C2/L5_gibbs_sampler.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "import seaborn as sns\n",
    "import pymc3 as pm\n",
    "import arviz as az\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, '..')\n",
    "from utils.plot_lib import set_default\n",
    "\n",
    "set_default(figsize=(6, 4))"
   ]
  },
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   "source": [
    "### Normal likelihood, unknown mean and variance\n",
    "\n",
    "The model is:\n",
    "\n",
    "$ \n",
    "\\begin{align}\n",
    "y_i \\mid \\mu, \\sigma^2 &\\overset{\\text{iid}}{\\sim} \\text{N} ( \\mu, \\sigma^2 ), \\quad i=1,\\ldots,n \\\\ \n",
    "\\mu &\\sim \\text{N}(\\mu_0, \\sigma_0^2) \\\\ \n",
    "\\sigma^2 &\\sim \\text{IG}(\\nu_0, \\beta_0)  \\, .\n",
    "\\end{align} \n",
    "$\n",
    "\n",
    "We chose a normal prior for $μ$ because, in the case where $σ^2$ is known, the normal is the conjugate prior for $μ$. Likewise, in the case where $μ$ is known, the inverse-gamma is the conjugate prior for $σ^2$. This will give us convenient full conditional distributions in a Gibbs sampler.\n",
    "\n",
    "Let’s first work out the form of the full posterior distribution.\n",
    "\n",
    "$ \n",
    "\\begin{align}\n",
    "p( \\mu, \\sigma^2 \\mid y_1, y_2, \\ldots, y_n ) &\\propto\n",
    "p(y_1, y_2, \\ldots, y_n \\mid \\mu, \\sigma^2) p(\\mu) p(\\sigma^2) \\\\ \n",
    "&= \\prod_{i=1}^n \\text{N} ( y_i \\mid \\mu, \\sigma^2 ) \\times \\text{N}( \\mu \\mid \\mu_0, \\sigma_0^2) \\times \\text{IG}(\\sigma^2 \\mid \\nu_0, \\beta_0) \\\\\n",
    "&= \\prod_{i=1}^n \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp \\left[ -\\frac{(y_i - \\mu)^2}{2\\sigma^2} \\right] \\times \\frac{1}{\\sqrt{2\\pi\\sigma_0^2}} \\exp \\left[ -\\frac{(\\mu - \\mu_0)^2}{2\\sigma_0^2} \\right] \\times \\frac{\\beta_0^{\\nu_0}}{\\Gamma(\\nu_0)}(\\sigma^2)^{-(\\nu_0 + 1)} \\exp \\left[ -\\frac{\\beta_0}{\\sigma^2} \\right] I_{\\sigma^2 > 0}(\\sigma^2) \\\\\n",
    "&\\propto (\\sigma^2)^{-n/2} \\exp \\left[ -\\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2\\sigma^2} \\right] \\exp \\left[ -\\frac{(\\mu - \\mu_0)^2}{2\\sigma_0^2} \\right] (\\sigma^2)^{-(\\nu_0 + 1)} \\exp \\left[ -\\frac{\\beta_0}{\\sigma^2} \\right] I_{\\sigma^2 > 0}(\\sigma^2)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "From here, it is easy to continue on to find the two full conditional distributions we need. First let’s look at $μ$, assuming $σ2$ is known (in which case it becomes a constant and is absorbed into the normalizing constant):\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "p(\\mu \\mid \\sigma^2, y_1, \\ldots, y_n) &\\propto p( \\mu, \\sigma^2 \\mid y_1, \\ldots, y_n ) \\\\\n",
    "&\\propto \\exp \\left[ -\\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2\\sigma^2} \\right] \\exp \\left[ -\\frac{(\\mu - \\mu_0)^2}{2\\sigma_0^2} \\right] \\\\\n",
    "&\\propto \\exp \\left[ -\\frac{1}{2} \\left( \\frac{ \\sum_{i=1}^n (y_i - \\mu)^2}{2\\sigma^2} + \\frac{(\\mu - \\mu_0)^2}{2\\sigma_0^2} \\right) \\right] \\\\\n",
    "&\\propto \\text{N} \\left( \\mu \\mid \\frac{n\\bar{y}/\\sigma^2 + \\mu_0/\\sigma_0^2}{n/\\sigma^2 + 1/\\sigma_0^2}, \\, \\frac{1}{n/\\sigma^2 + 1/\\sigma_0^2} \\right) \\, ,\n",
    "\\end {align}\n",
    "$\n",
    "\n",
    "Given the data and $σ^2$, $μ$ follows this normal distribution. Now let’s look at $σ^2$, assuming $μ$ is known: \n",
    "\n",
    "$ \n",
    "\\begin{align}\n",
    "p(\\sigma^2 \\mid \\mu, y_1, \\ldots, y_n) &\\propto p( \\mu, \\sigma^2 \\mid y_1, \\ldots, y_n ) \\\\\n",
    "&\\propto (\\sigma^2)^{-n/2} \\exp \\left[ -\\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2\\sigma^2} \\right] (\\sigma^2)^{-(\\nu_0 + 1)} \\exp \\left[ -\\frac{\\beta_0}{\\sigma^2} \\right] I_{\\sigma^2 > 0}(\\sigma^2) \\\\\n",
    "&\\propto (\\sigma^2)^{-(\\nu_0 + n/2 + 1)} \\exp \\left[ -\\frac{1}{\\sigma^2} \\left( \\beta_0 + \\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2} \\right) \\right] I_{\\sigma^2 > 0}(\\sigma^2) \\\\\n",
    "&\\propto \\text{IG}\\left( \\sigma^2 \\mid \\nu_0 + \\frac{n}{2}, \\, \\beta_0 + \\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2} \\right) \\, .\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "These two distributions provide the basis of a Gibbs sampler to simulate from a Markov chain whose stationary distribution is the full posterior of both $μ$ and $σ^2$. We simply alternate draws between these two parameters, using the most recent draw of one parameter to update the other.\n"
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   "source": [
    "To implement the Gibbs sampler we just described, let’s return to our running example where the data are the percent change in total personnel from last year to this year for $n=10$ companies. We’ll still use a normal likelihood, but now we’ll relax the assumption that we know the variance of growth between companies, $σ^2$, and estimate that variance. Instead of the $t$ prior from earlier, we will use the conditionally conjugate priors, normal for $μ$ and inverse-gamma for $σ^2$.\n",
    "\n",
    "The first step will be to write functions to simulate from the full conditional distributions we derived in the previous segment. The full conditional for $μ$, given $σ^2$ and data is:\n",
    "\n",
    "$ \\text{N} \\left( \\mu \\mid \\frac{n\\bar{y}/\\sigma^2 + \\mu_0/\\sigma_0^2}{n/\\sigma^2 + 1/\\sigma_0^2}, \\, \\frac{1}{n/\\sigma^2 + 1/\\sigma_0^2} \\right) $"
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   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def update_mu(n, y_bar, sig2, mu_0, sig2_0):\n",
    "    sig2_1 = 1.0 / (n / sig2 + 1.0 / sig2_0)\n",
    "    mu_1 = sig2_1 * ((n * y_bar / sig2) + (mu_0 / sig2_0))\n",
    "    mu_cand = norm.rvs(size=1, loc = mu_1, scale = np.sqrt(sig2_1))[0] # draw a candidate\n",
    "    return mu_cand"
   ]
  },
  {
   "source": [
    "The full conditional for $σ^2$ given $μ$ and data is: \n",
    "\n",
    "$ \\text{IG}\\left( \\sigma^2 \\mid \\nu_0 + \\frac{n}{2}, \\, \\beta_0 + \\frac{\\sum_{i=1}^n (y_i - \\mu)^2}{2} \\right) $"
   ],
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   "execution_count": 3,
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   "source": [
    "from scipy.stats import gamma\n",
    "\n",
    "def update_sig2(n, y, mu, nu_0, beta_0):\n",
    "    nu_1 = nu_0 + (n / 2.0)\n",
    "    sumsq = np.sum( (y - mu)**2 ) # vectorized\n",
    "    beta_1 = beta_0 + sumsq / 2.0\n",
    "    rv = gamma(nu_1, loc = 0., scale = 1/beta_1)\n",
    "    out_gamma = rv.rvs(size = 1)[0] # rate for gamma is shape for inv-gamma\n",
    "    return 1 / out_gamma # reciprocal of a gamma random variable is distributed inv-gamma"
   ]
  },
  {
   "source": [
    "With functions for drawing from the full conditionals, we are ready to write a function to perform Gibbs sampling."
   ],
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   "source": [
    "def gibbs(y, n_iter, init, prior):\n",
    "    y_bar = np.mean(y)\n",
    "    n = y.shape[0]\n",
    "\n",
    "    ## initialize\n",
    "    mu_out = []\n",
    "    sig2_out = []\n",
    "\n",
    "    mu_now = init\n",
    "\n",
    "    for i in range(n_iter):\n",
    "        sig2_now = update_sig2(n = n, y = y, mu = mu_now, nu_0 = prior['nu_0'], beta_0 = prior['beta_0'])\n",
    "        mu_now = update_mu(n = n, y_bar = y_bar, sig2 = sig2_now, mu_0 = prior['mu_0'], sig2_0 = prior['sig2_0'])\n",
    "\n",
    "        sig2_out.append(sig2_now)\n",
    "        mu_out.append(mu_now)\n",
    "\n",
    "    return mu_out, sig2_out"
   ]
  },
  {
   "source": [
    "Setting up the problem"
   ],
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   "execution_count": 5,
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "y = np.array([1.2, 1.4, -0.5, 0.3, 0.9, 2.3, 1.0, 0.1, 1.3, 1.9]) # Data\n",
    "y_bar = np.mean(y) # Sample mean\n",
    "n = y.shape[0] # Data points\n",
    "\n",
    "## Prior\n",
    "prior = {}\n",
    "prior['mu_0'] = 0.0\n",
    "prior['sig2_0'] = 1.0\n",
    "prior['n_0'] = 2.0 # prior effective sample size for sig2 (2 samples)\n",
    "prior['s2_0'] = 1.0 # prior point estimate for sig2\n",
    "prior['nu_0'] = prior['n_0'] / 2.0 # prior parameter for inverse-gamma\n",
    "prior['beta_0'] = prior['n_0'] * prior['s2_0'] / 2.0 # prior parameter for inverse-gamma\n",
    "\n",
    "# Plotting the histogram of the random samples\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "sns.histplot(np.array(y), stat= 'density', bins = 6)\n",
    "# Sampling in all the domain of the function\n",
    "ax.plot(np.linspace(-2, 4, 100), norm.pdf(x = np.linspace(-2, 4, 100), loc = prior['mu_0'], scale = np.sqrt(prior['sig2_0'])), 'r-', lw=5, alpha=0.6, label='Normal Prior') # prior for mu \n",
    "ax.scatter(y, np.repeat(0, n), s = 30, c='green', label = 'Data points') # individual data points\n",
    "ax.scatter(y_bar, 0, s = 30, c='blue', label = 'Sample mean') # sample mean\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.xlim(-1, 3)  \n",
    "plt.title('Histogram of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Running experiment"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(53)\n",
    "\n",
    "init_mu = 0.0\n",
    "# Execute experiment\n",
    "mu_out, sig2_out = gibbs(y=y, n_iter = int(1e3), init = init_mu, prior=prior)"
   ]
  },
  {
   "source": [
    "### Plotting $\\mu$ posterior"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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zoidnZ2e1ffv2IkMfW3uaPHmy7jkYfZKMJCfJSDIy2iQ5af8OlU6ZQgghhCg3aVBYyYYNG/QuwfAkI20kp5JJRiWTjLSRnLSTBoWVeHp66l2C4UlG2khOJZOMSiYZaSM5aScNCivp0qWL3iUYnmSkjeRUMsmoZJKRNpKTdtKgEEIIIYRF6N6DtKInI1zl4eDgoHsORp8kI8lJMpKMjDZJTnKVh+EEBwfrXYLhSUbaSE4lk4xKJhlpIzlpJw0KK6lTp47eJRieZKSN5FQyyahkkpE2kpN20qCwkujoaL1LMDzJSBvJqWSSUckkI20kJ+2kQWElmzdv1rsEw5OMtJGcSiYZlUwy0kZy0k4aFFYycuRIvUswPMlIm6qak2MdHxrcH0zzF9+n9dgFtJnwBf5P/R/eXQdh7167VK9VVTOyJK0ZLV26lO+//76Cq7GMKVOmEB4ebtHXlG1JO2lQCCF05ejlQ8DwmbR97Usa3Pc0NQOCcG7YnBrefni270mjfqNp+/pXNOo3CjuXWnqXaxVLly5FKYVSiqysLOLj49m6dSvBwcGYTCar1jJ27FiGDRtm/j00NJSPPvrIqjUURylF//79i8z74IMPuO+++yp83RXRcKko1mwQSoPCSrZs2aJ3CYYnGWlTlXLy7voYbcZ9jnvzjkXm5+XmkJedZf7dxt4hf9nxi3BtfFuJr1sVMtq0aRP16tWjcePG9O3bl9DQUObMmcOPP/6Ira1tuV9fa0ZJSUkkJiaWe33WkJqaypUrVyz6mlVhW7Im3a9xrejJCONQdOnSRfccjD5JRtUoJ5ON8hs0XgXN/Nk8tX19hfLu9riyr1knfxkbG1Wjvr/yeeg/KvDdjeblbp+xRdW588EqndHSpUvV999/f8P8nj17KqWUeuGFF8zz3N3d1cKFC9X58+dVYmKi+vnnn1W7du3Mj0+ZMkWFh4erp59+WkVFRamrV6+qr7/+WvXq1cu8zKBBg9Rff/2l0tLS1KVLl9S2bdvMn5eFa1m6dKm6XuPGjdXx48fVhAkTitTapk0blZubq/z9/W/6PocNG6YOHz6s0tPTVWRkpBo1apT5MXt7ezVv3jx19uxZlZ6erqKiotSkSZMUoKKioorUEBUVVeS9Xp9jSEiIio+PVwkJCer//b//p2xtbdXMmTPV5cuX1enTp1VwcHCRut577z119OhRlZqaquLi4tTbb7+t7OzsFKCee+65GzJ47rnnNP0trp/8/PyUUkoNGTJE7d69W6Wnp6u///5bde/evchy3bp1U/v27VMZGRnq7NmzasaMGcrW1rbEv9+UKVNuqPX619YyleI7VP+dp6InIzQo5Ba4kpHklD+ZbGxVkyffMDcQOr63TTXqN0rZ2Dve9Dn2bp4qYPisIg2Q2kEPVNmMbtagAFR4eLjauHGj+fddu3apdevWqY4dO6pmzZqpWbNmqYsXLyoPDw8F+V+ySUlJ6ttvv1Vt2rRR99xzjzp79qwKDQ1VgKpXr57KyspS48aNU35+fuq2225To0aNUi4uLjfU4u7urnbv3q0WLlyovL29lbe3t7KxsVEhISHq77//LlLnhx9+qH755ZebvscXX3xRxcXFqUcffVQ1btxYPfroo+rSpUvq2WefVYCaMGGCiomJUffcc4/y9fVVXbp0UU888YQCVJ06dcxf5N7e3qpOnTrm93p9gyIxMVHNmzdPBQQEqODgYKWUUps2bVIhISGqWbNmavLkySozM1P5+PgU2X7uvvtu5efnp5YvX67OnTunJk6cqADl5OSkZs2apQ4dOmTOwMnJSdPf4vqpoEERGxurBg4cqFq2bKk+//xzlZiYqDw9PRWgGjRooFJSUtQnn3yiWrRoofr3768uXLigpkyZUuLfz8XFRa1atUr99NNP5lrt7e1LvT1q/Q61QwghrKjRgJepHZh/njsvN4eor6eT8NfOWz4nO/kKx5a8TqOHRuLddRAAjR8bT25aElcP7yl1Da3GzMfe1bo3fcpOuULk3NHlfp0jR47Qrl07AHr27Enbtm2pW7cuWVn5p4gmTpzIgAEDeOyxx1i0aBEANjY2DBs2jJSUFABWrFjBk08+CUD9+vWxt7dn7dq1xMbGAvD3338Xu+6kpCSysrJIS0vj/Pnz5vlLly7l7bff5o477uCPP/7Azs6Op59+mokTJ970fbz55ptMmDDBfH4/Ojqa1q1bM2LECJYvX46vry/Hjx/nt99+AzDXBnDp0iUArl69WqSO4ly5coUxY8aglOLYsWO89tprODs7M2PGDABmzJjBpEmT6NKlC6tXrwZg2rRp5ucfPXqUv/76iyFDhjBr1iwyMjJISUkhJyenyLq1/i2K88knn7B27VoARo0axQMPPMALL7zArFmzGD16NKdPn+a///2vuZ4GDRrw/vvv8/bbb5f490tPT8fR0bHEnCxBGhRWMmfOHL1LMDzJSJvKnJPXXQ9T965+AOTlZHFyxVskRu7V9uS8PE5vmA8ovLs+hsnGFv+n3iTyk5dIP3eqyKIlZWTv6olDLa+yvAXdmUwmlFIAdOzYEVdXVy5fvlxkmRo1atC0aVPz79HR0ebGBMC5c+fIyckB4ODBg2zfvp1Dhw6xZcsWtm7dyrfffsvVq1c11xQfH8/GjRt5/vnn+eOPP3j44YdxcnLim2++KXb5OnXq4Ovry5IlS4p80drZ2Zn7ayxbtoxt27Zx9OhRNm/ezI8//si2bds011Tgn3/+MecFcP78+SJfuHl5eVy+fJm6deua5w0aNIhx48bRrFkzXF1dsbOzIykp6Zbr0fq3KM7vv/9u/jk3N5ewsDBatWoFQKtWrYo8DrB7927c3Nzw8fGxyN/PUqRBYSWDBw/miy++0LsMQ5OMtKmsObk2vo1G/V82/x7z7WztjYlCTv+4ADvnmtTu2Bsbewf8h/4fkXNHk5edYV6mpIyyUyzbcU8LS62zVatWREVFAflHHs6dO0ePHj1uWK7wF0p2dnaRx5RSuLm5AflfqL1796Zz58706dOHl19+mWnTptGpU6dSDeq0ePFiVqxYwSuvvEJwcDCrV68mPT292GVtbPKvBxg+fDj79u0r8lhubi4A4eHhNGnShL59+9KrVy/WrFnD9u3befzxxzXXBMW/9+LmFdTUqVMnVq1axZQpU9iyZQu9e/fGzs6OCRMm3HI9Wv8WWhU0ggo3IAsUXOmjlLLY388SpEFhJfXr19e7BMOTjLSpjDnZODjR5IlJ2Njmf+TE//oNl/8s/X+bAChF9Lcf4lSvMS7/Xl7a6JHRxHw327xISRlZ4tSDHnr27Em7du3Ml23++eef1KtXj5ycHGJiYkr1WtdfKbJnzx727NnD22+/TUxMDI8++mixl4dmZWUVe5XJTz/9RGpqKqNGjaJv375069btpuu+cOECZ86cwd/fn5UrV950ueTkZNasWcOaNWv49ttv2bJlCx4eHiQkJNy0jvLq0qULMTExTJ8+HYAHHngAPz+/IssUt+7y/C3uuusudu3aBeT/XTp27Mgnn3wCwOHDhxk0aFCR5Tt37kxSUhJxcXHmeTf7+1VUTsWRy0atpPAfXhRPMtKmMubk8+B/cPTM/5JPPvUXZ376vFyvp3KzOfW/d8nNzP8P2KvTQ9Rsdbf58cqY0fUcHR3x9vamQYMGBAYGEhISwrp169iwYQPLly8HYPv27fz+++/88MMP9OnTBz8/P+6++27eeecdOnbseMvXLzgScOeddxISEkLHjh1p1KgRAwcOxMvLi8jIyGKfFx0dTadOnfDz86N27drm/5bz8vJYtmwZM2bM4MSJE+zde+ujT1OnTiUkJIQxY8bQvHlzbrvtNoYNG8Yrr7wCwLhx4xgyZAgtWrSgefPmPP7445w7d8783350dDT33Xcf3t7e1KplufFJTpw4ga+vL0OGDMHf359WrVrx6KOP3pBBkyZNaN++PbVr18bBwaFcf4uXXnqJAQMG0KJFCz799FM8PDzMR9jmz59Po0aNmDdvHi1atOCRRx7hrbfeYvbs2SilSvz7RUdH065dOwICAqhduzZ2dhV7HEH3Hs0VPRnhKg83NzfdczD6JBlVzZzcmnYwX5kR+O6PytGzvsVeu3bQ/dcuO530lTLZOVTKjK6fCl+emZWVpc6fP6+2bt2qhg0bpkwmU5FlXV1d1Zw5c9SZM2dUZmamiomJUStWrDBftXD9lQ+AGjt2rIqOjlaAatmypdq0aZM6f/68Sk9PV0eOHFEvvfRSkVoKX3HSvHlztWfPHpWamqqUUsrPz8/8WJMmTZRSSr366qua3ueTTz6p/vzzT5WRkaEuX76sfvnlFzVgwAAF+VeB/Pnnnyo5OVldvXpVbdu2TXXo0MH83IcfflgdO3ZMZWVllXjZaOF1hoaGqo8++qjIvKioKDV27Fjz7++//766ePGi+eqYsWPHqoSEBPPjDg4O6ptvvlFXrlwpctloSX+L66eCqzyeeOIJ9fvvv6uMjAz1zz//qJ49exZZ7laXjZb096tTp47asmWLSkpKkstGLTEZoUFR2S9jk4yMM1WmnEw2tuq2icvMX/p1Ow+w+DoC/vOB+fUb9BlW6TLSa6qIjDp37qyysrJU3bp1dX9/Rs6pYCpoULRv317393mrSet3qJzyEEJUGK+7++Pk1QiAlOi/ufD7OouvI/aHueTl5Heyq9djCI51Glp8HeLWHBwcaNq0Ke+88w5r1qzhwoULepckdKB7g6Jr166sX7+euLi4Ysdmv96jjz7K1q1buXDhAomJiezZs4c+ffpYqdqy27Fjh94lGJ5kpE1lycm2hhsNej9j/j12/Xy4rre6JWRciOX8rm8BsLFzoOH9wZUmIz1ZMqMnn3ySo0ePUrNmTV577TWLva4RyLakne4NChcXFw4ePGgetKMk3bp1Y9u2bTz44IN07NiR0NBQNmzYQIcOHSq40vIpuOZb3JxkpE1lyalBr2ewc3YH4NKBraSdOVph6zr381dkJycA4Nm+J9kulXOMCWuy5Hb05ZdfYmdnR1BQEGfPnrXY6xpBRe5vMTExmEwmDh48WGHrsCbdGxSbN2/mzTff1Hw3tFdeeYVZs2YRFhbGiRMnmDx5MsePH6dfv34VXGn5VIajKHqTjLSpDDnZ1/TC6+5HAMjNyiBu85IKXV9eVgbndly7/NCr51MVur6qoDJsR0YgOWmne4OivEwmE25ubha/w5wQouzq93wSGzt7AC78tpbsxEsVvs6L+zaQdTX/3P1F+zq4+Lau8HUKIa6p9A2KCRMm4OLiwpo1a0pc1tXVFTc3N/Pk4OBghQrzffbZZ1ZbV2UlGWlj9Jzsa9ahzp19AcjNTOf8r8UPv2xpKiebs9tXmH+vf58cpbgVo29HRiE5aVepR8p84oknmDp1Kv379+fixYslLh8XF1dkUI8dO3awbNkyNm7cyKhRowDYunUrdnZ23HvvvQDMnTuXQYMG0bBhQ86dO8eaNWsYO3YsAL/88guZmZncf//9ACxYsIAHHniAxo0bc+nSJZYuXVrk5jgbNmwwn5pZsmQJ3bp1o3nz5iQmJjJ//nxCQkIA2L9/P2fOnGHgwIEALF++nKCgIFq3bk16ejqzZ88mJCQEGxsbwsPDOXbsGEOGDAHg66+/plWrVnTo0IGcnBzef/99JkyYgJOTE//88w/h4eE8/fTTAHz33Xf4+fkRFBQE5N8QZ8yYMbi5uXH06FF2797N888/D8C6devw8vKic+fOAMycOZMXX3wRT09PTp06xbZt2xgxYgQAmzZtwtnZme7duwPw0UcfMXToULy9vTlz5gzr1q3jpZdeAvIH5gHo1asXjRo1YtKkSfTv3x8fHx/Onz/PypUrzQPd7Ny5k7S0NPr2zf+yWrhwIb1798bf358rV66wePFic4ewPXv2cPHiRXMn3y+++IIuXbrQokULkpOTmTt3LpMnTwYgLCyMmJgY82h0X331FYGBgbRp04aMjAw+/PBDXn/9dezs7IiIiCAyMtJ8Y6XVq1cTEBBAYGAgeXl5zJgxg/Hjx1OjRg0OHz5MWFgYzz77LABr167Fx8eHO++8E8i/KdHo0aOpWbMmx48f59dff+WFF14wbyuenp506dIFgFmzZhEcHB4c0HIAACAASURBVEydOnVwc3Nj1qxZjBw5EoAtW7bg6OhoHvJ3zpw5DB48mPr16xMXF8d3333HmDFjzNt8Tk6O+TDuZ599xkMPPYSvry8XL15kxYoVjB8/HoBdu3aRlJTEQw89BMCiRYvo2bMnzZo1IyEhgYULFzJp0iQA9u7dS3x8PAMGDCDSqTmxdvmN9WbqAt3/8zwff/wxb7zxBiaTiQMHDnDq1CnzEMorV66kbdu2tG3blqysLGbNmsXEiRNxcHDg0KFDHDp0iKFDhwLwzTff4O/vT8eOHVFKMX36dMaNG4eLiwuRkZHs+yMMp7wMMmycqNXqLno8MoQubZsB8N577zFixAg8PDw4ceIEoaGhDB8+HICNGzfi7u5O165dAZg9ezbPPPMMXl5exMbGWuUzYvfu3Vy5csVqnxH9+vUjKiqqUn1GAHz66adW/Yxo1KgR33//faX6jIiOjmbz5s0W+4wYMGAAWul+jWvBpJRS/fv317Ts4MGDVWpqqnrwwQc1X0Nbt25d5ebmZp4cHBys9t7kunjJqDrkZOdSS90+bZN5ECs7l5pWr6HuPQPN41I0fnyi7pkYdTLydmSkSXKq4uNQPPHEEyxbtoyhQ4fy008/aX5eSkoKycnJ5qngFrPWoOUISnUnGWlj5Jy87u6HjX3+0YmLe38kJzXR6jVc2v8Ttrn5+7Zn4H3Yu9exeg2VgZG3IyORnLTTvUHh4uJC+/btad++PYB5fPRGjfIHw5k+fTpffvmlefknnniC5cuXM2HCBPbu3Yu3tzfe3t64u7vrUr9WK1asKHmhak4y0saoOZns7KnbOf/wscrN5cJva3WpIy8rg/jdPwBgY2eP9z0DdanD6Iy6HRmN5KSd7g2KoKAgIiIiiIiIAPLPpUVERPD2228D+XcN9PX1NS8/YsQI7O3tmT9/PvHx8eZpzpw5utSvVcF5aXFzkpE2Rs3Js8N92Lt6AJBw6FfzFRd6eLxDA/Jy8o9S1LmjLyY763XAriyMuh0ZjeSkne6dMnfu3Gm+W11xgoODi/zes2fPii5JCFEG9bo9Zv75/C7rXNlxM44qi4SDO6ndsTd2Lu54tute9tulCyE00f0IRXVRcK97cXOSkTZGzMmtaQdq1GsCQHLUIVJPV9yomFrs2rWLC3vXm38vGGRLXGPE7ciIJCftpEFhJUlJSXqXYHiSkTZGzMmr08Pmny/s+UHHSvIlJSWRGnOYtLMnAXD1a02NBs10rspYjLgdGZHkpJ00KKyk4Fp+cXOSkTZGy8nOpRa1brsHgOyUBK7+/ZvOFV3L6MLv145S1L3b2MPzW5vRtiOjkpy0kwaFEKJc6tzxgHmY7Ut/bEblGufmZVfCt5ObkQqAZ4d7sbF30rkiIaouaVBYyaJFi/QuwfAkI20MlZPJRJ1O1/6Du7Rvo47FXFOQUV5WBlciQgGwdXTGo21XPcsyFENtRwYmOWknDQorkatTSiYZaWOknNyaBuJUuwEAiUf/IPPKOZ0rylc4o0thW8w/1w66X49yDMlI25GRSU7aSYPCSpo1kw5hJZGMtDFSTnUKfUFf2q991NqKVjij1NjDZFw8DYB7s0AcPLz1KstQjLQdGZnkpJ00KKwkISFB7xIMTzLSxig52Tg6mztj5qQlcfXw7zpXdM31GRU5StGxj7XLMSSjbEdGJzlpJw0KK1m4cKHeJRieZKSNUXLybNcdW4f8To5XwnegcrN1ruia6zO6/Oc2VF4eAHWkQQEYZzsyOslJO2lQWEnBbZ7FzUlG2hglp8L9ES4d2KpjJTe6PqPsxEsknfgTAMfaDXDxbaVHWYZilO3I6CQn7aRBIYQoNcfaDXBr0haA9Pho0s7oOzKmFlcidph/9uxwr46VCFE1SYPCSvbu3at3CYYnGWljhJw8A+8z/3zZYEcnoPiMrv79m/mGYR7tuoOpen/8GWE7qgwkJ+2q9x5lRfHx8XqXYHiSkTZGyKngP3yVl8fliJ91ruZGxWWUm5FK4pH9ADi418bNv521yzIUI2xHlYHkpJ00KKxkwIABepdgeJKRNnrn5NywOTXq+gKQEvUX2YmXdK2nODfLSE57XKP3dlRZSE7aSYNCCFEqnh2uDfRz+d9RKCuLxMi95GamA+DRtismWzudKxKi6pAGhZUsW7ZM7xIMTzLSRtecTCY82+c3KPJyc0g49Kt+tdzCzTLKy87k6uHdANg5u+PW7HYrVmUssr9pIzlpJw0KK+nUqZPeJRieZKSNnjm5+t2GQ626ACQdCyM3zZi3dr5VRgl/XWsEVed7e8j+po3kpJ00KKykVSu57r0kkpE2eubk2b6H+efC/RGM5lYZJR0LIzcr/7RHrTZdwKZ6fgzK/qaN5KRd9dyTdJCamqp3CYYnGWmjW04mE7X+/Y8+LzuLq4f36FOHBrfKKC8703y1h71LTdyaVM+rPWR/00Zy0k4aFFby8ccf612C4UlG2uiVk6vfbTi41wby7yya92/nRiMqKaOEQ7vMP3u07VbR5RiS7G/aSE7aSYPCSt544w29SzA8yUgbvXLyaHfti9eonTELlJRR4pG95GXnD3JV67YuYDJZoyxDkf1NG8lJO2lQWImpGn5glZZkpI0uOZlMeNz27+mOnGwSI41zZ9HilJRRXmY6ScfDAHBwr4NLo+p3nlz2N20kJ+2kQWElBw4c0LsEw5OMtNEjJ5dGrXCo5QVA0vED5GYY+7yylowS/v7N/HOt1ndXZDmGJPubNpKTdtKgsJJTp07pXYLhSUba6JFTkdMdfxn7dAdoyyjxyH7zLc1rtrqroksyHNnftJGctJMGhZU8/vjjepdgeJKRNnrkVKtNFwBUbq6hr+4ooCWjnJQEUk8fAcC5vj8OHt4VXZahyP6mjeSknTQohBC35OTth1PtBgAkR/1FbnqyzhVZTuG+INXxKIUQliQNCitZuXKl3iUYnmSkjbVzqtW6i/nnq/8Y/+gEaM/o6uFrt6au1ap69aOQ/U0byUk7aVBYSdu2bfUuwfAkI22snVPhDouV4XQHaM8oPf4UmQnnAXBr2h4bxxoVWZahyP6mjeSknTQorEQ2ypJJRtpYMyd7N09c/VoDkHbuFFkJ8VZbd3mUJqPEyPyjFDZ2Drg371hRJRmO7G/aSE7aSYPCSrKysvQuwfAkI22smVPhfgWV5egElC6jq4ev9aOoTqc9ZH/TRnLSzgQovYuoaM7Ozqxfv55HHnmEtLQ0vcsRotJoFjyNWv82Kg7PHU3amaM6V2R5Jjt7Okz5HlvHGmSnJHDwncdBVfmPRSE00/odKkcorGTixIl6l2B4kpE21srJxt4J92a3A5CVeIm0uGNWWa8llCYjlZNN0vH8wYvsXT1wadSyosoyFNnftJGctJMGhZU4ODjoXYLhSUbaWCsn94CO2Njnr+tq5O+V6r/20mZUHU97yP6mjeSknTQorOTQoUN6l2B4kpE21sqpVuvO5p8ry+WiBUqbUeKRfeafq8t4FLK/aSM5aScNCiuRjbJkkpE2VsnJZGP+Ys3NTCf5ZHjFr9OCSptRTkoCKbGRADg3aIpDrboVUZahyP6mjeSkne4Niq5du7J+/Xri4uJQStG/f/8Sn9OtWzfCwsJIT0/n5MmTjBgxwgqVls/QoUP1LsHwJCNtrJGTq19r7F1rAZB49A9UTnaFr9OSypJR4uHqNWqm7G/aSE7a6d6gcHFx4eDBg/z3v//VtHzjxo356aef2LVrF4GBgUyfPp25c+cycODACq5UiOqjVptrpzsSK9HlouVxtfBpjxZ36FiJEJWTnd4FbN68mc2bN2tefuTIkcTGxvLKK68AcOTIEYKCgnj11VdZu3ZtRZVZbt98843eJRieZKSNNXKq+W/HRJWXW+SLtrIoS0bp506SnZyAvZsHbk07YLK1Q+XmVEB1xiD7mzaSk3a6H6EorbvvvputW7cWmbdlyxaCgoKws7t1+8jV1RU3NzfzZM3eu/7+/lZbV2UlGWlT0Tk5etanRl1fAFJiDpObllSh66sIZcpIKZKOhQFg6+iMy78jhFZVsr9pIzlpp/sRitKqV68e58+fLzLv/Pnz2NvbU6dOHeLjbz40cFxcXJFGx44dO1i2bBkbN25k1KhRAGzduhU7OzvuvfdeAObOncugQYNo2LAh586dY82aNYwdOxaAX375hczMTO6//34AFixYwAMPPEDjxo25dOkSS5cuNV/DXLt2bc6ePUu/fv0AWLJkCd26daN58+YkJiYyf/58QkJCANi/fz9nzpwxn8ZZvnw5QUFBtG7dmvT0dGbPnk1ISAg2NjaEh4dz7NgxhgwZAsDXX39Nq1at6NChAzk5Obz//vtMmDABJycn/vnnH8LDw3n66acB+O677/Dz8yMoKAiAadOmMWbMGNzc3Dh69Ci7d+/m+eefB2DdunV4eXnRuXP+ofCZM2fy4osv4unpyalTp9i2bZu5L8umTZtwdname/fuAHz00UcMHToUb29vzpw5w7p163jppZcA2L59OwC9evUiICCAvXv30r9/f3x8fDh//jwrV640H43auXMnaWlp9O3bF4CFCxfSu3dv/P39uXLlCosXL+a1114DYM+ePVy8eNHcJ+eLL76gS5cutGjRguTkZObOncvkyZMBCAsLIyYmhkGDBgHw1VdfERgYSJs2bcjIyODDDz/k9ddfx87OjoiICCIjI3nyyScBWL16NQEBAQQGBpKXl8eMGTMYP348NWrU4PDhw4SFhfHss88CsHbtWnx8fLjzzjsBmDFjBqNHj6ZmzZocP36cX3/9lRdeeAGADRs24OnpSZcu+TfmmjVrFsHBwdSpUwcfHx/++OMPRo4cCeQ3qB0dHenRowcAc+bMYfDgwdSvX5+4uDi+++47xowZY97mc3Jy6NOnDwCfffYZDz30EL6+vly8eJEVK1YwaOybHPl3H3FOjDXntGjRInr27EmzZs1ISEhg4cKFTJo0CYC9e/cSHx/PgAEDAFi2bBmdOnWiVatWpKam8vHHH/PGG29gMpk4cOAAp06dMt8WeuXKlbRt25a2bduSlZXFrFmzmDhxIg4ODhw6dIhDhw6Zz2N/8803+Pv707FjR5RSTJ8+nXHjxuHi4kJkZCT79u1j2LBhBAQEcPr0aerVq8ddd+X3h3jvvfcYMWIEHh4enDhxgtDQUIYPHw7Axo0bcXd3p2mrBhR0wes+eDgdbOOJjY21ymfE7t27uXLlitU+IwYPHkz79u0r1WcEwKeffmrVz4iAgACUUpXqMyI6OprNmzdb7DOiYL/WQhllUkqp/v3733KZo0ePqkmTJhWZ17lzZ6WUUt7e3sU+x9nZWW3fvl3VrVtXubm5mScHBwervbc33nhD93yNPklGxsipWfA0FTTzZxU082dVo35T3d+vNTOyc/Uwv/dWYz7T/X0YMaPqNklO175DnZ2db7lcpTvlER8fT7169YrMq1u3LtnZ2Vy+fPmWz01JSSE5Odk8WXOM9unTp1ttXZWVZKRNReZksrPHrWkHALKSLpF+7mSFrasilTWjnJQE0uKOA+DiE4CdSy1LlmUosr9pIzlpV+kaFL///ju9e/cuMq9Pnz6EhYWRk2PcDlTjxo3TuwTDk4y0qcic3PzbY+vgBEDikT8qbD0VrTwZJf7bjwLAvfntlijHkGR/00Zy0k73BoWLiwvt27enffv2ADRp0oT27dvTqFEjIL91+OWXX5qXX7BgAX5+fnz44Ye0bNmS4OBgXnjhBT744ANd6tfKxcVF7xIMTzLSpiJzqtmyk/nnpKP7K2w9Fa08GSUVblAEVN3LR2V/00Zy0k73BkVQUBARERFEREQA+Z1zIiIiePvttwGoX78+vr6+5uWjo6N58MEH6dGjBxEREbz55puMGTPG0JeMAkRGRupdguFJRtpUZE41W+R3BlO5ueYbZlVG5ckoJfpvcjPTgfz7mVRVsr9pIzlpp/tVHjt37sRkMt308eDg4Bvm/frrr3TsWLl29H37Kt+1/NYmGWlTUTk5etbHycsHgJSYv8nNSK2Q9VhDeTJSuTkkn4ygVuu7cXCvTY36/qSfO2XB6oxB9jdtJCftdD9CUV0MGzZM7xIMTzLSpqJycm95p/nnxCOV93QHlD+jxGPX+o/UrKKnPWR/00Zy0k4aFEII4NrpDoDEStx/whKSjl073VOVT3sIYUnSoLCSH374Qe8SDE8y0qYicjLZOeDeLBCArMRLlf4Qf3kzyrx0hswr5wBwbdIWG3snS5RlKLK/aSM5aScNCiu5fuwMcSPJSJuKyMnNvz029o5A1Tg6YYmMCi4ftbFzwK1pu3K/ntHI/qaN5KSdNCispGD4X3FzkpE2FZFTzSrUfwIsk1HS0Wv9KKri5aOyv2kjOWknDQohhLn/RF5uDskn/tS5GmNIPhmBys0FwL259KMQoiQm8sfgrtKcnZ1Zv349jzzyCGlpabrUYGtrS+6/H06ieJKRNpbOydGzPm0nfQVA8qmDHF0w3mKvrRdLZdTypXm4/nvX0YPvDiY76dbD+1cmsr9pIzlp/w6VIxRWUnCXPXFzkpE2ls6p8FUMiUcr73DbhVkqo6RCR2vcmgZa5DWNQvY3bSQn7aRBYSUeHh56l2B4kpE2ls7Jrdm1BkVlHh2zMEtllHwi3PxzwVUwVYXsb9pITtpJg8JKTpw4oXcJhicZaWPRnEw2uDfLv7toTloSaXFV429gqYxSYv4hLzsTALcq1qCQ/U0byUk7aVBYSWhoqN4lGJ5kpI0lc3LxaY6dszsASSfCQeVZ7LX1ZKmMVE42KVF/A+Do4Y1jnYYWeV0jkP1NG8lJO2lQWMnw4cP1LsHwJCNtLJlT4asXqsrpDrBsRoX7UVSl0x6yv2kjOWknDQohqjG3wg2KY1WnQWFJSYX6Ubg1u13HSoQwNmlQWMnGjRv1LsHwJCNtLJWTjb0Trn5tAMi4fJashHiLvK4RWHJbSos7Tk5aMgBuTTvALe6OXJnI/qaN5KSdNCisxN3dXe8SDE8y0sZSObn6t8PGzh6oWqc7wMLbksoj+dRBAOxdalKjflPLvbaOZH/TRnLSThoUVtK1a1e9SzA8yUgbS+XkXoVPd1h6W6qK/Shkf9NGctJOGhRCVFPuzfP7A6i8PJJPhpewdPVWdDwK6UchRHGkQWEls2fP1rsEw5OMtLFETnauHjjX9wcg7cwxctNTyv2aRmLpbSnjQixZSZcAcPVvi8nWzqKvrwfZ37SRnLSTBoWVPPPMM3qXYHiSkTaWyKmqXi5aoCK2peTj+UcpbB1q4NKolcVf39pkf9NGctJOGhRW4uXlpXcJhicZaWOJnApOd0DVbFBUxLZU+PJR9+aVvx+F7G/aSE7aSYPCSmJjY/UuwfAkI20skVPBEYrcrHRSYg6X+/WMpiK2pcL9TKrCeBSyv2kjOWknDQorkWuZSyYZaVPenJzq+uFQsw4AKacOoXKzLVGWoVTEtpR19QIZl84A4OLbChsHJ4uvw5pkf9NGctJOGhRWMmrUKL1LMDzJSJvy5lTV+09AxW1LBac9bGztcG3SrkLWYS2yv2kjOWknDQohqpmq3n+iIiUfr3rjUQhhKdKgsJKtW7fqXYLhSUbalCcnk40tbk3bA5CdfIX0+ChLlWUoFbUtJZ+MMP9c2RsUsr9pIzlpJw0KK7Gzq/zXrVc0yUib8uTk4tsaW0dnAJIK/bdd1VTUtpSTlkRa3HEAnBteu/V7ZST7mzaSk3bSoLCSe++9V+8SDE8y0qY8OVWX0x0VuS0Vufto0w4Vtp6KJvubNpKTdtKgEKIaKdohs+oeoahIRRoUzSv/5aNCWIo0KKxk7ty5epdgeJKRNmXNydbJBZdGLQFIPx9D9r9DSVdFFbktpUT9RV5uDlC5+1HI/qaN5KSdNCisZNCgQXqXYHiSkTZlzcmtaQdMtrZA1T7dARW7LeVlZZAaGwmAUx0fHGrVrbB1VSTZ37SRnLSTBoWVNGzYUO8SDE8y0qasORW+S2ZVb1BU9LaUXOh25m5NK+dRCtnftJGctJMGhZWcO3dO7xIMTzLSpqw5uQfk95/Iy80h+dRBS5ZkOBW9LRXpR9GscnbMlP1NG8lJO2lQWMmaNWv0LsHwJCNtypKTQ626OHk1AiA1NpK8zHRLl2UoFb0tpcZGkpuVAYB7JT1CIfubNpKTdtKgsJKxY8fqXYLhSUbalCWn6jDcdmEVvS2p3BxSog4B4FDLC0cvnwpdX0WQ/U0byUk7QzQoRo0axalTp0hPTycsLIx77rnnlssPHTqUiIgIUlNTOXv2LF988QWenp5WqlaIyqfw5Y1Jx6p+g8IaioyaWUmPUghhSbo3KAYPHszHH3/MtGnTCAwMZNeuXWzatIlGjRoVu3yXLl1Yvnw5S5YsoU2bNjz++OPccccdLF682MqVl84vv/yidwmGJxlpU+qcTCZzh8yc9BRSzxyxfFEGY41tKalwx8xKePmo7G/aSE7a6d6gGD9+PEuWLGHJkiUcOXKEV155hdOnT9/0Dm933XUX0dHRzJs3j+joaHbv3s3ChQsJCgqycuWlk5mZqXcJhicZaVPanGrUb4q9ay0Akk8ehLy8iijLUKyxLaXFnSAnPQX4d8RMk6nC12lJsr9pIzlpp2uDwt7eno4dO95w85WtW7fSuXPnYp+zZ88efHx86Nu3LwB169blscce03TPeldXV9zc3MyTg4ND+d+ERvfff7/V1lVZSUbalDan6jLcdmFW2ZZUXn4DDbB3qUmNev4Vv04Lkv1NG8lJO13velKnTh3s7Ow4f/58kfnnz5+nXr16xT7n999/56mnnmL16tU4OTlhb2/PunXrePnll0tcX1xcXJEbvezYsYNly5axceNG8xGRrVu3YmdnZx6/fe7cuQwaNIiGDRty7tw51qxZY+6k88svv5CZmWne4BYsWMADDzxA48aNuXTpEkuXLmXixIkA1K5dm3bt2tGvXz8AlixZQrdu3WjevDmJiYnMnz+fkJAQAPbv38+ZM2cYOHAgAMuXLycoKIjWrVuTnp7O7NmzCQkJwcbGhvDwcI4dO8aQIUMA+Prrr2nVqhUdOnQgJyeH999/nwkTJuDk5MQ///xDeHg4Tz/9NADfffcdfn5+5qM706ZNY8yYMbi5uXH06FF2797N888/D8C6devw8vIyN/RmzpzJiy++iKenJ6dOnWLbtm2MGDECgE2bNuHs7Ez37t0B+Oijjxg6dCje3t6cOXOGdevW8dJLLwGwfft2AHr16kVAQAC1atWif//++Pj4cP78eVauXMkrr7wCwM6dO0lLSzM3JhcuXEjv3r3x9/fnypUrLF68mNdeew3Ib3hevHiR/v37A/DFF1/QpUsXWrRoQXJyMnPnzmXy5MkAhIWFERMTYx7A5quvviIwMJA2bdqQkZHBhx9+yOuvv46dnR0RERFERkby5JNPArB69WoCAgIIDAwkLy+PGTNmMH78eGrUqMHhw4cJCwvj2WefBWDt2rX4+Phw5513AjBjxgxGjx5NzZo1OX78OL/++isvvPACABs2bMDT05MuXboAMGvWLIKDg6lTpw4+Pj7Url2bkSNHArBlyxYcHR3p0aMHAHPmzGHw4MHUr1+fuLg49jm2NW/zTV1zaXzHHfTp0weAzz77jIceeghfX18uXrzIihUrGD9+PAC7du0iKSmJhx56CIBFixbRs2dPmjVrRkJCAgsXLmTSpEkA7N27l/j4eAYMGADAsmXL6NSpE61atSI1NZWPP/6YN954A5PJxIEDBzh16hSPP/44ACtXrqRt27a0bduWrKwsZs2axcSJE3FwcODQoUMcOnSIoUOHAvDNN9/g7+9Px44dUUoxffp0xo0bh4uLC5GRkezbt49hw4YREBBAmzZtqFevHnfddRcA7733HiNGjMDDw4MTJ04QGhrK8OHDAdi4cSPu7u507doVgNmzZ/PMM8/g5eVFbGzsTT8jYhy8KDiBNHDkRBxj9pf5M2L37t1cuXLFap8RAQEBvP7665XqMwLg008/tepnREBAAPfff3+l+oyIjo5m8+bNmj8jvvvuO8aMGQPkfy/m5OQU+Ywo2K+1UGWZ7O3ty/S8wlP9+vWVUkrdddddRea/8cYbKjIystjntGrVSsXFxalXX31VtW3bVvXp00cdPHhQLV68+KbrcXZ2Vtu3b1d169ZVbm5u5snBwaHc70HrVLt2bautq7JOkpHlczLZ2avbp/2kgmb+rNqGrNS9diNmVJ7JydtPBc38WQXN/Fk1C56m+/s2YkaVfZKcrn2HOjs733K5Mp/yiIuLY/r06TftPKnFpUuXyMnJueFoRN26dW84alEgJCSE3bt388EHH3Do0CG2bt3K6NGjeeGFF256VKNASkoKycnJ5ikrK6vMtZfWAw88YLV1VVaSkTalycm1cVts7B2B6nUzMGttSxnnY8hOTgDAzb8dJhtbq6zXEmR/00Zy0q7MDYoNGzYwZswYTp48ydq1a8t0i9fs7GwOHDhA7969i8zv3bs3e/bsKfY5zs7O5F3XqSw3NxcAk4E7RTVu3FjvEgxPMtKmNDlVx/4TYN1tKelk/qiZto7OOPu0sNp6y0v2N20kJ+3K3KB44YUX8PHxYfLkybRv356tW7dy+PBhXnrpJVxdXTW/zuzZs3nxxRcJDg6mZcuWzJ49G19fXxYsWADA9OnT+fLLL83Lb9iwgYEDBzJy5EiaNGlC586dmTt3Lvv27TP0EKmXLlXdOztaimSkTWlyKjygVXKh4aKrOmtuS4Vzda9Ew3DL/qaN5FQ6FjnH0q9fP7VlyxaVk5OjEhMT1bx581SLFi00PXfUqFEqKipKZWRkqLCwMNW1a1fzY0uXLlWhoaFFlv/vf/+r/v77b5Wamqri4uLUihUrVIMGDcp9/qciJ2v216isk2Rk2ZzsnN1Vx/e2qaCZP6vWYxfoXrcRM7LIujzrzOSGrgAAIABJREFUm/tRBAyfpft7N2JGlXmSnEr1HWq5lXbo0EH9/PPPKjc3V+Xm5qqcnBz17bffKi8vr8oSRoVNkydP1n2jMPokGVk2J4/2PcxfdD4P/kf3uo2YkaWmtpP+p4Jm/qxun7ZJmewqxxeQ7G+Sk9apwjtlFrC1teWJJ55g165dhIWF4e/vz+uvv07jxo0ZN24cXbt2Zfny5eVdjRCilKrT7cr1VnD3URt7B1z9WutcjRD6KPM4FA0aNGDEiBEMHz4cb29vdu3axeDBg/n+++9RSgHwySefEBcXx1dffWWxgiur3bt3612C4UlG2mjNqaD/RF52Fsn/3siqurD2tpR8MhyvO/PHPnBrFljkPh9GJfubNpKTdmVuUERHR5OTk8OqVauYM2cOBw8eLHa5U6dO3fQS0OrkypUrepdgeJKRNlpycqzTEEfP/MuoU6IPoXKsd4m0EVh7W7r+RmFnWWrV9ZeF7G/aSE7alfmUx1tvvYWvry/PP//8TRsTAAcPHsTfv3INSVsRCka/EzcnGWmjJaeipzuqz/gTBay9LWUnXSb9fAwALo1aYuPobNX1l4Xsb9pITtqVuUERGxt7w3gQBTw8PHjmmWfKXJQQonwKXy4q/Seso+DyUZOtLW5N2pawtBBVT5kbFEuXLqVp06bFPtakSROWLjX+IT9rWrJkid4lGJ5kpE2JOdnYmG+nnZ2aSNrZE1aoylj02JYKBriCynE7c9nftJGctCtzg+JWo1I6OTmZR68U+bp166Z3CYYnGWlTUk4uPi2wq5E/uFzyiT/h307S1Yke21LyyYOof4/auleCBoXsb9pITtqVqlNmo0aNigxDGhgYiJOTU5FlatSowX/+8x9iY2MtUmBV0bx5c71LMDzJSJuScqru/SdAn20pNz2ZtLMncPEJwLlBM+yc3clJS7J6HVrJ/qaN5KRdqRoUwcHBTJkyBaUUSinmz59/wzIFRy4Kbt8r8iUmJupdguFJRtqUlJN7gPSf0GtbSj4ZjotPAABuTTuQcOhXXerQQvY3bSQn7Uzkj3ClScuWLWndujUmk4k1a9bwxhtvcPz48SLLZGZm8vfffxMTE2PpWsvM2dmZ9evX88gjj5CWlqZLDTY2NjftxCrySUba3ConGwcnOkz9ARs7ezIuneHvmc9ZuTpj0Gtbcm9xJwEvzADgwp51xP4w1+o1aCX7mzaSk/bv0FL1oThy5Ahr167lu+++Izg4mEWLFrF27doi08aNGw3VmDCKkJAQvUswPMlIm1vl5ObfHhs7ewCSjlXPoxOg37aUEvUXebk5QNE7vRqR7G/aSE7alblT5vLly2XADyEMprrertwo8rIySI2NBMDJqxH2NevoXJEQ1lOqPhRvvvkmixcv5ty5c7z55pu3XFYpxbvvvluu4qqS/fv3612C4UlG2twqp4LxJ1RebqUY/rmi6LktJZ+MMI9D4da0A1f+3K5bLbci+5s2kpN2pWpQTJ06lc2bN3Pu3DmmTp16y2WlQVHUmTNn9C7B8CQjbW6Wk717bWrUawJA6umj5GakWrMsQ9FzW0o68ScNeuUP7OfeNNCwDQrZ37SRnLQr1SkPW1tb/vjjD/PPt5rs7Mp8m5AqaeDAgXqXYHiSkTY3y6nwYErV/XSHnttSakwkedmZgLEHuJL9TRvJSbty375cCGEMRYbbPlE9x58wApWbTUrU3wA4enjjWLuBzhUJYR1lblA4Ojri5uZWZN7jjz/OjBkzuO+++8pdWFWzfPlyvUswPMlIm5vlVNAhMzczndSYw9YsyXD03pYqwzDcemdUWUhO2pW5QbFixQrmzr12jfXLL7/MqlWreO2119iyZQt9+/a1SIFVRVBQkN4lGJ5kpE1xOTl5N8bBPf+KguRTB1H/XrpYXem9LSUXOkLk3tSYDQq9M6osJCftytyguPPOO9m8ebP59zFjxvDVV19Rq1Yt1q5dy6uvvmqRAquK1q1b612C4UlG2hSXU82Aax961Xn8iQJ6b0upccfJSU8BwK1ZB7jFvY/0ondGlYXkpF2ZGxReXl7ExcUB0LhxY/z9/Zk3bx7JycksWbKE2267zWJFVgXp6el6l2B4kpE2xeVUdLjtMGuWY0i6b0t5eaRE/QWAvasHNbwb61tPMXTPqJKQnLQrc4MiLS2NmjVrAtC1a1dSUlIIC8v/IMvIyMDV1dUyFVYRs2fP1rsEw5OMtLk+J5OdPW7+7QHIunqBjAtyYz4jbEtJxwv1ozDgaQ8jZFQZSE7alblBcejQIV566SVuu+02Ro8eTWhoqPkxX19f4uPjLVJgVSHDt5ZMMtLm+pxcG7fFxt4RgEQ53QEYY1tKLtQx07258RoURsioMpCctCvzYBHvvPMOP/74IxEREWRlZdGrVy/zYw899BB//imXrRVmYyNX6JZEMtLm+pyK9J+Q0x2AMbal9PPRZKckYO/qgWuTdmBjAwa6yZQRMqoMJCftytygCA0NpVWrVnTs2JGIiAiioqLMj+3YsYOIiOo77G9xwsPDS16ompOMtLk+p4L+Eyovj+Tj0pAHg2xLSpF8IgLPDj2xq+GKS8PmpJ4+qndVZobIqBKQnLQr13CWsbGxxMbeeL72888/L8/LVknHjh3TuwTDk4y0KZyTnasHzg2aAZAWd4yctCS9yjIUo2xLSSfD8ezQE8jvR2GkBoVRMjI6yUm7ch/L8fLyIigoiK5du94wiWuGDBmidwmGJxlpUzinIqNjSv8JM6NsS8knCvejMNbtzI2SkdFJTtqV+QhFvXr1WLFiBT179rzhMZPJhFJK7uchRAUrfLloovSfMJzMy2fJvBKPo2c9XBu3xWTngMrJ0rssISpEmb/xP/nkEwIDA3n99df566+/yMzMtGRdVc7XX3+tdwmGJxlpUzingg6ZMtx2UUbalpKO///27j0uyjL///hrhmGAgeEkCCieUFE0D6ym5tlWNLXUdGPLtTbT1kOtechK222/u/tVS3+h+d00K8O0tVXXSl3TzNTEs5iWCaKGJ1BBBDmfBu7fH8gIKzg3MMx9z8z1fDyuh8PNPXN/5u3lzOV9uO54Ans/jtZVj7FNF9XcuE1NGamZyEm+eg8oBg0axKuvvsratWutWI7jioiIIDk5WekyVE1kJE9lTh7BYbga/QHI/eW000+3XZWa+lLO+ZME9n4cAO/wnqoZUKgpIzUTOclX73MoJEni2rVr1qzFoXXv3l3pElRPZCRPZU7VZsc8Lw53VKWmvpRz8RTS3ctFvcPVc18INWWkZiIn+eo9oNi8eTOPP/64NWtxaCaT+N+jJSIjeSpzqvrlJM6fqE5NfamsMJeClIorBQwh9/YqKU1NGamZyEk+DSDV54mDBg3io48+YufOnWzfvp3bt2/ft45art81GAxs27aN0aNHU1BQoHQ5gtBgGp2eyL9uReuqpzgrjTOLJyhdkvAAzYZPotmvJwKQ/K/FZP6wR+GKBEE+ud+h9d5DsXfvXtq2bcvLL7/Mrl27OHHihLnFx8dz4sSJ+r60Q5o7d67SJaieyEieuXPnYmzTBa2rHhCHO2qitr5U9byJqpf6KkltGamVyEm+ep+UOWnSJGvW4fDc3d2VLkH1REbyuLu7VzvcIQYU91NbX8q/kkBZcSEubh6qGVCoLSO1EjnJV+8Bxbp166xWxPTp05k3bx4hISGcPXuWWbNmcfDgwVrX1+v1vPXWW0ycOJHg4GBSUlJYuHAhsbGxVqvJ2s6ePat0CaonMpLn7NmzeIePAiqm2865qI5Di2qitr4klZnITf4R34g+6L2b4BHchsKblyw/sRGpLSO1EjnJZ5W7noSHh9O3b18MBkOdnxsdHc3y5ctZuHAhkZGRxMXFsXPnTlq0aFHrczZt2sSvf/1rJk+eTIcOHXjmmWc4d+5cQ95Co1PL+SRqJjKS58ekZAwhYQDkpyRRVpircEXqo8a+VHVPkhqu9lBjRmokcpKvQQOKZ599lmvXrpGQkMCBAwfo0KEDABs3bmTKlCmyXmPOnDmsWbOGNWvWcO7cOWbPns21a9eYPn16jesPHz6cQYMGMXLkSL777juuXLnCiRMnOHLkSEPeSqObOHGi0iWonshInkG/fdH8WBzuqJka+1L18yiUn4ZbjRmpkchJvnoPKH7zm9+wdu1afvjhB15++WU0Go35dz/88APR0dEWX8PV1ZUePXqwe/fuast3795N3759a3zO6NGjiY+P57XXXiMlJYWkpCSWLl0q6ziXl5cXRqPR3PR6vcXnCILa3Nbdu+xQ3L/DfhSlX6XkTjoAxrBuaHSuClckCNZV73Mo5s+fT2xsLFOmTEGr1fL++++bf5eYmMgf//hHi68REBCATqcjLS2t2vK0tDSCg4NrfE5YWBj9+/enqKiIJ598koCAAFauXIm/vz+TJ09+4PZSU1Or3V9k7969rF27lh07dpj3iOzevRudTsejjz4KwIoVKxg/fjzNmzfnxo0bbNq0iVdeeQWA/fv3U1xczPDhwwH44IMPeOyxx2jdujUZGRnExsYyb948AJKTk+natStPPPEEAGvWrGHgwIG0b9+e7OxsVq5cyfz58wE4fvw4KSkpjBs3Dqg4X6Vnz5506tSJwsJCYmJimD9/PlqtllOnTnH+/HnzDWw+//xzIiIi6N69OyaTiXfeeYe5c+fi7u7O2bNnOXXqlHnEvWXLFlq1akXPnhW7XxcuXMjMmTMxGo0kJSVx6NAhXnjhBQC2bt1KYGCgeaC3ZMkSpkyZgr+/P8nJyXz77bdMnToVgJ07d2IwGBg0aBAAy5YtY8KECQQFBZGSksLWrVt56aWXANizp+LyuaFDh2I0GvH19WXMmDGEhoaSlpbGhg0bmD17NgDff/89BQUFjBgxAoDVq1cTFRVFWFgYmZmZfPzxx7z22msAHD58mFu3bjFmzBgAPvnkE/r160eHDh3Izc1lxYoVvPnmmwDEx8dz5coVxo8fD8Bnn31GZGQknTt3pqioiHfffZfXX38dnU7H6dOnSUxM5JlnngEq9saFh4cTGRlJeXk5ixcvZs6cOXh4eJCQkEB8fDzPPfccAF988QWhoaH06tULgMWLFzNjxgx8fHy4cOECBw4cMPfh7du34+/vT79+/QBYunQpkyZNoklAAPtcfAFwkUz88Xdj+PYbN9zc3Bg8eDAA7733HtHR0YSEhJCamsqWLVuYOXOmuc+bTCaGDRsGwKpVqxg1ahQtW7bk1q1brF+/njlz5gAQFxdHTk4Oo0ZVnK/x0UcfMWTIENq1a0dWVharV6/mjTfeAODo0aPcvHmTsWPHArB27Vp69+5NREQE+fn5LF++nAULFqDRaDh58iTJyck89dRTAGzYsIEuXbrQpUsXSkpKWLp0KfPmzUOv13PmzBnOnDnDhAkVl8Vu3ryZsLAwevTogSRJLFq0iFmzZuHp6UliYiLHjh3j+eefx2g00rlzZ4KDg+nTpw8Ab7/9NlOnTsXPz4+LFy+yb98+XnyxYm/Pjh078Pb2Nt/UMCYmhmeffZbAwECuXr1qtc+If185i963KVpXN55++Q22rHzH/Blx6NAhMjMzbfYZYTQaef311+3qMwLg/ffft+lnhNFoZPjw4XbzGREQEMDly5fZtWsX06ZNA+Cbb75p0GdE5b9rOaT6tIKCAmno0KESIGm1WqmsrEyKjIyUAKl///5SYWGhxdcICQmRJEmS+vTpU235ggULpMTExBqf880330gFBQWSt7e3edmTTz4plZWVSe7u7jU+x2AwSHv27JGaNm0qGY1Gc9Pr9fV67/Vpw4cPt9m27LWJjCw3j5C2Us8l30k9l3wntf393xSvR61NrX3Jr9sQ899f8xEviozsoImc7n2HGgyGB65X70MeBQUF+Pj41Pi75s2bk5WVZfE1MjIyMJlM9+2NaNq06X17LSrduHGD1NRUcnJyzMsSExPRarWEhoY+cHt5eXnk5uaaW0mJ7e76VznCF2onMrLMp8PD5sdquSeEGqm1L+Ve/MH82Cdc2ctH1ZqR2oic5Kv3gOLQoUO8/PLLNf7u+eefZ//+/RZfo7S0lJMnTxIVFVVteVRUFIcPH651u82aNcPT09O8LDw8nLKyMlJSUuS/AUGwQz4de5sf55w7rmAlQn2Y8rPJr5yGu3l7dF5+ClckCNZVr10gPXr0kAoLC6Xjx49Ls2bNkkwmk/T3v/9d2rZtm5Sfny917txZ1utER0dLxcXF0qRJk6SOHTtKMTExUm5urtSyZUsJkBYtWiR9+umn5vU9PT2lq1evSps2bZIiIiKkAQMGSElJSdKHH37Y4N01oomm5ubi7in1WLxb6rnkO+mheWsVr0e0+rXmw18wH/Zo0mOY4vWIJpql1uiHPE6ePMmIESPw8vLi3XffRaPRsGDBAsLDwxk5cqTsyUA2bdrErFmzeOuttzh9+jQDBw5k5MiRXL16FYCQkBBatmxpXj8/P5+oqCh8fX2Jj4/nn//8J9u3bzefUKJWaq9PDURGD+bdvgcaFxcAssXeiQdSc1/KTrr3d+fToZdidag5IzUROclX76s8oOIM5k6dOhEWFkZQUBAZGRlcuHChzq+zatUqVq1aVePvapriOykpyXwGqr0wGo1Kl6B6IqMH8+l478sn+9wxBStRPzX3pbyrCZgKctEZjBW3oNdq4e7tzW1JzRmpichJvnoNKAICApg6dSoDBw6kWbNmAFy/fp19+/bx4YcfkpmZadUiHUFSUpLSJaieyOgBNBq87/5vVlNWSu6lnxQuSN1U3ZfKy8m5cBL/boPRGbzxahFB3hXbT++s6oxUROQkX50PeTz66KNcuHCBv/3tbwwZMoQmTZoQEBDAkCFDWLhwIefPnzdfyy3cc+jQIaVLUD2RUe08Qtqi924CQMGVM0imUoUrUje196Wqhz28Oypz2EPtGamFyEm+Og0oAgIC2LhxI9nZ2URHR+Pj40OzZs0ICQnBx8eHp59+mvz8fP7973/j7+9v+QWdSOXkL0LtREa1863ypfOrEM8HrCmA+vtSTtIJ82OlzqNQe0ZqIXKSr04DismTJ+Pi4kK/fv3YsmULhYWF5t8VFhayefNm+vfvj6urq8VZKwVBkM+7ypdOQOltBSsRrKE0N5OC1IrzzTxDw8Xlo4JDqNOAYtiwYXzyySekpqbWus61a9eIjY3lsccea3BxjmTr1q1Kl6B6IqOauXgY8WrVCYDCtCt8+9VGhStSP3voS9nV9lI8/IA1G4c9ZKQGIif56jSgiIiI4ODBgxbXi4uLIyIiot5FOaLAwEClS1A9kVHNvMN7oNHevVw06bjISQZ7yKjqpb9KHPawh4zUQOQkX50GFL6+vqSnp1tcLz09HV9f33oX5Yhqu3uqcI/IqGY+He7Njpl97rjISQZ7yCjv6llMhXkA9y4ftSF7yEgNRE7y1akHu7m5UVpq+exyk8kkbg0uCNag0Zh3h5cVF5J36YzCBQlWU15Ozvl4AHQGbzxbdFS4IEFomDrPQ9GhQwdMJtMD1+nYUfzD+G9LlixRugTVExndz9C8Pa7GihP2ci7+gFRWKnKSwV4yyk46jn+3wUDFYY/8Kwk227a9ZKQ0kZN8dd7HtnbtWk6cOPHAFhsb2xi12rUpU6YoXYLqiYzuV/XYeuUxd5GTZfaSUbXLR208H4W9ZKQ0kZN8ddpDUdM02II8Yl4Oy0RG9/OJ6GN+nHN3MiSRk2X2klHl5aOG5u3xDO2AzssPU16WTbZtLxkpTeQkX50GFOvWrWusOhxecnKy0iWonsioOlejP14tK66WKrh+kZI7FSdEi5wss6eMss8dx9C8PVBxe/rb8btssl17ykhJIif5bHtasRP79ttvlS5B9URG1VXdO3En4Yj5scjJMnvK6E7ivb9b306P2Gy79pSRkkRO8okBhY1MnTpV6RJUT2RUnW+ne5erVR1QiJwss6eM8q+dozS34jCHd3gPNDrbXCFnTxkpSeQknxhQCIIKaV3d8W7/KwBKcjIoSD2vcEVCo5Ek814KF70H3u0iFS5IEOpHDChsZOfOnUqXoHoio3u82/8KrasbANkJR0GSzL8TOVlmbxllJ1Q97GGbiZTsLSOliJzkEwMKGzEYDEqXoHoio3t8qh3uOFztdyIny+wto5wLP1BeWgyAT6c+oNE0+jbtLSOliJzkEwMKGxk0aJDSJaieyOgujQbfuydklpUUknPxVLVfi5wss7eMykuLyLnwAwB67wAMzcMbfZv2lpFSRE7yiQGFIKiMZ4uO92bHPH8SyVSicEWCLVTdE2XLqz0EwVrEgMJGli1bpnQJqicyquD7gMMdIHKSwx4zyk48an5si/Mo7DEjJYic5BMDChuZMGGC0iWonsioQuX/TqXycrITj933e5GTZfaYUWluJnlXEwEwNGuL3i+oUbdnjxkpQeQknxhQ2EhQUON+ODgCkRG4+YfgEdwGgPyrCZjy79y3jsjJMnvNKLvqYY+Ixj3sYa8Z2ZrIST4xoLCRlJQUpUtQPZER+FQ5dl51MquqRE6W2WtGd2x4+ai9ZmRrIif5xIDCRrZu3ap0CaonMqp9dsyqRE6W2WtGhTcvUZx5EwCvtt1wcfdstG3Za0a2JnKSTwwobOSll15SugTVc/aMdJ4+GNt0BaAoI5Wi9Cs1rufsOclhzxlVnoirddHh3eHhRtuOPWdkSyIn+cSAQhBUwrdzPzQuLgBknYlTuBpBKVWv7PF7qL+ClQhC3YgBhY3s2bNH6RJUz9kz8ntogPlx1pkDta7n7DnJYc8Z5SX/RGl+NgA+HfuYp2C3NnvOyJZETvKJAYUgqICLhxfGuzcDK85KoyAlSeGKBKVI5WXcOXsIABc3D7zDeypckSDIIwYUNjJ06FClS1A9Z87It1NftC464MF7J8C5c5LL3jPK+uleH/DrOrBRtmHvGdmKyEk+MaAQBBXw63LvS8PSgEJwfLm/nMJUkAtUzEeh0bkqXJEgWCYGFDby/vvvK12C6jlrRlo3A97hPQAoyc4g/+5sibVx1pzqwt4zkspM5pMzXdw98W5v/cMe9p6RrYic5BMDChsZM2aM0iWonrNm5BvRB61OD9zdOyFJD1zfWXOqC0fIqOqeqqp7sKzFETKyBZGTfGJAYSOhoaFKl6B6zppRXQ93OGtOdeEIGeWcP0lZUT4Avp37orl7jo21OEJGtiBykk8MKGwkLS1N6RJUzxkz0urd8enYC7h7c6jLZy0+xxlzqitHyEgqKzXPlqrz8MLY7ldWfX1HyMgWRE7yqWJAMX36dJKTkyksLCQ+Pp7+/eVN5tK3b19KS0s5depUI1fYcBs2bFC6BNVzxox8OvY2zzOQ9fNBkMotPscZc6orR8moMQ97OEpGjU3kJJ/iA4ro6GiWL1/OwoULiYyMJC4ujp07d9KiRYsHPs/b25t169bx3Xff2ajShpk9e7bSJaieM2ZUn6s7nDGnunKUjLKTTlBWXAiAX+d+aLQuVnttR8mosYmc5FN8QDFnzhzWrFnDmjVrOHfuHLNnz+batWtMnz79gc9bvXo1GzZs4MiRmm+gJAhqp3V1w6djbwBK87PJTf5R4YoEtZFMJWQnHgVA5+mNV1g3hSsShNopOqBwdXWlR48e7N69u9ry3bt307dv7bfuff7552nbti1//etfG7tEq/n++++VLkH1nC0jn06P4OLmAVAxM2K55cMd4Hw51YcjZVR1z5V/10FWe11HyqgxiZzkU3RAERAQgE6nu++kl7S0NIKDg2t8Trt27Xj77bf53e9+R1lZWZ225+XlhdFoNDe9Xl/v2uuqoKDAZtuyV86WUZPIezPwZZ6Sf+jO2XKqD0fKKPvcMcpK7h726DrQald7OFJGjUnkJJ91r0OqJ+m/rrvXaDT3LQPQarVs2LCBv/zlL1y4cKHO20lNTUWnu/eW9+7dy9q1a9mxY4f5EMvu3bvR6XQ8+uijAKxYsYLx48fTvHlzbty4waZNm3jllVcA2L9/P8XFxQwfPhyADz74gMcee4zWrVuTkZFBbGws8+bNA6BJkyaYTCaeeOIJANasWcPAgQNp37492dnZrFy5kvnz5wNw/PhxUlJSGDduHADr1q2jZ8+edOrUicLCQmJiYpg/fz5arZZTp05x/vx5fvvb3wLw+eefExERQffu3TGZTLzzzjvMnTsXd3d3zp49y6lTp5g4cSIAW7ZsoVWrVvTsWTFpzsKFC5k5cyZGo5GkpCQOHTrECy+8AMDWrVsJDAw07zlasmQJU6ZMwd/fn+TkZL799lumTp0KwM6dOzEYDAwaVPG/qWXLljFhwgSCgoJISUlh69at5lsCV954Z+jQoYSHh/PKK68wZswYQkNDSUtLY8OGDeZjmN9//z0FBQWMGDECqDjsFRUVRVhYGJmZmXz88ce89tprABw+fJhbt26ZryH/5JNP6NevHx06dCA3N5cVK1bw5ptvAhAfH8+VK1cYP348AJ999hmRkZF07tyZoqIi3n33XV5//XV0Oh2nT58mMTGRZ555BoCNGzcSHh5OZGQk5eXlLF68mDlz5uDh4UFCQgLx8fE899xzAHzxxReEhobSq1cvSjSu7PWsuDW1W3kRj/UIJy7/JpMnTwZg+/bt+Pv7069fPwCWLl3KpEmTCAgIIDQ0lD/96U9MmzYNgG+++QY3NzcGDx4MwHvvvUd0dDQhISGkpqayZcsWZs6cae7zJpOJYcOGAbBq1SpGjRpFy5YtuXXrFuvXr2fOnDkAxMXFkZOTw6hRowD46KOPGDJkCO3atSMrK4vVq1fzxhtvAHD06FFu3rzJ2LFjAVi7di29e/cmIiKC/Px8li9fzoIFC9BoNJw8eZLk5GSeeuopoOKkty5dutClSxdKSkpYunQp8+bNQ6/Xc+bMGc6cOcOECRMA2Lx5M2FhYfTo0QNJkli0aBGzZs3C09OTxMREjh07xvPPP0/hOROqAAAgAElEQVR4eDhLliwhODiYPn36APD2228zdepU/Pz8uHjxIvv27ePFF18EYMeOHXh7ezNgQMUN2mJiYnj22WcJDAzk6tWrNvmMOHToEJmZmTV+RpwsvUWGviU6gzdT/rSUy4e/bvBnRHR0NAkJCXb1GQEVE03Z8jMiPDycDRs22PwzAmDx4sXMmDEDHx8fLly4wIEDB2R9Rly+fJldu3ZZ7TOi8t+1HJJSzdXVVSotLZXGjh1bbfny5cul/fv337e+j4+PJEmSVFpaam5lZWXmZUOGDKlxOwaDQdqzZ4/UtGlTyWg0mpter7fZe33zzTcVy9lemjNlFPjIaKnnku+knku+k0JH/kHkZOXmaBl5d+hl7i9hE98SGdmwiZzufYcaDIYHrqfoHorS0lJOnjxJVFQUX331lXl5VFQUW7duvW/9nJwcHnrooWrLZsyYwaOPPspvfvMbLl269MDt5eXlKbb7avXq1Yps1544U0ZNIn9tfnz7h7rdHtmZcqovR8so50I8pXlZuHr54RvxCC7unuZJr+rL0TJqLCIn+RS/yiMmJoYpU6YwadIkOnbsSExMDC1btuSDDz4AYNGiRXz66acASJLE2bNnq7X09HSKioo4e/asqo91RUVFKV2C6jlLRnr/ELxaVwyMC24kU3gzuU7Pd5acGsLhMiovJ/P0PgC0rnp8HxrQ4Jd0uIwaichJPsXPodi0aRNNmjThrbfeIiQkhJ9//pmRI0dy9epVAEJCQmjZsqXCVTZcWFiY0iWonrNk1KT7o+bHdTkZs5Kz5NQQjphR5qk9BPWvOGeiya+Gcjt+V4NezxEzagwiJ/kUH1BAxUkfq1atqvF3kyZNeuBz//rXv9rF5aOZmZlKl6B6zpKR/6+qXN1xem+dn+8sOTWEI2aUfy2JolspuAeGYgzrhqtPAKXZGfV+PUfMqDGInORT/JCHs/j444+VLkH1nCEjQ/P2eDSt2OOW+8tpSu6k1/k1nCGnhnLUjG6fqjjfRqPV4l9lT1d9OGpG1iZykk8MKGyk8lIloXbOkFGTKnsnbtfjcAc4R04N5agZVT1EVnUek/pw1IysTeQknxhQCIKtaLX4dRsCQLmpRPa9OwShUvHt6+RdSQDA0KwtHsFtFK5IEO4RAwobOXz4sNIlqJ6jZ+Td7lfovZsAkJ14jLLCvHq9jqPnZA2OnFHlYQ8A/yqXH9eVI2dkTSIn+cSAwkZu3bqldAmq5+gZBfQaaX5c9Uuhrhw9J2tw5IyyftyPdPe2A00ifw2a+n2MO3JG1iRykk8MKGykcnpXoXaOnJHO0xffThVTEpfmZpnvIFkfjpyTtThyRqb8bLKTjgOg922Kd3jPer2OI2dkTSIn+cSAQhBsoEnPYWh1rgBkxO9CKjMpXJFgzzJO7DQ/Dqyy50sQlCQGFDbyySefKF2C6jlyRoG9RpkfZxz/ukGv5cg5WYujZ5SdeJSSnNsA+HR6BJ2XX51fw9EzshaRk3xiQGEjlXeEE2rnqBkZw7rhHhgKQM7FUxTfvt6g13PUnKzJ0TOSysu4Hf8NAFoXHQE9h9f5NRw9I2sROcknBhQ20qFDB6VLUD1HzSig971d0reO7Wjw6zlqTtbkDBlV3dMV0GtEnZ/vDBlZg8hJPjGgsJHc3FylS1A9R8zIxeCNX5eBAJTmZ3Pn54MNfk1HzMnanCGj4swb5Fw4CYB7QCjGtt3r9HxnyMgaRE7yaai4j7lDMxgMbNu2jdGjR6v6jqSC42nafxwtR78EwM0Dm0n5zwcKVyQ4Er9uQ2j7uz8BFTOvXvp8kcIVCY5I7neo2ENhI2+++abSJaieI2ZkzZMxKzliTtbmLBnd+fkgpfnZAPh1GYCLwVv2c50lo4YSOcknBhSC0Ei8WnXGI7g1ALmXzlCUflXZggSHI5WVcvvktwBodfoG399DEBpCDChsJD4+XukSVM/RMgro87j58a1j/7Ha6zpaTo3BmTLKOH7vRN/A3vLnpHCmjBpC5CSfGFDYyJUrV5QuQfUcKSOdlx/+d28EZsrPIesn690IzJFyaizOlFFR+lVyL50BwCO4DV6tu8h6njNl1BAiJ/nEgMJGxo8fr3QJqudIGQX2edw8M+at4zuQTCVWe21HyqmxOFtGt47e2wPWtP84Wc9xtozqS+QknxhQCIKVaVx0NH1kNABSWRm3jmxTuCLB0WX99L155ky/h/qh9wtSuCLBGYkBhY189tlnSpegeo6SkV/Xwbga/QHIOnuQkjvpVn19R8mpMTlbRlJZqXngqtG60LTvWIvPcbaM6kvkJJ8YUNhIZGSk0iWonqNkFDTg3i7S9INfWv31HSWnxuSMGd06+h/KSysOrQX0GonWzeOB6ztjRvUhcpJPDChspHPnzkqXoHqOkJGxbXc8Q8MByE85T97lM1bfhiPk1NicMSNT/h1un/oOAJ2HF016DHvg+s6YUX2InOQTAwobKSoqUroE1XOEjIIHRZsf3/x+U6NswxFyamzOmlH6wS/Mj4P6jwONptZ1nTWjuhI5ySem3hYEK3EPas1Dc9cAFfdZOLPkOSgvV7gqwdmEv7gU7/a/AuBC7JtkJx5VuCLB3ompt1Xm9ddfV7oE1bP3jKrunUiL29Jogwl7z8kWnDmjtP/eS1ELZ86oLkRO8okBhY3odDqlS1A9e85I7xeEf+SvATAV5JBxYmejbcuec7IVZ84o+9xRijJSAfBu3wOP4LAa13PmjOpC5CSfGFDYyOnTp5UuQfXsOaPgwU+jdan44Ek/9CXlJY133NWec7IVp85IkqqdSxE85Lc1rubUGdWByEk+MaCwkcTERKVLUD17zcjVO4CAhx8DoKy4gLRGuFS0KnvNyZacPaOM+F3mu5D6dxuCW0Dz+9Zx9ozkEjnJJwYUNvLMM88oXYLq2WtGwYOeQqvTA5B+eCtlhbmNuj17zcmWnD2j8pIi0g78G6iY6CpkyIT71nH2jOQSOcknBhSC0ACuRn8CelfcVbSsyoe4ICgt/fBXmAoqBrdNfhWF3j9E4YoERycGFDayceNGpUtQPXvMKOTR3+GidwcqZio05d9p9G3aY062JjKC8uIC0g5uAUDj4kLIkKer/V5kJI/IST4xoLCR8PBwpUtQPXvLSO/blIDeowAoKy7k5r7PbbJde8tJCSKjCumHvsRUmAdAkx7D0fs2Nf9OZCSPyEk+MaCwETEfvGX2llHI0OfMtyhPP/iFTfZOgP3lpASRUYWywjzSD38FgFbnSvDge3spREbyiJzkEwMKGykXMyZaZE8ZuTdtScDdeyWYCvO4eaBxptmuiT3lpBSR0T1pcVsoKy4EIODhEbh6NwFERnKJnOQTU28LQj20e/7v+HbqC0DqrjXc2LtB4YoEoXbNR7xoPoci7eAXXNv2vsIVCfZETL2tMnPmzFG6BNWzl4y8wrqaBxMl2RkV02zbkL3kpCSRUXVpBzZTdneytcA+j6P3CxIZySRykk8VA4rp06eTnJxMYWEh8fHx9O/fv9Z1n3zySXbv3k16ejrZ2dkcPnyYYcMefJteNfDw8FC6BNWzi4w0GlqMmmr+MfWbTygvLbZpCXaRk8JERtWZ8u+YZ8/U6vQ0G/a8yEgmkZN8ig8ooqOjWb58OQsXLiQyMpK4uDh27txJixYtalx/4MCBfPvtt4wcOZIePXqwb98+tm/fTvfu3W1ced0kJCQoXYLq2UNGTSKH4tmiIwAFN5K5ffJbm9dgDzkpTWR0v5v7/4WpIAeo6MenL6cpXJF9EH2pbiQl29GjR6WVK1dWW5aQkCAtWrRI9mv8/PPP0p///Odaf28wGKQ9e/ZIBoNBsffZokULRXO2h6b2jLRuBqnbnzdLPZd8J/Vc8p3k3b6HyEmlTWRUcwsa+JS5/3Z5aZni9dhDE31J/neoonsoXF1d6dGjB7t37662fPfu3fTt21fWa2g0GoxGI5mZmRbX9fLywmg0mpter69X3fXx3HPP2Wxb9krtGTUbOhFXoz8AWWfiyLlwUpE61J6TGoiMapZ++CuKsyr2TLi16op3+MMKV6R+oi/Jp+h9WQMCAtDpdKSlVd/1lpaWRnBwsKzXmDt3Lp6enmzaZPmyvdTU1Gq3ot27dy9r165lx44dTJ8+HagYzOh0Oh599FEAVqxYwfjx42nevDk3btxg06ZNvPLKKwDs37+f4uJihg8fDsAHH3zAY489RuvWrcnIyCA2NpZ58+YB0KRJE7p27coTTzwBwJo1axg4cCDt27cnOzublStXMn/+fACOHz9OSkoK48aNA2DdunX07NmTTp06UVhYSExMDPPnz0er1XLq1CnOnz/Pb39bcUfBzz//nIiICLp3747JZOKdd95h7ty5uLu7c/bsWU6dOsXEiRMB2LJlC61ataJnz54ALFy4kJkzZ2I0GklKSuLQoUO88MILAGzdupXAwEDzQG/JkiVMmTIFf39/kpOT+fbbb5k6teLcgp07d2IwGBg0aBAAy5YtY8KECQQFBZGSksLWrVt56aWXANizZw8AQ4cOJTw8HF9fX8aMGUNoaChpaWls2LCB2bNnA/D9999TUFDAiBEjAFi9ejVRUVGEhYWRmZnJxx9/zGuvvQbA4cOHuXXrFmPGjAHgk08+oV+/fnTo0IHc3FxWrFjBm2++CUB8fDxXrlxh/PjxAHz22WdERkbSuXNnioqKePfdd3l5wd845vNIxTDcVMLoVi4Y3nyTjRs3Eh4eTmRkJOXl5SxevJg5c+bg4eFBQkIC8fHx5g+kL774gtDQUHr16gXA4sWLmTFjBj4+Ply4cIEDBw4wefJkALZv346/vz/9+vUDYOnSpUyaNImAgABCQ0Np0qQJ06ZNA+Cbb77Bzc2NwYMHA/Dee+8RHR1NSEgIqampbNmyhZkzZ5r7vMlkMp93tGrVKkaNGkXLli25desW69evN5+EFhcXR05ODqNGVUze9dFHHzFkyBDatWtHVlYWq1ev5o033gDg6NGj3Lx5k7FjxwKwdu1aevfuTUREBPn5+SxfvpwFCxag0Wg4efIkycnJPPXUUwBs2LCBLl260KVLF0pKSli6dCnz5s1Dr9dz5swZzpw5w4QJFfei2Lx5M2FhYfTo0QNJkli0aBGzZs3C09OTxMREjh07xvPPP094eDidO3cmODiYPn36APD2228zdepU/Pz8uHjxIvv27ePFF18EYMeOHXh7ezNgwAAAYmJiePbZZwkMDOTq1as2+Yw4dOgQmZmZjf4ZseXENtyGVrzv7s//ibg/jWPO7Fl28RkB8P7779v0MyI8PJzhw4db/Ix4/fXX0el0nD59msTERPM9QJT4jLh8+TK7du2y2mdE5b9rORTbjRISEiJJkiT16dOn2vIFCxZIiYmJFp//9NNPS3l5edKvf/1rWbtrmjZtKhmNRnPT6/U2e68RERGK77ZSe1NtRhqN1GHaMvOu4mZRvxc5qbyJjB7cOr70f+b+HNh3jOL1qLmJvmQnhzwyMjIwmUz37Y1o2rTpfXst/lt0dDRr1qwhOjqa7777Ttb28vLyyM3NNbeSkpJ6115XoaGhNtuWvVJrRgEPj8AY1hWAooxUbthoiu3aqDUnNREZPVjVeSiaD3senaePgtWom+hL8ik6oCgtLeXkyZNERUVVWx4VFcXhw4drfd7TTz/N2rVrmTBhAl9//XVjl2kVlbuwhNqpMSOdlx+hI/9g/vnql+8hmWw3EK2JGnNSG5HRg+VfO0ezkhsA6AzeNB/xosIVqZfoS/IpftloTEwMU6ZMYdKkSXTs2JGYmBhatmzJBx98AMCiRYv49NNPzes//fTTrFu3jrlz53L06FGCgoIICgrC29tbqbcgOLCWY2eiMxgBuP3DHsVOxBQEawsv+sV847DAXiPwbNVJ4YoER6D48Znp06dLly5dkoqKiqT4+HhpwIAB5t/FxsZK+/btM/+8b98+qSaxsbENPv7TmE2r1Sqes9qb2jLy6zbEfJy521++kHSevorXpMac1NhERvIyatp3rLmPd5r1oaTRuihel9qa6Et2cg5FpVWrVtGmTRvc3d3p2bMncXFx5t9NmjSJIUOGmH8eMmQIGo3mvjZp0iQlSpdtxowZSpegemrKSOflR6uxM80/X/3yPZvdTdQSNeWkViIjy2bMmEH60W3kp14AwNCsLUGDohWuSn1EX5JPFQMKZ+DjI056skRNGbV+6lV0nhWH0TJ/3E/WT98rXNE9aspJrURGlvn4+EB5OVe2LEMqLwOg2dDncA+seZZiZyX6knxiQGEjFy5cULoE1VNLRk37jsU3omLugtLcLK5+tULhiqpTS05qJjKyrDKjgpQk0uL+DYDWVU+r38wFjUbJ0lRF9CX5xIDCRg4cOKB0Caqnhow8gsMIrXLzr0sb38GUn61gRfdTQ05qJzKyrGpG13d/SlFGCgDGNl0IGvAbpcpSHdGX5BMDChupnN1MqJ3SGWndPAib+Ge0rhVTst888G9yzp9QtKaaKJ2TPRAZWVY1o/LSYi5v/n9I5eUANH/sBTyC2yhVmqqIviSfGFAIwl2tfzMXj6YtAShIvUDqzo8VrkgQbCfv0hnS4jYDFbc4b/P0fDQurgpXJdgTMaCwke3btytdguopmVHTfuPw71ZxNZGpMI9f1v8VqaxUsXoeRPQly0RGltWUUequWApuJAMVV32EjvrDfes4G9GX5BMDChvx9/dXugTVUyojY7tIWjw+zfzz5Y3vUJx5Q5Fa5BB9yTKRkWU1ZSSVlXLp88WUl1bMBhvUfxy+nfvZujRVEX1JPjGgsJHKO8IJtVMiIzf/ENpOfAuNiwsAN/Z9zp2E2qd9VwPRlywTGVlWW0aFN5O5tv3evT5aR7+G3k/e3Z8dkehL8okBheC0XDy8aDdpITpDxXwTdxKPkrrrE4WrEgTl3Tr6HzJ/3A+AzsOLdr//K1pXN2WLElRPQ8WUmQ7NYDCwbds2Ro8eTUFBgSI16PV6m97d1B7ZMiONzpXwKe9gDOsGQGHaFRL/8TLlxcr0j7oQfckykZFlljJycfck4o8rcQ+suNvm7dN7ubRhoa3KUw3Rl+R/h4o9FDai9qnB1cBmGWm0tPnt6+bBRGluFhdi37SLwQSIviSHyMgySxmVFeVz8dO3KLv776JJ90cJHvy0LUpTFdGX5BMDChsJCAhQugTVs1VGrcbNMl/RUVZSyIXYBZSo+CTM/yb6kmUiI8vkZFSUfoVL/3rb/HPoyBfx6zKwMctSHdGX5BMDChu5fPmy0iWoni0yCn18GoG9RwFQXmYi+bO/UZByvtG3a02iL1kmMrJMbkZ3zh4iddca889tnp7vVLc6F31JPjGgsJFdu3YpXYLqNWpGGg0tRr9E8MCnAJDKy7n0r8VknzveeNtsJKIvWSYysqwuGd3Yu4GMExXra131tJ+00Glm0hR9ST4xoLCRadOmWV7JyTVaRhotrX8zl6D+48yLrmyJIevuWez2RvQly0RGltU1oytfLCPn/EkAdAZv2k95Bzf/kMYoTVVEX5JPDCgEh6Zx0RE2YQEBD48AQCov49LGd8g4sVPhygTBvkhlJi6u/wt5VxMB0Hs3IXzqu+idYFAhyCMGFDbyzTffKF2C6lk7I41OT9tn/8d8Ama5qZTkf/4vt0/utup2bE30JctERpbVJ6Py4kIufLKAwpuXAHDzC6LD1Hcdek+F6EvyiQGFjbi5iUlhLLFmRq4+gXSc8R6+nR4BKu6m+Mu6t8g6Y/+3IhZ9yTKRkWX1zaisIIekD+dRePNyxev4BdFhxnKHPadC9CX5xIDCRgYPHqx0CapnrYy8WnWm08xVeIaGA1BWXMCFNfPt8gTMmoi+ZJnIyLKGZGTKyyLpw1fNgwq9dwAdpi3Dq1Vn6xSnIqIvyScGFIJDCeg1kvCp7+Jq9AOg+PZ1Ev/xR3KTf1S4MkFwLKa8LJI+mE3+1XMA6AxGwv/w//DvPkThygSliKm3bcTLy4u8vDxFtm0vGpKR1s1Ay9EzzCdfAuRcOMkv//xfygpyrFWiKoi+ZJnIyDJrZaTVu9P2ub/iE97TvOz6nvVc//ZTkOz/60X0JTH1tupER0crXYLq1Tcjr7CudJ79UbXBRFrcFs6vecPhBhMg+pIcIiPLrJVReUkRF2Pf5NaxHeZlzYY+S/sXFplvvGfPRF+STwwobCQkxHHPgraWumak0bkS+vg0OvzhXdz8K26vXFaUz6V/vc217SuhvLwxylSc6EuWiYwss2ZGUpmJK1tiuLZ9FVJ5GQA+HXoR8coH5nvm2CvRl+TTKV2As0hNTVW6BNWrS0a+nfoS+vhU3ANCzctyfznNpU1LKMlKa4zyVEP0JctERpY1RkZpcf+m4PpFwib8CVejH25+QYT/4f+RFreZ67s/pby02OrbbGyiL8knzqGwEaPRSG5uriLbthdyMvIIbkOLJ6bj3b6HeVl5aQmpu9aQdnCLQxyztUT0JctERpY1Zkau3gG0eWY+3m27m5cVZ97g6rb3yU440ijbbCyiL4lzKFRn5syZSpegeg/KSO8fQqvxs+k0a3W1wURu8o8krJhGWty/nWIwAaIvySEysqwxMyrNyeD8h69y7T8fUG4qAcDNP4T2z/8v7Z7/X/R+wY22bWsTfUk+cchDUDWPkLYED3ka/66D0GhdzMuLM29w7T+rufNznILVCYJQK0ki7cBmshOP0nLsH83/EfDt9Aje7X9F+pFt3Ny/EVNelsKFCtYiBhQ2snfvXqVLUL3KjDQurvhE9CGw9yh8OjxcbZ2yonxu7N1A2sEtSKZSJcpUnOhLlomMLLNVRkW3rnH+o9fw6zaYFo9PR+8TgNbVjeCBT9H0kdHcOraDm/s3UpqTYZN66kr0JfnEgMJGTCaT0iWoXqlXU1qMfokmkUPReVa/3Kw0L4v0g1+QfmQbZYXOfU246EuWiYwss3VGWT/uJ/vcMZoNfZamfceidXVD6+pGUP9xBPZ5nMxTe7l1bAf5VxNsWpcloi/JJwYUNjJs2DBOnDihdBmqonHRYQzrhk9En4p7bviHEPRf6xRn3uDm95u5Hb/LLs8QbwyiL1kmMrJMiYzKiwtJ2fEhN7/fTPCgaAIfGY2L3h2tTk/Aw48R8PBjFN68xK1jX3P71B5VzCMj+pJ8YkAh2IzGRYeheXuMbbri1aYLxrCuuLh73rdeeWkxWT/HcTt+NzkXT4HkmPNJCIKzMuVlkbJjNTf3byRo4FME9nkcnYcXUHElV8sxL9Hi8WnkXvqJOz8fJOvsIUqzbylctWCJuGzURvz9/cnMzFRk20rQ6PR4BLfG0KwdHiFhGJq1w9C8PS569xrXLy8zUXQtgfST35H14z7KivJtXLH9cLa+VB8iI8vUlJHW1Q2/roMI6DUSY5suNa6Tn3qB3IunyP3lNHmXf7bZZ4SaclKK3O9QsYfCRkaNGsX69euVLsPqXAzeuAc0xy2gOe4BobgHhOIREoZ7YGi1qzJqUpp3h5ykE9xJPELO+XgmPDWO9cf+Y6PK7Zej9iVrEhlZpqaMykuLuX1yN7dP7sa9aSsCeg7H96H+uAc0N6/j2bw9ns3bEzwoGqm8jILUC+RfPUd+ynnyU5IounW1UWbHVVNOaif2UNiAXq9n586djBgxgpKSEptvvyFcPIzofZui92uK3rcpbr5BFY/9gnEPaF6nufqLM2+Sd/lnci/9RN6lMxSlXzX/zp4zsiWRk2UiI8vsJSOP4Db4PtQf38798Gze/oHrlpUUUpR+laL0axSlX6Ew/RpF6Vcpvp2KVFa/EyvtJafGJvc7VBUDiunTpzNv3jxCQkI4e/Yss2bN4uDBg7WuP3DgQGJiYujcuTPXr19nyZIlrF69utb1lR5QGI1GcnJy8Pb2Vs2Ma1pXd1yNfrh6N8HV6H/fn3qfQPR+TXFxM9T5tctNpRSlXabg+i8U3PiFwhvJFFz/hbLC2t+7GjNSI5GTZSIjy+wxI53BG6+wbhjbdsO7bXc8gtvIep5UVkbxnTRKsu62O+kUZ6VRcqficWluFuXFNX8v2GNOjcFuDnlER0ezfPlyZsyYwaFDh5g6dSo7d+6kU6dOXLt27b71W7duzddff81HH33ExIkT6devHytXruTWrVt88cUXCrwD5Wld3dG6eaAzGNF5GHHx9EZnqN5cDEZcPX3MA4aaToasC6m8nJLsWxRnpFCUkUpxRmrFn7dTKb59vd7/IxAEQaiJqSCHOz/HmSezc3H3xNC8PZ6hHTCEhmNo3h43/+D7DrVqXFxwb9IM9ybNan3t8tJiSnOzKM3LwpSXZX7sUlrIroSbeLbrgZR5C1NRHmVF+ZQV5lFeUtSo79ceKT6gmDNnDmvWrGHNmjUAzJ49m+HDhzN9+nQWLFhw3/rTpk3j6tWrzJ49G4Bz587Rs2dPXn31VZsNKDyatcPV0wc0GtBo0VT7s8pjbcWf7h4Gvj57A++uQ9AXF6PRaEGjQaPVonFxReOiQ6tzRaPT33vs4opG54q28k9XPVo3Q8UlVm4GXNwMaPXuuLh5WDxXoT7KS4spuZNOSVZ6xej+7uOSypF+dgZSmXNOLCUIgvLKivLJ/eU0ub+cNi/T6FwrzuUKbIF705a4N22JR9OW6P1DzFeR1ETr6oabf7D5rsVV/XlHAqHP/Pm+5VJZWcXgojif8tISykuLqzWp6jJTxWOpzIRUVgblZUjmVl5xh9ZafkaSkJDuHkuQ7t5iQLr7h1RlGUh3fy4rKqAgJalB+daHogMKV1dXevTowdtvv11t+e7du+nbt2+Nz3nkkUfYvXt3tWXffPMNkydPRqfTPXASksDAQAoLC80/FxcXU1pa9y/Ftk+8WO1+EnIs2pVA6ycba054+UetyooLKM2tOgrPxJSTRUle5r0Rem7WAw9PuAAebq6Aa8NLv8vDwwOTyYSHhwdlZWVWe11HI3KyTGRkmUNnlJNGcU4axb/Ek/YmvZIAAAdcSURBVF1lsYubAVffwIpzwnwq/nT1boKrpy86oy86T190Ht5otBp529FqwdUIRmOjvI2GKLh+kaQP5ljt9Tw8PGStp+iAIiAgAJ1OR1pa9dtNp6WlERxc881jgoODa1zf1dWVgIAAbt68ed9zKsOo3Avi3Ax3W3NLK9rc999/z4YNG5QuQ/VETpaJjCwTGTmw7u1g5Darv6yHh4e6z6GAyt0092g0mvuWWVq/puWVbt++zcSJEyn/r0uK6ruHQhAEQRCciYeHB7dv337gOooOKDIyMjCZTPftjWjatOl9eyEq3bx5s8b1S0tLH/hma9pzIQiCIAiCZXKukNTaoI5alZaWcvLkSaKioqotj4qK4vDhwzU+58iRI/etP2zYMOLj48VNXARBEARBQZKSLTo6WiouLpYmTZokdezYUYqJiZFyc3Olli1bSoC0aNEi6dNPPzWv37p1aykvL0969913pY4dO0qTJk2SiouLpXHjxin6PkQTTTTRRBPNyZviBUjTp0+XLl26JBUVFUnx8fHSgAEDzL+LjY2V9u3bV239gQMHSidPnpSKioqk5ORkaerUqYq/B9FEE0000URz8qZ4AQ7XfH19pXXr1kl37tyR7ty5I61bt07y8fF54HNiY2Ol/3bkyBHF34s12/Tp06Xk5GSpsLBQio+Pl/r37//A9QcOHCjFx8dLhYWF0i+//OIUA8e6ZDRo0KD7+owkSVKHDh0Ufx+N2QYMGCBt27ZNSk1NlSRJksaMGWPxOc7Wl+qakTP2pTfeeEM6fvy4lJOTI6WlpUlffvmlFB4eLvpSw5riBThc+/rrr6WffvpJ6tOnj9SnTx/pp59+krZt2/bA58TGxkpff/21FBQUZG5+fn6KvxdrtcpDW5MnT5Y6duwoLVu2TMrNzZVatGhR4/qVh7aWLVsmdezYUZo8ebLDH9qqa0aVXwLt27ev1m+0Wq3i76Ux22OPPSb9/e9/l5588klZX5bO2JfqmpEz9qWdO3dKv//976VOnTpJXbt2lbZv3y5dvnxZMhgMoi/VvylegEO1jh07SpI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     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(len(mu_out)), mu_out, 'r-', lw=3, alpha=0.6, label='Trace plot mu') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "# plot density estimate of the posterior\n",
    "plt.title('Trace plot for mu')\n",
    "plt.show()\n",
    "\n",
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "# plot density estimate of the posterior\n",
    "sns.kdeplot(np.array(mu_out), bw=0.5, label = 'Density estimate post')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "# plot density estimate of the posterior\n",
    "plt.title('Density plot for mu')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "arviz - WARNING - Shape validation failed: input_shape: (1, 1000), minimum_shape: (chains=2, draws=4)\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "x  0.889  0.289   0.411    1.515      0.009    0.007     945.0   945.0   \n",
       "\n",
       "   ess_bulk  ess_tail  r_hat  \n",
       "x     954.0     783.0    NaN  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mean</th>\n      <th>sd</th>\n      <th>hdi_3%</th>\n      <th>hdi_97%</th>\n      <th>mcse_mean</th>\n      <th>mcse_sd</th>\n      <th>ess_mean</th>\n      <th>ess_sd</th>\n      <th>ess_bulk</th>\n      <th>ess_tail</th>\n      <th>r_hat</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>x</th>\n      <td>0.889</td>\n      <td>0.289</td>\n      <td>0.411</td>\n      <td>1.515</td>\n      <td>0.009</td>\n      <td>0.007</td>\n      <td>945.0</td>\n      <td>945.0</td>\n      <td>954.0</td>\n      <td>783.0</td>\n      <td>NaN</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "# Summary of sig2\n",
    "pm.summary(np.array(mu_out))"
   ]
  },
  {
   "source": [
    " ### Plotting $\\sigma^2$ posterior"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(len(sig2_out)), sig2_out, 'r-', lw=3, alpha=0.6, label='Trace plot sigma2') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "# plot density estimate of the posterior\n",
    "plt.title('Trace plot for sigma2')\n",
    "plt.show()\n",
    "\n",
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "# plot density estimate of the posterior\n",
    "sns.kdeplot(np.array(sig2_out), bw=0.5, label = 'Density estimate post')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "# plot density estimate of the posterior\n",
    "plt.title('Density plot for sigma2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "arviz - WARNING - Shape validation failed: input_shape: (1, 1000), minimum_shape: (chains=2, draws=4)\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "x  0.917  0.472   0.299    1.762      0.016    0.011     850.0   850.0   \n",
       "\n",
       "   ess_bulk  ess_tail  r_hat  \n",
       "x     782.0     814.0    NaN  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mean</th>\n      <th>sd</th>\n      <th>hdi_3%</th>\n      <th>hdi_97%</th>\n      <th>mcse_mean</th>\n      <th>mcse_sd</th>\n      <th>ess_mean</th>\n      <th>ess_sd</th>\n      <th>ess_bulk</th>\n      <th>ess_tail</th>\n      <th>r_hat</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>x</th>\n      <td>0.917</td>\n      <td>0.472</td>\n      <td>0.299</td>\n      <td>1.762</td>\n      <td>0.016</td>\n      <td>0.011</td>\n      <td>850.0</td>\n      <td>850.0</td>\n      <td>782.0</td>\n      <td>814.0</td>\n      <td>NaN</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "# Summary of sig2\n",
    "pm.summary(np.array(sig2_out))"
   ]
  },
  {
   "source": [
    "As with the Metropolis-Hastings example, these chains appear to have converged."
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}