06_GibbsSampling_for_MixtureOfGaussians.ipynb

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    "# Application of Gibbs Sampling to Mixture of Gaussians\n",
    "\n",
    "## Task\n",
    "The file `data_ex06.csv` contains data sampled from a mixture of $K = 4$ Gaussians. The standard deviations of the Gaussians are known and\n",
    "identical, $\\sigma_k = \\sigma = 0.5$. Reconstruct the unknown parameters and the latent variables:\n",
    "$$\n",
    "    p_k, \\mu_k, Z_i\n",
    "$$\n",
    "where $Z_i$ represents the assignment of each point to one of the mixture components. To perform the inference, use _Gibbs sampling_.\n",
    "\n",
    "\n",
    "## Gibbs sampling\n",
    "**Step 1** <br>\n",
    "Initialize randomly $p_k, \\mu_k, Z_i$. Compute $N_k = \\sum_i \\chi(Z_i=k)$ and $m_k=\\sum_i \\chi(Z_i=k) x_k$.\n",
    "\n",
    "**Step 2** <br>\n",
    "Perform Gibbs sampling iterations:\n",
    "- Sample $\\mu_k$ for all $k$ from a normal with mean:\n",
    "  $$\n",
    "    \\mu'_k = \\left(\\frac{\\mu_0}{\\sigma_0^2}+\\frac{m_k}{\\sigma^2}\\right)\\frac{1}{\\left(\\frac{1}{\\sigma_0^2}+\\frac{N_k}{\\sigma^2}\\right)}\n",
    "  $$\n",
    "  and standard deviation:\n",
    "  $$\n",
    "    \\sigma'_k = \\left(\\frac{1}{\\sigma_0^2}+\\frac{N_k}{\\sigma^2}\\right)^{-\\frac{1}{2}}\n",
    "  $$\n",
    "  Here $\\mu_0 = 0$ and $\\sigma_0 = 1000$ are the Gaussian prior parameters. Do this for all $k$.\n",
    "\n",
    "- Sample the $\\vec{p}$ from a Dirichlet distribution with parameters $\\gamma'_k=\\gamma_k+N_k$. Here $\\gamma_k=1$ are the Dirichlet prior parameters.\n",
    "\n",
    "- Sample the $Z_i$ from a categorical distribution:\n",
    "  $$\n",
    "    P(Z_i=k) = \\frac{p_k\\exp\\left\\{-\\frac{(x_i-\\mu_k)^2}{2\\sigma^2}\\right\\}}{\\sum_k p_k\\exp\\left\\{-\\frac{(x_i-\\mu_k)^2}{2\\sigma^2}\\right\\}}\n",
    "  $$\n",
    "\n",
    "- If $Z_i$ is updated, update $N_k$ and $m_k$, and consequentially $\\vec{\\mu}', \\vec{\\sigma}', \\vec{\\gamma}', \\vec{p}'$."
   ]
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    "## Mixture of Gaussians (MoG)\n",
    "Assume to have $N$ 1-dimensional points generated from a Mixture of $D$ Gaussians with parameters $\\mu_i, \\sigma_i$ for $i=1, \\dots, N$. Then, assuming i.i.d. points, the likelihood function can be written as:\n",
    "$$\n",
    "  f\\left(\\vec{x}|\\vec{p}, \\vec{\\mu}, \\vec{\\sigma}\\right) = \\prod_{i=1}^N f\\left(x_i|\\vec{p}, \\vec{\\mu}, \\vec{\\sigma}\\right) =  \n",
    "  \\prod_{i=1}^N \\sum_{k=1}^D p_k \\mathcal{N}(x_i|\\mu_k, \\sigma_k^2)\n",
    "$$\n",
    "Given the likelihood, the posterior becomes:\n",
    "$$\n",
    "  f\\left(\\vec{p}, \\vec{\\mu}, \\vec{\\sigma}|\\vec{x}\\right) = \\left(\\prod_{i=1}^N \\sum_{k=1}^D p_k \\mathcal{N}(x_i|\\mu_k, \\sigma_k^2)\\right) \\times f_{prior}(\\vec{p}, \\vec{\\mu}, \\vec{\\sigma})\n",
    "$$\n",
    "\n",
    "The problem with respect to Metropolis is that the order of operations involved in the computation of the likelihood is $\\mathcal{O}(DN)$, which is computationally heavy and makes the problem intractable. \n",
    "\n",
    "A strategy to simplify the problem and make the inference task more interesting is to write the generative process in a slightly different form, i.e. as the combination of 2 random processes:\n",
    "1. extract $Z_i\\in\\{1, \\dots, D\\}$ with probability $\\{p_1, \\dots, p_D\\}$\n",
    "2. extract $x_i$ from the corresponding component of the mixture: $\\mathcal{N}(\\mu_i, \\sigma_i^2)$\n",
    "\n",
    "The variables $Z_i$ are called _latent variables_ and are unknown. They represent the mixture component from which each point $x_i$ was sampled. Thus, they are distributed according to a categorical distribution:\n",
    "$$\n",
    "  Z_i\\sim Cat(\\vec{p}) \\quad \\text{i.e.} \\quad P(Z_i=k)=p_k\n",
    "$$\n",
    "Then the likelihood becomes:\n",
    "$$\n",
    "  f\\left(x_i|\\vec{\\mu}, \\vec{\\sigma}, Z_i\\right) = \\mathcal{N}(\\mu_{Z_i}, \\sigma_{Z_i}^2) \\iff f\\left(x_i|\\vec{\\mu}, \\vec{\\sigma}, Z_i=k\\right) = \\mathcal{N}(\\mu_k, \\sigma_k^2)\n",
    "$$\n",
    "meaning that when $Z_i = k$,  $x_i$ is sampled from a Gaussian with mean $\\mu_k$ and variance $\\sigma^2$. \n",
    "\n",
    "We can also rewrite the posterior using the latent variables:\n",
    "$$\n",
    "\\begin{align*}\n",
    "  f\\left(\\vec{x}|\\vec{\\mu}, \\vec{\\sigma}, \\vec{Z}\\right) &= \\prod_{i=1}^N f\\left(x_i|\\vec{\\mu}, \\vec{\\sigma}, Z_i\\right) = \\\\\n",
    "  &= \\prod_{i=1}^N \\mathcal{N}(x_i|\\mu_{Z_i}, \\sigma_{Z_i}^2) = \\\\\n",
    "  &= \\prod_{i=1}^N \\left(2\\pi\\sigma_{Z_i}^2\\right)^{-\\frac{1}{2}} e^{-\\frac{1}{2}\\frac{(x_i-\\mu_{Z_i})^2}{\\sigma_{Z_i}^2}} = \\\\\n",
    "  &= \\prod_{k=1}^D \\left(2\\pi\\sigma_{Z_i}^2\\right)^{-\\frac{N_k}{2}} e^{-\\frac{1}{2}\\sum_{i=1}^N \\chi(Z_i=k)\\frac{(x_i-\\mu_k)^2}{\\sigma_{k}^2}}\n",
    "\\end{align*}\n",
    "$$\n",
    "where $\\chi(Z_i=k)=1$ if $x_i$ is such that $Z_i=k$, else $0$. Here $N_k = \\sum_i \\chi(Z_i=k)$.\n",
    "\n",
    "Notice that the model with latent variables $Z_i$ allows to:\n",
    "1. Drastically reduce the computational complexity of computing the likelihood\n",
    "2. Use conjugate priors, which considerably simplifies the shape of the posterior, enabling Gibbs sampling\n",
    "   \n",
    "At this point we can infer all the parameters from the data, assuming for simplicity that $\\sigma_k=\\sigma=0.5 \\, \\forall k$. \n",
    "\n",
    "### Priors\n",
    "- The prior of $\\mu_k$ is Gaussian with parameters $\\mu_0$, $\\sigma_0$: \n",
    "  $$ \n",
    "    \\mu_k|\\mu_0, \\sigma_0 \\sim \\mathcal{N}(\\mu_0, \\sigma_0^2)\n",
    "  $$\n",
    "  Then:\n",
    "  $$ \n",
    "    f_{prior}(\\vec{\\mu}|\\mu_0, \\sigma_0^2)=\\prod_{k=1}^D f_{prior}(\\mu_k|\\mu_0, \\sigma_0^2) = (2\\pi\\sigma_{0})^{-\\frac{D}{2}}\\prod_{k=1}^D e^{-\\frac{(\\mu_0-\\mu_k)^2}{2\\sigma_0^2}}\n",
    "  $$\n",
    "\n",
    "- For $\\vec{p}$ we may assume a Dirichlet prior, which is the generalization of a Beta, i.e. the conjugate prior for Bernoulli trials:\n",
    "  $$\n",
    "    p_{k}|\\vec{\\gamma}\\sim Dir(\\vec{\\gamma})\n",
    "  $$ \n",
    "  or \n",
    "  $$\n",
    "    f_{prior}(\\vec{p}|\\vec{\\gamma})=(\\beta(\\vec{\\gamma}))^{-1}\\prod_{k=1}^D p_{k}^{\\gamma_{k}-1}\n",
    "  $$\n",
    "  This is the conjugate prior for the multinomial distribution. We can fix the hyperparameters to have a non-informative prior $\\gamma_{k}=1$\n",
    "  (uniform prior). \n",
    "\n",
    "- From the assumptions, we know that \n",
    "  $$\n",
    "    f_{prior}(Z_i=k|p_k)=p_k \\quad \\Longrightarrow \\quad f_{prior}(\\vec{Z}|\\vec{p}) = \\prod_{k=1}^D p_k^{N_k} \n",
    "  $$\n",
    "\n",
    "### Posterior\n",
    "The posterior simply becomes:\n",
    "$$\n",
    "f(\\vec{\\mu},\\vec{Z},\\vec{p}|\\vec{x})= \\frac{1}{E(\\vec{x})}\\times f_{likelihood}(\\vec{x}|\\vec{\\mu},\\sigma, \\vec{Z})\\times f_{prior}(\\vec{\\mu}|\\mu_{0}, \\sigma_{0})\\times f_{prior}(\\vec{Z}|\\vec{p})\\times f_{prior}(\\vec{p}|\\vec{\\gamma})\n",
    "$$\n",
    "where $E(\\vec{x})$ is the evidence. \n",
    "\n",
    "### Conditional posteriors\n",
    "We want to sample the above posterior using Gibbs Sampling. To do so, we need to compute the conditional distributions:\n",
    "$$\n",
    "\\begin{align*}\n",
    "  f&(\\mu_k | \\vec{\\mu}_{-k},\\vec{Z},\\vec{p}, \\vec{x}) \\\\\n",
    "  f&(p_k | \\vec{\\mu},\\vec{Z},\\vec{p}_{-k}, \\vec{x}) \\\\\n",
    "  f&(Z_i | \\vec{\\mu},\\vec{Z}_{-i},\\vec{p}, \\vec{x}) \n",
    "\\end{align*}\n",
    "$$\n",
    "Even if it looks very difficult, in the computation most terms cancel out. The computation is done using Bayes theorem and marginalization; for semplicity we report here only the final results. \n",
    "\n",
    "For $\\mu_k$:\n",
    "$$\n",
    "  \\mu_{k}|\\vec{\\mu}_{-k},\\vec{Z},\\vec{p}, \\vec{x}\\sim \\mathcal{N}(\\mu_k', \\sigma_k'^2)\n",
    "$$\n",
    "with\n",
    "$$\n",
    "\\begin{align*}\n",
    "  \\mu'_k &= \\left(\\frac{\\mu_0}{\\sigma_0^2}+\\frac{m_k}{\\sigma^2}\\right)\\frac{1}{\\left(\\frac{1}{\\sigma_0^2}+\\frac{N_k}{\\sigma^2}\\right)} \\\\\n",
    "  \\sigma'_k &= \\left(\\frac{1}{\\sigma_0^2}+\\frac{N_k}{\\sigma^2}\\right)^{-\\frac{1}{2}}\n",
    "\\end{align*}  \n",
    "$$\n",
    "\n",
    "For $p_k$:\n",
    "$$\n",
    "  \\vec{p}|\\vec{\\mu},\\vec{Z},\\vec{p}_{-k}, \\vec{x}\\sim Dir(\\vec{\\gamma'}) \n",
    "$$\n",
    "with\n",
    "$$\n",
    "  \\vec{\\gamma'}=\\vec{\\gamma}+\\vec{N}\n",
    "$$\n",
    "\n",
    "Finally, for $Z_i$:\n",
    "$$\n",
    "  Z_{i}|\\vec{\\mu},\\vec{Z}_{-i},\\vec{p}, \\vec{x} \\sim Cat(\\vec{p'})\n",
    "$$\n",
    "with\n",
    "$$\n",
    "  {p'}_k \\propto p_k e^{-\\frac{(x_{i}-\\mu_{k})^{2}}{2\\sigma^{2}}}\n",
    "$$"
   ]
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 1000 data points\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.stats import norm\n",
    "\n",
    "data = pd.read_csv('./data/data_ex06.csv', header=None).values.flatten()\n",
    "print('There are %i data points' %len(data))\n",
    "\n",
    "sigma = 0.5\n",
    "K = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot data distribution \n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "\n",
    "hist_val_div = ax.hist(data, bins=50, edgecolor='black', alpha=0.5, density=True, color='forestgreen')\n",
    "\n",
    "ax.set_xlabel('x', fontsize=10)\n",
    "ax.set_ylabel('Normalized counts', fontsize=10)\n",
    "ax.grid(alpha=0.5)\n",
    "ax.set_title('Data distribution', fontsize=15)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define Gibbs Sampling steps\n",
    "Notice that $Z_i\\in \\{0, 1, 2, 3\\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_N_vec(Z_vec):\n",
    "    tmp = np.zeros(K)\n",
    "    for i in range(K):\n",
    "        tmp[i] = np.sum(Z_vec==i)\n",
    "        \n",
    "    return tmp\n",
    "    \n",
    "def gen_m_vec(Z_vec, x=data):\n",
    "    tmp = np.zeros(K)\n",
    "    for i in range(K):\n",
    "        tmp[i] = np.sum(x[Z_vec==i])\n",
    "        \n",
    "    return tmp\n",
    "\n",
    "def sample_mu_vec(N_vec, m_vec, mu_0=0, sg_0=1000):\n",
    "    mu_vec = np.zeros(K)\n",
    "    \n",
    "    for k in range(K):\n",
    "        N_k, m_k = N_vec[k], m_vec[k]\n",
    "        \n",
    "        mu_prime = (mu_0/sg_0**2+m_k/sigma**2)/(1/sg_0**2+N_k/sigma**2)\n",
    "        sg_prime = (1/sg_0**2+N_k/sigma**2)**(-0.5)\n",
    "    \n",
    "        mu_vec[k] = np.random.normal(loc=mu_prime, scale=sg_prime)\n",
    "    \n",
    "    return mu_vec\n",
    "\n",
    "def sample_p_vec(N_vec, gamma_vec=np.ones(K)):\n",
    "    gamma_prime = gamma_vec + N_vec\n",
    "    p_vec = np.random.dirichlet(gamma_prime)\n",
    "    return p_vec\n",
    "\n",
    "def sample_Z_vec(mu_vec, p_vec, x=data): \n",
    "    Z_vec = np.zeros(len(x))\n",
    "    \n",
    "    for i, x_i in enumerate(x):\n",
    "        p_vec_prime = p_vec*np.exp(-(x_i-mu_vec)**2/(2*sigma**2))\n",
    "        p_vec_prime /= np.sum(p_vec_prime)\n",
    "        \n",
    "        Z_vec[i] = np.random.choice(a=np.arange(K), p=p_vec_prime)  \n",
    "        \n",
    "    return Z_vec  "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gibbs Sampling function and inference task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gibbs_Sampling_for_MoG(mu0, p0, Z0, n_samples, burn_in=0, x=data):\n",
    "    mu_vec_curr = mu0\n",
    "    p_vec_curr = p0\n",
    "    Z_vec_curr = Z0\n",
    "    \n",
    "    # initialize the chain object\n",
    "    f_sampled = {'mu': np.zeros((K, n_samples)), 'p': np.zeros((K, n_samples)), 'Z': np.zeros((len(x), n_samples))}\n",
    "\n",
    "    # initialize N and m\n",
    "    N_vec_curr = gen_N_vec(Z_vec_curr)\n",
    "    m_vec_curr = gen_m_vec(Z_vec_curr)\n",
    "    \n",
    "    # MCMC algorithm\n",
    "    i = 0\n",
    "    while i<(burn_in + n_samples):\n",
    "        if i%100 == 0:\n",
    "            print('Iteration %i ...' %i)\n",
    "            \n",
    "        # step 1: sample mu\n",
    "        mu_vec_curr = sample_mu_vec(N_vec_curr, m_vec_curr)\n",
    "        \n",
    "        # step 2: sample p\n",
    "        p_vec_curr = sample_p_vec(N_vec_curr)\n",
    "        \n",
    "        # step 2: sample Z\n",
    "        Z_vec_new = sample_Z_vec(mu_vec_curr, p_vec_curr)\n",
    "        \n",
    "        # step 3: if Z is updated, update N and m\n",
    "        if not np.array_equal(Z_vec_new, Z_vec_curr):\n",
    "            Z_vec_curr = Z_vec_new\n",
    "            N_vec_curr = gen_N_vec(Z_vec_curr)\n",
    "            m_vec_curr = gen_m_vec(Z_vec_curr)\n",
    "        \n",
    "        # store chain\n",
    "        if i >= burn_in:\n",
    "            f_sampled['mu'][:, i-burn_in] = mu_vec_curr\n",
    "            f_sampled['p'][:, i-burn_in] = p_vec_curr\n",
    "            f_sampled['Z'][:, i-burn_in] = Z_vec_curr\n",
    "            \n",
    "        i+=1\n",
    "    \n",
    "    print('Iteration %i reached!' %(burn_in + n_samples))\n",
    "    \n",
    "    return f_sampled\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial state:\n",
      "u =  [1.532 4.977 3.502 6.283]\n",
      "p =  [0.401 0.084 0.086 0.429]\n",
      "Z = \n",
      " [0 0 2 2 2 0 0 0 1 0 1 3 2 2 3 2 0 3 0 1 2 2 2 3 3 3 0 1 3 0 3 2 3 0 1 3 3\n",
      " 3 2 1 2 3 3 0 2 3 2 0 1 3 1 0 0 0 1 1 1 3 1 3 1 0 1 0 1 0 1 0 0 0 2 0 2 0\n",
      " 2 3 3 1 2 1 2 2 1 1 2 3 0 3 1 2 3 2 0 2 3 3 2 2 0 0 2 3 1 3 3 2 3 2 1 2 3\n",
      " 0 1 0 1 2 1 2 1 2 1 1 1 3 0 3 3 1 2 0 0 1 0 1 2 1 1 2 3 2 0 1 1 1 3 2 0 0\n",
      " 3 0 0 2 0 0 0 0 1 0 2 1 3 0 2 0 3 2 2 3 3 2 2 1 3 0 0 1 1 2 2 3 1 0 3 2 0\n",
      " 1 1 1 0 0 1 3 3 0 0 0 1 1 0 2 3 1 1 2 1 3 3 3 1 3 0 0 1 0 1 3 2 1 1 2 2 2\n",
      " 1 0 3 0 0 0 0 0 3 3 1 1 1 2 1 3 1 3 0 3 3 1 3 3 2 3 1 2 3 2 2 0 2 1 1 3 3\n",
      " 3 0 3 2 0 2 1 3 3 2 0 1 1 3 2 0 3 0 2 3 1 3 1 3 0 3 1 0 0 1 2 2 3 1 0 3 1\n",
      " 0 1 1 0 2 3 1 2 3 1 0 3 3 3 0 2 2 1 3 3 0 1 3 0 0 0 3 0 2 1 3 0 2 0 1 1 1\n",
      " 0 3 1 0 1 2 1 1 2 3 1 1 0 2 1 2 1 1 3 3 1 1 1 0 0 0 2 1 3 0 3 1 2 2 3 2 1\n",
      " 1 0 0 2 3 3 1 3 3 2 0 0 2 2 1 2 1 0 2 3 2 3 2 0 3 0 2 0 2 0 0 3 1 2 0 0 3\n",
      " 3 2 3 0 2 0 2 1 1 0 0 0 1 0 3 2 3 1 3 1 0 1 1 1 2 2 3 0 1 2 3 1 0 3 1 2 2\n",
      " 2 0 3 3 3 1 0 1 2 3 0 0 1 2 3 2 3 3 3 0 0 1 1 1 0 1 1 1 2 3 2 3 3 3 0 0 2\n",
      " 2 0 3 0 2 0 2 3 2 1 0 2 1 3 2 2 1 2 1 2 2 2 1 2 2 3 0 1 0 0 1 1 3 2 2 2 2\n",
      " 1 0 2 1 3 2 3 1 0 3 1 2 2 1 2 1 3 1 3 0 2 2 2 1 3 0 3 3 1 2 2 3 2 3 3 2 2\n",
      " 0 1 0 3 0 2 2 3 1 0 2 1 2 1 0 1 1 2 3 2 2 0 0 2 0 3 1 2 3 1 3 0 3 3 2 2 1\n",
      " 2 3 3 3 0 2 1 1 1 1 2 2 1 2 1 1 1 0 2 3 3 0 0 1 1 3 3 3 1 1 2 1 1 2 0 2 1\n",
      " 3 1 1 3 0 0 1 3 1 1 0 1 1 3 0 0 1 2 0 0 0 1 1 2 3 3 0 0 2 2 0 3 3 1 3 0 3\n",
      " 0 1 1 3 3 0 3 0 3 2 2 1 3 1 0 3 1 2 3 1 1 0 0 1 3 3 2 3 2 0 3 1 3 3 2 0 2\n",
      " 3 0 1 2 1 3 3 3 3 2 1 3 2 2 0 0 2 1 3 1 3 1 3 2 1 3 1 3 2 2 3 1 0 1 0 0 0\n",
      " 1 3 1 3 0 0 0 2 2 1 0 3 0 3 3 2 3 1 0 2 3 0 3 1 3 1 3 1 1 3 1 1 1 3 0 1 2\n",
      " 3 1 1 2 0 1 2 0 2 0 1 0 1 2 1 2 2 2 0 1 2 1 0 1 1 1 0 2 2 3 2 2 2 3 1 2 3\n",
      " 2 1 1 1 2 1 3 3 1 2 1 3 1 1 3 0 3 3 0 3 3 0 3 0 2 1 0 1 1 1 3 3 2 2 0 1 1\n",
      " 2 1 2 3 0 3 1 3 0 1 1 2 0 1 2 3 0 3 3 1 2 0 3 3 0 3 2 3 2 3 0 1 3 0 2 2 2\n",
      " 3 0 2 3 0 0 0 1 1 3 1 1 0 3 0 0 2 2 0 1 3 1 1 2 2 1 2 3 0 0 1 2 2 2 0 3 3\n",
      " 2 2 3 2 1 2 0 0 0 3 0 1 0 1 3 3 3 3 1 3 2 3 1 0 0 3 2 2 2 2 3 2 3 3 3 3 3\n",
      " 2 0 1 2 0 2 1 0 0 1 2 3 3 1 3 2 2 0 1 2 0 2 1 1 3 2 1 3 3 1 3 2 0 0 3 1 0\n",
      " 0]\n"
     ]
    }
   ],
   "source": [
    "# initialize randomly p, mu, Z\n",
    "np.random.seed(1234)\n",
    "\n",
    "mu0 = 8*np.random.uniform(size=K)\n",
    "p0 = np.random.dirichlet(np.ones(K))\n",
    "Z0 = np.random.choice(np.arange(K), size=len(data))\n",
    "\n",
    "burn_in = 0\n",
    "n_steps = 500\n",
    "\n",
    "print('Initial state:')\n",
    "print('u = ', np.round(mu0, 3))\n",
    "print('p = ', np.round(p0, 3))\n",
    "print('Z = \\n', Z0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 ...\n",
      "Iteration 100 ...\n",
      "Iteration 200 ...\n",
      "Iteration 300 ...\n",
      "Iteration 400 ...\n",
      "Iteration 500 reached!\n"
     ]
    }
   ],
   "source": [
    "chains_evol = Gibbs_Sampling_for_MoG(mu0, p0, Z0, n_samples=n_steps, burn_in=burn_in)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chain analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "    \n",
    "for i in range(K):\n",
    "    ax.scatter(range(0, n_steps), chains_evol['mu'][i, :], s=1.5, label='$\\mu_%i$' %i)\n",
    "    \n",
    "ax.grid(alpha=0.5)\n",
    "ax.legend(edgecolor='black', facecolor='linen', fontsize=10, loc='upper right', ncol=4)\n",
    "ax.set_ylim(top=8)\n",
    "\n",
    "ax.set_xlabel('Iteration', fontsize=10)\n",
    "ax.set_ylabel('$\\mu_k$', fontsize=10)\n",
    "ax.set_title('Convergence of Gibbs Sampling for a 1-D Gaussian mixture model', fontsize=15)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated values of u:\n",
      " u_0 = 0.947 +- 0.03418\n",
      " u_1 = 2.933 +- 0.03706\n",
      " u_2 = 5.007 +- 0.03820\n",
      " u_3 = 7.012 +- 0.03489\n",
      "\n",
      "Estimated values of p:\n",
      " p_0 = 0.255 +- 0.01462\n",
      " p_1 = 0.248 +- 0.01514\n",
      " p_2 = 0.242 +- 0.01389\n",
      " p_3 = 0.255 +- 0.01381\n"
     ]
    }
   ],
   "source": [
    "burn_in_after = 20\n",
    "\n",
    "mu_k_mean = np.mean(chains_evol['mu'][:, burn_in_after:], axis=1)\n",
    "mu_k_std  =  np.std(chains_evol['mu'][:, burn_in_after:], axis=1)\n",
    "p_k_mean = np.mean(chains_evol['p'][:, burn_in_after:], axis=1)\n",
    "p_k_std  =  np.std(chains_evol['p'][:, burn_in_after:], axis=1)\n",
    "\n",
    "print('Estimated values of u:')\n",
    "for i in range(K):\n",
    "    print(' u_%i = %.3f +- %.5f' %(i, mu_k_mean[i], mu_k_std[i]))\n",
    "   \n",
    "print('\\nEstimated values of p:') \n",
    "for i in range(K):\n",
    "    print(' p_%i = %.3f +- %.5f' %(i, p_k_mean[i], p_k_std[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s83WIyF2YeBN1YqmN+d///ufSdk1NTSI0NFSoVCqxf//+Lu+/8sor1qez9iwX6s4JtBBCLFy4UAAQs2bN6vLev//97x5vMk499dQu2xiNRpGeni4AiJ9++qlPn+svf/mLACBeeeUVp8c577zzut3W2U2SJdGora3t9dhXXXWVACAeeuihLu9VVlZav2/7hMZyIzhjxowu25w4caLbxKs7lpvGpUuXOt1fWFhYlxgsta579+7tsk1LS4tISkoSUVFRDjcZPSXeQggxc+ZMh/dNJpPQ6/Xi/PPPF5dffrnQarXWxK+qqkpIkiQmTpxo3b69vV3ExcWJiIgIh2TYoqKiQmi1WjFmzBjra9u2bbOWJWe1NJ999pn1Bs/CknirVCqxb9++LttYEvyBJob9/T139/qnn34qAIjLLrvMaRyWm9YXXnihS2xardZpUm05HgDxr3/9q8t7/fl+H3roIQHILU0627t3r5AkyWuJ99GjR6219b///e+77HvBggUCgNMaNrPZLMaPHy9UKpVDeexv4v3WW291OcYLL7zQ5TMcPHhQAHKLD2fnIEtLlRtuuMH62ttvv+00YbGw1Ip+8MEH1teuvPJKAUA89dRTXdb/+uuvXU5mLOdtZ4nEAw880OfEu7KyUgAQCxYs6NNx+5p4jx49utua3N4Sb/sHxBaW2srhw4c7vO6txHug1/O+lsf+KioqEgDEwoULnX6WoUOHOjxUEkK+BkRHR4vg4GDR1tZmfd0XympPersH6eu5zt7y5csFAPH555+7vC3RQLCPN1EnwoX+p/a2bNmClpYWTJ48GTk5OV3ev/LKKwEA69evd3qMM844o8trQ4cO7fY9y8BlzvpEA8Cll17a5bXg4GAsWrQIgNzvsrMff/wRTz75JG666Sb86le/wrJly/Cvf/0LAFBUVOT0OBdccIHT17szceJEAMBVV12FTZs2wWw2d7vuunXrAACXX355l/cSEhJw5plnwmw2O+23feaZZ3Z5LTY2FrGxsd1+Zz1x9n3GxsbijDPOcIjh+PHj2LFjB/Ly8jBixIgu24SEhOCUU05BXV1dt9+pM3PmzAEAax/Xbdu2ob6+HnPmzMGcOXPQ1taGDRs2AAB++OEHCCEwe/Zs6/bbtm3DiRMnMGPGDKej9yYmJiInJwe7d+9GS0sLAFj7wS1YsMBpv8oZM2YAADZv3tzlvaysLAwfPrzL65bX+vM7cMZdv2fLZ7Xve22vp886YcKEHkdsliQJ559/frfHdOX7tfzdXnLJJV3WHzFiBMaPH99tHO5UVFSE6dOnY+/evXjzzTdx3333ObxvNpvx7bffIiIiAvPmzeuyvSRJmD59OsxmM7Zs2TLgeJyVA2dlzfL9nXvuuYiKiuqyjeU8bTn32C87Ow8BwBVXXNFlm55+T2eeeSZiYmK6/zCdlJSUoLS0FKmpqTj11FO7vH/ZZZf1eV8JCQlIS0vDl19+iT/84Q9uGxfg/PPP7/d86s7OrWeffTaio6Oxf/9+l8YCcJeBXs/7Wh77oqioCC+//DJuvfVWXHPNNVi2bBmeeOIJ63vOzJkzB8HBwQ6vBQUFYejQoWhvb0d1dbX1dV8qq/25B+mJyWTCqlWr8Oijj+LGG2/EsmXLsGzZMnz//ff93ifRQHBUc6JO4uLisG/fPpcv9pYbmKysLKfvR0VFQa/Xo76+Hg0NDV1GUXV2424Zebmn95wNsAIAmZmZTl+3xGd/w1VfX4+FCxfiu+++c7oNADQ2Njp93dURa++55x78+OOP+OKLL/DFF19Ar9djypQpmD9/PpYtW4aIiAjruseOHYMkSS59Fou0tDSn24SHhzvcdPRVX2OwDHhXWFjY643oiRMnnCbnzsyZMwdPPPEE1qxZg2XLllkT8Llz51q/szVr1mDOnDnW9yzJOgDrgDP//e9/e42rpqYGqamp1m3uu+++LolV58/RWU/fP9B9uXWVu37Pls+6ZMkSLFmypNv1nH3W3v4GLIOKdXdMV75fSznr7pgZGRnYunVrj/G4w80334yOjg48++yz+PWvf93l/erqausggkFBPd9qOPtOXeWsHDgra72dp52dU/q7jSRJSE9Pd7pNRkYGampqnL7XWV9+56545513cOmll+Lee+/FvffeiyFDhmDWrFlYunSp04SxL/o7cnl0dLTDOd9eZmYmamtrcezYMcTHx/dr//010Ot5X8tjT4QQuPvuu7FixYpuKwS6uy67cv71hbI6kHuQ7hw9ehTz58/Hjh073LZPooFi4k3USX5+PtavX4+tW7daazJc0Zen/s7W6Wm7/tYkOOPsAn7ffffhu+++w6xZs/D4449j9OjRiIqKglqtxqpVq3DWWWd1e+EPCQlx6fiRkZH47rvvsH79enzxxRdYs2YNvv32W6xatQrPPPMM1q1b5/I0ZK5+n+7U+XsxmUwA5OmPeruJjY2N7fNxpk2bBo1GY02qf/jhB0RFRWHcuHFQqVRIS0tzeE+lUmHmzJld4srJyXFaE2HPkiRatpk5c6a19YUzzmrQvfX9u+s4ls96zjnnICEhodv1nE3P1NvfQHfv9+f7tZQ3b32/3VmyZAnef/99rFixAgsWLOjyAMny2SIiIrBw4cIe99XdQy1XuPp9dLe+5fX+nFM89Tvp7Xfu6nFPO+00HDhwAP/5z3/wv//9Dz/88APeeecdvPPOO7jkkkvw4Ycfuhyjq9eBvnC19VlPraf6yxPX87768MMP8eKLLyItLQ0vvfQSpk2bhvj4eAQHB8NoNEKr1Xb7HSl1fuhvWR3IPUh3rrvuOuzYsQMLFy7EfffdhxEjRiAiIgIqlQpvvvkmbrjhhn63cCTqLybeRJ2cd955eO211/Cvf/0Lzz33XK+1NRYpKSkAgMOHDzt9v76+HvX19QgLC+v2Cb87OZtqDJCbggG2eAHg008/hVqtxueff97lyf2hQ4fcHpskSZgxY4a1KW1VVRVuv/12fPDBB3jwwQetN34pKSk4fPgwiouLndYMWz6jN+b3LS4uxtixY7u83vn7tNQ0JCUlYeXKlW47fmhoKCZPnowff/wRhw4dwrp16zBr1iyoVHKPodmzZ+Ojjz5CWVkZdu/ejfz8fIemtJa4Ro8e3ee4LNssXrwYt912m9s+iy+yfNYbb7zR5e4TAz2mK99vSkoK9u/fj+LiYqdNYC3l0dOuu+46TJ8+HTfffDPmzp2LNWvWOHQtiIuLg1arRXBwsFv/Dgaqt/O0pRWC/Tmlt22cnYeSk5Nx5MgRlJaWIjs7u8s2rvyeLMfv7pze3es9iYyMxNKlS7F06VIAwIYNG3DxxRfjn//8J5YtW4ZzzjnH5X32R21tLRobG51eEy3fkf33qtFoAMhT8Flqby1KS0vdFpcvXM8//fRTAMDrr7+O+fPnO7znzuuyL5RVd9+DNDc3Y/Xq1UhMTMQ///lPqNXqAe+TyB3Yx5uok7PPPhujRo3C0aNH8dRTT/W4bkNDA/bs2QNA7rscGhqKTZs2Oe039O677wKQ+21642m0s1qLjo4OfPzxxwCA6dOnW1+vra1FRERElwseAPzzn//0XJAnxcfHW+dQ3bVrl/V1S43te++912WbqqoqrFq1CiqVqtcaXHdw9n3W1NRg1apVkCQJ06ZNAyAnUyNGjMDOnTu7vWlzxnJD2dHR0e06lqbjL730Eurq6jB37lyH99ra2qzzZNs3MweASZMmQa/X4/vvv0dDQ0OfYjr99NMBoMf5pAcLJT5rf45peVhl6fdob//+/da5k73hpptuwh//+EeUl5dba1EtgoKCMGfOHNTU1DidA10plu/vyy+/dDqnsuU8bd9apKfzkP3r9tv09HtavXp1n5vuAnKLgLS0NJSVleHnn3/u8n53c0q7YurUqdZ+y/bn4L6clwbK2bn166+/Rm1tLXJychxaoFiS8P3793fZprs52PvzGXzhel5bWwsATpuAu/O67AtltT/3ID39Xuvr62E2m5GcnNwl6e7o6LA+1CDyNibeRJ1IkoR3330XISEhePTRR/HAAw+gubnZYR0hBD7//HOccsop1oGPwsLCcM0118BsNuOWW25x2Gb//v148sknAQC33nqrVz7H+vXr8fbbbzvE/Mgjj6CkpATjxo1zSFaHDx+Ourq6LjdAK1assA5C4i5//vOfnSak//3vfwE49gG75ZZboFKp8PLLL+OXX36xvm40GnHrrbfCYDBg4cKFPQ5s5S7//Oc/8fXXX1t/7ujowJ133onm5mZccMEFDn3qfve738FkMmHRokXYvXt3l30dPHjQ4XcD2GoK9u3b120MlsHS/vKXvwBw7MNtWXb2HiA3H7/77rtRV1eHRYsWOa152Llzp0MZmDp1KubNm4fvv/8ed955p7XProXZbMaqVaucDtTnbxYvXozc3FysXLkSzz77LNrb2x3eNxqN+OSTTxySkoHqz/f7q1/9ChqNBn/7298cBvNqaWnB7bff7pHmtj255ZZb8PLLL6OsrAynnXaaQ03Sgw8+CJVKhauvvtppGTl27Bhee+01b4aLoUOH4rzzzkNjYyNuv/12h9/zzz//jNdffx1qtRo333yz9fVLLrkEiYmJWLduHd58802H/b3yyivYvHkz0tLScNFFF1lfv+GGGwAAL774IgoLC62v19TU4N5773U5bsv+fvvb3zo8ONu+fbtL32FJSQlWrlwJg8Hg8HpbW5v1XG9/Du7LeWmgHn/8cWtLA0Du82/5jux/D4DtHPjMM89YuzMAciLcXVLXn8/gC9dzSwuSN99806FJ9Lp16/CHP/zBbcfxhbLan3uQnn6vCQkJ0Ov12L17N9avX2993WQy4d5773X64IbIK7w7iDqR//jxxx+tc7fqdDoxb948sXTpUnHeeedZXw8JCRHffPONdZuGhgbr1DIJCQni4osvFueee64ICQkRAMRtt93W5Tg9TY/S3dQ6Qtimbeo8f7Nlio2bbrpJSJIkJk+eLC677DIxatQoAUBERESIrVu3Omzz7rvvWqcMmTlzprjsssvEyJEjhUqlEnfeeWe/pmjp7rNZptoaOXKkWLRokViyZInIz88XAERoaGiXac6eeuopAcjzaJ9++uni0ksvtU5XkpOTIyoqKvr8nXUXU08sU+HccsstQpIkMXv2bHHZZZeJIUOGCAAiJSVFFBcXd9nu3nvvFQCEWq0Wp5xyirj44ovFWWedZZ2ubty4cQ7rf/zxx9ZpjhYvXiyuvfZace211zqs09zcLDQajQAgoqOju8x5mpaWZp3Kq6ampktMJpNJXHbZZdYpsKZNmyaWLFki5s2bZ/08nacZqqiosM7lGhMTI0477TSxZMkSMWPGDBEfHy8AOMwx3125tOjt99NZb9OJufp7Rg9T2RQWFoqMjAwByPPwnnXWWeLiiy8WU6dOFVFRUQKA+PTTT3uNra/HE8L171cIIVasWGEtW/PmzRNLliwRKSkpIi0tzTq/r7fm8e4cU2Zmpjhy5Ij19VdffVWo1WoBQIwdO1YsWrRInHfeeWL06NFCrVYLvV7vsJ/+Tifmymc7evSotbxnZmaKSy+9VMybN88ap/2UcRbffPONCA0NFQDExIkTxWWXXSbGjx8vAIiwsDCxdu3aLttY5pPXarXivPPOE4sXLxYxMTEiPz9fTJ061aUpmlpbW63zpcfFxYmLL75YnH322UKj0Yibbrqpz9OJWaaw0+l0YtasWWLp0qViwYIF1rI2efJkh6mmfvnlFyFJktBqtWLBggXW89KJEyeEEH37e+5pOrGMjAwxf/58odPpxPnnny8WLlxo/VubO3euwzzUQsh/L5ZYhw8fLhYvXizGjRsn1Gp1t9eq3j5Dd2Xd3dfzvpwv7O3bt0+EhYVZr5eXXnqpmDlzppAkSdx9991Of+fdfRaL7n4XSpfV/tyD9PZ7tdw7qNVqccYZZ4glS5aIrKwsERoaKm655ZYevyciT2HiTdSDxsZG8fzzz4vZs2eL+Ph4ERQUJKKiosSUKVPEI488IkpLS7ts09TUJB577DExcuRIodVqRUREhJgxY4Z4//33nR7DU4n3999/L7744gsxbdo0odPphF6vFwsWLBB79uxxeqwvv/xSTJ06VURERIioqChx+umnizVr1vR7btTuPtvnn38urrnmGjFq1CgRFRUldDqdGD58uLj++utFUVGR0/385z//EfPmzRN6vV5oNBqRnZ0t7r33XqfJpacS78OHD4uVK1eK/Px8ERISImJjY8WVV17ptAxYfPvtt+Kiiy4SSUlJIjg4WCQkJIgJEyaIe+65R2zZsqXL+itWrLCWG8tNSGfTp093miALIcTll18uAIj8/PweP9NHH30kzj77bBEXFyeCg4NFcnKymDp1qnj00Uedzj1uMBjEiy++KKZMmSIiIiKEVqsVWVlZ4swzzxSvvfaawzzM/px4CyFETU2NePTRR8W4ceNEWFiY0Ol0YtiwYeKCCy4Qf/3rX0VjY2OvsblyPCFc+34t/vnPf4qJEycKrVYr4uLixNKlS8XRo0ddntvWXYm3EEI8//zzAoAYMmSIw8OoX375RVx++eUiPT1dBAcHi5iYGDF27Fhxyy23iDVr1jjswxuJtxDyXO+//e1vxbBhw4RGoxFRUVHizDPPdDrnuMXu3bvFZZddJhITE61/N1dccYXTvxkh5LnKX3/9dTFq1Cih0WhEcnKyuPHGG0VtbW23CVBPGhsbxd133y1SU1OFRqMRw4cPF88995wwmUx9TrwbGhrE888/L84991yRlZUlQkJCRFxcnJg0aZJ45ZVXhMFg6HLc9957T0yYMMH64ME+7oEm3pmZmaK1tVU8+OCDIisrS2g0GpGZmSmWL1/uNBYh5Adk8+fPFxERESIsLEzMmjVLfPfddz3+vnv6DD0lq+68nruaeAshREFBgTj//PNFQkKC0Ol0Yvz48dZ5z92ZeCtdVoVw/R5EiJ5/r0II8c4774jx48cLnU4nYmNjxYIFC8SOHTt6/Z6IPEUSgkP6EQ0my5YtwzvvvIPvv/++S3NjIiIiIiLyPvbxJiIiIiIiIvIgJt5EREREREREHsTEm4iIiIiIiMiD+pV4/+lPf8KQIUMQEhKCiRMnOkxp0tknn3yCM844A/Hx8YiMjMS0adMcpuQBgJUrV0KSpC7/Wltb+xMeUUBbuXKl03mciYiIiIhIGS4n3h9++CHuuOMOLF++HNu2bcPMmTNxzjnnoKSkxOn6a9euxRlnnIGvvvoKW7Zswdy5c3H++edj27ZtDutFRkaivLzc4V9ISEj/PhURERERERGRj3B5VPMpU6ZgwoQJeP31162v5eXl4cILL8QzzzzTp32MGjUKS5YswcMPPwxArqG74447UFdX50ooRERERERERD4vyJWVjUYjtmzZgvvvv9/h9TPPPBM//fRTn/ZhNpvR2NiImJgYh9ebmpqQmZkJk8mE/Px8PPHEExg/fny3+2lra0NbW5vDfmtqahAbGwtJklz4VERERERERESuE0KgsbERKSkpUKm6b1DuUuJ94sQJmEwmJCYmOryemJiIioqKPu3jhRdeQHNzMy655BLra7m5uVi5ciXGjBmDhoYGvPzyy5g+fTp27NiBnJwcp/t55pln8Nhjj7kSPhEREREREZHblZaWIi0trdv3XUq8LTrXKAsh+lTL/MEHH+DRRx/Fv//9byQkJFhfnzp1KqZOnWr9efr06ZgwYQJeffVVvPLKK0739cADD+Cuu+6y/lxfX4+MjAwcOXIEkZGRLn0ek8mEQ4cOYejQoVCr1S5tqxTG7B3+FnN/4t3861+jdssWRE+ciEl/+YuHI+zK375jgDF7y6brrkPd1q2ImjABk996S+lw+sQfv2fG7Bn259YJf/6zz8fbmT98x50xZtf09/rP79k7/C1mf4sXcF/MDQ0NyMrKQkRERI/ruZR4x8XFQa1Wd6ndPn78eJda8M4+/PBDXHvttfjXv/6F008/vcd1VSoVJk2ahKKiom7X0Wq10Gq1XV6Pjo7uV+IdGRmJ6OhovyoojNnz/C3m/sQbrtGgTaVCuEaD6OhoD0fYlb99xwBj9pZwjQZGBctmf/jj98yYPaPzudXX4+3MH77jzhiza/p7/ef37B3+FrO/xQu4L2bLtr1VRLs0qrlGo8HEiROxevVqh9dXr16NU089tdvtPvjgAyxbtgzvv/8+zjvvvF6PI4TA9u3bkZyc7Ep4RERERERERD7H5abmd911F6688kqccsopmDZtGt58802UlJTgxhtvBCA3AS8rK8Pf/vY3AHLSfdVVV+Hll1/G1KlTrbXloaGh0Ov1AIDHHnsMU6dORU5ODhoaGvDKK69g+/bteO2119z1OYmIiIiIiIgU4XLivWTJElRXV+Pxxx9HeXk5Ro8eja+++gqZmZkAgPLycoc5vd944w10dHTglltuwS233GJ9/eqrr8bKlSsBAHV1dbj++utRUVEBvV6P8ePHY+3atZg8efIAPx4RERERERGRsvo1uNrNN9+Mm2++2el7lmTaYs2aNb3ub8WKFVixYkV/QiEiIiIiIvIJTU1NOHbsGMxm84D2YzKZUFxcDJPJ5Bd9pv0tXqBvMatUKkRFRSEuLq7HqcL6ol+JNxEREREREdls2LABd915J4zGtgHvSwDoaG9HUHAwep87Snn+Fi/gSswSJkyciEceeQSpqan9Ph4TbyIiIiIiogFoamrCXXfeiQn5o3HtsisRHBQ8oP0JCBjb2qDRaiH5QSrrb/ECfYvZZDahrOwYXv/LX3HZZZfim2++hUaj6dfxmHgTBbj0hQsRO2UKdAN4gkfkCWkLFwLZ2UgbO1bpUIhcxnMr+TqWUfc6duwYjMY2XLvsSowZNXLA+xNCoLW1FSEhIb1OU+UL/C1eoO8xj8rLRUJCPG689bcoKSlBdnZ2v47HxJsowKUvXqx0CEROpS1ciJYxY5CWk6N0KEQusz+3mkwmBSMhco7Xf/ey9OkeaE03+aYQbQgAoKOjo9/7GFgPcSIiIiIiIiLqERNvIiIiIiIiIg9iU3OiAFf60UcwlJVBl5rKZmfkU45+8gmqd+5E6NixyLz4YqXDIXKJ/bk15aKLlA6HqAte/72jvr4BhhaDy9sJAbS1tUKrDYErXaZ1oTro9ZEuH488j4k3UYAr/eQTVG/ciNgpU3jhJZ9y9JNPULNpE3DgABNv8jv251Ym3uSLeP33vPr6BjzzygrUNNf2a/v+zIkdExaNB267s8/J9zU3/AZ/f/9DAEBQUBBioqMxZvRILFl8Ea6+4rI+z139t/f+gd/e9ztUHT3gUryBhIk3ERERERGRmxlaDKhprkVsfgzCo8Jc2lZAoKPDhKAgdZ+n52qqa0b19hoYWgwu1XqfdcZpeOv1V2AymVF5/DhWrf4Od923HJ/8+wt8+uG7CApiyugO/BaJiIiIiIg8JDwqDJGxrjX/lhPvDgQFBbk0L3Y1alwND1qNFkmJiQCA1JRkTMgfhymTT8GZ8xfinXc/wLXLrsSKV1/HO+9+gMNHihETHYXzzjkLv3/iYYSHh+OHdetx3U23AQA0kQkAgIceuAcPP3gv3vvHv/DKn97A/qIDCNPpMHf2TLzw7JNIiI93OU5/x8HViIiIiIiIyGru7JkYO2YUPvviSwCASiXhpT88je0b1+LtN/6INT+sw/0PPQ4AmDZlEl74/ZOIjIhASdEulB7YjbtuuxkAYDQa8djv7seWn9bgow/+hsNHSnDtjbcq9rmUxBpvIiIiIiIicpA7PAe7dhcAAG6/5Ubr60OyMvHoQ/fjN3fciz+ueA4ajQZ6fSQkSUJSYiIku9HgfnXV5dbloUOysOIPT+PUOWeiqakJ4eHh3vswPoCJNxERERERETkQQliT6DVrf8Tvn38JhXv3oaGxER0dJrS2tqK5uRlhYd33X9+2YyeeePoP2LFrN2pqa2E2CwBAydEyjMwd4ZXP4SvY1JyIiIiIiIgcFO4rQlZmBopLSnH+osswamQuPnz3r9i49lu88sLvAQDt7R3dbt/c3IxzF1yCsPAwvPOXP+HnNavx0fsrAchN0AMNa7yJiIiIiIjI6vsf1mH3ngLcfssN2LJtOzo6OvCHpx+3Ti/20aefOawfHBwMk8nk8Nre/QdworoaTz/2ENLTUgEAW7Zt90b4PomJN1GAi8zLc/ifyFdE5uWhpaWFZZP8Es+t5OtYRr2nqa7Z5W36O51Yf7QZ21BRWekwndizL76M884+E1cuXYJdewrQ0dGBP/75L5h/zln4acMmvPl/7zjsIyszHU3NzfhuzVqMGzMaOl0oMtJSodFo8Nqf38L1116NPQV78fSzL/QrxsGAiTdRgBv90ENKh0Dk1MjlyxFcVIScnBylQyFymf25tXMtEJEv4PXf83ShOsSERaN6e02/pvkymUxQq9UubRMTFg1dqM6lbb5e/R3Ss0cjKCgI0VFRGDtmFFY89zSuuvxSqFQq5I8dgz888wSeX/EqfvfoU5g5fSqefPR3+NX1t1j3MW3KZFx79RW4fNn1qK6psU4n9n9/fhUPPfYU/vjnv2D8uLF49qnHcNGSK1yKb7Bg4k1ERERERORmen0kHrjtThhaDC5vKwTQ1tYKrTYEUt+n8YYuVAe9vu9zhr/9xh/x9ht/7HW9O35zI+74zY0Or11x2SUOP6/4w9N4/dUXHUY1v/Tihbj04oUO67U3VvU5vsGEiTcREREREZEH6PWRLiXCFkIItLa2IiQkxCGRJf/FxJsowNUXFKC9oQHBkZHQjxypdDhEVg0FBTAUFqKhvR3RY8YoHQ6RS+zPreEjAmvKHPIPvP4TeRcTb6IAt+fJJ1G9cSNip0zBqe+/r3Q4RFYFTz+Nmk2b0DJ5MqZ/8IHS4RC5xP7cOuXvf1c6HKIueP0n8i7O401ERERERETkQUy8iYiIiIiIiDyIiTcRERERERGRBzHxJiIiIiIiIvIgJt5EREREREREHsTEm4iIiIiIiMiDmHgTERERERGRg+CIePz7i68AAEeKSxAcEY/tO3d5ZH8/rFuP4Ih41NXVDzxwFz3+9HOYeOocjx+H83gTEREREREFoGtu+A3q6xvw8T/+1uW90gO7ER0V5ZHjpqelovTAbsTFxnpk/76IiTdRgDv1/feVDoHIqanvvouioiLk5OQoHQqRy+zPrSaTScFIiJzj9Z96k5SY6LF9q9Vqj+7fF7GpORERERERETmwbxremdlsxg2/uRMj86eguKQUAPDfr1djyqzTER6XhuFjTsETz/wBHR0dTrfvrun61u07MGXW6YhMyMDMeedi3/4DDu//+a2/YsTYSdDFpGDU+Kl494N/OrxfUnoUC5dciaikTMSkDMFlV12LyuPHHdZ57oWXkTp0JGJShuCWO+5Ba1ubS99Lf7HGm4j6rL6+HgaDoV/b6nQ66PV6N0dERERE5JumzPoClZUt/d5eCAFJklzeLjExFBvXnt/v4/bGaDTiymtuwMHDR7Bm9X+QEB+Pr1d/i1/ffAdefO4pzJw+DYcOH8FNt/0WAPDQA/f0ed8PPfY0/vD0Y4iLi8Mtt9+NX998G9Z+Iyf/n33+Je66dzleePZJzJszG1/+bxWuu+k2pKWmYM6sGRBCYNFlVyFMp8O3//0cHR0duPWue7H06l/j2//+GwDwr08+w2NPP4dXXvg9pp86Fe+8+wHeeOuvGJKV6f4vqhMm3kTUJ/X19Xjq+adQ01TTr+1jwmOw/O7lTL6JiIgoIFRWtqDsWP8qLHxVU1MzLli8FC0tLfj2q39Dr48EAPz++Zdw52034arLL4UkSRg6JAuP/u5+PPDQYy4l3k888iBmzZgOALj3rttwweKlaG1tRUhICF585TVcdfmluOnX1wAAhufchE2bf8GLL7+GObNm4Nvvf8Cu3QUo2r0F6WmpAICVf/kTxk2agc1btmHSxPF45bU3sezKpbh22ZUQQuDhB+7B2nU/obWt1c3fVFdMvIkC3E9Ll6J640bETpnSY38vg8GAmqYaxObHIiwqzKVjNNc1o3p7NQwGAxNv6rMNV1yBmk2bUD15MqZ/8IHS4RC5xP7cOuXvf1c6HKIu+nr9p/5LTAwd0PYDqfH2lCuvuQGpKSlY9Z+PodPprK9v3b4Tv2zdhudf+qP1NZPJjNbWVhgMBod1ezJm1EjrclKS3Af8eNUJZKSnYe/+Ilz3q6sc1p82dTL++PpfAACF+/YjPS3VmnQDwMjcEYiK0mPvvv2YNHE89u7fj+uvvdphH1Mnn4I1637s4zfQf0y8icglYVFh0Me5njxXo9oD0RARERH5poE09xZCWGt6+5N8e8rZZ56O9z/8CBs3b8Hc2TOtr5vNZjx4z11YvHBBl3hDQkL6vP/g4GDrsmU/ZrO5y2sW9g8nuntQ0d8HGO7GwdWIiIiIiIioVzdctwxPPfY7XLTkCqz9cb319fHjxqDo4CFkDxva5Z9K5Z6UM3d4Dtb/vNHhtQ0bNyN3uDz7ycjcESgpPYrSo2XW9wv27kN9fQNyRww/uY/h2Lh5i8M+Nm7+xS3x9YY13kRERERERAGqvqGhy+jiMdHR3a7/mxt/DZPJhAUXX44vPv4HZpw6Fcvv+y0uvOQKZGakY/HCBVBJKuzaswe79xTi8YcfdEucv739N7js6uswPn8sTps9E//57yp8+vmX+PqLjwEA8+bOxpjRI3HVtTfihWefREeHCbfedS9mzTgVp0zIBwDcevOvcc0Nt2Li+HE4deoU/P39f6Bg7z4OrkZERERERESe88O69Zg0/TSH165cuqTHbW6/5UaYzQIXLL4M//nkQ5x5+mn457t/xR9WvIIXXn4NwcFBGDE8B9dcdYXb4lxw/rl48bmn8OLLr+HOex7EkMwMvPX6K5g9Ux6MTZIkfPzB33DH3Q/gtLMvgEqlwlmnn4aXnn/Guo9LFl2EQ4eO4MGHn0BrWysuOO8cXH/tMqz+9nu3xdkdJt5EREREREQB6O03/oi33/hjt+9ZZGVmoL2xyuH9O2+9CXfeehMAuR/16afNxvxzz+q2P7X99p33N3vm9C77zx87pstrN173K9x43a+6/TwZ6Wn45MOeB7S8/547cf89dzr0o//9E4/0uI07sI83ERERERERkQcx8SYiIiIiIiLyICbeRERERERERB7EPt5EAW7U736H9oYGBEdGKh0KkYORDz6Iw4WFGJKXp3QoRC7juZV8HcsokXcx8SbyQ/X19TAYDF1eN5vNaGxsREVFRbdzJup0Ouj1euvP+pEjPRYn0UBEjhwJXXAwInNylA6FyGX251aTyaRgJETO9XT97+4+A+j9XqPzfQYRyZh4E/mZ+vp6PPX8U6hpqunynkpSITszGweKD8AszE63jwmPwfK7l/OiSERERF30dJ8B9H6vwfsMIueYeBP5GYPBgJqmGsTmxyIsKszhPQkS9NAjPSsdAqLLts11zajeXg2DwcALIhEREXXR030G0PO9Bu8ziLrHxJvIT4VFhUEf1+miJoAQQwgidZGA8ykUUY1qh593P/EEGgoLEZmXh9EPPeShaIlcV/DUU6jcuhXtEyZgzMMPKx0OkUvsz615Dz6odDhEXfR2/Xd6nwH0eq/R+T6DiGRMvIkCXENhIao3blQ6DKIuGgoL0bJrFxpCQ5UOhchlPLeSr2MZJfIuTidGRERERERE5EFMvImIiIiIiIg8iIk3ERERERERkQcx8SYiIiIiIgpQP/60AaHRyWhra7O+dvhIMYIj4lFcUqpgZIMLB1cjIiIiIiLygKP//g/KPv+yx3UiRuRg5L13WX9u2LsfBc+9CLPZDJVKBUlyPlXNlP973eHnjdfehNQLzkPagvkuxbhj127kjhgOrVZre23nbkRF6ZGZke7Svqh7TLyJiIiIiIg8oOVYOWp+2erSNu2Njajdss3lY9X8shUxp0xwebudu/Ygf+xoh9d27NqNsaNHWX/+9xdfYe36n/DC7590ef8kY+JNRERERETkAaEpyb0mwxEjchx+Do6IQPTE8b3WeHcWc8oEhKYkuxzjjl27cenFixxe275jF8aOsSXeu/YUOCTi5Dom3kQBLn3hQsROmQJdaqrSoRA5SFu4EMjORtrYsUqHQtQn9fX1MBgMAICIefOgGTkS2uRkVFRUoLGxERUVFVCpnA+vo9PpoNfrvRkuBThe/70jbcF8l5t+R+YOx5T/ex2tra0ICQnpc+Lduel5X5hMJhQU7sP4cWMcXt+2YycWnH+u9eddu/dg/rlnob6+AVddeyMWnH8urrn6CpePF8iYeBMFuPTFi5UOgciptIUL0TJmDNJycnpfmUhh9fX1eOr5p1DTVOP4RvURqPZsRHZmNg4UH4BZmJ1uHxMeg+V3L2fyTV7D6z8BwL6iA2hpaUFyUpL1tZ83bkbZsXKHGu99+w9Aq9HivIuW4LGH7se8ubOVCNevMfEmIiIiGiCDwYCaphrE5sciLCrM4T0JEvTQIz0rHQKiy7bNdc2o3l4Ng8HAxJuIvGrHzt0AgNfe+At+c+OvcfDQYdx574MAgLY2IwD5/HasogJXXHM9/vZ/f8aovFzF4vVnTLyJiIiI3CQsKgz6uE7JswBCDCGI1EUC3bQYrUa154MjIupkx87dOP20OThypAT5U2YhL3c4nnrsIfz65tvx+l/exrQpk7C7YC+mTJqIsmMVCA4KVjpkv8XEmyjAlX70EQxlZdClprLZGfmUo598guqdOxE6diwyL75Y6XCIXBK+rgDBVQ1oj49E04yRSodD1AWv/wQAO3fvxoT8sXjqsYccXl+44Hzr8q7dezBj2lScPm8urrjmenz/v88RFhbWeVfUC+cjfBBRwCj95BPsf+UVlH7yidKhEDk4+sknqHn/fRxl2SQ/FLGuENGfbULEukKlQyFyitd/AuSpxMb0Mlr57oJCjBqZh4njx+G6X12FG35zp5eiG1xY401ERERERBRgKiorUXm8CmNG99wqZ8VzT1uXr7/malx/zdWeDm1QYuJNREREREQUYJISE9HeWKV0GAGDTc2JiIiIiIiIPIiJNxEREREREZEHMfEmIiIiIiIi8iAm3kRERERERAOgUslplclsUjgS8oT2jnYAtt9zfzDxJiIiIiIiGoCoqCgAEsrKjikdCnnA9h27AEhITk7u9z44qjlRgIvMy3P4n8hXRObloaWlhWWT/JIxI97hfyJfw+u/e8XFxWH8hAl4/S9/RUJCPEK0IQPan4CAsa0NGq0WEiQ3Rek5/hYv0LeY2zvasX3HLvzpjf/DhRctRERERL+Px8SbKMCNfughpUMgcmrk8uUILipCTk6O0qEQuaz6ilm2H4RycRB1h9d/91KpVHj00Udx2WWX4sZbfzvg/QkAHe3tCAoO9os01t/iBVyJWcKFFy3Egw8+OKDjMfEmIiIiIiIaoNTUVHzzzbcoKSlBR0fHgPZlMplQXFyMzMxMqNVqN0XoOf4WL9C3mFUqFZKTkwdU023BxJuIiIiIiMgNNBoNsrOzB7wfk8kEtVqNnJwcv0hk/S1ewPsxM/EmCnD1BQVob2hAcGQk9CNHKh0OkVVDQQEMhYVoaG9H9JgxSodD5BJNcRVUhjaYdVr28yafxOs/kXcx8SYKcHuefBLVGzcidsoUnPr++0qHQ2RV8PTTqNm0CS2TJ2P6Bx8oHQ6RS2LfW4vQvWVoyU1F+QOLlA6HqAte/4m8i9OJEREREREREXkQE28iIiIiIiIiD2LiTURERERERORBTLyJiIiIiIiIPIiJNxEREREREZEHMfEmIiIiIiIi8iBOJ0ZERANWX18Pg8Hg8nbt7e0IDg52+p7RaLT+X15e3uV9nU4HvV7v8jGJetLfslxZWWkts0Tu0t/yCPAcSeRrmHgTEdGA1NfX46nnn0JNU41L2xnbjNhXuA8jRo6ARqPp8v700iOIA3Ck9Ajee+6hLu/HhMdg+d3LeWNJbtPfsgwAhmYDCvYXIH1Ougcio0A0kPII8BxJ5GuYeBMFuFPff1/pEMjPGQwG1DTVIDY/FmFRYX3ervJIJRp2NCBydCQSUhK6vH90TiaMSMBxHEcGhMN7zXXNqN5eDYPBwJtKcpv+lmVALs9te9rQ0d4BACh/cJHtTdHNRkQ9GEh57Ms5ktd/Iu9i4k1ERG4RFhUGfVzfk+DGmkZ5O3032wkgxBCCSF0kIHV9uxrV/Q2VqEeulmXAVp6J3K0/5RHgOZLI13BwNSIiIiIiIiIPYuJNRERERERE5EFMvIkC3E9Ll+KLYcPw09KlSodC5CD5mY8Rc9PjSH7mY6VDIXJZ8tMfY+hVryD5aZZf8k28/hN5FxNvIiIiIiIiIg9i4k1ERERERETkQUy8iYiIiIiIiDyIiTcRERERERGRBzHxJiIiIiIKMGazAAAIIRSOhCgwMPEmClC7dlXhiSd+xt69NQCAqioD2to6FI6KiIiIPMVsFnjvvQJMm/Ye1q07CgBYv/4YrrnmfygqqlU4OqLBjYk3UYBpMahx/fXrMHbsO3j44fWoqGgGAOzZU40RI97G//53WOEIiYiIyN2qq1tw9tkf4YorvsKGDeWwVHR3dJjx17/uxtix7+DNN3coGyTRIBakdABE5D0nyiR8/kEWmhpLnL5fXNyAc875GM8/Pxu//e0kL0dHREREnnD8eDPmzv0nCgqqra/pdEGAAIKCJABAa2sHbrhhNQ4dGqdUmESDGhNvogDRWCPw7uNaNDXKDV3i4kLx0EPTcGrmNFQeOY5dH5cA5e0AgLvv/gE6XTBuuilfwYgp0FUvnYXI2mA0RLcrHQqRy6ovnwWVoQ1mnVbpUCjAtbebcPHFX1iT7sREHVauPAfTMs5Fe0MDJqpDUfJOFV57bTsA4Nlnd2DWWZHImKNczESDERNvogDQ3ibwl/tMqK2Uk+68vCh8882lSEkJt65z7m0CuY//jEcf/QkAcPvt32H8+ARMnZqiSMxExsx4dMRHwairUzoUIpcZM+NtP3DsKlLQAw+sw9q1cn/ulJRwrFt3KYYOjXJY54+TgIyMSNx331oAwE/fJSF/QRv0cd6Olmjw6lcf7z/96U8YMmQIQkJCMHHiRKxbt67bdT/55BOcccYZiI+PR2RkJKZNm4avv/66y3off/wxRo4cCa1Wi5EjR+LTTz/tT2hE5MSqd8woKZTv/HTh7Xj33bkOSTcASJKERx45FXfdNREA0N5uxiWXfIGamhavx0tEREQD9+OPFXjhhV8AAMHBKnz88QVdkm6Le++djGXLRgEAOtpV+NfzWpg6+NSIyF1cTrw//PBD3HHHHVi+fDm2bduGmTNn4pxzzkFJifM+o2vXrsUZZ5yBr776Clu2bMHcuXNx/vnnY9u2bdZ1fv75ZyxZsgRXXnklduzYgSuvvBKXXHIJNm7c2P9PRkQAgGMHBL59zwwAUKkFzrjgKJKTdd2u//vfz8KMGakAgNLSRjz88HqvxElERETuYzYBv/vdL9afn39+Tq+t2F59dR6GDYsEAJQfUuGnf5s9GiNRIHE58X7xxRdx7bXX4rrrrkNeXh5eeuklpKen4/XXX3e6/ksvvYR7770XkyZNQk5ODp5++mnk5OTgiy++cFjnjDPOwAMPPIDc3Fw88MADmDdvHl566aV+fzAikufm/PA5E8wm+eeZizoQl9DmsM7uJ57AT0uXYvcTTwAAgoPV+OCD+QgLCwYAvP76DuzYcdyrcRMBQOx7axHx4juIfW+t0qEQuSz23bVIfvpjxL7L8kvKKNgRjf376wEAU6Yk4ze/Ge/wfufrPwCEh2vw8svTrD//720zDI2s9SZyB5f6eBuNRmzZsgX333+/w+tnnnkmfvrppz7tw2w2o7GxETExMdbXfv75Z9x5550O65111lk9Jt5tbW1oa7MlEA0NDQAAk8kEk8nUp1gsTCYTzGazy9spiTF7hy/GbDaboZJUkCB17Tco7P4B2LVWoLhA/iEhE5h9cQfKf1I5fKb6ggLUbNoEIYT1teRkHR58cDKWL18Ps1ng1lu/xfvvz+z+uL2QIEElqZx+l774HfeGMTvqsUz2QIIEtVrd7Xaa4ioEF5VBo+ro8n5PZUpJLBve4amY+1uWga7lWVNShdC9ZfKbnc7Nzrb1tfLMcuEdPcU8kPLY1ixh20a5g7YkAS+9NAdCmGF/GGfXfwDIz4/BsNwGHNwbieZ6YPU7Ziy4RW3bsIfy7ItlGRh8ZcMX+Vu8gPti7uv2LiXeJ06cgMlkQmJiosPriYmJqKio6NM+XnjhBTQ3N+OSSy6xvlZRUeHyPp955hk89thjXV4/ePAgwsPDnWzRPbPZjJqaGhw4cAAqlX9Mbc6YvcMXY25sbER2Zjb00CPEENLl/ZCOEES1RMFsFlj1Vq319cuuiURKcATCMrU4duwYGhsbAQAtLS3W/4uKiqzrz58fiTffDENxcTPWrSvD558X9HjcnoQgBNpOx7Xwxe+4N4zZUW9lsjuqUBXmTp2LtOA0RBgiurwfZA6y/h9liHJ4r6cypSSWDe/wVMz9LctA1/IcZDpZfk1BiGqJsp6bnfHF8sxy4R09xTyQ8rjmvxKMbUYAwIUXpiEqqhFFRY5lq7vrf2NjIy5eEo4XngHajcD6T8246KJoREbZ4uuuPPtiWQYGX9nwRf4WL+C+mJuamvq0Xr9GNZckyeFnIUSX15z54IMP8Oijj+Lf//43EhISBrTPBx54AHfddZf154aGBqSnp2PYsGGIjIzsy8ewMplMOHDgALKzs6FWq3vfwAcwZu/wxZgrKipwoPgA0rPSEanrVNYFECWiUBdah23fm3H0sPwELiNPQtZcA47XNKK0uBSXL74cSUlJAIDq0FC0AAgNDUVOTo7D7p56Crjiiv8CAN5/vxIjJ3dz3F40tDR0Oa6FL37HvWHMjnoskz0oKyvD9xu+R1h+GJJ1yV3e14oOBAMwogN1nUY276lMKYllwzs8FXN/yzLQtTyHquXy26HuQF1onfXcDCe3Nr5YnlkuvKOnmPtbHttaBFZ93g5Agkol4ZlnzkB2dlSX9bq7/ldUVKC64QBOOWsofv4iCMY24Mv/1eKca07GZ3ev0bk8+2JZBgZf2fBF/hYv4L6YLS2ve+NS4h0XFwe1Wt2lJvr48eNdaqw7+/DDD3HttdfiX//6F04//XSH95KSklzep1arhVbbdW5MtVrdry9OpVL1e1ulMGbv8LWYVSoVzMIMAeH0Bk5ukSbw3fu2AVHO/bUKkkqCgIBZmK2fCbA99JIkqctnvPTSPDz66M84cKAO69dXIiZNg7TujtsDZ8ft/Jl86TvuC8bsuN8ey2Q3BOTmjfbbCSGwdbXAmg/NuLFBYEwocGinwP/9pgPzLldh1Kkq67Y9lSklsWx4hydi7m9ZBpyXZyup0z8n2/pieWa58I7uYu5vedzwHzMMDfIGF1yQgREjYp2u193133LcqRe0Y+NXQTCbgHUfm3HaUhW0oScD6aY8+2pZBgZX2fBV/hYv4J6Y+7qtS3XqGo0GEydOxOrVqx1eX716NU499dRut/vggw+wbNkyvP/++zjvvPO6vD9t2rQu+1y1alWP+ySi7h3ZLVC6T+58lT5CwohJLt5BnqRWq3D//VOsP+/8xfnFm8gdDI0Cb95jwt8fN1nLr8WhHQJ/udeE957sQHsbB/ohInLGbBZY97Htwfttt43u976i4gUmnC7fPxgagE1fcYRzooFwuTH7XXfdhbfeegtvv/02CgsLceedd6KkpAQ33ngjALkJ+FVXXWVd/4MPPsBVV12FF154AVOnTkVFRQUqKipQX19vXef222/HqlWr8Oyzz2Lv3r149tln8c033+COO+4Y+CckCkBrP7JdHGcuVvWpK0h3rrxyJJKTwwAAJYfC0VDd/30Rdae1WeC12zpQuMGWVGtD5f81dl0bN/9P4M17Teho93KARER+oGiLwImTY/qlZDQjNzdqQPs7bamtJu+nf5shBB98EvWXy4n3kiVL8NJLL+Hxxx9Hfn4+1q5di6+++gqZmZkAgPLycoc5vd944w10dHTglltuQXJysvXf7bffbl3n1FNPxT/+8Q/89a9/xdixY7Fy5Up8+OGHmDJlSpfjE1HPak+YsOMH+cIYHgVMmDewRFmjUeO668YAAISQsPUb/2k+RP7B1AGsfMiEspNj+4RFAdf/QY30XLnsZuRKuPx3amhOJuJFWwT+82cNeP9HRORo/We2B++5Y+oGvL+UYRKGjJHPxeWHgOI9PPES9Ve/Ble7+eabcfPNNzt9b+XKlQ4/r1mzpk/7XLx4MRYvXtyfcIjIzo+rW63zdk+7QIUgzcBrqK+7biyeemojzGaBLauCMP8GAXUQa77JPdb+Mwx7N8k3c7oI4LbXgpCYKQHfn1xBAiadrUJcGvCn201obwO2fRsErSlauaCJiHxM/QmB3T/K59KIaDMyh7pnVPGp56tweJd8Y7HhP2ZkjfKPEauJfA3/cogGESEE1n9jm99+6vm9/4mnL1yI4bfdhvSFC7tdJyMjEvPmpQAAGqpVDs2BiQaipTEem7+Sq7LVwcC1z6jlpBtA44w8tJw3C40z8gAAQ0arcNmDthYXm9fF48gR35muhshe48w81F44GY0z85QOhQLE5v+ZrQ/ex59ugqqXBmp9uf4DQP5cCSFyjzNs/VagtZn3AET90a8abyLyTcUFAhVH5atu9ngJscm910qn97GlyRVXZGP1arnj2C+rzBg9g8/taGBMHUDFwRmAkMvpudepMCzfVq6aZo5EkCEKTXZTiU2Yp8KR3QJr/2WGyaTCgw9uxnff5QxoHAMiT2iaOdL2A/MU8oKtq23NzMef1oGmfT2v39frvzZUwoQzVPjpMzOMLcDOtQJJswcSKVFg4p0z0SDyy9e2u7tJZ7v3z3vOnBSEhHYAAPb8KNBq4J0kDcy273RoM8QAANKGA3OW9K3MnvdrFSJj5RvMNWvK8dFH+z0WIxGRPyg/JHDsoLycOUpCTLJ7r9GTzrI93Nz2HUc3J+oPJt5Eg0RHu8DWb+WLYbAWGDfXvTWAwcEqDMmRm/W2G4Fda5l4U/+1GQQ2fnmy7aIksOS+oD6PG6DVSTj317ZhzR96aD1MJt4IElHg+mWV7Rw48Qz3twDKHCUhOlFe3rdZoLGe51wiVzHxJhokirYIGBrk5TEzJYTo+nbhLf3oI+x7+WWUfvRRr+sOy22wLm9ZxYsu9d/aj8xoaZQvQblT25A+omt5DV9XgND/rEH4uoIu7+VOMSEp1QAA2LevBh9+2EubSiIvC19XgOhPNjgtv0TuJITA1m/ka7JKDYyf17fbe1eu/yqVZN2v2QRsWd/WyxZE1BkTb6JBYscaWyKcP7fvf9qln3yC/a+8gtJPPul13YTkFkQlyMfZ94tAUy1rvcl1rQaB7963lFczZiwyOF0v4sdChH65FhE/FnZ5T5KA8VNPWH9+/PGfWetNihMCOLI7GB8+Z0LD2wWI/mwTjB8WoLKY50rynNK9ArUV8vLwiRIiovv44N2F6z8AjD/Ndm+x4Xsm3kSuYuJNNAiYOgR2rZNv7DRaIHeyZwaakiRg9Ax58DZhBnav580kuW7jl2a0NMnL+vgDiEk29Ws/yWkGTJ2aAECu9f7sswPuCpHIZfUnVCjZcy7++UwUfv7cVsZrK4HfX9mBv/+xEcY2njPJ/ey7fo2b47lb+7QRQFyavLxvdzua6lieiVzBxJtoEDi4Q6C5Xl4eO1kDTYjnRnjOm2pLknatYw0jucZsFlj3sa3cxKTs7ve+JAm47bbR1p//+MdtA4qNqL9KCs149/FYtDQkO31fCODbL1rxx1tNaG5gskLutfPktVh+OO65678kSRg7S04dhBko+JllmcgVnE6MaBDYucZ28TtlhhZAq8eOlZJtRmQs0FAtD7DSZhDQ9rE/OVHhzwInjsrLGXlt0IbVDmh/s2YlYcSIGOzbV4M1a0qxe3cVRo+Od0OkRH1zokzgjbtNaGmSExJ9vAkLfqPB0J8koAiITQE0tYCxFSgpFHjjtyb85lV1lwekxjYjKisr+xWDTqeDXq8f8Gch/1NZIlB5RF7OGi0hIsaz1+PRMyR89768vHu9GZPPZR0eUV8x8Sbyc0II7F4vP+1WBwPjJmvQ5sHEW6UCRs+U5/PsMAJ7NwmMm8PEm/pm7cf2I+8aUPjLwPanUkm45ZZ83HbbdwCA117bjtdfP2NgOyXqo5Ymgb/c12FtcRQaWYGrnwrC0JHJUG2UX4tOlHDHb4Lwxm/NqK8xo6RQ4JOXTbj0PtstWGtzK3bs3IHn/vwcdKE6l+OICY/B8ruXM/kOQLvW2s6pY2d5/lqcNUpCmB5orpev/+1tAsFa3gMQ9QUfUxH5ufKDQN1xeTlnvIRQnef/rO0v7jvXsrk59U1thcD+zXLrjNhkYOhYo1v2e/XVoxAeHgwA+PvfC9DU5J79EvXmk5dN1trGmOQOpOWuRkhY1+a3KdkS7n5KD02I/POGL4TD9E/tbe0wCiNixsUgY06GS/9i82NR01QDg8H5IIU0uO2xG2tlzCzPX/9VagmjTpXvAYwtQNFWNjcn6ism3kR+ruBn283byGneeeqcPV5CyMkpmAs3CJhNvPBS7zZ/bYY4WVQmnauC5KYrUGSkFpddlgcAaG5ux6efFrlnx0Q92LfZjM3/lQt0SDiw8PY6qIO6f+iTPjQIi3+rtv780YumLjNDhOnDoI/Tu/QvLCrMMx+QfJ6hQeDIHrkMJWQCcaneuQcYPcN28uYgq0R9x8SbyM/ZD24ycpp3/qSDgiUMP0W+wBsa5H6LRD0RQmDTf20PiSaf496yetVVI63Lf/87500mzzK2CfzzD7aBJi+4SY2ohN5H5598tgoTz5TPna1NwJdv9m9EfyIA2L9FQJw8reZN8d4t/YhJEoLkRkbYu9EMIXgPQNQXTLyJ/Fhzg8Dh3Sefdmf072l3ZF4eYqdMQWRenkvb5U21nT4KN/KiSz07vMs2qFrORAkxSb2XVWNGPNpzMmHM6H2wtOnTUzFkiNy/9ZtvilFW1jigeIl68tNnZlQfk5eH5UuYen7X8mzMiEdLbmqX8rvgFjW0J7txb/iPQOk+nj+pf/Zusj3M7M80ov29/mtDJeSMkjPvmnKgqtTlQxMFJA6uRuTH9m2yPe3ub2336Ice6td2eVNsF/nCDQLnXNuv3VCA2LLKllxMOrtvZbX68lkwGaJQp6vrdV1JknDVVSPx2GM/QwjgvfcKce+9k/sbLlG32gwC3/zdNn3TojvUUKm6Jj3VV8yy/WCXW0fGSjj7Vyr8+zW568WXb5ow/wZPR02DjRACe08+9A7SyA+AXNXf6z8AjJmoQeH2dgDyA4CEDHUvWxARa7yJ/Ni+zban3XlTvTuqaFSChORh8nLpXtGlryKRhdkkrIPwBWuAsbM9U1avvHKUdfnDD/d55BhEaz8yo6lOXs4/TUJKtuvleeZiFWJOTvm9d6NAxRHWg5BrKottA6sOGyd1mZ7O00ZP1FiX927i9Z+oL5h4E/kxy2iiQRpgyFjvT+dh6VMmBC+81L2DOwQaa+TlvKkSQjw07/uwYVGYODERALB1ayUOH67zyHEocBlbBb7/x8nabhVw9rX9q+ULCpYw73LbLdjGLzlAGrlm78aBNTMfqPShakTEyMsHtgp0GHkPQNQbJt5EfqqmQkJNubw8ZIwETT/n0awvKMCJDRtQX+D6gFT2tez7t3BaMXJux/e2G7Jxc/t+2dEUVyFo/xFoiqv6vM2iRcOty598wtHNyb22rBIwNMjLE06XkJjR/XlXU1yFkMKj3ZbfyeeoEBkrLxdtCUGbgXNwU9/ttRtbJbefA6sN5PovSRJGTDo5rVgrcGgXE2+i3jDxJvJTh3ba/nxzJvT/afeeJ5/Ez5dfjj1PPunytlmjJASdbG1WtEVwZFPqwmwS2PGD/FAmSAOMmt73shr7/lpErvgbYt9f2+dtFi3KsS5//DETb3IfIQR++JdtFPLZl/R8CxX73lqkPPMJYt9zXn6DtRLmXmrbR22FawNcUeAytgkc3C5fb/XxQNKQ/u1nINd/AMidZCu/B7bx+k/UGybeRH7q8E5bE8fhE73fzAyQbxyHjJGPXVsJ6yi/RBZHdts1M5/iuWbmFsOHx2D06DgAwM8/H8PRoxzdnNxj/y8CFYfl5SFjJGTkDvwWasp8FTQh8nJDVQ6MrQPeJQWAwzsF2k9OGZ87WYIkKXMPkD3edlwm3kS9Y+JN5IeEAA7vkhNvrQ5Iz1XmogsAObzwUg/22M0zP2aWdy45ixfbmpt//vkBrxyTBr/1n9m608y+2D1lWRchYcLp8jnUbNKg4KcQt+yXBjf7a+3wU5S7lY9KkBCXKi8XFwgYW3kPQNQTDqNJ5Idqq7Vorpdv1rLzJaiD+p54G9uMqKystP7c1tZm/b+8vLzb7SorK2E0Gru8njNRAt6Sl4u2mDF1Pp/n+av6+noYDAaXt+uubABAwc+2aZe8NfL+BRcMw6OP/gQA+PLLQ7j55vFeOS4NXk11AnvWy0lFRAwwZpb7yvL0C9XY8J8OAMD2b0Jw7q/ctmsapCzNzAHHWmclZI+XcKJMwNQOHNkjkJipaDhEPo2JN5EfOlaisy7nnNL3i25rcyt27NyB5/78HHSh8j6mlx5BHIAjpUfw3nPdz+lpaDagYH8B0uekO7yekSdBEwoYW+RR1oUQijV7o/6rr6/HU88/hZqmGpe37a5s1FYIlB+Ul9NzJUREe6dc5OcnICUlHMeONeG770phMLRDpwv2yrFpcNqy2gyTnBvjlLNULj3s7E16roSkIe2oOByM48XBOHZA9GuKMgoMxjaB4kI58Y5LA/RxSifeKmz4jzz2wcHtTLyJesLEm8gPHSu1TT0zfGLfa5jb29phFEbEjItBQkoCAEC7pwCoBrRRWmTMyeh228ojlWjb04aO9g6H19VBEoaOlbB3o0BDNXC8BLzw+iGDwYCaphrE5sciLMq1qY26KxsFG2xNc0ee6r2bQ0mScO65Q/DWW7vQ2tqB778vwXnnDfPa8Wnw2fxfW1mefI77W/WMmt6CisPyw6FfVplxQXb/pimjwa94j1y7DMgt3pQ2LN+xu9mpCxQMhsjHsU0okZ8xmcyoKAsFAIRH9W800zB9GPRxeujj9AgKlp+/BQUHWV9z9k8Xqet2f/ajqhdt5bRi/iwsKqzHcuBK2Sj4ydYcctQ0715uzjtvqHX5yy8PefXYNLgcOyBwdL+8nJEnIXmo+5OdEZNaAUk+d25ZZYbZxL6y5Jx9/+5h+crfxkcn2vp5H9kj0N6mbDxEvkz5v1gicklBQR3ajXJtyLB8CSqV8k+8c+xGVT+wlTeMJDeH3L/F1ic2dXgvG7jZ6adnQqOR/06+/PIQp7qjftv2re1h4qSzPXO+1UUIhEeVAgDqT3CgSuqeQ/9uH6jxBmz9zE3twNH9TC2IusO/DiI/s3lzlXV56FjfuOim5UgICZeXi7YJmM28aQx0B7baaj7ypnr/AVF4uAazZ6cBAEpKGrFvn+t914mEENj2/ckBAlVA/lzP3TZFxh+0Lv+yii2HqKsOo0DxHvn6GpMMRCf5xj2Afc37kd3sJkHUHfbxJvIzmzbZJ94Dvwksf3DRgPehUksYNk7CnvUCzXVyP++krAHvlvxY4Qa7Zuan9q+clj+wCFGGKNTp6vq1/RlnZGL16mIAwLffliA3N7Zf+6HAVXYAOHFUXs4eLyEipu+JjsO5tQ/PIsOjSxAcYkZ7qwq7fxQwdQi3DuJG/q+40DZ/9zA31Haf+v77A94H4Fjzfni3CsOS3bJbokGHNd5EfkQIgc2bjwMANCECKdkKB2RnyBi7C+8u1ngHun2b5Ro7lRoYMUmZ5OH0022j/H3zTbEiMZB/2/6dreY5f65ny7FKbcKwfDmrMjSwuTl1dXCbfTNz37mFj06SEHsy2S4rUsFkUjYeIl/lO3+1RNSrkpIGlJe3AADShpt9qjZkqEPizWaSgayuSuB4ibycOVJCSJgy5XTcuATExsoDEa5ZUwqTieWS+k4Ige12zczHzvb8LdPwSUbr8s4fmHiTowM+NH93Z1kn7wE6jBJqqkIUjobINzHxJvIj69cfsy6n5/lWEpGeK0F9cqrkwzt5wxjI7AfYsx94z9tUKgmnnSbPLV5X14atWysVi4X8T8Vhu2bm+d6Zh37IOCOCNPLyrnVmjpdBVmaTrX+3Pl7u4+1Lhoy2/X1UlocqGAmR72LiTeRHfvzxqHU5M889bbmSn/4YQ696BclPfzyg/QRrJaSPkC+8VUeBxlreMAaq/VtsD4Xsp5pzVfIzHyPmpseR/Ez/y+a8efbNzUv6vR8KPHvW28rx6Bmul+P+nFu1oQK5k+VjNVQDR3bzPEqy8kNAm9zgDUNGS5CkgT8I+mnpUnwxbBh+Wrp0wPvKGm1LKY4fY+JN5AwTbyI/YqnxliSBtBG+VeMNsJ83yc1zi05OIxasAbJGKdsc0r6f97ffsp839d0e+3nop3vvdmnMLNux7GOgwHZkj+2anzXat5qZA0DyUEBzMt8+XsHEm8gZJt5EfqKurhW7dskjmsfEtUHrg9c1Jt5UfQyoPdmie8gYCcFaz90gGtuMqKysRHl5ebf/QkMNSEsLAyC3GDl0qBTl5eWor6/3WFzk/5rqbLXNSVlAXKr3Ep2RU23HKtzgew9YSRn2rR+UfqDpjDpIQmaeHFdzYzCOHTMoHBGR7+F0YkR+YsOGcoiT193EVAMA3xu8hIk3FXmpf3drcyt27NyB5/78HHShuh7X1emTgKNRaGsz4zf3/AEpGQbEhMdg+d3LodfrPRYj+a+iLWrr+XbUDO/WUUTEyN12SvcJHDsA1J8Q0Mf5XqJF3mVJvNXBQNpw3ywPWaMk6zVgy5YqTJw4TOGIiHwLE28iP7F+fZl1OTG5Bb6YeEdES4hLkwckKt0n0N4mPFrjSb6nyE39u3vT3tYOozAiZlwMElISelx3rEqN/Xvk5UYpGbH5dajeXg2DwcDEm5za/4vaujx6uvfPYXnT5MQbAAo3CEydz/NoIGuul8dOAYD0ERKCNL5ZHrLsHr5v2XJCwUiIfBObmhP5iU2bKqzLCcktCkbSM0utt6kd1htHCgxC2Gq8tTp5pHtPC9OHQR+n7/Hf2Nlh1vXL9msQFhXWwx4p0JnNwKGdcuKti5CnxPO2PDY3JztH99keBPliM3ML+9h++aVKwUiIfBMTbyI/YDYLbNpUDgBISAhBWESHwhF1b+gY22mFzc0DS3WZGo018vKwfMln5pmPjJVbYgBAyV6BdmPP61NgO1EZgtZmuezmTJSgUnu/HGfmSdBFysv7NguYOnguDWSl+2zXVV8cWM0iTC8hNkV+ULRrVy1aW333XoVICUy8ifzAgQO1qKtrAwDk58fBDbOIeIz9TYFlzlEKDKV7g63L2fm+VUiHjrW1xDhWxEsfda+sxNYiIneyMmVFpZYwYpJcZlubOa1YoPOXxBsA0nPlxLu93YwtWyoVjobIt/Dug8gP2DczHz8+VsFIepeYKTczBoDiQt4sBpKy/bbEe+g437o5HDrWdrkrLuSlj7p3zC7xHj5JuXKcN9VWTgs28FwaqMxmoOzkw8KoBCAq3rfOrZ2ljzBZlzdsOKZgJES+h4OrEfmBjRvLrcvjx8di9Qb37bv68llQGdpg1mndsj+VWkJGrjyyaX0VUFclfLqGntzHkngHa9wz6m710lmIrA1GQ3T7gPc1zO5BQEmhGlkzB7xLGoSamtpRWS7P1RiXBsQm978cD/TcmjfFsZ/3+Teqe1ibBquaE1q0t8llwd213aN+9zu0NzQgODLSbftMzbGNSbB5c0UPaxIFHibeRH7A0r8bAMaNc2/ibcyMd9/OTsoYaZtSpKRQIHOk2w9BPqa9TYf6KjkxyBgpISh44DeIxsx4dMRHwairG/C+4tKA8GigqRYoLVTBPH3Au6RB6OefKyHMctkdccrAWkY4nFv7UWEdESMhbThwdD9w7ADQVCsQHs2nmIGm6uSDIMD9ibd+pPsvzgkZAmq1GSaTCr/8wqbmRPbY3o7Ix7W1dWD7dnl00BEjYqDXaxSOqHeZefa1i2wiGQhaGhOty5b+1L5EkiRrrXerQUJdtXtaeNDgsnatrYZuhILNzC1yJtpu0w5s57k0EJ04bps61P7a6qvUQUBsQisA4ODBOtTU+O4sLETexsSbyMft2FEFo1HuMzVlSpLC0fRNht30OyUFvFkMBC0NtsR7yBjfvDkcYvdAoOJYaA9rUqBau1ZuXSSpBLI9OA99X+XYxXBgK8+lgaiqUk68VWogNUf5MtkXcYmt1mXWehPZsKk5kY+zb2Y+eXKy2/cf++5aaEqqYMyIR/UVs9yyz6h4Cfo4oP6EPH2TmdPQDnqGkzXekuS+5pCx762F7nAt1EOi3VI27WviK8t0A94fDS5lZY0oKmoAAKTlmKGLGFg5dji3Xt6/8jt0nASVGjCbgKJtZgDs5x1IDIYOa+ucpCxAE+LexHv3E0+gobAQkXl5GP3QQ27br2PiXYEzz8xy276J/BkTbyIft3Gjrenj5Mnur/HWlFQhdG+Z2/ebkSdh1zqB1mag+ph/PKWn/jG2SGhrjgEAJA/FgBMWC01JFYKLyqBRu2cu2NRsCZpQwNgi13gLwRpEX1ZfXw+DweD0PbPZjMbGRlRUVECl6tp4T6fTQa/Xu3S8NWtKrctDxw38aaE7zq0hOgnpIyQUFwhUHgEaqgUiY3k+DRS7d9dACPn3neGBZuYNhYWo3rjR7fuNt0u8OcAakQ0TbyIfZ6nx1mjUGDcuAdXVxxWOqG8yRsqJNyBPhRLDe8VB69ihYFh6Lg0Z47s9mNRBErJGSdj/i4ChKRhlZc1ISVE6KnKmvr4eTz3/FGqaapy+r5JUyM7MxoHiAzCLrklyTHgMlt+93KXke+3ao9blrFGmHtb0rpyJcuINAAe2CUw4nSfTQLFjh638p+f6z+9dH21EeHgQmpo6mHgT2WHiTeTD6upasX9/LQAgPz8eGo3/NDO0HwSmrEiFmOEKBkMeVVZkN3+3Dw6sZm/IGDnxBoAtW05g0qQchSMiZwwGA2qaahCbH4uwqLAu70uQoIce6VnpEJ2GDG+ua0b19moYDAaXEu8ffpATb0klkDbCd/rH5EyQ8M3f5eWirQITTlc2HvKe7durrcsZub77ULMzSQLGjo3FTz9VoqysCeXlTUhODlc6LCLFMfEm8mHbttlqtydN8o+B1Szsn86XFakwhon3oOVPiXem3cB/27ZV97Am+YKwqDDo45wkzwIIMYQgUhcJOCly1XDtd1tZ2Yx9++TaxfjEFmhCetnAi4aMkaAOAkwdwIGt7OcdSHbskMuxOkggeZjCwbho3LgY/PSTPLDaL79U4vzzmXgT+c/jM6IAZJ94T5iQ2MOavic0XEJCprxccViFjg7fTsiof8wmgYrDcuIdHm1CdJJv/57tE+8tW04oGAn5knXrbM3Mk1J9a/ojTYhkLbdVR4G6Ko5NEAjq6lpx6FAjACBpiBlBwb59bu1s3LhY6/LmzeU9rEkUOJh4E/mwrVtt03CMH5+gYCT9k3Gy1tvUIaGW8yYPSpXFgLFVvpSkZLtnEDRPCtNLiE2RmxHv3l1jnaqPApt9/+6kVOcDuikpm9OKBZwtW2zX/5Rs3+n60Ff5+bbEm1OKEcmYeBP5MEviHRyswqhRcQpH47r0EbabxerjTLwHo2K7edqTh7UrGEnfpebIN7FtbWbs2OEfgxWSZ1kSb0kCElN8q8YbALLH286lB3cw8Q4Ev/xiG5Qs1Q8T7/T0MMTGhgKQRzbnLBJETLyJfFZzsxF798p9DseM8a+B1SzSHBJvH+o0SW7jkHj7QY03AKQNt93EbtzIJpCBrra2FTt3VgEARo2Khkbre0lO5kh5Pm8AOLzL9+Ij97MfDdzysNCfSJKEiRPlLnInTrSgrKxJ4YiIlMfB1Yh81M6dJ2B5QDxhgueamTfOzENrbira4yPdvu/UHFvifYKJ96BUXGC5ITQjaYh7a7wbZ+QBw4ahMVnj1v3aj1i9cWMFfvMbt+6e/Mz69WXWc+3UqQlwV72cO8+t2lAJqTkSSvcKVBwGDA0Cukj/6vNLrrE0zw4KNiMu1TO1xekLFyJ2yhToUlM9sv/x4xOwatURAMD27ceRlhbhkeMQ+Qsm3kQ+ylv9u5tmjvTYvkN0EuLTgapSoPaEFu3t/vfUnrrX1iJQfkhe1urq3D4SdNPMkQgyRKFJV+fW/SZmmqFWm2EyqbBhwzG37pv8j33/7qlTE/Dzbvfs1+Hc6oa8acgYOfEGgCN7BEZOY+I9WFVXt6C4uAEAEBvfam3t4G7pixd7Zscn5efb7l22bTuO+fP9bGh2IjdjU3MiH2WfePvbiOb20oafHGDNpEJRUb3C0ZA7Hd0vIE4+SwkJr1I2GBcEBQOxCa0AgAMH6lBd7Xt9esl77Ec0nzzZdwexHDrGlmgf3sn+soPZ9u22sSdi49sUjGRg7CsN7GdpIQpUTLyJfNTWrfJFSqWSMHZsvMLR9J/9AGu7dtUoGAm5W/Ee281/aIR/3VTFJ7Val9nPO3C1tnZYR48ePjwacXG+2yVmyFjbufTQLibeg5l9kmp5SOiPsrOjEBYmTzdp/zCBKFCxqTmRD2pr68CePfIcw3l5MdDpgj12rPB1BQiuakB7fKRHmp1barwBYNeuWrfvn5RjP7CaXOOd69b9h68rQGi5ER3JGjTNcm/ZTEhqwZ6Tyxs3luPcc4e6df/kH7ZurbR2gZk2LcWt+3Y4t84YePnVx0mISQZqyoGSAoGOduF3cztT39gn3jHxrQD0/dqPsc2Iysrup/I68dVXaCsvhzY5GXHnnmt9vbKyEkajsV/HtKdWqzB2bDx+/vkYDh+uR11dK6KifPfhFpGnMfEm8kF79lRbbwbHj/dsM/OIdYUI3VuGltxUjyTeqcNZ4z1YWRLvYK0ZWjf3wwaAiB/lsoncVLcn3vHJtublmzaxxjtQ/fyzrY+/uxNvh3OrGxJvQO7nXVMu0G6Uu3pkjWLiPRhZaoeDg1WIju1fU/PW5lbs2LkDz/35OehCdU7Xmb5+G+Kq63AiNgrrd/9sfd3QbEDB/gKkz0nv17HtjR+fYP0727GjCrNnD3yfRP6KiTeRD3Ls3+27fQ77IixSQlSCGXXHVdizpxYmkxlqNXu5+Lv6EwJ1JytlErM6IEn+1fQ1PKIDMTFa1NS0YcuWSgghIElMYgJN18Tbt6fEGzJGwpZV8t/a4V0CWaMUDojczmBot04lOny4Hup+DqzW3tYOozAiZlwMElKc30do9xQA1YA2SouMORnW1yuPVKJtTxs62gf+99B5gDUm3hTIePdL5IMGy8BqFinD5Np7g6EDRUVsbj4YlBTazd891L3TiHmDJAFjx8YAAKqqWnD0aKPCEZESNmyQWztERGgwalSswtH0bugY223bYfbzHpR27ToBs1n+3Y4eHT3g/YXpw6CP0zv9FxQs178FBQc5vK6LdF5D3h/2A6yxnzcFOibeRD7Ivn+X/dNif5U81DaNmGXQOPJvlmmNALh9/m5vsSTeAKwDbFHgKC1tQFlZEwBg8uQkv2iJkzQECAmTlw/vEhCCyfdgs22b7Vw0enRMD2v6h9Gj46BWy62JOLI5BTrfv8oQBZiODjN27JCnZho2LAp6vVbhiAYueZh94s0EZzAo3We74U/MZOJN/seT/bs9RaWWrP26G2uAmgqFAyK3s09O3VHjrbSQkCDk5cmtSQoKqtHW5tvdOYg8iYk3kY/Zt68GLS3yhcnf+3dbONZ4M8Hxd0IIa+KtiwD0ceZetvBNTLwD288/2wbVmzo1WcFIXJNpN6Ca/cwCNDhYEm9JAkaN8v/EG7A1N+/oMGPPnmqFoyFSDhNvIh8z2Pp3A0B4FKALl2tFt249zuaRfq7+BNB0sqt+2ggJ/jomWWpqGGJjQwHAOsAaBQ77Gu+pU/2jxhsAMkcy8R6sOjrM2LVLnko0Ozsa4eGem0rUm+z7ebO5OQUyJt5EPsbSzBwYHP27LeISWgEA9fVtOHy4XuFoaCCO2jUzTx/hp1k3AEmSMHGi/HDr+HGDtb8vDX6trR3Wh5zDh0dbH8D4g4w8299cCRPvQWXv3mq0tsot3uyTVX9nfy/DAdYokDHxJvIxO3faEu9x4+I9fjxjRjxaclNhzPDssWLjbXORsrm5fyv1UuJtzIhHe06mR8umJfEG2Nw8kGzdWon2drmLhKf6d3vq3BoeJSH2ZMhH9wmY2GV20LCvDfZG4u2t63/nKcWIAhXn8SbyMZbEOy4uFElJYR4/XvUVszx+DACIPVnjDcgX3sWLR3jluOR+9ol32ggJrc2eOU715bNgMkShTlfnmQOgc+JdgQULsj12LPIdmzfbRiXzVP9uh3OrmyumM0dKqD4m0G4EKov9t9UJOfJ24u2t6390dAiysiJx5EgDduw4DrNZQKViuaXAwxpvIh9SWdmMykoDALm2W/LXzrNOxMTbEm/75vTkf47aDawW6z9dY51ijXdgsk+8J01KUjCS/rHv5310v1rBSMidvJ14e5Ol1rupqR0HD9YpGwyRQljjTeRD7JuZjx3r+Wbm3hQe0YHIyGA0NLQz8fZj9ScEGk4OSps2XPL7h0OZmZGIiQlBTU2rdYA1f/9M1LtffpEfsmg0aowZ43/nWvvEu6xIhaSxCgZDbiGEsPZ/TkkJR0JCGMrLGxSOqn+MbUZUVjo+yMzO1lmXv/tuH8LDM51uq9PpoNfrPRofkVKYeBP5ECUSb01xFVSGNph1WhgzPXdMSQLy8qKwcWMVjh5tRE1NC2Ji/GdAI5KV7nVsZu5JmuIqBNXWQRPdDmOWZ8qmZYC11auLUVlpwLFjTUhNjfDIscg3NDS0Yd++GgByyyKNxjM1xg7nVjf3oU3NkaAOAkwdQNl+FSYy8fZ7xcUNqKuTx0LxVm23J67/rc2t2LFzB57783PQhdqS7eKD4QDSAAB/fvszbN57wun2MeExWH73cibfNCgx8SbyIUok3rHvrUXo3jK05Kai/MFFHj3WyJHR2LhR/ow7d1ZhzpwMjx6P3O/ofu8l3rHvy2Uz2MNl05J4A3Jzcybeg5t9l4JTTvHclI0O59YH3Ft+g7USUrIllO4VOFEmwdjGnoP+TokZTTxx/W9va4dRGBEzLgYJKbbPEZ4r4Zsv5OVWRCFjjq7Lts11zajeXg2DwcDEmwYlnqmJfMjOnfITYJVKwsiRsQpH434jR0Zbl9nc3D95a0Rzb2I/78Dyyy/+3b/bwtLcXAgJVZUhCkdDA2W5/gPemdHE08L0YdDH6a3/MkdGQHOykVtVaZDDe5Z/YVGeH1CWSElMvIl8RHu7CQUFcufZESOiERIy+BqkjBwZZV1m4u2fLAOrhYQDcakKB+Mm9om3fVJGg5P9wGqnnOL/iTcAVFWw246/273blngPtjFeALlCIXmIXGary4FWA+egp8DDxJvIR+zfXwuj0QRgcF50AWDEiCjrFCJMvP1PQ7VA/cl7w/RBMLCaRVaWHtHRco2hZYA1GrwsA6vpdEHIy/PflkUZdon3CdZ4+71du+STa0hIELKzo5QNxkNShtmWKw7xPEuBh4k3kY+wT0THjRtc04hY6HRByMmRm5vv2XMCHR1mhSMiV3Sev3uwsAywBgCVlQaUl3toYnJSXHV1Cw4frgcAjB+fiKAg/70Nik8DtCe7yZ44zsTbn7W0mFBUVAsAGDUqFmq1/5bLniQPs103jh1UMBAihQzOv2wiP+Q4sFqcgpF4lqXvWlubCfv31ygcDbliMPbvtsjPt7Uy2bHjeA9rkj8bLP27Abnpbtpw+e+wuTEY1dWtCkdE/XXgQCMsDW0Ga4s3AEgeartulLPGmwIQE28iHzGY5/C2Z//Z2Nzcv9iPaD74Em9bKxOWy8HL0swc8OyI5t5i3/Jk1y4+yPRX+/fb5usezNf/FIcabybeFHiYeBP5CEviHRWlRVra4J3OyH60ViY4/qWsSL5R0oYCsYNkYDUL+3K5fTtrvAcr+xpvfx5YzcL+AdjOnUy8/dW+fY3W5TFjBm+LtzC9BP3Jj1d+UHA8DQo4TLyJfEB1dQvKypoAyE+7B8ugVc44Jt5McPyFoVGg9mTOkpItWQfJGyxGjIiBVqsGAGzfzgdCg5VlRPPISI11vAl/Zp9479jBxNtfBUqNN2Brbm5ohHWwTqJAMfjmKyLyQ7t2KdfMvPzBRV49XlpaBKKjQ1Bb2+owbyn5tmMHbDUTqdneSbrLH1iEKEMU6nR1Hj9WcLAao0fHYcuWSuzfX4PmZiPCwjQePy55T3l5k/UB58SJiR5/eORwbvVQxV58OqAJETC2Sti5s9ozByGPEkJg3z458U5KCkN8vM5rx/b29R+QH9zu3ST/QZQfFIiKH1wPcYl6whpvIh9g3+R6sD/tliTJOnjcsWNNOHGiReGIqC/K7BPvnMF5o2RpjSEEsHs3k5jBxr5/t78PrGahUklIHirPDlFWZsCJEwaFI6Lu1NfXo7y8vMu/nTuPoK6uHQAwfHiEw3uVlZUwGo0KR+5e9gOssZ83BRrWeBP5APuB1eybYg9W48Yl4IcfjgKQHzpkZCgcEPXK0r8bAFKyFQzEgxwHWDuOKVOSFYyG3G2w9e+2SB5mRnGB3E1iy5ZKnHXWEIUjos7q6+vx1PNPoaapa3eAsuJwAGkAgJqmPXjouTXW9wzNBhTsL0D6nHQvRep59lOKcWRzCjRMvIl8gCXxliR5Ds/Bzv7hws6dVcjIiFQwGuoLS1NzSeVYYzGYcIC1wc0x8fb/Ec0tUoaZrctMvH2TwWBATVMNYvNjERYV5vBe6WfB1uWcmeHImBNq/bnySCXa9rSho73Da7F6WlImoFIDZhNrvCnwMPEmUpjZLFBQIDdrHTo0yuv9SpOf/hihe8vQkpvqtf5e9s3pd+6swvz5TLx9malDoPywvCz3KfVO4p38jFw2Q71UNseNs9V4c4C1wcfyO42ODkFWlt7jx3M4tz7gufLbOfEm3xUWFQZ9nGPZqynvgGUQgGH5YdDH2c6vjTWN8CQlrv9BGgkJ6UDFEaDyiHx9UQcNzoe5RJ2xjzeRwo4cqYfBID/NHj168E4jYm/UqFjrwEYcYM33HS8BTHIXRK8NrKYEvV6LIUPkm+KdO6tgNrM2ZrA4frwZx47JA6vl5w+umSNiUwSCguXkm4m3/7HU+qrUcm1wILA0Nzd1yNcXokDBxJtIYbt32xLPQGhmDgChocEYPlyeyqewsAYdHeZetiAllSkworlSLM3Nm5vbcfBgnbLBkNvYt2Cw78s/GKjUQGx8KwCguLgB1dUcsNJfmDoEKo/Iywnpcm1wILDvrsR+3hRImHgTKWzPHtvoyYFS4w0AY8bIn9VoNKG4uFnhaKgnjgOrDe4bw84DrNHgsG2brSZ4/PjBlXgDQFxCq3WZtd7+43iJXOsLOA46NtilDOPI5hSYmHgTKcyxxjtwEm/7hwxFRZ7tx0YDcywAphKzcBxgjf28B4vBXOMNALGJTLz9kX3SmTJIB610xmFkcybeFECYeBMpbM8eOfFWqyWMGBGtcDTew8TbPwghrDXe4VFA5CDvDWGflHFk88Fj2zb5d6nVqpGbG6NwNO7nWONd0cOa5EscEu8AqvGOSQK0JwdvrzjMxJsCBxNvIgV1dJixd688r2dOTjS02sCZaGDMGFvN4v79TLx9VUM10FQnL6fmSINqUCpnMjMjoddrAchzzJP/a242Yv9++Tw7enQcgoPVCkfkfvpoI3Q6+frBGm//Yd+/ebB347EnSRISs+TPW10OtLUw+abAwMSbSEEHD9ahrc0EIHAGVrMYOlSP0FD5RpE13r7Lvpl5INwYSpJkbW5+9GgjB6oaBHbuPAFxshgPxv7dAKBSAaNGyS2mjhxpQF1day9bkC+wnF9DwyREDc6i2a0ku+nmK4uZeFNgYOJNpCBLM3MgsAZWAwC1WoWRI+WHDSUlzWhp6VA4InLGfmC1wd6/28JxgDXWevs7+y4Dg7F/t4Ul8QZYbv2BoUGg7mTRTM9SD/rWRJ0lD7F93orDCgZC5EWB066VyAf5wsBq1ZfPgsrQBrNO6/Vjjx4dhy1bKiEEUFhYjUmTUrweA/VMyanEqpfOQmRtMBqi2716XMcB1o7jtNMyvHp8ci9L/27AuzXe3j632ife27cfx+zZ6V45LvVPuV3f5rShQQBMXo9Byet/kkPizRpvCgxMvIkU5AtTiRkz43tfyUPsP/Pu3SeYePsgS+IdpAESvJx/GjPj0REfBaOuzv37bjOistJ5X9iUFNsN4caNJSgvT3V4X6fTQa/Xuz0m8gxLjbckAWPHeu9853Bu9UJe0TnxJt9m340nLUuZxFvJ679D4n2EiTcFBibeRAqy1HgHB6uQnR2lbDAKsMzlDQC7d1f3sCYpwdgmUFUqLydlAeqgwdEUsrW5FTt27sBzf34OulBdl/c72iUAwwFI+G7NHjz03FcO78eEx2D53cuZfPuBjg4zdu2Sz7M5OdEID9coHJHnjBihh0olwWwWnArPD5Qfsi2nDwkC0KZYLEqISgC0OqDNwBpvChz96uP9pz/9CUOGDEFISAgmTpyIdevWdbtueXk5li5dihEjRkClUuGOO+7oss7KlSshSVKXf62tHByEBi+j0YT9+2sBALm5MYNypN3e2Nd429f+k2+oOCQgzPLyYBpYrb2tHUZhRMy4GGTMyejyb+gZ6YhNkW8E6+pCkDbT9l5sfixqmmpgMBgU/hTUF/v21aC1VR4/YjD37waA0NAg61Rpe/acgNHo/RpU6jv7ZDMlM/Cu/5IkIenkyOY15UCbgck3DX4u13h/+OGHuOOOO/CnP/0J06dPxxtvvIFzzjkHBQUFyMjo2g6xra0N8fHxWL58OVasWNHtfiMjI7Fv3z6H10JCQlwNj8hvFBXVoqNDzmqU6t8NALHvroWmpArGjHhUXzHLq8dOSQlHVJQWdXVtDv3dyTeUFdmWlRhYLfa9tdAdroV6SLRHymaYPgz6OOe11qk5Hag+JtBhlNDeFomEDNvnrwYfEvkL+ybX3h7R3OHcerl3zq35+QkoKKhGe7s8VaU3m9ZT3wkhrIm3Ph4IC1ehToE4lLz+A/LI5sUF8nJlsYCexZUGOZdrvF988UVce+21uO6665CXl4eXXnoJ6enpeP31152un5WVhZdffhlXXXVVj83yJElCUlKSwz+iwcxxYDXlphLTlFQhdG8ZNCXeb5ooSZK11rusrAm1tWzl4kuUHFgNkMtmcFGxImUzeajt89rPtUv+xX5gNW/XeCtxbs3PdxwYkHxTQzVgODmLpqXWVwlKXv8Bx37e5RzZnAKASzXeRqMRW7Zswf333+/w+plnnomffvppQIE0NTUhMzMTJpMJ+fn5eOKJJzB+/Phu129ra0Nbm60/TENDAwDAZDLBZHKteZXJZILZbHZ5OyUxZu/wZMy7dtkudCNHxvT5GGazGSpJBQlS1wF7hN0/JyRIUKvVzre1bN+NXrftgQQJKknl9LscOTIGP/5YBgDYufM4ZsxIdbYLnzIYy7KzcmU/lVjKsO5/7/0tG30uj07K9EDLY2/bptgl3scOCoybbdu2u7IMDM6yoYQez3NAj+c6+9/Rtm22AfTGjo3t9TP2etwe9FiuBnpu7uW4ls9rP27G1q2VuPzyXNd2ZscXy0VvfDXmzuWqwu5hXtIQqcey7MnznAO7dfp0bnZDzPYPHSoOCeRN7vn8OhC+WjZ64m8x+1u8gPti7uv2LiXeJ06cgMlkQmJiosPriYmJqKiocGVXDnJzc7Fy5UqMGTMGDQ0NePnllzF9+nTs2LEDOTk5Trd55pln8Nhjj3V5/eDBgwgPD3fp+GazGTU1NThw4ABUKv+Y2pwxe4cnY964sdi6rNM1oqioqIe1bRobG5GdmQ099AgxdO2OEdIRgqiWKKfbqkJVmDt1LtKC0xBhiAAABJmCrP9HGZxv1922fRWCEGgztTh27BgaGxsd3ktIMFuXv/uuAImJvt93djCW5c7lSgiB8oNyk+rYRBVS1NFAN7+a/paN3rYLMgdZ/+9cNgdSHvuy7YjUDgDyGAwn9gchyiC32OqpLAODs2woobfzHND9uc7yOyorK8OWLfK9SVycFg0Nx3DyGf2AjtudzuXK4dzaEuXyubmv7MtkRIRt8LgNG4r7fF1xxhfLRW98NebO5apunwFAMwBgWJqu27Lh6fNcd9f/vmzrjphHJJkA1AAAqg8GIQEJPZ5fB8JXy0ZP/C1mf4sXcF/MTU1NfVqvX6OaS5JjsxghRJfXXDF16lRMnTrV+vP06dMxYcIEvPrqq3jllVecbvPAAw/grrvusv7c0NCA9PR0DBs2DJGRkS4d32Qy4cCBA8jOzoZa7R8DXDBm7/BkzCUl6wEAISFqnHbaOKjVffuDr6iowIHiA0jPSkekrlNZF0CUiEJdaB3g5E+yrKwM32/4HmH5YUjWJQMAQtUdCAbQoe5AXQ/TNjnbtq8aWhpQWlyKyxdf3qUbydy5Wjz55B4AQFWVutuHbb5kMJblzuWqulyg9eRgN0nZwiNlo7ftQlUny6aqa9kcSHnsy7aaoQLBWqC9DSgpNlqP31NZBgZn2VBCj+c5oMdzneV3NPfUC1FfL88Bf8opyX06t/R63B50LlcO59bQOpfPzX3VuUwmJ/+E8vJm7N/fhOzs7H7fn/liueiNr8bcuVwdLuuwvhc5vAWtQaFOy4anz3PdXf973baHvz9XYpYyBELCgNZmoLTUiOOo7/H8OhC+WjZ64m8x+1u8gPtibujtqe5JLiXecXFxUKvVXWq3jx8/3qUWfCBUKhUmTZrU45NarVYLrVbb5XW1Wt2vL06lUvV7W6UwZu/wRMytrR04cKAOAJCXFwuNJtileMzCDAHh9AYOkt2/TgQETCZTz9t2o9dteyAgYBZm63dpb8wYW7/LPXuq/aZsDLay3Llc2fdrThkqeaRs9Lk8OinPAy2PvW2rCpKQNERC6V6BE2VAW6uANlTqsSxbtx1kZUMJvZ7ngG7PdZbf0Z499dbXxo9P7NNn69Nxu9FjuZIwsHNzL8e1L5P5+QkoLz+M2to2HDtmQEaGaw8Q7PlauegLX4y5c7mqOGJ7z9rPWYHznAO7dfq0bQ9/f309riTJ59kjuwVqK4DWlt7PrwPhi2WjN/4Ws7/FC7gn5r5u61KdukajwcSJE7F69WqH11evXo1TTz3VlV31SAiB7du3IznZtad7RP5i794amM1yYmM/pVYgiokJQUKC/BBt164TEIIDWfmCcrupbpKGunjHN0gkD5X/FwKoPMJy6W/27Km1Lnt7RHMl2Q8ixwHWfI/9iObRiUCILjDPrxZJQ2zLVaX+0TyZqL9cLuF33XUX3nrrLbz99tsoLCzEnXfeiZKSEtx4440A5CbgV111lcM227dvx/bt29HU1ISqqips374dBQUF1vcfe+wxfP311zh06BC2b9+Oa6+9Ftu3b7fuk2iw2bPHN0Y09xXDh8s1MrW1rSgvb1Y4GgKA8oOdBlYLQPaf+9hBBQOhftm9u8a6PNjn8LZnP7L5jh3KjFZN3as7LjetBhxH9Q5U9gOsVZXy+6DBzeU+3kuWLEF1dTUef/xxlJeXY/To0fjqq6+QmZkJACgvL0dJSYnDNvajk2/ZsgXvv/8+MjMzceTIEQBAXV0drr/+elRUVECv12P8+PFYu3YtJk+ePICPRuS7HKcSC+wabwDIyYnAjz/KN4i7d59ASoprAySS+1mamquDgIQMhYNRCKcU82+WGu/w8GAMGxalbDBeNG4ca7x9WYVda6LkAG1NZM/+4cPxEhVih/SwMpGf69fgajfffDNuvvlmp++tXLmyy2u9NR1dsWIFVqxY0Z9QiPzSnj3V1mWlm5o3zsxDa24q2uP73w9woHJybCOf7tpVhTPPzFIsFgI62gUqTw66n5AJqIOUuTlsnJEHDBuGxmRN7yt7gH2Nt30LAPJ9xjYVSkvlasWxY+OhUnm/DCt1bs3OjoJOFwSDoYOJtw+yT7yVrvH2heu/Q+JdqkIeE28axPqVeBPRwFiamoeFBQ9o4Bt3aJo5UtHjA8Dw4bbE2741ACmjqhQwn5ySMlnBG8OmmSMRZIhCUw8jqntSRIyE8CigqQ44xhpvv1JbbRt8dcyY+B7W9ByHc6sXi49arcLYsfHYsKEchw7Vo76+DXp918FoSRkO42conGT6wvVfHweEhAOtTWxqToMfRzEg8rLmZiMOHZJH2x01KlaRmhhfM3RoBCwz3jDxVt4xu9rd5ADt321h+fxNtUBjLZNvf1F7wj7xDrzuPPZ92nfuZD9vX1Jx2LacmBnY51dAHtnc8oC3vkoFo5GpCQ1eLN1EXrZvn22k3ZEjObAaAISGqq19MPfsqYbJZFY2oADXZSqxAObQz5vNzf1GTTUTbws2N/cdZjNQcXKGhNhkQBsa2OdXi6Qs23JdtTJdi4i8gU3NibysoMDWvzsvT/nEO3xdAYKrGtAeH6los7PRo+Nw4EAdWlo6cPhwPbKzoxWLJdDZJ95K1niHrytAaLkRHckaNM1Spmw6jGx+SCAxS5EwyEWONd7KNDV3OLfO8G75ZeLtm+qrJBhb5GVfmKbRV67/cj9v+bpTV8NuETR4scabyMsKC22Jty/UeEesK0T0Z5sQsa5Q0Tjsp1Vjc3NlWRJvrU6eZ1YpET8WIvTLtYj4UbmymTLMtswab/8gBFBzMvFOTQ1HdHSIInEoeW4dPTrW2n2HU4r5Dvs+zEoPrAb4zvXf/ruwH5+BaLBh4k3kZYWFtrllfaHG21fYNwfdtYuJt1LaWoCacnk5eagESVL+5lBJSUMkawJTfkjZWKhvGmskGNvUAAKzmTkAhIVpMHx4DAD5QWZ7u0nhiAiQp8uyUHLgSl/jmHizqTkNXky8ibzM0tRcq1UjK0vZEc19CWu8fcPxYrsbQx9oCqk0TYiE2FR5ueKwgJnDD/i8ymJbuVWqmbkvyM+XP3tbmwn79tX0sjZ5w/FS2/nVF2q8fUVkLBAaLi/XscabBjEm3kReZDSacOCAPLhabm4M1Gr+CVpkZ0dBo5FrqZh4K6eyxHYzaN/MOpBZBpgztgK1lbxZ9nWVdg+PRo8OzBpvQJ6/3GLnTp5TfYHlwaakAhIyFQ7Gh0iSZH0Q0dwUjKamdoUjIvIM3vUTedGBA7UwmeR+omxm7ig4WI28PLlp5L59NWhr61A4osBkX+PNGhmZ/QBz9t8P+Sb731GgNjUHHBPvXbvYz1tpQgAnjsrnkrgUQKPl+dWe/cCVBw40KBYHkSfxDoLIixxHNI9RMBLfNGqUfJNsMgns31/by9rkCfa1hSkBPoe3hX2Te/tmzOSbLGVYrZYC+gGnY403E2+lNdYHo90onz/4ULMr+znN9++vVzASIs9h4k3kRfYDq/nCiOa+xr5ZKJube58QttrCyFggTM+bQ8CxxruSNd4+zdQhrLWKQ4ZEICQkcGdNTU+PgF4v95dlU3Pl2Y/WzcS7K/vEu6iIiTcNToF7RSJSgP1UYoFcE9Md+8R7z57qHtYkT2gxqGFolG9+OLCaTXwqEKQBOoxAVYkKxnFGVFZWOl3XbDajsbERFRUVUKm6Juk6nQ56vd7TIQesqqNAR7tcdvPyopQNRmGSJGHMmDj8+GMZjh5tRG1tq2JTqxFQZzdaNxPvrhKz7BNvNjWnwYmJN5EXWZqaq9UScnKiFY5GZsyId/hfSRzZXFm1J2w1Mr6QeBsz4hFkCoIxQ9m/FZVaQmImUFYEnDgmYdv2XXjuz89BF6rruq6kQnZmNg4UH4BZdB0CPSY8BsvvXs7k20Ps51rPzY1SLhD4xrl17Nh4/PhjGQC5n/esWemKxRLo7Gu8feH8CvhGGbWITgSCtQLtbRIOHGCNNw1OTLyJvMRkMmPfPrnfcnZ2tHUEb6VVXzFL6RCssrL00OmCYDB0MPFWQI39jaEP9O+uvnwWTIYo1OnqlA4FSUMklBUJCLOEJkMoYsbFICEloct6EiTooUd6VjoEhMN7zXXNqN5eDYPBwMTbQ8oP+U7i7XBuFd2v50md+3kz8VaOJfFWqYEEH/k1+NL1X6WSEJcqUH5IwpEjTWhr64BWyzSFBheWaCIvKS5uQGurPFI3B1ZzTqWSMGpUHDZvrsChQ3UwGNqh0wUrHVbAsK/xTvGRGhlfkTxEgiV7MhqiEaYPgz7OSfIsgBBDCCJ1kYCTr7Aa7ELhScfsEu9Ab2oOOI7qvmsXH2YqxWQyo75WbmoelwYEaXh+dSY+3YzyQyqYzQJFRbUYPVr5mngid+IoMUReYj+iOQdW656lubkQjn3iyfMsNTKS5Di1Czn2yWxr8Y1uItSVpal5ULAZGRnhCkejPPtxMziyuXKOHGmCySTfciezf3e34tJs3XPsB6MlGiyYeBN5ia8OrKYprkJI4VFoin3jpowjmyvDZDJbE++4VEATovzNoaa4CkH7j/hE2XRIvA1MvH1Rm0Gg+pi8HB3TBpVK2TLsC+fWyEgthgyRW2bs2nUCZrNCbd4DnP30WL40sJovlFF78Wm28skH7zQYMfEm8hL7p7e+1NQ89r21SHnmE8S+t1bpUABwZHOlFBc3wdRxskbGB/p3A0Ds+2sRueJviH1f+bIZkwxoTg4I3WaIUjQWcq78sO2mPTquTcFIZL5ybrU0N29ubseRIxy0Sgl799ZZl32pxttXyqhFvF2Nt30rQaLBgok3kZfYX0Ryc30n8fY1o0axxlsJDjeG7N/dhUolWae7aW+NRLvyeR11Un7ItuwLibev6DzAGnnfvn2+WePta2KSBSSV/ACNTc1pMGLiTeQFQghrs6nMzEiEhWl62SJwpaaGQ6+Xmzwz8faevXttN4ZMvJ1LHmpZklB9jGOT+hr7qcRimHhbMfFW3v79dQAAdZBAvI+MaO6L1EFApN4IANi3rwYmU9cpGYn8GRNvIi8oL29GQ4N8MfGlZua+SJIka3Pz0tJGNDTwBtobHGq8faSpua9JyrJ9L9VHfWM6QLKxn0osOpbnDQuObK6s9nYTDh5sBADEpgiog3h+7UlUjHyv1NZmwpEjDQpHQ+ReTLyJvIAjmrvGMrI5wH7e3lJYWAcACNIIxKcqG4uvsm8JUHWUNd6+RAhhnUosPEogVGdSOCLfkZ0djZAQubyyxtv7DhyoQ3u7XHMbn84a3N5E2T004wBrNNgw8SbyAl8d0dxXcWRz72ppacfhw3KNTHyagErNGhln7PtmnmCNt09prAGa6+TlhEwmN/aCglTWh5lFRbUwGNoVjiiw2F/DEjJYNntjqfEGmHjT4MNH9kRe4Czxrq+vh8FgcHlflZWVMBqNva/oxxxHNmfi7Wl799ZYpxli0tK9qARAE2qGsUWFE6zx9in2zcwTWYa7GDs2Hlu2VEIIuQXWKackKR1SwLC/hiVkcDq33kTF2Nd4c4A1Glx450DkBfZNzfPyYlBfX4+nnn8KNU2uX1QMzQYU7C9A+pzBO0KLfVNz1nh7nn2/TyYt3ZMkCXEpHTh2UIOGE2q0GgRCdGwd4AuOHWTi3RP7ft47d1Yx8fYi++5SrPHunT7aVrHAKcVosGHiTeQFlqe2iYk6xMSEory8DjVNNYjNj0VYVJhL+6o8Uom2PW3oaO/wRKg+ISEhDPHxoaiqamHi7QW7dtn6fTJp6Vlsqpx4A0DFYYGsUUy8fYF9jXdCpoDpqILB+CCObK4cS423Sm1GdBJrvHsTHCyQlhaGo0ebUVhYDSEEJInnWRocmHgTeVh1dQuOH5eblHfu3x0WFQZ9nN6l/TXWNLotNgAof3CRW/fnLqNHx+H770tRWWnAiRMGxMXplA5p0HLog5jpOzeG5Q8sQpQhCnW6OqVDsYpLtT3wqjgMZI1SMBiyKj8o/y9J8gBWFT6QeDucWxX+s7JPvDmyufe0tXWgqKgOABAVbYTax4aG8NXrf05OJI4elWeDKS9vRkpKuNIhEbkFB1cj8jD7/t0c0bzvRo2y7+fN5maeZLkR12hNiIj2ncTbF8Wl2EbLrjjM78oXmE3C+ruISwU0WoUD8kHx8TokJsoPL3fsqIIQLLvesH9/LTo65FZEnOKu73JybBUSHGCNBhMm3kQeZj84COfw7juObO4dtbWtKCtrAgDExLWBLfp6Fpdmq/EuZ+LtE06UAe0nu4VyDvruWWq9q6tbUFHRrHA0gcH+oXFU7OAeFNWdmHjTYMXEm8jDOJVY/3Bkc++w798dHccamd7oIs1QBbUCYI23r7Dv320/1zo5YnNz77O/drHGu++ysyOtyxzZnAYT9vEm8jD7UTl9sal58tMfI3RvGVpyU32qv5fjyOZ84u0p9q0J5BtD32mnm/yMXDZDfahsShKg1dWhpSEJ9VWAoVFAF8FkT0n2I5qn+FCNt8O59QHly2/nkc3PPDNLuWAChH2Nty8m3r56/WeNNw1WrPEm8jDLRUOv1yIpybURzANZVFQIUlPlAVV27z7BPokeYl/zFcMa7z7RhtZal1nrrTzWePcNRzb3PsuDzZAQNcIj2xWOxn/ExGiRkCCPScAabxpMmHgTeVBTkxElJfIo5Hl5MZwSw0WW5ua1ta3sk+gh9om3L9bI+CKtzpZ42yd9pIzykzXewVp5cDVyLi8vFmq1fA1i4u15ra0dOHiwDoBcg6viHbdLLGPiVFQ0o7a2VeFoiNyDpwEiD9q71/ak1hebmfs6x+bm7JPobkII6/eamqqDRss5vPvCPvGuOKJcHAQYWwVOlMnLSVkSVGo+3OxOSEgQhg+PBiDXIra3m3rZggZi794amM3yQ6ERI1ybNpQcx8Rhc3MaLJh4E3kQB1YbGI5s7llHjzaivl6u5c7NjVI2GD+isU+8WeOtqIojApZeKMnDlI3FH1iamxuNJuzfX9vL2jQQ9gOrDR/OxNtVjok3m5vT4MDB1Yg8yNcHVvN19on35s2lKC93vR2pTqeDXs+bHmfsm5nn5kaBjfn6Jii4DbpIMwwNKk4pprDyg7bl5CGs7e7N2LHx+PDDfQDk5uajRsX1sgX1l/3AaiNG6FG5TcFg/JD99Kus8abBgok3kQdxDu+BsX/i/c33u/HQc1+6vI+Y8Bgsv3s5k28n7KcSy8uLwrYDCgbjZ+LSO1CyR4OmWqCpViA8mkmfEo7ZD6zmQyOa+6rOU4pddpmCwQxy9q20cnOjsJaJt0vY1JwGIybeRB5kuViEhgYhM5OJn6vCwzXIyAhHSUkT6uq0SJ+dAVfGp2uua0b19moYDAYm3k50rvFm4t13caly4g0A5YcFcph4K4Ijmrum85Ri5DmWpuZhYcFITeWMJq5KTQ1HRIQGjY1GNjWnQYOJN5GHtLV14MCBOgBAbm4MVCreFPbHiBF6lJQ0ob1VBbMpEjFJrn2P1eCT8u5YamTUagnDhkUqHI1/iUu3DUxVcVggZ4KCwQQwS+Idpgci2ZunVxkZkYiM1KChwcjE24MMhnYcPlwPQO5mxuu/6yRJQm5uDDZvrsCRI/VoaWlHaGiw0mERDQgTbyIPKSqqtY5o6ssDq1VfPgsqQxvMOq3SoTg1YoQeq1fLwxaXHxIuJ97kXHu7yVqLMGJEDLRatcIRdVW9dBYia4PREO1789/GpXZYl8sPKxhIAGuoM6PxZEVY8lDJ56Zr9MVzqyRJGDs2Hj/+WIbS0kbU1bUiKipE6bAGncLC6v9n777j26jv/4G/TpJlWbYl771H7Oy9SUgZYRNSaEIZbRn9toW2jPKghPGjpYSUsFJaAoUGKBB2wk4zWNkkIctJ7HjFI/GQHU/ZsjU/vz8ulk7xkmxJp5Pez8fDj5zlO+md88efu/d9ln3SP+HqHP7GH8uo0LhxsThwoBGMAaWlbZgyJUHskAgZFZrVnBAvkcr4blNmPHrHpsGUGT/8ziIQzrZNayZ7Tnl5G0wmvtVW2P3Un5gy42EZk+WXZTMuzbnFm/jemWrHww9/HN/tr3Wr8O9dONyEeI5wfLdwklB/469ltI/w3kk4WS0hUkWJNyFeQjOae0ZBQZR9mxIczxHecE+c6J83Xf5MFc6gPXfaGk8xMEZl09fqBIl3Co3vdplwgjXqbu4dwhnNaeb4kaMJ1kigocSbEC+hNbw9IzdXA47jkxpKvD1HKi0y/izp3PJVBj3QSfeEPne6ytHrIDlHxEAk5vyZzYnnCdfw9ueu5v6OEm8SaGiMNyFe0tfVXKGQIS8vStxghhD7zg4oa5thyohHyy0LxQ6nH5VKDk2UCR1todBVAzYrg0xOrVuj5dziHQegR7xgBhG7fgfUVW2QZ0f7ZdlMzuZQut/xUEgbR+XSl4RdzZP8sMXbqW692X/Kr/BBG7V4e0dfi7dGo0RaWiQaG7tFjmhg/n79z87WQqmUw2Sy0szmJCBQizchXmC12lBayl8k8vKiEBLifxNX9VHWNiPsZB2Utf57AxYdawQAmE1AS73IwQSIvjW8w8NDkJXln0utKWubEVJe47dls6/FG+CXFCO+Y7Mxe1fz2GRApfa/xNtf61aNJhRZWfwqBseONdsnASWeodebUFPTCYDvZu5vk/4J+WsZ7aNQyDBmTDQAfl4Si8UmckSEjA4l3oR4QXV1J4xGvhskdTMfvehYk32bJlgbva4uE06d4pe6mTAhjpa6GSFh92YaBuFbrY2AsZff9seJ1fxdX3fzri4zamo6RI4msAjnd6Fu5qPXN8Ga2WxDZWW7uMEQMkqUeBPiBc7ju/13RnOp6GvxBqhl0ROEE//464zmUpCUJWjxPiViIEGoodJRDyT7YTdzfyecULGoiMZ5e5Lz+G6qX0eLxnmTQEKJNyFeQBOreVZ0nCPxppbF0evrZg7QxGqjEarmEJPMbzdW0czmviTs+UIt3u6bNInGeXuLMPGm+nX0nBNvGudNpI0mVyPEC6SyhrcvmYwm6HS6fq/bbDbo9Xo0NjZCJuv/LFCn00EV1gW5gsFq4airuQfQUmKek5TNobWBwWgA2nVAdKLYEQWHekE9QEuJDV6/DiYpybF98CBNnOFJx49TV3NPEi7HSmt5E6mjxJsQLxC2eBcWUuLd292Lo0VHsfqV1VCHqZ1+JuNkyMvMQ0VNBWys/8Qphm4DisuKEZMyDs21CjTVAhYzgyKEbrZHSriUGHU1H52kLA7Fe/gksKGKITqRyqUv9HU1l4cA8ekiByOyoerXwdhsgFw+BlarDDt3laOjowNarX9Osig1fS3e0dEqJCWFixyN9I0ZEw2ZjIPNxqirOZE8SrwJ8TDGmL3FOyMjEuHhSpEjEp/ZaIaJmRAzOQYJKQlOP+PAQQst0rPSwdC/NVtXrYPxhBFxqRY01ypgswLNp2nd3tHo62qemKhGfLxrN+pkYMLxxY1VDOPmiBhMkLCYGJrP8NuJmYBcEdwPO4aqX4eS8CU/N0Fbqxxnz3ZS4u0B7e29qKvrAsC3dvvzjOZSoVIpkJ2tRWVlO06ebIXNxmhCUCJZlHgT4mGNjd3o6ODHJNP4bmfh2nBo4867uWOAyqCCRq0BBriW6lv1AIC4NKv9tYYqRhMqjZBO143mZn7NbupmPnq0pJjvNdYAtnPVAXUzdxiwfh1CeqEFDacYGONQXt6B3Nwg7zrgAcKJK2l8t+eMHRuDysp2dHebceaMHhkZGrFDImREKPEmxMOcx3f7f+KtXzAWvYWpMMf794UsLs1i36YJ1kbOeXy3f98Y6i8YC+TmQp/sv71GErMAjgMYAxqrxI4mOEhlRnN/r1tTcjngXC+jkpJ2XH65uPEEAucZzen67yljx8biyy/5pSNKSloo8SaSRYk3IR5WXOy48EphYrWuBePEDsElcemCxJsmWBsx4cQ//t4i07VgHBSGKHSp28UOZVDKUA6xqcDZM4CumsFmo7LpbVKZ0dypbvXDYiF8aFFS0i5eIAFE2OIthaXEpHL9F95LlZS04rLLskWMhpCRo+XECPEwqbV4S0VUvA0hofw2zWw+cjSxmuf1dTc39QKtjSIHEwTqK2lGc09IyRMm3m0iRhI4pNbiLRXjxjmuVTSzOZEySrwJ8TDnNbz9v8VbKjgZP4M0AJytB0xGSr5Hoi/x5jhptMhIQbJgnDf1xvC+vgdv6ggOWpqmYMQiozlERPHnsri4ndah94C++jU+PgwJCTSjuacIV4ehmc2JlFHiTYiH9bV4x8WFIS7O/2eMjthZjOiNPyBiZ7HYoQwr6dxM5swGNNWIG4sU2WzM3lqQmxsFtTpE5IiGFrGzGGFffu/3ZZMmWPMdQydDBz8pP9KyFH49a7QU6taETH4Jx9ZWI3Q6g8jRSFtLS4/9HErloaYUyigAaLWhSEmJAODcq5AQqaHEmxAPam/vRWNjNwDpdDOP3FmC6E/3I3JnidihDEvYskjdzd13+rQBBgM/Vl4KM5pH7ipB2Fc7ELnLv8vm+UuKEe8R/t2nZctFjGR4UqhbE88l3gBQVNQsYiTSJ8Vu5lIoo336ehC2tPSguZkeEhFposSbEA9yHt9N3cw9TdiySAmO+8rKOu3bEyZI48ZQChLSAdm5HJBavL1LOL47LYvmhx2tpCxH4n3sGCXeoyGcP8PfJ66UImFjBnU3J1JFiTchHuQ8vpsSG08TtixSguO+sjK9fVsKLd5SoVByiD+3BHJTLWC1Utn0loZTju30bEq8RyuBWrw9RmozmkvN+TObEyJFlHgT4kE0sZp3RSUAqnPz1VBXc/eVlwsTb7ox9KS+if8sJkBXZxU5msAl/LtPzfLvruZSEJ/OwHH8OS0qOjvM3mQoUuxqLiXjxjnOKc1sTqSKEm9CPIiWEvMujuPs3c3bGoFeAyXf7ujrah4aKkdeXrTI0QQWYW+MuhpKvL2BMWZPvKMTAXU43cKMVogS0EabAPDJjNlMZXckGGM4fpxPBpOSwhETEyZyRIGHupqTQEBXLUI8qO9iEB4egvT0SJGjCUzJ2Y5tGuftut5eC2pq+In/xo2LhUJB1b8nOSfeFhEjCVxtOqCXL8JO55uMTnSsEQBgMllRXk7reY9EU5MBLS09AGh8t7ckJKgRHa0CQF3NiXTRnRchHtLTY0ZVVQcAvpu5Py9zI2XOE6yJGIjElJS0wnZuOCd1M/c8YSJ4pooSb29oEEysRom358TEG+3b1N18ZJzHd1NvN2/gOM4+hO/MGT30epPIERHiPkq8CfGQsrI2sHP3hdTN3HtogrWRoRl3vSsuFVAo+e0z1dRd1xvqT1Hi7Q0xccLEmyZYGwnn8d1Uv3qL8N7q5Enqbk6kh6YEJcRDpDq+25QR7/Svv3NaM5kmWHPZsWOOG0OpzGhuyoiHwqqAKcP/x6PL5BySsoAzZYCu3gqzkUOIipJDTxK2eKdIIPGWSt3a19UcoCXFRkr4YFNKLd5SKaN9hJPWFhe3YObMZBGjIcR9lHgT4iFSndG85ZaFYofglohoIFwLdHfQzObuEN4YSqWrecvNC2E1RKFd3S52KC5JyuZwpoyB2QBdLZA2RuyIAkvf37tMDiRkAjCLG89wnOpWP66qIjRmREQo0NVloRbvEZLqUmJSu/4LZzancd5EiqirOSEeQmt4+4ZwZvPOFqC704/vaP1IX+IdHR2KlJQIkaMJTCm5gmEQlVQuPcliZtDV8NsJGYAixP9bvKWC44CxY/leJbW1erS394ockbQwxuxdzdPSIqHVhoocUeCimc2J1FHiTYiH9D19DQmRITc3StxgApxTd3Ma5z2s1tYe1Nfz00FPmBBHE/95iXDiP5p/wLOaagHbuaHzNL7b88aOjbJvC3vHkOE1NHSjvZ3vri+lbuZSlJGhgVrNd9alFm8iRZR4E+IBFosNZWX8Miz5+dGSWqpJWdMMVckZKGuk08UwSbCkGHU3H54Uu5kDfNlUlFVLpmzS/APe4zS+O1caibeU6lZh4k3dzd0j5YkrpVRGAUAm41BQwA/lq6xsh9FIK0gQaZFOdkCIH6uq6oDJxDfHSGl8NwDErt+BlFUbEbt+h9ihuMy5xVvEQCRCOLGalFpkYt/dAc0LbyH2XWmUzagEQHWuFz+1eHuWFGc0l1Ld6px4U4u3O5xnNJdO/QpIq4z26etubrMxWneeSA4l3oR4AI3v9i2nLr3UsjgsYeIttRYZKeE4DsnnymabDujporLpKcK/82SJtHhLSWFhlH2bZjZ3j1QnVpOq82c2J0RKKPEmxAMo8fatcA0HzbnT3FjFwBglOEMR3khT4u1dNP+Ad9RX8OdSFQ7EJIkcTADSaJTIzNQA4B/U2WxUdl0lbPEWzrpNvINmNidSRok3IR7gvIa3tLqaS1VfgtPdAXRRb7NBMcbsYxCTk8Noxl0vS3aaf0C8OAKJQc/Q3sRvJ+dwNDmgl0yaxK/lrNebUFPTIXI00mCzMXuLd2amBhERSpEjCnw0szmRMkq8CfGAvsqf42Cf+IN4V1IOdTd3xenTenR2mgAAY8ZEihxN4BO2eNM4b8+gbua+0Zd4AzTO21U1NR3Q6/n6VXj+iPfk5UXZJ7ClFm8iNZR4EzJKjDF75Z+ZqYFaHSJyRMEhmcZ5u0TYzTw/nxJvb3Oaf4DW8vYI5xnNRQwkwAlXPKBx3q4Rzp8hpRUjpCwkRI68vCgAQGlpK6xWm7gBEeIGSrwJGaX6+i77E28a3+07wiXFaCzt4I4eddxAFxRoRIwkOEREcdDG8JfWhlM0/4An1Fc6tqWylJgUObd4U+LtCufEm1q8faXvXstotKK6ulPkaAhxHSXehIwSje8Wh1PLIi0pNihKvH0vLVMOgOYf8JQGCS4lJkX5+dEIDeXLLnU1d43wAcWkSdTi7Ss0szmRKkq8CRklmtFcHCo1h+hzsxvTzOaD60u8Q0PlyM4OFzma4JCWrbBv0zCI0bHZgPpzXc2jk4CwCEq8vUWhkNlnjC4vb0NPj0XkiPxfX5d8pVKO/PxokaMJHs4zm1PiTaRDMfwuhJChSD3xbnj4erFDGLHkHA5tjQy93UB7ExCdKHZE/sVgMKO8nG9yHT8+1j4hjVQ0rLgeUYYotKvbxQ7FLalZcvt2/SmGMTNEDEbiOpo5GA38dorEWrud6laJPH+ZNCkehw83wWZjKC5ugYY6yQyqt9eCsjK+fh07NgYhIfJhjvA/Ur3+08zmRKqkdRdGiB+irubioQnWhnb8uGM9Xppx13fSMh3PtBupXI6KrsZxm0Lju71PWE8Ixy+T/kpKWmC1Uv0qhoICR+8CmtmcSAkl3oSMUt/T1oQENWJiwkSOJrgIx3nTBGv9Ccd304y7vpOSKexqLmIgAUBX7fgbT86jxNvbnGc2p8R7KDSjuXjCw5XIzOS7Y5SUtNBQMyIZlHgTMgptbb3Q6fh+kNTa7XvJtJb3kJwn/qEWGV9RhXGITeG3G6uYvdcBcZ9Ti7fEuppLkXOLN81sPhTh+aEZzX2v756rs9OEhoZukaMhxDWUeBMyClIf3w0AyU9tQM4vXkTyUxvEDsVtiZmA7NywuroKSm7OJ2zxnjxZejeGyas2IOZ3TyB5lfTKZt9DIWMP0NYocjAS1pd4y0OA+HSRg3GTFOvWxMRwJCSoAVCL93CEM79LtcVbimW0j/Cei2Y2J1JBk6sRMgrO47ulmXhLWUgoh4R0oLEa0FUDFjODIoRaxQCAMWZv8U5Li0RMjAotdG/iM8nZHI7v4h8GNZxiiE2hcukui4VDSz1/3pKyALmCzqEvTJwYh2++qUVzcw/OnjUiP1/siDyro6MDBoNhRMeq1WpotVoAjhbvmBgVUlIiPBZfsDMZTdDpdMPul5LiSGF++KEK48crnX4/hPgjSrwJGQXnFm/qai6GlDwOjdUMVgvQVAOk5IkdkX+oqelER4cRgDRbu6UuSTgMoophwgUiBiNR7a1KMBt/HmliNd+ZNCke33xTCwAoLe3E3LkiB+RBHR0dWPnsSrR2jWxCrpiIGDzywCOwWJT27s0TJ8aB46h8ekJvdy+OFh3F6ldWQx2mHnJfXX0YgEwAwPqPtqG65R3774eSb+KvKPEmZBQCoau51KXkcTj0Nd+yWFfBkEITMAGQfjdzqROOR6aZzUem7WyofZsSb98RjvMuLe0UMRLPMxgMaO1qReyUWIRHhbt1bHd7N1qOtMBgMKC0tMP+Oo3v9hyz0QwTMyFmcgwSUhKG3DdOD3z5Ib/da9MgdorF/vuhxJv4K0q8CRmFvq7mkZFKpKZSVzMxpAoS7Xoa52139GiTfZsSb9+LT+fnH7BZ+bW8iftaz6rs28mUePtMICfefcKjwqGNcz85awH/sF04vpsmrvS8cO3wvx9tHBARbUZXG9BSL0d4VLj990OIv6LJ1QgZoZ4eM6qr+afehYUx1NVMJMIWbppgzcG5xXvolgPieYoQDgkZ/HZTDWC1UNl0Vyu1eIti3LhYKBT87eHJk4GZeI+W84zm0pxYLRAkZvL1gr4VMOhFDoYQF1DiTcgIlZa2oW/pSBrfLR5NLBARxW/XVzBaz/OcvsQ7LEyBvLwocYMJUn0zm1stQPNpkYORoL6u5hFRQCRVsT6jUins17TKyi709lpEjsj/CGd8Hz+eEm+xJGY5HsidPUMpDfF/VEoJGSEa3+0fOI6zt3p3tQOd1NMMer0JlZXtAPjWGLmcqnoxCNeZp+7m7jl7thc9Bn40XHIuRz2KfGzqVL6XjNXKcOIEVapCNhvD8eN84p2To0VkpFLkiIJXUpZju/kM1RHE/9HdGCEjJFw3khJvcdE4b2fCbpDUzVw8yTTB2oiVlLTbt6mbue9NmeKoN4TDVghQW9uF7m4zAJpYTWx9Xc0BoPk0pTTE/9HkaoSMkDDxHj9euol3y80LITMYYVOHDr+znzp/nPfYOSIG4wcCZUbzlpsWQtMWgs5os9ihjIgw8W6gxNstJSVt9m3heZQSKdetwsT7yJGmIfYMPsKHQlIf3y3lMgoM0NU8R8RgCHEBJd6EjFBf9zuVSoHsbOkuXWHKlG5i1kfY4l1XTglOoCTepsx4WOKjYFK3ix3KiMQkA0oVYOrl1/ImrnNq8c4TL47RcKpbJfbrd068qcVbKJASb6lf/7VxQKgaMBqoqzmRBuqXQcgIGI0WVFTwLTKFhTE0hlZkCZmA/NxjxPpKid3heoFwKTHqCikemYxDUjZ/M9hSxyfgxDV9yQ0nY0jKohtqX4uOViEzUwMAKCpqhs1G9Wqfkyfb7du0lJi4OI6zdzdvb5LBbKa6gvg3yhYIGYGysjZYrfyNyLhx0u1mHigUIRySsvntplrAZAzem0Sbjdln3M3K0kCrlWYXwkCRfK7rI2NAUy1dcl1htdpQVsYv1RiTxKBU0c20GPp6y3R1me2TNRLHQ6HQUDny8qLFDYYgMcux3dFGE90R/0ZdzQkZAeH47owMJRoaGtw6XqfTwWQyeTqsEYl9ZweUtc0wZcSj5ZaFYoczYil5HOrKGZgNaKxiyCgMzpv1o0dP2yf+KSjQ2MumzWaDXq9HY2MjZLL+CaA/lck+set3QF3VBnl2tGTLJj//AP8gqLGaQwLdFw6roqIdvb1WAEBilk3kaEbOqW692X/Lr8logk6n6/d6Xl6Yffu770oREZHZbx+1Wg2tVrpDrdxlsXCoquIXjBaudy5VgXD953vE8HVseys9aCb+bUSJ99q1a/HMM8+goaEB48ePx5o1a7BgwYIB921oaMCf/vQnHDx4EOXl5fjjH/+INWvW9Ntvw4YNeOyxx1BZWYnc3FysXLkSS5cuHUl4hHjdiROONTwPHP8Kj63+wK3jDd0GFJcVI31RuqdDc5uythlhJ+vEDmPUUvM4HDh38a2vADIKRQ5IBB0dHfjLytcA8DfCTe1H8NjqrwEAMk6GvMw8VNRUwMb6JzP+VCb7KGubEVJeB6VcuusIC2fk1lXLkDBGxGAkoqjIMaY4MVO6ibcU6tbe7l4cLTqK1a+shjpM7fSz2lORAFIBAGv/8yn2l5ztd3xMRAweeeCRoEm+21pC7d3upT6+G5BGGR2OcGbz9lZ6skn8m9uJ9wcffIB7770Xa9euxfz58/Hvf/8bV1xxBYqLi5GRkdFvf6PRiPj4eDzyyCN44YUXBnzPvXv3Yvny5fjb3/6GpUuX4pNPPsGyZcuwa9cuzJ492/3/FSFeJmzxzr5AjfTCGLeO11XrYDxhhMUs3YTC35w/s3kwMhgMqD3jmAF8zKJIZMzlb6Y5cNBCi/SsdLABZnqiMukdwon/GqtkmEiJ97CEy+ElZgbn37KvmI1mmJgJMZNjkJDivPSgdpwM2z7ntw3WaGQsck7Mu9u70XKkBQaDIWgS79ZmR4vq1KmJIkZC+ghnNu+gFm/i59xOvJ9//nnccccduPPOOwEAa9aswZYtW/Dyyy9j1apV/fbPysrCP/7xDwDA66+/PuB7rlmzBpdeeilWrFgBAFixYgW2b9+ONWvW4L333nM3REK8rm9Gc7nchtR8FbRx7t106Fv13ggrqNFa3ryWJpV9O39aOLRx584LA1QGFTRqDTBAL3wqk96h1nCISgDamwBdjQwseIumy4qKHC2rUm7xlpJwbXi/65gmhiE8woruLgZdjXzA61wLWvq9Fshamh3165QpNLGaP4hNBhRKwGKiFm/i/9xKvE0mEw4ePIiHHnrI6fXFixdjz549Iw5i7969uO+++5xeu+yyywbskt7HaDTCaDTav+/s7AQAWK1WWK1Wtz7farXCZrO5fZyYKGbfGChmk8mK8nJ+RnNtjAlyOef2UjEcOMjlcnDw8LFM8DWSzx0iFr+N+ZxwDQdtPNDRzLd4MxsDBw4yTubxcuevZdlms9kTb1UEf0NiP2ceOs+ePNbl8jhA3GLE63LM58WbmsehvYnBaOBg0Cv9ruz4W3nuWzc6RGlFdCJcPs99RvN3b7PZIONkflvP+fJYDhwychUoOWpGZwugb2GIjOGcfu6N+nU0hivLo/39tgoS7wkTYl3+fw/5ucOUZZ+VC8E+I6nnRIkZ/OoR8WlAwymgo10Jo9Ey4O/F3+o5V0gtZqnFC3guZlePdyvxPnv2LKxWKxITnbvXJCYmorGx0Z23ctLY2Oj2e65atQp//etf+71eWVmJiIgItz7fZrOhtbUVFRUVA0465I8oZt8YKOaysk77jOYZ6aFIgAYqg2qot+lHFibDT+b8BGkhaYg0RHr0WJVFhaieKJePVVgV9n+jDAMf528xDyYzuwNFzSb0dgHWag0SNGEIzQxFfX099HrPtej6a1muqmqBoZv/fWbnhiD6vHPqqfPsqWOHO05hU9j/Pb9sihGvq8eef56zM7pxYo8BAKDksjxeHkfLn8pzR4cJNTX8g/TUNBmSZAmD1q+DlWcVVCP+u9fr9cjLzIMW2lHX6051a0+U3/39uXJsTnYPSo7yw1faj4cjfYajRXE059lbhivLo/n9Km2haGvh/58pKWE4e/Y0zvYf9j6g4T53sLLh7XIx2PV/JPWcr2IeSHpaJxpOGcFsHPbvr0Rvb3e/ffypnnOV1GKWWryA52Lu6upyab8RTa7Gcc79FBlj/V7z9nuuWLEC999/v/37zs5OpKenIzc3FxqNxq3PtlqtqKioQF5eHuRyuXuBi4Ri9o2BYj5ypNT+c4WqBU3o5bvvuqGurg7f/fAdwqeEI1md7LljGRDFotAe1j5gd+KBjg2TWxACwCK3oF3dLomYB5Mwxgrs57dP1nUgQ9OF0zWncfMNNyMpKcmtmIfir2X5wAHHzW/SWKvz79OD59lTxw53XJjsXNmU9S+bYsTr0rEDnOfYsY7u0ieKW5GSkuLR8jha/lSev//+tH1brWkfvH4dojx39nSO+O++sbERFTUVSM9KH3W97lS3hrX73d/fsMcyICXPkSSWntYjfaGjfIzmPHvLcGV5NL/fqlN6mIz8+ZgxIwX5+fkuHzvk5w5Rlr1dLga7/o+knvNVzAOJybMCO/jttrbQAX83/lTPuUpqMUstXsBzMff1vB6OW4l3XFwc5HJ5v5bopqamfi3W7khKSnL7PUNDQxEa2n8SBblcPqITJ5PJRnysWChm3zg/5pKSNvvPtDG9YFAPeCM1FAYGq9XKT3Ll6WM5wddIjpVazAIp+YIJ1ioZ0scy2JjN/jv0JH8syydOtNu308Zw/c+Xh86zp451uTwOELMY8bp87HnnWVguW5qVXimPo+Uv5fnYMceY4Zi4XjCEunye+zCM/O9eJpPBxmyeLxsc/O7vz5VjM/Ict4l15c77jOY8e9NQZXk0v9+GKscBU6cmuPV/HvZzhyjLPisX5/1u3a3nRIn5nOQcx87l5Z2D/m78pZ5zh9Rillq8gGdidvVYt9rUlUolpk+fjm3btjm9vm3bNsybN8+dt3Iyd+7cfu+5devWUb0nId4iXEosOtY4xJ7E14QTrNWVB98sVsePt9q30wqCcx1zfxSfCoSce07ceta97q3Bpm98NwDExveKGAkBgOR0ORTnepcHY50q1FjluGWeMiVhiD2JryVlO653ZWUdIkZCyNDc7mp+//3349Zbb8WMGTMwd+5cvPrqq6itrcVvf/tbAHwX8Lq6Orz11lv2Y44cOQKA7//e3NyMI0eOQKlUYty4cQCAe+65BwsXLsTTTz+NJUuW4LPPPsPXX3+NXbt2eeC/SIhn9S0lFhoqQ6TWPMze/k+/YCx6C1Nhjnev250/ik/jExyzMThnNj92jO+NoVQxxKeJHIwH6C8YC+TmQp8s7ZlqZXIOyTkcaksYOttD0N0t/XrDW/oSb7mcQ1SsSeRoRicQ6laFgkNyNofTpQzNpwFjD0NoWHA+1AvExDsQyigAxKUCcgWD1cLh5Ml2scMhZFBuJ97Lly9HS0sLnnjiCTQ0NGDChAnYtGkTMjMzAQANDQ2ora11Ombq1Kn27YMHD+Ldd99FZmYmqqurAQDz5s3D+++/j0cffRSPPfYYcnNz8cEHH9Aa3sTv8DOatwMAcnM1kMjcEUPqWjBO7BA8RibnkJLLoaaY4WwdMMD8KgGrra0XtbX85B5J2TbI5NK/Oe5aMA4KQxS6hph7QCpS8oDaEgDgUFLSjry8DLFD8jsmk9X+YDM/XwOFQtoPz5zqVgn/V1LzgNOlAGNAQyVD1gTp1y0j0Xiuq7lGE4LMTGknqn0C5fovV3CIS2PQVXOoqtLDZLJCqZROV2cSPEY0udpdd92Fu+66a8Cfvfnmm/1eYy4sXHrDDTfghhtuGEk4hPhMeXkbLBZ+oqQxY9xbu5v4RnoBn3gDQMMpGYLl0nv4sKOLblI2rX3sb/hhEHy5LClpxzXXiBuPPyouboHZzJfd8eOjRY6G9EkdwwFf8WX3TDlD1gSRAxJBVxtDZwv/pH38+OhRTyhMPC8h3QZdtQwWC0NZWSsmTKB11on/CYD2OkJ8Rzi+mxJv/yQc21xfGTxV3KFDOvt2Si4l3v4mRTD/QHFx2xB7Bi/h+O7x42NEjIQIOc+dIWIgIqoTDF2ih0L+KT5DsHrEiZYh9iREPMFzV0qIB/R1gwSAgoIo8QLxoIidxYje+AMidhaLHYpHCBPvhlPBU8UJE+/knMBIvCN2FiPsy+8DomwKZ909cYIS74E4J97ST24CpW5NyePQ18B7pkzCfeZHQTixXCCUzT6BUkYBIDHD8Ts6ftzFBdYJ8bHguSslxAOET1Hz8wOjxTtyZwmiP92PyJ0lYofiEUlZgDyE324IqhZvPmmRyW2ITw+Mm+PIXSUI+2oHIndJv2yqIzlExfMPREpK2mGzBcbvyJOEife4cVHiBeIhgVK3qtQc4tP57fpKBos5+MpuoLZ4B0oZBajFm0hD8NyVEuIBfS3eSqUcWVkRIkdDBqII4SdYA4CWeg4mU+BXc3q9CWVl/FJiMXFGyEc0ewfxtsRzY++7uy2orqYlb4QYYzhypBkAkJYWidhYWnbNn6Sf60lkNQONVSIHI4K+Fm+ZjNEwMz8VncAgl/N1rHBYICH+JPDvSAnxEJPJirIyvotoQUE0FAr68/FXaWP4m0TGOLQ2h4ocjfcdPdqEvjksae1j/5WU5Wg1O3q0WcRI/E91dQc6OowAgClTaFIkf5Ne6BgqcfpkcLV4m4wMTecW64mKMdJs2X5KJgeiYvglCCsq2tHbaxE5IkL6o8yBEBdVVDhmNB8/Pk7kaMhQ0gXjvM82BX7LWV83cwCISzCKGAkZSmKWoyvk0aNNQ+wZfPpau4HAWSM5kAjr1NOlwZV4N1Yx2Kz8dmw81a/+LDqO//3YbAwnT7aKHA0h/VHiTYiLhGOGxo2LFTESMhzhTWJLECTehw87JlaLTaAWb3+V5JR4U4u3kHB8NyXe/id1jGOCtWBr8RbO5B5D9atfi4pxPBih7ubEH1HiTYiLhDOajx9Pibc/S86BfZxzMLV4y+Wc/Yk/8T/RSQyKED75LiqixFuIEm//plJzSMjkt+srGSym4Em+zwha+GOpfvVr0bHCxJsmWCP+hxJvQlwkfHpKLd7+TaHkkJzDb3e0KmEwBO5YL4PBbC+bY8ZooVAEzw2x1MhkjhvDU6c60NlJN/F9+hLvyEglsrNp8ip/ZJ9gzQI0nBI5GB8Sdq2nHkX+LTrWZN+mJcWIP6LEmxAXCWc0z8sLnOVEApVwgrXi4sBdN/nw4SZYrfyN4ZQp9EDI38XEOW7cjx2jG0MAaG3tQW2tHgAweXI8ZDJumCOIGIRDeGpP2obYM3BYLQz1lXz9GptigzI0OP7fUhWhMUOt5ru7UVdz4o8o8SbEBWZz4M5obsqIR09hKkwZgTWTcJrgJrGoKHAnWTlwoNG+HWiJtykjHub8zIAqm8LJmYRj84OZcLx7IHUzD7S6VZh4nwmSCdYaqgDLuUbUlNzAS7oDrYxyHOzLvVVVdaC72zTMEYT4Fq32SogLysvbYTbzF91A62becstCsUPwivQgSbz372+wb0+ZEouyhiF2lpiWmxfCaohCu7pd7FA8RthVVTgbfTAL1PHdTnVrAOSpqfkcOBnAbMEzs7lwIrmUvMBLvAPx+j9mjBZHjrSAMaCkpBUzZiSJHRIhdoHTbEeIF5WUCCdWo6XEpCA5l4NMxt80HT8eyIk33+KtUilQWBglbjBkWDHxRsjl/EOhw4cp8QbOT7wDo+UtEIWqOSSem2Ct4RRgDoLGROEDhkBs8Q5EwusgdTcn/oYSb0JcQEuJSY8ylEN8Bn/TVFragZ4es8gReV5raw8qK9sBANOmJSAkhKp0f6dQMOTnawDwk/8YjYE78Z+r+tbwVihk9GDTzwknWGuqCfz6pq/Fm+OApBxKvKWgoMAxOSPNbE78TeDXmoR4gLDyDrSlxJQ1zVCVnIGyJvCWN0o+d6NktTIUFQXek2/h+O6ZMwOvO52yphmKsuqAK5sTJsQAACwWW9DPvNvba7FPXFlYGAOVKnBGwAVi3Zpe6BjCU18Z2LeQFrNjYrX4dEClFjkgLwjEMto3xhugFm/ifwK71iTEQ/pujkNDA29G89j1O5CyaiNi1+8QOxSPE47JO3AggAY/n9PXzRwAZs1KFjES74h9dwc0L7yF2HcDq2xOnBhj3w72cd5FRc2wWPi/0+nTE0WOxrMCsW4Vzp1RXxHYt5CNVYD1XEcp4QOHQBKIZTQlRQ2NRgmAlhQj/iewa01CPKC314ry8nYAfDfzQJrRPNCljXEk3sIkNVAIW7xnzQq8Fu9ANXGi4+HdoUPBPbP5jz86yvCMGYGVeAeivgnWgMBPvIUTqwkfOBD/xnGcfchKba0een0QTEZAJCOwa01CPKCysgs2G38BnjiRxh9KSWKmDTI5n3zv2xdYLd6MMfuM5tHRKuTmRokbEHHZ+PHCFu/gTrwPHnT8/6dPp4dH/k6p4pCUxW83neZgsQRuQiqcWC1QW7wDlXBIYN9QFkL8ASXehAyjvLzTvj1xIs24KyWKEMe6yWVlbWhr6x3mCOk4fVoPnc4AgB/fzXF0YygVkZEhyM/nW72Lis7au1oHo77EWybjMHky1a9S0JeE2qwcWppCRY7Ge4QTq6XlU/0qJcJJGqm7OfEnlHgTMoyyMr19m1q8pSc+qce+LezWKnXUzVzapk3j16vu7bXg5MngbJHp7bXYJ64cNy4WanWIyBERV2SOcyShzY1hIkbiPRaTY2K1hEx+KTUiHRMmOO7VaII14k8o8SZkGOXlwsSbWmSkJj7J0codSN3N+7qZA4E5sVqgmzbNMZ45WCdYC+SJ1QJZ5njHrWOgJt4Np/gl0wAa3y1Fwq7mtKQY8SeUeBMyjLIyvqt5dLQKycnhIkdD3BWf6GjxDqQJ1oT/l0BcSizQTZ2aYN8O1nHeNLGaNCVnA0oVv93UqBI3GC9xGt9NibfkJCWFIzqaL5vU1Zz4E0q8CRlCa2svmpr4McITJ8bROFoJ0kSZERXFLy2yb18DGGPDHOH/rFabfWxsenokkpLogZDUOCfewdniTROrSZNcwdnHeXd1KtHc3DPMEdJz+qRj3gVKvKWHn9mcb/Wur+9Ce3vgzO9CpI0Sb0KGcOyY40kpje+WJo4DpkzhL8BNTQbU1nYOc4T/Ky1ttS+RQuO7pSkuTo2MjEgAwOHDOvvKCcGEJlaTLuE470OHAq8rb1+LNyfjl1Aj0iMc502t3sRfKMQOgBB/JqysA3V8d8PD14sdgtdNnRqH77/nx0Tv39+IzEytyBGNjnCseiB3M29YcT2iDFFoV7eLHYpXTJuWiNpaPbq6zKioaMOYMTHDHxQggmFiNae6NcCeq2SOFybeZ/GrX4kXi6eZjAz1lfx2YkZgT6wWyNf/8xPvuXNpLhQiPmrxJmQIzok3tXhL1dSpjolWAmGCtT176u3bc+emiBgJGQ3hBGuHDwdXd3PhxGo0vlt6ss5LvAPJmVIGm5XfFj5gINIyaZKjsaSoqFnESAhxoMSbkCEIu5oLn54SaQnUxFuhkGHGjMBt8Q50fUuKAcE3wZpwYjWa0Vx6tHEctHH8g5MjR1pgtQbOWvQ1JxzdE7LG022yVAkbS4qKAuvhEJEuqlEIGQRjzN4VMjNTA40mVOSIyEjFxqqQk8N3L//xRx1MJqvIEY1ca2sPiov5cjltWkJAdtENFsIW7x9/DK7EmyZWk77UMXyy3d1tsddJgaCm2JF4C8eyE2mJilLZ59EoKmoOiIlVifRR4k3IIGprO+0TWAnXhAw0yU9tQM4vXkTyUxvEDsWr5s9PBcCPLZVyt94ffnC02M+blypiJN6XvGoDYn73BJJXBWbZTE6OQEpKBAC+BTiYJlgLhonVAr1uTRvjaOUW1ktSV32uxVsZBiRlixyMlwV6Ge3rbq7Xm1BTI/2JVYn0UeJNyCCom3lgmTfPMRZ69+46ESMZHeH4buH/iUhT36z0nZ0mlJW1ihyNbwTDxGrBIL3AkXgHwhAeAOg4y9B+7rls5lgOMjm1eEuZcJy38J6OELFQ4k3IIGgpscDS1+INSDvxFsZOibf0zZrlmGl3//7GIfYMHDSxWmBIzrGBk/Gtwz/8UD/M3tIgHN+dQd3MJc95gjVKvIn4KPEmZBDHjjlmwaQWb+kbNy4WGo0SAN9qLMXxXmazFfv38y1LmZkapKZGihwRGS3hcnAHDgRH4t1XhgGaWE3KQkKB2LheAEBxcQs6O40iRzR61U4Tq1HiLXXCxJvW8ib+gBJvQgbR1+KtUHAoKIgWORoyWnK5zL70VmNjN6qqOkSOyH1FRc0wGCwAqLU7UAhbfIUJaSATjgeeM4fKsZTFJ/OJN2OB8eCIJlYLLPn50QgNlQOgrubEP1DiTcgATCYrTp7kx1tmZ0dAqZSLHBHxBKl3N6fx3YEnKkqFgoIYAMCRI82SnnHfVX3jgUND5U4tUkR64pN67Nt790q7u7nVwnD6JJ94RycBmlhKvKVOoZBh/Hi+x2JZWRt6ewO/fiX+jRJvQgZQVtZqH4OYn0/deQOFMFkVJrFS4Ty+O7BnNA8mfd3NTSYrioqah9lb2lpaelBR0Q6AX06NHmpKW2KyI/GW4sNMoYYqwMQ34FM38wDSN0ePzcZQWakXORoS7CjxJmQAwi5JY8ZQ4h0oZs9OhkzG31BJ7SaRMYbdu/mHBWq1gloKA0jfzOZA4Hc3F85+PXt28hB7EimI1JoRH68CwD/MtFptwxzhv6qPO2KnbuaBQ3itLC2lxJuIixJvQgbgnHhrRIyEeFJEhNK+ZvDx42fR3t4rckSuq6rqwJkz/E3DvHmpUCio+g4UwgnWAn1mc2HiPWcOJd5Sx3HA7NkJAPgl8aQ8jrbqGE2sFoicE29ay5uISyF2AIT4I+GM5oHe4t1y80LIDEbY1KFih+IVJqMJOp3O/v2UKVE4fLgJjAGbNp3AT34y+FhptVoNrVbrizCH9f33p+3bixalixiJ77TctBCathB0RpvFDsWrpkxJgEIhg8ViC4gJqoQ6OjpgMBjs3+/YUW3fzs6Wo6Fh4BZ+nU4Hk8k04s89/+/eVaP9XKFAr1v7zJoVjy+/rAUA7Np1BlOmJIgc0cicKuIT75BQIK1g4MTbH8qVJwVDGZ00ybEqTVkZJd5EXJR4EzKAo0f5xDsyUomUlDCRo/EuU2bgdlnu7e7F0aKjWP3KaqjD1ACA6sZIAPz46Kdf+BjfHhh8TG1MRAweeeARv0i+t293JN4XXpgmYiS+Y8qMhyU+CiZ1u9iheJVKpcDkyfE4eFCHkhJ+WSaNRvo3wh0dHVj57Eq0dvETVTIG7NmbD0AOldqCf7/7NLhBGhYN3QYUlxUjfQQPmQb6u3fVaD73fE51q/RWL3TZrFmORHvnzjr8/vfTRIxmZNp0DG3nnnlljuOgCOlfMP2lXHlSIF//+yQkhCMxUQ2dzoCTJzsluZQoCRyUeBNyntbWHpw+zXfpnTQpDtxgd4bE75mNZpiYCTGTY5CQwt8cRk8Gvvsf//NWfRQyFg38YKW7vRstR1pgMBj8IvHua/FWqRROXZNJYJg5MwkHD+rAGHDwoA4/+UmG2CGNmsFgQGtXK2KnxCI8Khxn6ziYjPxkapkTgMwh/o+6ah2MJ4ywmC1uf+5Af/euGs3nBqtx46IQERGCri4zdu48A8aY5K6bfa3dAJAzeeDYqVxJ16RJ8di2rQbt7WY0NnYjLU38azoJTpR4E3Ie4azCUu0yR5yFa8OhjeMvtNo4IDHLDF01UF8hh0qtQah64ButFrT4MMrBVVd3oLa2b3x3CkJDqeoONLNmJeGVV44C4NdDDoTEu094FP/3V3rABoBfzidvihLauMF7E+lbRz8JkvDv3lWe+Nxgo1DIMG9eKrZurUZDQzeqqjqQkxMldlhuqRIm3pOGfmhA5Up6+hJvADh2rIUSbyIamp2HkPMcOeJIvIVjgwJV7Ds7kPzUBsS+s0PsUHwmbwpf9dmswKlj/t/tLBi7mQNA7PodiHz+v4hdH/hlc9Ysx0RjgTqzec0Jx99aMMwaHUx16wUXOJY33LnzjIiRjMypIn5Gc04WXBOrBUsZFU6wJpzDhxBfo8SbkPMcPdpk3w6GJZuUtc0IO1kHZW3wXIzypjpurCoO+3/iLZxY7cIL/WuMoDcpa5sRUl4TFGWzsDAG4eEhABBwE6z1qSk+l9xwQMbYwE9ugqluXbDAkXjv2iWtpRoNeoaGU/x2ah6gCg/8stknWMqoc+It3Zn3ifRR4k3IefpavGUyDhMmBH6LdzBySrwP+X/ivX0734IUGiqntY8DlFwuw4wZiQCA2lo9Ghq6RI7Is0y9DPWV/HZiVnAlN8Fg1qxkhITwt5Q7d0or8a4+ztA331bOJLotDkRjx8ZALufrHEq8iZiohiFEwGSyoriYH9dbUBCNsDAaSxuIImM4JGbx26dLGXoN/pt819Z2oqqqAwC/7rFKRWUyUM2d61jabs+eehEj8bwzpQw2fnh3UHQzDzZqdQimT+cfHJWWtkKn6xY5ItedcmN8N5Gm0FAFCgtjAADFxS0wm60iR0SCFSXehAicPNkKk4mvkGlitcAmHOctnFjH3wjHdwfL+t3Bat48R3fdPXuk1Wo4nJpix99Y1ni69QhEwmEwwuEx/k6YeGdT4h2wJk7kezCazTaUlraKHA0JVnT1I0RAOL578uTAH98dzKQyzrtvJlaAEu9AN3euYxhBoLV4VwfZxGrB6KKLHDPxf/ttrYiRuM5kZKgt4ctmbAqgjaOyGaj6Em8AKCqi7uZEHJR4EyJw5Igj8aYW78CWN81xg1Xup+O8GWPYurUaABAeHuLUIkoCT1ycGmPGRAPg1/Lu7Q2MNX8ZA6rOrR4QqgaSskUOiHjF/Pkp9nHeUkm8q48zWEz8dv40SroDmXDOHmEjCyG+RIk3IQJHjzpm9pw8mRLvQBYZzdkTgNOlDN2d/pd8Hzt2FjqdAQDwk5+kQ6mUixwR8bb58/mHK2azDQcP6kSOxjPadBw6+akzkDWBg0xOCU4gCg9XYs4cfp6Ciop21NZ2ihzR8MoPOur9/Gl0SxzIhI0phw9T4k3EQbP0EHIOY8w+o3liohpJSeGwWmkCjkBWMEuGxiobmA0oO8Aw9WL/Sgj6WrsBYPHiLNHiIL4zb14K3njjOABg9+46eyIuZbUljoSGJq8KLCajCTqd4wHRzJnR9nW8N24swvLluYMeq1arodVqvR7jUIS9nfKoxVvyzi+PQjKZFdHRIWhrM+PgwUbU19eD4xy/c38ojyTwUeJNyDn19V1oaekBEFyt3foFY9FbmApzvEbsUHxu7GwO2z/gt0/ut2Hqxf7V4hHsibf+grFAbi70yUqxQ/GZefMCb2bz2mJHT41gSrwDvW7t7e7F0aKjWP3KaqjD1ACAxrowAJkAgJde3YLjNQ2DHh8TEYNHHnhEtGSnt9sxvjsxKzjHdwdSGR2oPArJOBniEvLR1sahtdWIP/2/JxAe6RjOI3Z5JMGBEm9CzhGO7w6midW6FowTOwTR5EzmEKIEzCbg5H4GxpjTE3Ax9fSYsWMH33KUmamxj/0NJl0LxkFhiEKXul3sUHymsDAWUVGhaG83Ys+eOr8qkyPV1+ItkwMZY6X9f3GHU93qfyNZRs1sNMPETIiZHIOEFP5hdYoZ2PoZg9nEoakpEukXhmCg4tvd3o2WIy0wGAyiJTqVRx1L3AVrN/NAuv4PVB6FOHDIqQlFeSk/qF+WlIaMmTYA/lEeSXCgxJuQc4Tju2liteCgDOWQO5XDyX0MHc1AYxWQnCN2VLwdO87AaOTvChcvzpJ88kVcI5NxmDcvBZs2VaG5uQeVle3Iy5PuQ5feHjmaz/BJTdoYDqFhVI4DTbg2HNo4R7KSM8WC0v0MnS0ymHo0SMgY+HfeghZfhTgg4fjuMdOpXAaK88ujHQNyCkIB8Il3m04NbZyjN47Y5ZEEh+B8xEfIAJwnVgueFu9gVzjbccN1cp9NxEicOXczzxQvEOJzzut5S7u7ua4+zL4dTN3Mg1m+04oR/lOnnq/sIB8bxwG5U6lsBoOMXEd7Y11ZAHZDIX6PEm9Czunrah4aKkdBQYzI0fhOxM5iRG/8ARE7i8UORRSFsxzVYMk+/7kQb93Kr98tk3FO6+MGk4idxQj78vugK5vCcd67dtWJGMnoBXPiHax1q7D1uPSA/9SpQt2dQH0Fv52aD4Rrgqts9gm2MpqYKofyXJV0ptw/yyYJbJR4EwKgu9uE8vI2APxajwpF8PxpRO4sQfSn+xG5s0TsUESRmAlEJ/Lbp4oYTL3iX4yrqztw/PhZAMDMmUmIiQkb5ojAFLmrBGFf7UDkruAqm7NnJ9vroO3bT4sczegIE+/sIEu8g7VuTRvDQX1urq6yHxmsFvHr1PNVH3d0Mc6fHjzX+/MFWxmVyTik5vL1UGsDYPDDZURJYAve2oYQgaKis2Dn6l/qZh5cOI5D4Sz+QmwxARWHxb8Qf/55pX372msHX46HBCa1OgQzZyYBAMrK2tDQ0CVyRCPT02PBWR2feMenA5HRwZV4ByuZ3FGn9nYDVcfEr1PPV3lYkHjTMmJBJXWM4/ddV+F/ZZMENkq8CQFw8GCjfXv69EQRIyFiGDvHURUe3yX+hfjTT8vt20uW5IkYCRHLokXp9u2+2e2l5siRFths/E1u9kRKboKJsE4t3it+nSrEGFB+iI9PoQTyaHx3UEnLd/y+z9A4b+JjlHgTAuDQIcdSYtOnJ4kYCRFDwSx+WTEAOL7LBptNvItxa2uPPdHKzY3CuHGxosVCxHPhhWn2bal2N9+9W2ffzptKtxvBpHA2Z19GrMSPJq0EgLazoehs4ctj3lQOShUl3sEkVZB419E4b+JjdCUkBMDBg/wNolzOYdKkOJGjIb4WGsah4FzXyM4WoOaEeBfjTZuqYLXyn79kSS4tIxak5s1LhVzO/+63b5dmi/fu3Y6eRNSdN7hERnNIL+R/5w2VQHuT/yQ4p6vD7dvj51G5DDbJ2YDs3EgDavEmvkaJNwl6vb0WnDjBT2Q1blwswsJCRI6IiGHiQkd1WLRDvIvxZ59V2Lepm3nwioxU2oe9FBe3oKmpW+SI3GMwmHHoEL8ubkySDdGJlOAEm7FzHL/zkh/8J8E5XR1h3xZ2iSfBQaHkkJTNbzfVAiaj/5RNEvgUw+9CSGDbs8fRwjh2rAYNDQ32n9lsNuj1ejQ2NkImc75A63Q6mEwmn8ZKvGfCfA4yOWCzAsd22HDhMt/HYDRasHlzFQAgNjbMaT1nEhhMRhN0Ot3wOwKYPj0a+/fzrcaffXYcy5YVQqvVejM8j9mzpx5mM9/FOGuif3U1Jr4xdg6HLW/w2yU/2DD3WvGT3PZ2I5rOzbSfkAHEpdIDoWCUms+hvoLBZgUaTzFo492rm8+nVqslUzcTcVHiTYJaR0cH/v7s2wD4tU9qm/bisdWb7D+XcTLkZeahoqYCNuZ882joNqC4rBjpgkmQiHSFaznkTuZQfojhbB3QVOP7G7Jvv61FV5cZAHD11TlBtaxdMOjt7sXRoqNY/cpqqMPUw+5fWx8OgK9f1rz0OcprN+CRBx6RxA3ed9/V2rdzJlpFjISIJaOQQ7gW6O4ASn9ksJgZFCHiJro7djSCMT6GsXOpfg1WafkcDvyPb3A5UwaEqt2rm88XExEjmbqZiIsSbxLUDAYDak47Eurxl2mRMTbS/j0HDlpokZ6VDgbn7ki6ah2MJ4ywmC0+i9cbTBnxTv8Gs4kL+cQbAEr2yZHj4wnuP/64zL5N3cz5MqmwKmDKiBY7FI8wG80wMRNiJscgISVh2P0TZgJff8HAbByaWyLR2lUBg8EgiZu7b791JN5ZE4Iz8Q72ulUm51A4m8PBrQxGA1B5hKFgpriJ97ff1tu3x82h1u5gLaNpgiXFzpQzZIx1r24W6m7vRsuRFsnUzURclHiToNfSpAIAcBwwZnoEQtWCizEDVAYVNGoNcN41Wt+q92GU3tNyy0KxQ/AbExfIsHEN/yCmZK8COdf57rONRgs2bOCXEYuICMHll2f57sP9VMvNC2E1RKFd3S52KB4Vrg2HNm74GzRtHJCaZ8aZMqD5jAK9PdJoodPrTThwgO8ir402IjJG5IBE4lS3Bukw0okXyHBwK//g5ej3DAUzxYvFZmP2xFupYsidTIl3sF7/nWY2F0yw5mrdfL4WtHgkLhL4pHEVJ8RLjEYr2s6GAgASMuGcdJOgE53IIWMsXwYaq2Vob1X67LM3b65GR4cRAHDddfk0yR8BAORPc1ymG06HD7Gn/9i164x93ozkdIPI0RAxjZ3jWKqxaIcNNqt4TyB++KEeZ8/2AgByJlmhUNL1PlipwjnEnZtCpb6CwSrtjotEQijxJkGttLQDNht/8RV2PSLBa9qljnJQcVLjs899770S+/bPf17os88l/m2MoGvumVppJN7ffedYdzyFEu+gFqrmu5sDQFcbUHVMvMR7wwbHUJ6xc4Jz+ANx6FvuzmwCWuqpAzDxDUq8SVA7dqzVvp1eEJyJt7KmGaqSM1DWNIsdil+YdrEM3LmasfKkBox5/0axq8uEzz+vBMDPZn7ppZle/0wpUNY0Q1FWHdRlM3cyB8W5FsP6mnCflMfR+uYbx/jupNTgTbypbuVNXuS41Tz6vTjllzGGjRv5oTycjKFgFiXeQHCX0YxCxz2frpoSb+IblHiToCZMvIO1xTt2/Q6krNqI2PU7xA7FL2hiORTMONdC06nEgQPevyH56KNS9PTwfd1uuGEMQkLkXv9MKYh9dwc0L7yF2HeDt2wqVRxyJp4rj/oQnDrl33NL6HTdOHSIX5JnwoRohKmDN8GhupU3bh4H+bm8pmiHDTab75Pvw4ebUF3dCQBISetGWMQwBwSJYC6j6YLEu7GahnYR36DEmwQ1SrzJQKYvdlSNH31U5fXPW7fuuH37V78a7/XPI9JSMMtRN+3Y0SBiJMPburXavv2Tn6SIFwjxG+pIDmPOPcxsbwJqS3yfePe1dgNAVl6Xzz+f+J+0MRy4c1VrYxUl3sQ3KPEmQctstqK4uA0AEJtigyqcEm/Cm7SQg1LF3xx++mk19HqT1z7r5MkW7N5dBwAYPz4Ws2cne+2ziDQVzHRcqrdvbxQxkuFt3lxt3/7JT6gsE56wu3nRdt8m3owxfPDBSQD86iWZuf7da4T4hiqcQ3wGv918RgGbjVIi4n1UykjQKilphdHILx2VnGsbZm8STELVHCYu5Lt+d3db8O67JcMcMXLr1h2zb99xx0RwHD0AIs5S8oBwLZ+s7NnTCLPZP7tvW602bNlSDQCIjFRi+vTgWhuYDG7CBRxk50bQHPraBpsPL7n79zeioqIdADB/fiLCwv3z74f4Xt84b5uVg9EQpOseEp+ixJsErYMHHS1HyTmUeBNnMy5zrC/y738f9cqkVj09Zrz55gkAQEiIDLfeOs7jn0GkTybjkDOJTxa6uizYv98/W70PHdKhpaUHAHDJJZkICaFbDMKLiHLMbt7eBFQf913ZWL++2L69dGm2zz6X+D/hOO/erjgRIyHBgq6KJGgdPKizb6dQ4k3Ok5LLEJfIJxGHDzd5JdlZv74EZ8/yn3HDDWMQF6f2+GeQwJA7xdFKJxxH7U+E3cwvvzxLtDiIf5pxmXB2c9/MIm2x2PDBB6UAgNBQOa66Kt0nn0ukIYMSb+JjlHiToOVIpBhS8ijxJv2NndRu337uuQMefW/GGNasOWj//r77pnv0/UlgyZ3iqKM2bTolYiSD27zZMRHh5ZdTyyJxNuECDqpzS9EX75HDYvb+sJqvv65BUxO/pN011+RCo1F6/TOJdKTmO4ZAUOJNfIESbxKUenstOHKkCQAQFWOy3wwQIpRT0In4eBUAYMOGclRUtHnsvb/+ugYnTrQAAObPT8XMmTQRFRmcJpYhJr4XAPDjjzrU1/vXzMxtbb344Qd+xvVx42KRkaEROSLib5ShHKZcxCfbpl4OVRWRXv9M4RwaN9881uufR6RFqeKQlMVvGw3RMBtFDYcEAUq8SVA6erQZZjPfghSf2CtyNMRfKRQMd95ZAACw2Riee+5Hj7wvYwxPPvmD/Xtq7SauyMxxJNtfflkpYiT9bd1abV+fmbqZk8HMusJx23myKMqrn6XTdePTTysAAImJalx1VY5XP49Ik2OctwxNtb4ZAkGCF5UwEpT273eshRuX1AMgeNdwbHj4erFD8Gu/+MUY/POfxejqMuONN45jxYrZSE0dXReJb76pxY4dZwAABQUxWLIkzxOhBpyGFdcjyhCFdnW72KH4hYwcPQ7v47tDfv55Jf7v/yaLHJHDJ5841km+6qpcESPxH051q++XrvZL2RM5JOcADaeApgY1TpxoQ3Kyd3r7vPHGcVgs/AP222+fiJAQuVc+R8ro+s8n3vu+4v9AGytDgEtEDogENGrxJkFJOFFWfBK1eJPBabVK3HXXFACA0WjF44/vHtX7Mcbw2GO77N//5S/zoFBQVUyGF5tgRFJSGAB+qEJ3t/fWl3eH0WjBpk38+O6YGBUWLkwTOSLirziOw/zrHPXdW2+VeeVzbDaG114rsn9/550TvfI5RPoyxjrmGmisovZI4l10t0eCUl+Lt1IpQ0wcJd5kaH/+8yxERYUCAP773xM4duzsiN9r48Zy+1jY8eNjsWxZgUdiJIGP44BLL00FwD8E2ratRuSIeN98Uwu9nn8IcM01ufQgiQxpxmUyKFV8C+OGDdVob/f8Nfirr07h1KkOAMCll2YiJyfK459BAkNKDgeZ/FyL9ylKvIl30dWRBJ22tl6UlfGTZE2YEA059T4jw4iJCcPDD88GADAG3Hff9yNa11uvN+Gee761f//kkxdAJvP+zL4kcCxe7GhN/vxz/xjnLexmvnRpvoiREClQhXOYtMgCADAYLHj55aMe/4znn3esGPHHP07z+PuTwKFQcohP48tjS4McvQYaF0K8hxJvEnR+/NHRzXzKFFo+IvmpDcj5xYtIfmqD2KH4tT/8YRoyM/mZmr///jQ++qjW7ff461/3oK6OnyDriiuyaWz3MJJXbUDM755A8ioqm33mz0+CWs23ynz5ZSWsVnGXQrRabfjsM34Cq7AwBS69NFPUePwJ1a2Dm7fEAo7jE5w1aw6ip8fssfcuKmrDzp11AIDCwhhceSVNqjYYKqO8pOxz5Y9xOH2SEm/iPZR4k6AjHN89bVqsiJEQKVGpFHj11cX271evLkF1dYfLx2/dWo3nn+dnRQ8NleOf/7wYHEet3cQ9KpUcixdnAQCam3uwZ0+9qPHs2VOP5uYeAPza3Wp18E5USVwXm8yQlacHADQ1GfDmmyc89t7r1jl6gjzwwEzqVUSGZU+8AdQUU+JNvIcSbxJ09u1zzGg+ZQol3sR1ixdn4fbbJwAAurstuO66z+xjW4dy+nQnbr75K/T1Tn/iifnIzY3yYqQkkP30p47u3O+/f1LESM7vZk49OIjrJs1ssW8/9dQ+j7R6Hzyow9at/MP1xEQ1rd1NXJKcI0i8T1DiTbyHEm8SVBhj9onVoqJCkZ0dKXJERGqee24R8vOjAADHj7dg2bLPh7xhrKvT45JLPsLZs3yr4NVX5+CBB2b6IlQSoJYsyYNKxXc3/+ijUvuSSb5mszFs3Mgn3nI5R+skE7fEJRhxySUpAIAzZ/T45z8Pj/o9H310t2B7jv3vhJChxCZbIZMbAfAt3iOZw4UQV1DiTYLK6dN66HQGAMCsWcnU1Ze4LSpKhc8+uw5aLd+ldvPmaixa9AEaGrr67Xv8eDMuvPAD+2R+2dla/Pe/V1DXRzIqGk0orroqGwDf3fzbb92fb8AT9u6tR01NJwDg4oszERMTJkocRLoefniqvT586ql9aGnpGfF7ffNNjX2m/6wsjV+tc0/8GycDwiKbAQCdLUBr4zAHEDJC9CiQBJW+1m4AmDUrScRIiJSNGRONF1+cgbvv/hFdXWbs39+IsWPfwG9+MwmLFqXDaLTiq69O4c03T9hbI3NytPj222UuJScdHR0wGAxux6XT6WAy+cfazsS7fv7zsdiwgW9tfu+9Evu4b196990S+zZ16SUjUVgYhdtum4B1646ho8OIBx/cjnXrLnf7fXp7Lbjrrq/t3//1r/OgVNKSJcR1qogmdLfzq0bUnGCITaYH5MTzKPEmQUU4sdqsWckiRkKkbtasWOzYsRxLlnyG06f16OgwYvXqA1i9+kC/fSdNiseXXy5Ferpm2Pft6OjAymdXorWr1e2YDN0GFJcVI31RutvHEmm58spsREYqodebsHFjOV5++VKfdqs1m6348MNSAPxs5rSMGBmpJ56Yjw8/LIVeb8Lrrx/HsmUFuOyybLfe48knf7D3LJo8OQo33ljgjVBJAAuLbLJvV59gmHaJiMGQgEWJNwkq57d422ydIkZDpG7SpHgcPHgrHn54p1Prdp+IiBDcf/8MrFgx2+WkyGAwoLWrFbFTYhEeFe5WPLpqHYwnjLCYLW4dR6QnLCwES5fm4a23itHZacLmzVW47jrfJb/bttXY5y249tpcREYqffbZJLCkpETg2WcvxG9+sw0A8Otfb8WhQ7ciLk7t0vG7dp3B00/vBwCEhMjwt79NhlxOIymJe8Iimu3b1cdpjDfxDkq8SdCwWGz48UcdACAjIxKJieFoaKDEm4xOfLwar712Gf72twuwdWs1KiraIJfLMGFCHBYvzhpxQhIeFQ5tnNatY/St+hF9FpGmn/98LN56qxgAsH59iU8T7//+17H80003UTdzMjq//vUkfPhhKb75phanT+tx/fWfY9u2nw3bXfzMGT1uuOFz+0PPP/95JvLzadJU4j55iAkxyRa0NihQV85gNjKEhFJ3c+JZlHiToHH0aBO6u/nZp+fNSxU5Gv/RcvNCyAxG2NShYociaUlJ4fjFL8aLHUZAablpITRtIeiMHv0yQ4Ho4oszEB8fhubmHnz2WQWamw2Ij3etlXA0mpsN9mXEEhLUuPxy97oFBwuqW13HcRzefPMKzJz5Dhobu7Fjxxn88pf/w3//e8WgyXdDQxeuuGKDfcLUiy7KwKOPzkFVVeWA+5P+qIw6S8nnE2+rBThTzpA9gRJv4lnUF4cEjT176u3b8+eniBiJfzFlxqN3bBpMmfFih0KIE1NmPCxjsqhsDiIkRI5f/pJ/2GM22/DWWyeGOcIz3n67GGYz38L4y1+Op0msBkF1q3vS0iLx6afXITSUL0/vv38SV165AWfP9p9o8tixZsyf/x6OHz8LAMjM1OCDD66GQkG3te6gMuosJY/W8ybeRTUUCRq7d9fZt6nFmxASCH7960n27ddeO+b19WcZY/jPf4rs399xx0Svfh4JLrNnJ+PDD6+xz4nxzTe1GDPmdTz00A588UUlPv64FLfd9j9Mm/Y2qqo6APBJ97ZtP3N5TDghgxEm3jTOm3gDdTUnQaOvxTs8PASTJtHTXUKI9I0ZE4MLL0zD9u1nUFraip07z2DhQu/Nar9z5xmUlPAz7i9cmIaCghivfRYJTtdem4dvv12Ga6/9BGfP9qCtrdc+edr5Jk2Kx6ZNP0VqKo3rJqMXl26FMgww9fAzmxPiadTiTYLC6dOdOH2an3hq9uxk6o4mEPvODiQ/tQGx7+wQOxRCnMSu34HI5/+L2PVUNocibPX+5z8Pe/Wz1qw5ZN/+v/+bNMSehOrWkZs7NwXHjv0Kv/rVeMjl/cfZajRK/OUv87B//82UdI8ClVFnMhmQOZYvb+1NQHszJd/Es6jFmwSF3btpfPdglLXNCDtZN/yOhPiYsrYZIeV1UMppebSh3HDDGDzwwHY0NnZj48ZyVFW1Izs7yuOfc+pUOz79lJ9ULTk5HD/7Ga2VPBSqW0cnKSkcb7xxBf7+94XYurUalZXtCAmRY8KEOFx6aSbU6hCxQ5Q8KqP9ZY7nUH6IT7hrTjBELaIJ1ojnUOJNgsKePY4Ly/z5NL6bEBI4QkMV+P3vp+LRR3fBZmP4xz8OYc2aizz+Of/852H0DSH//e+n0qRqxCcSE8Nx6620YgTxjazxjkS7+jjD5EXixUICz4j6265duxbZ2dlQqVSYPn06du7cOeT+27dvx/Tp06FSqZCTk4NXXnnF6edvvvkmOI7r99Xb2zuS8Ajpp6/Fm+OAOXOoxZsQElh+85tJCAvjn6WvW3cMra09Hn3/s2cNeO01flI1lUqB3/xmskffnxBC/IEw8a6iCdaIh7nd4v3BBx/g3nvvxdq1azF//nz8+9//xhVXXIHi4mJkZGT027+qqgpXXnklfv3rX+Odd97B7t27cddddyE+Ph7XX3+9fT+NRoPS0lKnY1Uq1Qj+SyQYdXR0wGDov+QIAHR3m3H0aBMAoLAwCgZDK/p21el0MJlMvgqTBJGhyuRQqEySkYiLU+OXvxyPV145iq4uM5577kesXLnAI+/d0dGBxx/fje5ufsbf5cuzYTK1o6GhfcjjqCyToZiMJuh0uhEdq1arodVqPRwRIUBENIeEDKCpFjh9ksHUy6BUUXdz4hluJ97PP/887rjjDtx5550AgDVr1mDLli14+eWXsWrVqn77v/LKK8jIyMCaNWsAAGPHjsWPP/6IZ5991inx5jgOSUlJI/xvkGDW0dGBlc+uRGtX64A/rz+thtXKPxRiiio8tvox+88M3QYUlxUjfZH3ZgEmwWe4MjkUKpNkpB56aBbWrTsGs9mGf/zjEO69dzri40e3xFJHRwce/utTePXVWAAyyOU2GBX/w2Orvxj2WCrLZDC93b04WnQUq19ZDXWY+2U0JiIGjzzwCCXfxCtyJnNoqmWwWoCaYob8aZR4E89wK/E2mUw4ePAgHnroIafXFy9ejD179gx4zN69e7F48WKn1y677DKsW7cOZrMZISH85BhdXV3IzMyE1WrFlClT8Le//Q1Tp04dNBaj0Qij0Wj/vrOzEwBgtVphtVrd+W/BarXCZrO5fZyYKGaHrq4utHe3I25KHMKjwvv9vOpDRzEfd1E4Mhdl2r/XVetgOWmB1WwFBupRxARf5+HAQS6XgwM38LFD8NqxQ8Tr0ucOEYvfxjzSz3XhWBknG7DMDleWhyuTQxm2TA4Ts5TOs8vlcYC4/fLvTxirF+qMwcpjn7S0CPz61xOxdu1RdHebsWrVPjzzzMJh33uo8tzV1YUd3ytgsfAj02ZcbsO4a1ybJ8NrZRkIvro5wGK2GC2wyqyInRyLhJQEt47tbu9G69FWdHV1ISIiwulnw9XNNpsNMk4mmfPs03Ih2Cfg/v7cjDlnkgw/fMGXocojDPmDpyMu1c0jJbV7fanFC3guZlePdyvxPnv2LKxWKxITE51eT0xMRGNj44DHNDY2Dri/xWLB2bNnkZycjMLCQrz55puYOHEiOjs78Y9//APz58/H0aNHkZ+fP+D7rlq1Cn/961/7vV5ZWdmvIh6OzWZDa2srKioqIJNJY5kpitlBr9cjLzMP2igtVGH9hyc0l7UD4LtIzpmahIQwx4RAUYlR4OZwSAtJQ6Rh4CVJVBYVonqi+r0uC5PhJ3N+MuSxg/HmsYPFO9ixCqvC/m+UYeDj/C1mT33uUFRQITQzFPX19dDr9U4/G64sD1cmh+JKmRyM1M7zcMcpbAr7v+eXTX/9+wO8U2cMVR6Fli+Px7p1MhiNNvzrX4dw6aWRyM4e+po4VHk+cqQRxUf5/0uIErjx5gREh7k2qZo3yzLg/3WzU93aE+V3f3+uHOvtmAviChAZ5t6xvehFTGbM6OpmaKEyuFc3i3GevV0uBrv+B8Lf32hinjrGinfB91g7fViOqOX9j7G/p4t180hI7V5favECnou5q6vLpf1GNKs5xzl3uWCM9XttuP2Fr8+ZMwdz5syx/3z+/PmYNm0a/vnPf+LFF18c8D1XrFiB+++/3/59Z2cn0tPTkZubC41G49b/x2q1oqKiAnl5eZDLpTFLK8Xs0NjYiIqaCqRnpUOjdv7d22wM5Sf5pYgiY4CQnE60C8pjXV0dvvvhO4RPCUeyOrn/mzMgikWhPawdOK+ID3vsELx27BDxDnZsmNyCEAAWuQXt6nZJxOyRzx1GZ08nTtecxs033NxvGMxwZXmoMunNmKV2noc7Lkx2rmzK+pdNv/z7A7xWZwxVHoXy84H77+/EqlX7YTYzPPfcKWze/NMhr9GDlWfGGO64Yz9sNv7YS26VgUvXo93FmKV4nj15rFPdGtbud39/wx7rh3UGEFx1s7fP8WDX/0D4+xtNzIpshqgEfi3v8pNmtCjbIFcMXIe6WjePhNTu9aUWL+C5mPt6Xg/HrcQ7Li4Ocrm8X+t2U1NTv1btPklJSQPur1AoEBsbO+AxMpkMM2fORHl5+aCxhIaGIjQ0tN/rcrl8RCdOJpON+FixUMyO97QxGxhYv8pUVwP0nnsIlT2RAyc77yEQGKxW64DH2nGCL3ePHYRXjx0k3sGO1S8Yi97CVJjjNUPG4k8xe+xzhznWxmz2Mnu+ocryUGXS2zFL6TwPd5x+wVggLxf6ZKV0/v4Ar9UZQ5VHoUcfnYt33z2JmppOfPNNLT74oAw33zxuyGMGKs+vv34Me/bwE1NGJ9pw0U0Kj/5+R32sn9fN/epWP/v7c+lYP405WOpmb5/jwa7/gfD3N5qYOY5DziQOh75mMPUAZ8oZMscN/Kbu1M0jIbV7fanFC3gmZlePdSvxViqVmD59OrZt24alS5faX9+2bRuWLFky4DFz587FF184T8KydetWzJgxwz6++3yMMRw5cgQTJ050JzxC+qk8YrNvZ09wsxYPEl0Lhr4hJ0QsXQvGQWGIQtcQPTFIf2p1CP7xj4tw3XWfAgB+97uvMXt2MvLyol1+j9LSVvzhD9/Yv7/iThNCBnjYTQbnVLe6OV6VEF+g6//gcibziTcAnDrKkEmniniA253Z77//fvznP//B66+/jpKSEtx3332ora3Fb3/7WwB8F/Bf/OIX9v1/+9vfoqamBvfffz9KSkrw+uuvY926dXjggQfs+/z1r3/Fli1bcOrUKRw5cgR33HEHjhw5Yn9PQkaq4ojjbid3KiXehJDgsGRJHm69lb9T1OtNWL78S3R3u7a0V2enEcuXfwGDgR+mUzChDQUzbcMcRQghgSN3siNFqiyiJ2fEM9we4718+XK0tLTgiSeeQENDAyZMmIBNmzYhMzMTANDQ0IDa2lr7/tnZ2di0aRPuu+8+vPTSS0hJScGLL77otJRYe3s7/u///g+NjY3QarWYOnUqduzYgVmzZnngv0iCFWMMlecSb1U4kJpHiTchJHisXXsJ9u1rQFlZGw4d0mHp0s/w+edLoVINfunv7bXguus+xdGjzQCA3FwNZl9YCoCWBCOEBI/ELECtAQydQFURg83GIJPRfSQZnRFNrnbXXXfhrrvuGvBnb775Zr/XLrzwQhw6dGjQ93vhhRfwwgsvjCQUQgbVVAvozy2jnDOJG3RijGAXsbMYIc2dMMdrqNsZ8SsRO4sR1mCCJVmJroVUNt0VEaHExx9fiwUL3kdHhxHbttXg6qs34t13r0JCQv9l7hobu/Hzn2/Czp1nAAAxMSq8/vpCvPXJfl+HHhCc6tYLqPwS/0PX/8HJZPw47+O7GLo7AF01kJwjdlRE6qQx1zshI1Bx2NE1MncKJd2DidxZguhP9yNyZ4nYoRDiJHJXCcK+2oHIXVQ2R2rixHhs2vRThIfzc6p8800tJk9+C2+8ccze9byry4SPP67FjBnv2JPu8PAQbNp0PfLztaLFLnVUtxJ/R2V0aDmTHPeOp4pouA0ZPUq8ScCqFI7vpsSbEBKk5s1LxebN1yMpiW/lbmzsxu23b0FU1L+QlLQWsbFr8dhjRWhsNAAAUlMj8O23yzB7tnvL+RBCSCDJmSxIvI/SOG8yeiPqak6Iv2OMoeIwX0mGhgHpBZR4E/eZjCbodLp+r9tsNuj1ejQ2NkIm6//8UqfTwWRybSIrQnzhggvScOTIL3DHHVvw1VenAAAWiw06ncFpv2uvzcVrry0esCs6IYQEk/QCDkoVYOoFKo8yMMbAcXQ/SUaOEm8SkM6eATpb+O3siTS+m7ivt7sXR4uOYvUrq6EOUzv9TMbJkJeZh4qaCthY/+5nhm4DisuKkb6IJqQi/iMxMRxffvlT7N5dh7ffLsYPP9SjtbUXcXFhKCgIw+9/Pxfz56eJHSYhhPgFuYJD1ngOZQcZ2puAlnogLlXsqIiUUeJNAhItI0ZGy2w0w8RMiJkcg4SUBKefceCghRbpWelgAyzQq6vWwXjCCIvZ4qtwCXHZ/PmpmD/fcfdotVpRXl6O/HzqWk4IIUJ50/jEGwDKDzHEpdI9JRk5SrxJQBJOrJZH47vJKIRrw6GNO2+CKQaoDCpo1BpggOKlb9X7JjhCCCGEeM2Y6Rw2vcZvl/1ow9xraHosMnJUekjAEY7vVqqA9EJKvAkhhBBCiHvSCzmEnhttVn6IH+dNyEhR4k0CTlMt0NHMb+dM4qAIocSbEEIIIYS4R67g7D0nu9qAxiqRAyKSRl3NScAp+9HRzXzMDEq6h2PKiHf6lxB/YcqIh8KqgCkjWuxQCHEb1a3E31EZdU3+dA4n9vAt3WUHbUjOkYscEZEqSrxJwCn90dENaMxM6tQxnJZbFoodAiEDarl5IayGKLSr28UOhRC3OdWt1DuV+CG6/rtmzHQZAL5Rp/wQw4U/EzceIl2UlZCAYrUwVBzi73DCo4CUXHHjIYQQQggh0pWUw99TAkDFYQablZ6kkZGhxJsElNMnGXq7+e0x0znIZNTVnBBCCCGEjIxMxiH/3NK0vV3AmTJKvMnIUOJNAkqZsJv5DCrerlDWNENVcgbKmmaxQyHEibKmGYqyaiqbRJKobiX+jsqo6/KnOxpyhPeahLiDMhMSUMoOChNvau12Rez6HUhZtRGx63eIHQohTmLf3QHNC28h9l0qm0R6qG4l/o7KqOuEjTmllHiTEaLJ1UjAMPUCVcf5yjAuFYhNpsSbEEIICTQmowk6na7f6zabDXq9Ho2NjZDJ+rct6XQ6mEwmX4RIAgx/Xwm0NACnjjIYDQyharrPJO6hxJsEjJpiGaxmfpu6mRNCCCGBp7e7F0eLjmL1K6uhDlM7/UzGyZCXmYeKmgrYmK3fsYZuA4rLipG+KN1X4ZIAwXEcCmfLsPtTG6wWfpK18fMp8SbuocSbBIyKQ451FambOSGEEBJ4zEYzTMyEmMkxSEhJcPoZBw5aaJGelQ42wBpuumodjCeMsJgtvgqXBJDC2Rx2f8pvl+xjGD9f1HCIBFHiTQJG+bnEWyanxJsQQggJZOHacGjjtM4vMkBlUEGj1gAD3AboW/W+CY4EpPzpHGRywGYFTu63AZAPewwhQtQflwSEzvYQtNTzxTl7Igd1JCXehBBCCCHEM1RqDtkT+fvLs2eAs3U0yRpxDyXeJCCcqQ63b4+dTUk3IYQQQgjxLOE95sl9/ecRIGQolHiTgHC6OsK+PXYOFWtCCCGEEOJZhbMd95gl+6jFm7iHMhQieT09FjSc4Wc21cYBKXkiB0QIIYQQQgJOSh4QEc1vlx9isJjFjYdIC02uRiTvhx+aYLXwz5DGzuHAcdTV3B0ND18vdgiEDKhhxfWIMkShXd0udiiEuM2pbqWGMeKH6PrvPpmMQ+EsDj9uYTD18EvZhogdFJEMavEmkvftt/X2bepmTgghhBBCvGX8PMe9Zul+mtmcuI6yFCJpjDF74i2TM1pGjBBCCCGEeE3hbA7yc32GSw/IwahHC3ERJd5E0k6ebEVVFb8uZ8ZYG8IiKPEmhBBCCCHeERbBIXcKf7/Z3iRDW0uoyBERqaAx3kTSPv20wr5dOMsqYiTSlfzUBoSdrENPYSqN9yJ+JXkVXzbDqGwSCXKqW1dQ+SX+h67/IzfhAg5lP/JN3bWnIobZmxAeJd5E0j77TJB4z6bEmxASuExGE3Q63YiONZvNCAkZeAogm80GvV6PxsZGyGTOHeF0Oh1MJtOIPpMQQgLV+PkybFzDr+NNiTdxFSXeRLLq67uwb18DACAmrhfRiTTIhhASmHq7e3G06ChWv7Ia6jC1W8eajCaUlpSiYFwBlEplv5/LOBnyMvNQUVMBG7M5/czQbUBxWTHSF6WPKn5CCAkksckcknOBhkqguVGFpqYeJCeLHRXxd5R4E8n64otK+3ZGbhcA925GCSFEKsxGM0zMhJjJMUhISXDrWF21Dp1HO6GZoBnwWA4ctNAiPSsd7Lx1r3TVOhhPGGExW0YVPyGEBJoJ82RoqLQB4PD113WYPDlH7JCIn6PEm0jWp5+W27czc/SgxJsQEujCteHQxmndOkbfqh/6WAaoDCpo1BqAG/hYQgghzsZfwGHb2/z25s1n8Kc/iRsP8X80qzmRpM5OI7799jQAIDlZjdgEo8gREUIIIYSQYJExlkNkDD88Z8eOBnR20r0oGRol3kSSNm+ugsnET6Z22WVp4GgVMUIIIYQQ4iMyGYexc/h7UZPJhi+/PCVyRMTfUeJNJOmjj8rs25dfniZiJIQQQgghJBiNn+dYUefjj8uG2JMQSryJBHV1mfDVV/xTxbi4MMyblyhyRIQQQgghJNhkjLVBpeYnn/zf/6rQ1UXLL5LB0eRqRHK+/PIUenr4Su7668dAoaDnR6PRcvNCyAxG2NShYodCiJOWmxZC0xaCzmiz2KEQ4jaqW4m/ozI6ejI5kJWrx8lj0ejttWDTplNYtqxQ7LCIn6LEm0jOhx+W2reXLy8QMZLAYMqMFzsEQgZkyoyHJT4KJnW72KEQ4janupUNvh8hYqHrv2dk5/OJN8B3N6fEmwyGmgqJpOj1JmzaxHczT0hQY+FCGt9NCCGEEELEkZRmQEwM32vgq69OwWCgXlpkYJR4E0n5/PMKGI38RBY33DAGcjkVYUIIIYQQIg6ZDLjiinQAgMFgwRdfVIocEfFX1NWc+I2Ojg4YDIYh93nrrSL79iWXxKGhoQE6nQ4mE01mMVKx7+yAsrYZpox4tNyyUOxwCLGLXb8D6qo2yLOjqWwSyXGqW2+m8kv8D13/Pee66zKxfn0FAOCdd4qxfDl1Nyf9UeJN/EJHRwdWPrsSrV2tg+5j7JXh62/yAMigDjfji+//ha92AIZuA4rLipG+KN13AQcQZW0zwk7WiR0GIf0oa5sRUl4HpdwidiiEuI3qVuLvqIx6zty5iUhLi8SZM3ps3lyN5mYD4uPVYodF/Awl3sQvGAwGtHa1InZKLMKjwgfcZ///FLBZ+a7lky8Gsi7KAADoqnUwnjDCYqabc0IIIYQQ4lsyGYebbirE6tUHYLHY8OGHpbj77qlih0X8DA2QJX4lPCoc2jjtgF/HdzmWu7hgaZj9dbWGnigSQgghhBDx3HLLOPv2O+8UixgJ8VeUeBNJ0NUy1Jzg12NJyQVS8zmRIyKEEEIIIYQ3cWI8Jk3il2j74YcGVFS0iRwR8TeUeBNJ+HGzzb498woqtoQQQgghxL/ccstY+za1epPzUQZD/J7NxvDjFj7xlsmB6ZdSsSWEEEIIIf7l5z8fC+5cp8y33iqGzcbEDYj4FcpgiN+rPMLQpuO3C2dx0MRSN3NCCCGEEOJf0tIicemlWQCAqqoOfPNNjbgBEb9CiTfxez98KehmfjkVWUIIIYQQ4p9+/euJ9u3//OeYiJEQf0PLiRG/1tXOcOQ7vptOuBaYcAG1dnuafsFY9BamwhyvETsUQpzoLxgL5OZCn6wUOxRC3EZ1K/F3VEa949pr8xAfH4bm5h588kk5relN7CjxJn5t/yYbrGZ+e9aVMoSEUuLtaV0Lxg2/EyEi6FowDgpDFLrU7WKHQojbnOpWGuZJ/BBd/71DqZTjV7+agGeeOQCz2Ya33jqBP/1ppthhET9A/XaJ37LZGPZ87uhmPu9aKq6EEEIIIcS/3XGHc3dzxujpG6EWb+JhHR0dMBgMA/7MZrNBr9ejsbERMplzEq3T6WAymZxeKz/IcPYMvz1mOof4dGrtJoQQQggh/q2gIAYLF6Zhx44zOHmyFTt2nMGFF6aLHRYRGSXexGM6Ojqw8tmVaO1qHfDnMk6GvMw8VNRUwMZsTj8zdBtQXFaM9EWOSmnPZ4LW7uuotdtbInYWI6S5E+Z4DXU7I34lYmcxwhpMsCQr0bWQyiaRFqe69QIqv8T/0PXfu37zm8nYsYNvQXrxxUOUeBNKvInnGAwGtHa1InZKLMKjwvv9nAMHLbRIz0oHO2/Am65aB+MJIyxmCwCgvYnh2E5+H00sMHEBtXZ7S+TOEoSdrENPYSpdeIlfidzFl00UplLiTSTHqW6lxJv4Ibr+e9cNN4zBAw98j4aGbnz6aQWqqzuQlaUVOywiImpGJB4XHhUObZy235cmVgNVmAqaWE2/n6k1zrM97vjYBpuV355zjQxyBSXehBBCCCFEGpRKOX73uykA+HmLXnrpsLgBEdFR4k38Tq/BMamaPAS4YCkVU0IIIYQQIi2/+c0kKJVyAPwka93dpmGOIIGMMhrid/Z9aUNvF789YzEHTSy1dhNCCCGEEGlJSAjHTTcVAgDa2414661ikSMiYqLEm/gVmw3Y/pFjUrVFy+UiRkMIIYQQQsjI3XPPdPv2Cy8chNVqG2JvEsgo8SZ+pfyAEq0N/HbhLA7JOdTaTQghhBBCpGnKlAT85Cf8jObl5W34+OMykSMiYqHEm/gNxoC9nzsmWVt0IxVPQgghhBAibQ8/PMe+/dRT+8AYG2JvEqgosyF+o6stA03VIQCAtDFAwUxq7SaEEEIIIdJ28cUZmDUrCQBQVNSML788JXJERAyUeBO/wBhw9vRU+/eX3y4Hx1Hi7QumjHj0FKbClBEvdiiEODFlxMOcn0llk0gS1a3E31EZ9R2O4/DII45W75Urf6BW7yCkEDsAQgDg1FEljN3RAPjW7vHzKen2lZZbFoodAiEDarl5IayGKLSr28UOhRC3OdWtdH9N/BBd/33r6qtzMXFiHI4dO4t9+xqwbVsNFi/OEjss4kOUeBPRMcaw94sI+/eLf0Wt3YQQQgghJHDIZHyr9403fgkAePjhnZg5Mwq9vT0D7m+z2aDX69HY2AiZrH8nZbVaDa1W69WYiWdR4k1EV7SDobGKH9udkGHBxAVULAkhhBBCSGD52c8KsGrVPhw92oyDRr6t4wAAL6tJREFUB3X41Z3PIT6jYcB9ZZwMeZl5qKipgI31X4IsJiIGjzzwCCXfEkIZDhGVxczwxctW+/fzb+gGx4WJGFHwUdY0Q2YwwqYOhSmTxnkR/6GsaYairR3KaDNMWVQ2ibQ41a00hpb4Ibr++55MxmHVqgW48sqNAIDvvw3Dr5+NhSYuvN++HDhooUV6VjrYeeNVutu70XKkBQaDgRJvCaHEm4hqz2c2nD3Db4dpGpA3jYqkr8Wu34Gwk3XoKUxFw8PXix0OIXax7/JlM4TKJpEgp7p1BZVf4n/o+i+Oyy/PxoUXpmH79jPobFei9KAWl9zcP/EGA1QGFTRqDTDACMwWtHg/WOJRNKs5EU1PF8OWNxxdZxKy9oOGdhNCCCGEkEDFcRz+/nfHxHbfvxeCni6agTEYUOJNRLPtLRu6O/jtsXN6EBZxVtyACCGEEEII8bI5c1Jw1VXpAICudg6b3+g/hpsEHkq8iSgaTjF8/wFfychDgAt+2iVyRIQQQgghhPjG449Pg1zB3wvv/NiGhlPU6h3oKPEmPmezMXz4jBW2c3OqXXKLDNo4etJHCCGEEEKCQ1paBCbP5Mdp26zAx89bwRgl34GMEm/ic/s3MVQd4yuWuDQ+8SaEEEIIISSYTJzeipgkvvGp8gjDj1so8Q5klPEQn+pos+FzwfJhP/uTHCGhNKMaIYQQQggJLgoFwxV3muzff/IPKzrOUvIdqCjxJj7DGMMba/QwdPLfT7uEQ8FMKoKEEEIIISQ4jZlhw7RL+EYogx74cDV1OQ9UlPUQn/nhS4YjP/BP9SKigKX3yMUNiBBCCCGEEJFdf58ckTH89ok9DAc2U+IdiBRiB0D8T0dHBwwGg9vH6XQ6mEymAX92to7h0386upjf+JAckdHUxdwfNDx8vdghEDKghhXXI8oQhXZ1u9ihEOI2p7qV7qGJH6Lrv2eYjCbodDq3jxPeN4drOfzsATlef5i/V964xoqciRyioj0aKhEZJd7ESUdHB1Y+uxKtXa1uH2voNqC4rBjpi9KdXreYGN76ixXGHv77OVdzmHABdbYghBBCCCHS1dvdi6NFR7H6ldVQh6ndOvb8++ZJC2WYcZkNP25h6O0G3vx/Fvy/5xjg3tsSP0aJN3FiMBjQ2tWK2CmxCI8Kd+tYXbUOxhNGWMwWp9c3vmhDbQn/uD8+WYbr/kBJNyGEEEIIkTaz0QwTMyFmcgwSUhLcOnag++Yb7pej5oQFzWeAM2XAB6924ZoHPR01EQsl3mRA4VHh0MZp3TpG36rv99q+TTbs+ZRfJiFECfz+UQ1U6m6PxEgIIYQQQojYwrWeuW9WhXP41d8UWPMbC8wm4JsvepE8RY4Zl1GjVSCgxJt4TfVxGz5+VrB02ANyZOaFoF28kMgAkp/agLCTdegpTKXxXsSvJK/iy2YYlU0iQU516woqv8T/0PXfP6Xmc/jpvXJ8sJq/h37v71bEJAM5kyj5ljr6DRKvaKpleO3PVpjPzbU27zoZZl1BxY0QQgghhJChzLmGw9xr+ftmqxlY97AVZ+tolkapo0yIeFx3B4d/P2BBdwf/ff40Dj/9IxU1QgghhBBChsNxHG64T4bxU0MAAN3twL8fsEDfSsm3lFE2RDzKYg7FR3+PQks9/31yLnD7U3IolLR0GCGEEEIIIa6QKzjc9agGCZn8982ngbX3WtDVTsm3VFHiTTzGoOdw+sQVaKrlpw6ISgB+84wCYRGUdBNCCCGEEOKO8AgZfvusAlHnJkxvOAW8cr8FPV3ixkVGhhJv4hEdZxk+fCYaRkMsAEATC/xujQJRCZR0E0IIIYQQMhIxSRzuflEBDX+LjTNlwBuPqNDdRXNkSw0l3mTUGqsY1vzGgrNn+HEoEdFW/P6fCiRmUNJNCCGEEELIaMSn8cl3RDT/va5Ghi8/yERlZae4gRG3UOJNRqXsoA1rfmdBm47/XqHswo2PdiCBkm5CCCGEEEI8IjGTwz1rFYhJ5r/v0ofg2mu3YNu2alHjIq6jxJuMiM3GsO0tK16+z4rec+NMEjPNyJr0OWKSrEMfTAghhBBCCHFLfDqHe15WICnLBgBoazPh8ss34O9/3wfGaNI1f0eDA4jbOlsY3ltlRckPjj/wcfM4XHJLG7a+0yNiZGQkWm5eCJnBCJs6VOxQCHHSctNCaNpC0BltFjsUQtxGdSvxd1RGpUkbx+G2lb1Y/5gVtaciYbMxrFixE9u3n8a6dZcjJSVC7BDJICjxJi5jjOHAZoZPX7TCoOdf4zjgsttlWPwLGeor6UmbFJky48UOgZABmTLjYYmPgkndLnYohLjNqW6lyyPxQ3T9ly5VOHDJNXWIVvwMzz13DACweXM1Jk58Ey+9dAmWLy8Ax9GwT39DXc2JSxpOMbzyJyveXelIuiOigd+9IMflt8khk9MfNyGEEEIIIb7AccCf/jQJ//vf9UhODgcAtLb24uc//xKLF3+MkpIWkSMk56PEmwyp4yzDx89Z8cxtFpTudzyyn3YJh4feVmDMDCpChBBCCCGEiOHyy7Nx7NivsGxZgf21r7+uwaRJ/8Xvf/816utp0W9/QV3NyYDadBy2vGHFvk02WAXDK6MTgZ/eK8fEBZRwB4rYd3ZAWdsMU0Y8Wm5ZKHY4hNjFrt8BdVUb5NnRVDaJ5DjVrTdT+SX+h67/gSM2Ngzvv381brppLO6991tUV3fCYrHhpZeOYN264/jtbyfjj3+ciuzsKLFDDWqUeBM7q9WG77+vxzdfpaD2RRVsNpv9Z8ow4JJbZFh0owzKUOpWHkiUtc0IO1kndhiE9KOsbUZIeR2UcovYoRDiNqpbib+jMhpYOI7DkiV5WLw4E08/vR/PPvsjurvN6O21YM2ag3jxxUO49tpc/OEP07BoUTpkMrqf9zVKvIMcYwxHjjRh48ZyvPXWCdTW6gFo7D8PVQMXLJVh0XIZImPoD5QQQgghhBB/FRYWgr/8ZT7uvnsqnn56P1566Qh6ey2w2Rg+/bQCn35agcxMDW68sRA33TQWEyfG0URsPkKJdxDq6DBi584z2LatBp99VoGams5++0REMSy4QY4FP5VBraE/RkIIIYQQQqQiPl6NZ59dhD//eRZefbUIa9cesY/3rqnpxNNP78fTT+9Hbm4ULr88C1dckY1Fi9IRHq4UOfLARYl3gLNYbDh5sgWHDjXh0CEd9uypx8GDOths/dc2kck4XHRRMphqP+b/KgYxSVoRIiaEEEIIIYR4Qny8Go88MgcPPjgTGzaU47//PY5t22pgtfK5QGVlO1566QheeukIFAoZJk+Ox5w5yZgzJwWzZiUhNzcKcjnN7eQJI0q8165di2eeeQYNDQ0YP3481qxZgwULFgy6//bt23H//ffjxIkTSElJwYMPPojf/va3Tvts2LABjz32GCorK5Gbm4uVK1di6dKlIwkv6FgsNuh03aiu7kRFRRsqKtpRXs7/W1zcgp6ewcdHKhQy/OQn6Vi6NB9LluSB4/R4bPW3kCtifPg/IIQQQgghhHhLSIgcN95YiBtvLERTUzc+/rgMH31Uhl276mCx8PM6WSw2HDyow8GDOrz00hEAQGioHIWFMRg3LhbjxsUiO1uLjAwNMjIikZISgZAQuYj/K2lxO/H+4IMPcO+992Lt2rWYP38+/v3vf+OKK65AcXExMjIy+u1fVVWFK6+8Er/+9a/xzjvvYPfu3bjrrrsQHx+P66+/HgCwd+9eLF++HH/729+wdOlSfPLJJ1i2bBl27dqF2bNnj/5/6ccYYzAarejttaC3t+9fCwwGCzo6jIIvE9rbe9HRYcTZsz1oaOhGbW0rWlu/wdmzPWD9G7AHNWFCHBYtSsdPfpKOiy7KQFSUyv6zhga9F/6XhBBCCCGEEH+QkBCOu+6airvumorOTiO+++40Nm+uwq5ddThx4qxTXmE0WnH0aDOOHm3u9z4yGYeUlAgkJqoRG6tCaKgF2dl1iI9XIzY2DBqNEhERSkREhNj/DQ8PQURECNTqECiVcsjlXNCMMXc78X7++edxxx134M477wQArFmzBlu2bMHLL7+MVatW9dv/lVdeQUZGBtasWQMAGDt2LH788Uc8++yz9sR7zZo1uPTSS7FixQoAwIoVK7B9+3asWbMG77333kj/b37n7bdP4LHHdjsl2Uaj1WufJ5NxyMnRYtq0REybloDp05MwdWoCYmPDvPaZhBBCCCGEEGnQaEKxZEkelizJA8DPBXXgQCN++KEehw41oaSkBeXlbfau6UI2G8OZM3qcOSNsuHNvpnyOA5RKueBLBqVSjpAQ/t+cHC2++OKno/kv+g23Em+TyYSDBw/ioYcecnp98eLF2LNnz4DH7N27F4sXL3Z67bLLLsO6detgNpsREhKCvXv34r777uu3T1+yPhCj0Qij0Wj/vqOjAwDQ1tYGq9W9ZNZqtaKzsxNtbW2Qy73XXeLs2VbU1DR57P0UChmSktRISAhHQkIYUlMjkJOjRU5OFHJytMjM1ECpPP//04u2tt5B37OjowMWkwVtDW0wGoyD7jfgsU0dAAPaG9uh4PoXLQ4cGBjOtpwFA3Pr2NF8bjDFPFS8gx0b0dMLZrOhq6cXTbWDl09/itkTn0sxix/zcMdF9BjPlU1jv7Lpj+cYkF6dQTF7L2Zh3dp8utnv/v6GO9Yf64xgi9nb8Q52/Q+Ev79Aj9nQYYDFZEFHRwdUKlW/Y0dr+nQNpk/XACgEAJhMVlRWtqO8vB1nzuhx+rQedXVdqKvrwunTerS29g44f5QrGAOMRv5rIGazAW1tbSP8nwzNUzlgZyc/UTUbrgsyc0NdXR0DwHbv3u30+sqVK9mYMWMGPCY/P5+tXLnS6bXdu3czAKy+vp4xxlhISAhbv3690z7r169nSqVy0Fgef/xxBoC+6Iu+6Iu+6Iu+6Iu+6Iu+6Iu+6EvUr9OnTw+ZS49ocrXz++Ezxobsmz/Q/ue/7u57rlixAvfff7/9e5vNhtbWVsTGxro9TqCzsxPp6ek4ffo0NBrN8Af4AYrZN6QWs9TiBShmX6GYfYNi9g2pxSy1eAGK2VcoZt+gmL1PavECnouZMQa9Xo+UlJQh93Mr8Y6Li4NcLkdjY6PT601NTUhMTBzwmKSkpAH3VygUiI2NHXKfwd4TAEJDQxEaGur0WlRUlKv/lQFpNBrJFJQ+FLNvSC1mqcULUMy+QjH7BsXsG1KLWWrxAhSzr1DMvkExe5/U4gU8E7NWqx12H7cWZVMqlZg+fTq2bdvm9Pq2bdswb968AY+ZO3duv/23bt2KGTNmICQkZMh9BntPQgghhBBCCCFEKtzuan7//ffj1ltvxYwZMzB37ly8+uqrqK2tta/LvWLFCtTV1eGtt94CAPz2t7/Fv/71L9x///349a9/jb1792LdunVOs5Xfc889WLhwIZ5++mksWbIEn332Gb7++mvs2rXLQ/9NQgghhBBCCCFEHG4n3suXL0dLSwueeOIJNDQ0YMKECdi0aRMyMzMBAA0NDaitrbXvn52djU2bNuG+++7DSy+9hJSUFLz44ov2pcQAYN68eXj//ffx6KOP4rHHHkNubi4++OADn63hHRoaiscff7xf13V/RjH7htRillq8AMXsKxSzb1DMviG1mKUWL0Ax+wrF7BsUs/dJLV7A9zFzjA037zkhhBBCCCGEEEJGyq0x3oQQQgghhBBCCHEPJd6EEEIIIYQQQogXUeJNCCGEEEIIIYR4ESXehBBCCCGEEEKIFwVF4r1y5UrMmzcParUaUVFRLh3zl7/8BYWFhQgPD0d0dDQuueQS7Nu3z/7z1tZW/OEPf0BBQQHUajUyMjLwxz/+ER0dHR6Jua2tDbfeeiu0Wi20Wi1uvfVWtLe3D3kMx3EDfj3zzDP2fSorK7F06VLEx8dDo9Fg2bJl0Ol0osRsNpvx5z//GRMnTkR4eDhSUlLwi1/8AvX19f323bt3Ly666CKEh4cjKioKixYtQk9Pj9sxrl27FtnZ2VCpVJg+fTp27tw56L4bN27EpZdeaj9Xc+fOxZYtW5z2WbRo0YDn/KqrrnI7Nk/EDADr16/H5MmToVarkZycjNtuuw0tLS1O+2zYsAHjxo1DaGgoxo0bh08++cQjse7YsQPXXHMNUlJSwHEcPv300yH337VrF+bPn4/Y2FiEhYWhsLAQL7zwgtM+GzduxIwZMxAVFYXw8HBMmTIFb7/9tkfiHUnMgGvnuL29HXfffTeSk5OhUqkwduxYbNq0ySMxr1q1CjNnzkRkZCQSEhJw3XXXobS01OXjd+/eDYVCgSlTpvT7mTfKxkjjfemllzB27FiEhYWhoKDAvkxlH2+WjZdffhmTJk2CRqOx//3/73//c+nYoc6vN8vFSGIe7hybzWY88cQTyM3NhUqlwuTJk7F582aPxDuQVatWgeM43HvvvYPu8/333w9Y7548edK+z2uvvYYFCxYgOjrafg3fv3+/R2L8y1/+0u+zk5KShjxm+/btmD59OlQqFXJycvDKK684/fzNN98c8P/U29srSsyunGMAWLNmDQoKChAWFob09HTcd999HosZAOrq6nDLLbcgNjYWarUaU6ZMwcGDBwfdv6GhATfddBMKCgogk8kGLEcnTpzA9ddfj6ysLHAchzVr1ngs3pHEDABGoxGPPPIIMjMzERoaitzcXLz++usD7vv++++D4zhcd911o4617xyc/3X33XcPuL8r59fb90XuxvyrX/1qwP3Hjx/vtJ+37osAwGKx4NFHH0V2djbCwsKQk5ODJ554AjabbdBjXLkH9eY1cCQxu3quvXkd1Ov1uPfee5GZmYmwsDDMmzcPBw4cGHR/V86zR6+DLAj8v//3/9jzzz/P7r//fqbVal06Zv369Wzbtm2ssrKSHT9+nN1xxx1Mo9GwpqYmxhhjx44dYz/96U/Z559/zioqKtg333zD8vPz2fXXX++RmC+//HI2YcIEtmfPHrZnzx42YcIEdvXVVw95TENDg9PX66+/zjiOY5WVlYwxxrq6ulhOTg5bunQpKyoqYkVFRWzJkiVs5syZzGq1+jzm9vZ2dskll7APPviAnTx5ku3du5fNnj2bTZ8+3Wm/PXv2MI1Gw1atWsWOHz/OysrK2EcffcR6e3vdiu/9999nISEh7LXXXmPFxcXsnnvuYeHh4aympmbA/e+55x729NNPs/3797OysjK2YsUKFhISwg4dOmTfp6WlxemcHz9+nMnlcvbGG2+4FZunYt65cyeTyWTsH//4Bzt16hTbuXMnGz9+PLvuuuvs++zZs4fJ5XL21FNPsZKSEvbUU08xhULBfvjhh1HHu2nTJvbII4+wDRs2MADsk08+GXL/Q4cOsXfffZcdP36cVVVVsbfffpup1Wr273//277Pd999xzZu3MiKi4tZRUUFW7NmDZPL5Wzz5s2jjnckMbtyjo1GI5sxYwa78sor2a5du1h1dTXbuXMnO3LkiEdivuyyy9gbb7zBjh8/zo4cOcKuuuoqlpGRwbq6uoY9tr29neXk5LDFixezyZMnO/3MW2VjJPGuXbuWRUZGsvfff59VVlay9957j0VERLDPP//cvo83y8bnn3/OvvrqK1ZaWspKS0vZww8/zEJCQtjx48eHPG6o8+vtcuFuzK6c4wcffJClpKSwr776ilVWVrK1a9cylUrlVA96yv79+1lWVhabNGkSu+eeewbd77vvvmMAWGlpqVP9a7FY7PvcdNNN7KWXXmKHDx9mJSUl7LbbbmNarZadOXNm1HE+/vjjbPz48U6f3XdvMJBTp04xtVrN7rnnHlZcXMxee+01FhISwj7++GP7Pm+88QbTaDT9ruOe4m7Mrpzjd955h4WGhrL169ezqqoqtmXLFpacnMzuvfdej8Tc2trKMjMz2a9+9Su2b98+VlVVxb7++mtWUVEx6DFVVVXsj3/8I/vvf//LpkyZMmA52r9/P3vggQfYe++9x5KSktgLL7zgkXhHGjNjjF177bVs9uzZbNu2bayqqort27eP7d69u99+1dXVLDU1lS1YsIAtWbJk1PE2NTU5/X63bdvGALDvvvtuwP1dOb/evi9yN+b29nan/U+fPs1iYmLY448/bt/Hm/dFjDH25JNPstjYWPbll1+yqqoq9tFHH7GIiAi2Zs2aQY9x5R7Um9fAkcTsyrn29nVw2bJlbNy4cWz79u2svLycPf7440yj0Qxa97tynj15HQyKxLvPG2+84XLifb6Ojg4GgH399deD7vPhhx8ypVLJzGbzCCPkFRcXMwBOf/B79+5lANjJkyddfp8lS5awiy66yP79li1bmEwmYx0dHfbXWltbGQC2bds2v4h5//79DIBTYjl79mz26KOPjio+xhibNWsW++1vf+v0WmFhIXvooYdcfo9x48axv/71r4P+/IUXXmCRkZEuJUCucDfmZ555huXk5Di99uKLL7K0tDT798uWLWOXX3650z6XXXYZu/HGGz0Scx9XktiBLF26lN1yyy1D7jN16lSPlInzuRKzK+f45ZdfZjk5OcxkMnk8xoE0NTUxAGz79u3D7rt8+XL26KOPsscff7xfYuirsuFKvHPnzmUPPPCA02v33HMPmz9//pDv7a2ywRhj0dHR7D//+c+Q+wx1fn1dLhgbOmZXznFycjL717/+5bTPkiVL2M033+zROPV6PcvPz2fbtm1jF154oUuJd1tbm8vvb7FYWGRkJPvvf/876lgH+t0O5cEHH2SFhYVOr/3mN79hc+bMsX8/mvsTV7gbsyvn+O6773a6x2CMsfvvv59dcMEFI4zS2Z///OdRvddw5YgxxjIzMz2aeI8k5v/9739Mq9WylpaWIfezWCxs/vz57D//+Q/75S9/6ZHE+3z33HMPy83NZTabbdh9XTm/jHn+vuh87sTMGGOffPIJ4ziOVVdX21/z9rXvqquuYrfffrvTaz/96U+Hvdc533D3oIx57hroiZgHOtfevA4aDAYml8vZl19+6fT65MmT2SOPPOLy+5x/nj15HQyKruajZTKZ8Oqrr0Kr1WLy5MmD7tfR0QGNRgOFQjGqz9u7dy+0Wi1mz55tf23OnDnQarXYs2ePS++h0+nw1Vdf4Y477rC/ZjQawXGc0yLxKpUKMpkMu3btEj1mgD+HHMfZhwQ0NTVh3759SEhIwLx585CYmIgLL7zQ7XhNJhMOHjyIxYsXO72+ePFil+Oz2WzQ6/WIiYkZdJ9169bhxhtvRHh4uFvxDWQkMc+bNw9nzpzBpk2bwBiDTqfDxx9/7NTFa+/evf3e87LLLnPr9+Qthw8fxp49e3DhhRcO+HPGGL755huUlpZi4cKFPo6O58o5/vzzzzF37lzcfffdSExMxIQJE/DUU0/BarV6Jaa+IS5DlU0AeOONN1BZWYnHH398wJ/7qmy4Eq/RaIRKpXJ6LSwsDPv374fZbO63vzfLhtVqxfvvv4/u7m7MnTt30P2GO7++LBeuxOzKOR5sn9FeM853991346qrrsIll1zi8jFTp05FcnIyLr74Ynz33XdD7mswGGA2m4f9G3FVeXk5UlJSkJ2djRtvvBGnTp0adN/B/q5+/PFHp7Lc1dWFzMxMpKWl4eqrr8bhw4c9EutIYu4z1Dm+4IILcPDgQXsX/lOnTmHTpk0e61L8+eefY8aMGfjZz36GhIQETJ06Fa+99ppH3ttbRhJz3zGrV69GamoqxowZgwceeKDfcLonnngC8fHxTvd1nmQymfDOO+/g9ttvB8dxHntfT94XnW8kMa9btw6XXHIJMjMz7a95+9p3wQUX4JtvvkFZWRkA4OjRo9i1axeuvPJKl99juHtQT18DPRHzQOfam9dBi8UCq9U6qmvWQOfZo9dBt1N1CXP3ifIXX3zBwsPDGcdxLCUlhe3fv3/Qfc+ePcsyMjLceqIymJUrV7L8/Px+r+fn57OnnnrKpfd4+umnWXR0NOvp6bG/1tTUxDQaDbvnnntYd3c36+rqYnfffTcDwP7v//5P9Jh7enrY9OnTnZ4g9bWax8TEsNdff50dOnSI3XvvvUypVLKysjKX46urq2MA+nXdWrlyJRszZoxL77F69WoWExPDdDrdgD/ft28fA8D27dvnclxDGWnMfd2BFAoFA8CuvfZapyeLISEhbP369U7HrF+/nimVSo/E3QdutHinpqYypVLJZDIZe+KJJ/r9vL29nYWHhzOFQsFCQ0PZunXrPBprH1djHu4cFxQUsNDQUHb77bezH3/8kb333nssJiZm2CfVI2Gz2dg111wzbCtLWVkZS0hIYKWlpYyxgVvAfFE2XI13xYoVLCkpif3444/MZrOxAwcOsISEBAaA1dfX2/fzZtkoKipi4eHhTC6XM61Wy7766qtB93Xl/PqiXLgTsyvn+Oc//zkbN24cKysrY1arlW3dupWFhYV5tEy89957bMKECfbr1XAtaSdPnmSvvvoqO3jwINuzZw/73e9+xziOG7IHxV133cVyc3OdrokjtWnTJvbxxx+zoqIiewt9YmIiO3v27ID75+fns5UrVzq9tnv3bqfzvHfvXvb222+zI0eOsB07drDrr7+ehYWFuXWd82TMrp7jF198kYWEhNjrwt/97nceiZcxxkJDQ1loaChbsWIFO3ToEHvllVeYSqVyudeCGC3eI4n5sssuY6Ghoeyqq65i+/btY1999RXLzMxkt912m32fXbt2sdTUVNbc3MwYY15p8f7ggw+YXC5ndXV1Lu3vyvn19H3R+dyNub6+nsnlcvbBBx84ve7ta5/NZmMPPfQQ4ziOKRQKxnGcy/fGfQa7B/XWNXC0MQ92rr19HZw7dy678MILWV1dHbNYLOztt99mHMeN6l7fk9dBySbejz/+OAMw5NeBAwecjnE38e7q6mLl5eVs79697Pbbb2dZWVkDJl0dHR1s9uzZ7PLLLx+y64SrMQ+WWOXl5bFVq1a5FHtBQQH7/e9/3+/1LVu2sJycHMZxHJPL5eyWW25h06ZNG/Ri6auYTSYTW7JkCZs6dapTV/i+m5MVK1Y47T9x4kS3uoj3JbF79uxxev3JJ59kBQUFwx7/7rvvMrVaPWSX/P/7v/9jEyZMcDmm4Ywk5hMnTrDk5GS2evVqdvToUbZ582Y2ceJEp+5CISEh7N1333U6rm+snie5k3ifOnWKFRUVsVdffZXFxMT0i89qtbLy8nJ2+PBh9uyzzzKtVjvoeC5vx+zKOc7Pz2fp6elO4yGfe+45lpSU5PGY77rrLpaZmclOnz496D4Wi4XNmDGDvfzyy/bXBku8vV02XImXMb7L2G233cYUCgWTy+UsJSWFPfjggwyAUz3szbJhNBpZeXk5O3DgAHvooYdYXFwcO3HiRL/9XD2/vigXrsbMmGvnuKmpiS1ZsoTJZDIml8vZmDFj2F133cXCwsI8Em9tbS1LSEhwGt/nahdWoauvvppdc801A/6s70H00aNHRxPqoLq6ulhiYiJ77rnnBvz5QA+gd+3axQAMOo7barWyyZMnsz/84Q8ej5ex4WMeyPnn+LvvvmOJiYnstddeY0VFRWzjxo0sPT19wIenIxESEsLmzp3r9Nof/vAHpy76QxEj8R5JzJdeeilTqVSsvb3d/tqGDRsYx3HMYDCwzs5OlpWVxTZt2mT/uTcS78WLFw87l5CQK+fX0/dF53M35qeeeorFxsYyo9Ho9Lq3r33vvfceS0tLY++99x4rKipib731FouJiWFvvvmmS8cPdQ/qrWvgaGMe7Fx7+zpYUVHBFi5cyAAwuVzOZs6cyW6++WY2duzYYY8d7Dx78joo2cS7ubmZlZSUDPl1/pPt0Y6hysvL63fx7OzsZHPnzmUXX3zxsE/SXY153bp1A8ap1WrZ66+/PmycO3bsYACGnKigubnZPnYrMTGRrV69WrSYTSYTu+6669ikSZP6PX0/deoUA8Defvttp9eXLVvGbrrppiHfV8hoNDK5XM42btzo9Pof//hHtnDhwiGPff/991lYWFi/MSNC3d3dTKPRDDnphLtGEvMtt9zCbrjhBqfXdu7c6dSykp6ezp5//nmnfZ5//nmWkZHhsdgZG/kY77/97W/DPpm844472OLFi0cY2eBcidmVc7xw4UJ28cUXO+2zadMmBqDfRWg0fv/737O0tDR26tSpIfdra2uzX4T6vjiOs7/2zTffMMa8XzZcjVfIZDKx06dPM4vFYp8MbKjJIL1VNhhj7OKLLx6wd5Cr59dX5cKVmIVcOcc9PT3szJkzzGazsQcffJCNGzfOI/F98skn/c4dAPvDYeHN2VCefPLJfuOoGePnZNBqtf0exHvaJZdc0m8+jj4LFixgf/zjH51e27hxI1MoFEM+rL/zzjv7jTv1pKFiHsj55/iCCy7oN0fA22+/zcLCwjwyYWtGRga74447nF5bu3YtS0lJcel4MRLvkcT8i1/8guXm5jq91jdvTllZGTt8+PCA9Uvf38hwE7e5orq6mslkMvbpp5+6fMxw59cb90VC7sZss9lYXl7egJP/efval5aW1m+M8N/+9jeXGn5cuQcV8tQ1cDQxD3WufXUd7Orqst+TLVu2jF155ZVD7u/KefbEdXB0g5FFFBcXh7i4OJ9+JmMMRqPR/n1nZycuu+wyhIaG4vPPP+/X//98rsY8d+5cdHR0YP/+/Zg1axYAYN++fejo6MC8efOGPX7dunWYPn36kOPR++L49ttv0dTUhGuvvVaUmM1mM5YtW4by8nJ89913iI2Ndfp5VlYWUlJS+i09VFZWhiuuuGLYuPoolUpMnz4d27Ztw9KlS+2vb9u2DUuWLBn0uPfeew+333473nvvvSHHrX344YcwGo245ZZbXI7JGzEbDIZ+cwzI5XIAfPkF+N/Vtm3bcN9999n32bp1q0tlyxfO/zsb6T7e4so5nj9/Pt59913YbDbIZPxUGmVlZUhOToZSqRx1DIwx/OEPf8Ann3yC77//HtnZ2UPur9FocOzYMafX1q5di2+//RYff/yx/XhvlQ134xUKCQlBWloaAH4Znauvvtp+Tgf7LG+VjcHe29Xz6+1y4U7MQq6cY5VKhdTUVJjNZmzYsAHLli3zSHwXX3xxv3N32223obCwEH/+85/tf1vDOXz4MJKTk51ee+aZZ/Dkk09iy5YtmDFjhkfiHYjRaERJSQkWLFgw4M/nzp2LL774wum1rVu3YsaMGQgJCRnwGMYYjhw5gokTJ3o8XmD4mAdy/jk2GAz9yolcLgfjG3VGHeP8+fMHvPYLx4v6m5HEPH/+fHz00Ufo6upCRESE/RiZTIa0tDRwHNfvb+TRRx+FXq/HP/7xD6Snp4867jfeeAMJCQkeXQrVG/dFQu7GvH37dlRUVAw4Rt7b90WD/a0MtTQX4Po9qJCnroEjjRkY+lz76joYHh6O8PBwtLW1YcuWLVi9evWg+7p6nj1yHXQ7VZegmpoadvjwYfbXv/6VRUREsMOHD7PDhw8zvV5v36egoMDestjV1cVWrFjB9u7dy6qrq9nBgwfZHXfcwUJDQ+3LsnR2drLZs2eziRMnsoqKikGX2xipyy+/nE2aNInt3buX7d27l02cOLFfdxphzH06OjqYWq126vIo9Prrr7O9e/eyiooK9vbbb7OYmBh2//33jzrekcRsNpvZtddey9LS0tiRI0eczqHwqdcLL7zANBoN++ijj1h5eTl79NFHmUqlcvspb9/SXOvWrWPFxcXs3nvvZeHh4fbZFh966CF266232vd/9913mUKhYC+99JJTbMLuYH0uuOACtnz5crfi8UbMb7zxBlMoFGzt2rWssrKS7dq1i82YMYPNmjXLvs/u3buZXC5nf//731lJSQn7+9//7rFlM/R6vf3vCwB7/vnn2eHDh+2z1J8f77/+9S/2+eefs7KyMlZWVsZef/11ptFonOZKeOqpp9jWrVtZZWUlKykpYc899xxTKBTstddeG3W8I4nZlXNcW1vLIiIi2O9//3tWWlrKvvzyS5aQkMCefPJJj8T8u9/9jmm1Wvb99987lU2DwWDf5/y4zzdQV2hvlY2RxFtaWsrefvttVlZWxvbt28eWL1/OYmJiWFVVlX0fb5aNFStWsB07drCqqipWVFTEHn74YSaTydjWrVsHjPd8A51fb5cLd2N25Rz/8MMPbMOGDayyspLt2LGDXXTRRSw7O9utGcXddX5L2vlxv/DCC+yTTz5hZWVl7Pjx4+yhhx5iANiGDRvs+zz99NNMqVSyjz/+2KnMCa/7I/WnP/2Jff/99+zUqVPshx9+YFdffTWLjIwctF7uW07svvvuY8XFxWzdunX9lhP7y1/+wjZv3swqKyvZ4cOH7UMAPDU21t2YXTnHjz/+OIuMjGTvvfceO3XqFNu6dSvLzc1ly5Yt80jM+/fvZwqFgq1cuZKVl5ez9evXM7Vazd555x37PgP9HfbV59OnT2c33XQTO3z4sNNwC6PRaN8nOTmZPfDAA+zw4cOsvLxclJj1ej1LS0tjN9xwAztx4gTbvn07y8/PZ3feeeegn+PJruZWq5VlZGSwP//5z/1+NpLz28db90UjiZkxvrfa7NmzB3w/b94XMcb/vlJTU+1Lc23cuJHFxcWxBx98cNC4XbkH9eY1cCQx9xnqXHv7Orh582b2v//9z14nTZ48mc2aNcveu2gk59mT18GgSLx/+ctfDjg2WTgGAoB9jcGenh62dOlSlpKSwpRKJUtOTmbXXnut0+RqfUttDPQlvGkZqZaWFnbzzTezyMhIFhkZyW6++eZ+v2BhzH3+/e9/s7CwsAGTQ8b4pS4SExNZSEgIy8/PZ88995zLSzB4OuaqqqpBz+H541NWrVrF0tLSmFqtZnPnzmU7d+4cUYwvvfQSy8zMZEqlkk2bNs1pophf/vKX7MILL7R/f+GFFw4Y2y9/+Uun9ywtLWUA7De3nuZOzIzxk92MGzeOhYWFseTkZHbzzTf3W7/wo48+YgUFBSwkJIQVFhY63UyNxmB/F33n7Px4X3zxRTZ+/HimVquZRqNhU6dOZWvXrnXqpvjII4+wvLw8plKpWHR0NJs7dy57//33PRLvSGLui3u4c7xnzx42e/ZsFhoaynJyctjKlSs98lCOMTbo342wPhgobqHBlhfyRtkYSbzFxcVsypQpLCwsjGk0GrZkyZJ+SxN6s2z8//buH5S6N4AD+PMqF4VF8if/YrlKYnhNFpHFIovJYmQgZbKYlEU2ZTUpGyky3EFKLDLYlJTFYlOU5zf86vb68/u9XnneW/d+PuO9d/j2nHM6z/c8554zPT2dP+7q6+vj8PDwq2P8q+Obcr/408yfGeNcLhe7u7tjRUVFrKuri1NTU59+kNFXvS3eb3Ovrq7Grq6u/HYfHBx89xC59vb2D/e5X98n+1WTk5OxqakplpeXx+bm5jgxMfGqeHy0b+Ryudjf3x8zmUzs6Oh4d3F8fn4+trW15bfd6Ojou+d7/M3Mnxnj5+fnuLy8nP9da2trnJmZ+daLMru7u7GnpydWVFTEbDYbNzc3X33/0Vh/tN3b29vz3//X3OP/jufUma+uruLIyEisqqqKLS0tcWFh4dWFybe+s3gfHBzEEEL+wZC/y/q78Y0x/bzoTzM/PDzEqqqqd9viV6nmRTH+u1g3NzcX29raYmVlZezs7IxLS0uvFpm+MgdNeQ78SuYYPzfWKc+D29vbsbOzM2YymdjY2BhnZ2dfdaKvjPN3ngd/xPgN9wMBAAAAH/IebwAAAEhI8QYAAICEFG8AAABISPEGAACAhBRvAAAASEjxBgAAgIQUbwAAAEhI8QYAAICEFG8AAABISPEGAACAhBRvAAAASEjxBoASdH9/HxobG8PKykr+s9PT05DJZMLh4WEBkwFA8fkRY4yFDgEA/H37+/thfHw8nJychGw2G/r7+8PY2FhYX18vdDQAKCqKNwCUsNnZ2XB0dBR+/vwZLi4uwtnZWaisrCx0LAAoKoo3AJSwx8fH0NPTE25vb8P5+Xno7e0tdCQAKDr+4w0AJez6+jrc3d2Fl5eXcHNzU+g4AFCUrHgDQIl6enoKAwMDoa+vL2Sz2bC2thYuLy9DQ0NDoaMBQFFRvAGgRC0uLoadnZ1wcXERqqurw9DQUKipqQl7e3uFjgYARcWt5gBQgnK5XFhfXw9bW1uhtrY2lJWVha2trXB8fBw2NjYKHQ8AiooVbwAAAEjIijcAAAAkpHgDAABAQoo3AAAAJKR4AwAAQEKKNwAAACSkeAMAAEBCijcAAAAkpHgDAABAQoo3AAAAJKR4AwAAQEKKNwAAACT0Dy9iGf4L/r2QAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def MoG(x, p_vec, mu_vec):\n",
    "    f_x = np.zeros(len(x))\n",
    "    \n",
    "    for p_k, mu_k in zip(p_vec, mu_vec):\n",
    "        f_x += p_k*norm.pdf(x, loc=mu_k, scale=sigma)\n",
    "        \n",
    "    return f_x\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "\n",
    "hist_n, hist_bins, _ = ax.hist(data, bins=50, edgecolor='black', alpha=0.5, density=True, color='forestgreen', label='Data')\n",
    "\n",
    "x_plot = np.linspace(-1, 9, 1000)\n",
    "ax.plot(x_plot, MoG(x_plot, p_k_mean, mu_k_mean), color='darkblue', linewidth=2, label='Likelihood')\n",
    "\n",
    "ax.set_xlabel('x', fontsize=10)\n",
    "ax.grid(alpha=0.5)\n",
    "ax.set_title('Comparison between inferred likelihood distribution and data', fontsize=15)\n",
    "\n",
    "# (hist_bins[1:]+hist_bins[:-1])/2\n",
    "binwidth = (hist_bins[-1]-hist_bins[0])/50\n",
    "a_left = 5\n",
    "a_righ = 6 \n",
    "xticks_list = np.linspace(hist_bins[0]+binwidth/2-a_left*binwidth, hist_bins[-1]-binwidth/2+a_righ*binwidth, 50+a_left+a_righ)\n",
    "\n",
    "ax.set_xticks(xticks_list[0::3])\n",
    "\n",
    "ax.set_ylim(top=0.25)\n",
    "for i, mu_k in enumerate(mu_k_mean):\n",
    "    if i==0:\n",
    "        ax.vlines(x=mu_k, ymin=0, ymax=0.25, color='firebrick', linestyles='dashed', linewidth=1.8, label='$\\mu_k$')\n",
    "    else:\n",
    "        ax.vlines(x=mu_k, ymin=0, ymax=0.25, color='firebrick', linestyles='dashed', linewidth=1.8)\n",
    "\n",
    "ax.legend(edgecolor='black', facecolor='linen', fontsize=10, loc ='upper right')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.7"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "dabd4eacb9e3ddd54eefcebcf933935be170cfdef29c95630fe9376e024beb9c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}