diff --git a/notebooks/contrib-dev/Stochastic-Kinetics.ipynb b/notebooks/contrib-dev/Stochastic-Kinetics.ipynb index f6b14c80..da0a6112 100644 --- a/notebooks/contrib-dev/Stochastic-Kinetics.ipynb +++ b/notebooks/contrib-dev/Stochastic-Kinetics.ipynb @@ -1 +1,2048 @@ -{"cells":[{"cell_type":"markdown","metadata":{"id":"Clm-BGLJK54N"},"source":["# Stochastic Simulation of Chemical Reactions\n","**Prepared by:** Raghav Saxena (rsaxena@nd.edu) and Sarah Nano (snano@nd.edu)\n","\n","**Reference:** [Chemical Reactor Analysis and Design Fundamentals by Rawlings et al. (Nob Hill Pub, LLC, 2002)](https://sites.engineering.ucsb.edu/~jbraw/chemreacfun/)\n","\n","**Intended Audience:** This problem is intended for Chemical and Biomolecular Engineering juniors and seniors from the University of Notre Dame who are either enrolled in or have taken Reaction Engineering.\n","\n","\n","## Learning Objectives\n","\n","After studying this notebook, completing the activities, and asking questions in class, you should be able to:\n","\n","* Understand stochastic simulations and how to use them to model chemical reactions. \n","* Highlight similarities and differences between stochastic and deterministic rate models for chemical reactions.\n","* Properly graph and visualize data using matplotlib. \n","\n","## Coding Resources\n","Relevant Modules in Class Website: \n","\n","* [Functions and Scope](https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-and-Scope.html)\n","* [Visualization with matplotlib](https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html)\n","* [Preparing Publication Quality Figures in Python](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"rsDgYreOSduc"},"outputs":[],"source":["import numpy as np\n","import matplotlib.pyplot as plt"]},{"cell_type":"markdown","metadata":{"id":"l5G8OHITGIWE"},"source":["## 1. Introduction\n"]},{"cell_type":"markdown","metadata":{"id":"fZPqZ8Z_IDOO"},"source":["Kinetic reactions are mostly modeled using deterministic rate laws, which involve solving nonlinear differential equations. Deterministic models work excellently with large systems involving many thousands of atoms.\n","\n","\n","However, in some cases, we might want to model systems with only a few hundred atoms, such as when modeling reactions at an interface or a catalyst surface. For such systems, the random behavior of the molecules becomes essential. Such systems can be modeled using random simulation techniques (also called kinetic monte carlo) which we explain later below in detail. "]},{"cell_type":"markdown","metadata":{"id":"CN-9WKlnT3u1"},"source":["**The objectives of this excercise are:**\n","\n","1. To perform random simulation on a two reaction batch system using Gillespie algorithm.\n","\n","2. Compare reaction profiles (concentrations vs. time) from random simulation with those of deterministic rate laws.\n","\n","3. Explore effect of number of molecules and rate constant on reaction profiles from Gillespie algorithm.\n","\n","4. Discuss similarities and differences between the rate law model and the random simulation model."]},{"cell_type":"markdown","metadata":{"id":"QM2N2vLsTafc"},"source":["## 1a. Random Simulation - Gillespie Algorithm\n","In a random simulation, one can directly capture the random nature of molecules by using random molecular motion and probability of collision as the basis of reaction rates. \n","\n","Through this exercise, we will highlight similarities and differences between a random simulation model and a deterministic model.\n","\n","We will use the following two reaction constant volume batch system for the purpose of this excercise.\n","\\begin{equation}\n","A \\xrightarrow{k_1} B\n","\\end{equation}\n","\\begin{equation}\n","B \\xrightarrow{k_2} C\n","\\end{equation}\n","\n","For stochastic (random) modeling, the systems are generally small and consist of about a few hundred molecules. Thus, we will model the system using the exact number of molecules instead of using concentrations. We will assume that these reactions are actual molecular events, i.e., a molecule of A converts to B in the first reaction, and a molecule of B converts to C in the second reaction. \n","\n","Which reaction takes place is governed by their probabilities; this is proportional to the rate constant and the number of molecules as shown below: \n","\n","\\begin{equation}\n","r1 = k_1x_a\n","\\end{equation}\n","\\begin{equation}\n","r2 = k_2x_b\n","\\end{equation}\n","\n","These reaction probabilities look very similar to rate equations from the deterministic models. However, **x$_i$** is the number of component **$i$** molecules in the reactor volume, not concentration **C$_i$**. \n","\n","Given these reaction probabilities, we will simulate the random behavior of this reaction network using the Gillespie algorithm. The basic idea behind the Gillespie algorithm is to (i) randomly choose the time at which next reaction occurs and (ii) randomly choose which reaction occurs at that time. The choice is not made completely randomly but rather using reaction probabilities. The following protocol describes the Gillespie algorithm: \n","\n","1. Initialize the number of starting molecules x$_i$ for each species in the reaction network.\n","2. Compute total reaction probability, $r_{tot} = \\sum r_ix_i$, it is intuitive that higher total reaction probability would mean time to next reaction is small.\n","3. Select two random numbers, p1, p2, from a uniform distribution on the interval (0,1).\n","4. Compute the time to next reaction $\\tau = -ln(p1)/r_{tot}$.\n","5. Select the reaction that takes place at this time. The idea here is to partiton interval (0,1) by relative sizes of individual reaction probabilities, then select the reaction that occurs using randomly generated number p2.\n","6. Update reaction time $t = t + \\tau$ and adjust number of molecules x$_i$ for each species. For example, if reaction 1 is selected in step 5, we will reduce number of A molecules by 1 and increase number of B molecules by 1.\n","7. Return to step 2 and continue until total reaction probability is zero."]},{"cell_type":"markdown","metadata":{"id":"kMG0-L38Hnbo"},"source":["## 2. Random Simulation Model - Gillespie Algorithm\n","Complete the function \"gillespie\" to perform stochastic simulation of the two reaction batch system. \n","\\begin{equation}\n","A \\xrightarrow{k_1} B\n","\\end{equation}\n","\\begin{equation}\n","B \\xrightarrow{k_2} C\n","\\end{equation}\n","**Write a pseudocode for the while loop to complete the code.** Submit this answer on an attached pdf file. "]},{"cell_type":"code","execution_count":null,"metadata":{"id":"SKnfMn39SpXn"},"outputs":[],"source":["def gillespie(k1, k2, A, B, C):\n"," \"\"\"\n"," Function to implement Gillespie algorithm to perform stochastic simulation of the two reaction batch system\n","\n"," Arguments:\n"," k1,k2: Reaction rate constants of the two reactions\n"," A,B,C: Initial number of A, B and C molecules\n","\n"," Returns:\n"," y: A numpy array of simulation time and number of A, B and C molecules\n"," \"\"\"\n"," # Random Simulation using Gillespie algorithm\n","\n"," # Index counter\n"," n = 0\n","\n"," # Initialize list for storing simulation time\n"," time = [0]\n","\n"," # Initialize list for storing number of A, B and C molecules\n"," x_a = [A]\n"," x_b = [B]\n"," x_c = [C]\n","\n"," # Total reaction probability at time t = 0\n"," r1 = k1 * x_a[0]\n"," r2 = k2 * x_b[0]\n"," rtot = r1 + r2\n","\n"," while rtot != 0:\n"," ### BEGIN SOLUTION ###\n","\n"," # Generating two random numbers from a uniform distribution between 0 and 1\n"," p = np.random.rand(2, 1)\n","\n"," # Time to next reaction event using one of the two generated random numbers\n"," tau = -np.log(p[0, 0]) / rtot\n","\n"," # Determining which reaction to take place at that time using other random number\n","\n"," if p[1, 0] < r1 / rtot:\n"," # This means reaction A-->B takes place. Adjusting the number of molecules\n"," x_a.append(x_a[n] - 1)\n"," x_b.append(x_b[n] + 1)\n"," x_c.append(x_c[n])\n","\n"," else:\n"," # This means reaction B-->C takes place. Adjusting the number of molecules\n"," x_a.append(x_a[n])\n"," x_b.append(x_b[n] - 1)\n"," x_c.append(x_c[n] + 1)\n","\n"," # Update simulation time with tau every iteration\n"," time.append(time[n] + tau)\n","\n"," # Update index counter\n"," n += 1\n","\n"," # Update total reaction probability\n"," r1 = k1 * x_a[n]\n"," r2 = k2 * x_b[n]\n"," rtot = r1 + r2\n","\n"," # Make a numpy array of simulation time, and number of A, B and C molecules.\n"," y = np.array([time, x_a, x_b, x_c])\n","\n"," ### END SOLUTION ###\n","\n"," return y"]},{"cell_type":"markdown","metadata":{"id":"ih9h_XHiCXz0"},"source":["Initialize the number of molecules and rate constants in the next block and then run the gillespie function. Plot the number of molecules of A, B, and C over time. "]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Xv0izRelW7MZ"},"outputs":[],"source":["# Define initial number of molecules and rate constants\n","\n","k1 = 0.5 # s-1\n","k2 = 1 # s-1\n","A = 1000\n","B = 0\n","C = 0"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"VcdxHpaNVnjD"},"outputs":[],"source":["# Run gillespie function\n","\n","x = gillespie(k1, k2, A, B, C)\n","time = x[0]\n","xa = x[1]\n","xb = x[2]\n","xc = x[3]"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":396},"executionInfo":{"elapsed":140,"status":"ok","timestamp":1670899890789,"user":{"displayName":"Raghav Saxena","userId":"07786690188932311494"},"user_tz":300},"id":"nquXZWxeYRZf","outputId":"4775f450-de49-4039-adc8-ae5c7c9e2435"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["# Plot number of A, B and C molecules vs Simulation time\n","\n","### BEGIN SOLUTION ###\n","fig = plt.figure(figsize=(6, 6))\n","plt.plot(time, xa, \"+\", label=r\"A\")\n","plt.plot(time, xb, \"*\", label=r\"B\")\n","plt.plot(time, xc, \"--\", label=r\"C\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=15)\n","### END SOLUTION ###"]},{"cell_type":"markdown","metadata":{"id":"3ICN865nJ1Lz"},"source":["## 3a. Deterministic Equations\n","Deterministic rate model for the same reaction network would result in the following rate expressions: \n","\\begin{equation}\n","r1 = k_1C_a\n","\\end{equation}\n","\\begin{equation}\n","r2 = k_2C_b\n","\\end{equation}\n","\n","Where $C_i$ is the concentration of species $i$, unlike number of molecules of stochastic model.\n","\n","**Using these rate laws, write down the differential equations for the concentration of each species?** Submit this answer on an attached pdf file.\n","\n","**Answer:**\n","\\begin{equation}\n","\\frac{dC_a}{dt} = -k_1C_a\n","\\end{equation}\n","\\begin{equation}\n","\\frac{dC_b}{dt} = k_1C_a - k_2C_b\n","\\end{equation}\n","\\begin{equation}\n","\\frac{dC_c}{dt} = k_2C_b\n","\\end{equation}"]},{"cell_type":"markdown","metadata":{"id":"GkO3k1sgGCoA"},"source":["Note: These equations would be exactly same for number of molecules, i.e, one can replace $C_i$ with $x_i$ in the differential equations above. Concentrations can be converetd to number of molecules using avogadros number $N_A$ and volume V of the reactor and these constants will cancel out in the equations."]},{"cell_type":"markdown","metadata":{"id":"ItSF2Lx5gGTm"},"source":["## 3b. Deterministic Rate Model - Solving Differential Equations"]},{"cell_type":"markdown","metadata":{"id":"02wez7jgFL21"},"source":["**Solve the differential equations to find the analytical solution of the deterministic rate models.** Submit this answer on an attached pdf file. Add these solutions to the code below to plot this deterministic rate model profiles."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":396},"executionInfo":{"elapsed":734,"status":"ok","timestamp":1670899899072,"user":{"displayName":"Raghav Saxena","userId":"07786690188932311494"},"user_tz":300},"id":"qIOQXFQTPjoW","outputId":"5137b4e5-0d41-4b4b-fc8c-b072ece8d23a"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["# Analytical solution from solving differential equations of deterministic rate models\n","# These models were solved mathematically on paper and in this section we are just plotting the obtained solutions\n","\n","t = np.linspace(0, 16, 1000)\n","\n","X_a = xa[0] * np.exp(-k1 * t)\n","\n","\n","if k1 == k2:\n"," X_b = xa[0] * k1 * t * np.exp(-k1 * t)\n"," X_c = xa[0] * (\n"," 1 + (k1**2) * (-t * (np.exp(-k1 * t) / k1) - (np.exp(-k1 * t) / k1**2))\n"," )\n","\n","else:\n"," X_b = xa[0] * (k1 / (k1 - k2)) * (np.exp(-k2 * t) - np.exp(-k1 * t))\n"," X_c = xa[0] * (\n"," 1 + (k1 * k2 / (k1 - k2)) * ((np.exp(-k1 * t) / k1) - (np.exp(-k2 * t) / k2))\n"," )\n","\n","\n","# Plot deterministic solution of number of A, B and C molecules vs time\n","\n","### BEGIN SOLUTION ###\n","fig = plt.figure(figsize=(6, 6))\n","plt.plot(t, X_a, label=r\"A\")\n","plt.plot(t, X_b, label=r\"B\")\n","plt.plot(t, X_c, label=r\"C\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=15)\n","### END SOLUTION ###"]},{"cell_type":"markdown","metadata":{"id":"avlhWMB84eAe"},"source":["## 3c. Stochastic vs Deterministic Solution\n","Plot the stochastic solution and deterministic solution for the species profiles in the same plot starting with 1000 molecules of A. **Write a few sentences to explain what you observe?** Submit your answer on an attached pdf file."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":316},"executionInfo":{"elapsed":986,"status":"ok","timestamp":1670899905357,"user":{"displayName":"Raghav 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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["### BEGIN SOLUTION ###\n","\n","fig = plt.figure(figsize=(15, 4))\n","\n","# Creating a subplot\n","plt.subplot(1, 3, 1)\n","plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n","plt.plot(t, X_a, \"c\", label=r\"A$_{deterministic}$\", linewidth=3)\n","plt.plot(time, xa, \"k-.\", label=r\"A$_{stochastic}$\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of A molecules\", fontsize=15, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=15)\n","\n","plt.subplot(1, 3, 2)\n","plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n","plt.plot(t, X_b, \"r\", label=r\"B$_{deterministic}$\", linewidth=3)\n","plt.plot(time, xb, \"k-.\", label=r\"B$_{stochastic}$\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of B molecules\", fontsize=15, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=15)\n","\n","plt.subplot(1, 3, 3)\n","plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n","plt.plot(t, X_c, \"g\", label=r\"C$_{deterministic}$\", linewidth=3)\n","plt.plot(time, xc, \"k-.\", label=r\"C$_{stochastic}$\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of C molecules\", fontsize=15, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=15)\n","\n","plt.subplots_adjust(left=0.1, bottom=0.1, right=0.9, top=0.9, wspace=0.4, hspace=0.4)\n","\n","### END SOLUTION ###"]},{"cell_type":"markdown","metadata":{"id":"i37i8E7r7MXE"},"source":["**Answer:** For N = 1000 molecules, we see that the profiles for the stochastic solution are similar to the deterministic solution with little noise. For even larger systems, the profiles will be even more accurate. Intuitively this is what we would expect; the random behavior becomes less important for large systems. In the next section, we will see that random behavior is important for small systems."]},{"cell_type":"markdown","metadata":{"id":"YhLRGavgfvHG"},"source":["## 3d. Effect of number of molecules in stochastic simulation "]},{"cell_type":"markdown","metadata":{"id":"aesb6BjnDXxy"},"source":["\n","**How does changing the starting number of molecules affect the reaction profiles?** Run the gillespie function with A = 100 and A = 1000 molecules and create a subplot for the species profile. Submit this answer in a few sentences on an attached pdf file."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":522},"executionInfo":{"elapsed":787,"status":"ok","timestamp":1670899911645,"user":{"displayName":"Raghav 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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["### BEGIN SOLUTION ###\n","\n","# stochastic model for with 100 total molecules\n","x = gillespie(k1, k2, 100, 0, 0)\n","# stochastic model for with 1000 total molecules\n","y = gillespie(k1, k2, 1000, 0, 0)\n","\n","### END SOLUTION ###\n","\n","# creating a subplot for the two stochastic simulations\n","fig = plt.figure(figsize=(8, 8))\n","\n","plt.subplot(2, 1, 1)\n","plt.plot(x[0], x[1], \"+\", label=r\"A\")\n","plt.plot(x[0], x[2], \"*\", label=r\"B\")\n","plt.plot(x[0], x[3], \"--\", label=r\"C\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","plt.title(\"N=100 molecules\", fontsize=14, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=13)\n","\n","plt.subplot(2, 1, 2)\n","plt.plot(y[0], y[1], \"+\", label=r\"A\")\n","plt.plot(y[0], y[2], \"*\", label=r\"B\")\n","plt.plot(y[0], y[3], \"--\", label=r\"C\")\n","leg = plt.legend(fontsize=13)\n","plt.subplots_adjust(hspace=0.5)\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","plt.title(\"N=1000 molecules\", fontsize=14, fontweight=\"bold\")\n","plt.xticks(fontsize=13)\n","plt.yticks(fontsize=13)\n","leg = plt.legend(fontsize=13)"]},{"cell_type":"markdown","metadata":{"id":"GYu8xOxB2G0q"},"source":["**Answer:** For N = 100 molecules, we can clearly see more noise in the species profile compared to N = 1000 molecules, where the profile is more smooth and closer to the analytical solution. This reinforces our idea that stochastic modeling is important if the system of interest is small."]},{"cell_type":"markdown","metadata":{"id":"dS55dJKRH6_r"},"source":["## 4. Effect of rate constants k1 and k2\n","Plot reaction profiles using different rate constant values (using the same number of starting molecules. *Hint:* Change the value of one rate constant while keeping the other the same; this will make any changes obvious.\n"]},{"cell_type":"markdown","metadata":{"id":"i_eHPDS6Dd5b"},"source":["**How does changing the rate constant affect the reaction profiles?** Submit this answer in a few sentences on an attached pdf file."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":519},"executionInfo":{"elapsed":541,"status":"ok","timestamp":1670899918991,"user":{"displayName":"Raghav 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5bTjTrOeVUe5eHbAs5EKV6l6RdvAAqQ1faVqxhjDxGUTeW/je7iNG0EY3nU4TWObctmJl3H6cafToVkHOjTrQIv4FtrpTKkQ0KQfIK3pK1W1Q3mHOJJ/hLziPHKLckt6jXuGjj3141PM2jCLQScM4obuN3BSyknEueIA6N+2fyRDV6rBcNSRry4KVkc+0B78Snm4jZtNhzfx68FfuarzVQDc+sWtfL/n+zL7dUrqxIdXfAjAH+b9gZNanMQDvR/QjnZKhVAwO/I1aFrbVw3ZwdyDLNi+gGV7lrF833Iy8zMBq5beqlEr/njSH7mi0xUkuBJKxqwnxpYuzDlt0DTio+MjFb5SiiAkfRFpA6QAa73mzK+X9Lm+akjcxk1GTgZxrjiaxzdn0a5FTFw2kbZN2jKg3QDOaH0GZxx3Bq0atQKgX9t+VZ5PE75Skeco6YvIaKzV7j41xkwXkb9izdAnwA4RGWSM2RyCOJVSIXAw9yAGQ0pCCjmFOTy/8nl2Zu9kR/YO0rPTKXAXcP/p93Nzz5u5KO0ieqX0olPzTpEOWylVTU6X1h2JtRTuHhFJBv5in0OA9lg3APXWkrED6dMhuUJ5emYew6cujUBESlXf/K3zueC9C5i+ejoAMVExfLj5Q/Yc20PHZh25vvv1PH7W45ybei5gzXKnCV+pus1p8353+3UFcJZ9/GfAEmAiMCBokdVS2sSv6rr9OfuZvmY676x/h6S4pJJFP2JcMSy9bqkOlVOqHnNa029uv2YAJ2EttPM28Ixd3ipIcdValXXa0858qrbamb2Tz7d9XvL5qR+f4p3179Dn+D6M7zuenik9S7ZpwleqfnNa0z+MldgvAwbbZZuAJvb7o0GKq9bSmr6qSyZ+P5FZG2YRJVEMbD+Q6KhouiV345IOl3B++/MjHZ5SKsyc1vRXYD2/fx84H8gCVgGeB33bghZZLVVZjT49M49+kxeGORqlKrcqYxUzN8zk/Hbn88HlHxAl1v/uo3uN1oSvVAPlNOn/FWtZWwHcwKPGmGJgmL392yDGVivNur0vTeN8LyR4JLcwzNEo5dtXO77i1i9uJd4Vz6N9HqVjUseSpK+Uargc/RUwxvyE1Uu/N5BqjHnJ3jQF6AA8HtzwaqcebZo5KlcqHArdhazZvwaAU1qdwqATBvHmxW9yXOPjIhyZUqq2cDw5jzEmR0SOAVeKSLIxZpIxJiMEsdVaa3dnOSpXKpTe2/geX+34il8P/kpSXBIfX/kxzeOb83/n/F+kQ1NK1TKOk76IPA/cidXEb4BJIvITcDJwvTFmVnBDrH16tGnGsq2HfJYrFS45hTnc//X9LNm9hFaNWtG3TV8uaHdBpMNSStViTmfkuwu428em54DXgGuAep/0taavwskYw7K9y/hyx5f8euBXerTowWNnPUZ8dDxbs7bSv21/JvWfRFJ8UqRDVUrVck5r+ndg1e6fBR7wKv/Cfj01GEHVdqP6d+S5hZsqlGfnFzN86lJm3d43AlGp+uijzR/x/sb3WbV/FQnRCfRM6Un7xPYAREkU86+er2PrlVIBc5r0O9uv4yib9A/ar21qHFEdMGZQF15dvIXs/OIK27S2r2oityiXXw78QsdmHWmR0ILfMn/jWNEx7jvtPkZ2H1lh0RpN+EopJ8QYE/jOIplAU+B4YC9gjDEuETkbWAxkGmMqTk4fQb179zbLly8PybmHT13q89l+nw7JWttXVXIbN1ESRU5hDu9vep89x/awKmMV6w6uo8gU8bez/8awzsMwxmhiV0o5IiIrjDG9fW1zWtNfgTW//gteJ78HeAir2T802bWW0tn5lBNZ+Vn8d/1/WbFvBae1Oo27TrmLnKIcnvrxKeJccZzU4iRuOukmTm11KqceZz0p04SvlAomp0n/KayZ+K7CSvIA/6S0J//TwQut9ktt3oj0zDyf5Up5+3Hvj0xYOoHtR7aTlphG2yZtAUiOT2bxiMU0imlETFRMhKNUStV3Tifn+Ry4FcjGSvSen2zgTmPMF1Uc3mAs23qIKQs2RjoMVUscKzzGPV/eQ2FxIVMvnMqnwz7lik5XAFZnvGZxzTThK6XCwvG8nMaYV4C2WAvu3AAMAdoaY6YFObZab9btfWmbFO9z2+wVO8McjapNjhUeY+6WuYCV2Lsnd2fSOZM4u+3ZEY5MKdWQVWsybmPMMWPMAmPMf40xXxhj6v3qepW55vR2Pst1AZ6Gp8hdxN5je/lhzw9cN/c6Hlv8GDuP7CQhOoHJ50zmtONOi3SISqkGzu8zfRHZ4uB8xhhzYg3iqXPGDOrC7BU7fT7bVw3H7qO7ueSDSyg21jDOxNhEpl80nXaJ1k2hzn+vlKoNAunIl+bgfIGP/6tHtENfw/XcT88xqucoWia0ZHSv0Rzf+HiOb3w83Vt0Jzm+Vo1eVUqpgJL+IhpoMg+UTsvb8OQV5fH8yud5c+2bJMUlcdNJN3HPqfdEOiyllKqS36RvjBkQhjjqtDUThvicqEen5a1/th/Zzpc7vuT9Te+z/ch2Bp0wiCs7XRnpsJRSKiCOV9lTvmltv2E4VniM51c+T0pCCmPPHMvI7iMjHZJSSgXM6TS8f/C3jzHmTQfni8d6fBCHdQMy2xgzTkQ6ADOBFlizAN5ojCkQkTjgTeB0rPn+hxtjtlV1jVBOw1ueTstbPxW7i/nkt08Y2nEosa5YcgpzaBSj/TWUUrVTMKfhfZ2qn+8brKQcqHzgAmPMURGJARaLyDzgfmCKMWamiLwEjAb+Y78eNsZ0EpERwN+B4Q6/Q8jotLz1izGGpbuXMumHSWw7so1iU8w1Xa7RhK+UqrOq07wftMnAjdXM4BnjH2P/GOAC4Hq7/A1gPFbSv8J+DzAb+LeIiHHSXKFUAJakL+GvS/5KRm4GAM+c9wyDThgU4aiUUqpmnCb988t9dmEN6bsHa9ndm50GICIurCb8TlgL+fyGtVpfkb3LLqwZALFfdwIYY4pEJAvrEcCBcue8DbgNoH379k5DqrbKhu6lZ+YxZcFGxgzqErZYVM3syt5FYlwid51yF91bdKdHix6RDkkppWrMUdI3xnzjq1xEPsBaavdy4D2H5ywGThGRJOBDoJuT4ys55zRgGljP9Gt6vkDNur1vpc/1v99yMFxhqGrYe2wvDy96mB4tevDwmQ8zvNtwru16ra5yp5SqV4LVe98zAf1l1T2BMSZTRL4C+gJJIhJt1/ZTgXR7t3SgHbBLRKKBZlgd+moNfa5ft2TlZzFx2UQWbl9IgbsAt3GTX5xPnCtOE75Sqt5xlPRF5EsfxfFATyAWhwlYRFoChXbCTwAGYXXO+wq4BqsH/03Ax/Yhn9ifl9rbv6xtz/N1dr66o9BdyJ8W/olV+1dx+YmXM6LrCHq17BXpsJRSKmSc1vQH4Lv3vqdK9JbD8x0PvGE/148C3jXGzBGRtcBMEXkSWAm8Yu//CvCWiGwGDgEjHF4v5HS8ft0RExXDee3OY2SPkQxJGxLpcJRSKuScjtPfRsWkn4/V2W42MN1+Rl9rhHOcvoeO16/9dh7ZSesmrXUde6VUvRO0cfrGmLSgRFTP6XP92uVY4THm/DaHfTn72HtsL+sOrWNz5mYeOfMRru9+vf8TKKVUPaHT8IbAkdxCR+UqtIrcRTy57Elc4qJlo5Z0bNaRIWlDdNy9UqrBcdq8/yxwJfC8MWaKV/kYrLH6HxhjHgx6lDUQieZ90Cb+SDHGsOvoLn7c+yPL9ixjWOdh9Gndh4ycDFISUnBFuSIdolJKhVQwp+G9EjgBqxe9t4+AZ4BhQK1K+pGiTfzhdyD3ADfNu4kd2TsASI5P5uw2ZyMiHNf4uAhHp5QKt8LCQnbt2kVeXsURVXWZy+UiKSmJlJQUoqKiHB3rNOm3sV/3lCvfV257g6dD98Jv/Hfj2ZG9g1E9R3H5iZfTsVlHHWuvVAO2a9cumjZtSlpaWr35W2CMobCwkH379rFr1y7Hs846TfrHgCRgMNbseR6DvbYrtKYfCf93zv/x64Ff6dtGH58opSAvL69eJXwAESE2Npa2bduyYcMGx8c7axeAZVhj8t8UkadEZLSIPIW1KI6xtytgydiB3Duwc4Xy9Mw80sbOZcqCjRGIqv4wxvDrwV95ec3L3L3wbjLzMkmMTdSEr5Qqoz4lfG9Om/VLjnO4/9NYyb0R8ADW/PYPAE3s8n9UK4p6asygLjSN891x7NXFW8IcTf1xIPcAw+cMZ8ScETz303OkZ6ezKXNTpMNSSqlaz+k4/S9F5BbgWax57z2ygDHGmK+DGFu9kJgQQ3Z+xfmKEhN0UpjquvWLW9mStYVHznyEIR2GkByfHOmQlFKqTnDcPmCMeQ1rEZzBwA32a6ox5vXghlY/XHN6O5/l6Zl5DJ+6NMzR1G1Fbmu15dt+dxsvXfgS13e/XhO+UqremDhxIiLCG2+8EbJrVO+hgJX0OwInGGMWGGO0A18lxgzqQp8Omphqamf2Tv608E8UuYu4uMPF+uxeKRU24eiD5Xa7mT59OsnJyUybNi1k13Gc9EXkeeBX4EXgCbvsJxEpFpHhQY6vXtBFeGruv+v+y5LdS9h9dHekQ1FKNTDPLQx9n6HPP/+c9PR03nzzTb777jt++eWXkFzHUdIXkbuAu+3jhNLV9Z6z318T1OjqiR5tmjkqV6WK3EW8vfZt3l73Nhe2v5D2ic7GpCqlVF0wbdo0Lr74YoYOHcrvfvc7pk6dGpLrOK3p34HVS/+ZcuVf2K+n1jiieqiysfnLth7SoXt+PLr4Uf7+49/pltyNUT1HRTocpVQDMWXBRtLGziVt7FyAkveh+Ju9e/du5syZw6hR1t+40aNH8/bbb5Obmxv0azlN+p6B5+PKlR+0X3VGPh+WjB1Y6XP977cc9Fne0LmNG2MM3ZK78ceT/sh7l71Hr5a9Ih2WUqqBGDOoC9smD2Xb5KEAJe/HDOoS9Gu98sorJCcnc+mllwJwww03kJuby6xZs4J+LadJP99+bVKu3DOxf/2a4DiIdIa+wO04soOrP7maIncRo3qO4oHeD0Q6JKWUCgm3280rr7xCZmYmqamptG7dmh49elBcXBySJn6n0/CuAAYAL3gKROQe4CGsZv/wL2en6pWX17zMv376F64oFz9l/ESf4/tEOiSlVAPna3bVYJk/fz47d+7khx9+oG3btiXlP//8M0OGDGHNmjX06hW8Vk6nS+sOBuZhJfgym+yyi40xX1Q4MIIitbSuL10e+4yC4oq/71iXsHHiJRGIqHYxxnD5R5fTJKYJ/7rgX7Rs1DLSISml6rB169bRvXv3SIdRpSuuuILo6Gjef//9CtvOPvtsTjvtNP7973/7PLay7xe0pXWNMZ+LyK1YHfkSvTZlAw/VtoRf27RsGudz5b2WTeMiEE3tM2PdDLYd2cafz/izJnylVIPw8ccfV7rtu+++C/r1nDbvY4x5RURmAmcDLYEDwHfGmKPBDq6+0eV2fTPGICK0atSKAakDGNF1RKRDUkqpeqlaM/IZY47ZM/H91xjzhSb8wMy6va/PBXiWbT1Er3HzIxBRZOUU5jD689E8tOghAC5Ku4h/XfAvYly6LoFSSoWC35q+iDhZDs4YY06sQTz1Xo82zVi29ZDP8obm651f88PeH7i689UlZfV1GUyllKoNAmneT3NwvsB7BTZQK3ccdlReX206vInJP0ymVaNWPHTGQ5EORymlGoRAkv4iNJkHzcaJlzB86tIKtf2CYsPwqUuZdXv9X0imoLiA6+deT2JsIq8OfpXGMY0jHZJSSjUIfpO+MWZAGOJoUHSiHjij9Rk8dMZDnJB4QqRDUUqpBsNx730AETkXuIjS3vufG2MWBTOw+uxIbqGj8vqiyF3EpsOb6N6iOy9e+GKkw1FKqQbH6Sp7UfZwva+AR4BbgLHAVyIyU0SqNRqgoVkzYYjPXvzZ+cX1uhf/rA2zuG7udWw+vDnSoSilVIPkNEmPAa6ldFld75/f29tVbbT5S5iQDFu+icjlD+cd5q21b9GjRQ86Ne8UkRiUUqqhc5r0b8Lq1Pcl1hz8nezXhViJ/4/BC00FTfZeePsqMMXwTvgnvsnKz+LqT65m37F9uniOUkpFUHWX1h1hjFlkjNliP8u/3i7XMfoBGtW/o8/y7Pzi4K7XPL4ZPNOVkgEYhTlW2fjwzQswe+Ns9ufuZ8r5Uzj9uNPDdl2llKorBgwYQFxcHE2aNKFJkyZ06tSJf/7zn0G/jtOkX2C/Hleu3PPZUU80EWknIl+JyFoR+VVE7rXLk0VkgYhssnE40hsAACAASURBVF+b2+UiIv8Skc0islpETnMYf60xZlAX2ibF+9w2e8XO6p20fBP+31KqGV1wXZR2EX2P78uAdgMiHYpSSjmTvRdeuxiy94X8Uo8//jhHjx7l6NGjvP322zz22GMsWLAgqNdwmvRX2q/zRORxEfmjiPwFmItVlVxZ+aE+FQEPGGN6AGcBd4tID6zOgQuNMZ2xHh2Mtfe/GKu1oTNwG/Afh9erVWrUi9/7H2L2XnjpHHh7mNWE/+blVk3e7ec8Yartt2vajqmDgr8utFJKhdw3T8GO7+Gbv4f1smeddRY9evRgzZo1QT2v06T/DNaz+7bAeOAVYALQzt7+rJOTGWP2GGN+st9nA+vsc18BvGHv9gZwpf3+CuBNY/keSBKR4x1+h1qjqib+Knvxr55tNdlv/w6m9LTe711dvSB8Jf49q2FSO9j7S7VOmV+czzPLn2HEnBHc//X97M/Zr9PrKqXqlidbWX8fl78Cxm29jm9mlYeYMYYlS5awfv16+vYN7oRtjpK+MeZT4G7gKGV77h8F/p8x5pPqBiIiacCpwDLgOGPMHnvTXkofH7QFvNu+d9lldVJVTfyVPtt/oiV8MLr0s7ug4j5OjW8GT7YuTfJvXQP5R+Cl/tVK/C+sfIHXf32dIwVHOJB7gCaxTWoeo1JKhdO9q6Hn7yE6wfocnQC9fg/3Brfm7W3ixIkkJSXRuHFj+vfvz8iRIznzzDODeg3H4+qNMf/BSrRDgBvs17bGmBeqG4SINAHeB+4zxhwpdz2Dw2mAReQ2EVkuIsv3799f3bDCYsnYgYE929/8pZWci4OQ5H0pyoWX+lnXyPE8uzKlZQFKP5rOh5s/5IJ2F/DZVZ/x5sVvkuD5n0YppeqKpq0hrikU50N0vPUalwhNy3dpC57HHnuMzMxMcnJy2LlzJ2vXrmXUqFFBvUZ1l9Y9ai+p61laN7u6AYhIDFbCn2GM+cAu3udptrdfM+zydEofJQCk2mXl45tmjOltjOndsmXL6oZWO2TvhekDref1kTS+WUCdWfbn7KdRdCP+dOqfwhSYUkqFyLEMOP1muOV/1uvR0Hfm80hNTeXaa6/lgw8+8L+zA46n4RURF9AHK/nGld9ujHnTwbkEq1/AOmOMd3+AT7DmBJhsv37sVf4ne1bAPkCW12OA+umZrpGOoNT27+CZLqWfW50EN35o3flm74XZN3PKNa8zZ9gcYlwxkYtTKaWCYcSM0veXOuqyVmN79+7lvffe4+STTw7qeR0lfXuI3AeUrW17M0DASR/oB9wIrBGRVXbZo1jJ/l0RGQ1sx5oFEOAz4BJgM5AD3Owk/toqtXkj0jPzypStj7uJ+LzqzsUfBeN9LNX7dFc4urea5/Qh41f49P/BZc/B86ez051Lk/f+QNLN9XcqYaWUCpUnnniCyZMnA9C4cWPOO+88nn766aBeQ6xH5gHuLPI9UFWvAmOMqTipfAT17t3bLF++PNJh+FV+ud2tcddTrQ7v3S4te3fqyxOtrOdTQZQVJVyc2pYoDJ/t2k1iVCz8JcP/gUopFSLr1q2je/fukQ4jZCr7fiKywhjT29cxTpv3e2LV5p8D5lE6WY+qoWovq5t2LqR0tp41+Uv2Ho9nWInfFFuf3UXVu7aXJQkJZLuieGFvBoluA+7g3lQopZSqOadJfw1WTf9vxpjMEMTTYC0ZO7Cktr8+7qbAavmB1Oor83i5WvgTrSAmAfqPgcVTIM/Zf94XmzejXWEh/XK9HlOMbwbjs6oXn1JKqaBzmvTvBBYAb4nIM8AOrFn1ShhjdgQptgZn1u196TVuPnH+ZjMORSL1vgnof5/1OnMkrJ/j99B7WqWwPSaGwUePUaue7SillCrDadJPB9Zjdaa7xMd2U41zKi+rGV51LT+cNWdfrQhenQFXxcXStaCQp/cfYGphM0YcORq+2JRSSjnmdJz+q8DZlJ2Nr/yPqq4nUipN+MY4nKEoVB7cAN0u5dPEJG5s05pJLZoTZ+D/Hc6iVXFxxf3HJ4VloQqllFL+Oa2VX2C/LgaWAHlV7KucqGLWO2PAjXD98fOYFcaQKrP3smd4dPYg2jVtx4PXzYT8nCrmEzDwbHe4fRG07hnWOJVSSpXlNOlvB7oCQ2syC58qx0/CB1jg7s2yrYcYPnUps24P7gIMTuQW5XLTvJtoFN2Iif0nkhibCLGJVR9kiq3pfKPjdBifUkpFkNPm/fuwhumNEZEKs/Gp0NhnkrijcAxQg6F9QbLn6B52H9vNP877B6e2OrV0Q7dL/R9clB+25XyVUkpV5DTpvwQUAuOATBHZISJbvH5+C36IDZcxkE80ZxW8WFK2Pzsy49+3ZG5h3tZ5pDRK4c6T7+SctueU3WHEDBCdelcppWozp0k/DWiM1WEvDmvBm7RyPypQ45v5rfl2yy87q/Gp7ZuHMiKfMvMyuXXBrUxfM52mMU2565S7EF89DscdAAlg0J7W9pVSqoLly5dz5ZVX0rJlSxITE+nSpQv33Xcfe/YEb4kZp0l/kf3zTSU/i4IWWQNnDPzo7lKhfO3u8E52k1uUy4PfPEhGTgZ3nnyn72TvrXFLiG2C34EcmviVUqrEggUL6N+/P127dmXVqlUcOXKEb775hhYtWvDNN98E7TqO5t6vi2rt3Pt+kp4b6Jj3X5/bmsa5WDNhSAiCKmvdwXWM/XYsW7O2Mq7vOK7ucrWzEzzVCXL2V72PztinlAqRujT3fufOnTnnnHN49dVXAz4mHHPvq2B4spXfXaJccdw7sDPPLdxUYVt2fjH9Ji9kydiBoYiuxIbDG9iStYV/X/Bvzmt3nvMT/HmzNU6/qhkGdKpepVQY3Ty/4uKsg9MGM6LbCHKLcrnrf3dV2H5Fpyu4stOVHM47zP1f319h+/CuwxnSYQh7j+3lkW8fAeC1Ia8FHNPGjRvZvHkz//nPfxx8k+px2ryvgqHIT2c8Vxw8nsGYQV2IqqSVfE9WaKdIyC/O58pOV/LTjT9VL+F7dBvqf5+9v1T//EopVcft32+1iLZt2zbk19Lm/Uioqmk/PgnGbi9T1GvcfLLzK8521zYpPiS1/U9/+5Svd37N0+c97f8ZfiACnMOfE86Ga16HpsfV/JpKqQavrjTvb9y4ka5du7JgwQIuvPDCgI+rTvO+1vTDzV8HtnIJvyrpmXlMWbCxhgGVKiwuZPrq6Ty6+FG+3PklRUFYchewhvM1ae1/v+3fwbw/B+eaSilVR3Tp0oVOnTrxzjvvhPxamvRrFd+16jUThtA0zvdQuFcXbwnKlTNyMrj606v518p/0S25G1MGTCHGFcRx9w9uIKB/bms/sm6MnmgZvGsrpVQt9+KLLzJjxgweffRRdu/eDcC+ffuYNGkSM2fODNp1Ak76IhInIpfbPylBi6Ah8deBb3zla9gnJvhOwJWVO7UkfQmH8w4zsf9E3r30XQa0GxCU85Yx/rDVXyEQxQXBv75SStVSgwYNYvHixaxdu5ZevXrRtGlT+vfvT0ZGBgMGDAjadRw90xeRAqwbheONMX7GYtUOteqZflVN+50GwQ2zK908ZcFGnz35oWbP9o0xuI0bV5SL/OJ84gJNyjUV6Dh9na9fKVVNdeWZfnWF45n+OnQJ3dCoIuEDjBnUpdIm/iO5hdW6ZKG7kN9/+numr5kOEL6ED5T804v3M8Ogv5EOSimlAuY06T+EteDOC9rE71AQZqALZhN/kbuI6+dez4bDG9hwaENNQ3Nu/GFrfP7Ybf47+Y1vBluCNyOVUko1VE6T/lSgCLgK2Csiu3XBnSB4ILAe+JU14adn5pE2dq6jS36z8xvWH1rPjT1u5OnznnZ0bNA9uAESkqve583LYUJzTf5KKVUDTpP+CUAjrOb9KKA1uuCOf/5q+Q7Gpffp4Ds5Vtb0X5lv078FYFTPUbiinB0bEg9v9b9Yj3FbyV8n81FKqWpxOg3vIqqcU1U5lnauo90rW3AnO7+YLo99xsaJlwR0njZN2nBjjxtJSahFT2kat4S8LCjKrXq/l/pZrzp9r1LKD2NMcCYZq2WqO7GezsgXDlXV9KuRuGrSk/9w3mESohOIj453fN2wcdL/QRO/UqoSGzduJC0tjdjY2EiHEnQ5OTns3r2bTp06VdgW9Bn5RKSriNwuImOrc7yqmTGDulTazJ+emcfwqUsrPXbyD5O5ef7NuI07VOHVXJPW0LIbRAXQEKWT+CilKpGUlMS+fftwu2vx3zuHjDHk5OSQnp5Oq1b+F28rz/EqeyLyPHAnpcP2JovIT8DJwPXGmFmOo6jPqqq1RlV/Yp1Zt/el4yNzcTtsqJm/bT6DTxhMlNTiyRgf9BpN4G/e/uICmNACYhvBzfOgdc/Qx6eUqhNSUlLYtWsXGzZEYIRSCMXExHDccceRmJjo+FhHSV9E7gLu9irypJzngNeAawBN+oEa82uNDm8c6/K5EM+yrYd8Lr17IPcAbuOmSWyTGl03rEbM8N/cb4og/wi81B9u/AgW/V0X7lFKERUVRfv27SMdRq3itLp3B1aif6Zc+Rf266k1jqi+eLJVUHvt+7JmwpBKm/lTmzcq87mguICHFz1MlETx+y6/r9F1w258FnS71H/vfgy8dYW1cM9L/SB7X1jCU0qpusJp0u9sv44rV37Qfm1Ts3DqEX8zyTnstV+Zszq28Fm+bOsheo2bX/J54Y6FHMw9yCNnPkL3FnVwWsoRM6ze/YE85wc4th+e6WLdeL14tt4AKKUUzpO+J5OVbx/29BLMq1k4DcgfPw3Kaaqanjc7v5jfT13E3C1zubjDxbx1yVuM6DYiKNeNiAc3QJchkHQCNE8L/LiMX0uX7N2zGia1gx9ehQnJOtmPUqpBcZr0V9ivL3gKROQeYCZWs7+jsXEi8qqIZIjIL15lySKyQEQ22a/N7XIRkX+JyGYRWS0ipzmMvfYIZG15B9ZMGEKsy8c4VClkbdQ4Jv8wmUJ3IU1jmwb1uhExYgbctxqO6wm9Rwe+ap9nyd6p51jP/z8bA6bYmuxHWwKUUg2E06T/FFav/aso7cT3TyDVfu90PtfXgSHlysYCC40xnYGF9meAi7EeL3QGbgP+4/Ba4VPVs3yJLts7PUhObV9x4ZqYpGVExR4gc3c/YmowUqBWGjEDLn0WOg+C6ISanSvjV+tRgFJK1XOOkr4x5nPgViCb0tX2xP58pzHmiyoO93W+RcChcsVXAG/Y798ArvQqf9NYvgeSROR4J9erFe5fG5LTzrq9L9smD/UqKSI25StMcRzZGWfTb/LCkFw34kbMgL/sLf0c06jyff0Z30z7ACil6jXH4/SNMa+IyEzgbKAlcAD4zhhzNEgxHWeM2WO/3wt4uri3BXZ67bfLLttDOSJyG1ZrQO0brhHiYWSxLqGg2BDT/Aeioo+Rv38Q4GJ/dj1forb8zHxPtILi8t9ZCGgW6Yxf4T/9IDkNhs/QoX9KqXqjWjO0GGOOGWMWAPOMMV8EMeGXv46hGnP9G2OmGWN6G2N6t2wZ5hnbqhymF/r5nzdOvIQogaKjXck/MICCg/0BKCg2ZXrz13uPZ5TO7HfNa9YrYr8GIGc/7PrRavbXDn9KqXqiOjPynQ1MwKrpx4tIHrAEGGeMqXz+18DtE5HjjTF77Ob7DLs8HWjntV+qXVZ3PBD6WaEW7VqEq8kvFGb3oGB/2e4SxwoqTuRTr3n3neh5Vel7n60AVfB0+Es9Q2v+Sqk6zVFNX0SuBr4BLgASsKquCcBAYJGIDAtCTJ8AN9nvbwI+9ir/g92L/ywgy+sxQN0Q4mRR5C7ioW8eIj71bSSmfFcJcBvq77N9Jx7PsCf7iYLYptAowNYgT81fa/1KqTrKafP+k4BnUPi3WEP1vrU/u4CJTk4mIu8AS4GuIrJLREYDk4FBIrIJuND+DPAZsAXYDEwH7nIYe7338/6fySnK4fGzHqdN41Sf+6Rn5jFlwcYwR1YLjZgB4w7Do7ugfR/rBkCiISqA1bjevBz+lgKvXawd/pRSdYqjpXVFJBeIBa42xnzkVT4MeB/IM8bUoPt08IV1aV1/i+v89UDILr3p8Cau+uQqYqJimH/1fFo1akW/yQtJz/Q9X1LZnv6qxMyRsHE+uIsC2z8hGVqcqM3+SqlaI5hL666xX8u3Ef/Pfl3t8HwNRw0X1/Fn/aH1AIw9cyytGvlfblGb+SsxYgY0Sgl8ad/cQ6XN/kopVcs5Tfr/D8gB/iIicQAiEgv8BTgK3Bfc8OqRENUC3/j1Db7b/R2XdryURcMXcW3Xa0u2XXN6u0qPS8/MI23s3JDEVOc9uAHuXgZ/PWg9+w907P/4Zlazf/ZebfpXStVKfpO+iGzx/AD/xRpC9yCQKSK7gCz7M8CMkEVa20VgqN7C7Qt5evnT7D66GxGheXzZWfnGDOrie3peL5r4/RgxA068IPD93YXwzVPWSn9TToK9v/g/RimlwiSQmn5auZ8mWFksDmtVvTj7cxN7uyovREP13t34LgBntzm70n02TrzE7/P7jo9o4q/SiBlWjT/pBDhpmP+a//JXrFd3obXE74QWWvNXStUKgYzTX0Q1JshpUKqs5UeFpGl/9f7VfLf7O0b3HE2bJv5XNL53YGeeW7jJ5za3sWr8bZPiWTJ2YLBDrR9GeDVizRwJu1fCkQCniTBFVs3/mS7Q6iS48UPt9KeUighHvffrorD03q8q6Xe7tGzCCJKrPrmKTYc3MXfYXNonBjbVcJfHPiMuOors/Mon6dHE78CTraEot3rHxjaBUZ9D655WH4DZN8M1r+vNgFKqxqrqve846YuIC+iDNTtehXVNjTFvVifIUAl50q+ylk/FOeGDZN+xfWzK3ET/tv0dH1vVUD7QxB+wmSNh7xo4utcakhkdD7mHrRn8AvXABph6LhzNgN+NgKztcM6f4d0brMcJsY10OKBSypGgJX17DfsPKDsdrjdjjHE8tW8oRTbpR8P4g0G/5A97fuCM1mcgUv0Ogr3Gzdcaf6g83dUayldcEJzz9bgSjmVoS4BSKiDBHKf/ItCessvqlv9pOPzV8h8I/jK6z698ntFfjObhRQ/X6DxrJgzh3oGdK92enpmnY/mr68EN1qQ9LbtBm9Nqfr61H5X2CZg+EF6+UDsFKqWqxWmtvCdWp77ngHlAkKoy9VSQa2VvrX2LaaunAfBIn0dqfL4xg6wJZSrr4OcZy6+z91WD92I/Thf4qUq63Wr1zd/hvD9bjxhE9BGAUiogTpv3lwJnAi2MMZkhiyqIQtq8H8YOfFsyt3DFx1eQHJ/MtEHT6JrcNWjnHj51KT9uO4S7kn8KbZPiOZJbyJoJQ3zvoPx7uisUHIWiAsCN1ShmrOl+xeWsH4AvUTEwbBp8eg+06ATXv6s3AUo1UMF8pn8KsAD4HngG2AGUmaTcGLOj+qEGX8iS/pOtoKiK2luQO/At3b2UCUsnMPmcyZzS6pSgntuj4yNzK038AE3jXJr4g2nmSGhyHPS+2XoPkH8U8rPA7ca6OaimqBi47WtrdIBSqkEJZtJvidWRr7LZYBpGRz5/Cf+OJUH9Y7ti3wpObnky0YHMBV8D/nr1g1XrB7STX6h5bgjWfwZHa7iCdJD/PSqlardgduR7FSvhN+yOfFUlfAjqH9gXVr3AH+f/kUnLJgXtnJVZMnYg2yYPLUnsvqRn5pGemcfwqUtDHk+DNmIGXPospJ4OvUdD2rnW2P4mx1u9+WObBH6ul/ppxz+lFOC8pn8MiAeW2D8VqoXGmAlBiy4IQlLTr+pZfpPWZTtx1cCB3AOc/+75AHx33Xc0jW0alPMGIpA5+WNdwp0DOpV0CFRh5JkjIOeg1VcgUCGaN0IpVXtUVdN32l68HegKDDXGZNc4svooSAl/77G9DJo9CIBxfceFNeGD1Yyf2rwRy7YeqnSfgmLDcws38eriLfqsP9w8nUSf7grNUiF7D+Qdwe+M2U+2gtH/g9eHws3ztNlfqQbGaU3/IuBjYBLwd2NMkMYhhU7Qa/phmoHvlwO/8Mi3j3BFpysY3XN0jSbiqYkpCzYye8VOv8/6tZNfLfF0VyjMgfwj/vdtlmrdKGjyV6peCWZHvi1ACtAYa4z+fsr23jfGmBNrEGvQhTfpC4yv2UjGP8z7A83imvH8Bc/X6DzBNmXBxkrH83voLH61xMyRsH4ujtbJ0mZ/peqNYHbkS8NK+J6ldVOpuPRuw1WDJXSPFBzh5vk3szJjJQdzgz91b02NGdQloE5+aWPn0mvcfHqNm8+UBRvDGKEqMWIGdBsKTkZ7jG9m/XiWAM7e6/u9UqpOc/pMX5fZrUoNJkN5cdWLLN9ntUi8OPDFYEUUdEvGDvQ7tM8zp/9zCzfx/ZaDzLq9b7jCUx4jZpROCJR6JhzeAkf2WpMBmaLKj9vxvTXbn/f7ghxrGuCX+lnD/3TSH6XqLF1a14kQTciTlZ/FNZ9eQ/O45swYOoOYqJhqBhg+/SYvZE9WXpWT+Xg0jXNVKNPn/xFSk+WAvaWeAUOnwPw/60JAStUyQV1at64JatKv6nl+NSdAMcYgIhwtOEqMK4Y4V4XVimu1QIb2+eIZHfDjtkPcc0FnHfYXLp5Jf5a/RoUZ/6ITrBsCsW/S/E0N3LIb7N8AjVIgOc3//P/Ze2H2zXqToFSIBbMj3x/87WOMedNBbCEXtqRfjVp+Zl4mw+cM546T72BY52E1CCzyqpv8PbZNHkq/yQtJbd6IlTsOc+eATjz/5Sa2TBrKlAUb9aYg2J7uCglJcN7DVhP+4e3WokCuWCiyH9244pwtFCRRMO5w5ds/uANWvwONW+pjAqVCKJjj9F+n6mf6BqhVSb+2WrN/DQ8teojdx3aTGJsY6XBq7N6Bnf327vfHM9sflF35z/P+uYWbdMW/YPGeT6LnVb7XARgxA14dEvjkP8Zt3RhHx8FfMkrLyz8WO7bfWiYYsTq/avJXKmyqM5l7w5hqN4RWZqzk1i9uJb84nxu638DAE+r+MLcxg7rw/JebcJvSZ/ij+ncM+EbAX0uB5zz9Ji8EILV5I87q2KLk2p5WgrW7s7S/QHV4rwh53+rS9x0HWDP/tT0Ndq+Ew9sqP4e4oOslMPSZsuWVVhMMPNsN7l9nNfsPeUr7CCgVYk6T/vnlPruwhundA3QGbg5CTLWTv+f5DqzZv4b84nxu6XUL9552bw0Dqz22TKpYC69p7b/8zYCnJSA9M69ktsAxg7qUaSUYPnUpZ3VsUXIzAGUXCNLHBQ543wzMHAnGWDcAO763auxur5EAphiatKqYsO9bDc9UshS0cZdu++AWOLDRetxw3p+t67kLrUcO/voLKKUC4micvjHmm3I/XxpjXsW6GYgGLg9JlLVdAB34DuYe5OL3L2ZX9i5u7HEjK29cWa8SfmX6dEimaZyrzI8vwWy2X7b1UMnNhvfNgIdnW69x84N2zQZhxAwrgf/+dXhgPXQZAkknwEnDrEWAkk6Aoz7G8jdtba1J4c/+9dZNwPJXrBuB9OWw52fY9SNMPbfsPAE6d4BS1RKstVo9M7ZcFqTz1Qs7juzg3yv/zZHCIyzdvRS3cfPh5g+559R7iJZatQJxyPgao+/dRP/jtkNVDvsLpK9AZY8G/CX17Pzikn3WTBjClAUbdV4BJ7xbAfxJ7Q0b55dtGSgRRYWRBOUd3Wv1A/D0F1gw3po7YN6f4ViG9UgAo6MDlPLDUeYRkS99FMcDPYFYoPZNJRdmO4/s5Nv0b7m++/VsztzMvG3z6J7cnd+l/I5hnYdxVeerIh1ixJWfqtczc59nGJ937/0xg7r4TfqV3Rh4JgmCijcGns/e+3jO4Yln9oqdJZMRXXN6O77fcpBdh3N0quHq8EwWlJAEMY3g0BarD0DjlnBgvfXeFOP3BqAov+yjtrUfWa/PdoPTby6dUOjSZ0v38TVUUIcPqgbK6ZA9N7675Xg69z1ljBkbjMCCJWhD9gIYrjfys5Gs3r+axNhE/vf7/1HkLqLQXUhyfHLNr9+AeZ7RV5b8t00e6rO2713ur8WgaZyrzA1AVee+d6A1r4AnrlcXb2FU/45lWgk8rQZgtXZ4Fi4CuOb0dtqnwMMzauDAJqvG3rgVHM2wbgTKExdgrEcAgfC0Csy5H1a8Zt0UeG4GfJU5EehNQzhvLvRGRtmCOWRvBxWTfj6wC5gNTHcenjMiMgR4DqsT4cvGmMmhvqY/U1ZM4c21b1JkN11OOmcSCdEJEY6q/vBubvckTu/e++B/KeAxg7qUJGpf+/hK+JV5bqHVArFs66GSc5W/oajqc/npiT0tC2MGdSnpZNhgOhv6ekQwc6Q1SVBxAeRnlw4ZNMXwu+tg5zJrWmFvEgWItU90AnS/FNZ+UvZmffkr1o83T1n5YYb+fPOU71aF6u4XDMG4lt6k1HuOkr4xJi1EcQRERFzAC8AgrBuNH0XkE2PM2pBe+MlWPovXxsbQvaCQk1uezPXdrichOoFRPUfRKKZRSMNpqDyJ2xdPk7unhu25ISi/QNCs2/uSNnZupa0D5VW2T00nI/K+8fDcEHgeZXg/0vDcHAyfurSkxcCzL5TeMHjvd1bHFiW/g8paF/pNXsiSsQPpNW5+mSGO3jcb3u+9R0SUv0nxCOQmZfjUpSWPSHxda8qCjYyxbwSmLNjIpese4lhsCmtaD+PG6C+tjoL22gHFCC4MBhC79l8ksUQX50NcotXp8PO/wPo51k1EdAJ0GggIbP5faVn3S+GiiX5jByrOOVDZTUOg+wVDMK/1zVO4ty8lKkw3KWG7VlWy97Jr+ghSb50VmZuPMF/fb9IXkbOdnNAY8131w/HrTGCzMWYLgIjMBK4AQpv0fcy3XwAMb3s817a7kMfbX8AF7S8IaQgqMOUTj6/n7/cO7FyhLJBHBIHwtW9VNw6+YvHwbh0o36Lg+Z7lWxS8Wx/K31h4/248IxrKt3B47+f93nNe7xuS8v0tAkn6C2Wx+gAAIABJREFUlcXkfbPjXfYct1k7b4MbJ9uJYeZI6DSI75d9T7/WxXy310W/FlZrwGX77mBev83WzUHT1hDXFIrzyTMxxBfnW48SjClbFpcY+B/be33cSPi6aQh0v2AIxrW8bhyiIGw3KSG/ViC+eYo2WavC0xpTC64fSE1/MYGvrGcCPGd1tQV2en3eBfQJ4fUquKV1K3JEWBNvzZF/ygma7OsaT1Lp0yGZtbtLp092MqtgVTcJUDbRV3Xj4H09zz7l99UlisuxWwJGLp7LtruHMnLsXLbdZ/3e142dC5feVbrvsQw4/WaGLelUejMAvssC4etGwtdNQ6D7BUMwrlXXblKCwfvmQwj/zUeEru+3I5/deS9QxhjjeyB2EIjINcAQY8wt9ucbgT7GmD+V2+82sKoI7du3P3379u01u/Ce1dY4YQz3t0ohR+x+i64Y/n3LGqKdrFuuajXvBOur976nphqMpF9+32BMZVwbeDo6elTWjyLU+nRIDvi65WOuzJQFG+m+6C4yTDPeKR7Ida6FtJIs1p37YpnjA90vGIJxrSkLNtLym7Fc7/qSAqKJpYgZxQM5cN6kkMQbrmtVZdrc72i19AkGu5aTIAXkmljmF59BRt+/cPtQRw3cte76NVpwR0TGVbG5G3ANViuNEPqk3xcYb4wZbH9+BOuikyo7Jmi99yckl111TFwwLvx/yFRkeT/Prknvfe91BDxJ33NzUP4mwVe50xYF72M8x3mft3y5r/flr+ErTn98fdfK4in/Xcqfv7JjfMXhq7yyfQMV6PE1vY4TNbqWPZLiYu8WECdzMdTWa1Xl0zHw0+vkuV3ERxVXfzRHLbt+jXrvG2Mm+DjhKcBjwJVYvegN8BHwfzUL1a8fgc4i0gFIB0YA14f4mpbGLcuuSpabGZbLqtrFuybiSfC+aifly8p3QvTcEEDZPgZVPeNXKqTspLtucblHJHX9WlWp7PFPPb6+08l5+gOPAoOxavZFwNvAJGPMuuCHV5YxpkhE/gR8jnWz8aox5tdQXxeouCqZUjXgPQzR+2bA896T/D03B306JJcp9/C1X2W99715RjWUnxa5shsQz3mr2icQfToks+twTqXncXJuX7+Tyo7xVV7TG6xAjw/njVwwrlXX4q0R++bjoriNMCgCNx8RuH5Ak/PYY+MfAfpjJft84DWsyXi2hTLAmgpa875SSilVB9SoeV9EVgCn2B+LgfeAZ4C99vY23vsbY3bXKFqllFJKhUQgzfunUjpkz4X1HH1EJfuGesieUkoppaop0AQt/ndRSimlVG0WyJC915yc0Bhzc40iCjIR2Q/UcKB+GSnAgSCer67Q792w6PduWPR71y8nGGNa+trgaJU9BSKyvLIOEvWZfu+GRb93w6Lfu+GIinQASimllAoPTfpKKaVUA6FJ37lpkQ4gQvR7Nyz6vRsW/d4NhD7TV0oppRoIrekrpZRSDYQmfQdEZIiIbBCRzSIyNtLxhIOIvCoiGSLyS6RjCScRaSciX4nIWhH5VUTujXRM4SAi8SLyg4j8bH/vCgtu1Wci4hKRlSIyJ9KxhIuIbBORNSKySkQazJzlIpIkIrNFZL2IrLNXca33tHk/QCLiAjYCg4BdWCv+XWeMWRvRwEJMRM4FjgJvGmN6RjqecBGR44HjjTE/iUhTYAVwZQP47y1AY2PMURGJARYD9xpjvo9waGEhIvcDvYFEY8ylkY4nHERkG9DbGFMfx6tXSkTeAL41xrwsIrFAI2NMvV8+VWv6gTsT2GyM2WKMKQBmAldEOKaQM8YsAg5FOo5wM8bsMcb8ZL/PBtYBbSMbVegZy1H7Y4z90yBqBiKSCgwFXo50LCq0RKQZcC7wCoAxpqAhJHzQpO9EW2Cn1+ddNIAkoEBE0rDWoFgW2UjCw27iXgVkAAuMMQ3iewP/hP/P3p2HR1FljR//nuyQBEIgyBIgIARE3FFEGUURRdHRcQFe92XcnVHUUVzRUV9xRkVnfi44ouLICAqubIogOgL6AoqiKIvsu0ACAbL3+f1R1aEJ2SrpTifd5/M8/VT3reqqk4g5dW/dhXsAX7gDqWcKfCoii0TkhnAHU086A78Br7uPc14VkeRwB1UfLOkbUwURSQEmA3eo6u5wx1MfVLVUVY8GMoETRCTiH+uIyLnANlVdFO5YwqCfqh4LnA3c6j7Si3RxwLHAS6p6DLAXiIp+Wpb0a24j0CHgc6ZbZiKU+0x7MjBeVd8Ldzz1zW3u/BwYFO5Y6sHJwO/d59sTgNNF5K3whlQ/VHWju90GvI/zKDPSbQA2BLRiTcK5CYh4lvRrbgHQTUQ6u50+hgEfhTkmEyJuh7axwM+q+my446kvIpIhImnu+yY4HVd/CW9Uoaeq96lqpqpm4fy/PVtVLw9zWCEnIsluR1Xc5u0zgYgfqaOqW4D1ItLdLRoARHQnXb+aLq0b9VS1RERuAz4BYoHXVPWnMIcVciLyNtAfaCUiG4CRqjo2vFHVi5OBK4Al7vNtgPtVdVoYY6oPbYFx7miVGOAdVY2a4WtR6BDgfecelzjgP6o6I7wh1Zs/AePdStwqoEGtEBsqNmTPGGOMiRLWvG+MMcZECUv6xhhjTJSwpG+MMcZECUv6xhhjTJSwpG+MMcZECUv6xkQQd8U0rcGrv4hcHfg53LH7icgxIuITkTwRaeHhey1EZI/73WNCGaMxjZUlfWNMQ/MkIMBYVc2p6ZfcY8e63/3fEMVmTKNm4/SNiVBu7f1z9+M4Vb06fNHUjIj0BPyTXh2rqt95/P6xOMsgA/RQ1WXBjM+Yxs5q+sZEqYqa991mf3/ZLe7qY3kiss49PlZEHheR7SKyWUT+LiJx5c7bR0Q+EpEdIlIkIstF5CF3LYPq+GdFWx2Y8N3rPiQiP4vIXjemX0Tk3yLSzn+cuxzyGvfj1XX49RgTkWwaXmNMZR4D0t33KcBrwIXAeQHH3A38CrwMICJnAR8DgQm+G/BXnIVcAr9bkQHu9uty5Xe75wjU3X09D2wKKP8ayALOAO6r5nrGRBWr6RtjKrMPJ2H7E7UAg3FW3esM7HHLLw74zgs4CX8eTuJtAgx3950rIpWu2OfO93+k+7H8uhb93O08oAWQChyFsxzqznLH+heMOVpE7G+cMQGspm+MqcwbqrrSXWjJb66qfgIgIkuAvrhLTotINnCoe9xJ7G9mD3QaUNmCLi1xFrMC2FFu31p32xN4GFgCLAb+pgd3TPJ/N84952+VXM+YqGNJ3xhTmbUAqlrgrsIGsC5gf5G7TXS3GTU4Z3r1h1ToMZyafT/2txwALBeRs1R1TUCZYIypkDV9GWMqU1LDMr/tAe+fU1Up/wJuqOL7O4BS933LwB2qulVVfwdkAmcD9+A8XsgGHih3Hv93Szi46d+YqGZJ3xgTLMuB1e77P4rI2SKSJCIZInKxiHwBdKrsy6paCvzgfuwVuE9EbhCRy4EEnGGIE9mf0Mu3MPi/u9g9pzHGZc37xpigUFUVkduAD3F6+0+rxWlmAcfg9BUIdBJwVSXfKd9H4ER3+1ktrm9MRLOavjEmaFR1GvA74COc5voiYD0wHadpf1Pl3wbgdXfbyZ1ox2+ye871QAGwC/gOuE1VX/YfJCLHsb814Y26/CzGRCKbkc8Y06CIyAzgLOAfqnq7x+/+A/gTMF1VzwlFfMY0Zpb0jTENilvDXwjsBTrWdP59d3Ge9UBT4DivU/gaEw0s6RtjjDFRwp7pG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpG2OMMVHCkr4xxhgTJSzpGxMEIrJGRFRE3gh3LI1RTX5/ItLfPUZFpH/9RWdM5LCkb0w9EZEkERknIj+JSKmbvNbU4/UfFJGvRSQ/IHlm1df164uI3CUis0Vko4gUisgGEXlXRI6oh2u3FZG3RWRlwO94Tqiva0xNWdI3pv4kAVcCLYCcMFz/YqAnsC0M165PfwJOA/YCa4D2OD/7/Hq4yTkEGAbEA3tCfC1jPLOkb0wIiEhXEdnk1vRmikgTIA/IVNV2wJwwhHUu0Bz4u5cvicggEfmviGwTkSIR2e1+PjvgmKyAmu1dIvKWiOS5te0Hy53vcBH5SkQKROQXEbmgtj+QiNzqXtMnIje6xa8CnVU1W1W7A3e55cnAH2p7rRpaBmSoaif3vTENiiV9Y4JMRDoCs4C2wCfAeaqar6qlqrqxlud8JCCpVvbqX9U5VHWDqmotLt8L6INz0/IjIEA/4CMROaqC458ETgcKgHbAYyIy0P05koDpwMlALFAK/Ado4zUoEbkG+CfgA65X1TEAqvq4qq4JOHRmwPvCas65pprf8Zqqvu/+d97u9Wcxpr7EhTsAYyJMG5yE3xGYClykqlUmmhraAHxTzTG7g3CdikwCXlXVXAARaQGsBVJxms2/L3f8QqA/0AzYhNPUPQAn+f4P0ME97mJV/VBEzuDAxFwTQ4EbAAWuVdVxVRx7p7vdAbxbzXm/A7ZUsX9zjSM0pgGypG9McJ3lbhcBF6pqUTBOqqqv4jRbh0MC8IaInAS05MAWwnYVHP+O+3NvF5FtOM/UD3H3+TvTFQIfAajqZyKyE0j3ENNN7vbuyhK+iCTg/M6uwLkhukBVf6vqpKoa6uZ/Y8LKkr4xwbUHSAGOBs4DJgfjpCLyR+CP1Rx2i6p+G4zrlTMV6AqUAEtwmu2PwbkZiK3g+NyA9yXuVoIck//3fKOI/FtVD+icKCKtgPdxHkNsBgar6nfVnVRE3sd5LFOZzXZjYBozS/rGBNdknAR3JfAfETlPVT8NwnkzcZ6rV6VZEK5zABFpiZPwAR5W1SfdHvC/1PKUP7rbRJyboo9E5HS81fIBbsHpO9AN+ERE+qvqLjfmw4ApQBdgMU6fig01PO8xQKcq9q/1GKcxDYp15DMm+P6I04EvAXhPRPr6d7jjt1cCg9yi9v4yEWlf2QlV9RFVlWpec6oKSkTGu9ceGVA8x732hZV8bSdOfwKAR0VkCfAt+2vwXv0n4HyTReRHnJaEYo/nWQ+cDezCaVWZ4o6QAKeG38V9HwdMcucn+NptMamUqmZV8zvOqur7ItI+4L9xL7e4T0CZMWFlSd+YIFPVYuAinA5tycDUgIlhDnVfye7nuICy+BCH1t69TquAsk5uWYWtBG5v/4uABTg97WOBy4Ba9VBX1QLgHGAeTq/7JsC1OB3+vJ5rCXA+Tv+Afjg3EfE48yH4+Uce+F+ZtYnbg3j2//dMdMuSAsqMCSup3QgeY4wxxjQ2VtM3xhhjooQlfWOMMSZKWNI3xhhjooQlfWOMMSZKWNI3xhhjokTET87TqlUrzcrKCncYxhhjTL1YtGjRdlXNqGhfrZO+iLyiqjeIyBBgsaour3WEIZSVlcXChQvDHYYxxhhTL0Sk0pkj61LTf8bdngYMF5HOwCqcaS8Xq+ordTi3McYYY4Ks1klfVZe525sBRESAbJwpMY8OSnTGGGOMCRpPHflEpNIFPdzpOktVdaKq3ufhnLEi8p2ITHE/dxaRb9y5qie6y2MiIonu55Xu/iwvsRtjjDHRzmvv/R9F5MyKdojIHThN+17dDvwc8PkpYLSqdgVygOvc8uuAHLd8tHtcvRs6Zn44LmuMMcbUmdeknwlMF5GXRSQZymrmc3Ce8Tep6svliUgmMBh41f0swOnAJPeQccAF7vvz3c+4+we4x9erb1bvZPTMBtln0RhjjKmS12f63+CsVHU9cKaIjAfuYP+KYW97PN9zwD1Aqvu5JZCrqv5lOzfgrAyGu10PoKolIrLLPb5Wq33VxfOzVjB8YHZ9X9YYY6LWZ2s/46uNX+FTHz71oSjd0rpxda+rAXj868fJKchB0bJjjml9DNf0ugaAO+fcyd7ivc53VfHho1/7flzb61oArph2Rdn3fDjHnNP5HK7udTWFpYUM+XgIijrfdY8b1mMYVx1+FTkFOVz80cVl1/ZvbzrqJi477DLW563noo8uQlX3H6PKfX3uY0j3IfX6e/Sa9E8CbgMeB7KA+wHBSc63qOqUmp5IRM4FtqnqIhHp7zGO6s59A3ADQMeOHet8vqFj5vPN6p0HlGWNmEqfzulMvLFvJd8yxpjIVuwrJk7iEBG27N3Clr1b2Feyj33F+9hXso+CkoKypDZr7Sx+2vETRaVFFPuKKfIVkRCTwH19nC5gr/zwCgu3LCzbV1xaTLPEZrx65qsAvPXzW6zMXUlibCIxEkNMuYbqVbtWsSN/BzHilMdIDJ2adSrbv7toN/kl+cQQU3ZM4CqzyfFO3VVEiJEYBCElIcU5FzEcmnZo2XX9x7RNbgtAQmwC/TL7ITjl/u93bt4ZgNT4VIZkD0FEnO+6MfRI7xHc/yA14HlpXbcD3b9xbgAEUJwa/i2qutvDeZ4ErgBKcNabbga8D5wFtHFr832BR1T1LBH5xH0/X0TigC1AhlbzA/Tu3VvrOk7/5FGz2JhbUOG+2wd0s1q/MabRK/WVklOYw478HeSX5JeVd2vRjeT4ZLbnb2dD3gZ86mPJ9iXMXjeb77Z9x4LLF5AYm8io/xvF+J/HH3DOGInh+yu/B+DhuQ/z0a8fkRCbQFxMHAkxCbRIasH7578PwOhFo1m4dSHxMfEkxCQQHxtP2+S2PHjigwCs3rWaTs06lSVsUzkRWaSqvSvc5yXpi8g9wMM4z+4F+AXogZP4NwG3qeqHtQiwP3C3qp4rIu8Ck1V1goi8DPygqi+KyK3AEap6k4gMAy5U1WrbRYKR9KHi2j5gtX1jTL0o9ZWyq2gXRaVFFJUWUVhaSJGviLbJbUlPSmdX4S4WbFnglAcc87vM39G5eWd+zf2VcT+NI78k/4DXvSfcy1EZRzF11VRG/HfEQdcdf854jsw4kvdWvMfIeSPLynuk96Bf+37cdNRNJMYmsiJnBVv3baVpXFOS45NpGteUJvFNaJnUEhFBVQlDN6yoVFXS99q8P8rdbgCuU9WZbjIehfPMfXItzlnevcAEEXkc+A4Y65aPBf4tIiuBncCwOl7Hk6WbdnkqN8YYcJrA42PiKSwt5OG5DwNQqqVlyXlwl8H8/tDfsz1/O9d+cm1Zsi4sLaS4tJjbj72dy3teztrdazn/w/MPOv8jfR/houyLWJ+3nuFzhh+0v1WTVnRu3pndRbuZu2muk4zjmpAUl0RqQmpZM/mRrY7k/j730zKpJcnxyQhOgs5qngXASe1OYswZYwDo1LwT7VPaH3Cdbi260a1Ft0p/D5bwG4baJOjXgDv9Tfmq+oKITAPeAPrVJghVnQPMcd+vAk6o4JgC4JLanD8YmjWJJ6+wtMJyY0zk8qmvrEl52qpprMtbR2FpIQUlBRSUFnBI00O46aibAHho7kOs2rXK2VdSwI6CHRzb+lhePONFSn2l/Lj9R8Bp9k6KSyIhJoHi0mLAeS6c3SKbxNhE4mPiSYxNJDE2sey5b6umrbjvhPtIjE0kITahbNu9RXcADk07lEnnTTpgX0JsAk3jmgJwTOtjmHXJrEp/zg7NOvA/zf6n0v1tktvQJrlNHX+bJty8Jv3Bqjq9fKGqrgZOFZE/BSeshufi4zrw/KwVB5VvzC1g9Mzl9lzfmEbgs7WfMW/TPHYW7CyracfFxDFmoFODfeLrJ5i9bjZFvqKymnbLJi357JLPAPhg5QfM3zyfOIkjMS6RpNgkDm91eNn5YyWW5LhkWia1JCk2ifQm6WVJu2l8U6ZeOLXS2JolNOPpU5+ucv+lh11a6f4mcU3ont7d0+/DRB9PSb+ihF9u/z/rFk7DNXxgNpMWra+wQ9+kRest6RvTwGzI28DSHUuZsWYG/9vvf0mKS2LR1kV8tvYzWjZxkrK/VuzXNa0rRb6iA2razRObl+3/+6l/p2l8U+JjKm7he+SkR0L9YxlTJxG/tG4wZbZoWmHSz2zRNAzRGGPK21e8jznr5/DJmk+YvX424NSA1+WtI7tFNn85/i/ce8K9lX5/aI+hVZ4/8AbAmMbIkr4HG3L2eSo3xgTfsp3L2FW4i7ziPPYU7WFP8R46pHbglMxT2Fu8l3v/ey+pCalcffjVDMoaRNcWXctq8zbcy0Q7S/rGmAZFVckvyWd30W7yivLYXbT7gGfnN312E9vzD5yIc1DWIE7JPIWMphlMOm8SXdO6EhsTG47wjWnQLOl7UFVnvqFj5tt4fWNqYV/xPuZtmkffdn1Jjk/m0fmPMnnF5AOOSY1P5ZOLPyE1IZX/7fe/xEosKQkppMankpKQQkp8Stmx1pnNmMrVOemLSDugFbA0YM78iDR8YDZfr9pR4SQ9xpj98oryWLd7Hevz1pNbmEteUR6DOg+iQ2oHFm5ZyAuLX2B7/na27dvGvhLn8djMi2eSHJ/M6R1Pp0NqB5olNqNZQjNSE1JpntC8rPNc33Z2c21MbXlK+iJyHc5qdx+r6r9E5GGcGfoEWCciA1V1ZQjibPD8q+9ZL34TjYpLi9lTvIcWSS34YOUHPDT3oYOO6ZrWlQ6pHRARfOoju0U2/dr3o1WTVmSmZtKqSSsATsk8hVMyT6nvH8GYqOB1Gt7ZwKk4iX8ezvz3/hsHBcar6pXBDrIugjUNb6DK5uJvn5bE3BEDgnotYxqyvcV7mbtxLqMXjea0jqdxz/H3UOorZcKyCbRJbkOH1A6kJ6XTLKEZCbEJ4Q7XmKgQzGl4D3O3i4AT3e9PA+YCTwD9axljo7I7v9hTuTGRaO7Gudzx+R0UlBbQPLE5SbFJAMTGxHLZYZeFOTpjTEW8jl9p4W63AYfj1O7fAp5xy1sHKa4G7dp+XSoszyssZfTM5fUcjTH1Y2XOSuZtmgc4ne9u+uwmRITXznqNOUPm8Odj/xzmCI0x1fGa9HPc7Xk4S+ACrAD8XWf3BCOohm74wGzapyVVuG/SovX1HI0xoZNbkMuCLQt4+fuX+cNHf+C1H18DnCll7zvhPsYNGsfxbY4nLsYGAhnTGHj9P3URcA7OanoAu4DFwHHu5zXBCavhs7n4TaTYnr+dz9Z+xm/5v7GzYCcXdbuIXq168fm6z/nz5/tr7+lJ6dxy1C1ln6uaB94Y0zB5TfoP4zzLTwdKgftVtVRE/uDu/28wg2vIbC5+EwleXPwir//4OgWlBcRIDGmJaZzU7iR6tepFz5Y9ubv33XRN60q3Ft3IaJJhy6Ma08h5XXDnWxHpCPQANqrqVnfXaOBlYEeQ4zPGBMmuwl0s2LKAH377gTt73wnA5+s/p2Ozjvz1pL9yWMvDDpim9pDkQ7jq8KvCFa4xJgQ8P4hT1X0ishe4QETSVfVJVd0WgtgaPJuhzzR0y3Yu46NfP2LBlgX8svMXFCUtMY0rD7+SVk1aMfHciTYfvTFRxPP/7SLyT+An4EXgMbfsWxEpFZGql6iKMFV16LNFeEx9K/YV8/6K93n5+5fZsncLAL/m/sqEXyaQkpDCzUffzLhB45h9yeyyiXAs4RsTXbzOyHcLcGsFu54HXgcuBiYGIa5Gw5bbNeG2KncVC7Ys4IOVH/Djjh8BaJbQjEsPu5QBnQYwoNOAA9aMN8ZEL6/N+zfhjM1/FrgroPxTd3tMMIKKBDYtrwk1VcWnPh6d/yjfbvuWpnFNOTvrbB49+VGaxDUBsGRvjDmA12l484EEIBVnTL6qaqyIJAAFQIGqNqgqbiim4S1v6Jj5FS7C06dzuj3XN0GVU5DD5BWTmb1uNgM7DeSi7ItIjktm055NZKZmWu96Y0xQp+EtxEn6KeXK/Sc/uJ07ClT2/N6e65tgWfLbEj5Y+QEz1sxgd9Fujsw4koTYBJLjkomNiaVDsw7hDtEY0wh47cWzyN2+4C8QkT8BE3Ca/UNbpW6gLj6u4j+4/ol6jKmr6WumM2XVFI7MOJJXz3yV8eeM57LDLiM2JjbcoRljGhGvzftnAdNxEvwBu9yys1X104O+GEb10bwPtvKeCb7JyycTHxvPeV3OI684jziJo2l8g3p6ZoxpgKpq3vdU01fVT4DrgTycRO9/5QE3N7SEX5/mjhhAn87pB5X7x+wb48W4n8bxyPxHePn7lykoLaBZQjNL+MaYOqvN5DxjRWQCcBKQAWwH5qlqVCy2UxvWk9/U1Evfv8Sk5ZPYtm8bbZPbMm7QuLKe+MYYU1e1mplDVfeq6kxV/Y+qfmoJ3zHxxr62+p7xpKCkgBcWv4D/MduO/B0c3vJwrup5FS8MeIGMphlhjtAYE0mqremLyCoP51NVPbQO8RgT0VbmrOSd5e/gUx/zNs1j055NlGopF3a9kLYpbXmgzwM27M4YEzI1ad7P8nC+mvcKjDK25G70yinIIacghy5pXUhLSmP66ukAdGzWkTM7ncmJ7U6kbUpbAEv4xpiQqrb3vojMwUMyV9XT6hhTUNVX7/1A1pM/uhWUFLB291pKfCXMXDuT8T+Pp2fLnow7exzgzKRnyd0YEyp1mpxHVfsHPaIItzu/2FO5adx86qNUS4khhtiYWL7a+BXD5wwv2980rikPnvhg2WdL+MaYcPE0Tr8xCkdNH6y2Hy2KS4s5/8PzWZ+3nssPu5zhxw0nryiPhVsXkhSbhIhwVMZRNE9sHu5QjTFRImjT8IrIldUdo6pvejhfEvAlkOjGMklVR4pIZ5xZ/lrizAJ4haoWiUgi8CZwHLADGKqqa7z8DPXFVt+LfNNWTWPkvJF8H1mZAAAgAElEQVQUlBZwQpsTyEzNpMRXQssmLTkr66xwh2eMMQfxOk7/Dap+vq84SbmmCoHTVXWPiMQDX4nIdOBOYLSqThCRl4HrgJfcbY6qdhWRYcBTwFCPP0O9sPn4I9u+4n08s/AZOjXrxJlZZ3LDkTeEOyRjjKlWbcbpSzWvGlOHf4x/vPtS4HRgkls+DrjAfX+++xl3/wBpoA9IK6vRb8wt4ORRs+o5GhMseUV5qCpN45vy2qDXeHvw25bwjTGNhtekf1q51xnAH4HvgX3AMK8BiEisiCwGtgEzgV+BXFUtcQ/ZALR337cH1gO4+3fhPAIof84bRGShiCz87bffvIYUFBNv7FvhtLxgTfyN1a+5v/KHD//A1TOuBqBTs07Ex8aHNyhjjPHAU/O+qn5RUbmIvAdsAX4PvOvxnKXA0SKSBrwP9PDy/UrO+QrwCjgd+ep6vtqyJv7IsLNgJ2/+9CZjfxwLwHmHnhfmiIwxpnY8z71fCf/cs7X+a6iquSLyOdAXSBOROLc2nwlsdA/bCHQANohIHNAcp0Nfg1RZZz6bqKdxuWr6VazZvYbBXQZzWY/LOKzlYeEOyRhjasVr7/3ZFRQnAb2ABDwmYBHJAIrdhN8EGIjTOe9z4GKcHvxXAR+6X/nI/Tzf3T9bG/CYw4k39qXLfVPxVRDhP2evsKTfgH279VuyW2STkpDCzUfdTHJ8MqdknmJj7I0xjZrXmn5/Ku697/9L+G+P52sLjBORWJz+Be+o6hQRWQpMEJHHge+Ase7xY4F/i8hKYCe16ENQ347PSueb1TsrLDcNU0FJAcPnDOeibhfx52P/zDldzgl3SMYYExRek/46Dk76hTid7SYB//JyMlX9ATimgvJVwAkVlBcAl3i5RrjZc/3GZW/xXkb8dwQ7C3ZyZMaR4Q7HGGOCymtHvqwQxRGxKnuub1PyNjyrcldx/ofnA3D9EddzauapYY7IGGOCqzbj9I0HJ3Y5aEQhAHmFpTZev4H5Zss3ADx60qP86Zg/2fN7Y0zE8ZT0ReRZEVklIsPLlQ93y58ObniN3/CB2STEVpw8Nu86uAXA1L+8ojwA/qfH/zDlD1O4sNuFlvCNMRHJ04I7IrIK6ARkq+qvAeWdcSbVWa2qhwY9yjoI14I75VW2AA9An87pTLyxbz1HZFSVj1d9zANfPcC9x9/L5T0vD3dIxpggKi4uZsOGDRQURFYFKzY2lrS0NFq1akVMzMF196AtuAO0c7eby5VvLbfflDN3xIBKh+99ty6n/gOKcjsLdjLq/0YxffV0UhNSOSLjiHCHZIwJsg0bNpCamkpWVlbEtN6pKsXFxWzdupUNGzbQsWNHT9/3+kx/r7stv4TYWeX2mwpUNkyvqFQZPXN5PUcTvV5a/BL9J/Zn+urpDOs+jKl/mMpRGUeFOyxjTJAVFBTQsmXLiEn4ACJCQkIC7du3Z+9e7ynXa03/G2AQ8KaIvAQsA7oDN+EM5fvGcwRRZOKNfRk6Zn6F4/a/XtVgJxaMCKrKVxu/on1Ke2466iaymmdxaNqhZLewCZKMiWSRlPADVdSsXxNek/7TOLX6psBdAeUC+IC/1yqKKLJ00y5P5aZuNu3ZxCs/vML6vPX835b/49pe1zL8uOGc3fnscIdmjDH1ztOtgqrOxllVbzcHLqe7C/ijqs4JdoCRZsmjgypcfS+vsJShY+aHIaLItWDLAm6bfRuTV0xm897N3N37bm475rZwh2WMMWHjuX1AVV/HWQTnLOByd5upqm8EN7TIVVnHPevQV3f5JfmsyFkBgCDsK97Hc6c9x7QLp3HV4VcRH2NL4RpjGqYnnngCEWHcuHEhu0ZtJ+fJBLoAnVR1pqpaBz4Plj9xToVj94tKlewHpoUhosiwp2gPF3xwAU8vdKaL6N2mN9MunMaAjgPCHJkxpjGrj47WPp+Pf/3rX6Snp/PKK6+E7Dqek76I/BP4CXgReMwt+1ZESkVkaJDji1gZqYmeyk31ZqyZwaa9m+jfoX9ZWYzYpJPGmLp5ftaKkF/jk08+YePGjbz55pvMmzePH3/8MSTX8Toj3y3Are73/M/zAZ53318c1OiMqSGf+pi8fDIdUzsyrHuDX3zRGGMO8Morr3D22WczePBgjjzySMaMGROS63itBvmH5j1TrvxTd3vQinmmYnNHDKiwiX9jboE18dfC9NXT+XHHj1x/5PURO0THGFN/Rs9cTtaIqWSNmApQ9j4UTf2bNm1iypQpXHvttQBcd911vPXWW+Tn5wf9Wl6Tfjd3O7JcuX+Quc3IFwRFpWo9+T3KaJJB88TmDO4yONyhGGMiwPCB2awZNZg1o5y/Kf73wwcGf26PsWPHkp6ezrnnngvA5ZdfTn5+PhMnTgz6tbwm/UJ3m1Ku3D/Hb2RNcBxiy584h/ZpSRXu25Czr56jaZy27t2KqnJC2xOYfN5k651vjGlUfD4fY8eOJTc3l8zMTNq0aUPPnj0pLS0NSRO/16S/yN2+4C8QkT8BE3Ca/cO/sk2E2JhbYFPzVqHYV8zQKUM5Y9IZ3P/V/QAcknxImKMyxkSi2wd0q/6gWpoxYwbr169n3rx5LF68uOw1ZcoUvv76a5YsWRLU63lN+n/D6bB3IU6SB3gOZwgfODP2GQ/mjhhQ4WQ9YFPzVqbYV8yj8x5l6Y6ldE3ryq1H3xrukIwxESwUTfp+Y8aM4YILLuC4446jTZs2Za+zzjqLvn37Br2272kaXlX9RESux+nI1yxgVx7wF1X9tOJvmtr4ZvVORs9cHtJ/cI3NrsJdXPjRhWzbt42BnQbybP9nwx2SMcbU2ocffljpvnnz5gX9el7n3kdVx4rIBOAkIAPYDsxT1T3BDi5aTLyxL0eMnEFeYelB+177apUl/QDNE5vzzKnPsHHPRs7odEa4wzHGmEbFc9IHcGfgmxnkWKJasybxFSb9Zk2sYxrAt1u/ZcKyCTz1u6c4uvXRHN366HCHZIwxjU61SV9EVnk4n6rqoXWIJ2pltmjKxlwb/FCZ5759jo15G8ktzKVFUotwh2OMMY1STWr6WR7Op9UfYrzYmFvA0DHzmXhj33CHEhb5Jfn864d/8d2277j+iOst4RtjTB3UJOl/iSXzkJt4Y1+GjpnPN6t3HrQvmjv0Pb3gad5Z/g6HpR/GpYddGu5wjDGmUas26atq/3qIw1B1hz7/gg/RkPhX5KwgNSGVNslt6NWqF6t3r+a1s14Ld1jGGNPo1WoJMhE5RUQeF5ExIvKEiJwS7MCi1ZJHB5GaGFvhvmgZtz/2x7FcOf1KVJVzupzDq2e+Gu6QjDEmInjqvS8iMcB/gEvK7RohIu8Cl6qqL1jBRavCkop/hd+ty6nnSOpfcWkxX6z/goGdBiIiJMbaUsPGGBMsXmv6w4Eh7F9WN/B1ibvf1NExHSvurBYNC/FMWz2NPcV7bAy+McaEgNekfxVOp77ZQH+gq7udhZP4rw5eaNFr4o19K52aN5IV+4p57tvnSE9Kp0/bPuEOxxhjIk5tl9YdpqpfquoqVf0S8HertjH6QXJil5YVln+zeicnj5pVz9HUjx35Ozik6SHc3ftua9Y3xkSV/v37k5iYSEpKCikpKXTt2pXnnnsu6NfxmvSL3G355cz8n4u9nExEOojI5yKyVER+EpHb3fJ0EZkpIivcbQu3XETkHyKyUkR+EJFjPcbfaAwfmF1pbT+zRdN6jqZ+tEluw2MnP8aAjgPCHYoxxjjytsDrZ0Pe1pBf6qGHHmLPnj3s2bOHt956iwceeICZM4M7+a3XpP+du50uIg+JyNUi8iAwFafZ/7vKv1qhEuAuVe0JnAjcKiI9gRHALFXthvPoYIR7/Nk4rQ3dgBuAlzxer1FZumlXheX+cfuRYvG2xVw69VKW7VxGtxbdaBofmTc1xphG6Iu/wbqv4Yun6vWyJ554Ij179gz70rrP4Dy7bw88AowFHgU6uPs9LXmmqptV9Vv3fR7ws3vu84Fx7mHjgAvc9+cDb6rjayBNRNp6/BkajSWPDqJ9WlKF+yYtWl/P0YTGTzt+4srpV/Lzzp9ZnxcZP5MxJgI83hoeaQ4Lx4L6nO0jzZ3yEFNV5s6dyy+//ELfvsGdjdVT0lfVj4FbgT0c2HN/D/BnVf2otoGISBZwDPANcIiqbnZ3bWH/44P2QGBm2OCWmUZIVblmxjUkxSXx6UWfWo99Y0zDcfsP0OsSiGvifI5rAkdcArcHt+Yd6IknniAtLY3k5GT69evHZZddxgknnBDUa3ienEdVX8JJtIOAy91te1V9obZBiEgKMBm4Q1V3l7ue4nEaYBG5QUQWisjC3377rbZhNQgXH9ehwnL/nPyN2dKdS8kvyeeMjmeQ0TQj3OEYY8x+qW0gMRVKCyEuydkmNoPU8l3agueBBx4gNzeXffv2sX79epYuXcq1114b1GvUakY+Vd2jqp+q6n/cbV5tAxCReJyEP15V33OLt/qb7d3tNrd8I/sfJQBkumXl43tFVXurau+MjMadTIYPzK50hr5vVu9slIm/1OdMM9wyqSUntTuJ4cfZ9A7GmAZo7zY47hr442fOdk/oO/P5ZWZmMmTIEN57773qD/bA04x8ACISC/TBSb4HjatS1Tc9nEtw+gX8rKqB/QE+wpkTYJS7/TCg/DYRmeDGsCvgMUDEWvLooEoX42lMVJWpq6fy9wV/Jz0pnXfPe5cxA8eEOyxjjKnYsPH735/rqctanW3ZsoV3332Xo446Kqjn9ToN77HAexxY2w6kQI2TPnAycAWwREQWu2X34yT7d0TkOmAtziyAANOAc4CVwD7gGi/xN2YbcvZ5Km+Ivv/te+77730A/PWkvxIX4/me0xhjItZjjz3GqFGjAEhOTubUU0/l6aefDuo1vP7VfRHoGKyLq+pXOB0BK3LQYG33+f6twbp+YzJ3xABOHjWLjbkFB5RvzC3g5FGzmDuiYY9tV1WeWfgMABPOncDhLQ8Pc0TGGNNwzJkzp16u4zXp98KpzT8PTGf/ZD2mHvyWV+ipvCEp8hWRX5LPsa2PtYRvjDFh4jXpLwFOAP6qqrkhiMdU4ZiOLSp8ru9fiGfijcEdzxlMibGJ3HncnXRP7x7uUIwxJmp57b1/M7AT+LeI9BeRLiLSMfAVghiNa+KNfVkzajAxFTwQ+Wb1TrrcN7X+g6qBD1d+yKtLXuXEdifSsknFawoYY4wJPa9JfyPwC05nulnACmB1wGtVUKMzFWrbvOJZ+iorD6fF2xbzyPxH+GL9F8RIrUaIGmOMCRKvf4VfA07iwNn4yr9MiM0dMaDC2v7G3AKOGDlj/wIRP0yGR9Nh1Rf1HyRO571xP42jxFfCqFNGhSUGY4wx+3l9pn+6u/0KmAsUVHGsCaHkhFjyCksPKs8rLOXH5y+kV8lPsHaeU/jm7+GScXD4BQcdT94WmHAZ7NsBOasBgSs/hC6nOvsmXQMXv+F5FipV5dUlr/LZus+4/LDLaZ9isyUbY0y4eU36a4HuwOC6zMJn6q78hD0Z5PBN4m3EiDprF5b37lXwLjiNMQrnPQ/HXQ3v3QgbFwYcqM5NAkCbo2DL9/BMNkgMXPGBczNQA4qyYMsCTmx7Inf1vqv2P6gxxpig8dq8fwfOML3hInLQbHwmfJ6P+wdSoyUK3GM+vt1ZMWr1nMoP3fJ9wNd8zs3AI81h0RtVrjG9r3gfMRLDrcfcypiBY2wSHmOMaSC8/jV+GSgGRgL3ichvHFivVFU9NFjBmapNvLEvhSNbkigVVe1D6OPbISEFivbAC8fDrQvKmv+X7VzGpVMvZfRpozkl85T6jcsYY0yVvNb0s4BknDbiRJwFb7LKvUw9SqjvhO9XtMfZFuxymv8fb82sdbO45ONLUJSk2IY3ksAYYxqyhQsXcsEFF5CRkUGzZs3Izs7mjjvuYPPm4C0x4zXpf+m+vqjk9WXQIjOV++JZp5n9keaVDpdQ3f+qD/8XB3d8fgcpCSlMOm8SJ7QN7hrQxhgTyWbOnEm/fv3o3r07ixcvZvfu3XzxxRe0bNmSL74I3ggsT837qto/aFc2tZO3BT5/tMpDAhO9/22ox1JOS0kmrbSUKRdOp3li8xBfzRhjIsstt9zCpZdeylNPPVVW1rZtWx566KGgXsd6WDUmj9Q8mZYifObrzU3Fw4kRWHXUf2DlLCjJr+Yau8p9bgH4qr3e8J05nLIvn+ZPdjz4HMYY00BcM+PgxVnPyjqLYT2GkV+Szy2f3XLQ/vO7ns8FXS8gpyCHO+fcedD+od2HMqjzILbs3VK2kujrg16vcUzLly9n5cqVvPTSSx5+ktqxKdIai8daV3uI4tTyTyh8ka6F47mpeDgAPoWsxZcyNON9iK1i0EWPcysoOwfSOlV5zb0iNPcpp+9zbyg83JwYY0y0++233wBo3z7085lYTb+xKK1+JT0BiG/CrpIWUHrww/xvVu+EUducyXhSDoHe18DC12HPVhg2vuKTVlb+SEughFebN+Mf6WmM2radwXv3BexvDvHJMPBxmH43XPF+jcf4G2NMqFRVA28S16TK/S2SWlS5v01yG081fL+MjAwANm7cyGGHHeb5+15Y0m/oHm8NJTVdOjcGug5w1kKsRPYD07i5/0iGD8x2Cs59tnZx9RiE75cpTGiWQhOfj7MCE75f8V6Y5rQ28ObvnRaDlNYwdLznGf6MMSZSZWdn07VrV95++23OOOOMkF7Lmvcbupok/KQ0p9n+kRwYNp7lT5xDQmzFXfeKSpXnZ63giJEzGD1zee3jGjaeOU2bsC0ujhE7cmp295i7FjYsgHevrv11jTEmAr344ouMHz+e+++/n02bNgGwdetWnnzySSZMmBC069Q46YtIooj83n21CloEpnI1eTZ+13IYsRYe2nZA8fInzmHNqMGVfi2vsJTnZ62odWj5Jfm81usMmvp8nLdnr7cvr5tXNuSQBa/Dkx1gy4+1jsUYYxq7gQMH8tVXX7F06VKOOOIIUlNT6devH9u2baN///5Bu06Nm/dVtVBEJuHcKLQNWgSm9uKaVNtMHiNOR77KdLlvKquerPzmoLwSXwmCsGznMloktuCuk0YSv/b6Gn//IFPvcLZvnAtaCtdMhza9an8+Y4xppHr37s0HH3wQ0mt4bd7/GVtCt35UV8tP6+Q8v6/GqicHk5oYW+l+n0LWiKk1aupftHURx791PE8vfJqjWx/N86c/z5DuQyClDdR1fv2CHCjcDS+fHLalgI0xJtJ5Tfp/wVlw5wVr4g+h6hJ+TDzc8UPlPevLWfLooCqb+gG+XrWj2vO8v+J9SrSE49sc74Qh7j+fu5dB9iCn5SEY/Av7GGOMCSqvSX8MzgI7FwJbRGSTiKwKeP0a/BCjTE2S3cPba3Xq2wd0o31axXPif7N6J9kPTKv0uzsLdvLhrx9yYbcLOb3j6QcfMGw8PLjFGevf+zrIOgUyekCTlrWKFbDEb4wxQea1TbYTznws/ib+NuX219NM7xGqJkkupfyvvOaGD8xm+MBsutw3tcLn/EWlSvYD01j+xDkH7bt99u0AHN7y8KovUlnrw4TLajYjYHmPt4bbf4BJ18DFb9hQP2OMqQOvSf9LLLGHRk0SfmyC05ReR6ueHMzQMfOdyXrKyUiteMa+M7PO5LojruPUzFpOsOO/GZhwGWxZAu2PhZ/er/57JYXwTHfn/TPZcOVHNsmPMabGVBWRyOuGprVcTc0W3GlMHvotaKdauqni+fE35hZw8qhZzB0xAJ/6mL56On3a9uGKnlcE58KBLQGXvOFML6yl4KvhEsFv/h4QuGuZ1fqNMVWKjY2luLiYhISEcIcSdPn5+cTHx3v+Xq0m5xGR7iJyo4iMqM33TTkrZ1e9P65JxfPi18GSRwfRp3N6hfs256+h5/+7lIs/vpgR/x3B0I+HsiO/+o5+tfLQNnh4B3T1MguVOrX+V8+AvK2hicsY0+ilpaWxdetWfL7qFw1rLFSVffv2sXHjRlq3rn5NlvLEaxOBiPwTuBl32J6qxorIt8BRwKWqOtFzFCHUu3dvXbhwYbjDqNzmH2DM76o+JoSr1mU/MI2igHn6E1rOJrH1p6jG0CqhMxvXH85Nx1zOXWeGdj5ooPYd92xVP2NMBXw+Hxs2bGDvXo8TiDVw8fHxtG7dmmbNmlW4X0QWqWrvCvd5Sfoicgvw/wKK1E36VwGvA5NV9ZKahx56DTrp13TGvRA3Y2eNmBrwyUd8+lx8Be0o3XfoAcf16ZzOxBv7hi6Qty6ClZ/V8sux0KmPdfYzxkS9qpK+1+b9m3A68j1TrvxTd3uMx/NFr5rWaushga0ZNZgO3T4mNvkXIIbinb87KOGDM6zv5FGzQhfI5ZOp/XIQpbB2Hky/J5gRGWNMRPH6F7abux1Zrtz/wLdd3cIxBwjyc/yKFPuKGf75cHLj5pLUcl61x2/MLQhtQD3OcfowxDeF1Hb7J/yp6Yx/Sz9wbqge9/6syxhjIp3XIXuFQAKQUq7c34wQ4owQIWpSy4+Jr/GMe7Wlqtz75b18tu4zDks/jH8N+xf9/nc+Pds1r3A4n1/WiKm0T0ti7ojqpwH2rKpx/r9Mqfl5arwcsTHGRA+vz/RnAf2B94CLcJr678CZnrc9MEtVz/RwvteAc4FtqtrLLUsHJgJZwBpgiKrmiDPQ8nngHGAfcLWqflvdNRrUM/1vXoXpd9Xs2HronLZs5zIu/vhiurfozoRzJxAXUJs+YuQMljw6qNzz/oOlJsZSWOKrcEKfkHm6O+zbAb7i6o9tmQ0JTaBoH+xYCa17whXv23N/Y0zECuYz/b/h9Nq/kP2T9DwHZLrvn/Z4vjeAQeXKRuDcPHQDZrmfAc7GebzQDbgBeMnjtcJr8w81T/ixFU+QEyz+G70OqR24+aibefvctw9I+OAM6QMqnbbXL6+wlKJS5YiRM0ITbEXuXgZNazi9747lsPl72LECUNj2kz33N8ZErdoM2bsOpyNf4FiBPOAvqvqK5wBEsoApATX9ZUB/Vd0sIm2BOaraXUTGuO/fLn9cVedvEDX9mnba63FuyJv0cwpyuG3WbWQ0zWB0/9E1mqlq9MzlPD9rRY3O7x/7H9Je/n61ndq3TAwkNIWWXeHSd6z2b4yJCEEbshdwwmTgJCAD2A7MU9U9tQwuiwOTfq6qprnvBchR1TQRmQKMUtWv3H2zgHtV9aCMLiI34LQG0LFjx+PWrl1bm9CCo6YJPzkD/rIytLEA9//3fj5e9THPn/Z8xQvnVKO65n6/hFipvyb/Jzs4y/LWRUwc3PAFtOkVnJiMMSZMgtm8D4Cq7lXVmcB0Vf20tgm/BtdRajHXv6q+oqq9VbV3RkZGCCILMompl4Q/ffV0Pl71McnxybVK+F4ETvgTcvetr/s5fCXw8snOTdpzR9pMf8aYiOQ56YvISSIyU0T2AttFZK+IfCoiwWrP3eo26+Nut7nlG4EOAcdlumWNX/fQ14hfXPwi93x5D13TuvLB+R/U+jxrRg3m9gHduH1At2qPzRoxtcrleoPL/085CAtr5K6FZ3vCmFMt+RtjIorX3vsXARNw/sIG/nVVwIfT074GS6cdcM4sDmze/zuwQ1VHuXP7p6vqPSIyGLgNp/d+H+AfqnpCdecP6zP96pr2M3pAfm5QVs6rTomvhPmb5tO7TW+a+Me+11H2A9NIjIshr7C02mPXjBoclGt68nR3KNoDmSfA6jmgPpx/uh7n4bZpfo0xjUhVzftex+k/DsTiJPn/4tS02wP93PIngBonfRF5G2cIYCsR2YAz6c8o4B23w+BaYIh7+DSchL8SZ8jeNR5jb1hOuQdOfyDkl5m3aR6frvmUod2H8rvMaub498j/zP7kUbNCP2lPbVR0M/VYa4hv4twM1HRlP//NW+bxMHS8dfgzxjRaXmv6+TiT81ykqh8ElP8BmAwUqGrToEdZB2Gr6T/euuoJYuqh9uhTHxd8eAE+9fHW2W+RlpQWsmsNHTO/ygl9gNBN6FMbte35n5Tm3Cxc+4l1+jPGNEjB7Mi3xN2Wn4Ddv0rKDx7PF7kawIxw434ax+pdq7nt6NtCmvDBGaK3ZtRg1owaXOmSvRtzCxg6Zn5I46ixYePhwS3OMEkvjzsKcp1WgpdPDl1sxhgTIl6T/p9xmtYfFJFEABFJAB4E9uDMzmeqc9PckF9iZc5Knl30LAADOw0M+fUCVTVG/7t1OfUYSQ34k/8ju5wbgNiqJyM6wCPNnderZ1iHP2NMo1Bt0heRVf4X8B+c5/l3A7nuc/hd7meA0M4s01hU14GvHpqFdxbsJDU+lTEDxxAbExvy65VX2Ux+RaVK9gPTGD1zeT1HVAPDxsNDW70lfoANC+CZ7vDf5+DRdFj1xf59K2fDIy3gxZPsxsAYE3Y1qelnlXul4PTcT8RZVS/R/Zzi7o9u1a3u1qRFyC49e91sBk0exKY9m+jaoiuvD3qdk9qdFLLrVWXuiAFVJv6azvAXFt3OAPF6o6QwayRoKbxzJeRtgdfPhneuAHz7p/99/Wwn+fv3/zD54BsFY4wJkWo78onIHDxMkKOqp9UxpqCq94581dXyQ9SBb+mOpQydMpS4mDhmXTKL9KSKn6vXt6p69qcmxpbN8d/gTLgMtiyB9sfCuq9hzzYnoQdLzwucZYD9JNaZEXDKHSACg0fDjHvg4jdstIAxxpOgT8PbmDSopB8TDw9vD+rldhbs5MrpV7JpzyZKfCWM7j+aAZ0aSA95V02m7u3TOb1+5uuvi8daO2P9a7K6X13FJIKv0Lk5GDIu9NczxkSMoCZ9EYnFmRynA07T/gFU9c3aBBkq9Zr0w1DL37xnM39f+HcAbj7qZrq1qH6mvHCoyVj+9mlJ7M4vrv+ler2YcBn8MiUMFxa4a5nV+o0x1Qra5DwicizwHgdOhxtIgQaV9BuM5OCvAbBl7xZaNWnFs/2fDfq5g23uiAEcMYiQgZMAABekSURBVHJGlbP3NcgJfsobNn5/039pEeSVX+QxFmJjnX1BpU6fAKv1G2PqwOvkPF8DVU19q6pa/13Fq1BvNf16rOWrKi8sfoExP4zh+iOu58/H/jlo5w61rBFT6dM5vdqJfGIEjs+qx2V6g2nCZZByCGxfAZu+hYRUKNwFxfuCd42W2dCkuc0QaIw5SDCn4e2FU5t/HpgOBLs60zhV12O/x7lBvdw/v/sn/1ryL7qmdWVYj2FBPXeo+efgr+45v0+p9sagwRpWwcjVijoGJrd2xr0U5kFsIpQWgs8HJTW4OdjhDnl8+WS4/H3r9GeMqRGvNf35ODX9lqqaG7KogqheavpV1fKTM4K6bO7/++7/MeaHMbRLbseUP0whPjY+aOeuT6NnLue1r1ax5NFB1d4ApCbG0rNd88ZX46+N2k4PDNBtEKybB0P+DV8+ZTcBxkSpoHXkE5GjgZnA18AzwDrggFVLVHVd7UMNvrAn/SA16+cW5JKWlMY7y95hxpoZ3HXcXRze6vCgnDvcatK738+/pO/wgdmhCqdheKQFxMY5NX+t4cJA5aW0gcsmWSuAMVEmmEk/A6cjX2Uzvqiqen1kEFIhT/pVPssXeKTuDSIrclZw4UcX8u0V3xIf0zhr9tUZPXM5kxatZ3d+ccNdqjccnu4OJQVQsAsP02UczH8D4J8HwPoCGBOxgpn0P8ZZ3lYqOST6OvJVlfTvWl6nP6x7i/fyxNdP8PGqjwF4rv9zDW4MfijUpOZ/+4BuTFq0nswWTVm6aVdkN//7OwZ++2bAcsB1nF8jJh5umAPJrWDSNdYSYEwECWbS3wskAXPd10FjrFT10VrGGRJhTfp1aNpXVS748AJW7VrFIU0PYcQJIzij0xm1Pl9jcvKoWWzeVUByQmyNav1+CbFCUalGfitAYKfA5Z/UbVSAxDgTDvlvAmy5YGMavWAm/aVAdyBNVfOCFF9IhTTpP9666iV065D0i0uLeWHxC8zbNI+J505EpLLGlcg2dMx8z73426clkdmiaeTW/AP5WwF++gCK8uo+P0BcIjy4zVkbwN8CgDrvB/3N+gcY0wgEM+mfCXwIPAk8parhXzS+GiFN+lXV8m+a67nWlF+Sz8vfv0xOQQ4PnvggIkKsxBIjXldAjizVTepTmfZpSVx8XAcmLVrP3BGR/1jkgPkB9m6DPb856wUU1KJfSe/rYNHrcNw1zudFr0PzjpC7xqYGNqaBC2bSXwW0ApJxxuj/xoG991VVD61DrEEXtqTvsZb/z+/+ySs/vAJASnwKk34/ifYp7esSXUQZOmY+363L4eb+XWu1Ql+fzo10op+6Kj9RUHF+cBcOSkiBaz+xxwLGNCDBTPo+nB5E1pGvqoTfpAXcu6bGp3p/xfs8PO9hwJk/f0j3IbRq0qqOAUYuL0P8ymuflsTcEQM4edSsA7ZR4+nu0CQNTr0XPvoTFO05cH96V2h3jLO+QEm+s/pfdTcJLbKgaSsbFWBMAxHMGfm+pM7dhqOAh4QP0CG1Aw/2eZCzss4iLSktNDFFkD6d0zmxS8uDeu/X5Nm/f37/wO3Jo2YBkNmiKSd2aRnZcwDcvWz/+14XHngT8MVTkJ8LianO7IBxSc5wwerkrHFeAB/9GfZttxsAYxooW1q3NoK4fG6pr5TYmAbVONJoZT8wjaLSmv97XjNqcIWtBrcP6BbZib86/kcCva9x3oPTP6Am0wMH6n0dnHrPwUMCAzsJ2k2BMUEX1KV1G5t6T/oenuVv27eNIR8P4Z7j7+GcLg10KdlGxj/JT2aLpnWau79P53SWbtpFsybOZEhR9QigIoEtAh/fDoW7vX2/93Vwrrsa5JQ793cSPPdZ5yZgwmXgK3b2xyYc3EpgNwrG1Fgwn+lfWd0xqtqgltYNetKvKuFLLIysWaJZtnMZQ6YMwac+nj/teU7veHqQAjR+J4+aVdZ7P3DZ3spq+FW5fUA3vl61gxO7tOSlOSu5uX9Xvl61I/o6BoKToJdND16HQP9cAYECbxLAuVFYONbmEzCmBkLRka8ykT8NbxBq+W/8+AbPLHoGgJPbnczLA18ORmSmCoHj/f1JvzbJvzz/qACIspEBgaMC1vyXSv8s+DsCxjWBrgMAgZWf1W5BoUD++QT8yrcWQMUtBsZEgaqSfm0GgEs1r8hV3RK6NbR131Z+1/53TPnDFEv49WTijX25fUA32qclARy0ra1vVu8sewFlnQLBedQQsYaNd2riV3/sJP+MHtDuWIiJc5YJ7nmBM5xPS50OgaWFznHJGfs7CSKQ1pEK/wxJLPQ4D278quLrlxQeeAP+xd9g40LY/P3+14YFMP0eeP1syNsait+CMY2O15r+qeWKYoEs4E9AN+AaVX03aNEFQVBr+nWcZz+nIIe0xLSonV2voQrsvV+XfgCBLQhA2fsjRs4oWxtg6Jj5kT9CwC+wQ+DC12GPm3gDy1bOhNxKFub0N/FPvBJ+/vDAfWkdYdjb8OrpVc+KGSjzeKfm759h0PoHmAgVtCF7qvpFJRd4D9gC/B5oUEm/3lTzx2PGmhmMnDuSPm378I/T/1FPQZmaCOyk53UEQCD/o4KhY+Yf0NSfV1hadjPhbxUYPjA78m8Aho3f/z7w+Xxg2YTLAHGmDy7Idd4nNXea5v03CVoKiWlQGDCzYHxT57n+7T/AlLtg2TTAd/A1Am1YAM/2cDoQrvvaGaJYUVwV8XcktKmITSMXrOfv/jbS84J0voiSV5THX774CwDXHXFdmKMxVVn+xDmMnrmcr1ftOKD3fmBHwOp8s3pn2Q1AVX0G/DcAkxat5+LjOjB8YPYBjwT8oxAiuq9A4I1BVcc83R2a9ThwPgGA1DaQ0ppqE76f+pwOgeBsF449uH9ARb74m3Oj8N4fYfvymt0wlB9xsPkHeGMwDPk3fPlU7W4cbBSDqSOvzfuzKyhOAnoBKcBmVW1Qc8fWW/N+JZ341u9ezznvO8PxrJd+4+W/EQjsvV9+OuDA5v3arBdQWcfCNaMGl41EGD4wu+w9ELmtBF74Vx30txYUV9NJMLBz4WHnwplPVJ5Aq1tUq6obhvJDE1/oA7/9AklpzpBHf7kX5c9ZlZreIHi9kbAbjwYvmB35+gOnlnv1wUn4AP+uZYwNX3WL61TCP8PeXcfdZQm/ERs+MJuJN/Zl+MBslj/x/9u79yAryjOP498fw/2SKBelABGyAQbKGNF4WVCTDaFAwFx2TdZo2OjWLluV6CJJKoUxJpvVNS67iqTWihovSUVKrMJU1iwqS0yKigquF1hQMYRFEIiEi8rVYWDm2T+6e6an51z6zMw5Z+b086k6dfr2vv1O19R5n3777fedw6KZE7l4/NCWT9LmH8wGaDPNb7Epfwt1/NvzfkNLkBEtL3v2Dy1p/vr+dS3fS9dsbflE+SaXo+OjbfH1XOWJlpMdFaP15HKutIX+1mSakly9HG7aBN98E27ZC/Xzgv4A4y4PKtikeOfCfh8qXHEt3ATnfBHqEh0+e/eHj30RFm5un+b2M4Lfi5cfam1Z+KcPBxU+BIFJfHuaDsL58iyUNmqdWPuvhfNOHndkb+HOj2uXwM518OPp8OBnCneSLJaXq7hSm/ffpv27OSeA3cBK4CddUahCJM0GlhF0InzQzO4s9zmLGnkOBz44wK4ju1o2Ld+ynE+O+STzPjKPlVeuZNLQSVUsoCuHeLN7VGHF3wZYOGNC3rSjT+vf7pFBvomECj0iWPbsH1g0c2K7PgORRTMntuQbX05z3ijv+HK8zPF0uZaTafPlnasMuVowotaWfI87WoKGYd8HYP2Jgzw+7j94/61X2Tt4CgD1h56HwWfw83F3ML/3b1r7DeQzZGQwLHFzI830ohfNwXdTY/6AYeEmWP3d1vkLevWDujo4mRjRsK4fTPls0NJQTDLPeCtFUrJ1It9jjHzHqRfNZvRKPsJIHn98f/C5ux6+/17ucscDilJbNZLTO6+41od37gKlduQbV6ZypCKpDrgXmEkQaLwk6Ukze6OsJ84RTZ8QbOrXj7NOnmIk8Lvdv2uZNCeyesdqZo2b5RV+BkSVVLxTYLRtSL86powKWoqieQMWzZzYrjJPM25Arv2dHWugO0kGDLn2FUvbxp3LOW/xKgifvu248wkAbl28ivl3pqyEju2DC65n3YvrmT6yiXV765h+8SX5A4YoUGg6QYP1ob+dhF4DgOOYBfVWs0Gv5pPFWxry5VmolSJtgJA8LmLNQRNwMlhYuAnuntx+ICVrDlod4kFF2sCjkLVLaN65Lgg+ANsTPKZVRwKI7uzIXnb/5GrG/P3jFQlmilb6kqaVkqGZvdDx4hR1EbDNzLYDSFoBfA4ob6Uf++ddMWQwqwcNZEP/fjRJnN9wgp8B00ZN4/6Z97dJNnnoZPrW9S1r0Vz3FzX1Q9vWgSgAKFaZxYOBhTMmlNQiEN+W3F9sPV/6QunSLBfaFlm6Zmv36a8Qdja89rlV7Pj6XK5dvIod8wo/qokChS88/1Genr4NNjwKI+rZuPckUwcd5N3jTQy/4EvFWxoK5Zk26MgXICSP0ykYOh4Ov5M7WBgyEj72Jdi0oiV4AYI+EpPmwNy7WvMupWUiKRYwtAQfxAaB6UgA0Z2tXcKoQxs71hrSAWnu9J8j/cx6ljLPjhoN7Iqt7yboU1Be6g12iuMS/zI8eH57+fEP+ERDAxf91WMAnDnoTM4c5E1OLr0oAIh670PbRwLJ4YMhdxN9oREG49uS++PjCcTXI7nGHEhuK3SOZNp8eS9ds7Xd3xT1Wbh4/NB2YydE+acJmtIEKIUmWEqWLRn45Eq7dM1Wlm28pjXNc2cDM+BYuCF68zAcd2jhsOIBTu48c6ddumYrk/9nM/vs0zzWNIMv1z3LGS9uYku/tsfmOu5TB/6XMWqgkT70PdnA8g3vceBDh1g0M/xtazwKw+th/5tEfcBFU/AGRTyoKKVlIqldC0Qv2rydkSvI6IniwY2oWDCTtoLuUaPJSFoALAAYO3Zs5zP8xutwVz0Dzbj+/cN89dBhhjWH/4RjL+t8/i7Tcj0SiJajDnajT+vfEhhEy8VaCHqKfIFMUr7gJLpm+d58yBfoFOtYGeUdzz8Z+KRNE/8b0uRRSp65jmXmrwH43uJV/M3twSON2WmOCwdUiloT5h/9E4TnjQKP+/osZbJGsKn5IwCc22s7WxJBRdrAI5el6w8zYuO7XFMXBB/9ONn2AGvi0dc+4MCwWDDSAz0w9Zecse42ZtW9zAA18oH15ZmmC9l34Xf5hzKeN02l/4MC++qBqwhCsUoEBnuAs2LrY8JtbZjZA8ADELyy1+mzDhkZtGWZ8Y33YgOE1M/rdNbOFRK1BsQDg1wz/kVvEER3v3Hx1oNoef32g222xdcLpUt2VFz5yq6cy/nyybctWq+VQKbHCh9lbHluFcz7WptdrYFH+0DqbNoGFWkDj1wWzZwIBwfA4L8Ngo8z74Oj+/hVw7kAXDl8L/NH9m8JRnqqBXOnQXM9vLqehuY+DOh1ii9cWA9zS3qiXrKilb6Ztav0JZ0H3AJ8nqAXvQG/BO7o6gImvARMkDSeoLK/GrimcJIuMmlO+yFF0wws4lyZxO+YouAgV8/2ZOtBof3F0iVbJaLtyeVi+ac5JilfcBLfHxcdmyboSCNKU0ra5LFRcNaR8+fLsyuOTROoVVQ8+LhpEwA3hoHGlTelbyHp9tL20+hCpQ7OcynwHWAWwZ39KWAF8EMz21KWErYvwxzgHoJg42EzK9gzpMtn2XPOuYyLj6mQpj9CRztlxtNG5+w2HTy7UFd3XO301Lrhu/E3A5cSVPYngEeAJWa2o8tKWgZe6TvnnMuSTk24I+kV4LxwtYlgQp27CCbYQdKo+PFm9sdOldY555xzZZGmI99UWl/ZqyN4jn51nmPL/cqec8455zqoJl/Zc84551x7RZ/pS3qklAzN7PpOlaiLSdoP7OzCLIcDB7owP1ecX/PK8utdeX7NK6vWr/fZZjYi146Seu87kPRyvg4Srjz8mleWX+/K82teWVm+3qVOreucc865Hsorfeeccy4jvNIv3QPVLkAG+TWvLL/elefXvLIye739mb5zzjmXEX6n75xzzmWEV/olkDRb0u8lbZO0uNrlqWWSzpL0W0lvSHpd0sJqlykLJNVJ2iDpv6pdliyQdJqklZLelLRFUvsZk1yXkrQo/E15TdJjkvoXT1U7vNJPSVIdcC9wBTAF+LKkKdUtVU07BXzTzKYAlwBf9+tdEQuBikye5QBYBjxjZvXAx/FrX1aSRgP/CHzCzM6hdZTZzPBKP72LgG1mtt3MGglmF/xclctUs8zsHTN7NVw+QvBjOLq6paptksYAc4EHq12WLJD0YeBy4CEAM2s0s/erW6pM6A0MkNQbGAhkar4Yr/TTGw3siq3vxiuhipA0jmAOiBerW5Kadw/wbaC52gXJiPHAfuCR8JHKg5IGVbtQtczM9gD/DrwNvAMcMrP/rm6pKssrfdetSRoMPAHcZGaHq12eWiVpHrDPzF6pdlkypDdwPvBjM5sKHAO8r1AZSTqdoIV2PDAKGCTpK9UtVWV5pZ/eHuCs2PqYcJsrE0l9CCr85Wb2i2qXp8ZNBz4raQfBo6tPS3q0ukWqebuB3WYWtWCtJAgCXPl8BnjLzPab2UngF8C0KpeporzST+8lYIKk8ZL6EnT+eLLKZapZkkTwrHOLmd1d7fLUOjO72czGmNk4gv/t35hZpu6AKs3M9gK7JE0KN80A3qhikbLgbeASSQPD35gZZKzzZNqpdTPPzE5JugFYTdDj82Eze73Kxapl04H5wGZJG8Nt3zGzp6pYJue62o3A8vBGYjvQrWYprTVm9qKklcCrBG8IbSBjo/P5iHzOOedcRnjzvnPOOZcRXuk755xzGeGVvnPOOZcRXuk755xzGeGVvnPOOZcRXuk7V0Mk7ZBkKT6fknRdfL3aZY9ImiqpWdKRcAS1tOlOl3Q0TDu1nGV0rqfySt851938EBDwkJm9lzZReOxDYdo7ylQ253o0f0/fuRoV3r3/Nlz9mZldV73SpBNOnxwNenW+mW0oMf35QDR/QL2Z/b4ry+dcT+d3+s5lVK7m/bDZP9r2tXDmtyOS3g6Pr5N0u6QDkt6R9G/hFKXxfC+W9KSkg5IaJW2VdGs4l0Ix0Yh0b8Ur/PC8t0raIulYWKY3Jf1c0qjouHA65h3h6nWduDzO1SQfhtc5l89twNBweTDwMPCXwJWxY74F/B9wH4CkWcCvgHgFPwH4Z+CiRNpcZoTf6xPbvxXmETcp/Cyj7Zzo64FxBJOr3FzkfM5lit/pO+fyOU5QYUcVtYC5wGyCqUmPhtuviqW5l6DCf4Gg4h0ALAr3zZM0O9/JJNUB54aryXktLg2/XwBOB4YAHyeYivbdxLGvhd/nSfLfOOdi/E7fOZfPT81sm6TdsW3Pm9lqAEmbgT8nnHJa0kTgz8LjptHazB73F8Azec43jGAyK4CDiX07w+8pwPeAzcBGYIm175gUpe0d5rk/z/mcyxyv9J1z+ewEMLOGYBZSIJiaNNIYfvcLv0ekyHNo8UNyuo3gzv5SWlsOALZKmmVmO2LbhHMuJ2/6cs7lcyrltsiB2PI9ZqbkB1hQIP1BoClcHhbfYWZ/MrPLgDHAFcC3CR4vTARuSeQTpT1F+6Z/5zLNK33nXFfZCrwVLv+dpCsk9Zc0QtJVktYCZ+dLbGZNwKZw9Zz4PkkLJH0F6EvwGuLjtFboyRaGKO3GME/nXMib951zXcLMTNINwH8S9PZ/qgPZPAtMJegrEDcN+GqeNMk+ApeE37/uwPmdq2l+p++c6zJm9hRwGfAkQXN9I7ALeJqgaf+P+VMD8Ej4fXY40E7kiTDPXUADcAjYANxgZvdFB0m6gNbWhJ925m9xrhb5iHzOuW5F0jPALOBHZrawxLQ/Am4EnjazOeUon3M9mVf6zrluJbzDfxk4BoxNO/5+ODnPLmAgcEGpQ/g6lwVe6TvnnHMZ4c/0nXPOuYzwSt8555zLCK/0nXPOuYzwSt8555zLCK/0nXPOuYzwSt8555zLCK/0nXPOuYz4f4yKaagoa6fNAAAAAElFTkSuQmCC","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["### BEGIN SOLUTION ###\n","\n","# stochastic model with 400 total molecules, k1 = 2 and k2 = 1\n","e = gillespie(2, 1, 400, 0, 0)\n","# stochastic model with 400 total molecules, k1 = 1 and k2 = 1\n","f = gillespie(1, 1, 400, 0, 0)\n","\n","### END SOLUTION ###\n","\n","# creating a subplot for the two stochastic simulations\n","fig = plt.figure(figsize=(8, 8))\n","\n","plt.subplot(2, 1, 1)\n","plt.plot(e[0], e[1], \"+\", label=r\"A\")\n","plt.plot(e[0], e[2], \"*\", label=r\"B\")\n","plt.plot(e[0], e[3], \"--\", label=r\"C\")\n","leg = plt.legend(fontsize=15)\n","plt.title(\"k1 = 2 and k2 = 1\", fontsize=14, fontweight=\"bold\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","leg = plt.legend(fontsize=13)\n","\n","plt.subplot(2, 1, 2)\n","plt.plot(f[0], f[1], \"+\", label=r\"A\")\n","plt.plot(f[0], f[2], \"*\", label=r\"B\")\n","plt.plot(f[0], f[3], \"--\", label=r\"C\")\n","plt.subplots_adjust(hspace=0.5)\n","leg = plt.legend(fontsize=15)\n","plt.title(\"k1 = 1 and k2 = 1\", fontsize=14, fontweight=\"bold\")\n","plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n","plt.ylabel(\"Number molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n","leg = plt.legend(fontsize=13)"]},{"cell_type":"markdown","metadata":{"id":"T3wxijtF-6-q"},"source":["**Answer:** We see that for the top figure with higher k1, the maximum in B was reached faster and in a steeper way than the bottom figure with lower k1; this makes sense because a higher k1 means a higher probability of the first reaction, meaning faster conversion of A to B molecules. With the same logic, we can explain the decay in A and growth in C is also fast in the top figure compared to the bottom figure. \n","\n","All of these characteristics would also be expected in the deterministic model. This exercise shows us the beauty of the Gillespie algorithm and how it can capture features of deterministic models while keeping the random behavior of the system into account."]},{"cell_type":"markdown","metadata":{"id":"LhKZC4yM45J6"},"source":["## 5. Final Discussion"]},{"cell_type":"markdown","metadata":{"id":"H9fS7IBv4-jg"},"source":["Through this project, we aimed to highlight the importance of stochastic (random) modeling (aka KMC simulations in the present time). We used the famous Gillespie algorithm for stochastic modeling and compared it to well-known deterministic reaction engineering models for a simple two irreversible reactions constant volume batch system. We showed that the stochastic solution has more noise in the profiles for smaller systems because of the random behavior of the molecules moving in the gas phase and colliding with each other. We showed that this random behavior becomes less critical for larger systems, and profiles were closer to deterministic models as captured by the Gillespie algorithm. "]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0} +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "Clm-BGLJK54N" + }, + "source": [ + "# Stochastic Simulation of Chemical Reactions\n", + "**Prepared by:** Raghav Saxena (rsaxena@nd.edu) and Sarah Nano (snano@nd.edu)\n", + "**Edited by:** Tiago Thomaz Migliati Zanon (tmigliat@nd.edu)\n", + "\n", + "**Reference:** [Chemical Reactor Analysis and Design Fundamentals by Rawlings et al. (Nob Hill Pub, LLC, 2002)](https://sites.engineering.ucsb.edu/~jbraw/chemreacfun/)\n", + "\n", + "**Intended Audience:** This problem is intended for Chemical and Biomolecular Engineering juniors and seniors from the University of Notre Dame who are either enrolled in or have taken Reaction Engineering.\n", + "\n", + "\n", + "## Learning Objectives\n", + "\n", + "After studying this notebook, completing the activities, and asking questions in class, you should be able to:\n", + "\n", + "* Understand stochastic simulations and how to use them to model chemical reactions.\n", + "* Highlight similarities and differences between stochastic and deterministic rate models for chemical reactions.\n", + "* Properly graph and visualize data using Matplotlib.\n", + "* To solve differential equations related to reaction kinects problems numerically.\n", + "\n", + "## Coding Resources\n", + "Relevant Modules in Class Website:\n", + "\n", + "* [Functions and Scope](https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-and-Scope.html)\n", + "* [Visualization with matplotlib](https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html)\n", + "* [Preparing Publication Quality Figures in Python](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html)\n", + "* [Euler Forward Method](https://ndcbe.github.io/data-and-computing/notebooks/07/Forward-and-Backward-Euler.html)\n", + "* [Crank-Nicolson (Trapezoid Rule)](https://ndcbe.github.io/data-and-computing/notebooks/07/Trapezoid-Rule.html)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "id": "rsDgYreOSduc" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import root" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "l5G8OHITGIWE" + }, + "source": [ + "## 1. Introduction\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "fZPqZ8Z_IDOO" + }, + "source": [ + "Kinetic reactions are mostly modeled using deterministic rate laws, which involve solving nonlinear differential equations. Deterministic models work excellently with large systems involving many thousands of atoms.\n", + "\n", + "\n", + "However, in some cases, we might want to model systems with only a few hundred atoms, such as when modeling reactions at an interface or a catalyst surface. For such systems, the random behavior of the molecules becomes essential. Such systems can be modeled using random simulation techniques (also called kinetic Monte Carlo) which we explain later below in detail." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "CN-9WKlnT3u1" + }, + "source": [ + "**The objectives of this exercise are:**\n", + "\n", + "1. To perform random simulation on a two-reaction batch system using Gillespie algorithm.\n", + "\n", + "2. Compare reaction profiles (concentrations vs time) from random simulation with those of deterministic rate laws.\n", + "\n", + "3. Explore the effect of the number of molecules and rate constant on reaction profiles from the Gillespie algorithm.\n", + "\n", + "4. Discuss similarities and differences between the rate law model and the random simulation model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QM2N2vLsTafc" + }, + "source": [ + "## 1a. Random Simulation - Gillespie Algorithm\n", + "In a random simulation, one can directly capture the random nature of molecules by using random molecular motion and probability of collision as the basis of reaction rates.\n", + "\n", + "Through this exercise, we will highlight similarities and differences between a random simulation model and a deterministic model.\n", + "\n", + "We will use the following two reaction constant volume batch system for the purpose of this exercise.\n", + "\\begin{equation}\n", + "A \\xrightarrow{k_1} B\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "B \\xrightarrow{k_2} C\n", + "\\end{equation}\n", + "\n", + "For stochastic (random) modeling, the systems are generally small and consist of about a few hundred molecules. Thus, we will model the system using the exact number of molecules instead of using concentrations. We will assume that these reactions are actual molecular events, i.e., a molecule of A converts to B in the first reaction, and a molecule of B converts to C in the second reaction.\n", + "\n", + "Which reaction takes place is governed by their probabilities; this is proportional to the rate constant and the number of molecules as shown below:\n", + "\n", + "\\begin{equation}\n", + "r1 = k_1x_a\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "r2 = k_2x_b\n", + "\\end{equation}\n", + "\n", + "These reaction probabilities look very similar to rate equations from the deterministic models. However, **x$_i$** is the number of component **$i$** molecules in the reactor volume, not concentration **C$_i$**. \n", + "\n", + "Given these reaction probabilities, we will simulate the random behavior of this reaction network using the Gillespie algorithm. The basic idea behind the Gillespie algorithm is to (i) randomly choose the time at which the next reaction occurs and (ii) randomly choose which reaction occurs at that time. The choice is not made completely randomly but rather using reaction probabilities. The following protocol describes the Gillespie algorithm:\n", + "\n", + "1. Initialize the number of starting molecules x$_i$ for each species in the reaction network.\n", + "2. Compute total reaction probability, $r_{tot} = \\sum r_ix_i$, it is intuitive that a higher total reaction probability would mean that the time to the next reaction is smaller.\n", + "3. Select two random numbers, p1 and p2, from a uniform distribution on the interval (0,1).\n", + "4. Compute the time to next reaction $\\tau = -ln(p1)/r_{tot}$.\n", + "5. Select the reaction that takes place at this time. The idea here is to partition interval (0,1) by relative sizes of individual reaction probabilities, then select the reaction that occurs using the randomly generated number p2.\n", + "6. Update reaction time $t = t + \\tau$ and adjust number of molecules x$_i$ for each species. For example, if reaction 1 is selected in step 5, we will reduce the number of A molecules by 1 and increase the number of B molecules by 1.\n", + "7. Return to step 2 and continue until the total reaction probability is zero." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kMG0-L38Hnbo" + }, + "source": [ + "## 2. Random Simulation Model - Gillespie Algorithm\n", + "Complete the function \"Gillespie\" to perform stochastic simulation of the two reaction batch system.\n", + "\\begin{equation}\n", + "A \\xrightarrow{k_1} B\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "B \\xrightarrow{k_2} C\n", + "\\end{equation}\n", + "**Write a pseudocode for the while loop to complete the code.** Submit this answer on an attached pdf file." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "id": "SKnfMn39SpXn" + }, + "outputs": [], + "source": [ + "def gillespie(k1, k2, A, B, C):\n", + " \"\"\"\n", + " Function to implement Gillespie algorithm to perform stochastic simulation of the two reaction batch system\n", + "\n", + " Arguments:\n", + " k1,k2: Reaction rate constants of the two reactions\n", + " A,B,C: Initial number of A, B and C molecules\n", + "\n", + " Returns:\n", + " y: A numpy array of simulation time and number of A, B and C molecules\n", + " \"\"\"\n", + " # Random Simulation using Gillespie algorithm\n", + "\n", + " # Index counter\n", + " n = 0\n", + "\n", + " # Initialize list for storing simulation time\n", + " time = [0]\n", + "\n", + " # Initialize list for storing number of A, B and C molecules\n", + " x_a = [A]\n", + " x_b = [B]\n", + " x_c = [C]\n", + "\n", + " # Total reaction probability at time t = 0\n", + " r1 = k1 * x_a[0]\n", + " r2 = k2 * x_b[0]\n", + " rtot = r1 + r2\n", + "\n", + " while rtot != 0:\n", + " ### BEGIN SOLUTION ###\n", + "\n", + " # Generating two random numbers from a uniform distribution between 0 and 1\n", + " p = np.random.rand(2, 1)\n", + "\n", + " # Time to next reaction event using one of the two generated random numbers\n", + " tau = -np.log(p[0, 0]) / rtot\n", + "\n", + " # Determining which reaction to take place at that time using other random number\n", + "\n", + " if p[1, 0] < r1 / rtot:\n", + " # This means reaction A-->B takes place. Adjusting the number of molecules\n", + " x_a.append(x_a[n] - 1)\n", + " x_b.append(x_b[n] + 1)\n", + " x_c.append(x_c[n])\n", + "\n", + " else:\n", + " # This means reaction B-->C takes place. Adjusting the number of molecules\n", + " x_a.append(x_a[n])\n", + " x_b.append(x_b[n] - 1)\n", + " x_c.append(x_c[n] + 1)\n", + "\n", + " # Update simulation time with tau every iteration\n", + " time.append(time[n] + tau)\n", + "\n", + " # Update index counter\n", + " n += 1\n", + "\n", + " # Update total reaction probability\n", + " r1 = k1 * x_a[n]\n", + " r2 = k2 * x_b[n]\n", + " rtot = r1 + r2\n", + "\n", + " # Make a numpy array of simulation time, and number of A, B and C molecules.\n", + " y = np.array([time, x_a, x_b, x_c])\n", + "\n", + " ### END SOLUTION ###\n", + "\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ih9h_XHiCXz0" + }, + "source": [ + "Initialize the number of molecules and rate constants in the next block and then run the Gillespie function. Plot the number of molecules of A, B, and C over time." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "id": "Xv0izRelW7MZ" + }, + "outputs": [], + "source": [ + "# Define initial number of molecules and rate constants\n", + "\n", + "k1 = 0.5 # s-1\n", + "k2 = 1 # s-1\n", + "A = 1000\n", + "B = 0\n", + "C = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "id": "VcdxHpaNVnjD" + }, + "outputs": [], + "source": [ + "# Run gillespie function\n", + "\n", + "x = gillespie(k1, k2, A, B, C)\n", + "time = x[0]\n", + "xa = x[1]\n", + "xb = x[2]\n", + "xc = x[3]" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "nquXZWxeYRZf", + "outputId": "350f3261-0852-457d-d96f-2324b3f91216" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# Plot number of A, B and C molecules vs Simulation time\n", + "\n", + "### BEGIN SOLUTION ###\n", + "fig = plt.figure(figsize=(6, 6))\n", + "plt.plot(time, xa, \"-.\", label=r\"A\")\n", + "plt.plot(time, xb, \"-.\", label=r\"B\")\n", + "plt.plot(time, xc, \"-.\", label=r\"C\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "### END SOLUTION ###" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3ICN865nJ1Lz" + }, + "source": [ + "## 3a. Deterministic Equations\n", + "A deterministic rate model for the same reaction network would result in the following rate expressions:\n", + "\\begin{equation}\n", + "r1 = k_1C_a\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "r2 = k_2C_b\n", + "\\end{equation}\n", + "\n", + "Where $C_i$ is the concentration of species $i$, unlike the number of molecules of the stochastic model.\n", + "\n", + "**Using these rate laws, write down the differential equations for the concentration of each species.** Submit this answer on an attached pdf file.\n", + "\n", + "**Answer:**\n", + "\\begin{equation}\n", + "\\frac{dC_a}{dt} = -k_1C_a\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "\\frac{dC_b}{dt} = k_1C_a - k_2C_b\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "\\frac{dC_c}{dt} = k_2C_b\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "GkO3k1sgGCoA" + }, + "source": [ + "Note: These equations would be the same for the number of molecules, i.e., one can replace $C_i$ with $x_i$ in the differential equations above. Concentrations can be converted to the number of molecules using Avogadro's number $N_A$ and volume V of the reactor and these constants will cancel out in the equations." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ItSF2Lx5gGTm" + }, + "source": [ + "## 3b. Deterministic Rate Model - Solving Differential Equations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "02wez7jgFL21" + }, + "source": [ + "**Solve the differential equations to find the analytical solution of the deterministic rate models.** Submit this answer on an attached pdf file. Add these solutions to the code below to plot these deterministic rate model profiles." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "qIOQXFQTPjoW", + "outputId": "de02f96d-9765-405d-9ad9-d035bf440e87" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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nVFrsvY6ntz2duwfcTeeIzl6OTgjhCyTJ8UEGnZaEsAByS6rIKqyQJEc0O4sPLOaF1S+QU54DQK+oXtw76F4Gxw32bmBCCJ8iSY6PahcVeDTJqWRQ+0hvhyMEAAdKD/D8mudZmrMUgNjAWO4beB/ndDhHhlWFEG4nSY6PahcVyMq9hWQVVng7FCGosdbw0ZaP+GTLJ9TYatBpdFzT4xpu7XMrgfpAb4cnhPBRkuT4qHZRR4uPZYaV8LKNhzfy5Mon2WfcB8Cw+GFMGzqNlLAUL0cmhPB1kuT4qHZHN+rMlLVyhJdUmit5a8NbzN4xGxWVKP8oHh76MGe1O0uGpoQQTUKSHB/l6MnJluEq4QVr8tbw+IrHyS3PBeDCjhfy4OAHZX8pIUSTkiTHRyUfXRCwuNKMscpMWIDeyxGJ1sBsNfPWxreYuXUmKirxQfE8MewJRiSO8HZoQohWSJIcHxVs0BEdbKCg3ER2YSW928r/oIVn7SvZx7Rl09hRtAOASztfygODHyBIH+TlyIQQrZUkOT6sXVQgBeUmsooqJMkRHqOqKt/s+oaX175MtbWacEM404dPZ0zyGG+HJoRo5STJ8WHtogJZl1UsG3UKjymvKeeJlU8495sanjCc/zvt/4gNjPVyZEIIIUmOT2t3zB5WQrjbnuI93Lv4XjJLM9FpdNwz4B6u7nE1GkXj7dCEEAKQJMenOXYjl2nkwt1+3vczM1bNoMpSRZvANrwy+hX6xvT1dlhCCFGLJDk+zJHkZEuSI9zEbDPzwuoX+HrX14B9Yb/nT3+eSH/ZOkQI0fxIkuPDHGvl5JVWU2224q/Xejki0ZKVVJdw35L7WJ23GoBb+97KrX1uRauRP1dCiOZJkhwfFhGoJ8RfR1m1heyiSrq0CfF2SKKF2mfcx3//+i8Hyg4QqAvkhdNfYHTSaG+HJYQQJyQVgj5MURTnkJXMsBKnamXuSq5ecDUHyg6QGJzIF+d+IQmOEKJFkCTHxzk36pQZVuIUfLf7O/7z138oM5fRP7Y/s8+dTZeILt4OSwghGkSGq3ycY6NO6ckRjaGqKh9s/oB3Nr4D2PeeenLYk/hp/bwcmRBCNJwkOT6u/dGenEzpyRENZLVZeTb9Wb7Z/Q0AU3tP5Y7+d8jO4UKIFkeSHB/n2Kgzu0h6csTJmawmHlr6EH9l/4WCwsNDH2Zyt8neDksIIU6JJDk+ztGTk1NchdlqQ6+VMixRv0pzJXcuupP0Q+noNXqeH/k8Z7U/y9thCSHEKZNvPB/XJtRAgF6L1aZyQHpzxHFUmCv4z5//If1QOoG6QN4f+74kOEKIFk+SHB+nKAodou29OfsLpC5H1FVaU8rNC29m/eH1BOuD+WDcBwyJH+LtsIQQwmWS5LQCkuSI4ympLuGm329i85HNhBnC+Pjsj+kX28/bYQkhhFtITU4r4Ehy9kmSI45hNBmZunAqO4t2EukfyYfjPqRrZFdvhyWEEG4jSU4r4EhyMiXJEUdVmCu47c/bnAnOp2d/Skp4irfDEkIIt5LhqlagQ4wMV4l/VFmquP2v29lcYB+i+uisjyTBEUL4JElyWoGUoz05h4zVVNZYvByN8KYaaw13L7qbdfnr7EXGYz+QbRqEED5LkpxWIDzQj/BAPQCZBTKNvLWy2Cw8sOQBVh5cSYAugHfHvkvP6J7eDksIITxGkpxWwlmXI9s7tEqqqvJM+jP8feBv/DR+vHnmm/SP7e/tsIQQwqMkyWklZBp56/bh5g/5dve3KCi8cPoLpManejskIYTwOElyWglHXc6+I5LktDY/7PmBtze+DcC0IdMY226slyMSQoimIUlOK9EhOhiA/QXlXo5ENKVlOct4atVTANzY60au7H6llyMSQoimI0lOK9E+2r4buQxXtR47i3Zy35L7sKpWLki5gLsG3OXtkIQQoklJktNKOHYjL640U1JZ4+VohKcVVBVwx993UGWpYmj8UJ4a/hSKong7LCGEaFKS5LQSQQYdcaH+gPTm+Loaaw33LLqHvIo82oe255VRr6DX6r0dlhBCNDlJcloRmWHl+1RVZcaqGWw8spEQfQhvnvkmYYYwb4clhBBeIUlOKyLbO/i+z7d/zk97f0KjaHh51Mt0COvg7ZCEEMJrJMlpRTpESZLjy1bkruDVda8C8ODgBxmeONzLEQkhhHdJktOKyHCV7zpUfoiHlj2ETbVxaedLubKbTBUXQghJclqRY4erVFX1cjTCXWqsNdy35D6MJiM9onrw8NCHZSaVEEIgSU6rkhQRiFajUFlj5XCZydvhCDd5ac1LbCnYQqhfKK+OfhWD1uDtkIQQolmQJKcV8dNpSIoIAGR7B1+xYN8Cvtr1FQDPjXyOxOBEL0ckhBDNhyQ5rYyjLmefbO/Q4u0t2evcsmFq76mc3vZ0L0ckhBDNi9uSnM6dO7Nnzx4AFixYQFZWlrsuLdyoY4x9D6u9h6UnpyWrtlRz/5L7nSsa397vdm+HJIQQzY7OXRe65ZZb0Ovtq6pefPHFWK1WgoOD6dmzJ71796ZXr17O5+joaHfdVjRSx9ijSc4R6clpyV5d9yoZJRlE+UfxwsgX0Gq03g5JCCGaHbclOffff7/zdUVFBTt27GDr1q1s2bKFrVu38vvvv5OdnY2iKMTExJCXl+euW4tG6CRJTou3NGcpX+78EoCnRzxNVECUlyMSQojmyW1JzrH0ej19+vShT58+zmNWq5XKykq2bNnCtm3bPHFb0QCO4arckiqqaqwE+EkPQEtSUFXA4yseB+Dq7lczInGElyMSQojmy6WanP/85z9UVVWdtN3evXsZMWIEISEhDB8+nKlTp7py25MqLy/n2WefpXfv3oSEhBAdHc3w4cOZOXNmnfVh0tPTGTt2LCEhIYSGhjJ+/Hg2btxY73UPHjzIlClTiImJISAggEGDBjF37lyPfhZ3iwzyIyJQj6pK8XFLY1NtPLb8MYqqi+gS0YW7B97t7ZCEEKJZcynJ+eCDDxg4cCAbNmw4bpuPP/6Y/v37s3r1aldu1WA2m41zzjmHxx9/nMGDB/PKK6/w2GOPYbVauf7665k2bZqzbVpaGqNGjWL//v3MmDGDp556ij179jBy5Ei2bNlS67pFRUWMGDGC77//nv/85z+88cYbBAcHM2nSJD799NMm+Wzu8s+QlRQftySzd8xmxcEVGLQGXjz9RVkPRwghTkZ1gaIoqkajUQ0Gg/rcc8+pNpvNea6goECdMGGCqtFonO2awsqVK1VAvfvuu2sdN5lMaocOHdSwsDDnscGDB6shISFqTk6O81hOTo4aEhKijhs3rtb7H3jgARVQ582b5zxmsVjUwYMHq5GRkWpZWVmDYzQajSqgGo3GRn4693jo201qu4d+Vl/5Y5dX7i8ab2/xXnXA5wPUXjN7qV/t+Mrb4QghhNc05jvULVPIa2pqePTRRznjjDPIzs7mt99+o3fv3sybN8/ZJjQ01B23OqnS0lIAEhISah338/MjOjqaoCD7OjEZGRmsWbOGiRMnkpj4zwJqiYmJTJw4kT///LNWcfScOXPo2LEjF1xwgfOYVqvljjvuoKioiF9++cWTH8utnNPIpfi4RbDarDy+4nFqbDWclngak7pO8nZIQgjRIriU5Pz111+0b98eAFVVWbZsGT179uS8884jLy8PVVVRVZVx48bVGf7xlCFDhhAeHs6LL77I3Llzyc7OZufOnTz88MOsW7eO6dOnA7BmzRoAhg0bVucaqampqKrKunXrADh06BC5ubmkpqbW2/bY67UEHWPtid7ew5LktASfb/+czQWbCdYHM33YdNmXSgghGsil2VVnnHEGmzdv5qGHHuK9994D7NPHHUJCQnjxxRe55ZZbXIuyESIiIpg3bx433XQTkyb98z/ekJAQvvvuOyZMmADYi4iBWr04Do5jubm5jW5bH5PJhMn0z15Rjt4mb+kUEwLYN+q02lS0GvnSbK72lezj7Q1vA/Dg4AeJC4rzckRCCNFyuDxcFRQUxBNPPMGAAQNQVRVFUZyPyy67jBtvvNEdcTZKcHAwvXr14v777+f777/n448/plOnTlx55ZUsXLgQgMrKSgAMhrrFm/7+/rXaNKZtfZ577jnCwsKcj6SkJBc+nesSIwLw02kwWWzkFp98dpzwjmOHqUYkjmBCpwneDkkIIVoUl5OcWbNm0bNnT9avX4+iKM4hKoCZM2cyaNCg407J9oQtW7YwfPhwxo0bx0svvcTFF1/MjTfeyPLly4mLi2Pq1KlYrVYCAwMBavWwOFRXVwM42zSmbX0efvhhjEaj83HgwAHXPqSLtBqFlKN7WEldTvPlGKYK0Yfw5LAnZZhKCCEayaUk5/zzz+faa6+lsLDQmdxce+21DB482JnobN68maFDh/LEE0+4JeCTee2116iurmbixIm1jgcGBnLeeeeRlZVFZmamszC5vmEmxzHHUFRj2tbHYDAQGhpa6+Ftsr1D85ZVmuUcpnpg8AMyTCWEEKfApSTn2BlFUVFRfP/993z66aesXLmSRx55BI1Gg6IomM1mnnnmGZeDbQhH0mG1Wuucs1gszufBgwcDsGrVqjrt0tLSUBSFgQMHAhAfH09iYiJpaWn1tgUYNGiQez5AE3HMsMqQ4uNmR1VV/i/t/6ix1TA8YbgMUwkhxClyebhKVVXOOusstmzZ4izq1Wq1PP300yxatIh27dq5eotG6dGjB2AfKjtWSUkJP/30ExEREXTq1IlOnTo5Vyx2FBaDvch47ty5nHnmmcTF/fO/58mTJ7N3717mz5/vPGa1WnnrrbcIDw/n3HPP9ewHc7OOMTJc1Vz9vO9n0g+lY9AaeCz1MRmmEkKIU6So6r/2OWiEwMBAXnzxRf773/8et01ZWRm33347s2fPrrd3xd2ysrIYMGAAxcXFXHXVVZx22mkUFRXx0UcfkZmZyTvvvMNtt90GwMqVKznjjDNo27Ytd9xxBwBvvfUW+fn5rFixgr59+zqvW1hYyMCBAyksLOTee+8lMTGRL7/8ksWLF/Pxxx83qsC6tLSUsLAwjEaj14autuYaOf+t5UQG+bH+8XFeiUHUZTQZufDHCymqLuLO/ncytY9nt0ARQoiWplHfoa6sOrh9+/YGt507d64rt2qUjIwMdcqUKWpiYqKq0+nUkJAQdeTIkep3331Xp+3KlSvVM888Uw0KClKDg4PVs846S123bl29183JyVGvvvpqNSoqSjUYDGr//v3Vr75q/Oqz3l7xWFVVtdJkUds99LPa7qGf1cJyk9fiELU9ueJJtdfMXupFP1yk1lhqvB2OEEI0O435DnWpJ0ecmubQkwNw2vN/k1tSxdxbhzG4faTX4hB2Gw5vYMqvUwCYOX4mA9sM9HJEQgjR/DTmO9Qt2zqIlsk5w0qKj73ObDUzY9UMAC7pfIkkOEII4QaS5LRinWQPq2Zj9o7ZZJRkEGGI4J4B93g7HCGE8AmS5LRijj2sZBq5dxVUFfD+5vcBuGfgPYT7h3s3ICGE8BGS5LRinWPte1jtzpckx5veWP8GFeYKekX14qJOF3k7HCGE8BmS5LRiXdrYh6tyS6qoMFm8HE3rtLVgKz9m/AjAtKHT0CjyV1IIIdxF/kVtxcID/YgJsW86ukeGrJqcTbXx3OrnALgg5QL6xvQ9yTuEEEI0hiQ5rZyjN2d3fpmXI2l9FuxbwOYjmwnQBXD3wLu9HY4QQvgcnScuWl5ezi+//EJWVhadOnXioosuQqORfKo56hwbwoqMQvZIktOkKs2VvLbuNQBu7nMzsYGxXo5ICCF8j0tJzsKFC3nppZcAuOmmm5g0aRIHDhxg9OjRZGZmOtudfvrp/PHHH+j1epeCFe7X2dmTI8NVTWnmtpkcqTpC2+C2TOkxxdvhCCGET3Kpe2XBggX8+eef/PXXX3To0AGAZ599lv379zvbqKrK0qVL+fDDD12LVHhElzb2GVbSk9N0jlQeYea2mQDcPfBu/LR+3g1ICCF8lEtJzurVqwGIjIxk8ODBAMyfPx9FUVBVlWN3jPj2229duZXwkC5Hp5EfNFZTVm32cjStw3ub3qPKUkXv6N6c1e4sb4cjhBA+y6Uk58CBAyiK4uzFycvL4+DBgwDMmDGDjIwMQkNDUVWV7du3ux6tcLuwQD2xMsOqyewr2cf3e74H4L5B96EoipcjEkII3+VSklNQUABAQkICADt37nSeu+SSS0hJSSE1NRWAkpISV24lPEiGrJrO6+tfx6paOSPpDNmfSgghPMylJMfxv9CioiIAduzY4TzeqVMnAAICAgDw9/d35VbCgxzFx3uk+Nij1uWvY9GBRWgVrUwZF0KIJuBSkhMfH4+qqqSlpfH888/z9ttvA9ChQwf8/OzFlI7enujoaBdDFZ7i6MnZLcNVHqOqKq+uexWw7zKeEpbi5YiEEML3uTSFfPjw4ezfvx+r1cqjjz4K2HtxzjjjDABsNhvbtm2rVbcjmp8uzp4cGa7ylCU5S5wL//2n73+8HY4QQrQKLvXk3HPPPc61bxyzqbRaLbfffjsAS5YscdbijBgxwrVIhcd0OjrD6pCxmlKZYeV2NtXG2xvsvZxXdruSmMAYL0ckhBCtg0tJzoABA1iwYAFjxoyhW7dunH/++SxevJi+fe178GRlZXHeeedx7rnncv7557slYOF+YQF64kLtNVNSl+N+C7MWsqt4F8H6YK7vdb23wxFCiFbD5W0dxo4dy9ixY+s9d91113Hddde5egvRBDq3CSavtJo9+WUMbBfh7XB8htVm5Z2N7wAwpccUwgxhXo5ICCFaD7duKGUymcjMzJQ1cVogZ/Gx9OS41S/7f2G/cT9hhjCu7nG1t8MRQohWxS0bdKalpTF9+nQWL16M2WxGURQsFgtPP/00+/btQ6fT8e6776LTeWQ/UOEGzuLjw1J87C5mm5l3N74LwPU9ryfEL8TLEQkhROvictYxc+ZMbr75ZqxWa61tHACCgoKYOXMmiqJwzjnncPHFF7t6O+EhnZ09OZLkuMtPGT+RU55DpH8kk7tN9nY4QgjR6rg0XLVt2zZuueUWLBYLQJ0l6idNmuQ89ssvv7hyK+FhnWPtPTn5pSaMlTLDylVmm5kPN9s3pb2p900E6gO9HJEQQrQ+LiU5r7zyinN4KikpicTExFrnExMTSUmxL3q2du1aV24lPCzEX09iuH116l3Sm+Oyn/f+zKGKQ0T5RzGxy0RvhyOEEK2SS0nOokWLAAgLC2P9+vUMHTq0TptOnTqhqiqZmZmu3Eo0gW5x9iGrnXmlXo6kZbParHy85WMArut5Hf462dJECCG8waUk59ChQyiKwrBhw4iMjKy3jaPYuKKiwpVbiSbQLd6e5Ow4JD05rvg983eyy7IJM4Qxqeskb4cjhBCtlktJjsFgAKCysvK4bXbv3g1AcHCwK7cSTaBbXCggPTmusKk2PtryEQDXdL9GanGEEMKLXEpyUlJSUFWVVatWsWfPnjrnZ8+ezZ49e1AUhc6dO7tyK9EEuh/tydmVV4bNpp6ktajPouxFZJRkEKwPZnJ3mVElhBDe5NIU8nHjxrFp0ybMZjOpqan4+/9TezB27FiWLFlSq61o3tpHBeGn01BZYyWnuIrkKOmFaAxVVflwi31G1eRukwn1C/VyREII0bq51JNz1113ERJi/99/cXExeXl5gP0f+0WLFmG1WgH7UNVtt93mYqjC03RajXMq+Q4Zsmq0FQdXsL1wOwG6AK7pcY23wxFCiFbPpSQnMTGRL774wlmbA/a1co5dL8fPz4/PPvuMhIQEV24lmoizLkeKjxvNsS7OxC4TifCX/b+EEMLbXN676sILL2T16tVccsklBAUFoaoqqqoSGBjIxRdfTHp6OhMmTHBDqKIpOOpypPi4cTYc3sCGwxvQa/Rc2/Nab4cjhBACN+1d1atXL7799ltUVaWgoACAqKgoNBq37v8pmsA/M6ykJ6cxZm6dCcCFHS8kNjDWu8EIIYQA3JTkOCiKQkxMjDsvKZqYY62czMIKKmssBPrJpqonk2nMZNEB+8KYU3pM8XI0QgghHBr1Dfb555+7dLMpU+QLoLmLDjYQHexHQXkNu/PL6ZcU7u2Qmr0vtn+BisqotqNICU/xdjhCCCGOalSSc91119XZhLMxJMlpGbrFhbI8o4BdeaWS5JxEUXURP+39CUBqcYQQopk5paIZR3FxQx6O9qLlcOxhJds7nNzXO7/GZDXRM6ong9oM8nY4QgghjtHoJKexCYskOC1Pt3jZ3qEhqi3VfLnzSwCu6+VaL6cQQgj3a9RwlWPXceHb/tmNvAxVVeXL+zjm7Z1HsamYxOBExiaP9XY4Qggh/qVRSc6oUaM8FYdoRjrFBqPVKJRUmskvNREX5n/yN7UyVpuVz7fbC/Gv6XENOo3MQhNCiOZGFrIRdfjrtXSIDgJke4fjWZa7jKzSLEL8Qri408XeDkcIIUQ9XPrvZ3Z2dqPaJycnu3I70YS6xYWQcbicHYdKOaOrLG73b7N3zAbgss6XEaiXjUyFEKI5cinJad++fYPrNRRFwWKxuHI70YS6x4fy8+ZDbD8oPTn/tq9kH2mH0tAoGi7vdrm3wxFCCHEcbikkkBlUvqdngn2G1fZDkuT825ydcwAY1XYUicGJXo5GCCHE8bhck3O8BMexG7nMzGmZeiaEAbC/oIIKk/TAOZTVlDFv7zwArux+pZejEUIIcSIu9eQ8+eST9R7Pz89n1apVbNq0CUVRuPTSS+nVq5crtxJNLCbEQGyIgcNlJnbmlTKwXaS3Q2oWfsr4iSpLFR3DOjI0bqi3wxFCCHECHklyHF5++WUefPBBli5dyptvvunKrYQX9EgI5fCuI2w7KEkOgE21ORf/m9xtsvRSCiFEM+fRKeT3338/kZGRFBQU8MQTT3jyVsIDHHU523KlLgdgRe4KssuyCdGHcEHHC7wdjhBCiJPwaJJjs9mce1gtWLDAk7cSHuCoy5HiYztHwfFFnS6SaeNCCNECuDRctXTp0nqPW61WiouLmTlzJsXFxQDOZ9FyOHpyduWVYbba0Gtb79qRWaVZLM9djoLC5G6TvR2OEEKIBnApyRk9enSD6hIURaFDhw6u3Ep4QVJEICEGHWUmCxmHy+l+dOPO1uibXd8AMCJxBMmhsqilEEK0BG75r7ljSOrfD8CZBN16663uuJVoQhqNQndHXU4rXhTQZDU5p41f3lUW/xNCiJbCY+vkOM4FBATw+OOPc+edd7p6K+EFPeIdSY7Ry5F4z59Zf1JiKqFNYBtGJI7wdjhCCCEayKXhqk8//fS45/z8/IiLi2Pw4MEEBwe7chvhRT2lJ4dvd38LwKWdL0Wr0Xo5GiGEEA3lUpJz7bXXuisO0Uw5ZljtOFiKqqqtbm2YfcZ9rM1fi0bRcHFn2W1cCCFaktY7XUY0SOc2wfhpNZSZLBwoqvJ2OE3uu93fAXB64unEBcV5ORohhBCNIUmOOCG9VkOXOPtwY2uryzFZTfy09ycAJnad6OVohBBCNJZLSc7LL79MZGQkkZGRzJkzp875L7/80nn+lVdeceVWwot6xtuHrFpbXc6fWX9iNBmJC4rjtITTvB2OEEKIRnIpyfn5558pKSlBo9EwadKkOucnTZqETqejpKSE+fPnu3Ir4UU9ElrnDKu5u+cCcEnnS6TgWAghWiCXkpzdu3ejKAqDBg1Cp6tbw6zVahk4cKCzrWiZHDOstrainpx9xn2sy19nLzjuJAXHQgjRErmU5BQWFgL2bRyOx2Kx1GorWp4eCaFoFDhSZiK/tNrb4TQJZ8FxWyk4FkKIlsqlJCcoKAhVVdm0aRNVVXVn3lRWVrJx40ZnW9EyBfrp6BwbAsDmHN8fsjJbzczfax9evazzZV6ORgghxKlyKcnp0qULYO+lufXWW6msrHSeq6ys5NZbb6WwsBBFUejcubNrkQqv6t3WXny8JafEu4E0gaW5Syk2FRMdEM1piVJwLIQQLZVLSc7ZZ5/tfD1r1izatWvHmDFjGDNmDO3atWP27NnO8+PHj3flVsLL+hxNcjbn+n5Pzk8Z9mnjF6RcgE7j0nqZQgghvMilJOf2228nIiLC+XNhYSGLFy9m8eLFtWpwwsLCuO2221y5lfCy3omOnhzjCfcra+kKqwpZlrMMgIs6XeTlaIQQQrjCpSQnNjaWWbNm4e/vX2fJf0VRUFUVf39/Zs2aRZs2bVwOVnhP9/hQdBqFwooaDhp9t/h4wb4FWFQLvaN70zG8o7fDEUII4QKXVzw+55xzWL16NZdddpmzEFlVVYKCgrjssstYvXo15557rjtiFV7kr9fSNc5efOyrdTmqqvLj3h8BmNBpgldjEUII4Tq3FBz07NmTb775BpvN5hymioqKQqORXSN8SZ+2YWw7WMrmHCPje8V7Oxy321G0gz3Fe/DT+HF2+7NP/gYhhBDNmlurKs1mMxUVFVRWVhITE+POS4tmoHdiOF9ygC0+Wnz8Y8aPAIxJHkOYIcy7wQghmi2z2XzC9eFEw2k0GvR6fa1yF3dyS5KTlpbG9OnTWbx4MWazGUVRsFgsPP300+zbtw+dTse7775b76rIouVwzrA6WnzsqT+U3lBjreGX/b8AUnAshKhfaWkpBQUFmEwmb4fiU7RaLYGBgcTGxuLn5+fWa7ucdcycOZObb74Zq9VaZ9ZNUFAQM2fORFEUzjnnHC6+uOmWxy8qKuLZZ5/lxx9/JCcnh5CQEHr16sWMGTMYOXKks116ejqPPvoo6enpKIrC8OHDef755+nXr1+dax48eJBp06bx66+/Ul5eTs+ePXnooYeYOLF17FDdpU0IfloNxiozB4qqSI4K9HZIbrP4wGKMJiOxgbGkxqd6OxwhRDNTWlpKbm4uwcHBREdHe7T3obVQVRWr1UpVVRVGo5HMzEzatm1LYKD7vltcSnK2bdvGLbfcgsViQVEU54wqh0mTJnH//fcD8MsvvzRZkpOVlcXo0aMpLy/nxhtvpEuXLhiNRjZv3kxubq6zXVpaGqNHjyYxMZEZM2YA8PbbbzNy5EhWrlxJ7969nW2LiooYMWIEhw8f5t5776Vt27bMmTOHSZMm8cknn3D99dc3yWfzJj+dhu7xIWzKMbI5t8SnkhzHUNWFHS+UzTiFEHUUFBQQHBxM27ZtJblxs+DgYCIjI8nKyqKgoIDk5GS3XdulJOeVV15xDk8lJSVhs9nIyclxnk9MTCQlJYV9+/axdu1al4NtqKuvvhqLxcLmzZuJjz9+geydd96Jn58fS5cuJTExEbAnZt27d+e+++7jjz/+cLZ9/vnn2b9/P/PmzeOCCy4A4MYbb2TYsGHcf//9TJw4keDgYM9+sGagd9swNuUY2ZJj5Pw+Cd4Oxy0KqwpZeXAlYE9yhBDiWGazGZPJRHR0tCQ4HqLVaomMjOTQoUNYLBa3lbe4NP1p0aJFgH2xv/Xr1zN06NA6bTp16oSqqmRmZrpyqwZbunQpy5cv58EHHyQ+Ph6z2VxruwmHjIwM1qxZw8SJE50JDtgTs4kTJ/Lnn3+Sl5fnPD5nzhw6duzoTHDA/ptyxx13UFRUxC+//OLZD9ZM9EkMB3xrD6vfMn/DqlrpFdWLDmEdvB2OEKKZcRQZ6/V6L0fi2wwGA/DPxt7u4FKSc+jQIRRFYdiwYURGRtbbxpGNVVRUuHKrBnMkG8nJyVxwwQUEBAQQFBREly5dmDVrlrPdmjVrABg2bFida6SmpqKqKuvWrQPsnzM3N5fU1Lq1Go5jjuv5uj5J9uLjrblGbDbfWPl4wb4FAJzf8XwvRyKEaM6kF8ezPPHr61KS48i66uspcdi9ezdAkw3l7Nq1C4CpU6dSVFTEZ599xieffIKfnx/XXHMNn376KWAvIgZq9eI4OI456nca07Y+JpOJ0tLSWo+WqlNMMP56DWUmC/sLmyZx9aSs0iy2FGxBq2hlbRwhhPAxLiU5KSkpqKrKqlWr2LNnT53zs2fPZs+ePU26C3lZWRkAISEhLFq0iKuuuorrr7+eZcuWER4eziOPPILNZnMmZo5E7Vj+/v7AP8lbY9rW57nnniMsLMz5SEpKcuETepdOq6FngmMqeYl3g3GDX/bZe/5S41OJDoj2cjRCCCHcyaUkZ9y4cYC9KCs1NZWVK1c6z40dO5brrruuTltPCwgIAGDy5Mm15ttHRERw4YUXkpeXx65du5xT1Opb76C62r43k6NNY9rW5+GHH8ZoNDofBw4cOJWP1mz0TwoHYEN2iVfjcJWqqizYbx+qOi/lPC9HI4QQwt1cSnLuuusuQkLs+xkVFxc7C3VVVWXRokXOYq3g4OAm24W8bdu2AMTFxdU555hpVVxcTEKCfWZQfcNMjmOOoajGtK2PwWAgNDS01qMl65ccDsDGAyVejcNV2wq3kVWaRYAugDHJY7wdjhBCtFirV692LiXjWJKlOXApyUlMTOSLL76oNYzj+JAOfn5+fPbZZ85EwdOGDBkCUGsqu4PjWGxsLIMHDwZg1apVddqlpaWhKAoDBw4E7MlRYmIiaWlp9bYFGDRokHs+QAvQPzkCgO0HS6k2t9ylzX/e9zMAo5NGE6j3nTV/hBCiqX3xxRfO17Nnz/ZiJLW5vIPmhRdeyOrVq7nkkktq7UIeGBjIxRdfTHp6OhMmTHBDqA0zYcIEQkJCmDVrFuXl5c7jhw4d4scff6RLly506tSJTp06MWjQIObOnessLAZ7kfHcuXM588wza/UGTZ48mb179zJ//nznMavVyltvvUV4eHir2mk9IcyfmBADFpvKtoMtcyq5xWbh1/2/AnB+isyqEkKIU2U2m/nqq68A+yjK7t27SU9P93JUdm7ZJrxXr158++23GI1G8vPzyc/Px2g08t1339G3b1933KLBIiIiePnll51Tvl999VWef/55UlNTqamp4a233nK2feONNzCZTIwcOZLXX3+d119/nZEjR2Kz2XjllVdqXXfatGm0a9eOK6+8kieffJIPP/yQsWPHsmbNGl5++WXnsF1roCgK/Vp4XU76oXSKqouIMEQwLKHuMgJCCCEa5rfffqOgoIDTTjvNWZpybM+ON7klyXFQFIWYmBhiYmLQaNx66Ua5+eab+e677wgODubxxx/nmWeeoWvXrixatIizzjrL2W748OEsXryY9u3b89hjj/H444/TqVMnli5dWic5i4qKYsWKFUyYMIF33nmHO++8E6PRyFdffcWNN97Y1B/R6/ofrcvZ0ELrchxr45zV/iz0GlngSwghTpVjDbqrr76aq6++GoCvv/4as9nszbCARm7r8Pnnn7t0sylTprj0/sa45JJLuOSSS07abtiwYfz1118NuqajBkng7MnZ2AJ7cqosVfyVbf89l6EqIYQ4dUajkXnz5uHn58ekSZOIjIxk+PDhrFy5kt9++63WLgHe0Kgk57rrrnNpRcKmTHKEZ/VpG45GgdySKg6XVhMb6u/tkBpsac5SKi2VJAYn0jemaYdThRC+RVVVqlrYBIwAvdZtqwt/++23VFdXc9FFFzl3Prj66qtZuXIlX3zxRctKchyO3Wn8ZBw7k8ty2L4l2KCjS5sQduaVseFACWf3rDtlv7n6PfN3AM5uf7b8uRRCuKTKbKXHE797O4xG2T7jbAL93LMBpmN0wzFMBfaNru+66y7mz5+P0WgkLCzMLfc6FY0unGlMgnMq7UXL0b8FrpdTaa5kWc4yAMa3H+/laIQQouXKzs5m6dKlhIeH1+qxiYqK4txzz6W6upq5c+d6McJG9uQ4dh0XAux1OV+uPsCG7GJvh9JgS3KWUG2tJjkkmW6R3bwdjhCihQvQa9k+o2Xtexeg17rlOrNnz0ZVVS677LI62x5dffXV/PTTT8yaNYubbrrJLfc7FY1KckaNGuWpOEQL5FgUcHOOEatNRatp/kM/MlQlhHAnRVHcNvTT0jiGqhYvXsyIESNqnaupqQFg6dKlZGVl0a5duyaPD06xJqc+JpOJVatWkZWVBUBycjLDhw+vd1NL4Rs6xgQTbNBRbrKwO7+M7vHNe7uK8ppy51CV7DguhBCnbt26dezYsQOAjIwMMjIy6m2nqiqzZ8/mkUceacrwnNyymM1LL71EXFwcY8aM4YYbbuCGG25g7NixtGnThhdeeMEdtxDNkFaj0DfJXlDWEupyFucspsZWQ/vQ9nSJ6OLtcIQQosVyrI1z//33O3c6+Pdj8eLFtdp6g8tJzm233ca0adMwGo11PmBpaSmPPPIIt9xyiztiFc2QY72c9VnNvy5HhqqEEMJ1VquVL7/8ErBveXQ8I0eOJDExkR07drBu3bqmCq8Wl5Kcv//+m/fffx+g3i8Nx/Txjz/+uMEL7omWZWA7e13OumZefFxaU8qK3BWADFUJIYQr/vjjD/Lz8+nSpQsDBgw4bjuNRsPll18OeG+bB5eSnA8++MD5OjAwkJtvvpk33niDN954g5tvvpnAwEBn8vPhhx+6FqlolgYcLT7ed6SCwnKTl6M5vsUHFmO2mekY1pHOEZ29HY4QQrRYjoTlRL04Do42X375JRaLxaNx1celwuO0tDQAAgICWLVqFb169ap1/o477mDIkCFUV1ezatUqV24lmqnwQD86xwaz53A567KKOauZLgp47FCVEEKIUzdnzhzmzJnToLaDBg3y6np5LvXk5OfnoygKqampdRIcgJ49e5Kamoqqqhw5csSVW4lmbFD7o0NWzbQux2gysvLgSkCSHCGEaE1cSnL8/PwAKC4+/pdbSUkJAHq97PTsqwa2s+9XsraZJjmLDizCYrPQOaIzKeEp3g5HCCFEE3EpyWnfvj2qqrJx40beeeedOuffffddNmzYgKIoXlsISHjeoKPFx1tyjFQ3w43q/sqyF72PSx7n5UiEEEI0JZdqcsaMGcPWrVsBuPPOO3nppZfo1s2+VP7OnTs5cOCAs+24cfIF46vaRQUSHexHQXkNW3ONDGof6e2QnCrMFc6hqjHtxng5GiGEEE3JpZ6cu+66i8DAQMC+qmF2djYLFy5k4cKFZGdnO4uNAgICuPPOO12PVjRLiqIw6OiQ1ZrM5jVktTx3OTW2GpJDkukcLrOqhBCiNXF5uGrmzJnOeptj18pxvNbr9XzyySe0b9/elVuJZu6f4uMiL0dSm2Ooaky7MbIAoBBCtDIur3h82WWXkZaWxoQJEwgMDHSudhwYGMiECRNYtWoVkyZNckesohlzLgqYVezV6YLHqrHWsDR3KQBjkmWoSgghWhu3bNDZr18/vv/+e2w2G4WFhQBERUWh0bhlayzRAvRMCMOg01BcaWbvkQo6xQZ7OyTSDqVRYa4gNiCW3tG9vR2OEEKIJubWLESj0RATE0NMTIwkOK2Mn05D36P7WDWXIau/su1DVWcmn4lGkT+PQgjR2rilJwfAYrFQWFiIyXT8pf2Tk5PddTvRDA1qF8Hq/UWsySzm8sHe/b222Cwsyl4EwNh2Y70aixBCCO9wOclZsmQJTz31FCtXrsRsNh+3naIoXtm3QjSd5rTy8YbDGyg2FRNmCGNgm4HeDkcIIYQXuJTkLFy4kPPOOw+r1dpsik2F9wxMjkRRYH9BBYfLqokN8fdaLI6hqtFtR6PTuK3DUgghRAviUqHCk08+Kb0zwiksUE/XNiEArN7vvbocVVWdSY4MVQkhROvl0n9xN23a5Fx7ZOjQoYwYMYLgYO/PqhHek5oSxc68MtL3FXF+nwSvxLC9cDt5FXkE6AIYljDMKzEIIYSvq2/tMZ1OR0xMDMOGDeO+++5j+PDhXojsmHhceXNQUBDV1dX07duXlStXymJrgqEdIpm5MpP0/YVei+HP7D8BGJk4EoPW4LU4hBCiNbj22mudr8vKyti0aRPff/89P/zwA7NmzeLKK6/0WmwuJTlnnXUWc+bMwd/fXxIcAcCQDvbtHXbnl1NUUUNkkF+TxyBDVUII0XRmzpxZ62ebzcYjjzzCCy+8wJ133snEiROdOyM0NZdqcp599lmioqJIT0/ntddeO+HsKtE6RAUb6NLGPmS52gu9OfuN+9lv3I9Oo2Nk4sgmv78QQrR2Go2GGTNmoNPpKCwsZNu2bV6LxaWenOTkZBYtWsTQoUO5//77mTFjBikpKYSFhdVpqygKf/31lyu3Ey3E0A5R7M4vJ21fEeN7xTfpvRcfWAzAkLghBPtJfZgQQniDn58fYWFhFBYWenWCkktJTlFREVdddRXV1dWoqorRaGTDhg11hq5UVZXhrFZkaEokX6Rlke6FGVaOJGd00ugmv7cQQgi7/fv3U1hYiF6vp1OnTl6Lw6Uk56GHHmLLli0oiiJJjHBy1OXszCulpLKG8MCmqcspqS5h45GNAIxqO6pJ7imEaOVUFcyV3o6icfSB4KHv7PLycjZu3Mg999wDwH/+8x/Cw8M9cq+GcCnJmTdvHoqiOBcCjIiIIDg4WPatauViQ/xJiQli35EKVu8v4qyecU1y32W5y7CpNrpGdCUh2DvT14UQrYy5Ep5tYf/ePHIQ/ILcdrn6OjlCQkJ46623uP322912n1PhUpJTWWnPXuPi4li2bBkdO3Z0S1Ci5RvaIYp9RypIb8IkxzFUNSpJenGEEKKpHDuF3GQykZWVRXp6OjNmzKBjx46cc845XovNpSRnwIABLF++nN69e0uCI2pJTYnky9XZTbZejtlqZsXBFQCckXRGk9xTCCHQB9p7RloSfaBbL/fvKeQAGzZsYNSoUVx44YVs3bqVrl27uvWeDeXytg4A6enp7Nu3zy0BCd+QmhIFwPaDpZRWe35pgTX5a6gwVxAdEE2PqB4ev58QQgD22ha/oJb1aIIa2v79+3PLLbdgsVh47733PH6/43GpJycnJ4fx48fz66+/MnDgQK644gp69OhR7xRygClTprhyO9GCtAn1p31UIJmFlazNLOLMbm08ej/nUFXbUWgUqQkTQghv69ChAwB79uzxWgwuJTnXXXeds+DIaDTy4YcfnrC9JDmtS2pKFJmFlazMKPRokqOqKksOLAFk6rgQQjQXjhEeb+5p6Zb/8v57Crmqqs6H42fR+gzvFA3Air2ercvZXbybgxUH8df6MzR+qEfvJYQQ4uQ2bNjg7Pg499xzvRaHSz05cPIERhKc1mt4R3tdzo5DpRSWm4gK9sxmmUty7L04qfGpBOgCPHIPIYQQ9bvuuuucr2tqasjKyiItLQ2bzcYFF1zANddc47XYXEpyFi1a5K44hA+KDjbQLS6EnXllrNpXyPl9PLOWhKxyLIQQ3vPZZ585X2s0GsLDwzn99NO55ppruO6667y6dp5LSc6oUbIeiTix0zpFszOvjBUZBR5JcgqqCthSsAWA09ue7vbrCyGEqF9LGKmRaSjCo07rZB+yWpHhmbocR8Fx7+jexATGeOQeQgghWiZJcoRHDekQhU6jkF1UyYEi9+/v4qjHkb2qhBBC/JskOcKjgg06+iWFA7Byb4Fbr11jrSHtUBogWzkIIYSoS5Ic4XHOqeRuHrJal7+OKksVMQExdI3wzpLhQgghmi9JcoTHnXZ0KvnKvQVuLVRblrsMgBGJI+rdBVcIIUTrJkmO8Lj+yREE6LUUlNewK7/MbdddnrscsCc5QgghxL81KslZunQpS5cuZceOHZ6KR/ggP52GIR0iAfcNWeWU5bDfuB+tomVYwjC3XFMIIYRvaVSSM3r0aM444wymT59uf7NGg1ar5fLLL/dEbMKH/DOV3D3Fx45enP6x/QnxC3HLNYUQQviWUxqu+nddRUtYEEh412lHi4/T9hVislhdvt6x9ThCCCFEfRqV5DiKO3Nzcz0SjPBdPeJDiQkxUFljZV1msUvXMllNrD60GoCRbUe6IzwhhBA+qFHbOoSFhWE0GklLS6Nt27bO47/++ispKSknfK+iKOzdu/fUohQtnqIonN45hu/W57BkzxHntPJTsTZvLdXWatoEtqFzeGc3RimEEMKXNCrJ6devH0uW2FeYPXjwIGAfqqqoqKCiouKE75UpvuL0LtH2JGfXER4+p/spX0emjgshhGiIRg1X3X333YDU4IhTM7JzDIoCO/PKyC+tPuXrLMuxJzkyVCWEEOJEGtWTc+GFFzJ//nw+//xzDh8+zOLFi1EUhaioKHr27OmpGIWPiAzyo0/bcDYdKGHJ7iNMGpTU6GtklWaRXZaNTqMjNT7VA1EKIYRojIqKCj744APmz5/P9u3bKS4uJigoiG7dujFu3DhuuukmkpOTvRJbo5IcgHPPPZdzzz0XsE8hB/vU8m+++ca9kQmfNKpzNJsOlLD0FJMcx9TxgbEDCdIHuTs8IYQQjbBy5UouvfRS8vLyCAwMJDU1lTZt2mA0GlmzZg1paWm8+OKL/Pzzz4wdO7bJ42t0knOsKVOmoCgKQ4YMcVc8wseN6hrDm39nsGxPAVabilbTuJoaRz2ODFUJIYR3bdy4kTFjxlBdXc1DDz3E448/TlDQP//5tNls/Pjjjzz44IPk5OR4JUaXkpyZM2e6KQzRWvRtG06ovw5jlZlNOSUMSI5o8HurLFWsObQGkPVxhBDCm1RV5ZprrqG6uprp06fz5JNP1mmj0Wi45JJLGDNmDAcOHPBClC4mOccymUysWrWKrKwsAJKTkxk+fDgGg8FdtxA+QKfVMKJzNL9syWPJriONSnLW5K2hxlZDQlACKWEnXrJACCGE5/z2229s3bqVtm3b8uijj56wbVhYGGFhYU0UWW1u2aDzpZdeIi4ujjFjxnDDDTdwww03MHbsWNq0acMLL7zgjlsIHzKqSwwAS3YfadT7HLOqZOq4EEJ414IFCwCYOHEiOp3b+kvczuUk57bbbmPatGkYjUZUVa31KC0t5ZFHHuGWW25xR6zCR5x+NMnZlFNCcUVNg9+34uAKQIaqhBDC2zZu3AjAgAEDvBvISbiUfv3999+8//77KIqCoih11s9xHPv444+ZNGkSY8aMcSlY4RviwwLo2iaEXfllLNl9hAn9E0/6ngOlBzhQdgCdRsfQ+KFNEKUQQpycqqpUWaq8HUajBOgCXO4NLywsBCAmJsYdIXmMS0nOBx984HwdGBjIVVdd5VwvZ9u2bcyePZvKykoAPvzwQ0lyhNOZ3WPZlV/GXzsPNyjJWXlwJQD9YvoRqA/0dHhCCNEgVZYqhs5pWf/xSr8yvdX8O+pSkpOWlgZAQEAAq1atolevXrXO33HHHQwZMoTq6mpWrVrlyq2EjxnbPZb3Fu9lya7DmK029NoTj5w6kpzhCcObIjwhhBAnEBUVBcCRI42rrWxqLiU5+fn5KIpCampqnQQHoGfPnqSmprJo0aJm/wshmla/pAgig/woqqhhbWYxwzpGHbet2WZmdZ5913FJcoQQzUmALoD0K9O9HUajBOgCXL5Gv379WLFiBevXr+fqq692Q1Se4VKS4+fnh9lspri4+LhtSkpKANDr9a7cSvgYrUZhdNcYvl+fy98780+Y5Gwt2Eq5uZxwQzjdIrs1YZRCCHFiiqK0mqGfY5133nm88847zJ07lxdffLHZzrByaXZV+/btUVWVjRs38s4779Q5/+6777JhwwYURaFdu3au3Er4oDHd2gDw147DJ2znGKoaFj8MrUbr8biEEEKc2Pjx4+nZsyc5OTk888wzJ2xbWlrKtm3bmiiy2lxKco4tJL7zzjtp374948ePZ/z48bRv35477rjDeX7cuHGu3Er4oNO7RKPTKOwrqGDfkfLjtnMmOQnDmio0IYQQJ6AoCrNmzcLf35/p06fz8MMPU1FRUauNqqrMmzePQYMGsWbNGq/E6VL/0l133cVHH31EVVUVqqqSnZ3tXLr52OnkAQEB3Hnnna5FKnxOiL+eoSmRrMgo5O+dh0mJCa7TxmgysrVgKyBJjhBCNCf9+vXjzz//5NJLL+X555/nzTffZNiwYc4NOteuXUt+fj7+/v4kJTV+Q2Z3cHm4aubMmc56m2Pn3Tte6/V6PvnkE9q3b+/KrYSPOtmQ1eq81dhUGx3DOhIXFNeUoQkhhDiJ0047jYyMDF5++WUGDx7M5s2b+eabb1ixYgXt27fnySefZM+ePV5bQsblFY8vu+wy0tLSmDBhAoGBgc7VjgMDA5kwYQKrVq1i0qRJ7oj1lFRWVpKSkoKiKPz3v/+tc37Xrl1MmDCBiIgIgoKCGDlyJH///Xe91zIajdxxxx0kJibi7+9Pz549ee+99+osgigabkz3WADWZBZhrDLXOb8i177KsfTiCCFE8xQcHMx9993H4sWLOXz4sHNCUlpaGtOnT6dt27Zei80t5dD9+vXj+++/x2azOVdBjIqKQqNxy9ZYLnniiSeOO3197969DB8+HJ1Ox4MPPkhYWBgfffQRZ599Nr/++itjx451tq2pqWHcuHFs2LCBO+64g+7du/Prr79y2223kZ+fz/Tp05voE/mWdlFBdIoNJuNwOUt3H+GCvgnOc6qqsuqgfX0lmTouhBCisdyahWg0GmJiYoiJiWkWCc769et5/fXXeeqpp+o9//DDD1NSUsLvv//Oww8/zG233cayZctISEjg9ttvr9VD8/HHH7NmzRpeffVVXn31VaZOncr333/PJZdcwrPPPuvcfV003phu9t6chdvzax3PKs3iYMVB9Bo9A9sM9EZoQgghWjDvZyIeYrVamTp1KuPHj+eSSy6pc76iooJ58+YxevRo+vXr5zweHBzMTTfdxO7du2tVg8+ZM4fAwECmTp1a6zp33303ZrOZr7/+2mOfxded1dNel7No52FqLDbnccesqgFtBrTKdSiEEEK4xmeTnNdee42dO3fy9ttv13t+8+bNmEwmhg2rW+uRmpoK4ExybDYb69evp3///vj7+9dqO2TIEBRF8dr0OF/QPymCmBADZSYLK/cWOI/LUJUQQghX+GSSs3//fp588kmeeOKJ487qOnjwIACJiXU3h3Qcy83NBaC4uJiqqqp62xoMBqKjo51t62MymSgtLa31EP/QaBTO6mHvzfl9Wx4AZqts5SCEEMI1Ppnk3HrrraSkpHDvvfcet41jd3SDwVDnnKO3xtHmRG0d7R1t6vPcc88RFhbmfHhrvYDmbHwv+/TwhdvzsdpUNh3ZRKWlkkj/SLpEdPFydEIIIVoin0tyZs2axcKFC3nvvfdOuF9WYKC9xsNkMtU5V11dXavNido62jva1Ofhhx/GaDQ6H44FE8U/UlOiCPXXUVBew7qs4lqrHGsUn/tjKoQQogm4NIV86dKlzteOqdjeZDKZuPfeezn33HOJi4sjIyMD+GfYyWg0kpGRQXR0NAkJCbXOHctxzDE8FRERQUBAQL1tTSYTBQUFjBo16rhxGQyG4/YCCTu9VsPY7m34fkMuv2/LYxv2JEeGqoQQzYWsieZZnvj1dSkrGT16NIqikJyczP79+90V0ymrqqriyJEjLFiwgAULFtQ5P2vWLGbNmsVLL73ErbfeisFgYNWqVXXapaWlATBo0CDAPjV+wIABbNiwAZPJVCthWb16NaqqOtuKU3dWzzi+35DLL9syqIjbDtg35RRCCG/Sau0bA5vNZgICArwcje9yjJa4s8PEpStFRERQUlJCz5493RWPS4KCgpg7d26d40eOHOG2225j/Pjx3HjjjfTp04fg4GAuuOACvv/+ezZt2kTfvn0BKC8v5+OPP6Zz584MGTLEeY3JkyezYsUKPvzww1obj77++uvodDouv/xyz39AHzeqSwz+eg1HLJsJQKVzRGdiAmO8HZYQopXT6/UYDAaMRiMhISG1tjAS7mG1WikqKiIoKKj5JDmpqan8+uuvzWYhPL1ez2WXXVbneGZmJgAdO3asdf65557jr7/+4qyzzuKee+4hNDSUjz76iNzcXBYsWFDrD/LUqVP59NNPuffee8nMzKR79+788ssv/PDDDzz22GOyN5cbBPhpGdUlhsWFewEYGjfUyxEJIYSdYxZtTk4OYWFh6PV6SXZcpKoqVquVqqoqjEYjNpuN+Ph4t97DpSTnySefZOHChWzfvp1Zs2Zx9dVXuyuuJtGpUydWrFjBtGnTeP7556mpqWHAgAH89ttvtbZ0APDz8+PPP//kscce48svv6SwsJCOHTvy1ltvcfvtt3vpE/ie8b3iWL7GnuQMiRtyktZCCNE0QkNDASgoKDjhkiGi8bRaLYGBgcTGxuLn5+fWayuqC5U+n3/+OT///DPffvstiqJw9tlnM3LkSOLj4+vd1mHKlCkuBesrSktLCQsLw2g0Ov/iCLuMwlwu/nk8qqrwxdjf6N824eRvEkKIJmQ2m7Fard4OwydoNJpG94o15jvUpZ6c6667DkVRUBQFVVX5/fff+f3334/bXpIccTI7StYDYKtOZNGOcvp7b/NaIYSol16vP+ESJaL5cNsCJMdmYaqqOh+On4VoiDV59u0xLBUd+XnzQfmzI4QQ4pS5nOQcm9Acm9gce16IhnJs5aCYOrHvSAU7DpV5OSIhhBAtlUvDVYsWLXJXHEKQU5ZDbnkuOkXH0LaD+HO7kZ83H6RHgtQtCSGEaDyXkpwTrfIrRGM5hqp6RffiosQU/ty+gZ83H+KBs7vKVE0hhBCN5tZNgUwmE5mZmWzfvt2dlxWthGOoakj8EMZ0jyVAryW7qJItuUYvRyaEEKIlckuSk5aWxvjx4wkLC6Njx4706dMHgKeffpobbriBm2++GYvF4o5bCR+lqiqrDx1NcuKGEOin48zusQD8vPmQN0MTQgjRQrmc5MycOZPTTz+dhQsXUlNTU6v4OCgoiJkzZ/K///2P+fPnuxys8F1ZpVkcrjqMn8aPvjH2LTYu6GNf+XLB5kNSwC6EEKLRXEpytm3bxi233OLspfl33cSkSZOcx3755RdXbiV8nGOoqm9sX/x1/gCM7hpLkJ+W3JIq1meXeDE6IYQQLZFLSc4rr7yC2WxGURSSkpJITEysdT4xMZGUlBQA1q5d68qthI9z1uMcs5WDv17LWT3jAPhpoyyjLoQQonFcSnIcU8jDwsJYv349Q4fW3VCxU6dOqKrq3CRTiH+zqTbnzKp/71c1ob89cZ6/6SA1FluTxyaEEKLlcinJOXToEIqiMGzYMCIjI+tt49gyvaKiwpVbCR+WUZJBUXURAboAekf3rnXutI5RxIQYKK40s2T3ES9FKIQQoiVyKckxGAwAVFZWHrfN7t27AQgODnblVsKHOXpxBsQOQK+tvR+MTqvhor72TTp/3CBDVkIIIRrOpSQnJSUFVVVZtWoVe/bsqXN+9uzZ7NmzB0VR6Ny5syu3Ej4s/VA6AIPjBtd73jFktXBHPsYqc5PFJYQQomVzKckZN24cYN92PjU1lZUrVzrPjR07luuuu65OWyGOZbVZWZtvL0ofGl+3pgugZ0IoXdoEU2Ox8esWWTNHCCFEw7iU5Nx1112EhIQAUFxcTF5eHmBf2G3RokVYrVbAPlR12223uRiq8EU7i3dSVlNGsD6YbpHd6m2jKAoX928LwA8yZCWEEKKBXEpyEhMT+eKLL5y1OWD/Qjp2vRw/Pz8+++wzEhISXLmV8FFrDtnrcQa1GYROc/yt1C7ql4CiQPr+InKKj18DJoQQQji4vOLxhRdeyOrVq7nkkksICgpyrngcGBjIxRdfTHp6OhMmTHBDqMIXpeeduB7HISE8gNQOUQD8tPGgx+MSQgjR8rm0C7lDr169+Pbbb1FVlYKCAgCioqLQaNy6/6fwMWabmfX564Hj1+Mc6+IBiazaV8h363K4bXRH2ZlcCCHECbk1C1EUhZiYGGJiYiTBESe1rWAblZZKwg3hdI44+ey7c3vHE+inZV9BBWuzipsgQiGEEC2ZWzKR7du385///Idu3boRFBREUFAQ3bp149Zbb2Xbtm3uuIXwQY71cQbHDUajnPyPYrBBx3m97Zt2fr3mgEdjE0II0fK5nOS8+eab9O/fnw8//JDdu3dTVVVFVVUVu3fv5qOPPmLAgAG8/vrrbghV+JqG1uMc6/LBSYB9Z/KyalkzRwghxPG5lOT89NNP3H333ZjN9i8bx8yqY2dYmc1m7rvvPn766SfXoxU+o8Zaw8bDGwEYGnfyehyHge0iSIkJosps5efNsmaOEEKI43MpyXnhhRcAe3Kjqip+fn506tSJTp06YTAYUFXVec7RVgiATUc2YbKaiA6IpkNYhwa/T1EULh9k7835Zq0MWQkhhDg+l5KcTZs2OXtsHnzwQY4cOcKuXbvYtWsXR44cYdq0aaiqCsDmzZtdj1b4jGPrcRo7S+qSAW3RaRQ2ZJewJ7/ME+EJIYTwAS4lOQEBAYB9Cvnzzz9faxPOoKAgnn32WXr3tu8q7e/v78qthI9x7Fc1JG5Io98bE2LgzG6xgBQgCyGEOD6XkpzTTz8dVVWJiYk5bpuYmBgUReG0005z5VbCh1RZqthcYO/Za0w9zrEmHR2y+n5DLjUWm9tiE0II4TtcSnKeeeYZAgICSE9PZ9euXXXO79ixg7S0NPR6PU899ZQrtxI+ZMPhDVhsFuKC4mgb0vaUrjG6awxtQg0UVdTw+7Y8N0cohBDCFzRqxePPP/+8zrGrrrqKjz/+mCFDhnDVVVfRo0cPwL52zuzZs6mqquLyyy9n8+bN9OvXzy1Bi5Zt9aHVgH2o6lRXLdZpNVwxOJk3/trDF2lZXNBX9kYTQghRm6I6KoMbQKPR1Pul5LjEv885Zlc5OHYlb+1KS0sJCwvDaDQSGhrq7XCa3FULrmJzwWaePu1pLup00SlfJ89YzWkv/I3VpvL73afTNS7EjVEKIYRojhrzHXpKw1WOTTiPTW7qS34cxxqRRwkfV15TzrZC+yrYp1J0fKy4MH/GdW8DwKy0LJdjE0II4VsaneT8O2E5NuE53kMIh/WH12NVrSSFJBEfHO/y9a4Z1g6A79fnUG6yuHw9IYQQvqNRNTmLFi3yVByilXBl6nh9hneMIiUmiH1HKvhxQy5Xp7Zzy3WFEEK0fI1KckaNGuWpOEQr4VgE0F1JjqIoXDW0Hf/383ZmpWVx1dDkUy5mFkII4Vvcsgu5EA1hNBnZWbQTgCHx7klyAC4b0BZ/vYadeWWszSp223WFEEK0bI3qyTkRi8VCYWEhJpPpuG2Sk5PddTvRAq3NW4uKSkpYCtEB0W67blignov6JvL12gN8viqLwe0j3XZtIYQQLZfLSc6SJUt46qmnWLlypXM38vooioLFIoWhrVl6nnvrcY51zbB2fL32AL9uOUTeud2JC5NtRIQQorVzabhq4cKFjBs3jiVLllBTUyOzrMQJOetx3DhU5dArMYzB7SOw2FQ+X5Xp9usLIYRoeVxKcp588knpnRENUlBVQEZJBgCD2wz2yD1uHJECwJzV2VTWyJ9LIYRo7Vwartq0aZNzJsvQoUMZMWJErZ3IhXBYm7cWgG6R3Qj3D/fIPcb1aENyZCDZRZV8tz6Xa2Q6uRBCtGouJTlBQUFUV1fTt29fVq5cKVN3xXE56nEGx3mmFwdAq1G4/rT2PDV/O58s389VQ5LRaOTPpBBCtFYuDVedddZZqKqKv7+/JDjihBybcg6NG+rR+0wclESIv479BRUs2nXYo/cSQgjRvLmU5Dz77LNERUWRnp7Oa6+9dsLZVaL1yqvII7ssG42iYUCbAR69V7BBx+Qh9qUKPl6236P3EkII0by5NFyVnJzMokWLGDp0KPfffz8zZswgJSWFsLCwOm0VReGvv/5y5XaihVqdZ+/F6RnVkxA/z+8Ufu3w9vxv+X5W7Stk20EjPRPq/nkUQgjh+1xKcoqKirjqqquorq5GVVWMRiMbNmyoM3SlqqoMZ7VijqEqT9bjHCsxPIBze8czf9NBPl62n9cu79ck9xVCCNG8uDRc9dBDD7FlyxbA3lPjeAjhoKqqsyfH0/U4x7ppRAcA5m06yIGiyia7rxBCiObDpZ6cefPmoSiKc6G/iIgIgoOD0WhkSyxhl1Oew6GKQ+g0OvrF9muy+/ZNCmdEp2iWZxTw4dJ9/N+EXk12byGEEM2DS0lOZaX9f8hxcXEsW7aMjh07uiUo4TscQ1V9ovsQqA9s0nvffkYnlmcU8PXaA9wxphOxIbLVgxBCtCYudbkMGGCfKdO7d29JcES9HENVTVWPc6zUlEgGJIdTY7Hxv+Uy00oIIVobl7d1AEhPT2ffvn1uCUj4jlr1OPFNV4/joCgKt5/RCYBZq7IwVsoSB0II0Zq4NFyVk5PD+PHj+fXXXxk4cCBXXHEFPXr0qHcKOcCUKVNcuZ1oYfaX7qegqgA/jR99Yvp4JYYzu8XSLS6EnXllfLYqkzvHdPZKHEIIIZqeorqwPbhGo6lVeHyymVVWq/VUb+VTSktLCQsLw2g0Ehoa6u1wPOarnV/xTPozDI0bysdnf+y1OOZtOsidX24gPFDPiofOJMjgUm4vhBDCixrzHeqWaVD/njquqqrz4fhZtD7erMc51nm942kfFUhJpZk56dlejUUIIUTTcTnJOTahOTaxOfa8aEVUFUoOYNu/jDW5KwAYqo+AqhKvhaTVKNx2tDbn/SV7qTBZvBaLEEKIpuNSv/2iRYvcFYdoyVQVDqTDus9g799QnscevZ6StvEE2Gz0/GaqvV1MN2g/EnpcCO1GQBOup3RJ/0TeXZRBZmElM1dmOguShRBC+C6XanLEqfGpmpzcdfDrQ5Cz5p9jGj1fxCbwYoDKaVYd7xeWQ8W/dgQPS4bBN8CgG8G/aX4NftiQwz1fbyIsQM+yh84g1F/fJPcVQgjhPk1ekyNaIasZfn8UPhpjT3B0/tD/GpjyEzycw+rOowAYMuQOeGAPPLgfJn0BA6aAIRSM2fDndHi9Fyx5CcxVHg/5wr6JdIoNxlhl5hNZN0cIIXyeSz052dmNK+JMTk4+1Vv5lBbfk1NZBF9fA1nL7T/3uQLGzYCQNgBYbBZGfjWScnM5X533FT2je9Z+v7kKtn4Py1+Dwj32Y2HJcNb/QY+LwIP7ny3YfIjb56wnxKBj2UNnEB7o57F7CSGEcL/GfIe6VJPTvn37Bm/IqSgKFosUfLZ4FYXw+UWQvwX8QuDi96D7BbWa7CzaSbm5nBB9CN0iu9W9hj4A+l8Ffa+wJzt/Pmnv2Zl7LXQ9Dy54HYJjPRL+Ob3inOvmfLh0Hw+Oryc+IYQQPsEtw1X1zbA62awr0QKZyuCLowlOUCzctLBOggP/TB0fGDcQrUZ7/OtptNBnIvx3DYx6CDR62LUA3hkK2370yEfQaBTuO6srAJ+uyKSg3OSR+wghhPA+t0whr49j7ZyG9vSIZs5mg+9vgbwtEBQD1/0Msd3rberYlHNI3JCGXdsvCM54BG5eDG16Q1WRvVdn/l1grnbTB/jH2O6x9G0bRpXZylt/7XH79YUQQjQPLg1XOfau+rf8/HxWrVrFpk2bUBSFSy+9lF69erlyK+FtS16w97JoDTD5K4jpWm8zs9XM+sPrgUYkOQ5xvWDq37DkeVj2KqybCQc3wqTPIaKda/EfQ1EUHjqnG1d+lM7s9GyuHd6elJhgt11fCCFE8+DRKeQvv/wyDz74IDExMWzcuJH4+HhP3apFaXGFxzlr4X/jQLXBhPeh3+TjNt1weANTfp1CuCGcJZcvQaOcYmdhxp/w3U1QVQz+4XDZ/6DT2FO71nHcMHMNf+88zPiecbx/zUC3XlsIIYRnNJsp5Pfffz+RkZEUFBTwxBNPePJWwlNqKuGHW+wJTp/LT5jgwD9DVYPjBp96ggP2hOaWpZAwAKpLYPZEWP3RqV+vHg+f0w2NAr9ty2NtZpFbry2EEML7PJrk2Gw2Z9HxggULPHkr4SnLXobCDAiJh3NeOGlzR9Fxo4eq6hOeDDf8Bv2usidZv9wPv04Dm3s2eu3cJoTLBycB8MwvO6Q4XgghfIxLNTlLly6t97jVaqW4uJiZM2dSXFwM4HwWLUhxJqx82/763JchIOKEzU1WExsPbwRgSLwbkhwAnQEuegeiOsJfMyD9PSjeD5f+Dwyu19HcM7YLP208yIbsEn7Zksd5fWRIVQghfIVLSc7o0aMbNHtKURQ6dOjgyq2EN/zxOFhN0GEUdDvvpM03Hd5Eja2GmIAYOoS68fdbUWDkfRCZAj/cCrt/g88vhCvnQlCUS5eODfVn6sgU3vhrDy/8tpNxPdrgp5OFwIUQwhd4dJ0cwJkE3Xrrre64lWgqB9bAjnmgaGD8cw1ahdgxVDU4brBnlg7oeTFc+zMERNr3zPp0PBhzXL7szaenEBNiILuokk9WyHYPQgjhKzy2To7jXEBAAI8//jh33nmnq7cSTWnpi/bnvldCm54nbnuUI8kZGj/UU1FB0mB7nU5oIhTshv+dDUd2u3TJIIOOaUdXPn7zrz3kGd2/No8QQoim59Jw1aeffnrcc35+fsTFxTF48GCCg2UNkhYldz3s+cPeizPy3ga9pdJcyZYjWwB7T45HxXSFG36HLy627331ydlw9beQeOrTwC/un8ic1dmsyyrm2V928Obk/m4MWAghhDe4lORce+217orDbXbv3s2sWbP4448/2Lt3L9XV1XTs2JGJEydy9913ExQUVKv9rl27eOihh1iyZAk1NTUMGDCAp556ijPPPLPOtY1GI4899hjff/89hYWFdOzYkf/+97/ceuutvrWy89KX7c+9J9kLfhtgw+ENWFQLCUEJtA1u68HgjgpPsvfozL4MDm6Azy6EK7+B9qed0uU0GoWnLuzJBW8vZ96mg1w5NJnUFNfqfYQQQniXz1VYfvLJJ7z22mt07NiRJ554gpdeeomuXbvy2GOPMXz4cKqqqpxt9+7dy/Dhw1m1ahUPPvggL730EuXl5Zx99tn8+eefta5bU1PDuHHjeP/997n88st566236Nq1K7fddhtPPfVUU39MzynaB7t+sb8eeV+D35aelw54sB6nPkHRcO186HA61JTDrEth3+JTvlyvxDCuHJIMwPR527BYbW4KVAghhDc0asXjGTNmuHSzplgQcO3atXTu3JmwsLBaxx977DGeeeYZ3nrrLf773/8CMGnSJL777jvWrVtHv379ACgvL6dnz574+/uzc+dO5xf2u+++y+23386bb77JHXfc4bzupZdeyvz589mzZw/t2jVs64FmveLxb49A2jv2xfiu/q7Bb5v882S2Fm7l2RHPckHHupt2epS5Cr6+2r5Kss4fLp8NnU9tdeTiihrOeGUxJZVmpl/Qg+tOk1mBQgjRnDTqO1RtBEVRVI1Gc8oPb9q8ebMKqLfccouqqqpaXl6uGgwG9cwzz6zTdsaMGSqgpqenO4+ddtppamBgoFpVVVWr7dKlS1VAfeGFFxoci9FoVAHVaDSe4qfxkOoyVX02SVWfDFXVXb83+G2lplK1z2d91F4ze6mHyg95MMATMFer6pwr7LHPiFbVnb+c8qW+WJWptnvoZ7XXE7+pecaqk79BCCFEk2nMd6hHhqvU40wn96acHPtU4zZt2gCwefNmTCYTw4YNq9M2NTUVgDVr1gD2lZvXr19P//798ff3r9V2yJAhKIribNuibfkGTEb7ejSN2CdqXf46bKqNdqHtiAuK82CAJ6AzwMTPoPuFYK2x9+xs/+mULjV5SDJ924ZRZrIwfd42NwcqhBCiqTQ6yakvgakvoVEUxfnwNqvVyv/93/+h0+m48sorATh48CAAiYmJddo7juXm5gL21ZqrqqrqbWswGIiOjna2rY/JZKK0tLTWo1naMMv+POgG0DT8j0b6oX/qcbxK5weXfQq9LgObBeZeD5vnNvoyWo3Cc5f0QatR+HVrHn9sy/NAsEIIITytUbOrFi1adNI2RUVFvPbaayxfvrxWgqNpxJemu919992sWrWKZ599lq5duwJQWVkJ2JOUf3P01jjanKito72jTX2ee+655l+cfGS3fYE9RWvfiLMR1uTZe7GGxnlwfZyG0urgkg9B6web5sD3U8Fmhn5XNuoyPRJCufn0FN5bvJcnftrGsI5RhPjrPRS0EEIIT2hUkjNq1KjjnispKeHVV1/lrbfeorS0FEVRUFUVjUbDpEmTvLYL+eOPP87bb7/NzTffzMMPP+w8HhgYCNh7Wf6turq6VpsTtXW0d7Spz8MPP8y99/6z3kxpaSlJSUmN/CQetmmO/bnzOAiObfDbiquL2VW8C4BBcYM8EVnjabT2/a60elj/Gfx4m71nZ8CURl3mrjGd+XXLITILK3nxt13834ReHgpYCCGEJ7jcvVJSUsLjjz9O+/bteeaZZygtLUVVVRRF4YorrmDr1q18+eWXdO/e3R3xNsr06dN5+umnuf7663n//fdrnUtISACod5jJccwxPBUREUFAQEC9bU0mEwUFBfUOZTkYDAZCQ0NrPZoVmxU2f2N/3Xdyo97q6MXpFN6J6IBod0d26jQaOP91GDwVUGHeHbDmf426hL9ey7MX9wZgVnoW67KK3B+nEEIIjznlJKe4uJjHHnuM9u3b8+yzz9ZKbiZPnszWrVuZM2cO3bp1c2e8DTZ9+nSeeuoprr32Wj7++OM6tUG9e/fGYDCwatWqOu9NS0sDYNAge8+ERqNhwIABbNiwoU5vzurVq1FV1dm2RcpaAaW54B8GXc9p1Fsd9Tge3crhVGk0cO5LkHqb/ecF90L6h426xPBO0Uwc2BZVhQe+3Uy12eqBQIUQQnhCo5McR3LToUMHnnvuOWdyo9FomDx5Mtu2bWP27NleS27Avp7PU089xTXXXMMnn3xSbz1QcHAwF1xwAYsXL2bTpk3O4+Xl5Xz88cd07tyZIUOGOI9PnjyZyspKPvyw9pfk66+/jk6n4/LLG1fH0qw4ZiF1v9A+S6kRHPtVDYkbcpKWXqIocPazMPzo3mm/PgCr3mnUJR49rzuxIQb2Hangxd92eSBIIYQQntCompxHH32Ut99+m/LycucsKq1WyxVXXMHjjz9Oly5dPBJkY7zzzjs8+eSTJCcnM3bsWObMmVPrfJs2bRg3bhxgLwj+66+/OOuss7jnnnsIDQ3lo48+Ijc3lwULFtTq/Zk6dSqffvop9957L5mZmXTv3p1ffvmFH374wdmj1SLZbLBjvv11j4sa9da8ijwySzPRKJrmU49TH0WBcTPsNTrLXoHfHwGrGUbc3aC3hwf68cKlfbh+5ho+WbGfcT3aMKyjbPkghBDNXaNWPNZoNM6CYrBPE09NTXXOWDrhjRSF//2vcTURp+K6667js88+O+75UaNGsXjxYufPO3bsYNq0abX2rpo+fTpjx9ZdJ6akpKTO3lW33XYbt99+e6OmyjerFY+zVsGn48EQBg9k2KdhN9C8vfN4dPmj9IrqxZfnf+nBIN1EVWHx87DkefvPZz4Gpz/Q4Lc//P1mvlx9gMTwAH67e6TMthJCCC9ozHfoKSU5Do4anJNxtLNapZ4BmlmS8+s0SH8P+lwBl3zQqLc+uvxR5u2dx429buTugXd7Jj5PWPISLHra/nr0wzDqIXtvz0mUmyyc88ZSDhRVcfmgJF64rI+HAxVCCPFvjfkOdWl2VXNY6E+4QFVPeahKVVVn0fGQ+GZaj3M8ox6AsdPtrxc/B38/bf+1OIlgg46XL+uLosDXaw/w5/Z8z8YphBDCJR5Z8bi5bekgjuPwdijNAV0AdDyjUW/NLssmvzIfvUZP/9j+HgrQg0bcA2c9Y3+97GX488kGJTpDU6K4aYR9084Hv9tMnrHak1EKIYRwQaMKj/fv3++pOIQ37Flof+4wEvQBjXqroxenb0xfAnSNe2+zMfy/9mLkXx+EFW/Yi5HPfvakQ1f3n92VlXsL2XawlLu/3sDsm1LRaqRXUwghmptGJTnt2rXzVBzCGxxJTuezGv3WFjtU9W9DbwGNzr6GTtq79pWRz3nxhImOQafl7SsHcP6by0jbV8Tbf2dw19jOTRi0EEKIhvDehlLCu6qNcMC+6GFjdhwHsKk250rHqfGp7o6s6Q2+ES54E1Bg9Yfw8z32qfUn0CE6iKcvtm/z8MZfu0nfV9gEgQohhGgMSXJaq32L7b0WUZ0hskOj3rqneA/FpmICdAH0ivKR/ZwGXgsT3gUUWPcpzL/zpInOxf3bcumAtthUuOurjRRV1DRNrEIIIRpEkpzWKuNP+3PncY1+q2OoamCbgei1PrRWTL8r7TuYKxrY8AX8dJt9X68TmHFRT1Kig8grreaurzZgtUmhvRBCNBeS5LRW+5bYnzue2ei3OrZyGBrXDPerclWfSXDpx6BoYdOX8MMtYLUct3mQQce7Vw8gQK9l2Z4CXvlDtn0QQojmQpKc1qg4C0qy7AW3yY2rqbHYLKzNXws000053aHXpTDxU/uvz5a58P1NYDn+UFS3uFDnwoDvLt7Lb1sPNVWkQgghTkCSnNYoc5n9OWEAGEIa9dZthduoMFcQZgija+TJt/NosXpcBJM+B40etv0AX10JNZXHbX5h3wTn+jn3fbOJjMNlTRWpEEKI45AkpzXafzTJ6TCy0W91Th2PG4JG8fE/Pt3Og8lf2RdLzFgIX0yAquLjNp92TjdSUyKpqLFy8xfrKK02N12sQggh6vDxbylRh6rC/qX21x1Ob/TbVx+y1+MMiWvh6+M0VOexMOUn8A+DA+kw83woy6u3qU6r4e0rBxAf5s++IxXcPns9ZuuJZ2gJIYTwHElyWpuifVB2ELR+kNS4mhqT1cSGwxsAH1gEsDGSh8J1v0BwG8jfCp+cDUX1r/4dHWzgoymDnIXIT87bJlubCCGEl0iS09pkLrc/Jw5q9FYO6/PXU2OrITYwlg6hjVtbp8WL6wU3/A4R7aE4Ez4ZD/nb6m3aKzGMNyf3R1FgTno2/1su26EIIYQ3SJLT2uTYh5saO6sKYNXBVQAMix/WOnegj+xgT3Rie0J5Hnx6DmSn19t0XI82PHpudwCe+WWH7FguhBBeIElOa3PgaJKT1PjhppUHVwIwPGG4OyNqWULi4PoF9qG+aiN8fiHsmF9v0xtHdGDykGRUFe74cgMbso9ftCyEEML9JMlpTSqLoGC3/XXbxiU5BVUF7Cq2L3SXmuAD+1W5IiACrvkBOp8Nlmr4+hpIe79OM0VRmHFRT07vEkOV2cr1M9fI1HIhhGhCkuS0Jjn2RfyI7AhBUY16a9oh+2ae3SO7E+kf6e7IWh6/ILhiDgy6AVDht4fgt0fq7Hel12p476oB9E0Kp6TSzJT/reZgSZV3YhZCiFZGkpzWxFGP08hZVXBMPU7CMHdG1LJpdXDeqzD2KfvPae/A3GvBXDuJCTLo+PS6wXSMCeKgsZopn6ymWDbzFEIIj5MkpzVx1uMMbtTbVFWVJOd4FAVG3A2X/s8+LX/HPPjsQqgorNUsMsiPz28cSnyYPxmHy7nu09WyWKAQQniYJDmthc0KuevsrxvZk5NRksGRqiP4a/3pH9vfA8H5gN6XwTU/2hcNzFkNH58Jh3fUapIYHsDnNwwhIlDPphwj136ymjJJdIQQwmMkyWktDm+HmnLwC4GYbo16q6MXZ2DcQAxagyei8w3tT4MbF0J4O/taOh+Pg12/1WrSuU0Is24aSliAng3ZJVz36RrKTcff5VwIIcSpkySntXAMVbUdCBpto9668pB96viweBmqOqmYrjB1EbQfCTVl8OUVsPw1+3YaR/VMCGP2TUMJ9dexLquYGz5dQ2WNJDpCCOFukuS0Foc22p8TBzXqbSariXV59mGuVr0+TmMERdmnmDtmXv05HX64BczVzia9EsOYddNQQvx1rM4s4nrp0RFCCLeTJKe1OLTJ/hzft1Fv23h4I9XWamICYugU3skDgfkorR7Ofw3OfRkULWz+GmaeB8ZcZ5M+bcP5/IYhBBt0pO8v4qqP0ymplFlXQgjhLpLktAYWE+Rvt79uZJLjWOV4WEIr3crBVUOmwjXfg3845K6FD06HfYudp/snRzBn6lB7MfKBEiZ9sIr80urjXk4IIUTDSZLTGhzeATaz/Ys2PLlRb5Wp426QMhpuXgRxvaGyAL64GJa94lw4sE/bcL65ZRhtQg3szi9n4vurOFBU6d2YhRDCB0iS0xocO1TViN6YI5VH2FFknwadGt/Kt3JwVWSKfeZVv6tBtcFfM+CrK6HKvp9V5zYhfHvrcJIjA8kuquSy91ey/WCpl4MWQoiWTZKc1uAU63GW5y4HoFdUL6IDot0dVeujD4AJ78CFb4HWALt/hQ9HO39/kiID+fbWYXRpE0x+qYmJ769k8a7D3o1ZCCFaMElyWoNTTHKW5S4DYGTbke6OqHUbMAVu/OOY9XTGwqp3wGYjNtSfubcMJzUlkooaKzd+tpY56dnejlgIIVokSXJ8ndUC+Vvtr+P7NfhtZpvZWY8zMlGSHLdL6Ae3LIGu54G1Bn5/BOZMhPLDhAXq+fyGoVzSPxGrTeWRH7bw3K87sNnUk15WCCHEPyTJ8XUFu8BSbV/pODKlwW/beHgj5eZyIv0j6Rnd04MBtmIBEXDFbDjvFdD5Q8af8N5pkPEnfjoNr0zqy91jOwPwwZJ93DJrnWwDIYQQjSBJjq9zDlX1AU3Df7sdQ1WnJZyGRpE/Jh6jKDD4JvsqybE9oOIwzLoUfn8UxWLi7rFdeHVSX/y0GhZuz2fCOyvYe6Tc21ELIUSLIN9evu7QZvtzXJ9GvW1Zjj3JOb3t6e6OSNSnTQ+Y+jcMudn+86q34cNRkLuOSwa05ZtbhxEX6s/eIxVMeHsFC7fnezdeIYRoASTJ8XWHjy4C2KbhQ06Hyg+RUZKBRtHI+jhNSR8A574Ek7+GoFg4stO+yedfM+gXH8D8O0YwpH0kZSYLUz9fyyt/7MJitXk7aiGEaLYkyfF1h+3r3BDbo8FvcQxV9YvpR5ghzBNRiRPpOh5uT4feE0G12hcO/HA0MWXbmT11KNcNbw/AW39nMPmjNA6WVHk3XiGEaKYkyfFlFQX2Gg+w747dQI6hKpk67kWBkXDpxzDpCwiMtvfIfTQG/aL/Y/o5Kbw5uT/BBh1rMos5541l/LEtz9sRCyFEsyNJji9z9OKEtwNDcIPeYrKaSM9LB2TqeLPQ40J7r07Pi+29OstfhXdTuTBwOwvuHEGftmEYq8zc/MU6nvxpK9Vmq7cjFkKIZkOSHF92CkNVa/LWUGWpIjYgli4RXTwUmGiUoGiYOBMunwUhCfYFBGdfSru/b+fbq1KYOrIDAJ+tyuK8N5exIbvYq+EKIURzIUmOLzviSHK6N/gti7IXATA6abTsOt7cdL8A/rsaUm8DRQPbfsDv/aE8GrOCT6cMICbEwN4jFVz63kpe+G0nJov06gghWjdJcnxZI3tybKqNRQfsSc4ZyWd4KirhCkMIjH/Ovq5OQn8wlcIv93PG4ktZdInChH4J2FR4b/FeLnhrOVtyjN6OWAghvEaSHF+lqv9MH29gT87Wgq0cqTpCkD6IIXFDPBiccFlCP7jpLzjnJfAPg8PbCP76El7nZT6fEE10sB+788u56J3lPDV/m6yULIRolSTJ8VVlh6DaCIoWojs36C1/Z/8N2AuO/bR+noxOuINGC0Nvhjs3wuCp9t/rnT9z+h/nsaz/Yib1CsWmwqcrMhn76hIWbD6Eqsr+V0KI1kOSHF/l6MWJ6gQ6Q4Pe8vcBe5JzZvKZnopKeEJgJJz3MvxnBXQ8E2xmAta8zYu51/D3sM10jtSSX2ri9jnrufbTNewvqPB2xEII0SQkyfFVhxtXdLzPuI/9xv3oNDpGJI7wYGDCY2K7w9Xfw5XfQHQXqComZcPz/KG9m497biFQa2Pp7iOc9doSZszfTklljbcjFkIIj5Ikx1c1sujYMatqaNxQQvxCPBWV8DRFgS5nw39WwUXvQFgSStkhxu59jk3Rj/FQ4hasViufrNjPqJcW88ny/dRYZGsIIYRvkiTHVxXstj/HNGytGxmq8jFaHfS/Gu5YB+Ofh8Bo9MZM/lP4HFtjn+D2iDVUVFUx4+ftnPXaEn7ZcgibTep1hBC+RZIcX6SqULDH/jrq5EXHueW5bD6yGQWFM5Jk6rhP0Rkg9T9w10Y441HwDyOwdB8PVL3GxoiHmRq4hIOFRm6bvZ7z3lrOwu35UpwshPAZkuT4osoiqC4BFIjqeNLmv2f+DsCguEHEBMZ4NjbhHYYQGPUg3L0Vxk6HwGiCq3J51PYB60If4HbDr+QcymPq52u56J0VLNp1WJIdIUSLJ0mOLyo82osTlgT6gJM2/23/bwCMbz/ek1GJ5sA/FEbcA3dvsQ9jhcQTUnOYB5QvWBd4JzMMX1Ccu5vrP13DhHdX8tvWQ1hlGEsI0UJJkuOLnENVJ+/FySrNYkfRDrSKlnHtxnk4MNFs+AUeHcbaBBe8ATHd8LNVMkX5laWGe/nQ8Bp+OWncOmsd415dwpers2XzTyFEi6PzdgDCAxw9OQ1YBNDRizM0figR/hGejEo0RzoDDLwOBlwLe/+CVe+i7P2Ls5Q1nGVYwy7a8UXxmTz7/Wm8ujCCa4e144ohyUQHN2ztJSGE8CZJcnxR4V77cwOKjn/LlKEqgX3qeaex9sfhnZD2Lmz+mq6WLJ7Wf8qj+jnMqxrGnIVn8uZfnTmvTwLXDGtH/6Rw2chVCNFsSZLjixo4XLW3ZC8ZJRnoNDqZOi7+EdsNLnzTXqC8+WtY+ykBBbu4XLeYy3WL2WZrx9zNo5i6YRjxiUlMSW3P+X3jCfSTf06EEM2L/Kvka6wWKNpnf32S4ap5e+cBMCJhBGGGME9HJlqawEh73c7QWyE7DdZ9Ctt+pCdZ9NR8zmO6WSw53JcffziN5+cPZUzvdlw2sC1DOkRK744QolmQJMfXlGSBzQw6fwhte9xmVpuVn/f+DMCFnS5squhES6Qo0G6Y/TH+edgyFzZ9he7gesZoNzBGu4Ey9X/8umkIb24YzsGwQVw8qB2XDEikbUSgt6MXQrRikuT4Gkc9TmRH0Bx/8tzKgys5XHWYcEM4o9uObprYRMsXGAlDb7E/CvbA5q9RN39NSEk2k3RLmMQSiiuDWbhoII//NYTKtiM4u087zu0dT1yYv7ejF0K0MpLk+BrnzKpOJ2z2Y8aPAJyXch56rd7DQQmfFN0ZznwMZfQjcCDdnvDsmE9EZYEz4SnNf5u/fh/Ak78MprLtSMb07cg5veNpEyoJjxDC8yTJ8TUN2M7BaDKy6IB9Q84JnSY0QVDCp2k0zuEs5dyXIXsVbP8J6/Z5hFbkc7F2BRdrV1CT/xarf+vGh7/051DMSLr1GsCYHm3oER8qNTxCCI+QJMfXFGbYn09QdPzzvp8x28x0i+xGt8huTRSYaBW0OugwEjqMRHvOi5CzBnbMw7L9Z/yMmYzQbmOEdhuUzCJzaRsWLe7H//wHEdZtFCN7tWdYSjQBflpvfwohhI+QJMfXFO23P0em1Hvaptr4audXAFzS+ZKmikq0RhoNJA+F5KHoznraXi+253dMO35Dd2Al7TX5XK/5HSy/Y97yPJs2d+RTtSeFsUOJ7jaCoV3b0icxDJ1WFmYXQpwaSXJ8icUEpbn21xEd6m2SdjCNzNJMgvRBXNhRZlWJJqIo9jqx6E4Yht0OpjLYtwTLrt8w71lEQEUOg5TdDGI3FP6AabmedUs7876mF6aEIbTpNpz+ndvSLS4UrUaGtoQQDSNJji8pOQCooA+CoOh6m3y580vAXosTpA9qwuCEOIYhBLqfj677+fZ/hIozUfcvpWLXYjSZywg0HWa4djvD2Q6HvsF6UGHnX8l8o3SlJKo//inD6NK1F/2SIwgyyD9jQoj6yb8OvqQ40/4c0d7+P+d/yS7NZknOEgCu6HpF08UlxMlEtEeJaE/wgCmgqlCYgW3fEow7l6DNXUOo6RA9lSx6kgVFf0ARHFkTxkq1E4eDumKL60NoymA6p3Smc1wIehniEkIgSY5vKT5ajxPRvt7T/9v6P1RURiaOpH1Y/W2E8DpFgejOaKI7EzHkJvux0oNYs1dTsmsZtux0Iow7iFGMjFPWQdU62D8H9sORP8NYqXYgP7grlti+hHXoT4dOPejYJgSDTgqahWhtJMnxJcf25PxLXkWecxuHm/vc3HQxCeEOoQloe00gqtcE+8/maji0EePe1ZTuX4vhyFaiq/YToxgZpWyEyo2Q+TVkQuXfBnapiRwytKcirAvaNt0Jb9+H9h26kBQZhEZqfITwWZLk+JITJDmfbv0Ui83C4LjB9Ivt15RRCeF+en9ITiUsOZWwM44eq6nElreVor1rqNi/FkPBFqIqMwlUTPRR9tHHvA8K/oYCYBuUqgFsIZFCQzJVoe1RojoSGN+FmOQeJCe0IcRfFskUoqWTJMeXOJKcyNozqw6UHWDu7rkATO09tYmDEqKJ+AWiSR5CdPIQoh2Jj9WCWrSPkqxNlGRtxpq/g+CSPUTXHCBUqaIvGVCTYU98CoBd9rcdUUPZq0mg2D8JU0h7tFHtCIjpQFh8Cm0S2hETGigLGArRAkiS4ytU9bg9Oa+tew2zzcyw+GGkxqc2eWhCeI1WhxLThYiYLkQMmvjPcUsNliN7KMjcTGnOTmyFezGUZhJRfYBwWwkxSikxailU7YQq4DCww/7WGlVLDlEU6GIp94+nJrgtSlgShph2hMYkEx6bTEx0NP5+8s+rEN4mfwt9RWUh1JQDCoQlOQ+vzVvLwqyFaBQNDwx+QP73KQSAzg9dfE/i4nsS9+9z1aWU5+2iMGsHlYd2oxbuw1CRQ0j1ISJtBfgpVpI4TJL1MFRshQogH9j9zyUqVQPZSgRGbRQVftGYAtugBsWiC0vAEJlIUFQiYVHxhEfFEmjQy99LITxEkpxGsNlsvPHGG3zwwQdkZmYSExPDpEmTmDFjBkFBXl5zxtGLE5pgr1cAqixVTF81HYBLO19K54jjb/UghDjKP5Tg9oMJbj+47jmrBbMxl6LcvRjz9mEqyEQtOYBfeS7B1XmEWwsJppJAxUQyeWDNs/cEVQGF9VxOVSgihFJNGOXacKr04Zj9I7EFREJgDLqQaPxCYwkMjyUwNIqgsGhCwyLw08tMMSEaQpKcRrjnnnt48803ufjii7nvvvvYsWMHb775Jhs2bODPP/9Eo/Hi2hxFdaePv7zmZbJKs4gNjOWuAXd5Jy4hfIlWhz6yHW0i29Gm95n1NlFN5ZQX5FJy+ADlBTnUFOdiLc1DW5GHofoIQTUFhFsLCaESraISRSlRailYDoAFe0JUfPwQrKpCCUGUK0FUakOo1gZTowvF4heC1RAO/mEoAeFoA8PRBYShDwhFHxiCf1Ao/sFhBAaFERQcik6m1ItWQJKcBtq2bRtvvfUWl1xyCd99953zeIcOHbjzzjv56quvuPLKK70X4L/qcb7a+RXf7P4GgBnDZxBmCPNOXEK0MoohmJDEroQkdj1hO9Viosp4BGNBHuXFeZiM+dSUHsFWUYBSUYi2uhD/mmICLSUEWUsJoRw/LGgVlXDKCaccrPlgBWqAyobHaFMVKjBQqQRQrfhTrQmkRhOAWRuERReIVReEVRcA+gDQ+YM+AEUfgMYvEI2fP1pDEBq/APSGQHSGIPz87Q9DQCB+AUH4BwSj9/OTYTjhdZLkNNCXX36JqqrcfffdtY5PnTqVadOmMWvWrGaR5Kjh7Zi9fRYvrnkRgDv738lpiad5Ly4hRL0UnYHAqLYERrVt8HuspkoqjIWUGwuoKi2iuqwIc0UxlooibFVGqC5BYzKiqynFz1yGn7UCg60Sf1sV/lQRpFajUVQ0ikoQ1QRRDSr2RMkKmN33+SyqBhN+mBQ9FvRY0GFR9FgUHRbFD6tGh1Xxw6bRY1P0WDV6VI0fNq0fqtb+Gq0faPWoWgOK1g90/xxTNDoUrR5Fq0PR6tBo7T9rNDo0Ov3RY3o0Oh1arR6NVodWp0ej06PV6tDq/ezHdTr0Oj80Oj06nb2N47ho+eR3sYHWrFmDRqNhyJAhtY77+/vTr18/1qxZ46XIQFVV1hbvJCc4iF+KVpCWZR+6uqLrFdzU+yavxSWEcC+tIZDQ2EBCY5NO3rg+qkpNdQWVZSVUVRgxVZRhqjBSU1WGpaoUS1UZNlMZqqkcjbkSLNUolmo0lmoUazU6axVamwmdzYT+6MNPNeFHDQa1Bn9q0CgqADrFhs6RSDnvf/QB9qSqGbOpClY0qNifbSioaLAp9tc2NNiOnrc/a7Ap/7xWlWOP/3NMdZ63HwcFVfnnmPPZ8fro++xb9Sio2F+rHC2POHrcfuyf18eeU4/e55/jjtKKY96nKEeP/6uNoqlzPfuz5l8/O67xrxjQoBiCGHrFw574bTopSXIa6ODBg0RHR2MwGOqcS0xMZOXKldTU1ODn51fnvMlkwmQyOX8uLS11e3x3kk95TBSU7Uev0XNn/zu5tue10l0shPiHouAXEIxfQDDhNLwHqaFUm41qUxWmqkpMVRVYTRXU1Jiw1lRjNZuwmKuxmWuwmquxWmqwWUyoZhOq47WlBtVqBosJrDUo1hr7s60GxWpGY6tBYzOjsVlQVAsa1YqiWtEcfe18xopGtaJVrWgdrznmodrQYUGLDb1Sf7alUVQ0jc3E1OO8buUKCAckyWnWKisr601wwN6b42hTX5Lz3HPP8dRTT3ksNgUYpAvFZK6ke/eJXNZzCkmhp/g/PSGEOEWKRoN/QBD+AUFAjLfDaRDVZsNqtWKxmJ0P1WLGZjOjWizYbDZsNis2mw3VZjna3gY2CzbVhs169Lhqw2a1otpsqKr92WazgM2GzWYDm/XocdXZnqPvQbW/B6sNm2pvCzaw2fuMsNnbgoqqHu0OU21He8ZsRz+ICtjsT0df42yr1n7tfP5XG0BVbShHXzvueWwb5eizerRbTvnXPRRqX09BxaoPJroJfi/ro6iqKvlmA/Tu3ZvDhw+Tn59f59ykSZOYO3cuJpOpwT05SUlJGI1GQkNDPRq3EEII4UtKS0sJCwtr0Heo9OQ0UEJCAtu3b8dkMtXp0cnNzSU6OrreBAfAYDActxdICCGEEJ7hxYVdWpbBgwdjs9lYvXp1rePV1dVs3LiRQYMGeSkyIYQQQtRHkpwGuvzyy1H+v727D4rivOMA/j30kLc73zAoL4KIqCiNRd6KUrAVo1ipYG0aqSFqSYyGkRgnjWkRDW1SG6MpL8GoMwnR1GkY09oE69SMJA2eBEUdk4gk6HkG0Kig8iYg8PQP57ZcOfUOONZbv5+ZG/eefW7v+wy6/Nx9dlelwptvvmnSvnPnTrS0tCA5OVmeYERERGQWT1dZKDg4GKtXr0Zubi6SkpIQHx8v3fE4JiZG3nvkEBERUQ8scqzw5ptvws/PDzt27EBRURHc3d2RlpaGV155Rd5HOhAREVEPvLpKBtbMDCciIqL/seZ3KA8/EBERkSKxyCEiIiJFYpFDREREisQih4iIiBSJRQ4REREpEoscIiIiUiQWOURERKRILHKIiIhIkVjkEBERkSKxyCEiIiJFYpFDREREisQih4iIiBSJTyGXgfGZqA0NDTInISIisi/G352WPF+cRY4MGhsbAQA+Pj4yJyEiIrJPjY2NGDp06D37qIQlpRD1q66uLtTW1kKj0UClUvXLNhsaGuDj44Pvvvvuvo+etxcck33gmB58ShsPwDHZC1uMSQiBxsZGeHp6wsHh3rNueCRHBg4ODvD29rbJtrVarWL+cRhxTPaBY3rwKW08AMdkL/p7TPc7gmPEicdERESkSCxyiIiISJFY5CjEkCFDkJmZiSFDhsgdpd9wTPaBY3rwKW08AMdkL+QeEyceExERkSLxSA4REREpEoscIiIiUiQWOURERKRILHKIiIhIkVjk2Lmuri5s27YNkyZNgpOTE3x8fPDCCy+gublZ7mi98s0332DDhg2IjIzEqFGjoNFoMG3aNPzxj3+02zH9v5aWFvj7+0OlUuG5556TO06v1dfXY926dQgICICTkxNGjRqFWbNm4fPPP5c7Wq80NTXh1VdfRXBwMDQaDdzd3REVFYV3333XomfkyOm1117D4sWLpb9Xfn5+9+z/xRdfYPbs2dBoNNBqtZg7dy5OnTo1IFktZemYWltbsXPnTvz85z+Hn58fnJ2d4e/vjyeeeAIVFRUDG/o+rP05dffb3/4WKpUKbm5utgtopd6MZ/fu3ZgxYwa0Wi3c3NwwdepUZGVl2Swjr66yc2vWrEF2djYSExMxb948VFRUICcnB9HR0fjkk0/ue8vrB81LL72EvLw8JCQkIDIyEmq1GsXFxfjggw/wgx/8AKWlpXB2dpY7Zp+sW7cOb7/9NpqamrB69Wrk5ubKHclqBoMBsbGxaGpqwooVKxAYGIibN2/i9OnTeOyxx/CrX/1K7ohW6erqQkxMDHQ6HVJSUhAZGYmWlhbs3bsXZWVlePHFF7F582a5Y96VSqXCiBEjEBISgvLycmi1Wly4cMFs39LSUsTGxsLLy0sqsnNzc3HlyhXodDoEBwcPYPK7s3RMZ8+exeTJkzFz5kzMmTMHnp6eOH/+PPLz89Hc3IyDBw9i1qxZAz8AM6z5OXV36tQphIWFwcnJCUIINDU12T6sBawdz/Lly1FQUIBFixZh1qxZcHBwgF6vx7Vr17Br1y7bhBRkt7766iuhUqlEUlKSSXt2drYAIN5//32ZkvXesWPHxI0bN3q0/+53vxMARE5Ojgyp+k95ebkYNGiQeOONNwQAsXr1arkj9crMmTOFt7e3qK2tlTtKv9DpdAKASE9PN2lva2sT48aNE0OHDpUnmIXOnTsnLU+ZMkX4+vretW9YWJjQaDSiurpaaquurhYajUbExcXZMqZVLB3TtWvXxMmTJ3u0f/3118LR0VFMnz7dRgmtZ83Pyaijo0OEhoaKBQsWiJiYGOHq6mrDhNaxZjy7du0SAMR77703AMn+x77+m08m9u7dCyEE0tPTTdpTU1Ph4uKCPXv2yBOsD0JDQ80+k+Txxx8HAHz11VcDHanfdHZ2IjU1FXPnzkVSUpLccXrtP//5D0pKSvDiiy9izJgxuH37NlpaWuSO1ScNDQ0AAE9PT5N2R0dHuLu7w9XVVY5YFvP397eoX1VVFY4dO4bFixfDy8tLavfy8sLixYvxySef4PLly7aKaRVLxzRy5EhMmzatR3tQUBCmTp36QO0zLB1Td9nZ2Thz5gxycnJskKhvLB2PEAKvvfYaQkJCsHTpUgB3niAuBuBEEoscO3bs2DE4ODggPDzcpN3JyQnTpk3DsWPHZErW/6qrqwEAHh4eMifpvW3btuHs2bN2eXqquwMHDgAAxo4diwULFsDZ2Rmurq4IDAy0y8IaAMLDwzFs2DD8+c9/RmFhIS5evIizZ89i/fr1KC8vx8aNG+WO2C+M+4Qf/ehHPdZFRkZCCIHy8vKBjmUTXV1duHTpkl3vMwwGAzIyMpCZmQlfX1+54/RaZWUlzp07h6ioKGRlZWHkyJHQarUYNmwYVq5cadPTb3wKuR2rra2Fu7u72dtle3l5QafTob29HY6OjjKk6z+dnZ3IysrC4MGDsWTJErnj9Iper0dmZiY2bNgAPz8/i87DP6gqKysB3DliOGHCBBQUFKC9vR1vvPEGli5ditu3b2PZsmUyp7TO8OHD8c9//hO/+c1v8Mtf/lJq12g02LdvHxYuXChfuH5UW1sLACZHcYyMbTU1NQOayVa2b9+OS5cuISMjQ+4ovfbss8/C398fa9eulTtKnxj3GX/729/Q3t6O3//+9xg3bhw+/vhjvP3226isrMThw4ehUqn6/btZ5NixlpaWuz4PxMnJSepj70VOeno6jh49ildffRUTJ06UO06vrFy5UhE7K+DOYWbgTgFQXFws/f1auHAh/P398fLLLyMlJcXuJr0br/RISEhAVFQU6uvrkZeXhyVLlmD//v2Ii4uTO2KfGU8rmttvdN9n2DudToe1a9fi0Ucfxcsvvyx3nF7Zu3cvDh48iJKSEgwebN+/qo37jKtXr+LQoUOYPXs2AGDRokUQQqCgoAAHDx7EvHnz+v277WsvRCZcXFzQ1tZmdl1ra6vUx55lZGQgNzcXTz/9NNavXy93nF7Zs2cPDh06hPz8fKjVarnj9Jnx6rYnnnjCpIAePnw4EhIScPnyZel/bvbiyy+/RFRUFOLi4vD6668jMTERK1asQElJCUaPHo3U1FR0dnbKHbPPjPsDc/sNpewzysvLMX/+fHh6eqKoqEgq3uxJfX090tPTsWLFCkRFRckdp8+M+wwvLy+pwDFKSUkBAHz66ac2+W4WOXbM09MT165dM7vDqqmpgbu7u10fxdm4cSP+8Ic/YNmyZdi+fbvccXqlra0Na9euRXx8PEaPHo2qqipUVVXBYDAAAG7evImqqircuHFD3qBW8Pb2BgCMHj26x7oxY8YAAK5fvz6gmfpq27ZtaG1txeLFi03aXVxcMH/+fBgMBrs+xWhknFht7pSUsc3cqSx7ceLECcTFxWHo0KEoLi6227Fs2rQJzc3NSE1NlfYZVVVVuHXrFoQQqKqqwnfffSd3TIvJuc9gkWPHwsLC0NXVhbKyMpP21tZWnDp1CqGhoTIl67uNGzdi06ZNSElJwa5du2xyrnYg3Lp1C1evXkVRUREmTJggvWJjYwHcOcozYcIE290jwgaME92Nk8G7M7Y98sgjA5qpr4y/4M0dreno6DD5056FhYUBAI4ePdpjXWlpKVQqFaZPnz7QsfrFiRMnpBscFhcX2/VEXYPBgObmZkRERJjsN8rKytDS0oIJEybY5NSOrQQHB8PJyclscW3zfcaAXrBO/er06dP3vE/O7t27ZUrWN5s2bRIAxNKlS0VnZ6fccfqkvb1dFBYW9ni99dZbAoCYO3euKCwsFJWVlXJHtVh9fb3QaDTCy8tLNDY2Su21tbXC1dVVBAYGypiud9LT0wUAsXnzZpP269evizFjxojhw4eLjo4OmdJZ5373KwkNDRUajUbU1NRIbTU1NUKj0Yif/vSnA5DQevcb04kTJ8SIESOEj4+Pyb1bHmT3GpNOpzO73wgKChJOTk6isLBQ/Pvf/x7YwPdxv59RcnKyACA+/PBDk/akpCQBQBw5csQmuXjHYzuXlpaG3NxcJCYmIj4+HhUVFcjOzsaMGTNw+PBhu5v8mZeXh+eeew5jx45FVlZWj/weHh6KmAB64cIFjBs3zm7veLxjxw4888wzmDJlCpYvX4729nbk5+fj0qVL+PjjjzFnzhy5I1rFYDAgJCQE169fR3JyMmbMmIH6+nrs3LkTFy5cQF5eHlatWiV3zLvavXu3dAo0JycH7e3teOGFFwAAvr6+0r1JgDuTcmfNmgVvb2+kpaVJn/n+++9x5MgRPProowM/ADMsHZPBYMD06dNRX1+PzMxMjB8/vse2EhMTH4h7HVnzczInNjYWx48ff2DueGzNeC5evIjw8HDcvHkTaWlp8PPzw4EDB1BUVIQnn3wSBQUFtglpk9KJBkxHR4fYsmWLCAwMFI6OjsLT01M8//zzJv/DticpKSkCwF1fMTExckfsF3q93q7veCyEEPv27RMRERHCxcVFuLm5ibi4OFFSUiJ3rF6rqqoSTz75pPDy8hKDBw8WGo1GREdHi3379skd7b5iYmKs+jej0+nET37yE+Hq6irc3NzEnDlzRHl5+cAHvwdLx1RcXHzPfQYAodfrZRtHd9b+nMx9/kG647G149Hr9WLJkiXC3d1dqNVqMWnSJLFlyxabHrHnkRwiIiJSJPs6l0FERERkIRY5REREpEgscoiIiEiRWOQQERGRIrHIISIiIkVikUNERESKxCKHiIiIFIlFDhERESkSixwi6nd+fn5QqVRWv4xP+u7e9tRTT8k6lv7Q1dWFH/7wh9KYPv300z5tb+PGjdK21qxZ0z8hiRSIRQ4RkY3t2bMHp06dAgBERERIT6HvrbS0NOlZTNu3b8f58+f7mJBImQbLHYCIlCc+Ph5Xrlwxafvss89w7do16f28efPg4uJi0sf4i3vRokVSW1hYmA2T2l5HRwc2bNggvTc+wLAvRo4ciaeeegp5eXlob29HZmYmdu/e3eftEikNn11FRAMiNjYWn332mfRer9fDz89PvkAD5O9//zuSkpIAABqNBleuXIGTk1Oft3vkyBHMnDkTAODo6Iiamhq4u7v3ebtESsLTVUT0wLnXnJzu831iY2Nx5coVpKamwsPDA25uboiOjpbmvHR2duL1119HYGAghgwZgnHjxiEjIwO3b982+711dXXIyspCREQEhg8fDkdHR3h5eeHxxx/HkSNHejWWHTt2SMsJCQlmC5xvv/0WzzzzDCZOnAgXFxc4OjpizJgxCA0NxcqVK1FYWNjjM1FRUfD29gYAtLe3o6CgoFf5iBTNZs83JyLqJiYmRgCQXnq9/q59u/dLSUkxWefr6yutCwoKEn5+fib9AQi1Wi0OHz4sFi5c2GMdALF8+fIe36nT6YSHh4fZ/gCESqUSr7zyilVjbm5uFmq1WtrGrl27evT58ssvhUajuev3AhDjx483u/3k5GSpT3R0tFXZiB4GPJJDRHbrzJkzuHDhAsLDwxESEiK13759G/Pnz8c//vEPeHt7Y/bs2XB0dJTWv/POO9Dr9dL7y5cvY8GCBfj+++8B3DmSFBkZifj4eHh4eAAAhBDYsGEDPvjgA4vz6XQ6k6NG5uYX/eUvf0FjY6NJn4SEBEREREjffTfh4eHScllZGVpbWy3ORvQwYJFDRHZt8+bN+OKLL3D8+HFpjgoA3Lp1C2FhYaisrMShQ4ewbds2aZ0QwmR+0JYtW1BXVwcAGDRoEEpKSnD06FEUFRVBr9cjNDRU6puRkWFxtpMnT5q8nzx5co8+1dXV0nJqairKysqwf/9+lJaW4vLlyzh9+jTWr19vdvtBQUHScltbG77++muLsxE9DHh1FRHZLa1WK90nRqVSISwsDCUlJdL6559/XrqC68c//rHJZy9duiQtHzhwQFp2dXXF1q1bsXXrVqmtoaFBWv7mm29w7tw5jB8//r75ul9hptVqoVare/QJCAiQlv/1r39h69atmDp1KiZNmgQfHx8EBwcjODjY7PZHjBhh8t54JIqI7mCRQ0R2y9/fH0OGDJHeu7m5mazvfqTj/9e1tbVJy8abEAJ3Cpp9+/bd83sNBoNFRc6NGzekZY1GY7bPmjVr8O6776KpqQnV1dUml5iPHDkSc+fOxUsvvYSpU6f2+KxWq73r9xERT1cRkR0bOnSoyXsHB4d7ru8vLS0tFvUbNmyYtNx93k13AQEBOHnyJNLS0jB58mQMGjRIWldXV4f3338f0dHRuHjxYo/P3rx5867fR0QscoiI4OvrKy37+/tDCHHP189+9jOLtvvII49Iyw0NDejo6DDbLyAgANnZ2Thz5gxu3bqFyspKvPXWW1LBc+PGDfz1r3/t8bn6+nqT96NGjbIoF9HDgkUOET305s2bJy2fP38ef/rTn9DV1WXSp66uDjt37rTqWVHTpk0zeV9RUdGjz4cffoiPPvpIOn2mVqsRGBiIJUuWwNnZWepnMBh6fPbMmTPSslqtNntKi+hhxjk5RPTQW7duHd555x1pTsv69euRn5+PoKAgODg4QK/Xo7KyEl1dXYiJibF4u1FRURg8eLB0BOf48eM9JhEfPnwYeXl5cHV1xZQpU+Dh4YGOjg4cP34cTU1NUr/uE5SNysrKpOWwsDCTooiIWOQQEcHT0xMfffQRFi1aJF0RdfHiRbPzYLrPmbkfV1dXzJ49GwcPHgQAFBcXY9myZWb7Njc3mxQt3U2cOBGpqakmbf9/GXxCQoLFuYgeFixyiIgAzJw5ExUVFdi+fTuKiopQUVGBhoYGODs7w8fHByEhIXjssceQmJho1XaffvppqcjZv38/2traTK4IW7VqFTw9PfH555/j22+/xdWrV9Hc3AytVovAwEAsWLAAaWlpPa6kKikpQU1NDYA7p6ruVjwRPcz4gE4iIhvq6OhAQECANKemsLAQv/jFL/q83VWrViE/Px8AkJycjD179vR5m0RKwyKHiMjG3nvvPaSkpAAAIiMjcfTo0T5tr66uDmPHjkVLSwvUajUqKiosum8P0cOGV1cREdnYr3/9a+lKq9LSUukp6b2Vk5Mj3avn2WefZYFDdBc8kkNERESKxCM5REREpEgscoiIiEiRWOQQERGRIrHIISIiIkVikUNERESKxCKHiIiIFIlFDhERESkSixwiIiJSJBY5REREpEgscoiIiEiR/gs9F8N+x0fvqQAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ], + "source": [ + "# Analytical solution from solving differential equations of deterministic rate models\n", + "# These models were solved mathematically on paper and in this section we are just plotting the obtained solutions\n", + "\n", + "t = np.linspace(0, 16, 1000)\n", + "\n", + "X_a = xa[0] * np.exp(-k1 * t)\n", + "\n", + "if k1 == k2:\n", + " X_b = xa[0] * k1 * t * np.exp(-k1 * t)\n", + " X_c = xa[0] * (1 + (k1**2) * (-t * (np.exp(-k1 * t) / k1) - (np.exp(-k1 * t) / k1**2)))\n", + "\n", + "else:\n", + " X_b = xa[0] * (k1 / (k1 - k2)) * (np.exp(-k2 * t) - np.exp(-k1 * t))\n", + " X_c = xa[0] * (1 + (k1 * k2 / (k1 - k2)) * ((np.exp(-k1 * t) / k1) - (np.exp(-k2 * t) / k2)))\n", + "\n", + "# Plot deterministic solution of number of A, B and C molecules vs time\n", + "\n", + "### BEGIN SOLUTION ###\n", + "fig = plt.figure(figsize=(6, 6))\n", + "plt.plot(t, X_a, label=r\"A\")\n", + "plt.plot(t, X_b, label=r\"B\")\n", + "plt.plot(t, X_c, label=r\"C\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "### END SOLUTION ###" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1. - Solving Differential Equations Numerically" + ], + "metadata": { + "id": "ayMYvWWhEH9A" + } + }, + { + "cell_type": "markdown", + "source": [ + "What if instead of solving on paper the found differential equations we decided to do it numerically coding? Two simple alternatives could bring expressive results. They are the Forward Euler Method and the Crank-Nicolson (Trapezoid Rule).\n" + ], + "metadata": { + "id": "hbppJVnlcvIo" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1.1 - Forward Euler Method" + ], + "metadata": { + "id": "IZGXRXGFaUL-" + } + }, + { + "cell_type": "markdown", + "source": [ + "The Forward Euler Method is a numerical technique for approximating the solutions to ordinary differential equations (ODEs). It is well known to be a simple and straightforward method that's useful for solving ODEs when you can't find an exact analytical solution.\n", + "\n", + "Basically, it approximates the solution to a first-order ordinary differential equation of the form:\n", + "\n", + "\\begin{equation}\n", + "\\frac{dy}{dx} = f(x, y)\n", + "\\end{equation}\n", + "\n", + "The Forward Euler Method also works through an iterative approach that breaks down the continuous ODE into discrete steps, by using the following formula to update the solution at each step:\n", + "\n", + "\\begin{equation}\n", + "y_(n+1) = y_n + h * f(x_n, y_n)\n", + "\\end{equation}\n", + "\n", + "In this formula,\n", + "\n", + "$y_(n+1)$ is the new approximation of the solution at the next step.\n", + "\n", + "\n", + "$y_n$ is the previous approximation of the solution at the current step.\n", + "\n", + "$h$ is the step size, which represents the size of the interval over which you're approximating the solution.\n", + "\n", + "$x_n$ is the current value of the independent variable at the nth step.\n", + "\n", + "$f(x_n, y_n)$ is the rate of change of y at the current point $(x_n, y_n).$\n", + "\n", + "This way, by applying the formula and" + ], + "metadata": { + "id": "rbgjRVf7aVcq" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Now, implement the found differential equations into the Forward Euler Method to find and plot the numerically solution.**" + ], + "metadata": { + "id": "bQllXd0omV3H" + } + }, + { + "cell_type": "code", + "source": [ + "def solve_differential_equations(k1, k2, xa0, t_max, h, print_flag=False):\n", + " # Create arrays to preallocate the results\n", + " num_steps = int(t_max / h) + 1\n", + " t_values = np.linspace(0, t_max, num_steps)\n", + " Ca_values = np.zeros(num_steps)\n", + " Cb_values = np.zeros(num_steps)\n", + " Cc_values = np.zeros(num_steps)\n", + "\n", + " # Set initial conditions\n", + " Ca_values[0] = xa0\n", + " Cb_values[0] = 0.0\n", + " Cc_values[0] = 0.0\n", + "\n", + " for i in range(num_steps - 1):\n", + " Ca_next = Ca_values[i] - k1 * Ca_values[i] * h\n", + " Cb_next = Cb_values[i] + (k1 * Ca_values[i] - k2 * Cb_values[i]) * h\n", + " Cc_next = Cc_values[i] + k2 * Cb_values[i] * h\n", + "\n", + " # Store the results in the preallocated arrays\n", + " Ca_values[i + 1] = Ca_next\n", + " Cb_values[i + 1] = Cb_next\n", + " Cc_values[i + 1] = Cc_next\n", + "\n", + " # Print intermediate results if the flag is True\n", + " if print_flag:\n", + " print(\"\\nt =\", t_values[i])\n", + " print(\"Ca =\", Ca_next)\n", + " print(\"Cb =\", Cb_next)\n", + " print(\"Cc =\", Cc_next)\n", + "\n", + " return t_values, Ca_values, Cb_values, Cc_values\n", + "\n", + "# Define the parameters and initial conditions\n", + "k1 = 0.5\n", + "k2 = 1.0\n", + "xa0 = 1000.0 # Initial concentration of Ca\n", + "t_max = 16.0 # Maximum time\n", + "h = 0.1 # Time step\n", + "\n", + "# Solve the differential equations using the function\n", + "t_values, Ca_values, Cb_values, Cc_values = solve_differential_equations(k1, k2, xa0, t_max, h, print_flag=True)\n", + "\n", + "# Plot the concentration profiles\n", + "fig = plt.figure(figsize=(6, 6))\n", + "plt.plot(t_values, Ca_values, label=r\"A\")\n", + "plt.plot(t_values, Cb_values, label=r\"B\")\n", + "plt.plot(t_values, Cc_values, label=r\"C\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "plt.title('Forward Euler Method')\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "8nuMtwo0cH4f", + "outputId": "ffeea791-8b13-4b1e-a194-9d69f261201c" + }, + "execution_count": 47, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\n", + "t = 0.0\n", + "Ca = 950.0\n", + "Cb = 50.0\n", + "Cc = 0.0\n", + "\n", + "t = 0.1\n", + "Ca = 902.5\n", + "Cb = 92.5\n", + "Cc = 5.0\n", + "\n", + "t = 0.2\n", + "Ca = 857.375\n", + "Cb = 128.375\n", + "Cc = 14.25\n", + "\n", + "t = 0.30000000000000004\n", + "Ca = 814.50625\n", + "Cb = 158.40625\n", + "Cc = 27.0875\n", + "\n", + "t = 0.4\n", + "Ca = 773.7809375\n", + "Cb = 183.2909375\n", + "Cc = 42.928125\n", + "\n", + "t = 0.5\n", + "Ca = 735.091890625\n", + "Cb = 203.65089062500002\n", + "Cc = 61.25721875000001\n", + "\n", + "t = 0.6000000000000001\n", + "Ca = 698.3372960937501\n", + "Cb = 220.04039609375002\n", + "Cc = 81.62230781250001\n", + "\n", + "t = 0.7000000000000001\n", + "Ca = 663.4204312890625\n", + "Cb = 232.95322128906253\n", + "Cc = 103.62634742187501\n", + "\n", + "t = 0.8\n", + "Ca = 630.2494097246094\n", + "Cb = 242.8289207246094\n", + "Cc = 126.92166955078126\n", + "\n", + "t = 0.9\n", + "Ca = 598.736939238379\n", + "Cb = 250.05849913837892\n", + "Cc = 151.2045616232422\n", + "\n", + "t = 1.0\n", + "Ca = 568.8000922764601\n", + "Cb = 254.98949618645997\n", + "Cc = 176.2104115370801\n", + "\n", + "t = 1.1\n", + "Ca = 540.360087662637\n", + "Cb = 257.930551181637\n", + "Cc = 201.7093611557261\n", + "\n", + "t = 1.2000000000000002\n", + "Ca = 513.3420832795052\n", + "Cb = 259.1555004466051\n", + "Cc = 227.5024162738898\n", + "\n", + "t = 1.3\n", + "Ca = 487.67497911553\n", + "Cb = 258.90705456591985\n", + "Cc = 253.4179663185503\n", + "\n", + "t = 1.4000000000000001\n", + "Ca = 463.29123015975347\n", + "Cb = 257.4000980651044\n", + "Cc = 279.3086717751423\n", + "\n", + "t = 1.5\n", + "Ca = 440.1266686517658\n", + "Cb = 254.82464976658162\n", + "Cc = 305.0486815816527\n", + "\n", + "t = 1.6\n", + "Ca = 418.1203352191775\n", + "Cb = 251.34851822251176\n", + "Cc = 330.53114655831087\n", + "\n", + "t = 1.7000000000000002\n", + "Ca = 397.2143184582186\n", + "Cb = 247.11968316121946\n", + "Cc = 355.66599838056203\n", + "\n", + "t = 1.8\n", + "Ca = 377.3536025353077\n", + "Cb = 242.26843076800844\n", + "Cc = 380.377966696684\n", + "\n", + "t = 1.9000000000000001\n", + "Ca = 358.4859224085423\n", + "Cb = 236.909267817973\n", + "Cc = 404.6048097734848\n", + "\n", + "t = 2.0\n", + "Ca = 340.5616262881152\n", + "Cb = 231.1426371566028\n", + "Cc = 428.29573655528213\n", + "\n", + "t = 2.1\n", + "Ca = 323.5335449737094\n", + "Cb = 225.05645475534828\n", + "Cc = 451.4100002709424\n", + "\n", + "t = 2.2\n", + "Ca = 307.35686772502396\n", + "Cb = 218.72748652849893\n", + "Cc = 473.91564574647725\n", + "\n", + "t = 2.3000000000000003\n", + "Ca = 291.98902433877277\n", + "Cb = 212.22258126190025\n", + "Cc = 495.78839439932716\n", + "\n", + "t = 2.4000000000000004\n", + "Ca = 277.38957312183413\n", + "Cb = 205.59977435264886\n", + "Cc = 517.0106525255172\n", + "\n", + "t = 2.5\n", + "Ca = 263.52009446574243\n", + "Cb = 198.9092755734757\n", + "Cc = 537.5706299607821\n", + "\n", + "t = 2.6\n", + "Ca = 250.3440897424553\n", + "Cb = 192.19435273941525\n", + "Cc = 557.4615575181297\n", + "\n", + "t = 2.7\n", + "Ca = 237.82688525533254\n", + "Cb = 185.4921219525965\n", + "Cc = 576.6809927920712\n", + "\n", + "t = 2.8000000000000003\n", + "Ca = 225.9355409925659\n", + "Cb = 178.8342540201035\n", + "Cc = 595.2302049873308\n", + "\n", + "t = 2.9000000000000004\n", + "Ca = 214.6387639429376\n", + "Cb = 172.24760566772144\n", + "Cc = 613.1136303893412\n", + "\n", + "t = 3.0\n", + "Ca = 203.9068257457907\n", + "Cb = 165.75478329809619\n", + "Cc = 630.3383909561134\n", + "\n", + "t = 3.1\n", + "Ca = 193.71148445850116\n", + "Cb = 159.3746462555761\n", + "Cc = 646.9138692859229\n", + "\n", + "t = 3.2\n", + "Ca = 184.0259102355761\n", + "Cb = 153.12275585294356\n", + "Cc = 662.8513339114805\n", + "\n", + "t = 3.3000000000000003\n", + "Ca = 174.8246147237973\n", + "Cb = 147.011775779428\n", + "Cc = 678.1636094967749\n", + "\n", + "t = 3.4000000000000004\n", + "Ca = 166.08338398760745\n", + "Cb = 141.05182893767508\n", + "Cc = 692.8647870747177\n", + "\n", + "t = 3.5\n", + "Ca = 157.77921478822708\n", + "Cb = 135.25081524328795\n", + "Cc = 706.9699699684852\n", + "\n", + "t = 3.6\n", + "Ca = 149.89025404881573\n", + "Cb = 129.6146944583705\n", + "Cc = 720.495051492814\n", + "\n", + "t = 3.7\n", + "Ca = 142.39574134637496\n", + "Cb = 124.14773771497424\n", + "Cc = 733.456520938651\n", + "\n", + "t = 3.8000000000000003\n", + "Ca = 135.2759542790562\n", + "Cb = 118.85275101079557\n", + "Cc = 745.8712947101484\n", + "\n", + "t = 3.9000000000000004\n", + "Ca = 128.5121565651034\n", + "Cb = 113.73127362366883\n", + "Cc = 757.7565698112279\n", + "\n", + "t = 4.0\n", + "Ca = 122.08654873684823\n", + "Cb = 108.7837540895571\n", + "Cc = 769.1296971735948\n", + "\n", + "t = 4.1000000000000005\n", + "Ca = 115.98222130000582\n", + "Cb = 104.00970611744381\n", + "Cc = 780.0080725825504\n", + "\n", + "t = 4.2\n", + "Ca = 110.18311023500553\n", + "Cb = 99.40784657069972\n", + "Cc = 790.4090431942948\n", + "\n", + "t = 4.3\n", + "Ca = 104.67395472325525\n", + "Cb = 94.97621742538003\n", + "Cc = 800.3498278513648\n", + "\n", + "t = 4.4\n", + "Ca = 99.44025698709248\n", + "Cb = 90.7122934190048\n", + "Cc = 809.8474495939029\n", + "\n", + "t = 4.5\n", + "Ca = 94.46824413773786\n", + "Cb = 86.61307692645894\n", + "Cc = 818.9186789358033\n", + "\n", + "t = 4.6000000000000005\n", + "Ca = 89.74483193085096\n", + "Cb = 82.67518144069994\n", + "Cc = 827.5799866284492\n", + "\n", + "t = 4.7\n", + "Ca = 85.25759033430842\n", + "Cb = 78.8949048931725\n", + "Cc = 835.8475047725192\n", + "\n", + "t = 4.800000000000001\n", + "Ca = 80.994710817593\n", + "Cb = 75.26829392057067\n", + "Cc = 843.7369952618365\n", + "\n", + "t = 4.9\n", + "Ca = 76.94497527671335\n", + "Cb = 71.79120006939326\n", + "Cc = 851.2638246538935\n", + "\n", + "t = 5.0\n", + "Ca = 73.09772651287768\n", + "Cb = 68.45932882628959\n", + "Cc = 858.4429446608328\n", + "\n", + "t = 5.1000000000000005\n", + "Ca = 69.4428401872338\n", + "Cb = 65.26828226930452\n", + "Cc = 865.2888775434618\n", + "\n", + "t = 5.2\n", + "Ca = 65.97069817787211\n", + "Cb = 62.213596051735756\n", + "Cc = 871.8157057703922\n", + "\n", + "t = 5.300000000000001\n", + "Ca = 62.6721632689785\n", + "Cb = 59.29077135545579\n", + "Cc = 878.0370653755658\n", + "\n", + "t = 5.4\n", + "Ca = 59.538555105529575\n", + "Cb = 56.49530238335913\n", + "Cc = 883.9661425111113\n", + "\n", + "t = 5.5\n", + "Ca = 56.5616273502531\n", + "Cb = 53.822699900299696\n", + "Cc = 889.6156727494473\n", + "\n", + "t = 5.6000000000000005\n", + "Ca = 53.733545982740445\n", + "Cb = 51.26851127778238\n", + "Cc = 894.9979427394773\n", + "\n", + "t = 5.7\n", + "Ca = 51.04686868360342\n", + "Cb = 48.828337449141166\n", + "Cc = 900.1247938672554\n", + "\n", + "t = 5.800000000000001\n", + "Ca = 48.49452524942325\n", + "Cb = 46.497847138407224\n", + "Cc = 905.0076276121696\n", + "\n", + "t = 5.9\n", + "Ca = 46.06979898695209\n", + "Cb = 44.27278868703766\n", + "Cc = 909.6574123260103\n", + "\n", + "t = 6.0\n", + "Ca = 43.76630903760448\n", + "Cb = 42.1489997676815\n", + "Cc = 914.0846911947141\n", + "\n", + "t = 6.1000000000000005\n", + "Ca = 41.57799358572426\n", + "Cb = 40.12241524279358\n", + "Cc = 918.2995911714822\n", + "\n", + "t = 6.2\n", + "Ca = 39.49909390643805\n", + "Cb = 38.189073397800435\n", + "Cc = 922.3118326957616\n", + "\n", + "t = 6.300000000000001\n", + "Ca = 37.52413921111614\n", + "Cb = 36.34512075334229\n", + "Cc = 926.1307400355416\n", + "\n", + "t = 6.4\n", + "Ca = 35.64793225056034\n", + "Cb = 34.58681563856387\n", + "Cc = 929.7652521108758\n", + "\n", + "t = 6.5\n", + "Ca = 33.86553563803232\n", + "Cb = 32.9105306872355\n", + "Cc = 933.2239336747323\n", + "\n", + "t = 6.6000000000000005\n", + "Ca = 32.1722588561307\n", + "Cb = 31.312754400413567\n", + "Cc = 936.5149867434558\n", + "\n", + "t = 6.7\n", + "Ca = 30.56364591332417\n", + "Cb = 29.790091903178745\n", + "Cc = 939.6462621834971\n", + "\n", + "t = 6.800000000000001\n", + "Ca = 29.03546361765796\n", + "Cb = 28.33926500852708\n", + "Cc = 942.625271373815\n", + "\n", + "t = 6.9\n", + "Ca = 27.58369043677506\n", + "Cb = 26.95711168855727\n", + "Cc = 945.4591978746678\n", + "\n", + "t = 7.0\n", + "Ca = 26.20450591493631\n", + "Cb = 25.640585041540294\n", + "Cc = 948.1549090435235\n", + "\n", + "t = 7.1000000000000005\n", + "Ca = 24.894280619189495\n", + "Cb = 24.38675183313308\n", + "Cc = 950.7189675476775\n", + "\n", + "t = 7.2\n", + "Ca = 23.64956658823002\n", + "Cb = 23.192790680779247\n", + "Cc = 953.1576427309908\n", + "\n", + "t = 7.300000000000001\n", + "Ca = 22.467088258818517\n", + "Cb = 22.055989942112824\n", + "Cc = 955.4769217990687\n", + "\n", + "t = 7.4\n", + "Ca = 21.34373384587759\n", + "Cb = 20.973745360842468\n", + "Cc = 957.68252079328\n", + "\n", + "t = 7.5\n", + "Ca = 20.27654715358371\n", + "Cb = 19.9435575170521\n", + "Cc = 959.7798953293642\n", + "\n", + "t = 7.6000000000000005\n", + "Ca = 19.262719795904523\n", + "Cb = 18.963029123026075\n", + "Cc = 961.7742510810695\n", + "\n", + "t = 7.7\n", + "Ca = 18.299583806109297\n", + "Cb = 18.029862200518693\n", + "Cc = 963.6705539933721\n", + "\n", + "t = 7.800000000000001\n", + "Ca = 17.38460461580383\n", + "Cb = 17.14185517077229\n", + "Cc = 965.4735402134239\n", + "\n", + "t = 7.9\n", + "Ca = 16.51537438501364\n", + "Cb = 16.29689988448525\n", + "Cc = 967.1877257305011\n", + "\n", + "t = 8.0\n", + "Ca = 15.689605665762958\n", + "Cb = 15.492978615287406\n", + "Cc = 968.8174157189496\n", + "\n", + "t = 8.1\n", + "Ca = 14.905125382474811\n", + "Cb = 14.728161037046814\n", + "Cc = 970.3667135804784\n", + "\n", + "t = 8.200000000000001\n", + "Ca = 14.159869113351071\n", + "Cb = 14.000601202465873\n", + "Cc = 971.839529684183\n", + "\n", + "t = 8.3\n", + "Ca = 13.451875657683518\n", + "Cb = 13.308534537886839\n", + "Cc = 973.2395898044297\n", + "\n", + "t = 8.4\n", + "Ca = 12.779281874799342\n", + "Cb = 12.65027486698233\n", + "Cc = 974.5704432582183\n", + "\n", + "t = 8.5\n", + "Ca = 12.140317781059375\n", + "Cb = 12.024211474024066\n", + "Cc = 975.8354707449166\n", + "\n", + "t = 8.6\n", + "Ca = 11.533301892006406\n", + "Cb = 11.428806215674628\n", + "Cc = 977.0378918923191\n", + "\n", + "t = 8.700000000000001\n", + "Ca = 10.956636797406086\n", + "Cb = 10.862590688707485\n", + "Cc = 978.1807725138865\n", + "\n", + "t = 8.8\n", + "Ca = 10.408804957535782\n", + "Cb = 10.32416345970704\n", + "Cc = 979.2670315827572\n", + "\n", + "t = 8.9\n", + "Ca = 9.888364709658994\n", + "Cb = 9.812187361613127\n", + "Cc = 980.2994479287279\n", + "\n", + "t = 9.0\n", + "Ca = 9.393946474176044\n", + "Cb = 9.325386860934763\n", + "Cc = 981.2806666648892\n", + "\n", + "t = 9.1\n", + "Ca = 8.924249150467242\n", + "Cb = 8.862545498550089\n", + "Cc = 982.2132053509827\n", + "\n", + "t = 9.200000000000001\n", + "Ca = 8.47803669294388\n", + "Cb = 8.422503406218443\n", + "Cc = 983.0994599008377\n", + "\n", + "t = 9.3\n", + "Ca = 8.054134858296685\n", + "Cb = 8.004154900243792\n", + "Cc = 983.9417102414595\n", + "\n", + "t = 9.4\n", + "Ca = 7.651428115381851\n", + "Cb = 7.6064461531342475\n", + "Cc = 984.742125731484\n", + "\n", + "t = 9.5\n", + "Ca = 7.268856709612758\n", + "Cb = 7.228372943589916\n", + "Cc = 985.5027703467974\n", + "\n", + "t = 9.600000000000001\n", + "Ca = 6.905413874132121\n", + "Cb = 6.868978484711562\n", + "Cc = 986.2256076411564\n", + "\n", + "t = 9.700000000000001\n", + "Ca = 6.560143180425515\n", + "Cb = 6.527351329947011\n", + "Cc = 986.9125054896276\n", + "\n", + "t = 9.8\n", + "Ca = 6.232136021404239\n", + "Cb = 6.202623355973586\n", + "Cc = 987.5652406226224\n", + "\n", + "t = 9.9\n", + "Ca = 5.920529220334027\n", + "Cb = 5.893967821446439\n", + "Cc = 988.1855029582197\n", + "\n", + "t = 10.0\n", + "Ca = 5.624502759317325\n", + "Cb = 5.6005975003184965\n", + "Cc = 988.7748997403643\n", + "\n", + "t = 10.100000000000001\n", + "Ca = 5.343277621351459\n", + "Cb = 5.321762888252513\n", + "Cc = 989.3349594903962\n", + "\n", + "t = 10.200000000000001\n", + "Ca = 5.076113740283886\n", + "Cb = 5.056750480494834\n", + "Cc = 989.8671357792214\n", + "\n", + "t = 10.3\n", + "Ca = 4.822308053269691\n", + "Cb = 4.804881119459545\n", + "Cc = 990.3728108272709\n", + "\n", + "t = 10.4\n", + "Ca = 4.581192650606207\n", + "Cb = 4.565508410177076\n", + "Cc = 990.8532989392169\n", + "\n", + "t = 10.5\n", + "Ca = 4.352133018075897\n", + "Cb = 4.338017201689679\n", + "Cc = 991.3098497802346\n", + "\n", + "t = 10.600000000000001\n", + "Ca = 4.134526367172102\n", + "Cb = 4.121822132424506\n", + "Cc = 991.7436515004035\n", + "\n", + "t = 10.700000000000001\n", + "Ca = 3.9278000488134968\n", + "Cb = 3.9163662375406605\n", + "Cc = 992.155833713646\n", + "\n", + "t = 10.8\n", + "Ca = 3.731410046372822\n", + "Cb = 3.721119616227269\n", + "Cc = 992.5474703374\n", + "\n", + "t = 10.9\n", + "Ca = 3.544839544054181\n", + "Cb = 3.535578156923183\n", + "Cc = 992.9195822990227\n", + "\n", + "t = 11.0\n", + "Ca = 3.367597566851472\n", + "Cb = 3.359262318433574\n", + "Cc = 993.273140114715\n", + "\n", + "t = 11.100000000000001\n", + "Ca = 3.1992176885088983\n", + "Cb = 3.19171596493279\n", + "Cc = 993.6090663465584\n", + "\n", + "t = 11.200000000000001\n", + "Ca = 3.0392568040834536\n", + "Cb = 3.032505252864956\n", + "Cc = 993.9282379430517\n", + "\n", + "t = 11.3\n", + "Ca = 2.887293963879281\n", + "Cb = 2.8812175677826333\n", + "Cc = 994.2314884683382\n", + "\n", + "t = 11.4\n", + "Ca = 2.742929265685317\n", + "Cb = 2.737460509198334\n", + "Cc = 994.5196102251165\n", + "\n", + "t = 11.5\n", + "Ca = 2.605782802401051\n", + "Cb = 2.6008609215627665\n", + "Cc = 994.7933562760363\n", + "\n", + "t = 11.600000000000001\n", + "Ca = 2.475493662280998\n", + "Cb = 2.4710639695265426\n", + "Cc = 995.0534423681926\n", + "\n", + "t = 11.700000000000001\n", + "Ca = 2.3517189791669484\n", + "Cb = 2.347732255687938\n", + "Cc = 995.3005487651452\n", + "\n", + "t = 11.8\n", + "Ca = 2.234133030208601\n", + "Cb = 2.2305449790774916\n", + "Cc = 995.535321990714\n", + "\n", + "t = 11.9\n", + "Ca = 2.122426378698171\n", + "Cb = 2.1191971326801724\n", + "Cc = 995.7583764886217\n", + "\n", + "t = 12.0\n", + "Ca = 2.0163050597632624\n", + "Cb = 2.0133987383470635\n", + "Cc = 995.9702962018897\n", + "\n", + "t = 12.100000000000001\n", + "Ca = 1.9154898067750992\n", + "Cb = 1.9128741175005204\n", + "Cc = 996.1716360757245\n", + "\n", + "t = 12.200000000000001\n", + "Ca = 1.8197153164363442\n", + "Cb = 1.8173611960892233\n", + "Cc = 996.3629234874745\n", + "\n", + "t = 12.3\n", + "Ca = 1.728729550614527\n", + "Cb = 1.7266108423021183\n", + "Cc = 996.5446596070834\n", + "\n", + "t = 12.4\n", + "Ca = 1.6422930730838008\n", + "Cb = 1.6403862356026329\n", + "Cc = 996.7173206913136\n", + "\n", + "t = 12.5\n", + "Ca = 1.5601784194296107\n", + "Cb = 1.5584622656965597\n", + "Cc = 996.8813593148739\n", + "\n", + "t = 12.600000000000001\n", + "Ca = 1.4821694984581302\n", + "Cb = 1.4806249600983843\n", + "Cc = 997.0372055414435\n", + "\n", + "t = 12.700000000000001\n", + "Ca = 1.4080610235352236\n", + "Cb = 1.4066709390114525\n", + "Cc = 997.1852680374534\n", + "\n", + "t = 12.8\n", + "Ca = 1.3376579723584623\n", + "Cb = 1.3364068962870683\n", + "Cc = 997.3259351313545\n", + "\n", + "t = 12.9\n", + "Ca = 1.2707750737405392\n", + "Cb = 1.2696491052762846\n", + "Cc = 997.4595758209832\n", + "\n", + "t = 13.0\n", + "Ca = 1.2072363200535123\n", + "Cb = 1.206222948435683\n", + "Cc = 997.5865407315108\n", + "\n", + "t = 13.100000000000001\n", + "Ca = 1.1468745040508368\n", + "Cb = 1.1459624695947903\n", + "Cc = 997.7071630263544\n", + "\n", + "t = 13.200000000000001\n", + "Ca = 1.0895307788482949\n", + "Cb = 1.088709947837853\n", + "Cc = 997.8217592733138\n", + "\n", + "t = 13.3\n", + "Ca = 1.0350542399058802\n", + "Cb = 1.0343154919964825\n", + "Cc = 997.9306302680975\n", + "\n", + "t = 13.4\n", + "Ca = 0.9833015279105862\n", + "Cb = 0.9826366547921283\n", + "Cc = 998.0340618172971\n", + "\n", + "t = 13.5\n", + "Ca = 0.9341364515150569\n", + "Cb = 0.9335380657084448\n", + "Cc = 998.1323254827763\n", + "\n", + "t = 13.600000000000001\n", + "Ca = 0.887429628939304\n", + "Cb = 0.8868910817133532\n", + "Cc = 998.2256792893471\n", + "\n", + "t = 13.700000000000001\n", + "Ca = 0.8430581474923388\n", + "Cb = 0.8425734549889831\n", + "Cc = 998.3143683975185\n", + "\n", + "t = 13.8\n", + "Ca = 0.8009052401177218\n", + "Cb = 0.8004690168647017\n", + "Cc = 998.3986257430174\n", + "\n", + "t = 13.9\n", + "Ca = 0.7608599781118357\n", + "Cb = 0.7604673771841176\n", + "Cc = 998.4786726447039\n", + "\n", + "t = 14.0\n", + "Ca = 0.7228169792062439\n", + "Cb = 0.7224636383712977\n", + "Cc = 998.5547193824224\n", + "\n", + "t = 14.100000000000001\n", + "Ca = 0.6866761302459317\n", + "Cb = 0.6863581234944801\n", + "Cc = 998.6269657462595\n", + "\n", + "t = 14.200000000000001\n", + "Ca = 0.6523423237336351\n", + "Cb = 0.6520561176573287\n", + "Cc = 998.695601558609\n", + "\n", + "t = 14.3\n", + "Ca = 0.6197252075469534\n", + "Cb = 0.6194676220782777\n", + "Cc = 998.7608071703747\n", + "\n", + "t = 14.4\n", + "Ca = 0.5887389471696057\n", + "Cb = 0.5885071202477976\n", + "Cc = 998.8227539325826\n", + "\n", + "t = 14.5\n", + "Ca = 0.5593019998111255\n", + "Cb = 0.5590933555814981\n", + "Cc = 998.8816046446074\n", + "\n", + "t = 14.600000000000001\n", + "Ca = 0.5313368998205692\n", + "Cb = 0.5311491200139046\n", + "Cc = 998.9375139801655\n", + "\n", + "t = 14.700000000000001\n", + "Ca = 0.5047700548295407\n", + "Cb = 0.5046010530035425\n", + "Cc = 998.9906288921669\n", + "\n", + "t = 14.8\n", + "Ca = 0.4795315520880637\n", + "Cb = 0.4793794504446653\n", + "Cc = 999.0410889974672\n", + "\n", + "t = 14.9\n", + "Ca = 0.4555549744836605\n", + "Cb = 0.45541808300460196\n", + "Cc = 999.0890269425117\n", + "\n", + "t = 15.0\n", + "Ca = 0.43277722575947747\n", + "Cb = 0.43265402342832476\n", + "Cc = 999.1345687508122\n", + "\n", + "t = 15.100000000000001\n", + "Ca = 0.4111383644715036\n", + "Cb = 0.41102748237346615\n", + "Cc = 999.177834153155\n", + "\n", + "t = 15.200000000000001\n", + "Ca = 0.3905814462479284\n", + "Cb = 0.39048165235969473\n", + "Cc = 999.2189369013923\n", + "\n", + "t = 15.3\n", + "Ca = 0.371052373935532\n", + "Cb = 0.37096255943612166\n", + "Cc = 999.2579850666283\n", + "\n", + "t = 15.4\n", + "Ca = 0.3524997552387554\n", + "Cb = 0.3524189221892861\n", + "Cc = 999.295081322572\n", + "\n", + "t = 15.5\n", + "Ca = 0.3348747674768176\n", + "Cb = 0.3348020177322953\n", + "Cc = 999.3303232147908\n", + "\n", + "t = 15.600000000000001\n", + "Ca = 0.31813102910297675\n", + "Cb = 0.3180655543329066\n", + "Cc = 999.3638034165641\n", + "\n", + "t = 15.700000000000001\n", + "Ca = 0.3022244776478279\n", + "Cb = 0.3021655503547648\n", + "Cc = 999.3956099719974\n", + "\n", + "t = 15.8\n", + "Ca = 0.2871132537654365\n", + "Cb = 0.2870602192016797\n", + "Cc = 999.4258265270329\n", + "\n", + "t = 15.9\n", + "Ca = 0.2727575910771647\n", + "Cb = 0.27270985996978353\n", + "Cc = 999.454532548953\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1.2 Crank-Nicolson (Trapezoid Rule)" + ], + "metadata": { + "id": "v9urNjZgaT1h" + } + }, + { + "cell_type": "markdown", + "source": [ + "Alternatively, the Trapezoid Rule is a numerical method used to approximate the solutions of ordinary differential equations (ODEs). It is a widely used method that provides a straightforward approach to solving ODEs when an exact analytical solution is not available.\n", + "\n", + "It also approximates the solution to a first-order ordinary differential equation of the form:\n", + "\n", + "\\begin{equation}\n", + "\\frac{dy}{dx} = f(x, y)\n", + "\\end{equation}\n", + "\n", + "The Trapezoid Rule also operates through an iterative approach that discretizes the continuous ODE into discrete steps by using the following formula to update the solution at each step:\n", + "\n", + "\\begin{equation}\n", + "y_{n+1} = y_n + \\frac{h}{2} \\left[f(x_n, y_n) + f(x_{n+1}, y_{n+1})\\right]\n", + "\\end{equation}\n", + "\n", + "In this formula:\n", + "\n", + "$y_{n+1}$ is the new approximation of the solution at the next step.\n", + "\n", + "$y_n$ is the previous approximation of the solution at the current step.\n", + "\n", + "$h$ is the step size, representing the size of the interval over which the solution is approximated.\n", + "\n", + "$x_n$ is the current value of the independent variable at the nth step.\n", + "\n", + "$f(x_n, y_n)$ and $f(x_{n+1}, y_{n+1})$ represent the rate of change of y at the current point $(x_n, y_n)$ and the predicted point $(x_{n+1}, y_{n+1})$, respectively." + ], + "metadata": { + "id": "r1EYn2umKwWW" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Now, implement the found differential equations into the Crank-Nicolson (Trapezoid Rule) to find and plot the numerically solution.**" + ], + "metadata": { + "id": "ZqnzYbpfnvHm" + } + }, + { + "cell_type": "code", + "source": [ + "# Define the parameters and initial conditions\n", + "k1 = 0.5\n", + "k2 = 1.0\n", + "xa0 = 1000.0 # Initial concentration of Ca\n", + "t_max = 16.0 # Maximum time\n", + "dt = 0.1 # Time step\n", + "\n", + "# Function to calculate the derivatives\n", + "def derivatives(variables, t):\n", + " Ca, Cb, Cc = variables\n", + " dCadt = -k1 * Ca\n", + " dCbdt = k1 * Ca - k2 * Cb\n", + " dCcdt = k2 * Cb\n", + " return [dCadt, dCbdt, dCcdt]\n", + "\n", + "# Function to perform Crank-Nicolson method\n", + "def crank_nicolson(t, variables, dt):\n", + " sol = root(lambda x: x - variables - 0.5 * dt * np.array(derivatives((x + variables) / 2, t + 0.5 * dt)), variables).x\n", + " return sol\n", + "\n", + "# Perform the Crank-Nicolson method\n", + "numsteps = int(t_max / dt)\n", + "t_values = np.linspace(0, t_max, numsteps+1)\n", + "variables = np.array([xa0, 0.0, 0.0])\n", + "results = [variables]\n", + "for t in t_values[1:]:\n", + " variables = crank_nicolson(t, variables, dt)\n", + " results.append(variables)\n", + "\n", + "# Plot the concentration profiles\n", + "results = np.array(results)\n", + "fig = plt.figure(figsize=(6, 6))\n", + "plt.plot(t_values, results[:, 0], label=r\"A\")\n", + "plt.plot(t_values, results[:, 1], label=r\"B\")\n", + "plt.plot(t_values, results[:, 2], label=r\"C\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "plt.title('Crank-Nicolson (Trapezoid Rule)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 574 + }, + "id": "y8QFkj-FKvMX", + "outputId": "9ceb09ca-079b-4420-bbe7-cb9703e172af" + }, + "execution_count": 48, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1.3 Comparing Errors" + ], + "metadata": { + "id": "MbPgBJepqeDn" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1.3.1 Understanding Convergence" + ], + "metadata": { + "id": "dn_JGwH5Cvmp" + } + }, + { + "cell_type": "markdown", + "source": [ + "The convergence difference between the Forward Euler Method and the Trapezoid Rule it is defined by their order of convergence.\n", + "\n", + "But **what is convergence?** In numerical methods, convergence refers to how quickly the numerical solution approaches the exact solution as you use smaller time steps.\n", + "\n", + "The **Forward Euler Method** is a first-order method, which means its **convergence is linear**. This way, when you reduce the step size $h$ in the Euler Method, the error in the approximation decreases linearly. Therefore, the Forward Euler Method is relatively less accurate for solving ODEs.\n", + "\n", + "Analogously the **Trapezoid Rule** is a second-order method, which means its **convergence is quadratic**.\n", + "This way, when you reduce the step size $h$ in the Trapezoid Rule, the error in the approximation decreases quadratically. This results in a **much faster convergence compared to the Euler Method.**" + ], + "metadata": { + "id": "xf-z6yaHrJZX" + } + }, + { + "cell_type": "markdown", + "source": [ + "## 3b-1.3.2 Visualizing Error Rates" + ], + "metadata": { + "id": "35-bPV-6DIsz" + } + }, + { + "cell_type": "markdown", + "source": [ + "Let's visualize the error rates of these methods by plotting the logarithm of the error against the step size. This will help us understand their convergence behavior more intuitively." + ], + "metadata": { + "id": "SJhyX6mpDYtw" + } + }, + { + "cell_type": "code", + "source": [ + "# Updated Crank-Nicolson method\n", + "def crank_nicolson(RHS, y0, Delta_t, numsteps):\n", + " \"\"\"Perform numsteps of the Crank-Nicolson method\n", + " Args:\n", + " RHS: function for the differential equation\n", + " y0: initial condition\n", + " Delta_t: time step size\n", + " numsteps: number of time steps\n", + "\n", + " Returns:\n", + " t: time array\n", + " y: solution array\n", + " \"\"\"\n", + " t = np.linspace(0, Delta_t * numsteps, numsteps + 1)\n", + " y = np.zeros(numsteps + 1)\n", + " y[0] = y0\n", + "\n", + " for n in range(numsteps):\n", + " y_half = y[n] + 0.5 * Delta_t * RHS(y[n], t[n])\n", + " y[n + 1] = y[n] + Delta_t * RHS(y_half, t[n] + 0.5 * Delta_t)\n", + "\n", + " return t, y\n", + "\n", + "# Code for Crank-Nicolson Method Error Analysis\n", + "RHS = lambda y, t: -y\n", + "Delta_t = np.array([1.0, 0.5, 0.25, 0.125, 0.0625, 0.0625 / 2])\n", + "t_final = 2\n", + "error = np.zeros(Delta_t.size)\n", + "t_fine = np.linspace(0, t_final, 100)\n", + "count = 0\n", + "\n", + "for d in Delta_t:\n", + " t, y = crank_nicolson(RHS, 1, d, int(t_final / d)) # Ensure numsteps is an integer\n", + " plt.plot(t, y, label=\"$\\Delta t$ = \" + str(d))\n", + " error[count] = np.linalg.norm((y - np.exp(-t))) / np.sqrt(t_final / d)\n", + " count += 1\n", + "\n", + "plt.plot(t_fine, np.exp(-t_fine), linewidth=3, color=\"black\", label=\"Exact Solution\")\n", + "plt.xlabel(\"t\")\n", + "plt.ylabel(\"y(t)\")\n", + "plt.legend()\n", + "plt.title(\"Solution with $\\Delta t$ = \" + str(Delta_t))\n", + "plt.show()\n", + "\n", + "plt.loglog(Delta_t, error, 'o-', color=\"green\")\n", + "slope = (np.log(error[-1]) - np.log(error[-2])) / (np.log(Delta_t[-1]) - np.log(Delta_t[-2]))\n", + "plt.title(\"Slope of Error is \" + str(slope))\n", + "plt.xlabel(\"$\\Delta t$\")\n", + "plt.ylabel(\"Norm of Error\")\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 932 + }, + "id": "lelUKn5D8XIe", + "outputId": "3fd609c7-d69b-4168-f780-16daa3f7af7a" + }, + "execution_count": 39, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Updated Forward Euler method\n", + "def forward_euler(RHS, y0, Delta_t, numsteps):\n", + " \"\"\"Perform numsteps of the Forward Euler method\n", + " Args:\n", + " RHS: function for the differential equation\n", + " y0: initial condition\n", + " Delta_t: time step size\n", + " numsteps: number of time steps\n", + "\n", + " Returns:\n", + " t: time array\n", + " y: solution array\n", + " \"\"\"\n", + " t = np.linspace(0, Delta_t * numsteps, numsteps + 1)\n", + " y = np.zeros(numsteps + 1)\n", + " y[0] = y0\n", + "\n", + " for n in range(numsteps):\n", + " y[n + 1] = y[n] + Delta_t * RHS(y[n], t[n])\n", + "\n", + " return t, y\n", + "\n", + "# Code for Forward Euler Method Error Analysis\n", + "RHS = lambda y, t: -y\n", + "Delta_t = np.array([1.0, 0.5, 0.25, 0.125, 0.0625, 0.0625 / 2])\n", + "t_final = 2\n", + "error = np.zeros(Delta_t.size)\n", + "t_fine = np.linspace(0, t_final, 100)\n", + "count = 0\n", + "\n", + "for d in Delta_t:\n", + " t, y = forward_euler(RHS, 1, d, int(t_final / d)) # Ensure numsteps is an integer\n", + " plt.plot(t, y, label=\"$\\Delta t$ = \" + str(d))\n", + " error[count] = np.linalg.norm((y - np.exp(-t))) / np.sqrt(t_final / d)\n", + " count += 1\n", + "\n", + "plt.plot(t_fine, np.exp(-t_fine), linewidth=3, color=\"black\", label=\"Exact Solution\")\n", + "plt.xlabel(\"t\")\n", + "plt.ylabel(\"y(t)\")\n", + "plt.legend()\n", + "plt.title(\"Solution with $\\Delta t$ = \" + str(Delta_t))\n", + "plt.show()\n", + "\n", + "plt.loglog(Delta_t, error, 'o-', color=\"blue\")\n", + "slope = (np.log(error[-1]) - np.log(error[-2])) / (np.log(Delta_t[-1]) - np.log(Delta_t[-2]))\n", + "plt.title(\"Slope of Error is \" + str(slope))\n", + "plt.xlabel(\"$\\Delta t$\")\n", + "plt.ylabel(\"Norm of Error\")\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 932 + }, + "id": "gVLYoVp3Cnvd", + "outputId": "042b6767-0842-4ba1-e6fa-31f4d9e1ed7d" + }, + "execution_count": 49, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Question**:\n", + "\n", + "What does the slope of the log-log plot representing the error against the step size signify in the context of error analysis for numerical methods solving differential equations? How can this slope be interpreted regarding the method's accuracy and convergence?\n", + "\n", + "Options:\n", + "\n", + "**A**. The slope represents the computational efficiency of the method. A steeper slope indicates higher efficiency in converging to the exact solution.\n", + "\n", + "**B**. The slope shows the order of convergence of the method. Higher-order methods exhibit a steeper slope.\n", + "\n", + "**C**. The slope indicates the absolute error of the method. A steeper slope implies a lower absolute error.\n", + "\n", + "**D**. The slope has no correlation with the method's accuracy or convergence.\n", + "\n", + "**Select the most appropriate option and provide a brief explanation for your choice.**" + ], + "metadata": { + "id": "60otxH7hrJ6e" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Your Answer:**" + ], + "metadata": { + "id": "6UiitI2_uAyH" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "avlhWMB84eAe" + }, + "source": [ + "## 3c. Stochastic vs Deterministic Solution\n", + "Plot the stochastic solution and deterministic solution for the species profiles in the same plot starting with 1000 molecules of A. **Write a few sentences to explain what you observe.** Submit your answer on an attached pdf file." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 316 + }, + "id": "-lmg13md6E1C", + "outputId": "fb997f24-9d4c-4c7a-956e-0e16999d81f5" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "### BEGIN SOLUTION ###\n", + "\n", + "fig = plt.figure(figsize=(15, 4))\n", + "\n", + "# Creating a subplot\n", + "plt.subplot(1, 3, 1)\n", + "plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n", + "plt.plot(t, X_a, \"c\", label=r\"A$_{deterministic}$\", linewidth=3)\n", + "plt.plot(time, xa, \"k-.\", label=r\"A$_{stochastic}$\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of A molecules\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "\n", + "plt.subplot(1, 3, 2)\n", + "plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n", + "plt.plot(t, X_b, \"r\", label=r\"B$_{deterministic}$\", linewidth=3)\n", + "plt.plot(time, xb, \"k-.\", label=r\"B$_{stochastic}$\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of B molecules\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "\n", + "plt.subplot(1, 3, 3)\n", + "plt.title(\"Stochastic vs. deterministic\", fontsize=13, fontweight=\"bold\")\n", + "plt.plot(t, X_c, \"g\", label=r\"C$_{deterministic}$\", linewidth=3)\n", + "plt.plot(time, xc, \"k-.\", label=r\"C$_{stochastic}$\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of C molecules\", fontsize=15, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=15)\n", + "\n", + "plt.subplots_adjust(left=0.1, bottom=0.1, right=0.9, top=0.9, wspace=0.4, hspace=0.4)\n", + "\n", + "### END SOLUTION ###" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "i37i8E7r7MXE" + }, + "source": [ + "**Answer:** For N = 1000 molecules, we see that the profiles for the stochastic solution are similar to the deterministic solution with little noise. For even larger systems, the profiles will be even more accurate. Intuitively this is what we would expect; the random behavior becomes less important for large systems. In the next section, we will see that random behavior is important for small systems." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "YhLRGavgfvHG" + }, + "source": [ + "## 3d. Effect of number of molecules in stochastic simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aesb6BjnDXxy" + }, + "source": [ + "\n", + "**How does changing the starting number of molecules affect the reaction profiles?** Run the Gillespie function with A = 100 and A = 1000 molecules and create a subplot for the species profile. Submit this answer in a few sentences on an attached pdf file." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 729 + }, + "id": "rA7OYZnLz6Oa", + "outputId": "e8a1f568-1b63-429d-9f5c-2ba12bc25099" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "### BEGIN SOLUTION ###\n", + "\n", + "# stochastic model for with 100 total molecules\n", + "x = gillespie(k1, k2, 100, 0, 0)\n", + "# stochastic model for with 1000 total molecules\n", + "y = gillespie(k1, k2, 1000, 0, 0)\n", + "\n", + "### END SOLUTION ###\n", + "\n", + "# creating a subplot for the two stochastic simulations\n", + "fig = plt.figure(figsize=(8, 8))\n", + "\n", + "plt.subplot(2, 1, 1)\n", + "plt.plot(x[0], x[1], \"-.\", label=r\"A\")\n", + "plt.plot(x[0], x[2], \"-.\", label=r\"B\")\n", + "plt.plot(x[0], x[3], \"-.\", label=r\"C\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.title(\"N=100 molecules\", fontsize=14, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=13)\n", + "\n", + "plt.subplot(2, 1, 2)\n", + "plt.plot(y[0], y[1], \"-.\", label=r\"A\")\n", + "plt.plot(y[0], y[2], \"-.\", label=r\"B\")\n", + "plt.plot(y[0], y[3], \"-.\", label=r\"C\")\n", + "leg = plt.legend(fontsize=13)\n", + "plt.subplots_adjust(hspace=0.5)\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number of molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "plt.title(\"N=1000 molecules\", fontsize=14, fontweight=\"bold\")\n", + "plt.xticks(fontsize=13)\n", + "plt.yticks(fontsize=13)\n", + "leg = plt.legend(fontsize=13)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "GYu8xOxB2G0q" + }, + "source": [ + "**Answer:** For N = 100 molecules, we can see more noise in the species profile compared to N = 1000 molecules, where the profile is smoother and closer to the analytical solution. This reinforces our idea that stochastic modeling is important if the system of interest is small." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dS55dJKRH6_r" + }, + "source": [ + "## 4. Effect of rate constants k$_1$ and k$_2$\n", + "Plot reaction profiles using different rate constant values (using the same number of starting molecules. *Hint:* Change the value of one rate constant while keeping the other the same; this will make any changes obvious.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "i_eHPDS6Dd5b" + }, + "source": [ + "**How does changing the rate constant affect the reaction profiles?** Submit this answer in a few sentences on an attached pdf file." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 727 + }, + "id": "9N5NTozx4pxA", + "outputId": "690979fc-3993-4d4d-fe77-fe86792b7d62" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "### BEGIN SOLUTION ###\n", + "\n", + "# stochastic model with 400 total molecules, k1 = 2 and k2 = 1\n", + "e = gillespie(2, 1, 400, 0, 0)\n", + "# stochastic model with 400 total molecules, k1 = 1 and k2 = 1\n", + "f = gillespie(1, 1, 400, 0, 0)\n", + "\n", + "### END SOLUTION ###\n", + "\n", + "# creating a subplot for the two stochastic simulations\n", + "fig = plt.figure(figsize=(8, 8))\n", + "\n", + "plt.subplot(2, 1, 1)\n", + "plt.plot(e[0], e[1], \"-.\", label=r\"A\")\n", + "plt.plot(e[0], e[2], \"-.\", label=r\"B\")\n", + "plt.plot(e[0], e[3], \"-.\", label=r\"C\")\n", + "leg = plt.legend(fontsize=15)\n", + "plt.title(\"k$_1$ = 2 and k$_2$ = 1\", fontsize=14, fontweight=\"bold\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "leg = plt.legend(fontsize=13)\n", + "\n", + "plt.subplot(2, 1, 2)\n", + "plt.plot(f[0], f[1], \"-.\", label=r\"A\")\n", + "plt.plot(f[0], f[2], \"-.\", label=r\"B\")\n", + "plt.plot(f[0], f[3], \"-.\", label=r\"C\")\n", + "plt.subplots_adjust(hspace=0.5)\n", + "leg = plt.legend(fontsize=15)\n", + "plt.title(\"k$_1$ = 1 and k$_2$ = 1\", fontsize=14, fontweight=\"bold\")\n", + "plt.xlabel(\"Time (s)\", fontsize=15, fontweight=\"bold\")\n", + "plt.ylabel(\"Number molecules x$_i$\", fontsize=15, fontweight=\"bold\")\n", + "leg = plt.legend(fontsize=13)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "T3wxijtF-6-q" + }, + "source": [ + "**Answer:** We see that for the top figure with higher k$_1$, the maximum in B was reached faster and in a steeper way than the bottom figure with lower k$_1$; this makes sense because a higher k$_1$ means a higher probability of the first reaction, meaning faster conversion of A to B molecules. With the same logic, we can explain the decay in A and growth in C is also fast in the top figure compared to the bottom figure.\n", + "\n", + "All of these characteristics would also be expected in the deterministic model. This exercise shows us the beauty of the Gillespie algorithm and how it can capture features of deterministic models while keeping the random behavior of the system into account." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LhKZC4yM45J6" + }, + "source": [ + "## 5. Final Discussion" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "H9fS7IBv4-jg" + }, + "source": [ + "Through this project, we aimed to highlight the importance of stochastic (random) modeling (aka KMC simulations in the present time). We used the famous Gillespie algorithm for stochastic modeling and compared it to well-known deterministic reaction engineering models for a simple two irreversible reactions constant volume batch system. it is also presented in the notebook two different options to solve differential equations through numerical coding. Besides that, we showed that the stochastic solution has more noise in the profiles for smaller systems because of the random behavior of the molecules moving in the gas phase and colliding with each other. We showed that this random behavior becomes less critical for larger systems, and profiles were closer to deterministic models as captured by the Gillespie algorithm." + ] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file