{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.004723, "end_time": "2026-05-16T13:42:20.193863+00:00", "exception": false, "start_time": "2026-05-16T13:42:20.189140+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Two-dimensional Disk Distribution Functions\n", "\n", "galpy includes several distribution functions (DFs) for razor-thin axisymmetric disks:\n", "**dehnendf** ([Dehnen 1999](http://adsabs.harvard.edu/abs/1999AJ....118.1201D)), \n", "**shudf** ([Shu 1969](http://adsabs.harvard.edu/abs/1969ApJ...158..505S)), \n", "and **schwarzschilddf** (the Shu DF in the epicycle approximation, see [galaxiesbook.org](https://galaxiesbook.org/chapters/II-04.-Equilibria-of-Galactic-Disks_2-Distribution-functions-for-razor-thin-disks.html#the-first-and-simplest-example-of-a)).\n", "These DFs are functions of energy and angular momentum, $f(E, L_z)$, and can be used to describe\n", "stellar populations in a thin disk with a flat or power-law rotation curve." ] }, { "cell_type": "code", "execution_count": 1, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:20.316934Z", "iopub.status.busy": "2026-05-16T13:42:20.316719Z", "iopub.status.idle": "2026-05-16T13:42:21.461937Z", "shell.execute_reply": "2026-05-16T13:42:21.461135Z" }, "papermill": { "duration": 1.151327, "end_time": "2026-05-16T13:42:21.463214+00:00", "exception": false, "start_time": "2026-05-16T13:42:20.311887+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from galpy.util.quadpack import AccuracyWarning\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)\n", "warnings.filterwarnings(\"ignore\", category=AccuracyWarning)" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.003686, "end_time": "2026-05-16T13:42:21.471071+00:00", "exception": false, "start_time": "2026-05-16T13:42:21.467385+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Types of 2D disk DFs\n", "\n", "All three DFs assume an exponential surface-density profile and an exponential\n", "velocity-dispersion profile by default. They differ in how they construct $f(E, L_z)$\n", "(see Section 10.2.2 in [galaxiesbook.org](https://galaxiesbook.org/chapters/II-04.-Equilibria-of-Galactic-Disks_2-Distribution-functions-for-razor-thin-disks.html#Distribution-functions-for-razor-thin-disks) for more details):\n", "\n", "- **dehnendf**: Dehnen's 'new' DF (Dehnen 1999)\n", "- **shudf**: Shu's DF (Shu 1969)\n", "- **schwarzschilddf**: Schwarzschild DF\n", "\n", "All operate in a potential with a power-law rotation curve $v_c \\propto R^\\beta$." ] }, { "cell_type": "markdown", "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "papermill": { "duration": 0.003715, "end_time": "2026-05-16T13:42:21.478597+00:00", "exception": false, "start_time": "2026-05-16T13:42:21.474882+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Initializing a Dehnen DF\n", "\n", "We initialize a `dehnendf` with a flat rotation curve (`beta=0.`). The default\n", "`profileParams=(1/3, 1, 0.2)` set the disk scale length, velocity-dispersion\n", "scale length, and velocity dispersion at $R_0$ (all in natural units)." ] }, { "cell_type": "code", "execution_count": 2, "id": "72eea5119410473aa328ad9291626812", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:21.487357Z", "iopub.status.busy": "2026-05-16T13:42:21.487045Z", "iopub.status.idle": "2026-05-16T13:42:23.110454Z", "shell.execute_reply": "2026-05-16T13:42:23.109464Z" }, "papermill": { "duration": 1.628915, "end_time": "2026-05-16T13:42:23.111516+00:00", "exception": false, "start_time": "2026-05-16T13:42:21.482601+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.df import dehnendf\n", "\n", "dfc = dehnendf(beta=0.0)" ] }, { "cell_type": "markdown", "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "papermill": { "duration": 0.003679, "end_time": "2026-05-16T13:42:23.119411+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.115732+00:00", "status": "completed" }, "tags": [] }, "source": [ "The `profileParams` tuple is `(xD, xS, Sro)` where:\n", "- `xD = 1/3`: disk surface mass scale length (in units of $R_0$)\n", "- `xS = 1.0`: velocity dispersion scale length\n", "- `Sro = 0.2`: velocity dispersion at $R_0$ (in units of $v_c(R_0)$)\n", "\n", "We can also use custom profile parameters:" ] }, { "cell_type": "code", "execution_count": 3, "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:23.128148Z", "iopub.status.busy": "2026-05-16T13:42:23.127742Z", "iopub.status.idle": "2026-05-16T13:42:23.131473Z", "shell.execute_reply": "2026-05-16T13:42:23.130673Z" }, "papermill": { "duration": 0.008969, "end_time": "2026-05-16T13:42:23.132156+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.123187+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "dfc2 = dehnendf(beta=0.0, profileParams=(1.0 / 3.0, 1.0, 0.15))" ] }, { "cell_type": "markdown", "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "papermill": { "duration": 0.003681, "end_time": "2026-05-16T13:42:23.139663+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.135982+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Evaluating the DF for an orbit\n", "\n", "The DF can be evaluated for a given orbit (a point in phase space).\n", "We create an `Orbit` object and pass it to the DF:" ] }, { "cell_type": "code", "execution_count": 4, "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:23.150768Z", "iopub.status.busy": "2026-05-16T13:42:23.150581Z", "iopub.status.idle": "2026-05-16T13:42:23.155135Z", "shell.execute_reply": "2026-05-16T13:42:23.154151Z" }, "papermill": { "duration": 0.009858, "end_time": "2026-05-16T13:42:23.155862+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.146004+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(orbit) = 0.3014411904461411\n" ] } ], "source": [ "from galpy.orbit import Orbit\n", "\n", "# An orbit at R=0.9, vR=0.05, vT=1.0\n", "o = Orbit([0.9, 0.05, 1.0])\n", "print(\"f(orbit) =\", dfc(o))" ] }, { "cell_type": "markdown", "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "papermill": { "duration": 0.003762, "end_time": "2026-05-16T13:42:23.163749+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.159987+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DF moments: surface mass, velocity dispersions, and mean velocities\n", "\n", "We can compute various moments of the DF by marginalizing over velocity.\n", "These are useful for comparing the DF to observations." ] }, { "cell_type": "code", "execution_count": 5, "id": "b118ea5561624da68c537baed56e602f", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:23.172747Z", "iopub.status.busy": "2026-05-16T13:42:23.172545Z", "iopub.status.idle": "2026-05-16T13:42:24.352069Z", "shell.execute_reply": "2026-05-16T13:42:24.351094Z" }, "papermill": { "duration": 1.185171, "end_time": "2026-05-16T13:42:24.352877+00:00", "exception": false, "start_time": "2026-05-16T13:42:23.167706+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Surface mass at R=1.0: 0.050968080499022066\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "sigma_R^2 at R=1.0: 0.03733043742309621\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " at R=1.0: 0.9171527697944728\n", " at R=1.0: 0.0\n" ] } ], "source": [ "# Surface mass density at R=1\n", "print(\"Surface mass at R=1.0:\", dfc.surfacemass(1.0))\n", "\n", "# Radial velocity dispersion squared\n", "print(\"sigma_R^2 at R=1.0:\", dfc.sigma2(1.0))\n", "\n", "# Mean tangential velocity\n", "print(\" at R=1.0:\", dfc.meanvT(1.0))\n", "\n", "# Mean radial velocity (should be ~0 for an axisymmetric DF)\n", "print(\" at R=1.0:\", dfc.meanvR(1.0))" ] }, { "cell_type": "markdown", "id": "938c804e27f84196a10c8828c723f798", "metadata": { "papermill": { "duration": 0.003791, "end_time": "2026-05-16T13:42:24.360991+00:00", "exception": false, "start_time": "2026-05-16T13:42:24.357200+00:00", "status": "completed" }, "tags": [] }, "source": [ "Let's plot the surface mass profile and compare it to the target exponential profile:" ] }, { "cell_type": "code", "execution_count": 6, "id": "504fb2a444614c0babb325280ed9130a", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:24.369855Z", "iopub.status.busy": "2026-05-16T13:42:24.369639Z", "iopub.status.idle": "2026-05-16T13:42:31.293069Z", "shell.execute_reply": "2026-05-16T13:42:31.291975Z" }, "papermill": { "duration": 6.928845, "end_time": "2026-05-16T13:42:31.293769+00:00", "exception": false, "start_time": "2026-05-16T13:42:24.364924+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Rs = numpy.linspace(0.01, 2.0, 51)\n", "smass = numpy.array([dfc.surfacemass(R) for R in Rs])\n", "plt.plot(Rs, smass / smass[25], label=\"DF surface mass\")\n", "plt.plot(Rs, numpy.exp(-(Rs - 1.0) / (1.0 / 3.0)), \"--\", label=\"Target exponential\")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$\\Sigma(R) / \\Sigma(R_0)$\")\n", "plt.legend()\n", "plt.title(\"Surface mass density profile\");" ] }, { "cell_type": "markdown", "id": "59bbdb311c014d738909a11f9e486628", "metadata": { "papermill": { "duration": 0.004122, "end_time": "2026-05-16T13:42:31.302441+00:00", "exception": false, "start_time": "2026-05-16T13:42:31.298319+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Asymmetric drift\n", "\n", "The asymmetric drift is the difference between the circular velocity and\n", "the mean tangential velocity: $v_c - \\langle v_T \\rangle$. The DF can \n", "calculate this directly as $v_c - \\langle v_T \\rangle$ or we can also\n", "estimate this from an approximation to the Jeans equation using ``asymmetricdrift`` (see [galaxiesbook.org](https://galaxiesbook.org/chapters/II-04.-Equilibria-of-Galactic-Disks_1-The-axisymmetric-Jeans-equations-and-the-asymmetric-drift.html#The-asymmetric-drift) for more details):" ] }, { "cell_type": "code", "execution_count": 7, "id": "b43b363d81ae4b689946ece5c682cd59", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:31.311799Z", "iopub.status.busy": "2026-05-16T13:42:31.311581Z", "iopub.status.idle": "2026-05-16T13:42:58.635895Z", "shell.execute_reply": "2026-05-16T13:42:58.635076Z" }, "papermill": { "duration": 27.330426, "end_time": "2026-05-16T13:42:58.637036+00:00", "exception": false, "start_time": "2026-05-16T13:42:31.306610+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated asymmetric drift at R=1.0: 0.09000000000000002\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " vs. correct one from mean tangential velocity: 0.0828472302055272\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(f\"Estimated asymmetric drift at R=1.0: {dfc.asymmetricdrift(1.0)}\")\n", "print(f\" vs. correct one from mean tangential velocity: {1.0 - dfc.meanvT(1.0)}\")\n", "\n", "# Plot asymmetric drift as a function of R\n", "ad = numpy.array([dfc.asymmetricdrift(R) for R in Rs])\n", "ad_correct = numpy.array([1.0 - dfc.meanvT(R) for R in Rs])\n", "plt.plot(Rs, ad, label=\"Estimated\")\n", "plt.plot(Rs, ad_correct, label=\"Correct\")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$v_c - \\langle v_T \\rangle$\")\n", "plt.title(\"Asymmetric drift\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "8a65eabff63a45729fe45fb5ade58bdc", "metadata": { "papermill": { "duration": 0.004307, "end_time": "2026-05-16T13:42:58.646213+00:00", "exception": false, "start_time": "2026-05-16T13:42:58.641906+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Sampling orbits from the DF\n", "\n", "We can draw random samples from the DF. The `sample` method returns `Orbit` objects:" ] }, { "cell_type": "code", "execution_count": 8, "id": "c3933fab20d04ec698c2621248eb3be0", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:42:58.655984Z", "iopub.status.busy": "2026-05-16T13:42:58.655744Z", "iopub.status.idle": "2026-05-16T13:43:01.427818Z", "shell.execute_reply": "2026-05-16T13:43:01.426792Z" }, "papermill": { "duration": 2.777859, "end_time": "2026-05-16T13:43:01.428432+00:00", "exception": false, "start_time": "2026-05-16T13:42:58.650573+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of sampled orbits: 500\n", "First orbit R, vR, vT: 0.24207749508260903 0.5832560359657737 0.633604070684058\n" ] } ], "source": [ "numpy.random.seed(1)\n", "samples = dfc.sample(n=500, returnOrbit=True, nphi=1)\n", "print(\"Number of sampled orbits:\", len(samples))\n", "print(\"First orbit R, vR, vT:\", samples[0].R(), samples[0].vR(), samples[0].vT())" ] }, { "cell_type": "markdown", "id": "4dd4641cc4064e0191573fe9c69df29b", "metadata": { "papermill": { "duration": 0.004357, "end_time": "2026-05-16T13:43:01.437569+00:00", "exception": false, "start_time": "2026-05-16T13:43:01.433212+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Plotting the velocity distribution\n", "\n", "We can sample velocities at a specific radius and plot their distribution.\n", "The `sampleVRVT` method samples $(v_R, v_T)$ at a given $R$:" ] }, { "cell_type": "code", "execution_count": 9, "id": "8309879909854d7188b41380fd92a7c3", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:01.447536Z", "iopub.status.busy": "2026-05-16T13:43:01.447331Z", "iopub.status.idle": "2026-05-16T13:43:03.844692Z", "shell.execute_reply": "2026-05-16T13:43:03.843530Z" }, "papermill": { "duration": 2.403401, "end_time": "2026-05-16T13:43:03.845420+00:00", "exception": false, "start_time": "2026-05-16T13:43:01.442019+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "vrvt = dfc.sampleVRVT(1.0, n=1000)\n", "plt.scatter(vrvt[:, 0], vrvt[:, 1], s=1, alpha=0.5, label=\"Samples\")\n", "\n", "# Evaluate DF on a (vR, vT) grid at R=1 and overplot contours\n", "vR_grid = numpy.linspace(vrvt[:, 0].min() - 0.1, vrvt[:, 0].max() + 0.1, 60)\n", "vT_grid = numpy.linspace(vrvt[:, 1].min() - 0.1, vrvt[:, 1].max() + 0.1, 60)\n", "vR2d, vT2d = numpy.meshgrid(vR_grid, vT_grid)\n", "\n", "df_grid = numpy.array([[dfc(Orbit([1.0, vR, vT])) for vR in vR_grid] for vT in vT_grid])\n", "\n", "levels = numpy.geomspace(0.02 * df_grid.max(), 0.9 * df_grid.max(), 6)\n", "plt.contour(vR2d, vT2d, df_grid, levels=levels, colors=\"k\", linewidths=1.0)\n", "\n", "plt.xlabel(r\"$v_R$\")\n", "plt.ylabel(r\"$v_T$\")\n", "plt.title(\"Velocity distribution at R=1\")\n", "plt.axhline(1.0, color=\"r\", ls=\"--\", label=r\"$v_c$\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "3ed186c9a28b402fb0bc4494df01f08d", "metadata": { "papermill": { "duration": 0.004728, "end_time": "2026-05-16T13:43:03.855324+00:00", "exception": false, "start_time": "2026-05-16T13:43:03.850596+00:00", "status": "completed" }, "tags": [] }, "source": [ "The distribution is centered slightly below $v_c = 1$ due to the asymmetric drift,\n", "and has a spread set by the velocity dispersion.\n", "\n", "## Other 2D DFs\n", "\n", "The `shudf` and `schwarzschilddf` classes have the same interface:" ] }, { "cell_type": "code", "execution_count": 10, "id": "cb1e1581032b452c9409d6c6813c49d1", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:03.866031Z", "iopub.status.busy": "2026-05-16T13:43:03.865782Z", "iopub.status.idle": "2026-05-16T13:43:04.100392Z", "shell.execute_reply": "2026-05-16T13:43:04.099421Z" }, "papermill": { "duration": 0.240894, "end_time": "2026-05-16T13:43:04.101018+00:00", "exception": false, "start_time": "2026-05-16T13:43:03.860124+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Shu DF surface mass at R=1: 0.062193623796354555\n", "Schwarzschild DF surface mass at R=1: 0.0689371283692479\n" ] } ], "source": [ "from galpy.df import shudf, schwarzschilddf\n", "\n", "dfs = shudf(beta=0.0)\n", "dfsw = schwarzschilddf(beta=0.0)\n", "\n", "print(\"Shu DF surface mass at R=1:\", dfs.surfacemass(1.0))\n", "print(\"Schwarzschild DF surface mass at R=1:\", dfsw.surfacemass(1.0))" ] }, { "cell_type": "markdown", "id": "cbb8fde1", "metadata": { "papermill": { "duration": 0.004661, "end_time": "2026-05-16T13:43:04.110830+00:00", "exception": false, "start_time": "2026-05-16T13:43:04.106169+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Corrected DFs\n", "\n", "The input profiles are only approximately reproduced by the DF. We can correct\n", "this by calculating a set of corrections (see Dehnen 1999). galpy supports\n", "these corrections and comes with pre-calculated corrections bundled with the code:" ] }, { "cell_type": "code", "execution_count": 11, "id": "9d755629", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:04.121496Z", "iopub.status.busy": "2026-05-16T13:43:04.121280Z", "iopub.status.idle": "2026-05-16T13:43:17.946418Z", "shell.execute_reply": "2026-05-16T13:43:17.945229Z" }, "papermill": { "duration": 13.831337, "end_time": "2026-05-16T13:43:17.947171+00:00", "exception": false, "start_time": "2026-05-16T13:43:04.115834+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigma_R (corrected vs. uncorrected): 0.1999998506941359 0.19321086259083936\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "meanvT (corrected vs. uncorrected): 0.9035516117477274 0.9171527697944728\n" ] }, { "data": { "image/png": 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HDgmOc/r0aXLnzn1fcZzY98VXX33F/v37CQkJoUyZMgwaNChBcfIkHvVZ+7eoqCg++eQTe3/jwMBAgoKCCAsLIzw83L7diRMnHvs5O3bsGAcOHLjvmuXNmxf4+5o9SpYsWe67lr6+voSEhNy3DEhQaCb2XD799FPCwsLImzcvRYoU4d1332Xv3r329a6urnz55ZcsWbKEDBkyULlyZb766isuXbr0yOxJ+T1x7NgxwsPDSZ8+/X3XKyIi4r5r9e/PJtz9fP7z/B93XkmVP39+SpcuzdSpU+3Lpk6dSrly5e77vS+pl/rISprh4+NDcHAw+/fvT9LzEju59qNaiP697l7hNmzYMIoXL/7A53h5eXHjxo3EhXyIe8eZPHkyGTNmvG/90xzd26BBAzw8PJg5cyYVKlRg5syZmM1m+0A0uHsd1q5dy+rVq1m0aBFLly5lxowZvPTSSyxbtgyLxZKkYz7stbFarQ/c18P2/89W5OTwsPfGg5bbbDZq1qxJ//79H/ice0XTf3HvfdGmTRvatWv3wG2KFi36n48D0KxZMypVqsS8efNYtmwZw4YN48svv2Tu3LnUqVMHSPrrmJSZHd566y0mTJhAnz59KF++vP1mCS1atEjyH1A2m40iRYowfPjwB67/dzH6IA97DybmvZnYc6lcuTInTpxgwYIFLFu2jPHjx/Ptt98yduxYOnfuDECfPn1o0KAB8+fP548//uDjjz9m6NChrFq1ihdeeOGx5/E4NpuN9OnTJygS/ykoKCjB48Scf2LOK6natm1L7969OXfuHDExMWzevJnvvvvuifYlKZMKWUlT6tevz48//simTZse25E/W7Zs2Gw2jh07Zh84BXcHyYSFhdlHST+JewNufHx87C1tDxIUFISPj89ji++HFQL3jpM+ffpHHufeuTzoK7sjR4488tj3eHp6Ur9+fWbNmsXw4cOZMWMGlSpVIjg4OMF2ZrOZ6tWrU716dYYPH86QIUP46KOPWL169SMzPoi/vz9hYWH3LT99+vRDZ1F4lHvXa//+/Q/Ncu9aPei6HD58mMDAwAdOr5WUDBEREY+9Frly5eKPP/7gxo0bj2yVfdB7IygoCG9vb6xW62OPky1bNvbv349hGAn2ldj3BUCmTJl44403eOONN7hy5QolSpTg888/txeyT/t1/KfZs2fTrl07vvnmG/uy6Ojo+46XK1eux37OcuXKxZ49e6hevbpD7h6V2HMBCAgIoEOHDnTo0IGIiAgqV67MoEGDEhR8uXLl4p133uGdd97h2LFjFC9enG+++YYpU6Y88PhJ+T2RK1cuVqxYQcWKFZ/qlHKJOa9/e9Rr1aJFC/r27cu0adOIiorC2dk5wbdIkvqpa4GkKf3798fT05POnTtz+fLl+9afOHHCPs1S3bp1ARKMEgfsrTH16tV74hwlS5YkV65cfP3110RERNy3/t6cmGazmVdffZXffvvNPqXSP91rrbhXOP37H7RatWrh4+PDkCFDiIuLe+hxMmXKRPHixZk0aVKCryiXL1/OwYMHE31ezZs358KFC4wfP549e/bc9w/Cg1qY77VI/3P6osOHD3PmzJnHHi9Xrlxs3ryZ2NhY+7Lff/+ds2fPJjrzP5UoUYIcOXIwYsSI+67lvWv9z2v1z23279/PsmXL7O+bJ9WsWTM2bdrEH3/8cd+6sLAw4uPjgbujzg3DYPDgwfdt989WLE9Pz/vOxWKx0LhxY+bMmfPA4u3e+wLufg4uXLiQoB/hnTt3+PHHHx97LlarNcH7Ce7+URUcHJzg9X7ar+M/WSyW+1rcR48ejdVqTbCscePG7Nmz54HTMd17frNmzTh//jzjxo27b5uoqKj7upQ8bYk9l+vXryd47OXlRe7cue3X/M6dO0RHRyfYJleuXHh7ez9yGrGk/J5o1qwZVquVzz777L79xMfHP7D4fpzHndfDPOgzcE9gYCB16tRhypQpTJ06ldq1axMYGJjkbJJyqUVW0pRcuXLx66+/0rx5cwoUKEDbtm0pXLgwsbGxbNy4kVmzZtnnsyxWrBjt2rXjxx9/JCwsjCpVqrB161YmTZrEq6++SrVq1Z44h9lsZvz48dSpU4dChQrRoUMHMmfOzPnz51m9ejU+Pj789ttvwN270ixbtowqVarYp/y5ePEis2bNYv369fj5+VG8eHEsFgtffvkl4eHhuLq68tJLL5E+fXrGjBnD66+/TokSJWjRogVBQUGcOXOGRYsWUbFiRfvXaEOHDqVevXq8+OKLdOzYkRs3bjB69GgKFSr0wGL7QerWrYu3tzf9+vWzF0v/9Omnn7J27Vrq1atHtmzZuHLlCt9//z1ZsmSxz68Kd/uaVqlSJcFcuA/SuXNnZs+eTe3atWnWrBknTpxgypQp9pbVpDKbzYwZM4YGDRpQvHhxOnToQKZMmTh8+DAHDhywF5fDhg2jTp06lC9fnk6dOtmn3/L19WXQoEFPdOx73n33XRYuXEj9+vXt0w9FRkayb98+Zs+ezalTpwgMDKRatWq8/vrrjBo1imPHjlG7dm1sNhvr1q2jWrVqvPnmm8DdP5pWrFjB8OHDCQ4OJkeOHJQtW5YvvviC1atXU7ZsWbp06ULBggW5ceMGO3fuZMWKFfY/Orp06cJ3331H27Zt2bFjB5kyZWLy5Mn2qZ4e5fbt22TJkoUmTZpQrFgxvLy8WLFiBdu2bUvQqvi0X8d/ql+/PpMnT8bX15eCBQuyadMmVqxYQbp06e677rNnz6Zp06Z07NiRkiVLcuPGDRYuXMjYsWMpVqwYr7/+OjNnzqR79+6sXr2aihUrYrVaOXz4MDNnzrTPCZxcEnsuBQsWpGrVqpQsWZKAgAC2b99unwIN4OjRo1SvXp1mzZpRsGBBnJycmDdvHpcvX04wEO1BEvt7okqVKnTr1o2hQ4eye/duXn75ZZydnTl27BizZs1i5MiRCQYQJsbjzuthHvYZuKdt27b2LA8qvCWVc8RUCSLJ7ejRo0aXLl2M7NmzGy4uLoa3t7dRsWJFY/To0UZ0dLR9u7i4OGPw4MFGjhw5DGdnZyMkJMT44IMPEmxjGHenj3nQtDD3pguaNWvWA3Ps2rXLeO2114x06dIZrq6uRrZs2YxmzZoZK1euTLDd6dOnjbZt2xpBQUGGq6urkTNnTqNnz54JppIaN26ckTNnTsNisdw3LdLq1auNWrVqGb6+voabm5uRK1cuo3379sb27dsTHGfOnDlGgQIFDFdXV6NgwYLG3LlzjXbt2j12+q1/at26tQEYNWrUuG/dypUrjYYNGxrBwcGGi4uLERwcbLRs2fK+qaaABNMuPco333xjZM6c2XB1dTUqVqxobN++/aHTNv37dbg3ZdM/pzgyDMNYv369UbNmTcPb29vw9PQ0ihYtaowePTrBNitWrDAqVqxouLu7Gz4+PkaDBg2MgwcPJtjm3lRAD5pu7GHvGcO4O23aBx98YOTOndtwcXExAgMDjQoVKhhff/21ERsba98uPj7eGDZsmJE/f37DxcXFCAoKMurUqWPs2LHDvs3hw4eNypUrG+7u7gaQYBqiy5cvGz179jRCQkIMZ2dnI2PGjEb16tWNH3/8MUGe06dPG6+88orh4eFhBAYGGr1797ZPo/So6bdiYmKMd9991yhWrJj9WhYrVsz4/vvv79v2v7yOhvHw6bdu3rxpdOjQwQgMDDS8vLyMWrVqGYcPH37glF/Xr1833nzzTSNz5syGi4uLkSVLFqNdu3YJpiiLjY01vvzyS6NQoUKGq6ur4e/vb5QsWdIYPHiwER4e/tBrYRh3p98qVKjQfcsf9l4AEkxdlthz+d///meUKVPG8PPzM9zd3Y38+fMbn3/+uf29c+3aNaNnz55G/vz5DU9PT8PX19coW7ZsginWHiUpvyd+/PFHo2TJkoa7u7vh7e1tFClSxOjfv79x4cKFx57/v1//x52XYTx4+q1HfQYM4+771N/f3/D19TWioqISdQ0k9TAZRjKPghARERFxkPj4eIKDg2nQoAE//fSTo+PIU6Y+siIiIpJmzZ8/n6tXr9K2bVtHR5FkoBZZERERSXO2bNnC3r17+eyzzwgMDExwUwlJO9QiKyIiImnOmDFj6NGjB+nTp+eXX35xdBxJJmqRFREREZFUSS2yIiIiIpIqPXeFbKNGjfD390/y/HYiIiIikrI8d10L1qxZw+3bt5k0aVKCO9kkhs1m48KFC3h7ezvk9oUiIiIiaZ1hGNy+fZvg4GDM5ke3uT53d/aqWrXqY+8m9DAXLlwgJCTk6QYSERERkfucPXuWLFmyPHKbVFXIrl27lmHDhrFjxw4uXrzIvHnzePXVVxNsExoayrBhw7h06RLFihVj9OjRlClT5qkc39vbG7h7YX18fJ7KPkVERETkb7du3SIkJMRedz1KqipkIyMjKVasGB07duS11167b/2MGTPo27cvY8eOpWzZsowYMYJatWpx5MgR0qdP/5+Pf687gY+PjwpZERERkWSUmG6cqaqQrVOnDnXq1Hno+uHDh9OlSxc6dOgAwNixY1m0aBE///wz77//fpKPFxMTQ0xMjP3xrVu3kh5aRERERJJFmpm1IDY2lh07dlCjRg37MrPZTI0aNdi0adMT7XPo0KH4+vraf9Q/VkRERCTlSDOF7LVr17BarWTIkCHB8gwZMnDp0iX74xo1atC0aVMWL15MlixZHlnkfvDBB4SHh9t/zp49m2z5RURERCRpUlXXgqdhxYoVid7W1dUVV1fXZEwjIiKSdDabjdjYWEfHEHkizs7OWCyWp7KvNFPIBgYGYrFYuHz5coLlly9fJmPGjA5KJSIi8nTFxsZy8uRJbDabo6OIPDE/Pz8yZsz4n+flTzOFrIuLCyVLlmTlypX2KblsNhsrV67kzTffdGw4ERGRp8AwDC5evIjFYiEkJOSxk8WLpDSGYXDnzh2uXLkCQKZMmf7T/lJVIRsREcHx48ftj0+ePMnu3bsJCAgga9as9O3bl3bt2lGqVCnKlCnDiBEjiIyMtM9iICIikprFx8dz584dgoOD8fDwcHQckSfi7u4OwJUrV0ifPv1/6maQqgrZ7du3U61aNfvjvn37AtCuXTsmTpxI8+bNuXr1Kp988gmXLl2iePHiLF269L4BYCIiIqmR1WoF7n4LKZKa3ftDLC4u7j8VsibDMIynFSqtu3XrFr6+voSHh+uGCCIi8sxFR0dz8uRJcuTIgZubm6PjiDyxR72Xk1JvqXONiIiIiKRKKmQTITQ0lIIFC1K6dGlHRxEREZHnTPv27e0D2SUhFbKJ0LNnTw4ePMi2bdscHUVERCTVqVq1Kn369Llv+cSJE/Hz83vmeZ4FFZ/PhgpZEREReS496KYShmEQHx/vgDTyJFTIioiIiMPda8H8+uuvyZQpE+nSpaNnz57ExcXZt4mJieG9994jJCQEV1dXcufOzU8//WRf/+eff1KmTBlcXV3JlCkT77//foKitGrVqrz55pv06dOHwMBAatWqxZo1azCZTCxZsoSSJUvi6urK+vXrsdlsDB06lBw5cuDu7k6xYsWYPXt2gswHDhygfv36+Pj44O3tTaVKlThx4gSDBg1i0qRJLFiwAJPJhMlkYs2aNQCcPXuWZs2a4efnR0BAAA0bNuTUqVP2fVqtVvr27Yufnx/p0qWjf//+aFz+w6Wq6bdERETkb4ZhEBVndcix3Z0t//muTP+2evVqMmXKxOrVqzl+/DjNmzenePHidOnSBYC2bduyadMmRo0aRbFixTh58iTXrl0D4Pz589StW5f27dvzyy+/cPjwYbp06YKbmxuDBg2yH2PSpEn06NGDDRs2AHDx4kUA3n//fb7++mty5syJv78/Q4cOZcqUKYwdO5Y8efKwdu1a2rRpQ1BQEFWqVOH8+fNUrlyZqlWrsmrVKnx8fNiwYQPx8fH069ePQ4cOcevWLSZMmABAQEAAcXFx1KpVi/Lly7Nu3TqcnJz43//+R+3atdm7dy8uLi588803TJw4kZ9//pkCBQrwzTffMG/ePF566aWneq3TChWyKZVhQFwUuGjCaxERebCoOCsFP/nDIcc++GktPFyebhnh7+/Pd999h8ViIX/+/NSrV4+VK1fSpUsXjh49ysyZM1m+fDk1atQAIGfOnPbnfv/994SEhPDdd99hMpnInz8/Fy5c4L333uOTTz6x3wUtT548fPXVV/bn3StkP/30U2rWrAncbfkdMmQIK1asoHz58vZjrV+/nh9++IEqVaoQGhqKr68v06dPx9nZGYC8efPa9+vu7k5MTAwZM2a0L5syZQo2m43x48fb/wiYMGECfn5+rFmzhpdffpkRI0bwwQcf8NprrwEwduxY/vjDMa9xaqBCNqXaNp6/tn5PdI1PKJi/kaPTiIiIJLtChQolmBw/U6ZM7Nu3D4Ddu3djsVioUqXKA5976NAhypcvn6CVuGLFikRERHDu3DmyZs0KQMmSJR/4/FKlStn///jx49y5c8de2N4TGxvLCy+8YM9TqVIlexGbGHv27OH48eN4e3snWB4dHc2JEycIDw/n4sWLlC1b1r7OycmJUqVKqXvBQ6iQTYmscURv/p5+7nc4uflj3j6xmDa1x2C26OUSEZG/uTtbOPhpLYcdO7F8fHwIDw+/b3lYWBi+vr72x/8uCk0mEzab7e7x/v+2pv+Vp6fnY5dHREQAsGjRIjJnzpxgO1dX1yfOExERQcmSJZk6dep964KCgpK8P1EhmzJZnIlrt4CsC1tyzHaLYdc2s2lKRf5X7xfSBeZzdDoREUkhTCbTU/96Pznky5ePZcuW3bd8586dCb6Of5QiRYpgs9n4888/7V0L/qlAgQLMmTMHwzDsrbIbNmzA29ubLFmyJClvwYIFcXV15cyZMw9tAS5atCiTJk0iLi7uga2yLi4u9lsK31OiRAlmzJhB+vTpH3rHqkyZMrFlyxYqV64MQHx8PDt27KBEiRJJOofnhWYtSARH3BDB2zcr37Zex8eZquNqM1jPHRovbMzGbd89swwiIiJPQ48ePTh69Ci9evVi7969HDlyhOHDhzNt2jTeeeedRO0je/bstGvXjo4dOzJ//nxOnjzJmjVrmDlzJgBvvPEGZ8+e5a233uLw4cMsWLCAgQMH0rdvX3v/2MTy9vamX79+vP3220yaNIkTJ06wc+dORo8ezaRJkwB48803uXXrFi1atGD79u0cO3aMyZMnc+TIEXvee+d67do14uLiaN26NYGBgTRs2JB169bZz6FXr16cO3cOgN69e/PFF18wf/58Dh8+zBtvvEFYWFiS8j9PVMgmgqNuiGAym2n28gimVx5ObpuZ6xYT3Q7+wPDZjYiLjXymWURERJ5Uzpw5Wbt2LYcPH6ZGjRqULVuWmTNnMmvWLGrXrp3o/YwZM4YmTZrwxhtvkD9/frp06UJk5N1/DzNnzszixYvZunUrxYoVo3v37nTq1IkBAwY8UebPPvuMjz/+mKFDh1KgQAFq167NokWLyJEjBwDp0qVj1apVREREUKVKFUqWLMm4cePsrbNdunQhX758lCpViqCgIDZs2ICHhwdr164la9asvPbaaxQoUIBOnToRHR1tb6F95513eP3112nXrh3ly5fH29ubRo00VuZhTIZ6DyfarVu38PX1JTw8/KFfCSSX6KibfL2wNTOiz1IiOpqfyIRTkwmQLtczzSEiIo4THR3NyZMnyZEjB25ubo6OI/LEHvVeTkq9pRbZFOrAhXD+9/tBYuPvdnJ3c/dnQPPFjMzzOl/cisfp4h4YWwnrrql3p+oSERERec6okE2B4qw23vp1F+PXn6TJ2I2cuX7Hvu6lCv3J1HU9ZHsR4iL5et2HfPBrNSJuX3RgYhEREZFnT4VsCuRsMfNh3QL4eTiz91w49UavY+n+fxSqvpmh3ULOvtib6T7e/B5/nWazXmb/wVmOCy0iIiLyjKmQTaFqFMzAol6VKJHVj9vR8XSfspOBC/YTE///U3mYLYTU+JQJJT8g2ApnLfD61sH8/FsHbNb4R+9cREREJA1QIZuCZfZzZ0a38nSrcvcWfJM2nabJmE2cvv73jAXFi7RmVuPF1LL4EW8y8e2N7XSbUoGrVw44KraIiIjIM6FCNoVztpj5oE4BJrQvjb+HM/vOh1N/1HoW7f27q4GPbwjDWv3J4My1cLcZbCaKDr81I/7IYgcmFxEREUleKmRTiWr507OoVyVKZfPndkw8PX/dycfz9xMdd7ergcls5rUaXzO96ijy2cy8df06TtNawpL3IT7GwelFREREnj4VsongiDt7PUiwnzvTupajR9W7c8dO3nyaxmM2cura310NcuZ4iemtNlCrSLu7C7aMYfvPVfjr5CpHRBYRERFJNrohQhI48oYI/7bmyBX6ztzDjchYvFydGPpaERoUC0640ZGlXPvtDRoHuBFlMvN+SG0avfQVpiTeqk9ERFIG3RBB0grdEOE5VzVfehb3qkSZ7AFExMTz1rRdfDRvn72rAQD5akPb38hj8STKbGLg+T/o/2tVboWfdVxwERGR58zEiRPx8/NzdIw0SYVsKpbR141fu5TlzWq5MZlg6pYzNPp+I39djbBvE5i+ED+22UifgJI4GQZLrTdpOqcuu/dNdWByERF5Hl26dIm33nqLnDlz4urqSkhICA0aNGDlypWOjnYfFZ+pgwrZVM7JYqZfrXxM6lCGdJ4uHLp4iwaj17Ng93n7NmaLM50aTGRS6Y/JbIULFmi/Yyg/LnwdQ3POiojIM3Dq1ClKlizJqlWrGDZsGPv27WPp0qVUq1aNnj17PtE+Y2NjH7g8Li7uv0SVVESFbBpROW8Qi3tXomyOACJjrfSevpsP5ibsalC0UHNmN/2DupZ0WE0mzpxZj2nyq3DrguOCi4jIc+GNN97AZDKxdetWGjduTN68eSlUqBB9+/Zl8+bNAJw5c4aGDRvi5eWFj48PzZo14/Lly/Z9DBo0iOLFizN+/PgEfStNJhNjxozhlVdewdPTk88//xyABQsWUKJECdzc3MiZMyeDBw8mPv7vBpywsDC6detGhgwZcHNzo3Dhwvz++++sWbOGDh06EB4ejslkwmQyMWjQIABiYmLo168fmTNnxtPTk7Jly7JmzZoE5zpx4kSyZs2Kh4cHjRo14vr168l4ZZ9vTo4OIE9PBh83pnYuy6iVxxi9+jjTtp5h15mbhLYuQa4gLwC8vIP5otUqqq0dSOWNP8G1dTCmAnENRuNcsIGDz0BERJLEMCDujmOO7ewBJlOiNr1x4wZLly7l888/x9PT8771fn5+2Gw2exH7559/Eh8fT8+ePWnevHmCQvH48ePMmTOHuXPnYrFY7MsHDRrEF198wYgRI3BycmLdunW0bduWUaNGUalSJU6cOEHXrl0BGDhwIDabjTp16nD79m2mTJlCrly5OHjwIBaLhQoVKjBixAg++eQTjhw5AoCX191/R998800OHjzI9OnTCQ4OZt68edSuXZt9+/aRJ08etmzZQqdOnRg6dCivvvoqS5cuZeDAgU96leUxNGtBEqSkWQseZ/2xa/SZsYtrEbF4uFj4vFFhGr2QJeFG147DnI7YLu6hZ4YgsgTk5Z1XpuLm7u+Y0CIi8kj3jfSOjYQhwY9/YnL48AK43F+UPsjWrVspW7Ysc+fOpVGjRg/cZvny5dSpU4eTJ08SEhICwMGDBylUqBBbt26ldOnSDBo0iCFDhnD+/HmCgoLszzWZTPTp04dvv/3WvqxGjRpUr16dDz74wL5sypQp9O/fnwsXLrBs2TLq1KnDoUOHyJs37315Jk6cSJ8+fQgLC7MvO3PmDDlz5uTMmTMEB/993WvUqEGZMmUYMmQIrVq1Ijw8nEWLFtnXt2jRgqVLlybY1/NOsxbII72YJ5DFvSpRPmc67sRaeXvGHvrO2E1EzD/6xAbmhk7L2VmyJes93JkefZZW06ty4sRyxwUXEZE0JzFtZocOHSIkJMRexAIULFgQPz8/Dh06ZF+WLVu2BEXsPaVKlUrweM+ePXz66ad4eXnZf7p06cLFixe5c+cOu3fvJkuWLA8sYh9m3759WK1W8ubNm2C/f/75JydOnLCfR9myZRM8r3z58ok+hiSNuhakYel93JjSuSyhq48zYsVR5u46z84zNxnV8gWKZvG7u5GTK6UajGXM1tF8dOAHjpltNF/7Nv1P1KRpjW8056yISErm7HG3ZdRRx06kPHnyYDKZOHz48H8+7IO6JjxoeUREBIMHD+a11167b1s3Nzfc3d2TfOyIiAgsFgs7duxI0K0B/u56IM+WqpQ0zmI20at6HmZ2K09mP3dOXb/Da99v5Me1J7DZ/v4L+cUybzGn/iwq4E6M2cRnF1fQd2plwsNOOzC9iIg8ksl09+t9R/wksn8sQEBAALVq1SI0NJTIyMj71oeFhVGgQAHOnj3L2bN/z3V+8OBBwsLCKFiwYJIvTYkSJThy5Ai5c+e+78dsNlO0aFHOnTvH0aNHH/h8FxcXrFZrgmUvvPACVquVK1eu3LfPjBkzAlCgQAG2bNmS4Hn3BrPJ06dC9jlRKnsAi3tVom6RjMTbDIYsPky7CVu5cjvavk1gUAHGtNnIO+nK4mQYrLCF03d2PTi9yYHJRUQkLQgNDcVqtVKmTBnmzJnDsWPHOHToEKNGjaJ8+fLUqFGDIkWK0Lp1a3bu3MnWrVtp27YtVapUua/bQGJ88skn/PLLLwwePJgDBw5w6NAhpk+fzoABAwCoUqUKlStXpnHjxixfvpyTJ0+yZMkSli5dCkD27NmJiIhg5cqVXLt2jTt37pA3b15at25N27ZtmTt3LidPnmTr1q0MHTrU3ie2V69eLF26lK+//ppjx47x3Xff2fcpT58K2UQIDQ2lYMGClC5d2tFR/hNfD2dCW5Vg6GtFcHM2s+7YNeqOXMeaI1fs25gtTrSvP54pZQeTywpvX7kME+vCmi9Ac86KiMgTypkzJzt37qRatWq88847FC5cmJo1a7Jy5UrGjBmDyWRiwYIF+Pv7U7lyZWrUqEHOnDmZMWPGEx2vVq1a/P777yxbtozSpUtTrlw5vv32W7Jly2bfZs6cOZQuXZqWLVtSsGBB+vfvb2+FrVChAt27d6d58+YEBQXx1VdfATBhwgTatm3LO++8Q758+Xj11VfZtm0bWbNmBaBcuXKMGzeOkSNHUqxYMZYtW2YvnuXp06wFSZCaZi14nGOXb/PWtF0cvnQbgC6VcvBurfy4OP39t401KgzL0vdhzzQAVmR9gUJ1hpMpUwmHZBYRed49aqS3SGqiWQvkP8mTwZv5PSvSrvzdv0zHrTtJ4zEbOXnt775LFnc/aDQWGv3IEQ9f3jNdo/HStixfP8RBqUVERET+pkL2OebmbGFww8KMa1sKPw9n9p0Pp96odczZcS7hVCnFmuPRcjr5cOa22UTfE9P4dHptou7ccFx4ERERee6pkBVqFszA0t6VKZczgDuxVt6ZtYe3Z+zmdvTf96oOCanApNbr6eSVF5NhMCvmPC2nV+XI8cUOTC4iIiLPMxWyAkBGXzemdi5Hv5fzYjGbmL/7AvVGrWf32TD7Ns4unvRpPIcfivQk0GpwwmLQan1/Zv7R6+5tEkVERESeIRWyYmcxm3jzpTzM7FaOzH7unLlxhyZjNjL2z4RzzpYv2YM5DedRyeRJrMnErYPzYHprUFcDEREReYZUyMp9SmYLYHHvStQrkol4m8EXSw7T9uetXLn195yzAenyENpmI8MyvUyHiGg4sgjGVCT2xCoHJhcREZHniQpZeSBfd2e+a/UCXzYugruzhfXHr1Fn5DpWH/57zlmT2Uztl7/B0nkFpMtDdMRFWq7swah5zYmLi3JgehEREXkeqJCVhzKZTDQvnZXf3qpIgUw+XI+MpcPEbQxaeIDouH/cti9TMej2JysK1uSoqwvjbh2kw5SKnD+/1XHhRUREJM1TISuPlTu9N/PeqECHitkBmLjxFA2/28DhS7f+3sjFk/pNZzEsRxO8bQZ7zHE0WdaRpWs/dUxoERERSfNUyEqiuDlbGNigEBM6lCbQy5Ujl2/zyncb+Hn9yQQDwWpXHsisl3+mmM2ZCLOJd0/O4pNpNblz55oD04uIiMh/UbVqVfr06ZPo7desWYPJZCIsLCzZMoEKWUmiavnSs7RPJarnT09svI1Pfz9I+4nbEgwEy5y5DBPbbKSrT0FMhsG82EsMnVodLu51YHIREXEEk8n0yJ9BgwY5NNv8+fMddvyU6GEF6Ny5c/nss88cE+oRVMhKkgV6uTK+XSk+e7Uwrk5m1h69Su2R61h+8LJ9GydnN95qNIOfir1N3niDnpfOwvjqsHmM5pwVEXmOXLx40f4zYsQIfHx8Eizr169fkvYXGxubTEnlUQICAvD29nZ0jPuokJUnYjKZeL1cNhb1epGCmXy4ERlLl1+289G8fUTF/j0QrPQLnZjd4k8y5q4N1lhY+j6zp7zM9evHHJheRESelYwZM9p/fH19MZlM9seRkZG0bt2aDBky4OXlRenSpVmxYkWC52fPnp3PPvuMtm3b4uPjQ9euXQEYN24cISEheHh40KhRI4YPH46fn1+C5y5YsIASJUrg5uZGzpw5GTx4MPHx8fb9AjRq1AiTyWR//CBnz56lWbNm+Pn5ERAQQMOGDTl16hQAhw8fxsPDg19//dW+/cyZM3F3d+fgwYMAtG/fnldffZXBgwcTFBSEj48P3bt3T1CUx8TE0KtXL9KnT4+bmxsvvvgi27Zts6+/11K6cuVKSpUqhYeHBxUqVODIkSOJPme4++/3+PHjadSoER4eHuTJk4eFCxcCcOrUKapVqwaAv78/JpOJ9u3bA/d3LZg8eTKlSpXC29ubjBkz0qpVK65c+Xtmo2fGkMf67rvvjAIFChh58+Y1ACM8PNzRkVKU6Lh44/NFB41s7/1uZHvvd6Pa16uNfefCEm5ksxnGlh+N1cMyG4UnFjaq/lTI2LDte8cEFhFJpaKiooyDBw8aUVFRCZZHxkY+9Cc6PjrR20bFJW6/T2rChAmGr6+v/fHu3buNsWPHGvv27TOOHj1qDBgwwHBzczNOnz5t3yZbtmyGj4+P8fXXXxvHjx83jh8/bqxfv94wm83GsGHDjCNHjhihoaFGQEBAgn2vXbvW8PHxMSZOnGicOHHCWLZsmZE9e3Zj0KBBhmEYxpUrVwzAmDBhgnHx4kXjypUrD8wcGxtrFChQwOjYsaOxd+9e4+DBg0arVq2MfPnyGTExMYZhGEZoaKjh6+trnD592jh79qzh7+9vjBw50r6Pdu3aGV5eXkbz5s2N/fv3G7///rsRFBRkfPjhh/ZtevXqZQQHBxuLFy82Dhw4YLRr187w9/c3rl+/bhiGYaxevdoAjLJlyxpr1qwxDhw4YFSqVMmoUKFCos/ZMAwDMLJkyWL8+uuvxrFjx4xevXoZXl5exvXr1434+Hhjzpw5BmAcOXLEuHjxohEWdvff8ypVqhi9e/e27+enn34yFi9ebJw4ccLYtGmTUb58eaNOnTr29ffy3rx584HX9WHvZcMwjPDw8ETXWypkkyApF/Z5tO7oVaPM58uNbO/9buT+cJHxw5/HDavVlmCbI8cWGw1/KmIUnljYKDyxsPHN7NeM2Jgn/6UoIvI8edg//vd+pz7op8fyHgm2LT2l9EO3bb+kfYJtK02r9MDtntS/C9kHKVSokDF69Gj742zZshmvvvpqgm2aN29u1KtXL8Gy1q1bJ9h39erVjSFDhiTYZvLkyUamTJnsjwFj3rx5j8wzefJkI1++fIbN9ve/ZzExMYa7u7vxxx9/2JfVq1fPqFSpklG9enXj5ZdfTrB9u3btjICAACMy8u9/78aMGWN4eXkZVqvViIiIMJydnY2pU6fa18fGxhrBwcHGV199ZRjG34XhihUr7NssWrTIAOzvh8Se84ABA+yPIyIiDMBYsmRJguP8uwD9dyH7b9u2bTMA4/bt24/czz1Pq5BV1wJ5al7ME8jS3pWpVSgDcVaDIYsP0+anLVwK/3sgWN7cdZjWYg3NXDMDMCHiKG2nVuTs2Q2Oii0iIg4SERFBv379KFCgAH5+fnh5eXHo0CHOnDmTYLtSpUoleHzkyBHKlCmTYNm/H+/Zs4dPP/0ULy8v+0+XLl24ePEid+7cSXTGPXv2cPz4cby9ve37CQgIIDo6mhMnTti3+/nnn9m7dy87d+5k4sSJmEymBPspVqwYHh4e9sfly5cnIiKCs2fPcuLECeLi4qhYsaJ9vbOzM2XKlOHQoUMJ9lO0aFH7/2fKlAnA/pV+Ys/5n/vw9PTEx8cnyd0CduzYQYMGDciaNSve3t5UqVIF4L7XLrk5PdOjSZrn7+nC2DYlmbHtLIN/O8jGE9epNWItX7xWhDpF7n7g3D0C+LjFUsqvH8rAY1PZb46nyYpuDM7ZmNpVBjv4DEREUp8trbY8dJ3FbEnweE2zNQ/d1mxK2L61tPHS/5Trcfr168fy5cv5+uuvyZ07N+7u7jRp0uS+AV2enp5J3ndERASDBw/mtddeu2+dm5tbkvZTsmRJpk6det+6oKAg+//v2bOHyMhIzGYzFy9etBeZT5uzs7P9/+8VyzabzZ41Mef8z33c28+9fSRGZGQktWrVolatWkydOpWgoCDOnDlDrVq1nvlgPBWy8tSZTCZalMlKmRwB9J6+m33nw+kxdSfNS4XwSYOCeLrefdvVePEDCueqxXt/dGGnORbzlh/gxmWoOwxcU97ISBGRlMrD2ePxGyXztk9iw4YNtG/fnkaNGgF3C7F7g6geJV++fAkGQgH3PS5RogRHjhwhd+7cD92Ps7MzVqv1oevv7WfGjBmkT58eHx+fB25z48YN2rdvz0cffcTFixdp3bo1O3fuxN3d3b7Nnj17iIqKsi/bvHkzXl5ehISEEBgYiIuLCxs2bCBbtmwAxMXFsW3btiTN3ZqYc34cFxcXgEdel8OHD3P9+nW++OILQkJCANi+ffsTH/O/UNcCSTY5g7yY06MCb1TNhckEM7afpd6odew5G2bfJmOmEvzceiOjg6rwclQM7JkGP1Qm6swmxwUXEZFnIk+ePMydO5fdu3ezZ88eWrVqlaiWwbfeeovFixczfPhwjh07xg8//MCSJUsSfJ3/ySef8MsvvzB48GAOHDjAoUOHmD59OgMGDLBvkz17dlauXMmlS5e4efPmA4/VunVrAgMDadiwIevWrePkyZOsWbOGXr16ce7cOQC6d+9OSEgIAwYMYPjw4Vit1vumFYuNjaVTp04cPHiQxYsXM3DgQN58803MZjOenp706NGDd999l6VLl3Lw4EG6dOnCnTt36NSpU6KvZ2LO+XGyZcuGyWTi999/5+rVq0RERNy3TdasWXFxcWH06NH89ddfLFy40GFzzKqQlWTl4mSmf+38TOtSjmBfN05dv0PjMRsJXX0c6//fEczi7ErVut9B+8Xgk4Wr4aeov7wTE3/vjM0a/5gjiIhIajV8+HD8/f2pUKECDRo0oFatWpQoUeKxz6tYsSJjx45l+PDhFCtWjKVLl/L2228n+Pq8Vq1a/P777yxbtozSpUtTrlw5vv32W3uLJ8A333zD8uXLCQkJ4YUXXnjgsTw8PFi7di1Zs2bltddeo0CBAnTq1Ino6Gh8fHz45ZdfWLx4MZMnT8bJyQlPT0+mTJnCuHHjWLJkiX0/1atXJ0+ePFSuXJnmzZvzyiuvJLgZxBdffEHjxo15/fXXKVGiBMePH+ePP/7A398/0dczMef8OJkzZ2bw4MG8//77ZMiQgTfffPO+bYKCgpg4cSKzZs2iYMGCfPHFF3z99deJPsbTZPr/EWySCLdu3cLX15fw8PCHfr0gDxd+J44P5+9j0d6LAJTO7s/wZsUJCfjHV1dRNxk/tzkj4+9uUwF3Pq87icCgAo6ILCKSokRHR3Py5Ely5MiRpH6ez4MuXbpw+PBh1q1b5+go92nfvj1hYWG6i9g/POq9nJR6Sy2y8sz4ejjzXcsX+LppMbxcndh26iZ1Rq5j9o5z2P+ecvenU8ulDAyuiZvNYCNRNP69Keu2jnJseBERSVG+/vpr+4wCo0ePZtKkSbRr187RseQZUyErz5TJZKJJySws6V2JUtn8iYiJp9+sPbwxdSc3I++OdDSZzTSpOZzplb8lj83MDbOJNw6N46tZDYmNue3gMxARkZRg69at1KxZkyJFijB27FhGjRpF586dHR1LnjF1LUgCdS14uqw2g7F/nuDb5UeJtxmk93bl66bFqJz37+lMYqLDGb6wFb9G3Z2X7o04N3q8Og0Cn3xEpohIaqWuBZJWqGuBpHoWs4me1XIz742K5Ary5MrtGNr+vJVBCw8QHXd32g9XN18+aLaI0Xnb8UKslXbnj8EPlWHXVNDfYCIiIs81FbLicEWy+PL7W5VoW/7uqMqJG0/RYPR69p8Pt29TtXw/JjVbjke2FyEuEtuCN5gwrR63b513VGwREYfRl6mS2j2t97AKWUkR3F0sfNqwMBM7lCbI25VjVyJo9P0Gxqw5YZ+my+SbGdougJc+ZrKvL8PjztJ0dm327J/u4PQiIs+GxXL3Ll3P+u5JIk/bvVvm/vsuY0mlPrJJoD6yz8aNyFg+mLuXPw5cBqBM9gC+aVYswTRde/ZP472tQzhvAYth8GZASTrUHYfFycVRsUVEkp1hGJw5c4a4uDiCg4Mxm9UeJamLYRjcuXOHK1eu4Ofn98Bb+Sal3lIhmwQqZJ8dwzCYteMcgxceIDLWirerE4MbFqLRC5ntd265fes8ny5syVLr3buxlMWNIbUnkD5DYUdGFxFJVrGxsZw8eTJRd8ASSan8/PzImDFjgrux3aNCNpmokH32zly/w9szd7Pj9N1itV6RTHzeqDB+HndbXg2bjfmr32fomcVEmU342Qy+KtSV8mV6OTK2iEiystls6l4gqZazs7O9m8yDqJB9ykJDQwkNDcVqtXL06FEVss9YvNXG2D9PMGLFMeJtBhl8XPmmaXFezBNo3+bkqTW8t7o3x0xWply4RKHiHaHmp+Cs6WlERERSExWyyUQtso6191wYfWbs5q+rkQB0rJiD/rXz4eb8/4MfYm6z+4++lNk58+4TMhQm8tVQPDMVd1BiERERSSrNIytpUtEsfix6qxKvl7s7TdfPG07yynfrOXDh7jRdLq7elHllHLSaBR6BHL55hJeXtGbO8r4Y6ksmIiKS5qhFNgnUIptyrD58hXdn7+VaRAzOFhN9a+aja+WcWMz/32n89iX+N7cxM7gFwMsWPwY2mIqPb1YHphYREZHHUYuspHnV8qfnjz6VeLlgBuKsBl8uPUyLHzdx5vrdeenwzsiHbf7knXRlcDIMllnDaDKnLrv2TnFscBEREXlq1CKbBGqRTXkMw2D2jnMM/u0gETHxeLpY+KRBQZqVCrFP6bH/4Cz6b/6UsxYwGwY9/IvTpd7PmnNWREQkBVKLrDw3TCYTTUuFsKR3JcrkCCAy1sp7c/bR5ZftXL0dA0Dhgk2Z1Ww5DZyCsJlMhIbtYfHkmhCu29uKiIikZipkJU0ICfBgWpdyfFg3Py4WMysOXaH2iLUsO3AJAE+vjAxpvYohWRtSPSqWeqd3w9iKcOh3xwYXERGRJ6auBUmgrgWpw6GLt3h7xm4OX7oNQLNSWfi4fkG83f7/fs7XT8CcznBhJ1EmExMLVKFDg4m4ufs7MLWIiIiAuhbIc65AJh8WvFmRblVyYjLBzO3nqDNyHVtP3ri7Qbpc0PEPqNibrwP8+D7qL1pOq8Kx40sdG1xERESSRIWspEmuThY+qFOA6V3KkcXfnXM3o2j+4yaGLjlETLwVnFyg5qdUL/cu6awGxy0GLdf1Y8YfvTTnrIiISCqhrgVJoK4FqdPt6Dg+/e0gs3acAyB/Rm9GtChO/ox3X8Pr147y0aK2bODuHcNeMvvwaYOp+Ppld1RkERGR55a6Foj8g7ebM8OaFuPH10uSztOFw5du88roDfy49gRWm0G6wLx832Y97wZVwMkwWGW7ReO59Tmwb6qjo4uIiMgjqJCV58bLhTKytE9lahRIT6zVxpDFh2k5bjNnb9zBbHGibd0fmFr+f2S3QjQ2Ahf0glWfgzXe0dFFRETkAdS1IAnUtSBtMAyDGdvO8unvB7kTa8XL1YmBDQrSpGQWTCYTdyKucPKPfhTat+DuE0LKEt7gW3zTF3JscBERkeeAuhaIPILJZKJFmaws6V2Jktn8iYiJ593Ze+k+ZQfXI2Lw8EpPoca/QOOfwNWHVdf3UmdRc/5Y95mjo4uIiMg/qEU2CdQim/ZYbQY/rD3Bt8uPEmc1CPRyYehrRalZMMPdDW6eouf8xqw1xwLQ2CUT/Rv+iodHoANTi4iIpF1qkRVJJIvZxBtVczO/Z0XyZfDmWkQsXX7ZTv/Ze7gdHQf+2RnRZh1dvAtgMgzmxF6kxfSXOHJUdwQTERFxNLXIJoFaZNO26Dgr3y4/yo/r/sIwILOfO980K0a5nOkA2LJzHB/uHskViwlnw+CdDJVpVes7TGb9PSgiIvK0JKXeUiGbBCpknw9bT97gnVm7OXsjCpMJOlXMQb9a+XBztnDzxgk++f111hh3b3870ZKNko0mgqe6GoiIiDwNKmSTiQrZ50dETDyfLzrItK1nAciT3otvmxencGZfDJuNact6cfbYYt67fh28MsJrP0LOKg5OLSIikvqpkE0mKmSfPysPXea9Ofu4FhGDk9lE7+p56FE1F04WM1zaD7M7wrUjXLFYmFOoJp0bTMDZ2cPRsUVERFItDfYSeUqqF8jAsrcrU6dwRuJtBt8sP0rjsZs4cTUCMhaGrmswSrTjw6B0fH/7IO2mVOTs2U2Oji0iIvJcUCGbCKGhoRQsWJDSpUs7Ooo4QICnC9+3LsGI5sXxdnNiz9kw6o1ax6SNp7A5uWN6ZRTNCrfH22awzxxP0xVdWPznQEfHFhERSfPUtSAJ1LVALoRF0X/2XtYfvwbAi7kD+apJUYL93Ll4YQfvL+vKTtPdOWcbOmfgw1d+xcMrvSMji4iIpCrqWiCSTIL93PmlYxkGv1IIN2cz649fo9aItczfdZ6MmUrwU+sN9PApjNkwWBB3mWYzq3Pm+B+Oji0iIpImqZAVSSKz2US7CtlZ1KsSxUL8uB0dT58Zu+n5605uxZp5o9E0fnqhHxmsBmZrHIHT2sDG78Bmc3R0ERGRNEVdC5JAXQvk3+KtNsasOcHIlceItxkEernyZeMiVC+QgfCwU9xc8i7ZjywDwJarOuF1v8Q/XR4HpxYREUm51LVA5Blxsph5q3oe5vesSJ70XlyLiKHTpO28N3svZrfMZG8xE+p/C05uTLq2lUYLGrFxW6ijY4uIiKQJapFNArXIyqNEx1n5+o8j/LThJIYBWfzd+brp3Vvcxl/aT6vFrTlkudu9oL1nbno1mIKzq6eDU4uIiKQsapEVcQA3ZwsD6hdkWpdyZPF359zNKFqO28z/fj9IfLoC/NJyDc3dQgCYGHmcNr9W5PTpdQ5OLSIiknqpkBV5ysrlTMfSPpVpUToEw4Dx609Sf/R6jl43MaD5YkbkeR1fm8FBs5Wmq3qwcPWH6IsRERGRpFPXgiRQ1wJJqlWHL9N/9t1b3FrMJt6slps3X8rN9at7+WBpZ7abYnAyDH7zfIEsDULBTe8rERF5viWl3lIhmwQqZOVJ3IiM5eP5+1m07yIARTL78m3zYuQIcGX8ok54nlhDm1u3wD87NP4ZspR0bGAREREHUiGbTFTIypMyDIOFey7wyYIDhEfF4eJkpn+tfHSsmAPzua0wpzOEn+GgmzubCtWhQ91xmC1Ojo4tIiLyzKmQTSYqZOW/uhQeTf85e1l79CoAZXME8HXTYoS4xxL9Wy+a3NrKaWdnyuHOkDoTCEpfyMGJRUREni3NWiCSQmX0dWNSh9J83qgwHi4Wtpy8Qe0Ra5mx/xYujSfQMXt93G0Gm4mi8aLmrN0y0tGRRUREUiy1yCaBWmTlaTp9PZJ3Zu5h++mbAFTPn56hjYsQcW0j/de8zRHz3Tln27hn5+2Gv+Li6u3IuCIiIs+EWmRFUoFs6TyZ0a08H9TJj4vFzMrDV6j17VoO3S7A1JZraeOeHYApUado/euL3Di3zbGBRUREUhgVsiIOZDGb6FYlFwvfqkjBTD7cvBNHz1930n/+X3SvP5fQ/B3xtxkEREfiN+kV2DkZ9CWKiIgIoK4FSaKuBZKcYuNtjF51jNDVx7EZkMHHlS8bF6WQ/1VMS/oTeHI9AFEFGxJX63N8fEMcnFhEROTpU9cCkVTIxcnMOy/nY06PCuQM9OTyrRjaT9jGtxtsuDefBzUGgdmJLy+vo+mcuuzeN9XRkUVERBxKLbJJoBZZeVaiYq18ufQwEzeeAiBrgAdfNy1GfvbTfHVPzlnAYhi8EfACner+hMXJxbGBRUREnhK1yIqkcu4uFga9UohfO5cls587Z27cofmPm/juUBCTGy2hrlM6rCYTo2/upsuUCly+vNfRkUVERJ45FbIiKViF3IEs6VOJpiWzYBjw49q/aDXxBG0qz+PzkAa42wy2mWJovLgVqzd97ei4IiIiz5QKWZEUzsfNmWFNizGubSkCvVw5ejmCRmM2cdLWgWlVQylosxBuNjHw0M9E/NYH4qIcHVlEROSZUB/ZJFAfWXG0G5GxDJi/j8X7LgFQNIsvXzbKzeKN3Sn512aqRkVB+kLQ5GdIn9/BaUVERJJOfWRF0qgATxdCW5VgZIvi+Lg5sfdcOA3H7MI343AqN5oCnkFw5QCrfnmZmcvexrDZHB1ZREQk2ahFNgnUIispyaXwaN6bs5c/j14FoGyOAIbXC8Z11Vs0jD/OLYuFGmZfBjWYgq9fdseGFRERSSS1yIo8BzL6ujGxQ2k+b1QYDxcLW07e4OUfD7E87wi6ZqiIk2GwwhZOk7n12bFnkqPjioiIPHVqkU0CtchKSnX6eiT9Zu1h26mbALyUPz1div3F57v+x2kLmA2Dbn5F6VrvZ5yc3RycVkRE5OHUIivynMmWzpPpXcvzYd38uFjMrDp8hR6/+dOp0FRecU6PzWRiTPg+Ok2tSOz1vxwdV0RE5KlQISuSRljMJrpWzsXvvV6kcGYfwu7E8fa8s4QzjEGZG+JpM8hz+zou46rCwQWOjisiIvKfqWtBEqhrgaQWcVYb3606znerj2O1GQR5u/JxtVhePjAMt/M7AbjxQmvca/4Pd48AB6cVERH5m7oWPGWhoaEULFiQ0qVLOzqKSKI4W8y8XTMv896oQO70Xly9HUOvhQaD/b4hplxvrJh49+JyWsyoypFjixwdV0RE5ImoRTYJ1CIrqVF0nJWv/zjCTxtOYhiQ2c+dT8ue5n8nv+GaxYSLYdAvY1VavDwKk1l/24qIiGMlpd5SIZsEKmQlNdv813X6zdrDuZt3b2HbuZSF85GDWE8kAFVN3nzaYAr+/jkdGVNERJ5z6logIvcplzMdS/tUpmWZrACM327lyNUhdPcui7NhsMa4TZN5r7B113gHJxUREUkctcgmgVpkJa1YfeQK783ey5XbMVjMJrqXOMvaW6Gcshjkjo1ldo5WWKp9CBZnR0cVEZHnjFpkReSRquVLz7K3K/NKsWCsNoPQ7Vmw3B5CQ3MGvrhyHcv64TChLtw87eioIiIiD6VCVuQ55efhwqiWLxDaqgT+Hs7svmhi5uF3OJP3MwxXHzi3lamTX2Lp2sGOjioiIvJA6lqQBOpaIGnVldvRfDBnHysPXwGgdpZY3nD+lnauN4g3mWjkkoH3G07HwyPQwUlFRCStU9cCEUmS9N5ujG9Xiq8aF8XL1Yml51xoda4f9U25MRkG82Iv03z6Sxw8Mt/RUUVEROxUyIoIACaTiWalQ1japxLlc6YjIs7C5ENdqBr9GumtBqcsBm02DWDy4m4YNpuj44qIiKiQFZGEsvh7MLVzWQY2KIirk5mFp8oSda4/5a2exJlMfHV1I29PqYhx+4qjo4qIyHNOhayI3MdsNtGhYg4W965E8RA/LtxJx7KjH/FydDFcDINS185i+uFFOLHK0VFFROQ5pkJWRB4qV5AXs7uX591a+XC2WJhzsiVZL7TnFTJAxGWY3IjzS94hLibS0VFFROQ5pEJWRB7JyWKmZ7XczO9ZkfwZvdl1qwBlrnzEBv9XiDSZ6Hp+EW1/fZGzZzc4OqqIiDxnVMiKSKIUCvZlwZsV6VE1F7EmV1pfbME77h0Js1jYb46nyYpu/LZmgKNjiojIc0SFrIgkmquThfdq52dW9/JkT+fB0hvViT/Rg0KxTtwxm/jw9AI+nPoSkRGXHB1VRESeAypkRSTJSmYLYHHvSrQtn43L8TnYemIQ5cNDMBsGv8VfpdnMmhw4NMfRMUVEJI1TISsiT8TDxYlPGxZmSqeyZPD1YtmFnoScrUv6eIMzFhi75n3YMBI056yIiCQTFbIi8p+8mCeQpX0q81qJzOyPrMKVE/2oGOHJwKvXYPknMOU1uH3Z0TFFRCQNUiErIv+Zr7szw5sV54fXS+LinpmlZwfwbWxH4syu8Ndqhk+uwrqtoxwdU0RE0hiTYRiGo0OkFrdu3cLX15fw8HB8fHwcHUckRboWEcNH8/bxx4HL5Dado2tAKJ+lv/tr5nWPnPR5ZQourt4OTikiIilVUuottciKyFMV6OXK2DYlGd6sGJdds/PxjQGUCAsAYPKdv2jzayVOnlrj2JAiIpImqJAVkafOZDLxWoks/NGnMmVyZ+PPi/3Jc64ivlYbh8xWmq9+k3kr+2NoIJiIiPwHKmRFJNkE+7nzS8cyfNawEIeiXyXmr57kj7IQZTbxybklDJ1WE6LDHR1TRERSKRWyIpKsTCYTr5fPzuLelciauTg7Tg2m+LUQnAyDF8/th7Evwtltjo4pIiKpkApZEXkmcgR6MrNbed6tXZgtN94i84kW5IryhrAz8HMt/loxAGt8rKNjiohIKqJCVkSeGYvZRI+quVj4VkWsgVWoHT2U36zluGCBNmfm0XVKBS5f3uvomCIikkqokBWRZy5/Rh8W9KxI22pF6B3/Fh+YGxBnMrHVFEOTxa1Ys/kbR0cUEZFUQIWsiDiEi5OZd2vlZ3aPipxx6YD7qbZkj4Ews4m3jkxkyIz6xGggmIiIPIIKWRFxqBJZ/VncqxIvlazHkZMDeeFmOgCmRZ+m1bTKnDix3MEJRUQkpVIhKyIO5+5iYdArhZjQqSrHoz4m97nK+FltHDXbmL2kO+yYCLoJoYiI/IsKWRFJMSrmDmTp25XJmacrUSd6UTnMhT7Xr8FvvWFWO4i66eiIIiKSgqiQFZEUxcfNmW+aFePzVg3ZEj6Eb2JbEmdYsB5cwAeTK7Fz72RHRxQRkRTCZBj6vi6xbt26ha+vL+Hh4fj4+Dg6jkiady0iho/m7ePiwY3UCBzDuEAnzIZBd79idK0/AYuTi6MjiojIU5aUekstsiKSYgV6uTK2TUnaNXmNKbcHUfSWBzaTie/D99JpSnkuXdzl6IgiIuJAKmRFJEUzmUw0LpmF+X1eweQ+ioIXi+Nhs7HDFEvjpa+zcsMXjo4oIiIOokJWRFKFYD93fulYhnpVPsPzbCdyRMMts4k+x6cyfmYjiItydEQREXnGVMiKSKphNptoWz4743t0xSX+W164EYSbzUaVY+uIH1sVLh90dEQREXmGVMiKSKqTM8iL6d1fomzxH8l7qgl+sR44XT+M9YeqHFo7BMNmc3REERF5BlTIikiq5GQx07Nabj7s1peePt+x2lqM/c4GLf/6ld5TXiQ87JSjI4qISDJTISsiqVqhYF8m967HlvJjGWmugglYbdym8dz6bNv9s6PjiYhIMlIhKyKpnquThffrFqRH8x/Jf60VwbEGly0mOu8ezqi5zYmPi3Z0RBERSQYqZEUkzSidPYDxb/WntF8oxcO9sJlMjLt9kLaTy3Ph/DZHxxMRkadMhayIpCmerk78r2kVOtZaQMlrZfC02dhniWflzObE75vr6HgiIvIUqZAVkTSpWr70jOgxhkrmD2hw00yb8Os4zelA+IzuEBvp6HgiIvIUqJAVkTTLz8OFYe3aUL7KQsbxGjbDhOXwdLpOLMfBIwsdHU9ERP4jk2EYhqNDpBa3bt3C19eX8PBwfHx8HB1HRJLg8q1oJkz9hci4b5jv64KzYfBGQAU61R+Lyay/6UVEUoqk1Fv67S0iz4UMPm68170LeYqOp3CkC3EmEyNvbqLzhHJcv37M0fFEROQJPHeF7O+//06+fPnIkycP48ePd3QcEXmGTCYTbatWYmjTNVSNKISLzWCrUxSN57/Kio2hjo4nIiJJ9Fx1LYiPj6dgwYKsXr0aX19fSpYsycaNG0mXLl2inq+uBSJph9Vm8P1vE1h8ZTjnXEyYDIPeTkXp1HISWJwdHU9E5LmlrgUPsXXrVgoVKkTmzJnx8vKiTp06LFu2zNGxRMQBLGYTbzXsyJc1F1Em0o90Vhuv/rWE08MqcfuSuhqIiKQGqaqQXbt2LQ0aNCA4OBiTycT8+fPv2yY0NJTs2bPj5uZG2bJl2bp1q33dhQsXyJw5s/1x5syZOX/+/LOILiIpVNHs2fi+6xo6u3bEyepGtuhDmMdW4rdF/3N0NBEReYxUVchGRkZSrFgxQkMf3JdtxowZ9O3bl4EDB7Jz506KFStGrVq1uHLlyjNOKiKpiauThdZt+nG62TL2mgvwp6eJD6/NoMe4StwIu+DoeCIi8hCpqpCtU6cO//vf/2jUqNED1w8fPpwuXbrQoUMHChYsyNixY/Hw8ODnn38GIDg4OEEL7Pnz5wkODn7o8WJiYrh161aCHxFJu4oWKkKud9ew3q8cZsNgvUsYrWa/zNKNUx0dTUREHiBVFbKPEhsby44dO6hRo4Z9mdlspkaNGmzatAmAMmXKsH//fs6fP09ERARLliyhVq1aD93n0KFD8fX1tf+EhIQk+3mIiGN5ursxpMs83g/uTlC8jfPOJj44OpRPJrYiJi7W0fFEROQf0kwhe+3aNaxWKxkyZEiwPEOGDFy6dAkAJycnvvnmG6pVq0bx4sV55513HjljwQcffEB4eLj95+zZs8l6DiKScrR8+U0m1plPyRh34k0m5pn20eHncuw6ttPR0URE5P85PekT4+LiuHTpEnfu3CEoKIiAgICnmSvZvPLKK7zyyiuJ2tbV1RVXV9dkTiQiKVXW4Dz83GkTI2b34Nc7G9nnFsfFOU24WuAzajRohdlscnREEZHnWpJaZG/fvs2YMWOoUqUKPj4+ZM+enQIFChAUFES2bNno0qUL27ZtS66sjxQYGIjFYuHy5csJll++fJmMGTM6JJOIpH5mi4W+zX9kTMkv6Bpmom70dV7e9QZLhnfmwvVwR8cTEXmuJbqQHT58ONmzZ2fChAnUqFGD+fPns3v3bo4ePcqmTZsYOHAg8fHxvPzyy9SuXZtjx57tPIwuLi6ULFmSlStX2pfZbDZWrlxJ+fLln2kWEUl7Shetz5s9NnM4pDkAL0TP451ZlZi6ai7P0X1lRERSlER3Ldi2bRtr166lUKFCD1xfpkwZOnbsyNixY5kwYQLr1q0jT548Ty0oQEREBMePH7c/PnnyJLt37yYgIICsWbPSt29f2rVrR6lSpShTpgwjRowgMjKSDh06PNUcIvJ8Mrl4kL/Tj1zaUotPd37IfneDE6c/Zs+4JbzXcjTpvN0cHVFE5LmSqm5Ru2bNGqpVq3bf8nbt2jFx4kQAvvvuO4YNG8alS5coXrw4o0aNomzZsk/l+LpFrYjcc/7CLt5d3Il9znEAFI/woHXF8dQuXsTByUREUrek1FupqpB1NBWyIvJP1vhYRsxtx+Q7+7CaTGSMs1HBtQPvNuuDl+sTj6UVEXmuPdNC9ubNmyxbtsx+o4Hg4GBq1aqFv7//f9ltiqRCVkQeZOvuKXy04wsuOZlwMgzqXSvGq41HUipHoKOjiYikOkmpt/7TPLI//fQT5cuXZ8uWLdhsNmw2G1u2bKFChQr89NNP/2XXKUpoaCgFCxakdOnSjo4iIilQmeJtmNNkCVUNX3LFxvFx5O/ETHiF7xauJzbe5uh4IiJp1n9qkc2XLx87d+7E09MzwfKIiAhKlCjB0aNH/3PAlEQtsiLyKIbNxtXNP+K7fCCuRjSXDW8GB7SiV/MB5M+o3xkiIonxzFpkTSYTt2/fvm/57du3MZk0UbiIPF9MZjPpK3TH9Y113PIrwFx/E+v8ljB0RgPGrt6L1aYhCSIiT9N/Go3w9ddfU6VKFQoXLkzmzJkBOHfuHAcOHOCbb755KgFFRFKdoLz4vPknYbObQMwpdvrd4Pqx1uw41INPWrQnJMDD0QlFRNKE/zzYy2q1snXrVi5cuADcHexVpkwZLBbLUwmYkqhrgYgk1Z+bv2XAwfGEWcy42QwKXC9KvcpDaVY6q765EhF5gGSdteD06dMcOXKEokWLPvDWrxcuXCA4ODhpiVMJFbIi8iSuXjnAe4vasc0cA0CR2274eg7ms6bVCfRydXA6EZGUJdn6yE6bNo3cuXNTu3ZtcubMyeTJkwE4c+YMX3zxBWXLliVr1qxPnlxEJA0KSl+I8W030zugFE6GwVHPO7Q534v+3/7I8oOXHR1PRCTVSlIh+9lnn/HWW2+xb98+atasSY8ePfj444/JlSsXEydOpFSpUsyaNSu5soqIpFpmixOdG0zgl9ID+STCTMX4q/wY/wl7pn5E/5k7uB0d5+iIIiKpTpK6Fri6unL06FGyZcvGuXPnyJo1K1WrViU0NJQCBQokZ84UQV0LROSpiL6F9fe+WPbPYrerC0P8gom6/RYfN32NMjkCHJ1ORMShkq2PrNls5tKlS6RPnx4ADw8P1q9fT4kSJf5b4hQuNDSU0NBQrFYrR48eVSErIk+Fbfc0Gm/7lOMuTvhYbWS6VJGSxd+m78t5cXVKewNmRUQSI1nnkf311185fPgwABaLJU3eivbfevbsycGDB9m2bZujo4hIGmIu3pIRL/9IQZuFWxYzRzJv4uCxrjQevZRDF285Op6ISIqXpBbZKlWqsHv3biIiIvD39yc8PJyePXtSoUIFChcuTN68eXFy+k9T06Zo6logIskhLiaSUb+1YWLkcQBCYgziLraicdXmdKmUE4tZ03SJyPMjWaffAjh27Bg7duxg586d9p+wsDBcXFzImzcve/fufeLwKZkKWRFJThu2fceH+8Zyw2LC1WZQ/kx5LqfvwDfNi+smCiLy3Ej2QvZBTp48yfbt29m1axdDhgx5GrtMcVTIikhyu3btMB8taodr5DVGXrnGH9bSfGrqTp9XytK0ZBbdREFE0jyHFLLPAxWyIvIs2KzxRG8ajfuqzzHZ4jhGAG+bm5I5RzOGNCpCOt1EQUTSsGQZ7HXmzJkkhTh//nySthcRkbvMFic8XnwbU+cV2AJyMj7IxNmsi4m6+iF1vl3JykO6iYKICCShkC1dujTdunV75Mj98PBwxo0bR+HChZkzZ85TCSgi8twKLo61y2qc/XNiM5nYle4imYPeZ8DUGXwwdx+RMfGOTigi4lCJ7lpw/fp1Pv/8c37++Wfc3NwoWbIkwcHBuLm5cfPmTQ4ePMiBAwcoUaIEH3/8MXXr1k3u7M+cuhaIiKMsWvMJn52cS6TZhJfVRpZL5bji3IbhzYpTMlvanwZRRJ4fydpHNioqikWLFrF+/XpOnz5NVFQUgYGBvPDCC9SqVYvChQv/p/ApmQpZEXGks2c38d6KN9hnvtsSWzzcmx2XetGp6gv0qp4HZ0uSpwYXEUlxNNjrKdOdvUQkpYiLu0Powrb8fPswgVYrX5018XHMmzgFF+Xb5sXInd7b0RFFRP4TFbLJRC2yIpJSbN7xA5b131L65kVicGZIXCumm2rxfp2CtCufHbNuoiAiqVSy3aL2pZdeIiws7KHrr127Rs6cOZOySxEReQLlSnajdOf1kKcWrsRR2m8WLwR/wsjFq2j781Yuhkc5OqKISLJLUiG7Zs0aYmNj7Y9jYmISrLdarZw+ffrpJBMRkUfzDIRWM4iq9TlfpfPngGcsfjmHE35xBrW+XcvCPRccnVBEJFk98ciA/fv3kzt3bgYMGIB6J4iIOIjJhHv5Nxn34lfksJq47mTmdMgyivsOo++0zfSatovwO3GOTikikiyeqJBdt24dlStXplq1aowbN44aNWpw5cqVp51NREQSKV/e+kxvsYrGLpkwTCZ2BVymcI5BbD/0J7VGrGXD8WuOjigi8tQluZCdN28etWvXZsCAAfzyyy/s3LmTmJgYihcvzpo1a5IhooiIJIaHRyCDWi7j65zN8LYZnHAzIPs4ikctofX4LXz620Gi46yOjiki8tQkadYCs9mMi4sLP/30E61bt7Yvt1qt9O/fnxEjRtgfp0WatUBEUosLF7bz3rKuFA+/zjs3w5gVX5mB8e3JnD6QES2KUyjY19ERRUQeKNmm3+rQoQOtWrWiZs2aD1w/f/58FixYwIQJE5KWOJVQISsiqUl8XDTG2q9wXv8tGDa2OmXio/gWnIorQ9+a+ehaOScWTdMlIilMsk2/lSVLFgICAh66/tVXX02zRayISGrj5OyGc/VPoN1vxPlkZmSQjevZZ1PO7we+WnqAlj9u5uyNO46OKSLyxJJUyJ4/f546deqQJUsWevTowZIlSxJMxyUiIilQ9heJ6fQHgR5BxJlM7E7/F2WyDeL42f3UGbmO2TvOafYZEUmVknxnL5vNxoYNG/jtt99YsGABFy9epGbNmjRs2JD69es/ssU2tVPXAhFJzQybjZnL+zDswipizCYCrDb8L1Rnd0Qt6hTOyJBGRfD3dHF0TBF5zj3TW9QeOnTIXtTu2LGDMmXK8Morr9CyZUsyZ878X3adYoSGhhIaGorVauXo0aMqZEUkVTt2fCn91/bnuOXur/8SN4PYeKkn/t6+fNWkKFXzpXdwQhF5nj3TQvafrl69ysKFC1m4cCGVKlWiX79+T2vXKYJaZEUkrYiOusnXC1oxI+Yc+WNi+eSSJ29G9eS0kZG25bPxQZ0CuLtYHB1TRJ5DDitk0zoVsiKS1qzc+CU5N4wlR+QNYswevBfdlvm2yuQM8mRk8xcokkXTdInIs5Vssxb8U1xcHGfPnuXIkSPcuHHjSXcjIiIOVL3Ce+Toug6yVcTVdoc86adRJeQzrlw/R6PvNzB65THirTZHxxQReaAkFbK3b99mzJgxVKlSBR8fH7Jnz06BAgUICgoiW7ZsdOnShW3btiVXVhERSQ6+WaDdb1yq1Ifxfj7s9Iokc64vyOW6iW+WH6XZD5s4fT3S0SlFRO6T6EJ2+PDhZM+enQkTJlCjRg3mz5/P7t27OXr0KJs2bWLgwIHEx8fz8ssvU7t2bY4dO5acuUVE5GkyW8hYfTA/lXiPTFaDC04mrmSbR7X0P7DrzDXqjFzH9K1nNE2XiKQoie4j27JlSwYMGEChQoUeuV1MTAwTJkzAxcWFjh07PpWQKYX6yIrI8yA8/AyDF7ZmuS0MgMLRzhw705Vr1hBqFszAF68VIZ2Xq2NDikiapcFeyUSFrIg8LwybjTkr3+XLc38QbTaRKd5GlpPNWRVfkkAvV4Y1KUq1/JqmS0SevmQd7HX69GmWLVvGpUuXHrj+woULSd2liIikMCazmSY1v2F6lRHksZnpGnaTn52+YbjPdG5FRNBh4jY+nr+fqFiro6OKyHMsSYXstGnTyJ07N7Vr1yZnzpxMnjwZgDNnzvDFF19QtmxZsmbNmixBRUTk2cuVswbTW66jcf7WALwWu5Afgz4lq8sBJm8+Tb3R69h7LsyxIUXkuZWkQvazzz7jrbfeYt++fdSsWZMePXrw8ccfkytXLiZOnEipUqWYNWtWcmUVEREHcHHzwVRvGLScTrhHAEP8oojO8QsvpZ/OX1dv89r3G/lu1TGsNvVUE5FnK0l9ZF1dXTl69CjZsmXj3LlzZM2alapVqxIaGkqBAgWSM2eKoD6yIvK8u3blAO8tbsdWUwwAZaK92Hr6DW7bAiiVzZ9vmxcnJMDDwSlFJDVLtsFeZrOZS5cukT793Q7+Hh4erF+/nhIlSvy3xKmEClkREbDGxzJhcRe+u7EDq8lEpngDj8uvsvtWeTxdLAx6pRBNSmbBZDI5OqqIpELJOtjr119/5fDhwwBYLBb8/f2fLKWIiKRKFicXOr8yiUmlBpDZChedTJwKnk/9rD8QFRvDu7P30mPKTm5Gxjo6qoikcUkqZCtVqsTAgQMpVKgQgYGBREdHM3LkSGbOnMnBgweJj49PrpwiIpLCFCvcgllNllLHEoDVZMLCAf7MOJLM5pssPXCJWiPW8ufRq46OKSJp2BPNI3vs2DF27NjBzp077T9hYWG4uLiQN29e9u7dmxxZHSY0NJTQ0FCsVitHjx5V1wIRkX8wbDYWrRnAi1sm4RcTQbyrPwPN3Zl6swgA7Stk5/06+XFztjg4qYikBg65IcLJkyfZvn07u3btYsiQIU9jlymO+siKiDzCteMwuwPGpb28F5SOGJccLP2rGzGGJ7nTezGieXEKZ/Z1dEoRSeF0Z69kokJWROQx4mPYv/RtWl5fB0DueBO2q23ZE1YAZ4uJt2vmpVvlXFjMGggmIg+WLIO9zpw5k6QQ58+fT9L2IiKSBji5Urj+94wp0JUAm8FxJ4MLGSbSJMdM4qxWvlp6hJY/bubsjTuOTioiaUCiC9nSpUvTrVs3tm3b9tBtwsPDGTduHIULF2bOnDlPJaCIiKQ+L5Z5izn1Z1Eed6LNJv5w20ntvEPI6HaDraduUHfkOubtOoe+FBSR/yLRXQuuX7/O559/zs8//4ybmxslS5YkODgYNzc3bt68ycGDBzlw4AAlSpTg448/pm7dusmd/ZlT1wIRkaSxWeP5ZUl3Rl7bTLzJRNE4g6wRbzHtUhYAGhQL5n8NC+Pr4ezgpCKSUiRrH9moqCgWLVrE+vXrOX36NFFRUQQGBvLCCy9Qq1YtChcu/J/Cp2QqZEVEnsz+g7P4YPOnfHzlMqVj4tgS0pnXj1chzmYi2NeNb5oVp3yudI6OKSIpgAZ7JRMVsiIiTy4+6iZOS96HvdMBWB5cjNDw19l9PRiTCbpWyknfl/Pi6qRpukSeZ8l2Z6+XXnqJsLCwh66/du0aOXPmTMouRUTkOeHk7g+v/QCNfuSMuw8DnK9zNXAkr+ddiWHAD2v/olHoRo5dvu3oqCKSSiSpkF2zZg2xsX/fcjAmJibBeqvVyunTp59OMhERSZuKNcfceiY5ceGW2cR8y3KaFfiWjB7RHLx4i/qj1zNxw0kNBBORx0pSIftP+/fvJ3fu3AwYMEC/bEREJEmyZCnPL63W09ErDwBLuEyGLINpkOMvYuJtDPrtIO0nbOPKrWgHJxWRlOyJCtl169ZRuXJlqlWrxrhx46hRowZXrlx52tlERCQNc3b15O3Gc/mhUA8CrQZ/WQw2uv5A9yJzcXUy8efRq9QeuY5lBy45OqqIpFBJLmTnzZtH7dq1GTBgAL/88gs7d+4kJiaG4sWLs2bNmmSIKCIiaVmFUm8w+5W5VDJ5Emsy4XJtBTtyT6RsBrgRGUvXyTt4f85eImPiHR1VRFKYJM1aYDabcXFx4aeffqJ169b25Varlf79+zNixAj747RIsxaIiCQfw2bj9+V9qb11Ks7WWAzvTEzO/AED9wRiGJA9nQffNi/OC1n9HR1VRJJRsk2/1aFDB1q1akXNmjUfuH7+/PksWLCACRMmJC1xKqFCVkTkGbi4B2Z3JO76cTpkykAB78IsPtWF87dsWMwmer2Uh57VcuFkeeJhHiKSgmke2WSiQlZE5BmJiWDZwo68c+cQAEVtzmQy92X2obutsSWy+jGi+QtkTefhyJQikgySbR5ZERGRZ8LVi5ebzmRYjiZ42Qz2muPYaPuCfqX/xNvViZ1nwqgzci2ztp/VzDkizzEVsokQGhpKwYIFKV26tKOjiIg8V2pXHsismuMpanPmttnEDxFLaJBnGBWyWoiMtfLu7L30/HUnYXdiH78zEUlz1LUgCdS1QETEMeLi7jDmt/aMv3UQw2SidpyZUhmG8NEmE/E2g4w+bgxvVowKuQMdHVVE/iN1LRARkTTF2dmDXq/NZHyxPmSPN+h56RzNd7fnz8qHyZnOg0u3omk1fgtDFh8iJj5tzpwjIvdTi2wSqEVWRMTxrBFXsPzWG44sBuC3nGXZ6tabyTvvri+YyYeRLYqTJ4O3A1OKyJNSi6yIiKRZFq/00OJXqPs12zy8+Mh2gQ0R7/Fp5UMEeLpw8OIt6o9ez6SNpzQQTCSNUyErIiKpj8kEZbrg22gcOW1mrlpMfH1lIi3zfU/VPD7ExNsYuPAAHSdu4+rtGEenFZFkokJWRERSrbx56jKtxRqaumbGMJn4Jeo4MeZefFQlBhcnM6uPXKX2iLWsPHTZ0VFFJBmokBURkVTN3SOAT1osZXiulnjbDPab4/np0icMqriO/Bm9uR4ZS6dJ2xkwfx9RsRoIJpKWqJAVEZE0oeaLHzKn1iRKGC5Emk24HZjIoqy/8kb59ABM2XyG+qPXsf98uIOTisjTolkLkkCzFoiIpHzxcdGsWPY2tbZPx2TYICAnW0t9yVtrzFy+FYOzxUTfmvnoWjknFrPJ0XFF5F+SUm+pkE0CFbIiIqnI6Y0wpwvhERdoGZyRRukrsONmV5YeugZA2RwBfNu8OMF+7g4OKiL/pOm3REREslWA7uuYn6sMZ52dGHVzKwa9+Ly2Jx4uFracvEHtEWv5bc8FRycVkSekQlZERNIujwDatlzCJ5mq42Yz2Mgdfjz5Jl++dIjiIX7cio7nrWm76DtjN7ej4xydVkSSSF0LkkBdC0REUq8TJ5bz7tp+HDPbAGjrkQuz92BC/zyHzYCQAHdGNC9OyWwBDk4q8nxT1wIREZF/yZWrJr+2WEMLtxAAfrlzAsv5zixomZEs/u6cvRFF07Gb+Hb5UeKtNgenFZHEUCErIiLPDTd3fz5qvpiReV6nQJyVDuePUeS3Bix/6TyvFQ/GZsDIlcdo9sMmzly/4+i4IvIY6lqQBOpaICKSdhhh5zDN7w6n1mEA0/NVwiXHZwxaeoXb0fF4uTrxacNCNHohMyaTpukSeVbUtUBEROQxTH5ZoO0CqDaAed7eDIk9zfiDbfmu3hVKZ/cnIiaevjP30Gv6bsKjNBBMJCVSISsiIs8vswWqvEvOl78isxXOWaDPgS95OfhH3qlx94YJv+25QN2R69jy13VHpxWRf1EhKyIiz73iRVoxq/ESalv8iTeZGHVzB3vOt2VCiwCypfPgfFgULcZtZtgfh4nTQDCRFEOFrIiICODtm4WvWq3h08y1cbcZbCGaATs6M6jiHpqVyoJhQOjqEzQZs5GT1yIdHVdEUCErIiJiZzKbaVRjGDOqjia/zUyYCbzWDuErz2mMbVEYX3dn9pwLp96odczYdgaNlxZxLBWyiRAaGkrBggUpXbq0o6OIiMgzkCNHNaa2Wk+oXxlKR8fAljHU3tSa31r5Uy5nAHdirbw3Zx89puzkZmSso+OKPLc0/VYSaPotEZHn0NE/YH4PTsWG0y44I2+F1OGqUze+WX6MeJtBBh9XhjcrTsXcgY5OKpImaPotERGRpyVvLeixkRkh+blhMTP4wh8cP9+JX9tlJ2egJ5dvxdDmpy0MXXyI2HgNBBN5llTIioiIPI53Rt5t8yd9AkrhZBgss97k4w3NGVrjLK3KZsUw4Ie1f9Ho+w0cvxLh6LQizw0VsiIiIolgtjjRqcEEfik9kCxWuGCBbru/JJv5K8a2LoK/hzMHLtyi/uh1TN1yWgPBRJ4BFbIiIiJJUKRQU2Y1XUY9p3RYTSa+C9vNre1tWNYpNy/mDiQ6zsZH8/bTdfIObmggmEiyUiErIiKSRF7emfii1WqGhDSgbHQsjU7vIWjKS/xS4Qof1S2As8XE8oOXqT1iLeuPXXN0XJE0S4WsiIjIkzCZaPDSEMY1XoRzpuIQdRPrzDaYL/djZqfC5Ary5MrtuwPBhiw+REy81dGJRdIcFbIiIiL/gSkwN3RaDhXeYrS/HyPuHOPTPxswsn4UrcpmBeDHtX/x2vcbNRBM5ClTISsiIvJfObnAy/+jbIV3CbAZHDfbaL/xXYp7jOeH1i9oIJhIMlEhKyIi8pRULP0mcxrMpiIexJhNfHZpFUt2N2VWh2wJBoJ100AwkadChayIiMhTFBiYn+/bbKBfYHmcDIOVtlt0X96Yd0sfsw8EW6aBYCJPhQpZERGRp8xscaJdvR+ZUu4zslnhtsnA//c+dLFOZ173svcNBNMdwUSejMlQR51ES8q9f0VERADuRFzh8NK3KbH/97sLQspxve63fLPZyq9bzgBQKNiHkS1eIHd6LwcmFUkZklJvqUVWREQkGXl4padEk6nw2nhw8WbL1V00XNqUqoEL+OH1kgkGgv265YwGgokkgQpZERGRZ6FoU+i+jmkZshJuNvPOXzPYtLct87sXtg8E+3DePrpN3sFNDQQTSRQVsiIiIs9KQA6GtVlLZ698mAyDObEX6fV7bT6qdCXhQLCRa9lwXAPBRB5HhayIiMgz5OzsQe/Gs/mxSC+CrAZ/WQzabPoAj8hvmNu9PLmCPLl86+5AsKEaCCbySCpkRUREHKBcya7MfnUBlU1exJpMfHFlLbf+fJ3fOxWkZZmsGAb8sPYvGo/ZyF9XdUcwkQdRISsiIuIgAQG5+K7NBt5PX5mGEVFUOL4O958qM7T4Dca2KYmfhzP7zodTb9R6Zm47q4FgIv+i6beSQNNviYhIsrm0D2Z3hGtHCTNbmFWkFnUqfc+7c4+w6a/rANQtkpGhjYri6+Hs4LAiyUfTb4mIiKQ2GYtA1z8xSrRjYKA/o27t573fXuLLOgbv1c6Pk9nE4n2XqDNyLVv+v7AVed6pkBUREUkpXDwwvTKKekU64G0z2GuOp/mKLmQz/cKcHhXIns6DC+HRtBi3mW+WHSHOqoFg8nxTISsiIpLCvFxpALNrTeQFw4UIs4n3Ts1l9romzOqcj2alsmAYMHrVcZqO3cSZ63ccHVfEYVTIioiIpEDBwaX4ufUGuvsUxmwYzI+7TMd5tehR7ALftXoBbzcndp8No+6odczbdc7RcUUcQoWsiIhICuXk7EbPRtMYX7wvGawGsbZ40k1vS/3IeSzpVZHS2f2JiInn7Rl76D19F7ei4xwdWeSZ0qwFSaBZC0RExFHCw05xeXFf8h5dCYCRqwZhdYcxZbeVESuPYbUZZPF3Z2SL4pTMFuDgtCJPTrMWiIiIpDG+ftnJ23IO1BsOTm7MubKJRgteoaTvcmZ2K09IgDvnbkbR7IfNjFxxjHgNBJPngApZERGR1MJkgtKdsHVeyVz/IK5bTHQ7MIY/t3VkQY8SNHohM1abwbcrjtJy3GbO3dRAMEnbVMiKiIikMuaMhfm55Rqau4UAMCHyOG/Mrsrb5SP4tnkxvFyd2HbqJnVGruO3PRccnFYk+aiQFRERSYXc3P0Z0HwxI/K0wcdmcMBspenK7jiFjWFxr0q8kNWP29HxvDVtF/1m7SEyJt7RkUWeOhWyIiIiqVj1Cu8xp/ZkShqu3DGbGHB6AfGrujKzfSHeeik3ZhPM3nGO+qPXs/dcmKPjijxVKmQTITQ0lIIFC1K6dGlHRxEREblPxkwv8FObjbzpV5weYbfJeeA3nMdV5Z1CEUzrUo5Mvm6cvBbJa99vZOyfJ7DZNGGRpA2afisJNP2WiIikeGc2w5zOEH6Wky6urC3agFeqfseH8w+yZP8lACrmTsfwZsXJ4OPm4LAi90tKvaVCNglUyIqISKoQdZO4hb1pHb6FQ64ulMedz+tMYOUpbwb/dpCoOCv+Hs4Ma1KMGgUzODqtSAKaR1ZEROR55u6PU9OJNM9RHzebwSaiaLKoOZmNefz21osUzOTDzTtxdP5lO58s2E90nNXRiUWeiApZERGRNMhkNtO45jfMqDqSfDYzN8wm3jg8nrl/tmJG5yJ0qZQDgF82nabhdxs4cum2gxOLJJ0KWRERkTQsZ47qTG25ltbu2QGYfOcknWZWoWux20zqWIZAL1eOXL5Ng+/W88umU6jHoaQmKmRFRETSOFc3X95v9hvf5WuPv83AOTYKv0mvUiViKUt7v0jVfEHExtv4ZMEBuvyynRuRsY6OLJIoGuyVBBrsJSIiqd2Vy/uxLn2XTCc3AhBX8FWian3OnP1xDF18mFirjfTergxvVpwX8wQ6OK08jzTYS0RERB4ofYbCZHr9d6g+EEwWRl1cQ7M5dXjBdxPze1Ykd3ovrtyOoc1PWxi6+BCx8TZHRxZ5KBWyIiIizxuzBSr15U67haz09uG8BdpvH8KG7W8yv3sZWpfNCsAPa/+i8ZiN/HU1wsGBRR5MhayIiMhzyiP7i8xospQ6lgCsJhOjbu6i98xK9KpgMLZNSfw8nNl3Ppz6o9czc/tZDQSTFEeFrIiIyHPM2yczX7Zazf9C6uFuM9hqiqHJ4pa43Z7Ckt6VKJczgDuxVvrP3stb03YRHhXn6MgidipkRUREnnMms5mGL33BzGqhFLBZCDObef/wBNzXvc/U9sV5t1Y+LGYTv++9SN2R69hx+oajI4sAmrUgSTRrgYiIpHWxMbcZtfB1CpzaQr3IO5C+EDT5mV3RGeg1fRdnb0RhMZvoXT0PPavlxmI2OTqypDFJqbdUyCaBClkREXluHFsB87tD5FU2e/pwtlgTar34BZ8sPMj83RcAKJMjgBHNixPs5+7gsJKWqJBNJipkRUTkuXL7MuHzuvBq3HGuOVmoafZlYIOprPzLwsfz9xMZa8XX3ZkvGxehduFMjk4raYTmkRUREZH/zjsD3q3n0i5DBZwMg+W2cJrMrUd2yyoW9apEsSy+hEfF0X3KTj6Yu4+oWKujE8tzRoWsiIiIPJTZ4kT7+uOZUnYwWa1wyWKiw66vWLK+K9M7l6R7lVyYTDBt6xkafLeegxduOTqyPEdUyIqIiMhjFSrQmJnNlvOKcxA2k4nvw/fSffqL9CptYUqnsqT3duX4lQhe/X4DEzac1Jyz8kyokBUREZFE8fTKyOetVjEkW0M8bAaZIm/iPr46FWM3sKR3JWoUSE9svI3Bvx2k06TtXI+IcXRkSeM02CsJNNhLRETkrrNnN+C/5EO8LuwG4NYLbXCq+Smzdt/m88WHiI23EeTtyvBmxaiUJ8ixYSVV0WAvERERSVYhIRXx6rgcKvbBAD46v5RW06tRPuggC3pWJE96L67ejuH1n7Yy9P8LW5GnTYWsiIiIPBknF6g5mMvNfma/mzsnLAYtN/Rnz56PWPBGBVqXzQrAD2v/osnYjZy6FungwJLWqJAVERGR/yRjwcbMfmUulUyexJpMfH55De/PrMK7Vb0Y26Ykfh7O7D0XTr1R65iz45wGgslTo0JWRERE/rN0gXkJbbOR99JXxNkwWG3cpvG8BqSLW8SS3pUomyOAyFgr78zaQ58Zu7kdHefoyJIGqJAVERGRp8JkNtOmzlimlv+c7FYTVywmPtnxNYHbvuLXjiXp93JeLGYTC3ZfoO6odew6c9PRkSWV06wFSaBZC0RERBLnTuRVvlrYildP7aZ4TCxkKQONx7Pjlg+9p+/i3M0onMwm+r6cl+6Vc2E2mxwdWVIIzVogIiIiDuXhGcSglssp3mAsuPrAua3Mn/QSV0+PYnHvStQvmol4m8FXS4/Q5qctXL4V7ejIkgqpRTYJ1CIrIiLyBG6e4tSc9jSxXCXGbKaRSwbee2Uaiw5FM3DBAaLirPh7OPN102JUL5DB0WnFwdQiKyIiIimHf3Yyt1tMW99CmAyDebGXaTGjOkW8d/J7rxcpFOzDzTtxdJq0nUELDxAdZ3V0YkklVMiKiIhIsnN29qDXazMZX6wP6a0GpywGrTd9xKbt/ZjTvRydXswBwMSNp3g1dAPHr9x2cGJJDdS1IAnUtUBEROS/u3njBJ/8/jprjLvFalWTFyNfW8Cf56HfzD1cj4zFzdnMwAaFaFE6BJNJA8GeJ+paICIiIimWf0AuRrVZz4cZquBiGBS8cQ7z2Bep5nSAJX0qUSlPINFxNj6Yu483pu4k/I7mnJUHU4tsEqhFVkRE5Ok6eWIZIUsH4HT1/9q77/imqv4P4J8kTZruQfcetIWyyqxs0EJRZKkICrKdoIwHEX8qBX0UHkEFhEecDFEBleEjiECh7KFlyCwtLR3QDd0jaXJ+f6QEQhktbUnTft6vV15N7j335ntPbk++PT333DgAEmQ98hLs+kZh9dEMfLw9DhVaAQ87JZY81x6d/RyNHS49BOyRJSIiIpPgH9gfZi/GAB3Ho1wi8FrKFoz7sQce98/Ar692g28zS1zNL8OILw9j8a6LqNBojR0yNSBMZImIiMi4FJbAoMW49MQCXJXLcUZageG7XkbqpU+w9Y2eeKqDJ7QCWLwrHs9/fRRX8kqNHTE1EBxaUAMcWkBERFS/0q/GYvaOl3BcogIADJY74/8G/4gd8RV4d9MZFKs0sFWa4T9Pt8XjbdyNHC3VBw4tICIiIpPk7tER3446iNfs2kAqBH5TZ+PZDf0QrDyKbVN7op2XHQrKKvDqD8fx9sbTKFVxztmmjIksERERNShmciVeHfojvmv/Jtw0Aiky4JN9b8Pnwrf4+eVH8ErvQADAT8dSMHjZAVzIKDByxGQsHFpQAxxaQERE9HDl56fg499G47XkM/Cs0ACBjwJDV+BAhgzTN5xEdmE5FGZSvDewJUY/4ss5ZxsBDi0gIiKiRsHOzgcfjt4LzwGfAGZK4NJufLmmN3D9J2yf2hN9Q5yhqtDivS1n8dL3sbherDJ2yPQQsUe2BtgjS0REZERZ53Fs41hMtNDNWjDGMgBvDF6LtX/lYMEf56HWCLjbKfHZiDA8EtDMyMHSg2KPLBERETU+Li3RduyfGKn0BgCsKUnECz/2xGPeqdj0WncEOFkhPb8Mz399BJ/u5JyzTQETWSIiIjIZSgsHvDNiG5YGj4WdVuC8VINnd7+GhLj5+G1yNwzv6AWtAJZGx2PkV0eQdr3E2CFTPeLQghrg0AIiIqKGIzPzH7z9xwT8JSkHAAw3c8Gcpzdhy4VCvLPpDIrKKzjnrAni0AIiIiJq9Fxd2+Lr0YfwukMYZEKg09VzwIoeGOKUjm1v9EQ7b3vOOdvIMZElIiIikyUzU+Clwd/jt67z8YSZE5CXDHwXCcmphdjwUme82icQEgnnnG2smMgSERGRyfMJGQS8sh9o9RRyocULSesx+cfumNChAt9PCIezjTnis4oweNlBfH/4MjiysnFoconssGHD4ODggGeeecbYoRAREVFdsrAHnvkOcb2no0QqxVGU4emtI6HN/Z5zzjZSTS6RnTp1KtasWWPsMIiIiKg+SCTo1nsO1vddhhZaKa5LJZgc9x2+2fYMVjwXgjlPhkIhk2LnuUw8vmQ/jiTmGjtiqoUml8j26dMHNjY2xg6DiIiI6pG/Xx/88PwBjLb0BwCsLb2MUT/1Qh/PJGx8rRsCnKyQUVCG574+gk93xHHOWRPVoBLZffv2YdCgQfDw8IBEIsHmzZurlFm+fDn8/PygVCoRHh6OY8eOPfxAiYiIqMFTmNvgreG/YXmLiXDUCsRJtVj9x8tonbkF/5vSHc928oIQwNLdCZxz1kQ1qES2uLgY7dq1w/Lly++4fv369ZgxYwaioqJw/PhxtGvXDpGRkcjKytKXCQsLQ+vWras8rl69+rAOg4iIiBqQXuHT8MvA9XgKNpiVnQ389jqsfpuEjwf6Yulz7WFjboa/k6/jiSX78cfpdGOHSzXQYG+IIJFIsGnTJgwdOlS/LDw8HJ07d8ayZcsAAFqtFt7e3nj99dcxe/bsau87JiYGy5Ytwy+//HLPcuXl5SgvL9e/LigogLe3N2+IQEREZIq0WuDQUmD3BxDaCnzo7oMnu82Go8cwvLHuBE6m5gEAng/3wZwnQ6GUy4wbbxPVKG+IoFKpEBsbi4iICP0yqVSKiIgIHD58uF7ec/78+bCzs9M/vL296+V9iIiI6CGQSoEe04AJO7DJ1RfrlcC42PnYduAlrJvUEa/0DgQA/HhUN+dsXEahceOl+zKZRDYnJwcajQaurq4Gy11dXZGRkVHt/URERGD48OHYtm0bvLy87pkEv/3228jPz9c/UlNTHzh+IiIiaiC8OqL/6D/xpJkTNBIJluedwqs/9cC49mX4fmIXONuY42JmEQYvO4C1R5I552wDZjKJbF3ZtWsXsrOzUVJSgrS0NHTt2vWuZc3NzWFra2vwICIiItNnbeOO+aP24COfwbDUCvwtKcczf4yGKvs7/DG1J3oHO6O8Qot3N5/Baz8cR36J2tgh0x2YTCLr5OQEmUyGzMxMg+WZmZlwc3MzUlRERERkygb1/RAbHv0CoVoZ8qUSTItfi1//GImVo1rj3YEtIZdJ8MeZDDy+ZB/+unzN2OHSbUwmkVUoFOjYsSOio6P1y7RaLaKjo+/Zq0pERER0L76+PbH2+YMYb9UcZkKga8IBSL99DJOCy/Drq93g18wSV/PLMOLLw1gaHQ+NlkMNGooGlcgWFRXh5MmTOHnyJAAgKSkJJ0+eREpKCgBgxowZ+Prrr7F69WqcP38er776KoqLizF+/HgjRk1ERESmTm5uhRnPbMK2znPR1sweyDoHfN0XVpe/wv+mdMdT7T2hFcCnOy/i+a+PID2/1NghExrY9FsxMTHo27dvleVjx47FqlWrAADLli3DwoULkZGRgbCwMCxduhTh4eEPJb6aTAdBREREJqooC9j8KuKT9+I5D1f0MLPHvEE/IDrRDO9tPoNilQb2lnIsfKYd+oW63n9/VCM1ybcaVCLb0DGRJSIiaiK0WvxvxzTMydiNCokErhqBBR1mopnXcLzx0wmcvpIPABjb1RdvP9GSc87WoUY5jywRERHRQyOVYtCApfjhkX/DVwNkyiSYeHIRtu2fhPUvdsCkHv4AgNWHkzHsv4eQkFVk5ICbJiay1bB8+XKEhoaic+fOxg6FiIiIHqLQFkOx4dloDJW7QiuRYEXBGbyyricmdCjByvGd0cxKgfPpBRj0+QGs/yuFc84+ZBxaUAMcWkBERNR0bYuJwgdJv6JIKsHUgjJMevRjZHk/jhkbTuFAQg4A4Mm27vjoqTawVcqNHK3p4hjZesJEloiIqGlLSzuMH3ZMxcyUOMgAoMNYaPt/hC+PZOKTHXGo0Ap4O1pg6cj2aO/jYOxwTRLHyBIRERHVAy+vrnhr7EHIeswAIEH5idV4c213POpxHhte6QovBwukXivF8BWH8UXMJWg552y9YiJLREREVBMyORARBYzZjBUuntgh1+K5Q7Nx/uw72Pp6dzzZ1h0VWoH/bL+AsSuPIauwzNgRN1pMZImIiIgeREAfvDDiN/SSWEMtkWBB1n6880sfvD/ADv95ug2Ucin2x+fgiSX7sfditrGjbZSYyBIRERE9IEfH5lg2+iBmu/SEXAjsFUV4ZvMQ+Mm2439TeqCFmw1yilQY+90xzN92HqoKrbFDblSYyBIRERHVgkQqxajH/4ufui2Av0aCbJkEL/6zFKePvI7Nr3TBC4/4AgC+3JeI4SsOITm32MgRNx5MZImIiIjqQEjwk1g3cjeeVrjDWivQ9Z/foPx+ID7obY0VozvCzkKOU2n5GLj0ALacvGLscBsFJrLVwBsiEBERUXVYWjph7nM7sKX9W3A3swau/A2s6Anf4p+xbWpPdPZzQFF5BaauO4k3fz6FElWFsUM2aZxHtgY4jywRERFVW14K8Osk7Ms5hcluLhgid8WsJ9fim6MF+Hx3PIQAApyt8Plz7dHKw87Y0TYYnEeWiIiIyNjsfYBx25DUoj+kQmCLOhPP/9IPA7zP4cdJj8DNVonE7GIMW34Iqw4m8fa2D4CJLBEREVF9kZlh7JDv8U3YDLhqBJJlwKgj7+Ji3Nv4/fWuiGjpApVGi7n/O4cX18TierHK2BGbFA4tqAEOLSAiIqIHlXc9CVG/j8ZubQEAoDus8O+Bq/C/OHPM33YBKo0WbrZKLB4ZhkcCmhk5WuPh0AIiIiKiBsbewR+LR+3Hu259Ya4VOIhiHP9xCMa7JmLja90Q4GSFjIIyPP/1EXy68yIqNJxz9n6YyBIRERE9JBKpFCMil+KnnoswpVyO/tcygLVPofXZRfjfa13wTEcvaAWwNDoez399FFfzSo0dcoPGRJaIiIjoIQtqPgAvjz8IdJoIAMg5sgxvruuBN8ILsXhEGKwUMhy7fA1PLN2PHWczjBxtw8VEloiIiMgY5BbAk58CI9biPy6u2C9TY3j0K5Dl/Rdb3+iJNp52yCtR46XvYxG15QzK1BpjR9zgMJElIiIiMqaWg/CvIT+hozBHiVSC/0v5DV/++SRWvxCAF3v6AwBWH07GsP8eQkJWkZGDbViYyFYD7+xFRERE9cnNvT2+HX0IU+zbQSYEfq/IweiNkRjifxYrx3dGMysFzqcXYNDnB7Dh71TOOVuJ02/VAKffIiIiovp28vRavPXXAlyVSWAmBJZ4DECL8PcxbcM/OHQpFwAwJMwD/x7aGjZKuZGjrXucfouIiIjIRIW1GY2fn96G/jJ7eFZUoOPhb+Cy5Xl8/6wv3owMgUwqwZaTV/Hk5wfwT1qescM1KiayRERERA2MrZ0PFj2/F9+3mQormRJI3APplz3Qw3YPNrz8CDztLZCcW4KnvziEr/clQqttmv9gZyJLRERE1ABJpFI4hL8KvLwXcG2DH8zKMfrMUuw6Ng6bXw7D463doNYIfLjtPCas/gs5ReXGDvmhYyJLRERE1JA5hwCTdiHLuyMAYG1JEl7b/Cje7F6Afw9tDXMzKWLisvH4kv04mJBj5GAfLiayRERERA2dXIkZw7dgWcg4OGgFLkg1GBnzOqyKl2PLa90Q5GKN7MJyjP72KBb+eaHJ3N6WiSwRERGRiej9yL/wyxPrEA4lSqUSzEn7A9/uHowfxvjjuS4+EAJYvucSRnx1BGnXS4wdbr1jIktERERkQlxcW+PLUQcx1bEjZEJgV0Uusn4aiPmdS7H8+Q6wMTdDbPJ1PLFkP/44nW7scOsVE1kiIiIiEyMzU2DSoFVY0/k9vFsiQevcFOC7ARiY9wO2vd4NYd72KCirwKs/HMc7m0432tvbMpElIiIiMlFtW43A0xMOAK2fAYQGcfsX4KPfH8XyYVZ4tU8gJBLgh6MpGLLsIOIzC40dbp1jIktERERkypR2wNPfQAz5L+a5OOGApAwj/xyNcPutWDOhC5yszRGXWYhByw5g3bGURnV7Wyay1bB8+XKEhoaic+fOxg6FiIiIqCqJBJL2o/BRvy/RUitDnlSC1+NWYf/xcdjySlv0DHJCmVqL2RtP4/WfTqCgTG3siOuERDSmtLye1eTev0RERETGoC4vxpLfRmF1ySUAQJBWiv/0WoTotAAs+jMOFVoBb0cLfP5cB4R52xs32DuoSb7FHlkiIiKiRkRuboWZwzdjRejLcNQKxEu1eH7fdPSS/oyfX34EXg4WSL1Wime+OIQv914y6dvbMpElIiIiaoS6d56CXwf9gu6wRNvycoREz0f7I1Ox9aU2GNjGHRVagfl/XMC4VX8hu9A0b2/LoQU1wKEFREREZGq0mgoUH1oCmz3zAa0aZbZeiOv3fzhX2hNzfzuL8gotnKzNsXhEGHoEORk7XA4tICIiIiIdqcwMNj3/BUzaCTgGYJG8GGNi5yPv6mxsfrUTgl2tkVNUjhe+O4qPt1+A2oRub8tEloiIiKgp8GgPzYt7UNosEFqJBP/NP40FOwfgq6ct8Xy47va2/425hBFfHkbqNdO4vS0TWSIiIqImQmZhjw+fj8Z836Gw0gocl6jwfPR49HX+n+72tkozHE/JwxNL92ObCdzeloksERERURPzZJ8P8HPEl2ijNUOhVIIZl35C7Lnx2PRSK4R526OwrAKv/XAc/9fAb2/LRJaIiIioCfL27o7Vow9ionUwJELgz5IUWG8ehp+H2epvb/tj5e1tLzbQ29sykSUiIiJqouRyS0x7+ld81WYKPirSwi3rIuTfPoa3HPdjzfjO+tvbDl52AD8dSzF2uFUwkSUiIiJq4h7p+Ap6TzwABPUHNOWI2fMefjkyFOvHeetvb3sqNc/YYVbBeWRrgPPIEhERUaMmBFSHl+Px8/9FlpkMLhqBj8KmIUHdD0+194KFQlbvIXAeWSIiIiKqOYkEim5TsLzHAvhpJMiSSfDiP4uRe3UW5BK1saOrgolsNSxfvhyhoaHo3LmzsUMhIiIiqnctQgZj/cjdeErhBiGR4ETmcUjWv2DssKrg0IIa4NACIiIiamr+3P8+2h36Fm6DPgdCB9f7+9Uk32IiWwNMZImIiKhJKrkGWDo+lLfiGFkiIiIiqjsPKYmtKSayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIlsNy5cvR2hoKDp37mzsUIiIiIiokkQIIYwdhKkoKCiAnZ0d8vPzYWtra+xwiIiIiBqdmuRbZg8ppkbhRs5fUFBg5EiIiIiIGqcbeVZ1+lqZyNZAYWEhAMDb29vIkRARERE1boWFhbCzs7tnGQ4tqAGtVourV6/CxsYGEonknmULCgrg7e2N1NRUDkN4QKzD2mMd1g7rr/ZYh7XHOqw91mHtPcw6FEKgsLAQHh4ekErvfTkXe2RrQCqVwsvLq0bb2Nra8pemlliHtcc6rB3WX+2xDmuPdVh7rMPae1h1eL+e2Bs4awERERERmSQmskRERERkkpjI1hNzc3NERUXB3Nzc2KGYLNZh7bEOa4f1V3usw9pjHdYe67D2Gmod8mIvIiIiIjJJ7JElIiIiIpPERJaIiIiITBITWSIiIiIySUxkiYiIiMgkMZElIiIiIpPERJaIiIiITBITWSIiIiIySUxkiYiIiMgkMZElIiIiIpPERJaIiIiITBITWSIiIiIySUxkiYiIiMgkmRk7AFOi1Wpx9epV2NjYQCKRGDscIiIiokZHCIHCwkJ4eHhAKr13nysT2Rq4evUqvL29jR0GERERUaOXmpoKLy+ve5ZhIlsDNjY2AHQVa2tra+RoiIiIiBqfgoICeHt76/Oue2EiWwM3hhPY2toykSUiIiKqR9UZxsmLvYiIiIjIJDGRJSIiIiKT1CCHFuzbtw8LFy5EbGws0tPTsWnTJgwdOvSe28TExGDGjBk4e/YsvL298e6772LcuHH69XPnzsW8efMMtgkJCcGFCxfq4QiIiIgaH7VGi1K1BmUqDcrUuuelag1KVRqUVeiW31hWptairHKd7vXNnxqtgFbork7XCkArbr4W+td3L6MVAlotIJUCZlIp5DIJzKRSmMkkUMh0P81kUsillT9lEshl0ptlK8srzKQwk+rWWZnLYKEwg5VCBguFDFYKM1gqZLA0v7lMIZNy1qIGpkEmssXFxWjXrh0mTJiAp5566r7lk5KSMHDgQLzyyiv44YcfEB0djUmTJsHd3R2RkZH6cq1atcKuXbv0r83M6v7whRCoqKiARqOp830TNURyuRwymczYYRBRNQkhUKzS4HqxCvmlalwvUSGvRI28UjXyilXIq1yWX1K5rlSN/BI18kvVqNAKY4dvVGZSyW1JrgyWlc9vLLNRymFnIYedhRnsLG881z1sK3+am7HNrCsNMpF9/PHH8fjjj1e7/IoVK+Dv749PPvkEANCyZUscOHAAn332mUEia2ZmBjc3tzqP9waVSoX09HSUlJTU23sQNTQSiQReXl6wtrY2dihETZYQAgVlFcgsKEN6fhky8kuRkV+OjIJSZBeqkFeZkOaVqJFfqoJaU7uEVCIBLOQyWMhlUMp1vZVKufTm61t+6tbdWCaFUi6DmUwCqUQCqUTXhtx8DkglkspluGMZ3XrdMq0QqNAIVGi0UGsrf2q0UFcuq9AK/XO1QRmBCq0W6goBtVYLVYUWpSoNSlQalKgqKn9qUFz5XFWhBQBUaAUKyypQWFZRq/pTyqUGCe6tSe6Nh6OVAs2szNHMWoFm1go4WipgJuOI0Ns1yES2pg4fPoyIiAiDZZGRkZg2bZrBsvj4eHh4eECpVKJr166YP38+fHx87rrf8vJylJeX618XFBTctaxWq0VSUhJkMhk8PDygUCj47wdq9IQQyM7ORlpaGoKCgtgzS1QPtFqB3GKVYZKqf16GjALdzxJVzf4TqDCTwsFSDnsLBewt5bC3lMPBUgG7ymUOlcvsLXXrbZVyWCnMoFRIm9y/2Cs0WpSoNSgpr5rolqo0KC6v0L8uKK1AfqkaBaW6XuxbHwVlagiBymEX5cgsKL//m9/C3lKOZlYKNLM2r/ypS3adrHXLHK0UuudW5rCzkEMqbfyfUaNIZDMyMuDq6mqwzNXVFQUFBSgtLYWFhQXCw8OxatUqhISEID09HfPmzUPPnj1x5syZu85TNn/+/Crjau9GpVJBq9XC29sblpaWtT4mIlPh7OyMy5cvQ61WM5ElekD5pWok5RTjck4xEit/pueXIj2/DJkFZdXuQbW3lMPNVgk3OyXc7ZRws7WAs405HCzlNxNUK91PCwV/X6vLTCaFrUwKW6W8VvvRVvbo3p7gVkl4S9W4VqxCbnE5rhWrcK1YBa2AbghIiRqXsovv+14yqQQOlrrE1tVWCRcbc7jaKuFqaw6XW14725hDbsI9vY0ika2OW4cqtG3bFuHh4fD19cWGDRswceLEO27z9ttvY8aMGfrXNybovZf73UqNqLFpSr0yRLVRqtLgcm4xknIMH5dzipFbrLrnthIJ4GRtDnc7JVxtK5PUymRV99oCbrZKJqcNnFQq0Y2btaxZQqzRCuSVqJBbrEJukS7BzS1SIbeovMqynKJyFJRVQKMVyCkqR05ROS5kFN5z/82sFHCpTHJdbZRwqUx2XSuTXRdbczhZN8yEt1Eksm5ubsjMzDRYlpmZCVtbW1hYWNxxG3t7ewQHByMhIeGu+zU3N4e5uXmdxkpERI2XqkKL1OslSMouxuVcXe/qjefp+WX33NbZxhz+Tlbwb2YFPycreDta6BNVFxslFGYNL4mgh0MmleiGE1ibA673L6+q0OJ6iS6pzS4sR1ah7mdmQVnloxxZBWXILiqHWqMbupJbrML59LvvUyIBnu/igw+Htam7A6sDjSKR7dq1K7Zt22awbOfOnejatetdtykqKsKlS5fwwgsv1Hd41MiNGzcOeXl52Lx5s7FDIaKH6FqxCueuFuBcej7Opxfi3NUCJGQXQXOPK/vtLOTwd7JCgJMuWfWvfPg5WcHavFF8JVMDoDCTVg4jUN6znFYrcL1EhcyCcmQWliG7oDLZLaxMdgt1CW9WYTk0WtEgz9GGFxF0SeatPaVJSUk4efIkHB0d4ePjg7fffhtXrlzBmjVrAACvvPIKli1bhlmzZmHChAnYvXs3NmzYgK1bt+r3MXPmTAwaNAi+vr64evUqoqKiIJPJ8Nxzzz3042tI+vTpg7CwMCxevNhg+apVqzBt2jTk5eUZJa76Zozkc+/evRg9ejRSU1OrxLJ69eq7bufr64vLly/Xc3R3xiSdSPdln3KtBOfSCyoTV93PjII797BaKmTwa2YFf2dd76q/083nDlaKhxw90d1Jb+npDYXtXcvduOBQ1gAvHmuQiezff/+Nvn376l/fGKc6duxYrFq1Cunp6UhJSdGv9/f3x9atWzF9+nQsWbIEXl5e+Oabbwym3kpLS8Nzzz2H3NxcODs7o0ePHjhy5AicnZ0f3oFRjahUKigUho2+EAIajaZe5gCub1u2bMGgQYOqLF+yZAkWLFigf+3u7o6VK1diwIABAFDjC6juVG9EVD1lag3iMgr1yer5dN2j+C4zAvg1s0Sohy1C3W0R6mGLFm62cLdTcuw4NSpSqQTONg10qKWgasvPzxcARH5+fpV1paWl4ty5c6K0tNQIkT243r17i6lTp1ZZvnLlSmFnZ6d/PXbsWDFkyBCxcOFC4ebmJhwdHcVrr70mVCqVvkxZWZmYNWuW8PLyEgqFQgQGBopvvvlGvz4mJkZ07txZKBQK4ebmJt566y2hVqsNYpk8ebKYOnWqaNasmejTp4/Ys2ePACC2bdsmOnToIORyudizZ4/QaDTio48+En5+fkKpVIq2bduKn3/+2eAYzpw5IwYOHChsbGyEtbW16NGjh0hISBBRUVECgMFjz549QgghUlJSxPDhw4WdnZ1wcHAQgwcPFklJSfp9VlRUiOnTpws7Ozvh6Ogo3nzzTTFmzBgxZMiQ+9Z1YGCg+OOPP+5bDoDYtGmT/vWsWbNEUFCQsLCwEP7+/uLdd981qPeoqCjRrl078fXXXws/Pz8hkUiEEEKcP39edO/eXZibm4uWLVuKnTt3Vtn3vY73XvV0K1M994nK1RpxIuW6+GZ/onjjp+Mi4pMY4T/7d+H7VtVH8DvbxODP94vZv54Saw4lib8v54rCMvX934SIauxe+dbtTK9by0QIIVCqNs7dvSzksnrpDdizZw/c3d2xZ88eJCQkYMSIEQgLC8OLL74IABgzZgwOHz6MpUuXol27dkhKSkJOTg4A4MqVK3jiiScwbtw4rFmzBhcuXMCLL74IpVKJuXPn6t9j9erVePXVV3Hw4EEAQHq6buT57NmzsWjRIgQEBMDBwQHz58/H2rVrsWLFCgQFBWHfvn0YPXo0nJ2d0bt3b1y5cgW9evVCnz59sHv3btja2uLgwYOoqKjAzJkzcf78eRQUFGDlypUAAEdHR6jVakRGRqJr167Yv38/zMzM8O9//xsDBgzAP//8A4VCgU8++QSrVq3Cd999h5YtW+KTTz7Bpk2b8Oijj96z7s6ePYusrKz7lrsTGxsbrFq1Ch4eHjh9+jRefPFF2NjYYNasWfoyCQkJ+PXXX7Fx40bIZDJoNBoMHToUPj4+OHr0KAoLC/Gvf/3LYL/3O9671RORqbperMLxlOv4O/k6YpOv41RqHsorJ7q/VTMrhUEva6i7LfydrDgZPVEDxES2npSqNQid86dR3vvc+5GwVNT9R+vg4IBly5ZBJpOhRYsWGDhwIKKjo/Hiiy/i4sWL2LBhA3bu3Km/OUVAQIB+2//+97/w9vbGsmXLIJFI0KJFC1y9ehVvvfUW5syZo5+2LCgoCB9//LF+uxuJ7Pvvv49+/foB0N2o4qOPPsKuXbv0F/QFBATgwIED+PLLL9G7d28sX74cdnZ2WLduHeRy3TQnwcHB+v1aWFigvLzc4E5va9euhVarxTfffKP/Q2DlypWwt7dHTEwM+vfvj8WLF+Ptt9/W3zp5xYoV+PPP+3/OW7ZsQWRk5AP9y//dd9/VP/fz88PMmTOxbt06g0RWpVJhzZo1+qEy27dvx6VLlxATE6M/xg8//FBfhwCwfv36+x7vneqJyBQIIXApuxjHk6/j7+RriE2+fse5N+0t5ejo44D2PvZo5WmHUHdbuNiYc2gAkYlgIkvV1qpVK4Pxmu7u7jh9+jQA4OTJk5DJZOjdu/cdtz1//jy6du1q8OXQvXt3FBUVIS0tTX+HtY4dO95x+06dOumfJyQkoKSkxCApA3TJXPv27fXx9OzZU5/EVsepU6eQkJBQ5QYZZWVluHTpEvLz85Geno7w8HD9OjMzM3Tq1AlC3Huy8i1btmDKlCnVjuVW69evx9KlS3Hp0iUUFRWhoqICtraGg/J9fX0NxnvHxcXB29vbIAHt0qWLwTb3O14iU1Km1uBUah5iU64j9vJ1xKZcR16Jukq5QGcrdPR1QCdfR3TwdUCgsxWTViITxkS2nljIZTj3fuT9C9bTe1eXra0t8vPzqyzPy8uDnZ2dwbLbk0KJRAKtVvdvubvN11tTVlZW911eVFQEANi6dSs8PT0Nyt2Y9/dB4ikqKkLHjh3xww8/VFlXm4sC09PTceLECQwcOLDG2x4+fBijRo3CvHnzEBkZqe9l/uSTTwzK3a3e7qW+jpfoYcgvUeNwYg7+uqwbKnD2Sj4qbpv2ytxMinbe9pWJqwPa+zjAkbMGEDUqTGTriUQiqZd/79e1kJAQ7Nixo8ry48ePG/wr/n7atGkDrVaLvXv36ocW3Kply5b49ddfIYTQ934cPHgQNjY28PLyqlHMoaGhMDc3R0pKyl17gNu2bYvVq1dDrVbfsVdWoVBAozEcw9yhQwesX78eLi4uVXo8b3B3d8fRo0fRq1cvAEBFRQViY2PRoUOHu8b7v//9D926dXug8aWHDh2Cr68v3nnnHf2y5OTk+24XEhKC1NRUZGZm6m/f/NdffxmUqc7x3qmeiIxBVaHFiZTrOJCQg/3xOfgnLQ+3T9fqYmOOTn4O6ODjgE5+jgh1t+VNBIgauYafaVG9evXVV7Fs2TK88cYbmDRpEszNzbF161b89NNP+N///lft/fj5+WHs2LGYMGGC/mKv5ORkZGVl4dlnn8Vrr72GxYsX4/XXX8eUKVMQFxeHqKgozJgxo8a39bWxscHMmTMxffp0aLVa9OjRA/n5+Th48CBsbW0xduxYTJkyBZ9//jlGjhyJt99+G3Z2djhy5Ai6dOmCkJAQ+Pn54c8//0RcXByaNWsGOzs7jBo1CgsXLsSQIUPw/vvvw8vLC8nJydi4cSNmzZoFLy8vTJ06FQsWLEBQUBBatGiBTz/99L5z7f72228YPHhwjY7xhqCgIKSkpGDdunXo3Lkztm7dik2bNt13u379+iEwMBBjx47Fxx9/jMLCQv1Y2xt/SFTneO9UTzUZrkH0oG6Mcd0fn40D8Tk4kphbZQqsQGcrdA1shk6+jujo6wAvBwsOEyBqYpjINnEBAQHYt28f3nnnHUREREClUqFFixb4+eef9fOYVtcXX3yB//u//8Nrr72G3Nxc+Pj44P/+7/8AAJ6enti2bRvefPNNtGvXDo6Ojpg4caLBhUw18cEHH8DZ2Rnz589HYmIi7O3t0aFDB/37NWvWDLt378abb76J3r17QyaTISwsDN27dwcAvPjii4iJiUGnTp1QVFSEPXv2oE+fPti3bx/eeustPPXUUygsLISnpycee+wxfY/lv/71L6Snp2Ps2LGQSqWYMGEChg0bdsfhGQBQXFyM6OjoKjecqK7Bgwdj+vTpmDJlCsrLyzFw4EC89957BjM93IlMJsPmzZsxadIkdO7cGQEBAVi4cCEGDRoEpVJ3pxdLS8v7Hu/d6omoPuQWlePgpVzsv5iNAwk5VW7p6milQPfmTugZ5IQezZ3gYV83Q5qIyHRJxP2uUiG9goIC2NnZIT8/v8q/YsvKypCUlAR/f399okC0ceNGvPvuuzh37pyxQ8HBgwfRo0cPJCQkIDAwsM72y3OfHlSZWoPY5OvYH5+D/fHZOHu1wGC9wkyKzn4O6BnkjB7NnRDqbgtpA7yzEBHVrXvlW7djjyxRPbK2tsZ//vMfo7z3pk2bYG1tjaCgICQkJGDq1Kno3r17nSaxRDWVlFOM6POZ2Befg2NJuShTG87j2sLNBj2DnNAzyBmd/RxhoajZne2IqGlhIktUj/r372+09y4sLMRbb72FlJQUODk5ISIiospsB0T1TasVOH0lHzvOZWDH2UzEZxUZrHexMUePIN1wge7NneBiw159Iqo+JrJEjdSYMWMwZswYY4dBTZCqQosjibnYeS4TO89lIqPg5lhXM6kEXQOboXewM3oFOyPIxZoXaBHRA2MiS0REtVZUXoGYuCzsOJuJPReyUFheoV9npZChTwsX9A91RZ8QF9hZcOYLIqobTGSJiOiBZBWWYde5LOw4l4FDCblQaW6Od3WyNke/UFf0b+WKboHNYG7Gsa5EVPeYyBIRUbUlZhdhx7lM7DibgROpebh13ht/Jyv0b+WK/qFuaO9tzxkGiKjeMZElIqJ7Ssgqwm8nr2DbmQwk3HaxVjtve/QPdUVkK1cEOnO8KxE9XExkiYioioz8Mvzv1FVsOXUFZ67cnN/1xsVa/Vu5oV9LV7jZcZYBIjIeJrJERAQAyC9R448z6dhy8iqOJOXqhw2YSSXoFeyMwe080LcFL9YiooaDiSw1aatWrcK0adOQl5dn7FCIjKJMrUH0+SxsOXkFMXHZBhdsdfZzwOAwTwxs4w5HK4URoyQiujOpsQMg48vIyMDrr7+OgIAAmJubw9vbG4MGDUJ0dLSxQ7ujVatWwd7e/qG+Z2lpKaysrJCQkFAlFolEcs/H5cuXH2qst8b2sOuJTEOFRot9F7Pxrw2n0OnfuzD5x+PYcS4TKo0WLdxsMGtACA681Rc/v9INLzziyySWiBos9sg2cZcvX0b37t1hb2+PhQsXok2bNlCr1fjzzz8xefJkXLhw4YH2q1KpoFBU/fJTq9WQy03v35I7d+6Er68vmjdvbrB8xIgRGDBggP71U089hdatW+P999/XL3N2dq72+wghoNFoYGbGX02qW0IInEzNw5aTV/H7P+nIKSrXr/O0t8DgMA8MCfNAC7d739eciKghYY9sE/faa69BIpHg2LFjePrppxEcHIxWrVphxowZOHLkiL5cSkoKhgwZAmtra9ja2uLZZ59FZmamfv3cuXMRFhaGb775Bv7+/lAqdReASCQSfPHFFxg8eDCsrKzw4YcfAgC2bNmCDh06QKlUIiAgAPPmzUNFxc0J1PPy8vDyyy/D1dUVSqUSrVu3xu+//46YmBiMHz8e+fn5+h7PuXPnAgDKy8sxc+ZMeHp6wsrKCuHh4YiJiTE43lWrVsHHxweWlpYYNmwYcnNzq1VPW7ZsweDBg6sst7CwgJubm/6hUChgaWmpf71z506Eh4fDxsYGbm5ueP7555GVlaXfPiYmBhKJBH/88Qc6duwIc3NzHDhwAIWFhRg1ahSsrKzg7u6Ozz77DH369MG0adP0297reO9VT9S0XMouwqc74tBnUQyG/fcQVh26jJyicjhYyjH6ER/88kpX7J/VF28NaMEklohMDrt96osQgLrEOO8ttwSqMQXOtWvXsH37dnz44YewsrKqsv7Gv6W1Wq0+id27dy8qKiowefJkjBgxwiBRTEhIwK+//oqNGzdCJrs5+fncuXOxYMECLF68GGZmZti/fz/GjBmDpUuXomfPnrh06RJeeuklAEBUVBS0Wi0ef/xxFBYWYu3atQgMDMS5c+cgk8nQrVs3LF68GHPmzEFcXBwAwNraGgAwZcoUnDt3DuvWrYOHhwc2bdqEAQMG4PTp0wgKCsLRo0cxceJEzJ8/H0OHDsX27dsRFRV133rSarX4/fffsXnz5vuWvZ1arcYHH3yAkJAQZGVlYcaMGRg3bhy2bdtmUG727NlYtGgRAgIC4ODggBkzZuDgwYP47bff4Orqijlz5uD48eMICwvTb3Ov471XPVHjV6rSYOvpdKz/KwV/Xb6uX24hl6F/K1cMDfNEjyAnyGXsyyAi08ZEtr6oS4CPPIzz3v93FVBUTUxvl5CQACEEWrRocc9y0dHROH36NJKSkuDt7Q0AWLNmDVq1aoW//voLnTt3BqAbTrBmzZoq/0p//vnnMX78eP3rCRMmYPbs2Rg7diwAICAgAB988AFmzZqFqKgo7Nq1C8eOHcP58+cRHBysL3ODnZ0dJBIJ3Nzc9MtSUlKwcuVKpKSkwMNDV+8zZ87E9u3bsXLlSnz00UdYsmQJBgwYgFmzZgEAgoODcejQIWzfvv2ex3+jZzo8PPye5e5kwoQJ+ucBAQFYunQpOnfujKKiIoPE8v3330e/fv0AAIWFhVi9ejV+/PFHPPbYYwCAlStX6o+rusd7p3qixu3MlXz8dCwFv528qr9FrFQC9A52xtD2nugX6gpLBZt9Imo82KI1YeLWW/Lcw/nz5+Ht7a1PYgEgNDQU9vb2OH/+vD6R9fX1veN40E6dOhm8PnXqFA4ePKgfZgAAGo0GZWVlKCkpwcmTJ+Hl5aVPYqvj9OnT0Gg0VbYpLy9Hs2bN9McxbNgwg/Vdu3a9byK7ZcsWPPnkk5BKa957FRsbi7lz5+LUqVO4fv06tFrdFeEpKSkIDQ3Vl7u1jhITE6FWq9GlSxf9Mjs7O4SEhOhfV+d4qWnIL1Xjt5NXsO6vVJy9enO+V29HC4zs7IOnO3hxrlciarSYyNYXuaWuZ9RY710NQUFBkEgkD3xB1+3uNDzhTsuLioowb948PPXUU1XKKpVKWFhY1Pi9i4qKIJPJEBsbazCsAaj9v9R/++03LFiwoMbbFRcXIzIyEpGRkfjhhx/g7OyMlJQUREZGQqVSGZS9W93dTX0eLzV8Qgj8dfk61v2Vgm2n01Gm1v2BpJBJEdnaDSM7e6NrQDPeIpaIGj0msvVFIqnWv/eNydHREZGRkVi+fDneeOONKslUXl4e7O3t0bJlS6SmpiI1NVXfK3vu3Dnk5eUZ9CpWV4cOHRAXF1dlBoAb2rZti7S0NFy8ePGOvbIKhQIajcZgWfv27aHRaJCVlYWePXvecb8tW7bE0aNHDZbdekHbncTHxyM5OVn/b/+auHDhAnJzc7FgwQJ9vf3999/33S4gIAByuRx//fUXfHx8AAD5+fm4ePEievXqBaB6x3uneiLTll1Yjo3H07D+r1Qk5hTrlwe7WmNkZx8Ma+8JB06VRURNCBPZJm758uXo3r07unTpgvfffx9t27ZFRUUFdu7ciS+++ALnz59HREQE2rRpg1GjRmHx4sWoqKjAa6+9ht69e1cZNlAdc+bMwZNPPgkfHx8888wzkEqlOHXqFM6cOYN///vf6N27N3r16oWnn34an376KZo3b44LFy5AIpFgwIAB8PPzQ1FREaKjo9GuXTtYWloiODgYo0aNwpgxY/DJJ5+gffv2yM7ORnR0NNq2bYuBAwfijTfeQPfu3bFo0SIMGTIEf/75Z7WGFURERMDSsnq93Lfy8fGBQqHA559/jldeeQVnzpzBBx98cN/tbGxsMHbsWLz55ptwdHSEi4sLoqKiIJVK9fexr87x3qmeHuQ4yLg0WoH98dlY/1cqdp7LRIVWNyTIUiHDoLYeGNHFG+297fXnBhFRkyKo2vLz8wUAkZ+fX2VdaWmpOHfunCgtLTVCZLVz9epVMXnyZOHr6ysUCoXw9PQUgwcPFnv27NGXSU5OFoMHDxZWVlbCxsZGDB8+XGRkZOjXR0VFiXbt2lXZNwCxadOmKsu3b98uunXrJiwsLIStra3o0qWL+Oqrr/Trc3Nzxfjx40WzZs2EUqkUrVu3Fr///rt+/SuvvCKaNWsmAIioqCghhBAqlUrMmTNH+Pn5CblcLtzd3cWwYcPEP//8o9/u22+/FV5eXsLCwkIMGjRILFq0SNjZ2d21bnr06CG+/vrr+1dipd69e4upU6fqX//444/Cz89PmJubi65du4rffvtNABAnTpwQQgixZ88eAUBcv37dYD8FBQXi+eefF5aWlsLNzU18+umnokuXLmL27Nn6MtU53jvVU10z5XO/IUu9Viw+3REnun60S/i+9bv+MWTZAfHT0WRRWKY2dohERPXiXvnW7SRCVPOKH0JBQQHs7OyQn58PW1vD+RbLysqQlJRkMIcqmbacnBy4u7sjLS0Nrq6uRo2luLgYnp6e+OSTTzBx4kSjxnI7nvt1RwiBgwm5WHXoMqIvZOJG62xnIcew9p4Y0dkbLd051ysRNW73yrdux6EFRHdx7do1fPrpp0ZJYk+cOIELFy6gS5cuyM/P198pbMiQIQ89Fqp/xeUV2HjiClYfuoyErCL98q4BzTCyizciW7lBKZfdYw9ERE0TE1miuwgODq7RFGB1bdGiRYiLi4NCoUDHjh2xf/9+ODk5GS0eqnuXc4qx5nAyfo5NRWGZbt5XK4UMT3f0wpiufmjuwhkoiIjuhYksUQPUvn17xMbGGjsMqgdarcD+hBysOpiEmIvZ+uED/k5WGNPVF8909IKNUm7cIImITAQTWSKih6CwTI1fY9Ow5nCywdRZfUKcMa6bH3oFOXPeVyKiGmIiS0RUjxKzi7DmcDJ+iU1DUeVtY63NzTC8k274gL9Tw55vmoioIWMiW8c4CQQ1NTznq9JqBWIuZmHVoWTsu5itXx7obIWx3fzwVAcvWJuz+SUiqi22pHVELteNaSspKXmgW6wSmaobt9u9/Va5TVFBmRo//52G7w9fxuXcEgC6m/w9GuKCcd390KO5E29cQERUh5jI1hGZTAZ7e3tkZWUBACwtLfmFRY2eVqtFdnY2LC0tYWbWdJuT9PxSrDx4GT8eTdEPH7BRmmFEJ2+80NUXvs04fICIqD403W+eeuDm5gYA+mSWqCmQSqXw8fFpkn+4xWUU4qt9ifjt1BWoNbohFs1drDGumx+GtfeEFYcPEBHVqwbZyu7btw8LFy5EbGws0tPTsWnTJgwdOvSe28TExGDGjBk4e/YsvL298e6772LcuHEGZZYvX46FCxciIyMD7dq1w+eff44uXbrUWdwSiQTu7u5wcXGBWq2us/0SNWQKhQJSqdTYYTw0QggcTszFV/sSERN3c/xrF39HvNwrAH1DXDj7ABHRQ9IgE9ni4mK0a9cOEyZMwFNPPXXf8klJSRg4cCBeeeUV/PDDD4iOjsakSZPg7u6OyMhIAMD69esxY8YMrFixAuHh4Vi8eDEiIyMRFxcHFxeXOo1fJpNxvCBRI1Oh0WL72Qx8tS8R/6TlAwCkEmBAaze82DMA7X0cjBwhEVHTIxEN/JJjiURy3x7Zt956C1u3bsWZM2f0y0aOHIm8vDxs374dABAeHo7OnTtj2bJlAHRj+7y9vfH6669j9uzZ1YqlJvf+JaLGoURVgZ//TsM3BxKReq0UAGBuJsXwTl6Y1CMAfpw+i4ioTtUk32qQPbI1dfjwYURERBgsi4yMxLRp0wDorqqOjY3F22+/rV8vlUoRERGBw4cP33W/5eXlKC8v178uKCgAAJw8eRLW1jdvHeng4AB/f3+UlZXh3LlzVfbToUMHAEBcXByKi4sN1vn5+cHR0RHZ2dlITU29uWLHu7DJPoEgJzk0QuBUuhpA5b8rK3+0cTOHXCbBpVw18stv/D2iW+lpZwZXGzNcL9Ei6Zpad+l05XoLuQQt3ZQAgBNXynHzLxldmZauSlgopEi+pkZuieaWaCVwtTGDp70chWUaxGergFu2lsskaOOhBARw+moZ1Nob63Q/g5wUsFHKcCVPjcxCtcG6ZpZm8HUwQ6lai/OZt+xXCEgkQHtPJQCB85kqlKpujQnwdzSDg6UMmYUVuJKvMdivnVKKwGZyqDUCpzMM4wWAdu4KyKQSxOeoUViuNVjnbWcGZ2sZrpVocPl6hcE6K4UEIc4KAMDxK+W4XaiLAkq5FEnX1Lheeut+JXC3lcHd1gwFZVok5BgOQTE3k6CVmzkA4J/0clQYhoRgZwWszaVIy1Mjq0ij3ycAOFnJ4OMgR4lKiwtZKoPtpFIJwjx1n/m5jHKUVRjWQ0AzOewtZMgoqMDVAsNjtbeQIqCZAqoKgTMZ5fr3uyHMwxxSqQQXs1Uouq0OfRzM4GRlhpziCqTcVofW5lIEOyug1QqcvFq1Dlu7mUNhJkFirgp5pYb79bA1g5utGfJKK5CYa1iHSjMJQivr8OSVMmi1hsfawkUBS4UUKdfVyCm+9VwScLGWwctejqJyLS5klaOsQovyCi08BfC+FGjjJoeFXIbEXA3UewSu7QGuVW7d3EkBW6UU6QVqpBcYnqMOllL4O8pRptbiXGbVYUcdvHTxxmWpUKwy/L3xczCDo6UM2UUapOYb1qGNuVTXRmgFTqUbfuYA0MZNcbONKDOsQ09bWWUboUGS/rPRfbYWcglauurO7xNXynF7d0dLVwUs5FIkX1cjt9jwWG+2EVrE5xjGJJdJ0MZdd6yn01X6ccU3BDkpYGMhw5V8NTILDffbzNIMvo7yW9qImyFLIEF7L935fT6zHKVqw2P1d1Tc0kYY1r+dUoZAJ4WujUgvu70K0c5DqWsjslUoLDeMydteDmdrM10bca0ypspDslJIEOKiO9bjaWW4ve0Jda1sI3JVuF5iuF93WzO428pQUKa5dxtxtQwVt9XhzTaiAllFhueLk5X0ljbCcL9SiUCYh26/5zJVVdsIRzNdG1FYgau3nd/2SikCmsl1bURm1fMwzF1xs41QGe7Xx94MTlYy5BRrkJJ3rzai6n5buykq24gK5JUaxuRhZwY3WznySjVV2wi5FKGut7QR+q9P3fl/9zYCcLE207cRF7MNYzKTAm09lIBEgrMZ5Si/rQHXtRGyyjbC8FgdLGTwb6aobCPKbz9d0KHy/I7LKr+ljQAAAT9HeWUbUYHUvHu0EXdoZ9u4V+YROeVV2wh9HqHR5REAEPI4EP4yLCws0LJlSwDAiRMnqkzD2LJlS1hYWCA5ORm5ubkG61xdXeHp6YnCwkLEx8cbrJPL5WjTpk2VOO9J1BOtViu0Wm2t9wNAbNq06Z5lgoKCxEcffWSwbOvWrQKAKCkpEVeuXBEAxKFDhwzKvPnmm6JLly533W9UVJSA7nS652PUqFFCCCHi4+PvuP6GRx55pMq677//XgghxLJly6qs6x8oEyLKVuTPtrnjfrNmWgsRZSsGBZtVWfdJf3MhomzFhmcsqqxr7yYVIspWiChboZBV3e+ZV62EiLIVE9vLq6yb3V0hRJSt2DPWsso6TxuJfr+eNpIq6/eMtRQiylbM7q6osm5ie7kQUbbizKtWVdYpZNDvt72btMr6Dc9YCBFlKz7pb15l3aBgMyGibEXWTOs71mH+bBshomxF/0BZlXXLHlcKEWUrvh+mrLLuES+ZPqY77Tf+dd1nM6pN1TqM6q2rw+2jqtZhoMPNOnSyrFqHhybo6nD6I1Xr8LVOujqMfalqHdoobtZhqHPVOtwyUleHHz1atQ6fCdXVYer0O9dh2Tu6OuztW7UOvx6kq8OvB1Wtw96+ujose+fO53fqdF0dPhNa9fz+6FHd+b1lZNXzO9T55vlto6i639iXdOf3a52qfjbTH9F9NocmVP1snCxvfjaBDlU/m+2jdJ9NVO+qn82oNrrPJv71O9fhjf0+4lW1Dr8fpqvDZY9XrUO2EWwjbl/PNoJtxK2Pemsj2rfX5zYKRdXjOXPmjBBCiIkTJ1ZZN3v2bCGEEHv27KmyztPTUwghRH5+vu73Lz//nvmfEELU+dCCNWvWYOHChfosOzg4GG+++SZeeOGFB9pfdYYWBAcHY/z48QY9rtu2bcPAgQNRUlKC69evw9PTE4cOHULXrl31ZWbNmoW9e/fi6NGjd9zvnXpkvb29sXfv3vrvkS3Kho3SDEEBvtBoNDh15nzlCqH/2aZFEORyOS5dTkZ+QRFudpsIeLq7wNWpGa7n5SMpJc1gUwsLBVoGBQBC4MSZCxCi8q+wyu1bNveDhYUSyanpyL2ef3NDIeDq3Aye7i4oLCpGfNKNeHV/xcrNzNCmZXMAwOkLCVBXGP5lGOTvAxtrK1xJz0JmTq5BL3EzBzv4enmgtKwc5+OTDPYrkUrQvo3uL7/zF5NQWlZ2y7aAv48XHOztkJmdgyvpt8wYIZHAztYagX4+UKvVOH3e8C8/AGjXqgVkMhniEy+jsMjws/H2cIezkyOuXc/D5dQrBuusLC0Q0twfAHD8n9s+cyEQGhwIpdIcSclpuJ5fYLDa3dUZ7q5OKCgsQkJSisE6c4UCrVro6vCfsxdQUWHYGxAc6AdrK0ukXc1AVs413DwfACdHB/h4uaOkpBQXEpJubiQqe2RbtwAAnLt4CWVlhj0JAb6esLezRUZWDq5mZBuss7ezQYCvF1QqNc5cqFqHYa1DIJVKcfFSMoqKSwzW+Xi6wamZA3JyryPlSsatlQRrKysEB/pCq9Xi5Jm4Kvtt3aI5FAo5EpPTkJdfaLDOw80Zbi5OyMsvQGLyVYN1SqUCocGBAICTZy5U7ZFt7gdLSwukpKUj51qefnlSbhEOp6lwLk9AXV6G4mtZ8HW0xGMtXdHO2x7mcjO0DQ0BAJyNS0B5ucrgPGzu7wNbG2ukZ2YjPTPH4D0d7Gzh7+uFsrJynLt4qcqxdmgbCgCIS0hCcUmpwTo/bw84OtgjO+caUq9mGKyzsba62UacrVqHbVreaCNSdG3ELTzdXeDq7FTZRhie3xZKc7SsrMMTp8/f0ttS2UYEBVS2EVeRez0Pt3bZ6toIV10bkXjZYL9yuRnatAwGhMDp8/FQq29rIwJutBGZyMw27MVp5ljZRpSW3dJG6N5XIpGgfeX5fT4+EaVlhj1P/t6ecLC3RWZ2Lq5kGM4qY2djjUA/b6jVKpy+UPWzaRcaXNlGJKPwtvPb28MVzs0cce16Pi6n3XoeSirbCD8AwPF/zuN2+jYiJQ3X8wzPb3dXJ7i7OqOgqLhqG2GuQKuQIADAP+fiDNsIieQObcTNmJwc7eHj5VG1jUBlG9FGdx6ei0tAWfntbYRXZRuRXbWNsLVBgJ83VCoVzlxIqHKsYa1bVLYRl3VtxC3ni4+n+y1tRPotWwlYW1kiONCvso24UGW/rVsEQSE3Q2Jy6h3aCJdb2ohUg3VKc3OEhtzaRmhvbUrv2kYAAi5OjvDycEVRcQkuXko22K+ZmQxtW+o+m7Nxl1CuMqzD5n7eN9uIrDu0ET6eujYiPrFy6c32pUNb3XdgXMLlu7QRdsjOvYbUK5kG62ysLSvbCC1Onb2I27UJvdFGpCK/wLAOPd1dq7YRSjvA2rnee2RrMrSgThPZTz/9FO+99x6mTJmC7t27AwAOHDiA5cuX49///jemT59e431WJ5Ht1asXOnTogMWLF+uXrVy5EtOmTUN+fj5UKhUsLS3xyy+/GOxn7NixyMvLw5YtW6oVC8fIEjUuQgjsj8/Bsj0JOJZ080u/b4gzXuoViEcCHJvktGJERMZktDGyn3/+Ob744guMGTNGv2zw4MFo1aoV5s6d+0CJbHV07doV27ZtM1i2c+dOfe+rQqFAx44dER0drU9ktVotoqOjMWXKlHqJiYgaLq1WIPpCFpbtjsepyhkI5DIJhoR54qVeAQh2tTFyhEREVB11msimp6ejW7duVZZ369YN6enpd9jizoqKipCQcPPfE0lJSTh58iQcHR3h4+ODt99+G1euXMGaNWsAAK+88gqWLVuGWbNmYcKECdi9ezc2bNiArVu36vcxY8YMjB07Fp06dUKXLl2wePFiFBcXY/z48bU4YiIyJRqtwLbT6Vi+JwEXMnT/RlPKpXiuiw9e6hUAdzveXpqIyJTUaSLbvHlzbNiwAf/3f/9nsHz9+vUICgqq9n7+/vtv9O3bV/96xowZAHRDAVatWoX09HSkpNwcN+Tv74+tW7di+vTpWLJkCby8vPDNN9/o55AFgBEjRiA7Oxtz5sxBRkYGwsLCsH37dri6uj7o4RKRiVBrtNhy8ir+uycBiTm6sdDW5mZ4oasvJvbwh5O1uZEjJCKiB1GnY2R//fVXjBgxAhEREfoxsgcPHkR0dDQ2bNiAYcOG1dVbGQXHyBKZlvIKDX7+Ow0r9l5C2nXdBRJ2FnJM6O6Pcd38YGcpN3KERER0O6ONkX366adx9OhRfPbZZ9i8eTMA3ZVrx44dQ/v27evyrYiI7qpEVYGfjqXiq32XkFmgu4LdyVqBST0DMPoRX1ibN4optImImrwGf2evhoQ9skQNW2GZGmsOJ+O7A0nILdZNfeNup8TLvQIwsosPlHLeOpqIqKF7qD2yBQUF+je5ceeru2HyR0T14XqxCisPXcaqg0koKNPNTerjaIlX+wTiqQ6eMDdjAktE1BjVOpF1cHBAeno6XFxcYG9vf8c5F4UQkEgk0Gg0d9gDEdGDySosw7f7k7D2SDKKK29d3NzFGpP7BmJQWw+YyaRGjpCIiOpTrRPZ3bt3w9HREQCwZ8+eWgdERHQ/WYVl+HJvItYeSdbfzzzU3RavP9ocka3cIJXyJgZERE1BrRPZ3r1765/7+/vD29u7Sq+sEMLw9qtERA8gu7AcX+69hLVHk1Gm1iWw7X3s8fqjzdE3xIV34SIiamLq9NJdf39//TCDW127dg3+/v4cWkBEDyS7sBxf7buE748YJrDTI4LRM8iJCSwRURNVp4nsjbGwtysqKoJSqazLtyKiJiCnqBxf7UvEmsOX9QlsmLc9pvcLRi8msERETV6dJLI37rwlkUjw3nvvwdLSUr9Oo9Hg6NGjCAsLq4u3IqImIKeoHF/vS8Saw8koVev+kxPmbY9pEUHoHezMBJaIiADUUSJ74sQJALoe2dOnT0OhUOjXKRQKtGvXDjNnzqyLtyKiRiy3qBxf7U/EmkM3E9h2XnaY1i8YfZjAEhHRbeokkb0xW8H48eOxZMkSzhdLRDVyrVilH0JQUjmNVlsvO0yPCEafECawRER0Z3U6RnblypV1uTsiauSuFavw9f5ErD5kmMBOiwjiLARERHRfdX7D8b///hsbNmxASkoKVCqVwbqNGzfW9dsRkQm6fksCe+NGBq09bTE9IhiPtmACS0RE1VOniey6deswZswYREZGYseOHejfvz8uXryIzMxMDBs2rC7fiohMUH6JGl/vT8TKg0n6BLaVhy2mRQQjoiUTWCIiqpk6TWQ/+ugjfPbZZ5g8eTJsbGywZMkS+Pv74+WXX4a7u3tdvhURmZDCMjVWHryMr/cnorCsAoDuTlzTIoLQL9SVCSwRET2QOk1kL126hIEDBwLQzVZQXFwMiUSC6dOn49FHH8W8efPq8u2IqIErUVVgzeFkrNh7CXklagBAiKsNpvcLRmQrJrBERFQ7dZrIOjg4oLCwEADg6emJM2fOoE2bNsjLy0NJSUldvhURNWBlag1+OJqCL2ISkFOkGysf4GyFaRHBeLKNO6RSJrBERFR7dZrI9urVCzt37kSbNm0wfPhwTJ06Fbt378bOnTvx6KOP1uVbEVEDpKrQYv3fqVi+OwEZBWUAAB9HS0x9LAhDwjxgJpMaOUIiImpM6jSRXbZsGcrKdF9e77zzDuRyOQ4dOoSnn36aN0QgasTUGi02Hk/D0ugEXMkrBQB42Cnx+mNBeKajF+RMYImIqB7UaSLr6Oiofy6VSjF79myUlZVh+fLlaN++PTIyMury7YjIyDRagd9OXcGSXfG4nKsbPuRiY47JfZtjZBdvmJvJjBwhERE1ZnWSyJaXl2Pu3LnYuXMnFAoFZs2ahaFDh2LlypV49913IZPJMH369Lp4KyJqALRagT/OZOCzXReRkFUEAHC0UuC1PoEY/YgvlHImsEREVP/qJJGdM2cOvvzyS0RERODQoUMYPnw4xo8fjyNHjuCTTz7B8OHDIZPxi43I1AkhsPNcJj7deREXMnQXdtpZyPFSrwCM6+YHK/M6v8cKERHRXdXJt87PP/+MNWvWYPDgwThz5gzatm2LiooKnDp1itPrEDUCQgjsvZiNT3dexD9p+QAAG3MzTOjhj4k9/WGrlBs5QiIiaorqJJFNS0tDx44dAQCtW7eGubk5pk+fziSWqBE4dCkHn+y4iNjk6wAAC7kM47v74aVeAbC3VBg5OiIiasrqJJHVaDRQKG5+oZmZmcHa2roudk1ERhKbfA2f7LiIQ5dyAQDmZlK88IgvXukTCCdrcyNHR0REVEeJrBAC48aNg7m57sutrKwMr7zyCqysrAzKbdy4sS7ejojq0em0fHyyMw4xcdkAALlMgue6+GBy3+ZwtVUaOToiIqKb6iSRHTt2rMHr0aNH18VuieghOp9egM92XsSOc5kAAJlUguEdvTDl0ebwcrA0cnRERERV1Ukiu3LlyrrYDREZQUJWERbvuojf/0kHAEgkwLAwT7zxWBD8nKzuszUREZHxcK4coiYqObcYS6LjsfnEFWiFbtnAtu6YHhGE5i42xg2OiIioGpjIEjUxV/JKsWx3PH7+Ow0VlRlsREtXzOgXjFAPWyNHR0REVH1MZImaiKyCMizfk4CfjqVCpdECAHoFO2NGv2CEedsbNzgiIqIHwESWqJHLLSrHl/sSsfrQZZRX6BLYcH9HzIwMQWc/RyNHR0RE9OCYyBI1UteLVfhqvy6BLVFpAAAdfOzxr/4h6BbYjDcsISIik8dElqiRyStR4ev9iVh18DKKKxPY1p62+Fe/EPQJcWYCS0REjQYTWaJGIq9EhW/2J2HVocsoKq8AAIS622JaRBD6hboygSUiokaHiSyRicsvUePbA4lYefAyCisT2JaVCWx/JrBERNSIMZElMlH5pWp8dyAJ3x1MQmGZLoFt4WZTmcC6QSplAktERI2b1NgB3M3y5cvh5+cHpVKJ8PBwHDt27K5l1Wo13n//fQQGBkKpVKJdu3bYvn27QZm5c+dCIpEYPFq0aFHfh0FU5wrK1FiyKx49/7MbS6LjUVhWgRBXG/x3VAdse6MnBrR2ZxJLRERNQoPskV2/fj1mzJiBFStWIDw8HIsXL0ZkZCTi4uLg4uJSpfy7776LtWvX4uuvv0aLFi3w559/YtiwYTh06BDat2+vL9eqVSvs2rVL/9rMrEEePtEdFZapsergZXy9PxEFlT2wwa7WmPpYMB5vzR5YIiJqeiRCCGHsIG4XHh6Ozp07Y9myZQAArVYLb29vvP7665g9e3aV8h4eHnjnnXcwefJk/bKnn34aFhYWWLt2LQBdj+zmzZtx8uTJB46roKAAdnZ2yM/Ph60t74BED0dReQVWHUzC1/uTkF+qBgA0d7HG1MeCMLANe1+JiKhxqUm+1eC6JFUqFWJjY/H222/rl0mlUkRERODw4cN33Ka8vBxKpdJgmYWFBQ4cOGCwLD4+Hh4eHlAqlejatSvmz58PHx+fuj8IojpQVF6B1Yd0PbB5JboENtDZCm88FoQn23pAxgSWiIiauAaXyObk5ECj0cDV1dVguaurKy5cuHDHbSIjI/Hpp5+iV69eCAwMRHR0NDZu3AiNRqMvEx4ejlWrViEkJATp6emYN28eevbsiTNnzsDGxuaO+y0vL0d5ebn+dUFBQR0cIdG95ZeqsfZIMr7Zn4jrlQlsgLMVpjKBJSIiMtDgEtkHsWTJErz44oto0aIFJBIJAgMDMX78eHz33Xf6Mo8//rj+edu2bREeHg5fX19s2LABEydOvON+58+fj3nz5tV7/ESA7lay3x1MwppDyfpptPydrPDGY80xuJ0nE1giIqLbNLhE1snJCTKZDJmZmQbLMzMz4ebmdsdtnJ2dsXnzZpSVlSE3NxceHh6YPXs2AgIC7vo+9vb2CA4ORkJCwl3LvP3225gxY4b+dUFBAby9vWt4RET3lp5fiq/2JeKnYykoU2sB6C7ieq1PczzZ1h1msgY7uQgREZFRNbhEVqFQoGPHjoiOjsbQoUMB6C72io6OxpQpU+65rVKphKenJ9RqNX799Vc8++yzdy1bVFSES5cu4YUXXrhrGXNzc5ibmz/QcRDdz+WcYqzYewm/Hk+DWqO75rKtlx0m922Ofi1deREXERHRfTS4RBYAZsyYgbFjx6JTp07o0qULFi9ejOLiYowfPx4AMGbMGHh6emL+/PkAgKNHj+LKlSsICwvDlStXMHfuXGi1WsyaNUu/z5kzZ2LQoEHw9fXF1atXERUVBZlMhueee84ox0hNV1xGIZbvScDv/1yFtnLOkHB/R0x5tDl6NHfinbiIiIiqqUEmsiNGjEB2djbmzJmDjIwMhIWFYfv27foLwFJSUiCV3vx3a1lZGd59910kJibC2toaTzzxBL7//nvY29vry6SlpeG5555Dbm4unJ2d0aNHDxw5cgTOzs4P+/CoiTqZmoflexKw89zNYTN9Q5wxuW9zdPJzNGJkREREpqlBziPbUHEeWaopIQQOJ+biv3su4UBCDgBAIgGeaO2OV/sEorWnnZEjJCIialhMeh5ZosZACIE9cVlYtjsBx1PyAAAyqQRDwzzxap9ANHexNm6AREREjQATWaI6pNEK/HEmHcv3XML5dN28wwozKUZ08sZLvQLg7Whp5AiJiIgaDyayRHWgqLwCP/+dilWHLiM5twQAYKWQYfQjvpjY0x8uNsr77IGIiIhqioksUS2kXivBqkOXseGvVP1NDOws5Bjf3Q/juvnB3lJh5AiJiIgaLyayRDUkhMCxpGv47mASdp7L1E+hFeBshQnd/fFUB09YKvirRUREVN/4bUtUTeUVGvx+Kh3fHUzC2asF+uW9gp0xobsfegU58yYGREREDxETWaL7yCkqxw9HUvD9kWTkFJUDAJRyKZ7q4IXx3fwQ5Gpj5AiJiIiaJiayRHdx7moBVh5MwpZTV6Gq0AIA3GyVGNPNF8919oGDFce/EhERGRMTWaJbaLQCuy9k4bsDSTicmKtf3s7bHhN7+OPx1m6Qy6T32AMRERE9LExkiXDn6bNkUgkeb+2GCT380cHHwcgREhER0e2YyFKTJYTAX5ev45fYVGz9Jx3FKg0A3fRZz3XxwZiuvvCwtzBylERERHQ3TGSpyUm7XoKNx6/g1+Np+t5XgNNnERERmRp+W1OTUKKqwPYzGfglNg2HLt0c+2qlkOHJth54ppMXOvk6QCLh9FlERESmgoksNVp3GzoAAN0Cm+GZjl4Y0NqNva9EREQmit/g1OjcbeiAj6Mlnunohac6eMLLwdKIERIREVFdYCJLjcK9hg4MbOuOZzp6o7Mfhw4QERE1JkxkyWRptQJ/J1/Hr7Fp2Ho6HUXlFfp1HDpARETU+PEbnkzKtWIV9sdnY8+FLOyLz8G1YpV+3Y2hA8Pae8LbkUMHiIiIGjsmstSgabUCp6/kIyYuG3visnAqLQ9C3FxvY26GAa3d8ExHL3Txd+TQASIioiaEiWwDJYRosknZ9WIV9sVnY29cNvZezEbuLb2uANDCzQZ9QlzQJ8QZHX0deMtYIiKiJoqJbAP14dbz+OvyNTwS2AxdA5qhs58jrMwb58el1QqcuarrdY2Jy8LJ1Dxob+l1tTY3Q/fmzdA3xAW9Q5zhbse7bRERERET2QbrQEIOLmQU4lRaPr7cmwgzqQRtvezQNbAZugY4oaOvAywUMmOH+cDySlTYF5+DmLgs7LuYjZwiw17XEFcb9AlxRp8QF3T0dYDCjL2uREREZEgixK0jDuleCgoKYGdnh/z8fNja2tbre13NK8WRxFwcvpSLw4m5SLtearBeLpOgvbeDvse2vY89lPKGl9iWqTVIzC5GQnYREjILEZ9VhISsIlzKLjLodbVSyNC9uZN+yICHPXtdiYiImqKa5FtMZGvgYSayt0u9VoLDibk4UpnYpueXGaxXmEnR0cdB12Mb2AztvOwfai9mUXkFLmUV6RPVhKxCJGQVIeVaiUHCeqsgF2v0beGCPsHO6OTnyF5XIiIiYiJbX4yZyN5KCIHkXF1ie6PHNruw3KCMhVyGTn4OeCSgGR4JcISjlTlkEgkkEkAmlUAmrXwuufFc99OgTOXzWy86yytRIeGWhDU+S9fTevW2xPpWdhZyBLlYo/ktjxZutnCzU9ZbHREREZFpYiJbTxpKIns7IQQuZRfre2yPJOZWudK/NqSVia1EIoGqQnvXck7W5vqENcj1ZtLqbG3eZGdgICIiopqpSb7Fi70aAYlEok8aX3jEF1qtQHxWEQ5fysHhxFwcT8lDmUoDjRDQCgGtFvrn1fkzRisArUYA0BX2sFOiuavNzaS18qe9paJ+D5SIiIjoFkxkGyGpVIIQNxuEuNlgXHf/e5YVQkArAI22MskVQvdcC93z25JfOws5rBvpNGBERERkWpiRNHESiQSyyqEDRERERKaEl4kTERERkUliIktEREREJomJLBERERGZJI6RrYEbM5UVFBQYORIiIiKixulGnlWdGWKZyNZAYWEhAMDb29vIkRARERE1boWFhbCzs7tnGd4QoQa0Wi2uXr0KGxub+07wX1BQAG9vb6SmpjaomyeYEtZh7bEOa4f1V3usw9pjHdYe67D2HmYdCiFQWFgIDw8PSKX3HgXLHtkakEql8PLyqtE2tra2/KWpJdZh7bEOa4f1V3usw9pjHdYe67D2HlYd3q8n9gZe7EVEREREJomJLBERERGZJCay9cTc3BxRUVEwNzc3digmi3VYe6zD2mH91R7rsPZYh7XHOqy9hlqHvNiLiIiIiEwSe2SJiIiIyCQxkSUiIiIik8REloiIiIhMEhPZGli+fDn8/PygVCoRHh6OY8eO3bXs119/jZ49e8LBwQEODg6IiIioUn7cuHGQSCQGjwEDBtT3YRhNTepv1apVVepGqVQalBFCYM6cOXB3d4eFhQUiIiIQHx9f34dhVDWpwz59+lSpQ4lEgoEDB+rLNLVzcN++fRg0aBA8PDwgkUiwefPm+24TExODDh06wNzcHM2bN8eqVauqlKnJ52LKalp/GzduRL9+/eDs7AxbW1t07doVf/75p0GZuXPnVjkHW7RoUY9HYVw1rcOYmJg7/h5nZGQYlGsq5yBQ8zq8UzsnkUjQqlUrfZmmdB7Onz8fnTt3ho2NDVxcXDB06FDExcXdd7uff/4ZLVq0gFKpRJs2bbBt2zaD9cb6TmYiW03r16/HjBkzEBUVhePHj6Ndu3aIjIxEVlbWHcvHxMTgueeew549e3D48GF4e3ujf//+uHLlikG5AQMGID09Xf/46aefHsbhPHQ1rT9AN+nyrXWTnJxssP7jjz/G0qVLsWLFChw9ehRWVlaIjIxEWVlZfR+OUdS0Djdu3GhQf2fOnIFMJsPw4cMNyjWVcxAAiouL0a5dOyxfvrxa5ZOSkjBw4ED07dsXJ0+exLRp0zBp0iSDZOxBzm1TVdP627dvH/r164dt27YhNjYWffv2xaBBg3DixAmDcq1atTI4Bw8cOFAf4TcINa3DG+Li4gzqyMXFRb+uKZ2DQM3rcMmSJQZ1l5qaCkdHxyptYVM5D/fu3YvJkyfjyJEj2LlzJ9RqNfr374/i4uK7bnPo0CE899xzmDhxIk6cOIGhQ4di6NChOHPmjL6M0b6TBVVLly5dxOTJk/WvNRqN8PDwEPPnz6/W9hUVFcLGxkasXr1av2zs2LFiyJAhdR1qg1TT+lu5cqWws7O76/60Wq1wc3MTCxcu1C/Ly8sT5ubm4qeffqqzuBuS2p6Dn332mbCxsRFFRUX6ZU3pHLwdALFp06Z7lpk1a5Zo1aqVwbIRI0aIyMhI/evafi6mqjr1dyehoaFi3rx5+tdRUVGiXbt2dReYCalOHe7Zs0cAENevX79rmaZ6DgrxYOfhpk2bhEQiEZcvX9Yva8rnYVZWlgAg9u7de9cyzz77rBg4cKDBsvDwcPHyyy8LIYz7ncwe2WpQqVSIjY1FRESEfplUKkVERAQOHz5crX2UlJRArVbD0dHRYHlMTAxcXFwQEhKCV199Fbm5uXUae0PwoPVXVFQEX19feHt7Y8iQITh79qx+XVJSEjIyMgz2aWdnh/Dw8Gp/JqakLs7Bb7/9FiNHjoSVlZXB8qZwDj6ow4cPG9Q5AERGRurrvC4+l6ZEq9WisLCwSjsYHx8PDw8PBAQEYNSoUUhJSTFShA1XWFgY3N3d0a9fPxw8eFC/nOdgzX377beIiIiAr6+vwfKmeh7m5+cDQJXfy1vdry005ncyE9lqyMnJgUajgaurq8FyV1fXKuOU7uatt96Ch4eHwYc8YMAArFmzBtHR0fjPf/6DvXv34vHHH4dGo6nT+I3tQeovJCQE3333HbZs2YK1a9dCq9WiW7duSEtLAwD9drX5TExJbc/BY8eO4cyZM5g0aZLB8qZyDj6ojIyMO9Z5QUEBSktL66RtaEoWLVqEoqIiPPvss/pl4eHhWLVqFbZv344vvvgCSUlJ6NmzJwoLC40YacPh7u6OFStW4Ndff8Wvv/4Kb29v9OnTB8ePHwdQN99PTcnVq1fxxx9/VGkLm+p5qNVqMW3aNHTv3h2tW7e+a7m7tYU3zjFjfieb1eveCQCwYMECrFu3DjExMQYXLI0cOVL/vE2bNmjbti0CAwMRExODxx57zBihNhhdu3ZF165d9a+7deuGli1b4ssvv8QHH3xgxMhM07fffos2bdqgS5cuBst5DtLD8uOPP2LevHnYsmWLwfjOxx9/XP+8bdu2CA8Ph6+vLzZs2ICJEycaI9QGJSQkBCEhIfrX3bp1w6VLl/DZZ5/h+++/N2Jkpmn16tWwt7fH0KFDDZY31fNw8uTJOHPmjEmPB2aPbDU4OTlBJpMhMzPTYHlmZibc3Nzuue2iRYuwYMEC7NixA23btr1n2YCAADg5OSEhIaHWMTcktam/G+RyOdq3b6+vmxvb1WafpqQ2dVhcXIx169ZVqzFurOfgg3Jzc7tjndva2sLCwqJOzu2mYN26dZg0aRI2bNhQ5d+Tt7O3t0dwcDDPwXvo0qWLvn54DlafEALfffcdXnjhBSgUinuWbQrn4ZQpU/D7779jz5498PLyumfZu7WFN84xY34nM5GtBoVCgY4dOyI6Olq/TKvVIjo62qDX8HYff/wxPvjgA2zfvh2dOnW67/ukpaUhNzcX7u7udRJ3Q/Gg9XcrjUaD06dP6+vG398fbm5uBvssKCjA0aNHq71PU1KbOvz5559RXl6O0aNH3/d9Gus5+KC6du1qUOcAsHPnTn2d18W53dj99NNPGD9+PH766SeDqd/upqioCJcuXeI5eA8nT57U1w/Pwerbu3cvEhISqvVHfWM+D4UQmDJlCjZt2oTdu3fD39//vtvcry006ndyvV5K1oisW7dOmJubi1WrVolz586Jl156Sdjb24uMjAwhhBAvvPCCmD17tr78ggULhEKhEL/88otIT0/XPwoLC4UQQhQWFoqZM2eKw4cPi6SkJLFr1y7RoUMHERQUJMrKyoxyjPWppvU3b9488eeff4pLly6J2NhYMXLkSKFUKsXZs2f1ZRYsWCDs7e3Fli1bxD///COGDBki/P39RWlp6UM/voehpnV4Q48ePcSIESOqLG9q56AQumM+ceKEOHHihAAgPv30U3HixAmRnJwshBBi9uzZ4oUXXtCXT0xMFJaWluLNN98U58+fF8uXLxcymUxs375dX+Z+n0tjUtP6++GHH4SZmZlYvny5QTuYl5enL/Ovf/1LxMTEiKSkJHHw4EEREREhnJycRFZW1kM/voehpnX42Wefic2bN4v4+Hhx+vRpMXXqVCGVSsWuXbv0ZZrSOShEzevwhtGjR4vw8PA77rMpnYevvvqqsLOzEzExMQa/lyUlJfoyt3+fHDx4UJiZmYlFixaJ8+fPi6ioKCGXy8Xp06f1ZYz1ncxEtgY+//xz4ePjIxQKhejSpYs4cuSIfl3v3r3F2LFj9a99fX0FgCqPqKgoIYQQJSUlon///sLZ2VnI5XLh6+srXnzxxUbb8AhRs/qbNm2avqyrq6t44oknxPHjxw32p9VqxXvvvSdcXV2Fubm5eOyxx0RcXNzDOhyjqEkdCiHEhQsXBACxY8eOKvtqiufgjamMbn/cqLexY8eK3r17V9kmLCxMKBQKERAQIFauXFllv/f6XBqTmtZf796971leCN10Zu7u7kKhUAhPT08xYsQIkZCQ8HAP7CGqaR3+5z//EYGBgUKpVApHR0fRp08fsXv37ir7bSrnoBAP9nucl5cnLCwsxFdffXXHfTal8/BOdQfAoG270/fJhg0bRHBwsFAoFKJVq1Zi69atBuuN9Z0sqTwoIiIiIiKTwjGyRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSETVSvXv3hkQigUQigUKhQMuWLfHjjz8aOywiojrDRJaIqBESQuDEiRNYtGgR0tPTERcXhwEDBmDMmDFISkoydnhERHWCiSwRUSMUHx+PwsJCDBgwAG5ubvD398fEiROh0WgQFxdn7PCIiOoEE1kiokYoNjYWDg4OCA0NBQCkpaXhnXfegbm5Odq2bWvk6IiI6oaZsQMgIqK6d/z4ceTn58PGxgYajQZlZWWwsLDAihUr4OHhYezwiIjqhEQIIYwdBBER1a3HHnsMrVq1whtvvIG8vDzMnDkT3bt3x4cffmjs0IiI6gwTWSKiRsjBwQFffPEFRo4cCQA4d+4c2rZti4SEBPj5+Rk3OCKiOsIxskREjUxiYiLy8vLQunVr/bLQ0FAEBgZy+i0ialSYyBIRNTKxsbGQy+UIDg42WP7YY49h06ZNRoqKiKjuMZElImpkjh8/jqCgICgUCoPlERERiI2NRVpampEiIyKqWxwjS0REREQmiT2yRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZJCayRERERGSSmMgSERERkUliIktEREREJomJLBERERGZpP8HojogVxZruv4AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dfc_corr = dehnendf(beta=0.0, correct=True)\n", "\n", "# The corrected DF reproduces the target velocity dispersion much better\n", "print(\n", " \"sigma_R (corrected vs. uncorrected):\",\n", " numpy.sqrt(dfc_corr.sigmaR2(1.0)),\n", " numpy.sqrt(dfc.sigmaR2(1.0)),\n", ")\n", "print(\"meanvT (corrected vs. uncorrected):\", dfc_corr.meanvT(1.0), dfc.meanvT(1.0))\n", "\n", "# Compare surface mass profiles and ratios to target\n", "Rs = numpy.linspace(0.3, 2.0, 31)\n", "smass_uncorr = numpy.array([dfc.surfacemass(R) for R in Rs]) / dfc.surfacemass(1.0)\n", "smass_corr = numpy.array([dfc_corr.surfacemass(R) for R in Rs]) / dfc_corr.surfacemass(\n", " 1.0\n", ")\n", "target = numpy.exp(-(Rs - 1.0) / (1.0 / 3.0))\n", "\n", "fig, (ax1, ax2) = plt.subplots(\n", " 2, 1, sharex=True, figsize=(7, 7), gridspec_kw={\"height_ratios\": [3, 1]}\n", ")\n", "\n", "# Top panel: profiles\n", "ax1.semilogy(Rs, smass_uncorr, label=\"Uncorrected\")\n", "ax1.semilogy(Rs, smass_corr, label=\"Corrected\")\n", "ax1.semilogy(Rs, target, \"--\", label=\"Target exponential\")\n", "ax1.set_ylabel(r\"$\\Sigma(R) / \\Sigma(R_0)$\")\n", "ax1.set_title(\"Corrected vs. uncorrected surface mass density\")\n", "ax1.legend()\n", "\n", "# Bottom panel: ratio to target\n", "ax2.plot(Rs, smass_uncorr / target, label=\"Uncorrected / Target\")\n", "ax2.plot(Rs, smass_corr / target, label=\"Corrected / Target\")\n", "ax2.axhline(1.0, color=\"k\", ls=\"--\", lw=1)\n", "ax2.set_xlabel(r\"$R$\")\n", "ax2.set_ylabel(\"Ratio\")\n", "ax2.legend()\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "e07e9722", "metadata": { "papermill": { "duration": 0.005149, "end_time": "2026-05-16T13:43:17.957872+00:00", "exception": false, "start_time": "2026-05-16T13:43:17.952723+00:00", "status": "completed" }, "tags": [] }, "source": [ "galpy will automatically save any new corrections that you calculate." ] }, { "cell_type": "markdown", "id": "befc0d74", "metadata": { "papermill": { "duration": 0.005159, "end_time": "2026-05-16T13:43:17.968435+00:00", "exception": false, "start_time": "2026-05-16T13:43:17.963276+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Oort constants\n", "\n", "galpy can calculate the Oort constants (A, B, C, K) for 2D disk DFs by direct\n", "integration over the DF and its derivatives:" ] }, { "cell_type": "code", "execution_count": 12, "id": "78ed0c6d", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:17.980320Z", "iopub.status.busy": "2026-05-16T13:43:17.980061Z", "iopub.status.idle": "2026-05-16T13:43:33.198960Z", "shell.execute_reply": "2026-05-16T13:43:33.197994Z" }, "papermill": { "duration": 15.225874, "end_time": "2026-05-16T13:43:33.199632+00:00", "exception": false, "start_time": "2026-05-16T13:43:17.973758+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Oort A: 0.4319078088921877\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Oort B: -0.4852449609022851\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Oort C: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Oort K: 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "A + B (should be ~0 for cold DF w/ flat rotation curve): -0.053337152010097366\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Cold DF: A = 0.4991755666614268 , B = -0.4999282474249216\n" ] } ], "source": [ "print(\"Oort A:\", dfc.oortA(1.0))\n", "print(\"Oort B:\", dfc.oortB(1.0))\n", "print(\"Oort C:\", dfc.oortC(1.0)) # zero for axisymmetric DFs\n", "print(\"Oort K:\", dfc.oortK(1.0)) # zero for axisymmetric DFs\n", "# In the epicycle approximation for a flat rotation curve, A = -B = 0.5\n", "print(\n", " \"A + B (should be ~0 for cold DF w/ flat rotation curve):\",\n", " dfc.oortA(1.0) + dfc.oortB(1.0),\n", ")\n", "\n", "# For a cold DF, the epicycle approximation is better:\n", "dfccold = dehnendf(beta=0.0, profileParams=(1.0 / 3.0, 1.0, 0.02))\n", "print(\"Cold DF: A =\", dfccold.oortA(1.0), \", B =\", dfccold.oortB(1.0))" ] }, { "cell_type": "markdown", "id": "ecc53307", "metadata": { "papermill": { "duration": 0.005434, "end_time": "2026-05-16T13:43:33.210857+00:00", "exception": false, "start_time": "2026-05-16T13:43:33.205423+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Line-of-sight sampling\n", "\n", "galpy supports sampling along a given line of sight in the disk, useful for\n", "interpreting surveys with a finite number of pointings:" ] }, { "cell_type": "code", "execution_count": 13, "id": "aff773fd", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:33.223166Z", "iopub.status.busy": "2026-05-16T13:43:33.222914Z", "iopub.status.idle": "2026-05-16T13:43:33.655810Z", "shell.execute_reply": "2026-05-16T13:43:33.654808Z" }, "papermill": { "duration": 0.44013, "end_time": "2026-05-16T13:43:33.656539+00:00", "exception": false, "start_time": "2026-05-16T13:43:33.216409+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample distances along a line of sight at l=30 degrees\n", "ds = dfc.sampledSurfacemassLOS(30.0 / 180.0 * numpy.pi, n=10000)\n", "hists, bins, edges = plt.hist(ds, range=[0.0, 3.5], density=True, bins=101, alpha=0.5)\n", "# Compare to the predicted distribution\n", "xs = numpy.array([(bins[ii + 1] + bins[ii]) / 2.0 for ii in range(len(bins) - 1)])\n", "fd = numpy.array([dfc.surfacemassLOS(d, 30.0) for d in xs])\n", "plt.plot(xs, fd / numpy.sum(fd) / (xs[1] - xs[0]), \"r-\", lw=2)\n", "plt.xlabel(\"distance\")\n", "plt.ylabel(\"density\")\n", "plt.title(\"Distance distribution along l=30 deg\");" ] }, { "cell_type": "markdown", "id": "c20a8901", "metadata": { "papermill": { "duration": 0.005664, "end_time": "2026-05-16T13:43:33.668172+00:00", "exception": false, "start_time": "2026-05-16T13:43:33.662508+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Non-axisymmetric, time-dependent DFs: evolveddiskdf\n", "\n", "galpy supports evaluation of non-axisymmetric, time-dependent 2D DFs.\n", "These are constructed by assuming an initial axisymmetric steady state\n", "that is then acted upon by a non-axisymmetric perturbation. The DF at any\n", "time is evaluated by integrating orbits backwards to the initial time\n", "(using Liouville's theorem). This is implemented as `galpy.df.evolveddiskdf`." ] }, { "cell_type": "code", "execution_count": 14, "id": "a43df859", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:43:33.680400Z", "iopub.status.busy": "2026-05-16T13:43:33.680209Z", "iopub.status.idle": "2026-05-16T13:44:03.343721Z", "shell.execute_reply": "2026-05-16T13:44:03.342986Z" }, "papermill": { "duration": 29.670943, "end_time": "2026-05-16T13:44:03.344742+00:00", "exception": false, "start_time": "2026-05-16T13:43:33.673799+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean v_R (warm disk): -0.029476364282585484\n" ] } ], "source": [ "from galpy.potential import LogarithmicHaloPotential, EllipticalDiskPotential\n", "from galpy.df import evolveddiskdf\n", "\n", "# Set up an elliptical perturbation to a logarithmic potential\n", "lp = LogarithmicHaloPotential(normalize=1.0)\n", "ep = EllipticalDiskPotential(twophio=0.05, phib=0.0, p=0.0, tform=-150.0, tsteady=125.0)\n", "\n", "# Initial steady-state DF (warm disk)\n", "idfwarm = dehnendf(beta=0.0, profileParams=(1.0 / 3.0, 1.0, 0.15))\n", "\n", "# Set up the evolved DF\n", "edfwarm = evolveddiskdf(idfwarm, lp + ep, to=-150.0)\n", "\n", "# Mean radial velocity at R=0.9, phi=22.5 deg\n", "mvrwarm, gridwarm = edfwarm.meanvR(\n", " 0.9, phi=22.5, deg=True, t=0.0, grid=True, returnGrid=True, gridpoints=51\n", ")\n", "print(\"Mean v_R (warm disk):\", mvrwarm)" ] }, { "cell_type": "markdown", "id": "0873f9fc", "metadata": { "papermill": { "duration": 0.005607, "end_time": "2026-05-16T13:44:03.356280+00:00", "exception": false, "start_time": "2026-05-16T13:44:03.350673+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Example: The Hercules stream\n", "\n", "We can combine galpy's orbit integration capabilities with the\n", "disk distribution functions to see the effect of the Galactic bar\n", "on stellar velocities. By backward-integrating orbits starting at the\n", "Solar position in a potential that includes the bar, we can\n", "see what the velocity distribution should look like today if\n", "the Galactic bar stirred up a steady-state disk (see [Dehnen 2000](http://adsabs.harvard.edu/abs/2000AJ....119..800D) and [Bovy 2010](http://adsabs.harvard.edu/abs/2010ApJ...725.1676B))." ] }, { "cell_type": "code", "execution_count": 15, "id": "9c7d2b96", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:03.368605Z", "iopub.status.busy": "2026-05-16T13:44:03.368396Z", "iopub.status.idle": "2026-05-16T13:44:07.014842Z", "shell.execute_reply": "2026-05-16T13:44:07.014211Z" }, "papermill": { "duration": 3.654232, "end_time": "2026-05-16T13:44:07.016126+00:00", "exception": false, "start_time": "2026-05-16T13:44:03.361894+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import LogarithmicHaloPotential, DehnenBarPotential\n", "from galpy.df import dehnendf\n", "\n", "lp = LogarithmicHaloPotential(normalize=1.0)\n", "dp = DehnenBarPotential()\n", "\n", "# Integrate back to before bar formation\n", "ts = numpy.linspace(0, dp.tform(), 1000)\n", "\n", "# Grid in velocity space at the Solar position\n", "ins = Orbit(\n", " numpy.array(\n", " [\n", " [\n", " [1.0, -0.7 + 1.4 / 100 * jj, 1.0 - 0.6 + 1.2 / 100 * ii, 0.0]\n", " for jj in range(101)\n", " ]\n", " for ii in range(101)\n", " ]\n", " )\n", ")\n", "ins.integrate(ts, lp + dp)" ] }, { "cell_type": "markdown", "id": "5aef5fa5", "metadata": { "papermill": { "duration": 0.005604, "end_time": "2026-05-16T13:44:07.030418+00:00", "exception": false, "start_time": "2026-05-16T13:44:07.024814+00:00", "status": "completed" }, "tags": [] }, "source": [ "Evaluate the weight of each orbit using a Dehnen DF at the time of bar formation:" ] }, { "cell_type": "code", "execution_count": 16, "id": "bbc535b1", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:07.042917Z", "iopub.status.busy": "2026-05-16T13:44:07.042669Z", "iopub.status.idle": "2026-05-16T13:44:10.412600Z", "shell.execute_reply": "2026-05-16T13:44:10.411471Z" }, "papermill": { "duration": 3.377239, "end_time": "2026-05-16T13:44:10.413396+00:00", "exception": false, "start_time": "2026-05-16T13:44:07.036157+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "dfc = dehnendf(beta=0.0, correct=True)\n", "out = [[dfc(o(dp.tform())) for o in j] for j in ins]\n", "out = numpy.array(out)" ] }, { "cell_type": "markdown", "id": "fc441cbf", "metadata": { "papermill": { "duration": 0.005778, "end_time": "2026-05-16T13:44:10.425221+00:00", "exception": false, "start_time": "2026-05-16T13:44:10.419443+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plot the velocity distribution:" ] }, { "cell_type": "code", "execution_count": 17, "id": "25d32106", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:10.438210Z", "iopub.status.busy": "2026-05-16T13:44:10.437955Z", "iopub.status.idle": "2026-05-16T13:44:10.634516Z", "shell.execute_reply": "2026-05-16T13:44:10.633562Z" }, "papermill": { "duration": 0.2042, "end_time": "2026-05-16T13:44:10.635456+00:00", "exception": false, "start_time": "2026-05-16T13:44:10.431256+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.util.plot import dens2d\n", "\n", "dens2d(\n", " out,\n", " origin=\"lower\",\n", " cmap=\"gist_yarg\",\n", " contours=True,\n", " xrange=[-0.7, 0.7],\n", " yrange=[0.4, 1.6],\n", " xlabel=r\"$v_R$\",\n", " ylabel=r\"$v_T$\",\n", ");" ] }, { "cell_type": "markdown", "id": "f6dae84c", "metadata": { "papermill": { "duration": 0.006061, "end_time": "2026-05-16T13:44:10.648081+00:00", "exception": false, "start_time": "2026-05-16T13:44:10.642020+00:00", "status": "completed" }, "tags": [] }, "source": [ "This entire calculation is encapsulated in the `evolveddiskdf` module:" ] }, { "cell_type": "code", "execution_count": 18, "id": "dfec15aa", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:10.661593Z", "iopub.status.busy": "2026-05-16T13:44:10.661372Z", "iopub.status.idle": "2026-05-16T13:44:25.924873Z", "shell.execute_reply": "2026-05-16T13:44:25.923782Z" }, "papermill": { "duration": 15.271303, "end_time": "2026-05-16T13:44:25.925583+00:00", "exception": false, "start_time": "2026-05-16T13:44:10.654280+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import evolveddiskdf\n", "\n", "edf = evolveddiskdf(dfc, lp + dp, to=dp.tform())\n", "mvr, grid = edf.meanvR(1.0, grid=True, gridpoints=101, returnGrid=True)\n", "dens2d(\n", " grid.df.T,\n", " origin=\"lower\",\n", " cmap=\"gist_yarg\",\n", " contours=True,\n", " xrange=[grid.vRgrid[0], grid.vRgrid[-1]],\n", " yrange=[grid.vTgrid[0], grid.vTgrid[-1]],\n", " xlabel=r\"$v_R$\",\n", " ylabel=r\"$v_T$\",\n", ");" ] }, { "cell_type": "markdown", "id": "a0db39bc", "metadata": { "papermill": { "duration": 0.006074, "end_time": "2026-05-16T13:44:25.938314+00:00", "exception": false, "start_time": "2026-05-16T13:44:25.932240+00:00", "status": "completed" }, "tags": [] }, "source": [ "The Hercules stream is the feature at $(v_R, v_T) \\approx (-0.3, 0.8)$. Note that the $v_R$ axis here is defined as the negative of the convention in [Dehnen (2000)](http://adsabs.harvard.edu/abs/2000AJ....119..800D) and [Bovy (2010)](http://adsabs.harvard.edu/abs/2010ApJ...725.1676B)." ] } ], "metadata": { "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": "3.13.13" }, "papermill": { "default_parameters": {}, "duration": 127.246669, "end_time": "2026-05-16T13:44:26.562410+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/distribution_functions/disk_df_2d.ipynb", "output_path": "doc/source/tutorials/distribution_functions/disk_df_2d.ipynb", "parameters": {}, "start_time": "2026-05-16T13:42:19.315741+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }