notebooks/02.01-Production-Models-with-Linear-Constraints.ipynb

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   "source": [
    "# Production Models with Linear Constraints\n",
    "\n",
    "Keywords: linear programming, cbc usage, production models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ihMeDuJ5ecIF",
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   "source": [
    "This notebook demonstrates the use of linear programming to maximize profit for a simple model of a multiproduct production facility. The notebook uses [Pyomo](http://www.pyomo.org/) to represent the model with the [COINOR-CBC](https://github.com/coin-or/Cbc) solver to calculate solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2JKaLcN8edkz",
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   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import shutil\n",
    "import sys\n",
    "import os.path\n",
    "\n",
    "if not shutil.which(\"pyomo\"):\n",
    "    !pip install -q pyomo\n",
    "    assert(shutil.which(\"pyomo\"))\n",
    "\n",
    "if not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n",
    "    if \"google.colab\" in sys.modules:\n",
    "        !apt-get install -y -qq coinor-cbc\n",
    "    else:\n",
    "        try:\n",
    "            !conda install -c conda-forge coincbc \n",
    "        except:\n",
    "            pass\n",
    "\n",
    "assert(shutil.which(\"cbc\") or os.path.isfile(\"cbc\"))\n",
    "\n",
    "from pyomo.environ import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zywBNq7gecII",
    "pycharm": {}
   },
   "source": [
    "## Example: Production plan for a single product plant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "izk2tTP1ecII",
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   "source": [
    "Suppose you are thinking about starting up a business to produce Product X. You have determined there is a market for X of up to 40 units per week at a price of USD 270 each. The production of each unit requires USD 100 of raw materials, 1 hour of type A labor, and 2 hours of type B labor. You have an unlimited amount of raw material available to you, but only 80 hours per week of labor A at a cost of USD 50/hour, and 100 hours per week of labor B at a cost of USD 40 per hour. Ignoring all other expenses, what is the maximum weekly profit?\n",
    "\n",
    "To get started on this problem, we sketch a flow diagram illustrating the flow of raw materials and labor through the production plant.\n",
    "\n",
    "![LP_ProductX.png](https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/figures/LP_ProductX.png?raw=1)\n",
    "\n",
    "The essential decision we need to make is how many units or Product X to produce each week. That's our *decision variable* which we denote as $x$. The weekly revenues are then\n",
    "\n",
    "$$ \\mbox{Revenue} = \\$270 x $$\n",
    "\n",
    "The costs include the value of the raw materials and each form of labor. If we produce x units a week, then the total cost is\n",
    "\n",
    "$$ \\mbox{Cost} = \\underbrace{\\$100 x}_{\\mbox{Raw Material}} \n",
    "    + \\underbrace{\\$50 x}_{\\mbox{Labor A}} + \\underbrace{2\\times\\$40 x}_{\\mbox{Labor B}} = \\$230 x$$\n",
    "    \n",
    "We see immediately that the gross profit is just\n",
    "\n",
    "$$\\begin{eqnarray*}\\mbox{Profit} & = & \\mbox{Revenue} - \\mbox{Cost} \\\\\n",
    "& = & \\$270x - \\$230x \\\\\n",
    "& = & \\$40 x\n",
    "\\end{eqnarray*}$$\n",
    "\n",
    "which means there is a profit earned on each unit of X produced, so let's produce as many as possible. \n",
    "\n",
    "There are three constraints that limit how many units can be produced. There is market demand for no more than 40 units per week. Producing $x = 40$ units per week will require 40 hours per week of Labor A, and 80 hours per week of Labor B. Checking those constraints we see that we have enough labor of each type, so the maximum profit will be\n",
    "\n",
    "$$\\max \\mbox{Profit} = $40 \\mbox{ per unit} \\times 40 \\mbox{ units per week} = \\$1600 \\mbox{ per week}$$\n",
    "\n",
    "What we conclude is that market demand is the 'most constraining constraint.' Once we've made that deduction, the rest is a straightforward problem that can be solved by inspection.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6fkeTeNqecIK",
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   },
   "source": [
    "### Pyomo model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oTNbhNemecIM",
    "pycharm": {}
   },
   "source": [
    "While this problem can be solved by inspection, here we show a Pyomo model that generates a solution to the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 527
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1545,
     "status": "ok",
     "timestamp": 1555698907390,
     "user": {
      "displayName": "Jeffrey Kantor",
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      "userId": "09038942003589296665"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 1600.0\n",
      "  Upper bound: 1600.0\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 4\n",
      "  Number of variables: 2\n",
      "  Number of nonzeros: 0\n",
      "  Sense: maximize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.0\n",
      "  Wallclock time: 0.01\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: None\n",
      "      Number of created subproblems: None\n",
      "    Black box: \n",
      "      Number of iterations: 0\n",
      "  Error rc: 0\n",
      "  Time: 0.2884402275085449\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    }
   ],
   "source": [
    "model = ConcreteModel()\n",
    "\n",
    "# declare decision variables\n",
    "model.x = Var(domain=NonNegativeReals)\n",
    "\n",
    "# declare objective\n",
    "model.profit = Objective(\n",
    "    expr = 40*model.x,\n",
    "    sense = maximize)\n",
    "\n",
    "# declare constraints\n",
    "model.demand = Constraint(expr = model.x <= 40)\n",
    "model.laborA = Constraint(expr = model.x <= 80)\n",
    "model.laborB = Constraint(expr = 2*model.x <= 100)\n",
    "\n",
    "# solve\n",
    "SolverFactory('cbc').solve(model).write()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vvul9a6zecIU",
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   },
   "source": [
    "The results of the solution step show the solver has converged to an optimal solution. Next we display the particular components of the model of interest to us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit : Size=1, Index=None, Active=True\n",
      "    Key  : Active : Value\n",
      "    None :   True : 1600.0\n",
      "x : Size=1, Index=None\n",
      "    Key  : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "    None :     0 :  40.0 :  None : False : False : NonNegativeReals\n"
     ]
    }
   ],
   "source": [
    "model.profit.display()\n",
    "model.x.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of variables, objectives, and constraints can be accessed and formatted using standard Python string and formatting functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 722,
     "status": "ok",
     "timestamp": 1555698912767,
     "user": {
      "displayName": "Jeffrey Kantor",
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    {
     "name": "stdout",
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     "text": [
      "Profit = 1600.0 per week\n",
      "X = 40.0 units per week\n"
     ]
    }
   ],
   "source": [
    "print(f\"Profit = {model.profit()} per week\")\n",
    "print(f\"X = {model.x()} units per week\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BYe4eDmAecIZ",
    "pycharm": {}
   },
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5-cCaUWKecIZ",
    "pycharm": {}
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   "source": [
    "1. Suppose the demand could be increased to 50 units per month. What would be the increased profits?  What if the demand increased to 60 units per month?  How much would you be willing to pay for your marketing department for the increased demand?\n",
    "\n",
    "2. Increase the cost of LaborB. At what point is it no longer financially viable to run the plant?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7R9q6sDcecIa",
    "pycharm": {}
   },
   "source": [
    "## Production plan: Product Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uHrtxXrhecIb",
    "pycharm": {}
   },
   "source": [
    "Your marketing department has developed plans for a new product called Y. The product sells at a price of USD 210/each, and they expect that you can sell all that you can make. It's also cheaper to make, requiring only USD 90 in raw materials, 1 hour of Labor type A at USD 50 per hour, and 1 hour of Labor B at USD 40 per hour. What is the potential weekly profit?\n",
    "\n",
    "![LP_ProductY.png](https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/figures/LP_ProductY.png?raw=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 527
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 254,
     "status": "ok",
     "timestamp": 1555698921323,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
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     "user_tz": 240
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    "id": "rHGr9LwqecId",
    "outputId": "e790827b-02b5-459f-c744-82e383e1051a",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 2400.0\n",
      "  Upper bound: 2400.0\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 3\n",
      "  Number of variables: 2\n",
      "  Number of nonzeros: 0\n",
      "  Sense: maximize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.0\n",
      "  Wallclock time: 0.0\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: None\n",
      "      Number of created subproblems: None\n",
      "    Black box: \n",
      "      Number of iterations: 0\n",
      "  Error rc: 0\n",
      "  Time: 0.03715109825134277\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    }
   ],
   "source": [
    "model = ConcreteModel()\n",
    "\n",
    "# declare decision variables\n",
    "model.y = Var(domain=NonNegativeReals)\n",
    "\n",
    "# declare objective\n",
    "model.profit = Objective(\n",
    "    expr = 30*model.y,\n",
    "    sense = maximize)\n",
    "\n",
    "# declare constraints\n",
    "model.laborA = Constraint(expr = model.y <= 80)\n",
    "model.laborB = Constraint(expr = model.y <= 100)\n",
    "\n",
    "# solve\n",
    "SolverFactory('cbc').solve(model).write()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 257,
     "status": "ok",
     "timestamp": 1555698923529,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "b9SY8ZPRecIh",
    "outputId": "ad099558-2549-4d70-8f10-2581d78feaa8",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Profit = 2400.0\n",
      "Units of Y = 80.0\n"
     ]
    }
   ],
   "source": [
    "print(f\"Profit = {model.profit()}\")\n",
    "print(f\"Units of Y = {model.y()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oEl-VQeyecIk",
    "pycharm": {}
   },
   "source": [
    "Compared to product X, we can manufacture and sell up 80 units per week for a total profit of \\$2,400. This is very welcome news. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uqfCBHxjecIm",
    "pycharm": {}
   },
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2LnLKNbfecIm",
    "pycharm": {}
   },
   "source": [
    "1. What is the limiting resource?  That is, which of the two types of labor limits the capacity of your plant to produce more units of Y?\n",
    "\n",
    "2. What rate would you be willing to pay for the additional labor necessary to increase the production of Y?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Df2vj9GiecIn",
    "pycharm": {}
   },
   "source": [
    "## Production plan: Mixed product strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uMh4W-ijecIo",
    "pycharm": {}
   },
   "source": [
    "So far we have learned that we can make \\$1,600 per week by manufacturing product X, and $2,400 per week manufacturing product Y.  Is it possible to do even better?\n",
    "\n",
    "To answer this question, we consider the possibilty of manufacturing both products in the same plant. The marketing department assures us that product Y will not affect the sales of product X.  So the same constraints hold as before, but now we have two decision variables, $x$ and $y$.\n",
    "\n",
    "![LP_ProductXY.png](https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/figures/LP_ProductXY.png?raw=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 527
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 267,
     "status": "ok",
     "timestamp": 1555698938250,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "RgjGjPrFecIr",
    "outputId": "8b0b6119-171d-4e1c-8ab6-bc95c0f8f1a3",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 2600.0\n",
      "  Upper bound: 2600.0\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 4\n",
      "  Number of variables: 3\n",
      "  Number of nonzeros: 2\n",
      "  Sense: maximize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.0\n",
      "  Wallclock time: 0.0\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: None\n",
      "      Number of created subproblems: None\n",
      "    Black box: \n",
      "      Number of iterations: 2\n",
      "  Error rc: 0\n",
      "  Time: 0.036074161529541016\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    }
   ],
   "source": [
    "model = ConcreteModel()\n",
    "\n",
    "# declare decision variables\n",
    "model.x = Var(domain=NonNegativeReals)\n",
    "model.y = Var(domain=NonNegativeReals)\n",
    "\n",
    "# declare objective\n",
    "model.profit = Objective(\n",
    "    expr = 40*model.x + 30*model.y,\n",
    "    sense = maximize)\n",
    "\n",
    "# declare constraints\n",
    "model.demand = Constraint(expr = model.x <= 40)\n",
    "model.laborA = Constraint(expr = model.x + model.y <= 80)\n",
    "model.laborB = Constraint(expr = 2*model.x + model.y <= 100)\n",
    "\n",
    "# solve\n",
    "SolverFactory('cbc').solve(model).write()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 367,
     "status": "ok",
     "timestamp": 1555698941635,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "16AtkqK1ecIy",
    "outputId": "56621172-1eec-458b-fd61-e856b70517b0",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Profit = 2600.0\n",
      "Units of X = 20.0\n",
      "Units of Y = 60.0\n"
     ]
    }
   ],
   "source": [
    "# display solution\n",
    "print(f\"Profit = {model.profit()}\")\n",
    "print(f\"Units of X = {model.x()}\")\n",
    "print(f\"Units of Y = {model.y()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "x7WugdoxecI1",
    "pycharm": {}
   },
   "source": [
    "The mixed product strategy earns more profit than either of the single product srategies. Does this surprise you?  Before going further, try to explain why it is possible for a mixed product strategy to earn more profit than either of the possible single product strategies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "o_K5Y2OaecI2",
    "pycharm": {}
   },
   "source": [
    "## What are the active constraints?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "PhCCA3bWfRTy",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fvTuDkoyvZLfBuZX05x+b+GPDHzz51JMkFUJwzpDddp9SFRjC/NpRI3gEZ1KWcy7l21yv8VatAfSdFx3oH0if6/pyS/c7iVRmZOtvcA74yYmUMjMraNagOZUrRqEoCg3rNOK/c//lWL998w6s++tXjpw8gs1uo0Gtht5+WwZ5EBeT4JWvovDU00/x4IMj+GPjn7z15tukpV9uuPSU7PaV1KpVm0oVK3LgwIFsz2eV3b6Swshuu2oFny3/nOHDH2T79u1c3+26PGsIuclu//nHJj755FPS0nJvQDVkt31IzZCxhFpacTD+uVz7G7ydNbj6G1RZAUmiZxcvyLYQKELJ7G8QKEg06kXXY++Rvdn+s2iaxv5/91GnhlOUzWK2ZL6mKiqOXP6R3tn7br5c8wVf/vS5kS0YZOIL2e0ruXDhAsdPHKd69erZnjdktz1DqQsMijDROPwthLCwP/bZXD8leDNrAGd/QwXbSkxEe3xtdwl1PEM5+/MIFKKr1KRxncbM+WRW5utzPplFk7pNiK5S0+01mzdswdkLZ/hu7bf0vb5/wTcYlDr0kt120a9/Xzp37Uy//n2Z8tzzVKpUKcc1hux28Sm1stux6ZuwKOUJMtfL9d6Pvg7h/qejqBZpY/WiU8We8pYbGsnEm54n0HEXfrKt5w1cwcyP3iYwIIhhdzyY+ZxV7CRJnYsS+wIvz5nGjv3bkUhaNGzJc2NeIDQ4lL92bGLRF+/z3ovOY3Ivzp5C03rXcFuvO7jvyQE89eAzXFPfuf86f/lc9v27j7ee8dz59OJiyG4blFW8JbtdKk4l5Ua4X/vMn1PtJwkwZU85vXlC6TIaVmUL6cpGKlq/QyWi4FuKwSP3PZbTA3GBNHU1geGVeOPpt3K979rm7bm2+eU/r+eyHHX96PXsWwNb92xhyP+GesZhAwODEkmp20q6khNJC9hyoX+OeoO3aw1QkvSUHiRF/YhUZVWR10lISuDGYd3ws/jToaUxC8LAoDRT6gNDpYC+eeopebvWACVtXvSEIs9vCA0OZfXCX3l30mzPOmdgYFDiKPWBwV+tTKOw13LVU/JF1gCX+xuS1YVoPj6pBNnnRSeZFvncvoGBwdVFqQ8MAOX9r8uzv8EXWYOrv6GC9SsUQty65/jpYzw/+3n2/7uv4IvdwERVKtg+o5z9OY+sZ2BgUHopE4EBnP0N5f1uQBUB2Z73VdagEIKJakgkqcqqPOsNew7tZtRLY7hxWA8++fZD5n32nsd8MMt6CEw4uEC6+NNj6xoYGJQuykxgUISJa8rPo0JAjxyv+SJrcJGu/Eqs+eFs9QYpJZt2/MmAp+/jtkf6s3bjDwhFoV+PO3j8/nEe9yHeNJkY80hjXrRBoYmoEE7nrp1p3+FaOnXpxKzZs3LtMtaD/GS+P/n0Ezp0bE/7Dtdybft2HpUDL45U9p133UFcfFy+13y87GPOnDlTpPWLSpkJDFk5lbSEQ/EvZT72VdYA4Kd1y9RTSpV/8fMfP9Hv4VsZ/PRA/tmxEYtfAPf9bxjrlvzOG0+8Ro0qnm+SC7VPBlRjXrRBoQkICGDD7xvY9OdffP3l16z5+Semvzpdb7fyZc2aNcydN4cvv/iKTX/+xW/rfic01HMihPlJZRfU4Pb5ZysIKxeW7zXLPlnG2bNGYPA6Vu0i/yUvzVZv8FXWIBAEpr7A6h/C6DVsOGNeHMWhI7sIDC7HmEGPsX7pRiaNnEhkhcpe88FEVcLtb2ToKeU94MjAID8qVqzIO2+9w/sL5iOlxOFwMPm5SdzQ/Xo6du7IB4udBx3Wb1hPn759GPLAYFq3bcXzL0zhs88/o1uPG+jYqQNHjzqPkucl352XRDXAGzNep0271tzyv/4cPnwoVz/ffPtNXnrx5UyZCn9/fwYPHgLAzl076dGzOx07d2TgfQOJi4sF4OZ+NzPl+efo1uMGWrdtldnhvG/fPrr1uME5LKhzR44cOZJDKjs3+fB7B93LdTd0pX2Ha1m8+INM365pfg2XLl3KU/p75cqv2b59Gw+OfJDOXTtnyoF7m1Lb4JYfNUPGEmfdwsH45wixNCHQVDsza7j/6SjmLgvj1h5JHu+GTk5N5rMfljNvxfvEZQwOCS8fzEN3Ps6dve8i0N89ATFP4OpvSDa9j5/WkQDtRp/ZNig+Ye+W88q6cY/GF+r6mjVroWkaFy5cYNWq7wkNLcfaX9aRnp7OjTf14oYbugGwe/du/t70N+Hh4bRo1Zz7Bt3Prz+vZe68ubw3fz7Tp03PV747N4nqPXt28+WXX/L7uvXY7Xauu6ErLZq3yOHjvn17adEi5/MAox4axWuvvkbnTp2Z+spUpr/6KtOnOTMgu93Brz+v5ac1P/Hqa9NZ+dU3LFq8iFEjH+KuO+/CarXicDhySGWv37A+h3z47JmzCA+PIDU1lW7db6B//1uIiMje8JqX9Pf8Be/z8osv0bJlq0L93RSHMhkYXHpKWy7cwp6Yx2hV8TNU4e+1buiY+BiWrFzChys/JCXZ+R+vatU6jLy3HTdf35tgtYtH7BSWUMcTCFT8tGt1sW9QOnCp6vy69lf27N3Dym9WAk5xvX+PHMFssdCqZUsqV3ZmwTVr1qJbRsBo3Lgx6zesB5zy3Q8MfYBz585htVmJrnF5G9UlUe3n55cpUf3Hn39y8819CcxQNr2pd59C+R2fEE9CfDydO3UG4N4BAxj8wODM1/v17QdAi+aXZbjbtW3HjBlvcPr0f/Tr2586dXKXKLlSPnzee+/x3fffOd/nf/9x5MiRHIEhL+lvPSiTgQEu9zfsinmI2PQ/qODfzeNZw+nz/zF/xQJW/Lgcm9XZXFe/XnMeu3cMN1zbLXPCFDh1lRRyaj55E4GZUIdzBq3ECkgEfvnfZFAiKOwne29x7NhRVFWhYsWKSCl5bfprdO+e/YDH+g3r8fO7/O9KURT8/CyZPzsypKyfevopxoweQ5+b+rB+w/pstYu8JKqvlPXOjUYNG7F9+3au63pdod6by0dVVbFnFB7vvONO2rRuzeqffuK2O/7Hu+/MpGbNmjnuzSrDvX7Den77bR1rVq8hMDCQm/vdTFp6Wo57rpT+TrXnvMZXlMkag4vy/tdxbaXVVPDvlvmcJ2oNR04cZtxrT9B9yPV88s0SbNY02rbswtLXP+Wbd7+ke4ce2YJCkrKEC5ZePp3fkBVJOhfNAzLnNxgYuMPFixcZ9/g4Hhw+AiEE3bt1Z+EHi7DZnMOcDh8+THJystvr5SffnRsdO3bku++/IzU1lcTERH5c/UOu140b9zhTnn+Oc+fOAZCens689+ZRLrQc5cLCMusHny5fTqeOnfO1eezYUWrWrMWokaO4qXcf9uzZU6BUdkJCAuXCwggMDOTgwYNs2VK4IV4FyXx7gzKbMbhwievFpv+JnxpJoKl2kbOGHfu3886y2Wz8+xcAhFDo0eVmHhkwmoa1G+V5n59sQwLTiDONJ8K+EOHjeC3ww6K1Jtm0AD/tWgK0m31q3+DqITU1lc5dO2O32VBNJu65627GjHkYgPvvH8yJkye47vquSCkpX6ECHy/92O21XfLdVaKq0KZNG46fOJ7v9S2at+C2//2PLtd1pnq16nRo3zHX63r17MX58+e59X+3ZA6nGjhwEABz58zl8cfHkZKaSs2aNZkzK3/Jly+/+pLPPvsMk9lMZKVKPP3UU4SHX5bK7tGjB716Za/X9ejegw8+WETHzh2pV7cubdoUTmn53gH38vj4cfj7B7Bm9RoCAgIKvqmYlFrZ7cLg0FLYdL4HFqUCrSp+hnT407hPTQ4dtzB13IV8aw1SSjZsXc87n8xm1x7nJwHVZOGWHrfz0F0j3D5umqwsJd78HCH2p3w6L9qFxMZF8z3YxSEqWr/BRE2f+1BUDNltg7KKt2S3y/RWkgtVCaRh2LRMPSV3+hocDgffr/uW3qNuZvikIezasxm/gCAeuGMEv324nmmPTS1UD0L2edFbCr7Bw2TVUzL6GwwMyjZlfivJhUtP6UTSfMIsbRnQt1+uJ5TSrel8teYLZi9/j/PnTwIQElqeYbcPZVDfgYQEFa1xxqWndNF8EIc4BrKNp96a27j6GxLU6Ti4iImqPvfBwMBAf4zAkIWs/Q1tK7Zm8uiQzFpDj45nWL7qYxZ8uYiE+IsAVKxUjdF3j+T2nndkO1FQVBRCqGj7DoG52GsVFX+tO35aV119MDAw0BcjMGTB1d9wMe1n/NQoBvRNZMpMO0dPz6bzoDnY0p2S2dHRDXj0nofo3bUPJtWzf4SuX8ipyioc4jzBjiEeXd9dHzRSSTBNI9g+9KqqN5RuZGbx1MDAWR/2To3YCAxX4K9WplrQII6ePMkL783m+JnvQbNiS4cmjdry2MDRdGnd1ev/OVOVH0hTfsSsNfHJvOgr0YghVfkWm3kbFWwrjP6GEoDd6iA+IZ5yoeWM4FDGkVISnxCP3eodYbcyHRg0TcvWTwCwc/9+psydz8qffkBmqEYGhfQhOXES9/auS9c2vjlPHGZ/hQuW3cSax/pkXvSVuOoNMeYHiTdNJcz+ok/tG+Qk7oIzY7106SJgBIayjcRudWT+m/A0ZTYwfLF6NcMmPceP779H+xYtWL9lC5Nnz+O3P5zt+Yqq0qNXJPfdG48pfgL3ju3A3GU2r2go5YZrXvQF8+269Tc49ZSGG/0NJQSpSWLPJejthkEZoMwFhnSrlbHTXuXj1T8j6nZi1EtTEUJh+67tAJgtfgy9406eGT6UyMoqWy7cgkV5kMZ1/2Lv4XIe1VAqCNe86Hjzc6Rrv+Gv3eATu1kJdTyJVdlKgukV/K09EVh87oOBgYFvKVOB4ejJk/R7ZCxnKEfYoLcRqplDn04g5fQhgoJDefS+QTx+/31UyCJu5dRTGsGrUx+m390feU15NS8CtYGYrHXxk+19Y/AKLvc32I2gYGBQRigzgeGrNWsY/Oxk/NrdQXCr/pnFO7+G11E71Myfy5YSnEsHtau/Ic3/PPVrpnLwWIBPswaByAwKNrEfRVbSpd4AIJFYxV+6BSkDAwPfUOo7n61WK6Nfmsr9U14m6JZJBLW+JTMoSLsVU3gUew8dIC4x7yJOrZBxNI54lUkPxQHen/KWGxqJXDTfQ5xpfJ7zor1NqvIVlyz3kqqs0sW+gYGBbyjVgeHoyZO0uuselm85RNigtzGXr0bqkc0k/L6E5M8mcHbWQMrv/pLRg+4jKB9hKiGcf0z9e//Da9Pv5Hys3euzoa9EIYRQ+3jS1d+yzYv2JQFaP8xaS+JME4x50QYGpZireitp624/Qrs0Y1D/RMYPjaVODVvma1+tWcOgp5/BUa4KQVXKk7JiIsmXznBNoyb0at+WG9r1oX3z5rluH+WFndO0vXYFDz8cwdyPZ/m01gAQqA0i3fEXieoMLFprn/c3uOoNFyx9iTU/YvQ3GBiUUnTJGIQQ44QQe4QQu4UQnwgh/IUQEUKINUKIQxnfw91ZKzFZZcHn5WjWP5offnMOx5i1dCm3PfwwQhF0qhPF0zc04vs3XyFh819s/nQpUx8bS4+OHQsVFMBZb6gWOIJ+/ebToOnnPs8aXHpKKtWINY/VZX6DMS/awKD043PZbSFEVWAD0FhKmSqE+AxYBTQGYqSU04UQE4BwKeXT+a/VRsJlJdLAAI2d3xxHEf+SkpZGozp1cjSwFRdN2llzcAgOdR9TJv7JkqlBPs0aAKxiN6nKt4Q6xut2UihRnYVZa46/1GcsaVbKiuy2gYE7XM2y2yYgQAhhAgKB08AtwJKM15cAtxZ2UZtN8NbicGpVr06TevU8HhTAqafUueYbaA4/ut/4hs+zBgCLbEo5xzMILEhsBd/gBUIcD2cGBb18MDAw8A4+DwxSyv+AN4ATwBkgXkr5ExAppTyTcc0ZoFJh17bZBR+tDPGku7kS5FeZpGOf8+ab7+lyQsmFTRzkvKUn6aJwowI9SZK6kIvmO435DQYGpQifB4aM2sEtQC2gChAkhBhUiPtHCCG2CJH7NJukZN+8pTu6V6VmFUFcchK/btvhE5tXosooQOhWbwAwyZrYlJ1GvcHAoBShx1ZSD+ColPKClNIGfAl0BM4JIaIAMr6fz+1mKeV8KWUbKXOfZBMc5Jsz/q4pb489NoY6re4jTfvXJ3az4tJT0ojRrb/BpaeUon5k9DcYGJQS9AgMJ4D2QohA4ew06w7sA74BBmdcMxhYWdiFzYqD+27xjtpgbgzom8jq717GavXjpPVRJGk+s+3Cqac0Udf+hlDHk0Z/g4FBKUKPGsNfwArgH2BXhg/zgelATyHEIaBnxuNCYdbSGBe5zIPe5o/JBI8MCOCVVz4iqNxeYpWXfGY7K4HaIPwdfbAqf+mSNbj6GwR+WJXtPrdvYGDgWXQ5lSSlnCKlbCilbCqlvE9KmS6lvCSl7C6lrJfx3e1Nc7NZI8CSxufcQZ23HoYVK7zpfjYG9E0k9lx3Pv54AmnmT0hVvvOZbRfO/obXibAt8Lk0twsTValkXUegdqsu9g0MDDzHVS+JERoKI0Yo7NrrT59p12H3lzBpks+Cg6vWsGjRS6z6bhyK7Vqf2L0ShQAEKg7OkaDO0CVzUHA2DKYpP5OqrPa5fQMDA89wVQeG1q0hPh5mzYI6dSD+oevYtDKAuGa+DQ4D+iZSp7rG6zPe5NufayFx6HZ8M01ZS5JpNknq+7rYl2gkqvOIMz1p1BsMDK5SrurAcCVBQU0xh1Zn72shWMv5Lji4sgaA9z4N5qJpMPEmfUZhBmp34++4mUT1DdJzP9HrVQQK4bZ3AJVY8yNGf4OBwVVIqQoMJlMITZp8jt3fxr4P6iLxXXAY0DeRetFWTpwJ4Oi/bUhRPyFFKfTBqmJj6CkZGBgUl1IVGACCg5tRt+67xIYd5sTiXiB9ExyyZg0Tp0zH7GhNvGkSdqFnf8MlEk1v+Nw+ZO9vsIp/dPHBwMCgaJS6wAAQFTWcSpXuJe3aaOS0V3wWHLJmDX/+shCBhRjTw7r1N0TY3iPUPsHntl2EOp4k3DYHs2ypmw8GBgaFp1QGBiEEDRsuoUGD+YgJz8C0aT4JDlmzhncWNSYkfQZSJOMQp71mMz/85XUohCJJ1yVzEZgJ0HojENjFv0a9wcDgKqFUBgYARXHOIEpK2sXB244jp031SXBwZQ2nzpn54ae+VLL+hEnW9po9d4g1jeei+T7d9JQcnOeCub9RbzAwuEootYHBRULCJk6fnsfxezSfZA5Zs4a5y8JwOPyQWIlXp+vyqR0gxPEQGpeIMz2hS3+DSiUCHfcaekoGBlcJpT4wuOoNx45NIXZke58Eh6xZw9c/B6MRS6r6ua71hnL2SaSr63TrbzD0lAwMrh5KfWAQQlC//jwCAuqyb98ArI8/4PXgcGXWIB2RhNlnYFf2E2/SS09poM79DU49JaO/wcCg5FPqAwNk6W+wx3HixKswYYLXg8OVWYO/dj3B9lG69zf4a91QCPO5fbjc32CWrXSxb2Bg4B5lIjCAs7+hefNfqV07Q7TVy8HhyqzB7oAQx+NYtNYkmF7WZUtJIYQI+3uYpbP5T+Lbed/g7G8Is7+AwE8X+wYGBgVTZgIDQLlyHVAUCzZbDImJ27weHK7MGgQmwm3vUt72MQJ/j9oqDBIrcabxJKnv6eaDTezjgrmfUW8wMCiBlKnA4GLv3nvYtetmrNbzXg0OuWUNKlGYZX0ArGKrx2wVDjMSK4nqDN3mRQsZikP8Z9QbDAxKIGUyMNSp8wZ2eyz79g1CSs2rweHKrMFFqrKKi5Y7DT0lQ0/JwKDEUSYDQ6aeUuwajh/P+KXkpeCQW9YA4K/1wqLpqacUSrhtpjEv2sDAIAdlMjBA9v6GuLjfnE96KTjkljW46g166ilZZFPK2SdhVbbhEMd8bh8u9zekKF/pYt/AwCAnZTYwuPoboqKGEhjY8PILXggOeWUNKlElor+hkvVn3WQ7BGbK2xYQYZ+ri30DA4OclNnAAM7+hgYN3sdiiUTT7M56A3glOORVa/DXrifEPh4/rWuxbRQFgUClAhJJsvKhLvUGhXAEJhxcIFlZ6nP7BgYG2SnTgcGFw5HMjh09OHFi2uUnPRwc8soaAEIcYwjQbgRAYi+WnaLiEEeJN72iW70BIFn9mHjzc1dtvaH3/3rw2tvTMx87HA7uHnw7z708EYA///6D5V98Umw7O3Zvz1zzyudvG9ifMY+P5MGHh7J0+YfFsnPrgL5Fuu/I0cP8vfWvXF9LS0/j1bdeYdTY4Yx8dDiPPzOW1NRUkpKT+PaHoh3E+HTFsiLdZ5A3RmAAFCUQP7+qHD363OV6A3g8OOSVNbhIVj7lovl2XeoNJlmbcvaJpKu/kaTO97l9cAbIq1lPyd/fn+MnjpKe7jx++8/2rZSPqJD5eod2Hbn79gFe9aFpo2uY/eZ7zHxjNr/+9guHjhzM9rrD4cjjTs9x5OgRNm/9O9fXvv7uS8LKhTPvnQW89+4Cxj38BKpJJSk5ie9++DbXewry+dMvjMDgaUx6O1AScNUbEhO3sHfvANq02Y7FUsn54oSMQTfPPOMMDgB33FEkO66s4f6no5i7LIxbeyRhUi+/rlIZm7KLeNNLhNmnFuMdFY1AbRDpjr9IVGdg0VrjJ9v61L5LT+mCpS+x5keoYFuBwM+nPhSXNq3a8ffWv+jSsSvrNvzK9V1uYPfeXQD89OtqDh0+yJgRj/D8K5Pp3KELPW7oxferv2P33p08Pe5Ztm7fwkefLMFmtxEVWYXxjzxJQEAAW/75m3mL5hIaEkrdOvUK9MPfP4B6depx5uxpNm3+k5iYS5w7f47Q0FAeGDSct2a9QVxCHGGhYTz+yBNUqhjJ2XNnmP7mKzg0B21aXv6737F7O198/TkvTnL+m5w9fyb16tanV7cbOXBoP/MWziEtPQ2zycy051/lo08WY7Va2bNvN3fffg/Xdb4hc62Y2BgiK0ZmPq5etToAH3y0gDPnTjN63EhaNm9FuzbX8vHyj4gIj+Dfo0eYP3MRL0x7jgsXL2C1Wbm17//o06sviz58H6vVyuhxI4muEc3T457ll3U/s/L7r7Db7TSo35CHRzyKqqr8+PMPfP7lp0RElKdqVFXMZgsP3DeMhx4bwcLZizGZTCSnJPPQYyNYNGcJJlPZ/fVoZAwZXNZTcvU3ZPmU4sHMIb+soWToKU1DpRpx5nG6NJ5l7W9IVGf53H5xua7zDfy2YS1Wq5Wjx47SoH7DXK8bO/pxPv5sKbv37uLLlZ8zevjDxCfE88nnHzP9hdeYPWMe9evW58tvVmC1Wnl7zlu88OxLzHjlbWJjC64DJSTEs+/APmpUrwnAoSOHmPLMi0x4fCJz3p9J9+t7Mu/t97mhazfmLpgNwNyFc+jbux8zX59DeFhEgTZsNhvTZrzMqGGjmfvWfKa98Br+/gHcN2AIXTtdz5y33ssWFABu7N6bz75czmNPP8Lijxfx3+lTADxw33CiIqsw5633eHDISAAOHDrAkIFDmT9zEQCPP/wEs2bMZebrc1j53dckJMQz9P4HsVgszHnrPZ4e9ywnTh7n943reHPaO8x56z1URWHt779wKeYiyz5bytuvzmTa869x8r+TAAQGBNKsafPMra/fNqylc4cuZToogBEYsuHqb0hNPUx6+pnsL3ooOORXa4DLekp6z4sOs72h26d1f607YbbXCXYM08V+cahdszbnzp9j3fpfadu6XZ7XhYeFc/+AwTw1eTwPPjCKkJBQ9h/Yx4mTx3n8mccYPW4kP6/9iXMXznHyvxNUjqxM1SrVEELQ7boeea67e98uxjw+kmdfmMDdt91DzRo1AWjfrgN+fs6/z30H9nJD124AdL++J3v27QZg777dXN/F9XzeNlycOn2SiPDyNKjnDH5BgUGoqprvPXVq1WXxvI+449a7SEpK5NEnx3Di5PFcr21QrwGVI6MyH3/9/Vc8NG4Ej014hAuXzvPfmf9y3LN91zYOHTnEo0+OYfS4kWzbuY0z585w4NABmjVpRkhIKCaTiS4dr8u8p3ePm/jplx8B+OmX1fTqdmOB7720U7bDYi5ERQ0nMvJeVDUo54se2lYa0DeRl+aU59BxC1//HMwdNyZlvubqb7hg6U+6+EuXY6Rm2STzZwenUanicx8CtdsBp66TRjwqFX3uQ1Fp37YD7y9+j9denkFCYkKe1x09fpTQkFAuxTg/KEgkLZu35pnx2QvLR44eRiDcst200TWZWz5Z8ffLW5tLCJHrzy5URUXKy4KHVpvV6W8RNRADAgLo3KELnTt0QQiFzf/8TacOXfL1ecfu7Wzb8Q9vTX8Xfz9/npz0eKYfWZFS0uOGngy9b3i25zdu2pCnP00aNWXW/HfZuXsHmqZRM7pW0d5YKcLIGK5ACIGqBqFp6fz777NOPaWseCBzKChrUImikvUXgjTvFioLIlVZxTnLDbrpKQHEmEYRYx56Vekp9erem4F33Uet6LyD+oGD+9nyz2ZmvzmPL1Z+ztlzZ2hYvxF79+/mdMYn4bT0NE79d4rqVWtw9vwZTp9xzg5ft35tsfxr1LAJ6zY41/j1919o0qgpAI0bNc1ce+3vv2ReH1kpkuMnj2O1WUlOTmL7zm2Asz4QE3uJA4f2A5CSmoLD4SAwIIDU1JRcbe/Zt5vEpETAuRV14uRxKlWMJNA/gNS03O8BSElOJiQ4BH8/f06eOsH+g/syXzOpJux252m+Fs1aseHP9cTFxQKQmJjAufPnaFCvITv37CQxKRGHw8HGP9dnW7/H9T2Z/uYr9OpuZAtgZAx5kpp6hFOn3iIxcQvNmv2IEFliqAcyh/yyBnBKVgCki41oIoEA7aYiv5ei4qd1QaUKseaxVLR+h0rB+86eJkgbSIz5QeJNUwmzv+hz+0WhYoWK3Nrvtjxft9qsvD33TR5/+EnKR1TgwSEjeXPWG7z64huMf+Qppr05FZvNBsDgex+gWtVqjH1oHM9NnUhoSChNGzXl2IljRfbvoeFjeGvmG6z4+rPM4jPAQ8NGM/3NV/j6+y/p3P7yJ/iKFSrRtdN1PPTYCKpGVaVOrboAmM1mnhk/ibkLZpFuteJnsTDt+ddp3rQFy7/8lNHjRuYoPp85e5qZ770DUqJJSbvW12ZkDoLGDZsw8tHhtGnVlnZtrs3mc+tWbfl+9XeMeuxBqlWpTsP6jTJfu6nXzTz02Ajq1qnL0+OeZfC9Q3j2hQloUsOkmhgz4hEaNWjMPXcM4LGnHiYiojw1qtcgKPDyrsANXbuzZNkHmVtpZR0hi5oPlgDatGkjt2zx3jSy06ff5+DBEdSq9TLR0TnPjTN9ujM4CAEvv1zo4PDR1yHc/3QU1SJtrF50KtsJJXBuLVwyD8Am9lDRtlKXbSWb2MMF8+34aR2IsC9E6JBkxquvkGxaQLhtJgHazTleb7DJ+efyY/Offe2awVVEamoqAQEBOBwOXpw+hV7de9OpfWcA1v/xO3/+/QdPPTZBZy+Lzy139TuTZk0p1v6vsZWUDy49paNHnyM2dl3OC4q5rVRQX4NAEG57S1c9Jee8aH37Gy7Pi37mquxvMCgZLF3+IaPHjWTk2OFERlam47WdAJjz/kwWfbSAe+8cpLOHJQcjYygAuz2RrVvbABrt2u1HiFxOXRQjcygoawBIU9YRYx5KoGOALv0NEkmcaTwWrQVB2v0+tw9g5z9izWMJs0/DLLOf4zcyBgODyxgZgw9w9jd8QdOm3+QeFKBYmUNBWQNk729IF38W5W0UC2d/wwzdggI4+xsq2D7PERQMDAw8jxEY3CA4uClBQY2QUpKUtCP3i4oYHAo6oeQixPE4Yba3sMj2RXkLxcZ1XDJV+ZFY06O66CkJBJI04kxPk6p87/H1NU1j/8F9vP/hAp55aZJP5CMMDEoixqmkQnDmzHwOHhxN8+a/EB5+fc4LinhaqaATSuDsbwjUbgHAzilUKugyN1rjIqnqd5hkY0Ico3xuH1Rs4jCpph8wW5tgomaxVrPZbOzcs4Pf/9zIH3//QWLcpczXjh7/l7q1jQzFoOxhBIZCUKnSvZw8+Sb79t2bXU8pK0UIDgVpKGVFI5YLln4EaH100lMaWOL0lApLckoyW7dtZu0fG9n6z19Ys5yfDw2vSOf2nejavlPmsUwDg7KGERgKgUtP6Z9/rmXfvkE5+xtcFCE4uJM1gHN2QZBjAEmmeVi0dplZhK9wzYu+YNmtW3+DS0/J1d/gDjGxMfz59x+s/XMje/dsR7PbMl+rXLUmXTt0okv7TtStXS/X7l8Dg7KEERgKiUtP6eDBEZw4MS33/gYodHAoTNYQ4ngcq7KZeNMkLLZrfN7foBBCuG0mF813kKZ8p0tR+vK86E8pb4FLOdUR+O/0KTb+tZG1f2zk6JF9lzUchKB2/aZ069CRjtd2okpUVd86b2BQwjECQxGIihpOUtJ2goKa5n9hIYODu1nDZT2lvsSYHqai7Uuf1xsssimVbD9gkvrpyoQ6niTIcT+XrM7pd1JKDh4+wIZNG/lt00bOnz6Rea1qMtOkaSu6dezEtW07EB4WrpfbBgYlnqs6MKSkHODs2SVUrjzYp3ad8xtmZz6WUua9/VCI4FCYrME1LzpV+R6J5qbEmmdxBQWb2I8kDYts4VP7AjPSHglHoOoxM3e9fU+24rFfQBBtWrfn+g6daN2yDYEBgT71z8DgauWqDgwABw+OJiSkLUFBjXWxf+rUTGJifuSaawrocwC3goO7WQM4+xv8tesBZxOauwqcnkSiEWsahybifVZvSE5NZv2W3/huw2rW/70WUuE/bMAlQsIq0OnajnTt0IlmTZqXeV19A4OicFX/rwkIqI2qnmXPnrto3fpvVNX3nwgVxZ+YmFUcPz6NmjUn5X2hm8GhMFmDC7v4l1jTeMLtM3xebxAohNvf4IL5duJM472mp3Qx9gK/bvqFb9evZuvOP3HYLxcVRMUAmre3MupmB7WqjkTab8hnJQMDg4K4qhvchDDTqNFSUlL2cujQI7r44NJTOnZsSvZ50bnhZhOcO93QWREyAIc4obOe0iSP6ykdP32MBSve55axt9Pp3vZMfudZ/v7nNxwOGw3qt2D80KdZvfAX5JhUdrVxUK9OI8xBb4GSc4CLgYGB+1zVGQNARERPoqMnce7cMmy2GMxm3x6dzHdedG64kTkUNmtw1RtizEN1nBc9kHTHJhLVGfhpHbDI5oVeQ0rJnsO7Wb3xJ1ZtWM2pU4czX1NNZlo160C/zjfSrX0PKkZkGdxzEhwSbMmTsISMwhw4FVvSLK7yzz0GBrpx1QcGgJo1p1C9+hOYTKG62L/c39CR2NhfiIwsYMCOG8GhMLUGuKynpHd/Q7LaCLNsVPANGdjsNrbs+ptVG39izR9riI05m/maX0AQXdreQN/OvenSpivBgQVkTzISe8ozSBSMoGBgUHRKRWAQQsVkCsXhSOPkydepXv3x3EdzepHg4Ga0b/9v/tlCVgoIDkWpNbj6G1LUzwjQ+vu8GK0QSohjDAAaCQiCc603pKSlOIvH61ezfvNaUlMSM18rF1aRHh16clOnXlzbvD0Ws6VQPmj2LHOWRSLIkKK9GQODMkypCAwuEhM3c+zYFNLSjtKw4SKf23cFhZiYNSiKH2FhXfO/oYDgUNiswdnfMA+FEF1OKLlwcIGLllsJdNyXqacUE3eJXzf9wjcbVrN1xx/YbZdHdVapUpubOveid6cbaVrvGhSl+J/2FfNPmALmYk2aBZrRwGZgUBhKVWAIC+tCdPQkjh9/ibCw66lc2fcduZpm5/DhsdjtcQXXGyDf4FCUrEGlvNMP4klVVukyN1qhAmatFQfOvcHW387ww/q97D+wDSkvK7LWq9eM/p1706NjL2pX9/xJKs3urHGYA1/ClvQuULjMw8CgLFOqAgM46w3x8es5ePChjP4G9/e7PYGimGjc+NOC9ZSykk9wKGzW4CJZ/ZhE0xsIW6DP6g1SSvYe3sPqjT/x/cb9nDqpAR8BoKgmWl3TkX5dbqR7+55UKu/mlluRnYnEnvIU5uDJmALew56qz6k1A4OrkVIXGIRQadRoGVu2tODAgaG0bPmHz0XRnHpKMzl48MH89ZSykkdwKErWABDsGEG6stbrekp2h50tuzfzw4bV/PTHT8RcylI89g+gdTvo3aUmfVotIySonFd8yAvN3gF72p2Y/D9HszdDs13nU/sGBlcrpS4wAPj5RdGkyQoslkq6KWVGRQ0jLm4dR48+R/ny/QgOblbwTXkEh6JkDd7UU0pJS2Hj1vV8t2E1v/+9lpTk+MzXQsMq0KN9T/p0vpFrm12Lzf8zUtWfCLLpc0rIkTYMxbQfRJwu9g0MrkZKZWAAZ70BnNsbqamHCQz07cAVV39DeHh3goKucf/GXIKD6Y47ipQ1ZO1vSFDfpJzj2QLv2XNoN/7+AdSpXifb8zHxMfy66Re+27Cazds3ZiseR1aOpk/nG+nd6UaaNWierXhs1gYRqA30Sje0e5iwJb0BuPEHZmBgAJTiwODixIlXOX78JVq33uxzPSWTKZioqAcASEs7iZ9flbz1lLKSS3AYcOsdRao1+GvXE2Z7Fb8MTaW8OH3+P6YtfI1f/1xD62va8+HURZw8e5Kf/1jDtxt+ZO++f7IVj+vWbUbfzjfSq1OvHEEkK87TUQIH50gwTSXU/rzP5ze4goJi+gNh2ocjbZiP7RsYXF2U+sBQufJgTp16iz177szQU/JtfwNAauoxtmxpTvXqT+avp5SVK4KDCZg8+oFCZw0AgdqdAEgcaMSgcrlrOCk5kVmfzOGTHz4hsEUfIofPY9ui0fQccRMnThzIvE5RTbRs2oH+XXrTrUMPIstHumc8A4e4QKryE5op0Wt6SgUhTLsw+X+OdNQ16g0GBvlQ6ttD/fyiMvSU9ummp+TvH0358n3d01PKyhXaSgPSFxdKQ+lKYk2Pcck8GEkadoedj79dyvUPdGPloX8pP/hdQjoPwhRSAb/GN3DixAEsfoFc3+km3pzwDn9/toVPXv2IAX0HFjoogHN+Qzn7RI/rKRUGR9owNHsjTIEzDD0lA4N8KPWBAS7rKZ09+wFnzy7xuX1XvSEgoC579w7Aaj3v/s1ZgoNpykQmt/0RgLnLwrA7CudHoHY7NrGf77eMoueDN/Luqi8Jvm0KIb3HYgqpkHmduUI0ra5pz9bPt/Le5NncfH0/QoKKLzcSqA3C33EzieoM0sXmYq9XeEzYkieBVDEHvgTkMvbNwMCg9G8luahZcwrJyXsxmysUfLEXcHtedG5k2VYasOJ2Xip/Fse5OFKfeZkWh1egpCajBQSR2O0WYm8bjq1KdK7LHD1UiUnzanD03F4Cu44htHYbtLQkrBeO40iOxZEUgyM5Bu3iCfYf3Yu5kHIUBZF1XnSi6Q0stk9936Gdpb9BMa9Ds/XyrX0Dg6sAIV1zcK9C2rRpI7ds2VKke/OduuZFTp9+n4SETdSvPwdF8SvczdOnwzPP8AvdaM8mzNiwcHmovVRNSJOZ05Nmk9L2+sznrTYrE96eyPe/fokQCqFVqmJPiSctIQWT2UJYWEUqRFSickQlqlaIJKpCJNFVatK9Qw8Pvevs2MW/KLICCp4RPWywydmj8WPzn92+R6j7kY4GoKN0iIGBN7jlrn5n0qwpVYqzhi4ZgxAiDFgANAUkMBQ4ACwHagLHgLuklLHesH/ixBukph6kQQPf73VHRQ2nSpUHi3bzhAlw6RLd3ngj119nwmFHOOxUeXkMx+euyswcNE2jVlR1Jo6cTMWISpSPULBEvk2t0KmU82td9DdTRFzNdpJ00sXf+MsuPvdBOhoCIJTjSMygFev/kYFBqUKvGsM7wI9SyoZAc2AfMAH4RUpZD/gl47FXcDgSOHPmfd3qDQDJyXvYvr174eoNzhsRBYjMCbuN8C8XZj729/PnkUGPcv+tQ7ipax/aNe1N84o/6BIUspKoziTGPFSnegOADXPwBMyBL2LUGwwMLuPzwCCECAW6AgsBpJRWKWUccAvg+k29BLjVWz7UrDmFsLDrOXhwNMnJe71lJl+kdJCQ8Af79g3K1h9QIEuXgpb/9cJhJ+TXr/O/BoHESrz6IinKSvfte5BgxwhUqhFrHouDGB08MGNPeRTFdBhTwDwd7BsYlEz0yBhqAxeAD4QQ24QQC4QQQUCklPIMQMb3XFXWhBAjhBBbhBBbLly4UCQHXHpKqhrMnj134nAkF/GtFB2nntK7xMau4cSJae7fmOReY5uS6s57UrApu4g3TcIu/nXfBw+hEEqEbRYaMcSZxiMpRID0EC49JdXvGxTzOp/bNzAoiegRGExAK2CulLIlkEwhto2klPOllG2klG0qVqxY8A154OpvSE09RGzs2iKvUxxc86KPHn3O/f6GYPf6F7SAghv5XHpKAkuJmBedrC7wuX3I2t/wJiindfHBwKAkoUdgOAWcklL+lfF4Bc5AcU4IEQWQ8b2Qm++FJyKiJ9dee4QKFfp621SuZO1vOHXqHfduGjQIzOZ8L5GqicRut7q1nEtPya7sJ970kns+eJhAbSDB9ofw07rpYt/V3+BI7wuaPseZDQxKEm4FBiFERyHEvUKI+11fRTUopTwLnBRCNMh4qjuwF/gGGJzx3GDAJxvf/v7VAbh06UeSk/f5wmQ2TKYQmjdfQ+PGn7p3w/jxBQcGIYi9zX09INe86FTlK+yccvs+TyEQhDqexCzrIpFI0gu+ydPISBxpI3AO9DEK0QZlmwIDgxDiI+ANoDPQNuOrTTHtPgJ8LITYCbQAXgGmAz2FEIeAnhmPfYLDkcz+/UMy6g0pvjKbib9/DRTFgs0Ww/nzK/K/uE4dWLECAgNzBAgrZiTOU0kBu/4ulA8hjsepaPsOE9UK6b1niTc9Q4xplC71BgCUM1hChhr1BoMyjTsZQxugk5RytJTykYyvR4tjVEq5PaNO0ExKeauUMlZKeUlK2V1KWS/ju8+OqahqEI0afURKyl4OHXrYV2ZzcOzYi+zde3fB9YabboKdO2HECAgNRSoKiUoo8xnBh53nI4DItycQuvpzt20LTJn9BanKKl3qDQBmrYmuekpoFZEyPKPeYOgpGZRN3AkMu4HK3nZEb/TWUwKoVeulLHpK5/K/uE4dmDUL4uMRDgdfL47nEWYx6diDnBk3HSFloYMDgE3sI9b8sI71hkH4O/oYekoGBjriTmCoAOwVQqwWQnzj+vK2Y3qQtb8hLe2Ez+279JTs9tiM/gb3VfIGDIB69eDUKfigwtNcGD+tSMHBLBsRbB9FivqJLv0NLj0lXfsbMvSUjP4Gg7KKO4HheZzNZq8AM7J8lTpc/Q11676Fn191XXy43N/wMydPvuX2fSYTTJ7s/HnuXLgwdEKRg0OI43EsWmtd+xvCbTMBhy724XJ/g1CPYWQNBmWNAgODlPI3YD8QkvG1L+O5UomfXxRVqoxACFHwdo6XiIoaTu3ar1G58n2Fui9r1vD11xA7omjBIXt/wyNI7EV4F8XDIpsSaf0dP1nccw5Fx5E2DFvS6zhPKhkYlB3cOZV0F/A3cCdwF/CXEOIObzumN0lJO/nrr3qcPfuhz20LIahR40kslkg0zY7dHu/WfVdmDXZ70YODShRhtrcIcTyK0EmdXeCHRCNJXaBbvQFUELGoAbMwMgeDsoI7W0kTgbZSysFSyvuBdsBk77qlP0FBTQgJac3Bgw/pqKck2b27H3v23Om2ntKVWQMUPTj4y64EaDcCoJFYlLdQbCSpJKsf66inBIp6AJPf15gC3tPFvoGBr3EnMChSyqxdyJfcvO+qpiToKQkhqFDh9kLpKeWWNUDRgwM4j6+es1ynU70hiHDbTJ31lNpn6CmtRDGX2l1UA4NM3PkF/2PGiaQhQoghwPfAKu+6VTIoCfOio6KGUanSwELpKeWWNUDRg4NFa4lA6KanZMyLNjDwLe4Un58E5gPNcM5OmC+lfNrbjpUUXP0NQpgKdXzUU1zWU6rn9rzovLIGKFpwKBl6Sq7+hrdxoMehgMv9DcYRVoPSjltbQlLKL6SUj0spx0kpv/K2UyWNmjVfoEGD+Qih6mLfZAqmSZPPMJnC3R7sk1fWAEULDi49Jb37G8rbPkQl0uf2AZCR2JKnYk95Uh/7BgY+Is/AIITYkPE9UQiRkOUrUQiR4DsX9cc1dS0paQe7d/9Pt/kNbdvuIji4qVvX55c1QNGCg7O/oR0Ocaaw7nsEhVD8ZDsArGKHLvUG6WgMMhSwIdRDPrdvYOAL8gwMUsrOGd9DpJShWb5CpJSemeJ+lWG1nufixZW61RuEUNC0dA4detStekN+WQMUPjgITJS3LSXEMaqI78AzWMUOLppv009PCTAFzMEcPN6oNxiUStxVVy3wubJASdBT0jQrMTGr3ao3FJQ1QNGCA0C62EiC+nqR3kNxMctm+Gt66imBPe0eQ0/JoNTiTo2hSdYHQggToO8UeR3Re150Tj2l/LdTCsoaoGjbSunKRpJMc0uEnlKoHv13hp6SQSkmvxrDM0KIRKBZ1voCcA4fDdEpiWTtbzh58g1dfCjMvGh3sgYofHDQX08pJHNe9DMNQfjcA2NetEHpJb8awzQpZQjw+hX1hfJSymd86GOe2O3xpKf7vhDq5xdFixbrqF9fv05Y17zoEydew2a7lO+17mQNULjgUHLmRU/h7xiQPrfuxJE2DIe1B9JRQycPDAw8jztbSX8LIcq5HgghwoQQt3rPJfdJS/uXffsG6tJfEBTUCEUxY7VeJCbmZ5/bd/Y3vEerVn9hNpfP91p3swYoXHDI2t+QohRu7oOnCNIG8NVp1yPf/zsAE/aUCUitto4+GBh4FncCwxQpZaaKm5QyDpjiNY8KgZ9fDeLi1nLsmD5NVwCHDz/K7t236FRvCCYoqCFSSi5e/C7feoO7WQMULjj4a9dT3voZgdqgIr4Lz3BtBJhDRoJwT3DQ82iYAmZgCpitk30DA8/hllZSLs/pI7d5BWZzeSIjB3P8+IvExv6iiw916szQVU8JIC5uLbt398u33lCYrAEKFxz8ZBsEAjsnsXOsCO+g+FyyglD+wxT4KugyL1pBymCj3mBQKnAnMGwRQrwphKgjhKgthHgL2Optx9ylfv3ZBAY2ZO/egdhsvlffLAl6SmFhN1Cp0r0F6ikVJmuAwgUHiZ1L5vuJMY/Wpd5wOAnsqQ+hmv9G9dNnW+uynpIxL9rg6sadwPAIzoPay4HPgTRgjDedKgyqGkSTJp9Tq9YLmEzhuviQtb/h3LllPrd/WU+pbr79DYXNGsD94CAwUc4xRVc9Jc3aD4f1OlT/hQh1tw4eGPOiDUoH7ojoJUspJ0gp20gpW0spn5FS6rNnkgdBQU2oUmUkQghstjhdfKhZcwo1ajxDeHgPXexn72+4DylzP6dT2KwB3A8OeuspgcCe8jholVHMm3SwT2Z/g1DPINSj+vhgYFBM3Ol8XiuE+PXKL184V1ji4/9g06ZoXeoNQqjUrv0KFkslNM2Ow5Hqcx+Cg5tRv/58qlYdnanvdCVFyRrA/eCgd38DBGFNmo0jbbgOtp1o9g5YE5YiHQ1088HAoDi4s5X0BPBkxtdkYDuwxYs+FZng4Ob4+VVl796BpKef1cUHTbOzY0cPDh3SZ7etcuX7qFDhFoA8g1NRsgZwLzi4+hsCtNtQZOWivIXiI0Ocvij/olh+0NEHiWJZadQbDK463NlK2prla6OU8nHgWh/4Vmhc9QaHI4F9++7Vpb9BUUyEhXXVVU8J4MyZxfz9d0Os1pyzC4qaNYB7wcHZ3/ACCoFIHffZVf/PMAW8hVB36eOAiMPkv9ioNxhcdbizlRSR5auCEOJGQKePggUTFNSEevXmEBe3luPHX9bFB731lABCQlphs53P0FPKGSCLmjWA+9tKDs5ywdyXFOWbIryD4mNPeQS0ypiDXtGnv0GGZ9FTMuZFG1w9uLOVtBXn1tFW4E9gPDDMm04Vl6ioIURGDsZqPZ9nEdabZJ8XfRcOR4rPfbisp/Qzx4/n7G8oTtYA7gUHhQoolCPeNFG3eoMtZbLzk7tO/Q2X9ZSMedEGVw/ubCXVklLWzvheT0rZS0q5wRfOFYeGDRdSv/7sPIuw3sbV3yCllfT00wXf4AVcekrHjk3Jtb+hOFkDFBwcSoKeknTUy+xvUCxrfG4fruhvEEm6+GBgUBjyU1e9Lb8vXzpZFFxjOBMTt7F//zBd6g0RET1p23YPgYF1fW4bLvc3BAY2JClpZ47Xi5s1QMHBoSTMi9as/bAlP4Vm7aaLfVd/gy15MshgnXwwMHCf/DKGfhlfw4CFwMCMrwWAvsI4hSApaQdnzy7STU9JUcw4HGkcOjRWt/kNbdr8Q7VquXdlFzdrgIKDg6u/wSZ2o+H7bTUQaLZegNlZa9Cl3hCJtLdxeqOc8r19A4NCkJ/s9gNSygdwKho3llLeLqW8nSsG95R0XPUGPfWU7PZYzp//VDc9JUXxAyAmZg2nTr2b7TVPZA1QcHAIcTxOBdtnKAQWzYBHsGMOflRHPSUQpq2YQ4YaekoGJRp3is81pZRZhx6cA+p7yR+vkFVPSY/+hpKgpwRw7tyHHD48Lke9wRNZA+QfHAQmBH5oxBOvvqJLvQFMONJvz9BT+kwH+yDtzZGOBoaekkGJxp3AsE4IsVoIMUQIMRj4HljrZb88Stb+hpMn9ZlTnH1e9Ie6+FCv3pxc9ZQ8lTVAwZmDVewk2bSgBOgpLdKpv8HQUzIo+bhzKulhYB7QHGgBzJdS6vext4gEBTWhRYvfqV37Vd18cPU3HDnylC6SGfnNi/ZU1gD5Bwd/2aXE6CmZg6bqVm8w+hsMSjLuZAwAfwC/Ar8AG73njncJDW2DopiwWi+QkLDZ5/Zd/Q0tW/6Gqgb43D5knxd94cKKzOc9mTVA/sGhJOgp2VImoznqoFetwdnfcA9Sq4x+g0kNDHLHnc7nu4C/gTuAu4C/hBB3eNsxb7Jv30B27eqnW70hMLABUkpiY9f53D44+xuuuWYVFSveme15T2YNkHdwyNrfEG96vviGioB01MOePBVkOHr9YnakDceRficgdPPBwCA33MkYJgJtpZSDpZT3A+1wiuldtdSt+5auekoAFy6sYMeOG3SpNwghKF/+JoQQpKYeyaw3eDprgLyDg0oUEbb5hNlmFN9IcRCxmIOe0k9PCVBMmzAHPYVRbzAoKbg12lNKmXXyyyU37yuxZNVT0qu/oWLF2yhX7joOHnyI5OR9uvjgcKTyzz+dstUbPJ01QN7BwSJbo1IRiQOb0OfPAGlBKOf0qzc4nUAxb8MUME8n+wYG2XHnF/yPWU4lDcF5KmmVd93yPtn7G3w/XkIIlcaNl6GqQRn9Db5v/FLVAGrVeonY2DWZ86K9kTVA/jWHBPVVLprv0llPKb4E6Cl9Y+gpGZQI8g0Mwik09C7wHtAM58mk+VLKp33gm9epX382VaqMJiiomS72/fyqZPQ37NWtv8Glp5R1XrQ3sgbIOzgEOx4oMXpKevU3XNZTmmH0NxjoTr6BQTqlSb+WUn4ppXxcSjlOSvmVj3zzOqoaRP36s7BYKqBpNp30lHpRu/Z0KlT4n89tQ+7zor2VNUDuwaGk6Ck5rNdlDPbRY6//cn+Dai6RAxINyhDubCVtEkK09bonOuJwJLN9+/W61Rtq1HiKChX6AqBpNp/bd/U3lC/fH1V1irx5K2uA3INDSZkXbUuaDVh0sA/ISKyJ7+FIv2qkyAxKKe4EhhtwBocjQoidQohdQoicUp1XMaoaREBAPV31lAD++28uW7e21UVPKTi4GQ0azENVA5HS4dWsAXIPDiGOxwlw9Mckoz1rzG2CMtRPrSiWb9Clx0FWAgRCOY5i+tv39g0McC8w3ATUBrrhVFvtm/G9VKG3nhJAQEBdkpN36qqnlJr6L5s3Nycu7jevZg2QMziUW/0V4fa3scgWAEidms8U8wbMge+i+uU+mc4XmAJmYwp62ag3GOhCfvMYKgkh3gZmA6OAWCnlcdeXrxz0FSVhXrRTT2mirvOizeZKSGln794BaNp5r2YNkHvmIJHEqy8Tb9KnXUaz3ZChp7RQt/4GW8p4Q0/JQDfyyxg+BJKBmUAwztNJpRpXf0N6+knS088UfIMXiI6ektHfoM+8aJMpmCZNPsvUU7rnHs2rWQPkljmsQGDRvd5QcvSUjP4GA9+SX2CoLKWcKKVcnSGap8+ZTh8TFTWENm124u9fTRf7imKiceNlmEzlSEj4UxcfsuopnT49zetZA+QMDlV/qFEi9JQQ8ZgC3tbB/hX9Daa/dPHBoGySX2AQQohwIUSEECICUK94XGpR1QAcjlQOH35CJz2lKrRrd5CoqGE+t+3C1d9w6dIq7rnH7vWsAbIHh8pvTaT6z730729IeQpH2hCf23bhSBuGPXUEmr2lbj4YlD3yCwzlgK1ZvkKBfzJ+3uJ91/QlLe04p0/P0a3eYDI5j41euvQj588v97l9IQQNGsynRYu1mM0mn2QNkD04VJs+nSp/3YpDnMAq9Nnr12w3ILVoQIKI1cEDE470uwALiCSMeoOBL8hvtGdNKWVtKWWtXL5q+9JJPQgKaqi7npKUkpMnX2P//qG66CmpahCKYsFmi6FTpxepX1/zetYA2YNDnWcXU2f1E/hJfVtpVP9FWEJG66inlIol+CFjfoOBT7iqxfC8jd7zooUQNGr0MaoarJueEsClS99x4sQUXn3Vqafk7awBsgeHqq+9ROjqz0lRvtCp3gCarSuIOB3nRQfgsHVG9VtpzIs28DpGYCgAV3/DwYOjdNlSujwvWj89pcjI+6hU6V7Cwp7j5pt/80nWANmDQ8TCp0nUphh6SvZGxrxoA6+TXx/DKiFETR/6UiJx9jd8wTXXrEIIVRcfLs+LXqSTEuxlPaVx4wYQFnbeJ1kDXA4OlgRoNCWlROgpGfOiDUo7+WUMi4GfhBAThRBmH/lTIgkKakRgYD2klCQk6FN3r1lzCo0bf05Y2A262HfpKZnNsUyYMM5nWQNcDg4V/oLqy9C9v0E66iGE72d2A5n9Dcgg0MsHg1JPfsXnz4CWOE8jbRFCPCGEeNz15TMPSxCnT8/jn3/a6VRvUKlU6Q6EEKSkHNal3hAc3IwmTb6gWrU3Ad/UGly4gkOthRC6CxLE0ziI8Y3xbARhS5qFZm+ng20nmr0DtuQ3QJbTzQeD0k1BNQYbzu5nPyDkiq8yR+XK9+uup2SzXWLr1ja61RvKl+/D3XdH0qCBHU077LOsAZzB4dK4aTR+ERq9YCV8tV6Ch84ZzarfZ7rVG0CAiMUU+LxRbzDwOPnVGHoD24FAoJWUcoqU8gXXV3ENCyFUIcQ2IcR3GY8jhBBrhBCHMr6HF9eGpykJekpmc3mqVXuUs2cX6TIvGpxT3t54YxTvvNOVjz8+77OsAZzBIXHwNCpugMi3J+C/Xr/jm0I9gOq/QMd50VYU0w6j3mDgcfLLGCYCd0opJ0gpvbFvMRbIejh/AvCLlLIe8EvG4xJH9nnRL+riQ82aUwgLu17XedFdujxKaGgsQ4YM4uuvfXt807WtFN9EcvS6V+leyafmMyhpekpGf4OB58ivxtBFSrnHG0aFENWAm4EFWZ6+BXBJii4Bbi14JYlzyJxviYoaQrVqjxEa2t7ntsFZb2jUaJmu/Q3lyjUjKeld2rZdw3//TfNp1gDO4GDt/TIh++HxelA9wLf2nZSkedErjXnRBh5Drz6Gt4GnyP4/KVJKeQYg43uunwOFECOEEFuEEFvi43dz9uwHXnc2N+rWfYvy5W8CQErf/0Jw9TeUK9cR55637+nXbzh//XUvt932HL/+6vtfSnEPTqTyuQnYJExpDFG/futzH1z9DYppC0LVJ3tz9Teo/h8Bvt/eNCh9+DwwCCH6AuellFuLcr+Ucr6Uso2Uso3Z7MehQ2NIStJrjxdOnpzBzp29dZvf0KDBfFQ1QJfMyWwWVK06jy1bevHZZ0E+zxoAku6fxiv7oU4w+JnfocrPP/rcB83aD1viPKSjic9tOzFhS56CLWkGoE+vjUHpQo+MoRPQXwhxDPgU6CaEWAqcE0JEAWR8P1/QQgEBtTCZwti79y7s9iRv+pwnJlN5YmPX6KanBJCcvI+tW1vrUm+4554QFi78gfXr2/D11+gSoP6OgaXHwXIJmsx5Q4fgIJCaUz5MmP7Rqd5QIeP4qg3FvN739g1KFT4PDFLKZ6SU1aSUNYF7gF+llIOAb4DBGZcNBgrsYBLCTKNGy0hJOcihQw/pVm/QU08JwGQqR3r6KV3qDa7Z0IriIDn5YRISXvGpfRcLj4EteDyKhKZzZuiSOSBiMQdN1lFPCVTLt5iDXjDqDQbFoiRpJU0HegohDgE9Mx4XSHj4DdSsOYWEhM3Y7XHe9C9P9J4X7edXRVc9pQEDoE4dBSFiSUp6jvR0fX4pHR0ygl3P38nOVyWNFuiQOchw7Kkj9dVTsvbP0FOaYfQ3GBQZXQODlHKdlLJvxs+XpJTdpZT1Mr673dYaHT2R1q23YDbr0/rg6m/QtFTi4/X5pRgR0StjXrTv+xucWYPgzTfncfZsXWJjB+BwFLgT6BXO3tiT2LZwZIw+mYOhp2RQGihJGUOREULFZArG4Ujh6NHJutQbgoKa0L79USpVutvntl3UrPk8YWHXc+7cUp9vqw0YANWqhTBp0ufYbLHExQ3S5bSWZroOu3kEZ/rB+W5Sh+BwZX+DDrWvLP0NasCCgq83MLiCUhEYXCQlbeP48Vd0qzeYzc6Jp5curdJJBVXNUIL9HiF8e4TVVWv4999mfPDBTNLTN2K37/apDy4clrFoSiv2P20mtZoewcHZ32BPu9spdqcDmr0D9tRRaOm9dbFvcHVTqgJDuXKdqFlzCufOLdWtv0HT7Bw58hR7996rS73BbI5AUcxYrRc5dWqmT20PGAD16sHHHw9jy5YDmM3NfGo/E2HC5v8mmjmIPRPbIKTvg4N01EOz/g9nj4k+KqiO9DsyT0vp5YPB1UmpCgzgrDeEhXXXrb9BUUw0abJcVz0lgLNnF3L48KOcPbuk4Is9hCtrAME771TDZpOkpHyoT71BicIauIKYVks5OGa8LsEBQKh7sITeq6OeEqj+8zAHj8OoNxi4S6kLDEKoNG78MSZTGAcOPKjLllJ2PSV9+huqVRtPuXLXcfDgaJKT9/rMritrOHUKfvzxBHFxI3WrN6BUByE4ev9N7HzpNp0yh5ogQ/TTUwKkvXmGntI8XewbXH2UusAAYLFE0qTJlzRqtNTne+0usvY3JCXt9Ll9RTHRuPEyVDUoo78h2Sd2L2cN8Pbb0YSEvEt6+hqSkqb5xH6uPqVP5VLnH9n79AM6BIeSpKf0jTEv2sAtSmVgAChXrgOBgXWRUvr0E3NW6tefTaNGHxEUdI0u9p39DR+TkrKPo0cn+8xu1qxh9erhBATcS2Kifv0Ndr/nAQtn+/zBgUce9XlwyD4v+nOf2LwSY160QWEotYHBxYkT09i6tbUu9QZVDSIyciBCCFJTj+qmp9Sw4YfUqOE7FfOsWcPcuYKgoHmoal1iY+9F03yTuWRDqYzd/zUU7QCn7jqnS83B1d8glNOA77c3M/sbtFCEckYH+wZXE6U+MERFDdNdTyk19RhbtjTTrd5QufIgLJZKaJqd9PTTPrGZNWv45psQIiI+p1y5OSiKTsc3M/obVPtyjg+qpUNwENhTnsGeOg691HCRkVgTFyPtbfSxb3DVUOoDg8USqbueUkBATSpUuF1XPSWAvXvvYceOnj6pN2TPGkCIZgQE3AKAw6HPWFSHZSx2y+NoaieODhmhQ3AwASCUfzEFzEQfPSUTIFEsXxl6SgZ5UuoDA1zWU9Kzv0FvPSWAKlVGkpKyz2d6SlmzBtds6LS0VZw7V5P09HU+8SEbwoTDMhJEIMgUjg6+X5dtJWHajeq3Usd50Q5Uy6+GnpJBnpSJwADO/oZKlQbg51dNF/slYV50RERPoqMncfbsBz7pb7gya7DbwWLpgqpGZ+gpnfO6D7ki0zCn3oUp/RVdMgdDT8mgpFNmAoOzv2EZERG9AH3mBrj6GwIDGyClDlNtcM6L9mV/w5VZg6I46w2aFkds7CB9GgCFP5p6A6p9OYrtWx2CQ0mbF230Nxhkp8wEhqwcPz6NAweG6ja/oX79uSiKny72XQEyOLg5Utq8bi+3rMFsbka5cu9itf6sW3+DS0/JlP4cQvtXh+Bwub9B9VvuZVu54+pvUCzfIpRjuvhgUDIpk4FBShtnzy7Wrd4AkJS0k23buug2v6Fly40EBzf3ib3cag2BgcMJCLgP3U7oCBM2/7cAC6a0x0Cm+Tw4SEc9bEmv40h7wKt28sORNgxb0ltIraZuPhiUPMpkYNBbTwmcn9yTkv7Rrd4ghEDT0jl4cLTX5zfkljUIIQgLW0JIyESv2s6XjP4G8APp3M7xfXBoCphBJCCUf71qK3dMGT6AUPdi1BsMoIwGhqx6Snr1N5QEPSUhTKSk7OPgwYe8Xm/ILWtwyZWkpa0hNnagbvMbbAHLQYnMfE6PgrQ58CXMwc/qpqeEchpz8GOYAt7Tx75BiaJMBga43N+QmnqU+PjfdfHBqad0v279DUKoNGq0DFUN9rqeUm5ZgwuH4xipqcv001MSCsh4TGnjEZrzU7uvg4M9bYSuekpoVXCk347qt9LobzAou4EBnP0N7dsfpXz5Prr5UL/+HAIDG/Lff3N1se/nF5UxL9r7/Q25ZQ3gqjfoq6eETEWxb8isN4Bvg4NTT2mUvvOiM/WUjP6Gsk6ZDgzg/MUIcPHiN7rpKTVvvobGjT/1uW0Xzv6GiZw//xmpqce8ZievrEEIQblyLj0lneZFZ9FTMqW/kvm0L4ODZu2Pw9rV6G8w0J0yHxgAHI5kDh4cpVu9wc+vKopiwmq9wLlzy3xuHyA6egpt2+4kIKCmV+3klTVc7m+IJSVFnznFWfWUFNu3mc/7Ljg4+xs0ay+kpk8jpqu/QbN1B8z6+GCgO0ZgwPmp3SlPrZ+eEjiVYPftG6RLvUFRTAQE1EZKyblzy7xWb8iv1mA2N6NixS0EBz/jFdvukNnfYH0XsvR5+C44BGNPfQJkOOBAr/kNjvQ7cR4l1qcR00BfjMCQQUnQU6pV6yXd9ZSSk3exb98gr9Yb8soaAMzmJgghsNuPYLX+5TUf8kSYsPm/jTXgYxDZPzH7tiCdijn4SR31lECYtmMJHWzUG8ogRmDIQnT0RMLDe3Do0BjS0k743H5J0FMKDm7mdT2l/LIGcMqVxMbeS0zM/3SqN0SCUgmkA8WePXvzXXDwR2rhOtYbQDqigBSj3lAGMQJDFpzHN5dSv/48/Pyq6+KDs79hNnFxazl5coYuPtSsOYWwsOu9qqeUX9bgbH57H02L1W9eNKDYV2BOG52t3gC+Cg4lTU/J6G8oSxiB4QoslkgqVx6MEIL09P90qTdUrjyEunXfpnLloT63Da4A+TGqGsTevXejaZ7fZy4oa3DqKc3UdV60Zrotm55SVnwTHErSvGijv6EsYQSGPEhK2sFffzXQpd4ghKBatbFYLBXQNBs2W6zPffDzq0Ljxp9Qq9Y0FMXkFRv5ZQ0AgYHDMvsbrNY/vOJDvghzDj2lrPgiOLj6GxTlBIgYj6/vDq7+BsW0XRf7Br7HCAx5EBTUlNDQ9rrqKUkp2bXrZvbsuV2XekN4eHcqVOgL4JXgVFDW4OpvCA6egMnUwuP23SJbf0POzMUXwUGz9sea+D7ICh5f2z1M2JJew576qE72DXyNERjyoCToKQkhqFTpXl31lADOn1/Opk01vVJvKChrUJQQQkOnoiiBaFqybnpKdssEHObbc33d+8FBAAGAFdV/kU56SgGAQCjHdZMJN/AdRmDIh5IwL9qppzRY13nR5cp1RVH8vaKnVFDW4ELTYrh4sbWO8xseQKrNnA9kao7XfZE5COUUqt/n+ukpAYplDaaA9416QynHCAwF4OpvUNVy6PWfUe950d7WUyooawAQIhyzubW+ekqAmj4Tc+o9OeoN4P3gILXa2FMfytBT+tyja7uLI22IoadUBjACgxtER0+mfv1ZCKHqYt/V32CxVMZu930hGi7rKXmjv8GdrKFE6CkBUm2Gou3PpqeUFW8Hh8vzohci1N0eXds9DD2lsoARGNzANTcgMXErO3ferNv8hjZtthEU1Mjntl1ER08hLKw7NttFj6/tTtaQVU9Jr/6GvPSUsuLd4HC5v8EUOAOnbIaPydLfoPp94Xv7Bl7HCAyFwG5PICbmR93qDUIIHI5UDhwYpZueUvPmq6lefbzH13a31uCaF61pCUgZ53E/3OHKedG54d3gEIQt+Xnsyc8D+mSxmr0DtuQXcKTnXpA3uLoxAkMhyK6ntEgnLzTi43/Xrd7g2k67dOlHDh/2bIBwJ2sA5/yGChU2oCgRHrXvNq550SIsz8AA3g0OUquN1KIBqdNIUNBsnQALiCQQ53TxwcA7GIGhkFyeF/2wbvMb9NZTAkhI2MipU296tN7gbtYghEAIE5oWQ2zsUML1UIdWKmMNXI1m6pHvZd6uOSiWbzCHjNKp3gAgMQc9hTloCka9ofRgBIZCkrW/4dSpt3XxoSTMi46OnkK5ctd5XE/J3awBwOE4RWrqJzzbSKd/yMICgGL7EsW2Ks/LvBkcNGsPffWUEDjS7jP0lEoZV3VgsNvjSE/3/ZE5iyWSFi1+p359/f4juPobTp16G5vtks/tK4qJxo2XoapBHu1vcDdrgMv1hjbhcG8Nj5gvPNKBaluBKX2iTttKLj2lOENPycBjXNWBIS3tKHv3DvCKyFtBBAbWy5i6do5Ll37wuX1w9je0br0Zs7m8Lvb9/Kpk9jecPfuhx9YtTNYQGDicn8/BkJog7HrMb1Cx+b9JXnpKWfFWcHDqKend32DMiy5NXNWBwc8vmvj49Rw7NkU3Hw4ffpw9e27Trd4QGFgPKSUXLnypS70hIqIXrVptokqVUR5bszBZgxCCNw/Bf6lgsr4Kekzfy2NedG54Kzho1n440vsiHTqNBM3ob9BsLUH66eSDgae4qgOD2RxB5crDOHHiFWJiVuviQ926b+qqpwQQF7eWPXtu163eEBraDiEEKSmHSEk54JE1C5M1pDpg0m6w+c+HjJ4TX5O1v0E48i8Eeyc4COypj6HZO2U81iFAykjsKS9kiP3pMx7XwDNc1YEBoF69dwkKasq+fYOw2XwvS1wS9JTCwm4gMvJ+XfWUNM3Orl192L37No/UGwqTNQCcTAWUCiDtCMffxbZfFByWsVj9FyPVpgVe682CtGr5ClPQc+gl4YJIxBz0tFFvuIq56gODqgbSuPHn1K79Omaze+fag4ODPepD1v6Gc+c+LvT9ffr0IS4ursj2hRDUrz+HuLjaVK7cg+bNm9K4cWNGjRqFprn/yyE9PZ0ePXrQokULli9fzvDhw9m713ni6JVX8t8iURQT9erN8aieUmGyBheqbQHm1MH6BAdhQpo6OH907Mm33gBerDmgoJr/1G9etAwAkWrUG65irvrAABAU1JCoqCEAPjuhY7/iI2x09ESio6dQvvxNhV5r1apVhIWFFcsfVQ2ifv05VK0qWLKkMjt27GDv3r18fcVv1Cv9zsq2bduw2Wxs376du+++mwULFtC4cWOg4MAALj0lz82LLmzWAOAwD0KKGpjTHgfN96e1ANDOYE69u8B6A3gnOGjW/jisXXWcF23oKV3tlIrA4CI+fiObNtV0u96wbt06rr/+eu644w4aNmzIwIEDM7eCNm/eTMeOHWnevDnt2rUjMTGRxYsXc+edd9KvXz969epFcnIyQ4cOpW3btrRq1YadO1tiNpfn338P0rlzJ1q1akWrVq344w/n9LEzZ87QtWtXWrRoQdOmTVm/fj0ANWvW5OLFixw7doxGjRrx4IMP0qRJE3r16kVqamqmP82aNaNDhw48+eSTNG2ac7siMLA+FktVqlcfj9lspmPHjhw+fDiH3zExMdx66600a9aM9u3bs3PnTs6fP8+gQYPYvn07LVq04MiRI1x//fVs2bKFCRMmkJqaSosWLRg4cGC+f6bZ50Xvd/vvLi8KnTWIYOz+74BMwJz+JOjRAKhE4TA/kK+eUlY8HxyMedEGxaNUBYbg4Fb4+9di375Bbvc3bNu2jbfffpu9e/fy77//snHjRqxWK3fffTfvvPMOO3bs4OeffyYgIACAP//8kyVLlvDrr78ydepUunXrxubNm1m7di1PPvkkiYnxnDkzmFmzotm6dSvLly/n0Uedk6+WLVvGjTfeyPbt29mxYwctWrTI4c+hQ4cYM2YMe/bsISwsjC++cIqUPfDAA8ybN48///wTVc1bH8dkKkf58jeRkpLCL7+s4Zprrsnh95QpU2jZsiU7d+7klVde4f7776dSpUosWLCALl26sH37durUqZO55vTp0wkICGD79u18/HH+W2XOedHLqFJlFP7+0W79HeRHUbIGqTbE7jcJxbER1abPLyV39JSy4vngEJzR35CEYvqnmGsVDVd/g2L+E0SiLj4YFI1SFRhUNYDGjT/D4Uhl79573epvaNeuHdWqVUNRFFq0aMGxY8c4cOAAUVFRtG3bFoDQ0FBMJufc4549exIR4axl/PTTT0yfPp0WLVpw/fXXk5aWxqlTpwkJ6cZTT31C48bVufPOOzP36du2bcsHH3zA888/z65duwgJCcnhT61atTIDRuvWrTl27BhxcXEkJibSsWNHAO69994838+RI0do0aIF7do1pFmzg3Tr1jKH3xs2bOC+++4DoFu3bly6dIn4eM99qvTzi6Ju3RmoagAOR/777O5QlFqDZroTu3kYmtq52PaLhEtPyY3+BheeDg7SUQ9rwkdothuKtU5xcKQNw5o4D2TOf+sGJZdSFRjAWW+oX38e8fG/c+zY8wVe7+d3+cy1qqrY7XaklJlS2znXD8r8WUrJF198wfbt29m+fTsnTpygUaNGfPGFSlRUDebOvci6dR9gtTr3WLt27crvv/9O1apVue+++/jww5xNYXn54y516tRh+/btbNq0isGDHRl6SloOv68kr/dbHNLSTrFlS7Ni1xuKkjUgBA6/p7JMXbMVy4cikdHfoKk9AfcEnTyeOchwAIRpi27zG5ChgC2j+c6oN1wNlLrAAFC58iAqVx6WMSO48MdHGzZsyOnTp9m8eTMAiYmJuRZtb7zxRmbOnJlpY9u2bQAkJCTSuPEDWCzhzJjRB4fDuc99/PhxKlWqxIMPPsiwYcP45x/3Uvzw8HBCQkLYtGkTAJ9++mmB9wQHN83UU7p48Ztsr3Xt2jVzS2jdunVUqFCB0NDQfNczm83YbIX75WqxVMZiqeIRPaWiZA0u1PRXMaeNAp3mNzj8HgGhgnSvQ9/z20p2TAEzMQe9rJOeEgjTHkwB7xn1hquEUhkYABo0mE/dum8V6ZOwxWJh+fLlPPLIIzRv3pyePXuSlpZzK2Dy5MnYbDaaNWtG06ZNmZzxsXb06NF8/PGXPPpoOCdO2AgKCgScv4RbtGhBy5Yt+eKLLxg7dqzbPi1cuJARI0bQoUMHpJSUK1euwHtcekqXLq0kPf1U5vPPP/88W7ZsoVmzZkyYMIElSwr+RD9ixAiaNWtWYPE5K57UUypS1pCBVGqhODboVm8AEI7tmFP6uFVvAE8HBxP2lEkg4nXTU5L2Foae0lWE0KMhy1O0adNGbtmyJd9rEhL+5r//ZtKgwQcoislHnl1G0+wesZuUlJTZfzF9+nTOnDnDO++8U+B9Dkcy//zTkSpVRlK16uhi+1EUYmJ+YufO3lSuPISGDYs+x8Juh8aN4dAhmDoV7rjD+XyDT5zB/8eb8+i6lhJT+hMo9lXYApYg1XZF9qHIaGexpNyCVCKxBXwGwt+t22otnk/92TOQQrB79HhO9+hdZBcUy0rMgTOxpw7HkX5PkdcpOnbMweMQ6nGsiXNBq6qDD6WfW+7qdybNmlKlOGuU2ozBRWrqIc6dW6qbnpKimHA4Ujh48KFi6Sl9//332Y65Tpo0ya37VDWI1q236BYUwKmnFB09kZSU/fpkDUJg93shS3+D50eTFkgh9JSy4snMwdnfcJ2zv0E5VuR1ik7W/obXMGQzSi6lPjBERg4kKmq4rnpKDkciFy9+XSw9pbvvvpvt27eze/duvv/+eypWrOj2vYriLHxeuvQ9J068UST7xSU6egotWvyGqgYVfHE+FLnWkNnfYENoxe+vKAruzIvODc8FB2d/gz11XMb0N89z4eJ5Bo8cRGJiAgCJSYkMHjmIc+czJrzJSGwpk7CnjOXCxYs8/8pkho4ezAOj7mPugtlu1bHuHzGQ+AR9aiVlhVIfGADq1n0nU09Jr/kNeuspAVy4sIJ//31Kt3nRimLGar3IoUOPFjlzKFatQW2INehXpEmnI6xc7m9QHIXbZ/dccAhCs94ECBAX8HS9oWKFSvTt3Y9FHy0AYNFHC7ipVx8iK0VmXiPtrdEctXjp1efp2P4aFs1ZwoLZi0lNS2Xxx3qNzDXISpkIDC49JYcjlZMn39LFh+zzoj/QxYd69WYRGNhQt3nRAMnJO/jvv1nF0lMqzgklRBBIiWL7XDc9JVvA+9j9Xi/0rR4tSCunsYQO84qe0v/63c6+g/v46tsv2LNvN7f3vzPHNdt3bcPPL56+/1sKyn+oqsrIoQ/x0y8/kpaexk+/rubF6c8z8cUJDB09mAVL5udYY8myD/j62y8zHy9euoivv/vK4++nLFImAgM4+xtattxAnTqv6uaDa1700aMTcThSfW6/JMyLDg/vTnT0xGLpKV2ZNRSedFTrAv30lESwUx5cO4lqXVCoWz0WHLQoNFtbr+gpmUwmhg8ewXuL5jJq6GjM5pw9HMdPHKdu7RbZ9JSCAoOoVLESp8+cBuDfY4d5dvwk5r39Pr9vXMeFi+ezrXFjj5tYs+4n59vRNH7bsJZuXbt59L2UVXweGIQQ1YUQa4UQ+4QQe4QQYzOejxBCrBFCHMr4Hu5p2yEhLRBCJT39LPHxf3p6+QJxzYtu2XIDqhrgc/uQfV70hQtfFnyDF/DEvOisWUOhEf5X6CnpI0+t2r7CZH29UPUG8FRw8K6e0pZ/NhMRXp5jJ47mfoGUQFAWPaV5mU+7Tpi3uKYlQUHBWCwWalSLvlynyKBypcqEhoRy+N9D/LN9C3Vq1yU0tOBj3AYFo0fGYAfGSykbAe2BMUKIxsAE4BcpZT3gl4zHXmH//vvYvbu/bvWGgIA6SCmJiVmtS70hKmoIzZv/QsWKd/jcNmTvbzh8+LEirZE1aygK2fWU5hV9oWLgsIwulJ5SVjwTHFzzoj3b33Dk6GH+2bGVt199l6++/YJLMTmzsho1ojl05GCWedHfkGpbzYWL54mq7DxpaTZbMq9XFAWHljPD7d3jJtb8+hM//bqaXt2LfpTXIDs+DwxSyjNSyn8yfk4E9gFVgVsA197CEuBWb/lQt+7MDD0lfeZFA1y48Dk7d/bWrd4QHt4tY+raAdLTz/jcvp9fFa655jsaNVpa5DVcWUNR0Ux34jD1RbXOAu1k0RcqKkXQU8qKJ4KDc170KNAicH5mKx5SSmbOe4dRQ0dTqWIkd9x6FwuW5GwsbNmsFenp6fy89iccacOwpbVm/oJf6NntRvz93OvxAOh4bWe2bNvMwcMHaN2iTbH9N3Cia41BCFETaAn8BURKKc+AM3gAlbxl97Kekn7zoitWvJ2wsO4cOjRGl3nRAA5HCtu2dWXfvoG61BtCQ9thsVRC0+wkJm4t9P1XZg2Owv5ey+hvsPvPBaV6oe17hCz9Dao1Z4G1IDwRHDRrf+ypTwCWAq8tiB/WfE+lipVo1aI1AH179+fkqZPs3L0j23VCCJ6b8Dzr//idoaOHMXjIacym6gwZNLRQ9sxmM82btqBrx+vyVR02KBy6dT4LIYKB34CpUsovhRBxUsqwLK/HSilz1BmEECOAEQA1atRoffz48SL7sH//cM6eXUizZj8REdGzyOsUFav1HFu2tMBkCqNVq82YTJ6dLOcOZ84s5sCBB4iOnkKtWs/73D7A4cPjOX16Hq1bbyYoqHGh7rXbwTzVuSk9znGGG/snFNkP4TiAVOo6dY18jGL/EU3tCiKwSPd7okNaKEcxBczFljIRpD579Yrla4RyGkeaew2Zmqbx8PiHmPjkZKpWqeZl764OrtrOZyGEGfgC+FhK6aqAnhNCRGW8HgWcz+1eKeV8KWUbKWWbwjR55Ua9eu9Srdo4QkL0SUGz9zeM0cUHl56SnvOiq1cfX2Q9JVMWtZFlCyMKnzVkIBwHMKfeppuekmbq7QwKMgW004W+3yM1B2FHmHbppqcEIJRzmPy/RDGvK/Da4yePM3T0/bRo1tIICh5Gj1NJAlgI7JNSvpnlpW+AwRk/DwZWetsXVQ2kbt03MZvD0TSrLvWG8PAbqFNnBpGR7ovTeZr69Wdn9Dfcq0t/g59fFRo1WlrsedHnTlv4eVX+KrF5IZX6aKbeqNaZ+vQ3AEiJOXVEhhJs4edYFDc4OOsND6Ga/9ZtXrQjbRiavRGmwDcLnBcdXT2axfOWMuKBUT7yruygR8bQCbgP6CaE2J7x1QeYDvQUQhwCemY89gkORzLbtnXWrd5QvfpjRET0AkDT0n1u39XfUKnS3ZhMYT63D5f1lIo7L7rIWUMOPSU9+hsEDsuDhdZTykpxg4Nm7WfMizbQ5VTSBimlkFI2k1K2yPhaJaW8JKXsLqWsl/E9xlc+qWoQQUHNdNVTAjh1aiZbtrQusp5ScXD2N7yLqvrrdlIrOnoKlSsPISjomqLdX9tarKwh57xofeY3FEVPKSvFCw6X+xtUP336XFzzooX6r25jScs6ZabzuSDq1ZtJUNA1uukpAQQFNc3YTtFPTykl5TCbNzfRTU+pYcMPCAlpBVDok1Kjn3B+yi9OrcHZ3zAZTW2NXuqfhZ0XnRvFCw7BWJNfw57ybJFsewLN3gFb4iI0e3vdfCjLGIEhg+zzovXpbygJekp+flEIoeqqpySl5ODBhzlw4MFC3df3tsTiZw2AZr4Th2VMxtQ1HYJDRn+DprZBujkSNDeKFRy0yoAZRAKKeX2RfSgOUnMWlIVpe4H1BgPPYgSGLAQFNaRBg/ew2S5gs50r+AYv4NJT0qu/oSToKQkhMJsjMuoNOedi54XJ5JmsIdMPx9+YU2/Vb35DwPvO/opiBKfi1hxM/kswBb6kU70BIBVz4MtGvcHHGIHhCiIjB9KmzXb8/PSZLuXSUzKbKxap6csTZNVTOnbsJV18qFlzCmFh13Pw4EMkJ+9z+z5PZQ1OQhHaUczpT+mmp4RMwpQ2psj1BihacDh+8jjT336Vi2du85qeknsEYE8Zn01PycD7GIEhFxTFD4cjmUOHHtVNT6ldu/1ERQ3xuW0Xrv6GuLi1umyrCaHSqNEyVDU4o78hxa37PJk1ZNdT0mtetD9Cxhar3gDuBwebzcaHn37EQ+NGsu63NXz13Wqv6CkVhqx6Su70NxgUHyMw5EF6+inOnFnE3r336vKLUVWdHbAXL37L2bNF1xMqDvXrz6V58190mZUNznpHo0ZLSU8/SVLSdrfv82TWcFlP6V395jcUQ08pKwUFhwMH9zPi8YdYtnwJmsNO9+59uPN/d2XqKTn7G/SZd5Ctv0Fc0MWHsoQRGPIgMLBBhp7S7xw79rwuPkgp+e+/dzl48EGd6g0BKIoJq/UC//47SZd6Q0RET9q3P0a5ch3dvsejtYYs/Q2qbVUxFioGRZwXnRu5BYe0tFRmL5zLYxMe5cypY5SvFMWrL77Bkw8/TnCQU6bFqac0DIdVr3kHzv4GR+oQkBV08qHsYASGfKhceRCVKw/Trb9BCEGjRksxmcKKNS+6uMTG/sSJE1N1qzeYzeFIKTl9+n235zd4tNYggrEFfoLdT58GSLjc36A4fil2813W4HBu9hsMHzmYb7/7AoBb+9/Fwnffp/k1La64S+BIHwAyHHAARRvNWixkJA7rbTjHkib63n4ZwggMBVCv3rsEBTXh0KGHdfnEXBLmRUdGDtRdT8luj+Xo0Uns2XOXW/UGT59QQkRkTF07gWL7opiLFQ2HZSzWgJWglC/2Wjtvu5v+jZrRE7iYEEON8pG889pMRj0wogDZa4k56FlMQVPRT0/pXywh96OYCzc328B9jMBQAKoaSJMmX9Cs2WqEDqqbkL2/IS5urS4+XNZT0qe/wWyOyNBT2uu2npJnTyg5MVnfx5Q+Sbd6A0oFkA4U69Ii1xs2/LqaB26/iW/37URVTTyvqBy6dI7rj+UxbS27EzhsnXTVU5JaDaRWDVPgDKO/wUsYgcENAgPrExBQGykl8fF/6OJDdPREmjZdSVjYDbrYz9rfcOTIeF18iIjoSXT0JM6eXeRWf4PHswbA7jcBKaL101MChLYDs/WlQtcbYi5eYPL4h3n56UdJirtEnSYtmPfpNwx46DEs4PZRVqee0nWGnlIpxggMheD06bls29ZJp3qDSoUK/TOnrumlp9S06dfUrfuOz227uNzfMBqrteDGM49nDSIIu//buuopSbVVofSUpJT8uHIFD9x+E5t/X4PZP5CHnpjMzEWfUL1mnSL0OXh3XrRbZOgpOfsb9DpKXHoxAkMhcAq8NdVVT8lmu8TWrW11qzdERPTCYqmAptlISTngc/uu/oYmTT7DYin4dIo3sgaXnpLi2Ihi/6T4CxYBd/WUzpw6yfhRQ3j75YmkpyTSrF1nFn7+PbfcPQhFufzfv/DBwTkvWspAhIj10LsqHK7+BkQyzoK4gacwAkMhUNVAGjf+XFc9JbO5PNWrP6GrnhLAwYMj2bbtOp3mN0RRvnwfAFJSDhV4vTdqDZrpDmx+L6OZbvPIeoUmW3/DkzlkMxwOBys+/oAH7+7L3n82ERBSjideeI1XZy2gUuXch3sVNjhIRz1sie8jtZoeelOFx5E2HHvK04Ax1tOTGIGhkJSEedF66ymBc+qannpKAHFxG/j770bcGJn/dd7IGhACzXwniACQyeA7lfjLKJWx+b+N3e8554mpDI4dPsiYwXex4O3p2K1pdOzehw+++JEefW5BZLkuNwqfOaiAFTVglk71BhUQCOU4psBpGPUGz3CVBwapy3ZK5cqDqF79KZ8Ugs+cOcOTTz3Nt99e3kt26Snp2d9QEvSUypXrQFhYF8bWg+gCRiV7I2sAQDowpw7EnDYedAiQ0tQBqTYHwJp2ig/mvsPoQf/j2IHdhEZU4vkZc3lu+luEhUe4vWbhg4MN1fS3jnpKIJTTqJZfjHqDh7iqA0NKyn7OnJmvi+06dV4lIqIHgFe2lA4fPszgocOpHh3N/AULaNy4cbbXXf0NYWHdEUIfyQq950W76g2pDni+MWha3v0NXskaAISKw3wviuMPHfWU4MC2VxkxoC/LF81Bc9i58dZ7+OCLH2jftWidyoULDkElSE9ppdHf4AGu6sAghIlDh8aSmLhdNx9OnHiVnTt7eiw4/PPPP/T73x00b92OFb/vQFVM/PTDKurUqZPj2vDwG6hffxaq6o/USf2zfv3ZlC/fD5Op+E1XRcHPL4pX9kONQIg/nX/m4q2s4bKeku/nRaemJPPuay8xduQHnD2VSsWoIF6ft4hxE18gKDi4WGsXJjiUrHnRRn9DcbmqA4O/fy3M5vIZ2ykJuvhgsVQlLm5dseoNUkp+/fVXOl/fnet63sQfieGUu/1FRMxxPlv+Cddee22+9ycl7Wbz5ma6zW+45pqVhIS0ANBla29rLCw5DiZLdL72vZc16DMveuumDTxwx82s+nwpQijcPvAmPvogmZZNPHecujDB4XJ/wzIQevx/vNzfYPJbpoP90sNVHRiEMNG48aekph7hwIERutUbnHpK0wrd36BpGl9++SVNW7TmtoFD2R/YlIih7xHYpBtJq15n2otTuOWWWwpcx2KpiN1+SVc9JU2zc+DACI4de0EX+x8eh5BKoxBC5PvvwGu1hox50VKphbcLoInxcUyb/BQTHxlG3IUzVKvTkJkfruDBx95GDS7evOjccD84OPsbbIkzQXrwz7YwyEhsya9jTx2rj/1SwlUdGADCwrpQq9bLJCfvxm6P08UHl55SYfobfv/9d2rWbcDwxydxoc5NlLt/JsHNeiE1jaRvX2H4oLt45OExbq1VEvSUFMWEpll11VMCSEvcyKWj9+dZb/Ba1oCzv8Hm/yEoUZ5bNOv6UvL7mh8YcvtN/PbjSlSzhcGjH2fe0hXUbeCsQTksY9HUznh6n9/94BCE1KIBiWLa5HE/3EE66gIWEEk6Tp67urnqAwNAjRpP07r135jN4brYd/U3SGl3WzIjKSmJCxcvEnTLZALrd0QIBak5SF79Fje0bswbr71aKB9KwrxovfWUXFiTN+dbb/Ba1gDOY6MyHlPqGI/WGy5dOMfEcQ/xyrOPkRwfQ/1rWvPeJ98w4IGRmExZ5kILEzb/BWjmgjPNwlKYbSVh+gdz8CTd6g0ApoB3MAdPNOoNRaBUBAYhFFQ1ELs9iSNHntal3hAU1JD27Y9RqdKdbl3frVs3akVXJ+HP5UjpPHab/Nsi6pYTfLL0w2xdqe7i6m+4cOFzXbKGkjAv2j+kE8GVHiI19ktSYnMfKuPNrMGJitAOe6TeIKVk1VfLGXpHH/7ZuBaLfyAPP/08by9YSrXoWrnflNGroNi+RE2fWiz7V+JucJD2VjisXXXUUwJ76nBDT6mIlIrA4CI5eRcnT87Qrd5gMpUD4MKFr4mJ+SnP6w4fPkyLNteyb/cuEjavJHnr1yRvXUlo7AFWf/8Nfn5+RbIvhEqTJito2vTbAhuZvIWrvyExcTPJyXt08SGk0sNYgtoR/98L2NIO53qNd7MGZ72huHpKp08eZ9yI+3j3ledIT0miRYfrWLjiB/reMcCtDw5CO4rJ9qFH6w3gbnAQ2FPGlyA9JWNedGEoVYGhXLkO1Kr1EhcuLNetv0HT7Bw7NoV9+wbmWm/49NPlXNO8BQf27KRK9Zp89dVXWLd+Dbu/Z93PqwkLCyuWfbM5LGPq2nlOnpyhS4CMihpCu3aHCA5u5nPb4AyQ4dVnINRAUuO+zvUab2cNxZkX7bDbWb7kfR68uy/7t28mMDScp1+ewbR33qNiZGX313FTT6kouBccruxv8P2/xezzon/3uf2rlVIVGMBZbwgPv1G3/gZFMdG48fIMPaXL86LT0tIYNmIUAwbcQ1pKMn1vvY29u7Zz66238vPqVWz8bS01atTwmB9nzy7hyJEnOHt2kcfWLAx+fpUzp66lp5/xuX3VXImKdb4gJDJviXCvZg1k6W+wfQqy4OFCAP8e3M9D99/JB7PewGGz0rlXPz74YhU33Ni38FmgB+dF54Y7wcHZ3zAWLf1mQJ8s1pE2DHv6/9DsjQu+2AAohYFBCIVGjT7CbC7PwYMjdfnEHBTUkAYN3sucF+3aOlr0/nuoJjPvzpzFN1+uoFw559ZTu3btaNCggUd9qF798Qw9pYd101NKTz/J4cNj2bdvoC71BtUShRACe/ox0hJ+zfG612sNGf0N1oAvQOSv2WFNT2fBrDcZc/9tnDi0l7CKlXnx7flMmvoG5cLcl7PIQca8aKEdRLHn/DMoLu4EB83aG83eKeORHnv9JhypYzJmRTsAmw4+XF2UusAAznP9TZt+TePGy3Xba4+MHEhU1HAWL3mFps2bZ24d/f3XJh55eIzX/SoJekr+/jV011MCiD8zndgTj2NLO5LjNW9nDYjgjKlrdudI0FzqDbu3b2HY3f1ZseQ9pKZx0+33sujz72nX6TqPuKCZrsMW+B2auY9H1rsSdwvSiuVHLCFDddNTAodzLGnAXJ3sXz2UysAAEBraloCAmkgpSUra6XP7aWlpvPoGvPSiJD0lJXPrqFWrVj7zIWt/w7Fjk31mNyt66ykBhFV9EaEGEntibI7+Bu+fUHKiONZhTn82W70hJTmJt6e9wBMPDuTCf8eoVK0mb76/jLETphAYVDw5iyuRSl0AhGMnQnNnhGfhcG9bqQ4ol3TTUwIVzVE7o96wTgf7Vw+lNjC4OHHiFbZubefTeoNr6+iDBQsyt44+XTqNkJAgn/ngIjz8Bho3/oTo6Ek+t+3C1d+wb98gHI5kn9tXzZUIq/Y69vTDufY3eD1rADS1e4ae0rsI+1/8tWEdD9zRhx+/XIZQVe4cMooFn35D4+Ze/OAg0zGnjcaUNtbj9QYoODg46w2jSoie0ptGf0M+lPrAEBU1wqd6SleeOvr7r00MH3YzW7e21G1+Q6VKd2E2l0fTbKSlnfS5fVd/Q4MGi1BV3wdHyN7fkBqfXbrEJ1lDRr0hLr4qU58dw5RxI4m/eI4a9Roz+6MvGTZmHJYiHlN23wc/7H5TUbQDhZ4X7S4FBQfN2l/n/gZjXrQ7lPrAYLFU9ImeUl6njlq1akVAQE0iI+/lxIlXdJkX7WLv3rvZsaOnbvMbype/CYC0tFM+tw/O/obQyk/jH5Jz797bWYOUkl9Xr2XQffH8vjYRk8XE0EeeYu6Hn1O7XkOP28sLzXRdlnnR33nFRv7BwamnJLUqCDVnzccnZPQ3CCUBoZzXx4cSTqkPDHBZT8lb/Q0FnToCqFv3XYKCrtF1XnTVqo+QmnpINz0lgEuXvuevv2rrNr8huOJQhOKP5khC01IzX/Nm1nDh7BkmPDqC1yY/QUpiAg2b1+f9ZW9z1/3DUE2+n6Vxub9hMmjeySDzDw7B2BLno1lv9Yptd9DsHbAmLEZq1XTzoSRTJgIDOPsbIiMHExBQz6Pr5rZ1lNupI1UNoHHjz3L0N/gSp57S87rqKYWFXU9AQF1d9ZSklsbFI3eScEW9wdNZg6ZpfPP5Mobd2Ycdm37HLzCYR599ibfe/4ao6J4ZzsQV206hyehvcFhGgsh9/rMnyD84WDJc2YJiWek1H/LHAthQ/RcY9YYrKDOBwdnfsJjwcOdEq+J+Ys5v6ygvXP0NwcEt0OdUBkRHP0t4eA/d5kWXBD0lofjjX643KbFfkBL7debznswaTh0/ytjhA5nz2gtY01Jo3bkbi1asos//7sr80KBa52NJ6euz+Q3ZUCrjsIwCoYL03tZiQTUH1fIjpoDZ+qmgijhUy/dGveEKykxgyMqxYy+yb9+gIgcHd7aO8iIyciD16r2Dolh02c5xjsNcSmhoe/TqRC0J86Iv6yk9n01PqbhZg91uY9kH7zHynv4c2vUPQeUieHba27z85hzKV4zMdq2mdi22nlJxEdpRLCk3elxPKSv5BQd7ymM66ylVzKKnZMyLdlEmA4MQZs6fX1akeoO7W0cFkZi4jX/+uVaXeoPFEkmLFmsJDm7qc9suoqKGULnyMN1OKWXVU8ra31CcrOHQ/j2MGng7H855E4fdynU33criL36ga4+bcv334dRTmlwkPSVPIUV1pKjhFT2lrOQdHIJL2LzodT63XxIpk4GhKHpKRdk6yg9FCSA5eS979w7Qpd4AoGnp7N8/nDNnFupiv0GD96lR40ldbMPl/gZFDUVm6a8obNaQnpbGe++8zqOD7+TUvwcIr1SFqTMX8syLrxJSLizfezXTHThM/Zz9DT6eFw14XU8pK3kFh6z9DYp5g9fs50dmf0PAbCBdFx9KEmUyMGTVU3Knv6E4W0d5cVlPaT3Hjj1f5HWKgxAm0tKO6aan5PoUfenSKvbsuVO3+Q3lay9DNVfMfK4wWcPOrX8z7O5+fLV0AVJq9L3rfhZ9/h2t23d2zwHXvGilEUK7WJy3UnQy9JS82d/gIq/goFn7Y0t6Gc3Wxav288bZ32BLehXwcj/JVUCZDAxwub8hPf1UvlPXsm4dRVWP9qjWkUtPSa/+hpKgpwRgtZ7nwoUVutUbhBBo9lhijj+aWW8oKGtITkpkxsuTeWrUfVw8fYLIGrV5a+GnPPzkRAICC7k9JoKwBazwmpaRO7j6G5AXQXpXZC734CDQ7Bl1L+W0bvMbpFYbAKHu9739EkSZDQzg7G9o3/4Y5cv3zvFaWloaQx8cmW3raN+uHR7XOnL2NzTlzBl95LFLwrzokqCnJKUNa8qWzHpDflnDn7//wgO392HNys9QVBP3DBvD+5+spNE1LYrugFBAShTb56jWBcV7M0XEYXkMu/9sEOaCLy4medccUrEEP6qjnhIo5nVYQh5GMf+mi/2SQJkODAAWSyUALlz4IrPecPjwYZq3bscHC+Z7bOsoL1Q1gGbNfqJx42UeX9tdXPOiL15cSVracV180Hte9GU9pSOZekpXZg1xMZd4/umxvDB+NAkx56nV8BrmfPw1Q0Y9isVi8YgfimMTqnWGTvUG1TkWVDuJKW2CV+sNkFdwCMCedr+uekqarXOGntKMMtvfUOYDA4DDkcyhQ2PZu/culi1bzDXNW3Bw7y6fyWT7+VVGCJX09LOcPbvEa3byIzp6Im3b7iYgoKYu9rP2N5w9u1gXH7LPi/46S9YgWThzFUNu782mX3/EZPHnwceeYdbi5dSs48GGSVe9QdTwyLzoIruhHUW1f+X1egPkHhw0az8c1usMPSUdMQIDzl9KtWsv5oWXjzNw4AMeOXVUFE6efJ39+x/Qrd7g718DKSVnzizWTU+pTZvt1KjxtM9tu3D1NySen4uUNlq13Y9/SE8S4oaRlpRA41btWfDZd9w+cAiqqnreAQ/Niy4O0tQ1i56S9/obXOQMDquxpzxeguZFl735DUZgwLl1dF33x/nhOyuKSeGll+/x2tZRftSq9RJBQU101VNKTt7FgQPDdKs3BAbWRwhBSsoB4uM3+tT2kUNHWDRnCeHV3ySi1lI+nP8JfbrcTFriL6CGEho2n9dmLaZy1epe9SPrvGjh+NOrtvLCm/OicyNncFiPLWUymu1akPqcEnL2N9yHZm+pi309KfOBwXXqyLV19PFH19Kl81ekp+shTx1I48afZ+gp6dPfEBzcjJo1p+iqpySlZN++wezefbvP6g2HDxxmQL/BvPPGfJYuXMWdfR7mlYlTsaWl0rV3L6pV3UVC3IP88oNvPixopjuxBqxAmjoVfLE3yNLfoFrf8YnJK4ND1Ooj2FPHAf44R3L6HkfaYDRbV9cjXXzQgzIbGHI7dbR313Zuu20lDRsuwt+/hi5+BQU1pH79ecTHr+fkyTd08SE6emLGvGh99JSEEDRsuNBnekoH9x1kQP/BmNvfT1jfJ5k25f/tnXl0VfW1xz/7DklIwpQqyByeoMjUCC70CRVHBsuq0ifrUaA1TrTigK+oxcezyuparVWRWp9oKVZ40IJPSy211LaKBTsIgobIlALmCTJTJAQIGW72++OcS++NSQgh95ybe/dnraycc3Lu2b+zc+/Z9zfs7/4hW4uKaNuxHbNnw7PPXct9M52VOoms8haHCBoc5GxGinzTU6pu8zI1mT/wzGS9E9KBvYTbftM/PSUgkLGScO4DpMt8Q1oGhsZWHWVknE/nzpMAOHXqE1+GUy64YAp9+86ja9epntuGuvkNE33puXilp1SypYTJNxWScWUhOQOuIavnYNoPn0z33vm8te73XD92GGV7ZjPmyx8mvMpbvWgZ4Yrb/ZtvCPYHyQY9iUQ+8MRm3eBwwar3Ear8m28AqO1IILSVUJsX/bHvMWkXGJYuXXZ66KixhLXjxzeybl2/hNRvaArdut1NOJxHbW0VVVXeZ8RmZHSmf/9l9Okzl0DA+5oBEJ/fcPRoy0slbNu0jck330bGiDvI6X/16eO5BWM5eOAwO0o+Pq2ndGzPA9z7kDO86FmvAUDaU5M501c9JYBQ5fcIV9zhyXwDxAeHwT/+bzq8c12S6CmtSIv8hrQJDNGho0mTvtakhLWcnEG0bz/yrPSUWhpVpbh4LJs3/5sv39o7dBhJXt4oAF+CEzj5Dfn5j9G27WUtet0txVuYMv42Mr90FzmXOGPI1Uf3c+zPS/hsyXS69+pBKBSKqxc94opZvvQaakMT/lkv2o/8BqAmYzpe6CnFEhscCr6/hNwPR7r5Da96Yr8u/6wXnfr5DWkRGJqTsHa2ekqJQETo0uV2ysrW+FYvGuDAgaWsXdvbt/oN+fmPEQxmUVNT3iLzDZuKNvH1r95O1shvkd1nGCe2rObY8kcpW/Ygoy8O8YvlP+V3775OwWUFgJPf0L7Lf5F73r8nvjZ0fdTNb9AjHhmOwUM9pVhig8PQB98iY/fFBMJ/xZ+J4Gh+Q4hA6EMf7HtHygeGpg4d1YdX9aIbw289JYCOHa8lGMz1VU+puvoI69dfes7zDcUfFHPrLXcSHDCGyJ5iDv6kkB7/eJfvPvwN/rZ5DbOffJR+Az9fgznnvClktBnAuK+Wc9ElR7yfa3DzGyLhSYC3y6ijeFEvuj6iwSGgMOybJZz361FAAnJImoJ2pqp8EbVV4/yx7xEpGxjOduioIaL1ojMzu+KXdovf9aKTQU8pHM6jffsR56SntHHDRqbcXMiJY2UEd/6JiSPzWfnu6yxbsYgbx99IZtaZ18ufPDyXuc9cSVbWCW97DTj5DZGMaW7VNW+Gc+oSyZhOJDyJ2uAXPbUbDQ6hChj0/I+4YPWvCGYuwZfPpLYFQEJFBELe5tp4RUoGhpbWOurZcyZ9+jyDiD/fUqL1orOyehOJ+PONPaqn5OQ3+CP4d656Sk8+/jTDr/kSL/3vAv5SvIrpM++jW49uZ3WNjJxhZGf9nUdm3eN9r8FFIlvIOHk9UrPWc9tIiJrMxyDQA1QTrsQaS+yw0vklzxNqs9A3PSVQQlkLCeX8MCXnG1IyMIwaO65ZQ0cNEX3tsWPr2LjxBl/mG3Jy+jFkyFqysy/23HaUXr1mkZc3hkhMURsvia8XPfms5xt+/pvFvLDoWYZfPZxAoHlv/aie0lUjFjFq1P943msA0EBPlBzClTPArxoOWkvo1H2EKr2VSo8Ghy6/g/PfgVDmS0hwk6dtcBCqTzySsnpKKRkY5jz5BBOnfKPFZbJrayv57LNVvs03iAiRyEm2bbvdNz2lQYN+S/fu93tuO0o0v6G2tpKSknKmTQO+fxQejzAk/0Ief6gTu0oTKxvdttO9hLOH8e1v301maKf3vYY4PaWH/akXLQE00NszPaVYSgunsv2eGVz8NGTtU7KCjyaBnlJq1YtOusAgImNEpEREdojIzOZcY/z4m1m6eFGLax1F5xsOHXrFt/wGEMrL1/s23yDivGUOH/4N27ff71v9hv37VzN0aAcWLACq2gMBThwP8uqS9nzlql6sfis7YfZFguT1nIPK+XTrtsOfXkOMnpJf+Q1e6ynFUlo4lY9vm8GAx0FD5bT77Lue2o8SWy9aght9aUMiSKrAIM4g/vPAWKA/8DUR6e9vq+JpTr3oliQ63+CnnhLA8eNF7NnznC96Sjt3woQJQU6ehOo6Q9w11UJFRYDpt3VNaM8hGO5Ej8G/Ze+B0b7NNUTzG6S2xBnv9xoP60XXR2nhVPaNdoLDkBmbY4r9eEvk1B1Un/gOGhnsi/1EkFSBARgG7FDVj1W1ClgG3ORzm+KIzW/Yu3eeL22IrxftT35Dr17/SceO1/uipzRnzucDQl2qa4SFL3ZMaDvC4TDTHjzMuHHz2bXtTc97DU5+ww+oyZzrFNjxAze/QfQIUrvLc/OlhVM5MmQGmUdgwItP0/lvyzxvA4Sorb4BEJADpMJ8g/gxFNAQInILMEZV73T3vw5crqr31nd+QcGF+t577/gieFdRUUpWVk/fVioBlJTcxaFDv+Tyy7cTDn/Bc/tVVQdYv76AUKgDQ4a8TyiU64nddu2gvPzM5+W2jbChdGdC21JdHWHN63eT3+t9/lq0kmEjuyTUXkOI7iYjspjK4Hec5axeoycdTSWfuHDxfALt5nDkMgi/N539Q8d63gYJlJHT6U6qK0ZSWVbvI8sTJhSO33+q6uQ5vRGTLTBMAEbXCQzDVPW+mHOmAlF1uYGAH0sSko3zAJ+Wp/jB0KFNPjVjw9YENiSGYBBC/ohKRYlE2hEMer9kLokIRGo6BIMhf5bNJQk1VVWdarU261yu4e8b+fN8CsRWQekO7I09QVXnA/MBRGS9qrasiE4rxPxgPgDXBzXVae+DSE1N2vvgXK+RbHMM7wN9RaS3iGQAE4EVPrfJMAwjrUiqHoOq1ojIvcDvccRQfqaqm31ulmEYRlqRVIEBQFVXAiubeLpfyQTJhvnBfADmAzAfQAv4IKkmnw3DMAz/SbY5BsMwDMNnWm1gaAnpjNaGiPQQkXdEZKuIbBaR6e7xPBH5o4hsd38nNrMrCRCRoIh8KCJvuPtp5QMR6SAir4nINvf98K/p5gMAEfkP97OwSUSWikhWqvtBRH4mIgdFZFPMsQbvWUQecZ+TJSIyuik2WmVgaA3SGQmiBpihqpcAVwD3uPc9E3hbVfsCb7v7qc50IDZHId188Czwpqr2A76I44u08oGIdAPuBy5T1YE4C1Ymkvp+WAiMqXOs3nt2nw8TgQHua+ZJE7JyW2VgoBVIZyQCVd2nqh+42+U4D4NuOPe+yD1tEXCzLw30CBHpDnwZWBBzOG18ICLtgKuAlwBUtUpVj5JGPoghBLQRkRCQjZP3lNJ+UNU1QN36rg3d803AMlWtVNVSYAfO87NRWmtg6Absjtn/1D2WNohIPnApsBborKr7wAkeQCcfm+YFPwIeJr58Vzr54F+AQ8DL7nDaAhHJIb18gKruAZ4GdgH7gDJV/QNp5geXhu65Wc/K1hoY6lMMS5vlVSKSC/wSeEBV00oCQUTGAQdVdYPfbfGREDAEeEFVLwVOkHrDJWfEHUe/CegNdAVyRGSKv61KOpr1rGytgeGM0hmpioiEcYLCz1V1uXv4gIh0cf/eBTjoV/s8YDjwFRH5P5whxGtFZAnp5YNPgU9VNVrb8zWcQJFOPgC4HihV1UOqWg0sB64k/fwADd9zs56VrTUwpKV0hjg1Rl8CtqrqMzF/WgHc6m7fCvza67Z5hao+oqrdVTUf5/++SlWnkF4+2A/sFpFondfrgC2kkQ9cdgFXiEi2+9m4DmfeLd38AA3f8wpgoohkikhvoC+w7oxXU9VW+QPcCPwd2AnM8rs9Ht3zCJxuYDFQ5P7cCHwBZyXCdvd3nt9t9cgfVwNvuNtp5QOgAFjvvhdeBzqmmw9cP8wGtuGoLC8GMlPdD8BSnDmVapwewR2N3TMwy31OlgBjm2LDMp8NwzCMOFrrUJJhGIaRICwwGIZhGHFYYDAMwzDisMBgGIZhxGGBwTAMw4jDAoORMrjqs6Uikufud3T3e9VzbkREilxVzldFJPsc7P5JRM66zrCrkDotZr+riLzW3HYYRkthgcFIGVR1N/AC8IR76Algvqp+Us/pFapaoI4qZxXwrdg/NkWBsgXoAJwODKq6V1Vv8cCuYTSKBQYj1ZiLkw37AE5C4JwmvOZdoI+IXO3Wu/gF8JGr7f+yiHzkitVdAyAibURkmYgUi8grQJvohUTkeMz2LSKy0N3uLCK/EpGN7s+VOIHrQrfn8pSI5Ec19huxXSgiy0XkTVd7/8kW8JlhxJF0NZ8N41xQ1WoReQh4Exiljix7g7hyzWPd88GRJB6oqqUiMsO95iAR6Qf8QUQuAu4GTqrqYBEZDHzQhKb9GFitquPd3kgujvDdQFUtcNuSH3P+PQ3YBifr+VKgEigRkefc3pJhtAjWYzBSkbE4kgEDGzmnjYgU4chK7MKtbQCsU0e3Hpwex2IAVd0GfAJchFMLYYl7vBhHluJMXIszzIWqRlS17AznN2QbnIIsZap6Ckcj6XNzKIZxLliPwUgpRKQAuAGnwt2fRWSZujr1daiIflOPeS04EtanDzViqiEtmdjjWWdqbyM0ZrsyZjuCfY6NFsZ6DEbK4CpsvoBTp2IX8BROIZfmsgaY7F77IqAnjhBZ7PGBwOCY1xwQkUtEJACMjzn+Ns4QVLRedTugHGh7lrYNI+FYYDBSibuAXar6R3d/HtBPREY283rzgKCIfAS8AhSqaiVO8MkVkWKcSnKxMsYzgTeAVTjDWVGmA9e419oADFDVfwB/cZfMPtVE24aRcExd1TAMw4jDegyGYRhGHBYYDMMwjDgsMBiGYRhxWGAwDMMw4rDAYBiGYcRhgcEwDMOIwwKDYRiGEYcFBsMwDCOO/wc541JMUbVREQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
    "ax.set_aspect('equal')\n",
    "ax.axis([0, 100, 0, 100])\n",
    "ax.set_xlabel('X Production')\n",
    "ax.set_ylabel('Y Production')\n",
    "\n",
    "# Labor A constraint\n",
    "x = np.array([0, 80])\n",
    "ax.plot(x, 80 - x, 'r', lw=2)\n",
    "\n",
    "# Labor B constraint\n",
    "x = np.array([0, 50])\n",
    "ax.plot(x, 100 - 2*x, 'b', lw=2)\n",
    "\n",
    "# Demand constraint\n",
    "ax.plot([40, 40], [0, 100], 'g', lw=2)\n",
    "\n",
    "ax.legend(['Labor A Constraint', 'Labor B Constraint', 'Demand Constraint'])\n",
    "ax.fill_between([0, 80, 100], [80, 0,0 ], [100, 100, 100], color='r', alpha=0.15)\n",
    "ax.fill_between([0, 50, 100], [100, 0, 0], [100, 100, 100], color='b', alpha=0.15)\n",
    "ax.fill_between([40, 100], [0, 0], [100, 100], color='g', alpha=0.15)\n",
    "\n",
    "# Contours of constant profit\n",
    "x = np.array([0, 100])\n",
    "for p in np.linspace(0, 3600, 10):\n",
    "    y = (p - 40*x)/30\n",
    "    ax.plot(x, y, 'y--')\n",
    "    \n",
    "arrowprops = dict(shrink=.1, width=1, headwidth=5)\n",
    "\n",
    "# Optimum\n",
    "ax.plot(20, 60, 'r.', ms=20)\n",
    "ax.annotate('Mixed Product Strategy', xy=(20, 60), xytext=(50, 70), arrowprops=arrowprops)\n",
    "\n",
    "ax.plot(0, 80, 'b.', ms=20)\n",
    "ax.annotate('Y Only', xy=(0, 80), xytext=(20, 90), arrowprops=arrowprops)\n",
    "\n",
    "ax.plot(40, 0, 'b.', ms=20)\n",
    "ax.annotate('X Only', xy=(40, 0), xytext=(70, 20), arrowprops=arrowprops)\n",
    "\n",
    "ax.text(4, 23, 'Increasing Profit')\n",
    "ax.annotate('', xy=(20, 15), xytext=(0,0), arrowprops=arrowprops)\n",
    "\n",
    "fname = 'LPprog01.png'\n",
    "fname = os.path.join('figures', fname) if os.path.exists('figures') else fname\n",
    "plt.savefig(fname, bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "02.01-Production-Models-with-Linear-Constraints.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}