diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb
index c1fa790d..ffdf1716 100644
--- a/notebook/problems.ipynb
+++ b/notebook/problems.ipynb
@@ -1 +1 @@
-{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":1,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the point estimate of the binomial distribution\n","    \"\"\"\n","    result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def pbinom(q, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the cumulative of the binomial distribution\n","    \"\"\"\n","    result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def qbinom(p, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the quantile function from the binomial distribution\n","    \"\"\"\n","    result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def rbinom(n, size, prob = 0.5):\n","    \"\"\"\n","    Generates random variables from the binomial distribution\n","    \"\"\"\n","    result = binom.rvs(n = size, p = prob, size = n)\n","\n","    return result"]},{"cell_type":"code","execution_count":2,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":3,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 500x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":4,"id":"98d5f012","metadata":{},"outputs":[],"source":["# TODO"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}
+{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":1,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the point estimate of the binomial distribution\n","    \"\"\"\n","    result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def pbinom(q, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the cumulative of the binomial distribution\n","    \"\"\"\n","    result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def qbinom(p, size, prob = 0.5):\n","    \"\"\"\n","    Calculates the quantile function from the binomial distribution\n","    \"\"\"\n","    result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n","    return result\n","\n","def rbinom(n, size, prob = 0.5):\n","    \"\"\"\n","    Generates random variables from the binomial distribution\n","    \"\"\"\n","    result = binom.rvs(n = size, p = prob, size = n)\n","\n","    return result"]},{"cell_type":"code","execution_count":2,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":3,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 500x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":4,"id":"98d5f012","metadata":{},"outputs":[],"source":["from scipy.stats import norm\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n","    \"\"\"\n","    Calculates the density of the normal distribution\n","    \"\"\"\n","    result = norm.pdf(x, loc = mean, scale = std)\n","\n","    return result\n","\n","def pnorm(x, mean = 0, std = 1):\n","    \"\"\"\n","    Calculates the cumulative of the normal distribution\n","    \"\"\"\n","    result = norm.cdf(x = x, loc = mean, scale = std)\n","\n","    return result\n","\n","def qnorm(p, mean = 0, std = 1):\n","    \"\"\"\n","    Calculates the quantile function from the normal distribution\n","    \"\"\"\n","    result = norm.ppf(q = p, loc = mean, scale = std)\n","\n","    return result\n","\n","def rnorm(n, mean = 0, std = 1):\n","    \"\"\"\n","    Generates random variables from the normal distribution\n","    \"\"\"\n","    result = norm.rvs(size = n, loc = mean, scale = std)\n","\n","    return result"]},{"cell_type":"code","execution_count":5,"id":"3f9633ae","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 500x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"code","execution_count":6,"id":"bd35340a","metadata":{},"outputs":[],"source":["from scipy.stats import uniform\n","\n","#Uniforme\n","def dunif(x, low = 0, high = 1):\n","    \"\"\"\n","    Calculates the point estimate of the uniform distribution\n","    \"\"\"\n","    result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n","    return result\n","\n","def punif(q, low = 0, high = 1):\n","    \"\"\"\n","    Calculates the cumulative of the uniform distribution\n","    \"\"\"\n","    result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n","    return result\n","\n","def qunif(p, low = 0, high = 1):\n","    \"\"\"\n","    Calculates the quantile function from the uniform distribution\n","    \"\"\"\n","    result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n","    return result\n","\n","def runif(n, low = 0, high = 1):\n","    \"\"\"\n","    Generates random variables from the uniform distribution\n","    \"\"\"\n","    result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n","    return result"]},{"cell_type":"code","execution_count":7,"id":"59950e8a","metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAeEAAAKyCAYAAADiuGbKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABluElEQVR4nO3dfVhUdcI//jeDMqACasggOIaa+SwoyICud9Z3NirXzd274mv+hFizMlCY+e6WlMG63YnbXQ6mJGaZ1eZKtWVtspQ3Za7JiPLQqgnmIyTNCJUMoc7gzPn9we0YKygHGM6ZmffruuYSPp7DvOdc6Hs+Z86DjyAIAoiIiKjPKaQOQERE5K1YwkRERBJhCRMREUmEJUxERCQRljAREZFEWMJEREQSYQkTERFJhCVMREQkkX5SB+gKh8OB+vp6BAYGwsfHR+o4REREnRIEAc3NzQgPD4dCcf25rluUcH19PdRqtdQxiIiIuqyurg4jRoy47jJuUcKBgYEA2l5QUFCQxGmIiIg6Z7FYoFarnd11PW5Rwld2QQcFBbGEiYjILXTl41MemEVERCQR0SW8Z88ezJs3D+Hh4fDx8cGOHTtuuM7u3bsxffp0KJVK3HLLLdi6dWs3ohIREXkW0SXc0tKCqKgo5Ofnd2n5U6dOYe7cubj99ttRVVWFzMxMPPzww/jkk09EhyUiIvIkoj8Tvvvuu3H33Xd3efmCggKMGjUKL774IgBgwoQJ2Lt3LwwGAxITE8U+PRERkcdw+YFZpaWl0Gq17cYSExORmZnp6qcmohs5dAj44gupU3RMoQB+9Stg5EipkxC5jMtL2GQyQaVStRtTqVSwWCy4ePEiAgICrlnHarXCarU6v7dYLK6OSeSd7roLqK+XOkXnPvgA2LVL6hRELiPLU5Ryc3OxatUqqWMQeb7GxrY/f/UrYMAAabP8nMkE7NlzNR+Rh3J5CYeFhcFsNrcbM5vNCAoK6nAWDABZWVnQ6/XO76+c+ExEvUwQ2v7cuBG4wZV9+tSuXcCdd17NR+ShXF7CCQkJKCoqaje2a9cuJCQkdLqOUqmEUql0dTQiIiJJiT5F6aeffkJVVRWqqqoAtJ2CVFVVhdraWgBts9jk5GTn8o899hhOnjyJJ554AtXV1Xj55ZfxzjvvQKfT9c4rIKLuuzLTlNuNUa7k4UyYPJzoEj548CCmTZuGadOmAQD0ej2mTZuG7OxsAMB3333nLGQAGDVqFHbu3Ildu3YhKioKL774Il599VWenkQkB3IvObnnI+oh0buj58yZA+E6/zA6uhrWnDlzUFlZKfapiKivyHUmTOTheO1oIm/G3dFEkmIJExERSYQlTOTNOBMmkhRLmMibyb3k5J6PqIdYwkQk35kwkYdjCRORfEuPM2HycCxhIpIfub4pIOplLGEib/XzWabcSo8HZpGXYAkTERFJhCVM5K04EyaSHEuYyFu5Q8G5Q0aiHmAJE5F8Z8JEHo4lTOStuDuaSHIsYSIiIomwhIm8FWfCRJJjCRN5K3coOHfISNQDLGEiku9MmMjDsYSJvJWcd0dfwZkweTiWMBHJj1zfFBD1MpYwkbeS80yYB2aRl2AJExERSYQlTOStOBMmkhxLmMhbuUPBuUNGoh5gCRORfGfCRB6uWyWcn5+PyMhI+Pv7Q6PRoKys7LrL5+XlYdy4cQgICIBarYZOp8OlS5e6FZiIeomcd0dfwZkweTjRJVxYWAi9Xo+cnBxUVFQgKioKiYmJOHfuXIfLb9u2DStWrEBOTg6OHj2K1157DYWFhXjqqad6HJ6IPJRc3xQQ9TLRJbx27VosWbIEqampmDhxIgoKCjBgwABs2bKlw+X37duHWbNm4cEHH0RkZCTuvPNOLFiw4IazZyJyMTnPhHlgFnkJUSVss9lQXl4OrVZ79QcoFNBqtSgtLe1wnZkzZ6K8vNxZuidPnkRRURHuueeeTp/HarXCYrG0exBRL3OHgnOHjEQ90E/Mwo2NjbDb7VCpVO3GVSoVqqurO1znwQcfRGNjI37xi19AEARcvnwZjz322HV3R+fm5mLVqlViohFRT8h1Jkzk4Vx+dPTu3buxevVqvPzyy6ioqMD777+PnTt34tlnn+10naysLDQ1NTkfdXV1ro5J5H3kvDv6Cs6EycOJmgmHhITA19cXZrO53bjZbEZYWFiH6zzzzDNYtGgRHn74YQDAlClT0NLSgkceeQRPP/00FIpr3wcolUoolUox0YjIk8j1TQFRLxM1E/bz80NMTAxKSkqcYw6HAyUlJUhISOhwnQsXLlxTtL6+vgAAge9yiaTDmTCR5ETNhAFAr9cjJSUFsbGxiIuLQ15eHlpaWpCamgoASE5ORkREBHJzcwEA8+bNw9q1azFt2jRoNBocP34czzzzDObNm+csYyKiduT6poCol4ku4aSkJDQ0NCA7OxsmkwnR0dEoLi52HqxVW1vbbua7cuVK+Pj4YOXKlTh79iyGDRuGefPm4bnnnuu9V0FE4sl5JsxTlMhL+AhusE/YYrEgODgYTU1NCAoKkjoOkWf48Udg6NC2r61WwM9P2jw/99VXQHQ0EBYGfPed1GmIRBHTWbx2NBHJdyZM5OFYwkTeSs67o6+Q/446oh5hCROR/Mj1TQFRL2MJE3krOc+EeWAWeQmWMJG3coeCc4eMRD3AEiYi+c6EiTwcS5jIW8l5d/QVnAmTh2MJE5H8yPVNAVEvYwkTeSvOhIkkxxImIvmR65sCol7GEibyVnKeZfIUJfISLGEib+UOBecOGYl6gCVM5O3kuOtXjpmIXIAlTOStrswy5Vx4nAmTh2MJE5H8yPmNAVEvYgkTeSvOhIkkxxIm8lZyLjgeHU1egiVM5O3kOBOWYyYiF2AJE3kr7o4mkhxLmIjkR85vDIh6EUuYyFtxJkwkOZYwEcmPnN8YEPUiljCRt5LzTJhHR5OX6FYJ5+fnIzIyEv7+/tBoNCgrK7vu8ufPn0daWhqGDx8OpVKJW2+9FUVFRd0KTES9xB0Kzh0yEvVAP7ErFBYWQq/Xo6CgABqNBnl5eUhMTERNTQ1CQ0OvWd5ms+GXv/wlQkND8d577yEiIgJnzpzB4MGDeyM/EfWUnGfCRB5OdAmvXbsWS5YsQWpqKgCgoKAAO3fuxJYtW7BixYprlt+yZQt++OEH7Nu3D/379wcAREZG9iw1EfWcnHdHX8GZMHk4UbujbTYbysvLodVqr/4AhQJarRalpaUdrvPRRx8hISEBaWlpUKlUmDx5MlavXg273d6z5ETkueT8xoCoF4maCTc2NsJut0OlUrUbV6lUqK6u7nCdkydP4rPPPsPChQtRVFSE48eP4/HHH0draytycnI6XMdqtcJqtTq/t1gsYmISUVdwJkwkOZcfHe1wOBAaGopXXnkFMTExSEpKwtNPP42CgoJO18nNzUVwcLDzoVarXR2TyPvIueB4dDR5CVElHBISAl9fX5jN5nbjZrMZYWFhHa4zfPhw3HrrrfD19XWOTZgwASaTCTabrcN1srKy0NTU5HzU1dWJiUlEYshxJizHTEQuIKqE/fz8EBMTg5KSEueYw+FASUkJEhISOlxn1qxZOH78OBwOh3Ps2LFjGD58OPz8/DpcR6lUIigoqN2DiHoZd0cTSU707mi9Xo/NmzfjjTfewNGjR7F06VK0tLQ4j5ZOTk5GVlaWc/mlS5fihx9+QEZGBo4dO4adO3di9erVSEtL671XQUSeRc5vDIh6kehTlJKSktDQ0IDs7GyYTCZER0ejuLjYebBWbW0tFIqr3a5Wq/HJJ59Ap9Nh6tSpiIiIQEZGBp588sneexVEJB5nwkSS8xEE+f+WWywWBAcHo6mpibumiXrL8ePA2LFAYCAgtzMQzp4FRowA+vcHOjl2hEiuxHQWrx1N5K04EyaSHEuYyFvJueB4ihJ5CZYwkbeT40xYjpmIXIAlTOStuDuaSHIsYSKSHzm/MSDqRSxhIm/FmTCR5FjCRN5KzgXHA7PIS7CEibydnGfCRB6OJUzkreS8O1qOmYhcgCVMRPLDEiYvwRIm8lZyngn/HD8XJg/GEibyVnIut5+/MZBzTqIeYgkTeTu5z4SJPBhLmMhbyXmGyZkweQmWMJG3k+NMWI6ZiFyAJUzkrXhgFpHkWMJEJD9yf2NA1EtYwkTeijNhIsmxhIm8lZzLjQdmkZdgCRN5O7nPhIk8GEuYyFvJeXc0Z8LkJVjCRCQ/cnxjQOQCLGEibyXnmfDPcSZMHowlTOSt5Fxu3B1NXqJbJZyfn4/IyEj4+/tDo9GgrKysS+tt374dPj4+mD9/fneelohcQe4zYSIPJrqECwsLodfrkZOTg4qKCkRFRSExMRHnzp277nqnT5/G73//e8yePbvbYYmoF8l5hsmZMHkJ0SW8du1aLFmyBKmpqZg4cSIKCgowYMAAbNmypdN17HY7Fi5ciFWrVmH06NE9CkxEvYwzYSLJiCphm82G8vJyaLXaqz9AoYBWq0VpaWmn6/3pT39CaGgoFi9e3KXnsVqtsFgs7R5E1MvkfGAWZ8LkJUSVcGNjI+x2O1QqVbtxlUoFk8nU4Tp79+7Fa6+9hs2bN3f5eXJzcxEcHOx8qNVqMTGJyN3J8Y0BkQu49Ojo5uZmLFq0CJs3b0ZISEiX18vKykJTU5PzUVdX58KURF5KzjPhn+NMmDxYPzELh4SEwNfXF2azud242WxGWFjYNcufOHECp0+fxrx585xjDoej7Yn79UNNTQ3GjBlzzXpKpRJKpVJMNCISS87lxt3R5CVEzYT9/PwQExODkpIS55jD4UBJSQkSEhKuWX78+PE4dOgQqqqqnI9f//rXuP3221FVVcXdzERyIPeZMJEHEzUTBgC9Xo+UlBTExsYiLi4OeXl5aGlpQWpqKgAgOTkZERERyM3Nhb+/PyZPntxu/cGDBwPANeNE1MfkvDuaM2HyEqJLOCkpCQ0NDcjOzobJZEJ0dDSKi4udB2vV1tZCoeCFuIioB+T4xoDIBXwEQf5vMy0WC4KDg9HU1ISgoCCp4xB5htJSYOZMYPRo4MQJqdO0Z7UC/v5tX58/DwQHSxqHSAwxncUpK5G3kvP7b+6OJi/BEibydtz1SyQZljCRt5LzDJMzYfISLGEib8eZMJFkWMJE3oqnKBFJjiVMRPIjxzcGRC7AEibyVnKeCf8cZ8LkwVjCRN5KzuXG3dHkJVjCRN5O7jNhIg/GEibyVnLeHc2ZMHkJljAREZFEWMJE3oozYSLJsYSJvJW7lJu75CTqBpYwkbeT40yYyEuwhIm8ldxnmFfeHMg9J1EPsISJvB1nwkSSYQkTeSs5H5gFcCZMXoElTETyJNc3B0S9iCVM5K3kPhO+gjNh8mAsYSJvJfdy4+5o8gIsYSJvJ/eZMJEHYwkTeSu5747mTJi8AEuYiIhIIt0q4fz8fERGRsLf3x8ajQZlZWWdLrt582bMnj0bQ4YMwZAhQ6DVaq+7PBH1Ec6EiSQnuoQLCwuh1+uRk5ODiooKREVFITExEefOnetw+d27d2PBggX4/PPPUVpaCrVajTvvvBNnz57tcXgi6gG5lxtLmLyA6BJeu3YtlixZgtTUVEycOBEFBQUYMGAAtmzZ0uHyb7/9Nh5//HFER0dj/PjxePXVV+FwOFBSUtLj8ETUC+Q6EybyAqJK2Gazoby8HFqt9uoPUCig1WpRWlrapZ9x4cIFtLa2YujQoeKSElHvkvsMkzNh8gL9xCzc2NgIu90OlUrVblylUqG6urpLP+PJJ59EeHh4uyL/d1arFVar1fm9xWIRE5OIxOBMmEgyfXp09Jo1a7B9+3Z88MEH8Pf373S53NxcBAcHOx9qtboPUxJ5CR6YRSQ5USUcEhICX19fmM3mduNmsxlhYWHXXfeFF17AmjVr8Omnn2Lq1KnXXTYrKwtNTU3OR11dnZiYREREbkFUCfv5+SEmJqbdQVVXDrJKSEjodL3nn38ezz77LIqLixEbG3vD51EqlQgKCmr3IKJexpkwkeREfSYMAHq9HikpKYiNjUVcXBzy8vLQ0tKC1NRUAEBycjIiIiKQm5sLAPjzn/+M7OxsbNu2DZGRkTCZTACAQYMGYdCgQb34UohIFLmXG0uYvIDoEk5KSkJDQwOys7NhMpkQHR2N4uJi58FatbW1UCiuTrA3btwIm82G++67r93PycnJwR//+MeepSeinpPrTJjIC4guYQBIT09Henp6h3+3e/fudt+fPn26O09BRK7G3dFEkuO1o4mIiCTCEibyVpwJE0mOJUzkrdyl3NwlJ1E3sISJvJ3cZ8JEHowlTOSt5D7D5O5o8gIsYSJvxxknkWRYwkTeigdmEUmOJUxERCQRljCRt+JMmEhyLGEibyX3cmMJkxdgCRN5O7nOhIm8AEuYyFtxdzSR5FjCREREEmEJE3krzoSJJMcSJvJW7lJu7pKTqBtYwkTeTu4zYSIPxhIm8lZyn2FydzR5AZYwkbfjjJNIMixhIm/FA7OIJMcSJiIikghLmMhbcSZMJDmWMJG3cpdyc5ecRN3AEibydnKfCRN5sG6VcH5+PiIjI+Hv7w+NRoOysrLrLv/uu+9i/Pjx8Pf3x5QpU1BUVNStsETUi7g7mkhyoku4sLAQer0eOTk5qKioQFRUFBITE3Hu3LkOl9+3bx8WLFiAxYsXo7KyEvPnz8f8+fNx+PDhHocnIiJyZ6JLeO3atViyZAlSU1MxceJEFBQUYMCAAdiyZUuHy69btw533XUX/vCHP2DChAl49tlnMX36dGzYsKHH4YmoBzgTJpJcPzEL22w2lJeXIysryzmmUCig1WpRWlra4TqlpaXQ6/XtxhITE7Fjxw7xaXtDSwvgcEjz3ERycvGi1Am6pqUFaG6WOgV5A4UCGDiwT59SVAk3NjbCbrdDpVK1G1epVKiuru5wHZPJ1OHyJpOp0+exWq2wWq3O7y0Wi5iY13fbbUB5ee/9PCJ3J/eZ8H/8h7Q5yHvMnAl8+WWfPqUsj47Ozc1FcHCw86FWq6WOROSZFArgl7+UOkXH7rpL6gRELidqJhwSEgJfX1+YzeZ242azGWFhYR2uExYWJmp5AMjKymq3C9tisfReEe/dy8+YiK5QKAClUuoUHdu8GVi/nv9eqe8o+n5eKqqE/fz8EBMTg5KSEsyfPx8A4HA4UFJSgvT09A7XSUhIQElJCTIzM51ju3btQkJCQqfPo1QqoXTVfwz+/q75uUTU+/jvlTycqBIGAL1ej5SUFMTGxiIuLg55eXloaWlBamoqACA5ORkRERHIzc0FAGRkZOC2227Diy++iLlz52L79u04ePAgXnnlld59JURERG5GdAknJSWhoaEB2dnZMJlMiI6ORnFxsfPgq9raWih+NqWfOXMmtm3bhpUrV+Kpp57C2LFjsWPHDkyePLn3XgUREZEb8hEE+X/gYrFYEBwcjKamJgQFBUkdh4iIqFNiOkuWR0cTERF5A5YwERGRRER/JiyFK3vMe/WiHURERC5wpau68mmvW5Rw8/9eso4X7SAiInfR3NyM4ODg6y7jFgdmORwO1NfXIzAwED5yvcReL7hyUZK6ujoegCYSt133cLt1D7db93jLdhMEAc3NzQgPD293tlBH3GImrFAoMGLECKlj9JmgoCCP/gV1JW677uF26x5ut+7xhu12oxnwFTwwi4iISCIsYSIiIomwhGVEqVQiJyfHddfN9mDcdt3D7dY93G7dw+12Lbc4MIuIiMgTcSZMREQkEZYwERGRRFjCREREEmEJuwGr1Yro6Gj4+PigqqpK6jiydvr0aSxevBijRo1CQEAAxowZg5ycHNhsNqmjyU5+fj4iIyPh7+8PjUaDsrIyqSPJWm5uLmbMmIHAwECEhoZi/vz5qKmpkTqW21mzZg18fHyQmZkpdRRZYAm7gSeeeALh4eFSx3AL1dXVcDgc2LRpE44cOQKDwYCCggI89dRTUkeTlcLCQuj1euTk5KCiogJRUVFITEzEuXPnpI4mW1988QXS0tJgNBqxa9cutLa24s4770RLS4vU0dzGgQMHsGnTJkydOlXqKPIhkKwVFRUJ48ePF44cOSIAECorK6WO5Haef/55YdSoUVLHkJW4uDghLS3N+b3dbhfCw8OF3NxcCVO5l3PnzgkAhC+++ELqKG6hublZGDt2rLBr1y7htttuEzIyMqSOJAucCcuY2WzGkiVL8NZbb2HAgAFSx3FbTU1NGDp0qNQxZMNms6G8vBxardY5plAooNVqUVpaKmEy99LU1AQA/N3qorS0NMydO7fd7x25ybWjvZEgCHjooYfw2GOPITY2FqdPn5Y6kls6fvw41q9fjxdeeEHqKLLR2NgIu90OlUrVblylUqG6ulqiVO7F4XAgMzMTs2bNwuTJk6WOI3vbt29HRUUFDhw4IHUU2eFMuI+tWLECPj4+131UV1dj/fr1aG5uRlZWltSRZaGr2+3nzp49i7vuugv3338/lixZIlFy8kRpaWk4fPgwtm/fLnUU2aurq0NGRgbefvtt+Pv7Sx1HdnjFrD7W0NCA77///rrLjB49Gg888AD+/ve/t7t1o91uh6+vLxYuXIg33njD1VFlpavbzc/PDwBQX1+POXPmID4+Hlu3br3h7cS8ic1mw4ABA/Dee+9h/vz5zvGUlBScP38eH374oXTh3EB6ejo+/PBD7NmzB6NGjZI6juzt2LEDv/nNb+Dr6+scs9vt8PHxgUKhgNVqbfd33oYlLFO1tbWwWCzO7+vr65GYmIj33nsPGo3Gq27tKNbZs2dx++23IyYmBn/5y1+8+h94ZzQaDeLi4rB+/XoAbbtXR44cifT0dKxYsULidPIkCAKWLVuGDz74ALt378bYsWOljuQWmpubcebMmXZjqampGD9+PJ588kmv353Pz4RlauTIke2+HzRoEABgzJgxLODrOHv2LObMmYObb74ZL7zwAhoaGpx/FxYWJmEyedHr9UhJSUFsbCzi4uKQl5eHlpYWpKamSh1NttLS0rBt2zZ8+OGHCAwMhMlkAtB239iAgACJ08lXYGDgNUU7cOBA3HTTTV5fwABLmDzMrl27cPz4cRw/fvyaNyvc6XNVUlISGhoakJ2dDZPJhOjoaBQXF19zsBZdtXHjRgDAnDlz2o2//vrreOihh/o+EHkE7o4mIiKSCI9WISIikghLmIiISCIsYSIiIomwhImIiCTCEiYiIpIIS5iIiEgiLGEiIiKJsISJiIgkwhImIiKSCEuYiIhIIixhIiIiibCEiYiIJMISJiIikghLmIiISCIsYSIiIomwhImIiCTST+oAXeFwOFBfX4/AwED4+PhIHYeIiKhTgiCgubkZ4eHhUCiuP9d1ixKur6+HWq2WOgYREVGX1dXVYcSIEdddxi1KODAwEEDbCwoKCpI4DRERUecsFgvUarWzu67HLUr4yi7ooKAgljAREbmFrnx8ygOziIiIJCK6hPfs2YN58+YhPDwcPj4+2LFjxw3X2b17N6ZPnw6lUolbbrkFW7du7UZUIiIizyK6hFtaWhAVFYX8/PwuLX/q1CnMnTsXt99+O6qqqpCZmYmHH34Yn3zyieiwREREnkT0Z8J333037r777i4vX1BQgFGjRuHFF18EAEyYMAF79+6FwWBAYmKi2KcnIiLyGC4/MKu0tBRarbbdWGJiIjIzM1391ETkxi5eBCwWqVOQN+nfHxg6tG+f0+UlbDKZoFKp2o2pVCpYLBZcvHgRAQEB16xjtVphtVqd31v4L5HIq5w6BUydCvz0k9RJyJvMnAl8+WXfPqcsT1HKzc3FqlWrpI5BRBL5+OOrBcyL5FFfkeJ3zeUlHBYWBrPZ3G7MbDYjKCiow1kwAGRlZUGv1zu/v3LiMxF5h3372v589llg5UppsxC5kstLOCEhAUVFRe3Gdu3ahYSEhE7XUSqVUCqVro5GRDJ1pYRnzpQ2B5GriT5F6aeffkJVVRWqqqoAtJ2CVFVVhdraWgBts9jk5GTn8o899hhOnjyJJ554AtXV1Xj55ZfxzjvvQKfT9c4rICKP8u23QG0toFAAcXFSpyFyLdElfPDgQUybNg3Tpk0DAOj1ekybNg3Z2dkAgO+++85ZyAAwatQo7Ny5E7t27UJUVBRefPFFvPrqqzw9iYg6VFra9mdUFDBokLRZiFxN9O7oOXPmQBCETv++o6thzZkzB5WVlWKfioi8EHdFkzfhtaOJSFZYwuRNWMJEJBsXLwIVFW1fs4TJG7CEiUg2Dh4ELl8Ghg8Hbr5Z6jRErscSJiLZ+PmuaF6kg7wBS5iIZIOfB5O3YQkTkSwIAkuYvA9LmIhk4fhxoLERUCqB/70MAZHHYwkTkSxcmQXPmNFWxETegCVMRLLAXdHkjVjCRCQLLGHyRixhIpLc+fPAkSNtX1/nBmtEHoclTESS27+/7ejoW24BQkOlTkPUd1jCRCS5L79s+5O7osnbsISJSHL8PJi8FUuYiCR1+XLb7miAJUzehyVMRJI6fBj46ScgKAiYOFHqNER9iyVMRJK6sis6Ph7w9ZU2C1FfYwkTkaT4eTB5M5YwEUmKJUzejCVMRJL57jvg1Km2ewdrNFKnIep7LGEikkxpadufU6a0HZhF5G1YwkQkGe6KJm/HEiYiybCEyduxhIlIEpcuAeXlbV+zhMlbdauE8/PzERkZCX9/f2g0GpSVlV13+by8PIwbNw4BAQFQq9XQ6XS4dOlStwITkWeoqABstrYbNoweLXUaImmILuHCwkLo9Xrk5OSgoqICUVFRSExMxLlz5zpcftu2bVixYgVycnJw9OhRvPbaaygsLMRTTz3V4/BE5L5+vivax0faLERSEV3Ca9euxZIlS5CamoqJEyeioKAAAwYMwJYtWzpcft++fZg1axYefPBBREZG4s4778SCBQtuOHsmIs/Gz4OJRJawzWZDeXk5tFrt1R+gUECr1aL0yrkG/2bmzJkoLy93lu7JkydRVFSEe+65p9PnsVqtsFgs7R5E5DkE4WoJz5olbRYiKfUTs3BjYyPsdjtUKlW7cZVKherq6g7XefDBB9HY2Ihf/OIXEAQBly9fxmOPPXbd3dG5ublYtWqVmGhE5EZOnQLMZsDPD5g+Xeo0RNJx+dHRu3fvxurVq/Hyyy+joqIC77//Pnbu3Ilnn32203WysrLQ1NTkfNTV1bk6JhH1oSuz4JgYwN9f2ixEUhI1Ew4JCYGvry/MZnO7cbPZjLCwsA7XeeaZZ7Bo0SI8/PDDAIApU6agpaUFjzzyCJ5++mkoFNe+D1AqlVAqlWKiEZEb4efBRG1EzYT9/PwQExODkpIS55jD4UBJSQkSEhI6XOfChQvXFK3v/96vTBAEsXmJyAOwhInaiJoJA4Ber0dKSgpiY2MRFxeHvLw8tLS0IDU1FQCQnJyMiIgI5ObmAgDmzZuHtWvXYtq0adBoNDh+/DieeeYZzJs3z1nGROQ9LBbg0KG2rzt5707kNUSXcFJSEhoaGpCdnQ2TyYTo6GgUFxc7D9aqra1tN/NduXIlfHx8sHLlSpw9exbDhg3DvHnz8Nxzz/XeqyAit7F/P+BwAKNGAcOHS52GSFo+ghvsE7ZYLAgODkZTUxOCeKsVIre2ahXwxz8CCxcCf/mL1GmIep+YzuK1o4moT/HzYKKrWMJE1GfsdsBobPuaJUzEEiaiPvT1120HZg0aBEyeLHUaIumxhImoz1zZFa3RAP1EHxZK5HlYwkTUZ/h5MFF7LGEi6jMsYaL2WMJE1CfOnQOOH2/7Oj5e2ixEcsESJqI+ceVup5MmAYMHSxqFSDZYwkTUJ7grmuhaLGEi6hMsYaJrsYSJyOVsNuDAgbavWcJEV7GEicjlKisBqxW46SZg7Fip0xDJB0uYiFzu57uifXykzUIkJyxhInK5KyU8a5a0OYjkhiVMRC4lCDwoi6gzLGEicqnaWqC+vu1a0bGxUqchkheWMBG51JVZ8PTpQECAtFmI5IYlTEQuxV3RRJ1jCRORS335ZdufLGGia7GEichlfvoJ+Oqrtq8TEqTNQiRHLGEicpmyMsDhAEaOBEaMkDoNkfywhInIZfh5MNH1sYSJyGVYwkTX160Szs/PR2RkJPz9/aHRaFBWVnbd5c+fP4+0tDQMHz4cSqUSt956K4qKiroVmIjcg8Nx9R7CLGGijvUTu0JhYSH0ej0KCgqg0WiQl5eHxMRE1NTUIDQ09JrlbTYbfvnLXyI0NBTvvfceIiIicObMGQzmXb2JPFp1NXD+PDBgADB1qtRpiORJdAmvXbsWS5YsQWpqKgCgoKAAO3fuxJYtW7BixYprlt+yZQt++OEH7Nu3D/379wcAREZG9iw1EcnelV3RcXHA//7TJ6J/I2p3tM1mQ3l5ObRa7dUfoFBAq9Wi9Mp+p3/z0UcfISEhAWlpaVCpVJg8eTJWr14Nu93es+REJGv8PJjoxkTNhBsbG2G326FSqdqNq1QqVFdXd7jOyZMn8dlnn2HhwoUoKirC8ePH8fjjj6O1tRU5OTkdrmO1WmG1Wp3fWywWMTGJSAZYwkQ35vKjox0OB0JDQ/HKK68gJiYGSUlJePrpp1FQUNDpOrm5uQgODnY+1Gq1q2MSUS9qbARqatq+jo+XNguRnIkq4ZCQEPj6+sJsNrcbN5vNCAsL63Cd4cOH49Zbb4Wvr69zbMKECTCZTLDZbB2uk5WVhaamJuejrq5OTEwikpjR2Pbn+PHATTdJm4VIzkSVsJ+fH2JiYlBSUuIcczgcKCkpQUIn16SbNWsWjh8/DofD4Rw7duwYhg8fDj8/vw7XUSqVCAoKavcgIvfBXdFEXSN6d7Rer8fmzZvxxhtv4OjRo1i6dClaWlqcR0snJycjKyvLufzSpUvxww8/ICMjA8eOHcPOnTuxevVqpKWl9d6rICJZYQkTdY3oU5SSkpLQ0NCA7OxsmEwmREdHo7i42HmwVm1tLRSKq92uVqvxySefQKfTYerUqYiIiEBGRgaefPLJ3nsVRCQbra1t14wGWMJEN+IjCIIgdYgbsVgsCA4ORlNTE3dNE8ncwYPAjBnA0KFAQwOg4MVxycuI6Sz+8yCiXnVlV3RCAguY6Eb4T4SIehU/DybqOpYwEfUqljBR17GEiajX1NW1PXx92z4XJqLrYwkTUa+5MguOjgYGDpQ0CpFbYAkTUa/hrmgicVjCRNRrWMJE4rCEiahXtLQAlZVtX7OEibqGJUxEveLgQcBuByIiAN74jKhrWMJE1Ct+vivax0faLETugiVMRL2CnwcTiccSJqIeEwSWMFF3sISJqMeOHQN++AHw9287R5iIuoYlTEQ9dmUWPGMG4OcnbRYid8ISJqIe465oou5hCRNRj7GEibqHJUxEPfLjj8DXX7d9nZAgbRYid8MSJqIeMRrb/hw7Fhg2TNosRO6GJUxEPcJd0UTdxxImoh5hCRN1H0uYiLrt8mVg//62r2fNkjYLkTtiCRNRtx061Hb3pOBgYMIEqdMQuR+WMBF125Vd0QkJgIL/mxCJxn82RNRt/DyYqGe6VcL5+fmIjIyEv78/NBoNysrKurTe9u3b4ePjg/nz53fnaYlIZljCRD0juoQLCwuh1+uRk5ODiooKREVFITExEefOnbvueqdPn8bvf/97zJ49u9thiUg+6uuB06fbdkPHxUmdhsg9iS7htWvXYsmSJUhNTcXEiRNRUFCAAQMGYMuWLZ2uY7fbsXDhQqxatQqjR4/uUWAikocrs+CpU4HAQGmzELkrUSVss9lQXl4OrVZ79QcoFNBqtSgtLe10vT/96U8IDQ3F4sWLu/Q8VqsVFoul3YOI5IW7ool6TlQJNzY2wm63Q6VStRtXqVQwmUwdrrN371689tpr2Lx5c5efJzc3F8HBwc6HWq0WE5OI+gBLmKjnXHp0dHNzMxYtWoTNmzcjJCSky+tlZWWhqanJ+airq3NhSiIS6+JFoKKi7WuWMFH39ROzcEhICHx9fWE2m9uNm81mhIWFXbP8iRMncPr0acybN8855nA42p64Xz/U1NRgzJgx16ynVCqhVCrFRCOiPlReDrS2AmFhQGSk1GmI3JeombCfnx9iYmJQUlLiHHM4HCgpKUFCB/cwGz9+PA4dOoSqqirn49e//jVuv/12VFVVcTczkZv6+a5oHx9psxC5M1EzYQDQ6/VISUlBbGws4uLikJeXh5aWFqSmpgIAkpOTERERgdzcXPj7+2Py5Mnt1h88eDAAXDNORO6DnwcT9Q7RJZyUlISGhgZkZ2fDZDIhOjoaxcXFzoO1amtroeD164g8liCwhIl6i48gCILUIW7EYrEgODgYTU1NCAoKkjoOkVc7fhwYOxbw8wMsFoCHbxC1J6azOGUlIlGuzIJjY1nARD3FEiYiUbgrmqj3sISJSBSWMFHvYQkTUZc1NQGHD7d93cFZiUQkEkuYiLps//62o6NHj267UAcR9QxLmIi67Mqu6FmzpM1B5ClYwkTUZfw8mKh3sYSJqEvsdsBobPuaJUzUO1jCRNQlR44Azc1AYCAwaZLUaYg8A0uYiLrkyq7o+HjA11faLESegiVMRF3y5Zdtf3JXNFHvYQkTUZfwoCyi3scSJqIbMpmAkyfb7h2s0UidhshzsISJ6IZKS9v+nDwZCA6WNguRJ2EJE9ENcVc0kWuwhInohljCRK7BEiai67JagYMH275mCRP1LpYwEV1XRQVgswHDhgFjxkidhsizsISJ6Lp+vivax0faLESehiVMRNfFz4OJXIclTESdEgSWMJErsYSJqFOnT7ddqKN/fyAmRuo0RJ6HJUxEnboyC54+HQgIkDYLkSfqVgnn5+cjMjIS/v7+0Gg0KCsr63TZzZs3Y/bs2RgyZAiGDBkCrVZ73eWJSD64K5rItUSXcGFhIfR6PXJyclBRUYGoqCgkJibi3LlzHS6/e/duLFiwAJ9//jlKS0uhVqtx55134uzZsz0OT0SuxRImci0fQRAEMStoNBrMmDEDGzZsAAA4HA6o1WosW7YMK1asuOH6drsdQ4YMwYYNG5CcnNyl57RYLAgODkZTUxOCgoLExCWibmpuBgYPBhwO4OxZIDxc6kRE7kFMZ4maCdtsNpSXl0Or1V79AQoFtFotSq9c4f0GLly4gNbWVgwdOlTMUxNRHysrayvgyEgWMJGr9BOzcGNjI+x2O1QqVbtxlUqF6urqLv2MJ598EuHh4e2K/N9ZrVZYrVbn9xaLRUxMIuoF3BVN5Hp9enT0mjVrsH37dnzwwQfw9/fvdLnc3FwEBwc7H2q1ug9TEhHAEibqC6JKOCQkBL6+vjCbze3GzWYzwsLCrrvuCy+8gDVr1uDTTz/F1KlTr7tsVlYWmpqanI+6ujoxMYmohxyOq/cQZgkTuY6oEvbz80NMTAxKSkqcYw6HAyUlJUhISOh0veeffx7PPvssiouLERsbe8PnUSqVCAoKavcgor5z9CjQ1AQMHAhMmSJ1GiLPJeozYQDQ6/VISUlBbGws4uLikJeXh5aWFqSmpgIAkpOTERERgdzcXADAn//8Z2RnZ2Pbtm2IjIyEyWQCAAwaNAiDBg3qxZdCRL3lyy/b/tRogH6i/5cgoq4S/c8rKSkJDQ0NyM7OhslkQnR0NIqLi50Ha9XW1kKhuDrB3rhxI2w2G+677752PycnJwd//OMfe5aeiFyCnwcT9Q3R5wlLgecJE/WtW28FvvkGKCoC7r5b6jRE7sVl5wkTkedraGgrYACIj5c2C5GnYwkTUTtXjoqeOBEYMkTaLESejiVMRO3w82CivsMSJqJ2WMJEfYclTERONhtw4EDb1yxhItdjCRORU1UVcOkSMHRo2xHSRORaLGEicvr5rmgfH2mzEHkDljAROfHzYKK+xRImIgCAIFy9XCVLmKhvsISJCABQVwfU1wO+vsCMGVKnIfIOLGEiAnB1V/S0acCAAdJmIfIWLGEiAsDPg4mkwBImIgBXS3jWLGlzEHkTljARoaWl7RxhgDNhor7EEiYiHDgA2O2AWg2MGCF1GiLvwRImIn4eTCQRljARsYSJJMISJvJyDgdLmEgqLGEiL1dTA/z4IxAQAERFSZ2GyLuwhIm83JVZcFwc0L+/tFmIvA1LmMjLcVc0kXRYwkRejiVMJB2WMJEX+/57oLq67ev4eGmzEHkjljCRFzMa2/4cNw4ICZE2C5E36lYJ5+fnIzIyEv7+/tBoNCgrK7vu8u+++y7Gjx8Pf39/TJkyBUVFRd0KS0S9i7uiiaQluoQLCwuh1+uRk5ODiooKREVFITExEefOnetw+X379mHBggVYvHgxKisrMX/+fMyfPx+HDx/ucXgi6hmWMJG0fARBEMSsoNFoMGPGDGzYsAEA4HA4oFarsWzZMqxYseKa5ZOSktDS0oKPP/7YORYfH4/o6GgUFBR06TktFguCg4PR1NSEoKAgMXGJqBOtrcDgwcCFC8CRI8DEiVInIvIMYjqrn5gfbLPZUF5ejqysLOeYQqGAVqtFaWlph+uUlpZCr9e3G0tMTMSOHTs6fR6r1Qqr1er83mKxiIl5XcuXA99802s/jshtXbzYVsCDBwPjx0udhsg7iSrhxsZG2O12qFSqduMqlQrVVw6x/Dcmk6nD5U0mU6fPk5ubi1WrVomJ1mX79gHl5S750URu6f/8H0DBQzSJJCGqhPtKVlZWu9mzxWKBWq3ulZ+9alXbaRlEBPTrByQmSp2CyHuJKuGQkBD4+vrCbDa3GzebzQgLC+twnbCwMFHLA4BSqYRSqRQTrcvmznXJjyUiIhJN1E4oPz8/xMTEoKSkxDnmcDhQUlKChISEDtdJSEhotzwA7Nq1q9PliYiIvIXo3dF6vR4pKSmIjY1FXFwc8vLy0NLSgtTUVABAcnIyIiIikJubCwDIyMjAbbfdhhdffBFz587F9u3bcfDgQbzyyiu9+0qIiIjcjOgSTkpKQkNDA7Kzs2EymRAdHY3i4mLnwVe1tbVQ/Owoj5kzZ2Lbtm1YuXIlnnrqKYwdOxY7duzA5MmTe+9VEBERuSHR5wlLgecJExGRuxDTWTwxgYiISCKyPEXp312ZrPfmRTuIiIhc4UpXdWVHs1uUcHNzMwD02rnCRERErtbc3Izg4ODrLuMWnwk7HA7U19cjMDAQPj4+UsdxmSsXJamrq+Nn3yJx23UPt1v3cLt1j7dsN0EQ0NzcjPDw8HYHKnfELWbCCoUCI0aMkDpGnwkKCvLoX1BX4rbrHm637uF26x5v2G43mgFfwQOziIiIJMISJiIikghLWEaUSiVycnJcdt1sT8Zt1z3cbt3D7dY93G7XcosDs4iIiDwRZ8JEREQSYQkTERFJhCVMREQkEZYwERGRRFjCbsBqtSI6Oho+Pj6oqqqSOo6snT59GosXL8aoUaMQEBCAMWPGICcnBzabTepospOfn4/IyEj4+/tDo9GgrKxM6kiylpubixkzZiAwMBChoaGYP38+ampqpI7ldtasWQMfHx9kZmZKHUUWWMJu4IknnkB4eLjUMdxCdXU1HA4HNm3ahCNHjsBgMKCgoABPPfWU1NFkpbCwEHq9Hjk5OaioqEBUVBQSExNx7tw5qaPJ1hdffIG0tDQYjUbs2rULra2tuPPOO9HS0iJ1NLdx4MABbNq0CVOnTpU6inwIJGtFRUXC+PHjhSNHjggAhMrKSqkjuZ3nn39eGDVqlNQxZCUuLk5IS0tzfm+324Xw8HAhNzdXwlTu5dy5cwIA4YsvvpA6iltobm4Wxo4dK+zatUu47bbbhIyMDKkjyQJnwjJmNpuxZMkSvPXWWxgwYIDUcdxWU1MThg4dKnUM2bDZbCgvL4dWq3WOKRQKaLValJaWSpjMvTQ1NQEAf7e6KC0tDXPnzm33e0ducgMHbyQIAh566CE89thjiI2NxenTp6WO5JaOHz+O9evX44UXXpA6imw0NjbCbrdDpVK1G1epVKiurpYolXtxOBzIzMzErFmzMHnyZKnjyN727dtRUVGBAwcOSB1FdjgT7mMrVqyAj4/PdR/V1dVYv349mpubkZWVJXVkWejqdvu5s2fP4q677sL999+PJUuWSJScPFFaWhoOHz6M7du3Sx1F9urq6pCRkYG3334b/v7+UseRHV62so81NDTg+++/v+4yo0ePxgMPPIC///3v7e6fbLfb4evri4ULF+KNN95wdVRZ6ep28/PzAwDU19djzpw5iI+Px9atW294T09vYrPZMGDAALz33nuYP3++czwlJQXnz5/Hhx9+KF04N5Ceno4PP/wQe/bswahRo6SOI3s7duzAb37zG/j6+jrH7HY7fHx8oFAoYLVa2/2dt2EJy1RtbS0sFovz+/r6eiQmJuK9996DRqPxqvsri3X27FncfvvtiImJwV/+8hev/gfeGY1Gg7i4OKxfvx5A2+7VkSNHIj09HStWrJA4nTwJgoBly5bhgw8+wO7duzF27FipI7mF5uZmnDlzpt1Yamoqxo8fjyeffNLrd+fzM2GZGjlyZLvvBw0aBAAYM2YMC/g6zp49izlz5uDmm2/GCy+8gIaGBuffhYWFSZhMXvR6PVJSUhAbG4u4uDjk5eWhpaUFqampUkeTrbS0NGzbtg0ffvghAgMDYTKZALTdvD0gIEDidPIVGBh4TdEOHDgQN910k9cXMMASJg+za9cuHD9+HMePH7/mzQp3+lyVlJSEhoYGZGdnw2QyITo6GsXFxdccrEVXbdy4EQAwZ86cduOvv/46Hnroob4PRB6Bu6OJiIgkwqNViIiIJMISJiIikghLmIiISCIsYSIiIomwhImIiCTCEiYiIpIIS5iIiEgiLGEiIiKJsISJiIgkwhImIiKSCEuYiIhIIixhIiIiibCEiYiIJMISJiIikghLmIiISCIsYSIiIon0kzpAVzgcDtTX1yMwMBA+Pj5SxyEiIuqUIAhobm5GeHg4FIrrz3XdooTr6+uhVquljkFERNRldXV1GDFixHWXcYsSDgwMBND2goKCgiROQ0RE1DmLxQK1Wu3srutxixK+sgs6KCiIJUxERG6hKx+f8sAsIiIiiYgu4T179mDevHkIDw+Hj48PduzYccN1du/ejenTp0OpVOKWW27B1q1buxGViIjIs4gu4ZaWFkRFRSE/P79Ly586dQpz587F7bffjqqqKmRmZuLhhx/GJ598IjosERGRJxH9mfDdd9+Nu+++u8vLFxQUYNSoUXjxxRcBABMmTMDevXthMBiQmJgo9umJiIhcwu6ww1fh26fP6fLPhEtLS6HVatuNJSYmorS0tNN1rFYrLBZLuwcREVFvszvseP/o+5j9+mxkf57d58/v8hI2mUxQqVTtxlQqFSwWCy5evNjhOrm5uQgODnY+eI4wERH1pmZrM9YZ12Hs+rH4z3f+E3tr92JL1RZcdlzu0xyyPEUpKysLer3e+f2Vc66IiIh64vT501i/fz1erXwVFmvbXtahAUPxaMyjSJuRhn6Kvq1Flz9bWFgYzGZzuzGz2YygoCAEBAR0uI5SqYRSqXR1NCIi8gKCIKD021IYjAa8f/R9OAQHAGDcTeOQGZ+J5KhkDOg/QJJsLi/hhIQEFBUVtRvbtWsXEhISXP3URETkxVrtrfjb0b/BYDSg7GyZc1w7WgtdvA533XIXFD7SXi5DdAn/9NNPOH78uPP7U6dOoaqqCkOHDsXIkSORlZWFs2fP4s033wQAPPbYY9iwYQOeeOIJ/O53v8Nnn32Gd955Bzt37uy9V0FERPS/frz4IzZXbMb6svX41vItAEDpq8TCKQuRGZ+JKaopEie8SnQJHzx4ELfffrvz+yuf3aakpGDr1q347rvvUFtb6/z7UaNGYefOndDpdFi3bh1GjBiBV199lacnERFRr/rm+2+wbv86vF71Oi60XgAAhA4MxeOxj2PpjKUIHRgqccJr+QiCIEgd4kYsFguCg4PR1NTEa0cTEZGTIAjYfXo3DEYDPj72MQS0VdqU0CnQxeuwYMoC+Pfz79NMYjpLlkdHExERXY/1shXbD2+HwWjAV+avnONzx86FLl6HO0bd4Rb3n2cJExGR22hoaUDBwQLkH8iHuaXtzJuAfgF4KPohZGgyMC5knMQJxWEJExGR7B05dwR5xjy89a+3YLVbAQARgRFIj0vHIzGPYGjAUIkTdg9LmIiIZMkhOPDpiU9hMBrw6YlPneOx4bHQxetw/8T70d+3v4QJe44lTEREsnKh9QLe+uotrNu/DkcbjwIAFD4KzB8/H7p4HWapZ7nF571dwRImIiJZqG+uR35ZPjaVb8L3F78HAAT6BWLxtMVYrlmOUUNGSZyw97GEiYhIUpXfVcJgNGD74e1odbQCACIHR2J53HIsnr4YQUrPPTWVJUxERH3O7rDj42Mfw2A04IszXzjHZ6lnQRevw73j7+3zmylIwfNfIRERycZPtp/weuXrWLd/HU78eAIA0E/RD/dPvB+6eB1mRMyQOGHfYgkTEZHL1TbVYv3+9dhcsRlN1iYAwBD/IXgk5hGkx6VjRNAIiRNKgyVMREQuY/zWCIPRgL99/TfYBTsAYOzQsciMz0RKVAoG+g2UOKG0WMJERNSrLjsu4/2j78NgNMD4rdE5fseoO6CL1+GesfdIfgtBuWAJExFRrzh/6TxerXgV68vWo7ap7W56fr5+eHDKg8jUZCIqLErihPLDEiYioh458cMJrNu/Dlsqt6CltQUAMGzAMCyNXYqlM5YibFCYxAnliyVMRESiCYKAPWf2wGA04KOaj5y3EJw0bBJ08TosnLqwz28h6I5YwkRE1GU2uw2FhwthMBpQaap0jt99y93QxeugHa31mEtK9gWWMBER3VDjhUZsOrgJ+Qfy8d1P3wFou4VgclQyMjQZmDBsgsQJ3RNLmIiIOnW04SjyjHl4819v4tLlSwCA4YOGIz0uHY/GPIqbBtwkcUL3xhImIqJ2BEHArpO7YDAaUHy82Dk+ffh06OJ1eGDSA/Dz9ZMwoedgCRMREQDgYutFvH3obeQZ83Ck4QgAwAc+uHf8vdDF6zB75Gx+3tvLWMJERF7O9JMJLx94GRsPbkTjhUYAwCC/Qfhd9O+wXLMcY4aOkTih52IJExF5qa9MX8FgNOCvh/8Km90GABgZPNJ5C8HB/oOlDegFWMJERF7EITiw89hOGIwGfH76c+d4wogE6OJ1+M2E33jFLQTlgluaiMgLtNhasLVqK9btX4dvfvgGAODr44v7Jt4HXbwOmhEaiRN6p25dQTs/Px+RkZHw9/eHRqNBWVnZdZfPy8vDuHHjEBAQALVaDZ1Oh0uXLnUrMBERdV1dUx2e3PUkRhhGIP0f6fjmh28QrAzGH2b+ASczTmL7fdtZwBISPRMuLCyEXq9HQUEBNBoN8vLykJiYiJqaGoSGhl6z/LZt27BixQps2bIFM2fOxLFjx/DQQw/Bx8cHa9eu7ZUXQURE7ZWdLYPBaMC7R9513kLwlqG3IEOTgYeiH8Igv0ESJyQA8BEEQRCzgkajwYwZM7BhwwYAgMPhgFqtxrJly7BixYprlk9PT8fRo0dRUlLiHPt//+//Yf/+/di7d2+XntNisSA4OBhNTU0ICgoSE5eIyGtcdlzGjuodMBgN2Fe3zzl+2823QRevw69u/RV8Fb4SJvQOYjpL1EzYZrOhvLwcWVlZzjGFQgGtVovS0tIO15k5cyb+8pe/oKysDHFxcTh58iSKioqwaNGiTp/HarXCarW2e0FERNSxpktNeK3yNby0/yWcaToDAOiv6I//O/n/Qhevw7Th0yROSJ0RVcKNjY2w2+1QqVTtxlUqFaqrqztc58EHH0RjYyN+8YtfQBAEXL58GY899hieeuqpTp8nNzcXq1atEhONiMjrnPzxJF7a/xK2VG5Bs60ZAHBTwE14LPYxpM1Iw/DA4RInpBvp1oFZYuzevRurV6/Gyy+/jIqKCrz//vvYuXMnnn322U7XycrKQlNTk/NRV1fn6phERG5BEAT888w/8dvC32Ls+rFYt38dmm3NmBAyAZt+tQl1ujr81x3/xQJ2E6JmwiEhIfD19YXZbG43bjabERbW8U2bn3nmGSxatAgPP/wwAGDKlCloaWnBI488gqeffhoKxbXvA5RKJZRKpZhoREQezWa34d0j78JgNKD8u3LneOKYRGTGZyJxTCIvKemGRJWwn58fYmJiUFJSgvnz5wNoOzCrpKQE6enpHa5z4cKFa4rW17ftwACRx4QREXmdHy7+gE0HN2HDgQ2ob64HAPj388eiqYuQocnApNBJEieknhB9ipJer0dKSgpiY2MRFxeHvLw8tLS0IDU1FQCQnJyMiIgI5ObmAgDmzZuHtWvXYtq0adBoNDh+/DieeeYZzJs3z1nGRETUXk1jDfKMeXjjqzdw8fJFAEDYoDCkzUjDozGPYtjAYRInpN4guoSTkpLQ0NCA7OxsmEwmREdHo7i42HmwVm1tbbuZ78qVK+Hj44OVK1fi7NmzGDZsGObNm4fnnnuu914FEZEHEAQBJadKYDAaUPRNkXM8OiwaungdkiYlQdmPH9V5EtHnCUuB5wkTkSe7dPkSth3ahjxjHg6dOwSg7RaC88bNgy5eh9tuvo2f97oRl50nTEREvcf8kxkbD27ExoMbca7lHABgYP+BSI1OxXLNcoy9aazECcnVWMJERH3skPkQDEYD3j70tvMWguogNZbFLcPD0x/GkIAhEiekvsISJiLqAw7BgX988w8YjAaUnLp6GV9NhAa6eB1+O+G36O/bX8KEJAWWMBGRC7XYWvDmV29i3f51qPm+BgCg8FHgtxN+C328HgnqBIkTkpRYwkRELnDWchYbyjZgU/km/HjpRwBAkDIID097GMs0yxA5OFLagCQLLGEiol50sP4gDEYD3jnyDi47LgMARg0ehQxNBn437XcIVAZKnJDkhCVMRNRDdocdH9Z8CIPRgL21V2/ROnvkbOjidfj1uF/zFoLUIZYwEVE3WawWbKncgpf2v4RT508BAPop+iFpUhJ08TrEhMdInJDkjiVMRCTS6fOn8dL+l/Ba5WuwWNvudz40YCgejXkUaTPSEBEUIXFCchcsYSKiLhAEAaXflmJt6Vp8UP0BHIIDADDupnHIjM9EclQyBvQfIHFKcjcsYSKi62i1t+JvR/8Gg9GAsrNlznHtaC108TrcdctdUPi4/Nbs5KFYwkREHfjx4o/YXLEZ68vW41vLtwAApa8SC6csRGZ8JqaopkickDwBS5iI6Ge++f4brNu/Dq9XvY4LrRcAAKEDQ/F47ONYOmMpQgeGSpyQPAlLmIi8niAI2H16NwxGAz4+9jEEtN1cbkroFOjidVgwZQH8+/lLnJI8EUuYiLyW9bIV2w9vh8FowFfmr5zjc8fOhS5ehztG3cFbCJJLsYSJyOs0tDSg4GAB8g/kw9xiBgAE9AvAQ9EPIUOTgXEh4yROSN6CJUxEXuPIuSPIM+bhrX+9BavdCgCICIxAelw6Hol5BEMDhkqckLwNS5iIPJpDcODTE5/CYDTg0xOfOsdjw2Ohi9fh/on38xaCJBmWMBF5pAutF/DWV29h3f51ONp4FEDbLQTnj58PXbwOs9Sz+HkvSY4lTEQepb65Hvll+dhUvgnfX/weABDoF4jF0xZjuWY5Rg0ZJXFCoqtYwkTkESq+q4DBaEDh4UK0OloBAJGDI7E8bjkWT1+MIGWQxAmJrsUSJiK3ZXfY8fGxj2EwGvDFmS+c47PUs6CL1+He8fein4L/zZF88beTiNzOT7af8Hrl61i3fx1O/HgCQNstBO+feD908TrMiJghcUKirunWVcfz8/MRGRkJf39/aDQalJWVXXf58+fPIy0tDcOHD4dSqcStt96KoqKibgUmIu9V21SLP3z6B4xYOwLLi5fjxI8nMMR/CJ6c9SROZZzCtv/cxgImtyJ6JlxYWAi9Xo+CggJoNBrk5eUhMTERNTU1CA299pqqNpsNv/zlLxEaGor33nsPEREROHPmDAYPHtwb+YnICxi/NcJgNOBvX/8NdsEOABg7dCwy4zOREpWCgX4DJU5I1D0+giAIYlbQaDSYMWMGNmzYAABwOBxQq9VYtmwZVqxYcc3yBQUF+O///m9UV1ejf//unYtnsVgQHByMpqYmBAXx4Aoib3DZcRnvH30fBqMBxm+NzvE7Rt0BXbwO94y9h7cQJFkS01mifoNtNhvKy8uh1Wqv/gCFAlqtFqWlpR2u89FHHyEhIQFpaWlQqVSYPHkyVq9eDbvdLuapichLnL90Hi/sewFjXhqDpPeSYPzWCD9fPzwU/RCqHq1CSXIJfnXrr1jA5BFE7Y5ubGyE3W6HSqVqN65SqVBdXd3hOidPnsRnn32GhQsXoqioCMePH8fjjz+O1tZW5OTkdLiO1WqF1Wp1fm+xWMTEJCI3dOKHE1i3fx22VG5BS2sLAGDYgGFYGrsUS2csRdigMIkTEvU+lx8d7XA4EBoaildeeQW+vr6IiYnB2bNn8d///d+dlnBubi5WrVrl6mhEJDFBELDnzB4YjAZ8VPOR8xaCk4ZNgi5eh4VTF/IWguTRRJVwSEgIfH19YTab242bzWaEhXX8LnX48OHo378/fH19nWMTJkyAyWSCzWaDn5/fNetkZWVBr9c7v7dYLFCr1WKiEpGM2ew2FB4uhMFoQKWp0jl+9y13Qxevg3a0lpeUJK8gqoT9/PwQExODkpISzJ8/H0DbTLekpATp6ekdrjNr1ixs27YNDocDCkXbZzjHjh3D8OHDOyxgAFAqlVAqlWKiEZEbaLzQiE0HNyH/QD6+++k7AG23EEyOSkaGJgMThk2QOCFR3xK9O1qv1yMlJQWxsbGIi4tDXl4eWlpakJqaCgBITk5GREQEcnNzAQBLly7Fhg0bkJGRgWXLluGbb77B6tWrsXz58t59JUQkW0cbjiLPmIc3//UmLl2+BAAYPmg40uPS8WjMo7hpwE0SJySShugSTkpKQkNDA7Kzs2EymRAdHY3i4mLnwVq1tbXOGS8AqNVqfPLJJ9DpdJg6dSoiIiKQkZGBJ598svdeBRHJjiAI2HVyFwxGA4qPFzvHpw+fDl28Dg9MegB+vh3vDSPyFqLPE5YCzxMmch8XWy/i7UNvI8+YhyMNRwAAPvDBvePvhS5eh9kjZ/PzXvJoYjqL144mol5h+smElw+8jI0HN6LxQiMAYJDfIPwu+ndYrlmOMUPHSJyQSH5YwkTUI1+ZvoLBaMBfD/8VNrsNADAyeKTzFoKD/QdLG5BIxljCRCSaQ3Bg57GdMBgN+Pz0587xhBEJ0MXr8JsJv+EtBIm6gP9KiKjLWmwt2Fq1Fev2r8M3P3wDAPD18cV9E++DLl4HzQiNxAmJ3AtLmIhuqK6pDhvKNuCVildw/tJ5AECwMhiPxDyC9Lh0jAweKW1AIjfFEiaiTpWdLYPBaMC7R9513kLwlqG3IEOTgYeiH8Igv0ESJyRybyxhImrnsuMydlTvgMFowL66fc7xOZFzoIvXYe7YufBV+F7nJxBRV7GEiQgA0HSpCa9VvoaX9r+EM01nAAD9Ff2xYMoCZGoyMW34NIkTEnkeljCRlzv540m8tP8lbKncgmZbMwDgpoCb8FjsY0ibkYbhgcMlTkjkuVjCRF5IEATsrd0Lg9GAD2s+hENwAAAmhExAZnwmFk1dhID+ARKnJPJ8LGEiL2Kz2/DukXdhMBpQ/l25czxxTCIy4zOROCaRl5Qk6kMsYSIv8MPFH7Dp4CZsOLAB9c31AAD/fv5YNHURMjQZmBQ6SeKERN6JJUzkwWoaa5BnzMMbX72Bi5cvAgDCBoUhbUYaHo15FMMGDpM4IZF3YwkTeRhBEFByqgQGowFF3xQ5x6PDoqGL1yFpUhKU/ZQSJiSiK1jCRB7i0uVL2HZoG/KMeTh07hCAtlsIzhs3D7p4HW67+TZ+3kskMyxhIjdn/smMjQc3YuPBjTjXcg4AMLD/QKRGp2K5ZjnG3jRW4oRE1BmWMJGbOmQ+BIPRgLcPve28haA6SI1lccvw8PSHMSRgiMQJiehGWMJEbsQhOPCPb/4Bg9GAklMlznFNhAa6eB1+O+G36O/bX8KERCQGS5jIDbTYWvDmV29i3f51qPm+BgCg8FHgPyf8J3TxOiSoEyROSETdwRImkrGzlrPYULYBm8o34cdLPwIAgpRBWDJ9CZbFLcPNg2+WOCER9QRLmEiGDtYfhMFowDtH3sFlx2UAwKjBo5AZn4nU6FQEKgMlTkhEvYElTCQTdocdH9Z8CIPRgL21e53js0fOhi5eh1+P+zVvIUjkYVjCRBKzWC3YUrkFL+1/CafOnwIA9FP0Q9KkJOjidYgJj5E4IRG5CkuYSCKnz5/GS/tfwmuVr8FitQAAhgYMxaMxjyJtRhoigiIkTkhErqbozkr5+fmIjIyEv78/NBoNysrKurTe9u3b4ePjg/nz53fnaYncniAI+LL2S9z3zn0Y89IYGIwGWKwWjLtpHDbO3Yg6XR1W/5/VLGAiLyF6JlxYWAi9Xo+CggJoNBrk5eUhMTERNTU1CA0N7XS906dP4/e//z1mz57do8BE7qjV3or3vn4PBqMBB+oPOMe1o7XQxetw1y13QeHTrffEROTGfARBEMSsoNFoMGPGDGzYsAEA4HA4oFarsWzZMqxYsaLDdex2O/7jP/4Dv/vd7/DPf/4T58+fx44dO7r8nBaLBcHBwWhqakJQUJCYuESS+vHij3il/BVsOLAB31q+BQAofZVYOGUhMuMzMUU1ReKERNTbxHSWqJmwzWZDeXk5srKynGMKhQJarRalpaWdrvenP/0JoaGhWLx4Mf75z3+KeUoit/TN999g3f51eL3qdVxovQAACB0YisdjH8fSGUsROrDzvUZE5D1ElXBjYyPsdjtUKlW7cZVKherq6g7X2bt3L1577TVUVVV1+XmsViusVqvze4vFIiYmkSQEQcDu07thMBrw8bGPIaBtJ9OU0CnQxeuwYMoC+PfzlzglEcmJS4+Obm5uxqJFi7B582aEhIR0eb3c3FysWrXKhcmIeo/1shXbD2+HwWjAV+avnONzx86FLl6HO0bdwVsIElGHRJVwSEgIfH19YTab242bzWaEhYVds/yJEydw+vRpzJs3zznmcDjanrhfP9TU1GDMmDHXrJeVlQW9Xu/83mKxQK1Wi4lK5HINLQ0oOFiA/AP5MLe0/ZsY0H8AUqJSkKHJwLiQcRInJCK5E1XCfn5+iImJQUlJifM0I4fDgZKSEqSnp1+z/Pjx43Ho0KF2YytXrkRzczPWrVvXabEqlUoolUox0Yj6zJFzR5BnzMNb/3oLVnvbxyYRgRFIj0vHIzGPYGjAUIkTEpG7EL07Wq/XIyUlBbGxsYiLi0NeXh5aWlqQmpoKAEhOTkZERARyc3Ph7++PyZMnt1t/8ODBAHDNOJGcOQQHPj3xKQxGAz498alzPDY8Frp4He6feD9vIUhEooku4aSkJDQ0NCA7OxsmkwnR0dEoLi52HqxVW1sLhYLnO5JnuNB6AW999RbW7V+Ho41HAbTdQnD++PnQxeswSz2Ln/cSUbeJPk9YCjxPmPpafXM98svysal8E76/+D0AINAvEIunLcZyzXKMGjJK4oREJFcuO0+YyNNVfFcBg9GAwsOFaHW0AgAiB0diedxyLJ6+GEFKvgkkot7DEiavZ3fY8fdjf4fBaMCeM3uc47PUs6CL1+He8fein4L/VIio9/F/FvJazdZmvF71Ol7a/xJO/HgCQNstBO+feD908TrMiJghcUIi8nQsYfI6tU21WL9/PTZXbEaTtQkAMMR/CB6JeQTpcekYETRC4oRE5C1YwuQ1jN8aYTAa8Lev/wa7YAcAjB06FpnxmUiJSsFAv4ESJyQib8MSJo922XEZ7x99HwajAcZvjc7xO0bdAV28DveMvYe3ECQiybCEySOdv3Qer1a8ivVl61HbVAsA8PP1w4NTHkSmJhNRYVESJyQiYgmThznxwwms278OWyq3oKW1BQAwbMAwLI1diqUzliJs0LXXOCcikgpLmNyeIAjYc2YPDEYDPqr5yHkLwUnDJkEXr8PCqQt5C0EikiWWMLktm92GwsOFMBgNqDRVOsfvvuVu6OJ10I7W8pKSRCRrLGFyO40XGrHp4CbkH8jHdz99BwAI6BeA5KhkZGgyMGHYBIkTEhF1DUuY3MbRhqPIM+bhzX+9iUuXLwEAhg8ajvS4dDwa8yhuGnCTxAmJiMRhCZOsCYKAXSd3wWA0oPh4sXN8+vDp0MXr8MCkB+Dn6ydhQiKi7mMJkyxdbL2Itw+9jTxjHo40HAEA+MAH946/F7p4HWaPnM3Pe4nI7bGESVZMP5nw8oGXsfHgRjReaAQADPIbhN9F/w7LNcsxZugYiRMSEfUeljDJwlemr2AwGvDXw3+FzW4DAIwMHum8heBg/8HSBiQicgGWMEnGITiw89hOGIwGfH76c+d4wogE6OJ1+M2E3/AWgkTk0fg/HPW5FlsLtlZtxbr96/DND98AAHx9fHHfxPugi9dBM0IjcUIior7BEqY+U9dUhw1lG/BKxSs4f+k8ACBYGey8heDI4JHSBiQi6mMsYXK5srNlMBgNePfIu85bCN4y9BZkaDLwUPRDGOQ3SOKERETSYAmTS1x2XMaO6h0wGA3YV7fPOT4ncg508TrMHTsXvgpfCRMSEUmPJUy9qulSE16rfA0v7X8JZ5rOAAD6K/pjwZQFyNRkYtrwaRInJCKSD5Yw9YqTP57ES/tfwpbKLWi2NQMAbgq4CUtjl+LxGY9jeOBwiRMSEckPS5i6TRAE7K3dC4PRgA9rPoRDcAAAJoRMgC5eh/9v6v+HgP4BEqckIpIvRXdWys/PR2RkJPz9/aHRaFBWVtbpsps3b8bs2bMxZMgQDBkyBFqt9rrLk/zZ7Da8/a+3MWPzDPzH1v/AB9UfwCE4kDgmEf9Y+A8cefwIlsQsYQETEd2A6JlwYWEh9Ho9CgoKoNFokJeXh8TERNTU1CA0NPSa5Xfv3o0FCxZg5syZ8Pf3x5///GfceeedOHLkCCIiInrlRVDf+OHiD9h0cBM2HNiA+uZ6AIB/P38smroIGZoMTAqdJHFCIiL34iMIgiBmBY1GgxkzZmDDhg0AAIfDAbVajWXLlmHFihU3XN9ut2PIkCHYsGEDkpOTu/ScFosFwcHBaGpqQlBQkJi41AtqGmuQZ8zDG1+9gYuXLwIAwgaFIW1GGh6NeRTDBg6TOCERkXyI6SxRM2GbzYby8nJkZWU5xxQKBbRaLUpLS7v0My5cuIDW1lYMHTpUzFNTHxMEASWnSmAwGlD0TZFzPDosGrp4HZImJUHZTylhQiIi9yeqhBsbG2G326FSqdqNq1QqVFdXd+lnPPnkkwgPD4dWq+10GavVCqvV6vzeYrGIiUk9cOnyJWw7tA15xjwcOncIQNstBOeNmwddvA633XwbbyFIRNRL+vTo6DVr1mD79u3YvXs3/P39O10uNzcXq1at6sNkZP7JjI0HN2LjwY0413IOADCw/0CkRqdiuWY5xt40VuKERESeR1QJh4SEwNfXF2azud242WxGWFjYddd94YUXsGbNGvzP//wPpk6det1ls7KyoNfrnd9bLBao1WoxUamLDpkPwWA04O1DbztvIagOUmNZ3DI8PP1hDAkYInFCIiLPJaqE/fz8EBMTg5KSEsyfPx9A24FZJSUlSE9P73S9559/Hs899xw++eQTxMbG3vB5lEollEp+3ugqDsGBf3zzDxiMBpScKnGOayI00MXr8NsJv0V/3/4SJiQi8g6id0fr9XqkpKQgNjYWcXFxyMvLQ0tLC1JTUwEAycnJiIiIQG5uLgDgz3/+M7Kzs7Ft2zZERkbCZDIBAAYNGoRBg3jh/r7UYmvBm1+9iXX716Hm+xoAgMJHgf+c8J/QxeuQoE6QOCERkXcRXcJJSUloaGhAdnY2TCYToqOjUVxc7DxYq7a2FgrF1WuAbNy4ETabDffdd1+7n5OTk4M//vGPPUtPXXLWchYbyjZgU/km/HjpRwBAkDIIS6YvwbK4Zbh58M0SJyQi8k6izxOWAs8T7p6D9QdhMBrwzpF3cNlxGQAweshoZGgykBqdikBloMQJiYg8j8vOEyb5szvs+LDmQxiMBuyt3escnz1yNvQJesy7dR5vIUhEJBMsYQ9hsVqwpXILXtr/Ek6dPwUA6Kfoh6RJSdDF6xATHiNxQiIi+ncsYTd3+vxpvLT/JbxW+Ros1raLmgwNGIpHYx5F2ow0RATx+txERHLFEnZDgiBgX90+GIwG5x2MAGDcTeOQGZ+J5KhkDOg/QOKURER0IyxhN9Jqb8V7X78Hg9GAA/UHnOPa0Vro4nW465a7oPDp1t0piYhIAixhN/DjxR/xSvkr2HBgA761fAsAUPoqsXDKQmTGZ2KKaorECYmIqDtYwjJ27PtjWGdch61fbcWF1gsAgNCBoXg89nEsnbEUoQOvvX8zERG5D5awzAiCgN2nd2OtcS12HtsJAW2ncU8JnQJdvA4LpiyAf7/Ob35BRETugyUsE9bLVmw/vB0GowFfmb9yjs8dOxe6eB3uGHUHbyFIRORhWMISa2hpQMHBAuQfyIe5pe3uVAP6D0BKVAoyNBkYFzJO4oREROQqLGGJHDl3BHnGPLz1r7dgtVsBABGBEUiPS8cjMY9gaMBQiRMSEZGrsYT7kENw4NMTn8JgNODTE586x2PDY6GL1+H+iffzFoJERF6EJdwHLrRewFtfvYV1+9fhaONRAG23EJw/fj508TrMUs/i571ERF6IJexC9c31yC/Lx6byTfj+4vcAgEC/QCyethjLNcsxasgoiRMSEZGUWMIuUPFdBQxGAwoPF6LV0QoAiBwcieVxy7F4+mIEKXk7RiIiYgn3GrvDjr8f+zsMRgP2nNnjHJ+lngVdvA73jr8X/RTc3EREdBVboYearc14vep1vLT/JZz48QSAtlsI3j/xfujidZgRMUPihEREJFcs4W46c/4M1petx6sVr6LJ2gQAGOI/BI/EPIL0uHSMCBohcUIiIpI7lrBIpXWlMBgNeP/o+7ALdgDA2KFjkRmfiZSoFAz0GyhxQiIichcs4S647LiM94++D4PRAOO3Ruf4HaPugC5eh3vG3sNbCBIRkWgs4es4f+k8Xq14FevL1qO2qRYA4OfrhwenPIhMTSaiwqIkTkhERO6MJdyBEz+cwLr967ClcgtaWlsAAMMGDMPS2KVYOmMpwgaFSZyQiIg8AUv4fwmCgD1n9sBgNOCjmo+ctxCcNGwSdPE6LJy6kLcQJCKiXuX1JWyz21B4uBAGowGVpkrn+N233A1dvA7a0VpeUpKIiFyiW0cT5efnIzIyEv7+/tBoNCgrK7vu8u+++y7Gjx8Pf39/TJkyBUVFRd0K25saLzTiuT3PITIvEsk7klFpqkRAvwA8GvMovn78axQtLMIvx/ySBUxERC4jeiZcWFgIvV6PgoICaDQa5OXlITExETU1NQgNDb1m+X379mHBggXIzc3Fr371K2zbtg3z589HRUUFJk+e3CsvQoyjDUeRZ8zDm/96E5cuXwIADB80HOlx6Xg05lHcNOCmPs9ERETeyUcQBEHMChqNBjNmzMCGDRsAAA6HA2q1GsuWLcOKFSuuWT4pKQktLS34+OOPnWPx8fGIjo5GQUFBl57TYrEgODgYTU1NCArq/nWXbXYbwl8Md95MYfrw6dDF6/DApAfg5+vX7Z9LRER0hZjOEjUTttlsKC8vR1ZWlnNMoVBAq9WitLS0w3VKS0uh1+vbjSUmJmLHjh2dPo/VaoXVanV+b7FYxMTslJ+vH5bGLsXhhsPQxeswe+Rs7m4mIiLJiCrhxsZG2O12qFSqduMqlQrV1dUdrmMymTpc3mQydfo8ubm5WLVqlZhoXfan2//E4iUiIlmQ5WWesrKy0NTU5HzU1dX12s9mARMRkVyImgmHhITA19cXZrO53bjZbEZYWMcXsAgLCxO1PAAolUoolUox0YiIiNyOqJmwn58fYmJiUFJS4hxzOBwoKSlBQkJCh+skJCS0Wx4Adu3a1enyRERE3kL0KUp6vR4pKSmIjY1FXFwc8vLy0NLSgtTUVABAcnIyIiIikJubCwDIyMjAbbfdhhdffBFz587F9u3bcfDgQbzyyiu9+0qIiIjcjOgSTkpKQkNDA7Kzs2EymRAdHY3i4mLnwVe1tbVQKK5OsGfOnIlt27Zh5cqVeOqppzB27Fjs2LFDknOEiYiI5ET0ecJSaGpqwuDBg1FXV9ej84SJiIhczWKxQK1W4/z58wgODr7usm5x7ejm5mYAgFqtljgJERFR1zQ3N9+whN1iJuxwOFBfX4/AwEDRpxhdeUfCWbR43Hbdx23Xfdx23cdt1329ue0EQUBzczPCw8PbfTzbEbeYCSsUCowYMaJHPyMoKIi/lN3Ebdd93Hbdx23Xfdx23ddb2+5GM+ArZHmxDiIiIm/AEiYiIpKIx5ewUqlETk4Or8DVDdx23cdt133cdt3Hbdd9Um07tzgwi4iIyBN5/EyYiIhIrljCREREEmEJExERSYQlTEREJBGPKOH8/HxERkbC398fGo0GZWVl113+3Xffxfjx4+Hv748pU6agqKioj5LKj5htt3nzZsyePRtDhgzBkCFDoNVqb7itPZnY37srtm/fDh8fH8yfP9+1AWVM7LY7f/480tLSMHz4cCiVStx6661e++9W7LbLy8vDuHHjEBAQALVaDZ1Oh0uXLvVRWnnYs2cP5s2bh/DwcPj4+GDHjh03XGf37t2YPn06lEolbrnlFmzdutU14QQ3t337dsHPz0/YsmWLcOTIEWHJkiXC4MGDBbPZ3OHyX375peDr6ys8//zzwtdffy2sXLlS6N+/v3Do0KE+Ti49sdvuwQcfFPLz84XKykrh6NGjwkMPPSQEBwcL3377bR8nl57YbXfFqVOnhIiICGH27NnCvffe2zdhZUbstrNarUJsbKxwzz33CHv37hVOnTol7N69W6iqqurj5NITu+3efvttQalUCm+//bZw6tQp4ZNPPhGGDx8u6HS6Pk4uraKiIuHpp58W3n//fQGA8MEHH1x3+ZMnTwoDBgwQ9Hq98PXXXwvr168XfH19heLi4l7P5vYlHBcXJ6SlpTm/t9vtQnh4uJCbm9vh8g888IAwd+7cdmMajUZ49NFHXZpTjsRuu393+fJlITAwUHjjjTdcFVG2urPtLl++LMycOVN49dVXhZSUFK8tYbHbbuPGjcLo0aMFm83WVxFlS+y2S0tLE+644452Y3q9Xpg1a5ZLc8pZV0r4iSeeECZNmtRuLCkpSUhMTOz1PG69O9pms6G8vBxardY5plAooNVqUVpa2uE6paWl7ZYHgMTExE6X91Td2Xb/7sKFC2htbcXQoUNdFVOWurvt/vSnPyE0NBSLFy/ui5iy1J1t99FHHyEhIQFpaWlQqVSYPHkyVq9eDbvd3lexZaE7227mzJkoLy937rI+efIkioqKcM899/RJZnfVlz3hFjdw6ExjYyPsdjtUKlW7cZVKherq6g7XMZlMHS5vMplcllOOurPt/t2TTz6J8PDwa35ZPV13tt3evXvx2muvoaqqqg8Syld3tt3Jkyfx2WefYeHChSgqKsLx48fx+OOPo7W1FTk5OX0RWxa6s+0efPBBNDY24he/+AUEQcDly5fx2GOP4amnnuqLyG6rs56wWCy4ePEiAgICeu253HomTNJZs2YNtm/fjg8++AD+/v5Sx5G15uZmLFq0CJs3b0ZISIjUcdyOw+FAaGgoXnnlFcTExCApKQlPP/00CgoKpI4me7t378bq1avx8ssvo6KiAu+//z527tyJZ599Vupo9L/ceiYcEhICX19fmM3mduNmsxlhYWEdrhMWFiZqeU/VnW13xQsvvIA1a9bgf/7nfzB16lRXxpQlsdvuxIkTOH36NObNm+ccczgcAIB+/fqhpqYGY8aMcW1omejO793w4cPRv39/+Pr6OscmTJgAk8kEm80GPz8/l2aWi+5su2eeeQaLFi3Cww8/DACYMmUKWlpa8Mgjj+Dpp5++4b1uvVVnPREUFNSrs2DAzWfCfn5+iImJQUlJiXPM4XCgpKQECQkJHa6TkJDQbnkA2LVrV6fLe6rubDsAeP755/Hss8+iuLgYsbGxfRFVdsRuu/Hjx+PQoUOoqqpyPn7961/j9ttvR1VVFdRqdV/Gl1R3fu9mzZqF48ePO9+4AMCxY8cwfPhwrylgoHvb7sKFC9cU7ZU3MwJvG9CpPu2JXj/Uq49t375dUCqVwtatW4Wvv/5aeOSRR4TBgwcLJpNJEARBWLRokbBixQrn8l9++aXQr18/4YUXXhCOHj0q5OTkePUpSmK23Zo1awQ/Pz/hvffeE7777jvno7m5WaqXIBmx2+7fefPR0WK3XW1trRAYGCikp6cLNTU1wscffyyEhoYK//Vf/yXVS5CM2G2Xk5MjBAYGCn/961+FkydPCp9++qkwZswY4YEHHpDqJUiiublZqKysFCorKwUAwtq1a4XKykrhzJkzgiAIwooVK4RFixY5l79yitIf/vAH4ejRo0J+fj5PUbqe9evXCyNHjhT8/PyEuLg4wWg0Ov/utttuE1JSUtot/8477wi33nqr4OfnJ0yaNEnYuXNnHyeWDzHb7uabbxYAXPPIycnp++AyIPb37ue8uYQFQfy227dvn6DRaASlUimMHj1aeO6554TLly/3cWp5ELPtWltbhT/+8Y/CmDFjBH9/f0GtVguPP/648OOPP/Z9cAl9/vnnHf7fdWVbpaSkCLfddts160RHRwt+fn7C6NGjhddff90l2XgrQyIiIom49WfCRERE7owlTEREJBGWMBERkURYwkRERBJhCRMREUmEJUxERCQRljAREZFEWMJEREQSYQkTERFJhCVMREQkEZYwERGRRFjCREREEvn/AaE4nnG+0FtoAAAAAElFTkSuQmCC","text/plain":["<Figure size 500x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["np.random.seed(42)\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}