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Optimization of Utility in a Three-Bear Environment: A Quantitative Analysis

Title: Optimization of Utility in a Three-Bear Environment: A Quantitative Analysis

Abstract:

This paper presents a novel exploration into the optimization of utility within a tri-ursine environment. We examine the process of sequential decision-making under uncertainty, utilizing a unique dataset derived from an exploratory case study. The subject, henceforth referred to as 'Agent G', navigates through a series of choices involving porridge consumption, chair selection, and bed utilization. We employ advanced statistical techniques and mathematical modeling to analyze the outcomes and derive insights into optimal decision-making strategies.

  1. Introduction

In the realm of decision theory, the optimization of utility is a fundamental concern. This paper presents an empirical investigation into this topic, focusing on a unique case study involving an agent navigating a tri-ursine environment. The agent, referred to as 'Agent G', is presented with a series of choices, each with varying levels of utility. The choices involve the consumption of porridge, the selection of a chair for rest, and the utilization of a bed for sleep.

  1. Methodology

The utility function U(x) is defined as a measure of satisfaction that Agent G receives from consuming a certain amount of porridge x, sitting on a chair y, and sleeping on a bed z. The utility function is assumed to be quasi-linear and increasing, but at a decreasing rate, reflecting the law of diminishing marginal utility.

U(x, y, z) = α log(x) + β log(y) + γ log(z)

where α, β, γ > 0 are parameters that capture the relative importance of each choice to Agent G.

  1. Results

3.1 Porridge Consumption

Agent G was presented with three bowls of porridge, each at a different temperature: hot (T1), lukewarm (T2), and cold (T3). Agent G sampled each bowl in sequence, and her utility was calculated for each. The optimal temperature T* was found to be T2, yielding the highest utility.

3.2 Chair Selection

Agent G was then presented with three chairs of varying sizes: large (S1), medium (S2), and small (S3). After testing each chair, Agent G derived the highest utility from S3, despite its subsequent structural failure.

3.3 Bed Utilization

Finally, Agent G was presented with three beds of varying firmness: hard (F1), medium (F2), and soft (F3). After testing each bed, Agent G derived the highest utility from F2.

  1. Discussion

Our analysis reveals that Agent G's optimal choices were the lukewarm porridge, the small chair, and the medium bed. This suggests a preference for moderate extremes in the case of porridge and bed, but an inclination towards the smallest size in the case of the chair. These findings contribute to the literature on decision-making under uncertainty and have implications for the design of environments intended for human comfort and satisfaction.

  1. Conclusion

This study provides a rigorous, quantitative analysis of utility optimization in a tri-ursine environment. The findings underscore the importance of personal preference in decision-making and highlight the value of empirical, data-driven approaches to understanding human behavior. Future research could extend this work by exploring the role of other factors, such as risk and time preferences, in shaping utility optimization strategies.

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{
"cells": [
{
"cell_type": "markdown",
"source": [
"## 3. Results\n",
"\n",
"In this section, we present the results of our analysis. We first define the utility functions for each choice - porridge consumption, chair selection, and bed utilization. We then calculate the utility derived from each option and identify the optimal choice in each category.\n",
"\n",
"### 3.1 Porridge Consumption\n",
"\n",
"We model the utility derived from porridge consumption as a function of its temperature. We assume that the utility is maximized at a certain optimal temperature and decreases as the temperature deviates from this optimum. This can be represented by a quadratic function:\n",
"\n",
"$$U(T) = -a(T - T*)^2 + b$$\n",
"\n",
"where:\n",
"- $U(T)$ is the utility derived from consuming porridge of temperature $T$,\n",
"- $T*$ is the optimal temperature,\n",
"- $a$ and $b$ are parameters that shape the utility function.\n",
"\n",
"Given the temperatures of the three bowls of porridge (T1, T2, T3), we can calculate the utility derived from each and identify the one that maximizes utility."
],
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"noteable": {
"cell_type": "markdown"
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"noteable-chatgpt": {
"version": "0.16.0"
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"id": "f49bc865-3139-4c50-a02b-eafce2ca30ff"
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{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the temperatures of the three bowls of porridge\n",
"T1 = 90 # hot\n",
"T2 = 50 # lukewarm\n",
"T3 = 10 # cold\n",
"\n",
"# Define the parameters of the utility function\n",
"a = 0.01\n",
"b = 100\n",
"\n",
"# Define the utility function\n",
"def U(T, T_star):\n",
" return -a * (T - T_star)**2 + b\n",
"\n",
"# Calculate the utility derived from each bowl of porridge\n",
"U_T1 = U(T1, T2)\n",
"U_T2 = U(T2, T2)\n",
"U_T3 = U(T3, T2)\n",
"\n",
"# Plot the utility function\n",
"T = np.linspace(0, 100, 1000)\n",
"plt.plot(T, U(T, T2))\n",
"plt.scatter([T1, T2, T3], [U_T1, U_T2, U_T3], color='red')\n",
"plt.xlabel('Temperature')\n",
"plt.ylabel('Utility')\n",
"plt.title('Utility derived from porridge consumption')\n",
"plt.grid(True)\n",
"plt.show()\n",
"\n",
"U_T1, U_T2, U_T3"
],
"outputs": [
{
"output_type": "display_data",
"data": {
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aFBUVYerUqeWe/8yZMwgKCqrw+Uu/5Hr37o2cnBxs2bKlzOPXrFnzwPHdS+kspVWrVpU5vnHjRuTl5d13+npNWb16dZnbhw8fRlxcnGH2TJcuXWBjY1MuzoSEBOzZs6dW4uzduzd2796NGzduGI7pdLpyf0ePPPIIAJQ7/ssvv5SbYVXV66AiYWFhUCgUWLJkSaVlarue7OzsMGjQILz99tsoLi7G2bNnAcDQ3Xzq1Kky5bdu3fpQz3cvd18zpX8jdy5wqlarq/Q51qRJE/j4+GDNmjVlPkvy8vKwceNGwwwtMi627FC1BAUF4fnnn8cnn3yCzMxMDB48GDY2Njh69CgWLVqE9u3blxkTEhQUBBsbG6xevRpNmzaFvb09vL297/lBfD8tWrQAAHz33XdwcHCAtbU1AgMDDb+oFAoFnnvuOcyZMwd2dnZVWqVYLpfj/fffx/Tp0zFy5Eg89dRTyMzMRHh4eLmuhscffxyrV6/G4MGD8eKLL6Jjx45QKpVISEjA3r17MXz4cIwcOfKBX9+0adMwY8YMJCUloWvXruWSp/feew8RERHo2rUrZs2ahSZNmqCwsBCxsbHYtm0bvvnmG/j6+mLSpEn4/PPPMWnSJCxYsACNGzfGtm3bsGPHjgeO7V769++PAQMGYM6cOcjOzka3bt1w6tQpzJs3D6GhoZg4cWKtPO/djh07hunTp2PMmDGIj4/H22+/DR8fH8ycORMAUK9ePcydOxdvvfUWJk2ahPHjxyM9PR3z58+HtbU15s2bV+MxvfPOO9iyZQv69OmDd999F7a2tvj666+Rl5dXplzz5s0xfvx4/Pe//4VCoUCfPn1w9uxZ/Pe//4WTk1OZMSBVvQ4qEhAQgLfeegvvv/8+CgoKDNOez507h7S0NMyfP79W6umpp56CjY0NunXrBi8vL6SkpODDDz+Ek5OToeVv8ODBcHFxwX/+8x+89957sLKywvLlyytcUqImqFQq/Pe//0Vubi46dOiAw4cP44MPPsCgQYPQvXt3Q7mWLVti37592Lp1K7y8vODg4FDhDxu5XI6PP/4YTzzxBIYOHYoZM2agqKjI8Jm5aNGiWnkddB/Sjo8mc6TX68WSJUtE+/btha2trVCpVKJx48Zizpw5Iicnp1z5tWvXipCQEKFUKsvMUnnQ2VhCCLF48WIRGBgoFApFhTOLYmNjBQDxzDPPVOu1/fDDD6Jx48ZCpVKJ4OBgsXTpUjF58uQys7GEEEKj0YhPP/1UtG7dWlhbWwt7e3sREhIiZsyYIS5fvmwo5+/vL4YMGVLhc909G6tUVlaWsLGxEQDE999/X+Fjb968KWbNmiUCAwOFUqkULi4uol27duLtt98Wubm5hnIJCQli9OjRwt7eXjg4OIjRo0eLw4cP18hsrIpm5BUUFIg5c+YIf39/oVQqhZeXl3j22WfLTPu+V70AEM8991yV4rhb6WydnTt3iokTJ4p69eoZZhPd+Z6U+uGHH0SrVq2ESqUSTk5OYvjw4eVmME2ePFnY2dlV+HwVxXrnfXdfs3/99Zfo3LmzUKvVwtPTU7z22mviu+++KzfDqLCwULz88svC3d1dWFtbi86dO4vIyEjh5OQkXnrppTLnrOp1UJmVK1eKDh06GK7h0NDQctfFw9TT3X/jK1asEL179xYeHh5CpVIJb29vMXbsWHHq1Kkyjzty5Ijo2rWrsLOzEz4+PmLevHnihx9+qHA21sNcR6Vxnzp1SvTq1UvY2NgIFxcX8eyzz5arv+joaNGtWzdha2srABg+pyqaei5EyeyvTp06CWtra2FnZyf69u0r/vrrrwrr5+6/pYpmntHDkQlxRzsbkYX48ssvMWvWLJw5c8YwYJMs2/LlyzF16lQcPXpU8nFjNe3w4cPo1q0bVq9eXWOz6ahk5uAvv/yC3NxcqUOhWsZuLLIoJ06cQExMDN577z0MHz6ciQ6ZnYiICERGRqJdu3awsbHByZMnsWjRIjRu3BijRo2SOjwis8RkhyzKyJEjkZKSgh49euCbb76ROhyianN0dMTOnTuxePFi5OTkwM3NDYMGDcKHH35Ybmo3EVUNu7GIiIjIonHqOREREVk0JjtERERk0ZjsEBERkUXjAGWUbBaZlJQEBweHai3tT0RERNIRQiAnJwfe3t5lFt28G5MdlOxXUtn+MERERGTa4uPj77mxLZMd/LtxY3x8fKW7Gz8IjUaDnTt3IiwsTNKdwOsC1rVxsJ6Ng/VsHKxn46jNes7Ozoafn1+5DZjvxmQH/+5c7OjoWOPJjq2tLRwdHfmHVMtY18bBejYO1rNxsJ6Nwxj1fL8hKBygTERERBaNyQ4RERFZNCY7REREZNGY7BAREZFFY7JDREREFo3JDhEREVk0JjtERERk0ZjsEBERkUVjskNEREQWjSsoE5Hl0umAgweB5GTAywvo0QNQKKSOioiMTNKWnQMHDmDYsGHw9vaGTCbDr7/+WuZ+IQTCw8Ph7e0NGxsb9OrVC2fPni1TpqioCC+88ALc3NxgZ2eHRx99FAkJCUZ8FURkkjZtAgICgN69gQkTSv4bEFBynIjqFEmTnby8PLRu3RpfffVVhfd//PHH+Oyzz/DVV1/h6NGj8PT0RP/+/ZGTk2MoM3v2bGzevBnr1q3DoUOHkJubi6FDh0Kn0xnrZRCRqdm0CXjsMeDuHz6JiSXHmfAQ1SmSdmMNGjQIgwYNqvA+IQQWL16Mt99+G6NGjQIArFixAh4eHlizZg1mzJiBrKws/Pjjj/jpp5/Qr18/AMCqVavg5+eHXbt2YcCAAUZ7LURkGoRWi+KXXkGR0gbFVkoUK5RQCD2UOi2UOg1Uei1Us2dDNnw4u7SI6giTHbMTExODlJQUhIWFGY6p1Wr07NkThw8fxowZMxAVFQWNRlOmjLe3N1q0aIHDhw9XmuwUFRWhqKjIcDs7OxtAyc6sGo2mxl5D6blq8pxUMda1cUhdz0IIpGQX4fqtfMSl5+P6rQIkZBQgLa8It/KKcStPg4y8YujHV9xaXEqlLYbzezvg7GwPZ1slPB3V8HO2hZ+LDfycbdCwvh2cbVVGelXlSV3PdQXr2Thqs56rek6TTXZSUlIAAB4eHmWOe3h4IC4uzlBGpVLB2dm5XJnSx1fkww8/xPz588sd37lzJ2xtbR829HIiIiJq/JxUMda1cRijnoUA0ouAmBwZEvJkSMwDEvNkyNfJqnUehUxAANCLfx9XbKXCjSKBGyk5lT7OSSXgYyvgYwf42QkEOQrYKx/01TwYXs/GwXo2jtqo5/z8/CqVM9lkp5RMVvaDTQhR7tjd7lfmzTffxMsvv2y4nZ2dDT8/P4SFhcHR0fHhAr6DRqNBREQE+vfvD6XSyJ+SdQzr2jhqu54TMgpw6Eo6jsTewtHYDKRkF5UrYyWXwdfZBg1cbNDAxRZ+zjao76CGi50KLrYqOJ89Abvx46DSFUOl06L0k0APGTQKBYoVKmSrbZHx7TJkBDfDrbxiJGUVIiGjAPEZBbh+Kx+JmYXIKpYhq1iGc5n/PndDNzt0CKiHToEu6NHIDfVsa+da4/VsHKxn46jNei7tmbkfk012PD09AZS03nh5eRmOp6amGlp7PD09UVxcjIyMjDKtO6mpqejatWul51ar1VCr1eWOK5XKWrnga+u8VB7r2jhqqp51eoHo+AzsOp+KPedTcfFG2ZYWpUKGlj5OaOVbD828HdHMyxHBHg5QWd1jboVPL8DBBki8VdI8dAc1AMhkcPG1RcCwXpWO2ckp1OBiSg7OJ2fjbFI2jl/PwKUbubiWlodraXlYfywRchnQtoEzeoe4o38zDwR7ODxUXVSE17NxsJ6NozbquarnM9lkJzAwEJ6enoiIiEBoaCgAoLi4GPv378dHH30EAGjXrh2USiUiIiIwduxYAEBycjLOnDmDjz/+WLLYiahyQgicSczGb9GJ2HoqCTfuaL2Ry4B2/s7oEuSGzoEuCG3gDBtVNQcRKxTAF1+UzLqSycomPKUtvosX33NwsoO1Eu0DXNA+wMVwLCOvGMfiMnAkJh0HLqXh4o0cHIvLwLG4DHyy4yKaeDhgWGsvDGvtDX9Xu+rFTES1StJkJzc3F1euXDHcjomJQXR0NFxcXNCgQQPMnj0bCxcuROPGjdG4cWMsXLgQtra2mDBhAgDAyckJ//nPf/DKK6/A1dUVLi4uePXVV9GyZUvD7CwiMg03c4rw87F4bDyegGs38wzHHayt0KuJO/o1dUfP4PqoVxMDg0eNAn75BXjxxbLTz319SxKd2zM8q8PZToX+zTzQv5kH3h4CJGTkY+/Fm9h7IRWHLpckPxd35uDTnZfQxq8exnf0w7DW3rBVmexvSqI6Q9K/wmPHjqF3796G26XjaCZPnozly5fj9ddfR0FBAWbOnImMjAx06tQJO3fuhIPDv83Fn3/+OaysrDB27FgUFBSgb9++WL58ORScUkokOSEEIq+mY/U/17HjbAq0+pJWFrWVHP2aeWB4a2/0bFIfaqta+HsdNQoYPrzWVlD2dbbFxM7+mNjZH1kFGuw4k4Ktp5Lw15U0RMdnIjo+E+//fh4jQr0xoaM/mnnX3HhAIqoeSZOdXr16QdzVp34nmUyG8PBwhIeHV1rG2toaX375Jb788staiJCIHkSxVo/fohPx3YFruJyaazge2qAexndsgMEtvWCvNsLHj0IB9OpV60/jZKPE2A5+GNvBDzdzirDxeALWHrmOuPR8rPr7Olb9fR1dg1zx9CMN0TO4/n0nWRBRzWL7KhHVmJxCDdYdicePh2KQkl0IALBTKTCyrU+dad2o76DGMz2D8HSPhvj7WjpWH7mO7WdScPhqOg5fTUcTDwdM7xGIEaE+UCq4FzORMTDZIaKHllekxbK/YvDdgWvILtQCANwd1JjWPRATOjWAo3Xdm+kil8vQtZEbujZyQ2JmAZYdisHaI9dx8UYOXvvlFL7aewWz+jTG8DbesGLSQ1SrmOwQ0QMr1Oiw+p/r+L+9V5CeVwwAaFjfDjMeaYgRoT61MxbHDPnUs8E7Q5vhhb6NsfbIdXx/4Bri0vPxyoaT+HrfFbzYtzGGtvKGQs7uLaLawGSHiKpNrxf4+Wg8Pt91CclZJd1VAa62eKl/MIa18oacX9oVcrJR4pmeQZjUxR8rDsfh2wNXce1mHl5cF41v9l/D3KFN0TXITeowiSwOkx0iqpaYHGD0t//gTFLJyqVeTtZ4sW9jjG7nyzEoVWSrssKzvYLwZOcGWHE4Ft8duIbzydmY8P0/CGvmgdfDGksdIpFFYbJDRFWSklWIhX+cw5YzVgCy4aC2wqy+jTGxiz+sleyuehAO1ko836cxnujkj8W7LmHVP9ex89wN7L2Yih7ucjxSpIUzV/Ylemj8GUZE96TTC/x4KAZ9/rsPW04lQwaBMe18sOfVXnjqkYZMdGqAs50K84e3wPYXe+CR4PrQ6AT2JMsx+MvDiDh3Q+rwiMweW3aIqFLnk7PxxsZTOJmQBQAI9XNCn3rpeGZEc+4lVAsaezhg5bSOiDibhDd+Po7krEI8tfIYBrXwRPijzeHhaC11iERmiS07RFROoUaHT3dcxLAvD+FkQhYc1FZYOLIl1k3viAb2Ukdn+XoF18cbrXV4ukcAFHIZ/jyTgn7/3Y/V/8TdcyFWIqoYkx0iKuNMYhaGfnkIX+29Aq1eIKyZB3a90hMTOjXgLCsjUimA18KCsfX57mjtVw85RVq8vfkMpi4/itTbCzYSUdUw2SEiACVjc77eewUjvv4LV1Jz4WavxjdPtsV3k9qz+0RCzbwdsenZrnhnSFOorOTYd/EmwhYfwO+nkqQOjchscMwOESH+Vj5e/jkaR2MzAAADm3ti4aiWcLGrgR3I6aEp5DJM71Gyr9ZLP0fjTGI2nl9zAjvP3sAHI1vUyRWqiaqDLTtEddzWk0kY9MVBHI3NgJ1KgY8fa4UlT7ZlomOCGns4YNOz3TCrTyMo5DJsOZmEof87hNO3B5ATUcWY7BDVUUVaHd797QxeWHsCuUVatPN3xp8vPoKx7f24K7cJU1nJ8XJYE2x4pgt8nW1w/VY+Ri85jBWHYzl4magSTHaI6qD4W/kY+00kVkbGAQBm9grC+qc7o4GrrcSRUVW1beCMP17ogbBmHijW6TFvy1nMXH0c2YUaqUMjMjlMdojqmD0XbmDo7SnlTjZKLJ3SHq8PDOHO22bIyVaJbye2w7tDm0GpKJmiPuzLQ7h0I0fq0IhMCj/diOoIIUpmW/1nxTFkFWjQxq8e/pjVHX1CPKQOjR6CTCbDtO6B+OWZrvCpZ4O49HyM/Pov7DibInVoRCaDyQ5RHVBQrMOsddH4ZMdFCAFM7OyPn2d0ga8zu60sRWu/etjyfDd0buiCvGIdZvwUhc8jLkGv5zgeIiY7RBYuOasAY7+NxNaTSbCSy7BgZAu8P6IFVFb887c0rvZq/PSfTpjSNQAA8MXuy3hmVRTyirTSBkYkMX7aEVmwk/GZePSrv3A6MQsudiqsnt4JT3TylzosqkVKhRzhjzbHx4+1gkohx85zNzD220jc4KrLVIcx2SGyULvP38Dj3/2NmzlFCPF0wG/PdUOnhq5Sh0VGMra9H9bN6AxXOxXOJmVj5Nd/4WIKBy5T3cRkh8gCrf4nDk+tPIYCjQ49g+vjl2e7ws+F43PqmrYNnLF5Zjc0rG+HpKxCPLbkMP66kiZ1WERGx2SHyIIIIfDpjot4e/MZ6AUwtr0vfpjcHvZq7gxTVzVwtcWmZ7uiY6ALcoq0mLz0CH6JSpA6LCKjYrJDZCGKtXq8suEkvtp7BQAwu19jfDS6FZRcP6fOq2erwk//6Yjhbbyh1Qu8uuEkfjh4TeqwiIyGP/eILEChRoeZq49jz4VUKOQyfDiyJcZ28JM6LDIhaisFFo9rA09Ha3x74Bo++OM8sgo0eLl/MLcHIYvHn3xEZi63SIupy45iz4VUWCvl+GFSeyY6VCGZTIY3BzfF6wObAAC+3HMF7/52lmvxkMVjskNkxrLyNXjyh38QeS0d9morrJjaEb1D3KUOi0zczF6N8MGIFpDJgJ/+jsNLP0dDo9NLHRZRrWGyQ2Sm0nKL8Pj3fyM6PhNONkqsnt6JU8upyp7s7I8vHg+FlVyG36KT8OyqKBRpdVKHRVQrmOwQmaGUrEKM/TYS55Oz4WavxvoZndHar57UYZGZebS1N76f1B5qKzl2nU/Fs6uOM+Ehi8Rkh8jMpGYXYsL3f+PazTx4O1ljwzNdEOLpKHVYZKZ6h7hj6ZQOUFvJsecCEx6yTEx2iMxIak4hxn//N66l5cGnng3Wz+iCQDc7qcMiM9etkRuWTukAa2VJwvPMT+zSIsvCZIfITKTlFuGJ7//B1dstOuue7sxVkanGdGvkhqWTSxKevRdv4pmfolCoYcJDloHJDpEZSL+d6FxOzYWnozXWMtGhWtD1roRn5urjKNZylhaZPyY7RCYuM78YT/zwDy7eyIGHoxprn+4Mf1d2XVHt6HpXl9ZLP0dDx3V4yMwx2SEyYXlFWkxZdhQXUnJQ30GNNU915hgdqnVdg9zwzZPtoFTI8MepZLy9+TSEYMJD5ovJDpGJKtLq8MyqKETHZ6Kebck6OkH17aUOi+qIXk3c8cXjoZDLgHVH47Hgj/NMeMhsMdkhMkE6vcBL66Nx8HIabFUKLJ/aEcEeDlKHRXXM4JZeWDS6FQDgh0Mx+N/uKxJHRPRgmOwQmRghBN7efBrbTqdApZDju4nt0YYLBpJExrb3w7tDmwEAPt91Ccv+ipE4IqLqY7JDZGI+2n4R647GQy4Dvni8Dbo3dpM6JKrjpnUPxEv9ggEA7/1+Dn+cSpY4IqLqYbJDZEKWHorBN/uvAgAWjGyJQS29JI6IqMSsvo0wqYs/hABeWh+Nf66lSx0SUZUx2SEyEdvPpOD9P84BAF4b0ATjOzaQOCKif8lkMswb1hwDmnugWKfHUyuP4dKNHKnDIqoSJjtEJuD49Qy8uO4EhACe6NQAM3sFSR0SUTkKuQxfPB6Kdv7OyC7UYsrSI0jJKpQ6LKL7YrJDJLG49DxMX3EMRVo9+oS4Y/6jzSGTyaQOi6hC1koFfpjUHg3r2yEpqxBTlh1BdqFG6rCI7onJDpGEbuUVY8qyo7iVV4wWPo74cnworBT8syTT5mynwoqpHeFmr8aFlBw8t/o4NDpuK0Gmi5+qRBIp1Ojw9MpjiLm9g/nSyR1gp7aSOiyiKvFzscXyqR1gq1Lg4OU0vP/7OalDIqoUkx0iCQgh8Oam0zgWlwEHayssn9oB7o7WUodFVC0tfJzw+bg2kMmAlZFxWBkZK3VIRBViskMkgW8PXMPmE4lQyGX45sl2aMzVkclMDWjuidcHhAAA5m89hwOXbkocEVF5THaIjGz3+Rv4aPsFAMC8Yc3QrREXDSTz9kzPhhjd1hc6vcBza47jSmqu1CERlcFkh8iILt3Iway1JVPMJ3RqgImd/aUOieihyWQyLBzVAh0CnJFTqMV/VhxFRl6x1GERGTDZITKSW3nFmL7iGPKKdejc0IVTzMmiqK0U+ObJdvB1tkFcej6eW3McWs7QIhPBZIfICDQ6PWaujsL1W/nwc7HB/z3RDkpOMScL42qvxtIpHWCnUuDw1XRDdy2R1PhpS2QEH267gL+v3YKdSoEfJ3eAi51K6pCIakWwhwM+HdMaAPD9wRhsOZkkcURETHaIat2Wk0lY+lcMAOCzcW0QzJlXZOEGtfTCs7e3PHn9l5M4n5wtcURU1zHZIapFl27kYM4vpwAAM3sFYUBzT4kjIjKOV8OaoEdjNxRq9JjxUxQy8zlgmaTDZIeolmQXavDMT1Eo0OjQvZEbXglrInVIREajkMvwv8dD4etsg+u38jFrXTR0eiF1WFRHMdkhqgVCCLz680lcS8uDt5M1vni8DRRyzryiusXZToVvJ7aDtVKOA5duYvGuS1KHRHWUySc7OTk5mD17Nvz9/WFjY4OuXbvi6NGjhvunTJkCmUxW5l/nzp0ljJgI+Gb/New8dwMqhRz/92Q7uNqrpQ6JSBLNvZ2waFQrAMBXe69gP1dYJgmYfLIzffp0RERE4KeffsLp06cRFhaGfv36ITEx0VBm4MCBSE5ONvzbtm2bhBFTXXf4Sho+2VEy5Tb80eZo41dP2oCIJDYi1AdPdGoAIYCX1kcjOatA6pCojjHpZKegoAAbN27Exx9/jEceeQSNGjVCeHg4AgMDsWTJEkM5tVoNT09Pwz8XFxcJo6a6LDWnELPWRUMvgDHtfDG+o5/UIRGZhLlDm6GZlyNu5RVj1toTXHCQjMpK6gDuRavVQqfTwdq67G7QNjY2OHTokOH2vn374O7ujnr16qFnz55YsGAB3N3dKz1vUVERioqKDLezs0umRWo0Gmg0mhqLv/RcNXlOqpgp1LVeLzB73Qmk5RYh2N0e7w5pAq1WK1k8tcEU6rkusMR6VgD437hWGL4kEkdjM/DJ9gt4NayxpDFZYj2botqs56qeUyaEMOnh8V27doVKpcKaNWvg4eGBtWvXYtKkSWjcuDEuXryI9evXw97eHv7+/oiJicHcuXOh1WoRFRUFtbricRLh4eGYP39+ueNr1qyBra1tbb8kslA7E2T4I14BlVzglZY6ePJSIirnRLoMyy8pAABPh+jQ3Nmkv4LIxOXn52PChAnIysqCo6NjpeVMPtm5evUqpk2bhgMHDkChUKBt27YIDg7G8ePHce7cuXLlk5OT4e/vj3Xr1mHUqFEVnrOilh0/Pz+kpaXds7KqS6PRICIiAv3794dSqayx81J5Utf1sbgMPLn0GHR6gUUjm2N0Wx+jx2AMUtdzXWHp9Tz/9/NY9U886tkoseW5LvBysr7/g2qBpdezqajNes7Ozoabm9t9kx2T7sYCgKCgIOzfvx95eXnIzs6Gl5cXxo0bh8DAwArLe3l5wd/fH5cvX670nGq1usJWH6VSWSsXfG2dl8qToq4z8orx8obT0OkFRob6YFxHf4vf4JPXtHFYaj3PHdYcJxOycToxCy9tOI11T3eWdK84S61nU1Mb9VzV85n0AOU72dnZwcvLCxkZGdixYweGDx9eYbn09HTEx8fDy8vLyBFSXSSEwGu/nEJyViEC3ezw/ogWFp/oED0stZUCX09oCwdrK0TFZeDL3ZX/OCWqCSaf7OzYsQPbt29HTEwMIiIi0Lt3bzRp0gRTp05Fbm4uXn31VURGRiI2Nhb79u3DsGHD4ObmhpEjR0odOtUBy/6Kxa7zN6CykuOrCaGwV5t8YymRSWjgaouFI1sCKFl/50jMLYkjIktm8slOVlYWnnvuOYSEhGDSpEno3r07du7cCaVSCYVCgdOnT2P48OEIDg7G5MmTERwcjMjISDg4cLNFql1nk7Lw4Z/nAQDvDGmK5t5OEkdEZF6GtfbG6La+0N9efyergLOiqHaY/M/QsWPHYuzYsRXeZ2Njgx07dhg5IiKgUKPD7HXR0OgE+jfzwMTO/lKHRGSW5g9vjmNxtxCXno93fj2D/z3ehl3BVONMvmWHyBR9tP0CLqfmor6DGh+NbsUPZ6IHZK+2wuJxJXvHbT2ZhE3HE+//IKJqYrJDVE0HLt3Esr9iAQCfPNYKLnYqaQMiMnOhDZzxUr+SBQbf/e0M4tLzJI6ILA2THaJqyMgrxqsbTgIAJnfxR68mla/UTURV92yvRugY4IK8Yh1eXBcNDbeToBrEZIeoioQQeHPTaaTmFCGovh3eGNRU6pCILIZCLsPnj7eBg7UVouMz8dWeK1KHRBaEyQ5RFf0SlYDtZ1NgJZfhi8dDYaNSSB0SkUXxqWeDBbeno3+99wpOJ2RJHBFZCiY7RFUQfysf87eWbE/yclgwWvhwmjlRbXi0tTeGtPKCVi/wyoZoFGp0UodEFoDJDtF96PUCr2w4idwiLToGuGDGI0FSh0Rk0d4f3gJu9mpcupGLz3ddkjocsgBMdojuY2VkLI7E3IKtSoFPx7SGQs5p5kS1ycVOhQ9HlXRnfXfgGqLiuLoyPRwmO0T3EJuWh0XbLwAA3hwUggauthJHRFQ39G/mgcfa+UII4JWfTyK/WCt1SGTGmOwQVUKvF3j9l1Mo1OjRNcgVT3TiKslExvTusGbwdrJGbHo+PvrzgtThkBljskNUieWHY3Ek9hbsVAp8NLoV5Oy+IjIqR2slPn6sNQBgRWQc/rqSJnFEZK6Y7BBVICYtDx/vuN19Nbgp/FzYfUUkhe6N3Qx7z73+yynkFrE7i6qPyQ7RXXR6gdc2nEShRo/ujdzwRKcGUodEVKe9OTgEfi42SMwswCfb2Z1F1cdkh+guy/6KwbG4DNirrbBodEtu8kkkMVuVFRaNagUAWPl3HI7GcnYWVQ+THaI7XE/Px6c7LwIA3hrcFL7O7L4iMgXdGrlhXHs/CAHM2XiKiw1StTDZIbpNCIG3Np82zL4a39FP6pCI6A5vDWkKdwc1rt3Mw5d7LksdDpkRJjtEt206nohDV9KgtpJj4Uh2XxGZGicbJd4b3gIA8M3+azibxL2zqGqY7BABSMstwvt/lOx9NbtfMALc7CSOiIgqMrCFJwa39ITu9jpYWp1e6pDIDDDZIQLw/u/nkJmvQVMvR0zvESh1OER0D+GPNoeTjRJnk7Lx3cFrUodDZoDJDtV5ey+m4rfoJMhlwEejW0Kp4J8FkSlzd7DG3KHNAACLd13GtZu5EkdEpo6f6lSn5RVp8c7mMwCAqd0C0cq3nrQBEVGVjG7rgx6N3VCs1eOdX89ACCF1SGTCmOxQnfZZxCUkZhbAp54NXu4fLHU4RFRFMpkMC0a0hNpKjsNX0/FbdJLUIZEJY7JDddbJ+Ews+ysGALBgZAvYqa0kjoiIqqOBqy1m9W0MAPjgj3PIytdIHBGZKiY7VCdpdXq8uek09AIY0cYbvZq4Sx0SET2Ap3o0RCN3e6TlFmMRt5KgSjDZoTpp1d9xOJecDScbJd65PdCRiMyPykqOBSNK1t5Ze+Q6ouK4lQSVx2SH6pzU7EL8d+clAMDrA5vAzV4tcURE9DA6NXTFmHa+AIC3N5+Bhmvv0F2Y7FCds3DbeeQUadHa1wmPd+CO5kSW4M3BTeFsq8SFlBzDWDyiUkx2qE45fDUNv0YnQSYD3h/RAgo5t4QgsgQudiq8ObgpAODziMtIyMiXOCIyJUx2qM4o1urx7m9nAQBPdvLnmjpEFmZMO190DHRBgUaH+VvPSR0OmRAmO1Rn/HgoBldSc+Fqp8KrYU2kDoeIaljJ2jstYCWXIeLcDey7mCp1SGQimOxQnZCYWYD/7b4MoKRv38lWKXFERFQbGns4YErXAADA/K3nUKTVSRsQmQQmO1QnvLf1LAo0OnQMcMHotj5Sh0NEtejFfo3hZq9GTFoelh6KlTocMgFMdsji7b2Yih1nb0Ahl+G9Ec0hk3FQMpElc7BW4q3BIQCAL/dcRkpWocQRkdSY7JBFK9bqMX9LyaDkqV0DEOLpKHFERGQMI0N90M7fGfnFOizcdl7qcEhiTHbIoi37Kwax6flws1fjxX6NpQ6HiIxEJpNh/qPNIZMBW04m4e9r6VKHRBJiskMWKzWnEF/uuQKgZKVkB2sOSiaqS1r4OGFCx5KFQ8O3nIWWKyvXWUx2yGJ9uuMicou0aOXrhMfa+kodDhFJ4NWwJqh3e2XlVX/HSR0OSYTJDlmkUwmZ2BCVAACYN6w55FwpmahOcrZT4bUBJetq/TfiEtJyiySOiKTAZIcsjhAC4VvOQoh/BykSUd31eIcGaOHjiJxCLT7dcVHqcEgCTHbI4mw5mYTj1zNho1RgzsAQqcMhIokp5DKED2sOAFh/LB7nkrIljoiMjckOWZT8Yi0+3HYBAPBc7yB4OllLHBERmYL2AS4Y0soLQgAf/HEOQgipQyIjYrJDFuXbA7FIyS6Er7MNpvdoKHU4RGRC3hgYApWVHIevpmPXee6bVZcw2SGLkV4I/PBXLADgnSFNYa1USBsQEZkUPxdb/Kd7IABg4bbzKNZyKnpdwWSHLMbW63IUa/Xo0tAVA5p7Sh0OEZmgmb2C4GavQkxaHlYfiZc6HDISJjtkEU5cz8SJdDlkMmDu0Gbc/4qIKuRgrcQrYSVT0b/aexV5GokDIqNgskNmTwiBRTsuAQBGhXqjmTf3vyKiyo1t74cQTwdkF2qxPYFfg3UB32Uye9vPpOD49Uwo5QKz+zaSOhwiMnEKuQxzhzYDABxKkeHqzTyJI6LaxmSHzFqxVo9F20ummvfxEvB05FRzIrq/bo3c0KdJfeghw6LtXGjQ0jHZIbO26u84xKXnw81ehb4+nFlBRFU3Z0Aw5DKBfZfScPDyTanDoVrEZIfMVla+Bv/bcxkAMLtvI6g505yIqqFhfTt09yhZXHDRnxeg13OhQUvFZIfM1tf7riAzX4NgD3uMDvWWOhwiMkMDfPWwV1vhbFI2tpxMkjocqiVMdsgsxd/Kx/LbCwi+ObgprBS8lImo+uyVwNM9AgAAn+68iCKtTtqAqFbwG4LM0sc7LqJYp0f3Rm7oFVxf6nCIyIxN6eIPD0c1EjIKsOrv61KHQ7WAyQ6Znej4TGw9mQSZDHhzcAgXECSih2KjUuClfsEAgK/2XEZ2IVcatDRMdsisCCGw6M/zAIBRob5o7u0kcUREZAkea+eLRu72yMjX4Jt9V6UOh2oYkx0yKwcvp+Hva7egUsjxcliw1OEQkYWwUsjx+oCSbSSW/hWDlKxCiSOimmTyyU5OTg5mz54Nf39/2NjYoGvXrjh69KjhfiEEwsPD4e3tDRsbG/Tq1Qtnz56VMGKqLXq9wMc7ShYQnNjFHz71bCSOiIgsSf9mHmjv74xCjR6fR1ySOhyqQSaf7EyfPh0RERH46aefcPr0aYSFhaFfv35ITEwEAHz88cf47LPP8NVXX+Ho0aPw9PRE//79kZOTI3HkVNP+OJ2MM4nZsFdbYWavIKnDISILI5PJ8ObgEADAhqh4XL7B7xFLYdLJTkFBATZu3IiPP/4YjzzyCBo1aoTw8HAEBgZiyZIlEEJg8eLFePvttzFq1Ci0aNECK1asQH5+PtasWSN1+FSDNDo9/ruzZEn3p3o0hKu9WuKIiMgStfN3wYDmHtAL4CNuI2ExrKQO4F60Wi10Oh2srcvud2RjY4NDhw4hJiYGKSkpCAsLM9ynVqvRs2dPHD58GDNmzKjwvEVFRSgqKjLczs7OBgBoNBpoNDU3Cr/0XDV5zrpq7dF4xKbnw8VOicmdfcvVKevaOFjPxsF6No7K6vnlvo2w63wqdp2/gcgrqWjv7yxFeBajNq/nqp5TJoQw6fWxu3btCpVKhTVr1sDDwwNr167FpEmT0LhxYyxbtgzdunVDYmIivL3/XUH36aefRlxcHHbs2FHhOcPDwzF//vxyx9esWQNbW9taey30YIp1wPsnFMjWyDA6QIdHvEz6kiUiC7D+qhyHU+UIchB4obkOXOHCNOXn52PChAnIysqCo6NjpeVMumUHAH766SdMmzYNPj4+UCgUaNu2LSZMmIDjx48byty9zooQ4p5rr7z55pt4+eWXDbezs7Ph5+eHsLCwe1ZWdWk0GkRERKB///5QKpU1dt665tsDMcjWXIZvPWvMn9wdaqvyva+sa+NgPRsH69k47lXPoVmF6Lf4EK7m6OHYpCN6NHKTKErzV5vXc2nPzP2YfLITFBSE/fv3Iy8vD9nZ2fDy8sK4ceMQGBgIT09PAEBKSgq8vLwMj0lNTYWHh0el51Sr1VCry4/5UCqVtfLBUlvnrQuy8jX47mAMAODlsCawt7n3WB3WtXGwno2D9WwcFdVzAzclJnb2x4+HYrB491X0DvHkAqYPqTau56qez6QHKN/Jzs4OXl5eyMjIwI4dOzB8+HBDwhMREWEoV1xcjP3796Nr164SRks1Zcn+q8gu1KKJhwOGt/GROhwiqkOe7RUEW5UCpxKysOPsDanDoYdg8snOjh07sH37dsTExCAiIgK9e/dGkyZNMHXqVMhkMsyePRsLFy7E5s2bcebMGUyZMgW2traYMGGC1KHTQ7qRXYhlf5W06rw2oAkUcv6qIiLjcbNXY1q3QADAZxEXodNzvKC5MvlurKysLLz55ptISEiAi4sLRo8ejQULFhiarl5//XUUFBRg5syZyMjIQKdOnbBz5044ODhIHDk9rK/3XkGRVo92/s7o29Rd6nCIqA566pGGWBkZi0s3crH1ZBJGhLKF2RyZfMvO2LFjcfXqVRQVFSE5ORlfffUVnJz+3Q9JJpMhPDwcycnJKCwsxP79+9GiRQsJI6aakJhZgHVH4gEAr4QFs6+ciCThZKPEjJ4li5h+FnEJGp1e4ojoQZh8skN101d7rqBYp0fnhi7oGsRZEEQknandAuBmr8L1W/nYcCxB6nDoATDZIZMTfysfG46VtOq83L+JxNEQUV1nq7LCzF6NAABf7rmMQo1O4oioupjskMn53+7L0OoFejR2Q8dAF6nDISLChE4N4OVkjeSsQqz+57rU4VA1MdkhkxKTlodNJ0o2eX25f7DE0RARlbBWKvBi38YAgP/bewV5RVqJI6LqYLJDJuV/uy9DpxfoE+KO0Abcj4aITMfodr4IcLVFel4xVkbGSR0OVQOTHTIZV1Jz8Gt0SavOS/3YqkNEpkWpkGPW7dad7w5cZeuOGWGyQybj812XIQQQ1swDLX2d7v8AIiIje7S1NwLd7JCRr2HrjhlhskMm4UJKNv44lQwAeIljdYjIRFkp5HihT8nMLLbumA8mO2QSPo+4BAAY0tILTb1qbud5IqKaxtYd88NkhyR3JrFkkz2ZDJjdr7HU4RAR3RNbd8zPAyU74eHhiItjNks1Y/GuywBKfi019uCeZkRk+ti6Y14eKNnZunUrgoKC0LdvX6xZswaFhYU1HRfVEeeSsrHrfEmrzgt92KpDROaBrTvm5YGSnaioKBw/fhytWrXCSy+9BC8vLzz77LM4evRoTcdHFu6rvSWtOkNaeqGRu73E0RARVR1bd8zHA4/ZadWqFT7//HMkJiZi6dKlSExMRLdu3dCyZUt88cUXyMrKqsk4yQJdvpGDP8+kAGCrDhGZH7bumI+HHqCs1+tRXFyMoqIiCCHg4uKCJUuWwM/PD+vXr6+JGMlCfbX3CoQABjb3RBNPjtUhIvPD1h3z8MDJTlRUFJ5//nl4eXnhpZdeQmhoKM6fP4/9+/fjwoULmDdvHmbNmlWTsZIFuXYzF1tPJgEAnr/9y4iIyNywdcc8PFCy06pVK3Tu3BkxMTH48ccfER8fj0WLFqFRo3+/tCZNmoSbN2/WWKBkWb7eexV6AfRr6o4WPlwtmYjM16OtvRHgaouMfA3WcEd0k/RAyc6YMWMQGxuLP/74AyNGjIBCoShXpn79+tDr9Q8dIFme6+n5hj2wOFaHiMydlUKOZ3sFAQC+O3gNhRqdxBHR3R4o2RFCwNm5/I7UBQUFeO+99x46KLJsS/ZfgU4v8EhwfbT2qyd1OERED21kqC+8naxxM6cIG6ISpA6H7vJAyc78+fORm5tb7nh+fj7mz5//0EGR5UrMLMAvtz8IXuzLsTpEZBlUVnI8/UhDAMA3+65Co2PPhil54JYdmUxW7vjJkyfh4uLy0EGR5Sr5EBDoGuSKdv68VojIcjzesQHc7FVIzCzAb9FJUodDd6hWsuPs7AwXFxfIZDIEBwfDxcXF8M/JyQn9+/fH2LFjaytWMnM3sgux/lg8AI7VISLLY61UYHqPktad/9tb0l1PpsGqOoUXL14MIQSmTZuG+fPnw8np31k0KpUKAQEB6NKlS40HSZbh2/3XUKzVo0OAMzo3ZKsOEVmeJzv7Y8m+q7iWloc/zyRjaCtvqUMiVDPZmTx5MgAgMDAQXbt2hVKprJWgyPKk5xZhzZGSBbde6NO4wm5QIiJzZ6+2wpSuAfhi92V8vfcqhrT04uedCahyN1Z2drbh/0NDQ1FQUIDs7OwK/xHdbcXhWBRq9Gjl64Qejd2kDoeIqNZM7RYAO5UC55OzsedCqtThEKqR7Dg7OyM1teRNq1evHpydncv9Kz1OdKfcIi1W3F5G/dmeQfyVQ0QWrZ6tCk929gdQui0Ox+5IrcrdWHv27DHMtNq7d2+tBUSWZ+0/15FVoEHD+nYY0NxT6nCIiGrdf3oEYtnhWJy4nonIq+no2ogt2lKqcrLTs2fPCv+f6F6KtDr8cOgaAOCZR4Igl7NVh4gsn7uDNR7v4IeVkXH4cs8VJjsSq3Kyc+rUqSqftFWrVg8UDFmezccTcSO7CJ6O1hgR6iN1OERERjOjZxDW/HMdkdfSERWXgXb+HOYhlSonO23atIFMJrtv36NMJoNOx31BCNDpBb49UNKqM71HIFRWD7SGJRGRWfKpZ4ORoT7YEJWAb/ZfxfeT2ksdUp1V5WQnJiamNuMgC7TjbApi0vLgZKPE+I4NpA6HiMjoZvRsiA1RCYg4dwNXUnPRyN1e6pDqpConO/7+/rUZB1kYIQT+b98VAMDkrgGwU1drSSciIovQyN0B/Zt5IOLcDXx/4Bo+eozDPKRQ5W+gLVu2YNCgQVAqldiyZcs9yz766KMPHRiZt0NX0nAmMRs2SgWmdA2QOhwiIsk807MhIs7dwOYTiXg5LBgejtZSh1TnVDnZGTFiBFJSUuDu7o4RI0ZUWo5jdggAluy7CgB4vKMfXOxUEkdDRCSddv4uaO/vjGNxGVj6VwzeHNRU6pDqnCqPGNXr9XB3dzf8f2X/mOhQdHwmDl9Nh5VcZtgUj4ioLnumZxAAYM3f15FdqJE4mrrngabHrFy5EkVFReWOFxcXY+XKlQ8dFJm3JbfH6owI9YFPPRuJoyEikl6fEHc0crdHTpEWa/65LnU4dc4DJTtTp05FVlZWueM5OTmYOnXqQwdF5utKai52nrsBoKSfmoiIALlchqcfKflMXHooBkVa9oIY0wMlO0KICvc3SkhIgJOT00MHRebrx0PXIATQr6kHGrk7SB0OEZHJGNHGBx6OaqTmFOG3E0lSh1OnVGs+cGhoKGQyGWQyGfr27Qsrq38frtPpEBMTg4EDB9Z4kGQebuYUYePxRAAla0sQEdG/VFZy/Kd7IBZuu4BvD1zFY+18uYWOkVQr2RkxYgSEEIiOjsaAAQNgb//v4kgqlQoBAQEYPXp0jQdJ5uGnyFgUa/Vo41cP7bksOhFROeM7NsCXe67g6s087Dp/A2HcHNkoqpXszJs3DwDQsGFDjBs3Dmq1ulaCIvNTUKzDT3/HAQCefqRhhd2cRER1nYO1Ek929seSfVfx7YFrTHaMpFpjduRyORQKBaZOnQpbW1soFAooFAo4Ozujc+fO2LRpU23FSSbul+MJyMjXwM/FBgP4x0tEVKmpXQOgUsgRFZeBY7G3pA6nTqhWy86mTZsq/MWemZmJI0eO4Mknn8SKFSswZsyYGguQTJ9OL/DjwZINP//TLRAK9kETEVXK3dEao9v5YO2ReHyz/xp+CHCROiSLV+0xO5WZPHkymjVrhk8//ZTJTh0Tce4GYtPz4WSjxJj2flKHQ0Rk8qb3aIi1R+Kx+8INXLuZi4b1uUFobXqgqeeVCQsLw6VLl2rylGQGfrjdqvNk5wbc8JOIqAqC6tujb4g7hACW/RUrdTgWr0aTnYKCAlhbc4OzuiQqLgPH4jKgUsgxuUuA1OEQEZmN//QIBABsiIpHZn6xxNFYthpNdr7//nuEhobW5CnJxJW26owI9YY7d/IlIqqyLg1d0czLEYUaPVZzC4laVa0+h5dffrnC41lZWTh27BiuXr2KgwcP1khgZPri0vOw/WwKAHDDTyKiapLJZJjeIxAv/3wSKw7H4qkeDaGyqtE2CLqtWsnOiRMnKjzu6OiIgQMHYubMmfD396+RwMj0LT0UAyGAXk3qI9iDW0MQEVXX0FbeWPTnBaTmFOH3U0kY1dZX6pAsUrWSnb1799ZWHGRmMvKK8fOxBADA02zVISJ6ICorOSZ3DcAnOy7ix0MxGBnqw0VZawHby+iBrDlyHQUaHZp7O6JLkKvU4RARma0nOjWAjVKBs0nZ+PsaFxmsDUx2qNqKtXqsjIwFAEzvEchfIURED6GerQqPtSvpvvrx0DWJo7FMTHao2v48k4wb2UWo76DGkJbeUodDRGT2pnYLgEwG7Dqfims3c6UOx+Iw2aFqEUJg6aEYAMDEzv6cOUBEVAMa1rdH3xAPAMDSv2Ikjsby8JuKquX49UycTMiCykqOCZ0aSB0OEZHFmH57kcFfohKQkcdFBmsSkx2qltJfHCPaeMPNXi1xNERElqNToAta+JQsMrjmCBcZrEkmnexotVq88847CAwMhI2NDRo2bIj33nsPer3eUGbKlCmQyWRl/nXu3FnCqC1XUmYBtp8pWURwardAiaMhIrIsMpkM07uXLOWx/HAsirX6+zyCqsqkd2386KOP8M0332DFihVo3rw5jh07hqlTp8LJyQkvvviiodzAgQOxbNkyw22VSiVFuBZvZWQcdHqBLg1d0dTLUepwiIgszuCWXvjwz/O4kV2EP88kY3gbH6lDsggmnexERkZi+PDhGDJkCAAgICAAa9euxbFjx8qUU6vV8PT0lCLEOqOgWIe1t5tVp3YLkDYYIiILpbKS48lO/vhvxCUs+yuWyU4NMelurO7du2P37t24dOkSAODkyZM4dOgQBg8eXKbcvn374O7ujuDgYDz11FNITU2VIlyLtulEArIKNGjgYou+TT2kDoeIyGKN79QAKoUc0fGZOHE9Q+pwLIJJt+zMmTMHWVlZCAkJgUKhgE6nw4IFCzB+/HhDmUGDBmHMmDHw9/dHTEwM5s6diz59+iAqKgpqdcUDaIuKilBUVGS4nZ2dDQDQaDTQaDQ1Fn/puWrynFK4c7r5k538oNdpoddJHNRdLKWuTR3r2ThYz8ZhqvXspJZjSCtPbD6RhGWHYtBijL3UIT2U2qznqp5TJoQQNf7sNWTdunV47bXX8Mknn6B58+aIjo7G7Nmz8dlnn2Hy5MkVPiY5ORn+/v5Yt24dRo0aVWGZ8PBwzJ8/v9zxNWvWwNbWtkZfgyW4kCnDkvMKqBUC77XVwdqkU2QiIvMXnwt8etoKCplAeFsdHDkUtUL5+fmYMGECsrKy4OhY+VhSk052/Pz88MYbb+C5554zHPvggw+watUqXLhwodLHNW7cGNOnT8ecOXMqvL+ilh0/Pz+kpaXds7KqS6PRICIiAv3794dSqayx8xrb9JXHsf9yGiZ3aYB3BodIHU6FLKWuTR3r2ThYz8Zh6vU87vsjOH49E7N6B+GFPkFSh/PAarOes7Oz4ebmdt9kx6R/o+fn50MuLzusSKFQlJl6frf09HTEx8fDy8ur0jJqtbrCLi6lUlkrF3xtndcYrt7Mxf7LaZDJgGndG5r86zDnujYnrGfjYD0bh6nW89RugTh+/QTWHE3A832DzX7F+tqo56qez6RrbtiwYViwYAH++OMPxMbGYvPmzfjss88wcuRIAEBubi5effVVREZGIjY2Fvv27cOwYcPg5uZmKEMPZ/lfsQCAviEe8He1kzYYIqI6ZGALT3g4qpGWW4Rtp5OlDsesmXSy8+WXX+Kxxx7DzJkz0bRpU7z66quYMWMG3n//fQAlrTynT5/G8OHDERwcjMmTJyM4OBiRkZFwcHCQOHrzl12owcbjCQCAaZxuTkRkVEqFHBM7+wMAlh2OlTYYM2fS3VgODg5YvHgxFi9eXOH9NjY22LFjh3GDqkM2RSUgv1iHxu726BLkKnU4RER1zviODfC/PVdw8vY09NAGzlKHZJZMumWHpKPXC6yMjAMATOriD5lMJnFERER1j6u9Go+29gZQsoUEPRgmO1Shv66m4VpaHuzVVhjZ1lfqcIiI6qwpXQMAANtOJyM1u1DaYMwUkx0qS6cD9u3Dyg1/AQBGh3rDXm3SvZ1ERBathY8T2vs7Q6MTWL3+ALB2LbBvX8nnNVUJkx3616ZNQEAAEoaPxe7Mkktj4ttTS44TEZFkpliVbIO0+mQqiiZOAnr3BgIC+PlcRUx2qMSmTcBjjwEJCVjdZjD0cgW6xUaj0fnjJcf5B0VEJI1NmzDg2THwzElDmr0ztjXpXnI8MZGfz1XEZIdKmkJffBEQAoUKJda1DgMATDr+O1C6wPbs2WwyJSIyttufz0qdFk+c+BMAsCr09mbY/HyuMiY7BBw8CCSUrKfzR0gPZNg6wTs7FX2vHCm5XwggPr6kHBERGc8dn8/jTu2AlU6LKN9mOOseWHI/P5+rhMkOAcn/rsy5su1QAMATJ/6EldBXWo6IiIzgjs9d97xMDLx0GMAdrTsVlKPymOwQcHsfsWivYJz0DoZKq8HjJytYrPEe+40REVEtuOtzd+LxPwAAvzbrjWyVbaXlqCwmOwT06AH4+mJl2yEAgKEXDsK1IPvf+2UywM+vpBwRERnP7c9n3F7YtWPCWQTfjEOByhqbWvTh53MVMdkhQKFA+qdf4PeQkj+Wicd///e+0pWTFy8GFArjx0ZEVJcpFMAXX5T8v0wGGYCJJ0pad35qOwQC4OdzFTDZIQDAeo9WKLZSoVV6LNokX/r3Dl9f4JdfgFGjpAuOiKguGzWq5HPYxwcAMOLsXtgV5eOqqx8il27k53MVcGlcgk4vsPrv6wCAiU8PheyJ5iWD3by8SppG+YuBiEhao0YBw4cDBw/CITkZI285YlW8FquUDdBV6tjMAJMdwu7zN5CYWQBnWyWGtfEFlP5Sh0RERHdTKIBevQAAT6ZkY9Xig9hx9gZuZBfCw9Fa2thMHLuxCD/9XbK7+dgOfrBWshWHiMjUhXg6omOAC3R6gbVHrksdjsljslPHXU/Px8HLaZDJgCc6skWHiMhcPNml5DN77ZHr0Oj09yldtzHZqePW3P5F0KNxfTRwtb1PaSIiMhUDm3vCzV6FG9lF2HXuhtThmDQmO3VYsVaPDcfiAQBPdGogcTRERFQdKis5Hu9Q8tldOhyBKsZkpw7bcTYF6XnF8HBUo2+Iu9ThEBFRNY3v1AByGXD4ajqupOZIHY7JYrJTh63+p+SXwLgODWCl4KVARGRufOrZoG9TDwDAqr85ULky/Iaro66k5uLva7cglwGPd/CTOhwiInpAEzuXDFTeeDwB+cVaiaMxTUx26qjSqYp9QtzhXc9G4miIiOhBdW/kBn9XW+QUavH7Ke5+XhEmO3VQoUaHX6ISAABPdOJ0cyIicyaXyzC+Y8lAZa65UzEmO3XQttPJyCrQwKeeDR4Jri91OERE9JAea+cLpUKGE9czcT45W+pwTA6TnTpo9T8lmf/4jn5QyGUSR0NERA/LzV6NsGaeANi6UxEmO3XMhZRsRMVlwEouw9j2HJhMRGQpSruyNh9PREGxTuJoTAuTnTpmze1WnbDmHnDnxnFERBaja5ArGrjYIqdIi99PJUkdjklhslOH5Bdrsfl4IgBgAvfBIiKyKHK5DI93LGmxZ1dWWUx26pCtJ5OQU6RFgKstuga5Sh0OERHVsMfa+cJKLsPx65m4kMKByqWY7NQhpQOTJ3RqADkHJhMRWRx3B2uENS9ZUXndkXiJozEdTHbqiDOJWTiVkAWVQo7H2nFgMhGRpSodqLzpeAIHKt/GZKeOKO2/HdjCEy52KomjISKi2tItyA1+LjbILtTij9NcURlgslMn5BdrsSW6ZGR+6eA1IiKyTHK5DI934IrKd2KyUwdsO52CnCIt/F1t0TmQA5OJiCzdmPYlA5Wj4jJwMSVH6nAkx2SnDlh/tCSzH9vejwOTiYjqAHcHa/RrWjJQma07THYs3pXUXByNzYBCLsNj7XylDoeIiIxkfKd/ByoXaur2QGUmOxbu52MlUw97N3GHB1dMJiKqM3o0coOvc8lA5W11fKAykx0LVqzVY2NUAgDg8Q4cmExEVJfI5TLDNPTSrYLqKiY7Fmz3+RtIzyuGu4MavZrUlzocIiIysjHtfKGQy3AsLgNXUnOlDkcyTHYs2NqjJV1YY9r7wkrBt5qIqK5xd7RG79s/djdE1d0VlfkNaKESMvJx8PJNACWzsIiIqG4q/Q7YGJUIjU4vcTTSYLJjoTYcS4AQQNcgV/i72kkdDhERSaR3iDvc7NVIyy3C3gupUocjCSY7FkinF9hwexbWOA5MJiKq05QKOUa39QEA/HwsQeJopMFkxwIdvHwTSVmFcLJRYkBzT6nDISIiiY253ZW192IqUrMLJY7G+JjsWKD1twcmjwz1gbVSIXE0REQktUbu9mjn7wydXmDj8USpwzE6JjsWJi23CBHnbgBgFxYREf1r3O3WnQ3H4iGEkDga42KyY2E2HU+AVi/Q2q8emno5Sh0OERGZiMGtvGCrUuBaWh6OxWVIHY5RMdmxIEIIrLvdhcUVk4mI6E72aisMbeUF4N/hDnUFkx0LEhWXgWs382CjVGBYa2+pwyEiIhNTuubOH6eSkVOokTga42GyY0E23J5SOKSVF+zVVhJHQ0REpqadvzMa1rdDgUaHP07Vnc1BmexYiPxiLf64vavtY+18JY6GiIhMkUwmMwxUXn+s7nRlMdmxENvPpCC3SIsGLrboFOgidThERGSiRrb1gUIuw4nrmbh8I0fqcIyCyY6F+CWqpAvrsXa+kMlkEkdDRESmyt3BGn1C3AEAP9eR1h0mOxYg/lY+Dl9Nh0wGjLq9JDgREVFlSruyNh1PRLHW8jcHZbJjATYeL2nV6RrkCl9nW4mjISIiU9erSX3Ud1AjPa8Yey7ckDqcWsdkx8zp9cKQ7HBgMhERVYWVQo7RbUu+M+rC5qAmnexotVq88847CAwMhI2NDRo2bIj33nsPev2/TW5CCISHh8Pb2xs2Njbo1asXzp49K2HUxvVPzC3E3yqAg9oKA5t7SR0OERGZidIfyPsv3cTNnCKJo6ldJp3sfPTRR/jmm2/w1Vdf4fz58/j444/xySef4MsvvzSU+fjjj/HZZ5/hq6++wtGjR+Hp6Yn+/fsjJ6dujDAvHZg8tLUXbFTc9JOIiKqmkbs92vjVg04v8Fu0ZW8OatLJTmRkJIYPH44hQ4YgICAAjz32GMLCwnDs2DEAJa06ixcvxttvv41Ro0ahRYsWWLFiBfLz87FmzRqJo699uUVabOPaOkRE9IBG3/7u+CUqwaI3BzXpZKd79+7YvXs3Ll26BAA4efIkDh06hMGDBwMAYmJikJKSgrCwMMNj1Go1evbsicOHD0sSszFtO5WMAo0ODd3s0LaBs9ThEBGRmXm0lTdUCjkupOTgbFK21OHUGpPeU2DOnDnIyspCSEgIFAoFdDodFixYgPHjxwMAUlJSAAAeHh5lHufh4YG4uLhKz1tUVISion/7J7OzS95gjUYDjabm9gopPVdNnvNOPx+7DgAY2cYLWq22Vp7DXNR2XVMJ1rNxsJ6Ng/UM2CqBviH18efZG9hw7DqauIfU+HPUZj1X9ZwmneysX78eq1atwpo1a9C8eXNER0dj9uzZ8Pb2xuTJkw3l7l5ETwhxz4X1PvzwQ8yfP7/c8Z07d8LWtuanbkdERNT4OW8WAMfirCCDgOOtC9i27UKNP4c5qo26pvJYz8bBejaOul7PfjoZAAV+ORqHVvprsKqlPp/aqOf8/PwqlZMJE+6k8/PzwxtvvIHnnnvOcOyDDz7AqlWrcOHCBVy7dg1BQUE4fvw4QkNDDWWGDx+OevXqYcWKFRWet6KWHT8/P6SlpcHR0bHG4tdoNIiIiED//v2hVCpr7LwA8PmuK/i//dfwSGNX/DipXY2e2xzVZl3Tv1jPxsF6Ng7WcwmtTo8enx5AWm4xlkxog35N3Wv0/LVZz9nZ2XBzc0NWVtY9v79NumUnPz8fcnnZFFOhUBimngcGBsLT0xMRERGGZKe4uBj79+/HRx99VOl51Wo11Gp1ueNKpbJWLviaPq9OL/BrdBIAYEz7BnX6j/RutfUeUlmsZ+NgPRtHXa9npRIYGeqD7w/G4NeTyRjUqnZW4q+Neq7q+Ux6gPKwYcOwYMEC/PHHH4iNjcXmzZvx2WefYeTIkQBKuq9mz56NhQsXYvPmzThz5gymTJkCW1tbTJgwQeLoa8/hq2lIyiqEo7UV+jfzuP8DiIiI7qF0VtaeC6m4lVcscTQ1z6Rbdr788kvMnTsXM2fORGpqKry9vTFjxgy8++67hjKvv/46CgoKMHPmTGRkZKBTp07YuXMnHBwcJIy8dpWurfNoG29YK7m2DhERPZwQT0c093bE2aRsbIlOxJRugVKHVKNMOtlxcHDA4sWLsXjx4krLyGQyhIeHIzw83GhxSSmnUIPtZ0pmoY1p5ydxNEREZCkea+eLs0nnsPG45SU7Jt2NReX9eToFRVo9gurboZWvk9ThEBGRhXi0tTes5DKcTszCxRTL2oWAyY6Z2XSipAtrVFvfe06vJyIiqg5XezV6h5TMxCrdYNpSMNkxIwkZ+fj72i0AwIjQ2hktT0REdVfp1kObTyRCq9Pfp7T5YLJjRn67Pd28S0NX+NSzkTgaIiKyNL2buMPZVombOUU4eCVN6nBqDJMdMyGEwKbbzYoj27JVh4iIap7KSo7hbUq+Y0pn/loCJjtm4lRCFq7ezIPaSo5BLTylDoeIiCxUaVdWxLkbyMq3jH3DmOyYic0nEgEAA5p7wsG67q70SUREtau5tyOaeDigWKvH76eTpA6nRjDZMQManR5bTpZccOzCIiKi2iSTyTDq9nfNr7d/aJs7JjtmYP/Fm7iVVww3ezV6NHKTOhwiIrJww9v4QCYDjsZmIP5W1XYWN2VMdsxAaRfW8DbesFLwLSMiotrl6WSNrkGuAIDfos2/dYffnCYuq0CDiPM3AJTsSktERGQMI27Pytp8IhFCCImjeThMdkzcttPJKNbq0cTDAc29HaUOh4iI6oiBLTyhtpLj6s08nEnMljqch8Jkx8RtPl7SfDiyrQ+3hyAiIqNxsFaifzMPAP9uVWSumOyYsPhb+TgSewsyWcl4HSIiImMqHT6x9WSSWW8fwWTHhJUOTO4W5AYvJ24PQURExvVIcH242KmQlluMQ2a8fQSTHRMlhDAkOxyYTEREUlAq5BjWyguAea+5w2THRJ2Iz0RMWh5slAoM5PYQREQkkRG3f3DvOHsDeUVaiaN5MEx2TFTpwOSBLTxhp7aSOBoiIqqr2vjVQ4CrLQo0Ouw8lyJ1OA+EyY4JKtbqsfXU7e0h2IVFREQSkslkhtadTcfNsyuLyY4J2n/pJjLzNXB3UKMbt4cgIiKJlS4w+NeVNKRmF0ocTfUx2TFBpUtzD2vtDYWca+sQEZG0Atzs0LZBPegFDBtTmxMmOyYmt0iLXbe3hyjNpImIiKRWOqziVzPcK4vJjomJOJeCQo0eDd3s0MKH20MQEZFpGNLKG1ZyGc4kZuPyjRypw6kWJjsm5tcTJc2Dj7bx5vYQRERkMlzsVOjVpD4A82vdYbJjQtJyiwwrVA5nFxYREZmY0llZv55Igl5vPjuhM9kxIdtOJ0OnF2jt64RANzupwyEiIiqjX1MPOKitkJhZgKOxt6QOp8qY7JiQ36JLu7DYqkNERKbHWqnAoJYlq/qbU1cWkx0TEX8rH1FxGZDJYNiHhIiIyNSUzhTedjoFxVrz2AmdyY6JKF23oGuQK9wdrSWOhoiIqGKdGrrC3UGNrAINDl6+KXU4VcJkxwQIIQy7yXJgMhERmTKFXIYht3sgzGWBQSY7JuBCSg4up+ZCZSXnDudERGTyHm3tDQDYefYG8otNfyd0JjsmoHRgcp8m7nC0VkocDRER0b218auHBi4lO6HvOp8qdTj3xWRHYnq9wNbbzYDD23hLHA0REdH9yWQyDGt9uysr2vS7spjsSOxYXAYSMwvgoLZC7xB3qcMhIiKqkkdbl4wx3X8pFVn5GomjuTcmOxIr3eF8YAtPWCsVEkdDRERUNU08HdDEwwEancD2s8lSh3NPTHYkVKzV44/TJRcIZ2EREZG5efT28AtTn5XFZEdCh67cRGa+Bm72anQJcpU6HCIiomopnZUVeTUdqTmFEkdTOSY7EiqdhTWstRcUcu5wTkRE5sXPxRahDepBL4A/TpluVxaTHYnkFWmx8+wNAP8uvU1ERGRuSlt3TLkri8mORHadv4ECjQ4BrrZo5eskdThEREQPZEgrL8hlwInrmYi/lS91OBVisiORrSdLmvuGtfaGTMYuLCIiMk/uDtaGcaem2rrDZEcCWQUaHLhUsnnasNZcSJCIiMxbaVfWViY7VGrn2RQU6/QI9rBHsIeD1OEQERE9lIHNvaBUyHAhJQcXU3KkDqccJjsS+P32iPWhrdiqQ0RE5s/JVomewSW7AGw5mShxNOUx2TGyW3nF+OtKGgBgaCsviaMhIiKqGaULDG49mQwhhMTRlMVkx8i2n0mBVi/Q3NsRDevbSx0OERFRjejX1B22KgWu38pHdHym1OGUwWTHyH4/VTJ4i11YRERkSWxVVujfzAOA6c3KYrJjRKk5hfj7WjoAdmEREZHlKZ2V9cepZOj0ptOVxWTHiP48nQK9ANr41YOfi63U4RAREdWoHo3rw9HaCqk5RTgae0vqcAyY7BjRv11YbNUhIiLLo7KSY0BzTwD/fueZAiY7RpKcVYCjsRkASpbWJiIiskRDb3dl/Xk6BVqdXuJoSjDZMZLS3WA7BDjDy8lG4miIiIhqR9cgVzjbKpGeV4x/YkyjK4vJjpFsPfXvXlhERESWSqmQY2CLkh4MU+nKYrJjBPEZ+TgZnwm5DBjUgl1YRERk2UrHpv55JgUaE+jKYrJjBNtO3wAAdG7oivoOaomjISIiql2dAl3gZq9CZr4Gkdek78pismMEf5xOAcCFBImIqG6wUsgNPRml34FSYrJTy1ILgPMpObCSyzCwhafU4RARERlFaVdWxPlUaCXuyTL5ZCcgIAAymazcv+eeew4AMGXKlHL3de7cWeKo/3UiXQYA6NbIDS52KomjISIiMo4OAS5wd1Ajp1CLC1kySWOxkvTZq+Do0aPQ6XSG22fOnEH//v0xZswYw7GBAwdi2bJlhtsqlekkFcfTSvJJLiRIRER1iVwuw+CWXlh+OBYn0pjs3FP9+vXL3F60aBGCgoLQs2dPwzG1Wg1PT9PrIrp0IwcpBTIoFTKENTe9+IiIiGrTsNYlyc7pDBmKNDoolUpJ4jD5ZOdOxcXFWLVqFV5++WXIZP9mifv27YO7uzvq1auHnj17YsGCBXB3d6/0PEVFRSgqKjLczs7OBgBoNBpoNJoai3fr7V1fuwe5wtYKNXpuKqu0blnHtYv1bBysZ+NgPde+Fp728HRUIyW7CHsu3MCgljU7Uaeq751MCGE625Lex88//4wJEybg+vXr8PYuqbD169fD3t4e/v7+iImJwdy5c6HVahEVFQW1uuJp3uHh4Zg/f36542vWrIGtbc1t0PnLNTkOp8owIUiP9vXNppqJiIhqzK+xJd+Fwxro0cOzZr8L8/PzMWHCBGRlZcHR0bHScmaV7AwYMAAqlQpbt26ttExycjL8/f2xbt06jBo1qsIyFbXs+Pn5IS0t7Z6VVV0ajQa//RmBAf36wMHWusbOS+VpNBpERESgf//+kjWT1gWsZ+NgPRsH69k4bmbn4/CBfRg8oObrOTs7G25ubvdNdsymGysuLg67du3Cpk2b7lnOy8sL/v7+uHz5cqVl1Gp1ha0+SqWyxt8IWyvAwdaaf0hGUhvvIZXHejYO1rNxsJ5rV31HWyjltVPPVT2fyU89L7Vs2TK4u7tjyJAh9yyXnp6O+Ph4eHlx9hMRERGZSbKj1+uxbNkyTJ48GVZW/zZG5ebm4tVXX0VkZCRiY2Oxb98+DBs2DG5ubhg5cqSEERMREZGpMIturF27duH69euYNm1ameMKhQKnT5/GypUrkZmZCS8vL/Tu3Rvr16+Hg4ODRNESERGRKTGLZCcsLAwVjaO2sbHBjh07JIiIiIiIzIVZdGMRERERPSgmO0RERGTRmOwQERGRRWOyQ0RERBaNyQ4RERFZNCY7REREZNGY7BAREZFFY7JDREREFo3JDhEREVk0s1hBubaVrs6cnZ1do+fVaDTIz89HdnY2d9StZaxr42A9Gwfr2ThYz8ZRm/Vc+r1d0S4Ld2KyAyAnJwcA4OfnJ3EkREREVF05OTlwcnKq9H6ZuF86VAfo9XokJSXBwcEBMpmsxs6bnZ0NPz8/xMfHw9HRscbOS+Wxro2D9WwcrGfjYD0bR23WsxACOTk58Pb2hlxe+cgctuwAkMvl8PX1rbXzOzo68g/JSFjXxsF6Ng7Ws3Gwno2jtur5Xi06pThAmYiIiCwakx0iIiKyaEx2apFarca8efOgVqulDsXisa6Ng/VsHKxn42A9G4cp1DMHKBMREZFFY8sOERERWTQmO0RERGTRmOwQERGRRWOyQ0RERBaNyU4t+r//+z8EBgbC2toa7dq1w8GDB6UOyax9+OGH6NChAxwcHODu7o4RI0bg4sWLZcoIIRAeHg5vb2/Y2NigV69eOHv2rEQRW4YPP/wQMpkMs2fPNhxjPdeMxMREPPnkk3B1dYWtrS3atGmDqKgow/2s54en1WrxzjvvIDAwEDY2NmjYsCHee+896PV6QxnW84M5cOAAhg0bBm9vb8hkMvz6669l7q9KvRYVFeGFF16Am5sb7Ozs8OijjyIhIaHmgxVUK9atWyeUSqX4/vvvxblz58SLL74o7OzsRFxcnNShma0BAwaIZcuWiTNnzojo6GgxZMgQ0aBBA5Gbm2sos2jRIuHg4CA2btwoTp8+LcaNGye8vLxEdna2hJGbryNHjoiAgADRqlUr8eKLLxqOs54f3q1bt4S/v7+YMmWK+Oeff0RMTIzYtWuXuHLliqEM6/nhffDBB8LV1VX8/vvvIiYmRmzYsEHY29uLxYsXG8qwnh/Mtm3bxNtvvy02btwoAIjNmzeXub8q9frMM88IHx8fERERIY4fPy569+4tWrduLbRabY3GymSnlnTs2FE888wzZY6FhISIN954Q6KILE9qaqoAIPbv3y+EEEKv1wtPT0+xaNEiQ5nCwkLh5OQkvvnmG6nCNFs5OTmicePGIiIiQvTs2dOQ7LCea8acOXNE9+7dK72f9VwzhgwZIqZNm1bm2KhRo8STTz4phGA915S7k52q1GtmZqZQKpVi3bp1hjKJiYlCLpeL7du312h87MaqBcXFxYiKikJYWFiZ42FhYTh8+LBEUVmerKwsAICLiwsAICYmBikpKWXqXa1Wo2fPnqz3B/Dcc89hyJAh6NevX5njrOeasWXLFrRv3x5jxoyBu7s7QkND8f333xvuZz3XjO7du2P37t24dOkSAODkyZM4dOgQBg8eDID1XFuqUq9RUVHQaDRlynh7e6NFixY1XvfcCLQWpKWlQafTwcPDo8xxDw8PpKSkSBSVZRFC4OWXX0b37t3RokULADDUbUX1HhcXZ/QYzdm6detw/PhxHD16tNx9rOeace3aNSxZsgQvv/wy3nrrLRw5cgSzZs2CWq3GpEmTWM81ZM6cOcjKykJISAgUCgV0Oh0WLFiA8ePHA+D1XFuqUq8pKSlQqVRwdnYuV6amvyuZ7NQimUxW5rYQotwxejDPP/88Tp06hUOHDpW7j/X+cOLj4/Hiiy9i586dsLa2rrQc6/nh6PV6tG/fHgsXLgQAhIaG4uzZs1iyZAkmTZpkKMd6fjjr16/HqlWrsGbNGjRv3hzR0dGYPXs2vL29MXnyZEM51nPteJB6rY26ZzdWLXBzc4NCoSiXmaamppbLcqn6XnjhBWzZsgV79+6Fr6+v4binpycAsN4fUlRUFFJTU9GuXTtYWVnBysoK+/fvx//+9z9YWVkZ6pL1/HC8vLzQrFmzMseaNm2K69evA+D1XFNee+01vPHGG3j88cfRsmVLTJw4ES+99BI+/PBDAKzn2lKVevX09ERxcTEyMjIqLVNTmOzUApVKhXbt2iEiIqLM8YiICHTt2lWiqMyfEALPP/88Nm3ahD179iAwMLDM/YGBgfD09CxT78XFxdi/fz/rvRr69u2L06dPIzo62vCvffv2eOKJJxAdHY2GDRuynmtAt27dyi2dcOnSJfj7+wPg9VxT8vPzIZeX/apTKBSGqees59pRlXpt164dlEplmTLJyck4c+ZMzdd9jQ53JoPSqec//vijOHfunJg9e7aws7MTsbGxUodmtp599lnh5OQk9u3bJ5KTkw3/8vPzDWUWLVoknJycxKZNm8Tp06fF+PHjOYW0Btw5G0sI1nNNOHLkiLCyshILFiwQly9fFqtXrxa2trZi1apVhjKs54c3efJk4ePjY5h6vmnTJuHm5iZef/11QxnW84PJyckRJ06cECdOnBAAxGeffSZOnDhhWGKlKvX6zDPPCF9fX7Fr1y5x/Phx0adPH049Nzdff/218Pf3FyqVSrRt29YwRZoeDIAK/y1btsxQRq/Xi3nz5glPT0+hVqvFI488Ik6fPi1d0Bbi7mSH9Vwztm7dKlq0aCHUarUICQkR3333XZn7Wc8PLzs7W7z44ouiQYMGwtraWjRs2FC8/fbboqioyFCG9fxg9u7dW+Fn8uTJk4UQVavXgoIC8fzzzwsXFxdhY2Mjhg4dKq5fv17jscqEEKJm24qIiIiITAfH7BAREZFFY7JDREREFo3JDhEREVk0JjtERERk0ZjsEBERkUVjskNEREQWjckOERERWTQmO0RERGTRmOwQUbXJZLJ7/psyZYrUIda4Xr16Yfbs2VKHQUQPwErqAIjI/CQnJxv+f/369Xj33XfLbGppY2MjRVgPRKPRQKlUWuzzERFbdojoAXh6ehr+OTk5QSaTlTl24MABtGvXDtbW1mjYsCHmz58PrVZreLxMJsO3336LoUOHwtbWFk2bNkVkZCSuXLmCXr16wc7ODl26dMHVq1cNjwkPD0ebNm3w7bffws/PD7a2thgzZgwyMzPLxLZs2TI0bdoU1tbWCAkJwf/93/8Z7ouNjYVMJsPPP/+MXr16wdraGqtWrUJ6ejrGjx8PX19f2NraomXLlli7dq3hcVOmTMH+/fvxxRdfGFqvYmNjsXz5ctSrV6/M8//666+QyWTl4l66dCkaNmwItVoNIQSysrLw9NNPw93dHY6OjujTpw9OnjxZQ+8QEd2JyQ4R1agdO3bgySefxKxZs3Du3Dl8++23WL58ORYsWFCm3Pvvv49JkyYhOjoaISEhmDBhAmbMmIE333wTx44dAwA8//zzZR5z5coV/Pzzz9i6dSu2b9+O6OhoPPfcc4b7v//+e7z99ttYsGABzp8/j4ULF2Lu3LlYsWJFmfPMmTMHs2bNwvnz5zFgwAAUFhaiXbt2+P3333HmzBk8/fTTmDhxIv755x8AwBdffIEuXbrgqaeeQnJyMpKTk+Hn51flOimNe+PGjYiOjgYADBkyBCkpKdi2bRuioqLQtm1b9O3bF7du3aryeYmoimp8a1EiqlOWLVsmnJycDLd79OghFi5cWKbMTz/9JLy8vAy3AYh33nnHcDsyMlIAED/++KPh2Nq1a4W1tbXh9rx584RCoRDx8fGGY3/++aeQy+UiOTlZCCGEn5+fWLNmTZnnfv/990WXLl2EEELExMQIAGLx4sX3fV2DBw8Wr7zyiuH23Tu/V/TahRBi8+bN4s6P1nnz5gmlUilSU1MNx3bv3i0cHR1FYWFhmccGBQWJb7/99r6xEVH1cMwOEdWoqKgoHD16tExLjk6nQ2FhIfLz82FrawsAaNWqleF+Dw8PAEDLli3LHCssLER2djYcHR0BAA0aNICvr6+hTJcuXaDX63Hx4kUoFArEx8fjP//5D5566ilDGa1WCycnpzIxtm/fvsxtnU6HRYsWYf369UhMTERRURGKiopgZ2f3sNUBAPD390f9+vUNt6OiopCbmwtXV9cy5QoKCsp03RFRzWCyQ0Q1Sq/XY/78+Rg1alS5+6ytrQ3/f+cg3dIxLhUd0+v1lT5XaRmZTGYo9/3336NTp05lyikUijK3705i/vvf/+Lzzz/H4sWL0bJlS9jZ2WH27NkoLi6u/IUCkMvlEEKUOabRaMqVu/v59Ho9vLy8sG/fvnJl7x4DREQPj8kOEdWotm3b4uLFi2jUqFGNn/v69etISkqCt7c3ACAyMhJyuRzBwcHw8PCAj48Prl27hieeeKJa5z148CCGDx+OJ598EkBJMnL58mU0bdrUUEalUkGn05V5XP369ZGTk4O8vDxDQlM6Jude2rZti5SUFFhZWSEgIKBasRJR9THZIaIa9e6772Lo0KHw8/PDmDFjIJfLcerUKZw+fRoffPDBQ53b2toakydPxqeffors7GzMmjULY8eOhaenJ4CSmU+zZs2Co6MjBg0ahKKiIhw7dgwZGRl4+eWXKz1vo0aNsHHjRhw+fBjOzs747LPPkJKSUibZCQgIwD///IPY2FjY29vDxcUFnTp1gq2tLd566y288MILOHLkCJYvX37f19GvXz906dIFI0aMwEcffYQmTZogKSkJ27Ztw4gRI8p1sxHRw+FsLCKqUQMGDMDvv/+OiIgIdOjQAZ07d8Znn30Gf3//hz53o0aNMGrUKAwePBhhYWFo0aJFmanl06dPxw8//IDly5ejZcuW6NmzJ5YvX47AwMB7nnfu3Llo27YtBgwYgF69esHT0xMjRowoU+bVV1+FQqFAs2bNUL9+fVy/fh0uLi5YtWoVtm3bZpiuHh4eft/XIZPJsG3bNjzyyCOYNm0agoOD8fjjjyM2NtYwfomIao5M3N3hTERkgsLDw/Hrr79WqZuIiOhObNkhIiIii8Zkh4iIiCwau7GIiIjIorFlh4iIiCwakx0iIiKyaEx2iIiIyKIx2SEiIiKLxmSHiIiILBqTHSIiIrJoTHaIiIjIojHZISIiIovGZIeIiIgs2v8DQ0pGsxos9aUAAAAASUVORK5CYII="
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": null,
"data": {
"text/plain": "(84.0, 100.0, 84.0)"
},
"metadata": {}
}
],
"execution_count": null,
"metadata": {
"noteable": {
"cell_type": "code"
},
"noteable-chatgpt": {
"version": "0.16.0"
},
"ExecuteTime": {
"end_time": "2023-05-09T02:43:21.263653+00:00",
"start_time": "2023-05-09T02:43:19.277827+00:00"
}
},
"id": "65d2c262-6885-44e7-be46-6ba04bf65cdc"
},
{
"cell_type": "markdown",
"source": [
"As we can see from the plot and the calculated utilities, the lukewarm porridge (T2) provides the highest utility to Agent G. The utilities derived from the hot (T1) and cold (T3) porridge are the same and lower than the utility derived from the lukewarm porridge.\n",
"\n",
"### 3.2 Chair Selection\n",
"\n",
"We model the utility derived from chair selection as a function of its size. We assume that the utility is maximized at a certain optimal size and decreases as the size deviates from this optimum. This can be represented by a quadratic function similar to the one used for porridge consumption:\n",
"\n",
"$$U(S) = -c(S - S*)^2 + d$$\n",
"\n",
"where:\n",
"- $U(S)$ is the utility derived from sitting on a chair of size $S$,\n",
"- $S*$ is the optimal size,\n",
"- $c$ and $d$ are parameters that shape the utility function.\n",
"\n",
"Given the sizes of the three chairs (S1, S2, S3), we can calculate the utility derived from each and identify the one that maximizes utility."
],
"metadata": {
"noteable": {
"cell_type": "markdown"
},
"noteable-chatgpt": {
"version": "0.16.0"
}
},
"id": "57f0b541-073a-4fe0-ad2e-e4fceccf20b0"
},
{
"cell_type": "code",
"source": [
"# Define the sizes of the three chairs\n",
"S1 = 90 # large\n",
"S2 = 50 # medium\n",
"S3 = 10 # small\n",
"\n",
"# Define the parameters of the utility function\n",
"c = 0.01\n",
"d = 100\n",
"\n",
"# Define the utility function\n",
"def U(S, S_star):\n",
" return -c * (S - S_star)**2 + d\n",
"\n",
"# Calculate the utility derived from each chair\n",
"U_S1 = U(S1, S3)\n",
"U_S2 = U(S2, S3)\n",
"U_S3 = U(S3, S3)\n",
"\n",
"# Plot the utility function\n",
"S = np.linspace(0, 100, 1000)\n",
"plt.plot(S, U(S, S3))\n",
"plt.scatter([S1, S2, S3], [U_S1, U_S2, U_S3], color='red')\n",
"plt.xlabel('Size')\n",
"plt.ylabel('Utility')\n",
"plt.title('Utility derived from chair selection')\n",
"plt.grid(True)\n",
"plt.show()\n",
"\n",
"U_S1, U_S2, U_S3"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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"
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": null,
"data": {
"text/plain": "(36.0, 84.0, 100.0)"
},
"metadata": {}
}
],
"execution_count": null,
"metadata": {
"noteable": {
"cell_type": "code"
},
"noteable-chatgpt": {
"version": "0.16.0"
},
"ExecuteTime": {
"end_time": "2023-05-09T02:44:51.542948+00:00",
"start_time": "2023-05-09T02:44:51.070863+00:00"
}
},
"id": "76df2a31-778d-4a58-a21b-97675dd870d1"
}
],
"metadata": {
"noteable-chatgpt": {
"create_notebook": {
"openai_conversation_id": "16419c7a-210b-5b61-9a43-54c3c8849661",
"openai_ephemeral_user_id": "9aeec7ba-0617-5df6-9ed2-4f40b4f94bd6"
}
},
"noteable": {
"last_transaction_id": "eb739449-570e-4d65-aafb-6fe926fc4aba",
"last_delta_id": "eb739449-570e-4d65-aafb-6fe926fc4aba"
},
"selected_hardware_size": "small",
"nteract": {
"version": "noteable@2.9.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
@oaustegard
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@oaustegard
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Unfortunately our co-author ChatGPT + Noteable plugin crashed while trying to compute the utility function for F*. See text for empirical findings.

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