notebooks/ERI-visualisation-tril-indices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "637bae21-d231-4cda-ba21-65104a296d25",
   "metadata": {},
   "source": [
    "# Visualising ERI index compression using lower-triungular matrix indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8b66b088-20e3-48e9-8dc9-6fc32deec5a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from plot_utils import plot2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9966a38e-10ca-4785-bb0c-b77d8275b703",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> tril_indices test passed!\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5\n",
    "\n",
    "original_tensor = np.zeros((N, N))\n",
    "\n",
    "# populate tensor with tril_indices\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    original_tensor[i, j] = c # c = 0,1,2,3,... (enumerated)\n",
    "\n",
    "# check values with forloops\n",
    "for i in range(N):\n",
    "    for j in range(i+1):\n",
    "        assert original_tensor[i, j] == i*(i+1)/2+j # c = i*(i+1)/2+j (compressed index)\n",
    "print('> tril_indices test passed!')\n",
    "        \n",
    "plot2D(original_tensor, N, show_values=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "668a00a5-e3fe-4e34-8a4c-db03e6e18d52",
   "metadata": {},
   "source": [
    "Extract i, j from c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "82e58d82-3b32-4eb0-9378-e25c040311fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "# plot i computed from c\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    dist_tensor[i, j] = np.floor((np.sqrt(1 + 8*c) - 1)/2)\n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a822a84-b14a-462e-a4c1-484aecf1fa62",
   "metadata": {},
   "source": [
    "Problem is np.floor((np.sqrt(1 + 8*c) - 1)/2) overflows in 8*c! Let's visualise that with int8 (but we will see this happening with int16, int32, etc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "973207b8-3c61-4ccc-8890-7d56d93853a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c is fine in uint8\n",
      "N is fine in uint8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ------------------------------- #\n",
    "# ignore Python casting warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "# ------------------------------- #\n",
    "\n",
    "N = 10\n",
    "\n",
    "max_c = 0\n",
    "\n",
    "# plot i computed from c\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    dist_tensor[i, j] = np.floor((np.sqrt(1 + np.array(8*c, dtype=np.uint8)) - 1)/2)\n",
    "    if c > max_c: # could have just taken the last c :-)\n",
    "        max_c = c\n",
    "\n",
    "assert max_c == np.uint8(max_c)\n",
    "print('c is fine in uint8')\n",
    "assert N == np.uint8(N)\n",
    "print('N is fine in uint8')\n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))\n",
    "\n",
    "# ------------------------------- #\n",
    "# enable Python casting warnings\n",
    "warnings.resetwarnings()\n",
    "# ------------------------------- #"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "239f06e9-ce06-4fbc-b5f4-454ac5cac265",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4trL9RMZnUrT2DXa993v2ff4kdQVb+r0+v+KnCRtxdEwrqlQq4kjGRkPoDDQQR3LQsniSsXfRXjJJJsk08DMd06fpsmXLlgU9fv3110lKSmLHjh3MmtV5rr8/FMVPcf4izLHZRJm7nj6yNxyhpnQ7E2fd12Wb2KThxKeOwRgZh7OlgaMHl7Fv66uMn3k3KlXv66ui+Dma9xnRCdlExnQ9X5kwaBIeVwv71jwHioKi+EnKPYv0UecHtWu1VZG/+p/4fV40Wj3DZtzS41RZe9/GKg5+8Y/2vrmzbyUipnd9Q3E1NVB3aBPJo88hdez5tDSUUbrtE1RqDQlDzuzz+jy4UFDQEzw812OgBUfIPm6c6DGc0N6IG2efty+ZJJNkGhiZjjmpazJ2ux2AuLiuLyy5XC5cLlf7Y4cj9As+pmjvp7Q21TBuxp1dtvF6nRTkvcuQcVejM0R12S4xfUL7/0eZU4kyp/L1msex1xcRkzi02xzHO7LjE1rt1Yw+/+5u29lrC6k8sIbBk67CFJ+Fs7meo3mfUb5vJRmjL2hvZ4xOZNyF9+P1OLGW76Fo27uMmn1nrwqN0ZzIqEt/js/TRuPRPRzd8A7D5911EoVGITI+g4xJFwMQGZ9BW2M1dQWb+1VkhBDieP0uMn6/n/vuu48ZM2YwZsyYLtstWLCARx99tFfrLNr7KdaaA4ybcSeGiJgu2zlbrLjaGtm//fWOhYoCwIbFDzJ59gNERMV36meMikerj6KtpaHXRebIjo+xVe5n1Hl3YYjsOhNA+d7lJAyaRFLuVAAiY1Lxed0c+fpD0ked3z56Umu07Rf+TXEZNFvLqC7YQM6Z1/SYR63Rtl8viYrPpKWhjJoD68k+69pevZ4T6SLMRMQED5mNlmQaS/b0b30YUKHqdDbkxtXpLOuYwNmT64T2zi7bSybJJJkGfqZj+v05mbvvvpv8/Hzefffdbts99NBD2O329p+ysrJObRRFoWjvpzRU5zP2rDu6vIh/TKQpkYnn3M/EWfe1/8Qlj8KSkMvEWfdhiAh9Z4SrzYbX3YreGN3j61MUhSM7PsZakc/I2T/GaOpctE7k97lBpQpa1j4tp3S3MT9+v7fH9XcRFMXXz76AKSkbp70uaJnTUYfeFNuv9alVaqKJwUrtcREVrNQSQ+h9GEN8UHsAKzVYumgvmSSTZBr4mdqz9afTT37yExYvXsyXX35JRkZGt20NBgNmszno50RFez+ltnwnwyd+B43WiNvZhNvZhM/naW9zKO9djh5YGgit0RFlTgn60eqMaDQGoswpqNVafF4XR/YvxtFYgrPViq3uMPu3v4ExKp7YxOE9vsajOz6mvmQnQ6fdiEZrwN3mwN3mwO/tyFS45R1K93zR/jgmbRS1hZupL83D2dyArbqAsvxlxKSNQqUO7OrSPV/gqC3C2WKl1Vb1zeNiEgZN6jFT+Y4lNFUX4Wq20tpY1f44LifQ98j6hZTvWNLe3u/z0mqtoNVageL34W6102qtwOmob2+TPGoWLXUlVO1ZhdNRT0PxTuoPbyFpxIwe83Qli2FUcoRK5SgtioOD7MSHl1SyAchXtlGo7G1vn8kQGqimRCmgRXFQpOzDQSOZ5PY7g2SSTJLp9GeCPk6XKYrCT3/6Uz755BPWrl3L4MGhP5vSV9UlmwHYu/nFoOVDJ1xHcuYZQGAUokLVqW+XVGpaHNXUlu3A63GiN5qJSRzKoBFzUWt6ftk1RYFM+798Pmh5zpTrSRocuFbham0MGrlkjJqDChVle5fhbrOjM5iITRtF5tiL2tt4nM0Ubn0Xj9OBRmckMiaNEefcTkzKsB4zeZ3NHNnwDp42Bxp9BBGxqQy94HYsaYGi6WqxBeXxtDnY//lTHa9p31pq9q3FlJzLiHl3AYHbnHNn30rFziVU7l6JITqOzDMvJz5nco95upKiysSjuChmPy6cRGNhIjMxfHOvvpPWoN9ljCqBMcpUisinkHwiMTGe6af0Xn3JJJkk07efCUClKEp3EzlB7rrrLhYuXMhnn33G8OEdowGLxUJERO8+vOdwOLBYLEyb9we0ulM793cyvJED7xt2vMY+FNVvScybm093BCHEaeRVPKzlM+x2e8iZqRP16cj6/PPPY7fbOffcc0lNTW3/ee+99/odWAghxP+uPk+XCSGEEL018OaIhBBC/M+QIiOEECJspMgIIYQIGykyQgghwkaKjBBCiLCRIiOEECJspMgIIYQIGykyQgghwkaKjBBCiLCRIiOEECJspMgIIYQIm5P688snoyVVg0avOV2b78RnGHjfeOzXn+4EnTU/NP10R+gkY8Gm0x1BCNEFGckIIYQIGykyQgghwkaKjBBCiLCRIiOEECJspMgIIYQIGykyQgghwkaKjBBCiLCRIiOEECJspMgIIYQIGykyQgghwkaKjBBCiLCRIiOEECJsTtsXZB6vft8m6vdvwt1kBcAYm0LK5AswZ43ssW9jYR4lq9/CnD2anLk/CHrO2VhD5dbFNFcVg9+PITaZwRfcjD46tsf1NuzZiHXvJtyOQCZDfArJUy4kOjt0puKPnqOloqjT8ujskWRfdnun5RVrPsCav5nUsy8nYeI5Pebpjbqtq6ldv4S4SWeTet6VXbazH9pF7cZleOxW9LEJJM+6hOicUSe9/YZNq6lbu4TYM88m+YLQ27flbca+92tc9dUAGFMySDz3YiLSBoVsX730A2x5m0maczlxU05uP5UphZRQgBsnJiwMZyIWVVyX7WuUcorYh5MWIjAxlLEkqFJPKoNkkkz/3zINiCKji7KQNnU+BksCigKNBds5svw1hl19PxFxKV32czVZqdzyOVEpOZ2fs9dz+LNniR8xhZQz5qLRGXE2VqPS9u4l60wxJM+YjyEmERSFxgNfU7L4VYZ85+cY4ztnypp/C4rP1/7Y52zl8MK/YRkyvlNbe9EeWqtL0EaZe5WlN9qqSmncvRlDYvdvkNaKI5Qvfovksy8mOnc0tgM7Kfv0NXJuuh9jD3273X5lKba8zRiSeth+aRHm0ZOIyMhGpdFi3bKGsndeZPAdv0QXHRPUtunQHtoqStCaTn4/VStlFLCHkUzCTBxlHCaP9UxX5qJXGTu1tyn15LOVXMaQSCrVlLKbTUxV5mBSWU46j2SSTP8fMsEAmS6zZI/GnDUSgyURY0wiqVMuRq3T01pb0mUfxe+ndPXbpJwxF725c6Wu2r4Uc9ZI0qZdSmRCBgZLApbsMegionuVyZwzGnP2KAwxiRhik0iZ/k2m6qMh22uNUeiizO0/zaWHUGt1WIYGFxlPs43KtZ+QOfd7qNSn5k8d+Nwuyr94m7S516ExRHbbtmHnekyDR5Aw5TwM8ckkz7wIY3I61l0b+r19v9tF5aK3Sbn4OtTG7refdvn3iJ08A2NyOoaEZFIuvh4Uhdajh4PaeZps1Kz4hLTLvweak99PpRSQzmDSVNmYVGZGMAkNGio5GrJ9GYXEk0y2ajhRKjO5qjFEE0sZnUerkkkySaauDYgiczzF76exMA+/x01UcugpFIDqHSvQRpiIHzG18zoUP47SAxgsiRQteZH8N35PwSd/x3Zkb78z2QoCmSJTsnvVx7p/K5ZhE1HrDEG5ylYsJHHy7JCjof6qWvURppyRmAYN67FtW+VRTIOGBi0zZY+gtfJov7dfvfwjTLkjiRrc8/ZP5Pe4Ufw+NMcVJ0XxU7VoIXFTZ2NIPPn95Ff8NGEjjqT2ZSqVijiSsdEQso+NBuJIDloWTzL2LtpLJskkmUIbENNlAG0NVRz+9B/4fV7UOj2D596KMTb0Aaa5qhjroW0Mv/r+kM9725rxe1zU7lpDypnzSJ16CU1lBzm64g2GXHonprTcXmVy1ldS9ME/8HsDmbIuubVXxaG1ugRXQzUZ518ftLzu6zWoVGrix5/dq+33hv1gHs7acnK+97Netfe2NKGNDB7NaSOj8bY09Wv7jn15uKrLGXRr77Z/orovF6M1WYg8rkBZN68BtZrYM0/NfvLgQkFBT/CUgR4DLThC9nHjRI/hhPZG3Dglk2SSTH0wYEYyhphEhl/zc4ZdeQ8Jo6ZT8uU7OBurO7XzuZ2UfvkOmbOuRRthCr0yRQHAnD2apHHnEJmQTvLE8zEPGkn9/t7/FUV9bBJDvvNzhlx/L/Fjp1O+4h2cDZ0znahx/1aM8alEpnSMxNpqy2jYvZ6MC76DSnVq/gqnx9FI1ZpPyJj/PdRa3SlZZ1+3X7PyE1Iv79/2GzatxrE/j/Rrbm3v76wqw7p9PamXnLr9JIQ4fQbMSEat0WKwJAAQmZhJa10ZdXvXkznr2qB2LkcD7iYrxcte7Vj4TVHZ9dIDjLz+V+hMMaBWY4wNHgoaY5JpqT7St0wxiQBEJGXSWltGw+6vSD/vui77+D0ubAW7SJ42L2h5S0Ux3tZmDr72x+Ny+6nasIj6XV8x4tbf9jrXMW015fhamyl686mgdbaWF2PN28ion/0VlTr4PEIbFY23NXjU4m1tQhvVu2tVx3NWBbZ/9N/B228rLabx640M/1Xn7R/TsOVLGjavJvO7d2JMSmtf3lpWjK+lmaJng/dT7epFWLd/xZC7+76fdBhQoep0hubG1enM75jAGZ3rhPbOLttLJskkmUIbMEWmE0XB7/N2WmyMSWL4tb8IWla1fSl+t4v0GVegM8Wg1miJTMzEZasLauey16Hrxe3L3WfyddvEfng3is9LzPDJQctjRpyBKSv4msWRT18kdsQZxI6a0q84UYOGknvzA0HLKpa9iyE+iYQzzwt5gI9Iy6a55DDxkztuB24uKSAyLbvP24/MHsrgHwZvv2rJu+jjk4ifFnr7AA2b19CwaRWZN9xBRGpm0HOWMWcQlR28n8refRHz2DOwjOvfflKr1EQrMVipJYl0ABRFwUotmYSeOo0hHiu1ZNFx/cpKDRbi+5VBMkmm/2+Z2rOd0rX1U+XWJTRXFuFqstLWUNX+OG7oJABK1iykcusSANRaHRFxqUE/Gn0Ear2BiLhU1JpA3UwaPxtb0S4aDmzBZa+nLn8D9pL9JIya3qtM1RsX01JRhNthxVlfGXhcXkTM8ECmshULqd64uFM/6/6tmHPGoI2IClqujYjCGJ8a9KNSa9BGRmOITeq0nt7Q6I0YE1ODftQ6PRpjZPvtyOVfLKTmq46c8ZPOpvnoQeq3r8XVUEPtxmU4q8uImzCz79s3GDEkpQb9qHR6NBGR7bcyVy5aSO2XHdtv2Lya+q+WkjL/enSWOLzNDrzNDvzuwBmVJjKq0zrRaNBGRWOI799+AshiGJUcoVI5Sovi4CA78eEllWwA8pVtFCodN4ZkMoQGqilRCmhRHBQp+3DQ2OU/WMkkmSRTaANiJONta6bky3fwtjrQ6CMwxqeSO/92ojOGA+ButkEf5+djBo/Fd/bV1OStoXzjJxhikhh84c2YUjt/pqarTGUrFuJtcaA2RGBMSCX7ijuIzgpk8jQ1dsrkaqyltfII2Vf8qE9Zw8njaAy6thGZPpiM+d+jdsNSajcsQR+TSOYVt57UZ2R62v7x+6lx5yYUn4/Kj98Iahc/80ISZ807sfspk6LKxKO4KGY/LpxEY2EiMzF88/kBJ62o6MgZo0pgjDKVIvIpJJ9ITIxn+in9/IBkkkz/65kAVIryzQWNb4nD4cBisTD21sfQ6E/t3N/J8BkG3kVmv/50J+jMNwAzZSzo/c0cQoiT41U8rOUz7HY7ZnPPH5QeENNlQggh/jdJkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNictq/6b01WoRlA33zs132rX0bdK8q3/xeVe+TXDrz9dPjv0053hE6G3rvldEcQYkCQkYwQQoiwkSIjhBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcLmtH1BZlesG1ZTv3oJMVPPJmnelT22d+TnUf3Rf4gaPob0G37Qvrzg0ftDtk+YcwlxM87rU6bGdatpWPkFlrPOJnH+FV2287W1YV31Bc379uJra0UXE0vCxVcQNXwkAH6Xk4ZVy2jZn4+vpQlDajoJ86/AmJHVpzxd5vxyNdZlX2CZcTYJl4XOqfh8NH65mqYdX+Nz2NElJhJ/0SVEDh9xajIsX45txcqgZbrERDIe/FXI9u7qahqXLcddXo63sZG4yy/DMmvWSWWwfbEc+7LgDNqkRNIfDp2hadMWWrbtwFNVDYA+M4OYSy/CMKjj9+JzNNG4aAnOgwX429ow5OYQd80V6JISTyprmVJICQW4cWLCwnAmYlHFddm+RimniH04aSECE0MZS4Iq9aQySCbJFM5MA6rIOCtKse3YjD65dy/SY7NSv2IREVk5nZ7L+fkjQY9bDh+kZtF7mEaN71um8lLs27egT+k+k+L1Uvn6i2iiTKR852a0ZgteWyNqY0R7m9pP3sddW03yNd9BY7bQtGsHla+9SNa9v0RrtvQpV6ecZaU4tm5Bn9p9TuvypTTl7SDx6uvQJybRWnCI6jdfI/2un2JIzzipDMfoUpJJ+dGP2h+r1Jou2ypuN7r4OKLGj8P62aJTsn0AXWoyyXd3ZKCbDM7DRURNnoBhcDYqnQ77qjXU/Osl0h56AG2MBUVRqH3ldVQaNYm334LaaMTx5VfUPPciab9+ALXB0K+M1UoZBexhJJMwE0cZh8ljPdOVuehVxk7tbUo9+WwllzEkkko1pexmE1OVOZhUJ/f+kUySKRyZ4CSny/7yl7+gUqm47777TjqI3+2i6uO3Sb70OjTGyB7bK34/VR+/Rfy5c9HFxnd6XmsyB/00H8onYvAQ9CHadpnJ5aLmg7dJuuJa1D1kcuzchq+1ldQbbyVi0GB0sXFEDM7FkJoWWJfHQ/P+vcTPvYSIwbno4xOIP38uuvgE7Fs39TpTVzlr332bxKuvRR3Rfc6mnTuInX0+USNGoouPx3LWdCJHjMS2ft1JZTieSq1Baza3/2hMUV22NWRlEXfppZgmTkSlPYXnPGoNGrO546ebDIk330j02TPQZ6SjS04i/jvXgV/BWXAYAG9dPe6jJcRddzWGQVnokpOIu+4qFI+Hlh27+h2xlALSGUyaKhuTyswIJqFBQyVHQ7Yvo5B4kslWDSdKZSZXNYZoYimjqN8ZJJNkCmcmOIkis337dl588UXGjRt3SoLUfvERUUNHEpUzrFftG9atQBNlwjKp578l4m1uouXwfiwTp/QpU93nHxM5fBSRQ3rO1HJwH8asQdR9/jFHFvye0n88gXXtKhS/P9DA7wO/v9OBVKXV0lZypE+5OuX89GMiR4wicmjPORWfF5U2+A/VqHQ6nEdPLsPxPPV1lD76B8oe+zO1b72Nt7HxlK27t7x1dZQ//AcqHv0zdW+8jdfa+wyK2w1+H+rIQMFWvF6AoN+dSq1GpdXiKu7ffvMrfpqwEUdSxzpVKuJIxkZDyD42GogjOWhZPMnYu2gvmSTT6cx0TL+KTHNzMzfeeCMvv/wysbGxJx3CkZ+Hs6qchDnze9W+rbQYR95WUi69rnfr370dtd6AaWTvC2LTnjxcVeXEX3Bxr9p7rA207NuD4veT+v0fEjt7DraN62hcG7g2oDYYMWYOwvrlKrwOO4rfT9OuHTjLSvA1O3qdq1POXXm4K8uJm9e7nJHDhmNbvw53fR2K309rwSFa8vfidfQ/w/EMWVkk3nADKbf/kPirr8ZrtVL53HP4nc5Tsv5eZcjOIv7GG0i684fEXXc1vgYr1X/vfYbGRUvQmC1EDB8KgC45CU1sDLbPv8DX2ori9WJfuQafzY6vn/vNgwsFBT3B0xh6DLgJndONEz2GE9obu2wvmSTT6cx0TL/mJ+6++27mz5/PnDlz+NOf/tRtW5fLhcvlan/sOOEfpcfeSN2yT8i46ceotT3/KUi/y0nVJwsD02qRpl7ltedtwzx2cq/WD+CxNVK/5FPSbv0Ral0v/zyloqCJMpF0xbWo1GqM6Zl4HQ5s678k7ry5ACRf811qPnmPo3/9A6jVGFLTMY2biKuyvHfbOIHX1kjD55+S+sPe50y49ApqP3qfsr89DioVurh4os84k6bt2/qV4USRI0e2/78+DQyDsij702O07N5N9NSpp2QbPYkY1ZGB9ECG8kceoyVvN9FndZ/BvnINrTt3kfzTO1F9s09VGg2Jt91CwzvvU/7g70CtxjhsKMZRI0AZeH8pVIiBpM9F5t1332Xnzp1s3769V+0XLFjAo48+2uXzrqpyfC3NlLz4VMdCxU9bSTG2bRsZ+vBfUak7Blzuxga8NisV7/z7uPaBf+gFf/gF2T95EH1cQvtTrSXFeBpqsVxzUy9fIbgqA5nK/vV0x0K/H2dJMfatG8l95PGgTACaaDMqtSZouT4xCV9zE4rXi0qrRRefQMYP78bvduF3udBGm6l+982Q15R6lbOiHF9zM+X/OCHnkWLsmzeS81iInCYTqTf/AL/Hg7+1FY3ZjHXpErRx/cvQE01EBLrEBDz1p3YI3hfqyAh0SQl467rPYF+9FvuqNSTf/SP06WlBzxmyMkj71f3429pQvD400Saqnvw7+szMfmXSYUCFqtNZoxtXp7PRYwJnma4T2ju7bC+ZJNPpzHRMn4pMWVkZ9957LytXrsRo7F2Qhx56iPvv77id2OFwkHncP8zIwUMZdOcDQX2qP3sXfUIScTPO63SQ1CckdWpfv2YpfreLpHlXoLPEBD3nyNuKITUDQ0p6r/ICROYOJfOnvwhaVvvxe+gTkoiZNbtTJoCIrME07dmJ4ve3P++prwsUnxOuw6j1BtR6A762VloLDxE/95JeZwva5pChZPwsOGfdB++hS0wi5tzQOdsz6HSoLRYUn4/m/D2Yxk3oV4ae+F0uvPUNaCZHh2X9fcpwZtcZ7Ku+xL5iNcl33o4hq+vCoY4I3C3oqa3DXVpOzMXz+pVJrVITrcRgpZYkAu9NRVGwUksmuSH7xBCPlVqyGNq+zEoNFk7NCYJkkkynMtMxfSoyO3bsoLa2lkmTJrUv8/l8fPXVVzz77LO4XC40muBbRQ0GA4ZubvFUG4wYkoJvu1Xr9GgiItuXV32yEG20mcQ5l6DW6jq113xzm/CJy30uJ037d5N44WV9eZmBTCfcRq3S6VFHRrYvr/lwIRqzhYQLA9eRzFPOwrZ1A/VffIpl2tl4GupoXLcay1lnt6+j5fBBUECfkIjHWk/9ssXoEpIwT+rbDQlBOU+4tVql16OJjGxfXvPeQrRmC/EXBXI6S0vwOuwYUtPxOuw0rlwOikLMObP7leFEDYs+J3L0KLSxsfjsDhqXLwe1GtPEiQDULXwHjcVC3PzANSTF68VdUxP4f58Pn92Oq6ICtcGALiGhy+10p/HTz4kYPQptXCxeuwP70uWgUhM1KZCh/j+BDLGXBTLYV67B9sVyEm6+EW18bPt1FpXB0H57ckvebjSmKDSxsXgqq7B+/BmR48YQMXJ4v/dVFsPYz3bMSiwW4ijlMD68pJINQL6yDSMRDFGNBSCTIexgHSVKAQmkUE0ZDhoZyeR+Z5BMkimcmaCPReb8889n7969QctuvfVWRowYwa9+9atOBeZU8dobUalUfe7XlJ8HikL0mImnPJPHZoPjMuliYkm7+Q7qv/gMx7N/QxNtwXLW2cTO6vjgp9/ppGHFF3gdNjQRkZhGjyPugotQhWm/AXhttqB9p3i9WJcvw2ttQKXXEzliJEk3fBdNREQ3a+k9n91O3Vtv42tpQWMyYRw8mLR7forGZPomT2PQfvM6HFQ+1THdZ1+7DvvadRhzc0i9665+ZfDa7NS/0ZHBkDuYlPt/iib6mwyNwRmaNm4Gn4/6V98MWo9l3gXEXBy4nuZzOGj8ZBG+pmY05mhMU87AMndOv/Idk6LKxKO4KGY/LpxEY2EiMzF885kGJ62o6MgZo0pgjDKVIvIpJJ9ITIxn+in9TINkkkynMhOASlFO7srlueeey4QJE3jmmWd61d7hcGCxWMh98M9oDKd27u9k+HUD7wKu0st7Dr5Nfu3A20/+Abifht675XRHECIsvIqHtXyG3W7HbDb32F6+u0wIIUTYnPRHrNeuXXsKYgghhPhfJCMZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2J/3dZf3lSvKijvCers13phl43y7MAPzGY5XWf7ojdKIegPvpyLvjTneETgbfsOd0RxD/D8lIRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYXPaviDzeLbFK3AsWRW0TJucSNojD/TYt2X7LhpeXUjE+NEk/vjm9uV+pwvbp0tp270Pf0sLmvg4omfPIHrWWb3LtGgljsUhMv3xF1328be2Yft0Oa078/G3tqKNiyX2+kuJGDuivY230Y7t46U48w+huN1oExOIu+VaDNkZPWf6dCWORauDM6Ukkvbnn3fZx7FiA81fbsFntaE2RRF5xhhirpmHSqcDoOnLLTR/uQVvfSMAuvRkLJeeT8S44T3m6YrXasf2/nLadh9CcXvQJscT/8OrMeR0/RqdB4ppXPgF7ooatHEWLJfPxnT25H5v3/rOctp2F6C4PGhT4kn80VVdbt/b6MD69lJcxRV4a6yY555F/Pfnd2rna2mj8f2VtG7fh6+5DW1CDPE3zSdyYu/2ldfqoOHtFbTuOozi8qBLiSPxzisx5qaHbN92sATr2ytwV9YHXkdiDOY5ZxAzf3p7m8ZPvqJl237clfWo9DqMwzKJv/FC9GkJvcoUSplSSAkFuHFiwsJwJmJRxXXZvkYpp4h9OGkhAhNDGUuCKrXf25dM/1uZBkSRAdClJpN07x0dCzQ9D7K8DVZsHy/BMGRwp+caP/oc16Ei4m+9AW18LM79BVjf/RSNxUzk+NG9y5SWTNLPbu9YoO46k+L1Uvv0K6ijTST++HtoYsx4G2yoI43tbfwtrdT89XmMw3NIvOcHaKKj8NTUo46M6FUeCBSBpF/8sFeZWrbswvbhMuJ/cA2GIVl4quux/vsDUKmIveESADSxZmKumYc2OQEUhZaNO6n755ukPHIP+vTkXuc6xtfSRvWfXsQ4MoekX9yC2hyFt7oBdVTXr9FTZ6X2yTcwnTeVhB9fR9v+Ihr+/QkaSzQR44b1bfvNbVQ98hLGUTmk/PJm1OYoPD1sX/H60ERHEXPFbBxLN3bRxkv1gtfQmKNIuve7aOLMeOuDf7895ar43StEjBpM6kM3oTFH4alqQNNNLrVBj3neVAxZKagMOpyHSql7eVFg+ZwzAGg7cBTz3KkYc9NRfH6s766k6rE3yHzyp6iN+l5lO161UkYBexjJJMzEUcZh8ljPdGUuelXn12pT6slnK7mMIZFUqillN5uYqszBpLL0efuS6X8rEwygIoNGjcYS3evmit9P/avvYLnkAlyFR/C3OYOedxeVEDVtMsZhuQCYzp5G0/qtuI+W9brIoO59puaNX+NvaSX5V3eh0moA0CYEn0E4lq9DG2sh/pbr2ped2OZUZnIVlmAYOoioaRPatxU5dTzu4rL2NpETRgX1ibl6Ls1rt+AuKu1XkXEsXoc2zkLC7de0L9Mldv8am9dsQ5sYS9x3Lw60T0/CVXAUx/KNfS4y9s+/QhNvIfHHV3dsP6n77esSY4m/OVB0m9ftCNmmae0O/M1tpD3yo/bfry4xtte5bIvWo403k3TXlcfl6r6/YXAqhsEdZ5W6pFhatu6n7WBJe5FJ+/X3g/ok3XUVR29/HFdxJRGjsnud75hSCkhnMGmqQN8RyiTqqaKSo2QzolP7MgqJJ5lsVWA0l8sYGpRayihiJJP6vH3J9L+VCQZQkfHW1lPx4B9Bq8OQk0XMFRehjev6H6F9ySo00SZMM6bgKjzS6Xl97iDa9uwnavqZaCxmXAVFeGvrMF57ad8yPfAn0H2T6cp5aONDZ2rbvR997iCs73xK2679aKKjiJwyAfO8c1F9M9po3b2fiFHDqHvhLVyHi9HEWIg+dxqms6f2PlNNPRU/eyyQaUgWMVfPQxsfE7KtYcggWjbn4Souw5CTibe2gba9h4g6K/QbSPH7ad2+F7/LjSE3q9eZjteWdwDj2GHU/XMhzoNH0MSaiT5/GtGzz+yyj6uwFOPoIUHLIsYOw/r24j5vv3XnASLGDaXmmXdwHjyCNtZM9AVTMZ/X9fZ7td4dBzEMzaThtUW07DiAxhyFafp4LJfNav/9dqfl60NEjh9C9VPv0XbgKNq4aCwXTsF8/hm9zuA6UoWzoIy468/vso2/NXCypTb1fnTc3lfx04Qt6ICkUqmIU5Kx0RCyj40GBhF8IhBPMnVU9nn7kul/K9MxA6LIGLKz0H//erTJifgcDuxLVlHz5POk/vZ+1MbOwzxn4RFaNm0n5Tf3dbnOuOuuwPr2R1Q+9FhgSkmtIu7GazAOzeldpsGZ6G+5Dm1KIj67A/vnq6h54gVSH7kftdHQqb23zor3YBFRUyeQdM+teGobaFz4Kfh8WC69oL1N07otmC84G8vFs3EfLafx3UWg0WKa3vP1B0NOFvrbrv0mUxP2z1ZR85cXSP3Dz1BHdM4UNW0C/qYWaha8ACjg82M6dyqWS2YHtXOXV1Pz2L9QPF5UBj2JP7kJXT9GMQCeukY8a7ZinjeD5EvPxXWknMa3Pkel1WA6O3Rx89ma0IwzBS3TWEwobS78bg9qva7X2/fWNtK0ahvmi2YQc8U5uIrKsb6xGJVWQ/Ss/p+deWutePfbiJoxnpRf3oynpoGG1xah+HzEXt31Qf/4XI6V27HMP4vYK2fhKqqg/rUvQKvBfM7EbvsevfNv+Bwt4PMTe+1szOeHfq8ofj/1byzFODwLQ1bff38eXCgo6An+N6fHQAuOkH3cONFjOKG9ETfOkO0l0/+fTMcMiCITMeb4oVwqhuwsKn6zgNYdezDNmBLU1u900vD6u8TdeDUaU1SX62xauxHXkRIS7rwFbVwsrsJiGt/9BK3FjHHk0J4zHXexnoxUDIOzqHhwAa1f78Y0c0rnDoqCJjqKuJuuRqVWox+Ugc9mx7H8q/Yig6KgH5ROzJXzANBnpeOurKb5qy29KjJBF+MzUzHkZFLxwF9o3b4H06zOZ+rOg0XYl3xJ3E2Xo8/JwltTT+M7n2NftBrLZR0HRl1KAimP3IPS5qT163waXvmA5F/d0b9C41cwDE4n9tq5gdeYnYanvIamNVu7LDKnkuJXMOSkE3fDhQAYstPwlNfStGrbSRUZRVFQm6NI+OEVqNRqDDnp+KwO7EvW96rIKH4FQ24a8d8JvBcMg1Nxl9XgWLm9xyKT/uht+J1uXIfLaFi4El1KHNEzOv/lzfpXl+AuqyX90dv69yKFCIMBUWROpI6MQJecgLeu8zDPW2fF19BI3fOvdyxUAn9+t/TuB0l95AE0FjO2z5aR+KPvEzF2JAD6jFTcZZU4Vq3rVZEJnSkRb23ooafGEg0aTdDUiS4lCb+jCcXrRaXVorFEo0sLPnDrUpJo25nf5zy9yWT/ZCVR0ydhmhUoivqMFBS3B+sbH2O+ZHZ7VpVWiy45cDeSPjsD15FymlZtJO7mq/qcSRMTjS49KWiZLi2R1q/3ddvHZ28OWuazN6OKMPRpFAOgiY1Gl57Yafst2/q3j4/RxoT4/aYn4rM1t/9+u+0fa0J/Yq70RJq37u9x28eu3RiykvHZmmn84MtORabu1cW07DxE+iO3oY3v30VbHQZUqDqdybpxdTpDPiZw5us6ob2zy/aS6f9PpmMG5Odk/E4X3roGNObOF7h1KYmkPHw/Kb++r/0nYtwoDMNySfn1fWhjLeDzBX5UqqC+KrW6vSD1O5PFHPJ5w5BsvHUNKH5/+zJPbT0aS3T7AcgwJBtvdV1QP29NPZq4mJPMFPpGAL/b02kfdHociuJH8Xr7lckwNAtPVfBr9FQ3dHndCMAwJAvn/qKgZW35hzEM6ft1IeOwLDxV9Sdsvx5tQu8v0ofMOGwQ3poTfr9VDWhionssMADG4SFyVTWgTYzpUw5FUVC8vqDHda8upmXbAdJ+e2uPNxN0R61SE00MVmqD1m+llhjiQ/aJIT6oPYCVGixdtJdM/38ytWc7pWvrp8aPFuMsKMLbYMVVdJT6F98EtZrIMycAUP/6u9g+XQqASqdDn54S9KOOMKI2GtCnp6DSalFHGDEMzcH28ZLAeuutNG/+mpatO4gYP6Z3mT5YjPNQMd76bzI9/02mKeMDmV59D9vHS9vbm86Zhr+llcb3PsdTU0fbngM4vvgS07kdn2mInjMTV3Ep9i/W4Kmtp2VrHs3rtxI9e3qn7YfM9N6SjkyFJdQ/+x9QqYmc+k2ml9/D9uGy9vYR40fQ/OUWWrbuxltnpW3fYeyfriRi/Mj2M3Lbh8va1+kur8b24TJch44QOa37KZyumOfNxFVUhn3RWjw1DbRs2kXzl9swzZnW8TreX079ix907LvzpuCttdL47lI8lbU0rdpC67Z8zHNn9Hn7lotm4Cosw/bpWjzVDTRv3E3Tmu2YL+i4ucL67nLq/vVBUD/X0UpcRyvxO134HC24jlbiLu/4B2i+YAq+ljasby7BU1VPa95BbJ+txXxh727asFw8Hefhcho/WYenuoGmDXtwrP4ay4UdU68NC1dS8+xH7Y/ty7fSsuMg7qoG3FUNONbswLZ4E6aZHaOY+n8vpnn9HpLvuQZ1hB6vrQmvrSlwgtEPWQyjkiNUKkdpURwcZCc+vKSSDUC+so1CZW97+0yG0EA1JUoBLYqDImUfDhrJJLdf25dM/1uZYIBMl/ka7TS8uhBfSysakwlDbjbJv/wJmujAxWCf1YaqN2fgx0m47UZsny2l4dV38Le2oomLxXLZPEyzpvXc+VimV45lisIwJJvkB+/uMpM2Loake2+j8f3PqXr0GbQxZqLPn4F53rntbQzZmSTe9X1sHy/Dvng12oTAhzWjpvbugO5rtNPwwjuBTNFRGIZmk/zwXWjMx2VSd2SyXHoeKpUK+ycr8DXaUUdHETF+JDFXz+1Yp6OZhlfex2dvQh1hRJeRSuL9PyBidN+nFAEMORkk3vM9bB8sx/bZmsBrvPESTNMndGzT1oS3wdb+WJcYR9LPb8b69hIcKzahjbMQf9uVfb59GcCQm0Hyz27E+t4KbJ98Gbg1+qb5mGaeuH17UL/KXz/X/v/uI5W0bNqNNiGGzH8EPhCsjY8h5Ve3YH3rCyoe/CeaWDOWedOxXDarV7mMQ9JJ+fl3sL6zksaP1qFNjCHh5ouIPnt817n8Cg0LV+Gta0SlVqNNjiP+uxe0374M4Fi5PZD/0deCtpd455WYz+37iUKKKhOP4qKY/bhwEo2FiczE8M3nLJy0oqLjPRajSmCMMpUi8ikkn0hMjGf6Kf2chWT6780EoFKUfs4f9ZPD4cBisZDx1B9QR5zaub+TovlWd0PvaAdeJpXW33Ojb5l6AO4ntcbXc6Nv2eAb9pzuCOJ/gFfxsJbPsNvtmM2hLx8cb0BMlwkhhPjfJEVGCCFE2EiREUIIETZSZIQQQoSNFBkhhBBhI0VGCCFE2EiREUIIETZSZIQQQoSNFBkhhBBhI0VGCCFE2EiREUIIETZSZIQQQoSNFBkhhBBhc9q+6t+Y2IomcuB8o69WO/C+NVc3AL/JV6cZOL+zY/QDcj8NvEyaL9NOd4ROfLMrT3cEEWYykhFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNhIkRFCCBE2UmSEEEKEjRQZIYQQYSNFRgghRNicti/IPJGnwUHdWytp2VmI4vagS4kj9e7LMQ5J77Fv68FSyn77GoasJLKfvLN9ueLz0/D+Whxf7cFra0YbG4159gTir5mFSqXqVaaaN1bTvLMIv8uDPjWW9J9eRsTQrr9o0O/xUvfuV9jX5eNtbEYbZyLx+lnEzpkAgGPzAeo+2Ii72ori9WNIiyP+8mnEzB7X804C3PVNVL2+BseOYvwuD4bUWLLuu4TIoakh25c8/TmNq/d2Wm7MSmDEv+4AAvupeuF6Gtfm42lsQRdnIu78cSTfMKNX+8ld30TZq2uxf12E3+XFmBbL4J9dTNSw0JkAaj7fQe3nO3HV2DEkmkm94SwS5oxtf9668RBV723GVdkY2E/psaRcNYWE88f0mOfrm17EVePotDzl0gnk/vSCkH3qvzpE6esbcNbYiUiPZdAPzyFuSk778xsvfCJkv0E/PIeM66b0mGnzd18JmSntsvEMu/f8Tssrl+yhZsUBWo7WA2AalkzObTMwj+jYp3XrD1P5+R6aCmrwNjmZ/OL3iB6S1GOWY9Zd/xrOmqZOyzOvGMuo+2Z3Wl7zVSHFb31Na4UNxecnMj2G7OsnknbhyPY2exespHL5gaB+8WdmccYTV/Q6VyhlSiElFODGiQkLw5mIRRXXZfsapZwi9uGkhQhMDGUsCaqu34+SKXyZBkSR8TW3UfqbfxM5ZjAZD9+IxhyFp6oBtSmi574tbVT/4xMix+bgszcHPWf9dAO25dtJ+emVGDITcRZVUvXsZ2giDcTOn9ZjpiMPvk7UmGyyfvcdtJZI3JVWNCZjt/3K//oRXlsLaT+5BH1qHN7GZlCU9uc1pggSr52JISMelVZD09eHqfjHIrSWKEyTcrtdt7e5jcO/fJPocYPIeeR6tJZIXD1kyrjjAtJu6ThgKD4/h376bywzRrQvq/1oM/VLd5L1s0sxZiXQdriK0r8vQRNlIPGyM7vP1OTkwM//g3n8IIb98Tp0lkicFY3dZqpdvJPy19aRfe9FRA1LpeVQJUf/sQytyUjMtKEAaKONpF1/FsbMwH6ybSvkyFNL0MVEYpmc0+W6Acb/8yYUf8e3RbcerWffgx+QMGt4yPaOfRUc+vPnDPrBLOKm5VK35gAHH/mE8c99n6jBiQCc+e6dQX0atx+h8KllJJw9rNssx0z+13dR/B3vg5Yj9ez55UcknhO6v213OUnnDcc8ejZqvZayd7ez+5cfM+Xf38eQGA2Az+nBMiaNxHOGUfDUyl7lON5ZL16P4uvI1Hykga9/8Skp5wwN2V4XbSTnpjOJyopFrVVTt/ko+X9ZhT4mkoQpg9rbJUwZxJhfzWl/rNZr+pzteNVKGQXsYSSTMBNHGYfJYz3TlbnoVZ3fZzalnny2kssYEkmlmlJ2s4mpyhxMKstJZZFMfdfnIlNRUcGvfvUrli5dSmtrK0OGDOG1117jjDPO6HcI6ycb0CVYSP3JFe3L9Mmxvepb8+JizGePBbWK5m0Hg55rO1SG6cwRmCYH/iHrkmJxrM+nrbCCntZe/9EmdAlm0u+9rNeZmnYW0rKvhKEv/hRtdMQ3fWKC2kSNzQ56HH/pVGxr9tByoLTHIlP74Rb0CdFk3XdJ+zJDSkzXHQBNlBFNVMdj2+ZD+JrbiL9gfPuylgMVWKYOw3LmkMA6k2No/Go/rQU9fw171Qdb0CeaGXz//F5nql+zj6SLJxB/TuAM2JgaQ8vhKqo+2NpeZMzjBgX1SbniTBpW5dO0r7zHIqOLiQx6XP7eNoxpMZjHZYZsX/npDmLPHNw+Ihl0y0xsO49StSiPIfdeCIA+zhTUx7qpEMv4LIyp3b/WY/QnZCp9ZxvGNAsx4zNCth/164uDHg//+QXUrT9MY14ZKReOAiDlgsB/26rtvcrQU6bihTuISLMQOyH07EHcxOCsg66ZQMXyAzTurQwqMmqdBkN81Ind+62UAtIZTJoqG4ARyiTqqaKSo2QzolP7MgqJJ5lsVeCkIpcxNCi1lFHESCZJpm8xE/TxmkxjYyMzZsxAp9OxdOlS9u/fz5NPPklsbO8KQleavz6EMTeNir+9T+Gtf+XoL17AtnJHj/3sa/Lw1DQSf905IZ+PGJ5Jy95i3JWBKQfn0WraDpZimhj6TO14TdsKMOamUfb4hxz8/pMU3fcS1hU7e+wTkZtGw8ebOHTrMxy+8zmqX1uJ3+UJ2V5RFJp3H8FV0UDU6EEh2xzPvrWAyKGpHFnwMfk3PsOhe/5Nw7K8Hvsdz7piN9ETBqNP6jhTiRqZTtPuozgrGgBoK66hZX8Z0ZO7L3oAti2HiRqaQuFjn5B3wz/Yd/er1C3d1W0fxeNFpQ8+v1HrdbQUVOL3dv47LIqi4Mg7irPcSvSY0IWiK36Pj7rV+0maO7bLqb+m/ZXETAze/7FnZNN0IHSRdTe20LitmOR5Y0M+35tMNasOkDpvTK+mIwF8Li+K14c2uvuRdH/5PT6qVh4k4+JRvcqkKAoNO8poLWskdnxwUbLuKufLK15m/U1vsv+pL3Hb2/qfS/HThI04OqYBVSoVcSRjoyFkHxsNxJEctCyeZOxdtJdM4cl0TJ9GMo8//jiZmZm89tpr7csGDx580iE8NY3Ylm8n9tKziL/qbJyFFdS+uhSVVoNl9oSQfdyVDdS9tYqsP92KShN6OB535Uz8rS6O3PMsqNXg95Pw3fMxz+r5+oe7phH3sq+Jv3waCdfOoO1wFdUvL0et1RBz3viQfTzVNloPlKLSa8l86Fp8jlaqXlyKz9EWNCLytTgp+MEz+D0+VGoVqT++GNOE7s/OAdzVNuq/2EniFVNJvm46rYerKH9pJSqdhrjze35NnoYmHDuKGPTA5UHLk66Zjq/VzcEfv9i+n1JvOpe42T1f/3BV26hdkkfKVVNIvf4sWgqqKXlhFSqthoQLQh+ELZNzqF+2m9izhhE5JJnWw9XULd+N4vXjdbS1jxq8LU52f+85FI8P1CoG3X0hlkl9e79ZNx3G2+wk6cKuX4unsQVdbPCZty4mCo+1JWT72pX5aCL1xM/s3VTZieo3FuJtdpEyd3Sv+xS/vB59vInYyVn92mZPajcU4W12kTZvZLftPM0u1l3zavt7d+TPziXhjI5MCVMGkTwrl4hUM60Vdg6/sokdv1rEtOeuRaXp+31GHlwoKOgJLq56DLTQ+RoXgBsnegwntDfixtnn7Uumk9enIrNo0SLmzp3Ltddey7p160hPT+euu+7i9ttv77KPy+XC5XK1P3Y4Or9gRVEw5qaReGNgHteYk4qrrBbbiq9DFhnF56fqmY9IuP5c9GkJXW67adM+HOv3knrf1Rgyk3Aeqab2tWVoY6O7LF7HhcKYm0byTecBEJGTiqukFuuyHV0WGUVRQKUi4/4r0EQFftmKx0vZ4x+S+uOLUBt0AKgjDOQ8cwf+Njcte45Q/eoK9MkxnabSQmWKGJJK2s3nAhCZm4KzpI76L/J6VWSsq/eiMRmxTAu+NmFbv5/GtfkM+sXlGAcl0lZcQ8XLq9DFm3per6IQOTSVjFsCo8moISm0ldRR+0Vel0Um7TvT8VibOfCzN1EUBV1sFAnnj6H6w61BZ9GaCAOjn/sB/jY3jl1HKXt5DYbUmE5Tad2pWbaX2DNzMMSbem7cS7XL8kk8byRqff8uaVYtzSd+ymAMCb3LVPLONmq/PMiEJ69D089t9qT8i/0kTB2EsYdM2kg9Z73yHXxtHqw7yzj03HoiUy3tU2mp53cU3uicBKJzE1j/3Tew7qogfnLfRqHif0Of3rHFxcU8//zz3H///fz6179m+/bt3HPPPej1em6++eaQfRYsWMCjjz7afYiYaAwZiUHL9OmJNG85ELK93+nCWVSJ80gVNa98EVioKKDAoWsfJeN3NxE1Noe6N1cSd+VMzDMDBzvDoGS89TasH6/vschoY6MxZAYXMENmAo7NB7voAdpYE7q46PYCA2DISAAlcKeaIS0eAJVahSE1cMdHRE4KrrJ66j7c2GOR0caaMGYFZzJmxmPf2HWmYxRFoWHlbuJmj0GtCx75Vb62hqRrziL2nMCZdUR2Eu5aOzUfbOqxyOjiTERkxQcti8iMp3HjoS77qA06Bt8/n0H3zMP7zd1sdUt3oY7Qo7V0XCdQqVUY0wJTsZG5ybSVNVD13pZeFxlnjR1bXgkjfnd5t+10sVF4GoNHLR5bC7q4ztcV7HvLaSu3Mvw3l/YqQ+dMDhp3ljLmkd71L33/a0rf2c74J67GlJvYc4d+aKt20LCjjIl/uLjHtiq1iqiMGADMQxNpLrFSvPDrTtdrjolMs6CzGGmtsPWryOgwoELV6ezajavTWfsxgbNx1wntnV22l0zhyXRMn4qM3+/njDPO4M9//jMAEydOJD8/nxdeeKHLIvPQQw9x//33tz92OBxkZga/2SJGZOKuDJ4H9FQ1oE0MfYeDOsJA9tPBd/vYlm2nde8R0h64Dl1S4MDkd3ngxPlltTow4uhB5MiMTplcFVZ0XWQK9MnEsXE/vjY3mgh9oE+lFdQqdPHmrjemKCghrkWcKGpUBq7yEJmSer4TpHlvKe6qRuIu6DwK87u8qNTB+0mlVoO/U9NOTKMycJZbg5Y5K6xB13y6otZq0CcG9ot13QFipg7plCM4qILi8fYc6hu1y/PRxUQSN7X7a0vRo9Kw5ZWSdlXHzSu2nSVEj+x8q3rtsj1EDU0mKrf3twofr2pZPvqYSOKm9Tw9WvrudkoWbmXcX67CPDylX9vrjYql+9HHRJAwrR9T3wr43V2/d521TXgczn7fCKBWqYlWYrBSSxKBaz+KomCllkxC/15jiMdKLVl0XHu1UoOF+JDtJVN4MrVn60vj1NRURo0aFbRs5MiRlJaWdtnHYDBgNpuDfk4Ue+lZtBWU0/DRV7irGnCs34Nt5Q5i53V8/qDurVVU/eNjIHAANGQlB/1oLFGo9FoMWcmojYEDvOmMYVg/+ormHQV4ahtp2nqAxs83Ez21+3lngPjLptF6qIK6DzbgqrJiW7eXxhU7ibu440BU8+Zqyp/+tP2xZdYYNNGRVP5jEc7SOlr2lVDz+ipizp/QPlVW9+EGmncV465uxFVWR/2nm7Gt3UvMOT1fRE66fAothyqpeX8jrkorjWv30bBsFwnzJ7e3qXz9S0qeXNSpr3XlbiKHpxGR3fngaJ4yhJr3NmHfXoirxoZt0yFqP92K5ayerzkkX3EmLQcrqXx3E87KRhq+3Efd0t0kX9Jxd0rZa2sp/tvn7Y+d5Vbq1+TjrLDSfKiSogWf0VpSR8Ytszpex3ubse88grPKRltpPdUfbaVhzT7iz+v5OhGA4leoXZFP0gWjO10LKPjrEo7++6v2x2lXTMb29REqPtxOa2kDpW9upLmgmtTLJgb187a4qP+qgOSLeveZplCZqpftI/nCUahPyHTgL0spfmV9++PSd7Zx5PVNjPjFhRhTLLisLbisLXjb3O1tPI42mgpraS355oaNskaaCmtxdXEtqatMFcsOkD53JGptcKa9f15BwUsb2x8Xv72d+q9Laa2001xi5eh7O6lccZC0CwLTr95WN4ee34BtXxVtVYHRUd7Di4lMjyHhzP5fS8piGJUcoVI5Sovi4CA78eEllWwA8pVtFCodnwXLZAgNVFOiFNCiOChS9uGgscuDrWQKXybo40hmxowZHDoUPA1SUFDAoEG9nyMPJWJIOum/vJ66t1fT8ME6dEmxJN06L+gCvbexCU99327VTP7hxdS/s4aal5bgc7QErsVcMJmEa0PfjRaUaWgaWQ9dS81/1lD33lfokmNI+eGFxJzbUQy8jc146juuMWki9GT/4UaqXlpG8c9fQRMdiWXmKJJuPLe9jd/poeqFpXgaHKj1WvTpCWT87AosZ/d8EThyWBqDf3M1VW+spfqdDeiTY0i/fU7QBXpPYzPuuuDrXr4WJ7ZNB8m4PfQHETN+dCFVb31F+b+W4bW3ooszkXDRRJJvOLvHTKbhqQz57VWUv76OyoUbMaTEkPWj84k/r+P1eKzNuGs7Mil+PzUfbaOkwopKoyF6fBYjn7oJw3G3e/udHkqeW4G7vgm1XosxM57BD1zafttzT2w7j+KqdZA8t3PxdtU2BV37MY9OZ9hDl1Dy+npKXltPRFosIx65sv0zMsfUrz0IKCTO7l2GEzXuLMFV20TqvM6F0lnbFDTqrvh8D4rHx75HFwe1G/T9aQy+eXogz6ZiDj2xvP25/X9a0qlNTxp2lOKsaSL94lGdnmurCc7ka/Ny4OkvcdY1ozZoMWXFMvY3F5J6XuBkRKVR01RcT+XyA3iaXRjio0g4M4shPzir39evAFJUmXgUF8Xsx4WTaCxMZCaGbz774aQVFR05Y1QJjFGmUkQ+heQTiYnxTD+ln/2QTL2nUnozd/SN7du3M336dB599FGuu+46tm3bxu23385LL73EjTfe2Kt1OBwOLBYLQ/7zIJrI8NyO2R9abc/TVd82nWYgZurFHNq3TD8g99PAy2TQ9H6q8dvim93zZ7HEwOJVPKzlM+x2e8iZqRP1abrszDPP5JNPPuGdd95hzJgx/PGPf+SZZ57pdYERQgjx/0ufx7CXXHIJl1xySc8NhRBC/L8n38IshBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcImPH/LtReGJDSgi9Kfrs13oh+A31CrVw/Ab/JVD7z9FKHxnO4InRjUAzHTwPvdGXYPvEybxg+c49L/AhnJCCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibKTICCGECBspMkIIIcJGiowQQoiwkSIjhBAibE7bF2Qeb9V1b9JW3dRpefYVYxh7/znd9q1YfZidj64geeZgpvz54vbl3lY3B17cQvWGYtx2J5GpZgZfM47sy8f0KtPSq9+mtbq50/Kcq0Yx8ednh+zjbnKx76VtVK47itvhJDIlmnH3TCd1ehYAB9/Mo3LdEZpKbGgMGuLGpjD2zqlED4rpVaZFV75LS4hMQ68ayRkPzOi0fPVdi6nNq+60PG16Juc8OReALX9cx5EvDgc9nzI1g9nPzOtVpg+u+ICWqpZOy0dcPYJpv5wWss++d/Zx6ONDtNS0YLAYyD4vm0l3TUJr0PZ7nd3x+/x8/dJeCpYeobXBSVRCBMMvzWHybWNQqVRd9qv4uoZNT+/AWmzHlBzJ5NvGMOLS3H5tf8uL+zj4RSktDU5MiUZGXZrNlB+O6nL7LXVtfPX0bmr2W7GVNTPhhqGc+8DEoDZ7Py7iwOISGorsACSNjGXGT8aSMia+F5kUNrywn/1Lyr7JFMGYy7KYfvuILjMdWl1B3vtHqC2w4XP7Scg1M+PHI8mZntzeZsPz+9n44sGgfnHZJm7/9MJeZVr3/CH2Li6nucFJdKKR8ZdncvYdw7rMVLqzgVXP7KfhSDMepw9LaiSTrx3EtJs6fk9/n7cSe2Vbp75nXJ/Nxb8Z12OurpQphZRQgBsnJiwMZyIWVVyX7WuUcorYh5MWIjAxlLEkqFL7vf3/lkwDosic/dK1KD5/++OmI1a23L+I1NlDuu3XWuVg/782Ejeu807Z99xG6neWM/HhC4hMiaZuexl7n16HMT6KlJmDe8x03itXofiV9sf2Yisb7ltCxuzQBxm/x8eG+5ZgiI1g6p8uICIxitbqJnQmQ3ub+l2V5Fw1mriRifh9Cvte3MaGny3hgrevQxuh6zHTha9eHpypqJEv711K5vmhX8/MBXPwezv2q9vuYun3PybzvOD2qdMymPrwrPbHGp2mxyzHXPrapfj9HduwFdlY8dMVDDp/UMj2xcuL2fGvHcx8eCaJYxNxlDrY8McNoIIp903p1zp7kvfGfvZ9eJjzHj2L2BwLdfutfPmHzehNOsbdMCJkH0dFM1/c9yWjrx7KnD/NoHxbNWv/tJXIhAiyzkrr0/a/fv0gez4sYu6jU4jLtVC738qKR7ajN+mY+J1hIft4PX4iYg1M+eEo8t4uCNmmfEcdw+dlkTo+Hq1ew9evH+Tju77i+x/OxZQU2W2mra8dYtcHR5j/h8kk5Jqp2m9j6e93YDDpOOO7of/dle2oZ/C0JM756SgM0Xr2fnaUj+7ZxPffmk3yiJj2dgm5Zq5/cWb7Y7Wm60J+vI2vHubr949y+Z8mkpQbTeU+G4t+l4fBpGPqjTkh++gitEy5YTBJw8zoI7SU5jWw5A970EVomHxNNgA/XDgr6N9NbWETb92xmVEX9u33eLxqpYwC9jCSSZiJo4zD5LGe6cpc9Cpjp/Y2pZ58tpLLGBJJpZpSdrOJqcocTCpLv3MM9EwwQIqMISYi6HHh2zuJTDcTP6HrN4Hi87PzjysZfusUGvZU4Wl2BT3fmF9N5rwRJExMB2DQZaMpWbQP24GaXhUZQ2xwpkP/ySMq3UzCxNBV/ujiQ7gdLs598XLU2sBBOio1OqjNzKfmBz0+4zfnsviSN2k8VEdiN6/1GOMJmfa/uRtTupmkLjIZLMFvrJKVxWgMWrJOKDJqvYaI+O4PSl1nCt7G3jf2Ep0RTcqklJDta/fUkjwumZy5gYNGdFo0ORfmUJdf1+919qRmTx3Z52QwaGbgvWBOM3F4+VFq9zV02WffR4eJTjMx/WeTAYgdbKF6Vx17Fh7sc5Gp2t1A7jnpDD470M+SFsWhZaXU5Fu77GNJi2ofuez77EjINhc9Fjyqm/O7MyhcU07ptlpGXZLdbaaK3VaGnJtK7qzAe8eSHsWBZWVU5Td22WfOL8cHPT7nnjEcXltF4bqqoCKj1qgwJXQ+qPWkfHcjw2enMGxWYGQUkx5J/tIKKrvJlDrSQurIjgNiTHokB1dXUbrT2l5kouIMQX02/ruQ2MxIBp3R84ivK6UUkM5g0lSBbYxQJlFPFZUcJZvOJy5lFBJPMtmq4QDkMoYGpZYyihjJpH7nGOiZYABek/F7fJSvLCDr4pHdTmUUvLEdQ2wEWZeMCvl87JgUqjcepa2uGUVRqN9ZTnOZjcQzs/qVqXRFIdnzh3eZqXLDUeLGJJH35AYWX/ImK7/3Pgff2Bk0QjuRp8UNgN7c93+QPo+Po8sLybmk66mEExV/fohBF+R0GjXV7qzi44vfYvH1H7D9rxtw2Z19znMsU/GyYoZeOrTLTEnjkqg/WE/dvkBRaapoonxTORkzMvq9zp4kj0ukYns1thIHAPUFjVTvriNretfFomZvHRlTg4ta5lmp1Oyp7/P2U8fHU7qthsaSwJRwXYGNyl31ZM84tdMSXqcPn1fBaO7576Gkj4+jZGsd1m8y1R6yUZ7XQM6M5B56dlD8Cu5WL0ZL8PYaS5t57oIveGH+Mj5/aDuOqtZerS9jfCxHttbRcDQwJVx9yE5ZXgNDZvY+U9UBO2W7Ghk0OXQB8Xn87FlSzoQrsvr9fvIrfpqwEUdS+zKVSkUcydgIfeJio4E4gl9HPMnYu2j/v5DpmAExkjle9fpivM0uMi8a2WWbhj2VlC45wKx/X99lmzH3zmLPE1+y6uo3UGnUqNQw7oHZ3Y6OulL51VE8zS4GXTy8yzYtlU3U7awk68IhzPjbRTSX29n15Ab8Pj+jfnBGp/aKX2H33zcRPy4FS07Xc6ZdqVhXgqfZzeD5Q3vVvmFfLfbiRqb+Ovh6Uuq0DDLOzcaUGk1zhYPdL3zN2p8t54KXL0Wt6ds5SOm6UtzNbobM73qaM2duDk6bk6V3LEVRFBSfwvCrhjPultBz471ZZ08m3TIaT4uHd675HLVahd+vMPWu8Qy7qOsRbWuDk8i44OIfEWfE3eLB6/SiNfb+n86Zt47E3eLljauWotao8PsUpt89lhEX92/6rysb/rEHU6KRrKk9H5Sn/WA4rhYvL1+xsj3TrJ+MZvT83p+EbXvjMJ5WLyMuTG9fljo2jov/MJm47Gia651sfOEAb/9gHT/4cA6GqO6nhGfeNhRXi5fnLl/Tnum8n45k7PzQJyDHe3rOClob3fh9fs65cziTrg69bw+uqcLZ5GHC5X0/2TzGgwsFBT3B7w89BlpwhOzjxokewwntjbjp3wndf0OmYwZckSldcoCkqYMwJkSFfN7b6ibvT6sY98DsTtNsxzv60R4a99dw5oKLiUyJpmFXJXuf/gpjQhSJZ2T2KdORxQdJnpZJRGLoTAAoCobYCCb9chYqjZrYEYm01bdyeOHukEUm78kNOIqtnPP85X3KckzR4kOkTssgsrtMx7f/vABLbizxo5OClg+6oOMaU8yQOGKGxPH5Ne9Tu7OKlDPTT1xNtw4vOkz6WelEJnY99Va1o4o9r+9h2i+nkTg6EUe5g21PbWP3v3cz/rbxndr3Zp09KVxZQsGyo8z50wzici3UH2pk41M7iEyMZMQloef6T6WClWUcXFrCRX+eRnyOmbpDNtY9uQtTYgSjLs0+JdvY/toBDi0v45qXzkVr6Pma2oEV5ez/ooxLF5xJYq6ZmkN2Vj8RKFJjL+u5+O3/ooyNLx7gqmfOIuq4Ypw7s2P0lzTMQtqYWJ6/eBkHV1Qw/srsbte5b3kl+UvKueovk0nMjabmkJ3lf80nOtHA+B6Kwi2vz8Dd6qNiTyOr/76fuMwoxlzcuTjlfVLKkBlJRCf1ffZA9M+AKjKt1Q7qdpRz5h+7vrOppcJOW3UT2x9a0r7s2EW9xbP/xey3bsSYEMWBl7dw5mMXkXxWNgDm3AQchfUUvburT0WmpbqJ2q8rOOvP3d8dY4yPRKVVozru7N88KAZnQyt+jw/1cRfT857cQPWmEs557jIik0y9ztKeqaqJmu2VzFwwp1ftvW0eSlcVMfb2yT22NaWbMcQYaS53QB+KTHNVM1Xbq5j9l9ndtst7MY/ci3IZdnnggnfskFi8bV42LdjEuFvHoVJ3TGH0dp092fyPPCbdPIqhc7MBiB8SS3NVC3mv7euyyETGG2m1Bp/RtVmd6KN0fRrFAKx/Zjdn3jKC4XMDB8qEoTE4qlvZ/tqBU1Jkdrx5kO2vHeTqF84hcVhMr/qsfTqfabcOY9S8wL+FxKEWHFWtbHn1UI9FZv+yMpb+YSdX/HUK2dOSum1rNOuJyzJhK+t8V+SJVj21jxm3DWXMRYH3XfIwM7aqNjb8u7DHIhObEdXep9nqYt3zhzoVGVtlK0e21HHd02f2mKU7OgyoUHU643fj6jSSOCYwQnCd0N7ZZfv/hUzHDKgiU/bFQQwxESR9UxhCMWXFcs7rNwQtO/jKVnytbkbfczYRSSZ8bh+K1w8nzrmqVUF3mfRGyZJDGGMjSDmr+zd5/NhkylYWoviV9gNlU5kdY3xke4FRFIVdT22k8qsjzHr2MqLSzH3KckzxkgIMsUbSpveuWJauOYLP4yd7Xs9TTq21LbjsTowJfRs5HF58GGOssctrK8f4nL6gQgK0P1YUBRUdz/V2nT3xOr1w4jY1KhSl6/dC8thESjdWBC0r21pF8riEfmzf13n7/XgvhvL16wfZ9uoBrnx2Fsmjej/t6uni96B0fQkRgP1Ly1j6yA4u+8uU9psGuuNu9WIrbyGqFzcCeJy+zv9k1d3/nkJR/ApeT+cXsuvTUqLiDAw9u/fXeEJRq9REKzFYqSWJQEFUFAUrtWQS+u7TGOKxUksWHdPbVmqw0P+bDwZ6pmMGTJFR/AplSw+QOW8Eam3wtYC8x1ZhTIhi5I/OQmPQYs4J3gnHbhM+tlyt0xA/IY0Dz29CY9ASmRxNw+4KypcfYvRPZtJbil+hZMkhsi4a1inT9j+uISIhijF3TgUg58rRFH20j93PbCT3mjE0l9s59GYeQ67t+FzOric3ULaykLP+MhddpA5nQ+s3+fVoDL37VSh+heIlhxl88dBOmTY/upaIxCgm3BV8plb8+SEyZg3qdLeZp9VD/r93kjl7MMb4CJrLHex6bhvRGWZSp/b+wK74FQoXF5I7P7dTpvWPrCcyMZLJdwdGURlnZ7B/4X7ihsWROCaRprIm8l7KI/PszKBrQN2ts6+yz85g56v5RKdEEZsTmC7b/fZBRlzW8Y9vy7N5tNS2cf4fpgMw+uqh5L9/iM1/38mIy3Op2F5D0apSLn7m3D5vf/CsNLb/+wDmlEjici3UHWwk760CRl2e3d5mwz/30FLbxtw/Tm1fVnsocFeVp9VLm81F7aFGNDo18TmBu6m2v36ALc/vY96fp2FOi6SlPvBZEF2kFn1k99c/hsxKYdMrBzGnRJCQa6bmkI3tbx1m3HGZ1v0jn6ZaJ5f8KTDdu/+LMpb87mvOf2AcqWPjaK4PnDXrDBoM0YHtrXlqL0NmpWBJjaSpzsmG5w+g0qjaR0zdGXZOCutfPow5NZKk3GiqD9rZ8p8iJlzRcYK3+u/7aapxcsWfA3c/bX/3SOA1DA7MCJTuaGDzG0VM+W7w9TbFr7D7szLGXZZ50u8ngCyGsZ/tmJVYLMRRymF8eEklG4B8ZRtGIhiiGgtAJkPYwTpKlAISSKGaMhw0MpKeZxf+mzPBACoydV+X0VbTTOb8zhf822qaOo9KejDp9xdy8KUt5P1xJW6Hk4iUaEbcPo1Bl4/u9Tpqt5fTWtNM9vzOF/xba5qD7k6JTDYx8+mL2fP3zay6+UMiEqIYcu0Yhn9vQnub4k/2A/DVTz4PWtfkX58bchuhVG+voLW6mZxLush0wtmpo8RG3e4azv175ylIlVqFrcjKkaWH8TS5iUiIJGVqOmPvmIxG3/vPylRuq6SluoWhl3a+CaG5pjnoHsbxt45HpVKR92IerXWtGGOMZM7MZOKdwR807G6dfTXzgTPY9sJuvvrLNtoaXUQlRDDqqiGccfvY9jat9U6aqzs+AGpON3HxM7PZ9NQO9rx7CFNSJOc+PLXPty8DzP7lRDb9K581C3bS2ugKXPe4Ooepd3TcGdlS78RRHXwX1sLvrGz//9oDjRxaWkp0aiS3LbkEgD0fFOHz+FnywKagflPvGMVZP+7+Q8dzHhzP+uf2s2LBLlqtLkyJEUy4ejAzftTx76+5zhl0Z9iuj47g9yqsXLCblQt2ty8fc2kW8/8YKERNNW18/tB22mxuImL1ZExM4KY3zyXyhNuIQ5n30FjWPnuQpY/tocXqIjrRyKRrBnHOjzve6811LuzVHR+sVPwKa/5+AFtFK2qtitiMKObcN5LJ12YHrbt4Sx32qjYmXtH/C/7HS1Fl4lFcFLMfF06isTCRmRi++TyKk9agUXmMKoExylSKyKeQfCIxMZ7pp/TzKAMxE4BK6etY9CQ5HA4sFgvzlt6OLqrnWy2/LXqN93RH6ESv9p3uCJ0Y1ANvP0VoPKc7QicG9UDMNPB+dwMx06bxA+e4NBB5FQ9r+Qy73Y7Z3POU/4D7nIwQQoj/HVJkhBBChI0UGSGEEGEjRUYIIUTYSJERQggRNlJkhBBChI0UGSGEEGEjRUYIIUTYSJERQggRNlJkhBBChI0UGSGEEGEjRUYIIUTYSJERQggRNqftq/6nxB7BaOr+b158m3SqgfiNxwPvm3yNqgGYSfZTr+hUA+8bjwfifppdPPAyPZYz4XRH6DcZyQghhAgbKTJCCCHCRoqMEEKIsJEiI4QQImykyAghhAgbKTJCCCHCRoqMEEKIsJEiI4QQImykyAghhAgbKTJCCCHCRoqMEEKIsJEiI4QQImxO2xdkHs/vU1j9r8PsWlxJU70Lc6KBSVdkMPtHuahUqh77l+xs5OVbt5I8xMRPP5rZvtzV4mXlPwvYv7qGZqubtBFmLnlwJBljY/qVccVzRexcXElTvRtzkoEzLk9jzo9zus3odftZ+XwROz+van9tc+7MZcpV6f3KsPTZI2z/vOabDHqmXpHK3DsHdZnhrYcOsO3T6k7LU3Ij+fXiqQCseKmEPSvrqCluRWdUM3iihct+nkvy4MheZfr82VK2LKrFUe/BkqRn+pVJzL8zs9v9svXzWpa/Uk5NiZOIaA1jzo7lmgcGY4oNfGnqzhX1LH2xnNrSNnxehaRBEVxwazpnXZ7UY56P/1nOpkUN2OvcxCbpmXlVIpffldZtnlVvVbPyrRrqK1zEpxm47MdpzLwyMWTbLYsb+Nf9hUw6P5b7nh/W4z4CaGv28d4zlWxbacfe4GHwqEhueTiDIeOiuuyzb2sTb/65nLLDTuJT9Vx9VwrnXh0f1MZa7eatJyrY9ZUDV5uflEEG7vrLIHLHdr3e4zMtfKaGrSvs2Bu8DB4VwW2/TWPouNC/d2uth9cXVFG4t5XqEjfzb07gtofTgto8/N0i9m1r6dR38rnRPPzK4B4ztTb7ePPpOjavaMLW4CN3lJEf/S6Z4eMiQrbfuNzBkrdtFB1w4nErDBpq4Hv3JDB5lqm9zc2zCqmt6Pyll5d8L5a7H03pRSY/rz7VwIblLTQ2+Bg62sBPfpfAiPHGkO33bm/jxccbKCty42xTSE7Xcul3LVx7W0x7G59P4Y1nrKz8tAlrnY+EZA1zrzZz009je3XM60qZUkgJBbhxYsLCcCZiUcV12b5GKaeIfThpIQITQxlLgiq139sPZUAUma/+XczW90q55rFxJA8xUb7PzkcP78Vo0jL9e9nd9m1zePjg17vJnRpPc4Mr6LmPf7eXmsJmrl0wHnOSgbzPK/n37du577OzsSSHfoN05ct/H2Hze2Xc8OcxgYz5dt5/eB8R0Vpmfm9Ql/3+c/9umhvcXPvH0SRkReKoc6H4lT5t+5hVr5Sw4d1KvrdgBClDoyjNb2Lhrw8SEa3lnJsyQva5+tdDuez+nPbHPp/C41dsZ8K8joN14XYbZ383nawx5kDReLqIf922i18vnoohUtNtpmUvl7P2nSpu/csw0oZEUpLfzOu/PkyEScv5308L2adwp4NXf1XAdQ/mMP68OBprXLz9SBH/+V0hd/5zJABRFi0X/ziDlJxINDoVe9daeePXBZjjdIw+O7bLPItfqmTNwlrueDyH9KGRHMlv5pWHiomM1nDh90MfUFYvrOH9J8v4wZ9yyBkbRfGeFl79bTFRFi0TzwveVl25i3ceL2H4GdHd7pcTvfCbEsoKnPzkiUHEJev46jMrf7z5ME8vHUVcir5T+9oyF3+5vYgLvpPAT5/MJn9zEy/8poSYJB0TzjYD0Gz38tsbChg91cSvXxmCOU5L1VEXUebe/bN+7tfllBY4ufdvmcQl6Vj3WSOPfL+YfywbTnxK529I97oVzHEarr07mc9frQu5zl/9axBeT8f7u6nRx88uLWD6RZZeZfr7Q1UcPeziF0+mE5+kZc1ndn59UykvLs8hIUSmvdtamTgjipt/kYgpWsPKj2w8ckcZT380mCGjA//G//5JNn5/R5+SAhe//n4pZ1/Uu9/hEw/WcqTAzUNPJZOQrGHlp0384qZKXluRRWJK531tjFRz5fct5IzQExGpZu92J0/9phZjhIpLvxvYD++80Mhnb9t58G/JDB6m59AeF4//soaoaDVX3xrTq1wnqlbKKGAPI5mEmTjKOEwe65muzEWv6ny8syn15LOVXMaQSCrVlLKbTUxV5mBS9e731Rt9KjI+n49HHnmEt956i+rqatLS0rjlllt4+OGHT6r6luxqZOTsZEacEzjwxaZHsueLKsr32nvs++kf9jF+fhoqtYoDa2ral3ucPvatquF7/5jE4DMClXzO3UM5uK6Wre+VcuE9vTsD7choY/R5SYw8J3B2G5ceQd4X1ZTudXTZ5+D6eoq/buShZWcTGaNr79dfR/IcjD0vgdHnJgAQnx7BziW1lHSTISJaS0R0x695z6o62hxepl3ZcbZy18vjg/rcuGAkv5mxkbJ9TQw5M6bbTEV5DiacH8+4cwP7OCHDyLYldRzd29Rln+I8B/HpxvYilJBhZNZ1KSx7pby9zfCpwds9//vpbPq0lsKdjm6LzOG8ZibNiWXC7ECbxAwDWxY3ULynucs+Gz+rZ/YNyUybHxglJGUZKd7bzOKXKoOKjN+n8MIvCrnqngwOfd1Eq6N3fx7C7fSzdbmNXz6fy6gpgQPbdfeksWONnRUL67nh/s7FeMU79SRl6Pn+Q4GTh4whERzc0cKS12rbi8xnL9UQn6rjrsez2/slZRp6lcnl9LN5uZ2HXshm9JTAWf8N96awfU0TyxY2cOP9nQtyUoaeH/42MAJf/YE15HqjY4IPKRsW2zAY1Uy/KKZXmTYsb+L3L2YwdkpgNPW9exPZurqZJW83cvPPO49if/zb4Jy3/CKJzaua2Lqmqb3IxMQHZ3r/hXpSs3SMndrzSN3l9PPVsmb+9FIq46cG/u3ecl88m1a3sugtO7f9Ir5Tn6GjDQwd3fF7SMnQsX55M3u3O9uLzL6dTmZcEMVZ50W1t1n9eRMHdzt7zNSVUgpIZzBpqmwARiiTqKeKSo6SzYhO7csoJJ5kslXDAchlDA1KLWUUMZJJ/c5xoj5dk3n88cd5/vnnefbZZzlw4ACPP/44f/3rX/nnP/95UiEGTYilaGsD9UcDw+yqgw6O7mxk2NkJ3fbb8Uk5jeWtnHfnkE7P+X0Kfp+C1hD8EnUGDSU7G/uRMYbCLQ3UfZOx8mATR/NsjOgm4/4va8kYbWbtq0f44+x1PH7xBj5/4hAeZ//+ds3giWYKtjRSe6QVgIqDzRTvtDHy7K6Hwyfa/FEVw86KJS6965Gcsynwd0ciLT2fg+RONHNws42aI20AlB1spnCngzGzui4EORPNNFa72LvOiqIoOOrd7Fhez9gu+iiKwoFvtjH0DHO3eYZONLF/s52qb/KUHmihYEcT42bFdNnH6/ajMwSfJOmNaor3tuD1dJwCf/psBeY4Hedc2/2U3Yl8XgW/j5DbOLgjdPE7nNfC2OnBZ9rjZ5opyOto//VqOzljonjqp8X8cOoefnnZAVa9V9+rTP5vMuk7ZVJx4OvO0139teqDRmZeEoMxsudDTft+0ge31RtV7NvR1qvt+f0Kbc1+oi2hR+Aet8KXnzm48NqYXp0Y+7yE3E8Go4q9X/cu0+F9LvJ3OBk/tePf3OhJRnZubKOs2A1A4X4X+dudTDm352nOUPyKnyZsxNHx3lSpVMSRjI2GkH1sNBBHctCyeJKxd9G+v/o0ktm0aROXX3458+fPByA7O5t33nmHbdu2nVSIWT/Mwdni5elLv0KlUaH4FC64ZxgTLun6ukV9SQvLnj7Ej96chkbb+Q1siNKSNT6GL18oIinHhCnewO4vKind3Uh8Vt9/kbN/OBhXs5cnLtnYnnHevUOYdEnX85cN5W0c3WlDZ1Bz898n0GJz88kfD9Bq83D9Y2P6nGHO7YNwNvt4bP7W9gzz78vhzEt7nlcGsNe6OLDeyvefGNVlG79f4eMFheRMspA2zNRlu2Pm3ZGBs8XH7y7e0Z7pivsGMfXSrg/EQyaZue2J4bz0s0N43H78XoVxs+P4zu9yg9q1Nnn51Tnb8LgV1Gr47u9zGTWj6+IFcMmP0mhr9vHgvD2oNSr8PoVrfpbB9Mu6PhkYOzOGdR/UMXlOHNmjIzmS38K6D+rweRSaG73EJOk59HUT6z6s5U+fje1xn5wowqRh2MQoPnqumvRcIzEJOjYstlKQ10LKoNAjD1u9B0tCcEG1JGhpa/bjdvrRG9XUlrlYubCO+T9I4sofp1C0t5XX/liGVqfi3Ks6n2GfmGn4xEjef7aWjFwjlgQt6z+3UZDXSsqgztN3/VGwu5XSAid3Lwg9lXuiSJOGkRMjeOe5erKG6IlJ0LLucwcH89pI7WWmj1620tbqZ9bFoU9GNq9sotnh44KrezcdFGlSM3qSkf/808qgIXpiEzSsWdTM/p1O0gd1/0cXrz3rCHarD58Xbr43jvk3dGzzu3fG0trs5+Y5pag1gUJ22y/iuOCKvk3DHuPBhYKCnuCTRz0GWgg90+HGiR7DCe2NuOn/aCqUPhWZ6dOn89JLL1FQUMCwYcPYvXs3GzZs4Kmnnuqyj8vlwuXquFbicHR+wXuXVbF7cSXXPT6e5CHRVB10sPjxA5iTDEy6vPMb1O9TeO+Xu5lz91ASsrsuGNcuGMdHv9vLX877ErVGRdpIM+MvSqNif8/TcCfas6yanUuq+O5fx5I8xETlwSYW/eUQ5kQDZ1wRuhgqCqCC7zw+lojowBvS+0s///nZbq767Uh0xu6vd5wob2ktXy+u4ftPjCJ1aBTlB5r5eMFhLN/cANCTrZ9WExGtZdz5XR9wP/hDAVWHW7j37Ym9yvT10nq2fl7LbX8bTtqQSMoOtvD+n4u/uQEgOWSfysJW3nusmEvuzmT0zFjstW4+fOIIbz9SxM2PDW1vZ4zS8NtPJuJq9XFgs40P/nKExAxjp6m04237wsrmzxu488khpA+NoPRAC2/9uZSYJD1nXxX6Qv7ld6djq/fwh+v2oSgKlngdM69MYMnLVajUKtqafbz4yyJ+8KccouP699dcf/JENs8/VMKPZ+aj1sDg0ZHMuCSWI/mt/VofgF+B3DGRfPfngfff4NGRlBa0sfKd+h6LDMC9f8vk2QfLuW3GAdQayBkdwcxLYija17sz9J6s/sDKoOFGho3veVrqmF88mcbTD1bxvemFqDUwZLSRcy41U5jf84Hvy0V23v5nHb9/MZOYhNCHtuUf2DjjHBPxyb3/PT70VDJ//WUN1047iloDw0YbOO9SEwX5rm77/eP9DNpa/OzPc/LyXxtIz9Zx/mWBIrJ2STOrPmvm4b8nkz1UT+F+F8/9sZ74ZC3zru5+tP7fpk9F5sEHH8ThcDBixAg0Gg0+n4/HHnuMG2+8scs+CxYs4NFHH+12vcuePMSsH+Yw/uLA3HTKsGgaq9pY+0pxyCLjavFSsc9O1UEHn/95PwCKX0FR4OHxy7j1pTPJnRpPfFYUd7w+DXerF2eLF3OikXd+nkdcRu/f9McsfrKA2bcNZsLFgYN56rBoGiudrHnlSJdFxpygx5JkaC8wAEk5USgK2GqcJA7q24jqs78VMeeHWUyeHzh4pw0z0VjpZOVLpT0WGUVR2PpRFWdeloxWH3rq4oM/FrBvXQP3/mcisSm9uzHioyeOMO/2DKbMDxzAM4ZHYa10svSl8i6LzNKXysidFM3c2zLa++gj1Txx414uv3cQMUmBs1a1WkXSoMA8eOZIE9XFbSx9qbzbIvPuX0u55I5Upl0SOMhmDo+kvtLN4hcruywyeqOa2xfkcOsfsnE0eIhJ1PPle7UYo9REx2kpO9hKfbmLp398qL2P8s0s2i0jt/L48vEkZ3W/v1IGGXh04TCcrT7amv3EJul4+t7iLq+hxCTosNcH3xFlr/cSYVKjNwZ+f7GJOjKGBG83I9fI1hW2brMckzrIwGPv5OJs9dPa7CMuScff7ikhJfPkRzLOVj8bFtu44b7ejbKPSRuk54l3BgVlWvDTclIyuy8Kaz+38/eHqvj1s+lMnBH631VNhYddG1t4+F+9G1kdkz5Ix9/fy6Ct1U9rs5/4JC2P/qSa1KzuM6V+kzlnhIHGeh9vPGNtLzIvLGjgOz+O4bxLo9vb1FR4Wfivxn4VGR0GVKg6jULcuDqNbo4JjFpcJ7R3dtm+v/pUZN5//33efvttFi5cyOjRo9m1axf33XcfaWlp3HzzzSH7PPTQQ9x///3tjx0OB5mZmUFt3E4fJ06PqtWqLu/CMpi03PPJzKBlW98tpWhbA999amKni+v6SC36SC1tdg+HN9Uz7/7hvX3J7TxtflTq4JBqTcfBJpTsibHsWVGDq8WLISqwq+tKWlGpIaaPd7cBuNt8nTKoNF3vp+MVbrdRV9rGtKs7FyNFUfjwT4fZs6qOn74xkfiM3t+c4A61X7r53R3ro9F27vNNmC77+f0KXnc3O5zAhdrOeQJn/T3R6tTEpQQO+luWNDBhdixqtYrU3Aj+vDh4muzDp8txtvj43sODiA9xd1hXjJEajJEamu1edq9v4nu/DH2CMnRiFHnrgkfcezY6GDaxYwpz+KQoKo8EH1Qqj7pITOtbkTBGqjFGqmm2e8lb38TNvzr5W1g3LbXhcSucc3lMv/ofy9Rk97FjfQs/+FXX069rF9l5+sEqHvx7OlNmdz3dtPJDG5Z4DVNm9zwNHEpEpJqIbzJt/6qVHz3Y82jxGL8CbnfHm9DV5u94z3+jp+NJd9QqNdFKDFZqSSLwnlIUBSu1ZJIbsk8M8VipJYuO2QMrNVjo/evqjT4VmQceeIAHH3yQG264AYCxY8dSUlLCggULuiwyBoMBg6H7O15GnpvE2peLiEmNCExFHXCw4c0jnHFlxxnH8qcP4ah1cu2C8ajVKlKGBr+ZouL06PTqoOUFG+tAgYTsKBpKW1n25EESB0cx+Yq+nckEMiay5qViYlONJA8xUXHAwVdvlHDmlR0HiS+ePoy91sl3FgQOSBPnp7DqxSLef3gfF96dS4vNzZK/FXDmlel9nioDGDM7gRUvlhCXaiBlaBTl+5v58vUypl3VcVBY9FQR9hoXNz0efN1l84dVDBpnDnmd5YM/FLBjSS0/fHYMxigNjrrA2Y0xWou+h5zjZsfxxQtlxKUaAtNlB5pZ+XoFM67uGMV8/ORRbLUufvB4oLiPnx3Hm78rZO07VYHpsjo37/25mOxxJmKSA++VpS+WMWiMicSsCLxuP3vXWdmyqI4bfx/6H8wxE2fHsOj5CuJT9aQPjaRkfwvLXqtm1jUdo5j3/1ZKY42HHz0RWFfVkTaK97SQO95Ei93LsteqKD/cxh2PB57XG9RkDAse/UaaA/vlxOVd2bXeAYpC2mAj1SUu/vN4Bek5hvbPvSz8WwXWGg8/eSIbgAu/k8Dyt+p46/FyZl+TQP6WJjYvbeTBlztucpl/axK/vf4QHz9fzfSLYyjc3crq9+q5449ZvcqU91UTigLpOQaqSly88XgVGTlGzrs6cCPJf56owlrj4d6/dazvyP7AVJqz1Y/D6uXI/ja0OhWZQ4NPmlZ9YGXqBWbMsX37lMSOr5pRFMjI0VNZ4ubff6klI1fPhdfEAPDaE7U0VHv5xZOBWY8vF9l58oFKfvzbZIZPiMBaF7hpxWBUERXd8d71+xVWfmhjzlUxnU5werJtXeBGiMwcPRVHPbywoJ6sXB0XXRsYcbz813rqqn38+qnAe/6TN20kp+nIyg2MZHZvc/L+y41cdXNM+zrPOj+Kt56zkpSmZfAwPYf3ufjg37b2dfZHFsPYz3bMSiwW4ijlMD68pJINQL6yDSMRDFEFjk+ZDGEH6yhRCkgghWrKcNDISCb3O0MofXoHtLa2olYHT7VoNBr8/n6W329c+utRrPxnAYv+tI9mqxtzooEp12YF3TXWVO/CVtW3C1LOJi8rnjmEvcZJpEXP6AuSufCeYWh0ff+igyt+M4Ll/yjk4z8eCGRMMjDt2gzm3Nlx0HPUBWc0RGm54+Uz+PTPB/j79VuIjNExfm4K8+7pfDdcb1zz8FCW/P0I7/+hgGarB3OSnhnXpTHvruzjMrhprAoeArc1edm9so6rHxpKKBverQTgnzfvClp+459HMPXK7s9qv/NwDp/9o5SFfyiiqSHwYcxZ16dyyV0do1V7nRtrZUem6Vcl42zx8eXbVXzw+BEio7WMmGbhql90vA5Xm5+FfyiisdqNzqgmZXAEt/11GGdeHHrK65ibfpvNR38v541Hj+Jo8BCbpGf2DUlccXfHyYCtzkPDcfvI74Olr1ZRfcSJRqti5FQzv3t3FIkZvbsduDdam3y887cKGqo9mGI0TJ0by3fuT0OrCxzwGms91Fe629snZRp48OVc3nisnC/eqCM+RcePHxvUfvsywJBxUfziuVwWPlnBR89WkZSh5+bfZHD25b2727C1ycd//lZNQ7WH6BgN0+ZauPHnKR2Z6rzUVQZP2d1/2eH2/y/Kb+OrRTYS03W8tG5k+/KKYicHvm7l96/3/OHLE7U0+Xntb7XUV3uJtqiZOc/MzT9PbM9krfVSW9WRaem7NnxeeO73NTz3+46PMMy5ysLPn+i4NTxvYwu1lV4uvLbvn/9oafLzyhMN1FV7ibZomDXPxG2/iGvP1FDro/a4/aT44eUnGqgu86DRqkjL0nHHrxK49Lsdv7t7Hknk1aca+Ptv62hsCHwY89LvWPj+Pb2/U/REKapMPIqLYvbjwkk0FiYyE8M3n5Fx0oqKjgIbo0pgjDKVIvIpJJ9ITIxn+in9jAyASlG6mZ84wS233MKqVat48cUXGT16NHl5edxxxx384Ac/4PHHH+/VOhwOBxaLhd9tmYPR1L+LqOGgU/XvtuJwMqg7f0r5dDOqBmAm2U+9olN5T3eETgbifhqI76fHciac7gjtvIqHtXyG3W7HbO555NWnkcw///lPfvvb33LXXXdRW1tLWloaP/rRj/jd737X78BCCCH+d/WpyERHR/PMM8/wzDPPhCmOEEKI/yXyLcxCCCHCRoqMEEKIsJEiI4QQImykyAghhAgbKTJCCCHCRoqMEEKIsJEiI4QQImykyAghhAgbKTJCCCHCRoqMEEKIsJEiI4QQImz69sceTqGZkYeJ+r/27jM8inLv4/g3u9mSnpBkQ0IICQGklyR0AUWUIkiTonD0gB4LASmKcrCAhdAUglQpwrEgoKKCCojwSFE41ASxcQQCSNiShGQ32dSdeV4kppC2QJZd9P5c177IZuee38zOzn/qPV6uU+O0LthDrcrt5h6h4AhaF+ytWnV9jwe5JbTXPoXPBahwvUwaN6etgqqlcrv+Zz052q7UJGdHKGW2SAQ0s//zrrOWFwRBEP5yRJERBEEQHEYUGUEQBMFhRJERBEEQHEYUGUEQBMFhRJERBEEQHEYUGUEQBMFhRJERBEEQHEYUGUEQBMFhRJERBEEQHEYUGUEQBMFhRJERBEEQHMZlikxOtkTia+kM636Ru5un8OTwVH5Jzrdr2FPH8ujZ5DyPDrhcZ23mZEu8+epV7u+eSrc7/mDcMAM/1TDssUN5xEZeqvRKM9puuE17c85/NZO+3fR0bHaZfww1cTq5oNrPv/TsVdo2ulzpNbSP4aZylJedLTFntpm7uhpp01TPqKHpnEourHGYbZ/lMqhvGm2b6ekea+Tfz2Vx9WrddRCanS3x2mwz3bsYad5Ez/Ah6SQn1ZzpvQ059LnbRPMmenr3MvHpJ7k3PP5Dh/N55J8ZtI81EBp+hR078yr8X5ZlFiy00C7GQFT0FUaOTufcudo7bV2/IYeOXYxERl9hwMA0Tp6s/ru/1g+H83n4n+m0itUTFJ7K1zsrTp8sy8xdaKZljJ7w6FSGjU7jbC2ZamuzNgcP5zHiUSNNYy7j0+Ai23daK2V6Y2EmTTr8QXD0JQaNMvD7uZq/xzeXZtFrgJ7QZpeIavsHo8ebOPN7zcOUd+BwLsMe0RPV4SLasPNs25FTKdOrC64S2f4i/o1T6D/ySq2ZVv/HTNw9fxDcLIXgZin0GpTKrr3WKj974HAuDzySSnj78yhDf+fzHdmVxj9rQToN2p3HK+os9428zP/O1bwcrPxPFu17X8S/6Vn8m56l+8BL7NhTcbrOphQybNwVQlqdw7/pWUY9ocdguv6OhF2myMybkcbRg7m8siiY93c2oFMPDyb/4womfc0TZTHbeP1ZE7HdPOqsTYDXX8jgvwfzeH1RPTbvCqFLDy1PjzVhrGXYrXvrs+tIWOmrXlDZLL7RNmsy+4VMDh/IZ87iAD79JoSuPTU8MSYNg77q3pJfmOXH3qP1S1/fHK6Pn78b995fef7dqBefN/P9gQIWJvrz5e4guvdQ88+HM9BXk+n40QKen5rFiFEefPVtEEtW+nMqqZCXXsiqs0wzpps5eKCARYn+7NwdRI+eav7xcAb6K1Vn+uA9KwvnZzNlqjff7Ali6jRvZr1k5tvdeVV+vjZWq0zLlioS3vCr8v/LV+Swbn0O8+f68dX2IDw93XhobAZ5eXK1bX6xLZfZr5l5dqo3u3YE0bKlOw+NzSAtzb6esq1WmdYtVSyoJtPSFdmsWZ/Dm3P92LU9GE9PBSPHpteYqbY27cnUpqWat+YEVPn/xSssrHrXQuK8evzf9hA8PRUMHWOsMdP3h/P516Pe7N0ewraPdBQWygx52EiO1b6NGKtVpk0rNYkJgVX+/63lWax418zSeYEc+DIML08FAx/Wk5dXffsNQt15Y2Y9Du1swA87GtCru5YHxxn4+bfKxcFqlWnXUsPShOAq21q4PJOl67JYMT+YQ1+F4+mpoP9DqTWOPzzUnYQXAzm6qyFHdjbk7u6eDB13hZ9+K97ozbFK9Bt9GTc3+PaTBhzYFk5BgczgR64gSdXP66q4ybJ8fUPcJLPZjJ+fH9+caoSXT/EKOD9P4t7WF5i3OoRuvT1LPzt+0GW69PLgiefqVdveK5OMhEeqUCph/zdW/vN1gxtqs3xX/3l5Ej1bXeatNUH06F228h0zUE/3uzyY8FzlH9CxQ3k8+ZCJ75Ib4ONXuXbfSJu1dfWflyfTtWUqS9YE0vMeben7o+43cuddWiZN961xeIC9u3KZ+mQGOw6GEBZee7frtXX1n5cn06GFgRVr/bm7XKahA9LoebeGqdN9Kg2z7p0cNr5vZc/Bsh/Re+tzWLMyhwNHdLVmqq2r/7xcmdYtDKxe50/vcpkGDUij110annu+cqbhQ9KJjVMx86WyefjGa2aSkwr5eGvVK5vyaurqPzT8Cu+uDaB/v+IssizTPtbIU0948fRT3gCYzRJtOxhIXOTPkMFVbwAMGJhG+3YqEuYULzuSJBPb0cj4cV5Mmuhd6fM1dfUfFJ7Ke2sDGNDPozRTq1gDE57wZmK5TC066Fm6KIBh1WSqqc2q1NTVv0+Di2xcF8Sgfp6lmZrGXGbSk75Mfqr4e8kyS0S3/4NViwN5cLBXrZkATOk2Gre9zI5PddzZRVvp/zV19a8NO8+WdToe6O9VmimqwyUmP+nH1Kf9SjNFtLvImsVBjBxS+XuoTmjLCyS8VI9xD1deHv/MpAz9nU/frc+Q/t6l4w9vn8K0p/x59umAkvHbCG2bwruJOkYPqdxWdYJanGP+y0E89rAv33xn5f4xqaT/2hjfkvV0ltlGYPPzbH23PkPH6cnKysLXt/Z1jEvsyRQVgc0Gak3FH4FG68apY9UfTvrqYwupFwsZP9m/ztoEsJUMq6li2KSjNQ/70AA993W8zISxRpLKjedm2qw+p1wyjRXf12rdOFnLNP5p62YrXe7U2FVg7FFUkqmq6Tx+tOpd+PYxKvRXbHy3Nx9Zlkkz2dj1dR697tZU+fnrzmSrOpNW68axajIVFMhVfj45qZDCwrrdLrt40YbRKNGjR9n0+voq6NBezbHj1ec79WNhhWEUCjd69NBw/IT9h8yqc6EkU69rMsXUkMnRUi7aMBgl7r6zrDD4+SqI66DhyHH7f0Nmc/HGWz3/m1/9nb9YhN5oo3ePipk6dtDwXzsz2WwyWz7PJscq0SXu+pb5P8d/T4+yDWk/XyWdO2g4fMy+vW6bTWbT5xZyrBJdY4unI79Axs0NNOqy34BWo0ChgMPHr29v3iWKjJe3gtYxGjYszcRkKMJmk9n1WTanT+RXOKdR3qXzhaycn8Eri3W4u1feQruRNssP2zZGzdq3zZgMNmw2ma8/y+HHEwWkmaoeNkinZOacABauCmLhqiBCQt15YrSRX04X3HCbtfHyVtAuRs3qpRaMJW1+udVK8okCTMbaDwUYDTa+/y6PYaM9a/2svby9FXSIVbHi7WwM+uJMX2zNJelEYbWZYjuqeXOJP1PjM2kVbaBbrAkfHwWz3qh9K8neTDGxKpYuKcv02dZcThwvxFhNpp49NWzelMuPpwqRZZlTyYVs3pRLYSFczajbh8kZTcXtBQdV/DkGByswmaoeV0aGhM1W/JkKwwQpqp2musikC1ZguMHl9WYZSn63uuCKexq6ICUGO6dZkmRemHWVLh01tGyudlimkGBl6f+qc/qXAgKbpOAbmcKkGelsWRdCi2bXl0lvLCodX3m6YHf0tXxPP/6Sj2/0WTwanWXCCyY+fTeUlncUj79LjBYvTwUz3kjDapXIsUpMfy0Nm41a272WSxQZgJcXBSPLMKTLJe6+I4WPN2TRZ5AXiioS2mwys6cYeWxqABGNVXXS5rVeWxyILEO/zql0bfYHmzZk0/cBT6o7ChIZrWL4GG9atFHTLlbDrIX1aBejYeM6yw23aY+ExABkGfp00hPXNJWNG7Lp/4AHCjva3PaJFR9fBb3vq7vzMQALF/shy9Cjk4nWTQy8t97KwMFa3KqZ77+fKWLObDPxk73Z+lUg694P4PIfNmbNNNdZpkWJxZm6dDRxR7SBDe9aGTRYW+2yMGmyN3fdpWHY4HSaRhl44rGrDH+weD5VNx2C65s28yq//FbIhhW1H/J0tGbRKo7sbsCBr8L41yM+PD7ZxC9nbt1e4h3Rak5825BDX4Xz1CO+jHum7JxQcJCSzavr8+XuHHybnCOg2TkysyRi2mjsWn+W5zLPPg1vpGL55lByrRI52RJBOndenmgkLKJyRGuOxK+nCvjfT+ksnpUOgCSBLEPPJudZ/F59Yrt5XFeb12rYyJ01W3TkWiWys2WCdUpmxKfRwI5h/9SqvbrCobC6aLOqnOu3BBdvbVhkgkOUTI/PIDyi5kfIyrLM51tyGDjMA5W6bh/LGxHpzocfB2K1SmRbZHQhSiZPyKRhNdO5ank2MXEqHn+q+Dh38xbg4eHGww9mMOU5b3QhN/843EaR7mz+pGKmiU9nElFNJq2HGwve8mPOPF/S0iR0OgUffZiLt7cbgYF1W2V0JXsjpjSJkHLTajJJtGpVdb569RQolVTa0zGVZK3LTPXLZTKaJNq0qn7DzpFCdMqSDLaKmdJstLUj07MvZrDz21x2bg2hQVjdrPrKZwoNKWvTYLLRrlXNeyVqtRvRUcW5Y9pqOJ6Uz7K1ZpYvCLJ7/PV17qXjKz9+o6mIdq1qPvSmVrvRJKo4Y2w7LceS83l7bSarFhafB73vLk/+dziStHQb7u7g76ckrO15Bve379zXn1xum8zDU0GQzh1zlo0j+3Pp0afyoRwvbwXv72zAhq/KXkPG+BDRWMWGrxrQsr3mutusKU+wTok5S+LQ/jzuutf+rf4zPxcQpKu8gryZNqvj6akgOKS4zR/253F3LXsnxw4XcDHFxtBR17fAXG8mXYiSrEyJg/vzuefeqhf6vDwZt2t2vZQls62uL0spn2n//nz63FfzD1GlciM0VIlS6cb2bbn0vkeDwp7dxOsQEaFEp1Nw8GDZBonFInEyqYC42KpXVGq1G23bqCoMI0kyBw/mExtz84eBGpVk2n9NphM1ZHK0yAglIToF3x0sOydgtkgcO5lPp9jqv0dZlnn2xQy278zlyy06Im9io+5aURHu1Ncp+b9rMh09mU/nGjJVRZKLz4XcyPj3Hiy7/NlskfjvyXy6xFW+qKHG8UtVjz8oUIm/X/E4jGk2+ve+vsPrLrMn8999VmQgorGKP1KKWD43g4hoFfePKL46YuWCDNL0Nl5eFIxC4UbjOyou6AGBStSaiu/X1mZNftiXCzI0ilZxKaWIJQmZREarGDSieKW8dH4mJoON1xYV73ZvXGchrKE70c3cyc+X+XxTDkd/yGf5+8F2t3kjvt+XhyxDZGN3Ll0oYlGCmchodwaPKF4QlszPwqC3kbC44tV0n23OoU0HFU3vqPut0gP78pFliGqs5GKKjfkJFhpHuzN8ZHHhe3OeBYPexsJEfwB699Hw0gtmNr5v5c6eakxGiTmvmmnbXkVI/ZvfiwHY910+yNA4WklKio25cyxER7szoiTTgnkW9Hobi0oynTtXRHJSIe07qMjKlFi3xsqZ34p4a/GNXZqbkyNxPqXsWPbFS0Wc/qkQf38F4Q2U/OsxLxLfziYqyp2Ihkrmv2khJERJv75lK4oRo9Lp30/L+HHFy8uTT3gxeWom7dqpaN9exZq1Vqy5MqNH2bfRkn1NpguXbPz4UyEB/m6EN3Dnqce8WPS2hcZR7jRqqGTumxbqhygZUC7T0FFp3N/Pg8dLMtXWpj2Zzp0vu9LzwsUiTp0uICBAQcMG7kx43JeFb2cR3didyIbuvL4wi9AQJQP7lq34Bo40MKi/J0+OK/6dT5t5lY8/z2HTu8H4eCtKz5X4+rjh4VH7dnZ2jsTZ82X3vaRcKiL5dD4B/koiwt2Z+Lgv85Zk0iTKncgIFa8uuEpoiJIH+pVl6jfyCoP7efH0+OLzjC8lZNC3twcNG7iTnS2z6bNs9v+Qx/aN9asc/4WUsnmScrGIpNP51PNXEBGuYvK//JmTeJUmUWqiItx5ZX4GYSFKhvQrW6/cO+IyQ/p7ET/eH4CZc9Lo19uLiHB3LNkSH2218N0Puez4KKx0mPWbzLRoqiY4UMmhY3lMfcXElCf8adr4+jYyXKbIZFskVi28iklfhK+fkl79PHnyuXq4l1yfmm60YUi9vvtJamuz5mFlli3IxKi34eun4J7+nkx4zg9VybBpRhv6y2U/psJCmcVzMjHpbWg93GjSXMWKD4Lp2E1rd5s3ItsisWS+GYPehp+fgj79PZg03be0TZNRQp9a8USdxSzx7Y48np99YyvM2ljMEm/Nz0avt+Hvp+C+AVqmTfcul8nGlXKZho3wJDtb5oMNVua9bsbXV0GX7mqe+7f9l1/WmskisXBecSY/fwX9+mt57vmyTEaDjdRy36dkg7Wrczh3tgiVyo0uXdV88nkg4Q1v7CeTnFzI8JEZpX/PftUCWBg5woMli/2Jn+CF1Soz/YUszGaJTh3VbPygHlpt2bKRcsFGRrmLDgY/4EF6usSCN7MxmWy0aqli4/v1CA62rzAnJRcyZGR66d8vv1p8Dmz0CA+WLQ5g0gRvcqwyz76QSZZZonNHNZs/CKyUKT3DZnebtTmZXMCAEcbSv//9aiYAD4/w4p3EQKZO8MFqlXjm+QyyzBJdO2rY+oGuQqbzF4oqZFr7XvHNi/0fLGsXYOWieowdVfslxseT8+n7oL707+dnF3+PY0d6szYxmGfj/cixysQ/n06mWaJbRw3bP6yPVltWwM6lFJFWLpMpzcZjz6ShNxbh56OgdQs12zfWp0+vyhsI147/2dlpADwy0of1S0KYHu9PjlXiqelGMs0Sd3bS8vXGsArjP5tSWGH8xnQb/3zGwBVjEX4+Stq2VLPjozDu7VVWGM+cLeDFhHQyMm1ENlQx85kApjzpjyX7NrxPxhWUv0/GVdR2n4wz1HafjDPcRI12mJruk3GWmu6TcZaa7pNxlpruk3EWV8pktkgENDt3e90nIwiCIPw1iSIjCIIgOIwoMoIgCILDiCIjCIIgOIwoMoIgCILDiCIjCIIgOIwoMoIgCILDiCIjCIIgOIwoMoIgCILDiCIjCIIgOIwoMoIgCILDiCIjCIIgOMwt753uz/44c7Jdq/PHIhfsjNIVO8h0xflUxdO3na5QdJBpl3wXXJ5UrvjduVAmc8m6296+lW95kbFYih9HPLTbpVs9akEQBKGOWCwW/Pxqf1zILe/qX5IkUlNT8fHxwe0mqrPZbKZhw4ZcunTJru6m/67EfLKPmE/2EfPJPn/l+STLMhaLhbCwMBSK2s+43PI9GYVCQXh4eJ215+vr+5f7Eh1BzCf7iPlkHzGf7PNXnU/27MH8SZz4FwRBEBxGFBlBEATBYW7bIqPRaJg1axYajcbZUVyamE/2EfPJPmI+2UfMpzK3/MS/IAiC8Pdx2+7JCIIgCK5PFBlBEATBYUSREQRBEBxGFBlBEATBYW7bIrN8+XIiIyPRarV07tyZI0eOODuSS5k7dy4dO3bEx8cHnU7HkCFD+O2335wdy6XNmzcPNzc3pkyZ4uwoLufy5cuMHTuWwMBAPDw8aNOmDceOHXN2LJdis9l4+eWXiYqKwsPDg+joaF5//XW7+/j6q7oti8zmzZuZNm0as2bN4sSJE7Rr146+fftiNBqdHc1l7Nu3j/j4eA4fPszu3bspLCzkvvvuIycnx9nRXNLRo0d55513aNu2rbOjuJyrV6/SvXt3VCoVO3bs4Oeff+att94iICDA2dFcyvz581m5ciXLli3jl19+Yf78+SxYsIClS5c6O5pT3ZaXMHfu3JmOHTuybNkyoLg/tIYNGzJp0iRmzJjh5HSuyWQyodPp2LdvHz179nR2HJeSnZ1NTEwMK1as4I033qB9+/YkJiY6O5bLmDFjBt9//z0HDhxwdhSXNnDgQEJCQli3bl3pe8OHD8fDw4MPPvjAicmc67bbkykoKOD48eP06dOn9D2FQkGfPn04dOiQE5O5tqysLADq1avn5CSuJz4+nvvvv7/CMiWU2bZtG3FxcYwYMQKdTkeHDh1Ys2aNs2O5nG7durFnzx7OnDkDQHJyMgcPHqR///5OTuZct7yDzJuVlpaGzWYjJCSkwvshISH8+uuvTkrl2iRJYsqUKXTv3p3WrVs7O45L2bRpEydOnODo0aPOjuKyzp07x8qVK5k2bRozZ87k6NGjPPPMM6jVah599FFnx3MZM2bMwGw207x5c5RKJTabjTlz5jBmzBhnR3Oq267ICNcvPj6e06dPc/DgQWdHcSmXLl1i8uTJ7N69G61W6+w4LkuSJOLi4khISACgQ4cOnD59mlWrVokiU86WLVv48MMP2bhxI61atSIpKYkpU6YQFhb2t55Pt12RCQoKQqlUYjAYKrxvMBioX7++k1K5rokTJ/Lll1+yf//+On3Ewl/B8ePHMRqNxMTElL5ns9nYv38/y5YtIz8/H6VS6cSEriE0NJSWLVtWeK9FixZ8+umnTkrkmqZPn86MGTMYPXo0AG3atOHChQvMnTv3b11kbrtzMmq1mtjYWPbs2VP6niRJ7Nmzh65duzoxmWuRZZmJEyfy2WefsXfvXqKiopwdyeXcc889/PjjjyQlJZW+4uLiGDNmDElJSaLAlOjevXuly9/PnDlDo0aNnJTINVmt1koP8VIqlUiS6z1i+la67fZkAKZNm8ajjz5KXFwcnTp1IjExkZycHMaNG+fsaC4jPj6ejRs38sUXX+Dj44NerweKHzbk4eHh5HSuwcfHp9I5Ki8vLwIDA8W5q3KmTp1Kt27dSEhIYOTIkRw5coTVq1ezevVqZ0dzKYMGDWLOnDlERETQqlUrTp48yaJFixg/fryzozmXfJtaunSpHBERIavVarlTp07y4cOHnR3JpQBVvtavX+/saC6tV69e8uTJk50dw+Vs375dbt26tazRaOTmzZvLq1evdnYkl2M2m+XJkyfLERERslarlRs3biy/+OKLcn5+vrOjOdVteZ+MIAiCcHu47c7JCIIgCLcPUWQEQRAEhxFFRhAEQXAYUWQEQRAEhxFFRhAEQXAYUWQEQRAEhxFFRhAEQXAYUWQEQRAEhxFFRhAEQXAYUWQEQRAEhxFFRhAEQXAYUWQEQRAEh/l/clQliDjY4mAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "# plot distance to top-left corner\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    dist_tensor[i, j] = np.around(np.sqrt(2)*np.sqrt(c), decimals=2)\n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a7a4fa16-89dc-4765-8801-850d45a181f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "# plot distance to top-left corner\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    dist_tensor[i, j] = np.round(np.sqrt(2)*np.sqrt(c)-1)\n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1b2b79fa-2732-4703-a720-6ab80da4fe9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zKJp37Rn3q+nCaTrJZdZQRzV+vKThZAozcRpZYfc3moepZTdeukgmjUlMI8coVJOa1DREMXkGk5DqpGjeIqZ89i4m/+tdOMZM5MCrT3K8tSHk/q6GAxxc8zTZU+Yx5bNLcJZW/HP/UTWpCYAG00U1OxnPRcylEgcZbGc9ftMbcn+72UwVmyiilHlUkkcRO9hAp+lWk5rUNEQxOWCcpReTXjIVuzOXpIxcCud+kriERLqb6kLuP7ZrPenFU8ib8VGSMvMpnHMNyTljaK76h5rUBMAhqhlDGUVGKWlGOuXMwoaNeg6G3O+ihmzyKTWmkGqkM8GowEEmLmrVpCY1DVFMDpgPMgMB2mq2E+jxk5o/LuSerqY60sZMDlpzjJ1CV+NBNamJgBmgg3ayyOtfMwyDLPJppyXkMe20kEV+0Fo2+bjD7FeTmtQ0UEw+BgNwvOUo+/76SwJ9vcQlJFK28GaSMgtC7u3t7iAhJS1oLSHFQe/xDjWpiR58mJgkkhS0noidLjwhj/HjJRH7afuT8BP67gY1qUlNA8XsgLFn5DLlc9+lz3+c9v07qXvjGSb9y21h/1CpSU0iElti9i6yOFs8dmcOKbnFFM1bRHJ2Ecd2rQ+5Nz7FQU93Z9BaT3cH8ckONamJBOwYGANumfnxDbjFd9KJW3K+0/Z7w+5Xk5rUNFDMDpgBTJNAX2/I/5SaN47OI/uC1jqOVJOaX6omNRFnxOEgg1aaPpBk0koTGWSHPCaD7KD9AK004gyzX01qUlOIroh9pwiq3/QSnfW1+DpaOd5ytP/rrEmzAKh7fSX1m17q35877cN4Du+lacdavG2NHH3nVY4fO0xOxQI1qQmAEiZTzwHqzYN0mR72so0+eimkFIAqczM15q7+/cVMpIUG6sxqukwPteZuPLRRzAQ1qUlNQxSTj8H0Hu+k7o1n6O32YEtMJim7kAmLbsExdgoA/s52MIz+/akFZZR+7Msc3fIyRzf/Hbszl7KFN5OcFbkXDKlp5DYBFBjF9Jg+9rMHH14cOJnJ5diNE3cHeOnG4FRXhpFDhTmPWqqooYoU0pjOfNIMp5rUpKYhMkzTNCP23YbA4/HgdDqZdvMD2BIjd1+fXLhyVrwd7QSRC0av2cNaVuF2u0lPTz/j3pi8i0xEREY+DRgREbGEBoyIiFhCA0ZERCyhASMiIpbQgBEREUtowIiIiCU0YERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELKEBIyIiloja2/V3FRrYkozBN4oMouu++dFOGGDcvRuinSASdTqDERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLaMCIiIglNGBERMQSGjAiImKJqL3Z5XC0vrmGltdeIuNDHyb3k58Ju6+j6l1aXn+F3vZWErJyyLn6WlInX6QmNcVsk8usoY5q/HhJw8kUZuI0ssLubzQPU8tuvHSRTBqTmEaOUagmNcVkU8yfwXiPHML9ztsk5p/5hz5+6AANf34a56y5lHzru6RNnUb9M0/iazyqJjXFZFOD6aKanYznIuZSiYMMtrMev+kNub/dbKaKTRRRyjwqyaOIHWyg03SrSU0x2XROA+anP/0phmFw5513RignWMDno+HPfyT/05/Hlpxyxr3tG9eTMrGczMs/RmJuPtlXXUNS4RjaN72lJjXFZNMhqhlDGUVGKWlGOuXMwoaNeg6G3O+ihmzyKTWmkGqkM8GowEEmLmrVpKaYbDrrAbNlyxaeeOIJLrnkkojFnK7ppb+QOnkqKRMmD7rX6zpIyvhJQWspE8vxug6qSU0x1xQwA3TQThZ5/WuGYZBFPu20hDymnRayyA9ayyYfd5j9alJTNJvgLAdMZ2cnN954I7/5zW/IzMyMWMwHdezajq/+MNmVi4a0v7ezg/g0R9CaLc1BX2eHmtQUc009+DAxSSQpaD0RO35C36Xhx0si9tP2J4XdryY1RbMJznLALF68mEWLFlFZWTnoXp/Ph8fjCboMpsfdxrG/P0/B575MXELC2SRGnJqGRk0ictKwn0X27LPPsm3bNrZs2TKk/cuWLeO+++4b1nX46g/T19XJoccfPrUYCHC8bj/tm//BxHt+hhEXPBvj0xz0nnbrsq+zA9tpt0LPlprUFMmmBOwYGANuLfrxDbgVetKJW5e+0/Z7w+5Xk5qi2QTDHDAul4s77riD1atXk5Q0tIi7776bJUuW9H/t8XgoLi4+4zEp4ydRsvh7QWuNzz9LYm4emZd/bMAfA4Ck4lKO799H5vwr+te6a6tJKi4dUudg1KSmSDbFGXE4zAxaaSKPMQCYpkkrTRQzIeQxGWTTShMlnHpsqJVGnGSrSU0x1wTDvIts69atNDU1MWvWLOLj44mPj2fdunX88pe/JD4+nr6+vgHH2O120tPTgy6DRtmTsOcXBl3iEhOxJadg/+fTSxv+spLm1S/2H5PxoQ/TVbOXtn+sxX+skZbXX8Fb7yJj3uXD+RHVpKbz0gRQwmTqOUC9eZAu08NettFHL4WUAlBlbqbG3NW/v5iJtNBAnVlNl+mh1tyNh7awf0DUpKZoNw3rDOaqq65i165dQWs333wz5eXlfP/738dms0UsbDC97jYwjP6vk0vKKPjcl2lZ8zItr71EQnYuRV+8uf8PiJrUFGtNBUYxPaaP/ezBhxcHTmZyOXbjxL0DXroxONWUYeRQYc6jlipqqCKFNKYznzTDqSY1xWSTYZqmeS7f4Morr2TGjBksX758SPs9Hg9Op5PxP3gQ2xDvZhMZacbduyHaCSKW6DV7WMsq3G73oPdIxfwr+UVEZGQ65/ciW7t2bQQyRERktNEZjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKWOOf3Ijtb/iI/ccmabzI6Vf92drQTBpj89XeinSAXGP2FFxERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLaMCIiIglNGBERMQSGjAiImKJqL3Z5Zm0r1qN54U1QWvxBbkUPfDdsMd0b9lJ+19X09vcRkJ+Nhmfu4bkS8rVpCY1DZPLrKGOavx4ScPJFGbiNLLC7m80D1PLbrx0kUwak5hGjlGoJjXF5oABSCjKJ+9/fv3UQlz4ky1fTR3NK54l47MLSb5kKl2b3uXYo/9JwT3fJnFsgZrUpKYhajBdVLOTqcwinSxc7GM765lvLiTRSBqwv91spopNTKCCXApp4BA72MA8s5I0w6mmC7wpdu8is8VhczpOXRypYbd2vPYPkiomk/6JK0goyiPjM1eTOK6IztffVpOa1DQMh6hmDGUUGaWkGemUMwsbNuo5GHK/ixqyyafUmEKqkc4EowIHmbioVZOaYvcMprexmSNLHoCEBOwTSsj47CeIz84IuddXW4fj6g8HrSVdPJnj23erSU1qGqKAGaCDdko5dbebYRhkmfm00xLymHZaGMfkoLVs8jlGvZou8CaI0TMY+/gSsr92Pbl3fY2sr1xHb3MrjT99nMBxX8j9fe5ObOlpQWu29DT6PJ1qUpOahqgHHyYmiQTfnZKIHT/ekMf48ZKI/bT9SWH3q+nCaYIYHTDJ06aQMucSEosLSa6YTN6dNxM4fpzud3aqSU1qEhkhYnLAnC4uJZmE/Fx6m0Kf6tmcA2/J9XkG3uJTk5rUFF4CdgyMAbdg/fgG3DI+6cQtXt9p+71h96vpwmmCETJgAl4fvU0t2JyOkP/dPmEc3vdqgta8e/ZhnzBOTWpS0xDFGXE4yKCVpv410zRppYkMskMek0F20H6AVhpxhtmvpgunCWJ0wLQ99xLe9/fT29x64umZv/pPiIsjZd50AJp/+xztf3mlf7+jcgHeqmo8r75Jz9Em2letxn/wCGkfu0xNalLTMJQwmXoOUG8epMv0sJdt9NFLIaUAVJmbqTF39e8vZiItNFBnVtNleqg1d+OhjWImqElNsfkssr42Ny1PPENfVzc2Ryr2iaXk//A2bI4Tdwf0tbZjGEb/fvvEceTccgPtz/837f/vVRLycsi9/SsRfX2AmtQ02psACoxiekwf+9mDDy8OnMzkcuz/fB2Fl24MTnVlGDlUmPOopYoaqkghjenMj9jrKNQ0spsM0zTNiH23IfB4PDidTsY++mPikiN3X5+InNnkr78T7QQZBXrNHtayCrfbTXp6+hn3xuRdZCIiMvJpwIiIiCU0YERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxRNTerj+vwI0tNXKf/SwiZ+b++8RoJwzg/GTN4JtkxNIZjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLRO3NLgfjb+7A9fu1uN+pJeDrJakok7K7Pknq5MKwx3h21uFa8TrH65pJzHVQ9MX55Hz8EjWpSU0juAnAZdZQRzV+vKThZAozcRpZYfc3moepZTdeukgmjUlMI8cI/zOoyZqmmBwwvR1e3vvuf5I+fRyT7/88Cc4UvEfasKUlhT3G19DOvnv+TO6iGYz/X5/C824dB5a/TEJWGs5Lx6tJTWoagU0ADaaLanYylVmkk4WLfWxnPfPNhSQaA9vazWaq2MQEKsilkAYOsYMNzDMrSTOcajqPTcMeMEeOHOH73/8+L7/8Mt3d3UycOJEnn3yS2bNnRyQI4Oh/bSQxN52yJYv61+wFGWc8puml7dgLnJTcchUAySU5dO4+TMPzWyLyD11NalLT+W8COEQ1YyijyCgFoNycRTNHqecgpZQP2O+ihmzyKTWmADCBClrMJlzUMpVZajqPTcMaMG1tbSxYsICPfvSjvPzyy+Tm5rJv3z4yMzMjEnNS+8Z9OC8to+aB5+nY5SIxO428a2eRe82MsMd07j1C+ozSoLX0S8twPbFGTWpS0whtCpgBOmgP+gNpGAZZZj7ttIQ8pp0WxjE5aC2bfI5Rr6bz2ATDHDAPPfQQxcXFPPnkk/1rZWVlEYs5ydfQTtNL2yn417kUfuEyuqobqHv8NYx4GzkfnxbymJ62LuIzU4PWEjJS6ev2EfD1EGdPUJOa1DTCmnrwYWKSSPBdPInY6cIT8hg/XhKxn7Y/CT+R+YBDNQ3dsAbMCy+8wMKFC7n++utZt24dY8aM4bbbbuOWW24Je4zP58Pn8/V/7fGE/mGDmCYpkwoZ+9UrAEidWMDxumM0/X172H/ollOTmtQkMizDepry/v37eeyxx5g0aRKvvvoq3/rWt/jOd77DU089FfaYZcuW4XQ6+y/FxcWDXk9CVhrJJdlBa8nF2fiPhR9OCZmp9LZ1Ba31tHdhS7Gf860oNalJTVFqwo6BMeBWtR/fgFvrJ524Fe47bb837H41WdMEwxwwgUCAWbNm8eCDDzJz5kxuvfVWbrnlFh5//PGwx9x999243e7+i8vlGvR60i4ai/dwa9Ca90griXnhn9mQVj4Gz466oDXP9oOkTi0a9PqGQk1qUtP5b4oz4nCQQStN/WumadJKExlkhzwmg+yg/QCtNOIMs19N1jTBMAdMYWEhF110UdDa1KlTOXToUNhj7HY76enpQZfB5F83h6699dQ/uwFvfRstb+zm2Ms7yL/21DMbXE+uZf9//K3/67xFM/Edbcf1uzc47mqh6cVttL75HgWfmTOcH1FNalJTDDUBlDCZeg5Qbx6ky/Swl2300UshpQBUmZupMXf17y9mIi00UGdW02V6qDV346GNYiao6Tw3GaZpmkPd/KUvfQmXy8X69ev71+666y42bdrEhg0bhvQ9PB4PTqeTWX++C1uqPey+9k01HP7DOrxHWrEXZFDwmTlBz2bZ//MX8Te6Kf/Zjae+9846XE+s4fihFhJzHBR9KbIv+FKTmtQU2SbnJ2uGtO/kCwh9eHHgZAozcBonbmm/Y64lmVQuNk4NtRMvIKziON2kWPyixgutqdfsYS2rcLvdg54wDGvAbNmyhfnz53Pffffx+c9/ns2bN3PLLbewYsUKbrzxxsG/AUMfMCIy+g11wEjsGM6AGdZdZHPmzOH555/nmWeeoaKigvvvv5/ly5cPebiIiMiFY9iv5L/22mu59tprrWgREZFRRO+mLCIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLaMCIiIglhv1eZJEyJ+8QiWnn/ol3IjKCbY3an6Cw3ru0N9oJo4bOYERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYIvbeaQ74w6IX6DjaPWB92vUTufLu2SGP2bf6EBsf20VHfRcZJQ7mf2c6pZcXqUlNalJTRJtOcpk11FGNHy9pOJnCTJxGVtj9jeZhatmNly6SSWMS08gxCkd1U0wOmC88fTWBPrP/65ZaN6u+tZaJHy8Ouf/ojmZe/cHbzL/9Eko/XET1K3W8tOQtblh5NdkTM9SkJjWpKWJNAA2mi2p2MpVZpJOFi31sZz3zzYUkGkkD9rebzVSxiQlUkEshDRxiBxuYZ1aSZjhHbVNM3kWWnJlEak5y/+Xgm/U4x6Yx5tK8kPvfXfk+4y4rZNZNU8ka7+RDt11CbnkmO5/bpyY1qUlNEW0COEQ1YyijyCglzUinnFnYsFHPwZD7XdSQTT6lxhRSjXQmGBU4yMRF7ahuiskB80F9PX28//JBpn66DMMwQu5p2NVC8bz8oLWSywo4urNFTWpSk5oi2hQwA3TQThanhpxhGGSRTzuhr6edFrII7somH3eY/aOhCUbAgNn/xhF8HT1M/ZfxYfd0N3tJyQ4+BUzJTqK75bia1KQmNUW0qQcfJiaJBF9PInb8eEMe48dLIvbT9ieF3T8ammAEDJg9f93PuPmFpOUmRzuln5qGRk1Do6ahicUmObOYHjCe+i5cmxu5+DPhb7EApOQk0d0SPHW7W7ykZEf+H6Ka1KSmC7spATsGxoBb+n58A84gTjpxZuA7bb837P7R0AQxPmDee2E/yVn2QZ9iWDAtG9fmxqA116YGCi/JVpOa1KSmiDbFGXE4yKCVpv410zRppYkMQl9PBtlB+wFaacQZZv9oaIIYHjBmwOS9Fw5Qfm0ZcfHBmf/9o41seGRH/9czvjSFQ28fZdt/7qX1gIdNj++iaU8bl3xhkprUpCY1RbyphMnUc4B68yBdpoe9bKOPXgopBaDK3EyNuat/fzETaaGBOrOaLtNDrbkbD20UM2FUN8Xk62DgxK2OjoZuLvp02YD/1tnQhfGBf2eF03O4+oHL2PjrXbz96E4yShwsevjyiD7vXU1qUpOaTiowiukxfexnDz68OHAyk8ux//P1Jl66MTj1TLcMI4cKcx61VFFDFSmkMZ35EXu9Saw2GaZpmoNvixyPx4PT6eQbb36WxLSE83nVIiKDeu/S3mgnxLRes4e1rMLtdpOenn7GvTF7F5mIiIxsGjAiImIJDRgREbGEBoyIiFhCA0ZERCyhASMiIpbQgBEREUtowIiIiCU0YERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELBG1t+uvTN9NisMWrasXEQnpEzXRLhjoFxOnRjvhrOgMRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLaMCIiIglovZml2fS12ey8v808cYqN23HesnKj6fyXzO44fZcDMMIe9zOjV389sEG6vb5yC1I4AuLc/j45zLVpCY1qWlUN53kMmuooxo/XtJwMoWZOI2ssPsbzcPUshsvXSSTxiSmkWMURqwnJgfMn59o5u8r27jrf49h3CQ7+3YdZ/n360l12PiXr2aHPKbB5efHX6/jk1/K4n8+PJYdGzr55Q/qycpL4NKPpKlJTWpS06htAmgwXVSzk6nMIp0sXOxjO+uZby4k0UgasL/dbKaKTUygglwKaeAQO9jAPLOSNMMZkaZhDZi+vj5+/OMf8/TTT9PQ0EBRURFf/epX+fd///czTu7hem9bN/MqHcz9qAOA/LGJrPubm/d3Hg97zN9XtlIwNpGv/6AAgJKJdva8081ff98Skf+BalKTmtQUq00Ah6hmDGUUGaUAlJuzaOYo9RyklPIB+13UkE0+pcYUACZQQYvZhItapjIrIk3DegzmoYce4rHHHuPRRx/lvffe46GHHuJnP/sZjzzySERiTpo6K4UdG7o4csAHwP73vOx5p5vZV4T/H7F3+3FmLEgNWpv1kTT2bu9Wk5rUpKZR3RQwA3TQThZ5/WuGYZBFPu20hDymnRayyA9ayyYfd5j9Z2NYZzAbNmzg05/+NIsWLQKgtLSUZ555hs2bN0csCOD6b+bQ3RngGx+vIc4GgT74t+/m8dFPZ4Q9pu1YLxk5wT9ORnY83Z0BfN4A9qRzez6DmtSkJjXFalMPPkxMEgm+KywRO114Qh7jx0si9tP2J+HHe04tHzSsATN//nxWrFhBdXU1kydPZseOHbz11ls8/PDDYY/x+Xz4fL7+rz2e0D/sB61/ycPaVe187xdjGTfZzv49Xlb8pIGsvAQqP5sxnOSIUZOa1KSmWG2KVcMaMEuXLsXj8VBeXo7NZqOvr48HHniAG2+8Mewxy5Yt47777htW1O9/2sD138zhik+deKCpdEoSTUd6+K/Hj4X9H5iZG097c2/QWntLLylpced860BNalKTmmK5KQE7BsaAsw8/vgFnNSedOFvxnbbfG3b/2RjWT/anP/2JP/7xj6xcuZJt27bx1FNP8R//8R889dRTYY+5++67cbvd/ReXyzXo9fi8JkZc8JMG4mwQCIQ/pnxmMu9u6Apa2/5WF+UzUwa9vqFQk5rUpKZYbYoz4nCQQStN/WumadJKExmEfmZbBtlB+wFaacQZZv9ZdQ1n8/e+9z2WLl3KDTfcwLRp0/jKV77CXXfdxbJly8IeY7fbSU9PD7oMZu7HHDz362NsfqODxsN+Nrzq4fnft3DZ1Y7+PX/43438/LuH+7/+5JeyaHD5+f1PG3DV+njx6VbW/93NdV+LzC9LTWpSk5pitQmghMnUc4B68yBdpoe9bKOPXgopBaDK3EyNuat/fzETaaGBOrOaLtNDrbkbD20UMyFiTcO6i6y7u5u4uOCZZLPZCJxpdJ+Fb95bwNO/aOLX9xzF3XLihUzX3JDJF7+d27+ntamXY0d7+r8uKE7kx78dx28eaGDVU63kFMTznQeLIvYUQDWpSU1qitUmgAKjmB7Tx3724MOLAyczuRz7P18D46Ubg1NnXhlGDhXmPGqpooYqUkhjOvMj9hoYAMM0TXOom7/61a/y2muv8cQTT3DxxRezfft2br31Vr72ta/x0EMPDel7eDwenE4n//VuOSkO21mHi4hcKH4xcWq0E/r1mj2sZRVut3vQe6SGdQbzyCOP8KMf/YjbbruNpqYmioqK+MY3vsE999xzTsEiIjL6DGvAOBwOli9fzvLlyy3KERGR0ULvpiwiIpbQgBEREUtowIiIiCU0YERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJYb1XmSRVJniJz1F801EZDCfqH832gn9PB0BMicPba/+wouIiCU0YERExBIaMCIiYgkNGBERsYQGjIiIWEIDRkRELKEBIyIiltCAERERS2jAiIiIJTRgRETEEhowIiJiCQ0YERGxRMwOmI7OAHf96Bhlsw+SWlbL5Z86zJZ3vWc8Zu2GbmZ/3EXyuBomX1bHH57zqElNalKTmqLUFLMD5pbvNvHam8d56pF8drxezMevSObqz9dz5GhvyP0HDvXwqS8f5coFyWxbXcIdtzi59btNvPpGl5rUpCY1qSkKTYZpmmbEvtsQeDwenE4nbdXjSXeEnm/HjwdwTtrP838oZFFlav/6nKtdfOJjKdy/NHvAMUt/0szfX+tm59qS/rUvfrOBdneAl58pOuduNalJTWpS08m369+P2+0mPT39jF0xeQbT2wd9fZBkN4LWk5MM/rH5eMhjNr7j5aoPJwetXX1lChu3nvkUUU1qUpOa1BT5JojRAeNIi+Oy2Uk88ItW6ht66eszefrPHby91cvRpr6QxzQc6yM/1xa0lp9rw9MR4PjxgJrUpCY1qek8NkGMDhiApx7JxzSheOZBksfV8ujv2rnhujTijMGPVZOa1KQmNUW/KWofmTyYCaUJvPH8WLq6A3g6AhTmx3PDNxooG5cQcn9Bro3GY8GTuvFYH+mOOJKTIzNH1aQmNalJTUMXs2cwJ6WmxFGYH09bex//vbabf1mYGnLfh2Yn8fpbwfc1vvZmNx+6NElNalKTmtQUhaaYHTCvvtHFK693ceBQD6vXdXPV545QPjGBm2848ayFHzzQzE3fbuzf/41/c7K/rofv39/M3n1+HvuDm/96oZM7b3WqSU1qUpOaotAUs3eRuTsC/PDBFg4f7SUrw8a/LkrjJ0uzSEg4cYfi0aY+XEd6+veXlSTwt6cL+e69zfzyt+2MLYxnxc/zWPjR0NNbTWpSk5rUZG1TTL4ORkREYtOIfx2MiIiMfBowIiJiCQ0YERGxhAaMiIhYQgNGREQsoQEjIiKW0IARERFLaMCIiIglNGBERMQSGjAiImIJDRgREbGEBoyIiFjivL+b8sn31vR0RuYjOUVE5Pw5+bd7KO+TfN4HTEdHBwDjZh0831ctIiIR0tHRgdN55s+OOe9v1x8IBKivr8fhcGAYZ/9h0R6Ph+LiYlwu16BvGX0h0+9paPR7Ghr9noZmNP+eTNOko6ODoqIi4uLO/CjLeT+DiYuLY+zYsRH7funp6aPuf6AV9HsaGv2ehka/p6EZrb+nwc5cTtKD/CIiYgkNGBERscSIHTB2u517770Xu90e7ZSYpt/T0Oj3NDT6PQ2Nfk8nnPcH+UVE5MIwYs9gREQktmnAiIiIJTRgRETEEhowIiJiiRE7YH71q19RWlpKUlIS8+bNY/PmzdFOiinLli1jzpw5OBwO8vLyuO6663j//fejnRXTfvrTn2IYBnfeeWe0U2LOkSNH+PKXv0x2djbJyclMmzaNd955J9pZMaWvr48f/ehHlJWVkZyczIQJE7j//vuH9J5do9WIHDDPPfccS5Ys4d5772Xbtm1Mnz6dhQsX0tTUFO20mLFu3ToWL17Mxo0bWb16NT09PVx99dV0dXVFOy0mbdmyhSeeeIJLLrkk2ikxp62tjQULFpCQkMDLL7/Mnj17+PnPf05mZma002LKQw89xGOPPcajjz7Ke++9x0MPPcTPfvYzHnnkkWinRc2IfJryvHnzmDNnDo8++ihw4v3NiouL+fa3v83SpUujXBebjh07Rl5eHuvWreMjH/lItHNiSmdnJ7NmzeLXv/41P/nJT5gxYwbLly+PdlbMWLp0Kf/4xz9Yv359tFNi2rXXXkt+fj6/+93v+tc++9nPkpyczNNPPx3FsugZcWcwfr+frVu3UllZ2b8WFxdHZWUlb7/9dhTLYpvb7QYgKysryiWxZ/HixSxatCjo35Sc8sILLzB79myuv/568vLymDlzJr/5zW+inRVz5s+fz5o1a6iurgZgx44dvPXWW1xzzTVRLoue8/5ml+equbmZvr4+8vPzg9bz8/PZu3dvlKpiWyAQ4M4772TBggVUVFREOyemPPvss2zbto0tW7ZEOyVm7d+/n8cee4wlS5bwgx/8gC1btvCd73yHxMREbrrppmjnxYylS5fi8XgoLy/HZrPR19fHAw88wI033hjttKgZcQNGhm/x4sVUVVXx1ltvRTslprhcLu644w5Wr15NUlJStHNiViAQYPbs2Tz44IMAzJw5k6qqKh5//HENmA/405/+xB//+EdWrlzJxRdfzLvvvsudd95JUVHRBft7GnEDJicnB5vNRmNjY9B6Y2MjBQUFUaqKXbfffjsvvvgib775ZkQ/JmE02Lp1K01NTcyaNat/ra+vjzfffJNHH30Un8+HzWaLYmFsKCws5KKLLgpamzp1Kn/5y1+iVBSbvve977F06VJuuOEGAKZNm0ZdXR3Lli27YAfMiHsMJjExkUsvvZQ1a9b0rwUCAdasWcNll10WxbLYYpomt99+O88//zyvv/46ZWVl0U6KOVdddRW7du3i3Xff7b/Mnj2bG2+8kXfffVfD5Z8WLFgw4Cnu1dXVjBs3LkpFsam7u3vAB3DZbDYCgQv34+FH3BkMwJIlS7jpppuYPXs2c+fOZfny5XR1dXHzzTdHOy1mLF68mJUrV7Jq1SocDgcNDQ3AiQ8KSk5OjnJdbHA4HAMek0pNTSU7O1uPVX3AXXfdxfz583nwwQf5/Oc/z+bNm1mxYgUrVqyIdlpM+dSnPsUDDzxASUkJF198Mdu3b+fhhx/ma1/7WrTTosccoR555BGzpKTETExMNOfOnWtu3Lgx2kkxBQh5efLJJ6OdFtOuuOIK84477oh2Rsz529/+ZlZUVJh2u90sLy83V6xYEe2kmOPxeMw77rjDLCkpMZOSkszx48ebP/zhD02fzxfttKgZka+DERGR2DfiHoMREZGRQQNGREQsoQEjIiKW0IARERFLaMCIiIglNGBERMQSGjAiImIJDRgREbGEBoyIiFhCA0ZERCyhASMiIpbQgBEREUv8f1ffqno4AP6BAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "# plot distance to top-left corner\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    dist_tensor[i, j] = np.round(np.sqrt(2)*np.sqrt(c+1)-1)\n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9ab17858-ceb4-4aac-a24c-4cdd8f2f3883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "\n",
    "# plot distance to top-left corner\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    my_i = np.round(np.sqrt(2)*np.sqrt(c))\n",
    "    my_i = np.where(my_i*(my_i+1)/2 == c, my_i, my_i-1)\n",
    "    dist_tensor[i, j] = my_i\n",
    "    \n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "73b1212b-56b8-4c1e-b4ee-23e145adecf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 255\n",
    "\n",
    "# plot distance to top-left corner\n",
    "dist_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    my_i = np.round(np.sqrt(2)*np.sqrt(c)).astype(np.uint8)\n",
    "    my_i = np.where(my_i**2 - c == c - my_i, my_i, my_i-1)\n",
    "    my_j = (((c - my_i) - (my_i**2 - c))//2).astype(np.uint32)\n",
    "    assert my_i == i, (my_i, i)\n",
    "    assert my_j == j, (my_j, j)\n",
    "    dist_tensor[i, j] = my_i\n",
    "    \n",
    "\n",
    "plot2D(dist_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19d718d2-d7d0-4a2e-88a1-d9da6272a917",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2858194/1492026618.py:9: RuntimeWarning: divide by zero encountered in remainder\n",
      "  i = i + np.where(i%2==0, val%(i+1)==0, val%i==0).astype(np.uint32) - 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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pa0dxeTpREJO63cc5qcDXHK1CyR+OiA/K2fojCkKspDh0P5riVTgmZEMJMYGIgovcSYqCRnOsioYfjoYaEaF1KETkR2z3kTSaoxWoP8hFxP/u5g2/REFC7kpKB60oDv+ORpuK+km5UIxS/31FRN0kd5KioNQco8BRMBYGi0XrUIjIx6T+c5SPjw9ezTEK1Ik5iFi7i0/4JQpgcldSOmg/cWg3Gm0G1E8eylV/RAFM7iRFQa85RoWjYDQMkVatQyEiH5C63ef5q5qCWnOsCmViDiyrd7L1RxRgpE5SAlyCTh0abSrc1w6F9c3P+eBEogAidZJiJUVna45RgZtGI2pNBVynTmkdDhH1Ac5JUeBQgOY4FXX5WdyUlihASF1JcccJ6kqjTYX7xhGIemsbH5xIJDmpkxTbfXQ+zbEqlBtHIWo1W39EMmO7jwJWU7yKU1dnQQ0N1ToUIuohVlIU0JpsKtw/vgTRb30Bd1OT1uEQkZekTlKck6LuaI5VUHfDCLb+iCTEdh8FhcYEFScnZ0Exm7UOhYi8IHUlxXYfeaPJpsJ9y2jEvL2DO1MQSULqJMV2H3mrOU7BqeuGIvp9tv6IZMB2HwWdxkQVx6/L5u7pRBLwKkkVFxfj0ksvRUREBOLj43HDDTegoqKi0zktLS0oLCxETEwMwsPDUVBQgJqamk7nVFZWYvLkyQgLC0N8fDxmz54Np9PpffQ6eFwEh5yjOV7BiZ+M4e7pRDrnVZLasGEDCgsL8emnn2LdunVob2/HxIkT0djY6DnngQcewHvvvYc333wTGzZswJEjR3DjjTd6jrtcLkyePBltbW345JNPsGzZMixduhTz5s3zPnodfNhxyDta4hScnJLDREWkY4oQQvT0m48dO4b4+Hhs2LABV155Jerr6xEXF4fly5fjpptuAgCUl5cjJycHpaWlGD9+PFavXo0pU6bgyJEjsNlsAIAlS5Zgzpw5OHbsGEymi7dgHA4HrFYrsmY+AYOZN2pS74QeE4j5axl3TyfyI6dox4d4F/X19bBYLOc9r1dzUvX19QCA6OhoAEBZWRna29uRl5fnOSc7OxupqakoLS0FAJSWlmL48OGeBAUA+fn5cDgc2LlzZ5c/p7W1FQ6Ho9MA/rtwgoOjN6M5XsGJ28fAEBXVm/8ciMgHepyk3G43Zs6cicsvvxzDhg0DAFRXV8NkMiEyMrLTuTabDdXV1Z5zzk5QZ46fOdaV4uJiWK1Wz0hJSek4oHBw9M1ojldw4tpsGC7wFx0R+V+Pk1RhYSF27NiBFStW9GU8XSoqKkJ9fb1nVFVVAdD+L3COwBqnByio/fFQ3vBLpCM9SlLTp0/HqlWr8MEHHyA5OdnzekJCAtra2lBXV9fp/JqaGiQkJHjOOXe135mvz5xzLrPZDIvF0mkQ+UJznIITt42GISZa61CICF4mKSEEpk+fjpUrV2L9+vXIyMjodHzMmDEICQlBSUmJ57WKigpUVlbCbrcDAOx2O7Zv347a2lrPOevWrYPFYkFubm5vfheiPtFkU3D82iyoERFah0IU9LzacaKwsBDLly/Hu+++i4iICM8cktVqRb9+/WC1WjFt2jTMmjUL0dHRsFgsmDFjBux2O8aPHw8AmDhxInJzc3H77bdj0aJFqK6uxty5c1FYWAizt20W5ZtB1McakxS4bh2G+D9v5YMTiTTkVSW1ePFi1NfX4/vf/z4SExM944033vCc8+yzz2LKlCkoKCjAlVdeiYSEBLz99tue4waDAatWrYLBYIDdbsdPfvIT3HHHHXj88cf77rci6gMtsQqO3XYJDLExWodCFLR6dZ+UVs7cJ5U5m/dJke+FVQvE/Y3PoyLqS365T0pzCgeH70dTooLa20dC7d8fRORfcicpIj9pjlNw7NYRbP0R+ZncSUoHf2VzBM9oSlRQ+8MhUEPZYibyFz5PisgLjYkK3HdeAttf+eBEIn+QOkkB6Pgrl8iPmuMVHLt5GOLf2QPX8RNah0MU0ORu9xFppHGAgpqCIdxCicjH5E5SOpin4Aje0ZSooGYaH5xI5EtSt/s4J0Vaa7YBtT/KRfzbFXCdOKl1OEQBR+5KikgHTicrOHpzNlt/RD4gdSUFRXQMIo01JwA1Px2DxBXlrKiI+pDkSYrtPtKPpgSBmpuyYPt7OVynTmkdDlFAYLuPqA+dTgaO/CSHrT+iPiJ9JQVWUqQzzTaBmrvHIHFFBe+jIuolJikiH2hKFKj+0RAk/G0XXHX1WodDJC22+4h8pDEZODx1KPf6I+oFqSsp3idFetdsEzh692gkrdgL17FjWodDJB2pkxTbfSSDpiSBoz8ejMS/tMLlcGgdDpFU5G736WBrHA6O7ozGFIHD04ZBDQsDEXWf3EmKSCLNNoGj00bBYIvXOhQiaUjd7hPfDCJZNA4QOHJzJhJfbYS7sVHrcIh0T+5KSgdtHA4Ob0fjAIHDPxsJNSICRHRhcicpIkk12wSO3jmcrT+ii5C63ef565RIQo3JAodvzUTSEgfcLS1ah0OkS1InKd4nRbJrHCBwuHA0kl/dyZ0piLrAdh+RxpoSBI7cMRSGuDitQyHSHakrKT5PigLF6VSBQ3cMxoCXGtj6IzqL5EkKnJOigNGU5MahGaOR8hofnEh0Btt9RDrSnODG4duzYYiN0ToUIl2QupLiwgkKRKdT3ai6KwvJz3/O1h8FPamTFNt9FKiaEt049IvRSHmdu6dTcGOSItKppiQ3Dv9kMAb82cU5KgpanJMi0rHTaW5U3p3NBydS0JK6khLgnBQFPk/rb9k+uGpqtQ6HyK+kTlK8T4qCRWOyC1W3ZyLl1Xa4Tp3SOhwiv2G7j0gSjakuHLw3hw9OpKAieSUFLpygoNKc5ELVjFFIW/YVnNU1WodD5HNMUkSSaUpxofKOQUhe3AR3Q4PW4RD5FNt9RBJqTHXh4C+G88GJFPBYSRFJqiXJhaqfD2frjwKa1ElKKAKCq/soiDWmOXHgzkFIff403I2NWodD1OfY7iOSXFOKEwcfGAlDpFXrUIj6nNSVFNt9RB2aBzhRee9QpC1l648CC5MUUYBoTHfiwF2DkPpMPXdPp4DBdh9RAGlKdeLAw6P5PCoKGExSRAGmJcmJyp9mwWCL1zoUol6TvN3HvfuIutKY0Y4D92Qi7SkHW38kNcmTFDgnRXQezSntOPDwaGS8wt3TSV5s9xEFsJbkdhy8KxOGuDitQyHqEVZSRAGuaWA79hcORvrCBrb+SDqSJynOSRF1R0tyGw7MGY2Br/A+KpIL231EQaIlpQ37pw3i8nSSiuSVFNjuI/JC88A2fP2LIchY+AXcTU1ah0N0UUxSREGmNbkdBx4ehYF/PADn4SNah0N0QWz3EQWhltQ27L8rHYaoKK1DIbogySspLpwg6qnmga346sFsDHxyB5/wS7oldZJSlI5BRD3TntyGAw8OZ+uPdEvqJMVKiqj3WjNa8PXd6Uh/uoEVFekO56SICK0ZLfiqaBgfnEi6I3klBa7uI+ojzuRW7J85lK0/0hWpk5QCAYXtPqI+0zaoGfvuTcPAhfVwNzZqHQ4R231E1JkzvQVfzR3BnSlIF6SupNjuI/INV0oLvp6RhUFLvobzaLXW4VAQkzpJcQk6ke84M5uxd0YGBi1wcAsl0oxX7b7FixdjxIgRsFgssFgssNvtWL16ted4S0sLCgsLERMTg/DwcBQUFKCmpvOOy5WVlZg8eTLCwsIQHx+P2bNnw+l09s1vQ0R9yp3Wgq/mjeSj6EkzXlVSycnJWLhwIQYPHgwhBJYtW4brr78eW7duxdChQ/HAAw/gX//6F958801YrVZMnz4dN954Iz7++GMAgMvlwuTJk5GQkIBPPvkER48exR133IGQkBA88cQT3kfP+6SIfM6d2oyvCwdh0MsKH/NBfqcIIXr1KR8dHY2nnnoKN910E+Li4rB8+XLcdNNNAIDy8nLk5OSgtLQU48ePx+rVqzFlyhQcOXIENpsNALBkyRLMmTMHx44dg8lk6tbPdDgcsFqtSH91LtSw0N6ET0TdVdkPmY9z93TqG07Rjg/xLurr62GxWM57Xo9X97lcLqxYsQKNjY2w2+0oKytDe3s78vLyPOdkZ2cjNTUVpaWlAIDS0lIMHz7ck6AAID8/Hw6HAzt37jzvz2ptbYXD4eg0AEBRBAcHh58GUpuxb95IGBMTevqxQeQ1r5PU9u3bER4eDrPZjHvvvRcrV65Ebm4uqqurYTKZEBkZ2el8m82G6uqO1UHV1dWdEtSZ42eOnU9xcTGsVqtnpKSkeBs2EfWSoggoaU3YV5jBOSryG69X92VlZWHbtm2or6/HW2+9halTp2LDhg2+iM2jqKgIs2bN8nztcDg6EpXCOSkifxOZjdj74CBk/uo0W3/kc14nKZPJhMzMTADAmDFjsGXLFjz33HO4+eab0dbWhrq6uk7VVE1NDRISOtoDCQkJ2Lx5c6f3O7P678w5XTGbzTCbzd96nUvQiTSS2oh980ZiyIuVcB46rHU0FMB6veOE2+1Ga2srxowZg5CQEJSUlHiOVVRUoLKyEna7HQBgt9uxfft21NbWes5Zt24dLBYLcnNzexsKEfmJogBqRiP2/jyVO1OQT3lVSRUVFeHqq69GamoqGhoasHz5cnz44YdYu3YtrFYrpk2bhlmzZiE6OhoWiwUzZsyA3W7H+PHjAQATJ05Ebm4ubr/9dixatAjV1dWYO3cuCgsLu6yULurMhC4RaULJPI09RYMx+FdtfMwH+YRXSaq2thZ33HEHjh49CqvVihEjRmDt2rX4wQ9+AAB49tlnoaoqCgoK0Nraivz8fLz88sue7zcYDFi1ahXuu+8+2O129O/fH1OnTsXjjz/eo+DZ7iPSXkhqI/bNHYYhL1bBWXVI63AowPT6PiktnLlPatCfi2DgfVJEuuD8KhyDF+6Cq65e61BIAt29T0ryvfvY7iPSi5DMBlTMy0HW47uZqKjPSJ6kwCRFpCOhaQ3YW5TL1h/1GT5Pioj6lCnTgYpfpECNiNA6FAoAAVBJaR0FEZ0rdJADe34zFFkL9sJ1/ITW4ZDEJE9SnJMi0quwNAf2zh6CIS/whl/qObb7iMhnQofUo+KBFKj9+2sdCkmKlRQR+VTYoHpUPDEcOcX7+Twq8prcSeqbQUT6FpFWjz2zBmLI80a2/sgrUicpVRFQWUkRSSE86xTKH0rBkEdPcfd06jbOSRGR31gy6lBRPALGAUlah0KSkLqS4pwUkXwiM06hYmYasp5xw3n0/A87JQKYpIhIA9bsE9j9aBqyHmmAu7FR63BIx9juIyJNRKWfQkXxMBhTkrUOhXRM6kpKVToGEckpZuApVMxMxpBFbXDV1F78GyjoSJ2k2O4jkl909gnsnp+O7DnNfHAifQvbfUSkubi0U6j4bS6MaSlah0I6I3UlpYL3SREFivjMEyh/YACyFjRxU1rykDpJsd1HFFjis45h94JByHnEyQcnEoAASFKspIgCS1L6cZT/Jhs5Tx+F80Cl1uGQxjgnRUS6kzj4GHY/mAhDpFXrUEhjcldS4AazRIEqafAx7F6YhZxf7oPrxEmtwyGNSJ2kuMEsUWBLyTiG8vmDkfP0ETgPVmkdDmmA7T4i0rXkrFrsmpMINSJC61BIA6ykiEj30jJrUf67bOTMO8idKYKM1EmKS9CJgkf6wFqUz81Azu/MbP0FEbb7iEgaadnV2FWUCLV/f61DIT+RupJiu48o+AzMrEb573OR+6vDcB4+onU45GNMUkQkncyB1dhdlIKchQqchw5rHQ75ENt9RCSlQTlHsGt+Elt/AU7uSgoCKlhJEQWrIQOPdrT+Hj8KZ9UhrcMhH5A6SXF1HxFlDTqCXUUDkPsbJ5xHq7UOh/qY1EmKc1JEBAA5OYew67fJyL6/kQ9ODDCckyKigJCTcQTlz2bBmJ6qdSjUh6SupBQFrKSIyGNo5mHsfCQFOfNbuDNFgJA6SbHdR0TnGp5TiR1PpiD7Fy1wORxah0O9xHYfEQWcYRmHsfvpLBgz0rQOhXpJ7kqKS9CJ6DxGDqnEF0WpyClq4POoJCZ3klLcUBW31mEQkU5dkn0A255NR/YDYKKSFNt9RBTQRqVXYffCQWz9SUrySooLJ4jo4sZk70fZ3HTkPFgHV1291uGQF5ikiCgoXJq1H2UvDETWQ4e5PF0ibPcRUdAYk1GJ3b9NZetPIqykiCiojMv5GpvnZyBrxkluoSQBuZMUl6ATUQ+MH/w1Ni/JRNbDNXxwos7JnaRYSRFRD43P2I+Pf52J3AVGOA9Uah0OnQfnpIgoaF2euw/lv4nhgxN1TPJKijfzElHvXJ75FT75wxBkPXoczoNVWodD55A7SUHAwHYfEfXSdwftw4fzs5A7X/AJvzrDdh8REYDv51Zgz5OxUCMitA6FziJ9JcXVfUTUV64cuA8blgxG1tyTcO4/qHU4BNmTFFf3EVEfuypzD0rmZyPnl+1cnq4DbPcREZ1jQk459j4dC4PFonUoQU/ySoqr+4jIN64auBcli7MxZH4dXPv2ax1O0JI6SRkUru4jIt+ZOGQ31szLRfbsRm5KqxG2+4iILmBSzi58/YINhqgorUMJSlJXUirA1X1E5HN5GXuw5sVcDJkfydafn8mdpDgnRUR+ck3WDrz/+FAMmRHNR9H7keRJikvQich/pmTtwL9fyUZ6oZFzVH7COSkiIi9MzCjHnmcGwJCZoXUoQUHuSgpuGMB2HxH51/XZX+C9BcOQeY8FLodD63ACmtxJiu0+ItLI9UO24/3Xc5H+i1PcmcKH2O4jIuqhazJ2oWKRDcaB6VqHErBYSRER9UJB7lb888nhSL8rAu6GBq3DCTi9qqQWLlwIRVEwc+ZMz2stLS0oLCxETEwMwsPDUVBQgJqamk7fV1lZicmTJyMsLAzx8fGYPXs2nE6n1z/f8M2cFAcHB4eW44eZX6BqWSqMaSm9+UilLvQ4SW3ZsgWvvPIKRowY0en1Bx54AO+99x7efPNNbNiwAUeOHMGNN97oOe5yuTB58mS0tbXhk08+wbJly7B06VLMmzev578FEZHGrsvYjoriGBjTU7UOJaAoQgiv+2WnT5/G6NGj8fLLL2PBggUYNWoUfv/736O+vh5xcXFYvnw5brrpJgBAeXk5cnJyUFpaivHjx2P16tWYMmUKjhw5ApvNBgBYsmQJ5syZg2PHjsFkMl305zscDlitVsz6eArM4SHehk9E5DPvfD0CKVMr2fq7CKdox4d4F/X19bBcYLf5Hs1JFRYWYvLkycjLy8OCBQs8r5eVlaG9vR15eXme17Kzs5GamupJUqWlpRg+fLgnQQFAfn4+7rvvPuzcuROXXHLJt35ea2srWltbPV87vlnyaVDcMHDHCSLSkYJB2/CPZaOQ9lAjnF8f0Doc6Xnd7luxYgU+//xzFBcXf+tYdXU1TCYTIiMjO71us9lQXV3tOefsBHXm+JljXSkuLobVavWMlBT2fYlIvwoGbcPe31phTEnWOhTpeVVJVVVV4f7778e6desQGhrqq5i+paioCLNmzfJ87XA4kJKSwsfHE5Fu3Za7BW+/MBID7uANv73hVZIqKytDbW0tRo8e7XnN5XJh48aNePHFF7F27Vq0tbWhrq6uUzVVU1ODhIQEAEBCQgI2b97c6X3PrP47c865zGYzzGbzt15X2e4jIh370cCteGPZaKTMbubu6T3kVZKaMGECtm/f3um1O++8E9nZ2ZgzZw5SUlIQEhKCkpISFBQUAAAqKipQWVkJu90OALDb7fjtb3+L2tpaxMfHAwDWrVsHi8WC3Nxcr4JnJUVEenfroDL8+YnLMOiBJO5M0QNeJamIiAgMGzas02v9+/dHTEyM5/Vp06Zh1qxZiI6OhsViwYwZM2C32zF+/HgAwMSJE5Gbm4vbb78dixYtQnV1NebOnYvCwsIuqyUiItndkb0Z/1gyErY7ouA6dUrrcKTS5ztOPPvss1BVFQUFBWhtbUV+fj5efvllz3GDwYBVq1bhvvvug91uR//+/TF16lQ8/vjjXv8sru4jIln8OH0r/vLqZUh9JBquPV9pHY40enSflNbO3Cf1q00TEBou9c5ORBRkllaMR9q9tXAdO6Z1KJrq7n1S3GCWiMiP/l/Wpzi+NBKGuDitQ5GC1GWIAQIGLpwgIsncklaG116xI/URC1t/FyF1klIVN1TOSRGRhH6a9TFeW2RH8p1cTHEhbPcREWnkrsGlOP7XWBgTu75HlCSvpNjuIyLZ3Z6+Ga+8dAVS54TBtfdrrcPRHamTlMJ2HxEFgPuyN+LVp7+DhJ9wC6VzSZ2kzjxwjIhIdtMyP8Ff37gM0fda4TxYpXU4usE5KSIiHTDAjalpn+LgsxYYMjO0Dkc3pK6kVEVAVTgnRUSB4xc5H+BPz12OmFsi+OBESJ6k2O4jokD004Ef4/W/2xFdGBP0D05ku4+ISGcMcOOn6R+j6pl+MGakaR2OpuSupLjBLBEFsFnZJfjT4itg+XHwrvqTOkmpcENlu4+IAthP0z/CH/9+BawzYoPyPiq2+4iIdEyFGz9L34ijvzPBmJKsdTh+J3UlZVAEDFzdR0RB4KHsdfjTa1eg34+scNXVax2O30idpFQIru4joqDxs9SNeO5v/wdRM+PgqtindTh+wXYfEZFE7h+4HseeVoNmU1rJKyk3VEXROgwiIr+aPWQt/vjXKxFycwxcx09oHY5PSZ2kuAs6EQWre1M24Hd/+QGiZkXDtXuv1uH4jNxJSnHDwEqKiILUnMy1ePKZfETdHrgVFeekiIgkNidzLVxv9AvYOSqpK6mOm3lZSRFRcCtMXY8nXr0G0Q9kBtyqP6mTFNt9REQdHhuyCk8+fzXCb4mC69QprcPpM2z3EREFiDmDVsP9j7CA2plC7kqKq/uIiDqZmfq/+NUr1yJ65iC49nyldTi9JnWSUjgnRUT0LY8PeRdPLZ6EkB/Kv3s6231ERAFodtoa4N1wGAemax1Kr0hdSXHhBBHR+T2YuhZzX7oBUTMy4Nq3X+twekTuJMU5KSKiCyoeshK/+1M+cJ2crT+2+4iIAtxDKWuh/rM/DEMGaR2K16SupFRFQOXj44mILurh1NV49PkbYb0vDc79B7UOp9ukTlIGuGHQOggiIkk8OeQtPL0sH+I6eR6cKHmS4pwUEZE3Hkxei+J3JgM/k+PBiZyTIiIKIgYIzE1dheYX26XYmULqSkpV3FC5Ap2IyGtPZr6F3/1tEk5fHw3XiZNah3NecicptvuIiHpszoDVeOytG2AoHALXrj1ah9MltvuIiILYb9LfgeuFJhgTbFqH0iWpKykunCAi6r0nB/4Di/4xCfUFNjira7QOpxOpk1THfVJMUkREvfXIgNV4eHkBDNP11fpju4+IiAAAiwb+A8bFDhhiY7QOxUPqSortPiKivlWcthLF/7wap25OhrPqkNbhyJ2kVAioTFJERH3ql0nv44FlP4KhcDBcu/dqGgvbfURE9C3PDnwTYX84BUNUlKZxSF1JGRQBAxdOEBH5xBOp72LB+1fjxP/VblNauZMU56SIiHxqftL7KHz1Zhjuy9Rkrz+pk5QC9iuJiHxt8aA38NjrU3Bykv8fnMjPeCIiuqjfDFiF2LXw+4MTpa6kDErHICIi31sw4H38/A8/Au4eCNfer/3yM6VOUipYChIR+dOSgW9i/l8m4egk/zw4kZ/xRETklV8nrYFtjRuGnME+/1lSV1KGbwYREfnXE0mrcd+SArT/P98uT5c7SSkKDAonpYiItPCHgW/jV3+fgAOTfPfgRLb7iIiox36VUILYVU4Yhmb55P2lrqS4cIKISHvPJK/Gz1+5Do23DIDz0OE+fW+pk5QBCgxgu4+ISGuvpL2HX797JfZcEw9XTW2fva/USUpRFKickyIi0oX58Rtx/zuTcOzubLh3lPfJe7JbRkREfUJVFLyQshZxfzwCgy2+T95T6kqK7T4iIv15OeXfmP/+d1B+fe/nqKROUuo3/yMiIn35je1T3PP3iTh5dxZcOyt6/D78hCciIp/4Q+q/MeC1QzDERPf4PaSupHgzLxGRvr2Y/CHmrrsMu25MhfNApdffL3WSYruPiEj/nrB9hjuXW3Hyp0Pg2rXHq+/lJzwREfnc62klyPzzfhiiorz6PskrKQUqV/cREUnh2cRNeHT9aGy/eRCcFd27j0rqJGVQVBgUFoNERLJ40rYNdyyzoPr2gcDei58vZZISQgAAHKfdGkdCRETeejH6QyxckoqSCf/9PD8fKZPUiRMnAABpow9oGwgREfVQx+PnGxoaYLVaz3uWlEkqOrpjzX1lZeUFf7lg53A4kJKSgqqqKlgsFq3D0S1ep+7hdeoeXqfuEUKgoaEBSUlJFzxPyiSlqh3zUFarlf8SdIPFYuF16gZep+7hdeoeXqeL606RwVUHRESkW0xSRESkW1ImKbPZjPnz58NsNmsdiq7xOnUPr1P38Dp1D69T31LExdb/ERERaUTKSoqIiIIDkxQREekWkxQREekWkxQREemWlEnqpZdeQnp6OkJDQzFu3Dhs3rxZ65D8auPGjbj22muRlJQERVHwzjvvdDouhMC8efOQmJiIfv36IS8vD3v3dt7J8eTJk7jttttgsVgQGRmJadOm4fTp0378LXyruLgYl156KSIiIhAfH48bbrgBFRWdH2Hd0tKCwsJCxMTEIDw8HAUFBaipqel0TmVlJSZPnoywsDDEx8dj9uzZcDqd/vxVfGrx4sUYMWKE58ZTu92O1atXe47zGnVt4cKFUBQFM2fO9LzGa+UjQjIrVqwQJpNJvPbaa2Lnzp3i7rvvFpGRkaKmpkbr0Pzm/fffF7/85S/F22+/LQCIlStXdjq+cOFCYbVaxTvvvCO++OILcd1114mMjAzR3NzsOWfSpEli5MiR4tNPPxX/+c9/RGZmprj11lv9/Jv4Tn5+vnj99dfFjh07xLZt28Q111wjUlNTxenTpz3n3HvvvSIlJUWUlJSIzz77TIwfP1585zvf8Rx3Op1i2LBhIi8vT2zdulW8//77IjY2VhQVFWnxK/nEP//5T/Gvf/1L7NmzR1RUVIhHH31UhISEiB07dggheI26snnzZpGeni5GjBgh7r//fs/rvFa+IV2Suuyyy0RhYaHna5fLJZKSkkRxcbGGUWnn3CTldrtFQkKCeOqppzyv1dXVCbPZLP72t78JIYTYtWuXACC2bNniOWf16tVCURRx+PBhv8XuT7W1tQKA2LBhgxCi45qEhISIN99803PO7t27BQBRWloqhOj4Y0BVVVFdXe05Z/HixcJisYjW1lb//gJ+FBUVJf70pz/xGnWhoaFBDB48WKxbt05873vf8yQpXivfkard19bWhrKyMuTl5XleU1UVeXl5KC0t1TAy/di/fz+qq6s7XSOr1Ypx48Z5rlFpaSkiIyMxduxYzzl5eXlQVRWbNm3ye8z+UF9fD+C/mxOXlZWhvb2903XKzs5Gampqp+s0fPhw2Gw2zzn5+flwOBzYuXOnH6P3D5fLhRUrVqCxsRF2u53XqAuFhYWYPHlyp2sC8N8nX5Jqg9njx4/D5XJ1+ocMADabDeXl3XvKY6Crrq4GgC6v0Zlj1dXViI+P73TcaDQiOjrac04gcbvdmDlzJi6//HIMGzYMQMc1MJlMiIyM7HTuudepq+t45lig2L59O+x2O1paWhAeHo6VK1ciNzcX27Zt4zU6y4oVK/D5559jy5Yt3zrGf598R6okRdQThYWF2LFjBz766COtQ9GlrKwsbNu2DfX19XjrrbcwdepUbNiwQeuwdKWqqgr3338/1q1bh9DQUK3DCSpStftiY2NhMBi+tWKmpqYGCQkJGkWlL2euw4WuUUJCAmprazsddzqdOHnyZMBdx+nTp2PVqlX44IMPkJyc7Hk9ISEBbW1tqKur63T+udepq+t45ligMJlMyMzMxJgxY1BcXIyRI0fiueee4zU6S1lZGWprazF69GgYjUYYjUZs2LABzz//PIxGI2w2G6+Vj0iVpEwmE8aMGYOSkhLPa263GyUlJbDb7RpGph8ZGRlISEjodI0cDgc2bdrkuUZ2ux11dXUoKyvznLN+/Xq43W6MGzfO7zH7ghAC06dPx8qVK7F+/XpkZGR0Oj5mzBiEhIR0uk4VFRWorKzsdJ22b9/eKaGvW7cOFosFubm5/vlFNOB2u9Ha2sprdJYJEyZg+/bt2LZtm2eMHTsWt912m+f/81r5iNYrN7y1YsUKYTabxdKlS8WuXbvEPffcIyIjIzutmAl0DQ0NYuvWrWLr1q0CgHjmmWfE1q1bxcGDB4UQHUvQIyMjxbvvviu+/PJLcf3113e5BP2SSy4RmzZtEh999JEYPHhwQC1Bv++++4TVahUffvihOHr0qGc0NTV5zrn33ntFamqqWL9+vfjss8+E3W4Xdrvdc/zMkuGJEyeKbdu2iTVr1oi4uLiAWjL8yCOPiA0bNoj9+/eLL7/8UjzyyCNCURTx73//WwjBa3QhZ6/uE4LXylekS1JCCPHCCy+I1NRUYTKZxGWXXSY+/fRTrUPyqw8++EAA+NaYOnWqEKJjGfpjjz0mbDabMJvNYsKECaKioqLTe5w4cULceuutIjw8XFgsFnHnnXeKhoYGDX4b3+jq+gAQr7/+uuec5uZm8fOf/1xERUWJsLAw8cMf/lAcPXq00/scOHBAXH311aJfv34iNjZWPPjgg6K9vd3Pv43v3HXXXSItLU2YTCYRFxcnJkyY4ElQQvAaXci5SYrXyjf4qA4iItItqeakiIgouDBJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbjFJERGRbv1/iyt5HlrIUTUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# testing\n",
    "\n",
    "N = 500\n",
    "\n",
    "def get_i_j(val):\n",
    "    # we also need it to work for val.dtype == uint64, hence we do not cast val directly\n",
    "    sqrt_val = np.sqrt(val.astype(np.float32)).astype(np.float32)\n",
    "    i = np.round(np.sqrt(2)*sqrt_val).astype(np.uint32)\n",
    "    i = i + np.where(i%2==0, val%(i+1)==0, val%i==0).astype(np.uint32) - 1\n",
    "    j = np.where(i%2==0, (val%(i+1)).astype(np.uint32), ((val-(i-1)/2-1)%(i+1)).astype(np.uint32))\n",
    "    return i, j\n",
    "\n",
    "# plot distance to top-left corner\n",
    "i_tensor = np.zeros((N, N))\n",
    "j_tensor = np.zeros((N, N))\n",
    "for c, (i, j) in enumerate(zip(*np.tril_indices(N))):\n",
    "    my_i, my_j = get_i_j(np.array(c))\n",
    "    i_tensor[i, j] = my_i\n",
    "    j_tensor[i, j] = my_j\n",
    "    assert my_i == i, (my_i, i)\n",
    "    assert my_j == j, (my_j, j)\n",
    "    \n",
    "\n",
    "plot2D(i_tensor, N, show_values=(N<=12))\n",
    "# plot2D(j_tensor, N, show_values=(N<=12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd2bec07-e556-4806-9b15-48ddf4d11933",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "434932b0-7f6c-4208-b637-d32ca217b31e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/localdata/mihaip/workspace/envs/poplar_sdk-ubuntu_20_04-3.2.0+1277-7cd8ade3cd/3.2.0+1277_poptorch/lib/python3.8/site-packages/numpy/ctypeslib.py:137: DeprecationWarning: \n",
      "\n",
      "  `numpy.distutils` is deprecated since NumPy 1.23.0, as a result\n",
      "  of the deprecation of `distutils` itself. It will be removed for\n",
      "  Python >= 3.12. For older Python versions it will remain present.\n",
      "  It is recommended to use `setuptools < 60.0` for those Python versions.\n",
      "  For more details, see:\n",
      "    https://numpy.org/devdocs/reference/distutils_status_migration.html \n",
      "\n",
      "\n",
      "  from numpy.distutils.misc_util import get_shared_lib_extension\n",
      "ic| N: 5\n",
      "ic| nonzero_indices.dtype: dtype('int64')\n",
      "ic| nonzero_indices.dtype: dtype('uint64')\n",
      "ic| 'Accessing values with uint64 vs int64 is fine'\n",
      "ic| nonzero_indices.shape: (33,)\n",
      "/tmp/ipykernel_2858194/82872427.py:14: RuntimeWarning: divide by zero encountered in remainder\n",
      "  i = sqrt_val + np.where(sqrt_val%2==0, val%(sqrt_val+1)==0, val%sqrt_val==0).astype(np.uint32) - 1\n",
      "ic| i: array([ 0,  1,  1,  2,  2,  2,  3,  4,  4,  5,  5,  5,  5,  6,  7,  7,  8,\n",
      "               9,  9,  9,  9,  9, 10, 11, 11, 12, 13, 14, 14, 14, 14, 14, 14],\n",
      "             dtype=uint32)\n",
      "ic| j: array([ 0,  0,  1,  0,  1,  2,  3,  3,  4,  0,  1,  2,  5,  6,  6,  7,  8,\n",
      "               0,  1,  2,  5,  9, 10, 10, 11, 12, 13,  0,  1,  2,  5,  9, 14],\n",
      "             dtype=uint32)\n",
      "ic| np.max(np.diff(nonzero_indices_2d, axis=0)): 4294967295\n",
      "ic| i: array([[0, 0],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [1, 1],\n",
      "              [2, 2],\n",
      "              [2, 2],\n",
      "              [2, 2],\n",
      "              [2, 0],\n",
      "              [2, 1],\n",
      "              [2, 1],\n",
      "              [2, 2],\n",
      "              [3, 3],\n",
      "              [3, 3],\n",
      "              [3, 3],\n",
      "              [3, 3],\n",
      "              [3, 0],\n",
      "              [3, 1],\n",
      "              [3, 1],\n",
      "              [3, 2],\n",
      "              [3, 3],\n",
      "              [4, 4],\n",
      "              [4, 4],\n",
      "              [4, 4],\n",
      "              [4, 4],\n",
      "              [4, 4],\n",
      "              [4, 0],\n",
      "              [4, 1],\n",
      "              [4, 1],\n",
      "              [4, 2],\n",
      "              [4, 3],\n",
      "              [4, 4]], dtype=uint32)\n",
      "ic| j: array([[0, 0],\n",
      "              [0, 0],\n",
      "              [0, 0],\n",
      "              [1, 0],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [0, 0],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [2, 0],\n",
      "              [2, 0],\n",
      "              [2, 1],\n",
      "              [2, 2],\n",
      "              [0, 0],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [2, 2],\n",
      "              [3, 0],\n",
      "              [3, 0],\n",
      "              [3, 1],\n",
      "              [3, 2],\n",
      "              [3, 3],\n",
      "              [0, 0],\n",
      "              [1, 0],\n",
      "              [1, 1],\n",
      "              [2, 2],\n",
      "              [3, 3],\n",
      "              [4, 0],\n",
      "              [4, 0],\n",
      "              [4, 1],\n",
      "              [4, 2],\n",
      "              [4, 3],\n",
      "              [4, 4]], dtype=uint32)\n",
      "ic| np.max(np.diff(nonzero_indices_4d, axis=0)): 4294967295\n",
      "ic| nonzero_indices_4d.shape: (33, 4)\n",
      "ic| 'Reconstructing indices is fine'\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'Reconstructing indices is fine'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pyscf\n",
    "from icecream import ic\n",
    "\n",
    "natm = 1\n",
    "\n",
    "skip_dense = True\n",
    "\n",
    "def get_i_j(val, precision='x32'):\n",
    "    # we need it to work for val.dtype == uint64 when called with the main index\n",
    "    if precision == 'x32':\n",
    "        sqrt_val = np.round(np.sqrt(2)*np.sqrt(val.astype(np.float32))).astype(np.uint32)\n",
    "    else:\n",
    "        sqrt_val = np.round(np.sqrt(2)*np.sqrt(val.astype(np.float64))).astype(np.uint32)\n",
    "    i = sqrt_val + np.where(sqrt_val%2==0, val%(sqrt_val+1)==0, val%sqrt_val==0).astype(np.uint32) - 1\n",
    "    ic(i)\n",
    "    j = np.where(i%2==0, (val%(i+1)).astype(np.uint32), ((val-(i-1)/2-1)%(i+1)).astype(np.uint32))\n",
    "    ic(j)\n",
    "    return i, j\n",
    "\n",
    "mol = pyscf.gto.Mole(atom=\"\".join(f\"C 0 {1.54*j} {1.54*i};\" for i in range(natm) for j in range(natm)))\n",
    "mol.build()\n",
    "N = mol.nao_nr()\n",
    "ic(N)\n",
    "\n",
    "if not skip_dense:\n",
    "    dense_ERI = mol.intor(\"int2e_sph\", aosym=\"s1\")\n",
    "distinct_ERI = mol.intor(\"int2e_sph\", aosym=\"s8\")\n",
    "\n",
    "nonzero_indices = np.nonzero(distinct_ERI)[0] # int64 by default\n",
    "nonzero_distinct_ERI_int64ind = distinct_ERI[nonzero_indices]\n",
    "ic(nonzero_indices.dtype)\n",
    "nonzero_indices = nonzero_indices.astype(np.uint64)\n",
    "nonzero_distinct_ERI_uint64ind = distinct_ERI[nonzero_indices]\n",
    "ic(nonzero_indices.dtype)\n",
    "\n",
    "assert np.equal(nonzero_distinct_ERI_int64ind, nonzero_distinct_ERI_uint64ind).all()\n",
    "ic('Accessing values with uint64 vs int64 is fine')\n",
    "\n",
    "ic(nonzero_indices.shape)\n",
    "\n",
    "last_index = nonzero_indices.shape[0]\n",
    "\n",
    "# test_index_casting = True\n",
    "# for i in range(last_index-10, last_index):\n",
    "#     if nonzero_indices[i] != nonzero_indices[i].astype(np.uint32):\n",
    "#         test_index_casting = False\n",
    "# if test_index_casting:\n",
    "#     ic('Casting indices to uint32 is fine')\n",
    "# else:\n",
    "#     ic('Casting indices to uint32 is NOT FINE')\n",
    "\n",
    "nonzero_indices_2d = np.stack(get_i_j(nonzero_indices, precision='x64'), axis=1) # ijkl x64 -> ij,kl x32 -- shape=(?, 2)\n",
    "assert np.equal(nonzero_indices_2d, nonzero_indices_2d.astype(np.uint32)).all()\n",
    "nonzero_indices_2d = nonzero_indices_2d.astype(np.uint32)\n",
    "ic(np.max(np.diff(nonzero_indices_2d, axis=0)))\n",
    "a = nonzero_indices\n",
    "b = (nonzero_indices_2d[:,0].astype(np.uint64)*(nonzero_indices_2d[:,0].astype(np.uint64)+1)/2+nonzero_indices_2d[:,1].astype(np.uint64)).astype(np.uint64)\n",
    "assert np.equal(a, b).all(), (a, b, np.nonzero(np.abs(a-b)))\n",
    "\n",
    "nonzero_indices_4d = np.concatenate(get_i_j(nonzero_indices_2d), axis=1) # ij,kl x32 -> i,j,k,l x32 -- shape=(?, 2)\n",
    "nonzero_indices_4d = nonzero_indices_4d.astype(np.uint32)\n",
    "ic(np.max(np.diff(nonzero_indices_4d, axis=0)))\n",
    "\n",
    "ic(nonzero_indices_4d.shape)\n",
    "a = nonzero_indices\n",
    "b_ij = (nonzero_indices_4d[:,0].astype(np.uint64)*(nonzero_indices_4d[:,0].astype(np.uint64)+1)/2+nonzero_indices_4d[:,2].astype(np.uint64)).astype(np.uint64)\n",
    "b_kl = (nonzero_indices_4d[:,1].astype(np.uint64)*(nonzero_indices_4d[:,1].astype(np.uint64)+1)/2+nonzero_indices_4d[:,3].astype(np.uint64)).astype(np.uint64)\n",
    "b = (b_ij*(b_ij+1)/2+b_kl).astype(np.uint64)\n",
    "assert np.equal(a, b).all(), (a, b, np.nonzero(np.abs(a-b)), np.nonzero(np.abs(a-b))[0].shape)\n",
    "\n",
    "# for val in range(last_index-10, last_index):\n",
    "# # for val in range(nonzero_indices.shape[0]):\n",
    "#     # ic(val, type(val))\n",
    "#     index = nonzero_indices[val] #.astype(np.uint32)\n",
    "#     # ic(index.dtype)\n",
    "#     ij, kl = get_i_j(index, precision='x64')\n",
    "\n",
    "#     # check reconstruct\n",
    "#     # ic((index, index, ij, kl))\n",
    "#     rec_index = ij.astype(np.uint64)*(ij.astype(np.uint64)+1)//2 + kl.astype(np.uint64)\n",
    "#     assert index == rec_index, (index, rec_index)\n",
    "    \n",
    "#     i, j= get_i_j(ij)\n",
    "#     k, l = get_i_j(kl)\n",
    "\n",
    "#     # ic(i, j, k, l)\n",
    "#     # ic(i.dtype, j.dtype, k.dtype, l.dtype)\n",
    "#     if not skip_dense:\n",
    "#         assert np.allclose(nonzero_distinct_ERI_uint64ind[val], dense_ERI[i, j, k, l]), (nonzero_distinct_ERI_uint64ind[val], dense_ERI[i, j, k, l])\n",
    "\n",
    "\n",
    "        \n",
    "ic('Reconstructing indices is fine')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4a5b3dc0-1845-4491-9305-24ffbc392b73",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| np.iinfo(np.uint32): iinfo(min=0, max=4294967295, dtype=uint32)\n",
      "ic| np.iinfo(np.uint64): iinfo(min=0, max=18446744073709551615, dtype=uint64)\n",
      "ic| np.finfo(np.float32): finfo(resolution=1e-06, min=-3.4028235e+38, max=3.4028235e+38, dtype=float32)\n",
      "ic| np.finfo(np.float64): finfo(resolution=1e-15, min=-1.7976931348623157e+308, max=1.7976931348623157e+308, dtype=float64)\n",
      "ic| max_uint32: array([4294967295], dtype=uint32)\n",
      "ic| max_uint64: array([18446744073709551615], dtype=uint64)\n",
      "ic| test32 == test32.astype(np.float32).astype(np.uint32): array([False])\n",
      "ic| test32_128 == test32_128.astype(np.float32).astype(np.uint32): array([ True])\n",
      "ic| test_sqrt_32 == test_sqrt_64: array([ True])\n",
      "    (test_sqrt_32, test_sqrt_64): (array([8192.], dtype=float32), array([8192.]))\n",
      "ic| test32_11: array([2097150], dtype=uint32)\n",
      "ic| test32_12: array([1048574], dtype=uint32)\n",
      "ic| np.power(test32_11, 0.5): array([1448.15399734])\n",
      "ic| np.power(test32_12, 0.5): array([1023.99902344])\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "(3259, (1,))",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[21], line 54\u001b[0m\n\u001b[1;32m     51\u001b[0m result \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mequal(test_sqrt_32, test_sqrt_64)\n\u001b[1;32m     52\u001b[0m \u001b[38;5;66;03m# ic(test_sqrt_64[test_sqrt_64!=test_sqrt_32])\u001b[39;00m\n\u001b[1;32m     53\u001b[0m \u001b[38;5;66;03m# ic(test_sqrt_32[test_sqrt_64!=test_sqrt_32])\u001b[39;00m\n\u001b[0;32m---> 54\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m result\u001b[38;5;241m.\u001b[39mall(), (N, result[result\u001b[38;5;241m==\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m]\u001b[38;5;241m.\u001b[39mshape)\n\u001b[1;32m     55\u001b[0m \u001b[38;5;66;03m# ic('PASSED v2 '+str(N))\u001b[39;00m\n",
      "\u001b[0;31mAssertionError\u001b[0m: (3259, (1,))"
     ]
    }
   ],
   "source": [
    "ic(np.iinfo(np.uint32))\n",
    "ic(np.iinfo(np.uint64))\n",
    "ic(np.finfo(np.float32))\n",
    "ic(np.finfo(np.float64))\n",
    "\n",
    "max_uint32 = np.zeros(1).astype(np.uint32)-1\n",
    "ic(max_uint32)\n",
    "\n",
    "max_uint64 = np.zeros(1).astype(np.uint64)-1\n",
    "ic(max_uint64)\n",
    "\n",
    "test32 = max_uint32\n",
    "ic(test32 == test32.astype(np.float32).astype(np.uint32))\n",
    "\n",
    "test32_128 = max_uint32//128-1 # 32-7 = 25\n",
    "ic(test32_128 == test32_128.astype(np.float32).astype(np.uint32))\n",
    "\n",
    "test_sqrt_32 = np.round(np.sqrt(2)*np.sqrt(test32_128.astype(np.float32)))\n",
    "test_sqrt_64 = np.round(np.sqrt(2)*np.sqrt(test32_128.astype(np.float64)))\n",
    "ic(test_sqrt_32 == test_sqrt_64, (test_sqrt_32, test_sqrt_64))\n",
    "\n",
    "test32_11 = max_uint32//(2**11)-1\n",
    "ic(test32_11)\n",
    "test32_12 = max_uint32//(2**12)-1\n",
    "ic(test32_12)\n",
    "ic(np.power(test32_11, 0.5))\n",
    "ic(np.power(test32_12, 0.5))\n",
    "\n",
    "# # size = test32_11.astype(np.uint64)\n",
    "# ic(size)\n",
    "# for N in range(1024, 2048):\n",
    "#     size = N*N\n",
    "#     test_sqrt_32 = np.round(np.sqrt(2)*np.sqrt(np.arange(size).astype(np.float32)))\n",
    "#     test_sqrt_64 = np.round(np.sqrt(2)*np.sqrt(np.arange(size).astype(np.float64)))\n",
    "#     result = np.equal(test_sqrt_32, test_sqrt_64)\n",
    "#     ic(test_sqrt_64[test_sqrt_64!=test_sqrt_32])\n",
    "#     ic(test_sqrt_32[test_sqrt_64!=test_sqrt_32])\n",
    "#     assert result.all(), result[result==False].shape\n",
    "#     ic('PASSED '+str(N))\n",
    "\n",
    "####################\n",
    "\n",
    "for N in range(3250, 4096):\n",
    "    size = N*N\n",
    "    # ic(size)\n",
    "    # test_sqrt_32 = np.round(np.sqrt(2)*np.sqrt(np.arange(size).astype(np.float32)))\n",
    "    # test_sqrt_32 = np.where(test_sqrt_32**2 - size == size - test_sqrt_32, test_sqrt_32+1, test_sqrt_32)\n",
    "    test_sqrt_32 = np.floor((np.sqrt(1 + 8*np.arange(size).astype(np.float32)) - 1)/2)\n",
    "    test_sqrt_64 = np.floor((np.sqrt(1 + 8*np.arange(size).astype(np.float64)) - 1)/2)\n",
    "    # test_sqrt_64 = np.round(np.sqrt(2)*np.sqrt(np.arange(size).astype(np.float64)))\n",
    "    result = np.equal(test_sqrt_32, test_sqrt_64)\n",
    "    # ic(test_sqrt_64[test_sqrt_64!=test_sqrt_32])\n",
    "    # ic(test_sqrt_32[test_sqrt_64!=test_sqrt_32])\n",
    "    assert result.all(), (N, result[result==False].shape)\n",
    "    # ic('PASSED v2 '+str(N))\n"
   ]
  }
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