{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c5a9be36",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:27.312422Z",
     "iopub.status.busy": "2024-09-30T14:48:27.312202Z",
     "iopub.status.idle": "2024-09-30T14:48:27.707950Z",
     "shell.execute_reply": "2024-09-30T14:48:27.707178Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "69a01195",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:27.710353Z",
     "iopub.status.busy": "2024-09-30T14:48:27.710046Z",
     "iopub.status.idle": "2024-09-30T14:48:27.718566Z",
     "shell.execute_reply": "2024-09-30T14:48:27.717985Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/runner/work/gala/gala/docs/tutorials/nb_setup:1: DeprecationWarning: `magic(...)` is deprecated since IPython 0.13 (warning added in 8.1), use run_line_magic(magic_name, parameter_s).\n",
      "  get_ipython().magic('config InlineBackend.figure_format = \"retina\"')  # noqa\n"
     ]
    }
   ],
   "source": [
    "%run nb_setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1156cb4",
   "metadata": {},
   "source": [
    "# Defining a Milky Way potential model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0a7d823b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:27.720558Z",
     "iopub.status.busy": "2024-09-30T14:48:27.720349Z",
     "iopub.status.idle": "2024-09-30T14:48:28.322989Z",
     "shell.execute_reply": "2024-09-30T14:48:28.322218Z"
    }
   },
   "outputs": [],
   "source": [
    "# Third-party dependencies\n",
    "import astropy.units as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from astropy.io import ascii\n",
    "from scipy.optimize import leastsq\n",
    "\n",
    "# Gala\n",
    "import gala.potential as gp\n",
    "from gala.units import galactic\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce029bfb",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "`gala` provides a simple and easy way to access and integrate orbits in an\n",
    "approximate mass model for the Milky Way. The parameters of the mass model are\n",
    "determined by least-squares fitting the enclosed mass profile of a pre-defined\n",
    "potential form to recent measurements compiled from the literature. These\n",
    "measurements are provided with the documentation of `gala` and are shown\n",
    "below. The radius units are kpc, and mass units are solar masses:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d4483974",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:28.325721Z",
     "iopub.status.busy": "2024-09-30T14:48:28.325195Z",
     "iopub.status.idle": "2024-09-30T14:48:28.335526Z",
     "shell.execute_reply": "2024-09-30T14:48:28.334899Z"
    }
   },
   "outputs": [],
   "source": [
    "tbl = ascii.read(\"data/MW_mass_enclosed.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9683e2c0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:28.337719Z",
     "iopub.status.busy": "2024-09-30T14:48:28.337474Z",
     "iopub.status.idle": "2024-09-30T14:48:28.344203Z",
     "shell.execute_reply": "2024-09-30T14:48:28.343662Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><i>Table length=16</i>\n",
       "<table id=\"table140488490858384\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>r</th><th>Menc</th><th>Menc_err_neg</th><th>Menc_err_pos</th><th>ref</th></tr></thead>\n",
       "<thead><tr><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>str27</th></tr></thead>\n",
       "<tr><td>0.01</td><td>30000000.0</td><td>10000000.0</td><td>10000000.0</td><td>Feldmeier et al. (2014)</td></tr>\n",
       "<tr><td>0.12</td><td>800000000.0</td><td>200000000.0</td><td>200000000.0</td><td>Launhardt et al. (2002)</td></tr>\n",
       "<tr><td>8.1</td><td>89502860861.52429</td><td>4994562473.797714</td><td>4858963492.608627</td><td>Bovy et al. (2012)</td></tr>\n",
       "<tr><td>8.3</td><td>110417867208.19055</td><td>4475949382.696884</td><td>4387023236.020782</td><td>McMillan (2011)</td></tr>\n",
       "<tr><td>8.4</td><td>102421035406.90356</td><td>16733918715.629944</td><td>15468328224.531876</td><td>Koposov et al. (2010)</td></tr>\n",
       "<tr><td>19.0</td><td>208023299175.30438</td><td>44317988008.38101</td><td>34833267089.920685</td><td>Kuepper et al. (2015)</td></tr>\n",
       "<tr><td>50.0</td><td>539884832748.48975</td><td>19995734543.31433</td><td>268490735257.4718</td><td>Wilkinson &amp; Evans (1999)</td></tr>\n",
       "<tr><td>50.0</td><td>529886965173.18726</td><td>9997867269.659302</td><td>38536752776.21277</td><td>Sakamoto et al. (2003)</td></tr>\n",
       "<tr><td>50.0</td><td>399914690706.92847</td><td>109976539940.53711</td><td>72696676468.2511</td><td>Smith et al. (2007)</td></tr>\n",
       "<tr><td>50.0</td><td>419910425325.7268</td><td>39991469076.968506</td><td>38172735113.64386</td><td>Deason et al. (2012)</td></tr>\n",
       "<tr><td>60.0</td><td>399914690957.5188</td><td>69985070910.63354</td><td>64344945146.92987</td><td>Xue et al. (2008)</td></tr>\n",
       "<tr><td>80.0</td><td>689852841359.0248</td><td>299936018002.3314</td><td>110361048549.1029</td><td>Gnedin et al. (2010)</td></tr>\n",
       "<tr><td>100.0</td><td>1399701417307.7747</td><td>899808054059.3811</td><td>831336271726.1903</td><td>Watkins et al. (2010)</td></tr>\n",
       "<tr><td>120.0</td><td>539884832260.29584</td><td>199957345314.72906</td><td>123854764645.32489</td><td>Battaglia et al. (2005)</td></tr>\n",
       "<tr><td>150.0</td><td>750000000000.0</td><td>250000000000.0</td><td>250000000000.0</td><td>Deason et al. (2012)</td></tr>\n",
       "<tr><td>200.0</td><td>679854974257.2006</td><td>409912558030.05396</td><td>313652012195.06256</td><td>Bhattacherjee et al. (2014)</td></tr>\n",
       "</table></div>"
      ],
      "text/plain": [
       "<Table length=16>\n",
       "   r           Menc        ...    Menc_err_pos                ref            \n",
       "float64      float64       ...      float64                  str27           \n",
       "------- ------------------ ... ------------------ ---------------------------\n",
       "   0.01         30000000.0 ...         10000000.0     Feldmeier et al. (2014)\n",
       "   0.12        800000000.0 ...        200000000.0     Launhardt et al. (2002)\n",
       "    8.1  89502860861.52429 ...  4858963492.608627          Bovy et al. (2012)\n",
       "    8.3 110417867208.19055 ...  4387023236.020782             McMillan (2011)\n",
       "    8.4 102421035406.90356 ... 15468328224.531876       Koposov et al. (2010)\n",
       "   19.0 208023299175.30438 ... 34833267089.920685       Kuepper et al. (2015)\n",
       "   50.0 539884832748.48975 ...  268490735257.4718    Wilkinson & Evans (1999)\n",
       "   50.0 529886965173.18726 ...  38536752776.21277      Sakamoto et al. (2003)\n",
       "   50.0 399914690706.92847 ...   72696676468.2511         Smith et al. (2007)\n",
       "   50.0  419910425325.7268 ...  38172735113.64386        Deason et al. (2012)\n",
       "   60.0  399914690957.5188 ...  64344945146.92987           Xue et al. (2008)\n",
       "   80.0  689852841359.0248 ...  110361048549.1029        Gnedin et al. (2010)\n",
       "  100.0 1399701417307.7747 ...  831336271726.1903       Watkins et al. (2010)\n",
       "  120.0 539884832260.29584 ... 123854764645.32489     Battaglia et al. (2005)\n",
       "  150.0     750000000000.0 ...     250000000000.0        Deason et al. (2012)\n",
       "  200.0  679854974257.2006 ... 313652012195.06256 Bhattacherjee et al. (2014)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tbl"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a049382b",
   "metadata": {},
   "source": [
    "Let's now plot the above data and uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c8a0247e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:28.346184Z",
     "iopub.status.busy": "2024-09-30T14:48:28.345974Z",
     "iopub.status.idle": "2024-09-30T14:48:29.036621Z",
     "shell.execute_reply": "2024-09-30T14:48:29.035864Z"
    },
    "lines_to_end_of_cell_marker": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 384,
       "width": 387
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "\n",
    "ax.errorbar(\n",
    "    tbl[\"r\"],\n",
    "    tbl[\"Menc\"],\n",
    "    yerr=(tbl[\"Menc_err_neg\"], tbl[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a692faf",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "We now need to assume some form for the potential. For simplicity and within\n",
    "reason, we'll use a four component potential model consisting of a Hernquist\n",
    "([1990](https://ui.adsabs.harvard.edu/#abs/1990ApJ...356..359H/abstract))\n",
    "bulge and nucleus, a Miyamoto-Nagai\n",
    "([1975](https://ui.adsabs.harvard.edu/#abs/1975PASJ...27..533M/abstract))\n",
    "disk, and an NFW\n",
    "([1997](https://ui.adsabs.harvard.edu/#abs/1997ApJ...490..493N/abstract))\n",
    "halo. We'll fix the parameters of the disk and bulge to be consistent with\n",
    "previous work ([Bovy\n",
    "2015](https://ui.adsabs.harvard.edu/#abs/2015ApJS..216...29B/abstract) -\n",
    "please cite that paper if you use this potential model) and vary the scale\n",
    "mass and scale radius of the nucleus and halo, respectively. We'll fit for\n",
    "these parameters in log-space, so we'll first define a function that returns a\n",
    "`gala.potential.CCompositePotential` object given these four parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "31fa7f1f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:29.038980Z",
     "iopub.status.busy": "2024-09-30T14:48:29.038556Z",
     "iopub.status.idle": "2024-09-30T14:48:29.043754Z",
     "shell.execute_reply": "2024-09-30T14:48:29.043045Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_potential(log_M_h, log_r_s, log_M_n, log_a):\n",
    "    mw_potential = gp.CCompositePotential()\n",
    "    mw_potential[\"bulge\"] = gp.HernquistPotential(m=5e9, c=1.0, units=galactic)\n",
    "    mw_potential[\"disk\"] = gp.MiyamotoNagaiPotential(\n",
    "        m=6.8e10 * u.Msun, a=3 * u.kpc, b=280 * u.pc, units=galactic\n",
    "    )\n",
    "    mw_potential[\"nucl\"] = gp.HernquistPotential(\n",
    "        m=np.exp(log_M_n), c=np.exp(log_a) * u.pc, units=galactic\n",
    "    )\n",
    "    mw_potential[\"halo\"] = gp.NFWPotential(\n",
    "        m=np.exp(log_M_h), r_s=np.exp(log_r_s), units=galactic\n",
    "    )\n",
    "\n",
    "    return mw_potential"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b941134",
   "metadata": {},
   "source": [
    "We now need to specify an initial guess for the parameters - let's do that (by\n",
    "making them up), and then plot the initial guess potential over the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "67158a75",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:29.046002Z",
     "iopub.status.busy": "2024-09-30T14:48:29.045522Z",
     "iopub.status.idle": "2024-09-30T14:48:29.054309Z",
     "shell.execute_reply": "2024-09-30T14:48:29.053587Z"
    }
   },
   "outputs": [],
   "source": [
    "# Initial guess for the parameters- units are:\n",
    "#     [Msun, kpc, Msun, pc]\n",
    "x0 = [np.log(6e11), np.log(20.0), np.log(2e9), np.log(100.0)]\n",
    "init_potential = get_potential(*x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9650e660",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:29.056519Z",
     "iopub.status.busy": "2024-09-30T14:48:29.056128Z",
     "iopub.status.idle": "2024-09-30T14:48:29.994925Z",
     "shell.execute_reply": "2024-09-30T14:48:29.994137Z"
    },
    "lines_to_end_of_cell_marker": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 384,
       "width": 387
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xyz = np.zeros((3, 256))\n",
    "xyz[0] = np.logspace(-3, 3, 256)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "\n",
    "ax.errorbar(\n",
    "    tbl[\"r\"],\n",
    "    tbl[\"Menc\"],\n",
    "    yerr=(tbl[\"Menc_err_neg\"], tbl[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "fit_menc = init_potential.mass_enclosed(xyz * u.kpc)\n",
    "ax.loglog(xyz[0], fit_menc.value, marker=\"\", color=\"#3182bd\", linewidth=2, alpha=0.7)\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b2b03a7",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "It looks pretty good already! But let's now use least-squares fitting to\n",
    "optimize our nucleus and halo parameters. We first need to define an error\n",
    "function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7f58ba2f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:29.997182Z",
     "iopub.status.busy": "2024-09-30T14:48:29.996869Z",
     "iopub.status.idle": "2024-09-30T14:48:30.000917Z",
     "shell.execute_reply": "2024-09-30T14:48:30.000332Z"
    }
   },
   "outputs": [],
   "source": [
    "def err_func(p, r, Menc, Menc_err):\n",
    "    pot = get_potential(*p)\n",
    "    xyz = np.zeros((3, len(r)))\n",
    "    xyz[0] = r\n",
    "    model_menc = pot.mass_enclosed(xyz).to(u.Msun).value\n",
    "    return (model_menc - Menc) / Menc_err"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b97afca7",
   "metadata": {},
   "source": [
    "Because the uncertainties are all approximately but not exactly symmetric,\n",
    "we'll take the maximum of the upper and lower uncertainty values and assume\n",
    "that the uncertainties in the mass measurements are Gaussian (a bad but simple\n",
    "assumption):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0d2af7ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:30.002880Z",
     "iopub.status.busy": "2024-09-30T14:48:30.002676Z",
     "iopub.status.idle": "2024-09-30T14:48:30.134020Z",
     "shell.execute_reply": "2024-09-30T14:48:30.133389Z"
    }
   },
   "outputs": [],
   "source": [
    "err = np.max([tbl[\"Menc_err_pos\"], tbl[\"Menc_err_neg\"]], axis=0)\n",
    "p_opt, ier = leastsq(err_func, x0=x0, args=(tbl[\"r\"], tbl[\"Menc\"], err))\n",
    "assert ier in range(1, 4 + 1), \"least-squares fit failed!\"\n",
    "fit_potential = get_potential(*p_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1a5cd05",
   "metadata": {},
   "source": [
    "Now we have a best-fit potential! Let's plot the enclosed mass of the fit potential over the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "75268e6c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:30.136414Z",
     "iopub.status.busy": "2024-09-30T14:48:30.136180Z",
     "iopub.status.idle": "2024-09-30T14:48:30.713986Z",
     "shell.execute_reply": "2024-09-30T14:48:30.713252Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 384,
       "width": 387
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xyz = np.zeros((3, 256))\n",
    "xyz[0] = np.logspace(-3, 3, 256)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "\n",
    "ax.errorbar(\n",
    "    tbl[\"r\"],\n",
    "    tbl[\"Menc\"],\n",
    "    yerr=(tbl[\"Menc_err_neg\"], tbl[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "fit_menc = fit_potential.mass_enclosed(xyz * u.kpc)\n",
    "ax.loglog(xyz[0], fit_menc.value, marker=\"\", color=\"#3182bd\", linewidth=2, alpha=0.7)\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc5cd185",
   "metadata": {},
   "source": [
    "This potential is already implemented in `gala` in `gala.potential.special`,\n",
    "and we can import it with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "81e28ae4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:30.716245Z",
     "iopub.status.busy": "2024-09-30T14:48:30.716004Z",
     "iopub.status.idle": "2024-09-30T14:48:30.719160Z",
     "shell.execute_reply": "2024-09-30T14:48:30.718630Z"
    }
   },
   "outputs": [],
   "source": [
    "from gala.potential import MilkyWayPotential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "56d0e294",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-09-30T14:48:30.720994Z",
     "iopub.status.busy": "2024-09-30T14:48:30.720794Z",
     "iopub.status.idle": "2024-09-30T14:48:30.730071Z",
     "shell.execute_reply": "2024-09-30T14:48:30.729528Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<CompositePotential disk,bulge,nucleus,halo>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "potential = MilkyWayPotential()\n",
    "potential"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}