{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7fb27b941602401d91542211134fc71a",
   "metadata": {
    "papermill": {
     "duration": 0.013977,
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     "exception": false,
     "start_time": "2026-06-30T01:15:56.459718+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Integration and Plotting\n",
    "\n",
    "This tutorial covers integrating orbits in potentials, plotting their\n",
    "trajectories, accessing orbital quantities, and working with\n",
    "non-inertial reference frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "acae54e37e7d407bbb7b55eff062a284",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:56.498316Z",
     "iopub.status.busy": "2026-06-30T01:15:56.498075Z",
     "iopub.status.idle": "2026-06-30T01:15:58.810597Z",
     "shell.execute_reply": "2026-06-30T01:15:58.809431Z"
    },
    "papermill": {
     "duration": 2.325919,
     "end_time": "2026-06-30T01:15:58.811365+00:00",
     "exception": false,
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy\n",
    "from astropy import units\n",
    "from galpy.orbit import Orbit\n",
    "from galpy.potential import MWPotential2014, LogarithmicHaloPotential\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a63283cbaf04dbcab1f6479b197f3a8",
   "metadata": {
    "papermill": {
     "duration": 0.011356,
     "end_time": "2026-06-30T01:15:58.837765+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:58.826409+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Basic integration\n",
    "\n",
    "Use `o.integrate(ts, pot)` to integrate an orbit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8dd0d8092fe74a7c96281538738b07e2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:58.862084Z",
     "iopub.status.busy": "2026-06-30T01:15:58.861706Z",
     "iopub.status.idle": "2026-06-30T01:15:58.882661Z",
     "shell.execute_reply": "2026-06-30T01:15:58.881790Z"
    },
    "papermill": {
     "duration": 0.034623,
     "end_time": "2026-06-30T01:15:58.883668+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:58.849045+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integration complete. Final R = 1.0478229328266577\n"
     ]
    }
   ],
   "source": [
    "o = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 10.0, 10000)\n",
    "o.integrate(ts, MWPotential2014)\n",
    "print(\"Integration complete. Final R =\", o.R(ts[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72eea5119410473aa328ad9291626812",
   "metadata": {
    "papermill": {
     "duration": 0.011672,
     "end_time": "2026-06-30T01:15:58.907034+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:58.895362+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Automatic time determination\n",
    "\n",
    "You can pass just the potential and galpy will integrate for ~10 dynamical times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8edb47106e1a46a883d545849b8ab81b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:58.931761Z",
     "iopub.status.busy": "2026-06-30T01:15:58.931550Z",
     "iopub.status.idle": "2026-06-30T01:15:59.306565Z",
     "shell.execute_reply": "2026-06-30T01:15:59.305579Z"
    },
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     "end_time": "2026-06-30T01:15:59.307304+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:58.918829+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_auto = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "o_auto.integrate(MWPotential2014)\n",
    "o_auto.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10185d26023b46108eb7d9f57d49d2b3",
   "metadata": {
    "papermill": {
     "duration": 0.012245,
     "end_time": "2026-06-30T01:15:59.333267+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.321022+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Physical units for time\n",
    "\n",
    "When using `ro=` and `vo=`, you can pass time arrays in physical units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8763a12b2bbd4a93a75aff182afb95dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:59.359068Z",
     "iopub.status.busy": "2026-06-30T01:15:59.358844Z",
     "iopub.status.idle": "2026-06-30T01:15:59.407253Z",
     "shell.execute_reply": "2026-06-30T01:15:59.406439Z"
    },
    "papermill": {
     "duration": 0.062825,
     "end_time": "2026-06-30T01:15:59.408299+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.345474+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R at 5 Gyr = 7.704903471220543\n"
     ]
    }
   ],
   "source": [
    "o_phys = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "ts_phys = numpy.linspace(0.0, 5.0, 1000) * units.Gyr\n",
    "o_phys.integrate(ts_phys, MWPotential2014)\n",
    "print(\"R at 5 Gyr =\", o_phys.R(ts_phys[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30e0fbf8",
   "metadata": {
    "papermill": {
     "duration": 0.011786,
     "end_time": "2026-06-30T01:15:59.432187+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.420401+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Warning**\n",
    "\n",
    "When the integration times are not specified using a Quantity, they are assumed to be in natural units.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7623eae2785240b9bd12b16a66d81610",
   "metadata": {
    "papermill": {
     "duration": 0.011976,
     "end_time": "2026-06-30T01:15:59.456147+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.444171+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Parallel integration of multiple orbits\n",
    "\n",
    "Multi-orbit objects are integrated in parallel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7cdc8c89c7104fffa095e18ddfef8986",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:59.481345Z",
     "iopub.status.busy": "2026-06-30T01:15:59.481078Z",
     "iopub.status.idle": "2026-06-30T01:15:59.607917Z",
     "shell.execute_reply": "2026-06-30T01:15:59.607002Z"
    },
    "papermill": {
     "duration": 0.140383,
     "end_time": "2026-06-30T01:15:59.608576+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.468193+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All 100 orbits integrated.\n",
      "R shape at all times: (100, 1001)\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "vxvvs = numpy.column_stack(\n",
    "    [\n",
    "        numpy.random.uniform(0.8, 1.2, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.uniform(0.9, 1.1, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.uniform(0.0, 2 * numpy.pi, 100),\n",
    "    ]\n",
    ")\n",
    "os = Orbit(vxvvs)\n",
    "ts = numpy.linspace(0.0, 10.0, 1001)\n",
    "os.integrate(ts, MWPotential2014)\n",
    "print(\"All\", os.size, \"orbits integrated.\")\n",
    "print(\"R shape at all times:\", os.R(ts).shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b118ea5561624da68c537baed56e602f",
   "metadata": {
    "papermill": {
     "duration": 0.012482,
     "end_time": "2026-06-30T01:15:59.633337+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.620855+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Continuing integrations\n",
    "\n",
    "galpy supports *continuing* orbit integrations in both forward and backward time\n",
    "directions. For forward continuation, if the first time of the new integration\n",
    "matches the last time of the previous integration, the two are merged into a single\n",
    "continuous orbit. Backward continuation works similarly: if the first time of the new\n",
    "integration matches the first time of the previous one and goes in the opposite\n",
    "direction, the orbit is integrated backward and prepended.\n",
    "\n",
    "The two time arrays do not need the same number of points or spacing. The only\n",
    "requirement is that the starting time of the new array matches the appropriate\n",
    "endpoint of the existing one.\n",
    "\n",
    "Continuation is not supported when ``t`` is per-orbit (shape ``orbit.shape + (nt,)``); each per-orbit integrate restarts from the original initial conditions. It is also disabled after a ``bruteSOS`` or ``SOS`` call, which rewrite ``self.t`` into a non-standard (NaN-padded crossings) form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "938c804e27f84196a10c8828c723f798",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:59.658802Z",
     "iopub.status.busy": "2026-06-30T01:15:59.658598Z",
     "iopub.status.idle": "2026-06-30T01:15:59.863282Z",
     "shell.execute_reply": "2026-06-30T01:15:59.861961Z"
    },
    "papermill": {
     "duration": 0.218604,
     "end_time": "2026-06-30T01:15:59.863998+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.645394+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time range now covers t = -5 to 10\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_cont = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "\n",
    "# Forward integration\n",
    "ts_fwd = numpy.linspace(0.0, 5.0, 5000)\n",
    "o_cont.integrate(ts_fwd, MWPotential2014)\n",
    "\n",
    "# Continue forward\n",
    "ts_ext = numpy.linspace(5.0, 10.0, 5000)\n",
    "o_cont.integrate(ts_ext, MWPotential2014)\n",
    "\n",
    "# Backward integration from t=0\n",
    "ts_bwd = numpy.linspace(0.0, -5.0, 5000)\n",
    "o_cont.integrate(ts_bwd, MWPotential2014)\n",
    "\n",
    "print(\"Time range now covers t = -5 to 10\")\n",
    "o_cont.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "504fb2a444614c0babb325280ed9130a",
   "metadata": {
    "papermill": {
     "duration": 0.012667,
     "end_time": "2026-06-30T01:15:59.890661+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.877994+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Displaying orbits: various projections\n",
    "\n",
    "Use `o.plot()` with `d1` and `d2` to select projections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "59bbdb311c014d738909a11f9e486628",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:59.917589Z",
     "iopub.status.busy": "2026-06-30T01:15:59.917359Z",
     "iopub.status.idle": "2026-06-30T01:15:59.936638Z",
     "shell.execute_reply": "2026-06-30T01:15:59.935648Z"
    },
    "papermill": {
     "duration": 0.033778,
     "end_time": "2026-06-30T01:15:59.937306+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.903528+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "o = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 10.0, 10000)\n",
    "o.integrate(ts, MWPotential2014)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc5362ed",
   "metadata": {
    "papermill": {
     "duration": 0.012742,
     "end_time": "2026-06-30T01:15:59.962827+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.950085+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The default projection is $R$ vs. $z$ (meridional plane):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b43b363d81ae4b689946ece5c682cd59",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:15:59.989388Z",
     "iopub.status.busy": "2026-06-30T01:15:59.989139Z",
     "iopub.status.idle": "2026-06-30T01:16:00.169805Z",
     "shell.execute_reply": "2026-06-30T01:16:00.168896Z"
    },
    "papermill": {
     "duration": 0.195144,
     "end_time": "2026-06-30T01:16:00.170578+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:15:59.975434+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Default: R vs. z (meridional plane)\n",
    "o.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b0341ed",
   "metadata": {
    "papermill": {
     "duration": 0.012865,
     "end_time": "2026-06-30T01:16:00.198106+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.185241+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Face-on view in the disk plane (`x` vs. `y`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a65eabff63a45729fe45fb5ade58bdc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:00.225442Z",
     "iopub.status.busy": "2026-06-30T01:16:00.225203Z",
     "iopub.status.idle": "2026-06-30T01:16:00.363758Z",
     "shell.execute_reply": "2026-06-30T01:16:00.362726Z"
    },
    "papermill": {
     "duration": 0.153509,
     "end_time": "2026-06-30T01:16:00.364603+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.211094+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Face-on view: x vs. y\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "161fe1c0",
   "metadata": {
    "papermill": {
     "duration": 0.01328,
     "end_time": "2026-06-30T01:16:00.391489+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.378209+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Phase-space projections (`R` vs. `vR`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c3933fab20d04ec698c2621248eb3be0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:00.419731Z",
     "iopub.status.busy": "2026-06-30T01:16:00.419518Z",
     "iopub.status.idle": "2026-06-30T01:16:00.632696Z",
     "shell.execute_reply": "2026-06-30T01:16:00.631720Z"
    },
    "papermill": {
     "duration": 0.228381,
     "end_time": "2026-06-30T01:16:00.633407+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.405026+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Phase space: R vs. vR\n",
    "o.plot(d1=\"R\", d2=\"vR\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07fefe67",
   "metadata": {
    "papermill": {
     "duration": 0.015903,
     "end_time": "2026-06-30T01:16:00.663308+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.647405+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Sky coordinates can also be plotted when `ro` and `vo` are set. Here we plot Galactic `(l, b)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4dd4641cc4064e0191573fe9c69df29b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:00.696527Z",
     "iopub.status.busy": "2026-06-30T01:16:00.696309Z",
     "iopub.status.idle": "2026-06-30T01:16:00.917864Z",
     "shell.execute_reply": "2026-06-30T01:16:00.916830Z"
    },
    "papermill": {
     "duration": 0.239312,
     "end_time": "2026-06-30T01:16:00.918615+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.679303+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sky coordinates (requires ro/vo)\n",
    "o_sky = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "o_sky.integrate(ts, MWPotential2014)\n",
    "o_sky.plot(d1=\"ll\", d2=\"bb\", marker=\"o\", ms=5, ls=\"None\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "991595f7",
   "metadata": {
    "papermill": {
     "duration": 0.016475,
     "end_time": "2026-06-30T01:16:00.952817+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.936342+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "And equatorial `(RA, Dec)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8309879909854d7188b41380fd92a7c3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:00.987263Z",
     "iopub.status.busy": "2026-06-30T01:16:00.987024Z",
     "iopub.status.idle": "2026-06-30T01:16:01.210249Z",
     "shell.execute_reply": "2026-06-30T01:16:01.209290Z"
    },
    "papermill": {
     "duration": 0.241999,
     "end_time": "2026-06-30T01:16:01.211375+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:00.969376+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_sky.plot(d1=\"ra\", d2=\"dec\", marker=\"o\", ms=5, ls=\"None\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed186c9a28b402fb0bc4494df01f08d",
   "metadata": {
    "papermill": {
     "duration": 0.01691,
     "end_time": "2026-06-30T01:16:01.246582+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.229672+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Custom expression plotting\n",
    "\n",
    "You can use arbitrary expressions in `o.plot()` calls using `numexpr` syntax (requires the `numexpr` package). For example, `o.plot(d1=\"t\", d2=\"R*cos(phi)\")` will evaluate the expression and plot it directly. If `numexpr` is not installed, you can install it with `pip install numexpr`.\n",
    "\n",
    "Let's demonstrate both approaches:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cb1e1581032b452c9409d6c6813c49d1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:01.282195Z",
     "iopub.status.busy": "2026-06-30T01:16:01.281959Z",
     "iopub.status.idle": "2026-06-30T01:16:01.489244Z",
     "shell.execute_reply": "2026-06-30T01:16:01.488145Z"
    },
    "papermill": {
     "duration": 0.226388,
     "end_time": "2026-06-30T01:16:01.490038+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.263650+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Pf84///lPbN68GSkpKXj99dcxYcIEpKSkYNu2bRf9mc5nsVhw4sQJCoYkioIhIhnJyckoLS3t8nslJSUA2mdwAECn0+Hee+/Fli1bUFNTgx07diAnJwePPPJIv8fCfQ73uR31ZgbKFbGxsQCAuro6j35OZGQkQkNDkZmZye+kOf9r+fLl/PNbW1tx7bXXIjw8HA888AD+/ve/d7nDrLuxFhcXX1DYr7/1f7hgqOOMnUqlwp///GdYLJZOMw0dccUK8/Lyun3vxMREqNVqFBUVXfA97rGBAwfyj11++eVYt24dioqKUFhYiAEDBuCGG264IKCvq6uDTqcD4Aguc3Jy+FmUDRs2wGq14vrrr+/x577uuuuwZMmSHp8DOAKSl19+GdnZ2aiqqsLSpUvx+OOPu7UKO3eccjNJR44cQXBwMDIyMmAwGPDVV19h8eLFF8w0ne/mm2+GTqfDu+++i9OnT2P79u1YuXIlf3PAueqqq7B+/XqcOnUKJ0+eRHh4OFasWOHSbreO8vLyYDKZkJmZ2avXEXGgYIhIxjXXXIPq6uouL7jvvvsu1Go1f0FoaGjotD1YoVBg3rx5GDx4sFtaHHB3oO+88w4/MwI4TqgHDhzo9/t3NGrUKCgUCuzcuZN/jDHW7YW9r5RKJW677TZ89dVXyM3NveD7jY2NaGlp4f+9atUq5OXlYcOGDXj55ZdxySWX4He/+12Xsy/r1q3rNLP1yy+/4NixY7juuutcGpurW+sPHToEtVp9wQVtzpw5iImJweeff97l60aNGoXx48fj9ddfR2NjY6fv1dbWgjGGgIAAXH755diwYUOnY8hkMuHNN99ERkYGH8ScOXOm03tkZGRg0aJFaGlpgV6v7/S9pKQk6PV6HDx4kF9SGjt2LMrKyvDUU0/hsssuu+jMkCvOH1NUVBQf3Lqz7Qc3e7hr1y4AjmCI+//x0EMPobW1FU899dRF3yc8PBzLli3Dhx9+iLfeegsAsHLlSv77jDGcPXu202uGDBmC+fPnQ6/X83//xcXFyMrKwrlz53r8PG7GOD093YWfkogNFV0kkvHAAw9g165dWLZsGe677z6MHz8eBoMBWVlZ2LVrF9544w1+pqGkpATLli3D0qVLMWrUKAQEBGDHjh04evQoPvzww36PRaVS4d1338Xll1+ORYsW4cYbb0R9fT22bt2K5cuXY8OGDf3+DE5aWhpuvvlmPPfcc7BarYiPj8emTZuwYMECZGVlue1zAGD16tXIz8/HlClTcN9992HUqFHQ6/U4evQotm7dil9//RWBgYFYu3Yt3nvvPfz3v//FxIkTAQAff/wxxo0bh+uuuw67d+/mlxYBYMaMGVi8eDGuueYaVFZW4h//+AdmzJiBhx56yKVxff7553j66afx/fff91gU8ODBg13mtyiVSixZsgRvv/02cnJyulyi+eSTT7BgwQKMGTMG999/PxISEnD8+HFs2rQJJ0+ehEKhwGuvvYbZs2dj6tSpeOihhxAQEIC1a9fi3Llz2Lp1Kz9rcckll2D8+PGYMmUKBgwYgPz8fLz66qu44447LsiJuueee7B+/XosW7aMz1XbuHEj7r//fkRERGD9+vVuqZj9xz/+EdXV1Vi4cCFSU1NRWVmJV155BePHj8cll1zS7/fnjB07FtOmTcP7778Pu92OI0eOYODAgZg1axZ+++03vPfeexddIuPccccd+OSTT/D3v/8d8+fPR3JyMv89xhhmzJiBqVOnYsqUKYiJiUFubi7efPNN3HffffyS51dffYVHHnkEmzZt6rEC9vDhw6FWq/Gvf/0L119/PdRqNRYvXnzBTBQRJwqGiGRoNBps2bIF3333Hb777jt89dVX0Gg0mD59Ol577TUMHjyYf+64ceOQnZ2Njz76CHv37oXJZEJaWhpyc3M7Pe/8dhxxcXFYsmTJBRcsjUaDJUuWdHrt3LlzceTIEbz99tvYvn07RowYgS+++IK/SF7MwoULMWTIkAseHzdu3AUXv3feeQeTJk3Cr7/+ioqKCjz99NNISkrCzp07Oy01TZ8+vdPsDWfatGldFjqcOnVqpzthf39/fPvtt9i2bRu2bduGLVu2ICYmBhMmTMC//vUvBAYGorm5GTt27MCTTz6J++67j39tbGwsPvvsM7z00kv49ttvO114li5diunTp+ODDz6AwWDACy+8gDvvvLNTwDRnzpxu862GDBmCJUuW9JhTxC1xzJo1q8vv33bbbaiurkZxcXGXF+NBgwYhJycHH3zwAfbt24cTJ05gzJgxOHDgAH9BTE5OxtGjR7Fu3Trs378fNpsNixcvxqZNmxAfH8+/V25uLrKysvDLL79g7969iIuLQ1ZWVqd8F86kSZOwefNmrF69Gjt27IBarUZeXh7uvvtuPP744wgNDe32Z+6NTz75BD///DO2bt2KrKwsRERE4K9//SuuvfZa/v9DV+045s2b1+XvfcyYMd22rMjKysLjjz+OHTt2QK/Xo6amBgMHDsTPP/+MadOmuTzmuXPn4ne/+x2am5tx//33d/qeUqlEfn4+Nm7ciD179mDPnj188v+cOXP456Wnp2PJkiWIi4vr8bOGDBmC77//Hp9++ik++ugjhIWFubT0SMSBGrUS4mVTp06FQqHgqynL2bp167By5Urk5eVh6NChQg/H582cORMqlQo//vij0ENxi88++wwrVqzA8ePHXZ4NIsQTaH6PEA/R6/WwWq2dHtu3bx/27t0rioaUxLfY7XZkZ2eLon+Xqw4dOgR/f38MGzZM6KEQmaNlMkI8pLS0FLfccguuv/56JCcnIy8vD6+88gpf34iQ3igoKIDBYJBUMHT48GGMHj0aKpVK6KEQmaNlMkI8KC8vD59++ikKCwuh0+kwc+ZM3HTTTZ1yYeRs165dePXVV7FmzRokJCQIPRyf1tTUhLy8PIwYMaLHgoRicvToUQQEBFy0BhIhnkbBECGEEEJkjXKGCCGEECJrFAwRQgghRNYogdoFdrsdZ8+eRXBwsFuKmxFCCCHE8xhj0Ov1iI+P77FAJgVDLjh79uwFDSgJIYQQIg4VFRVITEzs9vsUDLmA27lRUVGBkJAQgUdDCCGEEFc0NzcjKSnpojswKRhyAbc0FhISQsEQIYQQIjIXS3GhBGpCCCGEyBoFQ4QQQgiRNQqGCCGEECJrFAwRQgghRNYoGCKEEEKIrFEwRAghhBBZo2CIEEIIIbJGwVAP1qxZg+HDh2PixIlCD4UQQgghHqJgjDGhB+HrmpubERoaiqamJiq6SAghhIiEq9dvmhkihBBCiKxRMEQIIYQQWaNgiBBCCCGyRsEQIYQQQmSNutaTTo5WNOL930qRXdEIxoDh8SG4aXIypqVHCT00QgghxCMoGCIAAKvNjtVbT2LtLyWdHi+pbcE3x85h2dgEvLBsFPz9VAKNkBBCCPEMCoYIrDY7Hv4sG98cOwcAWDY2AcvGJkClVGBrzjl8sr8Cm46cwekGI9bfPpkCIkIIIZJCwRDB37eexDfHzkGjUuDVFWNx2ag4/nvTM6Jw5eh43LX+IA6UNuDBT47g7VvGQ6FQCDhiQgghxH0ogVrmtuVU4h3n0tgr5wVCnClpkXjvtonwUyuxI6/qgqU0QgghRMwoGJKxplYLnt6cAwC4Z1YaLu8iEOJMSI3A01cOBwC8uC0fp2oMXhkjIYQQ4mkUDPVA6r3JXvouHzV6E9KiA/HowsEXff7Nk5MxZ0g0zDY7ntlyAtTJhRBCiBRQMNSDVatWITc3FwcOHBB6KG5XWtuCj/eXAwD+unQktOqLJ0UrFAo8d9UI+KmV2F1Yi5151Z4eJiGEEOJxFAzJ1Ks7C2GzM8wZEt2rGkIpkYG4ffpAAMB/dhTQ7BAhhBDRo2BIhoprDMjKPgMAeHTBxZfHznfPrDQE+qlw4mwztudWuXt4hBBCiFdRMCRD634thZ0Bc4fGYHRiWK9fHx7oh5XO2aH//ljs5tERQggh3kV1hmSmuc2CLw+fBgDcMWNgn9/ntumpeOvnUzha0Ygj5Q0YmxzuriESQgivuc2CtbtLsC2nEnUtJqREBmL5xCRcOy4RSiXVOyPuQcGQzGw4eBpGsw2DYoIwLT2yz+8TFaTFVZnx+OLQabz3aykFQ4QQtztxtgl3rz+EM42t/GO1BjMOlTVgc/YZvHHzeIToNAKOkEgFLZPJCGMMH+0tAwDcOi2131Wkb5uWCgD49vg5VDe39Xd4hBDCy6/U46Z39uFMYyuSIvzx8vJMfP3gDDx+6VAE+Knwa1Edblm7H20Wm9BDJRJAwZCMZFc04lRtC/w1Kiwdm9Dv9xuZEIpxyWGw2hmfkE0IIf2lb7Pg7g8OotFoQWZSGL55aCaWjk3AyIRQ3DcnHZ/fMxVhARpkVzTi6awcoYdLJICCIRnZeNgRsCwaEYsgrXtWSK8dnwQA+OLQadpmTwhxi2e2nEBZnREJYf5Yt3LiBUthIxNC8d8bx0GpADYcOo1dJ2lXK+kfCoZkwmy146tjZwEAV49LdNv7XjE6Dlq1EgVVBhw/0+S29yWEyNOB0npsPHwGCgXw6g2ZCAvw6/J50zKicOfMNADAXzbl0HIZ6RcKhmTih/xqNBotiAnWYnqG60UWLybUX4OFIwYAcMwOEUJIX9ntDM9sPgEAWDExCeNTInp8/iPzByMhzB9nm9rwoTMfkpC+oGBIJr4+dg4AsCQzHio3b0e9Zpwj/+ibY+dgs9NSGSGkb747UYncc80I1qnxx4VDLvp8fz8VHpqXAcBR88xgsnp6iESiKBjqgVQatZqsNvxw0tFH7NKR3Xem76vpGVEI9degrsWM/SX1bn9/Qoj0Mcbw+g9FAICV01IRGaR16XXXjEtEamQA6lvM2HCwwpNDJBJGwVAPpNKodU9xHQwmK2KCtRibFOb299eolFg4PBYAsC3nnNvfn4hHk9GCN34sxp3vH8SDnxzB5uwzNFtIXPJjQQ1OnG1GgJ+Kr3DvCrVKiTucuUPv7ymFnY430gcUDMnA9hOVAIAFw2M9VrH1slGOvKGtOZV0MpKpw+UNWPCfn/CPbSexI68KXx09i4c/zcYNb+9FQ4tZ6OERH7d+TykA4MZJyQgP7DppujtXj01AsE6N0jojfsiv9sDoiNRRMCRxNjvD985mqpeOHOCxz5meEYVgrRrVehMOlzd47HOIb8o924xb1u5Htd6EtKhA/L8rh+PBuRkI9FNhf0k9bnpnH+VzkG5V1BvxY0ENAODmKSm9fn2gVo3lExxlPj7ZT0tlpPcoGJK4I+UNqDWYEaJTY0pa39tvXIxWrcK8YTEAgG05lR77HOJ7WkxW3P3BQRhMVkweGIGvHpyB22cMxB8WDkHWqumICtIi91wz/rLpONWiIl369EA5GANmZEQhNSqwT+9x/URHMPRjfjXqDCZ3Do/IAAVDEvdjvuNua86QGGhUnv3fvWC4Y+aJpqnl5e9bT+J0QysSwvzx1i0TENihoOeg2GC8cfM4qJQKZGWf5WcpCeFYbXZ8dsBRluPGycl9fp/BscEYlRAKq53hq6Nn3TU8IhMUDEncz4WOYGjW4GiPf9bMwVFQKRUormlBeZ3R459HhFdYpcdH+xz1XV68djRC/S9smjkxNQJ3z3IkuD7/TS4VxyOd7CmuQ63BhPAADRY4N2L01dXOMh8bj1B7INI7FAxJWH2Lma8KPWuQ+wotdidEp8GEFEf3+h8LaHZIDv61vQB2BiwcHttjMc8H52ZgQIgOFfWt+OwA5XSQdtwszuWj4vo9e33VGEcdtWOnm1BRTzdkxHUUDEnY7sIaMAYMHRCMmBCdVz7zkqGOvCGurhGRroIqPbadqIRCAfxxUc8F8gL81Fg111Ec782fimG22r0xROLjTFYbtjl3uy4eE9/v94sM0mJiquOG7LsTlLtIXEfBkIT95NydMdsLS2ScS4Y4gqE9xXVoNdNyiJS979wKvWj4AAyODb7o868bn4iYYC3ONbVhczYtYxDgp/wa6NusGBCiw6TUnltvuGqRsz3Q9hOUn0ZcR8GQRDHGsLuwFoB38oU4g2ODkBDmD5PVjt9O1Xrtc4l3NbVasPGwI6C5dVqqS6/RaVS4bbrjuR/tK/fQyIiYcG2Crhwd57YaaFyvxANl9ailXWXERRQMSdTJSj1q9Cb4a1SY4Jw29gaFQoHZQxzBFxeMEenZdPg0Wi02DIkNxpQ01+/or5+QBI1KgeyKRpw42+TBERJfZ7HZ+Z2nl41yX5ughDB/jEoIBWPADtq9SFxEwVAPxNyb7LfiOgDAxIER0KpVXv3s6elRncZApGdTtiPp9YZJSVAoXL+jjwrS8nfuH9PskKwdKKmHvs2KyEA/ZLq5TRC3K41LFSDkYigY6oGYe5PtK3EEIr25a3cX7jNPVuppmlqCSmtbcLSiESqlAleM7n3S6w0THbVkvjl+jhKpZWxHnmNW6JKhMVC5uU0QlxrwS1EtrDY6xsjFUTAkQXY747vHTx7ouarT3YkM0mJYXAgAmh2Sos3OWaHpGVGIDnats3hHU9MjERWkRaPRgl+LaClVjhhj2HnSsYQ1z7kD1Z1GJYQiLEADfZsVR083uv39ifRQMCRBRTUGNBgt8NeoMCohVJAxTEt3BGF7KBiSnC1HHYnTS/q4FVqlVOAKZ2NfqhQsT8U1LSirM8JPpcRMD2zwUCkVfN2rnwso4CYXR8GQBO075QhAxqWEwU8tzP/i9mCITkRScqrGgOKaFmhUCiwY0fdqwVxNme25VVSRWoZ2OWeFJqdFIKhD+xZ34grNclX4CekJBUMStFfAJTLOpIERUCkVKKsz4nQDVYKVip3OPI/JAyMRoruw9YarxiWHY0CIDgaTlQJmGeJ2mnJ1yTxh5iDHjNPRikY0GS0e+xwiDRQMSQxjDPtOccGQ95OnOcE6DUYnOpboaKlMOnbkOfM8hvXvIqZUKvj32EXVymWlzWLjcxpneLBNUHyYP9KjA2FnwP7Seo99DpEGUQZDVqsVjY2NfXpdZWUl9Hq9+wflI07VtqDWYIKfWokxbt6u2ltT0hwzUwdK6EQkBU1GCw6WNQAA5g3tX0NNoD2g2pVXDcZYv9+PiMPh8gaYrHZEB2sxKCbIo5812XkO2l9CN2SkZ6IKhhhjePzxxxEaGoq4uDgkJydjy5YtLr/+3nvvRVxcHJ5++mkPjlJYXOAxNikMOo136wudjyuvz11Aibj9WFANm51hUEwQkiMD+v1+09KjoNMocbapDScrpXuDQjrjdhDOyIjqVY2qvuBmx/fTDRm5CFEFQ//5z3/w1ltv4aeffoLBYMDvf/97XHvttcjPz7/oaz///HNkZ2dj+PDhXhipcA6XOwIPb1ad7s645HAoFEBJbQtq9FRvSOy4PI+5btoKrdOo+AKdtFQmH78WOWZpuE0WnjTReUOWc7YZBpPV459HxEtUwdBrr72GO++8ExMmTIBKpcKjjz6KxMRE/O9//+vxdSUlJfj973+Pjz76CBpN35M+xeBIeSMAYGyS8MFQaIAGQ5wNPA+V0Z2ZmDHG+JpR3JZld5jrXCr7gYIhWWhqteCYs+6PO4+j7sSH+SMpwh82O8MhmqEmPRBNMFRTU4PS0lLMmDGj0+MzZ87E/v37u32dxWLBihUr8Mwzz2DIkCGeHqagmlotKKw2AAAyk8OEHYwTN0N1oJRORGJWXm/EmcZWaFQKt846znLu+MmuaEQL3blL3r5TdbAzIC06EPFh/l75zEmplDdELk5UwRAAREV1vpuIjo5GdXX3d5VPPfUUYmNjcc8997j8WSaTCc3NzZ2+xOBoRSMAICUyAFFBva8M7AncNPVB2s0hatyOwLFJ4Qjwc19dmKSIACSG+8NqZzhAx4jkcccRtzzqDZQ3RFwhmmCIS7SzWjvfPVqtVqhUXScK//TTT1i7di3+9re/obKyEpWVlbBarTAajaisrOz2s1avXo3Q0FD+KykpyX0/iAe1L5GFCTqOjjqu2RvNdOcvVtxFbKoH8jy43BFq3SJ9XEDC7TT1hknOYOhoRRNMVirwSbommmAoPt5RsbaqqqrT41VVVfz3znfq1Cn4+flhwYIFyMzMRGZmJvLz8/HRRx8hMzMTNlvXfxhPPvkkmpqa+K+Kigr3/jAecqTCsRQ1Nln4fCFOfJg/EsIca/bZzmCNiIsjX8iRPO2JpNdpzlmCX6n4oqQ1t1lwstIxyz7Rixs8UiIDEBHoB7PNjtyz4pjll5ufC2pQWKWH3S5ciQ3RBEOhoaEYM2YMvv/+e/4xq9WKnTt3YtasWfxjzc3NqKtz3GGuXLmSnxHivkaMGIG77roLlZWV3c4oabVahISEdPrydXY7a58Z8pF8IQ7lDYlbYbUBtQYzdBqlR3LRuADrxNlmNBrNbn9/4huOlDfCzhzBSUyIzmufq1AokOmcLc92phIQ38EYw4OfHMGC//yMEwIGq6IJhgDgL3/5C95//32sXbsWubm5uPvuu2G323Hffffxz3n00Ucxe/ZsAUcpjJK6FjS1WqBVK/mO8b5iQoojGDpIO8pE6aAziB2XHA6t2v21q2JCdMiICQJjwN5TtFQmVVze4IQU71fG54KhIzQ77XNK64xoarXAT63E0LhgwcYhqmDo2muvxXvvvYf//e9/uOyyy1BdXY0ff/wRMTHtdU9CQ0MvSLLuKCoqShQzPb3F/ZGPTgyFRuVb/1u5ZbujFY2CToOSvuG2JI9P8dzSxlRnDsk+SnKVLC5B3ptLZBxutpxmhnxPtjO9Y2R8iKDXLs+0C/agm266CTfddFO33//Xv/7V4+t37Njh7iH5hCPlvpcvxBkyIBhatRLNbVaU1LUgPdqzJfiJe3GFPMd5MBiakBqOD/aWUS0YiTJb7fwN24RU788MjU4MA+AoEVFnMCHSR3bbEuDY6SYA7f+PhOJbUwikz7gDaozAB1RXNColRiU4mrZSErW41BlMKKltAQCM82AhT27W6QTtOpSknLNNMFntiAj0Q3p0oNc/P9Rfw3/uUWfRR+IbjvPBUKig46BgSALMVjvynb2duKDD13BNY+lEJC6HncHroJgghAZ4rnp7Qpg/BoToHLsOaSlDctrzhcI93o+sO9ysOeUN+Q6bnfFJ0xQMkX4rqNLDbLMj1F+DpAjvVHXtLdrNIU7cstU4Dy+/KhQKjHfmkhympTLJ4XaSThRgiYxD5yDfU1xjQKvFhgA/FQZGCZs+QcGQBBw/45hmHJkQIthd18VwJ6K8c81os1DhM7Hg8oU8mTzNad91SMGQlDDG+JxGT+adXQx3Djpa0QjGaCOHL+CWyEbGh0KlFPbaRcGQBLQHQ765RAYAieH+iAz0g8XGBK0lQVxnsdn5Fi/euIhxW64PlzXQrkMJOdPYilqDGRqVAiPihdvJO2RAMPxUjo0cFfWtgo2DtPOlaxcFQxKQ4zygfDVfCOhc+OwoTVOLwslzepisjuXXtCjPJ70OiwtGgJ8KzW1WvuEwEb+jFY7z07C4EOg07q9T5SqNSokhAxx1bE6cbRJsHKQdFwwJnS8EUDDUozVr1mD48OGYOHGi0EPpltlqx8lzvp08zaE1e3E53iHIVnphClutUvLHCLc8R8SPqyPjCztdRyY4ZqZyKBgSnNVm54NSmhnycatWrUJubi4OHDgg9FC6xSVPh+jUSI4IEHo4PRpDwZCoCDGFzR0jx2jXoWRwM0NjfKCB9PB4x7Gcc4aW6oVWXNOCNosdgX4qr8w8XwwFQyLXMbL21eRpDncyLK83or6FelD5OiGWX8c4p8u5CygRN6vNzgfVmUnC3/2PdOYsnTjbREnUAuNueEZ4aeb5YigYErnjIsgX4oT6azDQeQfAXWiJbxKqdhVXhTa/Sk+7DiWgoMqxdTpYq0aawFunAUfekkqpQK3BjGq9SejhyBp3DRjtI9cuCoZE7rhzutcX1lxdwe0mOU7BkE8TqnZVXKgOUUF+nYqxEfHiiqyOTvKNu3+dRoUMZzsguiET1jHuRt4HkqcBCoZEzWKzI++c44IhhpkhoH2ctJvDt3HtXUZ5eflVoVDws0OUNyR+3M5RX0ie5nA3ZJQ3JBybnfHXrhHxvnHtomBIxIqqDTBb7QjW+n7yNIebwaITkW8Tsv4Ht82WK8hGxIvbLJHpA8nTnBHcOYhuyARTUutIntZplHzqhNAoGBKxk5WOgGJYXIhPTEG7grsrK683osloEXg0pDtC1q7iZhGoj524tZisKKhy5J35UjDEJ1HTMplguFmhIQNCBK88zaFgSMTynPWFhsYFCzwS14UF+PE5KLRU5puEbvzLzQydqm2Bvo0CZrHKOdMEO3PkgcWE6IQeDm+4Mxg629SGBtrVKgguGBruQ9cuCoZEjDughsUJV+K+L0bG0zS1LxO68W9kkBYJYf5gjBLtxSznrG/mMwbrNEgMdxzXJ51BP/EuX7x2UTAkYvzM0ADfia5dQXlDvi2Xv2sTrvHvmCTKGxK7Ez7Ud+p83Dkzv5LOQULgrl0UDJF+q9GbUGswQaEA329HLNqDIbrQ+aKTPnCi4naYcHeQRHy40ghCNmftDnfOzK+imSFva2gxo7K5DYBv3chTMCRSXPJ0amQgAvzUAo+md7iTI+WE+Cbu2BIyF224MxDLpWBIlNosNhTVOJrt+uLM0JABjuOLlsm8j7vBSYrwR7BOI/Bo2lEw1ANfbtTafvfuO5G1q6KCtIgLdSRUctOlxDcw1l7/Y9gA4e7ouSRXR/8iqkQtNicr9bDZGaKC/BATrBV6OBcY5pyRKKjUw26nthzelOsD55euUDDUA19u1MpdsIb62AHlKloq8001ehMajBYoFcCgWOHaJ8QEaxER6KhEXUBLGaLD/V2PiPfNnompUYHwUynRYrbhdEOr0MORFV/MFwIoGBKtvErfPKBcxe8oo2DIp3DH1cCoQOg0KsHGoVAo2pfKqC2H6PhyvhAAaFRKpMc4gv2TlETtVb64kwygYEiUzFY7iqrFuZOMMzKB6x5NJyJfcpKbcfSBExW3VEZ5Q+LD1RDzxXwhTvuOMpp59BaLzY6iakcu2XAfOMd0RMGQCJ2qNcBiYwjWqvl6GWLD3RUU1xhgslJOiK/gEkqH+UCQTTND4mSx2fnjyFdnhoD2YOgkLcN6TXGNAWabHUE+eO2iYEiE+HyhuGCfXI93RVyoDqH+GljtjL9TIMLzpVw0bmYo71wzJbmKCN8zUefbPROH0MyQ17WfX4J9roUUBUMi5At1YPpLoVDwd2a0o8w3mK12FDu3Q/tCi5e0qED4qR1JruX1RqGHQ1zELX0LWbTTFVzA72gaSrPT3uCrydMABUOilOtDd+/9wf1BnKScEJ/Qcfk1IUz4KWy1StkhYKZjRCw67iTzZbEhWoT6a2Cj2Wmv4ZZPfeFm63wUDImQLx9QvcHVSMqj3Rw+4WSHxr++ckdPxRfFh8vx4jZJ+CqFQkFLZV5W6MzPGhLre9cuCoZEptFoRo3eBAAY7IMHVG9wM0N55/RgjHJChMYFpb7U3oU7RmjXoTjY7YzfSebrM0MAMNhZS4urlk08p7nNgnNNjjYcg3zw2kXBkMgUVDn+aBPC/BGkFVcbjvMNjg2GUgHUt7QHeEQ4hc5jy5fu2mj7s7iU1xvRYrbBT61EenSg0MO5qEExjuOLO/aJ53CzQtzypK+hYEhkCp31hYSsDuwuOo0KA6McJ0xaBhEelzfhS3dt3OznmcZW6mMnAtwS/uDYIKhVvn95yXAWXiymmSGP427kfXVFw/ePVgH5Ym+yQh8/oHqLT6KmO39BtZptqGhw7NjiLhC+IDywvbdVISW5+jy+ya9INncMch7rZXW0o8zTuLY6vnrtomCoB77Ym4w7oAb50AWrP9rzhmhmSEjFNQYwBoQHaBAZ6Cf0cDoZ0qGpJvFt3HKmWCrjRwdrEaxTw86A0roWoYcjae3BkG9euygYEhluqtGXljL6g9tRdpJqDQmKXyKL8Z2dZBzuTjKfKgX7PH6nq0hmhhQKBX9jSXlDnuXr1y4KhkSkocWMWoMj0VhqM0PUlkNYXDCU7oPHFT8zRMGQT2s12/jZFTGV/eCWhanWkOd03AXtq9cuCoZEhMuZSAjzR6DId5JxBoS0t+WgOzPh8In5Pnii4na35VfS8eHLCqr0YAyICvJDVJBW6OG4jNtRRsGQ53TcBR2s872dZAAFQ6Li62uufaFQKNqXyignRDCF/E4y3zu2uDHVGkyoM1AJBl8ltuRpDs0MeR63xO2L5xcOBUMiUsgfUOKZgnYFd/KkJGphmK12lNX53k4yToBfe8NPyhvyXdzNjC8V7XQFd8yX1LbAarMLPBpp8uXK0xwKhkSET0DzwQtWfwynHWWCKq1rgc3OEKRVY0CITujhdIlLoqYdZb6Lb+cismAoIcwf/hoVzDY7NQT2kAIR3MhTMCQiXF6Hr9Zp6Kv2BFmaphYCl6uVERPkczvJOEMGOG4A8ukY8UmMMX6ZzBc7kvdEqVQgzVktm5bKPKO94KLv3shTMCQS9S1m1BrMAHxzKaM/uJ+n1mBCfYtZ4NHIT/u2et89rviZIVom80k1ehMajBYoFeI8P/Hb6ykYcjvuvK7w8WODgiGR4NZcpbSTjBOoVSMpwh8AXeyEwM04+vKJqmPhRWrq63u4fKGBUYHQaVQCj6b3+LYcFAy5HXdOTwoPQICf7167KBgSiYJq359m7I8hdOcvmCIf3knGSYsKglqpgN5k5TtfE98h1p1knAyuYSsFQ25XKIIlMoCCIdEo9PG+Lv01iIIhQVhtdpyqdRTK4+qt+CI/tZJv6ksd7H2PWJOnOR0bttrtNPPoTvkiSJ4GKBjqkS81ahVDNn5/8DNDVFjPqyoaWmG22qHTKJEQ5i/0cHrEzVxRkqvv4dtwiCx5mpMSGQC1UgGj2YYqPc08ulOhSOrjUTDUA19q1Fok8WWyjv2nKCfEe7jjKi0qCEqlb+4k42REUzDkiyw2O///RKwzQxqVkq9ldaqGGra6U3GN7888AxQMiUJDh51k6dHSDIbSogOhVABNrRa+hw3xvFM1vtuT7HzcGItqKBjyJaW1LTDb7AjSqn1+drEn3DIst2xM+q++xczvEObKF/gqCoZEoLhGej3JzqfTqJDK5YRQ3pDXlDhP/GlRvn2iAjq3TaDZQ9/BLZENivX92cWecBfrEpoZcpuO1y5f3kkGUDAkCtwB5euRdX8NjuEaclIw5C3ckoAYjq306CAonLOH3EwpER63A8uXWy24YmCUI9g+VUszj+7ClSoQw/ml16Ga3W7H4cOHkZ2djYaGBoSGhmLkyJGYNGkS1GrfjvzEiltzleoSGWfwgGBsO1FJ3eu9iFsSGCiCmSGdRoXEcH9U1LeiqNqA6GDxdEaXMi5B1pfrVLmC+xsooWUyt+Fu5MVw7XI5eqmvr8d//vMfvP3226iqqkJoaChCQ0Oh1+vR0NCA8PBw3H777fjDH/6AuLg4T45ZdrjoOl0E0XV/DOmQRE08r7nNglpnF3gxBEOAI4m6or4VRTUGTE2PFHo4BO0zQ2Iv+8GdXyvqjTBZbdCqxVc80tdwN/JiCJRdWibbtWsXhg4diqNHj+KVV17BuXPn0NjYiLKyMtTX16OmpgZr165FeXk5Ro0ahS+//NJjA25tbcWmTZvw5ptv4tdff3XpNYWFhfjggw/wySefoKSkxGNj8xQxRdf9we2UK6QdZV7B5UZEB2sRrNMIPBrXUKVg32K22lHK1akS+U7X6GAtAv1UsDNHQET6r6haPNcul2aG1Go1fvjhB4wYMaLL70dFRWHZsmVYtmwZSkpKUFBQ4NZBciorKzF79mz4+fkhMzMTf/nLX3DllVdi3bp1XT6fMYarr74aeXl5mDRpEoxGI26//XY8++yzePzxxz0yRnczWW2oaGgFII4dP/2RGhUIjUqBFrMNZxpbkRgeIPSQJK1EREtknI7F8YjwSutaYLUzBGvVGBCiE3o4/aJQKJAWHYTjZ5pQXNPCV6UmfdNmsaGiwRFUpsf4/jnGpWBo1KhR0GpdW58fOHAgBg4c2K9BdeeJJ56Av78/9u7dC51Oh2PHjmHs2LFYtmwZlixZcsHzGWO49dZbsWTJEr4b96effoobb7wR11xzDTIyMjwyTncqrzPCZmcI0qoRI/EcCY1KifToIJys1KOgSk/BkIdx+UJiWn7tuKOMCI8rBpsRG8SfY8VsYFQgjp9porwhNyitawFjQIhOjegg3792ubRMtnbtWgQFBeHZZ5/FDz/8gFdffRU///wzmpqaPD0+nt1ux5dffonbbrsNOp3jDmT06NGYPn06Pv/88y5fo1QqsXTp0k5/pHPnzgVjzGOzV+7WvkQWKImTzcW0t+Wgi52ncTWGRDUzFO04Ps41tcFgsgo8GsL3nZLILAq36+kUzTz2W3G182YrRhyBskszQ/fccw+mTp2KwMBAlJSU4M0330RBQQHsdjtSU1ORmZnJf02ZMgUxMTFuH2h5eTkMBgOGDh3a6fGhQ4f2qkJ0VlYW1Go1MjMzu32OyWSCydRe+K+5ubnX43WXYn7rs7SXyDhDYoPwFRzdyYlntS+TiefYCg3QICpIi1qDCcXVBoxJChN6SLJWWN1eY0gKaEeZ+4gpXwhwcWYoODgY06dPR2ZmJpYtW4bc3FwYDAbs27cPTz31FOLj4/H999/jd7/7HV588UWPDFSvd/zRhYWFdXo8PDyc/97FHD9+HH/84x/x+OOPIz4+vtvnrV69mt8tFxoaiqSkpD6Pu7/kspOMM4h2lHkFY6y94KLIjq0MZ/4BLZUJj5sZkkrPxDTnjQEFQ/3HrWqIYScZ0Ic6QxydToeJEyd2amLKGENLi2cOooAAR/7I+YFPc3Mz/72eFBQUYOHChbj66qvx/PPP9/jcJ598Eo8++minzxAqICqulUeNIQ63vb6o2gCbnUEl4oq2vqyq2QSj2QaVUoEkkeVmZcQEYe+pemrLITCz1c4HDYNEcsG7mIHOG4NagxlNrRaE+otjl6UvEtsu6D4FQydOnMDOnTsRHByMUaNGYeTIkdDpdFAoFAgK8swPnpycDK1Wi+LiYixYsIB/vLi4GIMGDerxtQUFBbjkkkuwYMECvPvuuxddv9RqtS4njHsSYwynuJkhiZxsLiYpIgA6jRJtFjvK642iymcRE67KbnJEAPzU4ipETw1bfUOZcydZkFaNuFBx7yTjcBtVqvUmlNS2IJOWYfvEbmd8dXuxrGr0+iyYl5eHsWPH4rXXXsNzzz2HSZMmISgoCCNGjMBNN92E7du3e2Kc0Gg0uPzyy/Hxxx/DbrcDcOQR/fjjj1i6dCn/vB07duDDDz/k/11UVIRLLrkE8+bNw7p166BUiufEX6M3QW+yQqkAUiLFdffeVyqlgr+TKKSlMo/hTlRiDDbTqdaQT+A2OWSIJEHWVZRE3X9nm1rRarFBo1IgOUIc165ezwz98MMPmDdvHrZu3QrAsYSUnZ3NfxUVFWHhwoVuHygA/OMf/8C0adNw2WWXYfLkyfj4448xa9Ys3HjjjfxzPv30U+zduxc333wzWltbMXfuXFitVmRmZuLVV1/ln7dgwYJu6yb5Cm4ZICkiQFbVUDNignDibDOKagzwzJFExFhjiMPlIJTVG2G22kU3syUVXPL0YIkkT3MGRjmWYSlvqO+4jT+pkYFQq8Tx99nrYCgmJgYJCQn8v0NCQjBr1izMmjXLrQPryqBBg5CTk4OPPvoIVVVVePbZZ7FixQqoVO2BwoIFC/hlM7vdjquvvhqAYxapI1eTroUkl55k5xtEtWQ8TqzJ0wAwIESHIK0aBpMVZXUtkkneFRs+eVoi2+o56fzMEAVDfVUssp1kgIvBUEFBAVpaWjBixAhcfvnlWLNmDerr6xEREeHp8V0gNja2U3Lz+ZYvX87/d2BgIF5++WUvjMoz5LaTjEOF9TxPjDWGOAqFAunRgTh6uglF1QYKhgQitW31HO5v4hTNDPUZnzwtgsrTHJfmr7Zv345x48YhKCgIU6dOhdlsxtSpU7FhwwavFl6Um1My20nG6dh/inqUuZ/ZaudbvKSJqMZQR+nUlkNQFluHnWQSC0a5mm4ltQbY7XT+6QvuRlYs2+oBF4OhBx54AHV1ddi2bRtuvfVWpKenQ6vV4qabbkJYWBjS0tJw9dVX4//+7/+QnZ3t4SHLR7HMdpJxUiIDoVY6epSda2oTejiSU9HgaPES4KdCbIjwuyb7Io3u3gVVVtcCi40h0E+FeInsJOMkhvtDpVSgzWJHtd508ReQC4gxxcPlnKGIiAjMnTsXc+fO5R8zmUw4ceIEnzy9Y8cOAOixujNxTauzWSkgrgPKHTQqJVKjAlFUbUBRtQHxYf5CD0lSOu4kE+suIO7unfI6hMHvJIsNFu0x1B2NSonEcH+U1RlRWteCARIL9jytyWhBrcERRIqpc0Kfiy4Cjno848aNw7hx49w1HuLE1YEJC9AgItBP4NF4X0Z0EIqqDSisNmDW4GihhyMpJbXizRfidNz+zBiT3AXZ17X3JBPPxa43UiMDHcFQbQumpEUKPRxR4XZBx4U6NjqIRZ/2vL3zzjsYOnQogoKCkJaWhvvuuw/FxcXuHpusiXGa0Z0oidpzSmqNANqXmsQoNTIQCgXQ3GZFfYtZ6OHIToFEk6c5qc66bqV1RoFHIj5iqzzN6XUwtG/fPtxzzz24/PLL8fbbb+Pee+/FyZMnMWrUKGzYsMETY5SlUzXy3EnGyaDCeh5TVucItFMixXts6TQqxIc6lk+pHoz3FUmsJ9n5uL8N7m+FuO5UjTjLdvR6DuvgwYO49tpr8e9//5t/7E9/+hO2b9+O6667DmPHjkVGRoZbBymUNWvWYM2aNbDZbF7/bJoZclahrvb9elBiU+a8202NEkdl2O6kRQfiTGMrTtW0YEKq98t8yJXFZueX8aXSk+x83N8GzQz1HrcML7aZ517PDKWmpnbZt2vhwoW4+eab8cUXX7hlYL5g1apVyM3NxYEDB7z+2dyMiJgS0NwpPToICgXQYLSgzkA7OtylzWLD2SZHYr6YZ4YA2lEmlLI6I7+TLEGimxs6zgxReY/e4avbi+za1etgaNGiRSgvL8e+ffsu+F5oaCjMZlq/7y/GmKgrBLuDf4cTLeUNuc/pBiMYczSkjBR5Yj5fHI9qDXlVUYcbNakmrieG+0OpAIxmG2roZsxldjvjZ9MGiuxmq9fB0Ouvv478/HzMmDEDt912G7KyspCdnY2PP/4Y69evx3XXXeeJccpKVbMJrRYbVEoFksLFvZTRH3xbDrrYuQ23RJYSGSD6C1l7cTyaGfImLkFWTAX1ekurVvElPcpoqcxlZ5taYbbaoVEpkBAurlnDXucMLVmyBEqlkq8t9Omnn8JkckTOY8eOxaeffooxY8Zg9OjRSE9PF/0JVwjcyT0x3F/WTSgzYoLwQ34Nv42X9F9ph2BI7LiZobI6RxFJlZLONd4gh2AIcBxfpxtaUVrbgomUk+YS7tqVEhkour/HXgdDAwcOxEMPPcT/22KxIC8vjw+Odu/ejddffx319fV47LHH8OKLL7p1wHLAHVCpIptmdLcMarngdlLYScZJCHPcLJitdpxpaEWyBAI8MWjf3CH+Y6gnKZEB2F0IlNKOMpeVivja1e+KSBqNBqNHj8bo0aNxyy238I+Xl5dT/lAfcX98Yi6K5w5Ua8j9uJmhVAkEDkqlAgMjA5FfpUdxrYGCIS9gjOGUCDuS9wV3QacdZa47JeJcV5fWYHbv3o2TJ0+69IalpaX47rvvkJycLJkt9t7GZ+PLPRiKdtQwOdfUBn2bReDRSEO5hGaGgPaTbgm15fCKGr0JepMVKqVC8sEn1RrqPTFfu1wKhiwWC2bPno1rrrkGmzdvRn19fafvNzY24uuvv8YNN9yA8ePHw2CgO/n+EPMB5U6hARpEBzvKOBTTxa7fLDY7Tju71YtxGrsr/I6yWjrneAO3mSE5IgBatUrg0XgWN3taVmuk7fUuEvMymUvB0Ny5c5Gbm4uhQ4fizjvvRFRUFKKjo5GRkYHY2FhERETg5ptvxoABA3D8+HFcc801nh63ZNnsDOXc1kSZB0OAo0cZQEtl7nC2sRVWO4NWrURMsDi71Z+PGrZ6l1zyhQAgKSIACgWgN1HLF1eYrXZUOG+2xLhM5nLOUGRkJP72t7/hueeew8GDB3H8+HE0NDQgJCQEI0aMwOTJk+HnJ+66Jb7gbGMrzDY7/FRK6tYOR97Qb6fqqBK1G3TcSaYU2U6P7nA3DLS93juKZZIvBDhavsSF6HC2qQ2ldUZEBknjBsJTKhocuzoD/FSivNnqdQK1Wq3GlClTMGXKFE+MR/a4k3pyZIDotiZ6AtcIknqU9Z+UdpJxuBmKc01tMJqtCPATT5dsMRJrE86+So0KxNmmNpTVtWB8SrjQw/FpHZfIxFhSp09FbAoLC/HWW2/hk08+QU5ODqxWq7vH5RPWrFmD4cOHY+LEiV77TMoX6oyWydynTEI7yThhAX6IcFbSptkhz+NnhmLkcX5KoR1lLmtvwyHOY6PXt1EFBQUYPXo0YmJiYDabUVVVBa1WixEjRiAzMxM333wzLrnkEk+M1etWrVqFVatWobm5GaGhoV75TAqGOuO215fXG9FmsUGnkXbSpidxM0PJEpoZAhx/K/UtZpyqacGIeO/8ncpRi8mKs01tAIC0KJnMDDlvHEop0L4o/tol0vNLr2eGdu7ciVmzZqGsrAyVlZWoqqrCli1bsHz5crS2tuLYsWOeGKdscDWGxJiN7wnRwVqE6NSwM7rz7y8p1RjqKI3yhryC+/1GBvohXOR97VxF2+tdJ/Yb+V7PDEVFRSElJYVfE4yJicHChQuxcOFCtw9OjsR+QLmbQqFARkwQDpc3oqjagGFxIUIPSZTsdobyei4YktaxxU3LU8NWz5JbvhAApEY5Z4ZomeyixL5M1uuZocsvvxzZ2dloamryxHhkzWxtrwNDwVA7asvRf5XNbXwDxbhQndDDcStuyYZmhjxLbvlCgKOeEgA0tVrQaKTt9d1pNdtwzrmEKptlsu3bt8Pf3x/Tp09HVlYWFVh0I25ror9GhdgQ8W1N9BSulgwVXuw7bvk1KTwAapW0mv+m8TNDLVQcz4PaawzJZ2YowE/Nn4tpdqh73PklLEAj2iXUXp8Vw8PDER4eDoPBgGXLliE0NBRDhw7FDTfcgBdffBE5OTmeGKcs8FsTo8S5NdFT0vnCehR49xW3k0yKLRRSItuL49Ua6O7dU+S4TAa0LytT3lD3pJDe0eucoTlz5mDOnDkAgKamJhw9epT/2rBhAwwGA0aOHOnuccoCd0ClifiA8oT0Dnf+djuTTMFAb5JyYr5WrUJiuD8q6ltxqsbAt3Ah7mOzM74JJ7dsLRepkYHYV1KP0lqaGeqO2HeSAS4GQ4cOHcKpU6cwZcoUJCUl8Y+HhoZi1qxZmDVrlscGKCcl/MyQ9O7e+yMpIgAalQKtFhvONbchgSpz91pZbXv1aSlKiwpCRX0rSmpbMDktUujhSM6ZhlaYrXZo1fKrjJ/iPB/TzFD3ZDMzdOLECfz+97/H7bffjqFDh+Lzzz9HZmYm/zVkyBCoVFT/pb/aDyh53XldjEalREpkIIqqDSiuNlAw1AdlEt1JxhkYFYifCmpQQhcsj+CWyAZGBcquMj73N0PHVvfEvpMMcDEYuuWWW3DLLbfAZDIhPz8fBQUFOHr0KNavX4+qqir4+/tj5MiRyMzMxE033YTZs2d7etySVMoHQ9K8e++PtChHMHSqxoBZg6OFHo6oMMY6tOKQ5rHFJVGXUJK9R/D5QjJbIgPad5SVUwJ1t8TcrZ7Tq5whrVaL0aNH48UXX+Qfq6ysRHZ2No4ePYrs7GxkZ2dTMNQHbRYbX91VzAeUp6THBAG5VbSjrA9qDCYYzTYoFUBiuDSDIWrY6llyTZ4G2m8g6lrM0LdZEKzTCDwi39LUakFdi2PjguSXyc7322+/IT4+HikpKRgwYAAuvfRSXHrppe4em6xwCa4hOjXfa4m0S4+mWkN9xe0kiw/zh59aWtvqOe07fhzlKeS2lONpRXy3evFe7PoqWKdBVJAfag1mlNUZMTKBWr50xM0KxQRrEagVb6PkXp8Zq6ursXz5cv7flZWVuPTSS7FkyRLJteLwZqPW0g4JaLSt/kLcSZiCod5rb9Aq3QsZF+iZbXacbWwVejiSI8caQx1xS2VltFR2ASkkTwN9LLo4bdo0pKSkAABefPFFVFZWIiEhAfPmzUNzc7PbBymUVatWITc3FwcOHPD4Z52SyAHlKVzhxapmEwwmq8CjERep5wsBgEqp4HuunaKlMreqbzGj3rkMkibDmSGg/UailJKoL8D9vYn92Oh1MGQ2mxEWFsb/e9OmTfjvf/+L//73v5g7dy6+/PJLd45PNjoWXCQXCvXXICrIUT+Gii/2TqkMZoaADnlDdHy4Fff3lhDmjwA/8S6D9AdXrJSSqC8kheRpoA/B0Pjx4/Hdd9+hubkZ3333HfR6PaZOnQoAGD16NEpLS909RlmQylSjJ9FSWd9wM0NSrD7d0UDqUeYR3N+b2O/8+4NmhronlWtXr4OhMWPGYMGCBUhMTMRVV12Fu+66i89xKSgo4JfPSO+UOIviif2A8iRuW29xNZ2QekMqd24Xw1Vup2Uy95J7vhDQvsRcXk8zQx0xxto7J4g8WO7TnOdbb72F22+/HTU1NbjiiisAAOXl5fjqq6/wz3/+060DlAN9mwW1BhMAWibrCd+jrJZmhlzVaDSjuc2RY8UlgUoVV/CNZobcq71bvZyDIcexda6pDW0WG3QaKjIMALUGMwwmK5QKR6cAMevzAvCUKVM6/dvPzw9ZWVmIiYnp96Dkhut5ExXkhxCqYdEt7s6DZoZcx+ULDQjRwd9P2idwblb1TGMrXbDcqL3GkHxv1MIDNAjWqaFvs6K83ojBscFCD8kncDceCeH+0KrF/ffmtqIjAwYMoB5lfVQi4Saa7pQR3Z4TYrMzgUcjDnLJFwKAyEA/BOvUYIyWM9zFZLXxv8sMGS+TKRQKfqmMtte3K6nl2rSI/9iQZgU2keFaCFC+UM/iw/yhddaSOd1AJyRXcCfuFJFPYbtCoVC05w1RpXK3KKszws6AYK0a0cFaoYcjqBS+sCcdWxw+11UCN1u9CoaMRiOqqqoAAPX19WhsbPTEmGSH26FA+UI9UykVfMBIFzvX8MGQBE5WruCOD9r14x4d84XkXgw2lWaGLtA+MyT+a1evgqGCggI89NBDAICnn37aK8UI5YAvWiWBA8rTqC1H75TXc8tk8ji2+O31FCy7hZx7kp0vJYIC7fO1d6sX//HRq2AoMzMTsbGx+PDDD9HY2IgFCxZ4alyywRjji8TRzNDFUa2h3uHyPeSwTAbQjjJ347fVx9C5iXKGOrPbGb9BY6AEbrZcDoa+/vprrFixAkVFRbjllltw7tw5rFixAh999JEnxycob/QmazBa+K3PlEB9cVRryHVtFhuqmh0lG6S+rZ5DtYbcq71Bq/jv/PuLyxk609gKi80u8GiEd7apFWarHRqVAgnh/kIPp99c3lo/a9YsjBw5Elu3bkVDQwPmzJmDW265BaGh0u3gu2rVKqxatQrNzc0e+zm5O9i4UOlvfXYHqjXkOm5WKFinRliAPEo2cLOrtQYTmtssVKqiHxhjtEzWQUywFjqNEm0WO840tMp+Jp8rCZMSGQiVUvz5ZC7PDIWEhGDAgAH49NNP8f333+PHH39EaGgowsPDPTk+ySuVSClzbxnIX+zMaDSaBR6Nb+uYPC2X5NegDrueSml2qF8qm9tgNNugVipkk4DfE6VSwecNlVHpBj55WiorGr3KGcrNzcX999+PoKAgPPHEEzh8+LCnxiUbJdSgtVcCtWrEheoAtOczkK7x3eoj5HVs8Q1bKRjqF24pOjkyABoVVWEB2ut10fZ66XSr5/SqAvW4ceMwbtw4AMDChQs9MiC54QouSiEBzVvSo4NwrqkNxTUGjE+hmcnucMtkcii42FFaVCD2l9RT+YV+oiWyC3Hb67klIjmTWs9DCvcFRgUXe4/bUUYXu57JqeBiRzQz5B4UDF2IK1HBlayQM6l0q+dQMCQgxhgVXOwDfkcZba/vkVxnhigYcg/qSXYhfmZI5tvrLTY7KhpaAUhnmYyCIQFV600wmm1QKuSz9dkd0qIoGLoYm53xLUtSJDKN7aq0DrWGGKMedn3F5QzJuVv9+VL5mSEj7DLuj1hRb4TNzhDgp0KMRNq09CoYMpvN+Oyzz3DbbbchMzMTKSkpGD16NG688UasX78era2tnhonb8+ePbjpppswf/58PPLII3x7EHe/xhu4O9fE8AD4qSkudRVXAK68zkj1PrpxrqkVFhuDn0qJASE6oYfjVUkRAVAqAIPJihqDSejhiJLBZEVlcxsAIF0CTTjdJS5UB7VSAbPVzv9+5KikQ76QVHaqunQFttlsWLNmDZKSkvDwww/DYDDgyiuvxAMPPIClS5eCMYannnoKCQkJ+Pvf/w6z2TNbnn/++WfMmTMHSUlJePDBB5GTk4Pp06fDYOh+hqAvr/EW2lbfNwNCdAjwU8FqZ9SdvBvlzmn8xAh/SdQA6Q2tWoXEcMdMK7Xl6JtTzlnXqCAtQmVSo8oVapUSSRHcUpl8j632NhzSuXa5tJvs9ddfx1dffYUPPvgA8+fPh1J5YQzFGMPu3bvxn//8B8888wxWr17t9sH++c9/xtKlS/H3v/8dADB//nzExcXhrbfewqOPPuq213iL1BLQvEWhUCA9OgjHzzShuNpACZ5d4OqgyHX5dWBUIMrrjSipbcHktEihhyM6lC/UveSIAJTUtqC8zohp6UKPRhj8tUtCS/AuzQzdfvvt2LFjBxYuXNhlIAQ4LlCzZs3Cpk2b8NRTT7l1kABgNBqxZ88eXHXVVfxjgYGBmD9/Pr7//nu3vcab2qca5XnB6o/2HmXyvTvriVx3knH4JGoZ3733B+ULdY+SqKV5I+9SMHTgwAH885//xNGjR1160+Dg4H4NqisVFRWw2+1ISEjo9HhCQgLKy8vd9hoAMJlMaG5u7vTlCVLq+OttadS9vkdy61Z/Pj6JmoLlPqFt9d1Loe317SkeEpo5dGmZrLm5GR9//DEMBgN27dqFN954A5mZmZ2+4uPjPTpQi8UCANDpOieD+vv7d5uj1JfXAMDq1avx3HPP9We4F8UYg9FsAyCtqUZv4XuUUTDUJZoZou31/UHLZN1LkXnhxVazDWebHMnjUrp2uRQMLV26FEuXLgUAlJaWQqvV4ujRo9i8eTP+9re/wWg0IiYmBmPGjMF9992HZcuWuX2gERERAIC6urpOj9fV1fHfc8drAODJJ5/slE/U3NyMpKSkPo27OwqFAr8+MRfNbRYE+fWqEDhB+46y4hrH9mmp7GhwB8YYn0At155SXDBUVufYAiy3JPL+sNrs/IWeZoYuxM0MldXJ89zDJY6HBWgQHugn8Gjcp9dX4dTUVNx///38v+12OwoKCnD06FFkZ2d7bJdWfHw8YmNjcejQIVx55ZX84/v378f06dPd9hoA0Gq10Gq9UzuBumr3jWNLJ9DUakFdixlRQdKodeEODUYL9CYrAPA7X+QmPtQffmolzFY7zja2yvb30BenG1phttmhVSuREOYv9HB8TlKEPxQKoMVsk+W5R6q7oPtd3EapVGLo0KFYvnw5Vq9ejd/97nfuGFeXVq5ciXfeeQfnzp0DAGRlZSEnJwcrV67kn/OPf/wDt9xyS69eQ8RHp1EhMdxxoi6upqWyjrgmkgNCdNBpVAKPRhhKpYJPdD1FS2W9wi2RpUUHQUkzahfQqlWID3Wce+TYsPWUBHeSAX2YGbLb7XjkkUewdetWBAcHY9SoUcjMzMSYMWOQmZmJ8HDPNc585plnkJ+fj4yMDKSkpKC0tBSvvPIKJk+ezD+nsLAQhw8f7tVriDilRwehor4Vp2j7dCdybcNxvoFRgSioMqCkxoDZg6OFHo5ocD3/pNJmwRNSIgNwprEVZXVGjE/pPuVCiqS4kwzoQzC0ZcsWrF+/Hs8++ywsFguOHTuGd999FydPnoTFYsH/+3//z2PJxzqdDhs3bkR5eTmqqqowePBghIaGdnrOE088Ab1e36vXEHFKjw7Cj/k1NDN0nnKZJ09zBkYFAaiiJOpeop1kF5cSGYA9xXWy3F7Pd6uXezB09uxZLF++HA8//HCnx00mE06cOAGVyvPT8snJyUhOTu7yexkZGb1+DRGndNpe3yW5F1zkpDlP1rRM1ju0k+ziOiZRyw3NDDlNnjwZ33zzzQWPa7VajBs3zi2DIsQVVHixa9zMkOyXyaJpe31fcH9PNDPUPW7WtUxmM0PchhVAesGQSwnUn332Ge644w689tprMBqNSEhIwKeffurpsRHSI67wYkWDEW0Wm8Cj8R1lzmJwcutWfz7uZH2msZWODxc1tJhR77zYUc5Q9+Q6M8QtkcUEaxGolVZJGJd+msTERLS2tuKNN95AQUEBbDYb3n77bbzxxhtYtGiR1wovEtJRVJAfQnRqNLdZUVZnxJAB7q98LjZtFhuqmh2d2uWeMxQZ6IdgnRr6NivK640YHEvHx8WcqnUskcWH6hBA9c+6xdXvajBa0NRqQai/PEqkSHWJDHBxZmj69On4+OOPkZubC71ej3379uF///sfRowYga+//hrLly9HQkICYmJisGbNGk+PmRAAzoatMZQ31BG3kyxYp0aYzLuNKxSK9rwhWkp1CfUkc02gVs3XFyqX0VKZlIOhXof+/v7+mDRpEiZNmsQ/ZrfbUVRUhOzsbERG0hZn4j3p0UE4Ut6IItpRBqBDG47IANlVxu3KwKhAHD3dxFfNJT2jnWSuS40MQK3BhNK6FoxKlMcOZQqGzmOz2fDDDz/g9OnTiImJwcyZMzF48GAMHjzY3eMT1Jo1a7BmzRrYbJRv4KuoR1lnXA5DSoT0TlZ94dheTw1bXUU7yVyXHBmAg2UN/GysHFAw1IHRaMSsWbNw+PBhhIeHo6GhAf7+/nj44Yfx3HPPQaORztT8qlWrsGrVKjQ3N1NtIh/FnbSLKBgCQAUXz0c7ynqHdpK5LtWZRF0qk2OLMcb/HUkxub7X7Tg2b96M6upqFBYWoq6uDnq9HuvXr8c333yDJUuWgDHmiXES0qUMLmeougV2Ox17cu9Wfz6qNeQ6s9XOB9NpFAxdFJdELZft9bUGMwwmK5QKafY87HUw1NTUhCuvvBLp6ekAgMDAQFxzzTXYt28fysvLsXnzZrcPkpDuJEUEQKNSoNViw7nmNqGHI7gKmhnqhKuSW2swobnNIvBofFt5fQtsdoZAPxViQ+TVfLQv+O319fIItLlZoYRwf2jV0ut52OtgaO7cuTh27NgFM0A6nQ7XXXcdDh486LbBEXIxGpWSPynJvS2Hzc5Q0UDVpzsK0qoRE+y4sMtlOaOvijrsJKPk+4vjGgFXNZvQapZ+XmmJs+wCl4cnNb0OhkwmE8LCwnDnnXeiurq60/eOHTtGLS+I12VQWw4AwLmmVlhsDBqVAnHOrtqkfXaI8oZ6RjvJeicswFHnDIAskqi5peY0CSZPA31IoN67dy+2b98Oi8WCTz75BNOmTUNqaipyc3OhUqlwyy23eGKchHQrPSYQOAHZb6/n6p0khQdApaQ7e05aVCD2l9RTraGLoJ1kvZcaFYhjztINUi/6yjdolegSfK9nhu666y7o9XocOnQIr7/+OoYPH46CggLk5ubil19+QUJCAubOnYvf//73+PXXXz0xZkI6oYatDmWUL9SlgTQz5BLaSdZ7cmrLwW+rl+jx0ac6Q1xT1o6NWRljKCkpQXZ2Nv+1Z88eTJ8+3W2DJaQr/I4ymd/5006yrlEwdHGMMb5WF+0kc51cGrba7Qylzp9R1stkjLGLJtQpFAqkpaUhLS0Ny5YtowQ84jXcybtGb5JVn6DzlTt3tSTLvEHr+dI61Bpy5VwmRzUGE/Rtjm3TKTSz6DK5bK8/29QKs9UOP5US8WHSzEd0aZns9ddfx+9//3ucPn26x+dVVlbiz3/+M5599ll3jI0QlwRp1YgL1QGQ91IZzQx1LSkiAEoFYDBZUWMwCT0cn8T1JEuKCIBOI71t054il+313KxqcqR08xFdmhm6+eab8fTTTyM9PR2zZs3CrFmzMHjwYISGhkKv16OwsBA///wzdu3ahRtuuAH/+Mc/PD1uQjpJjw7CuaY2FFUbMC45XOjheB1jjE+gpjv7zrRqFRLDA1Beb0RJTQtignVCD8nn0E6yvuGSic80OGdO1L1OwxUFKbfh4Lj0fy48PByvv/46ioqKMGXKFGzevBm33norLrvsMtx000347LPPMHr0aOTm5uL999/HgAEDPD1uQjrhdsDIdWaowWiB3mQFIM3qsP1FeUM9o51kfRMdrIW/RgU7A043SHepjNuJKdV8IaCXCdRJSUl4/vnn8fzzzwNw9CkLCJDuiZcatYpHx7YccsTVOYkN0dIyRxcGRgXip4IalMhg109fcJsPKHm6dxQKBVIiA3CyUo+yeqNkf3+lzr+bVAkHQ32a09u2bRvy8/MlHQgBjkatubm5OHDggNBDIRch9+311K2+Z3wStcx3HHbnFC2T9RmfRC3hWUdaJuvC6dOncffddyMsLAwAUFpaigkTJmD69On45Zdf3D0+QlyS7pwZKq83wmSV30wely9ENYa6Rstk3Ws123CmsRUALZP1RXsStTSXycxWO9/zUMrLZL0Ohnbu3IlZs2YhNjYWAPDiiy9Cq9Vi3rx5WLx4Merq6tw+SEIuJiZYi2CtGjZ7eyKxnHAnYtpJ1jUuGCqrM8JmZxd5trw4Sg4AYQEaRAT6CT0c0ZH69vryeiPsDAj0UyE6WLoNfHsdDDHGoNPp+P/evHkzXnvtNfzf//0fFi9ejC+//NLtgyTkYhQKBdKcs0NybMtBM0M9iw/1h59aCbPNjrPOWRDi0HEnGdVg6r1U58xQqUTz0fg2HFGBkj4+eh0MTZ48Gdu2bUNlZSW++OIL2O12vhL1kCFDcObMGbcPkhBXyLlhK1fnJIUKLnZJqVRgoPN3c4qWyjrh/l6kvATiScnO2djT9a2SnHWUQ74Q0IdgaNiwYbj55puRmJiI66+/Hg888AD/vePHjyMjI8OtAyTEVekxjj9Wuc0MtZptqGp2FBOkZbLupUY5fjclMgyWe8Jtm+by7kjvxIf5Q6NSwGyz41yT9GYdpd6tntOn3WR///vfkZeXhz179uDPf/4zAKCgoAA7duzA4sWL3TpAQlzVvqNMXnf+3Lb6EJ0aYQHybEXiioFRjuODkqg7o4KL/aNSKpAU7gi0pZiv2HGZTMr6XC5z0KBBmDp1Kv/v6Oho7Ny5k99lRoi3tTdsNYAx6U1Xd6fjNLaU1/T7i7uzpWWydnY7a58Zop1kfcYlUZdKMBiiZbIeHDhwAAsWLEBiYiIyMzPxyCOPoKGhAWPGjHH3+AhxWXJEANRKBYxmG841tQk9HK/hawxRvlCPBkbT9vrznWtuQ6vFBo1KQZXL+4HfXi+xJOoWkxWVzY5zKQVD56msrMTChQuRnJyMv/zlL1i2bBkOHTqEkSNH4ttvv/XEGAlxiUal5O/Q5JREzd2NptJOsh5xJ/Mzja1os8ivFlVXip35dckRAdCopNlXyxukur2e2yEXEeiHsABpl13oVTsOANi+fTtmz56NtWvX8o8988wz2Lx5M373u9/hxIkT1JuMCCYjJgjFNS0oqjZg5qBooYfjFXJZ0++vyEA/BOvU0LdZUV5vxODYYKGHJDiqPO0eUt1eX1ornxutXt8KmEwmvuBiR0uWLMGyZcuozhARlBzbctAymWsUCkV73pDMkuy7U0w7ydyCq+9VXm+UVL5iSa3jPMptPpCyXgdDM2bMwObNm1FdXX3B9xITE1FVVeWWgfmCNWvWYPjw4Zg4caLQQyEuklvD1jaLDWed+VFyuHvrL26pTGp38H3FlaGgmaH+SQz3h1IBGM021BhMQg/Hbfht9TJIru9TnaHly5dj8uTJWL9+Perr6wEA+fn5+OijjzBq1Ci3D1Io1KhVfLiTepFMZoa4bfXBOjW1UnABv72eZoYAtP+dZNDMUL9o1SrEh/kDkFbeEL8EL4NZ5z5lzL388su4++678eCDDyIyMhIajQZDhw7FmDFjcM0117h7jIS4jLuDqdGb0NRqEXg0ntfxZEXb6i+OdpS1azJaUKN3zGJQMNR/Ukyilsu2eqCPwZBCocCTTz6JyspK/PDDD/jkk09w5MgRfPHFF1AqaUcCEU6wToMBIY7eeadkMDvELfdQ8rRrqNZQu6IaPQAgLlSHIG2v99KQ80hte31DixkNRscNJVe9Xcr6FLnccccd+O233+Dv7485c+bg2muvRWZmppuHRkjfyKktB22r7x0uaKw1mNDcJv2Zw54UVtESmTtxrXCkMjNU4gzq4kJ1CPCTfrDc62Bo165dOHbsWKfq0wBQVFSEdevWuWtchPSZnNpy0E6y3gnSqhETrAXQvsQoV9zNAgVD7iG1mSFux6UclsiAPgRDubm5fJf6jjIyMvDBBx/g6NGjbhkYIX3FndxlMTPkrAMyUAbT2O7CndzlnjdU6Pz7GBRD9ZbcgVtKkkpLDrn1rOt1MJSWloaDBw92+b0ZM2Zg69at/R4UIf3B/fFKPWfIsa3e0SWbZoZcN5BqDQGgmSF3S3YukzW1WtBoNAs8mv5rL8gpj3NLr4Oh+fPno66uDs8///wF3ystLYVGQ12zibC4YKis3giz1S7waDzndIMRjDmWfiJpW73LaGbI0XPqTKMjkB5EwZBbBPi1L8FKIW+ISzNIk8nMUK+zovz8/LBx40Zceuml+Oabb7BixQrExcXh4MGD+PTTT/HHP/7RE+MkxGWxIVoEadUwmKwoq2vBIIm2XSjhSuVHBdC2+l6gYKh9CSQqyA/hFEi7TUpkAKr1JpTVGzEmKUzo4fSZ1Wbnc5/kUp28T7vJxo0bh2PHjmHSpEl45ZVXcOutt2Lz5s1Yu3atpIouEnFSKBT81K6U23JQ8nTfpHWoNSSl1gm9QZWnPYNPohZ5oF3R0AqLjcFfo0Kcs1SJ1PV5v9yAAQPw6quv4tVXX3XneAhxi/SYIBw93STpJOoSvuAiJU/3RlJEAJQKwGCyosZgQkywPE72HfHJ07EUDLkT97co9iTq4mquJ1kglEp5zDpThcQeUG8y8eLbckg4GCrjawzRzFBvaNUqJIY7LlpybcvBJ0/TzJBbJTv/FsvrxX1cnXI2aJXLEhlAwVCPqDeZeA125gkVVEk3GKLq030n97yhIn5mSJr5dEKRzsyQM19IJjvJgF4GQ2azGXV1dQCA5uZmGI3i/h9OpIvbIVNcY4DNLr28EJPVhrON3LZ6WibrLT4YkkiBvN4wWW18vhltq3evlIj23ohGs1Xg0fQdl2spl51kQC+DoWPHjuHhhx8GADzzzDP48ccfPTEmQvotKSIAWrUSJqsdFfXSC9or6lthZ0CgnwrRQVqhhyM6fBK1DJfJSmpbYGdAsK59Kzhxj9AADcICHOVlxLy9nuvdRzND3ZgwYQKCgoKwceNGnDlzBpdffrmnxkVIv6iUCv6ut6BKL/Bo3K/jTjLaVt97cl4m61hskY4d92vvUSbOY6u+xYz6FkfRyLQomhm6wPbt23HnnXeiuroa119/PfR6Pe68805s2LDBk+MjpM+4vKFCCSZR8zvJqA1Hn3DBUFmdUZLLqD3hGrRSsUXPaO9RJs6ZIa7ydEKYP/z9VAKPxntc3lo/fvx4xMfHY9euXSgpKcHEiRNx/fXXIyoqypPjI6TPuG3D0pwZop1k/REf6g8/tRJmqx1nG1uRFCGfoLKohtpweJLYk6hP8ZWn5XVucXlmKDIyEoMHD8bGjRvxww8/YPfu3UhOTsaAAQM8Ob4umc1m1NbW9qpgWktLC0wmkwdHRXwN14BSijvK2msMyeuE5S5KpQIDnb+7UzJbKiuqogatniT27fVya9DK6XUC9cqVKxEWFoZHH30Ue/fu9dS4umS32/GHP/wBYWFhSE1NRWJiIjZt2tTjaz766COMHTsWcXFxCAsLw+TJk2mrvEwMjpXujjIuGJLb3Zs78XlDEq5Sfj6rzc4fOzQz5Bn8zFCtOGeGimXWoJXT6wTqW2+9FQCwePFiLFy40COD6s6//vUvvPfee9izZw+am5vx+OOPY/ny5cjLy+vy+TabDVu3bsW6devQ1NSExsZGjBkzBpdddhnq6+u9OnbifUnhAdBpHEshYk1m7Eqr2cY32ZTT1ld3S5VhEnV5vRFmmx06jRIJYf5CD0eSkp3B0NmmVpisNoFH03vcMhnNDPmwNWvW4M4770RmZiaUSiUeeughJCcn46233ury+SqVCh9++CHGjBkDhUIBrVaLZ599FnV1dTQ7JAPKDjvKpJREzV28wwI0iKAmm32WFiW/ZbKOPcnk0mbB26KDtAjwU4Ex4HRDq9DD6RWz1Y4yZykSOVWfBkQUDFVXV6OsrAzTp0/v9PiMGTOwf/9+l9+nqKgIAATJdSLeN9iZF1EooSRqrlT+QKo83S8Do+U3M8T3JJPZhc6bFApFhx1l4jq2yutbYLMzBPqpZFeDqs+NWt2hoaEBLS09HyxxcXFQqVSoqakBgAt2r0VFRWHPnj0ufZ7RaMRDDz2ESy65BGPGjOn2eSaTqVOydXNzs0vvT3xPBr+jTEIzQ9xuDxnVAPEELpg809iKNosNOo30txEXV9NOMm9IiQhA3rlm0eUNFXNLZDKsQdWrYOi3337DK6+8gpaWFlx55ZW46667oFQ6JpdaWlrwzTffQKVS4ZprrnHp/Z5//nl8/vnnPT7nl19+QWpqKv85VmvnEucWiwUq1cVPYmazGddeey2MRiO2bdvW43NXr16N55577qLvSXzfYH5HmZRmhih52h0iA/0QrFND32ZFeb2Rr0slZYV8MCT9n1VIKc76X+Uiq34v151kQC+Wyc6ePYt58+bh8OHDaGlpwR/+8Ac89dRTOHnyJG666SZER0djxYoVKCwsdPnD//3vf+P06dM9fqWmpgIAEhISAACVlZWd3qOqqor/Xne4QKigoAC7du266BLZk08+iaamJv6roqLC5Z+J+BbuAneqpgVWm13g0bgHVxQtjZbJ+kWhULTnDcmgLYfNzlBY7bgpGDKAgiFP4nqUlYpsmYxr0CrHc4vLwdCOHTuQmZmJkydPYteuXcjJycFnn32GOXPmIDs7Gy+88ALKysrwxBNPeGSgISEhyMzMxPfff88/ZrVasXPnTsyaNYt/rKGhAVVVVfy/LRYLrrvuOuTm5uLHH39EYmLiRT9Lq9UiJCSk0xcRp8Rwf/hrVDDb2hMDxYwx1mFmSH53b+7GLZWJ7aLVFxX1RrRZ7NCqlUiWUZFJIbRvrxfXccUV5JRb8jTQi2WympoaTJkyhV+uSk1NxbXXXotffvkFu3fvhlrt+fSjp59+GsuXL8fEiRMxdepUvPTSSwCA++67j3/OY489hr179yInJwd2ux0rVqzA3r17sXnzZgDA6dOnAQAREREICKATgtRxO8qOn2lCYZVB9NO/tQYz9G1WKBTUrd4dBjrzruTQsDXfuVQ8KDYIKtpJ5lHcjUpFg2N7vVbt+/lojDEUOY8RrkabnLg8M8QY4wMhTmxsLKZMmeKVQAgArr76anz44Yd4//33sWzZMjQ3N+Onn35CdHQ0/5yIiAh+GaypqQn79u2DRqPBtddeiylTpvBfXHBEpI/bOSOFHWXcElliuL8sEn49TU47ygoquQsdLZF5WmyIFkFaNWx2hnKRtOU429SGFrMNGlX7bjg56VUU8+677yInJwejRo3CqFGjUFpaCp1O56mxdWn58uVYvnx5t99/8cUX+f8ODw/nZ4KIfA1ynvwLJFBriLtoD6SdZG4hp1pD3MzQEAqGPE6hUCA9OhBHTzehuMbAn4N8GXezODAqEBqVaKruuI3LwdBVV10Fi8WCw4cP48svv+SXqPz9/bF3715MmjQJkyZNwuzZsxEXF+exARPSW9yUryRmhmrlm+DoCVwV6lqDCc1tFoToNAKPyHMKqmhmyJvSo4Nw9HQTX+jS1xXKvGedy8HQ4MGD8eSTT/L/bmhowKFDh3Do0CEcPnwYW7Zswcsvv4xHH32UD5QI8QXn7yhTi/iu55RM+wZ5SpBWjZhgLar1JpyqaUFmUpjQQ/IIs9XO75gbTDvJvIJLQi4WST4at9NwkAzzhYB+FF0MDw/H/PnzMX/+fP6xxsZG6PXiv/sm0pIQ5thR1mqxobTOKOqCc6domcztBsUGoVpvQmGVXrLBUEltC6x2hiCtGvGh3k1tkCtus0axSBoBt1cnl2ew7NZb5LCwMCQlJbnzLQnpt449yoqqxRusW2x2PhmTCi66D3fyl1L/uvPld9glJLfKwkLJiHH8jRZXG8AYE3g0PXPsJHMc/3LcSQaIqDcZIf3BTf3mV4r3gldRb4TVzuCvUWFACN3du8sgCeWUdYfbSUbFFr0nOSIQKqUCLWYbKpvbhB5Ojyqb26A3WaFWynMnGUDBEJGJYQMchTPzq8TbZ47L+UiNCqSO427E5ZRJqX/d+fIpedrr/NRKvhYYV9nZV3HHfmpUIPzU8gwL5PlTu2jNmjUYPnw4Jk6cKPRQSD8NjXNcBE6eE+/dfwn1JPMIrg7VmcZWtJisF3m2OBXQtnpBiCVvqFDGxRY5FAz1YNWqVcjNzcWBAweEHgrpp6HOmaGSuha0mm0Cj6ZvTtU6d5LRtnq3CgvwQ3SwFgBEsw26N1rNNr5hKO0k8y6xBENF1MCXgiEiD9HBWkQF+YEx8Xaw505Ycuwb5Gnc7JBYj42eFFUbwBgQGeiHqCCt0MORlfaNG74dDBXQzBAFQ0Q+uNmhk5XiyxtijPHr+mIuDeCruFwaX79o9UXHnmTEu7h6YL48M8QYk/22eoCCISIjQ51LBHkizBuqNZjR1GqBQgHRN5v1RRkSnhmifCHhcA1bq5pN0LdZBB5N1xxjs0KlVCA1Sr7NnykYIrIxNE68M0PcjEVyRAA1aPUAbmZIirWG8rkGrZQv5HWh/ho+H+2Uj1ai5ipPp0YGQKuW77mFgiEiG9zM0MlKvc8XQTsfVyxyEC2ReQT3ez3dIL0dZTQzJKyMaN/OG5J7TzIOBUNENjJigqBSKtBotKCq2ST0cHqlkJKnPSq8Q3KxL+d39FZTqwXnmhwF/8TQOV2K0mN8O2+IkqcdKBgisqHTqPhu73kiWyqjuzfPa99R5psXrb44ec5xnMeH6hDqrxF4NPKU7uMzQ3nOZVQujUCuKBgissLnDYksibp9t4e87948ibszLhRx/7rz5TmDoWEyv9AJibuB8cVgyGZnfKuWoTLPKaNgiMgK9wefL6KZoUajGbUGx7IeLZN5TgaXRC2hmSFu5yQFQ8IZPMDxN1ta14I2i28VfC2vN6LVYoNOo5RtTzIOBUNEVobFtSdRiwV3R5kQ5o8grVrg0UjX4BgJzgxV0syQ0KKDtAgP0MDOfG92iFtGHRwbDJXM+x1SMERkhSu8WFRtgNlqF3g0rqHkae/gEowr6lthNIt/R5nVZue31XM3AcT7FAoFX7oh38duwvJoiYxHwVAPqFGr9MSF6hCsU8NqZz67u+N87cnTFAx5UkSgH6KC/AD43h18X5TWtcBktcNfo5L9EojQuGDD14p6cukC3E2inFEw1ANq1Co9CoUCw0TWlqOQagx5TYaEdpTlOvOFhgygJRChcQUv830sGDrJ7ySjmSEKhojscH/4YmnLwc1SUG8pz+PukMWUYN8d2knmO7iClwU+tEzWYrKirM4IgGaGAAqGiAxxFwfuYuHL9G3tRfMyounuzdOGiSxQ7gl3fA+nu37BcfloZ5va0OwjPcq4WaqYYC0iAv0EHo3wKBgisjMyPhQAkHOmyefbcnCzQtHBWoQGUNE8TxsqsiXUntDMkO8I9dcgLlQHACj0kaUyrtaa3IstcigYIrIzeEAQ1EoFGowWnHXOuviqfNrt4VWDY4OhUAC1BjNq9OJq2dJRfYuZbzlDFzvf0L6jzDfy0biAfxidWwBQMERkSKtW8SemnDNNAo+mZ1yCIzXZ9A5/PxUGOndeiXl2iJsVSo4IoNpUPmKIj+0oa58ZonMLQMEQkamRCY675RM+Hww5t77S3b3XcBcHsbVs6ah9iYwudL6CuwHzhSCbMdZ+bqHkaQAUDBGZGpngzBs6K/yJqTuOExYtk3kbd3EQWzPfjnIpX8jnDOlQeFHoXMXTDa1obrNCo1LwjWTljoIhIksj4p0zQ2d9d2aoWm9Co9ECpaK9/g3xPC7wFPOOMupJ5nsyYoKgUAANRgtqDWZBx8Kd94YMCIafmsIAgIIhIlPD4kKgUABVzSZU630ziZpb6kiLDoJOoxJ4NPLBBRBF1XpYbOJo2dKR2WpHkbNQ53AKhnyGv58KqT6Sj3bcmR7A7awlFAwRmQrwU/PTwyd8dKmM20k2hJbIvCox3NEQ12JjOFXTIvRweq2gSg+LjSFEp0ZiuL/QwyEdcMGp0OecnDOOzx+RQMEQh4KhHlBvMmkbGe/bSdRcvhBtffUuhULBL5UJfQffF9wOyZEJoVAoqA2HLxkeL3wwxBjjj5FRFAzxKBjqAfUmkzY+ifqMb17w+G31tNvD68TWsqWj43Sh81m+kKtY1WxCXYsZKqWCNmZ0QMEQka0RXCVqH0yittja8z7ohOV9/I4yEbRsOV/HmSHiW7hzTkltC1pMVkHGwB0fg2IoF7EjCoaIbHFT1qcbWtFk9I1+QZyS2hZYbAxBWsr7EAJXn0dsy2QWmx15zhlFmhnyPdHBWsQEa8GYcMcWN3M4gpKnO6FgiMhWqL8GyREBAHxviz03IzFkQDDlfQiAK5BX1WxCfYuw26B7o7DKALPVjmCdGimRAUIPh3SBWyoTanmeO9eNSqDl944oGCKyxt09Hz3tW8HQSdpJJqhgXXugnOujuw27ksPf9YdQEO2juBkZoW7AuCCMllE7o2CIyNqYJMcJIbuiQeCRdJZDdUAEx7Vs8cWcsu5Q8rTvGyHgjrIavQmVzW1QKKgg5/koGCKylpkUDgA4WuE7FzzGGH+iHElT2YLh7pyP+2jpha5wgRvd9fsubmaooEoPs9W7RT2Pn2kEAKRFBSKQGvh2QsEQkbWRCSFQKRWobG5DZZNvVKI+19SG+hYz1EoFn7tCvI+blfPVOlTns9rsfK4ZzQz5rqQIfwTrHEU9C6u9W7rhSHkjAGBscrhXP1cMKBgishbgp+YDDl9ZKuO3vsYG09ZXAXGzK6V1RjS3+dZuw64U1RjQZrEjSKvm2z4Q36NQKASrRJ1d0QgAyEwK8+rnigEFQ0T2uBPDEeeJQmg53BJZPC2RCSki0A8JYY6yBid8tDBnR8dPtydPK5WUPO3LRic6N2548ZxjtzNk8zNDYV77XLGgYIjI3lhnMMSdKIR2gorm+QwuZ8vXSi90hYotigeXq5jtxWDoVK0BepMV/hoVhtDy+wUoGCKyl+m8Szp+pgk2OxN2MOiYBEszQ0Lj8obEkESd7ZwZ4mYdiO/izjknK/VoNdu88pmHnTd7oxJDoVbRpf989BvpATVqlYf06CAE+qlgNNu8ntB4vmp9G6qaTbT11UeMTOT61/l2MGSy2pDnXF4dm0TJsb4uPlSH6GAtbHbmtdIN3CzUWMoX6hIFQz2gRq3yoFIqMDoxDIDwS2VcQmV6dBAC/Gjrq9C4maFTtS0wCNRLyhUnzjbDbLMjItAPSRHUvsXXKRQKPlfRW+ecI5Qv1CMKhghB+7S1N9fwu8LnC1HytE+IDtZiQIgOjPl201Y+MTYpjCpPiwQfDHnhnNNisiLf2Qstk2YOu0TBECEAxnAzQwIHQ1xbEEqC9R18JWofXiqjLdPiM9aLwdDR042wMyAuVIcBoTqPf54YUTBECIDxKY67pfwqPZpahakpwxijqWwfJIZK1HwwRMeNaIxKDIVCAZxpbEW13rMFX/eX1AMAJqZGePRzxIyCIULgWA4ZGBUIxoDDZcIUXzzT2IpagwlqpYIv2U+EJ0RNmN6oM5hQXm+EQgGMoZkh0QjWaTAoJghAez6Pp3DB0KSBFAx1h4IhQpwmOGeH9pfWC/L53AlxeHwIVZ72IVyORXFNC5qMvleJmpsVSo8OQohOI+xgSK9wM9KHPHgDZrbacbjc8f5T0igY6o7ogiGj0YgNGzbg9ddfx08//dSr1+bn5+Oll17CDz/84KHRETGb6LxrOlAibDBEW199S0SgH1IjAwAA2acbhR1MFyhfSLy4mZp9p+o89hnHzzSizeLYaZgeHeSxzxE7UQVD586dw5gxY/C3v/0Nhw4dwnXXXYebb77Zpde2trbimmuuwbPPPovNmzd7eKREjCY519OPnW5Cm8U7hdA6OuLsjUZNFH0P9//kSLlv9K/riAuiKRgSn8kDIwE4WvB4qnTDPm6JLDWCdhr2QFTB0OOPP47g4GDs27cP7733Hnbt2oVPPvkEWVlZF33tQw89hHnz5iEjI8PzAyWilBIZgOhgLcw2O46d9m6yrMlq4/tf0UXN93hzG3Rv2O0MR52zVZR0Lz7xYf5IDPeHzc48tlRG+UKuEU0wZLPZsHHjRtx6663QarUAgJEjR2LGjBn4/PPPe3zt559/jr179+If//iHN4ZKREqhUGBiqmMG4ICX84byzulhttkRHqBBinNJhvgOLtA4Ut4IxoRv2cIpqNZD32ZFgB/1mxIrbnbIE0tlVpsdh0odQRYFQz0TTTBUUVGBlpYWDBkypNPjQ4cORV5eXrevKykpwYMPPoiPPvoIOp1r9RVMJhOam5s7fRF54Lae7vdy3hC3/DI2OZymsn3Q0AEh0KqVaGq1oKS2Rejh8Lj8tnHJ4dRvSqQmO5Oa93ngnHP0dCP0JivCAjTU3uciBK33v23bNuTk5PT4nDvvvBNhYWHQ6x09o8LCwjp9v+P3zmexWHDDDTfgiSeewOjRo10e1+rVq/Hcc8+5/HwiHVwwdLisATY7g0rpncDkoPPujZKnfZOfWolRCaE4WNaAI+WNSPORRNT9zuOG6seI1+SBXK5iI1rNNvj7uW8n6c8FtQCA6RlRXjuXiZWgtxJNTU2orKzs8ctmcySyBgQ4lg7On6VpampCYGBgl+//4Ycf4uTJk7BarXjppZfw0ksvoaamBocPH8ZLL73U7XT3k08+iaamJv6roqLCjT818WXD4kIQrFNDb7J6reIwY6w9yZGmsn2Wr+UNMcb4maGJAynpXqySIwIQF6qDxcbcvjz/c2ENAGDWoCi3vq8UCToztHz5cixfvtyl56akpECr1aK4uLjT48XFxRg0aFCXrxk8eDDuvPNOVFVV8Y9ZLBa0tLSgsrISjLEulyS0Wi2fl0TkRaVUYGpaJLbnVuGXolqvFLE7VduCWoMJfmolFc3zYY4dZSX8rj+hnW5oRWVzG9RKBXWqFzGFQoGZg6Lw+cHT+LmgBrMGR7vlfZuMFr5Q6MxB7nlPKRNNW2y1Wo0rrrgCH330Ee655x4olUqUlpbip59+wnvvvcc/b/v27Th79ixuu+02TJ8+HdOnT+/0Pjt27MDMmTPx0ksveftHICIxY1AUtudW4deiWqy6xPO7D7n8pMykMCq26MO4JOq8c3q0mKwI1Ap7+uRmEUYmhLp1aYV43+zBMfj84Gn8WFCDv7jpPX8troWdARkxQYgP83fTu0qXqDLuXnzxRRQWFmLhwoV46qmnMHfuXFxyySVYsWIF/5zPP/+cAh3SL9MzHFPKB0sb0Gr2fL0hbhfJFFoi82nxYf5ICHNsgz7sA/WGDtAuIcmYkREFpQIoqjbgdIPRLe/5c4FjiWwmLZG5RFTBUHp6OnJycnDVVVdBoVDghRdewLfffguVqv2uaNGiRVi5cmW373Hrrbdi7ty53hguEam0qEDEh+pgttk9vsW+c75QpEc/i/Qfl+zq7d2GXeGOTUqeFr/QAA3GOQt7cknP/WG3M+zIqwYAzBkS0+/3kwPRLJNxoqOj8dBDD3X7/euuu67H1z/yyCPuHhKRGIVCgekZUdhw6DR+Lap12xp+V043tOJckyPvY1xKmMc+h7jHpIER2HjkjEe2QfdGfYsZRdUGAO099Yi4zR4cjYNlDfgxvxo3Tk7u13sdqWhArcGEYJ0aU9PoJssVopoZIsRbZjinln8p6v9dWk9+cy6RjUoMRYCf6O5NZIdbksquaBSkZQuHW1odFBOE8EA/wcZB3IebwfmlqLbfy/PfnXBsGpo7NAZ+arrMu4J+S4R0YVq6Ixg6cbYZtQaTxz6HW9efkUHr+mIwMCoQUUFamK3eb9nS0a/F7fVjiDSMTAhBQpg/jGYbfiqo7vP7MMbw3YlKAMDC4QPcNTzJo2CIkC5EB2sxMsFRsXXXyb6fmHpiszN+5smTS3HEfRQKRYe8Ic91Gr+YPUWOz56WTksgUqFQKHD5KEfw8s3xyj6/T945PcrqjPBTKzF7CJ1XXEXBECHdmDc0FgCwM6/qIs/sm+NnmtBotCBYq6bmrCLCLZUJlTd0trEVp2pboFQAUygYkpQrRscDcJxz+roMu+nIaQDAvKExCBK4/IOYUDBESDcWDHcEQ7sLaz2SH8ItkU3LiISG+kqJBhcMHSprgMVm9/rn/+qcTRydGIYQncbrn088Z0xiKL9U1pcZaavNjqzsswCAq8clunt4kkZnYEK6MSI+BANCdDCabXyisztxwRAtkYnLkNhghAVoYDTbcOx0o9c/f0+x41icnkGzQlKjUChwVaZjduizA71vA/VLUS1q9CZEBPphNp1XeoWCoR6sWbMGw4cPx8SJE4UeChGAQqHAvGGOHR7uXiprNJpxxFkqfxaVyhcVpVKB6c4Ee3fUhOkNxtrzzCh5WppWTEwC4Ogr1tsCjJ/sLwcALB4dR7vIeol+Wz1YtWoVcnNzceDAAaGHQgQyf5hjqWxHbjXs9q4b+/bFzrxq2OwMQwcEIykiwG3vS7yDq+q729kI01uKqg2o0ZugVSv5In1EWlIiAzEtPRKMAZ/3Ynaoot6I73MdN203T0nx1PAki4IhQnowNT0SwVo1KpvbcLDMfS0YtnFbX0fQ1lcx4upQZVc0oqnV4rXP/SHfkUcyaWAE9bGTsBsmOYoufrSv3OWaQ+/vKYWdOQL1QbHBnhyeJFEwREgPdBoVFo10BCxbjp5xy3sazVY+X+hSCoZEKTE8AGnRgbAz4Ldi722x55Jq5w6lFgtSdunIAUiK8Eddi5lf+upJjd6Ej53PWzk91cOjkyYKhgi5iKvGOBIavz1e6ZbdQz/l18BktSM5IgDD4ugOTqy4XC9vLZU1t1lw0NmclYIhadOolLh3djoA4H8/F8Notvb4/P/+WASj2YYxiaG4hHqR9QkFQ4RcxLT0SEQF+aG+xcxva+6Pr4+dAwAsGhELhULR7/cjwmjPG/JOEvXuglpY7Qzp0YFIiQz0ymcS4Vw7PhEJYf6oajbhtV1F3T4v71wzPvitDADw2KKhdE7pIwqGCLkItUqJy0fFAQA2Hu7fUlmT0YLvnTvTlmQm9HtsRDhT0iKhUSlQXm9EcY3B45+382R7vykifVq1Cs9eNQIA8M7uUzhSfmHOYpvFhse+OAqrnWHh8Fg+l430HgVDhLjguvGO7a7bcipR149eZV8fPwuz1Y6hA4IxIj7EXcMjAgjUqjHF2RGc28XjKXY7w0/5juW4SygYko0Fw2Nxxag4WGwM9314GKW1Lfz3LDY7/rDhKHLONCPUX4O/Lh0p4EjFj4IhQlwwKjEUYxJDYbbZseHQ6T6/z5fO114zLpGmsyVgobNKuaeDoUPlDahrMSNYp8bE1AiPfhbxLX+/ZhQyYoJQ2dyGZf/9FW/9XIxNR07jujd/wzfHzkGtVOCNm8YhJkQn9FBFjYIhQlx002RH7Y6P95X3qebQibNNOFzeCLVSgSVj4909PCKA+c5g6HB5A6r1bR77nG+ceWYLhsdS6xaZCdZp8PFdkzEqIRQNRgte+PYkHvnsKLIrGhHop8Lbt0zANCrA2W/0V0WIixaPiUeITo3yeiOf99Mb7/1aCgC4fFQcYoLpLk4K4kL9MSYxFIw5Cml6gt3OsDXHEQxd4cxdI/ISE6zDxvun4a9LR2LW4GhMTA3H3bPSsPMPc2jZ1E0oGCLERf5+KtwyNRUA8NquQjDm+uxQjd6ELc4GilQHRFq4wpnbnYU03e1weQOqmk0I1qopQVbGNColbp6SgvW3T8KGe6fhqcuHYUAo3VS5CwVDPaDeZOR8t88YCH+NCjlnmvFjvuv1Zd74sRhmmx1jk8MwltooSAqXN/RLUS0ajWa3v/83x9uXyLRqqjpNiCdQMNQD6k1GzhcR6IebpzhK5b/wbZ5LRRjPNLbiw72OOiCPLhjs0fER7xsUG4xhcSGw2Bi+Pe7e2SGrzc7nC11GS2SEeAwFQ4T00qpLMhAR6IfCagPe31N60ef/7ZtcmG12TEmLwAxKdJSkZc6E+Kwj7mnZwtldWItqvQkRgX6YPTjare9NCGlHwRAhvRQW4Ic/LRoCAHhpez4KqvTdPnfr8XP49nglVEoFnr5yOG2nl6irxiRAoQD2l9ajot7otvfdcMjRtXxpZgL81HS6JsRT6K+LkD64fkISZg6KQpvFjns/PNRlIcaCKj0e++IYAOCeWWkYER/q7WESLxkQqsNUZwHGzdnumR2qbzHz9Yuum5DolvckhHSNgiFC+kCpVOA/yzMxIESHUzUtuOHtvSiqbp8h2neqDje8tRcGkxWTBkbg9/MpV0jqrh7nCFg+2V8BWx/qUJ1v4+HTsNgYRsSHYFgcVSsnxJPUQg+AELGKCtLio7sm44a39qKgyoCF//kZE1Mj0Ga142hFIwBgRHwI3rx5PC1xyMCVo+Pw129ycaaxFbtOVmOBc5dZX9jsDO//VgoAuGFSsptGSAjpDp2hCemH9OggfPXgDMwbGgM7A/aV1ONoRSMUCuCGSUn49O4piAj0E3qYxAt0GhWWT3T0sFvvDGT6akdeFSrqWxEWoME142iJjBBPo5khQvopNkSHtbdNRFG1AUcrGqFWKTBpYATiQv2FHhrxspsnp+Ctn09hd2EtCqr0GBwb3Kf3WftLCQDgxknJ8Pej2kKEeBrNDBHiJhkxQbhmfCKWZCZQICRTSREBWDTcUZH6tV1FfXqP34rrsL+kHhqVAr+bmuLO4RFCukHBECGEuNFD8wYBAL4+dhaFPZRd6ApjDP/+Ph+AI1eIgmpCvIOCIUIIcaPh8SG4dMQAMAb8Y1t+r167I68aB0oboFUrseqSDA+NkBByPgqGCCHEzf6wcDDUSgV25FVhZ16VS68xmq14dssJAI4eeLEh1ISTEG+hYKgH1KiVENIXg2KDccfMgQCA/7f5BJpaLRd9zd+3nsSZxlYkhPnjwbk0K0SIN1Ew1ANq1EoI6auH5g5CUoQ/zjS24rENR2HvoRDj18fOYv1vjma+f1s2EgF+tNGXEG+iYIgQQjwgUKvGmhvHwU+lxPbcKvy/LTldBkQ/5lfj0c+OAgDumZ2GOUNivD1UQmSPgiFCCPGQ0YlhePHa0VAogA/3luPW9/Yjv1IPxhiajBb8a3s+bl93AGabHZeNHIDHFg4ResiEyBLNxRJCiActHevoaP/4l8ewu7AWi17+GcFaNVrMVnATRVePS8Dfrx4NtYruTwkRAgVDhBDiYUsyEzAiPgQvfVeA7/OqoDdZAQBDBwTjgbkZuGJUHBQKhcCjJES+KBgihBAvyIgJxpu/G49Wsw1nGo0I8dcgJpi2zxPiCygYIoQQL/L3UyEjpm89ywghnkEL1IQQQgiRNQqGCCGEECJrFAwRQgghRNYoGCKEEEKIrFEw1APqTUYIIYRIn4Ix1n3DHAIAaG5uRmhoKJqamhASEiL0cAghhBDiAlev3zQzRAghhBBZo2CIEEIIIbJGwRAhhBBCZI2CIUIIIYTIGgVDhBBCCJE1CoYIIYQQImsUDBFCCCFE1qhrvQu4UkzNzc0Cj4QQQgghruKu2xcrqUjBkAv0ej0AICkpSeCREEIIIaS39Ho9QkNDu/0+VaB2gd1ux9mzZxEcHAyFQgEAmDhxIg4cONCv921ubkZSUhIqKir6XdnaHeOR6vvQ79l770O/a++8D/2evfM+9Hv2zvt48vfMGINer0d8fDyUyu4zg2hmyAVKpRKJiYmdHlOpVG5rzRESEtLv93LXeKT6PgD9nr3xPhz6XXv+fQD6PXvjfQD6PXvjfQDP/Z57mhHiUAJ1H61atUroIXTirvFI9X3cxdd+Ll97H3fytZ/N197HXXzt5/K193EXX/u5fO193KWv46FlMgFRA1jvoN+z99Dv2jvo9+wd9Hv2Dl/4PdPMkIC0Wi2eeeYZaLVaoYciafR79h76XXsH/Z69g37P3uELv2eaGSKEEEKIrNHMECGEEEJkjYIhQgghhMgaBUOEEEIIkTUKhgSyfv16XHHFFZg3bx5eeOEFtLW1CT0kyamursZzzz2Hyy+/HMuWLcMrr7wCk8kk9LAk7aeffsKUKVPwxz/+UeihSNbGjRtx3XXXYeHChXjppZdgtVqFHpLk5Ofn44EHHsD8+fNx5ZVXYvXq1XwnAtJ3+fn5eOSRRzB16lR88cUXXT7n5MmTuP322zF79mzcdtttyMnJ8crYKBgSwOrVq/HAAw9g6dKluO+++7Bu3TqsWLFC6GFJisFgwJQpUwAADz74IJYvX47XX38dixcvht1uF3h00lRXV4fbbrsNjY2NOHnypNDDkaRHH30Ud999N+bOnYs///nPaGxsxPPPPy/0sCSlvLwcU6ZMQV1dHZ544gncdtttWL9+PZYsWSL00ETtk08+wZIlS5CYmIicnBxUVlZe8JySkhJMnToVdrsdTzzxBNRqNaZNm4aCggLPD5ARrzIYDCwgIIC99tpr/GO//fYbA8D27t0r4MikxWq1MqPR2OmxX3/9lQFgR48eFWhU0nbllVeyF154gV1zzTXsiiuuEHo4krN7924GgO3YsaPT462trQKNSJref/99plQqmclk4h/bsGEDA8CampoEHJm4dfzdhYaGdroGcu6++242cuRIZrfbGWOM2e12lpmZyW677TaPj49mhrzst99+g9FoxOLFi/nHpkyZgtjYWOzYsUPAkUmLSqWCv79/p8eCgoIAAGazWYghSdrLL7+MpqYmPP7440IPRbI++OADDB48GPPmzev0uE6nE2hE0jR27FgoFArs27ePf+zXX3/F0KFDERwcLODIxM2VYoo7d+7ElVdeyfcAVSgUuOqqq7xybaTeZF5WVlYGAIiLi+v0eFxcHP894hl/+9vfkJqaijFjxgg9FEk5fPgwVq9ejf379/fYCJH0T25uLiZMmID33nsPH3/8MQICAjB37lzcd9998PPzE3p4kjFq1Ch88803uPbaaxETE4Pm5mbEx8dj165d/EWaeEZZWRni4+M7PRYfH4/Tp0/DZrNBpVJ57LMpGPIyi8UCpVIJjUbT6XF/f39YLBaBRiV9L7zwArZs2YKdO3de8LsnfWcwGLBixQr85z//QUpKitDDkbS2tjZ88803MBgMeOyxx1BbW4unnnoKu3fv7jYZlfTeuXPn8MADD2Du3LlYuXIlGhsb8eyzz+Lxxx/H+vXrhR6eZDHGYLPZLqhCzc3wW61WCoakJCIiAna7HU1NTQgLC+Mfr6urQ2RkpHADk7D//Oc/eP7555GVlYVp06YJPRxJ+fXXX1FSUoJXX30Vr776KgCgsLAQdrsdU6ZMwWeffUZBkptERERAoVDg888/5y8YgYGBWLp0Kc6ePXvBHTXpm1dffRUWiwUffvghf/FNS0vDxIkT8cADD2DSpEkCj1CaFAoFwsLCUF9f3+nxuro6BAYGerxVBwVDXjZu3DgAwIEDB7BgwQIAjv/Zp06dwtixY4UcmiS98soreOqpp7Bp0yYsWrRI6OFIzpQpU7B79+5Ojz311FMwm8146aWXEBsbK9DIpGfChAkoKirqdFHgltsbGhooGHKT+vp6xMbGdpqF4H6351+oiXuNGzcOBw4c6PTYvn37vHJtpAV+L8vIyMCsWbOwevVqPpH3r3/9K8LCwnDVVVcJPDppee211/DEE09g06ZNuPTSS4UejiSFhoZiypQpnb4iIiIQFhaGKVOmUHKvG61cuRJnzpzBt99+CwCw2Wx48803kZiYiCFDhgg8OumYNWsWDh8+zAf5jDG89tprCAwM5G9miWfccccd+Pbbb/mA6MiRI9iyZQvuuOMOj382NWoVQHl5OZYsWYKysjIEBgbCZrPh008/xaxZs4QemmScOXMGSUlJiIyMRHp6eqfv/fWvf8X8+fMFGpn0XXvttWhra8PXX38t9FAkZ8OGDbj33nsRGxuLhoYGhIeHY/369ZgwYYLQQ5OUxx57DK+//jrS0tLQ1NQExhj++9//Uq2hfjh58iRuu+02AMDBgweRlJSE2NhYzJ07Fy+88AL/vMcffxyvvPIKUlJSUFpaivvvvx///ve/PZ68TsGQgAoKCmAymTBs2DCo1bRi6U4mkwlHjhzp8nuDBg2i/CwP4nKGaLbCM0wmE06ePImwsDAkJyfTDicPaWlpQWlpKfz9/ZGcnEzn6H5qaWnB8ePHL3g8MjISgwYN6vRYXV0dysrKkJycjKioKK+Mj4IhQgghhMga5QwRQgghRNYoGCKEEEKIrFEwRAghhBBZo2CIEEIIIbJGwRAhhBBCZI2CIUIIIYTIGgVDhBBCCJE1CoYIIbL25JNPYu/evUIPgxAiIAqGCCGy1djYiH/84x9UXZgQmaNgiBAiS/v378cdd9wBxhjeeOMN3Hvvvdi2bZvQwyKECIBuhwghsqTVamGz2ZCWloaJEycCAAYOHCjwqAghQqDeZIQQ2Vq5ciUYY1i3bp3QQyGECIiWyQghsnX06FGMGTNG6GEQQgRGwRAhRJasVityc3MpGCKEUDBECJGnkydPwmQyYfTo0UIPhRAiMAqGCCGyVFJSAp1Oh6ioKKGHQggRGAVDhBBZyszMhFKpxGWXXYZ7770XhYWFQg+JECIQ2lpPCJGlpKQk5OXl4eeff4bBYEBsbKzQQyKECIS21hNCCCFE1miZjBBCCCGyRsEQIYQQQmSNgiFCCCGEyBoFQ4QQQgiRNQqGCCGEECJrFAwRQgghRNYoGCKEEEKIrFEwRAghhBBZo2CIEEIIIbJGwRAhhBBCZI2CIUIIIYTIGgVDhBBCCJG1/w/S8DH6N8weeQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numexpr\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Using numexpr expressions directly in o.plot()\n",
    "o.plot(d1=\"t\", d2=\"R*cos(phi)*sin(phi)\")\n",
    "plt.title(r\"Using numexpr: $R\\,\\cos\\phi*\\sin\\phi$ vs. $t$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cddf14fe",
   "metadata": {
    "papermill": {
     "duration": 0.015378,
     "end_time": "2026-06-30T01:16:01.523030+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.507652+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Without `numexpr`, you can specify the computation manually using a lambda function of time given as ``d1`` or ``d2``, which is useful for functions that cannot be parsed by ``numexpr``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f73e762f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:01.554922Z",
     "iopub.status.busy": "2026-06-30T01:16:01.554700Z",
     "iopub.status.idle": "2026-06-30T01:16:01.715704Z",
     "shell.execute_reply": "2026-06-30T01:16:01.714571Z"
    },
    "papermill": {
     "duration": 0.178068,
     "end_time": "2026-06-30T01:16:01.716428+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.538360+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plot(\n",
    "    d1=\"t\",\n",
    "    d2=lambda t: o.R(t) * numpy.cos(o.phi(t)) * numpy.sin(o.phi(t)),\n",
    "    ylabel=r\"$R\\,\\cos\\phi\\,\\sin\\phi$\",\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43a35ea4",
   "metadata": {
    "papermill": {
     "duration": 0.015736,
     "end_time": "2026-06-30T01:16:01.747558+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.731822+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Animating the orbit\n",
    "\n",
    "In a [jupyter notebook](http://jupyter.org) or in [jupyterlab](http://jupyterlab.readthedocs.io/en/stable/) (jupyterlab versions >= 0.33) you can also create an animation of an orbit *after* you have integrated it. For example, consider the following orbit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "837cf516",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:01.780245Z",
     "iopub.status.busy": "2026-06-30T01:16:01.780002Z",
     "iopub.status.idle": "2026-06-30T01:16:01.787589Z",
     "shell.execute_reply": "2026-06-30T01:16:01.786506Z"
    },
    "papermill": {
     "duration": 0.02503,
     "end_time": "2026-06-30T01:16:01.788290+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.763260+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "lp = LogarithmicHaloPotential(normalize=1.0)\n",
    "op = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "op.integrate(ts, lp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60bfdd2a",
   "metadata": {
    "papermill": {
     "duration": 0.015505,
     "end_time": "2026-06-30T01:16:01.819466+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.803961+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "If we then do ``op.animate()`` we get the following"
   ]
  },
  {
   "cell_type": "raw",
   "id": "4f7a7408",
   "metadata": {
    "papermill": {
     "duration": 0.01595,
     "end_time": "2026-06-30T01:16:01.851646+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.835696+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
   "source": [
    "<style>\n",
    "  .galpybutton {\n",
    "      background-color:#ffffff;\n",
    "      -moz-border-radius:16px;\n",
    "      -webkit-border-radius:16px;\n",
    "      border-radius:16px;\n",
    "      border:1px solid #1f77b4;\n",
    "      display:inline-block;\n",
    "      cursor:pointer;\n",
    "      color:#1f77b4;\n",
    "      font-family:Courier;\n",
    "      font-size:17px;\n",
    "      padding:8px 10px;\n",
    "      text-decoration:none;\n",
    "      text-shadow:0px 1px 0px #2f6627;\n",
    "  }\n",
    "  .galpybutton:hover {\n",
    "      background-color:#ffffff;\n",
    "  }\n",
    "  .galpybutton:active {\n",
    "      position:relative;\n",
    "      top:1px;\n",
    "  }\n",
    "  .galpybutton:focus{\n",
    "      outline:0;\n",
    "  }\n",
    "  </style>\n",
    "\n",
    "  <div id='galpy-knpeaurozjomyixuoikkmtea' style='width:600px;height:400px;'></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-play\" style=\"margin-left:70px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-playpause\" style='width: 108px !important'>Play</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-timestwo\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>x<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-timeshalf\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>/<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-replay\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Replay</button></div>\n",
    "\n",
    "  <script src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"></script>\n",
    "  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/3.6.1/jquery.min.js\"></script>\n",
    "\n",
    "  <script>\n",
    "  require.config({\n",
    "    paths: {\n",
    "      Plotly: 'https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.16.4/plotly.min',\n",
    "    }\n",
    "  });\n",
    "  </script>\n",
    "\n",
    "  <script>\n",
    "  require(['Plotly'], function (Plotly) {\n",
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    "    let layout = {\n",
    "    xaxis: {\n",
    "      title: 'R (kpc)',\n",
    "      domain: [0,1],\n",
    "  },\n",
    "    yaxis: {title: 'z (kpc)'},\n",
    "    margin: {t: 20},\n",
    "    hovermode: 'closest',\n",
    "    showlegend: false,\n",
    "  };\n",
    "    let numPerFrame= 5;\n",
    "    let cnt= 1;\n",
    "    let interval;\n",
    "    let trace_slice_len;\n",
    "    let trace_slice_begin;\n",
    "    let trace_slice_end;\n",
    "\n",
    "    setup_trace();\n",
    "\n",
    "    $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-play' ) {\n",
    "        clearInterval(interval);\n",
    "        interval= animate_trace();\n",
    "        document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Pause';\n",
    "        document.getElementById('galpy-knpeaurozjomyixuoikkmtea-play').id = 'galpy-knpeaurozjomyixuoikkmtea-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-knpeaurozjomyixuoikkmtea-pause').id = 'galpy-knpeaurozjomyixuoikkmtea-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-timestwo' ) {\n",
    "        cnt/= 2;\n",
    "        numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-timeshalf' ) {\n",
    "        cnt*= 2;\n",
    "        numPerFrame/= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-replay' ) {\n",
    "        $(\"#galpy-knpeaurozjomyixuoikkmtea-playpause\").removeAttr('disabled');\n",
    "        document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Pause';\n",
    "        try { // doesn't exist if replay with pressing pause\n",
    "        document.getElementById('galpy-knpeaurozjomyixuoikkmtea-play').id = 'galpy-knpeaurozjomyixuoikkmtea-pause';\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "        cnt= 1;\n",
    "        try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea',[1, ]);\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "          Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea', [0]);\n",
    "        clearInterval(interval);\n",
    "        setup_trace();\n",
    "        interval= animate_trace();\n",
    "      }\n",
    "    });\n",
    "\n",
    "    function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
    "         },\n",
    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "      let trace2= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "\n",
    "\n",
    "      let traces= [trace1,trace2];\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "      Plotly.newPlot('galpy-knpeaurozjomyixuoikkmtea',traces,layout,{staticPlot: false});\n",
    "    }\n",
    "\n",
    "    function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "        // Make sure narrow and thick trace end in the same\n",
    "        // and the highlighted length has constant length\n",
    "        trace_slice_len= Math.floor(numPerFrame);\n",
    "        if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "        trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "        trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.extendTraces('galpy-knpeaurozjomyixuoikkmtea', traces, [0, ]);\n",
    "        trace_slice_begin-= trace_slice_len;\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.restyle('galpy-knpeaurozjomyixuoikkmtea', traces, [1, ]);\n",
    "        cnt+= 1;\n",
    "        // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "        if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "            document.getElementById(\"galpy-knpeaurozjomyixuoikkmtea-playpause\").disabled = \"disabled\";\n",
    "            document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Finished!';\n",
    "            // making sure the whole orbits is plotted when finished\n",
    "            trace_slice_begin = trace_slice_end;\n",
    "            trace_slice_end = -1;\n",
    "            traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "            Plotly.extendTraces('galpy-knpeaurozjomyixuoikkmtea', traces, [0, ]);\n",
    "            // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "            Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea', [1, ]);\n",
    "            clearInterval(interval);\n",
    "        };\n",
    "          }, 30);\n",
    "      }\n",
    "  });\n",
    "  </script>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b881565b",
   "metadata": {
    "papermill": {
     "duration": 0.015577,
     "end_time": "2026-06-30T01:16:01.882989+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.867412+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "**Tip**\n",
    "\n",
    "There is currently no option to save the animation within ``galpy``, but you could use screen capture software (for example, QuickTime's [Screen Recording](https://support.apple.com/kb/ph5882?locale=en_CA) feature) to record your screen while the animation is running and save it as a video.\n",
    "\n",
    "</div>\n",
    "\n",
    "``animate`` has options to specify the width and height of the resulting animation, and it can also animate up to three projections of an orbit at the same time. For example, we can look at the orbit in both (x,y) and (R,z) at the same time with ``op.animate(d1=['x','R'],d2=['y','z'],width=800)``, which gives"
   ]
  },
  {
   "cell_type": "raw",
   "id": "6ff006f3",
   "metadata": {
    "papermill": {
     "duration": 0.015611,
     "end_time": "2026-06-30T01:16:01.914312+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.898701+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
   "source": [
    "<style>\n",
    "  .galpybutton {\n",
    "      background-color:#ffffff;\n",
    "      -moz-border-radius:16px;\n",
    "      -webkit-border-radius:16px;\n",
    "      border-radius:16px;\n",
    "      border:1px solid #1f77b4;\n",
    "      display:inline-block;\n",
    "      cursor:pointer;\n",
    "      color:#1f77b4;\n",
    "      font-family:Courier;\n",
    "      font-size:17px;\n",
    "      padding:8px 10px;\n",
    "      text-decoration:none;\n",
    "      text-shadow:0px 1px 0px #2f6627;\n",
    "  }\n",
    "  .galpybutton:hover {\n",
    "      background-color:#ffffff;\n",
    "  }\n",
    "  .galpybutton:active {\n",
    "      position:relative;\n",
    "      top:1px;\n",
    "  }\n",
    "  .galpybutton:focus{\n",
    "      outline:0;\n",
    "  }\n",
    "  </style>\n",
    "\n",
    "  <div id='galpy-inbxvjdspcnngdiraredcdou' style='width:800px;height:400px;'></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-play\" style=\"margin-left:170px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-playpause\"  style='width: 108px !important'>Play</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-timestwo\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>x<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-timeshalf\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>/<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-replay\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Replay</button></div>\n",
    "\n",
    "  <script src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"></script>\n",
    "  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/3.6.1/jquery.min.js\"></script>\n",
    "\n",
    "\n",
    "  <script>\n",
    "  require.config({\n",
    "    paths: {\n",
    "      Plotly: 'https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.16.4/plotly.min',\n",
    "    }\n",
    "  });\n",
    "  </script>\n",
    "\n",
    "  <script>\n",
    "  require(['Plotly'], function (Plotly) {\n",
    "    let data= JSON.parse('{\"x1_0\": [8.0, 8.00760157841249, 8.014403703227323, 8.020407343941182, 8.025613581274285, 8.030023605886074, 8.033638717057238, 8.03646032133981, 8.03848993117692, 8.039729163494036, 8.040179738263237, 8.039843477042336, 8.038722301490411, 8.036818231861506, 8.034133385478093, 8.030669975185948, 8.026430307792094, 8.02141678248736, 8.015631889255172, 8.009078207268116, 8.001758403273806, 7.99367522997157, 7.9848315243813985, 7.975230206206632, 7.964874276191785, 7.953766814476874, 7.941910978949617, 7.929310003596785, 7.915967196856022, 7.901885939969304, 7.887069685339312, 7.871521954889818, 7.855246338431233, 7.838246492032417, 7.820526136399737, 7.80208905526445, 7.78293909377933, 7.763080156925454, 7.742516207930091, 7.7212512666964646, 7.699289408246248, 7.676634761175553, 7.653291506125122, 7.629263874265413, 7.604556145797273, 7.579172648468751, 7.553117756108688, 7.526395887177581, 7.49901150333626, 7.470969108032839, 7.442273245108376, 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    "    let layout = {\n",
    "    xaxis: {\n",
    "      title: 'x (kpc)',\n",
    "      domain: [0,0.45],\n",
    "  },\n",
    "    yaxis: {title: 'y (kpc)'},\n",
    "    margin: {t: 20},\n",
    "    hovermode: 'closest',\n",
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    "      domain: [0.55,1],\n",
    "  },\n",
    "    yaxis2: {\n",
    "      title: 'z (kpc)',\n",
    "      anchor: 'x2',\n",
    "  },\n",
    "  };\n",
    "    let numPerFrame= 5;\n",
    "    let cnt= 1;\n",
    "    let interval;\n",
    "    let trace_slice_len;\n",
    "    let trace_slice_begin;\n",
    "    let trace_slice_end;\n",
    "\n",
    "    setup_trace();\n",
    "\n",
    "    $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-play' ) {\n",
    "        clearInterval(interval);\n",
    "        interval= animate_trace();\n",
    "        document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Pause';\n",
    "        document.getElementById('galpy-inbxvjdspcnngdiraredcdou-play').id = 'galpy-inbxvjdspcnngdiraredcdou-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-inbxvjdspcnngdiraredcdou-pause').id = 'galpy-inbxvjdspcnngdiraredcdou-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-timestwo' ) {\n",
    "        cnt/= 2;\n",
    "        numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-timeshalf' ) {\n",
    "        cnt*= 2;\n",
    "        numPerFrame/= 2;\n",
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    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-replay' ) {\n",
    "        $(\"#galpy-inbxvjdspcnngdiraredcdou-playpause\").removeAttr('disabled');\n",
    "        document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Pause';\n",
    "        try { // doesn't exist if replay with pressing pause\n",
    "        document.getElementById('galpy-inbxvjdspcnngdiraredcdou-play').id = 'galpy-inbxvjdspcnngdiraredcdou-pause';\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "        cnt= 1;\n",
    "        try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou',[1, 3, ]);\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "          Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou', [0, 1]);\n",
    "        clearInterval(interval);\n",
    "        setup_trace();\n",
    "        interval= animate_trace();\n",
    "      }\n",
    "    });\n",
    "\n",
    "    function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
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    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
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    "\n",
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    "      let trace3= {\n",
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    "        y: data.y2_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        xaxis: 'x2',\n",
    "        yaxis: 'y2',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
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    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
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    "        y: data.y2_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        xaxis: 'x2',\n",
    "        yaxis: 'y2',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "\n",
    "\n",
    "      let traces= [trace1,trace2,trace3,trace4];\n",
    "\n",
    "\n",
    "      Plotly.newPlot('galpy-inbxvjdspcnngdiraredcdou',traces,layout,{staticPlot: false});\n",
    "    }\n",
    "\n",
    "    function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "        // Make sure narrow and thick trace end in the same\n",
    "        // and the highlighted length has constant length\n",
    "        trace_slice_len= Math.floor(numPerFrame);\n",
    "        if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "        trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "        trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.extendTraces('galpy-inbxvjdspcnngdiraredcdou', traces, [0, 2, ]);\n",
    "        trace_slice_begin-= trace_slice_len;\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.restyle('galpy-inbxvjdspcnngdiraredcdou', traces, [1, 3, ]);\n",
    "        cnt+= 1;\n",
    "        // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "        if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "            document.getElementById(\"galpy-inbxvjdspcnngdiraredcdou-playpause\").disabled = \"disabled\";\n",
    "            document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Finished!';\n",
    "            // making sure the whole orbits is plotted when finished\n",
    "            trace_slice_begin = trace_slice_end;\n",
    "            trace_slice_end = -1;\n",
    "            traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "            Plotly.extendTraces('galpy-inbxvjdspcnngdiraredcdou', traces, [0, 2, ]);\n",
    "            // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "            Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou', [1, 3, ]);\n",
    "            clearInterval(interval);\n",
    "        };\n",
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     "end_time": "2026-06-30T01:16:01.945340+00:00",
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     "start_time": "2026-06-30T01:16:01.929848+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n",
    "You can also animate orbit in 3D with an optional Milky Way galaxy centered at the origin with ``op.animate3d(mw_plane_bg=True)``, which gives\n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "69c79251",
   "metadata": {
    "papermill": {
     "duration": 0.015589,
     "end_time": "2026-06-30T01:16:01.976515+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:01.960926+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
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    "      let layout = {\n",
    "              scene:{\n",
    "                  // force the scene always look like a cube\n",
    "                  aspectmode: 'cube',\n",
    "                  xaxis: {\n",
    "                      title: 'x (kpc)',\n",
    "                      domain: [0,1],\n",
    "                          },\n",
    "                  yaxis: {title: 'y (kpc)'},\n",
    "                  zaxis: {title: 'z (kpc)'},},\n",
    "                  margin: {t: 20},\n",
    "                  hovermode: 'closest',\n",
    "                  showlegend: false,\n",
    "                  };\n",
    "      let numPerFrame= 5;\n",
    "      let cnt= 1;\n",
    "      let interval;\n",
    "      let trace_slice_len;\n",
    "      let trace_slice_begin;\n",
    "      let trace_slice_end;\n",
    "\n",
    "      // guess on plotly current axis limit\n",
    "      let xaxis_min_guess;\n",
    "      let xaxis_max_guess;\n",
    "      let yaxis_min_guess;\n",
    "      let yaxis_max_guess;\n",
    "      let zaxis_min_guess;\n",
    "      let zaxis_max_guess;\n",
    "\n",
    "      setup_trace();\n",
    "\n",
    "      $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-play' ) {\n",
    "          clearInterval(interval);\n",
    "          interval= animate_trace();\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Pause';\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-play').id = 'galpy-srgqzhsgyxwdxovzaqreowll-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-pause').id = 'galpy-srgqzhsgyxwdxovzaqreowll-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-timestwo' ) {\n",
    "          cnt/= 2;\n",
    "          numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-timeshalf' ) {\n",
    "          cnt*= 2;\n",
    "          numPerFrame/= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-replay' ) {\n",
    "          $(\"#galpy-srgqzhsgyxwdxovzaqreowll-playpause\").removeAttr('disabled');\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Pause';\n",
    "          try { // doesn't exist if replay with pressing pause\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-play').id = 'galpy-srgqzhsgyxwdxovzaqreowll-pause';\n",
    "          }\n",
    "          catch (err) {\n",
    "          }\n",
    "          cnt= 1;\n",
    "          try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll',[1, ]);\n",
    "          }\n",
    "          catch (err) {\n",
    "          }\n",
    "          Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll', [0]);\n",
    "          clearInterval(interval);\n",
    "          setup_trace();\n",
    "          interval= animate_trace();\n",
    "      }\n",
    "      });\n",
    "\n",
    "      function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "          x: data.x1_0.slice(0,numPerFrame),\n",
    "          y: data.y1_0.slice(0,numPerFrame),\n",
    "          z: data.z1_0.slice(0,numPerFrame),\n",
    "          customdata: data.time,\n",
    "          hovertemplate: '<b>Object 0</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>z (kpc)</b>: %{z:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "          mode: 'lines',\n",
    "          name: '',\n",
    "          line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "          type: \"scatter3d\",\n",
    "      };\n",
    "\n",
    "      let trace2= {\n",
    "          x: data.x1_0.slice(0,numPerFrame),\n",
    "          y: data.y1_0.slice(0,numPerFrame),\n",
    "          z: data.z1_0.slice(0,numPerFrame),\n",
    "          customdata: data.time,\n",
    "          hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>z (kpc)</b>: %{z:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "          mode: 'lines',\n",
    "          name: '',\n",
    "          line: {\n",
    "          shape: 'spline',\n",
    "          width: 8.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "          type: \"scatter3d\",\n",
    "      };\n",
    "      let mw_bg = {\n",
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    "              [255, 255, 255, 255, 253, 247, 243, 235, 227, 216, 197, 184, 192, 197, 189, 161, 134, 121, 117, 119, 129, 135, 132, 126, 119, 105, 92, 95, 124, 162, 176, 136, 151, 189, 174, 155, 149, 140, 170, 209, 213, 211, 229, 237, 243, 248, 253, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 251, 245, 239, 231, 221, 205, 193, 198, 200, 191, 158, 104, 100, 124, 134, 145, 160, 160, 162, 166, 165, 154, 134, 102, 90, 105, 151, 156, 155, 180, 177, 165, 148, 124, 153, 199, 208, 205, 226, 235, 241, 248, 252, 255, 255, 255],\n",
    "              [255, 255, 255, 254, 248, 243, 235, 227, 214, 201, 202, 205, 197, 165, 112, 103, 127, 151, 159, 169, 161, 153, 161, 147, 161, 171, 172, 151, 120, 73, 110, 158, 160, 170, 177, 169, 153, 115, 137, 190, 199, 204, 223, 232, 239, 245, 251, 254, 255, 255],\n",
    "              [255, 255, 255, 253, 247, 241, 233, 222, 207, 203, 206, 201, 177, 135, 116, 145, 161, 162, 156, 143, 139, 132, 152, 174, 173, 161, 162, 179, 156, 108, 90, 139, 158, 158, 175, 169, 151, 134, 143, 176, 199, 204, 219, 230, 237, 243, 250, 254, 255, 255],\n",
    "              [255, 255, 255, 251, 246, 238, 231, 216, 206, 208, 206, 186, 125, 120, 154, 163, 167, 163, 139, 129, 124, 78, 92, 167, 177, 179, 151, 171, 176, 139, 92, 116, 147, 145, 175, 166, 144, 138, 140, 171, 196, 200, 216, 228, 234, 242, 249, 254, 255, 255],\n",
    "              [255, 255, 255, 250, 244, 235, 228, 214, 209, 209, 200, 150, 112, 133, 161, 170, 170, 148, 144, 142, 60, 25, 68, 124, 147, 172, 182, 162, 171, 165, 116, 109, 135, 138, 172, 166, 143, 117, 130, 173, 195, 204, 216, 228, 234, 241, 247, 252, 255, 255],\n",
    "              [255, 255, 255, 249, 242, 233, 224, 213, 208, 208, 179, 126, 131, 156, 162, 175, 154, 125, 148, 94, 67, 59, 38, 76, 119, 128, 154, 173, 161, 172, 117, 91, 133, 130, 164, 158, 141, 118, 126, 168, 196, 210, 216, 227, 234, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 255, 249, 242, 233, 220, 211, 211, 205, 158, 131, 151, 164, 173, 173, 133, 132, 133, 81, 129, 115, 39, 15, 31, 64, 106, 165, 170, 163, 115, 79, 132, 142, 163, 148, 146, 120, 127, 174, 191, 210, 220, 226, 232, 241, 246, 252, 255, 255],\n",
    "              [255, 254, 253, 248, 242, 232, 215, 208, 215, 191, 140, 134, 154, 168, 177, 165, 130, 144, 91, 93, 162, 153, 89, 17, 0, 8, 54, 127, 170, 156, 122, 99, 131, 158, 147, 144, 142, 123, 145, 174, 194, 208, 219, 226, 232, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 253, 247, 242, 231, 214, 211, 215, 182, 131, 139, 157, 170, 175, 156, 129, 144, 99, 115, 170, 175, 127, 59, 4, 0, 21, 83, 145, 156, 121, 117, 125, 149, 140, 137, 142, 131, 150, 178, 198, 209, 217, 227, 233, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 253, 248, 242, 231, 216, 214, 213, 184, 136, 137, 161, 171, 177, 158, 142, 139, 97, 136, 165, 175, 155, 120, 70, 27, 12, 40, 113, 145, 100, 111, 126, 138, 146, 153, 119, 118, 156, 187, 196, 208, 219, 226, 232, 241, 248, 252, 255, 255],\n",
    "              [255, 255, 253, 249, 241, 231, 219, 216, 211, 183, 140, 137, 168, 171, 176, 160, 145, 145, 88, 119, 162, 173, 183, 149, 136, 113, 67, 40, 81, 95, 79, 113, 131, 140, 154, 141, 102, 123, 167, 192, 192, 201, 220, 227, 235, 241, 247, 253, 255, 255],\n",
    "              [255, 254, 253, 249, 242, 231, 221, 220, 215, 181, 133, 140, 164, 173, 176, 155, 149, 156, 92, 97, 160, 166, 184, 184, 164, 148, 126, 67, 33, 49, 106, 137, 146, 162, 156, 125, 120, 154, 184, 190, 180, 199, 222, 229, 235, 242, 249, 252, 255, 255],\n",
    "              [255, 255, 254, 250, 243, 232, 222, 223, 216, 190, 125, 128, 166, 176, 173, 165, 161, 160, 108, 83, 139, 164, 155, 180, 195, 183, 169, 120, 50, 86, 127, 140, 160, 155, 126, 107, 124, 167, 184, 163, 178, 215, 226, 229, 236, 243, 248, 255, 255, 255],\n",
    "              [254, 255, 254, 250, 244, 234, 223, 222, 219, 193, 140, 141, 157, 175, 174, 173, 171, 165, 142, 97, 102, 148, 156, 146, 166, 179, 191, 172, 128, 107, 127, 148, 144, 131, 114, 117, 141, 168, 175, 176, 205, 221, 225, 232, 238, 245, 250, 253, 255, 255],\n",
    "              [255, 255, 254, 251, 245, 237, 224, 219, 222, 199, 161, 134, 148, 169, 175, 179, 176, 168, 157, 132, 95, 104, 150, 156, 140, 145, 147, 153, 154, 144, 147, 143, 121, 91, 108, 158, 171, 174, 181, 205, 215, 221, 228, 233, 240, 245, 250, 255, 255, 255],\n",
    "              [255, 255, 255, 252, 246, 239, 229, 223, 222, 210, 165, 128, 150, 165, 178, 185, 181, 170, 150, 154, 133, 87, 91, 123, 141, 151, 147, 144, 145, 139, 129, 106, 91, 113, 149, 180, 191, 186, 192, 211, 218, 224, 229, 236, 242, 248, 253, 255, 255, 255],\n",
    "              [255, 255, 254, 252, 247, 241, 233, 227, 225, 217, 184, 145, 140, 159, 176, 187, 184, 180, 143, 150, 164, 134, 96, 86, 91, 97, 112, 116, 104, 90, 84, 108, 138, 170, 189, 190, 179, 169, 199, 215, 221, 226, 232, 239, 244, 250, 254, 255, 255, 255],\n",
    "              [255, 255, 254, 252, 248, 243, 236, 231, 227, 221, 201, 161, 142, 159, 170, 184, 188, 186, 168, 149, 158, 164, 154, 129, 113, 94, 96, 108, 111, 105, 123, 168, 185, 187, 180, 170, 170, 188, 211, 220, 225, 229, 235, 242, 247, 252, 255, 255, 255, 255],\n",
    "              [255, 254, 254, 253, 249, 245, 239, 234, 231, 226, 213, 180, 152, 158, 168, 179, 188, 188, 190, 165, 143, 145, 161, 168, 169, 170, 159, 161, 175, 179, 190, 187, 170, 163, 163, 181, 201, 214, 218, 221, 227, 232, 239, 245, 250, 254, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 254, 252, 249, 243, 237, 234, 230, 222, 204, 164, 135, 163, 175, 183, 189, 193, 187, 169, 169, 170, 148, 159, 177, 174, 178, 180, 185, 185, 181, 177, 179, 194, 210, 212, 216, 219, 225, 230, 236, 243, 248, 253, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 254, 252, 248, 241, 236, 234, 229, 219, 191, 151, 152, 163, 175, 182, 188, 194, 188, 183, 190, 177, 158, 165, 173, 161, 161, 173, 184, 188, 199, 207, 209, 211, 214, 220, 224, 228, 234, 241, 246, 251, 254, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 254, 252, 246, 240, 236, 234, 229, 214, 187, 144, 147, 173, 176, 180, 186, 186, 182, 187, 195, 194, 188, 188, 184, 181, 191, 198, 202, 205, 208, 212, 215, 222, 223, 229, 233, 239, 245, 249, 253, 254, 255, 255, 255, 255, 255],\n",
    "              [255, 254, 255, 255, 255, 255, 254, 251, 245, 241, 237, 235, 227, 207, 173, 151, 151, 162, 177, 178, 180, 185, 187, 192, 197, 199, 198, 201, 203, 202, 205, 207, 210, 214, 216, 221, 223, 228, 233, 239, 243, 248, 252, 254, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 251, 245, 241, 239, 236, 226, 206, 184, 149, 141, 168, 176, 180, 185, 189, 190, 193, 197, 200, 205, 207, 209, 210, 211, 214, 215, 217, 221, 227, 233, 237, 242, 246, 251, 254, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 253, 250, 247, 244, 241, 236, 226, 214, 198, 177, 169, 166, 175, 186, 194, 191, 194, 196, 198, 205, 212, 215, 215, 213, 213, 214, 218, 225, 232, 238, 241, 245, 249, 253, 254, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 252, 249, 246, 242, 238, 231, 223, 215, 201, 190, 188, 184, 186, 196, 199, 201, 202, 207, 212, 214, 215, 215, 217, 218, 225, 234, 239, 242, 245, 248, 252, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 253, 251, 248, 245, 240, 234, 228, 222, 218, 217, 211, 203, 205, 207, 206, 204, 206, 211, 216, 220, 223, 226, 228, 234, 240, 244, 246, 249, 251, 253, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 255, 254, 252, 250, 247, 244, 238, 234, 231, 227, 225, 224, 219, 217, 216, 214, 216, 221, 226, 230, 232, 235, 238, 242, 245, 248, 250, 252, 253, 254, 255, 255, 255, 255, 255, 255, 254, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 253, 252, 250, 247, 244, 241, 240, 236, 235, 232, 230, 230, 231, 232, 234, 236, 238, 239, 242, 246, 249, 250, 252, 253, 254, 254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 254, 252, 253, 250, 247, 246, 245, 244, 244, 243, 243, 243, 244, 245, 247, 247, 250, 252, 253, 253, 254, 254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 255, 254, 253, 252, 251, 252, 250, 251, 250, 251, 252, 253, 253, 254, 254, 254, 255, 255, 255, 255, 255, 255, 254, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255]\n",
    "          ],\n",
    "              hoverinfo:\"skip\",\n",
    "              showscale:false,\n",
    "              cmax:255,\n",
    "              cmin:0,\n",
    "              type: 'surface',\n",
    "              };\n",
    "\n",
    "      let traces= [trace1,trace2,mw_bg];\n",
    "\n",
    "      Plotly.newPlot('galpy-srgqzhsgyxwdxovzaqreowll',traces,layout);\n",
    "      }\n",
    "\n",
    "      function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "          // Make sure narrow and thick trace end in the same\n",
    "          // and the highlighted length has constant length\n",
    "          trace_slice_len= Math.floor(numPerFrame);\n",
    "          if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "          trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "          trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "          traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "          Plotly.extendTraces('galpy-srgqzhsgyxwdxovzaqreowll', traces, [0, ]);\n",
    "          trace_slice_begin-= trace_slice_len;\n",
    "          traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "          Plotly.restyle('galpy-srgqzhsgyxwdxovzaqreowll', traces, [1, ]);\n",
    "          cnt+= 1;\n",
    "          // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "          if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "              document.getElementById(\"galpy-srgqzhsgyxwdxovzaqreowll-playpause\").disabled = \"disabled\";\n",
    "              document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Finished!';\n",
    "              // making sure the whole orbits is plotted when finished\n",
    "              trace_slice_begin = trace_slice_end;\n",
    "              trace_slice_end = -1;\n",
    "              traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "              Plotly.extendTraces('galpy-srgqzhsgyxwdxovzaqreowll', traces, [0, ]);\n",
    "              // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "              Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll', [1, ]);\n",
    "              clearInterval(interval);\n",
    "          };\n",
    "      }, 50);\n",
    "      }\n",
    "      });\n",
    "      </script>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d38d457",
   "metadata": {
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     "exception": false,
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n",
    "If you want to embed the animation in a webpage, you can obtain the necessary HTML using the ``_repr_html_()`` function of the IPython.core.display.HTML object returned by ``animate``. By default, the HTML includes the entire orbit's data, but ``animate`` also has an option to store the orbit in a separate ``JSON`` file that will then be loaded by the output HTML code.\n",
    "\n",
    "``animate`` and ``animate3d`` also work for ``Orbit`` instances containing multiple objects."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379cbbc1e968416e875cc15c1202d7eb",
   "metadata": {
    "papermill": {
     "duration": 0.015484,
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     "start_time": "2026-06-30T01:16:02.023601+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Orbit characterization\n",
    "\n",
    "After integration, compute orbital parameters numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "277c27b1587741f2af2001be3712ef0d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.072258Z",
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     "shell.execute_reply": "2026-06-30T01:16:02.076349Z"
    },
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     "start_time": "2026-06-30T01:16:02.055006+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eccentricity: 0.07484773934372554\n",
      "Apocenter: 1.0847070212241001\n",
      "Pericenter: 0.9336384271952163\n",
      "Max |z|: 0.04328778107544663\n"
     ]
    }
   ],
   "source": [
    "print(\"Eccentricity:\", o.e())\n",
    "print(\"Apocenter:\", o.rap())\n",
    "print(\"Pericenter:\", o.rperi())\n",
    "print(\"Max |z|:\", o.zmax())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fa5554e",
   "metadata": {
    "papermill": {
     "duration": 0.015279,
     "end_time": "2026-06-30T01:16:02.108929+00:00",
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     "start_time": "2026-06-30T01:16:02.093650+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "These parameters can also be computed analytically using the Staeckel approximation, without any orbit integration (see [Fast Orbit Characterization](fast_characterization.ipynb)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "db7b79bc585a40fcaf58bf750017e135",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.141347Z",
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     "iopub.status.idle": "2026-06-30T01:16:02.156908Z",
     "shell.execute_reply": "2026-06-30T01:16:02.155610Z"
    },
    "papermill": {
     "duration": 0.033256,
     "end_time": "2026-06-30T01:16:02.157835+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.124579+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytic e: 0.07494364311796002\n",
      "Analytic rap: 1.0844978863649968\n",
      "Analytic rperi: 0.9332783818295365\n",
      "Analytic zmax: 0.043063219299077755\n"
     ]
    }
   ],
   "source": [
    "# Analytic computation using the Staeckel approximation (no integration needed)\n",
    "o_new = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "print(\"Analytic e:\", o_new.e(analytic=True, pot=MWPotential2014, type=\"staeckel\"))\n",
    "print(\"Analytic rap:\", o_new.rap(analytic=True, pot=MWPotential2014, type=\"staeckel\"))\n",
    "print(\n",
    "    \"Analytic rperi:\", o_new.rperi(analytic=True, pot=MWPotential2014, type=\"staeckel\")\n",
    ")\n",
    "print(\"Analytic zmax:\", o_new.zmax(analytic=True, pot=MWPotential2014, type=\"staeckel\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "916684f9a58a4a2aa5f864670399430d",
   "metadata": {
    "papermill": {
     "duration": 0.01562,
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     "start_time": "2026-06-30T01:16:02.173894+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Energy and energy conservation\n",
    "\n",
    "Energy can be computed at any time using `o.E(pot)`, where ``pot`` is the potential object that does not need to be specified if the orbit has been integrated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1671c31a24314836a5b85d7ef7fbf015",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.222232Z",
     "iopub.status.busy": "2026-06-30T01:16:02.221796Z",
     "iopub.status.idle": "2026-06-30T01:16:02.230690Z",
     "shell.execute_reply": "2026-06-30T01:16:02.229715Z"
    },
    "papermill": {
     "duration": 0.026248,
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     "start_time": "2026-06-30T01:16:02.205096+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy at t=0: -0.8633506513947898\n",
      "Energy at t=10: -0.8633506513947993\n",
      "Relative energy error: -1.093054796920349e-14\n"
     ]
    }
   ],
   "source": [
    "print(\"Energy at t=0:\", o.E(0.0))\n",
    "print(\"Energy at t=10:\", o.E(ts[-1]))\n",
    "print(\"Relative energy error:\", (o.E(ts[-1]) - o.E(0.0)) / abs(o.E(0.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f85563e6",
   "metadata": {
    "papermill": {
     "duration": 0.015981,
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "You can also conveniently check energy conservation by plotting the energy over time using ``o.plotE`` or the normalized energy error using ``o.plotEnorm``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c26241d3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.295065Z",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plotEnorm();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33b0902fd34d4ace834912fa1002cf8e",
   "metadata": {
    "papermill": {
     "duration": 0.01575,
     "end_time": "2026-06-30T01:16:02.536523+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.520773+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Accessing raw orbital data\n",
    "\n",
    "Evaluate orbital quantities at any time, or get the full array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f6fa52606d8c4a75a9b52967216f8f3f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.569861Z",
     "iopub.status.busy": "2026-06-30T01:16:02.569633Z",
     "iopub.status.idle": "2026-06-30T01:16:02.586848Z",
     "shell.execute_reply": "2026-06-30T01:16:02.585901Z"
    },
    "papermill": {
     "duration": 0.035472,
     "end_time": "2026-06-30T01:16:02.587905+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.552433+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R(t=5): 1.0248822021703112\n",
      "phi(t=5): -1.3550275501315028\n",
      "Full orbit shape: (10000, 6)\n"
     ]
    }
   ],
   "source": [
    "# At specific time\n",
    "print(\"R(t=5):\", o.R(5.0))\n",
    "print(\"phi(t=5):\", o.phi(5.0))\n",
    "\n",
    "# Full orbit array: shape (ntimes, ndim)\n",
    "orbit_array = o.getOrbit()\n",
    "print(\"Full orbit shape:\", orbit_array.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4d66d9d",
   "metadata": {
    "papermill": {
     "duration": 0.015595,
     "end_time": "2026-06-30T01:16:02.619321+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.603726+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Sky coordinates and many other quantities are also available as attributes (see the [API documentation](../../reference/orbit.rst) for a complete list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f5a1fa73e5044315a093ec459c9be902",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.652639Z",
     "iopub.status.busy": "2026-06-30T01:16:02.652368Z",
     "iopub.status.idle": "2026-06-30T01:16:02.674817Z",
     "shell.execute_reply": "2026-06-30T01:16:02.673843Z"
    },
    "papermill": {
     "duration": 0.040077,
     "end_time": "2026-06-30T01:16:02.675434+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.635357+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RA(t=5): 204.3700933860205\n",
      "Dec(t=5): -64.02927160795768\n"
     ]
    }
   ],
   "source": [
    "# Sky coordinates at specific time (requires ro/vo)\n",
    "print(\"RA(t=5):\", o_sky.ra(5.0))\n",
    "print(\"Dec(t=5):\", o_sky.dec(5.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdf66aed5cc84ca1b48e60bad68798a8",
   "metadata": {
    "papermill": {
     "duration": 0.015552,
     "end_time": "2026-06-30T01:16:02.706615+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.691063+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Creating a new orbit from evaluated position\n",
    "\n",
    "Calling an orbit as a function returns a new Orbit at that time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "28d3efd5258a48a79c179ea5c6759f01",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.739362Z",
     "iopub.status.busy": "2026-06-30T01:16:02.739101Z",
     "iopub.status.idle": "2026-06-30T01:16:02.743770Z",
     "shell.execute_reply": "2026-06-30T01:16:02.742836Z"
    },
    "papermill": {
     "duration": 0.022039,
     "end_time": "2026-06-30T01:16:02.744467+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.722428+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New orbit at t=5: <galpy.orbit.Orbits.Orbit object at 0x7f5e5f3cb350>\n",
      "R: 1.0248822021703112\n"
     ]
    }
   ],
   "source": [
    "o_at_5 = o(5.0)\n",
    "print(\"New orbit at t=5:\", o_at_5)\n",
    "print(\"R:\", o_at_5.R())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f9bc0b9dd2c44919cc8dcca39b469f8",
   "metadata": {
    "papermill": {
     "duration": 0.015733,
     "end_time": "2026-06-30T01:16:02.776336+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.760603+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Non-inertial frames\n",
    "\n",
    "The default assumption in galpy is that the frame that an orbit is integrated in is an inertial one. However, galpy also supports orbit integration in non-inertial frames that are rotating or whose center is accelerating (or a combination of the two). When a frame is not an inertial frame, fictitious forces such as the centrifugal and Coriolis forces need to be taken into account. galpy implements all of the necessary forces as part of the [NonInertialFrameForce](../../reference/potentialnoninertialframe.rst#noninertialframe-potential) class. objects of this class are instantiated with arbitrary three-dimensional rotation frequencies (and their time derivative) and/or arbitrary three-dimensional acceleration of the origin. The class documentation linked to above provides full mathematical details on the rotation and acceleration of the non-inertial frame.\n",
    "\n",
    "We can then, for example, integrate the orbit of the Sun in the LSR frame, that is, the frame that is corotating with that of the circular orbit at the location of the Sun. To do this for ``MWPotential2014``, do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0e382214b5f147d187d36a2058b9c724",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:02.809336Z",
     "iopub.status.busy": "2026-06-30T01:16:02.809052Z",
     "iopub.status.idle": "2026-06-30T01:16:02.983204Z",
     "shell.execute_reply": "2026-06-30T01:16:02.981963Z"
    },
    "papermill": {
     "duration": 0.191673,
     "end_time": "2026-06-30T01:16:02.983910+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:02.792237+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator dopr54_c instead)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import MWPotential2014, NonInertialFrameForce\n",
    "\n",
    "nip = NonInertialFrameForce(Omega=1.0)  # LSR has Omega=1 in natural units\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o.turn_physical_off()  # To use internal units\n",
    "o = Orbit(\n",
    "    [o.R(), o.vR(), o.vT() - 1.0, o.z(), o.vz(), o.phi()]\n",
    ")  # Convert to the LSR frame\n",
    "ts = numpy.linspace(0.0, 20.0, 1001)\n",
    "o.integrate(ts, MWPotential2014 + nip)\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4923f1a6",
   "metadata": {
    "papermill": {
     "duration": 0.016039,
     "end_time": "2026-06-30T01:16:03.016430+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.000391+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "we can compare this to integrating the orbit in the inertial frame and displaying it in the non-inertial LSR frame as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "70a08bdf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:03.050383Z",
     "iopub.status.busy": "2026-06-30T01:16:03.050117Z",
     "iopub.status.idle": "2026-06-30T01:16:03.221505Z",
     "shell.execute_reply": "2026-06-30T01:16:03.220592Z"
    },
    "papermill": {
     "duration": 0.18985,
     "end_time": "2026-06-30T01:16:03.222541+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.032691+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plot(d1=\"x\", d2=\"y\")  # Repeat plot from above\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o.turn_physical_off()  # To use internal units\n",
    "o.integrate(ts, MWPotential2014)\n",
    "o.plot(\n",
    "    d1=\"R*cos(phi-t)\", d2=\"R*sin(phi-t)\", overplot=True\n",
    ");  # Omega = 1, so Omega t = t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2faecf4f",
   "metadata": {
    "papermill": {
     "duration": 0.016043,
     "end_time": "2026-06-30T01:16:03.255101+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.239058+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can also do all of the above in physical units, in which case the first example above becomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3ff85f4f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:03.289142Z",
     "iopub.status.busy": "2026-06-30T01:16:03.288891Z",
     "iopub.status.idle": "2026-06-30T01:16:03.482125Z",
     "shell.execute_reply": "2026-06-30T01:16:03.481190Z"
    },
    "papermill": {
     "duration": 0.211398,
     "end_time": "2026-06-30T01:16:03.482960+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.271562+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import MWPotential2014, NonInertialFrameForce\n",
    "from astropy import units\n",
    "\n",
    "nip = NonInertialFrameForce(Omega=220.0 / 8.0 * units.km / units.s / units.kpc)\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o = Orbit(\n",
    "    [\n",
    "        o.R(quantity=True),\n",
    "        o.vR(quantity=True),\n",
    "        o.vT(quantity=True) - 220.0 * units.km / units.s,\n",
    "        o.z(quantity=True),\n",
    "        o.vz(quantity=True),\n",
    "        o.phi(quantity=True),\n",
    "    ]\n",
    ")  # Convert to the LSR frame\n",
    "ts = numpy.linspace(0.0, 20.0, 1001)\n",
    "o.integrate(ts, MWPotential2014 + nip)\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "773db6d9",
   "metadata": {
    "papermill": {
     "duration": 0.016213,
     "end_time": "2026-06-30T01:16:03.515551+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.499338+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can also provide the ``Omega=`` frequency as an arbitrary function of time. In this case, the frequency must be returned in internal units and the input time of this function must be in internal units as well (use the routines in [galpy.util.conversion](../../reference/conversion.rst#bovyconversion) for converting from physical to internal units; you need to divide by these to go from physical to internal). For the example above, this would amount to setting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7f1413dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:03.549610Z",
     "iopub.status.busy": "2026-06-30T01:16:03.549392Z",
     "iopub.status.idle": "2026-06-30T01:16:03.552747Z",
     "shell.execute_reply": "2026-06-30T01:16:03.551907Z"
    },
    "papermill": {
     "duration": 0.021526,
     "end_time": "2026-06-30T01:16:03.553430+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.531904+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "nip = NonInertialFrameForce(Omega=lambda t: 1.0, Omegadot=lambda t: 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adefd943",
   "metadata": {
    "papermill": {
     "duration": 0.016452,
     "end_time": "2026-06-30T01:16:03.586421+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.569969+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Note that when we supply Omega as a function, it is necessary to specify its time derivative as well as Omegadot (all again in internal units).\n",
    "\n",
    "We give an example of having the origin of the non-inertial frame accelerate in the [orbit examples](examples.ipynb) tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9db57e",
   "metadata": {
    "papermill": {
     "duration": 0.01611,
     "end_time": "2026-06-30T01:16:03.619025+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.602915+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Surfaces of section\n",
    "\n",
    "galpy can compute surfaces of section (SOS) for 2D and 3D orbits using a special\n",
    "integration method that exactly determines intersections between orbits and a surface.\n",
    "The implemented method follows [Hunter et al. (1998)](https://ui.adsabs.harvard.edu/abs/1998NYASA.867...61H/abstract) in re-writing the integration in terms of an independent angular variable 𝜓 that is equal to a multiple of 2⁢𝜋 at intersections of the orbit with a surface of section (see Section 13.1 of [galaxiesbook.org](https://galaxiesbook.org/chapters/III-02.-Orbits-in-Triaxial-Mass-Distributions-and-Surfaces-of-Section_1-Surfaces-of-section.html#while-the-method-we-have-used-so)).\n",
    "\n",
    "Supported surfaces:\n",
    "- **3D orbits:** $z=0, v_z>0$ surface\n",
    "- **2D orbits:** $x=0, v_x>0$ or $y=0, v_y>0$ surfaces\n",
    "\n",
    "Surfaces of section are most useful for static, axisymmetric potentials (3D) or\n",
    "static, non-axisymmetric potentials (2D)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2d72d937",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:03.653265Z",
     "iopub.status.busy": "2026-06-30T01:16:03.653008Z",
     "iopub.status.idle": "2026-06-30T01:16:04.148773Z",
     "shell.execute_reply": "2026-06-30T01:16:04.147718Z"
    },
    "papermill": {
     "duration": 0.513916,
     "end_time": "2026-06-30T01:16:04.149451+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:03.635535+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Surface of section for the Sun's orbit in MWPotential2014\n",
    "o_sun = Orbit()\n",
    "o_sun.turn_physical_off()\n",
    "o_sun.plotSOS(MWPotential2014);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff5dd71b",
   "metadata": {
    "papermill": {
     "duration": 0.016358,
     "end_time": "2026-06-30T01:16:04.182394+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.166036+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "You can also retrieve the SOS crossing values directly using `o.SOS()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2df4ef51",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:04.217120Z",
     "iopub.status.busy": "2026-06-30T01:16:04.216882Z",
     "iopub.status.idle": "2026-06-30T01:16:04.509452Z",
     "shell.execute_reply": "2026-06-30T01:16:04.508510Z"
    },
    "papermill": {
     "duration": 0.311323,
     "end_time": "2026-06-30T01:16:04.510156+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.198833+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of SOS crossings: 500\n"
     ]
    }
   ],
   "source": [
    "# Get the SOS values directly\n",
    "Rs, vRs = o_sun.SOS(MWPotential2014)\n",
    "print(\"Number of SOS crossings:\", len(Rs))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e3527f0",
   "metadata": {
    "papermill": {
     "duration": 0.016524,
     "end_time": "2026-06-30T01:16:04.543513+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.526989+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "For 2D orbits, we can compute surfaces of section in the `x` or `y` planes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bca5328a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:04.578438Z",
     "iopub.status.busy": "2026-06-30T01:16:04.578183Z",
     "iopub.status.idle": "2026-06-30T01:16:04.893059Z",
     "shell.execute_reply": "2026-06-30T01:16:04.892045Z"
    },
    "papermill": {
     "duration": 0.333282,
     "end_time": "2026-06-30T01:16:04.893743+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.560461+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2D example: box orbit in a non-axisymmetric cored logarithmic potential\n",
    "lp_2d = LogarithmicHaloPotential(normalize=True, b=0.9, core=0.2)\n",
    "orb_2d = Orbit([0.1, 0.0, lp_2d.vcirc(0.1, phi=0.0), numpy.pi / 2.0])\n",
    "orb_2d.plotSOS(lp_2d, surface=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0253e81",
   "metadata": {
    "papermill": {
     "duration": 0.01657,
     "end_time": "2026-06-30T01:16:04.927212+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.910642+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Surfaces of section can also be computed for Orbit instances that contain multiple orbits, e.g., for the following two orbits defined to have the same energy and angular momentum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a5e5e607",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:04.962386Z",
     "iopub.status.busy": "2026-06-30T01:16:04.962129Z",
     "iopub.status.idle": "2026-06-30T01:16:05.578915Z",
     "shell.execute_reply": "2026-06-30T01:16:05.577868Z"
    },
    "papermill": {
     "duration": 0.635759,
     "end_time": "2026-06-30T01:16:05.579653+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:04.943894+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import evaluatePotentials\n",
    "\n",
    "\n",
    "def orbit_RvRELz(R, vR, E, Lz, z_init=0.0, pot=None):\n",
    "    \"\"\"Returns Orbit at (R,vR,phi=0,z=z_init) with given (E,Lz)\"\"\"\n",
    "    return Orbit(\n",
    "        [\n",
    "            R,\n",
    "            vR,\n",
    "            Lz / R,\n",
    "            z_init,\n",
    "            numpy.sqrt(\n",
    "                2.0\n",
    "                * (\n",
    "                    E\n",
    "                    - evaluatePotentials(pot, R, z_init)\n",
    "                    - (Lz / R) ** 2.0 / 2.0\n",
    "                    - vR**2.0 / 2\n",
    "                )\n",
    "            ),\n",
    "            0.0,\n",
    "        ],\n",
    "        ro=8.0,\n",
    "        vo=220.0,\n",
    "    )\n",
    "\n",
    "\n",
    "R, E, Lz = 0.8, -1.25, 0.6\n",
    "twoorb = Orbit(\n",
    "    [\n",
    "        orbit_RvRELz(R, 0.0, E, Lz, pot=MWPotential2014),\n",
    "        orbit_RvRELz(R, 0.1, E, Lz, pot=MWPotential2014, z_init=0.1),\n",
    "    ]\n",
    ")\n",
    "twoorb.plotSOS(MWPotential2014);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7f81ca",
   "metadata": {
    "papermill": {
     "duration": 0.0173,
     "end_time": "2026-06-30T01:16:05.615544+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.598244+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "For some force fields, the reparameterization of the orbit in terms of $\\psi$ does not work, because the angle $\\psi$ does not increase monotonically with time. This is notably the case for many orbits integrated in a non-inertial frame (e.g., bar orbits in the bar’s rotating frame). In these cases, you can use a brute-force approach to determining the surface of section implemented in ``Orbit.bruteSOS`` and ``Orbit.plotBruteSOS``, which work similarly to the ``Orbit.SOS`` and ``Orbit.plotSOS`` methods discussed above, but simply look for surface crossings using a regular orbit integration. In this case, you have to specify how long to integrate the orbit for and you can, therefore, not directly control the number of crossings that you will get."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "345088ed",
   "metadata": {
    "papermill": {
     "duration": 0.016837,
     "end_time": "2026-06-30T01:16:05.649398+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.632561+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Warning**\n",
    "\n",
    "Computing the surface of section leaves the Orbit instance in a state where its internally-stored integrated orbit is that computed during the surface-of-section integration (any previously integrated orbit is overwritten). However, the orbit is only output at intersections with the surface of section. Furthermore, with an Orbit like that of the Sun above whose initial condition is not in the surface of section, the first point along this orbit is not the initial condition, but the first surface-of-section crossing instead. This is because for orbits like this, internally galpy first integrates to the first crossing and then re-starts the integration to obtain many subsequent crossings to create the surface of section.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60066829",
   "metadata": {
    "papermill": {
     "duration": 0.017206,
     "end_time": "2026-06-30T01:16:05.683863+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.666657+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Integration of the phase-space volume\n",
    "\n",
    "galpy supports the integration of the phase-space volume through the method\n",
    "`integrate_dxdv`, for both two-dimensional (planar) and fully three-dimensional\n",
    "orbits. This can be used to, for example, explicitly verify Liouville's theorem\n",
    "(that phase-space volume is conserved along the orbit), quantify an orbit's\n",
    "sensitivity to its initial conditions, and compute Lyapunov exponents with the\n",
    "`lyapunov` method. See the\n",
    "[Phase-Space Volumes and Chaos](phase_space_volumes_and_chaos.ipynb) tutorial\n",
    "and the `integrate_dxdv` API documentation for details."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1c504ae",
   "metadata": {
    "papermill": {
     "duration": 0.016983,
     "end_time": "2026-06-30T01:16:05.718330+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.701347+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Fast orbit integration and available integrators\n",
    "\n",
    "For fast integration of many orbits, galpy provides fast C integrators accessed via the `method=` keyword.\n",
    "\n",
    "**C integrators (recommended for speed):**\n",
    "- `rk4_c`, `rk6_c`: Runge-Kutta methods\n",
    "- `dopr54_c`, `dop853_c`: Dormand-Prince methods\n",
    "- `ias15_c`: IAS15 integrator (Rein & Spiegel 2014), adaptive timestepping for high precision\n",
    "\n",
    "**Symplectic C integrators:**\n",
    "- `leapfrog_c`, `symplec4_c`, `symplec6_c`\n",
    "\n",
    "**Pure Python integrators:**\n",
    "- `leapfrog`, `odeint`, `dop853`\n",
    "\n",
    "For most applications, `symplec4_c` or `dop853_c` are recommended. The `ias15_c` integrator from [Rein & Spiegel 2014](https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1424R/abstract) is a good choice when extreme high-precision is required, but it is slow compared to other C integrators. The higher order symplectic integrators are described in [Yoshida (1993)](http://adsabs.harvard.edu/abs/1993CeMDA..56...27Y)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "adfc44a8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-30T01:16:05.753739Z",
     "iopub.status.busy": "2026-06-30T01:16:05.753491Z",
     "iopub.status.idle": "2026-06-30T01:16:05.770842Z",
     "shell.execute_reply": "2026-06-30T01:16:05.769874Z"
    },
    "papermill": {
     "duration": 0.03589,
     "end_time": "2026-06-30T01:16:05.771498+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.735608+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MiyamotoNagaiPotential has C: True\n",
      "Integration with dop853_c complete.\n"
     ]
    }
   ],
   "source": [
    "# Check if a potential has a C implementation\n",
    "from galpy.potential import MiyamotoNagaiPotential as MNP\n",
    "\n",
    "mp_test = MNP(a=0.5, b=0.0375, amp=1.0, normalize=1.0)\n",
    "print(\"MiyamotoNagaiPotential has C:\", mp_test.hasC)\n",
    "\n",
    "# Integrate using the fast dop853_c method\n",
    "o_fast = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 100.0, 10001)\n",
    "o_fast.integrate(ts, MWPotential2014, method=\"dop853_c\")\n",
    "print(\"Integration with dop853_c complete.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68567952",
   "metadata": {
    "papermill": {
     "duration": 0.017061,
     "end_time": "2026-06-30T01:16:05.805913+00:00",
     "exception": false,
     "start_time": "2026-06-30T01:16:05.788852+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "If no C implementation of the potential (or one of its components) is available, galpy will automatically fall back to using a pure Python integrator. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py312",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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