzBc4nMmfv1CLT5FEo0gkW94MDilA8oIpKCVMhJxnBhP+bc1lx2Z6Zj1BCu27PHOZ3e5sTdK4fNwfiG46lbsC5v/v4mvxz/xepIIiIABIdEJnI8Arx8oP2XUDAQvusKJ9ancDoRkZSjQk7SvyvHMOe05JrTRuvwQXRpUS9DzIm7Vz52HyY1nkRg3kCG/DaEladWWh1JRCTR3ROxx32yQMfvIGdx+PppOLc3BdOJiKQcIzUPAK5Ro4a5detWq2NIWhYahDmzOTeuh9LyxlAea/IgfZqWtjpVmhLuDKfnrz3Zf2U/Ux6cwgMBD1gdSUQysIU7ghKcM/dE5QJMeabazQOhZ+Czh8Htgm6/Qo6iKZxURCRpGIaxzTTNGrce14qcpEsLdwTx6Kj5HHm/KeFXL9L+xgAebtSQV5qUsjpampPZkZmPHvqIUv6l6Lu6L1vObbE6kohkYC0DAxjVulLsroqC/r5ULZydH3efZfbGEzcvzF4IOv0AMREwtzWEX7IqsohIstCKnKQ7C3cE8e78zcwy3qKkEcz/ogez3SjP+LaVaVUt4w38TipXI6/SdWlXzoaf5fNmn3Nf7vusjiQiAoDT5ealL7ezfN95RreuRIdaRW6ePLUJ5jwJ+e6DZ38C78yJP5GISCqkFTnJMCYv3c00YyxljdO86OzLFrMcLrfJ+F8PWR0tTcvhm4PpD00nh28OXljxAkdDjlodSUQEAIfdxrRnAmlQJg9DFuxh6MLd1Bu9iuKDF1PvqxtsqjYegnfAt8+Cy2l1XBGRJKFCTtIXVwyv3xhHLeMArzlfZI27auwpzYm7d/ky52PGQzPwsnnR89eenLl+xupIIiIA+HjZmd6pOiVyZ+bLTacJConAxDNnruvvedhR5U04shwWvQxut9VxRUTumQo5ST/cbvixNw/ZtzE8pgs/uuvGOa05cUmjcLbCfPLQJ0S6Ium5vCcXb1z89weJiKQAP287N6Jd8Y5HOF28fKASNH4Ddn8DK0ZYkE5EJGmpkJP0wTTh1zdg11dMcLblK/dDcU5rTlzSKp2jNB81/YhLEZfoubwnoVGhVkcSEQHgXOht5sw16A81e8DGKfD7BymcTEQkaamQk/Tht/dh0wfMcjVnc+FujGlTWXPiklnlPJWZ8uAUTl47yUsrXuKG84bVkUREbj9nzjCgxRio8CQsex32/pDC6UREkk6SFHKGYTQ3DOOgYRhHDMMYnMD5RoZhhBqGsfOvj+FJ8X1FANj6Oax6h0XuB1iY72U+61qLdjUKs2Hwgxwf/SgbBj+oIi6Z1ClQh3ENxvHn5T95ZfUrRLuirY4kIhncgGZl8XPY4x3vXOevTpY2O7T6BIrcDwtegBMbUjihiEjSuOdCzjAMO/AB0AKoADxtGEaFBC79zTTNqn99vH2v31dk4Y4g3hj5Du6fXmWlK5CxPr2Z9Vxtsvh4WR0tQ2lStAlv13ubzWc3M3DdQGLcMVZHEpEM7NY5c/my+ZDVx87MjSc4feWvnQMOX+jwFeQoBt88DRcOWBlZROSuJMWKXC3giGmax0zTjAa+AZ5MgucVSdTCHUH8OP9LhkdPZKtZhl7OV7gcYbLmoBpvWOGJkk8wuNZgVp5aydu/v01qnk8pIulfy8CA2F0Zm19vyncv1iXS6abjp5s5f+2ve+gy5YSO34OXL3zZFq6fsza0iMgdSopCLgA4/Y9fn/nr2K3uNwxjl2EYvxiGoUnCck9+/GUJU2zvc9QsSPfo/kTiQ2SMm3HLDlodLcPqWL4jPSv3ZMGRBUzZMcXqOCIiscrlz8bs52pxOSyKJ6et5/5RKz0z5qYfZXX1D+DGFfiyHURdtzqqiMh/lhSFnJHAsVvfjt8OFDVNswowFViY6JMZRk/DMLYahrH14kWtrkgCLh9lbNTbhJCFZ6MHc43Msac0K85aL1d9mbZl2vLpnk/5Yt8XVscREYlVtbA/z9YrxrlrUZwNjYydMffSKhcbq78P5//UwHARSVOSopA7AxT+x68LAcH/vMA0zWumaYb99fUSwGEYRu6Ensw0zU9M06xhmmaNPHnyJEE8SVeun8c1pzU23PwvejAXyBHntGbFWcswDN6o/QZNizRl7Jax/HzsZ6sjiYjEWrQjON6xCKeLATvzweOT4OhK+LmvZ6SNiEgqlxSF3BagtGEYxQ3D8AY6AD/+8wLDMPIbhmH89XWtv77v5ST43pKRRF7DNbctztCzdHcO5Iy9UJzTmhWXOthtdkY3GE3N/DUZtn4Y64PWWx1JRARIfNdGcEgEVPsfNBwEO+bC2jEpnExE5M7dcyFnmmYM8DKwDNgPfGua5p+GYbxgGMYLf13WFthrGMYuYArQwVQ3BLkTMVG4v+mEef5PXnT25cVOHRirWXGplo/dh8mNJ1MqRyleXfMquy/utjqSiMhtZsz5er5oNASqdoQ1ozwFnYhIKmak5nqqRo0a5tatW62OIVZzu3F//xy2fQvoF/0i9dq8TNvqhf79cWK5SxGX6LykM9ed15nTfA4l/EtYHUlEMrCFO4IYMn8PEU5XnONNyuXlsy41Pb9wOT2NT078Bp1+gBKNUj6oiMg/GIaxzTTNGrceT5KB4CLJYeGOIOqNWsnM4R2w7VvAe86nua9FTxVxaUhuv9x88tAneBlePL/iec6Fq723iFjn1hlzAf6+1C2Zk5UHLjBj3THPRXYHPDUbcpeBef/TjDkRSbVUyEmq9Pe7pk+EfUtXr2V8GtOCz83HyZ3Fx+pococKZyvMR00/Iiw6jOeXP09oVKjVkUQkA/vnjLkNg5vwRbc6PFq5ACOX7Of7bWc8F/lmh2e+9QwO/7IdhF2wNrSISAJUyEmqNG7ZQVq4VjPI8Q0LXXUZGdORGDeaE5dGlc9VnikPTuH09dO8suoVolxRVkcSEQHAbjOY8FQVHiiVm0E/7Obdn/dRb/Qqio/eTbfo/sSEXYSv2kP0DaujiojEoUJOUqWS1zYzxjGD9a77GOB8AfOvP6qaE5d21cxfk/ceeI/tF7Yz5LchuNyuf3+QiEgK8PGyM71zdQpm9+XT9ccJConABFZeC6BPdC/M4B0wvwe43VZHFRGJpUJOUp+zu/jIexJHzABedPbDiVfsKc2JS9uaF2/OwJoDWX5yOWO2jCE1N1sSkYwls48XMe74P5MWO6sxxasrHPgZVgy3IJmISMK8/v0SkRR09STOOW0INTPTNXog18kUe0pz4tKHzhU6cz78PLP3zSZfpnx0q9TN6kgiIgCcC41M8PiksCb0aeAFG6dCjuJQUz+3RMR6WpGT1OPGFaLntCYi4gaD/Ibz0pMPaE5cOvVqjVdpUawFk7ZP4qejP1kdR0QEuN2cuUzQbBSUbgZL+sPh5SmcTEQkPq3ISergjCT6yw5w9QSv2Ybxdvd2FM+dmf/dX9zqZJIMbIaNdx94l8uRlxm+YTi5/HJRt2Bdq2OJSAY3oFnZeHPmDAP6NCkFdi9o+znMbAHfdYHnlkH+itaFFZEMTytyYj23C+f33fEO2sxg98v0fq4LxXNntjqVJDNvuzeTGk+iuH9x+q3ux/7L+62OJCIZ3K1z5nJm9sY04Ze953C63OCTBZ6ZBz7Z4OsOcP281ZFFJAMzUnOzgRo1aphbt261OoYkk4U7ghi39ADdw6fT1WsZ7zg70fDZN2lQJo/V0SQFnQ8/T+dfOhPtimbuI3MplFUD30Uk9fhq8yleX7CHttULMa5tZQzDgOCdnpW5vBWgy8/gUCMuEUk+hmFsM02zxq3HtSInlvh74HeLsB9iB37P4VGuhEdbHU1SWL7M+fi46cc43U5eWvmSBoaLSKryTO0i9G1amu+3nWH8r3/NMi1YFVrPgKBtsPAlSMVviotI+qVCTiwxbtlBGrs28IbjS3521WZkTEecLlMDvzOoEv4lmNx4Mmeun6HP6j5Eu1TQi0jq0adJaZ6uVYQPVh/l1W93egaGzzb4wKsz/Dkf1oy2OqKIZEAq5MQSBUJ3MtHxEVvcZXjN+aIGfgs18tfg3Xrvsu38Nt7Y8AZuU4N3RSR1MAyDd568j4oFszF/e1DswPBxYc34wd0I1o6G3d9ZHVNEMhgVcpLyLh9lhs8Egsxc9Ih+jSi8Y09p4HfG9kiJR+hTrQ+/HP+FqTumWh1HRCSWl92WwPZ/g8HRz7HDqACLesHpPyzJJiIZkwo5SVnhl4iY2RK3Cc85BxFC1thTGvgtAN0qdqNtmbZ8uudTvjukd7hFJPU4m8DAcCdePBfRB7IHwDfPwNWTFiQTkYxIhZykHGcEN2a3w7h+lrezDKdnqyYa+C3xGIbB0NpDqR9Qn5GbRvLbmd+sjiQiAiS+aySTf1545ltwRXvGEkReS+FkIpIRafyApAy3m4ivOuFzZAmvew3glZdf1TZKua0bzht0WdqFE9dOMKv5LCrkqmB1JBHJ4P7uuBxnYDgwqnVFOtQqCsfWwNw2UKKxZ96czW5ZVhFJPzR+QFLcwh1Bns5egxfz1chn8TuymPFmZ7p0760iTv5VJkcmpjWZRnaf7PRa2YuzYWetjiQiGdytA8NzZfbc4714z18Dw0s0gkfGw5HlsHy4pVlFJP1TISfJ4u93LYNCIuhk/5VnXD8yM6YZ3P8S5fJnszqepBF5M+XlwyYfEhkTyUsrX+JatLYriYi1WgYGsGHwgxwf/Sjbhj3EmLaV+e3wJQb/sAfTNKFGV6j9Avw+DbZ/YXVcEUnHVMhJshi37CARThcP2rbzptdsfnVV552YzizaqVUVuTOlc5RmUuNJnAg9wWtrXsPpdlodSUQk1lM1CtOvaRl+2H6GicsPeQ4+PNKzvfLnfnDyd2sDiki6pUJOkkVwSAT3GceZ5pjKXrM4fZy9cGPTnDi5K7UL1GZE3RFsOruJkZtGkprv7RWRjOeVJqVoX6MwU1Ydoepbv1J86DKaBz3Hdb8AmNdJnSxFJFmokJNkUSV7OJ95j+cKWeke3Z8IfAHNiZO717JUS3pU6sEPh39g5p8zrY4jIhLLMAxqFc+BzYCQCCcmcCDUzlPX+hDtjIavn4aoMKtjikg6o0JOkl7UdT62jSUzkTwXPYCL+AOaEyf37uXAl2lerDkTt01k+cnlVscREYk1Yflh3LdsFtjvzMdA+sHFAzC/J7jd1oQTkXRJhZwkLVcM1+Z2JveNo7zpM4Dr2UprTpwkGZth451671A5T2WG/DaEPRf3WB1JRAQg0VsHFl0vC83eg4OLYfXIFE4lIumZl9UBJB0xTa4v6k+206sZ43iRQb17kTerr9WpJJ3x9fJlSuMpdFzSkd6revPVo19RMEtBq2OJSAZX0N+PoASKufzZfaH283BhH/w2HvKUg8rtLEgoIumNVuQkyUT89gFZd89kFo/TpudQFXGSbHL55eLDJh8S7Yqm18peXI++bnUkEcngBjQri58j/gDwLD52ol2mZ75c0XqwqBec2WZBQhFJb1TIyT35e+h3j9ffxmflGyx11aRc54mUypvV6miSzpXwL8HExhM5EXqC/mv7ayyBiFjq1mHhAf5+PF2rMIcvhPP6gj2Ydgc89QVkzQ/fPAPXNI5HRO6NtlbKXft76HfJmMNM9p7GbrM4A9y9eOdatNXRJIOoXaA2w+8fzvCNwxm1eRTD6gzDMAyrY4lIBtUyMCDeveB5s/oyeeVhiuTMxCtNSsPTX8OnD3nGEnRZDA7tXhGRu6MVOblr45YdJLvzQuyYgR7R/bnu8mbcsoNWR5MMpFXpVnSr2I3vDn3H3P1zrY4jIhJH36alaR0YwITlhxi6cDf1Zp7n+fCeELSVU3OeB83FFJG7pEJO7lpIyFU+8x5PJqLijBnQ0G9Jaa9Ue4WmRZoybss41p1ZZ3UcEZFYhmEwuk1lSuXJzJebThMUEsEyd00mOttQ5PRC9vww2uqIIpJGqZCTu+N28aHfh5QzTvGy8xUOmYVjT2not6Q0m2Fj5AMjKZezHAPWDuDQ1UNWRxIRieXtZSM82hXn2BRXK5a6alJh71g4utqiZCKSlqmQk7ty9cfXaWhu5e2Y/7HWXSX2uIZ+i1UyOTIx9cGpZHFk4eWVL3Mp4pLVkUREYp0LjYzzaxMbrzpf5LA7AL7rApePWhNMRNIsFXJyx8I2fkaOnR/zrdGcIi36xunQpaHfYqV8mfMxpckUrkZepc/qPkS5oqyOJCICJLxb5Qa+DPN9HQzD08kySqNUROS/M8xUfJNtjRo1zK1bt1odQ/4h+vBqbF+24Xd3RbI89wOBxfJYHUkknhUnV9BvTT9aFG/BmPpj1MlSRCz3d6fnCOfNLZZ2A8a3rUKrHEfhi1ZQpjm0nws2vc8uIjcZhrHNNM0atx7XTwr5z9wXDhHzdSeOufMT2fJTFXGSajUt2pQ+1frwy/Ff+Hj3x1bHERGJN2cum68XLhOOXgqHEg2h+Sg4uBjWjLI6qoikEZojJ7e1cEcQ45Yd5EbIBRb5DCcTNrbU/ZiO1cpYHU3ktrpV7Mbx0ON8uPNDimcrTvPiza2OJCIZ3D/nzJmmyZD5e5i2+ghFc2WiXa2ecG43rBsL+e6D+1paG1ZEUj2tyEmi/t4GciHkOh97TyQfV3gx5jUy5S1hdTSRf2UYBiPuH0G1vNV4Y8Mb7L642+pIIiKxDMPgnZYVeaBUbl5fsIffj12BRydAoZqw8CU4v8/qiCKSyqmQk0SNW3aQCGcMI70+o7btAAOcPdniKs34X9XaXdIGb7s3ExtPJLdfbvqs7sO58HNWRxIRieWw2/igYzWK5crMC3O3MX3jGZ68+AIXoh2c+bgVizermBORxKmQk0QFh0TQw76Yp7zWMjmmFT+668UeF0krcvrmZNqD07jhvMErq14hIkZ/fkUk9cju5+DzLjWJcbkZveQAu0L9eCG6L3ndF8m25AUWbj9ldUQRSaVUyEmi2mbZwxCvr/nZVZtJMW1ij2vgt6Q1pXKUYmyDsRy4coA31r9Bau7WKyIZT+GcmfDz9uLvn0zbzTIMj+lKfWMX1xcPtzSbiKReKuQkQdFBu3krZiJ7zWL0d76A+dcfFQ38lrSqYeGG9Kvej19P/qpOliKS6lwOizv38hvXg8yNaUJn1wLYO9+iVCKSmqmQk3jM6+cJm9WWa6YfSytOIJe/vwZ+S7rQ5b4uPFHyCT7c+SHLTiyzOo6ISKyEdru8FfMsu4xysKgXnNtjQSoRSc00EFzickZybupDZA89wIIqM3imdUurE4kkqWhXNM8te46DVw4yu8VsKuSqYHUkEZEEB4Y77AZTHitIi40dwO4NPddAppzWhRQRS2gguPw70yToix7kv7abrwNe5+lWT1qdSCTJedu9mdR4Ejl8c/DKqle4eOOi1ZFEROINDPe223C7TQoWKgbt58L1s/B9V3DFWB1VRFIJrchlcH8P/A4OiaB/psX0cn/JV5k707rvZHwddqvjiSSbg1cO0vmXzpT2L83nzT/Hx+5jdSQRkViXw6Jo+eEGIp1uFvWqR8HjP3i2WNbtDQ+/a3U8EUlBWpGTeP7exhEUEsHDtj/o5f6SRa66xNR7TUWcpHtlc5Zl1AOj2H1pN29ufFOdLEUkVcmVxYfPnq1JZLSLbrO3El6hA9TsARunwp7vrY4nIqmACrkMzDPw28V9xgkmOj5ih7sUA509mb7uuNXRRFJEk6JN6B3Ym5+P/cznez+3Oo6ISBxl8mVlWsdqHDx3jT7f7MT18Egocj/82BvO7bU6nohYTIVcBhYcEkEeQvjE+31CyEzP6H5E4a2B35Kh9KjUgxbFWjB5+2TWnVlndRwRkTgalsnDm0/cx4r956ny7hpqHurMJacPYV90gIirVscTEQupkMvAimW3M917Ajm5To/o17hIDkADvyVjMQyDt+q9Rbmc5Ri4biDHQo5ZHUlEJI5svg7sNoOwqBgu4k/PqD54hwVzbtb/wO22Op6IWESFXEZlmryfaSbVbEd4zfkCf5rFAQ38lozJz8uPKQ9OwdfuS+9VvQmNCrU6kohIrHHLDuJy37yPd7tZhrdj/kf+8+tg7WgLk4mIlVTIZVCnF4+m2tWlzPZ5mp3ZGmngt2R4+TPnZ1LjSQSHBzNg7QBi3GrxLSKpQ0K3PMx1NeXbmIawdgwcWGJBKhGxmsYPZEAXty0i10/Pss6rLlX7zcc/s6/VkURSjQWHFzB843A6le/EoFqDrI4jIkK90asISqCYK5rNxtpco+HKMeixCnKXtiCdiCQ3jR8QAMJP7yHTT89zgGIUeW62ijiRW7Qq3YpO5Tsxd/9cFhxeYHUcEREGNCuLXwJjgXwzZSam3RywO2BeJ4i6bkE6EbGKCrkMxBV2ifDZ7Qg3fQhr9QUlCuaxOpJIqvRajdeoU6AO72x6h50XdlodR0QyuJaBAYxqXYkAf7/YWyHa1yzEwXPXeXd9GLSdCZcOeQaGp+KdViKStLS1MgNYuCOIiUv3MiZiBIHGEaaXmMorzz5tdSyRVC00KpSnFz/NDecNvnnsG/Jnzm91JBGRON75eR+frT/OyFYV6RizCJYPg6ZvwgP9rI4mIklIWyszqIU7ghgyfzc9w6dTx7afQc4efHQkBwt3BFkdTSRVy+6TnakPTiXSFUmf1X2IjIm0OpKISByvP1KexmXzMGLRn2zM9zTc1wpWvg3H1lgdTURSgAq5dG7csoO0dS+lo9dKPop5nIXuB4hwuhi37KDV0URSvZL+JRlTfwz7L+/nzd/fJDXvYBCRjMduM5jydCDFc2em2+ytNDrUhkOuAlyd05llG7ZYHU9EkpkKuXSu6LWtjPCawwpXIONi2sceT6iVsYjE17BwQ14OfJnFxxYzZ98cq+OIiMSR1ddBh5qFiXC6OXHdxgvOfniZTgr8+jw/bj1udTwRSUYq5NKx8HOH+cAxmWNmAfo6e+H+x3/ugv5+FiYTSVt6VOrBQ0UfYsK2CWwI2mB1HBGROD7fcCL262NmQfo7X6CycRT3LwOtCyUiyU6FXDrliggl5LM2GJi86BpAGJliz/k57AxoVtbCdCJpi2EYvFvvXUr6l2TAugGcunbK6kgiIrFu3WWzzF2TD2OeoKXrV9j+hUWpRCS5qZBLj9xujn3SkXzRp/mj5kR6t304TsviUa0r0TIwwOqUImlKJkcmpjSegs2w8cqqVwh3hlsdSUQESHiXzfsx7dhiqwyLX4PgnSkfSkSSnQq5dOjg1wMpffU3lhTqw0OPPkXLwAA2DH6Q46MfZcPgB1XEidylQlkLMb7heE5cO8Hrv72O23RbHUlEJMGB4S7sbKk+DjLngXmd4cYVi9KJSHJRIZfOHF89i7KHZ7AiUwtadB2GYRhWRxJJV+oUqMNrNV5j1elVTN813eo4IiLxBoYXyO5LnizefLr9OuebfwJh5+CH7uB2WR1VRJKQBoKnAwt3BDFu2UFyhf7Jt95vsc8oRfFXV5AjWxaro4mkS6Zp8saGN/jx6I9MajyJJkWaWB1JRCSOYxfDaPnBBgr6+7GozmF8lr4KDQbAg29YHU1E7pAGgqdTnoHfe4gOCWa69wQukZ2XYvqx9mio1dFE0i3DMBh+/3Aq5qrI67+9zpGrR6yOJCISR4k8WfigYzUOXwjj5YOVMat2gnXj4OAvVkcTkSSiQi6NG7fsIG5nBNO9J5KNcLpH9+dcTBYN/BZJZj52HyY1nkQmRyb6rO5DaJTePBGR1KV+6Ty88Wh5lu+/QK+rT3PAKMG1r57jqfe+ZOGOIKvjicg9UiGXxgWH3OBdr8+pZjvCq84XOWAW+eu4Bn6LJLd8mfMxodEEgsODGfzbYFy6/0REUpkudYtxf4mcLDkYSvfIV3Bj8GbkGN6cv03FnEgap0Iujevlt5x2XuuYFNOaZe5ascc18FskZQTmDWRIrSGsD1rPBzs/sDqOiEgchmFw8vINAM6YeenrfIlyximGmjMYt/SAxelE5F6okEvDTm35mX7u2Sx11WRyTOvY4xr4LZKy2pVpR5vSbZixZwbLTy63Oo6ISBxnQyNjv17jDmSqqxXtvNbRIGyJhalE5F6pkEujrp7ej//i5zluK8yVhyZT0D+zBn6LWMQwDF6v/TqV81Rm6PqhHL562OpIIiKxbt2lMzmmNetclXjLMQuCtlsTSkTumcYPpEHR4SGcn1ifLM4rnHvqF8rfV9nqSCICXLhxgfY/t8fPy4+vH/2a7D7ZrY4kIhLb4TrCefM+3lxGGL/5jyCTtwOeXwuZclqYUERuR+MH0gnT7eLIx89QwHmGfQ9MUREnkorkzZSXiY0mcjb8LIN+G6TmJyKSKtw6MDyrrxeXzSwsu2+cZ1j4/B4aFi6SBmlFLg34e+B3cEgEQ3y/pyfzWV6sPw91GWZ1NBFJwHeHvuPt39+me6Xu9KnWx+o4IiJxuN0mL3+9naV7z/HLA0cou2U4NBoCjQZbHU1EEqAVuTTq7+0QQSERPGLbRE/mM8/ViOsVu1gdTUQS0a5MO9qWacunez5l2YllVscREYnDZjMY364KZfNno+2Wslwr1w7WjIbDK6yOJiJ3QIVcKjdu2UEinC4qGCcY7/iYre4yDHN25f0VaqYgkpoNqTWEKnmqMGzDMA5dPWR1HBGRODJ5ezHjf9Xxttt55HBLDhtFuDr3WVqP+kbz5UTSCBVyqVxwSAQ5ucYn3hO4ShZeiO5HNA4N/BZJ5bzt3kxsNJEsjiz0Xd2X0KhQqyOJiMRRKEcmOtYpwplwg26RfbHjZkTEGIbP365iTiQNUCGXyhXK7sVH3pPITSjPR7/KJTxd8DTwWyT1y5MpDxMaTeBs+FkG/zZYzU9EJNX5YZunYDtl5qO/83mq2I4xwJzFuGUHLU4mIv9GhVwq97bPl9S2HWCQswd7zBKABn6LpCVV81ZlSK0hrA9az4e7PrQ6johIHP/c4fOruyYfxzxGZ68V1Ly23MJUIvJfqJBLxXYvmkzja4v4MVMbtmZrqoHfImlUuzLtaF26NZ/s/oSVp1ZaHUdEJNatO3zGxbRns7sco7w/gwv7LUolIv+Fxg+kUse2r6DQoqf406cKFfovw8fb2+pIInIPolxRdPmlC8evHeerR7+iRPYSVkcSEUlwWHgerrIu23D8suaEnqvBJ6uFCUVE4wfSkKtnj5P9x26cN/JSqMfXKuJE0gEfuw8TG0/Ex+5Dn1V9CIsOszqSiEi8YeF5s/oQYs/Ju34DMa8cgx97Qyp+018kI1Mhl8o4I8O58nk7fMwobrSZQ548+a2OJCJJJH/m/IxvOJ7T10/z+vrXcZtuqyOJiNAyMIANgx/k+OhH+WNoU6Y+HciX5wuzOE8P+HMBbJ5udUQRSYAKuVRi4Y4g6o1ayU8jn6Kk8zALS4ygbKVaVscSkSRWM39N+tfoz+rTq5mxe4bVcURE4mlesQB9mpTm5VP1OZmnEfw6FE7/YXUsEbmFCrlU4O/96S3CfqC1fT3jne0YeaS4ZriIpFMdy3fk0RKP8sHOD1h3Zp3VcURE4unTpDTN7svPE2c6EpGpIHzXBcIvWR1LRP5BhVwqMG7ZQWq4djDE6ysWu2oxzdWSCKdLM1xE0inDMBhx/wjK5izL4HWDOXXtlNWRRETisNkMJjxVlfx58/NM6EtEXrvI+tFPUn/Ucr3RLJJKqJBLBRyhx5nmmMIhsxADnC8ABhB3touIpC9+Xn5MajwJm81Gn9V9uOG8YXUkEZE4Mvt48VSNQuxwFmGYswsP2PfSJvwrhszfo2JOJBVQIWexiOshzPB+Hzc2ejhf4wa+sedune0iIulLQJYAxtYfy9GQo7y58U1S8zgYEcmYPt9wAoDvXI34NqYhr9gXUNO1XbuGRFIBFXIWMt0uDk3vSHHO0tfVhzNm3thzfg47A5qVtTCdiKSEugF1eaXaK/xy4he+2PeF1XFEROL45+6g4TFdOGgWYpLjA8yQMxamEhFQIWeprXOGUCVsPb+X6kerNh1jZ7gE+PsxqnUlWgYGWB1RRFJAt4rdaFKkCRO2TWDLuS1WxxERifXP3UGR+PCSsy8OXEz3mwYx0RYmExEjNW/lqVGjhrl161arYySLPSu+pNL6l9iUrRm1+36DYVNNLZKRhUWH8cySZwiNCmXeY/PIn1kzJEXEen931o5wumKPtbBt5iPvyVDnJWg+ysJ0IhmDYRjbTNOscetxVQ8WOHVgGyXWv8pBe2kqv/C5ijgRIYt3FiY1nkSUK4p+q/sR5YqyOpKICC0DAxjVulLsrqH82XxZ76jLt16PwaYP4c+FVkcUybC0IpdCFu4IYtyyg4SFXGSRz3CyEIGz2yoKFClldTQRSUVWnlxJ3zV9aVO6DW/WfdPqOCIi8ew4dZVO09ezMNNIShlnMHqugdz694xIctGKnIX+3pZwNiScqY6pFOQivVyvsvmyulKKSFxNijahe6Xu/HD4B74/9L3VcURE4gkskoO3Wgfyv+svEeGywXfPQrRGqIikNBVyKWDcsoNEOF0M9PqGBvY9DI/pyuaY0mrdKyIJernqy9xf4H7e2/weey7usTqOiEg8basXonm96rwQ8QLu83/y85iOFB+8mHqjV2nGnEgKUSGXAoJDInjCtoEXvH7mi5imfON6MPa4iMit7DY7YxuMJW+mvPRd05fLEZetjiQiEs/QR8pzNnddpsa04jHXKtra1xAUEqGB4SIpRIVcCqiXJYixjk/Y7C7H2zH/iz2ugd8ikhh/X38mNppIaFQoA9YNIMYdY3UkEZE4vOw2wqJcTI5pzW+uirzjNZPyxkkinC7tOhJJASrkktmV82cYFzOay2Tjpeg+OPECNPBbRP5d+VzlGVZnGFvObWHy9slWxxERiedcaCRubPR19iKELHzgmEwWbmjXkUgKUCGXjJzRUZz7rAM5zGusC5yIr39+DfwWkTvyZKknaV+2PbP+nMWyE8usjiMiEsffu4suk52Xo3tTxLjAGMcnFMzua3EykfTPy+oA6dmOGS9SK3oPW6qP4eknnuRpqwOJSJo0qOYg9l/Zz7ANwyjlX4qS/iWtjiQiAsCAZmVjB4ZvNcsxNqY9rzu+pnDpLUATq+OJpGtakUsmW+ZPotbFH/g939PUfOIFq+OISBrmsDuY0HACfl5+9F3dl+vR162OJCICxB8Y/oXxOCtc1ai4bzycSR+zgEVSKw0ETwYHt66g+E/tOehbmfL9l+Hl8LY6koikA1vObaHHrz1oWKghExtPxGbovTgRSV2uRzrpNG0ZH4b1JV9Wb7xeXA+ZclodSyRN00DwZLZwRxD1Rq+i9uC5+P/UjfNGLgr3+EZFnIgkmZr5a/Jq9VdZdXoVn+/93Oo4IiLxZPV1MPHZRrzKq5jXz+P6oSe43VbHEkmXVMglgYU7ghgyfw+XQkL52HsiWYjgxZj+rDmtduEikrQ6V+hMi2ItmLpjKhuDN1odR0QknhJ5svBCh7a87eyM/ehyzPUTrY4kki6pkEsC45YdJMIZw9teswi0HeFV54vsjQnQDBURSXKGYfBm3Tcpkb0Eg9YNIjgs2OpIIiLxNC6XlwJNe/Gj637cq96hw+vjqDd6lQaFiyQhFXJJIDgkgv/Zf6W91xomx7RimbtW7HERkaSWyZGJSY0n4XK76LemH1GuKKsjiYjEUyC7H2/EdOeEOz9THVOJDjnLkPl7VMyJJBEVckng4UyHGO71Bctd1ZgU0yb2+N+zVUREklrRbEV5r/577Lu8j/c2v2d1HBGReMb/eohrph8vOvuShQimOKYR5XRqx5JIElEhd4/OnjzIKNf7nDDz08/5EuZfv6V+DjsDmpW1OJ2IpGeNCjeiZ+WezD88n+8PfW91HBGROP7emXTILMywmK7cb99HX6/vtWNJJImokLsHEeHXuTGnA1642Fr3A7L758IAAvz9GNW6Ei0DA6yOKCLp3EtVXqJuwbq8t/k99l7aa3UcEZFY/9yZ9L2rIfNiGvGK10JaZt1nYSqR9ENz5O6S6XazfWIbAq+tZk/DT6jy4FNWRxKRDCokMoT2P7fHjZt5j80jp69mNomI9f7u6h3hdAHgSxQLvIdT2CuULH1+h+yFLE4okjYk6xw5wzCaG4Zx0DCMI4ZhDE7gvGEYxpS/zu82DKNaUnxfK22eO4Lq11exucRLKuJExFL+vv5MaDyBKxFXGLhuIDFujT4REeu1DAxgVOtKBPj7YQC5/LPzcd7h4Irm6uyO4HJaHVEkTbvnFTnDMOzAIeAh4AywBXjaNM19/7jmEaA38AhQG5hsmmbtf3vu1LYit3BHEOOWHaTUtU3MdIxlo+8D1Bv0I4ZNO1RFxHoLDi9g+MbhdKvYjb7V+1odR0QknqgYF1Mmj2HA9TFcqdyTnK3HWR1JJNVLzhW5WsAR0zSPmaYZDXwDPHnLNU8Cc0yPTYC/YRgFkuB7p5i/twd4hR5nimMqB83C9L7RjUW7zlodTUQEgFalW9G2TFs+2/sZK0+utDqOiEg8Pl52/tfjVb61NSfn7k8I37nA6kgiaVZSFHIBwOl//PrMX8fu9JpUbdyyg9icYcxwvI8LGz2cr3LV6a0WuiKSqgypNYSKuSoydMNQjocetzqOiEg8+bL5UqrTZPa4S2Au7EXb976k+ODFGhgucoeSopAzEjh2637N/3KN50LD6GkYxlbDMLZevHjxnsMlleCQCPIYIXjhopezD2fMvLHHRURSC2+7NxMaTcDb5k2/1f244bxhdSQRkXiqlcjP4vLv4TJNRkSOxZtogkIiNDBc5A4kRSF3Bij8j18XAoLv4hoATNP8xDTNGqZp1siTJ08SxEsaBf39OGEW4OHosfzuvi/OcRGR1KRAlgKMbTiW49eOM3zjcFJzd2IRybh+OunDa84XqWQ7wRtecwGIcLq020nkP0qKQm4LUNowjOKGYXgDHYAfb7nmR+B/f3WvrAOEmqaZpm4uG9CsLH4OOzF4xR7T0G8RSa3qFKjDK4GvsOzEMr7Y94XVcURE4gkOiWCFuzofxzxGZ68VPGHbGHtcRP6d179fcnumacYYhvEysAywA5+bpvmnYRgv/HX+Y2AJno6VR4AbQNd7/b4p7e/h3uOWHSQ4JIKC/n4MaFZWQ79FJNV6ruJz7Lm0hwnbJlAhVwVq5I/X8EpExDIF/f0IColgfMxTVLcdYpRjBn9GFyUyeymro4mkCRoILiKSjoVFh/H04qe5Hn2dbx//lryZ8lodSUQEiDswPD+XWezzOpdMf/Y/Op+WtctYHU8k1UjWgeAiIpI6ZfHOwsRGE7kRc4PX1ryGUwN4RSSV+OfA8PPkYpjtFUobZyi8+U2ro4mkCVqRExHJAJYeX8qAdQN4ptwzDKk9xOo4IiIJ2vBJX+oFz2Rzpbep3aaP1XFEUgWtyImIZGDNizenc4XOfHXgK34+9rPVcUREElTnufHs86lK5d3v8ueOjVbHEUnVVMiJiGQQ/ar3o3q+6ry18S0OXlF7bxFJfexeXhTq9iURtkxkXtSN8xcvWR1JJNVSIScikkE4bA7GNxxPVu+s9FvTj2vR16yOJCIST7a8hQh/fDqFzbPs+fhZ6r63guKDF1Nv9CoNCxf5BxVyIiIZSG6/3ExoNIGzYWcZ+ttQ3Kbb6kgiIvEUrtactQE9aOpaT+PwxZhAUEgEQ+bvUTEn8hcVciIiGUzVvFUZUHMAa86s4dM9n1odR0QkQcMvN2OtqzLDveZwn3EcgAini3HLtDVcBFTIiYhkSE+Xe5pHSzzKtB3T2BC0weo4IiLxBIVG0df5EpfJxoeOyWQjHIDgkAiLk4mkDirkREQyIMMwGF5nOKVylGLQb4MICtNWJRFJXQr6+3GVbLwc/QoFjcuMdXwCmBT097M6mkiqoEJORCSDyuTIxKRGk3C73fRb3Y8oV5TVkUREYg1oVhY/h53tZhnGxHSguX0Lz9mX0qdJKaujiaQKKuRERDKwItmK8F7999h/ZT8jN43ENE2rI4mIANAyMIBRrSsR4O/HZ65HWENNhnh9xYlda/WzSgQwUvP/CDVq1DC3bt1qdQwRkXRv6o6pfLL7E0bcP4K2ZdpaHUdEJL6Iq1ybXJfrEVH8Unce3ZvVtDqRSIowDGObaZo1bj2uFTkREeGlKi9Rt2Bd3tv8Hnsv7bU6johIfH45yNr5S/LZrlFifX9W7jtrdSIRS6mQExER7DY7Y+qPIY9fHvqt6ceVyCtWRxIRiccIqIb58Hs8aN/Jjq/fpNZIDQuXjEuFnIiIAODv68+ExhO4EnGFgesG4nK7rI4kIhKPo04PjuVrRj/bPIqH7dSwcMmwVMiJiEis+3Ldxxt13mDz2c1M3THV6jgiIvEZBs+HPMsJMz9TvKeSm1BAw8Il41EhJyIicbQq3Yo2pdvw2d7PWHlqpdVxRETiORIKvZx9yE44kxzTsOEGNCxcMhYVciIiEs+Q2kO4L9d9DF0/lOOhx62OIyISR0F/Pw6YRRgW05UH7H/Sx2t+7HGRjEKFnIiIxONj92Fio4l427zpt7ofN5w3rI4kIhLr72Hh37ka8r2rAb3tC6hv202HWoWtjiaSYlTIiYhIggpkKcDYhmM5fu04wzcO1wBeEUk1bg4Lz8QwZ1eO2Qoz2fsDlm/awaWwKKvjiaQIFXIiIpKoOgXq8ErgKyw7sYwv9n1hdRwRkVgtAwPYMPhB9o9uTamXfiC7w82IqPH0/uIPomPcVscTSXYq5ERE5Laeq/gcTYo0YcK2CWw5t8XqOCIi8eUpg/2JKVQ3DtIw6GPe+ulPqxOJJDsVciIicluGYfBuvXcpnLUw/df253z4easjiYjEV6kt1OjGC14/c37LAuZuOml1IpFkZaTmex5q1Khhbt261eoYIiICHA05ytOLn6ZMjjLMbDYTh91hdSQRkbhiojA/e5gb54/QPOJdIjIX4nJYNAX9/RjQrCwtAwOsTihyxwzD2GaaZo1bj2tFTkRE/pOS/iV5p9477Lq4i7FbxlodR0QkPi8fjHazcNgMpjmmcC0sHBMIColgyPw9LNwRZHVCkSSjQk5ERP6zZsWa8WyFZ/nm4Df8dPQnq+OIiMSXszjDjV5UsR1jqNfc2MMRThfjlh20MJhI0lIhJyIid6Rv9b7UzF+Tt35/i/2X91sdR0QknnnXK/NJzKM867Wcx2y/xx4PDomwMJVI0lIhJyIid8TL5sW4BuPI7pOdfmv6ERoVanUkEZE4Cvr7MTamPVvdZRjtmEEJIzj2uEh6oUJORETuWC6/XExsNJELNy4waN0gXG6X1ZFERGINaFYWh8OHl6N7E4WDDx2T8SWK5hXzWx1NJMmokBMRkbtSOU9lBtcazIbgDXy460Or44iIxGoZGMCo1pWw+xein7MXZWxnmJh5Dt/8cZJD569bHU8kSXhZHUBERNKudmXasffSXj7Z/QkVc1WkcZHGVkcSEQE8xZxn3MCDsNqkxdoxbPUqR485vizqVQ//TN5WRxS5J1qRExGRu2YYBkPrDKVCrgq8vv51ToSesDqSiEh8DQdBiUYMNT4ne8hBXv5qBzEut9WpRO6JBoKLiMg9Cw4Lpv3P7cntl5svH/mSTI5MVkcSEYkr7CJMr891l4O6V4YTWLoIRy+GExwSoYHhkqppILiIiCSbglkKMqbBGI6FHmPExhGk5jcJRSSDypIH2s4ka0QQn+eYxbrDFwkKidDAcEmzVMiJiEiSqFuwLr0De7P0xFLm7JtjdRwRkfiK3g9N36RmxHqesy+Nc0oDwyWtUSEnIiJJplvFbjQp0oSJ2ybyx9k/rI4jIhJf3d786qrOEK+vqGYcinNKA8MlLVEhJyIiScYwDN6t9y5FshVhwLoBnAs/Z3UkEZG4DIP3M/XjrJmTad5TyMG12FMaGC5piQo5ERFJUlm8szCp8SSiXFH0W92PKFeU1ZFEROJ4sXk1+pmvkovrTHJ8iIEbuwH9Hy5jdTSR/0yFnIiIJLkS2Uswst5I9l7ey6jNo6yOIyISR8vAADq3fpJJju40tO/mNd8fcZlw5qq2VkraoYHgIiKSLJoUbUKPSj2YsWcGFXNXpG2ZtlZHEhGJ1TIwAKqOggVX6bV7Hl6lazF6OZTOl5XmFfNbHU/kX2lFTkREkk2vqr2oV7Ae721+j90Xd1sdR0QkLsOAxyZg5CnH85dH0aRgDK9+u5P9Z6/9+2NFLKZCTkREko3dZmdMgzHkzZSXfmv6cSniktWRRETi8s4M7b/AiIniY58p+PtA99lbuRym+3sldVMhJyIiySq7T3YmNZ7EtahrDFg7AKfbaXUkEZG4cpeGJ6biOLuVRWV/5VJYFO0+/p26o1ZSfPBi6o1epWHhkuqokBMRkWRXLmc5ht8/nK3ntzJx20Sr44iIxFexNdR+gTx7P+PNUkc4dimc4NBITCAoJIIh8/eomJNURYWciIikiMdLPk7H8h35Yt8XLD622Oo4IiLxPfQOBNTgiRMjKWacjXMqwuli3LKDFgUTiU+FnIiIpJjXarxGtbzVeHPjmxy8on8QiUgq4+UN7WYRZdr5yDEJX+LeJxccovEEknqokBMRkRTjsDl4v9H7ZPPJRp/VfQiJDLE6kohIXP6Fede7H2WNM7zrmAmYsacK+vtZl0vkFirkREQkReX2y83ERhO5cOMCA9cNxOV2WR1JRCSOBo88zUdma9ra19HevgYAA+jVuKSVsUTiUCEnIiIprnKeyrxR5w1+P/s7U3ZMsTqOiEgcLQMDCGj5JpttVXnbaxb1Mp/BMGDJnnPEuNxWxxMBVMiJiIhFWpduTbsy7fh87+csO7HM6jgiInG0rFaE2q/Nxyd7Xr7MOo0Jjxdl/ZFLvPPzPqujiQAq5ERExEKDaw2mSp4qDNswjMNXD1sdR0Qkrsy5oN1suHaWlifeoccDRZn9+0nmbjppdTIRDNM0//0qi9SoUcPcunWr1TFERCQZXbhxgfY/t8fPy4+vH/2a7D7ZrY4kIhLX5k/glwG4Gw+j27EGrDl4kVxZvLkcFk1Bfz8GNCtLy8AAq1NKOmUYxjbTNGvcelwrciIiYqm8mfIyodEEzoafZfBvg9X8RERSn1o9oGJbbGtG8r98xwG4FBatYeFiKRVyIiJiucC8gQyuOZj1Qev5cNeHVscREYnLMODxyZCrNFX/6E9ersQ5rWHhYgUVciIikio8VfYpWpVqxSe7P2HlyZVWxxERicsnC7Sfi8OM5kPvyTiIiXNaw8IlpamQExGRVMEwDIbWGUql3JV4ff3rHA05anUkEZG48pRhjPfLVLcdZojXV3FOaVi4pDQVciIikmr42H2Y0GgCfl5+9Fndh2vR16yOJCISR/VHnmOOuwXPeS3lUdum2OP3l8xlYSrJiFTIiYhIqpI/c34mNJpA0PUgBq0bpOYnIpKqtAwMIPuTo9hjlGWsYzr3Z7tEhQJZWbAjiN8OX7Q6nmQgKuRERCTVqZavGkNqD2F90Ho+2PmB1XFEROJ4snpxKvVbSOYs2fg62zTmdalIqTxZeOnL7Ry5EGZ1PMkgVMiJiEiq1K5MO9qUbsOMPTP49cSvVscREYkrW0Fo+zlcPkLWZf349H/V8bbb6DZ7C1fDo61OJxmABoKLiEiqFe2Kpuuyrhy+epgvH/mS0jlKWx1JRCSu9ZNgxQho9h7bCj7N059spnBOPyKiXZwNjdTAcLlnGgguIiJpjrfdm4mNJpLZkZlXVr1CaFSo1ZFEROKq1wfKPQa/DqM6B2hXM4CjF8MJDo3UwHBJVirkREQkVcubKS8TG03k3I1zDFw3UM1PRCR1MQxo+SHkLA7fdWHP/kPxLtHAcEkOKuRERCTVq5q3KkNrD2Vj8EYm75hsdRwRkbh8s0P7uRB1nWERY/G6ZVg4aGC4JD0VciIikia0LdOWp8o8xcy9M1lybInVcURE4spbHp6YSk3bQQZ7fR3vtAaGS1JTISciImnG4FqDqZa3GiM2jmD/5f1WxxERiatSW46W6ER3r1/iDAsH6NmguEWhJL1SISciImmGw+7g/Ubvk90nO31W9+FyxGWrI4mIxFHymYlczhnIOO9PKGUEkTerD952g++2neFGdPwtlyJ3S4WciIikKbn9cjP5wclcibzCq2texelyWh1JROQmL29ydfmaTJmzsaLgJ/zxWi0+6lSdfcHX6PvNTtzu1Dv6S9IWFXIiIpLm3JfrPt6q+xbbL2xnzJYxVscREYkrWwFoNxOuHINFL9GkXF6GPlqBX/edZ8yyA1ank3TCy+oAIiIid+PREo9y8MpBZv45k7I5y9KuTDurI4mI3FTsAXj4HVj2OmyYxHP1+nL8UhjT1x4jJDya9UcuExwSoYHhctdUyImISJrVp1ofDoUc4r3N71HKvxSBeQOtjiQiclOdl+DMVlj5NkaBqrz5eEO2HL/CvK1nYi/5e2A4oGJO7oi2VoqISJplt9kZU38MBTMXpN/qfpwLP2d1JBGRmwwDnpgKucvC98/hdf0M1yLjNzzRwHC5GyrkREQkTcvuk50pD04h0hVJn9V9iIyJtDqSiMhNPlmgw5fgjoF5nbkSei3ByzQwXO6UCjkREUnzSvqXZNQDo9h3eR8jNo7ANNUVTkRSkVwlofUncHYn72eeA8T/GaWB4XKnVMiJiEi60LhIY3oH9mbJ8SXM/HOm1XFEROIq2wIaDOAx1yqe9V4d55TdgP4PlbEomKRVKuRERCTd6FGpB82LNWfStkmsO7PO6jgiInE1GgKlmjLCPouHsp3GALL5euEy4fDFMKvTSRqjQk5ERNINwzB4u97blMtZjoHrBnIs5JjVkUREbrLZofUMbNkDmOEzmeNv1GTXiId5ulYRPlxzlHlbTlmdUNIQFXIiIpKu+Hn5MeXBKfjafXl51cuERoVaHUlE5KZMOaH9XIi4At91xXDH8PaT91G/dG6GLtjL+sOXrE4oaYQKORERSXfyZ87PpMaTOBd+jtfWvkaMO367bxERyxSoDI9PgZPr4ddhOOw2PuhYjZJ5stBt1h/UGrmC4oMXU2/0KhbuCLI6raRSKuRERCRdqpq3KsPqDGPz2c2M3zre6jgiInFVae8ZGL75I9j1Ddl8HXSoVZgol8mF61GY3BwWrmJOEqJCTkRE0q1WpVvRuUJnvtz/JT8c+sHqOCIicT30NhSrDz/1geCdfPrb8XiXaFi4JEaFnIiIpGuvVn+VugXr8u7md9l+frvVcUREbrI7oO1MyJQL5nUmIuR8gpdpWLgkRIWciIika142L8Y2GEuhLIXot6YfwWHBVkcSEbkpSx5o/wWEnWd6pg+x44p3SUF/XwuCSWqnQk5ERNK97D7ZmfLgFJwuJ71X9eaG84bVkUREbgqoDo9NpKZ7N697fxvvdI2iOS0IJamdCjkREckQimcvzviG4zkScoQhvw3BbbqtjiQiclNgR6jZg262n/hf1q0YeFbiqhTKxqJdwSzefdbqhJLKqJATEZEMo25AXQbWHMiq06uYumOq1XFEROJq9h4UuZ+3zY843rcoGwc3Yd7zdalRNAf9vt3J1hNXrE4oqYgKORERyVCeKfcMbcu05dM9n/LT0Z+sjiMicpOXN7SbDX7+8M0zcOMKvg47M/5XgwB/P7rP2cqxi2FWp5RUwjBN0+oMiapRo4a5detWq2OIiEg643Q7eX758+y6sIvPmn1G1bxVrY4kInLTma0wswUUrQcdvwe7Fycvh9P6w42YmHh72TkfGklBfz8GNCtLy8AAqxNLMjIMY5tpmjVuPa4VORERyXAcNgcTGk4gX+Z89Fndh7NhuvdERFKRQjXgsYlwbDWsGAFA0VyZ6Xx/Ua6EOzkXGqmB4aJCTkREMiZ/X3+mPTiNaFe0OlmKSOoT2Alq9YTfp8FuTyfL77aeiXeZBoZnXCrkREQkwyrhX4JxDcdxOOSwOlmKSOrT7D0oVh9+7A3BOxIdDK6B4RmTCjkREcnQHgh4gP41+rPq9Cqm7ZhmdRwRkZvsDmg3CzLngW86cl/2qAQvK+jvl7K5JFVQISciIhlep/KdaFO6DTP2zFAnSxFJXTLnhg5fwo0rzMoyjWyO+I0KG5TJbUEwsZoKORERyfAMw2Bo7aHUyl+LERtHsP38dqsjiYjcVKAKPDmN3Je3sbDkTwT4+3kGhmf3pUzeLHy79QxrDl6wOqWkMI0fEBER+UtoVCgdl3TkWtQ1vnz0SwpnLWx1JBGRm5YPhw2T4fHJUL0LANcjnbSfvokTl8OZ1/N+KhXKbm1GSXKJjR9QISciIvIPJ0JP0HFJR3L75eaLR74gm3c2qyOJiHi4XfBlOzi+DroshiK1AbhwLZJWH24kKsbFiw1L8vmGEwSHRGjOXDqhOXIiIiL/QbHsxZjYaCKnrp2i/5r+xLhjrI4kIuJhs0Pbz8C/MMzrBKGe+XF5s/ky+7lahEfF8O7i/QSFRGjOXAagQk5EROQWtQrUYtj9w/j97O+M/mM0qXn3iohkMH45oMPX4IyAb56BaM8MzFJ5s5DZx4tbf1ppzlz6pUJOREQkAa1Lt6brfV2Zd3AeXx34yuo4IiI35S0HbT6Fs7vgx5fhrzebLodFJ3i55sylTyrkREREEtG3el8eLPwgY7eMZd2ZdVbHERG5qWxzaDoC9v4A6ycAic+T05y59EmFnIiISCJsho1R9UdRNkdZBqwdwKGrh6yOJCJyU72+UKkdrHwHDixhQLOy+DnscS7xshkMaFbWmnySrFTIiYiI3EYmRyamPjiVLI4svLzyZS7euGh1JBERD8OAJ6ZCwaowvwctA64xqnWl2Dlzmb3txLhNLoVFWZ1UkoHGD4iIiPwH+y7vo8vSLhTPXpyZzWaSyZHJ6kgiIh7XguGTRuDwgx6rIVNOAFxuk1e+3sHiPWeZ2L4KrQILWZtT7orGD4iIiNyDCrkqMK7BOA5cOcDg3wbjcrusjiQi4pGtIHT4Cq6dhW//By4nAHabwYT2VahbMhcDvtvN6oMXLA4qSUmFnIiIyH/UsHBDBtYcyOrTq3l/2/tWxxERualQDXh8Mpz4DZa9HnvYx8vO9M7VKZs/Kz1nb6XmuysoPngx9Uav0ny5NE6FnIiIyB3oWL4jHct35It9X/D1ga+tjiMiclPVp6Fub/jjE9j6eezhrL4O2tcsTIzb5GJYlIaFpxMq5ERERO7QgBoDaFSoEaP/GK2xBCKSujR9C0o/DEsGwPGbP5+mrz2mYeHpjAo5ERGRO2S32RnTYAxlc5Sl/9r+HLhywOpIIiIeNju0+QxylYJ5neHyUSDxoeAaFp52qZATERG5C5kcmZjWZBrZvLPRa0UvzoWfszqSiIiHbzZ4+hswbPBVe4gISXQoeP7svikcTpLKPRVyhmHkNAxjuWEYh//6nCOR604YhrHHMIydhmFonoCIiKQLeTPl5YMmHxAeE87LK18m3BludSQREY+cxaH9XLh6Ar7rwsCHSsYbFg6eWXORTnXhTYvudUVuMLDSNM3SwMq/fp2YxqZpVk1oBoKIiEhaVTZnWd5v+D5HQo7w2trXcLqdVkcSEfEoVg8emwjHVvPk+WlxhoUH+PvRqU4RjlwMp/fXO4hxua1OK3fongaCG4ZxEGhkmuZZwzAKAGtM0yybwHUngBqmaV66k+fXQHAREUkrvj/0PW/9/hZtSrdhxP0jMAzD6kgiIh7LhsLv0+CR8VCrR5xTszeeYMSPf9KmWiHGta2MzaafXalNYgPBve7xefOZpnkW4K9iLm8i15nAr4ZhmMB00zQ/ucfvKyIikqq0LdOW4LBgZuz5f3v3HVdl3f9x/PU9DBkKKG4UcRSmlblLG+6d2nSPytG0Yd6Vjd/dXZbdLc3SysxRjtRMK9M0R2WaucutqbgFVEAZipzv7w/IOxNSE7jOgffz8eABXOc657zx8U17c43PWMoFl2NgrYFORxIRydTyPxC/A+Y9lXkTlKpNzz7Up1EUCSnpvP3dduJPpLEz7iQHE9IoHxbIkNbRdK4d4WBw+TsXLHLGmO+Astk89OwlvE9ja+3BrKK30Biz1Vqb7f2ajTEDgAEAkZGRl/AWIiIiznqk9iMcTj7Mu+vfpVzRcnSs2tHpSCIiWXey/AjGtYIZfaDfYihZ7ezDg5pXY3XMMb7f8b+T5/6YMweozHmoC14jZ61tYa29OpuPOcCRrFMqyfocm8NrHMz6HAt8ATT4m/f70Fpbz1pbr1SpUv/kZxIREXGEMYYXG71Iw7IN+b+f/o+fD/3sdCQRkUwBIdB9Grh8YcrdkHLs7EPGGH6PO3neUzRnzrNd7s1OvgT6ZH3dB5jz1x2MMcHGmGJ/fA20AjZe5vuKiIh4JD8fP95u+jZRoVE8vuRxth/f7nQkEZFMxaOgy2RI3AfTe8OZ02cfOpSQlu1TNGfOc11ukRsOtDTG7ABaZn2PMaa8MeabrH3KAMuMMRuAX4C51tr5l/m+IiIiHquYfzHGtBhDkG8QD3z3gGbMiYjnqHQDdHwX9vwIXz8OWTc+zGnOXE7bxXmXVeSstUettc2ttVdkfT6Wtf2gtbZd1te7rLW1sj5qWmuH5UZwERERT1Y2uCyjW4wmOT2ZhxY9xMnT55+2JCLiiFpd4JanYP2nsOxtAIa0js52zlz7a7O7VYZ4gss9IiciIiI5iC4RzVtN3mJXwi4eX/o46RmaMSciHqLJM3D1nbDoRdg0m861I86ZM1cuNICIsAAmLo9hxe9HnU4r2bisOXJ5TXPkRESkIJi9czbP//Q87au055UbX8Fl9HtUEfEA6Wkw8VY4/Cv0/QYq1D3n4aMnT9Hlw585lJDKp/0aUjuyuENBC7ec5sjpXxIREZE81rlaZwbVHsTcXXMZsWaE03FERDL5BUC3qVC0DEztCgl7z3k4vGgRJvdrSHjRIvT5+BfeW7KTxsMXU/npuTQevpjZ6w44FFxARU5ERCRf9LumH12iuzB+03g+2fyJ03FERDIFl4QeM+DMKZjSBdKSznm4TEgAk/s1xBh4/dttHEhIxfK/OXMqc85RkRMREckHxhieafAMLSJb8N9V/2X+bt3AWUQ8RKlo6DIJ4rfDzHsg48w5D1csEUQR3/NvhKI5c85SkRMREcknPi4fht88nDql6zB02VBWHlrpdCQRkUxVmkD7N2HndzD/qbNjCf4Qd+JUtk/TnDnnqMiJiIjkoyI+RXin2TtUCqnEo0seZdsx/TZbRDxE3b7QaBCs+ghWvHvOQ5oz53lU5ERERPJZaJFQxrQYQ1G/ojzw3QMcOKlrTETEQ7R4EWp0hgXPwabZZzdnN2fOAANvqZKv8eR/VOREREQcUDa4LO+3eJ+0jDTuX3g/CWkJTkcSEQGXC277ACo2hFkDYG/mKeB/nTNXsqg/vi7Dpz/HcPRk9qddSt7SHDkREREHrT2ylgELBxBdPJqxrcYS5BfkdCQREUg+CuNaQupx6PcdhFc9b5flO+O5Z8IqqpQqytT+DQkL8ncgaMGX0xw5FTkRERGHLdq7iCeWPsEN5W5gVLNR+Pn4OR1JRASO/p5Z5gJC4b7vIDj8vF1+2B5Hv4mrKV2sCBnWcjgxjfJhgQxpHU3n2hEOhC54NBBcRETEQzWPbM6/b/g3Px38iWeXPYvbup2OJCKSeRSu2zRIOpg5MDz9/DtU3nxlKfo0qsT+hFQOJaZpxlw+UpETERHxALddcRuP132ceXvm8erKV/HkM2ZEpBCp2ABu/xD2r4Iv7gf3+b9o+ua3w+dt04y5vKciJyIi4iHuvfpe+tbsy7Rt03h/w/tOxxERyVSjE7R6CTbPhu9eOO/hnGbJacZc3vJ1OoCIiIj8zxN1n+B42nFGbxhN8YDidK3e1elIIiJww8NwPAaWj4LQSGg44OxD5cMCOZBNaSsbGpCfCQsdHZETERHxIMYY/t3o3zSp0IRXVr7CvN3znI4kIgLGQNvXILodzPsXbP7y7EPZzZgDCPB1cfLUmfxMWaioyImIiHgYX5cvr9/yOrVL12bosqEsP7Dc6UgiIuDygTvGQYX68Hk/iFkBnD9jLiIskL6NKrH3eCp9Pv6FE2npzuYuoDR+QERExEMlnU7i3vn3svfEXsa2GkutUrWcjiQiAinHYFwrSI6FexdA6erZ7jbvt0M8MnUd11YIZeK9DSgWoNEq/4TmyImIiHih+NR4es/rTcKpBMa3Hk90iWinI4mIZF4vN64luPyg30IIKZ/tbvM3HuLhKeuICAvgdIbmzP0TmiMnIiLihUoGlmRsq7EE+gYycOFA9iTucTqSiAgUrwQ9ZkBaInx6Z+bnbLS5uhy9bqhEzDHNmcttKnIiIiIeLqJoBGNbjcVt3fRf2J9DJw85HUlEBMrVgi6fQPw2mNYDzpzKdrcFm46ct01z5i6fipyIiIgXqBJahQ9afkDy6WT6L+xPfGq805FERKBqU+g0Gvb8mOPAcM2ZyxsqciIiIl7iqvCreK/Fe8SmxDJw4UAST2V/KpOISL6q1QVavAibZsGC5857uHxYYLZPKxOiOXOXQ0VORETEi9QuXZsRTUewO3E3Dy56kJT0FKcjiYhA40ehwUD4+T34aeQ5D+U0Zy7D7eZQoo7K/VMqciIiIl6mUflGvH7z62yK38SgxYM4lZH9dSkiIvnGGGgzHGreDgtfgHWfnn0ouzlzg5pXIzXdzd0frGDfMf1C6p/Q+AEREREv9eXvX/LssmdpUqEJbzV9Cz+XZjSJiMPOnIYpd8Pu76HLZKjeLsddN+xLoPfHvxDs78M9jSszYfkeDiakajzBX2j8gIiISAHTsWpHhjYcytL9S3n6h6c54z7jdCQRKex8/aHLp1C+Nsy8B/b8lOOutSqGMbX/9SSmpjPsmy0cSEjVeIJLoCInIiLixbpV78bguoNZELOA5396ngx3htORRKSwK1IUus+AsEiY2hUO/5bjrjXKhxBcxPe87RpPcGEqciIiIl6u79V9eaT2I3y962v+8/N/cNvzb/8tIpKvgsOh5ywoUgw+uR2O7c5x17gT2V/nq/EEf09FTkREpAAYcO0ABlw7gFk7ZvHKylfw5GvgRaSQCKsIvb4Adzp80hlOnD8YHHIeT5DTdsmkIiciIlJAPHzdw9xT8x4+2/YZr69+XWVORJxXKhp6zISTcfDpHZB2/vzLnMYTtKxROj8Sei0VORERkQLCGMPjdR+nx1U9+GTzJ4xcO1JlTkScV6EedPkE4rbClK5w+txxA38dT1AuNIDK4UFMWhHDZ6v2OpPZC2j8gIiISAFjreWln19ixvYZPHjdgzxQ6wGnI4mIwMbPYeZ9UK0FdJ2SeYfLHKSezuD+T9fw/fY4OtUqz+qY44V2NIHGD4iIiBQSxhieu/45OlXtxOj1o/not4+cjiQiAlffAbeOhJ0LYVZ/+Ju77Ab6+zC2dz2uqxjKnA0HNZogG+ff61NERES8nsu4eLHRi6S70xm5diQGw33X3Od0LBEp7Or2gVMnYMGz8FVRuHUUuLI/tuTv6yI2mzta/jGaoDAdlcuOipyIiEgB5ePyYdiNw7BYRqwdAaAyJyLOa/QwnEqC718D/2LQ5lUwJttdDyWkZbtdowlU5ERERAo0X5cvr9z4CoDKnIh4jibPQFoSrBwDASHQdGi2u5UPC+RANqWtbGhAXif0eLpGTkREpID7o8y1rdyWEWtH6Jo5EXGeMdD6FajdM/PI3PJ3s90tp9EEBohNyv5oXWGhIiciIlII/FHm2lVux8i1I1XmRMR5Lhfc+g7U6Jx5zdyaCeft8tfRBBFhgdx/SxUSUtO5fcxydsWdzO/UHkOnVoqIiBQSvi5fht04DICRa0cC0O+afk5GEpHCzuUDt4+F08nw1WPgXxSuufOcXTrXjjjvxibtrinHPeNXcef7K+h9QyVmrN5f6MYT6IiciIhIIfJHmdORORHxGL7+cPckqNQYZg2AzXMu+JRrK4Tx+QONAMuI73YUyvEEKnIiIiKFzF/L3Ie/fuh0JBEp7PyDoPs0iKgLM++FbfMu+JSoksH4+5x//dwf4wkKOhU5ERGRQuiPMtehSgdGrRvFqHWjsNY6HUtECrMixaDnTCh7LUzvDTu+u+BTjuRww5PCMJ5ARU5ERKSQ8nX58nLjl7njijv48NcPeXP1mypzIuKsgFDoNQtKRcNnPWDX0r/dvXxYYLbby13CeAK3dTN923TS3emXktRxKnIiIiKFmI/LhxdueIGu0V2ZuHkir6x8Bbd1Ox1LRAqzwOLQaw6UqAJTu0HM8hx3zWk8QaC/D4kpFy5mGe4Mnv/peV76+SUW7118WbHzm4qciIhIIecyLoY2HErfmn2Ztm0aL654kQx3htOxRKQwCw6H3nMgtAJMvgv2/ZLtbtmNJ+h5fST7jqVy25if2Hs0Jce3OOM+wzM/PsOXv3/JQ9c9ROuo1nn0w+QN48mnUNSrV8+uXr3a6RgiIiKFgrWW99a/xwe/fkD7Ku15ufHL+Lo0qUhEHJR0CCa0g+T4zGIXUeeinvbzrqMM/GQNvi5Dr2zGE7SvVZqnfniKhTELeazOY9x3zX15/IP8c8aYNdbaeudtV5ETERGRPxv761jeWfcOLSu15LWbXsPPx8/pSCJSmCXuh/HtIC0xs8yVv+6invZ73Enuen85x5LPPcUy0M9ydZ0v2Zq0giH1htC7Zu88CJ17cipyOrVSREREztH/2v4MqTeEhTELeWLpE5zKOOV0JBEpzEIrQJ+vMu9qOakTHFx/UU+rWqoo/r5/uX7OpEPZCWxNWsHQhkM9vsT9HRU5EREROU/vmr15ruFzLN2/lAe/e5Dk9GSnI4lIYVa8EvT9GoqEwKSOcHDdRT3tSOKfxhOY0wRWmIRv0W2kHbqNbtW75VHY/KEiJyIiItnqUr0Lr970KmuOrKHft/1ISEtwOpKIFGbFozLLXEBo5pG5A2su+JSz4wnMaQIrTsAneCepB+8k3H1L3mbNBypyIiIikqMOVTowoukIdiTsoO/8vhxJPuJ0JBEpzIpXgr5zISAMJt0G+/++zA1pHU1gkdMERn6MT9Bu0g7ezZnEeqSln2HTwcT8yZxHVORERETkbzWp2IQxLcZwOOUwvef1JiYpxulIIlKYhUVmlrmg4vBJZ9if880Rb74qkMiak/AN3MupA10p42rE4FZXEujvy51jVjB/4yFmrztA4+GLqfz0XBoPX8zsdQfy72e5DLprpYiIiFyUTUc38cDCB3AZFx+0/IDoEtFORxKRwixxP0xoDynHoOcsqFj/nIePJB+h/8L+HDx5kLeavMXNFW4++1hsUhoDPlnD+n0J+LoMZ9z/60SBfj68evs1dK4dkW8/yt/RXStFRETkstQMr8mEthPwdflyz/x7WBd7cTcbEBHJE6EVoO83EBQOn9x2ztDwvUl76TO/D7Epsbzf4v1zShxA6ZAApg24nkA/n3NKHEBqegavf7stX36Ey6EiJyIiIhetSmgVJrWdRInAEgxYMIBlB5Y5HUlECrPQCLjnGyhaKrPM7VnG9uPb6TO/D8npyYxrPY56Zc87mAVAgJ8PaekZ2T52MCE1L1PnChU5ERERuSTli5ZnYpuJRIVG8ciiR/jq96+cjiQihVlI+cwjcyER/Da9K/d80wsXLia0mUDN8Jp/+9Szd7W8yO2eREVORERELll4YDgft/6YOmXqMHTZUMb9Ng5Pvu5eRAq4kHL80n4Y/UoXJzQ1iYlX9qVqWNULPm1I62gC/c4dGh7o58OQ1p5/DbCKnIiIiPwjxfyLMabFGNpGtWXE2hEM/2U4Ge7sT1MSEclLS/Yu4YFlT1M+rDITbRkqzHkUfpt5wed1rh3Bq7dfQ0RYIAaICAv0qBud/B1fpwOIiIiI9/L38Wf4zcMpFVSKSZsnEZcax6s3vUoRnyJORxORQmLm9pm89PNL1AyvyZgWYwjFBVO6wOf9ID0V6vT62+d3rh3hFcXtr1TkRERE5LK4jIsh9YdQOqg0b6x+g+NpxxnZbCQh/iFORxORAsxay/u/vs/o9aO5KeIm3rjlDYL8gjIf7DETPusBXz6cWeYaDnA2bB7QqZUiIiKSK/rU7MNrN73G+rj19JnXhyPJR5yOJCIFVIY7g5d+fonR60fTqWonRjYb+b8SB+AfBN2mQXR7mDcElo1wLGteUZETERGRXNOuSjvGtBjDoeRD9JzXk53HdzodSUQKmLQzaTyx9AlmbJ9B/2v681Ljl/Bz+Z2/o28RuHsiXH0HfPd/sPhlKEA3ZVKRExERkVx1fbnrmdBmAhnuDHrN68Xyg8udjiQiBUTiqUQGLBzAkn1LGNpwKIPqDMIYk/MTfPzg9rFQpzf88DrMfQIKyE2ZVOREREQk11UvUZ3J7SZTrmg5HvzuQWZuv/Dd40RE/s6hk4foPa83G+M38sYtb9CtereLe6LLB259B258HFZ/DDPvhTOn8jZsPlCRExERkTxRrmg5JrWZxPXlr+fFFS/y1uq3cFu307FExAttO7aNnvN6EpcSxwctP6BVVKtLewFjoMW/odXLsHk2TLkbTp3Mi6j5RkVORERE8kxR/6K82+xdukR3Yfym8QxeOpjUM6lOxxIRL/Lj/h/pPa83ABPaTqB+2fr//MUaPQKdx8DuH2FSR0g+mksp85+KnIiIiOQpX5cvzzZ8ln/V/xeL9i7i3vn3Ep8a73QsEfEC07ZO4+HFD1MppBJT2k3hyuJXXv6LXtcduk6GI5tgfBtI3H/5r+kAFTkRERHJc8YYetXoxcimI/k98Xe6z+3OjuM7nI4lIh4qw53Ba7+8xrCVw7g54mYmtJlAmeAyufcG0W2h5yw4cRjGtYa47bn32vlERU5ERETyTdPIpoxvM54z7jP0mteLH/b/4HQkEfEwKekpPLb0MT7d8ik9r+rJiKYjzp0Rl1uiGkPfuZBxGj5uDQfW5v575CEVOREREclXNcNrMqX9FCKLRfLwoocZ99s4bAGa7SQi/1xsSix95/flh/0/MLThUJ5q8BQ+Lp+8e8Ny18J930J4VSgSknfvkwdU5ERERCTflQ0uy8S2E2kd1ZoRa0fw9I9Pk3YmzelYIuKgbce20X1ud2KSYhjVbNTFjxe4XCWqwH0LoWS1/Hm/XKIiJyIiIo4I9A3kvzf/l0G1BzFv9zz6zO/D4eTDTscSEQcsillEr3m9sFgmtZ3EzRVuzt8AfzdU3EOpyImIiIhjjDH0v7Y/7zR7h5ikGLp+3ZX1seudjiUi+cRt3YxZP4bHlj5GtbBqTG0/legS0U7H8goqciIiIuK4JhWbMLndZIL8grj323v5YscXTkcSkTyWkp7C4KWDGb1hNB2rdmR8m/GUDirtdCyvoSInIiIiHqFqWFWmtp9K3TJ1eWH5C7y68lXS3elOxxKRPLDvxD56fNODxfsW86/6/+Llxi9TxKeI07G8ioqciIiIeIzQIqGMaTGGnlf1ZMrWKdz37X3EpsQ6HUtEctHKQyvpNrcbsSmxjGkxhl41emG88Bo1p6nIiYiIiEfxdfnyVIOn+O/N/2Xrsa3c9dVdrDq8yulYInKZrLVM3jKZgQsHUjKgJFPbT6VR+UZOx/JaKnIiIiLikdpWbsuUdlMI8Q+h/4L+jN84XvPmRLxU6plUnv/peYb/MpybK9zM5PaTiQyJdDqWV1ORExEREY9VrXjmXeyaRTbjrTVv8cTSJzh5+qTTsUTkEuxN2kvPb3oy5/c53F/rfkY0HUGwX7DTsbyeipyIiIh4tKL+RXnzljd5st6TLNm3hK5zu7Lj+A6nY4nIRVgUs4guX3fhSMoRRjcfzUPXPYTLqILkBv0pioiIiMczxtCnZh/GtR5HcnoyPb7pwVe/f+V0LBHJwRn3Gd5c/SaPLX2MqJAopneYzk0VbnI6VoGiIiciIiJeo26ZukzvMJ0a4TUYumwozy57lpT0FKdjicifxKXEcd+39zFh0wS6RHdhYtuJlC9a3ulYBY6KnIiIiHiVUkGl+KjVRzxQ6wG+3vU1Xb7uwpajW5yOJSLAqsOruOuru9hybAvDbxrOc9c/h7+Pv9OxCiQVOREREfE6vi5fHrzuQT5q9REpZ1Lo8U0PJm+ZrLtaijgkw53BBxs+oP+C/hTzL8aUdlNoX6W907EKNBU5ERER8Vr1y9Zn5q0zaVS+EcN/Gc6gxYNISEtwOpZIoXI4+TD9FvTj3fXv0jqqNdM6TKNa8WpOxyrwVORERETEqxUPKM6oZqN4usHT/HTwJ+746g4NEBfJJ4tiFnHHl3ew6egmht04jOE3DddogXyiIiciIiJezxhDj6t68Gm7Twn0DaTfgn6MXDuS9Ix0p6OJFEhpZ9J4acVLPLb0MSoUq8CMW2fQsWpHjDFORys0VORERESkwKgRXoPPOnxGp6qd+Oi3j+j+TXfNnBPJZduPb6fb3G5M3z6dvjX78mnbT6kUUsnpWIWOipyIiIgUKMF+wfyn8X8Y2XQksSmxdPm6CxM2TiDDneF0NBGvZq1l6tapdPu6G8fTjvN+i/cZXG8wfj5+TkcrlFTkREREpEBqFtmMWR1ncVPETby55k3uW3Af+0/sdzqWiFc6nHyYgQsH8srKV6hfrj6fd/ycxhGNnY5VqKnIiYiISIEVHhjOiKYjeKnxS2w9tpU7vryDL3Z8oTEFIhfJWsucnXO4bc5trI9bz3MNn2NM8zGEB4Y7Ha3QU5ETERGRAs0YQ+dqnfm84+fUCK/BC8tfYNDiQRxJPuJ0NBGPFp8az6DFg3jup+e4sviVfH7r53Sp3kU3NPEQKnIiIiJSKEQUjWBc63E8We9JVhxaQec5nZmxfQZu63Y6mojHmb9nPp3ndGb5weU8We9JPm79MRVDKjodS/5ERU5EREQKDZdx0admH2Z1nMVV4VfxnxX/od+CfuxN2ut0NBGPkJCWwJDvhzDk+yFEFotkRscZ9KnZBx+Xj9PR5C+MJ58jXq9ePbt69WqnY4iIiEgB5LZuZu2YxZur3yTdnc6D1z1I7xq98XX5Oh1NJN9Za/l619e8sfoNkk4n8WCtB7nn6nv034MHMMassdbW++t2HZETERGRQsllXNx55Z3M6TyHxuUb8/aat+k+tztbj211OppIvtqXtI+BCwcydNlQKhStwGcdPqP/tf1V4jycjsiJiIhIoWetZWHMQoatHEbiqUR61+jN/bXuJ8gvyOloInkm3Z3OpE2TGLNhDL4uXx6t8yh3X3m3TqP0MDkdkVORExEREcmSeCqRN1a/weydsykdVJoh9YfQulJr3aVPCpxf437lxRUvsv34dppHNueZBs9QJriM07EkGypyIiIiIhdpfex6hq0cxtZjW2lYtiFDGw6lSlgVp2OJXLYTp08wat0opm2dRqmgUgxtOJTmkc2djiV/Q0VORERE5BJkuDOYvn06o9aNIjU9lV41ejGw1kCC/YKdjiZyydzWzeydsxm5diTH047TrXo3Hqn9CEX9izodTS5ARU5ERETkHziaepSRa0fyxc4vKB2YdbpllE63FO+xPnY9r/7yKpuPbua6UtfxdMOnqRle0+lYcpFU5EREREQuw/rY9byy8hW2HNtC7dK1GVxvMLVK1XI6lkiOjiQf4e21bzN311xKB5XmibpP0K5yO/0SwsuoyImIiIhcpgx3BrN2zuK9de9xNO0orSq14rE6j1ExpKLT0UTOOpVxikmbJjH2t7FkuDPoU7MP/a7pp7uweikVOREREZFckpyezIRNE5i4aSLp7nS6Rndl4LUDCQsIczqaFGJu62be7nmMWjeKAycP0KxiM56s/yQVi+kXDd5MRU5EREQkl8WmxDJ6/Wi+2PkFwb7BDLh2AN2u6kYRnyJOR5NCxFrLsgPLGLl2JNuObyO6eDSD6w3mhvI3OB1NcoGKnIiIiEge2XF8B2+teYtlB5ZRLrgcA68dSMdqHfFz+TkdTQq49bHrGbF2BGuOrKFC0Qo8XPth2lZui8u4nI4muURFTkRERCSPrTi4gnfWvsPGoxuJKBrBwGsH0qFqBxU6yXU7j+/knXXvsGTfEsIDwhlYayB3XnEnfj5aawWNipyIiIhIPrDW8uOBH3lv/XtsPrqZisUqMuDaAXSo0gFfl6/T8cTL7UrcxUe/fsTc3XMJ8g2ib82+9KrRSzcyKcDypMgZY+4C/g1cBTSw1mbbuowxbYCRgA/wkbV2+MW8voqciIiIeCtrLd/v/57R60ez5dgWIotFcn+t+2lbua0KnVyybce28eGvH7IwZiFFfIrQJboL911zH8UDijsdTfJYXhW5qwA38AHwZHZFzhjjA2wHWgL7gVVAN2vt5gu9voqciIiIeDtrLYv3LWbM+jFsO76NisUq0rtGbzpV60Sgb6DT8cTD/Rr3K2N/HcvS/UsJ9gumW/Vu9LyqJ+GB4U5Hk3ySU5G7rF8HWWu3ZL343+3WANhprd2Vte80oBNwwSInIiIi4u2MMTSPbE7Tik1ZsncJH2/8mGErh/He+vfoWr0r3ap3o0RACadjigex1rL6yGo+/PVDfj70M6FFQnnouofoVr0boUVCnY4nHiI/jutHAPv+9P1+oGE+vK+IiIiIx3AZF80rNadZZDPWxq5lwqYJvL/hfcZvHE/Hqh3pU7MPlUIqOR1THJSekc78PfOZsmUKG49uJDwgnMF1B3N39N26Bk7Oc8EiZ4z5DiibzUPPWmvnXMR7ZHe4LsfzOY0xA4ABAJGRkRfx8iIiIiLewxhD3TJ1qVumLrsSdzFp0yRm75zNzO0zaRbZjO7Vu1O/bP0LnfEkBUh8ajwzts1g+vbpxKfGExUSxXMNn6NTtU4E+AY4HU88VK7ctdIYs5Scr5G7Afi3tbZ11vfPAFhrX73Q6+oaORERESkM4lPjmbJlCp9t+4yk00lEhURx15V30alaJ51KV4BtOrqJyZsnM3/PfNLd6dwUcRM9rurBDeVv0Bw4OStPxw9coMj5knmzk+bAATJvdtLdWrvpQq+rIiciIiKFSdqZNBbELGD6tulsiNuAv8ufNpXbcNeVd1GrVC0dpSsAUtJT+HbPt3y+43M2xG0gyDeITtU60b16d6JCo5yOJx4or+5aeRswCigFJADrrbWtjTHlyRwz0C5rv3bACDLHD3xsrR12Ma+vIiciIiKF1bZj25ixfQZf7/qa5PRkrih+BXddeRdto9oSFhDmdDy5BNZa1sauZfbO2Xy751tSz6QSFRLF3dF307laZ4r5F3M6ongwDQQXERER8UIp6Sl8s/sbpm+bzpZjW/A1vjSOaEz7Ku1pUrGJRhh4sMPJh/nq96+YvXM2e0/sJcg3iDaV23Bbtdt0hFUumoqciIiIiBez1rLt+Dbm7prLN7u/ITYlliDfIJpHNqdDlQ40KNdAg8Y9wLG0Yyzeu5gFexaw8vBK3NZNvTL16FytMy0rtdTdJ+WSqciJiIiIFBAZ7gzWHFnD3N1zWbhnISfSTxAeEE7LSi1pGtmU+mXq4+fj53TMQiM+Nf5seVt1ZBVu66ZisYq0rdyWzlU7UzGkotMRxYupyImIiIgUQKcyTvHj/h+Zu2suyw4sIy0jjWC/YG6MuJEmFZtwU8RNuvNlHjh48iBL9y1lYcxC1hxZg8USFRJFy0otaRXViuji0Tp1UnKFipyIiIhIAZd2Jo2Vh1ayZN8Svt//PfGp8fgYH+qUqUOTCk24ofwNVAurpoLxD6Skp7D6yGqWH1zOTwd+Yk/SHgCqhlalVVQrWlZqqT9byRMqciIiIiKFiNu62RS/iSX7lrB0/1J2HN8BQImAEtQrU48GZRtQv2x9KodWVvnIRoY7gx0JO1h+cDnLDyxnbexa0t3pBPgEULdsXRqXb0zjiMZUCa3idFQp4FTkRERERAqxgycPsvLQSlYdXsUvh3/hSMoRAEoGlqR+mfrUK1uPq0tezRVhVxTK6+sSTyXya9yvbIjbwIa4DfwW/xvJ6ckAXFH8ChqXb0yj8o2oU6YORXyKOJxWChMVOREREREBMu+Aue/EvrOlbtXhVcSlxgHg5/LjyuJXUiO8BjXCa1AzvCbVwqoVqHKXdDqJ3xN+Z8fxHWyM38j6uPXsTtwNgMu4uLL4ldQqVYtapWrRsFxDSgeVdjixFGYqciIiIiKSLWst+0/sZ9OxTWw+upnN8ZvZfHQzJ9JPAJnlrmpYVaJCoqgUUolKIZWICokiMiTSY2+kYq3lRPoJ9iXtY0fCDnYe38nOhMyPP45GAoQWCaVWqVpcV+o6apWqxdUlr9aIAPEoKnIiIiIictH+OGq3+ehmNh3dxM6EncQkxXDg5AHc1n12vxIBJYgsFknZ4LKUDCxJycCSlAoqRcmAkpQMyvw+rEgYLuPKtVypZ1JJOp1E0ukkEk8lcjj5MIeSD539OJJ8hEPJh86eGgng7/KnalhVqoVVo2pYVa4ofgXVwqpRLricrhEUj6YiJyIiIiKXLT0jnX0n9xGTGENMUgx7kvYQkxRDbEoscalxpJ5JPe85LuMi0DfwnI8A34CzX/u5/HBb99mPDJtxzvfJ6cmcOH2CpNNJnDh9ggybkW22EgElKBtclnLB5SgXXI6ywWWpULQCVcOqUrFYRXxcPnn9xyOS63Iqcr5OhBERERER7+Tn40eV0Co53q0xJT2F+NR44lPjiUuNIz41nmNpx0hJTyH1TOo5H2ln0khISyDdnY7LuPAxPriM6+zXxhh8jA9hAWFEhkQS4h9CMf9i53wOKRJC2aCylAkuQ6BvYD7/aYg4R0VORERERHJNkF8QkX6RRIZEOh1FpEDLnZOVRUREREREJN+oyImIiIiIiHgZFTkREREREREvoyInIiIiIiLiZVTkREREREREvIyKnIiIiIiIiJdRkRMREREREfEyKnIiIiIiIiJeRkVORERERETEy6jIiYiIiIiIeBkVORERERERES+jIiciIiIiIuJlVORERERERES8jIqciIiIiIiIl1GRExERERER8TIqciIiIiIiIl5GRU5ERERERMTLqMiJiIiIiIh4GRU5ERERERERL6MiJyIiIiIi4mVU5ERERERERLyMipyIiIiIiIiXUZETERERERHxMsZa63SGHBlj4oAYp3NkoyQQ73QIKdC0xiQ/aJ1JftA6k7ymNSb5wcl1VslaW+qvGz26yHkqY8xqa209p3NIwaU1JvlB60zyg9aZ5DWtMckPnrjOdGqliIiIiIiIl1GRExERERER8TIqcv/Mh04HkAJPa0zyg9aZ5AetM8lrWmOSHzxunekaORERERERES+jI3IiIiIiIiJeRkXuEhhj2hhjthljdhpjnnY6jxQMxpiKxpglxpgtxphNxphHs7aXMMYsNMbsyPpc3Oms4t2MMT7GmHXGmK+zvtcak1xljAkzxsw0xmzN+jvtBq0zyW3GmMez/r3caIyZaowJ0DqTy2WM+dgYE2uM2finbTmuK2PMM1mdYJsxprUTmVXkLpIxxgd4D2gL1AC6GWNqOJtKCogzwGBr7VXA9cBDWWvraWCRtfYKYFHW9yKX41Fgy5++1xqT3DYSmG+trQ7UInO9aZ1JrjHGRACDgHrW2qsBH6ArWmdy+SYAbf6yLdt1lfX/aV2BmlnPGZ3VFfKVitzFawDstNbustaeBqYBnRzOJAWAtfaQtXZt1tcnyPwfnwgy19fErN0mAp0dCSgFgjGmAtAe+OhPm7XGJNcYY0KAm4FxANba09baBLTOJPf5AoHGGF8gCDiI1plcJmvtD8Cxv2zOaV11AqZZa09Za3cDO8nsCvlKRe7iRQD7/vT9/qxtIrnGGBMF1AZWAmWstYcgs+wBpR2MJt5vBPAvwP2nbVpjkpuqAHHA+KxTeD8yxgSjdSa5yFp7AHgD2AscAhKttQvQOpO8kdO68oheoCJ38Uw223TLT8k1xpiiwOfAY9baJKfzSMFhjOkAxFpr1zidRQo0X6AOMMZaWxtIRqe3SS7LukapE1AZKA8EG2N6OptKCiGP6AUqchdvP1DxT99XIPNQvshlM8b4kVniJltrZ2VtPmKMKZf1eDkg1ql84vUaAx2NMXvIPC28mTHmU7TGJHftB/Zba1dmfT+TzGKndSa5qQWw21obZ61NB2YBjdA6k7yR07ryiF6gInfxVgFXGGMqG2P8ybzA8UuHM0kBYIwxZF5TssVa+9afHvoS6JP1dR9gTn5nk4LBWvuMtbaCtTaKzL+7Fltre6I1JrnIWnsY2GeMic7a1BzYjNaZ5K69wPXGmKCsfz+bk3ltudaZ5IWc1tWXQFdjTBFjTGXgCuCX/A6ngeCXwBjTjszrTHyAj621w5xNJAWBMeZG4EfgN/53/dJQMq+Tmw5EkvkP113W2r9ehCtySYwxTYAnrbUdjDHhaI1JLjLGXEfmDXX8gV3APWT+0ljrTHKNMeZFoAuZd31eB/QDiqJ1JpfBGDMVaAKUBI4A/wfMJod1ZYx5FriXzHX4mLV2Xr5nVpETERERERHxLjq1UkRERERExMuoyImIiIiIiHgZFTkREREREREvoyInIiIiIiLiZVTkREREREREvIyKnIiIiIiIiJdRkRMREREREfEyKnIiIiIiIiJe5v8BGAniwJ/FcEMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pylab.figure(figsize=(15,10))\n",
"pylab.plot(np.sin(ts),marker=\"o\",label=\"sin exact\")\n",
"pylab.plot(ys[0],label=\"sin?\")\n",
"pylab.plot(ys[1],label=\"cos?\")\n",
"pylab.legend()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21334e04-059c-4967-b6f9-d6b9f2027624",
"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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