Single_Item_Newsvendor.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "99c1caf1",
   "metadata": {},
   "source": [
    "## Robust Optimization of Single-Item Newsvendor Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8ea062b",
   "metadata": {},
   "source": [
    "In the single-item newsvendor problem, a seller is uncertain about the demand of a certain product and has to decide in advance how many units of the product he/she wishes to order. The uncertainty in demand induces a loss, either in unsold items or in unmet demand. Let $d_i$ be the realization of the demand in state $i$. Let $c$ be the cost of one unit of order, $v>c$ be the selling price, $s<c$ be the salvage value per unsold item returned to the order factory, and $l$ be the loss per unit of unmet demand. Denote $y$ to be the number of items ordered. The profit function $\\pi(d_i,y)$ is defined as\n",
    "\\begin{align}\n",
    "    \\pi(d_i,y)&:=v\\min\\{d_i,y\\}+s(y-d_i)_+-l(d_i-y)_+-cy\\nonumber\\\\\n",
    "    &= (s-v)(y-d_i)_+-l(d_i-y)_++(v-c)y.\n",
    "\\end{align}\n",
    "Here, we assume that $d_i\\in \\{4,8,10\\}$ with three possible realizations corresponding to low demand, medium demand, and high demand. The nominal probability of these realizations is assumed to be $\\mathbf{p}=\\{0.375,0.375,0.25\\}$. We assume the number of items ordered will not exceed the maximal demand, i.e., $y\\leq 10$. For the parameter values we take $v=6,l=4,s=2,c=4$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb8f609f",
   "metadata": {},
   "source": [
    "We assume the risk preference of the seller is represented by a risk measure induced by the distortion function $h_{cv}(x)=\\min\\{x/(1-\\alpha_0),1\\}$ and the seller's uncertainty in the probability $\\mathbf{p}$ is measured by the Kullback-Leibler divergence function $\\phi_{kl}(x)=x\\log(x)-x+1$. This leads to the following robust optimization problem, where the worst case risk evaluation is minimized\n",
    "\\begin{align}\n",
    "\\min_{0\\leq y\\leq 10, t\\in \\mathbb{R}}\\{t|\\sup_{(\\mathbf{q},\\mathbf{\\bar{q}})\\in \\mathcal{U}_{\\phi_{kl},h_{cv}}}-\\sum^3_{i=1}\\bar{q}_i\\pi(d_i,y)\\leq t\\},\n",
    "\\end{align}\n",
    "where\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{split}\n",
    "   \\mathcal{U}_{\\phi_{kl},h_{cv}}=\\{(\\mathbf{q},\\bar{\\mathbf{q}})\\in \\mathbb{R}^{6}_{\\geq 0}&: \\sum^3_{i=1} q_i=1,~\\sum^{3}_{i=1} \\bar{q}_i=1,~\\sum^3_{i=1}p_i\\phi_{kl}(\\frac{q_i}{p_i})-r\\leq 0\\\\\n",
    "    &\\bar{q}_1\\leq h_{cv}(q_1),~ \\bar{q}_2\\leq h_{cv}(q_2),~\\bar{q}_3\\leq h_{cv}(q_3)\\\\\n",
    "    &\\bar{q}_1+\\bar{q}_2\\leq h_{cv}(q_1+q_2),~ \\bar{q}_1+\\bar{q}_3\\leq h_{cv}(q_1+q_3),\\bar{q}_2+\\bar{q}_3\\leq h_{cv}(q_2+q_3)\\}.\n",
    "\\end{split}\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea720914",
   "metadata": {},
   "source": [
    "Using reformulation technique, this robust optimization problem is eqvuialent to the following convex problem with finitely many constraints\n",
    "\\begin{align}\\label{newsvendor:robust}\n",
    "    \\begin{split}\n",
    "      \\min_{\\substack{y\\in[0,10]\\\\ t, \\alpha,\\beta, \\nu_j\\in \\mathbb{R}\\\\ \\gamma,\\lambda_j\\geq 0}}&~t\\\\\n",
    "     \\text{subject to}~\n",
    "        &\\alpha+\\beta+\\gamma r +\\sum^3_{i=1}p_i\\gamma \\phi_{kl}^*\\left(\\frac{-\\alpha+\\sum_{j: i\\in I_j}\\nu_j}{\\gamma}\\right)+\\sum^6_{j=1}\\lambda_j(-h_{cv})^*\\left(\\frac{-\\nu_j}{\\lambda_j}\\right)\\leq t\\\\\n",
    "        &-r(d_i,y)-\\beta-\\sum_{j:i\\in I_j}\\lambda_j\\leq 0,~i=1,2,3,\n",
    "    \\end{split}\n",
    "\\end{align}\n",
    "where $I_1,\\ldots , I_6$ are the subsets of $\\{1,\\ldots,6\\}$ that are not the empty set or the entire set. $\\phi^*_{kl}$ and $h^*_{cv}$ are the convex conjugates of $\\phi_{kl}$ and $h_{cv}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4628064e",
   "metadata": {},
   "source": [
    "We can solve the above problem using CVXPY. First we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "51074f6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cvxpy as cp\n",
    "import pandas as pd\n",
    "import mosek\n",
    "import matplotlib.pyplot as plt\n",
    "### importing the phi-divergence functions \n",
    "import phi_divergence as phi        \n",
    "### importing the distortion functions\n",
    "import distortion_function as hf    \n",
    "import scipy.stats\n",
    "from itertools import chain, combinations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9910514c",
   "metadata": {},
   "source": [
    "The reformulated robust problem can be solved by defining the following functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4a7f44d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "### This function makes all subsets given a number of indices.\n",
    "def powerset(iterable):                     \n",
    "    \"powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)\"\n",
    "    s = list(iterable)\n",
    "    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))\n",
    "\n",
    "\n",
    " ### This function can solve the reformulated problem\n",
    "def RC_newsvendor_riskmin(sets,p,d,r,par,par_news,phi_conj, h_conj):   \n",
    "    N = len(p)\n",
    "    M = len(sets)\n",
    "    v = cp.Variable(M)\n",
    "    lbda = cp.Variable(M, nonneg = True)\n",
    "    y = cp.Variable(1, nonneg = True)\n",
    "    alpha, beta, c = [cp.Variable(1), cp.Variable(1), cp.Variable(1)]\n",
    "    gamma = cp.Variable(1,nonneg = True)\n",
    "    [v_news, l_news, s_news, c_news] = par_news\n",
    "    z = cp.Variable(M)\n",
    "    t, z2 = [cp.Variable(N), cp.Variable(N)]\n",
    "    s = cp.Variable(N)\n",
    "    w2_phi = cp.Variable(N)\n",
    "    l1 = (v_news+l_news-c_news)*y*(np.zeros(N)+1) - l_news*d\n",
    "    l2 = (s_news-c_news)*y*(np.zeros(N)+1) + (v_news-s_news)*d\n",
    "    constraints = [y<=np.max(d), z2 <= l1, z2 <= l2]\n",
    "    for i in range(N):\n",
    "        lbdasum = 0\n",
    "        vsum = 0\n",
    "        for j in range(M):\n",
    "            if i in sets[j]:\n",
    "                lbdasum = lbdasum + lbda[j]\n",
    "                vsum = vsum + v[j]\n",
    "        constraints.append(-z2[i] - lbdasum - beta <= 0)\n",
    "        constraints.append(s[i] == -alpha + vsum)\n",
    "    constraints = phi_conj(gamma,s,t,w2_phi,constraints)\n",
    "    constraints = h_conj(lbda,v,z,par,constraints)\n",
    "    constraints.append(alpha + beta + gamma * r  + cp.sum(z) + p@t <= c)\n",
    "    obj = cp.Minimize(c)\n",
    "    prob = cp.Problem(obj,constraints)\n",
    "    prob.solve(solver=cp.MOSEK)\n",
    "    return(y.value, c.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "177554b3",
   "metadata": {},
   "source": [
    "To compare the robust solution to the nominal solution, we also solve the nominal problem, where the risk evaluation is minimized with respect to the nominal probability $\\mathbf{p}$\n",
    "\\begin{align*}\n",
    "    \\min_{0\\leq y\\leq 10, t\\in \\mathbb{R}}\\{t|\\sup_{\\mathbf{\\bar{q}}\\in M_h(\\mathbf{p})}-\\sum^3_{i=1}\\bar{q}_i\\pi(d_i,y)\\leq t\\},\n",
    "\\end{align*}\n",
    "where \n",
    "\\begin{align*}\n",
    "    M_h(\\mathbf{p})=\\{\\mathbf{\\bar{q}}\\in \\mathbb{R}^3_{\\geq 0}|~\\sum^3_{i=1}\\bar{q}_i=1, \\sum_{k\\in I_j}\\bar{q}_k\\leq h(\\sum_{k\\in I_j}p_k), I_1,\\ldots,I_6.\\}\n",
    "\\end{align*}\n",
    "Since the set $M_h(\\mathbf{p})$ consists of linear inequalities, the nominal problem can be easily reformulated to the following convex problem\n",
    "\\begin{align*}\n",
    " \\min_{\\substack{y\\in[0,10]\\\\ t,\\beta, \\nu_j\\in \\mathbb{R}\\\\ \\gamma,\\lambda_j\\geq 0}}&~t\\\\\n",
    "     \\text{subject to}~\n",
    "        &\\beta+ \\sum_{j=1}^6\\lambda_jh(\\sum_{k\\in I_j}p_k)\\leq t\\\\\n",
    "        &-r(d_i,y)-\\beta-\\sum_{j:i\\in I_j}\\lambda_j\\leq 0,~i=1,2,3.   \n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "868a26ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "### This function can solve the nominal problem\n",
    "\n",
    "def nominal_solve(sets,p,d,par,par_news, h_eva):\n",
    "    N = len(p)\n",
    "    M = len(sets)\n",
    "    lbda = cp.Variable(M, nonneg = True)\n",
    "    y = cp.Variable(1, nonneg = True)\n",
    "    beta, c = [cp.Variable(1), cp.Variable(1)]\n",
    "    [v_news, l_news, s_news, c_news] = par_news\n",
    "    z2 = cp.Variable(N)\n",
    "    l1 = (v_news+l_news-c_news)*y*(np.zeros(N)+1) - l_news*d\n",
    "    l2 = (s_news-c_news)*y*(np.zeros(N)+1) + (v_news-s_news)*d\n",
    "    constraints = [y<= np.max(d), z2 <= l1, z2 <= l2]\n",
    "    h_jsum = 0\n",
    "    for i in range(N):\n",
    "        lbdasum = 0\n",
    "        for j in range(M):\n",
    "            if i in sets[j]:\n",
    "                lbdasum = lbdasum + lbda[j]\n",
    "        constraints.append(-z2[i] - lbdasum - beta <= 0)\n",
    "    for j in range(M):\n",
    "         h_jsum = h_jsum + lbda[j]*h_eva(np.sum(p[sets[j]]),par)\n",
    "    constraints.append(beta  + h_jsum <= c)\n",
    "    obj = cp.Minimize(c)\n",
    "    prob = cp.Problem(obj,constraints)\n",
    "    prob.solve(solver=cp.MOSEK)\n",
    "    return(y.value, c.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a3a5a0a",
   "metadata": {},
   "source": [
    "We perform the following experiment to compare the robust solution to the nominal solution. We choose a range of (fictitious) sample size $n= 10, 20,\\ldots 200$. This sample size is purely artificial: we treat $\\mathbf{p}$ as estimated from a sample of size $n$. We also examine a range of quantile levels $\\alpha_0 = 0.4, 0.3, 0.2, 0.1$ for the distortion risk measure. For both the robust and the nominal solution, we compare their worst case risk evaluation. For the robust solution, the worst case risk evaluation is simply the objective value of the robust problem i.e. the worst case risk evaluation minimization problem. For the nominal solution, the worst case risk evaluation is the objective value of the robust problem evaluated in this solution, which can be calculated by the following function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a566d3f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "### This function compute the worst case risk evaluation given a solution y\n",
    "\n",
    "def robustcheck_newsvendor(y,d,r,p,par,par_news,h_func, phi_func):\n",
    "    N = len(p)\n",
    "    x = np.zeros(N)\n",
    "    [v_news, l_news, s_news, c_news] = par_news\n",
    "    for i in range(N):\n",
    "        x[i] = v_news*np.minimum(d[i],y)+s_news*np.maximum(y-d[i],0)-l_news*np.maximum(d[i]-y,0)-c_news*y\n",
    "    rank = np.argsort(x)\n",
    "    q_b = cp.Variable(N, nonneg = True)\n",
    "    q = cp.Variable(N, nonneg=True)\n",
    "    constraints = [cp.sum(q) == 1, cp.sum(q_b)==1]\n",
    "    constraints = h_func(q_b,q,rank,par,constraints)\n",
    "    constraints = phi_func(p,q,r,par,constraints)\n",
    "    obj = cp.Maximize(-q_b.T @ x)\n",
    "    prob = cp.Problem(obj,constraints)\n",
    "    prob.solve(solver=cp.MOSEK)\n",
    "    return(prob.value,q_b.value,q.value)\n",
    "\n",
    "def wc(y,d,r,p,par,par_news, phi_func, sets):\n",
    "    N = len(p)\n",
    "    M = len(sets)\n",
    "    x = np.zeros(N)\n",
    "    [v_news, l_news, s_news, c_news] = par_news\n",
    "    for i in range(N):\n",
    "        x[i] = v_news*np.minimum(d[i],y)+s_news*np.maximum(y-d[i],0)-l_news*np.maximum(d[i]-y,0)-c_news*y\n",
    "    q_b = cp.Variable(N, nonneg = True)\n",
    "    q = cp.Variable(N, nonneg=True)\n",
    "    constraints = [cp.sum(q) == 1, cp.sum(q_b)==1]\n",
    "    constraints = phi_func(p,q,r,par,constraints)\n",
    "    for j in range(M):\n",
    "        q_sum = 0\n",
    "        qb_sum = 0\n",
    "        for i in range(N):\n",
    "            if i in sets[j]:\n",
    "                q_sum = q_sum + q[i]\n",
    "                qb_sum = qb_sum + q_b[i]\n",
    "        h_cons = (1+par)*q_sum-par*(q_sum)**2\n",
    "        constraints.append(qb_sum-h_cons <= 0)\n",
    "    obj = cp.Maximize(-q_b.T @ x)\n",
    "    prob = cp.Problem(obj,constraints)\n",
    "    prob.solve(solver=cp.MOSEK)\n",
    "    return(prob.value,q_b.value,q.value)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cbfe5df-4497-45ea-ae89-a21591d9003d",
   "metadata": {},
   "source": [
    "Defining the parameter values of demands, nominal probability, costs, etc. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bcaa9b62-45f6-446a-970b-bff6cb0a337a",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = np.array([4,8,10])\n",
    "p = np.array([0.375,0.375,0.25])\n",
    "### parameter values of [v,l,s,c]\n",
    "par_news = np.array([6,4,2,4])    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e6c4b34-5154-4ad6-854a-9232e2837033",
   "metadata": {},
   "source": [
    "Defining the phi-divergence conjugate function, which in this case is the conjugate of kullback-leibler divergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "29344b82-305e-41d4-b3f2-2f87ba18083c",
   "metadata": {},
   "outputs": [],
   "source": [
    "### the epigraph of the phi conjugate function\n",
    "phi_conj = phi.kb_conj  \n",
    "### the epigraph of the phi function\n",
    "phi_func = phi.kb_cut   \n",
    "### evaluation of the phi function\n",
    "phi_eva = phi.kb_eva     \n",
    "### phi''_kl(1), second derivative of kl_divergence function evaluated at 1, which is equal to 1.\n",
    "### Note that this has to be calculated by hand, which is usually not hard.\n",
    "phi_dot = 1   \n",
    "\n",
    "### Number of realisations of the demand d, which determines the phi-divergence radius\n",
    "m = len(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1cbbcb2-cad3-48a2-baa4-07a524a87063",
   "metadata": {},
   "source": [
    "Similarly, we define the necessary variables for the distortion function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d1758742-82fb-4845-b042-421e08687e0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "### the conjugate of the h function writte in its epigraph representation\n",
    "h_conj = hf.h_cvar_conj   \n",
    "### h_eva can be used when we need to evaluate the h function\n",
    "h_eva = hf.h_cvar_eva   \n",
    "### the epigraph of the h function\n",
    "h_func = hf.h_cvar_cut \n",
    "### parameter of the h function, in the h_cv case, this is the quantile parameter\n",
    "par = 0.1  \n",
    "\n",
    "### making all the subsets of {1,...,m} except the empty set and the whole set.\n",
    "psets = list(powerset(list(range(m))))   \n",
    "for i in range(1,len(psets)):\n",
    "    psets[i] = list(psets[i])\n",
    "psets = psets[1:(len(psets)-1)]\n",
    "sets = psets"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3122b85",
   "metadata": {},
   "source": [
    "The following code performs the experiment and output the graph of the worst case risk evaluation of the robust and the nominal solutions, with respect to the sample size $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8313c52d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\gjin\\AppData\\Local\\Temp\\ipykernel_2596\\4155095990.py:7: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  wcrisk_rob[i] = RC_newsvendor_riskmin(sets,p,d,r,par,par_news,phi_conj, h_conj)[1]\n",
      "C:\\Users\\gjin\\AppData\\Local\\Temp\\ipykernel_2596\\475701882.py:8: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  x[i] = v_news*np.minimum(d[i],y)+s_news*np.maximum(y-d[i],0)-l_news*np.maximum(d[i]-y,0)-c_news*y\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
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uLg8//DB79uzB29ub++67r0rbr8lrBCUD4V9rr8w///lPwBLIP/vss+Lp6enp3HrrrSQkJBAeHs6ECROqtV6bdDGD60nV1ckAxT/9yzCe9jKM7x+23jZEpEo0QHHVcG6A4oosXbrUcHJyMgCjWbNmRp8+fYwWLVoYgGFnZ1dqQF7DOD/Q7RNPPGF4e3sbLi4uRq9evYzw8PDibd5///1lbu/OO+8sXiYiIsLo0aOH4eDgYHTs2NF4+OGHSw2+++233xYv7+/vb/Tu3dvo3r274ebmVjz4744dO0psY+3atcVt2rdvbwwdOtQYNmyYsWLFikpfs+7duxcP1tupUyejb9++xQPxAsakSZNKtXn77bcNk8lkAEZAQIDRp08fw8fHxwAMZ2fnUgM1X/galjUQcXVfI8OwDCrdrl07AzB8fX2NAQMGGMOGDTMefvjhKm3z8ccfL95maGio0bt3b8Pd3b34c7F169ZSbYpel6ioqDJfy4sZKPpiaYBiqVzYAMu/6rETERty1VVXsWPHDm655RZcXFz4/fffMQyDa6+9lvXr15cakPdC7du3Z+vWrYwbN44TJ04QFxdH9+7dmT9/frmHd+fNm8fs2bOLz1dLSEjgnnvuYdOmTfj4+JRafsiQIbz++uuMGzcODw8P9u3bx/Hjx2nbti0zZszgwIEDpXrshgwZwmeffUbfvn05deoUa9euZc2aNZw+fbrS1+PVV1/l4Ycfplu3biQmJvL7778DlsOQ33//PQsXLizV5r777mPdunVcc801FBYW8vvvv+Pm5sakSZPYuXMnf/vb3yrd7sW8RmC5AnX58uVcf/312Nvbs3XrVtasWVNcf2XmzJnDDz/8wJgxY8jIyOCPP/7Az8+Pe++9l927d9OnT59q7YOtMhmGzrSvC2lpaXh7e5OamlrmCb61IjMRXmwDrs3hkb2Ww7MiUi9ycnKIiooiIiICFxeX+i5HRBqY6vyNqE6G0LX2tsTdDx7YAc1bQy2NlyQiIiKNh4KdrfFrW98ViIiISD1Rt46IiIiIjVCwszW5mfDVnfBaD8irvfGRREREpOFTsLM1jm4QtRaSoyB2V31XIyIiInVIwc7WmEwlby8mIiIiTYaCnS1qZbn1isazExERaVoU7GxRcY/dFjh36xgRERGxfQp2tiigKzi6gzkVEvbXdzUiIiJSRxTsbJG9A4Seu7VK9Mb6rUVERETqjIJdBbZu3cpDDz3EoEGDcHd3x2Qy8dFHH9V3WVXTajAEdQcnj/quREREROqIgl0FfvzxR9566y1SUlLo0aNHfZdTPUP/AfeshR4T67sSERERqSMKdhW47777SEtLY+/evTzyyCP1XU71mEz1XYGIiIjUMd0rtgIBAQH1XcLFy8u23I3C3a++KxERERErU4+dLdv0FswJhdX/re9KREREpA4o2FmJ2WwmLS2txKPOeYdAYZ4GKhYRsaLbbrutQVxcN3z4cEwmE7/99lu91vFXx48fx2QyER4ebtPbbCgU7Kxkzpw5eHt7Fz9CQ0PrvoiwAZZ/4/dBdnLdb19ERMQK5s6dy8yZM0lJSanvUhqcJh/sCgoKOH36dIlHamrqRa/3iSeeIDU1tfgRExNTC9VWk0cLaN4GMCBmW91vX0SkCQgKCqJDhw54e3vXdylNxty5c5k1a1a5wc7R0ZEOHTrQpk2bui2sAWjyF0/ExMQQERFRYtqUKVMuukvd2dkZZ2fni1pHrQgbAElH4cQmaH9pfVcjImJz5syZw5w5c+q7DLlAy5YtOXDgQH2XUS+afLALDAxk1apVJaYFBwfXUzVWENYffl+k8+xERESagCZ/KNbFxYXRo0eXeHTu3Lm+y6o9RefZndoB+eb6rUVE5C9MJhOmc+NurlixgqFDh+Lp6Ym3tzeXX345u3btKrft2bNnmTFjBh06dMDV1ZVmzZoxfPhwPv30UwzDKLX8Rx99hMlk4rbbbiM7O5snnniC1q1b4+rqSocOHXjjjTdKrPvhhx+mVatWuLi4EBkZWe6RnPIunpg5cyYmk4mZM2eSmprK9OnTCQsLw9nZmbZt2/LMM8+Qn59fan3Z2dksXryYCRMm0KFDBzw8PPDw8KBHjx48++yzZGZmVuGVrRrDMFi4cCFDhw7Fx8cHJycnAgMD6dWrFzNmzODkyZOl2mRmZvLss8/SrVs33N3d8fLyol+/frz11ltl7k95qnKBw4WfDzj/HkZHRwMQERFRvMyFF45Utu6L+eyYzWZmzpxJ27ZtcXFxITQ0lEcffbRW35eL0eR77CoSHR3NJ598AsDevXsB+OGHH4o/6FdddRXdunWrt/qqxLcNdL8ZArtCQR44NIDDwyIifzFv3jzuv/9+AgMDad++PQcPHuSnn35i/fr1bNu2jY4dO5ZY/siRI4wcOZKYmBicnJzo0qULKSkprFmzhjVr1rBy5criL+O/ys3NZdSoUWzdupXIyEgMw+DQoUM89NBDJCcnc++99zJ48GCio6OJjIwkPz+fffv2cfvtt2MYBrfffnu19i01NZUBAwZw+PBhunTpgr29PUePHuU///kPJ06c4L333iux/I4dO7j55ptxcHAgMDCQTp06kZqayt69e9m9ezfffvst69evx9XVtfov9F889thjvPzyywCEhYXRvn17EhMT2bNnDzt37mTgwIGEhIQUL5+QkMCoUaP4888/sbOzo0uXLuTl5bF161a2bt3K0qVL+f7773Fxcbno2soSEBDAoEGD2L59O2azmd69e5c47akq5zlezGcnLy+PSy+9lHXr1tG5c2fCw8M5fPgwr776Knv27GHlypW1ur81Yki5Vq9ebQDlPhYsWFDldaWmphqAkZqaar2CRaTByM7ONvbt22dkZ2fXdykNWtHfUzc3txJ/U9PS0oxRo0YZgHHTTTeVaFNYWGj07t3bAIxhw4YZp0+fLp63YsUKw93d3QCMt99+u0S7BQsWGIDh6OhodO3a1Th27FjxvMWLFxuA4erqalx66aXGiBEjjDNnzhTPf+655wzACAoKMvLz80usd8qUKWV+Jzz99NPF2xs6dKhx6tSp4nnff/+9YW9vbwDG/v37S7Q7fvy4sWTJEiM9Pb3E9Li4OOP66683AGPmzJmlXsthw4YZgLF69epS88oSHx9v2NnZGd7e3sb69etLzMvOzjYWL15s7N69u8T06667zgCMyMhI48iRI8XTt23bZgQEBBiAMWPGjBJtoqKiDMBo1apVlaZfqOjz8VetWrUyACMqKqrMduWtuzY+O507dzYOHjxYPG/Tpk2Gl5eXARgrVqwod1/+qjp/I6qTIRTs6oiCnUjTUuU/2uaM8h+52dVYNusils2sYPnM0svWoqIv7gcffLDUvD/++MMADG9v7xLTV61aZQCGs7OzERcXV6rdCy+8UPylXlhYWDy96MvZZDIZO3fuLNVuwIABxeHuwhBmGIaRn59vtGzZ0gBKta0s2Lm6uhoxMTGltjd+/HgDMF555ZVS88qTlZVlODk5Ge3atSs1r7rBbtOmTQZgXHvttVVa/tChQ4bJZCrzNTAMw1iyZIkBGO7u7kZaWlrx9IYU7Grjs7Nt27ZS7R599FEDMB566KFy9+WvrBXsdCi2KTAMSI6CmK3Q9Uawa/KnVoo0HP+t4GKtdpfCLV+e//nFtpCXVfayrQbD7cvP/zy3K2SdLXvZ4Etg6m/nf36rH6SeKHtZ/44wbcv5n98bUfLnWnLXXXeVmta1a1dcXFxITU3l7Nmz+Pr6AhQf7rrhhhsIDAws1e7ee+/lqaeeIjo6moMHD5Y6jHvJJZdwySWXlGrXo0cPNm3axOWXX17qIjp7e3u6devGqVOnOHbsWJnty3PZZZeVOJxZpE+fPnzzzTccO3as1LzCwkJ++OEHVq5cybFjx8jIyCg+98tkMnH48GGysrJwc3Orch1/VTS+6pYtWzhx4gRhYWEVLr9q1SoMw2Dw4MFl7v91111HSEgIJ0+eZMOGDVx22WU1rs1aLvaz06NHD3r37l2qXZ8+fQDKfC/rmoJdU1CYD+8MsnwhBHWHFp3quyIRkRLKG2/M39+fmJgYMjIyioPdoUOHAMq90M3T05PQ0FCOHDnCoUOHSn05V7StqszPyMioZG9KKm99LVq0KHN9KSkpXHHFFWzatKnC9SYnJ19UsGvZsiU33HADX375JW3btmXEiBEMHz6cIUOG0L9/fxwcSkaEyl53Ozs7OnbsyMmTJzl06FCDDHbW+uyU917WBwW7psDeEUJ6Q9Ray3h2CnYiDce/YsufZ7Iv+fNjRypY9i898dP/rPqy07ZgOeJV5sIlf7x7dfnrvQju7u5lTrc7d4TBuOBKxaIvz6Iv07IEBARw5MgR0tPTS80rLwwVnSxf2XyjjKsmK1KdfQN49NFH2bRpEx06dOC///0v/fv3x8/PDycnJwBCQkI4deoUeXl51aqjLAsXLqRz5868//77rFy5srhHy9/fnxkzZvDoo48W11nV1x0o83VvCC72s1Pd97I+KNg1FWEDzgW7zdD7jvquRkSKOJX9RVG3y1aj16c6y1qJh4cHAPHx8eUuc+bMGcDSA9OY5Ofns2TJEgCWLl1Khw4dSs0/ffp0rW3PxcWFmTNnMnPmTA4cOMDatWtZtmwZy5cv57HHHgPgH//4B1D7r3tlQdkaw4fY8meniE62aiqKxrM7UXHXvohIQ9e+fXsA9u3bV+b89PT04ts4Fi3bWCQkJJCZmUnz5s1LhTqAPXv2UFBQYJVtd+zYkalTp/L999/z9ttvA5QYiqWy172wsLD4bg9Ved2Ler8SEhLKnH/kSPk91GUNRVIVtvzZKaJg11SE9LYc1kk5Aamn6rsaEZEaGzt2LABffvllmb1X7777LmazmVatWpUZjhqyorHp0tLSyM7OLjX/hRdeqJM6+vfvD0Bs7PlTBS699FJMJhPr168vc+Dob775hpMnT+Lu7s6gQYMq3Yavry/e3t5kZ2cXjxV7offff7/ctkWvU1mvUUVs+bNTRMGuqXD2tAxSDOq1E5FGbeTIkfTp0wez2czEiRNLHFZbuXIls2bNAuDxxx+vcc9OffHx8SkeFPmRRx4hNzcXgIKCAp5//nm++OKL4nPtLtYvv/zCY489Vqr3KiMjgxdffBGAnj17Fk9v27Yt48ePB+DWW28tcQXozp07eeihhwB44IEHqnwotihoPfrooyUuPPj444/58MMPy23bunVrANasWVPpdi5ky5+dIgp2TUnx4VjdN1ZEGi+TycRnn31GSEgIv/32G2FhYfTq1Yt27doxduxYMjIymDx5Mvfcc099l1ojc+bMwWQy8e677xIUFESfPn0IDAzk8ccf59///jdBQUG1sp309HReeuklIiMjadGiBX369KFHjx4EBATw6aef4u3tzauvvlqizTvvvEPXrl3Zs2cP7du3p0ePHkRGRtKrVy/i4uIYPXo0M2fOrHINs2bNwsPDg5UrVxbfyiw4OJjbbrut+I4YZbnpppsAuO++++jatSvDhw9n+PDh/P777xVuz9Y/O6Bg17Rccgvc9CkMf7y+KxERuSht27Zl165d/OMf/yAsLIy9e/cSHx/P0KFD+eSTT/j4448bbY/LuHHjWLFiBQMHDiQ7O5uDBw/Stm1bFi1axOzZs2ttO0OGDOH1119n3LhxeHh4sG/fPo4fP07btm2ZMWMGBw4cKNFjB5arZTdt2sTs2bPp1KkThw4dIjo6mj59+vDGG2/w448/Vut2Yh07dmTt2rVcdtll2NnZcfDgQSIiIvjhhx+49957y203efJkXnvtNbp168bRo0eLbweWkpJS6TZt+bMDYDIawrW5TUBaWhre3t6kpqbi5eVV3+WIiJXl5OQQFRVFRESE1e6bKSKNV3X+RlQnQ6jHTkRERMRGaBy7pubMPti3FHzCLIdmRURExGaox66pObkN1vwf/P5ZfVciIiIitUzBrqkpujL21HbIz63fWkRERKRWKdg1NX7twM0X8nMgbnd9VyMiIiK1SMGuqTGZdHsxERERG6Vg1xSFWW4Vo4GKRUREbIuCXVN0YY9dYWH91iIiIiK1RsGuKQrsBg6uUJgP6bGVLy8iIiKNwkWNY5eXl8e2bdtYv3490dHRJCQkkJ2djZ+fH/7+/vTs2ZMhQ4bQsmXL2qpXaoODE9y3AZqFg519fVcjYtN0cx8RKYu1/jbUKNitXr2a999/n++++46cnByg7AKL7rXWqVMn7rjjDm699Vb8/PwuolypNb5t6rsCEZvm4GD582o2m3F1da3nakSkoTGbzcD5vxW1pVr3iv3hhx944okn2L9/P4Zh4ODgQNeuXenTpw9BQUE0b94cV1dXkpKSSEpKYt++fWzbto0zZ84A4OTkxNSpU3nqqafw9/ev1R1p6HSvWJGm58SJE+Tn59OqVSvs7dU7LiIWBQUFREdH4+DgQFhYWKXLVydDVDnYDR06lA0bNuDq6sq4ceOYMGECY8eOrdLNrY8ePcrnn3/O4sWL2bdvH56enixcuJCrr766Kpu2CQ0u2BkGfP8AHN8At68Ar6D6rkjE5mRlZRETE4O9vT3e3t64urpib29ffDRDRJoOwzAoKCggOzub1NRUCgsLCQ0NrVKPvlWCXfPmzXnooYeYPn06Pj4+VdqJsqxevZpnnnmGESNG8NRTT9V4PY1Ngwt2APMGw+k/4YaPIPLa+q5GxCbl5uYSHx9PVlYWBQUF9V2OiNQze3t73NzcaNGiBU5OTlVqU50MUeUDu9HR0Xh6elZ18XKNGDGCESNGkJ6eftHrkosUNsAS7E5sVrATsRInJydCQkIwDIO8vDwKNcSQSJNlZ2eHo6OjVXvtqxzsaiPUWXN9UgNhA2DrfN2BQqQOmEymKv/vXESkpjSOXVNWdAeK03+CWT2oIiIijZ2CXVPmFQw+rcAohJPb6rsaERERuUgKdk1d0e3FonU4VkREpLFTsGvqWg2AFp3BrXl9VyIiIiIXqXaHO5bGp+cU6HVbfVchIiIitUA9dk2dBkoVERGxGXXSYzdjxgwSExMxmUx88MEHdbFJqa58M+SkgkeL+q5EREREaqha94qtqYiICKKjozGZTE125PUGeeeJIn8sge8fhLajYcKn9V2NiIiIXMAqd564GNdffz2JiYl1sSmpiWbhkJ9juQOFYejwrIiISCNVJ8HuxRdfrIvNSE0FdQcHF8hKhLNHwa9tfVckIiIiNaCLJwQcnKFlL8tz3V5MRESk0VKwE4ui24ud2Fy/dYiIiEiNKdiJRdEdKNRjJyIi0mhVOdjdf//9nDx5slY2+vnnn/PZZ5/VyrqkloT0AUyQdBTSz9R3NSIiIlIDVQ528+fPp23bttx1112sXbu22htKSEjgzTffpFOnTtxyyy1ERUVVex1iRa4+0PduGD0L7HRDEhERkcaoyuPY7dmzh3/+85+sWLECk8lEcHAwl19+OX379qVXr14EBQXRvHlznJycSE1NJSkpif3797N9+3bWr1/Pb7/9RkFBAb6+vjz55JPcd999ODo6Wnv/aswwDD799FOWLVvG9u3biY2Nxc/Pjx49evDvf/+bfv36VWt9DXocOxEREWmwqpMhqj1A8bp163jzzTdZunQpubm5mCoZ86xo9W3btuXuu+/m3nvvxdPTszqbrBc5OTm4urrSrVs3rrzySlq3bk1cXBzz5s0jNjaWhQsXMmnSpCqvT8FOREREasKqwa5IYmIi3377LWvXrmXjxo3ExMSQn59fPN/Ly4sePXowePBgLr30UoYOHVqTzdSb/Px81q1bx4gRI0pMP336NF26dMHBwYHY2Fjs7Kp2NLvRBLuUGMuVsR2vACf3+q5GRESkyauTYFeWlJQUcnJyig/J2qrx48fz7bffEhcXR2BgYJXaNJpg92pXSD0Bty6F1sPruxoREZEmrzoZolaHO/Hx8SEwMNCmQx3AqVOncHJywsfHp75LqX0az05ERKTR0jh21bR8+XK2bt3KjTfeiIuLS7nLmc1m0tLSSjysxTAMNhxJ5M6PtnE2w3xxKysOdhrPTkREpLGxyrgWy5Yt4/vvv2fv3r0kJSVhZ2dHUFAQgwcP5rbbbiM8PNwam7W6gwcPMnnyZIKDg3n55ZcrXHbOnDnMmjWrjiqD5386wB8nU/l443EevbRDzVdUNFBxzDYoyAd7DX0iIiLSWNTqOXapqalcffXVxePcmUwmDMPAwcGB7t27c/jwYcxmMy+99BLTpk2rrc1elIKCAhISEkpMc3V1xdvbu8S0qKgohg0bRkZGBr/99hvdunWrcL1msxmz+XzvWVpaGqGhoVY7x+7HP+O4/9OdeLs6svHxkbg71zCQFRbCC+GQkwp3r4aWPWu1ThEREameejvHbsaMGfz555988cUXpKenk52dzerVq2nfvj2DBw/m7NmzvP7660yfPp2lS5fW5qZrLCYmhqCgoBKPhx9+uMQyx48fZ8SIEaSnp7Ny5cpKQx2As7MzXl5eJR7WNDYykHBfN1Kz8/hiW0zNV2RnB6E6z05ERKQxqtUeu4CAAJ599lnuvvvuEtN37txJ//79iY+Px8fHh0ceeYQtW7awcePG2tp0jeXk5LB+/foS04KDg+ncuTMA0dHRDB8+nOTkZFatWkWfPn1qtJ26uCr20y3R/PvbPbT0ceW3x4bjaF/D3L7uFfhlFnS6Cm76pHaLFBERkWqpToao1ROo0tLSaNWqVanprVq1Ij8/n5MnT+Lj48OYMWN47733anPTNebi4sLo0aPLnHdhqFu5cmWNQ11dua5nCK+uOsyplGx+2B3L+J4hNVtR56uhecT58+1ERESkUajVYNejRw8+/PBDLr300hLTP/zwQ5ydnYmIiLBs1MEBB4eGfVJ+eno6I0aM4Pjx4zz44IMcOnSIQ4cOlVhmzJgxBAQE1FOFpbk42nP7oHBe/Pkg7645xrWXtKz0ziBl8m1jeYiIiEijUqvp6plnnuHyyy+nR48ejB07FicnJ7Zs2cIvv/zCP//5T9zdLXcy2LVrF5GRkbW56Vp39uxZoqKiAHjjjTfKXGb16tUNKtgBTOrfirdXH+HgmXR+O5jAiI4t6rskERERqSO1eo4dwJo1a5g9ezZbt27F3t6e9u3b89BDD5W4r+rOnTtxcnKiS5cutbnpBq0u7zzx3PJ9vLcuir4RzVlyTw0PpyYdgz1fg5MH9L+vdgsUERGRKqu3W4pJ+eoy2J1OzWHIC7+SV2Dwzf0D6RnWrPorOfQzfHYj+LaDB7fXfpEiIiJSJfU23Ik0DIHeLlzToyUA7645WrOVhPa1/Hv2MGQm1lJlIiIiYk31EuzWrVtXPIixWMc9w1oDsHLfGY4mZFR/Ba7NoIVlyBeNZyciItI41EuwGzlyJCNGjKiPTTcZbVt4MrpTAIYB7609VrOV6L6xIiIijUq9BLsPPviADz/8sD423aTcN9zSa/fNzlPEp+VUfwVF49gp2ImIiDQK9RLsbr31VqZMmVIfm25SerVqTu9WzcgtKOSDDVHVX0FRj13cbsjNrN3iREREpNbp4gkbd+8wy0DDn20+QVpOXvUae4eCV0uwd4KzR6xQnYiIiNQmq9z+YenSpfzwww/s37+fpKQkAJo3b06nTp246qqruOqqq6yxWSnDyI4taNfCg8PxGXy25URx0KsSkwlu//FcuHO0XpEiIiJSK2q1x+7s2bMMGDCAa6+9lvXr1xMYGMjgwYMZNGgQgYGBbNiwgWuuuYaBAwdy9uzZ2ty0lMPOzsTUoZZz7T5cH4U5v6B6K2gWrlAnIiLSSNRqj90jjzxCQkICW7dupXfv3mUus2PHDiZMmMCjjz7Kxx9/XJubl3Jc3aMlr6w6RFxqDt/uPMWEvmH1XZKIiIhYQa322C1btoznn3++3FAH0KtXL/7v//6PH374oTY3LRVwcrDjzsERAMxfe4zCwmrebOTnf8MbvS0XUYiIiEiDVavBLj8/Hzc3t0qXc3V1JT8/vzY3LZWY0DcMLxcHjiVmsnLfmeo1TjhouQOFBioWERFp0Go12I0YMYKnn36a+Pj4cpeJj49n1qxZjBw5sjY3LZXwcHZg8oBWAMxbc5Rq3SJYAxWLiIg0CrV6jt3rr7/O8OHDCQ8PZ8SIEURGRuLj44PJZCI5OZl9+/axevVqAgMDWbJkSW1uWqrgtoERvLcuit9jUtgalUS/1r5Va1g8UPFmMAzL1bIiIiLS4NRqsGvVqhV79uxh3rx5LF++nIULF5KcnAxAs2bNiIyM5Nlnn+Xuu+/Gw8OjNjctVeDv6cwNvUL4dMsJ5q05WvVg17In2DlCehwkH4fmEVatU0RERGrGZFTrmJzUVFpaGt7e3qSmpuLl5VVvdRxPzGTky79RaMBP04fQMbCKtbw/Bk5uhWvmQY+J1i1SREREilUnQ+jOE01MuJ87l3cJAmD+mmNVb6jz7ERERBq8Ogt2ubm5zJs3r642JxW4Z5hlwOLvd8dyKiW7ao3CBoBfe/AKtmJlIiIicjGsHuyysrJ4+eWXiYiIYNq0adbenFRBtxAfBrbxJb/Q4P11Vey163A5PLANhj9u3eJERESkxmp08URqaiorV67k+PHjuLm50aNHDwYNGlRimYyMDF555RVef/11kpOTMQyD4GD19jQU9w5rw8ajZ/l8awwPjWxHM3enihvoSlgREZEGr9rB7tNPP2XatGmkp6eXmD548GC+//57vL29+eyzz3j44YdJSkrCMAw6derEP/7xDyZNmlRrhcvFGdLOj85BXuyLS+OTzdE8NKpd1RoW5ENmvA7JioiINEDVOhS7fft2brvtNtLS0op76tq3b4+9vT3r16/n/vvv59VXX2Xy5MmcPXuWfv368d1337F3715uv/12HB11M/mGwmQyFZ9r99HG42TnFlTeKGod/F8YvDsUcjOtXKGIiIhUV7WC3WuvvUZBQQE33HADsbGx7Nixg/3797N37146derEkiVL+Pe//42vry/ffvstGzdu5KqrrrJW7XKR/tY1iNDmriRl5vLVjpjKG4T1Bw9/yEyALe9av0ARERGplmoFuw0bNuDq6sr8+fPx9PQsnt6uXTvmzp1LQUEBZrOZpUuXcvXVV9d6sVK7HOztuHuIpddu/rpj5BcUVtzA3hGGP2F5vuE1yEm1coUiIiJSHdUKdnFxcbRt2xZvb+9S8/r16wdA69atGTBgQO1UJ1Z3Q69Qmrs7EZOUzY97TlfeoOsN4NcBclJg01tWr09ERESqrlrBzmw2lxnqgOIevMDAwIuvSuqMq5M9UwaEA/DumqNUeiMSO3sY8S/L801vQ+ZZ6xYoIiIiVVbr49iZNCxGo3PrgFa4OtqzNzaN9UcSK2/Q6SoI7Aa56bBhrtXrExERkaqp9nAn8fHxLFy4sMbzb7311upuUqysmbsTE/qGsmDDceatOcqQdv4VN7Czg5FPwWc3QFYSGIbGuRMREWkATEalx97Os7Ozu6geOZPJRH5+fo3bN2bVuYFvfTiZnMWwF3+joNDghwcG0zWk7EPuxQwDEg+Df/u6KVBERKSJqk6GqFaPXVhYmA612qiQZm5c1T2Yb3edYt7ao7x1c8+KG5hMCnUiIiINTLWC3fHjx61UhjQE9wxrzbe7TrHizziiz2bSyte9ag2Tj8Px9XCJ7iwiIiJSn2r94glpvDoGejG8gz+FBsxfe6xqjVJOwBu94fuH4OxR6xYoIiIiFVKwkxLuHdYGgC93nCQh3Vx5A58waDMSjAJY/V8rVyciIiIVUbCTEvpFNKdHqA+5+YV8vPF41RqNfNLy756v4cxeq9UmIiIiFav2cCdlyczM5IcffmD37t0kJSWRl5dX5nImk4kPPvigNjYpVmIymbh3WBvuXbSDhZuOc+/wNng4V/IxCeoGna+Bfd9Zeu0mfFoXpYqIiMhfXHSw+/zzz7nvvvtIS0srnlY0gsqFV9AahqFg10iM6RxAaz93jiVm8vnWE9x17n6yFRrxL9j/PRxYBqd2QMte1i9URERESrioQ7GbNm1i8uTJFBQU8O9//5u2bdsC8N577/Gf//yHq666CpPJhIuLC8899xwffvhhrRQt1mVvZ2LqUEuY+2B9FLn5hZU38u8A3W6yPP/1WStWJyIiIuW5qB67l156icLCQj799FPGjRvH6tWrOXLkCHfeeWfxMgcOHOCGG27grbfeYseOHRddsNSNa3u25OVVh4hLzeH73bFc3yuk8kbD/gmHfoKQPlBYYLmvrIiIiNSZi+6x8/PzY9y4ceUu07FjR77++mvi4uJ4+umnL2ZzUoecHey5Y1AEAPPXHqWwsAo3KGkeAY/utxyWVagTERGpcxcV7M6ePUtYWFjxz05OToDlYooLtW/fnsjISFasWHExm5M6dkv/MDydHTh0JoPVB+Or1sjR1bpFiYiISLkuKtj5+vqSnZ1d/LOfnx8AR4+WHqi2oKCAM2fOXMzmpI55uThyc39LcJ+3ppqDDx/7zTJocdVvRSwiIiIX6aKCXXh4OHFxccU/9+zZE8Mw+PTTksNd7N69m0OHDuHv738xm5N6cMegCJzs7dh2PJkd0UlVa5SdDItvhp0fw4Hl1i1QREREil1UsBszZgwpKSns3WsZlPbmm2/GxcWFl156iUmTJvHWW2/xn//8h1GjRlFYWMh1111XK0XXlZdffpnhw4cTFBSEs7MzQUFBjBw5kqVLl9Z3aXUmwMuFay9pCcC8NVW8zZhrM+h/r+X56uegsApX1YqIiMhFu6hgd+ONNzJy5EgOHjwIQGhoKO+88w4ODg589tlnPPTQQzz33HMkJSXRr18/nn22cQ2DsXXrViIiInj00Ud55513+Pvf/05mZibXXHMNs2fPru/y6szUYa0xmWDVvjMciU+vWqOBD4KzN8Tvg73fWLdAERERAcBkGLV/EtSxY8dYsmQJx48fx9XVlcGDB3PNNddgb9/4r5TMz8+nZ8+eHD16lJSUFBwdHavULi0tDW9vb1JTU/Hy8rJylbVv6sLtrNx3hht7h/DC9d2r1mjNi7D6WWjeBqZtBftaudGJiIhIk1KdDGGVYGfr/va3v/Hjjz+SkZGBu7t7ldo09mC380Qy49/eiKO9iXUzRhLo7VJ5I3M6vNYdss7CVW9Cz8nWL1RERMTGVCdDVOtQbNeuXXnxxRc5derURRXY2CQlJZGQkMCBAwd47rnn+Omnnxg2bFiVQ50t6BnWjL4RzckrMJi/torn2jl7wuBHLM/XPA/5ZusVKCIiItXrsbOzs8NkMmEymRgxYgSTJ09m/PjxeHh4WLPGeufn58fZs2cBsLe35+qrr+add96hRYsW5bYxm82YzeeDTFpaGqGhoY22xw5g7aEEbv1wK/Z2JpY9OJhOQVXYj7xsWHQ99L4dIseD3UWd1ikiItLkWK3H7qWXXqJHjx4UFhbyyy+/cPvttxMYGMikSZP46aefKLTRqx+/+eYbfv75Zz788EPGjh1LXl4eGRkZFbaZM2cO3t7exY/Q0NA6qtZ6hrb357LIQAoKDZ745s+q3Y3C0RVuXw5dr1eoExERsbIanWN34MABFi5cyOLFi4mOjrasyGSiRYsW3HzzzUyaNIlLLrmk1ou1hoKCAhISEkpMc3V1xdvbu9w2EydO5LfffmPfvn00a9aszGVssccO4HRqDqNfWUOGOZ9nrunC5P6tqrcCwwCTyTrFiYiI2CCr9dgV6dixI//973+JiopizZo13HXXXfj4+HDmzBnmzp1L79696dKlCy+88AInT56s0U7UlZiYGIKCgko8Hn744QrbTJkyhdOnT/PNN+UP4+Hs7IyXl1eJhy0I9HbhsbEdAHhhxQHi03Kq1rAgD7a+B+8Mgpw0K1YoIiLSdF30sbEhQ4Ywf/58Tp8+zddff83VV1+Nk5MT+/bt44knniA8PJxRo0bx8ccfV3r4sj4EBgayatWqEo8ZM2ZU2KboNmpJSVW8E4ONmdS/Fd1DvEk35zNr2b4qtjLBlnchfi9sfseq9YmIiDRVVhnuJDU1lS+++IJFixaxYcOG4umurq4NMtyVJTMzE8MwSl0YUlBQwNixY/nll19Yu3YtQ4YMqdL6GvtwJ3+1NzaVq97cQEGhwYLb+jCiY/kXkhTb8zV8dQc4e8HDu8GtufULFRERaeSsfii2Mt7e3kydOpVff/2V119/HWdnZwzDKO7pagwOHz5My5YtufPOO3nhhRd4//33mTlzJpGRkfzyyy9MmTKlyqHOFkUGe3PHoHAAnvxuD1m5+ZU36nwtBHQFcxpsfN26BYqIiDRBVrkVwObNm1m0aBFLlizh7NmzFHUKdu3a1Rqbs4qQkBAmTZrE+vXr+fbbb0lPT8fb25tLLrmEp556iptvvrm+S6x300e358c/T3MqJZvX/neYJ67oVHEDOzsY+W9YPMFyWLbffeAZUDfFioiINAG1dij28OHDLFq0iM8++4xjxywD2BqGQWBgIDfffDOTJ0+me/cq3orKBtnaodgiv+w/w50fb8fezsQPDwymc3Al+2YY8P4oOLXDEuwu/7+6KVRERKSRqrNbiiUkJLB48WI+/fRTtm/fDljCnJubG9dccw233noro0ePxk7jl9lssAO4/9Md/PjnaXqE+vD1fQOxt6tkOJOjq+GTa8DBBR7dr3PtREREKlCdDFHtQ7FZWVl8++23fPrpp/zvf/+joKAAwzCws7MrvhvFdddd16Rut9XUPT0ukrWHEvk9JoXPtkQzeUB4xQ1aD7fcaqzz1Qp1IiIitahaPXaTJ0/mu+++Iysrq/i8uS5dujB58mRuueUWgoODrVZoY2fLPXYACzcd5z9L9+Lp7MD//j6MAC+X+i5JRETEJljtUGzRIdXAwEAmTpzI5MmT6dGjx0UV21TYerArKDQY/85Gdsek8LeuQbx1S8+qN85OBtey7+AhIiLS1FltuJOJEyeyYsUKTp48ycsvv6xQJ8Xs7Uz899ou2NuZWP5nHL8eOFN5o8JC+HEGvNwR4vdbv0gREREbV61g9+mnnxISEsKyZcvYvHlzldps2rSJ77//nn37qnqHAmmsIoO9uXNwBABPfbe38rHt7OwgPRbyc2D1f+ugQhEREdtWrWCXlZXFpZdeyg033EBhYWGV2hiGwfXXX88VV1yB2WyuUZHSeEwf3Y6WPq6cSslm7v8OV95gxL8BE+z/HmJ/t3Z5IiIiNq1awW7x4sXExcVx5513MnDgwCq1GThwIHfffTcxMTF8/vnnNSpSGg83JweevaYLAB+sj2JvbGrFDVp0gq43WJ7/+qyVqxMREbFt1Qp23333HSaTiYceeqhaG5k+fTqGYfD1119Xq500TiM6tuBvXYMoKDT417d7KCis5Pqc4Y+DyR6OrIITVTvELyIiIqVVK9jt2rWLoKAgOnbsWK2NtGvXjpYtW7Jr165qtZPG6z/jOuPp7MDumBQ+3RJd8cK+beCSWyzPf33WcncKERERqbZqBbvExERatmxZow0FBweTmJhYo7bS+AR4uTDjsg4AvPDTQU6n5lTcYOgMsHeCUzshpZIgKCIiImWqVrBzcXEhOzu7RhvKzs7GycmpRm2lcbq5Xyt6hPqQYc5n1g97K17YJxSu/xAe3g3NwuukPhEREVtTrWAXFBTE0aNHq311q9ls5ujRo7ozRRNjb2dizviu2NuZWLHnNP/bV8nYdp3GgYd/3RQnIiJig6oV7IYMGUJOTg5fffVVtTby5Zdfkp2dzZAhQ6rVThq/TkFe3DXEMrbd09/vJdNcydh2RaI3QW6WFSsTERGxPdUKdrfddhuGYfDPf/6TmJiYKrU5ceIEM2bMwGQyMWXKlBoVKY3bw6PaEdKsaGy7Q5U3+PouWHAZfHM3FBZYv0AREREbUa1gN3DgQG644QZiY2Pp168fX375ZbkDFRcWFrJkyRL69+/PmTNnuO666xg0aFCtFC2Ni5uTA8+cG9vuww3H2XOqkrHtet9puZDiwDJY9Z86qFBERMQ2mAyjemNLZGdnM2bMGDZu3IjJZMLf359BgwYRERGBu7s7mZmZREVFsXHjRuLj4zEMgwEDBrBq1Src3NystR8NXnVu4Gurpn22k+V/xNE9xJtv7h+EvZ2p/IX//Aq+vtPy/IqXoO/ddVOkiIhIA1OdDFHtYAeQn5/PzJkzeeONN0hPT7esyHT+S7polR4eHjz44IPMnDkTR0fH6m7GpijYQXxaDqNeWUN6Tj4zx3XmtkERFTdY+xL8+gyY7GDCYuhwWd0UKiIi0oBYPdhduKHly5ezceNGTp06RXp6Op6enrRs2ZKBAwdyxRVX4O3tXdPV2xQFO4tFm6N58rs9eDg7sOrRoQR5u5a/sGHA9w/Crk/A0R1u/xGCe9RZrSIiIg1BnQU7qToFO4vCQoPr5m1k14kULosMZN7kXhU3KMiDT2+AqDUw7jXoeWvdFCoiItJAVCdDVOviCZGLZXdubDsHOxM/7T3NqsrGtrN3hBs/hklfK9SJiIhUwqG+C6hMfHw8q1evZsuWLZw+fZrs7Gx8fX3p0KEDQ4YMoX///vVdolRTx0Av7hrSmnlrjvL00j0MbOOLu3MFH0UXb2gz8vzP2Sng5G4JfSIiIlKswfbYrV69mquvvpqQkBAmTpzIN998w6FDh0hISGDTpk3Mnj2bgQMHEh4ezrPPPktaWlp9lyzVUDS2XWxqDq+uqsLYdkWSj8MHY2D5o5Zz8ERERKRYgwx2l156KVdddRXe3t58++23JCUlcfz4cbZv38769evZu3cvaWlp/Pnnn9x777189dVXtG7dmh9//LG+S5cqcnWy59nise2iKh/brkjCQTh7BHYuhPWvWrFCERGRxqdBBrv+/fsTHR3NwoUL+dvf/oaPj0+pZUwmE5GRkTz++OP8/vvvfP755+Tl5dV9sVJjwzu0YFz3YAoNeOKbPykorEIPXPuxcNnzlue/zLKMdyciIiKAroqtM7oqtmzx6TmMetkytt3T4zpze2Vj2xX56QnY/DbYO8OU7yFM51qKiIht0lWx0mi08HTh8cs7AvDSzweJS82uWsNLn4WOV0KBGRZPhLNHrViliIhI49Dge+xs5apY9diVr7DQ4Pp5G9l5IoWxkQG8O7l31RrmZsFHf4PYnRAxzNJzJyIiYmNsYoDi1atXM3fuXFasWEF+fj5hYWH4+fnh4uJCcnIyJ06cIDMzk7CwMO666y4eeuihBh2YFOwqduB0Gle+vp78QoP5k3txaWRg1RpmxMPyv1vuJ+sZYN0iRURE6kGjPxSrq2Kbno6BXtw9tDUAT3+/lwxzftUaerSAmz5RqBMREaGBBjtdFds0PTSyHWHN3YhLzeGlnw/WbCW7v4Bfn6vdwkRERBqJBnso1tboUGzVrDmUwJQPtwLw+OUduXdYm6o3Pr0H5g2yPB/3GvS6rfYLFBERqWON/lCsNF3D2vszfXQ7AP5vxQHe+OVw1RsHdoFh/7Q8X/YoHPnFChWKiIg0XA3+XrGxsbE89dRTHDp0iMDAQLp06UL37t3p0aMH4eHh9V2eWMH00e1xtLfjxZ8P8vKqQ+QVFPLImPaYTKbKGw9/wnLbsT++gCVT4M6fISDS6jWLiIg0BA2+x27SpEl8/fXXtG7dmqysLObPn8/48eNp06YNzZo1Y/jw4fVdoljBtBFt+dcVlvHtXv/1CP/30wGqdNaAyQRXvQGtBkNuOnx6A6TFWblaERGRhqHB99ht2bKF9957j5tvvrl4WmJiIr///ju7du3ijz/+qMfqxJqmDm2Do70ds37Yx7trjpGbX8h/ruxcec+dgzNMWATvj4Gzh+GzG+GOn8HJrW4KFxERqScNPtiFhobSvHnzEtP8/PwYPXo0o0ePrqeqpK7cPigCJwc7/v3tHhZsOE5eQSGzr+qCnV0l4c61GdzyJXwwBtpdCg4udVOwiIhIPWrwh2Lvv/9+Fi9eXN9lSD26pV8rXri+GyYTLNp8gie++ZOCwioclm0eAdO2wqinwK7Bf9RFREQuWoP/tjt79izr16/n0Ucf5ezZs/VdjtSTG3uH8sqN3bEzwRfbY3jsy93kFxRW3tDtgt7evGw4+JP1ihQREalnDX4cu6CgIM6cOQOAg4MDl1xySYlHt27dcHFp+IfZNI5d7Vj2RywPf/47BYUG47oH88qN3XG0r8L/T3KzYOFVcHK75U4VncZZv1gREZFaUJ0M0eDPsYuLiyMhIYHdu3eze/du/vjjDzZv3syCBQvIy8vD3t5ed5xoQq7sFoyDnR0PLt7JD7tjycsv5PWJl+DkUEm4c3SFwG5wcht8fTfcthxCetVN0SIiInWkwffYlSc/P599+/bxxx9/MGnSpDrZ5ttvv820adMAS+AMDKzijepRj11t+2X/Ge5btJPcgkJGd2rBW7f0xNnBvuJGBfnw+UQ4vBLc/eGu/0Gz8DqpV0REpKaqkyEabbCra7GxsXTq1InCwkIyMjIU7BqAtYcSuHvhdsz5hQxt78/8yb1wcawk3JnTYcHlcPpP8OsAty4Fr6C6KVhERKQGGv0txaZOnUp0dHSVly8sLGTRokUsWrTIajU98MADtG7dmmuuucZq25DqGdrenwW39cHV0Z61hxK446NtZOXmV9zI2RNuXgKewZB4EN4dCqd21E3BIiIiVtYgg53ZbKZjx45cccUVfPLJJxw9erTUMmlpafz666/8/e9/JywsjKeffppWrVpZpZ7vvvuOpUuXMm/ePOztK+kRkjo1sK0fH9/RF3cnezYePcttH24jw1xJuPMKhtuXQ4tIMArAvUXdFCsiImJlDfZQ7J49e5g7dy5LliwhMzMTV1dXfH19cXJyIiUlheTkZAoLC+nZsydTp07l9ttvx9HRsdbrSEtLo3PnzowbN4533nmH2267jY8//liHYhuYnSeSmfLBVtLN+fQM8+GjO/ri5VLJ5yE3E5KOQWDX89MKC8BO4V1ERBoOmzrHLicnh40bN7Jt2zbi4uLIycmhefPmdOzYkcGDB9O6dWurbn/atGl8/fXXHDhwAB8fnyoHO7PZjNlsLv45LS2N0NBQBTsr+uNkCpM/2Epqdh7dQrz55I5+eLtVI+wfWA6//Z9lOBRdVCEiIg2EzQx3YhgGmZmZjBw5kpEjR9b59jdt2sS8efNYuHAhPj4+1Wo7Z84cZs2aZZ3CpEzdQnz47O5+TP5gK3+cTGXie5tZdFc/mrs7Vd64IB9WPmnpwXt3GFz/AbTVLetERKRxaZDn2BUxDIOAgACWLVtmtW0UFBRw+vTpEo/U1FTy8vK4++67GTFiBLfccku11/vEE0+Qmppa/IiJibFC9fJXkcHeLL67P34ezuyLS2Pi/M0kpJsrb2jvAFN+gOCekJMCi66HtS9Bw+7QFhERKaFB99jZ2dkREhKCnRXv8xkTE0NERESJaVOmTKFHjx7s37+fV155hePHjxfPy8jIKG5nNpvLvWDD2dkZZ2dnq9Ut5esQ6MnnU/tz83ubOXgmnQnzN/HZ3f0J8KrkDiXeIXD7ClgxA3Z+DL8+A7G74Jp3wEWHz0VEpOFr8OfYPffcc+zatYuvvvrKKuvPyclh/fr1JaYFBwczf/58XnvttQrbOjs7k5OTU6Xt6OKJunc8MZOb39tMbGoO4b5ufHZ3f4J9XKvWeMdH8ONjUJALfu3h7l8tQ6WIiIjUMZs5xw4sPWSbNm3i1ltv5YUXXqjWlahV4eLiwujRpc+luvPOOxk+fHip6a+//jqrV69mwYIF+Pr61motUrvC/dz54p4BTHxvM8fPZnHT/E18dld/Qpu7Vd64120Q0BWWTIbWwxXqRESkUWjwPXahoaGcOnUKsByaveSSS+jduzc9evTgkksuoVu3bri4VHKIrRZpuJPG51RKNje/t5nos1kEe7vw2d39Cfdzr1rjzERw9gKHcxdg5KSCk4eGRBERkTpjUz12MTExJCUlsXv37uLHli1bWLBgAbm5udjb25OXl1ffZUoD1tLHlSXneu6OJWRy0/xNfHpXf9q28Ki8sbvf+ecF+fD5LWDnANd/CG7NrVe0iIhIDTT4Hrvy5Ofns3//fv74448aXbVa19RjV/8S0s3c8v5mDp3JwM/Dmc/u7kf7gGocYo3dBQuugLws8AmDmxZBUHfrFSwiIoKNDVBsKxTsGoazGWYmfbCV/XFpNHd34qUbujGyY0DVV3B6D3xxCyQfBwcXGPcadJ9gtXpFRESqkyEa9Dh2IrXN18OZxXf3o1uIN0mZudzx0XZmfLWbtJwqHs4P7AJTf4O2YyA/B769x3L1bH6uVesWERGpCgU7aXJ83Jz4YuoA7hwcgckES7af5LJX17L+cGLVVuDaDG5eAsP+afl563z44WHrFSwiIlJFtXIo1mw28/nnn/Pzzz9z6NAh0tPT8fT0pH379lx66aVMmDChTq9cbYh0KLZh2nLsLP/4ajcxSdkATO7fiscv74i7cxWvKzq4ApY9CpO/hRYdrVipiIg0VXV6jt3GjRuZNGkS0dHRlLUqk8lEWFgYixYtYtCgQRezqVJmz55NUFAQkydPbvDBUcGu4co05zNnxX4WbT4BQFhzN166oTt9I6p41Wu+GRwuuMvImX3QohOYTFaoVkREmpo6C3Z79+6lb9++ZGdnExgYyF133UWnTp0ICAggPj6e/fv388EHHxAbG4urqytbtmyhS5cuNd1cKUW3GvP39+fRRx/ln//8Z62tu7Yp2DV86w8nMuOr3cSm5mAywR2DInhsbAdcHKsxZl30Rvh4HHS7Cf72MjhW8U4XIiIi5aizYHfttdeydOlSJk2axAcffICjo2OpZfLy8rjrrrv45JNPuOaaa/jmm29qurlSoqOjyczMZOPGjaxfv56PPvqo1tZd2xTsGoe0nDyeXbaPJdtPAtDa352Xb+jOJWHNqraCbR/Aj/8Ao9AyFMpNiyxDo4iIiNRQnQU7X19fCgoKOH36dIWHQnNycggMDMTOzo6kpKSabq5RU7BrXH49cIZ/fv0nCelm7Exw77A2PDy6Hc4OVei9O/YbfHk7ZCeBa3O48hXofI0OzYqISI3U2XAnubm5dOjQodLz21xcXOjQocNF3SEiLS2NVatWsXjxYlatWkV6enqN1yVSmZEdA1j1yFCu7hFMoQFv/3aUq9/cwJ5TqZU3bj0c7lkDQT0s4e7L2yyHZ8/ss3LVIiLS1F1UsOvUqRMnT56s0rIxMTFERkbWaDuzZ88mODiYyy67jEmTJnHZZZcRFBTEM888U6P1iVSFj5sTr024hHdu6YmvuxMHTqdzzVsbmPu/Q+QVFFbSOAzu+NkyJIqDCxxfBwn766ZwERFpsi4q2E2fPp24uDhee+21Cpd7/fXXOX36NNOnT6/2Np577jlmzpxJVlYWhmEUP7Kyspg5cyZz5sypYfUiVXN51yB+fmQol0UGkl9oMPd/h7n27Q0cOlNJr7GjC4z4F0zbagl4kePPz0s4CIUF1i1cRESanIse7uTFF1/kqaee4oorruD++++nU6dOtGjRgoSEBPbv38/bb7/N8uXLefbZZ/nHP/5R7fWHhIQQGxuLj48PEydOpGXLlpw6dYrFixeTkpJCcHBwlXsN65POsWv8DMPg+92x/GfpXlKz83Cyt+ORMe2ZOrQ19nbVOH8uOwXe6AWegXD58xA+2Go1i4hI41dnF0/Y21djGIjyCjCZyM/PL3e+u7s7OTk5bNq0ib59+xZP37x5MwMHDsTNzY2MjIyLrsPaFOxsx5m0HJ745k9+PRAPwCVhPrx8Q3da+3tUbQXRm2DxBMhJsfwceS2MeQZ8Qq1TsIiINGp1dvHEhYdGa/ooLKz4XKX+/fsD0L59+xLTO3a0jPI/eLB6O6RuBXi58MGU3rxwfTc8nB3YdSKFy19bxwfroygsrML/k1oNgAd3Qu87wWQHe7+FN/vAb89DXrb1d0BERGzWRQW7wsLCWnlU5I033qB58+ZMmzaNqKgo8vPzOX78OA8++CDBwcG8+eabF7MLIjViMpm4sXcoPz8ylMFt/TDnF/LMsn1MeG8zJ85mVb4Cd1/LMCj3rIVWgyA/G377L7zVF8y64ltERGqmVu4Va03VOdxb2WHd+qRDsbbLMAwWbTnBnB/3k5VbgJuTPf+6ohO39AvDVJWx6wzD0mu38imIGArXvmP9okVEpNGo03vFWpudnR0mk6nM+9D+lclkoqCgYV5pqGBn+06czeIfX+1ma5RlEO4h7fx4/rpuBPtU8bZiuVlQYAbXc3e5SIqCze/A8MfBrYr3rRUREZtjU8Fu+PDhVev1OGf16tVWrKbmFOyahsJCgwUbj/PCTwcw5xfi6ezAg6PaMrl/OK5O1bzYaPHNcHC5JeiNfBJ63Q52F3/BkoiINC4N9qrYhnyo1NoU7JqWowkZ/H3Jbn6PSQHAz8OZe4e1ZlL/Vrg4VvH3JmotrPgnxJ+7Y0VAFw2PIiLSBNVZsLOzq/61F5VdLGGrFOyanvyCQr7ZeYrXfz3MyWTL1a7+ns7cP7wNE/uGVS3gFeTD9g9h9XMaHkVEpImqs+FOKrrSNSMjg99//51p06bh5ubGvHnzqhzqpk6dSnR0dLXqWLRoEYsWLarprojUOgd7O27sE8qvfx/OnPFdaenjSkK6mVk/7GPYi6tZuOk45vxKzgm1d4B+U0sPj7L787rZCRERaVTq5By7jz/+mDvuuINly5Zx+eWXV7r8lClTWLJkCSNGjGDixIkMHDiQNm3alFgmLS2N7du3s3z5cr744gucnZ356KOPGDJkiLV246Kox05y8wv5ckcMb/56hLjUHACCvF24f0RbbuwdgrNDFXrw4v6ADa/B1W+C47mLMrKSLOfhVeNcVBERaTwa5MUTLVu2pE2bNqxdu7ZKy+/Zs4e5c+eyZMkSMjMzcXV1xdfXFycnJ1JSUkhOTqawsJCePXsydepUbr/9dhwdHa28FzWnYCdFzPkFLNkWw5urj3AmzQxASx9Xpo1oy/W9QnByqEZHemEBvDvMEvIGPQQdrtAFFiIiNqZBBrvevXtz6NAh0tLSqtUuJyeHjRs3sm3bNuLi4sjJyaF58+Z07NiRwYMH07p1aytVXLsU7OSvcvIK+HzrCd7+7Sjx6ZaAF9LMlQdHtmV8zxAc7asQ8E7thAWXQ76lB5DmbWDANOg+EZzcrFi9iIjUlQYX7DIzMwkMDMTe3p6UlBRrb65BUrCT8uTkFfDplhO889tREjMsAS+suRsPjGzL+Eta4lBZwEs/DVvnw7YPzl9g4eYLfe6GvneDu591d0BERKyqzi6eqIr9+/dz/fXXk5WVxaBBg6y9OZFGx8XRnjsHR7Buxgie/FsnfN2dOJGUxYyv/mD0K2v4esdJ8gsquPDIMxBG/Qce2QuXvwA+YZB1Ftb8H5zZU3c7IiIi9e6ieuwqOgxqGAYJCQlkZ2djGAYeHh6sW7eO7t2713RzjZp67KSqsnLz+WRTNO+uPUZSZi4Arf3ceWhUO8Z1D8berpKLJAryYf/3cHgVXPP2+Ysqdn8OPq0grL8utBARaUQa1Dh23t7ejB07llmzZtGhQ4eabqrRU7CT6so05/PxpuPMX3uMlKw8ANr4WwLeld2qEPAulJMGr0aCOQ1a9oaBD0KncbrQQkSkEaizYFfRWHMmkwl3d3d8fX1ruvoKxcfH89Zbb5GSkkKfPn0YP348bm4N92RxBTupqfScPD7eeJz31kWRmm0JeO1aePDw6HZc0SUIu6oEvIwEWP0s/L7Ycj9agGbh0H8aXHILOLlbbwdEROSiNLiLJ2qTYRiYTCaGDRtG+/bt6dy5Mzt27GDXrl18//33pca7aygU7ORipeXk8dGG47y/7hhpOZZb83UI8GT66HaMjQysYsCLh63vwbb3IDvZMs21GVz7LrQfa8XqRUSkphpEsEtLS2PFihXExsbSs2dPhg0bVivr9fPzo0uXLuzbt48333yTXr160aZNGzZv3swzzzzD8uXLa2U7tU3BTmpLanYeH66P4sP1UaSbLQGvtb87E/uEcV2vEJq7O1W+ktxM+P0z2PQWpETDQ7ssPXgABXlg33DHhBQRaWrqLNh98cUXPP/889x///3cddddxdMPHDjApZdeyqlTp4qnTZ48mY8++qimmyqWl5fH77//zvjx47n00kuLx7fr3r07f/75J2+88QZ9+/YlPDz8ordVmxTspLalZuXxwfpjfLjhOBnnAp6TvR2XRgYwsW8YA1r7Vt6LV1hgGQsvtM/5aV9Mgvxcy3l44YN1oYWISD2rs2A3fvx4li5dyv79+2nfvn3x9Msuu4yVK1fSpk0bunbtyi+//EJGRgY//PADV1xxRU03V8KECRO45pprmDBhAjk5OezatYvx48czZswYdu7cyZ49DWuYBwU7sZb0nDx+2B3H4q0n+PNUavH0Vr5u3NQnlOt7hdDC06WKKzsDr3QC49w9bIMvOXehxdWW+9aKiEidq7Ng16ZNG9LS0khISCieFhcXR0hICKGhoRw4cAAXFxfWrl3L8OHDufzyy2vtUGlCQgLXXnstBQUF9OrVi4MHD+Lq6sr3339fK+uvbQp2Uhf2nEpl8dYTLP09trgXz8HOxOhOAUzoG8qQdv6VX0179qjlEO3vn56/o4V3GPS7B7rdBB7+Vt4LERG5UJ0FOy8vL9q1a8eOHTuKp3322WdMmjSJxx9/nP/+97/F0yMiIjCZTBw7dqymmyvThg0b2LZtG15eXtx00024uzfMq/sU7KQuZeXms2x3HIu3nWDXiZTi6S19XLmpTyg39g4l0LuSXrzMRMvdLLbOh6xEy7Sr3oCet1qvcBERKaXOgp2LiwsdO3bk999/L5523333MX/+fH766SfGjBlTPL1///7s3r2b7Ozsam8nPj6e6OhoAgICCAsLq2m59UrBTurLgdNpfL41hm92niy+mtbOBCM7tmBi3zCGtfev+LZledmWwY3/+AJu/gJcvC3Td3wMJ7dZ7ksbNgCqMK6liIhUX50eio2Pj+fMmTPFY8hFREQQGxtLcnJyiXHlIiMjOXv2LKdPn67WNqZNm8b8+fMpLLTcUsnX15d7772Xf/3rX7i4VPG8oQZAwU7qW05eAT/+GcfnW2PYejypeHqglws39g7hxj6hhDSrxliQ7w6FuN2W595h0P0m6DYB/NrWcuUiIk1bnQW7e+65h/fff5/bbruNRx55hK+++orZs2czduxYVqxYUbxcdnY23t7edO/enW3btlV5/d988w3XX389V155Jb179yY7O5tNmzaxfv16IiMj+d///oe/f+M430fBThqSI/HpfL41hq93niT53F0tTCYY2s6fiX3DGNWpBY4V9eIZBkRvsPTk7f0OctPPz2vZy3K4ttdtVt0HEZGmos6C3YkTJ+jVqxdJSZb//RuGgaOjI+vWraNv377Fyy1ZsoQJEyYwffp0XnnllSqv/7rrrmPUqFHcf//9Jabv2rWLiRMnEhwczK+//lrT8uuUgp00ROb8An7ee4bFW06w6djZ4un+ns7c0CuECX3CCPOtpBcvLxsO/mgJeUd+sVxR2/FKmPDp+WU0Np6ISI3V6QDF0dHRvPTSSxw5coTQ0FCmTZtG9+7dSyxz//33s2nTJubOnVutgYr79evH5s2bMZUxjtaJEyfo1KkT33zzDWPHNvwR8xXspKGLSszki20xfLUjhsSM3OLpg9v6MaFvKJd2DsTJoZLz6DLi4c+vILArRAyxTDt7FN4fBZHXWg7VhvbV2HgiItXQIO48URvGjh3Lzz//XO78J598kujoaD755JM6rKpmFOykscjNL+SX/WdYvC2GdYcTKPoL4ePmyOhOAVzeJZBBbf1wcbSv2grXvQK/zDr/c7MI6D7BMnRK84ja3wERERtjM8GuZ8+e7Ny5s9z5x44d47LLLuPQoUNW2f7MmTOZNWtWmfMefvhh5s6dW+V1KdhJYxSTlMWS7TF8sS2G+HRz8XR3J3tGdGzB5V2CGN7BH3fnCgYvLiyA4+ssh2r3fQ95mefnhfaHa+cp4ImIVKA6GaJBDyW/f/9+OnXqxLXXXsvVV19Nv379Ssxv3bo1WVlZVq/j1Vdfxc/Pr8S0Tp06WX27IvUttLkbf7+0Aw+Pase248n8tCeOn/ee4XRaDsv+iGPZH3E4O9gxtL0/l0UGMrpTAN5ufzmXzs4eWg+3PP72MuxfBrsXQ9QaiN8HnoHnlz17FLxagmPjueJdRKQhadA9dgEBAeTl5ZGSkoLJZCIwMJCrr76aq6++mlGjRuHg4EDbtm05cuSIVbZf1GMXFRV10feeVY+d2IrCQoPdJ1P4ac9pVuw5zYmk8/+5crAzMaCNL5d1CeTSzoH4ezqXv6K0WDizD9qNtvxsGPBmH8v0NiOgw+XQbqzudCEiTZ7NHIodOnQoK1eu5PTp03zzzTcsXbqUjRs3UlhYiKenJyNHjuTHH38kJyfHKtu/MNj5+vri4uKCo2PNruxTsBNbZBgG++PS+WnvaX7ec5qDZ84Pe2IyQZ9WzRnbJZDLugTS0se14pWlxcJ7oyA99oKJJgjpbQl5HceBf/tym4uI2CqbCXbPPvssN998M61bty6elpSUxA8//MDSpUtZuXIl2dnZFBQUWGX7RcHOy8uLtLQ07OzsuOSSS3jssce46aabqrUuBTtpCo4lZBSHvN0nU0vM6xbizdjIQC7vEkhrf4+yV2AYlkGPD/1kGUKlaABkgF63w7i5lueFhVCYDw5O1tkREZEGxGaCXXJyMvPmzeOJJ54oc35qaiqjRo1i+/btVtn+3Llz2bt3L4MGDcLX15ejR4/y5ptvcvToUZ555hmefPLJctuazWbM5vMnm6elpREaGqpgJ03GqZRsft5zmp/2nmbb8SQu/EvTPsCDy7oEcVlkIJ2CPMsc0giA1FOWkHfoJ+h3L7QdZZl+YjN8eoPl5w5XQNvR4Nbc+jslIlIPbCbYAezbt4/OnTuXO//s2bP4+vrWWT3Z2dn06dOHgwcPcuTIEVq1alXmcuVdUatgJ01RQrqZVfvOsGJPHJuOniW/8PyfnVa+blwWGcjYLoH0CPHBzq4KY9yt/i+sef78zyZ7y/1qO1wG7S/Xbc1ExKbYVLCztoKCAhISEkpMc3V1xdvbu9w2H3/8Mbfddhvz58/n7rvvLnMZ9diJlC01K49fDpxhxZ7TrD2UgDm/sHhegJczQ9v5M7idH4Pa+uHnUc7FF4WFcGqH5XDtoZ8sV9de6O7V0LKnFfdCRKTu2MxwJ3UhJiaGiIiSY2hNmTKFjz76qNw2RVfI/jUQXsjZ2Rln5wquCBRporzdHBnfM4TxPUPINOez5lACK/ac5tf9ZziTZubLHSf5csdJADoFeTG4rS+D2/nTN7w5rk7nBkW2s4PQPpbH6Kch+Tgc/AkOrYCEQxB0wd1vVj0N6XGWCzDajAIX/cdKRGxXkw92gYGBrFq1qsS04ODgCtscPny4uK2I1Jy7swNXdA3iiq5B5OQVsDUqifVHEll3OJH9cWnFj/fWReFkb0evVs0Y3M6PIe38iAz2xr7osG2zcOh/r+WRn2sZOw8sPXu7P4eM0/DHF2DnCOGDLefmRQyFgK6WkCgiYiMa7KHYtWvX0q9fvxK9XmvXrqVv3764uLhUuFxtyM/PJzU1tdT5eykpKfTq1YuTJ09y7NgxWrZsWaX16apYkepJzDCz4UgiG44ksv5wIrGpJYc18nFzZGAbXwa39WdwWz/CfN1Kr6SwEE5ssvTkHVwBZ/8y5mXYQLhjxfmfDUP3sRWRBscmzrGzt7fn8OHDJYY6sbe3Z//+/bRvbxnLqqCgACcnp1LL1YaUlBSCgoIYP348Xbt2xdfXl2PHjvHhhx8SHx/P3Llzefjhh6u8PgU7kZozDINjiZlsONebt/noWdLN+SWWCWvuxqC2lt68gW188XErYyiUxMNw6GeIWgvRG+GSSXD5/1nm5eXAG70sh3fDh0DEMPBto6AnIvXOJoKdnZ0dR44cKRHY7OzsOHDgQIlg5+joWGq52mA2m5k2bRpbt24lJiaGjIwMmjVrRr9+/Zg+fTqjRo2q1voU7ERqT35BIbtPprL+cCLrjySw60RKiSttTSbo2tKbwW39GNzOj16tmuHsYF9yJQX5lvvWupy7UCpqLXw8ruQynkGWQ7bhQyyHb70qPk1DRMQaFOwaIAU7EevJMOez5dhZ1h22HLo9HJ9RYr6Lox19I3wtF2K09adjoGfpYVXyc+HUdohaZwl5J7dCQe75+Zc+BwMfsDzPSYPcDAU9EakTuipWRJoUD2cHRnUKYFSnAABOp+ZYzs0790hIN7P2UAJrDyUAB/B2daRnmA+9WjWjV6vmdA/1xs3JCVoNtDyG/xPysiFmy/mg13rY+Q0eWAbf3Qe+bc8dtj3Xq6f72opIPVOwExGbE+jtwnW9QriuVwiGYXDoTAbrDiew4UgiW6KSSM3OY/XBBFYftAxZZG9nonOQ17mg14ze4c0I8naF1sMtj79KPg4mO8vFGGePwI4FluktOlsC3uDp6s0TkXrRYA/FNm/enFWrVtGrV6/iaX89FHv27FlatGhBQkICzZs37NsJ6VCsSMOQV1DI/rg0dkQnsz06mR3HkzmdllNquWBvF3q2akbvc716nYI8cbC/YGiU7BTLBRjHz/Xondlzft5jR8Hdz/J831LITISQPpbgZ6//T4tI9djEodguXbqwbt26EsHur3777TcCAgIafKgTkYbD0d6ObiE+dAvx4fZBlsHJT6VksyM6mZ3RyWyPTmJ/XDqxqTnE/hHHsj/iAHB1tKdH6LnDt+HN6BnaDO+OV0DHKywrzkyE4+sh8dD5UAew7X1L8ANwdLfcESOktyXohfQBjxZ1ufsiYuMabI/dxx9/zFNPPcXu3btp1qwZULLHLjs7m/79+3PllVfy3HPP1XO1lVOPnUjjkWnOZ3dMCjuik9lxwhL40nLySy3XroUHvcOb0TOsGb3DmxPu64bpr8OjrH8Vjq2x3ALNnFZynosP/PP4+SFVko6BVwg4lDFUi4g0WTZxVaxhGFx66aUkJSXx+eef065dO+zs7Dh48CDOzs7ceuutnDlzhh07duDmVsbApA2Mgp1I41VYaHAkIcNy+PZ4MjtPJBOVmFlquebuTudCXjMuCfWhc7AXni6O51ZSYOnNO7nt3GM7eIfALV+eX8GrXSHjDAT3ONej1xtC+oJ31QZCFxHbZBPBDiAjI4OpU6fy1VdfMXToUH799Vf69evHjh07GDRoEJ9++mmlt/9qKBTsRGxLYoaZndHJll696GT+OJVKbn5hqeVa+7kT2dKbri296BLsTWRLb7xdLwh7Rbc/y0mF13pAdlLpjXkGQ7cbYcws6+2QiDRYNhPsiuzdu5elS5dy8uRJWrRowZgxYxg0aFB9l1UtCnYits2cX8CeU2nF5+n9eTK11G3QioQ1d6NrS28iW3rRtaU3XYK9aebuZLmlWdIxS49ezFbLv2f2glEAfe6Cv71sWUFeDnx8JQT1gKDuENQN/DvpEK6IjbK5YGcLFOxEmp7EDDN7Y9PYcyqVPadS+fNUKieTs8tctqWPK13OBT1LD583fh7OkJsJsb+DazMI6GxZ+MQW+PDSkiuwc4QWHSGwO3S9DtqMtO7OiUidUbBrgBTsRAQgJSuXPafS2BNrCXp7T6Vy/GxWmcsGernQpaV3ceDr0tKbAC8XyEqCo7/CqZ1w+g/LIyf1fMOx/4UB0yzPzx6FX5+19OoFdrP08F141a6INHgKdg2Qgp2IlCc1O499RT175wJfVGImZf119vd0pkvw+Z69joGehPq4Ypd2AuLOhbzO10BgF0uD3V/At1NLrsQz+HzQ63o9+Hew+j6KSM0p2DVACnYiUh0Z5vzzYe/cYdyjCRkUlvEX29XRnnYBHnQI8KRDoCftz/3bwtMZU+IhOLDcEvji/oCkoyUbT/wcOlxueX5iC+z/3tKrF9gN/Nqdv7hDROqNTQxQLCLSlHk4O9A3ojl9I84PwJ6Vm8/+uPTisLc3No0jCRlk5xXwx8lU/jiZWmIdPm6OlpAXcCntQ6+jYx9P2nuDd9rB80Ev+JLzDY7+CpvePP+zgysERFrO7fPvZOnd04DKIg1ag++xa926dZWXNZlMHD16tPIF64F67ETEGvILColOyuLQ6XQOnknn4Ll/jydmltm7B5Zz9zoEXtC7F+BJuwAPXE6sPd+7d3oP5P1lrL4Htlt68QD++BKiN0CLTpaHfyfw8Lfuzoo0UTZ1KNbOzg6TyYRhGKX+/SuTyURBQUE9VFk5BTsRqUs5eQUcTcgoDnqHTqdz6EwGp1LKvirXZIJwX3faFx3SDXCni0siIeYj2CcegISDcP2C8/e6/WYq/PFFyZW4+Vruh+vfEUb+23Ilr4hcNJsKduHh4SQnJ5Oeno6TkxPNmzcnKSmJ3NxcPD09S90nNioqqp4qrZiCnYg0BGk5eRw+k87B0xkcuqCHLykzt8zlneztCPdzo7WfB6393Wntb/m3Q9oW3E9vgYQDEL8fko8D575OTHbwrzhwdLH8vOo/liFbLuzda9ERXLzrYpdFGj2bCnbbtm1j9OjR3HfffcycORMXFxfMZjNPPfUU7777Lv/73//o06dPfZdZKQU7EWmoDMMgMSP3fNAr6uU7k05WbvlHQfw8nIoDX/vm9nRxOk2EEUPzwiTshz56fsH3R1sGW/4rz2DL+XsTvzjfE5ibCY5u5++fKyK2FewGDhzIli1bSE1NxcPDo3h6eno63t7eDBw4kPXr19djhVWjYCcijU1hocGplGyOJmRwLCGTY4mWf48mZHAmzVxuO0d7E2HN3Wjj70Frfw96OkXTvjCKQPNxXJIPWXr40mMtC3uHwSN/nm+84ArL+X2+bSzn8/m2veDRBpzcrbzXIg2PTV0Vu2vXLgA2bNjA2LFji6dv2LABgJ07d9ZLXSIits7OzkRoczdCm7sx/C9D3WWY84k6F/aOngt7xxIyiUrMICev8Ny0TODMuRahQCjN3UfR2s+dziGFXOIaTyu3PLwTMght5oaTg53llmrmVIjdaXlcyDMY/r7//M/7llp693zbgk+YhmYRoRH02LVu3Zro6GgcHBwYM2YMISEhnDx5klWrVpGfn094eHiDvRL2QuqxE5GmoLDQIC4th6PxGRxLyOBYYmZxL19cOffOBbAzQbCPK22bO9DdPZnOTmcIN2JpkXcSr8zj2CcdtQy9ctuy841e7nS+58/eCZq3Pt+7F9wDIq+17s6K1BGbOhT7zjvvMG3aNEx/Od+iqOx58+YxderUspo2KAp2ItLUZeXmnzukm8mxBEtP37GEDKISMys8lw8s5/O1bWZPkF9zwpq70aq5MyP+mIFnZjT2yccwFfzl0HCrQXD7j+d//vwWcPKA5hHQLAKahVueu/vrfD5p8GzqUOx9992Hu7s7Tz/9NNHR0cXTIyIieOaZZ7j55pvrsToREakqNyeHc/e+LXk1rGEYJKSbiU7KIvpsFtFnMy3/JmVx4mwmyVl5JGbkkpgBxJy6oOWtAHg6mejpnUlPj0Q6OcbTilgc/drimJRFkLcLDoVmy/h8lNGP4egOna+Ga985Py1qLXi1BO9QcHCq9ddBxJoafI/dhU6ePElsbCwtW7akZcuW9V1OtajHTkSkZtJy8jhx9lzoS8osfn4iKYvY1Owy76lbxMHORGsfe8a5/UFHx3hCiMc/Lxav7FM4ZsZiwoDuN58PdvlmeDYAMCzDtniFQLNW53r6wiGkD0QMrYvdFilmU4dibYWCnYhI7TPnFxCTlM2JpHO9fOcCX/TZTGKSs8nNLyy3rRN5tHE8i5+XGybfNoQ0c6W9Wwbj9z6IR2YMdgVlnBPYfSJcO8/yPD8XFlwGPq0soa/o8K53KHiHgL2jVfZZmh4FuwZIwU5EpG4VFhqcTss5F/YyOZGUxankbE4mZ3MqJZvTaTkV9PYZ+JNKG4cEursn0cHpLOH28SS36E9ap5sIaeZGK9NpWiwYUE57E/S7By5/3vJjfi78/qnl6l2fMEvwc3S1wl6LLbKpc+xERERqws7ORLCPK8E+rgxo41tqfm5+IXGp2cVh72RyFidTzgW/5GziUk0k5PuwOfWCRqeBP3YD4E42Q+z/The3JNo5JtLKLp6A/Di8ck9jX5hLUoELLrn5uDk5QNpJWDa9ZAHu/udCXih0vgq6XGeZXlgIuRngok4AqT4FOxERaZKcHOxo5etOK9+yBz3OKyjkdGpOcQ/fyeSs4tB3MiWLuBQTPxX04qf0ku1MFOJHGgXr7Uha/zPero709jjLg679CDQSaJ53GqeCLMhMsDxO7QC/9udXkHIcXr8EXHzAJ9QyiLNP2LnnoRDUzXLYV6QMOhRbR3QoVkTEthQUGpxJKwp+WZxMsvT2xaXlEJeSTVxqDhnm/DJaGniTSYgpkRBTAi1NiRxx6kiiT3eCfVwYYH+AO488UP6Ghz4GI5+0PE+OhqXTwCv43KPluSt6z/3r5qvhXGyAzrFrgBTsRESanrScPE6n5hB7LujFpZ4PfbGp2cSl5JCdV3oMP3eyCTadLQ5+IaZEWjueJcz+LOuaX09MyysI8HKhS+5uhm26o/wChj0OI56wPE8/DVvmKfw1QjrHTkREpAHwcnHEy8WR9gGeZc43DIO07HxLyEs9F/5SikJfCMfTctiYko05vxCKOv8ygBOWcV39MDPQbhpBpiQCTUmE2CcRap9MIGfxKUxm+XGIXXuMFl7OtM/aRaf1r5Yuwt7Z0ts35O/Qc7JlWnYyRG8EzyDLw90f7BUZGgO9SyIiIvXEZDLh7eaIt5sjnYLK7okxDIPkrDxL8EvJIS41mzNpZk6n5XAmzY+DaSGsTc8hJSvvfPgDHMnH7mAh5oOW++u2M53iZvuxBJvO0tI+mWDTWZobKVBghuQoNh5JIM0pjhZeLoSmbsf/6wtuAGCyA/cW4BloCXq9b4f25+7fbk6HpCjLdDdfsLOz0qslVaFgJyIi0oCZTCaauzvR3N2JyGDvcpfLySsgPs3MmfQcTqfmcCYth/h0M2fSLD/Hp7vzQmory6HfPEsbR/IJMCURRBLRO1sQv3MnAAPs9vJPh9YE2aXgRwr2RiFknLY84n5nl9sAsux60cLTmaCkrXh8Md6yQjvHc+Ev8HwIjBwPrc4NC5Nvhrwsy4UhOvxrFQp2IiIiNsDF0Z4wXzfCfN3KXcYwDNLN+cSn5XAm7VzoS8shPs2MX5olDJ5JM7M9vQvX5D4LgB2F+JJGC1MyAecem7e4E7V5CwAj7XbygqMXfqY0KMyD1BjL45w/C8LIpSMtPJ0JSNyM02fXgoOLJfh5BIJnAHgEWHoE24+1XPULUJAPGBrouZoU7ERERJoIk8lUfN5f2xZln/cHlsGdU7LzSEg3k5BuJj49p/h5QoaZoHQzDuee/5rVk97meTiQjz+pBJiSaWFKpoUphQBTMss3OnBgw0YArrLbyOtOQH4OJB+3PC6wJ90Vc9dQ/D2c8U/YgOvn14Nrc0vw82hR8t+2oyGg87mCCwCTDgOjYCciIiJ/YWd3/vBvh8DyAyBYbuuWmJF7PvgVB8Ac/kwz45phJiTdTHy6me/zB/JzTm/8TSkEkEygKRk/Uyp+plT8SeGzDYX8sd4SAq+1W8erTkB2kuWRsL/EdnclmsiKbIGvhxOBCRvx/vYWTO4twMP/L0EwAFqPAP9zYwXaeAhUsBMREZEac3awp6WPKy19Kr5FWtFh4PO9gJZ/z2aYOZmRy+5MM6aMXEIyzCRmmPkubxC/5XTH35SKvykFf879e+7njzYXsnuT5XDweLu1vOKUD+mxlsdfbOr6DKkdvPD1cKJl4gaClk8Bdz9M7v7g7me56rfoefvLICDS0jA/Fwrzwan8w9sNjYKdiIiIWN2Fh4Hb+HtUunxWbj6J6bkkZpo5m5FLYoYlBMZm5PJHhhm3jFzan5v3Q9ZANuR0KRH8zgfBFN7fXsiubTsAGG+3nlecCiDjjOXxFz9FQ1yEG83dnWibsonI3+6k0NENk7v/uSB4QRjsfBUEX1Lrr9XFULATERGRBsfNyYEwX4cKLwYpkl9QSHJWHmczzSSm51r+zcglPsPMvgwzvpm59MzMJSkzl9WZQ+mb0xU/Uyq+pjR8ScPXlIqfKQ0/Ulm414k/9+wDYLzdNl5xAru8LEiJtjwusDjKheMtXWh27rD11T2CcXawt8rrUVUKdiIiItKoOdjb4e/pjL+nMwRWvnxufiEpWbmcPRf2ih4xmbn0yMwlLNMSDvdkXM7QzMHYZyfSzEixBMFzYdDPlMqXxzzYd/RY8Xqv7hFsxb2sGgU7ERERaVKcHOxo4eVCCy+XKi1fWGiQlpNXHADPZuaSnJnL3zJzGXDueWZufr331oGCnYiIiEiF7OxM+Lg54ePmRGv/+q6mYrZ5rW8tW7VqFVdccQW+vr64uLgQERHBzTffTG5ubn2XJiIiIlJMPXaVmDNnDv/6178YMWIETz75JF5eXpw5c4a1a9eSn5+Pk5NTfZcoIiIiAoDJMAyjvotoqH799VdGjx7NE088wXPPPXdR60pLS8Pb25vU1FS8vMq+0bOIiIjIX1UnQyjYVWDUqFH8+eefnDp1CkdHRzIyMnB1dcXevvonRyrYiYiISE1UJ0PoHLtyZGZmsmbNGvr168cnn3xCq1at8PT0xN3dnauvvppjx45VvhIRERGROqRz7Mpx5MgRCgoK2LJlCytXruQf//gHvXv3ZteuXTz//PNs3bqV3bt306JFizLbm81mzGZz8c9paWl1VbqIiIg0UeqxK0d6ejoACQkJvPHGGzz33HNce+21zJ49m7fffpvTp0/z6quvltt+zpw5eHt7Fz9CQ0PrqnQRERFpopr8OXYFBQUkJCSUmObq6sqRI0fo3bs3dnZ2ZGVl4ezsXDw/Ly8PV1dXevfuzebNm8tcb1k9dqGhoTrHTkRERKqlOufYNflDsTExMURERJSYNmXKFJ5//nkAmjVrViLUATg6OuLn50dSUlK563V2di7VTkRERMSamnywCwwMZNWqVSWmBQcHExAQQHh4ONHR0WRmZuLu7l48Pycnh4SEBNq1a1fX5YqIiIiUq8kHOxcXF0aPHl3mvFtvvZXZs2fz1ltvMWPGjOLpb731FoWFhfztb3+rqzJFREREKtXkz7GrSHp6OgMGDGDfvn3ccccd9O7dm507d/LBBx8QGRnJpk2bSvTkVUTj2ImIiEhNaIDiWpSUlMTTTz/Nt99+S3x8PIGBgYwfP56ZM2fi4+NT5fUo2ImIiEhNKNg1QAp2IiIiUhO684SIiIhIE6RgJyIiImIjFOxEREREbISCnYiIiIiNULATERERsREKdiIiIiI2QsFORERExEYo2ImIiIjYCAU7ERERERuhYCciIiJiIxTsRERERGyEgp2IiIiIjVCwExEREbERCnYiIiIiNkLBTkRERMRGKNiJiIiI2AgFOxEREREboWAnIiIiYiMU7ERERERshIKdiIiIiI1QsBMRERGxEQp2IiIiIjZCwU5ERETERijYiYiIiNgIBTsRERERG6FgJyIiImIjFOxEREREbISCnYiIiIiNULATERERsREKdiIiIiI2QsFORERExEYo2ImIiIjYCAU7ERERERuhYCciIiJiIxTsRERERGyEgp2IiIiIjVCwExEREbERCnYiIiIiNkLBTkRERMRGKNiJiIiI2AgFOxEREREboWAnIiIiYiMU7CpgMpkqfDz33HP1XaKIiIhIMYf6LqAh++STT8qcPnPmTI4ePcq4cePquCIRERGR8inYVWDSpEmlpp08eZKoqCh69+5Nt27d6qEqERERkbLpUGw1LViwgMLCQu666676LkVERESkBAW7ajAMgwULFuDm5sbEiRPruxwRERGREnQothp+/fVXoqKiuO222/Dy8qpwWbPZjNlsLv45NTUVgLS0NKvWKCIiIralKDsYhlHpsgp21fD+++8DcOedd1a67Jw5c5g1a1ap6aGhobVel4iIiNi+9PR0vL29K1zGZFQl/tmwgoICEhISSkxzdXUt9cIlJycTFBREREQE+/fvr3S9f+2xKywsJCkpCV9fX0wmU+0U3wikpaURGhpKTExMpb2ctqgp77/2XfuufW9amvL+W3vfDcMgPT2d4OBg7OwqPouuyffYxcTEEBERUWLalClT+Oijj0pMW7RoEWazuUq9dQDOzs44OzuXmObj43MxpTZqXl5eTe4X/UJNef+179r3pqYp7zs07f235r5X1lNXpMkHu8DAQFatWlViWnBwcKnlPvjgAxwdHbn11lvrqjQRERGRamnywc7FxYXRo0dXuMz27dvZvXs348ePp0WLFnVUmYiIiEj1aLiTKvjggw8ANHZdDTg7O/P000+XOizdVDTl/de+a9+bmqa879C0978h7XuTv3iiMtnZ2QQFBeHp6Ul0dHSlJy2KiIiI1BcFOxEREREboe4nERERERuhYCciIiJiIxTspMYOHTrEf/7zH/r374+/vz+enp706NGD5557jszMzBLLzpw5E5PJVOZj+vTp9bMDF6m8/TGZTKSkpJRY9syZM9xxxx0EBATg4uJCt27deO+99+qn8FpQ0ftpMplwdHSs0rIN/b2fM2cON9xwA61bt8ZkMhEeHl7h8tV9nxcvXkyvXr1wdXXFz8+PiRMnEh0dXct7UTNV3XfDMFi0aBETJkygbdu2uLm5ERYWxlVXXcWWLVvKbFOd3536UJ33vSafb1t436Hi99FkMvHcc89VefmG8L5X5zsNGu7ve5Mf7kRq7sMPP+TNN99k3Lhx3HzzzTg5ObF69WqefPJJlixZwubNm3F1dS3R5tVXX8XPz6/EtE6dOtVl2bVqyJAhTJ06tdR0d3f34ucpKSkMHjyYU6dOMX36dCIiIli6dClTp04lNjaWp59+ui5LrhXjx4+nbdu2pab/8ccfvPjii4wbN67UvMb43v/rX/+iefPm9OzZs9Ivnuq+z2+++SYPPvgggwYN4tVXXyUxMZG5c+eydu1atm3bVuZ4mnWpqvtuNpuZPHky3bp146abbqJ169bExcUxb948BgwYwMKFC5k0aVKpdlX53akv1Xnfi1T1820r7zvAJ598Uub0mTNncvTo0TL/DjTk970632kN+vfdEKmhbdu2GcnJyaWm//vf/zYA48033yye9vTTTxuAERUVVXcFWhlgTJkypdLlHn/8cQMwvv766xLTx40bZzg6OhrHjh2zUoV1b+rUqQZgLFu2rHhaY37vjx49Wvw8MjLSaNWqVbnLVud9TkxMNDw8PIyePXsaeXl5xdO3bdtmmEwm484776y9naihqu57Xl6e8euvv5aaHhcXZ/j6+hoBAQFGQUFBiXlV/d2pL9V536vz+bal9708MTExhp2dndG7d+9S8xr6+16d77SG/PuuQ7FSY7179y7zNmk33ngjAH/++WeZ7dLT08nLy7NmaXUqNzeX9PT0cud/+umnREREMH78+BLTH330UfLy8vjiiy+sXWKdyMrK4vPPP6dly5ZcdtllZS7T2N771q1bV3nZ6rzPS5cuJSMjg4ceeggHh/MHTnr37s3QoUNZsmQJubm5F78DF6Gq++7g4MCIESNKTQ8MDGTo0KGcOXOG+Pj4MttW9rtTX6rzvl+oss+3Lb3v5VmwYAGFhYUVjvvaUN/36nynNeTfdwU7qXWnTp0CKPMuHd27d8fLywsXFxd69+7d6EPNV199hZubG15eXvj6+nLXXXdx+vTp4vmnT58mJiaGAQMGlGo7YMAATCYTW7durcuSrWbJkiWkpaVx++23Y29vX2q+rb33F6ru+1z0fODAgaWWHzhwIOnp6Rw4cMB6BdeRU6dO4eTkVOaXZWW/O41NVT7ftv6+G4bBggULcHNzY+LEiWUu0xjf979+pzX033edYye1qqCggNmzZ+Pg4MAtt9xSPN3Hx4e77rqLQYMG4evry9GjR3nzzTeZMGEChw8f5sknn6zHqmumT58+XH/99bRr146srCxWr17NggULWLlyJVu2bCEoKKj4D0JISEip9s7Ozvj5+XHy5Mm6Lt0qPvjgA0wmE3fccUeJ6bb43v9Vdd/nipYvmnby5Em6detmjXLrxPLly9m6dSuTJk3CxcWlxLyq/O40FtX5fNv6+/7rr78SFRXFbbfdhpeXV6n5jfF9L+s7rcH/vtfqgV1p8u6//34DMJ599tlKl83KyjIiIyMNBwcH4/jx43VQnfUtXLjQAIy7777bMAzDWLt2rQEYTz31VJnLh4aGGpGRkXVZolUcOHDAAIxRo0ZVafnG+N5XdL5Rdd/nkSNHGkCpc88MwzA++OADAzC+/PLLWqm7NlT3XKsDBw4YzZo1M4KDg40zZ85Uqc1ff3caipqcZ1be59vW3/cJEyYYgLFu3boqt2mo73uRsr7TGvrvuw7FSq158sknefvtt7nrrrv417/+Venyrq6uPPbYY+Tn57Ny5co6qND6Jk+eTHh4OMuXLwfAzc0NsFw5WJbs7OziZRqz6t5P2dbe++q+zxUtn52dXWKZxiYqKooxY8YAsGLFijJPySjLX393GrPyPt+2/L4nJyfz7bff0rFjRwYPHlzldg35fS/vO62h/74r2EmtmDlzJs899xy33nor7777LiaTqUrtisZISkhIsGJ1dSs8PLx4f1q2bAlQ5uHWnJwczp49W2b3fGOSn5/PwoULad68Oddee22V29nSe1/d97mi5Ss6bNPQHT9+nBEjRpCens7KlSurfWjpwt+dxq6sz7etvu8AixYtwmw2c+edd1a7bUN83yv6Tmvov+8KdnLRZs2axaxZs5g0aRILFizAzq7qH6vDhw8DlivobIFhGBw5cqR4fwIDAwkJCWHTpk2llt28eTOGYdCnT5+6LrNW/fDDD5w5c4bJkyfj7Oxc5Xa29N5X930uer5x48ZSy2/cuBEPDw86duxovYKtIDo6mhEjRpCSksLKlSvp3bt3tdr/9XensSvr822L73uRDz74AEdHR2699dZqtWuI73tl32kN/ve91g7qSpM0a9YsAzBuueUWIz8/v8xl8vLyjMTExFLTk5OTjdatWxtOTk7GyZMnrV1qrTp9+nSZ01977TUDMKZNm1Y8bcaMGeWOd+Tg4FBi3KjG6G9/+5sBGH/88Uepebb03ld2vlF13ueEhATDzc2t3HGt7rjjjlqv/2JUtu/Hjx83wsPDDW9vb2PLli0Vrqs6vzsNQWVj+FXn821r73uRbdu2GYAxfvz4cpdpLO97Vb7TDKNh/76bDMMwai8mSlPy1ltv8cADDxAWFsbs2bNLDXEREBDAmDFjSElJISgoiPHjx9O1a1d8fX05duwYH374IfHx8cydO5eHH364nvaiZqZPn87//vc/rrzySlq1akV2dja//fYbP/zwA+3atWPjxo3Fo9AnJyfTu3dvTp8+XWKE8mXLlvHUU08xe/bset6bmouNjSUsLIxevXqVefuoxv7ef/LJJ8W3/HnjjTfIzc3l73//O2C5GvKBBx4oXra67/Nrr73G9OnTGTRoEJMnTyYxMZFXX30VR0dHtm/fXnz4pr5Udd/T09Pp3r07UVFRPPjgg/Tt27fUusaMGUNAQABQvd+d+lLVfa/J59tW3vcL3XfffcybN48ff/yRyy+/vMz1Nob3varfadDAf99rNSZKkzJlyhQDKPcxbNgwwzAMIycnx7jzzjuNrl27Gj4+PoaDg4Ph7+9vXHnllcb//ve/+t2JGlq6dKkxduxYo2XLloazs7Ph4uJiREZGGv/+97+NlJSUUsvHxsYat912m+Hv7284OzsbkZGRxjvvvFMPldeu5557zgCM+fPnlzm/sb/3w4YNK/fzXVZPRnXf50WLFhmXXHKJ4eLiYjRv3ty46aabGsydSKq671FRURX+HQCM1atXFy9f3d+d+lDVfa/p59sW3vciWVlZhre3txESElLmVZ9FGsP7XtXvtCIN9fddPXYiIiIiNkIXT4iIiIjYCAU7ERERERuhYCciIiJiIxTsRERERGyEgp2IiIiIjVCwExEREbERCnYiIiIiNkLBTkRERMRGKNiJiIiI2AgFOxEREREboWAnIiIiYiMU7ERERERshIKdiIiIiI1QsBMRERGxEQp2IiL1wGQyYTKZAFixYgVDhw7F09MTb29vLr/8cnbt2lXPFYpIY2QyDMOo7yJERJqaolD3zjvvcP/99xMYGEhQUBAHDx4kMzMTDw8Ptm3bRseOHeu5UhFpTNRjJyJSj/7+97/z4YcfEhsby44dO4iLi2PUqFFkZGQwc+bM+i5PRBoZ9diJiNSDoh67Bx98kNdff73EvD///JNu3brh7e1NSkpKPVQnIo2Vgp2ISD0oCna7d++mW7dupea7urqSk5NDYmIivr6+dV2eiDRSOhQrIlKP2rRpU+Z0f39/ADIyMuqyHBFp5BTsRETqkbu7e5nT7ewsf551UEVEqkPBTkRERMRGKNiJiIiI2AgFOxEREREboWAnIiIiYiMU7ERERERshIKdiIiIiI3QAMUiIiIiNkI9diIiIiI2QsFORERExEYo2ImIiIjYCAU7ERERERuhYCciIiJiIxTsRERERGyEgp2IiIiIjVCwExER+f9260AGAAAAYJC/9T2+oggmxA4AYELsAAAmxA4AYELsAAAmxA4AYELsAAAmAmneiR7nt1/yAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsize = np.arange(10,210,10)\n",
    "L = len(nsize)\n",
    "wcrisk_rob = np.zeros(L)\n",
    "wcrisk_nom = np.zeros(L)\n",
    "for i in range(L):\n",
    "    r = phi_dot/(2*nsize[i])*scipy.stats.chi2.ppf(0.95, m-1)\n",
    "    wcrisk_rob[i] = RC_newsvendor_riskmin(sets,p,d,r,par,par_news,phi_conj, h_conj)[1]\n",
    "    res_nom = nominal_solve(sets,p,d,par,par_news, h_eva)[0]\n",
    "    wcrisk_nom[i] = robustcheck_newsvendor(res_nom,d,r,p,par,par_news,h_func, phi_func)[0]\n",
    "plt.plot(nsize, wcrisk_rob, label = 'robust solution')\n",
    "plt.plot(nsize, wcrisk_nom,'--', label = 'nominal solution')\n",
    "plt.xlabel('n', fontsize = 16)\n",
    "plt.ylabel(r'$\\sup_{\\mathbf{q}\\in \\mathcal{D}_{\\phi}(\\mathbf{p},r(n))}\\mathrm{CVaR}_{0.9}(.)$', fontsize = 16)\n",
    "plt.xticks(fontsize=13)  # Set font size for x-axis tick labels\n",
    "y_min, y_max = plt.gca().get_ylim()\n",
    "y_ticks = np.arange(np.floor(y_min), np.ceil(y_max) + 1, 1)  # Ensure only integer ticks\n",
    "plt.gca().set_yticks(y_ticks)\n",
    "plt.gca().set_yticklabels([int(tick) for tick in y_ticks], fontsize=13)\n",
    "\n",
    "\n",
    "plt.legend(fontsize=16)\n",
    "plt.tight_layout()\n",
    "plt.savefig('s_news01.eps', format='eps')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbea29bb",
   "metadata": {},
   "source": [
    "In the second experiment, we compare the robust solution and the nominal solution by computing its risk evaluation with respect to a sample of probability vectors. We use the Hit-and-Run algorithm to sample 5000 probability vectors $\\mathbf{q}$ in the $\\phi$-divergence uncertainty set $\\mathcal{D}_{\\phi}(\\mathbf{p},r)$ for $n=50$. For each sampled vector $\\mathbf{q}$, we calculate the risk evaluation $\\rho_{h_{cv},\\mathbf{q}}$ for $\\alpha_0=0.4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a8bfb160",
   "metadata": {},
   "outputs": [],
   "source": [
    "import Hit_and_Run as hr \n",
    "\n",
    "#### This function calculates the risk with respect to any probability vector\n",
    "\n",
    "def nominal_risk(y,d,p,par,par_news, h_eva):   \n",
    "    N = len(p)\n",
    "    [v_news, l_news, s_news, c_news] = par_news\n",
    "    x = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        x[i] = v_news*np.minimum(d[i],y)+s_news*np.maximum(y-d[i],0)-l_news*np.maximum(d[i]-y,0)-c_news*y\n",
    "    rank = np.argsort(x)\n",
    "    q_b = np.zeros(N)\n",
    "    q_b[rank[0]] = h_eva(p[rank[0]],par)\n",
    "    risk = -q_b[rank[0]]*x[rank[0]]\n",
    "    for i in range(1,N):\n",
    "        q_b[rank[i]] = h_eva(np.sum(p[rank[0:i+1]]),par)-h_eva(np.sum(p[rank[0:i]]),par)\n",
    "        risk = risk - q_b[rank[i]]*x[rank[i]]\n",
    "    return(risk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "0c9b9dc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(10)\n",
    "n = 50\n",
    "r = phi_dot/(2*n)*scipy.stats.chi2.ppf(0.95, m-1)\n",
    "### simulating the probability vectors in the phi-divergence uncertainty set\n",
    "prob = hr.hit_and_run(p,phi.kb_eva,r,1,5000)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee796ac1",
   "metadata": {},
   "source": [
    "The following code compute the robust solution and the nominal solution and calculate the risk of both solutions with respect to a sample of probability vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "8bb26d0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\gjin\\AppData\\Local\\Temp\\ipykernel_19988\\3558743789.py:10: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  x[i] = v_news*np.minimum(d[i],y)+s_news*np.maximum(y-d[i],0)-l_news*np.maximum(d[i]-y,0)-c_news*y\n"
     ]
    }
   ],
   "source": [
    "### computing the robust solution\n",
    "news_result = RC_newsvendor_riskmin(sets,p,d,r,par,par_news,phi_conj, h_conj)   \n",
    "### Computing the nominal solution\n",
    "news_nom_result = nominal_solve(sets,p,d,par,par_news, h_eva)  \n",
    "\n",
    "\n",
    "l = len(prob)\n",
    "risk_rob = np.zeros(l)\n",
    "risk_nonrob = np.zeros(l)\n",
    "for i in range(l):\n",
    "    risk_rob[i] = nominal_risk(news_result[0],d,prob[i],par,par_news, h_eva)\n",
    "    risk_nonrob[i] = nominal_risk(news_nom_result[0],d,prob[i],par,par_news, h_eva)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e058b501",
   "metadata": {},
   "source": [
    "Plotting the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "ea62656f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data1 = {'robust solution':risk_rob, 'nominal solution': risk_nonrob}\n",
    "dt1 = pd.DataFrame(data = data1)\n",
    "plt.hist(dt1,density = True, bins = 30)\n",
    "plt.xlabel('$\\mathrm{CVaR}_{0.6}(.)$',fontsize = 16)\n",
    "plt.ylabel('density mass',fontsize = 16)\n",
    "plt.xticks(fontsize=12)  # Set font size for x-axis tick labels\n",
    "plt.yticks(fontsize=12)\n",
    "plt.legend(dt1.columns,fontsize = 14)\n",
    "plt.savefig('snews_cvar04.eps', format = 'eps',bbox_inches='tight')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}