double-inverted-pendulum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{\\mb}[1]{\\mathbf{ #1 }}$\n",
    "$\\newcommand{\\bb}[1]{\\mathbb{ #1 }}$\n",
    "$\\newcommand{\\bs}[1]{\\boldsymbol{ #1 }}$\n",
    "$\\newcommand{\\norm}[1]{\\left\\Vert #1 \\right\\Vert}$\n",
    "\n",
    "$\\newcommand{\\der}[2]{\\frac{\\mathrm{d} #1 }{\\mathrm{d} #2 }}$\n",
    "$\\newcommand{\\derp}[2]{\\frac{\\partial #1 }{\\partial #2 }}$\n",
    "\n",
    "$\\newcommand{\\R}{\\bb{R}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Double Inverted Pendulum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a frictionless two-link pendulum. Torque $\\tau_1$ is applied at a fixed base, where the first link is attached. Torque $\\tau_2$ is applied at the opposite end of the first link, where the second link is attached. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first and second links are modeled as massless, with point masses $m_1$ and $m_2$ at lengths of $l_1$ and $l_2$ from the torque applications, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume the angle of the first link from upright $\\theta_1$ and the angle of the second link from the first link $\\theta_2$ are measured, along with the corresponding angular rates $\\dot{\\theta}_1$ and $\\dot{\\theta}_2$. Let $\\mb{q} = (\\theta_1, \\theta_2)$ and $\\dot{\\mb{q}} = (\\dot{\\theta}_1, \\dot{\\theta}_2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\mathcal{I} = (\\mb{i}_1, \\mb{i}_2, \\mb{i}_3)$ be an inertial reference frame and let $\\mathcal{A} = (\\mb{a}_1, \\mb{a}_2, \\mb{a}_3)$ and $\\mathcal{B} = (\\mb{b}_1, \\mb{b}_2, \\mb{b}_3)$ be body reference frames such that $\\mb{i}_3 = \\mb{a}_3 = \\mb{b}_3$. Let $\\mb{e}_1, \\mb{e}_2, \\mb{e}_3 \\in \\R^3$ be elementary basis vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\mb{f}_1^\\mathcal{I} = -m_1 g \\mb{e}_1$ and $\\mb{f}_2^{\\mathcal{I}} = -m_2 g \\mb{e}_1$ denote graviational forces on the first and second link, respectively, both resolved in the inertial reference frame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\mb{r}_{10}^\\mathcal{A} = l_1 \\mb{e}_1$ denote the position of the joint relative to the base resolved in the $\\mathcal{A}$ frame. Let $\\mb{r}_{21}^\\mathcal{B} = l_2 \\mb{e}_1$ denote the position of the end of the pendulum relative to the joint resolved in the $\\mathcal{B}$ frame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\mb{R}: \\R \\to \\R^{3 \\times 3}$ be a rotation matrix defined as:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\mb{R}(\\theta) = \\begin{bmatrix} \\cos{\\theta} & -\\sin{\\theta} & 0 \\\\ \\sin{\\theta} & \\cos{\\theta} & 0 \\\\ 0 & 0 & 1 \\end{bmatrix},\n",
    "\\end{equation}\n",
    "\n",
    "for all $\\theta \\in \\R$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The direction cosine matrix (DCM) relating $\\mathcal{A}$ frame coordinates to inertial frame coordinates is $\\mb{C}^{\\mathcal{A}\\mathcal{I}} = \\mb{R}(\\theta_1)^\\top$, while the DCM relating $\\mathcal{B}$ frame coordinates to $\\mathcal{A}$ frame coordinates is $\\mb{C}^{\\mathcal{B}\\mathcal{A}} = \\mb{R}(\\theta_2)^\\top$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since $\\mb{R}(\\theta)$ is orthogonal for all $\\theta \\in \\R$, $\\mb{C}^{\\mathcal{I}\\mathcal{A}} = \\mb{R}(\\theta_1)$ and $\\mb{C}^{\\mathcal{A}\\mathcal{B}} = \\mb{R}(\\theta_2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, the DCM relating $\\mathcal{B}$ frame coordinates to $\\mathcal{I}$ frame coordinates is $\\mb{C}^{\\mathcal{B}\\mathcal{I}} = \\mb{C}^{\\mathcal{B}\\mathcal{A}}\\mb{C}^{\\mathcal{A}\\mathcal{I}}$, and $\\mb{C}^{\\mathcal{I}\\mathcal{B}} = \\mb{C}^{\\mathcal{I}\\mathcal{A}}\\mb{C}^{\\mathcal{A}\\mathcal{B}} = \\mb{R}(\\theta_1)\\mb{R}(\\theta_2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The position of the joint relative to the base resolved in the inertial frame is:\n",
    "\n",
    "\\begin{align}\n",
    "    \\mb{r}_{10}^\\mathcal{I} &= \\mb{C}^{\\mathcal{I}\\mathcal{A}}\\mb{r}_{10}^{\\mathcal{A}}\\\\\n",
    "    &= l_1 \\mb{R}(\\theta_1)\\mb{e}_1\\\\\n",
    "    &= \\begin{bmatrix} l_1 \\cos{\\theta} \\\\ l_1 \\sin{\\theta} \\\\ 0 \\end{bmatrix},\n",
    "\\end{align}\n",
    "\n",
    "while the position of the end of the pendulum relative to the base resolved in the inertial frame is:\n",
    "\n",
    "\\begin{align}\n",
    "    \\mb{r}_{20}^\\mathcal{I} &= \\mb{r}_{21}^\\mathcal{I} + \\mb{r}_{10}^\\mathcal{I}\\\\\n",
    "    &= \\mb{C}^{\\mathcal{IB}}\\mb{r}_{21}^\\mathcal{B} + \\mb{C}^{\\mathcal{I}\\mathcal{A}}\\mb{r}_{10}^\\mathcal{A}\\\\\n",
    "    &= l_2 \\mb{R}(\\theta_1)\\mb{R}(\\theta_2) \\mb{e}_1 + l_1 \\mb{R}(\\theta_1) \\mb{e}_1\\\\\n",
    "    &= \\mb{R}(\\theta_1) \\begin{bmatrix} l_2 \\cos{\\theta_2} \\\\ l_2 \\sin{\\theta_2} \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} l_1 \\cos{\\theta_1} \\\\ l_1 \\sin{\\theta_1} \\\\ 0 \\end{bmatrix}\\\\\n",
    "    &= \\begin{bmatrix} l_2 \\cos{\\theta_1} \\cos{\\theta_2} - l_2 \\sin{\\theta_1} \\sin{\\theta_2} + l_1 \\cos{\\theta_1} \\\\ l_2 \\sin{\\theta_1} \\cos{\\theta_2} + l_2 \\cos{\\theta_1} \\sin{\\theta_2} + l_1 \\sin{\\theta_1} \\\\ 0 \\end{bmatrix}\\\\\n",
    "    &= \\begin{bmatrix} l_2 \\cos{(\\theta_1 + \\theta_2)} + l_1 \\cos{\\theta_1} \\\\ l_2 \\sin{(\\theta_1 + \\theta_2)} + l_1 \\sin{\\theta_1} \\\\ 0 \\end{bmatrix},\n",
    "\\end{align}\n",
    "\n",
    "making use of the facts that $\\cos{(\\theta_1 + \\theta_2)} = \\cos{\\theta_1}\\cos{\\theta_2} - \\sin{\\theta_1}\\sin{\\theta_2}$ and $\\sin{(\\theta_1 + \\theta_2)} = \\sin{\\theta_1}\\cos{\\theta_2} + \\cos{\\theta_1}\\sin{\\theta_2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding velocities are:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\dot{\\mb{r}}_{10}^\\mathcal{I} = \\begin{bmatrix} -l_1 \\sin{\\theta_1} & 0 \\\\ l_1 \\cos{\\theta_1} & 0 \\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} \\dot{\\theta}_1 \\\\ \\dot{\\theta}_2 \\end{bmatrix},\n",
    "\\end{equation}\n",
    "\n",
    "as well as:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\dot{\\mb{r}}_{20}^\\mathcal{I} = \\begin{bmatrix} -l_2 \\sin{(\\theta_1 + \\theta_2)} -l_1 \\sin{\\theta_1} & -l_2 \\sin{(\\theta_1 + \\theta_2)} \\\\ l_2 \\cos{(\\theta_1 + \\theta_2)} + l_1 \\cos{\\theta_1} & l_2 \\cos{(\\theta_1 + \\theta_2)} \\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} \\dot{\\theta}_1 \\\\ \\dot{\\theta}_2 \\end{bmatrix},\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding kinetic energy terms are:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\frac{1}{2}m_1\\norm{ \\dot{\\mb{r}}_{10}^\\mathcal{I} }_2^2 = \\frac{1}{2} m_1 \\dot{\\mb{q}}^\\top \\begin{bmatrix} l_1^2 & 0 \\\\ 0 & 0 \\end{bmatrix} \\dot{\\mb{q}},\n",
    "\\end{equation}\n",
    "\n",
    "as well as:\n",
    "\n",
    "\\begin{align}\n",
    "    \\frac{1}{2}m_2\\norm{ \\dot{\\mb{r}}_{20}^\\mathcal{I} }_2^2 &= \\frac{1}{2} m_2 \\dot{\\mb{q}}^\\top \\begin{bmatrix} l_1^2 + 2 l_1 l_2 (\\sin{(\\theta_1 + \\theta_2)}\\sin{\\theta_1} + \\cos{(\\theta_1 + \\theta_2)}\\cos{\\theta_1})  + l_2^2 & l_1 l_2 (\\sin{(\\theta_1 + \\theta_2)\\sin{\\theta_1}} + \\cos{(\\theta_1 + \\theta_2)}\\cos{\\theta_1}) + l_2^2 \\\\ l_1 l_2 (\\sin{(\\theta_1 + \\theta_2)\\sin{\\theta_1}} + \\cos{(\\theta_1 + \\theta_2)}\\cos{\\theta_1}) + l_2^2 & l_2^2 \\end{bmatrix} \\dot{\\mb{q}}\\\\\n",
    "    &= \\frac{1}{2}m_2\\dot{\\mb{q}}^\\top \\begin{bmatrix} l_1^2 + 2 l_1 l_2 \\cos{\\theta_2} + l_2^2 & l_1 l_2 \\cos{\\theta_2} + l_2^2 \\\\ l_1 l_2 \\cos{\\theta_2} + l_2^2 & l_2^2 \\end{bmatrix} \\dot{\\mb{q}},\n",
    "\\end{align}\n",
    "\n",
    "using the fact that $\\cos{\\theta_2} = \\cos{((\\theta_1 + \\theta_2) - \\theta_1)} = \\cos{(\\theta_1 + \\theta_2)}\\cos{\\theta_1} + \\sin{(\\theta_1 + \\theta_2)}\\sin{\\theta_1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total kinetic energy of the system can now be described as:\n",
    "\n",
    "\\begin{equation}\n",
    "    T(\\mb{q}, \\dot{\\mb{q}}) = \\frac{1}{2} \\dot{\\mb{q}}^\\top \\underbrace{ \\begin{bmatrix} (m_1 + m_2)l_1^2 + 2 m_2 l_1 l_2 \\cos{\\theta_2} + m_2 l_2^2 & m_2 l_1 l_2 \\cos{\\theta_2} + m_2 l_2^2 \\\\ m_2 l_1 l_2 \\cos{\\theta_2} + m_2 l_2^2 & m_2 l_2^2 \\end{bmatrix} }_{\\mb{D}(\\mb{q})} \\dot{\\mb{q}}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Coriolis terms matrix can be expressed in terms of the inertia matrix:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\mb{C}(\\mb{q}, \\dot{\\mb{q}}) = \\derp{\\mb{D}}{\\mb{q}}(\\cdot, \\dot{\\mb{q}}, \\cdot) - \\frac{1}{2}\\left( \\derp{\\mb{D}}{\\mb{q}}(\\cdot, \\dot{\\mb{q}}, \\cdot) \\right)^\\top.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, $\\derp{\\mb{D}}{\\mb{q}} \\in \\R^{2 \\times 2 \\times 2}$ is represented as a multilinear operator for all $\\mb{q} \\in \\R^2$, with:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\derp{\\mb{D}}{\\mb{q}}(\\mb{e}_i, \\mb{e}_j, \\mb{e}_k) = \\derp{D_{ij}(\\mb{q})}{\\theta_k},\n",
    "\\end{equation}\n",
    "\n",
    "for all $i, j, k \\in \\{1, 2\\}$ and elementary basis vectors $\\mb{e}_i, \\mb{e}_j, \\mb{e}_k \\in \\R^2$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We write:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\derp{\\mb{D}}{\\mb{q}} = \\sum_{i=1}^2 \\sum_{j=1}^2 \\sum_{k=1}^2 \\derp{D_{ij}(\\mb{q})}{\\theta_k} \\mb{e}_i \\otimes \\mb{e}_j \\otimes \\mb{e}_k,\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and contract along the second argument as:\n",
    "\n",
    "\\begin{align}\n",
    "    \\derp{\\mb{D}}{\\mb{q}} &= \\sum_{i=1}^2 \\sum_{j=1}^2 \\sum_{k=1}^2 \\derp{D_{ij}(\\mb{q})}{\\theta_k} \\dot{\\theta}_j \\mb{e}_i \\otimes \\mb{e}_k\\\\\n",
    "    &= \\sum_{i=1}^2 \\sum_{k=1}^2 \\left( \\sum_{j=1}^2 \\derp{D_{ij}(\\mb{q})}{\\theta_k} \\dot{\\theta}_j \\right) \\mb{e}_i \\otimes \\mb{e}_k\\\\\n",
    "    &= \\begin{bmatrix} 0 & -2 m_2 l_1 l_2 \\dot{\\theta}_1 \\sin{\\theta_2} - m_2 l_1 l_2 \\dot{\\theta}_2 \\sin{\\theta_2} \\\\ 0 & -m_2 l_1 l_2 \\dot{\\theta}_1 \\sin{\\theta_2} \\end{bmatrix}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, the Coriolis terms matrix is:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\mb{C}(\\mb{q}, \\dot{\\mb{q}}) = \\begin{bmatrix} 0 & -m_2 l_1 l_2 (2 \\dot{\\theta}_1 + \\dot{\\theta}_2) \\sin{\\theta}_2 \\\\ \\frac{1}{2} m_2 l_1 l_2 (2 \\dot{\\theta}_1 + \\dot{\\theta}_2) \\sin{\\theta}_2 & -\\frac{1}{2} m_2 l_1 l_2 \\dot{\\theta}_1 \\sin{\\theta}_2 \\end{bmatrix}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The potential energy is:\n",
    "\n",
    "\\begin{align}\n",
    "    U(\\mb{q}) &= -(\\mb{f}_1^\\mathcal{I})^\\top\\mb{r}_{10}^\\mathcal{I} - (\\mb{f}_2^\\mathcal{I})^\\top\\mb{r}_{20}^\\mathcal{I}\\\\\n",
    "    &= m_1 g l_1 \\cos{\\theta_1} + m_2 g (l_2 \\cos{(\\theta_1 + \\theta_2)} + l_1 \\cos{\\theta_1})\\\\\n",
    "    &= (m_1 + m_2) g l_1 \\cos{\\theta_1} + m_2 g l_2 \\cos{(\\theta_1 + \\theta_2)}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gradient of the potential energy is:\n",
    "\n",
    "\\begin{align}\n",
    "    \\mb{G}(\\mb{q}) &= \\left(\\derp{U}{\\mb{q}}\\right)^\\top\\\\\n",
    "    &= \\begin{bmatrix} -(m_1 + m_2) g l_1 \\sin{\\theta_1} - m_2 g l_2 \\sin{(\\theta_1 + \\theta_2)} \\\\ -m_2 g l_2 \\sin{(\\theta_1 + \\theta_2)} \\end{bmatrix}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load core/systems/double_inverted_pendulum.py\n",
    "from numpy import array, cos, identity, sin\n",
    "from core.dynamics import RoboticDynamics, SystemDynamics\n",
    "\n",
    "class DoubleInvertedPendulum(SystemDynamics, RoboticDynamics):\n",
    "    def __init__(self, m_1, m_2, l_1, l_2, g=9.81):\n",
    "        SystemDynamics.__init__(self, 4, 2)\n",
    "        RoboticDynamics.__init__(self, identity(2))\n",
    "        self.params = m_1, m_2, l_1, l_2, g\n",
    "        \n",
    "    def D(self, q):\n",
    "        m_1, m_2, l_1, l_2, _ = self.params\n",
    "        _, theta_2 = q\n",
    "        D_11 = (m_1 + m_2) * (l_1 ** 2) + 2 * m_2 * l_1 * l_2 * cos(theta_2) + m_2 * (l_2 ** 2)\n",
    "        D_12 = m_2 * l_1 * l_2 * cos(theta_2) + m_2 * (l_2 ** 2)\n",
    "        D_21 = D_12\n",
    "        D_22 = m_2 * (l_2 ** 2)\n",
    "        return array([[D_11, D_12], [D_21, D_22]])\n",
    "    \n",
    "    def C(self, q, q_dot):\n",
    "        _, m_2, l_1, l_2, _ = self.params\n",
    "        _, theta_2 = q\n",
    "        theta_1_dot, theta_2_dot = q_dot\n",
    "        C_11 = 0\n",
    "        C_12 = -m_2 * l_1 * l_2 * (2 * theta_1_dot + theta_2_dot) * sin(theta_2)\n",
    "        C_21 = -C_12 / 2\n",
    "        C_22 = -m_2 * l_1 * l_2 * theta_1_dot * sin(theta_2) / 2\n",
    "        return array([[C_11, C_12], [C_21, C_22]])\n",
    "    \n",
    "    def U(self, q):\n",
    "        m_1, m_2, l_1, l_2, g = self.params\n",
    "        theta_1, theta_2 = q\n",
    "        return (m_1 + m_2) * g * l_1 * cos(theta_1) + m_2 * g * l_2 * cos(theta_1 + theta_2)\n",
    "    \n",
    "    def G(self, q):\n",
    "        m_1, m_2, l_1, l_2, g = self.params\n",
    "        theta_1, theta_2 = q\n",
    "        G_1 = -(m_1 + m_2) * g * l_1 * sin(theta_1) - m_2 * g * l_2 * sin(theta_1 + theta_2)\n",
    "        G_2 = -m_2 * g * l_2 * sin(theta_1 + theta_2)\n",
    "        return array([G_1, G_2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "m_1, m_2 = 0.25, 0.25\n",
    "l_1, l_2 = 0.5, 0.5\n",
    "dip = DoubleInvertedPendulum(m_1, m_2, l_1, l_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feedback Linearization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import identity\n",
    "from core.controllers import FBLinController, LQRController\n",
    "\n",
    "Q, R = 10 * identity(4), identity(2)\n",
    "lqr = LQRController.build(dip, Q, R)\n",
    "fb_lin = FBLinController(dip, lqr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace\n",
    "\n",
    "x_0 = array([1, 0, 0, 0])\n",
    "ts = linspace(0, 10, 1000 + 1)\n",
    "fb_lin_data = dip.simulate(x_0, fb_lin, ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import figure, grid, plot, show, subplot, xlabel, ylabel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b05940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, us = fb_lin_data\n",
    "\n",
    "figure(figsize=(12, 8))\n",
    "\n",
    "subplot(221)\n",
    "plot(ts, xs[:, 0], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_1$', fontsize=16)\n",
    "\n",
    "subplot(222)\n",
    "plot(ts, xs[:, 1], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_2$', fontsize=16)\n",
    "\n",
    "subplot(223)\n",
    "plot(ts[:-1], us[:, 0], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_1$', fontsize=16)\n",
    "\n",
    "subplot(224)\n",
    "plot(ts[:-1], us[:, 1], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_2$', fontsize=16)\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Energy-Based Controller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from core.controllers import EnergyController\n",
    "\n",
    "K_p = identity(2)\n",
    "K_d = identity(2)\n",
    "energy = EnergyController(dip, K_p, K_d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "energy_data = dip.simulate(x_0, energy, ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107acb710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import legend\n",
    "\n",
    "figure(figsize=(12, 8))\n",
    "\n",
    "subplot(221)\n",
    "xs, _ = fb_lin_data\n",
    "plot(ts, xs[:, 0], linewidth=3, label='FBL')\n",
    "xs, _ = energy_data\n",
    "plot(ts, xs[:, 0], linewidth=3, label='Energy')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_1$', fontsize=16)\n",
    "\n",
    "subplot(222)\n",
    "xs, _ = fb_lin_data\n",
    "plot(ts, xs[:, 1], linewidth=3, label='FBL')\n",
    "xs, _ = energy_data\n",
    "plot(ts, xs[:, 1], linewidth=3, label='Energy')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_2$', fontsize=16)\n",
    "\n",
    "subplot(223)\n",
    "_, us = fb_lin_data\n",
    "plot(ts[:-1], us[:, 0], linewidth=3, label='FBL')\n",
    "_, us = energy_data\n",
    "plot(ts[:-1], us[:, 0], linewidth=3, label='Energy')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_1$', fontsize=16)\n",
    "\n",
    "subplot(224)\n",
    "_, us = fb_lin_data\n",
    "plot(ts[:-1], us[:, 1], linewidth=3, label='FBL')\n",
    "_, us = energy_data\n",
    "plot(ts[:-1], us[:, 1], linewidth=3, label='Energy')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_2$', fontsize=16)\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization-Based Controller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from core.controllers import QPController\n",
    "\n",
    "qp = QPController.build_care(dip, Q, R)\n",
    "qp.add_regularizer(fb_lin, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "qp_data = dip.simulate(x_0, qp, ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gu7TvuK73dY6OWFEUpdvzqDjbUAgZaN+bCQHXvAintkBtOeQdhW3/hokPX/BUo8lM8ukithzPY1tqPgczSzGZ29aDHejpQqS/Gz393An0dCbAwxk/D2f83J1xNehw1utxdtJh0AvMUlJbJzGatGEnFbV1FFXUUlRppLhSG5qSXVJNRnEVOaXVnCuEWpOZ4znlHM8p56tfM637w/3crEn4oJ7aK8hLDalUlLZSSXdb6HQQPR6OrNXKpzZzTfxM1uzLBOmMvnw8eGi9HysOrOCa6GvQCfXRnKIoit1U5ONstDxEaXBv8hDloYJDrDiwgn15+3BzcmNC+AQWxC/A39X/0u7pEw5XPa49TAmw5UUYOAsCW86+c6agks0peWw5nsf21PwL9mQHejrTP9SbAaHeDAjzpvTsMW68egLuzvb5M200mckuqeZsUSUn8ypIzS23vrJLq1s9J72oivSiKr4/lGPdF+rjyqCePgzu6cOgcB/ie/oQ6KkScUVpjUq62yp6YqOkewsTZy+wDDExkZOeQNCAJKpNlaQWp7IlfQuJEYkODVdRFKVbyz3SsB0Yq3WOAKuOr+KZnc9QJ+ush987/B7rTq7jtcmvMTDgEnvERy6E/Z9oUxWaarRhJnespbrOzM6TBSQdyyPpWC5pBZXnvIQQEBfiRUKUHyOi/EmI8qenr1uTOknFKXZLuAEMeh0R/u5E+Lsztk/T6TTLqo0czynncFYphzJKOJhZwvHscmpN5hbXySqpJqukmvWHGxLxMB9X4i0JeHy4L/E9ffD3UAtTKYpKutuq8bjutJ9wc4Ir+wWx7kA2mN3p6zaZA+VrAG2VyonhExFqAQVFURT7yDvasB08AIAt6Vt4asdTSFqOmyioLuDe9ffy0TUfEeEd0f776vTa3N3LrgRpgrSfWPnq07yQO5xqY8uktF64nxsTYoOY0DeIMb0DOvX4aC9XA8N7+TG8l591X22dmZTcMg5llnIwo4SDGSUcyiylpq5lmzNLqsksqW7SI97T182ShGvJeHmtfR4QVZTOTCXdbRXYFzx7aFNGVZdA1j6mDQrVkm4gP2M0Br9vMZqN7Mvbx+6c3YzoMcLBQSuKonRTjXu6g/txsuQkj2x5xJpw9/fvz99G/42siiyW7lhKaW0pJTUlPPDjA3xy/Sftmt7VaDKz90wxPx51IcZ5BnNqtIVyZue/zjLjc2QTYK3rZtAzure/lmjHBtE70KNLd8Q4O+kYaHmgcm6C9qalzmQmNa+c/elaEr4/vYQjWa0n4hnFVWQUV/HdoWzrvuf2/sjgcG1seLzl5euuesSV7ksl3W0lBPSeqH2sCHBqM1eNeABnJx21dWaOZ+qYE38N35/5CtDGdqukW1EUxU4a9XSX+kXx4I8PUm4sByDUI5Q3pryBv6s/8UHx9PDowV3f3UWtuZYTJSdYtn8ZDwx94IK3MJslR7JL2XGigG2p+fx8qtA6NtuN6xnlvJUIXR6+ooJ/Ob/O415PM6FfKFf2C2JktD8uTnr7tL2TcNLr6NfDm349vK2JuNFkJiWnXEvCM4o5kKFNgVjbSiJeP0a8vvMKIMLfjcE9fRnU04cBYd7EBHsS6u2KTtd137AoSj2VdF+M6AkNSffJzXj+5n+Y0DeQDUdyAQg0TUMn1mKWZrZlbuNwwWEGBAxwYMCK0rl98MEH3H///a0e8/HxobhYrfyntEJKa0+3CXj0zGrSStMAcNW78u8r/93kocnBQYN5eMTDPL3raQBWHljJjD4z6OXddAXLipo69qeX8OvZYvaeKeKXtEKKKo2thlCFK4+YF/G+7il0mBmtO8KGkckw8X9t394uxKDXMSBMexh07oiGRPx4ThkH0ks4kKG9DmeUUNfKCJOzhVWcLazimwNZ1n3uznp6B3nQJ0ibS7xPsCd9gjyJ8Hez67h3RbE19a/1YjQe1312F5iMTBsUak26dxwTTB00le/SvgO03u5/Jv7TEZEqSpeyatUqwsPDm+xzclK/nhxJCDEN+DegB5ZLKZ9rdtwFeBcYDhQAN0sp0yzHHgPuQcuJ/yil/N6mwZXnQlUhEnguKJifcnZbDz017in6B/RvccrcuLmsO7WOvbl7qZN1PL/z38wI+19Scso4nlvO8ewyUnLLzjmNXr0wH1cmxgVzZVwQ42KuRrejFpKe1Q4mPQtR4222aE53YdA3DE25xbJvw4+b6BE3jAOWYSkHM0o4ml3a6mJAlbUmDmaUcjCjtMWxQE9nwv3cCfdz0x4MtWz38HEl2MsFHzdDlx7Wo3Qv6q/axfCNAN9IKD4DxkrI2sfk/oNx0gnqzJJ9Z4v583XzrUn3+tPrOV16ukVviqIoTQ0ZMoSYmJbTrnWUmpoaXFzUNGf1hBB64DVgCpAO/CKEWCOlPNyo2j1AkZQyRghxC/A8cLMQYgBwCzAQCAM2CCFipZQ2W/1lz4FN1Lq68KWXJ+s8Xa37xwfNpbxwEJ/kn6Gq1kRpdR0lVUZKq4wUVRrJLJ8MnnsB2JK5ge+2DcBcE3reewV4ODOmTwBj+wQytk8AvQLcmyZx4/8MJzfDme0gzfDZXbAwCbx62Kq53ZKTTljn+p43UttXU2fieHY5+zOKOZhRQkpOOal55RSf49MGgPzyWvLLa/n1bOufijk76QjydCHY24VgLxeCvVwJ9HTBx80JX3dnfNwM+Lgb8HEz4Oumfe2Q1Til1P69mE1grtNeWPZJqb0al5scM7dyTLZ+zFpudswaR4vAmsRolhKTWWKWZsxmMBQcofS4AZPZjATtmNmMWUrMEkxmM2azdp7ZDGap1dP+Y9bCsFzbug1Iy/W0Q422zY0fi5bI+vMk2vMbsmF//be1ZaOatul88s6coW7cOJwM9nnQ2eFJdxt6UyKBdwBfS51HpZTrOjzQer3GaUk3wOlt+IYnMLp3AFtT87VdWX6M6zmObRnbkEjeOvgWS8YucVi4itLVvf3229x1113s2LGDV155hbVr1+Lp6cmcOXN44YUXcHVtSLoqKytZunQpn376KRkZGfTs2ZMFCxbw2GOPobNMKZeUlMSVV17J559/zrfffsvq1asxGo3WoSwfffQRS5cuJS0tjb59+/L000/z0ksvWc/Nzs4mMjKSF198kQcffLBJrEuWLOGFF14gIyOjq/fUjwRSpZQnAYQQHwMzgcZJ90xgiWX7M+BVoWWjM4GPpZQ1wCkhRKrlejtsFdzfjrzCmdCQJvuMJVew7sgQ1rHvPGcG4BbeHyevIwghcQ5IojpznvWoEBAb7MWQCF+GRvoyNNKPvsGe5x9PrHeCG9+EN34DVUVQlgWf3AZ3fg1O6o3cxXBx0muzm4T7WPdJKSmsqCU1t5wTeRWcyNPmEj+VX0FmcRV1F/hoorbObH2IE0CPCXdq8KAKD1GNB9V4iGrcadj20dfiqTfirjPhoavDTV+HmzDhqjPiKupwwYgBI87SiBNGDOZa9JjQYUIvTQwy1lC6Q4dOmtBJE0LWaV8xW8t6270HtSud5VVvHMABx8TSEUYBVbX3dc+ku429KY8Dn0op/2PpQVkHRHV4sPUix8C+j7Tt09th3INM7h9sTbo3HMnhD9MXsC1jGwBrTqxh0ZBFBLsHOypiRen0TCYTdXV1TfbpdDprogxw2223MW/ePL744gt27NjBkiVL8PPzY+nSpQDU1dVx9dVXc/jwYf72t78RHx/Pzp07eeqppygsLOSf/2w61OuBBx5g+vTpvPfee1RXa4uBrF+/nvnz5zNjxgxeeukl8vLyeOihh6iuriY2NhaAHj16cMMNN7Bs2bImSbfJZGLFihXMnTsXPz8/ysrK7PK96iA9gUbLPZKO9veo1TpSyjohRAkQYNm/s9m5PZvfQAixEFgIEBISQlJSUpuDi6ku4YxnQyJsLB5GdfZsmqYHravJn4yTlzYe3OB9gFHO19Pbw58wTx3hXjrcnMxAIVQWknUUso6e/3r1/Po+xOD9SxGYIf1nspbfyrG4P2iZfDuUl5df1Pekq2lP+8KAME8Y7wn0FphNzlSWF1NTVoCxohBzVQnUlKEzluFaV4aruRwfWY6vsLwox03Utu1mEm1wlAk4d0f7uXWNnFppxdZt2zA4u164Yjs4uiumLb0pEvC2bPsAmThSr3EN22d2gNnMpP4hLFmrhbz9RAGv+U3miqAr2Je3D6PZyPuH32dxwmIHBax0a0t8Llynoywpafep/fr1a7Hv2muv5euvv7aWb731VmuCPXnyZHbt2mXtlQath3rr1q1s3ryZCRMmADBp0iQAli5dyiOPPEJwcMOb35EjR7J8+fIm93ziiScYMGAAX375pXUIwaBBg0hISLAm3QCLFi3iyiuv5KeffmL8+PEAfPPNN6Snp3Pfffe1+/twOZFSLgOWASQkJMjExMS2nsiGjDH0qdxDXE0Z6Z4P4+k3FKcgHU46gV4I9DqBi0GHj5sBb1dtyIC3m4EePq6E+bjx6PbtJOcmgzAzdEQWDw2/2QYtSoQeTvDDXwEIzd5A6MCxMP5P7bpaUlISbf6edEEXbJ+U2tj94tNQdBqK07RPmcuyG14VebQyPqJBF1gYulbqMVn6yc0IQGBGIBt91QaQ6JCAudFXAClbq3++8xuO12v5HWx8TGgl638kQghtrxANNUXTegJhfb/Z+BrScrTJvUSj7UbXay0eIZqWZeMYmpzftEWy+T3Poba2lgkTxuPi6nHOOpfC0Ul3W3pTlgA/CCEeADyAya1d6FJ6Teq16Z23lIw1+OJsLIbqEn5Z9y4VnlGEewrSyyW1dWbeWL2ZUV6j2Gf5mPPDwx/Sr6Qf7nr3i47JVrpzr0l3bhs0tM/Hx6dF76mXg2JqTXt6ds1mbWzhhx9+SFhYWJNj9e2t74VOTExsco+4uDg2bNhg3bd27VoiIyOJj4+nqKjIWm/cuHEYjUY2bdrENddcQ2WltlLgtGnTmlzPZDKxe/duFi9eTHl5uXV/bGwsUVFRmEwma/3hw4fTr18/Xn31VYYMGQLAa6+9xqBBgxg4cCBlZWVN6jdWXV3dFf69ZgCNV5AJt+xrrU66EMIJrVOkoI3ntp8Q/GP+mwBs/nEDE69q9U/Ced028DYt6QY+S/mMRUMW4ay3wfzQY34P2Qdg/8daeeOT4B4Iw++49Gt3V1XFkH8c8o5B/jHIOw5FaVqCXVdlhxsKcPYEZw/t5eJpKWv7pLMHdU7u1AkXaoUzRpyowZlanKjGQI3ZiWppwIhBOy6cqJUGanHCiA6TWcep9EyCwyKok3qkzgmz0CGF3voyCyek0IPQWXNLLZcU2htHy6vxtr7RG0onvUAnBE463TnrOukEumbn6IW2z0mnnd+inr6hfv39mg+tuhzeDNor4QbHJ91tMQ94W0r5TyHEGOA9IcQgKWWTST/b3WvSSJv/MeUlwuHVAIwIqoVRicysOcprm04AkK0L4vnpV7Hxq42cKDlBjawhIyiD3w3+3UXHZCvd+X+U7tw2aGjfkSNH8PLqTGl2U+2JrX74yIgRI875IGX9mO2IiIgm9/Dy8qKmpsa6r6ioiDNnzuDv79/qdSorK/Hy8sLdXXvz27t37ybXy8nJwWg0trgPaENK9Hp9k/2///3v+fOf/8zrr79OeXk5GzZs4NVXX7XWKSsra/V74urqytChQ8//jXG8X4C+QohotIT5FuDWZnXWAHegjdWeA/wopZRCiDXAh0KIl9BGBPQFfrZHkFLXvj9hieGJhHmEkVmRSUlNCUlnk5gaNfXSAxICZvw/KMuEU1u0fV8/BK4+MPCGS79+V2aq05LqrH2QtY8rjm2H3bnagnOXwj1Qe2jVqwd4BIO7P7j5gpsfuPlrX90tX119teRad+4ucAEYLC+3dobU3f8mKe3n6KS7LT0i9wDTAKSUO4QQrkAgkNshEbam11hr0s3pbTBqIZP6h1iT7k3HckEK7o6/m79u1T5qfP/I+9w24DZcnewzTki5TF3CkI7uJiAggOjoaD799NNWj0dFRTUpN59GLDAwEIPBQG5uy18tOTk5REZGNtl3++2389hjj/H2229TVFSEu7s78+fPv7RGdBKWMdp/AL5He4B9pZTykBDiSWC3lHINsAKtEyQVKERLzLHU+xRtmGC/pZi9AAAgAElEQVQd8HtbzlxiC3qdnhkxM3hj3xsArE5dbZukG7SHJ2/5EN6+DrJ+tcxocjeYjDD4Jtvco7Mzm7XFi87usibZ5B6GumprFb/znG7l6gO+vcCvl+VrFHiHaatDe4VoSbaTWsFS6TocnXS3pTflDDAJeFsI0R9wBfI6NMrmeo1t2D6zA6RkSLgvgZ7ODdMXpRczPXo6r+x9heyKbAqrC1mduppb+t1y7usqitJu06ZN4/PPP8fT07PVMeIXotfrSUhI4PPPP2fJkiXWpDw5OZlTp061SLq9vb2ZP38+//3vfykvL2fevHl4e3u3dukuyTJL1Lpm+/7eaLsaaDWLlFI+DTxt1wAv0cw+M61J97bMbeRW5trugXcXL5j/Gbw1HQpSQJrgi99BbRkk3G2be3QmZjPkHYG0rZD2kzbJQGVB287Vu0BgXwiMhaA47WtAHy3JdvO1b9yK0sEcmnS3sTflT8CbQoj/QRuDf6eUF5ho0d6CB2jvwKtLoDwHCk+iC+jDVf2C+XR3OgAbDucwLNKPOwfeyXM/a7Mgvn3obebEzsGpnR+JKkp39euvv5Kfn99if0JCQpuvMX/+fN566y0mTZrEn/70J6644gpqa2s5ceIEa9asYfXq1dahJeeydOlSpk6dyqxZs1i4cCH5+fksWbKEHj16NJlJpd6iRYv473//C6AeoOxiwr3CGdljJD9n/4xZmll7Yi33xN9juxt4BsGd38B7N2i9vEj4+n+g4ARMeRJ0XXiJeLMZcg9Zkuyt2ie+VUUXPs8nAkKvgNArOJAnib9yjtZ73ZW/F4pyERye/bWhN+UwlqkhOw2dHiJGQ4plkbXT2yCgD5P6h1iT7o1Hcvnfaf2YFTOLN/a9QXFNMRnlGXyf9j3X9r7WgcErSudz002tf+yel9f2D7UMBgPff/89zz33HMuWLePUqVN4eHjQp08frr32WpydL/wx9JQpU/jggw9YunQps2bNIiYmhn/+8588+eST+Pi0nClm8ODBxMbG4u3tzbBhw9ocq9I53BBzAz9na8PNv0v7zrZJN2hDIO78Bt6bpQ01AdjxqraE/az/aol5V2A2Q87Bpkl2deuL0Vi5B2ifCvccriXaPa4AjwDr4YKkJK1HW1EuIw5PurusXmMbJd3bYdjtjO8biLOTjto6M8dyyjhbWEmEvzu39r+V1399HYAVB1dwTfQ1allaRUHrnb5QD/Gdd97JnXfe2WL/kiVLWLJkSZN9rq6ure5vLDExkfN9WHbrrbdy660No9zS09M5cuQIs2fPblH32LFjpKSk8Oabb563DUrndGXElTjrnKk113K08Kh9VhB299cS7y/vhaOWKTBPbIT/jIEZr0LcNNvezxbMJm0WlvoE+/Q27ZPd83EPhKhxEDUeon4DgXHnfWBRUS5HKulur8bzdZ/eDoC7sxNj+wSQdEzrndt4JIc7x0UzL24ebx18i6q6KlKKUvgp4ycmhE9wRNSKopxHVVUVixcvZvLkyQQGBnLy5EleeOEF3N3dWbBggbVeeno6qampPPHEE4SGhjZJ0pWuw9PZk3E9x7Hp7CYAfkj7wT6zTLl4wtz3IOkZ2PKitq8iDz66GfrPgKn/0B4WdBSzCbL3N+rJ3gE1F0iyPYK05LqXJdEOimv3QkCKcrlQSXd7hV4BBncwVmqT95ekg084k/uHWJPuDUdyuXNcNL6uvsyJncN7h98DYMWBFSrpVpROSK/Xk52dzR/+8AcKCgrw8PBg/PjxrFq1itDQUGu95cuX8+STTxIbG8uHH36Im1t7JxdTHG1q1NSGpPu0nZJu0Hp9r3pc+5R09SJtuXiAI2sg5QcYdgeMfQB8I85/HVuoq4XMvdpEAKe3a19rSs9/jkewlmTXvwJjVZKtdDvmprNR25xKutvLyRnCExrmYj2zE+LnMKl/MI9bZhPcdaqA8po6PF2cuH3A7Xx09CPqzHXsyd3D3ty9DA3u9HP1KsplxdnZmS+//PKC9S40hEXpOhLDE+0/xKSxPlfB/dvhu8caFtGpq4af/wu7V0DcdLhiHsJsw6nwynK0afvO7tIS7IzkJtP3tcqzh2W4yG+0nuyAGJVkK92GlJK8qjyOFh7lWOExUopSSClOoaKigqu4ym73VUn3pYgc25B0n94O8XMI9XFjQKg3h7NKMZokW1PymDYolB4ePbiu93WsTtUy8pUHVvLKpFccGLyiKIrSYUNMGnP3h9n/hRH3wLePQOYebb+5Do6shSNr+Y3OBTLHawlvj0EQ1F9bAOZcM32Y6rSFZgpPQdEpKDwJ2Qe1YSPlOReOySu06XCRgD4qyVa6BZPZxJmyMxwtPNrkVVhd2KKuQFBVV4Wbk30+vVRJ96XoNaZh+8wO6+ak/sEcztI+qtt4JJdpg7SPpe8aeBdfpX6FRJKUnkRKUQp9/fp2aMiKoihKU1N6TbEm3ZvTN3fc6sERI+F3P2oPVv70Mpzeaj2kN9dA6gbtZSUaVlcUluS7rlqbru9Cw0Oa84uGyDEQOVpLtv17qyRb6fKklJwpO8P+vP0cyD/A4YLDHC86TlVdVdvOR3K69DT9/C9+rYe2UEn3pQgfof3ikyZtHtbKQnD358p+wbzyYyqgrU5pNkt0OkFv395cFXkVG89sBOCtg2/xzPhnHNkCRVGUy974nuPRCR1maWZ/3n4KqgoIcAu48Im2IATETNZeecdh30dw6Eutt7oFqS0609aFZ+oZ3CFkEIQN1TqLIkaDd+iFz1OUTq6ouogD+Qe0V572tbS2bW9A3Z3cifOPI84vjlj/WPr69iXrYJbdEm5QSfelcfbQHqis/2jw7C6Im84V4b4EeDhTUKGtTnkgo4QrIrSVte4edLc16V53ah1/GPoHwjzDHNUCRVGUy56vqy9DgoawJ3cPEsnWjK3MjJnZ8YEExcLkJ2DyE+z89hNGB1dB5q/avN75xy6wAI2lF9wvGvyjta9BcdBjsDZURC1Ao3Rx9b3YyTnJJOckszd3L2fLzrbp3CC3IOL84+jv3584/zj6+fcjwisCnWg6rWWx7gLzz18ilXRfql5jG5Lu09shbjp6nSAxLpjP91gWyjmaa026BwcNtq6CZpIm3j70Nn8Z9RdHRa8oiqIAEyMmsidX+12+OX2zY5LuRqrdQmB4IgxvtNNk1Hq5q0ugfq55vUEbbuLqoxJrpVsxSzMpRSnWJHtP7h7yq1quXNycr4sv8YHxxAfFMyhgEP0D+hPoFtgBEV+YSrovVeQYbYUxaDGuuz7p/vFoDounxFqP3TPoHusqaF+kfMG9g+/tuI8yFUVRlBYmhk/k5eSXAdieuR2jyYhBb3BwVM3oDdrDlF49HB2JoticlNp46h1ZO9iRuYPdObspqy077zkGnYH+/v2JD4onPjCewYGDCfcK77QLEKqk+1JFNnqYMnMv1FaCszvj+wbipBPUmSUHM0rJLqmmh48rAGPCxtDfvz9HCo9QY6rhw6Mf8sDQBxzUAEVRFKW3T296evYkozyDCmMFu3N2MyZszIVPVBSl3Yqqi9iVtcuaaGdVZJ23vpfBi6EhQxkeMpxhwcMYEDAAZ70Np9e0M7VG66XyCNCWuwVtuqeMZAC8XA2MjPa3Vtt0LNe6LYTg7vi7reWPjn5EhbGiY+JVlE7ohx9+YPr06QQEBODq6kpcXByPPvooxcVNx9dFRUUhhEAIgU6nIyIigjlz5nD06FEHRa50F0IIEiMSreXN6ZsdF4yidFP1Dyu/svcV5q6dy4RPJvDwlof5IuWLVhPuANcApvSawqMjH+Wz6z/jp1t+4rVJr3H3oLsZEjykSyXcoHq6baPXGO0hF9CGmESPB+CqfsFsP6E9Zb7xSC7zRkZaT5kSOYUIrwjOlp2lrLaMT499yl2D7urw0BXF0Z555hn++te/csMNN7B8+XL8/f1JTk7m+eef54svvmDTpk307NnTWv/qq69myZIlmM1mjh07xhNPPMH48eM5dOgQwcHBDmyJ0tVNCJ/AB0c+AGBbxjYHR6Mo3UOFsYIdmTvYnL6ZLelbWp0fu56HwYMRISMYHTaaMaFjiPaJ7rRDRdpDJd22EDkWkt/Wtk9vt+6e1D+Ef3xzBIBtqflUG024GrQHXfQ6PXcNuosndzwJwNuH3ubmuJtxN7h3aOiK4khbtmzh8ccf56GHHuLll1+27p84cSKzZs1i+PDh3HXXXfzwww/WY4GBgYwePRqAsWPH0rt3bxITE3n//fdZvHhxh7dB6T6GhwzHRe9CjamGtNI0ssqzCPVUU+spysXKq8xjw5kNJJ1N4pfsXzCaja3W0ws98YHxjAkbw5iwMQwKHIRB18mepbAhlXTbQuTohu30X7SVwfRORAd60DvQg5P5FVQZTew8WUBiXENP3Mw+M1m2fxnZFdkUVhey6vgq7hh4hwMaoCiO8a9//Qt/f3+effbZFseio6N59NFHeeSRR9izZw/Dhg1r9RojRowAIDU11a6xKt2fi96FhJAEtmVqvdw7snYwu+9sB0elKF1DTkUOG85s4Ie0H9ibuxeJbLWev6s/43uOZ2LEREaHjsbL2auDI3UcNabbFnwjwdvy8XdtubbsrsVV/RqS7B+P5jY5zVnvzIJBC6zllQdXtnnVJEXp6urq6ti2bRtTpkzB1dW11TozZswAYMOGDa0eBzh1SltExNfX1/ZBKpedxg9Pbs/cfp6aiqJkV2Tz3uH3uP3b25n82WSe+/k563z3jcX6xfK7+N/x/jXvs2nuJv7xm38wpdeUyyrhBtXTbRtCaLOYHPxMK5/ZAT21Xrmr+gezfKuWFGw8ksvSGbLJ+KRZfWfx5oE3yanMobC6kE+Pfap6u5U2i38n3tEhWB2448BF1S8oKKCqqoqoqKhz1qk/dvr0aes+KSV1dXWYzWaOHz/Ovffei06nY86cOe0JW2lGCOEPfAJEAWnAXClli1VZhBB3AI9biv+QUr5j2Z8EhAL1PQhTpZS5zc/vrEaHNnxyuTNrJyazCb2a/1pRrMpry1l/ej1rT67ll+xfWq2jEzoSQhKY3GsyieGJapiWherptpVejaaWajSue0SUP14u2nubjOIqjueUNznNWe/MgviG3u63Dr6lersVpRmdruFX1YcffojBYMDFxYX4+HgyMzNZtWrVOYefKBftUWCjlLIvsNFSbsKSmD8BjAJGAk8IIfwaVZkvpRxieXWZhBu0HrkAV23dhJKaEo4WqplxFMVoNrIlfQtv5b1F4qeJ/H3731sk3DqhY1ToKP42+m9svGkjK65ewbx+81TC3Yjq6baVyLEN22d2aquFCYFBr2NCbBDfHNCmwtl4NIe4Hk0/TpnddzZvHniT3MpcCqoLWHVsFbcPvL0jo1eUDhcQEICbmxtpaWnnrFN/rPHsJdOnT+fJJ59Er9cTFhZGSEiInSO97MwEEi3b7wBJwCPN6lwNrJdSFgIIIdYD04CPOiZE+xFCMCZsDF+f/BrQxnUPDBzo4KgUxTFSi1L5POVz1p1a1+qsIzqhY0SPEVwddTWTIifh7+rfylWUeirptpWgfuDqC9XFUJkPBakQ2BfQxnXXJ92bjuayKDGmyanOemd+F/87nt71NABvHXqLuXFzcXVqfZyrotS72CEdnYmTkxNjx45l/fr1VFdXtzque82aNYA2m0k9f39/EhISOizOy1CIlLJ+wtxsoLV3NT2Bs43K6ZZ99d4SQpiAz9GGnrR4okoIsRBYCBASEkJSUtJFB1peXt6u8y7Er7yh037doXXEFMScp7Z92KttnUV3bl9Xb1utuZa9lXvZXr6dkzUnW60TZghjpMdIEjwS8HHygUzYn7m/1bpdib1/dirpthWdThvXffxbrXx6uzXpTowLQgit8zv5dBFFFbX4eTSd0L1xb3d+VT6rjq/itgG3dXQrFKVDPfjgg8yYMYO//OUvvPTSS02OnTp1iueff54hQ4YwZoxaGdCWhBAbgNbWEv9r44KUUgohWp+C4NzmSykzhBBeaEn3bcC7zStJKZcBywASEhJkYmLiRd4GkpKSaM95FzKwciDvrXoPgFPGU4wcN7LDp3O1V9s6i+7cvq7atpSiFD47/hlrT65tdfn1ILcgBhsGc//E+4nzj3NAhPZn75+dGtNtS43HdZ/ZYd0M8HRhaIQ2s4JZwubjeS1ObT62e+XBlVTXVdsvVkXpBBITE1m6dCkvv/wys2fPZvXq1WzevJmXX36Z0aNHYzab+fjjjx0dZrcjpZwspRzUyusrIEcIEQpg+dramOwMIKJROdyyDyll/dcy4EO0Md9dSpB7EDG+Wu92nbmOPbl7HByRothHnbmO9afXc8e3dzB7zWw+PPphk4TbSTgxpdcU3pj8BuvnrOcGvxu6bcLdEVTSbUuRrT9MCdpCOfU2Hm39uaLZfWcT7KZNMZhflc9nxz+zfYyK0sn8/e9/59tvv6WiooK77rqLxMREFi9eTGRkJAcOHCAuTv2C72BrgPoplO4AvmqlzvfAVCGEn+UByqnA90IIJyFEIIAQwgBcBxzsgJhtrvEsJruzdzswEkWxvZKaEt46+BbXfHENi5MWt3hjGe4ZzkPDHmL9Tet5KfElxvUcp2bxsQGVdNtS6BBwctO2i09Daab10JWNFsXZfCyXOpO5xekuehfuib/HWl5+YDmVxkr7xasoncS0adP4/vvvKSoqQkrJ/PnzOXz4MOnp6U3qpaWl8f777zsoysvGc8AUIUQKMNlSRgiRIIRYDmB5gPIp4BfL60nLPhe05Hs/8Cta7/ebHd+ES5fQo+G5gV9yWp8WTVG6mlMlp/jHzn8w5bMpvJT8ElkVWdZjTsKJqb2msmzKMr6Z/Q33xN9DoFugA6PtftSYbltycobwBEj7SSuf3g7x2tzB/UO9CPVxJaukmtLqOpJPFzGqd0CLS9wYeyMrD64kpzKHguoCPjr6UZNEXFEuBytXriQ9PZ1rr72WrVu30r9/f0eHdNmQUhYAk1rZvxtY0Ki8EljZrE4FMNzeMXaEhJAEBAKJ5FD+ISqNlR0+rltRbOVg/kGWH1jOxjMbWxzzc/HjpribuDnuZoLdg1s5W7EV1dNta5Gtj+sWQpx3dcp6LnoX7rviPmt55cGVlNaW2j5ORenEnJ2dSUpKoqCgQCXcikP4uPgQ6xcLgEma2Ju718ERKcrFkVKyK2sXC35YwLxv5rVIuPv69eXJsU/yw5wfeGDoAyrh7gAOT7qFENOEEMeEEKlCiBaLMFjqzBVCHBZCHBJCfNjRMV6UJg9T7mxyaFL/hn/Q5xrXDTAzZiYRXtozSqW1pbxz6B3bxqgoiqJc0IgeI6zb51p5T1E6G7M08+OZH5m/bj4LfljArqxdTY5PDJ/Iiqkr+Pz6z5nVd5aanrgDOTTpFkLogdeA6cAAYJ4QYkCzOn2Bx4BxUsqBwEMdHujFCB8JwvKwQc4hqCq2HhrbJxBXg/YtT80t53RBRauXMOgM/H7I763l9w6/R0FVgf1iVhRFUVpQ47qVrkRKSdLZJOauncuDmx7kQH7DOg46oePa3tfy+YzPeXXSq4wMHYkQwoHRXp4c3dM9EkiVUp6UUtYCH6OthtbY74DXpJRFAJ1+SWEXTwgdbClIONvwDtPVoGdcn4aHEs41xARgevR0+vpp83xX1VWx/MByu4SrKIqitK5+XDdgHdetKJ2NlJLtGduZv24+D/z4AMeKjlmPGXQG5sbO5etZX/Pc+OesQ6YUx3D0g5StrWo2qlmdWAAhxDZADyyRUn7X/EKdaXWzPrpwItDG/5356WNOZrpYj/XUGa3bn20/SrTx9Dmvc6XTlaSQAsDHRz6mb2lf/J3at8RqV18h63y6c9ugoX0+Pj6UlpZ2q94Jk8lEWVnLRRi6g9baJqWkurq6W/977U7qx3UfKzpmHdc9ruc4R4elKFa7s3fzyt5XWkz556p35ZZ+t3D7gNsJcg9yUHRKc45OutvCCegLJKItwLBFCBEvpSxuXKlTrW4WXAqfrgUgkgwiG10ztriKdw//CEBKMSSM+Q2eLq3/GCbKiexct5P9+fupo4797vtZMnZJu0LqqitktUV3bhs0tC81NRUnJyfc3bvPDAplZWV4eXk5Ogy7aK1tlZWVeHl5MXToUAdFpVysET1GWHsOf8n+RSXdSqeQUpTCS8kvsTVja5P9zjpn5sbNVdP9dVKOHl5yzlXNGkkH1kgpjVLKU8BxtCS882o8g0nGHjBWWYthvm70D/UGoNZkZmtK/jkvI4Tgj8P+aC2vTl1NWkmazcNVuobg4GAyMjKorKxEyotdmVtxJCkllZWVZGRkEBysZgjoStS4bqUzya/KZ8n2JcxZO6dJwu0knJgbO5dvZn/DIyMfUQl3J+Xonu5fgL5CiGi0ZPsW4NZmdVYD84C3LCudxQInOzTKi+UZBAF9oSAFzEbISIao31gPT+oXzJEsbRrAH4/mMG1Qj3NealToKEaFjmJX1i5M0sSrv77K/038P7s3Qel8vL21N2uZmZkYjcYL1O4aqqurcXXtnk/ON2+bwWAgJCTE+nNUugY1X7fSGVQaK3n38LusPLiSqrqGjjyB4Po+13P/FfcT7hXuwAiVtnBo0i2lrBNC/AFtSWE9sFJKeUgI8SSwW0q5hoblhg8DJuBhy+INnVuvMVrSDXB6R5Ok+6r+wby6KRWAH4/mYTZLdLpzj9P949A/Mj9rPgDfp33PHQPuID4o3n6xK52Wt7d3t0rakpKSuu1Qi+7ctsuJGtetOJKUkm9OfcPLu18mt6rp5Atjw8ayePhi4vzjHBSdcrEcPbwEKeU6KWWslLKPlPJpy76/WxJupGaxlHKAlDJeSvmxYyNuo8ixDduNFskBuCLclwAPZwDyy2s4kFFy3ksNDhrMlF5TrOX/2/1/aniBoihKBxke0rDIplokR+koKUUp3PX9XTz202NNEu4Y3xjemPwG/53yX5VwdzEOT7q7rcaL5Jz9Gcwma1GvE0yMa3ia+HwL5dR7cNiDOAntg4k9uXvYdHaT7WJVFEVRzmloSMMnFirpVuytvLacF355gZvW3kRyTrJ1f6BbIEvGLOGz6z9Tn7Z0USrpthffXuAVqm3XlkH2gSaHJ/ULsW5vakPS3cu7F3Pj5lrLLye/jNHcPcb1KoqidGZDgxqS7v15+9XvXsUupJR8c/Ibrl99Pe8dfg+T1DrrnIQTdwy4g69nfc2NsTei1+kdHKnSXirpthchms5i0myIyfjYQJws47gPZJSQU1p9wUved8V9eBo8AUgrTeOL41/YLl5FURSlVSEeIfT07AlAtamaowVHHRyR0t1klGdw34b7ePSnR8mvapjVbESPEay6fhV/HvFnPAweDoxQsQWVdNtTr0bjuk9vb3LI29XAyOiGhW7a0tvt5+rHPfH3WMuv73udCmPrS8kriqIotjMseJh1u/lCJIrSXiazifcPv8+sr2axPbMhTwhyC+KFCS+wYuoKYvxiHBihYksq6ban5j3dzR5+vKpfw3y9bRnXDfDb/r+lh4c2xWBhdSErD6689DgVRVGU81LjuhVbSy1K5fZvb+f5X563TgMoEPy2/29ZO2st06Ond6sViBWVdNtX8ABw9dG2K/Kg4ESTw5P6N4zr3pqST7XRxIW4OrnywNAHrOV3D71LTkWObeJVFEVRWtW4p3tv7l41g5TSbkazkf/s+w83fX0T+/P3W/fH+Mbw/jXv88jIR9RQkm5KJd32pNNBxOiG8pmmQ0yiAz2IDtT+x6oymth1qrBNl72u93X08+8HaOMLX9n7im3iVRRFUVoV7RONj4vWiVJYXcjp0tMOjkjpik6WnOS3637L67++Tp25DgAnnROLhizi0+s+ZXDQYAdHqNiTXZJuIUSYPa7bJTWeOrDZuG5oOsTkxyNt67HWCR2Lhy+2lr868RUH8w+2P0ZFURTlvHRC12QWEzXERLkYZmnmgyMfMHftXA4XHLbuHxw0mFXXreL+K+7HoDc4MEKlI9irp3unna7b9fRqWImSUz+1GNc9qdm47rZ+ZDkmbAyJ4YnW8nM/P6c+7lSUbk4I0UcIsUkIcVII8ZIQwrXRsZ9tdA9/IcR6IUSK5avfOep9J4QoFkJ83Wx/tBBilxAiVQjxiRDC2RZxdQZDgodYt9XDlEpbZVdkc+/6e3nu5+eoMdUAYNAZ+NPwP/HutHfVg5KXkXYn3UKIGed6Aa4XvMDlImwoOHtp26XpUHiyyeGEKH+8XLRFb9KLqkjJLW/zpR8e8TAGnfbOeF/ePr4++fUFzlAUpYt7DfgCuAkIAjYIITwtx2zVTfYosFFK2RfYaCm35kXgtlb2Pw+8LKWMAYqAe1qp0yUNC2k6rltRLuS7tO+YvWY2O7Ma+iLj/OL4+LqPuXPQnWrO7cvMpfR0fwk8BPxPKy+vSw+tm9A7QVSjlaNObW5y2NlJx4TYRqtTHmnbLCYAkd6R3Dag4W/ev5L/RaWxsv2xKorS2YVIKV+RUiZLKW8D1gPrhRBegK0+6poJvGPZfge4obVKUsqNQFnjfUKbauEq4LMLnd8VDQwYiLNO67g/XXqagqoCB0ekdFbVddUs3bGUhzc/TFmt9r+JQHD3oLv58NoPifWLdXCEiiM4XcK5qcDdUsq05geEEGcv4brdT/QEOP6dtn1qCyTc3eTwVf2C+eZAFgA/Hs3h/sQ+bb70wsELWXNiDflV+eRW5fLmgTd5cNiDNgtdUZROxa1xQUq5VAhhAn4APFs/5aKFSCmzLNvZQMj5KjcTABRLKess5XSgZ2sVhRALgYUAISEhJCUlXXSg5eXl7TrvUoQbwjlZo31i+f6m97nC/Qq73McRbetI3bl9J4tP8uynz5JpzLTu89f7c1vgbcSUxbD9p5bPd3UV3fnnBvZv36Uk3e8BwUBaK8eWX8J1u5/oCQ3bp7aA2azNbGKRGBeEENpw7+TTRRRX1uLr3sNVo9wAACAASURBVLZhkB4GDx4a9hCPb3scgHcOvcPsmNlEeEfYtAmKonQKKUKIq6SUP9bvkFL+QwihB55o60WEEBuAHq0c+mvjgpRSCiHs8rCIlHIZsAwgISFBJiYmXvQ1kpKSaM95l+LX5F85eVBLumuDakkcYZ/7O6JtHam7tu+r1K947cxr1Mpa676ro67miTFP4OXc9QcBdNefWz17t6/Nw0uEEM5CiCghRLgQQiel/IeUstUHd6SUS20XYjcQPBDcA7TtygLIPdzkcICnC0MifAEwS9h8PO+iLn99n+uJD4wHtPk/X9z94qXHrCiKwzX/vQv8FtjdvJ7ld+6gtl5XSjlZSjmolddXQI4QItRy/1Cg7WPeoADwFULUd+iEAxkXcX6np8Z1K62pNFby161/5fFtj1sTbhe9C38f83denPBit0i4lUt3waRbCOEthHgXKAFOAKeBSsvT6UuEENH2DrLL0+kganxD+dSWFlWazGJyEeO6QZvK6tGRDc86bTq7ie0ZXffjK0W53J3r9y7aMJLFrf3elVIebr6vndYAd1i27wD+P3t3HhdV1T9w/HNmhmHYERBUXNBw19JEMntU3E1L6ynbzKwny9JKf7ZoT5vaU2n5tG8upVb2VFqmlWm5YFpuuS+4b4giCIigbDNzfn/MMDAyuCBwZ4bzfr3mxT33njv3ewUvX86cZeHlnihtUyitBO6syPme4LraJd1JkjKS1DgaheSzyQz9dSiLDi5y7Gsc0pi5/ecyuNlgtaqk4nA5Ld3TgVuBN7H1v3saMAJhwIvAXiHEB6WnrlJccOpisqrM4R4tSrpNJu5Nw2yxXtHbX1v7WgZeM9BRfm39a46piRRF8ThaPncnA72FEPuBXvYyQog4IYSj66AQYjUwD+gphDguhOhrPzQO2x8GB7D18f6sCmLUTIhvCLGhtinezNKs1kio4dakrOHuX+5mX9Y+x774gHi+GfANzcOaaxiZ4o4uJ+nuD4ySUr4ipfwMKF7+8G6gHvBv+/YyIYRfOe+hNEko2T7yJ1jMTodb1g2ibojt9+fZfDObjmZd8SX+r8P/EeRj+wjrWM4xPtvhVb/rFKUm0ey5K6XMkFL2lFI2tXdDybTv/1tKObxUvS5SytpSSj8pZX0p5VL7/kNSyngpZayUcrCU0uv++i+9JPymtE0aRqJoxSqtTN8+nZHLRjpmJ/HR+TDhxgkMjRiKv4+/xhEq7uhyku4CwGUnYyllmpRyKnAtthaNFysxNu8S1gSC7YP4C3Pg5Fanw0IIupdenXLPlXUxAYjwi3CauWTmjplqqWJF8UzquevG2keVWpnylOrXXdPkFuYyZuUYPtjyAdI+U2eUfxRz+s3hjmZ3aByd4s4uJ+leDDx2sQpSylTgZVwvlKAACOHcxeRQYpkqpft1L92VWqEVJu9sdqfToMr/rPuPWqlSUTyPeu66sQ6RHRzb29K3YbaaL1Jb8SbJOckMWTyElckrHfviouL49pZvaVu7rYaRKZ7gcpLu8UC8EGKhEOJiE0jnAxGVE5aXatytZNvFYMqbYiMItK9OeSTjPEknc8rUuRS9Ts9LnV5CJ2zf2nUn1/Hr4V8rFq+iKFpRz103VjewLnUCbDMunjefZ2/WXo0jUqrDplObuO+X+ziUXbKy9P0t72d6n+mE+4VrGJniKS6ZdNsXSeiKbYGEfcAqbCufdRRCtBFCtBRC3Am8DbicQlCxK93SfWwdFDqPejf56OnZsqS1+9edJ6mIluEtua/FfY7yW3+/xXmrGmGvKJ5CPXfdX/tI1cWkJll0cBHDfxvOmYIzABh1Rl7/x+uMix+Hj85H4+gUT3FZ83RLKQ9LKTsBg4EsIA/4BNgG7AS+AwqBR6ooTu8QEg0R9tHMlgI4WnZav5vb1HVs/7LjZIW7hoxqN4pIP1sCfzrvND9n/Vyh91EURRvqueveSncx2Zy2WcNIlKpklVbe2/weL6x5wdGNKMwUxmd9P+PWa27VODrF01z24jgAUsofpJS3ArWA9sA/gbuAjlLK1lLK/VUQo3eJ7VmyfWBZmcMJzWvjb9QDcCj9HPvTcit0mUBjIM/FP+cor85dzaZTapS9onga9dx1T6UHU24+tVmNnfFCeeY8nk58mpk7ShbZjg2N5esBX9Musp2GkSme6oqS7mJSyiIp5TYp5UIp5fdSSpXNXa7SSffB5WUOm3z0dG9e0sVk8Y6KdTEB6NOoD13rl3RpeeWvV8g351f4/RRF0Y567rqX2NBYxyqDGfkZHMs5pnFESmU6k3+G4b8NZ9mxksaxLtFd+PLmL4kOjNYwMsWTVSjpVq5Co5vAYF/P4vQ+yCo7pd/Nbes4tpfsTK3wpYQQvNTpJQJ9AgE4evYoH2/7uMLvpyiKotjohM6pX/fmU6qLibdIyU1h6K9D2Z6+3bHv/pb380GPDwg0BmoYmeLpVNJd3Xz8bIl3MRet3d2bR+JrsH1r9qTmcDC9Yl1MAOoE1GFs3FhHec6uOWoFNUVRlEpQepEc1a/bO+zN3MvQxUM5cvYIAALB+PjxjIsfh16n1zY4xeNpnnQLIfoJIfYKIQ4IIcZfpN4dQggphIirzviqRGyvku0DZZPuAF8DCc1rO8pX09oNcGfTO2lmagbYBoW8/NfLFFmKruo9FUVRarrro0qS7i1pagYTT7fh5AYeXPIg6Xm2dal8dD682e1NhrQconFkirfQNOkWQuiBj4CbgVbAvUKIVi7qBQGjgfXVG2EVKZ10H1oFLhLg/m1LZjG5mn7dYOtmcm/YvfgZbKtF78/a7zQwRFEURblyrcNbY9QZAVv3vdN5pzWOSKmoJUeW8Niyx8gtsn2yHOgTyLTe0+gX00/jyBRvonVLdzxwQEp5SEpZCHwDDHJR71VgCraFIDxfRFMIaWjbLsyB4xvLVOnRIhKj3vbt2XXiLEczzl3dJX0ieLL9k47y9O3T2ZO556reU1EUpSYz6o20iWjjKKvWbs/0/b7veW7VcxRZbQ1gkX6RzO43m451OmocmeJtDBpfPxpILlU+DtxQuoIQ4nqggZTyFyHEs+W9kRDiUeBRgKioKBITE684mNzc3AqdVxHN/FtSL9s22v3o8s843KSwTJ1WYYKttk+5eO/HPxl4jbHC18vNzSVaRtPYtzGHCw5jlmaeWvIUz9Z9Fh/h2RP7V+f3TQvefH/q3hRPd33U9Y7+3JtPbaZ3o94aR6RciS93f8mbG990lBuHNObTXp9SL7CehlEp3krrpPuihBA6bCuuPXipulLK6cB0gLi4OJmQkHDF10tMTKQi51VIVA58uxSARkX7aeTiutmhKYz+ZisA27N9+W+3rgghKnS54ntrkt2EwT8NJt+Sz8mik2wJ3MJzHZ+79Bu4sWr9vmnAm+9P3Zvi6dRgSs8kpWTa9ml8tPUjx76WYS2Z1nsatUy1NIxM8WZaJ90pQINS5fr2fcWCgDZAoj3ZrAMsEkIMlFL+XW1RVoXG3UBnAKsZTm6DsychuK5Tld6tovDz0ZNXZOFAWi5JJ3NoVS/4qi4bExLDM3HP8J/1/wFsf+V3rd+VTnU7XdX7Koqi1ETXRV6HQCCR7Mncw7micwT4BGgdlnIRUkre2fQOs3bNcuxrH9mej3p+5Jh7vbKcPXuWtLQ0ioq8Y/KCkJAQkpKStA6jypS+Px8fHyIjIwkOvrq8qzStk+6NQFMhRGNsyfY9wH3FB6WU2UBEcVkIkQg84/EJN4ApGBp1hsN/2Mr7lkDcQ05V/I0G+rSOYuHWEwAs3JZy1Uk3wF3N72LV8VWsTlkNwItrXuT7gd8T4hty1e+tKIpSkwQbg2lWqxl7s/ZilVa2pW+jc73OWoellMMqrby27jW+2/edY1+nup14r/t7+Pv4V+q1zp49y6lTp4iOjsbPz6/Cn1S7k5ycHIKCKvcPE3dSfH9SSvLy8khJsbUDV1birelASimlGXgCWAokAd9JKXcJISYJIQZqGVu1aN6/ZHvfEpdVBl5X0q/sp60nsFqvfqlhIQSTbppEqG8oAKfOn+K19a9d9fsqiqLURGqRHM9gsVp46c+XnBLu7g2682HPDys94QZIS0sjOjoaf39/r0i4axIhBP7+/kRHR5OWllZp76v17CVIKRdLKZtJKa+RUr5m3/eylHKRi7oJXtHKXaxZqamIDiVCYdkZSro0rU2ov22g44nsfP4+mlUpl47wi2DCjRMc5V8P/8pPB3+qlPdWFEWpSTpEdXBsqxlM3JPFauHlv15m0cGS1KJ/4/78N+G/+Op9q+SaRUVF+Pn5Vcl7K9XDz8+vUrsGaZ5012hhjSHSPi25Od+WeF/AaNA5zdm9cGtKmToV1bNRT26Lvc1RfnXdqxzOPlxp768oimcRQoQJIX4XQuy3f3U5okwIsUQIcUYI8fMF+2cLIQ4LIbbaX+2qJ3JttYssuc3t6dvV4mNuxiqtTFg7wSnhvj32dl7/x+v46Kp29i7Vwu3ZKvv7p5JurTW/uWR772KXVQaV6mLyy46TFJqtlXb58fHjiQmOASDPnMfTq54m3+wd06ErinLFxgPLpZRNgeX2sitvAUPLOfaslLKd/bW1KoJ0N3UC6hAdGA1AviWfpEzvHWjmaazSyit/vcKPB3507Ptn038yofMEtay7Uu1U0q210v269y4Bq6VMlY4xYdQNMQFw5nwRaw6kV9rlA3wCmNptqmNVtf1Z+5mycUqlvb+iKB5lEDDHvj0HuM1VJSnlciCnuoLyBE5TB6p+3W7BKq1M+GuCU8J9e+ztvHLjK+iESn+U6qf17CVKveshIBLOpcH505CyCRrEO1XR6QQDr6vHtD8OAfDD5hR6tIiqtBCahzVnXPw4Xl33KgDz982nY1RH+jfpf4kzFUXxMlFSypP27VSgIg+a14QQL2NvKZdSFriq5GkLml1KQE7JNIFLdy8l5nTMVb2fO91bVajq+7NKK99kfsPa3LWOfZ0COpFQmMAfq/6osutCyb2FhISQk+Ndf5t++eWXjBo1yuWxhQsX0qRJE9q2beu0PywsjJYtW/L000/Tq1cvx/6jR4/Stm1bPvjgA4YNG1alcV8ui8VS5nuWn59faT+rKunWmk4HzfvB5i9s5b2LyyTdALe1j3Yk3b/tPkX2+SJC/CuvL9rgZoPZmLqRJUdss6hMXDuRVuGtiAmJqbRrKIqiPSHEMmxrHlzohdIFKaUUQlzpdEnPY0vWjdgWKxsHTHJV0eMWNLuERtmN+ObHbwA4aj5Kl65drqr7gjvdW1WoyvuTUvLa+tecEu5B1wxi0k2TqqWFu/jekpKSvG56PZ3O9u83b9486tev73SsVatWZGZmAvD8888zcKBtErpTp07x4Ycfctddd7FmzRpuuMG28HhgYCAAJpPJbf6dXE2JaDKZaN++fTlnXBn1+Yo7KN3FJOknkGV/z7WsG0ybaNs8kYVmK4u2Vd6ASrANFnjlxldoGNQQgPPm84xZOYZzRWVnVFEUxXNJKXtJKdu4eC0ETgkh6gLYv17RXFlSypPSpgCYBZRtQfBSMcEx1ParDUBOUQ57svZoHFHNVLzwzbd7v3XsG3jNQCZ2nqi6lFSidu3a0alTJ6dX6bmsmzRp4tg/aNAgFi5ciBCCH374QcOotad+At1BkwQw2v7iI+MAnNrlstrgDiWLd87bdLzSwwg0Bjr17z6YfZAX17yIdPFHgKIoXmkRUPw57zBg4ZWcXCphF9j6g++s1OjcmBCCjnU6OsobT27UMJqaa8aOGU4rTfZv3J9JnSepQZMaM5lMGI1Gr1mZs6JU0u0OfPyc5+ze/aPLaoPa1cOot33Lth/PZm9q5fcVaxneklc6v+IoLzu2jBk7ZlT6dRRFcUuTgd5CiP1AL3sZIUScEGJmcSUhxGpgHtBTCHFcCNHXfmiuEGIHsAPbasL/qdboNRZfp6Rhf33qeg0jqZnmJs3lgy0fOMrdG3TnP//4j0q4q4DFYsFsNjteFovzJBBWq9Vx7MSJEzz99NPk5+dzxx13aBSxe1B9ut1F69tg53zb9q4F0P0FuGB+yFB/I71bRfHLDts4p3l/J/PiLa0qPZSB1wwkKSOJr5K+AuDDLR/SIqwFXet3rfRrKYriPqSUGUBPF/v/BoaXKncp5/weVRed+4uvW5J0bz61mSJrUZXPA63YLNi/gMkbJjvKnep24q1ub7ndv3/M+F+0DsHhyOQBFT63RYsWTuWbbrqJNWvWOMojRoxgxIgRjrKvry/Tp0/npptuqvA1vYFq6XYXsb0uq4vJnXElAxd+3JpCkaXy5uwubWzcWMdHpRLJuD/GcSj7UJVcS1EUxRvUD6xP3QDbYmbnzefZnbFb44hqhqVHljJh7QRHuV3tdrzX/b0qW2lSgQULFrBx40bH67PPPnM6/uKLLzqOLV26lEceeYRHH32Ub775RqOI3YNKut3FhV1Mdi1wWa1r09pEBdseJKdzC1m554rGOV1+ODofpnab6vgFkluUy6hlo8jMz6yS6ymKoni6Mv26U1W/7qq2+vhqxq8ej1XaGqBahrXko14f4e/jr3Fk3q1NmzbExcU5Xs2bN3c63qhRI8exPn368MEHH9C3b1/GjBlTo8eJqe4l7qR0F5PdP0KPF8t0MdHrBP+8vj6fJB4E4NuNyfRp7Wr2r6sXZgrjve7vMWzJMPLMeRzPPc6TK57ksz6fYTKYquSaiqIoniy+TrxjufENJzcwvO3wS5yhVNTWtK2MTRyL2WoGoHFIYz7t/SnBxuBLnKmdq+nS4elat27N4sWLSUtLIyqq8tYa8SSqpdudlOli4nrg/11xJbOYrNibxvGs81UWUsvwlkzpMgWBLfnfnr6df6/5t6NVQVEURSlRejDllrQtFFoKNYzGex06c4gnVjxBviUfgOjAaGb0nkGYKUzjyJTybN++HaPRSEhIiNahaEa1dLuT4i4mxa3dO7+HOm3LVGscEcA/YiNYc+A0UsL/Nhzj2b4tytSrLN0bdmdc/DjHIJXfj/7Ou5veZWzc2Cq7pqIoiieqG1iXBkENSM5JJt+Sz47TO+gQ1UHrsLxK6rlURiwbQXZBNmD7VHZ67+lEBdTM1lN3dOjQIdatWwdAVlYWixYtYunSpYwcORKTyfmT8k2bNhEaGlrmPQYOHIjRaKyWeKuLSrrdTZs7SpLu7d9Bj5fAxXRH93dqyJoDpwFbF5PRPZthNFTdBxdDWg4hOSeZuUlzAZi1axa1/WsztNXQKrumoiiKJ4qvE09yTjIAG1I3qKS7EmUXZPP4ssdJPZcKgJ/Bj497fkzD4IYaR6aU9sYbb/DGG28AEBwczDXXXMNHH33Eo48+Wqbup59+yqefflpmf3p6OhEREVUea3VS3UvcTWwv8A+3bZ9NgSOrXVbr1TLKaUDl0l2pVR7as3HPktAgwVF+c+ObLNjvesCnoihKTVV6MOX6k2q+7sqSb87nqRVPceDMAQAMwsC7Ce/SOqK1xpHVHEOGDEFKSWxsrMvjMTExSCmdXtnZ2WzevJmRI0diMBguWrf0y9sSblBJt/sxGKHNnSXlba6n1zHoddwbX/KX/VfrjlZ1ZOh1et7s+ibtI9s79k1YO4FlR5dV+bUVRVE8xQ11b3Bsb0vbRm5hrobReAeL1cL41ePZnLbZse/Vf7xK5+jOGkalKFdGJd3u6Lp7SrZ3L4IC1w/sezo2RK+zDXBcfziT/acqf4XKC/kZ/Piwp22xHACrtPLcH8/x14m/qvzaiqIoniDCL8LxjDRLMxtSN2gckWeTUvLa+tdYfmy5Y98zcc9wS5NbNIxKUa6cSrrdUb32EGGf87LoHOz52WW1OiEmercsGThSHa3dAMHGYD7p9QmNghvZQrQWMWblGDUnraIoil3neiUtsKpR4up8uv1T5u2b5ygPazWMYa2HaRiRolSMSrrdkRDOrd1bvy636tAbGzm25206Tvb5oqqMzCHCL4IZvWcQ5W9L+vPMeYxcNpJ1J9dVy/UVRVHc2T+i/+HY/jPlTw0j8WyLDi7i460fO8oDmgxQM2cpHksl3e7q2rvBPjc2h/+ArCMuq3W+JpzmUUEAnC+08L+Nx6onPmxTY83sM5PafrUByLfk88TyJ1SrjqIoNV672u3wN9hWRTyee5xjZ6vv2ewtNqZu5JW/XnGUb6x7I692fhWdUKmL4pnUT667ComG2J72goRNc1xWE0LwcJfGjvLsP49QaK6+hWtiQmKY1W8Wkf6RABRYCnhy+ZOsSVlTbTEoiqK4Gx+9j9NCOX+eUK3dV+Jw9mHGrBzjWG0yNjSW/yb8Fx+9j8aRKUrFqaTbncX9q2R7y5dgdr2y2aB29YgItE0fmHo2n8U7TlZHdA6Nghsxu+9s6gTYlqMvtBby5IonWXJkSbXGoSiK4k5Kz6yhuphcvsz8TEYuG8nZwrOArTvjxz0/JsgYpHFkinJ1VNLtzpr2haB6tu1z6eUOqPQ16BlWqm/3jNWHkFJWR4QODYIb8Hnfz6kbUBcAs9XMc6uecyymoyiKUtPcVO8mx/aG1A0UWapnzI0nK7AUMHrFaI7nHgfApDfxYY8PqRtYV+PIFOXqqaTbnekN0KHUCO2/Py+36pBOjTD52L6du06cZe2hjKqOrowGQQ2Y028OjUNs3V0kkskbJvP+5ver/Y8ARVEUrTUMbkj9wPqAbbD5lrQtGkfk3qzSyotrXmRr+lYABILJXSerxW8Ur6GSbnd3/QMg7MvAH1kN6ftcVgsLMHLH9fUd5Y9XHqyO6MqoG1iXL/p9wbW1r3Xsm7FjBi//9bJq5VEUpca5KbqktXt1iusVhhWbD7d86NQt8Zm4Z+jZsOdFzlAUz6J50i2E6CeE2CuEOCCEGO/i+FghxG4hxHYhxHIhRCNX7+O1gutBs34l5Y0zyq36aNcmjsVy1hw4zeZjWVUdnUuhplBm9J5B1/pdHft+PPAjw38bTmZ+piYxKYpyeYQQYUKI34UQ++1fa7mo004IsVYIscv+bL671LHGQoj19mf6t0IIY/XegXsp/RxMTE7ULhA3t2D/AmbsKPn9dk/zexjaaqiGESmuzJ07FyGEy1doaKjW4bk9TZNuIYQe+Ai4GWgF3CuEaHVBtS1AnJTyWmA+8Gb1RukG4oeXbG/5Cs67TlwbhQcw6Lp6jvIHy/dXdWTl8vfx593u73Jb7G2OfZvTNnPvz/eyL8t1a72iKG5hPLBcStkUWG4vX+g88ICUsjXQD3hXCFH8G3cK8I6UMhbIAh6uhpjd1g11b8DP4AfAkbNHOJx9WOOI3M+6k+uYtHaSo9wlugvj4schhNAwKuVi5s2bx9q1a51ey5Yt0zost6d1S3c8cEBKeUhKWQh8AwwqXUFKuVJKed5eXAfUp6Zp0h2i2ti2i85ftG/3yO6xFD+nVu5NZ8fx7GoI0DUfnQ+TOk/i6Q5PI+xzjp84d4Khi4ey7Kj6z6kobmoQUDxH6RzgtgsrSCn3SSn327dPAGlAbWHLknpgayAp9/yaxFfv67Q65crklRpG434OnjnI2JVjMUvb1IDNazXnrW5vYdAZNI5MuZh27drRqVMnp1dcXFy1Xb+goKDarlWZtP6pjgaSS5WPAzdcpP7DwK+uDgghHgUeBYiKiiIxMfGKg8nNza3QedUhqlZPWp7aCUDBmg9ZZ74OqXM9X2nHKD0bUi0AvPLdWp663qTpvcUQw6O1H2XO6Tnky3zOm8/zf4n/R/eg7gysNRCDuLofQ3f+vlUGb74/dW9uKUpKWTzvaCoQdbHKQoh4wAgcBMKBM1LaMyjbMz26qgL1FN0bdGf5seUArDy2kn+1+dclzqgZTuedZtTyUeQU5QAQ6RfJhz0/JMAnQOPIlKsxe/ZsHnroIdauXcsHH3zATz/9RGBgIHfeeSdvvvkmJpPJUff8+fNMnDiR7777jpSUFKKjoxk+fDjPP/88Op2tXTgxMZHu3bvz/fff8+uvv/Ljjz9SVFTEmTNnAPjf//7HxIkTOXLkCE2bNuW1117j7bffdpybmppKw4YNeeuttxg9erRTrBMmTODNN98kJSWFWrXK9KSrdFon3ZdNCHE/EAd0c3VcSjkdmA4QFxcnExISrvgaiYmJVOS8amHuDO99Bzkn8S3MolutNGg/xGXVOi3O0u9d24CdzWkWIpq2h/1bNL23BBLol9WPJ1Y8QUpuCgArc1aSYcpgatepVzUdlFt/3yqBN9+fujdtCCGWAXVcHHqhdEFKKYUQ5U49JISoC3wJDJNSWq+kO4C3N5SUprfoEQgkkm3p2/hp+U8E6S8+57Sn3FtFZeZk8uCPD5JSaPt9YBRGHgx9kD0b97CHPRpHd3WKv3chISHk5ORoHU6lslpti++dPXuWrCzncWM6nQ6dTkd+fj4AQ4YM4c477+Srr75iw4YNvPHGG/j7+/PCC7bHjNlsZsCAAezZs4fnnnuO1q1bs3HjRl599VVSU1N5/fXXAVtiDvDEE0/Qu3dvpk2bRkFBATk5OaxYsYIhQ4bQv39//vOf/3D69GlGjx5Nfn4+sbGx5OTkEBAQwC233MKnn37Kv/5V8gevxWJh5syZ3H777RgMBnJycrBYLGW+Z/n5+ZX2f1HrpDsFaFCqXN++z4kQohe2XwbdpJSe+ZnC1TIY4YYRsGyCrfzXB3DdvaAr20OoRZ1g+raOYumuUwC8uXQv/2pSjbGWI7ZWLN/e8i0vrnmRxOOJAGxP387gnwczqfMkejTsoW2AilJDSCl7lXdMCHFKCFFXSnnSnlSnlVMvGPgFeEFKuc6+OwMIFUIY7K3dLp/p9hi8u6HkAvN+ncfmtM1IJOaGZhKaJly0vifd25WySivD5g/jaOFRAHRCx9vd36ZbA5dtah6n+HuXlJREUNAFf1xNCNEmKFcmXHn30+LW5w4dOpQ5NmDAAH7++WdHS/b999/PxIkTARg4cCBbt27lhx9+YPLkyQB8+eWXb8SYugAAIABJREFUrF27llWrVtG1q23A8a233oqvry8TJ07kpZdeIjIyEn9/fwBuuOEG5sxxXp17ypQptGrVip9++skxBqBjx47ExcXRvHlzx7//U089Rffu3dm6dStdunQBYNGiRaSkpPDkk0866uXk5JT5nplMJtq3b3/F/1auaN2neyPQ1D7a3QjcAywqXUEI0R6YBgyUUrp8+NcYHR4CY6BtOz0JkhaVW/XpPs2xT2TCH/vSScqwVEOAlxbiG8L7Pd7nmbhn0NunQswuyGb0ytG8uOZFcgq9q1VAUTzQIqB4gYBhwMILK9if1wuAL6SUxf23kbYJ+VcCd17s/JqodKPCiuQVGkaivXc3v8vW81sd5XEdx3lNwl1TLFiwgI0bNzq93n33Xac6AwYMcCq3bduWY8eOOcpLliyhUaNGdO7cGbPZ7Hj16dOHoqIi1q1b53T+7bff7lS2WCz8/fff3HHHHU6Dbjt06EDjxo2d6iYkJNCqVSumTZvm2Ddt2jSuvfZaOnXqVLF/hArQNOm2t4Q8ASwFkoDvpJS7hBCThBAD7dXeAgKBeUKIrUKI8jNNb+cXCvGPlJRXTQH7Rz0XahYV5DRv97x9hW6zQI0QgmGthzGr3yyi/Eu6iy48uJA7Ft3BhpMbNIxOUWq8yUBvIcR+oJe9jBAiTggx017nLqAr8KD9ubxVCNHOfmwcMFYIcQBbH+/Pqjd895TQIMGxvfbEWs4XnS+/shebt28es3bOcpTvb3k/97W8T8OIlIpo06YNcXFxTq/Y2FinOmFhYU5lX19fpwGQaWlpHD16FB8fH6dXfHw8ABkZzov81a3r3A319OnTFBUVERkZWSa+qKiyQ1Eef/xx5s+fT0ZGBkePHmXJkiU89thjV3bjV0nr7iVIKRcDiy/Y93Kp7XI/Bq2RbnwSNsyAwlxI2w1JC6H17S6r/l/vZizcdoJCs5VD2VaW7Ezl5rbus5Ru+8j2fD/we15f/zqLD9t+BE6eO8nDvz3M3c3vZvT1owkyXrzfo6IolUtKmQGUWZFESvk3MNy+/RXwVTnnH8I2M5VSSqPgRsSGxnLgzAEKLAUkJifSv0l/rcOqVn+l/MVr615zlBMaJPBM3DMaRqSBCnTp8Fbh4eE0btyY7777zuXxmJgYp/KFY0YiIiLw8fEhLa1sJ4hTp07RsGFDp30PPPAAzz//PLNnzyYrKwt/f3+GDHE9Nq6qaN29RLlSAeEQ/2hJObH81u56oX4Mu7FkLaE3l+6l0Oy6rlZCfEOY0nUKU7tNJcS3pK/bt3u/ZeCPA1lyZInbtNAriqJcjZsb3+zYLr3yYk2wP2s/Y1eNxSJtXR0bGBswpcsU9Dq9xpEpWunXrx/JyckEBgaWaTWPi4sjIiLioufr9Xri4uL4/vvvnfKETZs2cfhw2fnwg4ODGTJkCNOmTePzzz/n3nvvJTg4uNLv62JU0u2JOj/p3Ld7+7flVh2ZEEuQyfaBxuHT55j1p3suzNA3pi8LBi6gW/2Sfn2n807z7KpneXz54ySfTb7I2YqiKO6vX0zJ6sJrUtZwtvCshtFUn/Tz6YxaPopzRecAqBNQhxG1R+Dv469xZEpFbd26lXXr1pV5mc3mS59sN2TIEDp37kzPnj15++23Wb58Ob/++isffvghffr0ccxacjETJ05k165d3H777SxevJgvvviCwYMHU6dOHcegz9JGjhzJ/v37OXnyZLV3LQGVdHsm/zC4cVRJefkkKHT9w1krwMiYXs0c5feX7yc1O7+qI6yQ2v61+aDHB0ztNpXafrUd+/9M+ZNBCwcxdeNUsgvUR3OKonimhsENaRVuW3S5yFrEymPev1DO+aLzPLHiCU6es039HuATwIc9PiTE4EazeChXbPDgwdx4441lXsVzZ18OHx8fli5dyiOPPML06dPp378/Q4YMYc6cOXTu3Bmj0XjJ9+jduzdz584lKSmJ22+/nSlTpvDf//6XOnXqEBJS9mfs2muvpVmzZsTFxXH99ddf0T1XBpV0e6rOT0GgfaBAzglY+1G5VR+4sRHRgba+UOcKLbzxa1J1RFghQgj6xvRl4W0LubfFvY6VLIusRczZPYcBCwYwN2kuRdYijSNVFEW5cqVbu3894nKtN69hsVoYt3ocuzN2A6AXeqZ2m0rzsOYaR6ZU1JAhQ5BSlvuKiIjgwQcfREpZZmDlhAkTynQXNZlMTJgwgT179lBQUEBmZiYbN25kwoQJGAy2T+kTEhKQUtKrl+shfvfddx979+6loKCAXbt20bFjR5KSklwm1Xv37mX//v2atHKDSro9l28gdC+1jsWadyAn1WVVH72O+1v6OsoLt55g/aEMl3XdRZAxiH/f8G++HvA17Wq3c+zPLshm8obJDPpxED8e+BGz9fI/ylIURdFa35i+ju11J9aRmZ+pYTRVa+rfU0lMTnSU/33Dv/lH9D+0C0jxOnl5eTz++ON8//33rFq1ilmzZtG7d2/8/f0ZPny4o97x48dJTEzk0UcfpW7dutx3nzYz5qik25O1vx8ibR9VUnQOlr5QbtWW4XpuubZk5pIXftxJfpF7zN19MW0i2vDFzV8wtdtUogNLVpNOzknmpT9fYtCPg1ifu14l34qieIR6gfUcDQkWaWHxocWXOMMzzU2ay1dJJRPcPNT6Ie5qfpeGESneSK/Xk5qa6litcuzYsTRt2pQ//vjDaYrBmTNn0qNHD06dOsXXX3+Nn5+fJvGqpNuT6fTQ742S8s75cGBZudVfGNCSAKNtpPiBtFw+WLG/qiOsFMVdThbdtoinOzxNsLFktPGxnGN8lfEVty28je/2fke+2T37qyuKohQbGDvQsf3DgR+8boamxORE3tz4pqPcu1FvxnQYo2FEircyGo0sWLCAkydPUlhYSFZWFosWLaJNmzZO9SZMmIDVamXPnj1066bdQkwq6fZ0TRKgbanWg5/Hljuosm6IH+NvbuEof7rqEDtTPGdgolFv5ME2D7LkjiWMajfKaQ7vo2eP8uq6V+kzvw8fbvmQ03mnNYxUURSlfP1i+mHS25bK3p+1n92ZuzWOqPLsytjFc388h1Xapqe9NuJaXv/H6+iESjcURf0v8AZ9XwdTqG37zFFY+Vq5VYfc0Ij4xrZVoixWyTPztrnd3N2XEmQM4rHrHmPpHUsZ2W4kfqLkY6KsgiymbZ9G3/l9eenPl9ievt3rWpEURfFsQcYg+sT0cZQX7F+gYTSVJ/VcKk8uf5I8cx4A0YHRvN/jfUwGk8aRKYp7UEm3NwisDb0nlZTXfgSHV7usqtMJ3rzjWkw+tm/9ntQcpv62tzqirHRBxiAev+5xJtafyLNxz1IvoJ7jWKG1kB8P/MiQxUO446c7+Drp6xozJ66iKO7vttjbHNuLDy32+K5xuYW5jFw+kvS8dMD2fP6458eE+4VrHJmiuA+VdHuL9kPhmuKVmyUseAzyXM+XGRMRwHN9S7qZTP/jEKv2pVdDkFXDT+fHA60f4Jd//sJb3d6ibURbp+P7s/bzxoY36PFdD5774zlWJa+iyKKmHFQURTtxUXE0CGoAQE5RDr8f/V3jiCqu0FLImMQx7M+yjRMy6Ay81/09moQ20TgyRXEvKun2FjodDPoI/GrZymePw0+joZyuFQ92jiGheckCNE9/t5X0nILqiLTKGHQG+sX0Y27/ucztP5fbY2/Hz1DS9aTAUsCvh3/liRVP0H1edyauncjG1I1YrO4/i4uiKN5FCME/m/7TUZ6bNNcju8JZpZUX1rzA+pPrHfsmdp5IxzodNYxKUdyTSrq9SXBduPX9kvLuH2Hthy6r6nSCqYOvo3aQbf7u07mFPPW/LRRZPKt/tytCCK6tfS2TbprE8sHLeanTS7QIa+FUJ7sgm/n75vOvpf+ix7wevPzny6w8ttLRF1FRFKWq/bPpPzHqbKvu7crYxbb0bRpHdGWklLy18S2WHFni2Pdk+ycZeM3Ai5ylKDWXSrq9TauBEPdwSfn3l+HQKpdVIwJ9eeeudgjboo+sPZTBa7+472qVFRFkDOKu5nfx3S3fMf/W+Tzc5mHqBtR1qpOZn8mCAwt4auVTdP2mK0+ueJL5++ZzIveERlErilIThJnCGNBkgKNcel5rT/D5zs+dYr6n+T080vYRDSNSFPemkm5v1G8y1I+3bUsrzBuG/7lkl1X/0TSCsb2aOcqz/zrCd3+7ruvJhBA0D2vOmA5jWHLHEr64+Qvubn43YaYwp3r5lnwSkxOZuHYifb/vy4AfBvDq2lf5/ejvZBd4zvSKiqJ4hiEthzi2lx1dxsnckxpGc/kWHljIu5vfdZR7N+rN+PjxiOJWHMWr/fbbb9x8882Eh4djMplo3rw548eP58wZ57FkMTExCCEQQqDT6WjQoAF33nkne/bs0Shybamk2xsZjHDXFxAYZSvnZXHt9olw1nXL7RM9Yrm5TR1H+cUFO/nrgPfOc60TOtpHtufFTi+y8q6VfHnzlzzc5mGahJQd9HMs5xjf7fuOsYlj6fJNF+766S5eX/86iw8t5mTuSY/sg6koivtoHtac+Dq2RhKLtDB712xtA7oMq5JX8cpfrzjKcVFxvNHlDfQ6vYZRKdXl9ddfp2/fvphMJmbOnMnSpUsZMWIEs2bNIj4+npSUFKf6ffv2Ze3ataxZs4ZJkyaxYcMGunTpQlpamkZ3oB2D1gEoVSS4Ltz7P5h9KxSdw1SQDl/dAcN+goAIp6pC2Pp3Hz59jj2pORRarDz65Sa+ebQTbaJDNLqB6qETOtpFtqNdZDvGdBjD0bNHSUxOZO2JtWw6tYl8S8k0XhJJUmYSSZlJ/G/P/wCI9I+kXW3b+a3CW9EirAUBPgFa3Y6iKB7ooTYPsSF1AwDz983n4bYPX+IM7aw9sZaxiWOxSNsA9Ga1mvF+j/fx1ftqHJlSHf744w9efPFFxowZwzvvvOPY361bN26//XY6dOjAQw89xG+//eY4FhERQadOnQDo3LkzTZo0ISEhga+++oqxY8dW+z1oSSXd3iy6A9z9BXx9N1jNkLYbZt8CDyyEoCinqgG+BmYOi+POT9aSejaf3AIzD87ayPzHbiQmouYkkY2CGzGs9TCGtR5GoaWQbenbWHtiLetPrmdnxk7HKmvF0s6n8dvR3/jtqO0BIxA0Cm5Ei7AWtAxvScuwlrQIa0EtUy0tbkdRFA9wU72baBPehp0ZOym0FjJr5yxu4Aatwypj06lNjF45mkJrIWBb/OaTXp84rQ6seLd3332XsLAw3njjjTLHGjduzPjx4xk3bhybN2/m+uuvd/keHTvaZrY5cOBAlcbqjlTS7e1ie8FtnyB/eBSBhPQkmD0Ahv4AoQ2dqtav5c+cf8Uz+NO/OJtv5nRuAfdMX8fXj9xAk9qBGt2Adox6Ix3rdHRMfZVTmMP29O1sTd/KlrQtbE/fXma2E4nkyNkjHDl7xGlEf5gpjGtCr6FJSBOuCb2G2NBYmoQ0IcwUpvpAKm5DCBEGfAvEAEeAu6SUWRfUaQd8AgQDFuA1KeW39mOzgW5A8QCIB6WUW6sjdk8mhODxdo8zavkoAObtm0eLOi0ucVb12pG+g1HLRzmeeVH+UXzW9zMi/SM1jkypLmazmT///JNBgwZhMrleZXTgwIGMGzeOZcuWlZt0Hz58GIDQ0NAqi9VdqaS7Jrj2LpKSkmi15z2QFsjYDzN62rqf1I9zqtq8ThCfPdiR+2eup8BsJfVsPndPX8f/HrmB2Mia3ZoRZAzipuibuCn6JgDMVjP7s/azJW0LuzJ2kZSZxKEzhxwfu5aWmZ9JZmomG1M3Ou0P9Q2lYXBDGgQ1KPMKN4WrhFypbuOB5VLKyUKI8fbyuAvqnAcekFLuF0LUAzYJIZZKKYtHUD0rpZxfjTF7hS7RXWgV3ordGbspsBTw85mfGcQgrcMCYE/mHkYsG8G5onMARPhF8Fnfz4gOjNY4Ms/Tdk7bS1eqJjuG7bii+hkZGeTl5RETE1NuneJjR48edeyTUmI2m7Farezbt48RI0ag0+m48847KxK2R1NJdw2RFtWNVm3bwfyHwVoE59JgVn8YMNW2mmWp5K5jTBizHuzIw3P+Jq/IQnpOAXdNW8eMB+Lo0Eh1kyhm0BlsXUjCWzr25ZvzOXDmALszdtv6f2ckcfDMQae+4aWdKTjDmfQzbE/fXuaYn8GP+kH1MeWb+Gv9X9QJqEOUfxR1AupQJ6AOkf6R+Oh8quz+lBppEJBg354DJHJB0i2l3Fdq+4QQIg2oDbheAle5LEIIRl8/mhG/jwBg/bn17M7YTavwVprGtSN9B48te4ycwhzA1lAwo/cMGgU30jQuxb3pdCXzdHz99dd8/fXXjnJMTAzz5s0rtyXcm6mkuyZpNQgeiIBv74e8TLAUwKIn4eAKuOVd8Cv5qKdzbARz/hXPQ7M2cK7QQua5Qu6dsY6377qOW66tp+FNuDeTwUSbiDa0iWjj2GeVVk7knuBQ9iEOnDnAwTMHOXTmEAezD150MZ48c55jWeUde8q2SAgEEX4RjkQ80j+ScL9wIvwiCDfZv/qFE24Kx0evknPlskRJKYvnrEsFoi5WWQgRDxiBg6V2vyaEeBlYDoyXUnr2UrfVqHO9znSr341Vx1chkUzZMIXZ/WZr9onX5lObGbl8pKOFO8gYxPTe04mtFatJPIq2wsPD8fPz48iRI+XWKT4WHV3yKcjNN9/MpEmT0Ov11KtXj6ioiz5WvJpKumuamJvgkeXwv3sh3T5P5q4FcGw99HvDlpjbH/DxjcP4cvgNDJ/zN5nnCik0W3ni6y3sS81hdK9m6HWq68Pl0Akd9YPqUz+oPl3rd3Xsl1Jy6vwpknOSHa9jZ4+RnJPM8Zzj5BTlXPR9JZL0vHTS89LZmbHzonVDfENKEnFTOLVMtQj1DSXEN4RQ31Dbtqlk29/gr7q2eCkhxDKgjotDL5QuSCmlEKLcOTGFEHWBL4FhUjpGGD+PLVk3AtOxtZJPKuf8R4FHAaKiokhMTLyyGwFyc3MrdJ4762LtwmpWY8XK5rTNTP5lMjcG3ljtcezN28v09OkUStugyQBdAI+HPc6pHac4xamrfn9v/N4VK763kJAQcnKcn+N//fMvjaIq68LYLkfnzp357bffSE9Pd9mve968eQDExcWRk5ODlJKgoCCaN29+VdetLhaLpUx8+fn5lfazqpLumiisCTyyEpY+D5tm2/blnIB5w+CantDnVYhqDcD1DWuxYGRnHpq9kUPpttaO91ccYOORLN67px2Rwa4HUyiXJoRwdBUpHqxZTEpJdkE2yTnJ/L7hd8Jjwkk9l8qp86dIPZdK6rlUTuedRnJ584RnF2STXZDNoexDl1XfoDPYEnFjiCMxDzIGEWQMItAYSKBPoG3bJ5BAYyBBPrb9xft89b4qaXdTUspe5R0TQpwSQtSVUp60J9UuJ9IVQgQDvwAvSCnXlXrv4lbyAiHELOCZi8QxHVtiTlxcnExISLjie0lMTKQi57m7438fd8zXvejsIh7q/hB1Alz9nVQ1fjn0C9P+nEaRLAIg3BTOjD4zaFqraaVdw1u/d1Byb0lJSQQFeddYqNGjRzNw4EDeeOMN3n77badjhw8f5t1336Vdu3b06mV7zAgh8PHx8Zh/h5ycnDKxmkwm2rdvXynvr5LumsroD7e+Z0uyfxkL59Jt+w8uh0+WQ6vboOszUKctjcID+OHxzoz6ejN/HsgAbEvG93tvNa/c2oqB19VTCVYlE0IQagol1BRKRkAGCa0TytQpshSRlpfmlIRn5GWQkZ/htJ2Zn1lmqsNLMVvNnM47zem8ii2SZNAZHIl4oE8gAT4B+Pv442fww9/g79hOzU4lJSkFf4P9WKk6fj5+TvtV//VqsQgYBky2f114YQUhhBFYAHxx4YDJUgm7AG4DLv4RjOLSyHYj+WXvL6Sb08ktyuWlP1/i016fVvniM1JKZu6Yyftb3nfsi/KPYmafmcSExFTptRXPkJCQwMSJE3nllVc4cuQIDzzwALVq1WLz5s1MnjwZq9XKN998o3WYbksl3TVdq4HQuCus+A9snAnFLae7f7S9GnSCjsMJbXkLX/zrBj5YsZ/3lu9HSsg8V8job7by45YUXr2tDfVr+Wt6KzWNj96H6MDoS84gYLFaOFNwxpaI52eQkZdBVn4WZwrOkF2Q7fy10NYifrG+5pfDbDWTVZBFVkHWJev+vOHny3pPg86ASW/CV++LyWD7WnrbpDfha/Ats126XHx+6W2j3oiPzgej3ohRZ8RH7+MoF3/ViRqzeO9k4DshxMPAUeAuACFEHPCYlHK4fV9XIFwI8aD9vOKpAecKIWoDAtgKPFbN8XsFP4Mf94Xfx/un3kciWXdyHZ9s+4Qn2j9RZdcssBTw+vrX+WH/D45914Rcw8e9PqZeoBrHo5R4+eWXiY+P55133uGhhx5yLP0eFxfHggULqF+/vsYRui/Nk24hRD/gPUAPzJRSTr7guC/wBdAByADullIeqe44vZpfqG0Wkw7DYOUbsPeXkmPJ62wvYyD6Zn0Z0/JWOt/flv/76RgpZ2yJ2cq96fT47yoe7BzDqIRYQvxVi6Q70ev0tgGVfuGXfU6+Ob9MQp5blEtOYQ65RbnkFl6wXZRDbmEuuUW5nC08i9lqrvT7MFvN5Fpt16huBmFwmYz76Er2OfbbE/es9Cy2b97OU9c/Ve3xVpSUMgPo6WL/38Bw+/ZXwFflnN+jSgOsQWJNsQxvO5wZO2YAMG37NFqEtaBXo3J7B1VYSm4KTyc+za6MXY598XXieaf7OwQbgyv9eorn69evH/369XOU77//fhYsWMDx48edku6LDbqsiTRNuoUQeuAjoDdwHNgohFgkpdxdqtrDQJaUMlYIcQ8wBbi7+qOtAeq0hXu/hhNb4M/3IOkn20qWAIW5sPN72Pk98Qj+iGzNhqCWzEsJJ0k24oA5mul/HOKbDcd4sHMMQ2+MoXZQDV0WWEr7ywLSantdzjnl0FkKoPB8ccVKCLCkK5BEIiVYpa13uJTC1k9cQjABBPn6U99YDxksbHWkLQSJxCptH0dLLuhaJCWF1kJyi3I5bznPuaJc8i355JnP27/mkWfJI9+cz/6j+wiPCifPkmfff548s+1Ynvk858155NuPuZr/vLqYpRmz2UweV/YJQM7xHI9KuhX3MqrdKHac3sG6k7Zu88/98Rwf9/qYTnU7Vdo1Vh5byUt/vUR2QbZj361NbmVi54lq1iPlsn3++eccP36cAQMGsGbNGlq2bHnpk2ogrVu644EDUspDAEKIb7DNE1s66R4ETLBvzwc+FEIIKS+SpShXp157GDwbck7B5jmw7RvILD0jmESftpMb2cmNRtueQqknRUZw3FKb43/UZu7qCBo2aEi7ZjE0btAA4VcLjIFgMILet+SrzmBPSqU9QZUlZasFLIVgLij1tQDMhU5fI09tga0n7MeLbHUthVe2bTW7Pi6tYLUnzsVJtLVUMu1UvoIk+wp0BVhdqW/pIOwvTTtPXEavXwkUAfk6QYEQ5AtBgdCVbOuK95V8LRDigvpljxUK+wtBkX27SFCyjaDwKmbpsaTuu3QlRSmHXqdnStcpPPDrAxw9e5QiaxFPrXiKt7q+RbcG3a7qvbMLspmyYQo/HfrJsc8gDDzT8Rnua3GfGqejXBGj0ei1s9FUJq2T7mgguVT5OHBDeXWklGYhRDYQDlRshJdy+YKioNtz0PVZSNsNuxfCgeW2lvALWh2NwkJjcYrGpaeSOmF/VbFWAElVfx1FOwLbHHRGq72pHbCtQF71JGCmJBEvTsyLk3WzEBTay051gNyLT3OtKJcUZgpjeu/pDP11KGnn08gz5/HUyqcY22EsQ1sNveLxBmarmQUHFvDRlo/IyM9w7I/0j+S/3f5Lu8h2lX0LiqLYaZ10Vxo15+vFVcq9ic7QtDP6xucJyd5N8Nl9BOYeIeDcYfzyXc4sVmNZpcCKwIIOEJfVKaRMN42rrOfKxSIp79jFrlaR97uY8mO42HVc05U/xfQVEYAP4CMl/lf4Ads+Ib32maJUn3qB9fisz2c8tuwxUnJTsEorU/+eyqrjq3iu43O0CGtxyfcotBTy6+FfmbVzFgezDzod69+4P8/HP0+oKbScsxVFqQxaJ90pQINS5fr2fa7qHBdCGIAQbAMqnag5Xy+u8u+tv3OxIBeyk+HMMWTWUVKTD5J8IoUzGWkEWnOoJXIxUYBRmDFShC+2r3qsSCFA6GwfZwodovil04HBF2EwIvS+YPAFvbHkq307LTOb2nWiMeuMmPGhSPhQiIFCqSfPouecRcc5s+2VUwQ5RYKzRYLsAsGZAsgqgHMWHYXSQBG2VyEGzOixoENKW/JsdbxsZUnxfuE4Vly+eKoKRoOOQF8Dgb4GAnwNBPrqCfQ14O9rwGTQ4+ujw2TQY/LRcfL4MVo0vQaTjx5fgw6Tj22/r8FWNuh1GPQCg06g1wl89DrbV50OvV7gY99v0Osw6AQGvUAvbPu0/gjZLf/PlZdYl7Pf1gdelqmS+Eci3bom0Myg9WNW8QYxITF81f8rnlz+pGMxrI2pGxn802C6RHehf5P+xEXFEeUfhRACKSUZ+RnsPL2TVcdXseLYCjLzM53eM9Ivkn93+jc9G5YZO6tUEiml5s9ZpeIquyez1r8NNgJNhRCNsSXX9wD3XVCneN7YtcCdwArVn9sN+QZCZEuIbIkA6t4AdYH8IgvLk9KYn3SKxH3pZJ4rrNDbG/U6fH10+Bp0joF/VvvXgiIzhcmXfo/KZtAJagUYqeXvQy1/I2EBRkL9jYQF2Mq1/I3UCvAhyOTjSLCLk2yj4fI/Ek5MTCWh2zVVeCeKk/J+QZazX5SzrdMZ0KuEW6lEEX4RfHHzF3yy7RM+2/mZY/791SmrWZ1iG/hh0pvwM/hx3nyeAkuBy/fxN/jzcNtDknG0AAAgAElEQVSHGdpqKH4Gv2qLv6YxGAyYzWZ8fNSAVE9lNpsxVOJzXNPfCPY+2k8AS7FNGfi5lHKXEGIS8LeUchHwGfClEOIAkIktMVc8hMlHz4Br6zLg2rpYrJIdKdn8fSSTLcln2HrsjGPawUsptFgptFipqsVjffTCKVG2fTUS5m8k1N+HsACjPcG27asVYEukVQuGoijVyUfvw1PXP0W/xv34aMtHrEhe4XQ835JPviXf5blR/lHc0+IeBjcbTIhvSHWEW6OZTCZyc3OpVauW1qEoFZSTk+NyufuK0rwZRkq5GFh8wb6XS23nA4OrOy6l8ul1gnYNQmnXoKTf4JnzhRw6fY5D6ec4lJ5L6tl80nMKOJ1byOncAnLzzeSbLRebUc/B5KMjwGjAz6h3fA3x86GWvw+h9uS5lv1rqH9JC3Wov0qgFUXxLM1qNeO9Hu+RfDaZxYcXs+7kOvZk7nGax97P4EezWs24rvZ19GzYk+tqX1flq1oqJWrXrs2xY8fw9fXFz89P/Y7xIFJK8vLyOH36NA0bNqy099U86VZqtlB/I9c3NHJ9w/JbAqSUFJitFBRZKbBY0Alhf9mWS//rzzX06ZGA/iqmdlMURfFEDYIbMOK6EYy4boQtUTDncd58Hn+DP34GlehpyWQyERUVRWpqKgUFrrv6eJr8/PxKbfl1N6Xvz9fXl6ioKO9q6VaUSxFC2AcP6rHNI+HMzyBUwq0oSo0nhMDfxx9/H3+tQ1HsQkJCCAnxnq48iYmJtG/fXuswqkxV35+ma2IoiqIoiqIoSk2gkm5FURRFURRFqWIq6VYURVEURVGUKqaSbkVRFEVRFEWpYirpVhRFURRFUZQqppJuRVEURVEURaliwhtXVBdCpANHK3BqBHC6ksNxF+rePJc335+6t7IaSSlrV3Yw7kw9s13y5nsD774/dW+eqyL3d9nPbK9MuitKCPG3lDJO6ziqgro3z+XN96fuTbka3vxv7M33Bt59f+rePFdV35/qXqIoiqIoiqIoVUwl3YqiKIqiKIpSxVTS7Wy61gFUIXVvnsub70/dm3I1vPnf2JvvDbz7/tS9ea4qvT/Vp1tRFEVRFEVRqphq6VYURVEURVGUKqaSbkAI0U8IsVcIcUAIMV7reCqTEKKBEGKlEGK3EGKXEGK01jFVNiGEXgixRQjxs9axVCYhRKgQYr4QYo8QIkkIcaPWMVUWIcT/2X8edwoh/ieEMGkd09UQQnwuhEgTQuwstS9MCPG7EGK//WstLWP0JuqZ7dnUM9szedNzW6tndo1PuoUQeuAj4GagFXCvEKKVtlFVKjPwtJSyFdAJGOVl9wcwGkjSOogq8B6wRErZArgOL7lHIUQ08BQQJ6VsA+iBe7SN6qrNBvpdsG88sFxK2RRYbi8rV0k9s72CemZ7GC98bs9Gg2d2jU+6gXjggJTykJSyEPgGGKRxTJVGSnlSSrnZvp2D7SEQrW1UlUcIUR8YAMzUOpbKJIQIAboCnwFIKQullGe0japSGQA/IYQB8AdOaBzPVZFS/gFkXrB7EDDHvj0HuK1ag/Je6pntwdQz26N5zXNbq2e2Srr/n737jpOrKhs4/jt36vZsy24a6QkE0iAJhBJCR6QEVEBAQaQp6PtiQQTFVyzwyisIgiiCVAWlJopCCiyhhvTeN5u+2d53dqec9487e2dm+25mdndmn6+fcc45t52bhLvPnnuK+TDbH5Y/QAI94MIppcYAM4EV/VuTqPodcBcQ6O+KRNlYoBR4Nvga9mmlVEp/VyoatNYHgf8D9gGHgWqt9eL+rVVM5GmtDwfTxUBef1YmgcgzO77JMzsODZLndsyf2RJ0DxJKqVTgdeC/tdY1/V2faFBKXQyUaK1X93ddYsAOnAg8qbWeCdSTIN0Tgv3kLsP8ITUcSFFKXde/tYotbU4TJVNFiW6TZ3bcSdhnNgy+53asntkSdMNBYFRYfmSwLGEopRyYD++/aq3f6O/6RNFpwKVKqSLMV8xnK6Ve6t8qRc0B4IDWuqWF6zXMB3oiOBfYo7Uu1Vp7gTeAU/u5TrFwRCk1DCD4XdLP9UkU8syOX/LMjl+D4bkd82e2BN2wEpiolBqrlHJiDgxY1M91ihqllMLsY7ZVa/1wf9cnmrTWP9Zaj9Raj8H8e3tPa50Qv3lrrYuB/UqpycGic4At/VilaNoHnKKUSg7++zyHBBpwFGYRcH0wfT2wsB/rkkjkmR2n5Jkd1wbDczvmz2x7tE8Yb7TWPqXUHcC7mKNx/6K13tzP1Yqm04CvARuVUuuCZfdorf/dj3US3fMd4K/BwKIQ+EY/1ycqtNYrlFKvAWswZ2pYS5yvcqaUehmYD+QopQ4APwMeBP6hlPomsBe4sv9qmDjkmS0GsIR8ZkPiPbf765ktK1IKIYQQQggRY9K9RAghhBBCiBiToFsIIYQQQogYk6BbCCGEEEKIGJOgWwghhBBCiBiToFsIIYQQQogYk6BbCCGEEEKIGJOgWwwYSindjU9RcN/nWtIDhVLqMaXUv/rp2guUUkeCS0cLIUTMyTP7qK4tz+xBSObpFgOGUuqUVkVvAuuB/wkra9Jar1VKjQfStdZr+6p+nQnWZytwqtZ6VT9cX2EuVrBQa/2zvr6+EGLwkWf2UV1fntmDkATdYsAKtop8FA/LBCulfg+corWe3Y91+DbwC2CE1trTX/UQQgxO8szucR3kmT3ISPcSEZdav6pUSo0Jvsq8TSn1gFKqWClVq5R6SSmVrJSaoJR6VylVp5TapZS6vp1zTldKLVJKVSqlGpVSHyulzuhGXVzAdcDfWpWnKqV+r5Tap5RqUkqVKKWWKqWODdvHrpT6sVJqW3CfQ0qp3yql3K3OlaKUelAptTu4X7FS6nWlVF7Ybv8AhgBXdPfPUQgh+oI8s+WZLcDe3xUQIsp+DBQA1wNTgN8AAWAm8Gfg/4BvAc8qpVZprTcDKKVOBD7EfN13M9AA3AYsVUqdqrVe3ck1T8F8cH7YqvwR4FLgHmAnkA2cFty3xUvAJcD/Ap8Ax2G2fIwBvhSsmxNYAkwHHgQ+AzKAC4BM4AiA1rpMKbUVuJBWP0yEEGKAkme2PLMHD621fOQzID9AEfBSB9ueA4rC8mMADbzXar83guXXhZVlAj7gZ2FlyzD79znDymzBsre6qOePMH9IOFuVbwIe7uS4M4J1+3qr8muD5TOC+RuD+Uu78Wf2IrCjv//u5CMf+Qy+jzyz5Zktn84/0r1EJJr/tMpvC36/21Kgta4ESoBRAEqpJOBM4FUgEHx9aAcUsBSY18U1hwM1WuvmVuUrgRuUUvcopWYppWyttl8INAOvtVwzeN3Fwe0t1z0fKNZaL+qiHgClwfoIIUQ8kGe2PLMHDQm6RaKpbJVv7qS8pQ9eFmYLyU8Bb6vPHUCmUqqz/1bcQFM75d8B/oTZ6rESKFFKPaKUSg5uHwo4gfpW1ywJbs8O+z7YyfXDNYbdlxBCDHTyzJZn9qAhfbqFgCrMV41PAC+0t4PWOtDJ8eVE9vlrOaYOs7/ij5VSo4EvY/bva8Z8vVkOeDBfWbbnUPC7DDihy7swZQXPK4QQiUqe2SIuSdAtBj2tdb1S6kPMQS9runhYt2cb4FRKjdRaH+jgGnuB3yqlriX0MH4H80GeobVe1sn5FwNXK6Uu0Vr/s4u6jAW296z6QggRP+SZLeKVBN1CmL4HLAfeVUo9AxwGcoATAZvW+u5Ojl0e/J4DWA9wpdSnwCJgI1CH2QdxOvA8gNa6QCn1Mmb/wIeBzzFbb8YAFwE/0lrvwBwtfzPwslLqAWAFkIY5Ev53WuttweupYB3+cFR/EkIIMfDJM1vEHQm6hQC01muUUrOBnwGPYU7vVAqsAf7YxbFFSqnPMaeReiNs03LgSuBuzP/WCoE7tdaPhe1zHWY/whuBezH7GRZhDiJqmVbKq5Q6P1i3W4Lf5cDHQEXYuU7FHOX/Ss/uXggh4os8s0U8khUphYgCpdQNwKPAMK11Qz/V4UngBK11l4tDCCHEYCbPbNEfZPYSIaLjJcxBNN/uj4srpfIxF5e4tz+uL4QQcUae2aLPSdAtRBRorX3ANzBXResPY4Dva62Xd7WjEEIMdvLMFv1BupcIIYQQQggRY9LSLYQQQgghRIwl5OwlOTk5esyYMT0+rr6+npSUlOhXaACQe4tfiXx/iXxv0Lv7W716dZnWOjdGVRqQ5JndViLfGyT2/cm9xa9YP7MTMugeM2YMq1at6vFxBQUFzJ8/P/oVGgDk3uJXIt9fIt8b9O7+lFJ7Y1ObgUue2W0l8r1BYt+f3Fv8ivUzW7qXCCGEEEIIEWMSdAshhBBCCBFjEnQLIYQQQggRYxJ0CyGEEEIIEWMSdAshhBBCCBFjCTl7iYhPDc0+yuuaqWxopr7JT5PPj8cboMnnp8kXwFAKQ2F+G2baYTPYWeYnbW8FyU47yU4bSU6bmXbYMAzV37clhBAC8Pg8lHvKqW2updBTiPOQE4/Pg8fnwad9AChCz2ylFC6bC7fNjdvuDn3b3aQ4Ukh3pmM3JIwR8UP+tYro0RoCflAKUOa3igx6j9R42Higmt2ldRSVN7C3vJ79lQ2U1TbT6PX3/tqrPm1TZChIT3KQEfZJT3IwpFVZRpKDjOTIfKrLjlISsAshRHc1eBvYVbWLfbX72F+zn321+zhQe4CyxjIqPBU0+FqtuL7k6K+Z4kghw5lBuivd+k53ppPlziI7KZucpByy3eZ3TlIOKY4UebaLfiNBt+iarxkqCqF0G5TvhJrDUHcEag9DQwV4G6C5wfzWbQPnAAbNykW9dtIUcDIKFzk4mY6LBu2iATd12k29PYl6XNTrJOpxU6/d5jdu6nUSdbhp0G7zGze+Lv75BjRUNXipavD2+JZthiLdbWdIsrNV4G4nI8nBkCSnFcS3DtxTnDZ5qAshEpo/4GdbxTZWHVnFlvItbK3YSlF1ERrdp/Wo99ZT763nUP2hbu3vsrmsQDw7KZuhyUMZmjyUvOQ88zslj7zkPFIcibsAjOg/cRF0K6UuBB4FbMDTWusH+7lKia25Hgo/gL0fw77P4PB6CPQ8cG1hEMCtG3HTSHYURxF4lQOPSqZeO/EYKTTgpla7qQ24qQ24qA64woL3JBpwURcR0JtBfoN248VOM3Z82PBhwx+AygYvlb0I2O2GIsVlJ9VldndJdtlJCXZ5SXW1zttJdtlIdtpw2my47AYuh4HLbsNpN3DZDYrrAxysasRlN6wyp82QwF4I0adKGkp4f9/7fHLoE1YeWUltc22PjrcbdrLcWWS4MvDWe8nLyrO6izgMB0BE0B7QAZr9zXj8HqsbisfnodHXSL2vnpqmmh4H+U3+Jg7WHeRg3cFO90txpIQC8bDvvJQ8K1DPcmdhKBkaJ7pvwAfdSikb8ARwHnAAWKmUWqS13tK/NUswXg9sXQRbFsKuZeBr7NVp/BigNTYV+9YOh/bi0NWkAfhLIzcaHNUwYa+24Q0G4V7C0tqGDzte7PhRaBQBFBqDgJVWaL8iUG8QqFdozNb+ln3NNNYx4fxAQ/DTIhPY9FnbOhpKWT14FGb/R4NQr56WPBHlKrhveM8fFfb/YSXB8+rgjzUNBBQE0KAggJnWKniPSgfvNfhRGoUmEDyndY5gTgNN3mYWrXVaPzbDt2lAq9CPVB32IXhtAK1aynXEeXTrc0UcG9zWwbGE7asj0q3qE/bvXLc6xjxZekKv3iYSX1ljGf8u/DdL9y1lXcm6ToNcQxmMyxjH2IyxjEobZX3ykvPISsoizZFmNRZEY2XDgA5Q562juqmamuaa0LenmgpPBeWecsoayyhrLKO8sZxyTzmN3fzZVu+tp7C6kMLqwg73sRt2hiYNjQjEhyYNpay+jJTiFIYmDyU3KZdkR/JR3adIHAM+6AbmALu01oUASqlXgMsACbqjoWofrPgTrPsrNFZ2vF/GKMidDDmTYcgoSMuHtGFsrnbwwqoS3tlRS712tenyke62ccb4TOaNTWX2CDej0w1svgbwNga7pdQHP3XQVGd+R6Troam21T710FwLOtBBZY+eQ/lx0E4f8yg3LnuBesOgzlB4lEGTUniUokkpmgwVkbe+g+VeFF4FPqXMD2baG5EGH8GyYNqnwKsUAcCPCgbSEEDhDwahEeXSot5r45p61hIoxEAQ0AE+O/QZr+18jff3vW8NcmwtNymXOcPmMCN3BsdlH8ekzEkk2ZP6rJ6GMkh3mn24u0NrTYOvgfLGUDBe0lBCSUMJxQ3FVvpI/RGaA81dns8X8HGo/lC7XVuef/d5K53mSCM3OdcKzHOTwtLJueQl55GdlG219ovEFQ9B9whgf1j+AHBy652UUrcAtwDk5eVRUFDQ4wvV1dX16rh40PrenE3ljN77KsMOL8Fo54Fan3wM5dknUp0xheqM4/A5wh5qHig64ueNnVVsKGsJTEP939KdMDvfzpx8OxMzDQzVCL5G9u2FfW2ulBT85ISKnMFPZ7TGCDRj8zfSVFNOmtvA7mvE5m/E5vcEv81P23JPWLmZVtqH0n6MgA9Fz4L5JgVVho0qm0GlYVBlswW/DaoMGzU2gzqlgsG1Qb2hzG+laDLk1WQi05CwzxSReLx+L/8q/Bd/2fQXimqK2mw3lMHsvNmcdcxZzB0+l7HpY+Oqm5tSihRHCimOFI5JP6bD/bTWVDdVc6ThiPUJD8hbyrrbvabWW0ttdW2nreYKRZY7ywrEhyYPjeh7nu3OtgaHpjpS4+rPXYTEQ9DdLVrrp4CnAGbNmqV789oqGq+7Birr3nzN8MljsPIh8HkidxpyDJz4dZiygJScibQ3jKS0tokH/r2VN9a27Q93xsQcrp87hvmTc7Hb+i6YLCgoYHY0/94CAQj40P5mKhtKOVi7nyP1xRxpKKGksTT4KaekqZLSpkrq/Z6uzxnnFGBgoFDm/ytl5cxvZU7lGL5Py/+CfVVU8P9VWNrr9eJ0OiO20Wo/gtcKlQfPptqek2A9WuqsWm9Vra9C5LlV6zoQcZ2IOoT90Gt9zpacoYyEfaaIxOENeHltx2s8s/EZjjQcabN95tCZXDr+Us4+5myy3Fn9UMO+pZRiiHsIQ9xDmJw1ucP9GrwNlDaWWoF4aWMpJQ0lbN67GVLMPvAljSX4Au2/KQin0ZR7zC4wWyu2drqv03CSnRQKwsMD8mx3NllJWWS7s8l0Z5LhypAW9AEkHoLug8CosPzIYJnoqYNr4K1vmbOQhDtmLpz+PZhwDhi2dg8NBDQvrdjLQ+9up9YTeoAoBQtmjOD2s8YzYWhaLGsfM9VN1eys3ElRTRH7a/dHfOq99TG9tqEMq+UlyZ6E2+bGZXPhsrusdFVZFaNHjDbnq7W7rXlrHTYHDsOB3bBb33bDjl3ZrXS728P2M5SBoQxsypxxxaZsEWUt6Vi1qiTyL7ogrdxiYNNa8/7+93lk9SNtWrZTHaksmLCAL038EhMyJ/RPBQe4ZEcyox2jGZ0+OqK8oCH0XAvoAFVNVZQ2lFqt5SWNJZH5hhIqPBXdHhTaHGjmcP1hDtcf7tb+qY5UMlwZDHENYYhrSMdpdyidbE+W1vQYiIegeyUwUSk1FjPYvhq4pn+rFGe0ZuT+hbD8xchZSPKnwrk/h/Fnt5lPO1xxtYfvv7qOj3eVR5RfeHw+3z9/EhPz4iPY9gV87Kraxdbyreys2smuyl3sqtpFaWNp1wd3wq7sZquIawiZ7kzz22W2MGS6M0l3ppPqTCXVYX6SHcmkOlKtQLurB1tBQQHz584/qjoKIQYBrc3pXEu3Q80hqD0EdSXmeBhvo/nxe8HmYB8+7vcdZEUgsotElj2Zrw2bx1VjLyYtcyyk5vXTzSQGQxlkubPIcmd12mruDXgpbyynpMEMyI80HLHmNy/3lFPRaH6XN5bj6eHb1TpvHXXeui5nbAlnN+ykO9NJc6aR5kgj1ZlKmjONuvI6Vq1cZeXDt7f8rEtzppFiT8HWQSPeYDbgg26ttU8pdQfwLuaUgX/RWm/u52rFD28jvHkrE3YvDJU5U+Gse2HOLWDr/J/AO5uKufuNDRFzXY/NSeHnlx7PvEm5sap1VByuO8z60vVsLNvIxrKNbC3f2uOHVbI9mZFpI8lPyW8zn2tLOt2ZLi0CQoi+F/DDoXVQ+D4UfQTFG6GhrNNDfMBL6Wk8npkRMaYkNRDg5qpqrqnZj3vnNlj+VOgg9xBz8HxqnvlJy4PU/FBZy7crrdMGHNExh+EgPyWf/JT8Lvdt8DZYs7G0BOKtA/MKTwVVTVVUN1X3au50X8BHhaeCCk9Fm22fbmm7GF17ku3JJDuSSXGkkGxPJsmeZKYdyda28O+Otllvge2uuO8qM+CDbgCt9b+Bf/d3PeJOfRm8fDUcWBkqGz4TvvwsZI3t9NBAQPPbJdt54v3dVplS8K0zx/Nf507EZR94v8GWNJTwefHnrCxeyYrDK7r9W73L5mJcxjjGDRnHMWnHREx1leXOkoBaCDFwaA2H1sCGf8Cm16G++2/q9ttt3J2bwwa3yyoztObK2jq+VVlNVqCDQeSeKvPTumtiKz5bEvXOHGodOdTYs6ixZVNpy6JSZVKmMqkysqm2Z9FgS6e0zMOrB9cA5s8Wcw2C4FoFLR+HDaetZe0Cg2RncO2D4HeKyxZR5rQPjoHpyQ4zGB2VPqrLfQM6QG1zLVVNVVYQXtVURZUnMm+VB9M9baBqT4OvgQZfA2WNnf8i2BN2Zbe6X1rdLe1uqzumle5on2C50+bEZXOFvg0nTpuTEm8J/oA/Zq30cRF0i16oOQTPXQwVoaCZObfA+b8Ce+dTg9Q1+fjvV9aydGuJVTZiSBIPXzmdk8dlx6rGPeYP+NlQtoGFlQt55K1HOh0Z3mJYyjBOyDmBSZmTmDhkIhMyJzAydaS8BhOim7parEwp5QJeAE4CyoGrtNZFfV3PhBPwm2spfPyYGXR3xJECQ4+DzNGQNsz8uNJYUr+X+/Ytos7fZO06KSmP+0dcwPFGMjRWgafaDK4bK81uKXVH0HUlqHZWGm6P3d9IRuN+Mhr3d7pfk3ZQThrVlalU6lSqSKXK+k6hgjSqdQpVOpV6IlcjbsRFR3O32g0VCspdNlKcdpKcNmsxMjNQN8uSHTaSnDbcDhtJVtqIzNsj93HYVNw1whjKIMOVQYYrg9GM7vqAII/PQ523jprmGuqa66htrqXWW8vqjasZPna4mQ+WhW9vKY/VeCif9uHz+mI63uoC7wVkuDJicm4JuhNRbXGrgFuxc8I3mXjRQ10eWl7XxPXPfs6mgzVW2ZmTcnns6plkJPf/ax2v38vHhz5myd4lfHjgQyqbOp5bPMmexLTcaUzLmcbUnKlMzZ1KTlJOh/sLITrXzcXKvglUaq0nKKWuBv4XuKrva5tAdi2Dd++F0nZmtUjNM8fljD0TRs2BzLEQ1m3EF/Dx21W/5aU9r1pldsPObdNu48apN7Z5Xe8PaLYeruGzwnJW7KlgXX0ZgcYKhqoqclUVQ1UVQ2lJVzJUVZGH+e1W3VvB16W8DKeC4apt14WuBLQyVxW2VhZ204CbJu2gGQdNfjtNjQ6aGxw0ESzDQbO2W+labFRiw4+BXxvmdzAfwMBHZJlf24JrF9hw2u24HAYOuw2n3YbDZsNmGDhsCpvNwG4zqK2p4eM9pTgMA7tNYTNs2G3mMXYD7DY7dpuyjjUMMAxz0LphKAzDwGYEZ4QKfmyG+ddqKIWtpdxQ2AwVHASvMKyF0VpmY4pMQ/ivKypiYbWWRdOsxdKCOyYpSFZO8shGqWyUv4KT0k8k7DTt8ms/Hn8TDf5GGn0eGv2e0Hfw0+BvjMz7GvG02t7g99Dkb6Ip0EyTv8laFC2WHDEMjSXoTjT15fD8JaGA27DDl5/lYEk6E7s49FBVI9c9s4LC0tBvkLfOG8ddFx6Lzei/3+4DOsDakrW8Xfg2i/cuprqput39nIaTGUNnMDt/NnPy5zA1ZyoOW///oiBEAunOYmWXAf8TTL8GPK6UUlrr2P+0TDS1xfCvO2F7q96VNheccAVMvxrGnNHhrFO1zbX88IMf8vGhj62yEakjeGjeQ0zNnWqVNTb7+WBHKYu3FPPetpKIMTymDMp1Blt1ZEupUjA0zUVumovMJAfD3c2MctSSZ1SR6S8n3VdOmq+c1OYykprLcHtKcXtKsPsa6C1DadJoJI3GqC9W1m3+4Kepk31iO/FVv7kAYF3/XFtjjknwBBeJMxeMM6x8yyJy1scqM6yypuBx3uBic80Kmq20+dFeH7i6qk3vSNCdSHxN8Mo1ULbDzCsbfOU5OO4SKCno9NADlQ1c9afPOFhlLpFrKPj15VO5ek7HCwjEWlljGW/sfIPXd7ze7opfADlJOUyyTeKrc77KycNO7tPV0IQYhLqzWJm1T3AgfDWQDUR07JQFzTqXtm8Z3o+uw+ELzS7iN9wcGHkxB0Zegtc5xFxtbN+H7R5f7ivnjyV/pNhbbJVNS5rGtZnXUr65nPf1+2yrCLD8oJfVxX6aO1kTzG2DkWkGo9IMRqYZ5CUrcpIMspMUDkMRikLBXCgtBRhBA9AAtJ752+ZrpLm6mAxnAIe3FruvFoe3Lixdi91Xh8Nb13bBs26sFCkSkwIcgENr0vwtv8N3r+tTTyz55FMcTnfUzwsSdCcOrWHhHbD/s2CBgi89bQbcXThS4+Hap1dYAbfDpnj06plcNHVYDCvcPq01q46s4h/b/8HSvUvbXX54WMowvjD2C5w3+jymZE9h+QfLmT9qfp/XVQjRe7KgWQcCflhyHxQ+Hlk+4zps5/yU0Wn5XfbMLawu5BeLf0GJNzQu59Zpt/LtGd/G4w3w95X7ef6TIorK2x8sl5vm4pRx2Zw8NotTxmUxLicVI8pvOwsKCpjVm787v8+cArG5PvgdTPuazQXf/E1mA5SvCfzBstbb/OPIbfQAACAASURBVF7QfvPPOuCHgC+Y91mLo4XywX20n4Dfh9YBAgEd9q3RaHTA/EZrGhsbcLncaG3mNTqU1hrC8wBao4LHEuw+Yb0W0qESHbYh/LWRDtsQ8Tqp1bulnrxq0m0SwTroUNeTnpyv715KHN2VNJozTj8dd3JqlOoTSYLuRPHxo7DxH6H8+b8wXz92obyuieueXsHecvN1n9Nm8NTXT2L+5KGxqmm7/AE/y/Yt45lNz7ClfEub7enOdC4YcwFfHPdFZg6diaEGxyh1IQaY7ixW1rLPAaWUHcjAHFApuuKpgdduhF1LQmXpI2DBH2Dc/G6dYnvFdm5Zcos11ZvDcHD/afdzRv4F/H7Zbp77ZA+VbbqPwIShqVxwfB4XHJ/P1BEZA3fAoM0OSUPMTx9r+anT1bD7VYn4y2BQQv6iG6agoICRMQq4QYLuxLBvBSy7P5Q/6QaYe0eXh3m8fm56YRU7S+oAsBmKJ649sU8Dbm/Ay6Jdi3h287PsrdnbZvvMoTO5cvKVnDf6PFy2GHWyEkJ0V3cWK1sEXA98CnwZeE/6c3dDYxW8dAUcXB0qm3wRLHiy2wHm5vLN3Lz4ZmqbzS4pSfYkHj7zUXYU5XPmS++36aud5razYMYIrpo9ihNGxGa2BiFEiATd8a6hwmwZaZnSaeQcuOj/ulygIBDQ/ODV9azdVwWYuz9y1QzOm9I3q48FdIB39rzD4+seZ39t5PRSLpuLy8ZfxpWTr+x0BS8hRN/qaLEypdT9wCqt9SLgGeBFpdQuoAIzMBedaaiAFxfA4fVW0d5jvszoq/4cMRNJZwqrCrltyW1WwJ3mSOPmyb/mJy97KGr19nBkZhK3zBvHV04aRZJTpksVoq9I0B3v/vlfUHPATLuHwJf/At2YseORpTv414bDVv6+i6dw6fThsaqlRWvNRwc/4tE1j7K9cnvEtjRnGl899qtcc+w1ZCcNnPnAhRAh7S1WprW+LyztAb7S1/WKW80N8NcvRwTcfPG37KmfwOhuBtwH6w5y85KbqWoyG1HSHOlMUT/k569GTqFxTFYyd543kUumDcduky56QvQ1Cbrj2ea3zMUSWix4EoZ0vULVO5sO8/v3dln5r88dzQ2njolBBSPtr9nPA58/wIcHI0fbpzvTufGEG7n62KtJcaTEvB5CCDEgBPzw+k1hXUoUXPoYnPh16OasLBWeCm5ZfAslDeagSafhpnH/N1haGWp8SXfb+e45E/na3NEDcjVhIQYLCbrjVUMF/PsHofyJX4djL+rysD1l9fzw1Q1W/sxJudx38ZSYDppp9DXyzMZneHbTszSHTfeUZE/iuuOu44YTbiDdmR6z6wshxIC0+Cew/e1Q/qKHzGd5NzX7m7nz/TvZV7sPAAM7VXuuw98Qmnnq0unDue+SKeSkypgYIfqbBN3x6t17oL7UTKcNg/N/2eUhHq+fb720mtomcxq+UVlJPHb1zJi+Zvz88Ofc98l9HKwLTXCgUFwx8QrumHmHrBAphBicNr4Gn/0hlD/1OzDn5m4frrXm/k/vZ01JcEl4rag/eDX+hgmAuWjNg1+aytnH9s04HSFE1yTojkd7P4X1L4fyFz8C7q5Hnv/iX1vYVmwOsnHaDP5wzUkxW9q9wdvAI6sf4ZXtr0SUn5B9Aveeci8n5JwQk+sKIcSAV77bHI/T4tiL4dz7O96/Hc9tfo6FuxdaeU/JF/DVms/VMyfl8vCV08mW1m0hBhQJuuNNIADv3B3KT7kMJn+hy8M2lPr46+p9Vv5nl05h6sjYTBG1tmQt93x4DwfqDlhl6c507jzpTq6YeIXMsS2EGLy8HvjH9eaiLgCZY83xON0cNAmw4vAKHln9SOiUVSfhrTgDpeCHF0zmtnnjo76YjRDi6EnQHW/W/w0OrzPTdne3upVU1jfzl02hvtQXHp/PNTFY3j2gAzyz8RmeWPcEfh1amvXMkWfys7k/Izc5N+rXFEKIuLL8N3Bko5m2OeHK58Hd/TEtZY1l/Gj5j1rWJ8TXMAZP8eUkO+08dvVMzu2jaV+FED0nQXc8aaqFpT8P5U/9LgzpOnj+6cJNVDWZD+icVBe/uvyEqA+cLG8s556P7uGTQ59YZWmONO4++W4uGXfJwF3dTAgh+srh9fDR70L5838Jw6Z3+3B/wM/dH95Nucdc4DPgS8Vz8Bry01J5+vpZssCNEAOcBN3xZMUfod6cFoq04XD6f3d5yNsbDkfMx/3gFVOj3s9vXck6vl/wfUoaS6yymUNn8pt5vyE/JT+q1xJCiLjk98LC20MLmY0+DWZ3f+AkwJ83/pkVh1cAoLXCc+gqjsnI5683nczIzORo11gIEWUSdMeLxir45Peh/Fn3gLPzOa1rPF7+55+brfyVs0ZG/dXjot2L+J9P/gdvILS88E1Tb+L2GbdjN+SflxBCAOZMJcXBbiV2N1z6+x71495ctpkn1z1p5ZvLzmJ08gz+dtMp5Ge4o11bIUQMSFQULz59AjzVZjprPEz/apeH/Pbd7ZTWNgGQ4VL85OIpUauOP+Dn0bWP8uymZ62yIa4hPHDGA5w+4vSoXUcIIeJeXQl88FAof9Y9kD2+24c3+Zv43vs/IkAAMPtxjzIW8MrNc8lNkxlKhIgXEnTHg/ryyPlc5/8YbJ3/1a3fX8ULn+218tcc6yTdHZ3pARt9jdy1/C4K9hdYZROGTOCxsx9jVFrXK2IKIcSg8t4voNmcrpWcSXDKt3t0+K8+eYRDDebzXAecZNRex0u3niIBtxBxRoLueLDiydD0UrnHwQlXdLq7zx/gnjc3os2xk8yblMuc/PqoVKW6qZo7lt3ButJ1VtmZI8/kwTMeJNWZGpVrCCFEwji8Ada8GMpf8Guwdb8B5KP9n/Pm7r9BcCy6UXkJL91wEcMykqJcUSFErMmEyQNdUx18/udQ/sy7wLB1esg/Vh1g86EaAFx2g19cdnxUZg8paSjhhnduiAi4bzj+Bh4961EJuIUQoj1L7oPg9H5MOA8mntftQ5u8zdy57CegzOMD9RN59kvfZcLQtBhUVAgRa9LSPdCtfRE8VWY6c6y5GE4naj1eHl6y3cp/e/4ERmensOcoq7GvZh+3LLklYjn3u2bfxdemfO0ozyyEEAlq7ydQ+L6ZVgZc8KseHX7zov/Do8zZp7TfyV2z7uOk0VnRrqUQoo9I0D2Q+b3mAMoWp36ny1buJwt2U1ZnLoQzLMPNLfPGHXU19tbs5cZ3brSmBLQrO/efdj+XjL/kqM8thBAJ6/1fh9LTrobcyd0+9IPiYtY0vkrLAr4nZVzD9XNmRLmCQoi+JN1LBrLNb0L1fjOdnAMzrul09wOVDTz9UahN+64LJ5Pk7DxI78q+mn3c+G4o4Hbb3Dx69qMScAsxyCilspRSS5RSO4Pfme3sM0Mp9alSarNSaoNS6qr+qOuAsGc5FH1oppUNzvxhtw89XNXIqxWvogwfAEn6GJ667LuxqKUQog9J0D2Qhc9YcvJt4Oh84MxD726n2WdOKTVtZAaXTR9xVJffX7PfDLgbQgH3E+c8wbyR847qvEKIuHQ3sExrPRFYFsy31gB8XWt9PHAh8Dul1JA+rOPAUfBgKD3jGsjq3ltHf0Bz02vPolJ2mAVa8cg5v8Blj87sU0KI/iNB90B1cDUcWmumbS6YdWOnu285VMPCdYes/E8vnoJh9H7w5OG6w9y4+EaONBwBwGVz8fg5jzNn2Jxen1MIEdcuA54Ppp8HFrTeQWu9Q2u9M5g+BJQAuX1Ww4Fi/0rY+7GZNuwwr/ut3I+/v5Ui/Q8rP3/4pZw26sRo11AI0Q8k6B6oVj4TSp9wBaRkd7r7w0t2WOnzp+Qxe0zvB9tUeaq4demtFNcXA6GA++RhJ/f6nEKIuJentT4cTBcDnS5vq5SaAziB3bGu2IDzyWOh9NSvQObobh226WA1f1jzIoazHACnSuWXPeiWIoQY2GQg5UDUUAGbXg/lZ9/U6e7r91exdKvZIq0UfO/8Sb2/tLeB25fdzp5qs2+4w3Dw2FmPccqwU3p9TiFEfFBKLQXy29l0b3hGa62VCs5j1/55hgEvAtdrrQMd7HMLcAtAXl4eBQUFPa5vXV1dr46LJXfjYU7e+s+WabVZ6TiF+m7U0RfQ/GxFOY68pVbZRRnnsfbTtbGpaD8biH930SL3Fr9ifX8SdA9Ea18Cn8dMD5sOI07qdPfwVu4vTh3GsfnpvbqsN+DlBx/8gA1lGwBQKH59xq85dcSpvTqfECK+aK3P7WibUuqIUmqY1vpwMKgu6WC/dOBt4F6t9WedXOsp4CmAWbNm6fnz5/e4vgUFBfTmuJh6+wdY83KPP4fZF9/QrcN+v2wnZe5XcNrMZ3+mkcN9F/8URw8W0oknA/LvLkrk3uJXrO9PupcMNIEArArrWjL7ZrP5ugOriir4YEcpAIaC/z63d63cWmvu//R+Pjz4oVX2ozk/4sIxF/bqfEKIhLMIuD6Yvh5Y2HoHpZQTeBN4QWv9Wh/WbWBoqDAbTVqc+p1uHbbjSC2///ATHJmh31G+lL0gYQNuIQYrCboHmqIPobLITLsz4IQvdbr7bxeHWrkXzBjBhKG9Wxnyuc3P8daut6z8zVNv5trjru3VuYQQCelB4Dyl1E7g3GAepdQspdTTwX2uBOYBNyil1gU/g2dy6fWvgK/RTOedAOPmd3lIIKD50esbMLIWo5TZE+ekoScxLWla7OophOgX0r1koFn3t1B62lXgTO5w11VFFXxaaA64sRmK754zsVeX/GD/Bzyy+hErf+n4S/nOzO610AghBgetdTlwTjvlq4CbgumXgJda7zMoaA2r/hLKz+n8LWWL11YfYP2RbaSM22CVfX/W9ynfXB6LWgoh+pG0dA8kTbWwdVEo38ViOH/8IDQpwIIZIxiTk9LjS+6s3Mldy+9CB/sgnjj0RH4292eobvywEEIIEVT0EZTvNNPONDjhy10eUt3g5cF3tuHMWWKVzR81n6m5U2NVSyFEPxrQQbdS6ivBlc0CSqlZ/V2fmNuyELwNZnroFBjW8VvZ7cW1LN0aGsf0rfk9X+690lPJd977Dg0+85rDU4bz8PyHcdqcPT6XEEIMauGt3NOuBFfXXf1+u2Q7Vf5CHOmbrbI7ZtwRi9oJIQaAAR10A5uAK4Dl/V2RPhHetWTGNZ2+mvxTWCv3+VPymDA0rUeX8gf83P3h3RysOwhAsj2Z35/ze7KTOp8PXAghRCt1JbD1n6H8rG90ecjmQ9W89NleXLmhVu7zRp/H5KzJsaihEGIAGNB9urXWW4HB0dWhYk9oBTNlg6lXdrjrgcoGFq4PrT75rfnje3y5pzY8xSeHPrHyD5zxAJMyez+/txBCDFprX4KA10yPnAP5nXcP0Vrzi39tAdc+7KnbAXOK1ttn3B7rmgoh+tGADrp7It4XWhiz52XGBNNlWSeyafVWYGu7+760pQl/wOyDfVyWQXXhegoKOz9/+L1tbdzKkyVPWtsuSL8Ao9CgoLDgqO6hv8hk/fErke8NEv/+BOYAyvC3lN1o5S7YXspnhRUkjXzPKrto3EWMH9LzBhQhRPzo96C7sxXQtNZt5oHtSFwvtKA1bPy+lc05+w7mH99+PSrrm7lt2TIr/+MFs5g3KbfLS7TcW3F9Mff98z5r4OTJ+Sfzv+f9LzbDdnT30I9ksv74lcj3Bol/fwI4tCZsAGUqTLms0939Ac2D/9mG4TqMPW0bYLZy3zrt1ljXVAjRz/o96O5sBbRBo3gjlO8y085UmHRBh7v+7fN9eLzmXK5ThqVzxsScbl/GG/Dyww9+SGVTJQC5Sbk8OO/BuA64hRCiX61/JZQ+7lJwdj6L1OtrDrD9SC3u4R9YZeeOPpexGWNjVUMhxAAx0AdSDg6b3wilJ38BHEnt7ub1B3jx071W/punj+1Rf/enNjzFutJ1ANiUjd/M+w05Sd0P2oUQQoTxNcPGsIU3p1/d6e4er5+HF+9AOcqxp6+3yr859ZuxqqEQYgAZ0EG3UupypdQBYC7wtlLq3f6uU9RpDZvCgu7jr+hw13c3F1Nc4wEgJ9XJxdOHdfsyhZ5CntrwlJW/Y+YdzMpP/FkYhRAiZnYthcYKM50+Asac0enuz35cRHGNB2f2cpQyu/jNHTaX47OPj3VNhRADQL93L+mM1vpN4M3+rkdMHVoDVcHWa1cGTGiz4Jvl2Y+LrPQ1J4/GZe9et5C65jpeKH+BgDa7pczKm8U3ju96sI8QQohOrH85lJ52JRgdt2PVNfl4avlulK0WR8Zqq1xauYUYPAZ0S/egEN7KfewXwe5qd7cNB6pYvdfsi+2wKa475ZhuX+KBzx+g3GcuKZzmSOPXp/9a+nELIcTRaKyCHe+E8tM671rywqdFVDZ4cWR9hDJ8AEzNmcqc/DkxrKQQYiCRoLs/BQKw+a1Q/vjLO9w1vJX74mnDGZrm7tYlFhctZtHu0NLyP537U4aldr9bihBCiHZs/zf4m830sOkw9NgOd61v8vHn5YWgmnBmrrDKvzn1m4NjHQohBCBBd/86sBJqDphp9xAYN7/d3UpqPPxrQ2gxnG+cNqZbp6/wVPDLz35p5S8edzFfGPuFXlZWCCGEZXNYz8dOxuIAvPDpXrOVe8galM0clzM6fTRnjTorljUUQgwwEnT3p62hFmiOuxjsznZ3e2Xlfrx+c9DNSaMzmTZySLdO/8CKB6zpATNtmdxz8j1HV18hhBBm15Ld74fyxy/ocNf6YF9uCODM/Ngqv/a4azGU/AgWYjCR/+L7i9bm68kWx7W/oII/oHnl831W/utzR3fr9Mv2LuOdolB/w69mf5U0Z1rv6iqEECJk+79Dy74PmwGZYzrctaWV25a6A8NVBphjay4b3/kiOkKIxDOgZy9JaKXboSK4drsjBcbOa3e3D3aUcKjafB2ZleLkwhPaW7wzUnVTNb9cEepWsmDCAo7zHnf0dRZCCNFqLE7Hrdwer59nPtoDENHK/aVJXyLZkRyz6gkhBiZp6e4v2/4VSk88FxztD4z824pQK/dXThrZrWkCf7PyN5Q1mi0quUm5/GDWD46urkKIQU8plaWUWqKU2hn8zuxk33Sl1AGl1ON9Wcc+0VgFu98L5ad0HHS/ufYgZXVNGM4j2FPNpeINZfDVY78a61oKIQYgCbr7S3jXkslfbHeXQ1WNvLetxMp/dU7X0wR+eODDiNlKfnLKT8hwZfS+nkIIYbobWKa1nggsC+Y78gtgeZ/Uqq9t/09Y15LpkNX+8u3+gDZnLAEcWaFW7nOOOYfhqcNjXk0hxMAjQXd/qDkMB4OLIygbTDyv3d3+vnI/AXP8JKdNyGZMTkqnp230NfKrFb+y8l8Y8wXOPubsqFRZCDHoXQY8H0w/D7TbxKuUOgnIAxb3Ub361tZ/htKdTPO6ZMsRCsvqwVaPM2ONVX7dcdfFsnZCiAFM+nT3hx3/CaXHnAbJWW128fkD/H3lfit/zZyuB1D+ecOfOVh3EIAMVwZ3n9xZQ5QQQvRIntb6cDBdjBlYR1BKGcBvgeuAczs7mVLqFuAWgLy8PAoKCnpcobq6ul4d11uGv4nTdi6hpZPfipqhNLZzfa01D31mjsVxZKyG4GI4o5yjqN5STcHWtse01tf31tcS+f7k3uJXrO9Pgu7+sO3tULqDriXvby+luMZ8aOekOjlvSpufbxEKqwp5dvOzVv7OE+8ky902mBdCiI4opZYC7Y3Wvjc8o7XWSindzn7fBv6ttT7Q1aIvWuungKcAZs2apefPn9/j+hYUFNCb43pt+zsQCC6IkzOJky+6tt3dVhZVsPvdTzGnCfzcKr951s2cNbF7c3P3+b31sUS+P7m3+BXr+5Ogu6811cKesK6Ox17U7m5/W7HXSn9l1iic9o57Ammt+dWKX+ELmK0p03Onc/nEjl97CiFEe7TWHbZOK6WOKKWGaa0PK6WGASXt7DYXOEMp9W0gFXAqpeq01onx2i1iLE7HC4396YPdANiSCzGcoWkCLxhzQUyrJ4QY2CTo7muFBaGlg/OmwpC2gyOP1Hj4YEeplf/q7M4HUL69520+LzZbU2zKxk9P+aksuiCEiLZFwPXAg8Hvha130FpbTb9KqRuAWQkTcAcCsCO09gGT228wKSytY+lW8/cRZ+ZnVvkl4y+RaQKFGOQkMutrO8PGFk06v91dFq47aA2gPHV8Nsdkd/ygrmmu4aGVD1n5a4+7lslZk6NSVSGECPMgcJ5Saidmf+0HAZRSs5RST/drzfrCoTVQd8RMJ2fDyNnt7vbCp+ZbSmWvwZ62xSq/cvKVMa+iEGJgk5buvqQ17Fwayk9of9aSN9cestKXzxzR6Sn/sO4PVHgqABiaPJRvz/j20ddTCCFa0VqXA+e0U74KuKmd8ueA52Jesb4S3rVk0oVgtF0zodbj5bXVBwBwDFkJKgDASXknMX7I+D6pphBi4JKW7r5UsgVqgwG1O6PdlpJtxTVsPVxj7uIwOl2BsrCqkFe2vWLl75p9FymOzqcVFEII0Qvbw2ad6qBryeurD1DX5AP8JGWttMqvmnxVjCsnhIgHEnT3pZ1LQunxZ4Ot7YuGN9cetNLnTcknze3o8HS/WfUb/NoPwOz82Zw/uv3uKkIIIY5CxR6z0QTA5oLxbWcgCQS01bXElrqdgK0KgCx3Fucc0+YFgRBiEJKguy/t6rxriT+gWRjRtaTjVcuWH1jOxwfNVc4MZfCj2T+iqym6hBBC9EL4WJxx88HZ9o3ih7vKzMVwgOTs0DSBl0+4HKfNGeMKCiHigQTdfcVTA/s+DeUntJ2Za0VhuTU3d3aKkzMm5rZ7Kq/fGzF48oqJV8jgSSGEiJXwBpMOBsA/9/EeAJS9CpK3m2kUX5705ZhXTwgRHyTo7iuFBRCcR5v8aZDWdrGbN8K6llwyfTgOW/t/PS9ve5mimiLAnPv1OzO/E+3aCiGEAPB6YM+Hofz4tl1F9pTV8/52c5pXx5DVgDn91NzhcxmZNrIvaimEiAMSdPeVXWH9uSe27VrS2OznnU3FVr6jWUsqPBX8cf0frfyt02+VlSeFECJW9n0CvkYznT0Bssa22eXFT1sWMwuQnrPOKl8wYUEfVFAIES8k6O4L3ZgqcOnWI8FR7zAuJ4VpIzPaPdUf1v2BWm8tAGPSx3DNsddEv75CCCFMu5aF0u10C/R4/by+xpwm0Ja8hyZltninOdM4+5iz+6SKQoj4IEF3XziyucupAsNnLbl85oh2B0UWVRfx2o7XrPwPZv0Ah63j2U2EEEIcpYgB8G2D7v9sOkx1oxeAjKGhVu6Lxl6Ey+aKefWEEPFDgu6+EP7QbmeqwPK6pohl3y+b0X7XksfWPmZNETgnfw7zRs6Lfl2FEEKYqvZD6TYzbXPB6NPa7PLyiv1mwmhCJ2+wyi+fcHlf1FAIEUck6O4LhQWhdDuDcP65/hD+4Lrvs0Zntrvs+/rS9SzZG+oX/r2TvidTBAohRCztDutaMuY0cEY+m3ceqeXzInNFYFfGBny6CYCJmROZkj2lz6ophIgPEnTHmtcTOVXguPltdnlzXdjc3Ce2beXWWvPwqoet/IVjLuT4nOOjWUshhBCtddG15OXP91vp7Pz1VnrB+AXSKCKEaEOC7ljbvwJ85tzbZE+AIaMiNu8urWP9fnPlMqfN4ItTh7U5xQcHPmBNyRoA7MrOd2d+N7Z1FkKIwc7vhcIPQvlWQXf4AErlLKWWXYD5jL54/MV9Vk0hRPyQoDvWwruWjJvfZvPCsAGUZx2by5DkyJXLfAEfv1v9Oyv/lclfYVR6ZOAuhBAiyg6shKYaM50+EnImRWwOH0CZnRdq5Z43cp5M4yqEaJcE3bHWSdCttebNdZGzlrS2aPcidlfvBiDZnsyt026NQSWFEEJEiOhacg606i5iDaDEjy1jtVV++UQZQCmEaJ8E3bHUWAmH1pppZcCY0yM2r95byf4Kc9GFdLeds44dGnm4r5En1j5h5b9xwjfITsqObZ2FEELA7vdC6QmRA+B3lYQGUDrTdtHgrwQg253N6SMin/NCCNFCgu5Y2vMhLcsBM3wmJGVGbA5f9v2L04bjstsitr+y7RVKGksAyEnK4etTvh7T6gohREeUUllKqSVKqZ3B78wO9jtGKbVYKbVVKbVFKTWmb2saBY2VcCg457YyYGzk9Kx/WxEaQDl85EYrfcn4S7AbkVPCCiFEi5gF3Uqp4bE6d9zopGtJk8/P2xsOW/nWXUvqvfX8ZdNfrPxt024j2dF2KkEhhOgjdwPLtNYTgWXBfHteAB7SWh8HzAFK+qh+0VP0EVaDybDpEQ0mzb4Ab64NDqC01VOlZNl3IUT3xLKl+7MYnjs+dBJ0F2wvtQbhjMxMYtboyEajv239G1VN5qwmI1JHcMXEK2JYUSFEvFNKjVdKva+UKlRKPayUcodt+zwKl7gMeD6Yfh5oE2EqpaYAdq31EgCtdZ3WuiEK1+5b4bOWjD0zYtN720qobGgZQLkJv/YBMC1nGuOHjO+zKgoh4s9RvQdTSl3ayWZ3J9sSX9V+qDAHQGJPgpFzIja/uSbUtWTBjBEYRmiQTm1zLc9tfs7K3zrtVlnuXQjRlSeAN4BPgP8GliqlLtRa1wHReIDkaa1bXs8VA3nt7DMJqFJKvQGMBZYCd2sdXEo3jFLqFuAWgLy8PAoKCnpcobq6ul4d15XZm/9DSjC9vjaTyrBr/GmNx0o70lbQFEwfFzguqnWJ1b0NFIl8f3Jv8SvW93e0nc/eBD4A2lsFIO0oz41S6iHgEqAZ2A18Q2tddbTn7RN7wlpKjjkFHKHfQaobvLy3LfTGdUGrriUvbX2JmmZzqqpRaaNkzlchRHfkaa1/H0x/TSn1M2CJUup8rL4SnVNKLQXy29l0b3hGa62VUu2d0w6cAcwE9gF/B24Anmm9o9b6KeApgFmzZun58+d3p4oRVUNORgAAIABJREFUCgoK6M1xnao5BAVm9xFsTqZffIu1EmVZXRMbF5urVBqug9QZ5sJmLpuL/7rgv0hzHvWPPUtM7m0ASeT7k3uLX7G+v6MNuncBN2qti1pvUErtb7t7jy0Bfqy19iml/hf4MfCjKJw39jrpWvL2xsM0+wMATBuZwYShqda26qZqXtz8opW/bfptOAxp5RZCdCkpPKO1/rlSyg8sBlLbPySS1rrtsotBSqkjSqlhWuvDSqlhtN9X+wCwTmtdGDzmLeAU2gm6B6w9H4bSo06OWPp94bpD+ALm7xojRm2ipQXo3NHnRjXgFkIkpqPt0/0iMLSDbU8f5bnRWi/WOthhzuwjPvJoz9kntO406H5rbcdzc7+w5QVqvbUAjEkfw0VjL4pRJYUQCWanUurs8AKt9S+Bd4AJUTj/IuD6YPp6YGE7+6wEhiilcoP5s4EtUbh239nTcX/u11YHW8CVjyb3KqtcBlAKIbqjxy3dSqnHgfu11iXBB3q7tNY/P6qatXUj5qvKjuo1YPoHptQVMbu+FACvPY2Pt1fADvO8pQ0BPi8y5+Y2FGTVFVFQsNe8vr+O5w8+b53nTOeZfLT8o6OuDyR2P6xEvjdI7PtL5HuD2N9f+PMY+BrtdCMJtni/GoXLPQj8Qyn1TWAvcGWwDrOA27TWN2mt/UqpHwDLlFIKWA38OQrX7htaRw6iHBcKujcfqmbrYbPbnztjG41+s3FkeMpw5uRHjtkRQoj29KZ7ybcwp4SKyjRQnfUh1FovDO5zL+AD/trReQZU/8DPnrSSjklnM/+sUOPT4+/tBHYAMG9SLpddEHpYP7L6EZoOmMNyJgyZwJ1fuBObETl3d28lcj+sRL43SOz7S+R7gz65P+t53Nl4F631Ubc2a63LgXPaKV8F3BSWXwJMO9rr9YuKQqgJtmY702D4idYmq5UbyB+xgXKzhyCXTbgMQ8mSF0KIrvUm6G5v0GSvddaHEEApdQNwMXCO1rpbg4H6XVFY63TY60mtdcSCOOFdS8oby3l528tW/lvTvxW1gFsIkbCi+jwe9MK7BY45DWzmj8hmX4CF68xBk8peTUVgk7XbpeM7m8RLCCFCevvruau9QqXUyUqpHUdRn9bnuxC4C7g0buZ6DQQig+4xZ1jJjQerKSytByDFaeP8KaEG/r9s+guNPrPbyaTMSZw7utPfRYQQokWfPI8HhQ76cxdsL6GivhmArLyNaMxm7jn5cxiZFh9DjYQQ/a+3s5cUKKWKgA3A+uB3EeZiCVlRqZnpccwfKEvM7oF8prW+LYrnj76SzeAJvuVNGQo5E61Nb4TNzX3hCcNIcpot2aUNpfx9e6i7+u0zbpfXlUKI7uqr53FiCwQiZy4J688d6lqicWWupjk467gMoBRC9ERvg+7fAcmY/fbuJHJO7ifbPaIXtNbRGHHftyJauU8D85cFvP4A/1x/yNoU3rXk6Y1P0+Q3+3JPyZ7CWaPO6pu6CiESQZ88jxPekY3QWGGmk3Mg9zgAyuuarHUVbEl7qfWb6wOlOlLljaQQokd6G3T/XWttLSuslBoNDAfqtdYbolKzeBURdJ9uJT/aVUZ58PVkXrqLueOzASiuL+bVHaGJBW6fcTvBVn0hhOgOeR5HQ8TS7/PAMN82hs/NnT9iIzXBXS4YcwFJ9iSEEKK7jnZxHAC01nsxp5Aa3Drpzx2+7PtlM0ZgCy77/vTGp/EGvABMy5nGGSNCxwghRE/J87iXwp/d7XUtUc14XGsIdueWriVCiB7rTcfhe4nSdIEJJ6I/dy7kTAKgrsnH4i3F1m4LZphdSw7VHeL1na9b5dLKLYToIXkeR0PAD/s+DeWDDSZbDtWwJTg3d9KQTTQHzMHuYzPGMj13ep9XUwgR33rc0q21fiAWFUkIrbuWBAPodzYV4/GazSPH5qcxZXg6AE9teApfwFxw88ShJzJ3+Ny+ra8QIq7J8zhKijdCU7DjSGo+ZI0D4PU1obm5s4etozo4ae2CCQukgUQI0WMyRUY0ddCfO3zZ9wXBAZT7a/bz1q63rHJp5RZCiH6y9+NQOjgA3usPWM9u5SylWpuzL9qUTebmFkL0igTd0RIItHpwm68ni6s9fLy7DDAbvi+bMRyAP274I35tzjs1O382c4bJMsJCCNEvisKe3aNPA6Bge6k1+D1z6Fpr87yR88hJyunT6gkhEoME3dFSsgUaK810WH/uResP0rKO5txx2QzLSKKouoh/Ff7LOvT2Gbf3dW2FEEKA2WCy75NQPviW8rXV+4MFfmwZq63NV0y8og8rJ4RIJBJ0R0sH/bnDF8Rp6Vry5PonCWizj/fcYXM5Ke+kvqunEEKIkHYaTCrqm625ue2p2/AEqgHITcrl9BGnd3QmIYTolATd0VIUtpJZ8PXk1sM1bCuuBcBlN/jCCfnsrtrNf/b8x9r19pnSyi2EEP0mvFvg6FNBKRatO4jXb76izB623tp86fhLsRtRmWlXCDEISdAdDR30535rXaiV+7wpeaS5Hfxh3R/QmA/zM0acIdNOCSFEfwp/Szk62LUkOGuJstfQaN9kbb584uV9WjUhRGKRoDsawl9PJudA7mT8Ac3CtaFl3684cQTbK7azeO9iq0z6cgshRD/SGvaG9+c+ja2Ha9h00Jw+0J25Fh1cDeekvJMYnT66P2ophEgQ8p4sGtrpz71idxnFNR4AslOcnDExlx8uD02pe9aoszg+5/i+rqmIczU1NZSUlOD1evu7KlGRkZHB1q1b+7saMRN+f47/b+/ew6OqzsWPf98kE5JArgQCBCQBpIDcjYgoEisgikWp1VqxWluLSmuxaqtoT7n0gr1Y9Zx6fspBxVNvp1SoVK0ItkGxighiFQOI3OQawjUhF3J5f3/MZDIJkxCSmey5vJ/nmYe9114z+11DeLNYe+21XS66du1KSkqKw1G1johkAP8H5AA7gOtU9Yifer8FJuMe1FkBzFStu508xBzcDGXu1aVITIcuA3n59U2eg0py5nrKPXt2A6VpDcvZ4SXYOds63YGw89T1uZf4rM39tWE9+PzoJt7a9Za3bMbwGe0WnokMx48f58CBA2RnZ5OYmBgR67qXlJSQnJzsdBhBU9c+VaW8vJw9e9x5IUw73vcDb6nqQyJyv2f/Pt8KIjIGuBAY6ilaDYwDCtoxzpbzzd1njaFK66cFxiZup5wDAHRydWJC7wlORGjCmOXs8BPsnG3TS9qqtrbhGq85Yyk/WcMbn/o89n1ENv+94b+9+xN6T2BAxoD2jNJEgKKiIrKzs0lKSoqI5B1NRISkpCSys7MpKgrbp7ZfBTzr2X4WuNpPHQUSgHigA+ACT881FO1o+FCcVZsPUlzqXps7uet676HLcy8nMS6xvaMzYc5ydvgKVs62TndbHSyE8sPubc987hWFByitdD/ePTezIzEJu1i1exUAgnDHsDucitaEsaqqKhIT7Rd/OEtMTAzny8xZqrrPs70fyGpcQVXfA/4J7PO8lqtqaF6LVm20csmF9Y99jylDk+pXLbnm7GvaOTgTCSxnh79A52ybXtJWfuZzL6lL3MDUEdk8vuH33v1JOZM4O/3s9ozQRBAbLQlvof73JyIrgW5+Dj3ou6OqKiKnzNMWkX7AQKCnp2iFiIxV1Xf81J0OTAfIysqioKDgjOMtLS1t1fsAEsv2cH6pexC+OrYjb3xSzJsbKwFwpa2jFvcv2l7xvTj46UEK2nmGTFvaFg4iuX11bUtNTaW0tNTpcAKqpqaGkpISp8MIGn/tq6ioCNjPqnW628p3fe6ciygqqeDtLQe9RWefVcT//Mt9d3yMxHD78NvbO0JjjGkRVR3f1DEROSAi3VV1n4h0B/xdc50KvK+qpZ73/B24ADil062qC4AFAHl5eZqfn3/G8RYUFNCa9wGwbpF3M67PRRR36kuNfgYoyV3WUje29b1zv0d+/1aeow3a1LYwEMntq2tbYWFhxM1/jpY53b4SEhIYMWJEQD7fppe0xSnzuS9i2Ya91HrGf87LTef/vvgf7+Er+1xJn9Q+7RykMcYExDLgZs/2zcArfursAsaJSJyIuHDfRBma00sazeeuW5s7NukLqmLc/5/o5OrE5bmXOxGdMSYCWae7LRrM5+4MXQbwss9j30f2P8i6A+sAiJM4bh9mo9zG+Hr++ecREb+vlStXsmPHjlPKMzMzGTduHMuXL2/wWXV1Fy5c6FBrIt5DwAQR+RwY79lHRPJEpO5L/wvwBfAJ8DHwsar+zYlgm9VoPvf2TsO9a3N3yFjjLf9a36+R5Epq9/CMCVWWs9vGppe0RaP53J/tK6FwnydxxwkbSl/yHp569lR6Jfdq7wiNCQuLFy+mZ8+eDcoGDRrE4cPu/9TOmjWLKVOmAHDgwAH++Mc/cuWVV7J69WrOP//8do83GqnqIeBSP+UfArd6tmuA29o5tDN3dCcc9wyQxHfihV3pQCkSd5y45M+om6x+Xf/rnIrQmJBmObt1rNPdFg063WNZ+lH9DZTnDjzAJ4fdjw92xbiYPnR6e0dnTNgYPnw4/fr1O6W8LoH36dOH0aNHe8snTJhAWloaS5YsieoEblrJZ2pJba/zWfqx+4ZKV+palBoARnYdSb/0U38mjTGWs1vLppe0Vm1tg8uT1b3G8NcNdY99r+VI/DLvseu+ch3dOvpbEMAY0xoJCQnEx8eH8/J7xkk+ufuLpGGetblrSchY6y3/5le+6UBgxkQmy9luNtLdWgc3Qdkh93ZSZ1Yfy+RgyQ4A0rtsYXfZVgASYhO4dcitDgVpTHioqamhurrauy8ixMbGevdra2u9x4uKivjd735HRUUF11xj6yebVvC5SrnkcA4AsZ02oXFHAchIyGB87yYXcjEm6lnObh3rdLdWo4cqLPmofpQ7KWslx91XKPnWwG+RmZjZ7uGZ6JBz/2tOh+C146HJrX7vgAENn9B64YUXsnp1fcfotttu47bb6qcKd+jQgQULFnDhhRe2+pwmSh3b7Z7TDWhcIou2pwMQn/6et8rV/a4mPjbekfBMZLOcHd052zrdreUzUlKRfQHL33A/9j0u5d8cr3HP7e7o6sh3z/muI+EZE06WLl3a4Kacxuuk/uxnP+Oqq64C3HMG//a3vzF9+nSSkpK4/vrr2zVWE+Z85nPvSxlKeWksMfEHiOv0OeB+nsK1/a91KjpjwoLl7NaxTndrNFpualVlfyqrK4EaOnV7y3MbDtw48EbSEtIcCdGYcDJ48GC/N+XU6d27N3l5ed79iRMnsm3bNu666y6++c1vhvyTHk0I2Vk/YPJWmftnzpXxL29Zfs98eib3POVtxph6lrNbxzrdrVG8BU54njqZmM7TnycClbjS1lIT6y5Pjk/mpnNuci5GExXacnkw3J1zzjm8/vrrFBUVkZWV5XQ4Jlz4jHT/7VgfiCnDlbreW3bjoBudiMpECcvZ0Z2zbfWS1vCZWnKi2yjW7DgKUkmHLiu95bcOuZWU+BQnojMmKvz73/8mPj6e1NRUp0Mx4aJkPxz+AoBqiedj7Ut82lokxr2iwlfSv0JeVl5zn2CMaSXL2TbS3To+U0verxkIQHzn1UhcKQBZSVncMOAGR0IzJhJt27aN999/H4AjR46wbNkyli9fzowZM0hISGhQd926daSlnTqta8qUKcTH281xUc1nwGSD9qOSWDr6TC2ZNnBa1F72NiaQLGf7Z53uM6Xa4PLk03uykdhS4jNWect+MPwHJMQl+Hu3MaYV5s+fz/z58wFISUmhb9++PP7440yffupDp5544gmeeOKJU8oPHjxIZqatJBTVfAZM3q0eQFzyRmJcxwD3MoFX9LnCqciMiSiWs/2zTveZOrwNSt0rlVS5knmvpDvxWa8isScB6JfWjyl9pzgZoTFhY9q0adx+++1NHs/JyUFVmzze2romSvkMmLxfOxBXxtve/W/0/wYdYjs4EZUxYcNydtvYnO4z5XN5cmPcOajrCK70Nd6ymSNnEhsT6++dxhhjnFJ6EIo3A3BSY9nQIZ64JPd63XESZ0+gNMYEnXW6z5TP5cnXS/rQocubiLgXCRzZdSTjeo5zKjJjjDFN8cndH2tf6Fw/l3tyn8l0TerqRFTGmChine4zodpgpHuVKxNX6sfe/R+f+2O7CccYY0KRT6f773E5xCUXeve/O9geYmaMCb6Q7nSLyC9E5N8iskFE3hSRHo4GdGQHHN8DQCmJfNm1fm3X8WeNZ3jX4Q4FZowxplk+87lXplV6ty/pdQl90vo4EZExJsqEdKcb+J2qDlXV4cCrwM8djcZnpOSJxBxik3YB4Ipxcfe5dzsVlTHGmOaUHYaijQB8GePicMpO76HvDfmeU1EZY6JMSHe6VfW4z25HwNnbXD0jJWUiLO5c5S2+cdCN9Erp5VRUxhgTdCJyrYhsFJFaEWnyCTIiMklENovIVhG5vz1jbNKu97ybj6ZmI1ILwLlZ5zKsyzCnojLGRJmQXzJQRH4F3AQcAy5ppt50YDpAVlYWBQUFZ3yu0tLSZt93/uaVJALPpKZQ5nIvEdhRkhl4bGCrzteeTte2cBbJbYP69qWmplJSUuJ0OAFVU1MTcW3y5a99FRUV4frz+inwdeDJpiqISCzwODAB2A2sFZFlqvpZ+4TYBM+ASXFMDP9IqR+7+d5gG+U2xrQfxzvdIrIS6Obn0IOq+oqqPgg8KCKzgB8Cs/19jqouABYA5OXlaX5+/hnHUlBQQJPvO/olFBSxLzaWZ1LrH+/+0wvu5fKzLz/jc7W3ZtsW5iK5bVDfvsLCQpKTk50OJ6BKSkoirk2+/LUvISGBESNGOBRR66lqIXC6m8VHAVtVdZun7kvAVYCjnW7duRoBnklLoTrG3en+SvpXuCj7IifDMsZEGcc73ao6voVVnwdep4lOd9B55nM/nJFGZYz7l06PxH5c1fcqR8IxxpgQlA186bO/GzjfX8X2uDoJEFt9ggv3fcKh2Bj+nNzJW35x3MWsWrWqmXc6K1qu4EUiuzoZvoJ9ddLxTndzRORsVf3cs3sVsMmxYHas5l+JCSzv1NFbNG/sg/YgHGNMxDjdlcdAnivoVyfrbFkO1PJUahoVMe7bmAZmDOTOy+8M6SVeo+UKXiSyq5PhK9hXJ0P6RkrgIRH5VET+DUwEZjoVSMWOd/hl53Tvfr/EcZzfvcl7iYwxLfD8888jIn5faWlpTocXdVR1vKoO9vNqaYd7D+B7V3lPT1lg/eOXsHA8I9fdC1/8o9mqJ7asoig2lj/7/CL9wfAfhHSH25hQZTm7bUJ6pFtVr3E6BgCO72WhHuFLVyoAWpPA/PxZDgdlTORYvHgxPXv2bFAWFxfS6cn4txY4W0RycXe2rwduCPhZDn0Bu9eSAu7lAJtRsnkVT6emcNIzLXBw58Fc3PPigIdkTDSxnN069g21wLZNr/BUWv3Nk2e7rmdA12wHIzImsgwfPpx+/fo5dv7Kyko6dOjg2PnDgYhMBf4L6AK8JiIbVPUyz0PLFqrqFapaLSI/BJYDscDTqrox8MH4XKTVpleSrSo/zonyLSzunOUtu2P4HTbKbUwbWc5unVCfXuI4VWXelheo9iTpLuUdmXXRzQ5HZUz0WLRoESLC+++/z7Rp00hJSaFHjx786Ec/oqKiokHdsrIy7rvvPnJzc4mPjyc3N5df/epX1NbWeusUFBQgIixZsoTvf//7dOnShays+k7Ziy++yIABA0hISGDIkCEsW7aM/Px87/zT/fv3Ex8fz2OPPXZKrHPmzCEpKYkjR44E58twkKouVdWeqtpBVbNU9TJP+V5VvcKn3uuq2l9V+6rqr4ISjG+nWWubrPbRu8t5PCPFm79Hdj2XsdljgxKSMcbNcnbTrNN9Gq9ue5V1NUcBiFXlnKrJjMrNdDgqYyJLTU0N1dXVDV6+SRfg29/+Nn379mXJkiXccccdPP7448yfP997vLq6mssuu4yFCxcyc+ZM/v73v3Prrbfyi1/8gp/85CennPPOO+9EVfnTn/7EokWLAFixYgXTpk1jwIABLFmyhHvvvZe77rqLLVu2eN/XrVs3rr76ahYsWHBKG5566imuu+460tPTMUHkO9LdzDPT3vt0CSs6Jnn37827x0a5jQkAy9mtY9NLmlFcXsxDa+p/QL517ATDx33bwYiMaWROqtMR1JtzrNVvHTBgwCllkydP5tVXX/Xu33DDDcydOxeA8ePHs2bNGl588UVv2Ysvvsjq1atZtWoVF1/snrN76aWXAjB37lzuu+8+unbt6v28UaNGsXDhwgbnnD17NoMGDWLp0qXeztngwYPJy8ujf//+3nozZszgkksu4Z133mHsWPfI6Wuvvcbu3bu5/fbbW/09mBZqML3E/0j3pn3HKUion9ny1ZRzGNJlSLAjM6Z5lrOjOmfbSHczfr3m1xyvcq/X2KOqmnHHuzF+aG+HozIm8ixdupS1a9c2eD366KMN6kyePLnB/pAhQ9i1a5d3/4033qB3796MGTOmwejLxIkTqaqq4v3332/w/qlTpzbYr6mp4cMPP+Saa65pMBp67rnnkpub26Bufn4+gwYN4skn6x/O+OSTTzJ06FBGjx7dui/BtFwLOt2/fftZtia6R8HjVLn3Arv53ZhAsZzdOjbS3YTlO5azYucK7/6c4kMk9r6S2Bi7NGlMoA0ePPi0N+VkZGQ02O/QoQOVlZXe/aKiInbu3InL5fL7/kOHDjXY7969e4P94uJiqqqqGoys1PGdP1jnjjvu4N577+Wxxx6jtLSUN954gz/+8Y/NtsEEyGnmdO8+foiPSv/X+xvuuopYenUb1k7BGRP5LGe3jnW6/ThccZhfr/m1d/+aklIuqKik4vxJDkZljB9tuDwYaTp37kxubi5//vOf/R7PyclpsN94bm9mZiYul4uioqJT3nvgwAHOOuusBmU33XQTs2bNYtGiRRw5coSkpCSmTZvWtkaYFmq+033vyl9RHee+YSurupo7e1zaXoEZ0zzL2V7RmLOt092IqvLL93/J4Qr32q9Z1dXcc+gINRJHQu4FDkdnjGnKpEmTePnll+nUqZPf+YanExsbS15eHi+//DJz5szxJvh169axffv2UxJ4SkoK06ZN48knn6S0tJRvfetbpKSk+PtoE2jNLBm4fPubbCypv0o569AROo3Kb6fAjDEtFY052zrdjfzl8780mFby8+LDJKtS3WMExCc1805jTGtt2LCB4uLiU8rz8lr+1Ndp06bxzDPPcOmll3LPPfcwbNgwTp48yRdffMGyZcv461//SlJS8/+G586dy8SJE5k6dSrTp0+nuLiYOXPm0K1bN2JiTr0FZsaMGd45gnYDZTtqYk733tK9/Ozd2d79CSfK+GpZOfS+sD2jMybiWc5uHet0+9h3ch8Pf/Cwd3/o0TQuLndP+o/rY2u7GhMs1157rd/ygwcPtvgzXC4Xy5cv56GHHmLBggVs376djh070rdvXyZPnkx8fPxpP2PChAk8//zzzJ07l6lTp9KvXz8efvhh5s2bR2rqqasODB06lP79+5OSksLIkSNbHKtpIz+d7mOVx5ixcgYVNaUAdK+uZnbxISSjD6R09/cpxphWspzdOrZ6iUfJyRKeLn6ayhr3JP+aiix+evhofYUcGykxJtCmTZuGqjb5yszM5Dvf+Q6qespNO3PmzEEbTS1ISEhgzpw5bNq0icrKSg4fPszatWuZM2eO9xHF+fn5qCrjx4/3G9MNN9zA5s2bqaysZOPGjZx33nkUFhb6TdCbN2/m888/t1Hu9tZoekllTSUz/zmTL459AUCMCr8pKia1Vm2U25gAspzdNjbSDVTXVvOTt3/C/qr9AIi6cO25iiHyH+4KEgu9bBkwYyJdeXk5d999N+PHjyczM5Nt27bx29/+lqSkJG699VZvvd27d7N161Zmz55N9+7dueGGGxyMOgr5dLqraqu4t+Be1h1Y5y27+UACIypPundyLmrv6Iwx7STccrZ1uoGHP3yYd/e8690v2/t1Lq0uJibe8z+yHiOgQyeHojPGtJfY2Fj279/PD3/4Qw4dOkTHjh0ZO3YsixcvbrBc1cKFC5k3bx79+/fnhRdeIDEx0cGoo5Dnhqka4IF9Kyko2eo9VHXgMm4r+9/6BU56j2n/+Iwx7SLccnbUd7rX7FvDc4XPefc7lE6k5PgILohbVF8p9+L2D8wY0+7i4+NZunTpaevNmTOHOXPmBD8g45/EUAvMzszgDZ8Od2XxOAYdyaZjB89awKlnQdpZ/j/DGBP2wi1nR/2c7lHdRvGjET8CoJsOofjLfAAuiiusr5RrN1EaY0yoUISHMtJ5Jbn+CmTVkTGcPDiJ0TGb6ivavTjGmBAS9SPdIsL3h36fXh3P5p5njwAxZHKMfnzprhDjsvncxhgTIlSVR0sLeTE12VvWy5XPZ/snAsLETl9A3UPv7CZKY0wIifqR7jqrPu7MiZPu5WmuSK6/XEnP82x9bmOMCRFHK4/yavlu7/74xBy2bpwExBBDLUNrfa5S2ki3MSaEWKcb+PjLo7y0dpd3f3qvPfUHbWqJMcYgIteKyEYRqRURv0/AEJFeIvJPEfnMU3dmoONIT0hnUeY4squqyT9RxqSjAzhZ4z52TY/DxFW51+kmuQek5wb69MYY02pRP72kplb5j1c+9T5J+NIBXel57MP6CjnW6TbGGOBT4OvAk83UqQbuUdX1IpIMrBORFar6WSAD6eVK5k/79pNSW8vj1ce85bf13geHPTu9x3hXOTHGmFAQ9SPdG748ysa9xwGIi4F5l2TAIc/0ktgO7uklxhgT5VS1UFU3n6bOPlVd79kuAQqB7IAHIzF0qamlg0JtrfuJlEN7ptK3bEN9HZtaYowJMVE/0n1u73Re+9FF/PyVjfSILSH7qM8od69R4EpwLjhjjAlTIpIDjADWNHF8OjAdICsri4JGVonHAAASG0lEQVSCghZ/ds6uXeR4tmNwX6acmFVG9eZ3cHnKPzgQT9kZfGaoKS0tPaPvJNxEcvvq2paamkpJSYnT4QRUTU1NxLXJl7/2VVRUBOxnNeo73QADuqXwf9NH89Y/C2DH2/UHcsc5FpMx0eTNN9/kkUce4YMPPuDEiRP07t2bqVOncv/995OWluatl5OTw86dOwH3ykPZ2dmcf/75/PKXv2TAgAFOhR8xRGQl0M3PoQdV9ZUz+JxOwMvAXap63F8dVV0ALADIy8vT/Pz8lgeq74H7x4AYqWVM3878YGxHZKNnPnfHroy6YlpYTy8pKCjgjL6TMBPJ7atrW2FhIcnJyad/QxgpKSkhOTk5YnN2Xft8JSQkMGLEiIB8ftRPL6kjIsTFCGx/p77QbqI0Juh+/etfc9lll5GQkMDChQtZvnw5t912G8888wyjRo1iz549DepfdtllvPfee6xevZp58+bxwQcfMHbsWIqKihxqQeRQ1fGqOtjP60w63C7cHe7nVXVJMOLcX3Ky/nzAfZMGIDv/VV/B5nMbEzSWs1vPRrp9JJQfgKOe4RNXEvQY6WxAxkS4t99+m5/97GfcddddPPLII97ycePGMXXqVM4991xuueUW3nzzTe+xzMxMRo92r50/ZswY+vTpQ35+Ps899xx33313u7fB1BMRAZ4CClX1D8E6zztbi7nWs312lySG9UqDf62ur2DrcxsTFJaz28ZGun2kHf2kfues0RAX71wwxkSBRx99lIyMDObPn3/KsdzcXO6//35WrFjB+vXrm/yM885z3+y8devWJuuYthORqSKyG7gAeE1ElnvKe4jI655qFwLfBr4qIhs8rysCGUfZyWpE6n91XdAnHWprYYdPpzvnokCe0hjjYTm7bazT7aNBpzv3YucCMSYKVFdX8+677zJhwgQSEvzfsDxlyhQAVq5c2eTnbN++HaDBPEITeKq6VFV7qmoHVc1S1cs85XtV9QrP9mpVFVUdqqrDPa/Xm//kM5MUH8c38s7y7qcnxkHRZ1DuWSswKRO6DgzkKY0xWM4OBJteUke1Yac7xzrdJvQNeXaI0yF4fXLzJ6ev5OPQoUOUl5eTk5PTZJ26Y3U34oD7MeDV1dXU1tayZcsWbrvtNmJiYvjGN77RmrBNOPIZ6UZrYbvPDfA5F9l8bhOyLGdHd862ke46h7eRUHnIvR2fDN2HORuPMcYrJqY+Vb3wwgu4XC46dOjAkCFD2Lt3L4sXL2bkSLsHI2o06HQr7LAb4I0JJZaz/bOR7jq+IyW9x0CsfTXGBFPnzp1JTExkx44dTdapO5adXf98lcsvv5x58+YRGxtLjx49yMrKCnKkJvT4jGTXVsOOd+v37SqlMUFhObvtrGdZx0ZKTBg608uDoSQuLo4xY8awYsUKKioq/M4RXLZsGeC+M75ORkYGeXl57RanCUG+I937PoZKz6PgO2VB5tnOxGRMC1jOjm42vQQ8lyd97ny3myiNaRczZ87k0KFDPPDAA6cc2759O7/5zW8YPnw4F1xwgQPRmZDl2+ne6TvKPdbmcxsTRJaz28ZGugEOb4PSA+7thFTICp0bHYyJZPn5+cydO5fZs2ezY8cObrrpJtLT01m/fj0PPfQQtbW1vPTSS06HaUKNNDFeZFcpjQkqy9ltY51ugD3r6rd7ngcxdgHAmPby85//nFGjRvHII49wyy23cPToUQDy8vJYunQpPXv2dDhCE3Ka6nTnWKfbmGCznN16YdHpFpF7gN8DXVS1OOAn2PtR/Xa2zTsypr1NmjSJSZMmefdvvPFGli5dyu7duxsk8OZu4DFRxN8UkpRsyOjT/rEYE4UsZ7dOyA/pikgvYCKwK2gnOXGwfjsjN2inMca0zNNPP815553H5MmTKSwsdDocE2r8dbptPrcxjrGc3TLhMNL9CPBT4JWgnaGqvH7blRS00xhjWiY+Pp6CggKnwzChyt/0EpvPbYxjLGe3TEiPdIvIVcAeVf04qCeqKqvftk63McaENn+dbpvPbYwJcY6PdIvISqCbn0MPAg/gnlrSks+ZDkwHyMrKOqP/cQ0v3k+aZ/ujjZs5tsfxryXgSktLI/Z/oZHcNqhvX2pqKiUlJU6HE1A1NTUR1yZf/tpXUVER0T+v7aJxpzvtLEjv7UwsxhjTQo73LlV1vL9yERkC5AIfi3ueXk9gvYiMUtX9fj5nAbAAIC8vT/Pz81sexGYXeJ6tMGLUGOgx4ozaEA4KCgo4o+8kjERy26C+fYWFhSQnJzsdTkCVlJREXJt8+WtfQkICI0ZEXo5pV4073fYUSmNMGHC8090UVf0E6Fq3LyI7gLygrF5y0qaXmPCgqojdLBa2VNXpECJDYnrD/T7j/NczxmGWs8NboHN2SM/pbjcNbqRMdC4OY5rhcrkoLy8/fUUTssrLy3G5XE6HEf4aLw3Yz+8FU2McZTk7/AU6Z4dNp1tVc4Iyyg12I6UJC127dmXPnj2UlZXZiGmYUVXKysrYs2cPXbt2Pf0bQpCIXCsiG0WkVkSafaCBiMSKyEci8mpQgsnsD10HubeHXAdJGUE5jTFtYTk7fAUrZ4fs9JJ2de0iqCzhs3+vY1CHFKejMcavlBT3z+bevXupqqpyOJrAqKioICEhwekwgsa3fS6Xi6ysLO/fYxj6FPg68GQL6s4ECoHgNDYmFm59i/V/f5aRk78XlFMY01aWs8NPsHO2dbrBOx+w6EAnBsXFOxyMMU1LSUkJ507bKQoKCiL6psJIap+qFgKnnZ8qIj2BycCvgLuDFlB8EsdTB4LlbBPCLGeHl2C3zzrdxhhjAulR3A80a3ZZmrYs81onkpcLjeS2QWS3z9oWvoLdPut0G2OMAZp/boKqnvapwCJyJVCkqutEJL+5um1a5tUjkpcLjeS2QWS3z9oWvoLdPut0G2OMAZp+bsIZuBCYIiJXAAlAiog8p6o3tj06Y4wJb2GzeokxxpjQpqqzVLWnquYA1wP/sA63Mca4WafbGGPMaYnIVBHZDVwAvCYiyz3lPUTkdWejM8aY0GfTS4wxxpyWqi4Flvop3wtc4ae8ACgIemDGGBMmJBIXbBeRg8DOVrw1EwjOA3icZ20LX5HcvkhuG7Sufb1VtUswgglVlrP9iuS2QWS3z9oWvoKasyOy091aIvKhqjb7pLVwZW0LX5HcvkhuG0R++5wWyd9vJLcNIrt91rbwFez22ZxuY4wxxhhjgsw63cYYY4wxxgSZdbobWuB0AEFkbQtfkdy+SG4bRH77nBbJ328ktw0iu33WtvAV1PbZnG5jjDHGGGOCzEa6jTHGGGOMCTLrdBtjjDHGGBNk1ukGRGSSiGwWka0icr/T8QSSiPQSkX+KyGcislFEZjodU6CJSKyIfCQirzodSyCJSJqI/EVENolIoYhc4HRMgSQiP/b8TH4qIi+KSILTMbWWiDwtIkUi8qlPWYaIrBCRzz1/pjsZYySxnB3eIjVnQ2Tn7UjK2eBM3o76TreIxAKPA5cDg4BvicggZ6MKqGrgHlUdBIwGfhBh7QOYCRQ6HUQQPAa8oaoDgGFEUBtFJBv4EZCnqoOBWOB6Z6Nqk0XApEZl9wNvqerZwFuefdNGlrMjQqTmbIjQvB2BORscyNtR3+kGRgFbVXWbqp4EXgKucjimgFHVfaq63rNdgjsBZDsbVeCISE9gMrDQ6VgCSURSgYuBpwBU9aSqHnU2qoCLAxJFJA5IAvY6HE+rqerbwOFGxVcBz3q2nwWubtegIpfl7DAWqTkboiJvR0zOBmfytnW63cnsS5/93URQgvMlIjnACGCNs5EE1KPAT4FapwMJsFzgIPCM5zLsQhHp6HRQgaKqe4DfA7uAfcAxVX3T2agCLktV93m29wNZTgYTQSxnh7dIzdkQwXk7SnI2BDlvW6c7SohIJ+Bl4C5VPe50PIEgIlcCRaq6zulYgiAOGAn8P1UdAZwggqYneObJXYX7l1QPoKOI3OhsVMGj7rVZbX1W02KWs8NSxObtaMvZEJy8bZ1u2AP08tnv6SmLGCLiwp28n1fVJU7HE0AXAlNEZAfuS8xfFZHnnA0pYHYDu1W1boTrL7iTeaQYD2xX1YOqWgUsAcY4HFOgHRCR7gCeP4scjidSWM4OX5GcsyGy83Y05GwIct62TjesBc4WkVwRicd9Y8Ayh2MKGBER3PPLClX1D07HE0iqOktVe6pqDu6/t3+oakT8z1tV9wNfishXPEWXAp85GFKg7QJGi0iS52f0UiLkhiMfy4CbPds3A684GEsksZwdpiI5Z0PE5+1oyNkQ5LwdF8gPC0eqWi0iPwSW474b92lV3ehwWIF0IfBt4BMR2eApe0BVX3cwJtMydwLPezoW24BbHI4nYFR1jYj8BViPe7WGjwjjxwuLyItAPpApIruB2cBDwJ9F5HvATuA65yKMHJazTYiLyLwdaTkbnMnb9hh4Y4wxxhhjgsymlxhjjDHGGBNk1uk2xhhjjDEmyKzTbYwxxhhjTJBZp9sYY4wxxpggs063McYYY4wxQWadbhMyRERb8NrhqbuobjtUiMh/isirDp37ahE54HmKnTHGBJ3l7Dad23J2FLIlA03IEJHRjYqWAh8Dc3zKKlX1IxHpC6So6kftFV9zPPEUAmNU9UMHzi+41019RVVnt/f5jTHRx3J2m85vOTsKWafbhCzPqMjqcHhimYj8FzBaVc9zMIYZwC+AbFWtcCoOY0x0spx9xjFYzo4yNr3EhKXGlypFJMdzKfN2EZkvIvtFpEREnvM8trafiCwXkVIR2SoiN/v5zGEiskxEjohIuYi8KyJjWxBLB+BG4IVG5Z1E5L9EZJeIVIpIkYisFJEBPnXiRGSWiGzy1NkrIg+LSEKjz+ooIg+JyBeeevtF5GURyfKp9mcgDfh6S79HY4xpD5azLWcbewy8iTyzgALgZmAQ8FugFhgB/A/we+AO4BkR+bDu8dEiMhJ4B/flvu8DZcDtwEoRGaOq65o552jcifOdRuWPAFOAB4DPgc64H/Gc5lPnOeBrwG+AfwEDcY985ADXeGKLB1YAw3A/ovZ9IBW4DEgHDgCoarGIFAKTaPTLxBhjQpTlbMvZ0UNV7WWvkHwBO4Dnmji2CNjhs58DKPCPRvWWeMpv9ClLB6qB2T5lb+Ge3xfvUxbrKfvraeK8D/cvifhG5Z8Cf2jmfWM9sd3UqHyap3y4Z/+7nv0pLfjO/gRscfrvzl72slf0vSxnW862V/Mvm15iIs3fG+1v8vy5vK5AVY8ARUAvABFJBMYBi4Faz+XDOECAlcDFpzlnD+C4qp5sVL4W+I6IPCAieSIS2+j4JOAk8Je6c3rO+6bneN15JwL7VXXZaeIAOOiJxxhjwoHlbMvZUcM63SbSHGm0f7KZ8ro5eBm4R0j+A6hq9PohkC4izf1bSQAq/ZTfCTyJe9RjLVAkIo+ISJLneFcgHjjR6JxFnuOdff7c08z5fZX7tMsYY0Kd5WzL2VHD5nQbA0dxX2p8HPhffxVUtbaZ9x+i4Zy/uveU4p6vOEtEegPfwD2/7yTuy5uHgArclyz92ev5sxgYfNpWuGV4PtcYYyKV5WwTlqzTbaKeqp4QkXdw3/Sy/jTJ2p9NQLyI9FTV3U2cYyfwsIhMoz4Zv4E7kaeq6lvNfP6bwPUi8jVV/dtpYskFNp9Z+MYYEz4sZ5twZZ1uY9zuBt4GlovIU8A+IBMYCcSq6v3NvPdtz5+jAG8CF5H3gGXAJ0Ap7jmIw4BnAVS1QERexD0/8A/AB7hHb3KAK4D7VHUL7rvlvw+8KCLzgTVAMu474R9V1U2e84knhv9u0zdhjDGhz3K2CTvW6TYGUNX1InIeMBv4T9zLOx0E1gNPnOa9O0TkA9zLSC3xOfQ2cB1wP+5/a9uAH6vqf/rUuRH3PMLvAg/inme4A/dNRHXLSlWJyERPbNM9fx4C3gUO+3zWGNx3+b90Zq03xpjwYjnbhCN7IqUxASAi3wEeA7qraplDMfw/YLCqnvbhEMYYE80sZxsn2OolxgTGc7hvopnhxMlFpBvuh0s86MT5jTEmzFjONu3OOt3GBICqVgO34H4qmhNygHtU9e3TVTTGmGhnOds4waaXGGOMMcYYE2Q20m2MMcYYY0yQWafbGGOMMcaYILNOtzHGGGOMMUFmnW5jjDHGGGOCzDrdxhhjjDHGBNn/B7SgYrZpMXylAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106bacd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(12, 8))\n",
    "\n",
    "subplot(221)\n",
    "xs, _ = fb_lin_data\n",
    "plot(ts, xs[:, 0], linewidth=3, label='FBL')\n",
    "xs, _ = energy_data\n",
    "plot(ts, xs[:, 0], linewidth=3, label='Energy')\n",
    "xs, _ = qp_data\n",
    "plot(ts, xs[:, 0], linewidth=3, label='QP')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_1$', fontsize=16)\n",
    "\n",
    "subplot(222)\n",
    "xs, _ = fb_lin_data\n",
    "plot(ts, xs[:, 1], linewidth=3, label='FBL')\n",
    "xs, _ = energy_data\n",
    "plot(ts, xs[:, 1], linewidth=3, label='Energy')\n",
    "xs, _ = qp_data\n",
    "plot(ts, xs[:, 1], linewidth=3, label='QP')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_2$', fontsize=16)\n",
    "\n",
    "subplot(223)\n",
    "_, us = fb_lin_data\n",
    "plot(ts[:-1], us[:, 0], linewidth=3, label='FBL')\n",
    "_, us = energy_data\n",
    "plot(ts[:-1], us[:, 0], linewidth=3, label='Energy')\n",
    "_, us = qp_data\n",
    "plot(ts[:-1], us[:, 0], linewidth=3, label='QP')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_1$', fontsize=16)\n",
    "\n",
    "subplot(224)\n",
    "_, us = fb_lin_data\n",
    "plot(ts[:-1], us[:, 1], linewidth=3, label='FBL')\n",
    "_, us = energy_data\n",
    "plot(ts[:-1], us[:, 1], linewidth=3, label='Energy')\n",
    "_, us = qp_data\n",
    "plot(ts[:-1], us[:, 1], linewidth=3, label='QP')\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_2$', fontsize=16)\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Safe Controller"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the task of moving the pendulum from configuration $\\mb{q}_0 = (1, 0)$ at rest to $\\mb{q}_d = (-1, 0)$ while evading an obstacle above the base of the pendulum. Suppose the position of the obstacle relative to the base of the pendulum is resolved in the inertial frame as $\\mb{p}^{\\mathcal{I}} = R \\mb{e}_1$, with $0 < R \\leq l_1 + l_2$. Additionally, suppose we must keep the end at least $\\delta R$ m away from the obstacle, for $0 < \\delta < 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the function:\n",
    "\n",
    "\\begin{equation}\n",
    "    h(\\mb{q}) = \\frac{1}{2} \\norm{ \\mb{r}_{20}^{\\mathcal{I}} - \\mb{p}^{\\mathcal{I}} }_2^2 - \\frac{1}{2} \\delta^2 R^2.\n",
    "\\end{equation}\n",
    "\n",
    "This function is positive for any configuration satisfying $\\norm{ \\mb{r}_{20}^{\\mathcal{I}} - \\mb{p}^{\\mathcal{I}} }_2 \\geq \\delta R$. Denote the $0$-superlevel set of this function as $\\mathcal{C}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding time derivative is:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\dot{h}(\\mb{q}, \\dot{\\mb{q}}) = ( \\mb{r}_{20}^{\\mathcal{I}} - \\mb{p}^{\\mathcal{I}} )^\\top \\dot{\\mb{r}}_{20}^\\mathcal{I}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second time derivative is:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\ddot{h}(\\mb{q}, \\dot{\\mb{q}}, \\mb{u}) = (\\dot{\\mb{r}}_{20}^{\\mathcal{I}})^\\top\\dot{\\mb{r}}_{20}^\\mathcal{I} + (\\mb{r}_{20}^\\mathcal{I} - \\mb{p}^\\mathcal{I})^\\top \\ddot{\\mb{r}}_{20}^\\mathcal{I}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that $\\ddot{\\mb{r}}_{20}^\\mathcal{I}$ can be expressed as:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\ddot{\\mb{r}}_{20}^\\mathcal{I} = \\begin{bmatrix} -l_2 (\\dot{\\theta}_1 + \\dot{\\theta}_2) \\cos{(\\theta_1 + \\theta_2)} - l_1 \\dot{\\theta}_1 \\cos{\\theta_1} & -l_2 (\\dot{\\theta}_1 + \\dot{\\theta}_2) \\cos{(\\theta_1 + \\theta_2)} \\\\ -l_2 (\\dot{\\theta}_1 + \\dot{\\theta}_2) \\sin{(\\theta_1 + \\theta_2)} - l_1 \\dot{\\theta}_1 \\sin{\\theta_1} & -l_2 (\\dot{\\theta}_1 + \\dot{\\theta}_2) \\sin{(\\theta_1 + \\theta_2)} \\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} \\dot{\\theta}_1 \\\\ \\dot{\\theta}_2 \\end{bmatrix} + \\begin{bmatrix} -l_2 \\sin{(\\theta_1 + \\theta_2)} -l_1 \\sin{\\theta_1} & -l_2 \\sin{(\\theta_1 + \\theta_2)} \\\\ l_2 \\cos{(\\theta_1 + \\theta_2)} + l_1 \\cos{\\theta_1} & l_2 \\cos{(\\theta_1 + \\theta_2)} \\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} \\ddot{\\theta}_1 \\\\ \\ddot{\\theta}_2 \\end{bmatrix},\n",
    "\\end{equation}\n",
    "\n",
    "that is, $\\ddot{\\mb{r}}$ is an affine expression in $\\ddot{\\mb{q}}$. This means $\\ddot{h}$ is an affine expression in $\\mb{u}$ and can therefore be used in an inequality constraint of an optimization problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pick $\\alpha > 0$. Since the pendulum starts from rest, $\\dot{\\mb{q}}_0 = \\mb{0}_2$, and since $\\dot{\\mb{r}}_{20}^\\mathcal{I}$ is linear in $\\dot{\\mb{q}}$, initially $\\dot{h}(\\mb{q}_0, \\dot{\\mb{q}}_0) = 0$. If $h(\\mb{q}_0) \\geq 0$, that is, the system is initially safe, then:\n",
    "\n",
    "\\begin{equation}\n",
    "    \\dot{h}(\\mb{q}_0, \\dot{\\mb{q}}_0) \\geq -\\alpha h(\\mb{q}_0).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Picking actions $\\mb{u}$ such that:\n",
    "\n",
    "\\begin{align}\n",
    "    \\der{}{t}(\\dot{h}(\\mb{q}, \\dot{\\mb{q}}) + \\alpha h(\\mb{q})) &= \\ddot{h}(\\mb{q}, \\dot{\\mb{q}}, \\mb{u}) + \\alpha \\dot{h}(\\mb{q}, \\dot{\\mb{q}})\\\\\n",
    "    &\\geq -\\alpha ( \\dot{h}(\\mb{q}, \\dot{\\mb{q}}) + \\alpha h(\\mb{q}) )\\\\\n",
    "    &= -\\alpha \\dot{h}(\\mb{q}, \\dot{\\mb{q}}) - \\alpha^2 h(\\mb{q})\n",
    "\\end{align}\n",
    "\n",
    "for all $\\mb{q} \\in \\mathcal{C}$ and $\\dot{\\mb{q}} \\in \\R^2$ ensures the inequality $\\dot{h}(\\mb{q}, \\dot{\\mb{q}}) \\geq -\\alpha h(\\mb{q})$ continues to be satisfied by Nagumo's theorem. It it is always possible to pick such actions, then $\\dot{h} + \\alpha h$ is called a control safety function (CSF)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Applying this reasoning once more, if $\\dot{h}(\\mb{q}, \\dot{\\mb{q}}) \\geq -\\alpha h(\\mb{q})$ for all $\\mb{q} \\in \\mathcal{C}$ and $\\dot{\\mb{q}} \\in \\R^2$, then $h(\\mb{q}) \\geq 0$ continues to be satisfied by Nagumo's theorem. This means the actions maintain the safety of system by ensuring $\\mb{q} \\in \\mathcal{C}$, or that $\\mathcal{C}$ is a safe set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\bs{\\Lambda} \\in \\bb{S}_{++}^{2}$ be an action cost, let $\\mb{k}: \\mathcal{Q} \\times \\R^2 \\to \\R^2$ be a baseline controller, let $\\rho \\geq 0$ be a regularization coefficient. Consider the optimization-based controller solving:\n",
    "\n",
    "\\begin{align}\n",
    "    \\inf_{\\substack{\\mb{u} \\in \\R^2 \\\\ \\mb{x} \\in \\mathcal{Q} \\times \\R^2}} ~&~ \\mb{u}^\\top\\bs{\\Lambda}\\mb{u} + \\rho \\norm{ \\mb{u} - \\mb{k}(\\mb{x}) }_2^2\\\\\n",
    "    \\mathrm{s.t.} ~&~ \\mb{x} = (\\mb{q} - \\mb{q}_d, \\dot{\\mb{q}})\\\\\n",
    "    &~ \\dot{V}(\\mb{x}, \\mb{u}) \\leq -\\alpha' V(\\mb{x})\\\\\n",
    "    &~ \\ddot{h}(\\mb{q}, \\dot{\\mb{q}}, \\mb{u}) + \\alpha \\dot{h}(\\mb{q}, \\dot{\\mb{q}}) \\geq -\\alpha (\\dot{h}(\\mb{q}, \\dot{\\mb{q}}) +\\alpha h(\\mb{q})),\n",
    "\\end{align}\n",
    "\n",
    "for all $\\mb{q} \\in \\mathcal{Q}$ and $\\mb{\\dot{\\mb{q}}} \\in \\R^2$. Here, $\\mb{x}$ is denoted as a decision variable only for convenience of notation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The additional constraint may render the optimization problem infeasible. The stability constraint can be relaxed to find safe solutions. Let $\\sigma > 0$ be a slack coefficient, and consider the optimization-based controller solving:\n",
    "\n",
    "\\begin{align}\n",
    "    \\inf_{\\substack{\\mb{u} \\in \\R^2 \\\\ \\mb{x} \\in \\mathcal{Q} \\times \\R^2 \\\\ \\delta \\in \\R}} ~&~ \\mb{u}^\\top\\bs{\\Lambda}\\mb{u} + \\rho \\norm{ \\mb{u} - \\mb{k}(\\mb{x}) }_2^2 + \\sigma \\delta^2\\\\\n",
    "    \\mathrm{s.t.} ~&~ \\mb{x} = (\\mb{q} - \\mb{q}_d, \\dot{\\mb{q}})\\\\\n",
    "    &~ \\dot{V}(\\mb{x}, \\mb{u}) \\leq -\\alpha' V(\\mb{x}) + \\delta\\\\\n",
    "    &~ \\ddot{h}(\\mb{q}, \\dot{\\mb{q}}, \\mb{u}) + \\alpha \\dot{h}(\\mb{q}, \\dot{\\mb{q}}) \\geq -\\alpha (\\dot{h}(\\mb{q}, \\dot{\\mb{q}}) +\\alpha h(\\mb{q})),\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import concatenate, reshape\n",
    "\n",
    "class SetPointOutput(RoboticDynamics):\n",
    "    def __init__(self, robotic_dynamics, q_d):\n",
    "        RoboticDynamics.__init__(self, robotic_dynamics.B)\n",
    "        self.robotic_dynamics = robotic_dynamics\n",
    "        self.q_d = q_d\n",
    "        \n",
    "    def eval(self, x, t):\n",
    "        q, q_dot = reshape(x, (2, -1))\n",
    "        return concatenate([q - self.q_d, q_dot])\n",
    "        \n",
    "    def drift(self, x, t):\n",
    "        return self.robotic_dynamics.drift(x, t)\n",
    "    \n",
    "    def act(self, x, t):\n",
    "        return self.robotic_dynamics.act(x, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from core.dynamics import AffineQuadCLF\n",
    "from numpy.linalg import eigvalsh\n",
    "\n",
    "q_d = array([-1, 0])\n",
    "set_point = SetPointOutput(dip, q_d)\n",
    "lyap = AffineQuadCLF.build_care(set_point, Q, R)\n",
    "slack_coeff = 1e3\n",
    "alpha = min(eigvalsh(Q)) / max(eigvalsh(lyap.P))\n",
    "comp = lambda r: alpha * r\n",
    "\n",
    "lqr = LQRController.build(set_point, Q, R)\n",
    "fb_lin = FBLinController(set_point, lqr)\n",
    "\n",
    "qp = QPController(dip, 2)\n",
    "qp.add_regularizer(fb_lin, 1)\n",
    "qp.add_stability_constraint(lyap, comp, True, slack_coeff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "qp_data = dip.simulate(x_0, qp, ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107d3b780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, us = qp_data\n",
    "\n",
    "figure(figsize=(12, 8))\n",
    "\n",
    "subplot(221)\n",
    "plot(ts, xs[:, 0], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_1$', fontsize=16)\n",
    "\n",
    "subplot(222)\n",
    "plot(ts, xs[:, 1], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\theta_2$', fontsize=16)\n",
    "\n",
    "subplot(223)\n",
    "plot(ts[:-1], us[:, 0], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_1$', fontsize=16)\n",
    "\n",
    "subplot(224)\n",
    "plot(ts[:-1], us[:, 1], linewidth=3)\n",
    "grid()\n",
    "xlabel('Time (sec)', fontsize=16)\n",
    "ylabel('$\\\\tau_2$', fontsize=16)\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import dot\n",
    "from numpy.linalg import norm\n",
    "from core.dynamics import AffineDynamics, ScalarDynamics\n",
    "\n",
    "class SafetyFunction(AffineDynamics, ScalarDynamics):\n",
    "    def __init__(self, double_inverted_pendulum, height, prop, alpha):\n",
    "        self.dynamics = double_inverted_pendulum\n",
    "        self.height = height\n",
    "        self.prop = prop\n",
    "        self.alpha = alpha\n",
    "        self.p = array([self.height, 0, 0])\n",
    "        \n",
    "    def r(self, q):\n",
    "        _, _, l_1, l_2, _ = self.dynamics.params\n",
    "        theta_1, theta_2 = q\n",
    "        r_1 = l_2 * cos(theta_1 + theta_2) + l_1 * cos(theta_1)\n",
    "        r_2 = l_2 * sin(theta_1 + theta_2) + l_1 * sin(theta_1)\n",
    "        r_3 = 0\n",
    "        return array([r_1, r_2, r_3])\n",
    "    \n",
    "    def r_dot(self, q, q_dot):\n",
    "        return dot(self.r_ddot_act(q), q_dot)\n",
    "    \n",
    "    def r_ddot_drift(self, q, q_dot):\n",
    "        _, _, l_1, l_2, _ = self.dynamics.params\n",
    "        theta_1, theta_2 = q\n",
    "        theta_1_dot, theta_2_dot = q_dot\n",
    "        drift_1 = -l_2 * ((theta_1_dot + theta_2_dot) ** 2) * cos(theta_1 + theta_2) - l_1 * (theta_1_dot ** 2) * cos(theta_1)\n",
    "        drift_2 = -l_2 * ((theta_1_dot + theta_2_dot) ** 2) * sin(theta_1 + theta_2) - l_1 * (theta_1_dot ** 2) * sin(theta_1)\n",
    "        drift_3 = 0\n",
    "        return array([drift_1, drift_2, drift_3])\n",
    "    \n",
    "    def r_ddot_act(self, q):\n",
    "        _, _, l_1, l_2, _ = self.dynamics.params\n",
    "        theta_1, theta_2 = q\n",
    "        act_1 = array([-l_2 * sin(theta_1 + theta_2) - l_1 * sin(theta_1), -l_2 * sin(theta_1 + theta_2)])\n",
    "        act_2 = array([l_2 * cos(theta_1 + theta_2) + l_1 * cos(theta_1), l_2 * cos(theta_1 + theta_2)])\n",
    "        act_3 = array([0, 0])\n",
    "        return array([act_1, act_2, act_3])\n",
    "\n",
    "    def h(self, q):\n",
    "        return (norm(self.r(q) - self.p) ** 2 - (self.prop ** 2) * (self.height ** 2)) / 2\n",
    "    \n",
    "    def h_dot(self, q, q_dot):\n",
    "        return dot(self.r(q) - self.p, self.r_dot(q, q_dot))\n",
    "    \n",
    "    def h_ddot_drift(self, q, q_dot):\n",
    "        r_dot = self.r_dot(q, q_dot)\n",
    "        return dot(r_dot, r_dot) + dot(self.r(q) - self.p, self.r_ddot_drift(q, q_dot))\n",
    "    \n",
    "    def h_ddot_act(self, q):\n",
    "        return dot(self.r(q) - self.p, self.r_ddot_act(q))\n",
    "        \n",
    "    def eval(self, x, t):\n",
    "        q, q_dot = reshape(x, (2, -1))\n",
    "        return self.h_dot(q, q_dot) + self.alpha * self.h(q)\n",
    "    \n",
    "    def drift(self, x, t):\n",
    "        q, q_dot = reshape(x, (2, -1))\n",
    "        return self.h_ddot_drift(q, q_dot) + self.alpha * self.h_dot(q, q_dot)\n",
    "    \n",
    "    def act(self, x, t):\n",
    "        q, q_dot = reshape(x, (2, -1))\n",
    "        return self.h_ddot_act(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "height = l_1 + l_2\n",
    "prop = 0.2\n",
    "alpha = 2.5\n",
    "safety = SafetyFunction(dip, height, prop, alpha)\n",
    "\n",
    "alpha_stability = min(eigvalsh(Q)) / max(eigvalsh(lyap.P))\n",
    "comp_stability = lambda r: alpha_stability * r\n",
    "comp_safety = lambda r: 5 * r\n",
    "\n",
    "qp = QPController(dip, 2)\n",
    "qp.add_regularizer(fb_lin, 1)\n",
    "qp.add_stability_constraint(lyap, comp_stability, True, slack_coeff)\n",
    "qp.add_safety_constraint(safety, comp_safety)\n",
    "\n",
    "qp_data = dip.simulate(x_0, qp, ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b1c1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import axis\n",
    "\n",
    "xs, us = qp_data\n",
    "rs = array([safety.r(q) for q in xs[:, :2]])\n",
    "r_joints = array([array([l_1 * cos(theta_1), l_1 * sin(theta_1), 0]) for theta_1 in xs[:, 0]])\n",
    "hs = array([safety.h(q) for q in xs[:, :2]])\n",
    "\n",
    "thetas = linspace(0, 2 * 3.14, 1000)\n",
    "unsafe = array([array([prop * height * cos(theta), height + prop * height * sin(theta)]) for theta in thetas])\n",
    "base = array([0, 0])\n",
    "theta_1_d, theta_2_d = q_d\n",
    "target = array([l_2 * sin(theta_1_d + theta_2_d) + l_1 * sin(theta_1_d), l_2 * cos(theta_1_d + theta_2_d) + l_1 * cos(theta_1_d)])\n",
    "\n",
    "figure(figsize=(12, 4))\n",
    "\n",
    "subplot(121)\n",
    "plot(rs[:, 1], rs[:, 0], linewidth=3, label='End')\n",
    "plot(r_joints[:, 1], r_joints[:, 0], linewidth=3, label='Joint')\n",
    "plot(unsafe[:, 0], unsafe[:, 1], 'r', linewidth=3)\n",
    "ylabel('$x_1$ (m)', fontsize=16)\n",
    "xlabel('$x_2$ (m)', fontsize=16)\n",
    "grid()\n",
    "legend(fontsize=16)\n",
    "axis('equal')\n",
    "axis([-1, 1, -0.2, 1.2])\n",
    "\n",
    "subplot(122)\n",
    "plot(ts, hs, linewidth=3)\n",
    "xlabel('$t$ (sec)', fontsize=16)\n",
    "ylabel('$h$', fontsize=16)\n",
    "grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b3aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "fig = figure()\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "ax.fill(unsafe[:, 0], unsafe[:, 1], 'r')\n",
    "ax.plot(target[0], target[1], 'x', markersize=20)\n",
    "ax.axis('equal')\n",
    "ax.grid('on')\n",
    "ax.set_xlim([-1, 1])\n",
    "ax.set_ylim([-0.2, 1.2])\n",
    "\n",
    "link1, = ax.plot([], [], linewidth=3)\n",
    "link2, = ax.plot([], [], linewidth=3)\n",
    "\n",
    "def init():\n",
    "    link1.set_data([], [])\n",
    "    link2.set_data([], [])\n",
    "    return link1, link2\n",
    "\n",
    "def update(idx):   \n",
    "    base = array([0, 0])\n",
    "    joint = r_joints[idx]\n",
    "    end = rs[idx]\n",
    "    link1.set_data([base[1], joint[1]], [base[0], joint[0]])\n",
    "    link2.set_data([joint[1], end[1]], [joint[0], end[0]])\n",
    "    return link1, link2\n",
    "\n",
    "anim = FuncAnimation(fig, update, init_func=init, frames=500, interval=20, blit=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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