{ "cells": [ { "cell_type": "markdown", "id": "2998ca29", "metadata": {}, "source": [ "# Vector Field Decomposition" ] }, { "cell_type": "markdown", "id": "32deabca1764c1d5", "metadata": {}, "source": [ "This example shows how to generate a Gaussian random vector field and decompose it into its compressive (divergence) and solenoidal (curl) components. It also computes the power spectra of these components and performs some sanity checks to verify the decomposition." ] }, { "cell_type": "code", "execution_count": 1, "id": "284bcc5d3c786a31", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:01.600874Z", "iopub.status.busy": "2026-08-11T18:23:01.600597Z", "iopub.status.idle": "2026-08-11T18:23:02.131035Z", "shell.execute_reply": "2026-08-11T18:23:02.130618Z" } }, "outputs": [], "source": [ "from kspace import FourierAnalysis, GaussianRandomField, PowerLawBetaModel\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "2c70a18071d1ac19", "metadata": {}, "source": [ "First, set up the power spectrum model:" ] }, { "cell_type": "code", "execution_count": 2, "id": "eb5dab45e0343cb7", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:02.132391Z", "iopub.status.busy": "2026-08-11T18:23:02.132284Z", "iopub.status.idle": "2026-08-11T18:23:02.133833Z", "shell.execute_reply": "2026-08-11T18:23:02.133538Z" } }, "outputs": [], "source": [ "# Parameters for the power spectrum\n", "l_min = 30.0\n", "l_max = 200.0\n", "alpha = -11.0 / 3.0\n", "f_rms = 10.0 # normalization of the field" ] }, { "cell_type": "code", "execution_count": 3, "id": "80371b74a68cfa29", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:02.134811Z", "iopub.status.busy": "2026-08-11T18:23:02.134741Z", "iopub.status.idle": "2026-08-11T18:23:02.136224Z", "shell.execute_reply": "2026-08-11T18:23:02.135853Z" } }, "outputs": [], "source": [ "# Make a power-law spectrum\n", "power_spec = PowerLawBetaModel(l_min, l_max, alpha)" ] }, { "cell_type": "code", "execution_count": 4, "id": "365c28b6", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:02.137098Z", "iopub.status.busy": "2026-08-11T18:23:02.137036Z", "iopub.status.idle": "2026-08-11T18:23:02.138740Z", "shell.execute_reply": "2026-08-11T18:23:02.138410Z" } }, "outputs": [], "source": [ "# Renomalize the power spectrum to have the desired RMS value\n", "power_spec.renormalize(f_rms)" ] }, { "cell_type": "markdown", "id": "fd276e7aef843220", "metadata": {}, "source": [ "Next, we set up the Gaussian random field generator, and generate a realization of the vector field:" ] }, { "cell_type": "code", "execution_count": 5, "id": "b1e0d25c", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:02.139571Z", "iopub.status.busy": "2026-08-11T18:23:02.139499Z", "iopub.status.idle": "2026-08-11T18:23:02.140994Z", "shell.execute_reply": "2026-08-11T18:23:02.140665Z" } }, "outputs": [], "source": [ "# Parameters for the box and grid\n", "le = np.array([0.0, 0.0, 0.0])\n", "re = np.array([750.0, 750.0, 750.0])\n", "ddims = [256] * 3\n", "width = re - le" ] }, { "cell_type": "code", "execution_count": 6, "id": "df493c33", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:02.141920Z", "iopub.status.busy": "2026-08-11T18:23:02.141869Z", "iopub.status.idle": "2026-08-11T18:23:05.224896Z", "shell.execute_reply": "2026-08-11T18:23:05.224363Z" } }, "outputs": [], "source": [ "# Generate a gaussian random vector field\n", "vgen = GaussianRandomField(le, re, ddims, power_spec, seed=10)\n", "v = vgen.generate_vector_field_realization()" ] }, { "cell_type": "markdown", "id": "b30fc8533f247004", "metadata": {}, "source": [ "`v` is now a 3D vector field in the form of a NumPy array, with shape (3, 256, 256, 256), where the first dimension of the array corresponds to the three components of the vector field. Now, we can decompose the field into its compressive and solenoidal components, and compute their power spectra. First, we create an instance of the `FourierAnalysis` class, which will help us with these tasks." ] }, { "cell_type": "code", "execution_count": 7, "id": "db886f0e", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:05.226730Z", "iopub.status.busy": "2026-08-11T18:23:05.226618Z", "iopub.status.idle": "2026-08-11T18:23:05.228734Z", "shell.execute_reply": "2026-08-11T18:23:05.228265Z" } }, "outputs": [], "source": [ "# Give the FourierAnalysis class the same width and dims as\n", "# the GaussianRandomField created above\n", "fa = FourierAnalysis(width, ddims)" ] }, { "cell_type": "code", "execution_count": 8, "id": "fa387e1c", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:05.229798Z", "iopub.status.busy": "2026-08-11T18:23:05.229719Z", "iopub.status.idle": "2026-08-11T18:23:13.525152Z", "shell.execute_reply": "2026-08-11T18:23:13.524024Z" } }, "outputs": [], "source": [ "# Decompose the field into its compressive (divergence) and solenoidal components\n", "vc = fa.divergence_component(v)\n", "vs = fa.solenoidal_component(v)" ] }, { "cell_type": "markdown", "id": "b000708d6158a898", "metadata": {}, "source": [ "Now that we have the compressive and solenoidal components of the vector field, we can compute their power spectra and plot them:" ] }, { "cell_type": "code", "execution_count": 9, "id": "527e1c3c", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:13.531539Z", "iopub.status.busy": "2026-08-11T18:23:13.531296Z", "iopub.status.idle": "2026-08-11T18:23:16.666386Z", "shell.execute_reply": "2026-08-11T18:23:16.665880Z" } }, "outputs": [], "source": [ "nbins = 60 # Number of bins for the power spectrum, it will\n", "# use the min-max wavenumbers as boundaries\n", "kc_bins, Pkc = fa.make_binned_powerspec(vc[0], nbins)\n", "ks_bins, Pks = fa.make_binned_powerspec(vs[0], nbins)" ] }, { "cell_type": "code", "execution_count": 10, "id": "faa1590d", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:16.667898Z", "iopub.status.busy": "2026-08-11T18:23:16.667836Z", "iopub.status.idle": "2026-08-11T18:23:16.903351Z", "shell.execute_reply": "2026-08-11T18:23:16.902957Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Take the geometric mean of the bins since they are logspaced\n", "kc = np.sqrt(kc_bins[1:]*kc_bins[:-1])\n", "ks = np.sqrt(ks_bins[1:]*ks_bins[:-1])\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n", "ax.loglog(kc, Pkc, label=\"Compressive\", lw=2)\n", "ax.loglog(ks, Pks, label=\"Solenoidal\", lw=4)\n", "ax.set_xlabel(\"Wavenumber (k)\")\n", "ax.set_ylabel(\"Power Spectrum (Pk)\")\n", "ax.set_title(\"Power Spectrum\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "14f36a1d832ff4fd", "metadata": {}, "source": [ "Now, let's do some sanity checks." ] }, { "cell_type": "code", "execution_count": 11, "id": "2e85df5c38ac8eed", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:16.904334Z", "iopub.status.busy": "2026-08-11T18:23:16.904273Z", "iopub.status.idle": "2026-08-11T18:23:17.098213Z", "shell.execute_reply": "2026-08-11T18:23:17.097807Z" } }, "outputs": [], "source": [ "# Compute the velocity magnitude field for the following sanity checks\n", "vmag = np.sqrt(np.sum(v*v, axis=0))" ] }, { "cell_type": "markdown", "id": "e7c013e6d7b1e646", "metadata": {}, "source": [ "For a gaussian random field in 3D, 1/3 of the power should be in compressive motions\n", "and 2/3 should be in solenoidal, let's check it:\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "642f7e3b13f1f42b", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:17.099560Z", "iopub.status.busy": "2026-08-11T18:23:17.099491Z", "iopub.status.idle": "2026-08-11T18:23:17.272269Z", "shell.execute_reply": "2026-08-11T18:23:17.271828Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fraction of power in compressive motions: 0.3336281924898164\n", "Fraction of power in solenoidal motions: 0.6663718075101835\n" ] } ], "source": [ "print(\"Fraction of power in compressive motions: \", np.sum(vc*vc)/np.sum(vmag**2))\n", "print(\"Fraction of power in solenoidal motions: \", np.sum(vs*vs)/np.sum(vmag**2))" ] }, { "cell_type": "markdown", "id": "f56278d7452f380b", "metadata": {}, "source": [ "We can also check this by dividing the solenoidal power spectrum by the compressive power spectrum, which should be $\\approx$ 2. We can plot it:" ] }, { "cell_type": "code", "execution_count": 13, "id": "f9aca5756741e2b8", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:17.273703Z", "iopub.status.busy": "2026-08-11T18:23:17.273625Z", "iopub.status.idle": "2026-08-11T18:23:17.357683Z", "shell.execute_reply": "2026-08-11T18:23:17.357257Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Power Spectrum Ratio (Pk_compressive / Pk_solenoidal)')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3o7vnnnukpKTEDEDJzc01ZRsJCQkmcL7ppps83RwQpHHbFeUZsdFREh0lolUc9HEGAAB+C5w1y3z//ffLXXfdZUo2srOzpXv37pKamurppoA6lVNgH34S6/Sa1jrn3IJiJgcCAAD/Bc6W+Ph4EzAD4Txu297LWQNnMs4AAMCnwPm8884Td02cONHt2wJBWxxYKXAu66xRSMYZAAD4FjhrqzkgkgJnVxlnRcYZAAD4FDiPGzfOnZsBIS3bqatGxeJAey/nvMKK2wAAAPilxnn37t1mGIrq2rWrNG3a1NtNAUEv1bBnnHXCoC4YBAAA8KmPc05Ojlx99dXSsmVL04pOT61atZK//vWvpj0dEJalGuUZ59JSkYLikjrfNwAAEIGB8+233y4zZsyQyZMnmxHbevriiy/MdXfccUdg9hLwex9nV4sDy+QVEjgDAAA/lGp89tlnMmHCBBk0aJDjuuHDh0tSUpJceOGF8sorr3i6SSAk2tFZ8ou0zjmOnwoAAPAt46zlGM2bN69yfbNmzSjVQBiVarheHKjyyTgDAAB/BM59+/aVhx9+WPLy8hzXHTp0SB599FHzNSAcMs5pCXG1ZJwBAAB8LNV47rnnZOjQodKmTRvp1auXuW7JkiWSmJgo33//vaebA+pMTnk7uugozTA7f2a0X6bGGQAA+CVwPvLII+WPP/6Q999/X1atWmWuu+SSS+Syyy4zdc5AqJdqaH1z5XZzCbG2Ug0yzgAAwF99nJOTk2X06NHe3BUIeqlG5Y4aiowzAADwe43zu+++K19//bXj8t133y0NGjSQfv36ycaNGz3dHBCUjHNlZJwBAIDfA+cxY8Y4SjLmzp0rL774ojz99NPSpEkTue222zzdHFAnSkpKJaeguNrAmYwzAADwe6nG5s2bpUuXLub8pEmT5Pzzz5drr71W+vfv79TbGQgluYUVnTJSK7WiU2ScAQCA3zPOqampsnfvXnN+ypQpcuqpp5rz2lVD29IBId/DOZ6MMwAAqIOMswbK11xzjfTu3VvWrFljpgaq5cuXS4cOHbzYBSC447arZJxt2WkAAACvM84vvfSSGXSye/duM367cePG5voFCxaYtnRA6E8NrCXjXFRSZ/sFAAAiOOOsHTR0QWBlOjnQ7u9//7v885//NIsGgVDKONfaVYOR2wAAwB8ZZ3f973//k8zMzEBtHvBqamC1iwOdMs6UagAAgDoMnEtLSwO1aSAApRoVwXQeNc4AAKAuA2cglGTVWqpR8auQT40zAABwgcAZ9S7jnEbGGQAAeIHAGfVCbaUaZJwBAEBtCJxRL2R7UONMH2cAAOCXwLmwsLDar+3Zs8dx/vLLL5f09HRPNw8EPOPsegAKNc4AAMDPgfPFF1/ssmPGzp07ZdCgQY7Lr7zyCj2cEZLt6FJctKOjqwYAAPB74Lxp0yYzcttux44dJmg+4ogjPN0cEBIjt2OjoyQ6quw8XTUAAIBfAudvvvlG5syZI7fffru5vG3bNhk4cKAcddRR8sknn3i6OSAkFgdGRUU5ss70cQYAAH4Zud20aVOZMmWKnHjiiebyV199Jcccc4y8//77Eh3NWkOEdsY5PjZa4mJcv061zjm3oJiMMwAA8E/grNq2bStTp06Vk046SU499VQZP368ydgBoSqnoKjaMg1LWca5kIwzAADwPnBu2LChy8A4NzdXJk+eLI0bN3Zct2/fPnc2CQRlcaCrhYGVO2tQ4wwAALwOnJ999ll3bgaEfKlGSnxtGWdqnAEAgA+B85VXXunOzYCQVFhcIgVFJbWWatgzztpykfIjAABg5/ZqvpKSEnnqqaekf//+cvzxx8s999wjhw4dcvfuQMh21LAklGectU15QXFZoA0AAOBx4PzEE0/IfffdJ6mpqdK6dWt57rnn5IYbbnD37kDQZOXZejgn1l6qofIKCZwBAICXgfN7770nL7/8snz//fcyadIksyhQW9BpJhoIh44aKrWGGmfnsdsVkwYBAAA8Cpx1YuDw4cMdl4cMGWJqQHUAChAJpRr2jHM+GWcAAOBt4FxUVCSJiYlO18XFxUlhYaG7mwCCIru8FZ1KdaMdnSLjDAAAvB6Aol0GrrrqKklISHBcl5eXJ9dff72kpKQ4rps4caJEKp2SeMcdd5jylH/84x9yzTXXBHuX4NeMc0XgTI0zAADwOnB21ZLu8ssvl/pCM+633367/PTTT5KRkSHHHnusnHvuuU7DXxDaPZxr7aoRayvVoMYZAAB4GziPGzdO6rNffvlFevToYTqKqGHDhsmUKVPkkksuCfauwYOMc80jt8k4AwAAP9Q414V//etfZsHhrbfe6tftzpw5U8466yxp1aqV2b52BXHlpZdekg4dOpha7hNOOMEEyxZdBGkFzUrPb9261a/7iSD3cSbjDAAAwiFw/vXXX+W1116Tnj171ni72bNnu1yQuGLFCtm5c6fL++Tk5EivXr1MYFydjz/+2JRiPPzww7Jw4UJz+6FDh8quXbu8+G4QqosDU2pYHEjGGQAAhHzgnJ2dLZdddpm88cYb0rBhw2pvp4vydOjKpZdeKsXFFcHQ6tWr5ZRTTpF3333X5f20rOLxxx83NcnVGTt2rIwePVpGjRol3bt3l1dffVWSk5Pl7bffNl/XbLU9w6zn9TpETqkGGWcAABDygbMGw2eccYbpDV2T6Oho+eabb2TRokVyxRVXmED6zz//NEHzOeecI3fffbdXj19QUCALFixwenx9LL08d+5cc7lPnz6ybNkyEzBroP/tt9+ajLQrmtnW4FtHkyP46KoBAADqNHB+6KGHTHDpbx999JEpjXjyySfdur1meX/88UeZNWuWyTxr0KwB7iuvvOL1PuzZs8dksJs3b+50vV7esWOHOR8bGyvPPPOMnHzyyXL00UebtnTVddTQDwJaOqLlJwitrhpuZ5wLmRwIAAC87KqxZcsWU/IQHx9vFtqNGDFCBg8ebC57a/PmzXLLLbfI1KlTqwxXqUm7du1k/PjxMnDgQOnUqZO89dZbZtFfoOn3rCeE78htt/s4FzFKHgAAeJlx1lpfzb5++OGHkpaWZjpfNGnSREaOHCnvvfee7Nu3TzylGWxdfHfMMceYjK6eZsyYIc8//7w5b69jttNFgNdee60J4HNzc+W2224TX+j3ERMTU2VxoV5u0aKFT9tGaC0OTLaN1a4540zgDAAAfKhx1rrfk046SZ5++mmzIG/+/PmmbZt2w9ASigEDBsh//vMft9u0acZ66dKlsnjxYsfpuOOOMwsF9bwGs67KKvR+3bp1M1MKp02bZjpi3HnnneItzZrrQBPdlkXrp/Vy3759vd4uQkN2XqGjTCM6uvojEwlOGWdKNQAAgJelGq5o8KonXZS3e/du+fLLL81JuRPIaub6yCOPdLpOx3dr7XDl661gVstF2rdvb4JlzUrrIjwt9dBaZ+2t7Cr7rIv51q5d67i8fv16E5g3atTIlH0obUWn0xE1cNeFgM8++6xpY6ddNhDecsozzjW1olOJtmx0HjXOAADAn4GzXdOmTeWvf/2rOQWKZrzHjBljst722mrtufzDDz+YfXDlt99+M4v6LBokKw2U33nnHXP+oosuMsG/LoLUkhRdAPjdd99VWTCI8O2qUVN9s0qIrcg451PjDAAAAhU4+8v06dNr/Pqpp57q8vrevXtXe59BgwZJaWlprY994403mhMih/7crcWBNXXUUGScAQBAyPdxBgLlUGGxlJR/ZkqJJ+MMAAC8R+CMetPDOcWDjDN9nAEAQGUEzqgXCwNVai2LA6lxBgAAfg+cdfhI//79TQu6jRs3muu0C8UXX3zhzeaAoI/bVtQ4AwAAvwbOOtpau1IMHz5cDhw44BhS0qBBAxM8A+E4blvFRkeJ1eaZrhoAAMDnwPmFF16QN954Q+6//36nASXa/1iHmQDhmnHWse1W1pk+zgAAwOfAWYeHuGr9lpCQYAaGAOG6ONBe50zGGQAA+Bw4d+zY0Uzdq0yHhegUQSBcFwcqMs4AAMBvA1C0vvmGG26QvLw8M1zil19+kQ8//FCefPJJefPNNz3dHBAypRqKjDMAAPBb4HzNNddIUlKSPPDAA5KbmyuXXnqp6a7x3HPPycUXX+zp5oCQWRyoyDgDAAC/jty+7LLLzEkD5+zsbGnWrJk3mwHqNOOc6mHGWY+o6IJBAAAAr2qcH3/8cbNAUCUnJxM0I7IWB5Z31SgtFSkoLgnovgEAgPDiceD86aefSpcuXaRfv37y8ssvy549ewKzZ0AQSzVUXiGBMwAA8CFwXrJkifz+++8yaNAg+c9//mPqm8844wz54IMPTOkGEAmLA1V+UUVHDgAAAK9Gbvfo0UPGjBkj69atk59++kk6dOggt956q7Ro0YJnFCHbji7Fg3Z0Kp+MMwAA8DVwtktJSTFdNuLj46WwsNDXzQEBKdWIi4mShNjaA2cyzgAAwK+Bsy4OfOKJJ0zmWUdtL1q0SB599FHZsWOHN5sDAianoMjtMg2VGFfxK0GNMwAA8Kkd3V/+8hf59ddfpWfPnjJq1Ci55JJLpHXr1p5uBqjTGueUePde6vasNDXOAADAp8B58ODB8vbbb0v37t09vSsQtFINdzpqKDLOAADAb4GzlmgA4aCouMRRbuHOwkBFxhkAAPgUON9+++3y2GOPmYWAer4mY8eOdWeTQMDlFNg7apBxBgAAvnErmtDFf1bHDD1fHcYTI5zHbSsyzgAAoDpuRRPaq9nVeSCShp8oapwBAEDA+jhnZmbKpEmTZNWqVb5uCgjquO0qGedCJgcCAAAfAucLL7xQXnzxRXP+0KFDpo+zXnfUUUfJZ5995unmgDqZGuhVV42isoWFAAAAXgXOM2fOlJNOOsmc//zzz6W0tFQOHDggzz//vDz++OM8qwgZ2fmFHpdqOGecCZwBAIAPgfPBgwelUaNG5vx3330nI0eOlOTkZDnjjDPkjz/+8HRzQMBkO2Wc3WxH55RxplQDAAD4EDi3bdtW5s6dKzk5OSZwPu2008z1+/fvl8TERE83B4TY4sCKADuPGmcAAODLAJRbb71VLrvsMklNTZX27dvLoEGDHCUcWucMhOLiQPdLNSo+S+ZT4wwAAHwJnP/+979Lnz59ZPPmzXLqqadKdHRZoNGpUydqnBH2fZzJOAMAAL8Fzko7aehJFRcXy9KlS6Vfv37SsGFDbzYHhEypBhlnAADgtxpnLdV46623HEHzwIED5ZhjjjG1z9OnT/d0c0BILQ60Z5zp4wwAAHwKnCdMmCC9evUy5ydPnizr1683w09uu+02uf/++z3dHBAwZJwBAEBQA+c9e/ZIixYtzPlvvvlGLrjgAjn88MPl6quvNiUbQKjIKaCrBgAACGLg3Lx5c1mxYoUp09B2dLpAUOXm5kpMjHuHw4E676oR716Nc2x0lERHlZ2nqwYAAPBpceCoUaPMiO2WLVtKVFSUDBkyxFw/f/58OeKIIzzdHBDwUo2kuBiJsaLhWuhrWuuccwuK6eMMAAB8C5wfeeQROfLII007Oi3TSEhIMNdrtvmee+7xdHNAwOSULw5MTfTsZa6dNTRwJuMMAAB8bkd3/vnnm//z8vIc11155ZXebAohrKCoROJtA0HCtVTD3R7Ozp01Csk4AwAAJx5HRVrb/Nhjj0nr1q3N9MB169aZ6x988EFHmzqEvw17cmTEi7Pko182STgqLS11lGqkuNmKrnIvZzLOAADAp8D5iSeekHfeeUeefvppiY+Pd1yv5Rtvvvmmp5tDCJqyfIec9cIsWbUjSx76crks3XJQwo0GvUUlpeZ8ipsLAyv3cs4rrOgDDQAA4HHg/N5778nrr78ul112mVMXDe3trP2cEb6Kikvkqe9WybXjF0hWeba2bcMkSYqPDuuOGp6Watgzzpq5BgAA8KrGeevWrdKlS5cq15eUlEhhYSHPapjak50vN3+4SOb8uddx3RlHtZSnzu/pceAZrsNPLAnlGWeNmQuKSyQhljaLAADAi8C5e/fu8vPPP0v79u2rTBTs3bs3z2kYWrBxv9zw/kLZkZnn6GV87/BucnX/DqY9W9j3cPYy46zyCgmcAQCAl4HzQw89ZDpoaOZZs8wTJ06U1atXmxKOr776ytPNIYi0DOHdORvk8a9XOuqBm6UlyEuXHSPHd2gUEa3oVKqHiwOtGmeVX6TbifPrvgEAgPDkcfHq2WefLZMnT5YffvhBUlJSTCC9cuVKc501RRChL7egSG75aLE8MnmFI2g+oWMj+ermE8M+aPa1VMMpcC4s8et+AQCA8OVRRFFUVCRjxoyRq6++WqZOnRq4vUJA/bk7W/72vwWyZme247prB3SSu4d2ldiY8FsIGKjFgRUZZwAAAA8zzrGxsaYNnQbQCE87M/Pk3JdmO4JmDSpfvfwYuW94t4gJmn3PODvXOAMAACiPI6XBgwfLjBkzePbC1MKN+yUzryyoPKxZqnxxY385/ciWEml8WxxYucYZAADAi8WBw4YNk3vuuUeWLl0qxx57rKlzthsxYgTPawjLzKtoGTiqf0fp3DRVIpFviwPJOAMAAD8Ezn//+9/N/2PHjq3yNW1dpiO5EbqyyrPNKi0x/PozuyunwF7j7FlXDDLOAADAFY8jJ21Bh/BllWmo9KTIbbPmXKpBxhkAAPguclaDwS2ZhwrrR8bZp64a1DgDAAA/Bc7Tpk2TM888Uzp37mxOel77OiO8SjXS60ngTFcNAAAQlMD55ZdfltNPP13S0tLklltuMaf09HQZPny4vPTSS37ZKQROlm1xYFpi/SjV8CnjXEjNPgAAKONxylEHoPz3v/+VG2+80XHdzTffLP379zdfu+GGGzzdJILUVSO9HgTOMdFRTgNNPO6qUURNPwAA8DLjfODAAZNxruy0006TgwcPero5BKlUIzY6yilAjNR2dCnxMabbi/cZZwJnAABQxuPISfs0f/7551Wu/+KLL0ytM8IjcNaFgZ4GlOGYcfa0TEMlOGWcKdUAAABlPI4qunfvLk888YRMnz5d+vbta66bN2+ezJ49W+644w55/vnnnUo4EJo1zpHcis6+ONDThYGVM8551DgDAIByHkcVb731ljRs2FBWrFhhTpYGDRqYr1k0m0ngHFpKS0sdfZwjuRWdjsnOLSj2+vu0l7DkU+MMAADKeRxVrF+/3tO7IEQcKiyW4pJScz7Nw2l64WR3Vr7jfPP0RI/vnxhHxhkAAFQVuavDUG/Hbe+yBc7N0hI8vr+9CwcZZwAAYIn15nD/hAkT5KeffpJdu3ZVGcE9ceJETzeJIEwNjOQa512ZeY7zzXzMONPHGQAAeB0433rrrfLaa6/JySefLM2bN4/ozgyRxqpvVmScq0fGGQAA+CVwHj9+vMkq66RAhJf6MjVwpy3jTI0zAAAIWo1zRkaGdOrUyW87gODUOKdHco1zpq3GOd3zGmcdDhNdfiCFGmcAAOB14PzII4/Io48+KocOHfL0rgiy+jJue6e9q0aa5zXOWn5k1TnTxxkAAHgdOF944YWyf/9+adasmRx11FFyzDHHOJ0i2VdffSVdu3aVww47TN58800JN/Wmq0Z5qUZ8TLQ0SPbuA4JV50zGGQAAWDyOnq688kpZsGCBXH755fVqcWBRUZHcfvvtppuIlqsce+yxcu6550rjxo0lXNSXGmerHV3TtASvX59lGedCMs4AAMD7wPnrr7+W77//Xk488USpT3755Rfp0aOHtG7d2lweNmyYTJkyRS655BIJyxrnpMjMOBcUlci+nAKv65stZJwBAIDPpRpt27aV9PR08ZdXXnlFevbsabapp759+8q3334r/jRz5kw566yzpFWrViYDOWnSJJe3e+mll6RDhw6SmJgoJ5xwggmWLdu2bXMEzUrPb926VcK1j3OkZpx3Z/tW32yhxhkAAPgcOD/zzDNy9913y4YNG8Qf2rRpI//6179M+cdvv/0mp5xyipx99tmyfPlyl7efPXu2FBZWBICWFStWyM6dO13eJycnR3r16mUC4+p8/PHHphTj4YcfloULF5rbDx061Ax5iRT1ocbZefiJfzLOOvQHAADA48BZa5u1zrdz586SlpYmjRo1cjp5SjPB2hNaF9wdfvjh8sQTT0hqaqrMmzevym11SuENN9wgl156qRQXFzuuX716tQm43333XZePoWUVjz/+uKlJrs7YsWNl9OjRMmrUKOnevbu8+uqrkpycLG+//bb5umar7RlmPa/XhZP6EDjvtLWi86aHsyWhvKuGxswFxc7TMQEAQP3kcfT07LPPBmZPREww/Omnn5oMsZZsVBYdHS3ffPONDBgwQK644gozjGX9+vUmaD7nnHNMJtwbBQUFJuN97733Oj3WkCFDZO7cueZynz59ZNmyZSZg1sWBWk7y4IMPutyeZrb1ZA/uQ6kdnWZTE2IrxkpHkt1ZFRlnXRzoLfv0wLzCkoh9vgAAQIC7avjb0qVLTaCcl5dnss2ff/65yfq6olneH3/8UU466SSTedbAVgNcrZX21p49e0yQq11C7PTyqlWrzPnY2FhTpqKjxjXzrUF6dR01NCuup8zMTBNkh1rGOVLrm/2ZcbZqnFV+kX4AitznDAAAuMer4/UaZOoCu5UrV5rL2m1ixIgREhPjXVZOeyMvXrxYDh48KBMmTDDB+YwZM6oNntu1a2eyzQMHDjRTDN966606aYun36OewpWVcY7oqYG2jHMzHzLOToFzIaUaAADAi8WBa9eulW7duplSiYkTJ5qT1j1r8Pznn3969ZzGx8dLly5dTG/kJ5980izMe+6556q9vS4CvPbaa019dG5urtx2220+/SybNGligv7Kiwv1cosWLSQSlJSUSnZ+ecY5KXKzp36rcbaVapRlnAEAQH3nceB88803m4WBmzdvNt0n9LRp0ybp2LGj+Zo/aClEfn5FAFS5rGLw4MEmeNegfdq0aaYjxp133un142ngrkG7bsu+D3rZVa11OMouKDIL3SI/41z2uomLiZKGXk4NVIlxzjXOAAAAHkdQWkKhHS/sHTS01ldbyvXv39/jZ1QX5GnXCy2/yMrKkg8++ECmT59uhqxUpsGs3rZ9+/YmWNa6Yy3nmDp1qlkgqL2VXWWfs7OzTabcogsKtTREvwd9XKWt6LRE5LjjjjMLAXURpC5S1C4bkaA+dNSwt6NrlpboU/mOfTEgGWcAAKA8jqASEhJMgOsqONXMrae0T7KWfWzfvt0spNNhKBo0n3rqqVVuq50uxowZYxYG2h9LSzt++OEHadq0qcvH0P7QuqjPokGy0kD5nXfeMecvuugi2b17tzz00EOyY8cOOfroo+W7776rsmAwXDmN206IzFKNwuIS2Vs+NdCXjhqKjDMAAPA5cD7zzDNNfbEuyNPMrJo/f75cf/31Xi2c0+14wlVArXr37l3tfQYNGuTWEIsbb7zRnCJR5qHIH7e9u7xMQzX3YfiJIuMMAAB8rnF+/vnnTY2z1v7qaGo9aYmGLu6raUEfQijjHKHt6Kz6ZqtUwxdknAEAQGUepx4bNGggX3zxhakZttrR6UI9DZwRuupDjfNO27htMs4AAMDfvI6gNFAmWA7PjHM6GedakXEGAAA+l2qMHDlSnnrqqSrXP/3003LBBRd4ujnUkcx6kHG2OmqoZv6scS6kjzMAAPAicJ45c6YMHz68yvXaJk6/htCeGhjRNc6ZAapxLqKPMwAA8CJwrq7tXFxcnGRmZvKchqh6UeOcFaAaZwagAAAAbwLno446ygwfqeyjjz4yw0gQmjIPVWScM5IiO+McG61TAz3vKW6X4JRxplQDAAB4sTjwwQcflPPOO0/+/PNPM61P6WjqDz/8UD799FOe0xBVHzLOu8ozzs3SEiQ62vupgYqMMwAAqMzjCOqss86SSZMmmQl+EyZMkKSkJDPtTyf3DRw40NPNIQhdNVITYiN7amC6b/XNVWucyTgDAAAv29GdccYZ5lQTzUDrJMGUlBSe5xDKOKfEx0hsjMcVOiFvT3a+WMMhm/s4blslxlXUOOfRVQMAAHhT4+yu6667Tnbu3MmTHGJdNepFRw0fFwaqhNiKX418umoAAIBABs6lVvoPIZVxrhdTA31sRVc540wfZwAAoCLvmD2qKCoukdyC4ogOnHdlkXEGAACBReBczzpqpEdsKzr71ED/ZpypcQYAAIrAud61oouL/IyzHxYHai9oq6MdNc4AAEARONe7cdv1oMbZDxnnqKgoR9aZjDMAAPB74GxfENi+fXszhhvBVz+Gn1RMDWzk49TAyp01yDgDAACvAud///vfLq8vLi6WSy+91HF52bJl0rZtW57lEMs4p0doqcbO8nZ0Tf0wNdBCxhkAAPgcOL/11ltVguaLL75YFi9e7OnmUNeLAyMw46xdQ/bm5PutvtlCxhkAANh5HEV9/fXXctppp0lGRoacf/75UlRUJBdeeKGsWrVKfvrpJ083hzoetx2JiwP3ZBc4pgb6o6OGhYwzAADwKXA+/vjj5bPPPpNzzjlH4uPjTfZ57dq1Jmhu3ry5p5tDHcg8ZG9HF3kZ511ZtlZ0Aco4a/2+LhgEAAD1l1eLA0855RR57733ZOTIkbJ+/XqZMWMGQXMIi/SMs1Xf7K+OGpaE8q4ams0uKC7x23YBAEB4civ9eN5557m8vmnTptKgQQO59tprHddNnDjRf3sHv4j0rhqBzjhbWeeE2IqhKAAAoP5xK4rSemZXhg4d6u/9QQBk5ZNx9sf0wEjtSAIAAPwYOI8bN87NzSHka5wjMOO825Zx1nZ0gQic8wsp1QAAoL7zKIqaN2+eTJ48WQoKCmTw4MFy+umnB27P4PcaZ13blhIfeYFzwGqcnUo1iv22XQAAEJ7cjqImTJggF110kSQlJZmJgGPHjpWnnnpK7rzzzsDuIfxW45yaEOu34SChWOMcEx0ljVP8MzVQJcZVBM55ZJwBAKj33O6q8eSTT8ro0aPl4MGDsn//fnn88cdlzJgx9f4JDKfJgRE/NTDVf1MDlX0xIBlnAADgduC8evVqk12OiSkLJu644w7JysqSXbt28SyGuMzyjHMkdtQoLimVvdnlUwPT/VffrMg4AwAArwLn3NxcSU9Pd1zW4SeJiYmSnZ3t7iYQBJopLSgqidiMswbNJdbUwDT/1TcrMs4AAMDOoxTkm2++KampqY7LOm77nXfekSZNmjiuu/nmmz3ZJAIs0ns42xcGknEGAACB5HYk1a5dO3njjTecrmvRooWMHz/ecVlHEhM4h5bMQxU9nNOT4iJ6+ElzMs4AACAUAucNGzYEcj8QIGScvUeNMwAA8KrGGeEp0gNnp4yznxcHOtU4F9LHGQCA+s6twPmjjz5ye4ObN2+W2bNn+7JPCEArukhdHOhU4+znUg2njHP5AksAAFB/uRU4v/LKK9KtWzd5+umnZeXKlVW+rr2dv/nmG7n00kvlmGOOkb179wZiX+HD1ECVFoGBs33cdrOAZpwJnAEAqO/cOnY/Y8YM+fLLL+WFF16Qe++9V1JSUqR58+amHZ0OQ9mxY4fprHHVVVfJsmXLzNcQGiK9VMPKOOvck8Ypfg6cnTLOlGoAAFDfuR1JjRgxwpz27Nkjs2bNko0bN8qhQ4dMwNy7d29zio6mZDpUh59Eeo1z07QEM3Lbn8g4AwAAO48jKQ2UzznnHE/vhiCJ5HZ0OjVwd1Z+QOqbq9Y4k3EGAKC+I0Vcj0o10iMs47w3p2JqoL87aqjEuIoa5zy6agAAUO8ROEe4SF4cuMvWUaNpADLOCbEVvx75dNUAAKDeI3COcJHcji6QPZwrZ5zp4wwAAAic60mpRmx0lFPNbiQIZA9nRcYZAADY+RRJlZaWmhNCP3DWjhpRUf7tOhFKpRrUOAMAgJAMnN977z056qijJCkpyZx69uwp48eP9//ewW81zpFW36x22oefBCDjrFl6q8Odv2qccwuK5Ovft8vOzIp9BwAA4cHjNgtjx46VBx98UG688Ubp37+/uU77Ol9//fWmx/Ntt90WiP2EF/RogNXHOT0psjpq1EXGWTP0WuecW1Dst64aj3+9Uj6Yv0kOb54q3986IOKOAgAAEMk8jqZ0eqCO4L7iiisc1+lglB49esgjjzxC4BxCDhUWm17HKi0h8jLO1uJAMzUw1f+Bs1XnrIGzvzLOizYdMP+v2Zltfj7J8ZH3gQYAgEjlcanG9u3bpV+/flWu1+v0awgdkT5u28o4N0n1/9TAyp01/JVxPphbUHHeNpwGAABEYODcpUsX+eSTT6pc//HHH8thhx3mr/2CH0T81MDs8qmBASjTqNxZw18Z5wO2n0nmoYoPNgAAIPR5nIZ89NFH5aKLLpKZM2c6apxnz54t06ZNcxlQI3is+uZIzDjvyylwlKE0D8DCwEBknPOLik3Zh4WMMwAAEZ5xHjlypMyfP1+aNGkikyZNMic9/8svv8i5554bmL2EVyJ5aqC9K0VdZZx9bb1YOVC2HxEAAAChz6s05LHHHiv/+9///L83CFiNc3qEZZx3ZwV2+IkloTzjrDFzQXGJJMRWTBP01MFc50CZjDMAAOHFrWgqMzNT0tPTHedrYt0OwRfJ47brOuNsZZ19CZzt9c2Vfz4AACBCAueGDRuajhnNmjWTBg0auOw9q4ex9friYv90H4DvIrmrxi5bxrkuapytOmdfPoAcIOMMAEBYcyua+vHHH6VRo0bm/E8//RTofYKfUOPs38A5v9C3zhoHbK3oFF01AACIwMB54MCBjvMdO3aUtm3bVsk6a8Z58+bN/t9DeM0emEV0xjk9sY5KNXw7mlK5ppkaZwAAIryrhgbOu3fvrnL9vn37zNcQmhnnSOvjvKu8xlk/vzVOiQ/Y4yTGVfyK5PmccabGGQCAehU4W7XMlWVnZ0tiYuAyf/Bcfahx1qmBsTEev4zdZl8M6GvG+cAh51INMs51b83OLJm5ZreUlPcABwDAE25HU7fffrv5X4PmBx98UJKTkx1f0wWB2tv56KOP9ujBEViRGjhr0GO1o2uWFriOGgHPONPHuU5t3pcrI16cZX6Oz1zQS0Ye26ZudwAAEPbcjqYWLVrkyDgvXbpU4uMrDo/r+V69esmdd94ZmL2EV6x2Z1qn60sbtVCzL7dAiqypgQGsb/Z3xpkBKME1+fdtjg8/c9ftJXAGAAQucLa6aYwaNUqee+45+jWHUcY5oqcGhnPG2XZEAIE3ZflOx/mNe3N4ygEAHvP4+P24ceM8fxQENeOcHsEdNZqFUca5co1zdn6RFBWXBLRGGxUfthZvPuB4OjbszeWpAQB4zKuI6rfffpNPPvlENm3aJAUFzsHAxIkTvdkkAlAHrIFZpNU32ztqhHvG2Toq0DCAXUFQZuqKimyz0hr5nPwiSUmIrN8NAEBgeZzq+uijj6Rfv36ycuVK+fzzz6WwsFCWL19uhqRkZGQEZi/hseyCIiktjdRWdHXTw7lKxrnQ+4yzZpbtizUtdNaoG1MqBc5qA+UaAIBAB85jxoyR//73vzJ58mSzKFDrnVetWiUXXnihtGvXztPNIUAitaOG2pkVpIxzkfcZ5+rqma1yGgSOPsdz/9xT5fqNlGsAAAIdOP/5559yxhlnmPMaOOfk5JgWdbfddpu8/vrrnm4OdTFuO4GMs38yziV+G7dtIeMceNNX75bC4rLDLy0zKo5QkHEGAAQ8cG7YsKFkZWWZ861bt5Zly5aZ8wcOHJDcXBbchOK47fSkSMs4l5Vq6ByeJqmBrQ9OcMo4e1+qccDWs9k+P8j+c0JgTFm+w3F+VP8OjvMb9/B+BQAIcOA8YMAAmTp1qjl/wQUXyC233CKjR4+WSy65RAYPHuzp5lAXGecIa0e3u3xxYOOUwE4N9GfG+aBtYWBLW102GefA0k4omnFWGUlxcsGxbR1fI+MMAPCUx6nIF198UfLyygKX+++/X+Li4mTOnDkycuRIeeCBBzzeAQRGpNY4a7cQqx1doOubq9Y4+5JxrijVaNsoWbYdLPsdosY5sOb+udfRXWbwEc1MB5PGKfGyN6eAGmcAgMc8jqgaNWrkOB8dHS333HOP4/KhQ4c83wMERGaEZpz3O00NrIvAuSLjnOdDVw17K7r2jZNl/vp95jwZ57rrpnFaj+aO518D5x2ZeXKooFiS4iNnqiYAILD8cpw7Pz9fxo4dKx07dvTH5uDnjHMkDUDZaWtF1ywtsK3orHHllnwfumrYA+d2jZId5zNttc/w/9EJq3+z/hwHHN7UnO/QOMVxm037qHMGAAQgcNbg+N5775XjjjvO9HGeNGmSY5KgBszaok47ayA0RGrGeZetFV1dZ5x96eNszyy3swVuZJxrD36fmbJaHvtqhckOe2LxlgNm0Ik66bCmkhxf9gGyQ5OK5586ZwCAJ9xORT700EPy2muvyZAhQ0xNsy4MHDVqlMybN89km/VyTAyHPENFpNY424efNA3w8BP/ZpwLXGecq+nvjDLfLNsuL/y41pzXgT4PndXd7admyvKqZRpWqYZlYz0dgqIDeR7/eqUUFpeY59S+CBYAUD23I6pPP/1U3nvvPRkxYoRpQdezZ08pKiqSJUuWmD7OCC32EgDtJhCRGee0MKpxtv082jZMMi3pNBAMlYxzbkGRjJu9QTo3TZXTj2whoeLnNRWDS96bu0Eu/0s76dQ01a37TllR1oYuOqpsYaDFXqqxoZ4OQfl66XZ5Z84Gc/7I1hlySR+GVwGAX0s1tmzZIscee6w5f+SRR0pCQoIpzSBoDk2RmnHek12RuW1SB4FzbHSUCbz8WePcIDleUhPKfiZZIRI4vztno/z7+9Xyt/cXyKodmRIq5q3f6zivi0Kf/HaVW/dbuytb1u0uyyYf16GRNE5NcBk419eM828b9jvO/1q+UBUA4MfAubi42EwKtMTGxkpqqnuZHwS3j7MVpEUCe4a2YXJgh58o/WBoZZ19yThb+60LNWOioxxHAUIl47x4c1kgpVnwb5dWDAwJpm0HDlVpGaeL/ea4GJ9dXbZZnda9okxDZSTHSYPksud/Qz0dgvL7lgOO84s2V5wHANTM7YiqtLRUrrrqKpNpVtrL+frrr5eUlIrsjZo4caK7m0QdZJyT42MCPiSkLtlrheuqBEXrnHMLiv1S46zZZpVuFmweMos49Xcr2Edu7AGkBqe3nXq4BNu8dRXZ5sObp8qandnm/ONfrZTJN51oPoC4Vd/cvWrpSfvGKXIg94BsO3jIfCCyl+REuoKiElm5vWz6q1q/J0f25xSYHtcAgJq5HVFdeeWV0qxZM8nIyDCnyy+/XFq1auW4bJ0QWl01ygK0yGGvFa6rNntWUOVpVwd7Zwgrs2xlOq2gv7C4VA75kMn2B90/e3eJFdszZeuBQyExvMTyyFk95MjW6Y79+2zBlmrvtzMzTxaXZ1GPaJEm7WyLAS0dyq/TDPuW/fUr66ylOAXFJVU6kAAAaud25KFt5xB+GedIqm9WVgCq31ddZdI1S7z9YJ4ZvuJNdjgrv0jKZ7Y4Aub0pIqfS+ahIkertGDQQSCVs+nTVu6UK/p2kFCob46PjZZj2jeUB87oLhe/Ps9c9+8pq+WMni0lxUUZktW7WZ3Ww/VCR80427PtXZqlSX3x+5aDVa5bvOmAnNy1YgElAMC1yDmGD6dWU1paEJGBc65z5rYuNC1fhKjZYW9qkq19tpdq2MtMgl3nvGFPTo3BZzBoFnjzvrKsd++2DUzW/y+dGsvQ8rZy2p/51Rl/1j4tsFJ9c+WMc33s5Wyvb7ZQ5wwA7iFwjvSpgRHUik6zvVapRoOkuqvHbJJa8VjWQA1PHDhUUZfdwMo420po7MNqgmG9i8BR64uDuV/z1lV0eujbubHj/L3DuklcTFnG//WZ66qUlOg+zy1fPNi6QZL0aFVW3lFTxrnyAsT6knHWGvGG5R9AF2/ab0p2AAA1I3CO+FZ0kRM4Z+cXSXH5H/c6zTjbWpntzvYicHbKODvXOFfOSAc746yL8Kzs+ozVu0NiYaBmmi069e/K8hISLS/593fO7emmr95t9l2d2r15tWU1vmac9UPcA5OWyuBnpst8276GOu3XvWZn2cLAw5unybHtGzkG8bj6AAUAcEbgHPHjtiOnVMMegNblUBerVMP7jHPV/U4PoVKN9baOGtec1Mlx/oeV3pVr6AeB68cvkLsnLDGT6XxZGKgdTY5u28DpazcNPsyRKZ20eJtjIaCasnyHy2mBlTVKiZe08vpobzLOq3Zkyf/mbZI/d+fIDR8slH05FUcVQtnybZmOevtebTKkd7uK53bRJhYIAkBtCJwjUKQOP7EHmHUZODexZZztA1jcddDWQs9VjXPQSzX2ZDuC1LOPbuV4zfy0apdXge+z09bId8t3yCe/bZFPf6u++0V1Nu/LdZRgHNOuYZVWcfrc3Tqkol3eY1+tMBng/KJik3G2btOnQ1k21RXNRLdvkuyop9YWbZ6wB5n6mnj4y+USDpbYPmT0bNPA1I9bFm2qGIoCAHDNq6hq27ZtMmvWLNm1a5eUlDj/wbn55pu92ST8yB6IRVI7OlclD3Wdcd7ja6mGi64awcw4a+mLtQivfeNkSYiNkUFdm8nkJdvM4XudKtevSxO3t5eTXyQTbMHyF4u3yqUneDbOea6t9MFe32yn29QR3JrxXbBxvxkhrYN+tJxHDe7WrNauK1rnvGxrWQZWA/WOTZx70rszMMaiz9ewI1vI8KNaSrh01OjZJsOUvljj3+2ZewCAnwLnd955R6677jozRbBx48ZONYR6nsA5xBYHRmjGuW4XB/qvVMNVjbO2owvmdD6rp68VOA7pVhY4q6krd3oUOE9cuMW037PMX7/PPEarBkk+1zfbxcVEy/1ndJOr3/nNXP7Xt6vkhI6Naxx6UllHe0u6vTkeBc6uyhoemLRM+nRs5PR6CTVLtx50HF3o2iLNPI+HN0uT1TuzTPmJ1kAHszUiAERcqcaDDz4oDz30kBw8eFA2bNgg69evd5zWrVsXmL2E1+O2I2lxoL07hY5NDsuMc/l+248EBDPjrFPjLJp9VJpxji2fyqd1zloG4Q693btzN1a53grC3d3GvPL65sS4aOnVtvqhStp3+KTDyoL6LfsPyWcLtziCwgGH1x7sa4bdstFFS76afr/W7i4rb9GhLFaLPK1zfnDSMrefr7qmrzPr5929VboJmpVV56xHH5a66PEMAPAhcM7NzZWLL75YoqMpjw5V9gxmJNU4uyp5qAv6WNZ4Z28yzgftAX9SaNU42ztKWBlY3bcTOpXVB2sZh2Yj3TF77V5Zu6ssoOzUtCJ7+8Vi9wNnfbxtB/PM+WPbNzSlI9XRI1yada48efukw5q6lTW1PiioDR4sENRyBys27t22oTx+zlGOxYrfLtshX/2+XUKRPSju2briA4l9gSDlGgBQM4+j37/+9a/y6aefeno3BCnjHEl9nJ1KNcoX2dWF6OgoRy9nXzPOodZVw1XGWZ3araIjxQ9uDkN5Z84Gx/k7Tu0qvcoXnumI7D/cDL6dyjRspRfVOaJFulx0vHMNdU3dNKrNOHvQis0eXGrHDz0i8dg5Rzque/CLZbIrqyz4DyVLtjgvDLQc3bah4zydNQDAz4Hzk08+KTNmzJBBgwbJTTfdJLfffrvTCcEXqV01Dti6U9RlVw1l1a1qBwVPB0VYNc4p8TFmfLTSThHW+cwgBs72Hs72Gt/BtsDZnSmC2glj2qqy27VITzTB6zlHt/I46+zOwsDKbj/1cLMwUGn2efARzdzuz50cH+NxxtkeXB5dnq09s2crOaN8YaB+ULr/89Ar2bBPDLSXwHRplup4/hZVWvQIAPBD4Pz999/Lzp07ZenSpbJo0SLHafHixZ5uDgGQlR+hNc5B6qphr3PWOlD7Yj9P9rtyltyqcw5q4FweMGoA2cxWy922UbIc0SLNnF+y5aDszKw5g/q/eRsd5QuX/6WdqZ89o2dLRxnFF0u21hpImvrm8sA5KS7GKSta28/mmQt7SeemKXLPsCOksZuL80xLuvLyFA38dVR9bXQfrYyzLry1LzD859k9pHFKvOPDhiclKnXZUUOD5E5NygbdKC1DsgLpnZn5sv2g8zRGAIAPgfMzzzwjb7/9tqxcuVKmT58uP/30k+P0448/ero5BLjGOZK6argaJBLqnTU00LJqnCvvc0Z5Szpt+xYM2qNZA0alAWTlKXunda/IOk9buava7RwqKJaPft1szsfHRMvFfcpKJ5qlJUr/8o4cWru8sJYBGzqIZHt5ffNxHRo6MvLuGNqjhUy7Y5BcO6CzeMKaIFhUUirbDtReXqGLEK1yHS1F0TIeiwbsj9tKNrS3c20fOOqKlo5Yz60uaLTvt7IPmaFcAwD8GDgnJCRI//79Pb0bglDjrHFQSgS1lrIys9ptofJQjFDtrJFbUOwYAV05S24F0tp72J1sp79pEKgBo+pYPgzEbogtcJ66omIiX2Xaq9mq0z6zV0unDxlnH93acf7LxVt9bkPnb1bG2d3R2/b65t7tKmqDLcOOaikjepWVqOhzct/EpSFRsmFfGNjLRSZfFzlaGIQCAH4MnG+55RZ54YUXPL0bglDjrIdkK2eWwpmj5KEOezj7mnF21cPZYl8gaK9LD0Z9cwdbAGk5slWGNE8v+75n/7nXDDepTINC+6LAq/p1cPq6tmqzMsfabaKmDwhzgxA4WxlndxcIOgXOlUaBWx4d0cPxepm2apd8trDmDwx1QcttLK5KYKxabUVnDQDwY+D8yy+/yLvvviudOnWSs846S8477zynE4LPam8WSVMD7X2c67q+2ZeMs/OCRueAPyPInTWq66hh0Q9dQ8oXCepI6p//2FPlNr+s32cGZ1htzSoHZVpjrwNV1N6cApm1tuo2Ktc3a721TrWr+4xz7QsE7UGl1TWksoYp8TLm3IqSjUcnLw963bB9YaCr51YD/baNkhy10N6MWof78gqLZc3OrKAcaQJQx4FzgwYNTIA8cOBAadKkiWRkZDidEHxWzWwkddTQPzR5hSVBqW9WVjs6TzPOB2tY0Gj/YBOMXs720oRO1UzNcy7XqNpd4925FdnmK/s6Z5tdl2tsqzaI14Vp6rgOjRzDOQKtQxP3M84aTC4rn7ynrewalS8EdOW0Hi3kvN6tHUcT7vkseCUb+rjWwkDtN92moespjla5Rn5Riawu/zAE/zz/W/bnypdLtskjXy6XES/OkiMf/l5O++9MGfnqXK9aXAIIHo8jq3HjxgVmT+AX+UXFJjsYaRlne0Y2GIGzvePEbk8yzk5jwl3XOIdqxln169zYtNHLKSiWH1ftNF1FrGEwOkr7++U7HRnL4eXt2Cob1LWp+RCnAeT3y3eYxYRJ5W3gLPPW7XOc/0v58JW60Dwt0Uwa1GCxtozzqu1Z5naVF9NV5+GzepgM+66sfJmxZrfpZ92jVUZQatl1qqHSIwKVF4Fa9IiBBndWnfORtiEp/jD3z73y0BfLzOvhvuHdqt2PSHgP1g9YCzcekIWb9suCjfvNa8CVJZsPyMhX5sh7V/dxOvoBIHQx/i/CRG4P5+C1ovOpxrmmjHN5V43KnVDqOuOclhDraKNWmU7uG3B4U3N+f26hCQIsH8zfZAJpdekJ7artgqHbGH5kWVCtAbiO8a5pYWDfOqpvtspRrEEom/bmOr4fVxbbehy7EzjrWPhrB3TyW7cKzXi/NWu9WYzpCSvbrHrVUAITyM4aGkze+ekS+WNXtrzx83r55LeyLiyRRMuyxk5dI8c//oOMfGWuPPHNSjNJ0lXQrL2zrfIv7SZz3stznMppAIQujyOrjh071pgpWLduna/7BB/YewJH0tRAe61wXU4NtGeH42KiTIcMHYLiaV12qNU461GJrfsPObLNNf1Oa52zBgBKg94+HRuZ0pkPf9lkrouNjpLLTnCe3lfZ2b1bycflwZL2Nz6rvPOEdSjbWhio2W1/Zzpro5m+NTuzpaC4RHZk5knrBkm1Dz5xI3CuPM66LDBq7/V+TliwRR77aoXjaNLJbg56ca5vrn6/u7dKN+0E9Xnw9wLBD+dvkq0HKuq8/zl5hfTr3MT0Cw93e7Pz5c1Z6+W9ORvMB8PK9IOpLr7ULizH6P9tG5oPVVr3ftXbv5qR9lr/f/Hr8+Tly46RQV3d+7kCCJPA+dZbb3W6XFhYaIaffPfdd3LXXXdJJPvqq6/kjjvukJKSEvnHP/4h11xzjYSaSM04B7tUQwNLzTprL9xIqHHetC9XrORqdWUallOOaGYGmejtdfy2Hmb/+vft5o+91YKteXpijds4oWNj06FD65hnrNllPghZH4DW7clxPKd1Wd/samLixj051QbOVjCpwaUGme7o3jLDlLZoJtue+fWGfWHlqzP+9CBwtnXUsE0MdHVkoEfrdPMBQX8m+3MKzEJHX+UWFMmLP/3pdJ0GmJqB/nD0XwLW+Uefc12YqeVBKQmx0jA5vvwUZ74v/X10XE6Ol9YNk8zP3t0Skl2ZefL6zHXy/vxNcqiwImDWD5JatqSdYY5t39Bkl63yJruWGUnyyfV9ZfR7v5lFttq68pp3f5N/jewp5x/bxq/PhU471dePllfpftX2Ow+gerHetKNz5aWXXpLffvtNIlVRUZEZKa6DXnQR5LHHHivnnnuuNG5cd4eV63PgXFNbt7qih1Y1cN6Xk+9U6+ttqUYwM85Oo7ZtLdlc0SBDA1r9464B1dpd2U6LAq/qV3sWVZ+rs3q2Mpk5zdp/s3SHKe+wal89HbPtT1aphtI6535dXH8A0u9dadCsQaY7tJb78OZpsnJ7pumioEFkspe91RfbMt7z1+8z9bHVdfawB0zWgsaWGYlmKE1NNJNuZdYXbzkgJ/sh+/nunI2OBXAnd21qsvuafdbvYdycDfLXEzuKv+nv512fLpGJi6yyFn382tsN6u9k95bp5mes/+sHic5NU50+zGmm+NXpf8qHv252rCexPlBdeHwbuX5gZ2nT0L1Muj6e1jff9vFic1RH+6rrBwodnPP3QZ19rgPX8p7JS7aZD1r6vFt6tEo3kz11THwga6t1wa3+7GOio80HitiYKIktP6/vCfq86v/6e2KNfQdCnd9eqcOGDZN77703YhcPahu+Hj16SOvWrR3f75QpU+SSSy6RUGLPXEbSuG2nzG0Q+jjb65w186qLrewt6twp1ai83/ZSmroeu23vqOFO9unUbs1N4Kz+/f0qRxZTp9Ad42IQiCvn9G5tAmeldbpW4ByMwSd2HdwYgqJBpKdlGva6Yg2c9XWzfFumHN/B88WPmt20lzqoN35eJy9eekyN99NgP6u8//ZRbpTAaDnBuNkbHIG6r4Gzvh9p0Kb0c+b9Z3QzNb+XvjHfXPf0d6tk4OFNTVbWX/TDwj2f/e4ImjUwS4yNdllGUZl+gNWyIXtPcQ2ID2+RagJpNWnRNlPOYtHFpZf0aWcC5hYZNX8wcUWHOenP8Z+Tl8u7czea6/79/WoTPOsCU3c+oFempVRaR/7ajHVVXjdKX4d6evq71eZ3+IyjWpkgul0tH6LdtWJbpjwzZbXpY+6uw5qlmvUUJx3WxByhqryAOFTtOJhn3ucPa5bm1c8K9ThwnjBhgjRq5PkfhCeffFImTpwoq1atkqSkJOnXr5889dRT0rVrV3/tmsycOVP+/e9/y4IFC2T79u3y+eefyznnnOMya66327Fjh/Tq1csMeunTp4/52rZt2xxBs9LzW7cGf7BBdVMDI62rhlMAGqyMs22BoGZR3AqcQzTjbGVP3Q2ctS2dLnZSVicNqwWdu1kxzXJ1apoi63bnyC8b9pnDxpoFtTpqaMbpSDdLIAKWcbY9L9Vle+11y+7QrLA1klyzxN4Ezotc1Bx/s3S7GZleU52wvb65tux05aEurh7TU2/+vN7x2tYPTl2apZnTqP4dTICuXUru+GSxfPa3fhLrhxIdDZrvn7RMPl2wxVzWzOZLlx1jRrLrAkX9AK6LXPfnFphyoX05Zee1LGXt7mwT8FVezKdB8rKtmeZklxQXI//Xt71cc1LHWjP5tdGA65ERPaR5RqIJZtV7czeaEqb/XnS025NS9YPK+LkbZdzs9VXWYmjZiAalP67a5VS+Y31vT323yny40jITb4Podbuz5b8//GGy3J7ShaN60gWwutC4T4dGMuDwJnLSYU3liBZpIdOFRddkaIccbc+pJ/0AorTkRz9ontKtmfkA4OnfXw3AdQGyHtXUJI2Wv7VIT5Rm6Ql1PikXfg6ce/fu7fQC1heRBpq7d++Wl19+2dPNyYwZM+SGG26Q448/3pRD3HfffXLaaafJihUrJCWl6h/02bNnm2A2Ls75Ram317KJ5s0r+s5acnJyTCB89dVXVzuk5eOPPzalGK+++qqccMIJ8uyzz8rQoUNl9erV0qyZb1mXI444QqKja/6jcMwxx8iXX37pdN2IESNk4cKFtW5f91tPVqlGSX6ubHvzb3LzuDi5u5ZfuC+++MKUndjruK+//vpaHzM1NdV82LHTGvcPP/yw1vueccYZ8tprrzldd9xxx5nXUXU0I6s1gA1PHiUZSSc6rtefz+DBg8Udv/76q7RsWdEy7fXXX5d//vOftd7v8MMPlx9//FGapFVkjG++dpSsXFSWNatJ4pGniRw90mSlrDe/Nm3K6he1ra9mldS4uGiZdLdzRvp///ufDBo0yHF5+vTpcvnll7v1vW7ZUhY4WB599FF54403HJc1Y24dZj5zfKLJBirtz/7+++873feUU06RNWvWmA8LReXjw5XWpt76vwS5rfzyQw89JNdee63j6/ohVX+v7XS8eHZ5OVGPN2MlIS5G9mTlS/OLn5Dj+/V2BE8ffPCB3H333bV+ny1atKhSInbdddfJ119/Xet99WiRflDWWlNrUdz7d42Ub+6rmpnU4Cq/vI/49e8lSMzrr8mZZ57p+Lp+KD/77LNdPo4+Z1apwq1vxMhFG9ZKWlqa4+tjx441p5ro73Vhw/bSbORDJoOtkwA1gz1k2BmSs/WPGnu65+YXSfrx50jPvz5Zsb2sLOnWrZvL+2jgqAHoh1FR8uNDCV6/RyQlp0j8xc85AthbBx/ueI8oLV9Up8+NvlKbPBrrdKjem/eIsu+3UBL6XSEp3QeZYPT5S3pLh9iD0qbNceLue0RsaiNzhECDo4/Hj5O5E14rG01f/tLXv386pKcgIVZeHifysu09wu6yyy4zf99qM3r0aHn44YfNdv8+qItpkXjRyUebx9Pf2HdujJa42GjzOxodFWX+19vq+edefVNOP3Ww+V1+e/YGee2jL2XzxKedtp8QF21qvOfHRMt8WynLwx/ONGsVlpaX8hyY9YF8u+R7+VZEbtKfWYy+Z5W9b+nPz+LqPaL/gEHy+/KVZbXetsY0+jPQ33GjtFT6XXCdHDl4pBn8os9p5r7d8tlDV0hJaWnZ0B3bfbXNwEe295pLH31D+hx9pPk9zCsqlt9+mCxT3nnG2rSU6r/y+1tlIHpq07qlLPDxPUL37df1+2TKip3y9DXDpOBQ1daV+jpeKiLP64UokX5X3CNXXHSeDO7W3KyjsL9H6G4WFpWY7Wrpmr736O+cpdU1r0h0QsUHl8LFX8reeZ+Lvj3qz93KbJd932Vn9P9G7bvKwBv/I3kFxeZnodv//e375eCWNY7XT1SV11HZ5Vtvu03+cdedbr1HVKbvEb17H2NKKvVox8wfvpM7br1Jn4aQiiMsTz/9tFx66aVOccTJJ58sAQucK2dqNSBs2rSp+QOvAaKndFGh3TvvvGMCVX2RDRgwwOlruihPg+zDDjtMPvroI4mJiXF80/rHXYNHV39staxCTzXRP1z6BjZq1ChzWQNo/cV6++235Z577pFWrVo5ZZj1vJWNdpW51lNxcbEjgKhN27Ztq1ynH0bcyWpnZmZWGX5SnL1X9laUtFWroMA5K3Ho0CG3HtP+h9+yf/9+t+67b19Fz16LvtjduW9JYb5TplY/bLmb+bd+Hpbs7Gy37msN9rFnnHfv2ePWfVt0yJSEStlmV/fTt+Hcim5nRn5+fpXL3h7lOHjwYLX33W57nezZU3Wy386dO13eV5/N8mSL4/l0+npxcY37e8B289KSYqf65tzcXK+/V319uXNffb0q/SOkU/P+3J0jeQd2y9aCmqf87cgu+z2p/HvkzmNqPrvyIBT9/XXnvvEJZdngp8/vJWe/NMsMBNq8dYcccuf3piBXerauyCbrPrjzmFuzvH+PSEhKkRbl5REXHt/WZDCre484mC1y0E/vEXGF+SYY0EytZk+XL3fv9WC9ZlumJUjTtKYma5i7oJFMP1j1d0Jf9vb8s6vhX/q75M7j6u+m3chj20hxVkWpiD6DZR+vq7rl/V8laW5F2cihQ3nmvb/Ke4uL+2ppiZ60DePXS7fLv+cXycFs58fVd6DKS1p37654PvQD4Us/rZXfVq6Xgn1VyzJ0G/ZXz2mHN5DbL+jl9AF//E21l3PodqYs3SbTd1S8j2at2CLZLh6zMl2Tcu7Ls6VXG51smmFOe/e695pYvHaL3PrRIpOlt/625h3cI6W1vEeolVv2yuNfrzQnHTDVqXSr1+9pOdlZkn9wd623K0hsKDPXON9u797dUrC/9ufpyS8Wyv9yvjczC/QISkZsodv7+39vzJb8RmV9/s3+rvpF9oRwHKF/X+w0jnAnTvMqcNaNazs6zcS6yuz6g/Um4qrsQ4P0b775xgTUV1xxhYwfP17Wr19vgmYN6N3JULmifxg0UNcabftjDRkyRObOnWsua5C8bNky80PRN8lvv/1WHnzwQZfb0+BeT/oHUW+rWc7aMs764cPVdfbykOqkp6dXqZWNSW0sjVPja+1QEB/vnOXUchl3HlM/KVbWsGFDt+7r6mermcOaWBnS6LgEpyA0NjbWrcdU1gct+/fgzn2t13oTW2lGfGoDt+6bF5NYFjjb6pvt99MuExrE6KIZe69olZBQ9bK732tl+jq07qtvbTsPlv0p1kyWvYezTgN19f3r76VmL/Zah3+jyhZLxtiOPlV+Tejz7Wp/tRuHZlukPKul2aeo6Bin+ubk5GS3vldXrxt9fblzX3292uucNXCOTm0szRNLTAbGon8MrK4fmj3TQ7L6e1L596imx7R/z1q6YPuVNb+/te2vHpmISc4wXR+6tkiTC49raw7lS1K6NGjS3GQUq7ufxumNGzYwLdAsmmmq7jFz8osci4z1Pt68R2gGcW9+2XuPHna/6ZQuLt8j7Ecg9HegcWqCyVJ5+h6h+6v7rfQ94pkLe8mI8paHdfkeYae/S+7c11XQrffTTKSWk9TUWzwq1vnIa1x8gqQ1amZeD+7W2+oHmr8N6iy7ZnSXV1e3KpvSqtlQ28JHu4W7iuThL5ZJUnysvDd3gzkSGJXcQGJSc8zrKjUhRpITYl1mG919j1Cakdb3fC3nKSgqNu8Rdvpz1r9ztYlOaWgWvNrbSWauz5GEjCZlGdtSkRJ9V3TxNP+yrUD+qDTtNDa1scSV5psFwprNt78H6v7qc5dfWCxRsfFOpXErd+ypdn/1edN2p/q7oj+3O4ceLgcK48zvr7bIXLg0Q7LTGrvcRzt9j3Cc18WYuggzOcO95yk+2fwe6UnfC/XItTv3U/vzSiXB9jrV773W+0aJNGnWqE7jCPvfFzt9j9A4zd3gOarUwzmw+oArV66U9u2970daHc0oa3nCgQMHZNasWdXebtOmTXLSSSdJ3759TWCr2W7NVLtTA6W3qVzjbNUvz5kzx2zTooG4HmqbP7/sAJeWUtx5551mP/Vr9sPSrliBswYd9uA2kO74ZIl8trDsMP0Ptw8w9YSR4KwXZplDivpmsPaJYUGpd5u/bq9c9Po8c370SR3l/jO613h7/QN0xINlR1S09/En11W8tiwnPvWjmeymweuCB0+VuqDjlIc+O9OcP7d3a5OZc4f+Adefgx7Cvui4tvLU+T29enytv3x0clk/Ynuv28UPnxa0xTXaV/jt2WULFz+69i9OQfykRVvl1o8Xm/O3n3q43Dz4MI+3r6OW35lTtuhOuyhYQ2XcoXW3w5//2Zw/s2dLs5BMuxUM+s9080dfP8DM+sfJVTp9LN92UM54vux9VINILVtwx5y1e+TSN8ve87Q/9xPnHiWe0gmBJrAXMV0zHjzT9e+KBhrnvDTbvKbUdQM6yb3D3Ts8rPTP19Pfr5ZXppctQNS3hadH9pQLjqt6BC8c6YfKzfsPmQBaD4Ob/3P1/0LbdYXmQ4PWMF99YsdaW0O6S9cgTFm+Q75bvsMsDK4hfjclHaP6dzQ/v0D02df6dA189Xu1ykfKTtHmdW+uM//HmA9t+nrS9QRay611/rVNBa2Nvj8NOqKZnNq9uZl8WVv9sr4uNfjUaavTVu6S3zbud3wA0mD2iJZpZpGxZsF1zUSnJqm1tmXUUo59uQWmFnpXVp6UlIgpGUqMjzH19uakl8vPWwOpTG3/oUKTVLNeO3pZXzvm/9wCkxDRbWqZ1q7MfKf2irWJidakT7xJ/Oh7kT62/u3TbRzSspryshE9WedN6ZP+XezQSD6+7i8hUb/uSbzmcamGZl61b3MgAmfN0mpWt6agWbVr185km7XWqlOnTvLWW2/VyROvQb2eQllWhHbVsBYH6tjqYP2S2TPO7vRyPljDuG1L2RvwIVObqW+2dfG9OY3a9qAVlb5Bjv9rH1m5PcunsdjaBksHedj/EOsHi2CuSO/QpCIDoUGpPXC2DwPxtKOGpZetf7L+IfckcF7kYmKhthA7vUcL08JMX4s6VEaz0NX2b65hYmBlPdvqWO6yTJw3g1B0waI1HEf/sGs2szr6x33sRb1kxAuzTZ3n6z+vMwtR3V1A+d+paxxBs3ry3KMiJmi2jsiU9Rmv+77LrRokyVX9O5qT1qNrAKhB9Kw/9ji6imiW9LIT2svfT+7s8wLJmmhw7EnHHX392F9Duij0961lgbQG1JqE0QBSM/PatjUloawdnnXS61MTY03ArItqtctHdZNRXdH3ce0Uo6drB3Q2j79g0z7zfq8DnrxZ7KeBtQanZUcmMzx67pqlxbj989G/Q3okyAqiNaDW9xhd56FHTpukxUvT1EQTJGvArD3QPenFrkG1Jm50YqYuEtf3Ll04HE48Dpz//ve/myEgWpukC0YqL+Dr2dO7LNSNN95oFp1oBwxr8VR1tOZSs71nnXWWWcxx2223mQ4Y3tJDanrISLdb+XHcTf2HZju6yOmLaXWnsB9urmv2LhruTA90Z0y4Va+th2X1k7i3PX69b0Xn2cp5PZR+4mG1dxOpib6B9+/SRH7+Y09Q29DZ2XvZVs5O2btLuNOZwhXNLFkWb/ZsEIr9ELO2i7OMHtDJMdHxjZnr5IJj2zh98HJ3YmBlGjh0bZ4mq3ZkmdOhgmKPWoM9P+0P83pWV/fvWKUEqbIjWqTLbacebro6aLCuR82+veWkastPrD++2ubu+R/XOq577Jwj5eI+NU+whHf0917r1PWkyZnpq3ebQEq7SITD9Ef9u6HdOfQUrMc/5YjAlLf6m76HaNJNT9rD3N8S42JMB5lR4341l7Vbk3YiCacuYB7/lb744ovN/zfffLPTE21lyyovwKqN3u+mm24y5RPaNUBrqGuiCy60i4Ku9vz000/Nan8t1dD6z//85z/iDa3h0w8B06ZNc5RwaDmGXtaAPpxYtYl6OEgPmUTK4Urr+6ouc1sXNPugWQc9vOxOxtmdMeHpSRW/gpmHvB+O4fXwkyBNEDv76NZOgXMwBp/YdWjsnHG26GHOleUrILWVnrdTKzWzrx9k9XVsD2jdYWV9NbunLf0s2j/7uPYNzWFgbeM1fc1up77LS8oDdE0Gaa9eT2hmW4NmPbys2Tk9IuCOP3dnO0rF0hNjTXDvjmsHdJKpK3bIwk0HzFTLMd+sNJnqzfsOyeb9uSaLbU77D5mvV/79e+Ss7vJ/f/H/UVBUpQHVWeX144A39H3qtO7NTZcS/V1+duof8tBZNZc+hhKP/0rrYjx/l2do6yltZ6IrLK1WIlprUnkBjgaz2h1Dy0S0fZwWdHfv3l2mTp1qFghqnbJmnyvT1f5r1651+h4WL15sisu17ENpR44rr7zStDPRchRtR6dt7KwuG+HCCjD1j3Qo1A35g7WaOVjjti36fGpnDR0oYLUXc3faYXX7XbmXszcDFHwq1QhS4Dy0R3O57/OyDyH6Wu1WPlwiWHTRnX7Y1Nq7DXtyneqLrcPS3pZpKD2UqeUSs9fuNYdAtU7RnZ+1viZ0UqPq3qrqIV4NTH8bv8CRdbYCZ83Irt6ZZc7rYAZPP5Bp3aXVe3rRpv1uB85aOmGV4Fw3sLPbv69apvPMhUfL8Od+NkdedIy1ntzxwBndTDkBgPDx4JndZeYfu013IJ1Eq1M39ehTOPC44/zGjRtNgKrBq/2k1+nXPPXKK6+YYmzNGuuqRuukgXGVnY2OljFjxshnn33mtNJbezT/8MMPcsEFF7h8DO3zqv2n9WQFyXpe+85aLrroIpOx1uuOPvpoE1hrq7xAdQ8JdI1zRNU3u5G5res6Z12koZlwt6cdVlOqYT88ZS+zqYvAWRckBuvwmL4+7x7a1RzGv2to16BP3NJa0jYNkxwZZ2vNtL3G114m4Q17ucQSN7POS+yP7yJwH1LeI1bN+XOvY7y2DmWwFiN5Ut/s6nu1l4rURD9kfPV72ap0rX28ql8Hjx5Tv497h9fe0lRfMxrY64LH1//vWLnmJPey2gBCR9tGyXLDoLJuO/pe9dCk5VVadUZMxlmbRGvLjspDQTT41a95U6rhiVNPdd15wAqKXdGg3J3H0bKMcCvNsNPv0crO2ksAwp07mdu60jS1LHDXl5O2yGtWwwr2msZtu8w42wLtQNHV99ZktGBlmy0a8IRS0KPPh9Y362hmrWHXmnan+mIfMs5KB5dYtFxDp9l5Vt9c9fH1A4d2rXhg0jLHGO7nLu4tS+31zV7st9Y2aq2zLhJyd4Hg2KllE+/U3wZ1qbFGuTqXn9DeHNGZ9+de0x1C/7i2a5Rs+my3bZgsbRomh80oZgA10yNmWtq1oXyh4KTFW+Xc3jWvcQsFHr+zVbfyf+/evS4n/aHu6CFOK8uUlhA5GWen7hRBXBxYeYGgBqA1Bs7uZJyT6jbj7LQw0IOOGvVB2fOx25F11p+1FTTq5Eftn+yvjLO944W7HTV6t3Wd8R55TBsZO3WN+SCnGd+7Tz/Cafv2gN1dGpBrJxAtLdE+stsP6nj0pOr3c9N++WFl2ZAFHaOubey8LWm5d5j77egAhK/E8oWCV5UvFBzzzSozaTHUFwq6HThbo6o1aL7qqquchjNolvn333+Xfv36BWYv4VF9c6R11HAqeQhyxtneIaC2OmdvapwDzV6/q4vdUKG9bYGglrNo6YAuRFNHtc6odZhQbTSg1GBcF8NoCUZt7Qf161bgrmU1mnV1RTOwujDuuWl/mA/Ob89a7ygF0VHi3tYNaqCugbOV+W55VNXH12B91fZMeWbqGsd1N51ymFfttgDUP4O6NjNrXr5fHj4LBd2OrqzpRvpmrov47Av3tN74L3/5ixlZjeCxpgYqapyD35LOrRrnSl01Ao2Mc/XsGXjtMWqvQ/ZlYaBFg2TN/mpmVkuq9PBkTV1N9OvWUQst06gpyP6/vu1NezadsqY9lK0BBt1apnnUf9bO/j3rAAx9flbtyDQDdFZqq7rtmY6yH/uHjwuOC/1DrQBCa6HgjDXhs1DQ7cB53Lhx5v8OHTrIXXfdVWVkIUKr+0TE1jgnh07GubaWdE41ztUsaqzrjLNzRw1+h6vLOOsHDPt6xaNd1Bd7W65hlTRonXNNgbOWP7gbuOvrcuSxbeSD+ZvMCGTLUV6Uabj6nnXqoTX5sCb3nH6Ez5l5APVLm4bJcuPJXeQ/U9Y4FgqGykRBVzx+h7viiitk69atVa7/448/ZMOG2t9YETgROzUwN4QWBzplnPPd2m9tc5ZSzYKmuu6qYe/hTI1z1TdvK1jWjLN98Ik/Ms6VO1xYfZY9HXxSHV0kWPnvjCeDT1wF4/YPE5XpURSdIKndM54aeZT8cPsAGXZUS68fD0D9XijYofz9xlooGKo8TktqffPVV18thx12mNP18+fPlzfffNMMMUHwa5x1+ECkcGd0dUhmnMsDZw0wqvvkXOc1zuWLA5ulJXjV9SCSaUlD64ZJZuiGfsCwfmT6YUn7PPuD8wLBA24tDNT9cKelnHbC0PZ0U1fsdDmx0Bt3Dz1Cnvx2pemwcUSLNDmiZbr5X/tu62soVDNCAMJLQqzzQsEnvg7dhYIe/+VctGiR9O/fv8r1WuMczq3cIoE9YxmKL7ZI6OPsScbZCoRrypI7ddUIcOCsrw+rLjvYrehClWbhNXDOyi9yyjb7K0BsVL7ITx9j2baDphe49pCuTMdcr9peNsDk8GZpbh9BKpvAVxY4J8fHSJdmvo3MPaNnS3MCgLpcKLgnO3QXCnpcqqF/QLKyyt7QK/dx9rSHM/wrYrtq2ALKYGfSteQiMS661oxzYXGJ6YFbW7Cv3QesxVuBzjg7jdqmFZ1LrkoT/FWmUTkLrAthdFS2KyaoLm8t6cnj6wjugYc3NeeHHdky6INlAMDThYLW31hdKLhye6aEfeA8YMAAefLJJ52CZD2v15144on+3j94IGJrnMsDSv0w4Co7V+djt8uzzjVlnD0pL7GODtg/+ETqqO1Q56ru29fBJ5XZyyfskwGrWxjoavBJTa/P1/7vWPnqphPl6fN7+rinAFD3a01uOqWsFNgsFPxiWchNFPQ4fffUU0+Z4Llr165y0kknmet+/vlnyczMlB9//DEQ+wg32duZRVTG2VYrHAq0zlkPte/PLTSZZVddBJwWNNay3xlJsSYID3zGuaKHc0c6arjUvlLgrBUavnSmqHWB4JaDcnEf3xcGVj6KcWRr/+4zANSVa07qKBMWbDHJpEv6eDdMKZA8jq66d+9uhp28+OKLsmTJEtPPWTttaH1zo0aNArOX8DjjbK+dDWf6SdPKOFc3trquNbUtENybXSAtMqpODzzoxrjtyj8rLe2orubV7z2cyTi7ZK3qthzWLNXvR280qNUKCq3EqG6BoBU466I8X+uUASDcFgq+evmx5m9rsDtpueJVWrJVq1YyZswY/+8NfBKJNc4aTFpjxEPlF6iJbYGg1jm7CpzdGbdtsX9f+jNsmBIf+FINapxdatso2WSZrSOD1Y259kVKeTC8Zme2GSaSV1jsNGlPx1vrmGulY6+pUwZQ33RtkSahyqvUlpZmXH755WbEttXTefz48TJr1ix/7x/qeeDsSclDMDLO1dU5exI411UvZyvj3CojkZHI1dAAtmV6ot8Hn1TXlk4XAK6otPhlsa1Mw98LEwEAdRw4f/bZZzJ06FBTorFw4ULJz893dNUgCx1cVtClXRr0UEckCKUeztVlnGuddljLftdFL2dt6WcF85Rp1Mz+/AQqcO1l2+7vlRYI2gevBCLjDQCow8D58ccfl1dffVXeeOMNiYur+IOvvZ01kEbwM86R1MPZKXAOwYzz7moyzgc96D1tH49uX+DpT3TUcN/IY9qYGuQ+HRpJ1+aBOVzYq9ICwWpHbQco4w0A8I7Hx/NXr15tumpUlpGRIQcO1DwJC4F19tGtZGdmvhl8ECmcSh5CZXFgWrxHGecGIZBxti8MpIdzzUYe20YGd2tmfi6Bmox3RIt0iY+JloLiElliWyCoXVp+Lw+k2zVKdppUCQAIw8C5RYsWsnbtWunQoYPT9Vrf3KlTJ3/uGzx09+lHRNxzdsDWnSJ0apwTw67Geb2tFR2lGrUL9IRKLafq1jLNZJvX7c4xP3d9HehiwfyiEnMb6psBIAJKNUaPHi233HKLzJ8/32Rjtm3bJu+//77ceeed8re//S0we4l6yznjHBqBcxOPM87xQc8420s16OEcGqwFgmpZeZbZ28EnAIAQzTjfc889UlJSIoMHD5bc3FxTtpGQkGAC55tuuikwe4l6yx5Ihko7uuT4WDN6O6eguNqMs1XjrEf6a+twYu+5nRmoUo3ywFlrd7XlGoKv8iCUfl2a+DT4BAAQgoGzZpnvv/9+ueuuu0zJRnZ2thmKkppKk34EphtEXR0+97SzRs7e3FozzhrsR2u0GsSMsw6RsQLnVg2SIqbjSrizl2JYg1CsjhpaytG9ZXrQ9g0A4JrXI8ri4+MlLS1NWrZsSdCMgPGkVjgYnTUy84okv6i42v12p7zEucbZ/1019uYUSFZ+2XY7MjEwZHRqmmqOXChdELg/p8BRUnNkq3QTPAMAQovH78xFRUXy4IMPmi4aukBQT3r+gQcekMLCwA1vQP0UiqUayt7tYE92RVZc6aRDa5FfhhtZ8kBnnK1ssyJwDh06EVDHb6utBw7JDyt3Or52NP2bASAySjW0jnnixIny9NNPS9++fc11c+fOlUceeUT27t0rr7zySiD2E/WUFUgmxkWH1LS7prYhKHuy8qV1gyTH5ay8QsfIZncyzqm2GuhA1Dgzajt06SCU+ev3mfPvzt3guJ6FgQAQIYHzBx98IB999JEMGzbMcV3Pnj2lbdu2cskllxA4w68qSh5Cp765csa5cp2zp+UlmnnUBYQ6wCYQgbNTD2dKNUJ2geCyrRWjtwmcASBCSjW0g0blHs6qY8eOpu4ZCEQf51Aq06iSca7UWcOT4SeV65wD0cd5Az2cQ1YvW0s6+2vLfgQDABDGgfONN94ojz32mOTnVwQLev6JJ54wXwP8Ja+wWPIKS0Jq+ImlSWr1vZztnUDcqXE2tysPsLU0RbtgBKJUQzPbbRoSkIUS/Xk0Somv0m0jUBMLAQB1XKqxaNEimTZtmrRp00Z69eplrluyZIkUFBSY3s7nnXee47ZaCw14y75QLlSGn7iTcfZmv9OTyn4VC4tL5VBhsekV7bdWdOWlGm0bJklcDJ0aQokGyFquMX31bsd1lGkAQOjy+K9zgwYNZOTIkU7XaX0zUF9a0VWpca5cquHFfttLUTIPFfktcF646YDkFpS1y2PUduhOEHQKnOmoAQAhy+O/zuPGjQvMngCVOGVuQ2j4SdWuGgU+B872Xs76fbfISPRLtvnxr1c4Lp/avbnP24T/9bItENRZOfYFgwCA0OLzcdsZM2bIN998I/v37/fPHgGuaoVDrFRDW+OlJcS6zjiXL2hUGW52A3HKOPtpgeCXS7Y5Rjh3aZYqFx3HkaFQzThbDm+eJinlrysAQBgHzk899ZQZfGLPZp1++uly8skny5lnnindunWT5cuXB2o/UQ85dacIsVINa+y21cfZ7qA3GWf7EBTb/b11qKBYnvp2lePyA2d0k1jqm0OSHr34v7+0Ny0J/35yl2DvDgDAH4Hzxx9/LEceeaTj8oQJE2TmzJny888/y549e+S4446TRx991N3NAbWyB5ChlnG2j93WcdbaAcSXdnT+zji/+fM62XYwz5wf1LWpDOrazOdtInAeO+dI+f3h02REr1Y8zQAQCYHz+vXrzaATi5ZnnH/++dK/f39p1KiRGbmtEwQBf7GXPITaABTVJM11SzpvSkysrhr+GLu9MzNPXp7+p6MFnWabEfpoQQcAERQ4FxUVmeEnFg2S+/Xr57jcqlUrk3kG6kNXDXvGuXJLOivjrDXQ7pZHVO6q4Yunv1ttWtqpy09oJ12apfm0PQAA4GHg3LlzZ1OaoTZt2iRr1qyRAQMGOL6+ZcsWady4sbubA2plL3kIxVKN6sZuWyUmngxtqdxVw1tLtxyUzxZuKd9mrNw65HCvtwUAAJy5vXz7hhtuMJMBtaZ53rx50rdvX+nevbvj6z/++KP07t3b3c0BtcoM8cWBzkNQChyLZq2A35N99keNsz72P7+qWKB7y5DDpWGlqXQAAKAOAufRo0dLTEyMTJ482WSaH374Yaevb9u2Ta6++mofdgVwXaqhdbqpIdiiy1XGOTu/SIpLSj2uy3bqquFlxvmbpTvk1w1lbSE7NUkxnRoAAID/eBSNaGBcXXD88ssv+2ufAKfFgdqZIhQXTrkau22vy/akVMO5xtnzwFm7ejz57UrH5fuGd5P4WMZrAwDgT/xlRciygtBQrG+293G2Z5ydph16sN8JsdESX76Q0JuM89uz18uW/YfM+RO7NJHB3Wg/BwCAvxE4IyQVFZdIVl6Rx5nbutQkNb7GjLMnNc6aUbfKNazv2127svLkpR/XOkY2P3Bmt5DM0AMAEO4InBGSMm3BoyeZ27qUEBtjOlfYx2770nva6uXsacZ57JQ1klNQ1n7u4j7t5IgW6R7dHwAAuIfAGSHJPkSkQXLodoZoWmnstrc1zub25R8QdIGhZtzdsXzbQfn4t82OvtG3n0r7OQAAQiJwLiwslNjYWFm2bFnAdgionHUN1Rpne2cNzfjmFhR5XeNcuZezO+Ua2n7usa9WSGlZEw+58ZQuTp0+AABAEAPnuLg4adeunRQXlx0WBupi+Eko9nB22Vkjq8CnTLmnvZynrtgp89btM+fbNUqWq/p38OjxAABAgEs17r//frnvvvtk376yP9hAIFjT90K5xrlKL+fsPJ/GhFs1zu7WOb8/f5NT+zmtuQYAAIHj8VSJF198UdauXSutWrWS9u3bS0pKitPXFy5c6M/9Qz1lz9yGaleNyhnn3Zpx9qFUw7mXc82lGgVFJfLL+rIPr83SEmRoj+YePRYAAKiDwPmcc87x4mEAzzgHoCG8ONAp45zvlCm3TwP0tMa5tozz4s0H5FBhWclU/y5NaD8HAEAoBs6VR20DgeBLd4rg1TjnO9rRJcXFSGJcTMBqnGev3eM4369zY48eBwAA1GE7ugMHDsibb74p9957r6PWWUs0tm7d6uVuAM586U4RvBrnfEfA782CRnuGuraM85w/bYFzlyYePxYAAKiDjPPvv/8uQ4YMkYyMDNmwYYOMHj1aGjVqJBMnTpRNmzbJe++958VuADUEzmHQx9kau22VmHjTQs+5xrn6wDknv0gWbTpgzndonCytGyR5/FgAAKAOMs633367XHXVVfLHH39IYmKi4/rhw4fLzJkzvdgFoObFgdZ0vlDU2DZ2e/O+XLNoz+uMs5s1zr9u2CdFJWXNm8k2AwAQwoHzr7/+Ktddd12V61u3bi07duzw136hnrMyt2mJsRIbE7oDLuNioqVheZC8bk+OTwsanWucq++qMefPvY7z/TtTpgEAQF3xOCJJSEiQzMzMKtevWbNGmjZt6q/9Qj1ndacI5amBleucrWyz9zXO7vVxti8M7MvCQAAAQjdwHjFihPzzn/8047dVVFSUqW3+xz/+ISNHjgzEPqKe0VHSVsY5lKcGuqpz9qUTSFpi7TXO+3MKZMX2sg+u3VqmS6OU0K3/BgBA6nvg/Mwzz0h2drY0a9ZMDh06JAMHDpQuXbpIWlqaPPHEE4HZS9Qr2flFUlxewxvKPZxdddaweLPfMdFRkpYQW2PgPG/dXikte2qkP9lmAADqlMerrrSbxtSpU2XWrFmmw4YG0cccc4zptAHUpx7ONWWcvc2Ua0u6rPyiavs4z7a1odPBJwAAIIQD57y8PNNN48QTTzQnoL72cK454+x94Lz1wCHzHGjJipZC2c1ZW7YwMDY6So7v2MjLPQYAAHUSODdo0ED69OljSjROPvlk6du3ryQl0UcWgerhXH9qnM39yhcIFhaXSl5hiSTFV0wf3H7wkKNzR6+2DSS1vKwDAACEaI3zDz/8IKeffrrMnz/fLBRs2LChyTzff//9poQD8GepRnjUOFfdR2/3u6Zezla2WVHfDABAGATOGiTfd999MmXKFDN6+6effjKLA59++mkTUAO+OnCoYvhJOLSj82eNs3Mv58Jq65sZfAIAQN3z6liv9myePn2645Sfny9nnnmmDBo0yP97iHon7BYHpvp3caCrjLPWO1sZ58S4aOndroFX2wcAAHUYOOuEQG1Dp0GynrR/c8+ePassYgLqy+JA7aWsL3+rTVx8TLQkxVXUJnudcbY9D+v35MiOzDxz/vgOjSQh1rvtAwCAOizV0OmAubm5Zry2nnbu3GkCacDfUwNVg+TQr3HWkeCNbPupWXJvP0imJ7qeHjjbNma7H2O2AQAIj8B58eLFJmC+5557TImG1js3adJE+vXrZxYIAv6scQ6HrhqVW9L5kiW3l6bYM85zbGO2+3dp7PX2AQBAHdc4a0s67ajRv39/EzB/8cUX8uGHH5pOG0wPhF9rnMOgVMNaILh6Z5bPwb5zV40i839JSanMXbfXkZHu0SrD5/0FAAB1EDhPnDjRsShwxYoV0qhRI9NpQ0dxa29nwFdWiYIugkv0slY4mC3pMnxooeeqq8aK7ZmODxN9Ozc2o7kBAEAYBM7XX3+9DBgwQK699loTKB911FGB2TPUW1aQGC7Z5sot6XzKOLvoqjHH3oaO+mYAAMIncN61a1dg9gSoVOMcDsNP/F7j7KKrxmz74BPqmwEACK8a5+LiYpk0aZKsXLnSXO7evbucffbZEhMTHofVEbryCovNqOlw6eHs94xzpcmBBUUl8sv6feZys7QE6dw01cc9BQAAdRY4r127VoYPHy5bt26Vrl27muuefPJJadu2rXz99dfSuXNnr3cGyAyzHs6WE7s0keT4GBPoDurazOvtaF239oEuKC6RzLwiWbLlgBwqLDZf69+lCf3SAQAIp8D55ptvNsHxvHnzzMJAtXfvXrn88svN1zR4Brx1wB44h1HGuVl6osy9d7DkFxVLs7REr7ej/Z/Tk2JlT3aB+RAx29aGThcGAgCAMAqcZ8yY4RQ0q8aNG8u//vUv054O8FcrunAYflK1Ptn3YF8XCFqBszVm28o4AwCAMBqAkpCQIFlZZf1q7bKzsyU+PrwCHYSeA7kVw0/CqauGP1l1zln5RbJo835zvkPjZGndICnIewYAQP3mceB85plnmlZ0OuyktLTUnDQDrW3qdCgK4K9SjfoaONu/78LiUvN/P7LNAACEX+D8/PPPmxrnvn37SmJiojlpiUaXLl3kueeeC8xeot446FSqUT8DZ3svZ0t/+jcDABB+Nc46bltHbGt3DasdXbdu3UzgDPirh3O49XH2p4ykqr+Wf+lUsaYAAACEeOBcUlIi//73v+XLL7+UgoICGTx4sDz88MOSlETdJfzHmpZXrzPOtl7OqlvLdGlsG7ACAABCvFTjiSeekPvuu09SU1OldevWpizjhhtuCOzeoV531aDGuUx/2tABABBegfN7770nL7/8snz//fdmauDkyZPl/fffN5lowF/IOFf9wEAbOgAAwixw3rRpk5kYaBkyZIgZ1rBt27ZA7RvqccY5JjpKUhO8mggfUYsDY6Oj5PiO1DcDABBWgXNRUZHpoGEXFxcnhYUVh9YBfy0O1KyrfjCr7xnnXm0b1NsPEAAAhBq3/yJrv+arrrrKDECx5OXlmf7NKSkpjusmTpzo/71Evcs4N6inPZxVl2apJtNcVFIqp/doEezdAQAAngbOV155ZZXrLr/8cnfvDtSquKRUsvKKzPmMetpRQzVPT5T3rzlBNu7NlXOPaR3s3QEAAJ4GzuPGjXP3poBXMu2t6Opxxlmd0KmxOQEAgDCeHAjUxbjtBsn1c/gJAAAIXQTOCBkHciumBtbXHs4AACB0ETgjJDPOBM4AACDUEDgjZBy0TQ2sr+O2AQBA6CJwRkiWahA4AwCAUEPgjNBcHJjE4kAAABBaCJwRMg7aa5wp1QAAACGGwBmhWeNMVw0AABBiCJwRMujjDAAAQhmBM0JycWB6ottDLQEAAOoEgTNCLuOclhArsTG8NAEAQGghOkHI1TizMBAAAIQiAmeEhNLSUkfGmR7OAAAgFBE4IyTkFBRLcUmpOU8PZwAAEIoInBFyCwMp1QAAAKGI1gUICSnxsXLvsCNMuUbX5mnB3h0AAIAqCJwREhqmxMt1AzsHezcAAACqRakGAAAA4AYCZwAAAMANBM4AAACAGwicAQAAADcQOAMAAABuIHAGAAAA3EDgDAAAALiBwBkAAABwA4EzAAAA4AYCZwAAAMANBM4AAACAGwicAQAAADcQOAMAAABuIHAGAAAA3EDgDAAAALiBwBkAAABwA4EzAAAA4IZYd24E75SWlpr/MzMzeQoBAABCkBWnWXFbTQicAygrK8v837Zt20A+DAAAAPwQt2VkZNR4m6hSd8JreKWkpES2bdsmaWlpEhUVFZbP4vHHHy+//vqrRKpQ//6CtX919biBeBx/bdPX7Xh7f8186IftzZs3S3p6utePj8h9X4jk7y2Y+1cXjx3K73n+2NbxXtw/FN7zNBTWoLlVq1YSHV1zFTMZ5wDSJ79NmzYSzmJiYiL6j3eof3/B2r+6etxAPI6/tunrdny9v943lF+bkSzU3xci+XsL5v7VxWOH8nueP7YV48P9g/2eV1um2cLiQNTohhtuiOhnKNS/v2DtX109biAex1/b9HU7of7aQv382YX69xbM/auLxw7l9zx/bOuGEH99+QOlGgAQQvSwpWY+Dh48GNKZQQCoj+95ZJwBIIQkJCTIww8/bP4HgEiXEGbveWScAQAAADeQcQYAAAAInAEAAAD/IOMMAAAAuIHAGQAAAHADgTMAAADgBgJnAAhT5557rjRs2FDOP//8YO8KAATEV199JV27dpXDDjtM3nzzTQk22tEBQJiaPn26ZGVlybvvvisTJkwI9u4AgF8VFRVJ9+7d5aeffjJDUo499liZM2eONG7cWIKFjDMAhKlBgwZJWlpasHcDAALil19+kR49ekjr1q0lNTVVhg0bJlOmTJFgInAGgACYOXOmnHXWWdKqVSuJioqSSZMmVbnNSy+9JB06dJDExEQ54YQTzB8JAIgUM318H9y2bZsJmi16fuvWrRJMBM4AEAA5OTnSq1cv80fBlY8//lhuv/12M2p24cKF5rZDhw6VXbt2OW5z9NFHy5FHHlnlpH9MAKA+vA+Gmthg7wAARCI9pKin6owdO1ZGjx4to0aNMpdfffVV+frrr+Xtt9+We+65x1y3ePHiOttfAAi198FWrVo5ZZj1fJ8+fYL6gyLjDAB1rKCgQBYsWCBDhgypeDOOjjaX586dy88DQMQrcON9UIPkZcuWmYA5Oztbvv32W5ORDiYyzgBQx/bs2SPFxcXSvHlzp+v18qpVq9zejv6BWbJkiTkc2qZNG/n000+lb9++AdhjAPAvd94HY2Nj5ZlnnpGTTz5ZSkpK5O677w5qRw2zT0F9dACA13744QeePQARbcSIEeYUKijVAIA61qRJE4mJiZGdO3c6Xa+XW7Rowc8DQMRrEqbvgwTOAFDH4uPjTSP/adOmOa7Tw5B6mVILAPVBfJi+D1KqAQABoAtZ1q5d67i8fv160yWjUaNG0q5dO9OC6corr5TjjjvOLIB59tlnTa2ytbocAMJddgS+DzJyGwACNA5bF7RUpn8k3nnnHXP+xRdflH//+9+yY8cO07P5+eefNwMAACASTI/A90ECZwAAAMAN1DgDAAAAbiBwBgAAANxA4AwAAAC4gcAZAAAAcAOBMwAAAOAGAmcAAADADQTOAAAAgBsInAEAAAA3EDgDAAAAbiBwBgAE1COPPGJG6daladOmSbdu3aS4uNitffjuu+/M10tKSupwLwGEGwJnAPCTV199VdLS0qSoqMhxXXZ2tsTFxcmgQYOcbjt9+nSJioqSP//8k+c/AO6++2554IEHJCYmxq3bn3766ebn9P777/PzAFAtAmcA8JOTTz7ZBMq//fab47qff/5ZWrRoIfPnz5e8vDzH9T/99JO0a9dOOnfuzPPvpcLCQpfXz5o1y3wgGTlypEfbu+qqq+T555/n5wGgWgTOAOAnXbt2lZYtW5psskXPn3322dKxY0eZN2+e0/UaaKvx48fLcccdZ7LVGmRfeumlsmvXLvM1LR1o06aNvPLKK06PtWjRIomOjpaNGzeaywcOHJBrrrlGmjZtKunp6XLKKafIkiVLHLe3ShX0sTp06CAZGRly8cUXS1ZWluM2ev2zzz7r9Dh6H72vRbPkr732mpx55pmSnJxsyiHmzp0ra9euNVn1lJQU6devn8tMut6vbdu25n4XXnihHDx40Onrb775ptleYmKiHHHEEfLyyy87vrZhwwbz2B9//LEMHDjQ3Ka67PBHH30kp556qrlNdXT/OnXqJDfeeKOUlpaa68466yzzoYejAACqQ+AMAH6kwbBmky16XgNKDfas6w8dOmQy0FbgrJnTxx57zAS6kyZNMkGiZj/Nm3R0tFxyySXywQcfOD2OBo39+/eX9u3bm8sXXHCBCba//fZbWbBggRxzzDEyePBg2bdvn+M+GhDq9r/66itzmjFjhvzrX//y+HvUfb3iiitk8eLFJsDVQP+6666Te++91wSeGohqQGqngfUnn3wikydPNvXEGvj//e9/d/p+HnroIXniiSdk5cqVMmbMGHnwwQfl3XffddrOPffcI7fccou5zdChQ13un2b59YNIdX7//Xc58cQTzX6/+OKLJiBXegSgefPm5v4A4FIpAMBv3njjjdKUlJTSwsLC0szMzNLY2NjSXbt2lX7wwQelAwYMMLeZNm2apjhLN27c6HIbv/76q/l6VlaWubxo0aLSqKgox+2Li4tLW7duXfrKK6+Yyz///HNpenp6aV5entN2OnfuXPraa6+Z8w8//HBpcnKy2SfLXXfdVXrCCSc4Lrdv3770v//9r9M2evXqZe5r0f164IEHHJfnzp1rrnvrrbcc13344YeliYmJjst6/5iYmNItW7Y4rvv2229Lo6OjS7dv3+7YV32O7B577LHSvn37mvPr1683j/Pss8+W1iYjI6P0vffec7pO90G/l9mzZ5c2bNiw9D//+Y/L+/bu3bv0kUceqfUxANRPZJwBwI80u5yTkyO//vqryVwefvjhpnxCM85WnbOWaWiZgGY4lWaItUxAL2u5ht5Wbdq0yVEuoSUMVtZZM8WaXdYss9JMtdZWN27cWFJTUx2n9evXO5UdaCmGbt+iZSVWSYgnevbs6TivGVp11FFHOV2n32dmZqbjOv3eWrdu7bjct29fU4ayevVq83zpfv71r3912v/HH3+8StlETZlki2b0XZVp6POpJRya2b7jjjtc3jcpKUlyc3NrfQwA9VNssHcAACJJly5dTE2ylmXs37/fEQS3atXK1PfOmTPHfE1rkJUGjVpyoCctV9AgWwM8vVxQUODY7mWXXWYCZy1V0P+1C4QGykqD5sq11ZYGDRo4zmvXCDstUbC3X9OyEKvet6YFePbtWGUOrq5zt7Wb7r9644035IQTTnD6WuWuGFpDXZsmTZqY574yfW715/Dhhx/K1VdfbWrBK9PSFr0dALhCxhkA/ExrlzWI1ZO9Dd2AAQNMDfIvv/ziqG9etWqV7N2719Qan3TSSaZm2FUWWOtxly1bZrLTEyZMMIG0ReuZd+zYIbGxsSZwt580iHSXBozbt293XNaMsWat/UE/DGzbts1xWRdKaqCuCyo1Q60B7bp166rsvy6q9FTv3r1lxYoVLrPJWtut2Wj9YGJfGKk0S64Zbr0/ALhC4AwAfqZBsbZE08VzVsZZ6XntLKGZZCtw1hKG+Ph4eeGFF0zg+OWXX5rFd5VpmYV2q9ByBh3qMWLECMfXhgwZYkofzjnnHJkyZYpZXKiZ7fvvv9+pNV5tNAuuXTe0xGTp0qVy5ZVXut0HuTYarOr2tKxEt3/zzTebzhraRUQ9+uij8uSTT5p2cGvWrDGPP27cOBk7dqzHj6VBsT7/rmjG+uuvvzYfMoYNG+bIdlvBfEJCgnkuAcAVAmcA8DMNirXOVjOmVg2wFThrltNqW2dled955x359NNPpXv37ibz/J///MfldjXLrIHnueeea7Kn9tKIb775xmS0R40aZeqqtdWctqqzP35ttCuG7qO2mjvjjDNMIO6vPtP6XJx33nkyfPhwOe2000ydtL3dnLbS03Z0GixrvbTuhz4v3mSc9Xlavny5qZ92ReunNfOvZSn6fWq5jNISDr2vtssDAFeidIWgy68AABCm7rrrLlNqohl+d+zZs8d8oNEMvTfBOoD6gYwzACDiaJmK9rh2d4GilrdoBpygGUBNyDgDAAAAbiDjDAAAALiBwBkAAABwA4EzAAAA4AYCZwAAAMANBM4AAACAGwicAQAAADcQOAMAAABuIHAGAAAA3EDgDAAAAEjt/h+2/UA3ojkdogAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n", "ax.loglog(kc, Pks/Pkc, lw=2)\n", "ax.axhline(2.0, ls=\"--\", color=\"k\", lw=2)\n", "ax.set_xlabel(\"Wavenumber (k)\")\n", "ax.set_ylabel(\"Power Spectrum Ratio (Pk_compressive / Pk_solenoidal)\")" ] }, { "cell_type": "markdown", "id": "7a457a9ae89c68e5", "metadata": {}, "source": [ "Similarly, the solenoidal field should be divergence-free. We can take its divergence and check that it is small compared to the magnitude of the field. Since `v` (and therefore `vs`) comes from an FFT-generated, periodic field, we pass `periodic=True` so the finite-difference divergence uses wraparound differences at the domain edges, consistent with the periodic (Fourier-space) projection that produced `vs` -- otherwise the one-sided differences `divergence_of_field` uses by default at the boundary (appropriate for general, non-periodic data) would show up as a spurious residual there." ] }, { "cell_type": "code", "execution_count": 14, "id": "1ca645d7b47f91d5", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:17.358692Z", "iopub.status.busy": "2026-08-11T18:23:17.358620Z", "iopub.status.idle": "2026-08-11T18:23:17.455889Z", "shell.execute_reply": "2026-08-11T18:23:17.455478Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.2807221551813742e-16\n" ] } ], "source": [ "div_vs = fa.divergence_of_field(vs, periodic=True)\n", "print(np.abs(div_vs*fa.delta[0]/vmag).mean())" ] }, { "cell_type": "markdown", "id": "7a3a6395bc63e72c", "metadata": {}, "source": [ " The same goes for the compressive component, which should be curl-free (again passing `periodic=True` for the same reason):" ] }, { "cell_type": "code", "execution_count": 15, "id": "d9a87a8de09fe215", "metadata": { "execution": { "iopub.execute_input": "2026-08-11T18:23:17.456893Z", "iopub.status.busy": "2026-08-11T18:23:17.456822Z", "iopub.status.idle": "2026-08-11T18:23:17.730364Z", "shell.execute_reply": "2026-08-11T18:23:17.729943Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.171739745857824e-17\n" ] } ], "source": [ "curl_vc = fa.curl_of_field(vc, periodic=True)\n", "print(np.abs(curl_vc*fa.delta[0]/vmag).mean())" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all" }, "kernelspec": { "display_name": "py313", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }