{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.005048, "end_time": "2026-06-30T01:09:17.102744+00:00", "exception": false, "start_time": "2026-06-30T01:09:17.097696+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": "2026-06-30T01:09:17.111910Z", "iopub.status.busy": "2026-06-30T01:09:17.111652Z", "iopub.status.idle": "2026-06-30T01:09:18.202300Z", "shell.execute_reply": "2026-06-30T01:09:18.201456Z" }, "papermill": { "duration": 1.096372, "end_time": "2026-06-30T01:09:18.203409+00:00", "exception": false, "start_time": "2026-06-30T01:09:17.107037+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": 0.003876, "end_time": "2026-06-30T01:09:18.211855+00:00", "exception": false, "start_time": "2026-06-30T01:09:18.207979+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": 0.003323, "end_time": "2026-06-30T01:09:18.218616+00:00", "exception": false, "start_time": "2026-06-30T01:09:18.215293+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": "2026-06-30T01:09:18.229945Z", "iopub.status.busy": "2026-06-30T01:09:18.229472Z", "iopub.status.idle": "2026-06-30T01:09:19.854235Z", "shell.execute_reply": "2026-06-30T01:09:19.853356Z" }, "papermill": { "duration": 1.630016, "end_time": "2026-06-30T01:09:19.855107+00:00", "exception": false, "start_time": "2026-06-30T01:09:18.225091+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": 0.004314, "end_time": "2026-06-30T01:09:19.864528+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.860214+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": "2026-06-30T01:09:19.873108Z", "iopub.status.busy": "2026-06-30T01:09:19.872742Z", "iopub.status.idle": "2026-06-30T01:09:19.876469Z", "shell.execute_reply": "2026-06-30T01:09:19.875573Z" }, "papermill": { "duration": 0.008846, "end_time": "2026-06-30T01:09:19.877047+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.868201+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": 0.00338, "end_time": "2026-06-30T01:09:19.884062+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.880682+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": "2026-06-30T01:09:19.892442Z", "iopub.status.busy": "2026-06-30T01:09:19.892089Z", "iopub.status.idle": "2026-06-30T01:09:19.896536Z", "shell.execute_reply": "2026-06-30T01:09:19.895634Z" }, "papermill": { "duration": 0.009496, "end_time": "2026-06-30T01:09:19.897271+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.887775+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": 0.003284, "end_time": "2026-06-30T01:09:19.904273+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.900989+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": "2026-06-30T01:09:19.912291Z", "iopub.status.busy": "2026-06-30T01:09:19.911957Z", "iopub.status.idle": "2026-06-30T01:09:20.727815Z", "shell.execute_reply": "2026-06-30T01:09:20.726773Z" }, "papermill": { "duration": 0.820829, "end_time": "2026-06-30T01:09:20.728529+00:00", "exception": false, "start_time": "2026-06-30T01:09:19.907700+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Surface mass at R=1.0: 0.05096808049902209\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "sigma_R^2 at R=1.0: 0.037330437423096205\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " at R=1.0: 0.9171527697944727\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": 0.003657, "end_time": "2026-06-30T01:09:20.736839+00:00", "exception": false, "start_time": "2026-06-30T01:09:20.733182+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": "2026-06-30T01:09:20.745090Z", "iopub.status.busy": "2026-06-30T01:09:20.744895Z", "iopub.status.idle": "2026-06-30T01:09:26.121453Z", "shell.execute_reply": "2026-06-30T01:09:26.120494Z" }, "papermill": { "duration": 5.381748, "end_time": "2026-06-30T01:09:26.122216+00:00", "exception": false, "start_time": "2026-06-30T01:09:20.740468+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": 0.003687, "end_time": "2026-06-30T01:09:26.130709+00:00", "exception": false, "start_time": "2026-06-30T01:09:26.127022+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": "2026-06-30T01:09:26.139578Z", "iopub.status.busy": "2026-06-30T01:09:26.139381Z", "iopub.status.idle": "2026-06-30T01:09:47.812468Z", "shell.execute_reply": "2026-06-30T01:09:47.811487Z" }, "papermill": { "duration": 21.678611, "end_time": "2026-06-30T01:09:47.813104+00:00", "exception": false, "start_time": "2026-06-30T01:09:26.134493+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: 0.08284723020552731\n" ] }, { "data": { "image/png": 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mT5/O4sWLDdOV9zt/REQEnTt3pnPnzrRs2ZIzZ87QpEkT1q9fT1hYGAB79+6lc+fODB48mMaNGzNlyhRu3rxJSEiIWb+WElQJUUbl6hTnb6ZwNDqRo9EJHIlO5MLNOw+sY6MBF60drlo7nB1scdXaYW9rw+20LOJSMknJyCEzR0dsQjqxCen5tlHN25mmVSvQJNCTplU9qVvJHQc7uadFiL9TSpGenWuRczvZ2xZptDkuLu6ekaqGDRsyefJkMjIyWLNmDQcPHiQ0NBSAqVOnkpiYiK+vL3Xr1uXWrVsPHOkC/TYv27dvN6QlOHLkCDt27CAiIsIw1bhv3z5+++03Xn75ZQCaNGlCkyZNDG2MGjWKgIAADhw4QFhYGKGhofmev1u3bgwdOpRPPvnEcMzT05PXXnuNrVu3AvDaa68xdOhQfvjhBwDGjBlD9erVC/01Ky4JqoQoY47HJjJ/bxTrTl7nTmbOPa8HeTvTNNCTZkEVaOjvgZezgyGQcrS3eeAf24zsXOJSMom7k6n/mJLJzZRMYhPSOBaTyMW4VC7Hp3E5Po2lR68A4GBnQ4i/B82qetK5ri9h1byws5UgSzzc0rNzqf+f9RY59+n3euDsUPi3b61WaxjpyRMYGAiAo6Mj1atX5//+7/+YOnUqjRs3xsHBAV9f3yL1qXXr1kZJUWvWrIm9vb3R2q2aNWsSGxtrVG/z5s1s27aNmzdvkpubi729PWfOnDGMOP1TWloaW7duxcHBgbFjx6KUQilFZGQk4eHhgD7P1J49e5g6daqhnpubG7169SIuLq5I11VUElQJUQZkZOey6vg1ft4XxbGYRMNxZwdbGgd40izIk6aBFWha1RNv18ItMM2Po70tgV7OBHrlnxE6KS2b8NhEwqMTORqTwNHoRJLSszkclcDhqAS+3xlJBWd7utX3o1fDyrSp6Y3WruSbkAohzKegNVWbNm1ixowZDBgwgDt37jB48GA++OADPD09C32OvIzkeWxsbPI9lpdEFWDKlCnMnz+fZ599lkaNGqHValm5ciUpKSn3PU9CQgK5ubk0bNiQWrVqGY6HhYUxdOhQQD+VmJubi7e3t1FdHx8fCaqEsGYxt9NYsD+K3w7GkJCmz+LrYGtD75BKDGsVRLOqFbC1Kb1F5R7O9nSsXZGOtSsC+imOy/FpHI1OYO/FeDaduUFCWja/HYrlt0OxuGrt6FLXl54NK9GxdkVctPInRTwcnOxtOf1eD4ud25SqV6/Od999B8Dp06d5/PHHeeedd5g5c6bZbmpRSvH111+zYMEC+vfvD+iz1k+aNMmo3D/P7+Pjg4ODA9WrV79voOjr64tWqyUmJoaWLVsajkdFRZn4Ku4lfwGFKGU6nWLH+Th+3hvFloibhgXmVTwcGdYqiCEtAvEpwWiUKWk0Gqr7uFDdx4XHmgWQk6vjwOXbrDt5nfWnrnMjOZMVx66y4thVtHY2dKhdkcGhAXSp6ytThMKqaTSaIk3BlVW3b9/myJEjhjv56tevT926dYmPjwfAy8uLiIgIs53/76NSs2bNIi0tzej1f55fq9UyePBgPvroIwYOHIifnx8Ad+7cYefOnfTq1QuNRsOAAQOYPXs2/fv3x97ennPnzrFmzRo6depktmsBCaqEKFUXbt5h2p/HOXg5wXCsfS0fnm4VxCPlIBCxs7WhTbAPbYJ9eOfRBoTHJrL+5HXWnrxO9O00Np6+wcbTN6js4ciTLaryZFggfu6Olu62EA+1/BaqA3zxxRfY29vzf//3f7zyyiuEhIQQGxvL6dOn2bhxIwB9+/blk08+4bHHHsPLy4tXX33VJH3SaDS89tprjB49mhUrVhAXF0dUVBQVK1Y0Kpff+b/88ksef/xx6tevT8eOHcnIyODMmTO8/vrrhnozZsygQ4cONGnShPr167Nv3z4aNmxokr4/8LqUKuyN2KKkkpOT8fDwICkpCXd3d0t3R5Si7Fwd3+24xOebzpOVq8PZwZYhLQJ5ulUQwRVdLd29ElNKceZaCsvDr/Dbob+mMm1tNHSr58ewVlVpG+yDTSlOZQphShkZGURGRlK9enUcHcvPPwqHDx/m6NGj+b42fPhwwwbRJ0+e5MSJE1SoUIEOHToYLTqPjIzk4MGDJCcn07t3b6KiokhNTTWMbu3YsQOdTmc0CrR161bs7e1p166d4diGDRtwd3c3WjQfHh7OyZMn8fb2plOnTqxevZr69esb5bP65/mrVKkC6O8wPH36ND4+PrRs2ZIKFSoYXd+dO3dYv3499vb2tGjRgtjYWG7fvk2PHvlP2z7oe1zY928JqkqRBFUPp+Oxibz2xwnOXEsGoFOdirw/MAR/T6cCapZPGdm5rDt5nYX7o4xG5Kp5OzOsZRCDQgMkF5Yod8prUCUKzxRBlUz/CWEm6Vm5zNx0ju93XkKnoIKzPW8/2oD+TapYdUZzR3tbBjT1Z0BTfyKup7BwfxR/HrnC5fg03l9zho82RDAoNICxHYKp6p3/XYhCCFEeyUhVKZKRqofHnou3mPbnCaLi9Ysu+zWuwtuP1i9ROoTyLDUzhxXHrrJgXxSnrupH7GxtNPRrXIXxnYKp5edm4R4K8WAyUmX9ZKRKiDImOSObGWvOsPhADACV3B15f2BDHqnnZ+GeWZaL1o6hYVV5skUgByJv89W2i+w4F8fSo1dYevQKPRr48WLnWoQEeFi6q0IIUWwSVAlhIteS0nl23gHO3dBvJfN0q6q81rMubo72Fu5Z2aHRaGhZw5uWNbw5HpvI7K0XWXfqOutP3WD9qRt0qF2RCZ2CaVnDu+DGhBCijJGgSggTuHDzDsPn7udqUgZ+7lpmPdlUAoMCNArw5JtnQjl/I4Wvt11k+bGr7DgXx45zcbSoVoGXu9WmTbCPpbsphBCFVraT4ghRDhyNTmDwN3u4mpRBjYou/DGujQRURVDLz41PhzRh66udeKplVRxsbTh4OYGnvt/P8HkHOHU1ydJdFEKIQpGgSogS2BZxk6e+309CWjaNAzxYMrYNARXkjrbiqOrtzPSBIex8rTPDWwdhZ6Nhx7k4+szaxeRfjhJzO63gRoQQwoIkqBKimJYdvcKonw6Rnp1L+1o+LHqhFV6Sf6nE/Nwdea9/Qza90pFHG+uT/C0Lv0qXT7bxzopTxN/JtHAPhRAif+VuTdW1a9dYsGABN27cICQkhKeeegp7+wcvBE5KSuLnn3/m7NmzTJo0yWhn66K0W5xzC+s0d1ck/111GtCnS/h4cGMc7OR/FFOq5uPCF0ObMqZDDT5cd5ad52/x457L/H4ohtEdghnVvrps4CyEKFPKVZ6qc+fO0aZNG8LCwmjZsiULFy7E39+fTZs2YWub/67d3333He+88w6dO3dm0aJFbN269Z4NFQvTbnHO/U+Sp6r8U0rx4boIvtl+EYARbavxVp/6f22/osuFpFhIjYM7N/UfU2/Cnbi7z+8+0hMBBWhAo8n/o40tOHuBsw+4+ICz992PPn99dK0I7v76slZu1/lbfLjuLCeu6NdY+bg68Gr3OjzRPBBb2f5GmJk15Kk6ffo0kZGReHh4UK9ePby9y/baz5SUFNavX0+fPn1wcjL/DhQP3TY1AwcOJCEhga1bt6LRaIiNjSU4OJjvv/+e4cOH51vnxIkT1KhRg4SEBAIDA/MNqgrTbnHO/U8SVJVvObk6Xl96gt8OxQLwWrcajG2Qg+bacbh2TP+4fgKyU0u3Y7Za8KoBPjXBuyZ419J/9KmlD8qsiE6nWHPyGh+tjzAkVm1QxZ13+zWgeTXrulZRtpTnoGr37t2MHj2aW7duERoaSmpqKufPn6dr1658/fXXuLi4WLqL+Tp79iz16tUjJiaGgIAAs5/voUr+mZ2dzdq1a5k1a5Zhi4+AgAA6derE8uXL7xvYhISEAJCQkJDv64Vpt7jnFtZDKcX7i9Zjc3YT79tH0tP7Jt57z8POjHsL22rB1U8/muTqq//o4gsuFf/63MlLPyKlFKDy+QjkZkH6bUi9BWm39B///jwtXj8alpsJcWf0j39yqgA+taFyE/BvBv6h4BUMNuVzqtLGRkPfRlXo0aASP++N4rNN5zh1NZlB3+ylf5MqTOtVj0oe5esNTwhzOnr0KF27duXFF19k+vTphiUrOp2OxYsXk56ebgiqdDodhw4d4saNG9SqVYu6desatXXo0CGUUtSvX5/9+/eTnZ1Njx49WLt2LfXq1cPJyYnDhw/j5+dHaGgooA9G9u/fj52dHY0bN8bL695/flJSUjhw4AB2dnaEhYXh5OREVlYWGzZsAGDNmjV4eXlRuXJl2rZta84vV4mVm6AqOjqazMxMqlevbnS8Ro0a7N6926ztFvfcmZmZZGb+tag2OTm52P0UFhJ/EU4vJ27/b7x95wzkLaFLvPvRwQ0qN/7rUaWJfpSotKbjdLmQGA3xF/563Dqv73dyLKQnQMx+/SOP1gP8m0KVu0GWfyi4Vy6d/pqIva0Nz7erTv8mVfh4QwS/HIxhefhVNp6+wYTONRnZrjqO9tY/JSpEQd544w2Cg4P54IMPjJaq2NjYMGzYMMPncXFx9OrVi2vXrlG/fn0OHDhAnz59+Pnnnw31vvzyS44fP05qaiqBgYHUq1ePHj16MG7cOOrUqcPZs2cJCQmhb9++hIaGsmDBAiZOnEijRo2wtbXl6NGjfPnll0bn/fnnn5kwYQLBwcF4enpy48YNfv/9d6pWrcrq1asBWL58OU5OTjRv3lyCKlNJT08HwM3NeI8wd3d30tKKf6t1Ydot7rlnzJjBu+++W+y+CQtQCm6egTMr4PQKuHkKAF8gV2mI92qCb732+uCpchOoUN2yoz42tuBVXf+o1c34taxUuH0Jbp6Fq0fgyhG4Fg6ZSXBpm/6Rx60KVGsL1TtCjY7gWbUUL6L4vF21zHisEU+FBfHOylMcjkrgo/UR/Howhjf71KNbfT+r3rxaWJBSkG2hNB/2znfXXj5YdnY2mzdv5t///neBa3+nTp2KTqcjIiICV1dXLl68SNOmTfnhhx8YNWqUodzx48fZv3+/YSQqz4ULFzh69KhhJOrUqVOMHTuWzZs307JlSwA2b95Mv3796NSpE/7+/hw7dowRI0bw7bffMnLkSACioqKIi4vDzc2Nzz//nHr16vHtt9+WyvSfKZSboMrV1RWAxMREo+MJCQklWp9UmHaLe+5p06bxyiuvGD5PTk4mMDCw2H0VZhR/EcIXwunl+tGeu5SNHXty67MqpwUeTQYydXB7C3ayiBxcoFKI/tFosP5YbrY+aLxy+K9A6+ZpSLkKJ37XP0AfLNboqA+yqnfQT1mWYSEBHiwZ25oVx64yfc0Zom+nMfrnw7Sv5cM7/RoQXNHV0l0U1iY7DaZXscy5X7+q//0uQEJCAllZWQQFBRVY9pdffuHrr782vN8FBwfz1FNPsXjxYqOgqn379vcEVADDhw83mtqbP38+VatW5dq1ayxdupS85dv29vbs2bOHwYMH8/PPP1O3bl1DQAUQFBRUqP6WVeUmqKpatSqurq6cOXOGnj17Go6fOXOG+vXrm7Xd4p5bq9Wi1WqL3TdRCm6chp2fwKk/Qen0x2wdILgLd2r0ZvA2T84k2tEm2JufHguzbF9NwdYeKjfSPxihP5aVqg+yInfApe365wmRcDgSDv+oL+PXEGp0glrdIaiNvp0yRqPR0L+JP13r+TF72wW+3xHJzvO36DVzJ2M71mB855oyJSgeKnlrpeLj4x9Y7ubNm6SlpVGjRg2j4zVr1mTjxo1Gx6pUyT+Q/OfxyMhI7ty5w4IFC4yOd+3a1TDrExUVRZ06dQq+kHKk3ARVNjY2DB48mB9//JGxY8fi5OREeHg4e/bsYcqUKYZyixYt4vLly7z++usma7ew5xblyJXDsOMTiFj917GaXaHxUKjVnSw7V56fu58zibcJ8nZm9rBm2NuWz8XdBXJw0Y9GVe8AXd6EjGSI2gOR2/VB1s1TcOOk/rH3S3D00AdXdXrpv2aOHpa+AiMuWjv+3aMuTzQP5J0Vp9gaEcesLRdYfuwq/xvQkPa1Klq6i8Ia2DvrR4wsde5CcHFxoV69ehw4cOCB5SpUqICtre09szG3b9++J+3C/abT/3nczc2NgIAAlixZct/zenh4cOHChfu+Xh6Vq3eJDz74gOzsbEJDQ3nqqafo0qULzz33HI8++qihzJYtW1i0aJHh8/379/Piiy/y1ltvAfD555/z4osvsmbNmiK1W5gyohy4vBt+Hgjfd7kbUGmgfn8YswOe/gNCBqG0bry94hQHIm/jqrVjzvDmeDo/RJnSHd2hTk/oOQPG74F/XYBB86DJ0/rcWBlJ+mnCJc/D/wXD/AGw/ztIjLF0z40Eebsw77kWzB7WDD93LVHxaTwz9wAvLT7KzZR87toUoig0Gv0/JJZ4FGGd4Msvv8yyZcvYvn37Pa8lJCSQnp6Ovb09LVq0YOnSpYbXdDody5cvL/bC8B49enDgwAGOHTtmdDwpKcmwTrlbt27s3buXS5cuGZW5ffs28NfSm7/f8FXWlas8VaD/4q5fv96Q1bxVq1ZGr2/dupXr168zdOhQQJ/nYtOmTfe0ExYWRljYX9M5BbVb2DIPInmqLEQpuLAZdn4M0Xv1xzS20OgJaPcyVDQefv5pz2XeXnEKjQbmPduCznV9LdDpMkqXC7GH9AFpxFq4dc749UohUH8ANHxcv3i+jEjJyOaTDeeYv/cyOgVujnZM6VmXYWFV/0rcKsQDlOc8Va+88grffPMNI0aMoFWrVqSmpnLy5EnWrFnDvn378PX1Zffu3TzyyCM899xzhIWF8dtvv3H8+HGOHTtGxYr60d3nnnuOnJyce6b0qlWrxptvvmm09kqn0zFkyBC2bNnC5MmTqVq1KqdOneLPP/9kz549+Pr6otPp6N+/P0eOHGHSpEl4eHiwZMkSJk2aRN++fcnNzSUwMJAePXrQq1cv/P39zXr330OX/LO8k6DKAhKiYMWL+vVCoF8v1fRpaDsJKlS7p/iu87d49ocD5OoU03rVZUzH4NLtb3lz6wJErNEHWDH7/lqXBuDfXB9cNRhYZlI2nIhN4vWlJwxZ2ZsEevL+wIY0qFK2pjBF2VOegyqA8PBw/vjjD0NG9ZCQEIYNG2Z0V/uJEyf44YcfuH79OrVr12bs2LFUqlTJ8PpXX31Fbm4uL730klHb48eP5/HHH+eRRx4xOq6UYunSpWzYsIGMjAxCQkIYMWKE0YL23NxcFi9ezJYtW3BycmLQoEF07tzZqE9z587l2rVrNG3alKlTp5r6S2MgQVU5I0FVKVJKv8h6w5uQdQfsnKDFSGj94n3f4CNvpdL/y10kZ+TwWFN/PnmisdyOXxSpt/QB1sk/9EGsIcDSQLV2+gCrfn+LZ3nP1Sl+3nuZjzec405mDrY2Gka1q87krrVxcpCF7CJ/5T2oEgWToKqckaCqlCTFwoqJcHGL/vOqraH/V+B9/1Gn5IxsBn61m4txqTSt6sniF1rJnWIlkXJDn57i5BLjxKM2dhDcBRo/CXX6gL3l3pyuJ2Xw31WnWX3iGgDVvJ2Z8VgjWgeX7f3QhGVIUGX9JKgqZySoMjOlIHwRrJsKmclg5wiP/Adaji0ww/m4BYdZe/I6ldwdWfFiW3zd5Y+mySRGw8k/9QHW9RN/HXf0hJDB0HSYPpGqhUYFN52+wZvLTnI9Wb94fWhYVab1rou7Y9lLGyEsR4Iq6ydBVTkjQZUZJV+DVZPh3Dr95wEtYMDX+k2FC7Du5DXGLjiCnY2GP8e3oVGAp1m7+lCLOwcnfoPwxfptdPL4NtCvdWv0hEUSjSZnZPPB2rMs2h8NgJ+7lvcHhNC1vl+p90WUTRJUWT8JqsoZCarMQCn97f1r/g0ZifqF6J3fgDYTC7X/XlJ6Nt0+3c7NlEwmdA7m3z3qFlhHmIAuV79NTvhCOLNKvyk0gI091O4BTZ/R58CyLd1UevsuxTP1j+NcjtdvP9K3UWXe6dcAH1dJ4vuwk6DK+pkiqCo3yT+FuEdutn7t1LHF+s8rN4GB34BvvUI38cHaM9xMyaSGjwsTuxQ8qiVMxMYWaj6if6QnwIkl+gDr6lE4u0r/cPeH0Oeg2XBwq1Rgk6bQqoY36yZ34LNN55izM5JVx6+x68It3n60PgOa+MuNC0KIB5KRqlIkI1UmlJUKvz0LFzbqFz93nArtJhdp+5S9F+MZ+v0+AH4d3YqWNWSBssXdOAVHF8LxXyDt7tYaNnZQtw80H6nP+l5Kgc2J2CSm/HGcM9eSAehcpyIzHmtEJQ8ZpXgY5Y1iVKtWDScnJ0t3R5hBeno6ly9fLtFIVbnKqC4EAGm39Vm8L2zUp0oY+gt0/HeRAqqM7FxeX6pfNP1Uy6oSUJUVfg2g53R45Qw89j0EtgJdjv5Owvn94MsWsHe2fnTLzEICPFjxYlv+3aMODrY2bI2Io9tn21lyOBb5X/ThY2urX06QlZVl4Z4Ic0lL00/729sX/yYVGakqRTJSZQLJV+HnxyDujP7usWG/Q2DRNzr+v3Vnmb3tIr5uWja92lHu9CrLrp+EQ/Pg+K/6nGOgD6YbPg4tR0PlxmbvwvkbKfzr92Mci9UnDe1S15fpA0Nk1OohopQiOjqa7OxsqlSpgo2NjElYC6UUaWlp3Lx5E09PTypXvjeXoSxUL4MkqCqhWxf0+/YlRYNbZXhmaZHWT+U5fTWZR7/cRa5O8e0zofRoUDrrdUQJZabA8d/0AdaNk38dD2oLrcZBnd6FujmhuHJydXy/M5LPNp4jK1eHm6Md/+lbn0GhAbLW6iGRlZVFZGQkOp2u4MKi3PH09KRSpUr5/j5LUFUGSVBVAlePwoJBkHYLvIL1AVWFoCI3k5Or47Gv93A8NoleDSvx9dOhZuisMCulIOYAHPgOTi/TTw8CeFaFsDHQ7BlwNN+2M/8ctZK1Vg8XnU4nU4BWyN7e3jDFmx8JqsogCaqK6dJ2+OUp/dRP5cYw7A9wrVispubsvMT/Vp/BzdGOza90lCSf5V3yVTg4Rz96lbfOysEVmgyDlmMemEW/JGTUSoiHiwRVZZAEVcVwejn8MQpys/R3fg1ZCI7F+9pFx6fRfeZ2MrJ1fPBYCE+GVTVxZ4XFZKXpk4ru+xrizt49qNHnvGr9on7vQTMEO/mttZrxWAh+EqwLYVUkqCqDJKgqovBFsHyCfmPeeo/CY3OKvVecUorh8w6w8/wtWtXwYvELrWREwRopBZe2wr5v4Pz6v45XaQZtX4J6/Uy+7uqfo1YeTvb8d0BDHm1UWX7GhLASElSVQRJUFcHl3fpb6HU50OxZ6PtZid4M/zgcy6u/H0NrZ8O6yR2o7uNiws6KMunWBdj3lT44z9Hv60eF6tB6gn560MHZpKeLuJ7Cq7+Hc/KKPq9Vn5DK/HdAQ7xcHEx6HiFE6ZOgqgySoKqQEmPgu076RekNH4fH55Zo6ubWnUy6frqdxLRsXutZl3GdzLPORpRRd+Lg4Pf6he15666cvSFsNLR4AVxMl6MsO1fHV1sv8OWWC+ToFD6uDkwfGEJ3ucNUiHJNgqoySIKqQshKgx96wrVjUKkRPL++xCMKr/wWzp9HrlC/sjvLX2yLva3kl3koZaXqs7Xv/RISo/TH7Jz0Gzm3mVisu0nv50RsEq/+Hs65G/q8Wo818+ftRxvg4ST50IQojySoKoMkqCqAUvpF6SeX6EcSRm/T3yZfAudvpNB95g6UgmUT2tIk0NMkXRXlWG4OnFkOuz/XB+8AGlto9AS0exkq1jHJaTKyc/ls0zm+23EJpaCSuyP/N6gRHWoX785VIYTlyDY1ovzZM0sfUNnYwRPzSxxQAczcdB6loEcDPwmohJ6tnX5aefR2GL4CanQGlavfmPurlvDrM/q8aCXkaG/LtF71WDK2NdW8nbmenMHweQd4Y+kJUjNzTHAhQoiyRoIqUTZc2ASb3tE/7/mB/hb4Ejp9NZnVJ66h0cDL3WqXuD1hZTQaqNERhi+DF7ZA3b6AgjMr9Gv6fn4MovaU+DShQV6smdSe59pUA2Dh/mh6z9rJocu3S9y2EKJskaBKWF78RVjyvD51QtNnoMUokzT72aZzgP4urLqVZLpVPIB/KDy5EMbvg0ZD9NOBFzfDD71gXk84v0k/PV1Mzg52vNOvAQtHtaSKhyNR8Wk88e1ePlh7lsycXBNeiBDCkmRNVSmSNVX5yEiGOV3hVgQEhMFzq8BOW+Jmj8cm0u/L3dhoYMPLHanp62qCzoqHxu1I/Zqr8IX6xLMAVZpCx9egds8S3Y2anJHNuytO88eRWADqVnLj0yeaUL+K/E0QoqySNVWi7NPpYOkYfUDlVhmG/GySgArg0436UaoBTfwloBJF51UdHp0Jk47rM7LbO+vXWS1+Er7tAGdWFXvkyt3Rnk+eaMy3z4Ti7eLA2esp9P9qF19tvUBOrmzUK0R5JkGVsJztH0DEGrDV6refcTNNLp/DUQlsi4jD1kbDS4/UMkmb4iHlXhl6vA+TT+jvDHRwhevH4ddh8E17/TZKuuIFQj0aVGL9yx3oXt+P7FzFR+sjeOLbvUTeSjXxRQghSosEVcIyzqyE7R/qnz86EwJCTdb0pxsjAHi8mT/VJHO6MAUXH+j6jj64av8qOLjBjRPw23D4pi2c/LNYwZWPq5Zvnwnlk8GNcdPacSQ6kd6f7+TnvZeRlRlClD+ypqoUyZqqu9JuwxehkH4bWo2HnjNM1vS+S/E8+d0+7G01bHm1E4Fept2KRAhA/zO872vY/w1k6reloWJd6DgF6g8Em6L/v3olMZ0pS46x+0I8AO1r+fDRoMZU8pDNmYWwNFlTJcquLf/TB1QV60G390zWrFKKTzfo11I90TxQAiphPs5e0OUNmHwcOk0DRw+IO6u/i/WbtsWaFvT3dOLn51vyzqP10drZsPP8Lbp/tp3l4Vdk1EqIckKCKlG6robDoXn6530+BlvTbdux68ItDly+jYOdDS92qWmydoW4L6cK0Gmqflqw0+ug9YCbp/XTgt92gLOri7Sg3cZGw3Ntq7P6pfY0DvAgOSOHSb+E8+LioySkZpnxQoQQpiBBlSg9Oh2s+RegoOEgkyT4zKOU4pO7o1RPhVWlsoeTydoWokCOHtDpNZh8DDpM+WvN1S9PwXcd4dz6IgVXNX1d+WNcG17uWhs7Gw2rj1+j+8wdbD1704wXIYQoKQmqROk5tghiD+rvoOr+P5M2vS0ijvCYRBztbRjfOdikbQtRaE4V/poWbPcK2Lvo9xdc9ATMeaRISUTtbG2Y1LUWf45vQ01fV+JSMhnx40Gm/Snb3AhRVklQJUpHegJsfFv/vONr+lvVTUQpZchLNbx1NXzdZGGvsDBnL+j6tj64avMS2DnBlcOw8HGY1wMidxa6qUYBnqya2I6R7aoDsPhANL0+38lB2eZGiDJHgipROrZOh7Rb4FMHWo0zadMbTt/gxJUknB1sGdOhhknbFqJEXHyg+3/1wVWrCWDnCDH74ae+ML8/xB4qVDOO9ra81bc+i15oib+nE9G39dvczFhzhoxs2eZGiLJCgiphfteOw8E5+ue9PzLp4nSdTvHZ3VGqEW2r4e1qmozsQpiUqy/0nA4vHYXmI8HGHi5t008JLnoSrp8oVDNtgn1YO7k9g0IDUAq+3XGJ/l/u5tTVJPP2XwhRKBJUCfNSCtb8W79ZcoOBUKOjSZtfc/IaZ6+n4Ka144X2Mkolyjj3KtD3U5h4CJoMA40NnFsL37SD30fArfMFN+Foz8eDG/P98Ob4uDoQcSOF/l/u5sst52WbGyEsTIIqYV7HfoGYffoFu93fN2nTSim+2noRgJHtq+Pp7GDS9oUwmwrVYMBsGL8fGjymP3bqT/gqDJaNh4SoApvoVt+P9ZM70LNBJXJ0io83nGPQN3u5GHfHvH0XQtyXBFXCfDKSYON/9M87/hs8/E3a/JHoBM5cS0ZrZ8NzbaqZtG0hSkXF2jD4Bxi7C2r30o/ohi/U7ziwZgrceXAKBW9XLV8/3YzPhjTGzdGO8JhE+szayQ+7I9HpJGGoEKWt3AVVs2fPpk6dOnh6etK+fXsOHDhQ4jo+Pj44Ojre83j55ZcNZSZOnHjP66GhptuvziptnQGpN8G7ln6RronN36v/b75f4yoySiXKt0oh8NQvMGozVO8Iumw48C183hg2vwfpifetqtFoGNg0gPWTO9C+lg8Z2TreXXmap+fu50pieuldgxCifAVV8+fP55VXXuH999/n1KlTNGvWjG7dunHlypUS1bly5QqJiYmGx4oVK8jMzKRfv36GMtnZ2fTu3duo3N69e816veXajVNw4Dv9897/B3amDXpu3clkzYlrgD6NghBWIaA5PLsChi8H/1DIToOdn+iDq12fQVbafatW8XRi/vNh/Ld/AxztbdhzMZ6en+3gt0Mxss2NEKWkXAVVH374ISNHjmTQoEH4+/vz2Wef4eLiwuzZs0tUR6vVGo1ALViwgJo1a9KpUyejtmxsbIzKOTjI6Ei+lILV/wKVC/X6QXAXk5/i14MxZOcqGgd6EhLgYfL2hbCoGp30o1ZDFug3as5IhE3vwKwmcOB7yMl/yxqNRsMzrauxdlIHmlX1JCUzhylLjjPqp0PcTM4oxQsQ4uFUboKqhIQETp8+TefOnQ3HbGxs6Ny5M7t37zZZnaSkJJYsWcKoUaPQaDRGr23cuBEvLy+qV6/O8OHDiY2NNcGVWaETv0P0HrB3hh7TTd58rk6xaH80AM+0CjJ5+0KUCRoN1HsUxu2BAd+AZ1W4c0O/1dNXLeDYr/fdtLm6jwu/j23D1F51cbC1YfPZm3SfuYOVx66W8kUI8XApN0HVtWv6qR5fX1+j476+vly/ft1kdRYvXkx2djbPPfec0fGgoCDmzJnD2bNn+fPPP4mNjaV9+/akpKTct8+ZmZkkJycbPayeLhe2/Ff/vP2r4Blo8lNsOXuTK4npeDrb07eR6TKzC1Em2dhCk6Hw4iHo9RG4+ELCZVg6Gr5tf999BW1tNIztGMzKie1oUMWdxLRsJi4+yoRFR7gtmzMLYRblJqjKY2Njc8/nBa0XKEqduXPn0q9fP/z8/IyOT5s2jcGDB+Pr60vTpk1ZsmQJ165d45dffrnveWfMmIGHh4fhERho+gCjzIlYA4nR4OQFrU2/OB1g/t7LAAxpHoijva1ZziFEmWOnhZajYVI4dHkLtB5w46R+X8EfekH0vnyr1ankxrIJbZn0SC1s8zZn/mwHG0/fKN3+C/EQKDdBVV6QExcXZ3T85s2b9wRAxa1z/PhxDh06xAsvvFBgf7y8vKhatSrnzp27b5lp06aRlJRkeMTExBTYbrm3/1v9x9DnwN7J5M1H3kpl5/lbaDQwrKVM/YmHkIMLdPiXPrhq85J+65vovfo9BRc9qb9J5B/sbW14uVttlo1vSy1fV27dyeSF+Yd49bdjJKVnl/41CGGlyk1Q5e3tTa1atdi+fbvhmFKK7du307p1a5PUmTt3LlWrVqV79+4F9ic5OZnY2FgqVap03zJarRZ3d3ejh1W7fhIu7wSNLbQYZZZTLNynT6PQqXZFqno7m+UcQpQLzl76fQUnHoFmw//Kzv51W/hzjH6K8B9CAjxYObEdYzrUQKOBP47E0nPmDrafi7u3fSFEkZWboArg5ZdfZu7cuWzevJnU1FTeeecdbt26xZgxYwxlxo0bZ5Q/qjB1QL/+acGCBYwcOfKe6cLMzEyGDh3K8ePHyc7OJjIykmHDhuHk5MSwYcPMe9Hlyf5v9B/r9zN5ok+A9KxcfjukH+2TNApC3OXhD/2+0Gdnr98fUHD8F/ii+d0EosYBk6O9LdN61+P3Ma2p5u3MtaQMnp13gNeWHCc5Q0athCgJO0t3oCjGjRtHQkICQ4cOJT4+nnr16rFq1Spq1Phrz7fs7GwyMzOLVAdg2bJlJCUl8fzzz99zXq1Wy6BBgxg1ahTHjx/H3d2d9u3bs3fv3geOVD1UUuP1d/0BtBxnllOsPHaV5IwcAr2c6FC7olnOIUS5VbE2PDEfrhzWJwy9tE2fQDR8IbSZqF/jqHUzFG9ezYu1kzrwf+vP8sPuy/x6KIad5+P4cFAj2teS3y8hikOjymlWOJ1Od8+IEkBOTg46nS7fHFL3q5NXLzc3F61W+8DzKqXuSbVQWMnJyXh4eJCUlGR9U4E7Ptbf9Ve5CYzepr8d3ISUUjz65S5OXklmaq+6jO0YbNL2hbA6F7fqc1tdC9d/7uwDHadA6Ih7kvHuuxTPlCXHib6tTy46NKwqb/Sph6u2XP3fLYTZFPb9u1xN//3d/YIjOzu7+yblvF+dvHoFBVRAsQMqq5abDQfn6p+3GmfygAogPCaRk1eScbCz4YnmD8FdlEKUVHBneGErDPoBvGpA2i1YO0Wf4+r470Y5rlrV8Gbd5PY821p/88fiA9H0+GwHu87fslTvhSiXym1QJcqQMysg5ao+f06DgWY5xc93F6j3bVQZLxfJZC9EodjYQMPHYMIB6PPJXzmu/hwF33WA85sMOa6cHex4t39DFr3QkoAKTlxJTOfpuft5Y+kJ7mTmWPY6hCgnJKgSJZeXRqH58/pcOiZ2OzWLVcdlnz8his3WXn9H7qRw6PImaN3h+glY+Dj89Kh+HdZdbYJ9WD+5g2G3goX7ZdRKiMKSoEqUzJUjELMfbOz1QZUZ/HYohqwcHSH+HjSWff6EKD4HF+jwb3gpHFq/CLYO+jQo33eB34bDrQsAuGjt+O+Ahiwa1RJ/z79Grab+IXcICvEgElSJkslLo9DwMXDLPwlrSeTqFAvuTv090ypI1rQJYQou3tDjfZh4GBo/BWjg9HL4KgxWToYU/TZebWr6sOHlDgy/u9bql4MxdP90B1vP3rRc34UowySoEsWXcgNO/ql/3nLMg8sW0/ZzN4lNSMfDyZ5HG1cxyzmEeGh5VoWBX8O43VC7J6hcOPwDzGqqT8uQkYSL1o73+jfk19GtCPJ25npyBiN+PMgrv4WTmCZ7CArxdxJUieI7NA902RAQBv6hBZcvhp/36kepBocG4OQg+/wJYRZ+DeCpX2HEWv3vc3Ya7PwEPm8Me76E7Axa1vBm3aQOjGxXHY0G/jxyhW6f7WDDqfw3pxfiYSRBlSienEw4lJdGYaxZThEdn8a2u9tnPN1K9vkTwuyC2sDIDTBkIfjUgfQE2PAGfNkcwhfhZAdv9a3PkrFtCK7oQlxKJqN/PszExUe5nSqjVkJIUCWK59RSSI0DtypQr59ZTrFwfxRKQYfaFanm42KWcwgh/kGjgXp9Ydwe/fY3blUgKQaWjYNv2kHEOkKrerL6pfaM6xSMjUa/20HXT7ezPPwK5TSftBAmIUGVKDqlYN/X+uctRupv1zaxXJ3iz6NXAHi6ZVWTty+EKICtnX6j5peOQLf3wNEDbp6GxUPgh144XjvEaz3rsmxCW+pWcuN2ahaTfgnn+R8PciUx3dK9F8IiJKgSRRdzQL/1ha1Wv+WFGeyPjCcuJRMPJ3s61fE1yzmEEIVg7wRtJ8GkY9B2Mtg5QvRemNcdFg+lkcM1VrzYjle71cbB1oatEXF0/3Q78/deRqeTUSvxcJGgShTd/rujVI0G62/NNoOVx/TJPns1rISDnfyYCmFxThWg27sw8Yh+BEtjAxFr4Os2OKx6kYmhjqyZ1I7mQRVIzcrlP8tPMfjbvVy4mWLpngtRauTdShRNUiycXqF/3nKcWU6Rnatj3Ul9UNW3kaRREKJM8fDXr7Uavw/q9gWlg/CF8EUoNY9+wG/P1OG9/g1wcbDlcFQCvT/fxazN58nK0RXcthDlnARVomgOztXnsqnWHio1NMspdl+4RUJaNj6uDrSq4WWWcwghSqhiHXhyIYzcBEFtITcT9n6JzRdNGJ79OxsnNqdznYpk5er4dOM5+n25i/CYREv3WgizkqBKFJ5ScGyx/nnYaLOdJm/qr3dIZexs5UdUiDItsAU8txqGLQG/EMhMhi3/o8qPrZnX4BiznmiAl4sDZ6+nMHD2bt5efpIU2epGWCl5xxKFd+0YpFwDexeo1d0sp8jMyTUkE5SpPyHKCY0GanWDMTvgsTngGQSpN9Gs+Rf9dg5gR6/bPNakMkrBT3uj6PbpDtadlKShwvpIUCUK79x6/cfgzmDvaJZTbI+IIyUzh0rujjQPqmCWcwghzMTGRn8Dy4uHoNdH4FIREiJxXTWaTxMnsbJXBkFeTlxPzmDsgsO8MP8QVyX9grAiElSJwju3Tv+xdg+znWLl8bwF6pWxsZHNk4Uol+wcoOVoeCkcOr8BDm5w/TghW59nS8VP+F/zNOxsNGw8fYNun27nh92R5Er6BWEFJKgShZNyA64e0T8309RfWlYOm07fAKCvbJ4sRPmndYWOU2BSOLQaD7YO2Ebt4umTozha+0f6V0kiNSuXd1eeZuDs3Zy8kmTpHgtRIhJUicK5sFH/sUpTcKtkllNsOXuT9OxcAr2caBzgYZZzCCEswMUHes7Q57hq8jRobHC7vJ6Zt8ezucYv1HG8zfHYJPp/tZv/rTrNncwcS/dYiGKRoEoUjmHqr6fZTrHy2FUAHm1UBY1Gpv6EsDqegTDgK32Oq3qPokERfHUF62xe5odKS/DUJTJnVyRdP9nO2hPXZB9BUe5IUCUKlpMJF7fqn5tpPVVKRjZbI+IAuetPCKtXsQ4MWQCjtkD1jmh02XRO/JP9rq/yjutSUpNvM27hEZ774SBR8amW7q0QhSZBlShY1G7IugOulaBSY7OcYuPpG2Tl6Aiu6EK9ym5mOYcQoowJCIVnV8Azy6BKU+xy0ngu53cOuL7COPvV7D8XS/fPdjBr83kyc3It3VshCiRBlShYXiqF2t31t0ybgWHqr7FM/Qnx0AnuDC9shSfmg08dnHKSec12IXudX2WwWs8XG0/Tc+ZOdp2/ZemeCvFAElSJB1MKItbqn5tpPVVCahY77/6xlKk/IR5SGg3U7w/j98KAr8GjKhV0t/mf/Q9sdfw3jW+vZ/jcvUxcfJSbyRmW7q0Q+ZKgSjzYrXOQGAW2Wqje0SynWH/qOjk6Rb3K7tT0dTXLOYQQ5YSNLTR5CiYegt4fg4svAdxgpsNs1jpMJfPEcrp8so3vd1wiO1c2aRZliwRV4sHy7vqr3l6fc8YMVh7Pm/qrbJb2hRDlkJ0Wwl7Q57h65G1w9KCOTSzfOXzGAjWNHet+pdfMHTIlKMoUCarEgxnWU5ln6i8uJZO9F+MBfSoFIYQw4uAC7V+BSceh/b9Q9s40sbnEzw4f8H7Sa3w+7yfGLzzMFdnuRpQBElSJ+0u7DdH79M/NlEV97clr6BQ0DvQk0MvZLOcQQlgBJ0945C00k45Dq/EoWy0tbc7yu/Y9hpydzKRP5vLllvNkZMtdgsJyJKgS93dxC6hc8K0PFYLMcoq/En7K1J8QohBcK0LPGWheOgqhI1A2dnS0Pc4S2zeovXUMYz+Zz+YzNyzdS/GQkqBK3J+ZN1C+mpjOwcsJaDRy158Qoog8/OHRmWhePIRq/CQKG7rbHmZe+sukLnqWad/9wcW4O5bupXjISFAl8pebA+fv7vdnpvVUa05cA6BFkBeVPBzNcg4hhJXzqo5m4LdoJuwju94AbDSKfrZ7+d+VkYTPGsoXSzaQlJZt6V6Kh4QEVSJ/sQcgIxGcKkBAC7Oc4q+EnzL1J4QooYp1sB/yE4zZSWq1bthqFI/b7mDciSFs+b8nWLplDzmSgkGYmQRVIn95U3+1uuvzxphYVHwqx2KTsNFArxAJqoQQJlK5ES7PLYEXthBfuSN2Gh0D2UKf7X1Z9+FTHDp23NI9FFZMgiqRP0MqBfOsp1p1XD/11ybYBx9XrVnOIYR4iPmH4j1mBTkj1nPFqxUOmlz6Zq0l5M/ObPn0WWKjLlq6h8IKSVAl7nU7EuLOgsYWgh8xyyny1lP1lbv+hBBmZBfUCv+X1pPy5HIiXZui1eTQJXkZPvNacuDrMSTHxVi6i8KK2Fm6A0WVm5vLnj17uHHjBiEhIdSpU6fEdQ4cOMC5c+eMjnl6etK3b98Sn7tcOr9B/zGojT43jIndTM7g1NVkALrW9zN5+0II8U9udTvhVncbMUfWkbbuPepknSLsxi9kfPUHp6o+Qe3H3sTeU+5CFiVTroKqhIQEevTowfXr12nQoAG7du1izJgxfPzxxyWqM2/ePNauXUv79u0NxwIDA42CquKcu9wycyqFbefiAGgU4CFTf0KIUhXYrCeqSXfCty/Fftf/0SD3LA2iF5I583cu13ySoH6vo3GXEXRRPOUqqHrjjTdITk7m1KlTuLm5sWfPHtq1a0ePHj3o1q1bieq0aNGCBQsWmPTc5VJmClzepX9eyzxB1fYIfVDVqXZFs7QvhBAPorGxoUnnx8lpP4BN637H59CnNCGCahfmk/XpLyTVH0bFnq+BBFeiiMrNmiqlFIsXL2bkyJG4ubkB0KZNG8LCwli4cGGJ69y+fZs///yTzZs3c/v27RKfu9y6tA1ys6BCdfCpZfLmc3J17Dx/N6iq62vy9oUQorDs7Gzp2vdJgl/bxW/1vuSwqoMDWVQ8/QPZn4WQsvQVSL5m6W6KcqTcBFUxMTEkJibSsGFDo+MhISGcOHGixHVOnTrFjz/+yJQpUwgKCmLOnDklOjdAZmYmycnJRo8yzzD11xM0GpM3fzQmkeSMHCo429M4wNPk7QshRFG5OTnwxJBnqDx5G19X/ZSDutrYq2zcjs0l57NGZC6fDImyoF0UrNwEVUlJSQBUqFDB6LiXl5fhteLWeeqpp4iOjmbFihUcPnyY6dOnM27cOI4dO1bscwPMmDEDDw8PwyMwMLAwl2o5Ot3fsqibaT1VxE0A2teqiK2N6YM2IYQorioVnBn3/EicRm/kf94fcEBXBzuVhfboD+R+3oScZS/q744W4j7KTVDl5OQEwJ07xns5paSkGF4rbp0OHTqg1f61YHrixIl4enqybt26Yp8bYNq0aSQlJRkeMTFl/D+da+Fw5wY4uEJQW7OcYlveeqo6sp5KCFE2NQzw5I0Xx5I6dCVTXKazO7cBtioHu/Cf0X0Riu7PMXDrvKW7KcqgchNUBQYGYm9vT1RUlNHxqKgoatSoYbI6eVxcXLh161aJ2tFqtbi7uxs9yrS8hJ/BXcDOweTN/z2VQgdZpC6EKMM0Gg2d6/kx49Xx3Bj4G2McZrAttzE2Kheb47+gvmyBWvI83Dht6a6KMqTcBFVarZZHHnmE3377zXAsLi6OLVu20KdPH8Oxffv2sWrVqkLX0el0XL9+3ehcBw8eJDo6mpYtWxbp3OVeXn4qM22gLKkUhBDlja2NhseaBTBryhgu9fiJp20+YENuKBoUmpN/wNet4ZdhcOWIpbsqygCNUkpZuhOFdfz4cdq2bUvfvn1p3bo18+bNw97ent27d+PgoB9ZGTVqFPv27ePkyZOFqpOdnU3jxo3p2rUrDRo0IDo6mtmzZ9OpUyf++OMPbGxsCn3ugiQnJ+Ph4UFSUlLZG7XKzYbpVfR3/r0UDl7VTX6KCQuPsPrENV56pBavdKtt8vaFEMLcUjKy+X5nJDt3bmGk+pPeNgew0dx9G63RGdq/CtXameVGH2E5hX3/LjcjVQCNGjUiPDyc6tWrc+zYMZ577jm2b99uFNS0bt2aRx99tNB17O3tOXz4MA0bNiQ8PBylFIsWLWLp0qWGgKqw5y7X4i/oAyoHN/AMMnnzRqkUZD2VEKKccnO055Vutfnu3yM42PxTeud8xB+57clRNnBpK/zUF+Z2h4h1UH7GLISJlKuRqvKuTI9UnVgCf4yEwJYwcoPJmz94+TaDv9lLBWd7Dr3ZTe78E0JYhZjbaXy++Tz7jxzlBdtVDLHdhlaTrX/RryG0exnqDwDbcpVrW/yDVY5UCTO6oZ8uxa+BWZqXVApCCGsU6OXMx4Mb8+MrgzjY4A3aZX3ONzmPkqKc9H9X/xgJXzaHQz9AdoaluyvMTIIqoXfjlP6jmYKqrWdl6k8IYb2CK7ryxdCm/DzpUY7WmUzbzM/5OHswt5UrJETCqsnweSPY+SmkJ1q6u8JMJKgSeoagquGDyxXDzeQMTl9LRqORVApCCOtWt5I73z7TnAUv9uBkzdG0zZzFe9nPcFV56/MAbn4XPmsIG96E5KuW7q4wMQmqBKTdhuQr+ue+9UzevCGVgr+kUhBCPBwaBXjy44gwFozrzNlqT9Mh8zNeyRrLOV0AZKXAni9gZiNYPgHizlm6u8JEJKgScPNu8jrPquDoYfLmt9/Not6xjmygLIR4uIQGebHohVYsGtOemzUeo0fWB4zI+jcHdHVBlw1HF8BXYfpcVzEHLN1dUUJyO4Iw69SfpFIQQggIq+7FglEtORx1m5mbfHnifFOaac4xzn4V3WwOwdlV+kdAGLSZCHX7gI2tpbstikiCKmHWO/+OxiSSnJFDBWd7Ggd4mrx9IYQoT0KDvPh5ZEuORCcwa3NFXoioTbDmCmPsVvOY3W7sYg/Ab89AherQajw0HQYOLpbutigkmf4TZr3zb+tZfSqFDrUllYIQQuRpVrUCP44IY9mEtgTVacqU7NG0Tv+cL3IGkGrjpr9jcO2/4dP6sPk9SLlecKPC4iSoetjpcuHmGf1zvxCTN78tQqb+hBDifpoEejLvuRasfLEdzRvW5dPcJ2ie9jlvZT/HddvKkJEIOz+BmSGwbPxf/wSLMkmm/x52CZchOw3snEy+359RKoVaElQJIcT9hAR48PXToVy4eYdvtl9k8VEnFqZ2pZvNISY7r6dezhkIX6h/VO+onxqs1R1sZGykLJGg6mGXt57Kt57JF0X+PZWCt6RSEEKIAtX0deXjwY2Z3LUWc3ZGsviAHevvhNFMc47JLhton7MPTeR2iNwOXsHQciw0eQq0rpbuukCm/8R18y1Sl1QKQghRPAEVnHmnXwN2T+3C+E7BnHeoz/A7L9I+8zMW2PQn084Vbl/8a93V+jcgIcrS3X7oSVD1sDNTOoWcXB07JJWCEEKUiI+rlik967J7Whf+3aMOma4BvJk2hKZ3ZvE/9TzxjlUhMwn2fgmzmsCvT8Pl3aCUpbv+UJKg6mFnpnQKR6ITSZFUCkIIYRLujvZM6FyTXa915v8eb0QVXx/mZHaleeJ0RmZPIcKlOSgdnFkJP/aGb9rB4R8hK9XSXX+oSFD1MMtIhsS7w8UmDqq2RUgqBSGEMDWtnS1PtAhkw+QOzHuuOWHVfdic24Qe8a/QLfP/2OLSm1xbR/0/zCsnwaf19FODty9ZuusPBVmo/jDLS6XgVgWcvUzatKRSEEII87Gx0dClrh9d6vpxLCaR73ZeYu0JeD7+adwZwHiPfQyz2YBbeqx+anDvV/q7BcNGQ3AXuWvQTOSr+jAz09SfpFIQQojS0zjQk6+easb2f3fmuTbVyHXw4IOkrjRK+IAXNdO46NkaUHB+PSx8HL5sDntnQ3qCpbtudSSoepiZKZO6pFIQQojSF+ilv2Nw7+uP8GafegR4ubAqPYRHrk/kkaxP2eI5iFx7N/1dg+unwSd19QlFYw/JwnYTKVZQdfbsWT744ANat25NjRo1mDx5Mlu3biUnJ8fU/RPmZKY7/7Ybpv4klYIQQpQ2d0d7RrWvwbZ/debbZ0JpVcOLi7pKPH/9MUJSPudr1wkkudeBnAx9MtE5j8C3HeDQD5B5x9LdL9c0ShUcniql2LdvH8uWLWP58uVERUXRtWtX+vfvj5+fHytXrmTlypVkZWXRp08fBgwYQM+ePXF2di6Nayg3kpOT8fDwICkpCXd3d8t2RimYEQhZKTBuL/jVN1Gzimb/3UhCWjZ/jGtDaFAFk7QrhBCi+E5dTeLH3ZdZHn6VrFwdoOjscplXvXbT4PZmNLmZ+oIObtB4CDR/3iz5C8urwr5/FyqounXrFvXq1aNPnz7079+fHj163BMwKaXYv38/y5cvZ/ny5bz66quMHDmy5FdiRcpUUJUQBZ83Aht7eOMa2NqbpNnzN1Lo9tkOnOxtOfZ2dxzsZIZZCCHKilt3Mlm0P5pF+6O5npwBgJcmhamVj9I3ex3OKZf/KhwQBqHPQoOB4OBimQ6XESYNqpRS6HQ6bG2NtzFJTExEo9Hg4eFxT52cnBzs7OTmwr8rU0HV2TXwy1D9Jsrjdpms2YX7o3hj6UnaBHuz6IVWJmtXCCGE6WTn6th85gbz90ax52L83aOKxz0vMsF9B9VvbUOju7ukR+sOIYOg2XCo0tRifbakwr5/F2oYQaPR3BNQASxbtoxJkyblW0cCqjLOTIvUD0TeBiCsumlTNAghhDAde1sbejaszKIXWrHplQ4816Yablp7/kisSZfo5+mQ/QVr/UaT6VYVMpPh0Dz4rhN80x4OzoGMJEtfQpkkczMPKzOkU1BK/RVUVZOgSgghyoOavm68068B+15/hPcHNqRuJTdisj0YF9WJunHTec3lf0RW6omydYDrx2H1q/BxHVg6DqL2yp2Df1PioOrcuXNs27aNlJQUU/RHlBYzjFTFJqRzLSkDOxsNTavKAnUhhChPXLR2DGsZxNpJ7fl9bGsea+qPg50dv8bXoPPl4bTO+oplfi+S7lkLctLh2CL4oSd80Qx2fARJsZa+BIsr8Rzd7du3ef/99zly5Ah+fn6EhYXRokULHnnkEerWrWuKPgpTy0rT5ykBk6ZTyBulahTggZPDvdPFQgghyj6NRkOLal60qObF2482YOnRWBYfiCHiBkyOagO0pr/3FSa476bWrY1obl+CLf+DLe9DcGdoMgzq9gV7R0tfSqkrcVDVqlUrfvzxR5RSnD9/noMHD3Lw4EHS0tIkqCqr4s7qN9509gFX0+WSOnhZH1S1kPVUQghhFTyc7XmubXWebVONI9GJ/HIgmpXHr7I8PoDl8UPwtB3IqwFneFS3Bc+4g3Bxi/7h6AENB0HTYVClGWgejj1gSxRUaf72RdJoNNSuXZvatWszbNiwEndMmNHfp/5M+IOeN1LVUoIqIYSwKhqNhtCgCoQGVeCtR+uz/OgVFh2I4cy1ZN6KasxbNCbULZFXfQ8Rlrweu5QrcGiu/lGxLjQaAo2eAI8AS1+KWRUqpcLfbd++nYoVK1K/vj5Z5J07d3B1dTVL56xNmUmpsPY12P8NtH4RerxvkiZvpmQQ9v5mNBoI/093PJxMk/dKCCFE2aSU4tTVZH4/FMPyY1dJTMsGQIOO5ypF86zzboJubkaTk3G3hgaqtdMHWPX7g6OFUwsVgUlTKvzdlStXaNKkCaNGjeLKlSsSUJVHZlikfuiyfmPOupXcJaASQoiHgEajoaG/B+/2b8j+1x/hq6ea0alORTQaG364Xo1Ol4YRlvk1v1aeQqJvGKDg8k5Y8SJ8XAt+HwHn1kNutqUvxWSKHFQ99dRTHDp0iKtXr1KrVi1ef/11kpIkX0W5oZRZ0inI1J8QQjy8tHa29GlUmR9HhLFn6iNM6VmHGj4uxGVreS2yCU2iJ9PP7mu2+o8h07Omft/BU3/Coif0GzuvfQ1iDpb79AxFnv77u23btjFlyhQuXbrEm2++yfjx43FwcDBl/6xKmZj+S74Kn9YDjS28ftVkd2f0/nwnp68l89VTzejTqLJJ2hRCCFF+KaU4Ep3An0eusOr4NZLS80akFH29bzCmwkHqx2/ANj3+r0qeQdDwcX0G9zK096BJt6kpyO+//84bb7xBTk4Oc+bMoUuXLiVt0iqViaDq/EZYOEi/cHDCfpM0mZSeTZP3NqAUHHjjEXzdHr7baIUQQtxfZk4u2yLiWHb0CpvP3Ly7qTPYa3J4ofJlhjjup2rcNjTZqX9VqlgPQh7X30XoVd1CPdcz25qqv7tz5w4HDx4kPT2dfv36cePGDdasWVOSJoW5mWHq73DUbZSC6j4uElAJIYS4h9bOlh4NKvH106EcfKMrMx4LIay6F9nKjtlXa9Lx0jAap33JtxXf4FqlLvrs7XFn9PmvZjWB77vA3tmQdMXSl/JARU6psHHjRj799FNOnz5NTEwMSil8fX0JCQlh9OjRDBw40Bz9FKZihkXqByL1i9RlaxohhBAF8XC2Z2hYVYaGVSU2IY3l4VdZeewqZ6/DjJgGzKABFe2HManyWXqyG++4fWiuHIYrh2H9NAhsCfUH6O8g9PC39OUYKXJQlZCQQJUqVejRowchISGEhITg62u6BJLCzAxBlSkzqevnw2UTZSGEEEURUMGZCZ1rMqFzTc7dSGHVsausOHaVy/HwZnRT3qQpQdrnmFTpJF1yd+Nx6wiamP0Qs79MBlgmWVNVmvbs2cNXX33FjRs3CAkJYerUqfj5+ZWoTkJCAt999x179uzBzs6Odu3aMW7cOBwd/5rK+vjjj1m2bJlRuzVq1GD+/PmF7rvF11TlZML0KqDLgZdPmSQJW3pWLo3eXU92rmLnlM4EejmboKNCCCEeVnn5r1Ye049gXU3KMLwWrE1mQqVTdM7dg+etI2j4WwgTEAYNBurzYLl4m7RPhX3/LtRIlU6nIzc3F3v7wucfyszMRKvVFrp8YezYsYOuXbvyyiuv8MQTT/Dll1/Stm1bwsPD75svq6A6ubm5NG3alKFDhzJy5EjS0tJ49913WbZsGZs3b8bOTv8lunDhAvb29vz3v/81tO3i4mLS6zO7W+f0AZWjB7ibJqI/GpNAdq6isocjARWcTNKmEEKIh1de/quG/h681rMuR2MSWBF+lbUnr3MxxZ1XoloDranmkMQEv1M8ottLhfgjaGIPQOwBqNHJ5EFVYRUqqLp9+zY1a9akd+/eDBgwgF69euHm5mZUJjc3lz179rBs2TKWL1/O1KlTGTVqlEk7+8YbbzBgwAA++OADALp27UrlypX57rvveOWVV4pVx9bWlhMnThhdT926dWnatCkHDx6kdevWhuPe3t60a9fOpNdUqv4+9Wei7Wny8lO1qOZltG2REEIIUVI2NhpCg7wIDdJv7nwkOoE1J66z7uQ1LifBv2PaAG2oap/IeL/TtHWMwsujFpYa8ijU3X8+Pj5s2LCB6tWr89577+Hj40OvXr349ttvWbp0Kc8//zyVKlVi0KBBJCYm8umnn5p8/7+0tDT27NlDv379DMdcXFzo2rUrGzduLFGdfwaIHh4eAGRkZBgdP3ToEN27d2fw4MHMmjWL7OxylgXWDHf+5W2iLOuphBBCmJONjYbm1bz4z6P12T21C8smtGVMhxpU9XImOtuTqbFtaH9hKJdupVmsj4VeqB4WFkZYWBjvv/8+ly5dYvny5SxevJgbN27w6KOPsmzZMlq3bo2NTYmyNNxXTEwMOp0Of3/jaSt/f3+2bNlisjoAM2bMwM/Pj5YtWxqOOTk5MWTIEDp27MiVK1eYPn06S5YsYevWrdja2ubbTmZmJpmZmYbPk5OTC7xOszLxnX/ZuTqORCUCElQJIYQoPRqNhiaBnjQJ9GRqr7qcuprM2pPXOB6bREN/y+0pWOS7/0C/QPvll1/m5ZdfNnV/7itvVOjvi8dBH+xkZWWZrM7s2bP58ccfWb16Nc7Ofy26njFjhlE7HTt2pH79+ixZsoQhQ4bk29aMGTN49913C7iyUmTiO/9OXkkiPTuXCs721Kwoe0AKIYQofX9fg2Vp5hlWMgMvL/1ISHx8vNHx+Ph4w2slrTN37lxefvllFi9eTLdu3Yxe+2dgVrt2bYKCgggPD79vn6dNm0ZSUpLhERMTc9+yZncnDu7cADT6bOom8Pf1VDY2sp5KCCHEw63cBFVVqlTBz8+Pw4cPGx0/cOAATZs2LXGdH374gfHjx7NgwQIef/zxAvuTm5tLfHy80WjWP2m1Wtzd3Y0eFnPz7iiVV3XQmmZUKS+okqk/IYQQohwFVQAjRoxgzpw5XLt2DYBly5Zx8uRJRowYYSjz4YcfMnz48CLVmT9/PmPHjmXBggUMHjz4nvNmZWXxySefGKYTc3Nzef3110lNTS1UAFYmXDftInWdTskidSGEEOJvirWmylLefvttIiIiqFmzJkFBQVy+fJnPP//caEH5+fPnOXLkSKHrJCYmMmLECDw9Pfn888/5/PPPDXWnTp1K3759sbe359atW1SpUoWAgACuXr2Ks7MzS5cupX79+qX3BSgJE6+niriRQnJGDi4OttSvbMEROCGEEKKMKFFG9aVLl5KQkMDzzz9vyj4VKDo6mhs3blC7dm1D+oM8Fy5cICUl5Z7pvfvVycnJYd++ffmep1atWkaZ1zMyMoiIiKBChQoEBAQU+U5Hi2ZU/6Y9XD8OQxZAvUdL3Nz8vZf5z/JTtK/lw88jWxZcQQghhCinTJpR/X4uXrzI9evXS9JEsVStWpWqVavm+1rNmjWLVCdvW5rCcHR0pHHjxoXvaFmScvf75Blkkub2311P1VKm/oQQQgignK2pEsWkFGQk6p87eZqgOcXBv935J4QQQggJqh4O2emQezcvl6NniZuLik/jZkomDrY2NA4seXtCCCGENZCg6mGQN0qlsQGt2wOLFkZeKoXGgR442uefTV4IIYR42EhQ9TDISNJ/dPQwyUbKBySVghBCCHEPCaoeBumJ+o8mmPqDvyf99DZJe0IIIYQ1kKDqYWDCRerXkzKIvp2GjQaaVS15e0IIIYS1kKDqYWDCkaq8qb8GVTxwc7QvcXtCCCGEtShRnqqJEydSgtyhorT8fU1VCR2I1G9OLakUhBBCCGMlCqq0Wq2p+iHMyYTTf4cuJwAQVr1CidsSQgghrIlM/z0MTDT9l5aVw7kbKQA0rSpBlRBCCPF3ElQ9DEw0UnX6ajI6BX7uWvzcHUvcLSGEEMKamCSounTpEqdOnTJFU8IcTDRSdTxWvzYrxL9k7QghhBDWyCRB1Y4dO/joo48Mnx86dIi1a9eaomlhCiZaqH7iir6dRgElX/AuhBBCWBuTBFXu7u6kpaUZPj958iS//vqrKZoWpmCi6b9jsfp2JKgSQggh7mWSoKpFixbs3buX5ORkAFJSUnB2djZF08IUTDD9l5KRzaW4VABC/CWoEkIIIf7JJEFVYGAgEydOpG3btrz//vvMmjWL9u3bm6JpYQomGKk6eUUfMPt7OuHtKqk0hBBCiH8qclCVNxr1T1OmTGHu3LloNBqmT5/O0KFDS9w5YQI5WZB9d2q2BCNVx+9O/TUOlFEqIYQQIj9FTv753XffsX79ej788EOaNWtm9FpYWBhhYWEm65wwgbxF6lCiherHr8idf0IIIcSDFHmk6plnniE4OJhWrVoxbNgwIiMjzdEvYSp5U39ad7CxLXYzJ2Llzj8hhBDiQYocVPn5+fHNN99w4sQJMjIyqFevHi+//DLx8fHm6J8oKRMsUk9MyyL6tn4KsaEsUhdCCCHyVeyF6nXq1OGPP/5g+/btHDlyhODgYGbMmEF6erop+ydKygQ5qvKSflb3ccHDyd4UvRJCCCGsTok2VAZo2bIl27dv55tvvuHVV18lMTGRDz/80BR9E6Zggjv/ThjWU8kolRBCCHE/RQ6qbt26xf79+zl9+rThcebMGVJSUnB0dMTb29sc/RTFlZ6g/1iikapEQNZTCSGEEA9S5KDqxx9/ZMqUKdSoUYOQkBB69OjBv/71L0JCQqhVqxa2tsVfDC3MwAQjVX/t+SdBlRBCCHE/RQ6qRowYwbhx43BxcTFHf4SpGdZUeRar+s2UDK4lZaDRyCJ1IYQQ4kGKHFTJ9F45U8K7/07eXU9Vs6IrLtoSL8ETQgghrJZJtqkRZVgJp/8MU3+ynkoIIYR4IAmqrF0JR6rygqrGAcWrL4QQQjwsJKiydiUYqVJKyUiVEEIIUUgSVFm7EiT/vJ6cwa07mdjaaKhf2d3EHRNCCCGsiwRV1i69+Hf/HYvR163t54ajvaTKEEIIIR5EgiprpsuFzLtBVTGm/05cSQSgsUz9CSGEEAWSoMqa5U39QbGm/2Q9lRBCCFF4ElRZs7ygys4J7LRFqqqUMuz518jf08QdE0IIIayPBFXWrAR3/sXcTicxLRsHWxvqVHIzabeEEEIIa1Qug6qUlBQuX75Mdna2SeuYqkyZUYIcVcfvrqeqV9kNB7ty+WMihBBClKpy9W6Zk5PDmDFj8PHxISwsDD8/PxYuXFjiOqYqU+aUYKTqhKynEkIIIYqkXAVVH3zwAUuXLuXEiRPcvHmTjz/+mGeffZbjx4+XqI6pypQ5JchRdSw2EZD1VEIIIURhlaug6ttvv2XUqFHUrl0bgOeff56aNWvy/fffl6iOqcqUOcWc/tPpFCevJAPQKFBGqoQQQojCKDdB1fXr14mNjaVVq1ZGx1u3bs3hw4eLXcdUZcqkYk7/RcanciczB0d7G2pWdDV5t4QQQghrVG6Cqvj4eAB8fHyMjvv4+HDr1q1i1zFVmfxkZmaSnJxs9ChVxRypyltP1aCKB3a25eZHRAghhLCocvOOaWur3yYlKyvL6HhmZiZ2dnbFrmOqMvmZMWMGHh4ehkdgYOD9L9AcirmmKm89VYi/TP0JIYQQhVVugip/f380Gg3Xrl0zOn79+nUCAgKKXcdUZfIzbdo0kpKSDI+YmJjCXaypFHP6L2+kqrGspxJCCCEKrdwEVW5uboSGhrJu3TrDsaysLDZt2kSnTp0Mx65fv05kZGSh65iqTH60Wi3u7u5Gj1JVjOm/nFwdp67qpylD5M4/IYQQotDuP3dVBr377rv069ePRo0a0bp1az799FMcHR0ZO3asocybb77Jvn37OHnyZKHrmKpMmVOMkaoLcXdIz87FVWtHDR8Xs3RLCCGEsEblZqQKoHfv3ixbtoz169czbtw4HB0d2bVrF15eXoYylStXpkaNGkWqY6oyZU4x1lTlbaLc0N8dGxuNOXolhBBCWCWNUkpZuhMPi+TkZDw8PEhKSjL/VKBS8J43qFx4+TR4+Beq2lvLTvLzvihGd6jB673rmbePQgghRDlQ2PfvcjVSJYog644+oIIiTf8dv3J3exq5808IIYQoEgmqrFXeInUbe7B3LlSVrBwdZ+4uUm8ke/4JIYQQRSJBlbX6+yJ1TeHWRp27kUJWrg4PJ3uqehUuEBNCCCGEngRV1qoEi9QbBXigKWQgJoQQQgg9CaqsVTFyVB2XTOpCCCFEsUlQZa2KkaPq7yNVQgghhCgaCaqsVRFHqrJzdVy4eQfQb6QshBBCiKKRoMpaFXFNVVR8Klm5OpwdbPH3dDJjx4QQQgjrJEGVtSri9N/Z6ykA1PZzk0zqQgghRDFIUGWtijj9F3E3qKpbyc08/RFCCCGsnARV1qqII1URfxupEkIIIUTRSVBlrYq4pirihoxUCSGEECUhQZW1KsL0X1pWDtG30wCoI0GVEEIIUSwSVFmrIkz/nb9xB6XAx9UBb1etWbslhBBCWCsJqqxVEUaq8tZTySiVEEIIUXwSVFmj7AzIzdQ/L8Saqrz1VLJIXQghhCg+CaqsUd7UHxrQuhdYXNIpCCGEECUnQZU1Mkz9eYBNwd/is4bpv4IDMCGEEELkT4Iqa1SERerxdzK5dUc/VVjL19V8fRJCCCGsnARV1qgoi9Tvrqeq6uWMi9bOfH0SQgghrJwEVdaoCIk/5c4/IYQQwjQkqLJGRZj+O3d3pKqO3PknhBBClIgEVdaoCNN/Z2WkSgghhDAJCaqsUSFHqnQ6xTlJpyCEEEKYhARV1qiQa6quJKaTmpWLva2Gaj4updAxIYQQwnpJUGWNCjn9l7dIPbiiK/a28qMghBBClIS8k1qjQk7/5aVTkPVUQgghRMlJUGWNijhSJUGVEEIIUXISVFkjw5oqzwcWkz3/hBBCCNORoMoaFWL6LytHx8W4OwDUlhxVQgghRIlJUGVtcrMhSx8sPWikKvJWKjk6hZvWDn9Pp9LpmxBCCGHFJKiyNnlTf/DAlApnrycDULuSGxqNxty9EkIIIayeBFXWJi+ocnAF2/tvkJy3nkqm/oQQQgjTkKDK2hTyzr+8Pf9kkboQQghhGhJUWZuMBP3HAnJUyZ5/QgghhGlJUGVtCjFSdSczh9iEdADqyPSfEEIIYRL3X3RTRsXFxfHLL79w48YNQkJCGDRoELa2tiWus337dvbs2YOdnR3t2rWjdevWRq//8ccf7N271+hY5cqVefXVV01zYaZSiH3/8qb+fN20VHBxKI1eCSGEEFavXI1UXbx4kZCQEJYtW0Zubi7Tpk2jd+/e5ObmFruOTqcjLCyMd955h5SUFK5cuUKPHj146aWXjNrZuHEjGzZsoFKlSoaHt7e3Wa+3WAqRo0oyqQshhBCmV65Gql577TVq1qzJxo0bsbGxYcyYMdSuXZtffvmFYcOGFauORqNh9uzZNG/e3FCnR48e9O7dm9GjR9OwYUPD8dq1a/Ovf/3L7NdZIoWY/jMEVTL1J4QQQphMuRmpysnJYfXq1QwbNgwbG323q1WrRseOHVm2bFmx62g0GqOACqBp06YAxMbGGh2/dOkS//nPf/jkk084cOCACa/OhGSkSgghhLCIchNURUVFkZGRQXBwsNHx4OBgzp07Z7I6APPnz8fR0dEo2NJoNLi56YOQ06dP06FDByZPnvzAPmdmZpKcnGz0MLsCRqqUUkTckKBKCCGEMDWLTv/9+uuvHDx48IFlpk2bhre3N2lpaQC4u7sbve7h4UFqamq+dYtTZ8eOHbz11lt89NFH+Pj4GI5PmTKF6tWrGz4fOnQo3bp1o1+/fnTp0iXftmbMmMG77777wOszuQIWqsfdyeR2ahYaDdTylaBKCCGEMBWLBlUeHh5UqlTpgWXy7tJzdXUFIDEx0ej1xMREwwjSPxW1zv79+3n00Ud59dVX71mo/veACqBr164EBASwc+fO+wZV06ZN45VXXjF8npycTGBgYL5lTaaA6b9z1/X7AlbzdsHJ4cF3TQohhBCi8CwaVPXs2ZOePXsWqmzVqlVxcXEhIiLCqM7Zs2epV69eiescOHCAHj16MHbsWKZPn16oPuXk5JCZmXnf17VaLVqttlBtmUwB03+GPf/8XEunP0IIIcRDotysqbK1teWxxx7jp59+MgQyJ0+eZNeuXQwePNhQ7vfff+eTTz4pUp2DBw/SvXt3xo4dy4cffnjPuXNycti1a5fRsd9++43r16/TrVs3k19riRQ0UmVYT+We7+tCCCGEKJ5ylVLhww8/pH379rRs2ZJmzZqxatUqhg4dysCBAw1l1q9fz759+wxJOQuqk5qaSo8ePdBqteTk5BilTHjiiScICwtDo9Hw9ttvk52dTYMGDYiOjmbz5s28/fbbdO7cuXS/CA+i00HG3cXw91lTlXfnn+z5J4QQQphWuQqqKleuzPHjx1m1ahU3btxg+PDhdOrUyajME088Qbt27Qpdx8bGhtdffz3f8zk5OQH6Ea/Nmzdz4MABjh49SufOnZk9ezZBQUEmv8YSyUwGlP55PtN/Op3i3A39mqrakqNKCCGEMCmNUkpZuhMPi+TkZDw8PEhKSrrnjkSTSLgMnzcGO0d488Y9L0fFp9Lxo2042Nlw+t0e2NmWm9lfIYQQwmIK+/4t76rWpMBF6vqpv1q+rhJQCSGEECYm76zWpIAcVbI9jRBCCGE+ElRZkwLu/JNM6kIIIYT5SFBlTQqY/ssbqaotQZUQQghhchJUWZMHjFRl5uQSeUu/NY+kUxBCCCFMT4Iqa/KANVUXb6aSq1O4O9pRyd2xlDsmhBBCWD8JqqzJA6b/Im7ok4LWqeSGRqMpvT4JIYQQDwkJqqzJA6b/8tIpyCJ1IYQQwjwkqLImDxipOndd9vwTQgghzEmCKmuSN1KVz5oqw/Y0vq6l2CEhhBDi4SFBlTXJW6j+j+m/jOxcriSmA1BTgiohhBDCLCSosib3mf7LS6Xg7miHl4tD6fZJCCGEeEhIUGUtlLrvQvW8oKpGRVe5808IIYQwEwmqrEVWKuhy9M/vM1JVw8ellDslhBBCPDwkqLIWeeupNLbgYBw8XYzTL1KvLkGVEEIIYTYSVFmLv0/9/WOK7+/Tf0IIIYQwDwmqrMUDclTlBVUyUiWEEEKYjwRV1uI+i9Rvp2aRmJYNQDUf59LtkxBCCPEQkaDKWtxnM+XIW/r1VFU8HHF2sCvtXgkhhBAPDQmqrMV9pv8uxd2d+qsoU39CCCGEOUlQZS3uM/13yZBOQRapCyGEEOYkQZW1uF829ThZpC6EEEKUBgmqrMV911TJ9J8QQghRGiSoshb5TP/l6hSR8fqgKlim/4QQQgizkqDKWuQz/Xc1MZ2sHB32thr8KzhZpFtCCCHEw0KCKmuRz0hV3tRfkLcLtjaykbIQQghhThJUWQvDSNVfa6ou3d3zTzZSFkIIIcxPgiprYVio7mk4JIvUhRBCiNIjQZU1yMmEnHT9879N//2Vo0qCKiGEEMLcJKiyBnlTf2hA+/fpv7tBVUW5808IIYQwNwmqrEHeInVHd7DRf0szsnO5mqQfvZLEn0IIIYT5SVBlDfJJ/BkVn4ZS4O5oh7eLg4U6JoQQQjw8JKiyBvnkqMq78696RVc0GkmnIIQQQpibBFXWIJ8cVbJIXQghhChdElRZg3xGqiIlqBJCCCFKlQRV1iCfNVV/Tf9JUCWEEEKUhnIXVM2bN4/GjRtTqVIlunXrxtGjR0tc55VXXsHT09Po0aZNG5Ocu1Q8YIsaufNPCCGEKB3lKqhavHgx48aN49///je7d+8mODiYLl26cO3atRLVSUtLo2PHjly+fNnwWL9+fYnPXWr+Mf2XkJpFQlo2IEGVEEIIUVrKVVA1Y8YMRowYwdNPP01wcDBfffUVWq2Wr7/+usR17O3tjUaq3NzcSnzuUvOPkaq8ReqVPRxxdrCzTJ+EEEKIh0y5CaoSExM5ceIEjzzyiOGYra0tXbp0YdeuXSWus3nzZqpUqUK9evUYPXo0N27cKNG5S9U/9v2TqT8hhBCi9JWboOrq1asA+Pn5GR339fU1vFbcOv7+/syaNYt9+/Yxb948Tp8+Tdu2bUlNTS32uQEyMzNJTk42epjFP6b/Im/pF6nXkEXqQgghRKmxaFA1fvz4exaI//MRGRlpVMfGxrjLdnZ2KKUeeJ6C6rz11ls888wzVK1aldatW7N06VJiYmL45ZdfSnTuGTNm4OHhYXgEBgY+sJ/F9s/pv7i8kSrZ808IIYQoLRZdcPPxxx8zffr0B5Zxd3cH9KNCALdu3TJ6/ebNm4bX/qk4dQAqVqxIUFAQERERJWpn2rRpvPLKK4bPk5OTzRNY1egIyVfBVd8XQ44qGakSQgghSo1FR6qcnZ0LHKnKGx3y8fGhRo0a7Ny506iNHTt20LJly3zbL04dgNTUVGJjYw0BU3Hb0Wq1uLu7Gz3Mov9X8MxS8KyKTqck8acQQghhAeVmTRXApEmTmDNnDrt37yYrK4sZM2Zw/fp1xowZYyjz0ksvGeWYKqhOZmYmI0aM4Ny5cyiluHbtGsOHD8fBwYGhQ4cW6dxlwdWkdDJzdNjbavD3dLJ0d4QQQoiHRrm6337ixIncunWL3r17k5qaSrVq1Vi2bBm1atUylElLSzNaEF5QHa1WS9euXRk0aBDnz5/H3t6e9u3bs3v3bvz9/Yt07rIgb5QqyNsFO9tyFTMLIYQQ5ZpGFbTKuwxSSpGRkYGT070jMenp6eTk5NyTZ+pBdfJkZWXh4OBQ7HMXJDk5GQ8PD5KSksw2FfjTnsu8veIU3er78f3w5mY5hxBCCPEwKez7d7kaqcqj0WjuG9Tc7/iD6uQpKKAqbDuWJOuphBBCCMuQ+SErc0nu/BNCCCEsQoIqK3MpTp/4U3JUCSGEEKVLgiorkpGdy5XEdEC2qBFCCCFKmwRVViT6dhpKgZujHT6uBa8PE0IIIYTpSFBlRfKm/mr4uKDRaCzcGyGEEOLhIkGVFclbpC5Tf0IIIUTpk6DKikTG5d35J4vUhRBCiNImQZUVkZEqIYQQwnIkqLIikZKjSgghhLAYCaqsRGJaFrdTswCo5i1BlRBCCFHaJKiyEnlTf5XcHXHRlsvdh4QQQohyTYIqK/HXInUZpRJCCCEsQYIqKxEpi9SFEEIIi5KgykpcupW3558EVUIIIYQlSFBlJS7dnf4LlhxVQgghhEVIUGUFdDrF5XiZ/hNCCCEsSYIqK3AtOYOMbB32thoCKjhZujtCCCHEQ0mCKiuQd+dfVS9n7GzlWyqEEEJYgrwDW4FIwyJ1WU8lhBBCWIoEVVbgomGRuqynEkIIISxFgiorIDmqhBBCCMuToMoKSFAlhBBCWJ5sElfOKaVoVtUTdyc7akiOKiGEEMJiJKgq5zQaDTOfbGrpbgghhBAPPZn+E0IIIYQwAQmqhBBCCCFMQIIqIYQQQggTkKBKCCGEEMIEJKgSQgghhDABCaqEEEIIIUxAgiohhBBCCBOQoEoIIYQQwgQkqBJCCCGEMAEJqoQQQgghTECCKiGEEEIIE5CgSgghhBDCBCSoEkIIIYQwATtLd+BhopQCIDk52cI9EUIIIURh5b1v572P348EVaUoJSUFgMDAQAv3RAghhBBFlZKSgoeHx31f16iCwi5hMjqdjqtXr+Lm5oZGoylxe8nJyQQGBhITE4O7u7sJelj2WPs1Wvv1gfVfo7VfH8g1WgNrvz4w7zUqpUhJSaFKlSrY2Nx/5ZSMVJUiGxsbAgICTN6uu7u71f6S5LH2a7T26wPrv0Zrvz6Qa7QG1n59YL5rfNAIVR5ZqC6EEEIIYQISVAkhhBBCmIAEVeWYVqvl7bffRqvVWrorZmPt12jt1wfWf43Wfn0g12gNrP36oGxcoyxUF0IIIYQwARmpEkIIIYQwAQmqhBBCCCFMQIIqIYQQQggTkDxVZUhmZianTp3CxcWFOnXqmKxOcdo1l5s3bxIVFUVQUBC+vr4FlldKERkZSXp6OsHBwTg6Ohq9fvXqVS5dumR0TKPR0LZtW5P2uygiIiJITU2lYcOGODg4PLDssWPHDJn28/j5+VGrVq0StWtO6enpnD59Gg8PD2rWrPnAstHR0URHR+f7Wps2bbCxsSE9PZ3Dhw/f83pISEih8sKYw61btzh79ix169bFx8enUHWuX79OTEwMNWrUwNvbu9hlSsuZM2e4fft2oX9X0tPTiYiIwMfHJ998e4cPHyY9Pd3omL+/P9WrVzdJf4sqOzubw4cP4+XlRe3atR9Y9s6dO4SHh99zvHHjxri5uRkdS01N5ezZs3h5eVns2vLcuHGD8+fP07BhQzw9PR9Ydv/+/WRnZ99z3NfX1/D1iYyM5MqVK0avOzk5ERoaarI+F0Vqairnz5/H19eXKlWqFKqOTqfj1KlTKKVo0KABtra2xSpTbEqUCWvWrFHe3t6qRo0aqkKFCio0NFRdvXq1xHWK0665TJ48WWm1WlW/fn2l1WrV5MmTH1h+3rx5qnr16qp69eqqXr16ytPTU3399ddGZT777DPl7Oys2rZta3h07NjRjFdxf7Gxsapp06bKy8tLVa9eXfn4+Kj169c/sE5oaKgKCgoy6v/7779f4nbN5ffff1ceHh6qVq1ayt3dXbVr107Fx8fft/x3331ndG1t27ZV3t7eyt3dXWVnZyullDpz5owCVIsWLYzKHTx4sLQuy+D06dPqmWeeUZUrV1aAWrx4cYF1cnJy1MiRI5Wjo6PhZ/s///lPkcuUll9++UW1bNlSVahQQdna2hZY/ubNm2rkyJHKw8NDNW7cWHl5eamWLVuq8+fPG5ULDg5WwcHBRt/Dzz//3FyXcV/JycnqzTffVAEBAcrV1VUNGzaswDoHDx5UgGrVqpVR/0+dOmVUbv78+crV1VXVrl1bubq6qq5du6qkpCRzXcp9HT16VD3xxBPK19dXAWrt2rUF1unTp4/RtbVs2VIB6uWXXzaUmTRpkqpQoYJRuSFDhpjzUvIVGxurhg0bpjw8PFSTJk2Uh4eH6tixo4qJiXlgvePHj6vg4GBVuXJl5e/vr4KCgtSRI0eKXKYkJKgqA+Li4pSbm5t67733lFJKpaenq1atWqlevXqVqE5x2jWXH3/8UTk7O6vw8HCllFJHjhxRTk5O6qeffrpvnffff19dvnzZ8PnixYuVRqNRe/fuNRz77LPPVIMGDczX8SLo2rWrat++vcrIyFBKKfXGG28oDw+PBwYdoaGhasaMGSZv1xyioqKUVqtVs2bNUkrp37waNmyohg4dWug2cnJyVJUqVdS4ceMMx/KCqoL+YJaGP/74Q/30008qJSWl0EHVzJkzlaenp4qIiFBKKbVz505lZ2enli9fXqQypeXtt99We/bsUT/88EOhgqrDhw+ruXPnqqysLKWUUqmpqapbt26qRYsWRuWCg4Pv+afHEi5evKjee+89dfXqVdWjR48iBVUJCQn3LXP27FllZ2en5s2bp5RS6vbt26pWrVrqhRdeMFXXC23BggVq8eLF6sqVK4UOqv7pzz//VIA6duyY4dikSZNUnz59TNnVYtm1a5dauHChysnJUUrp/9a0atVKdevW7b51cnNzVd26ddWQIUOUTqdTSin19NNPqxo1ahj+gStMmZKSoKoMmD17tnJ2dlapqamGY0uWLFEajea+o0qFqVOcds2lQ4cO6sknnzQ6NmjQoCKPKnl6eqpPPvnE8Plnn32m6tatq44dO6ZOnz5t+MNf2qKjoxWgVq1aZTiWlJSktFqt+v777+9bLzQ0VE2dOlUdOHBAXblyxWTtmsP06dOVt7e34Q+dUkrNmTNH2dvbF/q/9ZUrVypAHT582HAsL6jasWOHOnLkiEpOTjZ534sqOzu70EFVo0aN1NixY42Ode3aVfXv379IZUpbYYOq/CxYsEBpNBpDoK+UPqh6//331YEDB9S1a9dM1c0SKWpQdfDgQXX06FF1586de8q8/vrrKiAgwOjYzJkzlbOzs9HXoTTFxcUVO6jq06ePCgsLMzo2adIk1a1bN3X48GF1/vx5o991S/vyyy+Vs7PzfV/fsWOHAtTJkycNxyIiIhSgNm7cWOgyJSUL1cuAo0ePUq9ePZydnQ3HwsLCUErlO89f2DrFaddcjh49es+8fFhYGEePHi10G+fPnycpKemedTwRERE8+eST9OjRg4oVK/L999+bpM9FkXcdf79Gd3d36tSpU+A1zpo1ixdeeIG6desSGhrKyZMnTdKuqR09epQmTZoYrT8ICwsjOzubU6dOFaqNuXPnEhoaSrNmze55bejQoTz99NN4e3szduxYMjMzTdZ3c8m79gf9bBemTHlz8OBBAgIC7kmyOGPGDF544QVq1qxJu3btuHDhgoV6WDyPPfYYQ4cOpUKFCkyePJmcnBzDa/f7G5aWlsa5c+dKu6slcvXqVdatW8cLL7xwz2tbtmzh2WefpV27dgQGBrJ8+XIL9PBeBw8eJDg4+L6vHz16FK1WS4MGDQzHateujbu7u+H3rDBlSkqCqjLg9u3b9yxazfv89u3bxa5TnHbNIScnh5SUlHz7kpycTG5uboFtZGVl8dxzz9G0aVN69+5tON6oUSPOnTvH6dOniY6O5qOPPmLMmDFs2bLF5NfxIHlfz/yu8UFf65deeolbt24RHh7OlStXqFy5MgMGDDAs+C1uu+ZQ0p+nGzdusGrVqnv+kLu6urJq1SpiY2M5deoUBw8e5LfffuM///mP6TpvJklJSeTm5j7w+1OYMuXJzp07mT17Nm+99ZbR8TfeeIP4+HjCw8OJiYnB3t6exx9/3CgwKasqVKjApk2biI6O5syZM+zatYu5c+cyY8YMQ5my8vfUFH788UecnJx48sknjY536dKF2NhYTpw4wdWrVxk5ciRDhgzhzJkzFuqp3po1a/j555/v+Zn7u/y+P2D8e1aYMiUlQVUZYG9vT0ZGhtGxvDfV+93lVZg6xWnXHGxtbbGxscm3LzY2NgXeeZGTk8OTTz7J1atXWbZsGXZ2f9202qVLF6ORqxdeeIFmzZrx66+/mvYiCmBvbw+Q7zU+6Gs9fPhwnJycAHBzc+Pjjz/m4sWLHDp0qETtmkNJf57mz5+PVqtl6NChRscDAgLo06eP4fPGjRszfvx4fvnlFxP02rwK8/0pS9/DkgoPD6d///6MHz/+nuB4xIgRhuupUKECM2bM4Pjx4xZ/Qy6M4OBgHnnkEcPnYWFhjBw50uhnsKz8PS0ppRTz5s1j6NChuLq6Gr3Wr18/KlWqBICNjQ3vvvsu7u7uLFu2zAI91du9ezdPPPEEb731FoMHD75vufy+P3Dv72JBZUpKgqoyICgo6J7bWPM+r1q1arHrFKddc9BoNAQGBubbl4L6kZOTw9ChQzly5Ahbt24lMDCwwPP5+fndcy5zCwoKAijWNf6dn5+fUTumatcUSvrzNG/ePIYMGYK7u3uBZS3xPSwODw8PPD09H/j9KUyZ8uDYsWN07dqVYcOGMXPmzALL//Nnubz5589gWfl7WlLbt2/n4sWL+U79/ZONjQ0VK1a02Pdw79699OrVi8mTJ/POO+88sGxQUBAJCQmkpaUZjmVmZhIfH2/0nlhQmZKSoKoM6NatGxcvXuT06dOGY8uXL8fLy8uw9iQrK4tdu3YRHx9f6DqFKVNaunXrxqpVq1B3t5pUSrFy5Uq6detmKHPlyhV2795t+Dw3N5ennnqKgwcPsm3bNqpVq3ZPu6mpqUafJyUlceDAARo2bGieC7mPFi1a4OHhwYoVKwzHjh49SkxMjNE1hoeHc/78eUD/35H6x9abGzZsADD0v7DtloZu3bpx9OhRYmNjDceWL19O1apVDXlu0tLS2LVrF0lJSUZ1d+3axdmzZ/P9Q/7P7yHAxo0bS/17WFjR0dHs37/f8HnXrl1ZuXKl4fOcnBxWr15t9P0pTJmy5NChQ0RGRho+P378OI888ghPPvkkX3zxxT3l//4mlWfDhg1oNBrq169v1r4WR0pKCrt27TLkiCvMz2C3bt3Ys2cPt27dMhxbvnw59erVw9/f3/ydLqJLly7lm/9tzpw5NG7cmBYtWtzz2j+/DpcvXzbkwSpt+/bto2fPnkycOJH//e9/9y2TlwevS5cu2NjYsGrVKsPra9asIScnxzAKWZgyJWaS5e6ixLp3767q16+vfv/9d/X5558rrVarZs+ebXg9JiZGAer3338vdJ3ClikNFy9eVJ6enmr48OFqxYoV6plnnlGenp7q4sWLhjIfffSR0d1IzzzzjHJ0dFQ///yz2rlzp+ERGRlpKNOhQwf17rvvqtWrV6uFCxeqZs2aqapVq1rk7qPPP/9cOTk5qS+++EL99ttvqk6dOqp3795GZRo3bqyeffZZpZQ+rUSrVq3Ut99+q9avX68++OAD5e7urkaMGFHkdktDTk6OatWqlQoNDVV//PGH+vDDD5WdnZ1auHChocyJEyfyvZPmueeeUw0bNsy33ddee02NGjVK/fbbb2rFihXq6aefVg4ODsW6o6mkEhIS1M6dO9W2bdsUoN555x21c+dOdeHCBUOZN954Q3l7exs+P378uHJ2dlZjx45VK1asUI8//rjy9fU1+hksTJnSEhERoXbu3Klef/11ZWtra/i9+vsdnEFBQWrSpElKKaXOnz+vKlasqNq1a2f0e7hz507DXW9bt25VHTp0UHPmzFHr169X7733nnJ2djbKgVSadu3apXbu3Klatmypunfvrnbu3KkOHDhgeH3v3r0KMKRnmThxoho3bpxasmSJWrZsmRo0aJBydHRU27ZtM9TJzMxUjRs3Vm3atFFLly5V7733nrK1tVXLli0r9euLi4tTO3fuVKtWrVKA+vjjj9XOnTuNUtBMmDBBBQcHG9VLSEhQTk5O6ssvv8y33bp166qPPvpIrV27Vs2dO1fVrFlTNWnSxOgO8tJw/Phx5eHhoXr06HHPz9zf70j08PBQb7/9tuHzl19+Wfn4+KgffvhBzZ8/X/n5+anx48cbtV2YMiWhUeof/yoLi0hLS+PTTz9lx44dODs7M2zYMKP547i4OAYOHMj//vc/OnXqVKg6hS1TWs6ePcvHH3/MpUuXqFGjBv/617+oW7eu4fVffvmFb775hm3btgHQt29fEhMT72ln6NChTJgwAYDk5GS++uor9uzZg1arJTQ0lBdffPGeLMil5ddff2Xx4sWkpaXRsWNHXnnlFcOaKdCvO6lVqxavv/46ACdOnODbb7/l/PnzVKlShf79+zNgwIAit1takpOT+eijj9i7dy8eHh6MGDGCvn37Gl6PjIzkmWeeYebMmTRv3hzQjzj26dOHYcOG8cwzz9zTplKKxYsXs3LlSpKTk6lTpw4TJkx44J0+5rJ//35effXVe44PGDCAf/3rXwB8//33LF++3Oi/3WPHjvHZZ58RHR1NnTp1mDJlyj3ZtgtTpjT897//Zf369fcc//rrrwkJCQFg8ODBtG/fnpdeeonNmzfz9ttv59vWkiVLDGtwDh48yNy5c4mMjCQgIIDBgwfTs2dP813IA3Tq1OmeBfK+vr78+eefAJw+fZrRo0fz3XffUb9+fXJzc/n5559Zu3Ytqamp1K1bl4kTJxqm3/MkJCTw4YcfcujQIby8vHjhhRcsMtp4v+/J008/zdixYwH47LPP2L9/v9G6sHXr1jF9+nRWrFiRbwb2mzdv8sUXX3D48GE8PDxo27Yto0ePLvU1Y8uXL+ejjz7K97V169YZ1oL16tWLwYMH8/zzzwP6TOnfffcdK1asQClFnz59GDdunNG63cKUKQkJqoQQQgghTEDWVAkhhBBCmIAEVUIIIYQQJiBBlRBCCCGECUhQJYQQQghhAhJUCSGEEEKYgARVQgghhBAmIEGVEEIIIYQJ2BVcRAghRH5yc3M5ePCg4XMPDw+Cg4PL1Qa7QgjTkeSfQghRTCdOnKBRo0Y0bdoUBwcHoqOj0el0LFq0iC5duli6e0KIUiYjVUIIUUxHjhzB1taWvXv3otVqycnJMWx7ERERYenuCSFKmaypEkKIYjp8+DC1a9dGq9UCYGdnR8eOHYmKirJwz4QQliBBlRBCFNPhw4cNmxDn2bNnD2FhYRbqkRDCkmT6TwghiiE3N5fw8HDq1q3Lvn37uHPnDr/++itHjhxh3bp1lu6eEMICJKgSQohiOHv2LGlpaRw8eJCTJ08SHR1NcnIymzZtolGjRpbunhDCAmT6TwghiuHIkSMAbNu2jf379xMTE0Pr1q156aWXLNwzIYSlSFAlhBDFcPjwYWrWrImXlxegX6Q+ZcoUDh06xIkTJyzcOyGEJUhQJYQQxXD48OF7FqR36dIFb29vfv/9dwv1SghhSRJUCSFEMTg6OtK7d2+jY3Z2drz44ouSUkGIh5RkVBdCCCGEMAEZqRJCCCGEMAEJqoQQQgghTECCKiGEEEIIE5CgSgghhBDCBCSoEkIIIYQwAQmqhBBCCCFMQIIqIYQQQggTkKBKCCGEEMIEJKgSQgghhDABCaqEEEIIIUxAgioh/r/dOhYAAAAAGORvPYmdRREADKQKAGAgVQAAgwDSAFKwNYXKDAAAAABJRU5ErkJggg==", "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": 0.003909, "end_time": "2026-06-30T01:09:47.821529+00:00", "exception": false, "start_time": "2026-06-30T01:09:47.817620+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": "2026-06-30T01:09:47.830689Z", "iopub.status.busy": "2026-06-30T01:09:47.830447Z", "iopub.status.idle": "2026-06-30T01:09:50.546247Z", "shell.execute_reply": "2026-06-30T01:09:50.545268Z" }, "papermill": { "duration": 2.721425, "end_time": "2026-06-30T01:09:50.546995+00:00", "exception": false, "start_time": "2026-06-30T01:09:47.825570+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": 0.004472, "end_time": "2026-06-30T01:09:50.556786+00:00", "exception": false, "start_time": "2026-06-30T01:09:50.552314+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": "2026-06-30T01:09:50.566523Z", "iopub.status.busy": "2026-06-30T01:09:50.566316Z", "iopub.status.idle": "2026-06-30T01:09:52.539318Z", "shell.execute_reply": "2026-06-30T01:09:52.538338Z" }, "papermill": { "duration": 1.979168, "end_time": "2026-06-30T01:09:52.540030+00:00", "exception": false, "start_time": "2026-06-30T01:09:50.560862+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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": 0.004255, "end_time": "2026-06-30T01:09:52.549064+00:00", "exception": false, "start_time": "2026-06-30T01:09:52.544809+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": "2026-06-30T01:09:52.558993Z", "iopub.status.busy": "2026-06-30T01:09:52.558747Z", "iopub.status.idle": "2026-06-30T01:09:52.746870Z", "shell.execute_reply": "2026-06-30T01:09:52.745879Z" }, "papermill": { "duration": 0.194146, "end_time": "2026-06-30T01:09:52.747626+00:00", "exception": false, "start_time": "2026-06-30T01:09:52.553480+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": 0.004385, "end_time": "2026-06-30T01:09:52.757570+00:00", "exception": false, "start_time": "2026-06-30T01:09:52.753185+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": "2026-06-30T01:09:52.767819Z", "iopub.status.busy": "2026-06-30T01:09:52.767614Z", "iopub.status.idle": "2026-06-30T01:10:03.396429Z", "shell.execute_reply": "2026-06-30T01:10:03.395506Z" }, "papermill": { "duration": 10.634812, "end_time": "2026-06-30T01:10:03.397092+00:00", "exception": false, "start_time": "2026-06-30T01:09:52.762280+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigma_R (corrected vs. uncorrected): 0.19999985069413592 0.19321086259083936\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "meanvT (corrected vs. uncorrected): 0.9035516117477272 0.9171527697944727\n" ] }, { "data": { "image/png": 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", "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": 0.004651, "end_time": "2026-06-30T01:10:03.407733+00:00", "exception": false, "start_time": "2026-06-30T01:10:03.403082+00:00", "status": "completed" }, "tags": [] }, "source": [ "galpy will automatically save any new corrections that you calculate." ] }, { "cell_type": "markdown", "id": "befc0d74", "metadata": { "papermill": { "duration": 0.004731, "end_time": "2026-06-30T01:10:03.417230+00:00", "exception": false, "start_time": "2026-06-30T01:10:03.412499+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": "2026-06-30T01:10:03.427889Z", "iopub.status.busy": "2026-06-30T01:10:03.427667Z", "iopub.status.idle": "2026-06-30T01:10:15.328145Z", "shell.execute_reply": "2026-06-30T01:10:15.327270Z" }, "papermill": { "duration": 11.90696, "end_time": "2026-06-30T01:10:15.328970+00:00", "exception": false, "start_time": "2026-06-30T01:10:03.422010+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Oort A: 0.4319078088921868\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Oort B: -0.4852449609022859\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): -0.05333715201009914\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Cold DF: A = 0.4991755666614284 , B = -0.4999282474249201\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": 0.004791, "end_time": "2026-06-30T01:10:15.338861+00:00", "exception": false, "start_time": "2026-06-30T01:10:15.334070+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": "2026-06-30T01:10:15.349731Z", "iopub.status.busy": "2026-06-30T01:10:15.349527Z", "iopub.status.idle": "2026-06-30T01:10:15.762004Z", "shell.execute_reply": "2026-06-30T01:10:15.761164Z" }, "papermill": { "duration": 0.419416, "end_time": "2026-06-30T01:10:15.763186+00:00", "exception": false, "start_time": "2026-06-30T01:10:15.343770+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": 0.005173, "end_time": "2026-06-30T01:10:15.774646+00:00", "exception": false, "start_time": "2026-06-30T01:10:15.769473+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": "2026-06-30T01:10:15.786901Z", "iopub.status.busy": "2026-06-30T01:10:15.786541Z", "iopub.status.idle": "2026-06-30T01:10:44.624260Z", "shell.execute_reply": "2026-06-30T01:10:44.623266Z" }, "papermill": { "duration": 28.845163, "end_time": "2026-06-30T01:10:44.624920+00:00", "exception": false, "start_time": "2026-06-30T01:10:15.779757+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean v_R (warm disk): -0.029476364282585495\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": 0.004972, "end_time": "2026-06-30T01:10:44.635249+00:00", "exception": false, "start_time": "2026-06-30T01:10:44.630277+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": "2026-06-30T01:10:44.646514Z", "iopub.status.busy": "2026-06-30T01:10:44.646286Z", "iopub.status.idle": "2026-06-30T01:10:48.632694Z", "shell.execute_reply": "2026-06-30T01:10:48.632250Z" }, "papermill": { "duration": 3.993367, "end_time": "2026-06-30T01:10:48.633700+00:00", "exception": false, "start_time": "2026-06-30T01:10:44.640333+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": 0.004865, "end_time": "2026-06-30T01:10:48.643795+00:00", "exception": false, "start_time": "2026-06-30T01:10:48.638930+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": "2026-06-30T01:10:48.654698Z", "iopub.status.busy": "2026-06-30T01:10:48.654491Z", "iopub.status.idle": "2026-06-30T01:10:51.250996Z", "shell.execute_reply": "2026-06-30T01:10:51.250186Z" }, "papermill": { "duration": 2.603322, "end_time": "2026-06-30T01:10:51.252041+00:00", "exception": false, "start_time": "2026-06-30T01:10:48.648719+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": 0.004959, "end_time": "2026-06-30T01:10:51.262396+00:00", "exception": false, "start_time": "2026-06-30T01:10:51.257437+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plot the velocity distribution:" ] }, { "cell_type": "code", "execution_count": 17, "id": "25d32106", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:10:51.273871Z", "iopub.status.busy": "2026-06-30T01:10:51.273671Z", "iopub.status.idle": "2026-06-30T01:10:51.456741Z", "shell.execute_reply": "2026-06-30T01:10:51.455836Z" }, "papermill": { "duration": 0.189695, "end_time": "2026-06-30T01:10:51.457413+00:00", "exception": false, "start_time": "2026-06-30T01:10:51.267718+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": 0.005335, "end_time": "2026-06-30T01:10:51.469335+00:00", "exception": false, "start_time": "2026-06-30T01:10:51.464000+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": "2026-06-30T01:10:51.481096Z", "iopub.status.busy": "2026-06-30T01:10:51.480904Z", "iopub.status.idle": "2026-06-30T01:11:05.609938Z", "shell.execute_reply": "2026-06-30T01:11:05.608934Z" }, "papermill": { "duration": 14.135876, "end_time": "2026-06-30T01:11:05.610645+00:00", "exception": false, "start_time": "2026-06-30T01:10:51.474769+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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k+vTpQ5cuXUhOTsbf39/p525KAI01DQXQVFVVcezYMfbv3y9elZWVNmPatWvHyJEjGTNmDPHx8UDTxVAlOzub//3vf/zwww/CenPppZeKBxAphhJXXHRiuHr1asrLy/nf//7HoUOHmDlzJgBXXXUVOp2O0tJSQkJCmDt3Lrfffju//fYb11xzDVOmTLExjXp4eDBu3LhGnVOK4T/P+SyGhw4d4q677iItLQ29Xs9jjz3GXXfdhbe3t9PjnK4YGo1GFi1axDfffCNMoFqtlsGDB3PZZZfRr18/UXqtOaNJrWlqNKnFYuHIkSMi2X7//v0219KhQweuvPJKrrrqKsLCwmz2tcaVGEL9325ubi4fffQR8+fPF/dw/Pjx/Pvf/xYPwc72lWLYcrnoxPCRRx6xydVSmT9/Pt7e3lRVVTFlyhQefvhhRowYwbfffus0atTPz4958+Y16pxSDM8+zZUPeLbTJX7++Weef/55ampqaN26Nf/973/p1auXW4FrihiqrZVWrlzJ559/TmZmJlCfkjFu3DgmTpwozI72JlRr3N2HMxFDexoSl7KyMjZt2sTatWvZvXu3uA6dTsfgwYMZN24cAwcOFA8SKtYi5uHhYbPNWigzMjL49NNP+fXXX7FYLHh5eXHvvffy4IMP4ufn53al2JRV5JmUhJNl3c4PLjoxPBdIMTz7nO9iWFdXx7/+9S9RqOHSSy/l/fffF+2LmksMDxw4wOuvvy66Q4SEhHDbbbcxfvx4h8n6QhBDa6qqqli7di1Lly7l0KFD4v9bt27NDTfcwMSJE0UFmsaKobr90KFDvPbaa2zevBmAqKgoXnrpJa6++mqbzyDFsOUixbAZkGJ49jmfxVBRFF588UX+97//odFoePzxx3nggQdsJsAzFUNFUViwYAHvv/8+RqMRPz8/pkyZwuTJk/H19W3wOBeCGFqLTUZGBkuWLOHPP/+kvLwcAH9/fyZPnsyUKVNsSiU2Rgyh/nOtWrWK1157jVOnTgH1Dy1vvPGGqPAjxbDlIsWwGZBiePY5n8Vw1qxZvPbaawB89NFHXH311U02fbobW1lZyeuvv87KlSsBGDp0KM8//zzBwcGNPm5ziaHFYsFsNmOxWPDw8HAQNHtOVwxVAaupqWH58uX8+OOPwv3h4+PDjTfeyC233EJISEijxVD9uaamhtmzZ/Pf//6X2tpaPD09eeihh3j44YfFg4X99Th7L8Xw4kKKYTMgxbB5cPdrcybtk6wn+uYUQ5PJxE8//cQTTzwBwL/+9S/uvvtusc0aNdzf2TZ3Y9PS0njqqafIyMhAp9Mxbdo0rr32Wpvcv8YcpzHCbrFYbPoSZmdnU1paKl41NTUOXeO9vb3x9fXF39+f8PBwIiMjiYiIoE2bNiQmJgozMbgXP/v3zoRn06ZNfPPNN8JE7OPjw/XXX8/UqVNFlCy4Xylabzt16hT/+c9/WLt2LQCdOnXigw8+oGvXrg1en/37fyrYRorj2UOKYTMgxbB5uNDEcOvWrUyePBmz2cx9993Hc889J7Y1hxgeO3aMBx54gLKyMqKionj11Vfp2LGjy32bKoaKopCVlUVKSgp79uzhwIEDzVKNxpqQkBDatm1LcnIyPXv2JC4uTkzoTRFDa1Pn5s2b+frrrzl69Kg4xwMPPMBVV12FVqtttBiq7//44w9efvlliouL0el0PProozz88MNug3bs30sxvPCRYtgMSDFsHi4kMbRYLFxxxRXs3buX8ePH8/HHH9tMVGcqhunp6UybNo2SkhI6duzIzJkzCQ0NtTmO/b6NFcOCggJWr17NmjVrHJLiPT09iY2NJS4ujpiYGEJDQwkKCiI4OBhfX190Oh1arVZ0uK+urqa6upry8nIKCgooLCwkPz+fjIwMsrOzHb6b4OBgunfvzsCBA+nbt6+NODVGDFV0Oh3r169n9uzZouVTcnIyzz//PJ07d3b4TK6Oo24rKiripZdeYsmSJQD06dOH2bNnExsb6/KapBheXEgxbAakGDYPF5IY/vTTTzzyyCP4+/uzdu1am5w4ODMxTE9P595776WwsJCOHTvy4Ycfis7vpyuGJpOJHTt2sGTJElJSUsQ98/Dw4JJLLqFbt25069bNZuWm4s5f626yrqmp4eTJk6SmprJv3z4OHjxos/L08/Ojf//+XHbZZXTv3r3B3EFr1O1Go5HffvuNL774gqqqKnQ6Hbfeeiv33nsvPj4+QOPEUOWPP/7gueeeo6KigsDAQN59910mTJjg9JqkGF5cSDE8A2bNmsWsWbMwm80cPXpUimETaShQw93YprQnau4AmqqqKoYOHUpeXh7PPfcc06ZNa1JQjL2gWb8vLS3ljjvuIDMzk6SkJN5//32bFkX2+6qtn5xtU3MSt2/fzs8//2zTAumSSy7h0ksvpU+fPnh7e7u9R6crhmA78ZvNZlJTU0WH+5KSErEtKiqK0aNHM3z4cAIDA52aM62xFjFPT0+Kior46KOP+PvvvwFo06YNzz77LH369HEY6+o46vuMjAweffRRdu/eDcBNN93EK6+84vC33ZTyce4CidyJY0P3V4pj8yHFsBmQK8PT40IVwzlz5vDqq68SHx/PX3/9hZeXV7OIoclkYvr06ezcuZPWrVszZ84ch9+npojhtm3b+Pbbb4UZ0cvLi9GjRzNq1CiHlew/IYbWP1ssFtLS0ti4cSMbN26kuroaqBe9ESNGcO211xIRESHGNySGKhs3buSDDz4gPz8fgFtvvZUHH3xQiFVjxBDq7+XHH3/MrFmzUBSFLl26MHfuXJdmUymGFz5SDJsBKYanx4UqhldeeSUpKSn85z//4bbbbgOali7hSgxnzpzJjz/+iI+PD59//jmJiYluV5HgXAyzs7P58ssvRV1eX19fxowZwxVXXCF+P+2v758WQ/g/AampqWHz5s389ddfpKeni22jRo1i8uTJRERENFoMof6ezJo1i0WLFgHQrVs33njjDVq1atVoMYR6Ad6wYQPTp0+nqKiI0NBQPv/8cwYPHmxz/fY/gxTDCxEphs2AFMPG0ZQaog35AZtSb9T6fVPy7ZyJ4YkTJxgyZAharZatW7eK1Ys7f539e2sBU9//+eefIlfxtddeE50W7MfaR3taH7eqqopffvmFxYsXYzab0el0jB07lgkTJjhM+u5qntpvs8edGNrjTgSc+eAOHTrEokWLOHz4sPi/K6+8kmuvvdYmB7Axps+///6bd999l6qqKgICAnjhhRcYOXKk07HO3qsCnJ2dzbRp0zh48CA6nY6XXnqJ22+/3SF/saHP5uo+uMtJbM6apxL3nI153H1jL4nkAuaPP/4AYNCgQTZmvDPh8OHDvP322wDceeedNi2HGkt6ejovvvgiixYtwmw20717d2bMmMFNN90kSpid76hdNp5//nlefPFFLrnkEkwmE7///jsPP/wwa9asaVJ1nGHDhjFnzhwuueQSKioqePbZZ/nss8+adAyo9z/++OOPXH311ZjNZl5++WWee+65Bh8aJBK5MpQ45WJYGU6cOJGdO3fy5ptvcuONN4ptp7syLC0t5ZZbbiE3N5chQ4bw5ptv2hyroZVhZWUlP//8M4sWLcJisRAQEMA999xD37593Zpmm7oyrK6uprKykrq6Ompra6mrq0Ov1+Pl5YWnpyc+Pj4EBAQ4rE6asjK0X2kpisKuXbv47rvvRApIcnIy06dPJyYmRoxtyPQJ9cFuakH+cePG8a9//Qu9Xt+olaH1+88++4wZM2aI1JpZs2bh7e0tV4YXAdJM2gxIMWwcF7oYlpSU0LVrV8xmM1u3biUqKkpsOx0xNJvNPPLII2zZsoXo6Gj+97//ERgYaCOA7sQwKyuLGTNmiDJl/fv354477iA4ONjhnI0Vw6qqKo4fP86JEyfIysqiuLiYoqIiEeDiDg8PD0JDQwkLC6NVq1YkJCSQlJRESEiIQ8d5aFgMra91+fLl/Pzzz9TW1uLj48M999zDyJEj0Wg0DYqheqzFixfz7rvvYjabGTBgAG+++aZoceVsX1d+yuXLl/Pggw9SV1fHkCFD+PLLLx2OI8XwwkOKYTMgxdA1p9t38GyJYVP6GdoLxpIlS7jnnntITExk3bp1bsXGXsScieHs2bP56quv8PLy4tNPPxXFoq0Fz34lqL7ftGkTn376KdXV1QQGBnLXXXeJMmLOrsGVGJrNZtLT09m7dy+HDx+moKAAV3h6euLp6YmHhweenp6YTCaMRqNYLbr6sw8MDKRDhw5069aNjh07ClFprBiq587Pz2fOnDmi8kyfPn249957iYyMdBhrjZeXl/h5586dvPTSS9TU1HDJJZfw4YcfiocH+33diezmzZuZNm0aVVVVdOvWjXnz5tlE6LpbKTaUk9iUmqeyT2LzIcWwGZBi6JqLSQyfeeYZvv32W6ZOncprr712RmK4atUqXnjhBaC+puno0aPFdndiWFZWxldffSWKdnfs2JGHHnqIkJAQh7GuxNBoNLJv3z527drFkSNHqKmpsdkvPDyc2NhYYmJiCAsLIzg4mODgYBtRscdsNlNWVkZpaSlFRUVkZ2eTkZFBTk6OzT328PCgY8eO9OvXj27dutlM/A2JIdR/X3/++Se//PILJpOJkJAQnn/+edq3b+8wVsX6uj09PTl06BBPPfUUZWVlJCYmMnv2bLGya0pO4qFDh5g6dSrFxcW0b9+ehQsXCkGUYnjhIcWwGZBi6JqLRQwtFgu9e/cmLy+Pr776ipEjR562GO7Zs4dp06ZRV1fHjTfeyP33328z1pUYZmdn8/rrr4v2QxMnTmTy5Mli8mxIDE+cOMGmTZvYs2ePjdnTz8+PTp06kZycTNu2bUXlFlf3yB32k7XJZOLUqVMcOHCAgwcPUlxcLLYFBgYyYMAABg8eTGhoaKPEUCUnJ4cPPviA7OxsPDw8mD59OpdddpnTsfZiCHDy5Ekee+wxCgoK6NixI59++in+/v5NEkMPDw9SU1OZMmUKubm59OjRg59++gl/f38phhcgUgybASmGrrlYxHDHjh1MmDCBgIAAdu/ejZeX12mJYVFRETfffDMFBQUMGTKEt956y2EF6kwMt23bxnvvvUdVVRXBwcE8+uijdOnSxe0qsq6uDrPZzJ49e1i5cqXI4QMICgqiV69edO/endjY2CbdI3e4m7x1Oh05OTmiAk1lZaUYM2DAAMaNG+dyZeVMmAwGAx9//DG7du0C4Oqrr+bWW291KLDtTAyhvmvFQw89RHFxMd27d+fjjz+2+fttrC/y2LFjXHfddZSUlDBkyBC++eYbUT5PRYrh+Y8Uw2ZAiuH/0RSBO5OxTalN2hxJ96+88gpz5sxh4sSJfPTRR0DDuYPW1NbWYjQaefDBB0lJSSEuLo45c+bg5+fnYKa0fm8wGFiwYAELFiwAoH379kyfPl2Y9azHWouh2Wxm06ZNrFy5UqzGdDod3bp1o0+fPkRHR7tsPtzQPbKmocnaVTSpyWQiNTWVrVu3kpqaKrb379+fMWPGOFTIsTfRqu8tFguLFi3it99+A2DAgAE8/vjjNmJqva/9cVRBrKysZMCAAbz//vuNrlZjfY5Dhw5x4403UlVVxejRo/niiy9crnTPVoJ+Q8E2jd3WUpFi2AxIMfw/LkYxNJvN9OvXj5ycHGbPns0VV1wBNE0Mq6ur+fe//83y5cvx8/Pjs88+E6W9XIlhZWUl7777Ljt37gTg8ssv5/rrr7eZTO3F0Gg0smXLFhsR9PX1ZcCAAQwYMKBRBb//CTGE/xOIEydOsHLlSiGKXl5ejB8/nqFDh4p9XImh+vOGDRv49NNPMZvN9O7dm6efflqIlzsx9PT0ZO/evTz++OPU1tZy3XXX8fTTT4tt9mOdXb+6bdOmTUydOpXa2lruueceXnnlFadjpRien0gxbAakGP4fF6MY/vXXX0ydOpWQkBC2bNkizHBNEcO3336b77//Hp1Ox1tvvUW/fv3ENmdieOLECWbMmEFOTg4eHh7cc889DBs2zKVwWiwWNm7cyOLFiyktLQXA39+fYcOGMWjQIIfJr6liWFdXh9FoRFEUcb+9vb0dxOV0xFAlIyODxYsXC59odHQ0119/PUlJSQ2KIcDevXuZOXMmdXV1dO/eneeeew4vL68GxRBgw4YNoh/lyy+/zPjx45sshlCfdnHPPfcA8MknnzBp0iSHsVIMz0+kGJ4BsmtFw6LVlLGnK5xNqWPamO719j9PnTqVVatWcffdd4sIULAVPFcpEAC//fabKLX2r3/9i0svvdRmrH0O35o1a/j000+pra0lLCyMBx98kISEBKdja2pqSE9P57fffhMFuYOCghg6dChdu3YVk7C9ODurnVpZWUlBQQEFBQUUFRVRVlaGwWDAYDC4rLai1+vx8fHBz8+P0NBQIiIiCA8PJyIiAm9vb5sJ2p2YqNstFgs7d+7kr7/+orq6Go1Gw2WXXcZVV11lIyLWombtIzx8+DDvv/8+tbW1dOnShaefftrGf+fOn/jVV1/xzTff4OnpyezZs+nWrZvD9bl6b/3zzJkz+eSTT/Dx8eH333+nU6dObuuYuhPHprSGclcX1tn2xm5rKUgxbAZa8srwYhfDzMxMBg4ciKIorFq1iqSkJLG9MWK4c+dOpk+fjslk4o477uCOO+5wWN2pAqcoCr/99htfffUViqLQtWtX7r77bpvJ3FoMy8vLWbBggTCjenp6ipWgh4eHzTU5E8OKigpOnTpFRkYGGRkZlJWV0RjUidPdd63RaIiKiiI+Pp74+HjatGnjIETugmRMJhNLliwRxcZjY2O5/fbbCQ8PB1yLIdRHis6YMYOamhp69+7Nc889J0TEnRhaLBZeeuklNm3aRKtWrfj+++8bHVBj/bPZbObOO+9k/fr1JCQksGTJEkJDQ8V2KYbnJ1IMmwEphq7fN2Xs+SiGTz/9NN9//z1Dhgzh22+/tRnbkBgePHiQBx54gKqqKkaMGMHLL7+MRqNxKoa1tbV88sknoh/fmDFjhP/JfqzFYmH9+vUsXrxYrJ769evH8OHDbYTTmRgWFxdz9OhRDh8+7NDlXqPREBISQlhYGGFhYYSEhODn54ePjw8+Pj42E76iKBiNRmpqaqiurqaiooKioiKKi4spLCx0EFY/Pz+6dOlCly5dRE1Xd2KoitT+/ftZsGABBoMBb29vbr75Zrp37+5WDL29vTl48CAzZszAaDRy+eWXc++996LRaNyKoXqf7rrrLrKysrjyyit59dVXnV6f/Xv7bRUVFVx55ZVkZWUxZcoUZs6cKbZJMTw/kWLYDEgxdP2+KWPPNzE8evQow4cPx2w2s3DhQnr27Gkz1p0YHj16lLvuuouysjL69OnDjBkzxMRrL4ZZWVm8/vrrpKamotVqufXWWxk7diwajcbBLJqamsp3330n/GoxMTFMnjyZuLg4h+Oq11RXV0dKSgp79uwhJyfHZkyrVq2IjY2lTZs2tGnTBi8vL4d70tAK0Bp1slZXnadOneLkyZM219a6dWv69+9Ply5dbPZ3JoZQX7/1hx9+EKkhEyZM4IorrhD7OhNDqE9Hef/991EUhdtvv52JEyc2KIZeXl7s37+f+++/H4vFwsyZMxk2bJjD9dm/d2YC3rx5M9dffz0AP/30E0OHDgWkGJ6vSDFsBlqaGJ6J4DV2bHPmJDamR6GKdWDJtGnT+P333xkxYgRz5851MDW6SmsoKSnh9ttvJysri06dOvHhhx/a7GcwGMTPWVlZvPLKKxQUFODv78/DDz9MYmKiw1iLxcLq1av5888/MZvNeHt7M3bsWLp16yYmPXsxzM3NZffu3Rw+fFhcu1arJTo6mri4OOLj40VbJOv70NDDhTUNRZN6eHhgNps5deoUx44d4+TJk+L4YWFh9OvXjw4dOqDVat2u9jw8PFiyZAmbNm0C6ruGqAUHXIkhwLJly5g/fz4ajYbHH3/cwV/rShznzJnDDz/8QGhoKD/88ANBQUFufZ72oqpue/HFF/nuu++Ii4vjr7/+ws/Pr0ExbEpOYlPqmLoTTntaojhKMWwGpBi63nahiuG+ffsYO3YsAH/++SedO3dulBgaDAYefPBB9u3bR+vWrZk9ezahoaE2Aqj+fOjQIWbMmEFFRQVRUVE888wzREVFOYwtKChg3rx5YmV0ySWXcM011xAQEGCzclSvp6CggC1btnDo0CFxbwIDA0lOTqZjx474+vo6RJOeTTG0/tlgMLBv3z5SUlLE/QwLC2PEiBGiNiu4Xu1t2LCBJUuWoCgKnTt3ZurUqQ5/c9b7KorC999/z19//YWXlxfvvfeeTccLV2JYW1vLtGnTSE9P5/LLL+ff//73aYlhZWUll19+OVlZWdx33328+OKLUgzPU6QYNgNSDF1vuxDFUFEUJk2axPbt25kwYQIff/wx4BiEYi+GdXV1PProo2zbto2AgAA++eQTEQVqL3Dr16/no48+wmQykZSUxJNPPklQUJDD2HXr1vHjjz9SV1eHl5cXV111Fb179xaTlbUY5uTksHbtWo4cOSL+Lz4+nl69ehEVFWUzwZ0rMVSpra3lwIED7Nq1S9zHrl27Mnz4cHx9fd2u9g4cOMD8+fMxGo106NCB6dOn2wiVs1Xl66+/zsGDB0lISODtt98W4uXObJqWlsZdd92FoijMnj3bJh3G/vO4EkOobzJ8xx134OXlxfr164mLi7MZK8Xw/ECKYTMgxdD1tgtRDH/55RceeughfHx8WLNmDa1btwbci6HBYODZZ59lzZo1+Pj48P7779O5c2eb7So//vgjX375JVDfdum+++6zmUwNBgN1dXXMnz+f9evXA9CuXTumTJniUDe0urqa6upq1q5dy/bt28Vn79ChA7179xYdHdzVSlXvQ01NjSi2XV5eTmVlpehKoY7X6XTo9Xr0ej2+vr4EBgYSEBBAUFAQQUFBTepE4eHhQU1NDevXr2f//v1AvTiNGTOGXr162Yy1F63s7GzmzJkjUijuu+8+cXz7sT4+PpSUlPD0009TXl7OFVdcwbRp05yOtTfVzpgxg99++40OHTowb948l4XF3YmhoijcdNNNbN26lZtvvpn33nvPZqwUw/MDKYbNwMUuhk0RtDPZtylj3SXdu+tZ6Cy/zpqioiKGDRtGfn4+Tz31lJg0wXWlGEVRmDFjBr/88gseHh68/fbbJCcn24w1GAwoisIPP/zAzz//DMDYsWO5+eabHYJkTpw4wddff01OTo7Isxs+fDhardZGVBVFYevWrWzatEmYaWNjYxkwYABhYWFuUyuMRiPV1dXk5eVRUFBAfn4+VVVVnAkeHh6Eh4cTHh5O69atHcTRXQHt3NxcNm7cSFFREVC/Shw5cqQQFfuHAB8fH9LT05k7dy5Go5EuXbpwxx13oNPpnI6FetP3O++8A8Djjz/OwIEDnQqn9fWVlJRw8803U1lZybPPPsvkyZOdfp6GEvT37NnD5MmT0Wq1rFmzxqbLxtkSQ5mg3zSkGDYDUgybZ9/zQQyfeOIJvvvuOxITE1myZInNhO1KDL/88ktmzZoFwKuvvsrw4cNtRAvqfUeff/45y5YtA2Dy5MlMnDgRjUZjI0KHDx9mzpw5VFdX4+/vz7XXXmvjS1OPW1paypIlS0RUaXh4OP379xcl3sB5aoXRaCQjI4O0tDTy8vKwx9fXF39/f/z8/PDz88PDw0OsBDUaDWazGYvFIsS0qqqKqqoqKioqHO5lcHAwSUlJxMfH4+3t7VYMoV4Etm/fzvbt2wGIjIxk0qRJBAUFuRS41NRUvv76a0wmE/369eOmm24SQUH2YwEWLlzIokWL8PPz47333qNNmzYux6rXt2DBAtH38LfffhPHb2qHi3vuuYfly5czceJEPv30U5vPbX8fVKQY/nNIMWwGpBg2z77nWgxXrlzJlClTAJg/fz59+/a1GetMDBcuXMjrr78OwEMPPSRC6a3F0Gw289Zbb7F27Vo0Gg233XYbo0aNEttVMVy3bh3z58/HYrGQkJDA7bff7jD5VVVVsXfvXlauXEldXR0eHh4MGTKErl27Oi0OrpKfn8/hw4c5ceKEzf0JCQkhKiqKkJAQQkND8fT0bPB7cdYpwWKxUFZWRklJCfn5+eTm5or9NBoN8fHx9OjRQ/hFwXW90YyMDJYvX051dTU+Pj5cc801Ng8EYCtaaWlpfPHFFyiKwrhx45gwYYLLsR4eHvzrX//i+PHj9O3blxdffNHm8zgTQ5PJxK233kpmZibTp09n6tSpQNPF8MCBA1xxxRXo9Xq2bdtGq1atACmG5wtSDJsBKYZnfhz77Q1NyE1pOeSsxJqKdTL6yJEjyc/P58477+TFF190WSlGZcmSJbz00kvCJ3THHXeIbWp7IpPJxAcffMCmTZvQarVMmzbNoSN9RUUFixcvFv7Brl27MmHCBBF9qVJbW8sff/zB8ePHgfp8vcGDB4vfOWel2goKCjh27JjNKtDf35/WrVvTunVrp6kVDeUZWk+O9pOzOpHX1dWRk5NDdna2qJUKEBcXR6dOnQgMDHRbb9RkMrF06VIKCgrQ6/VMmjTJJuXEWrR8fX3ZsmULixYtQqPRcPfdd9vcY+uVoo+PD6dOneJf//oXZrOZJ598kkGDBjk9rrUJdfny5bz55psEBQXxyy+/4OfnZ3O99v5QVzVQr7/+erZt28YjjzzCU0895XTfpuQZnm67p4bEsCWK49mYx7UND5FIzh8UReHZZ58lPz+fdu3aiUnKHXv27OE///kPiqIwYcIEbr/9docxJpOJ9957j02bNqHT6XjooYcYOHCgw5hvv/1WCOHll1/ONddc4zBBFhYW8vXXX3P8+HG0Wi2DBg3i6quvdvlHW15ezoYNG9iwYYMQQlU8hw0bRtu2bR3Mic2Jp6cn8fHxXHrppQwdOpSoqCigvmXSihUr2LNnj8t6pwABAQFMmjSJuLg4TCYTCxcu5PDhwy7HDxgwgP79+6MoCt98841TE7BKXFycWD1+/vnnVFRUNPh5Ro0aRWxsLGVlZaKd1umgriq/++47h0INkouPFiOGs2bNIjk52cGcJrmwmD9/PkuWLEGv1/P+++87BFXYk56ezmOPPUZdXR1Dhgzh8ccfd3haNpvNfPjhh2zZsgW9Xs+jjz5Knz59bMaYTCa++OIL9u3bh06n45ZbbmHUqFEOx8rMzGTevHmUlpYSEBDA5MmT6dWrl8PTPdSvig8dOsSyZcsoKChAq9WSlJTEiBEj6NOnD6Ghof/4k31ISAj9+/dn5MiRwkeXmprKn3/+SWFhocv9PD09ufLKK2nfvj0Wi4U//viDY8eOuRx/1VVXkZiYSG1tLV999ZVDxKw1EydOJDo6mrKyMn788ccGP4NOp+POO+8E6qOB7a0GjWXMmDFERUVRVFTEmjVrTusYkguHFiOGDz74IAcPHhQOf8mFR2pqKi+++CIATz/9NF26dHE7vrCwkIceeoiysjKSk5N5+eWXHUxXal7axo0b0ev1PP300/To0cNmjNls5osvviAlJQW9Xs+dd97pMAbq/WE//fQTtbW1tGnThuuvv16ssuyprKxk5cqV7NmzB7PZTGRkJKNHj6ZHjx74+fk1/qacJUJCQhg0aBBDhgzB29ubiooKVqxYwd69e12a0HU6HaNHjyY5ORlFUVi8eDGZmZlOx+r1em666Sb8/PzIyspi8eLFLq/Fw8OD2267DaivUuPqmNaMGjWK1q1bU1JSwp9//tmIT+z8vBMnTgRwe32SiwPpM7zAaU4/YFPGnq7PsCn1Rq2DTOrq6hg3bhz79+9n8ODBfPfddzbb7X1wBQUFTJ8+nSNHjhATE8N7771HcHAw8H9BMIqiMHfuXBYvXoxGo2H69On069dP+BCh/vflu+++Y9++fej1em688UbatWsntqvHOnLkCH/88QcWi4X4+HjGjh3rsNpRrzErK4stW7ZgNBrR6/V06dLFJtHe3iTnLpCorq4Og8FAdXU1ZrMZk8mE2WxGo9GIyFIPDw98fHzw9fW1WaHam3ddtV0yGo0cPnxYiFBUVBRDhgwRvjVnKQ/Lli0jLS0NLy8vbrnlFsLCwgAczL0nT55k7ty5ANx33302rZjsx86aNYsdO3bQs2dPnn32WRufoX0Eq7e3t4gsbdOmDQsXLnTZfNhdQM2BAwe46qqr8PHxYc+ePQ5zRlMCaP4Jn2FLyUmUPkNJi+Wtt95i//79BAcH8/777zs1O6qYzWb+/e9/c+TIEYKDg3n33XeFEFqzaNEi8cR/9913O1QtURSFX375RZhGp06daiOEKunp6SxevBiLxUK7du244oorHIRG5ejRo6xfvx6j0UhwcDDDhw8nPj6+0ZOUoihUVFSQlpbGnj172LlzJ4cOHeLEiRNkZGSQk5NDfn4+eXl5ZGVlcfLkSVJTU9m3bx/bt2/n4MGDZGZmNskH5uHhQZ8+fejduzdarZa8vDxWrlzp8ACiotVqGT16NFFRUdTW1vLLL7+4NFUmJyczYMAAoN6k6e66pkyZgk6nY/fu3SLx3x3jxo0jKCiI7Oxs0WGkqXTv3p24uDiqq6tZsWLFaR1DcmEgxVBy3vP333/zySefAPVd6F2ZHlU++ugjNm7ciKenJ2+//bZNfUuVnTt3ijZPU6ZMcSgKDbBx40a2bduGRqNh6tSpXHLJJQ5jysvL+eOPP1AUhQ4dOjB69GiHFYFKWloau3btAiAxMZGhQ4c2OjDGZDKRnZ3Nrl272L9/P3l5eUKMvLy8CAkJISIiglatWhEdHU2bNm2IjIwkNDSUgIAAdDqdSKnIyMhg165d7Nu3j4KCAoeIXlfExsZy6aWX4u3tTVlZGStXrnSZ/O/h4cH48eMJCAigtLSUZcuWubQ2jB8/npCQEEpLS90KTps2bUSay88//9yg9cLHx0eYORcuXNiYj+iARqMRATzLly8/rWNILgykGErOawoLC3n44YcBRLskd/z22298/fXXALzwwgs2ZdZUMjIyeO+991AUhTFjxjg95smTJ0WwxuWXX+5QpQbqV6C///47NTU1REVFicozzsjKyhL+6o4dO9K1a1e3q1sVi8VCdnY227dv5/jx4xgMBrRaLREREXTs2JHevXvTs2dPOnbsSNu2bYmPjycmJobY2FgSExPp0KEDnTt3pk+fPnTr1o3ExERhViopKeHQoUNs377dJtfQHcHBwQwdOhQ/Pz8qKytZs2aNy1Wfj48Pl19+OVqtlqNHj7Jnzx6n49Q6rlCfP5qfn+/y/JMmTUKv13P48GH27dvX4PWOHz8ejUbDtm3bGuVrdMaYMWMAWLNmjYwqvYjRNzxEcrFgb4prSu+7M/E3NqU2qbU/rLa2locffpiCggI6duzIU089ZTMZWU/C1dXVpKSk8J///AeAW265hcGDB4vVk/pveXk5r732GgaDgU6dOjFlyhSHybywsJDPPvsMk8lEx44dGTBggNjfeuzq1avJycnBy8tL+Ait/YTq2NLSUtasWYOiKMTExNCpUyeX/Qytfy4vLyctLU2c29vbm4iICJvSafbndJdnqNVqRV3S2tpaSkpKKCoqora2lqNHj5KZmUl8fDxBQUFu80G1Wi2DBw9m/fr1VFRUsHz5ckaMGCFMw9Yr46CgIDF2zZo1JCYmCv+h9dh27drRtm1bjh8/zs8//8w999zjYGquq6vD39+f4cOH89dff/H9999zySWXoNFoHPyqqi86MjKSvn37sm3bNn799VceeOABt4Ue7N9bLBa6du1KVFQUeXl5bNy4keHDhzu9383pZ7f+3s4krMPd3/HF4j9sLuTKUHLe8vnnn7NmzRq8vLz473//6zaNorCwkOeffx6TycTw4cNF9KE9n3zyCfn5+URGRvLoo486VBSB+ojF4uJiwsLCRI1KZ+fbtm0bACNHjrSp1mKNoigiWCYsLIyePXs2ahLKycnhwIEDVFdXo9friYuLo3PnzkRFRTm95qbi5eVFTEwMXbt2JSYmBp1Oh8Fg4NChQ5w8ebLBCdjX15fBgwfj6elJcXEx27Ztc7lPjx49iI2NxWQyuTSXajQaxo0bh1ar5eDBg6Smpro89/jx49Hr9Rw8eJCjR482+FnVVeeSJUschLAxqD5QQPoNL2KkGErOS3bs2MFbb70FwMsvv0zHjh1djjWZTLz44osUFxeTlJTEiy++6FTANm7cyObNm9HpdDzyyCMEBAQ4jCksLGTLli0A3HDDDQ5RitbXB5CUlORQfsyaEydOUFJSgoeHB/369XPpT7QmJyeHEydOABAREUGXLl2IjIw8K0/yWq2WVq1aidWPev79+/e7TbSH+uo4AwYMQKPRcOrUKVFtxx6NRsOoUaPQ6XScOnXKpYBFRESIQgfuRCc0NFSMU+vHumPAgAEEBgZSVFTE7t27GxzvDNWnvHHjxtPaX3L+I8WwBaPRaGxep4uiKG5fFotFvMxms83LZDLZvIxGI/n5+dx7772YTCbGjRvHddddR11dHbW1tU5fH3zwAXv27MHX15eXX34ZjUYj2iWpr4KCAubMmQPAFVdcQevWrZ0e6/fff8dsNtOuXTvi4+OFGVJ91dXVUVpaKvxVXbt2FdvsP0tNTQ179+4FEGKunqeurs7mpf7/qVOnhBBGRUURExOD2Wy2ucaamhrxcnVPnI119zKZTLRp04aEhAQ0Gg1FRUXs2rWL8vJyt+fx8/MT+Z47d+4kPz/fYYza37F79+4ArFq1iqqqKmprax3u76WXXopWq+XYsWMcOXLEZpv1vR02bBhQL07FxcUO9976d0yr1Yrxy5Yts/l9dPY7ab1N/R3u378/Go2G1NRUcnJynP6eN/R3cbp/U5J/BimGkvMKRVF48sknycrKIj4+ntdee82tUK9fv15EhT799NMOzVhVvv76a8rKyoiJiRFmM3sKCgqE6VMNmnBGSkoKZrOZqKgoUcDZGWlpaRgMBnx8fGzaALmioKCAtLQ0oN7X1aZNm3NSgaZ9+/bo9XoMBgP79+9vsIJLu3btiIqKwmKxsHPnTpfRqT179sTPz4+ysjKXwTQhISH07t0bcB+9qa7ITSYTq1evbvBzWQfBnE5FmqCgICH6cnV4cSLFUHJe8e2337J8+XI8PT358MMPnZoyVSorK3nzzTeB+jZLl112mdNx2dnZbNiwAYBp06a5zAHcs2cPFouF9u3bEx8f7/K8qmA15P9LT08HoFOnTg2aR6uqqoSZMSIigujo6HMW4KCu9ry9vamrq+PYsWNu0y80Gg29evXCw8OD0tJSTp486XSch4cHgwcPBupXka78d8OGDUOj0bB//37RM9EZqh9v7dq1Da6gunfvTmRkJFVVVeKBp6moptnT3V9yfiPFUHLesH//fl555RUAnn/++QbLrf33v/+loKCA2NhY7rnnHpfjlixZgqIo9OjRw+0KTRWvDh06uBxjMpkoKCgAIDo62uU4tQO9RqOx6VvoDEVROH78OIqiEBISQkxMzDmP9PP29uaSSy5Bp9NRVVUl7o0rrFe/e/fudSmel1xyCX5+flRVVbn1Hap+WNV/64wBAwbg4eFBVlZWg9en1WoZMmQIUN9+63To2bMnwGn7HSXnNy1GDC/WQt3N5fdrKk3xlbjzz6j+oNLSUu6++25qa2sZMWIEt912m4Nfzfq1fv16kUj9xBNPoNFobLarvqOKigpWrlwJ1JvK7P1Jqo/IbDaLFV9sbKxT/5HFYhFJ6t7e3gQEBLj8bOrkHBkZiVardTivtX/r1KlTVFVVodPpRNSlvZ/S1ashn6G7sfbHsj6nmt6hmp0zMjLIy8tzeg51n/j4eDw8PCgvLyc1NdXp9SuKIh5y9uzZ4+AzVF+q8GzZskV8n/bfm6enpxi3Zs0ah+3237G6Kl23bh0mk8nBL9jQS61He+jQIaqqqhq9X2P8i2cLd+c9V9d0vtJixFAW6j6/eemllzh+/DitWrXinXfecSvsRqOR1157DYCrr75a+JicsWHDBgwGg4iYdEVRURFVVVXo9XqHjurWqAnh1rVEnaF2tXe3eoT6gBrVrBgTE+NQJ/NcExwcTHh4OFBfKN1daoJerxfl6g4ePOhygu3SpQtarVaUjnNGcnIy3t7eFBcXi4cUZ6j9DTdu3NjghN6jRw98fX0pKiri0KFDbsc6o1WrVrRq1QqLxSICoyQXDy1GDCXnL6tXr+aHH35Ao9Hw/vvvExoa6nb8H3/8QXZ2NmFhYUybNs3tWHWF1rdvX7cVX9SyYgEBAW7z+NTmt+6usby8nLKyMjQajdsAG4Djx49jNpvx9/cXonO+ER0djbe3N0aj0W3vQYCEhAR0Oh0VFRWUlJQ4HePn5yd8sq7yCT09PcUK0p1w9ejRAw8PDwoKCsjKynJ7bZ6enuLBaefOnW7HukKNiD1w4MBp7S85f5FiKDmnlJaW8uSTTwL1xbLVos2uMJlMosvBzTff3GBtT3XlERkZ2ajracjUrDaXdVcpXy37FR4e7nalV1RURFFRERqNpknFuu2xWCwYDAbKysooKioiLy+PvLw8iouLqaiooLa29ozMYFqtVqxws7Oz3QbTWK+sMzIyXI5LSEgAcLvqU9NR3CXWe3p62vgqG0IVM7VGbFPp1KkTUL/ylVxcyHJsFxlnUkbNHe6OYz85umvTZF867JlnniE3N5fExESeeOIJm7ZM9i2QjEYjS5cuJSsri5CQEK644gqRGO6qxJa6kgkLC3M7ibv6fPb/X15eDtSvblSfk/3nVEUgKirKJnHd+vPU1taKVVHr1q3R6/Viu/U9UMdao57HaDRSUVGBwWBwev3WKQQ6nY6QkBC3Dw/u2gaFhoZy6tQpjEYjhYWFNsUI7JPz27RpQ0ZGBhkZGSQnJ9t8N+rPavH0rKwsDAaDaKtkPVYNosnIyKCiosKhApE6Njk5mYMHD7J3714uv/xywHWJNbVFlOqv1Ol0bksE2h9HrVHrzgzcGJpSju1MjtuU4zTXNVyoyJWh5Jzx559/snjxYnQ6HR988IHLai/WLFq0CIAbb7yxUeNVs6azFk5NRVEUysrKANcrw8rKStER3l13jaysLOrq6vD09GzQr2hPXV0d+fn55ObmikAOnU6Hj48P/v7+ov6on58fXl5eaDQazGYzhYWFFBYWNrpLhTVarVasrt11vId635pGo6GyshKDweB0TGBgIMHBwVgsFpcFtIODg4mKikJRFLfRomox9sYIVNu2bfH19aWqqsrtqtQVqhgePXq0wQo9kgsLKYaSc0JFRQX/+te/gPrcP2ed4+0xmUwcPnwYQFQUaQhVBF35r1TUPEB3QlFRUUF1dTUajcalz1A16bVq1cqlWFdUVJCdnQ1AfHx8o0q0qddWUlIiojqhPgUiLCyMqKgo0a7J19cXX19fAgMDCQ8Pp1WrViJf02AwkJube1oTuXVzZHei4+Hhgb+/P4BNo2R71ILd7r4b1eTqzlcZFxeHRqMRvlp36PV6YVZ1V//U3bl8fHxEtSDJxYM0k17knG71+4bGujMlueter/48Y8YMcnJyiIuL44EHHhD/72ysyrFjx6itrSUgIIDo6Ggbc6K9SUc180VHR5OZmUl+fr4QHWfmH3W8u44GqoCFhoaK/oDW12gwGMRqIykpycHMW1dXh8Vi4dChQyiKIlZvarkzFXuzqJrqUFJSIq7Py8uLgIAA8Vnsz2X/uXx9ffH09KS0tFTkSrZu3drmXrj7TtV0ErVDRHV1tTBbOjMz+vn5UVFRQUVFhc126+OqAl1aWirG2F9DREQEUO/7tb8mdR8PDw+ioqLIzc3lxIkTdOvWzW0nirZt25KSkkJqaqqDqdvZ57FGo9HQrl079u3bx5EjR2xyUmV6woXNOV0Z7ty5k7vvvpuAgIAGAydUsrKyuOaaawgKCiIqKoqHH374tMorSc4d+/bt46uvvgLg1VdfdduNwhq1hFfnzp0b1QsQ6v1xALm5uW7HqRGk7lIHcnJyANfmz8zMTEwmE35+fm7HqDmFzpoO26N2ti8sLBR1NoOCgggODm70ilLF09OT0NBQNBoNRqOxwdWyPVqtVqx21UAiV/j5+QG4bP4L/2dqVk3ZzrAWQ3eohQ3cBe2oqL5IV4XFG0JdWR47duy09pecn5yzlWFtbS333nsv9913HxqNplFVHcxmM1deeSWtWrUiJSWFkpISrr76agwGA1988cU/cNWS5uCdd97BYrEwceJEhg4d2uj9VF9VU3xs6tiGGruqq0xXAqMoio0J1B6TySRSABITE52uPgsLC8VkHR0d7bIsnPUxCwsLxcOej4+P8LOdLnq9nuDgYEpKSqioqCA4OLjRDxZQb5Y1GAwNNrlVH3DcjVODedR+jc4ICQkBaND8qZpTGxJNqP9+gNM2c6q5lKfjc5Scv5yzlaGXlxc7d+7k3nvvFU+RDbF8+XL27t3LnDlzSEhIoGfPnrz++ut89dVXokSW5Pxm06ZNrF69Gp1OxxNPPNGkfa3D+xuLWkGlITFUhda68aw1OTk5FBYWotPpxGRozf79+6mursbHx4ekpCSH7ZWVlWIl0bp16wZzKaurq8nOzqampgaNRkNwcDAhISFNEi5XeHt7i5Wwu5WbOxqKNFTNx+5yNlWzorvPpD4wNNSHUDW5NubzqKv2goKC0zJtqqvQhvIaJRcWF5TPcOPGjSQkJIgcJahvrGo2m9m6dSvjx48/dxd3kdFQR3pnKQWu3qsTo8ViEZ3ob775ZuLi4hzSCNytetRE7ZMnT6LRaGwmUfsJVX2vtiQqKyujoqLCaRSooijiYSo8PNzm+tVrV020SUlJovQb1KcvVFVViZZOnTp1EiXA1BWP2Wxm9+7dWCwW/P39iYqKcjDtW6+OSkpKRAqHXq/H398fvV4vztmU4BdrMbIWMG9vbyorK6mqqhIPo40RhsaKh3oP3Ymh+l27E0N1pe5MDK2vRQ3YUX2U7lIXVNNrXV0dZWVlDmb6hjrSq6vQzMxMt/dD+hAvLC6oaNKcnByH5Onw8HA0Go1Ln1BtbS3l5eU2L8m54c8//2Tfvn34+/vzyCOPNHl/1byVnZ3d6O/R29tbrATc+ZPUaEVnVWDUDvCAQ5NhRVHYsWMHZrOZ0NBQ4aNUsVgsHD58GIPBgF6vF+LsDIvFQmFhofhsPj4+hIWFNUtne3tU319tbW2Tur+rE3xjV4bu/JrqeRsjhg09AKiC7i56VcXDw0OszBuqqOMMdWWYnZ0t0ysuIi4oMXSG+kfp6ilsxowZIu8qKCiowQ4CkrPH999/D8DUqVNPq/RYSEiIMEG663Vnjzrxu5r06+rq2L9/P4BTE+e6deuoq6sjIiLCoW7pgQMHyMnJQafT0blzZ4fozEOHDokqM4mJiS79hLW1tWRnZwszn7+/P4GBgWct8Vmn04ljN8UHqa5gGwp6si5O0NAYdVXnDDVPsaGc0qbeJ9VCcDpm4vDwcLRaLRaLxW2LKcmFxQUlhlFRUQ6+wcLCQhRFcRm999xzz1FWViZejYk2kzQ/ubm5rF27FoDrrrvutI8zadIkoD75vrFmKHVCdTWB7927l5qaGkJDQx38gbm5ucIEOmrUKJtJNzs7W9So7NOnj40JVg24UYWwc+fOTid9RVEoLS0lNzcXs9mMXq8nNDQUf3//f6wCSGPPY93Nwl2fSbPZLCJVXflgASEk7krlNbZogmpCbmyhc/V34XQi0XU6nVhZSjG8eLigfIaDBg3izTff5NSpUyIwYvXq1Wi1Wvr37+90Hy8vL1HqSWKLO79KQ+WimuIzNJvN/Pzzz1gsFvr06UN8fLxLIbM2mdmb2HQ6HePHj+eTTz4hLS2NgwcPivJa7kxt6mrGx8cHRVEcrk9t1tq7d2/MZrOY8BVFYdWqVUC9eTQsLExENdbU1LBq1SoURSE2NpbIyEix0lEUhbS0NBHZqK4IrauxGAwGLBYLpaWlYnWi5g6aTCabSdr+et09BNjfB+t97e+ntcnTvgWYMx+s9SrN+sHC/rjl5eUoioK3tzeBgYE2261/Li4uBuofctXzWZ9Xo9EIMQwJCXEQbev36nemVtxxh6IoYk5wF8mqjnVGaGioqOjT0NjGbm8OWloJtebkvF4ZlpWVodfr+eabbwC44oorSE5O5sEHHyQvL49Dhw7x0ksvMWXKFLelryTnHlVUrr766jM6jr+/v+hwrvYpdIfBYBBi46wuZ0ZGhojy7NWrl822HTt2kJ2djU6ns8mDNRqNrF69GoPBILrCqyiKQmpqqohejYuLIygoyOG8dXV15OXliWvz8/MjMDCwWaJFG4P1w0xjz6kKkzuzJvxfPqbqz3dGVVWVeLBwtzJULUFqioUrVKFu7IOvuoJsKEXEFXJlePFxTsWwR48e6PV6PvroI3bu3Iler0ev14sJQn2KV/9w9Xo9S5YswWQyERcXR//+/Rk2bBizZ88+lx9D0gjUScOZT66pDBw4EED4+dyxc+dOzGYzUVFRDhOqoij89NNPKIpC9+7dbfyYWVlZ/PXXX0C9RUI1C5rNZtasWUNRURGenp707dtXBLhYLBYOHjwoUj9iYmIczISKolBcXExeXh4mkwmdTkdERAR+fn7/6FO9KgIeHh6NEkO1QDc4DzJSsW6SrEb/OkPN2YyOjnbrD1QfVKwjyJ2hCnBDLbNUrMvZnQ7W5e0kFwfn1Ey6c+dOp6YDdXIJDg4WleVVEhISWLp06T92jRc6p1uCraHUCmvzm7u0CxVX5i5XKRHutqmm0bS0NGpqavD29na4XvX6Nm3aBNT79NTIP9UEuXv3bo4ePYper2fEiBFiYisoKGDBggVYLBbi4+NJTEwUIft///03eXl56PV6BgwYgKIolJeXYzabSUlJoaKiQrRk0uv1NpVaKioqKC0ttREiX19f0dlexT5C0V03AXemQ3ucmRX9/PzEfbX+O7O/92qBbz8/P0JCQmwiXK2DgrKzs6mrq8PPz4+YmBi0Wq3NWPVnVQy7du1qs936GkpLSykqKkKr1dKhQweHa7L+PGrOX2xsrIPJ136sRqMR33Vjc5ztUQVciuHFwzldGep0OrEatH5Zo9frpR38AkcNEgGcmgybSlRUFGFhYZjNZre97mpqakTfuj59+jhs++233wAYMmSICNCwWCysWLFCVGcZNGgQGo1GpFBkZ2ej0Wjo16+f2MdoNLJ//34hhElJSQ4BH9XV1RQWFgoR8vHxsRGifxKLxSKuo6F+kFD/YKGuvKKjo13+PSqKIkqctWvXzuVnKywspKCgAK1WyyWXXOLyvGpR9oSEBLcrOEVRhFm6sdWJrP3Ip0Njys1JLizOa5+h5OJBNStt3rz5jI+l0WiEn8ldXcvFixdTU1NDVFSUyFGE+slz3rx5lJSUEBoayuDBg8X/L1u2jPT0dHQ6HVdeeSWenp4oisLWrVtFQ9cePXoIU6HBYGD37t2Ulpai1Wpp27atTaSloigUFRWRlZWF2WxGp9MRHh4uil6fC9RcPA8PjwZLwkG9CdJoNOLl5eU2OvTkyZOUl5ej1+tF/U9nbN26Fag3mbsTYzWwyZ1gQv1qtKKiAr1e3ygxVBRFRLue7sOZ6ps8XZ+j5PxDiqHkrKPRaJg2bRoA77777hkXVlcURdSVdJU3WlJSwq+//grUV7uxFp4NGzawd+9edDodU6dOFcEUGzduFBP1mDFjiIyMxGKxsHHjRo4cOQLUm2jVcxYVFbF7926qq6vx8vKiffv2NsElRqORzMxMMfH6+PgQHh7eKAE6WxiNRmHacxahaY91f8a2bdu6XO3V1NSINJOuXbu6DGTJyckRfkBXEeBQXzf05MmTDsFLzlDrGrs7rzXFxcUYDAa0Wq1DkYTG0lB+s+TC44JKrZCcGQ2lS7hqtQPuWxs1NCFoNBruuusu5s6dS1ZWFt9//z1333034BiWb31cV9U9CgoKROeH6OhoFEVxaGH0448/UlNTQ9u2benbt69YQWZmZooGwWPGjCE0NJTi4mIOHz4sAmb69OlDZGQkxcXF/P3332RkZKDRaOjRowf+/v6UlJSQn5/P0aNHURQFX19fEhISbApYV1VViRxYjUYjVouqec6+DJ2zbvAq7vyq9vfPfqy18Or1ehthtl8VWefoeXt7YzabhfmxdevWNhHb1qLj6enJrl27MBqNBAcH061bN5vrUI+rKAobNmwA6oXLWbFy9b1qQejbt68wOTtzocD/lcrr16+fuB/u/IvqZ4qKimpUKoYz1ONLMbx4kCtDyT+Cj48PTz31FAAffPDBaTVWVVH9hG3atHG6yjpx4oRI5bjpppvEZFdZWckXX3yByWSiQ4cOIio1LS1NVLTp2bMnnTt3xmw2s2HDBlGkoVevXsTExKAoCidOnODIkSMoikJgYCBJSUk2EaWqT0xRFFH663SjFpuTyspKamtrReFvd6jd5WtqavD09HRanFzl1KlTnDp1Co1GQ58+fVyuHo8cOUJWVhYeHh4MGTLE5fHy8/NFpPDw4cPdXmdxcbH4fejbt6/bsSrqd9qYFloNcSYdRCTnF1IMJf8Y1157Lb169aK8vJzbbrvNrb/PHX/88QfgmBcI9WbAmTNnYjab6dWrF507dwbqV2Kffvop+fn5BAUFcc0116DRaDh27Bh//PEHFouFjh07ctlll1FXV8eqVatIS0tDo9HQs2dP2rRpg9Fo5ODBgzZtmOLj48XkX1NTQ3Z2tvDJ+fr6nlbfwbNBbW2tuN+BgYEN1jvNyMgQ5lFrsbenpKRE+PY6duzoshtHSUmJqEA0YMAAlxVsFEVh0aJFWCwWunTp4lD+zp6lS5eiKArJycmNLvGnriTt68w2haZWvJGc/0gxlPxj6PV6/ve//xEfH09mZiavvvpqk49RUFDAmjVrgP8rzWbNvHnzSE9Px9/fn3vuuQeof3r/+uuvSU9Px9fXl9tuuw0/Pz+OHz/O999/j9lspl27dowdO5bq6mqWL19OTk4Oer2efv36ERMTQ2VlJRs2bKC4uBitVkvHjh1FBwtFUcjNzSU3N1fkDrZq1eofLanmDqPRKBLc/fz83JZSg/poTzVX0llkrIrBYGD79u1YLBbatGljU3zAGpPJxPLly23yg12xa9cuUlNT0ev1TJ482e11VlVVCQvANddc43asiqIo7Ny5E2j8StIZqrm7MdG4kguDFuMznDVrFrNmzWpShf6LHXe5hPbmn6b4RtylC0RGRvLRRx8xadIkFixYwPjx421MYe7Ew2Qy8csvv2A2m+nevTsxMTHCR6d2lliwYAEAt9xyCzqdjoqKChYvXszu3bvR6XRMmTIFvV5PSkoKixYtwmQyERMTQ//+/cnKymLlypWUlZXh6elJv379MJlMHDt2jGPHjonaoWp6QUFBASUlJRQXFwufpaenJ76+vtTW1joECrnLJWzK/bR+b28mtl+pqO2roF4IW7duLe6xfVqBj4+PjRAmJiaKxHn7SV+v17Nz507q6uoICQlh2LBh4lqsTcKKorB+/XqKiorw9fVl8uTJNue19j1WVlaKVf/YsWMdVoX2q9OlS5dSXV1NbGws/fr1s/ndceVLzczMJDc3F71eT/fu3RuVk+iMxhYQv5A4Hx7cziUtZmX44IMPcvDgQbZv336uL6XF06dPHxFA8/nnnzd6v6KiIn788Ueg3uRqv+29995DURSGDRsmTKh///03ixcvBmDixIkkJiZy4sQJfv31V0wmE4mJiVx22WWUlJTw559/iv52AwcOJDAwkKysLA4fPozZbMbf35+EhAQxAZaVlZGfn4/RaESj0eDn5/ePV5JxR21tLfn5+VgsFjw9PWnVqpXba8vNzRV5gqoJ2Bl1dXWsXbtW3KuRI0e6jJDdtm0bBw4cQKPRcOWVV7os5WY2m/nhhx+oqqqiTZs2jBgxwu1nKykpEXmikyZNavQ9VwN4unTpckZCZl1GT3Jx0GLEUHJ+cdVVVwGQnp7e6H0++OADKioq6NSpk81qsq6ujnfeeYfS0lJiY2O58847gfrqM2rbqGHDhtGnTx8OHDjAb7/9htlsJjExkfHjx5OVlcXy5cuprq4mODiYgQMH4u3tze7du4V/MCIiguTkZPR6PRaLhZycHHJyckTR56ioqPPGf6QoCgaDQRTM9vT0JCwszOWKXVEUsrKyOHnyJFC/em/fvr1TgamurmbTpk2UlJTg6enJkCFDXArCrl27RNGD4cOHi+L6zvjjjz9IS0vDy8uLW2+91a2fVVEUvvnmGwwGA+3atRN5og1hsVj4/fffAbj88ssbtY8r1CLs7uqqSi4sWoyZtKVwJp0o3I21x11JNXdP6ar5Va01mZOTQ21trTCXWZuxrdMPNm/ezF9//YVWq+Xxxx/HZDJRWVmJoih8/PHHHD9+HD8/Px544AHq6upYt24d8+bNA2Dw4MH06NGD9evXs2zZMhRFIS4ujoEDB7J161YRABIeHk737t3Jz88nNTVV+IUiIiIICgqipKSEkpISSktLhZnT09MTT09PDAaDW7NoY+6piv0qy948aC269nl1np6eIo8O6pPKIyMj0Wg0Ts2iZrOZ1NRUkXKRlJREXFycwwrOx8eHiooKtmzZgsFgwNfXlzFjxhAUFORgQvXx8WHXrl0iZ3PkyJEictc+qtbb25uNGzeyZcsWNBoNd9xxh/jdcPbZALZs2cLOnTvR6XRMnz4db29vl2kXKjqdjt27d5OZmYmfnx9XXnmlyzQM+84Z1qjv1Wbija2Feq44X6wUFwJSDCXnhLCwMHx8fKiuriYrK8ttAe/q6mrefPNNoL7rRYcOHcS233//nTVr1qDRaLjvvvuIiIjg8OHDzJ8/H0VR6Nu3L+PGjWP16tWiy0VSUhL9+/cnJSVFJIpHR0eTnJxMaWkphw4dwmQyodfradWqlRCR8vJyEWGp1WoJCgo6r3zQJpOJ0tJS8RAREhLitnNEdXU1x44dw2AwoNFoSE5OdrnSKSgoYPPmzdTW1uLv78/YsWNd9mfcsWMH69atA+qLqqtC6IyDBw+ycOFCAK688kq6d+/u9jOWlZUxd+5coD5opqEC3tZYn+dMAl9qa2vFw4PslnPxIMVQck6oqakRK6WGVkwzZ84kMzOT8PBw7rrrLvH/a9eu5auvvgLqGwYnJydz6NAhPv74Y0wmE5dccgkTJkxg7dq1Qgi7du1KcnKyTQ5h27ZtSUpKIiMjQ+QP+vr60r59ewwGA4qiUFhYKFITPD09CQoKQqfTnReFmhVFoaqqSlyLVqt1W/JN/TyqmVev19OxY0enQqjWG1XvS3BwMEOHDnUqhGpuplq2rk+fPm6rxxw8eJD58+djsVjo1asXI0eOdPs5TSYTH3zwAWVlZURHR3P99de7HW/N4cOHRWpHQ1GqDXHixAkAUbRccnEgxVByTti6dSs1NTW0bt3a7apw5cqVLFq0CI1GwwsvvCCe6FNSUvjvf/8L1PsfR48ezcGDB/n4448xGo107NiRG264gWXLlrFx40agPpS+R48eLFy4UHRDGDBgAH5+fhw8eFB0PggNDSUxMRGtVkt5eTm5ubnCZOrn53fepExA/SqloqJCmJ99fHwcukpYU1dXR0ZGhsiFDAoKom3btk79nXV1daSkpJCXlwfU92bs3bu302PX1tby119/iQeMyy67jF69erm8T/v27eOnn37CYrHQvXt3h5J59iiKwmeffcahQ4fw8fHh8ccfb3RZO0VR+PDDD4H6qkPuCgg0BlXsL7nkkvPm90By5kgxbEE0xWdoj/0fvTu/ir3p0Hq7eg41P2zo0KEu/YQnT57ktddeA2DKlCm0bduW8vJyMjMzeeGFFzCZTPTu3ZsJEyawY8cOvvzySyGEI0aMYP78+aLzgVpce968eRgMBjw8POjatSsajYaNGzeKVZVa1aaoqIjq6mry8/NFSTV/f38sFosQEvvrbUrrJfsAEWuBsRcm+/deXl6YzWbKysqESOv1esLCwhwSz1UTr9pqKi0tDbPZLHIlY2JinKZaVFVVsWnTJlHDs3///nTs2FGMtTYz1tTUsGjRIoqLi9Hr9VxzzTU2Ce3Wx/Xx8WHHjh38+OOPKIpCv379uO2228T9sPYpWvsMf/31V9atW4dWq+WJJ54gMTHR5r6487P+9ddf7N27F29vb6ZPn+5w75uSWqHRaIRpvXPnzlIMLyLOSAy3bt1K586dG+x8LZFYYzKZRB3QYcOGOR1jNpt57bXXRPToXXfdRUVFBYWFhbzyyitUVlaSlJTE3XffzfHjx/nqq6+EEF5//fV89913pKeno9FoGD16NHV1daxcuRKj0YiPjw/du3fHbDazY8cOamtr0el0JCQkEBAQQGlpqU2Bap1OR0BAAHq9XojPucJsNlNaWirMt1C/ugsJCXEZLVpZWUlGRoZIBwgICHBZLcZkMnH48GHS0tJQFAU/Pz8GDx7sshvEkSNHWLduHXV1dfj7+3P11Ve79OOp7bHUfqT9+vVj6tSpDbaxWrlyJT/99BMA99xzj9PKQ64oKSlh1qxZAEydOrVZfHz79u0DcFlkQHJhckZi+MQTT/Dmm2+6rTMokdizaNEiTp06RXBwsMvfnVmzZrFr1y58fHx48cUX0ev1lJaW8uKLL5KXl0erVq146KGHOHbsGP/973+pq6sjKSmJSZMm8fXXX3Pq1CnRhslgMLB27VoURSE8PJxOnTpRXl7OgQMHMJvNeHl5kZSUJFYi5eXlFBcXA/Wrk/PBLGoymaiurrZpGeTh4UFkZKTLTg11dXXk5OSIz6LVaomPj3fZkzA3N5d9+/aJVXJCQgK9e/d2ao6sra1l7dq1ogNFdHQ0EyZMcJlmUVtby4IFC8Sq6tJLL2XixIkNCuHy5cuFX3jSpEmMHTvW7XhrzGYzr7zyCkVFRSQkJHDzzTc3el9XVFRUsGPHDqBezCUXD9JMKvlHMZlMvP/++wDcf//9TifPtWvX8sUXXwDwzDPPEBcXh8Fg4NVXXyUrK4uIiAhef/11UlJS+OSTT0Th7fHjx/Pll19SUFCAl5cX48eP58SJE6L8Vnx8PH379mXPnj2iUHhISAjR0dHo9XqRb6eKR0BAAJ6enudUCM1mM+Xl5TbmWE9PTwICAvDy8nIqhCaTSVTHUVePYWFhtG3b1ul4g8HA4cOHxUrYx8eHvn37uqwLmpmZyaZNm6iqqkKj0TBw4EAGDBjgUtiKioqYN28eubm56HQ6rrvuOrcl2aDerLtw4UJ+/vlnAMaPH8+tt97qdh975s6dy86dO/Hx8eHNN99slmLpf//9N0ajkaSkJLe+bsmFxxmL4dy5cyksLKRfv34NFtWVND9nkjvozqdlP7E1pd2TvXhYb//55585ceIEoaGh3HrrrQ7NUY8ePcrzzz8P1E+AvXv3pqCggNdff53U1FT8/f157LHHOHDggCiv17lzZ7p168acOXOoqqrC39+f/v37s2XLFhEUEx8fT2xsLOvXrxcBISEhIbRp00YEoBQUFIhcQV9fXzw9PR2uz50/1H4FZX8PrX1VrloXQb3Y1dTUiC4TKmrhb+sIRmtxM5lMlJSUkJ2dLa4zNDRUNBx2VlLt6NGjHD58GIvFIjrPd+vWjcDAQJux3t7e1NTUsGHDBrG6CwkJYdy4cQ4BKdY+wn379rFgwQJqamoIDAxk2rRpNo1/7cXZ29sbi8XCt99+K8yp119/PTfeeKPLvEP7n6E+L/Wbb74B4Nlnn6V9+/Zimzt/rf12++9Q7W4yduxYt77GhmhKeUN3f6eS5uOMxVCr1fLdd9/xyCOPYDKZ6Nu3L/369eOee+4hIiKiOa5RcpFQUVHBO++8A8B9992Hn5+f8GOp259++mkqKiro3Lkzd955JyaTiXfeeYedO3fi6enJI488QlZWFnPmzBFCOHjwYL755htqamoIDQ1l7NixrFixQkSM9u3bF09PTw4ePEhRURFQ358vLCxMTCwlJSXU1NSIQJnGNIltThRFwWQyUVNTQ11dnc0DhL+/P8HBwS4r3NTU1JCfn09RUZGYOP38/EhISHDqIzObzZw4cYLjx4+LFWdkZCQDBw502vndYrGwf/9+Nm3aJHymffr04bLLLnMZ0VldXc3ixYvFqjwxMZHbb7+9wST16upqZs2aJUyRd955p6hW1Fh27drFiy++iKIoXHvttU0yrbqjuLiYFStWAGdewUZy/nHGYjh16lTh98nPz2fbtm1s376d0tLS80oMZaHuc8+bb75JXl4e8fHx3H777TbbTCYTTzzxBGlpaYSHh/PGG2+gKArvvPMOmzdvxsPDg+nTp5Obm8uXX36Joih07tyZHj16MHfuXIxGI5GRkQwfPpxly5ZRUlKCh4cHgwcPJjg4mLVr11JSUoJGoyEuLs5m5VNdXS0iRCMiIv6xHnWKomA2mzEajRiNRpvzarVafH198ff3d5ogruYWZmRkUF5eLv7fz8+PmJgYG6FXMZvNnDp1itTUVLHi9Pf3F412nZ0nJyeHTZs2CRNqSEgII0eOdJuecOTIERYuXEhpaSkajYaRI0faVHxxRXZ2NrNmzRI9D6dPn86ll17qdh979u3bx3PPPUdtbS2DBw/m0UcfbdL+7vjiiy+orq6ma9euTQrikVwYaJQzaNV8zTXX8OSTTzJo0KDmvKazSnl5OUFBQZSVlTmYgi5EGjJ9uutI727Sb4r51f4Bw74MWU1NDXv37mXcuHFYLBb+97//iQcotaPCO++8w88//4yXlxdvv/027dq146233mLdunXo9XqmT59Oenq6KM7cq1cvgoKC+Pvvv1EUhaioKDp27Mi2bdtEQ9ouXbrg4eHBgQMHqKysRKPROBSfVoNM1ET7wMBAG9NkQ8LoLgzfmSlUURSMRiN1dXVUVVXZpGNotVr8/f0JCwuzCdqxN4WWlZWRk5NjE9kaHh5OfHy8TVcKqDc7Go1Gjh8/zrFjx4QZ2M/Pj969e9O+fXthCrT2qVVXV7N+/XqOHDkiruHSSy+lb9++6HQ6m7Hqz5WVlfz+++9iNRgWFsatt95qE3XpytS5efNmZs+eLVb3zzzzDF27dnU61tl7Dw8PDh48yEMPPYTBYGDAgAG8++674nzW30VD5e6s36s/l5aWMnDgQKqqqvjyyy/FatN6rKtOGc62u9tmv91dWpP99oZMqO62X0jm17Mxjzd5ZfjKK69w1113ERMTI8obSSTuMBqNPPPMM1gsFsaNG+cQQfrjjz+KQImnnnqKdu3a8eWXX7Ju3TpRZq24uFgI4YABAwgNDeXPP/8EoEOHDkRERLBp0yZMJhOBgYF06tQJjUZDSkoKNTU1InXC19eXiooKoF7QrTvSN9Tn73RRV3+qD9D64UGtGRocHIyfnx9ardZBMNQcwaKiIkpKSoRA63Q6oqOjiYmJEYFI1hOawWDg6NGjpKWliQcUPz8/OnfuTLt27ZwGL1VWVrJjxw4OHDggztOtWzdGjRrlMlLUYrGwY8cOlixZIh46LrvsMsaPH9+gubmuro7vv/9e+Ae7dOnCk08+6bKHoiv27NnDU089hcFgoFevXsycObNZTd2fffYZVVVVJCcnM2bMmGY7ruT8oclieOzYMTp06MAjjzzCs88+69THIJFY8+GHH7J3716CgoJ47rnnbLatXr2a9957D6hvszVw4EC+/PJLfvnlFwBuu+02CgoKRJ7ZgAED8PX1FULYrVs34uLiWLp0KWazmfDwcPr3709ZWRn79u2jpqYGb29v4uLinIqMujLz9fVtlidj1fRpNpuprq7GaDQ6Nc37+vqKlysBNBgMlJaWUlZWZrOC9PX1pXXr1kRGRjrk+CqKQlFREenp6aKYNNSbQ7t16yYq69hTXl7Oli1bOHjwoLjexMRELr30UiIjI11GYp48eZI///yTzMxMoL5w9ZQpUxpVM/TEiRPMmTNH7DthwgSmTp3aoDnVntWrV/PGG29QV1dH9+7defvtt5slclQlJSWF2bNnA/D4449fUCsoSeNpshh+9913/P333zzzzDN8/vnnvPDCCzzwwAP/eMCB5MJgy5YtohTWjBkzbPzIe/bs4eWXX0ZRFK677jpuu+02Zs6cKYTw5ptvpqSkRLTdGTJkCBaLhdWrVwP1QRyRkZFCCKOioujfvz9arZZjx45RVlaGTqejc+fONqkJKlqtlsDAQMrKyqisrHRZy9MV1sJn/XKGXq8XqRCuUiIURaG6upqioiLKyspszM06nY7Q0FDCw8Od+gNra2vJzs4mJyfHJigpMjKSdu3a0aZNG6f9+4qLi0lJSeH48ePC9N2mTRuGDh3qtuVSSUkJK1asYO/evUC9qXTUqFEMHTq0wSLYZrOZxYsXs2jRIsxmM0FBQdx///307NmzSUKoKAo//vgjn3zyCVCfu/jKK680qxBWVlaK4MBx48bJwJmLmDPyGf7888+88MILGI1GXnvttQbrC54PXAw+w+Zqy9SUr97ed2b93pmPEOrv9YgRI8jMzOTqq69m5syZoth1ZmYmt99+OyUlJfTv35+XXnqJBQsWiI4EU6ZMITMzUxRXHjlypGi0CzBo0CDMZjPbt2/HYrEQFhZGcnIyWq2W9PR0Tp06BdSvboKCgmz8a/Y+waysLMxmMz4+Pvj6+qLT6dBoNDaFxC0WixA7k8mE0Wh02a1eXen5+fnh4+ODj48POp3ORgBVf5eaR6gm+tsLYHh4ODExMYSHhzv49iwWi1gFZmdni+v18PAgKSmJTp062URvqvspisLJkydJSUkRRaehvmD54MGDna6i1X3Ly8tZvXo1W7ZswWw2o9FoGDx4MBMnThR/T+5SILKzs/n0009FE+FBgwbxwAMPiH3dpUtY+/pMJhMfffQRv/76KwA33HADTzzxhBBTez+g9b6Nafek3qfHHnuMX3/9ldatW7NixQqHcnfW4n0mPkN3fsCGWqS58y/aI32GrjmjaNLrrruOq6++ms8++4wnnniCd999l5UrVzot8yRpeTz77LNkZmYSFxfHyy+/LP6/uLiYhx9+mJKSEtq2bcuzzz7L4sWLhRBed911lJSUCCG8/PLLycnJ4fDhw8If5ePjI3oTtmnThrZt26LVaikpKRFCGBsb26AZX23FVFxcTHV1dZPLrWm1WtHT0MfHB29vbzw8PNBoNE4LWqurv8LCQsrLy6moqLB5KNHpdERERBAREUFoaKiDiFosFvLz88nKyiIrK8tGPMPCwujUqRMJCQlOUx6qq6s5fPgwe/fuFQ8lGo2G9u3bM2DAAJed7aF+8lm7di2bN28W5+zYsSMTJkxoVOHrmpoafvnlF5YuXYrFYsHX15e7776bkSNHNnkSLiws5OWXX2bv3r1oNBoeeughbrvttmafzD/77DN+/fVXdDodn3zyiexQcZFz2mKYn5/PwYMHOXjwIIcOHSIhIYGtW7dSXFwsxVDCggULWLhwITqdjnfffVcEp1RVVTF9+nROnjxJ69atefXVV1m+fLnwyYwbN46ysjKRz3XFFVeQm5tLSkoKGo2GUaNGERAQwO+//46iKMTExNC7d28xuasJ9aGhoYSFhTXqWv38/NDpdKLcmdlsFgKl0WjQaDRotVr0er14eXh44OHhgV6vF5OwMwFSFIWamhrR/LeqqsrBlKp2og8NDSUoKMjBzGc2mykuLiY3N5e8vDwbAfTx8SE+Pl6sgO33VRSFnJwcDh06RHp6uji3p6cnXbt2pXfv3m6DVUpKStiwYQO7du0SK+G4uDgmTJhg01fSFYqisHnzZr7//nuR4zlgwADuuusuQkJCmixg+/bt48UXX6SoqAg/Pz9eeeUVhgwZ0uxC+NNPP/HGG28A8MILL9C3b99mPb7k/KPJYnjDDTewatUq8YsdHx9P165dGTFiBI888ggxMTHNfpGSC4uTJ0/y7LPPAvX1a9WcLJPJxLPPPsuRI0cICQnhk08+YdWqVUIIb7jhBgoLC0VHi3HjxpGbm8vu3bvRarWMHDmSiIgIfv31V0wmE5GRkfTu3VuYiVSzIdDkBzJvb28b86NKU8LaoV64ampqhLBWV1c7mKNVX6X68vHxcTAt1tXVUVRURGFhIcXFxTYC6unpSZs2bYiJiaFNmzYuA2KOHz9OWlqaiJ6F+jzKLl260KlTJ7fRsxkZGWzevNkmqjQ+Pp6RI0fSqVOnRvnlUlNT+eGHH4RJNCIiosmFtlUsFgvff/89n332GWazmYSEBN5++223fs3TZdmyZTzzzDMATJs2jXvvvbfZzyE5/2iyGKrC17VrV7p06XLB+t1aIg2Vj3LnX7THenK2XqkYjUbuvfdeKisr6du3L/fdd58wBf7nP/9h06ZNeHl58e9//5tNmzaJnoRXXnmljRBeddVVHD16lCNHjqDRaBgxYgTe3t78/vvvVFdXExQURHJysggWUbuPm0wmPDw8HIprW4tNQ33w3LVaUoVHzRc0Go0YDAaqqqqoqqpyKN8G9T6poKAgwsLCCAkJITAw0EFMdDodpaWl5OXliWoy1vj4+BAbG0t8fDzx8fHiOqz9apWVlaSnp3PkyBGbSFJPT0+Sk5NFvVH189n75HQ6HXv37mX9+vXC1AzQqVMnxo0bR/v27Z3ua3+cwsJC5s+fz+bNm4H6B42rr76aSZMmOQiwu7J06s/FxcW89tprbN26FYBRo0bxwgsv2JjAG/IDOssdtP7cKqtWrWL69OlYLBZuuOEGXnrppUb9PkDDf19ni6a0XpO4psli+K9//etsXIfkIuGtt94iJSWFoKAgPvjgAzF5zJo1i4ULF6LVannuuefIy8vj3XffBWDEiBFYLBYhhBMnTqSoqEgI4ciRI2nfvj1//fUXlZWV+Pj4MGTIEAfhUbstGI1GYYY9kyhnNfWirq6Ouro6amtrxau6utplQr6Pjw8BAQFC+Pz8/NBoNDaioSiKaElVWFhIUVGRQ0BOcHAw0dHRJCQk2ESQWk/AFRUVpKWlcfz4cbKzs8X/qwUGunXrRocOHfDw8HB5L4qKiti2bRu7du0SDxd6vZ5evXoxbNgwYmNjXZaCsz/OwoULWbduHRaLBY1Gw/Dhw7nllltO23Wybds2/vOf/1BcXIyXlxePP/44EydOPCuT/KpVq5g2bRpGo5GJEyfy9ttvSzFpQciuFZJmY+PGjXz00UdAfek1tQfevHnzRBcK9an7zTffxGKxMGTIEAICAkRC/YQJE1AUhQ0bNgAwfPhw2rdvj8FgIC0tDahPqfDx8XEQw6ioKAwGg0hOLy0tFXVGPTw8RAcK++o59pGiarSofYk0Z6jRon5+fgQFBeHv7y9WHtarHLPZLK5J/dc+CldtyRQdHU3r1q1FioK9iBYWFnLq1ClOnDghyqSptGnTho4dO9KhQwf8/PxcCmBtbS379+9n9+7dwowJ9b0RBw4cyKWXXtroIgQFBQX8+eefrFmzRnym3r17c9NNNxEfH9/ojvTWGAwGPvvsMxYtWgRAUlISr7/++lnrFLFy5UohhOPGjbN5kJO0DKQYXgCcQfbLaT/ZNlS6zXoVU1NTQ0lJCffffz+KonD11VczePBgysvLWbFiBTNnzgTqiy7r9Xpef/11LBYLgwYNwsfHRwjhFVdcgaIo/PHHH0C9Sb5169aUl5eze/duLBYLwcHBBAcHU1dXZ7NCUnPounXrRkVFBcePH6ekpISKigobn9npoEaK+vn54e/vj5+fHwEBAQ5io4qguupT0yUKCwspLS11uId6vZ6oqCjatGlDfHw8YWFhIjrVGqPRyKlTp0hPTyc9PV2sgKH++42NjaVTp04kJyc71AO2PpZGo+Ho0aPs3LmTffv2idxLjUZDcnIyw4YNo2vXruh0OgcBc5bmoJbH27x5s/hsnTt35vbbbyc5Odnhvqj72R/H/p7s3LmT119/nZycHKA+uvjhhx92KDDQWNOn/Xb7bcuXL+fBBx/EaDRy1VVXMWvWLHFdDaVLWL9vKF2iuVIgJGeHFiOGslD32UNRFJ555hlycnJITEwUwQc7duzg+eefR1EUJkyYQJcuXXj22Wcxm8307duXxMRE5s2bB9TnESYkJPD555+jKAodO3YUtSmNRiNHjx4F6kuvNTRRBAQECFGsqqoSKRNq/qOiKCiKItIf9Ho9Op1OpEioSfHe3t74+/u7zSUzm81UVFRQVlZGRUUFpaWllJaWOs1B9Pb2JiIigqioKKKjo4X4gWMOXXZ2NhkZGZw6dYr8/Hyb43h4eJCQkED79u1JTk52WSZNvb60tDT27NnD/v37bYQ0MjKSfv360b9/f8LCwhq1grNYLOzevZtly5aJVk4APXr04Oqrr6Zbt26NMqk6w2AwMGfOHFHmsU2bNrz44ov06dPntI7XGP7880+mT5+O2Wxm4sSJfPjhh6e1kpVc+LQYMXzwwQd58MEHRbKmpPn4+OOPWbp0KR4eHnz88cf4+vpy5MgRHn74Yerq6hg0aBBjxozh6aefpq6ujm7dutGvXz9ROWTYsGEMHTqUTz/9FJPJRFxcHCNGjBDdGFRTJvxfQn9jCAgIcGrqayjQwZn4mUwmIaxVVVVixWkwGJyu3HU6HSEhISLFIzw8nODgYKcBKEajkby8PHJycsjOziYvL8/hoU0txJ2UlERCQoJY6TgTHpPJRGpqqkh7shbAgIAAunfvTp8+fWwCYhrCYDCwYcMGli9fLlZsWq2WgQMHMnny5DM2X27bto23335bpMZMmjSJRx991K3Qnynbtm3j0UcfxWw2c9111zFz5kxpGm3BtBgxlJwdli5dKnoUvvbaa3Tv3p19+/Yxbdo0Kisr6dWrF1OnTuWZZ57BYDDQsWNHxo0bx7vvvouiKPTp04cRI0awdu1a8vLy8Pb2ZvTo0TaTkre3N927d2f37t0cOHCAsLCwZi+qbbFYqK2tpaamBqPRaLOaNBgMTqNEVTw8PAgKChKNd4ODg0UnemtUf2VlZSUlJSUUFBSQl5dn04dQxd/fn5iYGOLi4khKSrIxETpL5i8rKyM1NZXjx4/b9CmE+lqmak5hu3btxGq0ISFUFIVjx46xdu1atm/fLo7p6+vLyJEjueKKK4iIiDijlVRJSQmzZ88WtWbbtGnDc889R58+fZx+zubi6NGj3HXXXdTW1jJ27FgphBIphhcizRVK3ZTu9fZmv5qaGo4ePcp9990HwE033cT48eM5deoU9957L0VFRSQlJfHAAw/wzDPPUFpaSnx8PKNHj+bjjz+mrq6O9u3bM3jwYNLS0vj7778BGDhwIFqtltraWpvPkpycLFZNf//9NxEREaJBr4eHhyh5ptVqsVgsWCwWEQ2qlk5TI0Lr6uqoqakR+YDWJlR3eHt7ExQURFBQECEhIYSEhBAeHi6iRZ2F85eXl5Ofn09eXp4QP2dVboKCgkTqRPv27QkNDXWZzO/h4UFtba1oy3T06FGbVAqoj0S1XgHqdLoG0w/U82RnZ7N582bWr19vc9y4uDjGjBnDyJEjbVKqmtISSRWcuro6fv75Z7766isMBgMajUb4BlX/r704ufMDNuQztH6fl5fH1KlTKS8vp0+fPnz66ac2K+zT9QM2lIPqrtXSuUjDcJda9U9e0/mCFEPJaVFSUsIdd9wh8gmfeeYZampqePDBB8nMzCQyMpIXXniBV199laKiIlq3bs2DDz7IW2+9RWVlJa1bt+bmm2+moqKCrVu3YjabSUxMpG3btk7Pp9Fo6N+/Pxs2bKC4uJj8/HwHX9qZYt1QVw2SURPj1ZWeq4nebDZTWloqEuULCgooKChwuqLU6XQicEZNnreueelspWU2m8nMzOTYsWOkpaVx8uRJh1ZQagGMLl26EBMTg0ajafSqrbS0lJ07d7Jx40aOHTsm/t/b25vBgwczduzYRvlrG8P27dt59913ycjIAOrzGB9//HG6d+9+VleDUD/hT5s2jezsbNq2bcvcuXOdFjCXtDykGEqajMlk4v777yc9PZ2YmBjee+89tFotTzzxBHv27MHf359XX32Vjz76iJMnTxISEsKTTz7J/PnzKSoqIjg4mDvuuANvb28qKirEpB4bG+t2svXx8WH06NFUVlaK2pzq/iaTyWmlF7V0ml6vF8ExarUZLy8v0UZJrStqv8KzX2EYjUbKy8tFoExZWRklJSWUlZU5TcPQarWEh4cTGRlJ69atiYqKIiIiosEKLnV1dWRlZXHixAlOnTrFqVOnHDpvqLVIO3ToQPv27fHz82uSybKkpIRdu3axbds2Dh06JO6fVqule/fuopmvj49Ps4hUamoqc+bMEcnzoaGhPPTQQ1x++eVOq+icDZYuXcquXbvw9fVl3rx5st6oRCDFUNJkXn75ZdatW4ePjw9fffUVISEhvPbaa6xatQoPDw9effVVFixYQEpKCr6+vjz++OPs2bOH7du3o9Vquemmm2x8fuqEVFJS0qjz+/v707FjR4cC0appVKvVujVDuTN1qYW0KysrqaysxGAwiDQJNWDGFWqN0fDwcCIiImjVqhVhYWFCSFwJisVioaCggJycHDIzM8nOziY3N9dBXH19fWnbti0dO3akffv2hIeHN0mkLBYLp06dYu/evezevdumYwVA+/btGThwIIMGDXJI0TgTMjIy+Oabb1ixYgWKoqDX65k0aRJ33333PypGJpNJpPncc889snSkxAYphuchZ5JX2FzndeYjhPoCxmoJtTfffJOYmBjef/995s+fj0aj4fnnn2f16tWsXLkSrVbL9OnTKS4u5vvvvwfqUyjCw8NtREWdEFUBUJPNz2Q14kzwVKGzjgitrKy0+dd6peoKHx8fG9GLiIggMjLSxs8Hzn1cav3UU6dOkZGRQWZmJpmZmU77LQYFBdGuXTshfq1btxarXetjWmN/ToPBQEpKCrt372bfvn0iQhfqHxA6dOjAgAEDGDx4MK1btxbb7FeYTcnbU9+npqYyd+5c1q5dK363Ro8ezQMPPCCEyJ1vz/47dPdZG9MSacGCBRw/fpzQ0FDuv/9+8V2diW/P3Vh3PsQzOW5L8+X9U0gxlDSa3bt38+STTwLwwAMPMHbsWJYtW8acOXPE/9XW1oqk+bvuuouuXbsyY8YMzGYznTt3pn///g7HVVchBQUFfPnll8TFxREWFib8dtbBMTqdTjTVtVgsomKMWjLNumyaGiSjdoxwlQZhj0ajwd/fX0SIqq/Q0FAiIiJsfEzWE7L9JGU0GikoKCA3N5ecnByROuEsWMfT05Po6Gji4+Np27YtiYmJoqtDUx4KjEYjqamp7Nu3j3379pGenm7zmX18fOjSpQt9+/alf//+bjtWnC4HDhxg/vz5ogkzwODBg8Xvw7lC7YRy5513Nns0suTCR4qhpFHk5+dz5513Ultby5gxY5g+fTopKSkiwf7qq6+ma9euPPTQQ0B9ntill15KdXU1R44cAeorzDh7qg0PD2f06NHs3buXvLw8Tp48ycmTJ8/aZ7EPkgkICMDf318EygQHBwuRc7ciUlE7TKjpEmpwT3FxsVM/ol6vJzo6mtjYWPGy7j7RFPGrra0lLS2NI0eOcPjwYY4dO+ZQ5i0+Pp6ePXvSu3dvOnTo0KDZ9nQwmUysXbuWBQsW2CTjjxw5kjvvvNNlYNQ/SZs2bQCa3LNS0jKQYngBcrZKrFmbB63NdnV1ddxxxx1kZ2eTmJjIW2+9xf79+5k2bRq1tbX06tWLMWPG8MILL2A0GunatSujRo2ioqKC7du3YzabCQ8PJzw83MEcqD6hDxo0iEGDBpGfn09qaqoITikrK6O6ulrUDjWbzWKFqL7UwBhPT0+8vb1Fx3q1hJpaRk0VQPv8v4Y6kiuKQlVVFUVFRTYRo2rUaFlZmct77uvrS0xMjEibiIuLc1pA3F2VG+syb7m5uaSlpXHs2DGOHDlCenq6w/cYHBxMt27d6N27N7179xZFshtKVWiK2VFdoe/fv58VK1awatUq0VPSw8ODMWPGMGXKFJHW0djjNrZDhP3YxtCpUycADh06ZPP/7qwF7tKPzoQzMZM2dKzmwl0axsWIFENJgzz33HPs2LEDf39/YRJ95plnKCkpoV27djz00EO8/fbbFBUVER0dze233y4mrpSUFAC6dOnSqD8oVTSd0ZSgmKb4WRRFwWAwiCLaaoRoUVERxcXFFBcXO/XpWePv70+rVq1o1aqVSJuIjY0lKChInLupSd0Gg0Ek0av5hGpXCWvUqNIuXbrQvXt3kVZxOudsDJmZmaxcuZKlS5fadMoIDQ3lmmuuYfLkyS6/w3OJKoZ79uzh5MmTxMfHn+MrkpxPSDGUuOWHH37gq6++QqPR8MEHH5CQkMC0adNIT08nPDyct956i7/++otDhw7h7e3NU0895dBlAeD48eNO63WeTSwWCzU1NVRWVtoEzFRVVYnoUHX12ZhrCwwMJCwszCZ4JjIykoiICPz8/BoMZnFHVVWV6ERx4sQJ0tPTyc3NdViJeHh4kJSUJKJK7Ytzn60qKtnZ2WzatImVK1famEF9fX0ZNmwYY8eOFVVj/qk0iabSpUsXoqKiyMvLY/To0bz66qvccMMN5/qyJOcJLUYMZaHuprN//34RMPPQQw8xbNgw3nvvPVavXo2npydvvPEG3t7eotj29ddfT5s2bWzaCk2ePJnDhw+TkZHBG2+8IborJCYmNtpnpZZKU4Nj1MAY6woy6ktttGswGDAYDA22YLLG399fVJYJCQkRohcaGkpISAgeHh4Nmu4awmg0ioCarKwsMjMzycjIcGjmqxIZGSnyCNu3b09CQoKNifVsiV91dTX79+9nx44dbN682caHq9Vq6du3L2PHjmXYsGFntX5oc+Lj48Mvv/zC448/zrZt23jiiSdYvnw577zzDpGRkef68iTnGI1yruL4zxFqoe6ysjKbklLnE835lbjrXu8qfQLgxIkTTJw4kZMnT3LZZZcxY8YMVq9eLZo7P/roowwbNozZs2ezbNkyYmJi+Pe//41er3cIUEhJSeHbb7+1MfFpNBqRAO/j4yPqdiqKgsViEZGhal/BM8HX15egoCACAgJsIkTVsmphYWEEBweLdIKmlONy5g9TFIWysjIRQZqVlUV2djY5OTnk5+e7FOjIyEiSkpJo37497dq1o3379gQFBTXqnM62NeWzVFVVsW/fPvbs2cPu3bs5dOiQzYOjTqeje/fuXHbZZYwZM8ZmNdqQibop3eDdjXV3nqaUTVMUhc8++4z33nuPuro6QkJCeOWVV7jqqqtEBxOVhh5+mjK2Kb9Xp5tacbb8i+ebz/BszONSDM9DzrUYWiwWJk+ezJo1a4iOjuaPP/7g6NGjTJ06lZqaGqZMmcJ1111HXl4e06ZNQ1EUnnvuOTp27Ag4RusZjUbMZjOpqans2bOHlJQUKisrm/xZPDw8HAJkfH19bfoMqoEygYGB+Pv7ExAQgF6vP+2J0902g8FAYWEheXl55ObmihVfdna2U9+eip+fH3FxccTGxhIXF0diYiKJiYmiGHdTJuDTFcOKigoOHDjA3r172bVrF4cPH3awmrRq1YrevXszaNAgBg4caJOO0BR/7fkmhurPhw8f5rHHHuPgwYNAfb7r2LFjGT9+PEOGDMHT01OK4Rnud7Y4G/N4izGTShrPhx9+yJo1a/D09OSzzz7Dx8eH559/npqaGnr37s0DDzxAQUEBKSkpKIpC+/bthRC6QqfTiQ7s1157LZWVlTZFsi0Wi4gSVRvcWr+8vb3dlho7U/OlPRaLhcrKSkpLSykuLhYRpEVFRRQVFZGfn+9W0DUaDVFRUbRu3Zo2bdoQHR0t/g0JCXEwEZ9NP5vRaCQtLY2jR49y6NAhDh48SHp6usO46OhoevToIdIw1FSEs31954pOnTrx22+/MWvWLL755huKi4uZP38+8+fPJygoiPHjx3PDDTfQr1+/804MJM2PFEOJDRs3buS1114D4NVXX6Vz584899xzHD9+XJiTVOHZt28fgE1X88ag1WpFAWx3lfKbewJSFIXa2lqqqqqorKykvLzc5qWmc6j/NjaoRhU9+5d9Aeh/QlDKy8s5ceKEiEA9fvw46enpTk3NsbGxdOvWje7du7cI8XOGp6cnTzzxBI888gjbtm1jyZIlLFu2jPz8fObNm8e8efNISEjghhtu4JZbbqFVq1bn+pIlZwlpJj0PaegraShNwNV7ezOYfUeF48ePM3bsWPLy8hg3bhyvvPIKK1as4Pnnn0ej0fD666/Tq1cvoP4+3nPPPZSVlfH888/TuXNnl+dpSr5SU8xvgIgMtRa3srIy8bNaYk3d3lCKhP35rANpIiMjRfSomkLhynTo7PobayZrjMnPbDaTkZEhUi7UFAzr4CVrAgICSE5OFq9u3bo5pD+cbrkwe5rrIeZMjmNvKWiKSRVg69at/PrrryxdulSUDvTw8ODKK69kxIgRDB06lMjIyEaVpXP2vqGxTTEXW3O2Sredbytj6TNsBqQY/h/WYmgymbjyyivZvHkz7du3Z+7cudTU1DB58mTKysq46aabmDp1qhhfUFDAbbfdhqIohIWFce211zJkyBAxUbu6BlfXbjQaqaqqEi+1KLYqZPY1RNV/T+fX19PTk8DAQJuGvEFBQSJqNCwsTHSpt+8kb3/97sqxNYcYKopCaWkp6enppKenc/z4cdLS0khLS3PZcLhVq1Yi9UKtaxodHd2sfqqLWQyt962trWXZsmV8++237Nq1y2Zct27dGDVqFKNGjaJHjx4N1nOVYth8SDFsBqQY/h/Wk+lzzz3Hf//7X/z8/Fi8eDFBQUG8+uqr/Pbbb7Rr144PPvjA5im4oqKCzZs38/XXX4u0gLCwMCIjI0XUplqYWn05qxmqpkI0ZcVmj6+vrzC7qi81elQtsWb9Xo1eVWlKYMbZEkOz2Uxubi4ZGRnipeYdVlRUOP3cPj4+Iuq0ffv2tG3blrZt29qkOpxuQIoUQ8ef9+7dy5IlS9i0aRN79+612ScmJobJkydz7bXXiuR+KYZnj4tSDH/66SdWrVqFt7c31113HUOGDHE7vry8nK+//pqDBw/i6elJ//79uf766xuds3YhiOGZYP91Wgugvd9I7WCwcOFCHnjgAQDef/99Ro0axZIlS3j22WcB+Pjjjx1qS6r+tNraWhYvXsyCBQvctjdqDFqtVkSDWguZtaBZi50qcB4eHuesu4C7icl+gquqqhKpFtZ5hpmZmeTm5rrMgdVqtcTExIi0CzX1IjY2tkmBOGdromyoZJm7iGb7NBN3Y8+kNNrpiqH9NnX1V1hYyLp161i3bh3r16+3iR7u0qULt956K5MnT7bxG1t/V/arSHcFG5oSpXom3/H5JnjuuOjE8MEHH2TBggU89thjlJSU8P777/PFF19w2223OR1fVlZGnz59CAkJEV3WP/zwQ3r16sXvv//eqHNKMfw/ysvLOXToEFdeeSXV1dXcfffdPPLIIxgMBq644gqKi4u59tprmT59uoPQWQeXWCwWqqqqSEtLE01vS0tLRR1R9aWmRaj/WqdC+Pv74+vrazMpNGebm39CDNX2TNnZ2SKv0FrwrNsnOcPb25u4uDgSEhKIj48XHSzi4+NtEu2b8lncXfuFJIaqubigoMDGTG4wGDAajZhMJoxGo4hKViOTPT09bVJxVHN4UFAQ/v7+Yqw1jRFDFb1eT01NDatWrWLx4sWsXbtW/J0FBgYyYsQILr/8ckaNGmXjX5ZieGZcVKkVBw4c4JNPPmHFihWMHj0aqJ8MnnjiCW666SanYfR///03qamp5OXliYoRHTp0YNKkSeTl5REVFfWPfoYLnerqah544AGqq6sZNmwY06dPB+DXX3+luLiYNm3acM899zTqWH5+fi7b85xuztT5hJpIX1xcTGFhoehMoeYZqq+GCgQEBwc7pFqo+Ybh4eFoNJozLkh9IVNaWsqBAwc4ceIEJ0+e5MSJE2RnZ1NUVHTGxRfs8fDwIDIykqioKKKiooiOjhZ5nwkJCY2eZL29vRk3bhwTJ06kpKSEn3/+mW+++YbMzEwWLVrEokWL8PX1ZezYsUyaNImRI0e6TROSnBvOmRguWbKE0NBQRo4cKf7vxhtv5NVXX2XLli0MHTrUYZ/4+Hg0Gg2ZmZlCDDMyMggLCyMoKOgfu/aLATVR/tChQ4SHh/Pxxx8D9SvJb7/9FoAbbrjBobvCxYLa6FeNRFVrlFqnV5SUlFBSUiKKdTdmMtbpdERGRtoIXmxsLDExMURHRwt/XksWPGsqKipYt24dO3fuFAW03aFWDlKLLPj6+uLl5YVerxfVY9Rel6qfWs1lraqqEt+zuqLMysoiKyvL6bmioqLo1KmTqAHbvXt3mwbIzggJCeHee+/lrrvuYt++faxYsYLFixeTkZHBr7/+yq+//kqrVq244447uO222+QD/HnEORPDtLQ0YmNjbSaFhIQEsc2ZGPbo0YPvv/+eG264gc6dO1NVVUVxcTFLly7F29vb6XnUoA2VhkxVFxpNactkXRnm22+/Zf78+Wi1WmbOnImnpyclJSWsXr2arKwsAgMDGTt2rBhvL4quzHYNvT+TwAz7KMuamhqROmEddapGpKrv7Ytzq2kWp1OnNiQkhPDwcLGaiIqKolWrVrRu3Zro6GgiIiKEyetM7oOrz93Q2DMR1dM1Z7r7nbN/bzabKSsrY/PmzaxcuZKtW7c65HPGxsaSlJRETEwMcXFxREdHiwde6xWV9Xmb4k/UarXU1dVRUlIiWnHl5+fbmLWtV/xr164V+0ZHR9O1a1d69epF3759iY6OFtvsI487dOhAhw4dePDBB9m7dy8rVqzg999/Jzc3lxkzZjBz5kzGjx/PtGnT6Natm82+1sdqikm1KRHDElvOmRhWV1eL8lMqakdzV803DQYDX3/9NcHBwYwePZqqqipmzZrFzz//TN++fZ3uM2PGDF555ZVmv/4LmcOHD4umvI899hgDBw4U25YuXQpA9+7dXT5gNDe1tbViNabmCaq5guq/1qKnvm+OouteXl4iMEdNswgJCSE4ONimQ4X6r7tUCznRuCYrK4u1a9eydu1a9u7da/PdJSUlMXDgQLp27coll1wirDwNieyZ4OnpKR5mnAmI6gNPT08nNTWVQ4cOkZ6eLlaSy5YtAyAxMZH+/fszZMgQ+vfv79T8qdFo6N69O3379uXJJ59k+fLlfPfdd+zatUusFnv27MnNN9/MpEmTHOZFyT/DOQugefjhh1m1apVNO5iysjKCg4P5/vvvuemmmxz2+eCDD/j3v//NqVOnhD1/27Zt9O/fn61bt9KvXz+HfZytDGNjYy+aAJqGnuCtn7qrqqowGo2MHTuWlJQULr30UubMmSMmg5KSEhYtWsSbb74JwLRp07jxxhsB9xORs1VObW2tMC9amxrVn0tKSoQp8kyiUHU6nU3EqWo+s27qa93N3j461dvb+6wF5rT0laGiKGzatInvvvuObdu22YxJSkrisssuY/jw4SQmJjrs6+64zrY3dWXY2Pf26URHjhxh7969bN++ncOHD9tcg7+/P0OGDGH48OFceumlDq4b6wcpT09PUlJSmD17NsuXLxd/p4GBgUyZMoVp06YRExMD/HMrwwvpYe6iiib9/PPPeeSRRygsLMTX1xeADRs2MHToUPbt20eXLl0c9nn00UdZtWqVKAMG9RO8v78/8+fPb1RvsostmrSpYqiaZ0JCQvj9999tWteUlJQAMHfuXNHE94477qBLly7o9Xo8PDyoq6uzMUOqKzpV2FShc1eo2hk6nU4kwasrNetUCuvcQfVlnTPYlMo250rgWooY1tXVsWTJEr799lvS0tKA+s/Qs2dPhg4dypAhQ4R50d5E2pAYVldX20Tq5uXlCUuC6gu07nii0WjQ6XR4eHjg4eEhclLVhyH7AJrw8HAbcbEXHuv35eXlpKSksHHjRjZs2CD+fqA+qGbYsGFcccUVXHrppXh5eTmIoUpBQQG//fYb8+bN4/jx40D938PEiRN5/PHHHUyoUgwvMjHMz88nKSmJ//znPzz22GMAXHfddRw9elR0RzcYDNx7773cd999DB06lG+++Ya7776b3bt3i/Jf33zzDbfffjsHDx4Uya7uuNjEsKGnZ2uT8+LFi7n11ltRFIWPP/7YwS9rnfg+e/ZsvvzyyzO6Ni8vL2FiDA0NFWZH9b36fyEhIQQEBDQoamfyh9yUP/TTTU84k8T0cyFw7gTP3UMV2P6eqdssFgsbN25kzpw5HD16FKgviDBu3DiuueYaWrdu7VBcwT4oyfp9VVWVqLGanp5OWloaOTk5zdrVxR5fX1/hsxw5ciRJSUk22+1Xaep7s9nM8ePH2bRpE2vXriUnJ0eM8ff3Z8yYMdx7772EhYUBjv5Fb29vLBYL69atY+7cuWzZsgWo/+4nTJjAE088Qbt27QBH/731NTVUBcdd4Qd7zmdxvKjEEOq7qN99993069ePkpIS8vLyWLp0KT169ADqw6xDQkKYO3cut99+OxaLhVtuuYXff/+d4cOHU1VVxebNm3nllVd4+umnG3XOliqGlZWV9O3bl+zsbK6//nreeustysrKbMZaT1Rms5kffviBFStW2Dxpe3h42OQGBgcHizJmqripAujv7+8gcGersokUQ+f8E2JoNBpZuXIlX3zxheiG4e/vz2233cbEiRNtJm93Ymg0GklJSWHPnj0cOnSI1NRUp8XSAwICbOrEqtGlAQEB+Pr64unpKSwZ6rWbzWaMRqOoeqRaNdROJAUFBU57Tfbs2ZOJEyfStWtXNBqNSzGE/xM4RVE4evQoa9euZfXq1eTn5wP16Uf33Xcf1113nbCGqdj751NTU/nkk09YsmQJUP87ec011/D44487dIiRYngRiCFAXl4emzZtwsvLi8suu8ymlJTRaOTHH39k0KBBNk9oR48e5fDhw3h6etKjR48mVZJvqWL4wgsv8N///pfo6GhWrFiBr6+vWzFsqEP82Upil2LY8NimcLbF8NSpU7zxxhvCJ+jn58fEiRO5+eabCQkJAWwFz14Mi4uL2bBhA9u2bWPv3r02DaahPpWiY8eOJCUlER8fT0JCAsHBwTbX4Ox63eHKlGg0GoX5devWrWzbtk3co6SkJG655RaHQD1nYmi9zWKxsGvXLubMmcPhw4cBiIuL45FHHmHkyJHiu7UXQ/UB4sCBA3z44YesWLECqBe3m266iSeffJLY2Nj/1955h0V1bf3/O9QBbKAIKiJgCUUUEBQpFoSAXV+vGmOJGt9o1BgTO+q1azSJmuSS6zXFqDFRif3VxAIoYqOrKIqNogZQUIpIm9m/P/jNuTPDMDDDNJj1eZ55dM7Z+5x1hrPPOnutvdaqJQMpQ+XRujLUNM1BGcrz10gnb379+jXS0tIwbNgwCAQC7Nq1CwMHDgRQ20QlL6F2Y3xaqlIYiu5XR1t1yauIfPKGrCIKTp7Ck1Z+0vfKmzdvsG/fPuzfvx+VlZUwNjbG5MmTMW7cuFoPZPF7sry8HFVVVUhOTsbly5eRnJwsodRat24NNzc3ODs7w9HRkUtEAMhfQFMf8jK61OUXzMvLw4ULF3Dp0iXuGtzd3TFlyhRu0U99ylCEQCDA+fPn8fPPP+P169cAADc3N8ydOxeenp61+op/NzU1xe3bt/Htt98iNjaWO/bkyZOxYMECidhHaROq9HHlVdlQ5CVW25AyVAH6pgwLCwsxcuRIpKamIiwsDDt27OD2kTJUvC0pQyAtLQ2bNm3CgwcPAADe3t5YuHAhtyhG+h4Ufc/Ly8Pp06cRExMjEe9rb2+Pvn37onfv3rC1tZWYqYmjaWUI1Cid4uJinDhxAufOneNkWLBgAQICAhqsDEX737x5g0OHDuHw4cPcLHjWrFmYM2dOrbYixBVcSkoKvvvuO1y5cgVAzerTzZs3Y9y4cbXaypKJlGHdkDJsgiiiDH/99VfMnj0bFhYWOHPmjMTqUVKGirdVpbyMMS6vpugjyqkpWv0oKwG9tpRhUVER/vWvf+H48eNgjKFVq1ZYvHgxAgICJK5N/B5kjCE+Ph4nT55EcnIyJ5+lpSUCAwPh6+vLmfsASTOqrihDETdv3sTWrVsBAB988AGGDx+usDIUUVJSgu3btyMmJgatWrXChQsXJMZRXcpQ9F1UhDs9PR0AMGbMGGzcuFGiQLMsmUgZ1g1Vum/GVFZWYsuWLQCAjz76SEIREo2jurqaW4QhKiRc10c8E05paSnKysrw9u1blJWV1ftAb9WqFbf6tnPnzvDw8ECvXr3g6uqqsaQIAJCYmIjw8HAUFhYCAIYNG4a5c+fCyspKZl1FgUCAq1ev4vDhw9wMEqipARgSEoI+ffrA0NBQodJdotAKIyMjjacJfPv2LX799VcAgIuLi0R2JmVo27Yt1q1bhxs3bqC4uBgZGRkNWg0vwt/fH6dOnUJERAS+/fZbHD9+HJcuXcKaNWswZcqUev2BRG1oZtgEEX+ASr89i9e+++GHHxAeHo62bdsiJiam3geINuLrGipPY+HxeKiurubqJ759+7ZWujbRKkPRv+JFhcWz3xQXFyscR6lqjI2NERQUhDlz5qBPnz7cdnmzP+nZnvR3ccUk+j9jDL/++isiIiIgFArh4OCARYsWoUePHlxb8fAdxhguX76MgwcP4vnz5wBqZieBgYEICQnhFr/IOqdIpvz8fDx48AC5ubnIz89HYWEh9wIhwsjIiEukYG9vj9DQUImqEPJme9L75K0QNTIyQlVVFXbu3InExERYWVnhyy+/5BYHSbeVd1xZM86lS5fiypUrmD9/PqZOnVqnDPKOm56ejvDwcG6BjpeXF7744gu4uLjINZvKmzUC8mt1anumSDNDosFUVFRw/sGFCxeiRYsWKs/63xiqq6u5ivYiRVRWVoby8nK8ffuWyxwk+ojCOyorK1FRUYGqqqpa20TtRAWERf+KEjU3poBwXYiCuEX1FUWJAdq0aSNRj1G09L9FixZc+SpRkmlRKICRkREYY1wowNu3b7kqGS9fvsTDhw+RkpKC1NRUFBQU4OzZs7hw4QKOHz+O3r17q/za8vLysGHDBm6laGhoKBYtWgQ+ny8zZeK9e/ewd+9eznRnYWGB0NBQDBw4kHtgyZpFisjKysL58+dx+/btemMJq6uruUTqOTk5yM/P52pyqorc3FzExsZyPk4jIyMsWbKEU4SN5c6dO9wLg3gmLkXp3bs3Tpw4gf3792PHjh1ITk7GmDFj8Msvv2DQoEEqkVUfIGXYTDl16hRevHgBW1tbTJgwQe3nE9Wby83NRV5eHnJzc7mHeEFBAQoKCrjco69fv250IeDGYGhoyCmjli1b1krfZm5uLlFkWKTERJlwRNlLRIWFRajqbVn0Rm5ubo62bdtywdYiGGO4d+8e1q9fj8uXL2P16tU4fvy4Sk1jqampWLZsGV69egVTU1PMnz8fo0aNknmNL1++xC+//IK4uDgANTOOYcOGYeTIkTA3N68VLiGOQCDA/fv3ER0dzQXqA0C3bt1gZ2cHGxsbtGvXDhYWFlxdwps3byIyMlLi5c7Ly0sl111dXY3k5ORaqSItLS3xwQcf1IrxUxTGGJKSknDw4EEkJiYCqMnJHBYW1qjjGhkZYcaMGRg9ejQWLFiAa9euYdq0adi7dy8GDx7cqGPrC3qjDCMiIhAREaHSZL+6zJ49ewCgztqQylBRUYGcnBxkZWUhOzsbWVlZePr0KZfpv64E6/IwNTXlFJOoAKuZmRlMTU25j4mJCUxMTCT+b2JiAmNjY5n7+Xw+11d0PHNzc/D5fFhYWMDExKTBikvb5iBZ8Hg8uLi4YOfOnRg4cCBSU1MRGRnZoHSEDeHo0aPYvHkzqqur0aNHD2zatElmqaGqqiocO3YMBw4cQHl5OQwMDBAUFISxY8fCysqqzuMLBAJkZGQgOTkZycnJnMnZwMAAXl5eGDx4MDp06FDL5FtaWopdu3Zxgf3m5uYICgqCn5+fREV5ZXj58iUuXryI2NhYbqUrj1eTYDs4OBheXl61FpwoQkVFBaKjo3HkyBHcv38fQM1LT2hoKGbPnq1QrLQ8bG1tsW/fPsyZMwdRUVGYOnUqfvrpp0b7OPUB8hk2AeRVr5f2XZWWliI9PR0hISEwMjLC1atXuYUz0sepyw9QVVWFx48fIz09HXfv3kVGRgYePXqEp0+f1rvgo23btlxJo/bt26Ndu3awtrbm0q61adOGMyG2aNFCbhUITaGqc6orPELeCtFdu3Zhw4YNsLKywuXLlyWSVgCSfkFpM7H099LSUnzzzTeIjIwEAAwcOBBLly6FmZlZrfssNTUVu3bt4moBduvWDVOnTkWXLl1qvRSJ+x9jYmJqhVZYWFhweUvFTZCimW5xcTHu37+PixcvIi8vD8bGxhg4cCBCQkK4TC6K+AFF91xZWRlSU1Nx7do1JCcnc7+rpaUlgoODERISIlGiSdZx5fkiKyoqkJSUhOvXryMqKorz55uammLMmDGYMmUKFyMorWjlrX6V910kQ2VlJT799FP89ddfMDIywg8//IDg4GCFVr/K81uKWyG0MWbJZ0g0CJF5hzGG06dPY/r06TJvWKFQiOfPn+PBgwfIyMjgMvs8ePCgTv9aixYt4OjoyGUDsbe3R+fOndG5c2d07NhR5gpHXZxdNRdmzJiBb7/9FoWFhbhz547Myi0Nobi4GJ9//jlnupsxYwamTJlS629XVVWFAwcO4OjRo1x4xYQJE+Dn51evmfbs2bNciTBzc3P06tUL7u7ucHJyknigV1dX48mTJ3jw4AHu378vkeezVatWmDdvHtq3by8z7KQ+SktLcfv2bS7jjfjLQs+ePREaGgo/Pz+lji0UCvHgwQMkJCQgPj4et2/flnhx7dChA0aNGoWxY8eiXbt2Ch9fEUxMTPDdd98hKCgIOTk52L9/P4KDg9V6zqYOKcNmyMiRI3Hp0iUcO3YM69atw+3bt+Hr64uCggK8fPkSz58/x5MnT5CZmVmnP6dFixZwcXHhPt26dUPXrl1hbW1db75RQnPk5uaiqKgIhoaGcHFxUeoYOTk5+OSTT5CZmQlzc3OsXbsW3t7etdo9efIE27dvR2ZmJgBgwIABmD59eoN8lVFRUZwiHDp0KAYOHAgjIyNuNiYQCPDw4UMkJSXh7t27Ei9jPB4PdnZ2cHZ2hp+fX60VqfVRWlqKmzdvIiEhAenp6bUUlK+vLwYOHMiVTFJEEebl5SEpKQlJSUlITk6uleKwU6dO6NevHwYMGIB+/fppNOTByMgIHTt2RE5OjkTNUkI2pAybANJmMvEHhfTqPB6PBz6fj++++w7u7u7YuHEjjh49iqNHj8o8tpGRERwdHTml5+zsDFdXV9jb28s1hahKGeqrIpVnCq2vfJL4bxYTEwOgZgFJ69at5VaBkL5X3r59i5s3b2L58uUoKiqCtbU1Nm7cCCcnJwkzJmMMR44cwcGDB1FdXc3V3PPy8oJAIKhlQhWfbb1+/RpnzpxBQkICgBpFKD5DKSkpweXLl5GUlCQRFtSqVSu4uLjA1dUVzs7OtRYrAfKrwVdVVeH69eu4du0abt26JfEbOjg4ICAgAP7+/ujSpYtc86C0SVJk+oyPj0d8fDxycnIk9ltYWMDb2xt+fn4ICAiQSCgg/neTZ3aU/l5f7t+68o2+ePGC+91HjBgBHo8nNyxLkXtSXP76ykY1FUgZNlN4PB5mz54NV1dXfP/99zA0NES7du3Qrl072NjYwMnJCd26dUPnzp25G5tme02P8+fPA4BSKwZFQdqVlZVwdnbG2rVruRJDIt6+fYudO3fixo0bAGqU7qxZsxq0KCs/Px/bt2/nlLDIv3fq1Cm8fv0af//9N/Lz87kHrYWFBby8vODj4yNTSdVHSUkJp6jS0tIklLKjoyP8/f3h5+cnUUy4PhhjePLkCa5du4Zr164hLS1NYmZpaGgIV1dX9OvXD/7+/nBzc+PkbsyCm8bw8uVLXLhwAYcPH4ZQKETv3r0llDIhG1KGzZzAwECubqGuBc4SjSMtLQ0XL14Ej8dTeGl+ZGQkvvjiCwiFQgQGBmLdunW1Vlrn5eVh8+bNyMrKgpGRESZPnoyQkBDweLwGhcYIBAKJmUhZWRlnKhWne/fuCAwMhLOzs8JZdQoLC7lVqenp6RLn69y5M6cAu3Tp0uBjvn37FikpKbh+/Tpu3LiBvLw8if2iXKp9+/aFj48PWrRoAUAx86qqENV8vHv3LmeqFa22BWrG+Mcff6xxuZoipAwJoony1VdfAagxgUnHItYFYwz//ve/8cMPPwAARo0ahcWLF8PIyEjC3Hn79m1s27YNJSUlsLS0xMKFCxt8DhEdOnTA6tWrkZKSgoyMDBgaGoLP58PMzAwtWrRAhw4dYGdnp/BqwBcvXiA5ORkpKSlcZXgRXbp0gY+PD/z9/Rs8G2KMITs7GwkJCUhISMDt27clTIgmJibw8vJC//79ERgYKJH/UxOzP8YYCgsL8fjxYzx+/BiZmZlc0WNpM60INzc3DB8+HCNGjKhVoJiQDYVW6CDSfxJZ5XPq2ieNImnTlK3j15yRlVxbWRpaW7C+GpXV1dVISUnByJEjYWBggHPnzqFr164AZPsFRZSWluLrr7/G8ePHAQBTp07F5MmTuWsU3VdnzpzBzz//DKFQCEdHRyxcuLBWHJ90Mu66rgWQvK+UCYEAahYKJSYm4urVqxIzHwBwdnZGYGAg/Pz8uFCF+sIEKioqcP36dW72l5ubK9G+Y8eO8Pf3x8CBA+Ht7c1dv7yUZdLjR5Fagjwej1PKd+/excOHD/Hw4UM8fvwYT548kfDhSmNtbQ0XFxfOxOzl5cWFqDQmjWJDk5vL+01kXasqoNAKgiAgEAiwfv16AMDYsWM5RVhfn61bt+L//u//wOPxsHjxYplL7SMjI/H7778DqEkGPXPmTJiYmCiVUKGxPHv2DPHx8bhx4waysrK47QYGBnBzc4O/vz/69euHtm3b1oqZk0VFRQXi4+Nx6dIlxMXFSZh6TUxM4Onpyc3+HBwcwOPx1Drze/nyJVJTU5GSkoKbN2/i5s2bdSo90Yrarl27cp8ePXrgnXfekQjT0JeXVHVAypAgmhh79uxBQkICLCws8Nlnn9Xbvrq6GmvXrsXp06dhYGCAVatWITQ0FKWlpVwbxhgOHz6MgwcPAgDGjx+PkSNHavThyhhDZmYmEhMTkZSUxOXtBGoUoLu7O/z8/NC3b1+0atWqQQtsysrKEB8fzy2AEbeq2NjYIDAwEAEBAfDy8uL8lerw/THG8PjxYyQkJHDXJz3DBWqUco8ePeDs7Ixu3brByckJXbt2hYODAycfKTz1QMqQIJoQOTk52LZtGwBg9erVtTKkSFNdXY1Vq1bh7NmzMDQ0xD//+c9aM0LGGH788Uf88ccfAID3338fQ4cOVc8FSCEUCvHo0SPOB/jy5Utun6GhIdzd3eHj4wNvb+8GB6qLYv+uX7+OlJQUCVeCtbU1goKCEBwcDFdXV/B4PLUpv4cPH3Jm2ISEBLx48aJWu+7du8PDwwOenp7w8PDAO++8A2NjY61neNFHSBnqINI+I+lsMOI+GemB3NRLLTVlF3Z9ssvzCzYkzpAxhuXLl6OsrAx9+/bFhAkTat0b4kkUBAIBwsPDcf78eRgZGSE8PBy+vr7cjLC0tBSMMfzwww84e/YsAGDy5MkICwur5XuUlkl8Vlafr0y8rbGxMZep5fr164iPj+dqJAI1M6M+ffrAz88Pfn5+Eunl5PkBc3Nz8eeff+LSpUt4/PixRLvOnTtj8ODBGDx4MNzd3WuZVBuTCk1aacXFxeHIkSOIi4tDfn6+RFtTU1N4enpyK1G9vb25BAKKFNZtjP9e2bbyUkIqgi7HIOqNMtS3RN1E8+PIkSOIioqCiYkJNm/eLPfBwhjDpk2bcP78eRgaGmLTpk3w8PCo1S4mJgZnz56FgYEBZs6ciYEDB6pF9urqaty7dw/JyclITEzE69evuX3m5ubw9vaGr68vfHx8OHNgfWbQ4uJiXLp0CX/99Rdu377NbTcwMECvXr3g7++PwMBAODk5qTXs4cWLF4iMjMTBgweRnZ3Nbefz+ejTpw/69++P/v37S5hiabane+iNMpw3bx7mzZvHrUIiiKZEbm4uVq9eDQD49NNP5YY5MMawY8cOHD16FAYGBli7di0CAgIkfIRATf3An376CUBNdRNVK8KKigrcuXOHWyQivmDFzMwM3t7e8Pf3h4eHB6f46lsI8+rVK1y5cgWxsbFITU3lXm4NDAzQt29fhIWFwdfXt1byAFUjFApx5coVHDp0COfOneMC/Fu2bImxY8dixIgR6NOnj0TcpC7Pigg9Uoa6jrgZQroCubRJTZEK1IqYWxq6r7mjrKm2vhCDhiL9966qqsLSpUtRVFSEXr16YebMmZwfTDq37Js3b/DLL79g3759AGoKO/ft2xelpaUSi0eKioqwZcsWlJeXw83NDUOHDq2VWUUcecvnxWdwZWVluHXrFq5du4aUlBQJM27r1q3h5+cHf39/9O7dmyvDVdd5RCbVjIwMXL16FdeuXcOdO3ckftcePXpg6NChGDFiBFedBaiteMSPq4jpU3pffn4+Dh8+jN9//10ixq9Pnz6YMmUKRo0axZl2G5NiTRfMpA2lMSZUXXpBIGVIEDrOsWPHcOHCBZiYmODrr7+Wa/I7efIkF1C/YMGCOuvYfffdd3jx4gVsbGywYMECGBgYKO1CePXqFVJSUpCYmFirEkT79u05M6Gzs3OD6w4+e/YM586dw59//lkrBtDFxQVDhgxBcHAw7O3tAag/+L2yshI7duzArl27uN+pVatWGDduHCZPngxXV1ederATikPKkCB0mOzsbM48umDBArzzzju1FreIuHLlCpeVZvr06Zg4cWIt0yhQkzw7OTkZALBo0SK0bNlSIZmEQiGysrKQmpqK1NTUWiECHTt2hJ+fH/r16wdHR0eYmpo26LgvX77EtWvXEB0djZs3b3LbzczM4OPjg8DAQPj7+8Pa2hqA5nJ/3r9/HwsXLuRKo/n4+OD999/HiBEjatWPJJoupAwJQkeprq7G/PnzUVJSgj59+mDu3Ll1ts3IyMCSJUsgEAgQFhaGWbNm1dlWpGgcHBy4skX1UVZWhrS0NNy8eRO3b9+uFRzetWtXeHl5oW/fvnB0dGyQOU6UBPvGjRuIi4vD3bt3uX08Hg99+/bFsGHDMGDAAPD5fI3n/qyqqsL333+PnTt3oqqqClZWVti6davGwk4IzULKUEcQN1FJ+wwbkyZNkXCJ5uwnVMR/J+93UFU6Nmlk/f2/+eYbxMfHw8LCAl999RWEQiEqKyslssGUlZXhxYsXmDdvHt68eYPevXtjwYIFXBvxWaToHKJZYe/evSXuLfEZnEAgQE5ODtLT05GUlFSrDqCZmRk8PDzg4+OD/v37w8rKitsnLwQCAOLj43H58mVcv369lgnU3d0dQUFBCAsLk8gBCsj3wdWXAkxeKjRZoSH37t3DZ599hrS0NABASEgItm3bBltbW6WPqw2foS6MaWkfuDy0aWomZUgQOkhSUhK2b98OAFi3bl2dSaerqqoQHh6O/Px82NvbY82aNfWGJDx8+BAAEB0djfLycnTp0gWlpaUoLS1FUVERsrOzkZ2dXcuH2KlTJ/Tp0wd9+vSBu7t7g1eAMsaQkZGBs2fP4sKFC3j16hW3T5QEOzAwEIMGDeJyi2qTV69e4b333kNBQQHatGmDDRs2YOzYsTqhWAj1QcqQIHSMkpISfPLJJxAIBBg9ejRGjx5dZ9uIiAikpaWhRYsW+Oqrrxrk/xs5ciQOHTqEoqIiLtheFhYWFujatSsXKC6uqOpTuEKhEOnp6YiLi0NcXByePXvG7bO0tMTgwYM5v6KiZZvUzYYNG1BQUIAePXrg0KFDEqtUieYLKUOC0DFWrlyJ7Oxs2NnZYcuWLXXOSM6dO4dDhw4BAP75z3+ic+fOMhfMSBMSEoKgoCCkpqbi6tWrKCkpQYsWLbiPKCG0tbU1d+6G+OvKysq4VaXXr1+vlVkmICAAw4YNQ79+/bjjaaMGoDzi4uIQGRkJHo+Hbdu2kSLUI3TrTtQjpP1H4n5CbcUOqssMpAsp1hS5NnXFGTakTNORI0e4YPmdO3fCzMysViHdt2/fIjs7G//85z8B1ATM+/j4oLy8vFZJr7pS9xkZGXEhDyLE/TXSps+6/IBlZWW4fPkyzp8/j6SkJIn72MLCAgEBARgyZAj8/Pxgbm6uUHkf6bby/Gz1+eAa4tsrLy/HihUrANSsxvX29lao7Fl9PkPxvoq01cU0iqoa0/L8iZr2H5IyJAgd4fnz5wgPDwdQE0bRp08fme0YY9iyZQvKysrQu3dvfPjhh5oUE5WVlYiPj0dUVBRiY2MlFunY2dkhICAAAQEB8PT0hImJicZCIBpLQkICcnJyYG1tjWXLlmlbHELDkDIkCB2AMYZFixahuLgYvXv3xrx58+pse/r0aSQnJ8PU1BTLly/XiLKpqKhAYmIiLl26VKsUkr29PcLCwhAUFIQuXbronOmzoYj8mm5ubmjRooWWpSE0TdO8a5VA1xJ1y5NDnslEmqawzFoTJkptoYi84iYh6fCZvXv34uLFizA1NcXmzZtRXV3NtRFPuZafn48dO3YAAGbMmAFra2uJe0n63hE3d9aXYk06FdqbN29w5coVXLx4EdevX5cI6bC2tkZwcDCGDh2K3r17yzXVKVKOSJv3r6h+onhZrMakPpNGVaZPXQif0oRLRXpsqfvvrzfKkBJ1E7pKZmYmNmzYAABYunQpnJyc6my7bds2lJaWwsXFBRMnTlT5y111dTUSExNx7tw5xMbGSuQWtbGxQVBQEIYMGQJPT09OyTWXkIO///4bAGrFNxL6gd4oQ4LQRYRCIT7//HOUlZXB19cXM2fOrJV8W8STJ08QExMDHo+HFStWwMjISCXKkDGGe/fu4eLFi4iOjkZBQQG3z97eHoMHD0ZwcDCcnZ05xdcc83CKrruhRYSJ5gUpQ4LQIvv378eVK1dgZmaGL7/8Uq6SOXDgAAAgICAAjo6OjTovYwyPHj1CdHQ0YmJiJDLBtG7dGqGhoRg2bBh69OgBHo9Xb1xhc0CUYo4sR/oJKUMNUVf1chHK2v2bWoq1+nxsTU1eeW3rCp8AajLHPHv2DOvWrQNQkzDb1tYWlZWVtRJxV1VVobCwEKdPnwYATJw4kTtXfeWIxL8bGRkhJycH58+fx/nz55GVlcXtMzMzw6BBgxAaGgp/f/9agfDywhzq+5vJ+w1VVfZKWgZljiOuDBt6H2rCt6ctn2FD26rLz6/IfaMKSBkShBZgjGH58uV48+YNfHx8MHXqVLntb9y4gcrKSnTp0gXu7u4KnSsvLw8xMTGIjo7GvXv3uO0mJibw9/fHu+++i4CAAIWrVzQnhEIh8vPzAQBt2rTRrjCEViBlSBBa4MiRI4iJiYGJiUm95lEAXGX7p0+fIi8vr1bCaHEYY8jMzMSVK1dw9epVpKenc/sMDQ3h4+PDZaGhEIIabt26hcLCQlhYWKBHjx7aFofQAqQMNUR9mdsbU5lCHrqWVUYXzKCNMdXKM+vVV/FblB0mLy8Pa9asAQB88sknsLe3lwhbkLUopnv37vDx8UFCQgKOHDmCTz/9FMB/M8G8ffsWSUlJiI+Px9WrVyVygQKAp6cnhg8fjpCQEK7ChHRohbxsKvKQvrcV+Y0ag/jfSfq4isjP4/G4HK2DBw+WMBGrKwRClgzqQBPn1IUxrQpIGRKEhlm+fDmKiorQs2dPfPTRRw3u9/777yMhIQGnTp1CixYtUFZWhmfPnuH58+fIysqSSMVmYmICHx8fDB48GAMGDEC7du30YhGMMjDG8OeffwIAwsLCtCwNoS1IGRKEBomKisJff/0FIyMjbN26VSEF5evri3feeQf379/HTz/9VGt/hw4d4Ofnh/79+8Pb2xvm5uZNNhuMJjl06BAeP34MPp+PoKAgbYtDaAkaKQShISorKznz6PTp0+Hi4qJQfx6Ph++++w6nT5/GgwcP0LJlS3Tq1AmdOnWCvb09OnXqRMpPQZ4/f47169cDqFnRq8+LiPQdGjlqRJ6vRBEfoaL7NYEuyCAPeb4pVSzDl9VX2ncmnXLthx9+wKNHj9CuXTvMmTNHwqwp7ieUlk989ti2bVt88MEH3HfpkAfpmaZ0aIU48nxa9YU8iMurSEiJIiiSlrC+trL8oaIVvSUlJejTpw9mz54NAwMDpStRaCrFmq6FVjQGXUq/2PzSSBCEDpKXl8dVrl+2bBnNQHSA3bt3IzY2Fnw+H9u3b28y1TUI9aA3yjAiIgKurq7w8fHRtiiEHvLll1+irKwMXl5eGD9+vLbF0XsOHTqETZs2AQDCw8O50BVCf9EbZThv3jzcvXsXCQkJ2haF0DMePXrEpVILDw9vlnk9mxLHjx/H0qVLAQCzZ8/GzJkztSwRoQuQz1CNKOK3aui+xrRtDLpk228IisQKyvMh1uc7k1eWSfR98+bNEAgECAoKgpeXF6qrq+Wm46tvhan4fmk/oLx0bPX5SsW/S/v5pOUV/15fW0VQxF8nr6307yDaf+bMGXz22WdgjGHKlClYtWpVnW0bK4Mile51IX5RG+sAdGntASlDglAj6enpOHXqFHg8HhYvXqzx81dWViItLQ2PHj3CkydPkJmZCT6fjyVLlqBDhw4al0dbMMawZ88erF+/HkKhEBMmTMDmzZt16mFMaBdShgShRnbt2gUAGD58OJydndV+PlE1itjYWMTFxeHGjRsoKyur1S4+Ph6HDx/Wi9p9FRUVWLt2LX7//XcAwHvvvYetW7eSuZqQgJShGhE3O+liSjVF0AUZpNFEtnxFwgakzaRPnz7FsWPHAAAfffSRRF/pB7G46bM+k5+4adTQ0BACgQBJSUk4e/Yszp8/j8ePH0u0t7KygpubGxwcHODg4IB9+/YhKysLEydORGRkJDdDFL+W+sIjxPcrYhZVJgSiId/r+s1yc3Mxe/ZsJCcng8fjYeXKlZg7d67EedVlJpV3baoMl5B3HFW1VddxdMn9QsqQINTErl27UF1djX79+sHDw0OiarwqePHiBX7//Xf89ttvXJV2oCYVm6+vLwYOHIgBAwbAxcUFBgYG3INn5MiR+Mc//oGsrCxMmDABp0+fRqtWrVQqmy5w7do1zJ8/H/n5+WjdujUiIiIwePBgnXyxI7QPKUOCUAMCgYCbFc6bN0+lx7516xb27t2LkydPcgq2VatWGDJkCMLCwjB48GC51Sg6deqEffv2YdCgQcjMzER6ejr69eunUhm1ydu3b/HVV1/h559/BmMM77zzDn7++Wc4ODhoWzRCh9G6MiwqKkJ8fDz4fD769esHExOTBvV78OABnjx5gp49e+qF34NoWqSkpODVq1do1aoVAgICGn28iooKnDlzBr/++itSU1O57Z6enpg5cyaGDh0KPp/fYD9YbGwsAMDBwQHe3t6Nlk9XSExMxJIlS/DkyRMAwKRJk7BmzRpKckDUi1aV4YkTJzB16lT06NEDRUVFqKqqwp9//ik3Z2NhYSEmTZqExMRE+Pj4IDMzEzNnzuTihrRJfUv25UGmG8VRJHxCHopU1JbnSxP///nz5wEAgYGBMDQ0BGNMrs9IfJ+4D+vvv//GgQMHcODAARQUFACo8S+OHDkSH374Yb2KTFx+kU+zqqoK//nPfwAA//u//8vJXte1SB9HmsaECSgSfiDPlyqaDf74449gjMHW1hZfffUVl3hbXeESDf2bSu9vainWtFFiShp1+xe1pgwLCgowbdo0LF++HOHh4RAKhRg9ejSmTZsmNzB+woQJKC4uxuPHj9G6dWsIBAIcP35cc4ITRAMQzbwGDRqkVP8HDx5g165dOHbsGKfEOnTogKlTp2Lq1KmwtrZWWrZjx47h2bNnaNeuHcaNG6f0cXQBxhjOnDmDDRs24Pnz5wBqnhHr1q1D69attSwd0ZTQmjI8ceIEKioq8MknnwCoeYtatGgRBg8ejPT0dJmzw2vXriEqKgqxsbHcjW5oaNjkBzTR/CgqKgIA2NnZNbgPYwxxcXHYs2cPYmJiuO39+/fHjBkzEBoaCiMjo0bl0CwpKcEXX3wBAJg1a5ZEIdumxv3797Fu3TrExcUBADp37oxNmzYhKCiIwiYIhdGaMrx58yacnJwkbPkeHh4AahYIyFKGFy9eRMuWLdG/f38ufsrNzQ3t27ev8zwVFRWoqKjgvhcXF6vuIgiiDtq0aQPgv0pRHqWlpTh16hT279+P+/fvA6gxH7377ruYO3euSn1633zzDfLz8+Hg4IAZM2ao7Lia5Pnz59ixYweOHDkCxhhMTU0xd+5czJ07F2ZmZtoWj2iiaE0ZFhUVwdLSUmJbmzZtYGBggNevX8vsk5+fD0tLS4SEhODNmzfg8/lISEjAP//5T6xYsUJmny1btmDdunWqFl8miti0teFP1KWYHnXTmDJN8soySfvS6iplJLq3i4qKOFmkU6OlpaXht99+w7Fjx/DmzRsAgLm5OSZNmoSPPvqIW/0oz0+liE8zKysLP//8MwBgzZo1MDY2lmivSPpARVKAKetXk973+vVr/Pvf/8aePXu4F9wRI0YgPDwcjo6Oco+rCT+gLqRYU6VvT9fWMSgbe9lQtKYMTUxMamXGKC8vh1AohKmpaZ19srOz8dlnn2HhwoUAapLujh07FiEhITLfoFesWIHPP/+c+15cXIzOnTur7kIIQgYin97hw4fh7OwMQ0ND8Hg8vHjxAlFRUYiKiuJ8XADQrVs3TJs2DePHj4eVlZVaZPr6669RWVkJPz8/BAUFKV1nUNO8evUKu3fvxi+//MI9M3x9fbFq1Sp4enpqWTqiuaA1Zejk5IRjx46BMcZp+ezsbACo9ZYnomvXrgBqlkuLGDNmDPh8PuLj42UqQ1NT0zqVK0Goi5kzZ+L06dNISkrC6NGjZbbh8/kIDg7GtGnT4O/vr9Y38fT0dC7uccWKFTr31i+L3Nxc/PLLL9i3bx83c+7ZsycWL16MoKAgqj9IqBStKcOwsDCsWLECsbGxGDhwIAAgMjISbdq0ga+vL4CaJeCnT5+Gl5cX7O3tERYWBkNDQzx48AA2NjYAgJycHJSXl6NTp07aupQ60fVlzPpkNpWHvOoN8qo1SLcV/33d3Nxw+PBhhIeHIz8/HwKBgPNvBQYGIjQ0FIGBgZyPS/zBrkiF9/pCIETyfvHFF2CMYdiwYXB3d4dQKFQoXEIe9Zn4FDU73rlzB7t378bJkye5lbRubm5YvHgxQkNDuWMoclx1mT51IcWarj1nmio8psUn4owZM3Du3DmEh4ejsLAQGzduxLfffovZs2cDqPERWFpaYs+ePZg+fTqAmnpwv/32G5YuXQo+n4+dO3fCwsICsbGx9Za+AWrMpK1bt0ZRUZHKU1DJK8ujCFSWSfUokm9U/HtVVZXEPnnf61NM8vJhqkoZSn+vqqpCQkICxo4dC0NDQ5w7d46zsKiq9JIqlKEoxnjv3r0SoVW+vr6YPXs2QkJC5OYQbW7KUF1xhqropwuo4zmu1aD7n376CXv27EF0dDRMTU1x8uRJhIaGcvuNjY0xevRo2Nvbc9s2b94MLy8vnDp1CgYGBpgzZw5mzZrVIEVIEPqIqHLG+PHjOUWoK+Tk5CAyMhK//fYb8vPzAdS8GAwfPhxz5sxB7969tSwhoS9odWaoDWhm+F/06U+vrzPDrKws+Pr6QigU4vz58+jevXudbTU1MywrK8Nff/2FyMhIXLt2jdtnbW2NKVOm4P3334etra1KV33SzFB1/XSBZjczbOo09fRrjUlnpgn5NVGiSdZ3eeWJFFFw0shTeIpUpJcXDiGt4Pbv3w+hUAhfX18JRSjrPPLkb2yYQFlZGaKionD69GlERUWhvLyc2x8QEIBJkyZh+PDhEovdGqOIFEmF1pi0afL26eLzQBeeO7oKKUOCaKYIhUKuoK3I565JioqKEB0djbNnzyImJgZv377l9nXp0gXjx4/HhAkTFMrSQxDqgpQhQTRTysvL8fLlSwDAgAED1H4+xhgyMjIQGxuLS5cu4fr16xJmZHt7e4wYMQIjR45Ez549wePxKG0aoTOQMiSIZoq4OdXISPVDnTGGJ0+eID4+HvHx8bh69Spyc3Ml2nTr1g1hYWEICwtDr169SPkROgspQw3R1Gz1uiCvqlKq1ddXEZ+cNPIe7vL8gvL8VKryaYpi9ETnbqyPsKysDDdv3kRSUhJSU1ORnJyMFy9eSLQzNTWFn58fBg4ciKCgIHTr1k3pNGTqKg3VmIUumvILairlGvFfSBkSRDPFyMgIPB4PjDHs3r0b48aN45JVyEMgEOD58+d4/PgxMjIykJaWhjt37uDRo0e1lK+pqSk8PDzg6+sLX19f+Pj4wNzcXF2XRBBqQ29CKyIiIhAREQGBQICMjAyVLMlVV2JuQjaqmhnWtwJTfEYl/n9ZbRXJ4qLszFBaAcmTT/r7woULERkZyZ3D29sbAwYM4FZtMsZQUlKCvLw85OfnIzc3F5mZmRKVXsSxtbWFt7c3+vTpAw8PD7i7u9cqA6WqWVlTmxk2ZhbZmLaK0FyeQ+oIrdAbZShClT9iY0IrCMVpjDKUZ1qUpwzrC60Qpz4zZENjxxSRT1r5SfetqKjA3r17ceLECaSkpNR5TmlMTEzg6OiI7t27w83NDe7u7ujZsydXLk3XlIu22jb0OPUdt75jNXRfY9o2JUgZqgBShk0XUoa15atPGYrL++zZM5w5cwZpaWkS21u0aAFbW1vY2NjAxsYGDg4OsLe3b7BPsSkoLVKGzQsKuicIQmk6duyIWbNmcd9pkQZB/Bda50wQBEHoPTQzbAT09qxeVBlKoUhZJnEas+BDkRyj8sI5Glo2StY55bWVRl0LPDSxyESRa2tMeER9MhFNF5oZEgRBEHoPKUOCIAhC7yFlSBAEQeg95DMkmizyAukVCbqXRhH/kiL17JSVT5HAfkVCPxTZr6qQAkX7avo40vspjEF/oJkhQRAEofeQMiQIgiD0HjKTElqlMeET8vY1JnOMqrKVyJNRETNpfeETDUWVJj9NZFNpasclmjY0MyQIgiD0Hr1RhhEREXB1dYWPj4+2RSEIgiB0DErUTWgVVZlJ68sqIy8DjbImVOnviphJ5SXjlk7MrYi88iAzqe4clxJ1Nw5K1E00eVSl/KT3K9JWXZUI5J2zvn3KpliTRl2pxTT1cNbEeXRRXkL76I2ZlCAIgiDqgpQhQRAEofeQMiQIgiD0HvIZEiqnMWuylPWz1Ycm0nwp4rdURAZ5bTVVfkgbbXVdvsa0JXQPmhkSBEEQeg8pQ4IgCELvITMpoRSqCk9VxPSpKjNpY5bLK4Ii8upCXJmumQ91TR5NnofQPDQzJAiCIPQeUoYEQRCE3kPKkCAIgtB79MZnGBERgYiIiFp5H4mGoa5wicagC342VYV3KNNOk8fSlJ9N2X7akK+xfdVxHEJ5KFE30SA0pQwVWUCjKlSlDBWpqdiYxUCKoAsPa1KGqj0OLeJRz3OczKQEQRCE3kPKkCAIgtB79MZnSCiGLphFpdGUyUf8PJq6FkXOqa7fQRdMquo4TmOO1dxkIOqGZoYEQRCE3kPKkCAIgtB7yExKaBVpE5CqVlWqy7SkqhRr8tCWWUwT59VFE29zMusSykMzQ4IgCELvIWVIEARB6D2kDAmCIAi9h3yGhE7RlH0l9fk/m9K16YKsuuiD00WfJ6EaaGZIEARB6D16owwjIiLg6uoKHx8fbYtCEARB6BiUqJuQiS5WqdAG9YVSaCOxuCbQBbMdmUl197jaRh3PcfIZEhy6HuPXGDSRVq0p+wjViTZ+B12IO9TUcTV9juaK3phJCYIgCKIuSBkSBEEQeg+ZSQkOZas1NAVUdW3ywifIRKVedN182ZzT6OkDNDMkCIIg9B5ShgRBEITeo1Vl+Pz5c0yYMAFt27ZFp06d8Pnnn6OioqJBfQsKCuDo6Ag+n49nz56pWVKCIAiiOaM1n6FAIMDw4cPRtm1b3LhxA69evcK4cePw5s0b/Oc//6m3/4wZM+Ds7IzMzMxm59/SBdRVWqkpoKqq8/r0mymLpvxduu5v1PVz6gNamxmeO3cOqamp2L17N7p16wYfHx9s3rwZP/30E16+fCm3786dO1FaWorPP/9cQ9ISBEEQzRmtKcO4uDh06dIFTk5O3LYhQ4ZAIBDg+vXrdfZLSUnB1q1bsW/fPnpDIgiCIFSC1pTh33//jfbt20tss7a2Bo/HQ25ursw+paWlmDhxIr799lvY2dk16DwVFRUoLi6W+BAEQRCEOFqNMzQwkNTFopleXb6WTz75BP7+/hg/fnyDz7FlyxasW7dOeSEJAIr5KZqTr6wxvlNds1yoMr5SF9CX9Ga6IIM+oLWZoY2NDV68eCGx7eXLl2CMwcbGRmafmJgYHDhwAHw+H3w+H8OGDQMAdOvWDUuWLJHZZ8WKFSgqKuI+OTk5qr0QgiAIosmjtZlh//798cUXXyAnJwedO3cGUKPsDAwM0LdvX5l97t+/L/F2GxMTg2HDhuHOnTvo0qWLzD6mpqYwNTVV/QUQBEEQzQatzQyHDh0KZ2dnzJ8/Hy9fvsSDBw+wZs0aTJo0Cba2tgCAoqIi8Pl87N+/H0CNYhPNCvl8PoyNjbntRkaUWU5X4PF4Ep/mhPS1yfvoGorIrq1r0YZMun7dhGbQmjI0NjbG6dOnUVZWho4dO8LDwwN+fn7YtWsX14YxhoqKCggEAm2JSRAEQegBOlHcVygU1lpMI6K8vBzGxsYwNDSU2a+yshJ8Pr/B56LivppHB24xCTQlj65dd1NAX4PYdUGGpkSzLe5blyIEIFfRGRgYKKQICYIgCEIWOqEMieaNrpWGqu8tXFUyquptXxd+M0XQhVmOLsggjS7KRPwXqlpBEARB6D2kDAmCIAi9h5QhQRAEofeQz5DQKJry1zUGXSvLRL4m2eja76Jr8hCKQTNDgiAIQu/RG2UYEREBV1dX+Pj4aFsUgiAIQsfQiaB7TUJB900XXb9VdV2+poCumxp1XT59QR3Pcb2ZGRIEQRBEXZAyJAiCIPQevVtNKjJlUcX7poeumyF1Xb6mgK6bIXVdPn1B9PxW5ZjTO2VYUFAAAFwNRYIgCKJpUlBQgNatW6vkWHqnDK2srAAA2dnZcn9EHx8fJCQk1Hu8hrRTRZvi4mJ07twZOTk59TqMNSVTQ9s0VHZNytSQdiS3ZseBKuVWlUwNaUNjU7VtGtKuqKgI9vb23PNcFeidMhRVyGjdurXcP76hoWGDVik1pJ2q2gBAq1atNHY+VcoN1C+7pmVS1W+u73Kr+liqkFuVMtHY1N17XF7FI0WhBTR1MG/ePJW1U1WbhqJJmZqq3Iq0U8VxmrPcqj6Wqo6j7/d4U5VbkXaqhOIMmwhNVW6g6cpOcmsWklvzNFXZKc5QBZiammLNmjUwNTXVtigK0VTlBpqu7CS3ZiG5NU9TlV0dcuvdzJAgCIIgpNG7mSFBEARBSEPKkCAIgtB7SBkSBEEQeo/eKMOnT59i7ty5GDRoECZNmoSrV6/W2+fixYuYNm0aBg8ejHHjxmHPnj0QCoUakPa/lJSUYPXq1QgKCsLo0aNx5MiRBvWLjY3FtGnTEBQUhJUrV6KkpETNkkoiFAoRERGB0NBQvPvuu/jmm29QXV3d4P6zZs2Cr68vbt26pUYpZXPixAmMGTMGgwcPxooVK1BUVCS3fU5ODlauXInQ0FCMGzcOu3fvVuhaFSUxMRFTpkzBwIEDMXv2bDx58kQtfVSNomOwuroae/fuxXvvvYd3330Xn332GbKzszUk7X9RdgyK+oaFhcHX1xeVlZVqlLI2yo7BjIwMzJs3D0FBQZgzZ45WfnNFx2BZWRm2b9+OUaNGYciQIZg9e7bizw6mBxQWFjI7Ozs2cuRIdvr0abZkyRJmbGzMrly5UmefP//8kxkYGLDVq1ez6Ohotnv3bta6dWu2YsUKjcktFApZQEAA8/T0ZMePH2fffPMNMzExYT/88IPcfrt27WJ8Pp9t3LiRXbx4ke3YsYN98MEHmhH6/7NgwQLWvn17tn//fvbbb78xW1tbNnv27Ab13b59O+vZsycDwC5fvqxmSSXZt28fMzY2Zl9//TU7ceIE8/b2Zn379mXV1dUy22dnZ7Nu3bqxzZs3s7Nnz7K9e/cyOzs7NnHiRLXIl5yczPh8Pvv000/ZmTNn2Lhx45iNjQ3Lzc1VaR9Vo8wYHD9+PJsxYwb7/fff2dmzZ9m4ceOYpaUle/TokcbkVnYMipg8eTJ3L799+1bN0kqizBiMjY1l5ubmbM6cOSwqKort37+fDRgwQEMS16DoGGSMsbFjxzInJyd28OBBduHCBTZ9+nRmbm7O0tPTG3xevVCG69evZ9bW1qyiooLbNnz4cBYcHFxnn48//ph5e3tLbFu0aBFzcXFRm5zSnDx5kgFgjx8/5ratXLmS2djY1Hlj5OTkMFNTU/avf/1LYrsmB+LTp0+ZgYEBi4yM5LYdO3aM8Xg8iWuRRWJiIrOzs2NxcXEaV4ZCoZDZ2dmxZcuWcduys7MZj8djf/zxh8w+FRUVrLKyUmLbiRMnGAD27Nkzlcs4atQoNmTIEO57VVUVs7OzY8uXL1dpH1WjzBgsKSmR+F5dXc3s7OzY6tWr1SanNMqMQRE///wz69u3L9u/f7/GlaEyY7C6upo5OTmx6dOnS2zXpNzKjEGBQMCMjIzYjz/+KHGcli1bsm+++abB59YLM2lUVBRCQ0NhYmLCbRs9ejQuXbqEqqoqmX28vb3x5MkT/P333wCAiooKJCQkoG/fvhqRGaiRu2fPnnB0dOS2jR49Gnl5eUhLS5PZJzIyEjweDzNnzpTYzufz1SqrODExMWCMYfjw4dy2oUOHwsjICNHR0XX2Ky0txaRJk/D999/DxsZGE6JKcP/+fTx9+hQjR47ktnXu3Bmenp64cOGCzD4mJiYwNjaW2NaiRQsAULlZjDGG6OhoCfmMjIwwbNiwOuVTpo86UGYMin5HEYaGhjAzM9OouVGZMQjU3EsrVqzAgQMHYGSk+ayXyozBq1ev4vHjx5g7d67Edk0+O5QZgwYGBvD09MS1a9e4KhYpKSkoKyuDt7d3g8+tF8owKysLHTt2lNjWsWNHVFVVccpOmpkzZ2LVqlVwcXGBh4cHOnXqBEdHR+zatUsTIgOoW27RPlncvXsXrq6uuHjxIkaMGIGhQ4di7dq1Gi1ZlZWVBUtLS5iZmXHbTE1N0bZt2zrlBoCPP/4YQ4YMkRgImkQkm6zfXJ7c4giFQmzZsgW9e/eGg4ODSuUrLCxEaWmpQvIp00cdKDMGpYmMjMTDhw8xatQodYgoE2XGYEVFBd577z1s2rQJ3bp1U7uMslBmDN69exeGhoYwNDTEe++9h+DgYCxYsECjPkNlx+Dp06fx+PFjdO7cGb169UJISAj++OMP+Pn5NfjcTTJR94ULF7Bq1Sq5bRYvXox//OMfAICqqqpamQpEN0ldb6VXrlzB2rVrMX/+fAQFBSEjIwOrV6/Gjz/+iPnz5ysld1ZWFiZOnCi3zejRo7FixQql5S4vL8fDhw+xfv16hIeHQygUYv369Th58iSuX78u8WauCEFBQSgrK6tzf48ePbBv37465RbJXpfcv/zyCxITE5GUlKSUfHUxd+5cJCcny21z5coVGBoacrLJ+s1fvXrVoPMtXrwY8fHxuHLlinICy0GefHX9rsr0UQfK3MviJCUl4cMPP8SKFSsUesA1FmXkXrRoEZycnPDhhx+qXb66UGYMlpeXg8fjYfLkyVi5ciXat2+PXbt2wdPTE7du3UKnTp3ULbbSY3Dt2rXIysrCtm3bYG1tjYMHD2LBggXw8PBo8Etpk1SGnp6e2Llzp9w24mYNKysrFBYWSuwX1TWsqwTIqlWrEBwcjI0bNwKoUQbV1dVYsmQJPvroI6WUio2NTb1yt2/fXkLux48fy5S7bdu2MvtbWVmhuLgYBw8eRJcuXQAAzs7OcHZ2RlxcHIKCghSWGwC2bt0KgUBQ534LCwsJGaR/b5Hsdcm9d+9elJWVcfJVVFQAAGbPno0RI0Zg69atSsk9f/78emfFhoaGnNxAzWxK/M20oKAA1tbW9Z5r5cqV+PHHH3H27Fn07NlTKXnl0aZNGxgYGMi8l+v6XZXpow6UGYMiUlNT8e6772L69OnYtGmT2mSUhTJjcO/evbC3t4evr69E+4EDB+Ljjz/G9OnT1Sfw/0eZMWhlZYXq6mps3LgR48aNAwAMGjQIHTt2xIEDB7B06VK1yiySAVBsDN6/fx/ff/89zp8/j+DgYABASEgI3N3dsW3bNnz//fcNOneTVIZt27ZVaCB7eXnVqo1148YNODg4wNLSUmafwsJC9OrVS2Jbx44dUV5ejrKyMqWUIZ/P5wZIQ+U+fvw4KioquDelGzduwNDQEO7u7jL7eHt7g8fjwdbWltvWoUMHAGjw7EYWPj4+CsldUVGB27dvc3Lev38fxcXF8PT0lNknIiJCQmk9ffoU48ePx6effopBgwYpLberq2uD2/bs2RPGxsZISEjglFlVVRVSUlKwbNkyuX1Xr16N7777Dn/99Rf69++vtLzy4PP5cHFxQUJCgsQD9caNG3X+rsr0UQfKjEEAuHXrFoKDgzFp0iR8++236hazFsqMwejoaIkXxwsXLmD16tX48ssv0bVrV43JregYFPnXxJWQiYkJrKysGvXsUARlxqBI6UvPXDt06CDzhaBOlFry08SIjY1lPB6PnTlzhjHG2JMnT5i1tTXbsGED1yY6Opr169eP5efnM8YYmz9/PuvUqRPLyclhjDFWVlbGwsLCWM+ePTUm999//80sLCzYli1bGGM1q+s8PDzYuHHjuDY5OTmsX79+LC4ujjHGWHFxMWvfvj3bvn0712bz5s3M3NxcLasbZSEQCJiLiwsbP348EwgETCgUsvfff5917dqVVVVVce2Cg4PrXKL+4MEDrYRWvP/++8zd3Z0VFRUxxhj76quvGJ/PZ9nZ2VybTz75hC1atIj7vmbNGtayZUu5YQKqYvv27czS0pLdv3+fMcZYVFQUMzAwYH/++SfXJiIigg0bNkyhPupGmTF4+/Zt1q5dOzZv3jyNySmNMmNQmt9//13jq0mVHYOBgYFs2rRp3ErZv/76ixkYGLDz589rTHZFx2BJSQmztLRkc+fOZQKBgDHGWFJSEjMzM6u1ql4eeqEMGat5IJiZmbEePXowU1NTNnnyZIkl8ZGRkQwAp/yKiorYmDFjGJ/PZ+7u7szS0pL17t2b3bp1S6Nynzp1illZWTEHBwfWsmVL5u/vz168eMHtFymNU6dOcduuXLnCOnfuzJycnJijoyPr0KEDO3nypEblTktLY927d2ft27dnNjY2zMnJiaWmpkq0ad26NVuzZo3M/tpShoWFhWzQoEGsRYsWzNHRkbVp04YdPXpUos2QIUPY8OHDGWOM3bx5kwFgtra2rF+/fhKf+Ph4lctXXV3NPvzwQ2Zqasrdy5s2bZJos2zZMmZjY6NQH02g6Bjs378/MzAwqPW7ajLWlzHlxqA42lCGjCk3BrOzs5m3tzeztbVlLi4urGXLluzrr7/WqNyKjkHGGDt37hzr0qULs7W1ZW5ubszU1JR9/PHHnHJsCHpVtaK4uBiPHj2Cra0tZzoUUVhYiIyMDHh5eUmYQAsLC5GTk4N27dqhY8eO4PF4mhYbFRUVuHfvHlq2bAknJ6da+1JSUuDs7Iw2bdpw2wUCAe7duwcTExM4OjpqZXk3Ywzp6elgjMHFxaVWVerExETY2trCzs6uVl/Rdbm5uaFly5aaEpnjyZMnKCoqgrOzc62l5enp6TAwMMA777yDN2/e4Pbt2zKP4erqqrYacXl5eXj+/DkcHR0l/u5ATUacFy9ewMvLq8F9NIUiYzAtLQ2lpaW1jtG2bVt0795dUyIDUG4MiigoKMCDBw/Qr18/jT8/lB2Djx49Qnl5Obp27arR0ApxGjoGRQgEAuTk5KCkpASOjo61QnPqQ6+UIUEQBEHIQi/iDAmCIAhCHqQMCYIgCL2HlCFBEASh95AyJAiCIPQeUoYEQRCE3kPKkCAIgtB7SBkSBEEQeg8pQ4IgCELvIWVIEARB6D2kDAmiiRIWFoazZ89KbMvPz8eQIUOQnp6uJakIomlCypAgmii5ubm4fPmyxLZ169YBAFxcXLQhEkE0WZpkPUOCIAB3d3eJGeDDhw/x448/4sqVK1qUiiCaJqQMCaKJ4u7ujj179nDfw8PD8T//8z9ckdbMzEwsX74cANCyZUtMmDABISEhWpGVIHQdUoYE0URxd3fHw4cPUVVVhZs3b+LkyZO4e/cut//y5cvIzc3FnDlzkJOTg9GjRyMzMxPt27fXotQEoZuQz5Agmiju7u6orq5GRkYGli1bhtmzZ0vU2ktMTMTEiRPx3nvvYd68eWjdurVW6nESRFOA6hkSRBPGysoKY8aMwZEjR/Dw4UNYW1tz+/z9/cHn82FlZYVnz57h008/xcSJE7UoLUHoLjQzJIgmTM+ePbFnzx4sXbpUQhEKBALcuXMHs2bNwpAhQ5CZmQlXV1ctSkoQug3NDAmiCZOeno68vDz069cPZmZm3Pbbt29jypQpuHnzJgBg48aNKCoqwpdffqktUQlCp6GZIUE0YVxcXDBo0CAJRQjU+Av79OnDfR87diyOHj2qafEIoslAM0OCaIbcvn0bhoaGEqbRP/74AyNHjoSpqakWJSMI3YSUIUEQBKH3kJmUIAiC0HtIGRIEQRB6DylDgiAIQu8hZUgQBEHoPaQMCYIgCL2HlCFBEASh95AyJAiCIPQeUoYEQRCE3kPKkCAIgtB7SBkSBEEQes//A1Ctg8B72YU1AAAAAElFTkSuQmCC", "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": 0.005492, "end_time": "2026-06-30T01:11:05.623017+00:00", "exception": false, "start_time": "2026-06-30T01:11:05.617525+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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 110.098081, "end_time": "2026-06-30T01:11:06.345192+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": "2026-06-30T01:09:16.247111+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }