{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving a multitraces formulation problem coupled with ordinary differential equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code considerations:\n",
    "- We try to use numpy arrays for faster computations whenever it is possible (lists are very slow)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import of the numpy library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we solve a example associated with the electropermeabilization problem. See article [Cell Electropermeabilization Modeling via Multiple Traces Formulation and Time Semi-Implicit Coupling](https://arxiv.org/abs/2403.19371) where the model and formulation are described. In this notebook we present one of the simulations of Section 4.3.2 of the same article."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One sphere"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We assume that the center of the sphere is in the origin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters set up."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we set up the parameters of the problem:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Geometry and physical parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Radius of the sphere. It has to be a float number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius = 10."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable `sigmas` is a numpy array with the medium conductivities in the order $\\sigma_0$, $\\sigma_1$. The numbers have to be floats:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_e = 15. # extracellular conductivity, [microS / micro m]\n",
    "sigma_i =  1.5  # intracellular conductivity, [microS / micro m]\n",
    "sigmas = np.asarray([sigma_e, sigma_i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Capacitance of the membrane (needs to be a float):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "c_m = 1.\n",
    "# c_m = 9.5*10**(-3)  # capacitance [p F / (micro m) ** 2] (This unit is for the Kavian et al. problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Discretization parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximum degree of the spherical harmonics to be used for discretize ($L$). It has to be an integer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "big_l = 17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximum degree of the spherical harmonics to be used for quadratures ($L_c$). It has to be an integer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "big_l_c = 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters for the time scheme used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_time = 0.\n",
    "final_time = 10.\n",
    "number_steps = 2**13"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial conditions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up of initial conditions, for this model we need two arrays of length `(big_l + 1)**2`. Each array has the coefficients of the spherical harmonic expansion of each initial condition.\n",
    "In the following we give a couple of examples for building one of the arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial condition equal to zero\n",
    "v_0_zero = np.zeros(((big_l+1)**2))\n",
    "# Intial condition equal to a cte value\n",
    "cte = 4.\n",
    "v_0_cte_value = np.zeros(((big_l+1)**2))\n",
    "v_0_cte_value[0] = cte * 2* np.sqrt(np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we use initial conditions equal to zero. We need to set up both arrays in one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_conditions = np.zeros((2, (big_l+1)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set up of the external excitation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up the contributions to the right hand side made by $\\phi_e$. For this, we set up a function only dependent on time, to account for changes in time. In the module `biosspheres.formulations.mtf.timecouplings.righthands` there are implementations on how to do this. We show some of the predetermined, and how to make a new one:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pre-defined:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import of the module where pre-defined right hand sides are.\n",
    "import biosspheres.formulations.mtf.timecouplings.righthands as righthands\n",
    "# phi_e cte in time and space\n",
    "cte=5.\n",
    "phi_cte_space_time = righthands.phi_part_of_b_cte_space_and_time(\n",
    "\tbig_l, n=1, radii=np.asarray([radius]), cte=cte\n",
    ")\n",
    "# phi_e point source in space, cte in time\n",
    "phi_point_source_space_cte_time = righthands.phi_part_of_b_point_source_space_and_cte_time(\n",
    "  big_l, n=1, radii=np.asarray([radius]), center_positions=[np.zeros((3))], p0 = 25.*np.ones((3)),\n",
    "  sigma_e = sigmas[0], pii = np.asarray([sigmas[1]/sigmas[0]]), amplitude = 1.\n",
    ")\n",
    "# phi_e = cte * z_coordinate\n",
    "phi_point_source_linear = righthands.phi_part_of_b_linear_space_z_cte_time(\n",
    "  big_l, n=1, radii=np.asarray([radius]), center_positions=[np.zeros((3))],cte=cte, pii = np.asarray([sigmas[1]/sigmas[0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Custom made:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Space part, cte * z_coordinate\n",
    "import biosspheres.formulations.mtf.mtf as mtf\n",
    "import biosspheres.formulations.mtf.righthands as mtfrighthand\n",
    "\n",
    "# Parameters for the function\n",
    "n=1\n",
    "radii=np.asarray([radius])\n",
    "cte = 5.\n",
    "ps =[np.zeros((3))]\n",
    "pii = np.asarray([sigmas[1]/sigmas[0]])\n",
    "x_dia, x_dia_inv = mtf.x_diagonal_with_its_inv(\n",
    "        n, big_l, radii, pii, azimuthal=False\n",
    "    )\n",
    "# Pre-defined space part\n",
    "space_phi = mtfrighthand.b_vector_n_spheres_mtf_linear_function_z(\n",
    "    big_l, n, ps, cte, radii, x_dia)\n",
    "\n",
    "# Time part, custom made\n",
    "def time_function(time):\n",
    "  if time >= 5. or time < 0:\n",
    "    return 0.\n",
    "  else:\n",
    "    return 1.\n",
    "\n",
    "\n",
    "custom_phi = righthands.phi_part_of_b_separable_in_space_time(space_phi, time_function)\n",
    "\n",
    "b_phi_part_time_function = custom_phi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Parameters for the coupled currents and ordinary differential equations:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For Kavian et al. dynamics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_l = 1.9*10**(-6)  # [micro S / (micro m) ** 2]\n",
    "s_ir = 2.5*10**2  # [micro S / (micro m) ** 2]\n",
    "tau_ep = 1.  # [micro s]\n",
    "tau_res = 10.**3  # [micro s]\n",
    "k_ep = 40.  # [V ** -1]\n",
    "v_rev = 1.5  # [V]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up of internals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up of the time steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau: 0.001220703125\n"
     ]
    }
   ],
   "source": [
    "import biosspheres.formulations.mtf.timecouplings.solvertemplates as solve\n",
    "tau, times, medium_times = solve.tau_times_medium(\n",
    "\tinitial_time, final_time, number_steps\n",
    ")\n",
    "print(\"tau: \"+str(tau))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up of the coupled problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up of the non linear current. Different models for the current can be used, there are models ready to use in the module `biosspheres.miscella.forcouplings.currents`. See the internals of the module for making custom made currents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import biosspheres.miscella.forcouplings.currents as currents\n",
    "import biosspheres.miscella.forcouplings.oderesolutions as oderesolutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kavian et al. current:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_current_kavian = currents.i_kavian_leguebe_ea_2014_1_sphere_2d(big_l, big_l_c, radius, s_l, s_ir)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "ode_next_sol_kavian = oderesolutions.next_step_z_kavian_leguebe_ea_2014_2d(big_l, big_l_c, tau, tau_ep, tau_res, k_ep, v_rev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model to be used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_current = i_current_kavian\n",
    "ode_next_sol = ode_next_sol_kavian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we set up internal parameters used for requirements of numpy for threading:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "number = \"7\" # Maximum of threads\n",
    "os.environ[\"OMP_NUM_THREADS\"] = number\n",
    "os.environ[\"OPENBLAS_NUM_THREADS\"] = number\n",
    "os.environ[\"MKL_NUM_THREADS\"] = number\n",
    "os.environ[\"VECLIB_MAXIMUM_THREADS\"] = number\n",
    "os.environ[\"NUMEXPR_NUM_THREADS\"] = number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We implemented a direct solver (LU decomposition) that takes as parameters what we previously defined, including the current and the coupled ODE system. The complete list can be seen in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[47], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m solutions \u001b[38;5;241m=\u001b[39m \u001b[43msolve\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmtf_time_coupling_one_sphere\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m      2\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mbig_l\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      3\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mradius\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      4\u001b[0m \u001b[43m\t\u001b[49m\u001b[43msigmas\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      5\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mc_m\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      6\u001b[0m \u001b[43m\t\u001b[49m\u001b[43minitial_time\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      7\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mfinal_time\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      8\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mnumber_steps\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      9\u001b[0m \u001b[43m\t\u001b[49m\u001b[43minitial_conditions\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m     10\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mb_phi_part_time_function\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m     11\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mi_current\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m     12\u001b[0m \u001b[43m\t\u001b[49m\u001b[43mode_next_sol\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m     13\u001b[0m \u001b[43m)\u001b[49m\n",
      "File \u001b[1;32mc:\\Users\\there\\miniconda3\\envs\\biosspheresall\\Lib\\site-packages\\biosspheres\\formulations\\mtf\\timecouplings\\solvertemplates.py:108\u001b[0m, in \u001b[0;36mmtf_time_coupling_one_sphere\u001b[1;34m(big_l, radius, sigmas, c_m, initial_time, final_time, number_steps, initial_conditions, b_phi_part_time_function, i_current, ode_next_sol)\u001b[0m\n\u001b[0;32m     99\u001b[0m v_hat[:] \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m    100\u001b[0m     \u001b[38;5;241m3.0\u001b[39m \u001b[38;5;241m*\u001b[39m solutions[i, \u001b[38;5;241m4\u001b[39m \u001b[38;5;241m*\u001b[39m num : \u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m num]\n\u001b[0;32m    101\u001b[0m     \u001b[38;5;241m-\u001b[39m solutions[i \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m4\u001b[39m \u001b[38;5;241m*\u001b[39m num : \u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m num]\n\u001b[0;32m    102\u001b[0m ) \u001b[38;5;241m*\u001b[39m \u001b[38;5;241m0.5\u001b[39m\n\u001b[0;32m    103\u001b[0m q_hat[:] \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m    104\u001b[0m     \u001b[38;5;241m3.0\u001b[39m \u001b[38;5;241m*\u001b[39m solutions[i, \u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m num : (\u001b[38;5;241m5\u001b[39m \u001b[38;5;241m+\u001b[39m number_of_extra_unknowns) \u001b[38;5;241m*\u001b[39m num]\n\u001b[0;32m    105\u001b[0m     \u001b[38;5;241m-\u001b[39m solutions[i \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m num : (\u001b[38;5;241m5\u001b[39m \u001b[38;5;241m+\u001b[39m number_of_extra_unknowns) \u001b[38;5;241m*\u001b[39m num]\n\u001b[0;32m    106\u001b[0m ) \u001b[38;5;241m*\u001b[39m \u001b[38;5;241m0.5\u001b[39m\n\u001b[1;32m--> 108\u001b[0m b_i_current \u001b[38;5;241m=\u001b[39m \u001b[43mi_current\u001b[49m\u001b[43m(\u001b[49m\u001b[43mv_hat\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mq_hat\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    109\u001b[0m aux \u001b[38;5;241m=\u001b[39m half_iden_2n_n\u001b[38;5;241m.\u001b[39mdot(solutions[i, \u001b[38;5;241m4\u001b[39m \u001b[38;5;241m*\u001b[39m num : \u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m num])\n\u001b[0;32m    110\u001b[0m aux \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mconcatenate((\u001b[38;5;241m-\u001b[39maux, aux), axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n",
      "File \u001b[1;32mc:\\Users\\there\\miniconda3\\envs\\biosspheresall\\Lib\\site-packages\\biosspheres\\miscella\\forcouplings\\currents.py:271\u001b[0m, in \u001b[0;36mi_kavian_leguebe_ea_2014_1_sphere_2d.<locals>.i_current\u001b[1;34m(v, z)\u001b[0m\n\u001b[0;32m    269\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(v) \u001b[38;5;241m==\u001b[39m (big_l \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m) \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m \u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlength of v is not (big_l + 1)**2\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m    270\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(z) \u001b[38;5;241m==\u001b[39m (big_l \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m) \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m \u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlength of z is not (big_l + 1)**2\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m--> 271\u001b[0m v_evaluated \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msum\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m    272\u001b[0m \u001b[43m    \u001b[49m\u001b[43mv\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mnewaxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mnewaxis\u001b[49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mspherical_harmonics\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\n\u001b[0;32m    273\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    274\u001b[0m z_evaluated \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msum(\n\u001b[0;32m    275\u001b[0m     z[:, np\u001b[38;5;241m.\u001b[39mnewaxis, np\u001b[38;5;241m.\u001b[39mnewaxis] \u001b[38;5;241m*\u001b[39m spherical_harmonics, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m\n\u001b[0;32m    276\u001b[0m )\n\u001b[0;32m    277\u001b[0m temp \u001b[38;5;241m=\u001b[39m z_evaluated \u001b[38;5;241m*\u001b[39m v_evaluated\n",
      "File \u001b[1;32mc:\\Users\\there\\miniconda3\\envs\\biosspheresall\\Lib\\site-packages\\numpy\\_core\\fromnumeric.py:2344\u001b[0m, in \u001b[0;36m_sum_dispatcher\u001b[1;34m(a, axis, dtype, out, keepdims, initial, where)\u001b[0m\n\u001b[0;32m   2338\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mPassing `min` or `max` keyword argument when \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m   2339\u001b[0m                          \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m`a_min` and `a_max` are provided is forbidden.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m   2341\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m _wrapfunc(a, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mclip\u001b[39m\u001b[38;5;124m'\u001b[39m, a_min, a_max, out\u001b[38;5;241m=\u001b[39mout, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m-> 2344\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_sum_dispatcher\u001b[39m(a, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, dtype\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, out\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, keepdims\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[0;32m   2345\u001b[0m                     initial\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, where\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[0;32m   2346\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m (a, out)\n\u001b[0;32m   2349\u001b[0m \u001b[38;5;129m@array_function_dispatch\u001b[39m(_sum_dispatcher)\n\u001b[0;32m   2350\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21msum\u001b[39m(a, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, dtype\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, out\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, keepdims\u001b[38;5;241m=\u001b[39mnp\u001b[38;5;241m.\u001b[39m_NoValue,\n\u001b[0;32m   2351\u001b[0m         initial\u001b[38;5;241m=\u001b[39mnp\u001b[38;5;241m.\u001b[39m_NoValue, where\u001b[38;5;241m=\u001b[39mnp\u001b[38;5;241m.\u001b[39m_NoValue):\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "solutions = solve.mtf_time_coupling_one_sphere(\n",
    "\tbig_l,\n",
    "\tradius,\n",
    "\tsigmas,\n",
    "\tc_m,\n",
    "\tinitial_time,\n",
    "\tfinal_time,\n",
    "\tnumber_steps,\n",
    "\tinitial_conditions,\n",
    "\tb_phi_part_time_function,\n",
    "\ti_current,\n",
    "\tode_next_sol,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the functions is defined in the module `biosspheres.formulations.mtf.timecouplings.solvertemplates` shortened in `solve`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saving the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following saves all solutions, i.e. traces, transmembrane potential, and recovery variables, in numpy format. We have commented the line for the saving."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename=\"example.npy\"\n",
    "directory=\"\"\n",
    "# np.save(directory+filename, solutions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To load the solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solutions = np.load(directory+filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To save in `txt` format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename=\"example.txt\"\n",
    "directory=\"\"\n",
    "# np.savetxt(directory+filename, solutions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To load the solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solutions = np.loadtxt(directory+filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For plotting the evolution of time of the solutions evaluated in the north pole of the sphere:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'v')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# Auxiliary arrays for plotting\n",
    "import biosspheres.utils.auxindexes as auxindexes\n",
    "num = (big_l + 1)**2\n",
    "eles, l_square_plus_l, el_square_plus_el_divided_by_two = (\n",
    "        auxindexes.eles_combination(big_l)\n",
    "    )\n",
    "little_partial_spherical = np.sqrt((2 * eles + 1))\n",
    "plt.figure()\n",
    "plt.plot(\n",
    "\ttimes,\n",
    "\tnp.sum(\n",
    "\t\tsolutions[:, (4 * num + l_square_plus_l[0 : big_l + 1])]\n",
    "\t\t* little_partial_spherical[0 : big_l + 1],\n",
    "\t\taxis=1,\n",
    "\t)\n",
    "\t/ (2.0 * np.sqrt(np.pi)),\n",
    "\tlabel=\"Numerical solution\",\n",
    "\tmarker=\".\",\n",
    ")\n",
    "plt.title(\"v\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Additional variable')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "little_partial_spherical = np.sqrt((2 * eles + 1))\n",
    "plt.plot(\n",
    "\ttimes,\n",
    "\tnp.sum(\n",
    "\t\tsolutions[:, (5 * num + l_square_plus_l[0 : big_l + 1])]\n",
    "\t\t* little_partial_spherical[0 : big_l + 1],\n",
    "\t\taxis=1,\n",
    "\t)\n",
    "\t/ (2.0 * np.sqrt(np.pi)),\n",
    "\tlabel=\"Numerical solution\",\n",
    "\tmarker=\".\",\n",
    ")\n",
    "plt.title(\"Additional variable\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For plotting the transmembrane potential on the surface of the sphere at a given time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Auxiliary arrays\n",
    "import biosspheres.quadratures.sphere as quadratures\n",
    "(\n",
    "\tquantity_theta_points,\n",
    "\tquantity_phi_points,\n",
    "\tweights,\n",
    "\tpre_vector,\n",
    "\tspherical_harmonics,\n",
    ") = quadratures.gauss_legendre_trapezoidal_real_sh_mapping_2d(\n",
    "\tbig_l, big_l_c\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2944d6faff0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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D4TDmzZuHefPmAQASiQR/pseOHUMymZQk4HwIOJVKAYBPwLMQvoTrDZ9wZzjcHKMopTh69GjO2FpFUcoq4abTaRw4cACjo6PYtm0b6urqcO7cubKOUegGwS6tTU5OcrI4cuQI0uk0qqurUVdXh/r6esRisddFDHApG4NIJOIgYCYBiwTstqkRCZj9JZNJn4B9vC7gE+4MhlvRgfHxca7KzRVbW04b7vDwMFpbWxGLxdDS0oJQKMTHKBfK0VdFRQUqKiowf/58UEoxOTnJY4DPnj0LXddRU1PDySIWi83KBd/NQ7xYRCIRzJ8/H/Pnzwfg3NSkUilUV1dLErBIpCzUyyfg2QFfpewNn3BnIETHKHts7ZEjR/KuW1sOGy6lFKdOnUJHR4fkkCWO4UXqxSyc5VSBE0IQjUYRjUaxcOFCUEoxMTGRVxKOXP3OBEzVPO2bGlECFgmYPdPq6uqcBPzqq69i9erViEajPgFPdxBi/JXaxyyET7gzDLquI5PJSCrkTCaDQ4cOYXBwsKC6taXacFOpFNrb2zExMYHt27e7FjvIJUUXslhO9cJKCEFVVRWqqqqwePFiHj88NDSEgYEBdHV1SbVtWQywOK+ZkgnrUtmaCSGcgBcsWMC1CkwCPn/+PDKZDCfg2tpa1NTUcI0NYBDw8PAw/y7ZJWAxD7RPwD6mM3zCnSHIFVtbWVlZcN3aUlTKg4ODaGtrQ21tLVpaWjxDb8odenQpCY0QwsuDLV26FLquY3R0FENDQ+jt7cXx48elwvEsVGkm4HI5d4laBZGAmVbh3LlzEgEztT6lVJJqRQk4kUjwvkUCDgQCEnH7uDQgpAxOU7P0M/MJdwbA7hjFvoxdXV3o6upyVeXmg2KcpiilOHHiBE6cOIG1a9di8eLFWcctdz3cywlFUXgiiOXLl7sWjmeLfG9vLy8aMB0xXbyp3dT68XicS8Bnz57l3/uzZ8+ioaGBV5fyUkH7BHx54dtwveET7jSHGFvLFotssbWFoFAyTCaTaG9v5+PmUxh6Jku4ueBWOL6zsxODg4NS0YDpmIRjuhCuHYQQnlubEfDIyAhee+01TExM4Pz589A0zeHYVigBM2nZJ2AflxI+4U5TeMXWXrx4EQcOHPCMrS0ELLdyPujv70d7ezsaGhoKGnc2Sbi5EAgEUFVVhVQqhSuvvNI1ZaIYLlNbW1vWGOBCMF0J1w4mAQPAxo0bQQjBxMQEf67d3d2glEoEzMo7+gR8eeDH4XrDJ9xpiFyxtRs2bMCCBQtKHicfMtR1HZ2dnTh9+jTWr1+PhQsXFuzoNFslXDeI83NLmchslSxe1c1b91KgnGFBUw1m9mB+C8yxjVWXsnuWU0q56t8n4EsPX6XsDZ9wpxk0TUNPTw9isRgvGl5IbG0hyBUWlEgk0NbWhnQ6jZ07dyIWixU1xutFws0Fe8Ym0VmIeeu6qUqnAjNFwgUgaXjscPMsZ+UdWT1gRsCiBMzIG/AJ2Melg0+40wRibG1rayu2b9+OUCjEY2uXLFmC1atXl3UBzhYWxFTXc+fOxRVXXFG05PV6k3ALgT1cJh6PcwJmqlI3oigHZhrh5jtXe3lHkYBZPWCW31uUgH0CLh+IUrpKmMxOAdcn3OkA5hjFpE1FUZBOp9HW1obBwUFcffXVaGxsLPu4bhKurus4fvw4zpw5UzbV9etNwi1mnqKzEFOVuhGFGIIUjUaLfiYzjXCL3WjaCVjXdU8Ctic3yYeAmfezT8AWfBuuN3zCvYwQY2vtarP29nbEYrGCY2sLgV3CjcfjaGtrg67rZVNd51ooE4kEQqFQ3hL0dJdwy7m5sBMFS8LR19eHzs5OBAIBRxKOQuY5U4hBzKZWKhRFccRWj42NYXh4GAMDAzhx4gQP/2KObdkIWNd1n4DtUBTjr9Q+ZiF8wr1McHOMAozY2lQqhcWLF+OKK66Y0h+rqO7t6enBwYMHsWDBAqxdu7aszjtudmJN03D06FGcOXPGkb3JK33i627hEqAoCmpqalBTU4Nly5ZB13UeA3zhwgUcO3YM4XBYeo7ZNmoziXBZSNxUQHyuIgGLGxtVVSUJmGkWshHw8ePHsXjxYsRiMZ+AfXD4hHsZ4BVb297ejkQigYqKCsydO/eSpDLUNA2HDx/G+fPnsXHjRu7QU84x7IjH42htbQUANDc3I51OS+kTRcmtvr4ekUiEXzvdJdxLBUVRpOxWmqbxUJkzZ87g8OHDiEajUgiSmIRjJhFuOSXcXHDb2IyOjmJ4eFgiYPG5uhHwwMAAFi1aJEnAiqI4ijHMRgIWn0UpfcxG+IR7CcFia1l6RrfY2i1btuDll1+essLwIlix9kwmg5aWFh7vWE7YnaaYJL1w4UKsWbMGmqYhEolIKj4muZ0/fx7Hjh1DJBJBfX19Tq/q6YLLsVioqoqGhgY0NDQAsD5bZqecmJiQisZrmjZjFrXLGcIkZhcTCZil9+zo6EAgEJAk4IqKCui6LuV4FiXgZDKJRCIxawnYDwvyhk+4lwhuKmTmoGSPrS13nVo3nD9/Hl1dXQgGg9ixY8eUSRCMcHVdx7Fjx3Du3DkuSbMNiAhRcluxYgUymQyGh4cxODiIvr4+JJNJvPzyy6ivr7/sySPcMF0k8GAwiDlz5vBCFmISjs7OTsTjcQSDQXR1dTlq1k43lOI0VW64pfe059cOBoPQdR19fX2YM2cOL3BhL3LBvv+apiGRSGDXrl145JFHcNNNN13GO/QxlfAJd4rhVXSAxdYqioJdu3ZJ0uVUEq6maThy5Ah6e3uxZMkSDA8PT+lixqTSl156Cbquo7m5uSBnrEAggMbGRjQ2NqK2thanTp3CkiVLpOQRLHb19VRAvlDYk3B0dHRgdHQUyWSSl8wTY4BZvuLpgOlEuHaI6mXA+H0NDQ2hvb0dfX19OHHiBEKhkCQBRyIRvg6w+2IpLAtxfJuu8L2UveET7hRCjK0FLFVjrtjaqSLc8fFxtLa2IhAIoKWlBSMjIxgcHCz7OCKGhoZAKUUsFsP69etLlqIIITx5hFcB+draWi4B51O/9vUIVVURjUaxfv16R8k8VrHHHgN8uUhvOhOuHaqq8hzjW7Zs4UQqOreJFaZqa2s5ycbj8Skx61xykDJ4Kc/SQFyfcKcIomMU28mm02letzZbbG25CZdSinPnzuHIkSNYunQpVq1aBUVRMDY2NmUqUDElJGDkwS0VduJ0qzTDYizF+rWMfAsNnSkGM8UZSZynW8k8MQkHy9aUjyf5VM11phAuAKmql6IoUoELtwpTP/nJTzA0NITx8XGMj4/nPc5vfvMbPPTQQ3j11Vdx4cIF/OxnP8Ntt93Gz1NKce+99+If//EfMTw8jF27duHb3/42Vq9enbXfb33rW3jooYfQ09ODq666Ct/4xjewffv2wh+EDwd8wi0zvIoOMDVTPnVry0m4mUwGhw8fRn9/v6M4fbmzQDGwlJCpVApbtmzBK6+8UjYiylXM3h67Ojo6isHBQSl0RiTg6Vo+b6qR7fPIloRjcHCQx6raY4CnioBnkoQLGPNVVdX1ebhVmEqlUvjP//xPaJqGG2+8EUuXLsX111+PD3/4w9i6davnOBMTE7jqqqvw/ve/H29/+9sd5//u7/4OX//61/Ev//IvWL58Of7P//k/uOmmm3D48GHJ81/Ej370I9xzzz149NFHsWPHDm5TPnbsGDdH5EQZVMrwVco+ciFbbO2JEyewevVqLF26NOfCVC7CHR0dRWtrKyKRCFpaWhw/sqlQXQ8MDKCtrQ2NjY3YunUrfxblINxCrxcdXABwBywmtR06dIh77tbX16Ompqak6kszCYV8HtmScFy8eBEdHR0IBoMOT91yYSYVWgAMKTZf00kgEMBNN92Ea665Bt/73vdw4sQJHDp0CL/61a8wOTmZ9dpbbrkFt9xyi+s5SikeeeQRfP7zn8fb3vY2AMD3vvc9NDU14cknn8Qf/dEfuV731a9+FXfddRfe9773AQAeffRRPPXUU/jud7+Lz3zmM3ndEyEKSIkq4VKvn654fawulwC6riOVSklSrRhbu3379rzr1pZKhJRSnDlzBseOHcPy5cuxcuVKz0QS5SJcSim6urpw8uRJrFu3DosWLZL6L5ckXUo/ogMWYHjuMqlNrN7DJODp5DhUbpSyAbLHqoqeusUk4ciFmSbhFpOoIx6PAwDmz5+PJUuWeBJpvjh58iR6enpw44038mM1NTXYsWMH9u7d60q4qVQKr776Kj772c/yY4qi4MYbb8TevXtLmo8PAz7hlgjRMSpbbG0hklMphMvsxENDQ9iyZQuPy/QapxxEmK0wPVvUyzFOuaWcUCiEpqYmNDU1ATCq9wwODjocsAopHjCTbLjlIjG7p24mk+F2SpaEo7KyUnIUCgaDefc/0wiXqZQLwcTEBCKRSNlCs3p6egCAf7cZmpqa+Dk7+vv7oWma6zVHjx7Nf3CFlK4S9lXKPuzQdR2ZTMYRW3vs2DGcP38eV1xxRVHJ/4sl3JGREbS2tqKyshItLS05pYpy2HAHBwfR1taGuro618L0+RBuISQ1lXGuFRUVWLhwIXfAmpiY4AR88uRJyW5ZX18/o0M4pnJjEAgEPJNwnDhxwpGEo7a2NuuGdCY6TRVDuKUUo5hO8BNfeMMn3CKQT2xtKZmbmEdzIfM5ffo0Ojo6sHLlSixfvjyvH24pkjSlFCdPnkRXVxfWrFmDJUuWZM1/PB0l3FxjsTqrogPW0NAQenp6cPz4ca42ZSromeSAdSklcXsSjmQyyQm4o6MDiUQCsViME7A9CYeu6zPKtl6MSnliYqJsda4B8BStvb29mD9/Pj/e29uLzZs3u17T2NgIVVXR29srHe/t7S0o5asfh+uNmfMtniawO0blG1tbCAohwlQqhYMHD2J0dBTbtm3jar18UKyEm0qlcODAAYyNjeW0TZeTcMvZT6FwyzDEMmAxB6zKykqeni+TyUxrkricqu9wOCyp8hOJBA9BOnLkCNLpNKqrq/lmRtO0glTQlxvFqJTj8XhZQ62WL1+OefPmYffu3ZxgR0dH8dJLL+HDH/6w6zWhUAhbt27F7t27eXiRruvYvXs37r777rLM6/WO6bsiTEO4FR0QbablqlubL+EODQ2hra0N1dXVaGlpKVjCKsZpanh4GK2trYjFYnmNOZ0l3PHxSbz02kk8s/sgKKU4cvwC0ukMMjoQjycRCgaQTGmojEaQ0TTUVEfRNKcaiqLi+jesxpIljdhy5XKsXr2ap048deoUJiYm8Nvf/paTBpPappNadDrZmiORCObPn4/58+e7JjPJZDLcvllXV4dYLDZt5u6GYp2mCtWIjY+Po7Ozk78/efIkWltbUV9fjyVLluBjH/sY/uZv/garV6/mYUELFiyQYnVvuOEG/MEf/AEn1HvuuQd33nkntm3bhu3bt+ORRx7BxMQE91rOC4SUnrhiGn++pcAn3DyQLba2ra0NVVVVedlM80UuwhXVufmGGnmNw3K65uMM1N3djePHj2PVqlVYtmxZQWNeDgn3eOd5fOPR/8GL+7qQSqWNUAPzemp0ZrZU+A+cgBhnCcEEAAIFk3Gj2svw0DhOd/eBAHjplQ6jtWKGQBB2LQEIQUNdJW558xpc1xzCuXPnoGmalAErHwesqcR0tYu6JTNpbW2FqqoYGRnhiVTcCsZPFxRjwx0fHy9Ypbxv3z5cf/31/P0999wDALjzzjvx+OOP49Of/jQmJibwp3/6pxgeHsYb3vAGPP3001J4YFdXF/r7+/n7d77znejr68MXvvAF9PT0YPPmzXj66acdjlTZ4KuUveETbg5QSpFKpfDaa69hw4YNXKIrNLa2EGQj3GQyiQMHDmBiYqKgUCM3iNJntvmn02kcPHgQw8PDRamt2RilItscn97dhr/50r9jbCwhHRfHpdAA2OdDAOgmWQKUEN6GgIASqx0xz1FjMkY73ejTqvJiEG5f/yi+/6PX8P0fKwYNKypACNauqMUfv30pKqMhKWxmKhNHuGE6SbjZwIq619fX8yQcLAZYzCZ2OZ+lHcWqlAuVcK+77rqciWDuv/9+3H///Z5tTp065Th29913+yrkKYJPuFnASulpmoaLFy9i3bp1PASm0NjaQuBFuAMDA2hvb0ddXR1aWlpKtmuJidO9wJJnVFRUYNeuXUU5BpVr8RNtzg9/6z/w+Pd/7Tp3qlPxIuu9JMWy8+Y17DilYBIuk4I5GZutYLbj90UU6LpmtCMEgEG+OqUA0UCICmK2P9o5iC/83SAUxViQqypD+PCdKzBvbrWUAatc2hIvzBTCBWQVLSEE1dXVUjlHe7UeMVcxKxZwueabL5jn9qyAUoZcytNQ+1IO+ITrAnvRAVbTkhWgnjt3bsGxtYXATrhiUom1a9di8eLFZVkss0mflFKcPXsWR48ezZo8I99xSk2w0ds7hLe/60sYHZsE8BMQImiEYbsH8Xb4a3YBAQW1pFHzGAi1SFecO/8PI1vjtfQsRDU1qDk3Yh4mIIRCUVTjvKKDEBW6KRmPjSfx0LePmWMpuOaqBtx2y3wet1pfX58zbKYYzCTCzTZXN2c2e67iSCQiEfBUe5Nrmlbwhok5Tc0G+AXoveETrg3MMYoRBCMLSimOHz8u1a2dKoiEK2arsieVKMc4ABxkKOZfzpU8Ix9ky9mb7Ye1v7UL7/3Q16HpuimcWhIupTbGhfjW3qdBemD2WdYPs7sS4QrpUio4f9jasfOCzVeeiEnf5s5A1zIAUUCgAEQzzhIVRFFANQ1QVBAFeKV9AK+0DwCUYMWyWvz5nSuQSqUQi8W4BFwOB6yZRLiFJL5wy1VsT+dZShKOcs+XYTYRrg9v+IRrQoytFR2jWGwtpRSbNm2SYtqmCoxw+/v70d7ejsbGximRqN0k3PHxcezfvx+hUMg1/3Kx43iprUdGRgCAe56Ojcdx/S1/hclEyrKkKux6ClBq51n+nggSKLOlsvcmvwKKwvu12gKUkaPo/CQ2g5PGnZ6UVGhDzHF1gBAzNywF1TWjFVGgKDo0TQchChRCoGu6OW8FikJw4vQwPnl/KwDg5t9ZiT/8vQqcP3/eUTqvGK/dyxVeVQxKyTTlls6TEXBXVxfi8bgUA1xbW1tytqdiE1+UurGdNvDL83nCJ1x4Fx04c+YMjh49iiVLliCTyVzSWMBEIoH9+/dj/fr1WLhw4ZRII6xPJuGeO3cOhw8flkr4lWsc+wLPMnKdPXsWlFL8y7+9hJdfPcUuMP9VQKkOygRwmwTrIF5JKUwFJla5hAxKQVn3RLGeK7EpkwkVbLIQ+pXFXE7kwrz4ZLk+moJSQ4VMiLkQUx26RqGqAUMCzhgSsKKqANVBKZP+DUJ++pcn8D+/PAGiKPiXb96GcCiNoaEhnDp1CoQQRwas2ZKCEihvasdQKIS5c+fyyjfJZJKHIIn5tNnzrK6uLpg8iyXcJUuWFHTNdIXvpeyN1z3hesXWMq9cFlvb398/JUXh7ZicnMTx48eRyWSwa9euKXWkYCrdTCaDgwcP8iw0Ygm/co0jEm4ikUBrayvi8SQ++pmfIJ3OyO3Nf6mu8WMyuVLZTssvNKVIfsCQFGXVLzsmS7jGKcWURi2SZUTM7LH2WfK2FABXW9vmCossLOI15qppaRBFNQnFIGGiBABTElbUgDkOU6XreM9HfgZAwR++bQM+9mfXOir3MKchpoJ2sye+XgnXjnA4jHnz5vFMSmIMMNMm1NTUSNqEXHMpVqU8K4rP+8iK1y3hsthalp7RHlsbi8Ukr1xFUbgEPFVgBQ9qa2uRSqUumddia2srAoEAWlpapiQ/sEi4AwMD+K+nfokHHvoFONkRWXq0S8MO7WcWsrXGVM1r2TEKRQlYflJM/cvJzurckpOZhzIxo4AsguJmWj6gODn7YqvbjhmqZj5HXYduhhYZ7zPmvAionpGIV+zz339+EP/+80NYsawR33/0Hbxyz8jICAYHB3nhgGg0KnlABwKBaRuH64ZLOdeKigpUVFRgwYIFoJQiHo9zAj5z5kxeBS2KkXDj8fjs8VImSukqYV+lPHtQTN1aVVWnjHBF9eqGDRtQWVmJffv2TclYInp6ekApRU1NDTZu3DhlixpzPPv+v/0C9/3fH0NiKuZuTEzVq12J4FAbO48RosoniOpoREyyFTslasD8jJ2DUDDp1VI5C73xMFxKqeEIJV5O7QQLGLG+tkWY6laSdqpB16ihUoYh3etg303D6YooAXMassf0iVP9aLn5O6itrcJ/PfFHktMQKxwwODiIrq4uTE5OIhaLIZFIYGJioihyuNS4XNWCCCGorKxEZWUljwEeHx/nBHzy5ElJnV9XV4doNFpSasdZAb9akCded4TLpFp73dq2tjYkk0lPT2BVVadEpRyPx7lTVktLCyorKzE2Njal6mtd13H06FGcP38eqqpi6dKlU7qgHTx8Fh+4+7u2oyZpcdKhpjQqqHoFNa7FpzZVMJzkKhMSHNIvYEnATvGZXZrnD54aYUbO5k7SpdBspGsfW4eui5Ku5pR81QCXvi0vakMSHxkZx7W3/hNqamN46ok/AiHEUTiA5S3u6OjAmTNncPr0aa4yra+vn5ZpE6dLAXpCCGKxGGKxGC9owdT5LGQwEAggk8lgaGiIS8v5YDYRrl+A3huvG8K1x9Yysu3t7cXBgwcxd+5cbN261dMTeCpUyj09PTh48CAWLFiAtWvX8l1xqQXos8FO8C+99NKUeayeudCH6978CSlMBgCXKimlRliMZJOlgolWkD6p7b15nts2+TFFpGjzWmeMLaUaKKWukkjNnGUIBFisppG+cfDiBUCLc0ncAZovIViZqwCDVIkizIFqACdlaqiUSdDyKNc1EEm9bJAt5dmyCEaGx3HtrY9h+YpG/Os3f18aneUt7u7uxsqVK1FRUYGhoSEMDg6iu7sbABwS2+Umu+laD1dRFNTU1KCmpgbLli2Druu8RObAwAC6u7t5RalsCU1YKcjZQrg+vPG6IFx7bC0jz0Lq1pZTwhXH3rhxo6P0VSE5jgsBsxHPmzcP69atg6qqWUN2ioWmadiw7S6kUynuwmSQgW54HpvSGVcF2222gElg9gwWdunWvFR6RoygxWM6QBXYNbqG/lo4aPYz0ncKgAIlEAbVdYBmwB2oBCmcUpdx7Z7KtmPU5RWR9xDQtQxXLQPGezUQ5DdsEBCT7NlmghESizPWcfJEH65967/gf71tA/7ig9vkWzftonaV6djYGAYHByWJjdl/6+vrpzwDlh3sdzAdCdcOVi+ZEIKNGzciHA7zECTRni6GIDEfkdmVacpXKXthVhOuV9GB8fFxnhA937q15ZJwJyYm0NramrVmrphysRyEq+s6Ojo60N3djY0bN0qxxOWWpm9/1/14tdXInCRncaLcMxeUmlKd6HlEJCHXKUXKBMyI1kjHaG8vh+4YsJGrCS2TBlEDtgXdJFQtKb03yM2QJw1bsz3eV7hnCW4qZ/GsQMzc29nWQvwuMA9mRXH1H2PqbEopoGn40ZOH8O//cRQ/ePT3sWhBtTlN53dLTJsoOmCxrE1HjhzhhMEyYE11qBzbDM4EwgXA4/lZdrqGhgYeX8vs6Syca3x8HL/85S/R19eHkZGRkn6Hy5Yt44UdRPz5n/85vvWtbzmOP/74444KQOFwGIlEwtG2UPgF6L0xawk3V2xtobGm5ZBwz58/j0OHDmHx4sVYs2aN59hiBqhSFxpmn06n02hubnbsossl4b7y2lH80Xv+xpAIAVgSqW7wDa/UQy2nJjfVsTw7/oq6ERl1IzLZA1iErme4p7I4BtUz0HRDHauoAYi+UlK/GlNfyyTLpF75Xoi4hTAlbuJCpm7SuWPqoLoOIki9VM+AKiGhBzdHLZNYdQ0apXjXh36Oquoonvr+O/LazNmzNomEISaNEDNgldsBS9RKzQRkm6/dnp5KpTA2Noaf/exnmJycxA033ICtW7fid37nd/Anf/In2LBhQ97jvvLKK5JAcPDgQbz5zW/G7bff7nlNdXU1jh07xt9fbtPB6wGzknB1XUcqlZKkWjG2tph0hayoeDHQNA2HDx/GxYsXcdVVV/Gg+2xjsfsoBf39/Whra8PcuXNxxRVXuC6G5chzfFXzn2J8dJyH21DT65gTjuC0xKmJORvZ4UKsFtnazzHJz764Uei6xgsEiJfoegZEUWUPZBb6A4BqGaFiELM5A0YJP4ATKVdlG1Iv7HMkVCBgwX4s3p/Na9pJvvb3NvsvNZyJrHF0QbXMJHodlCogxND2jI9O4ro/+Df8/o312LChsAXWThgsacTg4KBUOJ4RcD4xq7kgplidCWCkl8/GIxQK4W1vextuvvlm/PSnP8WLL76II0eO4Je//CXOnDlTEOHaY+f/9m//FitXrsSb3vQmz2sIIQ5zVllAbFqfYvuYhZhVhFtobG0hUFUVqVSq4OvGxsbQ1taGYDCIXbt25ZUqsVTCpZSis7MTp06dwvr167Fo0aKsYxUr4f7Ps6/gzz/6MB9T7IfAIkpCBGqlxNScyk5NHndie++04brrak2ZjzINgY3ApfSKxnmDS20ELF1GzblbamVDO26SrF2LzZy8CAWgMFqG7AhGbKozN29r8xXVQU2VOKNYWep1e4bWJoDqhje4pmWgAviPZwfx/174JZ5+4g9crssPYtIIVjh+cHAQQ0ND6O7uBqVUyoBVjAPWTJNwGeEWcp8TExMAgNWrV2Pbtm1497vfXdIcUqkUvv/97+Oee+7JOo/x8XFecWnLli344he/WBDJe0IhZagW5BPutIau68hkMg4VcmdnJ06ePFly3dpC43AppdzuVaj6mmWAKoZwk8kkD3HauXMnYrFYzrGKGeeaN34Yg4MjoOZiLquFrdzHdqdei2Ds3sciPOygjuNM0hOkXBvrGURjlzaYtKkbamJCuJpYcbS1zUIXJXVhPGrUzrVCdsx/OSFzmhSIl0nGsMieqFCI4r6nsPmDEUrFR+4CpmYWPwQKnWpQdCART+CGP/x3fOETO/GmZu9NWT4QC8fb69b29/ejq6sLgUBAyoCVz+aThQTNFAmX2W8Lme/4+DgAlM1L+cknn8Tw8DDe+973erZZu3Ytvvvd7+LKK6/EyMgIvvzlL6OlpQWHDh3KukH3URpmPOGKRQeYXUqMrU2lUmWpslOIc1Emk8GhQ4cwMDDAU0NO5XgMg4ODaGtrQ11dXd7FDgqVcHsvDmLXDXcbc5OuEwlR9MW1F7zLdyyLXO2l+NzImFI5vEb0C2YpIokSEM67OFaZVX2chebZFeI1Igta5Ept8+ZtODES85koXNK36vCaErFNA0AoG1dmXEqo6zH5iQufhRmCZGS2UqAoGjSN4P6v7MW8BTX4wdffgnLBrW4ty4Alls0TM2C5OWDNFA9lhmKzTFVUVJTtPv/5n/8Zt9xyS9bIi+bmZjQ3N/P3LS0tWL9+Pf7hH/4BDzzwQGkT8FXKnpjRhGt3jGJkm29sbSHIV8JlBdsjkQh27dpVdBhFIV7RlFKcOHECJ06cKLhebiES7qf/6lH8f//xa0A3PI2l+FmREUVSkhybiv8RWaTrlH4tXjMkbSkXsgCqa6ZtWRH8i2x9eWaXco5NQU0ydLMxU7MAgW0TwooSEEj9ADCka0klYM1DtlN72XzNZyCWFHTMydiUUj0DHQEo0KATgp7zI3jzHU/ivx6/FeFw+T2PWchMXV0dAKts3uDgIE6ePImDBw+6Vu2ZrjG4Xii2+HxlZWVZpPjTp0/j2WefxU9/+tOCrgsGg7j66qvR2dlZ8hx8L2VvzFjCdSs6IMa3btiwoayl9HJJnJRSnDlzBseOHcOKFSuwYsWKkn5A+Uq4qVQK7e3tmJiYwPbt21FTU1PwOPlIuJt2fADxibghBbL8i4JKU5Ls+FV2O6gA6kYajkYe5y2PXEmty2ZCqYuXskVyFEYFIkPKZHbmPHflnPTNt4T/R5CARdurSLqK6eREzWGFJ0WYfRaCmhnmNayqkfzMFI9sPIJi3+Uk5eOyFJS6lgEQANJpvPV9v8CnP7wFN167OPezKAH2snli1Z6jR48ilUqhpqYG0WiUa7FmAvEWk9ZxYmKibIULHnvsMcydOxe33nprQddpmoYDBw7gd3/3d8syDx/umHGESylFKpVCb28vGhsbOdky56RCYmsLQTYJV/SA3rp1Kw+jKAX5EO7w8DBaW1tRXV2NlpaWomIic4UFTcQT2Lzz/dA1zbDXUliEwMNhKO/LOg64Vs/xrETgycz8nJzfQrR9Oq+llHm3mjZMGzPbba2U6gAV28n2VUlRzj2wZbWyk0hNqy1VeA5k6e6ZUxnP6SyomNnlinDcMt5Ko7I7sj8bSuwbIMDYrLD707nEq2sZKEoYWiqNh769H//xTDe+fv8ux3OdKrg5YA0NDaG3txeZTAa//e1vUVtby1XQ5ZIIy41iJFyW1rHU+9F1HY899hjuvPNOh1bvPe95DxYuXIgHH3wQAHD//fdj586dWLVqFYaHh/HQQw/h9OnT+OAHP1jSHADAL17gjRlFuEyFHI/HsX//frzlLYbNqdjY2kLgRYDDw8Noa2tDZWVl0R7QhYwHGM/h9OnT6OjoKNkZLNs4r7UdxzvffS90XTfVx0yipYJZMh9vY6udIWC5qWoNb17va21q4qy3K6h9KTUIilqqZk5oHqrnnKAUlFieyuJOwCJdhR8Xz7L2BrEqPI+02A8nXYUVSZCfNIER02yo2dlmx3nv8sbHfp/GM9V1ZnMk0DUNiqoik07jeNcgbvvA/8OT/1w+u26+EB2wIpEIkskkNm7ciKGhIQwMDEgOWOxvKqpcFYNibbjlEBCeffZZdHd34/3vf7/jXHd3t7QuDg0N4a677kJPTw/q6uqwdetW7NmzB1dccUXJ8wAhpXsZT8PNVDkwYwhXLDrAdm/JZBJHjx4tOra2ENglXJH0Vq1ahWXLlpV1x+2l6mXS9MjICLZt28ZtYsXCS8L90le/j3987L/AVLQQw36oRLMQqVco/y68Ettle0buyRuE2XocZ2MI14rqWsErmcuERDjOWjn10x5juUjtomTM1MoSuQpSLwWXatlxRVWga7o1b9MfgUnG3B5rJoYnqs0+LSWy8HrO5uekG0XtjY0Iy91MzRhlw8ataxoSiSR+986n8V+PveWyqXOZitZeNIBlwLpw4QKOHTuGSCQiZcAq18a32PkWgvHx8bJ4KL/lLW/x1FY999xz0vuHH34YDz/8cMljusEvXuCNaU+4YtEBMbYWAF588UVUV1eXVbL0gigJplIpHDhwAGNjY2UhvVzjMbDE6JWVlWhpaSnLPbs5Tf3hu/8PWls7YCzCuiTVGq/cbIPmP0Q8wByH5IbuUi7gdPJxG0QmSUmryyYh/FjtpCr+Q6lunSeU50YmzFuYNabwkBJFSdmN7JykayXdgCkpGy917vinAFDMtI3CzsYcX/aUludkPFebkxaId1Yps4llH6WmxEuMlJeKAj2Txu9/4Bk88Y3rUF11afMoA3D1UvZywGIl81heYqZ+Zg5YlwLFqpT94vOvD0xrwnUrOgAAJ06cAAAsWrQIq1atuiS2HCbhsiQajOinKpesSLjldsiyjyPuinfd8OfovTgAAFLojxh/Cv6K2EVd4RyTugCnKtNLtewBTlDsP/aYW8K516589ewLjLzkNvJ0RdW004ZMJSlZkOml+zaO8wQbXGI1z5sdG7mmVd7WQZIUIKpq2Z55F7Ja3CJd+/xtdnYRzFRAYHhym9WItEwGgWAQekbDH//Fr/HQ57Zj/epa5/VTiHycpewOWKlUimfAOnbsGJLJpJQBq7q6esok9td98XnAL16QBdOScMXYWjE94+TkJNrb25FKpaCqKpqami6Z4wQhBJlMBvv27cOaNWuwZMmSKR2bES6L6R0cHCybQ5YIUcLdcM27kUymBNUx5dKsTLTiAWFxJ3JL78fDpF9F9g527VPohDOqTYUr/Nc5JLXauamZpc6zvc8CBxubI5h2XJmnGZFSqa0iSL6UaiBEgaIGDEmTECujFGGuUmL8LqTxrel4SbtwHIPQnP3mqK6B0gB0XQN0gk998RXc+7Grcc1VhceVF4tiauGGQiE0NTWhqakJAKQMWGfPnoWu66itreUq6HI6YBXrpTyrSvP5TlOemJZ3xTyRRRVyb28v9uzZg8rKSjQ3NyMQCJS9Pq0XkskkDh06BAC45pprSnJSyheKoiAej2Pv3r1IJpNoaWkpO9mycSilWHv1uwyy1ZkDkxBnyyVLuzhrs8/a7Ee5w42ok1D5H3HhPOI4buaIgqMxI3KWpYiTDJsTLYhTHfPmr9g9MJurYpGnbQMiSv58mooqVYeyNiM6tEwSgVBYsOcSuR9RuU+pfI5/HHbtgnUtO0bEZ0Pl+RkhQ4CeyQCg+OuvteL//eZcvg+qZJQjHKiiogILFy7Exo0b8YY3vAFbtmxBXV0dhoaG8Oqrr+L555/HwYMHcf78eUxOTpY0lq9Svnz41re+hWXLliESiWDHjh14+eWXPds+/vjj/DfF/vLJfFYqpqWEy0iWxdYePXoUFy5ckGJrC021WCwGBgbQ3t7O41svleonmUyiv78fK1asmFK1OSEEv/9Hf208S8oWe+YoxVp5EW3uOeWqSuN+3k4Siu2sYIsVbbeSTVVuK3vxsmNEIiViJ3/eg71fOwFa8yF8zpa62LxR8zXlTiXOZBZEloCJCk1LQ1FVKKrK7bxiewlS/C4A05vZS9XASdfUZDB1NeHEbHgus1q8mpaBqgbwze8dQ0rX8XvXTW2sLlD+4vOEEIcD1ujoqOSAFQ6HpQxYhfhKaJpWcLKbiYmJorLRTVvkG9Oeq48C8KMf/Qj33HMPHn30UezYsQOPPPIIbrrpJhw7dsyzWMzlqJY0LQkXMEh3dHTUM7Z2qiVcsQDAunXrMH/+fDz77LNlrR3rBlZZaHx8HAsWLMDq1aundLy33XE/X8ilAgQC2VKJ1ETYF33LSUg8pusal/6cXejGUi9lR7JgVp8V3hG5WT6hPS42WR4i5CBNS1p1dCMbeF03CyJxWfRrkSxXMROhrUDGMOlOUQIWV5vl9cIVlUgl4h73K9qFIX8GbjHLLnsmNh+d6iBU5bZgrmLWDPuurmXwjz/oQiQQwI1vKF9yGTdMdcILRVFQW1uL2tpaLF++HJlMhqegPH36NA4dOoSqqiopA1a2zHXFzHdiYgLLli0r8U6mERSlDMULCrv+q1/9Ku666y5e4/fRRx/FU089he9+97v4zGc+43rNlFVLyoJpSbiUUnR3d2eNrZ1KCTeRSKC9vV0qAMCIaCpJfnx8HK2trQgEApg7d+6UxxZese1dhn1OUnXKqklXouWHPEjORaqyihm4ECQ1E08QBbKQaUmnVoZI6kKy4ljE2d6zre0+HHGzrjfn0sLlGN9gCOQt2lXNCVJ2n5Qa968wyVe0vxKA6khOjiMUqUQqMSkRvVUI0Dlz6Zw5hoOcFbk90SmgWh8jy0gFWISiaxq+8S/HUF0VwvbNUxeOd6lzKQcCAaloPHPAGhoawvHjx7kDFrP/2h2winGampycnF023DJidHRUeh8Ohx0ahFQqhVdffRWf/exn+TFFUXDjjTdi7969nn1PWbWkLJi2hNvX15c1tnaqCLevrw/t7e2YM2eOVACAEFJUQYF8ceHCBRw8eBBLlizB6tWrceTIkSmVpre+4f1GuUFKBXtfDrJ1cK8b+XjDKtfnRdQ6qJn+0C7JCgKgbVwXdbD43tUhS5ZAxddupOUxWXkOXMVs/WsNn+05GUk0WJUisb3sYGUQZmpyAkogBEUJQMukbD3ZRxEco2Am2pDmwz4Pm+pZmgMklbORkSoESjVQSvB/v3UAX/7cVqxenr0qVbG43Ckd3RywGAEfOHAAuq6jpqaGq6CLIVzfacqjDwCLF8tmi3vvvRf33XefdKy/vx+apvHPiKGpqQlHjx517f5yVUualoSrKAq2bduWlXDKTbi6rqOjowPd3d244oorsHDhwikfk4175MgR9PT0SMXpp5Lcf+fWv8DI6BgnWwMWydpVyMQQsDzgolbORloCqbr3Q80F3l4rlgj8JthFxfMesGJX7ZKwRcr8nl2J2y4BmwTLZWghi1U2vhZDgNg1RH4WlhexMZJMuqaUmUkDAYJwNIZkfEy6f2tPIqqRzaPEhcSJkKbSGftkjEcpFBYzzHZnhJj1eAk++cXX8P2v7kQsVv443WK8lKcSFRUVqKiowIIFC0ApxcTEBA9BOnnyJHRdh6ZpYLWAKyoqcs6fpXacNShjWNCZM2ekSm/FFoOxY0qrJWXBtCTcfFBO8pucnERbWxsymQyam5s9HaPKTYLxeBytra0ghKC5uVmyURdSLShfUEpx10e+iO7uHgCUS5wQvFdhSjTydQWPZF5E3G2sTGKy221tiz3VdQchSZBCbkTVsVt/8nXOQ26SsgeJOrXHkKVSq6Gd4AjfSNglfbeNCwAoQsyy9XnpmRQS8QwqqxsQHx2UrnXkY7ZJG6Lt2ZGdilIQ1a52tpyrQIhl04UOI0uVjnd/8mX89Nu7yi6NFhNmc6lACEFVVRWqqqqwePFi6LqOl156CZFIBL29vTh+/DjC4TC3/9bX17s6YM06wi0jWInHbGhsbISqqujt7ZWO9/b25m2jLWe1pGyYlmFB+UBVVWQymZL7YeFGsVgsK9myMctFgmzc2tpa7NixwxEWUG5yT6VS+Prffx/P/Xa/uVCKamO7o5T5lhZDtjZQwFLXmuACqiBhZ1Mzm0n2xXaWfCkQLCcxanEu78hFSnUZ1wqJybVDz+PBEFgeyYrhaQyB4MR4Z7FPw0OcmH+ifZ21Mf90HRMj/QiGos77AAsaEomVymOYx6ltfPuc5H0BtVqa8fIAQHUdb//wntzPpEBcbpVyIWDRFQsWLMCWLVvwxje+EWvXrkUwGER3dzeef/55vPTSS+jo6EB/fz/PnleqSvm+++7jXvPsb926dVmv+clPfoJ169YhEolg06ZN+MUvflH0+A6YmpvS/vKXkEOhELZu3Yrdu3fzY7quY/fu3ZIUmw2sWlI5K8y54XUr4eq6jmPHjuHcuXN5l/IrBwnquo7jx4/j7Nmz2Lhxo+cOrJyEOzIygv/+n1/iG4/+3JR+YJNuITErIUBhQ2e3UYKK0qz9OggSnDdBclU3haBqFsYUQ4FMNTC1XW/dr92Ga41ZvPpSLvHH7ld2Frapc0VQ4Rix5V9mKlzJK5pJpEA6OYGKWAMS8XFQXdyEEoDYPaGFa0XPaNa3qJTg48pT1akOFYpxJT9pOFbd/pE9+Mm3Wgp7dFkwkwgXkJ2mVFWVHLDS6TRXP3d0dODxxx9HW1sbenp60NHRgeuvv75olemGDRvw7LPP8vfZPKn37NmDO+64Aw8++CB+7/d+D0888QRuu+02vPbaa9i4cWNR40u4DGFB99xzD+68805s27YN27dvxyOPPIKJiQnutXxJqyVlwbQl3FwLn6qqSKfTRfXNVLmAocvPd3dZKskz1bWmaTnHLQfhUkpx9uxZHD16FJ9/4AdgFX+s9dMuPYlHCx7N/NdFhQxBzen6uVIzoX7uHyoBAF23Ss9J13hIsRC/TwYZ272lHffMJWSxT9FWyyRr+5jCxVlhbTYc87XZeqVjlB2zRHhKKSbHBhCprEcmnUQmnZDm6pWVyiIyi3QVkyzEa4y9g7AhELzZdV2zrtF1pDPAZ7/cjgc/eWUezyCPp3SJvZRLRbbEF8FgEHPnzuV+Gk1NTXjqqadw77334q//+q/xl3/5l7j22mvxqU99CjfeeGNB4wYCgbzVp1/72tdw880341Of+hQA4IEHHsAzzzyDb37zm3j00UcLGtcVlyEs6J3vfCf6+vrwhS98AT09Pdi8eTOefvpp7kh1SaslZcG0JdxcKDYO98KFCzh06BAWLlyItWvXFvRjLoUEmfdzU1MT1q9fn9MuVSrhsnjevr4+/PknvsPJ1oKw4DuOuoBkO2k/72rklAnEFUzFzMrSuZO33N5Qvzq8kh2Ts/51j7E1CdVF1eylfs52H/Kcrc0IFSRZhyTpeD5MKWzfvAjbBJOwKaVITAwiEIpCUUM2SVfoh5G7orpKzKImgs2HeVCz+yDCnC01tfUFONo5hsd+uBdv2NrIq/cUa4edbk5TuVCIzXnFihX4yEc+gi984QvYs2cP0uk0nn322aKS63R0dGDBggWIRCJobm7Ggw8+iCVLlri23bt3L+655x7p2E033YQnn3yy4HGnE+6++27cfffdrucuZbWkbJixhFuotClmrNq0aZPDhXwqxgSMH2BnZydOnz7t6f3shlIId2JiAq2trVBVFY88+jR0qgtSibEwutlmizbX8rU298LIYjqNNdSNUKk5P8OGSRRr8XInaxtBMacvYZFWbB6TFtEUSKRZsja5trU7TdnIzdmdQIwCoRnHFE6urKUjwQYlyKSTCISiCFTEkJwYkvqGYqSdFMeVHKgUxSJT87lwS67Qjn9PJFW3dYxCx3/9RsG2DUlePICFztTX1yMWi+VNojNJpcxywBcy32QyCU3TEIvFMH/+/KLiQHfs2IHHH38ca9euxYULF/DXf/3XuPbaa3Hw4EHEYs5wrZ6eHtcQmp6enoLHdsVlUCnPFExbws1HpZwv+Y2Pj6OtrQ2KomDXrl1FJ5Qo1HNYTKCRyyHLbaxiCLe3txcHDhzAwoULceHiOA4f6YIc0+NOq64qVftBr2OAsIKLvbn98FjhdmJea5P2pE6pUb2GGDVaQewNvSVW8a6orptzscZnrj+l1d20Ni5WiFAOO63dE5vZryWJUVQjK1a/NlusfIwVsqfIpIxsVJHKBiQmjMpPihLgfcrFE0zCZGRsU2MrgQCfEzM9KOI8BacuYqq3CQyivO/RCfz7N5t57Org4CC6u7sBgHvt5gqdmUmEy36vhUjz8bjxWZXiNHXLLbfw11deeSV27NiBpUuX4sc//jE+8IEPFN1v0fCLF3hi2hJuLuRLuOfOncPhw4d5QolSfryqquZNggMDA2hra0NjY6OUQCNfFEq4Yhzxpk2b0NjYiLf+r3eaEqUBK/EE4LS5yscIsXEnhOYOLrGrkCEQqh3ixW5zcCFU4w5N6dVMj5hVdSwesUuxIlEQUOiCSpq5lAGA4pilO5h06Z0z2v2cl+OUIpA23KVqiXQtNTAnUgqTdAmi1U1IjA/A+tzF64XPW1H5nER7u6KK6mT75ki+B+M+BXKmOj78hXY8+sBViEajWLhwISilGBsbw+DgoBQ6w8i3vr5eKnk5kwiXrUeFEO74+DgAlLV4QW1tLdasWeMZ4jJv3rySQmh8FI9ZS7iZTAZHjhzBxYsXsXnzZsyZM6fkMfORcCml6OrqwsmTJ7Fu3TosWrSoKBtUIYSbTCbR1taGVCrFJenVV/2hC9mCSyEG3Mk2J7I1cWiJ5UXZkQtZUCHL0qYXoTLHL6YSdiFfF6naMT4/7FKEIIelOX+42HIFtTA7Jnpp86MOj2abPZcaKmDKd0U29TUFtHQcCT2NcLQeqckh2AbgpKuoQVNqtY5TAKqpzhf7NfJB21Xa9nkbZEupgr7BBPa1D2LblUalK0IIj61ctmwZNE3D8PCwlLs4Fotx8p2JhFvI751VCirnPY6Pj6Orqwvvfve7Xc83Nzdj9+7d+NjHPsaPPfPMM3mH0OQEKYPTlC/hTi9ki8MdGxtDa2srQqEQdu3aVbayS7kk3FQqhfb2dsTjcezYsSNnwHY25Eu4Q0NDaG1tRX19PZekP/X5b5oFCUTHKFktaMB6zbSadknGTcoVNaD2a8wWjnmKsqqXfcbYIMgE6pp7WSJQU2Vs61NKD+mGstmIRIchb2mXCgRHqEj63pIv70ey51obE69xrHhMBaA69MwkKmJNmByzpBpilmVUVNVcG22qbIWYCTDkfsWFlKWLdLdtGw5thOr4u386gR9/3b20pD10JplMcvXzkSNHkEwmcfLkScTjcdTX16OqqmraOlExh6lC5sdicEu5p09+8pN461vfiqVLl+L8+fO49957oaoq7rjjDgDOkJiPfvSjeNOb3oSvfOUruPXWW/HDH/4Q+/btw3e+852i5yDBt+F6YtoSbjE2XDEMZtmyZVi5cmVZd47ZJFxGfLW1tWhubpbUYsWOlY1wKaU4ffo0Ojo6sGbNGixZsgSEEExOJvGz//iV1C4vqZXDTlzcTMffi/86ryHOV05ByHt0T3W3bQJwI1RLXSzdNh+fTO3vWHhQZrSz6/fYzVs7a4yucREIUcwNkNMWbIDFAqs8VplSinRqAlBUTrpEVU3nKbuXstEHCIGqBoxZiOprSqFKGwDbvRP5g2bVp3Rdx3s+3Ybv/d1VXk+OIxwOY968eZg3bx4opdizZw9qamowMjKCU6dOQVEUh/13uuBy1cI9e/Ys7rjjDgwMDGDOnDl4wxvegBdffJFr9ewhMS0tLXjiiSfw+c9/Hp/73OewevVqPPnkk+WJwfWRFdOWcHPBTriZTAYHDx7E4OBg1qIHpY5pl6oppTh16hQ6Ozsl4isV2QiX3evQ0BC2bduGuro6fm7Tjj82nYSETEYQ/801N5c2JNtV7mccR6UDuSViUcozJpAlpMgzzMc+psCJWTyO5exL8vTMinWCrVf03s1GpG5wUzGzuTIpwZIW3D2TBXWvWczernWglCKdGIWiqIjE5iCdGOH3ae8DAIiigijMlgs+R9FjnD0/qx0jYsWSss2muqYhkUjj+X1DeMM267uaC2x+TU1NqK2t5bVrBwcHee3aSCTCvZ9ra2tL3uiWglIKF5SyZvzwhz/Met4eEgMAt99+O26//faix8wK32nKEzOWcAOBAHTdSPnH6uZWVFRg165dZUtwbYddwk2n0zhw4ABGR0dxzTXXoLa2tqxjuRHu+Pg49u/fj0gkgl27dkm5We//23+G4ZFMZcLIE7KKGBBVy+4SqiUxUmpZGmU7qTeZ2l+7q4+ttxTUJLxcTlN5LF4sFMZNAs1KkrxR4WovN09kx2nCzzGadZd4hfEJ4RKrnTzFXtKpcQQJEKlqRGK839adSZKKAkW1q40NKIpNlc03C85wJuP7pxsqZ3Mu33riNJqvri6IlEQbrli7FjA2nsz+29XVhcnJScRiMS791tTUXFL7bzF5nycmJsrqMDUt4KuUPTFtCTcflTIALl2uWLECK1asmFL7jmjDHRkZQWtrK6qqqtDS0uKalLwUuBEuK+G3dOlSrF69WrpXTdPwvR/8F1903eHixAPAnaBsqmGbatnRmq/95kLskNyI/JJmG9edsC0iZ/VzAUCx0gu6ffZZVdBe95JFIs1XPZ+LXKWNiWkLNeeZrS/RcYoQxZRoDUcy7mnNiduSWGHadTOpCYQi1QhH65CMy45UFMSwQUpjGqOqakB6vHYp1pqb9Zyo9UUwvsuZDP7i/3bi77+wNr9naI7jRZqBQACNjY1obGwEYIThMfvv+fPnoWkaamtruQq6VEkyF4pRKc+60nw+smLaEm4uMDI6deoUtm7divp6d6eMckJRFGQyGZw+fRrHjx/HqlWrsGzZsin5ERNC+D2KeZ/FEn4irmr+Ew+itR1zsbXJ48qOUBLdEZMoCHEv10fcidKTQEXpOCtZyjORSVQAE7Mlo3F2EnadY4HIJRFL54XYWtd52GymotextasxiNZw2HZ3WGIbF6KwovaWF3N89AJidUtAdQ2pxCifiyqFrlljEl6xya75kD5AGGptaxMBYUMBM+HJ8GgSvQMJNDXk58hYiJdyJBLB/PnzMX/+fLCiAIODgxgcHMSJEycQCAQ4+dbX15ddE1aMSnlWVgq6DKkdZwpmJOEODw+jra0NALBlyxbU1NRcsrHHxsYwPj7usJ2WG0zCTSQSaG1tha7raGlpcVU/HTrShWQyab5z90KW32ZXN3O/GNdzbNHP0pUp+VC7FCuRbTZVcj5kmYWEJSFedGRyCp2eZF8WZNcciIRqbW/cbOhGxSEmpdofD7E6lFTlihrgiSjMBvx+x4bOINawDFomCV1LQwkE3G26FFACIokIDlqKZa+122/NFvy9TikIKLRMBp986AT+9W9z56xlDlfFfD5i6bwlS5ZA13WMjIxgcHAQ586dw5EjR1BZWckJuLa2tuBYeTuKUSnPRsKlhPBc56X0MRsxbQnXy7bGVMirVq1CZ2fnJbPRjI6OoqurC7qu441vfGPZVch2sPt64YUXcuZfvu2OT5nSMFPhCXAQIoV3UgoL0sLuWNmtz4faCMKutuUSc74/IFNCNSQyx7D2htYgudqIzWzabbsbdl42XBcHKeOo+N11UyfnoZamFFDMsn7EUB3LNyI7UEmbBmLlPnaXkI32ajCAybFzaFi4HsMXT0PXUrYpGNcqgYC1DbI5aNnbWk7i1JKozfOKuQOjug5d0/DEUxfxx7c6NTX2OQAoy2+ceTezTTKr3DM0NISOjg4kEglUV1dL6ScLHddXKZsgBKU7TfmEe1mRSqVw4MABjI+PcwelU6dOlaUmbjZQSvmOeO7cuRgdHZ1ysqWU8hR4q1atwtKlSz3b/vWD/wTo1N3A6iXIEs83WY55gQhqaNsZQRqWtdhe6mb79cJBmrWp7Rq3OZJsDTyl73LBqVZ2J0suxbpOVVbTSlIxUYSyheDEKNlzKbiKmWF04DSaFq9BT/cRI42mcL3KpV67V7Ri5qf23lAY6SKJ9N6aNcX/vDCYk3CZSWUqNtX2yj2Tk5MYHBzE0NAQzp49C13XpfCjaDSa83tRrEp51jlN+fDEtCZctkseHBxEW1sbamtr0dLSwl3/y1kQ3g2ZTAaHDx9Gf38/tmzZAgA4dOjQlI0HGDvv9vZ2nvItV53eH/xILBxNXV66qGd5qE0uMde8nNgXVpGcxH9dpGI41cdWjKyoHhVVwm6qZJvqWSJ4KlznFGMdKmZB5Vke2OyVefVrFQuX5u4ihruTtQFFNQiU6l4bBWs+RCEImL8davaVTsYxPHAWcxatxsXuY+yMkNKRT4KPK6d7NOZKKaCoRDpmTYda/5p250w6jXv/vht//efuFW3YfQNTQ7h2VFRUYOHChVL6yaGhIfT19aGzsxPBYFBKP+m26S7WS9nNJ2NGww8L8sS0JlyWJvHEiROuMa7FlujLB+Pj42htbUUwGERLSwsikQiGhoamlOBHR0exf/9+VFVVYefOnfjVr36VNfnFH733c6A6FbxB3SVNVwIoUMWbtS+IKmazjYNIrTZc+0iE9rY29rEcxznR23+YjGA8iO+SqqrYxgaC4xHbdNhr6wrtXV5LkipzmjIuNv8Vr7FLzoAaCJrj6sZchFnGR/sRrqhC7ZyFGO47K0i2bvbcoPM4ANl+KzjcuTjpGcRE0H0hkdUpaiol3GwQ008uXboUmqZx+293dzcOHz6MqqoqTsCs/GCxKuViyvFNZ/g2XG9MW8LVdR379u3LmiZxqiTc8+fP49ChQ1i6dClWrVrFf0SFFC8oFGfPnsWRI0cc4U3Zxnut9SikcvLU/oKfMf8VpVyWDjHXF1uOtc0HnEglO7C9TQ6JNst8cg4OGxFT4jEVb4LL57lYQwrkZzqMWTt091SV4i17SbDScUJAWNpAydGLSffsNZubQcyqiyOQnUSJomK0/xzq569ETeMCTIz0Sc+IkTcv3+foh7gQtO35SfM1oOs67vnKaTzyqeWOObLzlhbg8kFVVW7bBQzzFgs/Onr0KFKpFGpqaqBpGqqqqvL0ATAwOTk5+2y4PjwxbQlXURQsXrwYDQ0Nnt6D5SZcTdNw5MgR9Pb2uhY8KLQ8X6FjXn311TymkI3nRbhv/V9CAWkq1rfNy3Cb1zG7VMlstaLN1r6wSAQBqxCet0exczzJySoLyUtjS5K4fd7E1kQmCeOkYP+ELKU4iipIc3Yj1lIIwlL3K8QW0iNMQapPa1vgjVJ7ShYHLpFECRRzjNGBM2haugHpZBypxIQ0J5bFSnbAEpvIGwVFEZ2pBCcqQgBdBxQFekbD6FjG0/Y5XYvPh0IhNDU1oampCZRSbv89ffo0ent70dfXJ4UfZUs/OTudpnyVshemLeEChv0ym4RXTsJlRdsVRUFLS4vrj4RJuIXsYLMhHo+jtbUVhBDXMXlSAxccO37KeDbS+WwiqIuU63JMJFM3SS+775GTSIlN+smlkmadO4mYukjYXupn9xZO9bhrqwJQ6HVZVMZgxKdwFbQ0kuOBOwlUUVVDXcw8nOFNzIYHcpBLzACgpdOYGDqDdZuvwqF9L0MzHRLtcbwi6VJKLAcq85gllTorIVEh3oyZQj758Bk8/Mlljqc1EyoFEUIQjUYRjUYxODiI2tpa1NTUuJYfZCpoMf3kbAwLYpqekvuYhZjWhJsL5SLcnp4eHDx4EAsXLsTatWs9f+TseDHOEXZcvHgRBw4cwPz587Fu3TrXMb0k6ne869MARHLMU9fLDZ/svUyA3t6xHl9+SQp1k2Btl7KFmDtV28nfIgNnV+JCbvl9WeOLB9yJ2G3qLme8ThQAb/U08/IlhAD8XzMLlijCevUlSJcsC5PhdWyFA9nnItp/KWUJLgR1BWGUTzAyMIDhgYtYvWkTju7fL0i2biCuRCzW1mWqbUPjTfl3gIIC5nd7bMJ9Uz0TCFeErusIBAKoqalBTU0Nli9fztNPDg0N4eTJkzh48CBisRiGhoaQSqUwNjZWEuE++OCD+OlPf4qjR4+ioqICLS0t+NKXvoS1a72zeT3++ON43/veJx0Lh8NIJBJFz8NHfpjxhFtKWJCYwWnTpk1oamrKOR67rljCpZSis7MTp06dwoYNG7BgwQLPtl4q5QOHOmEsnpazlES6BB4cbJdovdTHecAmgXICpHI/cq4qaxaKylIS2s96z8Mh9QpOQWzhh0hcWYk4f+Qbl+vonxOpuFlQhL5ESZ4CXJUtS4bO8YnlVxAISpoDL29mAJyYRenZLfnG6WPHsGbz1Viyeg3OnTwp3aM4LymxI+uHONXYjoIOwpOilELXNPyfb53BAx9ZLLWbaYTr5jRlTz+ZTCYxODiI3/zmN/jGN76BoaEhfPGLX8SJEyfw5je/GZs2bSronn/961/jIx/5CK655hpkMhl87nOfw1ve8hYcPnw4K5FXV1fj2LFj/H1ZVfd+pilPTOu7yvUlKEXCnZycxEsvvYShoSG0tLTkJFvAknCLHTOVSmHfvn3o6enBzp07s5ItG89OuPf/7T9DEBEB5C/fAvAQ7QzydqqvJebKo1sipPaDY6FlYyuKQA6mM45pVpWJXJqDe1/yIUZswmtFAVGMeRGR+MzMTUzCc9y2OB/Whr+WUyYaCf9VLm2y1wob20FCcHmNLF5p1BpTNRyh2PhW/VuXa8z+jDmqUMTcy65jMo93oLvjOJoWL0Kstsb2fKhA8LbvoSm9O2ouE/B+QalR7N7WpnfAuXHOlkd5OiKfONxwOIz58+fjE5/4BLq6ulBXV4ddu3bhueeew65du/B3f/d3BY359NNP473vfS82bNiAq666Co8//ji6u7vx6quvZr2OEMLLIM6bNy+v9S9fMC/lUv9mI2a8hJtOpwu+jqlz582bh3Xr1uUtrTLnkmI8lYeHh9Ha2oqamho0NzfnlUbOjXB/8KOnrDdShiTkx7xc8rF/ofPxzGVjuZOqq0qaOq+RJWvxWkFlrDNHG5fLHXZlN8Z0HmebArf5yKpr+yIvSNN8jmwMoS3xiux1eyDmO0/p2SAvmJ7BjNyd9+buDMXmppiezdxrHACgg1JL0qaUmoXTje8bUVSkkkmc6ezEyo0bcWDvi7ZNprvK25qjMA+iSAkwpHSQBAC1gtqe+EUf/vh3LUfF6eo05YVCNV+KoiCVSuH9738/rrrqKqRSKSFFa3EYGRkBgJy55cfHx7F06VLouo4tW7bgi1/8IjZs2FDS2D5yY+ZsH11QqITLVMhtbW1Yv349NmzYULBquFBPZVYo/pVXXsGyZcuwefPmvHO22gn3pVcOGpKCi3TrlCbznqJjvo4O3KRAOxzkRixet6uC85goUYwxFZUYDotKHnNwmYc8TrYOSB5txLZOZK/SlLsdUQgUVYUaCEANBkFUM6OTQPYGdKkPu0Rp9BG0aRtgkyqN75Wl6mbaByv0p/fsGVSGJrHiinXCdYrzM+RStlhH2CwVaLgrsyOSxCrNRtfx3D7RM3p2qJSzgVIqOU2FQiHEYrGix9d1HR/72Mewa9eurMXk165di+9+97v4+c9/ju9///s8T/vZs2eLHlsC81Iu9W8WYlpLuLl2t4UkvkgkEmhra0M6nUZzc3PRweaFxOJmMhkcOnQIg4ODRRU7sBPue/70Xi7IUlNVx8WDfOEqGeXT3mguE7uHujdLF95tZbWobK9lKmdBqjQlI9lmbElS9rFcVa4ekvCUg4jqbaEoAQDZBsqkfnPG2aRhRbVd53ZfstOVoe52W9iY8xPBS795DX94x5swMTQX58/2S5K1nIwDjuNEUQz1sTF56TOklEI1Vc2E8ivReWYSqxYb3vozjXALlXATCSPxR7kSX3zkIx/BwYMH8fzzz2dt19zcjObmZv6+paUF69evxz/8wz/ggQceKHkelCigJRJmqddPV8zou8pXwu3v78eePXsQjUZLIlsgfwl3fHwcL774IpLJJFpaWoqqLCQSrqZpoDbJJidR5OQRkandVMz27lykaOmQZTN0nyOzZ/KTttE9VK+SCpwt8AZJMVsps58yD2CusnS9He8HUx7qpZw4JZsuk17NdIwkp9QuazNkGOpWRVVNtbEorepSH3aJms2DwVID2yVxIJXK4OW9R3HDTZsQqbCnMzQ/b1tCDLFf+/dV5E8xpzOoca9/910jlKa/vx/pdHpGEW6huZQnJgyJvhxhQXfffTf+67/+C7/61a+waNGigq4NBoO4+uqr0dnZWfI8AED0dSjpbxZi5nybXZCLcCml6OjowP79+7FmzRps2rSp5HCefEi+p6cHe/fuxZw5c7Bt27ai626KhPvuD35BUs1xUOtFzu9oVnUra+JUFxot7GQrS48Wh+b5QzFVzpx07OpPD7aUzxH5HJca2eKuQFGNP2L+qygs2YNqvCayQxUU+UcvOkdJjlAKIzs2hgoloEIJBKAEgpwI2RiSFAuPbExZCda8TlGgqAEoakC4V5eWDscly+lK+Agg70SopBI25qKgq6MHw0PjuPY6l5J6okQuXMtsx2L/iqpKYWwslYeULc0k6Y6ODnR0dGBsbAwnT57E6OhoFpX95QcrJVjIBmFiYgIsjreUce+++2787Gc/wy9/+UssX7684D40TeMhij6mFjNapZyN/JLJJNrb2zE5OYmdO3eWZBuxj+mlUtZ1HcePH8fZs2dx5ZVXluz5JxLuK68dclkgYeccJ7iW1etZClZgmzQqNqFEKEcnSabur+192AlGJE5GHBRuZGsjpqxSsTgT+bilsiUgsByQCKEwbEbMO8smrfF21jyczljuz9aRb1jo2f0ccT0nqovZZiJ7n4Ah5arm/VobC+ELwa7KGvbEPptf727HH95xLZYsnYPu033mvNwTYhDbppZVDrI2B8bcFXFIwtTLOvZ1NuBdt67FiRMn0N/fj/HxcZw5cwYAeAKJ+vp6RCL5FbG/FGC/00I29Mx+W4pJ4yMf+QieeOIJ/PznP0csFkNPTw8AoKamhifSec973oOFCxfiwQcfBADcf//92LlzJ1atWoXh4WE89NBDOH36ND74wQ8WPQ8RFGVQKc9sWdAT05pwc8GLcFl1obq6Olx99dUlF5YW4aVSZjbiTCaD5ubmsqiJWAhHX/+Q8aMUsvQAlsOxrLZzEZKy/p7z+LEzAYZ5znpd6SAicLOhFBZqJ1+BTFjeY2M8k+zAqQdeNlr7OaeF2p3OjZXemhxxuQ+LDKnw2o5ipS+n5oAQGEksOJmJJCvfu0yWwnkm7Suq8IXIQc5CH/xzpkZKjJHhOA7s70Tztetw7twgdD3buIptDCoUT6CCtsB69uJT2P3SGN51ayNUVUU0GsXGjRuh6zrGxsYwODiICxcu4NixY6ioqODkW44C8qWArQmFqpTzKfuXDd/+9rcBANddd510/LHHHsN73/teAEB3d7ckeQ8NDeGuu+5CT08P6urqsHXrVuzZswdXXOGiwSgG5VAJz1KV8ownXDHxBaUUJ0+eRFdXF9auXYvFixeX9GX2GtMu4Q4ODqK1tRWNjY1FeT57gUm4b/n9u81F08WuSqx8xYVDJD0glyOV0cQiJ7m1x3Ukh+Rr68nN5mv0wIiAWA5TDuneSeKuc7N/J8ryFcnWiYvkSsDJ1XKcsoiKbwCkzYlxbdZEHMQl4xSxjw/ImwdGhFZeaAs6QI35vfxiF7ZtqkfLtWvxwm+OQQSPB5bsuWbKSUWRxqUUIKrCNxOyhcToR9M0SUWrKIojgxMrIMAKyNfU1EgF5C+lMxwj3ELGLEct3HzU7M8995z0/uGHH8bDDz9c0rg+isOMJ1z2RRcL1G/fvh01NTVTMqYo4VJKcerUKXR2dmLdunVYtGhRWX/kjHDHxsahKCbl2H2JQEEUgPI9AFPPUmEhc5uTFznZ2rsRl5DRSSyDLrWSDoiLvJkA30U9bZdSZXlU9OQlXGlMufRnU0EJQ7rJta73WlZYoTKAqX41DJ7C8yauw7upabOaBEyydvvuZauly+bAlSd2UrSRM1EI9u7pwHv+YCk6jkTR1x+XtCmS3dacMyGAGpRL+jEJV7hh4RrjWX3pny/gnTd420QDgQDmzJnDC4ywAgKshB4hRCogMNXqZ+ahXMjvvxwS7rQEISi9eMEseyYmpjXh5mPD1XUdQ0NDaGtrQ3V1tVSgfirAxkyn0zhw4ABGR0enjOAVRcH5C/2O4wSM8zx2t5LUkP0Zup+17Jme7aSi9Iw4jGMyBcuqWOIgX/tcspG9jYwFVaT0XREYn9stGYnZ++XE4rYBMKVPLn0rnOxZWwKmZXBL3WjbihC4fKcdYro1MUF9Ldt1dRDFyIdsqeMFudLW1lIXQ8jeJF/HTBOuamIwG6yCtqNjOH12HO956xx8+buneb9GUXrnt8luzzXayqklVYU4pPZjp1IFZZoSC8hfDvVzsbVwZ0vhgi9+8Yv4q7/6KwDw6+FmwbQm3FxgX/BXXnkFa9aswdKlS6d8t6goCuLxOPbu3YtoNIqWlhaEQvZwifKN9b8//QhEP07KxQCrHSEElFCIMansOeTUOGV9Xk7bn3Ch8CqLjdDRv0wklkTEjonnvaRd+7y5iGa+s43rop6VpWVIbeX37B/rmUtaXkMk897WiARG3SVad1J1tlBMwmdqRKddl8GNrBXrlNjSk2SZs5OchIAQ4MdPX8Dn/mwlViyuwIkzk9xjWpaMDWc0w7wi29YVOwk7nhEFUSgyGR2BQOGS0uVQPxcaEgTMLsL9i7/4C9x+++1Ys2bN5Z7KtMaMJdx0Oo1Dhw4BADZv3oy5c+deknETiQSGhoawcuVKrFy5ckoJnhCC8fGEwB2UWzPd2lLb2itqEu1tze7sveQ5MfGlG6kKs5W9paSLJdUqYEnslPJFntOPfQy7elQWWrPeiV1uFvtx/zzdCTz3SCKh2Yk0y2bGJHBDM8fsuta4bvZpO1nbC8Ebl1ibMGaOcErAukXOiul0JdwLQNDTl8STu3vxwdsX4P6/P4N0xn5fpto4IF9LCEEgoLqQs9jGejb/+RsNb7+hdH8Iu/o5Ho9zAj59+jQURSlZ/VxMQZPZVJovFotZ9mS/Hq4npjXhepHZ6Ogo9u/fz7+s5crUkg26ruPIkSMYHh7GnDlzsGrVqikdT9M09PT0gmWaJaZ0xMqoAfLyTYgk4AqqVuNfKyexO0k5Fn5JLWonllxSsU0edfFEtXyPuQgpvbbHrIp2SMoIkAqXuhK5PH7Z4cq32UlYligNQmRkyKQ/N6coWeVLzf97hxYZhK3AImCBZDl528laGIxYqRplCdjofc9rw3jrdXPx5pY6/PdvBh17NzXIau2ygQ1pWVVV6ZiiBhzPjJpJMPYfV/CHby7/wsvq14rq54GBAZw/f96hfq6rq8uLSItRKc8mwhVBYZhYSu1jNmJaE64dlFKcOXMGx44dw4oVK7BixQrs3r27bEXovTA5OYn9+/eDEIKFCxdO6VjieF/7+/8PCuMVwV4rkq4IxbSF2Vc/b9Wj+N5OfuJLty8/BYFiIzIv1aZgr2XJO0RbqAPifM12bJEmlsOUFchpLujCf4Uth0v3ZfoxO9S/Ls9YUKvz4vKmGpo3AbsvdonX5yWrioVB+GniWPTt0ribRMykXCKRLTsnFzoAVFVBRgNe+u0JXP/G5fjNvmGMx3U+nBpUbSRtvA4EVMcx9lpUe/PnoJCCSaxQiOrnFStWIJ1Oc+n3+PHjSCaTXP3c0NCAqqoqV0Hg9a5SBgw7ro/smPaEy3bZYl7iLVu2oKGhAUD5itB7oa+vD+3t7Zg3bx7Wr1+PEydOIB6PT9l4AwMDaG1txbx587D/QJex4Hjwg6FezmmkNf5LrMo7zibWgp0TDtWqc/G0xrVeC/ILGPmKhRJkwdtGKg5pz/lAuPMPlxqFsYnlMGV3xqAETt6Ue3a5Z+tfkSwtxynn+KwrR3+293ZVsLdd15ACmSOXG7zVzHYpl5Gswvs1Trtt6syygAD+c18Gtyxvw1u3N+HfnkuCEAI1GHBKxpQiGArJ/VEzG5Xty22UibTe9/RrWLrU9famBMFgEHPnzsXcuXNBKZW8n5n6WUy+wbLIFaNSZl7KswH33nsvnnjiCQDwcylnwbQnXAAYGxtDa2srwuEwWlpapFSJU0W4lFJ0dXXh5MmTuOKKK7hkW0jxgkLHYyFG69evN/KhUhiSLXVR+zkgECtbUO1KXCKTnDA6TNHLs1/neQJDMnKXJJ3v3KQzYS45hFIJNrtwNrldlhotgmSrOq9mwzjRVaIS5HwivDZfsOP2sXi/QhIJTrrWzeR4b7sT077N6s7K7kj2fpzPnIjzgSF1i3ZT97F1EBIACz1i38VkBvjPdgXvvPIMnq5qwlgqIHxHLduwElC5Z7KzUD3l0xQ0zdye+08/TWHHVpcpXQIQQrj6edGiRdB1HaOjoxgcHMS5c+dw5MgRVFZWor6+HplMJsfv04l4PI558+ZN0ewvHf7mb/4G3/72t/Fv//ZvuPHGG+HbcL0x7Qn37NmzOHz4MJYtW4ZVq1Y5vtRTQbipVArt7e2Ix+OOtJCFlufLB5lMBgcOHMDIyAgPMZqIT+Z1rZuUm02alQkZknTEqESQO+HFhA4bI5OiAMChapavFclSOiY4S4Hq4OpYywANOyGIJMjnLEqM9itsEqrjtQfcbJyeY3j162pblg64a6XFexIcjbI7TxmfHVPVStcItlW71GkxnjVfRVGFPqxzFAQ/O1SB31uXxHs2j+HvX5FrsFJTilVVRZau4aYqZvNnaRKNb9/IeD5ql0sDRVFQW1uL2tpah/q5r68PmUwG+/fv59Kvl/qZIR6PXxL/k6kEpRQPPfQQRkdHDbIF/LCgLJjWhEspRV9fHzZv3sw9DO2wZ5sqFSMjI9i/fz8vFG+P6S23hDs+Po7W1laEQiEpxOjPP/q3APPkhDNOUbbjOr+chJUhdUi6jHTdr3NpzS6yHbExgyj5iRIeXEJmvCRUIr+WCBgwSdi0NZrrsCPSJg/181TD8Vl5ved2UZtHsSTNQn6e0v1Q4ZmY722fCc+jbL7nLYhIyIwIdRjqfka0iqVmFu28APdmVlUVT3dW4vaNE/jJ4Qz6JlTheoJAMCARLZ+XdIya90aF7yag6xSKOn0XXlH9HAgEuL13cHAQp06d8lQ/M8wGpylCCC96Pzo6OmUJh2YLprXcTgjBli1bPMkWKJ+ESylFd3c3Xn75ZSxduhSbN292TaBRTgm3t7cXL774Iq8qJMbz/ua3r7rO0Q1etOkaByvwp3jaYTdlbfmCT60/SdJ0lAmQJVJ2vajKzib52V7b+xYzKxtNxL69n9H0guyDyR8TmHZClOjh/R5u75mq3LKPWt8DKj0rj6mZFYnEpcE+jtFnIBCEogbw3x1RpHQFf3jFGG9LCIEakG2aVvyw/Zj1faJUN+245p+uo38wlX3O0wC6riMUCmHRokW48sorce2112LTpk2oqKjAuXPn8MILL+Cll15CR0cHuru7MTY2VhanqW9961tYtmwZIpEIduzYgZdffjlr+5/85CdYt24dIpEINm3ahF/84hclje8GZsMt9W82YsbfVSFF6L3AylN1dnZi69atWL58uadkVA4Jl5Ufa29vx8aNG7F27VqHik2nck1TN6ceUZXsJQcQIgiJIpeB5fH18BUWJVoukdgzRdkkWj6gKA2Lq6vZF80ybzshSO8ZubqoQU3vbPvnxkJMeD+2/p01YPMhbHlOxPZO2o4Q6z2h1DpnPlMxAQdsz9Z9PHcYnyeTSMU+sxE0k1zNHoiRC9mSbN3bEkUx6uma801lCP7fIQUti+MIB4ysVIFg0OR44XtMrPSPzudsEKyuU96WVRl6+LEzOe//csPuNMXUzytWrMC2bdtw7bXXYvny5dA0Df/0T/+EZcuWYd++fXjuuefQ1tZW1EbxRz/6Ee655x7ce++9eO2113DVVVfhpptuwsWLF13b79mzB3fccQc+8IEPYP/+/bjttttw22234eDBg0XftyvE3Xwpf7MQM55wS5VwJyYmsHfvXkxOTqKlpQX19fVZ25cq4aZSKbz66qu4cOECmpubcztN6MIPkboQBKwFyoJIlkzCsfUrqjDFQuiiChOMTpySCZem7HZEV4KE9SNitkPBecbbYSfHj86N6KkLGfJz5mGBgJ3xrs4xHWsBFBD+P7ONoRG1pm23j/L52p5Z1g2GPFfrvFAogBULkMha7MP+XuzHkkaJopplAO0kK382alA11cQAI2AKgp8dq0G8+wz+eNMYgiwGV5BaAdg2laJWwhqB6tb9Ut0g4eOnEs75TzPkisNl6ud169bhvvvuw3PPPYfKykp0dnbiDW94A+bPn4/vfOc7BY351a9+FXfddRfe97734YorrsCjjz6KaDSK7373u67tv/a1r+Hmm2/Gpz71Kaxfvx4PPPAAtmzZgm9+85sFjeujeEx7ws1lgyuFcHt7e7F37140NjbimmuuySvDTCnjjY6OYu/evVAUBc3NzZ4OEy/sbQVb7MQwCSvRgTusU86FkhdCB3umNmIiRKiXKvRD5GOMj43DzL4n9CWRie29eF6YizECFYZy78/uEGWXrh3Sth1u0qR9g1AsRLWtCGp7PtQ+JuC8X7f7p2YBeRWCCZtPO5uamYLKGzW26WGSLNuUOeZj9aUoikG04qB8HIoEDeCZk9XYOb4XEdWmATKvd9U+CFPSdcoUFZYWiQJ0CqICyo1C4nAVRcHGjRsRjUbxxS9+EQMDA/jxj3+M7du35z0e27gzRyXW74033oi9e/e6XrN3716pPQDcdNNNnu2LRjnUybNUpTytnabyQTEEqOs6Ojo6cObMGWzcuLEg1/xiVcrnz5/HoUOHeMKObMR57wOP8teGHGJKI9SUAGwLpKhktTyU3bIViWKseKXVA0+eYdytfL3RibM/vj4LJOYm4dlAbOQrkyC1QnRsNkwGm3LZ/V0+BFxuOCfmPaZgl5Vt7lRKqyhrLfKfN1NbU0tzbBKtKmk++Pj8WZs3QQyzjaI40zRaN6sgEFLxYnwpbq3pxPXR43h6bB03Ohj5mMWNhE0rwjzcBSc73ZRuZ4pqsdjUjlVVVQiFQnjjG99Y0LX9/f3QNA1NTU3S8aamJhw9etT1mp6eHtf2rGh9ueBnmvLGrCDcZDKZd/tkMonW1lak02ns3LmzYLf8QlXKuq7j6NGjuHDhQlZvaxEdXd0AnOZKwJByFdfdn0WexsLpvsAZCzDTVNolWmNQMauQtR5S266TWPZTpiml1HDnJ8w71uhELCRvHwviJoD3JxM3VwcT+Vpifw75LM5lWcDFybixq4fEL7Zg4TqsB2Kz59r7tN27VK3J9t54XFQiSaIwiZaN6HigYATL3qpBFYr5+XqleCQKEAwGQBQFPZkYjiUb8TuxTjw9tg6MbA1Vq0GmxnR1ECJ6PBt9GvtYo28towEgoJqxU5hMaKiIlKfO9FTAT+3oIx9Me7k9H5VyvmFBQ0ND2LNnDyKRSFFky8bLV8JNJBJ45ZVXMDQ0hObm5rzIVoax+Og2O670nh2kAER3HWnRti/gbh7Mzuo+ov1XIjdXiZMRrY0qiBEpTBSY3zbBduqlbuZztp2jMpE5HKL44CahuH53XOyZ0ulS1ZeC6t5+htlcTbsrk8CdjlM57LjGQaFjttEC1IAKRVWhKIx8mXOWPEdmruD9W/IoVNWw0ypcMrUPbZCzGlCNMndmEwU6nh1djhplEsvDQ1B5akZj/rL/gSjZO7/TVLNMKgDwg/8ccM5jGqFQCZdSWpKXcmNjI1RVRW9vr3S8t7fXU2M3b968gtoXC99L2Rsz/q7yUSmzLE779u3DypUrceWVVxZdD1NRFNObMvvCPDQ0hL1796KiogI7d+4sMIWbkxQcNjgOY+mm3EFJdHhh56nUmkEhgKIaUopDWhTspdy+y1iCS505yIt3RaSF33CktRGLXf1tO+asSmRziIItnMaV0A2bJRHnoygyKdkKuTvIkN2A9NqUIK2pSGTqublwSIziW+ezsYcHAcb3UVVVs/i5eEm+kryl/lcDKgKhEC+fJxOyzudEFAXBUMAYk58HdChoTSxAd6oab685AHAJW5DE2aiCY5auC97JoNAzxliUUuia8e8rByemdchXobmUJycnQSktOvFFKBTC1q1bsXv3bn5M13Xs3r0bzc3Nrtc0NzdL7QHgmWee8WxfNMQ1oui/8k5pumBWqJSzEa6Yxemaa65BbW1tyeMBxpfbTYXE4nmPHz+ONWvWYMmSJQXZ3Ox9sWt1ncIQOMzFV2cLpSFtiHZec7Xn/XC7rsc0nJmp7OpjyKpmk+xYNhgC+w8ki/qYS97UIm17KT5jUvLltunbCdkxBZd+cn8OLukZXebiaaQV2mUz47rfjTvBioRPCOE1ca2mAmnbtRBEKL3HSJMI1XoIBVECZk5jt/u0zwcIhgLy994xV4IXB+bi9nmdaFDGMaBXCvdq3wQSUJ0io5kJL8w+Mmnx92y0Gx5N4fnnn8+aSOJyolCV8sTEBACUpFK+5557cOedd2Lbtm3Yvn07HnnkEUxMTOB973sfAOA973kPFi5ciAcffBAA8NGPfhRvetOb8JWvfAW33norfvjDH2Lfvn0Fe0f7KB7TnnBzLZLZ4nBZDuZIJFK2QvGMcDVNc0jJmqbh0KFDGBgYwLZt21BXV1dw//0DQ+ALkueGnljmTxeCNcCI2LyCt3Gz34GrIA0pQjWFLJPUrQ54X8y72FDrCn3Z7bBAdvWxqH4lhNfPZQ48VOwjF2ykL9uIczTPG9mpNP/r3LUYVrwzzOcgSNyGsZc1lu+N29nN93YitL1XFNVUb8uVfZzOU8Y5RVWhqAGpeLy9QAHMfl/JrMJbTj6PXTWH8Z/6NbAyPrPvrXXvhmRr3Yem6WBZ1EQtkqIouPLKKzEwMMDzGFdVVXHyra2tnfLKQtlQqEp5YmIChBBUVFQUPeY73/lO9PX14Qtf+AJ6enqwefNmPP3009wxqru7W3omLS0teOKJJ/D5z38en/vc57B69Wo8+eST2LhxY9FzcAOFAlqi8rTU66crpj3h5oKXhMu8gr1yMBcLS+KUVcrxeBytra085KeYItYA8IMf/rf0nuq6XIQcbMEi3IvTIClAliTc7pcdF6RLdlhQLbKedMke7A7uhMW7FxIvcEccD7Jlb8U2TALmZG8QurSwAwArOiD2UQ491JSossxNCe9bkFr5W2P+iqLaiNeDYHMQqjS2OR4hxJBmJZL1APsemEku2BTtOZHZv4pZrJ4QglESQ0dqLjb2vYj/qL2G35uwGzDNMhp0wXta1ym0tPC70pm9X4Ge0Rxl9FgVn8OHDyOTyfAi8g0NDaioqCjbbz4fFKpSZh7Kpc7x7rvvxt133+167rnnnnMcu/3223H77beXNGYu+LmUvTHrCFf0Cr7qqqswd+7cso5HCHGM2d/fj7a2NsyfPx/r1q0raaf9H//9W4PABCcStsjZc+4aEgnkY9m+qHzxFsnWnRQJIVDAPIxhtSX23MjWYm6tyqw5EarvCJsAD/KQeiTW4mypnq15OkKK2DwgqqW9HsQlhCCdKkThHsmsXKCbZ7IzTtrqJ3fVKFFty8rpqVwjIW6qJDWzeS2FDgLVJFq7BGwbhlAACs8exaBQDa+ENuGP4r/AstQZnAotAf9khNvSM5YanOoUVDdIlz0f/hqwpZo0Ekk0NTWhqamJOyANDg6iv78fnZ2dCIfDaGho4EXki/XZyAfMp6NQlXI0Gr2km4JLBb88nzdmFeFOTk6itbUVlFI0NzdPWa1JRVGg60bO1xMnTuDEiRNSCb9ScOGCLS2bTVh1Shg2/hLfsNeUGhKhALaQgRE2v062YzLrMJ9KFjLgbxWB/JgalPOAi3NWTgK2bwic10iOTrA2BnzO1JoXezZsM2BtXwwVrv3e7BsAI5zHfPasf5HIxHmzEVgbcb6Sqt3VSp0HZILlKR4lZzA5w5NDKuZaFGMzqQaMUnzcO1r4blEYRQvY/fJQI8FmrBMVbaH1ePvks9iebMWp0DI+R0pNWs/I90sB03ZrHBM1SGwcLxBCUFVVhaqqKixZsgSapvEqPl1dXZicnORF5Ovr6xGLxcpKdGyuhUq4s6UWro/8Me0JN5+wIE3TuJTZ1NSE9evXFxyEXghY7G9XVxdGR0exY8cOVFdXl6XvdMbFHi2QC6U6dN2+4zdiGIkiSi8AGKkKC73x1iJEIrQRzwmNJZIwBGORfJySsfSeLZTELX+uTTr3gENBnnOtFKQ58SKRpD0IUiZXfhNCW9m26T4VQ/LLqm3wvM52xFVFbM2Y/cvCjQBWTk8gM0+p2LTzKwRqgOVQdm58xBq20nhiV8L3k8DIFHQkuBLrU8eh0gw0EuBaFS0jbEbMzySTEkP7CHTNqFxEKYVCAF3XcL4vjQVznAVF7FBVFY2NjWhsbASArEXkGxoaSvbtYBv+QiTc8fHx2Svhwk984YVpT7i5wBJR7N+/3yrcfglw6NAhVFZWorm5uSzOWA4wqQEwNHFmvCIBwGIaCVPh8sULwhosS3NCx+A2XLOdIYmKF3upfwmM7I/E1p5dozjai+/t0hbPJCRMz5DOrIWeS+DSHdglXvs8PUg6n99wXr9zJzHmdVUW+6rbwCwci8XDEmISESWAKMHmtMnan4YhiRKiQFGJGbcreDMTKl8rlEVUVCu0ip133BchIFRHW2AtrkodxtpUJw6HjcxTWsaodcs3g2YYkOF1rxgSsK7b9kZGmb/eIWBBoaHsACoqKrBw4UIsXLiQF5EfGBjA2bNnufMVUz/X1NQUbBIqhnBnc9ILX6XsjRlNuOl0GocOHQKAor2CC0VPTw8SiQSampqwefPmKdmh8vAbkSh5qVJLDUgJgarYCEyHSaLUSUqsHYTlV/QKti/+btKnJAmLUhQgS4GsD/vgNgK2zZ/HrTK7NVF47LNz8nxSLtOcqh1yoareLOdNRyrRjmvkvFaE7wCkZ2TYZHP9bO2bJxmKajpCuUnBpsmA2ZjZZ2WQPlf4Qkz7aXk2s2EJKFFxPLgC8YyKpYlTOBRaC01QI7PPU9d0cHcILgEbpEwp5ZqqQCiA7osarl6TW8LNBrGI/MqVK5FKpbj0e+jQIWiaxp2v6uvr81L7Mg/lQr5z5SjN52PmYdoTrteXeGRkBK2trTxwfKrtIZRSHD9+HGfOnEE0GsX8+fOnblE3hVDbDIQTBFIojnAhtQyzVoiN1ERSLtsut0vF4kTcJTDpNd8MsIMspZ8wnk3sFKUjN3Umk+itGGAqmQuYpO2MJXZDrs+rXJ8nkV6yT4AQ8AQZhroURpk7QLahCxsXp4o/l6TMHOnYMeNzUVTFDAUq4B4J4UQrbQzgNgfh8zfPaUoAr6RWYsvkK3iq4gZYzlnWnDMZDYCwwdCpq6YmEFDRM5j/1PNFKBTCvHnzMG/ePFBKMT4+jsHBQVy8eBEdHR2IRCJc9VxbW+vqfOWndZTheyl7Y9oTrhuYKmjlypVYtmwZnnnmmbIVhXdDKpVCW1sbEokEdu7cicOHD0/ZeGqAQMsYFV4ktTKsl6KXKXPYUGyJ7qUwSjuRmuo87utiO8cuJIKXMpdoBWJwOC6x61QWb0kgRk85HK5cNMO51MfuNmMzVSJ7LCCOeFHLDkvZ/2UCYf8ltoIN5kZC3LZQUIcTDwEBUYWQKJFM2XU6zNzEFgELAzmP5bUBEAnKYipjPiofz6l2tpO0LNESBYJNl9ra26+3fxWMc5RSvFzfjK0nX8XyxEmciKww1I2mB7KesebOCs7rTOUMK0sX81dIaFOrZiSEIBaLIRaLYenSpchkMhgeHsbAwAA6OjqQSCRQU1PD1c8srKfQkCBglhOub8P1xIwgXBYmoGkaDh8+jL6+PmzZsgUNDQ0ASq+Jmw0jIyPYv38/ampq0NzcbFZOKa0mrhcSiQRECYfdNwdlBGiFB7GMUxJEUoUojdgYjrWjzkIAnDztk7T4GNIC7EKEBICqCupgyFKoq8OU3WPZAW+it967SM6i2tzkECLE8hpCpwJLHhVJmRjExY4J7617t3kDO26BClVzxNuViwJQas97nE2ilUmPmOp3w+4bkPp12OXZHPmzNDclAjFLDnigtvasA5fPzzyl6xSDSjU0KFg9cghdkZWS2pjqrCtjbhbZml2Y0rgaMMhMUS/tIhwIBBzOVwMDAxgcHMSpU6egqirq6+sRCoV8CddHXpgRhAsYX9D9+/dDVVW0tLRIiSWminBFSXr58uV8ASq2RF82DA0NobW1FYSYjmAw70cSCgWysYX/6Lpu2T8FUI2CKCb5eqkTCSMXWP26SpIApeJiy0eBU1wlAjkT6wrRHksUaUPhqqJ3zAOONd4pJrs0cVwi7RzMNjZpWmwr3oPHmHbkjpl1Qza9OFOfUz4vVo2HhQLZ21pdUvGGpPnx/NJe3s1c3WuGBHE7rPidMaVac8BMOgOAQFfCOBtZhNUTR/E0eRsopUinNDPO3PjisZrP7LtgD7NimoI8a5RMGSoqKrBo0SIsWrQIuq5jZGQEg4OD6O3t5YVKmPq5uro6KwkzL+XZCN9pyhszgnB7e3vR3t6OhQsXYu3atY4vcrkJV9d1HDlyBD09Pbj66qv5Dpeh3BLumTNncPToUaxZswaBgIpMSuOxvm62STnDlLV4ggJQBQnZZFFu17WpDWVVbbYZWgTPJFtCBGrgmaDsasccBGwWvLdIVyZga1KSUc/Wr/eU5ffOa7LbQgtBvte5kan93pzHCXt0pge3QgzHKTebN7vWKIGnSOekYzDU2/bUjq5zsJka3O6V6pSnadY0tjEwkmB0VK7GjQO7EUqMYhxR6TOmMIhc0yB9hywhmiAQCoAQYCqCAYqFoiioq6tDXV0dotEozp07h0WLFmFgYAAHDhyAruuoq6vj6md7Csd4PI4FCxZcptlPLXyVsjem/TaCUorTp09jw4YNWL9+veuusZyEm0gk8NJLL2FkZAQtLS0OsmXjlUPC1XUdhw4dwvHjx7F161YsXbqU5zS24mxtC6BIsDbipKBWhiq7apYai6IhSdilSSKrGdn14r/S4s4OWckP7HO122tt8qE0ppWgwUi8oIhSG3Hr17yhrESX+wdb1p90NsE062jOCwmBIbmqilluT0EgFEQgaFbocWgqKORdmfAdsTmtEULMCkNWWJHZWO7DtKlaGhW3+xCJkyKT0QyyFcbViYrW2GbolGL96AEQPWONZ9qfDYJm/RnzYzWfg+GgYVutqUAkOD0XYV3XEQwGMW/ePGzYsAFveMMbsGXLFlRXV6O3txcvvvgiXnzxRRw/fhznzp3D6OgoT+1YLpw6dQof+MAHsHz5clRUVGDlypW49957kUqlsl533XXXSb8/Qgg+9KEPlW1ePmRMewmXEILt27fLko8NhdTEzYbBwUG0trZizpw5uOKKKzwdIcoh4SaTSezfvx+6rqOlpUXaAasBBVpGN1TBuqkSphQ8JaO5SBqp74xr+MKp69BBBbICawDAUttxZylmpyVupCbAbrvzsKHKmbD4xXBkmHIRlOy2QyJI1LxvhS3+LD2ic66WFGfZjl3hOFzuBT33+EZaRMXU4jPJ325/dbveTRq1n6PgHsAEfBNjtXFqE8SsU1ZPlnZCLG7AzBA6pdDNJFFiaBFrP6pUYQIRLE+cwsux7XxIXafG91z6XjHNhzFyOBICQFEZC0OOD54+sHspi85Xy5YtQyaT4ZmvfvzjH+OBBx5AZWUlkskk2tracOWVVxZhepBx9OhR6LqOf/iHf8CqVatw8OBB3HXXXZiYmMCXv/zlrNfedddduP/++/n7UlXdFGVQKU9/WbAozIi7yvVlLFXCZfVyX331VaxatQobN27M6nVYqoQ7PDyMPXv2IBqNYseOHRLZEmIQLiAG0lNLkyc5rDDbK1sNwaURaqaepHZJFca6RXVTqHFzuhJhLqCU2Y3h/DwkGcqcqEggznSOjBBkide+qbJLxZZEbSaEUI3EDWqAmAkcWBJ988+sf+t2fyKpSPdaFIijK4N8FG5jZdKqGlChBgNcYlUUAlW1sjw5NyuFz4k5Txnjqjz9olcBePOFeVzUdLirj3krSpFJawbZ2iVkEFCqQ9coMmkdp0JLsGzyJB+LAtB4VjWL/BXFGjNcETak8YCCYFBFVXT6SrjZ1otAIIA5c+Zg7dq1+NjHPobf/va3qK+vR3d3N3bt2oWFCxfi61//eklzuPnmm/HYY4/hLW95C1asWIHf//3fxyc/+Un89Kc/zXltNBrloVHz5s0rOWseUymX+lcovvWtb2HZsmWIRCLYsWMHXn755aztf/KTn2DdunWIRCLYtGkTfvGLXxR7y3ljVhButhJ9uaBpGtrb23Hy5Elcc801edWvLUXCPXv2LF555RUsX74cmzZtcvxQwyFjAWYSiXHeZeFji5tOeV5nO3ROurYTXBplf+KiSxwLJ3tPifljsC3SzlAe4b/E+uO3IaoyjY7EadmOOnt2g0jGikByimqoTznZmSpaQgBVNVIaqgHFJD3hWuFP7lM1/4RrAwpU1ciGxP8CAfO4asbAMklTvPf8FxXn52tTFZv9M5W88ytsI1irY5uNlm1EDOJ3eMlT4zulaxRaRvhuSb4ExnXppAYto0OhGk5HlqIyNYaglgAFbDVvjWuZtG/Ympl0C1RWhg2pMTp9Jdx8w4IIIdiwYQMaGhrwl3/5lxgcHMQPfvADbNu2rezzGhkZQX19fc52P/jBD9DY2IiNGzfis5/9LOLxeEnjGnG4Sol/hRHuj370I9xzzz2499578dprr+Gqq67CTTfdhIsXL7q237NnD+644w584AMfwP79+3Hbbbfhtttuw8GDB0u691yYEYSbC8VKuPF4HC+++CISiQRaWlryLk5fjISr6zoOHz6MY8eOYcuWLVi2bJkrsQdUZss0E+s7a31DUukyidbD5krZIimcsy+6VNOha7q3GdIxT2NBNfpkh9ycndhsLaIR/6QWDmccDw9fhxTsLYWJreTbYRmdiEzU5nHnn8JzFdvvwf1+2DPKMS1X2CVFt04s2znbAFjqd/GenddSptoQ+xefvUSwwvjm561nNGhpaiY3sc/VaKfrFOlEmvsT6ETFiYplAIDlY8ehM7uiYOuVw9IIwtGIuVMDqqojCAWBqlB2e+TlQjGJL1i1oFAohOuvvx4tLS1lnVNnZye+8Y1v4M/+7M+ytvvjP/5jfP/738evfvUrfPazn8W//uu/4k/+5E/KOpdLga9+9au466678L73vQ9XXHEFHn30UUSjUXz3u991bf+1r30NN998Mz71qU9h/fr1eOCBB7BlyxZ885vfnNJ5vm4Jt6+vD3v27EF9fT2uueYahMPhvK8tVMJNJpN45ZVXMDQ0hObmZh4/7Aa2UQ4GjReEEB6HaBGTCdviSHWDNCVVsnmd6DDlALffGYsl51BPdbN1jEm81CEZS1NzXs9DUgTCEqVgl6+m3T7o3rcHnGJ+vleWGR4kKDmBiW0UvhkxVMWqJS3b+nV7/JbjlPeGyHoWNimYyHVrmUQrpdkUCdkM+cmkWNUfa8ye0DxMKBEsT5y2qQuN75hYjCMQVBEMGykcQyEVwZCK6ioFIXV6SriFFp+nlObtNPWZz3wm6yaPEIKjR49K15w7dw4333wzbr/9dtx1111Z+//TP/1T3HTTTdi0aRPe9a534Xvf+x5+9rOfoaurK+/7cdxfGVXKo6Oj0l8ymXSMl0ql8Oqrr+LGG2/kxxRFwY033oi9e/e6znHv3r1SewC46aabPNuXC9PeaSofFEK4lFJ0dXXh5MmT2LBhQ1Gu+YVIuCxxRm1tLbZu3ZqzLichrJKeYZ/UNcOupRFNMq9R1tgGtyQW4jnjMisxhJsUqevGAk2I6ZIkqBzd1e3MnmyyJRULK3hIqo4135mCkknGIgHYL84rrMeVW10cucoOL0cmN8hSvr1AgGOzle94/LMTn53cjyM8iurcaYXqRh144uawxD4bs9gAi70lQrYu5oSl6xQXA41YmDpvOdSYY4q+CgBBWCgeX1tvOPDEKgmigXSO+788KDa1Yz6E+4lPfALvfe97s7ZZsWIFf33+/HkuMX/nO98paE4AsGPHDgCGhLxy5cqCrwdQ1tSOixcvlo7fe++9uO+++6Rj/f390DQNTU1N0vGmpibHZoShp6fHtX1PT09J886FGUG4+ThNue187Ein02hvb8f4+Dh27tyJWCxW1HzyJfhz587h8OHDWLVqlacK2Y6QoiEYIEimgFAogMRkWhhT5wsogagaNhdXQVIlCrEcX0QbHTUSxvOatTbVrtiWUkDXNJPA2aIvz9fVfkuIsPQrltaSdUpcHJaygI2hiKp0dv/2+Vtn+TGnuhoC2crSMnEQInG0k4nT6z7sx41nSGzEaSWeyLVguxG1uMGwpFNrs8Pa5Cl9mc9T1wEQS21MHJ+X+aQoBahZUpICbs/CqH2rAZqGC6F5uGaiTfqOiSk4CSGoqKyAGjSeRTiiIlIRhKIAlRUE9eE4KK3N63d0KTGVqR3nzJmDOXPyK5F07tw5XH/99di6dSsee+yxgjcBANDa2goAmD9/fsHXTgXOnDkjOXEVoomcjpgRhJsL+YQFjY2NYf/+/YhGo2hpaUEwWHzVEZaUwgu6ruPYsWM4f/48Nm/enPcPBgACioZQMIBkCtwLV9coVyMaUoQBwoiNOomPeSArHtmlqKk6JmChNhTUJvGalMwXVibRWGEhJomIJAiXZZepnM3+5NaAp2XDfk+2vt0ldHNTYBIYl+ohX8w2BrLtkrrMRdJz83GZileerput2J6w300dnAse7anuIaWz+bpL/HaJ1lBpm6XxNA2UGgkx5Pb8jdFeIdAyOnRNA2wbBtGcYYT9KFBAcS68ALvG9yGMFJIIc9szQyAU4KpkAKiuNaTb2hhBQKUY6zuDPWdOoaGhAQ0NDairq8upMboUKFSlrOt62VM7njt3Dtdddx2WLl2KL3/5y+jr6+Pn5s2bx9vccMMN+N73voft27ejq6sLTzzxBH73d38XDQ0NaG9vx8c//nG88Y1vxJVXXln0XCgloK7FVQrrAwCqq6tzek03NjZCVVX09vZKx3t7e/m92zFv3ryC2pcLl//bWgbkkjgvXLiAgwcPYtmyZVi1alXJO+Rs46VSKbS2tiKVSqG5ubngmLagokNVFQQDOtIZWcolhEAJqGbOWUvNaJfR7NKsoircZiouwgSm+tiUiI3TgoQLG8FRY42nMGvzEnDy9VY5y1Kp3Mblc+DqYw8brr1vRyPnNXye9r7EY4SAeJEhcSNX97ZZv1sUcMaSUpnQ5MbSEV3XTanFjUjdVMbuKmyxUIGRo5xm+UwsyZlB0zTQtOg/QG2XGdKxntHML4nhONUdWgglqGB16jSORtcJakcKNRBAhDlKAaiKhVERDYIAaKhVEQtOYsWyNZiboRgcHERXVxcmJydRU1PD0ymyYgKXGoWqlOPxOCilZU188cwzz6CzsxOdnZ2OmuDss0un0zh27Bj3Qg6FQnj22WfxyCOPYGJiAosXL8Y73vEOfP7zny9xNgpKj6PN//pQKIStW7di9+7duO222wAYv5Xdu3fj7rvvdr2mubkZu3fvxsc+9jF+7JlnnkFzc3Mpk86JGUG4xcbh6rqO48eP4+zZs7jqqqswd+7csszHS8IdHR3Fa6+9hpqaGmzZsqWo3XdAMcg0FALSGUPKDYUDSKU0gBql6QjMmqEiyVFhEbYRINUpJ2ZJ0hOlHJ2CwpCIifledGRxtDe8s0ChS6SbmxI9PkvuoOVCEtRdUrPfa6mY8sU6n/7Z/TASc9ivASep8ovhRsaiVsJQGbN/xVJO9mnYpGBdB6XErFVrjGVX1fMat0KRefG++tQ60FAQczP9OAbLOS8QVBGtivLmgYCC2nojNr2igqAiQhALJRCoakCDqqKhoQGrV6/G5OQkBgcHMTAwgNOnT0M1z7FatqVosQpBoRIuI7xySrjvfe97c9p6ly1bJm2cFi9ejF//+tdlm8PlxD333IM777wT27Ztw/bt2/km4n3vex8A4D3veQ8WLlyIBx98EADw0Y9+FG9605vwla98Bbfeeit++MMfYt++fUXZvQvBjCDcXHAjXJbFhUma5fxyu43HpOgVK1ZgxYoVRS/e0VAII0kNCAQQUHVkNCNelDlQASbhq8zGZoCI1kebJAuAx0dCUbj91zFFnUI3ddQ8fWAWQmMCm+XUZEi/IALR2yq82KVoNnc7oUjPz1zYjfFYhiNRkreRUj6S8CWCawEDab7mZ+VKrPJ7N1u0Uz0sq38ZeVMwBygNoARQsvcjOk5ZlX28pQ5dN/rVNcNDWXKcMnM4E0XBoFqHJgxCJyqM75mCSDTCv2+UUtQ3VvJY4nmNhkRfHUw4SK2iogILFy7EwoULoes6hoeHeSWfw4cPo7q6mku/sVhsyjZUhdpwJyYmoKqqVIBlNuFy5FJ+5zvfib6+PnzhC19AT08PNm/ejKeffpo7RnV3d0taiJaWFjzxxBP4/Oc/j8997nNYvXo1nnzySWzcuLGkeefCrCTc4eFhtLa2ora2tmhJMxvEsCCxMH05pOiVi+dj4NgZZDIBVEQIxiYM8guHDdUyNW2pRrIPI36WgS0oBme6EKapQnT3ZCbSWk51QKOaEXvKbZvyouzmMMXsvdRsK0lX5hzsyCK/2hpSroa0HJxsxEsU1w65GpW9J2WiYfG+XO7RngrRU/VutycXNTnLo5tLm5pufgXccnN73A8hPC5b1yzbtjVl85j5XdR1HTovPuDWv1UkoV+tR70+YhxVFFRWV0oLYXVNBJGKECiAqghBZVRBNJBEUM3upKgoCpdsV61ahUQiwaVfttiK0m+ojJUQilEpR6PRy6L+vhS4XMUL7r77bk8V8nPPPec4dvvtt+P2228veJxSMCMIN9cXU8w0xSrvFOIZXChYWJBYmL5cUvQtb70N+zu+BgLTlhukSKcNO2Q4EkQykTYXUwJVUUBgLI6ibdBQH7vnGWaglILqOlcDU0Kk9iYtWM5VRAdhu3juBJXdYYpSAJpukKQp9XJplhEDiItjl6X+tE3I2c5uh2WTEE2MxihOO6ON15iSU2pGCNvBSMfYZ8AJ1G0+rC3rR7qZLFK423eWUm47l4/rgClNssLulLI4WDZvDzuutDEwHKcM8tRBdWIrkiA9UFCY7TO64C0u98fSavKEIVRHn1qPLeljCFeEEQwHJaIKVwRRXWelOZ0/15CCGyLjiEwMAljufC4eiEQiWLBgARYsWCCV0uvu7nZIv9XV1SWtE4WqlCcmJlBZWekTbo4+ZiNmBOHmAvNSPnjwIC5evCgVp58KMBvu3r17EYvFeGH6cuCaa6+D+uUvI6wGkNBCqIgQZMyEA4qqIBgKIJW0PJUVMw0kd6QyJRnCiYLBkkgAwTzIvZMhkZxDSDQdsAAYDlYg3LvZU2qzD08pNMrq9oJLwFabHPZYF4k6H7g5QxE3pwzm2ewY1p1IJUmWtStyocirdi4zC7DPiBomAEJ1UNukBX8kuCX9Fx2ndJ2akrDolyBeY45nxtRSmN7HYluHyoCAqKo5D+vE6dAivCnxCiKRoJTgXg0oaGyK8SpBjbUEkTCBSnTUhOOovHgewNbsz8cDYim9lStXIplMcun37NmzIIRwybehoaFg6bdYCdfH6w+zgnAzmQzS6TTGxsbQ3NzsqD1ZbgwMDAAwYtVWr15d1p2qqqoIaGmEAiEkNQqFEFSEgbgZZhwIKABMJypzUVRVFQpRpJAhAKaW2CQ1mwpZIlRKhaxSBjHbHabE9obUaxC86N3qlNmcRMXV3tz2S6BlNF4bl8B0vnLYZ50Lmqsq2uWzuHSSRN7K8dw9GUHQPDzHsMEyuyrlmyUQJbtDp5v92FQDUyjQdY1/DqLdlc1BdLaioNAyrHi8MStrkyE6bFlSrShhU6Kgr2IBlFGKqDaBiYARB68GFMyZHzM1HRShIEFTo3FTcyvGoFINwZGBop6jG8LhMObPn4/58+dD13WMjY1x8j1y5AhisVjeheQNrUJhEi4rPu9LuNn7mI2Y8YQ7MDDAg7W3b99ecAB6IaCUoqOjA6dPnwaAKVNZB7QUlGAUFYE04pkQQkGCjE6RShvkEQyq0HWjCgsDUQjUIEuOYR5jik6m1hQWRjcJj9lfRcmTSSju9lpGmqa9VlAdG5Jz/vRDTbWtsbbr0KgwNgwhjQoET3UKJeCiep4BcLNrs2OWDZxpIKzP07jY0ZvbCOBPntmOYXgOG+piw+PY2sN4PD9TXW0krzCvcX3WItGaUq2wEWMIR8OoUJOASlCpjWMiEIOiEsydV42Amb6UKARLFgSgKApCSgYNFeOIxAdBAlNTfV5RFNTU1KCmpgYrVqxAKpXi0u+BAwdAKeWF5BsaGhyJF5ind6FeyuV04pxuKGcc7mzDjCBctx85K6nX2dmJ1atXe6bwKhfS6TTa2toQj8exc+dOvPDCC2UpQm8Hk2wUPY2gYqjUNCioCFuqZQAIhwNQFA2ppOVMwpLsy1KIAStNovHOHA3iwgxB+oTOwo4YadsmajtAucqZAMQgD547gdlriQKSF0EK8zAtq4rObL6W4VXX2T6YbQ5cpDnx9aUiZsl5SpZ6jQ2KYSPlszNzYNu/Tjy1ptS1oFXwsvVSw6zLHOR0zXSUkz53t0tlBy9jqkwC5rMSr4Ak0YpSrXDbiqqgojKKQDCAcT2GYEUIiFRAUQia5tcgELTIam6DoUoGgPrIOFRCER3vg7Juh+ucy41QKMTL1FFKufR7/vx5HD16FFVVVVz6ramp4b4jhaiUmQ3Xx+sPM4Jw7WD22uHhYVxzzTWIxWI4evQoMpnMlEi44+PjeO2111BZWYnm5mYEg0EQQkouQm8Hqyik6DqC6ST0cBCRQBoT6QgIASorKCYmLVVsMBQApcQsdWaqBQEEggHomm7adU3Y7awS8covObgEC1AiysguKR5FRyDzOh06H9NoT41E0fawGDt5e0xHagBwhy7xhCG1ifMjgG7GCuuClxR1knRedlRxNIGILOlUmBP3ypKlVEIIdLtdtci9gLg5YpoMTdOgaCwntjUmxGfi3puhtTBLPsoZpDw+FSKqj0Wp1jR3BFREKiv47zKhREADAawL9eHE3CUgAev32lBLMKfOeB9WU5hTMQY1lUQ4OYrgouLy+pYCQgjPdLR8+XKk02ku/R46dAiapvEsSKlUKm9T1qyXcH2VsidmDOGyBW1iYgL79+9HKBRCc3MzwuEwX/jKTYCAke6rvb3dkaWq1CL0diSTSezfvx+6rmPXm27Ab57/NRSqIaQQpEgaaRqEqiqoigJjEzpf20JhFaqqIJmQE7uzGqxu0q4hkYgCoCzxEumYecZIsCurifOUGq2avGY8p5nVinL+tRx4jH9K+bGJ0rE1TbnCDQxJWzwAcDuyo0fiMicCyKFVRqiVnOSfmqQlS4XOGGh3idOV5ExvYt4BpdBNpynxc9Ztc3Pri3IthvmMNFuqSMclcj+sPKDbBSy+NhAKOp7diFqLKElAVQjYLyhWCcxr5CoRLKwaNjaZYz1AjrStlwrBYBBNTU1oamoCpRTj4+O4cOEChoaG8OKLLyIajXLpt7a21lPq9Qk3vz5mI2YM4QLAxYsX0d7ejkWLFmHNmjX8C00IKbomrhcopejs7MSpU6ewadMmR47Nco7HMlTV1tZi06ZN2LRhA377/HMIZBJIh6oQDaQxllahw6iTWxlVEJ+kYNmQA6oCUhFCKpURpBqD1ALBoCNel0GSdrm6GQ7bq0TAprZQzxgxupyk7aE9grON1Y9lf2UKYt20C7IxKQVUGwlTF95xl9JK/ZGWcr0Hadrn7nYvpupcbmeqhhVR1W+kYVQUAkp1i2Bd0kw6w36YhlvUCuigumL2QyHH2lpSqvUeABTP8oCsDZdqA85MT9HKEPTxCEJawtwUUEQjChY1WXmV50VHUBVIgFBDnZzpueDo53KDEIJYLAZKKXp7e7Fz504MDQ1hYGAAR44cQTqdlmy/ovTrq5Rfv5gRhMuclU6ePImNGze6VrIQY3FLRSaTQVtbGyYmJjyrChVaE9cLLEPVypUrsXz5cuOHXFMDOjkJtYIgHdShKASVwSTG0kZmmmCAIFoBTExa/aiqgnA4iGQyLakS2TlVVaFlNOhMvSqAOHbiLjZeOwi4g49hWVUgOkwZb/J7BmKyDACG17KpHrWHlVhE7KECvoxOVA7JNadu3LsfwKjURCkxJFiBFFGoQwkFWNwsCyUy+nORyD1BTKL1Kr5AoAYUhCMVCISC/D5YW6IAtXVRVMbCSPeHgWAIIAoqIsDShYaWBgAqA5NorBgDCEHVyDkohCLZVz4P5XKDZZkKBoOYO3cu5s6dyzVxAwMDuHjxIjo6OlBRUYFoNIrOzk4MDw8XXanMC8uWLePOnAwPPvggPvOZz3hek0gk8IlPfAI//OEPkUwmcdNNN+Hv//7vHWXrCoUv4XpjRhAuYNg3s5XUK5fEOT4+jv3796OiooLba73GK0WlzDYR3d3d7hmqEgmQiiiC6QmkwzEEVIoKPYWEbpFuVZRgMkG5s42iEFSYkq4mOFgBsGy7ui54MsuMYDnjKAKZwkFgripngTQNe6GhYpXUxXkRoWFr5YmyzDlSjQIs/tfU/CqqC+mK3r8uc7/0sOy6YjyvPSMU1XVAEzYxLBRHjI11JXB3dTH3MDbtyrpOQfVsvw/3nYJhf/eucMSefygSQigSgqI4fy+KStAwN4aKCsPTOK1GUBUFamPA/LkBHg4UVDQsqhoyNDOpCVSNXoCemIR6xfYs8768cAsJIoSgqqoKVVVVWLp0KTKZDIaGhvDyyy/j05/+NPr7+7F06VKsXLkSN998c9lCC++//36p4HwuUv/4xz+Op556Cj/5yU9QU1ODu+++G29/+9vxwgsvlDQPijJ4KfuEe/lACMG6deuyElw5CJeprBcvXow1a9Zk/RGUIuFmMhmpLq9b1RCVKNAyaQQIoKcT0AIRRII6aCaNpBYAQBAMECACTMQBrtolBOFwEJmAjlQiY/NKtjyZqU6N+XsINYwceBYhwebpzGElq48NT2uYSS5g9KNTqIwgYR4zr8t7sTEJnQnQVNdklbVCQMx4Yi4YUypJcVMX+ygTKZuk8Q/lKmKY81cU50/PmT/a0QCOD4xvnOTnT3UAuvz5imFV+UizxvcpeznBQDCASGXE1V5JCBCtDKK2oYpLsACQDFSgVhvCwrkqz+msQMey6n6EAjqIrqN24CQIgPTpk6j+8AezzPXyIp+kF4FAAHPmzMGtt96KW265BW9/+9sRDofx1FNP4dOf/jTuuOMOPPbYYyXPJRaL5V1ebmRkBP/8z/+MJ554Ar/zO78DAHjsscewfv16vPjii9i5c2fJ8/HhRKk1lKYNSiFcSim6urrQ1taGDRs2YO3atTkX5mIl3Hg8jhdffBGapnmSLQB88LP3AePjAIBQehKEGtWCKgIZBBWNr8fBAEGsClCIHCMZUBVUVIagBszUiSIxEQJFVRAIBqAG7E4vkCREwvrl0hnJc9G2ujLSDVJompEG0BDgKO9fkkhLAHMcMrxsjXAYXdOhpTLQ0hq0tIZMKoNMSkMmLfxlNGhef5px3tE+rSGTzpj9ZZBJpY1/eRvd7DdjeIybz6DkW2XSr+DpzfrXzHkaxQZoHh8Pk47NrhTD41hVAzmJVg2qqKiOoqKqwp1sFYL6xkrUz4kJdRKMsVINpkmIGe1BsahqEBHVcI6KjvUgmI5DHx6CPjpeVCH1S4VCk14oioJQKIS3vOUt+J//+R8MDAzgvvvuK8tc/vZv/xYNDQ24+uqr8dBDD2WtEf7qq68inU7jxhtv5MfWrVuHJUuWYO/evSXNQwcpy99sxIyQcIHckkmxhJvJZHDgwAGMjo5ix44dOYsdMxQj4bIkHQsWLMDatWuzLiTXv/0d+PYDfwV1chKkogLB1ARS4WoAFJXBNCbSBBmqAiBQFYKqGJCYNEr6MRBCEKkIIZPRkU5qjsWeEAKiEh6po2U02UuVwRH7KThb8WM2OI5Z+YetcBrdyMegWLWOCDFSBxKBUPIfw6VJzhbgjmCubMgdmoSeqFXKUGo3BWsEZTZ3QXrVGXELKR2JxK5m3mXvXq3JmmE9xks5n7ajLYBAWEUoEslKMtHKIGrqolCFdKeUUihEwfy5KuaMDiOtRM3vGsXS2ABqwikABIHEOGLD50ChQzt3FuPnB1Cf9QldXhRaKQiQnaYqKyvL4kD1v//3/8aWLVtQX1+PPXv24LOf/SwuXLiAr371q67te3p6EAqFUFtbKx1vampCT09PSXPxbbjemDGEmwssn3IhYCFG4XAYzc3NBeVQLUTCpZSiu7sbx48fx/r16x0For2gJ9NQApNAKIQAAJqOIxOqBAhQGUwing4jTY2PUCEEFRUUaoogkZQ9XgMBFYGAinRKQzptn7OZ11gxPI2pWWKNqT/dlCAi+coJFfgdu96P8ydEuPrZ4m7dmIfl08zDb6SKP66l4gr4kU6Jc1Vp4itP+A/LNsqkYipmnNK9Mj4J08h6awoPgVJykAUbJxAKIBQOQlEDPN2kNRgAEASCKmrrKxGpCNk7QWUFwby5AVSEzc91zlwwso2FEgAlILqG+v5OEABaby+QSiG45uqs87vcKDSPMmCsO/kUn//MZz6DL33pS1nbHDlyBOvWrcM999zDj1155ZUIhUL4sz/7Mzz44IOO7FhTDT/TlDdmFeEWInH29fWhra3NEWKUL/KVcFkyi4sXL2Lbtm2oq6vLe4yAGjSSNUxOAlVVCGQS0NUAdDVsxCiGUohngJRufIyEEEQiRoanRALgUSPGSYTCAQSCFKmUZhYSdzpNEYVAUYOGCjhjVp3JwiNiBSDLfml3wOGzkK8152UHt3WalxMYccfEtPsaPlmCI5J7B5fWYSorATqduOSiDRAcpOyqYKXw23Cz9ZqmAVYmL8tk2QUghCAYDiIUDluFKuxDKYadt7qmAtGqMBQrvRjvq7oSmD9HRTBkjduQPo9g9TlYPokUdX3HoWSSgK5Dv9iL5OAo4u/7c4yMjJRc0WeqUKhKGci/eMEnPvGJnEXlV6xY4Xp8x44dyGQyOHXqFNauXes4P2/ePKRSKQwPD0tSbm9vb952YB+F43VHuJRSnDx5El1dXdiwYQMWLFhQ9Hi5JNxkMonW1lZomlZUUYVPPvItfOljH0JAUUDNRPah5DhSEQVUDQIEiAZSIBqQ1Czv0FCQIBQgmJjUDRWzsE4pCkFFNARN05GcTIM79phgJEgIgRIyvIypZthfrQYyGG1bkq/Y0CwVKGUs8ugoK4hFxBRQzLhVHlXKtK5i8gqW6Yk4ZXBPFnPq3aXjniQvdSETLOXcw2yvBBSaox9C1KL3CKJ0bPbGVdE83WIe8bpEMWLag+EQVFUxCNqrTB+AqqowqmoqXUsshkMEc+oV1FQRqeB9pqoGJKwhqGgAVIBS1AyeQig1DkIIMmdPg4Ai3jOMhFkCk1X0YTVty1nPthQUqlKmlCIej+cVFjRnzhzMmTOnqHm1trZCURTP+txbt25FMBjE7t278Y53vAMAcOzYMXR3d6O5ubmoMRmMr3upKuXZiRlDuOWw4YopIbdv346ampqi55NLwrUnsygm5eS2G26AlkwjEAkDY2OgsWoQRUEoMYZUJAaqGll8ooEUVKIjoYV5GI2iEMQqVSRTOpIpAinvBaVQTacqTaNIJzUzdteIpxWftEIUIEigBKjkkGR2BNmJyoIovTILLSEyuVvsItsUnZ25SMGwUTYTrnXhDWDW+dVtfRAQXRiShcC4qbEIgeEGYpEZJYIHsjwciOL8TrgmiShZWrM/AdmjmIXzSM1B4bUOEmKkCg2GQraEFfLmQVGMz7KyKoxYdRhqIOBCyIYKef5cBZGwmNKMIqxkUJPuBw02GWnGAMSGTiM6OQgA0C72gI6MIB1PIJ0CNm7cyCv69Pf3S/VsWVKJWCx22aTfYlTK5c40tXfvXrz00ku4/vrrEYvFsHfvXnz84x/Hn/zJn3CN2rlz53DDDTfge9/7Hl/7PvCBD+Cee+5BfX09qqur8Rd/8Rdobm4u2UPZVyl7Y8YQbi4EAgEkk0nP8/F4HK+99hpCoRBaWlpK3iFnk3B7enpw4MABrFixAitWrChpMaBpDelECsFIyPBajsVACBBOjiMZqQZVjY8wEtCgKklMpMOW1AcgHFIQDAKTCaPakAhCCIIBBYGAUWUolch47kyZgxVUApUyL2BdkOZEAnD2oUjSlixZOTWVuaXg/J8pdbf3Cumr2CbFdVtNrYIM8rWKuxnZrYu8Q5/cjK8ez4Io0qZGUQI5pVcHCDjJKirrL/tNRatCiNWYYT4uKuagStA0R0UsKpR4JECAaIgFE1hQNYJwYhSp2nUAIYgNnkbleB8oIaDj49B7LgAZDWPdF7Hkb75s3ptV0YfVsx0YGMDAwAC6u7uhKAon3/r6es/Y+amArusFryXlJtxwOIwf/vCHuO+++5BMJrF8+XJ8/OMfl+y66XQax44dQzwe58cefvhhKIqCd7zjHVLiCx9Th1lDuNkk3P7+frS1teXlHZwvFEVBKpWSjrF0kKdPn3ZPZlEE3vS2t+M3v/g59IBqVEJNTEKJVgKgCE+OIFVRDWqWLgsqOmrCCYylgjDqprLFmKCqUkE6Q5FMAmkNEBd3QojhWFWlQtOBdDIDTRMNwDIIMbIKqQG26VDM8m3M0zj3fRGBfEUSdhvUIo7C1dEzf59MTHIl/MESRZGlVwDZPaUMiZrlsFYDAQRCAaiqKtt0XQhUMZ3pKmMRVFaFoCiKo1YyG7uummBug2rUbLaJ/42RMTRGEyAEUNIpROIDCPdTVMTNLFKZNLSzpwGdIn5+ANpkBpXL3QsWhMNhLFiwAAsWLICu6xgZGcHAwABOnTrlkH6r/v/2zjvOjrpq49/fzG3bN7ub3WTTe0hCyqYRRAFBIBDIBkVUxIAICgKCoCBKVQTElxdFBQtK5EVREgJIlUAC0k02m957257tt8783j+m3LK9ZQvzfD4L2bn3zvzm7r3zzDnnOc9JTe3R6LejEa6u691OuAUFBXz00UetPmf06NHxpQ7A5/Px29/+lt/+9rfdthZwVMqtod8QbmdSyrEj/DqiDm4PEiPc9phZdAY3Pfor3nlpJRF/EHdqEgQCSEVF+HwIJJ5ALWFfOrrqNlJ+AtI9YYIaBOy6rvHeuV0ClyoJhwWNwbggz4alaNZ1STjOsar5tK9hpKGiugxXI13TQYoE7+aWU5mxEDEtKvYrZWzaOirMai56s9uJYmrIzWmou4xOtQC152Yhep5gfuZFc+TaMSiKgup24XK5UN2elr9LCWIrt1slJd1LckpS868R4HZLfF5BbpaK1xPz9xOGmYVHkQxPqSLJE1NjjoTwhhsQjUZvMuEQkQP7IRwmVNdIuCFAoLblbFXiuQ0aNIhBgwYxfvx4AoGAHf0eOHAAl8tFVlYWOTk5DBo0CJerey95HRVNNTQ0AHTb9aEvwkkpt4x+Q7htIZFwNU1j8+bNVFVVdble2xxia7hWutrr9XLKKad0u6BDhnVwS7RgCFeSF/yNSCFQvF4E4A3WEfKkoLu8YApvfK4wblWjIexBxlywhVDwesDjEQRCklBI0GSYEEZk4/W5EQgiYd0ejGCoVWOfGSO4EQLVpRo1W7fLFFzp0Tm50TOivYyVWIuMevOqTZS+Ik6s1caxWhNNxT0UW2du47WtwTwHg9LM9HpM/6vxWCK5Npvjpvn3Ll75pqoqqtuD2+2Ku4lpeeiA8X+3R8Xr9ZCc6sXtUVt9jc9rjNNLS028jBhryfLWk5vaaAjcUEDqCKnjCgXA57VtJ7VjRxHBAALwH6tCRnRCCy9q5hzbhs/nY9iwYQwbNgxd16murqayspI9e/bg9/vJyMggJyeH7OxskpOTuxz9dlQ0ZaV0neEFn04MKMK1+nD9fj9FRUW4XC5OPfXUHulDsyLcjphZdBZTPnc62z7+DyIEuqqiuFVEYwNSEeByowiBJ9SAJnXCHvOLLAQuRZLuCRKSEn8kPtoVQpDkFfi8EAwZNd7mYIhpVNweFV3TiWgQDkXis49NelpFNGWsKKhuQCj2nFUZV/uFGJ1zh96XeCtEEKLphc8y0ojbFhtBxkHa5JQ4dL1plKk0S7zW8+LXFt+KY9VKE8f2NYsmNwDNb1NU1RA8qaqZOm5fdKwqxg2Xx+MiKcWLL8mNK6EGGpvSF0Lg8whyshSSfc0J5iQeRSM/5TgpHs0Q3ZmLVSNBMit2Q7ARoRo3TJED+xD1dUgpqT9YjtR1GisbYF7X/ZMVRSErK4usrCwmTJiA3++3o9+9e/fi8Xjs1POgQYM6JWzsaEq5sbERl8t1wntjTyQk0HEPvqb7GIjoN4Tb3pSyRYBDhgzhpJNO6jFbOCEEDQ0NFBUVdXu6OhbBYJAzr7iCre++g/QpaP4gQvEZM+zq6xEpqUiPkSZ0h/0oWoSgL92O9oQAnxLGo2g0hN0YnZ7R90QRgmSfIMkrCQQlgTBNU8jWc1UFr0vB43WhaTrhkDnNprkQOQG2q5WqgNuwexSmUMmwJkz8inaOhFs6dtzvxNdE7e0xhg7xhJlAXOYNRrPq7I6IuWLPTRrq57ZfbUTGbo/bmHmsKqYgTYnpgW3lqDHtQy63QkqqD1+yN87ruKW1JvsEWZkqqSnN9fIalbu8pHqykxqbZBt89RVk1B1GCYVQFAXd70crPYasq0MIaCyvIdIYIFQbBKH2yPc2KSmJ4cOHM3z4cDRNs6PfnTt3EgqFyMzMtAm4PX2y0LmUcnJycp+2q+wqnJRyy+g3hNsWFEUhGAxSVFTE5MmTGTFiRI8dS9d1jh07ht/vZ968eR0ys+gIrNYiRTFG32khDdWrGvXclCTjetbYAEjw+pCAqodJ9h8n6E1Fd/vsfamKJM0TIqyr+CNe8w40Ph2c5BMkJQmCIQgEoZkRuvZzrVqv5V8cDhvewUbJNZqibAmKopjRD7afc+wsX13XkXpiJEyb++23aJaoBcL0vFZUaw6tcWMQR65tGjRbdXCjLmtFsqpqEXXLF38hID1FIWuQC5+naWZAMdXb6W4/uSl1eF0JNx1SJ636EMn+SuPGIBREKgJt1w5z6ZJgdQPByjr0kEbEHyb7F/9LZQ8PnVdV1SbX2Oi3oqKC3bt34/P57MczMzNbJNWORrjOLNxPNwYE4WqaxoEDBwiHw8yfP7/HCBCiZhaBQIDk5OQeO1ZpaSkbN25k7NixVFRU8N3//RW/vfl7yIjhras1BlCTvUYvY2Mj6DrCl2QPhfeG6tD0MCGPKc4QxgXXo2p41EaCuht/uKmARggjzez1QCQCwTCE7XYi2YTuFNPw3mXWbHVdomkQDmltR74JqWh7sLkQqKj2U8yVGX3AUprRcFu1TGH/1s5qcbue1Tm0LphSTLMOoahG5Koo0bQwIJpMFmofwYLx9nq8bnxJbrxeF6rb3aoq2YKqQmaaQkaqgsfTtOXI+tuluv0MTqkhyWV9SKLk4w7WkVlzCFckaPTvSgmhELorWn8PN/hpLDmOAgRq/Ahd4s7JQSkra+Mcuw9CCJKTk0lOTmbEiBH2OL3Kykq2b9/e6jD5jtZwrQh3IMNRKbeMfk+4fr+f9evXG+bopmKxpxBrZjF69Gh27NjR7ceQUrJ371727t3L9OnTycvL4/jx40yaO9dIv0Z0hKqgSw38IVwpPuPi5feDriNTDIIVQuCOBFD1MGFPKrrii0mFQpIrgleNENY9NEYskVd8xOt2g9drKJaDIUkgaH0RmqcxIQSqanjqen1ue4JNOKQnRMstCZma2WSlboUANfpEJUY0ZamjjdNTjfSsaezfIqU0KwRqJ9qZNhbCeL8UVTVqq2ZrjkSa21zx5NfOtHBb63G7XaguBV+yF19SK6pkG9G/R1qKICNdJSWpJb9m433yucLkJNWR6gnjUhOjbUlKbQmpDaWosS1fwQDs34+uGjdW4YYA9YcrEVISrAsgNUn6nLnout6rKVdrnN7gwYNpaZi8Rb6dEU11h1irL8NJKbeMfkO4zX1Aq6qqKC4uJjc3lzFjxvCf//ynAyYDHUOimUV1dXWXBtA3B0tZffz48bjJRYqioOs6E2fOYGfxBvRgBNXrQg9HiDQYka6iKBAKIfVaRGoqSMVQMksdb7AWTQsR8lpkbFzMFFPN7HVFCETcBCIumhtWoChGutnnlWi6kXIOhczLdCtvtaIIFI8Lt0fY52CMrdPRwu1ULrey/9g+XiM6bk40ZRBdLDkbQxBiRE8SdLP9SFVVI443+VfqEqGqRu+rFTXrhrhKUVWzFoypkhYopuAoTiTVXA1YaX38XUeguhTcbhcpqUm4PWZ9Vco2fJONmy+vx1hreppCWoqCSxXN13PNm7UkNcTg1FpS3EEjjrHOy3x/3aEGMmoO4dKCKNb7LiXU1qAdO4K70U/E44bGAHWHyhFSEm4ME2kMgyaZ+POHOHjwYJ8hJCGaDpOvqqqisrKSrVu3EolE2L17N7m5uWRnZ+Pz+VrdX3sHF/RnOBFuy+g3hAvYF04pJYcOHWLHjh1MmjSJESNGEDbznp0xE28NLZlZdGUAfXOw6s8ACxYsiFMxWmT14Iv/4uJRI5EStLCG6lGREQ2tIYCSaqa5IhGorYWkZJSk6JffFQng0kKE3MnovpS4dK4iINkdxquGCUsP/ohpnJGQcjScqQQet4JMNpyrNE0QsP0/2q7bejwKHg8gFGNIvS7RIro5ezZR7dzy/jp6YxVnspHg0gSgmlFz8y9uTjTVfDTa7jUlnlpCD2zzTwJFFaiKSnJqEh6PiuqKEnfiUPvWRvS5XYK0FIXUFJUkX1uXAUmKO0iWr5EkVwiXW40uDwxy1yOkVR8iJVwXbaQypztpR48gaquNjWGNutJq+7VaSCNcFwAp8fiMz3xvR7itweVykZubS25uLrqus2bNGtLS0igpKWHnzp0kJyfb0W9GRkaT8/g0pJQdtIx+RbjQ8vQdi2Q7M5+yJcSaWcyfPz/OcLyzA+ibg5WqHjRoENOmTWuyfotwFUXB7XERDkVAl+ghDcUk3XCdH3eqz8xjSmRjA1LXIDnZ0Ppatd1wA1IPmX27HkTMRV1VwK1ESHJFCGkqjREX0hgMSOKFX8RERylJENYEwZAeYx+ZUEtthiCFInCpinkBN2qLUsesA+tomhEN9zmRVLPkaKBzGZZmiFURtquTLzkJtzueXFW1vV/d6L4VBTLTFdLTVDxuKwpuZq1m25EAMjyNZCUH8bmav7l0BRtJDteRXF+KkEY2ADDm+IZChA8dgHAY1TxOOBAyU/4SPaITrG40VqdJpjzzLNC3CTcWVtZk1KhRuN1uwuGwHf1u3rwZKaXdlpSdnY3X6+12l6k1a9Zw5plnNvvYJ598wty5c5t97IwzzuCdd96J2/btb3+bJ554ostr0iXN9vZ3dB8DEf2KcAOBgB0FnnrqqXHpG+sLGolEusV4oi0zCyvC7WoKO1Yc1ZLvskW4AL//4GOumjPbuGhpEhnWDdLVdcL1AVxJHhS3WRsMBiAcQianQEzErOoRfIEaNNWN5kk21MwxEa8Q4HVpeFQNXegEIi6Cmst+LBFCCGNCkduoq4Z1gRYRhMKSiBZ9TnugKEbrkBVF2fNhAU0zarVaxKgJC1prSZKtH/eEpCxbMd0QxrmqqmkWYqbFvUleXKoSR4SK2hFvYGkfQwhBSrIgJUkhKUngUo0ovrU0s4LErUoGef2ke/2oQprfrVjlsVnHbagktb4UD1rMQ8ZjWlkpelWlQepmZipQXoMaMO7IpKYTON5oXFk1icfjwpORCfQfwrUyXNZa3W43eXl55OXlIaWkrq6OyspKjh49yvr167n33ntJSUkhMzOz2wKDU089lWPHjsVtu/POO3nrrbeYM2dOq6+9+uqrue++++zfuyvydlLKLaPfEK6Ukk8++YTMzEymTJnS5MNqCHY6NhO3JbTHzMI6fmcJtzlxVEuIJdysvDxUVdhex7qmQxiESwFdJ9IYxJ0MwmPMtBW6DvV1yEgErC+UMKqRLi2MK1CLHgkS8qQYgxASiNet6Lg9IVJkiJDmIiw9hPXmo17jNQKfRwEPpIApuIJwBHS95VYj89XNbzXJQ1EAtwoIexiC9V5qmkTXzbKDbg1XkGi6OTgBa5A7La69Y2hprYaZhDB/pA4ejxvVrdo3EwKJ4lJxuZoSacdFU/GKZJ9XkORTSPKAxytwudv4ilv8jE6aO0CGpxErURI9p6iwS40E8AUDpNSVomph4701FchC05CRCJEjhyAUQlWMOrmMaDSUHkcNhgkEwqAo+KsMspWa0RU+5q57okuSsl8SbiyEEKSnp5Oens6YMWOoqanhW9/6Fr/5zW/YvHkzubm5nHfeeXzxi1/k4osv7vQaPB5P3PzacDjMiy++yA033NDmdSk5OdmZfXuC0W8IVwjB3Llz8Xq9LX6QXC5XlwhXSsnBgwfZuXNnm2YW1pesM+O5WhJHtXas2PT1j5/+P+772mXmog3lsgIItzFbVGsMokc0XD63Lc6RAT8iFITkFKTHY0dAAsMBKEkLoakeNG+yYRGZ2LIjwOeKkCw0dKkQ0FwENDPl3IZwKsknSDaPp+uScAQCIYN89faol9uA0RfcfE1VSUi9GiIei6wtUY8lmjKN+WOCZk0zRhkqqmqnWY2MqzAcmYR1Q2D+v5mpPUIo8R7Rpmiq44h/f1TFIFiPR8HjEqSlJgwiaOkY1t9WgEeNMDi5jhR3wB5ZK4Qr/rmm8tjXUEVKfTkeEdMjK8z3VNeNqLam2tBjmSSsBcP4SyqRIQ2v20XtcXNajdnZJSS4klxkLjjN3mV36zB6CtY623PDnZGRwTXXXMOOHTvw+Xx89atf5dVXX2XdunVdItxEvPTSS1RWVnLllVe2+dxnnnmG//u//2PIkCFceOGF3Hnnnd0S5Toq5ZbRbwgXjDuy1uqmXYlwW6oNt3Ys63UdQWviqJagKIptWwkw67Ono6oCXYsO4pMRHV1ipJelhFCEiKbjSvGZLoRGzY6GevSQ25g45HLZEboR8YZw+UNI1UPYnYTman5tqiJJUcIku8KEpYuw7iakq+hSpa32GkUxar8+r+GQJMGwi4wYkbAuBU3e0oTvXleywdaAhCaWh6Jl0VQTwrTPpSejsKbkaqTtDRVxRrqKS21aV297f5IUd4hUT5AUV8BQJTd3HiYpq5EAKY11JDVUougRI9Ud895JXSKPV6GVl6FI3RSlGSnjYE0DgYoa42ZQCCLBSFT9LSVCB9WjkH3V1XEpVl3XT+iIvc6is7NwBw8ezIIFC7o86L05PPnkk5x77rltOt997WtfY9SoUeTn57Nx40Zuu+02duzYwfPPP9/lNUQzSV3bx0BEvyLcttBZwrXMLDRNY8GCBXGN7S3Burh15HiWOCorK4upU6e2+y4+McIFuOfZZ7n3q19Fi+hYU3+kLtGDESPSVQBNJ1LnR/W5ER5XtBUlHEbWVCO9XhRfEsLjsS+wAlD0MGowjB5S0LwpRNzJxkU2IeoVAryKhs9lDHiP6IJgxEVQKmYNxhIXtUwEhvLZUM2mJCt2vU/TDCIOhkHXjWHvcenoOOFSP7sbtpfbdP2KALcbPG6rRUeQlqIarlAxSPy95WMYU3tSXEE8Lo1BvhAu62MnW/7buEKNJDVW4PXX4E5oE7Ju0vSaGmRFGcJyRjGjXRnR8JceR/Mb8nUhBGF/GBkyvivSrNsKReBJcnNkyAj2/ec/DBo0iJycHMLhcLu+g72NztRh2yuauv3223nooYdafc62bduYPHmy/fvhw4d54403+Oc//9nm/q+55hr73yeffDJDhw7lrLPOYs+ePYwb1/xYRAddR78i3M6M6GsLsWYWJ598cru/QFbNuL0RbnvEUS2hOcKddspnUFSBphlpOSSGOlkItJCGy6OCeVHWAmFkWIuLdiUgQiH0UAiRlARJRipJYBgzCLOH1xWsxxtqIOLyEXYlgdI03WzBpUhcnjDpqoYuIaS5CGkqIc0Nwqz7ttW8i5UiBpcLknyKXa81XKYgHBEG+QoFTTPSvkZNuyUCib1d7mlybv1YVurZpRq1VpdL4FINAnWp4PU2/Uq2Sa5xxzZuRFyKRrI7xKCkIF4lYr/lRhSfsD+pmzdUOu6wn8yqElyRQPNnFgpDOEikvAwCgfjoWEKwuh5/ZS2KtENZgg1hXEIQCoSN6EeTCGGkkkd871YGLVhgm0uUlpZSXV1NbW0tmqaRnZ1Nenp6n6zpdib13djY2K4+3FtuuYUrrrii1eeMHTs27ve//OUvZGdnc9FFHZ+0NH/+fAB2797dZcLVEehd/J519fV9Ff2KcNtCRwk30cyio+Kn9vTidkQc1dpxmnoKw73/WMFdl3wRzfIwxryUSqO/UXEb4hwwxFWRukYUrxvV47a3AxAIGD9eH3g9CG88qQrAHQngjgTQw250l4+I24dUjJS0FRnHrdms+fpcEZAhdFQiUrVJWNrGE+0jYbBucsDlilpAJr5PulFONH+MerFlnWhti2gSISz1rH2vQsuq4mZXg6pYBGr8aLpRr1ZVBUUx0sC6FHg9itHWo5oCLmkaZ3TGVcqCPTHIeA9VIcn0BklyhfC5wigYx1BbOob5gRGAJ1CPL3Acj7/WIEIrojXXaUW0sr4evbIcEQzE7MZ4LOIPEqqoQQuGo4/pklBtABnWSUr3EYpEP8OeJA/eJBfpp52JlDLOXKK4uBiv10swGGTTpk1IKe3e1uzs7D6Tbu5MSrm9fbiW01V7IaXkL3/5C9/4xjc69f4UFxcDMHTo0A6/tulanBpuSxhwhBtph+m5ZWaxf//+ODOLzhyvtQi3o+KoltBchAswefYcXGbNVouY94QmAUoJelhH6hLVEyVGPRhGD0ZwJXtRvYaS2eA7o41IDwYQXi8iORlhDuuOVWK79AgiVI8n3ICuuAh7UtA9SZj5xGaJ01A7S9wYPb4Amq6g4SIiXYQ1lbBUY17ffhKOP45AFQbRmVtIbSYCaa4mK4SwBVaxNzeG9sgaHJCY1m369VGaEdEIoZik30nEkavxtqS4g3hdYXxqGI8aQRHED1c3hV0t7c8dqscTbCApWI1b6vaLmvNM1mtq0KoqDOWxwM42oBsZFX95DaG6RlRLrWwaswRqgyjmZycciH4vXR4Xqlsw6u6HkFLa31mrNUpKSXp6OsOGDUNKSW1tLZWVlRw8eJBt27aRnp5OdnY2OTk5pKSkdKktryvoyQi3o3j77bfZt28f3/rWt5o8duTIEc466yz++te/Mm/ePPbs2cPf/vY3zj//fLKzs9m4cSM333wzn/vc55g+fXq3r81BFP2KcLsjpWyZWdTV1XHKKafEmVl0FK1FuJ0RR7V2nOYIt7Kykq89+AjP/OCm6AXQzKzavKVJtEAYxePCumkUAiINAfRgGDXJg3TFDxoXIcO7UbrdyJQUhNsdjXLMYwuMfl41UIMI1aIrbiIuHxGXF6l4opf6lhTlqjTUrsKs60mISDc6CppUCesKYV2F2EgYuqejpw3E2zJaKuQTdVGPPUGJgjDJNYJHjeBVIqiKtCcstb07K10sUfQIqXXH8AXrUKTZ0iJEvJrZepsjYfSaWmT1cRQt/ibWUnYHq+sJVzcYkTDRG5VgfRA9ECVRAYQajcjX5XPhcqskZSQzaMYsdF2P+4lEIgSDQZuIFUUhIyODjIwMxo4dSzAYpKKigsrKSg4cOIDL5bLJt7MzbTuLztRwe8pp6sknn+TUU0+Nq+laCIfD7Nixg8ZGQyHu8XhYtWoVjz76KA0NDYwYMYIvfvGL/OQnP+mWtTiiqZbRrwi3LbRFuJaZhcfjYcGCBV02yGgpwu2sOKolNEe4hw8fZtu2bcycM4c3hw+j9OBhdGG490DTYFMPRUBVDDtIacyilZpOpD6A7lJwJ/sQ1hQX64XhMHp1NUJVEL4k8PnsqDcWBvmGUUNhvKE6dNWDdHnQXF40l9cm+pYiYDA2e5SIWa+NXuB1BLp0oaGiSYWIphCWmDXhZtDKMXoVsTn/hOUp6KiKjqJAmjeIW9HsH5EYubb7OAKhR/AF6/AE63CHGhDI+EED5vOMl5k3VKEg4coKZH2dsbaE1L2UEK5pIHC8DqHpcTciWkgjWBtA6NF0ta5JUlI8hCJhVK/hluVJ9TD5T4arlJU9AONmeMuWLQBkZ2c3G/263W6GDRvGsGHD0HXdnuqza9cugsEgmZmZ5OTkNJnq0xPoaEpZSkljY2OXbvJbwt/+9rcWHxs9enRc1mbEiBFNXKa6E47xRcv41BCuZWYxdOhQJk+e3C0ijOYiXKsuPG7cOMaMGdMtkVEs4Uop2blzJ4cPH6agoICsrCz+5813WDptIoQ0cCnomowKqWKgazr4JYpHtWcUCCHQIzqh2kZUt4qa5EVaka71fynB34j0N6J7fShJSYaUFjvJGXcclx5GhCMQbjQcolQvui8VKVR01R29yDd5ZVOoCriFBiJ6wyFEEBBIoRipaSnQdIWw9OJSpf27bvbZNvkbNFEJx2xMvLW2UwUy4antUUkbj7sVDbeq41IkqjAaUN2qJMljiJtis82udls2WocwrC+FoiC0CO5QA55QA65QI249aqnYEgQgQyH0mmr02loULRwf4RONXLVAiGDZcWREj3tMSkmkLohmqpDtV0fM+r4icKcY1p3uZDdpo0ag+uKVurqus2XLFhobG5k7dy4ejwdd1203N+vfECVfIYRd17XILHGqj0W+zfkadxWdTSkP9Hm4jrVjyxhwhBsKheK2xQ466O7B9LEE3x3iqJYQnbQTYdOmTXY63OpL1nWdi675Ni/94fcQ0hCqIQ6SelREFcsJekgDBcOFSLVEPAI9oqHXNaK5Xbi8nmjtN+bFMhgwhogLAR4v+LxIxUiXGzyUUL8EXFoQl2Xph0BT3UTcyUi3D6mokNgT2yZMFbWQqGr0Im/9O+74igspDBGHbv5o0pj+o2DdjYMuFTThwaPq2PopBGHdhdul41KsWwuJLhWEAl6XMMRJwtiLjsDnNm4SFGHU1I2MrYi/2JtipA5nPmKiVwAlEsQd9qOGA3i0IF4tGEf9zfkk25FsJALhEJGKCsMC1H5R/PN0XRKuqSdY3QC6bo/bs96iSGOYcGMIIY33BiFANwRTihAoqjCTDgK3z4XX52bcL/4QtyZN09i4cSPBYJA5c+bYop/Y6FfXdbNdTIsj39jnpaSkkJKSwsiRI+2pPhUVFXG+xhZBd4f9a2f7cAc64TpoGf2KcNuKFl0uF36/3/69o2YWHYWVUu4ucVRLsIwvPvnkE1RV5ZRTTsHtdtsXH0VR+NL3buWVJ/8IbkNApQqBjh4NzOwSqJFORgctGEGoCoo9/cUUXIUjRMIRNFVF9blRfNGLU5yTUTBgELCqgNeL9HjBdLFqyfJSIHFpIdxaGBGsNZ6rqIbLlTsJ6fI0IeGulG2N66FpaWRtE00vlIZoKkxzaEKYJpqLRpsTTXUYViEeEUOuIdSIH1ULo2phkiMNKJbYySTw5sw5rOjUMj7Rq48j6+qQAeN7oibUp62MvB6OoDUGCR2vt4leIYaIIzrhmoDRU2u80lhxREb/XgLcZpuT2+fG7XMx/Lpb49anaZrdAz979uwWFbbW+x9rjmF9/ptLPSuKYk/1sXyNKyoqOHz4MNu3byctLc2u/aampnbqb9bRCFfTNPx+/8An3G5QKeOolPs+YiPOzphZdBSKohAMBvnkk08QQnRZHNUS/H4/fr/frgkDcWRrXSx++/5/uf4z8xBCIxLSUF0KUrd6VGM4x8qSCsCcyiM9iiHEiRVHmd7Mmj+Iy+tB8boRzYh1pK4jrNYiIdAtMw2Px24raQ52ylrXUHQ/nkjA4Bch7PSz5vYhXR4QCrrqsonYds4yfumGd7kXYKaDo+1XAqGFUSMhVC2IqocRukay5kfI+Bq+0sqF3r7ZkRIZDCIb6tEb6hGWv3EMYmcFCyGINPgJ1TSi+YMgRJOUtBbSCDeEkBHdnndrT5yKWaKiCjw+F95kI5Xs8qh4kr3UDB+Lx+8nKSmJSCRCcXExUkoKCgo6VKtOjH5jf5qLfi1fY0t4VVlZaSufVVWNE161dx2apnUoUm5oaAAY+PNwHdFUixiQhNtZM4uOQtd1Dhw4QG5ubreIo5pDWVkZ27ZtQ1XVOLIFmrSqJKelM+WUBWz58H1Ut4LUpJE6FgJN06Mlx5gPs9V9I0M6WlgiXArCbV7MrHBHghYMowXDCJeCJ9mH4ooZ7B5LeFKC34/0+w3iVFXwetFTko1B7vZrmjtb48ItACE1lIiGx0yTWjcBUijoqhvp9iEUBV2o6IoLXXEjm2ndsWayxsXJPUnQFonGEGnsyQpdAySuSAiPFkLVw0bd1IxcPc0MfxdqQjq62cyB+XA4hGxsRI+E0Wtro0TdiphMD0UI1TUSrvej6NGbGKtGa6SgdQK1AeMzhS0BMKBFFyAAl1sxCNbrxu01Ila3z43njocpLy+358Zak71mz57dMWFYAlpKPdv15WaEV/n5+eTn56PrOtXV1VRWVrJnzx78fn+c8Ko1RXFHU8qWSnjAR7gOWkS/Itz2tAX5/X4+/vjjTptZtBclJSVUVFQwaNAgTj755G4/jpSS/fv3s3v3biZMmMDevXvtiwm03Kpy6x/+wrdmTjbJKapaVlUj0tRNRyaBiLsGG3VLCRFjBq3qVlBMgwnrMevCG65tNC5ebheK12VEvsRcnK20NYCmQWMjut94DW43wu0GjwfpS7LPoaUUdOx2g4h1VC2IooeaPN8YMCDQhYpUVCNK9iYbqVehIK0flwekatccJQKpKEjZdDC98c5EjSDsmwJhRKNCSpPUJFJ14QmHUKWOkJoxqUkouPUgLqkZXsTWe6koqIlE2t6Ld2wKOBQCLYLW0IDW2AAxfeiqEk/61s2OEAJd09GDYfzH6wwFu/VhSHhPtUCEcGMYqTWt30rzJk6x0t6AO8mFqiiGutpr3IC6fC7yvnwF2WMNByO/38+6desAY+Tme++9R05Ojv3TFWOLllLPrQmvrJm1EyZMsIVXFRUV7N69m6SkJLvum5mZGUewHU0pNzY24na7eyQL1pfgOE21jH5FuK1BSklpaSmNjY3MmjWrW0VLicexxFE91Xhv1Z7Ly8uZN28eiqKwa9cuAoEAXq+3zbvqx95fxw2fmYOGbvyFdYmuYQuNtIgeJcVY8a0i7AuvHtaRER2hCBSPiqKqcb24Qkr0cMSo9TUEUD0uw8HK42q9bzUcRobDyMZGFKXGiIDdHqPX1+s1yNhEa6MPW4zypESVEdAN4lE1f1NiVhSbJGL3Z6VbY7NZEqPOqShNbSSatNgArmaibEURzRyv2dOKh4wfEC8jEYNQI2EiDQ3IQMAet6QImj2n2Bs0GdEINwQINwTQAsYNixpLyNZxdIkWjqDVh+w3I1atHKuAt16jqEbaWFEMQZkvxYOqqqheQ4CXff4SAEKhEBs2bCAlJYUZM2YghKCmpoaKigoOHDjAli1byMjIYPDgwd3y/eqo8Co5OZnk5GRGjBhBJBLh+PHjVFRUsHXrVjRNixNedbQP1+rB7S2jjhMFJ6XcMgYE4Vrq3erqarxeb4+RbaI46tixY+1ytuoIwuEwxcXFhEIhTjnlFHw+H8FgkLS0NN5//33S09PJzc1l8ODBLaamklJSOPPSr7H6H38zrogKCEWihTWDQF0CdGELXqwGF6nLJsGd1CVaIIIUmmEH6Y5GvfYF2kw56yHjvVA8LjxJPqN/16rhtnSR0TTQ/MiAH1mH8XzTSFm43EivB9ye+KiuG76MrZJ5wr9FwrbE53QYcRl4w0QiLiuv6xAOG+9NJIzmbzQjWQ2kbP6Ggfh92kMggmEijQEijUEIa9FzFjEEG5O9CPrDxlQfQCXhxsb8PBCzXQgjglXNmwrFpeBNduNN9to3GpN/vxwwyHbdunUkJydz8skn20SYmZlJZmYm48ePJxAIUFFRQXl5OXv27MHr9dqRb1eNLTojvLIsFqWU1NfXU1FRwdGjR9mxY4f9nNTUVNLS0tok0oaGBied/ClHvyfcWDOLadOmsWnTph45juUcFSuOKisra9KG1BU0NjbaF6T58+fbNWlFUZg7dy6hUIjy8nL7YpSUlGRfEDIyMuK+8Jf96E7eW/kcIhJB18xWF7eC1AyhldkTgxaJkq4RIWKIbYQV8RoPSCnRwxqENXRVsdOF9mtjIjE9FCEcNgQihgrahfB54uu+9iubgRnJSQJQD7rphWy4/LsQbjd6UpIRAaoqJCiD40VaPRBNtGrgEb8OW9wl4mlcSokMhQwijUSQUodIGBk0UsTWcWIjb/MArS5Nj2hogRB6JIJe549RETcTAWMQaDgQJhKINDGysM7B7JuKEXeZ+3MJPFZGg6iLlOpSjXS5gFE/ehAwUsdFRUWkpaUxderUFrM0Pp+P4cOHM3z4cDRNs1t7tm3bRjgcJisry45+u5qa7ajwKi0tjbS0NMaMGUMoFGLt2rX2DbKiKGRlZZGTk0NWVlazNemecpnqa3C8lFtGvyLcxItBoplFQ0NDlwbQt4SWnKO6Mn83EVVVVaxfv578/HwmT54cl/qyak1er9e+GEUiESorKykvL2f9+vVxd+NZWVmUlpbypQf+l2d/cAOKqqBLDVVRjJ5UXRoiKiFQXcJIOesytlppRJGW/icBUtPR/IbwSVEVQ2gVI5qJbQuSmo6mhdADISPYdrvMHxWpuJukPZscK/ZfFhEHA8jGhvjHFaM1CQFCUQ0iVhSkz2cuTBjPMeuUTeqlrYXNTcLbprXOuP5WTUNqmpHudbvQA37jd01DasbjipS2wYh1fONGqGlauMl7EkPgesQ4TqiuES0YRka0KFG3QM5SSqSmE24IoYdjDEWs98GKfmMi2liyVl2GY5kSUzrwpHpRVMVQJ5utQMljJpEyfjKBQIC1a9eSmZnJ1KlT251SVVW12QjzyJEjbNu2jdTUVJt809PTeyT13JLwyuVyoSgKo0ePZtCgQdTU1FBZWcnevXvttHis8EoIQWNj46cipewYX7SMfkW4EK1LHTx4sImZhUWAraULO4rWnKNa8jjuKI4cOcLWrVuZNGkSI0aMsO+yrWM0dy4ul4u8vDzy8vJspWVZWRnbt28nGAwCMGrUKO589nnu/8rFtm2jHtERqkAIM7oVIFSBohiiEssswxb3mOIqaV6BrRjHqgHrER0iOlKA4jKFVmrLQigZ0dAiGpofIoDiUlHcKorLIGHFLdok4Wah6/FTbKzNtc3Uk4VAt0hXCBBmmtztMgVQ0bsH4XIZRGnv2Ij4FMX6t3V1MdfbTORmGf4nrqHV381tseQqdWMYhe4PEQyEDII1PyeqiH2vmqaLwei71oIR2xHKJmS75dc8nimGsh3HrL0q4HKpuMy+bQG4vC67dquarUCKqgCCMT95yBZIZWVlcdJJJ3X6eymEaBJhVlRUUFFRwcGDB1EUhZycHPuGs6uqZ2hbeKVp0RT9oEGDGDRoEOPHj8fv99vCq7179+L1ennxxRfRNK3L7Yn3338/r7zyCsXFxXg8Hqqrq5s85+DBg1x77bWsXr2a1NRUli5dygMPPNDqe1JVVcUNN9zAv/71LxRF4Ytf/CK/+tWvBnwL04lGvyNcS1BUWlraxMzC+kB1xnItEe1xjupqhCulZNeuXRw8eJBZs2bZQgyLbNrbcmClszIyMgiFQhw/fpzc3FwqKyupr69n6pnnsHn1v427c5eCrulGZKoYblRaREdRhDHKTUrjom62f0TTojGBnjCu0HGEKkFGdLSIwdiq27gIo0Yv5M2djzT7gDUM04mIEAiXahCxS0W4FEMFLaIk3i2Q0hYcGX0tILSmxheG2juBtKVEKiLe9L9LS4m/MbGGuAPogTChYBgtZCiFwchCJBJXc2pvXdPRQhpaMGL3zdonJczzAFs8Z+0f4oN6RcEgVVWxMyBCYNRpXYrp8iVw+9zGaD8pmfrnF+wSyeDBg5k0aVK3RnYej6dJa09FRQW7du2ye9at2m9X07jNRb/79u2z+3Ct6Nd6XlJSUlxavLy8nGPHjvHmm2/i9/spLCxk0aJFnH/++eTn53doLaFQiEsuuYQFCxbw5JNPNnlc0zQuuOAChgwZwgcffMCxY8fskX0///nPW9zvZZddZq8xHA5z5ZVXcs0117Tq0dwSHNFUyxCy265gPQ9d13n//fcJh8MUFBQ0uVvUNI0333yTz3/+812ybosVRxUUFLToHHX06FEOHTpkD2/u6DE2btxIbW0ts2fPJiUlxb57bimqbQ2W+lPXdWbOnGnXt/x+P+Xl5Tx6xVdprDlup2qsaMn4d7R9CKKOQrom41XMRAVWYM2ZxUxBGhFv7LKFNIhAqAKhGjNhYyMpiwDisgY0JROX2d4iXIrh5KQquJO8RkuOqtr1YzVm3xbU5lTDZso0druAFn2HFZGgMjbVw4kmEsZam24zzqnpeaJLw04zYkRKejBk1MjDMfVD0bT2GvcemRGwSzFKBXpYM/4fCMcZUQji9yOIURvL6BotqEKYAjsFtyv6HqqKSawua2QheLxuFNV4P1QhGP/wH4j4Uli7di1Dhw5lwoQJJzSN2tDQYEe/x48fJzk52Y5+u8NTef/+/ezfv9/+3sYKr2IzM9b32Drer371K9566y2+8IUv8Morr1BbW9tpzclTTz3FTTfd1CTCfe2111i0aBFHjx61g4QnnniC2267jfLy8mavi9u2bWPKlCn897//Zc6cOQC8/vrrnH/++Rw+fLjdNwW1tbVkZGTw9FvHSU7tmtteY30tl59lpOq727mvN9GvIlxFURg1ahTZ2dnNpkesD3ZXos5AIMD69evjxFEtobMRbqIAK9GmsaMXp4aGBtavX09aWhrTpk2Li+6TkpIYOXIkj7z9PtfOnoowo1ODqCSRiGaoST0ukIaS2TDDMOu7ZgrVcquKVScLi48tkZWdx8QmVgCpSaSmEQ5pcQSMKzon1jaoaKFmKQAZ1tBMMpKNwegThJHKdXldBukrCkIx/++1RD0ClGik2iUCaOW11o2M9X9FVdCDIaQm0TUNqRnbRUw60oJK0/R3a6uUulGLlZpOJKjFRajN3bhAjAhKxiae46EoArfXZbyHMftxuRU8Po9BxMLwSVZdKooq7JrxkMuvI+xNZt3atQwbNoxx48ad8Jql5ak8atQoW+tQUVHBhg0bkFLakW9nPJUPHDjAvn37mD17tj31p73Cq4aGBvLz87njjju44447ulVwaeHDDz/k5JNPjsvInXvuuVx77bVs2bKFWbNmNfuazMxMm2wBzj77bBRF4eOPP2bJkiUdWoNON9Rwu/byPot+RbgAQ4cObbFuKoToUpq3o2P1OlPDraurs2ta06ZNQwjRJbI9fvw4GzZsYNiwYYwfP77V1z++bgvXFkwxwiZTtKOoii2OEcLopdQ13XYUEkIYAmHFMLJHj0a9iSllS2hjw0xbNhEYmQSsh4xJOUIRZguRkU6OBm9Ws2cLJBybztZ0tMamZhgR0ZR4rHYVYb3fZo3V5XYZ9UuEzXSKSzXUu9EDRyN6e/6wkYZHSnvIQSyatNc0f0otnx+W0Mk4hhbU0CNWhsKYmZt4WBG7DzurYf2j+RKy6lZRXIrprxzdj+pWcHndqOYNiyKM2q1lcAECFUHySTNxzz6FtWvXMnLkSMaOHdv6SZ4AxGodrGH25eXlcT2/VvTbVs/vwYMH2bt3b4tZr7aEV++8805cG2F3DFBIRElJSZPyl/V7SUlJi6/Jzc2N2+ZyucjKymrxNQ46h35HuG2hs4TbmbF6HT1WWVkZGzZsYMyYMfbFKLb+01GyPXbsmC22Gj58eLte86sP13PTglmGDaKU0bSoClpEQ2BELajSFAZrmP5LqKo1/cVUNWvxNxtNSFCXhvVxrPCnOSGVLpG6WbMMRozoTDXEV0JR0F2KKTCOqeOKlgcktAldGlb7pjLbgiUmioVGM2ldaU0r6nrkligOkyZ5S83oidZCEfMGRdqZg3j1cTwpR/djbktUGVvZB0v+JgzVscutGttiMhVCEfhSvHGRrqIqqC4lmkXAiKbVlAyyrrmZdevWMXr0aMaMGdPl96a7IYSwh9kn9vzu3bsXj8djq54Te34PHTrEnj17KCgoICMjo81jxQqvpJQ8+uijbN68md/97ndNnnv77bfz0EMPtbq/bdu2NTtcvi/CqeG2jAFJuB0xo+jKWL32RrhSSg4cOMCuXbuYNm0aQ4YMiVMit+rM1MqaDx48yMyZM8nOzm73az1eL3e/+Dr3Fi40r6xRAZTLrZqCKd2O/Nwel3HB13Uzu2wQgaoqSPOCa6mbgThbRwHGGFthEgnEuVm1eH5gkKFu9CbJoEkrijBTxcJIRwsFKYx6arP9o5hK28RokdZTtd2BtlTWlmLcJlcgHNab5OJcLaWY46J/K9I2xjIq9naaRrMiGrVa1p2x6WcBqB4Vl8dluGuZ2xVVweVx2dOF7NdoOsLlJv/+X1NUVMTYsWMZNWpUR9+uXkFiz+/x48cpLy9n27ZthEIhe6BBOBxm37597SbbWEgpefzxx3n44Yd58803m9V73HLLLVxxxRWt7qe92YIhQ4bwySefxG0rLS21H2vpNWVlZXHbrPGGLb2mNTiE2zL6HeG2RUwdiTpjxVGnnHKKXZNpL9pzLF3X2bZtG6WlpcydO5eMjIxOKZFj97d161aOHz/O3LlzOyXbzxsxklv+9DSPXHW5Eb6ZaUEwCNElhJ0SEwiESyCkgpTYNVQwbxQwWkWsqNeqDwL2hC1BlCjsiUUWISrW4WMIIiE/ahOkJBrthXSjzhMrRFKtVLGxXQgBqlEntm4UMG8k2u1b3BxaSXHrmkGaxulFHZykeQMhzfeouR7ZlvpmzQPEZQmMf4DQTVOT5l4bV3A3bpIUVbFTw9HTMd4T1aXg9qp2ZCcw/haqS8VlTokSZrpZURRkREOEJcN/9SeKioqYMGFCt86bPpFQVdWu7cb2/O7fvx+/309ycjKVlZUIIdrd8yul5Mknn+SnP/0pr7zySoviSqvXuDuwYMEC7r//fsrKyuw08Ztvvkl6ejpTpkxp8TXV1dWsW7eO2bNnA/D222+j63qnBKEOWka/I9y20F7C7Yg4qiUoitLqsSwXmmAwyIIFC/D5fHZk25kUcjgcZsOGDUQiEebNm9clp51xswq47M77eOand4EirLKuAbMWbglsdN1o9VGEQPG6QOp2OxH2S4SRcjZTvVISp3xuCcLs+7XIWYrmo8PEqFQKYkfcGts0iUSPM5TQIT7iM/cTIUo0mDcOquVoFbs+BRRbYCTtnVovJWENzZFmYpTaKmIiV6sOi3UcqZsRa/z70pLNo1DMGyjVHL3YDBRTdayYmQNLqS2EJZyKtgIpmPV2adTgZSDCqN8/Q3FxMZMmTWLYsGHtP88+DKvnt66ujlAoxIwZM+z2ntieX0t41ZyAU0rJ008/zY9//GP+9a9/cdppp3XL2g4ePEhVVRUHDx60ZwkDjB8/ntTUVM455xymTJnC5Zdfzi9+8QtKSkr4yU9+wne/+137evHJJ5/wjW98g7feeothw4Zx0kkncd5553H11VfzxBNPEA6Huf766/nKV77S4bYlAF0K9C46RXX19X0VA45wXS5Xm4RbU1PD+vXrbeFSZ9sELFJqrpZoWU76fD5OOeUU+0ags2Tb2NjI+vXrSUlJYdasWd0yCvDUJV9ECPi/e+8ENSqAIZbwBKiKahgsmPwphIJQJYqqJkR00UhPCFA85nxdzJYVK2pOIAzzqPaGKJFaaWGLZBJEVCL2LsH4vbl0cXPbYmvNVj+qFZXGvdb8KMXXcCFWhW2eeMf+plaKPWEf9uGlkcJPjFybnEczv7s8Lls5DE1vAoQiUN0qqlvFFZs2FtGIVlUVO4Nh12qFAN2Yf6v7I4x6/Gk2bNjASSedxNChQ9t/7v0Ax44dY/v27cycOZOsrCwgKti0en737NnDpk2bGDRoEIMHDyY7O5uUlBSklPzzn//k1ltv5fnnn+eMM87otnXdddddLFu2zP7dUh2vXr2aM844A1VVefnll7n22mtZsGABKSkpLF26lPvuu89+TWNjIzt27CAcjvadP/PMM1x//fWcddZZtvHFr3/9606t0Ukpt4x+1YcLRhq4tRptUVER2dnZLdaROiOOagmhUIi3336bs88+O+4u9/jx46xfv54hQ4bYQoeuRLbV1dW2heXEiRO7vc1i9f89zYpfPoBw2fld+zqv6zJKdlaAF9GtwBDj2dHn6qbwyoIdM1rpUF23+z91XTbpDwXM/t34NTYXOVr9tMSswyL72OMrCcQsaD6V31JKV0lco7m+qBDJYGAhYubExjzfJWKcs8z/2nOJZHR/TYgx8bg0bfdRTPcnoSgIDHOR2P3Y+xBmHdZtRLvW38QV80f0ej1RcjUjXQXTvlNijyLUAzqjH/8rmzZtYurUqZ2q8/VllJSUsHXrVmbMmNGmPqKxsdEWXr333ns8/vjjjB07lo8++ohnn32WwsLCE7PoPgCrD/dPb1STnNLFPtyGWr51bqbTh9vX0VJKOVYcNWPGjCYy+M4eC4gTTh09epQtW7YwceJERo4cabcGQOeUyCUlJfb+eqo+dubXLyc1axDL7vihYcuoYIaVUTMIXUaJzOVRo8YZMbdrqmrMeBVEyVfKRIIw1NFCCFSM985SQUsrUm7nWxQbFdtIEGRJMIRVMS8wotlYAozfTdzhE+umEL2hsCJSAU0WHhOtyrjNVi05/kSaO+Xmtimm4YRi1t4tEVPCymyoLkPsJNQEsROm+tpt1nVF9LNprc8mbtN3Ww9GkBHJmCcMsj355JO75XvUl1BaWsqWLVvaRbYAycnJjBw5kpEjRzJu3DgOHDjAn/70J1JTU7nyyit59tlnufrqqznrrLNOwOr7BpwIt2V8Kgi3q+KolhBrtCGlZPfu3Rw4cICZM2eSk5MTJ47qjBJ537597N+/n+nTp3ebqKIlzD1/ERm5uTx21VKDdFXFJl0jEgI9lnRM71zLCL9JLVMRqF63QahmNGsPSEggYJsEVJPYYsnKJOH2tAA1V8+E5om5vQQXU9iO2RQjwLL2K2kamrcuxm4TQhXR1K4Qzc7VTYRiposVl9G2E0vIdgbAdJByKQJFKNFTEzHRvzDee2G+B1ogjGdQLvk/fZgtW7ackM/kiUZZWRmbN29m+vTp5OTkdPj1n3zyCU8//TTPPPMMl1xyCWvXruXll1+moqKiB1bbdyFl140vBirhdo8ZbB9CYltQIBDgk08+we/3s2DBgm4jWwDLti0cDrNx40aOHDnC/PnzbbJtawBBS7CUyIcPH2bu3Lkn7MI2cc487nzpdaQ5kABd2qlEy4oxNr1qK61NQ3vVZSmCsZlGUYwJMi63gser4vao9vCEWFgdsQYhGGlP1WW0p7i9LlS3YtQdXYpdn5SJLJ+InvrStvdP2Syriya/KoqwJ/C4vC5cPhfuJDcer9t0clKaKLctGASr4Pa68CS78aZ6cXld9mcu9nPnciu4fcb76VIVm1gVhP1c2xozYtxE6aEImj9C+rTZDLn3IbZt28aMGTMGHNmWl5fbUXtnzm3NmjV8/etf54knnuDLX/4yiqIwb9487rvvPi699NIeWLGDzqKqqorLLruM9PR0MjMzueqqq6ivr2/1NWeccUbcd0QIwXe+850OH7vfRbjtaQuyLNNqamrsmm5XxFGtQVEUNm3ahKIoLFiwAI/H0yVxlEXe4XCYefPm4bPGy50g5I4axf98Uswtc2YiXBIpFcOEIiFtqsRETVaAZ83ZFbpuK3iNqFbYtVxDORsVfEmJOcqOVgnSqFES185jRcaWmlrqMY5QpvjLDj67/M60gRYOoChE+1nN56hmPTUu1U6CkKuFQwhF2ASsqgJXjHjO1pWZb7YiMOq1ivG+xbpgidgXWRcRKW3BmtR09LCG0CVpJ00n/VvXsWPHjjgR0UBBLNl2JkX+3nvvcemll/Loo4/y9a9/vds1Fv0NfX0ebmcHNVx99dVx4rPODMXod4TbFqyUcneKo1pCXV0dkUgEj8dDQUGB3SbUWbL1+/2sX7+epKQk5syZ06URY12Bx+fjsc3bufHkyUirFcUIbU1lsFXnE3bK0dAlSTvqt85cUbFtD+3eW2IIWwCKy64XGkMTdLCnFbW9XovMhKKi0DT1HLtvawF2GdW+Y4gZvpCgYDacpkyiF4BuRvvWUAWIGoIoTYm0LeGTsVsR+0t04IFleWm298TeNKrWGxSbMlaNdQlViUsnK/G7R4nttTVvVixxmR4yZurKcITx195E5ORZ7N69m4KCAjIzM1v8O/RHVFRU2OKvzpDtxx9/zCWXXMKDDz7IVVdd9aknW+jbNdxt27bx+uuvxw1qeOyxxzj//PP55S9/2WobVHJycpcFggMupawoij2FY8aMGYwdO7ZHvgTl5eV8/PHHuFwum9C7QrbV1dV8/PHHZGVlMXPmzF4j21j8etN2UtMzQdONyUGaNEbayfhUsxW8KWY/r8nJQELK1GxFUdSm701srVt1qbi9RurTm+TG43PZzkiK3b7UUiDY8vtup4MUYZtAGClvJSYtrtriL3vNLiOVrbrM7XZqW7H7VxVFaXYyUbuzzy5heharRko52Y0nxWtM5jHXoChKfB3akEobQwTcqvFcj8sYbZiQTrbruKbfrzQLbUKz/p6SSDCMFggbf+9ABHH1TWzxJLNz506GDRvWpb7vvojKyko2btzIlClTOuQwZ6GoqIiLL76Ye+65h+uuu84hWxOW5XpXf8BQPsf+WLO+O4u2BjW0hmeeeYacnBymTZvGj370IxobGzt8/N6/qncQrX2orci2J+q1sTh48CA7duxg6tSp7N27l0gk0iUlsqWMHD9+PCNHjuyJJXcaP//Ph/zjnjv5YMVzhlJZmnU+RcHS2wiitT+rd1NRhO1UJYUV1WJc3FUVoUbJyHZgikFsGtgiYUv0Y8Z2douRdWwpMRW1xBFThzyXm5Uqt7K9HbCzAeaNidHGYxGi0cqTGAXHtQiJaPxrpYcVM+KNVRbH7iH6XpkpbfN3oyXL8Nu0g/twxLyZksiIjtAlp734BgeOHOHAgQPk5+dTV1fH+++/T0pKiu2M1F7Hpb6Iqqoqu4e4M1HLxo0bueiii7jtttu46aab+u370NeR2Jlx9913c88993R6f50d1PC1r32NUaNGkZ+fz8aNG7ntttvYsWMHzz//fIeO3+8ItyVYzlHhcJjU1NQeIVspJdu3b+fo0aPMmTOHzMxM9u/fT2VlJampqU3m87ZnfwcOHGDv3r2dFmucCFx6z0/53Ncv58HCi0zmBIkO0vQ1jmE3SbSWGGvwnzj5Jy6trApQDZKxjESkLps4SUUPYqRRRULPKYDwqHFkI6Ux1ccgpNh6r7SJSIJ9S20QYfQw9vMUY8SfNHtnFcVMKcewu2pGuojoTYBbbXoD1uzwgYRCs5Umt03wrdqt+VqVpgRrE7MwzErsdLOt+I56d6NLtIhmGllgiqQkruR0TnvuRfbs2cORI0eYM2eO/V0Kh8NUVlZSXl5OUVERiqLY5JuVldUtZiwnAsePH6e4uJjJkyd3yrBj69atXHjhhXzve9/jtttuc8g2Ad2ZUj506FBcH25LWZb2DoDoLK655hr73yeffDJDhw7lrLPOYs+ePYwbN67d+xkQhBsrjsrNzWXPnj3dfoxIJMKGDRtobGxkwYIFJCUloes6o0eP5uDBg7z//vukp6eTm5tLbm5umwV1XdfZvn075eXlzJkzp883dw8dP5Ffbd7OzdNPMsz2beI1KUdIo94IJlEaj0iiUS/EZygSxUxx/tJKNEqzSVKaphlCNHG2itlJnBJYCGF7LMeiuTpqi8YXopnnNvP6xH021wrW3BGs2qulRDaiVzXutapZX41/obB3oKqxYrLoeybQ7fqwANB0IprRqgVA2HD/QtMZ89WljLnim+zatYtjx44xe/bsOK9ut9vNkCFD7OEb1dXVlJeXs2PHDoLBIFlZWTYB99X0c3V1NevXr2fSpEmdsi3cuXMnF154Id/61re46667HLJtBt1JuOnp6e26NrZ3AER3DWqwPKZ37949sAk38QNuiaPGjx/P6NGjqaqq6tIA+ubg9/tZt24dXq+XU045xbaP1HWd3Nxc8vLyCAaDlJeXU1ZWxu7du0lJSbHJNzU1NW7dlhI5FAoxf/78E65E7gr+d+M2/vK969n49iqkFAhdoFtRoTSmDOmKSZpmmjcqRIrWaS0rxETCTSRGm1AFKKi2A5L9mKWcNkneyJZ24CIYm3puRnDV7PNFM/9uC2aErShm9BkzblBNIGbbQcuK5O19xKq9YwRR9tqs90Lar7W8rdEkMqLZ69Y0I3UsJEYKecXLeNLS2LFjB2VlZcyZM4eUlJQWT0dRFLKyssjKymLixIk0NDRQXl7O0aNH2b59O2lpaTb5Jn7+ewsW2U6cOLFTvs979+5l0aJFfPWrX+X+++/vE+fkwEB7B0B016AGy8O6oxmSfmftCBAMBpFSsmfPHvbt2xfnHGV9qc4888xuOVZ1dTVFRUXk5eVx0kkntUscFQ6HqaiooKysjIqKCrxer02+Ho+H4uJifD4f06dP7xPiqM6grrKSu08/zU6fGiphokPdpRHxYql5TSRaL8a2F8URhPX8hOOqSpRcEcImmybRILGqZBkXfUpT8GURvl2etdTLMVleI31srTPKtKoQ8W1mElyuGCWzuX93Qpo1Llo2SVEl5qDQ1KyC+AhWxLxvYKmVm3lM143JSqb/sQBk2Gyd0o2bldRho1jw1P8hpWTbtm1UVlYyZ86cDpdHYhEKhWy7w8rKStxut31BHDRoUI+057UFKws2fvz4Tjm2HThwgPPOO49Fixbx2GOP9co59HVY1o6/frGGpC5aO/obarlxcUaPWDsuXLiQ0tJSe1DDlVdeyZw5c+y2oCNHjnDWWWfx17/+lXnz5rFnzx7+9re/cf7555Odnc3GjRu5+eabGT58OO+8806Hjt0vr/a6rrNx40aqq6ubOEd1dB5ua7Ci5wkTJthipvYMjHe73QwdOpShQ4eiaRqVlZWUlZVRVFSEpmmkpKQwYsSIfv2lTcvO5pHN23i48EJK9uwGhBFdSh2rrxOzZih1YahpzfMVMYQZZ/ovo1YWNgETk1a2HhOY9BFfC7aQOG1IiOgUHAvNEbVlAJGIdqeUY48hY1pxEurXsSdi116tlLEQceQKTW86jGSCtNchY9ei6WimzFOxsgqa0WqlYL43pq7slD8uI23MWKSU9sjHrpItgMfjIT8/n/z8/Lg5s1u2bCESiZCTk2Ob/Xs8ni4dqz2ora2lqKiIcePGdYpsjx49ygUXXMA555zjkG070JfbgqDtQQ3hcJgdO3bYKmSPx8OqVat49NFHaWhoYMSIEXzxi1/kJz/5SYeP3e8iXE3T+M9//oMQglmzZjWpFTU2NvLuu+9y7rnndjrlk+i7PHjw4C4NjAfDNm7Tpk123ai8vBxN0+w7/5ycnH4jOklEdVkZPz3rdJs8jKjX1MEq0fSnVZPFrKti/m7Xas39xRKoLbyySDRGcQtmGjr2d6LRayzUBNJMjBINgrSiShHHcopIID0zKm1yjARST3yOEEafbty5JT4ndj9WFC6xzz8xI6CCMZZQGr3LirV2k3QtwRim77WQkDJsOJ/9698B4+Z1y5Yt1NXVUVBQ0KPlDSkldXV1lJeXU15eTn19PRkZGfZ3oLUUdmdRW1vLunXrGDt2bIsDTVpDSUkJCxcuZP78+fzlL3/pt9/REwErwv3VC90T4X6vsGci3N5Ev4twVVVlzJgx5ObmNnunaaVodV3v1JdD13U2b95MVVUV8+fPJy0trUsD46WUHDx4kD179sQ52UyePJna2lq75rt582Zb9DV48GDcbneH194bCIVC7Ny/n6/8+a9se/YZNv77DeyaqpCgYbhICZDmn0MAMiKjvUIx5AvERb2J94NSl3E2hxb5xqVgRVNSFs0QbtwxhVVDbv7v21Y0a95HxD0/3j1K2pGs0S4Vj9h+5tihEJaBpX0zYz4upUTRJBHLbMRch65roFnp8ujAe4ERwZ/54mt4TCGUruts2rSJxsZGZs+e3eNCJyGELYIZN24cgUDAJt89e/bg8/ls8s3IyOhyJFlXV0dRURFjxozpFNmWl5dz4YUXMmvWLP785z87ZNtO6Lqd3OrSPgYi+h3hAuTn58dN6ImF9aXQNK3DX5BQKMT69evRNI1TTjkFr9fbpbF6uq7bIpTZs2eTkZFhPyaEICMjg4yMDMaPH09DQwNlZWUcPHiQrVu3MmjQILvu21cVn36/n6KiIlJTU5k2bRpz585F13V+Mq+ASCgUbUexxFIRzCu/RNppVNDDhsuRRBrWjQnRL4kpYl3GhZz2/q0NsRkIk9xi08vWc2O3A03MIiwkRsex+7F2ZhF6c2Rqrwmij1sqYmGusTlCtmuxJunqepwpvDT3I3WJFtGjNW1J1ObS7IUef8VVTPjGlfZrrbJMIBBg9uzZJyS1mwifz8eIESMYMWKErRQtLy9nw4YNAHGp545qHerr61m3bh2jRo1i9OjRHV5bVVUVixcvZuLEiTz99NP9VmvRG+jrKeXexID7FMVO8OkIrC9oeno606dP77JNYyQSsS9o8+bNa7UuJoQgNTWV1NRUxo4di9/vp6ysjJKSEnbs2NGhdqMTBSt6yMvLY9KkSVHFrKLw87XFVJcc44FzzrIDXYt9jZ5XgRAybmCBFBj2kVIawh4rZBSgmwIlS0VspY0tCISdRjayr7KJh5qtgI6xl4w16+go4mvKwmxbiiFbk0Bjn2fZNUbXHTOE3iJkXTcvWEY6WLezBdE+ZSEx3KBiLkqG85du+FbHrCN1xGhOX/ZM3No1TWPDhg2Ew2Fmz57dJ7IpLpfL/oxLKampqbEj302bNtktRzk5OW3WmOvr61m7di0jR45kzJgxHV5LTU0NhYWFDBs2jGeffbZPvD8OBgYGHOEKIVqcidsSKioqKC4uZuTIkUyYMAFrhm1nydYy4fB4PMydO7fDX9ikpCRGjRrFqFGjOtRudKJgWeKNHj2a0aNHN7uGzCFDeWjjVra+/TZP33S9QQ4ihiglgEG0lhczOqCYRGVHrSI6exeMx4TlnmQSMlFlshVF2ilZa7u0jhMT0Zr/jyXFZluDrHA4dlNc/Tc+irbJNjbyjnm+RczSXJNFsHYK2nyvbMW2BKFJNPPfsfcSwoxghXWOppzMnZLCF156vUlaVtM0iouL0TSNgoKCPkkmQggyMzPJzMxkwoQJNDY2Ul5eTmlpKTt27GjV7aqhoYF169YxYsQIxo4d2+Fj19XVsWTJErKyslixYkWfzS71ZTgRbssYcIQLLQ+hbw6HDh1i+/btTJkyhfz8fJtsoXM2jbW1taxfv57BgwczefLkLtehvF4vw4cPZ/jw4XHtRgcOHMDj8djkm5GRcULI99ixY2zdupWTTjqpXcYBUz7/eR7YuJU1v/89b/z2V2ZUaT4ozD5QsznHiH4xxcvSJtdoBGwRGkZfqU2OEqvAIEwzZ6sl1XTKwG5fikGsFaWF2BQ2ELPe+LR2S7DIVGCogcGYmKQI08zKEkCZ6V8rwhXmwaVuDovQpTW/IVpvto8R/3tsT7Pi8nDua282mwKNRCKsX78eIQQFBQX9Jk2anJxs34Ba34Hm3K68Xi/r169n2LBhnSLbhoYGLrnkEnw+HytXruxX/fF9CTpdn4c7QEu4/ZNw27rotac1SErJjh07OHLkCLNnz2bQoEFdGhgP0TFfliKyuwmwuXaj8vJyiouLEUIwePBg8vLyeqzXcf/+/bZyu6MDus/49rc549vfpviVf/Hcj24zWdV80ODM+HQsIt5jwkyxWgSli6hfs6VYUqx96jq2/0WsellEldDRqDU6DEHQtMVIKDGvwbgtUDD8m6wtidG0xIxCE1PWIkqdQkYja12azk8xz1Wiz4xLg0dNLmKEWYDq8nLuv17F1QJJhMNh1q9fj6qqzJw5s98KgGK/A7FuV9u3bycQCJCUlITP5yMUCnUoOvX7/Vx66aXous4rr7zSI4rpTwsse9au7mMgol8SbltoK8K16qv19fWccsopJCcn2ylkIUSnyOrgwYPs3r2bqVOndmrySEehqqod3VoXnrKyMrZs2YKmaeTk5JCbm9st7UZSSnbu3ElJSUmXbShnXnAhMy+4kGM7dvDbSy6OppljUr8GOUqENfXANFXWzTSrTciaETIKQAphZKRNf2Nph4xRJrfrpdYv0jiOla4WMWlgC7oejT7jnxOfem4aPQPmaEOEjKoudWnXa600dJSmiQkNYgg9YYudvtYlvsFD+MJzK1r9zIbDYdspbfr06f2WbBNhuV0lJSVRWlrK0KFDSUlJsd2u0tPTbeFVa+WXYDDIZZddRkNDA//+9797bOiJAwefOsINBAKsW7cOt9vNggUL4mwaO5NCtiLl0tLSJkrkE4VYm71JkyZ1a7uR1SZVW1vL3Llzu020NXTSJH62cQuRUIhfnvV5GmuOgxIlIsvmyappJoqR0HVT6YyVg46JmqX9f5tvhUAnptZq1n5jna90ZNRW0YISs+sY8rclT2YKWbeO3Uy6WJLQW2ytScYLxyAm8I7NtFjbzUwAumTC1y5j2nXXt/k+h0Ih1q1bR1JSki0GHEjw+/2sXbuW3NxcW7w3ZswYQqGQ3XK0b98+PB5Ps25XoVCIb3zjG5SVlbFq1aoT9v199913efjhh1m3bh3Hjh1j5cqVFBYW2o9LKbn77rv54x//SHV1NZ/5zGd4/PHHmTBhwglZX1fg1HBbRr8k3LZI0SLRRFj2boMHD2bKlCkI0bUZtpFIhE2bNuH3+9tUIp8otLfdaPDgwW3WqMLhMBs2bEDTNObNm9cjrSMuj4fb//MeAB88/VfeeOhBhKoYNVuiieW4v0yc8MoiY4HUpREFmxvjiC7R7Sn2tbFfbhEf40rdEDPJ2NR09KAxS4qKvGKnHEmpR49hf75iInrM9ca83toebYvSkTqobi8XvPKq3UfbFoLBIOvWrbPbtgYa2Vo3zzk5OXFKeTDcgYYNG8awYcPQNI2qqioqKirsDNAzzzxDQUEBa9as4cCBA7z99ttkZWWdsLU3NDQwY8YMvvnNb3LxxRc3efwXv/gFv/71r1m2bBljxozhzjvv5Nxzz2Xr1q19vrYsu6EPVw7QIm6/c5oCQ2nZWo3WmhwU2+yeOORAStmlHttAIEBxcTFut5vp06f3SbVnIqx2o7KyMtvBpaV2I0tpbXk+n8g0pK7r/Pkbl3N4Q7HBS3FOVVHSEzF13tg/X2w0mejkZCl/rag3MaI1g9+YDRYpithNzUes1j4T1qMmsLOl/YrdT+wx7AjXnMp0ys8fYuTnz2zp7WoWFhllZGQwZcqUAUm2a9euJSsry/Y4bw+klFRXV/PTn/6Uv/3tb9TV1bFgwQK+9KUvceGFF/ZKBCmEiItwpZTk5+dzyy23cOuttwJGsJCXl8dTTz3FV77ylRO+xvbAcpp68NlqfMldc4cKNNZy+1cyHaep/oDYlLKUkn379rFnzx6mT59u1zwt44zOkG1dXR3r168nOzubk046qd9czNrbbgTGNAzrYnaiz09RFL71f0bvqBaJ8MdLLqF01w6EoiAVYUewiFhxUQxie3IhOlEIS5kcfR7ERK1N99QUv/agpgAAODtJREFUCa9tJtSNtvZYj8bdDMTvyhZRm+5RaBJdwpwf/oiJX2oa+bQH1nSrQYMG2ZmcgQQrch80aFCHyBYMcktPTycQCJCXl8dbb73Ff//7X/71r3/xv//7v+zfv7/Xa9z79u2jpKSEs88+296WkZHB/Pnz+fDDD/ss4VpwUsoto18SbntUylaqeMuWLVRUVDBv3jzS09O7ZNMIUSXymDFjWuxB7Q9ort2ovLycTz75BF3XSU9PJz8/v9fPT3W5+M7Klfbvqx75Xz78058QqukMZbYBQTQ6jUbAUcRpniVxpBsnfko0wpAJpCkTPTXiRwomvltx3sdgDg4w1yIlui5B1/Fm5jDnoQeod7upqKjgmKKgbdtmD3dv72e1sbHRTrNOnjy51/9+3Q2LbK3IvTPub7fccgvvvPMOa9asYdSoUcydO5frrruOcDjc62QLRjYOaCK+zMvLsx/ryzBtvLu8j4GIfkm4bUFVVYLBIGvXriUSibBgwYIu2zSC0bO7a9cupkyZ0qFhxX0dVquFqqqUl5czbNgwpJRs2LDBbjfKzc3t0IW/p3D292/m7O/fDBilhZfv+Alb/vUvI1RUhS28kkpMGlhYZNxyL22TGnECibb0aVFNJZNFq7bBRnRnxn9j/JH1iMSTnMpnfnoPo876fJN96rpuT9jZunVr3ISdnJycFssXlulDXl4eEydOHHBkawnA0tLSmDp1aqfI9kc/+hGvv/46q1evbuKv3B/KQg76NwYk4eq6TklJCVlZWRQUFMRFvJ1VIu/cuZNjx45RUFBAZmZmzyy8F2HdTMQOWIhtN9q6dWu3txt1FaqqsvihB1j80AP2tmObt/DyHT+hYudOQ3ilCoRiqIitOrAU0ajUMs6I+0gIkWAdmRAtxwbAsWIsXcfqIJZm978ldpq29HJmfucaXO0QnimKQnZ2NtnZ2UyaNIm6ujrKysrYv38/W7ZsaVb4ZlmT5ufnM378+AFLtqmpqZ0m27vvvpsVK1awevVqxo0b10Mr7Tqsm3mr1clCaWkpM2fO7KVVtR9OSrllDDjCrays5MiRIyQlJTFr1qwu2zRqmsamTZtoaGhg3rx5fcbLuLsgpWTPnj0cOnSoyc1ET7Yb9RSGTpvK1S+tjNtWWlrK2rdXo+w7yN5XX8VfUUVERhBKtEUoVo1lGGpgC6Z0aZGymQa2stMShG7sw+VJIi1/KLO+dSUTLjwfpZtcnGIn7IwfP94Wvlk2h6mpqWRkZFBSUsKIESMYN27cgCNbq484JSWlU2prKSUPPPAA//d//8fbb7/NpEmTemil3YMxY8YwZMgQ3nrrLZtga2tr+fjjj7n22mt7d3HtgNSjve1d2cdARL8k3JYuKIcPH2bbtm22MKqrNo3BYJD169fjcrmYN29enyGV7oKu62zbto2qqirmzp1LaivtJt3ZbnQiceTIEXbs2MG8s89i8ODBcMcPe3tJXUKs8C0UCnHo0CH27dsHGLU/a8ZyZmZmr6f/uwMW2SYnJ3eabP/nf/6HJ554grfffpupU6f20Eo7hvr6enbv3m3/vm/fPluoOHLkSG666SZ+9rOfMWHCBLstKD8/P65X10H/Q78k3ERYKd/Dhw9TUFBAY2Mjx44ds8m2MzaNdXV1FBcX20rPgXDxioWmafY0o7lz53aIJNs73ainhoq3F/v372ffvn3MmjWLQYMG9do6egqNjY0cPHiQ8ePHM2LECKqqqigrK2Pjxo0Advo/Ozu719P/nUE4HKaoqAifz8fJJ5/cKbJ97LHHePTRR/n3v//NjBkzemilHcfatWs588xoq9f3v/99AJYuXcpTTz3FD3/4QxoaGrjmmmuorq7mtNNO4/XXX+9TN7MtwRFNtYx+2YcrpSQUCgFR4qirq6OgoICUlBTKysrYsGEDubm55OXldfiCU1FRwaZNmxg5ciRjx44dcCk6a+6vqqrMmDGjWyP3UChEWVkZ5eXlVFZW2pNd8vLyTth0Iyklu3fv5siRIxQUFAyoPj4Lx48fp7i4mHHjxjFy5Mi4x6zxdlbPdTAYJDs723Za6o3Ztx1FJBKhqKgIt9vNjBkzOkW2f/jDH7j33nt57bXXWLBgQQ+t1IEFqw/3nmXHu6UP956lgwZcH26/JFww0r2BQICioiJUVWXWrFm43W40TUPTNOrr6+2RXqFQiJycHPLy8toU+xw+fJgdO3YwZcqUOMHCQEFjYyNFRUWkp6f3uPtQJBKxpxtVVFTgdrvtXt/MzMweIV8pJdu3b6eiosK+ARtoqKqqori4mIkTJzJ8+PBWnyulpKGhwe65rqurIyMjw1ae90VNgkW2LpeLGTNmdDg6l1KybNkybr/9dl5++WU+97nP9dBKHcTCIty7/lLVLYR735VZDuH2FVjjubKyspg2bVqLNo1SSurr6yktLaWsrAy/32+n2gYPHmyPKJNSsmvXLo4ePcqMGTMGZArSGh04ZMiQE942YtnrWdFvT7QbWb7PVrajL1htdjcqKirYuHEjkydPbtd4xEQEAgHbY7iqqork5GT7u5A4W7Y3YI0QVBSlU1ONpJT87W9/4/vf/z4vvvgin/9807YrBz0Dh3DbRr8k3HA4zJtvvsno0aMZO3Zsh2waY8m3oaHBTrWVl5fT0NDArFmzBmRUZF2ox44dy+jRo3t1LbHtRmVlZd3SbqRpGhs2bCAUClFQUNAv0qYdRXl5ORs3buy27IuVgSgvL6eiogJVVe20c2/0XGuaZs/r7ewIweXLl3PdddexfPlyzjvvvB5YpYOWYBHunX/uHsL96Tcdwu0zqKmpwev1ximROyqOamho4OjRoxw6dAhN0xg0aBBDhgwhNzd3QF2wjx49yrZt2/pkmlxKabcblZWVEQgEOtxuFA6HKS4uBmDmzJkDTk0ORmvT5s2bmTZtWo+Mf4w12ygrK2u32UZ3QdM0iouLkVIya9asTpHtSy+9xFVXXcXf//53Lrrooh5YpYPWYBHuT57sHsL92VUDj3D7rUrZ5/MRiUS6NDBeSklJSQmDBw9m7NixlJeX27M0MzMzycvLIzc3t0ODrPsSpJTs37+f/fv3M3PmTLKzs3t7SU0Q2240YcIE6uvrO9RuFAqFKCoqGnCzXmNRUlLCli1bmD59utHa1APojNlGd8EiW13XO022r776KldddRXLli1zyNZBn0W/jHCPHz/Oxx9/zPz583G73Z1KfVVWVrJx48ZmzQICgYAdcVVXV5ORkWGLffpLXTB2Tm9BQUG/HKrt9/tt4VvsdCOr3cjv99sCsKlTpw641i3AvgGcPn06OTk5vbKGxsZGu+5bXV1NWlqanXruqvJc13WKi4uJRCIUFBTYmoqO4K233uKrX/0qf/jDH/ja177W6bU46BqsCPeOP1V2S4T7829lD7gIt18S7gcffMDixYtRFIULL7yQJUuWcNppp7U77XXkyBG2b9/OSSed1KbwxJqqU1payvHjx0lLS7Mj376o8AQjYti8eTP19fUDRjxkDRQvKyujsrISn89HKBQiOzu7Uz2a/QGHDx9m586dzJgxo89kJ0KhUFzd1+v12uK3jIyMDv0ddF1nw4YNhMPhTpPtu+++yyWXXMJjjz3G0qVLe1309WmGRbg/+kP3EO4D1ziE22cQDod55513WL58OS+88AKRSIRFixaxZMkSTj/99GZrsFZ/5uHDh5kxY0aHB04nXvRTU1PtXt++IrSy6plSSmbOnDmgatEWrLYYn89HIBA4Ie1GJxqWt3VfNu1IVJ4DduTbVu+7ruts3LiRYDBIQUFBp2rEH3zwARdffDEPP/ww11xzzYD4u/dnOITbNvot4cYiEonw3nvv8dxzz/HCCy/Q2NjIokWLKCws5POf/zxer5eGhgbeeOMNcnNzu0WJbI20Ky0tpbKykqSkJDvyPVEGD4mw+pKTkpIGbD2zqqqKDRs22OMRT0S70YnGgQMH2Lt3L7Nmzeo3gzKswe7WDWlrZhu6rrNp0yb8fj+zZ8/uFNn+97//ZfHixdx3333ccMMNDtn2AViEe/sfKvAldZFw/bU8eE2OQ7h9HZqm8cEHH/Dcc8+xcuVK6urqOOOMM+z+0zfeeKPboz6rvaK0tJSKigp8Pp8d+aalpZ2Qi0F9fT1FRUX2HNT+SDRtwZpFPGnSJIYNG9bk8dbajbKzszuVsjzR2LdvH/v376egoICMjIzeXk6n0JrZRk5ODnv37qWhoYHZs2d36rtYXFzMBRdcwI9//GNuueUWh2z7CCzCve2JCrxdJNygv5aHvuMQbr+Cruv84x//4NprryUUCqGqKgsXLqSwsJBzzjmnR2qwmqbZ7krl5eW43W478s3IyOiRi4Nl8zdQrSgBjh07xtatW9vdFtNau1FOTk6fS7VLKdm7dy+HDh1i9uzZ/VLk1hJizTYqKytRFIXhw4czZMiQDpttbN68mfPPP5+bb76ZO+64Y0B+1vsrHMJtGwOacD/88EMuuOACvvOd73DfffdRVFTE8uXLef755ykpKeGcc86hsLCQ8847r9VJOZ2Fle4sLS2lvLwcVVXtyLe7ao2lpaVs2bKlXTZ//RVWPbMr4qFYq8/6+vo+Nd3I0hYcPXqU2bNn98hnsbchpWTLli3U1NQwatQojh8/3mGzje3bt7Nw4UKuueYa7rvvPods+xgswv3h4+XdQri/uHawQ7j9CYcOHWLNmjVcfvnlcdt1XWf9+vUsX76cFStWcPjwYb7whS9QWFjIwoULe+QPrOu6XWssKytDCGELfQYNGtSpFPDBgwfZvXs3J598co/1Z/YmpJTs27ePAwcOdGs902o3stq+0tPT7brviRa/WZOuSktLmT17dp8R33UnpJRs3bqV6upq5syZY/e1J5ptaJpmZyGys7Pjaru7d+/mvPPO4+tf/zoPPvhgr5ZM7rnnHu699964bZMmTWL79u29tKK+AYtwb/1d9xDuL69zCHfAwfLffe6553j++efZs2cPZ599NosXL+aCCy7okTRwbK2xtLQUKaU9Uac9Qp/YaTgzZ87sN8KajsAiopKSkh7tI05Unlvewrm5uT1ef48dtDB79uw+22bWFUgp2bZtG8ePH2f27NktZhOklLbZhmWzWl5ezsGDB1mwYAHXXHMNhYWFPProo72uT7jnnntYvnw5q1atsre5XK5e65PuK7AI95bflHUL4f7P9bkO4Q5kWHfiVtp5+/btnHnmmRQWFrJo0SIGDRrU7Rdga5Sa5e8ciUTsaKu51gpd19m6dSvHjx8fsNNwdF23L9IFBQUnjIhO5HQji4iqqqqYPXv2gOiVTkTsOc6ZM6dDqfvGxkZefvllHn74YbZu3crgwYO58cYbKSwsZOrUqb2aTr7nnnt44YUXbDtRBwYcwm0bDuG2ACvCstLOmzdv5vTTT7fJNycnp0fI1xL6NDdWUErJxo0bCYVCzJo1q99aTrYGq2WkoaGBgoKCXquv9mS7kXXTVFNT02rU159hOZ1VVFR0mGwtHDt2jPPOO485c+Zwzjnn8NJLL/HGG2/wgx/8oElK90Tinnvu4eGHHyYjIwOfz8eCBQt44IEHmswl/rTBItzvP9Y9hPvIDQ7hfiohpWTPnj125Lt+/XpOO+00CgsLueiii8jNze0R8rUmG5WWlhIIBFAUBa/X26tE1JOIRCJs2LCBSCTCrFmz+oySOLYEUF5ebhv7d6bdyCph1NfXM3v27AF502TdrJaVlTFnzpxORe9lZWUsXLiQgoIC/vrXv9qZnsbGRhobG3s1ffvaa69RX1/PpEmTOHbsGPfeey9Hjhxh8+bNA0pd3lFYhHvTr0q7hXAf/V6eQ7ifdlgDAVasWMHzzz/Pf//7XxYsWGCT79ChQ7udfK0eW0tEYo0VzMvLa/dEnb6OcDjM+vXrUVWVGTNm9NmeWSsLYdV9/X4/WVlZdhaitZsEK3pvbGzsdA9qX0cs2Xa2Ll1ZWcn555/P5MmT+dvf/tbnP9/V1dWMGjWKRx55hKuuuqq3l9NrcAi3bTiE2wVIKTl06JBNvh999BHz5s1j8eLFLF68mOHDh3eZfGtqali/fj35+flMmDABIQQNDQ122rm+vp6srCy71tgfL+KWQ1ZKSkq/80W22o0sg4dBgwbZqefYLISmaXFWhv3x79QWLDHfsWPHmDNnTqfI9vjx41x44YWMGDGC5557rt+8T3PnzuXss8/mgQce6O2l9Boswv3eoyXdQri/ummIQ7gOmoeUkqNHj/L888+zYsUK3n//fQoKCigsLGTx4sWMGjWqw+RrOSuNHz++xfqQ3++3BVe1tbV2f2l/GSvY2NhIUVERgwYN4qSTTupXZJuIxHajtLQ022hj165ddqq8r0dsnYFVdjly5Ahz5szplJivtraWiy66iOzsbF544YV+8fkF46Zr5MiR3HPPPdx44429vZxeg0W4Nz7SPYT76+87hOugHZBSUlpaysqVK1m+fDnvvvsu06dPp7CwkMLCwna5QVkTjaZOncqQIUPadVxrrKA1zi4jI8N2ueqLNd+6ujqKiooYMmQIEydOHFBGBla7keW1rSgKI0aMYMiQISfM7vNEYs+ePRw+fLjTZFtfX8+SJUvw+Xy8/PLLfVq1feutt3LhhRcyatQojh49yt13301xcbGtpv60wiHctuEQbg9DSklFRQUrV65kxYoVrF69milTptjka6WJY59vmT10ZqKRhWAwaJtsHD9+3J4l21fGClZXV7N+/XpGjRrFmDFjBhwBgSECW79+PUII8vPzqaio6PF2o97A3r17OXjwIHPmzOmUS1ZjYyNf/OIXAXjllVf6vNPWV77yFd59910qKysZPHgwp512Gvfffz/jxo3r7aX1KizCvf5/jnUL4f7mlqEO4TroPKSUVFVV8eKLL7JixQpWrVrFxIkTWbx4sU2+N954I5/73OdYtGhRtykeY6OtqqoqUlNT7ci3N/p4Kysr2bBhQ6up8v6OcDhsC91mzJhhq2ybG2lnkW9/nG5k3Rx2lmwDgQCXXnop9fX1vPHGGwPq4vppg0W43/3l0W4h3N/emu8QroPugWV48dJLL7FixQreeOMNXC4XLpeLP/3pT5x33nk9cvENh8PNOitZM317OtoqLS1l8+bNTJkyhaFDh/bosXoLoVCIoqIivF5vq2MSrXYj6+8RDofjTE/6qlLbwv79+9m/f3+nhy0Eg0G+/vWvU1payptvvtln5/46aB8cwm0bDuH2AVRVVXH++edz/Phxxo0bx5o1axg+fDiLFy9myZIlTJ8+vUfIt7mxglbk2xN1xiNHjrBjx44B6/0MBtmuW7eO5OTkDimuY60NY9uNrAELfU2ta83snT17dqcuiOFwmKVLl7J//37eeuutTg+lcNB3YBHutb840i2E+/gPhw04wu3bt9CfAkgpufjiixk6dCirV68mKSmJuro6Xn31VVasWME555xDbm6uTb4FBQXdRr4ul4shQ4YwZMiQuLGCa9euxePx2KnO7vCT3r9/P/v27WPmzJmdrkv3dQSDQdatW0dqairTpk3r0N9JCEF6ejrp6emMHz/ebv06fPgw27ZtIzMz0/579LYA7uDBg+zdu5eCgoJOXQwjkQhXX301u3btYvXq1Q7ZDjBIafx0dR8DEU6E2wewd+9eRo0a1WzqsaGhgddff53ly5fzyiuvkJWVxUUXXcSSJUuYO3duj0S+3TlW0GoXOXz4cKcv0P0BgUCAtWvXkpmZ2e1ev5b6PLHdqDdq8IcOHWL37t0UFBSQkZHR4ddrmsZ1113HJ598wpo1awZsWeHTCCvC/faDh/H6uhjhBmr5/e3DB1yE6xBuP4Lf7+eNN95gxYoVvPzyy6SmpnLRRRdRWFjIKaec0mKtsCvoylhBaxpOeXn5gB09B8bfZd26dWRlZXHSSSf1aB28N6cbHT58mJ07d1JQUNCpCVW6rvO9732PNWvWsGbNGkaMGNH9i3TQa3AIt204hNtPEQgEWLVqFStWrODFF1/E5/PZ5Hvqqaf2iODGEvlYRhutjRXUdZ0tW7ZQW1tLQUFBn+6r7AoaGxtZt24dgwcPZtKkSSe0xedETjey6u+zZs3qlLhJ13V+8IMf8Nprr7F69WrGjBnTbWtz0DdgEe41DxzC00XCDQVq+cOPRjiE66DvIRQK8fbbb7N8+XJefPFFFEXhwgsvZMmSJZx22mk94mwkpYyb6atpmq2wzczMZMuWLQPaxhCMdP/atWsZOnRok37qEw1d16msrGzSbjR48GCys7O7VHo4evQo27dv73T9Xdd1fvzjH7NixQrWrFnD+PHjO70WB30XFuFeff/BbiHcP/54pEO4Dvo2wuEw77zzDsuXL2flypVomsaiRYtYsmQJp59+eo+Qn2XoHzvZyO12M3HiRPLy8nok1d3bqK+vZ926dQwbNoxx48b1KfOK2Jshq93IGvPY0XajY8eOsW3btk6TrZSS++67j2XLlrFmzRomT57c4X046B9wCLdtOIQ7gBGJRHjvvfd47rnnWLlyJX6/n0WLFlFYWMjnP//5bveqtVpiVFUlMzOT8vJyAoGAPcpu8ODBfb63tD2ora2lqKiIkSNHMnbs2N5eTqvoSrtRSUkJW7duZcaMGZ1SEkspeeihh3j88cd5++23Ofnkk7tyKg76OCzC/dZPD3QL4f7pzlEO4Tron9A0jffff9+OfOvq6jj//PMpLCzkrLPO6nKN1e/3U1RURFpamt0SI6WkoaHBrvk2Njbao+z661jBmpoaioqKGD16dL+sQ1rtRtZ0o5bajSyDkhkzZnRq9qyUkl/96lf88pe/ZNWqVRQUFHTnaTjog7AI95v3dQ/h/vkuh3AdDADous5HH31kk29lZSXnnXcehYWFnHPOOR32Wm5oaKCoqIicnBwmT57cYnq1v48VtPyfx44dy6hRo3p7OV1GS+1Gqqqya9cupk+f3imDEikljz/+OPfffz9vvPEG8+bN64HVO+hrcAi3bTiE+ymHruusXbuW5cuX8/zzz1NSUsK5555LYWEh5557bpv+uFZ6ddiwYYwfP77dtczGxkb7Yt8fxgpWVVVRXFzMhAkTBmQ7i9VudPjwYWpra/F6veTn53e43UhKyZNPPsmdd97Jq6++ymc+85keXrmDvgKLcK+8Z3+3EO5f7hntEG5fwf33388rr7xCcXExHo+H6urqJs85ePAg1157LatXryY1NZWlS5fywAMPDIg6Yk9A13XWr1/P8uXLWbFiBYcPH+YLX/gChYWFLFy4sMkH//jx4xQXFzNmzBhGjx7d6eP29bGC1rCFSZMmMWzYsN5eTo+hvLycjRs3MmXKFBRFsS0/29tuJKXk6aef5gc/+AH/+te/OOOMM07sCTjoVViEe8Xd+7qFcJ+6d8yAI9z+NZokBqFQiEsuuYRrr7222cc1TeOCCy4gFArxwQcfsGzZMp566inuuuuuE7zS/gNFUZg9ezYPPPAA27dv56OPPmL69On88pe/ZPTo0Xz5y1/mmWeeobq6mn/84x98//vfZ8KECV0iWwCfz8fIkSOZO3cun/3sZxkyZAjl5eW89957fPLJJ+zfv5/GxsbuOckOory8nA0bNnDSSScNaLKtqKhg48aNTJs2jaFDh5KXl8f06dM544wzmDx5MpqmsWHDBt555x22bNlCeXk5uq7br5dS8o9//INbb72VFStW9Bmy/e1vf8vo0aPx+XzMnz+fTz75pLeX5OBTjH4b4Vp46qmnuOmmm5pEuK+99hqLFi3i6NGj5OXlAfDEE09w2223UV5e3i9qhn0FUkq2bt1qR75bt25FSsnXvvY1HnjgAQYNGtQjbTGhUMhOO/fGWMGysjI2bdrE1KlTGTJkSI8fr7dgRfAnnXRSq1aLzbUbffTRR+Tl5eF2u7nlllv45z//yQUXXHACV98y/vGPf/CNb3yDJ554gvnz5/Poo4/y3HPPsWPHDnJzc3t7eQMOVoT7jTv34fF1bbRoKFDHX3/qRLj9Bh9++CEnn3yyTbYA5557LrW1tWzZsqUXV9b/IIRg6tSp3H333XznO9/B6/Xy9a9/nS1btjB27FgKCwv5y1/+Qnl5Od15/+bxeBg+fDgFBQWcfvrpjBw5kurqaj766CM+/PBD9uzZQ319fbce00JpaSmbNm3i5JNPHtBkW1VV1S6yBeNzMGjQICZNmsRpp53GnDlzCAaD/PSnP+Xaa69lypQpdhq6L+CRRx7h6quv5sorr2TKlCk88cQTJCcn8+c//7m3lzagIaXslp+BiAFLuCUlJXFkC9i/l5SU9MaS+j3+/e9/85Of/IRVq1axbNky1q1bx9atWznrrLNYtmwZ48ePZ9GiRfzpT3+itLS0W780breb/Px8Zs2axemnn87o0aOpr6/n448/5oMPPmD37t3U1tZ2yzGPHTvG5s2bmT59+oCOhCwh2OTJkzs8RMCabnTqqafS0NDAI488whe/+EV+//vfM3ToUN55550eWnX7YPWEn3322fY2RVE4++yz+fDDD3txZQMfUpfd8jMQ0acI9/bbb0cI0erP9u3be3uZn1qcffbZFBUVsWDBAsC46I4fP57bb7+djz/+mJ07d3L++efz97//nYkTJ7Jw4UKeeOIJjh492q3k63K5GDp0KDNmzOCMM85g/PjxNDY2snbtWt5//3127txJTU1Np4555MgR21lpoM7shajgbdKkSeTn53dqH6tXr+byyy/niSee4KabbrI/B/v27ev1VqCKigo0TWv2ptu54XbQW+hTct1bbrmFK664otXntNfZZ8iQIU0EEqWlpfZjDjoORVFaFEgJIRgzZgw/+MEPuPXWWzl06BArVqzg+eef54c//CHz589n8eLFLF68mOHDh3dbzVdVVfLy8sjLy0PTNNtPuKioCJfL1SEz/0OHDrFr164BPbMXov3EEydO7LQQ7L333uMrX/kKv/rVr/j6178e994OHz68u5bqoB+iOyLUgRrh9inCHTx4cLdFFQsWLOD++++nrKzMTgu++eabpKenM2XKlG45hoPmIYRg5MiR3Hzzzdx0000cPXqU559/nhUrVvDjH/+YgoICCgsLKSwsZOTIkd1KvhbBWmMFS0tL2bBhgz1W0Jrpm2jmf/DgQfbs2dPp0XP9BTU1Naxfv54JEyZ0mhg//vhjLrnkEh588EG++c1v9ikfaQs5OTmoqmrfZFsoLS11brh7GDoSvYsZLZ2BSbh9KqXcERw8eJDi4mIOHjyIpmkUFxdTXFxMfX09AOeccw5Tpkzh8ssvZ8OGDbzxxhv85Cc/4bvf/W6fNFYYqBBCMGzYMG644QZWr17NoUOHuOKKK1i1ahXTp0/n9NNP55FHHmHPnj3dmnZWFIWcnBymTp3K5z73OaZNmwbApk2bePfdd9m6dSsVFRXous7+/fs/NWRbVFTEuHHjOm3eUVRUxMUXX8y9997Ldddd1yfJFgzB3ezZs3nrrbfsbbqu89Zbb9klEQcOTjT6bVvQFVdcwbJly5psX716td0DeODAAa699lrWrFlDSkoKS5cu5cEHH3SML/oApJRUVFSwcuVKVqxYwerVq5kyZYod+fbUuDurtcXydw6Hw0gp7YhvIE42AqNlY926dV2ypdy4cSPnn38+t912Gz/84Q/7LNla+Mc//sHSpUv5/e9/z7x583j00Uf55z//yfbt25vUdh10HVZb0Fd+uBOPt4ttQcE6nv3FxB5pC2qPaVIipJTcfffd/PGPf6S6uprPfOYzPP7440yYMKFDx+63hOtg4EBKSVVVFS+++CIrVqxg1apVTJw40Sbf1vyZu3LM3bt3c+jQIXJzczl+/DjhcNie6WulJAcC6urqWLduHaNHj+60ScnWrVtZuHAh119/PXfddVefJ1sLv/nNb3j44YcpKSlh5syZ/PrXv2b+/Pm9vawBCYtwL/3Bjm4h3H88PKlHCPfuu+8mMzOTw4cP8+STT7aLcB966CEeeOABli1bxpgxY7jzzjvZtGkTW7du7ZAbnkO4DvoUpJTU1NTY5Pvmm28yZswYFi9ezJIlS2zbwa4eY9euXRw7dozZs2eTmppqj7GzIl9rrGBeXh45OTn9NitSX1/P2rVrGTVqVKenG+3cuZOFCxdy5ZVXcv/99/cbsnVwYtFfCNdCS6ZJiZBSkp+fzy233MKtt94KGOWZvLw8nnrqKb7yla+0+5j98yriYMBCCEFmZiZLly5l6dKl1NTU8PLLL9t2gcOHD7fJd/r06R0mXyklO3bsoKysjDlz5tiOVVZfaXp6OuPHj6e+vp6ysjL27t3Lli1byM7OtmfI9pexghbZjhw5stNku3fvXhYtWsTXvvY1fvaznzlk66BNSF2id5NKuba2Nm671+s94Rqcffv2UVJSEtfTnZGRwfz58/nwww8dwnUwcJCRkcFll13GZZddRl1dHa+++iorVqzgnHPOIS8vzybfWbNmtUm+Ukq2bdtGZWUlc+fObXEGsBCCtLQ00tLSGDdunD3T9+DBg2zdujVupm9ftQhtaGhg3bp1jBgxot2tdIk4cOAAF1xwAYWFhTz88MNdziw4+HSgO9uCEsV9d999N/fcc0+X9t1RWH3b3dHT7XyDTjBGjx7dxMzjwQcf7O1l9QukpaVx6aWX8s9//pPS0lIeeughjh07xgUXXMC0adNs44VYU30Llh90VVUVc+bMaZFsm0NKSgpjx47llFNO4dRTTyUrK4vDhw/z7rvvsm7dOg4dOkQwGOzOU+0SGhoaWLt2LcOGDes02R49epQLLriAc889l1//+tcO2TroFRw6dIiamhr750c/+lGzz+svpklOhNsLuO+++7j66qvt39PSulbv+DQiJSWFL33pS3zpS1/C7/fzxhtvsGLFCi6++GJSU1O56KKLWLJkCfPnz0fTNO6//37OPvts5s6d26WRf8nJybb4yO/3U1ZWRklJCTt27OgTYwUbGxtZt24d+fn5jBs3rlMp4JKSEi644AI++9nP8vjjjztk66BD6A4vZOv1VpmnLXSnaVIirL7t0tLSOAvU0tJSZs6c2aF9OYTbC0hLS3Oa77sRSUlJtqI5EAiwatUqVqxYwZe//GW8Xi8ul4tIJMLVV1/drUSYlJTEqFGjGDVqFMFg0J7pu3PnTtLT022jjY5E012B3+9n3bp15OXlMX78+E6RbXl5ORdeeCGzZs3iySefHDBKbQcnDlLXkc1kmTq6j46gO02TEjFmzBiGDBnCW2+9ZRNsbW0tH3/8cYvjYVuCc+vaC3jwwQfJzs5m1qxZPPzww0Qikd5e0oCBz+dj0aJF/OUvf+HAgQOMHj2axsZGQqEQn/3sZ7nxxhtZvXo14XC4W4/r9XoZMWIEc+bM4XOf+xz5+flUVVXx/vvv89FHH7Fv3z4aGhq69Zix8Pv9rF27lsGDBzNx4sROkW1VVRUXXXQRkyZN4umnn+63yuyewPDhw/nd734Xt+2DDz4gOTmZAwcO9NKq+iZ0UzTV1Z+eQlumSQCTJ09m5cqVgKHpuOmmm/jZz37GSy+9xKZNm/jGN75Bfn4+hYWFHTq28406wbjxxhspKCggKyuLDz74gB/96EccO3aMRx55pLeXNqCgaRqXXnopmqaxe/duUlNTeeedd1i+fDnf/OY30TSNRYsWsWTJEk4//fRuFT9ZYwWHDx9OOBymvLyc0tJS9uzZQ0pKih35pqSkdIvqNxAIsG7dOnJycpg0aVKn9llTU0NhYSEjRozg2Wef7TdK7BOF+fPn89///tf+XUrJTTfdxM0339xpIxEHvYO77rorzjRp1qxZQLxp0o4dO6ipqbGf88Mf/pCGhgauueYaqqurOe2003j99dc7nDFz+nC7AbfffjsPPfRQq8/Ztm0bkydPbrL9z3/+M9/+9repr693LCe7GcuWLWPJkiVNakCRSIT33nuP5557jpUrVxIIBFi0aBGFhYWceeaZPfZ3iEQilJeXU1ZWRkVFBT6fz675pqWldYooA4EAa9euJSsri5NOOqlT+6irq2Px4sWkp6fz0ksv9Vr9uS/j4YcfZtmyZWzevBmAv/71r9x2223s2rWL1NTUXl5d34DVh1v43Y24u9iHGw7W8cJvpw+4AfQO4XYDysvLqaysbPU5Y8eObTaK2rJlC9OmTWP79u1MmjSpp5booAVomsb777/P8uXLWblyJXV1dZx//vkUFhZy1lln9Vj9VdM0Kioq7IHtHo/HjnzT09PbRZzBYJC1a9eSmZnJlClTOkW2DQ0NfPGLX0RVVV5++WW7L9lBPP7zn/9wxhlnUFNTgxCCSZMmce+993LVVVf19tL6DCzCXXzthm4h3Bcfn+EQroPuxTPPPMM3vvENKioqGDRoUG8v51MNXdf56KOPWL58Oc8//zxVVVWcd955LFmyhC984QskJyf3yHFjxwqWl5e3a6xgMBhk3bp1pKenM3Xq1E6Rrd/v55JLLiEUCvHaa685avlW0NjYSEZGBm+99RarVq3iX//6F+vWrXMU3DFwCLdtOIR7AvHhhx/y8ccfc+aZZ5KWlsaHH37IzTffzMKFC5sdxOCg96DrOv/973/tyLekpIRzzz2XwsJCzj333B5LI8aOFSwvL292rGAoFGLt2rWkpaUxbdq0TpFtMBjkq1/9KsePH+ff//43GRkZPXA2AwsFBQV89rOf5Y9//COvvvqqXe9zYMAi3Iu+XdwthPvS72c6hOug8ygqKuK6665j+/btBINBxowZw+WXX873v/99p37bh6HrOuvXr2f58uWsWLGCw4cP84UvfIHCwkIWLlzYYxcEXdc5fvw4ZWVllJWVIaUkOzub6upq0tPTOfnkkzsVYYVCIS6//HKOHDnCqlWryMrK6oHVDzxcd911PPHEEyxevNhWsDqIwiLcRd8uwu3pIuGG6nj59wUO4Tpw8GmGruts2rTJJt99+/Zx9tlns3jxYs4//3wyMjJ6bKxgeXk5W7duRdM0FEVh8ODB5OXlkZWV1e5+2XA4zDe/+U127tzJ6tWrycnJ6fa1DlT8/ve/58Ybb2TLli2MHz++t5fT5+AQbttwChAOHHQAiqIwY8YMfvrTn7Jlyxb++9//Mnv2bH79618zZswYvvSlL/HXv/6VqqqqLrvtxCISibB3714GDRrEGWecwaxZs/B4PGzfvp133nmHTZs2UVpaiqZpLe5D0zS+853vsG3bNlatWtVnybav2p8+++yzXH/99Q7ZtgGpR/2UO//T22fRM3AiXAcOugHWFKIVK1awYsUKNm/ezOmnn05hYSGLFi0iJyen05FvOBymqKgIr9fbZEJS7FjB0tJSgsFgs2MFNU3jhhtu4IMPPmDNmjXk5+d3y3n3BEaPHs1VV13VxP60NxTUuq5TXl7Ok08+ye9+9zu2bt06oCKu7oQV4Z5/1Trcnq5pHMKhel59cvaAi3Ad4wsHDroBQggmT57Mj3/8Y+644w727NnD8uXLWbZsGTfddBOnnXYaS5Ys4cILLyQ3N7fd5GuRrcfjaXYcYVtjBZ966ikWLFjAxo0bee+991i9enWfJlsLfcX+9N133+Xzn/88kydPZsWKFQPq4u/gxMNJKTuw8dvf/pbRo0fj8/mYP38+n3zySW8vqV9CCMH48ePt6UU7d+7k/PPP5+9//zsTJ05k4cKFPPHEExw9erTVtHMkEmH9+vW43e52zf61xgqOGzeOU089ldmzZ5Ofn8/999/P008/zahRo3jrrbfa7BnvC+gr9qdnnHEGuq6zdetW5s+f3ytr6G+whhd09WcgwiFcBwD84x//4Pvf/z533303RUVFzJgxg3PPPZeysrLeXlq/hhCCMWPG8IMf/IAPPviAPXv2sGTJElauXMlJJ53EOeecw29+8xsOHToUd5EJBAKsX78eVVWZMWNGp4YIpKen4/F4SEpK4s0332ThwoX8/ve/Z8iQIRw+fLg7T7NbceONN/Lss8+yevVqvv3tb/Pzn/+cH/7wh729LAfthK7r3fIzEOHUcB0Ahlfs3Llz+c1vfgMYX5oRI0Zwww03cPvtt/fy6gYepJQcPXqU559/nuXLl/PBBx8we/ZsFi9ezFlnncW3v/1tFi9ezC233NIpspVS8vOf/5w//elPrF69milTptiPHTlyhGHDhnXn6bQJx/504MOq4Z7zjY+7pYb777/OH3A1XIdwHRAKhUhOTmb58uVx0y+WLl1KdXU1L774Yu8t7lMAKSUlJSWsXLmSf/7zn7z77rskJSVx8803c+mllzJ27NgOCa6klPzP//wPv/71r3n77beZPn16D66+fXDsTwc+HMJtG45oygEVFRVomkZeXl7c9ry8PLZv395Lq/r0QAjB0KFD+eY3v8kLL7zAvHnz+NrXvsYrr7zCL37xC6ZMmWLP+50wYUKr5Cul5LHHHuPRRx/l3//+d58gW+javNLi4mIURSE3N7ebV+WgJyCljuxiX09XX99X4RCuAwd9BI888gj19fW8+eabpKWlccMNN1BVVcULL7zAihUreOCBB5g0aRKLFy+msLCQyZMnx5GvlJI//OEPPPjgg7z22mvMmTOnF8+mc2jJ/vTrX/+64zXeT2D10nZ1HwMRjmjKATk5OaiqSmlpadz20tLSPtGa8WnBrbfeyhtvvGEPERBCkJ2dzVVXXcUrr7xCSUkJt9xyCxs2bOC0005j7ty5/PSnP2Xz5s3ous6yZcu4++67eemll1iwYEEvn03n4PV6efbZZzn99NOZOnUq999/PzfffDN/+MMfentpDhx0GU4N1wFgiKbmzZvHY489BhiiqZEjR3L99dc7oqk+iJqaGl5++WVWrFjB66+/Tnp6OtXV1bz22muceeaZvb08B59CWDXcs7/6Pq4u1nAjoXpW/f0zTg3XwcDE97//fZYuXcqcOXOYN28ejz76KA0NDVx55ZW9vTQHzSAjI4PLLruMyy67jLq6Ov73f/8Xl8vlkK2DXocudfQu1mC7+vq+CodwHQBw6aWXUl5ezl133UVJSQkzZ87k9ddfbyKkctD3kJaWxl133dXby3DgwEEbcFLKDhw4cOCgy7BSymd++d1uSSmv/ufnnJSyAwcOHDhw0BKk1JFddIoaqG1BjkrZgQMHDhw4OAFwIlwHDhw4cNBtcPpwW4ZDuA4cOHDgoNvgOE21DCel7KDf4Z577kEIEffTnOm9AwcOTjx0HXRddvGnt8+iZ+BEuA76JaZOncqqVavs310u56PswIGDvg3nKuWgX8Llcjm2kw4c9EFIvRtUygM0xHVSyg76JXbt2kV+fj5jx47lsssu4+DBg729JAcOHBAVTXX1ZyDCIVwH/Q7z58/nqaee4vXXX+fxxx9n3759fPazn6Wurq63l+bAgQMHLcJJKTvod1i4cKH97+nTpzN//nxGjRrFP//5T6666qpeXJkDBw4clXLLcAjXQb9HZmYmEydOZPfu3b29FAcOPvVw+nBbhpNSdtDvUV9fz549exg6dGhvL2VA4v777+fUU08lOTmZzMzMZp9z8OBBLrjgApKTk8nNzeUHP/gBkUjkxC7UgYM+DodwByj+/ve/k5SUxLFjx+xtV155JdOnT6empqYXV9Z13Hrrrbzzzjvs37+fDz74gCVLlqCqKl/96ld7e2kDEqFQiEsuuYRrr7222cc1TeOCCy4gFArxwQcfsGzZMp566ilngtGnFJFQHeFg134ioQGqx5AOBiR0XZfTp0+X119/vZRSyrvuuksOHz5cHj58uJdX1nVceumlcujQodLj8chhw4bJSy+9VO7evbu3lzXg8Ze//EVmZGQ02f7qq69KRVFkSUmJve3xxx+X6enpMhgMnsAVOuhN+P1+OWTIEAl0y8+QIUOk3+/v7dPqVjg13AEKIQT3338/X/rSlxgyZAiPPfYY//nPfxg2bFhvL63LePbZZ3t7CQ5i8OGHH3LyySfHzU4+99xzufbaa9myZQuzZs3qxdU5OFHw+Xzs27ePUCjULfvzeDz4fL5u2VdfgUO4AxiLFi1iypQp3Hffffz73/9m6tSpvb0kBwMQJSUlcWQL2L+XlJT0xpIc9BJ8Pt+AI8nuhFPDHcB4/fXX2b59O5qmNbkgOvh04/bbb2/iR534s3379t5epgMHAwpOhDtAUVRUxJe//GWefPJJnnrqKe68806ee+653l6Wgz6CW265hSuuuKLV54wdO7Zd+xoyZAiffPJJ3LbS0lL7MQcOHBhwCHcAYv/+/VxwwQXccccdfPWrX2Xs2LEsWLCAoqIiCgoKent5DvoABg8ezODBg7tlXwsWLOD++++nrKyM3NxcAN58803S09OZMmVKtxzDgYOBACelPMBQVVXFeeedx+LFi7n99tsBwwpx4cKF3HHHHb28uk8H3n33XS688ELy8/MRQvDCCy/EPS6l5K677mLo0KEkJSVx9tlns2vXrt5ZbDtw8OBBiouLOXjwIJqmUVxcTHFxMfX19QCcc845TJkyhcsvv5wNGzbwxhtv8JOf/ITvfve7eL3eXl69Awd9B0JKOTAtPRw46CW89tprvP/++8yePZuLL76YlStXUlhYaD/+0EMP8cADD7Bs2TLGjBnDnXfeyaZNm9i6dWufFJxcccUVLFu2rMn21atXc8YZZwBw4MABrr32WtasWUNKSgpLly7lwQcfdMYmOnAQA4dwHTjoQQgh4ghXSkl+fj633HILt956KwA1NTXk5eXx1FNP8ZWvfKUXV+vAgYOehJNSduDgBGLfvn2UlJRw9tln29syMjKYP38+H374YS+uzIEDBz0Nh3AdODiBsPpSm+tbdXpWHTgY2HAI14EDBw4cODgBcAjXgYMTCKsv1epTtVBaWur0rDpwMMDhEK4DBycQY8aMYciQIbz11lv2ttraWj7++GMWLFjQiytz4MBBT8PR7Dtw0M2or69n9+7d9u/79u2juLiYrKwsRo4cyU033cTPfvYzJkyYYLcF5efnx7UOOXDgYODBaQty4KCbsWbNGs4888wm25cuXcpTTz2FlJK7776bP/zhD1RXV3Paaafxu9/9jokTJ/bCah04cHCi4BCuAwcOHDhwcALg1HAdOHDgwIGDEwCHcB04cODAgYMTAIdwHThw4MCBgxMAh3AdOHDgwIGDEwCHcB04cODAgYMTAIdwHThw4MCBgxMAh3AdOHDgwIGDEwCHcB04cODAgYMTAIdwHThw4MCBgxMAh3AdOHDgwIGDEwCHcB04cODAgYMTgP8HYbHVk39UKO4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_index = 3 * number_steps // 4  # time index of the simulation \n",
    "vector = pre_vector * radius\n",
    "surface_v = np.zeros((quantity_theta_points, quantity_phi_points))\n",
    "surface_v[:, :] = np.sum(\n",
    "\tsolutions[time_index, 4 * num:5*num, np.newaxis, np.newaxis]\n",
    "\t* spherical_harmonics, axis=0)\n",
    "surface_v_max = np.max(np.abs(surface_v))\n",
    "surface_v = (surface_v + surface_v_max) / (2. * surface_v_max)\n",
    "\n",
    "from matplotlib import cm, colors\n",
    "fig = plt.figure()\n",
    "ax_1 = fig.add_subplot(111, projection='3d')\n",
    "ax_1.plot_surface(\n",
    "\tvector[0, :, :],\n",
    "\tvector[1, :, :],\n",
    "\tvector[2, :, :],\n",
    "\trstride=1, cstride=1, \n",
    "\tfacecolors=cm.coolwarm(surface_v[:, :]))\n",
    "ax_1.set_xlabel('$x$')\n",
    "ax_1.set_ylabel('$y$')\n",
    "ax_1.set_zlabel('$z$')\n",
    "ax_1.set_aspect('equal')\n",
    "fig.colorbar(cm.ScalarMappable(\n",
    "    norm=colors.CenteredNorm(halfrange=surface_v_max), cmap=cm.coolwarm),\n",
    "    ax=ax_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That can be made a video too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For plotting a plane cut without $\\phi_e$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2944ef6fad0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uUKetrQ3bt29XFxWp44kBmbQphaIsdz7C7NUNzYTUWwTs1UWZkhlzrDxc9W1mv4Sn9OajD9GuDc2KkhkjA6GaPsSweJc6CCUjx9jy0/oytCUQ1w66DZliHTamrV/bOBql8mV2+TriYtVu02Zoc3DQkmiZJ5puQ/Zl9COtwAP26ggvg/l5h0MGCxy0GC5ZKC426E51FV2Hqmex9JW2Vxf31ShJeTGkjB+Iex8uLFmyBHPmzMFFF12ESy65BE8++STa29sxd+5cAMBNN92E0047DatWrQIA3Hbbbbj88svx+OOPY8aMGXjxxRfxzjvvYO3atQCAWCyGxYsX48EHH8S5556bTrUdNWoUZs6cCQDYvn073n77bVx66aX4gz/4A/yf//N/cO+99+Lss8+ObNcDKNPFByGEENLbuO6663Dw4EGsWLECzc3NmDhxIjZu3JgWjO7ZswdxX5r3lClTsH79eixfvhz33HMPzj33XLz66qtpjw8A+O53v4v29nYsWLAAhw8fxqWXXoqNGzemPT4GDx6Mn/3sZ1i5ciXa29sxcuRITJ8+HcuXL0dlZWVkr7UsfT7GLfpzJCqP+3w4GHoFD3Gz1Q0vtx4WV4S6Rrmxe6HVzX7nQ92tAAz/4cC4eex8WDNltDJl14E7Hz6485GxH+58ZFvXfecj2XEUu565pyg+H2++f1pBfD4uP39fpPPtq3DngxBCCBEkEUcyT1lkEaNEfY6yXHyE2avLdH3DO8Jvr25xHtX0F5oexKir6EGMusZuhcO1bCvn6C+Xc1B2GUyXVfEmS2t5bddE9KVt2qk7H7bdGEkqvK1BVDshvYE8djokmqeGWTd8l8G686HV1Y6kt+yS+Mcx+3HYzTDmJOoqfiLqzofh62G7dtg1ybAjkVW/Fp8P+Xc+4CeS9vlA0fAKoPnw8mzfn2G2CyGEEEKKSlnufBBCCCEarqmyYX2QzPSZxceqVavws5/9DLt27cKgQYMwZcoUPPzww/hP/+k/OfflJXxbgL7fjZSRWisaBlJTg0XSMl07FdYlJVYLsxj9GmV624A1u8NJuy4hGlsKr3FInX+bUoac5Pa2f/4yhVcVp4Z2EzKn7OvqHYdjDf2UAKvtucQh5BEcJ/u6hlW5NTyiCUNl34rgVLVi1+fkFErRwiVWe3WtLJ+2Wl3dSt4fOjFt5sV1FmJV472MkKQXR9KIDbn2UaDJ9EP6TNjlzTffxMKFC/HWW29h06ZN6OrqwlVXXYX29vZST40QQgghDvSZnY+NGzcGrtetW4cRI0agqakJl112WYlmRQghpD+SQgypPL+fp1y2P8uMPrP4kLS2tgIAhg0bFlqno6MjYA/b1tYW+bwIIYT0faj5iJY+ufhIpVJYvHgxvvzlLwec3CSrVq3C/fffb7b326v79AqWE7dVQy950rOhr/Dbq+dlHCavNSt2i0mX1lZL25VlUsMSMAoTZVoKL4SEQgTA1ZReGSw3TMf8gXao2PQjWt3gHPRxAmMYT5ToG5OrzsOP8iVR1Y9YTLr0unIOiobClgIbC/l/hjkFtAeuJmM5aj60fmRfLroN2ziarqOwabnKnHpSbWmc0W/oM5oPPwsXLsT777+PF198Ua23bNmywDHGe/fuLdIMCSGE9GV6BKf5Pkhm+tzOx6JFi7BhwwZs2bIFp59+ulq3srIyUm96Qggh/ZNjmo88D5Zj2CWUPrP48DwPt956K1555RW88cYbGDt2bKmnRAghhJAc6DOLj4ULF2L9+vX4+c9/jpNPPhnNzc0AgJqaGgwaNMipLy/hwRtwPKbuj2eKeKKpzcj8f0DXh9jaSsGIF6hrOxxOKwv3xTDb6gezBfrSDp2Drq9Q9SGivnw9pndHeJlVL6J0bOhH/Giv1UYf8P1w8vZweekWbYZa18kjJPza6gkSV8o0HYdFh2JoJgKaj+zb2jUfSr8uB83lpQ8R1w6aD2PcQNtjnwevu3ifi1QBznZhtks4fWbx8cMf/hAAcMUVVwSef/bZZ3HzzTcXf0KEEEL6LYUxGePiI4w+s/jQDhEjhBBCCkkKcfp8REifWXwUEm/AsXRbIHhSakxsrRrhEX9YxrbdK0MGTumz/n4cbNst/ephFz1MEVNOdlXbuoRoRH0tJGMfRzRV02Utdf3XCYdwjsRhAe0UzikgTsM6hGj002b1a6fUWy2t1eGkWqdQirWuMqeCptqG17XZoOccssknRGM55bYn1OKv65XlX6z+CX+UhBBCiCDpxZDM80tAvu37M1x8EEIIIYJkAQSnSYZdQqEDCiGEEEKKSlnufHgJX7zRvysm7cilla8vZmxoL6RtuAwv+5d5ih4EcLNXz9W2HUDQJtlqr66l2sq2OepDRH3NTv1YuTIntV9hn24Ez0Vfik26m/W6sgWrO+GXBscdYxdtRqCdRcugjmGzW49pZZoVu95vzmm5ck6WVNvAZ9SiJck1XVZeW1NgXebk13Uomg6jbsicZJ0oSXlxpPLMdkkxUSKUslx8EEIIIRoMu0QLwy6EEEIIKSrc+SCEEEIEKeSfreJwsHXZUZaLD2+Az1496dNMyHCyYZnu89RI6rFn1efDMo52tLeW2+9i2w4ENQlm2+zHkWFRvxbDXjdc7GDqNhz8RBS9iOYtkgndmj3HdlmM2+uw3Idz1nzY7u+56jasbZV52LxGXHQbLnoRVV+Ru1eH0zhR+XwkvKzryr572qbv20WgMCZjDC6EwXeGEEIIIUWlLHc+CCGEEI3CnO3C7/dhcPFBCCGECFKIIeWab56hD5KZslx8+H0+vJiDjiMQExbxS6FtiGt95aHjUK8tcV3VI8Soq2gxLJ4gAX2LXPgb2ozw83SkHMTw51D0IWZ6vU+H4nJmjCy25O3729r8Q1xwOkPGgbz0dHnpOMIrOOk2LHMqho5D8+bIVK5rPhzm5OIf4nLtoA+RrzUldB3IVUsCoREpgc8Hdz6ihe8MIYQQQopKWe58EEIIIRqFMRnj9/swynLx4SUyp9oae9uavbolXTYl+gqEKmwpsDmGUqxW7A7hHbn9GwiHWEI0/lCLETqxHHUfCNNYQjR6Wq5s6zue2zW1NnCt28N7oReOY2pTKBLOIZlcwzA2i3S1roPdel5W7KKtaq8u62YfSilYWq5DiMbWVrNFzy8tN3t7dfSk2sqwToSkvBhS+fp88FTbULgsI4QQQkhRKcudD0IIIUQjVYCwC03GwuHigxBCCBEU5lRbLj7CKMvFh5fw0rFDf8jYUzQeAICkF15mSbfz60c8qQfR+rLYtmtzsKXa6jqO8L4MLYmIaQdSbWV6rGGvLvry921Jnw2ktVrTZf0/aEtd1TJdvB5ZIUe7dWskO6pQdx4haRdthtk2eyt2TbdhnZODjiP3VFuL7XkeOo6cU21t/TrpRZT0WanT0Ma1ajzEOAmzrJiaDxItZbn4IIQQQjSSiCGZp0lYvu37M1x8EEIIIQKGXaKF7wwhhBBCikp57nwkvBN541o8WWhA/LHdWFIKB0Rb6eXhr2roQZS+HLQlql9IhraqjkOO44WXqV4dKVnZ1tYLratpM6y6DScr9vBxXSzTVQ8QS9teiaveIsu2LpbpLroNo76Tz0f2Ry246EOM+i5W5lY/Ed+FbU4u3h2arsPm3aHoQ0wNSLi2JF23iJqPJPIPm0gZITlBeS4+CCGEEAWGXaKFiw9CCCFEwIPloqU8Fx++sEsQGSqRKbG+MiNEI7dpZczAV24LhwQs0xWbdiAY1rBtScu2WihFSb21npbrD1M41D12HZ4Sq51ya0u1DfRl27l1Sr1VuimgvXopKJW9ulM/UYVSCmqvroxjsz3Xwkb5WJm7tHVJn83iZNqwORkKRH95ovhhFxIt5bn4IIQQQhQ8xJDKU/NhaMRIGu4JEUIIIYKesEu+D1dWr16NMWPGoKqqCvX19dixY4da/+WXX8a4ceNQVVWFCRMm4LXXXguUe56HFStWYOTIkRg0aBAaGxvx0Ucfpct/97vfYd68eRg7diwGDRqEs88+GytXrkRnZ6fz3F3g4oMQQgjpBbz00ktYsmQJVq5ciXfffRcXXHABpk2bhgMHDmSsv3XrVtxwww2YN28e3nvvPcycORMzZ87E+++/n67zyCOP4KmnnsKaNWuwfft2DBkyBNOmTcPRo0cBALt27UIqlcKPfvQjfPDBB3jiiSewZs0a3HPPPZG+1pjnuUSm+zZtbW2oqanB6DUrER9UBQDw/FoNmRaq6Ctisq7IqTLKAzoOh7qWI+mD/cb0ukpf1rqKZkJra52/Q0qsy5zMutl7m9vGVetqRFW3kLjsEjvUddF8WNNpA3ULqOPQ0u61I+hd9CGuc9KOulfr6noKNT3YRS9i03FksEg/0TZ7zUfsuNYj9R9Hsfd/3I/W1lZUV1cjCnr+Ttzxm2tQedLAvPrqONKFx7+8Iev51tfX4+KLL8YzzzwDAEilUhg9ejRuvfVWLF261Kh/3XXXob29HRs2bEg/N3nyZEycOBFr1qyB53kYNWoU7rjjDtx5550AgNbWVtTW1mLdunW4/vrrM87j0UcfxQ9/+EP867/+ay4vOyu480EIIYQIksdPtc33ARxb0PgfHR0dxnidnZ1oampCY2Nj+rl4PI7GxkZs27Yt4xy3bdsWqA8A06ZNS9f/5JNP0NzcHKhTU1OD+vr60D6BYwuUYcOGZf9m5QAXH4QQQkiEjB49GjU1NenHqlWrjDqfffYZkskkamtrA8/X1taiubk5Y7/Nzc1q/Z5/Xfr8+OOP8fTTT+M73/lOdi8uR5jtQgghhAhSXgwp53xzsw8A2Lt3byDsUllZmVe/UbFv3z5Mnz4d1157LebPnx/pWGW5+IjFU4gljosPfDFjLylNKcL7kL+TMekRovl8GHHe3D1BglbsFst3c9JKXXGtHHWvtpWeGRY7FNWPw8FeXfUPkTj5eoj4d1ReHn1A8+F0Xzb0FUrjqHw/CmnF7qL5cLBmd9N8KFbmhn5Cn5OTd4dS1xgnoXxINTt14MQ9GieOXYjF5Q0xOlKII5VncKCnfXV1tVXzceqppyKRSKClpSXwfEtLC+rq6jK2qaurU+v3/NvS0oKRI0cG6kycODHQbv/+/Zg6dSqmTJmCtWvX2l9cnjDsQgghhJSYiooKTJo0CZs3b04/l0qlsHnzZjQ0NGRs09DQEKgPAJs2bUrXHzt2LOrq6gJ12trasH379kCf+/btwxVXXIFJkybh2WefRTwe/dKgLHc+CCGEEI2kF0Myz7CLa/slS5Zgzpw5uOiii3DJJZfgySefRHt7O+bOnQsAuOmmm3DaaaelNSO33XYbLr/8cjz++OOYMWMGXnzxRbzzzjvpnYtYLIbFixfjwQcfxLnnnouxY8fi3nvvxahRozBz5kwAJxYeZ555Jh577DEcPHgwPZ+wHZdCUJaLj1jCS6duBQlu6XnGxpAXVtXcJZfhBTW9TolFGBbpeWxXGx7kyhy00IoWkhHlRje28I6/bT6W6S4hGokyrsuptsYcLMMGxyxN3EUNh9hwsVAPjFnAuvmEUhzqqt5RhbRXV06bdUr/LWT6rENKbyAsY6nrD7MACJxw3XO/znzfjoZCaj6y5brrrsPBgwexYsUKNDc3Y+LEidi4cWNaMLpnz57ArsSUKVOwfv16LF++HPfccw/OPfdcvPrqqzj//PPTdb773e+ivb0dCxYswOHDh3HppZdi48aNqKo6ZjexadMmfPzxx/j4449x+umnB+YTpRNHWfp8nPmXyxEfbPp8eOIPu6EB8X82DG8O3SMk4MHh4vNRSE8Q1edD/6MaUzQfVu8Opa7LgkKra9d8KHUltnG1cbIts8DFR451ufg49v9+uvhIfXEU/zbvwaL4fCx481pU5Onz0XmkC2svfznS+fZVqPkghBBCSFEpy7ALIYQQopFEDMk8D4bLt31/piwXH/F4CvHjKVuBVCrj90RoQLR0WYPw1NtYLLzseIXwcfJJy1XK5RyMUENAtGIZxx/ikNoYuaUru3LQcRRMHyJxSr3Nvh8N2U9vOA3TOdztEi7R2hUqtVaWu6TA2l57jumyZlsR/nBJ6VXSZ81U2wKmz/rLjTkp6bSiLCavE+HlPfdrFDPV1nPXbGTqg2SGYRdCCCGEFJWy3PkghBBCNFJeHClVWZxdHyQzXHwQQgghghRiSOUZ/sy3fX+mLBcf8YSHRDq+eCKGaLXSVWQPWl0xTAbJRLhowhb7j/nruniCyIlY9CEBzYrsV/PucPD1MK5d6kry0YcofZnaDIc5KXX7RGjY5T5q+9XTbM9d6tp0HC51VS8epa5N86GkzzrpQ1zSZy39qpoQa6pteF1TL2Kmy6avLRqQuE/fkb5fF9Hng0RLWS4+CCGEEI1SOJyWE1x8EEIIIQJqPqKF7wwhhBBCikpZ7nzE454vnuhff+lnu6gZ5tYjP8IPR9Hiy8aRK0ZdxefD8AnP3ppdjuP36zB8SQx7dcWnxGLN7hVB85FPXWe9SLZzEDj1W0Ccdokd6rpYqBdUx+FSV/MEcdFiKEfdG20d9CJm3cJYpBvllnGgeIIYZ6/4NR+GpkNqPoI3g4Svr577tfE6IiSFApztQsFpKGW5+CCEEEI0vAJku/QGs8DeChcfhBBCiKAUp9qWE2W5+EgkUkgkMgVRgvuNSRFPiPvKbQe5GtGGmFIqPXjjJ8o90bNMyw2EQGRYxQidKOEey6m8SChlxov1jaOFZDK2Dfm/7bqQIRqX8oj67ZUJhQ6W4xIne/U82hbKXt1e1+G0Wc0yHeFlx/rOMX1Whie0dF85rhZmAQLprjKUolmou4RZjtX3p9oe/3/G+zbpi5Tl4oMQQgjRYLZLtHDxQQghhAgYdokWLssIIYQQUlTKcucjEfOQOB7XDMY+ZTwxXAMSt6ThahoQI86rWpsrGg9Iq3Oh6TBEH9o42aflGktWTV9hjGnxJ/d9UzDSf5VxXOoa2OpqX16Yaht5v056Ea2tU11LOrx21L2LjXs+6bPacfa2VFu1ra75iCl1tXRaF42HbNtzvy7mB4Nnu0RLWS4+CCGEEA2GXaKFYRdCCCGEFBXufBBCCCEC7nxES1kuPuLxVDq+6H8Duo2NIGG37vl9PsI9QAAzHuuvbVpb2M6d93ckNCD+mKqh8RDxYyFM8dc37dTDY94xOQfFctzQXtheqn9cRQ9iHUd5C/PRh9hs6FVdh4tGwlKea+i7aPfCAnp3qFbm+bTVdB02fUWu/iFw8+4I6kMs/htaXU3jIa81jYeoGxe6jZjUpPl0HNLnQ9N4AMCAQNsee/Xi+Xxw8REtDLsQQgghpKiU5c4HIYQQosGdj2jpU4uPLVu24NFHH0VTUxM+/fRTvPLKK5g5c6ZzPwPjJ+zVu3zPx+UvirEvFJ5vKsMwSAXL4wl/3SB6GMayv+4LgXjyREklzHKsZ3/cwrZPHnphtlWyl41Tel1ykm1pusqccg3RWNsa41rKQ/p1pRT3tIKm4eYaSnGwPZdo6bJGuS10km0/GeYUCK1Ywy4O6bPaPrbFBt3f1maZ7g+1aGEWQKTLJvQwSzwWHpYZeLytDNVEiYf8U2V75TEJvYQ+FXZpb2/HBRdcgNWrV5d6KoQQQvoxPTsf+T5IZvrUzsdXvvIVfOUrXyn1NAghhBCSB31q8eFKR0cHOjo60tdtbW0lnA0hhJC+AjUf0dKvFx+rVq3C/fffbzwfj6eQOB47DP5yJAP1upOJwHXAUtkS/Nc0IDEZuxVtg7IHSy6nv9hwh1c0HgBifgGGTK2FopkQw8TEe+G/NHQmNn2FXwvgkqZr6DgUfYiiB8mEOmeHtFynfnsjhUyfzbVfm+25U6qtUldOQrVI19NanazZFS2GPFrBTLUN14cYv4x5WKb7dR6axkNe2zQeAxLB+2/Crxdhqm2/o09pPlxZtmwZWltb04+9e/eWekqEEEJI2dOvdz4qKytRWVlZ6mkQQgjpY3DnI1r69eKDEEIIyQXPi8HLc/GQb/v+TJ9afBw5cgQff/xx+vqTTz7Bzp07MWzYMJxxxhlZ95OIeekjmlPxcO8OT/qR+3QbRpzXgl8DErNEu/w9W63YPaW29MWQGhBfW8OaXUS9nXQcDp4gVqtzf13tpSsW72ZdB78QIDBnQ8eh3FsK6QnSK3C1NlfQdBx6XX1MJxt0OVCOfiKaJXrGvhR7ddXLw+Zp4m9r0aFoXh6GxsO41izTFc2HmG9C6DcS8fDynvu1oXshfZY+tfh45513MHXq1PT1kiVLAABz5szBunXrSjQrQggh/Y0UYnmbjOXbvj/TpxYfV1xxhTXLhBBCCMkXaj6ipU8tPgpFIiTVVm7pyW1Afy6ruQSyhFJ848jtx5TS1Jpt6j9h1pivJQzjP9VWbq0qe9QyZdcIpfh2U+WWtJaWK/uKiaiXcXqutk2uhIJcQj1GBYcQje1LT1/bQXazV88jlGL0pczBdu0fU+kXkLbnDumzLhbpQPBWoYVkZLkt1VYJ0dgs02NK2EXer/yfO3vYxRc6sYRZjLCM77oUqbYkWspy8UEIIYRoUHAaLVx8EEIIIQKGXaKFiw9CCCFEwJ2PaCnLxUc85qXjiwPimo4jSMoXzE0Y8ddgLNITgV9/LNRwQQ/P6DVQrdhT4hfdSQMi0mdlTDigLZGTCrdmt+orZIjbNydPpAbr6bOiH80O2zYH5W1z0ofIbnSpjKXfiG5ieQhPcrZTt5S7pMsabbVxIkqftVqk52HNrlqmK21dNB7y2tB4KLqOWEyWCV1HLLyuqQEJXvvvzT1zknMjfZeyXHwQQgghGl4Bwi7c+QiHiw9CCCFE4CH/wx+5TxNOvz5YjhBCCCG9j7JcfAyIpdKPWMxLPxLiEROPRPzEIx5PBR4xIPCIxz3x8NcPlsXEo0eTEo+ZZfIB38MoMybliQdOPGKeeATbenEv9KGNY61rjHPiIedrju2vG3x4MfHAiYc5X9FWPvz9iDK1L+W1qWNkeijvf14PdUz9kddr195T+fD3A/EQc9Z/luJ30fj9Ul6b8nkwPlf5fHbk5zDwevRxwu4Lme4NLvccp3uZcR88Udd//0zEM9xflfuv/55dLHocTvN9uLJ69WqMGTMGVVVVqK+vx44dO9T6L7/8MsaNG4eqqipMmDABr732WqDc8zysWLECI0eOxKBBg9DY2IiPPvooUOehhx7ClClTMHjwYAwdOtR5zrlQlosPQgghRKMn2yXfhwsvvfQSlixZgpUrV+Ldd9/FBRdcgGnTpuHAgQMZ62/duhU33HAD5s2bh/feew8zZ87EzJkz8f7776frPPLII3jqqaewZs0abN++HUOGDMG0adNw9OjRdJ3Ozk5ce+21uOWWW3J7s3KAiw9CCCGkF/AXf/EXmD9/PubOnYvx48djzZo1GDx4MP7qr/4qY/3vf//7mD59Ou666y6cd955+N73voc/+qM/wjPPPAPg2K7Hk08+ieXLl+O//tf/ij/8wz/E888/j/379+PVV19N93P//ffj9ttvx4QJE4rxMgFw8UEIIYQY9JiM5fvIls7OTjQ1NaGxsTH9XDweR2NjI7Zt25axzbZt2wL1AWDatGnp+p988gmam5sDdWpqalBfXx/aZ7Eoy2wX/9kuA/znm4hfFM3Lw/MSRp8BpFmH71IejmccFe/P15e/vA7eBLKq4QMS8BAQZco5MBLDE8Q/Z3k+i6hrnAvjP0ZFtDVn4HvtxotV+rX4fBjnYvivbV4d4dYpBjGHur0Bt7Ndsi+3ZgTEQv4P3avDNifTn8OhX3+5+NwZx74bfSn9aufCyN9L+VnyXUtPDXmPMX48ih+H6eUR7gki74P+24rh6yH7FdcDMpwLU8yzXTyvANkux9u3tbUFnq+srERlZWXguc8++wzJZBK1tbWB52tra7Fr166M/Tc3N2es39zcnC7veS6sTqngzgchhBASIaNHj0ZNTU36sWrVqlJPqeSU5c4HIYQQolFIe/W9e/eiuro6/bzc9QCAU089FYlEAi0tLYHnW1paUFdXl7H/uro6tX7Pvy0tLRg5cmSgzsSJE91fUAEpy52PWOyExXocJx494Ziehz/9TD5kXZk2JusHyjKmr2V+xOKp4EOmAMdx4iHKZNqemaaL8FRbI90xPA3XSC2MeemHljaZKbUw+7RJS9qn1q+WIpopTRRKaqdDumlBU2+jeji9x9m/9nxSn7V+7CniyuuRv18O/QbbeYGH9X3K+nMWLDdT6cXnO+y+kOHeIO8rTvekLO9zMXGf1O6nme6p/nvzif5RNAqZ7VJdXR14ZFp8VFRUYNKkSdi8eXP6uVQqhc2bN6OhoSHjHBsaGgL1AWDTpk3p+mPHjkVdXV2gTltbG7Zv3x7aZ7HgzgchhBAiSHkxU3OXQx8uLFmyBHPmzMFFF12ESy65BE8++STa29sxd+5cAMBNN92E0047LR22ue2223D55Zfj8ccfx4wZM/Diiy/inXfewdq1awEAsVgMixcvxoMPPohzzz0XY8eOxb333otRo0Zh5syZ6XH37NmDQ4cOYc+ePUgmk9i5cycA4JxzzsFJJ52U13sQBhcfhBBCSC/guuuuw8GDB7FixQo0Nzdj4sSJ2LhxY1owumfPHsTjJwIWU6ZMwfr167F8+XLcc889OPfcc/Hqq6/i/PPPT9f57ne/i/b2dixYsACHDx/GpZdeio0bN6KqqipdZ8WKFXjuuefS1xdeeCEA4PXXX8cVV1wRyWuNeTL1oh/T1taGmpoaNL72HQwcUgEA6EqeyFrpFuki/jIASPpWscmUrBu8Tolyf1tZlhJZKP5rWeaJtv6YpMwOMbJbPNmX71qKyOWKPaWUKdkjxjcHY5zwcY3EBXWcPPqV2PryoX6vyeeTVapPZT5f9JS26suR7bR+jLp6ZkmgvmWcYF1LxkogM8Yhu0X2rWW3iHIju0VmpfizXWTmm1FXZKX4M1jEOOa1LwvFyIQJ9jswYWashLUdmEgGrv1upj1lXe2d+OXVP0Jra2tAQ1FIev5OfOmFpUgMNsMjLiS/6MC/zP5/Ip1vX6Usdz564odA8AMh/9DLD0vKtxgxj4eWt9fs2xppcL4nzKPhg20DV6KyvFnJxUkwXVAuEuRNMBZepqXhQt70LAsXX9+e6Ff7u2idke99M1NtLeP4n5CpttpE5M9V1tWwVc51cVLAmLnTgsKhXF1gWPo124aPqY5jLApkW2VOtgVSPMsyWa4sNoxxjXuM7Z6j1RXX/unKBYVMu/e1lW+LmZYbnrbbUybrRMmxVNv8PjDl89XenbIUnBJCCCGkdJTlzgchhBCiUchUW2LCxQchhBAiSKeC59kHyUxZLj4GxJIYEDsmYEr5gp0JcVxzSgRG/Xa/hvBTajFE24TSNia1Gv44qSVO7e9JOrqbduri0hefNfUgcsXuZVeWaaBATRk/Vl6QCJhqWg0ZCtYs1M3ZyZ+dMo7RNntUfYgrpfhC5TKmizbDFsf31VU1HRmunUSkqj5E01fIfmzjaHoRRddhea3+uoY2wqoBCb/nmPo2vxYjWFeO678eYNN4xMLLe+7XXiwoSiV9l7JcfBBCCCEaDLtECxcfhBBCiIRxl0gpy8WHP9XWv7WnbRkCQEpJG7Omp/kayPx2uaUbTHsLjiRz7lO+nUqXE3CBYCqrLbyj9mug5JsaNS1hmCzHySct19i+VuIjttNz/X1ZswKVFN5egeOXNv13JnuzFKffPZf0WYeQTV4n07qEhpSUV1nudFKt4b9hS7X1Mv4fMO9XWl0tLdc4HdfhuhSptijAzofbUdDlBVNtCSGEEFJUynLngxBCCNE4ZjKWfx8kM1x8EEIIIQIKTqOlLBcfAc0HzLhi+hrhMUiZNuaSeivLjDhmoCuR/muk6fovFOt1ozIQU7QM8myIQNqutHWWKb3aJGwpmL4Gueo/jl1lrwHRe7KrVsJLsh+1N96inO+bDroOdRwHzYfTWS9WvYiDPkQrk9eKDbr1vBaXtFw1XVZMSTvbxaLj8KfX2nQbAzJYpKevlfurLC+J5oNESlkuPgghhBAVL5a/YJQ7H6Fw8UEIIYQIqPmIFma7EEIIIaSolOXOR9DnwxeTlDoBJQYpTX5dfD+MXH4HtFx/Q7dh8f3wlDJT+OB7whxIVg4vs3mRBKZQGA+QY1eKRbpF5KF9eclVD2LW7IXbs67xdRddR5btZLmTxkNe52OZbswpey2G2tYoC79WfT1Evzb/DRf0e1m4r4fEriWR16ZepLg+H6DJWISU5eKDEEII0WC2S7Qw7EIIIYSQolKWOx9xeOkQSmAbT2a8ytRVL3y70agrxvRv8SbF5qTWVtqrawIm05rZknrrP63VSA0WXfnmbF/M+7ekLfEchzCMa9puWON80nCt08/eWV78oPvA/qzDG2X9HXEIceR8Mq2tb6e6WojGbU5aerwaHnE4wsGGZq9uC224HEkR6NeSWquO03O/LnYcow98LPsqZbn4IIQQQjQYdokWLj4IIYQQCQWnkULNByGEEEKKStnvfGSKK2YqA4LptYZOQ9ZVttvioki2jSlaDDNW69NiaOmxot9jT/jmICep5aOaOX6hVe06AYuIIlBkeT0agaoWK/Y8tCVqWm4+mpWovkHlsStcqPRZa79aWqsDRmqthqu2RK2rWKg76EO01FqjSNF0ZLxWyuT9SsOmAVHrOmpCoieGvH7h0n2QTJT94oMQQggxYNglUhh2IYQQQkhR4c4HIYQQIuHOR6SU5eLDb6/u/+Xw2/keK5PH14frQ1zs1m06Dn+s05AJiMqabbtM8zK8PAIXlroBHYocR04ydBS3Ux5t/g++vq3W6w5iDFUDYrWhDy/TXro1vF2C0LFzlmCOGhCrZbrLmJqeykW3YR03ex2K5r9htT1X7htaX3atWLi+wqoP8ddVZ6T3a9ZNKWWlsFeP8VTbCGHYhRBCCCFFpSx3PgghhBANz9MdpbPtg2SGiw9CCCFEQs1HpJT94sMpD91/PotM3bfkt2u+H4XCjOsGr13OhVF1HBY/EV3cEF5kdJ7Pe5aPh4aiAbF6deR4tkteL9VygyvYr55LP/mc16L1VUjdhjFOgfQhLq9HFuV1Pkv2bQuFdpaLra7L2S6k/1H2iw9CCCHEgILTSOHigxBCCBHEPLfEq7A+SGbKcvERj6VOpHX50mmNbT7lF8f1aOdA+qxhzR4T1770NEsKrL+p6wmKWiRFDydYwizaNPL5MGrpmqLj3K3Xoc7ReKku4Slt3Dzel8i+XBUw1dZpjoW0UNdCNvng0q/2F8iWppvtfGQ7Bzt1WS7t1F3DJYG6Dr/Yegg8Ffi3KFDzESlMtSWEEEJIUSnLnQ9CCCFEhZqPSOHigxBCCJEw7BIpZb/40GKS+cQrpd16r8AlJdalW4eU3qjm4ISDxuNY/fCcWFUD4jKO65yiokDaDOuPNR8L9VLgMN/IUl77gHqxkHoQV10d6VuU/eKDEEIIMeDOR6Rw8UEIIYRIuPiIFGa7EEIIIaSocOcjIkphry6Ruf2qD4hFi+Hvy9VPRKVYWocCeWoUDQdr9oL229sp1vwjHEc9Wt5JW1L6X+R+bYHObJdI4eKDEEIIEdDhNFoYdiGEEEJIUelzi4/Vq1djzJgxqKqqQn19PXbs2FG0seMxL/3ojcRiXuDRJ4n5HnngxbzAI+c5FNqSu1D9uvQTxZi95H3J6+eszaMP0ts/+/77Z2+9hwbwCvRwxPVv3Msvv4xx48ahqqoKEyZMwGuvvRZ8GZ6HFStWYOTIkRg0aBAaGxvx0UcfBeocOnQIs2fPRnV1NYYOHYp58+bhyJEj7pN3wHnx8dRTT2H//v1RzMXKSy+9hCVLlmDlypV49913ccEFF2DatGk4cOBASeZDCCGEFArXv3Fbt27FDTfcgHnz5uG9997DzJkzMXPmTLz//vvpOo888gieeuoprFmzBtu3b8eQIUMwbdo0HD16NF1n9uzZ+OCDD7Bp0yZs2LABW7ZswYIFCyJ9rTHPUy2hDOLxOMaOHYs33ngDo0ePTj/f2dmJ//2//zcmTZpU8En2UF9fj4svvhjPPPMMACCVSmH06NG49dZbsXTpUmv7trY21NTU4Bubv4mBQyoAAN2pRLq80/d/WQYA3b5D6LqS4WUAkEwFr7t817LMvI6FlqWEgCnlqyuFoP6yTNeer2/5S+CJuv4KZpns13/anexYXoePAzmOxAv5fwYCB83Z5qSOo8/J6Qtdob78uRxglw8O/TiZjFnrhs/ButvhcgBcXJmTw4F1sbis64WXW9oGhokHD1WLi7r+a7n7YdQV5Qlf34l4eJm8HqiUAcAA30FwAxPJ0DIAGBAPllf4rnvKuto78f9d+f+itbUV1dXViIKevxNnPvwg4lVVefWVOnoU/3b38qzn6/o37rrrrkN7ezs2bNiQfm7y5MmYOHEi1qxZA8/zMGrUKNxxxx248847AQCtra2ora3FunXrcP311+PDDz/E+PHj8fbbb+Oiiy4CAGzcuBFXX301fv/732PUqFF5vQdh5BR2aWxsxOWXX469e/emn/v3f/93XHLJJQWbmKSzsxNNTU1obGxMPxePx9HY2Iht27ZlbNPR0YG2trbAgxBCCCkm8u9QR0eHUSeXv3Hbtm0L1AeAadOmpet/8sknaG5uDtSpqalBfX19us62bdswdOjQ9MIDOPY3Ph6PY/v27bm/aAvOi49YLIbvfe97mD17trEAcdxEceKzzz5DMplEbW1t4Pna2lo0NzdnbLNq1SrU1NSkH/6dGkIIISSUnlTbfB8ARo8eHfhbtGrVKmO4XP7GNTc3q/V7/rXVGTFiRKB8wIABGDZsWOi4hSDnVNvvfe97iMViuPzyy/Hmm2+ioqICscgONciNZcuWYcmSJenrtrY2LkAIIYTYKaDD6d69ewNhl8rKyjw77vs4Lz78uxsPPPBAegHy4osvFnRiklNPPRWJRAItLS2B51taWlBXV5exTWVlJX/IhBBCSkp1dbVV85HL37i6ujq1fs+/LS0tGDlyZKDOxIkT03WkoLW7uxuHDh0KHbcQOIddHnroIQwZMiR9ff/99+PGG2/EV7/61YJOTFJRUYFJkyZh8+bN6edSqRQ2b96MhoaGSMcmhBBSZhQ51TaXv3ENDQ2B+gCwadOmdP2xY8eirq4uUKetrQ3bt29P12loaMDhw4fR1NSUrvOrX/0KqVQK9fX12b8AR5x3PpYtW2Y8d//992PgwIF47LHHCjKpMJYsWYI5c+bgoosuwiWXXIInn3wS7e3tmDt3bqTj9iAzTXobBbU9LxUFkg3F8nkvopIuFbLfXLNq8vkVkWMW6tctj37lzzkvr49CvU8lwv/5741eH8b9s5e/x6VwOLX9jbvppptw2mmnpTUjt912Gy6//HI8/vjjmDFjBl588UW88847WLt27bHxYzEsXrwYDz74IM4991yMHTsW9957L0aNGoWZM2cCAM477zxMnz4d8+fPx5o1a9DV1YVFixbh+uuvjyzTBSigvfry5cuxfPnyQnWXkeuuuw4HDx7EihUr0NzcjIkTJ2Ljxo2GmIYQQgjpa9j+xu3Zswfx+ImAxZQpU7B+/XosX74c99xzD84991y8+uqrOP/889N1vvvd76K9vR0LFizA4cOHcemll2Ljxo2o8qURv/DCC1i0aBGuvPJKxONxzJo1C0899VSkr9XZ56Mvk6/Ph79c+m/0Bp+PlKgrf7J9wucjpZRJFJ8PdefDOidtzDx8Pkq18+Gn0M6kITj5fNj6dfDqMHY+XHw+/G1lQLoP+Hz49f5xmydICXw+ZFmF8PXobT4fYx58qCA+H79b/meRzrevwoPlIqI3hGicwjCWupGFdIq19O1rS+xShX5K/2urE1Xop4jjqOERIzQR/gOTn8lShFrkfS4RUq9PUsBsF2LS5852IYQQQkjfhjsfhBBCiKAUgtNygosPQgghROJzKM2rD5KRsl98pJRgrlZm1O0Lv2QRzdFJstwb3ifXbyPKnAsmMO0t35Bc0k0VXYRNyhB4wvb1sDekwDppMUTVgqUkZz+HUuGSTmu7v7rcfyOBmo9IoeaDEEIIIUWl7Hc+CCGEEAk1H9HCxQchhBAiYdglUspy8ZHy4kh5ZsTJRbfhGo/0920Yhcn4uK/c8L+Shl55aCjUz0UeRlua+VdeKGZgxbJTt36TKYHOwyqZyPWtcfW6ULQZVg1IPuMGxhGfD+1NLqTVvNavptWwvNZc5S7mfUJOyRPl/vuTMC+TfiK+64Tll89/n7R5gGj33577dab7NumblOXigxBCCFEpQNiFOx/hcPFBCCGESBh2iRTuYRFCCCGkqJT9zoceZ5TajPC6MsZaCt8PI67rsOq21s1HA6L1YztoLle0cayvVca4HcbJtkwQpSo+175Nbw7bQEpdVfZgE4hYxlXGccLTXoDDODY/DkXI4eIRon3eC+YtYkHe5+L53E/lGZMBL5icppcf3PmIlLJffBBCCCESptpGC8MuhBBCCCkqZbnzkfJiGcMitjSuYDqa5Qh6pa0tXTal1s2+X2NOstwhjKTNwayQ3RhWLCGaQAqgLZyjjlOgMIulPK9vQVF9g1J+PM4pvFpeqIsVuy0Mo/VrDONPW88jlGKMq4RoHEIp8nMWU3KSjbdQSZc17xPhdQEg5e/X5Z5jS7X11Y3b7NSN+2/KVxYz+iN9m7JcfBBCCCEq1HxEChcfhBBCiICaj2ih5oMQQgghRaXsdz4CtucI115o7Wx1zbbBa0PXoZVZ4rHBwvB+jbYuKbCGdkSbg0O/Fgpmoe6i8TDa6lWdvun0hm9FeaSx5iHFcOrX03J487FeV1+AQ56xtar2edHTigOXxvsU/sZpOo2M5YG28t4WrKzZpMv7YGCOWiotgFRMuaeWSurRGz6j/ZSyX3wQQgghBtR8RArDLoQQQggpKtz5IIQQQgQUnEZLWS4+Uoil9R1Oug6/Z4BF8+GiCZFlWr6+hi3O6+TrocWInfQhSlnGiSj9utRVxjVuCFF5d+ThNdIrcLU517w7XK3aM3dreoDk2pGtqVFXaez44gI26FA+ZxBeHhYNl7+xzV5du1ekRF3DfSPwWRIaD9lW0dTZNFyZ9Hiyj0hh2CVSGHYhhBBCSFEpy50PQgghRINhl2gpy8WH317db+mrhT8ylQfqyms1lJL71qGaeuuSWisrWEMP2vGaSiqhS5hFXBvbsi7z19JpHcMsuZ9q65JGnHXVomGGOOwtwtB6smWmBn4njKLcwzBGyMMpnTbgka5X1mJQttCWF16kpd7aTrg2bNwVtDRdo0zp1zgB12JtkIL/3pzKWCdSGHaJFIZdCCGEEFJUynLngxBCCFHhzkekcPFBCCGECKj5iJayXHwENB++uKOWWivLu1Px0LLM1yf+b03TTfnmJMbRYrnW1FotFVfGblNKW60s07VD3YDOw5o+6/+/xTI9H4v0HHUdfc5qXeCu+HBSdoSOk4fje8E0IKr+Qw5sG0J+XuI+K3NRFhOB8GBarp6/HHRtD9aV9w15Xwkk2IqiuHG/8qX0anbqCN4npc5EtVMX5Sc0etR89Beo+SCEEEJIUSnLnQ9CCCFEhTsfkcLFByGEECKg5iNaynLxEfT5UDQfmleH6FP13xDXSYe6Zqw2XNdh8/UwNSHhdd08NeR19roN1cujkJbpAf8QS12JNo5R11Kea91SYLGvkATeG4s9efAyOJDxHiu/TsYc5LBO4gx/Pw4eIK46E6XY8OMI+HzIz4qs7G8ndWTBqvF4sK12z5H3K91PJNz3I58jKUqi+SCRUpaLD0IIIUSFYZdI4eKDEEIIETDsEi1lufjo9hKIeQkAwW28pKenz/rTxlxSawEg6Wur2RXLclv6rH9cNT02w3WgvtXKXAulZB86sVqm+7eH80ifdbJEt42jtXUoL+iGca43tXwmYXECz3kaakgmOJJSlLFtIJszZhnH/4MXeYAFDcMEBrakz/o+D7G4/gPwf55lJq1Ma9RT9sNDMkDwXhaLJQNlWuqttCeQqbfy/hv3zaP7+P2651/S9ynLxQchhBCiwrBLpHDxQQghhEi4+IgUmowRQgghpKiU5c6HP9U2qeg4ktLa3P9/o65Mbcu+rX5kNdS6mhbD1IAo1yIVz6iraDH0tFaln4xtI0qfzSddNlcdRz7feqL6xuSaq+pSVZMyaPOQOg2jbizTf49XFmm6yjASNS1XirbkHOMOVuyysb/vuFImy43Pt5yT/8ahWK8Dxo1FO6bBuAf53nPVph1APOb/2QmNh2gbV8p7yoqZahtD/jotJgaHU5aLD0IIIUSFYZdIYdiFEEIIEfSk2ub7iIpDhw5h9uzZqK6uxtChQzFv3jwcOXJEbXP06FEsXLgQp5xyCk466STMmjULLS0tgTp79uzBjBkzMHjwYIwYMQJ33XUXuru70+Wffvop/vt//+/40pe+hHg8jsWLF+c0fy4+CCGEkD7G7Nmz8cEHH2DTpk3YsGEDtmzZggULFqhtbr/9dvzt3/4tXn75Zbz55pvYv38/vva1r6XLk8kkZsyYgc7OTmzduhXPPfcc1q1bhxUrVqTrdHR0YPjw4Vi+fDkuuOCCnOdflmEXz/PZ9fqicjIGqXl5GHoQB2t2aZGuXXuWcfxxX5sniKEB0XQcmgbEoomIqVoSpV+Ibwoypu2gxVD7dekH0pNCr+uyzdorDYg0629bANtFx+H/dbL9PGIZ/3u8qq7y0CzfDU8Q30fN1i8C/hsuHiBiIprGQ5TLOcXEV8fA+2jtV9zrjA9qODH/UfeyTPUE0fU5hgYk4dOWHO/X+F2Jkl4cdvnwww+xceNGvP3227jooosAAE8//TSuvvpqPPbYYxg1apTRprW1FX/5l3+J9evX44//+I8BAM8++yzOO+88vPXWW5g8eTL+4R/+Ab/97W/xy1/+ErW1tZg4cSK+973v4e6778Z9992HiooKjBkzBt///vcBAH/1V3+V82vgzgchhBCSCS/Px3Ha2toCj46OjrymtW3bNgwdOjS98ACAxsZGxONxbN++PWObpqYmdHV1obGxMf3cuHHjcMYZZ2Dbtm3pfidMmIDa2tp0nWnTpqGtrQ0ffPBBXnOWcPFBCCGERMjo0aNRU1OTfqxatSqv/pqbmzFixIjAcwMGDMCwYcPQ3Nwc2qaiogJDhw4NPF9bW5tu09zcHFh49JT3lBWSsgy7EEIIIRqFPNtl7969qK6uTj9fWVmZsf7SpUvx8MMPq31++OGH+U2ql1CWi49kKo7Y8fiidl6LPEo66Ali9unH0Iv4dRwWn4+Ar4GYu+r7ITQd9rNeHHw+FM1ETBvHpa64zsu7Q+sXFlx8PlTdiW2gHOsWC6mJcLGzMLwhRF3/z8Pw7giva5wib7TVzm+xeIL4dRy2fv2eGlKbpNU1cPH5EN4c4rMUePtth7kYP9tYaFV5HdCoGTYf8vyWE2e/yHsk4sITRDlLK378Z2f0ESUF1HxUV1cHFh9h3HHHHbj55pvVOmeddRbq6upw4MCBwPPd3d04dOgQ6urqMrarq6tDZ2cnDh8+HNj9aGlpSbepq6vDjh07Au16smHC+s2Vslx8EEIIIb2N4cOHY/jw4dZ6DQ0NOHz4MJqamjBp0iQAwK9+9SukUinU19dnbDNp0iQMHDgQmzdvxqxZswAAu3fvxp49e9DQ0JDu96GHHsKBAwfSYZ1Nmzahuroa48ePL8RLTEPNByGEECLozT4f5513HqZPn4758+djx44d+M1vfoNFixbh+uuvT2e67Nu3D+PGjUvvZNTU1GDevHlYsmQJXn/9dTQ1NWHu3LloaGjA5MmTAQBXXXUVxo8fjxtvvBH/9E//hF/84hdYvnw5Fi5cGAgV7dy5Ezt37sSRI0dw8OBB7Ny5E7/97W+dXkNZ7nx0e/H0vqQ/bCHDLJqFumaffqw83G5dlsntU3/IRpaZ6bLhdc1J5W6ZHgiX2MISvrou4ZBj44TPSe1L31V2m0M+oZRcQzQ2orKV1iZlma8WSrGGbFxCNP5UW0sGrBqWUUMywVRQI2whp+T/3Mk5iTCLEWr0f5SMkIwWhhFloq3/8+9iMw8EoyUiGpIhCTceWhpLBEcK3ifDrdcB8/7rD8N0H/+BdNt+MIWkF6faAsALL7yARYsW4corr0Q8HsesWbPw1FNPpcu7urqwe/dufPHFF+nnnnjiiXTdjo4OTJs2DT/4wQ/S5YlEAhs2bMAtt9yChoYGDBkyBHPmzMEDDzwQGPvCCy9M/7+pqQnr16/HmWeeid/97ndZz78sFx+EEEJIX2bYsGFYv359aPmYMWPgidV4VVUVVq9ejdWrV4e2O/PMM/Haa6+pY8t+c4GLD0IIIURQyGwXYsLFByGEECLp5WGXvk5ZLj5SXiytq/Cnc8k0Ls1CXcYnDQ2IlmqraDxkuabxMMpdNB4ANMt0NSXWkpYb1G2Ifl3SZy3W7LnqOpxs2m1tjbrZazN6xbcih/kaGgk1g1R/cYG+HPQhmh4E0DUhtjRdL+7/3dN/2fzzMPqxvSDfrUJ+zlQNiJyTogHR0nCPzTEcS0Zs4OMv04rlfdDfWLNez0RQrnNsxvJeGSlcfEQKs10IIYQQUlTKcueDEEII0aDmI1q4+CCEEEIkDLtESlkuPvz26n7thmGvngqPUcrYpunrIT1DfGWWo+4D1y6W6S4aD9HW0Hgoegsni3SbPiQf7w6trku/DjoOp28yeXiC9EYMPYVRwfd/W2w+ENDPXh9is2J38QgxNCBBMYPar+YJYvzOy74Ur/+YeCKoAbFYsfvLFQ+QDD25aUB8b5y8z5n4NHVmz8E5Kb4f8Z77dTHt1UmklOXigxBCCNGIeR5iefpZ5Nu+P8PFByGEECJh2CVS+szi46GHHsLf/d3fYefOnaioqMDhw4dz7ivpxdJpX8lAqq2eCuYPl9jCLKaFetz3/zws07Uwhi3MIk/f1NrKbVol1VYLcbiEaACxHexig+5U1xL6keRot55Xv70Ryw67GmnRsk9t8RwlRGOGQ8LbWuv6+7Wk5QafyD4t91ixYs1unLzrrytTdh2s2OX7JsqVV2Pg+UIpqQzm62HIsIp5Aq4c2Xeq7fEyaXFA+i59JoDW2dmJa6+9Frfcckupp0IIIaSf05sPlusP9Jmdj/vvvx8AsG7dutJOhBBCSP+HYZdI6TOLj1zo6OhAR0dH+rqtra2EsyGEEEII0M8XH6tWrUrvmPhJpeJpPYdf59GdTATrKRbpLhoPIGi37mSZbtFiGNeBsuClmk6rWaQDuafPyjnIObrYoNu0JtnOydFeXW1rjGspD+u3D+CSPWvTh6iW6bJqLOwiwzjamyrriqCzmtIr8GtCjPRYJS0XCP6KWK3ZfQPFhMbDk79s/nKZ12oE2MM1ILY03MDrk7o4RQNiaD7EnOT91/8i4rFjlQ379gihyVi0lFTzsXTpUsRiMfWxa9eunPtftmwZWltb04+9e/cWcPaEEEL6LV6BHiQjJd35uOOOO3DzzTerdc4666yc+6+srERlZWXO7QkhhJQn3PmIlpIuPoYPH47hw4eXcgqEEEIIKTJ9RvOxZ88eHDp0CHv27EEymcTOnTsBAOeccw5OOukkp766UnGkkmYMUdN4AEAyGQ8t0zQeAJBKOlim+8OmNo2Hi6eGpgHRrKYdx8nZf0PM0fQPKYyOQ7Ved20rKdI3nVy/UeVjk+A0poMniFHVxavDaKtUMMQMij+HogcxhjHs1C1zUuzVDXxtpcZDak38xZ6wV1e1YaKx5gECBF9uXMo0VA2IjPKLN04U++/NXcf/Laq9OrNdIqXPLD5WrFiB5557Ln194YUXAgBef/11XHHFFSWaFSGEkP4KwybR0WdMxtatWwfP84wHFx6EEEJI36LP7HwUkpTvVNvuVHgoRTu5VoZZzDBMHpbpyqm2ZngkR4t0Ud+aPhtIyxVzKGS6rHaCrMs4hQzDKBT0lNtc+3XAuvnuEpbR6or5G2EL7fUp9uQuIRqjrS0cEvAY1y3T/V/bbLbt5mv33QvkibhiXH+5kdJruJF74XWdwjDZW7EbESd5Aq5ixR6TlUV5t69tzx+qYqbawvMyvMk59EEyUpaLD0IIIUSD2S7R0mfCLoQQQgjpH3DngxBCCJEw2yVSynLxkfRi6UBs0DI9uBGUTIq4qaIPcbJMT8q6YoLKUfdqmqvUeBht5ThKv5otulW3oY1p0aEo6bMFqyvIJ31Wt3jPvd9SoUo+HCzT8yqT74tDW1V/4VTXktPrj+XL/WOLDiVQ37BBV94MQ+MhawZEK8EpiBdraEAC+czhU5CXth9dMNFW3F+NG1+4BiR5/OeRzCdX3JFYKsP9K4c+SGYYdiGEEEJIUSnLnQ9CCCFEhWGXSOHigxBCCBEw2yVaynLxkUzGgQz26prG41hdzatDtDV0HYofh4xjBvw3LFoMpV8X7w6bRkL1+VDGcepXlhdSx1Eonw/bnDR6gc+HjYL5fNjqumhAilVXs2I3dB2KRkL+8GRbTylTPks2T5DgZ0fXeBg+IP7GUneSCteH2OxQApI0UeauAQkecRE59PmIFGo+CCGEEFJUynLngxBCCNFg2CVauPgghBBCJBScRkpZLj5SqVj6bBe/zkP6fEhdh/9a1XRkvA4vU3UdLt4d2rkvsl+IVbmDFkP26+bzoV+rcyqUjsNVt6GdIaPUtdILb0x5+XwodQ0tgKav0Ppy0W1Y5qRdW8+i8ZdrehDA9Mnwn8FilCldGT4fDp4gUgPi8LmTc9KcPoxfaeV33DgXRhXA9Gj0iufzQaKlLBcfhBBCiAbDLtHCxQchhBAiYbZLpJTl4iOVjKUtzv2hFiPMYqTe+tNaxfafLQzjYGXub2u1SNfqal7HstzSNjBnpxBNeFkmcg67ONR1Dp1EZa+ebT8lwtnJWqlvhDG0dkpdY075pM+61JVo4RBLmm4skD6rpMvKtrY5aWm5ll9G1ZpdC604fFZcQjIAkAq8+GM3kpS8z5I+S1kuPgghhBANhl2ihYsPQgghRMJsl0ihyRghhBBCikpZ7nykUnHguNbDr+swNR9ibaakwKqptbDZoGv26g51XazLRbnRb1726gjFqksplI6jgJqPnHUdeXzrMayzi4Tny+10jq4rDWT2aXDM7Pux6kPkr3GOmg+1HwQ1FbGkpV9NEyKPPJDj+H8PNJt2WW5JtTWEkJo1u6iralZU4Y+cgqwrbg6ev8Q8DiNqGHaJlrJcfBBCCCEqKS/DuTY59EEywsUHIYQQIqHmI1Ko+SCEEEJIUSnLxYeXjJ14pHyPZDzwQArBR48/SDJ2TOPhe8SS+sPf1iyHeCh9pRD+MPpx6NfaVnkoc4ongw+XfvNpq/Xl+r75fwdiSS/7Ryr4iCezf+T188jrfXKYo3h9Lu9N8D3N/vcrqt+JfH431c9kVp9L7ZHjZ9Y6J5d+Xe5loq7/PinayvurvP8G780nHsUiBqR1Hzk/IpzfoUOHMHv2bFRXV2Po0KGYN28ejhw5orY5evQoFi5ciFNOOQUnnXQSZs2ahZaWlkCdPXv2YMaMGRg8eDBGjBiBu+66C93d3enyn/3sZ/iTP/kTDB8+HNXV1WhoaMAvfvEL5/mX5eKDEEIIUelxOM33ERGzZ8/GBx98gE2bNmHDhg3YsmULFixYoLa5/fbb8bd/+7d4+eWX8eabb2L//v342te+li5PJpOYMWMGOjs7sXXrVjz33HNYt24dVqxYka6zZcsW/Mmf/Alee+01NDU1YerUqfjqV7+K9957z2n+MU9KmfsxbW1tqKmpwRlr70V8cBUAeVickt0CBF1MpUrdcDgVbYvgWmrtV85ZaeuU7eKSWeKQ7ZJXBks+GSuqo6nFkVLBSfleqk+lw1c1JwdUI3tES42xXGtzyCPbRatrjBNXymxt/bcR41A60Tae+f/H6nrZ1xXXWvYO4uH92uoa4ySUD2lCbxtLnLhZxI6Pk/riKPYs+B5aW1tRXV2NKOj5O/HlK+/DgAFVefXV3X0Uv9l8X8Hn++GHH2L8+PF4++23cdFFFwEANm7ciKuvvhq///3vMWrUKKNNa2srhg8fjvXr1+PrX/86AGDXrl0477zzsG3bNkyePBl///d/j2uuuQb79+9HbW0tAGDNmjW4++67cfDgQVRUVGScz3/+z/8Z1113XWCRYqMsBadeKp5eaAS28Zxsz6W9evCyaOmzSrqsW6qtpa6WAqvZq7um5ea6oLDWzd73Oa/TczX62eJDWz9ITHt1/w9ar6un3mq+7cFiJ2t2Wwqv/+dj61dbYNgyVbXfce30XNsiWUvbLWRaru8FmafjKnMA4PkbHF+oeH001batrS3wfGVlJSorK3Pud9u2bRg6dGh64QEAjY2NiMfj2L59O/7bf/tvRpumpiZ0dXWhsbEx/dy4ceNwxhlnpBcf27Ztw4QJE9ILDwCYNm0abrnlFnzwwQe48MILjX5TqRQ+//xzDBs2zOk1MOxCCCGESLwCPQCMHj0aNTU16ceqVavymlpzczNGjBgReG7AgAEYNmwYmpubQ9tUVFRg6NChgedra2vTbZqbmwMLj57ynrJMPPbYYzhy5Ai+8Y1vOL2Gstz5IIQQQorF3r17A2GXsF2PpUuX4uGHH1b7+vDDDws6t3xYv3497r//fvz85z83FkM2uPgghBBCBDHPy9tpuKd9dXV1VpqPO+64AzfffLNa56yzzkJdXR0OHDgQeL67uxuHDh1CXV1dxnZ1dXXo7OzE4cOHA7sfLS0t6TZ1dXXYsWNHoF1PNozs98UXX8S3v/1tvPzyy4FQTraU5eIjkLLloPlQLdKTFr1FRCJS3bZdv3bSVzjYq+eqD7G1VXUc+YhgJYXSfEQlRi0SToJSwKLNyL7MxYo9JkWXqo6jgPoQ/++TTbOi6TosgtPAONJ9XNFtxCxaDKsGJFDXRVsixvVVNuckxwm/7vlvMVNt02nA+fbhwPDhwzF8+HBrvYaGBhw+fBhNTU2YNGkSAOBXv/oVUqkU6uvrM7aZNGkSBg4ciM2bN2PWrFkAgN27d2PPnj1oaGhI9/vQQw/hwIED6Z2MTZs2obq6GuPHj0/39dd//df41re+hRdffBEzZsxwe5HHoeaDEEII6UOcd955mD59OubPn48dO3bgN7/5DRYtWoTrr78+nemyb98+jBs3Lr2TUVNTg3nz5mHJkiV4/fXX0dTUhLlz56KhoQGTJ08GAFx11VUYP348brzxRvzTP/0TfvGLX2D58uVYuHBhOlS0fv163HTTTXj88cdRX1+P5uZmNDc3o7W11ek1cPFBCCGECHrCLvk+ouKFF17AuHHjcOWVV+Lqq6/GpZdeirVr16bLu7q6sHv3bnzxxRfp55544glcc801mDVrFi677DLU1dXhZz/7Wbo8kUhgw4YNSCQSaGhowDe/+U3cdNNNeOCBB9J11q5di+7ubixcuBAjR45MP2677Tan+Zdl2IUQQghR8WWr5NVHRAwbNgzr168PLR8zZowRbquqqsLq1auxevXq0HZnnnkmXnvttdDyN954w3mumSjPxUePvS8Q1HlYdBwB3Ybh6yGvHbw7lL60foy+bJoPTQfhog9x0G24+Hoca1sgHUc+dQW56jqctSW9DCO6bgm3axoRFx2HOhGLFkPTXxRUH+L7vbYZhWlaDauOw39t05JoeinpAWQYh3m+/4u2CW0cmyeIz+dD9CM/H54qjjlOMTUfhXAoLR8PT2cYdiGEEEJIUSnPnQ9CCCFEoZAOp8SkPBcfvrBLIKxhsUgPhEcsVuZqaMUSolFtz5XwiFO6rLx2SIl1ShW2pPip9uvWEE32/brMwelsF0vfWc/JRlQ3sTx2sU3L9Oz79Z/tYgvvBEMnjnNS0meNvgJnrjiEaGwhDS1cYgmlqOEdeRaKP2IpP7+anbqcpFEWfML/+oxfSyUtV352vISSwgsEwj3ppgy79BsYdiGEEEJIUSnPnQ9CCCFEIZbKsAOcQx8kM1x8EEIIIRKGXSKlLBcfsWTsRBqtL4ZoaBk0DYijlblT+qzLUfdOVuzhfbmMY5aJmHBE9ur5pNpqKbwSNw2I0lE/t1d3ScU19SH+H56tbvgYnhBu6Km2+jhBHYcokm396bIyhdfQW4RruqSOI5+03MC14/H1WpquatVus2l3SctNyHF8cziu/zDsD0ifpSwXH4QQQohKLzcZ6+tw8UEIIYQICnmqLTFhtgshhBBCikpZ7nzEkjHEunvs1YPPB+q5aDHEddywZs+uXwBOtue56kOMa4uOI3efD8ucXLQlimdIXjoNJ48Q/ZtMoTQgTv3mgWqJbmvspPGQbcMba1oMVTuSYaBAfYteJOjzoc8poNuQZbKt+CzpOo7s9SEuniC2a+3zbfqL+HRyoiyVCNd/GR8dxRMEAODv63jdomo+KDiNlLJcfBBCCCEqHowvlTn1QTLCxQchhBAioOYjWqj5IIQQQkhRKcudj1jyhIdHIIbooq9w0IfIvvPRceSjDzFen29VXlBPEKe6ues43DxBPKUMKrnqOPI5B6ZYOEXQC3hei//F2/Uh/jFkmfCGcDrbJfz8FkP34KIPcfAIMXQo8kwZf13bGTL+a4veS9OA2LQlmidIXHqC+PtKhH/WM137/UW8422l91KkeCiA5qMgM+mXlOXigxBCCFGh4DRSGHYhhBBCSFEpy52PWPeJVFs1xOFir27UFddaKCKPsEvg2ijzwuuKOZkhGWUcWwqvYr9sTdNVwy4ONu5qv27hEPVwqHzCLln2UzIcsxpVO3YtLVd+BVJTeGX4Izx0IvtyCtkYabkO6bKyX8VC3Xjt8vPhD4cocwCgpsDmE0qRn6XAx9uwkhfXCX8/8n0RryeB4HUGa/a0RUIxSMH5M5CxD5KRslx8EEIIIRrMdokWhl0IIYQQUlS480EIIYRIKDiNlLJcfARTbX3Py1Q2RdfhfHx9gVJtNV2HS7qsbRxT85GjjsNi2+6m+ZDjZD8nJ21GPlbtGg43oqjs1G2oug2JPM5eeaNUG3ftaHvIFF6LnbqiH3HSi2g27RA26A76EGNOcUV3Itsq2pFjdX3py4oeBNA1IVYrdr/eRdbV9CGGHsRir+7XhBzXgxQ31ZaLjyhh2IUQQgghRaUsdz4IIYQQFe58RAoXH4QQQoiEqbaRUpaLj1g3EO8+/n+fzsOIJ7r4b9h8Plws0wN1LV4dOVqxm211LYbu8+Hgv6F5goj6TtbsLlbsEs0/RGLTrGg41C1Vip6hi9BwePGG5iMePo5mke5cV/X5EH1ptueGd4en1JX9atbsuk+Jv63ND0XXbRTOI0S1Yld8PqyfUTmOTxPiHf88eN0oGky1jRZqPgghhBBSVPrE4uN3v/sd5s2bh7Fjx2LQoEE4++yzsXLlSnR2dpZ6aoQQQvojPZqPfB8kI30i7LJr1y6kUin86Ec/wjnnnIP3338f8+fPR3t7Ox577DHn/mJJn716jumz+YRdXGzQ8zsBV08hjS7VVqkr3yctzdVqme6FlzmEgiTW1FutbmAO+jgqJbppxVzCLhLlq4wZztHCFi515RzCU1eN02W1kI0tlOIPJ7iEaER9e6qtkj7rEKKxX+eWpmvtV0m1tab0+j8/iZ77dTHt1b38c97lPZik6ROLj+nTp2P69Onp67POOgu7d+/GD3/4w5wWH4QQQggpHX1i8ZGJ1tZWDBs2rNTTIIQQ0h9hqm2k9MnFx8cff4ynn37auuvR0dGBjo6O9HVbW1vUUyOEENIvKIRmg4uPMEq6+Fi6dCkefvhhtc6HH36IcePGpa/37duH6dOn49prr8X8+fPVtqtWrcL9999vPB/vBuI9dr256jhE3bg1TTd7G3Q3zUdu/QIIaiby0XxoOg5Lv2qaq5MVu0XfoszJwCX1Vrs59YHUWg2ntFtA9UTQtCSm9kLpSOoErJbpMaVM9h0LLTP0Iv7feWNO4locFR/UfFjaBtJ/pZZE1g3XbRjaEid7dSVN12Lb7v8IW1N4xfsU0Isc/38xU21JtJR08XHHHXfg5ptvVuucddZZ6f/v378fU6dOxZQpU7B27Vpr/8uWLcOSJUvS121tbRg9enTO8yWEEFImMOwSKSVdfAwfPhzDhw/Pqu6+ffswdepUTJo0Cc8++yzicXuWcGVlJSorK/OdJiGEkHIj5SHvsAmzXULpE5qPffv24YorrsCZZ56Jxx57DAcPHkyX1dXVlXBmhBBCCHGlTyw+Nm3ahI8//hgff/wxTj/99ECZl8O2Vix5Qqfg1yvYdRvBPoJlDjboTlbsDv3abM81H5CIdByxZPa6DWMcY05S1xH+s1e1JdqYmfDramy/bi6/j718S9ZQXjhZr+t1A/4bitX6sbrhx9dLfYih1VDm5Mkj3X0/XLuWJLwfVR8CBDQieelDFF2H5hdibeugzbD1G/cdX2G8NlFX3p9S/vo9Gj35XkaJlzr2yLcPkpE+4XB68803w/O8jA9CCCGk4NDhNFL6xM4HIYQQUlSo+YiUslx8xLuAHr2qUzjEt+1vTWtV+rLZoBejrlHukmpr69clxKGFZZzSZ23hHS0lVpQpO6VmSm9EYZZS7da67IXmE4ZxSKdVU28tYZdg+qwIj8gt/Fh42AIJOY7vWvwOm/bqypxkSEML0eRx2qw99dYhTTeF8LoyXdbfb0rW1d8nf0Snp63XBdJPKMvFByGEEKLCVNtI4eKDEEIIkXgowOKjIDPpl/QJwSkhhBBCTnDo0CHMnj0b1dXVGDp0KObNm4cjR46obY4ePYqFCxfilFNOwUknnYRZs2ahpaUlUGfPnj2YMWMGBg8ejBEjRuCuu+5Cd/cJa9lf//rX+PKXv4xTTjkFgwYNwrhx4/DEE084z78sdz4C9uq+GKuhkdB0Gw7psrJvmdLrZpkeroNwTf9VU2IVHYcxB9W23UG3AehprZreQtOdyLoOGo+MfWlzyrYM6HtiNEtKrKrjkHoL3/+tNu6Kxbj1Ou4v0utq6b+eOMrd31RqIoxx1JRYi+25TxdhpPBqmg8lZdfaVtGDAMEUWE0PYpuTJ37/zXIzTbeo9uq9POwye/ZsfPrpp9i0aRO6urowd+5cLFiwAOvXrw9tc/vtt+Pv/u7v8PLLL6OmpgaLFi3C1772NfzmN78BACSTScyYMQN1dXXYunUrPv30U9x0000YOHAg/vzP/xwAMGTIECxatAh/+Id/iCFDhuDXv/41vvOd72DIkCFYsGBB1vOPeWWUr9rW1oaamhqM/x9/jkRlFQAuPk605eIjDC4+jlPAxYefQi4+jL6c2vrbWfpVFh/aAkjWd1l82M92UTw1jMVHeF+2c2DUxYfDgsguVjVfT7LjKH675h60traiuroaUdDzd6JxxLcxIF6RV1/dqU788sBPCj7fDz/8EOPHj8fbb7+Niy66CACwceNGXH311fj973+PUaNGGW1aW1sxfPhwrF+/Hl//+tcBALt27cJ5552Hbdu2YfLkyfj7v/97XHPNNdi/fz9qa2sBAGvWrMHdd9+NgwcPoqIi8/vxta99DUOGDMFPf/rTrF8Dwy6EEEJIH2Lbtm0YOnRoeuEBAI2NjYjH49i+fXvGNk1NTejq6kJjY2P6uXHjxuGMM87Atm3b0v1OmDAhvfAAgGnTpqGtrQ0ffPBBxn7fe+89bN26FZdffrnTayjLsAshhBCiUsCwS1tbW+DpfM8da25uxogRIwLPDRgwAMOGDUNzc3Nom4qKCgwdOjTwfG1tbbpNc3NzYOHRU95T5uf000/HwYMH0d3djfvuuw/f/va3nV5DWS4+4t0e4sfjmMGwS7Ce5t0hy+K2sIWTZbo/HBJeBiAQMjDDRrr3RTC8o4ciglbscv4OoZOU9FAW42jhESVcYvXf0G4iRmjIIZTicHMy3ieNUkVDHbw7jHCDS7++a6uNuzaO1JJoYRi5z6u0NTxBDK+OuK+uLJOhCGUc+doM34/wuqY1u69u0tKvapmu1435tRgWe/WUf06Gz4e4NvQipkeI113Ez0UBFx/yNPWVK1fivvvuM6ovXboUDz/8sNrlhx9+mN+cCsQ//uM/4siRI3jrrbewdOlSnHPOObjhhhuybl+Wiw9CCCGkWOzduzeg+Qjb9bjjjjtw8803q32dddZZqKurw4EDBwLPd3d349ChQ6GHrdbV1aGzsxOHDx8O7H60tLSk29TV1WHHjh2Bdj3ZMLLfsWPHAgAmTJiAlpYW3HfffVx8EEIIIXlRQHv16urqrASnw4cPx/Dhw631GhoacPjwYTQ1NWHSpEkAgF/96ldIpVKor6/P2GbSpEkYOHAgNm/ejFmzZgEAdu/ejT179qChoSHd70MPPYQDBw6kwzqbNm1CdXU1xo8fH/4yUyl0dHRY5+2Hiw9CCCFE4HkpeHmeSptv+zDOO+88TJ8+HfPnz8eaNWvQ1dWFRYsW4frrr09nuuzbtw9XXnklnn/+eVxyySWoqanBvHnzsGTJEgwbNgzV1dW49dZb0dDQgMmTJwMArrrqKowfPx433ngjHnnkETQ3N2P58uVYuHBherdm9erVOOOMMzBu3DgAwJYtW/DYY4/hT//0T51eQ1kuPuJdJ8KyLumzcZezXZS0XXtKb/aptsHzZixprYYuJUcdh0UjERjHQbdxrO+UUtchfVaJ1drmH1n6bCF1HLn25XIei7Ur7XyWAqblahoJS9vAHG1akoA+RB40Isc58Xtq6EwSyhwQfA2Gn4iDPkSO4z9jxlZXO1PGngKrlYn5p/xzCtZNpSxz8utQSnG2i+flnw4foXbrhRdewKJFi3DllVciHo9j1qxZeOqpp9LlXV1d2L17N7744ov0c0888US6bkdHB6ZNm4Yf/OAH6fJEIoENGzbglltuQUNDA4YMGYI5c+bggQceSNdJpVJYtmwZPvnkEwwYMABnn302Hn74YXznO99xmn9Z+nz84ZyHkKg47vPBxcfxulx8ZNOWi48s++oliw/kuPjwrIsPxX9DLgqUxYdNnKq9dnOc8H7MxYeDz0cW/hvZ9Rusm7ItiDKIYJOdR/HPz/1ZUXw+rhx6EwbE8vT58Dqx+fDzkc63r1KWOx+EEEKIilcAzUf5fLd3piwXH/HuE7uq/l0Hp3RZa11l50PbgYDczbD1m/3uhUtb86h737VLuqxR12HXwdhRkbl4DrsMyi6PfTdD2Y0xhnW42fQ3h1MfakjmWAVfvxavQ39arkvoRBsTgJeQOaTKONq4cv7depprLJCmK8IUyq6JsXuRDN/NsIWC1B0K2zgZwiGZ+rH1K+9HWlimJPbqqZR5A3YlIs1Hf4AOp4QQQggpKmW580EIIYSoMOwSKVx8EEIIIQIvlYKXZ9glqlTb/kBZLj7iXR7ix32/45q9uqLriHfregrNntzWNnBt0YcET7VN6XUddBzytQdW8DbtReC03OzrGtcu+hCpLRF1PbVfyw3CxZrdpd/+pvnweZAbr8zBIl3rV/Zj12bEQ8tihjZDyYzRMnCEdsQ6J199mzYjMP9uXR8SzEIRcxIZdUZWjWLNLuumBmg27lLHcaI8Jf7aqCf4Inj/6vl4e1197DNDQinLxQchhBCiwrBLpHDxQQghhEhSHsyTMR3h4iMUZrsQQgghpKiU5c5HvPtEiFPz1NC0Gbaj7jUvj5hVLxKumdDcOQ2dRj46DkVD4aTjsNVVxjE8MzSthktd6S9QQJ+P0HYZ6GvmwlbvDptfR7CzrNsFxjWOlZdOpJrDqV5Xt2JXPEEUv5BM1wE9htShyHEc9CEB/5CEFJ1ZfD7849gs3/3+Gw427qavh9SSQJSbYxbV58PzYIj3cuqDZKIsFx+EEEKIhpfy4OUZdulrXzCKCRcfhBBCiMRLIf+dD6bahlGWi49EZwqJ478Uuu05xHX2oROjL1/4wVbXv13vFEoxLNL1UEogfGILh/jnbJQFr71UeIjD9GNWwiXJpKiqzNEhdGIN50h8c/Yc6lrpY9+KpBW4igxxGMVKOESOq9iGu1izy7pmGMPnG26zbdfSf41D6eLh5XIcJbxjpM8WKERzrNzvIyDLwu3W5Zw0G3dvQHhIBjDvdf6+vMSxMq+Lf8z7C2W5+CCEEEI0GHaJFi4+CCGEEAnDLpFSVouPnlVod9fR9HNOYRcvorCLmu0SYdhFC1s4hV3Edmk+YZfAqbaWsIuW7SLxh05kVae25Rt2ARzCLpYs/pjn78sSOvHVNWYg9+7NkULrxmRv/uNaUw5hF9FPzHg9ctbhbc0jcH2hB1lmvPbwLBrPeK3x8HJPtJXX/lCK7EerK+Ygw3iG46k/q+b4x6rn3l2MHYVudOXtMdaNrsJMph9SVouPzz//HADQ9Is/L/FMCOmDuNyIbXX5hZDkweeff46amppI+q6oqEBdXR1+3fxaQfqrq6tDRUVFQfrqT8S8MgpKpVIp7N+/HyeffLLds6BItLW1YfTo0di7dy+qq6tLPZ1eC9+n7OD7ZIfvUXb0xvfJ8zx8/vnnGDVqFOIuvjKOHD16FJ2dnQXpq6KiAlVVVQXpqz9RVjsf8Xgcp59+eqmnkZHq6upe8wHvzfB9yg6+T3b4HmVHb3ufotrx8FNVVcUFQ8TQXp0QQgghRYWLD0IIIYQUFS4+SkxlZSVWrlyJysrKUk+lV8P3KTv4Ptnhe5QdfJ9IlJSV4JQQQgghpYc7H4QQQggpKlx8EEIIIaSocPFBCCGEkKLCxQchhBBCigoXH72E3/3ud5g3bx7Gjh2LQYMG4eyzz8bKlSsL5rLXn3jooYcwZcoUDB48GEOHDi31dHoNq1evxpgxY1BVVYX6+nrs2LGj1FPqdWzZsgVf/epXMWrUKMRiMbz66qulnlKvY9WqVbj44otx8sknY8SIEZg5cyZ2795d6mmRfgYXH72EXbt2IZVK4Uc/+hE++OADPPHEE1izZg3uueeeUk+t19HZ2Ylrr70Wt9xyS6mn0mt46aWXsGTJEqxcuRLvvvsuLrjgAkybNg0HDhwo9dR6Fe3t7bjggguwevXqUk+l1/Lmm29i4cKFeOutt7Bp0yZ0dXXhqquuQnt7e6mnRvoRTLXtxTz66KP44Q9/iH/9138t9VR6JevWrcPixYtx+PDhUk+l5NTX1+Piiy/GM888A+DYOUajR4/GrbfeiqVLl5Z4dr2TWCyGV155BTNnziz1VHo1Bw8exIgRI/Dmm2/isssuK/V0SD+BOx+9mNbWVgwbNqzU0yC9nM7OTjQ1NaGxsTH9XDweR2NjI7Zt21bCmZH+QGtrKwDwXkQKChcfvZSPP/4YTz/9NL7zne+Ueiqkl/PZZ58hmUyitrY28HxtbS2am5tLNCvSH0ilUli8eDG+/OUv4/zzzy/1dEg/gouPiFm6dClisZj62LVrV6DNvn37MH36dFx77bWYP39+iWZeXHJ5nwgh0bJw4UK8//77ePHFF0s9FdLPGFDqCfR37rjjDtx8881qnbPOOiv9//3792Pq1KmYMmUK1q5dG/Hseg+u7xM5wamnnopEIoGWlpbA8y0tLairqyvRrEhfZ9GiRdiwYQO2bNmC008/vdTTIf0MLj4iZvjw4Rg+fHhWdfft24epU6di0qRJePbZZxGPl8/GlMv7RIJUVFRg0qRJ2Lx5c1o8mUqlsHnzZixatKi0kyN9Ds/zcOutt+KVV17BG2+8gbFjx5Z6SqQfwsVHL2Hfvn244oorcOaZZ+Kxxx7DwYMH02X89hpkz549OHToEPbs2YNkMomdO3cCAM455xycdNJJpZ1ciViyZAnmzJmDiy66CJdccgmefPJJtLe3Y+7cuaWeWq/iyJEj+Pjjj9PXn3zyCXbu3Ilhw4bhjDPOKOHMeg8LFy7E+vXr8fOf/xwnn3xyWjdUU1ODQYMGlXh2pN/gkV7Bs88+6wHI+CBB5syZk/F9ev3110s9tZLy9NNPe2eccYZXUVHhXXLJJd5bb71V6in1Ol5//fWMvztz5swp9dR6DWH3oWeffbbUUyP9CPp8EEIIIaSolI+ogBBCCCG9Ai4+CCGEEFJUuPgghBBCSFHh4oMQQgghRYWLD0IIIYQUFS4+CCGEEFJUuPgghBBCSFHh4oMQQgghRYWLD0IIIYQUFS4+COnjnH766fjBD34QeG7r1q0YPHgw/u3f/q1EsyKEkHC4+CCkj1NfX4+33347fe15HhYvXozbb78dZ555ZglnRgghmeHig5A+zuTJkwOLj5/+9KfYu3cvli1bVsJZEUJIOFx8ENLHmTx5Mj788EMcOXIE7e3tuOeee/Dggw/ipJNOKvXUCCEkIwNKPQFCSH5MmjQJ8Xgc7777Ln75y19i+PDhmDt3bqmnRQghoXDxQUgfZ/DgwZgwYQL+5m/+Bj/+8Y/x2muvIR7npiYhpPfCOxQh/YDJkyfj6aefxrRp03DFFVeUejqEEKLCxQch/YALLrgAAwcOxKOPPlrqqRBCiJWY53leqSdBCMmPqVOn4o/+6I/w+OOPl3oqhBBihZoPQvooqVQKBw8exF/+5V/io48+ws9//vNST4kQQrKCiw9C+ihbtmzBH//xH2PcuHH4m7/5G1RXV5d6SoQQkhUMuxBCCCGkqFBwSgghhJCiwsUHIYQQQooKFx+EEEIIKSpcfBBCCCGkqHDxQQghhJCiwsUHIYQQQooKFx+EEEIIKSpcfBBCCCGkqHDxQQghhJCiwsUHIYQQQooKFx+EEEIIKSr/P9P6XTPRHI1MAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import biosspheres.laplace.drawing as draw\n",
    "from matplotlib import cm, colors\n",
    "cut = 1\n",
    "# Size of the window to be plotted\n",
    "horizontal = 5.\n",
    "vertical = 5.\n",
    "# For the resolution of the plot\n",
    "inter_horizontal = 100\n",
    "inter_vertical = 100\n",
    "# For plotting without the external function we make the following function\n",
    "def zero(x: np.ndarray) -> float:\n",
    "    return 0.\n",
    "\n",
    "x1, y1, data = draw.draw_cut_representation_formula_one_sphere_azimuthal_symmetry(\n",
    "    cut, np.zeros((3)), horizontal, vertical, inter_horizontal, inter_vertical, solutions[time_index, 0 : 4 * num], radius, big_l, zero)\n",
    "plt.figure()\n",
    "plt.imshow(data, origin='lower',\n",
    "           extent=[-horizontal / 2, horizontal / 2,\n",
    "                   -vertical / 2, vertical / 2],\n",
    "           norm=colors.CenteredNorm()\n",
    "           )\n",
    "plt.xlabel('$y$')\n",
    "plt.ylabel('$z$')\n",
    "plt.title('$x = 0.$')\n",
    "plt.colorbar()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "biosspheresall",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}