{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prior Distributions with `Bilby`\n", "\n", "Prior distributions are a core component of any Bayesian problem and specifying them in codes can be one of the most confusing elements of a code.\n", "The `prior` modules in `Bilby` provide functionality for specifying prior distributions in a natural way.\n", "\n", "We have a range of predefined types of prior distribution and each kind has methods to:\n", "\n", "1. draw samples, `prior.sample`.\n", "2. calculate the prior probability, `prior.prob`.\n", "3. rescale samples from a unit cube to the prior distribution, `prior.rescale`.\n", " This is especially useful when using nested samplers as it avoids the need for rejection sampling.\n", "4. Calculate the log prior probability, `prior.log_prob`.\n", "\n", "In addition to the predefined prior distributions there is functionality to specify your own prior, either from a pair of arrays, or from a file.\n", "\n", "Each prior distribution can also be given a `name` and may have a different `latex_label` for plotting.\n", "If no name is provided, the default is `None` (this should probably by `''`)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2025-03-20T14:28:07.838553Z", "iopub.status.busy": "2025-03-20T14:28:07.838163Z", "iopub.status.idle": "2025-03-20T14:28:08.924007Z", "shell.execute_reply": "2025-03-20T14:28:08.923444Z" } }, "outputs": [], "source": [ "import bilby\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prior Instantiation\n", "\n", "Below we demonstrate instantiating a range of prior distributions.\n", "\n", "Note that when a `latex_label` is not specified, the `name` is used." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2025-03-20T14:28:08.926387Z", "iopub.status.busy": "2025-03-20T14:28:08.925844Z", "iopub.status.idle": "2025-03-20T14:28:10.221597Z", "shell.execute_reply": "2025-03-20T14:28:10.221055Z" } }, "outputs": [ { "data": { "image/png": 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Nxd7+6ldcKdS0wwFwNZ2t01BZIYQQTVv+pg9wKismzzWA5Iye1g7HImutjjlu3Di+/PJLvvvuOxwdHc09q5ydndHpdBQWFjJjxgxGjhyJl5cXR48eZerUqbi7u1dKoAnRYHLT4eeZALxd9giPOMgqkEKIcrL6nhD14GRe019dsTZWrlzJpEmTmDZtGrt27SI4OJiwsLBKK3pdLC0tjeHDhxMcHMyuXbuYOnUqEyZMYNWqVeYyX3zxBS+99BKvvvoqqampLF68mJUrV5qXuL5aZW06ANBBlVsv9QkhhGg6Tp7OxrT1IwBiTt0ONM0eFtZaHXPhwoXk5eUxePBgvLy8zNvKlSsBUKvV7N27l3vuuYfu3bvzxBNP0L17d5KTk3F0dGykZ0e0WorC+dUToLSIIs+bWG68zdoRCSGaEOkpBeVDr6aeZN/JfEbFb2Hmv3rxyvf7mDSkO3Eb/jY/fv/hfhQbjLy4ak+lnwG+jhxIL28nc3Li0qF5FXUD5voAIi8Mnfvo8f4Ed3PnZF4x+0/mM375LnOdlmw+nM0zy3ZUiaNiqJy3s67K/VT8+3VkeXdvS/FUXLNi2N/F801dGs/F91RxH5dey9J5V3qOKspX3OPXkQNxddBw97zybwTfGdXb/PxU3MfF17j0vi++x8s9p5ZcfI+XXu/i5/CrEttKPeqau7lz5zJ69GjGjBkDlPdwWrduHQsXLiQ2NrZK+fj4eDp16kRcXBwA/v7+7Nixg9mzZ5vfWCcnJ3PLLbfwyCOPANClSxcefvhh/vjjj3qJuaxN+dwaHqqceqlPCCFEE7Lzc1xUheRqfVh7/iZrR3NZ1lgds2Jy9OrodDrWrVt32TJCNJSz277A7divGBRbdvZ9DeWovFcTQvyPJKWgfC4gOwcUTRnF2OPk7AIaB2I3pAP2GG3bUIw9Y5anAqDTOODf2at8dTjKhx0pmjZg54B3e8tDuCrqBsz1AfTo5AmaTJ5Znsqy0Tfx+OIdFxJB9uY6LXF1LqsUExfqG7/qb/NE4oqm/DoV16v4V9G0AbAYT8U1e3Vx4Icpw9iedpZJK3dXOmbpnjzauVGMvsq1LJ13pefoRJGK7KPniFyeChoHXFxc8HbR8cOUYQDm5/3i+7j4GhX1XBxDpXuvxTA7Fxcb0Dhc+NnFfO1DOaZKz2FLmk/KYDCQkpLCSy+9VGl/aGgoW7ZssXhOcnIyoaGhlfYNGzaMxYsXU1paikaj4dZbb+Xzzz/njz/+4KabbuLIkSMkJCTwxBNP1EvcpRf1lDpdLzUKIYRoCvRnC3D7s7yX1OFuT2FKkY7+QjQbRdk4/foyAO+V3Y9NfjtAklJCiP+RpNRFKlbH83HRER8RyBNLqvbguHhVvZxarqZnycXX+ufCCnJw5VXwLMUEmJNIh7MKaVfD8y8XW06HttUed3WwQ6dRm3+G2q8waEnFin06jZqvIoPMcwNV/Fsfz3tN+bjozCv3VVxfp1GbE3UtUXZ2NkajscqqPh4eHlVW/6mQmZlpsXxZWRnZ2dl4eXnx0EMPcfr0aW699VYURaGsrIznnnuuSvKrQklJCSUlJebH+fmXX52lYvieO3mcNlleRVEIIUTzos8tJi7ubd610ZOtOJHW8R5IsbxanBCiadHnFuO69t+0Kckh1eTLR8a7Kf3lcK0+5wghWj5JSl2gzy0m8rMU8x9JSwkXgG4d2pqTE9WVqa1Lk0cfRgQS4ONc44maL44JPzd0GjWRn6UQ91DfOsdUExcnbKA8WfPuuoP1UvfFyT9ruziGinuuSIzpc4vNSbSWRnVJ7y9FUarsu1L5i/dv3LiRN998kwULFjBgwAAOHz7MxIkT8fLyYvr06VXqi42N5bXXXqtxvGU6d4yKCrVKwbb4NOBW43OFEEI0PfrcYrYfyWbshdVRPim7E1/11S+MIYRoePrcYmbMeY9F6q8xYcNLpWOZHzEAHxcdrg52TeI9vhA1owIuP0RaXB1JSl2QU2SguNTIp0/fZP4jWZFwqa5njqVeNPXBx0VX5/ou7nlV0x5Fl0uuXSnxdnGcX0UG8UB8crVlaxNHTRJS+txiig016xGjz62/iciv5v+nOXB3d0etVlfpFZWVlVWlN1QFT09Pi+VtbW1p164dANOnTyciIsI8T9X1119PUVERzzzzDNOmTcPGpvJwjJiYGKKjo82P8/Pz8fX1rT5wG1syccOHM2iKMoDranrLQgghmhh9bjFD5iQxyLiVe+305Cs6PjMO5d1L3pc0Zu9pIUTN5eXm8KrNIgCWlA3jb9vravWluxCi9ZCk1CUu7rVUk+FiTfEPa3XD9i5OzFycAArwca42uVabxNvF9QC17kVW2yTfxcP8rnSN96WrcI3Z2dkRGBhIYmJipWWiExMTueeeeyyeExQUxA8//FBp3/r16+nfvz8ajQaAc+fOVUk8qdVqFEWxOEGrVqtFq9XWKvaTSjt8VGfQFOprdZ4QQoimpfzLwjLe9kyEXFhmDCUfhyrvFSQpJUTT1GHHbNxV2Zxr40PQg/9hg4tLk/zcJISwPklKNSH12ZvnYhUJqIsTM7VJANXmBeTisnXpRVaTshcn1OIjAisPX7Tgw4hA6SpcS9HR0URERNC/f3+CgoL46KOPSE9PJzIyEijvxaTX61m2bBkAkZGRzJ8/n+joaMaOHUtycjKLFy9m+fLl5jpHjBjB3Llz6devn3n43vTp0/nXv/6FWq2ul7gzlPJeWaVn069QUgghRFMXbLMX19y/MKntWXI+zLxfXsuFaOJO7KDdX0sAyBr0Nr26eFk5ICGugkoFV1jhVFwdSUpZgaUhcZcmjerTxfMgXZyYaeg3dQ1Vf00TahVJPh8XHQE+zg0SS0sVHh7OmTNnmDlzJhkZGQQEBJCQkEDnzp0ByMjIID39f4kfPz8/EhISmDx5Mh988AHe3t7MmzePkSNHmsu8/PLLqFQqXn75ZfR6Pe3bt2fEiBG8+eab9Rb3ScUdgN9T/sQ+pFg+uAghRDP2vO23AJz1f4SzO5ysG4wQombKDPD9eFQorDLeynW+IVc+R9TIwoULWbhwIUePHgWgV69evPLKK4SFhV3+RCGaOElK1UB9TWhewVJSxVLSqD61tHmQLncvlnqGidqLiooiKirK4rGlS5dW2RcSEsLOnTurrc/W1pZXX32VV199tb5CrEJ/oadUByWbnCJDi/qdF0KI1qRN5h8E2BzAZKMh+/pnYcc/1g5JCFETm+dA1n7OKE7M5gm+lvfh9aZjx468/fbbdOvWDYBPP/2Ue+65h127dtGrVy8rR9eSVb/Qk6gfkpSqgfqY0PzSxJaluZvkA3T9qK5nmGj5Tl5ISnmrsq0ciRBCiKvRftd8AHK7j8LRozM6zVGgfr4cFEI0kFP7UDbPRgW8WvoEbz95m7wPr0cjRoyo9PjNN99k4cKFbN26VZJSolmTpFQNXe0f1IZaqU9YJkm+1qli+J636gyZVygrhBCiiTq5C8cTGzEqKrL7PEd3eQ8lRJNlni7DUYPhm+ewM5Wx3hjIz+pbiOnQ1srRtVxGo5GvvvqKoqIigoKCrB2OEFfF5spFqlqwYAF+fn7Y29sTGBjI5s2bL1s+KSmJwMBA7O3t6dq1K/Hx8ZWOL1q0iODgYFxdXXF1dWXIkCH88ccfV33dpqaxEyUNNXG6EE1VxfA9d1U+qrLzVo5GCCFEXRT/8i4Aa5RbcPDqDsiXTUI0RfrcYobMSWLInCT++eEd7E79Sb7SBlPYHDZMGSxttgHs3buXtm3botVqiYyMZPXq1fTs2dNi2ZKSEvLz8yttog5UMnyvodU6KbVy5UomTZrEtGnT2LVrF8HBwYSFhVWa9PhiaWlpDB8+nODgYHbt2sXUqVOZMGECq1atMpfZuHEjDz/8ML/++ivJycl06tSJ0NBQ9Pr/Lete2+u2ZjKnkmit8nGgVF3+BkhTlGHlaIQQQtRa1gF0h9cA4HX3VPlQK0QTllNkoLjUiGfZCXx2zQVglvI41/fsIW23gVx33XXs3r2brVu38txzz/HEE0+wf/9+i2VjY2NxdnY2b76+vo0cbUshSamGVuuk1Ny5cxk9ejRjxozB39+fuLg4fH19WbhwocXy8fHxdOrUibi4OPz9/RkzZgxPP/00s2fPNpf54osviIqKom/fvvTo0YNFixZhMpn4+eef63zdlq4i8WQp6VQxVPDH8beyYUqIvCiIVkTFOV35ssOaQv0VygohhGhyfiv/YLvWeCM6nwArByOEuBIVJlb5LMdeVUqhTzBRk1+Vzx4NyM7Ojm7dutG/f39iY2Pp06cP7733nsWyMTEx5OXlmbfjx483crRC1EytklIGg4GUlBRCQ0Mr7Q8NDWXLli0Wz0lOTq5SftiwYezYsYPS0lKL55w7d47S0lLc3NzqfF1o2V0WKxJP1SWdfFx0BPg4y4uCaHXO2VckpU5aORIhhBC1cjYN9n4NwPyye6wcjBCiJh5V/4xb9g7QONB21Af4uLaxdkitiqIolJSUWDym1WpxcnKqtIk6kOF7Da5WE51nZ2djNBrx8PCotN/Dw4PMTMvTCmdmZlosX1ZWRnZ2Nl5eXlXOeemll/Dx8WHIkCF1vi6Ud1l87bXXanRvzZEknISo6pzOEwC7whNWjkQIIUStbJ4DipGCjiH8dbirtaMRQlyBpuAEL9kuL38w5FVw7WzdgFq4qVOnEhYWhq+vLwUFBaxYsYKNGzeydu1aa4cmxFWp00TnqkuyhYqiVNl3pfKW9gO88847LF++nG+++QZ7e/uruq50WRSi9SnUdQRAky/zzQkhRLNxNg3lz/IPt1k3TLJuLEKIaulzi8sXU1IUvH+Loa3qPEUe/eHGsdYOrcU7deoUERERXHfdddxxxx1s27aNtWvXMnToUGuHJsRVqVVPKXd3d9RqdZXeSVlZWVV6MVXw9PS0WN7W1pZ27dpV2j979mzeeustNmzYQO/eva/qulDeZVGr1dbo3oQQLUOhQ3lSyq7gmJUjEUIIUVNFP7+Dg6mMzUofzml7AinWDkkIcYmK1fYAtoRl4noiiRJFg37Qu3S3qVNfB1ELixcvtnYIrdOFDjWi4dTqr4ednR2BgYEkJiZW2p+YmMjAgQMtnhMUFFSl/Pr16+nfvz8ajca879133+X1119n7dq19O/f/6qvK4RonQrblK8sYic9pYQQonk4m0ab/f8F4D+G+8gpMlg5ICGEJRWr7bUtPYNj0isAxJWNxOByjZUjE6IhSVKqodU6pR0dHc3HH3/MkiVLSE1NZfLkyaSnpxMZGQmUD5l7/PHHzeUjIyM5duwY0dHRpKamsmTJEhYvXswLL7xgLvPOO+/w8ssvs2TJErp06UJmZiaZmZkUFhbW+LpCCAH/S0ppik9zMivbytEIIYS4HH1uMUU/v4NKKSPJ2JudSvfyoUFCiCbrNc1SbEvyKHYP4CPjXdYOR4iGpZisHUGLV6vhewDh4eGcOXOGmTNnkpGRQUBAAAkJCXTuXD6xXUZGBunp/+uh4OfnR0JCApMnT+aDDz7A29ubefPmMXLkSHOZBQsWYDAYGDVqVKVrvfrqq8yYMaNG1xVCCIC2Lu7kKm1xURXy3PurWDDlcVkUQAghmiB9bjFPzvkvCTYrQQXvld0PwPu/HEanUePqYGflCIUQl7rT5g+Gq/9AUdmiHzQb45dnrR2SEA1LklINrtZJKYCoqCiioqIsHlu6dGmVfSEhIezcubPa+o4ePXrV1xVCCChflbKNZzc4tRtPYwY5RQZJSgkhRBOUU2RgtPINGpWRJGNvUm39+Wr0TeaElPztFqJpUZ/P5XXNJwAc6TGWv4ydAElKCSGuTp2SUkII0ZTZtb8GTu2mk+qUtUMRQghRDU3+MUaqNwPQ8b7X2NA1SBJRQjRR+txiHDZOp70qj79NPty962YMu3ZLr0YhxFWTpJQQouVx9QOgsySlhBCiyWq/+wM0KiMFHUO45obbrR2OEKIa+txiXpsTx0fq7zApKv5d+gwGNMSF9+VGPzdJJgshroqs3SmEaHncypNSnVRZVg5ECCGERWfTcP37awCybphk3Vjq2YIFC/Dz88Pe3p7AwEA2b9582fJJSUkEBgZib29P165diY+Pr1Jm1apV9OzZE61WS8+ePVm9enWl47Gxsdx44404OjrSoUMH7r33Xg4ePFipjKIozJgxA29vb3Q6HYMHD2bfvn1Xf8OixcvLOcOrNosASO/+BLuUawHo1qGtJKSEEFdNklJCiJbHVZJSQgjRpG2eY15xr9gj0NrR1JuVK1cyadIkpk2bxq5duwgODiYsLKzSIkAXS0tLY/jw4QQHB7Nr1y6mTp3KhAkTWLVqlblMcnIy4eHhRERE8OeffxIREcGDDz7Itm3bzGWSkpIYN24cW7duJTExkbKyMkJDQykqKjKXeeedd5g7dy7z589n+/bteHp6MnToUAoKChruCREtgscfb+OjOoPBsRNFt8ZYOxwhRAsjSSkhRMtzoaeUjyobTGVWDkYIIUQlZ4+g/LkcgHgeaFHz0cydO5fRo0czZswY/P39iYuLw9fXl4ULF1osHx8fT6dOnYiLi8Pf358xY8bw9NNPM3v2bHOZuLg4hg4dSkxMDD169CAmJoY77riDuLg4c5m1a9fy5JNP0qtXL/r06cMnn3xCeno6KSkpQHkvqbi4OKZNm8b9999PQEAAn376KefOnePLL79s0OdENHNpm2mX+hkA+kHvoNhKzyghRP2SpJQQouVp64nJVodGZcSu4Li1oxFCCHGxjW+jMpX3koqMeLjFDP8xGAykpKQQGhpaaX9oaChbtmyxeE5ycnKV8sOGDWPHjh2UlpZetkx1dQLk5eUB4ObmBpT3yMrMzKxUj1arJSQk5LL1iFaupBC+GwfAl2W3U+Q9EFcHO3QatUxwLoSoN5KUEkK0PDY2lDhfA4A295CVgxFCCGGWlQp7/gvAu2UP0q4FfajNzs7GaDTi4eFRab+HhweZmZkWz8nMzLRYvqysjOzs7MuWqa5ORVGIjo7m1ltvJSAgwFxHxXk1raekpIT8/PxKm2hlNsyA3GOcVNyZq4rA1cEOHxcdG6aEsGFKSItJKAshrEuSUkKIFqnEpRsA2pzDVo5ECCGE2S9vAAp5XcL4S+lq7WgahEqlqvRYUZQq+65U/tL9tanz+eefZ8+ePSxfvvyqYouNjcXZ2dm8+fr6VnsPogVK2wTbyyc3/7/SscyJCDYnoXxcdJKQEkLUG0lKCSFapIqkFNl/WzcQIYQQ5fQpcOBHFFTs8HvO2tHUO3d3d9RqdZWeR1lZWVV6KFXw9PS0WN7W1pZ27dpdtoylOsePH8/333/Pr7/+SseOHStdB6hVbDExMeTl5Zm348dlOHyrcdGwvbQuD/K76foW1atRCNG0SFJKCNEi2XpeB8CpI3vQ5xZbORohhBDn180E4BvjLYz+qbDFzUljZ2dHYGAgiYmJlfYnJiYycOBAi+cEBQVVKb9+/Xr69++PRqO5bJmL61QUheeff55vvvmGX375BT8/v0rl/fz88PT0rFSPwWAgKSmp2ti0Wi1OTk6VNtFKbJgBuemcVNy5+8CwFtdWhRBNi621AxBCiIbQrvP1APihJ72wRLqZCyGENR39Dfv0jZQqahyHTedHP3/z/DQtSXR0NBEREfTv35+goCA++ugj0tPTiYyMBMp7H+n1epYtWwZAZGQk8+fPJzo6mrFjx5KcnMzixYsrDb2bOHEigwYNYtasWdxzzz189913bNiwgd9++81cZty4cXz55Zd89913ODo6mntEOTs7o9PpUKlUTJo0ibfeeotrr72Wa6+9lrfeeos2bdrwyCOPNOIzJJq603sTaX/RsL03w4O40c+txbVVIepEUeAyw7FF3UhSSgjRMrldg6JS40QxtudOAS7WjkgIIVonRYGfXwdghfE2+vn5E+DjbOWgGkZ4eDhnzpxh5syZZGRkEBAQQEJCAp07dwYgIyOD9PR0c3k/Pz8SEhKYPHkyH3zwAd7e3sybN4+RI0eaywwcOJAVK1bw8ssvM336dK655hpWrlzJgAEDzGUWLlwIwODBgyvF88knn/Dkk08C8OKLL1JcXExUVBQ5OTkMGDCA9evX4+jo2EDPhmhu9h89idPXz4EKvii7g53qvrwjCSkh/sdkBLWkUOqbPKNCiJbJ1g6DU2e0eUfQ5h4GrrN2REII0Tod3gDHt2K00fJ+2X0ssXY8DSwqKoqoqCiLx5YuXVplX0hICDt37rxsnaNGjWLUqFHVHq+YHP1yVCoVM2bMYMaMGVcsK1offW4xu5dM5BGb05x38KHfqPfZ4CoJKSEqMZVKUqoByJxSQogWq8TlGoALSSkhhBCNzmTCsP41AD42DKFA4y5z0wjRBBn+/pVHbNYDYD9yAT39fCQhJcSljAZrR9AiSVJKCNFiVazAJ0kpIYSwktTvsTu9lwJFh+/dU9kwJUQ+6ArR1JQU4rPpRQDO+D8GXQdbNx4hmipjmbUjaJEkKSWEaLFKXLsDYH/2gJUjEUKIVshYBr++CcBiYxidfH0lISVEU7ThVewKj3NCcefUTVOtHY0QTYY+51ylxxk5+VaKpGWTpJQQosUqdusJXEhK1WC+DSGEEPVo9+eQ/TdlWhcWlw23djRCCEuOJMH2jwF4sfQZTHZtrRyQEE1HTmHlpFT+JY9F/ZCklBDCogULFuDn54e9vT2BgYFs3rz5suWTkpIIDAzE3t6erl27Eh8fX6VMbm4u48aNw8vLC3t7e/z9/UlISGioW8Dgcg0GRY3akA+56Vc+QQghRP0wFMGvsQAc7TWOAtpYOSAhRBUlhfD98wCc7PYIW0wBVg5IiKZFZSyt/Ngkw/cagiSlhBBVrFy5kkmTJjFt2jR27dpFcHAwYWFhlZaxvlhaWhrDhw8nODiYXbt2MXXqVCZMmMCqVavMZQwGA0OHDuXo0aN8/fXXHDx4kEWLFuHj49Ng96Go7TisdCx/cOqvBruOEEKIS2xdAIWZlDn5cv92f3QatUxwLkQTU7hmGuSmc97BhxEHQ6WdCnEJlclw2ceifsh6hkKIKubOncvo0aMZM2YMAHFxcaxbt46FCxcSGxtbpXx8fDydOnUiLi4OAH9/f3bs2MHs2bMZOXIkAEuWLOHs2bNs2bIFjUYDQOfOnRv8XlKVTvTkGPlHd+HU464Gv54QQrR6Rdnw23sA7Lp2Avm/2/Dp04Eyn5QQTYQ+t5jsPYn02bMUgKdynuScWsdXkUHSToW4iM0lq+3lFRVbKZKWTXpKCSEqMRgMpKSkEBoaWml/aGgoW7ZssXhOcnJylfLDhg1jx44dlJaWd3v9/vvvCQoKYty4cXh4eBAQEMBbb72F0Wi0WGdJSQn5+fmVttpydbDjkMoPgK3JSehz5YVECCEaij63mL/0eRQmvgWGAv5SuvLg717oNGq6dZB5aoRoCvS5xfxrzlrcNkQD5cP2po17lg1TQgjwcbZydEI0LSpT5eF7s37cI58nGoAkpYQQlWRnZ2M0GvHw8Ki038PDg8zMTIvnZGZmWixfVlZGdnY2AEeOHOHrr7/GaDSSkJDAyy+/zJw5c3jzzTct1hkbG4uzs7N58/X1rfW9+LjoGP3AvwC4TjlKTpF0uRUtQ0PM+bZq1Sp69uyJVqulZ8+erF69utLx2NhYbrzxRhwdHenQoQP33nsvBw8erNf7Es2XPreYIXOSGDf/a7S7lgIwx/QIS5++mQ1TQqT3hRBNRE6RgSnKp/janKbMyRfvB94hwMdZ2qgQFqgu6SllLCuVzxMNQJJSQgiLVCpVpceKolTZd6XyF+83mUx06NCBjz76iMDAQB566CGmTZvGwoULLdYXExNDXl6eeTt+/Hid7qP9NYEAdLbJwsZQUKc6hGhKGmLOt+TkZMLDw4mIiODPP/8kIiKCBx98kG3btpnLJCUlMW7cOLZu3UpiYiJlZWWEhoZSVFTU4Pcsmr6cIgPFpUY+6bQWjcrIJqUvUyKfIaR7e/mwK0QT0jb9Zx6x/RUFFbb3x4PW0dohCdFkXZqUslPJROcNQeaUEkJU4u7ujlqtrtIrKisrq0pvqAqenp4Wy9va2tKuXTsAvLy80Gg0qNVqcxl/f38yMzMxGAzY2VWeWFOr1aLVaq/+htq4UergiaYoE/sz+8Gv49XXKYQVNcScb3FxcQwdOpSYmBigPCmclJREXFwcy5cvB2Dt2rWV6v3kk0/o0KEDKSkpDBo0qKFuVzQTZ4oM9Fb9Q9dT61FQcd1jc/GQoUBCNC3nzuKz6UUAzgSMxr3LrVYOSIim7dLhe7ZYnnZEXB3pKSWEqMTOzo7AwEASExMr7U9MTGTgwIEWzwkKCqpSfv369fTv3988qfktt9zC4cOHMZlM5jJ///03Xl5eVRJS9a3YvQ8Ain5ng15HiIbWUHO+VVemujoB8vLyAHBzc7N4vD7mhRPNgz63mMjPdvCyXXkCU9XnYTyuDbRyVEKIKtZMQVN8mkMmH07d+KK1oxGiybu0p5QG6SnVECQpJYSoIjo6mo8//pglS5aQmprK5MmTSU9PJzIyEijvRfH444+by0dGRnLs2DGio6NJTU1lyZIlLF68mBdeeMFc5rnnnuPMmTNMnDiRv//+mzVr1vDWW28xbty4Br8fxaf8w9HBlI0yOaFo1hpqzrfqylRXp6IoREdHc+uttxIQEGCxTH3MCyeah5wiAzcbU7hJtR/UWrhtqrVDEkJc6q9VsO8bFJWa6NLnUGztrR2REE3epT2lJCnVMOqUlKrvCVb37dvHyJEj6dKlCyqVyjzE4GIzZsxApVJV2jw9PesSvhDiCsLDw4mLi2PmzJn07duXTZs2kZCQQOfOnQHIyMioNH+Nn58fCQkJbNy4kb59+/L6668zb94889AgAF9fX9avX8/27dvp3bs3EyZMYOLEibz00ksNfj/O3QYAcD2HZXJC0SLU95xvta3z+eefZ8+ePeahfZbU17xwohkwlRFj+2X5zzdHgoskIIVoUgoyYc0UAE73e569SlcrByRE86AyVf7cIMP3Gkat55SqmGB1wYIF3HLLLXz44YeEhYWxf/9+OnXqVKV8xQSrY8eO5fPPP+f3338nKiqK9u3bmz+wnjt3jq5du/LAAw8wefLkaq/dq1cvNmzYYH588dw0Qoj6FRUVRVRUlMVjS5curbIvJCSEnTsvPzwuKCiIrVu31kd4tePdDwUVvjanKSzOBmSeE9E8NdScb9WVsVTn+PHj+f7779m0aRMdO1Y/R1u9zQsnmjy3A1/ibaOnTOuK7a3Vv48TQliBonB+VRT2xTng1YesfhNgy7YrnyeEqDrRufSUahC17il18QSr/v7+xMXF4evrW+0KWhdPsOrv78+YMWN4+umnmT17trnMjTfeyLvvvstDDz102Tewtra2eHp6mrf27dvXNnwhRGtk70yJyzUA6E7/aeVghKi7hprzrboyF9epKArPP/8833zzDb/88gt+fn71cUuiuSvOocOOOQBk9Z8COlcrBySE0OcWm6cryPl9MfZHf6ZE0XBqyDzOFCtWjk6I5sOm7Hylx/YqGXHREGqVlGqoCVZr6tChQ3h7e+Pn58dDDz3EkSNHLlteJlkVQlQobt8XgDand1s1DiGuVkPM+TZx4kTWr1/PrFmzOHDgALNmzWLDhg1MmjTJXGbcuHF8/vnnfPnllzg6OpKZmUlmZibFxTJPW2tWkBiLbUkOf5t8ONvjEWuHI0Srp88tZsicJIbMSSLz2AGckl4B4N2yB9l93pPIz1LQadS4OjTsIjNCtAQ2ZZXf4+gosVIkLVutklINNcFqTQwYMIBly5axbt06Fi1aRGZmJgMHDuTMmTPVniOTrAohKhR36AuALkt6SonmrSHmfBs4cCArVqzgk08+oXfv3ixdupSVK1cyYMAAc5mFCxeSl5fH4MGD8fLyMm8rV65svJsXTUpm2j60KR8D8I7yOK6ObawckRAip8hAcamR86WlOP40AXVpEdtMPVhiDDMfi48IxMdFZ+1QhWjyVJKUahS1nlMKGmaC1SsJCwsz/3z99dcTFBTENddcw6effkp0dLTFc2JiYiody8/Pl8SUEK3UufZ9ANCd3gUmE9jI4qOi+WqIOd9GjRrFqFGjqj1e8dotRIU2G2dgpzKS6TGI1x6eKB9yhWhCnlb/hEPmNooULS+UPovpor4I7aSXlBA1cunwPZ0M32sQtfpU1lATrNaFg4MD119/PYcOHaq2jFarxcnJqdImhGidzrfrSZGixbYkD06nWjscIYRo3o5sxOnYesoUGwqCX5WElBBNSDfVCV60/S8Ab5Q9xkOhgwDM80wJIWrm0uF7baSnVIOoVVKqoSZYrYuSkhJSU1Px8vKqcx1CiFbERkOKqXv5z8csz4EnhBCiBkxGShNiAFiuhNKmYy8rBySEMDOVMlezEK2qlCMuA1luvJ1uHdqi06h5/5fDMp+UELVgY5The42h1sP3oqOjiYiIoH///gQFBfHRRx9VmWBVr9ezbNkyoHyC1fnz5xMdHc3YsWNJTk5m8eLFLF++3FynwWBg//795p/1ej27d++mbdu2dOvWDYAXXniBESNG0KlTJ7KysnjjjTfIz8/niSeeuOonQQjROvxh6sEg9V449jvcNNba4QghRLOjzy2mzd7Pcc3eT67iQNcHXpdeUkI0Ie13zcfDJo1cxYGHMh9Fp7ElwMeZDVNCyCky4OpgJ21WiBqqmFPKpNZiYyxBp5KkVEOodVIqPDycM2fOMHPmTDIyMggICKjRBKuTJ0/mgw8+wNvbu8oEqydPnqRfv37mx7Nnz2b27NmEhISwceNGAE6cOMHDDz9MdnY27du35+abb2br1q3m6wohxJX8YeoBgDHtd9SKArWY104IIVo7fW4x98z5ibU2r4MK3iu7n5FulqdvEEJYwYkUOuyaB8Cxm2eypPeISkkoSUYJUTsVw/eM9q7YFGWiQ+aUagh1muk3KiqKo0ePUlJSQkpKCoMGDTIfW7p0qTmRVKFigtWSkhLS0tLMvaoqdOnSBUVRqmwX17NixQpOnjxp7km1atUqevbsWZfwhRCtkKuDHQdtu1OiaFCfy+LvVFmFTwghauNwViHPKl/hrsoj36ELnxmHWjukJmnBggX4+flhb29PYGAgmzdvvmz5pKQkAgMDsbe3p2vXrsTHx1cpU/G+V6vV0rNnT1avXl3p+KZNmxgxYgTe3t6oVCq+/fbbKnU8+eSTqFSqStvNN998VfcqmgZ9bjEns7LhmzGoFCPfGQei7v0AAT7OkohqIWJjY7nxxhtxdHSkQ4cO3HvvvRw8eNDaYbV4FROdl9mXz4XdhvOXKy7qSJafEkK0Cj4uOhKmDKXYoy8Ay1Z8KRN+CiFEDelzi5n92bc8pV4LwM6e/6asbos4t2grV65k0qRJTJs2jV27dhEcHExYWFilUQQXS0tLY/jw4QQHB7Nr1y6mTp3KhAkTWLVqlblMcnIy4eHhRERE8OeffxIREcGDDz7Itm3bzGWKioro06cP8+fPv2x8d955JxkZGeYtISGhfm5cWI0+t5ghc5LYPP8ZOHsEg4M300uftHZYop4lJSUxbtw4tm7dSmJiImVlZYSGhlJUVGTt0Fo0lbmnlBsA9rL6XoOQdxNCiFbDx0UHPQZD1nYClb/IKTLIN4hCCFEDOYUlvMQn2KpMrDcGslcTCBy2dlhNzty5cxk9ejRjxowBIC4ujnXr1rFw4UJiY2OrlI+Pj6dTp07ExcUB4O/vz44dO5g9e7Z5qou4uDiGDh1KTEz55PIxMTEkJSURFxdnnqM1LCyMsLCwK8an1Wrx9PSsj1sVTUROkYFbjH8QbvczCir+6PMm+b9orR2WqGdr166t9PiTTz6hQ4cOVUYtifpVMXyv7EJSSlbfaxjSU0oI0br4hQBwq81eUExWDkYIIZoHpyM/cot6H0YbLe/wpKziZYHBYCAlJYXQ0NBK+0NDQ9myxfKqr8nJyVXKDxs2jB07dlBaWnrZMtXVeTkbN26kQ4cOdO/enbFjx5KVlVXrOkTTYnsui1majwD4sOwuHvtFK22zFcjLywPAzc3NypG0bGpDIQBluvaArL7XUKSnlBCidfEdgFHjQPvSfPLO7IeOt1g7IiGEaNpKCvHa9gYA2X2j+HTQA7KKlwXZ2dkYjUY8PCpP/u7h4UFmZqbFczIzMy2WLysrIzs7Gy8vr2rLVFdndcLCwnjggQfo3LkzaWlpTJ8+ndtvv52UlBS02qo9a0pKSigp+d8HsPz8/FpdTzQCRcFn0//hqCpgv6kzc8seIC68Lzf6uUnbbMEURSE6Oppbb72VgICAastJG756Noby56ysTQcAdKoSZPKP+ic9pYQQrYutHUVeQQC0PZFk5WCEEKIZ2DwHTVEG6ab2ZPd5Dh8XnUygfBmqS1Z2VRSlyr4rlb90f23rtCQ8PJy77rqLgIAARowYwU8//cTff//NmjVrLJaPjY3F2dnZvPn6+tbqeqLh5W5aiOPxXylRNEwsHYcBDd06tJW22cI9//zz7Nmzxzx8tzrShq+eurQAgFKH8i8GHGSi8wYhSSkhRKtT2LF8CF/bE5usHIkQQjRx2Ydhy/sAzCx7HMXW3soBNV3u7u6o1eoqPZiysrKq9HSq4OnpabG8ra0t7dq1u2yZ6uqsKS8vLzp37syhQ4csHo+JiSEvL8+8HT9+/KquJ+rXqSN/Yv/LKwDElj3MIaWjDNtrBcaPH8/333/Pr7/+SseOHS9bVtrw1bO5MHyvtK0PAI4Uy/QfDUCSUkKIVqciKdXm1A4oKbRyNEII0UQpCvz0IphKKfC9nQ2mG6wdUZNmZ2dHYGAgiYmJlfYnJiYycOBAi+cEBQVVKb9+/Xr69++PRqO5bJnq6qypM2fOcPz4cby8vCwe12q1ODk5VdpEE1FmwCkhCntVKafa38LYF97m95duZ8OUEOkl1UIpisLzzz/PN998wy+//IKfn98Vz5E2fJVMRtSlFUmp8gSgjUrBxlBgzahaJElKCSFaHQfv7qQrHtiYSjmz72drhyOEEE3TwQT452dMNnZs7f4CULvhYq1RdHQ0H3/8MUuWLCE1NZXJkyeTnp5OZGQkUN5z4fHHHzeXj4yM5NixY0RHR5OamsqSJUtYvHgxL7zwgrnMxIkTWb9+PbNmzeLAgQPMmjWLDRs2MGnSJHOZwsJCdu/eze7duwFIS0tj9+7dpKenm4+/8MILJCcnc/ToUTZu3MiIESNwd3fnvvvua/gnRtSvjbHosv8iR2lLztD/4OPqgI+LThJSLdi4ceP4/PPP+fLLL3F0dCQzM5PMzEyKi2WGowZT8r/kU5muHSZ1eU9hdUmetSJqsSQpJYRodXxcdKi7DwEg/88f0OfKC7oQQlRiKKJszYsALDCEMXZNrgwNqoHw8HDi4uKYOXMmffv2ZdOmTSQkJNC5c2cAMjIyzIkiAD8/PxISEti4cSN9+/bl9ddfZ968eYwcOdJcZuDAgaxYsYJPPvmE3r17s3TpUlauXMmAAQPMZXbs2EG/fv3o168fUJ4c69evH6+8Uj68S61Ws3fvXu655x66d+/OE088Qffu3UlOTsbR0bExnhpRX45tgd/+A8BLpWMoc/C0ckCiMSxcuJC8vDwGDx6Ml5eXeVu5cqW1Q2u5SsonOS9RNChqLUatMwBqgySl6pusvieEaJW0ve6GQ1/gcDSRwXN+JXHKbfINoxBCXFCw7k0cC05wQnGn8z3T+dG7g6y2V0NRUVFERUVZPLZ06dIq+0JCQti5c+dl6xw1ahSjRo2q9vjgwYPNE6RbotPpWLdu3WWvIZqB83nwzbOAwirTYDapg3hFEsWtwuXat2gg58uTUvmUv+4Ztc5ozp2SnlINQHpKCSFaJfeAIZjsnOigyqVH2UFyigzWDkkIIZqEU4dS0O1YCMCbpqe54dqOstqeEE1Bwv9BXjoGx068YoggPiJQ2qUQDeVCT6kCpQ0ARrsLPaUkKVXvJCklhGidbO2wuW4YAKHqHVYORgghmgiTCcfEKdiqTOi9Qnl5SrR86BWiKfhzJexZCSobjt8WRxE62kkvKSEazoWeUoUX9ZQCGb7XECQpJYRovXrcDcAwm+3lq0wJIUQrl7v5Q9pk7aJA0VFw2xuSkBKiKTh7BNZEl/8c8hLFHv2tG48QrcG5bADOKuWrFpqTUtJTqt5JUkoI0Xp1G4JJrcXP5hTanL+tHY0QQlhVhv4o6l9eAyBOeQjHDp2sHJEQQn8mD8PKp8BQCJ0Gou89jsNZhdYOS4iWr6g8KXUGSUo1NElKCSFaL21bCn2CAXA+8oOVgxFCCOvS/fwyjqpiclwCeHqS9JISwtr0ucUkvDceu1O7KbVzZmu/txnyn9+YtHK3rIYpREMrOg3AmYqeUjKnVIORpJQQolXL63YvAI5/r5YhfEKI1utQIi5HfsCoqDhz2zv4uLW1dkRCtHqGgxsYa/MdAM8XPsVDK08A8OnTN7FhSogkjoVoSOfOABclpbQu5f8WnbFWRC2WrbUDEEIIa1L7D6foZ3scio5zOnUz7XsOsnZIQgjRuAznzPPVfGK8k5vdA6wckBCComw6bpwMQHrXhxh/RzTjAVcHO0lGCdEIzudmYg8UqJ1xdbBD6+oFwLH0oxhyi6Ud1iPpKSWEaNW827ejoGsYADZ7/2vlaIQQwgp+fRNy0zE4eDO37AFrRyOEUBT49jk0xaf52+RDQchrBPg4E+DjLB+EhWgkyoU5pR6+7QZ8XHS08/AFoJ2SQ06RwZqhtTiSlBJCtHrFPUYCF+aVKpMXGSFEK3JiB8rWBQCkBLzMOeytHJAQrZs+t5jcje/DofWY1FrGl45HsZVElBCNTV1cPkyvjYtn+Y62HgB0UOVaKaKWS5JSQohWr8j7FrIUF2xLcuHQemuHI4QQjaOshNJvnkOlmPjGeCsPJ7nI5MlCWJE+t5jxc5bSZmP5KpiZN0/noCKrYArR6BQF2/PlSakye7fyfReSUg6qEmxKi6wVWYskSSkhhEULFizAz88Pe3t7AgMD2bx582XLJyUlERgYiL29PV27diU+Pr7asitWrEClUnHvvffWc9R1ZKPmG+Ot5T+nLLVqKEII0Rj0ucXkr49Fc/ZvTitOaO9+hx/H3yqTJwthRbm5ubyreg87VRn5nUM51Cnc2iEJ0Tqdz8PGWAJAWZv25fu0bTHatgHA9txpa0XWIklSSghRxcqVK5k0aRLTpk1j165dBAcHExYWRnp6usXyaWlpDB8+nODgYHbt2sXUqVOZMGECq1atqlL22LFjvPDCCwQHBzf0bdTKcuPtACiHN5B57KCVoxFCiIajzy3m+Tmfots2D4BXSp+ic8eOMl+NEFbmlTyDa2wyyFDc2NFnJpGf75Tei0JYQ74egLNK20rDZysSVLbnTlklrJZKklJCiCrmzp3L6NGjGTNmDP7+/sTFxeHr68vChQstlo+Pj6dTp07ExcXh7+/PmDFjePrpp5k9e3alckajkUcffZTXXnuNrl27Nsat1Iirgx1Ztj5sNgagQuHbxbHoc4utHZYQQjSInIIiXlctRKMyctxjCD+ZBlg7JCHEnq9wO7gCk6JicmkUWWUOFJcaiY8IlGSxEI0trzwplam0q7S7TFeRlMpq9JBaMklKCSEqMRgMpKSkEBoaWml/aGgoW7ZssXhOcnJylfLDhg1jx44dlJaWmvfNnDmT9u3bM3r06CvGUVJSQn5+fqWtofi46NgwJYTOoeMAGKn6hZwCGSsuhGiZ3Pd8SIDNUXIVB1ICplk7HCFavVNH9mL6YSIA7xvvZaupp/nLsXbSS0qIxnehp9RJxa3S7tK23gBoik42ekgtmSSlhBCVZGdnYzQa8fDwqLTfw8ODzMxMi+dkZmZaLF9WVkZ2dvlyqr///juLFy9m0aJFNYojNjYWZ2dn8+br61uHu6k5HxcdnQY+QKmuPe1VeRT/+a30lhJCtDinjuyhfUocADNLI/in2MG6AQnRyumzz5Lz6SPYlBaR4dqf98rKVwR+/5fDMnRPCGu5kJTKuKSnVGnbjgDYFZxo9JBaMklKCSEsUqlUlR4rilJl35XKV+wvKCjgscceY9GiRbi7u9fo+jExMeTl5Zm348eP1/IO6kCtobj34wDY/fEBQ+ZslMSUEKLF0J8tIPPTp1CbDPxq7MM3pmD54CuElek2TKOHKp3TihP/yngKrUbDV5FBsvCAENaUV5GUqtxTyuBY/iW5pqARPpe0InVKStX3qlz79u1j5MiRdOnSBZVKRVxcXL1cVwhRe+7u7qjV6iq9orKysqr0hqrg6elpsbytrS3t2rXjn3/+4ejRo4wYMQJbW1tsbW1ZtmwZ33//Pba2tvzzzz9V6tRqtTg5OVXaGoPToCgUtT19bI7Qx/gXOUWGRrmuEEI0NNvf4+ijOkyprSM9nvmE31+6Qz74CmFNe77C7cCXmBQVR0Pe45PxI9gwJYQbu7jJwgNCWFNeedKpSk+pC0kpu0LpKVWfap2UaohVuc6dO0fXrl15++238fT0rJfrCiHqxs7OjsDAQBITEyvtT0xMZODAgRbPCQoKqlJ+/fr19O/fH41GQ48ePdi7dy+7d+82b//617+47bbb2L17d4MPzasVB3dU/R4F4Bn1j1YORggh6snJ3XTYGQdAZvAbePleg4+LTj74CmEt2YfAPI/Ufeiuu0PaoxBNxdk0AI4plb+QN1wYvqcpOAEXRoWIq1frpFRDrMp144038u677/LQQw+h1Wrr5bpCiLqLjo7m448/ZsmSJaSmpjJ58mTS09OJjIwEyofWPf744+bykZGRHDt2jOjoaFJTU1myZAmLFy/mhRdeAMDe3p6AgIBKm4uLC46OjgQEBGBn18SGjQSNQ0HF7erdaM8etHY0QghxdUrPw+pnUSllrDHeRN4191o7IiFaNX32Wc5/+RiUFnHa/SbeK7vf2iEJISqUFkN+eU+oo0rlDjMVE52ry87BubONHlpLVaukVEOuylXf1xVC1F14eDhxcXHMnDmTvn37smnTJhISEujcuTMAGRkZlXop+vn5kZCQwMaNG+nbty+vv/468+bNY+TIkda6havT7hry/e4EwGnHPCsHI4QQV+mX1+H0AU4rzrzBWFzbWv4CUAjR8PS5xfw+bwz2Zw9wWnFi+Ikn0Go0Mq+bEE3EqfQDAOQrbSjWuFRqm4qtPZmKKwBZxw9YJb6WyLY2hRtiVS4vL68GuS6ULylfUlJiftyQS8oL0dJERUURFRVl8djSpUur7AsJCWHnzp01rt9SHU1JSdAUSPuJ9kd/5NDeP7j2+pusHZIQQtTe0d8g+QMA/l06lrefvE2GBwnRiPS5xeQUGXB1sMPHRYfpz5U8aPMzCioK71rIJz7B5mNCCOs7n3kIAKOLHxueGlypbbo62HEMLzzJYe6XPzI++gZpu/WgThOd1+eqXA153cZeUl4I0XJ06H4jeX5h2KgUjnz9sqzCJ4RofkoKKPsmElA44TeKX0w30E56YwjRaPS5xQyZk8Td7//GkDlJnDqyF+/NMQCcvmECfjfdLfNICdHE2OUfBUDlfk2VtunjoqNXn/IvqjubjsuCSPWkVkmphliVq6GuC1ZaUl4I0WI4h72Kgophqm0UH6t5LzAhhGgKzn7zArb5xzluas+dqXdaOxwhWp2cIgPFpUbG394NSotw/mE06rJzJBt7ktVvkrXDE0JYoM0tXxXc4NTF4vG2Pr0A6KY62VghtXi1Sko1xKpcDXVdsN6S8kKIFqKDP3nX3AOA029voM85Z+WAhBCiZs5s/y9uB1eULzUfPBujxhGdRi3z1jSCBQsW4Ofnh729PYGBgWzevPmy5ZOSkggMDMTe3p6uXbsSHx9fpcyqVavo2bMnWq2Wnj17snr16krHN23axIgRI/D29kalUvHtt99WqUNRFGbMmIG3tzc6nY7Bgwezb9++q7pXUTM+zva8pVmMfc5BSnXtmVA6DmzU1g5LCGGBfU75IkfnXa+zXKB9+f5uqhONFVKLV+vhe/W9KheUT2ResUy8wWBAr9eze/duDh8+XOPrCiFEQzgf/BIGxZYOp7fwxtz/yDA+IUSTl5n+N47rpwBwotezBA+9lw1TQtgwJUSGCTWwlStXMmnSJKZNm8auXbsIDg4mLCys0uIgF0tLS2P48OEEBweza9cupk6dyoQJE1i1apW5THJyMuHh4URERPDnn38SERHBgw8+yLZt28xlioqK6NOnD/Pnz682tnfeeYe5c+cyf/58tm/fjqenJ0OHDqWgoKD+ngBhUbdjK7hP/TuKSs3xOxZwGldrhySEsMRkQnumfALz8+38LZe5kJTqpMpCVXa+sSJr0Wo10TmUr8p15swZZs6cSUZGBgEBATValWvy5Ml88MEHeHt7V1mV6+TJk/Tr18/8ePbs2cyePZuQkBA2btxYo+sKIURD8OziT0H/Z7FL+YD/Uy0jN/8Z+VAnhGiy9GcLyFz8GJ6qfP5UuuF+xzQA+bvVSObOncvo0aMZM2YMAHFxcaxbt46FCxcSGxtbpXx8fDydOnUiLi4OAH9/f3bs2MHs2bPN75Xj4uIYOnQoMTHlcxHFxMSQlJREXFwcy5cvByAsLIywsLBq41IUhbi4OKZNm8b9998PwKeffoqHhwdffvklzz77bL09B6KyG1R/c0PquwDMMj5CP11vIMW6QQkhLMpMP4CnsZjzigYHr+6WC7X1wGjnhNqQT3HmQehc/XRCombqNNF5VFQUR48epaSkhJSUFAYNGmQ+tnTpUnMiqULFqlwlJSWkpaVV6d3UpUsXFEWpsl1az+WuK4QQDcVx6EuU6dzpapOJ275PrR2OEEJUS/PbbAJVBym1dcDj6S/waSdTFzQWg8FASkoKoaGhlfaHhoayZcsWi+ckJydXKT9s2DB27NhBaWnpZctUV6claWlpZGZmVqpHq9USEhJSq3pE7aiLs/nAbh42Simnfe8k3nAnf+nzrB2WEKIahhN7AChtdx0+bo6WC6lUlLUvn1dq1ZoEGUVRD+qUlBJCiFbF3olT/f8PgPYpcyFPb+WAhBDCgmNbaL9rHgCZwbF4du5h5YBal+zsbIxGY5VFeDw8PKos1lMhMzPTYvmysjKys7MvW6a6Oqu7TsV5Na2npKSE/Pz8SpuoBWMZvj8/j5fqLOddulE6Yj46jS3v/3JY5ncToomyP5sKQJl7NUP3LtB2CgTA33RYVuCrB5KUEkKImuj3GH8q3bAtK6L4u0mgKNaOSAgh/qc4h7Kvx6BSTHxrGoRNnwetHVGrpVKpKj1WFKXKviuVv3R/beusj9hiY2NxdnY2b76+vrW+Xqv2y+u0zdhCkaLl+JAP8e7Qng1TQvhx/K0yv5sQTZTudHlPqfPtel6+oHf51EO9bY40dEitgiSlhBCiBnzc2mK4ax4GRY3uyHrObl9p7ZCEEKKcolC8ahy2BXrSTB64h8+TD7xW4O7ujlqtrtLzKCsrq0oPpQqenp4Wy9va2tKuXbvLlqmuzuquA9SqnpiYGPLy8szb8ePHa3y9Vi/1R/g9DoAXS5+lxPVaoHxutwAfZ2mfQjRFioIuaycA5zoEXr6szw0A+KvSURmlp9TVkqSUEELUkHf3G/hIuQ8A05oXyciQYXxCCOvLTZqP7vAaShU1LyoT8PPxtHZIrZKdnR2BgYEkJiZW2p+YmMjAgQMtnhMUFFSl/Pr16+nfvz8ajeayZaqr0xI/Pz88PT0r1WMwGEhKSqq2Hq1Wi5OTU6VN1ED2Yfj2OQBOXPcUa0w3WzkgIUSNnPkH25JcziuaK/eUcvXDaOeEVlWKNudg48TXgklSSgghasjHRcd9E+aQ73gN7qo8bNdMkmF8QgjrOrEDp02vAXDg+v8jbspo6YVhRdHR0Xz88ccsWbKE1NRUJk+eTHp6unmRn5iYGB5//HFz+cjISI4dO0Z0dDSpqaksWbKExYsX88ILL5jLTJw4kfXr1zNr1iwOHDjArFmz2LBhA5MmTTKXKSwsZPfu3ezevRson9h89+7d5hWxVSoVkyZN4q233mL16tX89ddfPPnkk7Rp04ZHHnmk4Z+Y1qKkkNLlj0JJPiXeAwjbP0TmjxKiuTixHYC9ih+K+gptVqWiuH0fANqc2tnQkbV4kpQSQoha8HF34fyIhRgUNe1PrCfnt0XWDkm0QgsWLMDPzw97e3sCAwPZvHnzZcsnJSURGBiIvb09Xbt2JT4+vkqZVatW0bNnT7RaLT179mT16tWVjm/atIkRI0bg7e2NSqXi22+/rc9bErWgzy0uX+3n3Fn47xPYmEpJMN6E6ubnJCFlZeHh4cTFxTFz5kz69u3Lpk2bSEhIoHPnzgBkZGSYE0VQ3oMpISGBjRs30rdvX15//XXmzZvHyJEjzWUGDhzIihUr+OSTT+jduzdLly5l5cqVDBgwwFxmx44d9OvXj379yuc5iY6Opl+/frzyyivmMi+++CKTJk0iKiqK/v37o9frWb9+PY6O1awwJWrHZKL4q2fQnDnAacWFLTfMpqBURXxEoLRLIZqDE38AsMt0bY2KF3mW/w12yNjaYCG1FrbWDkAIIZqbDt0H8M8N/8c1u97GeeN06BEC7a+zdliilVi5ciWTJk1iwYIF3HLLLXz44YeEhYWxf/9+OnXqVKV8Wloaw4cPZ+zYsXz++ef8/vvvREVF0b59e/MH3+TkZMLDw3n99de57777WL16NQ8++CC//fab+YNvUVERffr04amnnqr0gVk0Ln1uMUPmJKHCxM5rFmGff4Jjiiev8hzfttVaOzwBREVFERUVZfHY0qVLq+wLCQlh587Lf9M+atQoRo0aVe3xwYMHmydIr45KpWLGjBnMmDHjsuVEHW2eje7wGkoUW541TOKWs+XtsZ30khKiWSg9shkNkGK6lpoMji7yvhlSwF6fjD7nHD6ubRo6xBZLekoJIUQdFAdGssl4PTbG85SuiOBk1mlrhyRaiblz5zJ69GjGjBmDv78/cXFx+Pr6snDhQovl4+Pj6dSpE3Fxcfj7+zNmzBiefvppZs+ebS4TFxfH0KFDiYmJoUePHsTExHDHHXcQFxdnLhMWFsYbb7zB/fff39C3KC4jp8hAcamRJ02rsT/6C+cVDRNNk/kk8g7pjSGEtRxYA7++CcDLZU+zU+nO+78clqF7QjQTGcf/QXP2EEZFxW719TVqt9ouN3FO0aI1nOW5uZ+X92AWdSJJKSGEqAuVDVNKn+OcXXs0Zw6y94NH0eecs3ZUooUzGAykpKQQGhpaaX9oaChbtmyxeE5ycnKV8sOGDWPHjh2UlpZetkx1dQrrCrLZxxTbrwCYXvYUkyNGEuDjbOWohGilslLhm2cAONPrSb4yDubDiEB+HH8rG6aESLJYiGbAePhXAPJcA/hmyl01arc+7Zyx6Vy+kEFf01/kFMkqfHUlSSkhhKgDVwc7CjXteKxgHAZFzTDVNvLWv81f+jz5pkQ0mOzsbIxGY5Ul3D08PKos9V4hMzPTYvmysjKys7MvW6a6OmuipKSE/Pz8Spu4erZFmczTzEetUvir/d18ZRwsw4OEsJbiHFjxCBgKKfQaSEqP8gnqfVx0BPg4S0JKiGai7YnyuTnLugyuVbu17zYIgGCbvxokrtZCklJCCFEHPi46NkwJYebzT6O/5Q0Aeuyfx/sf/Ichc5IkMSUalEqlqvRYUZQq+65U/tL9ta3zSmJjY3F2djZvvr6+da5LXFB6nk6Jz9BelUeqyZdRx0fK8CAhrMVYBl8/DWePoFfaE5z2OM98scfaUQkhastkoo2+PClV2DG4dud2HwbArTZ7UZXJe/+6kqSUEELUUcU3oX6hURT2fhIblcIC+w/oVbZPuvCKBuHu7o5ara7SgykrK6tKT6cKnp6eFsvb2trSrl27y5aprs6aiImJIS8vz7wdP368znUJQFFgTTRtTu8mV3Hg9F2f8PX4O2R4kBBWUpDwMvzzC+cULeNML/Bq+CB0GrUkioVoZk4f+A2782coUHRouwy48gkX8wjA0NYHncqA8s/GBomvNZCklBBC1IO298yB64ajNhlYbDeb4pP7rB2SaIHs7OwIDAwkMTGx0v7ExEQGDrS8VkxQUFCV8uvXr6d///5oNJrLlqmuzprQarU4OTlV2sRV+OMj2P0FCjaMK52AW8fuMjxICCs5u/VzHFPKF5eYanqONyIf5t5+PmyYEiKJYiGaGVXqDwCc6zIUH3eXWp6swnBNeW+p1I0rZaREHUlSSggh6oPaFkYupsSrP86qc3T88TEyjx2wdlSiBYqOjubjjz9myZIlpKamMnnyZNLT04mMjATKeyg9/vjj5vKRkZEcO3aM6OhoUlNTWbJkCYsXL+aFF14wl5k4cSLr169n1qxZHDhwgFmzZrFhwwYmTZpkLlNYWMju3bvZvXs3AGlpaezevZv09PRGue9WLW0TytoYAN4ofZid6r7SE0OIRqbPLeYvfR7/7PwZl/WTADh47TP835SXzAsN+LjoJCElGsymTZsYMWIE3t7eqFQqvv32W2uH1PwpCk5pPwFQcu1ddaqibe9/ATBYlcL2I6clMVUHkpQSQoj6YtcGbcRXFDldg5fqDG7/vQ/Oplk7KtHChIeHExcXx8yZM+nbty+bNm0iISGBzp07A5CRkVEpUeTn50dCQgIbN26kb9++vP7668ybN4+RI0eaywwcOJAVK1bwySef0Lt3b5YuXcrKlSsZMOB/3dh37NhBv3796NevH1CeHOvXrx+vvPJKI915K5VzDP77BCrFyDfGW7l+5FTpiSFEI9PnFjNkThKR87/B+bsnsTGVss7Yn9KQqdIWRaMpKiqiT58+zJ8/39qhtByZe7ArPE6xYkdBx5C61dH5FkxaZ9qr8lj59QqZW7YObK0dgBBCtCht3Dg+YgWaz/7FNUUnMSy5i7MPfINn5x7Wjky0IFFRUURFRVk8tnTp0ir7QkJC2Llz52XrHDVqFKNGjar2+ODBg80TpItGYiiClY9C8VkK3AKIOTmGVR6O8iFYiEaWU2TAtrSAhPbv41SQz15TFyaVRvGVSr7fF40nLCyMsLAwa4fRsuz9GoCNpj74atrUrQ5bO2x63Qs7P+XtbvsJ+bsXOUUGea2uBflLKoQQ9cyxvS9PKa/yj8kLu0I9LAlj+x+/y7cmQoiaMxlh1RjI3ItR145/nX4OG41Ohu0JYQ2mMj7QvIdTwT8YHTx5Xvk3aBykPYomraSkhPz8/EqbuIixFOPu5QD8SMjVtec+DwHQMSMRe0rqI7pWRZJSQghRz3xcdCyfci+lEd9T5HQNnqqzdF8zihfnfMhf+jxrhyeEaA4SX4GDCShqLb/1f5+0UlfiIwLlm1chGpui4JU8g0HqvZhsdagfXcmXU+6TYbSiyYuNjcXZ2dm8+fr6WjukpuXwBtTnTnNacSL80dFX1559bwaXTqhLCxlqk1J/MbYSkpQSQogG4OOio8e13XGI3GCe/HyxzRt8GP+e9JgSQlze9sWQXD5nyJTSSJ5IBJ1GTbcOba0cmBCt0LYPabd/GSZFxfHb5oF3X5nQXDQLMTEx5OXlmbfjx49bO6SmZdfnAKw2BuPm6HB1ddnYQO/y3lKPqH+52shaHUlKCSFEQ2rjhvapH+C64dirSnlfPQfDz2+DyWTtyIQQTYw+t5ijW79HSfg/APb3mMA3hgHEhfeVXhlCNDJ9bjHZu76HdeUrX75d9hAFXYZZOSohak6r1eLk5FRpExfk6VH+XgvAV8Y6TnB+qcAnUFRqgtT70Z49WD91thKSlBJCiIZm1wYe/IzCPk8D4Lc3juIvHoWSAisHJoRoKvS5xTw35zPa/fQMKsXI18ZBDN89AJ1GzY1+bpKQEqIR6XOLmTDnE3TfjgXFxNem2/jM5h6ZQ0qIFqJg8wJUpjK2mvw5Ydu5ftq2c0fyu4QC4Lb/06uvrxWR1feEEKIxqG1pe99/OGh/LV22Tkf3TwJ8PAQeWAod/K0dnRDCygqy0llgMwtHVTFFXjfjH7aEH9V2uDrYSUJKiEZWmHGYeJu3cVCd51S7AcTon+Ljp/tLWxRWVVhYyOHDh82P09LS2L17N25ubnTq1MmKkTUzJYW02bOs/Oebo9gwsP56Ip/t+STOaT/h/PcqTmZOw9vTu17qbemkp5QQQjSi0t6P8pBhOsXa9nD6AMqHg2H7x6Ao1g5NCGEtxbl0+SmCjqpsSpy74hCxnF6d2hPg4ywfgoVobEVn6LL2cdqr8kg1deK/18RSii3tpJeUsLIdO3bQr18/+vXrB0B0dDT9+vXjlVdesXJkzczuL1Eb8kkzedD2+rvr9XXWrtsgUpXO2BqL+WbBdJlHtoYkKSWEsGjBggX4+flhb29PYGAgmzdvvmz5pKQkAgMDsbe3p2vXrsTHx1c6vmjRIoKDg3F1dcXV1ZUhQ4bwxx9/NOQtNEmuDnYcsO1BcN5MNhr7oDKehzVTYMWjUHTG2uEJIRqZPvssJZ+HY59zkFOKC0fDPoM2btYOS4jWyXAOlj+ENu8IeqUdTxj+zZxNmeg0ahm6J6xu8ODBKIpSZVu6dKm1Q2s+Ss/Db/8BYLFxONio67V6H9c2dLhrGgARqgTycuS9fU1IUkoIUcXKlSuZNGkS06ZNY9euXQQHBxMWFkZ6errF8mlpaQwfPpzg4GB27drF1KlTmTBhAqtWrTKX2bhxIw8//DC//vorycnJdOrUidDQUPR6fWPdVpPg46Jjw5QQlo6/i9z7vmBmaQRGGw0cXEPZ+/05nrQMfc459LnF8u2KEC2c/mwBqe8/gFa/lVKNI08YXqLUUZbsFsIqTEaKVzwFJ/7AaOfEE4Z/83rEEH4cf6ssNCBES7HzUyg4SYbSjh9sbm+QZHO7/g9w3qUbzqpzKH8skvfzNSBJKSFEFXPnzmX06NGMGTMGf39/4uLi8PX1ZeHChRbLx8fH06lTJ+Li4vD392fMmDE8/fTTzJ4921zmiy++ICoqir59+9KjRw8WLVqEyWTi559/bqzbajJ8XHQE+DhzY1d3ltvczYji10g1+WJ7/iy+v47nwNzhjHr7K4bMSZIXMiFaKkVBt+4Fhqh2UKJo2BQ4jwOKzAkihFUoCoXfTkZ3ZC0lioa118dxWOlofr2WhJQQLUBpMcak8s8m88vuYV5EUMO0bRsbzg2YBIDP/kWMnLNG3s9fQZ2SUvU9rAdg1apV9OzZE61WS8+ePVm9enWl4zNmzEClUlXaPD096xK+EOIyDAYDKSkphIaGVtofGhrKli1bLJ6TnJxcpfywYcPYsWMHpaWlFs85d+4cpaWluLm13mEqFb2m3nn+MUxjfuVU4AsYbTTcod5Fovb/iDB9S25+gfSaEqKF0ecWk/XddNwOrsCoqBhf+jy7bXpZOywhWq28xFm03fMpJkXFpNIoxv1uL0P2hGhh8n6NQ30uixOKOz/Y3EG3Dm0b7FpuAx6h1N0fF1URY5SvySkyNNi1WoJaJ6UaYlhPcnIy4eHhRERE8OeffxIREcGDDz7Itm3bKtXVq1cvMjIyzNvevXtrG74Q4gqys7MxGo14eHhU2u/h4UFmZqbFczIzMy2WLysrIzs72+I5L730Ej4+PgwZMsTi8ZKSEvLz8yttLVHFt7C9OrXHY8R0jty/lu2m7rRVnWeqZjl+K+/gzTlzGDJnoySmhGgB9LnFrJw7iQ673wfg5bKnWW+6kfd/OSwfgoWwAn3ifJy3xAIQqzzB089MkiF7QrQ0eXoc/3gPgMz+L/LTlDsatn3bqNHc+SYAj6vXU5R5qOGu1QLY1vaEi4f1AMTFxbFu3ToWLlxIbGxslfIXD+sB8Pf3Z8eOHcyePZuRI0ea6xg6dCgxMTEAxMTEkJSURFxcHMuXL/9fsLa20jtKiEaiUqkqPVYUpcq+K5W3tB/gnXfeYfny5WzcuBF7e3uL9cXGxvLaa6/VNuxmr03HXtyjvMadhiT+rVmBR1E6C9TvstkYwPmjDui73Aggb5SFaKZsti4g2mYFAJk3xfD8wIk8D+QUGXB1sJO2LUQjOrv1S7x+exlUkN4zkidDZ0gbFKIl2jADm7Jitpu6o+sX3jjtvNsdnO98G/bHfqXw+3+j7/oDPq5tGv66zVCteko11LCe6spcWuehQ4fw9vbGz8+Phx56iCNHjtQmfCFEDbi7u6NWq6v0isrKyqrSG6qCp6enxfK2tra0a9eu0v7Zs2fz1ltvsX79enr37l1tHDExMeTl5Zm348eP1/GOmhcfFx2JU25j2KOTub1kDtt8nqREsSVY/RfXfDuC1P/cTdScZdJrSohmRp9bzMnE+XhtnQnAqRsm4zn8JXxcdDJvjRDW8Pc6XNeNx0aloL/2UTo98La0QSFaoqO/w97/YlJUvK08hWtbbaNd2v6utzHZaLhDtQPjvu9lSo5q1Cop1VDDeqorc3GdAwYMYNmyZaxbt45FixaRmZnJwIEDOXOm+mUWW8vwHyHqk52dHYGBgSQmJlban5iYyMCBAy2eExQUVKX8+vXr6d+/PxqNxrzv3Xff5fXXX2ft2rX079//snFotVqcnJwqba1FxQdUk6Yt4f+EcodhNl8bB2HChiGqHXynfpG234+BjD3y4iZEM6DPLeaDuTPw/r18meiFZSM4fcMk6wYlGow15l6tyXWffPLJKvOz3nzzzVd3s83V0d/gv4+jUsr41jiQnJA34TK9wYUQzZThHGWrowD4r3IHr0U+2rjJ5w49yO7zXPmPv73MvXN+koWMLKjTROcNMaznSnWGhYUxcuRIrr/+eoYMGcKaNWsA+PTTT6u9bmxsLM7OzubN11eWWRaiJqKjo/n4449ZsmQJqampTJ48mfT0dCIjI4HyXkyPP/64uXxkZCTHjh0jOjqa1NRUlixZwuLFi3nhhRfMZd555x1efvlllixZQpcuXcjMzCQzM5PCwsJGv7/moGIS9B/H38r0x8J4oTSST/uu4HtjEADOR36ED4M5+p9Qps95n6SDWfICJ0QTZdq9gjdUHwKwzBTGPNWjjfpNrWg81pp7tabXvfPOOyvNz5qQkNAwT0RTdnIXfPkQlJ3nFyWQ6YzDta3lqQSEEM3cL69jm3eUk4obHR98lwAf50YP4XTf5zli8sT+/GmilWUUlxpl4vNL1Cop1VDDeqorU12dAA4ODlx//fUcOlT9pGGtdfiPEFcrPDycuLg4Zs6cSd++fdm0aRMJCQl07twZgIyMjEpvdP38/EhISGDjxo307duX119/nXnz5pnnjYPyb3ANBgOjRo3Cy8vLvM2ePbvR76+5qOgxFeDjjE6j5rWtZUwoHc+dJW/znXEgZYoNt6j2sET9Ju5fDGHe3NfRZ+dYO2whxMV2fkbHjZOxUSmc7fEod0xewoYpg2WYUAt18dyr/v7+xMXF4evry8KFCy2Wv3juVX9/f8aMGcPTTz9d6bXx4rlXe/ToQUxMDHfccYd5vtbaXFer1eLp6WneWt0KuFkH4PORYCigyOtmnisZz/yIAdIehWiJjv4OW8v/BsaUjsXFtd0VTmgYLs5OzFCexaSoeNj2V4bZ/GGVOJqyWiWlGmpYT3VlqqsTyofmpaam4uXlVW2Z1jz8R4irFRUVxdGjRykpKSElJYVBgwaZjy1dupSNGzdWKh8SEsLOnTspKSkhLS3N3KuqwtGjR1EUpco2Y8aMRrib5u3iXlO/v3Q7i//9JNdEruCfhzdT2HcMJlsdvWyOMcvmAzwW9YP1L5N5dL/0nBLC2rYvhu+fR4XC52V3cPLWN/FxbSMfgFsoa829Wpvrbty4kQ4dOtC9e3fGjh1LVlZWtffT4qbBOP03fDoCzp0B734cC11MCXa0kxUvhWh5irJh1RhA4Vin+0ky9bFaKD4uOmKnPMeZvuWfjWZpFmFbmGG1eJqiWg/fa4hhPRMnTmT9+vXMmjWLAwcOMGvWLDZs2MCkSZPMZV544QWSkpJIS0tj27ZtjBo1ivz8fJ544omruH0hhGgeLp4IueLn63oE0PbeOdhE7+dU//9Dr7TDtiQHtryP59Igjv4nlP2JS9l37BR/6fPMSSqZh0qIhpf7y3uwJhooH7L3pmqsDBFq4aw192pNrxsWFsYXX3zBL7/8wpw5c9i+fTu33347JSUlFmNrUdNgZB+CT++GoiwM7r1IvWMpf+fKHFJCtEgmE6x+FgpOckTxJuzvu9Fp1LhaMQHt46Kj/YiZFLtfj4uqCM+fx4OxzGrxNDW2tT0hPDycM2fOMHPmTDIyMggICKjRsJ7JkyfzwQcf4O3tXWVYz8CBA1mxYgUvv/wy06dP55prrmHlypUMGDDAXObEiRM8/PDDZGdn0759e26++Wa2bt1qvq4QQrRabdwou3UKw7b142ZjCo+qNxBis4dbVHvg94nk//YSCcYBJKgGMf7pJ3h8yQ4ANkwJkR4bQjSAvMR3cPn9TQD2dH6KVw4O4dOn+0t7ayWsMfdqTcqEh4ebfw4ICKB///507tyZNWvWcP/991eJKyYmhujoaPPj/Pz85pmYOvMPLL0bCk9R6u5PyKlJZCzaB2D1D6pCiAbw2xw4vAGjWstz5ybwVvjN3OjnZv3XYFs78u+Kx7T0Dlyy/qDwh5doe69MYwJ1SEpB+bCeqKgoi8eWLl1aZV/FsJ7LGTVqFKNGjar2+IoVK2oVoxBCtCY+LjrWTbmdnKJbgYlklWXg8NeXaFO/xqlQz0O2G3mIjRStXMQEpT8/GW8ip/Bm8wu0PreYnCIDrg521n/RFqK5UhQK1kzHecf7AMSV3U/cwSHoNLZ069DWysGJhmatuVfrcl0ALy8vOnfuXO38rFqtFq22mU/Ib05IZXLe9Tp+6b+IjG/TiQvvS7cObeU1T4iWZv/38MsbALxa+iTptn5NIyF1gYdfAH8NmkvA5ija7l5ETocAXAc+ae2wrK5Oq+8JIYRoei6eGN2zcw8c75qJXfRf8OQazl73EPmKDofzGTxn+wPfa6fT9YsBZH89mdStPxE651fufv83hsxJYvvRs5WG+wkhasBYRtFXkTheSEjNMT3MLWPm8OP4YOmV2EpYa+7VulwX4MyZMxw/fvyy87M2a2ePUPbJ3VBwksNKR27JmETUt+noNGpu9HMzD4kXQrQQJ3dh+uYZAI74PcLnhhDiIwKbXDt3DbyfD0zlo8barHuB0/s3WTki66tTTykhhBDNhI0NdLmVYpdA7tp/FwON2xmu/oPbbHbhUJxJm7+W4P7XEpJsnMj0HcRCfVdGx+eRT1t0GrV8mBaiJgzn4OuncPh7LUZFxZ5+M3lo8FhpO61QdHQ0ERER9O/fn6CgID766KMqc6/q9XqWLVsGlM+9On/+fKKjoxk7dizJycksXryY5cuXm+ucOHEigwYNYtasWdxzzz189913bNiwgd9++63G1y0sLGTGjBmMHDkSLy8vjh49ytSpU3F3d+e+++5rxGeocZw6sgfXrx/A7lwmh0w+PKVMZ+7Td9DOwU56RwnRAmWmH8J1eTjasmI2GvswOjUMnUbdJHsp+7jouHfy+5xcmYt35s+4fPsYuK+DDv7WDs1qJCklhBCtgI+LjjVThpJTFIKrgx25ZcVk//0zqtQfcUpPxF2Vj/vpH/nADoyKikyn61l+9joyU+3wGTC4PLklhKjq3Fn4MhxO/MF5RUO0aRLTJCHVallr7tUrXVetVrN3716WLVtGbm4uXl5e3HbbbaxcuRJHR8dGenYaR9bf27H94n7sVPn8bfLhn7AvWel/nbRJIVqoDP1RDIvvRqs6xSGlI7bhS/nOtV2TTkD7uDpwcuQids8fRl/DIc4vvZfch9fg6dvN2qFZhSSlhBCilahYua+cDtwfQN/zboLn/Ex/UnnF/ySlB9bR3UaPT8EeXtDsgXVfYUpyxabLLeR63ExJx4F4XNMPfX6JuU4hWq0z/8DyhyD7b3IVB6JMLzI18ilpF62cNeZevdJ1dTod69atu+z5LcLx7bT7+n7Uqnz2mrrwjDKNryUhJUTLde4sTv8dhYMqk6I2PrR9+Huu9e1q7ahqxLt9O/Ie/5rDy4bT7Zye4o/v5sCj39Gj+3XWDq3RSVJKCCFaMR8XHWun3AHcAcDw1GF4GbNZFXoO48H12B/fTNvzOXDgR1wO/AiAQePMfkN3/lB6cefwe/G8NhDUGpkoXbQuR3/DtOIxbM7nUOrgxQNnJ/PyU/cT4ONs7ciEaJ3SNsGXD6EuLWK7qTv593/J1106ymuSEC3VubMYlt6DQ94hshRXTA+uwsv3GmtHVSv+13Qhc8z3nF9+N37nMjj6xT1kjE3Aq2PzSKzVF0lKCSFEK3fxG/YNU0IAcHXRob8+gtvm/My1ZYe42SaVATap9Lc5iENpHkNV2xmq2g5rl1L8kx17lK7sMnVjv6o7D48cSacu18gHAdEi6XOLUXZ+jvdvMdiYSvlT6cb+G+I5lJhFO1laXohGp88tpmx/Ar4/P4eNsYRCn1t5/J+n+ap9B3kdEqKlys+Az+7F7vQBziiOHLv7S27s0jznZPL07QZj13L+4+F0KdJTuPxfHPzXV7T16NJq/oZJUkoIIYTZxS9+Fb2oDmcNIPKzFD4BPnuiH665+3E/sx3tiS3YnExBV5rPANUBBtgcKD/x27lkKO0o7h6ErtMNZDv24LTDdTi19zHXX7GyX2t5sRUtgz6niJ/+E8kYm+8B+NF4M1NKIylJzEKnUeMqSSkhGpU+t5j4ua/wqupjbFQmflb6c6L7HIr/+cfaoQkhGkrOUcqW/gvbvGOcUlwZbXqZD6/tZ+2oro5rF3LDv6V08V34Fh2n7Zd3EWmKIX7KY63ivbIkpYQQQlSrYh6qih5U5S+MHsBtAPx1IoeJH3xFP5vDTL2+kLbZu9Fkp+KlOgOHfoRDP+IOuANZiisFnfqCZ2/e2WpDKl2Y++w9BHR0tdLdCVEL587itOopxthsBCDrhon0C/43v6hsZOiqEI1Mn1tMTmEJtptn8brNRwBk+t3PpMMjKfjpH0kSC9FS6XdS+kU4mnNZHDN1YLQynbjIe1rE669np+5kjvmJkq8fxCfvHz63eYW0vV74BN9t7dAanCSlhBBCXFF1L/aube05aduJk3Ri8p0huLnoOJmVzUvvf4q/6RC9bI4SYHMMP1UGHVQ5cPxXOP4r76nLzy9a9CIGzx7YefaE9j2gfQ8y7btgdPLFx9WhEe9QiMs4uQtWPo5jXjrFih3Zt8/GN+QJ8+GW8GZYiOZCn1vMsDm/8LLyEQ/ZbgQg/6bJeIa9ytq885IkFqKl2v8dpm+eRVNWzCGlI9n3r+TTFjZdhKdvN3h2AyWfPYhzxnZ6bniCs5r3cbv5EWuH1qAkKSWEEKLOqvaiAu8O7sROiSKnyACA1sEOlc7IP/v+4Itvf+BaUxrXq4/hrz6Og6kETv1Zvl3gCRQrdhS4XYva059S12vJ0/licPajjee1eHdo3+j3KVqxnctgzQtgLKG4bSfuOxPF7G734mvtuIRopfJyc5jHO9xuuxtFZUPubW/jOuhZ4NJVZoUQLYKiwG9z4eeZ2AAbjX2wDV/KrQEtdDLwNm5on/6B058+TvsT63Fb+xwFp//CcfhMULfM9E3LvCshhBCNxtIHAEsfDK654XZGdw0yf4udaSpjzH++opPxGNeq9Pir9QQ5ZeNQcASdygA5+8o34OL1zErs21Pm3AXaXYODV3dw60qWpiNlLn4odg7yLbmoFyezstFtiMH17/8CkO1zO8PTH6PA1kGGBQlhLbnpdPr2AXqqD2BS22PzwCe49hhu7aiEEA3lfB58Nw5SfwDgTK8nGZ1yB9+5trNyYA1Mo8Nw/ycsjotktM0POKZ8QGHmn7R99DNo42bt6OqdJKWEEEI0mkuTVR9PeZicIgNnigxEfpZCcbaRthr4cpQHxfp9bPr9N7ranGSweyGO545hV5KD9vxptOdPw6ntsL+8ng4X6jurtOWM0p59qvY4BfbD0eMazth6UObki4dvN7B3rhqUEJc4vHsztqvH4q3KwKiomFP2AAv/+Rf2Gg1fRQZJwlMIa0jfinH5I7QtPsNpxRll1Jd06HGrtaMSQjSUk7vhqycg5ygGRU2s8iS+XuMxVrz5a+F83NpyZ/Qi9m9fSZffXqSt/jfOf3Ar+Xd/RAf/lvW3T5JSQgghrObiJNWGKSGVejnpO/diSbJH+bEnQmjnouNkZibnMv8m5/gBNm/dRmebTPxUmXRRZeKmKjRvvUmDnX8AcPF3aUY7JwyOvuDsi869M3l27TG29cHNPwScfRr79kVTYzKR98scOm2OxU5l5HwbTzJue4/h3kEMB+mBJ4QV6HOLUXZ+hvdvU1GbSvnL1IXC+5Zxs38fa4cmhGgIigLbP0ZZNw2VsYRzOm8eyn2OPco18OP+VrWQgY+LDp+hT3LI0x+7ryPoXKTHdsUI8ge+gNPQl8BGbe0Q64UkpYQQQjQJl/aisjhflacneHqi73Iji/7oBED8Y4EUd2jLyZJ81PknOH86jSVrNtFRdRofVbb533aqAtSGfHRn9sGZfXDkf8MCz9h8RLubwhv1fkXTkpl+iLZrJ+J88ndQwWnfYbR/OB6/FthNXojmQJ9bzD8ZZzm6fAqP2/wEwBrjTUxnHD/4dbdydEKIBpF3Ar57Ho78igpINN7AlJxISjXOfDX6JnNCqrV9QXTt9QM42X4Tx3+Ixle/Bqfkdyg68isFwz/As/N11g7vqklSSgghRJNV3ZsOSwkr0IGHB3+16canxvJ9ceF9aefnxnlgf24OmkI92ScOsWbzH4zoYkKf/g/eqjO4azvSwmcnENUxmcj57SMcf34VB9V5zila3lKe5Ln7Z0CbNtaOTohWSZ9bzGNzVjFbFcfjNocAOHXDZDrfMJEf2tq3ug+kQrR4isLZ5GU4b3wZtSEfo42WN0oepM/Il/jSw7FVJqIu5e3piX7Ux7z4nzeZrlqM46ntKEtCOHnry3jfEQU2NtYOsc4kKSWEEKJZqu7NiauDHTpNeXfmG/3czOXK//WmTccAVv3uxuf/GM3n/Oge0ODxiibo7BH4fgKuRzeDCs643cCZO+bynE+PVv/mVwhrKj2wnlU2/8ZNVYjJzgmb++Px6HEXHtYOTAhR/3KOUfz9FNzSEgHYbbqG6JLnyLD1ZUzXdvJ6fBEf1zZMjH6ZkxnheP48EefsnbT9fRpF/3yHw6gF4H6ttUOsE0lKCSGEaFEs96KqejynyIA+t5hnP0tp7BCFtZUZYOsHsHEWlBVzTtEyV3mYpyLeorurg7WjE6LV0p8tQLP5XTrvmodKpVDsHoDukc/Bzc/aoQkh6luZgbxf43DcOged8TwGRc1h/3HY3jKJeTa20juqGj4uOnDpDddt4GTiPJy3xOKQ+QemBQM5fcNEym4eh4+7q7XDrBVJSgkhhGhxrvQm5tL5q0TroM8tRntsI+6bXoYzhwE47T6A+/UP8cZTI/CRhJQQVpOZto/spY/TR1XeNj8vu4N+IxbSy036RwnR4qRt5vx3k3HOLR+eu9Xkz+vKGD6681F5f1ZTNmq8h03mYOdQTi2PYpBpNx473iV9+zL+CpmBa7978XFtHtMQSFJKCCGEEC1eZvrf7Fs8jlBV+aqMpxVnYksf5psTweg0tnTr0NbKEQrRSikKpHxC+5+m4qkq5ry6Lf9X/CQ/mAbyo629taMTQtSn7MOQ+AocXIM9cEZxImvgdNr2epCP2molIVUH1/XoRdtJP3F8z1d02PomnYpPwabn+D1pIece+A/XBvS3dohXJEkpIYQQQrRc585SsOFt2u9eQqiqlDLFhk+Nw4hXPcjsJ4N52sFOhggIYS25x2FNNBxajxpIVgJoc/+HbFhxAp2aVrPsuxAtXlE2JM2CHUvAVIZJpeaL0tvoGv42t1zfPOdBakp8XNtAyBNw80gKNszCIWUht5j2UPbVUM7+9RBuw6eDk7e1w6yWJKWEEEII0fIYimDrAoyb38OxtACArUov2t47mwEdenGnJKKEsB6TEbZ9CL+8AaVFlCga/qM8zN3PzCSgoysbplwDXHkothCiiTufB1vjMW15HxtD+Wvxr8oNvFnyEHrbzmzw7WjlAFsYbVsc73odgp4i/7sXcTqWiNuBL1EOfYNqwFi4NRrauFk7yiokKSWEEEKIlqOkoPyb2C3zoSgLNZCqdKb0tlfx7RPWbOZXEKLFOrkbfpgIGbuB8lUvwzMeYvpT9xPQsXxyXklGCdHMnc8nP2k+bXbGY1uShw3wl6kLb5Y9ym51b+KfCqRbh7bS1huKW1ecnvqa3b8lYFg/g5s4CFvex7RjKTYDx8OAZ0HnYu0ozSQpJYQQQojm79xZ2BaPaWs8NiV5ABxXOvCeEs6Tz0yhd8fmtRKNEC2JPreYgtPH8d09lzb7VqBCIV9pw9tlD7P85G3YazQyr5sQLcH5PPhjEaYt83E6nwPAIZMP8YzkX48+z7S29jJkvhG1D7iNIetUDDCk8KLtf+lpOAYb38L4+zzO9XkKx8EToW17a4cpSSkhhBBCNGOZf8H2RbDnv1B6DhvgH5MXC43/Yp3NIJZHBhPg42ztKIVotfYdy+TnxdMZrfoOB1UJAN8bg5jNE7z+xBAekXndhGj+8k5QkPQ+bfZ+jrq0EBvgsMmbnBsno+s7imhHWfXYGnxcdGyYMpicooGcLhzLlC/mM5bV9Cg9juOO9zHu+oji6x+j7W3R4Gy9oZSSlBJCCCFE81JWwtmUb9DuWoJD5h/m3bnO/sScDmXYqDE86eHMZPmgK4T1GIrI2xyPx6b3mGBT3ntxt3Its0yPExnxMMtl6I4QzV/mXtjyPsreVTgqZQD8bfJhftm9/Ky+lfXBt0k7tzIfl4qEoDPdoqeSUxjNX3+vxZg0mz7Gw7TdvRjTn59yvvsI2gQ/Dx0bf7U+SUoJIYQQoukzmTidugn13pU4/vMjbqX5AJQpNqw13chnZaFsO9UDncaWl7u2lzfBQljLubPk/f4xDikLcT5/FlRQ7OCLLuw12vuEMVulkvYpRHNmLIND6+CPRXDkVwBUwDalJ20GR6O6dgjPqGz4t3wx1OSYE1QdH0bf7x7+3Lue4p/f4Wb20ebgaji4GoPnDdjdMg563gNqTaPEJUkpIYQQQjRNxjI4vg0OJlC27zva5x83H8pU3Dh//SNkdHuI/1ulB1v4NEImThXCajL2wB8fYdrzX5yN5cP0jpo8+JD7ef7pqfi0c8LHyiEKIa5CwSnytyxGt2cZmqIMAIyKijWmm1nGCGZEPibD5ZsRH9c2+Ay6F33vYaQc2MaxhLncpfodbeZOWDWa0rXTKO79OE5BT4GTd4PGYlOXkxYsWICfnx/29vYEBgayefPmy5ZPSkoiMDAQe3t7unbtSnx8fJUyq1atomfPnmi1Wnr27Mnq1auv+rpCiLqzVjsXQlxZi34dzj0Ou5fDN89iercbLB0OyfOxzT9OgaLjmO+9pA1fjnHiXrqMepOgvtezYUoIG6aEENJdekgJ62uq7VNRFGbMmIG3tzc6nY7Bgwezb9++q7vZ8orhs/vhw2DY9Rk2xhL2K104cPO7FI5N5vnoV/Fp53T11xFCNP7nYZMJ0jbBV0+izO2JU/IsNEUZnFEcWVg2glDTPJwjPuO9KU9LQqqZ8nHREXjzYAZEryTl/t943/QAWYoLmqJMnJLfQflPL4o/HQUHEsq/LGwAtU5KrVy5kkmTJjFt2jR27dpFcHAwYWFhpKenWyyflpbG8OHDCQ4OZteuXUydOpUJEyawatUqc5nk5GTCw8OJiIjgzz//JCIiggcffJBt27bV+bpCiLqzVjsXQlxZi3wdPpAA346jbO71EBcA30bCnhXYnM8hR2nLKuOtPGeYyCDTh9iOjMfvpuH4uP1vpa7/zZcghHU15fb5zjvvMHfuXObPn8/27dvx9PRk6NChFBQUXN1Nq1QU6bwpVdR8bwziEeNrmMYm0ePOZwjwbSdtU4h60qifh8+mwa+xlMX1hk9HwL7VqJQyUpTrSA2aQ+bonQQ/9wHLpjwgXwi1ED4uOgb28ef+6Pc5PXoHqUFz2K74o1JM6NISYcXDlM7pSda3L3MwdS/63OL6u7hSSzfddJMSGRlZaV+PHj2Ul156yWL5F198UenRo0elfc8++6xy8803mx8/+OCDyp133lmpzLBhw5SHHnqozte1JC8vTwGUvLy8Ksf2nshVOv/7R2Xvidwa1yfElX5vLvc715RZq51fzpWeS2nDoi4u93vTVNtvc30dvuzz+d14RXnVSVFedVJKX3FRdk3vpyyc9qjy2MtzlI2pJ5W9J3KVvSdylRM552p0LdF6NLU23FTbp8lkUjw9PZW3337bfPz8+fOKs7OzEh8fX6N7u9zzmXogVen/78+U1TtPSDsVtdLU2nBT1qCvw4qiKOfzFWXnZ4qyJMz8mqy86qTkveKhfD7tPuWelxfK++xW5kTOOWXb9q3Kx9MfVbJf8an0e7H9lZuUExsWKkpx9b8TNW3DtZpTymAwkJKSwksvvVRpf2hoKFu2bLF4TnJyMqGhoZX2DRs2jMWLF1NaWopGoyE5OZnJkydXKRMXF1fn6wKUlJRQUlJifpyXV77yR35+fpWyhQX5mErOUViQT36+qto6hbjYlX5vKn7XFEVp7NDqzFrt/FK1ab8gbVjUzeV+b5pi+21Or8O1asO+Q8guUDNtpyP33XUvnbzb0xcY3MYO70rfvpaSn19q8XqidWpKbbgpt8+0tDQyMzMrXUur1RISEsKWLVt49tlnq8RWmzacqzhwqkSLp86Eo420U1FzTakNN2UN+jpceh7WvgQH1kBZee8Xk6Ii2eTPGtUg7h75JNc4OfJ2Gzu8HVXVvhcXLY+jDfTo7o/TmDkcLigkM/0XXA99hUPGNrqTChteJOeXlyn1uwP7Ee+CzqXS+TVtw7VKSmVnZ2M0GvHw8Ki038PDg8zMTIvnZGZmWixfVlZGdnY2Xl5e1ZapqLMu1wWIjY3ltddeq7Lf19e32nOC4qo9JES1rvR7U1BQgLNz8xhnba12fqm6tF+QNizq5nK/N02p/Tan1+G6tuEVc1+/7HEhLGkKbbgpt8+Kfy2VOXbsmMXY5H20aExNoQ03ZY35Ovw/24BtfPDOu7WMVrQ+/72wWXalNlyn1fdUqspZbEVRquy7UvlL99ekztpeNyYmhujoaPNjk8nE2bNnadeu3WXPa27y8/Px9fXl+PHjODm1vokkm/L9K4pCQUEB3t4Nu2JBQ7BWO6/QWtovNO3f4cbQVO+/Kbff5vA63Jra8NVqqm2gObjcc2etNtyU26e04YYhbbjummIbbsoaqg3L7/DlyfNTvfpow7VKSrm7u6NWq6tkY7OysqpkbSt4enpaLG9ra0u7du0uW6aizrpcF8q7JWu12kr7XFxcqr/BZs7JyalVN5Kmev/N7Zsda7XzS7W29gtN93e4sTTF+29q7bc5vQ63xjZ8tZpiG2guqnvuGrMNN+X26enpCZT3mPLy8qpRbNKGa0/acN01hTbclDXW67D8Dl+ePD/Vu5o2XKvV9+zs7AgMDCQxMbHS/sTERAYOHGjxnKCgoCrl169fT//+/dFoNJctU1FnXa4rhKgba7VzIcSVyeuwEE1XU26ffn5+eHp6VipjMBhISkqSNixEMyCvw6JFq+0M7CtWrFA0Go2yePFiZf/+/cqkSZMUBwcH5ejRo4qiKMpLL72kREREmMsfOXJEadOmjTJ58mRl//79yuLFixWNRqN8/fXX5jK///67olarlbfffltJTU1V3n77bcXW1lbZunVrja/bmrX2lSla+/03BGu189aqtf8Ot/b7ry15HW55pA3UXVN77ppy+3z77bcVZ2dn5ZtvvlH27t2rPPzww8r/s3fnYVHW+//Hn/fMwIDsiCyiAu4m5oLllvuW7bsnS+uknTyWZVqdPHXKrG/W+aV5WtQ8p7TVrGzPSlxwX5Ig931BEUSQnYHZ7t8fAyQJJgpzz/J+XNdcwsw9M6/B+cx93+/5LDExMWpRUZET/jKezdXeh+5E/nYXrzH3w/L/cGHy96lbQ/xt6l2UUlVVffvtt9W4uDjV19dX7dGjh7p27drq2+677z514MCBNbZPSUlRu3fvrvr6+qrx8fHq/Pnzz3vMzz//XO3QoYPq4+OjduzYUV22bFm9nteblZeXq88//7xaXl6udRRNePvrbyxatXNv5O3vYW9//ZdC9sOeRdrApXPFv52rtk+73a4+//zzanR0tGo0GtUBAwaoO3fubJgX7eVc8X3oLuRvVz+NtR+W/4cLk79P3Rrib6OoqqyxKYQQQgghhBBCCCGcq15zSgkhhBBCCCGEEEII0RCkKCWEEEIIIYQQQgghnE6KUkIIIYQQQgghhBDC6aQoJYQQQgghhBBCCCGcTopSbmLWrFlcddVVBAUFERkZyS233ML+/ftrbKOqKjNmzKB58+b4+/szaNAgdu/erVHixjVr1iwURWHKlCnV13nT6xfuR9rw76T9Cm8wY8YMFEWpcYmOjq6+/WLe8xUVFUyePJmIiAgCAgK46aabOHnypLNfSqNbt24dN954I82bN0dRFL7++usatzfU3yo/P5+xY8cSEhJCSEgIY8eOpaCgoJFfnXBH0n7rR9qwZ/m///s/+vbtS5MmTQgNDdU6jubmzZtHQkICfn5+JCUlsX79eq0juYQ/a/f1IUUpN7F27VoefvhhtmzZQnJyMlarlREjRlBaWlq9zb///W/mzJnDW2+9xS+//EJ0dDTDhw+nuLhYw+QN75dffmHhwoVceeWVNa73ltcv3JO0YQdpv8KbdO7cmaysrOrLzp07q2+7mPf8lClT+Oqrr/j000/ZsGEDJSUl3HDDDdhsNi1eTqMpLS2la9euvPXWW7Xe3lB/qzFjxpCens5PP/3ETz/9RHp6OmPHjm301yfck7Tfiydt2LOYzWbuvPNO/v73v2sdRXNLly5lypQpPPPMM6SlpdG/f39GjRpFRkaG1tE092ftvl5U4ZZycnJUQF27dq2qqqpqt9vV6Oho9ZVXXqnepry8XA0JCVEXLFigVcwGV1xcrLZr105NTk5WBw4cqD722GOqqnrP6xeewxvbsLRf4U2ef/55tWvXrrXedjHv+YKCAtXHx0f99NNPq7fJzMxUdTqd+tNPPzVqdi0B6ldffVX9e0P9rfbs2aMC6pYtW6q32bx5swqo+/bta+RXJdyNtN9LJ23YcyxatEgNCQnROoamrr76anXixIk1ruvYsaP69NNPa5TINf2x3deX9JRyU4WFhQCEh4cDcPToUbKzsxkxYkT1NkajkYEDB7Jp0yZNMjaGhx9+mOuvv55hw4bVuN5bXr/wHN7YhqX9Cm9z8OBBmjdvTkJCAn/5y184cuQIcHHv+dTUVCwWS41tmjdvTmJiole1i4b6W23evJmQkBB69epVvU3v3r0JCQnxqr+nuHjSfhuGtGHhrsxmM6mpqTXelwAjRoyQ91wDM2gdQNSfqqpMnTqVa665hsTERACys7MBiIqKqrFtVFQUx48fd3rGxvDpp5/y66+/8ssvv5x3mze8fuE5vLENS/sV3qZXr1588MEHtG/fntOnT/PSSy/Rt29fdu/efVHv+ezsbHx9fQkLCztvm6r7e4OG+ltlZ2cTGRl53uNHRkZ61d9TXBxpvw1H2rBwV7m5udhstlrfu/Kea1hSlHJDjzzyCDt27GDDhg3n3aYoSo3fVVU97zp3dOLECR577DFWrFiBn59fndt56usXnsXb2rC0X+GNRo0aVf1zly5d6NOnD23atOH999+nd+/ewKW95721XTTE36q27b317ykuTNpvw5M2rK0ZM2bwwgsvXHCbX375hZ49ezopkfuQ49PGJ8P33MzkyZP59ttvWbNmDS1atKi+vmpFkD9WbXNycs6r7rqj1NRUcnJySEpKwmAwYDAYWLt2LW+88QYGg6H6NXrq6xeewxvbsLRfISAgIIAuXbpw8ODBi2rv0dHRmM1m8vPz69zGGzTU3yo6OprTp0+f9/hnzpzxqr+nuDTSfi+dtGHX8Mgjj7B3794LXqp67wuHiIgI9Hq9HJ86gRSl3ISqqjzyyCN8+eWXrF69moSEhBq3JyQkEB0dTXJycvV1ZrOZtWvX0rdvX2fHbXBDhw5l586dpKenV1969uzJPffcQ3p6Oq1bt/bo1y/cnze3YWm/QjiWO9+7dy8xMTEX1d6TkpLw8fGpsU1WVha7du3yqnbRUH+rPn36UFhYyLZt26q32bp1K4WFhV719xSXRtrvpZM27BoiIiLo2LHjBS8X6s3ujXx9fUlKSqrxvgRITk6W91xDu+Qp0oVT/f3vf1dDQkLUlJQUNSsrq/pSVlZWvc0rr7yihoSEqF9++aW6c+dO9e6771ZjYmLUoqIiDZM3nnNX71JV73v9wr1IG65J2q/wdNOmTVNTUlLUI0eOqFu2bFFvuOEGNSgoSD127Jiqqhf3np84caLaokULdeXKleqvv/6qDhkyRO3atatqtVq1elmNori4WE1LS1PT0tJUQJ0zZ46alpamHj9+XFXVhvtbXXvtteqVV16pbt68Wd28ebPapUsX9YYbbnD66xWuT9pv/Ugb9izHjx9X09LS1BdeeEENDAys/r8tLi7WOprTffrpp6qPj4/67rvvqnv27FGnTJmiBgQEVH8WeLM/a/f1IUUpNwHUelm0aFH1Nna7XX3++efV6Oho1Wg0qgMGDFB37typXehG9seTWm97/cK9SBuuSdqv8HSjR49WY2JiVB8fH7V58+bqbbfdpu7evbv69ot5z5tMJvWRRx5Rw8PDVX9/f/WGG25QMzIynP1SGt2aNWtq/Xy87777VFVtuL9VXl6ees8996hBQUFqUFCQes8996j5+flOepXCnUj7rR9pw57lvvvuq/X/c82aNVpH08Tbb7+txsXFqb6+vmqPHj3UtWvXah3JJfxZu68PRVVVtZE7YwkhhBBCCCGEEEIIUYPMKSWEEEIIIYQQQgghnE6KUkIIIYQQQgghhBDC6aQoJYQQQgghhBBCCCGcTopSQgghhBBCCCGEEMLppCglhBBCCCGEEEIIIZxOilJCCCGEEEIIIYQQwumkKCWEEEIIIYQQQgghnE6KUkIIIYQQQghxAYMGDWLKlCkXtW1KSgqKolBQUHBZzxkfH8/cuXMv6zGEEMLVSVHKC9x///0oisIrr7xS4/qvv/4aRVE0SiWEuFjShoUQQgghhLg0cizt2qQo5SX8/Px49dVXyc/P1zqKEOISSBsWQgghhBDi0sixtOuSopSXGDZsGNHR0cyaNavObZYtW0bnzp0xGo3Ex8cze/bsGrfHx8fz8ssv88ADDxAUFESrVq1YuHBhjW0yMzMZPXo0YWFhNG3alJtvvpljx441xksSwqtIGxbC/QwaNIhHH32Up556ivDwcKKjo5kxY0b17XPmzKFLly4EBATQsmVLJk2aRElJSfXtixcvJjQ0lO+//54OHTrQpEkT7rjjDkpLS3n//feJj48nLCyMyZMnY7PZqu9nNpt56qmniI2NJSAggF69epGSkuLEVy6EZ/voo4/o2bMnQUFBREdHM2bMGHJycs7bbuPGjXTt2hU/Pz969erFzp07a9y+adMmBgwYgL+/Py1btuTRRx+ltLTUWS9DCK8ix9KuS4pSXkKv1/Pyyy/z5ptvcvLkyfNuT01N5a677uIvf/kLO3fuZMaMGfzrX/9i8eLFNbabPXs2PXv2JC0tjUmTJvH3v/+dffv2AVBWVsbgwYMJDAxk3bp1bNiwgcDAQK699lrMZrMzXqYQHkvasBDu6f333ycgIICtW7fy73//m5kzZ5KcnAyATqfjjTfeYNeuXbz//vusXr2ap556qsb9y8rKeOONN/j000/56aefSElJ4bbbbmP58uUsX76cDz/8kIULF/LFF19U3+evf/0rGzdu5NNPP2XHjh3ceeedXHvttRw8eNCpr10IT2U2m3nxxRf57bff+Prrrzl69Cj333//eds9+eSTvPbaa/zyyy9ERkZy0003YbFYANi5cycjR47ktttuY8eOHSxdupQNGzbwyCOPOPnVCOEd5FjahanC4913333qzTffrKqqqvbu3Vt94IEHVFVV1a+++kqteguMGTNGHT58eI37Pfnkk+oVV1xR/XtcXJx67733Vv9ut9vVyMhIdf78+aqqquq7776rdujQQbXb7dXbVFRUqP7+/urPP//cKK9NCG8gbVgI9zRw4ED1mmuuqXHdVVddpf7jH/+odfvPPvtMbdq0afXvixYtUgH10KFD1dc99NBDapMmTdTi4uLq60aOHKk+9NBDqqqq6qFDh1RFUdTMzMwajz106FB1+vTpl/2ahPBWAwcOVB977LFab9u2bZsKVLfLNWvWqID66aefVm+Tl5en+vv7q0uXLlVVVVXHjh2r/u1vf6vxOOvXr1d1Op1qMplUVXXst19//fWGfzFCeBk5lnZt0lPKy7z66qu8//777Nmzp8b1e/fupV+/fjWu69evHwcPHqwxJODKK6+s/llRFKKjo6u7K6empnLo0CGCgoIIDAwkMDCQ8PBwysvLOXz4cCO+KiG8h7RhIdzLuW0OICYmprrNrVmzhuHDhxMbG0tQUBDjxo0jLy+vxvCdJk2a0KZNm+rfo6KiiI+PJzAwsMZ1VY/566+/oqoq7du3r27HgYGBrF27VtqxEA0kLS2Nm2++mbi4OIKCghg0aBAAGRkZNbbr06dP9c/h4eF06NCBvXv3Ao597uLFi2u005EjR2K32zl69KjTXosQ3kaOpV2PQesAwrkGDBjAyJEj+ec//1mjm7GqquetPKCq6nn39/HxqfG7oijY7XYA7HY7SUlJfPzxx+fdr1mzZg2QXgghbVgI91JXmzt+/DjXXXcdEydO5MUXXyQ8PJwNGzYwfvz46uE9dd3/z9qxXq8nNTUVvV5fY7tzC1lCiEtTWlrKiBEjGDFiBB999BHNmjUjIyODkSNHXtTwnKp9td1u56GHHuLRRx89b5tWrVo1eG4hhIMcS7seKUp5oVdeeYVu3brRvn376uuuuOIKNmzYUGO7TZs20b59+/MOauvSo0cPli5dSmRkJMHBwQ2aWQjxO2nDQri/7du3Y7VamT17Njqdo+P6Z599dtmP2717d2w2Gzk5OfTv3/+yH08IUdO+ffvIzc3llVdeoWXLloCjPddmy5Yt1QWm/Px8Dhw4QMeOHQHHPnf37t20bdvWOcGFENXkWNq1yPA9L9SlSxfuuece3nzzzerrpk2bxqpVq3jxxRc5cOAA77//Pm+99RZPPPHERT/uPffcQ0REBDfffDPr16/n6NGjrF27lscee6zWyeSEEJdG2rAQ7q9NmzZYrVbefPNNjhw5wocffsiCBQsu+3Hbt2/PPffcw7hx4/jyyy85evQov/zyC6+++irLly9vgORCeLdWrVrh6+tb3Xa//fZbXnzxxVq3nTlzJqtWrWLXrl3cf//9REREcMsttwDwj3/8g82bN/Pwww+Tnp7OwYMH+fbbb5k8ebITX40Q3kmOpV2LFKW81IsvvlijO2KPHj347LPP+PTTT0lMTOS5555j5syZta4kUpcmTZqwbt06WrVqxW233UanTp144IEHMJlMUikWooFJGxbCvXXr1o05c+bw6quvkpiYyMcff3zBZarrY9GiRYwbN45p06bRoUMHbrrpJrZu3Vrdq0MIcemaNWvG4sWL+fzzz7niiit45ZVXeO2112rd9pVXXuGxxx4jKSmJrKwsvv32W3x9fQHHvDRr167l4MGD9O/fn+7du/Ovf/2LmJgYZ74cIbyWHEu7DkWtbaCkEEIIIYQQQgghhBCNSHpKCSGEEEIIIYQQQgink6KUEEIIIYQQQgghhHA6KUoJIYQQQgghhBBCCKeTopQQQgghhBBCCCGEcDopSgkhhBBCCCGEEEIIp5OilBBCCCGEEEIIIYRwOilKCSGEEEIIIYQQQgink6KUEEIIIYQQQgghhHA6KUoJIYQQQgghhBBCCKeTopQQQgghhBBCCCGEcDopSgkhhBBCCCGEEEIIp5OilBBCCCGEEEIIIYRwOilKCSGEEEIIIYQQQgink6KUEEIIIYQQQgghhHA6KUoJIYQQQgghhBBCCKeTopQQQgghhBBCCCGEcDqD1gGcyW63c+rUKYKCglAURes4wguoqkpxcTHNmzdHp5Ma8OWQ9iucTdpvw5I2LJxN2nDDqvp7CuFsst9oGLIfFs52sfthrypKnTp1ipYtW2odQ3ihEydO0KJFC61juDVpv0Ir0n4bhrRhoRVpww2jqKiI0NBQrWMIL1RQUEBISIjWMdye7IeFVv5sP+xVRamgoCDA8UcJDg7WOI3wBkVFRbRs2bL6vScunbRf4WzSfhuWtGHhbNKGG4e0YeEsVW1YNAzZDwtnu9j9sFcVpaq6KQYHB0tDFE4lXWQvn7RfoRVpvw1D2rDQirThhiFtWGhF2nDDkDYstPJnbVgG2AshhBBCCCGEEEIIp5OilBBCCCGEEEIIIYRwOilKCSGEEEIIIYQQQgink6KUEEIIIYQQQgghhHA6TYtS8+bNIyEhAT8/P5KSkli/fv1F3W/jxo0YDAa6devWuAGFEEIIIYQQQgghxPms5st+CM2KUkuXLmXKlCk888wzpKWl0b9/f0aNGkVGRsYF71dYWMi4ceMYOnSok5J6t8wCE5kFJq1jCBcza9YsrrrqKoKCgoiMjOSWW25h//79f3q/tWvXkpSUhJ+fH61bt2bBggVOSCtETfK5JlxZZoGJXZmF8h4VwgNJ+xZCeBRLOczrBT88AaaCS34YzYpSc+bMYfz48UyYMIFOnToxd+5cWrZsyfz58y94v4ceeogxY8bQp08fJyX1XpkFJobNXsuw2WurT+JkJyrAUVx6+OGH2bJlC8nJyVitVkaMGEFpaWmd9zl69CjXXXcd/fv3Jy0tjX/+8588+uijLFu2zInJhbf74+eaEK6k6v15w5sb5D0qhIeR9i2E8DQFG/8LZ49g2/s9GPwu+XE0KUqZzWZSU1MZMWJEjetHjBjBpk2b6rzfokWLOHz4MM8//3xjRxRAfqkZk8WGyWJjV2ahnMiJaj/99BP3338/nTt3pmvXrixatIiMjAxSU1PrvM+CBQto1aoVc+fOpVOnTkyYMIEHHniA1157zYnJhbc793Mtv/Tyuxu7s/oMoU9JSUFRlPMu+/btc2Jiz1f1/pw8pK28R4XwMNK+hRCe5NSZPCxrHOdxLxZdT2apesmPZWioUPWRm5uLzWYjKiqqxvVRUVFkZ2fXep+DBw/y9NNPs379egyGi4tdUVFBRUVF9e9FRUWXHtpLtVDOcL/+J1pv/YZW1u7sV1uRX2omNtRf62jChRQWFgIQHh5e5zabN28+rxA9cuRI3n33XSwWCz4+PjVuk/YrGkPeOScBOnMRHEmD0lyIvwaCojVM5lxVQ+jnzZtHv379eOeddxg1ahR79uyhVatWdd5v//79BAcHV//erFkzZ8T1OrKPFcJzSfsWQngCZft7NFMKKDTG8HHhAO64jBqBphOdK4pS43dVVc+7DsBmszFmzBheeOEF2rdvf9GPP2vWLEJCQqovLVu2vOzM3sS34DBf+/6LCYYfaZexlG98/8VVyr4aJ3VCqKrK1KlTueaaa0hMTKxzu+zs7FoL0Varldzc3PO2l/YrGlpmgYmJH6bSnFxm+8yj0wfd4IObYdl4yPpN63hOdalD6CMjI4mOjq6+6PV6JyUWfyRD6oX0dnRN0jaFEB6vooRmv80DYF/7v2O5zL5OmvSUioiIQK/Xn9crKicn57yTVoDi4mK2b99OWloajzzyCAB2ux1VVTEYDKxYsYIhQ4acd7/p06czderU6t+LiorkxPYiZBaYwG6jxdqpNFGK2GtvSREB9NLt43Xfedz8YRu+nTZSvukRADzyyCPs2LGDDRs2/Om2tRWia7sepP2KhpdfauYa21beCngHo60UVLAGt8IW3BKjb4DW8Zymagj9008/XeP6PxtCD9C9e3fKy8u54oorePbZZxk8eHCd20pvx7pVnbDWtR/1sRQxXLed4A0poDsDZWdB7wOB0dCsPTkRVzP8o3xUdKycNlD2x15IejtqL7PARH6pmbAAX+D34Xnj3t0GcFFt89zHOHfbP/uMEEIITW2Zj6H8LEftURyLvRF+2XtZD6dJUcrX15ekpCSSk5O59dZbq69PTk7m5ptvPm/74OBgdu7cWeO6efPmsXr1ar744gsSEhJqfR6j0YjRaGzY8B6uahLGEWzhP/o0ilR/Tt/0MZERzbAuG06L4pPcbv+J/NLBsqMUTJ48mW+//ZZ169bRokWLC24bHR1dayHaYDDQtGnT87aX9isaWujBZSzweR29TeVXe1vMw2fx1xV2yIeVoUnEah3QSS5lCH1MTAwLFy4kKSmJiooKPvzwQ4YOHUpKSgoDBgyo9T6zZs3ihRdeaPD87q5qPwvnn7T6n07lDZ83uWHVdm73tUAdx3iRwCpdOB9bh1KU14HY0NqPg4TnOre3I8DcuXP5+eefmT9/PrNmzarzfpGRkYSGhjoppeeqascmi63Obaqmu6gqPP2x91RmgYk7F2zGZLHh76Ov/jzYlVnInQs2AxdX2BJCCKcqOwub3gBgjvVO+ukuv6SkSVEKYOrUqYwdO5aePXvSp08fFi5cSEZGBhMnTgQcvSQyMzP54IMP0Ol05w0LioyMxM/P74LDhUT9Ob7lsXK/73cALLKNYmhMPFfEhsCQf8I3kxhv+JEz9pc0Tiq0pKoqkydP5quvviIlJaXOwvC5+vTpw3fffVfjuhUrVtCzZ8/z5pMSosEdSSF27RMoisqRFrdw56HbmWSKw2Q5BOCVc+Vd7BB6gA4dOtChQ4fq3/v06cOJEyd47bXX6ixKSW/H2lX1pqj6OTbUH/IOw4p/0Wb/D7TRA3YoC0rg6/wEeiT1Qm3SlA83HiKGPCa0K8E3Yx0xlrM84fM5tk9/hEFPQa+JYDBKDwsvIL0dtXfupOVvrnbsR6p+NmDlGt0uoresoSJvB0rmYVpSRhQ+/OAbSkB6F+7Qx1Ka36LGY1RNfF5VqKp6HmnLQgiXsmEOVBRRHNaJ77N6068BHlKzotTo0aPJy8tj5syZZGVlkZiYyPLly4mLiwMgKyuLjIwMreJ5tQ7KCbrrDlGhGvjAOpyhVTd0uRPriueIMuVSfmIttLxdy5hCQw8//DCffPIJ33zzDUFBQdW9K0JCQvD3dxw8nVtYBpg4cSJvvfUWU6dO5cEHH2Tz5s28++67LFmyRLPXIbxE/jHsS+9Dp9r40nYNAb1n4Xt8R/WJhLep7xD6uvTu3ZuPPvqoztult+NFUFXY9l/sK/6FzmpCRcfn1v70uPMpyiO68M83N8DWqo2bAzB4yDUotgoWLnidvxl+oLPlOCQ/hyXtU9J7zWHct46FJ6SHheeS3o6u49w2Fh9g5XHDF9ytX02kUgCVgzyan1Prb6YUwqnjvOYD9lXvovj0wl/3ePXtVcWuJ0d24P/9vN9Jr0IIIS5SYSZs+y8A03Jvxs/Hp3oI8+XQrCgFMGnSJCZNmlTrbYsXL77gfWfMmMGMGTMaPpTgBv0WANbTjTKf8N/faAZfCtrcRMSu9wg59BX0laKUt6qaDHnQoEE1rl+0aBH3338/cH5hOSEhgeXLl/P444/z9ttv07x5c9544w1uv13eR6IR2e1UfDERY0UBafa2vMBDLG8RxsppA6uHUzz0YarWKZ2qvkPo65KWlkZMTExjRPQKflQQtvxBOLUCHbDR1pnnrPdzWI3l+4guNbadO7ob/r766veqqjfyjf0avjX3Zf3I08Rsexmf3D0kfn8Tw20P8q29n/Sw8ALS21E75y76o2DnHv0qbkj5CqOhAIAzajD6jtdRFtOLyT8XMWF4d95K3k0L5QyPXVGK7sBPXKE7zq36jagbNjHLMAi9qRM2f8d0Bk0b4CRPCCEaWmnyywRYyzkb0ZMVJ7vw/gNJDfJ5pWlRSrggVeUGnWMce49R41nZseY3rYVtbyVi13sEZ6wEawUY5Ftwb1Q1QfmF1FZYHjhwIL/++msjJBKiDr/8F2PmZkpVI2dGvM3yxK7Vn2nefMJenyH04JivJj4+ns6dO2M2m/noo49YtmwZy5Yt0/JluK1mFPBf39eIPXUEs6pnlnUMgQMe5vCaI9XbhAX44u/jWN3wqoTw6qE951LRsT10FMYBPQlc/jD99bt4w/dtWlhyQT2/Q70M7fMM0ttRW1Urufr76IlR8vjIZxb99LvBAofV5syx3MEKe0++GjCIvFIzaeo2igMT2KuWsFeNY2j7Ljy9ayCJyhEe9vmBUbrN3G1Yg2XZCE4OngvUXlgUnmXdunX8v//3/0hNTSUrK4uvvvqKW2655YL3Wbt2LVOnTmX37t00b96cp556qnq/LURjO310F013fgIKPJh5PaA0WAFdilKiBt/CwyToTmPXGwnvfhMYax64miKu5LQaSpS1AI5vhDbnr3oohBCuIOtUBpErX0QPvGK9m9EJneRkvFJ9h9CbzWaeeOIJMjMz8ff3p3Pnzvzwww9cd911Wr0Et1WUm8mnvi/SRpdFhW8o9xY/yi9qR14Jq7kCZGyoPyunDaz+uaoodSinBH9fffV2U5amA9DE5xm29lhL0K8LeMpnKWe2hULsq2QWlldvW9cE68K9SG9HbVUNsfvqRgNdVt+BQZ+LSfUlv+8z+F01npuySvnhw1QyC0xM+TQdfx99rcNbdqmtaXLvhxwp/g3rN4/S3pRJ/PJ7may/HVSZM9fTlZaW0rVrV/76179e1KiBo0ePct111/Hggw/y0UcfsXHjRiZNmkSzZs1k1IFwCr/1szAodg6HXUNqVoc/v0M9SFFK1BB4cj0AZVE9CTQGnr+BopBi68ZoQwocTJailBDCJWUWmFi/YCp/0RWz0x7PR7ZhjNY6lIupzxD6p556iqeeesoJqTxbVmYGUV/eThtdFtagWI6PWsIvH5ysc/tzC0dVPaeqilAA74xNqt4mLMCXoNDrOGWMpvnmGTTb8Q6Zii/Dfr0GgLl/6SaTJ3sQ6e2oret1W+i6+h10tgr22OOYZHmUtxLvJDE8iHyTHfi9ePX+A1fTNjKwuufjuQWqpgG+lAVcxR3ml9jUbSXh+z5mms8XHN5px8AtWrw04SSjRo1i1KhRF739ggULaNWqFXPnzgWgU6dObN++nddee02KUqLxnUon5Mj32FWF7J5P4v+T4wuvsADfWnty15cUpUQNgZmOolRJbH9qKUkBsMbejdGkYNm/Ap9r6152WAghtFJ2chd3KisBeMkyFhWdxomE1zOXEvrVGGKUU5Q3icbvrz8QoIvG3ycLgDZ1nLRWqeo59cvRs9WFqdhQfxJjQ2psp/aayEsbj/GsbjGxv73JGHs+79qua5CDRuE6pLejdkIOfcMbPm+is6kUxY3kjv2jKcOvzu2bBvjW6PkI1Gjr+aVmyjFyqv8sypteQdSGZ2lz8kvm+mSC3VFUziwwkV9qJqzysYT32bx5MyNGjKhx3ciRI3n33XexWCyykrVoXKtmAvCNvS/t4ruzcprjOOXcntyXQ4pS4nc2CwFZjknOS2KvqXOzTfYrsKsKPvmHyMrMICa2lbMSCiHERQn+5T/oFZWTUYPZeryT1nGEt7Pb4cu/4Z+7kzw1iLwbltI+PIFYqDFE79yfaxMb6k9+ZF1fGf2+zV+nvsKRlEhap/+bZwwfc1SNBrpc8H7C/UhvRw3sWkaLlMdQFJWzHf7Cqf6vULZ/U62bVs3hVuXcdl3b0NzMAhOHIm7lB0seC4xvcIN+KwVrp5F53VsMe30DJosNfx+9DL/1UtnZ2bWuuGm1WsnNza11KG5FRQUVFRXVvxcVFTV6TuF5zuxcSbPDq7ArBuZY72A+DT83pXx1LH6X9Rt6Swn5aiDlEXWPZS8ikP1qCwAsR2vfEQshhFZOH91FxLHvAci48jGN0whvk1lgYldmYc0T0tUzYd/32HW+/M08FXNIQvVNsaH+NSbfb4gDvdhQf1rf/E9KE8eiU1Te8HmLkOKDl/24QniTzAJTzXZ8bCN8NRFFtfOpdRCn+r8CyvmnUlVDbd9cfajO+aRqa+sPfZjKlKXpbND3Ykef/2BVdYQe+grLj//EZLExeUhbTBab9Hr0YrWtuFnb9VVmzZpFSEhI9UVWzxT1lZlfxqkv/gHAR5bBnFAvfjGN+pCeUuJ3J7YBsN3enphadrLw+452u70DnXQnaJK9DfiLE0MKIcSF+W529JLKjR1CXOfe+P/kmNy5thMDIRpSZoGJYbPX1uzRkLMeNrzuuH3ga6T+GHFZz3HuqnwXfE8rCgG3vk7J2cMEntpE31+n4c+/MF1gmJEQwqGqLUPlwgDWk/DpGLCZKUwYxfS99/Cdoqu1PVb1erzY4XbnPsaCsUm0rewN+Y8N+5mtvEH8wfe5W28gNlR6O3qz6OjoWlfcNBgMNG3atNb7TJ8+nalTp1b/XlRUJIUpUS+2ncvoqhzCrPPnTeutf36HSyRFKfG7k78AkGZvS11rsVTtaHM3n4StKwnI3ua8fEII8WeKThF68EsACntOoc1FDIkSoqFUTWw8eUhb3lx9iOLTx+HrhwAo6Tae1OBhQPplPcfFDPOrpvfhxNB5hH0wmOjSo8w0LOZJqywfLsSfqWrLAIX5eUR9cxeG8gKI7cnJQf9B3bsdqLs91qfXY12PMXXqP9nzE1yx7w1mGhazPq8vIPsxb9WnTx++++67GtetWLGCnj171jmflNFoxGg0OiOe8ETWCqK3vQrA/jYPcGZnaKM9lQzfE9WsGY4C0x5dhwt++xob6o+xtWPOKb+83WAudUo+IYT4U9vfQ1GtbLV3xBTZDWi4IVFCXKzYUH902Gm5ZjKYzmKOvJK+qYOZsrTu5eHr+/gX+562+YXzmPkR7Oi407COW3QbLuu5hfAuKmGrn8RQcIRTalOyrl+EaqjZ27Ah9jG1PUZsqD/2a6bxta0vPoqNPmlPEUHhZT2PcB0lJSWkp6eTnp4OwNGjR0lPT69eoGD69OmMGzeuevuJEydy/Phxpk6dyt69e3nvvfd49913eeKJJ7SILzxcZoGJrOQ38S05QbYaxr6EcX9+p8sgRSnhUJyNofgkNlVhwl9u/9OdqzUwhtNqKIpqh+ydTgophBAXYK3Atn0RAJ+oo2S4ntDUffqfHb2JfQNJ6zWHIouOuaO7aTJJ8Va1E7vbOXpIveCzGENp9p/cQwgBcI9+FTEnlmNR9TxinszW03oO5ZQ47fnDAo3M4O8cUFvib85jjs88MvNLz5+3Trid7du30717d7p37w7A1KlT6d69O8899xxw/gqaCQkJLF++nJSUFLp168aLL77IG2+8we23365JfuG5MgtM3D77B5psmQ3AbOudBIeE4u+jb5Av1mojw/eEw0lHN+QDaktCQ8P/dPOwAF/20JoofqXg8C+Eturd2AmFEOLC9nyDviyXLDWc2+/5m/SOEpoJLD3BU4alAORf8xz3f52Hv4+eqxLCNXtf7mnzIOr+H7lSd5Sy1f8gs9knxIY10SSLEO6grXKS5wwfAvBv62h+Vdvz69J0gEY7Mfuj2FB/fpg2HENeK+yfjGQAO3llyQs8ZLtJVuJzc4MGDaqeqLw2f1xBE2DgwIH8+uuvjZhKCMfw5QnqF4QoZexTW7FcN5gpsSGNOh2G9JQSDqccH3Bp9jYXtXlsqD8JXfoBoJ5Ka7RYQghx0ba+A8DH1qGEBwVoHEZ4L5Wrds3AXzFTEtOXzNZ3YbLYWDA2SdOTx5NFFp60PIRZ1ROTvYY5r8+SnhZC1MVu5TWfdzAqFo6E9uW/tut5Z2wS30++hu8nX+PUYlBsqD9RbbqR1XcmAI8bvmBGb0VW4hNCNArfomOM068AIOK2/8eKaYOrhxg31ueeFKUEAOUn0gE4qGt90d/8KM27AeCfK8P3hBAay94Fmdux63z41DZE6zTCi92lTyEqbxtlqpFNnZ/j0JkyAJpqNJz03OXpMwwJnOn+KAD/VBZx7GSmJpmEcHURO/9LN91hitQm3J09Bn8fA4mxIdUXTQrMPcaSovbAqFi5JWMWOuzOzyCE8HhR217FV7FR3GIQEV2vdcrnnQzfEwDoz+wG4KaRIy/6jWeKcCxNayw45Jjs3Fd6JgghNPLbEgCKWw0jd1+IxmGEt9JVFPIPw6cAvKneyfzvzwJnnTbUpzbnLU8fNBRLxg80PXuAI589Q3yLxTL8R4hznTlAZOocAI5f/S/e7XaTo+1o3E5iw5qge/Bd7B8MIPTsDh7Q/wgM0DSTEMLDnNhGyNEfsKkK2b2eIchJTys9pQSU5uFTOempsXniRd/NGhBdPdn5mUPbGyudEEJcmM0COxzz9xS0v0PjMMKbBW+dTVOlmPLQttz72CxNhvrUJjbU//feHXoffG74fwDcrayg7MQOMgtMMpRPCABVpeLrR9HZKlhj64rSdYx2PaNqEdOiNbprXwbgCcNn+BSf0DiREMJjqCr8/AwAn9kGURHewWlPLUUpAacdw++O2qOw+wZe9N3CAnzZRwIA8z79Rg5ohRDaOLQKSs9gaxJBurGn1mmElzp9OI3ofR8AUDL4/4htGqztUJ8LaT2IwoRRGBQ7gaumM2x2CsNmr+WXY2dlVS/h1c5u+xRj5mZMqi8v8SBhgUatI52v+1hKYvrgp1iI3vqS1mmEEJ5i5xdwchs2QxPmWJ37Ja8UpQRkO4pSe9W4et0tNtSfHj37AtDaflwmWxRCaCP9YwA+LOnFY5/v1nSolPBSqkrA6mcxKHbOtBhBRNdrtU70p0yDZ2JSfYkpSGWgbQsmi407F2zmhjc3MGz2WilMCa9zKieXJmueA+BYp4f4YNodrldQBlAUsvq+gFXVEXL0R3J3rNA6kRDCzZ06k4vl52cBeMN8EyU+EU49lpailHBMEAzstbeq912DWnUFoL3uZINGEkKIi1J2Fvb/CMCnlv7MHd1N86FSwgsdWUNg5gYqVANn+z2ndZqLEt2qPZbejwDwesS3BPo4lrl/7oYrZFUv4XUyC0x8/9ZU/MpzOG6PxN5nskvvRyrCO/KhbTgABcumsG7fKSkkCyEuSWaBiW/efBKf0mwy7M1YrF7P5xP7OPUzUIpS4pJ7SgEQ2QmADsoJxzhUIYRwpt1fgd1CcVgn9qmtaBsZ6NInEsIDqSrmn58HYKk6nMCYthoHunjBgx+HJk3xLzrC+pFZrJw2kKsTwrWOJYTTlWQd4j7lBwBmWseiGvw0TvTnXrfeTp4aRFslk9UfzpIejkKIS1KSdYgHlO8AUEf8H8unDScx1rmLBklRyttZzZC7H4A99ksoSkW0R1X0hCqlGMpON3A4IYT4E3u+BuCdvO4ybE9oY883+ObsoET1o+0dM9yrKOoXDP2fACBs62xiZRFd4YUyC0w02fgqRsXKBltnVtl7aB3pohQRyGzrXQBMD/genaVEejgKIeotfNOLGBULJc37EdfvLk2OY6Qo5e3OHga7FZtPIKdoWv/7+/hREeKY7Nx8alcDhxNCiAsoyYFjGwD42nI1C8YmuVdBQLg/mxVWOyYa/p/tOoKbxmgc6BL0fABCWkLxKdj2X63TCOFUmQUmJs3+gNgT3wPwivVuQNE2VD18ZhtIRXACRvNZJuiXax1HCOFmzuxMptmJn7GqOkqHvASKNp9/UpTydmccvaQqQttyqTthtVlHAH5cvVq6DQshnGfvt6DaKWvWlZNqJE2ll5Rwth2fQt5BrMYw/me9Tus0l8bHDwb/0/HzhjnoLKXa5hHCifJLzTzGJ+gUlawWo9ilttY60kUJC/DF30ePj4+RkmumA/Cg4QdyTmfKCppCiItjsxK0+hkATne4h6i22vUSlaKUt8s94PjH7xKG7lXyj70SgNb2DOk2LIRwnt1fA3Ck2TBtcwjvZLPC+tkAnOk2iRKaaBzoMlw5GsLbgCmfsL0faZ1GCKdpkrWVIfp0VMVAcd+ntY5z0WJD/Vk5bSArpw2kac87MUV0IVAp59iXL8gKmkKIi5O6CL/8/ZxVAynq9aSmUaQo5eXKTu0BYMkR/0ufj6VqsnPdCfKkKCWEcIaSHNTjGwGYmNZK5pMSzrfnazh7BJtfONsjbtE6zeXR6aH/NAAidizEiOzLhXeISnUUls92/Avmyuko3EVsqL9jyLpOR/bVjoLaPfqVTO8XJCtoCiEurOxs9fQDc6x3YvML1TSOFKW8nFLZU2pgv36Xvox6ZVGqrXKKv3/4i3wzI4RofHu/RVHtpNtb88Rdwy/980uIS2G3w7rXAHirbBiTlx10/8LolXdBSCt8TGf4i36N1mmEaHzHNxGQtQWzqudMt8nVQ+LcsS2XxvZni70TRsXKoLxPtY4jhHB1q2ZCeQGm8E58YhuqdRopSnk1ux1jwWEAwuO6XPoJXVg86Aw0USoIseTKNzNCiMZXOXTvB1tv2kYGSkFKONf+H+DMXopVfz5Wr+X9B652/8Ko3geumQLAQ4bvUGwV2uYRopGVr3oFgK/UQQRFxdUYEueObflN6y0AtMn4gggKtQ0jhHBdJ7dD6mIAsvrOxO4CJSHtEwjtFGags5VToRowB7e69MfR+0CYo8tza92pBgonhBC1y8o6WT10b7Wuj9t9o+0q5s2bR0JCAn5+fiQlJbF+/fqLut/GjRsxGAx069atcQO6KlXFvObfACy2jeT/jR3AwPbN3PIk9jzd7sHSJIrmyll8di3VOo0QjSZn70b8MtZiVXXE3/JsdfutHhLnhjbaE/nV3haDvYIJBlmJTwhxvsyzJZi+egxQoesYymJ6aR0JkKKUd8s9CMAxNRp0hst7rIh2ALRWsi43lRBC1CmzwMR/5r+NotrZq8bxn4k3u+0JhJaWLl3KlClTeOaZZ0hLS6N///6MGjWKjIyMC96vsLCQcePGMXSo9l29tZK7MxnfnB2UqUY+Ua6nbWSg1pEajo8fpT0nOX7c+jaZ+bISnyuTwvKlySwwsefTZwH4Vu1Pi9adNE7UUBTetN4KwFj9CvTl+RrnEUK4kswCE+/NfRb/vF0UqgFk9ZqudaRqUpTyYoUndgFwVIm9/J4GTdsC0EaRnlJCiMaTX2pmgLodgNjet5EYG6JxIvc0Z84cxo8fz4QJE+jUqRNz586lZcuWzJ8//4L3e+ihhxgzZgx9+vRxUlLX4/uL42+U3fp2vph2o8cVRUP7jcfqE0SCkoVl389axxF1kMLypTNlpDFI+RUVHX3/Ossj2nDVfFhb9EkUhV5BgFJBk18Xah1LCOFCis+c5DHFMefcv62jyVNd5xhailJezHZ6HwCdulx1+TvkiPaA9JQSQjQuxVrOQN1vAAR3vVnjNO7JbDaTmprKiBEjalw/YsQINm3aVOf9Fi1axOHDh3n++ecv6nkqKiooKiqqcXF7Zw4QfGI1dlXBetVEjziZPY8xiPxOYwCI2PlfjcOIukhh+dJF7HAUawrb3EB0QmeN0zSM3+fDGoSl31QAQna9z6kzuRonE0K4iuit/0ewYiIvJJEltiFax6lBilJezFhwCABdsw6X/2BVw/d0UpQSQjSegKzNBCgVWJpEQUw3reO4pdzcXGw2G1FRUTWuj4qKIjs7u9b7HDx4kKeffpqPP/4Yg+HihnvPmjWLkJCQ6kvLli0vO7vmtjpO+FfZe2AOidc2SyM62/l+rKqOwFObIGuH1nHEHzirsOyRik4Rcvg7AHK7PKhxmIZVNR9W06TbMAW2IlQpgXRZiU8IARxdR+ihr7CrCtsTn3WJyc3P5VpphPOoanVRqiKs7eU/XlNHUaqFkkt+YcHlP54QQtQi6HgyAEVxw0FRNE7j3pQ//P1UVT3vOgCbzcaYMWN44YUXaN++/UU//vTp0yksLKy+nDhx4rIza6rsLKQvAeBd2yiNwzQuS2Asy+2OyU/L1r2hcRrxR84qLHtab8fMAhNnVr2JolrZau9IebOuWkdqHDo9+VdOACB0x3/Bbtc4kBBCU1Yz5d88DsASdQQ07w7AoZwSDuWUaJmsmhSlvFXZWQwVBQBUhLS+/McLaIrNLxyAOUt+JLPAdPmPKYQQ57LbCa4sShXHjfiTjUVdIiIi0Ov155285uTknHeSC1BcXMz27dt55JFHMBgMGAwGZs6cyW+//YbBYGD16tW1Po/RaCQ4OLjGxa2lLgKrCVPTzmyxe8rEyLULC/DlI24AwLDnS7JOHtU4kahNYxeWPam3Y2aBiZtm/4xv+mIA/me9TttAja3bPRSqATQpPkZe2rdapxFCaKhwzVz8Cg6Rq4bQ/f7XSIwNwd9Hz5Sl6UxZmo6/j17zlaw1LUrVZ9WQDRs20K9fP5o2bYq/vz8dO3bk9ddfd2JaD3P2CACn1HBUQ8PMiaFv5ugtFWs7SX6puUEeU7imdevWceONN9K8eXMUReHrr7++4PYpKSkoinLeZd++fc4JLDxDVjo+ZacpUf0obe6986FcLl9fX5KSkkhOTq5xfXJyMn379j1v++DgYHbu3El6enr1ZeLEiXTo0IH09HR69XKN5YQblc0C2xzzKx1vdz/g2b30YkP9eX3aePLCe+Cr2DBvlrmlXImzCsue1Nsxv9TM9fbVhChlHFej2aS/SvOTsMbUPDKCws73AOC3/cLzjAnt1HcFzY8//piuXbvSpEkTYmJi+Otf/0peXp6T0gq3lHeYoC2vAXCm77+4onWr6jnovp98Dd9PvoaV0wZqPkemZkWp+q4aEhAQwCOPPMK6devYu3cvzz77LM8++ywLF8rKEpeksih13B7dcI9ZOYRPVuDzfKWlpXTt2pW33nqrXvfbv38/WVlZ1Zd27do1UkLhkfb/CMA6+5WoeqPGYdzb1KlT+d///sd7773H3r17efzxx8nIyGDixImA42R03LhxAOh0OhITE2tcIiMj8fPzIzExkYCAAC1filPkpX4JxVnYmjTjro0xLvGtYmOLDfVH6f0QAE12fUxmnnsP3fIkziose1RvR7uNB/Q/ARAy5FFWTBus+UlYYyvrOh6LqicgawucStM6jviD+p4Lb9iwgXHjxjF+/Hh2797N559/zi+//MKECROcnFy4DVWF76egs1Ww0dYZW+c7q2+KDfUnMTaExNgQl/gs1KwoVd9VQ7p3787dd99N586diY+P595772XkyJF/WlEWtSs6tR+ATCWq4Q6sIxxzU8lk555v1KhRvPTSS9x22231ul9kZCTR0dHVF71e30gJhScy7/kBgHVKT48vCDS20aNHM3fuXGbOnEm3bt1Yt24dy5cvJy4uDoCsrKw/XVreW2QWmDjwg2NepWNxd1Bk0bFgbJJLHMQ1tvAet2H2i6CZUoBtz/daxxHnkMJy/QSdWEW87jRWYwihfe73ivZrDYzhh8q54dgivaVcTX3Phbds2UJ8fDyPPvooCQkJXHPNNTz00ENs377dycmFq8ssMLErs5D8TYvg6DrseiPTrRNcei5WTYpSl7pqyLnS0tLYtGkTAwcOrHMbT5ugsSHZ8xw9pXp0b8AD68qeUgmKFKVE7bp3705MTAxDhw5lzZo1F9xW2q+ooegUvrm7sasKN97hHScUjW3SpEkcO3aMiooKUlNTGTBgQPVtixcvJiUlpc77zpgxg/T09MYP6QJKM/fSR9mFTVVY1cQxwXlTbymKGnwp6Hg3AOF7P9Q4jDiXFJbrJ3zPRwDkd/gL+Hp+Ea7KIuu1jh92fwWlMszLVVzKuXDfvn05efIky5cvR1VVTp8+zRdffMH1119f5/PIsbT3ySwwMWz2Wu5/8weUFc8CkJM0jQz1/KHdrkSTotSlrBpSpUWLFhiNRnr27MnDDz98wS6LnjRBY0PzLToOgCGiTcM9aFPHY8Urpx3dBYWoFBMTw8KFC1m2bBlffvklHTp0YOjQoaxbt67O+0j7FTUcdsx5skNNIKRpAw47FuJPhO/7BIA19m68vLHEK4bunSu/493YVYXAU5s4fWSn1nHEOaSwfJHOHiHoZAoA+Z3u0TaLk/2mtsEUkQg2M4WbF2kdR1S6lHPhvn378vHHHzN69Gh8fX2Jjo4mNDSUN998s87nkWNp73MopwSTxcZHsV8SqpRSHHYFuV1cf4inphOdX+yqIedav34927dvZ8GCBcydO5clS5bUua0nTdDY0HyLjgFgDolvuAcNczxWsFJGYX5Owz2ucHsdOnTgwQcfpEePHvTp04d58+Zx/fXX89prr9V5H2m/ooZDqwBYa/fQJbyFa7KYCD3wOQBhAye6zISgzhQY3Zq1OJaP/mnxy7K6rnA/2x3FmLW2KzEHx2ubxekUDsf9BYCC9QvJzC/VOI84V33Ohffs2cOjjz7Kc889R2pqKj/99BNHjx6tHrJbGzmW9i6ZBSYmfpjKKJ90OuYlY1V13J87lswii9bR/pRBiyet76oh50pISACgS5cunD59mhkzZnD33XfXuq3RaMRolMlwz2MqwFB+FgBzUFzDPa6PP9bA5hhKTvHGZz8T37KlVx24i/rp3bs3H330UZ23S/sV1ew2OOIY7rnOdiVDNY4jvMiebzBUFHBSjcDYYQSJsSFaJ3K62FB/jLdMhW/u5RYlhZOFhbJvF+7DUo7t14/QAx/ZhvGY1nk0sMrQn1ZqE+KU02za9j30uknasMYu5Vx41qxZ9OvXjyeffBKAK6+8koCAAPr3789LL71ETEzMefeRY2nvkl9qRm8p5vXwD6AMTl0xgdS0OPJLzVpH+1Oa9JSq76ohdVFVlYqKioaO5/nyjwJwRg3B7hvYoA9dNRwwxnbKLRqA0E5aWlqtO1AhznMqDUz5FKlN2G/o4FVDp4TGtr8HwCfWIaDz3oUZIrpehzmwJSFKGfZdX0pvKeE2zm7/HH35WU6p4WzWe9ciGWEBvvj76Hl9bSbLbP0BKN3wDsNmr5U2rLFLORcuKytDp6t56l61YJAq06aISk8YPsOvLBvC4inuPQ3ALdq7Jj2lwLFqyNixY+nZsyd9+vRh4cKF560akpmZyQcffADA22+/TatWrejYsSPgWBbztddeY/LkyVq9BPd11lGUOq5G4dfQjx2eAMfWE6+78Nxgwr2VlJRw6NCh6t+PHj1Keno64eHhtGrV6rz2O3fuXOLj4+ncuTNms5mPPvqIZcuWsWzZMq1egnAnlUP3NtgTeXvs1fINr3CK04d+JerEVuyKgc9tg7hO60Ba0uk52+luon/5N2Vb3+euLa29bhijcE/GdMfQvYJO9/LztUO86j0bG+rPymkDyS8106yiBXzwM8P0aYSVnya/1OxVfwtXVN9z4RtvvJEHH3yQ+fPnM3LkSLKyspgyZQpXX301zZs31/KlCBfRJGsr4/SVhc4b/0NoSAj+PnreXH3I5efD1KwoNXr0aPLy8pg5cyZZWVkkJiZecNUQu93O9OnTOXr0KAaDgTZt2vDKK6/w0EMPafUS3FbhqQOEACeJ5qqGfnOGtwYgTjndsI8rXMr27dsZPHhw9e9Tp04F4L777mPx4sXntV+z2cwTTzxBZmYm/v7+dO7cmR9++IHrrvPq0zxxkSr2J2ME1tmv5F4X3qEKz5FZYCL5g9e4Xwc/WXtwhlCtI2muoN0dNNv2/+il20dUxUk5qRWuL3sXAadTsah6dEnjvPL9GhvqX/m6u0J8f5Rj6/mLYTV5pXL8pbX6ngvff//9FBcX89ZbbzFt2jRCQ0MZMmQIr776qlYvQbgScymx655Ap6jktx9NWOtBxEJ1YToswNelPwM1K0qBY9WQSZMm1Xrb4sWLa/w+efJk6RXVQOy5hwHo2rVHw785K4tS8VKU8miDBg26YFfhP7bfp556iqeeeqqRUwlPdCo7i6hT20GBbbruTJailHCC/OJSblDWA/Atg13+G0ZnsAZEs85+JYP1v3GHfh1wp9aRhLiwX98HYIU9ibgmkRqHcQE9H4Bj67lTv55hH/7CimmDXfok1RvU51wY5HxY1K1k+b8ILDpOptqUwj7/Iqzy+t8L065N09X3hDaqVt6rmv+pQVX3lJLhe0KIy2c9uAa9olIc2JoPp93uFjtW4f6CMtYQoRRh8W/Gvx6fLEPVKn1mGwTA7fr1jgUIhHBVlnLsv30GwFLb4D/Z2Et0vB78w4hR8kiypcvcr0J4iDM7VxKY/i4Az9kfIiQsQuNE9SdFKS9UVZQyh8Q3/IOHOVZHDFdK0FUUNPzjCyG8SuDJtQBUxMs3usJ5wg58DkBBu9uIDQ+S916lVfYe5KuBxChnCcxcr3UcIeqUsfkLdBUFnFLDSdV38/qejgAYjNDlLgDu0q/VOIwQoiGcyskl4MdHATgadyczpz3qlscsUpTyNuZSfMpyAKgIjmv4xzcGYvFvBoBv0fGGf3whhPdQVYIqi1IlLQZqHEZ4jdJcgjIck+sXtLtD4zCuIyzAF72PH1/b+jl+379U40RC1C6zwMSxVf8FwJL4Fxmmdq7u9wIwXLcdfXm+xmGEEJcjs8DE2rcm0qQsk5NqBKZBL7jtZ50UpbzM6Yz9ABSoAYSEN874enNwPABGKUoJIS7Hmf34lGZRofpQGtNL6zTCW+z4DEW1km5vTUV4B63TuIyqlbw6jPo7AIHHV5CVlalxKiHOV3z6OP34DYC4IRPc9iStUcRcialpIkbFSsihr7VOI4S4DOYDq7hb51ht7ynL37D7Bmqc6NJJUcrLlGcfBEDXtE2j7aSrhgX6Fh5rlMcXQniJw47eKlvtHVENclIhnCT9EwC+sEnvvD+KDfUnrnNv9qjx6O0W3p3/bzILTFrHEqKGsIPL0CsqpdFXQ9NGmD/VzeW3dyxSEHbgM42TCCEuWXkRsesci0h9YB3OJnuixoEujxSlvIyxcj4pe+XcT42hqqdU1dxVQghxKcr3rgBgkyLzgQgnydoBp3diVg0k666R910tYkP9aT5oAgA3sE4mSxauRVUJrSy25Le/S+Mwrqmw7S1UqAb883ZD1m9axxFCXIqfp+NbkkmGvRmvWO/WOs1lk6KUl6me5LyycNQYquaqkqKUEOKSWUz4Zm4GYOgNd8vwC+Eclb2kVth78u+xsuJeXUKv+guqoqeb7gi+hUe1jiPE7zK2YCw6RqlqpKj19VqncUk2vzCS7T0dv/z6obZhhBD1t+dbSPsIFYUnLRMpw0/rRJdNilJe5veiVCNMcl7p955SMqeUEOISHd+IzlbBKTUc/+adtU4jvEDm2WJsOx2r7n1h609T6SVVt8BmlMT2B0C363N2ZRbKMD7hGtI+AuAHW2/sPgEah3Fdn1cOT7btXEZmXpHGaYQQF63oFHznWG0vt+tEtqqdNA7UMKQo5WWqCkUVlfM+NYaqgpeP6QxUFDfa8wghPNghx3xS62xXgqJoHEZ4sswCE2sPnOG51+ehL8vF7BvGBnsXrWO5vIK2twCg3/U5N7y5nmGz10phSmjLYoI9XwO/F11E7TbYE6kwRqAvP8tLc9+UtiuEO7Db4eu/gykfYrqSkzSt+iZ/H71bTzkgRSlvYq3Ap+QU0LjD9+zGEPLUIMcvZ6VbvxDiElQVpexXahxEeLLMAhPDZq/lvve2ca26AYDj0SOwYtA4mesrjh9JmWokQXea/7vKjMlik/mlhLb2/wjmEsyBLdiuttc6jUuzoedYzLUAXCdzwwnhHrbOhyMp2A3+nB7+FqreUYR6Z2wSK6e595QDUpTyJvnHUVApUf2w+TVt1Kc6rkYBkHdyX6M+jxDC82SfOAS5+1HRscHNVxMRri2/1FFMeeOOjtzqlwrA8ebXaZzKPdh9AlhhTwKgZ/FKjdMIAVQOvy1sezOqnOL8qWPNbwBguC4VnVlGNgjhyk4fTEVdOQOAF81jGLToFNuOngUcC5C4c0EKpCjlXc4eASoLRo08HOaYGg3A+9+tki7BQoiLlllg4u3/vgPAr/Y2WHxC3Lo7snAP3cq3YbCWclKN4Delg9Zx3MbXtn4AxJ36ET02jdMIr1Z2Fg4mA1DQ5hZts7iJXWoCh+0x+CkWgo/9pHUcIUQdMnPzKfzoPhSbmZyYwSwyD8FksTHz+z1uP2yvihSlvEllUepYZS+mxnTc7niO5vZs6RIshLho+aVm+qjpALToeYPbd0cW7iHk8DcA/KT25c01RzzmIK8xhQX4kqrvxlk1CD/zWfrpdpEn+3uhlT3fgN2CKbwTu62xWqdxaWEBvvj76HlzzeHqwnKT/V9qnEoIURdjyou0V05wRg1m4xXPAwrvjE3i+8nXeMxxskya4E2qe0pF03hr7zl2dqf0MQDEKTmN+ExCCI9jt3KNbhcAUd2vBw/Y0QrXFkQZQRmrAbhx7GP0btKOsABfjzjIa0yxof78NG0ovmvugN8WcbthExM/7OExB8jCvVSkfYoRmHu6G+8sTZfC8gXEhvqzctpA8kvN2POaw5dfEJK1iazMY8TExmsdTwhxrv0/ErHrXQCesjzESGNT4BSxof4kxoZom60BSU8pL1KecwiAU7qYRt1Rx4b68+Tdjjk54nTZjfY8QgjP438mnWClDKsxBGJ7aB1HeIGR+l/Q2SqgWUei2iaRGBsiRZWLFBvqT2DPMQDc4JuKaimT3tHC+QpPYszcAkCP68Z7VO+BxlJ1Qnvlld0pjOiOXlFh5zKtYwkhzlV4EvtXfwfgXeso1ti7e+y0OFKU8iJKvmMlvDuGD2j0HXVkXCcAmitnUazljfpcQgjPYTji6LFSGtsfdHqN0whvcJNuk+OHxDsafb5Fj9TiKghthd5axiDdb1qnEd5o5xcAbLV3JDa+vRSW66m0w+0AhB5yDOHLLDCxK7PQY09+hXALNiuln9yHrjyf3+ytecV6NwBvrj7kkT1BpSjlLWwWfItPAuAX2bbxn88/DJtvMAC+Rccb//mEEG4vs8BEwU7HZKv2NkM0TuP55s2bR0JCAn5+fiQlJbF+/fo6t92wYQP9+vWjadOm+Pv707FjR15//XUnpm0c+rIz9KscLkqX27UN464UBa64BYDr9Vu0zSK8U2VRqmp+JFE/ha1vwKLq8c/dxekjOxg2ey03vLmBYbPXSmFKCI0U//QCAae3U6z6U37zf0l5egQbnx7isT1BpSjlLQpPoKhWylUfrAGNP9E5ioI52DFzlRSlhBAXoyjvNF04DEBYl1Eap/FsS5cuZcqUKTzzzDOkpaXRv39/Ro0aRUZGRq3bBwQE8Mgjj7Bu3Tr27t3Ls88+y7PPPsvChQudnLxhhRz7Eb2iUtasG4S31jqO++p8CwBDdGkoVjmJdRYpLAM5e+H0TsyqnjW6vh7Xe8AZbH7hrLd3AaAsbRkmi43JQ9pisthkOK4QWji0kqBf3gAgo/+r9ErqSWyof/WwW08rSIEUpbxH9STnUaA457+9IjgekKKUEOLiBGauR6eolId1gODmWsfxaHPmzGH8+PFMmDCBTp06MXfuXFq2bMn8+fNr3b579+7cfffddO7cmfj4eO69915Gjhx5wZNgdxB8ZDng6CkgLkPzHpgDWxKgVMDBZK3TeAUpLFfa5ZgHaa29K6+O9bzeA87yg603AJYdy/D30XvUBMpCuJXibGzL/gbAEvtwQnvepXEg55CilLc465hP6rjqhF5SlczVRaljTntOIYT7Cjy5FoCSFgM1TuLZzGYzqampjBgxosb1I0aMYNOmTRf1GGlpaWzatImBA+v+v6qoqKCoqKjGxaWUnCEg2zHcrChBeuZdFkWhosONABxf97EM+XECKSwDqgq7vwbge1tvmkovqUuWbE/Cphhor5zgg5uCpbgnhBbsNlg2Ab0pj732VsTePddr2qIUpbxFZVHqmBrttKesGr5nlKKUEOLPqGp1Uaq4pRSlGlNubi42m42oqJpfUkRFRZGdfeEVU1u0aIHRaKRnz548/PDDTJgwoc5tZ82aRUhISPWlZcuWDZL/clVN4puf9hWKauc3e2ssQa6RzZ0F9bgDgIHKrxQUFmqcxrM5q7Ds8nL2QN5B7Hojq+yyWuvlKCKA7Ii+ALTKWqFxGiG81JqX4dh6rHp/HrY8SnhwkNaJnEaKUt7i3OF7TlJVlFLyj8q3pkKICzu9G5+yHEyqL2VRV2mdxisof1hpTlXV8677o/Xr17N9+3YWLFjA3LlzWbJkSZ3bTp8+ncLCwurLiRMnGiT35cgsMFVP4rtn5YcA/Gi7WuNUHuKcIXxBJ9ZoncajOauw7PK9HSt7SZ1u1pcSmmibxQOciBkJQMiR7zVO4j3qMy8cONrkM888Q1xcHEajkTZt2vDee+85Ka1oVPuWw/rXAJhqeoAsQ0uvmiNPilJewpJ7CHBuUco/pj0AfqWZjJq9SgpTQoi6HV4FwBZ7J1SDn8ZhPFtERAR6vf68k9ecnJzzTnL/KCEhgS5duvDggw/y+OOPM2PGjDq3NRqNBAcH17hoLb/UjMli48n+EfTCsereGl0frzrwazSKQmHr6wAIPvKDxmG8Q2MXll21tyMAqopl51cAvJrRySOXSHe2zKhBVKgG/AoOYjy7X+s4Hq++88IB3HXXXaxatYp3332X/fv3s2TJEjp27OjE1KJR5B2Grx4CYJF1JEPufNgjV9i7EClKeYHMsyWoeY7he9n65k7bacc0j8Nu8EevqIRbs2UFDyFE3Q45ilLr7FdqHMTz+fr6kpSURHJyzQmpk5OT6du370U/jqqqVFRUNHQ8p+hZvgWDYme3PY5/jr3eqw78GlNR5YTxgcdXcupMnsZpPJezCsuu2NuxWs5efPIPUqEaGHbLfV53AtcYLD7B1fvgkKPSW6qx1XdeuJ9++om1a9eyfPlyhg0bRnx8PFdffXW99tvCBZlLsXwyBiqKyAvvwcvWe2gbGeh1n2dSlPICJWcy8FWs2BUD7z9+q/Pe5IqCrmkbAOKV0855TiGE+zGXQsZmwLGCkmh8U6dO5X//+x/vvfcee/fu5fHHHycjI4OJEycCjpPRcePGVW//9ttv891333Hw4EEOHjzIokWLeO2117j33nu1egmXpfWZlQAk05u2kYEap/EcfnE9Oak2w2Az8cobb0kP6UbirMKyK/Z2rLbna8DxRUZ8bIzXncA1lqpV+By9HVVtw3iwS5kX7ttvv6Vnz578+9//JjY2lvbt2/PEE09gMsnnrNtSVcqWPYJP3j5y1FCuPTUeg4/RK3t9GrQOIBqfb+ExACzBrYgNd/KEaWHxcHoXcVKUEkLU5dgGsJkp82/OkfIYrdN4hdGjR5OXl8fMmTPJysoiMTGR5cuXExfnmAswKyurxhACu93O9OnTOXr0KAaDgTZt2vDKK6/w0EMPafUSLlkwJTTNcRRB775/MlFyMttgYsOaUNzzTkidx3A2kV9qlmJBI5k6dSpjx46lZ8+e9OnTh4ULF55XWM7MzOSDDz4AHIXlVq1aVQ/12bBhA6+99hqTJ0/W7DVclsr5pH60Xc0D2ibxGJkFJlbae2DXG/ErOER75aTWkTzWpcwLd+TIETZs2ICfnx9fffUVubm5TJo0ibNnz9Y5r1RFRUWNwrPLzQvn5QrWvkXo/i+xqjr293+DRZ0GERbg65X7TSlKeQHf4uOAY+Jxo7OfPLw1APHKhSfeFEJ4r5I9PxMIfF3cEX8fg1d+Q6SFSZMmMWnSpFpvW7x4cY3fJ0+e7L4nr38wTPcrOrsFIq8gqnUXreN4nKDud0DqPAbr0jluc8/hne7AmwvL5OyF3P3YdT6stCdJUeoyhQX44u+j583Vh/D3CaIibjD+R37iev0W4G6t43m0+swLZ7fbURSFjz/+mJCQEMAxBPCOO+7g7bffxt///ELGrFmzeOGFFxo+uLhsZ3anELrmeVDgZes93NZpEImxIVrH0owUpbyAb6FjPqmK4HicvrBkZVGqlZLj7GcWQrgJn6OOlbra9LmFlf1kXhDRuEbptzl+uOJmbYN4qubdsQREE1iaTUDmRmh1q9aJPJa3FpbZ8w0A62xdsPgEyxcZlyk21J+V0waSX2p2FKgyiuDIT9yg24JJlSF8jeFS5oWLiYkhNja2uiAF0KlTJ1RV5eTJk7Rr1+68+0yfPp2pU6dW/15UVORaCxZ4q4IThH0/HoNi4ztbb96zXcttWmfSmMwp5QV8i6p6SsU7/8mlp5QQ4kLOHsVYeASLqifoiiFSkBKNSmcuZoBup+MXKUo1Dp2OojjHPCnBx3/WOIzwSJVD976zXM2CsUmy32gAsaH+JMaGOP6W7a/FrvOljS4LY8FBraN5pEuZF65fv36cOnWKkpKS6usOHDiATqejRYsWtd7HpeeF8zKZBSZ2ZRZy6kwuLLkbgymXPfY4nrL8DbjwqqneQIpSXsBYdAwAc0i885+8sijVUskBu835zy+EcG2HHavu/aq2w+4rB0uicQWdWINRsVAR0gaayTLajaUofiQAwceTZd8vGtaZ/XBmL3adD8n2JJpKL6mG5xdMaWw/AAwHlmscxnPVd8GRMWPG0LRpU/7617+yZ88e1q1bx5NPPskDDzxQ69A94ToyC0wMm72WG99cx863xsDpnVT4hvOgeSom/LSO5xKkKOXpVLV6onNNekoFN8eu88VXseFTesr5zy+EcG2HHEWptTZZdU80vqBjjp47RfEjoY55O8TlK43pTaHaBIMpF07+onUc4Un2fAtAaWx/igjQOIznsra/HoDS376WVTQbyejRo5k7dy4zZ86kW7durFu37oLzwgUGBpKcnExBQQE9e/bknnvu4cYbb+SNN97Q6iWIi5RfasZksfFx2xRGKlsxq3rGFE8mk2YA+PvovX4Ysswp5emKs9HZyrGqOiyBsc5/fp0ec3Ar/AoOVQ4jTHR+BiGEa7KasR9JQQds0XXnHi/fIYtGZjUTdCIFgKK4EZWHgqJR6HxYZe/BbfoNsPc7aNVb60TCU+z7HoCi+GtBRpY1mrDuN6OuepJE5Qj7Tx+F0Cu0juSR6jMvHEDHjh3PG/InXF9eqZlRuq30Pfk/AJ6xjmfsXaN5IyG8ehtvH4asaU+pefPmkZCQgJ+fH0lJSaxfv77Obb/88kuGDx9Os2bNCA4Opk+fPvz8s8xV8KfOHgEgU41A1WtzwmcOdlT8fSuHEQr3t27dOm688UaaN2+Ooih8/fXXf3qftWvXkpSUhJ+fH61bt2bBggWNH1S4thNb0FnKOKOG8Ni9t3n9Dlk0nswCE8dSf0ZvKSZHDcUU2U3rSB5vha2n44d934NMliwaQuFJyEoHFIrihmmdxrMFRlIW5WjDVT1MhRD1l1lgYu6Hy5jt4zjvedc6is9tg2gbGUhsqH/1xdtpVpRaunQpU6ZM4ZlnniEtLY3+/fszatSoGt0Uz7Vu3TqGDx/O8uXLSU1NZfDgwdx4442kpaU5Obl7yc/cB8AJJVqzboFVwwarJlwX7q+0tJSuXbvy1ltvXdT2R48e5brrrqN///6kpaXxz3/+k0cffZRly5Y1clLh0g6tBGCd/UqaBsqYetE4quZyWPfd+wCkqEmEyfutUYUF+LJN351y1Qfyj0HOHq0jCU+wr3J+o1a9sflHaJvFCxTFXwtAsBSlhLhkxTkZvK17lSZKBcUtBvKydYzWkVySZkWpOXPmMH78eCZMmECnTp2YO3cuLVu2ZP78+bVuP3fuXJ566imuuuoq2rVrx8svv0y7du347rvvnJzcvVjPHAYgoX0XzaqwVUUppbLXlnB/o0aN4qWXXuK22y5uAdMFCxbQqlUr5s6dS6dOnZgwYQIPPPAAr732WiMnFS5N5pMSTuCYy8HKHYGOVfeG3Hq/fCvZyGJD/Xl9bD/W27sAUJT2lcaJhEeoHLpXGDeCQzklf7KxuFxVCxYEZG0lK+ukxmmEcD+ncs4Q/cM4mitnKQ9tS/EN7+Dr4ytzSNVCk6KU2WwmNTWVESNG1Lh+xIgRbNq06aIew263U1xcTHh4eJ3bVFRUUFRUVOPibaomOdc1baNdhkjHc589sU8mS/RSmzdvPq+9jxw5ku3bt2OxWGq9j7RfD1eUBad3oaKw3i5zzYnGlagcpUl5NvgEEJE44s/vIC5b28hAUpSrATi5+XPZ/4vLcio7C/XYBgDuSglnytJ0ObFrZIExbdmrxqFg5835b0obFqIedp3I49DbdxBauI9cNYSCWz+meXQMK6cNZOW0gfLl2B9oUpTKzc3FZrMRFRVV4/qoqCiys7Mv6jFmz55NaWkpd911V53bzJo1i5CQkOpLy5YtLyu3O6oaMlc1r5MWIlo6lt1uyWnySyo0yyG0k52dXWt7t1qt5Obm1nofab+eLX/njwD8Zm9NuU+YnFiIRjVCv93xQ9sh4CND95whNtSfRyY+goqOK5RjlGQf1jqScFOZBSbmznsLRbWxz96S/ZZmzB3dTU7sGllsqD+xfe4EYLC6jfxSs8aJhHAPmfll7PrvQwxQ0rHp/bDfvYToOMf5sMwhVTtNJzpX/rAcs6qq511XmyVLljBjxgyWLl1KZGRkndtNnz6dwsLC6suJEycuO7NbUdXqycUrQhK0yxHaClXR46+YMZSd1i6H0FRt7b2266t4ffv1cLrDjqF7fp1GyImFaHTDdamOHzreoG0QLxPTvCVl0VcBEHx8hcZphLvKLzUzSN0GwBquwt9Hz1UJ4bLfcILg7o5pGgbodqKzlGqcRgj3oN/8Bn/RJaOioL/zPSI79tM6ksvTpCgVERGBXq8/r1dUTk7Oeb0p/mjp0qWMHz+ezz77jGHDLrzyhtFoJDg4uMbFq5TmoreUYFcVLEEa9jLR+2AOagHIZOfeKjo6utb2bjAYaNq0aa338fr268lsVpqcdKy26tNhhJxYiEZVevownXQnUBU9tJOhe85WNS9N0DEpSolLo1jLGaj7DYDb73lIvshwpsgrqAiOw6hYCDyRonUaIVxaZoGJjHUfEb1tFgBZfZ6HjtdrnMo9aFKU8vX1JSkpieTk5BrXJycn07dv3zrvt2TJEu6//34++eQTrr9e/oP/VOXE4qdoiqo3ahrFHOQYPmg5c0jTHEIbffr0Oa+9r1ixgp49e+Lj46NRKqGVM/s342MupEANwC/+Kq3jCA+WWWBi9deLADDH9oImdc9DKRpHUdxwAAKyt4EpX+M0wh0FZm4gQKnAEhBDZPteUpByJkWpXoXPeOhHjcMI4bp2ZRby9Oz5RK2aAsAH9lGovSZqG8qNaDZ8b+rUqfzvf//jvffeY+/evTz++ONkZGQwcaLjP2/69OmMGzeuevslS5Ywbtw4Zs+eTe/evcnOziY7O5vCwkKtXoLrO+uYv+GY/cK9z5xBadoagDWbt8lEiR6gpKSE9PR00tPTATh69Cjp6elkZGQA57ffiRMncvz4caZOncrevXt57733ePfdd3niiSe0iC80ph5yFCjNcQOJDQ/SOI3wZI5hP475pIydb9Q4jXeyBMdxwB6LotqqV9wUoj6CKod+FsWNhIuY5kM0sMphz02OJZOZJ4vOCPFHmQUm/rVgCfN0/8aoWCiMv5ahU/4nBfR60KwoNXr0aObOncvMmTPp1q0b69atY/ny5cTFOXrUZGVlVZ/gArzzzjtYrVYefvhhYmJiqi+PPfaYVi/B9VX2lDquRmscBAJj2gPQQs2SiRI9wPbt2+nevTvdu3cHHEXm7t2789xzzwHnt9+EhASWL19OSkoK3bp148UXX+SNN97g9ttv1yS/0FbgibUAmOOHaJxEeDp9eQFX6fY5ful4nbZhvNhqew/HDwd+1jaIcD92G8HHHV9kFMXL8FstNOvYD7MxnCDFRO7uFK3jCOFySk8dYKHu/whSTBB3DSH3LCY2PFDrWG7FoOWTT5o0iUmTJtV62+LFi2v8npKS0viBPExZ9kGaAJm6GAZpvbJVuKOnVJxycasrCtc2aNCg6onKa/PH9gswcOBAfv3110ZMJdxCaR7+Zxxzg5S0GKBxGOHpgk6swqDYKQ/viF9YvNZxvNYqW3cmGr6DgyvAZgW9poefwp2c2IahPI9CtQmlMb20TuOddHosbYbju2cp6SuXEHHlcOkBIrxaZoGpupNFU/KJ//EefJUiTE0743/3J+Aj7aO+5KjAk1X2lLpuYD/tdx7VRanTZFygmCGE8HCHVqKgstfeCluA9r04hWcLquphETcCP42zeLNf1XZYjaEYygvg5DaIq3v+UCFq2Pc9AKvsPWivkzkotRKQeAPsWcpAUskvqdD+vEIIjWQWmBg2ey0mi41gSvjc+BIxygmO2qMov/YDOvmFaB3RLWk2fE80MlXFWHQMAGNkW22zAITGoaIQrJjQl5/VOo0QQisHfgJglb27xkGEx7NZCKxc5bG41VCNw3g3G3ryYip7Ru6XyZJFPVS+X1bYemocxMu1GYJd50u87jTGAlm0SHinzAITuzILMVlsvHl7B9a3fIcOSgan1VAeVJ8luFms1hHdlhSlPJUpH73ZMRmhObiVxmEAHz8sATEAmHJkZyaEV7JZqic6XmXroXEY4fEyNqO3FJOrBmNq1lXrNF4rLMAXfx89rx5JAKB8z3JZ8ERcnNxDcPYwZlXPL/puhGk9FYU3MwZS2rwPAEEZKzUOI4TzVfWQeujDVHyxMGjHE4ScScVuDKHojs94f9qd0oPwMkhRylPlOVbey1LDUQ2u0UDUMMcB6ac/rZUDUiG8UcYWqCjE6teU39Q2WqcRnq5yUu219q6gyOGOVmJD/fl8Yh82qF2xqHr8Cg7x19lL5ThA/LmDjja81d6JOWOvkRM+jRW3GgZA0HEpSgnvk19qxmSxYcDKWz5vEHRiDRj80d3zGe269JLPp8skR2meKu8gAEfsMRoH+V3VMMLm9lOyAp8Q3qhy6N6pZv2xy+5HNLaDjmXkV9tkqKjWEmND+GradVQ0d0xU3c++XY4DxJ+r3GestnenqfSS0lzVMOgmOalQJlNxCO+jx8Z/fN5ihD4Vu94Idy+BVr21juUR5KzAU+VWFqVU1ylKnTvZuRDC+1j2OU4wZh2Ow99HL0MxROM5ewRyD6Aqetbbu2idRuDoMRXY5XoAhujSNE4jXF55IRzfBDgmORfaswS1YK+9FYpq5+xv32sdRwjnstuY7TOf6/XbMKsGzt7wHrQZrHUqjyFFKU+VewBwzaJUgpKlcRAhhNPlHcYn/xBmVc/1t9zDymkDpauzaDwHHL2kCpv1pIgAjcOIau2vBaCXbi86c7HGYYRLO7wa7FbKQ9uSoUZpnUbgmB9uLUkAbP3xYxmCK7yH3U7s+qe4Rb8Ju2Kg+KZ3ieh+g9apPIoUpTyUJcdRlDqpa+E6vREi2gPQWskCVdU4jBDCqSqHYWy1dyI+NloKUi5g3rx5JCQk4OfnR1JSEuvXr69z2y+//JLhw4fTrFkzgoOD6dOnDz///LMT09ZT5Vw0C7PbSa88VxLRloqQ1vgqNgJPrtM6jXBllXPCnYkZpG0OUS021J/b7n4QgGuU3zicJUP4hBew2+H7KYQd+ByrquPk0LdomnSL1qk8jhSlPJHdhr7gGAATbh3hOid/4Qmoip5gxYTBlKN1GiGEM50zN4jQ3tKlS5kyZQrPPPMMaWlp9O/fn1GjRpGRkVHr9uvWrWP48OEsX76c1NRUBg8ezI033khamgsOw6oogWMbAPjZ0pUFY5NcZz8oquelCcpYpXES9+exhWW7DVtlUeqZXbFSWHYhkR36YGvSjCDFxOJPpLeU8HB2OyVfPQa/vo+q6JhqmURRwnVap/JIUpTyRAXH0dnNVKg+BDSL1zrN7wxGzEGtADAWHNY4jBDCaWRuEJczZ84cxo8fz4QJE+jUqRNz586lZcuWzJ8/v9bt586dy1NPPcVVV11Fu3btePnll2nXrh3fffedk5NfhKNrwWamtEkLDqvNZYJkF1O9gteJ1WC3aZzGfXlyYfnMvk3oTWcpVJuQRns+n9hHCsuuQqdD32EkAP1VWbBAeDC7jdIvJhK48wPsqsKuni/zrb2v1qk8lhSlPFHuIQCOqtGg02scpqaKUMe8UlKUEsKLVM4NclhtzhlDc/nGW2Nms5nU1FRGjBhR4/oRI0awadOmi3oMu91OcXEx4eHhjRHxspTuWg7A50VX4O9jkPebiymN7kmR2gRD+VnI/FXrOG7LkwvLamXP2uIWg/hp2lASY0M0TiRq6ODoKTJU96tMx3GZ6tPb8VwbN27EYDDQrVu3xg3orWwW+PJvBOxZilXVMcUyiRU+Q7RO5dGkKOWJ8lxw5b1KFaFtAfAtOKRxEiGEs5TtdKzSk6ImyTfeLiA3NxebzUZUVM3Jg6OiosjOzr6ox5g9ezalpaXcdddddW5TUVFBUVFRjUujU1UMh5MBaH/N7TKhvivS+bCuakXEQ8naZnFTziosO7sNZxaY2JVZiP9Rx/tCbT9S2q8raj0Iu95IK90ZjPkHtE7jturb27FKYWEh48aNY+jQoU5K6mWsZvj8ftj1BXbFwCOWR/nW3o83Vx+SocSNSIpSnijXUZQ6rDbXOMj5zCFtAOkpJYTXsJoxHnGshNZj5L3yjbcLURSlxu+qqp53XW2WLFnCjBkzWLp0KZGRkXVuN2vWLEJCQqovLVu2vOzMfybn4HaMptOUqUbiesoJrataa+/q+OGgFKUuhbMKy85sw5kFJobNXsuDb35DUOF+bKpCSYtBjfZ84jL4BlDavB8AQSfWaBzGfdW3t2OVhx56iDFjxtCnTx8nJfUembn5FL0/GvZ9j1k1MKFiCmv1ffh8Yh++n3yNfNHViKQo5YEqTu8H4KQu1uWquRWhlUWpQilKCeEVjq1Hby7ijBqCT1wvrdMIICIiAr1ef97Ja05OznknuX+0dOlSxo8fz2effcawYcMuuO306dMpLCysvpw4ceKys/8ZtXJy5LIW/YiNCGv05xOXJsVWWZQ6lQaludqGcWONXVh2ZhvOLzVjstiYecVJAH5V22HzkzbsqopbDgIgUIpSl+RSezsuWrSIw4cP8/zzzzd2RK9z6kwux968ieATqzGpvjxgeZKb7nyAldMGclV8OImxIVKQakRSlPJAusrhe6OvHeJyjad6+F5JJphLNU4jhGhsJb99DcAKW09QZJfjCnx9fUlKSiI5uWYvleTkZPr2rXsSzyVLlnD//ffzySefcP311//p8xiNRoKDg2tcGltQxmoAKhIuXDAT2jpDGMVhnQAVDskqfPXlrMKyFm34iuLNAKy2yaIYrqy45WAAArJ/gXInDM32MJfS2/HgwYM8/fTTfPzxxxgMhot6Hk2G0buhrKxMmiy5jX7KDiz6Jjxkn06qvhtXJYS73Lm0p5IzBE9TXoSP6QwAfjEdNA5zPptfGHlqkOOXPJlXSghPlnm2BNOObwBYo1ztcj03vdnUqVP53//+x3vvvcfevXt5/PHHycjIYOLEiYCjh8S4ceOqt1+yZAnjxo1j9uzZ9O7dm+zsbLKzsyksLNTqJZyvNBf/HMfE2cUtZa4NVxUW4Iu/j55P8hzHKGV7ftI4kftxVmHZ2fyoIDpvKwAbdUmyz3BhluA4DttjUFQrHEnROo7butjejjabjTFjxvDCCy/Qvn37i358LYbRu5vsjIOULRhG6NnfyFcDybj+E2ZN+7sM1XMyKUp5mspeUmfUEOy+jf+NVn2FBfhylFgAzh7frXEaIURjqji6hWZKIRZDEC9M+bvs3F3I6NGjmTt3LjNnzqRbt26sW7eO5cuXExcXB0BWVlaNyVbfeecdrFYrDz/8MDExMdWXxx57TKuXcL5Dq1BQ2WOPwxroegt9CIfYUH8+n9iH9Wo3ACr2JZN5tkTbUG7IEwvLfXW70dsrsAa1YP7Ue2Wf4eJS7N0cPxxcoWkOd1Tf3o7FxcVs376dRx55BIPBgMFgYObMmfz2228YDAZWr15d6/NoMYzereTspenSG2ijnCJTbcq99hfwa92b2FB/+fxxsovr+yfcR+7vK+8FaBylNrGh/ujaXgmH92HN2ad1HCFEIwo+5pjfpzR+GLFNZYJzVzNp0iQmTZpU622LFy+u8XtKSkrjB7pclSu5pdi7MkDjKOLCEmNDePXxCVjmzSbMWszZ49shfJDWsdzK6NGjycvLY+bMmWRlZZGYmHjRheWHH364+vr77rvvvPaulSG6NAAMHa8lNqyJxmnEn1lj78Z4fsR2IJns/DL5P6uHc3s73nrrrdXXJycnc/PNN5+3fXBwMDt37qxx3bx581i9ejVffPEFCQkJtT6P0WjEaDQ2bHhPkbEVPrkLn/ICDthjybrxYxa26yjFKI1IUcrT5OwF4IC9Bd01jlKniPZwmOoCmhDCA6kqwcd+BKAo/lpCtU0jPJ3dDocd3xSn2KQo5Q5iw4MobNmfkKPLsez7mV2R3QkL8JUTgnrwqMKyqjJI/5vj53Yjtc0iLso2e0esen8Mpdk8POcD3p52n7Tfepg6dSpjx46lZ8+e9OnTh4ULF57X2zEzM5MPPvgAnU5HYmJijftHRkbi5+d33vWibpkFJgBiT6/F/vn96KwmyiKTuDPjIT5u3lrevxqSopSnOePofXRAdd2ilE+0Yx6Js8d3YSkwyQeAEJ7o9C58i09gUn0pbjFQ6zTC02WlQ1keFkMAv5a30zqNuEj2tsPg6HLK9/7MLb9dg7+PXubx8FJlWftIVHKx643o4vtpHUdcBDM+nG7ai9icFPrY08gvvVvabj3Ut7ejuDyZBSaGzV7LGOVnntUvRqfaSVF7YOn3LoUZe7SO5/VkTilPk+NoVAfsrjuRXUSco6IfTxb5xSaN0wghGkNR2pcAbKQroaGh2oYRHq9ol2Oy7NUVnfDxMcoEyW4irMt1AHTVHWHeLa0wWWzkl5o1TiWcLbPAxOrvPgbAHNsbfF1xAgpRm72BVwMwSJ+ubRA3NWnSJI4dO0ZFRQWpqakMGPB7P9/FixdfsIfjjBkzSE9Pb/yQHiK/2MST6iL+pXsPRbXzmXUgEyqmsOO07HNcgRSlPElFCRQ4KuoH1FiNw1xAaBx2vR9+igXfYvkGQAiPo6oY9zlW3YvtO1q+ORWNTn/EMXQvqsf10tPGnQTHQFQXFFS6VKRqnUZoJL/UTF/VMZ+UXycZuucOqlbRnLHXcb6RpBxAV+E6k+YLca5TOblEfP9XHjA4vsD6t2U0T1n/hhUDb64+hL+PXr7M0pgM3/Mkufsd/6ghlPuEuW7j0umpCGuHf+5O/M7uA7ppnUgI0ZCyd2IsPEy56oPafpTWaYSnMxXQJOdXAPw7jZCClLtpNwxO7yToRApwp8ZhhBYUq4leusrFb9oO0zaMuCixof6snDaQ/FIzJZ++QWDxYQIz10Pre7SOJkQNWScOU/C/27hCOUa56sPJwa9zXbubuKfyPDm/1CzzGboA6SnlSSpXsztgj2XB2CSXblzl4R0BMJ6VFfiE8Di7vgBgtb07dt8gjcMIj3d0LYpq45C9OZYg1x26LurQdjgAgSfXomDXOIzQQsCpzRgVC+bAFo7FcIRbiA31JzE2hPL4oQAEnVijcSLhzTILTOzKLKyezBwgZ/8Wwj6+1lGQMjal6C9f03bQWBJjQ4gN9a9+D7vyObO3kKKUJzlTufKe2oKmrtpLqlJ5mGOyc2vW7hofHkIIN6eqWHc4ilLf2vpqHEZ4g9I9KwDYRFfX7SEs6tbyajAGYyg/y5XKEa3TCCfLLDBhP+BowyUtBoKiaJxI1Fdxy0EANMlIcayEKoSTVU1ifsObGxg2ey2/HDvL3p8XEvzJDfiV53DAHsvxW78lstM1WkcVdZCilCfJqSpKuf43xT7NHZOdl2fuZNjstVKYEsJDnNm7AUNxJiWqH1v0SVIkEI1LVfE56phPqtuQO+TbTnek94HWgwAYpPtN2yzCqapOJJXDqwBQ2w3XOJG4FL6t+1Gq+mEsP0POoV+0jiO8UH6pGZPFxuQhbTFbzOz43yQ6bX4SP8XCKlt37lFfIjC6jdYxxQVIUcqTnDN8z9VFtO4OQGvdaewWk6y2I4SH0O129JLKbzmcH6YNlyKBaFxn9uNbeopy1Qd9Qn+t04hLVVmMGKT/jTw5HvAa+aVmIq2ZJOhOo+p8aJoo80m5o9iIUEwtHZ+/6v4VGqcR3qy1v4kPfWYx3vAjAEVXP07HqT/w9bRRcjzq4qQo5SnKi6DoJOAYvufyAqPAPxwFO+2Uk1qnEUI0BLuN4CM/AGDrfLscAIjGd2glANvsHVENfhqHEZescnLrrsphnv5wjfSe9iIDK3vHKa16g1HmIHRXFfFDADAcXSXtV2iis3KUERv/Ql/9HkpUPzKGvUPwdTOIDQuQ41E3IEUpT3HG0UvqtBqGxSfE9YfMKApEdQago+6ExmGEEA3i2Hp8TGfIVwMpjZVx+8IJKof9rLV31TiIuCzBzSEqEZ2icpXtN+k97UWqh2zKqntuTd9hBACheencPvsHKUwJ51FVfHZ8zDLfGQSUZ3FcjeZu+0voE2/WOpmoBylKeYosx059tz3O5VfeqxZ5BQAdFClKCeEJyn75EICf1d6EBgdqnEZ4PHMZHNsIQIoUpdxfG0dPi/66HRoHEc6iWMvpo9vj+EWKUm4tumVbLE07oldUrralSWFZOMWpnFyy37+fDlun46dYKI8fgs/f17Jg2r3ucS4sqklRylNk7wRgjxrn8ivvVYuSopQQHqO8CL8D3wPQ/tqH5GBANL7jG8FWQZl/DIfV5lqnEZerrWNZ+f76naCqGocRzhCQvQ1/xYylSVR173nhvnwqe0sN0EthWTS8zAJTjR54B3duw/R2f6KPfY1NVci+6in8xi2jeXS0HIO6ISlKeYpsxw5gtz1e2xz1Eek4AOmgOyETmwrh7vZ8g85WzmF7DL6trtY6jfACJbt/BuDr4o74+xhcf9i6uLCWvbHr/YhW8jHmH9A6jXACwxHH8NuSFoMc0zoI91ZVWNbtIK+kQuMwwpNUrdRZtWJ7/sb3aPHF9bRRTlHhH8XZO78k+vpnQCelDXel6f/cvHnzSEhIwM/Pj6SkJNavX1/ntllZWYwZM4YOHTqg0+mYMmWK84K6OpsVTju6P+9R4zQOUw+RnVBRiFIK+OeHq2X8uZupT/tNSUlBUZTzLvv27XNiYtGo0j8B4AvbQDm5EE7hc3Q1AG363MLKaQPlm1F35+NHaUxvAAJPrtM4jGhsmQUmyvc5Vmqzt5Ohex6hVR/sBn+ilALmfPSVHNeLBpNfasZksaG3FNPkh4cJS34cf8XM2ehrMD68kWaJQ7SOKC6TZkWppUuXMmXKFJ555hnS0tLo378/o0aNIiMjo9btKyoqaNasGc888wxdu8rcETXkHgBbBTafQDLUSK3TXDxjIErTtgC0sx2S8edupL7tt8r+/fvJysqqvrRr185JiUWjyjsMGZuwqQrLdQOlx4pofPnHMRYexqrqCLpiqBSkPERJiwEA6I7KCnyeriT7CG2VTFRFT9PEEVrHEQ3BYESX0B+AXnaZV0o0jMwCE4dySuip7ONH3+mEHVyGTVV43f4XTKM/g8BmWkcUDUCzotScOXMYP348EyZMoFOnTsydO5eWLVsyf/78WrePj4/nP//5D+PGjSMkJMTJaV1c5XxS5eGdUN1tRGbz7gAkKkc1DiLqo77tt0pkZCTR0dHVF71e76TEolH99ikA6+1XMnPscCkQiEaXv/MnANJpT0hYhMZpREPRtXN82x1yeivXzU6WwpQHCzyZAkBZZA/wD9U0i2hAbaqG8O3UOIjwBJkFJq6dvYoTy/7JUt8Xaak7Q6ExhtHmf9Hj3peIDQvQOqJoIJpUMMxmM6mpqYwYUfObkREjRrBp0yYtIrm3yvmkTjdxw14nzbsBcKXuiLY5xEW7nPbbvXt3YmJiGDp0KGvWrGnMmMJZ7LZzhu4NcJ+FFoRb0x92zEXTtOt1UgT1IFGtu2ELjMFPsZBo2yM9LTxY0IkUAEpaDtIyhmholatoXq3bj2KVorKov3MnNC/N3MtHyr+YbPgavaLylX0g/QpfZLehM20jZZVnT2LQ4klzc3Ox2WxERUXVuD4qKors7OwGe56KigoqKn6faK+oqKjBHtuVlJ9Mxw+YfyAQfx+9ew2diekGQKLuKAfl4NMtXEr7jYmJYeHChSQlJVFRUcGHH37I0KFDSUlJYcCAAbXex1var9s7uAKKTmL2CSG5PImJWucRns9qJuDURgBsrWUeCY+iKOjbDoX0jxigkxW8PNY5bbi4xUCi/mRz4UYi2mEOjMVYkklA1haIu0XrRMKNVE1ormBn09DDtF3/EjpdOVZjCIab/sPVsdfyaamZsABf+ULKw2g61kv5w2S4qqqed93lmDVrFiEhIdWXli1bNthjuwxVRX/a0UX2umEj3G+y15grUVForpyVyc7dTH3ab4cOHXjwwQfp0aMHffr0Yd68eVx//fW89tprdT6+V7RfD1C+eSEAi0zXoPPxd6+iuHBPJ7eht5SQqwZTHpGodRrR0NoMBmCADP/xXCe2oLeUckbasOdRlOq54QJPrtU4jHA3+aVmoq0nWazMIDTlWXS2ctbbEjl0ezJ0vpXYUH8SY0Pc61xXXBRNilIRERHo9frzelXk5OSc1/vickyfPp3CwsLqy4kTJxrssV3F6WO78TEXUq760P7KXu7XSI1BKBGOYYcy2bl7aKj227t3bw4ePFjn7d7Qft3e2aMYjzmGYbYe+Yj7FcWFezrsWHVvvb0LKG42j6L4c60Ho6LQSZeBoey01mlEYzi0EoB19iulDXugkhYDAVlFU9ST3UbTHe/wo+/TXK3bj0XfhD09nmec5WmsAdFapxONTJM9ga+vL0lJSSQnJ9e4Pjk5mb59+zbY8xiNRoKDg2tcPI3l+DYAKpp1Ibapm76+yiF8XRSZV8odNFT7TUtLIyYmps7bvaH9urvijf9FQWWDeiVXdOkuBSnhFOYDjvmktipdpWeeJwpoiimiCwCBmRs0DiMaRWVheZ3tSo2DiMZQ0rwfVlWHX8EhsjPq/vJRiCqnD6dRNn8IMVv/Dz/FwjpbFwaVzuK6TR3cbxEvcUk0+1+eOnUq//vf/3jvvffYu3cvjz/+OBkZGUyc6JiRZPr06YwbN67GfdLT00lPT6ekpIQzZ86Qnp7Onj17tIjvMvxz0gGwRPfQNsjlqFyBr4tOVuBzF/Vtv3PnzuXrr7/m4MGD7N69m+nTp7Ns2TIeeeQRrV6CuFzWCvx3LwEgdMDfpSAlnKPsLD6nfwPg5tvGyPvOQ/0+/Ed6WnickpzqVaM32LtoHEY0hpDwZuygLQBv/2+hTM0h6mYxUbT8ecI+GEqTM+kUqU140vI3TKM/5+UHrsffR+9+8yWLS6JZUWr06NHMnTuXmTNn0q1bN9atW8fy5cuJi4sDICsri4yMjBr36d69O927dyc1NZVPPvmE7t27c91112kR32X4n0kHoCyym6Y5Lsu5K/CpqrZZxEWpb/s1m8088cQTXHnllfTv358NGzbwww8/cNttt2n1EsTl2vUlhvKznFLDof1IrdOISzBv3jwSEhLw8/MjKSmJ9evX17ltVlYWY8aMoUOHDuh0OqZMmeK8oOc6ug4FlQP2WIKatdImg2h0VUUpvxPryMwv1TiN63LLNnzEMc/QHjWeMp9wOdn0QLGh/rTtczMAvdV0mZpDVMssMLErs9BRqDzwM7zdi+Btc/FVbBwO68/win/zuW0QsWFNGNi+GSunDZSpIbyEpv3hJk2axLFjx6ioqCA1NbXGKlyLFy8mJSWlxvaqqp53OXbsmHNDuxJLOX55jp5ipmbdtM1yOWK6oSoGopV8SnKkt5S7qE/7feqppzh06BAmk4mzZ8+yfv16ry8ouzVVxbLhPwB8ZB0OOk0WchWXYenSpUyZMoVnnnmGtLQ0+vfvz6hRo877MqhKRUUFzZo145lnnqFr165OTnuOI445zKSHhWczJvSmVDXiV5HHI3M+lJ4WtXDbNlw9dK8LC8Ymycmmhwru7Piy6hrdLrBbNU4jXEHVynoPvvkNe16/ET65CwqOk6U2ZbJtGoeG/pfThNe4T2yov3xGeAkZpOnOsneis1vIVYOxBLnxymS+TbBEOk4wln39hRx8CuHicnf8hE/uXkpVI8t0I+Sbbjc0Z84cxo8fz4QJE+jUqRNz586lZcuWzJ8/v9bt4+Pj+c9//sO4ceMICQlxctpzHHYUpdZLUcqjxTYNQdfa8UXH1XbpaVEbt2zDqortUNVCBYk0lX2H54rtgdUYQohShiVju9ZpXFZ9ejt++eWXDB8+nGbNmhEcHEyfPn34+eefnZj28hQUlTDW/jVrmzzFcOUX7IqBg20fYGjF/+OOsX8nNqyJ1hGFhqQo5c4yHR/y6fY2oCgah7k8vgmOCbKvtO+Tg08hXJxx2zwAstvcyZfTrpdvsdyM2WwmNTWVESNG1Lh+xIgRbNq0SaNUF+HsESg4jl3nw1Z7J63TiEbm39Hx/hyg26FxEtfjrm349JF09KXZlKs+7NJfIV9oeDKdHnMrR2F548+fyRfOtahvb8d169YxfPhwli9fTmpqKoMHD+bGG28kLS3NycnrSVVh7/e0/mwI//RZgq/dxDZ7B64t/z+G7xqG6hNA28hAwgJ8ZQ4pL6HW7TAAACYhSURBVCZjLtzZ8Y0A/Gpvj9sPhGrVC7a8TU/dAWxaZxFC1C17F0GZ67CpCtarJkpByg3l5uZis9mIioqqcX1UVBTZ2dkN9jwVFRVUVFRU/15UVHR5D1jZS+psWFfKyvwu77GE62szBICeuv0cspQBGvbQczHu2obtBx29pAojr2b5PcNl/+HhmnQaAQe/oy+O3o7y/13Tub0dwbEo0M8//8z8+fOZNWvWedvPnTu3xu8vv/wy33zzDd999x3du3d3RuR6yznwC03W/IvArM34A2fUUIr7P8t9a1uAQeH9sUm0jQysfm+snDYQQN4rXkiKUu5KVeG449uwLfZO7l+UatkbgA7KCfZVFCIHn0K4qI1zAfjR3ov4YJlo2p0pf+hhq6rqedddjlmzZvHCCy802OOZ9q/CH1icnSDfpHqDpm0wB7bAWHKSgOytEH+L1olcjru14cBMx9Ake+vBctLpDdoMBaCrcpj9FQXIsf3vqno7Pv300zWur09vR7vdTnFxMeHh4XVu0+BfDv2JzAIT+aVmDGU5NN32/4g48Bk6RaVc9eG/tuvpdvcL9O8cz8qejp5zf/wckM8F7yXD99zVmf1Qlodd78dOtbXWaS5fUBTmoFboFJUmOS7eDVUIb3XmAOquZQAs4mYpCripiIgI9Hr9eT0qcnJyzut5cTmmT59OYWFh9eXEiROX/mB2G74ZjhPaq4bcJqvxeANFoaRFfwACT67TOIxrccs2bK0g4NRm4PfVFYWHC4mlPLQdekWlZO8qGcJ3jobo7Th79mxKS0u566676txm1qxZhISEVF9atmz4OYgzC0zVl1tm/8iq+Y/R8qN+NDu4FJ2iciTqWq63v8485W5axzper0xgLv5IilLu6vgGAAojemDxkA5vpdFXAdAk+xeNkwgharXu3yiqnRW2JB4de6ccULgpX19fkpKSSE5OrnF9cnIyffv2bbDnMRqNBAcH17hcslPp6M1FFKlNaNq+t7z3vERJrKN4EXhyrcZJXItbtuGMLehs5eSooVSEdWiwjMK1WRMGA3B487cMm71WClN/cKm9HZcsWcKMGTNYunQpkZGRdW7XoIXlWlStqHfD7BWUrHqNZN0jPGb4igClgnR7G26rmEHZTQv5YNod8mWSuCDPqGZ4o8qhex9mtfCYYQxl0b0IO7gM48kNWkcRQvzRmQOw8wsA/mO9nVc94DPHm02dOpWxY8fSs2dP+vTpw8KFC8nIyGDixImA40A2MzOTDz74oPo+6enpAJSUlHDmzBnS09Px9fXliiuuaPzARxxz0Wyyd6aFTt/4zydcQklsP2yqgl/BISg8CSEttI7kMtyvDVetnJlIBzdfnEdcvMArRkLaQm4O2sv0fKvMLVXpcno7Ll26lPHjx/P5558zbNiwC25rNBoxGo2XnfdcVYXF2FB/CopKuN3+E48aviJyZwEoUB7ajtM9n+SW7wMApXpbIS5EilLuSFXhmGOS842WDiz4a5JHNHZ9u8GwHgLO/Map06dp3oBd0IUQl6ds5cs0QaUobgS798drHUdcptGjR5OXl8fMmTPJysoiMTGR5cuXExcXB0BWVtZ5KwCdO5Fqamoqn3zyCXFxcRw7dqzxAx9OAWCDPZG/NP6zCRdhN4bym9qGHsohx0T3PcZqHclluFsbNh9YhS+wVelGb/lSw3vE9QW9kSambNoop7RO4zLO7e146623Vl+fnJzMzTffXOf9lixZwgMPPMCSJUu4/vrrnRG1hqqeUT5YWTsym3Zb5/KSj6P3VaExhheKb+aB2/8BOj0gnQzExZOilDs6sx9KHEvq7jO0p21koNaJGkR0q/aUBcXTpPgYlkNrIaruMdJCCOfJ2b+FyP1fAbA66gHYb9c4kWgIkyZNYtKkSbXetnjx4vOuU1W1kRPVoaIETmwFYL29ixSlvMx6+5X00B2ibF8yTaQoVYPbtOHSXHxzdgBwy+33eMQXqeIi+TZxFKaOrGGgbgcwWutELqO+vR2XLFnCuHHj+M9//kPv3r2re1n5+/sTEuKcSeQLCou4y76chwzfEbbyLABn1BDesN7Kp+VDMPgYmRbkaN/+Po5ezZ4wmkc0PilKuaHCncsJAbbRmY8netb4XFPLATTZc6xyhRYpSgmhOVUlIOV5AL6y9ePxdXaPGTIs3MTxTWC3cFJtRo6hubz3vEhYgC/blK7Al5TvX01+fimxYQFaxxL1dSQFgL32VgRHxGqbRThf26FwZA39dTvIKzVrncZl1Le34zvvvIPVauXhhx/m4Ycfrr7+vvvuq7UI3ZBO5ZwhYMdiOqQu4AWfXABMxmYc7ziBW7e2Y+7YfowO9ScswLf6vHTltIGADN0TF0eKUm5If2QVAM2TbqBtrGctr1oS25+mez4gMFO6fArhEvYvJyBrC+WqD+E3vcT3zdvUOOgQotFVzkWzzpbIgnE95b3nRWJD/fn3lAewzHuVcFsxqft/Ibb3IK1jifo6XNmG7V3op3EUoYE2Q4Fn6a3bS+8PN7N82nD5HK9Un96OKSkpjR/oj4pPU7R+Pk22LiREKQXghL0ZC2w38kX5ACq2Or4kig31J/EP56TyfyzqQ1bfczfmUppkbQPA3maoxmEaXmnzPlhVHcbCI5B/XOs4Qng3qxmSnwPgXdsomjZvQ2JsiBxoCKeyHHR8EbPB3oWm0kvK68Q2DcbaylHKWLN8qaze5W5UFduh39uw8EKRnSAwGn/FzBW2feRLbymXd/rgdkqXPoj6emeCt71OqFLKYXsMP7Z9jsHm2QwY8w8WPnAN/j566T0vGoT0lHI3R9ejs5vJsDfDHNJa6zQNLiQsgjQ6cBV7KUj/htDBj2odSQjv9f/bu/PwqOq77+PvyUZCVkggQAwQFkEIoATEWFJQNNzYKihtsVoK+rRViwi4VNxuWpcbbPURd+slbvVp4VarxaWW2LLJohAJu7JFAxiICZANMklmfs8fYTEmQZQ4v3NmPq/rykVy5szwmTPnO3POd875nVWPQ9kOykwCL3guZ5w2OiTAivcU0rnsU/zGw7rwgdrwDVExfUZBYR7nmo26epfL7C/cQGpVMV4Tycbw/qrhUOTxQI+RsGE+OWEbbaeRlvj9sCOPmuWPkbr7xBkra/1nMq9+DP/yD8W/KYyYyPDjX1DqFD1pLWpKuc2n7wCw1D+Ic4LwkrppSTEcyboCPn6AyG3vgJpSInYc2IVZ8kc8wP11V/Pw5BxtdEjA+bb/B4Dydv15bfKPtQ6Gqh4XAHBu2CfsrK8BgmvogmDmP3qkY3nHobxztU7bClk9L4QN8xmuppQz1VbDsyOhdBvRQL0J45/+c5lXfwmTf/YT7s5oz93AweraRkM4qJ6ltej0PTfx1ePb8jYA//GcF7TfNvnOvASAtvs+gupSy2lEQpAx1Lw5A4+vhhW+/rwXPiJorvIp7tJw0Quo7x5cF/WQb6lDH+raphLtqaPt/rW208i3ELenoYb9GSNVw6Gsx0gAMj2fEV5zwG4WaSoqFpK64Y+KZ3vPyYzwPsLUupsoML3o1TGOtKSY4+NGqY7l+6CmlJt8/gHhNQcoM/FMvvoXQfumENepJ1tMdzzGz8GCf9iOIxJ6Cv5KdNESvCaSw7l/4v1btDMhFhhD7NGLXlSl5VgOI1Z5PFSlDQdONCrFBeq9xBavAqDqjB9aDiNWxadS074vYZ4T7+viLPtyHmDokce5eHMue+kAoPGiJGDUlHKRqnWvA/Av3xCS49taTvP9SUuKoe3AsQBEfPKW5TQioWXf559Q/85tADxpxtNvwGA1pMSOkq1EHvmSIyaKw6lZttOIZdXHm1LaoXWN3R8RVn+EL00iNe372k4jlh37ckE17EylEZ0oq4ti7oSzWTHzQlbMvJD3b9FRyhIYakq5xN6ycrwb3gSC+9S9Y2r7jgMgds8yivfqKnwigbD3QCV7n/8lEfXVrDV9yf31bG2MiDWHNi8CYC1nkZQQbzmN2HbsSKno0k0UF++1nEZOyc6GMeE+8GeCR7scoe5EU2o5GGM5jbTkq6fraRtQAkWfEC5xqOAtkj0VHGnTgT/MmBL0bxKxaWdRYHoTZny8/Oc/6hLQIgEQufyPZHk+pS4iljOufZnM9Pa2I0kICy9cAkCXwWOC/jNPvll8h3S2mXQ8GB586lltF7hA7dFBzj/0DAr6L1Plm1V3HobXRBBVtRfKdtqOIyIOoqaUC+w9dITSZc8BUD/gStLaB/83xmlJMXQb9SsAxrKUg1Vey4lEgtzWt+i47jEA9uXMplO3PpYDSUir9xJbvBoAf8YFlsOIE6QlxdBl8BgAzjXrOVhdazmRnNThA0Tu3wDA2CuuVmNZSEpM5GMaTuM8tOk9y2lExEnUlHKBypIihlMAQHz2NXbDBFC7oRPwh7ehb9huYkrW2Y4jErxKPsH39+sAeMl/CWGDfmY5kIS8r4xF49VYNHJU3FkXAzA8bBNlako5264leDB84k8nvkO67TTiAGlJMaSe/V8AhB09ElZEBNSUcoW2Bc8T7jFUdxoGyT1txwmcmHaU97wMgORN8yyHEQlSFV9Q/5crCK+r5kPTj6xfP65vtMW+XYuBY2PReCyHEcfodj4mLJKuYV/ywF/e0Sl8TnZ0PKnl/gGWg4iT+DNGAhCzdyV7yyqsZhER51BTyuG+KPmSpM0vA1Az9AbLaQKvLPP/AJBY+C4c2m05jUiQOXIQXhlPROVedvo7Uz/+RTLTU2ynEoGdR5tSPu3Qyle0icOTfi4AQ/wbdAqfUxlzoobVlJKviOk2mIMmnsj6am6b+7wayyICqCnleJ6PXybBc5jDCT1IPmes7TgBF9P1bFaZTDzGR9WSR23HEQkeRxtSlGzhSHRHJtXNJDG5k+1UInD4AHzRcMr2B/5My2HEcXqMBGB42Ea7OaRlZTugYg/+sEg+9Ov0WzkhrV0sbfpcCGhsOBE5QU0pJ/NWkrL+aQAODroOwkLv5UpLiiH2wlsBiNnwIvuKtllOJBIEqr6EFy+FvfkcMnGMK7+ZsohOujqSOEPhMsBQEd+T/egKkPI1PRoGvj8/bDP4fZbDSLOOnrr3oa8Pnsi2+myRRtr2vQiAHDWWReSo0OtyuMnKJ4g88iWF/lQO9R5vO401yQNHs9r0J9xfx6rnbtWhviKnYf+ujXifvRj2b+RLk8gv/bO485qf8P4tIzSWlDhC9db3AXjtYG9iIsO1QyuNdTkHX1QCSZ5qYso22U4jzTnalFpan8kzE7P02SKNHW0sD/LsJKxW40qJiJpSznXwM/wrGk5Xm2uuIikhznIge9LataXHz/8EwFjPMko2L7OcSMSdSgveJealXNpUFLLHpPBL/+/5n+snMOLMDtppEMeI/HwpAGf9YKyapdJUeATVnbMBiN273HIYaaK+Fj77AIDl/oEkq6ksX5eUjjexBxEeP7FfrLKdRkQcQE0pJzIG3ppGWP0RPvT35Ypf/DbkN8o79v0B1f0mEOYxJCyazt7Sg7YjibhHfS2Vb99N8ptXkeA5TFn7wVROXMRzt/yczLRE2+lETjhQSFRlEXUmnMS+akhJ86rShgMQXrhUR087zZ41UFuFN6o9W0xX22nEoarSfghAxGdL7AYREUdQU8qJVj0Ju5bgC4/md3W/ITmuje1EjhD74znURqfQ0/MFLLrHdhwRdyhez5GnLyB+7eN4MLzqv5Caq97grF49tcMvjnNw0yIA1tObxHYaT0qaF967YaDkhC/z+fHDi9SYcpCKLQ01/N6RvkRHRur0W2lez4ZT+Oq3/Vv1KyJqSjnOriWQ19Bw+Z+6qyiJSNMH+jFt21OZ+38BSNv2Fw6ueMFyIBEHqy6Dt6Zj/jyCmLJNHDTxbM55kvNv/itpKUm204k0K6yw4TLyyQP/S01TaVFq9/7Ux6fRxlPPAN9mXcHLQSIKlwCQPuRHOv1WWpTc/0KMJ5xunn1U7dtpO46IWKamlJMUrYb5V4PxU5Q+jnm1ozRA5NckDx7LZ5lTAUh8/xbK1rxqOZGIw1SVUPnWnfjnDoD8F/BgeNv/A/b/4j/0H/ULvZ+Ic/l9xH6xsuHXjJFWo4jDeTxE9Go40uIHYRrs3DEOHyDmy/UAtD3rYn3eSMuiEzjc8RwA4jQ2nEjIU1PKIcrW/h3fy5dDbRWrTCYXbx9HTGQEvTqG7gDnLYkcdQcL/TmEGR8Jb1/HF3lPNIzDJRKqjIGi1VQv+DW+RzKJz3+SsLpqSuP78jPvPcT/4iX69j7TdkqRk/uigAhvORWmLUc6DLSdRpzu6BW8ctSUco7CpXgwbPOnUR/byXYacbiqtJyGX3Yu1il8IiHOalPqqaeeIiMjg+joaLKysli+/OSd8qVLl5KVlUV0dDQ9evTgmWeeCVDS71FNBWWvTiP57WsIrz/Mcl8mv/X/jmevHa7DnluQ1i6WrOnz2ZdxOZEeH11W3MXhv02Gyv22o4UU1a9lfj8UfQh5/03dY1nw/Ghit/4v4T4vBf6eXFt7K0O+vIeNEZlqbkuzHFfDuxouI7/S3x/CIlr3sSX4ZIwAoF/Y51SUFVsOY4fjanhnw+m3y/1qKss3C+s1CoC2e1eQ+3BoNqYcV8MillhrSi1YsIDp06dz1113sW7dOnJychgzZgxFRUXNzl9YWMgll1xCTk4O69at48477+Smm27i9ddfD3DyVnLkEOXv/wnv3MEkb34RgD1nTqLdb/7B27fk6hLt3yCtfRydfvkCu86+DZ/x0Hbbm/gey6Lynf+Gyn224wW9kK9fG2oqGk7x/WAu/O3n+P7YE57PhRWPEnlwJ4dNG173j2Tdxf9LhxkfcN/vbuXtqTlqbkuznFjD3k//DcCHnoEaS1G+WVwHalP6A/D6a/8v5HZoHVfDxnylKTWgdR5TglqHPtn4oxJo56miZ/2OkBsbznE1LGKRxxg75z0NGzaMwYMH8/TTTx+fdtZZZzFu3Dhmz57dZP7bb7+dhQsXsnXr1uPTrr/+etavX8+qVatO6f+sqKggMTGR8vJyEhISTv9JfBv1Xti/Cfbkw448/DsXE+avA+Bzk4q55GG6D7s0sJmCwN5DR5j28PPM8jzLgLDPADCeMKo7nUdl1ws40nEw0V3PoUuHZCv5rK5z36OQq99AqPdC9ZdQ8QWU74GKL6gq+QxTuo3og9uIrG56JECFacti/9ks8wzh8gnXkJHWWQ2ob2nT3nJ+/PgHvD11OJlpiY1uC+Z1znE17K3C/2B3wvx1fHjp+wzLGvrdnpiElkV3w8rHWVA/kv43vKwatlnDpTvgiSxqTQTn+efx1i2j9Xkk32z+1fDJ2/yx7mdc8tuHVMMWa/hk20MiJ9Ma29JWjo+vra0lPz+fmTNnNpqem5vLypUrm73PqlWryM3NbTRt9OjRzJs3j7q6OiIjI797oIpi2LMGjL/hB9Pwjc+xvxv9fuz2r97W8Hf54SN4aqtI8NSAt5LDlQcxFcVEVe0honofHk70/8KAT01XTPaNxA+9krRkFf93kZYUw6O3XMvBqqvY9Om71C6by2C2EVe8krjiE+uSN6Yj9QldqY9JwdcmCV+bRNrEJpEQFwvhURAeCWGRDb+HhR+9lwc8nhP/mcfTMO2rvx+7PTUTknsG4ilb57j6BSjb2dD0Pd5jP1qXx//lxN9f/b3Zf5u7f3O3NfM4AP76hgaTr/Zr/3qhvhbqa6g5UoX/cDlhteWEe8sJr60gzOdt8rS+ftLdfpNEgb8Xa/x92BTWl99eNZ6eCXEMiY3Sxr+cMkfW8OcrCfPXsdvfgdjU3qf3WBI6eoyElY8zPHwjB0NobElH1vCuhqOk1vrP5JGJP9BnkpyaHiPhk7dDbmw4R9awiEVWmlKlpaX4fD5SU1MbTU9NTWXfvuZPvdq3b1+z89fX11NaWkrnzp2b3Mfr9eL1ntjRKy8vBxo6do18uhz+/qvv8lQaOda++Nqjc+yA8oMmlo3+DNb5e7M8bAj3XjuOfl0Sm88kpyw+DOITwmHopXzR+yLySwqJ//x92u7PJ7pkHVHeA+DdD4f246FhpT+24rfaUh81C879dZPJx15XSwckfi8cV78AH/8d/nPft30qjlNnwikhiWLTnhLTjjJPe7KHDiG8Qx/2t+nKjX/fBcDcK8/hJymxdDm+0V9HRUWdveAuVlVZgd97mKrKCioqPI1uC8b6BYfW8MZ/gdfwr/o+ZFZVUlGh67DIKUjKxF8bQbwpZf/eDVQknN3oZtXwCYGq4ffr+pDrr9F2rZyajkPBa+htPmHngf1UxOtz2FYNn2x7SORkWmNb2upIoh5P49DGmCbTvmn+5qYfM3v2bP7whz80mZ6env5to7aSSmAfsAp4mbw/3WQph7S6ObcCt7Z4c2VlJYmJwXU0XOjVb6AcAj77yt+vNpnjR38KUJQQkj235duCsX7BqTX8LjzU9SS3i7RgzogWb1INtzx/c9OP+W41/BKzHn7pJLeLtODBPi3epBpuef7mph/zXWr4ZNtDIidzOtvSVppSKSkphIeHN+kEl5SUNOkAH9OpU6dm54+IiCA5ufnxgu644w5uvvnm43/7/X4OHDhAcnJyk+KtqKggPT2d3bt3B905y6dLy6Zl37RsjDFUVlbSpUsXC+m+H06sX9B6ejJaNi072bIJxvoF59ZwILi1FtyY2wmZVcMnaDs6eITSslYNn6AatkvLp2WtsS1tpSkVFRVFVlYWeXl5XH755cen5+XlMXbs2Gbvk52dzVtvvdVo2qJFixgyZEiL59C2adOGNm3aNJqWlJR00mwJCQla0VqgZdOyky2bYPtmx8n1C1pPT0bLpmUtLZtgq19wfg0HgltrwY25bWdWDTfQdnTwCZVlrRpuoBp2Bi2flp3WtrSxZP78+SYyMtLMmzfPbNmyxUyfPt3Exsaazz77zBhjzMyZM83EiROPz79r1y7Ttm1bM2PGDLNlyxYzb948ExkZaV577bVWyVNeXm4AU15e3iqPF0y0bFoWqsvGafVrTOi+FqdCy6ZlobpsnFjDgeDW19uNud2Y2U2cVsN6vQNHyzo4qIbdRcunZa2xbKyNKTVhwgTKysq49957KS4uJjMzk3fffZdu3boBUFxcTFFR0fH5MzIyePfdd5kxYwZPPvkkXbp04bHHHmP8+PG2noJIyFL9iribaljE3VTDIu6mGhb5ilZskrlaTU2NmTVrlqmpqbEdxXG0bFqmZeMcei1apmXTMi2b0OLW19uNud2YWb47vd6Bo2Ut3wetVyen5dOy1lg2HmOC7BqbIiIiIiIiIiLieGG2A4iIiIiIiIiISOhRU0pERERERERERAJOTSkREREREREREQk4NaWa0b17dzweT6OfmTNn2o5lzVNPPUVGRgbR0dFkZWWxfPly25Gs+/3vf99kHenUqZPtWHLUAw88wPnnn0/btm1JSkqyHccq1W/zli1bxqWXXkqXLl3weDy8+eabtiOJBW54r3BbDau2QpPb1lM3mj17NkOHDiU+Pp6OHTsybtw4Pv30U9uxxOWefvppBg4cSEJCAgkJCWRnZ/PPf/7TdixHmj17Nh6Ph+nTp9uOYl1r7wurKdWCY5fnPPZz9913245kxYIFC5g+fTp33XUX69atIycnhzFjxjS6RGmo6t+/f6N1ZOPGjbYjyVG1tbX89Kc/5YYbbrAdxSrVb8uqq6sZNGgQTzzxhO0oYpHT3yvcWMOqrdDjxvXUjZYuXcqUKVNYvXo1eXl51NfXk5ubS3V1te1o4mJnnHEGc+bMYe3ataxdu5YLL7yQsWPHsnnzZtvRHGXNmjU8++yzDBw40HYUx2jVfeFWuxZgEOnWrZt55JFHbMdwhHPPPddcf/31jab17dvXzJw501IiZ5g1a5YZNGiQ7RjyDV544QWTmJhoO4Y1qt9TA5g33njDdgyxyKnvFW6vYdVWaHD7eupWJSUlBjBLly61HUWCTLt27cxzzz1nO4ZjVFZWmt69e5u8vDwzYsQIM23aNNuRrGvtfWEdKdWCBx98kOTkZM4++2weeOABamtrbUcKuNraWvLz88nNzW00PTc3l5UrV1pK5Rzbt2+nS5cuZGRkcOWVV7Jr1y7bkUSOU/2KuJtqWNxA66k95eXlALRv395yEgkWPp+P+fPnU11dTXZ2tu04jjFlyhR+9KMfcdFFF9mO4iituS8c0Yq5gsa0adMYPHgw7dq146OPPuKOO+6gsLCQ5557zna0gCotLcXn85GamtpoempqKvv27bOUyhmGDRvGyy+/zJlnnsn+/fu5//77Of/889m8eTPJycm244mofkVcTjUsbqD11A5jDDfffDPDhw8nMzPTdhxxuY0bN5KdnU1NTQ1xcXG88cYb9OvXz3YsR5g/fz4ff/wxa9assR3FUVp7XzhkjpRqbjCur/+sXbsWgBkzZjBixAgGDhzIr371K5555hnmzZtHWVmZ5Wdhh8fjafS3MabJtFAzZswYxo8fz4ABA7jooot45513AHjppZcsJwte36aG5QTVr4SaYHuvUA2LG2g9Dawbb7yRDRs28Le//c12FAkCffr0oaCggNWrV3PDDTcwadIktmzZYjuWdbt372batGm88sorREdH247jKK29LxwyR0rdeOONXHnllSedp3v37s1OP++88wDYsWNHSB0Fk5KSQnh4eJNvukpKSpp8IxbqYmNjGTBgANu3b7cdJWidTg2HItWvhKpgea9QDYsbaD0NvKlTp7Jw4UKWLVvGGWecYTuOBIGoqCh69eoFwJAhQ1izZg2PPvoof/7zny0nsys/P5+SkhKysrKOT/P5fCxbtownnngCr9dLeHi4xYTOcbr7wiHTlEpJSSElJeU73XfdunUAdO7cuTUjOV5UVBRZWVnk5eVx+eWXH5+el5fH2LFjLSZzHq/Xy9atW8nJybEdJWidTg2HItWvhKpgea9QDYsbaD0NHGMMU6dO5Y033mDJkiVkZGTYjiRByhiD1+u1HcO6UaNGNbmi3DXXXEPfvn25/fbb1ZD6itPdFw6ZptSpWrVqFatXr+aCCy4gMTGRNWvWMGPGDC677DK6du1qO17A3XzzzUycOJEhQ4aQnZ3Ns88+S1FREddff73taFbdeuutXHrppXTt2pWSkhLuv/9+KioqmDRpku1oAhQVFXHgwAGKiorw+XwUFBQA0KtXL+Li4uyGCyDVb8uqqqrYsWPH8b8LCwspKCigffv2IfleH6qc/l7hxhpWbYUeN66nbjRlyhT++te/8o9//IP4+PjjR6clJiYSExNjOZ241Z133smYMWNIT0+nsrKS+fPns2TJEt577z3b0ayLj49vMmZbbGwsycnJIT+WW6vvC7fadfyCRH5+vhk2bJhJTEw00dHRpk+fPmbWrFmmurradjRrnnzySdOtWzcTFRVlBg8erEvPGmMmTJhgOnfubCIjI02XLl3MFVdcYTZv3mw7lhw1adIkAzT5Wbx4se1oAaf6bd7ixYubXUcmTZpkO5oEkBveK9xWw6qt0OS29dSNmqsrwLzwwgu2o4mLXXvttcdrt0OHDmbUqFFm0aJFtmM51ogRI8y0adNsx7CutfeFPcYY893aWSIiIiIiIiIiIt9NyFx9T0REREREREREnENNKRERERERERERCTg1pUREREREREREJODUlBIRERERERERkYBTU0pERERERERERAJOTSkREREREREREQk4NaVERERERERERCTg1JQSEREREREREZGAU1MqRIwcOZLp06ef0rxLlizB4/Fw6NCh0/o/u3fvzty5c0/rMUSkgWpYxN1UwyLuphoWcTfVsHOpKSUiIiIiIiIiIgGnppSIiIiIiIiIiAScmlIh6JVXXmHIkCHEx8fTqVMnrrrqKkpKSprMt2LFCgYNGkR0dDTDhg1j48aNjW5fuXIlP/zhD4mJiSE9PZ2bbrqJ6urqQD0NkZClGhZxN9WwiLuphkXcTTXsLGpKhaDa2lruu+8+1q9fz5tvvklhYSGTJ09uMt9tt93GQw89xJo1a+jYsSOXXXYZdXV1AGzcuJHRo0dzxRVXsGHDBhYsWMAHH3zAjTfeGOBnIxJ6VMMi7qYaFnE31bCIu6mGHcZISBgxYoSZNm1as7d99NFHBjCVlZXGGGMWL15sADN//vzj85SVlZmYmBizYMECY4wxEydONL/5zW8aPc7y5ctNWFiYOXLkiDHGmG7duplHHnmk9Z+MSAhSDYu4m2pYxN1UwyLuphp2Lh0pFYLWrVvH2LFj6datG/Hx8YwcORKAoqKiRvNlZ2cf/719+/b06dOHrVu3ApCfn8+LL75IXFzc8Z/Ro0fj9/spLCwM2HMRCUWqYRF3Uw2LuJtqWMTdVMPOEmE7gARWdXU1ubm55Obm8sorr9ChQweKiooYPXo0tbW133h/j8cDgN/v57rrruOmm25qMk/Xrl1bPbeINFANi7ibaljE3VTDIu6mGnYeNaVCzCeffEJpaSlz5swhPT0dgLVr1zY77+rVq48X1MGDB9m2bRt9+/YFYPDgwWzevJlevXoFJriIAKphEbdTDYu4m2pYxN1Uw86j0/dCTNeuXYmKiuLxxx9n165dLFy4kPvuu6/Zee+9917+/e9/s2nTJiZPnkxKSgrjxo0D4Pbbb2fVqlVMmTKFgoICtm/fzsKFC5k6dWoAn41I6FENi7ibaljE3VTDIu6mGnYeNaVCTIcOHXjxxRd59dVX6devH3PmzOGhhx5qdt45c+Ywbdo0srKyKC4uZuHChURFRQEwcOBAli5dyvbt28nJyeGcc87hnnvuoXPnzoF8OiIhRzUs4m6qYRF3Uw2LuJtq2Hk8xhhjO4SIiIiIiIiIiIQWHSklIiIiIiIiIiIBp6aUiIiIiIiIiIgEnJpSIiIiIiIiIiIScGpKiYiIiIiIiIhIwKkpJSIiIiIiIiIiAaemlIiIiIiIiIiIBJyaUiIiIiIiIiIiEnBqSomIiIiIiIiISMCpKSUiIiIiIiIiIgGnppSIiIiIiIiIiAScmlIiIiIiIiIiIhJwakqJiIiIiIiIiEjA/X966Bk8fAPW6AAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "\n", "priors = [\n", " bilby.core.prior.Uniform(minimum=5, maximum=50),\n", " bilby.core.prior.LogUniform(minimum=5, maximum=50),\n", " bilby.core.prior.PowerLaw(name=\"name\", alpha=2, minimum=100, maximum=1000),\n", " bilby.gw.prior.UniformComovingVolume(\n", " name=\"luminosity_distance\", minimum=100, maximum=1000, latex_label=\"label\"\n", " ),\n", " bilby.gw.prior.AlignedSpin(),\n", " bilby.core.prior.Gaussian(name=\"name\", mu=0, sigma=1, latex_label=\"label\"),\n", " bilby.core.prior.TruncatedGaussian(\n", " name=\"name\", mu=1, sigma=0.4, minimum=-1, maximum=1, latex_label=\"label\"\n", " ),\n", " bilby.core.prior.Cosine(name=\"name\", latex_label=\"label\"),\n", " bilby.core.prior.Sine(name=\"name\", latex_label=\"label\"),\n", " bilby.core.prior.Interped(\n", " name=\"name\",\n", " xx=np.linspace(0, 10, 1000),\n", " yy=np.linspace(0, 10, 1000) ** 4,\n", " minimum=3,\n", " maximum=5,\n", " latex_label=\"label\",\n", " ),\n", "]\n", "\n", "for ii, prior in enumerate(priors):\n", " fig.add_subplot(2, 5, 1 + ii)\n", " plt.hist(prior.sample(100000), bins=100, histtype=\"step\", density=True)\n", " if not isinstance(prior, bilby.core.prior.Gaussian):\n", " plt.plot(\n", " np.linspace(prior.minimum, prior.maximum, 1000),\n", " prior.prob(np.linspace(prior.minimum, prior.maximum, 1000)),\n", " )\n", " else:\n", " plt.plot(np.linspace(-5, 5, 1000), prior.prob(np.linspace(-5, 5, 1000)))\n", " plt.xlabel(\"{}\".format(prior.latex_label))\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define an Analytic Prior\n", "\n", "Adding a new analytic is achieved as follows." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2025-03-20T14:28:10.223590Z", "iopub.status.busy": "2025-03-20T14:28:10.223157Z", "iopub.status.idle": "2025-03-20T14:28:10.227620Z", "shell.execute_reply": "2025-03-20T14:28:10.227233Z" } }, "outputs": [], "source": [ "class Exponential(bilby.core.prior.Prior):\n", " \"\"\"Define a new prior class where p(x) ~ exp(alpha * x)\"\"\"\n", "\n", " def __init__(self, alpha, minimum, maximum, name=None, latex_label=None):\n", " super(Exponential, self).__init__(\n", " name=name, latex_label=latex_label, minimum=minimum, maximum=maximum\n", " )\n", " self.alpha = alpha\n", "\n", " def rescale(self, val):\n", " return (\n", " np.log(\n", " (np.exp(self.alpha * self.maximum) - np.exp(self.alpha * self.minimum))\n", " * val\n", " + np.exp(self.alpha * self.minimum)\n", " )\n", " / self.alpha\n", " )\n", "\n", " def prob(self, val):\n", " in_prior = (val >= self.minimum) & (val <= self.maximum)\n", " return (\n", " self.alpha\n", " * np.exp(self.alpha * val)\n", " / (np.exp(self.alpha * self.maximum) - np.exp(self.alpha * self.minimum))\n", " * in_prior\n", " )" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-03-20T14:28:10.229064Z", "iopub.status.busy": "2025-03-20T14:28:10.228902Z", "iopub.status.idle": "2025-03-20T14:28:10.314294Z", "shell.execute_reply": "2025-03-20T14:28:10.313747Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prior = Exponential(name=\"name\", alpha=-1, minimum=0, maximum=10)\n", "\n", "plt.figure(figsize=(12, 5))\n", "plt.hist(prior.sample(100000), bins=100, histtype=\"step\", density=True)\n", "plt.plot(\n", " np.linspace(prior.minimum, prior.maximum, 1000),\n", " prior.prob(np.linspace(prior.minimum, prior.maximum, 1000)),\n", ")\n", "plt.xlabel(\"{}\".format(prior.latex_label))\n", "plt.show()\n", "plt.close()" ] } ], "metadata": { "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 4 }