{ "cells": [ { "cell_type": "markdown", "id": "b1", "metadata": { "papermill": { "duration": 0.005883, "end_time": "2026-06-30T01:26:35.320166+00:00", "exception": false, "start_time": "2026-06-30T01:26:35.314283+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Particle-spray Stream Modeling with streamspraydf\n", "\n", "The particle-spray technique generates tidal streams by \"spraying\" particles\n", "from the Lagrange points of a progenitor cluster as it orbits in a gravitational\n", "potential. Each particle is given a small velocity kick and then integrated forward\n", "in the potential. galpy provides two implementations (described in \n", "[Qian et al. 2022](https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.2339Q/abstract)):\n", "\n", "- `chen24spraydf`: the spray model from [Chen et al. (2024)](https://ui.adsabs.harvard.edu/abs/2025ApJS..276...32C/abstract)\n", "- `fardal15spraydf`: the spray model from [Fardal et al. (2015)](https://ui.adsabs.harvard.edu/abs/2015MNRAS.452..301F/abstract)\n", "\n", "These are faster to set up than `streamdf` and work in any potential." ] }, { "cell_type": "code", "execution_count": 1, "id": "b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:35.330334Z", "iopub.status.busy": "2026-06-30T01:26:35.330047Z", "iopub.status.idle": "2026-06-30T01:26:37.978805Z", "shell.execute_reply": "2026-06-30T01:26:37.978085Z" }, "papermill": { "duration": 2.655102, "end_time": "2026-06-30T01:26:37.979989+00:00", "exception": false, "start_time": "2026-06-30T01:26:35.324887+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from astropy import units as u\n", "from galpy.df import chen24spraydf, fardal15spraydf\n", "from galpy.potential import LogarithmicHaloPotential\n", "from galpy.orbit import Orbit\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "b3", "metadata": { "papermill": { "duration": 0.003958, "end_time": "2026-06-30T01:26:37.988277+00:00", "exception": false, "start_time": "2026-06-30T01:26:37.984319+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Setup\n", "\n", "We set up a potential and a progenitor orbit. The particle-spray classes\n", "only need the potential and the progenitor orbit (no action-angle machinery)." ] }, { "cell_type": "code", "execution_count": 2, "id": "b4", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:38.001081Z", "iopub.status.busy": "2026-06-30T01:26:38.000678Z", "iopub.status.idle": "2026-06-30T01:26:38.004718Z", "shell.execute_reply": "2026-06-30T01:26:38.003733Z" }, "papermill": { "duration": 0.012995, "end_time": "2026-06-30T01:26:38.005360+00:00", "exception": false, "start_time": "2026-06-30T01:26:37.992365+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "lp = LogarithmicHaloPotential(normalize=1.0, q=0.9)\n", "prog = Orbit(\n", " [1.56148083, 0.35081535, -1.15481504, 0.88719443, -0.47713334, 0.12019596],\n", " ro=8.0,\n", " vo=220.0,\n", ")" ] }, { "cell_type": "markdown", "id": "b5", "metadata": { "papermill": { "duration": 0.004079, "end_time": "2026-06-30T01:26:38.013784+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.009705+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Initialize chen24spraydf\n", "\n", "We create a spray model for the leading tail. The key parameters are:\n", "\n", "- `progenitor_mass`: mass of the progenitor in solar masses\n", "- `progenitor`: the progenitor orbit\n", "- `pot`: the gravitational potential\n", "- `tdisrupt`: time since disruption began (in Gyr when using physical units)\n", "- `tail`: which tail to model (`'leading'`, `'trailing'`, or `'both'`)" ] }, { "cell_type": "code", "execution_count": 3, "id": "b6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:38.023031Z", "iopub.status.busy": "2026-06-30T01:26:38.022806Z", "iopub.status.idle": "2026-06-30T01:26:38.030850Z", "shell.execute_reply": "2026-06-30T01:26:38.030113Z" }, "papermill": { "duration": 0.013865, "end_time": "2026-06-30T01:26:38.031746+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.017881+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "spdf_lead = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"leading\",\n", ")" ] }, { "cell_type": "markdown", "id": "b7", "metadata": { "papermill": { "duration": 0.004269, "end_time": "2026-06-30T01:26:38.040509+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.036240+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Sample stream particles\n", "\n", "The `sample` method generates stream particles by spraying `n` particles\n", "from the progenitor's Lagrange points and integrating them forward." ] }, { "cell_type": "code", "execution_count": 4, "id": "b8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:38.049723Z", "iopub.status.busy": "2026-06-30T01:26:38.049475Z", "iopub.status.idle": "2026-06-30T01:26:38.603627Z", "shell.execute_reply": "2026-06-30T01:26:38.602700Z" }, "papermill": { "duration": 0.559684, "end_time": "2026-06-30T01:26:38.604293+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.044609+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "lead_stream = spdf_lead.sample(n=500)" ] }, { "cell_type": "markdown", "id": "8296078c", "metadata": { "papermill": { "duration": 0.00396, "end_time": "2026-06-30T01:26:38.612560+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.608600+00:00", "status": "completed" }, "tags": [] }, "source": [ "Let's visualize the sampled stream particles:" ] }, { "cell_type": "code", "execution_count": 5, "id": "b9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:38.622004Z", "iopub.status.busy": "2026-06-30T01:26:38.621785Z", "iopub.status.idle": "2026-06-30T01:26:38.901271Z", "shell.execute_reply": "2026-06-30T01:26:38.900147Z" }, "papermill": { "duration": 0.285252, "end_time": "2026-06-30T01:26:38.901981+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.616729+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(lead_stream.R(), lead_stream.z(), \"k.\", ms=1)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Leading arm (R, z)\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(lead_stream.R(), lead_stream.vR(), \"k.\", ms=1)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$v_R$\")\n", "plt.title(\"Leading arm (R, vR)\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "b10", "metadata": { "papermill": { "duration": 0.004138, "end_time": "2026-06-30T01:26:38.910671+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.906533+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Leading and trailing arms with tail='both'\n", "\n", "Using `tail='both'` generates both arms in one call. This is more\n", "efficient than creating separate leading and trailing instances." ] }, { "cell_type": "code", "execution_count": 6, "id": "b11", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:38.920172Z", "iopub.status.busy": "2026-06-30T01:26:38.919962Z", "iopub.status.idle": "2026-06-30T01:26:40.012756Z", "shell.execute_reply": "2026-06-30T01:26:40.011906Z" }, "papermill": { "duration": 1.098583, "end_time": "2026-06-30T01:26:40.013464+00:00", "exception": false, "start_time": "2026-06-30T01:26:38.914881+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "spdf_both = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "both_stream = spdf_both.sample(n=1000)" ] }, { "cell_type": "markdown", "id": "a8062c9f", "metadata": { "papermill": { "duration": 0.004315, "end_time": "2026-06-30T01:26:40.022724+00:00", "exception": false, "start_time": "2026-06-30T01:26:40.018409+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plotting both arms in Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "id": "b12", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:40.032708Z", "iopub.status.busy": "2026-06-30T01:26:40.032499Z", "iopub.status.idle": "2026-06-30T01:26:40.139320Z", "shell.execute_reply": "2026-06-30T01:26:40.138390Z" }, "papermill": { "duration": 0.112877, "end_time": "2026-06-30T01:26:40.140038+00:00", "exception": false, "start_time": "2026-06-30T01:26:40.027161+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6, 6))\n", "plt.plot(both_stream.x(), both_stream.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Both tails in Cartesian coordinates\")\n", "plt.axis(\"equal\");" ] }, { "cell_type": "markdown", "id": "b13", "metadata": { "papermill": { "duration": 0.004518, "end_time": "2026-06-30T01:26:40.150214+00:00", "exception": false, "start_time": "2026-06-30T01:26:40.145696+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Using fardal15spraydf\n", "\n", "`fardal15spraydf` provides an alternative spray model based on\n", "Fardal et al. (2015). The interface is the same." ] }, { "cell_type": "code", "execution_count": 8, "id": "b14", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:40.160365Z", "iopub.status.busy": "2026-06-30T01:26:40.160136Z", "iopub.status.idle": "2026-06-30T01:26:41.255458Z", "shell.execute_reply": "2026-06-30T01:26:41.254686Z" }, "papermill": { "duration": 1.101359, "end_time": "2026-06-30T01:26:41.256095+00:00", "exception": false, "start_time": "2026-06-30T01:26:40.154736+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "spdf_fardal = fardal15spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "fardal_stream = spdf_fardal.sample(n=1000)" ] }, { "cell_type": "markdown", "id": "b465061b", "metadata": { "papermill": { "duration": 0.004405, "end_time": "2026-06-30T01:26:41.265499+00:00", "exception": false, "start_time": "2026-06-30T01:26:41.261094+00:00", "status": "completed" }, "tags": [] }, "source": [ "Comparing the two spray models side by side:" ] }, { "cell_type": "code", "execution_count": 9, "id": "b15", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:41.275705Z", "iopub.status.busy": "2026-06-30T01:26:41.275504Z", "iopub.status.idle": "2026-06-30T01:26:41.497357Z", "shell.execute_reply": "2026-06-30T01:26:41.496498Z" }, "papermill": { "duration": 0.228037, "end_time": "2026-06-30T01:26:41.498137+00:00", "exception": false, "start_time": "2026-06-30T01:26:41.270100+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(both_stream.x(), both_stream.y(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"chen24spraydf\")\n", "plt.axis(\"equal\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(fardal_stream.x(), fardal_stream.y(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"fardal15spraydf\")\n", "plt.axis(\"equal\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "eb740819", "metadata": { "papermill": { "duration": 0.004492, "end_time": "2026-06-30T01:26:41.508307+00:00", "exception": false, "start_time": "2026-06-30T01:26:41.503815+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Progenitor self-gravity with progpot\n", "\n", "The `streamspraydf` models can include the progenitor's gravity using the\n", "`progpot` parameter:" ] }, { "cell_type": "code", "execution_count": 10, "id": "bc23e0d2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:41.518405Z", "iopub.status.busy": "2026-06-30T01:26:41.518178Z", "iopub.status.idle": "2026-06-30T01:26:45.200761Z", "shell.execute_reply": "2026-06-30T01:26:45.199735Z" }, "papermill": { "duration": 3.688595, "end_time": "2026-06-30T01:26:45.201439+00:00", "exception": false, "start_time": "2026-06-30T01:26:41.512844+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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7jQ8Xo9GIrl27OqxtURshhL0pveqxxMTEGuf6+Phg9uzZ2L17N1566SUUFhbW+Ed22LBhKC0txe7dux2OO5uh0VCjRo2CEALz589HUFAQbrvtNvvxPXv2YMeOHejXrx/atWtX53VsU8Gr/p92U7uS98XX1xd33HEHdu/ejYsXLzr8bOvWrfD19cWQIUPg5+dnP6/qbCTb81e/5l133YVdu3bh4sWLTv8ONNUaP8HBwQBq3l9XX1dDNeQ+1EcIUaM1eN++ffjtt99qnDtp0iQolUqsW7cOa9euRVBQEB566KF6n6O2+2MzePBg9OrVC6tWrcKqVavQtm1bl65LzYthhhrl/vvvx5gxY/CPf/wD69evx/nz52EymbBp0ya88MILDb7ehAkTcO+992LmzJn48MMPcfbsWZSUlOC3337DSy+9hGXLljX4mufOncPIkSNx/vx57N69G7fcckut5/r6+tYaoHx8fBzCxKxZs7By5UocP34cFRUVyMnJwfr16xEYGIh+/fo5XPfaa6/FnDlzkJubi/z8fMydOxe//PILli5d6tJrGDt2LIqLi7Fw4UIUFRXhzz//xKOPPoquXbs6Pf+xxx5DQEAAli9fjpCQEDz44IMOP58yZQp69OiBWbNmYe/evbh06RJ27dqFbdu22bspGqtPnz7o0KEDduzYgaFDh9rHR4wePRoWiwV79+51qYspKCgI1157LdLS0mCxWK6optpc6fuyZMkSFBYW4qGHHsIff/yBwsJCrFy5EmvXrsXTTz+NmJgYAEB8fDwkScJjjz2GM2fOoKCgAEuXLnUazlesWIHy8nJoNBqkp6fj0qVLOHfuHL7++ms88MADOHjwYJO89ptvvhkA8NVXX9VY8dnV19VQDbkPdRk7diw2bdqEPXv2oLS0FHv37sXs2bNxxx131Dg3ODgYkyZNwqZNm5CYmIiJEye69Dte1/2xeeKJJ/Djjz/im2++wcSJExEaGtqg10FNj2GGGsXHxweff/45nn/+ebz66quIjIxEjx498OWXXzaqyVWhUGDLli1YtGgR3njjDcTExCAiIgIPP/ww/Pz8oNVqG3zNLVu24NChQygoKED//v1rhBVny+W7Yv78+cjKysKYMWMQFBSE3r17w2w2Iy0tDddee63DuXFxcRgwYAAGDRoEtVqNr776Ch9//DEmTpzo0nONHj0aBoMBn376KcLCwjB8+HAMGjQIjzzyiNPzw8PDMWnSJADA5MmT7f+XaRMQEIDdu3fj1ltvRVxcHCIiIvDOO+9g1apVV7xwnUKhsHchVQ0tMTEx9rV9Ro4c6dK13n33XZw+fRrt27evdZ2ZK3Gl78utt96Kb775BiUlJejZsyfCw8Px73//GwkJCVi+fLn9vMGDB2PHjh347bff0KlTJ/To0QMBAQH429/+BuDy+2HTtWtXZGZm4sYbb8QDDzwApVKJm2++GcuWLcPkyZPtH7JXatCgQZg3bx5eeOEF+Pv7O6wz4+rraqiG3Ie6vPXWW5g4cSIeeOABtGvXDgsXLoTBYMBVV13l9PwZM2bAYrGgoKDA5X+X6ro/Ng8//LA9wLCLyU3IMoeKWo3a1iapqKhweRpyY69ZdU0KZ1+1rZniynPVxzat9+2333bp/IY+j+21OfP0008LAOKHH35w+XpCOH9PGvo+Wa1Wp6/FdtyZ+l571XVm6jrflVqb+31x1ZtvvlljGrWr6nrvq9db17lC1P5+XUkNDeHsPjTm2larVVRUVDj9me3vuzONvT8VFRUiKipKdO3atVl+P6jhuI4zNavalgpv7BiYhlyzKZYqb6mlzhv6PLW9tsrKSmzevBk333wzBg4c2KBrOntPGvo++fj4OB3bUdtxoP7XXv3nzfE75epzN5XPPvsMnTt3blS3TV2/19WP1/d3oK73pbE1NISz+9CYa9f1Guq6VmPvT1paGnJzc7F06VJuxeEm2M1E5CUqKyuxatUqnD59Gv/3f/8ndzn0P9OmTcOPP/6IS5cu4eTJk3j66aeRlpaGl156Se7SWpS33AeLxYIlS5YgLCwMs2fPlrsc+h+2zBB5gW3btmH8+PFQKpWYN28epkyZIndJ9D8PPPAAdDodDh48iJKSEvTo0QMbN250upeWN/OG+zBp0iRs3rwZXbt2xccff1zvzDxqOQohuM85UXOoqKiAr69vizRDCyFQWVnZLF0t3qYl3xfyLrbVvptqmjw1HYYZIiIi8miMl0REROTRvH7MTGVlJSRJglKpZLMyERGRhxBCwGKxQK1W19u15/VhRpKkRq9aSURERPI6depUvduMeH2YsW1lf+rUqSterp2IiIhahtlsRkxMjP1zvC5eH2ZsXUsqlYphhoiIyMO4MkRE1gHAf/75JxYtWoTrr78e99xzj9NzCgoK8MQTT6Bbt27o3bs3Xn311Vo3/yIiIqLWR7aWmdLSUgwZMgTTp09H//79cezYsRrnCCEwbtw4lJWVYf369SgoKMDf/vY3nD9/HitWrJChaiIiInI3soWZgIAAZGVlwcfHB08//bTTMLNnzx589913OHToELp37w4AePXVV/Hkk09i0aJFXH2RiIiI5O1mqm+qVVpaGjp27GgPMgBw1113oaysDOnp6c1dHhEREXkAtx4AfPr0aURFRTkci4yMBACcOXPG6WNKS0tRWlpq/95sNjdfgURERCQ7t14BuLKyssb27L6+vvDx8al1EPDSpUsRGhpq/+IaM0RERN7NrcNMhw4dcO7cOYdj58+fR2VlJTp06OD0MQsWLEBhYaH969SpUy1RKhEREcnErcPMgAEDcOLECeTm5tqPffvtt1AoFOjXr5/TxwQEBNjXlOHaMkRERN7PrcPM2LFjERMTg+effx6lpaU4d+4cXn75ZYwbN47dR0RERARA5gHAI0eOxJEjR1BYWIjS0lL73gvHjh1DUFAQAgMDYTQa8cgjj6Bdu3awWq2Ii4vDunXr5CybiIiI3IhCCCHkevK8vDyUl5fXOH711VfXWL64oKAAbdq0QUhISIOew2w2IzQ0FIWFhexyIiIi8hAN+fyWtWXGNs3aFe3bt2/GSoiIiMhTufWYGSIiIqL6MMxQrSRJQnx8PCRJatTPiYiIWgLDDNXKYDDAaDTCYDA06udEREQtgWHmCnhqy4QrdUuSBIvFgiFDhkCr1To9R6vVQqPROP25p94bIiLyPAwzV8BTWyZcqdtgMCA1NRUqlQpqtdp+vGpIUavVWLx4scPPG/IcRERETcGtN5p0d7YWidpaLtyVK3XXdo4tpADA4sWLr+g5PJUkSTAYDNBqtU6DHBERtSxZ15lpCVxnpmm56wd5S9YVHx8Po9EIjUZTZ6AjIqLG85h1Zsjz2LqW3I2rLUZNwZtbnYiIPBHHzJBXcDYYubkGIdc1Vqg5n5eIiJxjmCGv4CxgtPQgZFuI0ev12LJlC6ZOndqgQGN7fGZmJuLj45GcnIxhw4YhMzOzGasmIvJ8DDPkteqaOt4cbOFJoVAgJCQEhw4dQkJCgtNznbXe2B6v0+lgNBoxe/Zs/PTTT9DpdLU+jq1AREQcM0NerKXH91QdSyOEQHZ2NmobX191jI9Wq4XBYIBGowEAaDQaGI1GDBw4EMuWLYNer3f6uMWLFzsdK+Sug7SJiJoLwwxRE6kannQ6HVQqVZ0LDprNZlgsFiQkJCA1NRXAX4EkNjYWABAXF+fwOI1Gg9TUVIfgU/V7oGUHQxMRuQN2MxE1g/oGCavVaqhUKqSmpkII4XJ3mNFohMVisYeV6t8Df3WvaTQahy6ozMxMjsEhIq/ElhkimVTtlnK1O6j6tHBn08RtQcq2Hg5wuYVGp9PZx+Ds2bOnyV4HEZHcuGgekZfKzMyETqezj8mx/Vev19u7sYiI3BUXzSMiJCUl4ejRo5g3bx7Onz8PALW2yDgbNMyBxETkKRhmiLyUrdF1wIAByMzMxPz58+0/qx5U9Ho9Nm7cCLPZjKlTp0Kn06Fbt2745ZdfYDab7YOZGWqIyB0xzBB5KduMKrPZjJMnTyI9Pd0+O8o248kWVPLz82GxWFBcXAydTocff/wRx48fx6RJkwAAW7ZsQXJyMgYNGoS5c+dCrVbbA5FtKnn1sMOWHSJqKQwzRF7KNhBYkqQa08Rtf7bNhPL394dSqURISAj0ej0mTJiAwMBAKJVKaLVaZGRk4NChQ8jOzkZRURGOHj2Kjh07IiUlBcnJySgqKkJqair0er092HANHCJqKRwATNSK1da6Uj10SJIEvV4PhUKB77//Hvv370dYWBisVivGjRuHo0ePwmQyITw83P7fqsEGuNwaZLFYsHPnToSHhyMxMZGBhohq1ZDPb4YZImqQzMxMzJkzB9HR0cjJycHKlSsRFRVlD0U6nQ4mkwkTJkywt9CYzWakpaWhb9++2LlzJwIDAzF58mSHRf3YakNEVTXk85uL5hFRg8TGxiIuLg4//PADsrOzYTQa7V1asbGxSExMdAgytv2qNBoNlEollEoloqKiaizq19IbgxKR9+CYGSJqMK1WC4vFAiFEjZWLq27rUH1hQEmS7ONwqo+pcbY1AxGRK9jNRESyqN6tNGvWLCQlJWHKlCn2TTRtm23Onz8f6enpNb5nlxSR9+KYmSoYZog8w6BBg/Dzzz+jf//+iIuLg9FohMlkQl5eHgICAhATEwOLxYL8/HyEhYWhrKwMXbp0webNmxloiLwQx8wQkcdZuXIlBg8ejJUrV9o3y1y9ejXatWuHS5cuwd/fH6tXr8aAAQMwYMAAXLhwAceOHYNer3cYe2MjSZLT40TkfThmhojcQmxsrMN2C7ZxN507d0Z+fj7y8vLQs2dP7NmzB9OmTYMQAmq1Gvn5+Xj33Xdx/PhxdO3a1d71ZDAYsGXLlhrr37AVh8j7MMwQkVtbuXIlJkyYgLZt2yIhIQFKpRKHDx+GEAIhISE4fPgwLl68iJSUFBw+fBjA5SCk1WqRmpqK3Nxc3HvvvSgrK4PFYsGKFSucPg+nhhN5LnYzEZFbi42Nxd69ezFp0iQIIWA0GtG3b197l1S/fv0QFBSEESNGQKPRQKPRYNasWZg4cSLmz5+PqKgolJSU4OLFi6hriCCnhhN5LrbMEJHbc7Y1g22qd3BwMGbNmmXfMyo+Ph5JSUkoKSlBfHw8brvtNnTr1g3BwcGYOnUq4uPjHVYlrrq1w5AhQxymmrO1hsgzMMwQkceouoYNcDmMpKWlQaPR2MOGVquFJEk4ePAgevXqhbS0NAwdOhRKpRJr1qzB559/bt+PqqioyH4t2xo3VUOLs/2liMj9MMwQkcequiifjVqtxpo1awD81bJiNpvtAebixYs4cuQIgoODcdNNNzndgLPqnlXOjrOlhsi9MMwQkceq3lJT289t3VMajQaJiYkoLi5GcHAwdDodADgElMzMTPuu4QDsj7dN8zYajcjJyUF0dDRDDZGb4KJ5RNSqxcfHw2g0QqPRYPHixRg2bBh+/PFHREZGYu/evQCAqVOnwmQyISQkBNnZ2ejcuTPKysrsjyGipsdF84iIXGRboM/WlTR//nxERkZi9erV9vVqTCYTwsPDsXLlSsyaNQuLFy+GUqnkPlJEboLdTETUqlXvqkpPT0d4eDjS09MRFxdXY7NMAJgwYQL8/Pyg0+mg1+uRmJgIhUJhn1FFRC2LYYaIqApng4qr0ul09v2i2rZtizlz5uDAgQP2n1ddlI8DholaBruZiIiqsLXU2MJH9cX09Ho9br31VmzatAkTJkxAz5497YvxVR+CyIX4iFoGW2aIiOpQvaWm6h5ScXFxkCQJISEh9m6mqq0xWq0WZrMZFosFkiSxdYaomXA2ExFRE6o+Oyo+Ph5btmxBeHg4EhMTHQINu6GIasfZTEREMqk+O0qr1SI8PBwmk6lGd5Ner8eaNWug1+sdjldd14aI6seWGSKiZpaZmWmf+RQVFYWEhAQUFRXhl19+wR9//IGAgACMGzcOL774ItRqNZ599lls2LABXbp0webNm9lqQ61SQz6/OWaGiKiZGY1GWCwW+z5PSUlJsFgsCAoKQmVlJfLz87F+/XokJydjy5YtEELg4sWLyMrKgsFg4MJ8RPVgmCEiambVBxFbLBYUFRUhODgYffv2xbx581BWVoa8vDzodDokJiYCABQKRa1TxInoL+xmIiKSkW3AcL9+/XD06FHo9XrExsY6nMOBwtQasZuJiMhDOFthuDqDwYAtW7YgNTW1xowoIuJsJiIiWVVfpA9wnM2UmZmJ5ORkAMChQ4dqzHwiIrbMEBG5HdvKwQCQmpqK/fv3IzQ0FBcvXkRxcbHM1RG5H4YZIiI3U7XrSaPRQKfToWPHjkhJSUFISIjDuVXH0wCX167hppfU2nAAMBGRB7CFFo1GA6PRaB9jo9PpsHHjRgwfPhx79+5FUVER2rRpg1mzZnFKN3k0rgBMRORlbGNrjEajw+aVxcXFsFgs+Prrr5GXl4fAwEBMmTKFU7qpVWE3ExGRB6m+Zk1wcDCUSiWGDx+OM2fOOJ3aTeTt2M1EROTB6lqDhuvTkCfjOjNERK2ErfvJGb1ej40bN0KSJKjVaodQU9sYHCJPxDBDROSlFAoFrFYrduzYgfbt2wOAfXZUt27d8MsvvyA5ORnZ2dkwm81cw4Y8FsMMEZGXmjt3LjIyMpCbm4vw8HBotVpMnToVP/30EywWC5RKJTp27Ijs7GwoFAq5yyVqNM5mIiLyUmq1GomJiZg8ebJ9GwS9Xo8BAwage/fuOHr0KC5evIiAgACMGjVK7nKJGo1hhojIi1UdUxMfH4+oqCjs2bMHV111FQDgu+++w8mTJzF9+nRIkgTg8nganU6HZ5991n6MyJ0xzBARtQK2LRJs69PodDrMmjULkZGRAICCggL7zxISEvDuu+9iw4YN9mNV94sicjccM0NE1ApUX5/G1mKj0WgwZ84c9OrVy/4zIQSCgoIQExMDSZLw7LPPQgiBtLQ0AODKwuR2PGKdmV9//RWHDh2Cv78/+vXrh2uvvdblx3KdGSKihpEkCXq9Hj/88AOysrLg6+uLESNG4LvvvsPq1avRs2dPrl9Dzc5rtjOwWq2YMGECRowYgR07duCjjz7CTTfdhH/+859yl0ZE5LXUajVUKhWKiooQExODzp074/Dhw8jPz8eyZctqdFkRyc2tu5m+/vprfPbZZzhw4AB69uwJAFizZg2eeOIJPPXUUwgNDZW5QiIi76TVamE2m/HDDz+gqKgIvXv3hslkglarRUZGBoYOHcr9n8htuHXLjG3dg4iICPuxDh06wNfXFx7QO0ZE5LGqts6Eh4fjqquuQnh4OAwGA9LS0qBUKtnFRG7DrVtmRowYgTlz5uDee+/Fgw8+iOLiYmzatAnvvPMO2rVr5/QxpaWlKC0ttX9vNptbqFoiIu9SfdCwSqVy2P6Aez+Ru3DrMAMAUVFROHv2LDIyMlBcXAyr1VprkAGApUuXIj4+vuUKJCLyUtX3fbL92bYrd3x8PIxGI8xmM1QqFUMNycatZzNt3LgR06dPx8GDB3H99dcDAD799FNMmTIFR44cQZcuXWo8xlnLTExMDGczERE1gaqtMcDl9WssFgtSU1Oh0Wg4bZuajNfsmp2eno4bbrjBHmQAYMyYMaioqMDPP//sNMwEBAQgICCgJcskImo1bDOZgMstNYsXL4YkSVAqldBoNIiPj6+xEze7o6i5uXWY6dy5M7Kzs1FQUGDf8fXXX3+1/4yIiFpW9XE0wF/dUbZup+o7cSckJCApKQkWiwUrVqyQq3TyYm4dZmbMmIHVq1fjjjvuwLRp01BcXIzVq1fjvvvuw8CBA+Uuj4io1ak+jqYqW8DJyclx2Ik7NzcXJpMJubm59nPZWkNNya3DjEqlwv79+7Fx40YcPnwY/v7+eO+996DRaOQujYiIqrEFHUmSEB0dbe92OnjwICoqKnDkyBH7udW7q4iuhFuHGQAIDAzE9OnT5S6DiIhcVL3bqU2bNggKCkLfvn3t52g0GvugYaIr5fZhhoiIPJOt28k2IFij0UCn06G4uBgHDhzAhQsXoNPpkJiYCADsdqJGc+up2U2BG00SEbmH+Ph4rFmzBhaLBUFBQQgKCoJSqcSECRMAwB542O1EgBdNzSYiIu9h2+8pOzsbP/30E5YsWYLff//dYWZUXfs9cdAw1YYtM0RE1KKGDRuGn376CQMGDMCePXtcfpxtDA5bb1qHhnx+u/VGk0RE5H30ej0GDBgAvV4PSZIQHx8PSZLqfZxWq4VGo+Fu3VQDW2aIiEg2bG2h2nDMDBEReQRnKwoDHB9DDcNuJiIiko1tTZrqgcVgMGDLli2YOHEinn32WYduqIZ0TVHrwJYZIiJyO1qtFqmpqTh48CAOHjyIoqIi+6rCOp0OJpMJAFcPpsvYMkNERG5HrVYjMTERN9xwA4KCgnDgwAEYjUbodDrk5eWhoKAAOTk5bJ0hAAwzRETkptRqNTZv3ownnngCK1euhEajgV6vR7t27VBQUICtW7fCYDCw24nYzURERO6r6i7dsbGxkCQJZWVlEEIgJiYGWq3W6aaVHEDcujDMEBGRxzAYDMjOzkZFRQX69u0LtVrtdEYUd+VuXdjNREREHkOr1aJz585o06YNFAoFAOczomwL7Gk0GnZBtQIMM0RE5DHUajWGDBkClUqF4ODgOs9bvHgxjEYjjEYjDAZDC1ZJLY3dTERE5FF0Oh1UKpVL2xpoNBqkpqZCo9G0QGUkF7bMEBGRR6ltoT1njEYjLBYLkpKS2N3kxdgyQ0REXsvWeiNJEpKSkmA2m6HX62WuipoaW2aIiMhr2WY7HTx4EFar1T5omLwLwwwREXk1g8GA/Px8lJWVITY2lt1NXojdTERE5FWqLpgHABaLBaWlpSgtLcXChQsRHh4Oi8UCpVLJRfW8BMMMERF5laoL5gFAamoqhg4ditTUVNxyyy247rrrIITgonpehGGGiIi8irMVgSVJwoULF7B3715cddVVOHDgAPr16+fS9G5yfwwzRETkVaru5wRcXmvm3nvvha+vL/z9/fHLL7/g8OHDCAgIYBeTl2CYISIir6bT6WAymRAQEID27dujb9++UCqVnKLtRRhmiIjIa0mShBtuuAGlpaVYvHgx0tPTOejXCzHMEBGR17HNaLJYLMjIyIBGo0FcXBzi4uLkLo2aAdeZISIir2Ob0SSEgEaj4UBfL8cwQ0REXkej0cDf3x/FxcX2IMPF8rwXu5mIiMjrGI1GZGdn49ixY0hOTkZsbCx27tyJnJwcrF69Wu7yqIkxzBARkdfRarX4/fffsXnzZlgsFpw/fx6lpaU4cOCA3KVRM2A3ExEReR21Wo0TJ06goqIC/v7+GDFiBHr16oVevXqxq8kLMcwQEZFX6tWrFwIDAxEUFIS9e/faF8xLSEjg+BkvwzBDRERe6cUXX0T//v1htVpRXFyMsrIyDB061L4vk8FgkLtEaiIMM0RE5JXUajUSExPx6KOPolevXigrK4NSqYROp7NP15Ykia00XoBhhoiIvJZarcaKFSuwefNmjBo1ChaLBcDlnbLVarV9PRq20ng2zmYiIiKvZ9u+ICkpCUII6HQ6GAwGaDQaAOCieh6OYYaIiFoFhUJh/6+tRcZsNkOlUslcGV0phhkiImoV5s6dC6VS6dAKY7FYYDQaAVzueiLPpBBCCLmLaE5msxmhoaEoLCxk+iYiIge2DSm5k7b7acjnN1tmiIio1cvNzUVCQgIsFguUSiXmzp3LcONBGGaIiKjVSkhIQFJSEpKTk5GdnW0PMwDsXVIMNe6PYYaIiFot20iLnj17YtCgQThx4gS+//57bNiwAWFhYQA4lsYTMMwQEVGrpdPpoFKp7C0ww4YNQ35+PgCgpKTEPnWb3BsXzSMiolZLrVbbF9ADLq834+d3+f/zfX197TOdyL0xzBAREf2PwWBAZWUl/Pz8cOONN0Kr1SIzMxPDhg1DZmam3OVRLRhmiIiI/kev12PAgAF47LHHsHnzZqjVauh0Ovz000/Q6XRyl0e14DozREREdUhOTsbs2bOxZMkS/P7775zh1EK4zgwREVETyMzMxOzZsxEYGAiDwWDfqFKr1UKv10OhUHBNGjfAMENERFSLOXPm4PTp04iKioJer0dSUhLMZjP0ej02btwI4PJ6NJy+LS+OmSEiIqpFr169EBgYiHvuuQdRUVHIyMjArl27UFxcjM6dO2PEiBHIycmBTqeDJElyl9tqsWWGiIioFi+++CKio6Oh1WphMBhgMpkQHh6O4OBglJWV4fTp0zh69CisVisyMzORmJjILicZMMwQERHVwrYODQD7bttVd90+fPgwLBYLOnbsCJPJBIPBwC4nGTDMEBER1UOSJCQkJNi3P1Cr1VCpVEhJSUFZWRmKioowc+ZMh6BDLYdhhoiIqB4GgwFJSUn271UqFTQaDY4fP47U1FS89957iIuLk7HC1o1hhoiIqB5arRYWiwVCCCgUCvs2Bxs2bJC5MgIYZoiIiOqlVquxYsUKAJe7nJRKZY0uJUmSYDAYuKieDBhmiIiIGqDqoOCqDAYDjEYjzGazw07c1PwYZoiIiJqAraXGYrHYu6FsU7oZbJoXwwwREVETsLXY2BbPs60UnJaWBgCcst2MGGaIiIiakFqthlKpxJYtW+Dv7w9/f39oNBq5y/Jq3M6AiIioiWm1WoSEhODw4cPIysqydztR8/CIMLNx40bcfvvtUKvVuOeee3Do0CG5SyIiIqqVWq3GoEGDEBISgpiYGFgsFu7d1Izcvptp+fLlePnll7Fq1SqMGjUKR44cwYoVK7Bu3Tq5SyMiIqrV3LlzoVQqYbFYkJqayt21m5FC2NZmdkM5OTno1KkT3nrrLcyePbtR1zCbzQgNDUVhYSFUKlUTV0hERFQ3rj/TOA35/Hbrlhmj0YjKykpMnTpV7lKIiIgapbZ1aajpuPWYmd9//x2dO3fGp59+iu7du6NTp06477778Ntvv9X6mNLSUpjNZocvIiIiuUiShPj4eI6ZaUZuHWasVitOnjyJTZs2YcuWLdizZw9CQkIwbNgw5OfnO33M0qVLERoaav+KiYlp4aqJiIj+YlsZ2GAwMNg0E7cOM5GRkaioqMDKlStx00034brrrsO7776LgoIC/Oc//3H6mAULFqCwsND+derUqRaumoiI6C9arRYajQYajQYTJ07EqlWrkJCQgMzMTAwbNgyZmZlyl+jx3DrM3HbbbQCAgIAA+7E2bdrAx8cHFRUVTh8TEBAAlUrl8EVERCQX25gZo9GIY8eO4cKFCygqKoJOp8NPP/0EnU4nd4kez63DzB133IEBAwZg4cKFKCoqQllZGRYuXIi2bdti1KhRcpdHRETkMq1WixtuuAHt2rVDcHAw5s+fj7CwMHTs2JHdTlfIrcOMQqHA559/jgsXLiAsLAyhoaFITU3F9u3bORaGiIg8ilqttg+bmDp1KtLT02G1WpGSkgKDwSB3eR7NradmA0B0dDS+/PJLe7eSn5/bl0xEROSU0Wi076qt1WphNpuhUCjsO25T43hMMmCIISIiT2cLLRqNBgaDATqdzr6QHhfXazwmBCIiohaiVquh1WoxdepUmEwmAMDixYshSVKNY+Q6tx4zQ0RE5G0MBgNMJhPCw8PtLTW2Y/7+/khOTkZycjLXo2kAtswQERG1IFuAqdqdZDuWnJyM/fv3Y/bs2QgPDwfAVhpXuPVGk02BG00SEZGnSE5OxuzZs7FkyRL8/vvvrXr8TEM+v9nNREREJJPq2xukp6cjPDycqwI3ELuZiIiIZGLbtwm43J1k624ym80Ox6luDDNEREQyqTp+Bvhr64PMzExkZmZCo9HIWZ7HYDcTERGRTGzhpfq4mMTERBw6dAhz5szhjCYXMMwQERG5GYVCgYsXLyIrK4tbHbiA3UxERERuZu7cuRBCQKFQQKPRID4+vlXPbKoPwwwREZGbUavV0Ov1AID4+HgOBq4Hu5mIiIjcmEajgVKp5GDgOjDMEBERubGqO22TcwwzREREbowtM/VjmCEiInJjtpaZd999F8OGDePqwE4wzBAREbkxrVYLjUaDAwcOID09HRMmTODaM9UwzBAREbkx28J6K1euREREBIqKipCQkCB3WW6FYYaIiMiDCCEghKixSWVrxjBDRETkAXQ6HUwmE5RKJXQ6nX2TSq4Q3Igw8+mnnyI7O7sZSiEiIqLa6PV69OnTB6NHjwbAWU5VNTjMLFiwAAMGDMDBgwdr/Cw7OxtCiCYpjIiIiP4SGxuLuLg4ZGRkICEhATqdDrm5udDpdK2+q6lR3UxDhgzB8OHDawSakSNHIisrq0kKIyIiIke2mU1CCJhMJpSUlMBkMrX6rqZG7c20dOlSrFmzBsOHD0dKSgp69erV1HURERFRNbaZTZIkQaVSQaPRwGg0QqvVyl2arBq90eTy5cuhUCgwYsQIBhoiIqIWZAs1wOXuJ9vMpta6s/YV7Zr9+uuvA4A90BAREVHLi4+PR1JSEiRJwpo1a+Qup8U1OMxMnjwZwcHB9u9ff/11KBQKDB8+HFartUmLIyIiotpJkgSDwYAffvgBFy9eREZGhtwlyaLBA4BfeeUVREdHOxx77bXXMHPmTFy4cKGp6iIiIqJ62Naa8ff3R1BQELp3794qF9JrskXzli1bBpPJhGuuuaapLklERER10Gq16Nu3LwBg6tSpiIyMbJUL6V3RmJnqwsLCmvJyREREVAe1Wo1jx47h8OHDUCqVSExMBACYzWZIktRqBgNzOwMiIiIPptfrMWDAAOj1egBARkYGdu3a1apaZ5q0ZYaIiIhaVmxsLPbs2QPg8v5Nhw4dQpcuXVrV2jNsmSEiIvISCoVC7hJkwTBDRETkJebOnYubbroJRUVFraqbiWGGiIjIS6jVaiQmJmLChAmtqptJIbx8m2uz2YzQ0FAUFhZCpVLJXQ4REVGLkSQJCQkJEEJAp9N51Oymhnx+cwAwERGRl7CFF4vFAqVSiby8PHzyySdQKpVQqVT2/Zy8DcMMERGRlzAYDEhKSrKHGV9fX1RWVqJt27Ze3e3EMENEROQltFotLBaLPczExsZi4cKFWL16tUd1MTUUwwwREZGXUKvVWLFihf37Z599FqWlpdi1axfi4uJkrKx5cTYTERGRl8rLy4PJZEJeXp7cpTQrhhkiIiIvlZWVhcrKSqSmpkKSJEiS5JW7arObiYiIyEutXLkS9957Ly5duoSEhAQolUoYjUYA8KqZTWyZISIi8lKxsbF48MEH4e/vD4vFArPZjKFDh3rdzCaGGSIiIi+m0+kwa9YsKBQKbNy40b7VgTd1NTHMEBEReTG1Wo3FixcjODgYpaWl+OCDD/DRRx951d5NDDNEREStgE6nQ2VlJUpLS3H69GloNBq5S2oyDDNEREStgFqtxiuvvAJfX1/4+/sjMTFR7pKaDMMMERFRK7F582YoFAqUlJRAoVDIXU6TYZghIiJqJbRaLYKCgjB27FjMnTtX7nKaDMMMERFRK2EwGFBRUYHz58971V5NDDNERESthF6vx4ABA6DX6+UupUkxzBAREbUCkiTBaDRCr9fDaDR61Toz3M6AiIioFTAYDDAajUhNTYXFYgHgPVsaMMwQERG1ArYtDK6//nosXLgQAwcOlLmipqMQQgi5i2hOZrMZoaGhKCwshEqlkrscIiIiWQ0aNAg///wzevfuDY1GA41GA6PRCK1W61aDghvy+c2WGSIiolakV69eOHjwIADAaDQiOTkZ2dnZyMnJQXR0tNuFGlcwzBAREbUiL774IqKjo6HRaJCYmIjdu3fjwoUL2LZtGyIiIgB43lgazmYiIiJqRWwbT8bGxkKlUiE3NxdWqxVlZWUIDw+3j63xJGyZISIiaqW0Wi0sFgvy8vKQlZUFvV7vcV1MAFtmiIiIWi21Wo0VK1aga9euKCsrg9FolLukRmGYISIiaoUkSUJ8fDwkSYJGo4FSqcT111+PYcOGITMzU+7yGsSjupnWr1+PnJwcPPnkk1AqlXKXQ0RE5LFsi+iZzWb88MMPyMrKwrx583D+/HnodDrs2bNH7hJd5jFh5pNPPsFTTz0Fs9mMhx9+mGGGiIjoCtgG+ubk5ODAgQMAgNGjR+P06dMet3eTR3Qz/fHHH5g7dy6WLVsmdylERERewTarKTg4GMHBwejVqxdee+017NmzB7GxsXKX1yBu3zJTUVGBhx56CC+99BI6d+4sdzlEREReRafTAQAUCoXMlTSe24eZhQsXIjo6GjNnzsTu3bvrPb+0tBSlpaX2781mc3OWR0RE5NHUajVUKhWMRiOEEFAoFBBCQKfTecw0bbfuZtq5cycSExNhMBhcfszSpUsRGhpq/4qJiWnGComIiDyfbTZTcXExkpKS8NFHH2Hq1KmQJEnu0lzi1mHmmWeewS233IL33nsPy5Ytw6ZNmwAAq1atQkpKitPHLFiwAIWFhfavU6dOtWTJREREHsdoNMJisSA4OBhTpkxBly5dYDKZGtSYICe37mZ65JFHUFBQgAsXLgAAiouLAQCFhYW4dOmS08cEBAQgICCgpUokIiLyeLaZTbZNJiVJgsFg8JitDRRCCCF3Ea7avXs3Ro0ahVOnTqFjx44uPaYhW4gTERERHMKMXONmGvL57dYtM0RERNSyJEnC1KlTYTKZAHjGDtoeFWY6d+6MefPmsYWFiIioidlaY8xmM0wmk0ftoO1R3UyNwW4mIiKi+sXHx8NoNGLo0KFQKpWydjEB7GYiIiKiBqo6CBgAEhISPGa9GYYZIiIism9vAFxupUlKSgIAqFQqtx83wzBDREREdpIkwWKxYNy4cRBCwGKxQJIkt26dcetF84iIiKhlGQwGpKamIjo6Gmq1GqmpqW6/eB5bZoiIiMiu+tiZ6n92R2yZISIiIju1Wg2tVguDwYDc3Fy5y3EJW2aIiIjIgcFggNFoRHJyMrKzs2E2m6HX6+Uuq1YMM0REROTA1q10/PhxHDx40L43ortiNxMRERE5sE3TvuqqqxAUFIQDBw5AkiS5y6oVwwwREREBuDwtOz4+HpIkQZIkKBQKREZGYt++fRg3bpzbBhp2MxERERGAv8bKWCwWZGRkIDc3F5IkobS0FEeOHIHBYHDLBfQYZoiIiAjAX2NlbJtNFhUVwdfXF5GRkRg3bpzbTtFmmCEiIiIAf42VkSQJKpUKOTk52Lp1Kzp37owXX3zRbVcB5pgZIiIicmALNS+++CK6dOmCrKwsJCQkyF1WrRhmiIiIyCm1Wo3bbrsNAPD999+77QBghhkiIiKq1ejRo1FWVob8/Hy33aOJYYaIiIhqtWzZMpSWluLixYtITk5GZmam3CXVwDBDREREtdLr9bj11luhVquxf/9+6HQ6uUuqgWGGiIiIahUVFYWhQ4diyZIlGDBgAObPn29fWM9dcGo2EREROSVJEqZOnYrc3FykpqYiMTHRvrAeALdZQI9hhoiIiJwyGAwwmUwoKSmByWSCwWCAVquF2WyGxWKBJElusfYMwwwRERE5ZVvxV6PRwGg0QqvVQq1WQ6VSwWg0QqlUukXrjEIIIeQuojmZzWaEhoaisLAQKpVK7nKIiIg8kiRJ9pYZAPY/N1fLTEM+vzkAmIiIiOplMBiwZcsWTJ06FcDl8TLu0MUEMMwQERFRPSRJgsVigb+/Pw4dOuR2WxswzBAREVGdDAYDUlNT4e/vD19fX7jbCBUOACYiIqI6abVaWCwWWCwWDBo0CHPnzpW7JAdsmSEiIqI6qdVqKJVKZGRkQAgBg8HgVovmMcwQERFRvTQaDfz9/ZGWloYtW7a41aaT7GYiIiKiehmNRmRnZ8NqteKmm26yT9F2BwwzREREVC+NRoPk5GRcd911iIqKkrscBwwzREREVC+j0YiysjKcOHECX3/9NYQQ0Ov1cpcFgGNmiIiIyAVarRYajQa9evUCABQXF7vN7tkMM0RERFQvtVoNrVaL4OBgTJkyBcHBwTAajW4xEJhhhoiIiFySkJCAjz76CN9//z1Gjx4NpVIJjUYjd1kMM0REROQaIQSKiopw4MABxMfHw2KxwGg0yl0WwwwRERG5ZurUqQgNDYUQAl26dIFGo3GLKdoMM0REROQSo9EIq9UKAMjKyoJGo3GL1YA5NZuIiIhcotVqIUkSduzYgQsXLkCn08FisQAAFi9eLFtdDDNERETkErVaDbVajfbt2yM8PBx6vR5Go1H2riaGGSIiInLZwIED8cEHH2D58uWIjY1FbGys3CVxzAwRERG5btmyZcjPz8eyZcvkLsWOYYaIiIhcptfr0bt3b3Tr1k32gb82DDNERETkEkmSkJSUBAD4/vvv3WL1X4BhhoiIiFxkMBiwYcMGHDhwACEhIdBoNG6xPxPDDBEREblEq9WiS5cuaNu2LQAgMTHRLfZnYpghIiIil6jVamzevBk9evRAUVERFAqFW6wCzKnZRERE5DK1Wg29Xg+dTocpU6ZwajYRERF5HqPRCJPJBJ1OJ/t4GYBhhoiIiBpIq9UiPDwcJpNJ9vEyAMMMERERNZBarUZiYiImTJgg+3gZgGGGiIiIGiAzMxPDhg1Dbm4uFi9eDLVaLXdJDDNERETkGkmSMGHCBPz444/Q6XRyl2PHMENEREQuMRgMCAwMRGRkJPR6vdzl2HFqNhEREbnENj5Gq9W6RfeSDVtmiIiIyCVqtdo+TkaSJLfYygBgmCEiIqJGMBgMbrGVAcBuJiIiImqEql1OclMIIYTcRTQns9mM0NBQFBYWQqVSyV0OERERuaAhn9/sZiIiIiKPxjBDREREjeIug4AZZoiIiKhR3GUQsFuHmeLiYqxYsQK33HILQkND0aNHD7z55pvw8mE+REREHkGr1UKj0cg+CNitZzO9//77yMvLw/vvv49rr70W3377LR566CGUlJRg3rx5cpdHRETUqtnWnZGbx81m+vvf/47vvvsOv/76q0vnczYTERGR5/Hq2UwmkwlKpVLuMoiIiMhNuHU3U3Xff/89PvnkE6xdu7bWc0pLS1FaWmr/3mw2t0RpREREJBOPaZk5cuQI7rvvPkyfPh1/+9vfaj1v6dKlCA0NtX/FxMS0YJVERETU0jwizBw7dgzDhw/H3XffjTVr1tR57oIFC1BYWGj/OnXqVAtVSURE5P3cZW2Zqty+m+n333/HsGHDMHLkSLz//vvw8ak7fwUEBCAgIKCFqiMiImpdbGvLAHCLmUyAm4eZrKwsDBs2DCNGjMAHH3xQb5AhIiKi5uVOG0zauHU6eO+993DmzBkkJSXB398ffn5+8PPzQ0REhNylERERtUpV15Zxl+4mtw4zS5YsQXl5OUpKShy+8vLy5C6NiIioVXOXrQwAN+9m8vHxYdcSERGRG3Kn7iaPWwG4obgCMBERkefx6hWAiYiISD5Vp2a7yzRtt+5mIiIiIvdSdWo2ALeYps0wQ0RERPWSJAkGgwEajQaA41gZucfNMMwQERFRvWpbLM8dFs5jmCEiIqJ6udPspeo4m4mIiIjcDmczERERUYtwhxlNDDNERETUaO6wEjDHzBAREVGjucNYGrbMEBERkcuqdyvZNp5Uq9Wy1cQwQ0RERC5zh26l6hhmiIiIyCWSJMFsNmPo0KFuNUWbYYaIiIhcYjAYkJaWBqVSKWu3UnUcAExEREQucYfBvs5w0TwiIiJyO1w0j4iIiFoNhhkiIiLyaAwzRERE5NEYZoiIiKhO7rD/Ul0YZoiIiKhO7rhQXlWcmk1ERER1ctcp2Tacmk1ERERuh1OziYiIqNVgmCEiIiKXuOtAYIYZIiIicom7DgTmAGAiIiJyibsOBOYAYCIiInI7HABMRERETcpdx8sADDNERETkAncdLwMwzBAREVE9JEmCxWLBkCFD3G68DMAwQ0RERPUwGAxITU2FSqWCWq2Wu5waOJuJiIiI6uSus5hsOJuJiIiI3A5nMxEREVGrwTBDREREHo1hhoiIiDwawwwRERF5NIYZIiIi8mgMM0REROTRGGaIiIjIozHMEBERkUdjmCEiIiKPxjBDREREdZIkCfHx8ZAkSe5SnGKYISIiojoZDAYYjUYYDAa5S3GKG00SERFRnbjRpMy40SQREZHn4UaTRERE1GowzBAREZFHY5ghIiIij8YwQ0RERB6NYYaIiIg8GsMMEREReTSGGSIiIvJoDDNERETk0RhmiIiIyKMxzBAREZFHY5ghIiIij8YwQ0RERB6NYYaIiIg8mp/cBTQ326bgZrNZ5kqIiIjIVbbPbdvneF28PsxYLBYAQExMjMyVEBERUUNZLBaEhobWeY5CuBJ5PFhlZSUkSYJSqYRCoXB6jtlsRkxMDE6dOgWVStXCFbYevM8tg/e5ZfA+twze55bhjvdZCAGLxQK1Wg0fn7pHxXh9y4yPjw86duzo0rkqlcpt3kRvxvvcMnifWwbvc8vgfW4Z7naf62uRseEAYCIiIvJoDDNERETk0RhmAAQEBGDx4sUICAiQuxSvxvvcMnifWwbvc8vgfW4Znn6fvX4AMBEREXk3tswQERGRR2OYISIiIo/GMENEREQejWEGwK5duzBw4ED83//9n9yleKWKigqsWbMGGo0G99xzDzZs2CB3SV7JaDTioYcewrBhwzBp0iR8+umncpfk8crLy/HJJ59gzJgxGDJkiNNzhBAwGAy4++67MWrUKKxYsQLl5eUtXKlnq6iowNatW6HRaDBw4EBYrdYa5xw9ehRz587FqFGjMGnSJGzcuNGlZe7pL1arFdu2bcO9996LgQMH4tKlS3Wev2jRIgwcOBDJycktVGHjef2iefXJy8vDzJkzERAQgGPHjsldjtexWq3QaDQ4fvw44uPjERUVhcTERPj6+mLKlClyl+c1PvzwQ8yYMQNLly5Fv379cODAAUybNg05OTl46qmn5C7PY915553o2LEjYmJisH79eqfnLFq0CO+88w4SEhIQFBSE5557Dvv27cNHH33UwtV6rri4OCiVSnTu3BlffvlljZDy888/49FHH8XMmTMxZswYHD9+HE8++SQyMjKwYsUKmar2PBqNBr6+vujatSu2bdvmNDTabN26Fdu2bcPBgwdx9uzZFqyykUQrVllZKUaNGiUSEhLEPffcIyZMmCB3SV7nnXfeEYGBgSI7O9vh+KVLl2SqyDuNHz9ejB071uHY1KlTxbBhw2SqyDtcuHBBCCGEwWAQAQEBNX5uMplEmzZtxPvvv28/tmvXLgFA/Pbbby1Vpsez3eeNGzcKAKK8vNzh58XFxcJqtToc+/e//y0CAgJEWVlZi9Xp6Wz3eevWrQKAsFgsTs87efKkUKvVYv/+/QKA2LBhQ0uW2SitupvptddegxACTz/9tNyleK0NGzZgzJgx6NSpk8PxwMBAmSryTv369cN///tfFBYWAgCKioqwb98+DBgwQObKPFt9S6l/8803KC8vh0ajsR8bNmwYlEoldu/e3dzleY367nNQUFCNvXlCQkJgtVpRUVHRnKV5FVe2BrBarZgyZQoWLFiAm266qQWqahqttpspPT0d//rXv5CZmVnrBpR05Q4dOoS77roLr776Knbt2oWIiAiMHz+eXUxNbP78+SgpKUGnTp1w7bXXIjs7G9OnT8eSJUvkLs2rnTx5Ev7+/ggPD7cf8/X1RWRkJE6ePCljZd6ttLQUer0ecXFxaNu2rdzleJXFixdDpVJhzpw5HhUUW2WYKSwsxEMPPYRVq1ZBrVbLXY5XKykpgV6vx7Rp07Bo0SIcPXoU/+///T8cO3YML730ktzleY3t27fjzTffxIIFCzBgwADs378f8fHxuPXWWzFp0iS5y/Na5eXlTldMbdu2LQcBN5PKyko8+uijOHfuHHbs2CF3OV7l66+/xtq1a7Fv3z65S2mwVhlmUlNTIUkSXn/9dbz++usALo+U9/HxwcCBA7F161ZER0fLXKV3CAsLg1qtxttvvw0AGDFiBAoKCqDX6xlmmtDzzz+PadOmYf78+QCA4cOHw2Qy4ZlnnmGYaUZhYWGwWCwoLy9HmzZt7MdNJpNDaw01jcrKSsyYMQOpqalITU3F1VdfLXdJXmXDhg0QQuDee+91OP7SSy9h586d+PDDD2WqrH6tMszceeedSEtLczj27LPPwt/fH6+++irCwsJkqsz79OvXr8ax6OhoFBUVoaKiAn5+rfJXsMmdP3++xj/sarUaBQUFEEKwK7WZxMbGAgB++eUX3HbbbQCA06dPIycnB7fccoucpXkdIQS0Wi2++uor7NmzB926dZO7JK+zaNEizJo1y/691WrF4MGDMW3aNNx///0yVla/VvlJ0r59ewwcONDhWLt27RAYGFjjOF2ZWbNmYdKkSTh8+DC6d++O4uJifPDBBxgyZAiDTBO688478dFHH+Hxxx9HeHg4CgsL8cEHH2Dw4MEMMs2oT58+6Nu3L5YsWYIvvvgCvr6+ePnll6FWqxEXFyd3eV5DCIHHH38cO3bswJ49e9C9e3e5S/JKXbp0QZcuXezf28bMdOnSBT179pSrLJfw04Sa1ZgxY7Bw4ULceuut6Ny5M06fPo0ePXpg3bp1cpfmVd566y08/PDD6NSpE7p06YI//vgDPXv2hMFgkLs0j/bCCy9g165dOHv2LMrKyuz/s7N27VrcfPPNAIBNmzbhvvvuQ2RkJAICAuDr64vPPvuMM/YaYOnSpfjiiy9gMpkAAIMHDwYAvP322+jfvz+++uorvPfee7jmmmswffp0h8d+/PHHNWZLknN6vR6ffvopCgoKAFzujvbx8YFer8ftt98uc3VXhrtm/49tzMz1118vdyleyWw2IysrC1FRURyP1IzOnj0LSZIQGRmJqKgoucvxeMePH8e5c+dqHO/RowdCQkLs3wshcPToUVRUVKB79+7w9fVtyTI93okTJ5Cfn1/j+E033QSVSoWCggIcPXrU6WP79OnD4Oii7Oxs5Obm1jh+4403ol27dk4fk56ejq5duyIiIqKZq7syDDNERETk0Vr1onlERETk+RhmiIiIyKMxzBAREZFHY5ghIiIij8YwQ0RERB6NYYaIiIg8GsMMEREReTSGGSIiIvJoDDNERETk0RhmiMjjPPfcc1iwYIH9+8rKSsyZMwc6nU7GqohILtzOgIg8TkpKCkaPHo3//ve/uPHGG/HMM89g27Zt+P777xEZGSl3eUTUwhhmiMgjjRw5EhEREejfvz9ee+017N27lxvFErVSDDNE5JF+/vlnDBw4EMHBwUhJSUH//v3lLomIZMIxM0TkkbKysiCEwC233MIgQ9TKMcwQkcfZs2cPZsyYgYSEBOzduxcpKSlyl0REMmI3ExF5lAMHDuDOO+/E8uXLodVq8eijj+Lw4cP48ccf5S6NiGTCMENEHuPPP//EbbfdhpkzZyI+Ph4AcOLECXTr1g0ff/wx7r//fpkrJCI5MMwQkcc4fvw4cnNzMXjwYIfjGRkZCAoKQvfu3WWqjIjkxDBDREREHo0DgImIiMijMcwQERGRR2OYISIiIo/GMENEREQejWGGiIiIPBrDDBEREXk0hhkiIiLyaAwzRERE5NEYZoiIiMijMcwQERGRR2OYISIiIo/GMENEREQe7f8Dkuz/lW/8KbIAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "from galpy.potential import PlummerPotential\n", "\n", "progpot = PlummerPotential(2 * 10.0**4.0 * u.Msun, 4.0 * u.pc)\n", "spdf_with_prog = chen24spraydf(\n", " progenitor_mass=2 * 10.0**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", " progpot=progpot,\n", ")\n", "stream_with_prog = spdf_with_prog.sample(n=500)\n", "plt.plot(stream_with_prog.x(), stream_with_prog.z(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"chen24spraydf with progenitor gravity\");" ] }, { "cell_type": "markdown", "id": "60ac321e", "metadata": { "papermill": { "duration": 0.004693, "end_time": "2026-06-30T01:26:45.211370+00:00", "exception": false, "start_time": "2026-06-30T01:26:45.206677+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Time-dependent progenitor mass\n", "\n", "Real cluster progenitors lose mass over their lifetimes. The\n", "`progenitor_mass` argument accepts either a constant (as above) or a\n", "callable `M(t)`. The callable receives the progenitor-time coordinate\n", "`t` — `t=0` is now and `t<0` is the past — and may take/return astropy\n", "`Quantity` values, which are auto-detected.\n", "\n", "Here we compare a constant-mass run to one in which the progenitor mass\n", "declines by a factor of 10 from start of disruption to the present (so\n", "the cluster is more massive in the past and is now nearly dissolved).\n", "Earlier strippings happen at the higher mass and therefore a wider\n", "tidal radius." ] }, { "cell_type": "code", "execution_count": 11, "id": "67eadcc6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:45.222088Z", "iopub.status.busy": "2026-06-30T01:26:45.221838Z", "iopub.status.idle": "2026-06-30T01:26:47.649388Z", "shell.execute_reply": "2026-06-30T01:26:47.648333Z" }, "papermill": { "duration": 2.434508, "end_time": "2026-06-30T01:26:47.650612+00:00", "exception": false, "start_time": "2026-06-30T01:26:45.216104+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from astropy import units as u\n", "\n", "\n", "def M_declining(t):\n", " # t = Quantity time, t=0 now, t<0 past\n", " # M0 at t=-4.5 Gyr, 0.1*M0 at t=0\n", " return 2e4 * u.Msun * (0.1 - 0.9 * t / (4.5 * u.Gyr))\n", "\n", "\n", "spdf_evol = chen24spraydf(\n", " progenitor_mass=M_declining,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "spdf_const = chen24spraydf(\n", " progenitor_mass=2e4 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "\n", "numpy.random.seed(0)\n", "stream_evol = spdf_evol.sample(n=1000)\n", "numpy.random.seed(0)\n", "stream_const = spdf_const.sample(n=1000)\n", "\n", "plt.figure(figsize=(12, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(stream_const.x(), stream_const.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Constant mass\")\n", "plt.axis(\"equal\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_evol.x(), stream_evol.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Declining mass (1.0 → 0.1 M0)\")\n", "plt.axis(\"equal\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "8f73fc53", "metadata": { "papermill": { "duration": 0.004958, "end_time": "2026-06-30T01:26:47.661673+00:00", "exception": false, "start_time": "2026-06-30T01:26:47.656715+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Integrating sampled orbits\n", "\n", "The `sample` method can return integrated orbits (to the present time) using\n", "`integrate=True`. You can also get the stripping times with `returndt=True`.\n", "The returned `Orbit` object can be further integrated or analyzed:" ] }, { "cell_type": "code", "execution_count": 12, "id": "fc80e237", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:47.673445Z", "iopub.status.busy": "2026-06-30T01:26:47.673207Z", "iopub.status.idle": "2026-06-30T01:26:48.421066Z", "shell.execute_reply": "2026-06-30T01:26:48.420154Z" }, "papermill": { "duration": 0.755032, "end_time": "2026-06-30T01:26:48.422111+00:00", "exception": false, "start_time": "2026-06-30T01:26:47.667079+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "# Sample with integration and stripping times\n", "orbs_integrated, dt = spdf_both.sample(n=500, returndt=True, integrate=True)\n", "\n", "# Integrate the progenitor for context\n", "ts_prog = numpy.linspace(0.0, 3.0, 301)\n", "prog.integrate(ts_prog, lp)\n", "prog.integrate(-ts_prog, lp)\n", "\n", "# Plot the integrated stream with progenitor orbit\n", "prog.plot(d1=\"R\", d2=\"z\", color=\"k\", lw=1)\n", "plt.plot(orbs_integrated.R(), orbs_integrated.z(), \"r.\", ms=1, alpha=0.5)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Integrated stream particles with progenitor orbit\");" ] }, { "cell_type": "markdown", "id": "52865a9f", "metadata": { "papermill": { "duration": 0.005135, "end_time": "2026-06-30T01:26:48.434206+00:00", "exception": false, "start_time": "2026-06-30T01:26:48.429071+00:00", "status": "completed" }, "tags": [] }, "source": [ "You can also obtain the stream points at the time of stripping by using `integrate=False`:" ] }, { "cell_type": "code", "execution_count": 13, "id": "5a650fe8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:48.445906Z", "iopub.status.busy": "2026-06-30T01:26:48.445692Z", "iopub.status.idle": "2026-06-30T01:26:48.692680Z", "shell.execute_reply": "2026-06-30T01:26:48.691648Z" }, "papermill": { "duration": 0.254038, "end_time": "2026-06-30T01:26:48.693446+00:00", "exception": false, "start_time": "2026-06-30T01:26:48.439408+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", "# Sample with integration and stripping times\n", "orbs_not_integrated, dt = spdf_both.sample(n=500, returndt=True, integrate=False)\n", "\n", "# Integrate the progenitor backwards for context\n", "ts_prog = numpy.linspace(0.0, -4.5, 3001) * u.Gyr\n", "prog.integrate(ts_prog, lp)\n", "\n", "# Plot the integrated stream with progenitor orbit\n", "prog.plot(d1=\"R\", d2=\"z\", color=\"k\", lw=1, xrange=[0.0, 32.0], yrange=[-16.0, 16.0])\n", "plt.scatter(\n", " orbs_not_integrated.R(), orbs_not_integrated.z(), c=dt, marker=\"o\", s=20, alpha=0.5\n", ")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Stream particles at the time of stripping with progenitor orbit\");" ] }, { "cell_type": "markdown", "id": "7ae44cc9", "metadata": { "papermill": { "duration": 0.005739, "end_time": "2026-06-30T01:26:48.706256+00:00", "exception": false, "start_time": "2026-06-30T01:26:48.700517+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Different potential inputs\n", "\n", "When initializing a particle-spray DF, you can also specify a different potential for computing the tidal radius and velocity distribution of the tidal debris, which can be useful when the overall potential contains pieces that are irrelevant for computing the tidal radius and that don’t allow the tidal radius to be computed (using the ``rtpot=`` option). If you want to generate a stream around a moving object, for example, a stream created within a satellite galaxy of the Milky Way, you can specify an orbit for the center of the satellite (``center=``) and the stream will be generated around this center rather than around the center of the total potential (this was used in [Qian et al. 2022](https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.2339Q/abstract)); the center orbit is integrated in ``centerpot``, which can also differ from the potential that stream stars are integrated in (e.g., the stream stars may feel the potential from the satellite itself and/or the satellite could be experiencing dynamical friction which the stream stars do not feel)." ] }, { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.005713, "end_time": "2026-06-30T01:26:48.717902+00:00", "exception": false, "start_time": "2026-06-30T01:26:48.712189+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Smooth stream track from spray samples\n", "\n", "After drawing a set of stream particles with `.sample()`, we can construct a smooth phase-space track through them using `.streamTrack()`. The track is parameterized by an affine curve parameter `tp` along the progenitor's orbit: for the leading arm `tp` runs from `0` (progenitor today) up to a positive `tp_hi`; for the trailing arm `tp` runs from a negative `tp_lo` up to `0`. The exact range is auto-fit from the particle distribution and is much smaller than `tdisrupt` (typically a small fraction of an orbital period).\n", "\n", "At each `tp` the track gives the mean galactocentric phase-space position of the corresponding stream particles, plus a 6×6 covariance that captures the scatter around that mean. The returned object is a `StreamTrack` — or a `StreamTrackPair` with `.leading` / `.trailing` attributes when `tail='both'` — that exposes the same coordinate accessors as `Orbit`: `x`, `y`, `z`, `vx`, `vy`, `vz`, `R`, `vR`, `vT`, `phi`, plus heliocentric (`ra`, `dec`, `dist`, `ll`, `bb`, `pmra`, `pmdec`, `pmll`, `pmbb`, `vlos`).\n", "\n", "Accessors return `NaN` for `tp` values outside the track's valid range (rather than silent cubic-spline extrapolation); use `track.tp_grid()` to see what range is in scope.\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:48.731101Z", "iopub.status.busy": "2026-06-30T01:26:48.730837Z", "iopub.status.idle": "2026-06-30T01:26:56.418073Z", "shell.execute_reply": "2026-06-30T01:26:56.417165Z" }, "papermill": { "duration": 7.694966, "end_time": "2026-06-30T01:26:56.418756+00:00", "exception": false, "start_time": "2026-06-30T01:26:48.723790+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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p/N/boS9cuHD6fStXrtznOfF4nHg8Pv12OBye+UJFDlJpSQmtFgtHFRdzwvwa7n3sJR5sH6MjYqctEOdbj3TR7Mlw+fIYnzy/WqdmRCRvFFQAiUQilJWV7XGtpKQEm81GJBLZ73NuuOEGrr/++myUJ3LIDMOY3lopLoIPnXkUC6va2DGS5uneDOt6x9kdsfCD50ZYvf1xrj6uigtPXECZp9jkykVEDqygAkhxcfE+KxiRSIRUKkVx8f5/IV933XV8+ctfnn47HA4f0qkZkWyqr6ujvq6OdDrDh8cTrOsMctfznTzbPsS2oQT/8kgPv301yFfOXcY7FlRqsqqI5KyC+u20aNEiOjs7mZiYmL7W1tY2/b79cblclJaW7vFHJNdZrRYqPS7etaSGmy4/lm+9q56F5WABNvaP87E7X+byW5/jgZfbGR0bM7tcEZF9FFQAueiiixgfH+f++++fvnbHHXfQ3Ny83/4PkXw3FURWnbqIH166lK+dXslR1S4swNrdIa79/TY+cvvLPL2ll/6BQaLRqNkli4gAebYF8/Of/5zBwUFeeukl+vr6+M53vgPA1772NRwOB3PnzuX666/nE5/4BE899RTDw8OsXr2aP/7xj1itBZW1RPZQXFTE8oVzmddYw5nLgry4Y5j/WdPDtuEU63vHuOZX61lR5+LieQ4WVxtU+nzU19fr6K6ImCavAkg8HicWi3HOOecAEIvFAHjjKJNvfOMbvPOd7+SJJ55gwYIF3HDDDbS2tppSr0i2FRcVsWROEU1VXuaVpHlx1whPdqfZNDDOur44r/TFOMob4kPLIpzudGK43ZohIiKmyJtBZNmiQWRSKKLRKKHwKKF4hqfbhrh3/QBtQ5NbMHYrnDOvlMuXezmqpZrq6mqTqxWRQlCQk1CzRQFECo3f72coMEzK6eHJtmF+83I3fZE0AC6bhfcuLOMf37uU1lovoPvLiMjbdyivoXm1BSMih87j8Uz/b3N1OUeVp/jzawM81Z0kEMvwwJYRnuh4kctX1rNqeSWOdIxgMEhNTQ2NjY0mVy8ihUorIHvRCogUumg0Sv+gn+7hCA9uCfLQ9lGCsRQApU4LFyzycG6rm9amegUQETkk2oI5DAogMpt09w2wtWuQv24b5eG2ESKJyV8HFW4rq4728pl3L6OitMTkKkUkXyiAHAYFEJlNpvo9JjIWtvcO84fXAjy6Pcj4xOSvhXqPjS+9ZxEXH9ei+8yIyFtSADkMCiAym43Fk7yweRe3PrmN9f4MExkLAIur3Hz6lDrefUwLJW9yWwMREQWQw6AAIrOd3+9n247drN/l5+FdSTYHLaRff9+JjcV8/swWTphXQ3FRkal1ikjuUQA5DAogMttNbcuEQiF29g7SEbaweusoW4Ym77Fks8BZrSX803nLWNRQgcViMbliEckVCiCHQQFEZNJUECkuLmZ4fIKHX+3mf9YN0j40DoDhsPL+Y2o4v8VGva+Euro6zQ0RmeUUQA6DAojI/qXSGfyjMX7/cid3vbibgdHJFZFie4b3NNu4eGk5TXXVuseMyCymAHIYFEBEDmwilWbjjh5+8cQWnupKMJac3IKpcKZ5V12Kq05fyIJ5czVNVWQWUgA5DAogIm8tGo2ya3c3O/2j/LltnMfbQ8QnZ5nRUmrlEydUMscdw1dRQX19PclkUmFEZBbQKHYRmVGGYbBk0QKWLIITjx7lHS9s5Lcb/GwMWukMp/l/jw+y3Gfh6mOsOByOPZ4nIgIKICJymCrLSjjvxMW0VhWzdWiC328O8Vp/lFcDGb7x1AjnLszw+TPnTt+TRkQEtAWzD23BiLx9g4OD7Owb4tWhNHc810Xf2OQEkTK3jQ+vqOLqk5txWtF2jEiB0haMiJiipKSEhkSCWm+GecUJfr+uj7/1QSiW4pbn+7n/lX4+tLSI85c3MKe5SSFEZBbTzR1E5IgxDAOXy0U8FmVhYzVfOGcB/3Kqh1NrwWHJMBiFn6wd50urd/DI2jbGxsfNLllETKIVEBE5oqZ6PTweDz6fj1JPEcvmRtnYHeTX6/xsGs6wdTjFl/7SxVlbgnz9fUexsN5nctUikm3qAdmLekBEZk5nn58HXtzG77dE2BWaPLdr2C1cdkwlnzp9LoZN/SEi+UxzQA6DAojIzBobH2fd5jb+uK6bx7szjCQmB5lVF9v4wAIHlxzfwqIF802uUkTeDjWhikjOKi4qYm6tj/PmBTiuZoLnhlw8sXOcwbEUN7+S4m89O/n8aXFaPBkaGhrwer3T96XR6ohI4VAAEZGs8/l8LF60kMXA+aXlvLS9h1v+totXBpNs8ie4dvVOVvrSfOHMFGec4CUSiRAMBgENMxMpFAogIpJ1hmHQ2Ng4/fay2mK+dEoFbRE7v3p5gN3hFC8O2dj0QDefHrZx9SkteL1eDTMTKSAKICJiOp/Ph8vlYm4sxpyiJPe/0sdTvRYiE1ZufLKTP7zSxz+8o4EzF9u0FSNSINSEuhc1oYqYZ6rXIzw6xrMbtvGnjjjrA1aSmclG1RPqnKxa6GDlomZaW1tNrlZE9qYmVBHJS4ZhYBgGVVVV1NfVsGxbO0+8upMHOzPsHLPzcl+CDQNxzu3p4FPxJN6SInw+n1ZDRPKQAoiI5CTDMFi6aD7WTJL5lX7WDqR5qDPFUMzCA+0Jnu1q4+PHlXPBigxFhlvbMiJ5Rlswe9EWjEhumdqWGY2Msb17kHte8fNMX5pEevJOEsfVurh8sYPGUgeZTAafz0dLS4vCiIgJtAUjIgVjalsGoLWmnI8dn2bBxl08MeiiLeJgXX+cjYMxTqua4FRvhJpAAJvNRmNjo0KISA5TABGRvDB1BHdiYoIVzeU0l4+zOZzhoS4IxC08OeBkw3AZFyQmqK4NUl5ergAiksMUQEQkL0ythNjtdpxOJ0ucThYNDbHY289DO2O8NOxieMLGXTtsrB0e4EtnuTjt9dCio7siuUcBRETyitfrxev1AlBdXY3dZsOV2cGxFTEe7XOwfdTOphErX/hTNxduDXDZUeW4bBY8Ho+2ZURyiAKIiOQtwzBYtGgRJSUltAwNsbh+lOe6YzzSbSEQg/u2Rnl65xhXHWVwzhIHkUhEAUQkR+gUzF50CkYkP0WjUQKBAOlMBv/oBHc838kjHWNMpC1AhtOai/jn9y2h1JYC0PwQkRlwKK+hCiB7UQARyX/RaJTASJj1u4b48RMdtI/aAPA4LVzcauPcBSUsXriAqqoqkysVKSw6hisis5phGDQaBo11NcypcPM/z27nL7vShBIZ7t6a5PneIJ8Za2dZ/QCVlZXYbDY1qYpkmVZA9qIVEJHCExkb5+Fn1nD3K8O8ErSTxoLNkuGkihgXtNior/ZSVVVFa2urQojIYdAKiIjIG3iKizh2fgPFtiSb/BPct32CvqiF5wIGW8IpLps3yjlut5pURbJIAUREZoX6+npKS0s50WbjpPld3PHsTp4ZsBGcsHHb1gzrAsN8MgF1PT2Ulpbi9XpJJpPamhGZIQogIjIrvHGk+/GGgcua4oS2Pu7fkaItbGOtP8Pmh/28qybGSZUpKivK8fl8lJeXa36IyAxQABGRWccwDI5auoS6mmoW1HXy102DPNJrZzRp5U+9RawfjnNBrZ8l8TgOh+aHiMwEBRARmZUMw6CxsRGfz8fC1iFO3byT37w6wvqAle6Yi190OnhHJMonq+OkUina2tqorKycnsIqIodHAUREZjXDMGhuaqLE42FObTcb+mPc+sIgA1ErTw0Vs/2RQa5cHKDOEcfrLefYY49VCBE5AhRARESYvMfM8V4vTXWDeDOj3PPqMC8F3fRGrdz4SpqV5UneU9uDx+PhhBNOMLtckbynACIi8gYlJSUsbKrhykyCFYNxVnda6Rm38mKwiLZRBx9xBfB624nH49TX12s1RORt0iCyvWgQmYhM3VcGIJLI8B9/WsdT/VYmMlYsZFhRFuN9jUkWzW1kzpw5uq+MyOs0iExE5DBMNahO+dwZARatb+fP3Q52jdtZFzJoH0uyaiLAmZkMoVCIsrIyBRGRQ6AAIiLyFpYsXkSJp5h529p5cPsofx8yCCft3L49w7qhIBc1DVLutrJkyRIWL15sdrkieUEBRETkLUytiFitVprrw1wwmuKW5/vZMmJh/bCNthCcWzWKzd5OTU2N+kJEDoICiIjIQTAMg3nz5gHQ7PfjscT582uDPNxrJ5KycV9/OdujcVK2NSxsqVeDqshbUAARETlEHo+H5rpqPuSyc2zvCL/dmmBLyMqrIRffej7GqoEdnH9MnPLhYWKxmMKIyH4ogIiIHKKpLZny8nIWLbSzbG43v3tpN3/pTBOesHL7tgxrBzq5oD5GqdvGxMSEAojIXhRARETehjfe3G6Z281H7BZai9q4d0eGHeMuXhlx0jFq5dzKEaANt9tNTU2N7rAr8joFEBGRw2QYBvPnzSM6Po47086zfeM8M1LGaMrOvQM+to2Nsyq9iaMWRXE6nQwODurYrsx6CiAiIkeAYRgcffTRlJaW4mtrZ15XgIcHPeyKuXk1UkzXphRXTPRyTI0Dq9XK4OAgoVCI1tZWhRCZlRRARESOEMMwWLx4MTU1NdS2tdHa1ctju0b5W6CY4ISN/9qU4fjuEO+fZ8XjspNMJnG73ZSWlmpbRmYdjWLfi0axi8iREo1GWbtuHWva+1i928HOscn/5qt0TPCB5hiLfE5KSkqoqqqioaGBqqoqkysWOTwaxS4ikgMMw2BOSwsOu52j5iS595UBnuh3MDTh4Bc77Jw5Guc9DSHsdju1tbX4/X6thMisoQAiIjKDfD4fLpcLj8fDkgUjtP71WX7faWMw4eSJQTfbQnGuSgYpLt5NLBajoaFheuCZSCFTABERmUFvPK7bYBhcfNpRzKno4P7tY7wcLKIn7uKmTWk+EPNzUlVaW78yayiAiIhkUUtLCz6fj3kt3fz+mc08OOghlLTzmzbYNGzl464gpTt2UFdXp60YKWgKICIiWTS1IlJVVYXNAvVrN/JQv5tNEYMNAQv/8vcIH+p9jUtPilFVVYXdbtfwMilICiAiIiaZM2cOyWSSpppBnukc58E+F6NJG7dvs7Ax0Malc9toqq/G5/MBKIBIQVEAERExidfr5YQTTqCuu5tU4iWq7UEeGihhR9TFC0N22kMTXNy3jYvPOA6Px2N2uSJHlAKIiIjJfD4fS5cuwTcwwNGtKR7tTPCnHUmGJhzc1eNj5PndfNRipbqqEpvNpu0YKQgaRLYXDSITEbN17u7i1w89y/1dbgITDgAWeuJ8ZLGdpqoy3G43Cxcu1B12JedoEJmISB6zWS2cONdHbXGQP3elWD/iYnvExffXJ3lf1U6WV0/OFdlfAIlGo0QiEa2SSM5TABERyTE+n48lS5ZQVtZLmdFLa884D/a5GU3Z+V1/JbvjY1TVDlJfX79PCIlEIgSDQUBNq5LbFEBERHKMYRg0Njbi8/mor6+nubeXuVs7+W2Hje64i+eCHjqfHuGTgec47/Tj9+gLmWpWVdOq5DoFEBGRHDUVRABOyGQod3bx4K4wL4yU0BN38v31abpjGzitwUFFRQWLFi3aY/KqSC5TABERyXFT95OpqKjAYX2Fpp4ADwXKCSXt3L4pyfqeUS6dEyAej6s5VfKGAoiISI574/RUwzBo7OxkUdcg97bH2RJxsW7EoHtzgiuiO6moqMDr9aoZVXKeAoiISB5542pIqWs7D3WM8lSgmMGEk5u320mV9PExn49UKqVmVMlpBRVA0uk0mzdv3ud6Y2Mj5eXl2S9IROQIm1oN8Xg8pNNpykr6qN3Uw5/9ZYwkHfxkTZj1Pc/z5bPnUO4xiMfjRKNRhRDJOQU1iCwSiVBSUkJra+seP2zf/e53ufjiiw/qY2gQmYjki6ltlp6eHp5d+xqre9xsHy8CoMaZ4Iq5cRbXeykvL1dviGTFrB9Edvfdd3PyySebXYaIyIx6Y2+I2+3G9+pGHt0d5umAh4GEk/9qs3N+aIh3NI3hcDhwu91aCZGcUZABJBQK0dHRQXNzMw6Hw+xyRERmXEtLC6lUCp+3lzk7Avy+y2AkaecP/WXsGhvjKms3Y2NjNDc3U1RUpOZUMZ3V7AJmwvvf/37OOussiouL+cxnPkMkEjG7JBGRGWUYBq2trRx77LFccOIivrQ8w8LiGGBh/aiHf1+f4sVNHWzYsIHdu3cTCATMLllmuYJaAbHZbPznf/4nn/3sZ3E4HLz66qucd955pNNpbrvttv0+Jx6PE4/Hp98Oh8PZKldE5Iia2pKx2+0kEgk+ThePdI7y9LCH/oST23dXcElylHOMYYqLi/H7/VoJEdMUVBPq/vz0pz/ln/7pn4hEIthstn3e/+1vf5vrr79+n+tqQhWRfBaNRtmxYwfdPT083x7g9z1FjKbsWMhwhm+M9zRkqK2pYtGiRdPTVkUO16xvQn2jxsZGYrEYfr+f2trafd5/3XXX8eUvf3n67XA4TFNTUzZLFBE54qa2ZABOTCYptfv5Y6+H3TE3Twc89IxHuSi8E4vFAkzOF9FKiGRTQQWQRCKB0+nc49rTTz+N1+ulqqpqv89xuVy4XK5slCciklVTIaSsrIzy8t0UW7fx2OAEL4c9tEcNftlt55LELqLRKMccc4xWQiSrCiqA/PSnP2X79u1cdNFFlJeX8+CDD/LTn/6UH/3oR/vdfhERKXRvvLNucXExvvYOancGeWS4nGDSwa/7qhhOhSgv79QqiGRVQfWApNNp7r77bu699178fj+tra185jOf4Ywzzjjoj6FBZCJSyPx+P+vXr+eFbT2sHvQSmJgcVXBiRZxrlhdz3LHH7He7WuRgHMpraEEFkCNBAUREClk0GiUQCNDb28tr23Zw7y47W8cmVz0aXAn+YYWL01cu12qIvC1qQhURkf1645bM2NgYV1r7eLxngr8Pl9ATd/K9NSk+PrqW45rLaWpqoq6uTkFEZoQCiIjILGQYBkuWLAHgXZleapwB/uz3Mpq08bPN8J6BLk7t6mbevMnhZgohcqQpgIiIzFK1tbWUlZWxceNGiou7aa1Ocef2DH0xOw8OeRlMRLggswOXy8XcuXN1Mzs5ohRARERmMcMwOOqoo5gzZw6pVIra8g3csnaULWMGa8IehjpifMyxE0A3s5MjqiDvBSMiIgdv6o66NpuN5rpqPrHUxhnlYSxk2BVzc9NGG4+v28YTTzxBf3+/2eVKgVAAERERADweDx6Ph5bmRlYtK+Gy2iBua5pg0sFtHR4e2xbg6aefJhgMml2qFABtwYiICPC/J2TKyydPwLjdr9FYPsJdO5wEEnb+OFiBPzFK+csv09jQQH19vfpC5G1TABERkWlTd9SFyVtVzJkzRHP1Ln7ycogdUYNnRkoZfmmUD87ZQENvLytXrlQIkbdFWzAiIrJfXq+XBQsWsHxRK1e1RDmxdBTIsDni5tbtbjbv6qW9vd3sMiVPaQVEREQOqL6+nuNXLMdbvouanRH+OlhMX8LF7Z023GV+EolncTqdzJ8/X6shctAUQERE5IAMw+CYY46hubmZxoZ2yl/cxu97Swkn7dz4SpqLB3ax3JshkUjQ0tKiMe5yUBRARETkoHi9Xk444QSCwSAeay/39JUTmHBwX08ZQ9EwZ2d2Mj4+TmtrK6WlpXg8HgUReVMKICIickiWL19OIpHg4w4/9/aWsivq5onhMoYnxrgo2Ut5eTmpVApAAUTelJpQRUTkkNTW1rJ06VLmN9fzkTnjHFsSAeCV0WJ+1elhZ+8gdrsdj8djcqWSy7QCIiIih6yuro6SkhLq+vqwW1+loneEp4JldMbcfH9Nks/HNnLq8jhz5szRKojslwKIiIgcsql5IR6Ph3g8jqe4i8quEVb3lxGYsHPjqyn84Q0c391NU1MTLS0tCiKyBwUQERF526ZuZje5IrKFUkcvv+spZzRl5/YdxQyPD3BSOEwmk6GyslKNqTJNAURERA7L1Aj3KaWuAf57VzH+CSf39ZUznhnHbt9OPB6noaFBAUQABRARETlCfD4fS5Ysobi4GGtyC/f1lbMr5ubP/cX4o6O8L7yJRCKB3W7XwDJRABERkSPjjSsh4+PjXOnoZnVPio1jxbwYKmE0Oc4l8Y10dXWxcuVKWlpaTK5YzKQAIiIiR1RxcTEtLS1YLBYunOigdDjFc6ESNo8VEem2ctnEMMVbtlBUVKSekFlMc0BEROSISiaTZDIZ5syZQ2NjA+dUjXNu5QhWMuyOubmrt4ru4DgbN26kt7eXaDSK3+8nGo2aXbpkkVZARETkiJoaQObxeKioqKCzsxP3xo14bAEeGKxgaMLBjzel+OhoL6lUilgsNv1crYbMHgogIiJyRE3NCJn6u9frxWq1Yt+8mVLHML/r9TKatHH7rhJWRbtYNDDAsmXLNDl1llEAERGRGbdgwQLS6TTuXbuw4+d3/ZWEknb+p7+S96eHKSnZPb1toxMys4MCiIiIzDjDMKisrCQcDrM4neZqyyD39FcyOOHk9wM+4pkRThnfhtPpVACZJRRAREQkK3w+HwDV1dW4XB181NHP//R46Y67eGCwnPFUiNLSTtxuN/X19eoHKXAKICIikhVTc0L8fj+jo6OkUimuZJDf95XTHjV4NFBObOMoH0xtweVy7TFdVQqPAoiIiGSVx+OhvLycVCqFw+FgVaabP/vTvBYp5u/DHqKboiSTa0mlUhpWVsAUQEREJKumVkKm/nf+/Pl412/g/h1jvDBSzJoRg7GN41weeYYliwZYsGCB+kIKkAKIiIhk3d43sCspKcEw1mBsCfPUcAlbxor47x0Wrra0U1xcTDKZ1NTUAqMAIiIipqutrWXp0iVEo2txWkZ4JDDZF/LLdgslpbsYGBigpaWFefPmmV2qHCEKICIikhPq6+sBqKzsxLGuhweHvOyKublxbZyrW4amR7XrhExhUAAREZGcYBgG8+bNo7S0lEgkgsM6zAODFXTHXdy5y8Ll8V6SyaROyBQI3YxORERyisfjYdmyZZw9v5xLawLYLWn6Ek5+3VfJ7oHh6RvYSX7TCoiIiOSUqZUQgImJV3BYA9zX78OfcPLLLi9pNpNMJlmyZImaU/OYAoiIiOSk+vp6YrEYicSr2C1D3NNfyfCEgzt2e0mmtjE2NkZZWRler3f6WK/kD23BiIhITjIMg9bWVubNm8fCCgdX1PkpsqYIJe3c1V3B1q5BBgcHGRsbIxKJmF2uHCKtgIiISM4yDIOjjz6aRCJBJrOTKxjiN32VhFJ2ftHh4SNxP4lEgkQigd1u18CyPKIAIiIiOc0wDJYtW4bX66W+vx+bdTe/7vURStn5VXcFV6X8RKNRMpkMy5cv11ZMntAWjIiI5Dyv18uyZcvweDzUe6xcUeun2JYinLLz674qeoJROjo66OvrM7tUOUgKICIikjdaWlpobm6mrtjClXuFkO7hcTZu3EhHRwfBYBC/36/jujlMWzAiIpI3amtrKSsrw+VyUbR7Nx+xDXNXT8V0CPmEK0RJyW7S6TSZTAZAWzI5SgFERETyimEYrFixgrKyMqr6+7E7+rljVwnhlJ07Osv4p8oo4fBmvF4vVVVVZpcrb0IBRERE8s7UEd3q6mp8Ph+p5Cv8qruCUNLGD9cluaZxmEgkQmNjo07G5Cj1gIiISF4yDIOqqipaWlpoqTC4qnZyTsjIhI27uisIxdN0dXURjUaJRqPqCckxCiAiIpLXvF4vTU1NVLrTXFHnx7CmGJ6w88tdpezoGWDXrl10d3czMDCggWU5RFswIiKS16LRKEVFRXi9XmzhMFfUD/PrHh/+hJ1btmaw8RpV3hLcbjeVlZVmlyuv0wqIiIjktUgkgt1up6ysDMMwmFNm44qGIA5LmoGEg1u3O+jqHaCvr4+Ojg5tw+QIBRAREclrHo+HmpoampqaKC8vp6KiguUNJXy4YQS7JUNPzMnd3WVExmMMDQ0RCATMLlnQFoyIiOQ5wzAwDAOPx4PH4wEgEAgQj2/hg5kRftdTTmfUyW97Svl06QSJRMLkigW0AiIiIgXCMAwaGxtpbGzE5/NhGAaLSlO8vzaIlQw7oga/2m7BPzSkbZgccMgB5I477uDaa69lw4YNM1GPiIjIYUmnM9yxLsjGZA01NTWsqLJyQVUQCxm2RNz853N+RkdHzS5z1jvkALJkyRLWrFnDsccey/HHH8/PfvYzgsHgTNQmIiJyyJ7cNsgdz+3mtpcDPD9gxWq1srwsznsrQwB0hCGpDQDTHfK/wCmnnMJzzz3Hli1beOc738l3vvMd6uvr+fCHP8xjjz02PXtfRETEDOcsruY9c10A3LUlwZr+CdLpNKfXweVzJ7j2+CLGQkFtw5jsbUfAxYsX84Mf/ICuri7uuecedu/ezbvf/W7mzp3Ld7/7Xa2KiIiIKWKxGOfVjLGwKEoGC6sHK9gddRCPxzmpOkNd0WSTqk7DmOuw1qAmJiZYvXo1t956Ky+++CInnHACV155Jf/93//NkiVLaG9vP1J1ioiIHJRIJILb5eT9NcM0ueMkMxbuHaikbxzi8TiZTIbx8XHi8bjZpc5qbyuAvPbaa3zpS1+ivr6eT33qU8ydO5d169bx0ksv8d3vfpfNmzdz1llncffddx/pekVERA7I4/FQWlpKseHmQ3XDVDkniKet/Kavkt2BCH19fYTDYR3HNdkhB5BbbrmF5cuXs379en70ox/R29vLT37yE5YvX/6/H9Rq5dxzz50+jy0iIpIthmFQV1dHZWUlDdU+PrdogjJ7krGUjf/pq8QfGiccDuskjMkOeRDZSSedxPbt21mwYMEBH3fNNde83ZpEREQOS11dHalUing8zvj4OJ+3dHPTRgvBpIPf9ldydZ2f3t5egsEgXq/X7HJnJUtGx1b2EA6HKSsrIxQKUVpaanY5IiLyNkWjUQKBAENDQwwNDbFmxyC37yxhImOl1YjyodphKit9LFiwgIqKiunhZfL2HcprqA5Ci4hIQTIMA5fLhd1ux+VysbDSzQeqA9NTUR8OlBEIBNi8eTOdnZ1EIhGzS55VdC8YEREpWFO9iJWVlcTjcRaVh3hvaoS/DnlZF/ZQbk/yDvs4oVAIu10vidmk77aIiBSsqRvVAXR2duJ2uzm+fIzgxCgvhEp4criMcvswbvcIAwMDJJNJPB6PtmKyQAFERERmhZaWFhKJBKOjo7zPNUxwYpxt40U84PdSYh/CvXkzFRUVlJWVUVVVpZ6QGaYAIiIis0JtbS1lZZN9H36/n6tt2/jZ1gR9CSf39vsosg3SGI0Sj8dJp9O4XC4FkBmkJlQREZk1DMOgsbGRxYsX4/OW8aHaIcrsScbTNn7XX8nIWJxYLEYsFiOVShGNRvH7/bpvzAxQABERkVnHMAyWLl2Kr8TN5bVDuKxphicc3NtbRmB4hMHBQQKBAJFIhGAwqBMyM0ABREREZqXq6urJXg9nisteP567K+bmwT43wWCQnTt3EggEKCoq0mTvGaAAIiIis1IkEsHtduPxeGgpSvBu3wgAa8IeXh520tfXx4YNGxgdHVUvyAxQABERkVnJ4/HQ1NREfX09JSUlnORLcFzpGACPDJXTOW5nfHyc7u5u9YDMAAUQERGZlQzDoLS0lMrKSoqKirBYLJxbFabJHSeFhfsHfAyNpwiFQuzYsUMh5AhTABERkVnL4/FQU1PD0qVLqa2tpcJbzpXNY9MnY+4d8DEwNExnZyeBQMDscguKAoiIiMxahmFQVVXFggULOOuss2hqaqLYAatqAjgsaQYTTh4YrKC/f5Ddu3drFeQIKrgAEg6H+fKXv8wxxxzDSSedxI033kg6nTa7LBERyXGGYbBw4UKqqqpoLrNzYVUQCxm2jRv8ze+ko6ODXbt2mV1mwSi4SaiXXHIJIyMj/PjHPyYYDPLJT36SoaEhvve975ldmoiI5Div18tJJ53E9u3bsds7GEiM8uxIKX8LllLnGsK9cSPxeJyWlha8Xq/Z5ea1ggogTz31FE8++SQbN25k2bJlAAwODvLFL36Rr3/965SWlppcoYiI5Dqv18vy5cuJxWKcE+2gL+5kR9TN6sEKfE4/NtsOiouLFUAOU0FtwTz11FM0NDRMhw+A888/n3g8zvPPP29iZSIikk8Mw2D58uU0NzdxcfXwdFPq7/srmEhlKCkpMbvEvFdQKyBdXV3U1tbucW3q7e7u7v0+Jx6PE4/Hp98Oh8MzV6CIiOQNr9fLypUrSafTfCDZw696q+lLOLmnbYwi98ssWLCAlpYWDSl7mwpqBSSdTuNwOPa4ZrPZsFqtpFKp/T7nhhtuoKysbPpPU1NTNkoVEZE84PV6WbZsGUvrSnnv65NS14aLeXjbCH//+9959NFH6e/vN7fIPFVQAaSysnKfc9rBYJB0Ok1lZeV+n3PdddcRCoWm/3R1dWWjVBERyRM+n48VK1Zw5SlzWVE6DsDDgXL6Yzb6+/vZtm2byRXmp4IKICeccAIdHR0MDg5OX3vmmWcAWLly5X6f43K5KC0t3eOPiIjIFMMwmDdvHgsXLuQDc5LUOhNMZKz8YbCCeBr6+/tZv349wWDQ7FLzSkEFkAsuuIC6ujq+8Y1vkEwmCYVCfOc73+H888+nubnZ7PJERCSPeTweKiu8rKofwWVNMzzh4GF/OaOjEXbu3MnQ0JDZJeaVggogRUVF/OlPf+K5556joqKC6upqysvLufPOO80uTURE8pxhGBx77LEsaqzi4rpRADaOFbN+xEk0GsXpdJpcYX4pqFMwACtWrGDz5s309fXhcrmoqKgwuyQRESkQtbW1HH300cRiL9MWjrB+1MOjgXLq3YPYX3gBgJaWFpOrzA8FtQLyRnV1dQofIiJyxBUVFVFVVcV7KkNUOSZIZKz8caCCQDDEmjVr6O7u1j1jDkLBBhAREZGZ4PF4qKyspNRTzKWv37TOP+Hk0UAZgUCAtWvX6s65B0EBRERE5BAYhkFraytNTU3UFFl4b+UIAOtHi9kScTM4OKgTMQdBAUREROQQGYaBz+ejpKSEY8viLC0eByw8PFROOGGhp6dH2zBvQQFERETkbaivr6e+vp7Kyko+ODdFmT3FeNrGX4bK8Q8F2LZtm0LIARTcKRgREZFs8Hq9tLS04Ha7WVRUxFXJLfzXVis7ogZ/64vjdrXhcDhobW3V/WL2QwFERETkbfL5fLhcLuLxOPPLLJxYFuHFUAlPDZcyxxgknd6I2+1m3rx5Zpeac7QFIyIi8jYZhkFVVRU+n4/GxkYuaE5T5Zgc1f6nwQqGgyE2bdqkptT9UAARERE5TIZhMH/+fI479hiumBvHbsnQn3Dy92AJgUCA3t5es0vMOQogIiIiR0AymcThcDCvsoizvCEAXgiVsGsU2tvbtQqyFwUQERGRI8Dj8eD1eqmsrOQUX5xmd5w0Fh70e+nuG2DDhg06FfMGakIVERE5AgzDwDAM7HY7drudjxb38v9tSOOfcPBssARPZydOp5Pm5mZ8Pt+sPxmjACIiInIEeb1ejj76aHw+H5tGNnH/LngxVMKi4kHsO3dis9lwuVyzPoBoC0ZEROQIi0QipFIp3t3ioNEVJ4WFB4e8jEfjuFwuPB6P2SWaTgFERETkCJvqBykuLuai6hHslgwDCSdPD7kJhULEYjGzSzSdAoiIiMgRNjUfpKGhgbnVJZzuDQPwQqiUv73awcsvvzzrG1IVQERERGZIRUUF9fX1nFWbos6ZIJmx8NBQOR07drF9+3azyzOVAoiIiMgMSSaTlJeXM39eK5fUj2IlQ0/cxYZIEVu3bp3VqyAKICIiIjPE4/FQXV3NvHnzWN5SxQllEQCeHi6lNzDK448/TkdHx6wMIjqGKyIiMkOmZoO0tbUB8J66BFsiScIpO48FSimy9WK32yktLZ11x3K1AiIiIjLDKisraW5upr6mivdWjgCwaayIXTEngUCAVCplboEmUAARERGZYV6vl2XLllFbW8uSshQLiqKAhUeGyhkZHaO/v9/sErNOAURERCRL5syZQ319Pe/1jeCwpAlMOHhxxMPGjRvp7Ow0u7ysUgARERHJEq/Xy1FHHUVrXQXv8I4Ck3fM7QvFWLNmzaxqRlUAERERySKfz8eiRYs4szZFhX2CRMbKk8NlDA0FZtVsEAUQERGRLDIMg9bWVpYftYxzayaP5W4ZM+iKOWlvb581x3IVQEREREzQ1NTEu5bVM8+IkcHC44EywpFxOjs7iUQiZpc34xRAREREsiwSiRAMBikpKeHChhhWMvQlnKwL2Egmk9jthT+mSwFEREQky6bulltRUcHCei8nVUxuuTwZ8NDZO0gwGDS5wplX+BFLREQkx0xNSPV4PMRiMS4a386GkRSRlI3H+my07txJXV1dQU9H1QqIiIiISQzDoL6+Hq/H4JyqMQDWhT2s3bqTl19+uaCbURVARERETJRMJvF4PJxWZ8XnmGAiY+XvwVLa29vp7e01u7wZowAiIiJiIo/Hw5w5c5jXOpfz6uMAbIoU0TuWYceOHSZXN3MUQERERExkGAaNjY0sWLCAM+Z5aXDFSWPhqeEydu/uKtj7xCiAiIiI5IBkMonT6eT811dB2qNudkSsbNiwweTKZoYCiIiISA7weDxUVVWxck4FC4pigIWnhkvp7u6hu7u74BpSFUBERERywNSI9sbGRs5vSGAhQ0/cxdawjRdffJFdu3aZXeIRpQAiIiKSI6ZCyPELGlhaPLni8exIKYHhIJ2dnQW1CqIAIiIikkMMw6CkpIQzKkaxkKE37qQt4iAWixXUVowCiIiISI4pLS2lrsTO0uJxAJ55fRXE7/cXzI3qFEBERERyTH19PfPnz59eBemLO9kastLd3Y3H4zG7vCNCAURERCTHGIbBihUrWFDnnV4FeXaklFB41OTKjhwFEBERkRxkGAannnoq51RFp3tBOsacBXMaRgFEREQkR9XW1rJsTg1Lpk7EDBfx6msbCQaDJld2+BRAREREctxp5ZNbL11xF5sGxgpiFUQBREREJIfV19fTXO6g1Zicjvp80MP69a+wZs2avD6Saze7ABEREXlzCxYswOl0EnF38v21STrG3fSPh7Bu3Dg9uMwwDLPLPGRaAREREclhhmHQ0tLChacso8GdJI2FF0ZKSCQS9Pb25u1cEAUQERGRHBeJRBgYGOCMqhgAW8YMRpNWIpEIdnt+bmYogIiIiOQ4j8dDTU0NK6ptlNuTTGSsrA0V43A4SCaTZpf3tiiAiIiI5DjDMGhsbGTFscdwdsPktdciRQwOBdm5c2deHstVABEREckTCxYs4HPvPRanJc1oys76AOzcuZPOzk6zSztkCiAiIiJ5xE6Ko0smj9+uCxeTwUImkzG5qkOnACIiIpJHnE4n76ieAKAn7qR7DNxud97NBFEAERERySPFxcUsbqigxT05mOzJHgttbW0EAgGzSzskCiAiIiJ5ZGxsDIvFwqmVcQC2j7vpGRohFArl1SqIAoiIiEie8Xg8nDG/ghJ7iomMlXXDDvr6+vJqFUQBREREJI/4fD4WLVrEySedxElVaQBeC7vp7esnkUiYXN3BUwARERHJI4ZhUFVVhdfr5cKlPiBDf8LJjuAEXV1deTMTRAFEREQkz0SjUfx+P8cubKbFmFz1WBcuprOzM29mgiiAiIiI5Jmpe8P09/fzjloLAG3jbkbH43mzDaMAIiIikmc8Hg8ul4tkMsnKOgdua5po2sbWMXfeDCVTABEREckzU/eGaWlpobGuhmO9kzek2zhaREfHjrw4jqsAIiIikoemQkhdXR3vXlAKQFfcRf/IWF70gSiAiIiI5DGfz8fpS5sod6RJZixsGTMYGBgwu6y3pAAiIiKSxwzDoLS0lBNrJl/St0QM+vsnG1RzmQKIiIhInuvq6mKBcwSA3riT7uEx2tvbzS3qLSiAiIiI5Ll4PI7PHsfnmCCNhdfCLkKhkNllHZACiIiISB6LRqNUVlZSU1PDiooUMHmDuvHx3D4JowAiIiKSxyKRCFarlcWLF3P2Ai8A/XEnaZcnp4/jKoCIiIjkMY/Hg9frxeVy0VzmoMKZJo2FJ9uCbNiwwezy3pQCiIiISB6bujldcXExqVSKhZ4YANsiTjZv3kxbW5vJFe6fAoiIiEgBSCaTZDIZjvamAeiJOYnEUzl7GkYBREREpAB4PB7q6uo4pt6DYUuTyFjZFZucEZKL7GYXcCQlEgm+8Y1v7HP98ssvZ+XKlSZUJCIikh2GYeDz+Whvb2dBUZxXRw3aY0U4nU6zS9uvgloBSSQS/Md//AeJRILa2trpP4ZhmF2aiIjIjPN4PFRWVrKobPI4bte4jeHgSE6ehimoFZApV1xxBSeffLLZZYiIiGSVYRi43W4WlQHdEJyws6V7iOZdu1iyZInZ5e2hIAPIb37zG/7yl78wb948LrnkEsrLy80uSUREJGvKDRs1riQDcTsbh+GE4WGzS9pHQW3BAJSVlTE+Pg7Af/3Xf7F48WLWrVv3po+Px+OEw+E9/oiIiOSrlpYWWlpaWFw++fbumJtkMkkwGDS1rr1ZMplMxuwi3sz4+Dj/7//9vwM+5qijjuKaa64BYGJigoGBARobGwHIZDK8733vo7+//01DyLe//W2uv/76fa6HQqGc7RwWERE5kLa2Nh5ct5MfrZ+g2J7h31ZmmNPcwJIlS2a0LzIcDlNWVnZQr6E5vQVjsViora094GO8Xu/03x0Ox3T4mHr+Rz/6UT784Q8TiUTweDz7PP+6667jy1/+8vTb4XCYpqamI1C9iIiIOUpKSlhS6cBmSTCWtNARGKOpIUUkEsmZgxk5HUAMw+CrX/3qYX2MqcEsiURiv+93uVy4XK7D+hwiIiK5xGazkYiOUeOcoDfuZHvIyrvs9v3+h7hZCqoHZP369Xv0cMTjcW655RaOO+44KioqTKxMREQkezweD263m5aiJAC7xyz4/X6Tq9pTTq+AHKqBgQGuuOIKjj76aMrLy3n88cdxOBzce++9ZpcmIiKSNYZh0NjYyOLOCM8HYSDuoG9gkEAgsEergpkKKoCce+65nHLKKTz++OP4/X5WrVrF2Wefjd1eUF+miIjIW/J4PCyvL4G2GCNJG/7RBMFgUAFkppSVlXHppZeaXYaIiIipUqkU5W4rFc40wwkru6LOnBo1UVA9ICIiIjIpEAgwMjJCU9HkWPbBVFFOjZdQABERESlAPp9vcjxF8eS4r8CEg3A4nDMDyRRAREREClBRURE1NTUsqHQDMBiFbW3tbNmyxeTKJimAiIiIFCCPx0N5eTktZTYARpNWAuMTOXMcVwFERESkAE0dxZ1bX0356/M2+xIGTqfT3MJepwAiIiJSwEpLS2ktnzz0Oph0U1RURDQaNbkqBRAREZGCFYlE8Pv9lFtiAIRTDoqKiohEIiZXpgAiIiJSsDweDy6Xi/qSyRWQUNJOUVFRTtwTRgFERESkQBmGQWVlJQtqJ+d/BOMZHC53TtwRVwFERESkgBUXF9NSMRk4wgmIpnPjpT83qhAREZEZkUwmqSxx43FOvuR3DEXVhCoiIiIzy26343K5aCybPIu7dnsPO3bsMD2EKICIiIgUsGQySSKRwGNNALB7KEx3dzeBQMDUuhRARERECpjdbicej1P++vyx0aSFWCxGPB43tS4FEBERkQI2NjbGxMQEtWWT94SJ4cLhcDA6OmrqNowCiIiISIGz2+3Ul0+ehIlMgMUyuQpi5kAyu2mfWURERGZMNBolEolgt9ux2Wy4M2MAjE6AzW7H7XZjt5sXAxRAREREClAkEiEYDGKxWBgdHSUTDQFWxicydPf0kUmnaWhoMK0+BRAREZECNDVufWoFJO0ognX9TGQsjMWTxGIxU0eyK4CIiIgUIMMwpkeuu91urHYH0A9A2llMSUkJsVjMtLHsakIVEREpcH19fWzZtBGXNQPAhM3N2NgYvb29ptWkACIiIlLgotHo5GqHfTKAxLFjsViw2Wym1aQAIiIiUuDq6+upqKjAeD1vJC0OysrKTO0BUQAREREpcF6vl8rKShy2yZf94lIvc+fOxefzmVaTAoiIiMgs4PP5cDsml0DiqQw+n8+0BlRQABEREZkVbDYbNstkD8jQcNDUKaigACIiIjIr2O12nPbJl32H021q/wcogIiIiMwKyWQSl2Ny/JentMzU7RdQABEREZkVPB4P1teP3YZDIYLBoKn1aBKqiIhIgYtGowQCAdKTLSAk4jF6e3tJJpN4PB5TVkO0AiIiIlLgAoEAO3bsYDwaB8BiydDV1cXOnTtNa0bVCoiIiMgs4HQ6SWfGAZiIxxkZieJyuUxrRtUKiIiISIErLi7G5/NhszsAsFomr2sUu4iIiMyIaDRKb28vAwMDRCdSABS7nTidTpLJpLZgRERE5MiLRCIEg0GCwSBj8cmX/ea6aubWWSktLTVtC0YBREREpIB5PB48Hs/kHXFTSQDmNTew4qhaU+tSABERESlghmFQWVlJKpUimhwAoMww/+Xf/ApERERkRvl8PmwOJ7FkPwDp+BjRaLFuRiciIiIzKxAen/772PAAgUDAxGoUQERERApeJBJhy64eAAy7hUw8SjweN7UmBRAREZEC5/F4GEtOzvwocVooKy3G5XKZWpMCiIiISIEzDIOkowiAUreN+toafD6fqTUpgIiIiMwCUZzAZAAx3G5TG1BBAURERKSgRaNRuru76fKHAPB53MTjcaLRqKl1KYCIiIgUsEgkwsDAADv9owDUlLoZHx83bQT7FAUQERGRAma323G73Qy9vuDRUlmC1+s1bQT7dF2mfnYRERGZMdFolKGhIdLpNH2jCQBafEVUVVWZXJkCiIiISMEKBAIMDg4SjKWJJTNYAK81gd/vx+PxmNqIqgAiIiJSoBKJBOPj43QG0wB4DRtlho1gMAigACIiIiJHntPppKSkhLFQEghR7y2irqaS2Pi4ekBERERkZvh8PlwuF3/u7QVCzKn0UFJcTElxsdmlKYCIiIgUKsMwMAyD9qF2AFqrzF31eCMdwxURESlgmUyGrX2TM0DmK4CIiIhINgyOxhmJTmCxQGNRyvQJqFMUQERERArY5r4wADUeJ9aJMdMnoE5RABERESkg0WgUv98/vdLxWvfkPWDmVBZTW1lh+umXKWpCFRERKSCRSIRgMEg4HCYWi/H8tiEAFteVUVtTbXJ1/0srICIiIgXE4/Hg9XqJxWJ0d3ezeWAMgPk+1x4rI2bTCoiIiEgBmTp6a7fbyWQyfOe98HJfghp7lMHB+PRjzKYAIiIiUoC8Xi9er5d50Sit3t0kYuM4nZ6c6QHRFoyIiEgBCwQCjIaCOJ1OGhsbc2L1AxRARERECp7D4aCsrCxnwgdoC0ZERKSgTd0PJle2XqYogIiIiBSYaDRKJBLBbreTTCbxeDw5tfoBCiAiIiIFJxKJMDg4SDwex+l0Arlx8uWN1AMiIiJSYOx2O5FIhHA4jMViybntF1AAERERKTjJZJKJiQkmJiZwu905t/oB2oIREREpOFPTUB0OBy6Xy+xy9ksBREREpMAYhkFrayuRSCQnt19AWzAiIiIFZ+oUTC6efpmiACIiIlJgAoEAu3fvJhAIEI1Gc+omdFO0BSMiIlLAIpEIwWAQyK2juAogIiIiBWJq66W4uJjm5uY9+j9yrRck77ZgMpkMa9euZcOGDW/6mImJCdavX8+WLVuyWJmIiIi5IpEIAwMDDA0NTc8CAaiqqsqp1Q/IoxWQTCbDjTfeyK233orf72fevHmsWbNmn8c9+eSTfPjDH8YwDEZHR2loaOCBBx6gpaXFhKpFRESyx+PxMDIyQiKRYGhoiEwmA+TW1suUvFkBmZiYoLe3lz//+c989KMf3e9jwuEwq1at4qMf/Sg7d+6kr68Pn8/H1VdfneVqRUREss8wDBobG6murqayshKv15tzWy9T8mYFxOl08h//8R8HfMzq1asJh8Ncd911wOTth7/2ta9x7rnn0t7ezvz587NRqoiIiGkMw8jJFY+95c0KyMFYv349ra2tlJeXT1878cQTp9+3P/F4nHA4vMcfERERmVmmrYAkk0leeOGFAz7G5/OxZMmSg/6Yw8PD+Hy+Pa6Vl5djtVoZHh7e73NuuOEGrr/++oP+HCIiIrksH4aQgYkBZGxsjK9//esHfMwZZ5zB9773vYP+mA6Hg1gstse1RCJBOp2evh3x3q677jq+/OUvT78dDodpamo66M8pIiKSS3J17sfeTAsgZWVlPPPMM0f0Y7a0tPCnP/1pj2s9PT0ANDc37/c5LpcrZ2/UIyIicqimmk5ztfl0SkH1gLz73e9mYGCAl156afra6tWr8Xg8nHLKKSZWJiIikh2GYeTk3I+95c0pGJhsJB0bG6O3t5dIJDK9gnLqqaditVo56aSTeP/738+VV17Jd77zHYaHh/nmN7/Jt771LYqKikyuXkRERKZYMlNTSvLARz7yEXbs2LHP9UcffXQ66cXjcW666SaeeOIJXC4XH/rQh7jyyisP+nOEw2HKysoIhUKUlpYesdpFREQK3aG8huZVAMkGBRAREZG351BeQwuqB0RERETygwKIiIiIZJ0CiIiIiGSdAoiIiIhknQKIiIiIZJ0CiIiIiGSdAoiIiIhknQKIiIiIZJ0CiIiISJ6KRqP4/X6i0ajZpRwyBRAREZE8sXfgiEQiBINBIpGIyZUdury6GZ2IiMhsNhU4YPKutx6PB2D6f/OJAoiIiEie2DtwGIYxfTPWfKMAIiIikifyOXDsTT0gIiIiknUKICIiIpJ1CiAiIiKSdQogIiIiknUKICIiIpJ1CiAiIiKSdQogIiIiknUKICIiIpJ1CiAiIiKSdQogIiIiknUKICIiIpJ1CiAiIiKSdQogIiIiknUKICIiIpJ1CiAiIiKSdQogIiIiknUKICIiIpJ1drMLyDWZTAaAcDhsciUiIiL5Zeq1c+q19EAUQPYyOjoKQFNTk8mViIiI5KfR0VHKysoO+BhL5mBiyiySTqfp7e2lpKQEi8Vidjk5JxwO09TURFdXF6WlpWaXk3P0/Xlz+t4cmL4/B6bvz4Hlyvcnk8kwOjpKfX09VuuBuzy0ArIXq9VKY2Oj2WXkvNLSUv0SOAB9f96cvjcHpu/Pgen7c2C58P15q5WPKWpCFRERkaxTABEREZGsUwCRQ+JyufjWt76Fy+Uyu5ScpO/Pm9P35sD0/TkwfX8OLB+/P2pCFRERkazTCoiIiIhknQKIiIiIZJ0CiIiIiGSdAogcko6ODk477TRWrVpldik5JZ1O88tf/pKLL76Y8847j9tvv/2gRhHPBplMhrvvvptVq1Zx1llnceWVV/LII4+YXZZpRkZG+M///E/OPPNMrr322v0+ZmxsjG9961ucc845XHTRRdxzzz1ZrtI8AwMDfO973+O0007j3/7t3/Z5fzqd5r777uOqq67iXe96F5///OfZtm2bCZWao7Ozk3/+53/mlFNO4dZbbz3gY7du3cqpp57KlVdemaXqDo0CiBy0iYkJPvzhDxMOh1m/fr3Z5eSMTCbDqlWruP766/nABz7A//2//5e1a9fyi1/8wuzScsINN9zAZz/7Wd75znfy7W9/myVLlnDeeedx//33m11a1gUCAZYtW0ZbWxsOh4PNmzfv85hMJsMFF1zA6tWrufbaa3nPe97DRz7yEW655RYTKs6uzZs3s3LlSsLhMNFolI6Ojn0e83/+z//h3nvv5dxzz+XrX/86iUSCFStWzIrfSY8//jhnn302hmHQ09NDV1fXmz42Ho9z+eWXMzo6yoYNG7JY5cHTKRg5aF/5ylcYGhqiqamJ3/72t7S3t5tdUk749a9/zcc+9jFee+01Fi9ePH09FovhdrtNrCw3nHjiiRx//PHcfPPN09fOOussmpubueuuu0ysLPuSySSJRIKioiKuueYauru7eeyxx/Z4zF//+lfOP/982tramD9/PgDf/va3+dnPfkZfXx92e+EOsI5Go9jtdhwOB+9617tobGzkzjvv3OMxkUgEj8ezx7XjjjuOlStX8vOf/zyL1WZfJBKhqKgIq9XK4sWLueyyy/jOd76z38d+4QtfIJlMUlJSwkMPPcTGjRuzXO1b0wqIHJSHHnqIP/7xj/zkJz8xu5Sc89///d+cc845e4QPQOHjdStXrmTdunXEYjEA/H4/27dv58QTTzS5suyz2+0UFRUd8DGPP/44ixcvng4fABdffDFDQ0M5+1+yR4phGDgcjgM+Zu/wMXUtkUjMVFk5w+PxvOX9VQD++Mc/8thjj3HjjTdmoaq3TwFE3lJfXx8f//jHueuuu0y/x0Au2rx5M8cddxw//OEPOeecc7jsssu488471QPyuptuuokVK1bQ0NDAihUrmD9/Ptdeey3/8A//YHZpOamzs5P6+vo9rk293dnZaUZJOe3pp5/mmWee4ZJLLjG7lJzQ1dXFZz/7We6++26Ki4vNLueACnctT46IdDrNVVddxac+9SlOO+00s8vJSbFYjJtvvpnLLruMb3zjG+zYsYOvfOUrbNy4kR/+8Idml2e6u+66i3vuuYd//dd/ZenSpTz77LPccMMNnHTSSZx99tlml5dzJiYm9plmaRjG9Pvkf7W3t/PBD36Qj33sYwogQCqV4oorruCLX/wiK1euNLuct6QAIgfU1dXFE088QSgU4uGHHwagu7uboaEhTj75ZH7wgx9wxhlnmFyluSoqKrDZbNx2221YLBZgci/761//Ot///vex2WwmV2ieTCbDV77yFa677rrpFY9zzjmHjo4Ovva1r/HSSy+ZXGHuqaio2Kc5NRAIAODz+cwoKSft2LGDc845h3POOafgez8OVnt7O8888wzxeJzVq1cDsHv3bkZGRjj55JO56aabOPnkk02u8n8pgMgB1dbW8vzzz+9x7dZbb+Wxxx7jpptuYtGiRSZVljtWrlxJf3//dPgAqKurIx6PE41G97tnPVskEgkikQgNDQ17XK+vr+eZZ54xqarcdtxxx3HPPffs0cT84osvYrVaWb58ucnV5YadO3dy9tlnc8opp/DrX/96Vof8N2ppadnn9/VPfvITXnjhBW666SaWLFliUmX7px4QOSCXy8XJJ5+8x5+Ghobp616v1+wSTffpT3+a5557bvoYYCwW44477uCkk06a1eEDJv//c+KJJ3L77bczNjYGTM55+N3vfsfpp59ucnW56YMf/CBWq3V6+258fJwf/vCHXHjhhVRXV5tcnfk6Ozs5++yzOfnkk7n77rsVPt7A7Xbv8/u6rq4OwzA4+eSTKSsrM7vEPWgFROQwnXnmmXz/+9+fPlra19fH/Pnzufvuu80uLSfceeedXHXVVTQ0NNDS0kJ7eztnnHHGrO2PueiiixgcHKSjo4NEIsHJJ5+M3W6fXhGqrq7md7/7HR/5yEf4xS9+QTAYZNmyZbNmm2Fqi2DLli1s2LBh+kX0D3/4AwBf+tKX6OzspKqqine84x3TzzvmmGPecjBXvvP7/Vx44YXAZBC78847eeyxx/L2a9ccEDlkUz0gxx57rNml5JRIJEJ7ezvV1dX7nGKQydNUg4ODNDY2zupehvXr1xOPx/e4ZrFYOOmkk/a4lkgk2LJlCx6Ph3nz5mWzRFO98MIL+1xzuVysWLECgG3bthEMBvd5TGlpKUuXLp3x+syUSCRYt27dPtcP9LVP9YDk4vadAoiIiIhknXpAREREJOsUQERERCTrFEBEREQk6xRAREREJOsUQERERCTrFEBEREQk6xRAREREJOsUQERERCTrFEBEREQk6xRARCTnvfLKK9P3Apni9/v57W9/y9DQkElVicjh0M3oRCTnlZWVcc0119Df38/nPvc5MpkMV199NbFYjA9+8INmlycib4MCiIjkvLlz5/Kzn/2MT3/605x55pk8/PDDvPjii7z66qtYrVrIFclHuhmdiOSNK6+8kjVr1tDZ2cldd92l1Q+RPKYAIiJ5Y8eOHcybN49TTz2VZ5991uxyROQwaO1SRPLGV7/6VRYtWsRLL73Eo48+anY5InIY1AMiInnhtttu49FHH+WVV17hjjvu4JprruHVV1/F5/OZXZqIvA3aghGRnNfW1saKFSv46U9/yjXXXEMymeTUU0+lsbGR+++/3+zyRORt0BaMiOS8Bx54gC9+8Ytcc801ANjtdn7zm9/gcrnYuHGjucWJyNuiFRARERHJOq2AiIiISNYpgIiIiEjWKYCIiIhI1imAiIiISNYpgIiIiEjWKYCIiIhI1imAiIiISNYpgIiIiEjWKYCIiIhI1imAiIiISNYpgIiIiEjWKYCIiIhI1v3/auzqIwXTl1QAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(0)\n", "# Build the track for both arms\n", "track = spdf_both.streamTrack(n=3000, tail=\"both\")\n", "# Also draw a particle cloud to overlay\n", "orbs = spdf_both.sample(n=3000)\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "ax.scatter(orbs.x(), orbs.y(), s=1, alpha=0.2, color=\"0.6\", label=\"samples\")\n", "track.plot(d1=\"x\", d2=\"y\", spread=1, color=\"C0\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.005917, "end_time": "2026-06-30T01:26:56.432195+00:00", "exception": false, "start_time": "2026-06-30T01:26:56.426278+00:00", "status": "completed" }, "tags": [] }, "source": [ "The shaded band shows a +/- 1 sigma envelope using the projected covariance at each point along the track. Pass `spread=0` to suppress it." ] }, { "cell_type": "code", "execution_count": 15, "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:56.446092Z", "iopub.status.busy": "2026-06-30T01:26:56.445866Z", "iopub.status.idle": "2026-06-30T01:26:56.595536Z", "shell.execute_reply": "2026-06-30T01:26:56.594459Z" }, "papermill": { "duration": 0.158037, "end_time": "2026-06-30T01:26:56.596345+00:00", "exception": false, "start_time": "2026-06-30T01:26:56.438308+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Heliocentric view: track overlaid on sample (ra, dec)\n", "fig, ax = plt.subplots(figsize=(6, 5))\n", "ax.scatter(orbs.ra(), orbs.dec(), s=1, alpha=0.2, color=\"0.6\")\n", "track.leading.plot(d1=\"ra\", d2=\"dec\", color=\"C0\", label=\"leading\")\n", "track.trailing.plot(d1=\"ra\", d2=\"dec\", color=\"C3\", label=\"trailing\")\n", "ax.set_xlabel(\"RA [deg]\")\n", "ax.set_ylabel(\"Dec [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "72eea5119410473aa328ad9291626812", "metadata": { "papermill": { "duration": 0.006235, "end_time": "2026-06-30T01:26:56.609176+00:00", "exception": false, "start_time": "2026-06-30T01:26:56.602941+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Controlling the smoothness and iteration\n", "\n", "The `smoothing` keyword sets the spline smoothness; `None` (default) picks an automatic Generalized-Cross-Validation (GCV) value from the binned scatter via `scipy.interpolate.make_smoothing_spline` — for galpy's normalized-internal units the GCV optimizer is run on a y-rescaled problem so it is well-behaved at the small absolute scales of the covariance entries. A float scales it; a dict keyed by `'x','y','z','vx','vy','vz'` sets per-coordinate values; an array of length 6 (or 27 with `order=2`) supplies per-spline `s` values directly (e.g. from a previous `track.smoothing_s`).\n", "\n", "`smoothing_factor` (default `1.0`) is a second, simpler knob: it multiplies whatever `s` was selected (by GCV or by the user) by a constant, with `>1` smoother and `<1` rougher. The default GCV usually produces a good fit, but this dial lets you trade bias for variance if you have a particular reason to (e.g. a noisy short-stream sample where you'd rather oversmooth, or a long well-sampled stream where you want every wiggle of the predicted track resolved). See below for an example.\n", "\n", "`niter` runs additional refinement iterations that reassign each particle to the closest point on the current track before refitting. For typical streams, 1-2 iterations suffice." ] }, { "cell_type": "code", "execution_count": 16, "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:26:56.622889Z", "iopub.status.busy": "2026-06-30T01:26:56.622688Z", "iopub.status.idle": "2026-06-30T01:27:02.762066Z", "shell.execute_reply": "2026-06-30T01:27:02.761099Z" }, "papermill": { "duration": 6.147371, "end_time": "2026-06-30T01:27:02.762846+00:00", "exception": false, "start_time": "2026-06-30T01:26:56.615475+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compare default fit with niter=2 (closest-point reassignment) on a single sample\n", "spdf_both._tail = \"leading\"\n", "tr_default = spdf_both.streamTrack(n=3000, tail=\"leading\")\n", "xv_dt = tr_default.particles # save once, reuse below to skip the resample\n", "tr_iter2 = spdf_both.streamTrack(particles=xv_dt, niter=2)\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "ax.scatter(orbs.x(), orbs.y(), s=1, alpha=0.2, color=\"0.6\")\n", "tr_default.plot(d1=\"x\", d2=\"y\", color=\"C0\", label=\"default\")\n", "tr_iter2.plot(d1=\"x\", d2=\"y\", color=\"C2\", label=\"niter=2\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "papermill": { "duration": 0.006328, "end_time": "2026-06-30T01:27:02.776915+00:00", "exception": false, "start_time": "2026-06-30T01:27:02.770587+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Pulling the 6×6 covariance with `cov()`\n", "\n", "Beyond the mean track, `track.cov(tp, basis=...)` returns the 6×6 covariance of the particle distribution at the requested `tp`. Five output bases are supported: `'galcenrect'` (default; native), `'galcencyl'`, `'sky'` (equatorial), `'galsky'` (Galactic), and `'customsky'` (requires a `custom_sky_transform`). The non-native bases use analytical Jacobians — no finite differences — so the result is a self-consistent transform of the stored galactocentric covariance.\n", "\n", "The diagonal entries can be used directly to draw ±σ bands; the cross-terms encode correlations (e.g. between `pmra` and `pmdec`):\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:02.791487Z", "iopub.status.busy": "2026-06-30T01:27:02.791277Z", "iopub.status.idle": "2026-06-30T01:27:02.809791Z", "shell.execute_reply": "2026-06-30T01:27:02.808839Z" }, "papermill": { "duration": 0.027158, "end_time": "2026-06-30T01:27:02.810716+00:00", "exception": false, "start_time": "2026-06-30T01:27:02.783558+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tp= 0.000: σ(ra)=0.281 deg, σ(dec)=0.139 deg, σ(dist)=0.043 kpc\n", "tp= 0.303: σ(ra)=0.291 deg, σ(dec)=0.287 deg, σ(dist)=0.044 kpc\n", "tp= 0.606: σ(ra)=0.317 deg, σ(dec)=0.247 deg, σ(dist)=0.046 kpc\n", "tp= 0.909: σ(ra)=0.286 deg, σ(dec)=0.132 deg, σ(dist)=0.049 kpc\n", "tp= 1.212: σ(ra)=0.220 deg, σ(dec)=0.038 deg, σ(dist)=0.055 kpc\n" ] } ], "source": [ "tps = numpy.linspace(*track.leading.tp_grid()[[0, -1]], 5)\n", "for tp in tps:\n", " C = track.leading.cov(tp, basis=\"sky\")\n", " sigma_ra = numpy.sqrt(C[0, 0])\n", " sigma_dec = numpy.sqrt(C[1, 1])\n", " sigma_dist = numpy.sqrt(C[2, 2])\n", " print(\n", " f\"tp={tp:6.3f}: σ(ra)={sigma_ra:.3f} deg, σ(dec)={sigma_dec:.3f} deg, σ(dist)={sigma_dist:.3f} kpc\"\n", " )" ] }, { "cell_type": "markdown", "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "papermill": { "duration": 0.006628, "end_time": "2026-06-30T01:27:02.824153+00:00", "exception": false, "start_time": "2026-06-30T01:27:02.817525+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Stream-frame plots with `custom_sky_transform`\n", "\n", "For visualizing thin streams, it's often useful to rotate to a frame aligned with the stream itself — a `(φ1, φ2)` system in which the stream lies near `φ2 = 0`. Pass a 3×3 rotation matrix as `custom_sky_transform=` and the track exposes `.phi1`, `.phi2`, `.pmphi1`, `.pmphi2` accessors and `cov(basis='customsky')`. The helper `Orbit.align_to_orbit()` builds such a matrix from the progenitor's angular momentum:\n", "\n", "Calling `Orbit.align_to_orbit()` also stashes the rotation matrix on the orbit itself, so afterwards `prog.phi1(t)`, `prog.phi2(t)`, `prog.pmphi1(t)`, `prog.pmphi2(t)` (and `prog.plot(d1='phi1', d2='phi2')`) work without re-passing `T=`. Below: the same plot but also overlaying the progenitor's orbit in the aligned frame — it traces `phi2 = 0` by construction (the rotation maps the orbital plane onto the equator)." ] }, { "cell_type": "code", "execution_count": 18, "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:02.838130Z", "iopub.status.busy": "2026-06-30T01:27:02.837918Z", "iopub.status.idle": "2026-06-30T01:27:07.409546Z", "shell.execute_reply": "2026-06-30T01:27:07.408570Z" }, "papermill": { "duration": 4.579721, "end_time": "2026-06-30T01:27:07.410376+00:00", "exception": false, "start_time": "2026-06-30T01:27:02.830655+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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NmjXs2rWL9PR0Bg0axIoVK/K97QeJqfjdesD5R0lY2APCY1MyLVvW3pJqbrZUL2P78E83W6q62kjiVYQEBASwYsUKpk2bhoWFBVOnTqV8+fK88sorT/yMSI+MJHrlSqJXrjKMOzN1ccHpzeGU7t8fbalSBXEKopCTpCwb0lMmROGk1+u5c+cO5cqV4+zZszRq1IgWLVowYMAA+vXrly89YkopgiMTOR0cxZmb0Zy+GU3QvfjHymk0UNXFhjrl7Kn9v5/qZWyxL1XyxmkVZ3q9nt69e7N161YsLS3p378/7733Hk2aNMn+uMREHqzfQOTixaTfuQOAiZMTTm8Mw2HAALSF8ElfUXAkKcuGJGVCFC5Xr15l2bJl/P777zg6OuLn54dSipCQEMqXL5+nben0ioDbsZy4fp9TwdGcvRmd6RiwSs7W1PcsTe1y9tT1sMe7rB3WFgX/0IAwjpCQEJYuXcpvv/3G7du3CQsLw8XFBaVUtoP6VWoqDzZtInLhItLCwoCHC6E7DhuGw+BBslJACSVJWTYkKROicAgJCWHAgAEcP34ce3t7XnnlFYYOHUrz5s3z7Gk2pRRXwuM5fu0+x69F8tf1SGKT0zOUMTfVUrecPY0qOtCovAONKjjgZCNjgsTDJZ/8/Pxo3LgxycnJNG/enN69ezNixIhsl3lSaWnEbN3G/YULSLt5CwATe3ucRryFw+DBaC0tC+oURCEgSVk2JCkTwnjOnz/PiRMnePvtt0lLS2PIkCGGAful8mj8TdiDJA5djuD4tfucvB7J/fiMPWG2FqY0q+xI00qONKrgSO1ydliYyhgwkb2oqCimTJnC8uXLSUtLo3///rz//vvUr18/y2NUejqxO3Zw/+cFpN64AYCpmxvOI9+jdO/eaIwwZYsoeJKUZUOSMiEKVlJSEr6+vixYsICTJ0/i6enJ5cuX8ywJS03Xczo4ioNXIjh4+R5XwjOOCbM009KkoiPPVXHmuSpO1HK3K5ZLDomCER0dzZIlS5g7dy6Ojo6cPn0ajUaT7a1NpdMRs3kLEfPmkn774Zgz8woVcBk3FtvOndEU42W+hCRl2ZKkTIiCk5KSQoUKFQgPD6dTp0688847dO/eHTOzZxsgf/tBEgcu3+Pg5QiOB90nIVVn2KfVQIPyDrTycua5Ks7U87SXnjCR59LT07lz5w6enp6cPHmSMWPG8OGHH/LSSy9hksV8ZfrUVB6sWcP9nxegi44GwNLbG9cPJmHdvHlBhi8KkCRlmZApMYTIf3q9nu3bt7NkyRJWrVqFpaUlq1atolmzZlR5hmVpHo0N2/3PXfYE3OViWGyG/c425rxQzYW21V1p5eVMaSvzZz0VIXLs9OnTTJo0iYMHD1KtWjU++OADXnvttSy/fOjiE4hatpSoxUvQJyQAYNO+PW6T3se8YsUCjFwUBEnKsiE9ZULkvbi4OJYuXcpPP/1EUFAQzZs3Z9WqVVSqVOmp69TrFWdvRbMnIJzd/9zlZmSiYd+j3rA21VxoU92VWu52aLWy1I0wrr/++otZs2axceNGPv/8c6ZOnZpt+fToaO77zCd69WrQ6cDMDMfBg3F+711M5POp2JCkLBuSlAmR9zp06MDBgwfp168fY8eOpflT3orR6RWngqPYeu42u/8J5378/0/aam6qpVVVZzrXKkO7mq44yxOSopC6cOECZcuWxdnZmUWLFmFubs6QIUOyXIs15do1wmfNIuHwEeDhNBrOY0bj0L+/PAxQDEhSlg1JyoR4Nkopjh8/zuzZs5kwYQItWrTAz88PZ2dnPD09n6q+c6ExbPG/zfYLtzPMnm9raUr7Gq50qlWG1tVcZK4wUeQMHz6cxYsXU7VqVaZOncqgQYOyTM7ijxwhfNYsUoOuAWBRrRplpk/HqmGDggxZ5DFJyrIhSZkQT0cpxfbt25k5cybHjx+nevXq/PTTT3Tq1Omp6gq8G8fWc7fZev42IVFJhn12lqZ0rV2WbnXL0ryyE+am8mSaKNr8/PyYPn06W7ZsoWbNmhw6dAgXF5dMy6r0dKJ9fbk/5yfD0k32ffvgOnEipg4OBRm2yCOSlGVDkjIhns4PP/zAxIkTee655/jwww/p1q0b2lw+yh8Zn8Im/9usOx1C4N04w/ZSZiZ09HajZz13WlVzlqclRbF0+vRp1q5dyzfffINGo+Gff/6hVq1amZZNj47m3nffEbN+A/DwlqbrpPex79VLptAoYiQpy4YkZULkTHJyMkuXLgXgnXfe4d69ewQGBtKqVatczbifptNzIPAef5wJZX/gPdL1D3/lmJtoaV3dhZ713Glf0xUrc7k1KUqOI0eO8MILL9C7d2+++uorqlevnmm5xLNnuTttOilXrwJQqmFDyn42HQsvr4IMVzwDScoyIVNiCJEzsbGx/Pzzz/z4449ERETw9ttvM3/+/FzXc/luHOtOh7DJPyzDrPp1Pezp18iDHvXcZeoKUWLp9XpWrlzJJ598QlhYGCNGjODzzz/H2dn5sbIqLY2o5b8T4eODSkwEMzNc3nsXpzffRPOMc/6J/CdJWTakp0yIrIWEhFCvXj0SEhJ4/fXX+eCDD6hatWqOj09O07Hz4h1WnLzFmZvRhu3ONub0alCOvo08qV7GNj9CF6JISk5OxsfHhxkzZjBhwgQ+/fTTLMum3bnD3c8+J/7gQQAsatbE/asvsaxZs4CiFU+jWCdlqampbNiwgcDAQIYOHUrFXE60J0mZEBnFx8ezYcMGXn31VQBmz55N//79KVeuXI7ruBmZwKq/buF7OoToxDQATLUa2tVwpV9jT9pUd8FMljYSIksRERFYWVlhbW3NwoULqVy5Mh07dnysnFKK2G3bCP/iy4cPApia4jziLZzeeQetufQ8F0bFNilbuXIlkydPpk6dOuzatYsDBw7Qpk2bXNUhSZkQDyUkJODj48O3335LbGwsFy9exCsX41TSdXr2B95jxV+3OHwlwrDd3d6SgU3L80oTT1ztLPMjdCGKLaUUXbt2Zffu3fTs2ZMffvgh09Uw0iMiuPv5DOL+/BMAC6+qlJ35NaVqZ/7ggDCe3OQdReqra5UqVTh79iy//PKLsUMRokh79E38k08+oW/fvgQFBeU4IYtJSmPR4Wu0/vYgI34/w+ErEWg00LqaC7+81pjDH7RldHsvSciEeAoajYadO3eydu1a/Pz88Pb2Ztq0aeh0ugzlTF1c8Jj7E+Vmz8bE0ZGUq0EEDxjA/QULUOnpRopePKsi9bjTo1nCQ0NDjRyJEEVPamoqaWlpWFtbExUVxUsvvcSUKVOoUKFCjo6/GZnAkmPBrDsdYlgA3NHanH6NPRjctALlnazyM3whSgyNRkP//v3p3r07X331Ff/880+W08/YdemMVbOm3J3+GXG7dxMxew7xhw7j/s0szJ9iMmdhXEXq9uUjoaGheHp65uj2ZUpKCikp/z9DeGxsLJ6ennL7UpQYer0eX19fQ6/Y119/neNjlVL8fSOK347e4M9L4Tz6bVHNzYbhLSvxUv1yWJrJnGJC5CelFBqNho0bN7J+/Xq+//573NzcHisTs3kz4TO+QJ+QgNbKCrcpU7Dv3StXU9iIvJeb25dG7SnbtGkT/v7+2ZYZM2YMjo6OT93GzJkz+eyzz576eCGKsr179zJ58mTOnj1L9+7dGTx4cI6O0+kVOy7cYdHh61wIizFsb1PdheEtK9GyqrP8oheigDz6v6bT6di1axfbt29n1qxZvPnmm4YeNI1GQ+mXX8aqcRNufziZpNNnuDNlCvEHD1Dm889lNYAiokiNKXsaH330ETExMYafkJAQY4ckRIE4f/48HTt2xMLCgsOHD7N161bq1KmT7TEp6TrW/H2L9t8fZPRqPy6ExWBhqmVg0/LsnfACS4c1pZWXiyRkQhhB3759CQwMpFevXrz99tu0bNmSsLCwDGXMPcpRYdkyXCZMADMz4v7cy/WePYk/fNhIUYvcKPa3L/9Lnr4Uxdm1a9dYsmQJM2bMQKPRcOLECZo3b/7EJCoxNZ1Vf93i1yM3uBubDEBpKzOGPleR11pUxNFaHrUXojA5dOgQP/74I2vWrMHSMvOHapIDAgib9AGp1x4ucO74+uu4TJwgU2cUsGL79KUQInMxMTF88MEHeHt7s2TJEkOPcIsWLbJNyB4kpjJn71We/3o/X2y/xN3YZNzsLPikW02OTW7HuA7VJCETohBq3bo1mzZtwtLSkoCAAFq1asU///yToYyltzeV1v+Bw/+GLUQtW8bNgYNIvXnTGCGLHChST1/6+/uzadMmYmNjAVi6dCkHDx6kTZs2ue4xE6K4WLFiBRMmTCAhIYEpU6bw/vvvY2WV/ZOQMYlp/Hb0OouPBROf8vDx+QpOVrzbugq9GpaTBcGFKEJSU1OJjIykYcOGTJs2jQ8++ABT04cf71pLS8pM/QTr55/jzkcfk/zPP9zo1Zsyn32GfY/uRo5c/FeRSsoesbOzY9q0acYOQwijSk9Px9TUlOjoaLp27cpXX331xFn4Y5PTWHI0mF+PXicu+WEyVqOMLe+1rcqLtctgKrPuC1Hk1K9fn7Nnz/L5558zdepU1q9fz+rVq6lWrZqhjG27dlhu3kTY+++TdPoMtydNIuHECcp8MgXtE77EiYJTJMeUPQsZUyaKuqtXr/L+++/j6enJvHnzcnRMfEo6S4/d4JcjN4hJergMUnU3W8Z39KKTdxm0Whm4L0RxcOrUKcaPH8+aNWvw8PB4bL9KT+f+zwu4//PPoNdjXqkS5X78AcsaNYwQbckgY8oy4ePjg7e3N02aNDF2KEI8ldjYWCZOnEitWrU4d+4crVu3fuIxianp/HzwGq1m7ee7PVeISUqjqqsN8wY1YOfYVnSpXVYSMiGKkSZNmnD06FE8PDx48OABQ4YMyTDrgMbUFJfRoyi/ZAmmrq6k3rhBcP9XiF69mhLWR1MoSU+ZEEVATEwM3t7ePHjwgI8//pgJEyZQqlSpLMun6fT4ng5h9t6rRMQ9nDy5srM1Yzt40b2uOyaSiAlR7J07d47u3bsTHx/Pzz//zIABAzLsT4+O5s5HHxN/8CAA9i/1pMz06Wiz+d0icq/YLkieFyQpE0XJ5cuXqVq1KiYmJixcuJAXX3wRz2yWTlFKseviXb7dfZnr9xMA8HQsxfgO1ehZz13GjAlRwkRHR/Puu++ydu1ahgwZwrx587C3tzfsV0oRtXgJ9374AXQ6LKpVw+OnOZhXrGi8oIsZScqyIUmZKApiY2P57LPPmDNnDkuWLOHVV1994jEnr0cyc2cg50IeAOBkbc6Y9l4MbFoec1NJxoQoqZRSrFy5ktGjR7N161Zatmz5WJmEv/8mbMJEdPfvo7Wxwf3rmdh26GCEaIsfScqyIUmZKMyUUqxZs4aJEycSExPD1KlTGT9+PBYWFlkec+lOLN/sCuTA5QgArMxNeLNVZUa8UBkbiyL5gLUQIh/ExsZiZ2eHTqdjzZo1DBw4MMNC52nh9wgbP56ks2cBcHrrTVzGjUNjIlPkPAtJyrIhSZkozDZt2kSvXr3o27cv33//PeXLl8+ybERcCt/vucza0yEoBaZaDQOblmd0+6q42mY+w7cQQhw8eJB27drRsWNHfv/9d1xdXQ37VFoa9777nqhlywCwadMG9+++xcTGxljhFnmSlGVDkjJR2KSkpPDnn3/SvXt3dDodx48fp1WrVlmXT9ex5Fgw8/YHGSZ+7VanLO93rk4lZ+uCClsIUYT9+eefDB48GFNTU1atWvXYBOwx27ZzZ8oUVEoKFl5eePw8H/NMptgQTyZJWSZ8fHzw8fFBp9Nx5coVScpEoXDkyBFGjBjB9evXCQoKeuIg/t3/hPPVjkvcikoEoK6HPZ9296ZxRceCClkIUUzcuXOHwYMHc+jQIY4fP06zZs0y7E86f57QkaNIj4jAxMEBj7k/YdW4sZGiLbokKcuG9JSJwiA6OprJkyfzyy+/0KJFCxYtWkTt2rWzLB9wO5YZ2wI4cT0SAFdbCz7oUoPeDcrJPGNCiKem0+lYu3YtAwcORKPRkJycnGGB87TwcELffY/kgAAwM6Ps9OmU7tPbiBEXPTJ5rBCF3FdffcXatWuZP38+R48ezTIhi05I5eONF+g29wgnrkdibqplVNuqHHi/DX0beUhCJoR4JiYmJgwaNAiNRsP27dupUaMGp06dMuw3c3OjwsoV2HbpAmlp3JkyhYh5PjLRbD6RnjIhCkhISAjnz5+nW7duxMTEkJCQgLu7e6Zl9XrFujMhfL0zkOjEh8sidatblo+61sDDQdapE0LkvdDQUPr27Yufnx/z589n+PDhhn1Kryfip5+IXLAQgNL9+lFm2qdoTOUJ7yeR25fZkKRMFDSlFL/++isTJ07Ew8ODCxcuYJLNI+b/3I5h6qaLnL31AIBqbjZ8/lJtmld2KqCIhRAlVUpKCmPHjmXhwoWMGDGCn376KcOUPNFr1nD38xmg12PTti3lfvheVgB4Arl9KUQhERwcTKdOnRgxYgT9+vXj+PHjWSZksclpTN/yDz3mHuXsrQdYm5sw5cWabB/TShIyIUSBsLCwYMGCBfz222+cOnWK1NTUDPsdBgzA46c5aCwsiD9wgFtDh5EeHW2kaIsf6SkTIh916dKFgIAAfvnlFzp37pxpGaUUm/1v88X2S9yPf7hOZbe6ZZnazZsy9jLfmBDCOHQ6HSYmJgQFBRESEkLbtm0N+xLPniXk3ffQx8RgXrEinr/+irlHOSNGW3hJT1kmfHx88Pb2pkmTJsYORRRz169fx8/PD4BffvmFixcvZpmQhUQl8trivxm31p/78SlUdrbm9+FN8RnUUBIyIYRRPerVnz17Nh07duTnn3827LNq2JCKq1Zi6l6W1OBgbg4ZQsr1G8YKtdiQnjIh8oher8fHx4cPP/yQ559/nj179mRZNl2nZ+nxYL7fc4WkNB0WplpGt6vKWy9UxsJUljQRQhQe6enpTJw4kZ9++omRI0cye/ZsTP83wD8tPJxbw94g9fp1TJycKP/br1jWqGHkiAsX6SkTooDdunWLjh07MmbMGIYOHcr69euzLBtwO5bePx/ni+2XSErT0byyI7vGvcCodl6SkAkhCh1TU1PmzJnDwoULWbhwIf379zfsM3Nzo8KK37HwrokuMpKbr71Okr+/8YIt4qSnTIhnpNfrqVOnDrGxsSxZsoQOHTpkWi45TcdP+66y8PB1dHqFraUpU16syStNPNFoZL4xIUThd+DAAeLi4ujZs2eG7brYWELefockPz80VlZ4zp+PdfNmWdRSssiUGNmQpEzklfv376PT6XBzc+Ps2bNUqlQJBweHTMueDo5i0h/nuXE/AYCutcvwWc9auNrJuDEhRNGjlGLMmDG89NJLhi+i+sREQkaOJPHESTQWFpSbMxvb/6ypWRLJ7Ush8tn27dupU6cO48aNA6Bhw4aZJmTJaTq+2nGJfgtPcON+Aq62FiwY0oifhzSShEwIUWQlJydz9epVunTpYngAQGtlheeCBdi0a4dKSSF01Ghid+40cqRFiyRlQuRCfHw8b7/9Nt27d6dBgwb88MMPWZY9H/qA7nOPsujwdZSCvo08+HNCa7rULlOAEQshRN4rVaoU27ZtY+TIkbz33ntMnjwZvV6P1sICjzmzseveHdLTCZv4Pg+yGWMrMiox6yP4+Pjg4+ODTqczdiiiiEpLS6NZs2YEBwezYMECRowYkelYsNR0PfP2X8Xn4DV0eoWzjQVf965DB283I0QthBD549EDAJUqVWLChAnUrFmToUOHojEzw33W12itrHjg68udKZ+gUlNxGDjQ2CEXejKmTIgn0Ov16PV6TE1NWb16NY0bN8bLyyvTsoF3Y5mw9hwBd2IB6F63LDNeqo2DtXlBhiyEEAXq6NGjtGjRAhMTE8Oks0op7n09i6hlywBw+/hjHF971ciRFrxiO9A/Li6OxYsXc/z4cUxNTWnZsiXDhw/H3DznH3iSlIncuH37Nq+99hqNGjVi1qxZWZbT6xW/Hb3BN7sDSdMpSluZMeOl2vSol/mC40IIURwdPHiQsWPHsmnTJipVqoRSiogffiDyl18BcP3gA5zeGGbkKAtWsRzo/2jageDgYPr06UPHjh35/vvvefHFF+WWpMgXW7dupV69egQEBNCxY8csy92LTeb1JX/z5Y5LpOkUHWq6smf8C5KQCSFKnHLlypGQkECLFi04ffo0Go0GlwkTcHr3HQDuffMN9xf9YuQoC68i01OmlOLBgwcZnnA7c+YMjRs35uTJkzRrlrP5UKSnTDyJTqdj3LhxzJs3jx49evDbb7/h4uKSadm9AeF8sP48UQmpWJpp+bR7LQY2lXnHhBAlV0REBD169ODChQusX7+eLl26PNzu48P9ufMAcB49CpeRI40ZZoEplj1lGo3msSkHnJycAEhISDBGSKKYMjExISkpiblz57J58+ZME7LkNB2fbr7Im8tPE5WQindZO7aNbsWgZuUlIRNClGguLi7s37+f9u3bM2rUKFJTUx9uHzkSl/HjAbg/dx735syhiPQLFZgi01OWmZEjR+Lr60twcDDW1taZlklJSSElJcXwOjY2Fk9PT+kpExkopVi0aBEODg4ZlhDJTODdWMas9uNKeDwAb7asxKQu1WWJJCGE+Je0tDTu3r2Lp6cnKSkpWFhYABC5eAn3vvkGAKe33sRlwoRi/WU2Nz1lOZoSQymVq3FbWq0WrfbJnXDffvstu3fvzrbM8uXLcXd/fGzOb7/9xsKFC9m8eXOWCRnAzJkz+eyzz54ctCix4uLiGDFiBGvWrGHSpElZJmVKKVb9fYvPtgaQmq7H2caC7/vXo3W1zG9tCiFESWZmZmZIyFq3bk3Xrl359NNPcXpjGBpTE8K/mknkL7+i0tJxnfxBsU7McipHPWXfffcdkyZNynGlEydO5LvvvntiuYCAAG7fvp1tmeeff55SpUpl2LZixQreeOMNli5dyqBBg7I9XnrKRHYuXLhA3759uXPnDr/++muWCVlCSjofb7zAZv+H79e21V34tl89nG0sCjJcIYQocpRSzJo1i48++ohRo0YxZ84ctFotUatWEf75DAAchgzBbcrHxTIxy/OeMoD+/fvz7rvvPrHc2rVrc1ol3t7eeHt757g8wKpVqxg+fDiLFy9+YkIGYGFhYegyFeLflFK88847WFpacvr0aapVq5Zpuct343hv5RmuRSRgotXwQefqjHihcrH85SGEEHlNo9Hw4Ycf4uTkxDvvvENkZCRLly7FcdAgNKam3J02negVK1DpaZT59FM0ObjTVlzlKCmztbWlTp06tMnBwqKXL18mIiLiWePK1Jo1axg2bBiLFy9m8ODB+dKGKP4SExMJDw+nUqVK+Pr64ujo+Fhv7CN/nAnlk00XSE7T42ZnwbxBDWlS0bGAIxZCiKLvrbfewtHRkUGDBjFo0CC6d++OQ//+aEzNuDNlCg/WrEWlp1P2889LbGJWZAb6x8TE4OzsjL29PfXr18+wb+LEiXTt2jVH9ciUGCXbpUuX6NevH5aWlpw6dSrL3q6kVB3TtlzE93QoAK28nJn9Sn2c5HalEEI8k5s3b1KhQgXg4cMAZmZmxGzdyu3JH4Jej/1LL1H2qy/RmBSPh6fy5falsVlZWbEzi9Xmc3sLVJRMK1as4J133qFChQosX748y4Qs+H4C76w4Q+DdOLQaGNehGiPbVsVEK7crhRDiWT1KyObPn8/vv//Ozp07Kd2jBxoTE8ImfUDM5s0onQ73r2eiMS0yaUqeyHVP2aFDh9i6dWum+7RaLfb29rRo0YK2bdsWyjE30lNWMn3wwQd8++23vPrqq/z8889ZPrF7IPAeY9b4EZecjrONOT8NaMBzVZ0LOFohhCj+Tp8+TadOnahUqRJ79uzBycmJ2N17CJs4EdLTse3ShXLffoPGzMzYoT6TfF37cuPGjUyYMIHg4GC8vb1xd3cnIiKC8+fPU6ZMGTw8PPD396dv376sWrXqmU4kL/n4+ODj44NOp+PKlSuSlJUwO3bs4Pbt2wwfPjzTLwt6vWL+wSC+//MKSkHD8qX5eUgj3OwsjRCtEEKUDOfPn6dDhw64ubmxd+9e3NzciNu/n9Cx4yAtDduOHSj3/fdocrHGdWGTr0nZ3bt3ad68OatWreK5554zbD9//jw9e/Zk9+7daDQannvuOVavXp3tmoHGID1lJcfBgwdZvXo1CxYsyLbXNj4lnYm+/uz+JxyAwc3KM61HLcxNS+ZAUyGEKEiXLl2iffv2dOzYkWXLlgEQf+gQoaPHoFJTsWnblnJzZqMtoolZvi6zdPDgQdq0aZMhIQOoW7cuAwYMYNeuXVSrVo1XX32V06dP57Z6IZ6ZUooff/yRDh06EBQUlO0yXNci4nnZ5xi7/wnH3ETL173r8GWvOpKQCSFEAalZsyZHjhzhp59+Ah7+Drdp3RqP+fPRWFgQf+AAoSNHoU9ONnKk+S/XnzzR0dFZTnlx7949oqKigIfzg2U1zYAQ+SUhIYFBgwYxYcIEJkyYwO7du7Gxscm07N6AcF6ed4yge/G42Vmw9u3mDGhavoAjFkIIUaVKFezt7bl27RotW7YkODgYm5bP47lwAZpSpUg4coTQ90YW+8Qs10lZp06d2Lt3L5MnTyYoKIjExESCg4P54osvWL58Od27d0en07Fr1y7DyvBCFJQlS5awdetWfH19+eabbzDN5MkdpRRz913lzeWniUtJp0lFB7aObkmD8g6Z1CiEEKKgWFhYEB4eTtu2bbl58ybWzZtTftFCNFZWJBw/Xux7zJ5qnrIdO3YwduxYgoKCDNs8PDz45ptvGDhwIKGhoVy7do3WrVvnabB5QcaUFU/BwcFUrFgRvV5PcHAwlStXzrRccpqOD/44z5ZzD5dLerV5BaZ295bblUIIUUiEhITQpk0blFIcOnQIT09PEk+f5taIt1GJiVi3bImHzzy0RWS1nnwd6P/Io6cYb9++jZubG9WqVcO8CAzCk6SseFFK8eWXX/LZZ5/x119/0bBhwyzL3otLZsTyM/iHPMBUq+Gzl2oxuFmFAoxWCCFETty6dYvWrVtjbW3NuXPnMDExIfHUqYeJWVIS1q1a4TFvbpFIzPJ1oP8jqampJCUlUb58eWrXrl3oEzIfHx+8vb1p0qSJsUMReSQxMZEBAwYwdepUpkyZ8thKD//2z+0YXp53DP+QB9iXMmP58KaSkAkhRCFVvnx5Dhw4wJw5czD538z+Vk2aZBxjNmYM+tRUI0eat54qKVu3bh3lypWjUaNGLFy4EIBz587RsmXLPA0uL40cOZKAgABOnTpl7FBEHggLC6NVq1Zs27aNP/74g+nTp6PNYq203f/cpe/PJ7gdk0xlF2s2jXye56rIhLBCCFGYVaxYkfbt26PX65k2bRp3797FumlTPH/+GY2lJQmHDhM2ZiwqLc3YoeaZXCdlISEhvPXWWyxatIgvvvjCsL1evXrY2dmxe/fuPA1QiMyUKlUKBwcHjh8/Tp8+fTIto5TC50AQb/9+hqQ0Ha28nNn43vNUcs58Nn8hhBCFz927d/ntt99o164d4eHhWDdvhueCh4lZ/MGD3P7oY5Reb+ww80Suk7JDhw7RtWtX+vbti6VlxtnOGzVqxLFjx/IsOCH+a+XKldy6dQtHR0f27t1LvXr1Mi2Xkq5jou85vt19GYDXW1RgydAm2Jcq2st1CCFESePu7s7+/ft58OAB7du3JyIiAuvmzfGYMxtMTYndto3wL7/iKYfIFyq5TspiY2OxtbUFeGyW9AcPHmBWxNeoEoWTTqdj4sSJDBkyhJUrV2Zb9kFiKq/+9jcb/MIw0WqY8XJtPnupNqYm8oSlEEIURdWqVWP//v3cv3+fzp07Exsbi03r1rjPnAkaDdErV3LfZ76xw3xmuf6UatasGTt27CAuLi5DUhYUFMSKFSsK9bgyUTQ9ePCA7t27M3v2bObMmcOHH36YZdmQqET6/Hycv29EYWthytJhTXi1uQzoF0KIoq5GjRr8+eefPP/881hZWQFg36M7blOmAHB/3jxitmwxZojP7KmmxBg6dCiHDx/G3d0dnU5H5cqV2bhxI506dWLTpk35EGbekSkxihadTkfjxo0JDg7G19c327VUz4U8YPiyU9yPT6WsvSVLhjWhRhn5NxZCiOLIz88Pb29vLCwsuPf9D0T+8gsaMzPKL1+GVYMGxg7PIN/nKVNKsXTpUtauXUtYWBhOTk68/PLLjBo1KtMZ1AsDHx8ffHx8DPOrSVJWdGzdupUaNWrg5eWVZZk9/9xlzBo/ktP0eJe1Y8mwJrjZWWZZXgghRNEVGxtLpUqVaN26Nb6+vphotYSOGUP83n2YODlRaZ0vZu7uxg4TKKDJY4sq6SkrGlavXs3JkyeZPXv2Y2MX/2vpsRt8ti0ApaB1NRd8BjfExqJwfjkQQgiRN7Zu3Urv3r0ZNGgQS5YsgaQkggcPISUwEIsaNai4cgVaa+M/bZ+bvCNHn1yRkZHcuXMnR407OztTpkyZHJUV4r+UUsyYMYNp06bx2muvodPpsux91esVX+64xG9HbwAwsGl5ZrxUSwb0CyFECdCjRw+WL1/O4MGDsbOz46effsJzvg83+vUnJTCQO9M/w/2bWU/8Yl+Y5CgpW7JkCZMmTcpRhRMnTuS77757pqBEyZSSksJbb73F77//zowZM5gyZUqW/5mS03SMX+vPzot3AfigS3XebV2lSP3nE0II8WwGDhxIXFwc06dP5+OPP6asuzsec2Zz8/WhxG7dilWjhjgMGGDsMHMsR7cvk5KSSEhIAB4OvO7WrRt16tThnXfewcPDg/DwcJYvX862bds4efIkzs6Fd7Z0uX1ZeH3//fdMmTKFJUuWMHDgwCzLxSSl8day0/wdHIW5iZbv+tejZ73CMXZACCFEwYuNjcXOzg69Xo9WqyXyt8Xc+/ZbNGZmVFi1ilJ1ahs1tnwbU7Znzx5mzZrFvn37Hts3aNAgunbtyquvvpq7iAuQJGWFT3JyMpaWlqSlpfHPP/9ku4ZleGwyry/+m8C7cdhamvLLa41pXtmp4IIVQghRKCUkJPDiiy8yYsQIBg0aROjo0cTv3YdZuXJU2rAeE3t7o8SVrwuSX716lQoVMp/3qUKFCly9ejW3VYoS7NixY1StWpW///4bMzOzbBOy6xHx9J5/nMC7cbjYWuD7dgtJyIQQQgBgZWVF5cqVGTp0KH/++SfuX32FmacnaWFh3J78YZFYiinXSVm1atXYtGkT58+fz7D9+vXrrFixgmrVquVZcHnJx8cHb29vmjRpYuxQxP9s3LiRDh06ULVq1Wynu4CHc5D1XXCCsAdJVHK2ZsO7z1GzrPR0CiGEeEij0bBo0SI6d+5M7969OXv5Mh5zZqMxNyf+4EEif/vN2CE+0VNNiTFs2DCWL19O8+bNcXd3JyIigmPHjtGtWzfWr1+PiYlJfsSaJ+T2ZeEwb948xowZQ79+/Vi+fDkWFhZZlj18JYJ3VpwhMVVHnXL2LBnWBGebrMsLIYQouRITE2nfvj1BQUEEBgai3bePu59OA1NTKq5aSam6dQs0nny9fQkPn8Y8dOgQrVq1wtLSkiZNmrB9+3Y2bdqUrwlZSEgI7733HlWqVMHNzY127dplOrZNFG4PHjzgq6++Yty4caxevTrbhGyzfxhvLD1FYqqOllWdWT2iuSRkQgghsmRlZcW2bdv47rvvcHJyonS/fth27QLp6YS9PwldfIKxQ8xSkZo89p133qF58+a0b98eU1NT5s+fz6xZszh79iy1a+fsyQrpKTOe1NRUkpKSsLe3JyIiAhcXl2zLLz12g+lbAwDoXrcsP/Svj7mpzEEmhBAi59atW0eH5s25//rrpN++g/3LL+P+9cwCaz/Pn74MCQkhNTWVKlWqPLHx3JR9Vnq9HgsLCxYsWMDw4cNzdIwkZcYRGxtLnz59gIdP8D5pPjGfA0F8u/syAEOfq8in3b3RamUOMiGEEDl3//59vLy8aNCgARu+/JI7w98EvR73777Dvnu3Aokhz29frl27lp9//jlHjeem7LNISUnBx8eHUqVK0bZt23xvTzy9O3fu0Lp1a06dOpXthLDwcEb/WbsCDQnZ2PZeTOshCZkQQojcc3Z2ZsuWLRw7dowxP/+M0ztvA3B3+nRSQ8OMHN3jcrxA4J49e3jzzTefWO7ChQu0atXqmYLKzp9//kmPHj1ITU3F3t6eP/74g8qVK2dZPiUlhZSUFMPr2NjYfItNPC4wMJAuXbqQnp7OkSNHqFOnTpZl9XrF9K3/sPzETQCmvFiTt17I+t9WCCGEeJJWrVqxbNkyBg4cSJWKFXm9fn2S/P25PWkSFX5fjiaLpfyMIUc9ZTVq1MDb25v4+Pgn/lSqVIkGDRrkqPG33noLS0vLbH+uX7+e4Zj27dvz4MEDbt26xahRo+jVqxdnzpzJso2ZM2dib29v+PH09MxRbCJvHDx4EBsbG06cOJFtQpau0/PB+vMsP3ETjQa+7FVbEjIhhBB5YsCAAcycOZMdu3fj/OWXaG1sSPLz4/7PC4wdWgZGHeiflpaGTqfLtoyFhUW2t7saNmxIkyZNWLhwYab7M+sp8/T0lDFl+Sw4OJiKFSsC/z9jf1ZS0/WMX+vP9gt3MNFq+K5fXXo18CigSIUQQpQESilSU1OxsLDgwdat3Jn0AWi1VPh9OVaNGuVbu/k+JUZeMTMze2JP2ZMGhCulyC6vtLCwwM7OLsOPyF9r166lWrVq7NixAyDbhCw5Tcfbv59m+4U7mJlo8BnUUBIyIYQQeU6j0WBhYUFQUBBtpk5FtWkNej1hkyahi4kxdniAkZOy3EhISODVV1/l4sWLpKenExUVxeeff8758+cZNGiQscMT/7NgwQIGDhzIK6+8QseOHbMtm5Sq442lpzhwOQJLMy2/vt6ELrXLFFCkQgghSiJXV1eUUvTeuROtuzsqMYnU4GBjhwUUoaTM2tqal156iTfeeANbW1sqV67MgQMH2L17N23atDF2eCWeUoovv/ySd999l9GjR7Ns2TLMzMyyLJ+Yms4bS09x/Fok1uYmLBvWlNbVsp+3TAghhHhWdnZ2bN++nbj0dCZHR+O2ZjWl6tUzdlhAEZs89hGl1BNva2ZF5inLHykpKbzwwgt069aNqVOnZvvv8yghO3k9ChsLU5a90YRGFRwLMFohhBAlnb+/P61ataJz58788ccf+dZObvKOwvMcaC48bUIm8l56ejp37tzB09OTw4cPZ7tkEmSWkDWlUQWHAopWCCGEeKh+/fqsW7cOc3NzY4di8My3LwMDA/nxxx/x9/c3bDtz5gzr1q171qrzlI+PD97e3jRp0sTYoRQbycnJ9O3blzZt2hieaMlOQko6Q5c8TMhsLUxZPlwSMiGEEMbTpUsX2rVrZ+wwDJ4pKYuKiuL555/n0qVLjBw5kt9//x14OIHs9u3b8yTAvDJy5EgCAgI4deqUsUMpFuLi4njxxRfZvXs3P/300xO/aSSkpDNsySn+vvH/CVnD8pKQCSGEEI880+3Lw4cP06xZMxYtWkR6ejpDhgzBxsYmr2IThVR0dDRdunQhMDCQPXv2PHEFB0NCFvz/CVkDSciEEEKIDJ4pKXNyciI+Pv5hRaamLFu2jO7du+Pm5oZpIVq2QOStixcvEhoayv79+2n0hAn3ElP/lZBZmvL78GbU9yxdMIEKIYQQRcgzZU4tW7bE3NycAwcO0LZtWywsLPD19aVly5YydqsYioyMxMHBgVatWhEUFESpUqWyLZ+cpuOt5acNCdmK4c2oJwmZECITOp2OtLQ0Y4chRK6ZmZlhYmKSJ3U9U1Km0WjYtWtXhqWSHBwcOHXqlPznKmZCQkJo3749ffv25auvvnpiQpaarue9lWc5FvS/ecjeaCoJmRDiMUop7t69y4MHD4wdihBPrXTp0pQpU+aZZ4d4qqQsJSUFX19fAgMDcXFxoUuXLtSoUcOw38rK6pmCEoXL9evXadeuHRqNhjfffPOJ5dN1esau8WN/4D0sTLX8NrSJDOoXQmTqUULm6uqKlZWVTHkkihSlFImJidy7dw+AsmXLPlN9uU7KlFJ07tyZw4cP4+XlRXx8POPHj6dNmzb8/vvveHgUznULfXx88PHxeeIC6CKjwMBA2rdvj42NDXv37sXT0zPb8jq94v1159h58S7mJloWvdaY5pWdCihaIURRotPpDAmZk5P8nhBF06M7R/fu3cPV1fWZbmXmaEqM+Ph45s6dy/Hjxzl69ChHjx7l7NmzXL58mbCwMAIDAylTpgzNmjUjIiLiqYPJTzIlxtP5+eefcXBw4NChQ09MyJRSTNl4gU3+tzHVavAZ3FCWThJCZOnRMBe5uyKKukfv4WcdupWjZZaio6Np3bo1AQEB6HQ6LCws6Nu3Lw0bNqRhw4bUr1+f0qVL06NHD+rVq8cXX3zxTEHlJ1lmKWeSkpIoVaoU6enpxMXF4eCQ/e1HpRSfbQ1g6fFgtBqYM6ABPeq5F1C0QoiiKDk5mRs3blCpUiUsLS2NHY4QTy2793Ju8o4c9ZQ5ODhw/vx54uLiWLx4MSYmJlhaWrJixQo6d+6Mg4MDVapUISgoiK1bt7Jz507Cw8Of/uyEUf31119UqVKFv//+G1NT0ycmZADf7r7M0uPBAHzTt54kZEIIUQTodDr8/f1JSkoydihPlJqair+/P6mpqVmWKUrnk5lczehfqlQp+vbti1arZcCAAZw9e5b4+HjOnj3LlClTKFOmDNeuXaNfv36UKVOGn376Kb/iFvnk5MmTdOrUicqVK1OzZs0cHfPL4evMP3gNgC9erk3fRoVzXKEQQoiMoqOjadCgAZcvXwYermfs7+9PcnKykSN73O3bt2nQoAG3bt3KskxROp/M5HqZJVtbW3788Ud69uzJp59+yrVr16hVqxatWrUiLi6OAQMGEBsbS0BAAN27d8+PmEU+OXnyJJ07d6Zu3brs3LkTW1vbJx6z7nQIX+64BMDkLjUY0rxCfocphBAij5iamlKvXj3DYPX79+/ToEEDgoKCjBzZ0ynq5/NUa1+++eabbNy4kQ0bNlCzZk0sLCyoVq0aYWFhTJo0Ca1WS82aNalcuXJexyvySXp6Oq+//jp169Zlx44dOUrI/gwI58MNFwAY8UJl3mkt/95CiJLh8uXLhgfbQkJCuH37dpZl9Ho9QUFBBAcHG/bpdDquXLnCzZs3s2wjMTGRy5cvk5KSglIKf39/EhMTHyt38+ZNbt68yX+HiP/7dl96ejrXrl0zrMLziK2tLUuXLqV8+fIA/PPPP4bY/f39MyQz2cX877YSEhIICAggOjo6y3N71rrS0tK4evUqcXFxT30+hZJ6RoGBgWrdunVq69atKi4u7lmryzfz5s1TNWvWVNWqVVOAiomJMXZIhc6VK1dUbGxsjsqevHZfeU3ZoSpM3qYm+vorvV6fz9EJIYqbpKQkFRAQoJKSkowdSq7Vq1dP9evXT1WoUEFVqlRJmZmZqb59+6rk5OQMZfr3768qV66svLy81Pvvv6+UUmrr1q2qTJkyqmzZssrOzk7VqVNHBQQEZKh/xYoVysbGRpUrV06VLl1ajR07VgHqxIkThjJ//fWXqlGjhnJzc1MVK1ZUZcuWVdu2bTPsv3HjhgLUuHHjlIuLi6pSpYoyNzdXc+bMMZSJiIhQgPLz81Pp6emqVq1aClDVq1dX9erVU0OHDs1RzI/aGjNmjHJwcFB16tRR27dvz/TaPW1dj7aPGjVK2dvbq/LlyytLS0s1b968XJ9PXsvuvRwTE5PjvOOZk7KiJjcXpyQ4ceKE6tGjR64S6othD1TtT3epCpO3qeFLT6m0dF0+RiiEKK6KelJmYWFhSJJu3LihypUrp2bOnJmhjJ2dnTp//rxhW3h4uLK1tTWUS01NVb169VINGjQwfLm9ffu2srS0VD/99JNSSqnExETVvn37DElZRESEcnJyUosWLTLUvW7dOmVra6tCQkIMMQGqc+fOKj4+Ximl1MqVK5WZmZm6e/euoZ5HSYxSSt25c0cB6sKFC7mK+VFbL7zwQrZf7p+lrkfb69evryIjIw3nrNVq1T///JPj88kPeZWUyarhJdiJEyfo3Lkz9evXz/ExwfcTeH3x38SlpNO0kiPzBjXA1OSp7oILIUSW7ty5w507dzJsc3BwoFKlSiQnJxMQEPDYMQ0bNgQe3qpKSEjIsK9ixYo4OjoSERFBSEhIhn22trZ4eXnlOsbevXvTvHlzQ/2jRo3i119/5cMPPzSUGTRoEHXq1DG8Xr16Nba2tkyaNAl4uG7it99+S9WqVfn7779p1qwZq1evxs3NjVGjRgEPH7L7/PPP2bdvn6GeFStWYGdnR4sWLbhw4QJKKapVq0bp0qXZt28fr7/+uqHslClTsLa2BqBfv368+uqrXLp0CTc3txydZ05ifuTjjz/OdvhLXtT10Ucf4ejoCEDfvn1p0qQJixcv5rvvvsvR+RRmkpSVUMePH6dLly40aNCA7du3Y2Nj88Rj7sUm8+riv7gfn4p3WTt+fb0xlmZ5swirEEL828KFC/nss88ybBs8eDArVqwgNDSURo0aPXaM+t+YqqFDh3Ly5MkM+37//XeGDBmCr6+vIdl5pFOnTuzevTvXMf73CXVvb2+Cg4PR6XSGWd0rVqyYoUxQUBDVq1fPMOt7lSpVKFWqFEFBQTRr1ozr169TvXr1DEtO/XspQ4BLly4RGRnJkCFDMmx3dHR8bALTfy/9Y2ZmhpmZ2WNjy7KTk5gf+e/55kddmV33a9eu5fh8CjNJykqgsLCwXCdkcclpvL7kFCFRSVR0smLZG02xszQrgGiFECXR22+/Tc+ePTNsezRnooeHB2fOnMny2KVLl2baUwbQv39/WrRokWFfTh5sysx/B90nJCRQqlSpDAnHf5fcsba2fuy49PR0UlNTDb+LMyvz39cWFhZUrlwZPz+/p4o9N3IS8yNPWmIoL+rK7Lo/6gks6iQpK4HKlSvHzz//zEsvvZSjhCxNp+e9lWe5dCcWZxtzlr/RDBdbiwKIVAhRUpUtWzbLxZ0tLS0NtyozU7169Sz3ubi44OKSN8u/7d+/P8Prffv20aBBg2yPadSoEXPmzCEiIsIQx6PbkvXq1QOgQYMGzJ8/n5iYGOzt7QE4ePBghnpeeOEF5s+fT0BAAN7e3obtSinS0tIwNzd/qnN6NBv9v3vbchJzTuVFXfv37zf0qKWmpnL06FEmTpyY4/MpzGQwUAly/vx5li1bBjy8DZCThEwpxUcbLnDk6n1KmZmweGgTyjvJOnVCCOHn58e7777L4cOH+eqrr1i2bBlTp07N9pg+ffpQq1YtevXqxZ49e1i3bh1vvvkmI0aMMPTm9e3bFw8PD/r27cu+fftYtWqVYZzao1uavXr1om3btrz44ossX76cY8eOsXjxYpo2bfpMt/JKly5N2bJlWbFiBWfPniUoKChHMedUXtT17bffsmDBAg4ePMiAAQNQSjFixIgcn09hVmKSMh8fH7y9vWnSpImxQzGKS5cu0aFDB+bOnZurbwyz917ljzOhaDXgM7gBdT1K51+QQghRhHz66ac4Ozszffp0Dhw4wB9//EHHjh0N+6tXr46rq2uGY7RaLXv27KFFixZMnz6d+fPnM27cuAwr4JiamrJ37148PT355JNP2LFjB4sXLwYwTIpqYmLC9u3bGT9+PCtWrOCDDz7gxIkT/PLLL4YxV+bm5tSrVw8Li4x3NurVq2fogfvvZKsAa9asISgoiBEjRvDll1/mKOas2vqvZ6nr0fb169fz999/8/HHH2NpacmhQ4cMnQw5OZ/CLEcLkhdG8fHxBAYG4ubmhqenZ46PK4kLkl+9epXWrVvj7OzMgQMHcHJyytFxa0/dYvL6h5PDftWrDoOalc/PMIUQJUxRXpC8fv36DBkyhPfffz9f6k9LS8PM7P/H7W7cuJEBAwYQHR2NlZXcrShsCnRB8sLo1VdfpWnTpnz//ffGDqVQCw4Opn379tjb2/Pnn3/mOCE7ePkeH2+8CMDItlUkIRNCiAI0fvx45s6dy7Fjx/jtt9949913efvttyUhK+aKZFI2b9484uLiMsz9IjJnY2NDs2bN2LdvX47npLkYFsPIlWfR6RW9GpTj/U5ZD5oVQoiSKLNbk3lp2rRp3Lhxg48++ogtW7YwY8YM5syZk2/ticKhyD19ee7cOWbOnMnff/9Nt27djB1OoXXnzh10Oh0eHh6sW7cux8eFPUhi2NJTJKTqeL6qE7P61M0wV44QQghYu3Ztvtbv4uLCDz/8kK9tiMKnSCVlCQkJDBgwgDlz5lCuXDljh1NoRURE0KFDB5ycnDh06FCOk6r4lHSGLz1FRFwKNcrY8vOQRpibFsnOVCGEEKLIMWpSFhwczP3797MtU6dOHcMTGKNGjaJFixb07ds3x22kpKSQkpJieB0bG/t0wRYRMTExdOnShcjISDZu3JjjhEynV4xZ7Ufg3TicbSz4bWgTmRxWCCGEKEBGTcqWLVvG1q1bsy2zadMmPDw82LFjBxs3bmTTpk2cPn0agKSkJO7du8fp06dp3LhxpsfPnDnzsaU6iqukpCR69uzJ9evXOXToENWqVcvxsV/tuMT+wHtYmGr55bVGlCtd6skHCSGEECLPFJkpMXx9ffnmm28ybAsICMDW1hZPT0/++uuvTJdkyKynzNPTs1hOiXHo0CFefvllduzY8dgyItlZ9dctPt74cOqLeYMa0L2ue36FKIQQBkV5Sgwh/i2vpsQoMmPK+vfvT//+/TNsq1+/Pm3atGH27NlZHmdhYfHEyeyKOr1ej0ajoXXr1ty4cYPSpUvn+NhjQff5dPPDqS/Gd6gmCZkQQghhJDKKu4hTSjFy5EjGjx8PkKuE7FpEPO+uOEO6XtGznjtj2lfNpyiFEEII8SRFOimrVasW5cuX7ElNP/74YxYsWEDdunVzdVx0QirDl54iNjmdhuVL801fmfpCCCFy6qWXXuK7774rkLYGDRqUYXmggmxbFKwic/syMytXrjR2CEY1a9Ysvv76a3744QfeeOONHB+XptPz7sozBEcmUq50KRa+2hhLs8fH4wkhhMhcZGQk8fHxBdJWVFQUcXFxRmlbFKwinZTlho+PDz4+Puh0OmOHkie2b9/Ohx9+yNSpUw23LnPqi20BnLwehbW5Cb8NbYyLbfEecyeEEMXJli1bMDc3N3YYIh8U6duXuTFy5EgCAgI4deqUsUPJEx07dmTZsmW5nu7D91QIy07cBODHV+pTo0zxegJVCCGMZdGiRTRr1oxKlSrRqVMnDhw4kGH/W2+9RZkyZShbtix169Zl1KhRREVFZSiTkpLChAkTqFKlCk2bNmXWrFno9foMZYYNG8aCBQsMrzt06MDXX3/NqFGjqFOnDg0aNGDu3LkZjklKSmLMmDEZ6h0wYECG26LC+EpMT1lxsXfvXmxsbGjevDmvvfZaro49eyuaTzY9fNJyXAcvOtUqkx8hCiHEU1NKkZRmnDsapcxMnnps7bRp0/D19WX27Nl4eXlx6NAhunXrxoEDB2jWrBkA3377LTNmzAAgNDSUjz/+mMGDB7Nz505DPRMmTGDXrl388ssvODs7M2XKFPbu3UvDhg0NZf57+/L+/ft8+umn/PDDD4wbN45Tp07x6quvUrNmTTp06ADA2LFj2bdvH7/++ivOzs5MnTqVLVu2ULFixac6X5E/JCkrQk6fPs3LL7/Miy++iK+vb66ODY9N5p3fz5Cq09PJ240x7bzyKUohhHh6SWk6vD/dbZS2Az7vjJV57j8WHzx4wKxZszhw4IBhjsjKlStz8uRJ5s2bZ0jK/v10fJkyZfjtt98oX7489+7dw9XVlcjISH755Rc2btxIu3btAFi+fDmenp5PjGHAgAGMGjUKgKpVq/LLL7+wb98+OnTowP3791myZAmbNm2ibdu2wMPJ2z08PHJ9riJ/SVJWRFy9epUXX3yR2rVrs2TJklwdm5Ku450VZ7gXl0I1Nxt+eKU+Wq08aSmEEHnh7NmzpKSk0LdvXzQaDUoplFLExcVRu3ZtQ7krV67wxRdfcPbsWSIjI3k0d3twcDCurq5cunSJtLQ0nn/+ecMxDg4OeHt7PzGGWrVqZXjt6upqWMYwMDCQ9PT0DPXa29vnqF5RsCQpKwLu3r1L586dcXR0ZNu2bVhbW+f4WKUUUzddxO/WA+wsTVn0amNsLOSfXQhROJUyMyHg885Ga/tpPFo1Zs+ePTg5OWXYZ2ZmZijTvn17OnXqxLJly3BzcyMxMZHq1auTmpoKQFpaWoZjHsnJoP7MVrR5lPQ9qv9p6hUFSz6di4B79+7h4ODAhg0bcHZ2ztWxv5+8ie/pULQamDeoIRWdc57QCSFEQdNoNE91C9GYHvVSXbp0ib59+2Za5vLly4SGhvLdd9/h4OAAwOHDhzOU8fJ6OKzk3LlzPPfcc8DDZC4wMJCWLVs+dXyP6j1//rzh9mpaWhqBgYEZes+E8ZWYpy99fHzw9vamSZMmxg4lx1JTU0lOTqZu3bqcPn2aChUq5Or4k9cj+XxrAAAfdq3BC9Vc8iNMIYQo0cqXL8+gQYOYOHEif/31FwDx8fGsXLmSxYsXA1C2bFlMTU3ZunUrALdu3WLcuHEZ6vHw8KBHjx588MEHREZGkpaWxscff0xkZOQzxefp6cmLL77Ihx9+SFRUFOnp6Xz66aeG25ui8CgxSVlRmxJDr9czdOhQevXqhVIq108EhccmM2rVWdL1ipfqu/NWq8r5FKkQQojffvuN3r1707lzZ2xsbPDw8GDPnj107NgRABcXF+bPn8/o0aOxs7Ojbt26dO/e/bF6Fi5ciKmpKa6urri6uhIWFmbo3XoWixYtQimFi4sLLi4u3Lhxg0aNGsktzEJGox7ddC4hcrNau7EopZgwYQJz5szB19c3y+7wrKTp9AxcdJLTN6OpUcaWje89TylzmbFfCFG4JCcnc+PGDSpVqoSlpaWxw8mVqKgozM3NsbGxybBdr9cTExND6dKlM/0yrZQiOjqa0qVLo9VquXv3Lk5OTo+N94qNjcXa2hoTExOio6MxMzMztPXftiMjIylVqhRWVlaG42NiYtBoNI99zj2qV6PRUL58eaZNm8Zbb72VJ9ekJMvuvZybvKNo3bgvIb777jtmz56Nj49PrhMygJk7Ajl9MxpbC1MWDGkkCZkQQuQxR0fHTLdrtVrDmLHMaDSaDMeWKZP5fJH//vD+b33/bfu/DxfAw6cr/23Xrl1oNBo6dOhAeno606ZNIzo6mh49emQZqyh4Jeb2ZVFx+vRpPvjgAz755BPee++9XB+/7fxtFh+7AcD3/evJwH4hhBCGWf6dnJyws7Nj586d7Nq1K8ukUBiH9JQVMo0bN2b37t2GcQi5EXQvjg/+OA/Au22qyIz9QgghAHBzc2Pbtm2kpaWh1+uxsJA1jwsj6SkrJC5dusSKFSsA6NSpU64H9senpPP272dITNXRorITEztWy48whRBCFGFmZmaSkBViJaanzMfHBx8fH3Q646yplp27d+/StWtX7Ozs6N+/f66fhlFKMXn9ea5FJOBmZ8FPAxtgaiL5thBCCFGUlJhP7sI6JUZCQgLdu3cnNTWV7du3P9XjyUuOBbP9/B1MtRrmD26Ii618CxJCCCGKmhLTU1YY6XQ6Bg4cyOXLlzl8+HCOFp39rzM3o/hqxyUApnSrSaMKmT8RJIQQQojCrcT0lBVGMTEx3Lt3D19fXxo0aJDr46MTUhm1yo90vaJ73bIMfa5i3gcphBBCiAIhPWVGkpKSgqOjI8ePH0erzX1urJRi4rpz3IlJprKzNV/3qZvrhwOEEEIIUXhIT5kRrF+/Hm9vb+7evftUCRnAr0dusD/wHuamWuYNaoiNheTXQghRVH311Vds2rQpx69F8SRJWQE7efIkQ4YMoWnTpri6uj5VHWdvRTNrVyAAn3b3xtu9cC4XJYQQxdWMGTMMi4vnhR07duDv75/j16J4KjHdK4VhSoybN2/y0ksv0bhxY5YsWfJUvWQxiWmM/t84sm51yjK4Wfl8iFQIIUR2tm/fjkajybNliqZMmULZsmWfer8oHkpMUjZy5EhGjhxpWBi0oOn1enr16oW1tTUbN258qsV3lVJM+uMcYQ+SKO9oxcw+dWQcmRBCFLDZs2dz7do1NmzYQFBQEADz5s3jm2++4bnnniMxMZH9+/dTs2ZNRo4ciY+PD6dOnUKj0eDi4sILL7xA9+7dM9Tp5+dHSkoK9evXz7TN/+7/9NNPee6550hPT+fQoUOYmpoyePBgateuneG4HTt2sH37dpycnOjZsyeHDh2ifPny9OvXL8+vi3h2RSop279/P+fPn8+wzdnZmSFDhhgpopzTarV88803uLu74+zs/FR1LD0ezJ6AcMxNtPgMaoidpVkeRymEEOJJ6tSpg52dHZUqVaJNmzbAw5nyt2zZwi+//ELdunV56aWX8Pb2BqBWrVpYWz9chzg0NJS3336b1157jZkzZxrq3LFjB6mpqbz88suZtvnf/Vu2bOHXX3+lYcOGdOnShVOnTtG4cWMuXrxI1apVAZg/fz7jx49n3Lhx2NraMmDAAB48eMCbb74pSVkhVaSSMl9fX/bt20e3bt0M21JSUowYUc5s27aNrl270qFDh6eu43zoA8N8ZB+/WIM6HgXf2yeEEPlNKYVKSjJK25pSpXJ096F9+/a4uLjQoEEDhg4dmmGfp6cnu3fvzrDtUeL2SMeOHWnVqhVTpkzBxsbmqeOtXr0627ZtM7z29/dn9erVTJ06laSkJD799FO+//57Ro0aBUDPnj0NiaIonIpUUgZQr149Zs+ebewwcmzRokW8/fbbbNmy5anHHsQmpzFqlR9pOkXnWm68LvORCSGKKZWUxOWGjYzSdvWzZ9BYWT1THZ06dXpsW1paGuvWrePs2bNERkaSnp5OWloa165do169ek/dVvv27TO8rl69OqGhoQAEBAQQGRlJnz59Muz/7+1NUbgUuaTszp07LFq0CHt7e5o1a0bFihWNHVKW9u/fz8iRI3nvvfeeOiFTSvHxhgvcikrEw6EU3/SpJ+PIhBCikCpdunSG10opunbtyp07dxg0aBA1atRAr9ezYsUK4uLinqmt/45N1mq1hofZ7t+/D4CjY8ZVXv77WhQuRS4pi4iI4OTJk4SFhfH6668zY8YMJk2alGX5lJSUDLc4Y2NjCyJMrly5Qp8+fWjXrh1z5sx56nr+OBPKtv+tazl3YAPsrWQcmRCi+NKUKkX1s2eM1naOy+bwy3FQUBD79u3j1q1bhqX0AgMDnyq+3HjU1q1bt/Dy8jJsv3XrFs2aNcv39sXTMWpStmfPHgICArItM2zYMMPTkiNGjGD+/PmGqSRWrVrFkCFDeOGFF7J8k82cOZPPPvssbwPPgd9++40yZcqwdu1aTE2f7jLfuJ/AtC3/ADC+YzUalHfIyxCFEKLQ0Wg0z3wLsSA4OjoSFRX1xHKPkrfo6Gg8PT3R6/V89dVX+R0eNWrUoGbNmvz000/MnTsXeDi++fr16/netnh6Rk3K7t+/T3BwcLZl0tLSDH9v2LBhhn2DBg1iwoQJ7Nu3L8uk7KOPPmLChAmG17GxsU+18Hduff3110yaNOmxruycSk3XM3aNH4mpOppXduSd1lXyNkAhhBBPrXfv3owbN46wsDBKlSrFvHnzMi1XtWpVBgwYQLt27WjXrh2XLl3C1tY23+PTarX4+PjQs2dPTp8+jZOTE4GBgVSpUgUTE5N8b188HaMmZYMGDWLQoEHPVIe5uTkxMTFZ7rewsMDCwuKZ2ngaGo3mqae+APhx7xXOh8ZgX8qMH1+pj4lWxpEJIURhMXz4cJo1a8Y///xDUlISZmZmfP7551Sp8vgX6NWrV3P8+HGCg4MZO3YszZo1Y8WKFVSrVs1Q5r+Twz7pdWZtvfvuu5iZ/f8Ql7Zt23Lt2jUOHjyIk5MTTZs2pUWLFs/02STyl0YppYwdRE7odDquX7+e4d74gQMHaNeuXa6ebHw0eWxMTAx2doVzeaLjQfcZ/NtfKAULhjSkS22ZxVkIUfwkJydz48YNKlWq9FQTaovsXbhwAQ8PDxwcHg592bNnD507d8bf3/+ZnvoUj8vuvZybvKPIDPRXStGvXz+8vb2pVasWt27dYvny5QwfPvyxmZGLsuiEVMb7+qMUDGxaXhIyIYQQTyUtLY2mTZtSs2ZNkpKSOHLkCF988YUkZIVYkUnKTE1NOXPmDJs3b8bPz4/q1atz+PBhmjRpYuzQ8oxSisnrzxMem0JlF2umdq9p7JCEEEIUUQ0bNuT06dOcOHGCtLQ0Fi9eXCBjqsXTKzJJGYCJiQm9e/emd+/exg4lX6z+O4Q9AeGYmWj4aUADrMyL1D+PEEKIQsbe3p4uXboYOwyRQ1pjB1BQfHx88Pb2LrQ9a0H34vh828PpLyZ3qUHtcrKMkhBCCFGSlJikbOTIkQQEBHDq1Cljh/KYlHQdo1f7k5ymp5WXM288X8nYIQkhhBCigJWYpKww++HPK1y6E4ujtTnf96uHVqa/EEIIIUocScqM7K/rkSw6/HCG5a9718HVTh4LF0IIIUoiScqMKC45jQm+51AKXmnsSadaZYwdkhBCCCGMRJIyI/psawBhD5LwdCzF1B7exg5HCCFECZOamsqaNWt48OBBgbYbERHB9u3b87xevV7PmjVriIyMzLM6Y2Ji2LhxY57Vlx1Jyoxk18U7/HEmFK0GfuxfHxsLmf5CCCFEwYqNjWXgwIGGdaiTk5NZs2ZNtssX5oUJEyYYHrzLyzZTU1MZOHAgV69efea6HrGzs2P69Ols2LAhz+rMSolJygrTlBj34pL5aMMFAN5pXYXGFR2NHJEQQoiSyMLCgldeecWwFNODBw8YOHAgISEh+dbmhQsX2LBhA+PHjy+wNp+FRqNh8uTJfPzxx+T3ypQlJikrLFNiKKWY/Md5ohPT8C5rx7gO1Z58kBBCiEJl9+7dXL58mYiICP78808OHDhAenp6pmXu3bvHtm3bOHbsmGHf3bt32bJlC7t37yYuLi7TNi5fvszmzZu5ePEiOp0u09tysbGx7N69m927dxMeHp5hX0JCAmvWrCE+Pp7r16+zfft2zp07l6GMhYUFL7/8Mvb29iil2Lx5MwC7du1izZo17Nu3L0cx/7utixcvsmHDBm7evJnpefn4+ORJm49cvXrVcJ0y4+vry5o1a1i3bh1///03aWlpGfZv3rw50561jRs3EhQUBECvXr0ICwvLEFu+UCVMTEyMAlRMTIxR2l9xMlhVmLxNeU3ZoS7fjTVKDEIIURgkJSWpgIAAlZSU9Ez1xMXFqc8//1x5eHgorVarPDw81Oeff67i4uLyKNLH1atXT7Vu3VqVK1dOde3aVZUrV041aNBARUVFZSjTpk0bVaFCBdWjRw/1448/KqWUmjt3ripVqpRq06aNatCggXJ0dFQHDhzIUP/nn3+uLCwsVPv27VXt2rVV165dFaBOnDhhKPPHH38oBwcH9cILL6guXbooe3t7NW/ePMP+GzduKED16NFDeXt7q27duikbGxs1evRoQ5mIiAgFKD8/P6XT6dRLL72kANWlSxf1yiuvqGnTpuUo5kdtde/eXVWvXl3169dPHTlyJNNr5+HhoX799VellHqmNpVS6uuvv37idRo0aJB65ZVXVJ8+fZSXl5fy9vZWt27dMuwfPHiw6tWrV4Z6z507pwAVEBBg2NahQwc1duzYTM8pu/dybvIOScoK0PWIeFXjk52qwuRt6tcj1wu8fSGEKEzyIimLi4tTDRs2VFqtVgGGH61Wqxo2bJhviVm9evWUnZ2dCg4OVko9/GypWbOmmjBhQoYyZcuWVffu3TNsu3r1qjIzM1Nr1qwxbBs9erSqWLGiSk5OVkopdenSJaXVatXWrVuVUkrp9Xo1ZMiQDMnG9evXlbW1tTp48KChnlOnTilLS0t16dIlpdT/J0pvvPGG0uv1SimlDh48qDQajbp586ZSKmNSppRSd+7cUYC6cOFCrmJ+1Fb//v2VTqfL8rqFh4crQB0/ftyw7WnbvHLlijIxMclwnQYOHPhYUvZvOp1O9enTRw0dOtSw7eDBg8rMzCzDv9OYMWNUixYtMhw7fvx49dxzz2Vab14lZSXm9qWxpev0jF/rT1KajueqODHsuYrGDkkIIYq8H3/8EX9/f/R6fYbter0ef39/fvzxx3xru3///lSoUAF4OBj83XffxdfXN0OZAQMG4OLiYni9fv16PD09eeWVVwzbpkyZQnBwMH/99Rfw8LZZtWrV6N69O/BwTNP777+fod7Vq1fj5OREREQE69atw9fXl+vXr+Po6MiRI0cylH377bfRaB5OSt6yZUu0Wi1XrlzJ8XnmJOZHRo4ciVabdWpx//59AMMYtmdpc/369Xh5eWW4TpMmTcq0voCAALZt24avry8uLi78/fffhn2tW7emYsWK/P7778DDhwVWrlzJG2+8kaEOBwcHQ/z5RR75KyDzD17DP+QBtpamfCez9gshRJ5YtGjRYwnZI3q9nkWLFjF16tR8abtixYoZXleqVImwsDDS09MxNX348Vq2bNkMZW7evEnlypUzbHNzc8Pa2towBiskJOSxuv/7Ojg4mNTUVP74448M21u1aoWzs3OGbY6O//8wmYmJCaampiQnJ+foHHMa8yP/Pd//srGxAR6OQXvWNm/dupXpv8G/JSUl0aNHD/z8/GjSpAn29vaEhIRw7969DOWGDx/OkiVLmDBhAps3byY5OTlDQvgoZltb22zjflaSlBWAcyEPmLPv4SDCGS/Vxr10KSNHJIQQxcPt27efaf+ziI6Ofux16dKlDQkZYOihesTZ2fmx3qWUlBQSExMNyZSjoyN+fn7ZtmVnZ4eDgwNr1qx55vN4kpzE/Mh/z/e/3N3dsbGx4caNGzRq1OiZ2nRycuLs2bMZyvz3Ov3+++9cvXqVmzdvGhLCefPmMX369Azlhg4dytSpU/n7779ZvHgxffv2fSwBu3HjBtWrV8/2/J5Vibl9aawpMZLTdIz39UenV3SrW5aX6rsXaPtCCFGcubtn/zv1SfufxdatW9HpdIbXGzZs4Pnnn8/2mJYtW3Lu3DmuXbtm2PbHH39gaWlJw4YNAXj++ec5c+YMoaGhhjKPnlB8pEuXLly6dIlDhw5l2B4XF5flU4o58Shx+XdPWk5izilTU1NeeOGFDE+iPm2bLVu25OzZsxmm0vjvXGJ3796lXLlyhjbg4W3P/3Jzc6N79+588cUX/PnnnwwfPvyxMsePH6dDhw65Ot/cKjE9ZSNHjmTkyJHExsZib29fYO1+s+sy1yMScLW14MuXaz/xW4QQQoicGzFiBNOnT8/0FqZWq2XEiBH51nZUVBRdunShX79+HD16lF27dnH8+PFsj+nUqRMvvvgiHTt2ZNy4ccTExDBr1iymTp2Km5sbAF27duW5556jY8eOjBo1ivDwcBYvXgz8f09Uhw4dGDFiBN27d2f06NFUqVKFy5cvs3HjRvbs2fPUt9lsbGyoXr06s2bNolevXri5ueUo5tx46623GDVqFN999x0mJiZP3Wbnzp154YUX6NChA6NHj+bu3bssWbIkQ1vdu3dnxowZjBs3jtq1a7Nx40b8/f0xMTHJNK4XX3wRLy8vWrVqlWHfsWPHiI2NpV+/frk+39woMT1lxnDiWiSLj90AYFbfupS2MjdyREIIUbyMHz+e+vXrPza4XKvVUr9+fcMEpflh8uTJDB06FH9/f+zt7fnrr79o0KCBYX+XLl2oUaPGY8etX7+eKVOm4O/vz+3bt1m7di0fffRRhjI7duxg2LBhnD59GnNzczZt2gSQIdlauHAhf/zxB/Hx8Rw/fhw3NzdOnDhhGFdlbW3NK6+88liC1r9/f8qVKwc8PnkswLZt26hcuTI7duwwPDTwpJizaiszPXv2xMXFJcN4uKdpEx72Vr711lucOXMGS0tLTpw4wSuvvGK4xdmwYUOOHDlCeno6x44do1u3bmzYsIHevXs/FlenTp2wsrJi2LBhj+2bO3cu48aNy9Djli+e+HxmMVNQU2LEJqWq52buUxUmb1Mfrj+Xr20JIURRVNTnKfv222/zrf7IyMgMr3/55Rdla2urUlJS8q3NgnTixAk1depUY4eRwb59+5SZmZm6fft2hu1RUVHq9ddfV4mJiVkem1dTYpSY25cF7cvtlwh7kISHQymmdJPFxoUQIr/Y2NgwderUfHvK0hg++eQTNBoNDRs2JDAwEB8fH2bMmIG5efG449K8eXOaN29u7DCAh+PO/vzzT2bNmsUbb7zx2BOkDg4OLF26tEBikduX+WB/YDhrToWg0cB3/erJYuNCCFHMZHVrMq/Mnj2bevXq8ddff6HVatm1axcTJ07Mt/ZKsvDwcHbu3Em/fv344YcfjBqLRql8Xl2zkHk00D8mJgY7O7s8rz86IZVOsw8TEZfC8JaVmNpdesmEECIzycnJ3Lhxg0qVKmFpaWnscIR4atm9l3OTd5SYnrKCmhLj0y3/EBGXQhUXayZ1zt/5TIQQQghRfJSYpGzkyJEEBARw6tSpfGsjOU1HdEIqJloNP/Svj6XZ44/cCiGEEEJkpsgNdtLpdKxdu5b9+/cbHl399yPIxmRpZsLyN5pyPiyGep6ljR2OEEIUCSVsFI0ohvLqPVykespSUlLo3Lkz06ZNo169etSrV49Ro0bh7+9v7NAMtFoN9SUhE0KIJzIzMwMgMTHRyJEI8WwevYcfvaefVpHqKZs1axZ+fn4EBAQYZvR9/fXXn7iwqRBCiMLHxMSE0qVLGxaHtrKyklVPRJGilCIxMZF79+5RunTpTFcKyI0ilZT99ttvDBkyJMOyDqampgW6bJIQQoi8U6ZMGQBDYiZEUVS6dGnDe/lZFJmkLDo6mlu3btG4cWNmz57NmTNncHd3Z8iQIdSpUyfL41JSUkhJSTG8jo2NLYhwhRBC5IBGo6Fs2bK4urqSlpZm7HCEyDUzM7Nn7iF7xKhJmY+PDwcOHMi2zLx58yhTpozhFuXHH39M165d6dixI3/99RcNGzZky5YtdO3aNdPjZ86cyWeffZbnsQshhMg7JiYmefbBJkRRZdTJY0+fPk1wcHC2Zbp27Yq1tTXx8fHY2trSs2dPNm/ebNj/yiuvEBoayrFjxzI9PrOeMk9Pz3ybPFYIIYQQ4pHcTB5r1J6yxo0b07hx4xyVtbGxoXLlylSrVi3Ddi8vr2znHrOwsMDCwuKZ4hRCCCGEyG9FZkwZwNChQ1m9ejXTp0/H2tqapKQktm3bxnPPPZfjOh51DMrYMiGEEELkt0f5Rk5uTBaptS9TUlLo378/p06don79+pw/fx4PDw+2bNmCq6trjuoIDQ3F09MznyMVQgghhPh/ISEheHh4ZFumSCVlj1y4cIGbN29Svnx56tSpk6t5bfR6Pbdv38bW1jZXxz0aixYSEvJUY9GaNGny1Es8GevYZzm+JF4vuVYFc3xJvF4l7VoZq+2ier3kWhXutpVSxMXF4e7ujlab/Zz9Rer25SN16tTJdhqM7Gi12idmqtmxs7N7qjegiYnJUz9YYKxj8+L4knS95FoV7PEl6XqVtGtl7LaL2vWSa1X4287pfKpFapmlomzkyJFF7ti8ON4Y7RbFY59FUT1fuV4Fc+yzKKrvj5J2veRaFZ22n6RI3r40htw80irkeuWGXKvckeuVc3KtckeuV87Jtcof0lOWQxYWFkybNk2m18ghuV45J9cqd+R65Zxcq9yR65Vzcq3yh/SUCSGEEEIUAtJTJoQQQghRCEhSJoQQQghRCEhSJoQQQghRCEhSBgQGBnL06NEs9yuluHTpEv7+/qSlpT11meIgMTGRY8eOcevWrSzLhISEcP78eRISErIsEx0dzenTpwkLC8uPMAuNK1eucPTo0ScurxEaGsrRo0e5f/9+pvsDAwPx8/MjNTU1P8IsFJKTkzl+/Dg3btzIttzNmzc5f/486enpme6PiYnh9OnThISE5EeYhca1a9c4evRoltchLS2Ny5cv4+fnR0xMTJb1XLlyhbNnz5KSkpJfoRrd3bt38ff3z3Z5vbi4OE6fPk1wcPAzlSnqUlNTuXDhAjdu3ECv1z91GYCgoCDOnDlDUlJSfoVb/KgSzNfXV7Vo0UI5ODiorC7FtWvXVO3atZWzs7OqUKGCKlOmjDp06FCuyxR1d+/eVWPHjlVly5ZVlpaWasqUKY+V2bRpk6pVq5by8PBQderUUdbW1uqzzz57rNzXX3+tLC0tVc2aNZWlpaUaNGiQSk1NLYjTKDAbN25ULVu2NLy3kpKSsiz74MEDVaVKFQWo1atXZ9h369YtVa9ePeXk5KQqVaqkXFxc1N69e/M7/AJ1//599f777yt3d3dVqlQpNXbs2EzLBQUFqRYtWihHR0fVuHFj5eXlpQ4fPpyhzE8//aRKlSqlatasqUqVKqV69+6tkpOTC+AsCs727dtV27ZtlaOjowJURETEY2W2bdumypYtqypWrKjq16+vLC0t1fjx4zOUuXPnjmratKkqXbq0qly5snJ0dFTbtm0rqNMoEPv371dNmjRRZcqUUfXq1TO8v/R6fYZyv/zyi7KyslLVq1dX1tbWqmvXrio+Pj7XZYqyxMRE9f777ytHR0dVp04dVbZsWVW9enV14sSJXJVRSqnIyEjVsmVLZWdnp7y8vJS9vb1at25dQZ9SkVSik7Lp06ero0ePqt9//z3LpKxFixaqU6dOKi0tTSml1NixY5Wrq6uKi4vLVZmi7sSJE+rHH39UUVFRqnr16pkmZbNnz1YBAQGG1/v371empqZq/fr1hm179+5VWq3WkFjcuHFDOTs7qy+//DL/T6IAffHFF+rQoUNq3bp1T0zK+vfvryZPnpxpUtamTRvVpk0blZKSopRSavLkycrBwUFFR0fnZ/gFys/PT33zzTcqIiJCNWrUKNOkLC4uTlWqVEn169fPcC1v376tNmzYYChz8uRJpdFo1JYtW5RSSoWFhSl3d3f10UcfFch5FJRZs2apvXv3qh07dmSalOl0OlW6dOkM1/Ho0aMKUDt37jRs6969u2rWrJlKTExUSik1Y8YMZWNjo8LDwwvkPArCokWL1OnTpw2v/fz8lLW1tfLx8TFsO3/+vNJqtWrVqlVKKaXu3bunKlasqEaPHp2rMkVdWFiY+vbbbw2JZnp6unrjjTeUq6ur4UtzTsoopdSAAQNUvXr1DJ+BP/74o7KwsFA3b94s4LMqekp0UvZIVklZQECAAtTBgwcN2+7du6dMTEwMH545KVPcZJWUZaZ27doZvqEPGjRItWzZMkOZcePGqSpVquRpjIXFk5KyhQsXqubNm6u4uLjHkrLr168rQO3atcuwLTo6WpmZmaklS5bkd+hGkVVSNmfOHGVpaamioqKyPHbEiBGqfv36GbZ98sknys3NLa/DLBR27tyZaVKWmJiotFqtWrNmjWFbamqqMjU1VcuXL1dKPez51mg06o8//shwnLW1tZo7d27BnICRdOjQQQ0cONDwesKECapq1aoZynz99dfK3t5epaen57hMcXTy5EkFqH/++SfHZWJiYpSZmZlaunSpoUxaWppydHRUM2fOzPeYizoZU5YNPz8/ABo1amTY5uLiQoUKFQz7clKmpIqMjOTGjRtUrVrVsM3Pzy/DtQJo2rQp165dIy4urqBDNKqAgACmTp3KihUrMDV9fBnazN5bpUuXxsvLq8S9t/bt28fzzz+Pvb09586d4+rVq+h0ugxlsnpvhYeHc+fOnYIM16hKlSrFtGnT+Oyzz/D19WX37t28+uqrNG7cmD59+gBw7tw5lFIZrlepUqWoVatWsX5vJSUlcfHixRz9ToqJieH69es5LlMcnTp1CjMzM8qXL5/jMhcvXiQtLS3D9TI1NaV+/frF+r2VV4rkguQFJSoqCnNzc2xsbDJsd3JyIioqKsdlSiKlFG+99RYuLi68+uqrhu1RUVE4OTllKPvodVRUFLa2tgUap7EkJSXxyiuvMGvWLKpUqUJycvJjZR69fxwdHTNsL4nvrdu3b+Pg4EDDhg3R6/VERUVhZmbG8uXLadWqFfDk91bZsmULPG5j6du3L7t27WLSpEnY29sTHh7O7NmzsbKyAv7/vZXZ9SrO763x48eTlpbGu+++a9gWFRVFzZo1M5T79/smp2WKm6tXrzJ16lTGjx//2OdbdmVK6nsrr0hPWTbMzMxIS0t77Bt5UlIS5ubmOS5TEo0cOZLDhw+zdevWDImWmZnZYwnIoydzStL1mjFjBiYmJlStWpWjR49y/PhxAC5fvsy5c+eAh9cKeOypuJL43jIzM2Pv3r188803nD9/nlu3btGxY0f69etneCJV3lsPxcTE0Lp1a1q3bk1wcDDnz59ny5YtDB06lE2bNgH//97K7HoV12v12WefsWLFCjZt2pQhQc/J+6akvbdCQ0Pp3LkzrVu35ssvv8xVmZL43spLkpRlo0KFCiilMtz6ePT6UVdtTsqUNKNHj8bX15d9+/ZRu3btDPsqVKjw2DQYYWFhWFhY4OrqWpBhGlWpUqWwsbHhww8/5MMPP2Tq1KkArF69mrlz5wIPrxXw2PW6fft2iXtvVaxYkUqVKtGpUycAtFotb731FuHh4Vy5cgXI+r2l1Wrx8PAo8JiN5eTJk9y/f5/33nsPjUYDQLNmzWjcuDFbtmwBsn5vhYWFFcv31hdffMG3337L9u3badmyZYZ9Wb1vgAy/559UprgIDQ2lTZs21K5dG19f30yHVmRXpqS9t/KaJGXZeP755ylVqpThFxnA0aNHiYyMpGPHjjkuU5KMGTOGVatWsXfvXurVq/fY/o4dO7J79+4M821t3ryZdu3aYWJiUpChGtXUqVM5evSo4Wffvn0ATJ8+nV9//RV4+EFqa2ub4b116tQpbt++XeLeW507dyYyMjLDt+/Q0FDg4RhOePje2rt3L4mJiYYymzdvNvwfLSkeXY9H1wdAp9Nx+/Ztw7769evj7Oyc4b116dIlrl69WuzeW1999RUzZ85k27ZttG7d+rH9HTt25PDhwxnmctu8eTMNGjQw3ILLSZniICwsjLZt21KzZk3++OOPTHu2nlSmevXqeHp6Znhv3bx5E39//2L33soXxnzKwNiuXLmijhw5oqZOnaoAdeTIEXXkyBH14MEDQ5kvv/xS2draqgULFqjVq1erSpUqqf79+2eoJydlirqUlBTD9Slfvrx67bXX1JEjR9T58+cNZT766CNlYmKi5s6dayh75MgRFRgYaCgTGRmpPDw8VI8ePdSWLVvU2LFjlYWFhfr777+NcVr5JigoSB05ckTNmDFDAWrfvn3qyJEjWU5lkZSUlOmUGN9//72ysrJSPj4+au3atcrLy0v17NmzAM6g4KSnpxveK9WrV1f9+vVTR44cUX5+foYyqampqlGjRqpbt25q+/btatmyZcrT01O9/vrrhjKxsbGqcuXKqlOnTmrz5s1q8uTJytTUtNjNGXjjxg115MgR9d133ylAbdu2TR05ckTdv39fKfVwSoxWrVqpatWqqZUrV6odO3ao/v37Kysrqwz/FxcuXKgsLCzU7Nmz1bp161StWrVUu3btjHVa+WLOnDkKUF988UWG30n//r2VlJSkvL291QsvvKA2bdqkPv30U2ViYpJh+pCclCnqoqKiVLVq1VS1atUMv6/++5mYkzJKKbVixQplamqqvvnmG7V+/XrVsGFD1bx5c6XT6Yx1ekWGRqknTDVejH311Vfs2LHjse1z586lQYMGhte///4769atIyUlhQ4dOjB27NjHvh3kpExRFhERQa9evR7bXrduXebPnw/AsGHDuHr16mNlOnTowPTp0w2vQ0ND+frrr7l06RLu7u6MGTOGJk2a5FvsxvDdd98Zxu/82/fff0+zZs0e256amkq7du347LPPaN++fYZ9q1evZs2aNSQlJdG2bVvGjx+PpaVlfoVe4OLj4+nSpctj2728vFiyZInhdUxMDN9//z0nTpygdOnSdO7cmWHDhmXoYb179y5ff/01Fy5cwM3NjZEjR/L8888XyHkUFB8fH1avXv3Y9i+++II2bdoAD1femD9/PsePHycxMZFq1aoxevRovLy8MhyzYcMGfv/9d+Lj42nVqhUTJ07E2tq6IE6jQLz//vucPHnyse0NGjQwDBMAuH//PrNmzcLPzw8nJyfeeecd2rZtm+GYnJQpyi5fvszw4cMz3Td79mwaN26cozKPbNu2jSVLlhATE0OLFi2YNGkSdnZ2+RJ7cVKikzIhhBBCiMJCxpQJIYQQQhQCkpQJIYQQQhQCkpQJIYQQQhQCkpQJIYQQQhQCkpQJIYQQQhQCkpQJIYQQQhQCkpQJIYQQQhQCkpQJIYqN3377jcDAwKc+ftiwYTRu3JjGjRtnWM/2vy5evEjjxo0zLBf2rFJTUw1t9+zZM8/qFUIUHZKUCSGKhYSEBEaMGJFhfcLcunTpEk2bNmXBggXZrmkYHx/PmTNn0Ov1T93Wf5mZmbFgwQK6du3K+fPn86xeIUTRIUmZEKJY8Pf3R6vVUrdu3Weqx93dncaNGxf4MmkajYbGjRtToUKFAm1XCFF4SFImhCjSUlJSWLRoEdOmTcPS0pKZM2cSFhaWp20EBAQwcOBA2rRpw6hRo7h79+5jZa5fv867775Lq1at6NOnD2vWrMmwPzExkSlTptCqVSsGDBjAzp076du3Lxs2bMjTWIUQRZckZUKIIis2NpZmzZrx888/c/PmTapUqcLatWt5/vnnSUxMzJM2IiIiaNmyJaampkydOhUPDw+GDBmSoczly5dp0qQJDg4OzJgxgz59+vDBBx/w7bffGsoMGzaMtWvXMn78eAYOHMjEiRPZsmUL9+7dy5M4hRBFn6mxAxBCiKf1zjvvYG9vz969e2ncuDHDhg2jW7dueHl5sWfPHl5++eVnbmPOnDmUKVOG5cuXo9FoaN++Pbdv32bu3LmGMp988gl9+/blq6++Mmyztrbm9ddfZ9KkSQQGBrJu3TpOnjxJ06ZNAahYsSL169d/5viEEMWHJGVCiCLp7t27rF27luPHj6PX67l06RINGzakatWqmJmZERsbC8Dw4cMJDw/H3d2dRYsW5bqd06dP0759ezQajWFbx44dMyRlBw8exNbWlubNm6OUQilFUlISMTEx3LlzBz8/P6ytrQ0JGUC9evWyfZhACFHySFImhCiSdu7ciY2NDU2bNuXMmTOkp6dTv359bt++TVpaGl5eXgAMHjyYkJAQZsyY8VTtxMfHY2VllWGbtbV1htePnvzs1avXY8c7OTllWkdm9QghSjZJyoQQRVJYWBh2dnZoNBrOnj1L1apVsbW1ZenSpbi7u9O8eXMA2rVrR2ho6FMnZZUrV35s7rNLly5leO3l5UV4eDiNGzfOso6IiAiioqJwdHQEHo6Hu3379lPFJIQonmSgvxCiSCpfvjyhoaFcunQJPz8/GjZsSGBgINOnT+eLL77IcLvxWbzxxhvs2LGDI0eOAA9vm/74448ZyowZM4Zly5axdetWw7awsDC+/vprAFq3bk3FihWZOnUqSikApk+fTnp6ep7EKIQoHqSnTAhRJPXr148ff/yR5s2bo9VqMTc3Z+vWrYwbN45hw4blWTtt2rThww8/pH379lSoUIHIyEj69OnDtWvXDGWGDx9OdHQ0r776KjY2NpiZmaGUMgz8NzU1Zfny5fTt25f169ej1Wpp2rQpZcuWxdRUfg0LIR7SqEdf24QQoohJSUlh586d9O7dm2nTpvHqq69SuXLlx8qFhobSpk0bgoKCsq2vefPmhISEULZsWbZu3UrZsmUN++7fv8/9+/epUqUKqampXLp0iUaNGmXokUtLS+Pq1avY2NhQvnz5x+pPTU3l6tWruLu7Y21tjZ2dHRs2bODFF18kNTWV5557jvv37wMQHBz8lFdFCFFUSVImhCjSLl68SJ06dbh//36mTzN+8sknnDx5khMnTtC2bVuGDh1K3759M60rMDCQ+Ph4AOrWrZuns/pv376dOnXqUL58efR6PZMnT+bXX38lJCQEGxsblFKcOXMGAAsLC+rUqZNnbQshigbpNxdCFGlnz57F09Mzy+klevToQfPmzRk3bhwANWvWzLKuGjVq5EeIALi5udGuXTu0Wi2RkZHY2dmxadMmbGxsgP9fZkkIUXJJT5kQokiLi4sjOTkZFxcXY4fyREopgoODMTMzw8PDw9jhCCEKGUnKhBBCCCEKAZkSQwghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEJCkTAghhBCiEPg/yLwIh0tc9iwAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prog = prog() # Need to reset because we integrated it above\n", "T = prog.align_to_orbit()\n", "track_cs = spdf_both.streamTrack(n=3000, tail=\"both\", custom_sky_transform=T)\n", "\n", "# To overlay the progenitor's *orbit* in the aligned frame we have to\n", "# actually integrate it; `prog` is just initial conditions. The\n", "# progenitor sits in the middle of the stream so we integrate both\n", "# forward (to the leading-arm tip) and backward (to the trailing-arm\n", "# tip) — the second integrate() call extends the first rather than\n", "# overwriting it.\n", "tp_lo = float(track_cs.trailing.tp_grid()[0])\n", "tp_hi = float(track_cs.leading.tp_grid()[-1])\n", "prog.integrate(numpy.linspace(0, tp_hi, 201), lp)\n", "prog.integrate(numpy.linspace(0, tp_lo, 201), lp)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3))\n", "# `prog.align_to_orbit()` stashed the rotation matrix on `prog`, so\n", "# `prog.phi1`/`prog.phi2` work without re-passing T=.\n", "prog.plot(\n", " d1=\"phi1\", d2=\"phi2\", color=\"k\", lw=1.0, ls=\"--\", label=\"progenitor orbit\", gcf=True\n", ")\n", "track_cs.leading.plot(d1=\"phi1\", d2=\"phi2\", color=\"C0\", label=\"leading\")\n", "track_cs.trailing.plot(d1=\"phi1\", d2=\"phi2\", color=\"C3\", label=\"trailing\")\n", "ax.scatter([180.0], [0.0], color=\"k\", s=30, zorder=5, label=\"progenitor (today)\")\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "ba17f45c", "metadata": { "papermill": { "duration": 0.006879, "end_time": "2026-06-30T01:27:07.424146+00:00", "exception": false, "start_time": "2026-06-30T01:27:07.417267+00:00", "status": "completed" }, "tags": [] }, "source": [ "The `custom_sky_transform` is also exposed as a settable property on the `StreamTrack` (and on `StreamTrackPair`, which broadcasts the assignment to both arms), so you don't have to rebuild the track to look at it in a different frame — or to drop the rotation altogether (set to `None`):" ] }, { "cell_type": "code", "execution_count": 19, "id": "dd826b9d", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:07.438681Z", "iopub.status.busy": "2026-06-30T01:27:07.438471Z", "iopub.status.idle": "2026-06-30T01:27:08.704246Z", "shell.execute_reply": "2026-06-30T01:27:08.703355Z" }, "papermill": { "duration": 1.274217, "end_time": "2026-06-30T01:27:08.705167+00:00", "exception": false, "start_time": "2026-06-30T01:27:07.430950+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "before: None\n", "after : shape (3, 3)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Build the track without a rotation, then attach one after the fact —\n", "# the phi1/phi2 accessors and cov(basis='customsky') light up immediately.\n", "# (track_cs.particles is the both-arm sample from the previous cell; the\n", "# leading-only xv_dt from earlier in the tutorial would be wrong here.)\n", "track_bare = spdf_both.streamTrack(particles=track_cs.particles, tail=\"both\")\n", "print(\"before:\", track_bare.custom_sky_transform)\n", "track_bare.custom_sky_transform = T # broadcasts to both arms of the pair\n", "print(\"after : shape\", track_bare.custom_sky_transform.shape)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 2.5))\n", "track_bare.leading.plot(d1=\"phi1\", d2=\"phi2\", color=\"C0\", label=\"leading\")\n", "track_bare.trailing.plot(d1=\"phi1\", d2=\"phi2\", color=\"C3\", label=\"trailing\")\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "b118ea5561624da68c537baed56e602f", "metadata": { "papermill": { "duration": 0.007035, "end_time": "2026-06-30T01:27:08.719531+00:00", "exception": false, "start_time": "2026-06-30T01:27:08.712496+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Reusing samples for a smoothing sweep\n", "\n", "The expensive part of `streamTrack` is the orbit-integrated sample (and, on first call, the GCV per-spline `s` selection). The cheap part is the spline fit. To explore smoothing variants without redoing the expensive work, save the particles and pass them back as `particles=` to subsequent calls — only the bin-and-smooth step re-runs.\n", "\n", "There are three reuse handles depending on what object you have in hand:\n", "\n", "* `track.particles` (a single-arm `StreamTrack`) — the `xv` array the fit saw. Pass back as `spdf.streamTrack(particles=..., tail='leading')` (or `'trailing'`).\n", "* `pair.particles` (a `StreamTrackPair` from `tail='both'`) — concatenates the two arms' `xv` arrays in the leading-first order that `streamTrack(tail='both', particles=...)` expects.\n", "* `spdf.sample(tail='both', returndt=False, return_orbit=False, integrate=True)` — pre-sample without building any track at all; returns the same concatenated `xv` array.\n", "\n", "Two further knobs that take the cheap-refit path:\n", "\n", "* `track.smoothing_s` is the per-spline effective `s`. Passing it back as `smoothing=` (with `smoothing_factor=1`) skips the GCV step entirely and re-fits at exactly that smoothness.\n", "* `smoothing_factor=` is the simplest dial: rerun with the same `particles=` and a different multiplier.\n", "\n", "Below: the same `track_cs` sample fit at `smoothing_factor` $\\in \\{0.25, 1, 4\\}$ in the aligned frame, both arms. The factor `0.25` track follows individual bin means and the factor `4` track sands out the corners — the default `1.0` is a balanced fit." ] }, { "cell_type": "code", "execution_count": 20, "id": "938c804e27f84196a10c8828c723f798", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:08.734656Z", "iopub.status.busy": "2026-06-30T01:27:08.734404Z", "iopub.status.idle": "2026-06-30T01:27:11.136313Z", "shell.execute_reply": "2026-06-30T01:27:11.135412Z" }, "papermill": { "duration": 2.410586, "end_time": "2026-06-30T01:27:11.137135+00:00", "exception": false, "start_time": "2026-06-30T01:27:08.726549+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Reuse the both-arms sample from track_cs (built in the previous cell) —\n", "# pair.particles concatenates the two arms in the leading-first order that\n", "# streamTrack(tail='both') expects, so re-fitting only re-runs the splines.\n", "xv_dt = track_cs.particles\n", "tr_cs_rough = spdf_both.streamTrack(\n", " particles=xv_dt, tail=\"both\", custom_sky_transform=T, smoothing_factor=0.25\n", ")\n", "tr_cs_smooth = spdf_both.streamTrack(\n", " particles=xv_dt, tail=\"both\", custom_sky_transform=T, smoothing_factor=4.0\n", ")\n", "fig, ax = plt.subplots(figsize=(8, 3.5))\n", "for arm in (\"leading\", \"trailing\"):\n", " getattr(tr_cs_rough, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C3\",\n", " alpha=0.7,\n", " label=\"factor=0.25 (rougher)\" if arm == \"leading\" else None,\n", " )\n", " getattr(track_cs, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C0\",\n", " label=\"factor=1.0 (default)\" if arm == \"leading\" else None,\n", " )\n", " getattr(tr_cs_smooth, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C2\",\n", " label=\"factor=4.0 (smoother)\" if arm == \"leading\" else None,\n", " )\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend(loc=\"best\", fontsize=9);" ] }, { "cell_type": "markdown", "id": "1fa33ae5", "metadata": { "papermill": { "duration": 0.007043, "end_time": "2026-06-30T01:27:11.151842+00:00", "exception": false, "start_time": "2026-06-30T01:27:11.144799+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Non-uniform stripping times\n", "\n", "By default, `streamspraydf` draws stripping times uniformly between\n", "`-tdisrupt` and `0`. Real tidal streams, however, are stripped preferentially\n", "near pericenter passages of the progenitor's orbit, where the tidal field\n", "is strongest. The `stripping_pdf=` keyword lets you supply an arbitrary\n", "probability density over the progenitor time axis `t \\in [-t_\\mathrm{disrupt}, 0]`\n", "(`t=0` is the present day, `t<0` the past). Internally the PDF is\n", "converted to a CDF and inverted; samples are drawn via inverse-CDF\n", "transform.\n", "\n", "The PDF need not be normalized. It may accept and return floats,\n", "``numpy`` arrays, or astropy ``Quantity`` (input a time, output a\n", "``1/time``); the detection is the same as for\n", "``AnyAxisymmetricRazorThinDiskPotential``." ] }, { "cell_type": "markdown", "id": "25ad2350", "metadata": { "papermill": { "duration": 0.006974, "end_time": "2026-06-30T01:27:11.165939+00:00", "exception": false, "start_time": "2026-06-30T01:27:11.158965+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Example A: a custom Gaussian stripping window\n", "\n", "Suppose stripping was concentrated around 2.5 Gyr ago, with a width of\n", "0.3 Gyr. We pass a Gaussian PDF in ``Quantity`` form and sample the\n", "stream." ] }, { "cell_type": "code", "execution_count": 21, "id": "96f4819e", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:11.181799Z", "iopub.status.busy": "2026-06-30T01:27:11.181554Z", "iopub.status.idle": "2026-06-30T01:27:12.053812Z", "shell.execute_reply": "2026-06-30T01:27:12.052845Z" }, "papermill": { "duration": 0.881071, "end_time": "2026-06-30T01:27:12.054424+00:00", "exception": false, "start_time": "2026-06-30T01:27:11.173353+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.util import conversion\n", "\n", "ro_, vo_ = 8.0, 220.0\n", "\n", "\n", "def gauss_pdf(t):\n", " return numpy.exp(-0.5 * ((t - (-2.5 * u.Gyr)) / (0.3 * u.Gyr)) ** 2) / u.Gyr\n", "\n", "\n", "spdf_gauss = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " stripping_pdf=gauss_pdf,\n", " tail=\"both\",\n", ")\n", "numpy.random.seed(0)\n", "stream_gauss, dt_gauss = spdf_gauss.sample(n=600, returndt=True)\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.hist(dt_gauss * conversion.time_in_Gyr(vo_, ro_), bins=40, color=\"steelblue\")\n", "plt.xlabel(r\"$\\Delta t$ since stripping [Gyr]\")\n", "plt.ylabel(\"count\")\n", "plt.title(\"Gaussian stripping_pdf\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_gauss.x(), stream_gauss.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=6)\n", "plt.xlabel(r\"$x$ [kpc]\")\n", "plt.ylabel(r\"$y$ [kpc]\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "453d0ef1", "metadata": { "papermill": { "duration": 0.007383, "end_time": "2026-06-30T01:27:12.070379+00:00", "exception": false, "start_time": "2026-06-30T01:27:12.062996+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Example B: pericenter-driven stripping\n", "\n", "A common physical model is to bunch stripping into Gaussians centered on\n", "each pericenter passage. ``galpy.df.pericenter_stripping_pdf`` builds such\n", "a PDF from the progenitor and potential, given a width ``sigma``. The\n", "returned PDF can be passed straight into ``stripping_pdf=``, and it\n", "exposes a ``.pericenter_times`` attribute listing the pericenter times\n", "in internal units." ] }, { "cell_type": "code", "execution_count": 22, "id": "bd9ebfc1", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:27:12.086887Z", "iopub.status.busy": "2026-06-30T01:27:12.086683Z", "iopub.status.idle": "2026-06-30T01:27:13.688773Z", "shell.execute_reply": "2026-06-30T01:27:13.687788Z" }, "papermill": { "duration": 1.611432, "end_time": "2026-06-30T01:27:13.689734+00:00", "exception": false, "start_time": "2026-06-30T01:27:12.078302+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import pericenter_stripping_pdf\n", "from galpy.util import conversion\n", "\n", "ro_, vo_ = 8.0, 220.0\n", "peri_pdf = pericenter_stripping_pdf(\n", " prog, lp, 4.5 * u.Gyr, sigma=50 * u.Myr, ro=ro_, vo=vo_\n", ")\n", "spdf_peri = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " stripping_pdf=peri_pdf,\n", " tail=\"both\",\n", ")\n", "spdf_uniform = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "numpy.random.seed(1)\n", "stream_peri, dt_peri = spdf_peri.sample(n=600, returndt=True)\n", "numpy.random.seed(1)\n", "stream_uniform, dt_uniform = spdf_uniform.sample(n=600, returndt=True)\n", "peri_gyr = peri_pdf.pericenter_times * conversion.time_in_Gyr(vo_, ro_)\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.hist(\n", " dt_uniform * conversion.time_in_Gyr(vo_, ro_),\n", " bins=40,\n", " color=\"0.6\",\n", " alpha=0.6,\n", " label=\"uniform\",\n", ")\n", "plt.hist(\n", " dt_peri * conversion.time_in_Gyr(vo_, ro_),\n", " bins=40,\n", " color=\"C3\",\n", " alpha=0.6,\n", " label=\"pericenter\",\n", ")\n", "for tp in peri_gyr:\n", " plt.axvline(-tp, color=\"k\", lw=0.5, alpha=0.6)\n", "plt.xlabel(r\"$\\Delta t$ since stripping [Gyr]\")\n", "plt.ylabel(\"count\")\n", "plt.legend()\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_uniform.x(), stream_uniform.y(), \"k.\", ms=1, alpha=0.4, label=\"uniform\")\n", "plt.plot(stream_peri.x(), stream_peri.y(), \"C3.\", ms=1, alpha=0.6, label=\"pericenter\")\n", "plt.plot(prog.x(), prog.y(), \"yo\", ms=6)\n", "plt.xlabel(r\"$x$ [kpc]\")\n", "plt.ylabel(r\"$y$ [kpc]\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] } ], "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": 40.052837, "end_time": "2026-06-30T01:27:14.515324+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/streams/streamspraydf.ipynb", "output_path": "doc/source/tutorials/streams/streamspraydf.ipynb", "parameters": {}, "start_time": "2026-06-30T01:26:34.462487+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }