World_of_Process_Modeling.ipynb

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        "<a href=\"https://colab.research.google.com/github/MJAHMADEE/Industrial_Control_Course/blob/main/World_of_Process_Modeling.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.1 Process Variables](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1-Process-Variables)",
          "section": "2.1 Process Variables"
        },
        "id": "JiecULKV3bhl"
      },
      "source": [
        "# 2.1 Process Variables\n",
        "\n",
        "Of the many ways to characterize chemical processes, thermodynamics offers unique insights that are invaluable in the synthesis of effective control systems."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.1.1 Intensive and Entensive Variables](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.1-Intensive-and-Entensive-Variables)",
          "section": "2.1.1 Intensive and Entensive Variables"
        },
        "id": "KtmDy7MV3bhl"
      },
      "source": [
        "## 2.1.1 Intensive and Entensive Variables\n",
        "\n",
        "One of the first distinctions to describe in the difference between extensive and intenstive process variables. \n",
        "\n",
        "**Intensive variables** are those that do not depend on system size, such as concentration, temperature, or pressure. Examples of intensive variables: temperature ($T$), pressure ($P$), concentration ($C$), mole fraction, mass fraction, specific heat capacity, color, density, chemical potential.\n",
        "\n",
        "**Extensive variables** are variables that scale proportionally system size such as total volume or mass. Examples of extensive variables include mass ($m$), moles ($n$), internal energy ($U$), enthalpy ($H$), entropy ($S$), Gibb's energy ($G$), heat capacity ($C_p$).\n",
        "\n",
        "Roughly speaking, intensive variables tell us something about the state of the material making up the system of interest, while extensive variables describe the size of the system in various dimensions. The same distinction extends to process flows where extensive variables are given as rates rather than in static dimensions.\n",
        "\n",
        "One test that you can use to classify a process variable as extensive or intensive is to ask what is the value of the variable when combining two identical subsystems. For example, given indentical subsystems $A$ and $B$ with masses $m_A$ and $m_B$, the mass of the combined system $m_{A+B}$ is\n",
        "\n",
        "$$m_{A+B} = m_A + m_B$$\n",
        "\n",
        "which demonstrates that mass is an extensive variable. The temperature of the combined systems is\n",
        "\n",
        "$$T_{A+B} = T_A  = T_B$$\n",
        "\n",
        "which is the case for any intensive variable."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.1.1.1 Exercises](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.1.1-Exercises)",
          "section": "2.1.1.1 Exercises"
        },
        "id": "TwB-ufRS3bhm"
      },
      "source": [
        "### 2.1.1.1 Exercises\n",
        "\n",
        "1. Why is heat capacity an extensive variable, whereas specific heat capacity is an intensive variable?\n",
        "\n",
        "1. A common version of the ideal gas law reads $$P V = n R T$$ Which variables are intensive? Which variables are extensive? How could you rewrite the ideal gas law in terms using only intensive variables? When would you prefer one version over the other?\n",
        "\n",
        "1. The kinetic energy of a mass $m$ moving at velocity $v$ is $$E. = \\frac{1}{2}m v^2$$ Rewrite this equation using only intensive variables.\n",
        "\n",
        "1. The fuel efficiency of vehicles is often reported in liters of fuel consumed per 100 km traveled. Is this a satsifactory intensive variable for comparing vehicles of different sizes?  Why or why not?  Another measure is the [brake specific fuel consumption (BSFC)](). What are the typical units?\n",
        "\n",
        "1. Consider a system comprised of batteries. The subsystems are combined by connecting the batteries in series. Is system voltage an intensive or extensive variable? What about the system current? How does this change if subsystems are combined by connecting the batteries in parallel? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.1.2 Thermodynamic State](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2-Thermodynamic-State)",
          "section": "2.1.2 Thermodynamic State"
        },
        "id": "eyNWn-HF3bhm"
      },
      "source": [
        "## 2.1.2 Thermodynamic State\n",
        "\n",
        "A fundamental postulate of thermodynamics is that a system consisting of a single phase is completely specified by the internal energy $U$, the volume $V$, and the amount (in moles) of each chemical species $n_1$, $n_2$, $\\ldots$, $n_K$. This is a system of $K+2$ extensive variables for a system composed of $K$ chemical species.\n",
        "\n",
        "The second law of thermodynamics specifies that every state also has another well-formulated extensive variable called entropy, $S$. Collectively $U$, $S$, $V$, and $n_1$, $n_2$, $\\ldots$, $n_K$ form a redundant set of extensive variables where we can write one variable as a function of the others.\n",
        "\n",
        "Suppose we write $U$ as a function of $S$, $V$, and $n_1$, $n_2$, $\\ldots$, $n_K$. Then\n",
        "\n",
        "$$U = U(S, V, n_1, n_2, \\ldots, n_K)$$\n",
        "\n",
        "The fact that $U$, $S$, $V$, and $n_1$, $n_2$, $\\ldots$, $n_K$ are extensive variables has profound consequences. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.1.2.1 Conjugate Variables](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2.1-Conjugate-Variables)",
          "section": "2.1.2.1 Conjugate Variables"
        },
        "id": "PgNDFV2p3bhn"
      },
      "source": [
        "### 2.1.2.1 Conjugate Variables\n",
        "\n",
        "The total derivative of internal energy is constructed by taking the partial derivatives with respect to each of the independent extensive variables on which it depends.\n",
        "\n",
        "$$dU = \n",
        "\\left(\\frac{\\partial U}{\\partial S}\\right)_{V,\\bf n} dS + \n",
        "\\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n} dV + \n",
        "\\sum_{k=1}^{K} \\left(\\frac{\\partial U}{\\partial n_k}\\right)_{S,V,n_{j\\ne k}} dn_k$$\n",
        "\n",
        "Each of the terms is an extensive quantity contributing to a change in the internal energy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 4,
          "link": "[2.1.2.1.1 Pressure/Volume](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2.1.1-Pressure/Volume)",
          "section": "2.1.2.1.1 Pressure/Volume"
        },
        "id": "In6qP8bs3bhn"
      },
      "source": [
        "#### 2.1.2.1.1 Pressure/Volume\n",
        "\n",
        "The second term in the total derivative $dU$\n",
        "\n",
        "$$\\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n} dV$$\n",
        "\n",
        "describes the change in internal energy due to a change in system volume. If the system is expanding, it is experiencing a loss of internal energy by doing mechanical work dW on the surroundings. The amount of work is the product of system pressure times the change in volume, therefore \n",
        "\n",
        "$$\\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n} dV = -P dV$$\n",
        "\n",
        "where pressure must correspond to term\n",
        "\n",
        "$$ P = \\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n} $$\n",
        "\n",
        "What we see here is that pressure $P$ is an intensive conjugate variable corresponding to the extensive volume $V$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 4,
          "link": "[2.1.2.1.2 Temperature/Entropy](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2.1.2-Temperature/Entropy)",
          "section": "2.1.2.1.2 Temperature/Entropy"
        },
        "id": "5gP09QfJ3bhn"
      },
      "source": [
        "#### 2.1.2.1.2 Temperature/Entropy\n",
        "\n",
        "The term \n",
        "\n",
        "$$\\left(\\frac{\\partial U}{\\partial S}\\right)_{V,\\bf n} dS$$\n",
        "\n",
        "describes the change in internal energy due to thermal energy from the surroundings. In the case the \"displacement\" is the change in system entropy. The corresponding conjugate \"force\" is temperature.\n",
        "\n",
        "$$ T = \\left(\\frac{\\partial U}{\\partial S}\\right)_{V,\\bf n} $$\n",
        "\n",
        "This formula actually serves as a thermodynamic definition of temperature."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 4,
          "link": "[2.1.2.1.3 Chemical Potential/Molar Amount](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2.1.3-Chemical-Potential/Molar-Amount)",
          "section": "2.1.2.1.3 Chemical Potential/Molar Amount"
        },
        "id": "G7MAgZ3B3bho"
      },
      "source": [
        "#### 2.1.2.1.3 Chemical Potential/Molar Amount\n",
        "\n",
        "The terms in $dU$ come from an increase in the amount of species $k$ in the system. The change may be due to exchange of material with the surroundings or to chemical reaction. The corresponding conjugate variable is chemical potential defined as\n",
        "\n",
        "$$ \\mu_k = \\left(\\frac{\\partial U}{\\partial n_k}\\right)_{S,V,n_{j\\ne k}}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 4,
          "link": "[2.1.2.1.4 Conjugate Variables](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.2.1.4-Conjugate-Variables)",
          "section": "2.1.2.1.4 Conjugate Variables"
        },
        "id": "aVkj1v_C3bho"
      },
      "source": [
        "#### 2.1.2.1.4 Conjugate Variables\n",
        "\n",
        "The pairing of an extensive \"displacement\" variable with an intensive \"force\" variable appears throughout thermodynamics and chemical processes. Variables which share this relationship are called **conjugate variables**. In this case, the total derivative of internal energy can be expressed as\n",
        "\n",
        "$$dU = \n",
        "\\underbrace{\\left(\\frac{\\partial U}{\\partial S}\\right)_{V,\\bf n}}_{T} dS +\n",
        "\\underbrace{\\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n}}_{-P} dV +\n",
        "\\sum_{k=1}^{K} \\underbrace{\\left(\\frac{\\partial U}{\\partial n_k}\\right)_{S,V,n_{j\\ne k}}}_{\\mu_k} dn_k\n",
        "$$\n",
        "\n",
        "or \n",
        "\n",
        "$$dU = T dS - P dV + \\sum_{k=1}^{K} \\mu_k dn_k$$ \n",
        "\n",
        "which is comprised of contributions due to the exchange of mechanical work and thermal energy with the surroundings, and with a change in amount of each species."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.1.3 Homogeneous Equations](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.3-Homogeneous-Equations)",
          "section": "2.1.3 Homogeneous Equations"
        },
        "id": "n5HDug0g3bho"
      },
      "source": [
        "## 2.1.3 Homogeneous Equations\n",
        "\n",
        "Computing the total derivative of internal energy $U$ using partial derivatives revealed the existence of intensive/extensive conjugate variable pairs. We can gain additional insights by more carefully investigating the behavior of extensive variables.\n",
        "\n",
        "We start with a given system with specified values for all of the extensive variable. Then we look at a system where the only difference is that it is factor $\\lambda$ times larger. By definition, each of the extensive variables will also a positive factor $\\lambda$ times larger. \n",
        "\n",
        "$$U, S, V, n_1, n_2, \\ldots, n_K \\stackrel{\\lambda}{\\longrightarrow} \\lambda U, \\lambda S, \\lambda V, \\lambda n_1, \\lambda n_2, \\ldots, \\lambda n_K$$\n",
        "\n",
        "Because $U$ is a function of the other variables, we can write a relationship between the two systems that is a function of the positive scaling parameter $\\lambda$.\n",
        "\n",
        "$$ U(\\lambda S, \\lambda V, \\lambda n_1, \\lambda n_2, \\ldots, \\lambda n_K) = \\lambda U(S, V, n_1, n_2, \\ldots, n_K)$$\n",
        "\n",
        "Taking the partial derivative of both sides of this equation with respect to $\\lambda$,\n",
        "\n",
        "$$U(S, V, n_1, n_2, \\ldots, n_K) =\n",
        "\\left(\\frac{\\partial U}{\\partial \\lambda S}\\right)_{\\lambda V, \\lambda \\bf n} \\frac{\\partial \\lambda S}{\\partial \\lambda} + \n",
        "\\left(\\frac{\\partial U}{\\partial \\lambda V}\\right)_{\\lambda S, \\lambda \\bf n} \\frac{\\partial \\lambda V}{\\partial \\lambda} + \n",
        "\\sum_{k=1}^{K} \\left(\\frac{\\partial U}{\\partial \\lambda n_k}\\right)_{\\lambda S,\\lambda V, \\lambda n_{j\\ne k}} \\frac{\\partial \\lambda n_k}{\\partial \\lambda}\n",
        "$$\n",
        "\n",
        "From the chain rule we get\n",
        "\n",
        "$$U(S, V, n_1, n_2, \\ldots, n_K) =\n",
        "\\left(\\frac{\\partial U}{\\partial \\lambda S}\\right)_{\\lambda V, \\lambda \\bf n} S + \n",
        "\\left(\\frac{\\partial U}{\\partial \\lambda V}\\right)_{\\lambda S, \\lambda \\bf n} V + \n",
        "\\sum_{k=1}^{K} \\left(\\frac{\\partial U}{\\partial \\lambda n_k}\\right)_{\\lambda S,\\lambda V, \\lambda n_{j\\ne k}} n_k\n",
        "$$\n",
        "\n",
        "Since this has to hold for any value of the parameter $\\lambda$, we choose to set $\\lambda = 1$\n",
        "\n",
        "$$U(S, V, n_1, n_2, \\ldots, n_K) =\n",
        "\\left(\\frac{\\partial U}{\\partial S}\\right)_{V,\\bf n} S + \n",
        "\\left(\\frac{\\partial U}{\\partial V}\\right)_{S,\\bf n} V + \n",
        "\\sum_{k=1}^{K} \\left(\\frac{\\partial U}{\\partial n_k}\\right)_{S,V,n_{j\\ne k}} n_k\n",
        "$$\n",
        "\n",
        "Finally, we set the partial derivatives equal to the intensive variables identified above\n",
        "\n",
        "$$U = T S - P V + \\sum_{k=1}^{K} \\mu_k n_k $$\n",
        "\n",
        "This shows "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.1.3 Homogeneous Equations](https://jckantor.github.io/CBE30338/02.01-Process-Variables.html#2.1.3-Homogeneous-Equations)",
          "section": "2.1.3 Homogeneous Equations"
        },
        "id": "M-kRU0eL3bhp"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VzFcLHpl3OPe",
        "nbpages": {
          "level": 1,
          "link": "[2.2 Gravity Drained Tank](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2-Gravity-Drained-Tank)",
          "section": "2.2 Gravity Drained Tank"
        }
      },
      "source": [
        "# 2.2 Gravity Drained Tank"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.2.1 Summary](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.1-Summary)",
          "section": "2.2.1 Summary"
        },
        "id": "4DWAaghP3khh"
      },
      "source": [
        "## 2.2.1 Summary\n",
        "\n",
        "In the example we study the problem of constructing nonlinear process model for the liquid level in a gravity drained tank."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xSIqWFm93OPg",
        "nbpages": {
          "level": 2,
          "link": "[2.2.2 Torricelli's law](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.2-Torricelli's-law)",
          "section": "2.2.2 Torricelli's law"
        }
      },
      "source": [
        "## 2.2.2 Torricelli's law\n",
        "\n",
        "Torricelli's law states the velocity of an incompressible liquid stream exiting a liquid tank at level $h$ below the surface is \n",
        "\n",
        "$$v = \\sqrt{2gh}$$ \n",
        "\n",
        "This is the same velocity as an object dropped from a height $h$. The derivation is straightforward. From Bernoulli's principle,\n",
        "\n",
        "$$\\frac{v^2}{2} + gh + \\frac{P}{\\rho} = \\text{constant}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zGDdqtSj3OPj",
        "nbpages": {
          "level": 2,
          "link": "[2.2.2 Torricelli's law](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.2-Torricelli's-law)",
          "section": "2.2.2 Torricelli's law"
        }
      },
      "source": [
        "Applying this principle, compare a drop of water just below the surface of the water at distance $h$ above the exit, to a drop of water exiting the tank\n",
        "\n",
        "$$gh + \\frac{P_{atm}}{\\rho} = \\frac{v^2}{2} + \\frac{P_{atm}}{\\rho}$$\n",
        "\n",
        "$$\\implies v^2 = 2gh$$\n",
        "$$\\implies v = \\sqrt{2gh}$$\n",
        "\n",
        "Torricelli's law is an approximation that doesn't account for the effects of fluid viscosity, the specific flow geometry near the exit, or other flow non-idealities. Nevertheless it is a useful first approximation for flow from a tank."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H8dmoxAJ3OPk",
        "nbpages": {
          "level": 2,
          "link": "[2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.3-Mass-Balance-for-Tank-with-Constant-Cross-Sectional-Area)",
          "section": "2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area"
        }
      },
      "source": [
        "## 2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area\n",
        "\n",
        "For a tank with constant cross-sectional area, such as a cylindrical or rectangular tank, the liquid height is described by a differential equation\n",
        "\n",
        "$$A\\frac{dh}{dt} = q_{in}(t) - q_{out}(t)$$\n",
        "\n",
        "where $q_{out}$ is a function of liquid height. Torricelli's law tells the outlet flow from the tank is proportional to square root of the liquid height\n",
        "\n",
        "$$ q_{out}(h) = C_v\\sqrt{h} $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rcxaOAy73OPl",
        "nbpages": {
          "level": 2,
          "link": "[2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.3-Mass-Balance-for-Tank-with-Constant-Cross-Sectional-Area)",
          "section": "2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area"
        }
      },
      "source": [
        "Dividing by area we obtain a nonlinear ordinary differential equation \n",
        "\n",
        "$$ \\frac{dh}{dt} = - \\frac{C_V}{A}\\sqrt{h} + \\frac{1}{A}q_{in}(t) $$\n",
        "\n",
        "in our standard form where the LHS derivative appears with a constant coefficient of 1."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "56j29DiG3OPm",
        "nbpages": {
          "level": 2,
          "link": "[2.2.4 Step-by-Step Approach to Nonlinear Simulation](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4-Step-by-Step-Approach-to-Nonlinear-Simulation)",
          "section": "2.2.4 Step-by-Step Approach to Nonlinear Simulation"
        }
      },
      "source": [
        "## 2.2.4 Step-by-Step Approach to Nonlinear Simulation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C-BiES7y3OPn",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.1 Step 1. Initialize Jupyter and Python](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.1-Step-1.-Initialize-Jupyter-and-Python)",
          "section": "2.2.4.1 Step 1. Initialize Jupyter and Python"
        }
      },
      "source": [
        "### 2.2.4.1 Step 1. Initialize Jupyter and Python\n",
        "\n",
        "The first step in any Python application is to initialize graphics display (if you will be creating graphic output), and import any needed libraries.  \n",
        "\n",
        "The `%matplotlib inline` is a command telling the Jupyter notebook to display any graphics inside this notebook.\n",
        "\n",
        "We then import a standard graphics library (`matplotlib.pyplot`) that will be referred to with the prefix `plt`, a standard numerical library `numpy` that will be referred to with the prefix `np`, and the function `odeint` from the `scipy.integrate` library.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lAtqLB373OPp",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.1 Step 1. Initialize Jupyter and Python](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.1-Step-1.-Initialize-Jupyter-and-Python)",
          "section": "2.2.4.1 Step 1. Initialize Jupyter and Python"
        }
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy.integrate import odeint"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rz2LNFOP3OPu",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.2 Step 2. Define parameters](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.2-Step-2.-Define-parameters)",
          "section": "2.2.4.2 Step 2. Define parameters"
        }
      },
      "source": [
        "### 2.2.4.2 Step 2. Define parameters\n",
        "\n",
        "Provide values for all relevant parameters.  Use comments to describe the parameters and units."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qYEqVEsU3OPv",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.2 Step 2. Define parameters](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.2-Step-2.-Define-parameters)",
          "section": "2.2.4.2 Step 2. Define parameters"
        }
      },
      "outputs": [],
      "source": [
        "Cv  = 0.1     # Outlet valve constant [cubic meters/min/meter^1/2]\n",
        "A   = 1.0     # Tank area [meter^2]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QqTpi1bf3OPy",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.3-Step-3.-Write-Functions-for-the-RHS-of-the-Differential-Equations)",
          "section": "2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations"
        }
      },
      "source": [
        "### 2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nuIhX1VO3OPy",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.3-Step-3.-Write-Functions-for-the-RHS-of-the-Differential-Equations)",
          "section": "2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations"
        }
      },
      "outputs": [],
      "source": [
        "# inlet flow rate in cubic meters/min\n",
        "def qin(t):\n",
        "    return 0.15\n",
        "\n",
        "def deriv(h,t):\n",
        "    return qin(t)/A - Cv*np.sqrt(h)/A"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n1EJHyQd3OP1",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.4-Step-4.-Choose-an-Initial-Condition,-a-Time-Grid,-and-Integrate-the-Differential-Equation)",
          "section": "2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation"
        }
      },
      "source": [
        "### 2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HiA2HZcb3OP1",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.4-Step-4.-Choose-an-Initial-Condition,-a-Time-Grid,-and-Integrate-the-Differential-Equation)",
          "section": "2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation"
        }
      },
      "outputs": [],
      "source": [
        "IC = [0.0]\n",
        "t = np.linspace(0,200,101)\n",
        "h = odeint(deriv,IC,t)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UJ5008ZA3OP6",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.5 Step 5. Visualize and Analyze Results](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.5-Step-5.-Visualize-and-Analyze-Results)",
          "section": "2.2.4.5 Step 5. Visualize and Analyze Results"
        }
      },
      "source": [
        "### 2.2.4.5 Step 5. Visualize and Analyze Results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "DyQyXfpp3OP8",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.5 Step 5. Visualize and Analyze Results](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.5-Step-5.-Visualize-and-Analyze-Results)",
          "section": "2.2.4.5 Step 5. Visualize and Analyze Results"
        },
        "outputId": "be349d5d-4806-4249-e3c5-85f14d31ff28"
      },
      "outputs": [
        {
          "data": {
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sr8e31rJuSy0btjcEX3gKjS3M5bj5E5k7bSyHTR3L7CklFBUc+q/Qi4wGKgCS8XbuaWHN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\nkYhSARARiSgVABGRiPr/YZwA5Y19DxcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(t,h)\n",
        "\n",
        "plt.xlabel('minutes')\n",
        "plt.ylabel('meters')\n",
        "plt.title('Gravity-Drained Tank')\n",
        "plt.legend(['Liquid Level']);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "taamgWsu3OQB",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.6 Step 6.  Adjust and Repeat as Needed](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.6-Step-6.-Adjust-and-Repeat-as-Needed)",
          "section": "2.2.4.6 Step 6.  Adjust and Repeat as Needed"
        }
      },
      "source": [
        "### 2.2.4.6 Step 6.  Adjust and Repeat as Needed\n",
        "\n",
        "Rarely does a simulation provide you with the information you seek on the first try.  You will almost certainly need to revise parameter values, choose different time grids, and add visualization features to obtain the most informative results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fuPuM5fV3OQC",
        "nbpages": {
          "level": 3,
          "link": "[2.2.4.6 Step 6.  Adjust and Repeat as Needed](https://jckantor.github.io/CBE30338/02.02-Gravity-Drained-Tank.html#2.2.4.6-Step-6.-Adjust-and-Repeat-as-Needed)",
          "section": "2.2.4.6 Step 6.  Adjust and Repeat as Needed"
        }
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.3 Blending Tank Simulation](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3-Blending-Tank-Simulation)",
          "section": "2.3 Blending Tank Simulation"
        },
        "id": "G1-7uf4D3p_t"
      },
      "source": [
        "# 2.3 Blending Tank Simulation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.3.1 Summary](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.1-Summary)",
          "section": "2.3.1 Summary"
        },
        "id": "HItuVkzs3p_t"
      },
      "source": [
        "## 2.3.1 Summary\n",
        "\n",
        "This example provides an introduction to the use of python for the simulation of a simple process modeled by a pair of ordinary differential equations. See SEMD textbook example 2.1 for more details on the process."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.3.2 Basic Simulation of the Blending Tank](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2-Basic-Simulation-of-the-Blending-Tank)",
          "section": "2.3.2 Basic Simulation of the Blending Tank"
        },
        "id": "-cCFwPQF3p_t"
      },
      "source": [
        "## 2.3.2 Basic Simulation of the Blending Tank\n",
        "\n",
        "\\begin{align*}\n",
        "\\frac{dV}{dt} & = \\frac{1}{\\rho}(w_1 + w_2 - w)\\\\\n",
        "\\frac{dx}{dt} & = \\frac{1}{\\rho V}(w_1 (x_1 - x) + w_2 (x_2 - x))\n",
        "\\end{align*}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.1 Step 1. Initialize Python Workspace](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.1-Step-1.-Initialize-Python-Workspace)",
          "section": "2.3.2.1 Step 1. Initialize Python Workspace"
        },
        "id": "0XuSa8Zz3p_u"
      },
      "source": [
        "### 2.3.2.1 Step 1. Initialize Python Workspace\n",
        "\n",
        "Unlike Matlab, in Python it is always necessary to import the functions and libraries that you intend to use. In this case we import the complete `pylab` library, and the function `odeint` for integrating systems of differential equations from the `scipy` library.  The command `%matplotlib inline` causes graphic commands to produce results directly within the notebook output cells."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.1 Step 1. Initialize Python Workspace](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.1-Step-1.-Initialize-Python-Workspace)",
          "section": "2.3.2.1 Step 1. Initialize Python Workspace"
        },
        "id": "QdfvTqEp3p_u"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.2 Step 2. Establish Parameter Values](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.2-Step-2.-Establish-Parameter-Values)",
          "section": "2.3.2.2 Step 2. Establish Parameter Values"
        },
        "id": "9_r_AE7R3p_v"
      },
      "source": [
        "### 2.3.2.2 Step 2. Establish Parameter Values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.2 Step 2. Establish Parameter Values](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.2-Step-2.-Establish-Parameter-Values)",
          "section": "2.3.2.2 Step 2. Establish Parameter Values"
        },
        "id": "zbhgt1qQ3p_v"
      },
      "outputs": [],
      "source": [
        "rho = 900.0  # density, kg/m**3\n",
        "\n",
        "w1 = 500.0   # stream 1, kg/min\n",
        "w2 = 200.0   # stream 2, kg/min\n",
        "w =  650.0   # set outflow equal to sum of inflows\n",
        "\n",
        "x1 = 0.4     # composition stream 1, mass fraction\n",
        "x2 = 0.75    # composition stream 2, mass fraction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.3-Step-3.-Write-a-function-to-compute-the-RHS's-of-the-Differential-Equations)",
          "section": "2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations"
        },
        "id": "vSRbKhgP3p_v"
      },
      "source": [
        "### 2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.3-Step-3.-Write-a-function-to-compute-the-RHS's-of-the-Differential-Equations)",
          "section": "2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations"
        },
        "id": "pgnMUPDe3p_w"
      },
      "outputs": [],
      "source": [
        "def func(y,t):\n",
        "    V,x = y\n",
        "    dVdt = (w1 + w2 - w)/rho\n",
        "    dxdt = (w1*(x1-x)+w2*(x2-x))/(rho*V)\n",
        "    return [dVdt, dxdt]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.4-Step-4.-Set-the-Initial-Conditions,-Time-Grid,-and-Integrate)",
          "section": "2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate"
        },
        "id": "ekrUGlU13p_w"
      },
      "source": [
        "### 2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.4-Step-4.-Set-the-Initial-Conditions,-Time-Grid,-and-Integrate)",
          "section": "2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate"
        },
        "id": "9xwYm4703p_w"
      },
      "outputs": [],
      "source": [
        "V = 2.0      # initial volume, cubic meters\n",
        "x = 0.0      # initial composition, mass fraction\n",
        "\n",
        "t = np.linspace(0,10.0)\n",
        "y = odeint(func,[V,x],t)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.5 Step 5. Visualize the Solution](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.5-Step-5.-Visualize-the-Solution)",
          "section": "2.3.2.5 Step 5. Visualize the Solution"
        },
        "id": "Son8RGTI3p_w"
      },
      "source": [
        "### 2.3.2.5 Step 5. Visualize the Solution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.3.2.5 Step 5. Visualize the Solution](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.2.5-Step-5.-Visualize-the-Solution)",
          "section": "2.3.2.5 Step 5. Visualize the Solution"
        },
        "id": "07NqG8bZ3p_x",
        "outputId": "9f458d0d-8e10-40ed-8b0c-0ab5c576f1f9"
      },
      "outputs": [
        {
          "data": {
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CTyYvWyIikgqdfRtYDfzAzNab2ffMbHKyMiUiIqlx0KDg7ne5++nAuQQfl//b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\nSIyCgoiIxCgoiIhIjIKCiIjE/H+pGYB6y4fVzQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x111585f28>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(t,y)\n",
        "plt.xlabel('Time [min]')\n",
        "plt.ylabel('Volume, Composition')\n",
        "plt.legend(['Volume','Composition'])\n",
        "plt.ylim(0,3)\n",
        "plt.grid()\n",
        "#plt.savefig('BlendingTankStartUp.png')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.3.3 Steady State Analysis](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.3-Steady-State-Analysis)",
          "section": "2.3.3 Steady State Analysis"
        },
        "id": "m7vmAcDv3p_x"
      },
      "source": [
        "## 2.3.3 Steady State Analysis\n",
        "\n",
        "The blending tank is a system with two state variables (volume and composition). Suppose a mechanism is put in place to force the inflow to equal the outflow, that is\n",
        "\n",
        "$$w = w_1 + w_2$$\n",
        "\n",
        "The mechanism could involve the installation of an overflow weir, level controller, or some other device to force a balance between the outflow and total inflows.  In this case,\n",
        "\n",
        "$$\\frac{dV}{dt} = 0$$\n",
        "\n",
        "which means volume is at *steady state*. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.3.3 Steady State Analysis](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.3-Steady-State-Analysis)",
          "section": "2.3.3 Steady State Analysis"
        },
        "id": "904_2Xn83p_y"
      },
      "source": [
        " \n",
        "In that case there is just one remaining differential equation\n",
        "\n",
        "$$\\frac{dx}{dt} = \\frac{1}{\\rho V}( w_1(x_1 - x) + w_1(x_2 - x)) = 0$$\n",
        "\n",
        "Solving for the steady value of $x$,\n",
        "\n",
        "$$\\bar{x} = \\frac{w_1x_1 + w_2x_2}{w_1 + w_2}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.3.3 Steady State Analysis](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.3-Steady-State-Analysis)",
          "section": "2.3.3 Steady State Analysis"
        },
        "id": "HuCnmf3j3p_y",
        "outputId": "988328e8-f053-4e99-de28-00325460e66c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Steady State Composition = 0.5\n"
          ]
        }
      ],
      "source": [
        "w1 = 500.0   # stream 1, kg/min\n",
        "w2 = 200.0   # stream 2, kg/min\n",
        "\n",
        "x1 = 0.4     # composition stream 1, mass fraction\n",
        "x2 = 0.75    # composition stream 2, mass fraction\n",
        "\n",
        "x = (w1*x1 + w2*x2)/(w1 + w2)\n",
        "\n",
        "print('Steady State Composition =', x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 2,
          "link": "[2.3.3 Steady State Analysis](https://jckantor.github.io/CBE30338/02.03-Blending-Tank-Simulation.html#2.3.3-Steady-State-Analysis)",
          "section": "2.3.3 Steady State Analysis"
        },
        "id": "Kjy4xLxL3p_y"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.4 Continuous Product Blending](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4-Continuous-Product-Blending)",
          "section": "2.4 Continuous Product Blending"
        },
        "id": "sogldz3e3u3m"
      },
      "source": [
        "# 2.4 Continuous Product Blending\n",
        "\n",
        "This case study is modeled after an actual process used to prepare an over-the-counter pediatric medication. The situation has been simplified to the dissolution of a single active ingredient into a suspension, and adapted to continouous rather than batch operation.\n",
        "\n",
        "The process objective is to mix an active ingredient $A$ into a suspension $S$, providing enough time to fully mix and dissolve components coming from both streams. The feed concentration of $A$ is 200 grams/liter. Process requirements include:\n",
        "\n",
        "* The final product concentration must be in the range 7.8 to 8.2 grams/liter. \n",
        "* At all timses the mixer residence time, $\\frac{V}{q_{out}}$, must remain between 84 and 108 hours.\n",
        "* The volume cannot exceed the tank capacity of 15,000 liters, and cannot fall below the 8,000 liters required to fully cover the mixing blades.\n",
        "\n",
        "The outlet from the tank is fed directly to a packaging line. The flow demand can vary due to changes in speed of the packaging equipment.\n",
        "\n",
        "![](figures/Continuous-Mixed-Tank.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.1 Preliminary Control Analysis ](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1-Preliminary-Control-Analysis)",
          "section": "2.4.1 Preliminary Control Analysis "
        },
        "id": "iY1-VWGf3u3n"
      },
      "source": [
        "## 2.4.1 Preliminary Control Analysis "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.1 Parameters](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.1-Parameters)",
          "section": "2.4.1.1 Parameters"
        },
        "id": "BDwfaOmu3u3n"
      },
      "source": [
        "### 2.4.1.1 Parameters\n",
        "\n",
        "| Quantity | Symbol | Value | Units |\n",
        "|:-:|:-:|:-:|:-:|\n",
        "| Feed Concentration |$c_{A,f}$ | 200 | g/liter |\n",
        "| Maximum Tank Operating Capacity | $V$ | 15,000 | liters |\n",
        "| Minimum Tank Operating Capacity | $V$ | 8,000 | liters |"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.2 Control Objectives](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.2-Control-Objectives)",
          "section": "2.4.1.2 Control Objectives"
        },
        "id": "OUOnFlqd3u3o"
      },
      "source": [
        "### 2.4.1.2 Control Objectives\n",
        "\n",
        "* Maintain outlet concentration of $A$ at $8.0 \\pm 0.2$ grams/liter.\n",
        "* Maintain an average residence time (i.e., ratio $V/q_{out}$) of $96 \\pm 12$ hours.\n",
        "* Past operation has shown a liquid volume of 12,000 liters generally meets nominal demand. Demand, however, fluctuates and is determined by the downstream packaging line."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.3 Classification of Variables](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.3-Classification-of-Variables)",
          "section": "2.4.1.3 Classification of Variables"
        },
        "id": "HE6Dzow-3u3o"
      },
      "source": [
        "### 2.4.1.3 Classification of Variables\n",
        "\n",
        "What are the disturbances variables (DV), manipulated variables (MV), and controlled variables (CV)?\n",
        "\n",
        "| Variable | Symbol | Classification |\n",
        "|:-:|:-:|:-:|:-:|\n",
        "| Outlet Flow | $q_{out}$ | DV |\n",
        "| Feed Flow | $q_A$ | MV |\n",
        "| Water Makeup Flow | $q_W$ | MV |\n",
        "| Product Concentration | $c_A$ | CV |\n",
        "| Volume | $V$ | CV |\n",
        "\n",
        "In this case, we can assume the controlled variables are directly measureable."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.4 Degrees of Freedom Analysis](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.4-Degrees-of-Freedom-Analysis)",
          "section": "2.4.1.4 Degrees of Freedom Analysis"
        },
        "id": "hC48x3R93u3p"
      },
      "source": [
        "### 2.4.1.4 Degrees of Freedom Analysis\n",
        "\n",
        "At steady-state the balance equations become algebraic equations\n",
        "\n",
        "\\begin{align}\n",
        "0 & = \\bar{q}_A + \\bar{q}_S - \\bar{q}_{out} \\\\\n",
        "& \\\\\n",
        "0 & = \\bar{q}_A c_{A,f} - \\bar{q}_{out}\\bar{c}_A\n",
        "\\end{align}\n",
        "\n",
        "There are a total of five variables in these two equations. So we need to find at least three more specifciations or constraints to determine values for these variables. \n",
        "\n",
        "Additional pieces of information we have are the process specifications\n",
        "\n",
        "\\begin{align}\n",
        "\\frac{\\bar{q}_{out}}{\\bar{V}} & = 96 \\mbox{ hours} \\\\\n",
        "c_{A,f} & = 200 \\mbox{ g/liter} \\\\\n",
        "\\bar{q}_{out} & = \\mbox{ set by the downstream demand} \\\\\n",
        "\\bar{c}_A & = 8 \\mbox{ g/liter}\n",
        "\\end{align}\n",
        "\n",
        "This is a total of four new equations for steady-state.  The new equations introduced an additional variable $\\bar{V}$. This provides six variables in six equations provided we know the downstream demand."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.5 Steady State](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.5-Steady-State)",
          "section": "2.4.1.5 Steady State"
        },
        "id": "l61wR3vg3u3p"
      },
      "source": [
        "### 2.4.1.5 Steady State\n",
        "\n",
        "Let's assume a constant output demand $\\bar{q}_{out}$ = 125 liters/hr.  The equations may then be solved in order:\n",
        "\n",
        "\\begin{align}\n",
        "c_{A,f} & = 200 \\mbox{ g/liter} \\\\\n",
        "\\bar{c}_A & = 8 \\mbox{ g/liter} \\\\\n",
        "\\bar{V} & = 96\\ \\bar{q}_{out} = 12,000 \\mbox{ liters}\\\\\n",
        "\\bar{q}_A & = \\frac{\\bar{q}_{out}\\bar{c}_A}{c_{A,f}} = 5 \\mbox{ liters/hr}\\\\\n",
        "\\bar{q}_S & = \\bar{q}_{out} - \\bar{q}_A = 120 \\mbox{ liters/hr}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.1.6 Exercise 1. Determine Operating Range](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.1.6-Exercise-1.-Determine-Operating-Range)",
          "section": "2.4.1.6 Exercise 1. Determine Operating Range"
        },
        "tags": [
          "exercise"
        ],
        "id": "xtrSG6SX3u3q"
      },
      "source": [
        "### 2.4.1.6 Exercise 1. Determine Operating Range\n",
        "\n",
        "Solve the steady-state equations for other values of $\\bar{q}_{out}$. Given a maximum tank operating capacity of 15,000 liters, what is the largest possible value of $\\bar{q}_{out}$ which still meets process specifications?  If the minimum tank operating capacity is 8,000 liters, what is the minimum value of $\\bar{q}_{out}$?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.2 Modeling](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.2-Modeling)",
          "section": "2.4.2 Modeling"
        },
        "id": "7N5pDa-f3u3q"
      },
      "source": [
        "## 2.4.2 Modeling\n",
        "\n",
        "The balance equations are\n",
        "\n",
        "\\begin{align}\n",
        "\\frac{dV}{dt} & = q_A + q_S - q_{out} \\\\\n",
        "\\frac{d(Vc_A)}{dt} & = q_A c_{A,f} - q_{out}c_A\n",
        "\\end{align}\n",
        "\n",
        "where we have made the assumption of constant density among all of the streams, and of complete and uniform mixing in the stirred tank. \n",
        "\n",
        "For simulation, it is useful to isolate the derivatives of $V$ and $c_A$ on the left-hand side of these differential equations. Using the chain rule\n",
        "\n",
        "\\begin{align}\n",
        "\\frac{dV}{dt} & = q_A + q_S - q_{out} \\\\\n",
        "V\\frac{dc_A}{dt} + c_A\\frac{dV}{dt} & = q_A c_{A,f} - q_{out}c_A\n",
        "\\end{align}\n",
        "\n",
        "Substituting the first equation into the second gives\n",
        "\n",
        "\\begin{align}\n",
        "\\frac{dV}{dt} & = q_A + q_S - q_{out} \\\\\n",
        "V\\frac{dc_A}{dt} + c_A\\left(q_A + q_S - q_{out}\\right) & = q_A c_{A,f} - q_{out}c_A\n",
        "\\end{align}\n",
        "\n",
        "Rearranging terms, and dividing the second equation by $V$, gives us the final version of a dynamical model.\n",
        "\n",
        "\\begin{align}\n",
        "\\frac{dV}{dt} & = q_A + q_S - q_{out} \\\\\n",
        "\\frac{dc_A}{dt} & = \\frac{q_A}{V} \\left(c_{A,f} - c_A\\right) - \\frac{q_S}{V} c_A\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.3 Simulation](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3-Simulation)",
          "section": "2.4.3 Simulation"
        },
        "id": "xTPFpGpA3u3r"
      },
      "source": [
        "## 2.4.3 Simulation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.1 Step 1. Imports](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.1-Step-1.-Imports)",
          "section": "2.4.3.1 Step 1. Imports"
        },
        "id": "1jOvtPgs3u3r"
      },
      "source": [
        "### 2.4.3.1 Step 1. Imports\n",
        "\n",
        "We start the simulation by importing necessary Python libraries."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.1 Step 1. Imports](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.1-Step-1.-Imports)",
          "section": "2.4.3.1 Step 1. Imports"
        },
        "id": "KEqWEhgo3u3r"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import odeint\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.2 Step 2. Parameter Values](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.2-Step-2.-Parameter-Values)",
          "section": "2.4.3.2 Step 2. Parameter Values"
        },
        "id": "H7ujIgyB3u3s"
      },
      "source": [
        "### 2.4.3.2 Step 2. Parameter Values\n",
        "\n",
        "It is good coding practice to include all relevant parameter values in single block of code. This makes it easier for users of your code to understand what values are relevant to the problem, and to adjust and maintain your code. No 'magic' numbers should appear later in your code."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.2 Step 2. Parameter Values](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.2-Step-2.-Parameter-Values)",
          "section": "2.4.3.2 Step 2. Parameter Values"
        },
        "id": "nsaIDMyc3u3t"
      },
      "outputs": [],
      "source": [
        "# parameters\n",
        "caf       = 200       # g/liter\n",
        "Vmax      = 15000     # liters\n",
        "Vmin      = 8000      # liters\n",
        "\n",
        "# process setpoints\n",
        "ca_SP     = 8         # g/liter\n",
        "rtime_SP  = 96        # residence time in hours\n",
        "\n",
        "# nominal values of the disturbance variables\n",
        "qout_bar  = 125"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.3 Step 3. Computing Steady State](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.3-Step-3.-Computing-Steady-State)",
          "section": "2.4.3.3 Step 3. Computing Steady State"
        },
        "id": "rSYzM1vG3u3t"
      },
      "source": [
        "### 2.4.3.3 Step 3. Computing Steady State\n",
        "\n",
        "A good modeling practice is to begin with the determination of a nominal steady state. By nominal we mean operating conditions representative of typical, desired behavior of the process in question, and should be computed based on the parameter values given above."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.3 Step 3. Computing Steady State](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.3-Step-3.-Computing-Steady-State)",
          "section": "2.4.3.3 Step 3. Computing Steady State"
        },
        "id": "WomV8q2q3u3t",
        "outputId": "43e9e3cb-5144-4d6b-8dbd-102ff932e30f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Steady-State\n",
            "    V [liters]    =  12000\n",
            "   ca [g/liter]   =  8\n",
            "   qa [liters/hr] =  5.0\n",
            "   qs [liters/hr] =  120.0\n"
          ]
        }
      ],
      "source": [
        "# nominal steady state at process setpoint\n",
        "V_bar    = rtime_SP * qout_bar\n",
        "ca_bar   = ca_SP\n",
        "qa_bar   = ca_SP*qout_bar/caf\n",
        "qs_bar   = qout_bar - qa_bar\n",
        "\n",
        "print(\"Steady-State\")\n",
        "print(\"    V [liters]    = \", V_bar)\n",
        "print(\"   ca [g/liter]   = \", ca_bar)\n",
        "print(\"   qa [liters/hr] = \", qa_bar)\n",
        "print(\"   qs [liters/hr] = \", qs_bar)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.4 Step 4. Process Model Equations](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.4-Step-4.-Process-Model-Equations)",
          "section": "2.4.3.4 Step 4. Process Model Equations"
        },
        "id": "AB33zb3g3u3u"
      },
      "source": [
        "### 2.4.3.4 Step 4. Process Model Equations\n",
        "\n",
        "In our case the model consists of a system of two differential equations. For simulation with the Python function `odeint`, the model is encapsulated into a Python function that accepts two arguments.\n",
        "\n",
        "* `X` is a list of values for the model state, in this case `V` and `ca`.\n",
        "* `t` a variable containing value corresponding to the current time."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.4 Step 4. Process Model Equations](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.4-Step-4.-Process-Model-Equations)",
          "section": "2.4.3.4 Step 4. Process Model Equations"
        },
        "id": "HzPL8pij3u3u"
      },
      "outputs": [],
      "source": [
        "def deriv(X, t):\n",
        "    V, ca = X\n",
        "    dV = qa + qs - qout\n",
        "    dca = qa*(caf - ca)/V - qs*ca/V\n",
        "    return [dV, dca]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.5 Step 5. Numerical Solution of the Process Model](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.5-Step-5.-Numerical-Solution-of-the-Process-Model)",
          "section": "2.4.3.5 Step 5. Numerical Solution of the Process Model"
        },
        "id": "pHBsmybu3u3v"
      },
      "source": [
        "### 2.4.3.5 Step 5. Numerical Solution of the Process Model\n",
        "\n",
        "This block does the numerically intensive portion of the simulation. Here we establish values for all degrees of freedeom, specify initial conditions, and thne proceed to compute a history of the process behavior. The history is broken into discrete time step which is a bit more work now, but will later provide a means to test implementations of control algorithms.\n",
        "\n",
        "For the first simulation, it usually a good idea to pick an initial condition that will yield a known result. In this case we start a simulation at steady state."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.5 Step 5. Numerical Solution of the Process Model](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.5-Step-5.-Numerical-Solution-of-the-Process-Model)",
          "section": "2.4.3.5 Step 5. Numerical Solution of the Process Model"
        },
        "scrolled": false,
        "id": "3q199ZS93u3v",
        "outputId": "43d7f14e-e257-41d5-d998-64356c738d71"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[[0, 12000, 8],\n",
              " [1, 12000.0, 8.0],\n",
              " [2, 12000.0, 8.0],\n",
              " [3, 12000.0, 8.0],\n",
              " [4, 12000.0, 8.0],\n",
              " [5, 12000.0, 8.0],\n",
              " [6, 12000.0, 8.0],\n",
              " [7, 12000.0, 8.0],\n",
              " [8, 12000.0, 8.0],\n",
              " [9, 12000.0, 8.0]]"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# fix all degrees of freedom \n",
        "qout = qout_bar      # outlet flow -- process disturbance variable.\n",
        "qa = qa_bar          # inlet flow of A -- process manipulated variable\n",
        "qs = qs_bar          # inlet flow of suspension -- process manipulated variable\n",
        "\n",
        "# establish initial conditions\n",
        "t  = 0\n",
        "V  = V_bar\n",
        "ca = ca_bar\n",
        "\n",
        "# time step, and variable to store simulation record (or history)\n",
        "dt = 1\n",
        "history = [[t,V,ca]]\n",
        "\n",
        "while t < 500:\n",
        "    V, ca = odeint(deriv, [V, ca], [t, t+dt])[-1]\n",
        "    t += dt\n",
        "    history.append([t,V,ca])\n",
        "\n",
        "history[0:10]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.6 Step 6. Visualization and Analysis](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.6-Step-6.-Visualization-and-Analysis)",
          "section": "2.4.3.6 Step 6. Visualization and Analysis"
        },
        "id": "_j8VhjUl3u3v"
      },
      "source": [
        "### 2.4.3.6 Step 6. Visualization and Analysis\n",
        "\n",
        "To simplify future simulations, here we define a function to plot the results stored in the simulation record. The function `plot_history(history, labels)` takes two arguments. The first argument is the data history recorded during the course of the simulation, where the first element is assumed to be time. The second argument is a list of labels corresponding to each of the recorded variables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.6 Step 6. Visualization and Analysis](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.6-Step-6.-Visualization-and-Analysis)",
          "section": "2.4.3.6 Step 6. Visualization and Analysis"
        },
        "id": "O0Bh1uPO3u3v",
        "outputId": "d376738d-ca2a-4922-b77b-bb637db4efa3"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x115a434a8>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plot_history(history, labels):\n",
        "    \"\"\"Plots a simulation history.\"\"\"\n",
        "    history = np.array(history)\n",
        "    t = history[:,0]\n",
        "    n = len(labels) - 1\n",
        "    plt.figure(figsize=(8,1.95*n))\n",
        "    for k in range(0,n):\n",
        "        plt.subplot(n, 1, k+1)\n",
        "        plt.plot(t, history[:,k+1])\n",
        "        plt.title(labels[k+1])\n",
        "        plt.xlabel(labels[0])\n",
        "        plt.grid()\n",
        "    plt.tight_layout()\n",
        "        \n",
        "plot_history(history, ['t / hours','Volume','Concentration $c_A$'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.7 Exercise 2. Explore Dynamical Behavior](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.7-Exercise-2.-Explore-Dynamical-Behavior)",
          "section": "2.4.3.7 Exercise 2. Explore Dynamical Behavior"
        },
        "tags": [
          "exercise"
        ],
        "id": "Y-2nsekY3u3w"
      },
      "source": [
        "### 2.4.3.7 Exercise 2. Explore Dynamical Behavior\n",
        "\n",
        "Let's explore the behavior of this mixing tank under different assumptions.  We'll explore the following cases:\n",
        "\n",
        "1. The startup concentration of $A$ is $c_A = 0$. How long before the mixer is producing an acceptable product?\n",
        "2. The outlet flow increases by 10%.  How long before the product is out of spec?\n",
        "3. The outlet flow decreases by 10%.  How long before the product is out of spec?\n",
        "\n",
        "The following cell shows how you might get started with first question."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.4.3.7 Exercise 2. Explore Dynamical Behavior](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.3.7-Exercise-2.-Explore-Dynamical-Behavior)",
          "section": "2.4.3.7 Exercise 2. Explore Dynamical Behavior"
        },
        "scrolled": false,
        "id": "Qm0n5AUb3u3w",
        "outputId": "6774337a-c67f-4296-c1c2-8952e7b53e3e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x113124b38>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# fix all degrees of freedom \n",
        "qout = qout_bar      # outlet flow -- process disturbance variable.\n",
        "qa = qa_bar          # inlet flow of A -- process manipulated variable\n",
        "qs = qs_bar          # inlet flow of suspension -- process manipulated variable\n",
        "\n",
        "# establish initial conditions\n",
        "t  = 0\n",
        "V  = V_bar\n",
        "ca = 0         # <========= CHANGED TO AN INITIAL CONDITION OF ZERO\n",
        "\n",
        "# time step, and variable to store simulation record (or history)\n",
        "dt = 1\n",
        "history = [[t,V,ca]]\n",
        "\n",
        "while t < 500:\n",
        "    V, ca = odeint(deriv, [V, ca], [t, t+dt])[-1]\n",
        "    t += dt\n",
        "    history.append([t,V,ca])\n",
        "\n",
        "plot_history(history, ['t / hours','Volume','Concentration $c_A$'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.4 Control Residence Time](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.4-Control-Residence-Time)",
          "section": "2.4.4 Control Residence Time"
        },
        "id": "7f5vGncM3u3w"
      },
      "source": [
        "## 2.4.4 Control Residence Time\n",
        "\n",
        "From the exercises above, we know even small changes in the outlet flowrate results in substantial loss due to out-of-spec product.  Let's try a control strategy in which we change in the suspension flowrate, $q_S$, to compensate for excursions from the desired value of residence time.\n",
        "\n",
        "We'll try proportional control where the change in $q_S$ is proportional to the difference of the residence time from the setpoint.\n",
        "\n",
        "\\begin{align}\n",
        "q_S - \\bar{q}_S = - K \\left(\\frac{V}{q_{out}} - \\frac{\\bar{V}}{\\bar{q}_{out}}\\right)\n",
        "\\end{align}\n",
        "\n",
        "The negative sign is there because we expect a negative deviation in flowrate is needed to compensate for a positive deviation in residence time.  This can be written more directly as\n",
        "\n",
        "\\begin{align}\n",
        "q_S = \\bar{q}_S - K \\left(\\frac{V}{q_{out}} - \\frac{\\bar{V}}{\\bar{q}_{out}}\\right)\n",
        "\\end{align}\n",
        "\n",
        "In the following cell we will decrease qout by 10%, and attempt to find a value for $K$ that provides satisfactory control."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.4 Control Residence Time](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.4-Control-Residence-Time)",
          "section": "2.4.4 Control Residence Time"
        },
        "id": "kGammvTZ3u3x",
        "outputId": "3a52fa6f-a4cb-4c84-c202-1f6011b8043c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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yEpYvbWVJ6fuUlUQpL4lQVhKhvCRCeWmUsmiE8tJgviRCWTRKNGqURIxoJPUxQiRC8tHQ+UUiIr2YAo7slZkxpH8FQ/rv/dtXiYSztSXGpu2tbNjWyqbtbWzc3srG7W1s2t7Klh1tNLfE2d4ao7klxraWGGu3trCtNTm9rSVOazyR3Ni77/Ro/e3BJ7pHEIrsGk/+jhAxwwyM5DTtYynL2/uRDE67l9M+lrqc9m0kpy14TrpgC7vnu5jHMgW3TE/N/Jq7rd+wk9vff6VL28tcW4bndfKaAuvW7eTupbPCLqNXUc9zr97aaAi5BgUc2S+RiDGgTykD+pQyqrZqn7bRFk8w4+lnOOHEk2iJJWiJxWmNJYLp5HxLLLFrrDWWIJ5IEEs4iYQTSzjxlMfd08l14vHkfMJ9j3nHCf5Hwh1PmcZTx5yEgzuwazp4JDndvp6nPC+5XiJ43p7ShzzDSpn2i3VlW3tbMX1ka4vjza0Z1ttzzYyv2cU6Mv1evd22Hc72DdvDLqNXUc9zb0D/8P+/r4AjoSuNRqgoMWqqysIupVdpbGykoeHksMvodZJ9PzXsMnoV9Tz3Ghsbwy5B96ISERGR4qOAIyIiIkXHCvUYuZmtBT7I0uYHAeuytG3JTD3PPfU8HOp77qnnuZfNno9y98GdrVSwASebzGyWu08Ku47eRD3PPfU8HOp77qnnuZcPPdchKhERESk6CjgiIiJSdBRwMrsl7AJ6IfU899TzcKjvuaee517oPdc5OCIiIlJ0tAdHREREio4CThozm2Jm75rZQjO7Jux6ioWZ3WpmTWY2N2VsoJk9YWYLgseaYNzM7KbgPXjTzCaGV3nhMrMRZva0mc0zs7fN7OvBuPqeJWZWYWavmNkbQc9/HIwfaGYvBz2/18zKgvHyYH5hsHx0mPUXMjOLmtnrZvZoMK+eZ5GZLTGzt8xsjpnNCsby6rNFASeFmUWB3wDnAocDV5jZ4eFWVTRuA6akjV0DzHD3scCMYB6S/R8b/FwN3JyjGotNDPiWux8GTAa+Gvz3rL5nTwtwhrsfDUwAppjZZOCnwI1BzzcCVwXrXwVsdPcxwI3BerJvvg7MS5lXz7PvdHefkPJ18Lz6bFHA2dPxwEJ3X+zurcA0YGrINRUFd38W2JA2PBW4PZi+Hbg4ZfwOT5oJVJvZsNxUWjzcfZW7vxZMbyX54V+P+p41Qe+ag9nS4MeBM4AHgvH0nre/Fw8AZ1qm27tLh8xsOHA+8Idg3lDPw5BXny0KOHuqB5alzC8PxiQ76tx9FST/GANDgnG9Dz0s2A1/DPAy6ntWBYdK5gBNwBPAImCTu8eCVVL7uqvnwfLNQG1uKy4KvwC+CySC+VrU82xz4HEzm21mVwdjefXZoruJ7ylTitfXzHJP70MPMrO+wJ+Bb7j7lg7+saq+9wB3jwMTzKwaeAg4LNNqwaN6vp/M7AKgyd1nm1lD+3CGVdXznnWSu680syHAE2Y2v4N1Q+m59uDsaTkwImV+OLAypFp6gzXtuymDx6ZgXO9DDzGzUpLh5i53fzAYVt9zwN03AY0kz3+qNrP2f1Cm9nVXz4PlA/jwoVzp2EnARWa2hORpBWeQ3KOjnmeRu68MHptIBvnjybPPFgWcPb0KjA3Ovi8DLgemh1xTMZsOXBlMXwk8kjL+2eDM+8nA5vbdntJ1wXkFfwTmufsNKYvU9ywxs8HBnhvMrA9wFslzn54GLglWS+95+3txCfCU6+Jk3eLu33P34e4+muRn9lPu/inU86wxsyoz69c+DZwDzCXPPlt0ob80ZnYeyfQfBW519+tCLqkomNk9QAPJO8yuAa4FHgbuA0YCS4FL3X1D8If51yS/dbUd+Ly7zwqj7kJmZicDzwFvsfvchH8neR6O+p4FZnYUyZMroyT/AXmfu//EzA4iuXdhIPA68Gl3bzGzCuBOkudHbQAud/fF4VRf+IJDVN929wvU8+wJevtQMFsC3O3u15lZLXn02aKAIyIiIkVHh6hERESk6CjgiIiISNFRwBEREZGio4AjIiIiRUcBR0RERIqOAo6IFAwzqzazr4Rdh4jkPwUcESkk1YACjoh0SgFHRArJ9cDBZjbHzH4WdjEikr90oT8RKRjBXdEfdffxIZciInlOe3BERESk6CjgiIiISNFRwBGRQrIV6Bd2ESKS/xRwRKRguPt64AUzm6uTjEWkIzrJWERERIqO9uCIiIhI0VHAERERkaKjgCMiIiJFRwFHREREio4CjoiIiBQdBRwREREpOgo4IiIiUnQUcERERKToKOCIiIhI0VHAERERkaKjgCMiIiJFRwFHREREio4CjoiIiBQdBRwREREpOgo4IiIiUnQUcEQkr5nZCDN70MzWmtl6M/u1mR1sZk8F8+vM7C4zqw67VhHJHwo4IpK3zCwKPAp8AIwG6oFpgAH/BRwAHAaMAH4USpEikpfM3cOuQUQkIzM7EZgODHP3WAfrXQxc6+7H5Kw4EclrJWEXICLSgRHAB+nhxsyGADcBpwD9SO6N3pj78kQkX+kQlYjks2XASDNL/8fYfwEOHOXu/YFPkzxsJSICKOCISH57BVgFXG9mVWZWYWYnkdxr0wxsMrN64DthFiki+UcBR0TylrvHgQuBMcBSYDlwGfBjYCKwGfgL8GBYNYpIftJJxiIiIlJ0tAdHREREio4CjoiIiBQdBRwREREpOgo4IiIiUnQUcERERKToFOyVjAcNGuSjR4/Oyra3bdtGVVVVVrYtmannuaeeh0N9zz31PPey2fPZs2evc/fBna1XsAFn9OjRzJo1KyvbbmxspKGhISvblszU89xTz8Ohvueeep572ey5mX3QlfUKNuCIZJO7E084cXcSCYi3zwc/Cd9zOuHJ5yQcwHEnOUby+R6MeftYsL4Hr5Uch0QiOZYIBtqnk9tLLsN3j6Uu37293eumXueqfTLYCu+saGP97OXB2O7fe9d82vq7n797e3tbRnutqctSt73r+XsuY49le3/d9rrSL+O16zU88/of2l6GmlLXTdfRZcM6uqJY6vOWLm1l5o75Kc/r/kY7fq29L+2J+vd8zr69Vkc6rH8fXstxVq5o4clNb3XzeR0s2+vCfex9J/VnSzYvgzewLUZD9jbfJQo4EqqWWJzmnTHW7UiwsGkrO1oT7GiLJ39a4+xsi7O9NTm/MxhriydojSdoiydoi/me8/FgPpY2HyxPJCCWSBBPsCukJIIg0x5WYokP/+EsWm+9EXYFobPgDla2a972mN/b+hmXdXQ7rGBRIpEgsuz9TIu69XodvVbHNXb0Wh1scx82uM+vtQ/b7Gh7bW0xyjas7vZrdfQb7P196WBr+/jfTsc17p9sbfq4QYksbbnrFHCkR7TE4mzY1sq6ra2s29bCuq0trGtuZdOOVrbsiLFlZxtbd8bYsqNtj+mWWMr/CZ55ttPXMYOyaISyaITSkvZHo7R9LBqhNJqcryov2WO+NBohYkZJxIhEjGgEohZMmxGN7P6JWPo0u54bjex+zu7H5PJkjUbEkh9YEWv/cGqfTn6MRSLJ5ZY6Zu3zu5e1j0WCbewaC3rR/pqpz01dnv7HOnX+5ZdfZvLkE3Z9sKZ/iGZ+fvCY8pxdT+tgWYfbsfSx3c/p6HXpZJl19LrZ/IvRCR0uyT31PPcaGxvDLkEBRzoXiydYtXknKzftYMWmHazYGDxu2sHKTTtYu7WFLTtjGZ9bFo3Qv08p/StK6Bc81lf3oX+fEvpVJOf7lpew9P2FTDjyCPqURpM/ZWmPpVEqypIhJsw/TsVkSVWEUbU68VJEipMCjuzSGkuwsKmZBU1bWdTUzMK1zSxsambJuu20xvfc3Tiobxn11X0YV9ePk8cMorZvOYP6ljOobxm1fcsZ3LecQf3KqCzr2n9ijW0f0HD0Adn4tUREpBdSwOmlEgnnvaatvLFsE28u38zcFZuZt2rrriATMRgxsJIxg/ty+iFDGD2oivrqPtTX9KG+ug8VpdGQfwMREZG9U8DpJRIJ5901W5m5eD0zF6/n5fc3sGl7GwD9KkoYf8AAPn/SaI6oH8C4ur6Mrq1SiBERkYKlgFPEdrbFeWHhOp6ct4Yn5zWxdmsLACMG9uHsw+qYfFAtE0fVMGpgJZGIzmsREZHioYBTZNriCZ5fsI4HX1/BE++sZmdbgr7lJZw2bjANhwzmxINrGV5TGXaZIiIiWaWAUyQWr23mTzOX8sicFazf1kp1ZSkfnzicKUcM5YSDBlJeosNNIiLSeyjgFLBEwnlu4Tr+94X3aXx3LaVR46zD6vjYMfU0HDKEshLdS1VERHonBZwClEg4j729ml88uYB312xlcL9yvnnWOK44YQRD+lWEXZ6IiEjoFHAKiLszY14TNzzxHu+s2sLBg6u48bKjOf/IA7S3RkREJIUCToGYv3oLP3zkbV55fwOjaiu58bKjuejoeqL69pOIiMiHKODkueaWGD9/7F3unPkB/StKuO5j4/nkpBGURrXHRkREZG8UcPLYi4vW8Z3732Tl5h38w/Ej+c5HD6G6sizsskRERPKeAk4e2tkW5/q/zee2F5cwuraSB750IseOGhh2WSIiIgVDASfPLNuwna/e/RpvLt/MlSeO4t/OPbTLN6wUERGRJP3lzCON7zbxjXvnEE84t3zmWM45YmjYJYmIiBQkBZw8cedLS7h2+tscMrQ/N39qIqMHVYVdkoiISMFSwAlZIuH89LH5/P6ZxZx12BBuuuIYHZISERHZT/pLGqJ4wvnO/W/w4Osr+PTkkfzowiMo0de/RURE9psCTkjiCedb983h4Tkr+dezx/EvZ4zBTBftExER6QkKOCFIDTff+eghfPX0MWGXJCIiUlR0PCTH3J3vP/SWwo2IiEgWKeDk2K+eWsi0V5fxz6ePUbgRERHJEgWcHLp/1jJueOI9Pj6xnm+dMy7sckRERIqWAk6OvLRoPd978C1OHjOI6z9+lE4oFhERySIFnBxYvXkn/3LPa4yqreS3n55IWYnaLiIikk05+UtrZt80s7fNbK6Z3WNmFWnLP2dma81sTvDzj7moKxdaYwm+evdrbG+N87tPH0v/itKwSxIRESl6WQ84ZlYPfA2Y5O7jgShweYZV73X3CcHPH7JdV678v3+dx+wPNvLTTxzF2Lp+YZcjIiLSK+TqWEkJ0MfMSoBKYGWOXjdUT76zhtteXMLnTxrNhUcfEHY5IiIivUbWA467rwB+DiwFVgGb3f3xDKt+wszeNLMHzGxEtuvKtg3bWrnmwbc4dGg/rjn30LDLERER6VXM3bP7AmY1wJ+By4BNwP3AA+7+p5R1aoFmd28xsy8Bn3T3MzJs62rgaoC6urpjp02blpWam5ub6du37z4/39357RstvLYmzrUnVjCyf7QHqytO+9tz6T71PBzqe+6p57mXzZ6ffvrps919Umfr5SLgXApMcfergvnPApPd/St7WT8KbHD3AR1td9KkST5r1qwerxegsbGRhoaGfX7+I3NW8PVpc3Sl4m7Y355L96nn4VDfc089z71s9tzMuhRwcnEOzlJgsplVWvLiL2cC81JXMLNhKbMXpS8vJBu2tXLt9Lc5ZmQ1Xzz1oLDLERER6ZWyfrNNd3/ZzB4AXgNiwOvALWb2E2CWu08HvmZmFwXLNwCfy3Zd2fLff5/P1p0xrv/4UZREdb0bERGRMOTkbuLufi1wbdrwD1OWfw/4Xi5qyabXlm5k2qvL+KdTDuSQofpKuIiISFi0i6GHxBPODx6eS13/cr5+lu4zJSIiEiYFnB5y98sf8PbKLfzH+YfTtzwnO8ZERERkLxRwesDWnW3c+OQCTjyolguOGtb5E0RERCSrFHB6wP88u5gN21r53nmH6i7hIiIieUABZz+t3drCH55/n/OPHMZRw6vDLkdERERQwNlvv35qAS2xBN86RycWi4iI5AsFnP2wdP127n5lKZcdN4KDBusy4CIiIvlCAWc//OqpBUTM+PqZY8MuRURERFIo4OyjlZt28NDrK7j8uBHU9a8IuxwRERFJoYCzj/7nucUA/JPuNyUiIpJ3FHD2wYZtrUx7ZRkXTTiA4TWVYZcjIiIiaRRw9sFtL7zPzlicrzQcHHYpIiIikoECTjd+soIJAAAgAElEQVQ1t8S47cUlnHN4HWOG6IaaIiIi+UgBp5semLWMLTtjfOk07b0RERHJVwo43eDu3DHzAyaMqOaYkTVhlyMiIiJ7oYDTDS8sXM/itdv47Imjwi5FREREOqCA0w23v7SE2qoyzjtSdwwXERHJZwo4XbR843ZmzFvD5cePoKI0GnY5IiIi0gEFnC666+WlAPzDCTo8JSIiku8UcLqgJRbn3leXcfbhddRX9wm7HBEREemEAk4XzJjXxIZtrdp7IyIiUiAUcLrggdnLGdq/gpPHDAq7FBEREekCBZxONG3dyTPvreVjE+uJRizsckRERKQLFHA68cjrK4knnE9MHB52KSIiItJFCjgdcHcemL2cCSOqGTOkb9jliIiISBcp4HRg7ootvLtmK5ccq703IiIihUQBpwN/fm05ZSURLjzqgLBLERERkW5QwNmLWDzB9DdWcvZhdQyoLA27HBEREekGBZy9mLl4Axu2tXLBUbrvlIiISKFRwNmLv7y1isqyKA2HDAm7FBEREekmBZwM4gnnsbdXc8ahQ+hTphtrioiIFBoFnAzmb0iwYVsr5x+pw1MiIiKFKCcBx8y+aWZvm9lcM7vHzCrSlpeb2b1mttDMXjaz0bmoa29eXR3T4SkREZEClvWAY2b1wNeASe4+HogCl6etdhWw0d3HADcCP812XXsTiyeYvSamw1MiIiIFLFeHqEqAPmZWAlQCK9OWTwVuD6YfAM40s1Bu/PTy+xvY2oYOT4mIiBSwrAccd18B/BxYCqwCNrv742mr1QPLgvVjwGagNtu1ZfLom6soj6LDUyIiIgXM3D27L2BWA/wZuAzYBNwPPODuf0pZ523go+6+PJhfBBzv7uvTtnU1cDVAXV3dsdOmTevxemevibF8406mHqp7T+VSc3Mzffuq57mknodDfc899Tz3stnz008/fba7T+psvZKsvPqezgLed/e1AGb2IPAR4E8p6ywHRgDLg8NYA4AN6Rty91uAWwAmTZrkDQ0NPV5sA9DY2Eg2ti17p57nnnoeDvU999Tz3MuHnufiHJylwGQzqwzOqzkTmJe2znTgymD6EuApz/auJRERESlaWT9EBWBmPyZ5iCoGvA78I/B9YJa7Tw++Nn4ncAzJPTeXu/viTra5FvggSyUPAtZladuSmXqee+p5ONT33FPPcy+bPR/l7oM7WyknAafQmNmsrhzfk56jnueeeh4O9T331PPcy4ee60rGIiIiUnQUcERERKToKOBkdkvYBfRC6nnuqefhUN9zTz3PvdB7rnNwREREpOhoD46IiIgUHQUcERERKToKOGnMbIqZvWtmC83smrDrKRZmdquZNZnZ3JSxgWb2hJktCB5rgnEzs5uC9+BNM5sYXuWFy8xGmNnTZjbPzN42s68H4+p7lphZhZm9YmZvBD3/cTB+oJm9HPT8XjMrC8bLg/mFwfLRYdZfyMwsamavm9mjwbx6nkVmtsTM3jKzOWY2KxjLq88WBZwUZhYFfgOcCxwOXGFmh4dbVdG4DZiSNnYNMMPdxwIzgnlI9n9s8HM1cHOOaiw2MeBb7n4YMBn4avDfs/qePS3AGe5+NDABmGJmk4GfAjcGPd8IXBWsfxWw0d3HADcG68m++Tp7XiVfPc++0919Qsr1bvLqs0UBZ0/HAwvdfbG7twLTgKkh11QU3P1ZPnx/sanA7cH07cDFKeN3eNJMoNrMhuWm0uLh7qvc/bVgeivJD/961PesCXrXHMyWBj8OnAE8EIyn97z9vXgAODO4pY10g5kNB84H/hDMG+p5GPLqs0UBZ0/1wLKU+eXBmGRHnbuvguQfY2BIMK73oYcFu+GPAV5Gfc+q4FDJHKAJeAJYBGxy91iwSmpfd/U8WL4ZqM1txUXhF8B3gUQwX4t6nm0OPG5ms83s6mAsrz5bcnE38UKSKcXre/S5p/ehB5lZX+DPwDfcfUsH/1hV33uAu8eBCWZWDTwEHJZpteBRPd9PZnYB0OTus82soX04w6rqec86yd1XmtkQ4Akzm9/BuqH0XHtw9rQcGJEyPxxYGVItvcGa9t2UwWNTMK73oYeYWSnJcHOXuz8YDKvvOeDum4BGkuc/VZtZ+z8oU/u6q+fB8gF8+FCudOwk4CIzW0LytIIzSO7RUc+zyN1XBo9NJIP88eTZZ4sCzp5eBcYGZ9+XAZcD00OuqZhNB64Mpq8EHkkZ/2xw5v1kYHP7bk/puuC8gj8C89z9hpRF6nuWmNngYM8NZtYHOIvkuU9PA5cEq6X3vP29uAR4ynX11W5x9++5+3B3H03yM/spd/8U6nnWmFmVmfVrnwbOAeaSZ58tupJxGjM7j2T6jwK3uvt1IZdUFMzsHqABGASsAa4FHgbuA0YCS4FL3X1D8If51yS/dbUd+Ly7zwqj7kJmZicDzwFvsfvchH8neR6O+p4FZnYUyZMroyT/AXmfu//EzA4iuXdhIPA68Gl3bzGzCuBOkudHbQAud/fF4VRf+IJDVN929wvU8+wJevtQMFsC3O3u15lZLXn02aKAIyIiIkVHh6hERESk6CjgiIiISNFRwBEREZGio4AjIiIiRUcBR0RERIqOAo6IFAwzqzazr4Rdh4jkPwUcESkk1YACjoh0SgFHRArJ9cDBZjbHzH4WdjEikr90oT8RKRjBXdEfdffxIZciInlOe3BERESk6CjgiIiISNFRwBGRQrIV6Bd2ESKS/xRwRKRguPt64AUzm6uTjEWkIzrJWERERIqO9uCIiIhI0VHAERERkaKjgCMiIiJFRwFHREREio4CjoiIiBQdBRwREREpOgo4IiIiUnQUcERERKToKOCIiIhI0VHAERERkaKjgCMiIiJFRwFHREREio4CjoiIiBQdBRwRyToze8zMfpJhfKqZrTazkmD+PTMbl8U6RpuZt7+eiBQvBRwRyYXbgM+YmaWNfwa4y91jZnYwEHH393JenYgUHQUcEcmFh4GBwCntA2ZWA1wA3BEMnQ/8NVhWa2bTzWyLmb1iZv9pZs+nPPcjZvaqmW0OHj+SsmyJmZ2VMv8jM/tTMPts8LjJzJrN7MRs/LIiEj4FHBHJOnffAdwHfDZl+JPAfHd/I5g/D/hLMP0bYCcwDPhC8AOAmQ0M1rsJqAVuAP5iZrVdKOXU4LHa3fu6+0v79huJSL5TwBGRXLkduNTM+gTznw3GMLNK4DjgGTOLAp8Afuju29x9bvt6gfOBBe5+p7vH3P0eYD5wYa5+ERHJfwo4IpIT7v48sBaYamYHkQw0dweLzwRedPedwGCgBFiW8vQPUqYPSJtvX16fjbpFpDAp4IhILt1Bcs/NZ4DH3X1NMJ56eGotEANGpDxvZMr0SmBU2nZHAiuC6W1AZcqyoSnTvs+Vi0hBUcARkVy6AzgL+Cf2POx0LsEJxu4eBx4EfmRmlWZ2OHBlyrp/BcaZ2T+YWYmZXQYcDjwaLJ8DXG5mpWY2Cbgk5blrgQRwUM//aiKSTxRwRCRn3H0J8CJQBUwHMLPxQLO7L01Z9Z+BvsBqkl8x/9+Ubawn+e2rbwHrge8CF7j7umCVHwAHAxuBH7P7MBjuvh24DnjBzDaZ2eQe/yVFJC+Yu/bYikh4zOy7wCB3/24H63wO+Ed3PzlnhYlIQdPVPEUkbEuA/wu7CBEpLgo4IhIqd78v7BpEpPjoEJWIiIgUHZ1kLCIiIkWnYA9RDRo0yEePHp2VbW/bto2qqqqsbFsyU89zTz0Ph/qee+p57mWz57Nnz17n7oM7W69gA87o0aOZNWtWVrbd2NhIQ0NDVrYtmannuaeeh0N9zz31PPey2XMzS7+SeUY6RCUiIiJFRwEng0cXtfIfD78VdhkiIiKyjxRwMpi/McFdLy9lxaYdYZciIiIi+0ABJwN3xx3un7Ws85VFREQk7yjgZBAPLg10/6zlxBO6TpCIiEihUcDJIOEQjRgrNu3ghYXrOn+CiIiI5BUFnAwSDseOrKGmspS7X17a+RNEREQkr2Ql4JjZrWbWZGZzU8YGmtkTZrYgeKwJxhvMbLOZzQl+fpiNmroj4VBRFuWTx43giXlrWKmTjUVERApKtvbg3AZMSRu7Bpjh7mOBGcF8u+fcfULw85Ms1dRlCYeowWcmj8Ld+dPMLl1TSERERPJEVgKOuz8LbEgbngrcHkzfDlycjdfuCclzcCIMr6nkrMPquOeVpexsi4ddloiIiHRRLs/BqXP3VQDB45CUZSea2Rtm9jczOyKHNWWUcCcadOZzHxnNxu1tTJ+zMtyiREREpMvy4V5UrwGj3L3ZzM4DHgbGZlrRzK4Grgaoq6ujsbExKwXF4gnWr1tHY2Mj7s6IfhF+8fe3GNS8kIhZVl6zt2tubs7a+ymZqefhUN9zTz3PvXzoeS4DzhozG+buq8xsGNAE4O5b2ldw97+a2W/NbJC7f+j72e5+C3ALwKRJkzxrN0979q8MrRtCQ8NEAL5ds4KvT5tDvO5wzji8Ljuv2cvpZni5p56HQ33PPfU89/Kh57k8RDUduDKYvhJ4BMDMhpold4uY2fFBTetzWNeHJICSyO49NecfOYzhNX24uXEh7rrwn4iISL7L1tfE7wFeAg4xs+VmdhVwPXC2mS0Azg7mAS4B5prZG8BNwOUecopIOERSAk5JNMLVpx7Ea0s38cr76edOi4iISL7JyiEqd79iL4vOzLDur4FfZ6OOfZX8mvie59pceuwIfvXUQv6/x9/j3i9OxnQujoiISN7SlYwzSDiURPcMMH3KonztjDG8smQDzy7Q7RtERETymQJOBgn3jN+Wuuy4kQyv6cPPHpuvc3FERETymAJOBvHgZpvpykoifPOsccxdsYW/z10dQmUiIiLSFQo4GSScvV7v5uJj6hkzpC8/f/xdYvFEjisTERGRrlDAycB9z6+Jp4pGjG+fM45Fa7dxzyu607iIiEg+UsDJILGXQ1TtPnrEUD5ycC0/e+xd1je35LAyERER6QoFnAziadfBSWdm/GTqEWxvjfPTv8/PYWUiIiLSFQo4GSQ6OETVbsyQflx1yoHcN2s5sz/YmKPKREREpCsUcNK4O87eTzJO9bUzxjK0fwU/eHgubTrhWEREJG8o4KSJJ5LXt+noHJx2VeUl/Oiiw3ln1RZ+8/TCbJcmIiIiXaSAkybuXQ84AFPGD+Njx9Tzq6cW8ubyTdksTURERLpIASdNIjjS1NWAA/Cji45gcN9yvnnvHHa2xbNUmYiIiHSVAk6aXXtwunEzzQF9SvnZpUexaO02rv+bvlUlIiISNgWcNPF4MuB09DXxTE4ZO5gvnHQgt724hOlvrMxGaSIiItJFCjhpdu/B6f5zrzn3UCaNquHfHniTd1dv7eHKREREpKsUcNLs+hZVtPutKSuJ8NtPTaRvRQlfvHMWm3e09XR5IiIi0gUKOGl2BZxunIOTakj/Cm7+1ESWb9zBV+96jdaYro8jIiKSawo4aXZ/TXzftzFp9ECu/8RRPL9wHd++/w0SQWgSERGR3CgJu4B8k9h1ob/9y36XHDucpq07+e+/v8vgfuX8x/mHYfu4V0hERES6RwEnze4rGe//tr582sE0bWnhj8+/T1VZlG+ePU4hR0REJAcUcNLEgoDTlXtRdcbM+OEFh7OjNc5NTy2kJZbgmnMPVcgRERHJMgWcNIlu3qqhM5GI8V8fP5Kykgi/f3YxO9viXHvhEd2+zo6IiIh0nQJOmvZDVCU9GEAiEeMnU4+gojTC/zz3Pmu2tHDDZUdTWab2i4iIZIO+RZUm3oOHqFKZGf9+3mH84ILDefyd1Xzy9y+xevPOHn0NERERSVLASbP7JOOeP4RkZlx18oH84cpJvL92Gxf++nleXLiux19HRESkt1PASRPv4XNwMjnj0Doe/MpJ9K8o4VN/fJkbHn+XWFwXBBQREekpCjhpElncg5PqkKH9+L9/OZlPTBzOTU8t5NLfv8R7a3T/KhERkZ6QlYBjZreaWZOZzU0ZG2hmT5jZguCxJhg3M7vJzBaa2ZtmNjEbNXVVbD9v1dAdlWUl/PzSo/nl5RNYsm4b59/0HDc+8R4tsXjWX1tERKSYZWsPzm3AlLSxa4AZ7j4WmBHMA5wLjA1+rgZuzlJNXdK+ByeXX+OeOqGeJ//1NM47chi/nLGAs294lr+9tQp33eJBRERkX2Ql4Lj7s8CGtOGpwO3B9O3AxSnjd3jSTKDazIZlo66uaD8Hpye/Jt4VtX3L+eXlx3DHF46nojTCl+96jU/+/iVeWrReQUdERKSbLFt/PM1sNPCou48P5je5e3XK8o3uXmNmjwLXu/vzwfgM4N/cfVaGbV5Nci8PdXV1x06bNq3H635zbYwbZrfwH5MrGFMd7fHtd0U84Ty3IsZDC9vY3OKMqY5wwUGlHD04WrRXQW5ubqZv375hl9GrqOfhUN9zTz3PvWz2/PTTT5/t7pM6Wy8frjSX6S92xtTl7rcAtwBMmjTJGxoaeryY+Lw1MHsWxx17LEePqO78CVlyJnBNW5z7Zy3jd88s5hev7eDQof341AkjmXpMPf0rSkOrLRsaGxvJxvspe6eeh0N9zz31PPfyoee5/BbVmvZDT8FjUzC+HBiRst5wYGUO69pDNq+D010VpVE+c+JoGr/TwM8vPZqIGT945G1OuG4G37n/DV55f8Ouc4ZERERkt1zuwZkOXAlcHzw+kjL+z2Y2DTgB2Ozuq3JY1x56+l5UPaE0GuGSY4fziYn1vLViM/e8spRH5qzk/tnLqetfzrnjh3HekcM4dlRNXtUtIiISlqwEHDO7B2gABpnZcuBaksHmPjO7ClgKXBqs/lfgPGAhsB34fDZq6qpYHu3BSWdmHDW8mqOGV/P98w9nxrw1/OXNVdz9ylJue3EJ1ZWlnDxmEKeOG8ypYwczdEBF2CWLiIiEIisBx92v2MuiMzOs68BXs1HHvsjWvah6Wt/yEqZOqGfqhHqaW2I8Pb+JxnfX8tyCtTz6ZnIH2IiBfTh2ZA3HjqrhmJE1HDq0HyVRXdtRRESKXz6cZJxXEiF9TXx/9C0v4cKjD+DCow/A3Zm/eisvLFzHa0s38uKi9Tw8J3lKU3lJhEOG9uPQof04dGh/Dh3WjzGD+zK4X3nRfjtLRER6JwWcNLF4/h6i6goz47Bh/TlsWH8A3J0Vm3Yw+4ONzF2xmfmrt/LU/Cbum7V813P6lEYZVVvJ6NoqRg2qZOTASoYNqGBIvwqGDqhgYGVZTi98KCIisr8UcNK078Eplj/oZsbwmkqG11QydUL9rvG1W1uYv3oLS9ZtY8n67XywfhsL1zbz1PwmWtNu/FkaNYb0q6Cufzm1fcupqSylpqqMmsoyaipLqa5MTldXllJVXkLfshKqyqM6HCYiIqFRwEnT/rc9F/eiCtPgfuUM7jeYU8YO3mM8nnDWbNm562f15p2s3tJC05adrN6yk6Xrt/PGslY2bW/7UBBKV1YSoW95MuxUlZVQVZ78KS+JUF4SoawkQnlJlPKSCGtWtTK79d1gWTRYllynJBqhJGJEI0ZJxIgEj8n5yK7xaMo67csiESiJRDAj+YMRsWTwM4JzrYJlkZSx9re/fTp1XIfzRETynwJOmngefk08l6IR44DqPhxQ3afD9dyd7a1xNm5Php2N21vZvKONbS0xmlvibGuJsa01lnxsidPcEmN7a4zNO9poaYvTGkvQEvy0xuLsaI3x9yULKZS7Unwo9GB7hKhM639oLON2Mzw3YwH7sb1gqK2tjdJnH8/43K7WkTnr9c7/73RVa2srZc8/GXYZvYp6nnsnDkkQ9rUVFXDSxIO9Er014HSVme3aIzO8Zv+319jYyGmnnUZb3GmNJ5IhKJ6gpS1BLOHEE04skQgek/PxXeNOPJEgFncSvnt5LL57ueMkHHDHSd5UNZjddViyfdoJHoOwlb5ucjq5vH277dOZAlqm26FkXC9DXzKv17XtZZJay/IVKxhef8CHtrY/r1kg+TRUK1eu5IAD6sIuo1dRz3NvwM41YZeggJMuOMe46A9R5SMzo6zEdh3akuxqbFxHQ8P4sMvodRob19PQcGTYZfQq6nnuNTauD7uEnN6qoSC03/ogGlXAERERKVQKOGl2XclYe3BEREQKlgJOmt1fEw+5EBEREdln+jOeJq49OCIiIgVPASdNPI9vtikiIiJdo4CTJp5wDF3MTUREpJAp4KSJu6OdNyIiIoVNASdNIuHoG+IiIiKFTQEnTSyhPTgiIiKFTgEnTTzhe7m/joiIiBQKBZw0CZ2DIyIiUvAUcNLEdQ6OiIhIwVPASRNPOBEdoxIRESloCjhp4jrJWEREpOAp4KSJe/JCfyIiIlK4FHDSxBNOVF0REREpaCVhF5BvvnnWOCZWbgi7DBEREdkP2leRZvSgKkb1j4ZdhoiIiOwHBRwREREpOubuYdewT8xsLfBBljY/CFiXpW1LZup57qnn4VDfc089z71s9nyUuw/ubKWCDTjZZGaz3H1S2HX0Jup57qnn4VDfc089z7186LkOUYmIiEjRUcARERGRoqOAk9ktYRfQC6nnuaeeh0N9zz31PPdC77nOwREREZGioz04IiIiUnQUcNKY2RQze9fMFprZNWHXUyzM7FYzazKzuSljA83sCTNbEDzWBONmZjcF78GbZjYxvMoLl5mNMLOnzWyemb1tZl8PxtX3LDGzCjN7xczeCHr+42D8QDN7Oej5vWZWFoyXB/MLg+Wjw6y/kJlZ1MxeN7NHg3n1PIvMbImZvWVmc8xsVjCWV58tCjgpzCwK/AY4FzgcuMLMDg+3qqJxGzAlbewaYIa7jwVmBPOQ7P/Y4Odq4OYc1VhsYsC33P0wYDLw1eC/Z/U9e1qAM9z9aGACMMXMJgM/BW4Mer4RuCpY/ypgo7uPAW4M1pN983VgXsq8ep59p7v7hJSvg+fVZ4sCzp6OBxa6+2J3bwWmAVNDrqkouPuzQPpNvqYCtwfTtwMXp4zf4UkzgWozG5abSouHu69y99eC6a0kP/zrUd+zJuhdczBbGvw4cAbwQDCe3vP29+IB4EwzsxyVWzTMbDhwPvCHYN5Qz8OQV58tCjh7qgeWpcwvD8YkO+rcfRUk/xgDQ4JxvQ89LNgNfwzwMup7VgWHSuYATcATwCJgk7vHglVS+7qr58HyzUBtbisuCr8Avgskgvla1PNsc+BxM5ttZlcHY3n12aK7ie8pU4rX18xyT+9DDzKzvsCfgW+4+5YO/rGqvvcAd48DE8ysGngIOCzTasGjer6fzOwCoMndZ5tZQ/twhlXV8551kruvNLMhwBNmNr+DdUPpufbg7Gk5MCJlfjiwMqRaeoM17bspg8emYFzvQw8xs1KS4eYud38wGFbfc8DdNwGNJM9/qjaz9n9QpvZ1V8+D5QP48KFc6dhJwEVmtoTkaQVnkNyjo55nkbuvDB6bSAb548mzzxYFnD29CowNzr4vAy4HpodcUzGbDlwZTF8JPJIy/tngzPvJwOb23Z7SdcF5BX8E5rn7DSmL1PcsMbPBwZ4bzKwPcBbJc5+eBi4JVkvveft7cQnwlOviZN3i7t9z9+HuPprkZ/ZT7v4p1POsMbMqM+vXPg2cA8wlzz5bdKG/NGZ2Hsn0HwVudffrQi6pKJjZPUADyTvMrgGuBR4G7gNGAkuBS919Q/CH+dckv3W1Hfi8u88Ko+5CZmYnA88Bb7H73IR/J3kejvqeBWZ2FMmTK6Mk/wF5n7v/xMwOIrl3YSDwOvBpd28xswrgTpLnR20ALnf3xeFUX/iCQ1TfdvcL1PPsCXr7UDBbAtzt7teZWS159NmigCMiIiJFR4eoREREpOgo4IiIiEjRUcARERGRoqOAIyIiIkVHAUdERESKjgKOiBQMM6s2s6+EXYeI5D8FHBEpJNWAAo6IdEoBR0QKyfXAwWY2x8x+FnYxIpK/dKE/ESkYwV3RH3X38SGXIiJ5TntwREREpOgo4IiIiEjRUcARkUKyFegXdhEikv8UcESkYLj7euAFM5urk4xFpCM6yVhERESKjvbgiIiISNFRwBEREZGio4AjIiIiRUcBR0RERIqOAo6IiIgUHQUcERERKToKOCIiIlJ0FHBERESk6CjgiIiISNFRwBEREZGio4AjIiIiRUcBR0RERIqOAo6IiIgUHQUcERERKToKOPL/t3fv0XHWdR7H39+ZXHpvek1Lr0DLpZRLIRa8YQQWQavoikqVFQXt7lkUXHEXUM+yuy7nyGFXXFdXKJfD5UgBUYQjXkAkpahc2lJsS6H03tC06SVNmqRNMpnv/jFP0nSYtmmb53lmJp/XOTkz83t+efLtd3om3/x+v+f3iIiIFB0VOCKS18xslpktNbM9ZvaomT1iZv9pZqPN7NdmttvMdpnZIjPTZ5qIACpwRCSPmVkZ8CvgIWAk8HPg08HhG4BaYAxQCXwb8BjCFJE8pAJHRPLZeUAp8EN373D3x4FXg2MdwHhgSnBskburwBERQAWOiOS344B3sgqXjcHj7cAa4BkzW2dmN0UenYjkLRU4IpLP6oAJZmY92iYDuPsed7/B3U8APg5808wujCNIEck/KnBEJJ/9BUgB15lZiZn9LTAbwMzmmNm0oPhpAjqDLxERTFPWIpLPzKwKuBuYBvwmaH4b2AlcT2aRcQNwl7t/L5YgRSTvqMARkYJiZvcDte7+3bhjEZH8pSkqERERKToqcERERKToaIpKREREio5GcERERKToqMARERGRolMSxknN7D5gDlDv7jODttvJbMbVDqwFvuzuu4NjNwPXkNnD4jp3//3hfsbo0aN96tSpYYRPS0sLgwcPDuXckptyHj3lPB7Ke/SU8+iFmfMlS5bscPcxh+sXyhocMzsfaAYe7FHgXAz80d1TZnYbgLvfaGYzgAVkNu86DvgDcJK7H3LDrqqqKl+8eHGfxw5QU1NDdXV1KOeW3JTz6Cnn8VDeo6ecR1BrnakAABKGSURBVC/MnJvZEnevOly/UKao3P0FYFdW2zPungpevgRMDJ5fBjzi7m3uvp7MvWVmhxFXb2zY0cLGJm2GKiIiUsjiWoNzNfDb4PkEYHOPY7VBWyzu+MNqfrKsLa4fLyIiIn0glDU4h2Jm3yFzb5mfdTXl6JZz3szM5gHzACorK6mpqenz+HbUt5HqTIdybjm45uZm5Txiynk8lPfoKefRy4ecR1rgmNlVZBYfX+j7F//UApN6dJsIbMn1/e4+H5gPmTU4YczvPb39dVbtekfztRHTHHn0lPN4KO/RU86jlw85j2yKyswuAW4EPuHurT0OPQVcYWblZnY8MB14Jaq4siUTRlp7H4qIiBS0sC4TXwBUA6PNrBa4BbgZKAeeNTOAl9z9H9x9pZk9BrxBZurq2sNdQRWmTIGjCkdERKSQhVLguPvcHM33HqL/rcCtYcRypJIJo1P1jYiISEHTTsZZEqYpKhERkUKnAidLMmFohkpERKSwqcDJUqJFxiIiIgVPBU6WhNbgiIiIFDwVOFmSWoMjIiJS8FTgZEkmDAfCuAmpiIiIREMFTpZkInPniE4N44iIiBQsFThZugscjeCIiIgULBU4WRKZXZZJp2MORERERI6aCpwsJRrBERERKXiR3k28ECS6ChxdK15U3J20Zx4dSLt3b+jY9bxnu+dqo+tY0EaPfsHxXEu3ci1Yz/W/K3dN7Yft09tzeVbPzXvSrKprOqrvPVg/ObwNjZ2seKcx7jD6FeU8ejv3xj8NogInSzJT32gE5xi0pTppaeukpS1Fc1uq+7G1vZPmthRtqTRtHZ20pdK0p9K0pdKs3dDGsw3LM8dSadpTnUG/NJ1pJ5XuevTux/QBrzPHs/t0tclB/GlR3BH0T395Me4I+h/lPFJ/M6WET8ccgwqcLMlkZtZOvxQzUp1ptje3sbVxH9ua9rGjuZ3dre00tHbQ0NJOQ/B8d2s7u/d20NKWouMIR7/KkgmSlmbwzq2UJROUlyYpL0lQVpKgLJmgNJmgvLSEZMIoSRgJM0qSRjKRoCRh+9uDx2T3Y4JkIrO3kVnm+8wgYRDc0b67zXo+N8Mg6Lv/uHV///7j+/tacF7ItBzI3t2Uk+XomN2S61y9/Zk9m1asXMnM0047SGxHfr5Mn17+Q/uxFSuWM3Pm6XGH0a8o59HbunZl3CGowMmWtP51mXhn2tmyey8bdrawYWcrG3e0sGlXK1ub9rG1cR87mttyTrsMLktSMaiMEYNLGTGojMkjB1ExqJTB5SUMKS9hcFmSweUl3V9DyoPXZSUMKE1SVpLIFDHJBImEUVNTQ3V1deT//v5s4M63qD59fNxh9Dul9auonlEZdxj9inIevZr6VXGHoAInWzCAU3RTVO7O1qZ9rKprYlXdHlbVNfHm1j1s3NlywIjLgNIEk0cOYtzwgZwybijjhg2gcviAzOOwAYwZWk7FoFLKS5Ix/mtEREQOTQVOlv2XiRd2gdOW6mTFO00s3djAko0NLN7YwI7mtu7jE0cM5JRxw7jo1EqmjhrElFGDOX70YMYOLe9eaC0iIlKoVOBkKUkW5hSVu7OmvpmFq7ezcPV2Xlm/i7ZUZhX75JGDOH/6aM6cVMGM44Zx8rihDBtQGnPEIiIi4VGBk6VrBCdVAAWOu/N6bSO/WV7H03+t453dewGYNnYInz93MuceP5Kzp4xg7NABMUcqIiISrVAKHDO7D5gD1Lv7zKBtJPAoMBXYAHzW3Rssc9nF/wAfBVqBL7n70jDi6o2uWzWk83gNzuZdrTzy6iaeXLaF2oa9lCaND0wbzdcumMb5J41hQsXAuEMUERGJVVgjOPcDPwYe7NF2E/Ccu3/fzG4KXt8IXApMD77OBX4aPMaiJE9vtpnqTPPcm/U8/PImXnh7OwZ8cPoYrr9wOhfPGMfwQZpyEhER6RJKgePuL5jZ1Kzmy4Dq4PkDQA2ZAucy4EHPbPf6kplVmNl4d68LI7bDSeTZZeLtqTRPvFbL/9WsZePOVsYNG8DXL5jOFe+ZxHEaqREREckpyjU4lV1Fi7vXmdnYoH0CsLlHv9qgLZYCJ5knIzjtqTQLXtnEXQvXsqVxH6dPGM6dV57NRadWUpLULcREREQOJR8WGee6JjlndWFm84B5AJWVldTU1PR5MCu3pwB4dckSGtZGv9eLu7O0vpPH3mpnW6tz0ogEN5xTzszRHdiOt3hx0VuRxxSF5ubmUN5POTjlPB7Ke/SU8+jlQ86jLHC2dU09mdl4oD5orwUm9eg3EdiS6wTuPh+YD1BVVeVh7HybfHs7LHmFs86aRdXUkX1+/kNZv6OF7zyxnD+v3cn0sUO47XOn8qGTxvSL7e+1k3H0lPN4KO/RU86jlw85j7LAeQq4Cvh+8Phkj/avmdkjZBYXN8a1/gb236ohysvEU51p7nlxPXc8u5qykgTfu+w05s6erKkoERGRoxTWZeILyCwoHm1mtcAtZAqbx8zsGmAT8Jmg+2/IXCK+hsxl4l8OI6be6trFN6qdjDfvauXrC15j2ebdXDyjku99ciaVw7RvjYiIyLEI6yqquQc5dGGOvg5cG0YcR6P7MvEI9sH53Yo6/vnxv4LDj+bO4uNnjO8X01EiIiJhy4dFxnmlawQnzCmqzrRz2+/eZP4L6zhz4nD+d+7ZTB41KLSfJyIi0t+owMmSDPlmm63tKa5/ZBnPvrGNL753Ct/92AzKSrTWRkREpC+pwMkS5j449Xv2cfX9r/LGlib+7eMz+NL7j+/znyEiIiIqcN4lrHtRbW3cx+fvfomtTfu456oqLjilsk/PLyIiIvupwMmSDGENTm1DK5+/+2V2tbTz4NWzI99fR0REpL9RgZOlr+9FVde4l8/d9RJN+zp46JrZzJo8ok/OKyIiIgenAidLSR9OUTXu7eBL971K494OHv7quZwxseKYzykiIiKHp8t3suxfZHxs59nX0clXH1zMuh3NzP+7c1TciIiIREgjOFkS3QXO0Vc47s4Nj73OK+t38aO5s3jftNF9FZ6IiIj0gkZwsiTt2Edw7ly4jqeX13HzpafwiTOP66PIREREpLdU4GRJHuOtGv60Zge3//5N5pwxnnnnn9CXoYmIiEgvqcDJ0l3gHMUQzpbde7luwWucMGYIt336DN1XSkREJCYqcLJ0T1Ed4QBOZ9q5bsFr7Ovo5M4rz2FwuZY3iYiIxEW/hbMkk0d3L6p7Fq1j8cYGfvDZM5k2dkgYoYmIiEgvaQQny/4RnN4XOKu37eG/n1nNR06r5FOzJoQVmoiIiPSSCpwsiSAjvd3JuKMzzTcfW8bQASXc+qnTte5GREQkD2iKKkvyCG/VcNfCtax4p4k7rzyb0UPKwwxNREREekkjOFn272R8+AKntqGVHz+/ho+ePo5LZo4POzQRERHppcgLHDP7JzNbaWYrzGyBmQ0ws+PN7GUze9vMHjWzsqjj6hEfRu8KnFufXoVhfOdjM8IPTERERHot0gLHzCYA1wFV7j4TSAJXALcBd7j7dKABuCbKuLIl7PCLjBe9vZ3frtjKtR8+kQkVAyOKTERERHojjimqEmCgmZUAg4A64ALg8eD4A8AnY4irW9IOfZl4eyrNvz21kimjBvGVD2q3YhERkXwTaYHj7u8A/wVsIlPYNAJLgN3ungq61QKxXmudsENPUT388kbWbm/hX+fMYEBpMsLIREREpDcivYrKzEYAlwHHA7uBnwOX5uias7ows3nAPIDKykpqamrCiRNn4+bN1NTUv+tYW6fzg4V7OXlEgsTWN6jZtiqUGPqb5ubm0N5PyU05j4fyHj3lPHr5kPOoLxO/CFjv7tsBzOyXwPuACjMrCUZxJgJbcn2zu88H5gNUVVV5dXV1KEEmnnua8cdNoLp65ruO3blwLU3tb3Lv1efxnqkjQ/n5/VFNTQ1hvZ+Sm3IeD+U9esp59PIh51GvwdkEnGdmgyyzI96FwBvA88DlQZ+rgCcjjusAyYNMUe3Z18GdC9fyoZPGqLgRERHJY1GvwXmZzGLipcDy4OfPB24Evmlma4BRwL1RxpUtYZazwLn3xfXsbu3gWxefHENUIiIi0luR72Ts7rcAt2Q1rwNmRx3LweRaZNzY2sG9i9bzkdMqOX3i8JgiExERkd7QTsY55NoH56GXNrCnLcU3LjoppqhERESkt1Tg5JDI2gdnX0cn9/95A9Unj+HU8cNijExERER6QwVODgkg1aPA+cXSWnY0t/P3558YX1AiIiLSaypwckgYpIMpqs60c/cL6zhz4nDOO0FXTomIiBQCFTg59FxkvHB1PRt2tvKVD55A5sp2ERERyXcqcHLoeZn4A3/eyNih5Vwyc1zMUYmIiEhvqcDJoWsEZ/2OFhau3s4Xzp1CaVKpEhERKRT6rZ1D5jJxePAvGyhNGnPPnRR3SCIiInIEVODkkDBobUvxiyW1fOS0cYwdOiDukEREROQIRL6TcSFIGCzd1EDaYe7syXGHIyIiIkdIIzg5ZC4Th0kjB/LeE0bFHY6IiIgcIRU4OSSDq8E/c84kEgldGi4iIlJoVODkYGaYweXnTIw7FBERETkKWoOTwykjEsyaNpHjKgbGHYqIiIgcBRU4Ocw5sYzq6plxhyEiIiJHSVNUIiIiUnRU4IiIiEjRMQ/uml1ozGw7sDGk048GdoR0bslNOY+ech4P5T16ynn0wsz5FHcfc7hOBVvghMnMFrt7Vdxx9CfKefSU83go79FTzqOXDznXFJWIiIgUHRU4IiIiUnRU4OQ2P+4A+iHlPHrKeTyU9+gp59GLPedagyMiIiJFRyM4IiIiUnRU4GQxs0vM7C0zW2NmN8UdT7Ews/vMrN7MVvRoG2lmz5rZ28HjiKDdzOxHwXvwVzM7O77IC5eZTTKz581slZmtNLPrg3blPSRmNsDMXjGz14Oc/3vQfryZvRzk/FEzKwvay4PXa4LjU+OMv5CZWdLMXjOzXwevlfMQmdkGM1tuZsvMbHHQllefLSpwejCzJPAT4FJgBjDXzGbEG1XRuB+4JKvtJuA5d58OPBe8hkz+pwdf84CfRhRjsUkBN7j7qcB5wLXB/2flPTxtwAXufiZwFnCJmZ0H3AbcEeS8Abgm6H8N0ODu04A7gn5ydK4HVvV4rZyH78PuflaPy8Hz6rNFBc6BZgNr3H2du7cDjwCXxRxTUXD3F4BdWc2XAQ8Ezx8APtmj/UHPeAmoMLPx0URaPNy9zt2XBs/3kPnwn4DyHpogd83By9Lgy4ELgMeD9uycd70XjwMXmplFFG7RMLOJwMeAe4LXhnIeh7z6bFGBc6AJwOYer2uDNglHpbvXQeaXMTA2aNf70MeCYfhZwMso76EKpkqWAfXAs8BaYLe7p4IuPfPanfPgeCMwKtqIi8IPgX8B0sHrUSjnYXPgGTNbYmbzgra8+mzR3cQPlKuK12Vm0dP70IfMbAjwC+Ab7t50iD9Wlfc+4O6dwFlmVgE8AZyaq1vwqJwfIzObA9S7+xIzq+5qztFVOe9b73f3LWY2FnjWzN48RN9Ycq4RnAPVApN6vJ4IbIkplv5gW9cwZfBYH7TrfegjZlZKprj5mbv/MmhW3iPg7ruBGjLrnyrMrOsPyp557c55cHw4757KlUN7P/AJM9tAZlnBBWRGdJTzELn7luCxnkwhP5s8+2xRgXOgV4Hpwer7MuAK4KmYYypmTwFXBc+vAp7s0f7FYOX9eUBj17Cn9F6wruBeYJW7/6DHIeU9JGY2Jhi5wcwGAheRWfv0PHB50C07513vxeXAH12bkx0Rd7/Z3Se6+1Qyn9l/dPcvoJyHxswGm9nQrufAxcAK8uyzRRv9ZTGzj5Kp/pPAfe5+a8whFQUzWwBUk7nD7DbgFuBXwGPAZGAT8Bl33xX8Yv4xmauuWoEvu/viOOIuZGb2AWARsJz9axO+TWYdjvIeAjM7g8ziyiSZPyAfc/f/MLMTyIwujAReA6509zYzGwA8RGZ91C7gCndfF0/0hS+YovqWu89RzsMT5PaJ4GUJ8LC732pmo8ijzxYVOCIiIlJ0NEUlIiIiRUcFjoiIiBQdFTgiIiJSdFTgiIiISNFRgSMiIiJFRwWOiBQMM6sws3+MOw4RyX8qcESkkFQAKnBE5LBU4IhIIfk+cKKZLTOz2+MORkTylzb6E5GCEdwV/dfuPjPmUEQkz2kER0RERIqOChwREREpOipwRKSQ7AGGxh2EiOQ/FTgiUjDcfSfwJzNboUXGInIoWmQsIiIiRUcjOCIiIlJ0VOCIiIhI0VGBIyIiIkVHBY6IiIgUHRU4IiIiUnRU4IiIiEjRUYEjIiIiRUcFjoiIiBSd/wfCBs24f0bigAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x1125bcf60>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# fix all degrees of freedom \n",
        "qout = qout_bar      # outlet flow -- process disturbance variable.\n",
        "qa = qa_bar          # inlet flow of A -- process manipulated variable\n",
        "qs = qs_bar          # inlet flow of suspension -- process manipulated variable\n",
        "\n",
        "# establish initial conditions\n",
        "t  = 0\n",
        "V  = V_bar\n",
        "ca = ca_bar\n",
        "\n",
        "# time step, and variable to store simulation record (or history)\n",
        "dt = 1\n",
        "history = [[t, V, ca, V/qout, qs]]\n",
        "\n",
        "qout = 0.9*qout\n",
        "while t < 500:\n",
        "    qs = qs_bar - 5*(V/qout - V_bar/qout_bar)\n",
        "    V, ca = odeint(deriv, [V, ca], [t, t+dt])[-1]\n",
        "    t += dt\n",
        "    history.append([t, V, ca, V/qout, qs])\n",
        "\n",
        "plot_history(history, ['t','V','ca','V/qout','qs'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.5 Control Concentration](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.5-Control-Concentration)",
          "section": "2.4.5 Control Concentration"
        },
        "id": "4Dk4Wfwu3u3x"
      },
      "source": [
        "## 2.4.5 Control Concentration\n",
        "\n",
        "As shown above, it isn't enough to control only residence time. In fact, controlling residence time in response to a decrease in output causes the outlet concentration to increase beyond the product quality limits. We propose to fix this problem by controlling $q_A$, the inlet flow of $A$. A proportional control rule is given by\n",
        "\n",
        "\\begin{align}\n",
        "q_A & = \\bar{q}_A - K \\left(c_A - \\bar{c}_A \\right)\n",
        "\\end{align}\n",
        "\n",
        "where, again, we predict a decrease in $q_A$ is needed to compensate for a positive excursion in $c_A$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.5 Control Concentration](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.5-Control-Concentration)",
          "section": "2.4.5 Control Concentration"
        },
        "id": "vF4zM_TG3u3x",
        "outputId": "42c4127e-15ef-47df-f28a-217b849b2e25"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x112aa26d8>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# fix all degrees of freedom \n",
        "qout = qout_bar      # outlet flow -- process disturbance variable.\n",
        "qa = qa_bar          # inlet flow of A -- process manipulated variable\n",
        "qs = qs_bar          # inlet flow of suspension -- process manipulated variable\n",
        "\n",
        "# establish initial conditions\n",
        "t  = 0\n",
        "V  = V_bar\n",
        "ca = ca_bar\n",
        "\n",
        "# time step, and variable to store simulation record (or history)\n",
        "dt = 1\n",
        "history = [[t, V, ca, V/qout, qs, qa]]\n",
        "\n",
        "qout = 0.9*qout\n",
        "while t < 500:\n",
        "    qs = qs_bar - 5*(V/qout - V_bar/qout_bar)\n",
        "    qa = qa_bar - 3*(ca - ca_bar)\n",
        "    V, ca = odeint(deriv, [V, ca], [t, t+dt])[-1]\n",
        "    t += dt\n",
        "    history.append([t, V, ca, V/qout, qs, qa])\n",
        "\n",
        "plot_history(history, ['t / hours','Volume','Concentration $c_A$','V/qout','qs','qa'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.6 Exercise 3.](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.6-Exercise-3.)",
          "section": "2.4.6 Exercise 3."
        },
        "tags": [
          "exercise"
        ],
        "id": "xFLmah1K3u3x"
      },
      "source": [
        "## 2.4.6 Exercise 3.\n",
        "\n",
        "The algebraic formulae given above do not include any limits on flowrate.  Suppose the flowrate $q_s$ is limited to 0 to 200 liters/hour, and the flowrate $q_a$ is limited to 0 to 20 liters/hour. Modify the code above to incorporate those limits. Now try to find the minimum time necessary to bring the tank from initial concentration of 0 to state where it is producing an acceptable product."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.7 Proportional-Integral Control](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.7-Proportional-Integral-Control)",
          "section": "2.4.7 Proportional-Integral Control"
        },
        "id": "BODlyij03u3y"
      },
      "source": [
        "## 2.4.7 Proportional-Integral Control\n",
        "\n",
        "The above control laws do a reasonable job of control, but do not return the system to a desired steady-state operating condition. How can we modify the control laws?\n",
        "\n",
        "\\begin{align}\n",
        "q_A & = \\bar{q}_A - K_p \\left(c_A - \\bar{c}_A \\right) - K_i \\int_0^t \\left(c_A - \\bar{c}_A \\right) dt\n",
        "\\end{align}\n",
        "\n",
        "The second term will integrate any constant offset to produce a constantly changing value.  So the only possible steady-state is when $c_A = \\bar{c}_A$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.7 Proportional-Integral Control](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.7-Proportional-Integral-Control)",
          "section": "2.4.7 Proportional-Integral Control"
        },
        "id": "yBsyDmPi3u3y",
        "outputId": "20490d9e-865a-44db-c9ba-af9e36cb25f4"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x112c66ef0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# fix all degrees of freedom \n",
        "qout = qout_bar      # outlet flow -- process disturbance variable.\n",
        "qa = qa_bar          # inlet flow of A -- process manipulated variable\n",
        "qs = qs_bar          # inlet flow of suspension -- process manipulated variable\n",
        "\n",
        "# establish initial conditions\n",
        "t  = 0\n",
        "V  = V_bar\n",
        "ca = ca_bar\n",
        "error_sum = 0\n",
        "\n",
        "# time step, and variable to store simulation record (or history)\n",
        "dt = 1\n",
        "history = [[t, V, ca, V/qout, qs, qa]]\n",
        "\n",
        "qout = 0.9*qout\n",
        "while t < 500:\n",
        "    qs = qs_bar - 5*(V/qout - V_bar/qout_bar)\n",
        "    \n",
        "    error = (ca - ca_bar)\n",
        "    error_sum += error * dt\n",
        "    \n",
        "    qa = qa_bar - 3*error - 0.4*error_sum\n",
        "    V, ca = odeint(deriv, [V, ca], [t, t+dt])[-1]\n",
        "    t += dt\n",
        "    history.append([t, V, ca, V/qout, qs, qa])\n",
        "\n",
        "plot_history(history, ['t / hours','Volume','Concentration $c_A$','V/qout','qs','qa'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.8 Exercise 4.](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.8-Exercise-4.)",
          "section": "2.4.8 Exercise 4."
        },
        "tags": [
          "exercise"
        ],
        "id": "F6A4fJgZ3u3y"
      },
      "source": [
        "## 2.4.8 Exercise 4.\n",
        "\n",
        "Write an expression for the proportional-integral control of residence time.  Implement the control, and 'tune' the control constants until you get satisfactory feedback control for a 10% reduction in demand.  By satisfactory we mean:\n",
        "\n",
        "* Meet product quality specifications at all times.\n",
        "* There are no more than three observable peaks in any underdamped response.\n",
        "* The decay ratio is less than 0.25.\n",
        "\n",
        "Is it possible to meet these control specifications?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.4.8 Exercise 4.](https://jckantor.github.io/CBE30338/02.04-Continuous-Product-Blending.html#2.4.8-Exercise-4.)",
          "section": "2.4.8 Exercise 4."
        },
        "id": "sDNHLhps3u3y"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GZFOPAaKuBCU",
        "nbpages": {
          "level": 1,
          "link": "[2.5 Hare and Lynx Population Dynamics](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5-Hare-and-Lynx-Population-Dynamics)",
          "section": "2.5 Hare and Lynx Population Dynamics"
        }
      },
      "source": [
        "# 2.5 Hare and Lynx Population Dynamics\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.5.1 Summary](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.1-Summary)",
          "section": "2.5.1 Summary"
        },
        "id": "oTXmvfFO31Ps"
      },
      "source": [
        "## 2.5.1 Summary\n",
        "\n",
        "This notebook provides an introduction to nonlinear dynamics using a well-known model for the preditor-prey interaction of Snowshoe Hare and Canadian Lynx. Topics include limit cycles, the existence of multiple steady states, and simple phase plane analysis using nullclines. This notebook can be displayed as a slide presentation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "482JFcV_uBCW",
        "nbpages": {
          "level": 2,
          "link": "[2.5.2 Introduction](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.2-Introduction)",
          "section": "2.5.2 Introduction"
        }
      },
      "source": [
        "## 2.5.2 Introduction\n",
        "\n",
        "[Snowshoe hare](https://en.wikipedia.org/wiki/Snowshoe_hare) (*Lepus americanus*) are the primary food for the [Canadian lynx](https://en.wikipedia.org/wiki/Canada_lynx) (*Lynx canadensis*) in the Northern boreal forests of North America. When hare are abundant, Lynx will eat hare about two every three days almost to the complete exclusion of other foods. As a consequence, the population dynamics of the two species are closely linked. \n",
        "\n",
        "| Canadian Lynx | Snowshoe Hare |\n",
        "| :---: | :---: |\n",
        "|![Canadian lynx by Keith Williams](https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Canadian_lynx_by_Keith_Williams.jpg/256px-Canadian_lynx_by_Keith_Williams.jpg)| ![Snowshoe Hare, Shirleys Bay](https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Snowshoe_Hare%2C_Shirleys_Bay.jpg/256px-Snowshoe_Hare%2C_Shirleys_Bay.jpg) |\n",
        "|kdee64 (Keith Williams) [CC BY 2.0](https://creativecommons.org/licenses/by/2.0), [via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Canadian_lynx_by_Keith_Williams.jpg) | D. Gordon E. Robertson [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0), [via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Snowshoe_Hare,_Shirleys_Bay.jpg)|\n",
        "\n",
        "It has been known for over a century that the populations of the two species vary dramatically in cycles of 8 to 11 year duration. This chart, for example, shows pelt-trading data taken from the Hudson's Bay Company (from MacLulich, 1937.  See important notes on this data in [Stenseth, 1997](http://www.pnas.org/content/94/10/5147.full))\n",
        "\n",
        "![https://commons.wikimedia.org/wiki/File:Figure_45_06_01.jpg](https://upload.wikimedia.org/wikipedia/commons/1/16/Figure_45_06_01.jpg)\n",
        "\n",
        "(CNX OpenStax [CC BY 4.0](https://creativecommons.org/licenses/by/4.0), [via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Figure_45_06_01.jpg))\n",
        "\n",
        "The actual cause of the cycling is still a matter of scientific inquiry. Hypotheses include the inherent instability of the preditor-prey dynamics, the dynamics of a more complex food web, and the role of climate (see [Zhang, 2007](http://www.int-res.com/articles/feature/c034p083.pdf)). The discussion in this notebook addresses the preditor-prey dynamics."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OCZVhnPZuBCY",
        "nbpages": {
          "level": 2,
          "link": "[2.5.3 Historical Data](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.3-Historical-Data)",
          "section": "2.5.3 Historical Data"
        }
      },
      "source": [
        "## 2.5.3 Historical Data\n",
        "\n",
        "A digitized version of the historical data is available from [D. R. Hundley at Whitman College](http://people.whitman.edu/~hundledr/courses/M250F03/M250.html). The following cell reads the data from the url, imports it into a pandas dataframe, and creates a plot. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 409
        },
        "id": "T5DYualXuBCZ",
        "nbpages": {
          "level": 2,
          "link": "[2.5.3 Historical Data](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.3-Historical-Data)",
          "section": "2.5.3 Historical Data"
        },
        "outputId": "979898e0-7445-4703-917a-54694508be57"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x11dfab210>"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import pandas as pd\n",
        "\n",
        "url = 'http://people.whitman.edu/~hundledr/courses/M250F03/LynxHare.txt'\n",
        "df = pd.read_csv(url, delim_whitespace=True, header=None, index_col=0)\n",
        "df.index.name = 'Year'\n",
        "df.columns = ['Hare', 'Lynx']\n",
        "df.plot(figsize=(10,6), grid=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rsk5coxwuNbx",
        "nbpages": {
          "level": 2,
          "link": "[2.5.4 Population Dynamics](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.4-Population-Dynamics)",
          "section": "2.5.4 Population Dynamics"
        }
      },
      "source": [
        "## 2.5.4 Population Dynamics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "INpnjFyFuBCf",
        "nbpages": {
          "level": 3,
          "link": "[2.5.4.1 Model Equations](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.4.1-Model-Equations)",
          "section": "2.5.4.1 Model Equations"
        }
      },
      "source": [
        "### 2.5.4.1 Model Equations\n",
        "\n",
        "The model equatons describe the time rate of change of the population densities of hare ($H$) and lynx ($L$). Each is the difference between the birth and death rate. The death rate of hare is coupled to the population density of lynx. The birth rate of lynx is a simple multiple of the death rate of hare.\n",
        "\n",
        "$$\\begin{align*}\\frac{dH}{dt} & = \\underbrace{rH\\left(1-\\frac{H}{k}\\right)}_{Hare Birth Rate}-\\underbrace{\\frac{aHL}{c+H}}_{Hare Death Rate}\\\\\n",
        "\\frac{dL}{dt} & = \\underbrace{a\\frac{bHL}{c+H}}_{Lynx Birth Rate}-\\underbrace{dL}_{Lynx Death Rate}\n",
        "\\end{align*}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T618LCyXuBCg",
        "nbpages": {
          "level": 3,
          "link": "[2.5.4.2 Parameter Values](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.4.2-Parameter-Values)",
          "section": "2.5.4.2 Parameter Values"
        }
      },
      "source": [
        "### 2.5.4.2 Parameter Values\n",
        "\n",
        "| Parameter | Symbol | Value |\n",
        "| - | :----: | :---: |\n",
        "| Lynx/Hare Predation Rate | $a$ | 3.2 |\n",
        "| Lynx/Hare Conversion | $b$ | 0.6 |\n",
        "| Lynx/Hare Michaelis Constant| $c$ | 50 |\n",
        "| Lynx Death Rate | $d$ | 0.56 |\n",
        "| Hare Carrying Capacity| $k$ | 125 |\n",
        "| Hare Reproduction Rate | $r$ | 1.6 |"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NBHx2poouWeJ",
        "nbpages": {
          "level": 2,
          "link": "[2.5.5 Simulation using the scipy.odeint()](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5-Simulation-using-the-scipy.odeint())",
          "section": "2.5.5 Simulation using the scipy.odeint()"
        }
      },
      "source": [
        "## 2.5.5 Simulation using the scipy.odeint()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "awPZ2Q0CuBCg",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.1 Step 1. Initialization](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.1-Step-1.-Initialization)",
          "section": "2.5.5.1 Step 1. Initialization"
        }
      },
      "source": [
        "### 2.5.5.1 Step 1. Initialization\n",
        "\n",
        "The `SciPy` library includes functions for integrating differential equations. Of these, the function `odeint` provides an easy-to-use general purpose algorithm well suited to this type of problem."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OzhDjdKauBCi",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.1 Step 1. Initialization](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.1-Step-1.-Initialization)",
          "section": "2.5.5.1 Step 1. Initialization"
        }
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K2cJYWBKuBCk",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.2 Step 2. Establish Parameter Values](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.2-Step-2.-Establish-Parameter-Values)",
          "section": "2.5.5.2 Step 2. Establish Parameter Values"
        }
      },
      "source": [
        "### 2.5.5.2 Step 2. Establish Parameter Values\n",
        "\n",
        "Set global default values for the parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0M7WNJY2uBCl",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.2 Step 2. Establish Parameter Values](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.2-Step-2.-Establish-Parameter-Values)",
          "section": "2.5.5.2 Step 2. Establish Parameter Values"
        }
      },
      "outputs": [],
      "source": [
        "# default parameter values\n",
        "a = 3.2\n",
        "b = 0.6\n",
        "c = 50\n",
        "d = 0.56\n",
        "k = 125\n",
        "r = 1.6"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p2IyyIfBuBCn",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.3 Step 3.  Write function for the RHS of the Differential Equations](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.3-Step-3.-Write-function-for-the-RHS-of-the-Differential-Equations)",
          "section": "2.5.5.3 Step 3.  Write function for the RHS of the Differential Equations"
        }
      },
      "source": [
        "### 2.5.5.3 Step 3.  Write function for the RHS of the Differential Equations\n",
        "\n",
        "`deriv` is a function that returns a two element list containting values for the derivatives of $H$ and $L$. The first argument is a two element list with values of $H$ and $L$, followed by the current time $t$.\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{dH}{dt} & = r H \\left(1-\\frac{H}{k}\\right) - \\frac{a H L}{c + H} \\\\\n",
        "\\frac{dL}{dt} & = b\\frac{a H L}{c + H} - dL\n",
        "\\end{align*}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "joCefyE-uBCs",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.3 Step 3.  Write function for the RHS of the Differential Equations](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.3-Step-3.-Write-function-for-the-RHS-of-the-Differential-Equations)",
          "section": "2.5.5.3 Step 3.  Write function for the RHS of the Differential Equations"
        }
      },
      "outputs": [],
      "source": [
        "# differential equations\n",
        "def deriv(X,t):\n",
        "    H,L = X\n",
        "    dH =  r*H*(1-H/k) - a*H*L/(c+H)\n",
        "    dL = b*a*H*L/(c+H) - d*L\n",
        "    return [dH,dL]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yMXxd_1yuBCv",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.4-Step-4.-Choose-Time-Grid,-Initial-Conditions,-and-Integrate)",
          "section": "2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate"
        }
      },
      "source": [
        "### 2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EZ01UtcUuBCv",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.4-Step-4.-Choose-Time-Grid,-Initial-Conditions,-and-Integrate)",
          "section": "2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate"
        }
      },
      "outputs": [],
      "source": [
        "# perform simulation\n",
        "t = np.linspace(0,70,500)       # time grid\n",
        "IC = [20,20]                    # initial conditions for H and L\n",
        "sol = odeint(deriv,IC,t)        # compute solution\n",
        "H,L = sol.transpose()           # unpack solution "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jm7T2kqsuBCz",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.5 Step 5. Visualize and Analyze the Solution](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.5-Step-5.-Visualize-and-Analyze-the-Solution)",
          "section": "2.5.5.5 Step 5. Visualize and Analyze the Solution"
        }
      },
      "source": [
        "### 2.5.5.5 Step 5. Visualize and Analyze the Solution\n",
        "\n",
        "For this choice of parameters and initial conditions, the Hare/Lynx population exhibits sustained oscillations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        },
        "id": "y1nwBXFPuBC0",
        "nbpages": {
          "level": 3,
          "link": "[2.5.5.5 Step 5. Visualize and Analyze the Solution](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.5-Step-5.-Visualize-and-Analyze-the-Solution)",
          "section": "2.5.5.5 Step 5. Visualize and Analyze the Solution"
        },
        "outputId": "3b92c826-b9c4-4846-8747-d9be55b21ea3"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(t,H,t,L)\n",
        "plt.title('Hare/Lynx Population Dynamics')\n",
        "plt.xlabel('Year')\n",
        "plt.legend(['Hare','Lynx'])\n",
        "plt.grid(True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g8DzM85HuBC4",
        "nbpages": {
          "level": 4,
          "link": "[2.5.5.5.1 Phase Plane](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.5.1-Phase-Plane)",
          "section": "2.5.5.5.1 Phase Plane"
        }
      },
      "source": [
        "#### 2.5.5.5.1 Phase Plane"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        },
        "id": "Ls4VbFzHuBC4",
        "nbpages": {
          "level": 4,
          "link": "[2.5.5.5.1 Phase Plane](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.5.5.1-Phase-Plane)",
          "section": "2.5.5.5.1 Phase Plane"
        },
        "outputId": "b5fa3e5b-8851-421e-a558-3fd9a6bec177"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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7djc7D1cyNnrgjEgoTjz2F1bz+spDfLIp95g+p7S2idLaJtu+t5sJL7MJLzcT3mYTLa2SoqpGimsasXTyEOHuYsTTzYSXmxGjQZBRUkv7arvzq9idX9Xh3DNGhjIrMYTEMG+Gh3rhbVbppBUKR+JUQv/Rb9LYndfxxgFgsVgwGo1H/ZkjI3x4eP6obuvU19czbtw4235ZWRnnnnsuAKeccgrr1q1DCMHrr7/O008/zTPPPAPA5s2bWbVqFe7u7rz66qv4+vqyceNGSkpKmDt3LmeeeaZKpakY8KxKL8HX3YVLT4rmjVUZ1Da24OnmVLeOTtmaXUFiqDfzRofxt293syO3Qgl9hdNRWdfMp5tz+Pt3HddeifA1E+DlSm55PRV1zQCE+5o5KS6AQC9XvM0uNhHvbRPyLnbbJjauXcXsWbM6vbalVVJa20hRVSNF1Q0UVTVSqG8X2h0TQoDs3ajCj7sL+XF3YZtjgZ6uXD45hjmjwhgV4aNG1hSKfsT5e+t+wN3dnW3bttn2rTH6oOX5v/TSS8nPz6epqamNcD/33HNxd3cH4IcffmDHjh189tlntLa2Ul1dzYEDB5TQV7Rhxf5ivt6ex4Nnj8TXY2B4ujZklDFlSACT4wJ4dcUh9uRXMSkuwNFm9cj+wmqmDAkkzMeMr7sLu/OrHW2SQgFoAnvF/mLu/HgblfXNXdbLq2ygrtnC1CGBTEsIYvrQQOKDPI8qRt7QTV2jQRDibSbE2wz4dmtvWW0ThVUNNvGfX9lAWl4VW7PL24wedEZpbROLlqezaHk6AAGertw3J5HTR4YSpEJ+FIo+pVdCXwhxF3AjIIGdwPVAOPAREABsAa6WUnb/394D3XneHbVg1u23387dd9/NueeeS2pqKo888oitzNPT07YtpeSFF15gzpw5A2pxL0X/UdPYwjVvbgDA09XIowuSHWxRz9Q1tZBdVsfFE6NIjtSEwK7DlU4v9CvrmsmvbCAxzBshBCPCvdnTSZiBQtGfZJTU8uCXu1iVXtJlHXcXI5PjA5ieEMi0oUGMDO87D7iUklZJjxmpjAZBsLcbwd5utH8gkFKSXVbHluxytmRVsCW7nL0F1baQIBejwGwyUtPUYhsUKKtt4v7Pd8LnOwFYMC6Cq6bEMj7aD5PRKbJ+KxSDhh6FvhAiEvgTMFJKWS+E+AS4DDgLeE5K+ZEQ4hXgBuDlPrXWAVRWVhIZGQnA22+/3WW9OXPm8PLLLzN79mwA9u/fT2RkZJuHAcWJzQ9pBQBE+rnzzY58Hp4/yumHsA8W1QIwLNSLUB83grxcSesivM6ZSC/WvPfDQ730d2++2HIYKaXKGKLodzJKajnnPyupbbJ0Wn5SnD/ThgYxPSGIcdF+uJq6F7s1jS3sOlzJztxKdhyupLCygZbWVlpaJS0W2Wa7tq4e4+qfsLRKmi2t2nurxKK/AIK8XIny9yA6wIMof3ei/T2IDtDeI/zcu7VHCEFsoCexgZ6cPz4K0BwE23Mq2ZJdztbscrZkVyAbtfouRkGzpW0Y0Ffb8vhqWx4A3mYT985J5LQRoUT6ufeqfRUKRdf0NnTHBLgLIZoBDyAfmA1coZe/DTzCIBT6jzzyCBdffDGRkZFMmTKFjIyMTuvdeOONZGZmMmHCBCwWC6GhoXz55Zf9bK3CmVlzsJRAT1fuOH0Y9322g32F1YwI93G0Wd1yoEgTzAkhXgghGBLk1at0fo4mp0zLNBIT4Km/e1Dd2EJlfTN+Hq6ONE1xAiGl5I1VGZ3G37saDVw1JZbbZg3tNmNNQ7OF3flV7MipYMfhSnbkVnKwuMbmHY/0cyc6wB1PFxMmg8BoMOBiFBgNApNBUFLcRFRECCajwGQwaMeNWpnJoAn4wqoGcsrr2J5TwZKd+W2y/AgBYT5mov09iApw1x4I/N2JDtAeDMJ8zB1GBDxcTUwdGsjUoYG2dsgq1b3+uud/b0FVhwm+ANUNLTz0VRoPfaWlBD17TDiXTopmcnwAZpejn6enUJzo9Cj0pZSHhRD/ArKBeuAHYDNQIaVs0avlApF9ZmUfY59DH+C6667juuuuA2DBggUsWLCgwzn2ITwABoOBJ554gieeeEKF7ig6ZdfhSpIjfZk6ROv8NmeVO73QzyipxSAgNlAXzIEerDxQ7GCreia3XHsYifLXPILRAR4AZJfVKaGv6BeKqhqY9a/UDl58g4ALJkRx5+nDiPL3aFPW1NLK/sJqtudWsDO3ku25lewvPBIGE+ztxtgoX+aPiWBMlC+jo3x7jHFPTU0lJWVMr+22tEoKqhrIKasjt7yenLI6csrryC2rZ93BUvKrDreZl2syCCL83EkM8+bk+AAmxwcwMtynTQiOEIK4IE/igjy5YILm9a9tbGF7bgVbsyvYklXO+owyahpb2pvDdzvy+W5HPqCFPN55+nBmjwhhyFHOVVAoTlR6E7rjDywA4oEK4FNgXidVO52SL4S4CbgJIDQ0lNTU1Dblvr6+VFf3PEnOYrH0qp4z0J2tDQ0NHdrAUdTU1DiNLT0x0G1tskgOFNaR4NFA+vb1mI2QumUvUQ2djxD1Fz216+a9jfi5CVavXAFAa1UThVXN/PDzclyN/dvJHs1vYMPuRnxcBetWrwSgsEoTW0tXbqIsvO9zEAyk36vi+PPpphzu/WxHh+NnjAzl3jmJDA9t6wjKq6hn8ZpMPlyfTbUudv08XBgT5cdpSSGMjvJlbJQfoT5ufS5ujQZBpJ97l2EzTS2t5FXUaw8B5XX6g0A9uw5X2rLteLmZmBjrz+T4AE6OD2BMVMdwJE83E9OGBjFtaBAAjS0W1qSXsmRXPj/uLqS8ruMk5domC49/v4fHv9dGSK6aEsPNM4faHuQVCkVHetPjnQ5kSCmLAYQQnwPTAD8hhEn36kcBeZ2dLKV8FXgVYNKkSTIlJaVN+Z49e3rl/R5IXvLubDWbzYwfP76fLeoczdOT4mgzesVAt3VPfhWWH1dy5snJzBobQdLu1dS5GElJmeIYI3V6ateX961laJgkJWUaAJV+h/n8wDbikid1ECt9zdH8Bl5PX8+Q0BZSUqYDUN3QzENrfsA7PJ6UlKF9aKXGQPq9Ko4fVQ3NnP7MrxRVN7Y5Pjk+gIVzk5gY69/m+K7Dlby28hDf7chHAvOSw5iXHM6YKF+i/N2d0mPtajLYvPPtKaxqYENGGRsyylifUco/l+0DwM1kYEKMLvyHBDA+2h9317ZhOG4mI7OSQpiVFEKLpZUNGWUsTStgWVoBhVWNHa4F8N66bN5blw3Ag+eM5JJJUSpvv0LRjt4I/WxgihDCAy105zRgE7AcuAgt8861wFd9ZaRCMdDJLtNCSeICNc/TsBAvlu9z/hCYwxX1bcSJNRTmcEV9vwv9oyGvsp6ksCP2WfONF+oLfykUx5tlaQXc/O7mNsdGhPtw39xEUoYH20R7a6skdX8Rr63IYO2hUjxdjVwzNY7rp8cNeM90qI+Z+WMjmD82AtCy61iF/4bMUl745QD//lmbkDsmys8W6jMx1r+NQDcZDUxLCGJaQhCPzB/F1pwKlqUVsGRXPjll9QihjRpUNxwJ9Xns29089u1uQn3c+MeFY5gxLLjHbEIKxYlAb2L01wshPkNLodkCbEXz0H8HfCSE+Lt+7I2+NFShGMhk6xNYY/XJoXFBnpRszqWuqQUPV+dczsLSKimobGgzhB/mq20XVDq3YC6pbiQ4IajNsVBfsxL6/YAQwg94HUhGC+n8HbAP+BiIAzKBS6SU5Q4y8bjS0GzhvBdXs7fgSLimh6uRJy8YzfwxEbbMWg3NFr7cepjXV2WQXlRDmI+ZB+YlcdnkGHzdB6cXOsDTlbnJYcxN1lbTrmpoZnOmFo+/PqOUV1cc4qXUgxgEJEf6MjlOE/7TEoLw0hflMxgEE2P9mRjrzwPzktidX8WyXQUs2VVAdUNNh2sWVjVy3VsbAW0i752nDWOYEzslFIq+plcKQ0r5MPBwu8OHgMnH3SKFYhCSVVaLr7uLbZEsm2e8vN5pO6HSmkZaWiXhdkI/xNsNIZxb6De2WKhqaOkwSTHUx40CJfT7g38DS6WUFwkhXNEytf0Z+FlK+ZQQ4n7gfmChI408HjQ0W0h6cGmbY9EB7rx9/WSGBGupXctqm3h3bRbvrsukpKaJURE+PH/pOM4eE47LCZYz3sfsYgvPAS0N59bsCtYfKmV9RhnvrMvi9VUZuJkMzE4K4ewx4cxOCrE5Q4QQjIrwZVSEL3efmUh6UQ3L0gpYuquAnYcrO1zPfiLvwrlJXHpSNAGeajK+4sTCOV2JCsUgI6esnhi7YXmrlzy3wnmFfkmNtv5dsNeRjtHFaCDQ082pPeOlut3tUxaG+phZf6jMESadMAghfICZwHUA+iKKTUKIBUCKXu1tIJUBLvRbLK1Mf+qXNseSI31467rJ+sJSWjjPPZ9up7qhhVmJwfx+xhCmDg10yth7R+DhamJ6grZ+AGgP6VuyKli6K5/vdmpee3cXI6eNCOGcMRGkJAa3SbGZEOJFQkgCt81KILe8jmVphSzdlc+mrPI2mYEA/rF0L/9YupcAT1eeOD+Z2UmhPa5XoFAMBpTQB7y8vDqk2FQ4N1JKHv46jX0F1bx6zSSnH/ourGpok0ovUvfo51XUO8qkHimp0SbAtRfMYb7O7Rm32h3k1dZzF+pjpqi6gdZW6fQLlQ1ghgDFwFtCiLFoqZjvAEKllPkAUsp8IURI+xN7ytDWGY7KbiSl5LF1DZTWttqOJQcZuW1EC2mb12JplfzvQDPfZzQT72Pg/onuRHrX0ZS7i19z+9fWgZgBapYvnDrdyL4yM+sLWvh1Tz7f7sjHbITxIUYmh5tIDjLi0u7/eChwWxJUxLuzscBCak4zh2vaKv6y2iZueW8LoH3W/KEuBBvqB1wb9TcD8XfkCJyxnZTQVwxI1h4q5Z21WQC8uzaTP84e5liDeqCkppHxMUcmtYZ4mzEZBIfLnVfol9bqQr/dUHeYj5lcZ7Zb9+gHebfz6Hu70WyRlNc1dbtAkeKYMAETgNv1+V3/RgvT6ZGeMrR1hqOyG93+4VYOVR5JNHfBhEj+ceEYXIwGiqobuP2DrazPqOPKk2N4aP5I3EyOW+hpIGeAmg38AW30ZO2hUr7dns/StALW5jfibTYxZ1QY54wJZ3pCUIcwqPPQHsg2Z5Xz/vpsvtuZT1NLa5s6W4ssbC2yAII/nRbBFZNjCPM199fXG1AM5N9Rf+KM7aTGrTqhurqa+Ph4mpu1PL5VVVXExcXR3NxMSkoKCxcuZPLkyQwfPpyVK7U83c8++yy/+93vAEhLSyM5OZm6OudfQXSg8vW2PLzNJsZF+/GtHoPprLRYWimtbSLETngaDYJQH7NTe8a7CoEJ9HSjrLbJESb1imLdox/czu4Afb+8znltHwTkArlSyvX6/mdowr9QCBEOoL8XOci+Y+bppXv5ZvsRkX9rylCeuXgsLkYDGzLKOPs/q9ieW8Gzl4zl8fNHO1TkDxZMRgMzhgXzj4vGsPEvp/PWdSdxxshQlu0q4Lq3NnLS4z9x//92sOpACS2WI2JeCMGkuACeu3Qc6x84jb+ePYL4TtKCAvzn5wNMefJnZj69nB25Ff311RSKPse5PPpL7oeCnZ0WuVtawPgbzA0bDfOeOqpTvL29SUlJ4bvvvuO8887jo48+4sILL8TFRQsPaWlpYcOGDXz//fc8+uij/PTTT9x5552kpKTwxRdf8Nhjj/Hf//4XD4+BnSrNmdmSXc6kWH/GRvvx758PUN3Q7LT5k8tqm5ASW9yulWBvN4qrO88P7QyU1DThajTgY277fxfg5Up5XRNSSqeMNT4SctR2JCJAXxG3rLbjQjyK44OUskAIkSOESJRS7kNLx7xbf10LPMUATsf83rosXko9aNt/9NxRXDstDiklr644yD+W7iMmwIN3b5hMUlj/rXrd2qqNVBXXNFJU1UhxdSPFNdp72sEGPsrZjI+7SUsza9befdq/25U78yRhV5PBNqG3scXCiv0lfLsjj2+25/HRxhwCPV2ZNzqMs0dHMDk+wJZi09/TlRtnDOGGU+JZe7CU99dnsyytgJbWtqE92WV1nLtoNQAvXzmBOaPCVKgPrDcYAAAgAElEQVSfYkDjXELfibjxxht5+umnOe+883jrrbd47bXXbGUXXHABABMnTiQzMxMAg8HA4sWLGTNmDNdffz3Tp093hNknBNUNzRwoquHs0RFMjPVHStiWU8GMYcGONq1TrIvntBf6Id5uZJU676hPaU0jgV6uHcR8gIcrzRZJdWMLPk74cFVS3YSHq7FD2lJ/T81WZx6NGCTcDryvZ9w5BFyPNnr8iRDiBrS1WS52oH2/iZ92F/LXL3fZ9l+5agJzk8Opamjmvk93sDStgLmjwnj64jF98n9RXtvEigPF7C+s1oS8nZgvqWnC0tpxcXp3FyPeLq34WGqobmimuqGFuiZLj9dydzHibTbh4+5CXKAHI8N9GKG/YgI8nEb4upmMnDEylDNGhtLQbGH53iK+3ZHPZ5tzeW9dNiHebpwzJoIrp8QwVM+CJISw5egvqm7g0025vLViPyX1ErOLgRaLtIn/P7yvxfLfNzeR66bFOW0qZIWiO5zrV9uN572+n1fGnT59OpmZmfz6669YLBaSk5NtZW5ummAzGo20tBxZsOPAgQN4eXmRn+/coSQDnX0F1UgJo6N8GBGu/Sb2F9Y4rdAv7kLoB3u7sTHTebPAlNY2dfCKA7b0dGU1TU4p9EtrGzuk1oQjdqvQnb5FSrkNmNRJ0Wn9bcvxYmt2OTe+s8m2/6+LxzI3OZx9BdXc8t5mssvq+MtZI7hxRvxxG+VqbZWk5VWxfF8Ry/cVsS2nAim1sL8gL1eCvd0I9nJjZLiPbTvY20ywtxsh3m4Ee7vh6WbSY4ZPtX1ui6WVmsYWqupbqNLFf3VDM1X6u22/voWK+iYOFtfyy94irM8Rnq5GEsO8bcJ/RLgPSWHeeLo5Vk6YXYzMGx3OvNHh1Da28MveIr7dkce76zJ5c3UGM4YFcc3UOGYnhdi8/CHeZm6blcAIchARo/hgfTY/7yns8NlPL93H00v3ccH4SBbOSyLUR8XxKwYOziX0nYxrrrmGyy+/nAcffLDHupWVldxxxx2sWLGCW265hc8++4yLLrqoH6w88ThUUgvAkCAvAjxd8XV34VCx82ZNsgl9r/YefTPldc00tbQ6ZZq3kppGAj27FsxldU3E0Xm8qyMpqWnskHEHwN8WuqOEvqL3lNc2cf5La2z754+P5MIJkeSW13HFa+swGAQf/n4Kk+MDjvlalXXNrEwvZvneYn7dX0RJTRNCwJgoP/40exizkkIYHel7TCu+mowG/Dxc8fPofT75hmYL+wur2ZNfxZ78anbnV/H19jzeX58NgBAQF+jJiHBvRoTpDwARPkT4mh0S3ufpZrKt0Ftc3chHG7J5f302v39nE5F+7lw9NZZLJ0Xjr9/LDEKQkhjCrMQQ8ivr+WhDDh9vzOkwh+rzrYf5fOthRoT78MzFYxkZ0X/hWQrFb0UJfaCuro6oqCjb/t13383dd9/NlVdeyV//+lcuv/zyHj/jrrvu4tZbb2X48OG8+OKLzJ8/n5kzZxIS0iGLnOIYySypxWQQRPm7I4RgSLAnh4prHW1Wl9gmh7YP3fHR9ktqGomwW5TKWSitaSIhxKvDcWvnWO6kgrmkuomYwI7zY8wuRjxcjU5rt8I5ueS/a23bcYEePHZeMrVNFm5YvIkmSytf3Dy90/+T3mJd9Cl1XxFbsiuwtEp83V04dXgwKYnBzBwe3OkIVX9idjEyJsqPMVF+tmNSSnLL623if09+FWl5VXy/s8BWx9fdhWlDA0lJDCYlMcQhnvBgbzduP20Yt6QM5afdhby9NpOnluzl2R/3c+7YCK6dGtemfrivO3edMZzbZyfwy94i3l+fzYoDxW3y8u/Jr+Ks/2iJON68bhIpw0OcJpxJoWiPEvpAa2trp8dXrVrFRRddhJ/fkZubfX7UoKAgW4z+m2++aTseFRVFenp6n9iqgIySWmICPTDpE8aGBHmxKr3YwVZ1TXG1lgrOfqEXwNZ5O6PQl1LqnvGOAsOabrPUSQVzSU0jE2L9Oy3z93ClTIXuKHrJpswyDhQdGS184fIJuLsYuemdTaQX17D4+pN+s8jPLq3jmR/38dU2LYNPcqQPt6YMJSUxmHHR/sfkte8PhBBEB3gQHeDBmaPCbMdrGlvYV1DF7vxqduVWsuJAMUt2aeJ/ZLgPKYnBzEoKYXy0n+0e3h+4GA220J59BdW8szaTL7Ye5rPNuQz1NVDum8tZo8NtWZJMRgNnjgrjzFFh5JTV8cGGbD5Yn01lfdvJ/L9brIV0/W3BKC6ZFN3hPq9QOBol9Lvg9ttvZ8mSJXz//feONkXRjuyyOmLtVpmNDnCnqLrRaUNgiqob2qTWtOLvocW3l9c5XxaY2iYLjS2tHXLog3N79C2tkrK6pjar+drj7+lChRO2t8L5sLRKLnrliDf/r2ePYHSUL49/t5uf9xbx2IJRv2leUHF1I4t+OcAHG7IxGgS3pgzlumlxhAySuG8vNxMTYwOYGKuFMkkp2VdYTeq+YpbvLeK/Kw7xUupBfMwmZgwPJmV4MKcmBhPi3X/fPzHMm8fPH83CeUn8b3Mur/y8h7s+3s7fv93D5ZNjuOLkmDbOl+gADxbOTeK2WQm8vy6L11Zm2LJ7WXnoqzQe+iqN66fHcdusBIePwigUVpTQ74IXXnjB0SYouqCwqpExUb62/Qhfd6TUVp+NDnC+lKbF1Y0dwnYA/HShX+GEHuZS2+qyHe32dDXiajI4pWe8qr4ZKeky/tjfw1XF6Ct6xVNL9ti2ZyUG87vp8Xy8MZvXVmZw7dRYrm4X8tET1Q3NvLYyg9dXHqKxpZVLT4rmjtOGDfqJnUIIksJ8SArz4ZZTh1LV0MzqAyUs31dE6r5ivtPXQRkd6WsL8RkX7dcvIxo+Zheunx5PbFMmpshk3lmbyYup6bz860HOHBnK1VNjmTok0DbPwMvNxM2nDuXaaXF8ujmXV1IPcrjd6uZvrc7krdWZnJIQxEPzRzI8tP+SiCgUneEUQt9Z83Efb6TsmP5McXQ0W1oprW1s4/0J99O28yrqnVboj7aLbbViFaPO6BkvsS2W1VEwCyEI8HClrMb57LYOq/u6d54NKMDTlewy501pqnAOSmsaeW1lhm3/XxePZUNmGX/5YhczhgXx4Dkje/1ZjS0W3l+XzaLl6ZTVNnH26HD+78zhDAn+7XH9Axkfs4sthEZKye78Kpu3/8Xl6bzwSzp+Hi7MHBbMrKRgZg4L7vOVrA1CMHO4Nh8ip6yO99Zn8fHGHJbsKmBYiBfXTIvjgvGRtsxCZhcjV0+J5bKTovl6Wx4vpaZzsN08sVXpJZz53AqCvd1489qTGG3nnFIo+hOHC32z2UxpaSmBgYGDWuxLKSktLcVsHtzem76mpKYRKWnjBQv31YZY8yrruzrNoZTUNHUaAuOni9GKeucLJbF6vQM6sdt63BnTVPYk9JVHX9Ebpj75i237gxtPpqaxhVve20xsoAeLrpjQq9hyKSVfbjvMMz/sJ7e8nmlDA1k4N4mx0R0f+k9UhBCMivBlVIQvt81KoKKuiZW6t3/F/mK+3p6H0SBIGR7MxZOimJ0U2ufhmdEBHjwwbwR3nT6cr7fn8c7aTB78chdPL9nLhROj+N30eNtkfxejgQsnRnHe+Eh+SCtg0fJ00vKq2nxecXUj8xetwsds4tNbppEYpjz8iv7F4UI/KiqK3Nxciou7n0zZ0NAwYERyV7aazeY22X0UR09hlRZSEupzxMMTYfPoN3R6jiNp1nNW+3cSSmIyGvA2m5wyZrw3nnFnnIxrs9uja7urG1potrQ69eqfCsfxy95CmixagoabZg5hVKQvF7ykrZT6xrUndfk/YU9Ds4X7PtvB19vzSI704ckLRnNKQtCgdmYdD/w8XG1pMVtbJbvyKvl+ZwGfb8nl571F+Hu4sGBcJBdPimJURN96yM0uRi6ZFM3FE6PYmlPBO2syeX99Fu+uy+L88ZHcNiuB+CAtvbDRIJg3Opy5yWH8ur+YF5enszGzHDeTASmhydJKVUMLc55fQWygB29dd9IJO6Kj6H8cLvRdXFyIj4/vsV5qairjx4/vB4uOnYFk60CjSM9rbO/R93A14W022cqciSpdePp1ITz9PZzTM17Vk2fc05XccucLgenRo2+3aFZ/Tv5TDAwsrdKWRQXg9tkJPPxVGlmldbx348nEBfW8bkRpTSM3vbuZzVnl3DsnkT+cOlSlXvwNGAzCltLznjOHszK9hM825fLB+mwWr8lkRLgPF0+MYsG4iD4N7RFCMCHGnwkx/jxw1ghe+fUgH6zP5vMtuZw3LpLbZie0WXU3JTGElMQQNmSUsWh5Oiv2F+NqMtDUoj08ZpXWMfuZXxkT5cuLV0xwynBTxeDC4UJfoTgaCvXFp0J8Oq4yW+KEMeMVPQp9F6fMumMVzN5drHwb6OmcITA9jkTY5kU0K6Gv6MD9/9th277nzOEcKKrh862H+UPKUKYMCezx/PSiaq5fvJGiqkZeunICZ40O70tzTxhMRgOz9AWtKuqa+Hp7Hp9tzuVv3+7mySV7mJ0UwkUTo0lJDO7TkbpQHzMPzx/FH1KG8uqvh3hvfRZfbjvM/LER3D47gYSQI2E5k+MDeCd+MjtzK3lxeTpL0wrafNaO3EpmPL2cUxKC+NfFYwnzVfcjRd+ghL5iQFFU1YBB0GHF1iAvN9vCVM6ENSynK+Hp56Qe/cr6ZrzdTF1mvvD3cKXKCUNgevboa8dLaxsBFSurOEJTSyufbs4FwMUouGZaHNe8sYFgbzdum5XQ4/mrDpTwh/c342Yy8vHNUxmnYvH7BD8PV66ZGsc1U+PYW1DF/zbn8sXWwyxLKyTIy5XzxkVy8aToPo2FD/E289dzRnLzqUN5feUh3lmbxdfb8zh7dDh/Om1Ym0w7o6N8eeXqiRworObl1IN8tT0PS+uRxByr0kuY8uTPzEsO428LkjvN0KZQHAvO00MrFL2gsKqBYG+3DgI02NuNkmrnE/qV9ZqI7zrdo4tTCv2q+mZ8uolF9nXXfATVDS39ZVKvqKpvxs1k6HLRGusDQFW9c9mtcDzvrM20bd95+nB+3lPItpwK7puTiJdb9z6xDzdkc+1bG4j0c+fL26Ypkd9PJIX58JezR7L2gdN47ZpJTIz1Z/GaTOY8v4L5L6zinbWZfZq+ONjbjQfOGsGqhbO4eeZQftlbxJznV3Db+1vYW9B2Uu6wUG+evXQcqfekcOXJMbi2c5As2VXASY//xH2fbXfKlMuKgYsS+ooBRWFVY6d5p4MHsEe/otY5Q3e6m3RoDempcrKMQT3Z7WO1u8G57FY4nr9/dyRv/iWTovnHkn2MifLlwgldJ1BobZU88f0eHvh8J6ckBPHpLVOJ8lcx1/2Ni9HAGSND+e/Vk1j/59N46JyRtLRKHvoqjcmP/8ztH25le05Fn10/0MuN++clsWrhbG5NGcqv+4uZ+/xKbnl3M7vbZeGJDvDg8fNHs3LhLK6dGoupndPqk025jPvbj/ztm91Uq/uU4jighL5iQFFY1dBpbHWQl5ZNpaHZ4gCrusYaSuLXTbrH6kYtBMaZqGroQTDrZc7m0e/5AcU5RyIUjmVzVrlte+HcJN5dm0lBVQMPzx/Z5UTa1lbJHR9v49UVh7hmaixvXDupyzktiv4j0MuN350Sz5I7ZvDdn07hipNjSN1bxIIXV3PZq2tZvreoz9a0CfB05d45SaxaOIs/zU5gdXoJZ/1nJb9/ZxO7Dle2qRvqY+bRBcn8dPepnN3JXI43V2cw+pEfePaHfdQ1qfuV4rejhL5iQFFc3dgmtaYV6wqu7ZcldzRWj35XYTDWmHFnS7HZe8E8sOy2hmA4m90Kx3Lhy2ts26eNCOG/Kw5x7tgIJsYGdHnOouXpfLM9j3vnJPK3Bcm9yq2v6F9GRfjyyLmjWPPAbP5y1ggyS+q4fvFG5j6/ks8259oy4Rxv/DxcufvMRFYtnM2dpw9j/aFSznlhFTcs3siO3LYjC3FBnrx45QS+uHUak+M6/t7+80s6Ix9axiu/HnQ6R5ZiYKDuTIoBQ4ulldLaJpuot8eaNtEZBbOPuetJrdbYfWssv7MwUENgerLbZDTg6WpUHn2FDfuVqR+Yl8S/fz6AEHD/vKQuz/l5TyHP/bSf88dHcmvK0P4wU3EMeJtd+P3MIay4bxbPXDwWgHs+3c7Mp5fz6oqD1Lf0jYff18OFO08fzqr7Z3P3GcPZlFXOuYtWc/1bG9iaXd6m7vgYfz6+eQqvXzOJhBAtXad9t/HUkr0kPbiUd9Zm0uJkI8AK50YJfcWAwRoG09lqrbZVZp1M6FfUNXU5ERe0ybiA06XYrKxvxse96wmIVo9+lZMJ5p6EPmidvvLoK6zc8fE223ZSuA/f7cjnllOHEuHn3mn9Q8U13PnRNkaGawthqUWwBg6uJm0l26V3zuCt608iPsiTJ77fy92pdTy5ZA+FfbQWi4/ZhT+dNoxVC2dx75xEtuZUcP5La7hh8UbSi2ps9YQQnD4ylKV3zODJC0bbnFredpPBH/oqjYS/LGHlge4XGVUorCihrxgwWMVwZznpbR79AeYZ93O35nV3HrsbWyw0NLf2Kkbf6Sbj1nWfLQi0hxSVdUcB2gJZK/ZrgumWU4ey6JcDhPuauXlm5176msYWbn53Myaj4L9XT+wyu5PCuRFCMCsxhA9vmsLXf5zO6CAjr604xCn/+IV7Pt3O/sLqPrmut9mF22YlsGrhbO6dk8j6jDLmPr+CR75Oa9MHmIwGLp8cQ+q9KfzfGcORaKvv2oetXv3GBk5+4ieyS51v4UKFc6GEvsJGelE117y5gY2ZZY42pVOsKcf8O/GQO61Hv765y8Wy4MhDizPZ3VMuerCPdXcewWxplVQ3tvTCo2+iutF52lvhON5anWHbHhfty8bMcm44JR53144CXkrJPZ9s51BJLS9eMUFl1xkkjIny49ZxZlLvmcXlk2P4dkceZz63gt8t3si6Q6V9MnHXy83EbbMSSL03hUtPiuadtZmc+s/lvL7yUJt5Ax6uJm4/bRip96Zw1ckxlNY0YXYxEK4vrlVY1cjMfy7n3k+3U9PoPPdihXOhhL7Cxt2fbGfF/mL+8N6WNgt6OAtWj35nQt/XJpidxzMOmoe5N7Hu1U50k7Z6u7vzjBsNAi83k1PF6Ff14gEFrKE7ztPeCsdhTakZ4Wtm5YES3EwGLprYeTrNl1IPsjStgAfmJTEtIag/zVT0AzGBHvxtQTJr7j+Nu04fzracCi57dR3nvbia73fm90mfGOTlxuPnj2bJHTMZG+3H37/bw5nP/crSXQVtHjCCvNx4dEEyP959KqclhZJf2YCH3cPop5tzSX54GR9tyKbVCftuhWNRQl8BQE5ZHTtyKxkX7UdJTSMbMpzPq29dWKozD7mbyYiHq9GpPOPQs0ffywmz1/TGow/gYzY5lWDutd3uSugroKj6SDz2VVNj+XLrYc4ZE9HpnJrUfUX864d9LBgXwQ2nxPenmYp+JsDTlTtOH8bqhbN57LxkKuqbufX9Lcx5fgXL0gr6xMOfGObNuzeczOLrT8LFaOCW9zZz2avrOqTkjNcz9Hx+6zSSI3wB2iR6uP/znQz58/cdJvoqTmy6X+5PccKQqsepPn5+MgsWrWbFgWKmDg10sFVtscYw+ncyGRe08J0KJ4oZl1JSWd9si8PvDKNBOF0WmKPzjDtPe/dW6HubTU5lt8IxLPol3bbdYpHUNlm4akpMh3rVDc3c8+l2ksJ8eOqCMU4z+bah2UJOWR2HSmrJLKklQ39lltZSY3c/sVgsGH9ZSmfyVKDlnY/ydyfSz51If3ei/D2I9HMnyt+dMF8zLido2lB3VyNXT4nliskxLNmVz7M/7OfmdzczIcaPhXOTOHnI8e8fUxJDOCUhiA835vDcj/uZv2gVF4yP4t45iYT5Hlk/ZoKeoeenPUX8Y+neNhN6Ac5/aQ0TY/156coJnS4wqTixUEJfAcDO3AoCPF0ZGe7DsFBv0tqt5ucMlNc142LUhHFn+Hq4OlXoTk1jC5ZW2aPw9DKb2nTMjsYqmHua1Orj7lyTWq0xqmoyrqI3vLM2C4Bx0X58vzOfURE+jIv261DvxeUHKalp4s3rTuo0dr8/qGpo5pc9RWzOKieztJZDxbXkVdZj71wO9HQlPsiTGcOC2yzQl5ObQ3RUNADtn1EsrVBc00hueR2/7i+mqLrtOiQGAWE+ZtsDQFygJ+Nj/Bgf43fCLA5mNAjOGRPB3FFhfLIpl+d/2s+lr65jdlII981NJCnM57hez2Q0cPWUWBaMi+DFX9J5a3Um3+/M5+ZTh3DTzCF4uGqyTQjBGSNDmZUYzKebc3nux/1t/n6bs8o5+YmfuW3WUG6fPUxNHD+BUUJfAcDu/CpGRfgghCA5wodf9NUDncV7BUdSVXZlk7+Hi1OF7lht6ZVn3Ikmh/beM+7SJvzB0VhHRbzcur+t+ZhdaLK00tBsUZ3fCUp905GFh8ZF+7F4TSZPdZIqM6esjjdXZXDBhEjGRHV8COhLSmsa+XF3IUvTClidXkKzReLtZiI+2JNJcf7EBUYxJNiTuEBP4oI8u/x/TU0tIiVlZK+u2dBsIb+ygcPl9RyuqONweT255fXkVtSzIaOML7cdRkrtASAxzIeJsX5Mig1gYqw/Uf7uTtVfHG9MRgNXnBzD+eMjeWtNBi+nHmTev1dy/rhI7jpjONEBx3dyto/ZhQfOGsGVJ8fy1NI9PP/TAT7akMO9cxI5f3ykbcVma4ae+WMjeP7H/by1JrPNfIIXlx/kxeUHeeWqicwZFTqo/0aKzlFCX0GzpZX9BTVcPz0OgJERPny6OZfimkZCvJ1n2K+8rsmWd74z/Dxc2F9Y02V5f2MVnt3lowdrKInzeJitoTs+PXjsfMwm0oucx26rR9+a478rjqzq29JW6LdawKCE/4nA++uzbNv5lfV4m02cOy6iQ72nluzFaBDcN6frxbOOJ3kV9SxLK2DprgI2ZpbRKiE6wJ3rp8czZ1QY46P9bAKvLzC7GIkP8iQ+yLPT8uqGZrblVLAps5zNWeV8seUw763LBiDUx42Jsf5MjA1gUqw/IyN8BmXYj7urkVtTErhicgwvpR5k8ZpMvt2Rz1VTYvnj7IRO13k5FmICPXjpyolszCzjsW9383+fbuetNRk8ePbINuFDXm4m/nrOSC6cGMVfv9zF5qxyTAZBiy76b3lvM77uLnxy81QSw7yPq40K50YJfQWHy+tpsrTaVuOLC9Ru8tmldU4m9Ju7XXzK1935QncAvNx6CN1xMznVwlM1jS24mQy4mrrvpDuN0d/+Mez9Fi58HUwdVzDuS2p0W3ry6HvbTYAO9tZtXPsi/PQoXPU/iJ/Rp3YOdoQQmUA1YAFapJSThBABwMdAHJAJXCKldNiMQWu2nSHBnizfW8wVJ8fYQiKsbMgo47ud+dx1+vA28dHHGykly9IKeOXXQ2zLqQBgeKgXf5yVwJzkMEaG+ziNF9bb7MKMYcHMGBYMaClt9xZUsTlLE/6bMsv5fmcBAGYXAxNi/DlzZChzk8P7tA0dgZ+HK38+awTXTYvj+Z/2s3hNBp9syuGmmUO44ZR4PHu4Dx0tJ8UF8OWt0/lq+2GeXrqPS19dx9xRYdw/L4k4uwezEeE+fHrzVD7bksuT3++hsr4ZT1cT1Y0tVNY3M+f5FZw9JpzHz0vutj9VDB6U0FeQWVoLYLtZxARqQ5BZpXVMigtwmF3tqahr6tLTBEdCd5wl5MgqgnvyMPuYXcirqG97cMU/oSIHzvoXmPr3Zlzd2NKjzXBkJMLW3jVF8MVNWuH2j2DitX1saVusD1Y9dbC2lKbWh6tWC/zyd7A0aoJfCf3jwSwpZYnd/v3Az1LKp4QQ9+v7Cx1hmH36wSh/Dw4V13LlyTEd6jz27W7Cfc3cNHNIn9myJr2Efyzbx/acCoYEeXLvnETmJocxNNirz655PDEaBKMifBkV4cs1U+MAKKhssAn/lQeKeeSb3TzyzW7Gx/gxLzmMecnhxz3MxZFE+Lnz9EVj+f2MITy9bB/P/rifd9ZmccdpCVw2Oea4jmoYDILzx0cxd1Q4r688xMu/HuTnvYX8bno8d5w+zPawajAILpkUzRkjQnl62V4+3JCDl5sJKbVJ59/tyOe7Hfk8eM5Irp0ai2kQjrwojqD+ugqy9JX1YnWBr8VaQlaZc624V17X3GkOfSt+Hi60tGo3MmfA5tHvRShJm9CdihxNeG55G7Z/0JcmdkpNQ0uPXnHQJr22tErqm/X2zlx1pHDPN31kXddUH8VIBHBkDYC8bdBcB54hcGg5WJxndGUQsQB4W99+GzjPUYb8sLvQtl1U1cDEWH+GhbYNZfhi62F2Hq5k4dykPpmAuzO3kqvfWM8Vr6+nqKqBpy8cww93zeS2WQkDRuR3RZivmbPHhPPQ/JH8ePep/HT3qdxz5nCaWlp54vu9zHh6Oee8sJIXl6dzsNh5Qi2PlWGh3rx2zST+94epDAny5MGv0jj92V/5envecc9t7+5q1BbSuieF88ZF8t8VhzjzuRX8qmfPs+Lv6cqTF4zh81unERPgQW2ThUg/d1v5Y9/uJuEvS9jthMk3FMcPJfQVZJXW4eFqJNhLC2NwMxmJ8HUnS/f0OwNSSttk3K6wprG0X0rckVjFe29ixtsI/QPLjmwfSu0Dy7qnprGlx4cTaBvrDkDWGnD1gjGXQv426IN8091R09D7kQiwsztnvfY+9TZoaYCyg31l4omCBH4QQmwWQuhDPIRKKfMB9PcQRxl3/+c7bNt7C6o5Y2Rom/K6phaeXraXsdF+nDu2Y9z+sZBRUsttH2xh/qJV7DxcyV/OGsHye1K45KToQetVTQjx4o+zh/Hdn2aw4t5ZPDAvCZPBwD+X7eO0Z37lzOd+5dkf97Mnv6pPctT3N01OwcAAACAASURBVBNjA/j45im8ed0k3F2M/OnDrcxftIq1B0uP+7VCfMz88+KxfHzTFFxNBq59cwN3fLSVkpq22ZMmxPjz9R+n8/D8kVTWN+NqMjAy/Ei2oLP+s5L7/7eDhmbncJIpji8qdEdBTnkd0f4ebcJdIv3cya90nowqDRZotsgeJ+OCljUm2nqwphg2vQGjL4bAoX1vqB02od9jjL4L9c0WWiytWmeftw3c/SHhDM3DLGXHvHh9SK89+lbPeH2zlqu5MA3CRkPkJNjxMVTlgW9kX5tro6axd3Z7t1+krGQ/mP0g4XT46WEo2AnBiX1p6mBnupQyTwgRAvwohNjbm5P0h4KbAEJDQ0lNTe3xnJqaml7Vs8eaDSvKS5BbI/GpziI1NcdW/u3BJgqrmvn9CMGKFb8e1Wd3RUur5LP9zfyQ1YzJAPOHujAvzgWP1mzWrc4+Ltfoit/SRn1JIpA4CkqHuLOl0MKmwjpe+PkA//n5AKEeglOjTMyIcsHbtR/veX3QRgbgvrGStcGufH6gmstfW8e0CBOXJbri43b8v9sD4yXfHnTh2+15/JSWx2WJrpwSaWrTr8cDj0114aO9TazPryLALHA1QkGt5KONOXy0MYf7J5tJCug4iuVsvyNnxRnbSQl9BfmV9YT7tZ0oFeprZrs+McwZqGnSPD3dh+5oZW1SbK5+HtYu0iaI3rKqizP7hprGZowGgdmlp1ASk16/RfsO+dsgYjxEToCdn0BtCXgF94fJgBYCYz+82xVWu20TiUvTYfiZEJas7Rft6V+h39DbkYh2Mfql6RA0TBP3BhMU7e5LMwc9Uso8/b1ICPEFMBkoFEKESynzhRDhQFEn570KvAowadIkmZKS0uO1UlNT6U09KzlldbB0OQAmN3fi3ODys1NsYqjF0soDa5czY5gvN55/cq8/tzuKqxu57YMtbMis4/LJ0dx1xvB+TXJwtG3Un1yovxdXN/LD7gK+2pbHJ/vL+PKQhXNGh3PV1FjGR/v1+Zyrvmyj2cDdTRYWLT/AqysOsausifvmJnHF5JjjnkHpjNnwx8Jq/vzFTt7YVU5anRdPnD+aIe3Cwc6fC6sOlPDQV7s4VFJLQoiXbdGtpzY0kJIYzL8vG98mZasz/46cCWdsp8E5Vqg4KvIrGghvlxEh3NdMQVWD0wyl1jZrdvh249G33pQq6vXQHSk1zzJoXtryzL40sQPWUJKeOqk2oSStrVC8H0JHQeAwrULpgb42tQ01jc29CoGxes9rG1ugoQpqiyAwAfzjtQrlGX1pZgeqe+vRd+vkASVwGBhdwDcKyrO6OVvRHUKI/2fvvKOburIu/ruqtiT3DhjTe+/EFJOQ3pNJSCFtUoeQOkm+KZlMZtImvU8qyaSSQnoDQsCU0EIJYHovxgV3y+ry+/54kmxjyZZAT7ZBey2WrX4spPf23XeffYxCiDjv78AZQAHwLeDtzr4O+KYt6vtoVYN6frjKxtT+TXPFF2wtpajaxjXjcsLyeusOVHLey0vZeKiKF6YN44lLhrSrJLP2grQ4PVePzeGzW8cz/55JXDE6m/lbSrjkv8s57+VlfLL6QJPZBx0NsTo195/Zj5/umsiATvE8+HUBF7+2nILC6rC/Vu+MOD69ZTyPXzyYzYdrOOvFpbyycCcOV32T+03oncpPd0/kvjP6cLDCQoxW5dsVz99+hKH/ms/cgqKw1xdF5BEl+ic5bE435XUOshKaKriZ8TE4XPXtZgCVxcPJWsp29ynjXgJXuQ/qjsD4mfLlvUsVrLA5aoO0wDQh+uZiOf0lqTuk9pLvUBZhoh9k3cbGRN/ra0/uCaYM0MS0ycKqtShTkBMpDDo1FrsLnFaoLYJkT7JKYg5URYn+cSADWCaE2ACsBn6QJGku8B/gdCHETuB0z+WI4/XFDf0XDnc9p/Vv6s//YOU+OifGNrs+VEiSxEer9jPtjRXoNCq+/FMuFw2P3O5WR0afjDj+feEgVv7tNB69aBDueom/fLmJMY8v4N/fbenQDby90uOYffM4np82lMJKCxe8soyHv93cPKb4OKFSCa4a25Vf7p3M6f0zeGb+Ds57eSlr91c0uZ9eo2bmqb1ZcO9kTumZSpXF2WTy/G0fruOsF5ZQWtN+bLxRhI6giL4QIlEIMUcIsU0IsVUIMV4IkSyE+FkIsdPzM0npYqMIP0o8X+CjFX1v5nF78elbXbKi39LwqWZNlsWb5J8DLgJNbMQtGUErzD4ribOBHCd1g4RsUOsjquhLkhR0M673bzPbXVB9SL4ysSuoVHL9kSb6QcaCAhh0GuocLqiVM7+J9zRdJuVEFf3jgCRJeyRJGur5N1CSpMc815dLknSaJEm9PT8rWnsuJaHTqIiP0TCqW8Npa1dpLb/uKueqsV1RH4elwuZ085cvNvH3rwo4pWcq382cwIBO8a0/MIomMOk1TB+Xw093TeTz28YzpW86H6zcx2nPLmb626uYW1CMy13f+hO1MwghR2T+cm8eV43tynsr5L/p+42Hw76Dnh4fw6tXj+Dta0dhtrn4w+srePDrTQ2JYx5kJxuYdd0o3rhmpG9n3Ht831Zcy5jHf2HhAWe72eGPIjQEq+i/CMyVJKkfMBTYSkMucm/gF8/lKDoYiqu9RL+pop8RLxP9ktr2QfQtHutOS4q+UadBCJlgAzLRFyrZM57eT24WjSBqbc5Wp8vCUQuUxkRfpZatJF4SHQHYXfU43VJIir7F4fZDmLtFnDAH24wLYNKrqbM3qjsuU/6ZmCNbkBztK1o2iuOHxdGQbOVw1TOlX3qTjPMPVuxHp1Zxxehsfw8PCtVWJ9PeXMmnaw5y56m9eOf60dGhRMcJIQSjuyXz0pXDWf6X07j/zL7sOWLmtg/XMuHJRcxatrdDpsUkGLQ8etFgvpqRS1qcnpkfr+fad1azryz8aXdTB2Qw/97JXH9KNz5adYCpzy5mbkFRE+IuhODMgZn8fO9kpo/r2kw4eX+Lg6H/ms9eBeqLQlm0SvSFEPHAJGAWgCRJDkmSqmhHuchRHDuOeGK4fBNCPUjxjPGuMLePqMpgrDsqlcCk0zRsg5bvlImbNhbSB8rNoRFE8DGVHkXf7vSQYyGr+SAT55rDClbZFN7s/2CUcYNni9ds9yjjQg2GVPnG+E5QG7m6IfhmXPAo+naXbNsBiMuSf3rf9wi+51FEBt9vbOo3bmzPMdtdfLGukHOHZJFiOraJzjanm5vfX8OWw9W8Pn0k957R97h2BqJojrQ4PbdP6cWSB6bw1rWj6JZq4JHvtzDxqUW800EJ/7DsRL65XY6+XH+gijNeWMKLC3Zid4X3bzHpNfzz/IF8PSOXFJOe2z5cxy0frKWouumwRqNew6MXDeaDG8cQp9egEvgGVdbYXEx5Jp/nf96BswPuppysCOas2AM4ArwrhBgKrAXu4qhcZE+UWjMcS2SaP7THyKJA6Ci1ms1mVuyXVe7tG9dQtK3hpORV0Fdv3EpK7a42qa8xqi12QLB21TJULTS3aoWbXfsOkZ9/hBEHCnBpEtiYn0/XakGPulKWLvgJt6b1RJnjgff//0ilBVN9XaufhWq7/F6v27SVsdZ1pGoTWL5sOQD9rGoSq/ayUqHP09Gf1ZI6+eB9cM9O8u37WnysJEmoBWzduYei+vUkaxNZsWQJADllVrpbylm88GckVeu7GsdSa2M46yUc7nqOFB4gP7+41edy2awU2s3sWr+MXsCyjbtxaUtJrCxmGLB+2VyqEwcpUmsUbYMXFzRY4DQqweQ+DUlWX60vxGx3cc34Y2vCdddL3PXJelbvreClK4dz1qDM4643isDQqFWcPiCD0wdksHJPOS8u2Mm/v9/C64t386e8nlw5pisx2vAPOlMKGrWKG3K7c87gLB75fgvPL9jB178X8siFg5jQOzWsrzU0O5FvZ+byzrK9PL9gB1OfXcz9Z/blmvHdmixMJ/ZOY+49k3j0+y18tuYQSXqBWqulzOzgxV928uIvO/lu5gQGd0kIa31RhB/BEH0NMAK4Q5KkVUKIFwnBpnMskWn+0B4jiwKho9San59PojYT9fY9nDc1r0nUlyRJaPN/Iikzm7y8fm1YpYyPt87DpIdTp0xp8X6p6xdjTDSRlzcSVldAn1z5/2JTGez9gIlDukF6f0Vr9f7/u5b+TM+umeTlDW7x/janGxbNJTO7O52K1CBlN3x+nItgxa/kTZoke98VqtWLgsJqWLqM0cMGkzewdbJiWjKflIxOZNUKUHVteK61+2HfbCaP6AeJx26FaKnWxig322H+AoYM6EPe+G6tPtd7e1dTZnbQK8MI+/RMmHqePKugNBM2PMTwnpkw2P9rHW+tUbQNCqsalMshXRJ8XmRJkvhgxT4GdY5neHZiyM8rSRIPfl3AvM0l/PP8AWEfshVFyxjXI4Vxt6SwYnc5LyzYwb++8xD+yT25ooMR/oz4GF65agSXjzrCQ98UMH3WKs4f2omHzhvQbNf9eKBVq7h1ck/OHpTF37/exMPfbeH7jUU8P20Y2ckG3/3iY7Q89YehnDUok3tnr6XK4mRkThJr91cCcP4ry7h6bFcePHeAIhOkowgPgmEOh4BDkiR5xkcyB5n4l3jykAmUixxF+0dZrYNko65Znq8QgmSjrvmU2e1z4bmBsHtRBKsEqys4O4lJr5GtJPZasJTLXnGQLTwQUd94bZDWnRitGp1a1ZC6Y2qU+BHfCeqd8t8SAXgbmYO1wJj0Guq8Hn2v/QUaPO/mknCX6Bdey1GwHn2D3mPdMZfItXp3ieI8732E6o4iMqivb9pEOKpbsu/3gsIadpSYuXpszjHltb+wYCezVx9gRl5Pbsjtfty1RnFsGN8zhU9vHc/sm8eRk2Lk4e+2MPnpRby3fF+Hs/RM6pPG3LsncffU3szbXMyZLyxh/ubWdypDRdcUA+//cQzPXjaU7cW1nP3iUuasPdSs6fbUfhk8mhvL+UM7sXZ/Jd1TjQzqLDeYf7TqAP0fmsuafW3aXx9FC2iV6EuSVAwcFEJ4R0WeBmyhneQiR3F8KDPbSQ3gSU0y6ChvTPQlCb6/G2oOwff3yJcjBItLCrKxVSt79Ks8ky4Tu8o/kzxEv0rZKZRe2F1uHK76oGoGmVib7U4wl4KpkZLuJc8R8rv7PPpBxFSC7NOv83r04xrX7fm9NjI5zL4FSrDNuL7UnaKmdcckyklHteE/qUbRdlh/sLLJ5RFdG9J25m0uRiXgrCB2sI7GByv38+IvO7l8VBfuPzM6Tbk9YHzPFD69ZRwf3zyWnGQj//x2M3lP5/P+in1h970riRitmrun9uGHOyaQlRDDLR+s5f/mbPQdo8MFIQSXjuzCj3dNZEBWPPd9voGZH6+nytJU5DPpBM9PG8br00dSa3OyvbiWqf0bHNt/eH0FD3+7Oerdb4cI1gtwB/CREGIjMAx4nHaSixzF8UEm+v5TIVJMOirq7A1XFG+UiVHnkfIwpIo9EapS7hkIStGP0cipO95mynhPdrUxTY7YjFBGujlE4mnUq7HanLKSbGrU7uKtP0LNoWa73MgcrKJv1Guw2qxgKWu6QPH+HiHC7FP0g23GbZy605joCyGr+lFF/4TChyubLvBH5DRYdOZvKWZM92SSjKGl43gni57WL53HLx6s+PTWKIKHEIJTeqby6a3j+OimsXRJiuWhbzZz6jOL+XFTUYeKieydEcdXM3KZkdeTz9ce5JwXm+fhhwPZyQZm3zKOB87qy7zNxZz1wlJ+3VXW7H5nDcpk3t2TOGNAJgu2ljIgK55Jnn6X/y3fR++//xRN5mlnCIroS5L0uyRJoyRJGiJJ0kWSJFW2t1zkKI4NZWZHQO9fslFPRWNFf89i+ecZj3ouR86+YwnSuhOn18jqrlcB9yriQsiErp1aSYw6DZKtEupdTYlnvKf+SBH9UJVxvQad9Yh8oXHdxlQ5hSdSRP8Y6q5zuJCOthyBvEiJKvonFL5aX+j7vWuywTeddm9ZHTtKzJwZoppfY3PywJwNdE818spVI9Coo7Mn2yOEEOT2SuXz28bz4Y1jiYvRMOOjdUyftYqdJbVtXV7Q0GlUPHBWPz69dTwSEpe9voJn5m0Pu3quVglm5PXiqxm5GPRqrn57FY/9sKXZTkiKSc+rV4/g5SuHc7jayqo95ZwzuOE7NOWZfD5Yub9DLahOZESPTicxJEniiNlOWgDrTorxKOtOSQHEdYKu4yE2GYo2RqhSeWBWfGxwmfRmmwtqjopNBJmIRojAea0kwQ9wUqP3EubGir4xXZ4FECkLTAjxmiDvRMTYPKpPY6KvUst/hznCin7QOygaYiUbwl7TtG6IKvonOEblNLXtAJw+ILRJuI9+v4XiGhvPXjY02oTYASCEYELvVL6/YwL/vnAgmw5Vc/aLS3nshy1hn0qrJEZ3S+bHOyfyh5FdeGXRLi7573J2lYZ/wTK4SwI/3DGRa8bl8NbSvVz4yq8cqm2+qDh/aCfm3zOJib3T+HFTMf0y4+icKKfa/ePrAs5+cWlTsTCKNkGU6J/EsLrkwTGBPPrJRh21NhcOl+cLXrIZMgbK6nj6gIhOmrUGa93Ra7E63bhrCuVMd02j7fi4zMh7xkOwwMTYvUS/EfFUa+Tm3JrI1G22udCoBHpNcIcGo16DyelH0fdejtTCKkTrjlGnJl14fNtRRf+kwohGRH/+5mIGdY6nS5KhhUc0xcJtJXy25hC3Tu7J8K7RgfAdCRq1imvHd2PRfXlcNqoLby/by6nPLmb5YVeHUZ/jPEk4r08fyaFKC+e+tIz3lu8Le/2xOjWPXDSId64fRZnZzsMrrLyzbG+zxvb0uBjeunYkz142lMIqKxV1DkZ6vmPbimsZ8cjP5G+PZrW0JaJE/yRGjUP+wqbG+femJns8q5UWB7hdcGQ7ZAyQb8wYIA+gisDBUZIkLK6Wh2V54V0M1FcdbrC9+G7MirhnPNhmXINOjcHhSdYxHTWSIoLDp7xDvoL1Gxt1GkxOb91HEX1TJtRGyCplC62J2KjXkEq1fOHo9zsuA2xV4GwfU6GjOD6Ume1NLntJSGmNjXUHqjhzQPC2nSqLg798sYm+GXHcPbV3WOuMInJIMel54pIhfD0jl06Jsby50c5lr69g8+Hqti4taJw1KJN590xifM8U/vntZq59ZzUlNeE/Zp3aL4O5d09iYIqaf3+/hevebf463obe+fdMYnT3ZNbur6RXusl3+/Xv/sa9n/7e4dKPThREif5JDO+gpkCKvnc6brnZATWFcsxjSi/5xrS+4DBHxDtuc9bjlhomyLYEr6Ir1RY3J55xmXLNduW9md7t4FA8+g2E+SgbQSQXKDZX0DWDTJjjXZWAkH35jRHBHRSz3YlaJYjRBr8TkSw8nwNDStMbvZ+bCNmOolAWC7Y0LDZNeg19MuIAmO+5/owQ/Pn/+m4LFXUOnr18KHpN1LLT0TE0O5Gv/nQKfxykY29ZHee/vIx/fF3QLHGmvSI9LoZ3rx/NoxcN4rd9FZz5whJ+3BT+Y26qSc/dI/Q8dnHD68wtaP46WQmxvHeDXM+BCgupJj1jPFG2X64vpN8/5naoxdSJgijRP4lR7WiZ6HtTKCrqHA2xlAme4UeJ3TxPclDJEgG58Q0gPrZ1AhrvIfrCUi4n7TSGLwlGeZX5WFJg4l3loDOB3tT0RmOaHLsZAdTaQyP6Jr2aeKkGKTZJ9uU3RlymnMbjVt4D612ghLITkSTM8oWjiX5c5D4nUSiPz9Y0HKOGZSf6pn/O31JCtxQDfTJMgR7aBD9vKeGr9YXcPqUXgzpHp4GeKFCpBJO6aFl4Xx7Xju/GR6v2M+WZfD777WCHsPMIIZg+Locf75xITrKBGR+t495Pf/edN8P5OlePzeGHOyfSNdnAbR+u44E5G5rFfXrr+XpGLvExGtbsr2BK34Zz8bkvLeO/+buaWYCiUA5Ron8SoyZIRb/C4mgg9N5ceu/PCOTSe9XxoBR9vRaQUFvLwBiIwCmvMofajGvUaUh0VzZX80G2lljKZfuUwjDbXEHXDLIyniRqqY9Nbn6j1xJTdyRM1QVGqAsUo15NMh5F/+jaTdGhWScS1h2o8v0+sJM85MfucrNyTzmn9ssIanHoctfzxI9b6ZNhYuapvRSrVQm46yWqrU6KqmX/dDTn3D8SYrU8fMFAfrhzIr3T43jgi43c9N4aSms7hoWvR5qJOX86hbtO6803Gw5z9gtL5UnnYUbPNBNf/OkUZk7pxZy1hzxxn5XN7jegUzzf3TGBC4d1ZtH2IwzNTmRoF3mB/NTc7Ux8ahGHG02rjkI5BH9mjOKEg9kpE/0kg38C7fXoV5jt4PQq+l3kn4keZT8CufTV1uBJc1yMBiM2VPUOuRm3yY3e4VPKWzJqbS50alXQ2/sGnYYkqQrJmEoz2mFMAyRZHT+64TXMMNtdAecq+INRpyGJWlz6JJr9pd4dlbojcp+BgjjWBYpLHYtGd1Qjpm+BEm0gO9Hgte1sPFSNw1XPuB5+Fqh+8NX6QvaU1fHGNSPRtqMoTavDzc7SWrYV17K9uJYdJbUcqbVjcbips7sw213YXfUwf36Txxl0auJjtCTEaomP1RAfoyUzIYbe6SZ6Z8TRO8NEmkl/Us4G6J8Vzye3jOO9Ffv4z0/bOOuFpTx+8WDOGqTssTcc0KpV3HN6Hyb3TeOOj9dz6WvLefziwVw6skvYX+e+M/syuW8a93z6O5e/sYK/ndOfP+Z2a/KZMeo1PHf5UMb3TOGhbwow6bVcOSab2asPUlhl5ZT/LOSVq4Zz3hBlzw8nO6JE/ySG2SEn2QTKgE40eBV9J9QdlImyxqP+a2NlIlelvHXHq+gH09hqitGQLGrkC0dbd+Ii5702250hEk+1TDxjutHsr/QpzKURIfrdUo1B31/2uptx6LvQbF/I6CHMZuUVfXPIir7s0bfrEpsfBL0LxLrmw2Ki6Fg42nrRN1Mm+qv3ymNfRndrneg7XPW8+MtOBndO4IwQYzjDjdJaGz9vKWHpjjK2Fdewv8Liy0OI0aronR5HlyQDJr1aTsTSayg9fJCBfXth1GuwO93U2FzUWJ3U2JzUWF3U2JwU19hYs7+SamuD3SMhVkufDBO90uPom2FibI8U+mXGnRTkX6US3JDbnYm9U7n709+57cO1XDayCw+dPyConeW2xoiuSXw7M5eZH6/nz59vYOOhKh48b0DYF6mjuyXz410Tue+zDTzy/RY2HKziP5cOxqBrOKoKIbh8VDbDshO5/aN1fPLbQS4Z0ZklO8ooM9uZ+fF6vl5fyAtXDA/pGB5F8Ii+qycxzE6JJIN/2w7IwzPkAVROWbn3+vO9SOwaIeuON8EmOEU/FS/RP0rR18eB1hAxRT9Yfz7Iin6yqMWpT/ZD9COnMNeG3IwrL1Ds2kTijr7R5FX0la/bbHf5dqCCgUmnIZFarJpEmi1r1BrZzhOhvogolENhI2uASuBLAlm1t4I+GaagpuF+tuYghyqtPHrRoDYhuQcrLMzbXMzcgmLWHqhEkqBLUiyDOydw0fDO9MuMo29mPF2TDb7+g8bIzy8hb2KPVl/HO1dlZ4mZnSW17Cg1s6vEzE8FRcxeLS8AUk06xvdMJbdnCrm9UslODj6WtCOiV3ocX/4pl5cX7uTVRbtYsaecZy8bytgeKa0/uI2RYtLzwY1jeHLuNt5aupctRTW8evUI37C4cCE+Rsvr00fy2uLdPDt/O9uLa3n9mpF0P0ow6pMRxzczc/nnN5v5fO0hRuUkcfqADGavPsCCraUM+uc8fr5nEr0zmp1JojhORIn+SYw6JyQGsO14ER+rlVWe6oPQeVTTGxO7RmRoVkMzbhDxmnptg6J/tHXHOx03Ah79kNNrdCqSqKVOl0izU6d3ZyIiynhoOxEmnex1L9X6aU70KfoRIPo2F11DIB0GvZpkUYtFHeCEbUqPWndOACzfXe77vVuqkRitGpe7nnX7K7loeOt2AZvTzSsLdzEyJ4nJfdJavX+44HTX89X6Qt5bvo/Nh+XjWf+seO4+rQ9nDsqgb0b4lXUhBOlxMaTHxZDbq+HYKUkShVVWlu8uZ/muMn7dXc53G+S0tezkWHJ7pnJa/wwm90lDF+T8jY4EnUbFn8/oS17fdO797HeueGslt0zqwb2n92n3yUsatYq/nzuAwV0SeWDOBs5/eRmvTR/JiDDPf1CpBLdP6cWQLgncOXs9F7y8jOenDWPqUTtgBp2Gpy+TrTwPfl3AnrI67pnah+cX7ADg9OeX8OIVw7hwWOew1neyI0r0I4j6egmVH8WlrWB2SmQnt6xoxcdqqbXYofoQDLy46Y2JXWHbj1BfDyrlDvChNLbGaFWkqjxNlkcr+hCxYUi19tA84/EqOzrhplzr5wDsVfQVbg51uuuxOetDW6CoHOiFkzq1H6KvN8k7KBFoxjWH+H5r1SqShZladQCl05gWkYVVFMpi2c4G+1Vfj1K4tagWs93FmO6tq7IfrzpAcY2N56YNjYiab3O6+WzNQd5YvIfCKiv9s+J58Nz+nDEgk64pbaOeCyHokmTg8lEGLh+VjSRJ7Co186uH9P+wqYhPfjtIokHLOYOzuGhYZ0blJLWrc104MDIniR/vnMhjP27ljcV7WLz9CM9PG0b/rPi2Lq1VXDC0E73TTdz6wVqmvbGCf10wiKvGdg3760zsncZ3d0zgTx+u46b313DHqb24e2qfZjtNl4zowpAuicz8eB3PL9jBNeNy2FRYze8Hq7jrk99ZtrOMxy4efEIuHNsC0XcxQvj7V5vo94+5fLnuUFuX4kOdUwrYiOtFfIwGdV0J1Lsakna8SMgGt11x5bPG6kQtIFbbunoihCBT44lN9Ev00yOiMMsWmOC9nPGSnI5Qp/FDmHWRIcx13kjQEIh+fL2sNtaqAsQNGlMjRvRD9Xcmi1pqRICT4noNZAAAIABJREFUtDEtquifAPh2Q8OcD68/f9VeWeUf04o/3+Z089/8XZzSM4VTevo5loQRFoeLN5fsZuJTi3jom81kJsj56D/eOYGbJvZoM5LvD0IIemfEcX1ud966dhTr/nE671w/ikm90/hqXSGXv7GCiU8t4sm529herPzMkkjCqNfw+MWDPdNiHVz4yq/MWra3Q8Rw9s+K59uZuZzSM5W/fbWJv3yxEbsr/AOsuiQZ+Py28Vw+qgsvL9zFDf/7ze9cgl7pJr6+PZerxnblg5X7UQm4ZlwOAJ+vPcSYxxdQXN0xEo/aO6JEPwJYu7+Cj1YdwOGu51/fbfE/Hc5phdVvwYGVEavL7JBIbMUOkxCrxWD1nCybefTlL6XSPv1am4tYDUErahnqWhxCDzo/TaWmjAh5xkOzwMR5CHOd2g/xFCIiWfrenZNQeguMbjm6sEYE8FUalV9YueslLA53SAsr3E7iqaO6eWeBDFN6tBn3BINX0V+9t4KcFAOZCS17ledtLqbM7GBGnrJxmst3lXH6c0t4/Mdt9M2IY/bN45hz23im9EvvEI2vWrWKU/tl8NKVw1nz4FSenzaUXukm3lyyhzNfWMK5Ly3li7WHcLhOnFjPU/tlMO/uiUzum8Yj32/h3s82dIipr4kGHe9cP5qZU3rxyW8HmfbGSoqqwx9xGaNV8+SlQ3j84sGs3F3OeS8v8xv1GaNV8/jFg3npyuHsKDHz7YbD3DihOwBVFifjnviF5buix+HjRZToRwDfbShCr1Hx+vQRVFudrGjkG/Vh0WPw433w3vlQuU/xmlzueiyuhmSdQIiP1RJj83zRjk58SfD46GoKFaiwATU2JwZt8Ce8NJWZWnWi/xtNaWCrBqeySkGocY8mH2EOoIxHwDPuHXwSF4IybnDJdVcHUsZN6Yor+qEOJwPAKuc+l0uBFihpYK9R/HMSReTQNzMOSZL4bV9FUGk7H606QE6KgVN6KtN4WWd38Y+vC7jq7VXoNSo+u3U8H940lvE9UzoEwfcHo17DxcO78N4fx7Dqb6fx8PkDcLjq+fPnG5j41EJey9/dJNmnIyPFpOfNa0Zy7+l9+Gp9IdPeWNEhFGi1SnDfmX15ffpIdpbUcv7Ly1i1xw8nOU4IIbhqbFc+u2087nqJS19bzpy1/h0NFwztxPd3TCA7OZZZy/Zy4bBOGHTyDv5Vb6/ilYU7O8SuSXtFlOhHAL9sK2Fi71Sm9EvHqFOzcNtRhM1phd/egZxckOrht1mK11TjUW9bt+5oMTg8B4GjhzlFKJdeVvSDP/ElU0N1ICuJ929QkHxKkhRyek2sU1Y7qlVtp4wfC2HW2mXCXBlIGY/ATsSxLFCwyJ/pSgJMRY1m6Z9Q0KgEOSlGDlVaqbQ4GZYdQAjwYFepmdV7K7hidFdFvOYr95Rz1otL+HDVfm6a0J0f75rImO7BZfp3FKSa9Fyf253590zifzeMple6iSfnbmP8E7/wr+82c7DC0tYlHjeEENx5Wm/evGYku0rNnP/KMr/Do9ojzhqUyTczc4mP1XL126v436/KWJCGZSfy3R0TGNE1ifs+38CDX2/yu7vTLdXIF386havHduWb3w8zMieJqf3l4/Az83dw2esrwj7t92RBlOgrjNIaGwcrrIzrkYJeo2ZodiK/H6xqeqc9+eCsg4l/hm4TYdsPoPDqtdLjmWtN0U+I1RJfX4EkVGA4StmKTQK1TvEUm1qbE0MIHC6JaqoI5L1WPgnGWQ+ueimkvOUYp/yZqJRaUMaVJsy20D36wiLnkZfXt0D0LWVyw7ZCMB+D5QhP3UfcAYh+BJOOolAGVkeDlSLbEz3pTbDxTsgNhNmrD6BVCy4bFd5BQ5Ik8crCnVzx5krUQvDZreN58LwBxATRf9RRIYQgr286H900jh/unMBZAzP5YMV+Jj+9iJkfr2PPEXNbl3jcOGNgJl/dnotBp+bKN1fy2Rrl58uEA73S4/j69lym9Evn4e+28PiPW6mvDz/3SPVEfd46uQcfrjzAtDf9737oNWoeu3gwj1w0iOW7y9lXbmHmFNk6t2Z/JUMens/Wopqw13eiI0r0FcZ6D6kfkSOnqQzuksD24tqmK9o9i0ETK5P8PmdCxW455UZBVPmIfmvxmhrSqEYypILqqJORL65SWUW/xuoKybqTUF9DRSCiH4Fsd4tLPlCGQjx19kockppqd4C5BqZ0WYV2u8JRol/4lPGQLDAVuFBR6Q7gdzaly7tU1oowVOgfZrus8oTUjOtR9EsDEn2voh8l+h0V6w82KKve6NUtRTWoBPTLDEz0bU43X6w7xBkDMkk1BZ4zEipc7nr+/nUBz8zfwcXDO/PTXZOCshCdSBjYKYHnpg1j6f9N4eZJPVi0rZTTn1/CP74uoMxsb+vyjgt9MuL45vZcxnRP5oE5G3n428243O2/LyE+Rssb00dy/SndeGvpXu6bswGnAnVr1Cr+enZ/Xrt6BDuKaznv5aUBLUPXjMvhgxvHUGa288HK/fz17H6+285+cWm7CjXpCIgSfYWx6VA1apVggCeCa3DnBBzuenaUNEojKFwDnUeARgfZYxquUxBVFpkcJbXm0Y/RkiaqcMYGyJCOy4qAdccZvHVHkoirr+JIQGXcO2VWuahKj8AckpVEbaugknjMjgAHWGMaIPkIqhLwWXdCaWq1lFMj4jA7A6hAPmVcuYXVsTQRe9/HEmeAKcARHPYVhTL4tVETn4/oH66hR5qJWF1gBX3e5mKqLE6uHBO++EGrw81tH67j41UHmJHXk+cuH9piDSc6shJi+evZ/cm/fwpXjsnm49UHyHs6n1cW7myyE9PRkGjQ8b8bRvPH3O78b/k+rn1nNZV1zRNn2htUKsE/zx/An0/vw5frCrn1g7WK/T+cPTjLZxm6ZtbqJslYjXFKz1S+uT2X9Dg9T83bzr2n9/FFmd772Qbu/3yDIqlBJyKiRF9h7D5iJifF4Nua7eNJftjt3a502aFoA3QeKV/OGAxqPRxSluhXeoh+a4p+QqyWNFGNPSZAvFwkFH2bK3jrjsOMTnK0qSXD6lH0Q1LGLeVUizgsjgCKfQQWKMdmgSmnVpWANWDdynvdj8ejX+yM9X97BBYoJyqEEGohxHohxPeey92FEKuEEDuFEJ8KIYIfYXwcaJyhn+OJp9xaVOMTXQJh9urwNuFW1Dm46u2V/LKthH9fOJAHzurXYZttw420OD2PXjSYeXdPYnzPFJ6Zv4Mpz+Tz2ZqDuBWwkEQCGrWKh84fwNN/GMKafZVc8Ooydpa0/5hRIQR3nNabxy4exKLtpUyftYpqizKe+F7pcXz1p1yGdU3kztnreXPJbr/9ATkpRr6ccQp5fdJ47ucdDMtO8KXyfL72EBOeXNRk+nUU/hEl+gpj9xEzPdMaSGdOigGVgD1H6uQryneB2wFZQ+XLGh2k94eSAkXrqgrSox8fqyVVVGPRBSD6Cg+gctdLmO0hNON6IhGLXQGIvkYPMYmKEmarh/OGZiWpoFYVT509gEIRAcJca3chBBhC8QtbKqhTJQSu20uYFYyqPFaPvl1loNIR4G/VxoIuLmrdOTbcBWxtdPlJ4HlJknoDlcCNkShiw6GGOL/sZANVFgeFVVYGtODPLzPbWb23gguHdQ5LE67F4eL6d1ez+XANr109gmvHdzvu5zwR0SvdxFvXjuKzW8eTkRDDA3M2ctGrv3ZoP/Zlo7L55NZx2Jz1THtzJZsPN4+XbI+4emwOr141gk2HqrlcwSShBIOW9/84hnOHZPH4j9v413db/C7u4mK0vHntKG6b3JPZqw9SUFjNk5cOBuBIrZ3c/yzsMA3QbYUo0VcQLnc9+8os9EhrsAfoNWq6JBnYU+Yh+mXy6GdS+zQ8MK0fHNmhaG1VFicqIQ/EagnxMWrSqMKsCeAljcsEezU46hSosoHEBe3R9yi1Ra64wIqQwlGV1mPw6GMpx6xKCKzoR2AnwmxzYdJpQiM4lnIs2mDqVl7RD9Wjb9MmYHW6AzefmdKiRD9ECCG6AOcCb3suC+BUYI7nLu8BF0W6rpwUA1s8pLElRf+XrSXUS3DmwIyA9wkW7nqJO2evp6CwmlevGsFZg7KO+zlPdIzpnszXM07hpSuHU1Rt5YJXlvHSLzsV8YxHAiO6JvH5reOJ0ai46q1VbDg6iKOd4pzBWfzvhtEcqrRw6WvLFWuYjtGqefmK4dw8UbY6zfhord95BGqV4C9n9+P5aUNZf7CKVxbt4vXpI9B4zlWXvrac7zf6twBFAaGNkowiJByqtOJw1zdR9AG6pxrZW+b54hzZAQhI7d1wh7Q+sPETsNVAjDLjtSstDoxBDKFKVNWhE26q1YGIfqOIzZSeYa4SX5xW0NYdDzGrkOKwOt3+yZ8pQ1HiafH41eNDSN3BUk6dphd1gXyREbHAOENbnIBMmDXdA9cdmwQqrbI7EZ7FoFEXWhOxQydHLFqdboz+PicRiDQ9AfEC8AD48lZTgCpJkrwrwUNAZ38PFELcAtwCkJGRQX5+fqsvZjabg7rfvoK1LD4kl1C5t4D8w/6Pex+vtZESIyjdvo4jO45d0ZckiQ+3OvjlgIvp/XVoS7eSX7q19QcqgGDfo/aEeOCfYzR8tNXNcz/vYM7KXdw4WEdOvDJ9DUq/R/cMFTz1m4sr3viVe0fG0DupY/Rn3D9Sy7NrrVz40mJuGyCBQu9RrhHq+umYvbmE856dz10jYojTNf/+JQH/N0rHy+tt3D17HTcN0rPggJNdVfXM/Hg9C38r4Pwe2ja1xrXH71uU6CsIrw//aKLfJSmWjYc8K/uy7ZDYVbYKeJHa13PbTugyUpHaqixOjH6+SEcj3iWnpVSIALnT3iFaChP9UK075cRTZw+QZW9Mk/siFIItVOtOvZxKYzMlYLEHUMZ1JtAaFFfGQ1LFJbk52J6chKU2QN2+qb4K7kR46g51J8Kpl5Ow6hwu/0TflCZ/B6MICkKI84BSSZLWCiHyvFf7uavfLRRJkt4E3gQYNWqUlJeX5+9uTZCfn0/A+839AZD7kM6aOoUFn28g1XSEC8+c4vfudXYXWxf8zNVjc5gyZWCrr90S3lqyh18ObOXmid35+7kDjuu5jhctvkftHOefITdH//2rAh5ZaWfGlF7MnNILnSa8ZoRIvEcTcq1c9dYqnl9vY9Z1wxiv0CC2cGNybh3XzFrFywVWZo0eRG6vADbe40QeMHFTEXd9+jvPbRS8d8MYunp6a46+37lTbNzywRre2FTNvVP7cLjayuzVB/lypxOXIY1nLhsa9s9IsGiP37eodUdBNBD9pskenRJjqbQ45S2qIzsgrW/TB3ovl21XrLYqqwNTEHaYWLtMnMukAAOovIq+WRmffm3I1h0P0Zdkou8XCiv6VneI1h1bFUj12HVJgZVxH2FWVhkPSdG310C9C6e+hboBjKnK7kTYXBj1ISpklnJcMfIulaWl/oKooh8KcoELhBD7gE+QLTsvAIlCCO8HqwsQ0T32biny8XfPETO90gOkLAGLdxzB4arnzIGZAe8TDJbvKuPxn7ZyzuBM/np2/+N6rijgzIGZLLh3EucP7cRLv+zk4v/+2iGHbWUlxPLpLePonBjL9e+uZsmOjmEL7O4ZZJUaK7jh3d/4YaNyc3POHpzFxzeNpdLi4JLXfg1odcpMiOGzW8dz3pBOPPvzDursbu4/U+ZN3244zAWvLDthJjCHA1GiryD2HKkj1aRr1vCaGS9njhdV1kH5zqb+fICk7rLd4YhyRL+yzokxCPIsPEpscX0gou/xsirUkOsj+kFbd8pwq2OwEoMloA0mDRy14FDmZGFxQoxWhVYd5NfLM7zJqUsK7HUHxXsLQlb0Pf0QrpjklqPYTOmKet3NdldIw8kAsFQgxcpEvy5gf0G6nP+v4OyCEwmSJP1VkqQukiR1A64AFkqSdDWwCPiD527XAd8oXUvjz2NWgny83VduoXtqYKI/f3MxSQYtozwzT44FNTYn932+ge4pRp69bJgiU3VPRiQadDw/bRhvXjOSAxUWzn9lGUt3dgyi3Bjp8TF8css4eqSZuOm9NfyyVblQiHAiIz6Gv46NZUiXBGbOXqdojv2obsnMue0UYrRqrnhzZcD3KEar5qUrhnH/mX35dsNhft5Swn8ukZt0txXXMuKRnzvkglAJRIm+gthXXkdOSvMTS1aifOKpOLwbXLbmRF+tgZReDY26CqDKEpyi702nOewK0CsQkwiaGMWm49Z4VuVBK/p1ZTg9Sq25JUUfFCPNNpcUchY9gCs2OXB6DSjuGTfbXCFGgsoLFCk2CYe73u9Yc8BTt3In5RqbM7QFissB9hqkWHnrvMUFIfh2iaI4ZvwfcK8QYheyZ3+W0i/YeE5JRnwM1RYnFXWOgETf5a7nl22lTO2fgSbYBbof/OvbLZTU2nlu2rCTOidfKZwxMJPvZk4gIy6G695ZzRuL/ccytmekmPTMvnks/bLiuO3DtcwtUHayfLhg1Ao+uHEs43ukcP+cjfy8RblFSq90E1/OOIVe6SZufn8NH63a7/d+Qghun9KL16ePYEtRDW8v28trV48A5Gb4iU8tiibyECX6iuJwlY3Oic1zujslyNdZirbJVxxN9EFuzlWS6FudmIJJszaX4EBLqSPAhEiFp+PWhurRt5RRHyt7CAMnwXgaWxUin1aX1GqaURN4iL4Uk9y6oq+wdSekhlZv3R7CHFDVN6XJiyqFTsiyoh9aIy6AMHqsO4Hq9n1OovadUCFJUr4kSed5ft8jSdIYSZJ6SZJ0mSRJio9A9fVAIW/z7y2XU8G6+RFeAAoO11BrczGpT4DBgEFgbkExX6w7xO15PRmWHaCnKYrjRrdUOVv97EFZPPHTNmbOXt/ycbMdItGg48ObxjK4cwJ3zF7PygATYtsbYnVq3rx2FIM6xXP7x+tYsVu5utPj5N2PSX3S+PtXBTwzb3vARd1Zg7J474YxFFfbePSHrbx7w2jfbdFEnijRVwz19RJF1VY6JzUn+pmerWRX+T75iqSc5k+Q1A2qDsiNmmGG3eXG4nAHZd3BXEq1OpnaQOo4KDodt8Zj3YkNwbojGWTi2WomvUJZ+lbXsU1plQwpWBwtxT2my/dVyEoSsgXG4iXMnve7pYWV2wE2ZXKkzbZjsxxpTJ4FYaDPtvHkno4rhIjxc50ynXhhxqbChs9aZnyML+WsR5p/ou8lWmN7BEgXawUVdQ7+9tUmBnWO547Terf+gCiOC0a9hleuGs5fzu7HT5uKuPjV5RzuYIOT4mO0vHvDGLomG7jtw7XsK1MmojrcMOk1/M9T983vr2HTIeXmAxj1Gt6+dhRXjM7mlUW7+PvXBQHPj+N7pvDJLeOwOd3c99kGPrhxjK8/cubH63l10a4Ot/sTLkSJvkIorbXjdEt+Ff0YrZpkow5RfVD24pv8NH8l5cjkSIEm1yrPtLtgrTu1muTANhjwKPrKbD/W2pzEatW+vNxWUVeGMMpcJHAzrrJRlVaXdEzE06cw+8kRBjzEU/LdP5yo9wwmC3WaL4DaY3FpNUtfoaFZodctL1C0nrpbjTRV0HbUzvGbEGKc94IQ4lJgeRvWEzRW7a3w/Z4RH8PeMgsqIQ/O8nv/PeX0TDOSHtdsbRMUXlywg2qrk2cvGxZ8b04UxwUhBLdN7sl7fxzD4Worl7+xosN5shNitbxz/WgEcON7v3WYBtIko44PbhxDQqyW695dza5SZXL2QZ40/MQlg7ltck8+XnWAh74tCEjYB3VO4PPbxhOjVfOnD9fxj/MGcMYA2ar79Lzt/PnzDYEtpicwokckhVBYJR9w/Cn6IDeIxdYVQmI2qPz8NyR2k39W+vemHQ98RD+IeE3MpVh0Kb6mWL9QcDpujdVFfLByviSBpcxHPAMSOIWHOFldUuiEWROLPlaOHg+oMCu4E2H2kPSQ61Zp0Rvk/o1Wve4KLaxkRT/0nghtfGsWL2/dJy3Rvwp4WQjxtBDiI+Bm5CSddo/95Q2ELzMhhr1ldXROikWvae6bd7nr+W1fJWN7HFvc4Z4jZj5adYBpo7PpmxnX+gOiCCsm9k7j45vGYba7uPyNFYoNd1IKOSlGXp8uNxnP/Hgdrg4yHCwrIZYPbxqLSsC1s1ZRqOCOihCC/zurL7dO6sGHKw/wz283ByT7PdJMzPnTeLISYrjlg7VcMqILt02Wo7+/XFfIZW+s6DALqnAhSvQVQmGVPDban6IP8pck3l4kZ+j7g9fOUxV+ol9pcQDBK/o2fWrLRD8uExxmsNcGvs8xotbuDN5O4qgDlw11nEyIAxJmtRZikxUk+oRIPCvAkOKLiAysMCvXROydQBwy0TekYPD8rQGtUgp63evrJcyOEGNBPUQ/JkGuK2Dd+ji50fwkte5IkrQJeAy4DZgCzJQkSbm4DYWQEa9nX1ldQH/+lqIazHYX446R6D81dzs6jYq7p0YtO22FwV0SmH3zOByueqa9uZKdJeE/FymJsT1SeOziwSzdWcbD3wUmse0N3VONvPfHMdTaXFwzaxXlZuXab4SQp+PePLE776/Yz7++2xLwfcpKiOWzW8czICueGR+tpUeakccvlhN5Nhys4rRn8xWttb3h5CL66z+C9y+ETXNav+9xorBSXt0GJvoxpLpLICHb/xN4r1dE0ZeJvrE1Lup2yoOFYtMw2124A3nHG0/HDTNqQ0mC8Sivmrg0dGpVy9nupgwFPfrHoOgbkjF4GmEDWo58OxHhV5i9C7mQlfFGC5SAyrjPKhX+uuscLiQJ4kKySsm2jpj4VIQAa6C6IzDsqz1DCDELuBsYAtwAfCeEuL1tqwodBp2GQ5WWgLYdrz9/XPfQ/flr9lUwd3Mxt07qecy2nyjCg/5Z8Xx66zgEMO3NlWw+rJx3XAlcPirbp1i/t3xfW5cTNAZ2SmDW9aMprLRy3burfQEaSkAIwd/O6c+NE7rzv+X7+Pf3gcl+klHHRzeNJbdXKg/M2YjZ7vQ16ZaZHUx8ahGlNTbFam1POHmI/p7F8M0M+eeXt8ChNYq+XGGVhUSD1v/ETaCzCdKowhHXxf8TaGMgrpMiin7QHv26MkDCbZAJZkCffryX6Iffp19jdRIfrKLv9a4bUjHq1YEJM3iSYMJP4CRJwuo6NmXcm3gT2AKjXG+B2e75TITqdTckY9C1shMRmwwIRd5v72cyZEVfF4fQ6DHqNK0M+0o7aRV9oACYIknSXkmS5gHjgBFtXFNIyEqIwepwU2lxBhRdVu+toHuqkfT40In6U/O2kx6n5+ZJ3Y+31CjCgF7pcXx263hiNCqmv72K/eUdo8HViwfO6sfU/hn8+/st5G/vOMedMd2TeW36CLYV1XLz+2vkYaAKQQjBg+f254bcbrz76z4e/WFrQLJv1Gt4+7pRnDski8d/3MaqPRV8NeMUQD7PjnviF0UtR+0FJw/RX/Q4JHSF+3ZAbBIsflLRlyustAY8sQDkqGVVsTamU+AnScpRRNGvDJboexVvD8EMuFJvN4q+p9nTmIZBpwmcAgOKKfoWhxsJQm/GNaRg8Fl3AtStM4EmVhELTO0xW3cadiICW6U0YEhRpG6zbyci9LoBDDp1EEPKTk5FX5Kk56VGZ1BJkqolSbqxLWsKFdlJBoqq5RO5d3DW0dh4qJrhXUOPw9x4qIrVeyu4ZVIP33cgirZHt1QjH988jnoJbnpvjaIKc7ihVglevGIYfTPjuWP2eoqrO47ifGq/DJ69fCir9lZw1yfrA6fHhQFCCB46bwDXjc9h1rK9PPHTtoBkX69R89IVw7lqbFdeX7ybT387yNe35wJQL0HufxZ2uAVhqDg5iH7pVji4EsbdJp+4R98EO+dDtXJ200AZ+l5kIZOHck1G4CdJzFFI0Xeg06hodZ6Lh5ip4uRUoIA+fc/tiij6NifxscEq+l6iL9tJLK0On1JOYQ4tpvIoRT9Q3UIolqXvI/ohEeay4HYiQDHCXGs/9t4CkIl+y0PKUk9m606uEOJnIcQOIcQeIcReIcSetq4rFCQbdRR5yFJWQvPjcWmNjdJaO4M6BZj83QJmLduLSa9h2ugA9sso2gzdUo28dvUI9pTVcdcnvwe2nbZDGPUaXrt6BE53PQ9+HThhpj3iwmGd+fs5/Zm3uYQ3lyp7qBBC8PAFA7lmXA5vLtnDf+YGJvtqleCxiwZxx6m9+OS3g7yev5tvPGQfYPLT+ewq7Vh9HaHg5CD6m78GBAzyTGEffJn8c8u3ir3k4WprQAUJIMUlq8nFqhaIflIO1BTKXvkwosriJDFWixDBKfrqeJnIB7Tu6ONktVkBRb/mGDz6GFKDUPTTwVkH9vAmNHjVo6CtJG4X2KpkRd9rgWnRcpSukHUnRAtMvRuslWBI9U0AbVEZN6YpquiHPDDLR/Q1LS9QjJ4FigLzLDoAZgHPAROA0cAoz892jcYn+ySjzrc13ymx+fF48+EaQI7lCwXF1TZ+2FjE5aOyQ1vURxExnNIrlYcvGMjCbaU8NXdbW5cTErqlGvnz6X1ZsLWEHzZ1jMm5Xtw4oTvnDs7i6Xnb+W1fResPOA4IIfj3hQOZPq4rbyzew9MtDNUSQvDnM/ryj/MGMHdzMa8v3s2Pd0703T71uSVs8RwPTjScHER/x1zIHgtxHlKd2gvS+sGuBYq8nN0lUWtzkdEC0U90FOGU1BS5WzjBJOaAVA/VB8NaX6XFQZIhiLG4HqKvT/Qq+i0sOOIyoSa80+dsTjcOV33wHv26MtnaojNi0mtaJ8wQdtJcbQ2ReFo947kNyb5+jpYJszI7Ed7/26BJi7VK/mwaUz27Q600PyvkdT+eJmJA3vlpbUEouRv+n04uVEuS9JMkSaWSJJV7/7V1Ua2h8ecwxaijyJOAlunneFzgGaw1oFN8SK/x/op91EsSN+R2O+Y6o1Ae14zL4ZpxObyxZA9frO1YgVEVQNUMAAAgAElEQVQ35HZjSJcE/vnNZirrHG1dTtAQQvDEpYPpkhTLHR+vVzzdRgjBvy8YxJVjuvLf/N08O39Hi7sgN07ozoPn9uengmLeXraHn++Z5LvtnJeW8vvBqoCP7ag48Ym+tQqKN0KPvKbXd5sIB1aGXS0HqLTLH7LMFpq7DJZCiqRkyiwtkCNvxGaYffpVFieJhiCIkbkU9AmYTHI2dMsRm+Gfjut9vfhgSbOlXLZaCOHxXrdiJYGwq8xewhx8A7HHbtRY0W+x7jRlcvRtLoQAg7Y1P5cHvsZnmTDH6tSBPfrg2YkI/8CsY28iblD0W12gwMnq01/kydAfL4QY4f3X1kW1hsa+Ztm6YyXVpPeboV9wuJoeqcaQejyc7npmrz7A6QMyAib5RNF+8ND5AxjXI5mHvinoUNNzNWoVT146hGqrk0e+39LW5YSE+Bgtr141goo6B/d+tkFRvz6AymPN8U7QfXNJy7ahmyb24J6pffhyXSHvr9jPwj9P9t120au/snqvsjsRkcaJT/QPrJCVx24Tml7fbYJs3Tj8e9hfsspD9DNaIPrqmkMUiXSO1Law2k1UJku/yuoIjujXlYIp3Ue0a1ol+uHdYqzxkuZgPfp1RxoptZqWp/kqlO0e8uLESyCNqeg1KlQCrK3FglrKZctPGFFrd2HSaVAFO4G40QIFwKhTt06YHWZwhHdyZW2ozbhOm1yHIQnwNOO2+DlRdthXO8dYZLvO48Cznn/PtGlFQeBQZcNnLMWk43C1za9tB6CgsIaBIdp2lu48QqXFyeWjot78jgCtWsXTfxiKW5L457eb27qckNA/K54ZeT35cn1hh0rhAdkO94/zB7B4xxFeW7xb8ddTqQSPXzyYc4dk8Z+52/h5S8uC2J2n9eKWST34YOV+Pl1zkCX3T0HjOf9d/sYKlu1UZpJ7WyBooi+EUAsh1gshvvdc7i6EWCWE2CmE+FQIEYQXpA2wbxmo9dDlKGupl/jvWxr2l6y0tU70qTpAuTaT8pa25OI7gUobdkW/0uIM0rpTCqYMn52jVetObbE8nTZMCDkJpq5MVvTxWjJaIcwQdnW8oeYQ7EYAhlSEEJ64x9aIp9SgqIcJIaUbQaO6Pcq4XtPKAkUZq5SvtyBYom/1KDXBevQV2vnpIJgqSdKUo/61+8m4hyobVNskg44jtXbS4/TN7ldtcVJYZWVgiLadr9cfJtGgZWLvtOOuNYrIIDvZwN1T+/DzlhLmFigzxV0p3H5qL3qlm/j7VwUti1ftENPHduW8IVk8O387q/Yo7/pTqQTP/GEogzsncNcn61v03Ash+OvZ/bh6rOzv/+b3QvLvz8Po2VmfPmsVv2xVZtZOpBGKon8XsLXR5SeB5yVJ6g1UAu0zdm3vEsgeI+fSN4YxFdIHyAuBMKNB0W9+cgHAZYfaImr0WS3711RqSOgSVkVfkiSqLA4Sg/Xom9KJ0arQqETr1h23Paxe5hrPmOqEoBX9Mp9Sb9S14tE3pKBEtnuD1z0EuxH4FiixOnXbEGbbsU2X9S2sdOogFiiEvb/AbHNh0KlRB70T0dRy1KpH36jcsK8OgF0e607/ti4kFOw+0tBgn2zUUWa2k2pqfize5blf73RT0M9dZ3fx85YSzh2chU5z4m+In0i4cUJ3+mXG8fC3mztU5KZeo+bJS4dwuNrKfxftautyQoIQgicuGUxOipE7Zq+nLALTaGN1at6+dhTxMVpueu83SmsDR5QKIXjkwkFcMrwzz/68g3mbS1jw58kkeRwPN763hoXbOj7ZD+pIJYToApwLvO25LIBTAe+I2feAi5Qo8LjgsEBJAXQd5//27DFQuDasKjRApa0eo04dWNX1xHpaDZ1a/+CHOUvf4nDjdEvBe/RNGQghiIvRtHxwVGBoVrU1BL+7JMlkzEM8DToNdlc9LneAtBS1xhOdGN4vcY3NiUrg89u3Cq8yHivnuhv1rXnGvQpzmHci7M4Qs+iPUvR1mlbiTJXxuh/3TkRrHv3YJBDqk5XoDwF2ALOEECuFELcIIUKTv9sAmxupeHExGirqHKSYmgsbezxEv3uqMejnXrC1BKvTzYXDOh9/oVFEFFq1iv9cOoSSWhsvLNjZ1uWEhJE5SZw9KJMPV+5vWcBqh4iL0fLKVcOpsjq559PfFffrA6THx/D2daOotDi55f21LQ7wUqkET/1hCGcNzOSR77ewZMcR5t49ySfU/vF/a1i7v2N79oM9Q74APADEeS6nAFWSJHk/cYcAv0c+IcQtwC0AGRkZ5OfnH1OhZrO5xcfaXRKzCuwcrK3nmgF6BqSoiavZzkipnoJyDWV+HptVa6CvrYqVcz/FFpt5THX5Q1mdkziNKmC9SRW/MxQocRgoqmz57+pj1ZFatpPlx/i+NavNKhPfkoN76JJoD/jaKredSfYa9pSaOZCfj0ZysWt/Ifn5/rff4quLGQFs+HUelcnhIUVrDshEv2D9b2hdlhbfJ7XLwkS3nd3FNRzMz6f4kPzYeQsXYwwwGGwUBmz7tlIQpvcWYNtuOzFqicWLFwd1/947N5CuiePXpfLOkttu5cBhW8C/NdZSxFhg65ollBw6/iE93u/V4SNWTFoR9Pez184NZKpjWbZsBQCWWhtVding4/W2I4wHtq9bRlHxsTUw+jsG7DlkQ+WuD7ru9JKlDABWb96LZZ+L0sMOHK56Fixc5PNnHo3x2ngqdm5guzq41whUa0eDJEm1wFvAW0KIScBs4HkhxBzgEUmS2qW8uK2ogejXS+Cul0gxNlf095bVoVGJkBpqf9xURFZCDKNyksJSaxSRxbDsRC4e3pnZqw9w52m9g98tbge4cUIPftxUzBfrDnHt+G5tXU5IGNgpgYfPH8jfvtrErGV7uXlSD8Vfc1DnBJ6fNpTbPlzHA3M28uIVwwJGimvUKl68chi3vL+Wv3y5iRevGM53d0xgytP51DncXPraCn6+ZxK9M+L8Pr69o1WmIIQ4DyiVJGmtECLPe7Wfu/pdpkmS9CbwJsCoUaOkvLw8f3drFfn5+bT02Cd+3Mrq4j3E6TW8UeBm2f9NIm6TfB4adPpVkNi1+YMOJ8KO/zIuWweDjq0uf3hs5U90z0wiLy/ATsLa/bARUnqNwLzczISJk9CoA2yuqNbAwvnknTIGdMef8FBQWA2LlzFu+GD0R7YFfk8r98FS6DFkPD2G55G2YSnGhBjy8gLEaFd2g/V/YWj3dBge4DlDxNb83bBlG2efNpmVvy5t8f+f8t2wDHoOHU/PoXkUrT7A7G2bGDFmnN9BOQAc6IHJXtvy84aIb0p+x3jkcPDPWfouOLJ898/YthyNShX4s2OvhdXQPzuF/rlBvkYL8H6v/r02n65Z8eTlBRmqUv4RWDJ8dX9RtJ6awurAf7fLDiuhb+ck+k4+trr9HQPe2bOadK2TvLxc/w86Giu3wVYYk3cOGFPYpd7Dlzu3Mnr8hMAn/a1dyIrXkBXC56S141VHgBBCjbyTewPQDbkZ9yNgIvAj0KfNimsBjUMD7C5ZyUv149Hfc6SOrikGtIGOvUfB6a5n+a5yzhuaFXzTehTtDn/M7c6X6wr57LeDESGc4cLInCSGd03knWV7uXpsTvB2xXaCK8dks2BrCS/9spOLR3T2a6cLN84alMX9Z/bl6Xnb6Z1u4o7Tege8r16j5vXpI7nu3dXc++nvvD59JN/dMYFTn5VFu3NfXkb+fXl0amEQantFMEe4XOACIcQ+4BNky84LQKIQwrtQ6AKEN0Q9BFRbnPxv+T4uGdGZj28eR7XVyae/HYSijfLWe0KAdIT0AaDWQVF4k3eq7FJgfz5A1QEQamKSOyNJcnNsQCR1a3hMOGrzvFZia0pGrcca4vGEy9adluITPTsiNeG17ujUKvTBeGG9lgyfdcc7fKq1aa3hj9eM1YRwAK4rA0Oq76LcHNrC+6wzybMCFEgLCjopCHxTcb0w6lrxumv0EJOgQG+BM7RpvnVHQKjk4wIEN7vApMywrw6AncCFwNOSJA2XJOk5SZJKJEmaA8xt49qCQmWdfLxLNfqx7pSZ6RGCbef3g1XU2l1MijbhdmgM6pzAmO7JvLdiX4eamAtw04Qe7Cu3dMgmUSEEfzunPxanmxcW7IjY687I6+nz4P+wsWV+EqtTM+u6UQzsFM+Mj9dRXG3jyxmnAOBw1XPZ6ys61EwDL1plUJIk/VWSpC6SJHUDrgAWSpJ0NbAI8Iya5TrgG8WqbAXfbTyM3VXPH3O7M7hLAkO7JPDdxiIo2gCZQyDQBFiNDjIGwuH1YatFkiQq7VKLw7KoPgjxnUmJl08y5XWRi9istMgf0iQ/J74mMHuSCTzpNHExWl/cpV9oY2TyFEaPfo3NSXyspvUJvtBAID1ecK/fvNWhWebSsPZo1FhdxIbiqLGUgbGBMLea/y+EIsTTbHOF6NEvb75AaWlRBZ6hWWFuxrWHWrdngaKSD30G31TfIKbjnnwYIknSjZIkLfdeIYS4G0CSpDvbrqzg4T22Hq3ou+sl9pVb6JEWfCPu4u3/z955x7lx3df+O2iLBbb3yl323sQmUY2SZavEsmyrOU5kudc0+yVxe07iyHGv7yVO5CrJlmXJlvxkWV2WqEqKvYhcdm7vFb3P++NisA3A3MGCy11yz+fDD8jdGczlYDBz7rnnd359mE0KWxeV6W88hxmND1/eSPuQXzeCcabh+pWV1Bbl8rPXzp7voWSERRV5/PWWefzmzVZO9Lin5ZhaA68NDcX8r98d4FB7+oZY+XYr9394M42lDj75672UOGz89AMbAegY9vPBX+5KLwzNQEwlNuDzwOcURTmF8Oz/PDtDMo4Xj/Uyv8yZiEl7x8oqjrT1o/Yeheq16XeuXgedB7NG9oZ9YSIxqMxPH61J0TxK42R7wJNmhqhZjrKm6Itj6Rbjaop+viiyLdBT9AHya7LaNMvlDxvoiqvl0Qui77DFib5eokokIOwwWYIrEMaRoiYgKZIq+jqEOa8yq8p4OBrDH44a6y7rHRin6DviqTvpOhKei66+htOCvP2jhcGIdCZAp5C4TFxfWS7an+lQVdWT5Mefm/aBZIhcqzlxby2ZIGz0uAKEIjEaSuXtkK+c7GN9fdGs8nXPITnevqKKmkI7v9+b3a7z5xoWs4kPXd7IrrODuoR1puLvr1uCM8fC159q0t84S8ixmLn3rg2UOnP46P176HGlTuIBKHLY+NkHNqEoCh//1R62Lizla+9eBcDB9hE+8+A+wqmCPmYgDBF9VVW3q6r6zvjfz6iqullV1UWqqt6uquq5z01KglAkxs4zA1yxqCyh/F69pJzFSgdKNCRB9NdCcCRrinm3K3W79QSGW6GoPvHwGUy3FJRXIawaQ81ZGd9QwrojoeibLAkyp5u6A/Es/exad+SbZY3m0YOITQQdApfI0s8eaXYHIvLWnVhM5Lo7xxJ9nZhKyDph1lY9pNNrVHXySkSOmZgKwUiam19e+TmwShlU9L39kyYooDMhzMv+hHAWY9YYg6uL7InkronkXOuQKuu3dQfCHO4Y4fI5Nf+CgNmkcOXicnY3D01LCkw2ceemenKtZh7d236+h5IRSpw2/u7axWw/3sfLJ6ZvpbQsL4eff3Aj7kCEzz96KL0oBcwrdfCf71/PqV4P//T7g/zVlnl85pqFALx0vI/PP3po1lw7sz4IeH/rEL5QlCsWj96Al1cXsMEWV8D1iH7VGvHafTgr49Fmiqkz9EOCDBfNS9hnNDtNUiiKUPWzaN3Jy7HoZ0C7ewShjFsc8u1WPEEdxTa/OruKfiBirCuuvVDYsZBU9POy3/XUHQjjkOWd/iHRtXmsoq/X6AuyTpgT3WVliX7YJ4jvOI++hFXKWZHVSVUspuIJGawt8PaNU/QdMh79iztLfyJmx5MNqCqw4/KHcdjMkwpuO0fEfbomVaH+BBzuGEFVYf28oqyPcw7nB5vmlzDiD3OyN9nC1cxFvt3KJQ1F7G7OXs+a6cYHtjbQUOrgP548mjoC+xxgWVUBn79hKduP9/E7iYnSlYvL+cKNy3jqcDc/3n6af3zHUt67XgRMPravg289c+xcDzkrmPVE/7VT/ZgUuGzhKOkwmxSuyu/ERy6ULEz/BhXLRXFe16GsjEcj+hWprDuuDkHuiuZRlGtFUXSsOxAn+tmx7gx5QxQ7ZTL0uyG/MvHPfLuFmEr6zPH8KpHvHtMhqpJw+8PyJM7bN0rIGOvRl1D0szQ5icVUPMEIubLWHd/4AmIAh9VCKF3+P8Q94/0QzY5PMNHNV1YZn7B6ArJe93IIDIvJbhbgC0dRVQMTFIivRIyO2ylVtK01+7o4CnIVRXEriuJK8scN1Jzv8cmiMNfKiD+c1GrTFVf0q4vSrLyOwYE2YZNYVz9H9C8UbGoUBfm7m2dfRvqGhhKOdbtmXadcDTkWM1+8cRknejw8smd6VyY+cFkjW+aXcM8TR+ka8etu/7ErF/CutTV897njbD/RxzdvXcMV8ZW9e185w09fOXOuhzxlzHqi/+bZQVbXFU3yci/nLE2xeYT19CebA8qWZFHRFw6milSKvkbYC+uxmE0U5lrTK/qQ1aZZQ74wxTJdcd09o0k6jJIpT9ruuFWgRrOmfKZ6SCfFRO91jkbgdLr5QtaIvjcUIaaCQ9a6o52nscq4ZjlK0+BDJCGpo11epwhPwrojea6TTFBG02skCLO2/xShXYvStQWREARGkir6absRn6NmXzMVqqrmq6pakORPvqqqU2/eME3ItZpFQX+S67prJEBejkW6Buhg2zCNpQ65juJzmBWYV+KgIj+HPbOQ6G9sKCamwoHW2enTB7h+ZRWbG0v4/vPHp7VTscmk8J3b1hKJqXzh0cO6Fh5FUfjWrWtYVlXA3z20n45hP//915ewrEpk6v/HU00zPgVpVhN9VVU51uViVc2EZo2xGNX+kxyKNXK236v/RlWrs0b0u10B8q1ixpoUmgWnWKTplDhtDOjFNRU1CCU0MDLl8Q37QpJEv2uCoi8eiOm749aM7jtFqKoaT90xYN1xji9qBdIrHrnFov7B1TGVoSagKePSqTuJSNAxxFOmODRPs5JkR2HWPlNpZdwXfzCOmaDkynjdE119szNuT9DouOMTo7EefauBcWe5vmAO5xY5VnNKsaBz2E91ujqqCTjYNsLaOTX/goKiKDSWORN1dbMJ6+cVoSiwZxZ3bFUUhc/fuJR+T0g39jLbmFfq4As3LuPlE308ske/IDvXZuYnd23AYlL4+AN7UBSF+z+8OdEL4CP376F9yHeuh50xZjXR7xoJ4ApEEjOrBAZPY4n6OaI20jSmS2JKVK0GV/sogZkCel0BiuxpTms8Q5+COgBKHDb9XFYteScLqv6gL0SxXuJONCxUV03xZrRQ06Wn6ENWFPJAOEY4qhpL3RlDmM0mhVyrTra7oojJiSs7LSA0oi+t6Cez7iQsMNNJmDVl3Kh1Z7JHP+0EJYvXB4xei9KWo2TnO0fGchTf/iKx7lwoyLWacfkjFCSZeXe7AukDE8Zg2Bei2xVIpLrN4cJBjsVEIDx70lM05NutLK3MZ2/L7PXpA1wyr5j5ZU4ePzD9bZjuurSBSxeU8LU/NSWK89OhvsTBf77/Ek73efjHRw5SkZ/Dz+7emPj9Zx7cRyhdGMV5xKwm+se7RQrGsuoJN+Cug+L3zKepSyIpo2q1eM2Cqt/tClCck4boDbVAQS2YxcOn2GlLn7oDCfU/Gz79YW9YIkM/TmjyRhV9zSufVtHXJgZZIM6p0jKSIhoRkzTn+EY2zhwzHr1s96wSfTFmeUU/icIs43XPyy7R1yYo0vUQyZRxGUU/seKTnfPtMVpEPCGCFcBmNmExKektXmarmFxl6Tq5kKEoil1RlF2KohxUFOWIoihfjf98vqIobyqKclJRlIcVRTnnHhi71ZTSujPgCVEu2ZnzdJ9YFV5oIHN/DrMDdqs5fVLYDMbGxmL2tw7PmuSXZFAUhXetrWHn2QHdyMtsw2RS+Pata4mqKl94TN/CA3D5ojK+dNNynjnSzX+9dIp19UV86aZlgIjdnM7IUCOY1US/qVuo9UsqJyj6XQfBbEMtX8axbhlFX0vemXpBbo8rSJE9DdEfbhkl7kCpDNHPUtOsUCSGOxjRt+5ozbLyRz36o9YdHaVZMWWFEGnNuZKpcZPgGwDUcUotCN+4bmOLgtrsK/pGinHthYJIxuGQSa/JunXHIGH29YvoVXth4kdOGa97XqVYzRrJjlXKYzQWNDGxGr1OFEXRb1IGUJi96+QCRxC4VlXVtcA64AZFUS4FvgX8QFXVxcAQ8JFzPZBcqxlvMJK4NsdiyBfSFzziON0nUlmMNNeaw+xAjsVEMJKd8IjpRnVhLp5ghMgsJvoA71pXg6rCEwen//46r9TBF29cxisn+nh4t1xPhY9cMZ93r6vhe8+fYHfzIB+9YgFXLRHi0X1vNLO7e+YVSM9qon+8201tUe5k1bfrIFSsYEl1sZx1x1kmmj1NUdEPR2P0e4LpFf3h1lHijlD0h3yh9LPJ3GKw5U/ZujPsj3fFlW2WlTc+dQd0iL7ZIs7jyNSr6F1xRV/KuqMptXkV437stFnSE2YQKrO7U2TaTxGuhKJvoBjXMX5y4pApxrXlidqCLHrdNauTFLQs+jEdi50yir7JLFZ9skSYR4txM7fugJEJYXYmKBcyVAEtr9Aa/6MC1wK/j//8fuDd53osdquYwGmrTRoC4Si+UHRSE61UONPnxWpWqC+Wi+Kcw+xBMBLDLNN5fQZCRoGeDVhYnsfq2kL+eB6IPsBfbWngsgWlfO1JOQuPoih8/b2rqSnM5YuPHSYci/H9O9YmmpD+98EgzTK1odOIWZOgkAzHutwsnejPV1WhzC9/F4sK8nhsfwfuQFg/USQLBbn9niCqCsWpFP1wQBSqjlH0Sxw2wlEVdzCSmtQqithnitadIa8govrWnXSKvk51fFF9Voi+IetOEksGCOtO2thEEEQ/FhHvMab4OBO4Eh59yR28/ZNJp4zXXVGy2pzME286pcg+8HwDkyYoWjFu2nFD3CqVHcKsTazkawv6xIqCfXxRZa7NnD42FgTRP/tKJsO86KAoihnYCywC/gs4DQyrqqrNptqB2iT7fRz4OEBlZSXbt2/XPZbH4xm3XWwM+Wk5e5pgJEZPZxvbt4+mYgwGxKS+r/0s27fr36t2HwtQbofXXp2dn//EczSHURxs9tFQYMLjicy6c3TmrBDuXnnlZSymcz9ZOZfX0cq8ML89HuK3T75IlXP69ef31sXYfTbClx98hbtXyln67lwY4/t7/Xzhvj9zyyIbH1th5jt7wsRU+MC9r/C/L7VjM8+MSeSsJfqhSIzTfR7etny8istIm2hEVL2G+XYnAC0DPlbVFiZ5lzGoWg2nXhBk3CqfxjAW3fEmLEWpFP2R+NKQVlzLaGv2IW8ovXpd1ABDZzMalwYtxlPXuuPuBpRxufROmxlF0UmxASisg7Y3pzROGGvdkSH6k9NrQCi1uraogjjfcLVPmegnPPrS1p0BKJ4/7kdSxbggznOWLDCGu8t6eietnkg1KANB9HveMjrEpEgU40oXbMcnVqbxDxKnzYJPZuUn6IKAC+xzRZnpoKpqFFinKEoR8AdgebLNkuz3E+AnABs3blS3bdume6zt27czdjt/KArPPgPAokWLoOkoK5YsZNtVo/1UjnSOwPbXuHT9aratqpr4lpPwg7deY1GtjW3bNutuOxMx8RzNQcAbjND7zLPcdflC8swds+4cHY6ehJMn2Hb11VjM554cn8vraNn6AA9/889059Txvm1Lzskx9LAvcJhH97bzrbsupaJAnwNuA05F9vPkW9185l0b2VaRhzfvGD/efppWd4yXRkr5xnvXnPNxy2DWWndO93mIxNTJir7W+Kp6HY1lgug3D0hGbKpR6Mu8mEIrJklJ9DXrzRjrjkb0pQpyh1rEikWG0NJ9pIi+szxRMAxiuSovx5LeugNQWC+sGVNsmuXyGygQTSj6k9Vx3YmJViCaBTuJOxDBYlKwyX6rvP3gLB33I6liXIgT/ew0GnEFIvI+d4gT/fGTIrNJwW416Y9bq4nIwrKzyx8m327BLKtmefsnrUSAOOdSij7M+fQNQFXVYWA7cClQpCiKdpHVAefkRLrGrDhq1mVtEqohsbKpZ2GMo9cdlC7cncPswfGeFGEeswQXhnFHoKrQzqXzS8+bfQfgk1cvIBKL8fPX5AXVr7xzBbk2M1967DCxmMpn376EhYWCADy0q43H9k1vM7BUmLVEX0vcWZ4scUcxQ+VKGkodAHJ+qWqtIDdz+46m6JekiteckKEPBoh+0TwIe6fUJGnIp1l3dB5wnp6k6naB3TruQZoURfXCCjPFCEXNuiOn6PfFi0PHWzKcOWZ9K0mhiDnNSgFxnHhKWWBiUeEZn0CYpZXxwjpRW5CF7riG+hWoqrg+8son/cppk/C6F9ZC2Cf6QkwRLn/yRJWU8E22SoFY+UlbRAxi3DDn09eBoijlcSUfRVFygeuAJuAl4Lb4ZncDj5+L42v3DRglQhM9+lr/BZmVoFhMpc8dTN0AcQ6zFm+eEXHaszU2VdNKpC2XMxxXLinjTJ/3vHX7bSh18s41Nfx6ZwsjPrkGXuX5OXz5puXsah7kkT1tWM0mPrk2J1Gz9vlHD9Eh4fs/15i1RL+p24XVrDA/rton0H1IdLq15uKwWagsyKF5QKKRQVGjKHjtyjx5p9sVxGpWyEslmA+3gNk2ruOsPNGfevKOIetO3uQl7Xy7pKIPozalDOHyh3HYzFhlliQ9vfHEn/E3PGeORDGuo1R8JlkgcO5AxECDr35QY5OIvt1qQlF00mtAKMxqbLSeYgpwGelAHHRBNDhp3CAKiaU8+pC1CFbpcUPSmgjQPPrTt/JzgaMaeElRlDEGFxYAACAASURBVEPAbuB5VVX/BHwe+JyiKKeAUuDn5+LgwTGZ6Fqx4sQic23VSetCnQ7D/jCRmEpF/hzRv5AQi6n8dncrm+eXUFM0O4usz/Z7KMuzMQ32/GlBbfxz6B45f8T4U9sW4g1FuX9Hs/Q+t2+s49IFJXz9qSZ63QHKHSa+c/taAMJRdUZEbs5aon+8282iivzJRLDrIFSvTfyzodQpp+ibTFC1akqKfo8rQEW+HVOqGfZQiyDCYzzCxUasO9p7ZIghb4hcqxm7XrpKCkVfEH2dma5G9IenSPRT5F8nhbtrXOGwBqfNgjcUSZ9OkMWmWaLoW9IC45mcbCSGo+CwShQRJyZU2Sl8libMWtKPs2LSrxxWiwRhjivjWagvECsRBixHKaw7TpvEBCVfI/pzin46qKp6SFXV9aqqrlFVdZWqqv8e//kZVVU3q6q6SFXV21VVDZ6L44fHpGdp92GbZfwzQrNpTbT0JMOgVwxTNqFnDrMDr5/up2XAx19tmae/8QyEqqrsODPAZQvLLhhFvyrui+8aOX+dipdXF/C2ZRX88vWz+qvTcSiKwtffs5pAJMa/P3EUgJtWV3PNUrHq/eShLnacztyJkQ3MWqJ/rMvN8on+fE+vIH3VowUQ80udch59ED79nrcyjlrsHtHptjghQx8EybBZTAz6JLvjTknRD+s/sGLRuAc7maJvlVD041aYKSv6yTtaJoWnJznRz7EQU9HvfJilLH13IEJ+jixhTk70ARw5Fvxh2fN8noh+XhKinyORR1+QPQuMoXFHghAcmVSwDYLw6U5QLLZ406w5oj+TER7T/Eir3ZgoBmmF1zKKfkL9l5gUzGH24MGdrZQ4bdwgUYw9E3Gm30uPK8jWhaX6G88SaCsrXcPnj+gDfPqahQz5wjy0S57DLCjP42+vWcSfDnVxoFfcX75402gGwVefOEIkev4as81Koq+1JJ9UiNuxT7zWrE/8qKHMQb8npK9EgyD6IU/G6TY9rkBiVpoUEzL0QcwGSxy2RKFsSuTkQ27J1BR9XyiR9ZoSnl5RlKxZFcZAyrqTkydy/6dI9A2RuFSKfo5EtjtkLfLRbaSoVSP6SVZOnDYZRV9TxqdG9CMxFV8oaoDop56gSPUtyKvMXlM1f5pI2olId77jExTdXOosdlGew7lBaMzDVIvanEj0NUXfbpEn+hN9/nOYvTjUPsxzR7u5Y2M9ORLXwEzEG3GF+EIi+lodzPlU9AE2NJSwZX4JP33ljKFmap+4eiELy538/oToi7SkMp+/3CwE2mPdbh7aNbV49KlgVhL9Y90pquU79wkSMca6M790NGJTF1WZF+Sqqkq3K0BlKqIf9IhC2qLJS4XFMt1xAUrmw+AZw2PTMOQL6fvzNcKrKcZjkG+XSLEBYSuZIgGVtu5EQuK8JlmBcMp0mYVRAjfFJBiXTL8GDRrxTGKBybVZ9JXxnHzRmXaK51mrOZIm+imakwFyHWbNFvFZTbein2gCN/k6cdgsRGPqOJKYFFmMNJ3DuUF4zGcYjcfu2CY0sPOHItitJkwS5mZ/vHGdfY7oXxAIR2P88+8PUZ6fw6evWai/wwzFjtP91BTamVfiON9DyRpyLGbK8mx0u85/8eqnti2k2xXgxSb5ppQ2i4lPXr2Qdo+amIh99u2LEyLBd587oS/oniPMSqKvJe4sS6boly8H22iBbn38i9A2KEH0y5eJ9JZu4wW5rkAEXyhKVWGKoi2NoJcsmPSrUlmiX7oYBk4bHpuGIa9E23eNOBZM6mcTt+6E9ZXPonnZ8ejLkLiEUpvcugMS2f8FtRANjebxZwhDir67B3IKwDb5Ru20meX8gQV1UybM3rD4LA3ZpBSzWF2aACmiD1lZQQlFYvjDUfni50QTuCRWKUPNvuYU/ZmMUGT03hSOJlf0IzFVrsgfCMSvZ+mu0XOY0fjJK2c41u3ma+9ebSyxawbBH4ryxukBLl1YesH48zVUF+bSeZ6tOwCXLyrDYTOz44wxb/3Na2sosMEv4hGdFfl2Pnm1mFCO+MN87/njWR+rDGYl0T/W7aLYYR2fhKCq0LEXateP2zZB9IckiL7VDmVLM1L0tQz9lIr+YJygl05WEaQV/dJForFTSOL/kgRDvrB+drRG9AsnE/28HAvhqEowIqN8tk1JIR/xSaq1aYm+ZCZ9okA088lJOBrDE4zor5ho8PQktb+AZKdWGD3PU4AvTowMWXec5ZOaToGoLZCaoBROvSZCi3mVV/TjRD/dyo9MIXFwBIJu6XHOYXoxXtEXf7dMuFajMVW698IFxqMuapzocfOjP5/kL1ZX8/YVU2uOeD5x3xvNDPvC3Lmx/nwPJevIy7HoR3hPA6xmExsaihMRrLKwW81cU2/lxeO9nI2HwHz0yvlUxm1JD77ZytFOV9bHq4dZSvTdLK3KHz+bHW4B/yDUXDJu28JcKwV2C60yij4In34GRF/L0K8uTBHVNXBKvE5J0Y9PEjKw70SiMUb8YTnrjtU5KZMeRptX6X4RC+tFrUOGWemxmIo7GJFrluXuEq9TUfS1AunhzD10Wn63bg2EhjRE32mz4JcizFNvmqUp+vJEvy+pbQckawtAEOaRjilNBF2JPgtGViJMSeM1HUYnhHOq/oxFeJxHX7xaJrShj8ZULJJE3xyfJGg2oDnMTnSPBPjgL3ZRYLfyr+9acb6HkzFGfGH+e/sprl1WwZYFF44/X0PzgJfGUqf+htOASxeUcrzHzYDHWEDYNfMsWEwK97/RDAhr6P96x1JAPPL+7Ykj+q6ILGPWEf1YTOV4t5tlVRP8+R17xWvthkn7zCt10DYo6fuqXiPIo6fP0Li644p+ymLcgTMios82+SIudthwBSLjHlJJUboo/l6nDI0NRomolKJfWJtUytL857oFuUVTi9gc8YdRVSiSUccllFpdS0YWEo2G46lJhoh+EhsJCOIpRZgLa8E/BCHJVKkkMOzRTzNBcdgs+MNRfVJUUCuav02haZYrfg0aKth2VoBpsgXDUC0HZK0j8Ryyj7H3UGXCq4ZoTE0dgTwB2oRgjujPXoz4w3zwl7twBSLc96FNVOSnCcyY4fjxy6dwByP88w1Lz/dQsg53IEzXSIBFFXnneygAXLpA2FN3nTWm6hflmLh5TQ2/29OWEEVvvaQuYTXfdXaQg+0j2R2sDmYd0W8f8uMLRZP78805ULly0j71xQ456w4IRR+gx5iq3xNX9FN2UBw8ndS2A1AS71Q7pBexqe0/cNLQ2Ma+t65H39WR1J8PJPzn0k2zMlTItbFKZVe7u4VnPGnH03jqjh6BsxeKFYwpJBoN+zRFX9a605uGMJsTRYBpkcjSz9zv7o1oHn0D8ZqpFP34+dYduzaxmsL51iauhopxU0yscuMefd0mZdq4p2iXmsO5Qyg6mZBP5PRGrDvadpEMI5fncH4RCEf5+AN7ON3n4X/+egOragvP95AyRteIn/teb+Y962onC50XAE73CcFq8Qwh+qtri8i1mnnTINEH+NDl8/GGojyyWzwrzCaFT1+zKPH7R/ZM7zNk1hH9pm7hb5qUuNOxT5B08+QH/7wSB+2DfmIyqkzlKvFqsENutytAscOauhnVwOmkth2AEqeYHAx5dSwxNqcg4RkU5A75NEVfrxi3I6k/H8Yq+jrjLJkfP2hmMaXSkxKId/HVUWplbDDFDVNU9ONEX4Z4Bj3C2pTGuqM7OYExVpLMFWZD1p1oRCj6SaJXQaQFAfo+/eJG8TqF852w7kinHCXv9gxjrxOJYlyTFYaaZYc5h2nG2Bz9UYI/ntQrirxrbNT+Jx+zN4eZgWFfiLt/sYs3zw7y3dvXcsXiyWLQbML3njuBqsJn377kfA/lnOBkj6h9WlyZr7Pl9MBmMbGxsZidBgtyAVbXFbK5sYT73mhOrAZet7wiUdT/xMFOAjJiXpYw64j+8W43igJLKsfM+qJh6DqQ1LYDUFfiIBSN0euW8Fo5SoRSatCn35MuWtM/DL7+lIp+cVzRH/BKjK90YUbWnf74/700Lw15joTiRG5ytCYYUPRzi8WfDKNAtQmPrs0IBIFL4s+H0Ye0FGkuapiSR3/YiEc/TRY9CIU5GInp2wW0CNQpJBz5wip2q0kuT9ob77GQX530107Z9JpEl+dmAyMdj2wq+qMefZ3rxGQWtrQprETM4dwimf1xoqJvMZukFXrtHnS+YvHmkBma+72898dvsL91mB/euY5b1iUXr2YLHt7dyu/3tvPhK+YnAkYuNJzq82Azm6gvTlHneB6wZX4Jx7rdGX3/797aSPuQn93NYkXAYbNwXbwI3B2I8OyR7qyONR1mHdE/1u2iocQxvn1510EI+6DhsqT7aBeOIfuOQaLfla4rrpa4U5LKuiPIt66iD8KnnwnRjxeUlOelsBZBvLBVTaPox9UtPaIPUDwfBjNT9LUuwVIJNq6ulMTTZjFhM5vk1LjiONHPsEhm1KMvM+a41SaFMu6UVcYLakUc7BQIsy9igCy74oXPKcbtkF1ByYJVSvM+SlmOohGR/6+n6MtcJ0UNc4r+DEZkzORYC2uYaNKxmU2E9JLD4tDuzVJhCXOYEdjdPMh7fvw6Q74Qv/7oFt69fnaT/B2nB/jyH97iqiXl/OM7Lkw1H+BUj4cF5U4sktG304EVNcI5cqbfeB3cZfFmZofaR2vRbl4zylV+t2f6ar1mzhmVhJa4Mw4tr4vXeVuT7qM1lWiVaZoFonHWwElDMZZpu+L2xz31ZYuT/jrxMNHz6IMg+v4h8BpbTur3hFAUHd97mgx9gPwcQaqk4q9KFkxB0Tdg3RlpT9rcS4MjRzKTvqgBIoFRtd0ghn1hTArk50ikwGie+hTj1jzjUs2niuZlbJECYd2Rtr+442kzqSYosuk1IOw7U7DujPjD2Cym1Fa5sfD2AerUFX0Q454j+jMWY9N0NH99bMLk3WJSxk0I0qHAbsWkzBH92YBoTOV/Xj7NX/30TYodNv7w6cvZPH9yv4/ZhLP9Xj75673ML3Pyn+9fP6NIcDYx6A3xxukB1tVPTvs7n9BuHbIpXWNR4rRRW5TLoTGFt1cvLU8Ipq+f7qddVnyeImbVVRMIR2nu904uRGl5QxDgFA/y2uJcFMWgoq/GoLdJavNQJEa/J5TautPbJLy9KTz6mnI96JEk+mBY1e/3BCl22NLfKDTipXmoJyBP1roD4v860ibsQAYx5AtjM5sSVpCUCLhErnkaou+0SXbzLdLsJJmRz2F/iMJcq1S3zYSin8oCY4gwZ75yAsK6I6/ox4l+vo6iL3O+i6emjLv8EWP+fEip6DusRs53g4jxDUx/FvIc9DF24qc1xZpI6q0WE5EkRbvJYDIpVBfm0jF8/rt1ziE1mvu93HHvDr759DGuXVbBY5/eSmPZzIhpzBQjvjAfuW83ZpPCz+/eNGsbfMngvtfP4g9H+cgV88/3UMZBa7o3MaJXFqtrC3mrY5To51jMXL9SPIdUFR7dOz2d1mcV0T/Z4yGmTuiIG4tCyw5oSK7mgzi5VQV2Y1n6AN0HpTbXmmVVp7Lu9B0Tan6SQmEQD6QCu0U/dQfGEH1jyTv9niClegr5ULPIGi9M3ojDbFJw2sySRH++mCxlkFAy5A1R5LDqd/1LWGBSL806c8z6nnEYndxkSD6HfRI9CjS4OkVn2SRdccEgYS6ZP0VF34h1p1NMWB3J85sdsuk1MFoTkWGayYg/RKFshv5IequUxWzCZjFJFm03itcprEbM4dzBZhl9pGnP5omkPsdiIhSNEdGLM46jscyRaH4zh5kFVVX51Y5mbvzRq5zscfPDO9fx3399iXz62QyFNxjhk7/eS/uQn3vv2sC80gvTlw8i3OO+N5q5YWXVjCnE1aDV8sh20p6I1XWFNA/4GPGNuiBuXjv6HPr9vrZpydSfVUQ/aeJO9yGh6jZcnnbf+mKRvCOFonnCRyzp09fUntpURSS9TVC+LO17lDhtDMgsDxc1iBjRvmNSY9PQ7wlRls6fD4LkFtSCJfVNMt9u1U/dgdHViwzsO0O+kFy0ZqKLb+oOgc4ci3zqjmLK2G407AtTKJuhnybCFEbtP1IrEcXzITACPuMRYCCsO4ay6Auqk3bFBQPpNSAIczQ0qrYbxKA3RKlT53rWoE0I010nNskJ4RRXfuZwbmG3jl6bmpA/sUBXSw+T+n4BjaVOmgfmiP5Mw57mQd794zf4yuNH2NhYzLOfvYp3r6/VF4hmOLpG/Nz+Pzt48+wA375tDZsaZ7f9SA+/3tmKKxDh09ckr2E8n9ACMWTjeCdiTZ2Ic32rc1TV37qwNBHa0Tbop89gQ65MMKuI/vFuN3arKeG5B+DkC+J14bVp960ryZW37iiK8OlLEv3OONGvKUpC9ENeof5VLE/7HsVOm1xlt9kC5Uuh56jU2DT0e4KU5UsQ/RS2HQ35doucol8cX4LLkOhLpddoqwVprDt5OZJRlZYcQQQzKHQGYd2RitaEONFPri7DqEVKquh5ilGmnrAqVwsBQtFPYdsBo173OGHO0HY05A0n0qp0MdImJsdJei1ocNhkJ4SN8QFkvooyh3OH3DHWHc2bPzG9Sjo9LI75ZU6GfWHDHTLncG7QMuDlU7/ey23/s4PuET/fvX0tD3x4c+qu9LMIh9tHuOU/X6d10McvPrhp1hcS6yEQjvLz185w5eIy1tTNLH8+jFp3rCnELT2sqhFE//AY+47VbGLBGFtZm6zTZAqYVUT/WLeLpZX542dXp16A6nUpm/homFfioNsVIBiRzC6tWg09R0Rihw46huKKfjKi33dcvOoo+qVOm3zBV+VKMTYDGPCEKEsXrQlCpdQIWArk2y24gxKKfl4F5BSMFiIbwJAvLK/oK+aU8Zog7CRSaSqQcaIRZGDdSZFsBGJyAgYUfciIMAfCUYJRycZkIMZdkLyuAAym12gJVIPGe0KAKFyXHrfWGyKN0uewmeUsR7nFYrUvw5WfOZxbjI2J1VbEQxMUfc3rLBUqAIkmSwfbM+/kPIepo9cV4J4/HeW677/M9uN9fPa6Jbz0j9u4bUPdrFfxAZ55q5s77t2B1Wzi0U9tZdvS9JzmQsAje9ro94T4mzHNpGYSonHrTqYe/WKnjfqSXA5P6IRblpeTKPCVtpRPAbOK6B+fmLjjH4L2XbD47br71hc7UNVRUq6Luk0isrNbv3FWx7Cfsjxb8gQQzWKjp+g7DBJ9T7d08k4gHMUTjKS37oR84j11FX2rnNKsKKIuof+E1BjHYsgbkiPNI3FlPEmzLA3S1h0QPQoGz2QUsTkia90J+8E3IKXou6WIfqN4zUBh1q43KcKsqnHrTuoJit1qQlEkFf2ieWC2ZTSxUlVV/hoBXasUgCPHImc5UhQoXZzxhHAO5xY5Y6w7WmH8xMY0BQYV/TV1hZhNCvta5oj++cCZPg9fePQQV3zrJX75+lnes76W7f+0jb+/bvH4mO1ZClVVuffl03zqwb0srcrn/33m8snJghcgWga8/OD5E2xsKJ6x6UidwwEUZbQnTybIy7ESnBDnW5afg91qRlGgdeDcF/rPmm/JSFCl3xNi6djEnVN/FgWfi67T3V8rZmkd9LGgXKLFslbc2/I61F6SdtOOYX9yNR+E8m6xjyqvKVDitDHoC6Gqqr46UblSvPYegflXpd8W6HNLZOhrzaJ0xplvt8gvNZUtgTPb5baNIxZTGfZLquM60ZpgoMssCEU/6IpnrsurKeFoDHcwQlGuTIa+FlGZetxajKnUhMrmEOk9A8YVZo3oS53rwLCY+KZICgKRW+6wmuXSa0xmUcfRb5wwu4MRIjHVgKLfrvs9ER59A9fJ2Vfktp3DtGKs2KKJcBOvx2KD2fgOm4Xl1fnsax3KziDnoAtVVTnQNsy9L5/h2aPdWM0m7thUx8euXEBD6exO0xmLzmE/X/7DYV463sdfrKnme7evlYsMnuVwBcJ8+L7dqMB3b187Y1dknn6ri02NJfJ1bEkw6A2yunZ8UmRZXg7ekBBfp0PRnzVEv9UlbtYrxhbivvWoIB51m3T3ry8WRL9NVtHPrxL2gpY3YOvfpt20Y9jP0lTV4p0HoHKV8NanQYnTRigSwxuKJqwbKVERJ/o9ckRfa5ZVlp+GGGlpM0X61h2XpBJG2RI4+JAoFrUXSu3iDkSIxiR94yNtUL857SbOHIu8dUezkwycNkT0R4x0xdVplgVCGTebFDwyFikQxDODlRON6KTtlqxB675blLqgFYQyLqXoQ3zcGVi7jExQohGxEqEzIXTYLAz5JO8NZYvg0G8h6IEcCdFgDtMG+xjrjjmelDHRkqXFIGtpaTLY1FjCb95sxReKXBAq8kzFiD/M4wc6+O2uNo52uci3W/j0toV8cOt8yvVqzGYRYjGVB3e18q2njxGNqXzlnSv40NZGuXjmWY5INMZnHtxHy4CPX31ky4yNQT3Z4+ZEj4d/v2Vlxu8hVp/Dk/hMeZ4NVRXBG9Ph0Z81d6xWt1j6SBB9/xCcfB62fCKtdUNDRX4ONouJdiMntWErND0hIgBTFGOoqkrnsJ9rk/npYjHRtXftnbqHKk50xw3pE/28CnCUSfv0++P5/GlTSjTrh4R1Ryp1B0TRMAgyV7dRapehRFdcHdIci8a97ukJXF6OmVA0RigSGxe9lxSlGtE/lbLLcjKMdsWVKSDWkoJSj1tRFPJyLHKKPojzfOh3wl5jQBkZMtKBWIuT1JkIOo3WRJx4VnyWEt9hDYYsR55useqnZ92xSTZWg9GI28EzUL1Gbp85TAvGWnc0D6x/gnWn2GHFalbocckX1759eSW/fL2ZV070c8Oq1DVBczCOWExld/MgD+9u48nDXQQjMVZUF/Dvt6zkPetrEylJFwqEFekwu5oHuWJRGd9472rqSy7c+MyJ+NqTTbx6sp9vvnd1onvsTMSTh7tQFKb0ffcEI4SisUnR5pqNOtdmpmXw3Cd6zRqi3+KKUVecO+qDPvpHiIVh1a1S+5tMCnXFucaWSRouh/2/gr6mUbvMBAx6QwTCseTRmoOnIeQWxcI6KHGMLifrfukVBSpXGCD6mqKfhuj3nxSqe5pkEhAz0GBEkjiXxYl+33Fpoj8g2xXX1SE+f52Jiaa++UIRbGliQ4ExvnFjKnOfW4w5rTVKw1AzoKSNegRRkCvl0QexchIcEV190xQmT8RAYgIoQ/Tj1q6ieWk3c9gMKvqxsJhEpGgmlwyJCYqhCFYdi1eOpOUIhEcfxHUyR/RnFMZbdwTRnzjxVBSFinw7vQYU/c3zSyhyWHnuaPcc0c8CYjGVva1DPHW4i2fe6qZrJEB+joXbN9bxvk3zEgXQFxIi0Rg/ffUsP3jhBHaLiW/ftobbL5BCYln8amcL973RzEevmM/7Nqd/lpxvPHmoi82NJVTkp+iPJIEhrxBFJ4pp2rMrEI7KC2NTwKwh+q3uGGsb42q+qsKun4okm5r10u9RX+yQj9iEUZ9+8+spiX5HumjNzgPitUaC6OcZ841SuQr23ielhmoe/bSpO/0nBGHUuemMRtOFKdUjtsWNosGSAVuJNtYKvWVaLfVEhyCOTbDRbaJiMgvyqSUlSWLAK8asez5AJBsV1qXtVQDiPEsr+mVx4tl/whDRH/KFUJBsmDXUIlKUcovTbubMMaDoa+MeOG2I6A/Gb54lsnUcIGXdkffoj7F4zWFGYexqqMmkYDEpSVcgqwrtdI7IF8FZzCbetqyS54524w9FydXr2j2HSQhGouxpHuK5I908/VY3ve4gNouJq5eU8883LOX6lVUXpC0qFlN55kg333/+BKd6PVy/spJ7bllFRUHmBHI24qVjvfzbH49w7bIKvnhT+nCS840TPW5O9nq4Zwq2HRDpcDB59bl1QPBQfyjKwvJzb12aFd8qbzBCj1dlRXV8ln/2Zeg5DO/6v4asCvNKHOw3UlBV3CCU15bXYMvHk27Sni5as+uAyO/WidaE8Yq+FCpWiOLIwbPCM5wGXSMBSp22cdFzk9B/Ahbppxdpy6juQESf2JotceIs39xLax6h68fU4iQliodBPmGDiuXQvltu2zj6ZSZSGiR6FYAgLLINfRIrJ/0npGo2NAx4Q+TZkPOFDrcKNV/n+5ZrsyRqFnShWWD6T0glZ2lIePRlcvS1lQjdom0zvnCUWEzVPx/WXHFfyKC+YA7nFmOJfigSo8hhZTjJ9dhQ6uD1U/2G3vvOTfU8uq+dxw90zHg1ciZAVVVO93l55UQfr57sY+eZQfzhKDkWE9uWlnPT6mquXVZxwVlzNKiqygtNvXz/+RM0dblYVJHHvXdt4PqVF9eKkKqq/Py1s3z9qSaWVhXwo/ety7gB1XTh93vbMSlw/RRX77rjYsJEor+/bYjCXCvhmMqiinOfsDQriP6xbhcqsLKmQKj5r3wXnOWw+g5D71NfkosrEGHEH5avom68Ak48k1I5b4nPzBqStahu3y2W9s36xzKs6FetFq/dB3WJfo8rkChASwr/sLB9aAprGmjEWZqEVq6Atl1y2yIUfZOiU08AQtE35+h6rwvin7NLlnyWLxdF3gYKLQe8IUwKcm3Xh5qlUqLy7Bb5a6GgBmx50GesIHfIGyLfJnnDHW6RmqA4bWa6hiWVUmeZqDXpbZLbPo5BXwirWdGvZQFRe+Iog5z0N1NHjgVVhUAkKqcqli0Rlr45zCiMJRD+cJTCXOu49vMaFpbn8di+DjzBiNx1BGxqLGZZVT7372jhzk31F5XlQgaRaIxj3W72tQ6xp3mIPc2DdI4Ie9T8Mid3bKzjysXlXLawdEpxhTMdqqryysl+vv/ccQ62j9BY6uCHd67j5rU1M57gZhv+UJQvPHaIxw90csPKKr57x1rp79v5wr7WIX7+2lluWVc7JdsOwB/2d1DksLK8enzqzv7WYRaUO9nfOsziynMf6KB7xhVFqQceAKqAZdq2LAAAIABJREFUGPATVVV/pChKCfAw0Ag0A3eoqnpO8seOdroAWFFTAIcehuZX4S++B1ZjH4LWUbdt0EehrAdw8dtFckzH3qQJLy0DXkqdtsmqRMgHHfvgsk9LHSY/x4LFpCSWenRRuVLEdnbs061T6BoJUFOY5lxpmeBlS/THabDZDJWrBHH2D+naPkAQ/RJnjv4Ncehs3BqUvk5gtDmOrKIfX33pOw51G6R26fdIjjnsl+pVAEKZ1Jb3dJHoWWDUchQi3yrx4FFVoYzPv1p3U+HRN+A5rFhumOhrGfpSRGvw7Gj34DRwxK0Y3qAk0a9cAW++JlJ9dBK1LibMhOeFBncgTJHDxrB/8j1V60x5ts/L6jq5Z4GiKNy9tZEvPnaY1071c+Xi8qyOdzYhGlM52+/haJebpi4Xh9qHOdA6nOhFUZGfw8bGYj6zqIyrFpdfFMWmqqryxukBfvjCCXY3D1FblMu3b13Dey+pxWKeVS2LsoK2QR+f+NVemrpd/NP1S/n0toUzfnLsCUb47MMHqCqw82/vmpptp3PYz/NHe/jYVQvG1Q55ghFO9Li5fJGoh1xcMQOIPhAB/peqqvsURckH9iqK8jzwQeDPqqp+U1GULwBfAD5/LgZ5pNNFnhWqw63wzBegdiNs+LDh96krHiX60sU+C68V3VdPPJuC6PtSqPm7RKFhwxVSh1EUhWKnLWFL0IXZCtVrxQREBz2uAOvnpWkvrXnotZScNDBshdFWHnqOiNURHfS5g3IxapIErtCool+xIj6QJmmi3+eW6DoMY3oVNOpumm83YN0BYQ87/aL89gjCXCij6PuHIOTRLcSFuEdfthgXxIR136/SJltNxKDXQFfcoebRWps00Mi9VHdcEBG30aBYWSrXnyBfRDjvzwsNLn+EolxrQlUeC62Xyuk+jzTRB3jP+lr+66VTfOOpY1z+t2UXfByiOxCmZcBHy4CP5gEvzf1ejve4Od7tTjQBspgUllblc+uGOjY0FLOhoZjaotwZT+qyBU8wwh/2tfPAjhZO9nqoLMjhnnev4s6N9fqBFRcoXj/Vz9/8Zh+RmMov7t7ENctmR5ffr/7xCG2DPn778cumlJ0P8Js3W1GBv94yPqnuUPswMXXUZrh4Jlh3VFXtArrif3critIE1AK3ANvim90PbOcc3bjrzj7CF+2dKD//M5gscOtPpUnBWGiqgqGC3NxiqN8CJ5+Dt31l0q9bBrxsWZAkIqrlDVBMMO9S6UOVOm2J1Bkp1G6APb9MqyoGwlEGvSGq01l3+o6Lolmd6ESYAtHvfkuO6HskiL6qCqIv4UcvyBXjlV6BKG4UKyUGVOYBbzB912ENWq+CbHv0QaycHHwIPH2QJ6c0DnpD1JZIPIwT49a/PnJtZnxGUgQqlkPYCyOtUucFRBGxVCRoJCiKcXXqOEBYjgD5SUplfELYe2SO6I/BTHheaHAHwlQU5HBwQvt5gAXlTnIsJg53jPDu9entf2Nht5r55xuW8XcP7ecP+zu4dUP62o/zjY5hP23uWGJVHEBFxR8S3dK9wSjeUAR3IEKfOyj+eIL0ugL0uoOT7INleTksrcrjrksbWF5dwPLqAhZV5F2UhPZUr5sHdrQkLGCrawv5zm1ruHltzUXR9CoZYjHhx//G000sLM/jJx/YyPwZmpM/EU8e6uJ3e9v522sXTblTbzAS5be7W7l2acWk1az9raLDtsVswm41JU9szDIMrTkritIIrAfeBCrjN3VUVe1SFCXplE1RlI8DHweorKxk+/bthgYYU1Xudv+MfMXPkHMNx5d+msChVqDV0PtocFph51unWBJrk96n3rKYha33s/PphwnkViZ+HoqqdI0EUN294/5fHo+H4ZNPYnbOZ+/OfdLHUUJ+mju90ueoYiSXFRE/u5/+Fd685GSm1ydUl+GuZrZv7xj3O4/Hw/bt21nd9Bo5uTXsefU13WO6QyoA+w83UeaW6Gqqqmy1FjJw4HmOB/SLktv7fOSVmCedA22sALbgEFvDXk72R+jQOVfRmBjvwaaTbA+36I8X2GCvIXzsNQ7lpH/vsWNeVGRKjG/sWMeitv15FgOvN3UQPp0+O7e/K4QvFOXFl17CJKGMFQ1FWQccfO5Bhkr0U55iqsqgN4S9RNW93ip6XmEFsPtUH97u9Nv2doQIRWO88OJLiRzzdCgYCXIJcPjPDzNQtiXtttp5bevzUZ9v0h13rq+dLag09QTo0dn2VJ8g+K/t3E1Psf5D2hQNciUmWnY9RXPfZEtaqmvgYkImz4tsYsQfZnl1AQPeIOFoDOsY+4TVbGJVbSEH24YNv+/Na6oTZOaqJeUzupHTN55q4k+H/PD6q7rbWs0K5Xk5lOfnUFfs4JKGYuaVOGgsddBQ6mReieOC9tbLIBKN8UJTDw/saOGN0wPYzCbeuaaauy5rYF190UWzipEM+1qH+Oofj3CwfYTrV1byvTvWzXg/vobOYT9ffOwQa+uL+Lu36dcq6uGZt7rp94S467Lx4lgwEuX3e9spz8/hhaM9XL+yalrqNqQ/BUVR8oBHgX9QVdUle0GrqvoT4CcAGzduVLdt22Z4kN51B3l6515uvPEm5PXx5Jh/+FWi9hy2bUvfUXUchubDj+7n0rwOuHK0+dWpXjfq869w9YYVbFs/quy8+sKTFLmPw6Wfwsj/93cd+2jqcsnvMzgPmr7HpioVNibf580zA/DKTq7evI6rloxXerdv3y6OtfeTsPBqqeOGozF48Wkq6xvZtk3yC9G2nmp/P9U676+qKu7nn2H14ga2bRs/KUiMFUTc6Q5YfOn1LF6kP+a8l5+lpLKObdtWyI13eCuceIZtV18tlerkffEZViycl3j/cWMdi6efhhYnl7/9Ft33PW05yx9OHWXDpVfILSF6V8PBf2FtlRm2Jjn2BAx5Q6jPPk+JM0f/c9++E5oUNl1/p0icSYMz8XFfsuVyOXtNcAPs/2dWV5jgqvTj0M6r96VnWbWwjm3bdDyUJ56FXbB8600sn5d+EuFsHoS9O1i6cs2k70lKHF1IY66PxiTnL+U1cJEgk+dFJqJQugnVifY+apQhVBX++Nx2SnPHq85lBHmxLSI9KR2L2+fF+LeOEB+59yU+uyFnxhK89Y4oVctU7HaxoqsNM8cMdrNCjkXBboZci4LTSvz/EQE84o86AP3Q0w895+s/MQ1Idx2pqsrpkRhvdkXY1R1lJKhSale4bYmVq+qsFNiGGTkzzMtnpnfM041U52goEON3J8K80RmhKEfhY6ttbK1xs2eHvnA4E+AJqXx/b4BgOMZfNgZ5/dVXpvR+LreHH+04RKVDIdZ5hO1dRxO/e+pMiLP9YSodCqGIytb8oWkRhKSIvqIoVsRN+0FVVR+L/7hHUZTquDpTDfSeq0E6iyvJzc1OMc+8EgfHut3GdipugLpN8NZjcOXnEj8eTdwZvzRVOrBX+POXvdPQYUqcNvliXBCWBGcFtOyAjclrFrrjTWGqUxXjenrB3SXd+McaX26S7o4LULUG3vwfYaWwpFa/XH7RRU7X794b/+KUy2XxFtgt8tYdELUPB34d77ybflnfF4rgC0XlrDt9x0XRrAQpyB+T/y9F9J2lkF8tLFIS6I1HghblSBCU/pNQVK9L8mG0JmLEH5Yj+jn5wvsv2fzNF4rgDkbk0hC0CFaJWg7DljQQ9p2uQ/LbXyTI9HmRiSiUdEL1zJPigH6Fqzat4b4je1iwcj3r541feXEVd/LsQ/upWLKeNXVpaphSIFbWzL88foTTlgY+eqV8H4jpxDbmJp0ySHaOjnW7+OOBTp441EnbYACbxcS1Syu5dUMd1y6ruOgSdCaeo2Akys9fO8t/vXGKcFTl09sW8plrFs2qVZ+WAS8f+uVu2j3wf/5yQ1aa4X3q3uc4MxLmO7et4dqNo40xe1wBPvPidpZV5XO6z8Odm+dx51+snvLxZCCTuqMAPweaVFX9/phf/RG4G/hm/PXxczLCLKO+2MELR3vl8rLHYtWtohC452jCn9usEf0JHqyy/p2CgNdtMjS2YqeNEX+YSDQmV6WvKNB4ObS8LnzrSQhkT5zoV6Yi+hpRqV4rPc58u9WYf7xuI7wREiQ0TYFrn0eMVXcpvO+YaN5UUCN1+IJcq3wxLow2OOs6oEv0E91lZYpx+09I1SmAiNcE5JtmgfDp98gRfe26KLJLfAcGTo52g9XBWKIvjep10HVQatNel2RDNRDJTFaniOLVQUbjrloDRx8X8bS5xonihYiZ9Lzwh6NUF4rJafuQfxLRvyxeW/Xqyf6MiP5dlzbw+ql+/uOpJioL7Ny8Vu5+NIeZi5YBL08c7OSPBzs50ePBbFK4fFEZf/+2JbxjZWUixe1ihqqq/Lmpl3uePErLgI/rllfylXcunyR4znTsbRniYw/sIaaqPPixLWxqnJovH0T+/tNnw9x1aQO3jyH5AN98+hjhmEq+3YJJUfi7a6duEZKFTAXN5cBdwLWKohyI/7kJccN+u6IoJ4G3x/8941Ff4iAUjSUUTWmsvl3ktu/+aeJHp/s8FNgt45XLsJ+Swb2w7CbDBcOlTptIMjRCNhouB1eHIDVJ0DUSwGkzJxTiSeiOE6wq+Zllvt0iH1cJIiUJoGNP2s20z0SX6PceEykzksvlBblWYwSucpUopJYgn4kGX3qKftAtPieJCFMY29HXCPFcJVYNIvrXdoLo6yn6qgr9p6R6LAAUOTIgzDXrRHqNXz9tMTFxlekq2X9CdLGVqXHIFd/hZFGMKaF15ZacpFwkmFHPC61jecvA5JqY8vwcVtcW8tKxzBajFUXhR+9bz6aGEj73yAFePtE3pbHOYfoRjsbYeWaAR46HeMcPXubq72znu8+doDDXyj23rOTNL72NBz68mds21F30JF9VVfY0D3L3L3fz0Qf2YDWbeODDm/nZ3RtnHcl/+nAX7//pTvLtFh771NaskPy9LUN86bHDLC8x8S83j7cJ72ke5A/7O9i2pJw9LUPcvbWRqnSR51mGTOrOa0CqJ+Xbsjucc4+xyTuGTrSzDFbfBgd/C2/7V8gt4lSPhyWV+eP9mW89hiUagFW3GR5bcXzCMOQNyVlBYFQhbn4dSiYvH3cNB6gqtKf2kHYdFBYgu3zEXL7dasziUFgrbCXte2DLJ1Ju1ueWVGv7mmDZX0gfvsBupUO2iROAzSG6zXYe0N1UWtE3EGEKo4q+ofNcc4mwjHUfFqsoaSBt3XF1ilQcrYutDjJSxscS5gXb0m6qjbuiQOL70XsM5l8pNQS71YTNbMps3J37YYF+j4GLATPheVGWl0N/fALuC0WoLMhJrL5OxLal5fzXS6cY8YUpdBgncnarmZ99cCPvu3cnH7t/D9++bY2hFJ85TD/6PUG2H+/jpeO9vHKiD3cgglmBLQsKuGNjPTeurk7e6f4iRSQa45kj3Xx/Z4Azz+6gMNfKV965gg9c1jCuwH02QFVVfvbqWb7+dBPr64v46Qc2UirLtdKgc9jPJ361l+oiO59Zy7jzEoxE+dc/HqEsz0avO4jTZuFTVy+c8jGNYPaYqbKE+niUUeuAz/gsbssn4MCDsPunqFf+Iyd63dy4qnr096oKu+7F65iHU9KiMRYl8cjAAW8I6UWd8mWi82fzq3DJXZN+3TroSzQKS4rO/YIgGkCB3WLMow8iClRH0e+O511XpFNrPX3gG5D254OI2GzqMjjemnUilz6FJUpDt6zCrHWtLZMj+mM9+tLQyH37Hl2i3+MKUOSwYjPrEP2Bk+JVUtHP2LoDccK8Le2mGtGv1PPoB0bA3Sm+HxJQFMW4xctRIiJBO+WTteZw7nHFolL+34FOADqHAzSUOmnuT55yde2yCv7vi6d49mg3d0xYapdFgd3Kgx/dwid/vZd/ePgAZ/o8/MN1Sy74jP3ZgkA4yoG2YXaeGeCl430cah9GVcWKzo2rqrh2WQVq9zFuvG6qUR8XFlyBMI/sbuOXrzfTMeyn0qFwzy0ruXVDnVxTwRkGXyjC155s4jdvtvIXq6v53h1rsxKD6gtF+NgDewiEozz0sS10NI32NgqEo3ziV3s5Eo+37feE+PZtaxKi7nRh9n1aU0RtcS6KYjBLX0P1WlFg+9oPGVjyPoZ94fFdzVp3QNdBOhZ/kiUZpDCUjFH0paEosPAaOPUCxKJgGr1wVVWlbdDHpsbkHWlzAn2iidOlnzE0zrwcC11JmtCkRe0GOPYn8A6IwtEk6Bz2k2+3pF8i1QpxK+QIHIgHsaFiXBDjPfiQOD9p8uO7hv1YTIr+Ckz/cdEDQqIwFDJU9AtqIL9Gd0IFYlIlyHIs/Yb9caIv6dEvMNqgDMYQ5v26m/a6RFGc1h8hJfriXYIr5CeERQ4rwz6jE8L1Uk3r5jB92NhYkiD6HcN+FpY7efqtblRVnbSyua6+iPllTn6/tz1jog9iNfZXH9nC//5/h/k/L55ib+sQ33zvmouiI+xMgz8UZV/rEG+eGWDn2UEOtA0TisRQFFhbV8Rnr1vCtcsqWFFdkJiMbTfYVfxCRvuQj/teb+a3u9vwBCNsnl/Cv968AktvE9de1ni+h2cYqqry9FvdfO1PR+kcCfCJqxfw+euXZWUi3usK8DcP7edol4tf3L2JxZX5dMRb8HiDET56/x52nBlIbP+vN6+Y0n0mU1x0RD/HYqaqwE7rYAZEH+C6r8KPt8DTnwfez5LKeFezaASe/TLkV9NddQ2ZtNDRiL6hplkAS26Aw78TRGmMkjvsC+MORlI+bApH4kknEp1Dx+1n1PM+9hitb8Dym5Nu0jHs118y1dJZKiSjMhHj9QQjxgqwtUZnbW+mJ/ojASoL7PoJDH0noGSh6GgsAc0zbvg8120Qir4OetzBuP1Fx9LUexRyCqULn+1WMzkWgxYYEIS5bbfuZr3uIBX5EnGGWsMzSUUfMryua9bDkT+At1/Y++Zw3rGypiDx985hPyuqC3hoVxudI4FJ9xdFUbhtQx3fefY4LQPeKXmNbRYT37p1Devqi/n6U0284wev8E/XL+XurY0XXULLdGLIG+Jg+zC7zg7y5tlBDrUPE46qmBRYVVvI3Zc1sGV+KZsaSzKyZ10MiMVUdjcP8sDOFp55qxuAd66p5iNXzE8Uqm/vO3Y+h5gRTvV6+Lc/HuG1U/0sq8rnR3+5Pit+fIAdpwf424f24w1G+OGd68Z1/3UFwnz4l7vZ2zqEzWwiFI3x+RuW8aHL5YS+bOOiI/ogfPrtgwY822NRtgiu+RJlf/53/sbsYHHF24S94/mviCX8235BrD+zIovSPBuKImaJhrDwWlE8euLZcURfm8yksu4UDcdJXKVOHnmScQ56Q8aIc80lYHXA2VfTEP3JD+JJ6NwnVOt8+RisglwrqirUcekbfcUKkezTuhPW3JF6OMN+aookPm8J3/xYaJ5xwwpz7QZoeiLtygmIa2xxRRm6RL/7sCjUNrBCVZhrZcTouOu3CMI83CaiPFOgxxWQK8TtOyauN4luzxoKc62JYl9p1MX7cbTuhOXG4nTncG6wvHqU6LcP+XhPvMfJkY6RpPeX915Sy/eeO85vdrXyxRvlV4CSQVEU3r9lHtuWlvPlPxzm3/90lF/vbOHv3raYm9fWzBH+KcIXivBWh4tD7cMcaBvmUPtI4jlnMSmsrivkI1csYMuCEjY2FJN/kRfQ6qGpy8XjBzp54mAnHfEV9Y9eMZ+7tzYmCtlnI7zBCP/3xVP8/LUz2K1mvvqulfzVlnlyaYY6iMVU/vvl03zvuePML3Pym49tGRV8Ebn8d/3sTY50uih1inqhv3/bYj61bXp9+WNxcRL9YgdvnO7P/A2u+BwH977BPw7/DvX3rRANCTV98ydEDGeGDRCsZhMV+Tl0GrXFOEoEUTrxNFz75cSPE0S/NI2iP+/ScXYfGZTl5RCNqQzLZqUDWGxijM2pm2h0DPnY2JDcZjS60T6oNV5TAGKWLU30TWZBzFt3pt2sayTAunqdaD7fIIy0wuaPyh0bQRgKHVZGjKTAwCjxbNuZsmA5FlPpdQep1CtojUXFCsoldxsaQkbK+LzLxGvrzrREv9cdHG+XS4W+YyLhyEDyVVGuleNGe2zUXiLSuFp3zBH9GYKxvtuz/V6WV+djUuBIp4t3rJwsEFQX5nLj6mp+vaOFT129kCLH1P2zNUW5/OKDm3j2SDc/fOEk//DwAf7Piyf5+JULeOfamlnTMfR8YsQf5kSPm2Pdbg63C1J/osdNvNk5NYV21tQV8Zeb57G2rpC19UWzKsP9fKF9yMfjBzr544FOjve4MZsUrlxcxj9dv5S3r6ic1edQVVWePNzFfzzZRNdIgNs31PH5G5fJh5voYMgb4rOPHGD78T7etbaGb7x39bjzNeAJ8q3dATq9fuqKc2kZ8PGJqxfwD9dNX5RmMszeT3QKaCx18Oi+AN5gJLOLWlH4mu0fuCl/IR+K7ATFDO/8IWz44JTHVl2YS9dIBqsNy98Fz35RWETKhXFIq0OoL05C9EfacfraofHjhg+lfWn6PUF5og8iIejFe5Kqze5AGFcgQm1xGhXBPwSDp2H9Xxkab8GYAlFD7rj6S2H7N1LmpMdiKt0jAapX6yjMmvdcKzqVRFFuBp7x2g1gsYsUphREf8AbIhpThTKeLolz8AyEfYaiVyFDol+1Gmz5wtq15vaUm/W6AlyxSMcio6piJWLxOwwNwXAxLogGcLUboOUNY/vNYVpwsG0Eh83C4op89rWmjm/922sX8eShLn7x2lk+9w65gnk9KIrCDauqeceKKp490s2P/nySLzx2mK8+cZQbV1dx+4Z6tswvueiLdgPhKKd6PRzvdnOix83xHjfHu93j6sCKHVbW1BXxjpVVrK0rZE1dkX4M8xwSGPSGePJwF4/v72BPi/gebGgo5p5bVnLT6uqsJM+cT6iqyo4zA/zni6d44/QAK2sK+M/3X8IGPeHQAPa1DvE3D+6j3xPinnev4q+3zBtnIX3mrS7+5fEj9LpF3VvLgI8PXd7IF25Ydt47Z1+URH9plVhmOdHjntRERQaRaIzDXR5Wb/4g3PztrI6tpsjOsS6DqiLAqvfCc18WXv24qt826KMsz5Z8MnPsKfG69CbDh9KiJPvdwXFLVrqYf5V4PfuyGO8YdA6Lm3ra5UKNMNembrqVDFpxr+GC3MbLAVU0JEtCmge8IULRGDWFOkucWs66ZPdhDRkRZqtdNGprfjXlJuOy6NNFf3fHm6llQPQNr0qZzFC/Oe0KSjCq4gpE9B/wI+3g7RuNv5REYa4VdzAi37BOQ8NWeO0HEPRAjsRqwxymDZ5gBFcgzGULS3l4dxuhSAybZfJnu6yqgBtWVvHL15u567LGrJJIk0nhxtXV3LCqiv1tw/xuTxtPHOzisX0dlDhtXLW4jKuXlnPl4vKsKY8zDZFojI5hP2f7vbQM+OKvXpoHfLQMeBMqvc1sYmFFHpcuKGVJZT7LqvJZUpVPTbqI6DkkRfdIgO3He3nuaA+vnOgjElNZXJHHP12/lHetrbkgCsUD4ShPHOzkF68309TlotRp455bVvL+LQ1Zs8kNekP8+KVT3L+jmcoCO7//1GXjGux1jwT4l8ff4rmjPYmfFTus3PPuVbxzzcxoondREn3Nw3msOzOif6rPQyAcY229fPa8LKoLc3nxWG/ShIi0yK8SRPrwI3DNl0BR0kdrHnsCr6MOp2Rs4lhozaH6jRYN126A3GJRSzCJ6ItVjLQefS3dxKAyriW0GFZr6zaLzqqnX0xK9LWVl2q9fgxdB0SqTK6xa63IYU1MgAxh/lXw0tfFCkiSY2oxppUFdobTEf2uQ2CyGipohf/f3nmHx1Vde/vd0zSaGY3KqHdLlmS5yhV3jE0zIRhCQg0hhZDkhjRI+CAFEm5y0+5NA5JAGiGEQGjBNJtq3HDvVW6yJKv3PnV/f5zRWLZVR20k7/d55pkzZ9rSmaNzfmfvtX4LIi1Gjgw0BQY0wdzDjA9ATZumBlJ7m/WBs/vJAFO8Opt9NXV4BjZTlbEANvwvlG7T6mUUIcWxymbmZzl4anMRe0sbeizG+/ZVebx/pIofvXaQx24b2L7TH4QQzEqPZlZ6NA9dO4W3D1Ww7mg16wurAy5BOfE2pqVEMjUlkmmpkUxOso+JVIoOt5eKxg7KGtupaOygvLGD8sZ2SuvbOV3bRkldG55ONQ9YTHoyHVYmJUbw8elJ5CZqoj7TYR2SPOqLEbfXx67T9XxwtJp1R6sCx+CUqHC+sGQCq2akkJ8UMS4umKqbnfxz62me2XKamhYXeQkR/OLG6VxXkDwklpmgDRL8ZcMp/rThJG0uDzfOSuX7H5scSP/1+ST/3FbML946QnMXG+zZCXr+eNelITXjFPpHkGEgJSocW5iBI+VNQb1/X0kjANNShkPom+lw+2hsdw88V3TGrfDKlzRhOnEFRTU9WGu21UHRJmrSbiAYj4lA6s5Auwvr9Fo6xbG3L7ACLe2P0D/9kSY6u0mj6Y1O0VbXOtC0DJPWcOnE+90+3SnCk/oa0S/bo/nyD5DIcBOHg5ndyVyMNhOxudsLlM7ajbTocBp6+5yy3Zo9pWFg+2FQMxGg2cS+/99w8gOtOd15VLdrU6K99oUArWBbZ9Q6HA+Arj0ABiT00+aD3qTtJ0rohwQ3zUnl3ztKAdhf2sj1M1MQAjYeq+lR6E+Mt3HP8on86p1CPjGrkuWTEoYtvnCTnlUFKawqSMHnkxwsa2L9sWp2F9ez8XgNL+8+A2g18Il2M2kxFjJiLKTHWEh3WIiLCCPGaiLGYiLKYup2liJYpJS4vD7anF4a293Utrqob3VR1+rSlttc1La4qGt1UtnkpKKpg7puBn2iLUaSo8KZnGznmmmJZDisTIi1kuGwEGfrh3OWok+qmjpYV6gJ+w2FNTQ7PRh0gjmZ0Ty4chLL8uLJTbA/02/AAAAgAElEQVSNm219uLyJv248xat7ynB5fSyfFM8XFk9gYbZjyP5Gp8fLP7cU8/gHx6ltdXHVlAS+fWUeOV2yF45VNvPgy/sDaVCgnT8eWTUFe31hSIl8uEiFvk4nyEuM4HAwo47AvjMNRIQZyByGts+dqStlDR0DF/pTboB3HoKPHqc5dSlnGtq5LSH9wtftex6kl+q4RfTfk+QskeFG9DoR6D45IHKv1r6/dPtZC0u0EX2jXvTYFVf43JpwnT2wwlDoKvSDiDd7ORSugfoibVS+C4ER/d5cd5rKoeE0zPvigL86MtxIQ9sAZ00AUuaAyQbH3ulR6NvCDL2LWa9Hs+kcYD0EnLUzHXAKTNJMsDi0nhDdCn1tRLDPKeczuyBxqpY/PwCCavYFWrpO+gI4/h5c+eOBvVcxLFxfkBIQ+ntKGvjsognMTo9m7cEKvnVFz+bHX740m9f3lfH/XtrPa/dEjkibep3fLWZa6tmBo6qmDvafaeRgWRNFta2U1LWx/lg1lU3dH8NsYQaiLEbCjXpMBh1hBp3/Xk9TQwfPFu/AJyVen8QrtdFIbVnS4fbS6vTQ5jp733X0/XzCDDocVhPRVhMJ9jAK0qNIsptJigonOVK7T7SbCTcNzciq4ixOj5e9JY18WFjFuqPVgUZMCfYwPjY9iWV5cSyaGDuu3IZcHh/rjlbx1OYiNp+oJdyo5+a5aXxuUSZZcUOXKun1SV7eVcpv3j3GmYZ2FmY7+M5VeedkfbQ6PTy5/iS/X3cct/fs/8jl+fH8zw3TiLebWbfu2JDFNFRclEIfYFJiBK/tLRt4igzaCNHUlMhhKaLqTAMpb2xnchc/6H5hCIO5X4QPfkzp4W0A5J2fQ+/zwtYnIG0+LRFZQcWo0wkcVhO1LUGI0IkrtNHWw6+dI/SLa9tIjgrvcZtGNh4GT3ufnVO7I8ygxxZmGHh/Ajg7QnvsnQvEellDOyb/Sa9HTm/S7oPplGw10ury4vR4CTMM4KRpMGmj44Vru+3sW1zXRlqMpff9vmIfuFvP+Y36S6dgHnAKjE4HWZdpgtnnu8Axp7rNR7hR3/v29vm0mohpPRf09kRn6k5QF1cTL9csdhtLITJ14O9XDClzuoza7ynR5q2umZbEI68f4kR1C9k9CASTQcfvbp3Jjb/fzN3/2MG/v7RgyFIBBkK83cwKu5kV+efOKnS4vZTUtVHd4qShzU2df7S9vs1NQ5uLDo8Xp9uHy+vD6fbR0O6mrl3SXteGTgj0OoFOJ9AL0AltOcZqIi3agsWkxxpmwBqmx2IyYDXpiTAbibFpMwcxVhMOm4lwo37cjBCHOk0dbnaermf7qTp2FNWzp1Rr/qXXCWZnRHP/1XlclhfPpMTxkZLTidvr46MTtby+r4y1BytpbHeTFGnmgZWTuGVu2pA4Y3Xi8fp4+1Alv3qnkONVLUxLieTnN05ncc5Z04eqpg6e2lzEM1tO09SliWW0xcgPrp3MDTNTQnr7X7xCP8nOP7cWd9tEpTdanR4OljVx99LgRHJfBEb0B1rM2MncL8CWx4nZ+EPgGxcWyxaugfpTsOIhGITDaKwtLLgRfXMk5FwBB16CKx4JpO+cqG5hYi9X59H1ezV3o4xFQcXrsAV5YRKbo9k0Hnr1AqF/qqaNCQ5r7//gRRs0P/7EgRXiAgEnhLpWV9/pQeeTu1K7mKrYf0ERcHFdG9lxfcxGFX+k3XfaXg6AoFNgQBPMB16Eir0XFNNWt0vSYsL7vkBxNmlWrgMk6BF90Pbpd36gzUYMgfuWYnB0TWUpqm2jqrkjIPTf2FfO11f0XJs0KdHOb26Zyd3/2MF9L+zld7fMDBn/e7NRT05CxDlpBH2xbt06li1bOoxRKYaKqqYOthVpon7bqTqOVDThk1qPgCn+5l9zM2O4JMsROF6NFzxeH1tP1fH6vjLWHKigvs2NLczAlZMTuGZaEpfmxWEcwvqNoppW/r2jhBd3llLV7CQrzsofbp/F1VMTA+eYoxXN/GnDSV7ZfQZvl1muRLuZLy7N4tZ5aVhMoS+jQz/CYWK6P79+T3HDgIT+9qI6PD7Jwuzh6YIZawvDoBOUNwTZ0MsSA8u/T8Ib93GLaROp0V1SNzxOePdHEJOlNa3asCn4OCOCFPqgNaA6+qYmgrOW4fVJTta0sjQ3rse3xNT5u/6aBzjL0fl+q6nbPNJ+kX8dbPzVBd1PT9a0kBvfxwm3aKMmlgfYqwC6dEpuCULo51wBCDj61jlC3+eTFNe1sbxLF79uKf5IazbVz464XRmcYL5Su6A7/NqFQr/Nx6S0PtJ2Tn2o3U8YuLDptGEdcNE2aLUjUelw+HUl9EOQDYU13Dg7lQVZmvvOfy3L7jWt7IrJCTxw9SR++tYRpJT8+uaCgc2qKRR94PH6OF7dwr6SRrYV1bG9qI7TtVr9VLhRz6yMKL6+Iod5mTEUpEeNCUE5ULw+ybYu4r621YXFpOfy/ASunZ7E0ty4IZ1R63B7WXOggue2F7PlZB06AZflxXPT3DRWTIrHoNchpWTjsRr+tOEkHxae61YxIdbKly/N4vqZKWPqeDD+9px+MjnZTrhRz/aiOj42Panf7/voRC0mvW5I/Vm7otcJEiPNnAlW6APM/hxH3vkbj7j+hK74Ws0m0ueDN+6DmqNw+4ugH9xoQKzVxImqluDenLtSG+Xe8y/IWsaZ+nZcHh9ZsT2MMteeIKLlBCz8XNDxOqwmzgTjYAMw+TrNVeXIWRHn8foorm3jqm4a8ARoKoPa4zDrM0F9bWynjWkwF1S2eH+32Zfh0vsD6TtVzU5cHl/vee4+r+bDn3tVMGETPZiaCKtDK4A++Aos/0EgbiklNe2S1O56QnTl5IcQmwf2/v9Pd9J5gVI/0N4FoMU5+XrY8nut2F0x6twwM4VX/EWtHxZWc+PsVD67KJMv/WMn7xyqZOW03veRL12ajV4n+PEbh2lx7uSPn541LsWWYvjxeH0cq2ph/5lGDpxpZP+ZRg6XN9Hh1gwGYqwm5mREc8f8DOZkxjAl2T6ko9ehRIfby46iet45VMGbByqobnYSbtSzPD+ej09PYlle/JCnyx0sa+T57SX8Z/cZmjo8pMdY+M5Vedw4KzVQh+P2+nhldylPrj/F4fOMWqYk2/mvZRO5empiyMzuDYSL9qhl1OuYmR7F9qKBnZQ3n6ilID1qWAuNsuJsnKxuDf4DdHru8X2bZ00/IP7pVZpQrS/SbAeXfsc/2js4Okf0g6lxwGiGGbfAzqfgikc4UaO9P7unjqf7X0QiEFM+0f3z/SDGamL/mcbg3pw4HWKyYe9zAaFfWt+Oxyd7vjgBOPKGdp8TnGB2WLXUnaBSjkCbOXnj3nPSd07XavtVRm9Cv3Q7tNcFvZ8E7Febg4x7yg3w2jfOibuu1UWHt49CXI9Lm4mY+emgvjbMoMduNlAb7EzVlBtg8+/8v/uAWrMphoGvLZ8YEPrrj1Xj9vq4PD+BtJhw/rLx1DlT9D1x15Is7GYjD7y8j2sf3cjvbpnJ1GFwW1OMH9xeH8cqWwKCvlPUOz2aqLea9ExJieT2SzICVqrZcX2kgI5hvD7JobImNh6vYePxarYX1ePy+Agz6Fg+KZ6PTU9i+aT4Ib+Ibmxz89q+Mp7fXsL+M42YDDpWTk3k5rlpzJ/gQKcTeH2SLSdreWNfOf/Zc4bmLvn3APMmxPDVyyayNCd2TP8+F63QB61g67H3j9Hc4e5XlXp9q4sDZY18ffnwtjPOjrPyfFEdPp8MquC3psXJ8RYTa654ms+0/R0K39YsKa97FGbeMSQxxtpMOD0+Wpye4Cr8L/kybPsTbP8TJ4y3AXRfICclHHiRxsgpREWmBB1vXEQYNS2u4LapEDDrDnj3h4HOwydrtNmMrN5y3Q+/puX3xw/Mh76TzsZkQaccTbkB3rpf663gF8yd1pq9WlQefRN0Bi1fPgg6rcWqgxXMkz6uzT7te/6CuNN689Av3qx18s1aFtz3osUedNzJMzVnpgMvQvq3go5BMTR0deRoaHOzvrCaFfkJ3LU4i4dXH+SDo1X9stC8aW4aqdHhfOvfe/jE7zdz/9V5fH7RhIu+o+3FjpSSssYOCiubOVbZTGFlC8cqmzlc0YzLL+ptYQamJNu5Y34G01I1UT/BYR33+05xbRsbj9ew6XgNm07UBDq8T0qM4I75GSyeGMu8CTFD2iNCSsmJ6lbeP1LJu4er2Hm6Hq9Pkp9k50fXTWFVQTJRFhM+n2RXcT2v7yvn9X3lF8yYx1hNXDs9iRtmpgTVZykUuaiF/rzMGHwSdhU3cGkv+eGdvH2oAinh8vzh81cGzc+5zeWloqmj906xPbC7WHOZyM/OhMzfDnF0Ggn2TnegjuCEviNbs37c9iTlWcuIthi7L9w8/i7UFFKR93UG5p5/Lol2M16fpKbVSXxEEJZ5BbfD+z+GXX+Hq34SmHHJiu1hFqKtTsvPX/zNoGO2hRkwGXTUBJMCA1q9Rs5V2kzE8h+AIYxTNa3odaL3/eroGq3o2RzcyKXZqCcizED1QPssdGJ1aB2b9zyrxW00c6xSu7Ca2NOsD2jpPkar5twTJHERYcHHLYTWy2LdzzDH3RZ0DIrh4eXdZ1iRn8Ct89J5anMRP3njMEty+lfgt3BiLGu+sZT7X9rHj984zEu7zvDdayaxJKfv84ZibCOlpKKpIyDkC/2i/nhVCy1dGiXF2sLITbBx54IMreFZSiSZF4GoB20QdPOJ2sCofUmdlnqcaDdzeX4CiyfGsnCiI7hzby+4PD62F9Xx3uEq3jtSGahxyE+y85VLs7lqSiJTU7S6vj0lDbyx7zhv7C+n/DyzEyG0VL9VBSksynaMu6ZtF7XQn5URhcmg44MjVf0S+m/sryA9xhLYcYaLzpHt41UtQQr9egw6MSwNvTrp7E56pr79Qmef/nLZ9+CPi5hT9AR74r5y4fNSwvr/hcg0KhMuJbhxcY14/4VJZWOQQt8WrxUw73oaln6HUzWtRFmMgXz0CzjwEkivVsgbJEII4mxhVPXgnd0v5t0FR9/Q4im4jSMVzWTHWXtusFN5UKvjmPuF4L+TQY6MA8z5PBxerd2m38SRimZMOsjoqXeF1605I+WtBFPwrd3jIszsL+21jVjvFNwOW36PtfV08J+hGDJ++cnpfOfFfQC8c6iS2hYnDlsYD66cxN3/2MnfNxdx15L+OahFW008ecdsVu8t45drj3LHX7axNDeOe6/IpSBtMMMQilCg3eWlqLaV07WtFNW2UVTTyrGqFgorm89J6XBYTeQk2PjErBRyEiLIjbeRmxDR87lgnOH1SY5VNbOnuIHdxQ3sKWmgsKoZKSEizMD8bAd3Lc5icU4sWbFDn5JU2+Jk3dFq3jtSyfrCGlqcHkwGHYuyHdy1JIsVk+JJjgoPNKL72VtHeH1febd1j1dOTmBVQQrLJ8WP674PF7XQt5gMLM2JY+3BCh7++ORed8j6VhebjtfwxSVZw56r1Sn0T1S39OpE0xO7iuuZnGwfVv/nlChNTA2qaDhhMnL257li+185k3wVsPDc5wvXQskWWPlLZPvgdtXETqHf1ME0grwAWnyvNmq87UmOVy1hQk/5+dKn9SpInglJM4KMWCMp0kxFsFaroI1ux03SikRn3MqR8ibmTui+MygAO/+udXmdemHDqoEQaxvEyDjAhEu1uoiPHoNpn+JoZRMpNl3PhVAn10F7PUwNvo4DIH4wI/oAUWnw7ePUbtw8qDgUQ8ONs1IDQt/l8fHU5iLuuzKPKyYncHl+PL9Yc5T5WY5+590LIVhVkMLVUxP5x0enefT941z/+Camp0by6fkZXDcjeVR89xX9o83loaimjdO1rZyqbeV0TRtFta0cLWujYc2ac17rsJrIjrexqiCZ3IQIcuIjyE2wBWyPLxaqmjrYXdLA6qMu/lj4EftLG2l1eQGt90hBWhTXTk9iUU4s01Mih3w0vMPtZW9JA9tO1fHB0Sp2lzQgpXas/viMJFZMSmDhRAcWk4Hi2jY+LKxm0/EaXt9X3u3nLcx2sKogmaunJBFpGV8WpT1xUQt9gJVTE3n3cCV7Sxt7HZXp9FG9dgAOPcESazMRGW7keBCuNh6vj70ljdw8d3iLAeMiNBvQQQl94NSMe5Hb3uDTJQ9B7QItpQegoRhWfw3iJ2sFsIMUTp2pRhVNgxDNSdMhdyXyo8eoaM9k6czJ3b4spm4P1B6DG568oFnVQEmMNAe6HwaFELDgHlh9D617X6GsMYxJiT3MSLnatDSfyau09JlBEGcP49Bg4tbpYMm98OpXoXANRysM5Ef2cgLZ9iRYYiF7RfDfibZft/o7hAadP2q4OEb2xgI6ncCoF4Euln/fXMTdS7OIMBv5xSdnsPK36/n6v3az+muLsQ3g9w4z6LlrSRY3z03jld1nePqj09z/4j7+583DXD0lkSsmJ7BoYqwS/SNMq9NDWUM7pQ3tlDW0c6bef9/QzunaNqrOu4iPtZnIdFiZ4tCzYGoWGQ4rmQ4rGbEW7OOou2x/aXd5OVDWqI3Wl9Szp7gh0NNHL2BKipcbZ6cyMz2KgrRoMh19NF4MgvpWl9YkzG85uv9MY+D/d3pqJN9YkcPl+QlMSbZT0+Ji84kafrT6EO8dqaSmG+MKnYCPTU9mycRYLs2LC2iBi4mLXuhfnp+AQSd4bW9Zj0Lf4/Xx102nmJsZPSKOC0IIsuOsQQn9IxXNtLu9zEwf3qlkvU6QFGWmtH5wQn9XleSP7m+x1vJTeHIZLP02GMyw4Vea7/8n/zYkwinWZkIntBH9QXHFj+APi/im7yncKU9c+LzXw4RTT0NEslYMO0iSIs28e7gyOHejTmbcCpsfRff+Ixj4EflJPaRa7XwKnI1a2swgSY408+6hQcY9/WZY/0s87z5CfcuDpKb2kMZWeQiOva2lghkHdxBPsGujdRVNHT12T1WMLVbfs5iVv90AaN2an/jwJN++Ko8Yq4nf3DyT2/+8hS/9Ywd/uXPugIV5hNnIZxZkcsf8DLacrONf24p5fV85z20vIdyoZ2luLMvy4pmdEc3EONtFka89XHS4vVQ3O6lqdlLZ1KEJ+npNxHeK+YbzrHENfrvq5KhwlubGMSHWSobDool5hyVQX6Y1FRtek41QQkpJZZOTwxVNHK1o5kh5E0cqmjlW1RJoDJUaHc6sjGg+nxbFzPRoao/v4coVA+/w3lccpfXtflFfz46iOo75dY9RL5ieGsUXFmcxNzOa2RnR6HWCrSfreGlXKd96vibw2vNZNNHB4olxLMmJZXKS/aL/v7vohX6kxcjKaUk8v72Er6/I6bbb3FsHKiitb+f7H+t+BHc4yEuM4I195QMWSp0NHuZnDW5Etj9kOqwBu8Zg2VfaQLkxA+7+EF79CrzzkPZE0gxY9fugHWvOx6DXkRQZPugLE+LyKMy5ixuO/oGy1rXAXec+v+0JIlpOwaeeGpILlMTIcDrcPhrb3cG3/dYb4Mr/JvzZm/i64WXyk7qx+2yrgw9/rqX6BNEN93xSosJxenzUtrqIDXaqW2+Ey3+E4YU7uUv/Jnbbp7p/3bqfgtECc+/q/vkB0JmSVlrfroT+OCE/6dwZrCfWn+D6mSlMjLexINvBLz85g/te2Ms9z+7iD5+eHZR/uRCCBdkOFmQ7cHq8bDlZxzuHKnj3UBVrD1YCYDcbKEiPZnZ6NNNTI8mOs5ESHT4mfbmHCiklLU4PtS0uqpqdVDV3UNmk3Vc3nRX1Vc3ObhvwWU16UqLDSYkKpyAtKrCcEhVOSnQ48RHmi3r7gjbLUVjZzJGKZo5WNHPYL+q7bs+kSDN5iRGsyI+nIC2agrSogHtaJ+tODX47Oj1eCita2FWsjdjvKKoPzLJHmA3Mzojm+pkpzM2MYXpqJFVNTvaWNrDlZC0/X3OEwsruhX1eQgSX5sWxeGIsczNjxnW+fTBc9EIf4CuXZvPa3jKe3lzE185rjd7q9PCzt46QE2/jisnD67bTlRmpUfxrWwlFtW0954J3wwdHqpiaYh+R6amsWCsv7TozqFHbvaWNTEuNRB+TAZ97U2sy5fNAZNqg017OJz3GErBpHAwvWm/jUt9GFq3/f2A3aZalQsCh1fDOQ9Q45hI7+fohiFg7AAOUNXQEL/QBcq9ie9Q13NPwKqLidrBfefY5KeHt70NHI1z54yHZ7p1F5Gfq24MX+gCTV1EUdxn3Vr3IVgqA81JzDvkLdpd/X3MZGiRdi8wV44fn7p7PLU9uAcDtlXzvlf08+8X56HWCG2en0uby8INXD/L5p7bz6K0zB/W/FmbQc2luHJfmxvHfq7Su37tO17OruJ5dpxv4zXuFSG3QFJNBR1aslew4G9lxVlKiw0mwmwO3aItxTPh3Sylxenw0d3hocXpo7nDT0Oamvs1FXauL+lYXdW0u6lvd2uPO9W2uQFpGV4x6QXyEmbiIMLLirMzPchAfEUa8PYz4CDPx9jBSoyzYww1jYvuMBE6Pl5K6No5VtnDYP0p/tLI54EQD2oVRbmIE10xLYlJihP9mH5Zc9cZ2N4fKmjhY1sih8iYOlTVxvKoFj3/GICnSzLwJMczNjGZOZgwOf6+bvSUN/O69Y2w8XtPjZ6dEhTM/y8HS3FgWZsdecFGiOBcl9NG65F6eH88fPzzBqoIU0h1nXTt++tZhzjS08+KXF4zoyECBP/VmT0l9v4V+fauLXcX13HPZxOEMLUBWnI0Wp4fqZmfA1WYgdLi9HC5r4nOLMs+utCcPXYDnkR5j4b0jVYP+nL1lrRyKf5jFEb/T6gi2PqEVsJbtgpTZHMn8JouH6OTT6XdfXNfK5OTBuT094r2Tx4xHyXj+dvjY/0HB7QifWxP5e/4JS++HxKlDETYpfsFc1tDOjME4kgjBo9Z7+JbuMAuO/BiKCyB9vvZc2W5t+ydOh0XB25h2JcFu9teeDP6CUBE6nD/DufVUHb9ce5QHVmozhncsyCTMoOd7/9nPdY9t4k+fmUNeYpBuYl3Q0jBtZMfZ+NQcrW6qqcPN0YpmTlS1cLKmlRNVLRwsa+StA+X4ztO8Jr2OuIgw4iLCiDAbtFuY0b9sxGY2EOG34TXoBUa9DqNeYNDpAssnG7xEFtfjk5og90nNOaVz2SclXilxur04PT463F463GfvnR7/Y4+XDpeXpg4PLU53F1GvCfvuBPvZ7QDRFlPARjk9xkJBWhTRVhMxFhPRVlNAyCdEmIkaIxc4I43PJylrbOdUTSunalo5Wd0aWC6tbwvsPzoBmbFWpiZHcuOs1ICgT40OH/I0lk770YNnmjhY1sSh8kYOljWdM3seHxHG5GQ7K/LjmZwUSVaclfpWF3tLG9l0vJYfvHqw1+9YkhPLnIwYCtKjmJEaObhBr4sQJfT9PPzxKVzzuw189m/bePz2WaRGh/Pbd4/xzJZivrhkAnMyBz9aOBBy4iOwmw1sPVnHDTNT+/WedYVV+CRcNil+mKPT6GwWdbyqJSihv+VkLS6vj4UTY4c6tG5Jd1ioaXHS5vIE3YXP5fGx/4y/2PnaV2HXU5oTj9cDVzwC876EZ9OWIY0ZoKh2cMKzpsXJ/mov7674M18o+a4mkN/7bxY6W8HTCvPuhmUPDkXIAKRGa3GX1A8ubiklH5RIHNm/4lul92L820rNY19vhMOvQ0Qi3PwP7fEQoPfn9A46xUsRcmz77grm/c97gcd//PAEU5LtfHyGNrhw09w0suNtfPmZnax6fCNfW57DF5dk9WxFGyR2s5G5mTHMPe+c4vL4/GkqWvpKZZM/jaWpg+oWJ80dHsobO2ju0ER2m9/5pF9sCd7MwKATmI16zEYdYQY9EWYDdrORBLuZif6LD5v/4sNuNvgvPowB++EYiwl7uPGiT6HpL1JK6lpdmpD3i/hTfkFfVNsa6LAL2gj9hDgrM9KiuH5mSmB2KCfBNiyF4C1ODyerWzhR3cLh8ubAiH29vzZCCJjg0OK57ZJ08pPsRIYbqW91UVjZwoGyRh7/4ESv3zEpMYKF2bHMSItkZlo0aTHh6qJvkCih7yctxsJfPzuXu5/eESjcArhjfgYPrMwf8Xj0OsH8LAebTvQ8fXU+L+08Q0pUODNSR8bTudO95XBFc1Bifd3RasIMOi7pze5xCMn0e7CfrG4Nuqh6x+k62t1eFmY7NGeYOZ8fkuLVnrCbjTispkHXQmw7VQdAQe4EWPEmHH4VCt+muqqW5Cv+a1DdZLsjMlyLu7OxWLCcqG6hrtVFdt40diT+miXeTVrHYemDWZ+By74L1qG9UMx0WCmqGVzcitAj3m7mswszeWpzUWDdvf/eg0EnWDlNc1ObnRHN619bzEOvHuCXa4/yyu4zPLJqCguzh38wwmTQkRZjIa23rtVd8Hi1zuQtTg9ur8Tt9flvEo/Xh8vrw+OV7NqzlxnTp6PTCXQCdEIgBOiFCKwTQmA26Akz6jRRb9Duwwy6cdc8KBRo6nBTWtdOaX0bpfXt/pu2XFLfdo5vv1EvSI+xMCHWxqV5WkHxhFgrWbFW4iLChlwEd47Qn6hq5YRf1J+obuFQSRv1a9YGXmfS68hLjOCqKYnkJ9mJsZrQCW029EhFM0+uP3lBcfT5xNrCWJoby8w0zcUnLzFiyC+sFUron8PczBjeu28Zr+0to6ndzZLcuFFthLIkN463D1VyrLKZnD6aUp2ubWXj8RruvSJ3xCrM4yLCSLCHcfBMY1DvX19YzYJsx4hZ0OUlasWVhZXNQQv99YU1GHRa4d1IkeGwcGqQwnPLyVrCjXqmp0ZqFyhTboApN1C4bh3JWcuGJM7zyY6zcaJ64M5RXdnqv0CZN8HB6QMWuPwncNVPhiK8HpkYb+OFHSWDcwy6SBFC/BW4FqiSUk71r4sBngcygSLgJill/WjE98Prppwj9D0+yVef3cUvPzmDG2drM6cJdjNP3Nt1OsYAAB4bSURBVDGH9w5X8vDqg9z2p63MyYjmy5dms3xSfMg4eBj0OqIspj7TGHxlBpaN0CyvQqO5w32BgO8q6s8vLLaY9KRGh5MabWFOZjSZDisT4jQxnxIVPiwXWx1urUFYV0F/slpb7jpbFBFmICvexmSHnoXTsokwG/B4JS6vj1PVrWw4VsNz20v6/L55mTHMnRBNbkIEeYkRZMXalKgfIZTQP48Yq4k7F2aOdhiA1rXtoVcP8Ob+Cr7Rh9B/dlsxOgE3zRle//zzmZocyf4ghH6Rf1ryjgUZwxBV92Q6tI6wRyuag/6M9YXVzMqIDtiyjQS5CRGsPVgxKOG55WQtczKjg3IUCZbseBtrDnTftKS/bD5RS1xEGJkOCyPVazY73kary0t5Y0dQnakvcp4CHgOe7rLuAeA9KeXPhBAP+B//v1GIDYBjP1lJzvfeArQ6dJNBx30v7GV3ST3f/9jkwMDDivwEFmbH8tz2Yv684RR3Pb2DnHgbt85L59rpSUGlKyrGNj6fpLbVRWVTB+WNHVQ0dVDZed/UQUWjdmt2es55X7ixU8iHMys9mtTocNJiLAFxPxxF11JKalpclNS3UVLXedNmDIrr2jjT0B4oCgetwDU73sZNGWnYzQb0Oq3uo9XpYVdxPZtKPGwqO9rn905JtjM/y0FeQgS5iRHkxNuC70miGBLU1g9hEuxmLpkQw4u7Srhn+cQecxwrmzp4evNprpmWRGLkyJ58ZmVE896RKupaXcQMoAX4y7tKEQKumpI4jNGdi0GvY2KcjUPlwTVyqmrq4FB5E9+5Km+II+udycl2ntteQkVTB0mRAxeex6taKKxs4ea56cMQXc/kxNv4V5ubqqaOoIu1PzhSxaqClBEdWc+J12Z+jlY2K6E/QKSU64UQmeetXgUs8y//HVjHKAp9o17Hzu9fzqf/so3D5U04PT7CDDqe2VLM9lP1/N9NMwIzfuEmPZ9bNIFPz8/g9X1l/HnDKR55/RD//cYh5k9wcF1BMssnxV+UTXjGEz4pqW1xUtvqoqbZSXWL0y/cnX5R3x6w/Ty/6FgnID7CTEKkmaw4KwuzHSRFhZMWbQmI+xiraViOYa1Ojybca9soqW8/K+jrNVHf7j63jiPWFkZ6jGZFeskEBwadQK/X0rcOlTWxvrCa9X6L7r6YkmxndkY02XE28hIjyE2IGJAGUIwcSuiHOJ+en8E9z+5m7cEKrpnWfVfeX71diMfnG3EBCjA/S8uv33qyNpDn2hden+SFnaUszYkbcSFVkB7Fa3vL8PrkgIvDXtl9BhjZixPQDqgAB880BSX0X99XhhDwsX7+PkPF9FRNLO0tbeSKyQMXQuuOVtHm8o543JOT7QgB+0sbuSxPpTwMAQlSynIAKWW5EKLbjSqEuBu4GyAhIYF169b1+cEtLS39el133D9d8je9gfWlnkCB4/GqZq59dCMLkw3cmGPEEX52Biwa+M50KMsKZ2u5hy3ldTz4ci0AiVZBfoye/Bg9k2L02MNCI70HBreNxjJen6TZJWl0SZqckqbAMjT51zW6tPXNTh++te9e8Blheog2C6LDBBkWHQXRBu2xf120WWA3Cf+5xO2/tYAE6qC+DoLNUfP4JA1OSX2HpM5/q+/wBZar23w0n5cCb9ZDnEVHjFkwJQZ0Qo/OX4/R7pEUNbnYVexkV3FDv2JItAjyHXqSrTrsOicZDgux4QKDTgBeoAZcNXQUw77iIP/QcUYo/r8poR/irJyaxMT4Y/xizREuy4u/oBHE6/vKeH5HCV9aqrXvHmmmp0YREWbgg6NV/Rb6HxZWUd7YwUPXjlwDsk7mZETz7NZiCiubL2ik0xtSSv69o0TrcBk/so2U8pPsGHSCncX1XD7AXg5SSl7bW8a8zJgRn+2ZkhyJXifYW9IQVA+KN/ZXEGM1BS4mRwq72cjEOBu7i0cljfyiRUr5JPAkwJw5c+SyZcv6fI/W0bTv1/XEZZfBm/vL+a9/7gLAK7U0i20VXnZU+bhpTip3zM+8wGrzNi1eDpU3sel4DR+dqGV7UT0flDgBrcNyfpKdSYl28pMiyE+yk+GwEGYY+UY+g91Go42UklaXl/pWFw1tbhraXdS3uWnw+/LXt7m05c51fv/+rgWtXQkz6Ii1hREbEUZevAmHNYzWugpmT8nR1tvCiIswEW83ExE2PD79HW7v2fSfxs779kA6UHljBzUtznNSa0DL5U+MNGOLMGC3axcYnQNWtS1OTlS3UtLso2QA2amTEiO4ZEKM1jU41soEh9bP4fw0z7G+H40UobidlNAPcfQ6wSOrpnDbn7Zy3wt7+PXNBYGTxVv7y/n2C3uZnRHNfVeO/Gg+aNPgK/LjeftQJT/x+vrMAff5JL9+5xgpUeGsyB+5BmSdzPM7/Gw6XjMgob/jdD0nqlv5xY3ZwxVaj1hMBmakRfHRidoBv3d7kRb35xdPGIbIeifcpGdKsp2tpwYed1VzB2sPVnDL3LRRcf2YlR7NmoMVQc38bD1Zizz/DH1xUymESPKP5icBg29mMYRcMy2JzQ8sZ9Xjm6hudgbSHYSUPLOlmGe2FDNvQgy3X5LO8knxgfocIQRTkiOZkhzJ3Uuz8Xg1690dRfUcLm/icEUzm46fDKR6CAEJEeZAOkdqtIWU6HASI804rCZi/LdgrX9DEY/XR5vbS7vLS5vLG7AGbe5w09Rx1oO/qd1z9jln52vOPufy+nr8jogwA5EWI9EWE1EWIxkOK9EWI1EWE7ERYcRa/fe2MGJtJmzdiPd16+pYtmhwx0ifT1Lf5qK6xUl1s5Ma/7227AosVzV3BOwou2I3G3DYwtDrBDEWEw6rCb1O4PFKalu1z2hzeQfsZJYVZ2VORjQ58RGkRIeT7O8c7LCaQqawXDG8jJ8jyjhmYXYs3/9YPj9+4zBHyjewNDeOQ2VNbCuqY1Z6FE/cMXtUq9evK0jmP3vKWHuwgmun997w6vX95ew/08ivbpoxKjGnRluYlBjB2wcruWtJVr/eI6Xk1+8UEmM18bHpI5tG0smibAePrztBbYsTxwA6zT72wXEcVhOf6GcvhqFmaU4cf/jwBI3tbiLD+1/A/LdNRXi8Pj4/yJNvsCzNjeP5HSXsLq4fUA+NLSdrueXJLdw1zcRlwxjfGGM1cCfwM//9q6MbzoUkR4Wz7bsrWFdYzef+th3gnNHU7UV1bDtVh1EvWJAdyxX58azITzgn9dCg1zEzPZqZ6dGBdW6vjxPVLRwp1zqUdjqv7Cyu57V95XjP75AFmI26QBOpaIsJi0mPxaQn3GTA2nU5TI/ZqMeoF1rhpH9016ATGPRnHxfWe7EW1eHzyXOaZvmkxCclMrBMwJbT6fHh8t/cXv+y/97pX3a6fbS7NT//NlenmPfQ7vLS6n/cm0DvisV01p8/wmwg2qI11YowG7GHGwLNtqIspnOWoyzGYTUY6HB7u3T3dVPb6qS2pXsxX9vq6vb3DDPoiDAbkVLS+WyszYTL46Opy6xDU4fnnMf9IcygY96EGKalRAYuHFOizCRHhY+rC0bF4FB7whjhriVZZMfZeOyD47y4s5TESDMPrpzEZxdljsp0cFeW5caT4bDw+AcnWDk1qccR0LKGdh569QBTU+ysKkgZ4SjPcvXURH773jFK6tr65Vm9/lgNm0/U8tC1k0fNPeCqqYn87v3jrDlYwe2X9M+paOfpetYXVnP/1XkXpHyNFJdNiuexD47z9sGKQGfQvqhpcfLMltOsnJpEZj+7Qg81i3NiMegEaw9W9Fvo+3ySX649SnxEGPMSR/d/crQQQvwLrfA2VghRCjyMJvD/LYT4AlAMfGr0IuwZIQSX5cVz4n+u4bW9ZXzz+T2B5zpFv9srAwWLP3j1IKnR4czOiGZWunablBRxjvA06nVMSrQHeo50xeP1UdnspKKxnbpWN/WtLmpbXQFhWdeqpaRoTf46xbSHNrf3gpSOPtn6UTCb5ByE0LzTTQYdJr2OMIOOcJMei8lAuElPrM2ExWTxr9Nr90aDdqESpq2zBbr6nhX1tjDDiMzadbi9NLa7zxHudW0u6ltd7C908krFbi3tx7/t69tcfTYlE/6+BHr/zcuFP4zT48PZ4hxwvOkxFqam2MlPtJMYaSbBbladgxVBoYT+GOKySfEj1vV2IOh0gnuvyOUbz+3hzxtO8qVLL0xvqWlxctffd+DxSh69ddaodkm8eW4aj75/nL9uOsXDH5/S62vrW108+NI+MhwWbp8/sq41XZmcZCc3wcY/txRz27z0Pg/yHW4v97+4l6RIM3fMHzkL0/OZlR7FhFgrz20v6bfQf3j1QZxuH9+6ImeYo+uZyHAjl+cn8NKuM9x3ZV6/ej38c1sxO0/X84tPTsfU0nv3x/GKlPLWHp5aMaKBDAK9TnD9zBSun5nCobImfrbmSI9OJJ2+6K/uKQM0q86sWCvZ8Tay42xMjLcxMc5GhsNywSCBQa8jxZ9GMRCklHS4fbT6R8+9PonHJ/H6tKZZXR97fD527d5LwYwZgcZYOsE5jbJ0/nUCgUEvzhHyxk5hb9BmCEZTXLq9PlqdWkpPY7ubpg43Te1aak9juzuwLrAcWKc97/L0MbtwumzAMUkJXim7Ffg9kRVnZUpyJHkJNhLsSsArhh8l9BVDwnUzknlrfwU/W3MEt9fH3UuzMRl0+HySD45W8cPXDlLd7OSPn57NhFEape0kKTKcG2el8MyW09w8N63b0TbQrMv+65+7qGlx8dJXFo7qzIkQgrsWZ3H/S/tYc6Ci18Jnn0/yvVcOcKK6lac/P29EPf/PRwjBnQsy+OFrh9hwrJolOXG9vv4fW07zxr5yvn1lLhPje+8dMdx8ZmEGaw5W8MyW032mee0rbeCnbx5mSU4sn5qdyocfXpxCf7wxOdnO05+fh8frY+fpev6x5TSv7+u5N4TL4+NIRTNHuunVERFmIDHSrN3s5sAobbTFRGS4kSiLkchwI5EWY69FoEIIwv0j5v3BVaJncc7wd/btREqtmVKHy0e726vdXNp9R5flVn9X3xanx7/sPbvc4V/vOrvs7EuojxKxNhM58RHkJtjIcFiJjQjDYTXhsGmFvtEWo+ourBhVlNBXDAlCCH5zSwH3vbCX/327kCc+PElmrDXgHpAVa+XZL85nVpf81dHk/qsn8f6Rar749A7+eufcCzoPH61o5tsv7OVgWSP/d9MMpqUG10l3KPnErBT+trmI7//ngNZZMO5C9582l4fv/+cAL+86w7cuz2Vpbu/CeiS4ZV46f9tcxAMv7ec/X11EXMSFNQZSSp7+6DQ/fO0gKybFdzsrNNIszI7l0tw4/u/tQpbkxF3gvNLJ9qI6vvSPncRYTfzvp2aoEblxiEGv45IsB5dkOXj0VsmZhnZ2FTewes8Z3j3cv9riZqeH5qoWjlX13S1aJ7RZJZvZgNmgiXqzQY/ZpMds0GE26gk36jEbdeh1OvQ6bZTeoNNSSHRd7k8XuTimOxnIw9fy8rvm6Xfm7fvX+WQgH9/t9eH2ykCOvtvbNWdf4vavb3f5RbxfzHeTqj4mcFhNZDgsZDisZDgsJEWaiQzXagGiLEaiwk1EW42jni6rUAwEJfQVQ4bZqOfx22Zx85xq3jpQQVlDOznxNpbmxnHNtKSQancdawvjL3fO4bN/28Y1v9vAtdOTmZJsx+nxse1UHRuOVRMZbuSJO+YEZQ05HBj0Oh67bSaf/MNmVj22iW9flcfVUxOJsZqoaOzg/SNV/HnjSUrr2/nm5Tl8fcXE0Q4Z0PaL394yk1ue/IhVj23koY9PYfmkeEwGHS6Pj62nanniw5NsPF7D8knxPH77rBHt4NsbP79xOtc9tpGbnviI712Tz3UFyZiNeqSUnKhu4e+bT/PstmLSosN56nPzVOOkiwAhBKnRFlKjLVw3QzMf6HB7OVHdwvGqFracrGPNgfJunVX6i0/it4kM/jPO4ejhofmcMUCszURyVDjJkX6Hmehwoi1GIroU+nbOnnSm5IWiJaJCMVQooa8YcpbmxoXESHJfzEiL4p17L+X/3i5kzYHyQEOs9BgLX1mWzRcWZ4Vcp7/sOBuvfW0x33xuDw+vPsjDqw+e8/yMtCh+fuN0FmaP3FR9fyhIi+L5uxfwrX/v4cvP7MRk0BEVbqS+zYXbK3FYTTz88cncuSAzpCzfEiPNvPDlBdz7773c/9I+fvDqARLsZpo63DS0uTHoBDfPTePBlZNGNUVKMbqYjfqA1eaqghR++olpgDZSXtfqoryxg8qmDopq29hdXM/BsiZO1QzMJnE8E20xEhfR6WEfRpzf5z7GqtlhWkx6rGEGwo167H4nnpEq4lUoxjqDEvpCiKuB3wJ64M9Syp8NSVQKxQgRawvjp5+Yxk+un0qz04NBJ0bNWae/pEZbeOHLCzhY1sTO0/U0tLlx2EzMzYwhN8EWsqkjM9KiWPONpWw4Vs3WU3U0tLmItpqYnR7Nkpy4UXMG6osMh5UXvrSAjcdr2HCsmqpmJ7YwA/lJdi7PTxjxRmSKsYMQAoctDIctjKkpnel/3VvGSilpcXpoaNOKSDvOy29v7vAEnHmaO7RcdqfHi9Pjo8N99r7D7cPp8eLxSTxeidfrwWAwBIpudUIEinI7XWOMeh0GvQikCWlpQZ3OOf7UoS7pQp0pRUaDLpBKZPY/Zzb604yMOsKMesIMWmFvqB6XFIrxTtCKRgihBx4HrgBKge1CiNVSykNDFZxCMVLodGJAPu+jjRCCqSmRXcTD2MBk0LEiP2FUmqUNBp1OjJmZKsXYRAjhTy8x0j9/qv6h0lIUioubwcx7zQOOSylPSildwHPAqqEJS6FQKBQKhUKhUAyGwQj9FKCky+NS/zqFQqFQKBQKhUIxygwmGbm7hLsLTLWEEHcDdwMkJCSwbt26oL6spaUl6PeONGMl1rESJ6hYhwsV6/AwlmJVKBQKxfhlMEK/FM5JJUwFLmgtJ6V8EngSYM6cOTLYXMGxlGc4VmIdK3GCinW4ULEOD2MpVoVCoVCMXwaTurMdyBFCTBBCmIBbgNVDE5ZCoVAoFAqFQqEYDEGP6EspPUKIe4C1aPaaf5VSHuzjbQqFQqFQKBQKhWIEGJRhuJTyTeDNIYpFoVAoFAqFQqFQDBGqrZxCoVAoFAqFQjEOEVJeYJQzfF8mRDVwOsi3xwI1QxjOcDJWYh0rcYKKdbhQsQ4Pg4k1Q0p5UXfmGsC5YiztE6OF2kZ9o7ZR36ht1D9Gcjv161wxokJ/MAghdkgp54x2HP1hrMQ6VuIEFetwoWIdHsZSrGMZtZ37Rm2jvlHbqG/UNuofobidVOqOQqFQKBQKhUIxDlFCX6FQKBQKhUKhGIeMJaH/5GgHMADGSqxjJU5QsQ4XKtbhYSzFOpZR27lv1DbqG7WN+kZto/4RcttpzOToKxQKhUKhUCgUiv4zlkb0FQqFQqFQKBQKRT9RQl+hUCgUCoVCoRiHhLzQF0JcLYQ4KoQ4LoR4YLTj6YoQ4q9CiCohxIEu62KEEO8IIY7576NHM8ZOhBBpQogPhBCHhRAHhRDf8K8PuXiFEGYhxDYhxF5/rD/yr58ghNjqj/V5IYRptGMFEELohRC7hRCv+x+HapxFQoj9Qog9Qogd/nUh9/sDCCGihBAvCiGO+PfZBaEYqxAiz789O29NQohvhmKs44lQPi+MJmPpOD+ajJVj9mgyVo7Bo4kQ4lv+/7MDQoh/+bVLyO1LIS30hRB64HFgJTAZuFUIMXl0ozqHp4Crz1v3APCelDIHeM//OBTwAPdJKfOB+cBX/dsyFON1AsullDOAAuBqIcR84OfAr/2x1gNfGMUYu/IN4HCXx6EaJ8BlUsqCLj6/ofj7A/wWWCOlnATMQNu+IRerlPKof3sWALOBNuAVQjDW8cIYOC+MJmPpOD+ajKVj9mgxJo7Bo4UQIgX4OjBHSjkV0AO3EIr7kpQyZG/AAmBtl8cPAg+OdlznxZgJHOjy+CiQ5F9OAo6Odow9xP0qcEWoxwtYgF3AJWjd5gzd7RujGF8q2gFvOfA6IEIxTn8sRUDseetC7vcH7MAp/GYBoRzrefFdCWwaC7GO5dtYOC+Eym2sHOdHeJuMmWP2KG6jMXkMHuFtlAKUADGAwb8vXRWK+1JIj+hzdkN2UupfF8okSCnLAfz38aMczwUIITKBmcBWQjRe/9TqHqAKeAc4ATRIKT3+l4TKvvAb4H7A53/sIDTjBJDA20KInUKIu/3rQvH3zwKqgb/5p9f/LISwEpqxduUW4F/+5VCPdSwzFs8LI85YOM6PEmPpmD1ajNVj8IghpTwD/C9QDJQDjcBOQnBfCnWhL7pZp/xAB4EQwga8BHxTStk02vH0hJTSK7V0iFRgHpDf3ctGNqpzEUJcC1RJKXd2Xd3NS0Nln10kpZyFlvLwVSHE0tEOqAcMwCzgD1LKmUArIT5F7M/DvA54YbRjuQgI5f+xkGCsHOdHmjF4zB4txtwxeKTx1yesAiYAyYAV7dx6PqO+L4W60C8F0ro8TgXKRimW/lIphEgC8N9XjXI8AYQQRrSD/z+llC/7V4dsvABSygZgHVq+aZQQwuB/KhT2hUXAdUKIIuA5tKng3xB6cQIgpSzz31eh5ZHPIzR//1KgVEq51f/4RbSTTijG2slKYJeUstL/OJRjHeuMxfPCiDEWj/MjyJg6Zo8iY/EYPNJcDpySUlZLKd3Ay8BCQnBfCnWhvx3I8Vcxm9CmxlePckx9sRq40798J1qO5KgjhBDAX4DDUspfdXkq5OIVQsQJIaL8y+Fo/1CHgQ+AT/pfNuqxSikflFKmSikz0fbN96WUtxNicQIIIaxCiIjOZbR88gOE4O8vpawASoQQef5VK4BDhGCsXbiVs2k7ENqxjnXG4nlhRBhLx/nRYCwds0eTMXoMHmmKgflCCIv//65zG4XcvhTynXGFENegXXHrgb9KKX8yyiEFEEL8C1gGxAKVwMPAf4B/A+loO8KnpJR1oxVjJ0KIxcAGYD9ncxO/i5a/GVLxCiGmA39H+811wL+llI8IIbLQRmFigN3Ap6WUztGL9CxCiGXAt6WU14ZinP6YXvE/NADPSil/IoRwEGK/P4AQogD4M2ACTgKfw78vEHqxWtByxrOklI3+dSG5XccLoXxeGE3G0nF+tAn1Y/ZoM5aOwaOF0Ky/b0Zzu9oN3IWWkx9S+1LIC32FQqFQKBQKhUIxcEI9dUehUCgUCoVCoVAEgRL6CoVCoVAoFArFOEQJfYVCoVAoFAqFYhyihL5CoVAoFAqFQjEOUUJfoVAoFAqFQqEYhyihrxhXCI2NQoiVXdbdJIRYM5pxKRQKhSK0EEK0nPf4s0KIx0YrHoViODD0/RKFYuwgpZRCiC8DLwghPkDz2f4JcPVgPlcIYZBSeoYiRoVCoVCMfdR5QTEWUCP6inGHlPIA8Brw/9CamD0tpTwhhLhTCLFNCLFHCPF7IYQOQAjxpBBihxDioBDioc7PEUKUCiF+IITYBNwwKn+MQqFQKEYcIcTHhRBbhRC7hRDvCiES/Ot/6D9nvA08LYTQCyF+KYTYLoTYJ4T40iiHrlCcgxrRV4xXfgTsAlzAHCHEVDSxvlBK6RFCPInWAv1Z4AEpZZ0QwgB8IIR4UUp5yP85rVLKRaPxBygUCoViWAkXQuzp8jgGWO1f3gjM988S3wXcD9znf242sFhK2S6EuBtolFLOFUKEAZuEEG9LKU+N1B+hUPSGEvqKcYmUslUI8TzQIqV0CiEuB+YCO4QQAOFAif/ltwohvoD2/5AMTAY6hf7zIxu5QqFQKEaIdillQecDIcRngTn+h6nA80KIJMAEdBXuq6WU7f7lK4HpQohP+h9HAjnnvV6hGDWU0FeMZ3z+G4AA/iql/EHXFwghcoBvAPOklA1CiGcAc5eXtI5IpAqFQqEIJR4FfiWlXC2EWAb8sMtzXc8LAvialHLtCMamUPQblaOvuFh4F7hJCBELIIRwCCHSATvQDDT5R26uGsUYFQqFQhEaRAJn/Mt39vK6tcBXhBBGACFErhDCOtzBKRT9RY3oKy4KpJT7hRA/At71F+G6gS8DO9DSdA4AJ4FNoxelQqFQKEKEH6K5t50BtgATenjdn4FMYJfQ8kKrgetHIkCFoj8IKeVox6BQKBQKhUKhUCiGGJW6o1AoFAqFQqFQjEOU0FcoFAqFQqFQKMYhSugrFAqFQqFQKBTjECX0FQqFQqFQKBSKcYgS+gqFQqFQKBQKxThECX2FQqFQKBQKhWIcooS+QqFQKBQKhUIxDvn/+L1tZdJr4XgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 936x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(13,4))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(t,H,t,L)\n",
        "plt.title('Hare/Lynx Population Dynamics')\n",
        "plt.xlabel('Year')\n",
        "plt.legend(['Hare','Lynx'])\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(H,L)\n",
        "plt.title('Hare/Lynx Phase Plot')\n",
        "plt.ylabel('Lynx')\n",
        "plt.xlabel('Hare')\n",
        "plt.grid(True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4IPhCiZHuBC7",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        }
      },
      "source": [
        "## 2.5.6 Nullclines\n",
        "\n",
        "Nullclines are the points in the phase plane where the derivatives are equal to zero. \n",
        "\n",
        "The nullclines for hare are where \n",
        "\n",
        "$$\\frac{dH}{dt} = 0 \\implies \\begin{cases}\n",
        "\\begin{align*}\n",
        "H^* & = 0 \\\\\n",
        "\\\\\n",
        "L^* & = \\frac{r}{a}\\left(c+H\\right)\\left(1-\\frac{H}{k}\\right)\n",
        "\\end{align*}\n",
        "\\end{cases}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAlYA1RJuBC9",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        },
        "nbpresent": {
          "id": "c74a83fc-6f9e-40b0-9284-51276d079600"
        }
      },
      "source": [
        "The nullclines for Lynx are where \n",
        "\n",
        "$$\\frac{dL}{dt} = 0 \\implies \\begin{cases}\n",
        "\\begin{align*}\n",
        "L^* & = 0 \\\\\n",
        "\\\\\n",
        "H^* & = \\frac{c d}{a b - d}\n",
        "\\end{align*}\n",
        "\\end{cases}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PiR4jTmDuBC-",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        }
      },
      "source": [
        "For convenience, we create a function to plots the nullclines and steady states that occur where the nullclines intersect."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ouGX46OzuBC_",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        }
      },
      "outputs": [],
      "source": [
        "def plotNullclines():\n",
        "    # nullcline dH/dt = 0\n",
        "    Hp = np.linspace(0,k)\n",
        "    Lp = (r/a)*(c+Hp)*(1-Hp/k)\n",
        "    plt.plot(Hp,Lp,'b')\n",
        "    plt.ylim(0,130)\n",
        "    plt.xlim(0,150)\n",
        "    \n",
        "    # nullcline dL/dt = 0\n",
        "    Hd = c*d/(a*b-d)\n",
        "    plt.plot([Hd,Hd],plt.ylim(),'r')\n",
        "\n",
        "    # additional nullclines\n",
        "    plt.plot([0,0],plt.ylim(),'b')\n",
        "    plt.plot(plt.xlim(),[0,0],'r')\n",
        "\n",
        "    # steady states\n",
        "    Hss = c*d/(a*b-d)\n",
        "    Lss = r*(1-Hss/k)*(c+Hss)/a\n",
        "    plt.plot([0,k,Hss],[0,0,Lss],'r.',ms=20)\n",
        "\n",
        "    plt.xlabel('Hare')\n",
        "    plt.ylabel('Lynx')\n",
        "    plt.legend(['dH/dt = 0','dL/dt = 0'])  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xyRX89AAuBDC",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        }
      },
      "source": [
        "Here's a plot of the nullclines for the default parameter values. The steady states correspond to \n",
        "\n",
        "* No Hare, and no Lynx.\n",
        "* Hare population at the carry capacity of the environment, and no Lynx\n",
        "* Coexistence of Hare and Lynx."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KSo_J6tZuBDD",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        },
        "outputId": "a0433277-a5f6-4c7c-8d70-58ff88935bd9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plotNullclines()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-z62zBHruBDI",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        }
      },
      "source": [
        "Visualization of the nullclines give us some insight into how the Hare and Lynx populations depend on the model parameters. Here we look at how the nullclines depend on the Hare/Lynx predation rate $a$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "85sXKwQ3uBDK",
        "nbpages": {
          "level": 2,
          "link": "[2.5.6 Nullclines](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.6-Nullclines)",
          "section": "2.5.6 Nullclines"
        },
        "outputId": "9db17e16-dc90-41ac-82fd-969e0b9d8d48"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": [
              "<function __main__.sim(aslider=3.2)>"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from ipywidgets import interact\n",
        "\n",
        "def sim(aslider= 3.2):\n",
        "    global a\n",
        "    a = aslider\n",
        "    plt.xlim(0,150)\n",
        "    plt.ylim(0,130)\n",
        "    plotNullclines()\n",
        "    \n",
        "interact(sim,aslider=(1.25,4,.01))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3UUYg--euBDQ",
        "nbpages": {
          "level": 2,
          "link": "[2.5.7 Interactive Simulation](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7-Interactive-Simulation)",
          "section": "2.5.7 Interactive Simulation"
        }
      },
      "source": [
        "## 2.5.7 Interactive Simulation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.1 Visualization Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.1-Visualization-Function)",
          "section": "2.5.7.1 Visualization Function"
        },
        "id": "NZIIG2eZ31P1"
      },
      "source": [
        "### 2.5.7.1 Visualization Function\n",
        "\n",
        "The visualization function for this example accepts a list of time values, values of $H$ and $L$, and model parameters. The model parameters are needed to plot nullclines and steady states on the phase plane."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OX4x0ibWuBDS",
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.1 Visualization Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.1-Visualization-Function)",
          "section": "2.5.7.1 Visualization Function"
        }
      },
      "outputs": [],
      "source": [
        "# visualization\n",
        "def HLPlot(t,H,L):\n",
        "    # time axis\n",
        "    plt.figure(figsize=(12,5))\n",
        "    plt.subplot(1,2,1)\n",
        "    plt.plot(t,H)\n",
        "    plt.plot(t,L)\n",
        "    plt.xlabel('Time [years]')\n",
        "    plt.ylabel('Population Density')\n",
        "    plt.legend(['Hare','Lynx'],loc='upper left')\n",
        "    \n",
        "    # phase plane\n",
        "    plt.subplot(1,2,2)\n",
        "    plt.plot(H,L)\n",
        "    plt.xlim(0,150)\n",
        "    plt.ylim(0,130)\n",
        "    plotNullclines()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B7BXePuPuBDT",
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.2 Simulation Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.2-Simulation-Function)",
          "section": "2.5.7.2 Simulation Function"
        }
      },
      "source": [
        "### 2.5.7.2 Simulation Function\n",
        "\n",
        "An additional function is created to encapsulate the entire process of solving the model and displaying the solution. The function takes arguments specifing the initial values of $H$ and $L$, and a value of the parameter $a$.  These argument "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-7AyYkYJuBDV",
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.2 Simulation Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.2-Simulation-Function)",
          "section": "2.5.7.2 Simulation Function"
        }
      },
      "outputs": [],
      "source": [
        "# default parameter values\n",
        "a = 3.2\n",
        "b = 0.6\n",
        "c = 50\n",
        "d = 0.56\n",
        "k = 125\n",
        "r = 1.6\n",
        "\n",
        "# perform simulation\n",
        "t = np.linspace(0,70,500)\n",
        "\n",
        "def LynxHare(H=20,L=20,aslider=3.2):\n",
        "    IC = [H,L]\n",
        "    global a\n",
        "    a = aslider\n",
        "    sol = odeint(deriv,IC,t)\n",
        "    HLPlot(t,sol[:,0],sol[:,1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6X08RjWtuBDX",
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.2 Simulation Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.2-Simulation-Function)",
          "section": "2.5.7.2 Simulation Function"
        }
      },
      "source": [
        "Use the `aslider` to adjust values of the Hare/Lynx interaction.  Can you indentify stable and unstable steady states?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FaYQM0fGuBDY",
        "nbpages": {
          "level": 3,
          "link": "[2.5.7.2 Simulation Function](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.7.2-Simulation-Function)",
          "section": "2.5.7.2 Simulation Function"
        },
        "outputId": "862ee478-ce11-4747-82fc-94afcc30ac9f"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "from ipywidgets import interact\n",
        "interact(LynxHare, H = (0,80,1), L =(0,80,1), aslider=(1.25,4.0,0.01));"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lL04w6VVuBDb",
        "nbpages": {
          "level": 2,
          "link": "[2.5.8 Stability of a Steady State](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8-Stability-of-a-Steady-State)",
          "section": "2.5.8 Stability of a Steady State"
        }
      },
      "source": [
        "## 2.5.8 Stability of a Steady State"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.1 1. Unstable Focus ](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.1-1.-Unstable-Focus)",
          "section": "2.5.8.1 1. Unstable Focus "
        },
        "id": "cZ3pyZ0X31QA"
      },
      "source": [
        "### 2.5.8.1 1. Unstable Focus \n",
        "\n",
        "Any displacement from an unstable focus leads to a trajectory that spirals away from the steady state. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l9WDrpDTuBDb",
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.1 1. Unstable Focus ](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.1-1.-Unstable-Focus)",
          "section": "2.5.8.1 1. Unstable Focus "
        },
        "outputId": "787c6834-a1ab-45ce-b6d0-016155b5c01b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "LynxHare(H=20,L=20,aslider = 4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eKz3ZK8yuBDg",
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.2 2. Stable Focus ](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.2-2.-Stable-Focus)",
          "section": "2.5.8.2 2. Stable Focus "
        }
      },
      "source": [
        "### 2.5.8.2 2. Stable Focus \n",
        "\n",
        "Small displacements from a stable focus results in trajectories that spiral back towards the steady state."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gDnSiHh5uBDh",
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.2 2. Stable Focus ](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.2-2.-Stable-Focus)",
          "section": "2.5.8.2 2. Stable Focus "
        },
        "outputId": "cc6679dc-9c0f-4b8a-cba9-122fedcf18fe"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "LynxHare(H=20,L=20,aslider = 1.9)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KxrNJxAJuBDk",
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.3 3. Stable and Unstable Nodes](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.3-3.-Stable-and-Unstable-Nodes)",
          "section": "2.5.8.3 3. Stable and Unstable Nodes"
        }
      },
      "source": [
        "### 2.5.8.3 3. Stable and Unstable Nodes\n",
        "\n",
        "Displacements from a steady state either move towards (stable) or away from (unstable) nodes without the spiral structure of a focus."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WJ-TgtKYuBDl",
        "nbpages": {
          "level": 3,
          "link": "[2.5.8.3 3. Stable and Unstable Nodes](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.8.3-3.-Stable-and-Unstable-Nodes)",
          "section": "2.5.8.3 3. Stable and Unstable Nodes"
        },
        "outputId": "d76e2dd4-149f-4398-cabb-907da2cc6136"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "LynxHare(H=20,L=20,aslider = 1.4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fU7icbViuBDo",
        "nbpages": {
          "level": 2,
          "link": "[2.5.9 Summary](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.9-Summary)",
          "section": "2.5.9 Summary"
        }
      },
      "source": [
        "## 2.5.9 Summary\n",
        "\n",
        "Hope you enjoyed this brief introduction to the modeling of a small food web. This is a fascinating field with many important and unanswered questions. Recent examples in the research literature are [here](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0108243) and [here](http://science.sciencemag.org/content/320/5876/658). \n",
        "\n",
        "What you should learn from this notebook:\n",
        "\n",
        "* How to simulate small systems of nonlinear ODEs.\n",
        "* How to plot trajectories in a phase plane.\n",
        "* How to plot the nullclines of two differential equations with constant parameters.\n",
        "* Solve systems for multiple steady states.\n",
        "* Recognize limit cycles, steady-states, stable and unstable foci, stable and unstable nodes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CFCK9DgpuBDo",
        "nbpages": {
          "level": 2,
          "link": "[2.5.10 Suggested Exercise](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.10-Suggested-Exercise)",
          "section": "2.5.10 Suggested Exercise"
        }
      },
      "source": [
        "## 2.5.10 Suggested Exercise\n",
        "\n",
        "Explore the impact of the parameter $a$ on the nature of the solution. $a$ is proporational to the success of the Lynx hunting the Hare.  What happens when the value is low?  high?  Can you see the transitions from conditions when the Lynx done't survive, the emergence of a stable coexistence steady-state, and finally the emergence of a stable limit cycle?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cbOk899MuBDs",
        "nbpages": {
          "level": 2,
          "link": "[2.5.10 Suggested Exercise](https://jckantor.github.io/CBE30338/02.05-Hare-and-Lynx-Population-Dynamics.html#2.5.10-Suggested-Exercise)",
          "section": "2.5.10 Suggested Exercise"
        }
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.6 Exothermic Continuous Stirred Tank Reactor](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6-Exothermic-Continuous-Stirred-Tank-Reactor)",
          "section": "2.6 Exothermic Continuous Stirred Tank Reactor"
        },
        "id": "ITDQGAHR3-Gy"
      },
      "source": [
        "# 2.6 Exothermic Continuous Stirred Tank Reactor"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.1 Description](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.1-Description)",
          "section": "2.6.1 Description"
        },
        "id": "XxJwoaXb3-Gz"
      },
      "source": [
        "## 2.6.1 Description\n",
        "\n",
        "This example is intended as an introduction to the nonlinear dynamics of an exothermic continuous stirred-tank reactor. The example has been studied by countless researchers and students since the pioneering work of Amundson and Aris in the 1950's. The particular formulation and parameter values described below are taken from example 2.5 from Seborg, Edgar, Mellichamp and Doyle (SEMD).\n",
        "\n",
        "![Exothermic Reactor](https://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Agitated_vessel.svg/500px-Agitated_vessel.svg.png)\n",
        "\n",
        "(Diagram By [Daniele Pugliesi](https://commons.wikimedia.org/wiki/User:Daniele_Pugliesi) - Own work, [CC BY-SA 3.0](http://creativecommons.org/licenses/by-sa/3.0), [Link](https://commons.wikimedia.org/w/index.php?curid=6915706))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.2 Reaction Kinetics](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.2-Reaction-Kinetics)",
          "section": "2.6.2 Reaction Kinetics"
        },
        "id": "xAPDAzSO3-G0"
      },
      "source": [
        "## 2.6.2 Reaction Kinetics\n",
        "\n",
        "We assume the kinetics are dominated by a single first order reaction\n",
        "\n",
        "$$A \\xrightarrow{kc_A}{} \\text{Products}$$\n",
        "\n",
        "The reaction rate per unit volume is modeled as the product $kc_A$ where $c_A$ is the concentration of $A$. The rate constant $k(T)$ is a increases with temperature following the Arrehenius law\n",
        "\n",
        "$$k(t) = k_0 e^{-\\frac{E_a}{RT}}$$\n",
        "\n",
        "$E_a$ is the activation energy, $R$ is the gas constant, $T$ is absolute temperature, and $k_0$ is the pre-exponential factor. \n",
        "\n",
        "We can see the strong temperature dependence by plotting $k(T)$ versus temperature over typical operating conditions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.2 Reaction Kinetics](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.2-Reaction-Kinetics)",
          "section": "2.6.2 Reaction Kinetics"
        },
        "id": "f1Hp9IZp3-G2",
        "outputId": "dab389d5-0632-42f3-87bf-51becac0c830"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Arrehnius parameters\n",
        "Ea = 72750     # activation energy J/gmol\n",
        "R = 8.314      # gas constant J/gmol/K\n",
        "k0 = 7.2e10    # Arrhenius rate constant 1/min\n",
        "\n",
        "# Arrhenius rate expression\n",
        "def k(T):\n",
        "    return k0*np.exp(-Ea/(R*T))\n",
        "\n",
        "# semilog plot of the rate constant\n",
        "T = np.linspace(290,400)\n",
        "plt.semilogy(T, k(T))\n",
        "plt.xlabel('Absolute Temperature [K]')\n",
        "plt.ylabel('Rate Constant [1/min]')\n",
        "plt.title('Arrenhius Rate Constant')\n",
        "plt.grid();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.2 Reaction Kinetics](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.2-Reaction-Kinetics)",
          "section": "2.6.2 Reaction Kinetics"
        },
        "id": "5ox3ziBO3-G6"
      },
      "source": [
        "This graph shows the reaction rate changes by three orders of magnitude over the range of possible operating temperatures. Because an exothermic reaction releases heat faster at higher temperatures, there is a positive feedback that can potentially result in unstable process behavior."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.3 Model Equations and Parameter Values](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.3-Model-Equations-and-Parameter-Values)",
          "section": "2.6.3 Model Equations and Parameter Values"
        },
        "id": "0o7Lw8Df3-G7"
      },
      "source": [
        "## 2.6.3 Model Equations and Parameter Values\n",
        "\n",
        "The model consists of mole and energy balances on the contents of the well-mixed reactor.\n",
        "\n",
        "\\begin{align*}\n",
        "V\\frac{dc_A}{dt} & = q(c_{Ai}-c_A)-Vkc_A \\\\\n",
        "V\\rho C_p\\frac{dT}{dt} & = wC_p(T_i-T) + (-\\Delta H_R)Vkc_A + UA(T_c-T)\n",
        "\\end{align*}\n",
        "\n",
        "Normalizing the equations to isolate the time rates of change of $c_A$ and $T$ give\n",
        "\n",
        "\\begin{align*}\n",
        "\\frac{dc_A}{dt} & = \\frac{q}{V}(c_{Ai} - c_A)- kc_A \\\\\n",
        "\\frac{dT}{dt} & = \\frac{q}{V}(T_i - T) + \\frac{-\\Delta H_R}{\\rho C_p}kc_A + \\frac{UA}{V\\rho C_p}(T_c - T)\n",
        "\\end{align*}\n",
        "\n",
        "which are the equations that will be integrated below.\n",
        "\n",
        "| Quantity | Symbol | Value | Units | Comments |\n",
        "| :------- | :----: | :---: | :---- | |\n",
        "| Activation Energy | $E_a$ | 72,750 | J/gmol | |\n",
        "| Arrehnius pre-exponential | $k_0$ | 7.2 x 10<sup>10</sup> | 1/min | |\n",
        "| Gas Constant | $R$ | 8.314 | J/gmol/K | |\n",
        "| Reactor Volume | $V$ | 100 | liters | |\n",
        "| Density | $\\rho$ | 1000 | g/liter | |\n",
        "| Heat Capacity | $C_p$ | 0.239 | J/g/K | |\n",
        "| Enthalpy of Reaction | $\\Delta H_r$ | -50,000 | J/gmol | |\n",
        "| Heat Transfer Coefficient | $UA$ | 50,000 | J/min/K | |\n",
        "| Feed flowrate | $q$ | 100 | liters/min | |\n",
        "| Feed concentration | $c_{A,f}$ | 1.0 | gmol/liter | |\n",
        "| Feed temperature | $T_f$ | 350 | K | |\n",
        "| Initial concentration | $c_{A,0}$ | 0.5 | gmol/liter | |\n",
        "| Initial temperature | $T_0$ | 350 | K | |\n",
        "| Coolant temperature | $T_c$ | 300 | K | Primary Manipulated Variable |\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.4 Transient Behavior](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.4-Transient-Behavior)",
          "section": "2.6.4 Transient Behavior"
        },
        "id": "KO-Jcv7u3-G8"
      },
      "source": [
        "## 2.6.4 Transient Behavior\n",
        "\n",
        "The first simulation assumes a cooling water temperature of 300 K. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "jupyter": {
          "outputs_hidden": true
        },
        "nbpages": {
          "level": 2,
          "link": "[2.6.4 Transient Behavior](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.4-Transient-Behavior)",
          "section": "2.6.4 Transient Behavior"
        },
        "id": "UWOexfxP3-G8"
      },
      "outputs": [],
      "source": [
        "from scipy.integrate import solve_ivp\n",
        "\n",
        "Ea  = 72750     # activation energy J/gmol\n",
        "R   = 8.314     # gas constant J/gmol/K\n",
        "k0  = 7.2e10    # Arrhenius rate constant 1/min\n",
        "V   = 100.0     # Volume [L]\n",
        "rho = 1000.0    # Density [g/L]\n",
        "Cp  = 0.239     # Heat capacity [J/g/K]\n",
        "dHr = -5.0e4    # Enthalpy of reaction [J/mol]\n",
        "UA  = 5.0e4     # Heat transfer [J/min/K]\n",
        "q   = 100.0     # Flowrate [L/min]\n",
        "cAi = 1.0       # Inlet feed concentration [mol/L]\n",
        "Ti  = 350.0     # Inlet feed temperature [K]\n",
        "cA0 = 0.5;      # Initial concentration [mol/L]\n",
        "T0  = 350.0;    # Initial temperature [K]\n",
        "Tc  = 300.0     # Coolant temperature [K]\n",
        "\n",
        "def deriv(t, y):\n",
        "    cA,T = y\n",
        "    dcAdt = (q/V)*(cAi - cA) - k(T)*cA\n",
        "    dTdt = (q/V)*(Ti - T) + (-dHr/rho/Cp)*k(T)*cA + (UA/V/rho/Cp)*(Tc-T)\n",
        "    return [dcAdt, dTdt]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.4 Transient Behavior](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.4-Transient-Behavior)",
          "section": "2.6.4 Transient Behavior"
        },
        "id": "i1y-apkv3-G9"
      },
      "source": [
        "We first define a visualization function that will be reused in later simulations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.4 Transient Behavior](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.4-Transient-Behavior)",
          "section": "2.6.4 Transient Behavior"
        },
        "id": "5JwMpbQy3-G-",
        "outputId": "9c7db974-6646-46ab-a9b6-ffe5f6bcd406"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# simulation\n",
        "IC = [cA0, T0]\n",
        "t_initial = 0.0\n",
        "t_final = 10.0\n",
        "t = np.linspace(t_initial, t_final, 2000)\n",
        "soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n",
        "\n",
        "# visualization plots concentration and temperature on given axes\n",
        "def plot_reactor(ax, t, y):\n",
        "    ax[0].plot(t, y[0], label=str(Tc))\n",
        "    ax[0].set_xlabel('Time [min]')\n",
        "    ax[0].set_ylabel('Concentration [gmol/liter]')\n",
        "    ax[0].set_title('Concentration')\n",
        "    ax[0].set_ylim(0, 1)\n",
        "    ax[0].legend()\n",
        "\n",
        "    ax[1].plot(t, y[1], label=str(Tc))\n",
        "    ax[1].set_xlabel('Time [min]')\n",
        "    ax[1].set_ylabel('Temperature [K]');\n",
        "    ax[1].set_title('Temperature')\n",
        "    ax[1].set_ylim(300, 450)\n",
        "    ax[1].legend()\n",
        "    \n",
        "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n",
        "plot_reactor(ax, soln.t, soln.y);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.5 Effect of Cooling Temperature](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.5-Effect-of-Cooling-Temperature)",
          "section": "2.6.5 Effect of Cooling Temperature"
        },
        "id": "v6uurqbz3-G-"
      },
      "source": [
        "## 2.6.5 Effect of Cooling Temperature\n",
        "\n",
        "The primary means of controlling the reactoris through temperature of the cooling water jacket. The next calculations explore the effect of plus or minus change of 5 K in cooling water temperature on reactor behavior. These simulations reproduce the behavior shown in Example 2.5 SEMD."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.5 Effect of Cooling Temperature](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.5-Effect-of-Cooling-Temperature)",
          "section": "2.6.5 Effect of Cooling Temperature"
        },
        "id": "epNkE4Ye3-G_",
        "outputId": "74c34ec9-4e64-4797-9379-350eb3005e77"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n",
        "for Tc in [295, 300, 305]:\n",
        "    soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n",
        "    plot_reactor(ax, soln.t, soln.y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.6 Interactive Simulation](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.6-Interactive-Simulation)",
          "section": "2.6.6 Interactive Simulation"
        },
        "id": "VpL5cbld3-HA"
      },
      "source": [
        "## 2.6.6 Interactive Simulation\n",
        "\n",
        "Executing the following cell provides an interactive tool for exploring the relationship of cooling temperature with reactor behavior.  Use it to observe a thermal runaway, sustained osciallations, and low and high conversion steady states."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.6 Interactive Simulation](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.6-Interactive-Simulation)",
          "section": "2.6.6 Interactive Simulation"
        },
        "id": "O6dZ-sLL3-HA",
        "outputId": "01f4f4bb-9b27-4fbd-9cfe-9f77c16d5bbf",
        "colab": {
          "referenced_widgets": [
            "3f00b2b8607c4d4187d0875977a5b962"
          ]
        }
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "3f00b2b8607c4d4187d0875977a5b962",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "interactive(children=(FloatSlider(value=300.0, description='Tcooling', max=310.0, min=290.0), Output()), _dom_…"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from ipywidgets import interact\n",
        "from IPython.display import display\n",
        "\n",
        "# create an initial plot object, and close so it doesn't appear\n",
        "Tc = 300.0\n",
        "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n",
        "soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n",
        "plot_reactor(ax, soln.t, soln.y)\n",
        "plt.close()\n",
        "\n",
        "# function to update and display the plot object\n",
        "def sim(Tcooling):\n",
        "    global Tc\n",
        "    Tc = Tcooling\n",
        "    soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n",
        "    ax[0].lines[0].set_ydata(soln.y[0])\n",
        "    ax[0].legend().get_texts()[0].set_text(str(Tc))\n",
        "    ax[1].lines[0].set_ydata(soln.y[1])\n",
        "    ax[1].legend().get_texts()[0].set_text(str(Tc))\n",
        "    display(fig)\n",
        "\n",
        "# interactive widget\n",
        "interact(sim, Tcooling = (290.0, 310.0), continuous_update=False);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.7 Nullclines](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.7-Nullclines)",
          "section": "2.6.7 Nullclines"
        },
        "id": "T4iXDWEG3-HB"
      },
      "source": [
        "## 2.6.7 Nullclines\n",
        "\n",
        "The nullclines of two first-order differential equations are points in the phase plane for which one or the other of the two derivatives are zero.\n",
        "\n",
        "\\begin{align*}\n",
        "V\\frac{dc_A}{dt} & = 0 = q(c_{Ai}-c_A)-Vkc_A \\\\\n",
        "V\\rho C_p\\frac{dT}{dt} & = 0 = wC_p(T_i-T) + (-\\Delta H_R)Vkc_A + UA(T_c-T)\n",
        "\\end{align*}\n",
        "\n",
        "The intersection of the nullclines correspond to steady states. The relative positions of the nullclines provide valuable insight into the dynamics of a nonlinear system."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.7 Nullclines](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.7-Nullclines)",
          "section": "2.6.7 Nullclines"
        },
        "id": "Qzp78SgY3-HB",
        "outputId": "7daf7ec5-fa0b-4c7f-e2a4-45b63c86abd8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# plot nullclines\n",
        "\n",
        "def plot_nullclines(ax):\n",
        "    T = np.linspace(300.0,460.0,1000)\n",
        "    ax.plot((q/V)*cAi/((q/V) + k(T)), T, 'b:')\n",
        "    ax.plot(((q/V)*(Ti-T) + (UA/V/rho/Cp)*(Tc-T))/((dHr/rho/Cp)*k(T)), T, 'r:')\n",
        "    ax.set_xlim(0,1)\n",
        "    ax.set_ylim(300,460)\n",
        "    ax.grid()\n",
        "    ax.legend(['dC/dt = 0','dT/dt = 0'])\n",
        "    ax.set_xlabel('Concentration')\n",
        "    ax.set_ylabel('Temperature')\n",
        "    \n",
        "fix, ax = plt.subplots(1, 1, figsize=(8,6))\n",
        "plot_nullclines(ax)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.8 Phase Plane Analysis](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.8-Phase-Plane-Analysis)",
          "section": "2.6.8 Phase Plane Analysis"
        },
        "id": "m1vmjZQp3-HC"
      },
      "source": [
        "## 2.6.8 Phase Plane Analysis\n",
        "\n",
        "The final analysis is display the simulation in both time and phase plane coordinates. The following cell produces a "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.8 Phase Plane Analysis](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.8-Phase-Plane-Analysis)",
          "section": "2.6.8 Phase Plane Analysis"
        },
        "scrolled": false,
        "id": "Q9igYLoh3-HC",
        "outputId": "252ce2d0-c0c0-4928-b4d7-b765adf94627",
        "colab": {
          "referenced_widgets": [
            "fc96639dec6f4ae08c8aa0795911f7a3"
          ]
        }
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "fc96639dec6f4ae08c8aa0795911f7a3",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "interactive(children=(FloatSlider(value=0.5, description='cinitial', max=1.0, step=0.01), IntSlider(value=350,…"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": [
              "<function __main__.phase(cinitial=0.5, Tinitial=350)>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "def plot_phase(ax, t, y):\n",
        "    ax.plot(y[0][0], y[1][0], 'r.', ms=20)\n",
        "    ax.plot(y[0], y[1], 'g', lw=2)\n",
        "\n",
        "def phase(cinitial=0.5, Tinitial=350):\n",
        "    global Tc\n",
        "    soln = solve_ivp(deriv, [t_initial, t_final], [cinitial,Tinitial], t_eval=t)\n",
        "    \n",
        "    ax[0,0].lines[2].set_xdata(soln.y[0][0])\n",
        "    ax[0,0].lines[2].set_ydata(soln.y[1][0])\n",
        "    ax[0,0].lines[3].set_xdata(soln.y[0])\n",
        "    ax[0,0].lines[3].set_ydata(soln.y[1])\n",
        "    ax[1,0].lines[0].set_ydata(soln.y[0])\n",
        "    ax[1,1].lines[0].set_ydata(soln.y[1])\n",
        "    display(fig)\n",
        "    \n",
        "Tc = 300.0\n",
        "cinitial = 0.5\n",
        "Tinitial = 350.0\n",
        "fig, ax = plt.subplots(2, 2, figsize=(12, 9))\n",
        "soln = solve_ivp(deriv, [t_initial, t_final], [cinitial, Tinitial], t_eval=t)\n",
        "plot_nullclines(ax[0,0])\n",
        "plot_phase(ax[0,0], soln.t, soln.y)\n",
        "plot_reactor(ax[1,:], soln.t, soln.y)\n",
        "plt.close()\n",
        "\n",
        "interact(phase, cinitial=(0,1,.01), Tinitial=(300,400,1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.9 Suggested Exercises](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.9-Suggested-Exercises)",
          "section": "2.6.9 Suggested Exercises"
        },
        "id": "BeWEDYCA3-HD"
      },
      "source": [
        "## 2.6.9 Suggested Exercises"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.9 Suggested Exercises](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.9-Suggested-Exercises)",
          "section": "2.6.9 Suggested Exercises"
        },
        "tags": [
          "exercise"
        ],
        "id": "QmPQfu6n3-HD"
      },
      "source": [
        "**1.** Using the interactive simulation, adjust the cooling temperature over the range of values from 290K to 310K, identify the cooling water temperatures at which you observe a qualitative difference in system behavior. Try to identify the following behaviors:\n",
        "\n",
        "* Stable steady state\n",
        "* Oscillatory steady state\n",
        "* The onset of a thermal runaway condition\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.9 Suggested Exercises](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.9-Suggested-Exercises)",
          "section": "2.6.9 Suggested Exercises"
        },
        "tags": [
          "exercise"
        ],
        "id": "mAYIATsq3-HD"
      },
      "source": [
        "**2.** Repeat the exercise using the phase plane simulation. Describe the underlying behaviors in light of the nullclines.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.6.9 Suggested Exercises](https://jckantor.github.io/CBE30338/02.06-Exothermic-CSTR.html#2.6.9-Suggested-Exercises)",
          "section": "2.6.9 Suggested Exercises"
        },
        "tags": [
          "exercise"
        ],
        "id": "aQSRpuxc3-HE"
      },
      "source": [
        "\n",
        "**3.** Assume the reactor is start up with a tank of reactant feed with a concentration $c_A = 1$. What is the maximum initial temperature that would avoid thermal runaway during reactor startup?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.7 Fed-Batch Bioreactor](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7-Fed-Batch-Bioreactor)",
          "section": "2.7 Fed-Batch Bioreactor"
        },
        "id": "mM2A1IVZ3_yK"
      },
      "source": [
        "# 2.7 Fed-Batch Bioreactor"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.7.1 Model Development](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.1-Model-Development)",
          "section": "2.7.1 Model Development"
        },
        "id": "tnuqaLUD3_yK"
      },
      "source": [
        "## 2.7.1 Model Development\n",
        "\n",
        "Mass balances for a fed-batch bioreactor are given by\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{d(XV)}{dt} & = V r_g(X,S) \\\\\n",
        "\\frac{d(PV)}{dt} & = V r_P(X,S) \\\\\n",
        "\\frac{d(SV)}{dt} & = F S_f - \\frac{1}{Y_{X/S}}V r_g(X,S)\n",
        "\\end{align*}$$\n",
        "\n",
        "where $X$ is cell concentration, $P$ is product concentration, and $S$ is substrate concentration, all given in units of grams/liter. The reactor is fed with fresh substrate at concentration $S_f$ and flowrate $F(t)$ in liters per hour. The volume (in liters) is therefore changing \n",
        "\n",
        "$$\\frac{dV}{dt} = F(t)$$\n",
        "\n",
        "Rate $r_g(X,S)$ is the production of fresh cell biomass in units of grams/liter/hr. The cell specific growth is expressed as\n",
        "\n",
        "$$r_g(X,S) = \\mu(S)X$$\n",
        "\n",
        "where $\\mu(S)$ is the cell specific growth rate. In the Monod model, the specific growth rate is a function of substrate concentration given by\n",
        "\n",
        "$$\\mu(S) = \\mu_{max}\\frac{S}{K_S + S}$$\n",
        "\n",
        "where $\\mu_{max}$ is the maximum specific growth rate, and $K_S$ is the half saturation constant which is the value of $S$ for which $\\mu = \\frac{1}{2}\\mu_{max}$.\n",
        "\n",
        "For this model, the product is assumed to be a by-product of cell growth\n",
        "\n",
        "$$r_P(X,S) = Y_{P/X}r_g(X,S)$$\n",
        "\n",
        "where $Y_{P/X}$ is the product yield coefficient defined as\n",
        "\n",
        "$$Y_{P/X} = \\frac{\\mbox{mass of product formed}}{\\mbox{mass of new cells formed}}$$\n",
        "\n",
        "The model further assumes that substrate is consumed is proportion to the mass of new cells formed where $Y_{X/S}$ is the yield coefficient for new cells\n",
        "\n",
        "$$Y_{P/X} = \\frac{\\mbox{mass of new cells formed}}{\\mbox{mass of substrate consumed}}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 3,
          "link": "[2.7.1.1 Dilution Effect](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.1.1-Dilution-Effect)",
          "section": "2.7.1.1 Dilution Effect"
        },
        "id": "OxV_fjFW3_yL"
      },
      "source": [
        "### 2.7.1.1 Dilution Effect\n",
        "\n",
        "One aspect of the fed-batch model is that volume is not constant, therefore the cell, product, and substrate concentrations are subject to a dilution effect.  Mathematically, the chain rule of differential calculus provides a means to recast the state of model in terms of the intensive concentration variables $X$, $P$, and $S$, and extensive volume $V$.\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{d(XV)}{dt} & = V\\frac{dX}{dt} + X\\frac{dV}{dt} = V\\frac{dX}{dt} + F(t)X \\\\\n",
        "\\frac{d(PV)}{dt} & = V\\frac{dP}{dt} + P\\frac{dV}{dt} = V\\frac{dP}{dt} + F(t)P \\\\\n",
        "\\frac{d(SV)}{dt} & = V\\frac{dS}{dt} + S\\frac{dV}{dt} = V\\frac{dS}{dt} + F(t)S\n",
        "\\end{align*}$$\n",
        "\n",
        "Rearranging and substituting into the mass balances gives\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{dX}{dt} & = - \\frac{F(t)}{V}X + r_g(X,S)  \\\\\n",
        "\\frac{dP}{dt} & = - \\frac{F(t)}{V}P + r_P(X,S) \\\\\n",
        "\\frac{dS}{dt} & = \\frac{F(t)}{V}(S_f - S) - \\frac{1}{Y_{X/S}}r_g(X,S) \\\\\n",
        "\\frac{dV}{dt} & = F(t)\n",
        "\\end{align*}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.7.2 Python Implementation](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.2-Python-Implementation)",
          "section": "2.7.2 Python Implementation"
        },
        "id": "G_W_BVuw3_yL"
      },
      "source": [
        "## 2.7.2 Python Implementation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.7.2 Python Implementation](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.2-Python-Implementation)",
          "section": "2.7.2 Python Implementation"
        },
        "id": "jk-2OHO23_yM"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "# parameter values\n",
        "\n",
        "mumax = 0.20      # 1/hour\n",
        "Ks = 1.00         # g/liter\n",
        "Yxs = 0.5         # g/g\n",
        "Ypx = 0.2         # g/g\n",
        "Sf = 10.0         # g/liter\n",
        "\n",
        "# inlet flowrate\n",
        "\n",
        "def F(t):\n",
        "    return 0.05\n",
        "\n",
        "# reaction rates\n",
        "\n",
        "def mu(S):\n",
        "    return mumax*S/(Ks + S)\n",
        "\n",
        "def Rg(X,S):\n",
        "    return mu(S)*X\n",
        "    \n",
        "def Rp(X,S):\n",
        "    return Ypx*Rg(X,S)\n",
        "\n",
        "# differential equations\n",
        "\n",
        "def xdot(x,t):\n",
        "    X,P,S,V = x\n",
        "    dX = -F(t)*X/V + Rg(X,S)\n",
        "    dP = -F(t)*P/V + Rp(X,S)\n",
        "    dS = F(t)*(Sf-S)/V - Rg(X,S)/Yxs\n",
        "    dV = F(t)\n",
        "    return [dX,dP,dS,dV]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.7.3 Simulation](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.3-Simulation)",
          "section": "2.7.3 Simulation"
        },
        "id": "ozO7Ex3p3_yN"
      },
      "source": [
        "## 2.7.3 Simulation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 2,
          "link": "[2.7.3 Simulation](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.3-Simulation)",
          "section": "2.7.3 Simulation"
        },
        "id": "mI5QgEOl3_yN",
        "outputId": "dc425fd1-ef51-490f-c633-53c60b784a09"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x1152fb668>"
            ]
          },
          "execution_count": 84,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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27eOWW25Jl2QAlC1bNvX5wYMHsdlsvPvuu+nq2Ww2Jk2alK782LFjdOvWDT8/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\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x114f71710>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "IC = [0.05, 0.0, 10.0, 1.0]\n",
        "\n",
        "t = np.linspace(0,50)\n",
        "sol = odeint(xdot,IC,t)\n",
        "X,P,S,V = sol.transpose()\n",
        "\n",
        "plt.plot(t,X)\n",
        "plt.plot(t,P)\n",
        "plt.plot(t,S)\n",
        "plt.plot(t,V)\n",
        "\n",
        "plt.xlabel('Time [hr]')\n",
        "plt.ylabel('Concentration [g/liter]')\n",
        "plt.legend(['Cell Conc.',\n",
        "            'Product Conc.',\n",
        "            'Substrate Conc.',\n",
        "            'Volume [liter]'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 2,
          "link": "[2.7.3 Simulation](https://jckantor.github.io/CBE30338/02.07-Fed-Batch-Bioreactor.html#2.7.3-Simulation)",
          "section": "2.7.3 Simulation"
        },
        "id": "Mj1kcKgn3_yO"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "5UWGPMpD4Kt-"
      },
      "source": [
        "# 2.8 Model Library"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "kKRG45BU4Kt_"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "UxQl3t-n4KuA"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint,ode\n",
        "\n",
        "class GravityTank():\n",
        "    \n",
        "    def __init__(self, A=1, Cv=1, h = 0):\n",
        "        self.A = A\n",
        "        self.Cv = Cv\n",
        "        self.Qin = 0\n",
        "        self._h = h\n",
        "        self.IC = self._h\n",
        "        \n",
        "    def deriv(self,h,t):\n",
        "        h = max(0,h)\n",
        "        self._h = h\n",
        "        return (self.Qin/self.A - self.Cv*np.sqrt(h)/self.A)\n",
        "    \n",
        "    @property\n",
        "    def Qin(self):\n",
        "        return self._Qin\n",
        "    \n",
        "    @Qin.setter\n",
        "    def Qin(self,Qin):\n",
        "        self._Qin = Qin\n",
        "        \n",
        "    @property\n",
        "    def Qout(self):\n",
        "        return self.Cv*np.sqrt(self._h)\n",
        "        \n",
        "        "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "scrolled": false,
        "id": "QM9kYu4O4KuA",
        "outputId": "68faf13f-2418-4990-f552-1a47381cc770"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x118d16da0>]"
            ]
          },
          "execution_count": 186,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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REYlSM6tK2bG/hdci4OKPChMRkSh11rH55A9JiYhzThQmIiJRKjGQwOcmlvDa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\nkClMREQkZAoTEREJ2f8HIjfwRRpFyfwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x118b9e160>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "tank1 = GravityTank(2,1)\n",
        "tank2 = GravityTank(1.5,2)\n",
        "\n",
        "t = np.linspace(0,.1,50)\n",
        "tank1.Qin = 3\n",
        "\n",
        "def deriv(X,t):\n",
        "    h1,h2 = X\n",
        "    tank2.Qin = tank1.Qout\n",
        "    dh1 = tank1.deriv(h1,t)\n",
        "    dh2 = tank2.deriv(h2,t)\n",
        "    #print(\"{0:9.6f}  {1:9.6f}  {2:9.6f}  {3:9.6f}  {4:9.6f}  {5:9.6f}   {6:9.6f}   {7:9.6f}  {8:9.6f}\".format(h1,h2,tank1.Qin,tank1.Qout,tank2.Qin,tank2.Qout,dh1,dh2,t))\n",
        "    return [dh1,dh2]\n",
        "\n",
        "\n",
        "sol = odeint(deriv,[0,0],t)\n",
        "h1,h2 = sol.T\n",
        "plt.plot(t,h2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "19lAd2C84KuB",
        "outputId": "ca88831d-f707-43ea-8a28-bb1c81e64c5d"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/Users/jeff/anaconda/lib/python3.5/site-packages/scipy/integrate/_ode.py:869: UserWarning: vode: Excess work done on this call. (Perhaps wrong MF.)\n",
            "  'Unexpected istate=%s' % istate))\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x117ed0240>,\n",
              " <matplotlib.lines.Line2D at 0x117ed04e0>,\n",
              " <matplotlib.lines.Line2D at 0x117ed06d8>]"
            ]
          },
          "execution_count": 165,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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gcPOFDL7p759AtMfLthZ4JoPD3D8GPtE9Yp+GbI+6nOUdPYzE42R7PXBdVW0ErgM+OIls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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x116510128>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "tank1 = GravityTank(2,1)\n",
        "tank2 = GravityTank(1.5,1)\n",
        "tank3 = GravityTank(0.8,0.9)\n",
        "\n",
        "tank1.Qin = 3\n",
        "\n",
        "def deriv(t,X):\n",
        "    h1,h2,h3 = X\n",
        "    tank2.Qin = tank1.Qout\n",
        "    tank3.Qin = tank2.Qout\n",
        "    dh1 = tank1.deriv(h1,t)\n",
        "    dh2 = tank2.deriv(h2,t)\n",
        "    dh3 = tank3.deriv(h3,t)\n",
        "    return [dh1,dh2,dh3]\n",
        "\n",
        "\n",
        "de = ode(deriv)\n",
        "de.set_initial_value(IC,0)\n",
        "\n",
        "ts = []\n",
        "ys = []\n",
        "t_end = 10\n",
        "t_step = .2\n",
        "\n",
        "while de.successful() and de.t < t_end:\n",
        "    de.integrate(de.t + t_step)\n",
        "    ts.append(de.t)\n",
        "    ys.append(de.y)\n",
        "\n",
        "plt.plot(ts,ys)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "scrolled": false,
        "id": "H0TfUv-a4KuC",
        "outputId": "42c87fa2-ba84-42c6-b036-02a3e7df876d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0, 0, 0]\n",
            "[1.5, 0.0, 0.0]\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/Users/jeff/anaconda/lib/python3.5/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n",
            "  warnings.warn(warning_msg, ODEintWarning)\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x114d11d30>,\n",
              " <matplotlib.lines.Line2D at 0x114d11f60>,\n",
              " <matplotlib.lines.Line2D at 0x114d17198>]"
            ]
          },
          "execution_count": 107,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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sq6qZcfdjEjgWB3I8DuR4PKe1sXAJSJIaZQBIUqOmOQA2jLsDE8SxOJDjcSDH4zlNjcXU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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x1133d3b00>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "IC = [tank1.IC] + [tank2.IC] + [tank3.IC]\n",
        "print(IC)\n",
        "print(deriv(IC,0))\n",
        "t = np.linspace(0,45,500)\n",
        "sol = odeint(deriv,IC,t)\n",
        "plt.plot(t,sol)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "2DjQ2zvy4KuC",
        "outputId": "3e1b3aab-8de5-413d-a88f-218a1d0831c1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "tank3.Qin"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "nbpages": {
          "level": 1,
          "link": "[2.8 Model Library](https://jckantor.github.io/CBE30338/02.08-Model-Library.html#2.8-Model-Library)",
          "section": "2.8 Model Library"
        },
        "id": "kHpbUuWy4KuC"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.4"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}