{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bienvenidos  a Jupyter Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jupyter es un entorno interactivo de ejecución de código, aquí podemos mostrar de forma más ordenada y explicativa el código que estamos ejecutando."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos importar las librerías clásicas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Titulo pequeño\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## titulo mediano"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#esto es un ejemplo\n",
    "def suma(x, y):\n",
    "    return x+y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suma(15, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aquí acabamos de realizar una suma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y comprobar que es como si estuviesemos trabajando en cualquier script:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    }
   ],
   "source": [
    "a=100\n",
    "b=50\n",
    "print(a-b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hay q empezar a hacer la tarea de Opti\n"
     ]
    }
   ],
   "source": [
    "print(\"Hay q empezar a hacer la tarea de Opti\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "También podemos realizar informes o reportes de las tareas de forma más bacán por que se puede utilizar $LATEX$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sum_{0}^{n}\\frac{1}{x^{2}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P=\\{x\\in\\mathcal{R}^{n}|Ax=b, x\\geq0\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{x^{2}}{1000}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "aqui hemos definido un poliedro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora vayamos a $\\textbf{PULP}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pulp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El modelo resultante del problema anterior:\n",
    "\n",
    "$$\\begin{array}{cc} \\min & \\sum^{10}_{j=1}e_j(C_E)_j + \\sum^6_{i=1}\\sum^{10}_{j=1}a_{ij}(C_A)_{ij} &\\\\\n",
    "\\mbox{s.a}  & e_{j}\\in\\{0,1\\}&\\forall j \\in \\{1,2,3,4,5,6,7,8,9,10\\} \\\\\n",
    "            & a_{i,j}\\in \\mathbb{N}_0&\\forall i\\in\\{1,2,3,4,5,6\\}, j\\in\\{1,2,3,4,5,6,7,8,9,10\\}\\\\\n",
    "            &\\sum^{6}_{i=1}a_{i,j}- e_jP_j\\leq 0&\\forall j \\in \\{1,2,3,4,5,6,7,8,9,10\\} \\\\\n",
    "            & \\sum^{10}_{j=1}a_{i,j}=D_i&\\forall i \\in \\{1,2,3,4,5,6\\} \n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "donde $e_j$ nos dice si la escuela $j$ abre o no y $a_{ij}$ nos dice el número de niños que del área $i$ que asistiran a la escuela $j$.\n",
    "$C_E$ es un vector que nos dice cuanto cuesta abrir una escuela.\n",
    "$C_A$ es una matriz que entrega el costo anuel de que un niño del área $i$ asista a una escuela $j$.\n",
    "El vecotr $P$ nos entrega la capacidad de cada escuela y el vector $D$ la demanda de cada zona."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$C_E=\\begin{pmatrix}\n",
    "100000\\\\ 500000\\\\ 150000\\\\ 230000\\\\ 100000\\\\ 180000\\\\ 90000\\\\ 100000\\\\ 100000\\\\ 100000\n",
    "\\end{pmatrix}$   \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$C_A=\\begin{pmatrix}\n",
    "0 & 0 & 150 & 150 & 150 & 150 & 150 & 150 & 150 & 150 \\\\ \n",
    "150 & 150 & 0 & 150 & 150 & 150 & 150 & 150 & 150 & 150 \\\\ \n",
    "150 & 150& 150& 0 & 0 & 150& 150& 150 & 150 & 150 \\\\ \n",
    "150 & 150 & 150 & 150 & 150 & 0 & 150 & 150 & 150 & 150 \\\\ \n",
    "200 & 200 & 200 & 200 & 200 & 200 & 0 & 200 & 200 & 200 \\\\ \n",
    "200 & 200 & 200 & 200 & 200 & 200 & 200 & 0 & 0 & 0\n",
    "\\end{pmatrix}$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "P=\\begin{pmatrix}\n",
    "1500\\\\ 2000\\\\ 800\\\\ 2000\\\\ 800\\\\ 1000\\\\ 1200\\\\ 1500\\\\ 1500\\\\ 500\n",
    "\\end{pmatrix}\\;\\;\n",
    "D=\\begin{pmatrix}\n",
    "1200\\\\ 800\\\\ 1400\\\\ 2500\\\\ 1000\\\\ 1500\n",
    "\\end{pmatrix}\n",
    "$$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A continuación definimos los parámetros:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "CE=[0,100000,500000,150000,230000,100000,180000,90000,100000,100000,100000]\n",
    "CA=[[0,0,0,0,0,0,0,0,0,0,0],\\\n",
    "    [0,0,0,150,150,150,150,150,150,150,150],\\\n",
    "    [0,150 , 150 , 0 ,150 , 150 , 150 , 150 , 150 , 150 , 150],\\\n",
    "    [0,150 , 150, 150, 0 , 0 , 150, 150, 150 , 150 , 150],\\\n",
    "    [0,150 , 150 , 150 , 150 , 150 , 0 , 150 , 150 , 150 , 150],\\\n",
    "    [0,200 , 200 , 200 , 200 , 200 , 200 , 0 , 200 , 200 , 200],\\\n",
    "    [0,200,200,200,200,200,200,200,0,0,0]]\n",
    "P=[0,1500, 2000, 800, 2000, 800, 1000, 1200, 1500, 1500, 500]\n",
    "D=[0,1200, 800, 1400, 2500, 1000, 1500]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ojo que estamos agregando ceros ya que python indexa desde 0 y no desde 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ahora las variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Listas\n",
    "I=[1,2,3,4,5,6]\n",
    "J=[1,2,3,4,5,6,7,8,9,10]\n",
    "\n",
    "#Variables\n",
    "e = pulp.LpVariable.dicts(\"e\", (j for j in J),  cat='Binary')\n",
    "a = pulp.LpVariable.dicts(\"a\", ((i,j) for i in I for j in J), lowBound=0, cat='Integer')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora podemos definir el modelos agregándole restricciones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modelo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "asignacion:\n",
      "MINIMIZE\n",
      "150*a_(1,_10) + 150*a_(1,_3) + 150*a_(1,_4) + 150*a_(1,_5) + 150*a_(1,_6) + 150*a_(1,_7) + 150*a_(1,_8) + 150*a_(1,_9) + 150*a_(2,_1) + 150*a_(2,_10) + 150*a_(2,_2) + 150*a_(2,_4) + 150*a_(2,_5) + 150*a_(2,_6) + 150*a_(2,_7) + 150*a_(2,_8) + 150*a_(2,_9) + 150*a_(3,_1) + 150*a_(3,_10) + 150*a_(3,_2) + 150*a_(3,_3) + 150*a_(3,_6) + 150*a_(3,_7) + 150*a_(3,_8) + 150*a_(3,_9) + 150*a_(4,_1) + 150*a_(4,_10) + 150*a_(4,_2) + 150*a_(4,_3) + 150*a_(4,_4) + 150*a_(4,_5) + 150*a_(4,_7) + 150*a_(4,_8) + 150*a_(4,_9) + 200*a_(5,_1) + 200*a_(5,_10) + 200*a_(5,_2) + 200*a_(5,_3) + 200*a_(5,_4) + 200*a_(5,_5) + 200*a_(5,_6) + 200*a_(5,_8) + 200*a_(5,_9) + 200*a_(6,_1) + 200*a_(6,_2) + 200*a_(6,_3) + 200*a_(6,_4) + 200*a_(6,_5) + 200*a_(6,_6) + 200*a_(6,_7) + 100000*e_1 + 100000*e_10 + 500000*e_2 + 150000*e_3 + 230000*e_4 + 100000*e_5 + 180000*e_6 + 90000*e_7 + 100000*e_8 + 100000*e_9 + 0\n",
      "SUBJECT TO\n",
      "_C1: a_(1,_1) + a_(2,_1) + a_(3,_1) + a_(4,_1) + a_(5,_1) + a_(6,_1)\n",
      " - 1500 e_1 <= 0\n",
      "\n",
      "_C2: a_(1,_2) + a_(2,_2) + a_(3,_2) + a_(4,_2) + a_(5,_2) + a_(6,_2)\n",
      " - 2000 e_2 <= 0\n",
      "\n",
      "_C3: a_(1,_3) + a_(2,_3) + a_(3,_3) + a_(4,_3) + a_(5,_3) + a_(6,_3) - 800 e_3\n",
      " <= 0\n",
      "\n",
      "_C4: a_(1,_4) + a_(2,_4) + a_(3,_4) + a_(4,_4) + a_(5,_4) + a_(6,_4)\n",
      " - 2000 e_4 <= 0\n",
      "\n",
      "_C5: a_(1,_5) + a_(2,_5) + a_(3,_5) + a_(4,_5) + a_(5,_5) + a_(6,_5) - 800 e_5\n",
      " <= 0\n",
      "\n",
      "_C6: a_(1,_6) + a_(2,_6) + a_(3,_6) + a_(4,_6) + a_(5,_6) + a_(6,_6)\n",
      " - 1000 e_6 <= 0\n",
      "\n",
      "_C7: a_(1,_7) + a_(2,_7) + a_(3,_7) + a_(4,_7) + a_(5,_7) + a_(6,_7)\n",
      " - 1200 e_7 <= 0\n",
      "\n",
      "_C8: a_(1,_8) + a_(2,_8) + a_(3,_8) + a_(4,_8) + a_(5,_8) + a_(6,_8)\n",
      " - 1500 e_8 <= 0\n",
      "\n",
      "_C9: a_(1,_9) + a_(2,_9) + a_(3,_9) + a_(4,_9) + a_(5,_9) + a_(6,_9)\n",
      " - 1500 e_9 <= 0\n",
      "\n",
      "_C10: a_(1,_10) + a_(2,_10) + a_(3,_10) + a_(4,_10) + a_(5,_10) + a_(6,_10)\n",
      " - 500 e_10 <= 0\n",
      "\n",
      "_C11: a_(1,_1) + a_(1,_10) + a_(1,_2) + a_(1,_3) + a_(1,_4) + a_(1,_5)\n",
      " + a_(1,_6) + a_(1,_7) + a_(1,_8) + a_(1,_9) = 1200\n",
      "\n",
      "_C12: a_(2,_1) + a_(2,_10) + a_(2,_2) + a_(2,_3) + a_(2,_4) + a_(2,_5)\n",
      " + a_(2,_6) + a_(2,_7) + a_(2,_8) + a_(2,_9) = 800\n",
      "\n",
      "_C13: a_(3,_1) + a_(3,_10) + a_(3,_2) + a_(3,_3) + a_(3,_4) + a_(3,_5)\n",
      " + a_(3,_6) + a_(3,_7) + a_(3,_8) + a_(3,_9) = 1400\n",
      "\n",
      "_C14: a_(4,_1) + a_(4,_10) + a_(4,_2) + a_(4,_3) + a_(4,_4) + a_(4,_5)\n",
      " + a_(4,_6) + a_(4,_7) + a_(4,_8) + a_(4,_9) = 2500\n",
      "\n",
      "_C15: a_(5,_1) + a_(5,_10) + a_(5,_2) + a_(5,_3) + a_(5,_4) + a_(5,_5)\n",
      " + a_(5,_6) + a_(5,_7) + a_(5,_8) + a_(5,_9) = 1000\n",
      "\n",
      "_C16: a_(6,_1) + a_(6,_10) + a_(6,_2) + a_(6,_3) + a_(6,_4) + a_(6,_5)\n",
      " + a_(6,_6) + a_(6,_7) + a_(6,_8) + a_(6,_9) = 1500\n",
      "\n",
      "VARIABLES\n",
      "0 <= a_(1,_1) Integer\n",
      "0 <= a_(1,_10) Integer\n",
      "0 <= a_(1,_2) Integer\n",
      "0 <= a_(1,_3) Integer\n",
      "0 <= a_(1,_4) Integer\n",
      "0 <= a_(1,_5) Integer\n",
      "0 <= a_(1,_6) Integer\n",
      "0 <= a_(1,_7) Integer\n",
      "0 <= a_(1,_8) Integer\n",
      "0 <= a_(1,_9) Integer\n",
      "0 <= a_(2,_1) Integer\n",
      "0 <= a_(2,_10) Integer\n",
      "0 <= a_(2,_2) Integer\n",
      "0 <= a_(2,_3) Integer\n",
      "0 <= a_(2,_4) Integer\n",
      "0 <= a_(2,_5) Integer\n",
      "0 <= a_(2,_6) Integer\n",
      "0 <= a_(2,_7) Integer\n",
      "0 <= a_(2,_8) Integer\n",
      "0 <= a_(2,_9) Integer\n",
      "0 <= a_(3,_1) Integer\n",
      "0 <= a_(3,_10) Integer\n",
      "0 <= a_(3,_2) Integer\n",
      "0 <= a_(3,_3) Integer\n",
      "0 <= a_(3,_4) Integer\n",
      "0 <= a_(3,_5) Integer\n",
      "0 <= a_(3,_6) Integer\n",
      "0 <= a_(3,_7) Integer\n",
      "0 <= a_(3,_8) Integer\n",
      "0 <= a_(3,_9) Integer\n",
      "0 <= a_(4,_1) Integer\n",
      "0 <= a_(4,_10) Integer\n",
      "0 <= a_(4,_2) Integer\n",
      "0 <= a_(4,_3) Integer\n",
      "0 <= a_(4,_4) Integer\n",
      "0 <= a_(4,_5) Integer\n",
      "0 <= a_(4,_6) Integer\n",
      "0 <= a_(4,_7) Integer\n",
      "0 <= a_(4,_8) Integer\n",
      "0 <= a_(4,_9) Integer\n",
      "0 <= a_(5,_1) Integer\n",
      "0 <= a_(5,_10) Integer\n",
      "0 <= a_(5,_2) Integer\n",
      "0 <= a_(5,_3) Integer\n",
      "0 <= a_(5,_4) Integer\n",
      "0 <= a_(5,_5) Integer\n",
      "0 <= a_(5,_6) Integer\n",
      "0 <= a_(5,_7) Integer\n",
      "0 <= a_(5,_8) Integer\n",
      "0 <= a_(5,_9) Integer\n",
      "0 <= a_(6,_1) Integer\n",
      "0 <= a_(6,_10) Integer\n",
      "0 <= a_(6,_2) Integer\n",
      "0 <= a_(6,_3) Integer\n",
      "0 <= a_(6,_4) Integer\n",
      "0 <= a_(6,_5) Integer\n",
      "0 <= a_(6,_6) Integer\n",
      "0 <= a_(6,_7) Integer\n",
      "0 <= a_(6,_8) Integer\n",
      "0 <= a_(6,_9) Integer\n",
      "0 <= e_1 <= 1 Integer\n",
      "0 <= e_10 <= 1 Integer\n",
      "0 <= e_2 <= 1 Integer\n",
      "0 <= e_3 <= 1 Integer\n",
      "0 <= e_4 <= 1 Integer\n",
      "0 <= e_5 <= 1 Integer\n",
      "0 <= e_6 <= 1 Integer\n",
      "0 <= e_7 <= 1 Integer\n",
      "0 <= e_8 <= 1 Integer\n",
      "0 <= e_9 <= 1 Integer\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#Problema\n",
    "model = pulp.LpProblem(\"asignacion\", pulp.LpMinimize)\n",
    "\n",
    "#Funcion objetivo\n",
    "model += pulp.lpSum([e[j]*CE[j] for j in J])+\\\n",
    "            pulp.lpSum([pulp.lpSum([a[i,j]*CA[i][j] for i in I]) for j in J])\n",
    "\n",
    "#Restricciones\n",
    "for j in J:\n",
    "    model +=  pulp.lpSum([a[i, j] for i in I]) - e[j]*P[j]<=0\n",
    "    \n",
    "for i in I:\n",
    "    model +=  pulp.lpSum([a[i, j] for j in J])==D[i]\n",
    "\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora podemos resolver el problema."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Optimal'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Resolver\n",
    "model.solve()\n",
    "#Estado\n",
    "pulp.LpStatus[model.status]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y podemos analizar la solución encontrada:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a_(1,_1) = 1200.0\n",
      "a_(1,_10) = 0.0\n",
      "a_(1,_2) = 0.0\n",
      "a_(1,_3) = 0.0\n",
      "a_(1,_4) = 0.0\n",
      "a_(1,_5) = 0.0\n",
      "a_(1,_6) = 0.0\n",
      "a_(1,_7) = 0.0\n",
      "a_(1,_8) = 0.0\n",
      "a_(1,_9) = 0.0\n",
      "a_(2,_1) = 0.0\n",
      "a_(2,_10) = 0.0\n",
      "a_(2,_2) = 0.0\n",
      "a_(2,_3) = 800.0\n",
      "a_(2,_4) = 0.0\n",
      "a_(2,_5) = 0.0\n",
      "a_(2,_6) = 0.0\n",
      "a_(2,_7) = 0.0\n",
      "a_(2,_8) = 0.0\n",
      "a_(2,_9) = 0.0\n",
      "a_(3,_1) = 0.0\n",
      "a_(3,_10) = 0.0\n",
      "a_(3,_2) = 0.0\n",
      "a_(3,_3) = 0.0\n",
      "a_(3,_4) = 1400.0\n",
      "a_(3,_5) = 0.0\n",
      "a_(3,_6) = 0.0\n",
      "a_(3,_7) = 0.0\n",
      "a_(3,_8) = 0.0\n",
      "a_(3,_9) = 0.0\n",
      "a_(4,_1) = 300.0\n",
      "a_(4,_10) = 0.0\n",
      "a_(4,_2) = 0.0\n",
      "a_(4,_3) = 0.0\n",
      "a_(4,_4) = 600.0\n",
      "a_(4,_5) = 0.0\n",
      "a_(4,_6) = 0.0\n",
      "a_(4,_7) = 164.0\n",
      "a_(4,_8) = 0.0\n",
      "a_(4,_9) = 1436.0\n",
      "a_(5,_1) = 0.0\n",
      "a_(5,_10) = 0.0\n",
      "a_(5,_2) = 0.0\n",
      "a_(5,_3) = 0.0\n",
      "a_(5,_4) = 0.0\n",
      "a_(5,_5) = 0.0\n",
      "a_(5,_6) = 0.0\n",
      "a_(5,_7) = 1000.0\n",
      "a_(5,_8) = 0.0\n",
      "a_(5,_9) = 0.0\n",
      "a_(6,_1) = 0.0\n",
      "a_(6,_10) = 0.0\n",
      "a_(6,_2) = 0.0\n",
      "a_(6,_3) = 0.0\n",
      "a_(6,_4) = 0.0\n",
      "a_(6,_5) = 0.0\n",
      "a_(6,_6) = 0.0\n",
      "a_(6,_7) = 0.0\n",
      "a_(6,_8) = 1500.0\n",
      "a_(6,_9) = 0.0\n",
      "e_1 = 1.0\n",
      "e_10 = 0.0\n",
      "e_2 = 0.0\n",
      "e_3 = 1.0\n",
      "e_4 = 1.0\n",
      "e_5 = 0.0\n",
      "e_6 = 0.0\n",
      "e_7 = 1.0\n",
      "e_8 = 1.0\n",
      "e_9 = 1.0\n"
     ]
    }
   ],
   "source": [
    "#Valores optimos de las variables\n",
    "for variable in model.variables():\n",
    "    print(\"{} = {}\".format(variable.name, variable.varValue))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y la solución óptima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1145000.0\n"
     ]
    }
   ],
   "source": [
    "#Optimo de la funcion objetivo\n",
    "print(pulp.value(model.objective))"
   ]
  }
 ],
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