{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 MPC\n",
    "This notebook contains the CVXPY implementation of a MPC\n",
    "本篇笔记包含了一个基于CVXPY的MPC实现\n",
    "This is the simplest one\n",
    "这是最简单的一个"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MPC Problem formulation MPC问题的表述\n",
    "\n",
    "**Model Predictive Control** refers to the control approach of **numerically** solving a optimization problem at each time step.\n",
    "**模型预测控制**是指在每个时间步上**数值**地解决一个优化问题的控制方法。 \n",
    "\n",
    "The controller generates a control signal over a fixed lenght T (Horizon) at each time step.\n",
    "控制器在每个时间步上生成一个固定长度T（视野）的控制信号。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![mpc](img/mpc_block_diagram.png)\n",
    "\n",
    "![mpc](img/mpc_t.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear MPC Formulation 线性MPC表述\n",
    "\n",
    "Linear MPC makes use of the **LTI** (Linear time invariant) discrete state space model, wich represents a motion model used for Prediction.\n",
    "线性MPC使用**LTI**（线性时不变）离散状态空间模型，该模型表示用于预测的运动模型。\n",
    "\n",
    "$x_{t+1} = Ax_t + Bu_t$\n",
    "\n",
    "The LTI formulation means that **future states** are linearly related to the current state and actuator signal. Hence, the MPC seeks to find a **control policy** U over a finite lenght horizon.\n",
    "LTI表述意味着**未来状态**与当前状态和执行器信号之间是线性相关的。因此，MPC试图找到一个有限长度视野上的**控制策略**U。\n",
    "\n",
    "$U={u_{t|t}, u_{t+1|t}, ...,u_{t+T|t}}$\n",
    "\n",
    "The objective function used minimize (drive the state to 0) is:\n",
    "用于最小化（将状态驱动至0）的目标函数为：\n",
    "\n",
    "$\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\min_{} \\quad &  \\sum^{t+T-1}_{j=t} x^T_{j|t}Qx_{j|t} + u^T_{j|t}Ru_{j|t}\\\\\n",
    "\\textrm{s.t.} \\quad &  x(0) = x0\\\\\n",
    "  & x_{j+1|t} = Ax_{j|t}+Bu_{j|t}) \\quad  \\textrm{for} \\quad t<j<t+T-1    \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "$\n",
    "\n",
    "Other linear constrains may be applied,for instance on the control variable:\n",
    "其他线性约束也可以应用，比如对控制变量的约束\n",
    "\n",
    "$ U_{MIN} < u_{j|t} < U_{MAX}    \\quad  \\textrm{for} \\quad t<j<t+T-1 $\n",
    "\n",
    "The objective fuction accounts for quadratic error on deviation from 0 of the state and the control inputs sequences. Q and R are the **weight matrices** and are used to tune the response.\n",
    "目标函数考虑了状态偏离0的二次误差以及控制输入序列的二次误差。矩阵Q和R是权重矩阵，用于调整系统响应\n",
    "Because the goal is tracking a **reference signal** such as a trajectory, the objective function is rewritten as:\n",
    "由于目标是跟踪参考信号（例如轨迹），目标函数被重写为：\n",
    "\n",
    "$\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\min_{} \\quad &  \\sum^{t+T-1}_{j=t} \\delta x^T_{j|t}Q\\delta x_{j|t} + u^T_{j|t}Ru_{j|t}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "$\n",
    "\n",
    "where the error w.r.t desired state is accounted for:\n",
    "其中考虑了相对于期望状态的误差：\n",
    "\n",
    "$ \\delta x = x_{j,t,ref} - x_{j,t} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Formulation: Study case  研究案例问题表述\n",
    "\n",
    "In this case, the objective function to minimize is given by:\n",
    "在这种情况下，要最小化的目标函数为：\n",
    "\n",
    "https://borrelli.me.berkeley.edu/pdfpub/IV_KinematicMPC_jason.pdf\n",
    "\n",
    "$\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\min_{} \\quad &  \\sum^{t+T-1}_{j=t} (x_{j} - x_{j,ref})^TQ(x_{j} - x_{j,ref}) + \\sum^{t+T-1}_{j=t+1} u^T_{j}Ru_{j} + (u_{j} - u_{j-1})^TP(u_{j} - u_{j-1}) \\\\\n",
    "\\textrm{s.t.} \\quad &  x(0) = x0\\\\\n",
    "  & x_{j+1} = Ax_{j}+Bu_{j} \\quad  \\textrm{for} \\quad t<j<t+T-1  \\\\\n",
    "  & u_{MIN} < u_{j} < u_{MAX} \\quad  \\textrm{for} \\quad t<j<t+T-1 \\\\\n",
    "  & \\dot{u}_{MIN} < \\frac{(u_{j} - u_{j-1})}{ts} < \\dot{u}_{MAX} \\quad  \\textrm{for} \\quad t+1<j<t+T-1 \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "$\n",
    "\n",
    "\n",
    "Where R,P,Q are the cost matrices used to tune the response.\n",
    "R,P,Q是用于调整响应的成本矩阵。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRELIMINARIES 准备工作\n",
    "\n",
    "* linearized system dynamics 线性化系统动力学\n",
    "* function to represent the track 轨迹函数\n",
    "* function to represent the **reference trajectory** to track 跟踪的**参考轨迹**函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T06:09:14.320605Z",
     "start_time": "2024-10-23T06:09:13.499103Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "from scipy.interpolate import interp1d\n",
    "import cvxpy as cp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use(\"ggplot\")\n",
    "\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T06:09:15.094392Z",
     "start_time": "2024-10-23T06:09:15.092291Z"
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Control problem statement.\n",
    "控制问题陈述。\n",
    "\"\"\"\n",
    "\n",
    "N = 4  # number of state variables (x, y, v, theta)\n",
    "M = 2  # number of control variables (a, delta)\n",
    "T = 20  # Prediction Horizon (time steps)\n",
    "DT = 0.2  # discretization step [s]\n",
    "\n",
    "\n",
    "def get_linear_model(x_bar, u_bar):\n",
    "    \"\"\"\n",
    "    Computes the LTI approximated state space model x' = Ax + Bu + C\n",
    "    计算LTI近似状态空间模型x' = Ax + Bu + C\n",
    "    \"\"\"\n",
    "\n",
    "    L = 0.3  # vehicle wheelbase\n",
    "\n",
    "    x = x_bar[0]\n",
    "    y = x_bar[1]\n",
    "    v = x_bar[2]\n",
    "    theta = x_bar[3]\n",
    "\n",
    "    a = u_bar[0]\n",
    "    delta = u_bar[1]\n",
    "\n",
    "    A = np.zeros((N, N))\n",
    "    A[0, 2] = np.cos(theta)\n",
    "    A[0, 3] = -v * np.sin(theta)\n",
    "    A[1, 2] = np.sin(theta)\n",
    "    A[1, 3] = v * np.cos(theta)\n",
    "    A[3, 2] = v * np.tan(delta) / L\n",
    "    A_lin = np.eye(N) + DT * A\n",
    "\n",
    "    B = np.zeros((N, M))\n",
    "    B[2, 0] = 1\n",
    "    B[3, 1] = v / (L * np.cos(delta) ** 2)\n",
    "    B_lin = DT * B\n",
    "\n",
    "    f_xu = np.array(\n",
    "        [v * np.cos(theta), v * np.sin(theta), a, v * np.tan(delta) / L]\n",
    "    ).reshape(N, 1)\n",
    "    C_lin = DT * (\n",
    "        f_xu - np.dot(A, x_bar.reshape(N, 1)) - np.dot(B, u_bar.reshape(M, 1))\n",
    "    )\n",
    "\n",
    "    return np.round(A_lin, 4), np.round(B_lin, 4), np.round(C_lin, 4)\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "the ODE is used to update the simulation given the mpc results\n",
    "I use this insted of using the LTI twice\n",
    "ODE用于根据mpc结果更新仿真，而不是两次使用LTI\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "def kinematics_model(x, t, u):\n",
    "    \"\"\"\n",
    "    Returns the set of ODE of the vehicle model.\n",
    "    返回车辆模型的ODE模型\n",
    "    \"\"\"\n",
    "\n",
    "    L = 0.3  # vehicle wheelbase\n",
    "    dxdt = x[2] * np.cos(x[3])\n",
    "    dydt = x[2] * np.sin(x[3])\n",
    "    dvdt = u[0]\n",
    "    dthetadt = x[2] * np.tan(u[1]) / L\n",
    "\n",
    "    dqdt = [dxdt, dydt, dvdt, dthetadt]\n",
    "\n",
    "    return dqdt\n",
    "\n",
    "\n",
    "def predict(x0, u):\n",
    "    \"\"\"\n",
    "    预测车辆的真实轨迹，使用ODE求解 \n",
    "    \"\"\"\n",
    "\n",
    "    x_ = np.zeros((N, T + 1))\n",
    "\n",
    "    x_[:, 0] = x0\n",
    "\n",
    "    # solve ODE\n",
    "    for t in range(1, T + 1):\n",
    "\n",
    "        tspan = [0, DT]\n",
    "        x_next = odeint(kinematics_model, x0, tspan, args=(u[:, t - 1],))\n",
    "\n",
    "        x0 = x_next[1]\n",
    "        x_[:, t] = x_next[1]\n",
    "\n",
    "    return x_\n",
    "\n",
    "\n",
    "def compute_path_from_wp(start_xp, start_yp, step=0.1):\n",
    "    \"\"\"\n",
    "    Computes a reference path given a set of waypoints\n",
    "    给定一组路径点，计算参考路径\n",
    "    \"\"\"\n",
    "\n",
    "    final_xp = []\n",
    "    final_yp = []\n",
    "    delta = step  # [m]\n",
    "\n",
    "    for idx in range(len(start_xp) - 1):\n",
    "        section_len = np.sum(\n",
    "            np.sqrt(\n",
    "                np.power(np.diff(start_xp[idx : idx + 2]), 2)\n",
    "                + np.power(np.diff(start_yp[idx : idx + 2]), 2)\n",
    "            )\n",
    "        )\n",
    "\n",
    "        interp_range = np.linspace(0, 1, np.floor(section_len / delta).astype(int))\n",
    "\n",
    "        fx = interp1d(np.linspace(0, 1, 2), start_xp[idx : idx + 2], kind=1)\n",
    "        fy = interp1d(np.linspace(0, 1, 2), start_yp[idx : idx + 2], kind=1)\n",
    "\n",
    "        final_xp = np.append(final_xp, fx(interp_range))\n",
    "        final_yp = np.append(final_yp, fy(interp_range))\n",
    "\n",
    "    dx = np.append(0, np.diff(final_xp))\n",
    "    dy = np.append(0, np.diff(final_yp))\n",
    "    theta = np.arctan2(dy, dx)\n",
    "\n",
    "    return np.vstack((final_xp, final_yp, theta))\n",
    "\n",
    "\n",
    "def get_nn_idx(state, path):\n",
    "    \"\"\"\n",
    "    Computes the index of the waypoint closest to vehicle\n",
    "    计算最接近车辆的路径点的索引\n",
    "    \"\"\"\n",
    "\n",
    "    dx = state[0] - path[0, :]\n",
    "    dy = state[1] - path[1, :]\n",
    "    dist = np.hypot(dx, dy)\n",
    "    nn_idx = np.argmin(dist)\n",
    "\n",
    "    try:\n",
    "        v = [\n",
    "            path[0, nn_idx + 1] - path[0, nn_idx],\n",
    "            path[1, nn_idx + 1] - path[1, nn_idx],\n",
    "        ]\n",
    "        v /= np.linalg.norm(v)\n",
    "\n",
    "        d = [path[0, nn_idx] - state[0], path[1, nn_idx] - state[1]]\n",
    "\n",
    "        if np.dot(d, v) > 0:\n",
    "            target_idx = nn_idx\n",
    "        else:\n",
    "            target_idx = nn_idx + 1\n",
    "\n",
    "    except IndexError as e:\n",
    "        target_idx = nn_idx\n",
    "\n",
    "    return target_idx\n",
    "\n",
    "\n",
    "def get_ref_trajectory(state, path, target_v):\n",
    "    \"\"\"\n",
    "    Adapted from pythonrobotics\n",
    "    获取参考轨迹\n",
    "    从当前位置开始，截取路径上的一段作为参考轨迹，其中v=固定的，参考的方向转角为0\n",
    "    \"\"\"\n",
    "    xref = np.zeros((N, T + 1))\n",
    "    dref = np.zeros((1, T + 1))\n",
    "\n",
    "    # sp = np.ones((1,T +1))*target_v #speed profile\n",
    "\n",
    "    ncourse = path.shape[1]\n",
    "\n",
    "    ind = get_nn_idx(state, path)\n",
    "\n",
    "    xref[0, 0] = path[0, ind]  # X\n",
    "    xref[1, 0] = path[1, ind]  # Y\n",
    "    xref[2, 0] = target_v  # sp[ind] #V\n",
    "    xref[3, 0] = path[2, ind]  # Theta\n",
    "    dref[0, 0] = 0.0  # steer operational point should be 0\n",
    "\n",
    "    dl = 0.05  # Waypoints spacing [m]\n",
    "    travel = 0.0\n",
    "\n",
    "    for i in range(T + 1):\n",
    "        travel += abs(target_v) * DT  # current V or target V?\n",
    "        dind = int(round(travel / dl))\n",
    "\n",
    "        if (ind + dind) < ncourse:\n",
    "            xref[0, i] = path[0, ind + dind]\n",
    "            xref[1, i] = path[1, ind + dind]\n",
    "            xref[2, i] = target_v  # sp[ind + dind]\n",
    "            xref[3, i] = path[2, ind + dind]\n",
    "            dref[0, i] = 0.0\n",
    "        else:\n",
    "            xref[0, i] = path[0, ncourse - 1]\n",
    "            xref[1, i] = path[1, ncourse - 1]\n",
    "            xref[2, i] = 0.0  # stop? #sp[ncourse - 1]\n",
    "            xref[3, i] = path[2, ncourse - 1]\n",
    "            dref[0, i] = 0.0\n",
    "\n",
    "    return xref, dref"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MPC \n",
    "\n",
    "test single iteration\n",
    "测试单次迭代"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T08:23:39.847687Z",
     "start_time": "2024-10-23T08:23:39.780867Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "===============================================================================\n",
      "                                     CVXPY                                     \n",
      "                                     v1.5.3                                    \n",
      "===============================================================================\n",
      "(CVXPY) Oct 23 04:23:39 PM: Your problem has 124 variables, 166 constraints, and 0 parameters.\n",
      "(CVXPY) Oct 23 04:23:39 PM: It is compliant with the following grammars: DCP, DQCP\n",
      "(CVXPY) Oct 23 04:23:39 PM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)\n",
      "(CVXPY) Oct 23 04:23:39 PM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.\n",
      "(CVXPY) Oct 23 04:23:39 PM: Your problem is compiled with the CPP canonicalization backend.\n",
      "-------------------------------------------------------------------------------\n",
      "                                  Compilation                                  \n",
      "-------------------------------------------------------------------------------\n",
      "(CVXPY) Oct 23 04:23:39 PM: Compiling problem (target solver=OSQP).\n",
      "(CVXPY) Oct 23 04:23:39 PM: Reduction chain: CvxAttr2Constr -> Qp2SymbolicQp -> QpMatrixStuffing -> OSQP\n",
      "(CVXPY) Oct 23 04:23:39 PM: Applying reduction CvxAttr2Constr\n",
      "(CVXPY) Oct 23 04:23:39 PM: Applying reduction Qp2SymbolicQp\n",
      "(CVXPY) Oct 23 04:23:39 PM: Applying reduction QpMatrixStuffing\n",
      "(CVXPY) Oct 23 04:23:39 PM: Applying reduction OSQP\n",
      "(CVXPY) Oct 23 04:23:39 PM: Finished problem compilation (took 2.905e-02 seconds).\n",
      "-------------------------------------------------------------------------------\n",
      "                                Numerical solver                               \n",
      "-------------------------------------------------------------------------------\n",
      "(CVXPY) Oct 23 04:23:39 PM: Invoking solver OSQP  to obtain a solution.\n",
      "-------------------------------------------------------------------------------\n",
      "                                    Summary                                    \n",
      "-------------------------------------------------------------------------------\n",
      "(CVXPY) Oct 23 04:23:39 PM: Problem status: optimal\n",
      "(CVXPY) Oct 23 04:23:39 PM: Optimal value: 5.630e+02\n",
      "(CVXPY) Oct 23 04:23:39 PM: Compilation took 2.905e-02 seconds\n",
      "(CVXPY) Oct 23 04:23:39 PM: Solver (including time spent in interface) took 3.982e-03 seconds\n",
      "CPU times: user 60.9 ms, sys: 5.23 ms, total: 66.1 ms\n",
      "Wall time: 62.7 ms\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[0, 2] = np.cos(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:28: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[0, 3] = -v * np.sin(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:29: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[1, 2] = np.sin(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:30: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[1, 3] = v * np.cos(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:31: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[3, 2] = v * np.tan(delta) / L\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:36: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  B[3, 1] = v / (L * np.cos(delta) ** 2)\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "# 限制条件\n",
    "MAX_SPEED = 1.5  # m/s\n",
    "MAX_STEER = np.radians(30)  # rad\n",
    "MAX_ACC = 1.0\n",
    "REF_VEL = 1.0   # 目标路径参考速度\n",
    "\n",
    "#获取参考轨迹，线性插值，三个点[0,0],[3,0],[6,0]\n",
    "track = compute_path_from_wp([0, 3, 6], [0, 0, 0], 0.05)\n",
    "\n",
    "# Starting Condition 初始条件\n",
    "x0 = np.zeros(N)\n",
    "x0[0] = 0  # x\n",
    "x0[1] = -0.5  # y\n",
    "x0[2] = 0.0  # v\n",
    "x0[3] = np.radians(-80)  # yaw\n",
    "\n",
    "# starting guess 开始猜测\n",
    "u_bar = np.zeros((M, T))\n",
    "u_bar[0, :] = MAX_ACC / 2  # a\n",
    "u_bar[1, :] = 0.1  # delta\n",
    "\n",
    "# dynamics starting state w.r.t world frame 与世界坐标系相关的动力学起始状态\n",
    "x_bar = np.zeros((N, T + 1)) # 4x21\n",
    "x_bar[:, 0] = x0\n",
    "\n",
    "# prediction for linearization of costrains 用于约束线性化的预测\n",
    "# 这部分应用线性模型，得到预测的轨迹\n",
    "for t in range(1, T + 1):\n",
    "    xt = x_bar[:, t - 1].reshape(N, 1)\n",
    "    ut = u_bar[:, t - 1].reshape(M, 1)\n",
    "    A, B, C = get_linear_model(xt, ut) # 获取在t - 1时刻的线性近似模型\n",
    "    xt_plus_one = np.squeeze(np.dot(A, xt) + np.dot(B, ut) + C)\n",
    "    x_bar[:, t] = xt_plus_one  # 获取t时刻的状态\n",
    "\n",
    "# x_bar是根据猜测的u_bar获取的预测状态估计\n",
    "\n",
    "# CVXPY Linear MPC problem statement CVXPY线性MPC问题陈述\n",
    "x = cp.Variable((N, T + 1)) # 4x21维，状态向量\n",
    "u = cp.Variable((M, T)) # 2x20维，控制向量\n",
    "cost = 0\n",
    "constr = []\n",
    "\n",
    "# Cost Matrices\n",
    "Q = np.diag([10, 10, 10, 10])  # state error cost 状态误差成本\n",
    "Qf = np.diag([10, 10, 10, 10])  # state  final error cost 最终状态误差成本\n",
    "R = np.diag([10, 10])  # input cost 输入成本\n",
    "R_ = np.diag([10, 10])  # input rate of change cost 输入变化率成本\n",
    "\n",
    "# Get Reference_traj 获取参考轨迹，根据当前位置截取的路径上的一系列点，并赋值目标速度和转角\n",
    "# x_ref 表示参考状态，d_ref表示参考转角\n",
    "x_ref, d_ref = get_ref_trajectory(x_bar[:, 0], track, REF_VEL)\n",
    "\n",
    "# Prediction Horizon 预测视野\n",
    "for t in range(T):\n",
    "\n",
    "    # Tracking Error 跟踪误差\n",
    "    cost += cp.quad_form(x[:, t] - x_ref[:, t], Q)\n",
    "\n",
    "    # Actuation effort 执行努力\n",
    "    cost += cp.quad_form(u[:, t], R)\n",
    "\n",
    "    # Actuation rate of change 变化率\n",
    "    if t < (T - 1):\n",
    "        cost += cp.quad_form(u[:, t + 1] - u[:, t], R_)\n",
    "\n",
    "    # Kinrmatics Constrains (Linearized model) 运动学约束（线性化模型）\n",
    "    A, B, C = get_linear_model(x_bar[:, t], u_bar[:, t])\n",
    "    constr += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t] + C.flatten()]\n",
    "\n",
    "# Final Point tracking 最终点跟踪\n",
    "cost += cp.quad_form(x[:, T] - x_ref[:, T], Qf)\n",
    "\n",
    "# sums problem objectives and concatenates constraints. 求和问题目标并连接约束。\n",
    "constr += [x[:, 0] == x_bar[:, 0]]  # starting condition 初始条件\n",
    "constr += [x[2, :] <= MAX_SPEED]  # max speed 最大速度\n",
    "constr += [x[2, :] >= 0.0]  # min_speed (not really needed) 最小速度（实际上不需要）\n",
    "constr += [cp.abs(u[0, :]) <= MAX_ACC]  # max acc 最大加速度\n",
    "constr += [cp.abs(u[1, :]) <= MAX_STEER]  # max steer 最大转向\n",
    "# for t in range(T):\n",
    "#     if t < (T - 1):\n",
    "#         constr += [cp.abs(u[0,t] - u[0,t-1])/DT <= MAX_ACC]     #max acc\n",
    "#         constr += [cp.abs(u[1,t] - u[1,t-1])/DT <= MAX_STEER]   #max steer\n",
    "\n",
    "prob = cp.Problem(cp.Minimize(cost), constr) # 构建问题\n",
    "solution = prob.solve(solver=cp.OSQP, verbose=True) # 求解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T08:23:43.320874Z",
     "start_time": "2024-10-23T08:23:43.203207Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 4 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_mpc = np.array(x.value[0, :]).flatten()\n",
    "y_mpc = np.array(x.value[1, :]).flatten()\n",
    "v_mpc = np.array(x.value[2, :]).flatten()\n",
    "theta_mpc = np.array(x.value[3, :]).flatten()\n",
    "a_mpc = np.array(u.value[0, :]).flatten()\n",
    "delta_mpc = np.array(u.value[1, :]).flatten()\n",
    "\n",
    "# simulate robot state trajectory for optimized U\n",
    "x_traj = predict(x0, np.vstack((a_mpc, delta_mpc)))\n",
    "\n",
    "# plt.figure(figsize=(15,10))\n",
    "# plot trajectory\n",
    "plt.subplot(2, 2, 1)\n",
    "plt.plot(track[0, :], track[1, :], \"b\")\n",
    "plt.plot(x_ref[0, :], x_ref[1, :], \"g+\")\n",
    "plt.plot(x_traj[0, :], x_traj[1, :])    #根据mpc优化后的a和delta，预测的轨迹\n",
    "plt.axis(\"equal\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.xlabel(\"x\")\n",
    "\n",
    "# plot v(t)\n",
    "plt.subplot(2, 2, 3)\n",
    "plt.plot(a_mpc)\n",
    "plt.ylabel(\"a_in(t)\")\n",
    "# plt.xlabel('time')\n",
    "\n",
    "\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(theta_mpc) \n",
    "plt.ylabel(\"theta(t)\")  # 航向角\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(delta_mpc)\n",
    "plt.ylabel(\"d_in(t)\")   # 前轮转角\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 下图展示的结果并不准确\n",
    "# 这是因为在做约束条件中，xt+1 = Axt + But + C时，A，B，C是线性化的模型，且是基于猜测的x_bar和u_bar来线性化的\n",
    "# 所以需要通过滚动优化，获得更准确的猜测和状态猜测\n",
    "# 这里有一个问题，那是否要将这次计算的u，作为下一次的猜测基础？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## full track demo "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T08:19:27.567266Z",
     "start_time": "2024-10-23T08:19:11.796354Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[0, 2] = np.cos(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:28: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[0, 3] = -v * np.sin(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:29: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[1, 2] = np.sin(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:30: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[1, 3] = v * np.cos(theta)\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:31: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  A[3, 2] = v * np.tan(delta) / L\n",
      "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_12777/1770301921.py:36: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  B[3, 1] = v / (L * np.cos(delta) ** 2)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVXPY Optimization Time: Avrg: 0.0791s Max: 0.1699s Min: 0.0546s\n"
     ]
    }
   ],
   "source": [
    "track = compute_path_from_wp(\n",
    "    [0, 3, 4, 6, 10, 12, 14, 6, 1, 0], [0, 0, 2, 4, 3, 3, -2, -6, -2, -2], 0.05\n",
    ")\n",
    "\n",
    "# track = compute_path_from_wp([0,10,10,0],\n",
    "#                              [0,0,1,1],0.05)\n",
    "\n",
    "sim_duration = 200  # time steps\n",
    "opt_time = []\n",
    "\n",
    "x_sim = np.zeros((N, sim_duration))\n",
    "x_sim[0,0] = 0  # x\n",
    "x_sim[1,0] = -0.5  # y\n",
    "x_sim[2,0] = 0.0  # v\n",
    "x_sim[3,0] = np.radians(-60.0)  # yaw\n",
    "u_sim = np.zeros((M, sim_duration - 1))\n",
    "\n",
    "MAX_SPEED = 1.5  # m/s\n",
    "MAX_ACC = 1.0  # m/ss\n",
    "MAX_D_ACC = 1.0  # m/sss\n",
    "MAX_STEER = np.radians(30)  # rad\n",
    "MAX_D_STEER = np.radians(30)  # rad/s\n",
    "\n",
    "REF_VEL = 1.0  # m/s\n",
    "\n",
    "# Starting Condition\n",
    "x0 = np.zeros(N)\n",
    "x0 = x_sim[:, 0]\n",
    "\n",
    "# starting guess\n",
    "u_bar = np.zeros((M, T))\n",
    "u_bar[0, :] = MAX_ACC / 2  # a\n",
    "u_bar[1, :] = 0.0  # delta\n",
    "\n",
    "for sim_time in range(sim_duration - 1):\n",
    "\n",
    "    iter_start = time.time()\n",
    "\n",
    "    # dynamics starting state\n",
    "    # 获取当前时刻的状态，x_sim是通过ode计算出的真值\n",
    "    x_bar = np.zeros((N, T + 1))\n",
    "    x_bar[:, 0] = x_sim[:, sim_time]\n",
    "\n",
    "    # prediction for linearization of costrains\n",
    "    # 获取各参考点处的线性化模型参数\n",
    "    for t in range(1, T + 1):\n",
    "        xt = x_bar[:, t - 1].reshape(N, 1)\n",
    "        ut = u_bar[:, t - 1].reshape(M, 1)\n",
    "        A, B, C = get_linear_model(xt, ut)\n",
    "        xt_plus_one = np.squeeze(np.dot(A, xt) + np.dot(B, ut) + C)\n",
    "        x_bar[:, t] = xt_plus_one\n",
    "\n",
    "    # CVXPY Linear MPC problem statement\n",
    "    # 构建MPC问题和求解器\n",
    "    x = cp.Variable((N, T + 1))\n",
    "    u = cp.Variable((M, T))\n",
    "    cost = 0\n",
    "    constr = []\n",
    "\n",
    "    # Cost Matrices\n",
    "    Q = np.diag([20, 20, 10, 0])  # state error cost\n",
    "    Qf = np.diag([30, 30, 30, 0])  # state final error cost\n",
    "    R = np.diag([10, 10])  # input cost\n",
    "    R_ = np.diag([10, 10])  # input rate of change cost\n",
    "\n",
    "    # Get Reference_traj\n",
    "    x_ref, d_ref = get_ref_trajectory(x_bar[:, 0], track, REF_VEL)\n",
    "\n",
    "    # Prediction Horizon\n",
    "    for t in range(T):\n",
    "\n",
    "        # Tracking Error\n",
    "        cost += cp.quad_form(x[:, t] - x_ref[:, t], Q)\n",
    "\n",
    "        # Actuation effort\n",
    "        cost += cp.quad_form(u[:, t], R)\n",
    "\n",
    "        # Actuation rate of change\n",
    "        if t < (T - 1):\n",
    "            cost += cp.quad_form(u[:, t + 1] - u[:, t], R_)\n",
    "            constr += [\n",
    "                cp.abs(u[0, t + 1] - u[0, t]) / DT <= MAX_D_ACC\n",
    "            ]  # max acc rate of change\n",
    "            constr += [\n",
    "                cp.abs(u[1, t + 1] - u[1, t]) / DT <= MAX_D_STEER\n",
    "            ]  # max steer rate of change\n",
    "\n",
    "        # Kinrmatics Constrains (Linearized model)\n",
    "        A, B, C = get_linear_model(x_bar[:, t], u_bar[:, t])\n",
    "        constr += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t] + C.flatten()]\n",
    "\n",
    "    # Final Point tracking\n",
    "    cost += cp.quad_form(x[:, T] - x_ref[:, T], Qf)\n",
    "\n",
    "    # sums problem objectives and concatenates constraints.\n",
    "    constr += [x[:, 0] == x_bar[:, 0]]  # starting condition\n",
    "    constr += [x[2, :] <= MAX_SPEED]  # max speed\n",
    "    constr += [x[2, :] >= 0.0]  # min_speed (not really needed)\n",
    "    constr += [cp.abs(u[0, :]) <= MAX_ACC]  # max acc\n",
    "    constr += [cp.abs(u[1, :]) <= MAX_STEER]  # max steer\n",
    "\n",
    "    # Solve\n",
    "    prob = cp.Problem(cp.Minimize(cost), constr)\n",
    "    solution = prob.solve(solver=cp.OSQP, verbose=False)\n",
    "\n",
    "    # retrieved optimized U and assign to u_bar to linearize in next step\n",
    "    # 将本次计算出的u_bar作为下次猜测的起点\n",
    "    u_bar = np.vstack(\n",
    "        (np.array(u.value[0, :]).flatten(), (np.array(u.value[1, :]).flatten()))\n",
    "    )\n",
    "    \n",
    "    # 本次的执行值\n",
    "    u_sim[:, sim_time] = u_bar[:, 0]\n",
    "\n",
    "    # Measure elpased time to get results from cvxpy\n",
    "    opt_time.append(time.time() - iter_start)\n",
    "\n",
    "    # 用ode模型仿真车辆运动\n",
    "    # move simulation to t+1\n",
    "    tspan = [0, DT]\n",
    "    x_sim[:, sim_time + 1] = odeint(\n",
    "        kinematics_model, x_sim[:, sim_time], tspan, args=(u_bar[:, 0],)\n",
    "    )[1]\n",
    "\n",
    "print(\n",
    "    \"CVXPY Optimization Time: Avrg: {:.4f}s Max: {:.4f}s Min: {:.4f}s\".format(\n",
    "        np.mean(opt_time), np.max(opt_time), np.min(opt_time)\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-23T08:19:28.719495Z",
     "start_time": "2024-10-23T08:19:28.541069Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1500x1000 with 5 Axes>",
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fHjtIM05KU1W/wVq5I0W//k2/Zj3VJVq/AAAABBohOgAAANCJ/NUD3Vor7dwqu/xD2c8+looKfAeEhEqDhqj3iDGqiEtyAvP4RBmX64iveSwzxjh94ftEyaRmNNtvq6u096td+mzBHp2atl5hxVulXdtkykqUGrFD2rRD2rRU4fXj09yhypw0RDVrB2nhqmFavy9d6/cNlUTrFwAAgEAjRAcAAAA6iT96oNv8PbIrPpJd8ZG0Z0fjjl5hMmMnSsOynCrzhGS53G7FJCaqcs8eJ3SH35iQUMWOT9O3xqdJOtm7PX9TmT54Llfnjs5Wn9LNsju3SXu2y1VdpTHR66TqdTp+xFve8QVVfVWXMFgbK4ZowWfDteb1dM3/T6qkI2/9QrAOAABweAjRAQAAgE7SUT3Qbcle2c8/kV3+kbR1Q+MOd7CUdbxcEyZLo4+TCQlt/SQIiPghkbrkd5GSGqvXradOhd/ka+mLezQlM1vhJVukXdtk83MVF1okFRcpQSt1SpYz3iOXNu1PkVKGqrJ/hoqjMrWxKl1SRLtav9BTHQAA4PAQogMAAACd7Eh6oNvy/bIrl8ou/1DK+UpqqCQ3Lmn4GJkTT5MZO1EmPMKfU4cfGFeQ4kYm6sK7EyWN927/amWdfvPDUj3+u1UaoE2yO7dKu7bJtb9M6b23SkVbpaIlkqSTPEE64eShWvPUCM0tGanVpSN0/Lf7K2uc8/vk4NYvB6M6HQAAoHWE6AAAAIAfHU0PdFtVKbt6hdOq5auVUl1t484hw2QmnCZz/MkykTH+mTwCKm5AsM68dpBCzoiVq/8USU7v+2+W79e9Py3U76/9XH3LshWWl6PgAyUaHZWt0VHZuiJlgSTpwN5QffXyMP1u+Ah9MmekHisZoa0VA3X22VWS6KkOAADQXoToAAAAgJ8cSQ90W1sjfb1KdsWHsquWS9VVjQcmD3aC8xNOlYnt7+/pI8D69/foV7/a57PNGKN+qVEaf2WSIi4Zouj+Hllrtf5/JXrwxlzd++PPFVmUraCdGxSmAzqh72qd0He19/iS6kitKRmusRkj9M6fRupPJSOUVxVPT3UAAIA2EKIDAAAAftLeHujxcTWy2etkl38ou/J/UnmT4DS2v8yEyU54PiAlQCtBV3JwuG6MUW2feL2VO1I3nZyl/qNrZD0eKW+3dny8WYv/sUPfO261epdsUnRImU6LW67T4pZ7jz8Q2k95nkzFDBmj/A8H6evKNHl69aGnOgAAQD1CdAAAAMDPWuuBbqsqZd97Q5733pBKihoPiIx2qs0nnCalZsiY5j2sgabi4+v0y1/u8wbfxuWSEpNVOjxVd66L04kPFWjU8App13bt/HSzPnx6u04fvFbxtVsVVrVXg6uW6jeZS6XVklZLW8oHakfMMNUNHqFhfSbqqzV9JTntX1rqqS5RoQ4AAHouQnQAAACgA7WnB7qprZbn3YWyb74olZU4B4ZFyIw/SebEyVLmKBlXUKfPHd1XS61fJN9w3biDpUFDVFI2TLesjdNzt+5VSWSFehVsVMmqTdr20RadOWSt+hzYrdSIHVL1DinnHS0+9RGVvROhL18arS+Ks+RJG66IoPE+PdXj4+to/QIAAHosQnQAAACggxyqB3qQqdVtp72sjOf+KVta4OyMS5CZ+gOn8jw4WEBHailcbwjWhw+vUf/+QZIytTZplH7+5zi9fX+B+vcu0f6vNyl8zzeq2/CNehesV2RwuSbHLdPkuGWSpF+c49L6/w7VZ3PH6IviLI29aIgmXhDd7PoE6wAAoCcgRAcAAAA6SKs90P+vSCf3ek9xy55RaMkuqVRSdF+ZCy6VOeUsp0IY6CStVa03iE+NUHxqlqQsrV0brInn9dUrj36hxANfK2zPOrm3faPelbkaGZmjkZE5+tGgl6TN0oHH++nv48aoamGGNuZm6kDcEO0tad76hZ7qAACguyFEBwAAADqYtwe6tToz/mNd+NWj6lW42dnZu4/Mty6WOf1bMiGhbZ4H6CwH91RvyqMg9UpPVfLoZEnnau3aYP3oQumVBz9Rwf+ypc3rNSpqvcKq9+r8xPekTe9Jm6TKulC5zTDdmjlWe98fonUHMlQXFkVPdQAA0O0QogMAAABHobUe6OE7Vivh/af07+O/kQolhYXLnPNdmbO+I9MrPIAzBpprT0/1pvKq4rRv6ClKmXSS8vODtKm2Srv/t0Ur/rNJ52Ws0qDateobUqoMrVbGkNXSWklrpU37U2TCR+kHyeO1dVmqZBMlY+ipDgAAujRCdAAAAOAItdQDfWzUVxrw0l81OHaFJKnKhqrutG+r9/emyUT0CdRUgSPSVk/1+Pg69e/vqQ+3XbLuYfrbvafqlN/vVW7fOhWV7FLRZ9natHijThu4SgPMVg3pvV1DtF2nZL0prZAKP47RiuKxKsgaoYFThsmlvj7Xaq31C+E6AADoTIToAAAAwBFq2gN9VMwG9Vr8jAYU/k+SZF1uFY/6luy3Llb80OjAThToQIfqqd6vn0ejR9dK6q+1Mcm65aEf6Lnb9mpfRKnCc7/RvtXZKl2ZrQlxXyk2tFjnJ7wv5b8vvSCtOTtC5c+O0O7MkaoYMEpF7owWr0FfdQA9TXFxsWpra9scExcXp4KCgk6akf+wjq7lWFmH2+1WTEzMEZ+fEB0AAAA4CqkR23T6pj8rasNHkrWqsy6VjTxT/a68RHGx/QM9PaDTtNVXvV8/j0aO7iVpnNYOnqAf/C1Oby/crbVvbNfmRes1oe+XOj5mtaKC9yuy6DPpf59JkgbYEM07cZTsf0do8/YRqkgYprjkkBavT3U6gO6strZWNTU1re43xnjHWWs7a1odjnV0Layj/QjRAQAAgMPQ0APdvS9fvd5+Qe+euljuHCc03Jl4un74wg36600Rio1t/T/CQE90qNYvzQQF68wfD9boC4dIukCL1rj0r98X6qpJKxSdv1Yn9F2luNAindRvpbRtpbRNqvUEaU9whlxJo3R2/ERlr0yVFCZJ2rvX0FMdAAD4BSE6AAAA0E55eS7dNtPqpJKndEXKywoNqpFc0pK8U/WnnJ9q3b5MTZxYpfj44kBPFegS2t9TXZKCtW5fpgZeFat+/c5TgbX6bEWePvznRv3srOWKKvhKMcrVwLpvpB3f6MnjX5I+kb55c6iWF41TyMgR6h860eda9FQHAAAdgRAdAAAAaAfrqVPdW6/qkT7PKzymUpKUFz1G1795ky67PUUPja6RVOANBgG0rH091et/ksMk6Kd3jtaPLj1FvePrtGFjocJ3f63Kr9bJk/O10ntv1fDIjRoeuVEqly4/U9r3jwEqTB2hiqTR2h+RJSmu2TXoqQ4cW9atW6fXXntNW7ZsUXFxsX79619rwoQJrY7/+uuvdffddzfbPmfOHA0YMMD7etmyZZo3b57y8vLUv39/XXbZZW2eF0D3RYgOAAAAHILN3y3Pvx5W/03rJbd0oH+mIi6/Qntrj9fK5+N13+iCxtAPwBFps/WLVF+13lfSqVo7bIrOOy9OP7lsp3a8n60JMas0oe9KjYzMUZ8Du6R1uxSz7h0NkPTp6YmqfXG0tq8bpYrkLMUMjW3x/FSnAz1XVVWVBg8erDPOOEMPPvhgu497+OGHFR4e7n0dGRnpfZ6Tk6OHH35Yl156qSZMmKAVK1Zozpw5uueee5Sent6h8wcQeIToAAAAQCusx6Oy199W+Nv/lqu2StVB4brty19rws9P1ei6Wm3YyD+ngY5y2D3VJU2eGqZ+P8qSlKW1a6/VZbcF6bopnyt429ea2PcLZUWt08DwPVLuHil3sSSp2NVfYfFZujj5JG1ekS7ZfpIxLfZUlwjXgZ5g3LhxGjdu3GEfFxUVpYiIiBb3LVy4UFlZWZo2bZokadq0aVq3bp0WLlyoWbNmHc10AXRB/KsfAAAAaIEtKlDlE4+q96ZVkqRPC0/Qr9bcqd2VCXrpN43jnB7oLQd8AI5Oa61fGsL14cNrfILtstpoHfejLPXrN0rSpXrty1q98uA23X7xUoXvXKMBNd8oRnmKyX1HD2a9Iy2Tdr6foGV7j5MyRiolbJJkQ3yuResX4Nj1m9/8RjU1NUpOTtZFF12kUaNGeffl5OToggsu8Bk/ZswYvfnmm22es6amRjU1jT+9ZoxRWFiY93lrGva1NcaWFsvzxgtSQa5UV//nVbBbru9cITN4aJvz6iztWUd3wDq6ls5YByE6AAAA0IS1VvZ/78u+8A+FHCjXgbpQbRh9nWLOPF+/+CpUN98sPfBAibd9Cz3Qgc7XVl91n57qCtbHhROlC4eod3ydNu6qUfiedSr/8mtVfPmVxvf9Wslhufp+8kKpYqG+f4ZU/kSc9qZmqWLAaPUaM0qySc2uQXU60LPFxMToJz/5idLS0lRbW6uPPvpIv//973XnnXdqxIgRkqSSkhJFR0f7HBcdHa2SkpI2z71gwQLNnz/f+zo1NVWzZ89WXFzz+ze0JCEhodV9JYte1r73m4f4bo9H8bOfaNf5O0tb6+hOWEfX4s91EKIDAAAA9WxZiTzP/FVatUySVJEwTN+ad6/+9otwJ5QzTjA3enQNPdCBLqZ9PdWDJI3W2pTxuuhvcZp+eaE2Ltqkif2+0El9v9CY6K8VUVUgrX9X0evfld6VQkPjNCfrBO1fNFzrS0aoJipRe4tcVKcDPVhSUpKSkho/QMvIyFBhYaFef/11b4jeEmvtISthp02bpqlTp3pfN4wvKChQbW1tq8cZY5SQkKDc3FxZa1scU7d2Zf2ER8p12nlSbY08T/9FVV+t1O4vlktVlfLMnysz9VK5ho9pc57+0p51dAeso2tpzzrcbne7P6xq8fgjPhIAAADoQezKpU6Avr9M1uVW/ok/1Ichl2lLeT+tXVsiSdqwgX8+A13VkfRUP/sCox9clSYpTWvXXq4f3hqqx3+zVJ7sr9Rn9xpvqP695Del7DelbGn3gf6qisrSpcknKrgkVdbGdvsfgwdwaBkZGfr444+9r1uqOi8tLVVUVFSb5wkODlZwcHCL+9oTYlprWxxnrZXdvkmS5Lr0OpmUIc6OVSukVcvkWfii7IqPJeuR3bND+r9/ywQFHfJ6/tLaOrob1tG1+HMd/C8AAAAAxzRbvl/2hSdkl30gSdpaO1TX/+8effNGhnfMzTdHe5/TAx3oPg63p/qBumjFT85S/MUjlZ9/uTbVVCp36QatmZ+tS8ctV3z5eiWF5Smp+h2Ny3pHelqqXBCviuQsBQ0fragJo2T6HXmVG4Cua8uWLT7tWzIyMrR27VqfqvI1a9YoIyOjhaM7QUGuVFEuud1SUop3szn+ZNlVy2SXf9g4tqxEdvmHMpOmBGCiQPdEiA4AAIBjlv1qpTxPPSqV7JWMS4XHXayz/nCTHnykXOnpBVq7Nlg33xxND3Sgh2mrp3rDfud9HiQbPFoP/nGKcidcpZffCtJxMWt0Yt+VmtTvc42N/koh+/IV8s0S6Zsl8rwiKS5BZliWyieeJtt/oBQV02nrAtCyyspK5ebmel/n5+dr69at6t27t2JjY/X888+rqKhIN9xwgyRp4cKFiouL08CBA1VbW6uPP/5Yy5cv169+9SvvOc4//3zdeeedevXVV3XCCSfos88+09q1a3XPPfd0+vokyW5zqtA1YLCMu7HS3QwdLp+63IQBUu4u2VXLJEJ0oN0I0QEAAHDMsZUHZOf/W/bDt50N8UlyXTNL+RWjVe0JUXp6qU/Pc3qgAz3foVq/nH9+pa680iMpVWvXZuj7N/9UD92/Ryf0XaOIHasVlbdawbs3SAW5sgW5Kvp4sXNgQrLMsNEyw7KkjNEyfSI7b1EAJEmbNm3S3Xff7X399NNPS5ImT56smTNnqri4WIWFhd79tbW1euaZZ1RUVKSQkBANHDhQt956q8aPH+8dk5mZqVmzZumFF17QvHnzlJCQoFmzZik9Pb3zFtbUrq2SJJOS5ru9b5wUFCTVOX+2mW9fJvuPP0k7t3bu/IBujhAdAAAAxxS7YZ08/37Y+bFnSQcmfltbx10jW9FLa9c6lVsNj/RAB44dh9v6RZJGjHUrbfRoSaMl/VD2QIW04WvZ7LVyb1qvms3ZUu5O2dydsh+85Rw0YJDMsCyZYaOl9FEyEb39vzjgGDdy5Ei9+OKLre6fOXOmz+sLL7xQF1544SHPO3HiRE2cOPGo59chSvY6j/3ifTYbY6SQUOlAhfN6xFinMr0gV7aiXCY8onPnCXRT/K8AAAAAxwRbUy376nOy77wqWSv1jVXphbP04wfP0LLfhfqMpQc6gAaHav3SlAkLl7JOkGvMBCUkJmr3xg2y2WudX+vXSLu2Sbu2ye7aJvvu65Ix0sC0JqH6CJle4X5eEYCeyJYUOU+i+zbb57pmljyP3Sdz+fUyvSOlvrFSUaFTjZ4xsnMnCnRThOgAAADo8ey2TfL8a460e7skyZx8pswl12nXpmgtWxaqRx8tVnp6LT3QAbTLoVq/NDARvaVxE2XGOZWqdl+p5A3V10q5O6Xtm2S3b5JdvEByuaRBQxtD9SEjZEJD27wGAEiS6kN0E9U8RDdjJ8r16DwptJezYWCaVFQou2OLDCE60C6E6AAAAOixbF2d7JsvyS6c5/QCjYyW68qZMmNP9BmXnl5LD3QA7XY41elNmT5R0vGnyBx/iiTJluyVzf7KCdbXr3HaTG3Jkd2SI/vWfCnILQ3JlMnMcnqqp2X43DAQALxKW69ElyTTK6zx+cBU2dUrpJ1bOmNmQI9AiA4AAIAeye4rk+cfD0jfrHY2HDdJritmKL8iWvlrgySJHugAAspE95M5cbJ04mRJkt1bIJu9Rlq/1nksKpRyvpbN+Vr29f84fY2HjqivVM+SBqXJuIICvAoAgWZraqT99R/stRKi+0hKcY7bs8OPswJ6Fv6XAAAAgB7Hbt8sz1/vk/bmS6G9ZH44Q+bEycrPD9KMGTFatowe6AC6HtMvTmbSmdKkM2WtdW78t36NtH6N87ivVFr3pey6L50bA4ZFSBkjZYaPcUL1pBTnJoIAji1lxc6j2y1F9DnkcJOY7PwZsmenrLX8uQG0AyE6AAAAehTP8g9ln35Uqq6W4hLkmnm7zIBBkqT8/CB6oAPoFowxUnyiTHyidNq5Tqi+e7tsQ6Ce/ZV0oFxavUJ29QonEOsT5YTpw0Y7j3GJhGPAsaDhpqJRfdv3nu8/QDIuqWK/tK9Eiozx6/SAnoAQHQAAAD2CrauTfeVp5+Z8kjRynFw/vtm5sd9B6IEOoLsxxkgDBjkfCp75bVlPnbR9c2OovmGdtK9U9rOPpc8+dkL1vrEymVlSffsX0zc20MsA4A8lbfdDP5gJDpFi4537MOzeQYgOtAMhOgAAALo9u79Mnica+5+bb31P5rs/lHEF6auv3Hr66Qidf/4B7d7t/POXHugAujvjCpIGp8sMTpfO+55sbY20OccJ1bPXSJuypaJC2f+9J/3vPSdUj0+qr1TPkhk22rnRKYBuzzapRG+3xIFOy6g9O50/FwC0if81AAAAoFuzO7Y4/c8L86SQULmuvknm+FO8+59+OkLPPef8akAPdAA9jXEHO/3RM0ZKuky2qkratK6+Un2ttHWjlL9bNn+39NHbTqg+YFDjTUozRsmERxziKgC6pPqe6CYqut2HmMRk2TWfSdxcFGgXQnQAAAB0W57PPpGd+4hUXeX0P59xm0xyqs+Y88+v1HPPRejRR4tVWWnogQ7gmGBCQ6UR42RGjJMk2YpyacPXst+sdtq/7Nom7domu2ub7LuvO/2RBw91KtSHZUlDRjjnAND1le9zHiMi239M4kBJks3d6YcJAT0PIToAAAC6Heupk13wrOzbLzsbRoyT6ye/lonoI0nKy3MpPz9IkrR7t/NYWWnUq5eVJCUl1dIDHcAxxYRHSGMmyIyZIEmyZSWy2V9JDT3V83dLW3Jkt+TIvvWyFOSWhmTKZNZXqqdlONXuALqeinLnMaL9P01iEpKdn0ihEh1oF0J0AAAAdCu2fJ88//iT9PWXkiRz7kUyF13p9AeWE6DPmBGjZct8KyibtnB5880wnX56dafNGQC6GhMZLXPCKdIJTvsrW1TgtH1pCNWLC6Wcr2VzvpZ9/T9SSKg0dERj+5dBad4/dwEEli3f7zwJb34z9VbVV6KrpEi2opx2TsAhEKIDAACg27A7tzr9zwtypZBQmek/l+uEU33G5OcHadmyUD36aLHS02u1dm2wt4VLUlKd3nyzl666qjxAKwCArsn0jZOZNEWaNEXWWqlgjxOmr1/rPO4rldZ9KbvuS6d6NSzC6cE+fIwTqielyBgT6GUAx6YKJ0Rv+Im89jDhEc6NSEuLpNydUlqmv2YH9AiE6AAAAOgW7BefyvPvR6SqSqlfvFwzb5cZmNrq+PR035Yto0fXaPToGp1+elVnTBcAui1jjBSfJBOfJJ12nhOq795ef5PSNVL2V9KBcmn1CtnVK5xQvU+UE6Y39FSPSyRUBzpLQ0/0w6lEl6TEZKm0SHbPThlCdKBNhOgAAADo0qynTvbV52Tfmu9sGD5Grp/cLNO78eZZTXugr10b7PO4YQP/5AWAo2GMkQYMkhkwSDrz27KeOmn75sZQfcM6aV+p7GcfS5997ITqfWNlMutD9cwsmX5xgV4G0HM19EQ/zBDdJCY772H6ogOHxP8oAAAA0GXZ8v3y/PNB6asvJEnmnGkyF10lE9TYh7c9PdAnTqxSfHxdp8wZAHo64wqSBqfLDE6XzvuebG2NtGVDY6i+eb1UVCj7v/ek/73nhOpxCTKZo6XM0TLDRstE9wv0MoAewXo8R3RjUUnevug2d2cHzwroeQjRAQAA0CXZXdvleewP9f3PQ2SuulGuEyc3G9dWD/SGdi7x8XXq39/T2UsAgGOCcQdL6SNk0kdI3/6BbFWVtOkbJ1TPXitt3SAV5MoW5EqfvOOE6v0HOKH6sNEymaNkImMCvQyge6qskGz9v3EOtxI9Idl5P1KJDhwSIToAAAC6HLtyqTz/erix//mM/yeTktbmMa31QAcAdC4TGiqNGCszYqwkyVZWSBu+kc1eI7t+rbR9s5S3SzZvl/TR206IlzjQqVDPzJIyRsn0iWzrEgAalDs3FVVwiExIaNtjD1Zfia6CPNmaapngkI6dG9CDEKIDAACgy7DWyr79suwrTzsbhmXJ9ZPfNAtT6IEOAN2H6RUujT5OZvRxkiRbsV/asK6+/ctaaecWac8O2T07ZN9/0zkoebBMfesXpY+SiTjMGyYCx4oj7IcuSYqKkcIinBsF5+2Wkgd36NSAnoT/YQAAAKBLsJ462Rf+4Q1QzFnfkfn+1T79zyV6oANAd2fCe0tjJsiMmSBJsvvLpJyvZNevddq/7N4u7dwqu3Or7LuvS8ZIA9PqK9VHS+kjZcLCA7wKdCfr1q3Ta6+9pi1btqi4uFi//vWvNWHChFbHL1++XIsXL9bWrVtVW1ur5ORkXXzxxRo7dqx3zAcffKC//vWvzY599tlnFRLSiRXdFfWV6EfwQZMxRkpMljZny+7ZKUOIDrSKEB0AAAABZ6urnBuIfrlMMkbmkmvlOus7LY6lBzoA9Cymd6Q0fpLM+EmSJFtWIpv9lZRd31M9d5e0fZPs9k2yi1+VXC5p0FCnUj1jlDR0OKE62lRVVaXBgwfrjDPO0IMPPnjI8d98842ysrJ02WWXKSIiQu+//75mz56t++67T6mpqd5xYWFheuSRR3yO7dQAXZLK9zmPR1KJLskkJstuzqYvOnAIhOgAAAAIKLu/TJ6//EHatF5yB8t13S9ljjv5kMfRAx0AeiYTGS1zwinSCadIkmzJ3vpQfa3s+jXODae35MhuyZF9+2XJuKSUNJn0kTIZI6WhI+ipDh/jxo3TuHHj2j1++vTpPq8vv/xyff755/riiy98QnRjjKKjoztolkfGHkUluiQpaZBznh2bO2hGQM9EiA4AAICAsYV58jxyl1NlGB4h18zfOgHIQeiBDgDHLhPdT+bEydKJkyVJdm+BU6GevVZ2w9dOqL5to+y2jbJL/usclJTi/H1SH6yb6H4BXAG6O4/HowMHDqh3b9+gurKyUjNmzJDH49HgwYN16aWX+oTsnaLc6YluwiOO6HCTlunc3HfTellrnRYvAJrhfxwAAAAICLt9kzx/vkcqLZb6xsp1010ySSnNxtEDHQDQlOkXJzNpijRpiiTJFhU6YfqGr2VzvnbaUuzeLrt7u/TBW05AGJ8okz5SyhjpPMb2JyxEu73xxhuqqqrSSSed5N2WlJSkGTNmKCUlRQcOHNCbb76pO+64Qw888IASExNbPVdNTY1qahp/cs4Yo7CwMO/z1jTsazbmQOONRY/o9/TgoVKQW9pXKlOYJxPf+tw7Qqvr6GZYR9fSGesgRAcAAECns19/Kc/f7peqDkjJg+X6+Z0yMS1XCdIDHQDQFtM31rdSfV+ptGGd7IavZXO+knZskfL3yObvkT5d4oTqMbFOmJ45UiZ9lJQwoNuHSPCPTz75RC+99JJuvvlmRUVFebdnZGQoIyPD+zozM1O33HKL3nrrLV1zzTWtnm/BggWaP3++93Vqaqpmz56tuLi4ds0nISHB53VxkNF+SX3i4hXVRnjflrz04apev1ZRe3MVMWb8EZ3jcB28ju6KdXQt/lwHIToAAAA6lWfpe7JPPyrV1UnDsuT62W3t+hFkeqADANrD9ImSxp8kM96pGrYV5dKmb2RzvnYq1rdukIoLZVd8KK340AnV+0Q1tn5JHyklD5JxBQV0HQi8pUuX6u9//7t++ctfKisrq82xLpdLQ4YMUW5ubpvjpk2bpqlTp3pfN3x4U1BQoNra2laPM8YoISFBubm5stZ6t9ft3StJ2l9Tp4o9ew65ppbUDRwirV+r4i/+p7Lh7e8dfyRaW0d3wzq6lvasw+12t/vDqhaPP+IjAQAAgMNgrZV98yXZV5+VJJkJk2Wu/rmMO7jZWHqgAwA6igmPkEYfLzP6eEmSraqUNmfXV6p/LW3OlvaVSiuXyq5c6oTq4RHODUqHDpdJGyYNHioT2iug60Dn+uSTT/S3v/1NN910k8aPP3R1trVW27Zt08CBA9scFxwcrODg5v/2aThHe67TdJytrHAee/U64hDUDBkm+45kN67vtCD14HV0V6yja/HnOvgfCAAAAPzOeupkn39c9sO3JUnm3ItkLrpKxuVqNpYe6AAAfzKhvaThY2SGj5Ek2ZoaaduGxkr1jd9IFeXSms9k13zmhOoul5ScKjMkU0obJjNkGH3Vu5HKykqfCvH8/Hxt3bpVvXv3VmxsrJ5//nkVFRXphhtukOQE6I899pimT5+ujIwMlZSUSJJCQkIUHh4uSXrppZeUnp6uxMREb0/0rVu36tprr+3kxR1wHnuFHfk5hmQ6j7u2yR6okAkLP/p5AT0MIToAAAD8ylZVyfPPP0mrlkvGyFz6Y7nOnNrqeHqgAwA6kwkOrq86HyHpYtm6OmnnFidU3/SNtClbKtkrbd8ku32T9P6bTrAeGV0fqGc2VquHhLZ9MQTEpk2bdPfdd3tfP/3005KkyZMna+bMmSouLlZhYaF3/5IlS1RXV6cnn3xSTz75pHd7w3hJKi8v1xNPPKGSkhKFh4crNTVVd999t4YOHdpJq6pXH6KbowjRTXQ/qV+8tDdf2pIjjRjbQZMDeg5CdAAAAPiN3Vcmz19+7/yovDtYrut+JXPcpHYdSw90AEAgmKAgadBQmUFDpbMvlCTZogLZTdnS5vWym9ZL2zdLZSXSqmWyq5Y5oXpQUH21+jApLdN57BdPtXoXMHLkSL344out7m8Ixhvcddddhzzn9OnTNX369KOcWQdoqEQPPYpKdNW3dNmbL7vxGxlCdKAZQnQAAAD4hS3Ilefhu6T83VJ4b7lu+K1M+ogWx9IDHQDQlZm+cTJ946QTTpEk2Zpqadsm2YZQfVO2VFokbdsou22j9N4bTrAe1Veqr1Q3QzKdcD44JKBrQQ9T1dDO5ShbsGSOllZ8JLv8Q9mpl7bYcg84lvE/EgAAAHQ4u22jPI/c7dyorW+cXLPukkls+UZb9EAHAHQ3JjhEGjpcZuhwSfU3hCwqcAL1zdnO447NTrC+8n+yK/9XX63ullLSZNIypSFOb3XTNy6ga0E31xE90SWZCafJzp/rFD989YWUdcLRzw3oQQjRAQAA0KHsV1/I8/fZUlWllJwq102/c3pttoIe6ACA7s4Y47Ru6RcvTThNkmSrqxqr1Teulzavd1rAbMmR3ZIjvfu6bHCIXH9+QcZNPIPDZ63tuBC9V5jMqWfLLn5Vng/fVhAhOuCDP6UBAADQYTyfviv79KOSxyMNHyPXz26TCWvfjxfTAx0A0JOYkFApfYTTyuzc+sCzME92c7a0ab3z2CuMAB1Hrqba+TeXdNQhuiSZk8+SXfyq9PVK2X1lMn0ij/qcQE/Bn9QAAAA4atZa2bfmyy54RpJkJp4u86MbZdzBLY6nBzoA4FhjjJHiEmTiEqQTJ0uSrIefssJRaKhCl6TQXkd9OpOUIqUMkbZvkv38Y5kzLjjqc6JrsHV1kjH0uj8K/A8FAAAAR8VaK/vyU7KLXpEkmfO+J3PRVU5Y0AJ6oAMA4CDQwlFpCNFDe3XY7yVz0hmy2zfJLloge8o5MsEtF0S0xNbWSDlfS+5gqaxYSsv0a89/W1sjyUhF+VJM3GHNtafwtvQJDvYWr9iqSqm4UHb1Cqm2VirYI/vZJ1LiQOenRPtxH4YjQYgOAACAI2Y9dbLP/V32o0WSJHPx1XKdM63NY+iBDgAA0AE6qB96U+bUc2TffkXamy/70dsyZ377kMfYkr2yC1+U/fpLqSC3ycmM1DdO5tRzZL71/Q790Mjz0SLZF5907sEjOfckOPF0mUlTZPonHfX5rbXSzq1SWYlszlfOxr35TsX/gQoporeKQkNVZ4KctjrhvSVPndQnSnK5nJ84ie3vrD8ktM1rHda8PB7ZFR9J2zbKLv/QuXZVpRTSS4qIkOrqnHsvWNv84G0b5bn/Zrl+da9MwoAOm9OxghAdAAAAR8TW1sj+62HZzz6WjEvmyhlynXpOu4+nBzoAAMBR8Faid2CIHtpL5ts/kH32r7JvvyJ72nltVnjbwjx5Hrlbyt3ZuDEswgnQK/Y7Yfyrz8oue1+uS66TyTr+qOZnS4vleeL/nIr3pvbmy775ouz7C+X68a9kRh/Zdez+Mtm3Xpbd9I20aX2bY8vbOk/Dkz5RMsOypDETZCac1upParZrbnt2yLPgGenLZc13Vh1wfjWVkCxFxcj0jZM5bpI8rzwt7d4uz1/+INc9f5FxBR3xXI5FhOgAAAA4bLaqSp7HZ0trP5eC3HJd90uZ409pdTw90AEAADpYVcdXokuSmXSm7OsvSCV7Zf/3rsxp57U4zm5YJ8/Dd0rVVVJUX5kLL5cZP0kmordTyZ23S3b1Z7Kv/0fK3SXPX++VZt0jJSYe0bystfI89Wh9yxi3U91+6rlSaKjs0ndlP1ki7domz5/vkZl8nswVPzus0NruK5Xn/luk/N2NGyP6SANSpPA+MpHRUm2N8/Uu36/wqChV5OdKwSGy+8vq29iUOFXgebucCvF9pU7ByWcfy774pMxJU2S++8PDvqGwXb/G+VrX1UkulzT2RJkR42QGDJKiYqTCPKmi3LlhccIAmZPPalb570rLlOeOGc7cVi2Xxk86rDkc6/gfCwAAAA6LPVAhz19+7/wHJiTE6a046rhWx9MDHQAAoONZP7RzkSQTHCxzzndlX/qX7Py5ssPHOu1Jml67psYJtKurpKHD5brmFz5jjDFSQrJMQrLsaefK86850qrl8jz5oDwTjiy8te/81yngcLvluv0hmeTBjdc760LZ086TXfCs7Luvy374tnP9s77T/vMvfNEJ0KP7ypx+vvOBQGJyi2ONMeqbmKiqPXucDwwOPpfHI9XVOQH6lmzZj99xWsMsekX2y//JfOdyuepvMHzIeRXkyvPPh5wAfcgwuS6+RmbIMN9B9V97c1zrX1vTJ0pm8nmyb74kzzv/VRAh+mHhDhYAAABoN7uvTJ4Hf+sE6GHhcs26p80AXfLtgf722wV64IESSdIDD5To7bcL9PbbBfrrX4vpgQ7g/7N35/FR1df/x1/3ZpKQhSyELISwBQiCgOKCaKkoFrFIRdwogpUqagWtFsX+LLWKWJXaqv2iXdWKEiuKoggoFHdEwWorUSyggMiSlWyEkGRyP78/JhmISUiAzJa8n48Hj8zM/dw750MYzZycOUdERI6Gj5LoANbo8dD3BKg8gLNwQaNEsfngX56K5vhE7Jt/0yjJ3uBaUdHY02+HlG5QXEThvbMwxUVHFY/530bMi095rnfJ1Q0S6N7niYjEnnQt1hXXeM5Z+myrn8fsK/Ak3gH7p7diX3hFswn01rBsGys8HPus0dhTbsT+/dNY037uaXWTvxfzxB9wVi3F1B65iMSUFuPM/yWU7vMMBv3FvMYJ9KOJ69wLPZXsX32JObwFj7RISXQRERERaRVTXITz0J3wzVcQG+cZStR/UKvPr++BXt/3vP72kCE1SqCLiIiIHK26JLrliyS6y4V97SyIiIDNOZj17zQ4bja851l3/kSs6JiWrxcZif3TWyEikqrPP6X293M8LVBayXntec91vndei9Xl1nk/gn4DoboK5/m/NVkp3uj6i5/0tGrJOhEGntTquFrLio3D/t4PsH/3JNY5PwTALPkHzsN3Yaqrmj3PLH8eSos9CfRZ87Aij29IqZXQBU48xXPtdW8d17U6GiXRRURERKRFJn+Ppwpm77eQ2BX7jgexevVtdn1enk1OTrj3D+C9rR7oIiIiIm3ARz3R61nJaVgXTgLAvPysN9lriovgqy89a44wE6fR9foNJOzu/yMsOQ3yduM8+TCmprrFJLfZthm2fA5hLqyLprTY59yyLOwfXw9hYfDph5i3lh/5+l9+Bp+uA9vGnnz9cQ3/bInVKRrryp9hXfkzz/dty+eYpx5tuiVMUQHm/dUA2FNu9CTA24D9vfM819/wXqt+wSAeegcjIiIiIkdkdu3wDDIqLYaUbp4qmKSUZterB7qIiIiIHxw86Pka2clnT2GNmYB593XYV4hZ9hxcOg3z2XrP8My+J2B16Xp010tNJ+meR8m75Sr4/FOcGZdB53hI7Y511ugmB2KaT9Z5zj3te61+PqtXX6zLr8E8/3fMSwsxg0/FSk1vcq2z+hXPOaMuwMroc1T7ORaWZWGdOw7TvZenEv2TD+Dj97GGn91gnflkracPev9BWAMGt10Ag0/z/IKhKN8zkDS96b8XaUiV6CIiIiLSLLNtM85Dv/Ik0DN6eyrQj5BAB/VAFxEREfGL+jYgvkyih0dgXXI1AGbVUs/wzR1bPccGnnxM14zo3Q/7kp8ceqC8FL7ahHnmMcyTj3iGch7GfP6J58ZJw48u9tHjYdDJUFONk/3npqu9c3fB55+AZWH9YMLRbuW4WFknYo27zBPH0/+Hyfl3w9g+/dCz7iiq/Vv1vJGR0Lu/5zm2fN6m127PVIkuIiIiIk0yX36G8/hvoeog9D3BMzQqJrbV59f3QK93eD90ERERETlO1XWV6BHH1ye7JfYZo3DKSjAvPIl5Ndv7uNUr85ivaY2ZgN33BE8V+v4yzKb/Yl77J2bDu5CcinXxVMAz8JM9O8GysQadfHTPYVnYU2fg/GYGfPmZJ1k+5LQGa8xnH3tuDDoZK6XbMe/nWFnjLsd88zVs/BjnLw9i3zEfq1dfTGkxbNvsWXPyiLZ/3qwTMV//D7NZSfTWUiW6iIiIiDRi/vsRzv/d60mgDzwJ+9a5R0ygqwe6iIiIiJ9VV3u+RviuEr2ePWYC9QMxvXo2Px+nJZZlYWUO8PRd75OFfeEVWFf/HACzcomnDzpg/rfRc0JmFlZM56N/nuQ0z6BRwMn+C6aivMFxsznHs27QsGPdynGxXOHYN94Jg0+F6mqcvzyIqaqCr7/0tMzJ6HPULXNa9bxZnvYwZusXbX7t9krvaERERESkAeejtzH/+CM4DgwbgX3dbKzw8GbXqwe6iIiIiP+ZqvpK9Ai/PJ910RTMO68feiCxbZO79pnn4mz6D+ajd3D+8Ufsux6Bb3d4nrtP1jFf17pwkqc1SkGu57oz52BZFsapha82edYMGNIWWzi2+Fwu7Otux5l7MxTmYVY8D2Gen72Pp9r/iPoM8HwtyMXZX37ktQIoiS4iIiIih3HeXol57i8AWGeOxrr6ZqywsCOec3gP9P793eTkhDN7dgIPPVTibd+SklKrHugiIiJyRFdfffUxnTd37lx69+7dtsGEAj/0RD+c1TkOklI8Aykjo7Asq+2f48fXYb7cCLm7MMuew+ze4TnQvdexXzMqGvuGX+I8OBs+24B5c5mn//m326HyAETFQI/ebRL/MccYHYM9+Qacx3+LWf0KdEn2HPDRoFMrJha6dIV9hVTv2ApJ/m9lE2pCKom+evVqVq9eTUFBAQAZGRlcdtllDBsWmI9ciIiIiLQXxhjM60swS58FPIOYrEnTsezWd/9TD3QRERE5HgcPHmTYsGHExcW1ar3jOLz//vs4Tgf9RX1dJbrl457oh7NvvQfn2T9h//Ayn1zfiumMfdVMnMfmYf71KoR7quyt7r2P77q9+mJdcS3mub9iXnkOc9r3Pb3IAfpkYdlHLhrxB+vkM2DYCPjPR1CQ63msh2+S6IAnQb+vkJptW5REb4WQSqJ36dKFK6+8krS0NADeffddfve73/G73/2OHj16BDg6ERERkdBkjMG8tBCz6mUArPE/xrpo8hGri/LybPLzPW82Du+BDqgHuoiIiByzyy67jH79+rVqbW1tLe+//36L6zZt2sSyZcvYvn07xcXF3H777QwfPrzFcxYuXMiuXbtITEzkoosu4vzzz2+w5qOPPmLx4sXk5eWRmprK5MmTW7xum/JzJTqAlZZB2Oz7ffscJ50Op54Fn6zz/KLAsiC95/Ff95xxmA/fhu1bMK8sgroe61a3jOO+dluxf3w9zn8+OvSAjyrRAayMPpiNH1OzfSucPspnz9NehNQ7nNNOazhBd/LkyaxevZqtW7cqiS4iIiJyDIzjYLL/gnnvDQCsK67FHjPhiOeoB7qIiIj4wg9/+EMSEhJavd627VadU1VVRe/evTn33HP5wx/+0OJ18/PzeeCBBzjvvPO4+eab2bx5M0888QRxcXGMGDECgC1btvDoo48yadIkhg8fzoYNG3jkkUe499576d+/f6v3cFzqk+h+rET3F3vSdThf/AcOVkJyGlbk8e/RsizsSdNxHrwDs+5NSEjyHEjtftzXbitWl65YP7wM8/oS6BTlabviq+fq0RsDVG/f6rPnaE9CKol+OMdx+PDDD6mqqiIrq/nhAjU1NdTUHPoYsWVZREVFeW+HqvrYQ3kPIqFArzUR/9BrLTBMbS3m6T96KnIsG/vqm7BHjmnxvNb0QE9NdUhNNYC+p8FErzUR/9BrTeTYTJs27ajWW5bVqnOGDRt2VK2AV69eTdeuXb3XzsjI4Ouvv+a1117zJtFXrFjB0KFDmThxIgATJ05k06ZNrFixgltvvfWo9nHM2nES3UpMwrrkJ5jn/oqVNbjtrtv3BKzhozAb3oXiQs9jqeltdv22YF10JUTHHNcw1VbJ6A2Ae+fX2I7jqfiXZoVcEn3nzp3MmTOHmpoaOnXqxO23305GRvMfu1i6dClLlizx3u/Tpw/z588nOTnZH+H6XH1rGxHxLb3WRPxDrzX/MTU1FD30ayo/fBvsMJJmzyP67PNbPhHYu9fz9ayzEjnlFKj/sWr06AROOcVHAUub0mtNxD/0WhMJTVu3bmXo0KENHjv55JN5++23cbvduFwutmzZwoUXXthgzUknncTKlSv9F6i3nUv7S6ID2OdeiMkc0OaV4taPJnmS6PXSgqcSHcByubAuuNT3T9Q1DWwbU1UFJfsgMcn3zxnCQi6Jnp6ezkMPPURFRQXr16/n8ccfZ+7cuc0m0idOnMj48eO99+srAQoKCnC73X6J2RcsyyItLY3c3FyMMYEOR6Td0mtNxD/0WvMvU1ON8+cHMRs/BpcL+4ZfUtp/CKX12fEm5OXZ5OV5hox6ep8n8NZbJRQU1NT1QE+koKCAvXtD9+erjkCvNRH/0GtNOhqXy9XmxYqff/455eXlnHnmmQCUlJTw5z//mW3btnHSSSdx/fXXExER0abPWa+kpIT4+PgGj8XHx1NbW0t5eTmJiYmUlJQ0aiOTkJBASUnJEa99rB0TvvsJF2PMocGikZ1C5pMvR/tJHat327fGsbr1wImI9P4SwkrsetR/f+3hE0dWeDhOchrk7YH8PVhdugY6pGPmj+9HyCXRXS6X97f5ffv25euvv2blypVcf/31Ta4PDw8nPDy8yWPt4YcZY0y72IdIsNNrTcQ/9FrzPVN1EOfx38KXn0F4BPaMX2ENPuWIf++eHugJreqBru9faNBrTcQ/9FoTOXaLFy9uUA2+aNEivvzyS4YOHcpHH31EWloal112mc+e/7vJuPrX8pGSdMaYFpN4x9sxoT4nZmpq2OU4nsd69sb2Ye9sXwj0J3WKzjqXA+94ZgKldz/2SvRA7+N4FfTM5GDeHuIqy4nt1i3Q4Rw3X34/Qi6J/l3GmAa/wRMRERGRppnKAzgL7oWtmyCyE/bNd2ENGNLiea3pgZ6SUktqquPrLYiIiEgHsXfvXiZM8Aw7r62t5eOPP2bKlCmMHTuWZcuW8fbbb/ssid5URXlZWRlhYWHExsY2u6a0tLRRBft3HWvHhO9+wsVU7Pcey91XjFVW3pqtBVywfFLHXHwVVlkp1vBR7D3CpzGbEyz7OF5Ooqf6vHTLl5QPO/q/h2DRmu/H8X5iJqSS6M899xzDhg0jKSmJgwcP8sEHH/DFF18wZ86cQIcmIiIiEtRMRTnOH+fC9i0QFYN9y91YfU84qmv07+/2Js0BhgypaXBfREREpK1UVlYSExMDwLZt2zh48CCnnXYaAP369ePFF1/02XP379+fTz75pMFjn332GZmZmbhcnlRaVlYWOTk5DRLiGzduJCvryMMgj7djQv0nXExdKxfCXBAWFnKJ3IB/UiemM/aNd3pjOVYB38fxqhuqavJ2h/Y+6vjy+xFSSfTS0lIee+wxiouLiY6OplevXsyZM6fRsAcREREROcSUl+I8/BvYtR1iO2Pfei9Wr75HPCcvzyY/Pwyo74F+6KunB7qIiIiI78TFxbF3714GDhxITk4OycnJJCV5Bh8ePHjQm8xujYMHD5Kbm+u9n5+fz44dO4iNjaVr164899xz7Nu3j5tuugmA888/n1WrVrFw4ULOO+88tmzZwltvvcUtt9zivca4ceO4++67eeWVVzj99NP5+OOPycnJ4d57722jv4EW1CfRI9rnUFHxk7qhrSZ3d4ADCX4h9Q7oxhtvDHQIIiIiIiHFlBR5Euh7v4W4BOxZ87C69zriOZ4e6Imt6oEuIiIi4gsnn3wy//znP9m1axfvvPMOo0aN8h7bvXv3UbVl+Prrr5k7d673/jPPPAPAqFGjmDlzJsXFxRQWFnqPp6SkcOedd7Jw4UJWrVpFYmIiP/3pTxkxYoR3zYABA7j11lt5/vnnWbx4MWlpadx6663079/2gzCbVDcUk0gl0eXYWSl1fdCLCjBOLZYdFtiAglhIJdFFREREpPVMUT7OH34NBbmQ2NWTQE9reXCSeqCLiIhIoE2ePJnCwkLefPNN+vXrx6WXXuo9tnbt2hbbphzuxBNP5IUXXmj2+MyZMxs9NmjQIObPn3/E644YMaJBYt2vqlWJLm0goQuEhUGtG0qKoUvXQEcUtJREFxEREWmHTP4enD/cBfsKoGuqJ4GefHTT6tUDXURERAIlLi6u2Rl4d999NxEREX6OKMjUV6JHdApsHBLSLDuMsOQ0anN3Q1G+kuhHoCS6iIiISDtj9n7rSaCX7oPU7p4Eegs/EKsHuoiIiATaHXfcwYgRIxg+fDgZGRnNrouOjvZjVEGqSu1cpG24UtOpzd2NKcrD6j8o0OEELb0jEhEREWlHzLfbcR75DZSXQvde2LPuxYpLPOI56oEuIiIiweDEE0/kzTffZPHixaSnp3PGGWcwYsQIevfuHejQgo7xVqIriS7Hx5XSjSqAwvxAhxLUlEQXERERaSfM9i04j94NByqgVz/sW+/Bio1r8Tz1QBcREZFgcPXVV3P11Vfz1VdfsX79ej788EOWLl1KSkqKN6Her1+/QIcZHJRElzYSlpruuVGkJPqRKIkuIiIi0g6YLV/gLLgXDlZC3xOwf343VnTMUV1DPdBFREQkGPTr149+/foxZcoUduzYwfr161m/fj2vvfYaXbp0Yfjw4YwYMYITTjgBy7ICHW5gVHkGi1pKostxcqV2A8AoiX5ESqKLiIiIhDiz6b84j//WU5E0YAj2Tb/G6hR1xHPUA11ERERCQe/evenduzeTJk1i165d3oT6G2+8QXx8PH/7298CHWJg1FeiR2qwqBwfV0pdJXphXmADCXJ6hyQiIiISwszGj3H+/CC4a2DwKdg33tliRZJ6oIuIiEgoysjIICMjg0svvZTc3Fw2bNgQ6JACp0rtXKRthCWnem4UF2KM6bif7miBkugiIiIiIcp88gHO338PtbUwbAT2dbOxwsNbPE890EVERCTUpaWlcdFFFwU6jMDxVqIriS7HJ6xLV88NtxsqyqEVM5U6IiXRRUREREKQ8/H7mCf+AI6DNfxsrJ/eiuU6uh/t1ANdREREgpXjOLz++uusXbuWgoICamoa/4yycOHCAEQWJKo9PdFViS7HywqP8CTO95dBSZGS6M1QEl1EREQkxDRIoJ85GmvazVh22BHPUQ90ERERCSXZ2dksX76c3r17M3ToUFxHWSzQ7tVXokeoJ7q0gYQudUn0fZDRJ9DRBCX9F0hEREQkhDgb3sM88TAYB+t752H95KZWJdDVA11ERERCydq1a5kwYQJXXnlloEMJSqZKlejSdqyEJMyuHZiSfagjetOURBcREREJEc76dzFPPnJYAv1mLNtu8Tz1QBcREZFQU11dzdChQwMdRvDy9kRXJbq0gYQunq8lRYGNI4gpiS4iIiISAhok0EeOwbpqZqsS6IdTD3QREREJFUOHDmXr1q0MHjw40KEEpypPEt1SJbq0BW8SfV9g4whiSqKLiIiIBDnno3cwTz3qSaB//3ysqTNaTKCrB7qIiIiEsp/+9Kc8+OCDREZGcsoppxAbG9toTVOPdRjeSnQl0eX4WYlJGMAoid4svYMSERERCWLOR29jnvrjUSfQ1QNdREREQll0dDTp6eksXLiQhQsXNrlm8eLFfo4qiFSrJ7q0ofgkz1cl0ZulJLqIiIhIkHI+fBvzj7oE+tljsabcqB7oIiIi0iH87W9/48MPP+T000+ne/fuuFxKYTVQX4muJLq0AUvtXFqk/wKJiIiIBCFn3VuYp/8IxmCdfQHWlJ+pB7qIiIh0GB9//DGTJ0/moosuCnQowUmDRaUtxSd6vu4vxTjOUb/v6AiURBcREREJMs66NzFP/58ngT7qAqwrW06gqwe6iIiItCcul4s+ffoEOozgVaVKdGlDneM8X2trobICYjoHNp4gpHdUIiIiIkHE+eBNzMK6BPo5P8SafIN6oIuIiEiHM3z4cD777DOGDBkS6FCCjnEcqKn23IlQJbocP8sVDlExngR6WamS6E1QEl1EREQkSDgfrMEsXHAogX7lz7Asq8Xz1ANdRERE2pvvfe97/PWvf8XtdnPKKacQGxvbaE1mZmYAIgsC9a1cQJXo0nY6x3uS6OUl0C0j0NEEHSXRRURERIKAs/ZfmGceq0ugj8O68oZWJdAPpx7oIiIi0l7MmzcPgNdff53XX3+9yTWLFy8+qmuuWrWKZcuWUVJSQkZGBtOmTWPgwIFNrn388cd59913Gz2ekZHBww8/DMA777zDn/70p0ZrFi1aRERExFHFdlQaJNF9+DzSscTFQ/4eKC8LdCRBSUl0ERERkQBrkEA/90Ksyde3mEBXD3QRERFpz2688cY2vd66det4+umnmT59OgMGDGDNmjXcf//9PPLII3Tt2rXR+p/+9KdMmTLFe7+2tpbZs2czYsSIBuuioqL44x//2OAxnybQAaoO1j1R5FEXXYg0KzYeAFNegv5VNaZ3WCIiIiIB5Ly/2pNAB6zR47F+fF2rEujqgS4iIiLt2TnnnNOm11u+fDmjR4/mvPPOA2DatGl89tlnrF69miuvvLLR+ujoaKKjo733N2zYQEVFBeeee26DdZZlkZCQ0Kaxtqi6rh96pPqhS9ux4uIx4OmJLo0oiS4iIiISIA0S6Of9CGvSdPVAFxEREWljbrebbdu2cfHFFzd4fOjQoWzevLlV13jrrbcYMmQIycnJDR4/ePAgM2bMwHEcevfuzaRJk+jTp0+z16mpqaGm5lC7PcuyiIqK8t5uTv0xy7Kw6tu5hGAl+uH7CGXtch9xCZ4H95eG3L788f1QEl1EREQkAJz33sA86+mheTQJ9MOpB7qIiIi0J8uXL2fkyJFHVdm9fPlyzj77bOLi4ppdU1ZWhuM4xMfHN3g8Pj6ekpKSFp+juLiY//73v/z85z9v8Hh6ejozZsygZ8+eVFZWsnLlSu666y4eeughunXr1uS1li5dypIlS7z3+/Tpw/z58xsl55uTlpbGwfxdFACumNhmnyfYpaWlBTqENtGe9lHevQclQKeaarrq31UjSqKLiIiI+FmDBPoPLsK64lr1QBcREZEO79lnn+WEE05odRLdcRyeffZZBg0adMQker2mft5qTRHDO++8Q0xMDMOHD2/weFZWFllZWd77AwYM4Je//CWvv/4611xzTZPXmjhxIuPHj2/0/AUFBbjd7iPGnpaWRm5uLrV79wDgtm327t3bYvzB5PB9GGMCHc4xa4/7qDWef4uV+bnt8t+Vy+Vq9S+rmjz/mM8UERERkaPmrHvrsAT6BKwrrlEPdBEREZE6b731Fv/9739btdZxWte6Li4uDtu2G1Wdl5aWNqpO/y5jDG+//Tbf//73cbmOnEazbZu+ffuSm5vb7Jrw8HDCw8Obfa6WGGMaDBYN1QSuMSZkYz9ce9oHsXW/iCovDdk9+fL7oSS6iIiIiJ+Y/3yEWfh/QF0Ll1Yk0EE90EVERKTjePPNN9v8mi6Xi8zMTDZu3Nigmnzjxo2cfvrpRzx306ZN5ObmMnr06BafxxjDN998Q48ePY475iM+T1V9T3QNFpU2VN8TvbwkkFEELSXRRURERPzAfPkZzt9+B46DddZ5rWrh8l3qgS4iIiLt2eLFi3127fHjx7NgwQIyMzPJyspizZo1FBYWMmbMGACee+459u3bx0033dTgvLfeeov+/fvTs2fPRtd88cUX6d+/P926dfP2RN+xYwfXXnutz/YBwGGDRUXaTH0lesV+jFOLZYcFNp4goyS6iIiIiI+Zr/+H8/hvwe2GU87E+slNWLZ9xHPUA11ERESk7Zx11lmUl5fz0ksvUVxcTI8ePbjzzju9PZKLi4spLCxscM6BAwdYv34906ZNa/KaFRUV/O1vf6OkpITo6Gj69OnD3Llz6devn283U5dEtyKVRJc2FNPZ89UYqKiAzi3PGehI9A5MRERExIfMru04/zfX07ty0MnY02/HCjtyVYd6oIuIiIi0vbFjxzJ27Ngmj82cObPRY9HR0SxatKjZ602bNq3ZBLtPHdYTXaStWC4XRMVAZQXsL1MS/TuURBcRERHxEZO3B+eRu+FABfQ9AXvGr7CaGSR1OPVAFxEREZFm1bdziVRPdGljneMOJdGlASXRRURERHzA7CvAefguKCuBHn2wf/4brKN8o6Me6CIiIiLSSLUq0cVHYuMgf6+S6E1QEl1ERESkjZnyUpxHfgP7CiC1O/atc7GiY494jnqgi4iIiEireAeLqhJd2ljdcFGzvwwrwKEEG70jExEREWlD5kAFzqN3Q+5u6NIV+xf3YsUlHPEc9UAXERERkVarqk+iqxJd2pYVG4cBVaI3QUl0ERERkTZiqqpwFsyDndugczz2L+ZhJSW3eJ56oIuIiIhIaxlvT3Ql0aWN1VWiK4nemJLoIiIiIm3AuGtw/vIAfLUJomI8LVzSuh/VNdQDXURERMTjiy++4NNPP2Xz5s3s27eP6upqOnfuTEZGBoMHD+bMM88kLi4u0GEGRpV6oouP1CfRy0sDG0cQUhJdRERE5DgZpxbzxMPw+acQEYn987uwemYe8Rz1QBcRERFp7J133uHVV19lz549dOrUiV69epGZmUlERAT79+9n586dbNiwgWeeeYYzzzyTSZMmkZzc8if/2pW6SvSjHVov0qLYzgCY/eUBDiT46B2aiIiIyHEwxmCe/RPmkw8gzIU941dY/QYd8Rz1QBcRERFp7Je//CX5+fl8//vfZ+bMmWRmZmLbdqN1+/fvZ8OGDbz77rv84he/4KabbmLEiBEBiDhAqtUTXXzD6qye6M1REl1ERETkGBljMC88hVn7L7Bs7OtuxzpxWIvnqQe6iIiISGOnnHIKP/rRj4iOjj7iutjYWEaPHs3o0aPZtGkT+/fv91OEQUJJdPEV9URvlpLoIiIiIsfIrFiMWfMqANbVN2OdetZRna8e6CIiIiKHTJo06ajPGTToyJ8AbJfqe6JrsKi0tdh4z1cl0Rtp/JkYEREREWmR8+ZrmFefA8CaNB37e+cdcX1enk1OTrj3D+C9rR7oIiIiIg0tWbKEffv2NXmsuLiYJUuW+DmiIKJKdPGVznWV6JUHMG4V9xxO79hEREREjpKz7k3M838HwLroSuwfXHTE9eqBLiIiInJ0XnzxRU4++WS6dOnS6FhxcTEvvvgil112WQAiCyxjzGFJdA0WlTYWFQOWDcaB/eWQ0Pj111EpiS4iIiJyFMyn6zBPLwDA+sEErPEtf+xYPdBFRERE2s7BgwdxuTpoSsvtBqfuZ0ZVoksbs2wbYjtDeamnpYuS6F4d9L84IiIiIkfPbPoPzt9/D8bB+t4PsK64BsuyWn2+eqCLiIiINO+bb75hx44d3vuffvopu3fvbrCmurqatWvXkpqa6ufogkR9FTooiS6+ERt3KIkuXkqii4iIiLSC2bUD508Peqp/Tj0L6yczj5hAz8uzyc8PA2jQAx1QD3QRERGRJmzYsKFBr/OXXnqpyXURERHceOON/goruNQPFQ1zYXXUanzxrdjOAJjyMlpfLtT+6dUmIiIi0gJTVoLz2H1QVQkDhmBfexuWHdbsevVAFxERETl6P/jBDzj11FMxxvCrX/2KG2+8kZ49ezZY43K5SEtLIyIiIkBRBlh9JXqkqtDFR2LrhouqEr0BJdFFREREjsDU1OD8+QEoyoeUbtg/+yVWePgRz1EPdBEREZGjl5iYSGJiIgB33303mZmZdOqk4ZkNVNdVoquVi/iIFRuHASXRv0NJdBEREZFmGGMwzz4GX30JUTHYN92FVV+Z0QrqgS4iIiJybAYNGhToEIJTVV0leoR+uSA+okr0JtmBDkBEREQkWJlVL2M+fBtsG/tnd2B1y2h2bV6eTU5OuPcP4L2tHugiIiIiLXvggQfYvn17q9fX1NSwfPly3njjDR9GFVyMKtHF1zrHe74qid6A3tGJiIiINMH89yPMy88AYP34OqxBw5pdqx7oIiIiIscvPj6eO++8k/79+3P22Wdz4oknkp6e3mBNZWUlW7du5d///jcffPAB0dHR3HTTTa26/qpVq1i2bBklJSVkZGQwbdo0Bg4c2OTaL774grlz5zZ6/JFHHqF79+7e+x999BGLFy8mLy+P1NRUJk+ezPDhw49i10dJPdHF1+oq0Y2S6A0oiS4iIiLyHebb7ThPPAzGYJ0zDvvcC4+4Xj3QRURERI7fjBkz+OEPf8grr7zCP/7xD2pra4mIiCAuLo6IiAj2799PeXk5xhiSk5OZOHEiY8eOJbyFeTUA69at4+mnn2b69OkMGDCANWvWcP/99/PII4/QtWvXZs979NFHiY6O9t6PizvU2m/Lli08+uijTJo0ieHDh7NhwwYeeeQR7r33Xvr37398fxnN8bZzURJdfEM90ZumJLqIiIjIYUxpMc5j86DqIAw8CWvS9Fafqx7oIiIiIsenT58+/OIXv6C0tJTPPvuMLVu2UFxcTHV1NX369KF79+6ceOKJDBgwAMuyWn3d5cuXM3r0aM477zwApk2bxmeffcbq1au58sormz0vPj6emJiYJo+tWLGCoUOHMnHiRAAmTpzIpk2bWLFiBbfeemvrN300qpVEFx+r74leriT64ZREFxEREaljaqpx/nQ/7CuE1O7YN/wSy9X0j0t5eTb5+WEADXqgA+qBLiIiInKc4uPjOfvsszn77LOP+1put5tt27Zx8cUXN3h86NChbN68+Yjn3nHHHdTU1JCRkcEll1zC4MGDvce2bNnChRc2/MTiSSedxMqVK4875mZVeXqiW5EaLCo+EtvZ83V/GcaYo/plVXumd3giIiIigDEGs3ABbNsM0bHYN9+FFRPb5Fr1QBcRERHxrZ07d9KzZ882uVZZWRmO4xAfH9/g8fj4eEpKSpo8JzExkeuvv57MzEzcbjfvvfce8+bN4+6772bQoEEAlJSUkJCQ0OC8hISEZq8JnmGoNTWHPqloWRZRUVHe283xHqup9nyNiAzJ5GZ9zKEY++Ha9T7i6l4nNdVYNdUh8Qsbf3w/lEQXERERAczKFzHr34WwMOyf/RIrNb3ZteqBLiIiIuJbs2fPJjMzk3PPPZfvfe97zbZUORpNJdiaS7qlp6c3GGqalZVFYWEhr732mjeJ3pSWKneXLl3KkiVLvPf79OnD/PnzSU5Obs0WiA13UQbEdEkisVu3Vp0TjNLS0gIdQptoj/swxrArPAJqqkmJ7oQrJXT+nfny+6EkuoiIiHR45tN1mFcWAWBNvgFr4EmtOk890EVERER849prr+Xdd9/lySef5JlnnuH000/n3HPPZejQoUd9rbi4OGzbblQhXlpa2qg6/UiysrJ4//33vfebqjpv6ZoTJ05k/Pjx3vv1CfeCggLcbnez51mWRVpaGvv3FQFQUePm4N69rY49WNTvIzc3F2NMoMM5Zu1+H7GdobiI/K+3YoXAh2tb8/1wuVyt/mVVk+cf85kiIiIi7YD55mucJx8BwDrvR9ijLmhynXqgi4iIiPjP+eefz/nnn8+uXbt45513eP/991m3bh1dunThnHPOYdSoUa2uOnW5XGRmZrJx40aGDx/ufXzjxo2cfvrprY5p+/btDdq3ZGVlkZOT0yApvnHjRrKyspq9Rnh4OOHh4U0ea00y1tT1RCciMqSTt8aYkI6/XrvdR0wcFBdhykshhPbny++H3vGJiIhIh2VK9uE8dh9UV8GJw7Auv6bJdeqBLiIiIhIYGRkZTJ06lSuvvJL//ve/vPPOOyxbtoylS5fy/PPPt/o648ePZ8GCBWRmZpKVlcWaNWsoLCxkzJgxADz33HPs27ePm266CYAVK1aQnJxMjx49cLvdvP/++6xfv57bbrvNe81x48Zx991388orr3D66afz8ccfk5OTw7333tu2fwmHq6ryfI2IPPI6kePROQ4As7+M0O763naURBcREZEOyVRX4Tz+Wygpgm49sK+/AyssrMm16oEuIiIiEli2bZOWlkZqairR0dGUlZUd1flnnXUW5eXlvPTSSxQXF9OjRw/uvPNOb3uH4uJiCgsLvevdbjfPPvss+/btIyIigh49evD//t//45RTTvGuGTBgALfeeivPP/88ixcvJi0tjVtvvZX+/fu3zaabUl2XRA+BYY8SuqzYOAzA/qN7nbVnSqKLiIhIh2OMwTz9f7BjK8R0xr7p11jRLQ+rUg90EREREf+qrKxk3bp1vPPOO2zZsoXw8HCGDx/OOeecc9TXGjt2LGPHjm3y2MyZMxvcnzBhAhMmTGjxmiNGjGDEiBFHHcsxqz7UzkXEZ2I9leiUK4leT0l0ERER6XDM8sWYj9+HsDDsG+/EamLivHqgi4iIiATO559/zjvvvMP69euprq6mb9++XHvttYwcOZLo6OhAhxcwpq4S3YpUEl18qHPdcFxVonvpHaCIiIh0KM7HazHLngPAmnIj1oDBjdaoB7qIiIhIYM2bN4+4uDjGjBnD6NGjycjICHRIwaFKlejiB7GHeqKLh5LoIiIi0mGY7Vsx/3gUAGvMBOzvn9/kOvVAFxEREQms22+/nVNPPRXbtgMdSnCp1mBR8T2rc11P9PLSQIcSNJREFxERkQ7BFBd5BonWVMOQ07Aum9biOeqBLiIiIhIYp59+eqBDCE5VGiwqflDfE31/eWDjCCJKoouIiEi7Z2pqPAn00n3QrQf2dbdj2WEN1qgHuoiIiIgEPVWiiz94B4uqEr2e3hGKiIhIu2deXgjffAWxnbFvvgsrquEwKvVAFxEREZGQ4O2Jrkp08aH4RM/XinKM243lUgpZfwMiIiLSrpmNH2PWLAPAnnYrVnJaozXqgS4iIiIiwc7U1oK7rrWgKtHFl2I6g22D48D+UkhICnREAackuoiIiLRbpqQI5x9/BMA670dYJx25t6Z6oIuIiIhIsDL1rVwAIpVEF9+xbBviEqBkH5SWKImOkugiIiLSThmnFueJh2F/GfTog3XptAbH1QNdREREREKJOVjpuWFZEB4R2GCk/YtL9CTRy4oDHUlQ0DtEERERaZfM6y/B5hyI7IR9/Wys8HDvMfVAFxEREZFQY7z90COxLCuwwUj7V9cX3ZQWo39tSqKLiIhIO2S++hKz7DkArMk3YKVlNDiuHugiIiIiEmqc+kp09UMXP7DiEjAApapEByXRRUREpJ0xFftx/v57cBys4aOwzhrd7Fr1QBcRERGRUHF4JbqIz9VVolNWEtAwgoWS6CIiItJuGGNwnnkM9hVAchrW1Bu9H3VVD3QRERERCWXmoJLo4kdx9e1c9gU4kOCgd4wiIiLSbpj3VsGn6yAsDPu62VhR0YB6oIuIiIhI6PNWokd2Cmwg0iFY8fXtXEoCHElwUBJdRERE2gWz+xvM4icAsCb+BKtPf+8x9UAXERERkVBnqtQTXfworr6di3qig5LoIiIi0g6Yqiqcvz0ENdVw4jCsMROaXKce6CIiIiISqtTORfyqvid6yT6MMd42mR2VkugiIiIS8syLT8KenRCXgH3NrVi2rR7oIiIiItKuOPWV6JFKoosfJCR5vlZXwYEKiIkNbDwBpneQIiIiEtLMJ+sw774BgH3tL7DiEtUDXURERETanfqe6JYq0cUPrMhIiO0M+8uhuFBJ9EAHICIiInKsTFE+zjMLALDGXoI1aBigHugiIiIi0v6Yg/WV6BosKn6S0PVQEj2jd6CjCSgl0UVERCQkmdpanCf+4PloYZ8srIunNlqjHugiIiIi0l7UV6KrJ7r4TZeusGs7Zl8hHbsjupLoIiIiEqLMa/+Er76EqGjs624nvyhCPdBFREREpFmrVq1i2bJllJSUkJGRwbRp0xg4cGCTa9evX8/q1avZsWMHbrebjIwMLr/8ck4++WTvmnfeeYc//elPjc5dtGgRERERbR7/oSS6KtHFP6zEJAx4KtE7OL2jFBERkZBj/rcRs/JFAKypM8h30tUDXURERESatW7dOp5++mmmT5/OgAEDWLNmDffffz+PPPIIXbt2bbT+yy+/ZOjQoUyePJmYmBjefvtt5s+fz/3330+fPn2866KiovjjH//Y4FxfJNABnIOqRBc/S6x7bexTEl1JdBEREQkpprwM58mHwRis7/0Ae/jZ5OeoB7qIiIiING/58uWMHj2a8847D4Bp06bx2WefsXr1aq688spG66dNm9bg/pVXXsm///1vPvnkkwZJdMuySEhI8GXoXt5K9Egl0cVPuiQDYEqKAhxI4CmJLiIiIiHDGIPz9B+hZB+kZWBNvr7BcfVAFxEREZHvcrvdbNu2jYsvvrjB40OHDmXz5s2tuobjOFRWVhIbG9vg8YMHDzJjxgwcx6F3795MmjSpQZK9LXkHi6oSXfzE285FlehKoouIiEjoMG++Bhs/Blc4xZfewd4tnQH1QBcRERGR5pWVleE4DvHx8Q0ej4+Pp6SkpFXXWL58OVVVVZx55pnex9LT05kxYwY9e/aksrKSlStXctddd/HQQw/RrVu3Jq9TU1NDTc2hIg/LsoiKivLebo5lWd5KdCsy6ohrg1l93KEaf70Os4+kFM/XfQVHXhdg/vh+6B2miIiIhASz82vMS08DsP+Ca7hh3qnqgS4iIiIirdZUgq01Sbe1a9fy4osvMnv27AaJ+KysLLKysrz3BwwYwC9/+Utef/11rrnmmiavtXTpUpYsWeK936dPH+bPn09ycnKLceTVVaJ3SUsjqpkkfahIS0sLdAhtor3vwyQns8u2oaaa1MhwwpJa/ncaSL78fiiJLiIiIkHPVB3E+dvvwe2Gk89gZ58J6oEuIiIiIq0SFxeHbduNqs5LS0sbVad/17p16/jLX/7CrFmzGDp06BHX2rZN3759yc3NbXbNxIkTGT9+vPd+fRK/oKAAt9vd7HmWZUFdJfq+igPYe/ceMZZgZVkWaWlp5ObmYowJdDjHrEPto0tXKMwn7/PPsLJO9G+ArdSafbhcrlb9sqo5SqKLiIhI0DOvLIK83ZCQhH31zbDd82ZDPdBFREREpCUul4vMzEw2btzI8OHDvY9v3LiR008/vdnz1q5dy5///GduueUWTjnllBafxxjDN998Q48ePZpdEx4eTnh4eLPnH/H6B+sGi4ZHhHTiFjx7DfU9QAfZR3I3KMzHKdiL3X+QfwM7Sr78fiiJLiIiIkHNfP0/Ty90YOfZt7B/e5J6oIuIiIjIURk/fjwLFiwgMzOTrKws1qxZQ2FhIWPGjAHgueeeY9++fdx0002AJ4H++OOPM23aNLKysrxV7BEREURHRwPw4osv0r9/f7p16+btib5jxw6uvfZan+yhvic6kRosKv5jJadhvvwMCpr/hEVHoHecIiIiErRMTQ3OwgVgDO9WXcBVPxvX4Lh6oIuIiIhIa5x11lmUl5fz0ksvUVxcTI8ePbjzzju97R2Ki4spLCz0rl+zZg21tbU8+eSTPPnkk97HR40axcyZMwGoqKjgb3/7GyUlJURHR9OnTx/mzp1Lv379fLIHU+XpiU5EJ59cX6RJyXV9xpVEFxEREQlOZsVi2Pst7qgEbv7X7eqBLiIiIiLHbOzYsYwdO7bJY/WJ8Xr33HNPi9ebNm0a06ZNa4PIWmaMOVSJHqFKdPEfKzkNAxgl0UVERESCj/l2O+aNlwDYe84MSl5KoH//AvVAFxEREZGOx10DTl3BSKQq0cWP6ivR80NzmG1bURJdREREgo6praXqiQWE19ZS1vcs1lWeC6gHuoiIiIh0UFVVh26rEl38KbW75+v+Mkx5GVbnuMDGEyB6ByoiIiJBp/zlV4nZ8xWlNZ0572+/Ib8qEVAPdBERERHpoKrrkuguF1ZYWGBjkQ7FiuwESSlQlA97d0LnwYEOKSCURBcREZGgYnJ3EfVmNgBfn3IDz9xmyMkpUQ90EREREem4qtUPXQIovScU5WP27MTKUhJdREREJKCM4+AsfAy7toZ3C0aQfM5o9UAXEREREamvRFc/dAkAK70HJuffsOfbQIcSMCGVRF+6dCkbNmxg9+7dREREkJWVxdSpU0lPTw90aCIiInKc9u6FXdmr6PbVJmrCOnHn57/ils8jwLLUA11EREREOrYqVaJLAKX3BMDs2RngQAInpN6Rbtq0ibFjx9K3b19qa2t5/vnnue+++3j44Yfp1Em/iRMREQlVn3/u4tcz9vJ05tPggns33syuynRmzz60Rj3QRURERKSjMvWV6BHKf4n/Wek9MQB7dmKMwbKsQIfkdyGVRJ8zZ06D+zNmzGD69Ols27aNQYMGBSgqEREROV6b/xfGzYlziXUd4EC3QQw+ZwzcgXqgi4iIiIgAVNUn0VWJLgGQ3hPCwqC8FIoLoUtyoCPyu5BKon/XgQMHAIiNjQ1wJCIiInI8euz+F6ckf0StHU7sjJsYUuCpOFcPdBERERERvD3RLSXRJQCsiEhPIv3b7bBjq5LoocQYw8KFCznhhBPo2bNns+tqamqoqTn05tuyLKKiory3Q1V97KG8B5FQoNeaiO98/rmLzZtdRFbt4+ycvwDwRthPca/rz7ffhnnX6fUn0nb0/zUR/9BrTUTaXH1P9Egl0SUwrN79Md9ux2zfinXKWYEOx+9CNon+5JNPsnPnTu69994jrlu6dClLlizx3u/Tpw/z588nObl9/MYkLS0t0CGIdAh6rYm0vcmT4d134S+n3E90Wjk5pSdw07prqH3V8+NJr14wdGgy3boFOFCRdkj/XxPxD73WRKTNVKudiwRYnyx4fzVmx9ZARxIQIZlEf+qpp/jkk0+YO3cuSUlJR1w7ceJExo8f771fXwlQUFCA2+32aZy+ZFkWaWlp5ObmYowJdDgi7ZZeayK+M2eOi+mnfMiozW9TSxi3b/wNl1xWzdlnlwMwYIAbcLN3b2DjFGlP9P81Ef/Qa006GpfL1W6KFYOWtxJdg0UlMKze/T3DRXdsxdTWYoWFtXRKuxJSSXRjDE899RQbNmzgnnvuISUlpcVzwsPDCQ8Pb/Z6oc4Y0y72IRLs9FoTaXuDeu+j387/A+DT5B/zZXkWM84u5pJLKr1r9LIT8Q39f03EP/RaE5G2YlSJLoHWvSdEx8KB/Z6+6H1PCHREfmUHOoCj8eSTT/L+++9zyy23EBUVRUlJCSUlJVRXVwc6NBERETlKZvETuCpL2Freh4+Trwp0OCIiIiIiwWt/GQBWbFyAA5GOyrLD4IShAJj/bQxwNP4XUpXoq1evBuCee+5p8PiMGTM455xz/B+QiIiIHLW8PJsDGz6l54dvY7CYnXMXZ58awSmngGUZ8vJsUlOdQIcpIiIiIhI8yko8X+PiAxqGdGzWwKGYT9dhvvwMLrwi0OH4VUgl0V944YVAhyAiIiLH6YWFMGHj4xAFT27/MZ+WDOXTRz3HPv20C7NmlXPbbeUBjVFEREREJJiY8lLPjc4JAY1DOjZr0MmevuhfbcJU7MeKiQ10SH4TUu1cREREJPT9OOrPdI/KozI2jYSrrwTgoYdK+OQTeOONAqZOrQhwhCIiIiIiQabMk0S3OqsSXQLHSkmH7r2gthbznw8DHY5fKYkuIiIifmO2fE6XjSsAyB/zcwad7PlQ3JAhNZxyCgwd6lYrFxERERGR7yov8XyNSwhkFCJYp40EwHy8NsCR+JeS6CIiIuIXproKZ+FjAPxz58VU9BgW4IhERERERIKfqa6Cg5WeO6pElwCzTv++58aXn2Hy9wQ2GD9SEl1ERER8Li/PJv+pFyF/Dwcikvjt/24hJyecoiKbKVMqsPUTiYiIiIhI08rLPF9d4RAVHdhYpMOzUtNhyGlgHMyqVwIdjt+E1GBRERERCU0rnixi8tcvgw0///BOytydmT370PHUVIcxYwIXn4iIiIi0f6tWrWLZsmWUlJSQkZHBtGnTGDhwYLPrN23axMKFC9m1axeJiYlcdNFFnH/++Q3WfPTRRyxevJi8vDxSU1OZPHkyw4cPb9vA61q5hCV0wbIsjDFte32Ro2SPvQQn59+YD9ZgzhuPld4z0CH5nOq+RERExKeMMUx2/R8RtpvNrjM447qTAc8w0TfeKOCNNwq46qoDgQ1SRERERNq1devW8fTTT3PJJZcwf/58Bg4cyP33309hYWGT6/Pz83nggQcYOHAg8+fPZ+LEifzjH//go48+8q7ZsmULjz76KGeffTYPPfQQZ599No888ghbt25t2+DLPUNF7fjEtr2uyLHKOhFOGg61bpyn/w9TVRXoiHxOSXQRERHxrY0fE7H1E4zt4vo37yAl1VM5M2RIjfePhomKiIiIiC8tX76c0aNHc95553mr0Lt27crq1aubXL969Wq6du3KtGnTyMjI4LzzzuPcc8/ltdde865ZsWIFQ4cOZeLEiXTv3p2JEycyePBgVqxY0aaxmzJPEj0soUubXlfkWFmWhX3lDRAVA9u34Cy4F7Ov6V9ItRdq5yIiIiI+Y2qqcRY/AUDRsIlsX94LKA5sUCIiIiLSobjdbrZt28bFF1/c4PGhQ4eyefPmJs/ZunUrQ4cObfDYySefzNtvv43b7cblcrFlyxYuvPDCBmtOOukkVq5c2WwsNTU11NTUeO9blkVUVJT3dlOs8lIMYCckNrsmVNTHr30Eh+PZh5WUgvXzu6h95G7YnINz53RI6w5RMVjhEW0daovMg3/16fdDSXQRERHxmfKXlxFTkEtNTBfejb4KgPx8zzDRoiKbvDxbVegiIiIi4lNlZWU4jkN8fHyDx+Pj4ykpKWnynJKSkibX19bWUl5eTmJiIiUlJSQkJDRYk5CQ0Ow1AZYuXcqSJUu89/v06cP8+fNJTk5u9pwSx005EBbfhaS0tGbXhZI07SOoHPM+unWjpncm+x67n+ov/gt7vgUgMF37jU+/H0qii4iIiE+YfQVEvPkCALd98AteeTEdgHnzPG9GsrNjmDWrnNtuKw9YjCIiIiLScTRVpXqkytXvHqsf6Hmkc4wxRzw+ceJExo8f3+g5CgoKcLvdTV9z2JmEpXYneuAQcnNzQ3qwqGVZpKWlaR9Bok32ER4Fv5hHWEEupjAPDlRAbdP/ln3FArDDjrgPl8t1xF9WtURJdBEREfEJs+Rpws1BdoQN4fLfncb39pYwe3YCDz1UwpAhno+wpqTUBjhKEREREWnv4uLisG27UYV4aWlpo2rzek1VlJeVlREWFkZsbGyza450TYDw8HDCw8ObPNZsErNbD6z0nkR064bZuzekk7b1jDHaRxBpk310TcXqmto2AR0ly7KwwsJ8+v3QYFERERFpc2bz55iP38dgceO7vySpK97EuQaKioiIiIg/uVwuMjMz2bhxY4PHN27cyIABA5o8p3///o3Wf/bZZ2RmZuJyeWpSs7KyyMnJaXTNrKysNoxeRIKBkugiIiLSpkxtLc4//wpA8ZAf8kXZCQGOSEREREQ6uvHjx/Pmm2/y1ltvsWvXLp5++mkKCwsZM2YMAM899xyPPfaYd/35559PYWEhCxcuZNeuXbz11lu89dZb/OhHP/KuGTduHJ999hmvvPIKu3fv5pVXXiEnJ6fRsFERCX1q5yIiIiJtqmz5KmJ3f0NtZCzvxl8LQE5OOOnptUyZUoFlhf7HHUVEREQktJx11lmUl5fz0ksvUVxcTI8ePbjzzju9PZKLi4spLCz0rk9JSeHOO+9k4cKFrFq1isTERH76058yYsQI75oBAwZw66238vzzz7N48WLS0tK49dZb6d+/v9/3JyK+pSS6iIiItBlTXoZrZTYAv/lkJs8u7QXA7NkJ3jWpqQ6DB2uYqIiIiIj419ixYxk7dmyTx2bOnNnosUGDBjF//vwjXnPEiBENEusi0j4piS4iIiJtxryyiE5OOfsTMzEjx3JX31LmzYvXMFEREREREREJWUqii4iISJsw33yNeX8VAIWjf8aia+NYsKAYODRMVEREREREGqsfVtpW64Kd9hFcOsI+jneP7eNvSERERALKGOMZJmoM1vCzOdB9SKBDEhEREREJGYmJia1aV9/DPdRpH8FF+2iZ7bMri4iISIdh1r8DX/8PxxXJ5hOnk5MTDkB+vs2UKRUUFdnk5enHDhERERGRY1FZWckvf/lLKisrAx3KcdE+gov20XqqRBcREZHjYg4ewCxZCMBDX0zn8csHeY/NmxcPQHZ2DLNmlXPbbRooKiIiIiJytIwxbN++HWNMoEM5LtpHcNE+Wk9JdBERETkuZvkLULqP6vhulJ9xMdn3FrJnj4vZsxM0UFRERERERERCnpLoIiIicsxM7i7MmmUA5J59A8/cmMiVPykgKcmTONdAUREREREREQl1ak4qIiIix8QYg7P4Cah1w5DT2N/njECHJCIiIiLSLoWHh3PZZZcRHh4e6FCOi/YRXLSP1lMluoiIiBybjR/D559ibBdfn3yDd5hoTk446em1TJlSgWWFdm89EREREZFgEB4ezhVXXBHoMI6b9hFctI/WUxJdREREjpqpqfZUoQN/3jqFBycP8x6bPTvBezs11WHwYA0TFRERERERkdClJLqIiIgcNbP6FSjIpSYmibxTf0z2bzRMVERERERERNonJdFFRETkqJh9BZiVLwKQ971r+MetyUzSMFERERERERFppzRYVERERI6KWfI0VFdBv4GUDTg30OGIiIiIiIiI+JQq0UVERKTVzObPMR+/j8Fi+2kzyPk8AtAwURERERERX1m1ahXLli2jpKSEjIwMpk2bxsCBAwMdVrNeeOEFlixZ0uCx+Ph4/v73vwNgjOHFF1/kzTffZP/+/fTv359rr72WHj16BCJcr02bNrFs2TK2b99OcXExt99+O8OHD/ceb03cNTU1PPvss3zwwQdUV1czePBgpk+fTlJSUtDs4/HHH+fdd99tcE7//v357W9/G1T7WLp0KRs2bGD37t1ERESQlZXF1KlTSU9P967x5/dESXQRERFpFeM4OC88CcCiby5hzk/O9B7TMFERERERkba3bt06nn76aaZPn86AAQNYs2YN999/P4888ghdu3YNdHjN6tGjB3fddZf3vm0faobx6quvsmLFCmbMmEG3bt14+eWXue+++3j00UeJiooKRLgAVFVV0bt3b84991z+8Ic/NDremriffvppPvnkE2655RY6d+7MM888w4MPPsj8+fMb/B0Ech8AJ598MjNmzPDed7kapoiDYR+bNm1i7Nix9O3bl9raWp5//nnuu+8+Hn74YTp16gT493uidi4iIiLSKuaTD2Dn1ziRUfSfdTlTplRw112lADz0UAlvvFHAG28UMHVqRYAjFRERERFpH5YvX87o0aM577zzvFXoXbt2ZfXq1YEO7Yhs2yYhIcH7Jy4uDvBUDq9cuZKJEydyxhln0LNnT2bOnElVVRVr164NaMzDhg3jxz/+MWeccUajY62J+8CBA7z11lv85Cc/YejQofTp04ebb76ZnTt3snHjxqDYRz2Xy9Xg+xMbG+s9Fiz7mDNnDueccw49evSgd+/ezJgxg8LCQrZt2wb4/3uiJLqIiIi0yLhrMEufBSDsgonEdY8nOzuGlBQHODRMdMiQGlJTnUCGKiIiIiLSLrjdbrZt28ZJJ53U4PGhQ4eyefPmAEXVOrm5udxwww3MnDmTRx99lLy8PADy8/MpKSlpsKfw8HAGDRoU1HtqTdzbtm2jtraWoUOHetd06dKFnj17smXLFr/HfCSbNm1i+vTp3HLLLfzlL3+htLTUeyxY93HgwAEAb8Lf398TtXMRERGRFpn3/wUFuRCXgPWDCbA10BGJiIiIiLRvZWVlOI5DfHx8g8fj4+MpKSkJTFCt0L9/f2bOnEl6ejolJSW8/PLL/PrXv+bhhx/2xt3UngoLCwMQbeu0Ju6SkhJcLleDqu76NcH0/Ro2bBhnnnkmXbt2JT8/n8WLF3Pvvffy4IMPEh4eHpT7MMawcOFCTjjhBHr27An4/3tyTEn0bdu2kZmZeSynioiISIgxBysxr/0TgL2nTKF4axw5OeEA5OfbTJlSQVGRTV6erSp0EREREZE2ZllWqx4LFsOGDfPe7tmzJ1lZWdx88828++679O/fH2gcvzHGrzEeq2OJO9j2dtZZZ3lv9+zZk759+zJjxgw+/fTTI7aACeQ+nnzySXbu3Mm9997b6Ji/vifH1M7lzjvvZM6cObz//vu43e5juYSIiIiECLPmVSgvpSQ8ne/98iouuCDZO0h03jxPW5cpU5JYtCgmsIGKiIiIiLQjcXFx2LbdqGK2tLS0UfVtMOvUqRM9e/Zk7969JCQkADTaU1lZWVDvqTVxJyQk4Ha72b9/f6M19ecHo8TERJKTk9m7dy8QfPt46qmn+OSTT7j77rtJSkryPu7v78kxJdFnzJiBMYbHHnuMG2+8keeff56ioqJjuZSIiIgEMVNeinljKQD2JVNZ/noxb7xRwEMPlQAaKCoiIiIi4isul4vMzMxGAxA3btzIgAEDAhTV0aupqWH37t0kJiaSkpJCQkJCgz253W42bdoU1HtqTdyZmZmEhYU1WFNcXMzOnTvJysrye8ytVV5eTlFREYmJiUDw7MMYw5NPPsn69ev5zW9+Q0pKSoPj/v6eHFM7l1GjRjFq1Ci++uor3njjDV577TVeffVVTj31VH74wx9y4oknHstlRUREJMiYFS9AVSX07Ev1iSNZ/Vwnpk6tYMgQz/H6YaIiIiIiItL2xo8fz4IFC8jMzCQrK4s1a9ZQWFjImDFjAh1as5555hlOO+00unbtSmlpKS+99BKVlZWMGjUKy7IYN24cS5cupVu3bqSlpbF06VIiIyMZOXJkQOM+ePAgubm53vv5+fns2LGD2NhYunbt2mLc0dHRjB49mmeffZbOnTsTGxvLs88+S8+ePRsMtgzkPmJjY3nhhRcYMWIECQkJFBQU8M9//pPOnTszfPjwoNrHk08+ydq1a7njjjuIioryVpxHR0cTERHRqn9LbbkXy7RBQ5uysjLWrFnDmjVrKCoqIiMjgwsuuIBRo0YRERFxvJf3iYKCAmpqQvdNv2VZdOvWjb179wZdbyWR9kSvNenITEEuzl0zoNaN/Yu5fF47nAsuSOaNNwoAvLfbIomu15qIf+i1JuIfeq1JRxMeHk5ycnKgw2i3Vq1axbJlyyguLqZHjx5cffXVDBo0KNBhNevRRx/lyy+/pKysjLi4OPr378+Pf/xjMjIyAE+F8YsvvsiaNWuoqKigX79+XHvttd6BkYHyxRdfMHfu3EaPjxo1ipkzZ7Yq7urqahYtWsTatWuprq5m8ODBTJ8+na5duwbFPq677joeeughtm/fTkVFBYmJiZx44olMmjSpQYzBsI8rrriiycdnzJjBOeecA7Tu31Jb7aVNkugHDhzg7bffZtWqVeTl5ZGcnExBQQFdunThF7/4RVB+ZEFJdBFpDb3WpCNznnwY89E7MPAkwmbNIycn3Js4T0mpZdGiGKZOrWiTYaJ6rYn4h15rIv6h15p0NEqii0h7d0ztXOp98803rFq1irVr1+J2uxkxYgQ///nP6devH9988w1/+9vf+Pvf/85DDz3UVvGKiIiIH5hvt2PWvwvAtpOu5WBOODk54QDk5IQzZAicf/7BQIYoIiIiIiIi4hfHlERft24dq1at4n//+x9xcXGMHz+e888/v8FU0169ejF58mR++9vftlWsIiIi4ifOy8+AMWzufC5jfnJWg2OzZyd4b8+aVc5tt5X7OToRERERERER/zmmJPof//hHevfuzY033sjIkSNxuZq+THJyMt///vePK0ARERHxL7M5Bz7/BMLCSJ4+meyLClm5MorMTDfz5sXz0EMl3j7oKSm1AY5WRERERERExLeOKYk+d+5cTjjhhBbXpaamMmPGjGN5ChEREQkAYwzOSwsBsL4/luRBaSTVGrKzY1iwoBiAIUNq2mSYqIiIiIiIiEgosI/lpNYk0EVERCQE/edD2L4FIiKxxk8KdDQiIiIiIiIiAXdcg0VFRESk/TC1tThLnwXgwFkT2bEzBcA7UDQ/32bKlAqKimzy8mxSU52AxSoiIiIiIiLiL0qii4iICADmgzWQuxti43h691QevCO5wfF58+IByM6O0UBRERERERER6TCURBcRERFMVRVm2T8BsC68gnPTbL4trGDcuEr27HExe3aCBoqKiIiIiIhIh3RMPdFFRESkfTFvvQal+yApBWvUDzHGIjs7hqQk402c1w8UHTKkRq1cREREREREpMNQEl1ERKSDMxXlmNdfAsC6eApWeHiAIxIREREREREJHmrnIiIi0sGZlUugsgJ3Wm+2RP8AcmzvMNGcnHDS02uZMqUCyzIBjlRERERERETE/5REFxER6cBMUQHmreUALHf9jJ//MLXB8dmzE7y3U1MdBg/WMFERERERERHpWJREFxER6cDMa8+BuwayBjPyqhPJHlXIypVRZGa6mTcvXsNERUREREREpMNTT3QREZEOyuzeiVn3NgD2pVeTmmZISjJkZ8eQkuIZHKphoiIiIiIiItLRKYkuIiLSQTlLnwHjwClnYmUOCHQ4IiIiIiIiIkFJ7VxEREQ6ILN1E3y2AWyb4u9fzd7DBokC5OfbTJlSQVGRTV6erSp0ERERERER6bCURBcREelgjDE4Ly8EwPreD1i4agAPP9y5wZp58+IByM6OYdascm67TQNFRUREREREpGNSEl1ERKSj+Ww9fPUlRERg/WgyY3dXkpdnM25cJXv2uJg9O0EDRUVERERERETqKIkuIiLSgZjaWpyX6qrQfzABKzEJs8siOzuGq646QFKSJ3FeP0xURERERER8r7i4GLfbfcQ1ycnJFBQU+Cki39E+gk972cuR9uFyuUhMTDzmayuJLiIi0oGYtf+C3N0QG4c19pJAhyMiIiIiIoDb7aampvkiFsuyvOuMMf4Kq81pH8GnvezF1/tQEl1ERKSDMAcrMcueA2D/qMns/DoBODRMNCcnnPT0WqZMqcCyQveHJxEREREREZG2pCS6iIhIB2FWvwJlJZCcxlNfXcrvZ3ZpcHz27ATv7dRUh8GDNUxUREREREREREl0ERGRDsCUFmNWLwXAvuQnXNmjmmGnFbJyZRSZmW7mzYvXMFERERERkTqrV69m9erV3v7KGRkZXHbZZQwbNgwAYwwvvvgib775Jvv376d///5ce+219OjRI5Bhi4iP2IEOQERERHzPvPZPqDoIfbLg1O+RmuqQlGTIzo4hJcUBDg0THTKkhtRUJ8ARi4iIiIgETpcuXbjyyit54IEHeOCBBxg8eDC/+93v+PbbbwF49dVXWbFiBddccw0PPPAACQkJ3HfffVRWVgY4chHxBSXRRURE2jmTuwvz/moA7MumeQeuiIiIiIhI00477TROOeUU0tPTSU9PZ/LkyXTq1ImtW7dijGHlypVMnDiRM844g549ezJz5kyqqqpYu3ZtoEMXER9QOxcREZF2znn5GXAcOGk4+fFDyc8JAw4NFM3Pt5kypYKiIpu8PFtV6CIiIiIih3Echw8//JCqqiqysrLIz8+npKSEk046ybsmPDycQYMGsXnzZsaMGdPstWpqaqipqfHetyyLqKgo7+1mleyj+NVFOPv3Y505Gue/H2F//3ys5LTj36Af1e8x1At72ss+oP3sxdf7UBJdRESkHTNfbYL/fASWjX3p1SxaFMPDD3dusGbevHgAsrNjmDWrnNtu00BREREREZGdO3cyZ84campq6NSpE7fffjsZGRls3rwZgPj4+Abr4+PjKSwsPOI1ly5dypIlS7z3+/Tpw/z580lOTj7ieaVvv0bZa4s9d95eAYC18WO6/XXJEc4KXmlpoZX8b0572Qe0n734ah9KoouIiLRTxhicJU8DYH1/DFa3HowdW0lens24cZXs2eNi9uwEDRQVEREREWlCeno6Dz30EBUVFaxfv57HH3+cuXPneo9/t+LVGNPiNSdOnMj48eMbXaOgoAC3293seU7u3kaPuXftYO/exo8HM8uySEtLIzc3t1V/X8GqvewD2s9eWtqHy+Vq8ZdVR6IkuoiISHv1nw/h6/9BRCTWjyYDYIxFdnYMV111gKQkT+K8fpioiIiIiIgc4nK5vFWtffv25euvv2blypVMmDABgJKSEhITE73ry8rKGlWnf1d4eDjh4eFNHjtSAtMcbHpgaagmPY0xIRv74drLPqD97MVX+9BgURERkXbIuN04Lz0DgHX+RKyELgGOSEREREQktBljqKmpISUlhYSEBDZu3Og95na72bRpEwMGDPDNk1c1kUQPj/DNc4lII6pEFxERaYfM+6shfw90jqdw2CXk1Q0RzTnsa3p6LVOmVGBZoV9tICIiIiLSlp577jmGDRtGUlISBw8e5IMPPuCLL75gzpw5WJbFuHHjWLp0Kd26dSMtLY2lS5cSGRnJyJEjfRPQwYONH4uJ9c1ziUgjSqKLiIi0M+bgAcxr/wTA+tFknn0xudEw0dmzE7y3U1MdBg/WMFERERERkXqlpaU89thjFBcXEx0dTa9evZgzZw5Dhw4FYMKECVRXV/PEE09QUVFBv379mDNnDlFRUT6Jx1Q1lUTv3PgxEfEJJdFFRETaGbNqKZSXQko61vfPZ+qgCk49tYqVK6PIzHQzb168homKiIiIiBzBjTfeeMTjlmVxxRVXcMUVV/gnoKbauUTH+Oe5RUQ90UVERNoTU1KEWf0KAPalP8FyuUhNdUhKMmRnx5CS4gCHhokOGVJDaqoTwIhFRERERKRFTVWiu5oeUCoibU9JdBERkXbELPsnVFdB3xNg2JmBDkdERERERNpCUz3Ra93+j0Okg1I7FxERkXbC7NmJWbsGAPuyaeTnh5GfHwYcGiian28zZUoFRUU2eXm2qtBFREREREJBU+1catWWUcRflEQXERFpJ5yXnwHjwLARWP0GsegPMY0Gis6bFw9AdnYMs2aVc9ttGigqIiIiIhLMjDFNt3NxqxJdxF+URBcREWkHzObP4bMNYNvYl/wEgLFjK8nLsxk3rpI9e1zMnp2ggaIiIiIiIqGmuhqM8dzuOxC+/tJzW5XoIn6jnugiIiIhzhiDs+QfAFhnj8VKy6h73CI7O4akJONNnGugqIiIiIhIiDmslUvYjf/PM/8I1BNdxI+URBcREQlx5t8fwI6tENkJ60c/DnQ4IiIiIiLSlupauVidorASumBfOs3zuCrRRfxG7VxERERCmHHXYJY+A4A19hLyK5PI/6bhMNGcnHDS02uZMqUCyzIBi1VERERERI5BXSW61Snacz/M8/O+KtFF/EdJdBERkRBm3n0DCnIhPhFrzAQWPd54mOjs2Qne26mpDoMHa5ioiIiIiEjIOOipRLejojz3w+rSeUqii/iNkugiIiIhyhyowCx/HgDroslYnaI0TFREREREpL3xtnOJxsBhlej62V7EX5REFxERCVHmjZdgfzmkZWB9b4znsbpholdddYCkpIbDREVEREREJATVt3OJiqpLoqsSXcTfNFhUREQkBJl9BZg1ywCwL70aq74aRURERERE2hVT386lvie6qz6Jrkp0EX9RJbqIiEgIcv75d6iphv6DyE8bQX6O53/pGiYqIiIiItLO1Ldz8fZE12BREX9TEl1ERCTEmP98BP/9CMLCsKfcyKLsWA0TFRERERFpr+rbudRXote3c3G7McZgWVaAAhPpOJREFxERCSGm8gDOc38FwDp/Ilb3XkydWsGpp1axcmUUmZlu5s2L1zBREREREZH2oq4S3f5uJTqA4zS8LyI+oZ7oIiIiIcS8sghKiiA5DWv8JMBTaZ6UZMjOjiElxQEODRMdMqSG1FQnkCGLiIiIiMjxMAYiIhtXooNauoj4iSrRRUREQoTZvgXz9goA7KkzsCIiAxyRiIiIiIj4mn3xVKyJVxGflkZlbu6hwaKg4aIifqIkuoiISAgwbjfOM4+BMVgjzsUadDJ5eTb5+Z6PbtYPFM3Pt5kypYKiIpu8PFtV6CIiIiIi7YS39/nh7VtUiS7iF0qii4iIhACz5lXYtQNiO2NdcQ0AixbFNBooOm9ePADZ2THMmlXObbdpoKiIiIiISHti2WFgWZ42L6pEF/ELJdFFRESCnCnIxbz2TwCsy67B6uxJlE+dWsH553uGDOXkhDN7doIGioqIiIiIdARhYeB2e/6IiM9psKiIiEgQM8bgZP8ZqqthwBCss0Y3OL56dSdSUmq9iXMNFBURERER6QDqh4uqnYuIXyiJLiIiEsTMhvfgi/+AK9wzTLS+DyKQnx/Gww939vZFFxERERGRDqK+L7rauYj4hZLoIiIiQcpUlGMWPwGAdeEVWGndm12bklLLrFnlauEiIiIiItIRqBJdxK/UE11ERCRImSVPQ3kpdOuBdcElAOTl2d7K85yccO/XIUPw9kcXEREREZF2zptEVxGNiD8oiS4iIhKEzJbPMWv/BYB91UwslydhvmhRDA8/3LnB2tmzE7y3Z80q57bbyv0Wp4iIiIiIBIC3nYsq0UX8QUl0ERGRIGNqanCefRwA6+yxWP0HeY9NnVrBqadWsXJlFJmZbubNi+ehh0q8g0XVzkVERERE5PgtXbqUDRs2sHv3biIiIsjKymLq1Kmkp6d71xhjePHFF3nzzTfZv38//fv359prr6VHjx6+D1CV6CJ+pZ7oIiIiQca8/iLk7ob4RKxLr25wLDXVISnJkJ0dQ0qKA8CQITXeP6mpTiBCFhERERFpVzZt2sTYsWP57W9/y69//Wscx+G+++7j4MFDLRRfffVVVqxYwTXXXMMDDzxAQkIC9913H5WVlb4PsL4S3V3j++cSkdBLom/atIkHH3yQG264gSuuuIINGzYEOiQREZE2Y/buwry+BABr0nVY0bEBjkhEREREpOOZM2cO55xzDj169KB3797MmDGDwsJCtm3bBniq0FeuXMnEiRM544wz6NmzJzNnzqSqqoq1a9f6PkBVoov4Vci1c6mqqqJ3796ce+65/OEPfwh0OCIiIm3GOA7OosfB7YYhp2Gd9j3vsaYGiubn20yZUkFRkU1enq0qdBERERERHzlw4AAAsbGeIpf8/HxKSko46aSTvGvCw8MZNGgQmzdvZsyYMU1ep6amhpqaQ9XjlmURFRXlvd2c+mPeNa66lJ5Te8Tzgk2jfYSo9rIPaD978fU+Qi6JPmzYMIYNGxboMERERNqc+WANbPkCIiKxr7yhwf/8mxooOm9ePADZ2TEaKCoiIiIi4iPGGBYuXMgJJ5xAz549ASgpKQEgPj6+wdr4+HgKCwubvdbSpUtZsmSJ936fPn2YP38+ycnJrYolLS0NgLyoKKqBxLg4ort1O4rdBIf6fYS69rIPaD978dU+Qi6JfrSO9Td8wa69/JZIJNjptSb+YkqLMUueBsCeMAU7ueH/+C+44CB5eTYXXniQ3bvDmD07ocFA0dRUJ6T/neq1JuIfeq2J+IdeayLty5NPPsnOnTu59957Gx377uvcGHPEa02cOJHx48c3Or+goAC3293seZZlkZaWRm5uLsYY3LWeT6EWFxZQundvq/cSaN/dR6hqL/uA9rOXlvbhcrla/cuqprT7JPrx/oYv2LWX3xKJBDu91sTXip59jAMH9hPedwCpV12PFdbwf9F790J2NsyaFcOAAZ7HRo9O4JRTAhCsD+m1JuIfeq2J+IdeayKh76mnnuKTTz5h7ty5JCUleR9PSEgAPBXpiYmJ3sfLysoaVacfLjw8nPDw8CaPtSaBaYzxrKsbLGrc7pBMfHr3EeLayz6g/ezFV/to90n0Y/0NX7BrL78lEgl2eq2JPziff4Lz7iqwbJzJPyM3v6DRmoICF5BMQUH9Mc/tvXtD9/9lh9NrTcQ/9FoT8Q+91qSjOd4Kz2BkjOGpp55iw4YN3HPPPaSkpDQ4npKSQkJCAhs3bqRPnz4AuN1uNm3axJQpU3wfoHewaPt4PyAS7Np9Ev14f8MX7NrLb4lEgp1ea+IrpqoKZ9GfAbDOGw+9+nr/rTU1TDQnJ5z09FqmTKnAstrfv0u91kT8Q681Ef/Qa03k6C1fvvyYzjv77LOJi4trsziefPJJ1q5dyx133EFUVJS3B3p0dDQRERFYlsW4ceNYunQp3bp1Iy0tjaVLlxIZGcnIkSPbLI5muZREF/Gndp9EFxERCWbmtX9CYR506Yo1oWHFSlPDRGfPTvDeTk11GDxYw0RFREREpP149tlnj+m8QYMGtWkSffXq1QDcc889DR6fMWMG55xzDgATJkygurqaJ554goqKCvr168ecOXO8s/h8qq6dC7W1vn8uEQm9JPrBgwfJzc313s/Pz2fHjh3ExsbStWvXAEYmIiJydMy32zH/egUA+8qfYXVq+MP21KkVnHpqFStXRpGZ6WbevPgGw0RTUvQDs4iIiIi0P7fffju9e/du1dra2lpuueWWNo/hhRdeaHGNZVlcccUVXHHFFW3+/C0+d5gLA6pEF/GTkEuif/3118ydO9d7/5lnngFg1KhRzJw5M1BhiYiIHBXj1OI88xg4Dpx6FtZJwxutSU11yM83ZGfHsGBBMQBDhtR4k+giIiIiIu1RYmJiq3usO47j42iClCrRRfwq5JLoJ554Yqt+GygiIhLMzNuvw46tEBWN/ePrAh2OiIiIiEhQ+Mc//kGnTp1avd627aM+p12oHyzqViW6iD+EXBJdREQk1Jl9hZilnl6P1iU/wUpIanC8qYGi+fk2U6ZUUFRkk5dnk5raQStuRERERKRdi46O9ss5Ic9bia4kuog/KIkuIiLiR8ZxcJ5ZAFWV0PcErLMvaLSmqYGi8+bFA5CdHcOsWeXcdpsGioqIiIiIdFguT7GN2rmI+IeS6CIiIn5k3l4BX/wHwiOwf3ITlm03WjN2bCV5eTbjxlWyZ4+L2bMTNFBURERERDqEw+fgtcSyLH7zm9/4MJogpkp0Eb9SEl1ERMRPzO5vMEueBsC6/KdY6T2bXmcssrNjuOqqAyQleRLnGigqIiIiIh2BMQbLsrz39+zZQ0lJCV27diUhIYGSkhIKCwtJSEggPT09gJEGmAaLiviVkugiIiJ+YGqqcf7+e3DXwJDTsM4ZF+iQRERERESCzj333OO9/d///pe//vWvzJs3j6ysLO/jmzdv5tFHH+VHP/pRACIMEnWDRc2aZZhzx2GldOBfKIj4QePPkIuIiEibMy8/C7u/gc7x2NNublBdA55hojk54d4/4BkqWlTkGShqWSYQYYuIiIiIBMzzzz/P5Zdf3iCBDjBgwAAuu+wynn/++QBFFgSSUrw3zZplAQxEpGNQJbqIiIiPmU3/wax5FQD76p9jxSU2WtPUMNHZsxO8t1NTHQYP1jBREREREek4vv32W5KSkpo81rVrV3bv3u3niIKH9b0fYP691jNvqbIy0OGItHtKoouIiPiQ2V+G848/AmCd80Osk05vct3UqRWcemoVK1dGkZnpZt68eA0TFREREZEOLSEhgfXr13PSSSc1Ovbhhx+SkJDg/6CChGVZWENOw3zxH0/LSBHxKSXRRUREfMQYg/PMY1CyD9IysC67ptm1qakO+fmG7OwYFiwoBjRMVEREREQ6tvPPP5/nnnuO/fv3M3LkSO9g0ffff58NGzZw5ZVXBjrEwHJ52kAaJdFFfE5JdBERER8xa/8F//kIwlzY02/DiowMdEgiIiIiIiFjwoQJVFVVsWzZMtavX+99PDw8nEsuuYQJEyYEMLogUJdEVyW6iO8piS4iIuIDJm8PZvETAFgTpmD16tvkurw8m/z8MADvQNH8fM8w0aIim7w8m9RUxz9Bi4iIiIgEmSuuuILx48ezZcsWysvL6dy5M/379ycmJibQoQWeqy6tV6MkuoivKYkuIiLSxozbjfPkw1B1EAYMwRp7cbNrmxooOm9ePADZ2THMmlXObbdpoKiIiIiIdFzR0dGcfPLJgQ4j6Fjh4RhQJbqIHyiJLiIi0sbMisWwfQtEx2BfcyuWHdbs2rFjK8nLsxk3rpI9e1zMnp2ggaIiIiIiIoc5cOAAe/bsobq6utGxQYMGBSCiIOFt5+IObBwiHYCS6CIiIm3IfLUJs+JFAKypM7C6JB95vbHIzo7hqqsOkJTkSZxroKiIiIiICNTW1vL3v/+dd999F8dpusXh4sWL/RxVEFFPdBG/sQMdgIiISHthKg/gPPEwGAdrxLnYp38/0CGJiIiIiISsFStW8Mknn3DjjTcCcO2113L99dfTt29funXrxq9+9asARxhg9Ul09UQX8Tkl0UVERNqIee6vUJQPSSlYV97Q7Lq8PJucnHDvH/AMFS0q8gwUtSzjr5BFRERERILWe++9x8SJExk5ciQA/fr147zzzuP+++8nOTmZL774IsARBli4KtFF/EXtXERERNqA8/H7mI/eBsvGnj4LKyq62bVNDROdPTvBezs11WHwYA0TFREREZGOLS8vj969e2NZFgA1h1Vcjxkzhn/84x9ceeWVgQov8NTORcRvlEQXERE5TmZfAWbRnwCwLrwcq9+RhxtNnVrBqadWsXJlFJmZbubNi9cwURERERGR7+jUqRNutxvLsoiNjaWgoIABAwYAEBERwf79+wMcYYApiS7iN2rnIiIichyMU4vz1KNwoAL6ZGFdOKnFc1JTHZKSDNnZMaSkeAYk1Q8THTKkhtTUpocmiYiIiIh0JOnp6eTn5wOQlZXFihUrKCoqorS0lFdffZX09PQARxhgrrraWCXRRXxOlegiIiLHwax+BTbnQGQnTxsXl/7XKiIiIiLSFs466yz27NkDwBVXXMHdd9/NjBkzAHC5XNx2222BDC/w6nui17gDG4dIB6B3+iIiIsfIfPM15pVsAKxJ07FSjlwJk5dnk58fBuAdKJqf7xkmWlRkk5dnqwpdRERERKTO2LFjvbf79OnDww8/zMcff4xlWQwdOlSV6PXtXIyDqa3FCgsLbDwi7ZiS6CIiIsfAVFXhPPF7qHXDsBFYI8e0eE5TA0XnzYsHIDs7hlmzyrntNg0UFRERERGprq5myZIljBgxgszMTAC6du3KD3/4wwBHFkTqk+jgaemiJLqIzyiJLiIicgzMkqcgdzckdMH+yU1YltXiOWPHVpKXZzNuXCV79riYPTtBA0VFRERERJoQERHBihUrOPnkkwMdSvD6bhI9slPgYhFp55REFxEROUrms48x77wOgP3TW7Bi41p3nrHIzo7hqqsOkJTkSZzXDxMVEREREZGGMjIyyM/PZ9CgQQF5/k2bNrFs2TK2b99OcXExt99+O8OHD/ceN8bw4osv8uabb7J//3769+/PtddeS48ePfwTYFgYWBYYAzV6TyHiS3agAxAREQklpqwYZ+H/AWD9YALWoGEBjkhEREREpH269NJLefnll8nNzQ3I81dVVdG7d2+uueaaJo+/+uqrrFixgmuuuYYHHniAhIQE7rvvPiorK/0Sn2VZh6rR3Uqii/iSKtFFRERayRiD8/QCKC+F7r2wLrmqxXOaGiaakxNOenotU6ZUYFnGpzGLiIiIiISqt99+m6qqKn7xi1/Qq1cvEhISGrRRtCyLO+64w2fPP2zYMIYNa7poxhjDypUrmThxImeccQYAM2fO5LrrrmPt2rWMGdPyzKQ24QqHmmol0UV8TEl0ERGRVjLvrIScf4MrHPu627HCI1o8p6lhorNnJ3hvp6Y6DB6sYaIiIiIiIt+1c+dOXC4XXbp0oby8nPLyhj83t2Yuka/k5+dTUlLCSSed5H0sPDycQYMGsXnz5maT6DU1NdQc1nrFsiyioqK8t5tTf6zRmrpKdMvtDujfR2s1u48Q0172Ae1nL77eh5LoIiIirWB2bsO8+A8ArEuvxureq1XnaZioiIiIiMixefzxxwMdQrNKSkoAiI+Pb/B4fHw8hYWFzZ63dOlSlixZ4r3fp08f5s+fT3JycqueNy0trcH9PZ0iqS2H8DeWkHj9bbjSurdyB4H13X2EqvayD2g/e/HVPpREFxERaYEpLcZ5/D7PxyQHn4I1enzrz9UwURERERGRduu7Va/GHLld48SJExk//tD7ifrzCwoKcLvdR3yetLQ0cnNzGzxHreUZd3hw/Xvs/fp/uB588qj34E/N7SPUtJd9QPvZS0v7cLlcrf5lVVOURBcRETkCU12F8/hvYV8hpHXHnn47lq253CIiIiIiHVlCQgLgqUhPTEz0Pl5WVtaoOv1w4eHhhIeHN3msNQlMY0zDda7DrlWYHzJJ0Eb7CFHtZR/Qfvbiq30oCyAiItIMYwxm4QLYvgWiY7FvugsrJrbF8/LybHJywr1/wDNMtKjI1jBREREREZEjuPrqq9m2bVur1zuOw9VXX82OHTt8F1QTUlJSSEhIYOPGjd7H3G43mzZtYsCAAf4LxNV0Ql5E2pYq0UVERJphVizGbHgPwsKwb/x/WKnprTpPw0RFRERERI7NwYMHcRzH5+e09rq5ubne+/n5+ezYsYPY2Fi6du3KuHHjWLp0Kd26dSMtLY2lS5cSGRnJyJEj2zyWZjVT1S4ibUtJdBERkSaYf6/FvPocANaVP8M6YWirz506tYJTT61i5cooMjPdzJsXr2GiIiIiIiKtNGfOnECHAMDXX3/N3LlzvfefeeYZAEaNGsXMmTOZMGEC1dXVPPHEE1RUVNCvXz/mzJlDVFSU/4JUJbqIXyiJLiIi8h1mx1acfzwKgPWDi7DPHntU56emOuTnG7KzY1iwoBjQMFERERERkda47LLLjum8Ll26tHEkcOKJJ/LCCy80e9yyLK644gquuOKKNn/uVnM1TO0569/FGjQMq3NcgAISaZ+URBcRETmMKS7Ceey3UF0NQ07DuvyngQ5JRERERKTDuPzyywMdQmj5TiW6eeIPmF79CPv1w577xsDuHXDgAGRmYalyXeSYKIkuIiJSx1QdxHnsPijdB+k9sa+7HcsOa/X5eXk2+fme9fUDRfPzPcNEi4ps8vJsUlPbvlejiIiIiIh0UK4mUnvffHXo9saPPe9x8HzK1po03U+BibQvSqKLiIgAxnFwnnoUdn4NsXHYN/0aKyr6qK7R1EDRefPiAcjOjmHWrHJuu00DRUVEREREpI243Uc8bLZtPnQ7d5evoxFpt5REFxERAc8Q0U/XQZgLe8avsJLTjvoaU6dWcP75BwFPJfrs2QkaKCoiIiIiIr5TXXXk4wW5h24frPRtLBJyTE0N5oN/4R4zPtChBD070AGIiIgEmvPRO5iVnoFB1k9mYvUfdMzXWr26Eykptd7Eef1A0SFDatTKRURERERE2lYLiXFTmHfY2oM+DkZCjVn+PE72Xyi4++eYmppAhxPUlEQXEZEOzXz9P8zCBQBYF1yKfdZ5x3yt/PwwHn64s7cvuoiIiIiIiE81U4luaus+BXt4Er1KlehyiCkvw6x8EQD3N9swry8JcETBTUl0ERHpsExRPs7jvwV3DZx8BtbEq9rs2ikptcyaVa4WLiIiIiIi4jvNVaJXlGMOHoDy0pbXSodk1r/T4L7z1nJVox+BeqKLiEiHZA4ewFkwz/NDZUYf7GtnYdlH/7vlvDzbW3mekxPu/TpkCN7+6CIiIiIicmwOHDjA1q1b2bdvH9XV1XTu3JmMjAx69uwZ6NCCQ1Uz7zn2l4HznYIeJdHlMGbrJgDsi6divb+a2qJ8zKfrsM4YFeDIgpOS6CIi0uEYpxbniYdh9zcQl4B906+xOkUd07UWLYrh4Yc7N3hs9uwE7+1Zs8q57bby4wlXRERERKRDqa2t5aOPPuJf//oXmzdvxnEazxbq3LkzI0eOZOzYsXTr1i0AUQYH6wcXYV5Z1PjA/jKo2O+53TXV09alphpTW4sVpvaTHZ0xBr7+EgArazAxUVGU/fPvmH9/AEqiN0lJdBER6XDMy8/AZxvAFY49cw5WUvIxX2vq1ApOPbWKlSujyMx0M29ePA89VOIdLKp2LiIiIiIirffvf/+bZ599lvz8fIYOHcrkyZPp06cP8fHxhIeHs3//fvLy8tiyZQsff/wxq1at4txzz+XHP/4xcXFxgQ7f76wfXoqVNRjn0bsb9kffX44pKfLc7t7rUG/0qkqIjvV/oBJcCvOgtBjCXNC7H5Gd6/5N5O0ObFxBTEl0ERHpUJwP1mBWLQXAmvZzrMwBx3W91FSH/HxDdnYMCxYUAzBkSI03iS4iIiIiIq33+OOPc+GFFzJmzBji4+ObXNO/f39GjhzJNddcQ05ODi+//DKrV6/msssu83O0gWfZYdB/EMR0bpBEN/vLvK1erNjOmDAX1Lo9LV2URO/w6lu50DMTKyISV7cMz/2CXIzjHFOr0/ZOSXQREekwzJbPMc/+CQBr/CRsfUxNRERERCSoPPbYY8TExLR6/ZAhQxgyZAgVFRU+jCoEhEc0vL+/7FBSPaITRHaCA/vVF108Pv8EAOuEIQCEpaR5qtLdNVBcBMfxae32Sr9WEBGRDsEU5OL8+QGodWOd+j2sH00+ruvl5dnk5IR7/wDk59tMmVJBUZFNXp7+FysiIiIicrSOJoHeFue1G+HhDe9XlENVXRI9shPUzYBy/vwAZvPnfg5OgolxuzGffwqANXS452uYy9M7HyB/T6BCC2p6hy8iIu2eOVCBs2Ae7C+HXv2wfnrrcX88bdGiGC64IJkLLkj2DhKdNy+e7OwYpkxJYtGiDv5DvIiIiIjIcZo0aRJfffVVk8e2bdvGpEmT/BxREPvu8NXyMqj2tHMhMtKbRCd3N87vf+Xf2CS4fLUJKisgNg4ys7wPW6meAb0mf2+gIgtqauciIiLtmqmtxfnb72Dvt5DQBfumOViRkcd93bFjK8nLsxk3rpI9e1zMnp2ggaIiIiIiIn7iOA6WZQU6jOBhGibRTWUFltPJcyfiUCW697gx+vvroMxXXwJgDRrm6alfLyXd81VJ9CYpiS4iIu2aefEp+OI/EBGBfdOvsRKS2ua6xiI7O4arrjpAUpInca6BoiIiIiIi/rFt2zaio6MDHUbw+G4l+oEKDHVJ8si6nuiHK8o/1L7DT4xTi/PsnyhJ7YY576LGfdzFP3J3eb5m9GrwsJWSjgFM/XFpQEl0ERFpt5x3Xse8+RoA9jWzsHr1C3BEIiIiIiJyJCtXrmTlypXe+w899BDh3+n3XV1dTWlpKSNGjPB3eMHLmIb3KyvAVZf2O7ydS71vt/s9ic7WTZi1/6Ic4KP3sG+4A6tbhn9jEEzubgCs1O4NHrd69PHc+OZrf4cUEpREFxGRdsls+i/mn38FwLp4KtapZx33NfPybPLzPR93qx8mmpMTTnp6LVOmVGBZ5kini4iIiIhIC+Li4sjI8CRWCwoKSE1NbVRxHh4eTs+ePRk3blwgQgxOTVSiE+FpY2nVtXM5/N2K2bkNa5h/fwlhNuccurN7B84f78G+/2/HPa9KWs8YA3meJDppDZPo9MwE24bSfZjiIqzEtvkUd3uhJLqIiLQ7ZuPHOH+ZD46DdcYorHGXt8l1Fy2K4eGHOzd4rH6oKEBqqsPgweVt8lwiIiIiIh3RyJEjGTlyJABz585l+vTpdO/evYWzpFESvfIARMV4bkdEQnjDuVBm9w7/xHX4c9Yl0eOm3EDZS894Wsp88xX0yWrhTGkzpcVwsBIsG5K7NThkRXaC9F6wazvs2ApKojegJLqIiLQrzodvY57+o+eHyCGnYV19c5sNzJk6tYJTT61i5cooMjPdzJsXr2GiIiIiIiI+cvfddwc6hNBhmkiiV1V6bkd28iROD1ex3z9x1THVVbBtMwDRo8ZS/r8czCfrMBv/jaUkuv/U9ztPTsX6TpskAKtPf8yu7ZjtW/z+SYVgp89LiIhIu+GsWYZ56hFPBfqIc7Fn/AqrDYfVpKY6JCUZsrNjSEnx/JBaP0x0yJAaUlOdFq4gIiIiIiJHsnXr1qM+p7q6mm+//dYH0YSQ71aiGwfKSj23IyMxB76TNK+s8E9c9b74D7jdkNgVV3oPrCGne8LM+bd/4+jgzJ6dnhupzXy6o3d/z7q6X3jIIUqii4hIyDPG4LyyCLP4CQCsH1yE9dNbsFz6wJWIiIiISCi55557+N3vfsfGjRtbXFtSUsKyZcu46aab+OSTT/wQXRA7PIkeVvc+qL4SPaITuGsarq884J+46jjr3wHAOn0klmVhDTnVc+CbrzAl+/waS0dmPv0QAKv/oCaPW1knem5s24ypqfZXWCFB2QUREQlpxqnFZP8V894bQN0Q0XGXt1kLF2h6oGh+vs2UKRUUFdnk5dmqQhcRERERaQN/+MMfePbZZ/ntb39LQkICAwcOJDMzk7i4OCIiIti/fz+5ubls3bqVr776itjYWC6//HJ+8IMfBDr0gLImTMFk/xnr++dj/rseyksPHYzshH3ZNJzfz8E69SzMB2/CQf8l0U15GXz2MQD2iHM88cYnQq9+niT6559gjRzjt3g6KrOvELZ8DoA1/OymF6V2h/hET+/0bVtgwGA/RhjclEQXEZGQZWpqcJ78A3yyDiwLa8qN2KMuaPPnaWqg6Lx58QBkZ8cwa1Y5t92mgaIiIiIiIscrLS2N2bNns2vXLlavXs1//vMfPvzwwwZrIiIiyMrK4vrrr2fkyJGEN9HbuaOxRl2AdcJQSEnDbP78O0n0SKxe/bD/+ByUFHuS6JUHMMa0afFRU4wxmOw/eyrhe2ZCj8xDMQ89DfPNV56WLm2URDeVBzD/+Qh274DUdOyz2/79Yagyn3wAxkD/QVhJKU2usSwLK2sw5uP3MZtzsJRE91ISXUREQpI5WInzp/vhy88gzIU9fRbWaSN98lxjx1aSl2czblwle/a4mD07QQNFRURERER8KCMjg2uuuQaAsrIy9u3bR3V1NXFxcXTt2hVXELVuXLVqFcuWLaOkpISMjAymTZvGwIED/RqDZVmQVtfnOiq64cGITp41dhim/lhtLdRUQ0SkbwPbsdWTvA0Lw/7JTQ2S9taQ0zGvPQ9fbmyThL6pPIAz71YoyD30WOYArIw+x3Xd9qK+/7w17MwjLzxhKHz8PmbDe5gLr8AKC/NDdMFPPdFFRCTkmPIynIfv8iTQIzth//wunyXQAYyxyM6OISnJeBPnGigqIiIiIuIfcXFx9O7dm6ysLNLS0oIqgb5u3TqefvppLrnkEubPn8/AgQO5//77KSwsDFxQ0TGHboe5Gs6KiuwE9clqP/RFN+vfBcA69XtYvfo1PNi9Z10cFfDdwadH+zwHKjDP/cWTQI+MOvR4XRuZQDOVB3DeW0Xtw3dRO/Nyah+7r/GwV18+f9VB2PoFANbgU4+41hr+fYiNg7zdmHVv+iO8kKAkuoiIhBSzrwDnd/8Ptm+BmM7Yt92HNWhYoMMSEREREZEOaPny5YwePZrzzjvPW4XetWtXVq9eHbigog5Lokc2rDS3bBs61VWjV1b4NAzjdmP+/YHneZvowW1FREJnT5tMigqO/XkqynHm3Yr56B0A7Bl3Yl01w3Osrvo6kEzJPpz5v8Q8+7inEKy6Cj7bgFm11H9BfP4puN2QlHLoEwvNsDpFY/3wMgDM8uc1YLRO8PzqTkREpAVm7y6cR38D+wohsSv2L+Zidevhk+dqaphoTk446em1TJlSgWUZnzyviIiIiIgcsmnTJl5//XV2795NdXXDZJ5lWSxYsCBAkYHb7Wbbtm1cfPHFDR4fOnQomzdvDkxQgBUdg/fdSl0rlwaiojwJ9MpKn8VgDh7AWTAPSvdBdCw0V/jUJdnTv31fgadn+tE+z67tOM8/AYV5kNgV6/KfYg06GYqLPH8H2zZjykux6pP1R3PtbZtx3ngJvvkaOkVBeAQkJWNFRWOl9aC8a1ccB88vAmI6g22DZYNtear9qw5i1izzJveJjMIaPQ6qqjBvLcd8sg5z8dTjamNj3DWe+A5WglMLqelYKekN1+Tuwln0OADWsBGtej7r3HGYNctgXyHm5WdgwhSsTodV+BsDtW5PWyC3G2prwF3recwE6L1ySjefXl5JdBERCQlmx1acP86F/WWQ1h371nuxkpJ99nxNDROdPTvBezs11WHwYA0TFRERERHxlf/973/MmzePQYMGsXv3bk4++WQqKyvZsmULqampDBgwIKDxlZWV4TgO8fENE7Tx8fGUlJQ0eU5NTQ01NTXe+5ZlERUV5b3dnPpjrUq4NqhE79T4nKgYoBAOHvDJYFFTWoz5x6Ow5QvoFIU9/TbsiAig8T6spGTMN19BceFRx2K+/h/O7+d4eru7XITdNMfbMsbq0hWnZybs3Aaff4p11uijunbtoj9h3nm98YFvvsIABig5mgumdSds+m1YvftjKg9Q+94qyNuNtfdbrO69jio28PwdO8sXYz5+D/Y3fF9qDRgC/QZ6Bs06Ds7zf/es6ZOF3UTSvql/W1ZEJEy4Eufp//P8IuDtFZ5WQO66xHmt+6hj9jXXXzyV/b4alqskuoiIBD3z5Wc4j98PVZXQqx/2LXcfUyXB0Zg6tYJTT61i5cooMjPdzJsXr2GiIiIiIiJ+9MILL3DOOedw3XXXMXnyZCZNmkRmZibffPMN999/P8OHDw90iEDTSbvmEnlLly5lyZIl3vt9+vRh/vz5JCe3rkAoLS2txTWlqWmU1d0Oj40lrVvDCt28+ASqd39DYqdIoru1XfWuMYb9ry2m9OnHMFUHsSIiSb7/z0QOGNxobf0+inv0Zv+nHxJTdYCEo4il6vP/ULhgHtRUEzn0NBKm/4KIvg1/qVJ61mjKdm4jcksOXS+d0uprV/57HYXvvA62TfToC4kZNRZsG1N5AHdRAU5xEe7c3Rh3DU5pMbWlxTj7y8AxYBzPH8dAWBjhPTOJ/8kMIged1OA5Ck49k4Pr3yP683+TcNqIVscG4M7dTf7v7sTk7QbAjksgLCkFgJpvvsJszoHNOZgVL3jPCUtKJnXeAsISk5q97nf/bZnLruJAQiJli5/EvXcXHGih/Y8r3NN/3wpM9/C0tNS6ry2/Ro6FkugiIhLUzKfrcP7+e89vvE8Yij3zV1idols+8Tilpjrk5xuys2NYsKAYODRMVEREREREfO/bb7/lRz/6kfe+4zgA9OrVi0svvZSXXnqJ0047LVDhERcXh23bjarOS0tLG1Wn15s4cSLjx4/33q9PthcUFOB2N1/da1kWaWlp5ObmelppHIETFu69XWOHsXfv3gbHa21POrB4z25Kv3MM6oZQRkQeVUWvMQbnub9g3l7peaBPFvbl17AvLgkOe47v7sOJ9Ly32//NdiqbiKXJ5yopovY3P/cUWfUdiPuGX1IU2anB8wCYzIEAVH6yjj3f7sRyhTd1uUb7qP3r7z2xnvcjqidNp0ETod4DGu0DY5odOlkL7INGsTmnnAXr36N89TIO/OBirLCwljcOmLw91P7+V1BcBMlp2FNuxBp4Eqbu/LBdO3DeWwWlxZj/bYTO8Z5K94smk3+wulEc391Lo39bg0/DnHgqYfsKoKYGwsLAFV731QVhLs992/ZZBXhr5RXtO+JrxOVytfqXVU1REl1ERIKW8/5qzLN/8vwm/5QzsaffhhUeEeiwRERERETED6qqqujUqRO2beNyuSgvP9S2Ij09nV27dgUwOk9SLjMzk40bNzaoit+4cSOnn356k+eEh4cTHt50Mrel5Hj9mhbXDT3sufcVNl4f5Ulcm8r9jY6Zb7fjPDAbuqZi3/BLrO49W4wJwFmzzJNAtyysK67BGv0jT/V2M7F691HXotPsK2jV/gGcl57xJND7ZGHPuhciIps81/TqC9ExcKACs+db6NGnxWubr76EPTs9v0QYP6nFmFr1/WjK0NMhNg5K92G++BSGtO6XQf+/vTsPj6q8+z/+uSczgYSQBZKQsAQSIIjsriBYsP83eQAAee1JREFUEKpSxSpqFTdq1aoFrV3U1qp1F6lPrb/H5dFWK261IItSl4K44Fb3BQQrIoQ1IQnZE7LO/fvjZCEmgSQkc2aS9+u6uDJzzplzvjeTE8gnd753zT//5gToyYPk+c3tMrF96+uQJA0YLM95l7dY64EccCx9Dh4+t+vvoRO0+z05CHfm1wMAcADWWvlfXSb71IOS9cscf5I8V1wfkAB9zx6P1q/31f+RpOxsjy64oFR793q0Zw//dAIAAACBEB8fr8LCQknSwIED9dlnn9Xv27hxo6Kiotwqrd6sWbP0+uuv64033tDOnTu1aNEi5ebm6sQTT3StJhMd2/Bkb3bTA2pD9OYWFrUfvOn0GM/cIf8//9qq69mcLNlli5xrn3uZPD88XcbTyu+b6sLZvJzWXWtvtlOjJM95Vzi9u1tgPB4pobZFTO6e1p3/3dXOa4+cLBPZeZ9fxuuTmeC0cbGbv25dbdu3SOs/kYxHnqturA/QERjMRAcABBVrrezSJ2RXvyBJMj86S2b23ID9alhzC4recYfzq5jPPttLv/lNsX77WxYUBQAAADrb4Ycfrg0bNmjixImaMWOGHn/8ce3atUs+n09ffvllo7YobjnuuONUXFysZcuWKT8/X4MGDdINN9xwSG0jOoLn2rvl/9/bZM7+WdOd9SF60x7X9quGH1Ro9/ZWXcu+/q/69ptmehvfk9pe3irIk62sOGAoLkn2vdcla51rpQ4/6OlNQpLsts2yuXt0sO8ord8v+8VHzusm/7A11R+agUOc6+7a1qrD7VtOqxxz1GSZxP6dVRVaQIgOAAgatqZG9qkHZd9/XZJkfvIzeU6aHdAaTj55n/bs8eiUU/Zp926vrrsulgVFAQAAABecc845KikpkSSddNJJqqys1DvvvCNjjM4880ydeeaZLlfoOPnkk3XyySe7XUYjZsRoeR74p4ynmV7bEb2cj+WNZ6LbvJzGwXlRgWz5PpmeES1ex+4rk313jSTJ86Oz2j75KSraCfX3lTmzxfu33D7GWtvwveKUVs70T3AWm1RO1sGP3b1dKi2WevSUhh7WuvMfAtM/Rbbuugdha2pkP/+P87rjT+rcwtAsQnQAQFCwlRXy//Ve6cuPnEVJ5l4tz+QZga/DGj37bC9ddFGZ+vZ1gnMWFAUAAAACLzo6WtHR0fXPZ82aFRSzz0NFswG6JPWsnYle1ngmuv16nfMgbYSUtUsqK3GC7doZ082xX37k9CdPGiCNHN/2Go1xWq5s/07KzjxgiK49u532NL7w+lYoBxXvhOi2Fe1c7KavnAdDD5PxBiAyHTDY+Zi7R7aiXKZHz5aP3fSVVFIsRfWW0kd3fm1ogsauAADX2bJS+f/fbU6A7vXJ84vfuxKgAwAAAAget912m3bt2tXsvt27d+u2224LcEVdg4mrXYxy+3eNF2Dc+o2zf9hIKSHJ2XawGdzrP3FeM2FSu1twmkSnb7k9yLXsFqc+DR560LYv9eeOrx1HG0J0E6CQ2vSOkXrHOO1pMncc8Fi77mPnNeOOlQlr4Ycj6FSE6AAAV9mifPn/5w/OT9Z7Rsjzq9tkxrdyVkEHaW4x0fXrfdq711lQ1JjgWGUcAAAA6E42btyofc0sfilJ5eXl2rhxY4Ar6iJGTZB6RDgB+XcNi1rarZskSSY1XaY2RD9QsG1ramS/+tR5zdij219PbYiu7MwDH1cX8qeNaP25ExpC9EY/MGj2/N865x92eOvPf6hqZ6PbXQdu6WK/+6/zYOS4zq4ILaCdCwDANTZ3j/x/+aPzn6XeMfL86laZlKEBr6O5xUSvuy62/nG/fn6NHs1iogAAAECwyM/PV48erZuNjMZMj54yRx4n+/7r8q9aIU/aCGdh0J0ZzgGpI6TtW5zHB5odnvGt0xKmV28pLb39BdUF9gcJ0etmorcpRI+LlzweqapSKsyXYvs0f+7qKik/13mSPKD15z9Epm+i0xe9YG+Lx9iqKmmH8360aezoUIToAABX2M1fy//oQqkgT+qbKM+vb5fp584K4xdeWKojj6zQK69EKC2tWnfcEcNiogAAAIALPv74Y3388cf1z5cuXdqoL7okVVZWauPGjUpNTQ10eV2GmXaK7AdvSl98KLvyOZnRR0h+vxQTJ/WJbwi2c1oOtu2uDOdB6vCW+6+3ppbEZCdIPtC1qir3C/lbH9gbr9dZvLSoQCopbDFE194cp61KeA+pd2yrz3/Iomo/t0sOMGlrxxbnhxy9Y+p7vCPwCNEBAAFl/TWyry6TXfkP5z9p/VOcFi61ffnc0K+fX9nZVs8+20sPPJAvicVEAQAAADfs3LlTH3zwQf3zDRs2NOm17fP5lJKSoosvvjjA1XUdJnW4zIXzZJ96UPbdNVJMbbicMtT5++43wAm2M3e2fJLdTh9vkzzo0Iqp61u+N1vWX9N8IJ+b7Xz/2CPCmV3eFhG9nBC9rKzlY+p6psf3a3dv93aJqv2N6JKiFg+p7wWfmh7Y2tAIIToAIGBswV75H/+L9F9n1XdzzFSZC38hExHpcmUAAAAAgsHs2bM1e/ZsSdK5556rW265RcOGDXO5qq7JTDxBdvFjUmGe7MdvO9uSaluZ1PbqVl6ObFmpTGSvJq+3dYthHmqIHh0rGeOE5CXFzvPvqwu5E9oRctd9v7mvtMVD6nu/B3qmd+1MdFt6gJnotTPwzWDuAzcRogMAAsKu/1T+v//F+Ql7eA+Z86+UOW66qz9J37PHo+xsZ5ZD3YKi2dnOYqJ793q0Z49H/fr5XasPAAAA6M4WL17sdgldmvH5pMPHS59/IH1bu0hrbYhuekU5bV3ycqVd26ThzSy2WTcTvX/KodVR13KluFAqym82RLe5hxBy14bodl+pWvzuszakr1tQNVBMVG9nxv+BZqLvzXYeJAa2NjRGiA4A6FS2ukp2+VOyr73obBg4RJ7Lr5dJHuhuYWp+QdE77oiRJD37bC/95jfF+u1vWVAUAAAAQNdkxh4t+3lD+xzTb79FNQcMkfJyZXdmyHwvRLdlpQ2LYXbE93bRsbUhekHz++tC7naF6LWz6Pe13M6lIaRPbPv5D0V9T/SWQ3TVhuimT4BrQyOE6ACATmOzd8v/1/+Rtm2WJJkTTpX5yc9kfOEuV+Y4+eR92rPHo1NO2afdu7267rpYFhQFAAAAXDR//vxW/7aqMUYPPPBAJ1fUtZkxRzkzoevsF6KbgYNl138i1S0gur+s2l7pMXEykVGHXkh0rLRrm2xhQbOzxW19z/K2z8Y2EZHOGMtabuei3NqgOtDtXHrVhugttHOxfr/z2wCS1JcQ3U2E6ACATuH/cK3sMw9L5fukyCh5Lv6lzISJbpfViLVGzz7bSxddVKa+fZ3gnAVFAQAAAPccfvjhLJ4YQCYmTho8zJn41CNCiolr2DlgiCTJ7tre5HX1PcQTkzusDis57Vya08kz0ZVfG1T3SWj7+Q9F3Uz0slLZmhqZsO8tqlqYL9VUSx6PFNsnsLWhEUJ0AECHshXlss89Kvve686G4YfLc9lvZQL9nxEAAAAAIWf+/Plul9DtmLFHy27bLPXr3+gHGCa+nxNs5+U0fVHt7GjTUbOjo2vD+8IWQvScupno7e+J3lKIbq1taKcSFdP28x+KXr2cRVWtdWajf78ffF0/9Lj4pgE7AooQHQDQYez2LfL/7V4pa5dkjMyp58rMOjeo/rFvbjHR9et96t+/RhdcUCpj7IFeDgAAAABdivnBybKbvpI5/qTGO+LinY+FebJ+v4zH07Avrzbc7ag+3TGxtdcqaLLL7iuT9tW2YmlPz/LIuhC9hXYuZaWS3+887h3d9vMfAuMJkyKjnAC9pKhJiF6/qCitXFxHiA4AOGTWWtk3X5Z9/gmpukqK7ePMPh8xxu3SmmhuMdHrroutf9yvn1+jR7OYKAAAABAMioqK9NJLL2nDhg0qLi7Wddddp0GDBum1117TsGHDlJqa6naJIc/E9lHYtXc13RETJxmPVFPjLPq5X6sXu7d2dnrfDvqN49qZ6La5di51i432jJDp0bPt565t52JbaudSNwu9R4Q763f16l0bojfzfWjdoqId9feMdiNEBwAcEltaLP+i/5W++NDZMPZoeS6+RibAP8FvLRYTBQAAAEJDdna2br75ZpWVlWnw4MHas2ePqqqc/7dv27ZN3377rebNm+dylV2XCQtzZogX5Dk9w/fvl17b4qWj2rk09EQvaLqzuHZb7/a1WqlfWLSlmejFhbXnd+l72N7RUvbuhjB/f3WtdGiP6jpCdABAu9lNG+R//M9OPzyvV+asi2VmnBbUCwGxmCgAAAAQGp555hlFRkZqwYIFiomJ0fnnn1+/77DDDtPzzz/vYnXdRFy8E6IX7JU0XFJtD/G6NiMdFe7W9URvdiZ6bcj9/X7hrXWwhUXr+6G7FKL3cn5T2pYW6/vfSdu6HyrEsKio2wjRAQBtZv01sq88L7vyn5L1S4n95bn8OpnBQ90uDQAAAEAXsX79ev385z9Xnz595K/rWV0rLi5OeXl5LlXWjcQ64a3N39sQ8JaVSuX7nMcdFqLXzjIvKZatrpbxNkSWtn6meDsX/TzYwqKHev5DVD8LP39v0521tZlod2pDA0J0AECb2Py98j9+n/TNekmSmXiCzAVXyPSMdLmylrGYKAAAABB6qqqqFBUV1ey+iooKefZf6BKdwsTFNw1462ah946R6dGjYy7UK0oyRrLW6Q++f+uY2nYupt0het1M9BbaudT2IjdRvZvf39ni+zkfc7Ka7ityN+BHA0J0AECr2S8/ln/R/c5/Mnr0lLngF/JMOsHtsg6KxUQBAACA0NO/f3+tW7dOY8eObbJv48aNGjRokAtVdTNxfZ2P+4fondBixHjCnLYmJUVNFjFtCJJj23fyupno5ftk/TXOtfZX4nJQnZAsSbI5mU33FR/i2NFhCNEBAAdlq6pkly2Sff1fzoaUNHl+fp1M0gB3C2ulCy8s1ZFHVuiVVyKUllatO+6IYTFRAAAAIMjNmDFDTz31lPr06aMpU6ZIkqqrq/XBBx9o9erVuuSSS1yusBuIdUJ0m5/bsK28ti1KZAf/NnLvmIYQfX91z9vb0qRuJrrktKGJ/N5vNxS72xPdJCY5s/2/NxPdVlU1zJ6nnYvrCNEBAAdk9+yW/69/krZvkSSZH/5Y5syfyvh8LlfWev36+ZWdbfXss730wAPOQjUsJgoAAAAEt5NPPlkZGRl68skn9dRTT0mS/vjHP8paqxkzZmjatGnuFtgN1Pfrrlt8U5Kt64fe0S09e0dLmZItKWq0wOah9iw3Pp/k9UnVVU5f9O+F6NbthUUTkpyPRQWy5ftkekY4z2vb2CgsrGnwj4AjRAcAtMj/nzdln31EqtgnRfWW5+JfyYw72u2yAAAAAHQTV1xxhU444QR99tlnKiwsVO/evXXkkUdqxIgRbpfWPfSqDW9L92t/WTsTvT7s7ShRtSH592ei17aPaXdPdMlpFVOY57Qm7ZvYeF9tiG56uzQTPTLKqa+0WMrNkgamOjv2++GBMablEyAgCNEBAE3Y8n2y/3hE9j9vOhvSR8tz2W9l6vrhhYjmFhTNzvboggtKtXevR3v2eNSvn9/NEgEAAAAcRHp6utLT090uo3vqVbu2VGlJw7Z9nTMT3fSOdma9Fxc13lHfziW2/SfvHeOE6HWzu/fn9kx0yZmNXlosZe8XorOoaFAhRAcANGIzvpX/b3+WsndLxiPz4zkyp/yk6eIrIaC5BUXvuMP5D8izz/bSb35TrN/+lgVFAQAAAKBZdTPRqyplKytkwns4fcUlqaNnoteFxSUNM9FtTU3DLPhDCZNre4rb4satYiQ5LV6kjm9P0wYmIUk241vZ3Kz6+mxd4M+iokGBEB0AIEmy1VWyLy+RfeV5ye+X4uKd2efpo9wurd0uvLBUJ51ULsmZiX7ddbEsKAoAAAAEsXPPPbdNxy9evLiTKoEkqUeE05O7psaZjR7eo2Fh0YjOaedi92/nsq9UstZ53Kt3My9qHRMVUzvLvaDpzsoK52OPnu0+/yGr+63vgryGbbV/D4ZFRYMCIToAQHbnVvn/fr+0Y6skyRx9vMwFV8ocwn9SgsXq1T114YWlGjPGec6CogAAAEDwOuussxr1f37rrbdUXl6uI488UrGxscrPz9dnn32mHj166IQTTui0OpYvX67PPvtMGRkZ8nq9WrRoUZNjcnNz9dhjj2nDhg0KDw/X5MmTNXfuXHm9XSduM8Y4i1oWFzozwuP67jdzu6Nnote2U9m/nUvdrPfwcJmwQ/jt6Loguqhxv3Xr9+8Xovdo//kPVUwf5+P+ITrtXIJK17mrAQBtZmtqZP+9TPZf/5RqqqWo3jLn/0Keo6e4XVqHyM4O03339a6fjQ4AAAAguJ1zzjn1j//1r38pNjZWN998s3r2bJglvG/fPt1xxx3q0YmhZ3V1tSZOnKj09HS98cYbTfb7/X4tWLBA0dHRuv3221VcXKyHHnpIknTJJZd0Wl2u6NW7NkR3+qLb8s7qiV43W3y/oLui9nu5HocY2PduYdHSqsqGx+EuzkSPdUJ0W7hfiF5a+8OELjC5rSvwuF0AAMAdNnOH/PdcL/vCM06APv5YeW57sMsE6N+XmFij3/ymmBYuAAAAQIhYvXq1fvzjHzcK0CUpIiJCP/7xj7Vq1apOu/Y555yjWbNmKSUlpdn9X375pXbu3Kmrr75aqampGjt2rObOnavXX39dZWVlnVaXK+r6otf1Jq9t52IiOriHeN1M9JJmZqIfaquV3s20ipEaQnrJaVXjEhNbNxM9v2FjZW3A72abGdRjJjoAdDPWXyO7ZqXsimek6iopopfMeZfLTJzW6NcmQ9WePR5lZzu/5rd+va/+45gxYkY6AAAAEELy8vIU1kILj7CwMBUUFAS2oP1s2rRJKSkp6tOnT/22cePGqaqqSlu2bNHo0aNdq63DRTohui0qkF36hPTtRmf7oc4O/76ouoVFi2X9NTKesP1moh9akGyiY5vOcpcazh8eLuNxca5xXYhemCdrrYwxsh00dnSMkAzRV61apZUrV6qgoEADBw7UxRdfrJEjR7pdFgAEPZu9W/4n/p+0+Wtnw+gj5Jl7tUzdIiZdwDPP9NJ99zX+dbfrroutf/yb3xTrt78tDnBVAAAAANpqwIABeumllzR+/PhGfcarq6v10ksvacCAAa7VVlBQoJiYxr2qo6Ki5PV6DxjuV1VVqaqqYY0mY4wiahfoPNCkprp9bkx8MlG9ZSXZfy+T9mY3bI/s1eZ6DjiO6FjJGMn6ZUpLnOC7LkjuGXloY9+vnUuj89S1cwnv0abzd/j7EVv7PXlFuUxFuUxEpExlhawk06Nnp77vbn5udaTOHkfIhejvv/++Fi1apMsuu0wjRozQmjVrdPfdd+svf/mL4uPj3S4vYPbs8ejRR6UzzvA0ak2wZ49HzzzTSxdeWKp+/fwH3B4MxwZzbV1lHNR26LVde61afWzQjuPpCF02/HlFrX5CqqyQPzxCr/eZrwnnTlW/OOv633FHXu/CC0uVllalRx+N0owZ5br//mjde29B/WKitHMBAAAAQsOcOXN077336uqrr9Yxxxyj2NhYFRQU6KOPPlJBQYGuu+66Np1vyZIlWrp06QGPWbBggYYOHdqq8zUX1tXNIm7JihUrGtWQmpqqhQsXKiEhoVXXTEpKatVxHSk/MUklUqMAXZLiBw5SeHJyu87Z0jh2xcTJX5Cn+HCvwpOTVRrRQ3mSesbEKKGd15KkatUoU5IpKVTyfuepKNqrbElhEb0abW+tjnw/dvaKki0tUYIvTL7kZO3x16hSUp+kZEUcwthby43Prc7QWeMIuRD9pZde0vTp0zVjxgxJ0sUXX6wvv/xSq1ev1vnnn+9ydYGzZ49Ht90mTZrUOETffxG9/cOn5rYHw7HBXFtXGQe1HXptF1wg1f17FQy1tXUc+ZtzdfR7Dynqm4+dDSPG6LtJv9Wl54zWv8/JUb+kqg67XjC8//36+WWt0fr14frRj5xZC2PGVNWH6AAAAABCwxFHHKE//OEP+uc//6lVq1bJWmcC0LBhw/SLX/xCY8eObdP5Zs6cqcmTJx/wmNaG2bGxsdq8eXOjbSUlJaqpqWkyQ31/s2fP1qxZs+qf1wXuOTk5qq6ubvF1xhglJSUpKyur/u8hUPxq/ocCuSWlMpmZbTrXwcbh7xUtFeQp57tN8vSMkj8rS5JUIaPMNl5rf7bcmXFuKyq0O2OrTG2LFP/uXZKkGq+vTefvjPfDRsdJpSXK/va/8nh7qLrE+Q3qvLJ98hzC2A/Gzc+tjnSwcXi93lbf380JqRC9urpaW7Zs0RlnnNFo+9ixY/XNN9+4UxQABClrrey7ryntucc1PH6f/N4eCvvJT2WmnaKqDe4tmAIAAAAArTVmzBiNGTNGFRUVKi0tVa9evdSjR/u+n4mOjlZ0dHSH1JWenq7ly5crPz9fcXFxkqR169bJ5/MpLS2txdf5fD75fL5m97UmwLTWBjzotLU90Zts7xkhtbOWFscREyvtkmxBvnNMRcPCoocybhveQwoPlyorZQvzpYTa2crldT3Re7Tr/B36fsT2kTJ3yBbsdc5ZWeFs94UH5D1343OrM3TWOEIqRC8qKpLf72/yE72YmJgW+021t9dUMNqzx6M9e5xFDr76Krz+4969HuXledS3r1+7djUsptfc9vfeC9e33zpv+/4L7wXy2GCurauMg9o6trY33pAiInrK2tD53Czeka8h7/5F/XI+Vpikj/PGacvxv1XPgmTpheD7O+6I623eHKbt272KifHr88+dr5EbNnj1ox/t0yef+OTxSKNHtzyzA+7qKn34gGDHvQYEBvca0PF69OjR7vC8PXJzc1VSUqLc3Fz5/X5lZGRIclpF9OzZU+PGjdPAgQP14IMP6sILL1RJSYmefvppzZgxQ5GRkQGrMyB69W5+e0cvLCrJRMfVLgBa4GyoC7l7Htq1jDFSr2ipMlcqLa4P0W1l8CzeaWL6OGPP3+tsqF9YlElwwcDYEPoRQ15enq688krdeeedSk9Pr9++fPlyvf3227r//vubvOb7/a7qek2FoltvlW67ze0qAAQ3q9n9X9Xto+5VjK9Y5TXhunfTPD2+9Tz51fyq9t3F1KnSW2+5XQUAAACAUPDQQw9p7dq1TbbfcsstGjVqlCQnaH/sscf01VdfKTw8XFOmTNFFF13U4kzzA8nJyWk0CfT7jDFKTk5WZmZm4Geib9ss/52/abI97G8r23yug43D//wTsqtXyJx4ujznXCr/4sdl17woM/Msec76abvqr1Nz69XSrm3y/Oo2mVETnOu9+5rskw9IY45S2C//2GHjaA//i/+QfemfMsefJM/cq1Rz1TlSRbk8dz0qk9h5PdHd/NzqSAcbh8/n6z7tXKKjo+XxeJrMOi8sLGyx31R7e00FozPO8GjSpIaZ6NdeG6P/+Z9CJSdXN5qped11sbr33gL171/TZPvNNxcqMbGhl/Add0QH/Nhgrq2rjIPaOra2e++VIiLy62eiB+vnZu7WIvVc9pBmJr0lScqPGaEtP7hW6SWp8l8XFtR/xx1xvYgIf6OZ6EuXRurss8s0darzK3AjRlQrMzO0vu53J12lDx8Q7LjXgMDgXkN3c6i9hoPR/PnzNX/+/AMeEx8fr9///vcBqsg9ZvAwmfOvlF3xlLSvrHMvFhPrfCwscD7u187lkNXOqLdlJQ1d3itqW6aEhx/6+Q9VQj9Jks3d07idSxDMkkeIheher1dpaWlat26djjnmmPrt69at09FHH93saw6111QwSUysabSIqCSNHl3ZaLG89eudsX5/Eb267ZMnNxzv1rHBXFtXGQe1dWxt06dLycnlstYG7TjsJ++q8tNH5E0qkvV45fnxHPWdeZbiw8IUsb4q6P+OO/p60dFWS5dGaurUCp155r767SH2Zb9b6ip9+IBgx70GBAb3GoCuwnPCKbJTT5Z99hHZt1d13oWinf7ytq6dS11Lk54dECTX9XYvLWnYVhtUm3D3g2qTkOy0c8nOlCorG76BDaedSzAIqRBdkmbNmqUHHnhAaWlpSk9P15o1a5Sbm6sTTzzR7dIAIOBsSZHsPx6V/fgdeSVtKEpXzyuuUfr0QW6XBgAAAADoQownTPrhj50Q/YhJnXON6FgnSC7MlyTZ+r7gh95/3fSKcs5dWtywMYh6otcvdpqXK+0rbdhOT/SgEHIh+nHHHafi4mItW7ZM+fn5GjRokG644YYu92tDB9Ovn1+33OJ83F9iYo1+85viJjPWm9seDMcGc21dZRzUdui1JSf3btc5OvvYgXnvy//kg85/Ljwelf3gJ3o981KdP6pSkr9V5wiWv+OOvl56epUmTqxQenrLPQUBAAAAAG1jkgfJ85dnpMhenXOBGGcmuoqcEF3ltb9ZfIgLi0qSetXORC/bL6AOpsU7Y+KctjKVlVLmDmeb1+f88AKuC6mFRTvSwRZsCHZdpek/EOyC8V6zZSWy/3xM9j9vOBuSB8nzs1/JpA53tzDgEATjvQZ0RdxrQGBwr6G7OdQF+xDcC4t2pIONw5YWy/+rCyRJngcWy/8/N0rbNstz9c0yY5tv5dxa/peXyL7wjMzkH8pz8S+dbU8/LPv2v2VOO0+eH5/XYeNor5pbrpJ2b5c591LZxY9LvXor7P5nO+z8zekun1vdamFRAOju7IbP5X/yASk/VzJG5qQzZE6/QMYXBIugAAAAAABwCEyv3lJMH6kwT9q1bb+Z4h03E92W7d8TPYjauUhOS5fd22U3fO48D4YZ8pBEiA4AIcGWl8k+v0j27X87GxKTndnnw0a6WxgAAAAAAB1p4GCpME92/SdS9m5nW0e0c2lmYVFbu7BosCzeacYcJfvlR9JXnzkbgqQuEKIDQNCzmzfK//f7pZwsSZKZcZrM7Lky/EQaAAAAANDFmIFDZDd8LvvykoaNHTBT3PTq7Swsuv9M9GDqiS7J/OBk2Y1fSJ+972wID5IZ8iBEB4BgZaurZP/1T9lXl0nWL/VNlOfiX8ocNtbt0gAAAAAA6BwDhzTd1rMDwuS6meiNQnRnJroJknYuxhiZYSNl60L0IAn3QYgOAEHJ7t4u/+P3Sdu3SJLMpOky510uExHpcmUAAAAAAHQeM3CImiwL2YE90fdv51LfEz2IZnybvokN4w+ScB+E6AAQVKzfL/vmy7LLnpSqKqWo3vJcOF/myOPcLg0AAAAAgM6XnCKNGOPMGN+xVYqL75gwuS5EryiXra6S8frqZ6IH1Yzv+MSGx0EU7nd3hOgAECRsXq78i/6f9PWXzobRR8rz06tlYvu4WxgAAAAAAAFiwsIUdu1dkiSblyN5wmQ8nkM/8f6/2V1WIkXH7dcTPYjC6r79Gh4b98pAY4ToABAE/B+/I/vMw1JZqRQeLvOTS2Sm/kjG8C8mAAAAAKB7Mn0SOu5cnjApspfzfXdpbYheWTsTPTyIZqJH9mp4XFLsXh1ohBAdAFxkS0tk//Go7EdrnQ1Dhstz6a9lkga6WxgAAAAAAF1NVLQTohcXSckKzp7o+0+mKy50rxA0QogOAC6xX38p/xP/T8rPlTwemVPPkTnlHBkvX5oBAAAAAOhwvWOk7EyppFC2pkaqrna2B1NP9P0RogcNkhoACDBbVSm7/GnZNS86GxL7O7PP00a4WxgAAAAAAF1ZVLQkyRYVytT1Q5eCqye6JHP6+bIv/kOeC+e5XQpqEaIDQADZ7d/J/9h9UuYOSZKZOtPpfx5k/2ADAAAAANDVmOhYWUkqKWxo5WI8ktfnZllNmFPPlZl2ikxt6A/3EaIDQABYf43sqhWyL/5DqqmWomPl+enVMmOPdrs0AAAAAAC6h7pQurhIqqhdVLRHj8Z9yIOAMaahVgQFQnQA6GQ2J0v+v98vbd7obBg/UZ6582V6x7haFwAAAAAA3Urd9+HFhVJlbYgeHqT90BFUCNEBoJNYa2Xff132ub9JFfuknhEycy6XOW560P2UGwAAAACALq93bU/0kqKGnui0V0UrEKIDQCewxYXyP/2Q9PkHzoZhh8tzya9kEpLcLQwAAAAAgG7KRMU4PdGLChp6ojMTHa1AiA4AHcyu+1j+Jx9w/lEO88qcfoHMyWfIeMLcLg0AAAAAgO4ruradS8n+PdGZiY6DI0QHgA5iK8pll/xd9u1/Oxv6p8hz6W9kUtLcLQwAAAAAAEhRtSF6Yb5s9m7nMSE6WoEQHQA6gN3yjfyP3ydlZ0qSzA9PlznzIhlfuMuVAQAAAAAASQ0Li0qySxc5D2jnglYgRAeAQ2Crq2VfXiL7yhLJ75fi4uX52TUyI8e5XRoAAAAAANiP8fmabiNERysQogNAO9nMnfL//S9SxreSJHPMVJnzr5DpFeVyZQAAAAA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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot trajectory\n",
    "grid = plt.GridSpec(4, 5)\n",
    "\n",
    "plt.figure(figsize=(15, 10))\n",
    "\n",
    "plt.subplot(grid[0:4, 0:4])\n",
    "plt.plot(track[0, 0:200], track[1, 0:200], \"b+\")\n",
    "plt.plot(x_sim[0, 0:50], x_sim[1, 0:50])\n",
    "plt.axis(\"equal\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.xlabel(\"x\")\n",
    "\n",
    "plt.subplot(grid[0, 4])\n",
    "plt.plot(u_sim[0, :])\n",
    "plt.ylabel(\"a(t) [m/ss]\")\n",
    "\n",
    "plt.subplot(grid[1, 4])\n",
    "plt.plot(x_sim[2, :])\n",
    "plt.ylabel(\"v(t) [m/s]\")\n",
    "\n",
    "plt.subplot(grid[2, 4])\n",
    "plt.plot(np.degrees(u_sim[1, :]))\n",
    "plt.ylabel(\"delta(t) [rad]\")\n",
    "\n",
    "plt.subplot(grid[3, 4])\n",
    "plt.plot(x_sim[3, :])\n",
    "plt.ylabel(\"theta(t) [rad]\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "language": "python",
   "display_name": "Python 3 (ipykernel)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}