{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contravariant & Covariant indices in Tensors (Symbolic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "from einsteinpy.symbolic import ChristoffelSymbols, RiemannCurvatureTensor\n",
    "from einsteinpy.symbolic.predefined import Schwarzschild\n",
    "\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysing the schwarzschild metric along with performing various operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 - \\frac{r_{s}}{r} & 0 & 0 & 0\\\\0 & - \\frac{1}{c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0\\\\0 & 0 & - \\frac{r^{2}}{c^{2}} & 0\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡    rₛ                                 ⎤\n",
       "⎢1 - ──       0        0         0      ⎥\n",
       "⎢    r                                  ⎥\n",
       "⎢                                       ⎥\n",
       "⎢            -1                         ⎥\n",
       "⎢  0     ───────────   0         0      ⎥\n",
       "⎢         2 ⎛    rₛ⎞                    ⎥\n",
       "⎢        c ⋅⎜1 - ──⎟                    ⎥\n",
       "⎢           ⎝    r ⎠                    ⎥\n",
       "⎢                                       ⎥\n",
       "⎢                       2               ⎥\n",
       "⎢                     -r                ⎥\n",
       "⎢  0          0       ────       0      ⎥\n",
       "⎢                       2               ⎥\n",
       "⎢                      c                ⎥\n",
       "⎢                                       ⎥\n",
       "⎢                             2    2    ⎥\n",
       "⎢                           -r ⋅sin (θ) ⎥\n",
       "⎢  0          0        0    ────────────⎥\n",
       "⎢                                 2     ⎥\n",
       "⎣                                c      ⎦"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch = Schwarzschild()\n",
    "sch.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{r}{r - r_{s}} & 0 & 0 & 0\\\\0 & \\frac{c^{2} \\left(- r + r_{s}\\right)}{r} & 0 & 0\\\\0 & 0 & - \\frac{c^{2}}{r^{2}} & 0\\\\0 & 0 & 0 & - \\frac{c^{2}}{r^{2} \\sin^{2}{\\left(\\theta \\right)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  r                                   ⎤\n",
       "⎢──────       0         0        0     ⎥\n",
       "⎢r - rₛ                                ⎥\n",
       "⎢                                      ⎥\n",
       "⎢         2                            ⎥\n",
       "⎢        c ⋅(-r + rₛ)                  ⎥\n",
       "⎢  0     ────────────   0        0     ⎥\n",
       "⎢             r                        ⎥\n",
       "⎢                                      ⎥\n",
       "⎢                        2             ⎥\n",
       "⎢                      -c              ⎥\n",
       "⎢  0          0        ────      0     ⎥\n",
       "⎢                        2             ⎥\n",
       "⎢                       r              ⎥\n",
       "⎢                                      ⎥\n",
       "⎢                                 2    ⎥\n",
       "⎢                               -c     ⎥\n",
       "⎢  0          0         0    ──────────⎥\n",
       "⎢                             2    2   ⎥\n",
       "⎣                            r ⋅sin (θ)⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch_inv = sch.inv()\n",
    "sch_inv.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOCAYAAAD9lDaoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVQoFW2RMRKCMBBFg3qAjEeA1orRnsIjWNupR6CEVm8gpa2tnRY0tt5AjoDeIL4fBycqf+ZPsn//bnYhcs6ZsixjY0wOhSlsYY5+kzCEMmwRllmWnWBV1/UE7cB5JW4GMsAV/IACdX3Co0SZ5vBBwkoIcOFu0WOZFDQEquyDNRq8j0VR3CEp55/7q6ZriqiF/MZ6rg8auMK8UzJSuxAk9oo5N53+1YnE+tegeNS5MSy4J2EH7prrPTiBBp1xdr9GOUGFbcSacp+hvleIMUFKYaLntImMfh7OEP4HvwBvn1+w+m4NrAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch.order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ll'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining Christoffel Symbols from Metric Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABdEAAACvCAYAAAASRZccAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAgAElEQVR4Ae2dTc7dtpauvxhpHzg2cPo3AWoA/hmBnRk4LqBu284MHLhxUdUzkhkk7heQODNwzggcewAFOAM4gH9wBlC57yOLirY29bslkZJeAtqUKIpcfMgtkYtL1Gf/+Z//eevq6uq1tpj79b/+67++iZ1wmAmYgAlsmYDubb73bbkCR8iuun6g6F9qu1n6PyrstxFJOKoJmIAJmIAJmECGBPQ8fyuxeMafOZ377CzQASZgAiZgAiZgAibQQqCvX/F57boftE8npO7+qB943wRMwAR2SGDT9z7d5F+oTh7J/7hk3Sj9LSuin0v+L+Aj/7q8D9qiA2udX4UnstiZgAmYgAmYgAlcTOD7SApfK4x+i50JmIAJmIAJmIAJjCHQ2a+oK9GxzLPSfAxaxzUBE9gDgc3e+0qF73fyF1Wgl5U8WBGdYaO4XZMJa7UuXt/p/D/E9N5KXGuiedcETMAETMAETGAMAT2rf2rGVxhBVqI3wfjYBEzABEzABEygk0Bfv+Ja59U+aQImYAImkCUB3dyxmF5zAmCMIjorZmJVnyBmZrl1mbIyLop0+NqZgAmYgAmYgAmYgAmYgAmYgAmYgAmYwJWV6G4EJmACJrAxAlL03kdk+aut610qlwOpTkV0iJSbrzL8KJmw3O/kVp7/KN9WbLlVouUxARMwARMwARMwARMwARMwARMwgQQErERPAN1ZmoAJmMCFBApl8IVpTLp8qCJ6UuILXiS5UfyjQH9T7vfl9kwRYuuh9V3n8yZgAiZgAiZgAiZgAiZgAiZgAiZgAjsjUF8TfWdFc3FMwARMYH8EpAB+rFL9Ib++RMkqBS2Vz8Ua7OxrY9mT2ZzSo2wsG/O6TJSPgF4pnI+/9jrFu6VIWOmz5vlXOi7kk096nHuifXlXsOuUXfFQtsP5gbZfucjOBEzABEzABEzABEzABEzABEzABEzgmASsRD9mvbvUJmAC2yXAet5Yoi/ipDCeTRE9QUCU2yjOb0uOb7XxEVDk6XWl3E/lF+udyw+K+Cvt19dz702rFgHOT7VZiV6D4l0TMAETMAETMAETMAETMAETMAETOBoBK9GPVuMurwmYwNYJYGnd+mHMSwonZTMK67kV0YNFUv6/acNCPFiQo1SvLO5L+e6EBHX8U9iXXyzXEo51bqriPCSBz9rpL5TWdW1Yt9uZgAmYgAmYgAmYgAmYgAmYgAmYgAkckIDXRD9gpbvIJmAC2yQgRS4fumSJkaUUuiiiWQu8cMpnDkX0ldIZYzl/R/HfBBkaPtbpKM5/0fZV4xxW63WFOxbtFznlBWfSZOLCzgRMwARMwARMwARMwARMwARMwARM4KAEbIl+0Ip3sU3ABDZJ4K6kblMwz1GgM0V0qUi+NG3S7XXKC8U31t9tDqvwoJAPfoj7rXawon9VBtyQX7dUD/HG+vCGu5d0GUvO8U3ABEzABEzABEzABEzABEzABExgJwSsRN9JRboYJmAC+RKQYhcL8q+1vSylRKmMJTUf56ysp8tzXd6Jkrsr4sRzSymiB4kjFlh+R5eq0bkXOsdHTbFGR9n+UFs1oaAwlO9dCnidnuSon0Hrsk9K3ReZgAmYgAmYgAmYgAmYgAmYgAmYgAlkT8BK9OyryAKagAnsgABW0SiB2Z5J4fuDNj58iXJ2jBId5fE7bYu4BRXRc8j7sxK5Lxnfy78hfw4r8yFywZv6szMBEzABEzABEzABEzABEzABEzABEzgoASvRD1rxLrYJmMA6BKTsxXocC+n72ljP/Icy50faryypy7A+j7Sw1p7dSZY/pyaqaz+bem24bmz+it9cziUkNcofIDu8mbywMwETMAETMAETMAETMAETMAETMAETOCgBK9EPWvEutgmYwDoEpKQtLM3ls5xLtdyIjscq0HsFVppYtvNx0D7HkignFvA6vlgRTqZKB+U2yv6642OhYSmbEM765pU1ufZnyT8kPqOP5budCZiACZiACZiACZiACZiACZiACZjAgQlYiX7gynfRTcAEViWAJXp0vW+kkBIZBfgd9nE6rhTMn0KK306raF2DYh5lfTInGVhX/cQp7KW2pHKdCDTugKVcFrH+HyeGY5uACZiACZiACZiACZiACZiACZiACaQiYCV6KvLO1wRM4DAEpEDGMvu6/MoSPVJ4rMPDRzOfRs4ThFX0zZZzswdLHj6Iiuzkif9jTxkUZTmXSB6Wcjmx2l+uhE7ZBEzABEzABEzABEzABEzABEzABEwgRwJWoudYK5bJBExgbwRQQP/aUyiWNwnrfAe/eQnK3DXX534umb5ACPnk+0FbymVXUsjzlcrsJV0Ewc4ETMAETMAETMAETMAETMAETMAEjkrASvSj1rzLbQImsBoBKaCxQG+1Qtf5Fzr/nfxgif5QxyzN0nSvFXC2XEoz0ozHt2tpMRGQelmTVnnE7rHk4zyMcMVkg8LDh1w/hY7/ZYmdn8df5itMwARMwARMwARMwARMwARMwARMwAT2QuDaXgricpiACZjAhgmgpL0vhS/LpzyUH1sPneKhiGft9FWc5KgvY8IHS1vXdO8RqJ5OT9T20z3ykMdbbbdLflj+z5EvvPveIlAUOxMwARMwARMwARMwARMwARMwARMwgb0SsCX6XmvW5TIBE9gMASl9BylpUSJr+6gNhXurZfvcBVdeLC+DpXzMOr43O103q/V8TB6F/abtO+REIO2jQL9Iia40UKDD/KJ0kMfulICYMimDe6eNJXO+N2dw2HURcLvpouNzORFwW82pNiyLCZiACZiACZiACcxDwJbo83B0KiZgAiawFoFnymiqRfhoGUtFQKFArykFRqcz1wU98tzR+UmK/hb5UP4PmuBoud7BEQKqI5bceSWfdsVyO0x8vNT+l5HoDjKBgoDbjRvCVgi4rW6lpiynCZiACZiACZiACYwjYCX6OF6ObQImYAJJCZRKR5Z8WfwDo6Ui4IkK/EH7f8pnuZlkrkueksfc1vmsTc+khd1MBFRPrF1/XX41OaF91trnuO2DujPl7mS2SsDtZqs1dzy53VaPV+cusQmYgAmYgAmYwHEIeDmX49S1S2oCJrAfAqyZ/lRbsXTJUsWSMqD+Ic+lshmcbpc8OocidjYLfaXH5MGzMt3BMjpiLwHqKPa2wCuFPxFvFOzUpZ0J1Am43dRpeD9nAm6rOdeOZTMBEzABEzABEzCBCwjYEv0CeL7UBEzABFIQkJIR5fkD+V7+YoEKQJGrZL+Vz1IjdvMSuK/k3keSDIpzztuZQJOA202TiI9zJeC2mmvNWC4TMAETMAETMAETuJCAlegXAvTlJmACJpCIANZuXv5iGfjPlezXyyR93FTLyYk+ADf6Ivj8sQi43RyrvrdcWrfVLdeeZTcBEzABEzABEzCBfgJWovczcgwTMAETyI6ABussifG9/BfZCbdhgcSTiQmWcfljw8XIVfSgIA9W53U5g3U6bwHYmUCdgNtNnYb3cybgtppz7Vg2EzABEzABEzABE7iQgJXoFwL05SZgAiaQioAUvXxIc9F10VOVLWG+TEzE1uxOKNKhsr55qNK6sHMRcLuZi6TTWZqA2+rShJ2+CZiACZiACZiACSxE4POF0nWyJmACJrB5AlKmYhX7D21jrGO/qSthtf/n0iCUx9JZHCr9Pp46/9mhgMxX2GBtHksxWHC+i5102KEJuN0cuvo3VXi31U1Vl4U1ARMwARMwARMwgXEErEQfx8uxTcAEDkRAylKWnbh9SZGtcL2Enq/dEwH+T9ooUmxSKoR5GZ09VfoMZXG7mQGik1iFgNvqKpidiQmYgAmYgAmYgAkkI2AlejL0zriLgAYiD3SeD/u9LON9Kf8rbSy1YCVLCcWeCeRGoPzv8n/llXX8HxXGsjN2JgAB2gLtoumCJbrbSpOMjyHgduN2sBUCbqtbqSnLaQImYAImYAImYAIjCUxWokspckt5vW7J71ed/6blnINNYAgBFCp8MJGNj/z9oI32RruzEl0Qcnaqq7eSL6You9I5L4WRc+VdLttz1fEXJCMf6+IP2lznALGDAPf07yMoeOPjjdoMb3/YmUCTgNtNk4iPcyXgtpprzVguEzABE9g5AfWjraPbeR27eOMI6D8xu15qshK9JvoP2kewutuEklNAw0CeNVht5VyvwYT7qheUr1jy3Nf2h45pY7hH2vcH/z6xKH5TtuGevMN/qyZt8WYBbxjY7ZtAffkb/stWiu67vkeVTveNn7R9p+2Btl+5WD6TLQ+13ePYzgSaBNRG3G6aUHycJQG31SyrxUKZgAmYwNEIbFZHd7SKcnkXJzC7XmoOJTqv6m9CaV6vHsmMVTMWzvVB/Gsdf73F8tTLtvX9wJ+6UFmqV/t1bAV6rXLFI1kb7stb53+qiVrsKgzfSvSCxn5/VM/15wEPLb+VtN/qnloyJlqeqq2Et1Xu6viejn2Pn0r0GNe53RyjnvdQSrfVPdSiy2ACJmAC2yWwSR3ddnFb8lwJaHw5u15qDiV6rrxa5RLIxzp5XX6hQCei9vngGcc/akN5a5eeAJborQo41RevK90JYur47A8Szu3NV1mTteGUee+tHrdWHtX94G8VKC73UiyOrRjdWkUvLK/aBG8nfLdwNk5+ZwTcbnZWoTsujtvqjivXRTMBEzCBnRDQsypY6CZZlSF1/ktV417LNRevPfC5NheMjaWDYjam2Hml8PuqWF4tt0tIQHWAhSITHZUlekScb3Uexfkv2liO50guZRtOmfeR6jjHsoZvFTyXcF/q/8ergkxkMaFVOYXTKSsU6OV+dc47JmACJmACJmACJmACJmACJmACaQhofMYb7a/kM15jPIdxy0vth7dEFxUsdf5LFW6v5ZqL1174HFWJjoXz+0hjCGv3ct4uLQFu4NWbAi2ivNAfEWtXFHY/t8TZa3DKNpwy773WZ/bl0n+N/ySTWvjNbxVU/9Xy4fhEcT5o/0/5XsJHEOxMwARMwARMwARMwARMwARMICUBjc+ib7RLprAqw6Lipc5/qcLttVxz8doTn88FBWXyf2v737kA5ZyOKm+IlTnWlnYJCaieUNa1WqHr/AudZ+YUa3TqlI/Sxd4uUPC+XFnevkIt0oZT5t1X4AnnD3Xvm8Dn5BLVfbHWufzObxXofP3Doidp+MAETMAETMAETMAEViDwP8qD8W1yp34Rb+th9Rlzv+p869KVsQscZgImkIaA/qtvlTPGRGdO5z47C8w3oOut8icqC6sBBOPSJUqROv8lykSaey3XXLy2zqfqV1wTEZRt/6GN/SO4oFyM3RiCdfoQRfsRWOVcRizPWXoHK9eH8lnW5SguZRtOmffc9Xu0e99c/HgT4eVciTkdEzABEzABEzABE5iZwL8pPca3OTmWTPi2sfFGrZ0JmMA2CPD2e/M/XL2Nu40iFFKmfqs8df5LVdVeyzUXr63zqfoVn89FZGfp3NxZeXZXHCnNt/jAWrMeUrbhlHmvyfhweel/h/VF37cKDsfFBTYBEzABEzABEzCBHgI/qh9VvNXXE8+nTcAEMiQQM9pTGJJuZulKyTvEWDQYzc1eC6nzn71AZYJ7LddcvPbG54hK9GBtHmsT4YbBF4oP6dTAWcPY7kIC4rjkK10p23DKvC+sFV8+AwGU6J7AmgGkkzABEzABEzABEzABEzABEzCBFQkEfVeqVRlS578U6r2Way5eu+JzOCW6lJsftdEYYrNwIeywVgILK39b/4TK90ttm+KeSmblm6wNp8y7tfH4xGoEVP+d3ypYTRBnZAIrEFB7x7KIiSPersHHirD1Wx06b2cCJmACJmACkwnoGcNyETgMur7S9r3CVh0f5SADAHKRA1mO5sz+aDV+Vt7Ub5Wnzv8MyEwBey3XTHiK8dZcaS2azrVFU883cQbBDIibLsyQeJDcJLPgsR7UT5T8rQWzWCppFP/InsKlbMMp807B2nmawO4I6N71QluYOF6sfMrjAfdJbSgCyPP+YpnNn/BzyfuDtu+U9CNt0W8BlOVanOX8xXOKJmACJmACuRDQs4SPj77imaON9dN59rzUfmzMuojYOchAwXKRYxHImSdq9plX0OXipX6rPHX+lxOMp7DXcsVLOz50V3yOqkR/oXq/E6n72wp7o4fHx8g5By1AQKyx9Lspf3NLREjmYrKlLMMCdDqTTNmGU+bdCcUnTcAE+gnonsV/mEH6Gs+6QYrofqmTxKBPEBxKjDZeKDr+IZ5WpAda9k3ABEzABAYT0PPjsSLzzZlqPFQ+ozle5eOjOcgAsFzkQJajObPff42rjkNfNtZnDWGLvf2SOv+laniv5ZqL1974HFKJrkr8SQ3ivfzqIxDa56bxUBvWZnYrECiZP5WPAmI1p/wea+O1fHw2rCQnWZTrOixFKEN46KxSDuWXrA2nzHsVuM7EBHZMQP9fFOjc/xbrIDfwDVVENy5Lf9hgxCv238SkKuPxHIOtnQmYgAmYgAmMJcDz5U3kolcKu6/nzBrjjBxkAEEuckSqY/dBZr/7Ki4KmPqt8tT5L1XLey3XXLx2w+dwa6LXWgADe5SfWJfh7mq7p+NYB6aI4J9hBMRw6DqyKCVWsa5oSI7yiM7obcn6bdkGLllOhjJQlm+1relStuGUea/J2HmZwG4I6F5XLKUin07MKk551ZX1rYroVYSZmInKwD0ey/3W/gFMtfE8YfmaypJwYpa+zARMwARM4FgEeD5jINN0H8sAzi/9bMlBBoqbixwl+kN5Zn+M6sbogz550zG+X2NVhtT5N8s91/Fey2U+DQKfN44Pc6hBLp2SVS2gtwJXbFAwPy3lDZMMj0pmQ4rB6/tfELFM64N2P4tc+FDno4rn8jreDEApwQ19Nqf0UHZQ90X9ax8lT6Xo0TEK9Wq5Hx3HOrWVPJzX9kHbWssjFHkrv2RtOGXeFXjvmIAJjCWAMvjrsRfNEV/3jF5F9Bz5zJ2G5GaQUdzb2dfW1W94prh0oJdWdMxdTKdnAiZgAiaQiICeK4y7+lz4bldfvEnnc5ABwXORYxLEjV9k9huvwBHiq67RXdC3rQw/yvpH93JvRFKToqbOf5LQAy7aa7kGFH1QlD3xOawSfVBNHzcSioJKua19lB987IavxA9xdaU3SniUvSdOaTLTXSmu6yd1DiU253FDOpafYo77vaN82qwKUdyzkXeYTOhLnbLw4OlUuPcl4vMmYAImsAQB3c9Yb/UP+dH77hJ5hjSV5xhFdLhssF+WjecOzylc8dxQOMtt9TrFC88cnlVf6ThMsJIe51jyS17xzGpVoisO1jswrgYlXGRnAiZgAiZgAh0EgoKcZ1DTvS8Diuda8+SMxznIQHFykWNGtJtJyuw3U1WzCEq/OeWqDKnznwViJJG9litS1ElBu+BjJfqkut/9RY+lBHihLbzyjwKEsFva2hTPFRTFqStpuJb11ZqOsJD+ybkyD5QR1Zr1JxEuPFC6dESjeZdJU3YmDnDB/3TU/kt6WHhaid7OyGdMwATSEeCeO/R+NlpK3TNv6SImPy9SRI/O+NMFPHO4r49eoquUm0FE8ZySHxTxV9qnozfWwfipNlujjyXn+CZgAiZgAm0EbradWDE8Bxkobi5yrIg+m6zMPpuquEwQ9XHpr7cahlyWev/VqfPvl3BajL2WaxqN86v2wgcl+t/K4gX/vLQOORoBrNB/byu0Gj/KbRTGL8s4WJtjpY4Fe6VA1z7KhLZ1ZFkuZTGFjtJudeWfN6bYv9I5XsVH5mCJjnV578SB4rzVhgLJbjsEwj0v+NuR3JKawHgC3J+i973xSZ1eofslCvQ5FdGnGfQcKf9LlugqrORDFkrrdtif6DOhykTsdW0MUOxMwARMwATWJ/D39bOcnOP7jiuDdfC7jjhznMpBBsqRixxzMN1aGma/tRqzvCZgAmsSqPoV15Trv8qcg7+mIM4rQwIa+LNOVn3wj1KdV9TflOLSoUPZ/FzblwrnlXmU4re0FU5h4fV9LMrZbzqsBrse1s34ax3/rIzuS2YmClizfahlOWWhTHbbIRDuecHfjuSW1ARGECjvZ9zD6/f1ESn0RuUez3rghVM+lyqiQzpjJlr7lujiXv6LtuayZEwC1yd/L7qPl4xJz5OqgmBnAiZgAokI/DNRvqOzrT2bY8+fEFY9p0ZnMOCCHGRAzFzkGIBsd1HMfndV6gKZgAnMS6DqV2CJbmcCrQT0QEUxjkK5UIroGIUDlnYoCFDKoEDH8eHRQskuf8g6sjd0zVIKnUKgKT+Sfeor+HRuYWNnAiZgArkRuCuBwiToErKdKaJ1L53j/j7onqq8UDJMXaKLSWKs6F+VYHg2DZ08LS8582AN86nPk7MEHWACJmACJrBrAjzDYs88nkm4rmfcpxiX/+YgQyhrahaX09xmCrm0gW3Ss9QmYAKHIGAl+iGqeVohpVSgA4OFIevMFgoR+YUlhHyWc6k6dDquFDTan8UKsU1qpY9iP2bd3ryEJVlOLDd0/Gcz0tBjXftZR9wsJwU65PUpEzCBzAnonsMEZu/SWQOKwb385F444JoxUZZQRA/OX5x4PkWXqtG5ziW6dJ7nWPUsG5xpd0RY85yyMwETMAETMIEhBHhWxcY2jKl4q3eOiek+OXKQARlzkaOP1x7Pm/0ea9VlMgETmJWAleiz4txPYuqsFQp0+ShwruSjEPgoPyhisESPKi2IP8CRDtaDo51kQGFfyDX2Yl3bpQgfm1w9PmV5Xw/wvgmYgAlcSIDJOQY0bM90//pBW3jTJ9yLh2TB/Wmx9VQl0xKK6CHlGhLnZ0ViiS7uzzfkX2plPiRPWFN3diZgAiZgAibQS4Bnkza+yfRAW/EWk3ye3Xyb6V5vAjNEUH7JZaAYucgxA9LNJWH2m6syC2wCJpCAgJXoCaDnnqUeoCjQw0dBgzUdlobFF5zL83w07RLrPRQa5LMXh8JkjFJrL+V2OUzABBYgUN5nuccyYRldOmtEttxrP46IPziq5Fzq7Z5BMozNX/HHrLPeKoPS6ZqQhTXKDzsTMAETMAETGEoAq3OWFwvjI5YFu6djjIfWcjnIQFlzkWMt7jnlY/Y51YZlMQETyI6AlejZVUkWAmHpiAIAv3LqxKFIx9G5u3StVzqEdA7PXNl5JC+UR3y4FKXHW/lh/fWzazIIoMPxMgM5LIIJmMAOCOh+V0zKyW9dOmuuYioPJktjr5E3s4gtkdWlTG5e33osGbjPB8VBiMfHQpv31RcKq6zJtT9L/iHDmXwmie1MwARMwARMYDABPc+YgC0MlgZfNHPEHGSgSLnIMTPeTSRn9puoJgtpApsloHsMekbesmJciQ5tc85K9M1V2fICqzF/0ZWLzs/x6j6KkahFoNJHebRaJ1L5PVZ+/IHDpEFhQajwMUp7FP5DlFCKZmcCJmACgwlwb2ldOkv3KRTgd0JqOq4UzCFMPgPz4r5WC6t2dQ2TmpOWyKoSuXBHMoRJ2iolhb3UllSuSphxO7yZBHM7EzABEzABEzABEzABEzABEzg8AY3rGLcytsW1jk0/nc7310r0fOtm15LpD/Sbtiv+SNrWfE0xxhWlPX9iPqDKjBjWkPzBB7ky/pV8L+cyiJgjmYAJDCFQ3lv6ls7insXGPexpS7pYRt9sOTdrsOTgY6jcQ8kP/0eFXbL0l5K4zCWQibrw8+CyavPVJmACJmACJmACJmACJmACOyGgMRl6Pz6WzXhxs85K9M1W3S4Ex3Ib68MzC8Q1S4eCRxuW72HNd5QfYxQgXGcr9DUrzXmZwDEIoITuWzqL5U3CWz3Bb9LhfrbWbP9zyVO8zSSfPD9oS73kytoyfaUyM3FhZwImYAImYAImYAImYAImYAImsBMCVqLvpCK3WAwpWPgKPK/rs+75GKX1EsVl7d3RFvHILmGQP+lEwBJAnKYJmEBaArqvdC6dpfMvJOF33H+0obBmfbnYfYylqta6R9XXtuP++FFbatcqk7jNsZxXs3wsr/NzM9DHJmACJmACJmACJmACJpADAfWBgxHgO8mDAcj3CltNJ5M6/6XqYK/lWorXFtO9tkWhLfOuCLDWb5v15CoF1Y0O5dPU5QaQvXW94lUK4ExMwASOSgBF7X3dw3gl7qH82HrosOH+NniJKi6Y6iRDvfNN5/yS+2M9rakiXfXIRB5vtbGcF/yw/L80X1j3vUGgKHYmYAImYAImYAImYAImsC4B9XkxsHklH2McvgPHm/WFceMakqTOf6ky7rVcS/Haarq2RN9qze1Ebt1oPmrDivKxtjYF0KKlRQZlMFrRg8y6DtlzsLRclJETPy4Bte+kVgrHJd9fctXNIEWt4v3BfUobCvepE4b9AtViKB8mGOmYxyzjazHbd3XtrNbzMZkUdulyXicFUHoo0OF9qSL+JF0ffCIgrr4fuTFsgoDb6iaqyUKagAmYwOEI6PmEDoNvLlXjCO0zTuCY/vvXS0JJnf9SZdtruZbiteV0sURnoMdA1et3brkmNyy7bjgoHJIo0C/BhszIfkkavjYpAd/7evCrfSe1UugRz6fHEXim6KMnC8dl8Sm22g2KzkKBXu5PSWbWa3pkmrScV4uA9KeqQUlLHAdPIOD70QRoviQJAbfVJNibmTJhPOtEbDMDHy9LQP8jlHwYWdEXtTMBE5iPAOOBmJHLK4VjcMNb+ku61PkvVba9lmspXltLt+pXoET/UhszTje2VgrLawImYAIXEPC9rwMeAxedPrNSUFiwUui42qdyI6D65FVNlnxZtGOs9BnsPtH2Qft/yk/+9fUumUoec1rnsy49ExZ2MxJQPfl+NCNPJ7UcAbfV5diOTPm+4jO+tdsgAf2PeKuruO/LX7TfskE8FtkELiXA/TFmQBveruf8ki51/kuVba/lWorX1tKlfot+xedbk3yqvHoYM5Dn1ZSXZRoo0Fb/gEKZtz0TMAETyJ1A12z6E91TUbCHzlbuZc/6JbMAACAASURBVLF8nwjwxs9Tbax7uIhTm6h/xHORPMYm2iVT2YZp6xc7pcXkwbMyzYvTcwInBHw/OsHhg4wJuK1mXDkWbRsE9BzFSvaN/OQT8dsgZilNYBgB/aeGTEotZlybOv9hlMbH2mu5xpPovkKc0MHylhgK6S91jFL6rXyMvTbjDqNEV41wM3hRbgxyf9CGxRwz3V6SQxDsTMAETKBGgIdbbJmloDjnvJetqAHLfVfPPJZYoaPyozY/92asMPFkUMI3Mpict5ufgO9H8zN1issQcFtdhqtTNQETMAETuJxAUJCH8Vw9xWCdPkTRXr9uzH7q/MfIOibuXss1hkFv3HL8uZgxV68AM0X4fKZ0sk5GlcWMB69r07Fl/e0w0/FI+7H1oLIuzxGFUz35Y2KRik/JJWXeERQOmpGA6nZI5yl0FmbM2UmtQAArSWb9F/1o0ArlyC2L52a6TJX4frQMV6c6PwG31fmZHi3FHPrWOchwtHrPrbxuA7nVyOry3Fw9x9MMU+d/Ks18R3st13yENpLSUZTohcWdHggoDaq1T3VsBfoGGqrqiTcGeHugsHqVj4LvtfyvtR3WmlJlT8YlZd4baLJ7EDEoyFNZKeyBYZZl0H+X16O/1/ZC2yzLmGRZ0BWFEkcmJXhGHfZ5tDBu348WBuzkZyPgtjobyuMlpGdIsn59oJ2DDEEW+2kIuA2k4b5irsHaPJZleIa9i52cKSx1/jMV4yyZvZbrrKBTA3Rv4VtZnU5xPuuMkMnJaxfIQUP5b23/e0Eaa1+KJXpYE33tvJ3fBAL6I/ljYhFuKblckPf/qCjcM+z2QcCz6RutR/2HmUze/Kt0GeFnUuJNRvIcURTfj45Y69sss9vqNuttUakv6FvPJlcOMsxWGCc0iYDbwCRsuV3UqaNTHQcDqdhbxyFsMaOQ1PkvVVl7LdecvMTos75tzvx60rpIL3WJJTozVf+h7f/1CJjFaVUYS7rwIbzKEr0pmM7dUtidEK7j2HrA4bT9dQj4A01xzim5TM3731QU7hn/N14kh2ZEwLPpiStDz5/e2fpLRVQelybh60sCQ1gqziasKzKsVN+PMqwUixQl4LYaxeLAAQSm9q0HJD04Sg4yDBbWERch4DawCNZVEx2io0Mfhm6s6YIlequ+rHnBxOPU+U8Uu/eyvZart+AbjHCRXuoSJfrWWHGj6PsIHh8FY2MW7unWCrhTeXl7IDaZEWZROd9Xr3tEk5JLyrz3WJfZlUn3wI/akCtYJNRlDGGLWSnUMzvqvvhb4ZpR5as+Hkgc+hFYkeLzcdalBxnKxk6cfT9yM9gEAbfVTVRTrkLm0LfOQYZc6+cocrkNHKOmX6iY4Xtz9RLf1gHLPgY9S/3cnPup85+zLPW09lquehm9LwLXjkKBwa42Zle7HGvEsrYpN5WfuyL63PIEVBdBWdeVWZgx7Yqzq3MpuaTMe1eVuI3CeDZ9G/VkKdch8Fz3vx+0sQzOI21eGm4d7iEX348CCfu5E3Bbzb2GMpMvh751DjLUq0XyfKmN8ThGbewzcf2kHsf78xIQX4+750WabWqqawwU38vHQKRwZf0/1AF93EVd6vyXKtxey7UUry2n+/mWhZ9TdjV6Zo6+kx8s0bmJvJkzD6c1mkBQkMdmQ8Mrs0Me+KMzzvyClFxS5p15texOPM+m765K1yuQnqUMejfztsIAebHOCQ5L9NhzKZy3Pz8B34/mZ+oUlyHgtroM1z2nmkPfOgcZqjou+w/+dktFZJWdrNrAKiU+dib0a5/S/y0x3JV/T8dr6b9S579U7e+1XEvx2mS6VqL/VW1Ynt/XjQPl7A35sSVE/ortvVwI3MxFkMzkSMklZd6ZVcN2xeEeqI2JxQfaiiWT5DNpxQTjve2WzJIvTUDtBGsxFOibUaJLVpT+tPUfYnwUXi8L1nF9b7bFknHYRALi7/vRRHa+bF0Cbqvr8j5Qbjn0rXOQ4UBVnmVR3QayrJbxQulZhTFIsomq1PmPJzbsir2Wa1jp+2OJD28/fK0tvNHLJM5X2r7XufpYS0H5OpTofyvFC/6s0grG4h9Hm1XgMjHJzbIu2TjJc8T1cZnQaHNhtvxdW4Qdh6fkkjLvuas03POCP3f6e0jvtgqR0kphDwwPVQY9q+gc3ZQfVUbPDUP5PFaatNPXZdrF20lj81d8lny7pa2aNIrJqvP0DZhcehM777BFCfh+tCheJz4jAbfVGWFOTOrvE69b4jL6zv+t7X9bEud8m1trvJODDAUDPV97dQeKc8RxcVsbmSs8mzYwV4FWSud/lA//bzsTMIF+AjzTeGOP7Znu5SyVyRjulrbclehVvwIl+r+04YL/6WimXz/kZgJ5wGTUdvwxsUi9p+SSMu8IikuDwj0v+Jemt7vrqW8VKpmVwu6AJiqQ6nHyRzHHXKu4KLCZdEGBtJajw0W+t5Uvy7Fh0XBrSua6tujIyUehTts/cQrDAh0FOs8mLCb83zghtOwB3OG/bC5O3QQuJ+C2ejnDGVL45wxpzJXEDSX0H9r+XyxB2os2TvEsa7oQtqhyIQcZQsElixXkAcaKfk5tYMViz5HVvykR/t//d47EnIYJ7JWA7jGM0fhuzH1tf+g4GFw90v6bDZS76legRN+to6K0LdrpmBPe1uSds+wdafkDTXE4KbmkzDtOw6EmYAJdBPgo5hdEkM+A/IO2oYPUMdeiZI6+xVXmy1JAKLpnU7IrLRTeKFYL5ar2eeZXz30do1C/o61wOu5bqg35Kce3n6749KvrgpXEE+0TSB5W6ELCzgRMwARM4FICOfStc5DhUo6+/jICbgOX8fPVJmACLQQ0firGZ/JZzoV7TeF0vAUFehC38K+dHO3oQJXBmqyTrNESYkDpj9x2fxHgVY9KAfJXcPH6/hvxwjLtiC4ll5R5H7GuXWYTuJRAXWmNFcCY++aYax/qnnympFYYz2KWXUGBzza3u6M82jpgKO2R6RdtrLnX6cq4lONETh1j6f5ZbetNqzMjnzQBEzABEzCBvwjk0LfOQYa/iHgvBQG3gRTUnacJHIsAluhhTfRNlnyXSnQNcsOarMXH8NaoGeX5WNuPpc8+1mqjFOKKX8zIyEd+OxEQC5Qf7+tMtI9yA4vGR9oO6VJySZn3ISvbhTaBCwnoP1tZZiupUR/FHHqt4hWv5sVE1TkmPHllry5HLOroMKXL86CyZogk8EJxgnX5z5HzsSDk5BljZwImYAImYAKLE9BzKvl4JwcZFgftDDoJuA104vFJEzCBCwnoHoMx13X5XWO3C3NZ/vLNLOci0CiWgX6z9FFYn8FXGAPqtddkVZaFcoC8L1qXVfJ3rslKRgd0WEJSp9Q/7q62ezpuszwsIh3gJyWXlHkfoGpdRBMYTkD3Qp6PvV86V7zOj2LqPAp2Ptb8URsdnLBW3VXftYr/jbazZ7LCFnWSC1nJ+8zpHBZVrGGONTrPZxTjQ54blAOeZ1b1CrMzARMwARMwgSUI5NC3zkGGJdg6zeEE3AaGs3JMEzCBcQTQ561m6DxOtOGxL1Gi/63MJvituZaD16dlhKAIZQF5Br9D3dB1WVECoCg4c7VB9KxrspKR0p5zXdZgNXeyJutZgQ4SULYTrz3bqO+UXCbm/fdGEXxoAiYwDwE+WobCmO2Z/p9nXzpXGM/G1o9i6vxbnefZyLOM5Vf+oa1Qovddq3i4O9qiz97ibJofLM/vS/738m/IH6oUhwWW9XYmYAImYAImsAoBPaMYFycd7+QgA7AlxyDjgFUq5mCZ5NIGDoZ9zuIG3Vzw50zbaZnARQR0f8FQaXWjq4jQF+mlrkUSHBr0rzJi8Luu+17AGLyzYTHGgJaPdI1xzIoGhyK+TQGfak1WZJtlXVYxYqB/tiYrGdiZwIYJ/HPDslt0E8iSgJ4XPA/pjOA3v3RezPQrDs/bJ9o+aP9P+QxOK6cwlN9cGzo1LGdyjwgK67yWOKXD0ptnezZOsv+q7afgjxCMclAeOxMwARMwARMwgfUJBOOA58qab4Yxqc9kPZP8diZgAu0Egm4u+O0xfcYEMiSg+/0DbYxrBznFZYw71l2kl7rEEn2MoKwRzrqkYYCORRxht7S9GZKQ4tXXUuX6s9e3FQfLsXq8KukyH9ZlPVEeVBEu3FG6DLhD+WKphXVZOTfEWi+syTrUci6Wp8NMwARMwAR2TEDPnuKZJ7/1S+c6V5+EjtF4qMDqGxOKzyR18WwecG1IjwEv1412yoNBMc/1PoelfPWM1z4TApOcrv2s40LyGNx560jHp0zABEzABEzABEYQ0PM5GAcU43odF2/FKQneYh+kNxiRnaOagAmYgAlkQkD3+McSBcOuaryHaDrmucCbWrwtzHF4LhT7Omap79VW8VhLiU6BfqfAMacCD35lC0BKA4v22EM0yZqslEnyoDw4U+yX56asy4pC3muyAtDOBEzABEygjwCDzegzqO9CnWcSOPZMHXDp5VHK5znPu1FO13Upwkel1Yg8eUKgkY4PTcAETMAETMAERhDQs73XOGBEco5qAiZgAiawAQK69zMe/Vr+yXi2DEcH/I32P2p7rY03jevGWxgsF6ufrFHUa2tkEikkSnVmGMKgnQEriubOV7YAoziFAr3c1+GJ4zWvYnbiJDT9wc8S4b5kZrIgutxMRETKwYyLnQmYgAmYgAm0EtCzhWfFJV8651l88rxpeca2yqATDHrp/OzBUY73eyiIy2ACJmACJmACGyWAccDLjcpusU3ABEzABMYRQNcbW7Gj+O6XxqZBac4YjedD5XQOA2T0rauMRdeyRK8XkNe2USYXr5eroAzci0LLb67nGpTsV4rHuqxc+0T78ooBe/PjK1kOfCXvlC/Q0jhWaQTAtDMBEzABE9gsAZ6jU54zocDM+DNBHRTpPHuehZMDfZ5Z4fqTS8p0mTynw8PapnSQ3sqvXsU7uSD9ARP7J68RphfJEpiACZiACZjAMQiU/YZLjAOOAcqlNAETMIEVCOiezLrjN7W903ZXG+PG8NYQ5z5qY/xInGc6x/FVeV2xr8OvtL1TWNv4DyU448XK6ZixJeH1N5aj403FCzrlS8bEVd5dOyjR/1ZGCH5X/IvOlRCYYbit/QA2wAcMBS+czr8J+/g67lvTlWgMfEMlcTzYKX0U9MjW507WZCWyrl1iXVa4tDWQPhl93gRMoJ9AuOcFv/8KxzCBDAnoGcSzs3p+jhVR1/O8Oem0jE1D8Xlm06k6c2X6zUnvs3hzBCgv1tKjv8DEO+46Pwpv67Bxuum43tZvTSo+NgETMIHtEPh7RqKGfmbwMxItW1EYAy+uCMm29BZsSwRyutdsiZtl3QgBjaHQkTKpWYwV5WMMxT6KdMZLLKNSjEPlM+5iDPaV9jGeuim/GIPJ576OMfWZK8/F9LiMH5tjXNIpdMiNhF7pGJ3yUs+O6r+OEv1fZebBLw/n9UowAC5mEeSjtGZNmwAAyCfr38wrQXdqkgMFQH2Go/uC2lldu8S6rDeURawh1XL2rgmYwAUEwj0v+Bck5UtN4PAE6ETFXsFbGwx9CjpwTNYz6U1Hi/7GGEd/ZMik+pg0HdcETMAETGA9Av9cL6venEI/M/i9F6SMoOcmz9CH2niGDjFim11c5XuRccDsAjlBE2gnkNO9pl1KnzGBCQTK58ETXYoVeXCMkd7rHOOrEytxhRX6Xflcw32cVUR4pjBO5PgnbTHHeO195ARjMlYrCeMy4l3pGN1t06E7Lc43T8x0XP3XUaIv7lRICsPgmtmKMJgtZi/IvDw/xytbYfBMslt3NLZYQ9p6uSy/CZiACZjAzgjoOf6bNp7nt7TFOjarlFh5IwdWC4Xlu/bpF4TJ+l4ZFD90zgZf05uoI5iACZiACZjABgjoGVgoRUpRGYvamYAJ7JSA/u9BMckSHShJMXhdrf+bOv+lqnVn5eKbk1f1dhH25XMOxXXTEYYl+g/aMFJmTMa65jiOm5blhPO8iaXFuIwPihZjS/nolNsU8avpTq9JiDUcJv3MIuCH7bEgBFDAmcPsHnDFAFj+iVNerMPKjeKptmJNVh0zQ5KruyHBVruJ5QrBcpmACZiACWyGAM/YS5eFmaOwd/R8n6rIp6MXBhVzyOI0TMAETMAETGATBHh2auPVe49BN1FjFtIEphHQ/xyd3Cv5GLnyn6f/+1L7UV3atFzar0qdf7tkl53ZYbmKZ4HKhZK76X5XQCycNsS3r5iU/V3+19pYuYMxYtsYi3xiaSn45HnEW1JtaZDvKs+utSzRv6D0bU5Q53pli0Gz12RtA+1wEzABEzABE1iIgJ7lP2krOuDyV+nENIuifOmAxSwcmlHPjnUtnS8m2XOYCDiTzwEmYAImYAImYAImYAImcAkB9XP5fhCrQFRGrNpnGQ6OsfSdtMTxUJlS5z9UzrHx9lgulYmlVBhXYYgc3vJlrIVBNJbmTLw+0Fa0JfnFWErnsRbHiJoxVTGu0jnGidHluxVOOlzbdNV4Uudpm4/kV2GNyFz/thG2yOEqSvRFJI8n6jVZ41wcagImYAImYAJrEKBzxCt7i3bA2wqijtVHnYt20NquqYXTOZt6bS0Z75qACZiACZjAeAJ6hgULu3e6evXlFcZLvNwVZrEc276Uzb6P0ObP09eNvbHJhxmLNazL/vRSBU2dv8s1goDaApbkLPXD84ln05X2eXsBn29QcS4owHluEcakDFHwWf2D8RnnugyVUNhjzFRXkhP/aZkWhlrVxI/Cm46xZ1f6zfiTj3elRBdUr8k6uSn4QhMwARMwARO4jICew3SW+BgZFgpta9ZdlskCVyOvkkVuOnl2JmACJmACJrAqAT1/WF7hmfxg0Ye132sdo8CoKxVWlStFZmaRgvqnPM0+HfsVc8ZCONZHD31gzncpKy8VNXX+l8rfdv1ey3Wl+0JhhR4reNs5hdOGxrQjlPQowau8lMagFUsUj+fllfxVnpXXyGyiQ0AKyTrkObkAP7VMXpM1dQ04/9wIcBNcZXYwt4JbHhM4EgE6MNpinfNsMSDvWh2vbCFYsNkIqC3xaivWXFjnvNDGwMrOBEzABKIEdI+ILq+gyCggeEvqMM4s0lW12adjP2POnTo61XGhbOzJj2/zLeJS579IoZToXsu1FK9YumKIrui6/GDVHovWFsZyM2PeJr5IL3WJEp3C8VBf7E/WRqgrXNAZuPMawBT4XUkPPqe8uTlRMaNdKTfyb0oBMbqgvuCIBFAiHGogcMRKdplNwAT2TUD9E5TCQwZhk0Eo/a0roZ+rDKwViTXNI20sN3jmdH5xlmeZOsAETCBHAl3LG9zXvWLRe25mQMwiXYWYfTr2c+Xcp6MLuruPkQyDceyS95vU+UeKPUvQXss1C5yhiehZh8ElbwYPboOKyyQ0S73E2nRb1hfppS5RorcJlEM4D4BkyjoqUBsyTHHIPfXaKfn5GhMwARMwARMwARPoJaC+Devdfzeyo9qbbiTCICV05Lpcgm7XBGFA29axR8n+D/EcPFiopetdEzCB/RBgQB8UWPVShXvHkd5mMYt6C1h33+zX5Z1rbjcTC5Y6/6WKv9dyzcpLfeJqOZeBCf+iayYZMA9M/yza52chOwhgcKfNa7LuoC5dBBMwARMwARMwgfQE1K9Cgf6j/DXWGxyqhE4PJiJBgxHLDEaNI4injcFCso/xRsR3kAmYwIoEdA8YMokWrBwXlUyyMOmHJSDKVN6MxrjrrfziI3LaX9TlxGLRgmaYuNlnWCnLiBSbrAs5hftM8fHIEDiznzr/mYtTJbfLcum+8GdVwpV3lPfgHGNxFfbZ4ARGRtylEh0GgsYgb1NLokjmTck7sq05ugmYgAmYgAmYwAYJqH+CQoW+1SqWHsqnrqhvVULnjlLlQAGF5f6bNllhqg3DD5awGfMBprYkHW4CJrAtAkFxFazO69IHxcwQRXv9ukn7ugdx7x1rBTgpr5aLsmHRIt+eg81+z7Vblk3/cYxNOYrdU0JYvQ9WXjmPlzr/eUpxnsqOy7WYIvqc4nZC9rqcy3ZqwJKagAmYgAmYgAmYQN4ECmXw2iJqUBKU0Kso7+csn2RH+V8o0Mv9ruSf6STx7UzABEwgRsDLAPxFxSz+YrH2ntmvTXyZ/OhT8dZJ04WJlKX7XKnzb5Z7ruO9lmsuPr3pqL+MQUmsbUavVdwn0RMLB2KJzkwTr22Fme6Fs3TyJmACJpAFAd/7sqgGC2ECJpAzAXVQ+WAPy44sZpkUK7/yC0porKa+1za7daTSpGwsHfO6lKGwwlL4oKULFO+WrsNK/6O2r4KM8kmPc0+0L6/oa7fKrzhvtMHY1ujQsjOBywmgzGB8m9zx/5YQXdZ8XWPwoNRacnmFgpHk7H1tX3G6yjEH6yxYzFGQDaZh9hMqTf8JVhLY2moCLCEXm7inP0R/hD7Nki51/kuVba/l6uSl9kJfGqORrzoj9pws0zkbbygcpTp96LckoeOqj86+NpaaXON5X/UrUKIjFJY+BC79h1EW+TjBDjcPOiZUOoO0VQeJ+dDIWxLXVbx+UnJJmXecxujQw977RpPyBSZgAkcmsNjH2vUcmUUJfUHl0OdDcX5bsrCkCs8FZOp1pexP5RfrncsPivgr7TMQHevoiz/V5iVdxpJzfBM4J8DkFv+p5Mot3Q+4p3B/YKLtbJypsKTLK0iuwkmOpRXkIatWPxcWrQLu+ITZT6tccUOBiBIv+f9naAkk60/aUHpWE/fapy/0UNu9oelMjZc6/6ly912313L1lVvnf9fG83ayK9vf1/JPviFUhpP2N9rnWflaG+23rrd+oeNFjG0aBar6FSjRD+moABX8mfxisCKfGweVQuWddXAOCSmTQqs+XFeRukjJJWXeERQOMgETMAETKAno/kx/BmUsDqUw7pHC6x3OT6HDfuk0nnRqh13WHUvyoFiaUwndnWHkrGRgPXKsWworce3T/6v6gKWMd8KlOq4r5ApL+dq5KYrzcDk+xiwMBK5rm1pX9fS8bwImsB0C/P/D/bou9Y3ygPNHcWaRrqbNPh37tXOmz0IfLNx37ur4no55c2YNlzr/pcq413K18irbzKXthj51TBGPdT9949Av5o0ZxiWVwYnO0ZdHib5a//mQSnQBZsYQyHX4zGxwTOV9rc0uAwKuq3glpOSSMu84DYeagAmYgAnUCNCRrF5r1D79msIKshZn0K6ufaCIvFoZOq+DrhsYaW4ldJEt5dVWlX+ALHcUv63zj3U623WlEyYmQpIMPOsK94s678qDfijpnQwOQmb2TcAEdk3gkMsAtNSoWbSAWSHY7FeAnEMW9DkkR+syc0vLmDr/pcq343Kx9ngYC7CCxzuVlaVU6B9z37iv/eJtDPn0jwnjHEY4HLPd1bk2oxyuP+m7l+kQXtfNkk7MMQG4Wv/5WkyCA4RRebEB0yvgq6KocLs8CLiu4vWQkkvKvOM0HGoCJmACJhAIPFY/ho5kcCirv1TYoGVKwkWlf1d+rL/UiDbpkI7wiRJ6UirnF7V1sM9ilv29LgtPrF+YhIDhz40E6OxjxcXr0Ew28Br0pQ7WMLczARM4EAHdQ3jL5X15LylKrn3Go9xXHhUBB/kxi3QVbfbp2DtnE8iVgO4LjClucn8o7xH0iwun44/aaSq/6dujL6I/zvjjV22sY84+/eUTpzDikU7TMcnT7KOfjB1qF6DHrSvba6fm3/18/iQ3kSINof5KbhA6VB7nKyv1cNJ+EgKuqzj2lFxS5h2n4VATMAETMIFAgM7s7+Gg6ZcdWDqaL8tzdEjbvgvT1lltJjvlOCih6fjiWLYg1jcrTi7xIxb0++jonzmdw4qGNUODJTrKrGpCQeF07Jud+7N0RgYw8Jgy2TEyG0c3ARPIkMDhlgHoqAOz6ICz8CmzXxiwkzeBjRF4L3mfqN97XT5jB/q+9f4659tcvZ9MPMYVTUdYLA10TrwNiyELrrhWx28+HZ780p+PpX0Saa6Dz+dKaCvplJXfJ25Yf64vns8vSMB1FYebkkvKvOM0HGoCJmACJlAnoPt0vWPLKZTVdEJDp5M+DgpiNr4Nw+uYLPeC8rayDNc+jg7zu2Jv5h/luYQSek4psTzn7UQ69jfkN7nOmVdIC9bugwYa9k3gQAR0j0EJkGx5BVBLBqwEh06ycskiLgcWixRsA4ma/QYqySKawIoEdE94o43nAs8nxg44jusK8iKw+VPeT0Iwz7iYY6wRO4dSnA+KFuMX+VjAt/XF6auv5g6nRBfZMDiJVVSAT0XapSfguorXQUouKfOO03CoCZiACZhAlIA6nLd0AqUIlmVXOqZDSqc3WHfweiWOD48WndRPh9Uv8WP9pSrClB3l9eeU67hG1xZrLk69Plw3VgbFr15fDWlM8Xvkh7X7oFPA+hoTMIE5CNDPHzrJOkd+TsMETMAETCBjAuq3Mpb4XT6K8yv5fF8S6/BibEHYhQ4Dnra+b924hzdC2/JkvFKPe6FI3ZcfUYneTeTT2ZtDIjlOFgRcV/FqSMklZd5xGg41ARMwgYMRUCeXDmXRydV+oQiXX3Qw5Z9YkOg4pkDvJabr6FiH1yy74rMkStW51f5cinAU25Sz7vhQaFiqJoSztvmJ9cpcMoQMZvKDMcdMyTkZEzABExhGQPdE7qVjJlmHJexYJmACJmACWybAs4G3Wtmu6E9riy6FyPkOF1WUKy0s3Zt9eZKpjxvo72PwU4U18uH6t42wxQ6PqETvGqAw+45b5NXlT0n7dwQB11UcVkouKfOO03CoCZiACZjACYGyM/q9/GA1grL7Y63ziSX6kA4wyvdop5cMld4beUUeHK/tlH/Roa/nq7CX2pLJVJdlwj790GLCY8K1vsQETMAEJhPQfXPWSdbJgvhCEzABEzCB3Agwhngioeij8h2loFBnjPBc25XO/6gtfEeoMLCphWG9fkcbyyOiNG8uBcOyKjnp3gAAIABJREFUk3x4tK4kJ4+nCpN3Rd++65uV9PvPxgRcuIQ7nBJd8GkAsIwNCkNYvfKW4O40BxBwXcUhpeSSMu84DYeagAmYgAnUCeg+jTUGFht8FBPlOY6OZbHWbnn+uvxmB7aI2Phh4nSVt4skD8vOIDv5FWUYKKOiz+8SyUM/1H3Q+avTKZqACQwnMHSSdXiKjmkCJmACJrBJAuoPo7yOKrB17qPOnRjltITxNujJG6ENGCjdq7EK55QO45TesYriFTpc+av1nw+nRKdC5KgMBmhNFyzReyureaGPFyPguoqjTcklZd5xGg41ARMwARMIBPhIKB1K/MqpcxksNOj/RDvDVeS/duiQFp3Tv4IW23suGb8gdfnk+UHbLMu+kOYEl0IerHu63viaUAxfYgImYALDCOjey/Nh6CTrsEQdywRMwARMwAQ6COjZ85s2PiLatEbvuKo69VR7J4r86sxCOyjR/1amHfyFssoqWT6YElvD87bCeb3gY1bSHlsY11W8/lNySZl3nMa00HDPC/60VHyVCZiACWREQH2YQhHdJpLOMxHKNsShiA/K9yHxL4lDHyw4FDmp+2Kt8oghr6VyPkxUFBMNCg8fag3lGOvzquvPYy9yfBMwgTMCfz8LccAQAmMmWYek5zgmYAImYAIm0EtAfWiWgmEpymfaBo0BFI/+OEu9DIrfK0R3hKpfcU3x/lXGDX73pTs4K8i8SvBePq8OF077DID44uujTyH+zYGA6ypeCym5pMw7TmNyaLjnBX9yQnu+UPXNw4ztiTbWOmOAZWcCFxEo25Tb1UUUV7kYZfutNXJSm6i/homhw1Srkno6k0XvkYc8+IDRbcWjT4ll/xz5wnroWwKKapcrAd/jktfMP5NLsEEB1G4La8ANim6RTcAETGATBHSffaBt0Hha8ViH/DBO5S2WnhxR4F90zVDDoBHJRqNW/YqjLucCFSyIWKg+NOC7Or6n4zectMuKgOsqXh0puaTMO07DobMT0P0QK0tmgwuljnwmG1/L/1rbHAqj2WV2gvkTUNtxu8q/mgoJ+Z9r41sy97Wt0klVPmE990n9MV0/q+V8TB5YaKOjH9aZ53540T1R6aFAh/dF6RQV55+kBFSHvsclrQFnbgImYAImYAL5EVD/AMvps76ewtFJ0qfEQONKx8Wbjfjaig92En4Ep/IOtiofE3dOdodVopfAx850zMneaQ0k4LqKg0rJJWXecRoOnZuA6piHPOtiVlaR1Ht5jJKLr2DbmcAoAm5Xo3DlEvmZBMEqfHElutoHFuh8EJV7DW8qJO2n9chzR+cnKfpbKhblf3W/bYnj4MwJqE342Zl5HVk8EzgiAd2bRq81POWanNhOkX/KNTmV2bLkS0BtC2M0DNFO3rQswxlbsyY4/V8M1n5ivyzNC+0n7xPnS3Z9ya6tn6VzNAETMAET2AABHvAxBdErhWOVSkfAzgTGEnC7GksscXz917GGebj0f17pY73La6sftP+n/GrJPe2v7rrkKVnMPanAkoJMWNhtm4DvcduuP0tvArsjoGcWz9YpS7OheN/kchJHLPMWGy79KW2PtdEH3LvDUARledPxvTkU5UFp/l7H90MkhdPf9Ng7AMnAP6wlegbsLYIJmIAJ5EyAhzdr/TZdeMBz3laTTTo+7iPgdtVHKM/z3AuealvMMlyDBJYJy8Z1yVMOdE4siS4RXOmhpBj8IaVL8vK1ixPwPW5xxPvNQPcClCy4d9q+0ob14apLPOUgAwBykQNZlnQqJ8s4oEDkLaxYv/ui7JUmE9I35RfLQ8QS0zmeQTe1IQvPosKIRj5Ll93SxhrOm+nzIy/lkX+YMqu8m3OqHyZ2eGbikhpnSZbwH+Dee1cb/8fi3lueY/yLjPxPqv5a7ZyCi3v2O4W1tTsU4SdLDuqY/xzh9Te8CWu6QpGuwM38D5sF2NPxtT0VxmUxARMwARO4nIAe5EM6Mjcuz8kpHImA29V2a1t1h/J88IeQtlvS9SUv/xffym8bdK0vlHOcRMD3uEnYfFFJQO0HReor+ShvuB9w332p/ZhCpbxqXi8HGShRLnLMS7c1NeqXfvfsE8niSLp8A651AlznXioOS0gQ55E2rGIrp3DaImkMGRtU16XaKeU8VJlTsb40X9XVm7J9rTpR2JRbMjB5+ZX8cO/FErxQdiuM/wdysrwK/wXeGORefaVjJgCYrOEcE2AxK3OiEpf/+cfi4PSH/13zzUbiNpnwJnhd0X6aio9WJXBt1dycmQmYgAmYwBYIBAV57GFPxwK3ic70J1H9mwkBt6tMKmKiGFhetw4QJqbpy66unguCB0b7aAm+x+2jHlcvhRQs0bX0JQhWh6vcd3OQAfC5yIEsaziVFwXaF/JPLFRnyrtt+YgieeVZvPkgv7CAl0+/nyVcbjXypw2GtyQap7I7PGKZs6uErQikts54Fiv0evtmH2tz/gf35VdKbu3zH+HDoFzDmPiJ9vnwJ28/cNz2NgmK8TCG1m7lCkt8Xc9bR2zFJJb8N1WMTzvFf7MR5sNEBKxETwTe2ZqACZjAxgnwOpudCcxNwO1qbqIzpVd26KsO/kzJHjoZMUUxwUCtaXF0aC47L7zvcTuv4InFy2Et/RxkAF8uckysyvGX6RmAgmwJx/dMoko9haMgbCoPgwwo/CpXprH4t1GqDC/bOWKZJxFTvQbFbVAEn9T7pES3d9EdRBaLqh/Gvjb+k5yL/TcJw3IdRTdGEHBD+f1BW5Ge/Ka7roBYWlyLBXyxab9NER9TwDfz2MSxyrr5dndtE6QtpAmYgAmYwJoEuh7UwdKONePsTGAMAberMbQyjKuOL9Y4ra+FZyhy7iIxkHiTu5CWbzAB3+MGo3LEBgGsEWPtJyhdwrrBjctmPcxBBgqUixyzwl07MT1b4FgpBiP5P+V8+VwvTms/WKCHvn79MtJ6WA/Ibf+IZZ5aB2KVfPmoqbLPfF3xHxEPlNxN97sCYuEovt+W/5ff5X+t7TOF8TZJ3aJdh5Ujn1haRKj/T/mPxdIgz3o8rtucE6ddtLvPN0feApuACZiACSxKQA841kYkj9jDPoRt/kG+KEQnfkbA7eoMyewBYvzn7IlGEizvD5EzDhpLoI+lzjMws9sAAdWVn50bqKfcRFS7Cf2qLtFiSs2u+KPO5SADAucixyh4PZFVJhTTKLQ/agt1/e8Kv60NxRgWrPh8xBMr/Cv5XEM49f6LNpRqLBeBu6uNtfNZn7nLkVa1DEU9oq5FDtJrToojBy7WxyctrG6jlu1chCvTRl7KGxzyVh9ErMV5W0bgI7ovFF7Jq/1WbiHRiJ+kzBE5sg4S2+jyUQoPy0cdZok5lTlMJDGpVPwfFMb/47H8H7SxHnr1YV3t8x9h43/A/xrFebEUk86xNnrxH1bYiVM46YT/V/1c9V/Ted5OfCS/CqtF5Nrwf6kFb2dX5dpNu7MSfTvtzpKagAmYwJoE6MjGHvZ06HFVR/fToX9NYBABt6tBmKZFUgf1MApXlRUFAPcolsfAZ01K35cEwi4pAd/jkuLfZOahX1VXOoaCBOt0lDpLuhxkoHy5yDELaz2TqDfeODpRSuo4KN1QlqFMP1GO6Zg3lFguguUhYIISr1Cay7+l49fyf9UWU7bpdOFYVgKlXMyhzMI1n5ko6HGxdJERpWGrkzw8i7E0RRFYKM3lcw0KcpSVKBKRnwkCrHerfLTPR3RvaUNx2clN17a51cvcJkjm4Sh6aWNN90oBLO1yXVvsftSMv4tjlZW2WCwxogIVb1rrOPzf+H9yLoyJmfAhLEya47MsErw4V/y35ccc/wG+OVC1e0UiPh/CJT7/gWqyiYCa4x7SlXYtara7u2l3VqJn28YsmAmYgAkkJUAHN/Y62W2F0wk+TOcqaS3sL3O3q/3VaaoSPdd96Asyl8+AG2XDYSYRKLddlgR8j8uyWjYvVA5r6ecgAxWZixxDGhVK3Ts8o7TV+81NRVldqVZP93cd3Ne1lXWr9umDEwfldJdVOM/FMAlD/LoLSv2gvAvnmJxGKRiTh7RIs8tx/0NRWC9fuCaUnzixCQCsgJkcQLHPxMEQbop24lKU+USAjRy0tZ1QR5yv1+FGijVdTLW75lsZVWJt58p2PoYT42oU4VVeZXtvTmZVebOjOMV/SH7sf3kSN/OD3bS7zwWayqAy226ymdeFxTMBEzCBSQR87+vApgc1r6TxkZP6K2w8xFmr7V7HpT5lAq0E3K5a0fjEeAJM6AWHhVAY/IUw+yawOgHf41ZH3pYhSomtWO11jcFRJuIK68hPu4v85iADBUsuh/7D9HX/oa1QXCHUAPeNrnvTjKcwlmihTB/Yl/9SGwrkSonWvCZyjCI95vrko+20PRdR7lfLx5C4ZCI9lOjPOI44xk3BGvfsdHk9VuYny8woHCVjoWjUPudJ45W2E6dzYXKApW4Yf0zhtmqZTwqwkQNx7Ws3lASOizvJQlvgPo1yFQtt3pxgrfGTNqSwXTiVq/jPUW5tYxTiLDVTTaRtEYbKm027u4Bf1a9AiU7jpcES2Haj1an9OVVmsLKkY8LrF7yqMaZB7w9KpiVyXcUrJiWXlHnHaYwOPey9bwQplFRYqcAKd1fbPR2fDRSKs/4xgWEE3K6GcXKsDgK6D9X7a/TnNj3A6CiqT22PgO9x6esMpQzj2y5L3fRSSgLdy8KyADElQwir3+9mlzsHGShUDnIgg0SpT9Jeyru4HygR2iTPKvQNGKqknOShXaHQr7vw0dC2/0yXgpp0wliha8InxIFxm0PRjpub2xJl/iTptn6DgjxWB0xc4GC1uNN/gPvamAmlxWVaOgP+99q4BzzTFquDExEUh6WXWOalN+7JhfkdZNPuLkBT9StQoh/SqSG+VsFpvGFmlJsFrxCdrM91SDiZFdp1Fa+QlFxS5h2n4dAlCKieeWAfqnOzBEeneUrA7eqUh48uI6D2hKIMqzVP7l2G0lfPRMD3uJlAHisZjNmCgrFe8qB44PzSLgcZKGMuclzMW/cC6vS9/KIvLR99A8pqvuHBtuRzCwUl+Z24UgbCmnkjI8p9+v4xR1pByRo7HyZ6MExscyHOmVy1C4p1o3U8hdvaZa6Jvavdm7sqTWaF0X+MPmvXf6Au8S8d/8l6vD3sb6bdXdsD7bFlUEOMfhlW6aBQZzBmlwkB11W8IlJySZl3nIZDTcAETMAE9kxAzx2sdvjY1WP8UFbCtV8o0Mv9cMq+CZiACWyJAOtEs8RG02GNyzIXbYrNZvxLjnOQAflzkeMSluFarKrDRzyvqEdtWHqjc4jVd7huDh+F99nETKwtKYxlXJiw6TKc4XxQgmv31JXpopiPlos8tHGethzWZK8S0TmsPHHoYqZyW7XMhbTb+4FRm6OOcV1vE3yK4d+LCJT/l940hsbrTSh9hF21u6NaovPKLzfxpmN9rsN9kbgJIbNj11W8QlJySZl3nIZDTcAETMAEdklAA4i3Khivv7KWJANr1qr9Qfu8Ucgx/TZ5xeC+SwFAHDsTMAETyI6A7mHJv0OTgwxUTC5yzNhIWBaxaeGNFWrz7YKYZSpKzS7lU5eY6DrutkRAiV8o2CUb+TIhzXKNKLjbHBM6zSVgmnEZI/JmPxPe1bIw2if9YKjId5X+obCmJT5xeLYzaYRsQ7kpauVSlLnKfAs7Ypt8+Sg4SY4/+3gpzuIfix8iR5+cqc6vwWeusknWLNrdXOU5qhKdmc7qxl6DGR4cnC+Weamd824aAq6rOPeUXFLmHafhUBMwARMwgd0RUKebQTevdgdlA1ZwxYeNFcaA3s4ETMAE9kKAexqKw2A9jAJ07e/Q5CAD9ZmLHMhyiUO3gM7hoeoVZTXuprbiO2wKYyIY5XFhva1jlNQoomkDhHMe5RPhTBITj/M4JpfvagvHn0L/+uWaoLj+K/TT3iN5xRte8ll+Zchytoz/kKnVSRae1/9HEZ7Lpw6DbgWFeWHFLh8lOed4iyycp7wch2d9JzfFbXOrl7lNkMzDky+ZpLpeXEE+pA5ykWOIrDuIk7zdzcXw87kS2ko6+qOEB1iXyMz62iUm4LqKV0BKLinzjtNwqAmYgAmYwI4JsHYsg/3C6RnEwDr2JmEZw54JmIAJbJNAeX9L+jZNDjJQe7nIcWlLUjlQGgXF8FlyOs/z7GxpE4V1hccMAWNp8/bWlbZbZT5VHB3zLB38YVPFLyZ25Lcu5xISL9NuU+wX0cp0WvPX+U5uIa+mz3XarrStWuamHBs4Zsmk2IQIkxtrLR+1AUzzi6i2ydJJMO79L5G74vG25Q/zS5Ikxd20u2tJ8KXNNCjIeXg03fsyYIiivXmtj+cn4LqKM03JJWXecRoONQETMAET2CsB+mNWmu+1dl0uEzABEzCBJQmgKG1VVo/ImMmdmNJ1RBKrRT1imUfBlVKWiZj38lHoFk779LdODBfKU4f2xIWliVhW8GJHWkqEN0tOFOg6/lIbb2ugMK+++0OGOmaJo7Y3Si6Wac0EVI7dtLsjKtGHtBVes7LbBgHXVbyeUnJJmXechkNNwARMwAS2SAAFemEBF4RXJ3wrA/kgsn0TMAETMAETWJ1AqbRCQXfyHB0jSHktaQyygB+T9hJxj1jmiRxv6zqWAwqK2+c6Xnv5qImir3rZ78rtYiW2ODNJwbJJJ2+mlOGkz3JGWJz/exmm3cq9UNhe+r67aHeHW85FTTFYm1etsrYTrGz9ReIalIS7rqs4/JRcUuYdp+FQEzABEzCBvRLglXAGFkEBwCDk2V4L63KZgAmYgAmYwMwEeI6yjEJs2ZghWaHg61yeZUgiK8c5YplHIVa/6qMuSLp81CiBE0UWpzfKmu1ShxI8poznv4mSnPrAoWu5r636PqPOsUwR3zC4XotH3M25Uv7Nt7vDKdGpOG00OAZiTRfCTl6xaEby8ToEXFdxzim5pMw7TsOhJmACJmACeyWgZw79sTleRd8rIpdrRwTU3nm1ngkj3ujD5/XuE6s1hdmZgAmYwGAC5diNj5CyLMUoa3KuUUZcGxR8g/NNGRF5tR2qzCl5T81bdcQzj8kdPgiL47nHh26LD+8SsIaTHCyhEto4+b9TGMuooBtEyX1f+8WHUOUjI2GcY7KGY7auj/zqdJHGSX+2TIu06xNcpBVz9AVOlOuxSA5bh8DhlOglVhphrIEGS3R3WNdpf0NycV3FKaXkkjLvOA2HmoAJmIAJmIAJZEtAg0QGnY/kh4HqIrIq/S0rop9L/i8AI58B+gdtxcCdsLrT+VV41vP0vgmYwDYJ6H7BhPQoBTol1XWjr8mF0BHLnAv7EXKge+NZxvZMdYbi+rX2b2lbxahV+aGYvkne8q/koyMs1orXfjEZo+NqTXSF/aEN5TlhLHNUWIzLf63tQTjWucopjDRjfR8sspt6R+LGyv5K4SjbKwt17dslInBUJTp/1Ni6QqzR4y8SJ2qMLdm6ruJgUnJJmXechkNNwARMwARMwASyJKABJP0GluWJDSLnlnmwInrujGdIj3FIcG2D7nCewfc/xJQ1bNfgGvK1P53AW9VV8+pfFba1pTKaZfCxCRyCgP6rheL0EIVduJBiyTMOBTJKbBTThRJb+0y2z7F8ipIa5Fg+hXXhmbjGIh6Z6pNHnG9zdQU48ShTzBEeSyeUPegli+tbys9zvi39WJ4OW5DAtQXTzjZpNUz+GP4icbY19Jdgrqu/WNT3UnJJmXedgfdNwARMwARMwATyJqA+Awp0liWJWVYtIfwYRfQS+U9Os8GIQXWrcrWMiyIdvnZ5E6Dt8xp/bIutkZt3aSydCRyXAPfl2P/4ZJmO4+IZXnKeYeVzDOvqShmtsDfDU7k8ZpkfMqCg5nnKG2B3tPU6XVufwK7vN69FQR87T54YGBSb9lG01xX4OqxcTAlfnfTOugSOaokOZTrZT9Vow4zOXR37i8SQyc+5ruJ1kpJLyrzjNBxqAiZgAiZgAiaQDQH1sbGyupJfDZCXFk551ZX1nYropWWZmr7KgGKVQXWnMgGu2lj3N/oK+dT8h15HvorLOOpm6XsN9wg8cUJ50qYYiVzhIBMwgRwJ6L/s//H8FUM/oXXCeP7sTlNUnbJ0zO/yi3XJ5fMdAPoO6DrmcvRLUKTHXL3P8lAR2vLlWVuPG0vLYSsROKwSXX8QOjSb/zLsSu0kaTauqzj+lFxS5h2n4VATMAETMAETMIHMCKAMLgama8ulfsogRfTacvXlJ7kZvBdL37CvrW+s8kzxsZ5LsU7qlpfO6asKnzcBEzABE1iQgJ5vKIavy19toj1SHGQIbxdcSZaftE1R6rcpyUmT5aLJp+kqpbjO02dhKZsqrBGZ66u12RvnfLgygcMq0Vfm7OxMwARMwARMwARMwARM4BAENBDEmiu8rr1qmZX3WEX0KPnKsmEtxgfQcMXgWeFhTddPoS2/ioflG9Z3GPR8peNCUS4/fFCN9Vl1qrA661SiKx6DczinsEavW8wxwKc8diZgAiZgAiYwhADPjRQTwE3Z+IDoEwUWz2T5xfI8CuPZ/pzI2udNK978Iow+Rj2M/g5LwNzQeZ7JsUkBntN8iLSuJCcfVsaQd/VSfhcLDBIKuYhsl5aAlehp+Tt3EzABEzABEzABEzABE9gbASy5sKxaxGmwOZsieoKADIIZSN+WHAyqUQQgT68r5WbQXFi6yQ+K+Cvt15XSvWnVIsD5qbauAXgt+jy7kreuDECpMMh6T9exDEyh/B8iieIzqTBogmJIeo5jAiZgAiaQnoDu6yibYwrn1YSTDDw3o89OnUOpfvJcawljmZ++pX54RqIErybGh5Zf8ehvXMmvP3MJsktEYA4lur80nqjynK0J5EpAN3l/vTzXyrFcJmACJmACJhAhUA7UUMbiUAzjeL2YgeRYd18XnAw+xybQFl/yoLCeWxHdlt1ZuPJnLXIGwsGCnIFtNbgt5as+TKbj+uC6sJIPiercVMV5SAIfJcQLpcVr8VPq6krXYUnHMjJfkeAYp2tQ4veu4U6aZT5nbygonPYGz+J1dR1XSnP2tRVWgKRhZwImYAIm0EvAOrpeROtF0DOMfsM32prW6EOEoF+2SH9qSOZbjyPms+ulrl0Ahc4isymxjc6UnQmYwHEJhNnW2P3huFRcchMwARMwARPIl0CxBrcGHChEGbC911ZZSg8VW9diaYyidJJCd0A+9DGehXjKZw5F9JXSGTN+uaP4bR/+xDodxfkv2ppKaZTFdYV7YWEWyjLFV15wJk0mLqa633XhmPIX+SjvYlIAFuV+a/46T1m/ln9ieViGkzftDuX5v5dh9bSYJCAvOxMwARMwgXYC1tG1s0l6Rs+wQi8Seb61yqW4THCz1MtS/anWvHd0Yna91GRL9LIi65YVO+LsopiACVxCQPcH3xsuAehrTcAETMAETGB9Ao/1/EZZGZScDDwIu6WtTWEck/KuAsfEj6XRFXamiJZ8cwwwSbfXKS+UwYFRLD4Mg0I6+CEeg2is6F+VATfkz9Fngjfco6+ll3m1epKH60fVma4Zu4Y77anJA5n4MCrMQh2+1zETAlVZdA4rPiZ5JlvbKz07EzABE9g1gfI+OsczZdecUhVO9cNkMX2Ioe6Xsk6Hxne8BgHxm/3/MFmJ3pDNhyZgAiZgAiZgAiZgAiZgAtslgIIXi+So00AEC3M+bvWyjIDSGUtrlJuVdbWOT5TcZdw5vaUU0YNkLAe00VerdQ6FMIPk8AGyhzqulNMKR/nepYAfJEMkEvw712VX3uHDaVxOvb1TGEulMKBH7vva/0z+lXzqkDDOUVaO2e7qXFF2+WPfACB96q5yZT6E066CI5+Yg9uJcj0WyWEmYAImYAImkCsBPe/ChHGviGPi9ibmCLMRsBJ9NpROyARMwARMwARMwARMwAS2SUCDtaa1DgpPlmUJSmCspgurYfnPFI4CNlgj15XoKF7faVvEKc+lFNFzyPuzEkEpjDX1DflNpnPkEUsD3tRP1EkOlM835RdrjctHUc2kyJX2P2qjrov1yMsw6h1lebGWqPYLq3D5r7U9CMfEHeIUn/xiigPWQW9OKhC33p5CFq+0g7K9slAPJ+ybgAmYgAmYgAmYwBoErERfg7LzMAETMAETMAETMAETMIGNEJDSE6tmlKyFtXGpBA2WwChYw4cf+fBoULKH0rUpTMP5yb7y+nPqxbq2sLKeej3Xjc1f8WPLl4wWYYDsKKiZvGhzKPWfKB3i8CYBdVlX8HO+zdWV3MSjfsc6ronlgXKf9sRSL7gibR2/+XR48ksZp+R9kogPTMAETMAETMAETGAqASvRp5LzdSZgAiZgAiZgAiZgAiawMwJSYKKoRKl5W/soLq/kF5bB8rEErpSqOo4pO7mk1ekaFPRBadoaTydYEuXEIlnHFyvCyVDpoNxuKmT5WGhYqoZoONbqrpTN2p8l/09Jz/obU1BXGUhuPvxJ3WH5zdsEuJO6/BR0/qvrijZQnqnvn0duD7muU7FrqYNvkI9L5VMvFW/Caq6zjLV43jUBEzABEzABEzCBRQhYib4IVidqAiZgAiZgAiZgAiZgAtsiICVmoUCXj4IVpSYKb5b7CMpsLIej64ETv3QoS1GaRp3SQmFapB+NsEKgZDhZm5ssFfZSW1K5Lig6S7nElNRFkioX9fh7KJ/8xzouJkqKCMv/0H7a2kRoW0jBGvJta63TNutxiW9nAiZgAiZgAiZgAqsRsBJ9NdTOyARMwARMwARMwARMwATyJCDFKkpKLIH5MCZKVxzKZqyXr8rz1+VXluiERxwWwzcj4YsESR6WnUF28izKMEDGRWQh0UTyoKDuUjDDhbosJg8k40/a+iZDFP3MtSnCzyLWA5QXlvDI0HSVzDpP22N5oCqsEZnrq3XbG+d8aAImYAImYAImYAKLE7ASfXHEzsAETMAETMAETMAETMAEsifAR0JRkuJXTkorLB84AAAH/UlEQVTNYLWNEnPIRx1Rgk5StlaZjtt5Lhm/4BL55PtBW8plV1LI85XK3LfcCW8UPFG8j9qIHxTqMHuuDX4/amMZHcKKJXdqYViv39HGB1NRivdNpijqiWPt8y+11ZXkyPBUYUTkTYCu9sVbAqEtEt/OBEzABEzABEzABFYlYCX6qridmQmYgAmYgAmYgAmYgAnkR0AKzEIR3SaZzqM0HaI4RQm/prKzvvwHin6UxCldqzxiiCKa82GiAmX1lcLDh1o5nOJQbv/cdqHSRzkdVVDrHLxOrNJbwlirvG298ras6+Eo5WkXxZsNnFA+g9qU4gVOdQU8SdiZgAmYgAmYgAmYwGoErERfDbUzMgETMIHtEdDAtbBEk+TvtGG59r3CPIjdXlVmJbHbVVbVsRlh3G42U1UoRlmaYxXXeCbxzDpRCI8QYpZnW4885IFCmI+2YvGN0j8snTNC1LOopDG13GeJLRGgsv6mjY+INq3Rh2T3NPfyDSmE45iACZiACZiACWybwLVti2/pTcAETMAEliKggS6Wcq/ksz4uVnJYj/G6NYN+OxOYRMDtahK2w1/kdrOdJqC6QlHM0iH315Ra+YX13IdYy5+JputntZ6PyaMwZGNZkmKSQccscRK1ED8TsCVA16NAJ51ZJgFaspklWDLCOCwXMyhNXYP1Pn0PLObtTMAETMAETMAETCAZASvRk6F3xiZgAiaQL4Fy0MoH5KrBfTmA5Xg1C8N8CVmyKQTcrqZQ8zVuN5tsA88k9WqW0WojWKAz4cta3eENqmTgeuS5g5wzCodiunpWz5juIkmp7NVyLgMz+EXXTJoYGZi+o5mACZiACZiACZjAIAJWog/C5EgmYAImcDgCKD9ig/xXCr+vAW2xPunhqLjAlxJwu7qU4DGvd7vZWL3rGcHbSw/XeFYoD96a4oOZH7T/p/wH2pK5LnlKHnMrhB+qsExabMaJw2Cr8jFxNwPAgpqACZiACZiACWySgNdE32S1WWgTMAETWJwAr+HHPiAWBr6c34zl2+K0nMFQAm5XQ0k5Xp2A202dxnb2eYawlvVYy+NRJZSStf4hz1HXLhG5S55SITybhb7SY/LgWZnuEsVxmiZgAiZgAiZgAiZgAiUBW6K7KZiACZiACZwQ0GB8iJX5jZOLfGACPQTcrnoA+XSUgNtNFMsmAlV3KM8fyP9yEwJvTMjyv8H64lj925mACZiACZiACZiACSxMwEr0hQE7eRMwARPYIIGgIA9W5/UivC8Phija69d53wTcrtwGphBwu5lCLZ9rsLr2dzSWqY/nSpaPlNqZgAmYgAmYgAmYgAmsQMBK9BUgOwsTMAET2CGBmzssk4uUnoDbVfo62KIEbjeZ1pqspPm2xvfyX2Qq4ibFEk8mJljG5Y9NFsBCm4AJmIAJmIAJmMAGCViJvsFKs8gmYAImsDCBYG0eyyZYhb6LnXSYCXQQcLvqgONTrQTcblrRbOOEFL18SHPRddG3QWJWKZmYYILCzgRMwARMwARMwARMYCUCn6+Uj7MxARMwARPYCAENzD9qQ9rYki0hzNZvG6nPXMR0u8qlJrYlh9vNOvUlzn8unVP5XFk6m8Okf3SeKv9nh6lsF9QETMAETMAETCALAlaiZ1ENFsIETMAEsiOA5WDsY3DBEp3zdiYwloDb1Vhijg8Bt5uF24EVkssAFtcHSplnKUsO4f+oMD8/BcLOBEzABEzABEzABLZGwEr0rdWY5TUBEzCBdQiwfu33kaxuK+yNlACxj45GojvIBE4IuF2d4PDBQAJuNwNBOVp2BJ7refkFUsnnTa4P2mxBDRA7EzABEzABEzABE9gYAa+JvrEKs7gmYAImsAYBDfZ/Uj7v5WNFV7hSAfBQB4/KIHsmMIqA29UoXI5cEnC7cVPYMAEmnoPDEt0T0IGGfRMwARMwARMwARPYGAFbom+swiyuCZiACaxIgMH/UymwGPjj7mq7p2N/zKzA4Z+JBNyuJoI7+GVuNwdvAFssvp6X9e+H8HbXN1ssh2U2ARMwARMwARMwARO4urIS3a3ABEzABEwgSkCDfyzmvouedKAJTCTgdjUR3MEvc7s5eAPYePHVfn9UEb6T70nojdelxTcBEzABEzABEzguASvRj1v3LrkJmIAJmIAJmIAJmIAJmMAMBKQgx9L8nTYmoK/r+AeSLcNRoH9kX5snpwFjZwImYAImYAImYAIbI+A10TdWYRbXBEzABEzABEzABEzABEwgHwJSjL+VNC/lozj/XdtTpNPxa3lPtH3Q/p/yq++MaN/OBEzABEzABEzABExgQwRsib6hyrKoJmACJmACJmACJmACJmAC+RCQcpylWv6Q/1spFeug32NfYfUPi5an7ZmACZiACZiACZiACWyRgJXoW6w1y2wCJmACJmACJmACJmACJpADgYcS4lEQRIpzlnPx2ucBiH0TMAETMAETMAET2AkBL+eyk4p0MUzABEzABEzABEzABEzABFYncF05Wmm+OnZnaAImYAImYAImYALrEqhbor+V5UQz918V9k0z0McmYAImsCMCvvftqDJdFBMwARMwARNYmQAK9C+1sYxL4TR+8gdEA4yFfbFmPXr425mACZiACZiACZjARQT6+hUo0enwfduSS9UZbDnvYBMwARPYKgHf+7Zac5bbBEzABEzABPIhgMHRdxp0BUUulunP8hFv95J8v/sSuoAmYAImYAImYAJrEejsV/x/zSOtUG5PI1IAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0\\\\\\frac{r_{s}}{2 r^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}- \\frac{r_{s} \\left(- \\frac{c^{2}}{2} + \\frac{r_{s} c^{2}}{2 r}\\right)}{r^{2}} & 0 & 0 & 0\\\\0 & \\frac{r_{s} \\left(- \\frac{c^{2}}{2} + \\frac{r_{s} c^{2}}{2 r}\\right)}{r^{2} c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)^{2}} & 0 & 0\\\\0 & 0 & \\frac{2 r \\left(- \\frac{c^{2}}{2} + \\frac{r_{s} c^{2}}{2 r}\\right)}{c^{2}} & 0\\\\0 & 0 & 0 & \\frac{2 r \\left(- \\frac{c^{2}}{2} + \\frac{r_{s} c^{2}}{2 r}\\right) \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\0 & \\frac{1}{r} & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                      ⎡    ⎛   2       2⎞                    \n",
       "⎢                                      ⎢    ⎜  c    rₛ⋅c ⎟                    \n",
       "⎢                                      ⎢-rₛ⋅⎜- ── + ─────⎟                    \n",
       "⎢                                      ⎢    ⎝  2     2⋅r ⎠                    \n",
       "⎢                                      ⎢───────────────────          0        \n",
       "⎢                                      ⎢          2                           \n",
       "⎢                                      ⎢         r                            \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                        ⎛   2       2⎞\n",
       "⎢⎡                     rₛ           ⎤  ⎢                        ⎜  c    rₛ⋅c ⎟\n",
       "⎢⎢      0        ─────────────  0  0⎥  ⎢                     rₛ⋅⎜- ── + ─────⎟\n",
       "⎢⎢                  2 ⎛    rₛ⎞      ⎥  ⎢                        ⎝  2     2⋅r ⎠\n",
       "⎢⎢               2⋅r ⋅⎜1 - ──⎟      ⎥  ⎢         0           ─────────────────\n",
       "⎢⎢                    ⎝    r ⎠      ⎥  ⎢                                    2 \n",
       "⎢⎢                                  ⎥  ⎢                       2  2 ⎛    rₛ⎞  \n",
       "⎢⎢      rₛ                          ⎥  ⎢                      r ⋅c ⋅⎜1 - ──⎟  \n",
       "⎢⎢─────────────        0        0  0⎥  ⎢                            ⎝    r ⎠  \n",
       "⎢⎢   2 ⎛    rₛ⎞                     ⎥  ⎢                                      \n",
       "⎢⎢2⋅r ⋅⎜1 - ──⎟                     ⎥  ⎢                                      \n",
       "⎢⎢     ⎝    r ⎠                     ⎥  ⎢                                      \n",
       "⎢⎢                                  ⎥  ⎢                                      \n",
       "⎢⎢      0              0        0  0⎥  ⎢                                      \n",
       "⎢⎢                                  ⎥  ⎢         0                   0        \n",
       "⎢⎣      0              0        0  0⎦  ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢                                      \n",
       "⎢                                      ⎢         0                   0        \n",
       "⎢                                      ⎢                                      \n",
       "⎣                                      ⎣                                      \n",
       "\n",
       "                                                ⎤                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "          0                       0             ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥                             \n",
       "                                                ⎥  ⎡0  0  0        0       ⎤  \n",
       "          0                       0             ⎥  ⎢                       ⎥  \n",
       "                                                ⎥  ⎢      1                ⎥  \n",
       "                                                ⎥  ⎢0  0  ─        0       ⎥  \n",
       "                                                ⎥  ⎢      r                ⎥  \n",
       "                                                ⎥  ⎢                       ⎥  \n",
       "                                                ⎥  ⎢   1                   ⎥  \n",
       "      ⎛   2       2⎞                            ⎥  ⎢0  ─  0        0       ⎥  \n",
       "      ⎜  c    rₛ⋅c ⎟                            ⎥  ⎢   r                   ⎥  \n",
       "  2⋅r⋅⎜- ── + ─────⎟                            ⎥  ⎢                       ⎥  \n",
       "      ⎝  2     2⋅r ⎠                            ⎥  ⎣0  0  0  -sin(θ)⋅cos(θ)⎦  \n",
       "  ──────────────────              0             ⎥                             \n",
       "           2                                    ⎥                             \n",
       "          c                                     ⎥                             \n",
       "                                                ⎥                             \n",
       "                          ⎛   2       2⎞        ⎥                             \n",
       "                          ⎜  c    rₛ⋅c ⎟    2   ⎥                             \n",
       "                      2⋅r⋅⎜- ── + ─────⎟⋅sin (θ)⎥                             \n",
       "                          ⎝  2     2⋅r ⎠        ⎥                             \n",
       "          0           ──────────────────────────⎥                             \n",
       "                                   2            ⎥                             \n",
       "                                  c             ⎦                             \n",
       "\n",
       "                      ⎤\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "⎡0  0    0       0   ⎤⎥\n",
       "⎢                    ⎥⎥\n",
       "⎢                1   ⎥⎥\n",
       "⎢0  0    0       ─   ⎥⎥\n",
       "⎢                r   ⎥⎥\n",
       "⎢                    ⎥⎥\n",
       "⎢              cos(θ)⎥⎥\n",
       "⎢0  0    0     ──────⎥⎥\n",
       "⎢              sin(θ)⎥⎥\n",
       "⎢                    ⎥⎥\n",
       "⎢   1  cos(θ)        ⎥⎥\n",
       "⎢0  ─  ──────    0   ⎥⎥\n",
       "⎣   r  sin(θ)        ⎦⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎥\n",
       "                      ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chr = ChristoffelSymbols.from_metric(sch_inv) # can be initialized from sch also\n",
    "chr.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ull'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chr.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Changing the first index to covariant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r^{2}} & 0 & 0\\\\\\frac{r_{s}}{2 r^{2}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}- \\frac{r_{s}}{2 r^{2}} & 0 & 0 & 0\\\\0 & \\frac{r_{s}}{2 c^{2} \\left(r - r_{s}\\right)^{2}} & 0 & 0\\\\0 & 0 & \\frac{r}{c^{2}} & 0\\\\0 & 0 & 0 & \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & - \\frac{r}{c^{2}} & 0\\\\0 & - \\frac{r}{c^{2}} & 0 & 0\\\\0 & 0 & 0 & \\frac{r^{2} \\sin{\\left(2 \\theta \\right)}}{2 c^{2}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin{\\left(2 \\theta \\right)}}{2 c^{2}}\\\\0 & - \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}} & - \\frac{r^{2} \\sin{\\left(2 \\theta \\right)}}{2 c^{2}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                    ⎡-rₛ                                ⎤                    \n",
       "⎢                    ⎢────        0         0       0    ⎥                    \n",
       "⎢                    ⎢   2                               ⎥  ⎡0   0    0       \n",
       "⎢                    ⎢2⋅r                                ⎥  ⎢                 \n",
       "⎢⎡       rₛ       ⎤  ⎢                                   ⎥  ⎢        -r       \n",
       "⎢⎢ 0    ────  0  0⎥  ⎢            rₛ                     ⎥  ⎢0   0   ───      \n",
       "⎢⎢         2      ⎥  ⎢ 0    ──────────────  0       0    ⎥  ⎢          2      \n",
       "⎢⎢      2⋅r       ⎥  ⎢         2         2               ⎥  ⎢         c       \n",
       "⎢⎢                ⎥  ⎢      2⋅c ⋅(r - rₛ)                ⎥  ⎢                 \n",
       "⎢⎢ rₛ             ⎥  ⎢                                   ⎥  ⎢   -r            \n",
       "⎢⎢────   0    0  0⎥  ⎢                      r            ⎥  ⎢0  ───   0       \n",
       "⎢⎢   2            ⎥  ⎢ 0          0         ──      0    ⎥  ⎢     2           \n",
       "⎢⎢2⋅r             ⎥  ⎢                       2           ⎥  ⎢    c            \n",
       "⎢⎢                ⎥  ⎢                      c            ⎥  ⎢                 \n",
       "⎢⎢ 0     0    0  0⎥  ⎢                                   ⎥  ⎢              2  \n",
       "⎢⎢                ⎥  ⎢                               2   ⎥  ⎢             r ⋅s\n",
       "⎢⎣ 0     0    0  0⎦  ⎢                          r⋅sin (θ)⎥  ⎢0   0    0   ────\n",
       "⎢                    ⎢ 0          0         0   ─────────⎥  ⎢                 \n",
       "⎢                    ⎢                               2   ⎥  ⎣                 \n",
       "⎣                    ⎣                              c    ⎦                    \n",
       "\n",
       "                                                        ⎤\n",
       "          ⎡0       0             0              0      ⎤⎥\n",
       " 0     ⎤  ⎢                                            ⎥⎥\n",
       "       ⎥  ⎢                                      2     ⎥⎥\n",
       "       ⎥  ⎢                                -r⋅sin (θ)  ⎥⎥\n",
       " 0     ⎥  ⎢0       0             0         ─────────── ⎥⎥\n",
       "       ⎥  ⎢                                      2     ⎥⎥\n",
       "       ⎥  ⎢                                     c      ⎥⎥\n",
       "       ⎥  ⎢                                            ⎥⎥\n",
       "       ⎥  ⎢                                 2          ⎥⎥\n",
       " 0     ⎥  ⎢                               -r ⋅sin(2⋅θ) ⎥⎥\n",
       "       ⎥  ⎢0       0             0        ─────────────⎥⎥\n",
       "       ⎥  ⎢                                       2    ⎥⎥\n",
       "       ⎥  ⎢                                    2⋅c     ⎥⎥\n",
       "       ⎥  ⎢                                            ⎥⎥\n",
       "in(2⋅θ)⎥  ⎢         2        2                         ⎥⎥\n",
       "───────⎥  ⎢   -r⋅sin (θ)   -r ⋅sin(2⋅θ)                ⎥⎥\n",
       "   2   ⎥  ⎢0  ───────────  ─────────────        0      ⎥⎥\n",
       "2⋅c    ⎦  ⎢         2              2                   ⎥⎥\n",
       "          ⎣        c            2⋅c                    ⎦⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr = chr.change_config('lll') # changing the configuration to (covariant, covariant, covariant)\n",
    "new_chr.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'lll'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Any arbitary index configuration would also work!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r \\left(r - r_{s}\\right)} & 0 & 0\\\\\\frac{r_{s} c^{2} \\left(- r + r_{s}\\right)}{2 r^{3}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}- \\frac{r_{s}}{2 r \\left(r - r_{s}\\right)} & 0 & 0 & 0\\\\0 & - \\frac{r_{s}}{2 r \\left(r - r_{s}\\right)} & 0 & 0\\\\0 & 0 & - \\frac{1}{r} & 0\\\\0 & 0 & 0 & - \\frac{1}{r}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & r - r_{s} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\frac{1}{\\tan{\\left(\\theta \\right)}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\left(r - r_{s}\\right) \\sin^{2}{\\left(\\theta \\right)}\\\\0 & 0 & 0 & \\frac{\\sin{\\left(2 \\theta \\right)}}{2}\\\\0 & \\frac{1}{r} & \\frac{1}{\\tan{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                       ⎡    -rₛ                             ⎤\n",
       "⎢⎡                      rₛ           ⎤  ⎢────────────       0         0    0 ⎥\n",
       "⎢⎢       0         ────────────  0  0⎥  ⎢2⋅r⋅(r - rₛ)                        ⎥\n",
       "⎢⎢                 2⋅r⋅(r - rₛ)      ⎥  ⎢                                    ⎥\n",
       "⎢⎢                                   ⎥  ⎢                  -rₛ               ⎥\n",
       "⎢⎢    2                              ⎥  ⎢     0        ────────────   0    0 ⎥\n",
       "⎢⎢rₛ⋅c ⋅(-r + rₛ)                    ⎥  ⎢              2⋅r⋅(r - rₛ)          ⎥\n",
       "⎢⎢───────────────       0        0  0⎥  ⎢                                    ⎥\n",
       "⎢⎢         3                         ⎥  ⎢                            -1      ⎥\n",
       "⎢⎢      2⋅r                          ⎥  ⎢     0             0        ───   0 ⎥\n",
       "⎢⎢                                   ⎥  ⎢                             r      ⎥\n",
       "⎢⎢       0              0        0  0⎥  ⎢                                    ⎥\n",
       "⎢⎢                                   ⎥  ⎢                                 -1 ⎥\n",
       "⎢⎣       0              0        0  0⎦  ⎢     0             0         0   ───⎥\n",
       "⎣                                       ⎣                                  r ⎦\n",
       "\n",
       "                                                          ⎤\n",
       "                          ⎡0  0    0            0        ⎤⎥\n",
       "  ⎡0  0    0       0   ⎤  ⎢                              ⎥⎥\n",
       "  ⎢                    ⎥  ⎢                          2   ⎥⎥\n",
       "  ⎢0  0  r - rₛ    0   ⎥  ⎢0  0    0     (r - rₛ)⋅sin (θ)⎥⎥\n",
       "  ⎢                    ⎥  ⎢                              ⎥⎥\n",
       "  ⎢   1                ⎥  ⎢                  sin(2⋅θ)    ⎥⎥\n",
       "  ⎢0  ─    0       0   ⎥  ⎢0  0    0         ────────    ⎥⎥\n",
       "  ⎢   r                ⎥  ⎢                     2        ⎥⎥\n",
       "  ⎢                    ⎥  ⎢                              ⎥⎥\n",
       "  ⎢               -1   ⎥  ⎢   1    1                     ⎥⎥\n",
       "  ⎢0  0    0     ──────⎥  ⎢0  ─  ──────         0        ⎥⎥\n",
       "  ⎣              tan(θ)⎦  ⎣   r  tan(θ)                  ⎦⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr2 = new_chr.change_config('lul')\n",
    "new_chr2.tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining Riemann Tensor from Christoffel Symbols and manipulating it's indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  0  0  0⎤\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎣0  0  0  0⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm = RiemannCurvatureTensor.from_christoffels(new_chr2)\n",
    "rm[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ulll'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm.config"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  0  0  0⎤\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎣0  0  0  0⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm2 = rm.change_config(\"uuuu\")\n",
    "rm2[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABkCAYAAABNcPQyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAF7UlEQVR4Ae1c0W0cNxRcBf42jBhIAXIHsV1BnA4cd5C4BCNf0q/dgdNC1EHSgWF1oBQQwIaRCjLvjk8gj9TykUvyuMAQOC35dsmhZkjuLXdwF1dXVz8uy/IZn1S6ub6+/iV1grE5GIA+d+jJZao3OHfxyDvxAXm52E//+AXmp2TgfaJXPyP2WuK+wB+hOAVNsDVzCJr9cdo/xCQUCXx6XVRGRR0tX3DyGT7vRw0KYi9VnH8XqfhAAATLffoTju/wkeX8HT5/IZ9c/x9opipM7HrOTQKD4N+gzBMcb1Qh5L8hL+WPGutxJPY2zk0CQzj5Jn2bEPATYq8gwpPEuVYhYodMFnFuFfgVML6GOIeSzGJJcr5XInbIbBHnWYGNs/P7sA9tSsRe5dHEeVZgQGhDOnJ8VJ3VvZZoYvtsH/NFnFsEjiHiyNM4NCxC7BWqLQLriEk1ozNMntF6JGLHrBZxnhUY90FdmlPLsMa67IARe1F+fZk1ZuI8K7Br+W8cL30Ul9fRJOd7JWKHzBZxbhX4T2C8CHEOpef4e+vNtMQlm0PEDiks4twkMASUDe2vOB42sAUPeVkq3uDzq5R7JWJv4/xRgTAycn4H4bpUv0T5J5RvC9qovZTYR+aKOb/wXvg/g1imG3etSqw3hgHoKO8O5PXvhWmJHtMtovRggAL3YHWiNinwRGL06AoF7sHqRG1S4InE6NEVCtyD1YnapMATidGjKxS4B6sTtUmBJxKjR1cocA9WJ2qzZC96wdYXje87M/ybZzDEpfF9h4Z/k8AQl8Z3t+yCi2/I7sbwbxIY/xDN5+F9tch8HlY1l5pwbhWY5vNQF5nFkoSXXqkJ51mBsSSpyWvtH1Gf0No1xeeIvUqZifOswIDQhnTU+qhqa7UMAr+eNU/smKkizi0CxxBx5GkcGhYh9grVIvBjd16Pp5friDmNS1lnGI3vKXbqY1s5/0GhszPYPRbI9allWGNdvFzE3s65CPyfU1uPrhgcaD4P6LhfuWY1/P+r3c3OYHchzefK2PEoNt5dGP5NAmOppPHdCewe3XZj+C952UDz+VHkYvO5Gxs1h82c0/heQ/vkdbDK0Pg+uUbNume6BzdDY0PDGaDAwykfC0iBx/I9HI0CD6d8LCAFHsv3cDQRWPaR3+KztsE9vGME3MSAbKGKposIfImP/KCovhlClmnnDIgb5PAjsVyid65krvsUOMfQzs+X7EUv2AKj8Z3G9/ZDHgOLpvtK071piXab1/zFd4xdcCHmQxrfG87jJgbwyv7sHts0g0FOExN2JcnEDomTFUSS8JJNWYGxJKmxbq2xLs/QxF6j3LZvkRUYECqejhwfVXe/LIPAr2fNEztmqohzi8AxRByh+TzmpHfExLlFYB0xqQ7rDKPxPcVOfawZ51mB3WOBdDW1DGuMxvd6MaOaLTnPCuzQaXwPZdCVa1bj+31vrQLT+H5P2SEjdlYa30NO6kpYrmi6d9S5x8Yi033Jy4bNJuw6iQ+1iH0kr9h0T+P7hlE3a1XMdBrfZxWndb+sX7Ja47K9QQxQ4EFEnwuGAp+L+UG4FHgQ0eeCocDnYn4QLgUeRPS5YCjwuZgfhEuBBxF9LhgKfC7mB+GW7EUv2AKj8Z3G9/ZDEwOLxnca37sMrN3/0r31Hrx7A3il/Lv/v60C03wejhC1EJvM52FVc6kJ51mBcf9TY91az9SjtHZN8Tlir1Jm4jwrMCC0IR21PqraOy2DwK9nzRM7ZqqIc4vAMUQcMZmw42pNIsReodEisI6YVDM6w2h8T7FTH2vGeVZg3Ad1aU4twxqj8b1ezKhmS86zAjt0Gt9DGXTlovE95KWqRNN9SJtYiM2me9MMxpJB87kj2T26FZnPQ31spVacl7xsoPn8qE2x+dwmafKqzZzT+J7kdd9BzH4a3/ctob33pnuwvTleORsDFHg2RRr3hwI3JnS25ijwbIo07o//mHSHb1+nzd8gJi+9mSZlAPrcoWuXD3VPBNZffE9d02WPOQXEWDUDaoRMNvA/20zdf1aRE9YAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  0  0  0⎤\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎣0  0  0  0⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm3 = rm2.change_config(\"lulu\")\n",
    "rm3[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  0  0  0⎤\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎢0  0  0  0⎥\n",
       "⎢          ⎥\n",
       "⎣0  0  0  0⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm4 = rm3.change_config(\"ulll\")\n",
    "rm4.simplify()\n",
    "rm4[0,0,:,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### It is seen that `rm` and `rm4` are same as they have the same configuration"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}