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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "ZB7hIRdzvTep"
+ },
+ "source": [
+ "# Entrance Length Estimation for Channel Flow\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "0_WncgpRkWH5"
+ },
+ "source": [
+ "**Prepared by**: Stephen Cini (scini@nd.edu) and David Gazzo (dgazzo@nd.edu)\n",
+ "\n",
+ ">\n",
+ "\n",
+ "**Editted by** Farbod Shirinichi (fshirini@nd.edu)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Reference**:\n",
+ "\n",
+ "[1]Truskey, G. A., Yuan, F., & Katz, D. F. (2004). Transport phenomena in biological systems.\n",
+ "\n",
+ "[2]Chaudhry, M. H. (2008). Open-channel flow (Vol. 523). New York: Springer.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "qO2qu5ttfkgD"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# 1-Introduction:\n",
+ "\n",
+ "Estimating the entrance length of channel flow is a fundamental concept in fluid dynamics, with wide-ranging applications in various engineering and scientific disciplines. The entrance length, often referred to as the hydrodynamic entrance region, represents the distance over which a fluid undergoes a transition from a disturbed, uneven flow pattern to a more uniform, steady-state flow within a conduit or channel. Accurate estimation of this entrance length is crucial for optimizing the design and performance of fluid transport systems, spanning pipelines, heat exchangers, and microfluidic devices. Understanding and characterizing the entrance length is essential for predicting pressure drops, flow profiles, and heat transfer rates, thereby ensuring efficient and cost-effective operation in a multitude of engineering applications. [1][2]\n",
+ "\n",
+ "The study of entrance length has been a topic of great interest to fluid dynamicists and engineers for many decades, as it provides critical insights into the behavior of fluid near the entry of a channel. The phenomena associated with entrance length have significant implications for industrial processes, energy systems, and the transportation of fluids. By comprehending the factors that influence entrance length, researchers and engineers can make informed decisions about channel design, fluid transport efficiency, and the mitigation of undesired effects like turbulence and heat loss. [1][2]\n"
+ ],
+ "metadata": {
+ "id": "2IkaSRHHnOdD"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "i9wwxaH-vTeq"
+ },
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "**Intended Audience**: his problem is tailored for junior and senior students majoring in Chemical and Biomolecular Engineering at the University of Notre Dame, especially those currently enrolled in or having completed the Transport course and possessing a keen interest in fluid dynamics. However, any student intrigued by fluid dynamics is encouraged to explore this problem.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "yLqvejeuvTet"
+ },
+ "source": [
+ "## 1-1-Learning Objectives:\n",
+ "\n",
+ "\n",
+ "Upon completing this notebook and actively engaging in class discussions and activities, you will achieve the following learning objectives:\n",
+ "\n",
+ "* Utilize Python-based integration methods proficiently to solve ordinary differential equations.\n",
+ "* Demonstrate competence in generating and visualizing data through matplotlib, ensuring effective data representation.\n",
+ "* Apply integration techniques to practical scenarios, particularly analyzing entrance length flow in diverse channel flow systems.\n",
+ "* Successfully solve real-world problems related to entrance length calculations.\n",
+ "* Adapt acquired skills to analogous problems by making minor formula adjustments, showcasing your adaptable problem-solving capabilities."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "sDQW_Y8IvstJ"
+ },
+ "source": [
+ "## 1-2-Coding Resources:\n",
+ "\n",
+ "Relevant Modules in Class Website:\n",
+ "\n",
+ "\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",
+ "* [Lambda Functions](https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-as-Arguments.html#lambda-functions)\n",
+ "* [Preparing Publication Quality Figures in Python](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html)\n",
+ "* [Scipy](https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html#scipy)\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "DuQsLLTnvTer",
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "# load libraries\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy import integrate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "ZLUihthfR0Yz"
+ },
+ "source": [
+ "## 1-3-Problem Statement:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "n2b8uykvR0Y0"
+ },
+ "source": [
+ "
\n",
+ "
Homework Problem
\n",
+ " Complete the following problem outside of class to practice the concepts discussed.\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "37pz7pp1R0Y1"
+ },
+ "source": [
+ "In this notebook, we delve into the concept of estimating the entrance length for flow in a rectangular channel, particularly when the channel's width \"w\" significantly exceeds its height \"H,\" as shown in the figure below.\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "The velocity field within the channel's entrance depends on both the x and y directions, creating a boundary layer as the fluid enters. The lecture focuses on the crucial point when the boundary layer grows to half the channel's height, H/2, marking the transition to fully developed flow.\n",
+ "\n",
+ "It's important to note that we assume the \"no slip condition\" throughout, where the fluid's velocity at the channel walls is zero, a fundamental concept in fluid mechanics.\n",
+ "\n",
+ "Additionally, the formulae provided here are only valid for laminar flow.\n",
+ "\n",
+ "The goal of this notebook is to offer a foundational understanding of entrance length in channel flow, its relevance in different systems, and the limitations of applying experimental formulae to broader fluid dynamics scenarios."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "Kw1O2l0kR0Y2"
+ },
+ "source": [
+ "## 1-4- Estimating Entrance Length:\n",
+ "\n",
+ "As a first approximation, assume that the boundary layer is described by the results for flow over a flat plate. That is, the development of the boundary layer $δ$ is given by\n",
+ "\\begin{equation}\n",
+ "δ(x)=5.00xRe_x^{-1/2}\n",
+ "\\end{equation}\n",
+ "\n",
+ "where,\n",
+ "\\begin{equation}\n",
+ " Re_x=ρUx/μ\n",
+ "\\end{equation}\n",
+ "\n",
+ "Develop an expression for the entrance length in terms of the channels Reynolds number, $Re_x=2ρUH/μ = 2ρQ/wμ$, where $〈v〉$ is the average velocity in the channel.\n",
+ "\n",
+ "Show that the entrance length $Le$ is equal to $0.005ReH$.\n",
+ "\\begin{equation}\n",
+ "Le=0.005ReH\n",
+ "\\end{equation}\n",
+ "where\n",
+ "\\begin{equation}\n",
+ " Re_x<2000\n",
+ "\\end{equation}\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "mLe463wyR0Y4"
+ },
+ "source": [
+ "Submit your answer and written work via **Gradescope**."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "It is worth mentioning that\n",
+ "\\begin{equation}\n",
+ "Le=4.4Re^{1/6}H\n",
+ "\\end{equation}\n",
+ "or\n",
+ "\\begin{equation}\n",
+ "Le=10ReH\n",
+ "\\end{equation}\n",
+ "where\n",
+ "\\begin{equation}\n",
+ " Re_x> 3500\n",
+ "\\end{equation}\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "wr3Cd0DIXHFm"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## 2- Some Real-life Simple Applications:\n",
+ "#### 2-1-Air Tunnel:\n",
+ "Wind tunnels are devices used to test and study the aerodynamic properties of objects, such as aircraft, cars, buildings, and more. They work by creating a controlled flow of air over a model or prototype, simulating the conditions that the object would experience in the real world."
+ ],
+ "metadata": {
+ "id": "Z3a1i5XMNwsT"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "(Truss-braced wind model installed in the Ames 11x11 Foot Wind Tunnel for testing as part of the Subsonic Ultra Green Aircraft Research Project (SUGAR) Shown here with test engineer Greg Gatlin, Langley Research Center.) NASA ID: ACD16-0013-015"
+ ],
+ "metadata": {
+ "id": "Pm5s-drJVYmd"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "Calculating the entrance length is a critical aspect of wind tunnel testing, particularly in the context of aerodynamic research. Understanding and accurately determining the entrance length, which is the distance required for the flow to transition from an initially turbulent or non-uniform state to a fully developed, stable flow, is vital for ensuring the reliability and validity of aerodynamic measurements. It helps researchers establish a controlled and consistent testing environment by allowing them to place the object of interest in the fully developed flow region. This not only enhances the accuracy of aerodynamic data but also ensures that the testing conditions closely resemble those experienced by real-world objects, such as aircraft or vehicles, enabling engineers and scientists to make informed design decisions and improvements.\n"
+ ],
+ "metadata": {
+ "id": "-UW_1JD-PN-r"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "####2-2-Finding The Etrance Lenght of a Formula One Wind Tunnel:\n",
+ "First Let's explore a scenario with a wind tunnel that has a length of 141 meters and a Square side of 9.4 meters. If the wind is flowing in this tunnel at a velocity of 100 m/s and the air kinematic viscosity is given as 1.5×10−5 m²/s, the objective is to calculate the entrance length of this wind tunnel\n",
+ "\n",
+ "\n",
+ "1. Find the Rynolds Number\n",
+ "\\begin{equation}\n",
+ " Re_x=ρUx/μ\n",
+ "\\end{equation}\n",
+ "\\begin{equation}\n",
+ " Re_x=Ux/ƴ\n",
+ "\\end{equation}\n",
+ "where here ƴ is kinematic viscosity\n",
+ "\n",
+ "\\begin{equation}\n",
+ "Re=100*9.4/1.5*{10^-5}\n",
+ "\\end{equation}\n",
+ "2. check if it is laminar or turbulent\n",
+ "\\begin{equation}\n",
+ "Re>3500; terbulant\n",
+ "\\end{equation}\n",
+ "\\begin{equation}\n",
+ "Re<2000; laminar\n",
+ "\\end{equation}\n",
+ "\\begin{equation}\n",
+ "3500>Re>2000; transition\n",
+ "\\end{equation}\n",
+ "3. use the coresponding equation if transition average it\n",
+ "2. report the data\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "G5HiD_rPPVmj"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Given values\n",
+ "wind_speed = 100 # m/s\n",
+ "tube_diameter = 9.4 # meters\n",
+ "air_viscosity = 1.5e-5 # m^2/s\n",
+ "\n",
+ "# Calculate Reynolds number\n",
+ "Re = (wind_speed * tube_diameter) / air_viscosity\n",
+ "\n",
+ "# Determine the flow regime\n",
+ "if Re < 2000:\n",
+ " flow_regime = \"Laminar\"\n",
+ " Le = 0.005 * Re * tube_diameter\n",
+ " equation_used = \"Le = 0.005 * Re * D\"\n",
+ "elif Re > 3500:\n",
+ " flow_regime = \"Turbulent\"\n",
+ " Le = 4.4 * (Re ** (1/6)) * tube_diameter\n",
+ " equation_used = \"Le = 4.4 * (Re^1/6) * D\"\n",
+ "else:\n",
+ " flow_regime = \"Transition\"\n",
+ " # For transition, use the average of laminar and turbulent equations\n",
+ " Le_laminar = 0.005 * Re * tube_diameter\n",
+ " Le_turbulent = 4.4 * (Re ** (1/6)) * tube_diameter\n",
+ " Le = (Le_laminar + Le_turbulent) / 2\n",
+ " equation_used = \"Average of laminar and turbulent equations\"\n",
+ "\n",
+ "# Output the results\n",
+ "print(f\"Reynolds number (Re) is {Re:.0f}, the flow is in the {flow_regime} regime.\")\n",
+ "print(f\"Entrance Length (Le) is {Le:.2f} meters, calculated using the equation: {equation_used}\")\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "cL0KtuvfQ2xn",
+ "outputId": "a428e0d1-1a12-4de2-ba01-f59b8f36530e"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Reynolds number (Re) is 62666667, the flow is in the Turbulent regime.\n",
+ "Entrance Length (Le) is 824.30 meters, calculated using the equation: Le = 4.4 * (Re^1/6) * D\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Activity** Why should the Reynolds number be high?\n",
+ "Based on the obtained results, where should the object be located relative to the entrance length?\n",
+ "Submit your answer and written work via **Gradescope**."
+ ],
+ "metadata": {
+ "id": "RmZKcUTqSJoQ"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "###2-3-Water Flow Example:\n",
+ "You have a water tank connected to a pipe with a diameter of 0.5 meters. Water flows out of the tank and into the pipe. The kinematic viscosity of water is 1.004×10−6 m²/s. Plot the relationship between entrance length (Le) and water velocity."
+ ],
+ "metadata": {
+ "id": "Qm97UnetRIrZ"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "\n",
+ "# Given values\n",
+ "pipe_diameter = 0.5 # meters\n",
+ "water_kinematic_viscosity = 1.004e-6 # m²/s\n",
+ "\n",
+ "# Initialize lists to store data\n",
+ "speeds = np.arange(0, 100.01, 0.01) # Water speeds from 0 to 100 m/s with a step of 0.01 m/s\n",
+ "entrance_lengths = []\n",
+ "\n",
+ "# Calculate entrance lengths for different speeds\n",
+ "for speed in speeds:\n",
+ " Re = (speed * pipe_diameter) / water_kinematic_viscosity\n",
+ " if Re < 2000:\n",
+ " Le = 0.05 * Re * pipe_diameter\n",
+ " elif Re > 3500:\n",
+ " Le = 4.4 * pipe_diameter * (Re ** (1/6))\n",
+ " else:\n",
+ " Le_laminar = 0.05 * Re * pipe_diameter\n",
+ " Le_turbulent = 4.4 * pipe_diameter * (Re ** (1/6))\n",
+ " Le = (Le_laminar + Le_turbulent) / 2\n",
+ " entrance_lengths.append(Le)\n",
+ "\n",
+ "# Create the plot for Entrance Length vs. Water Speed\n",
+ "plt.figure(figsize=(8, 6))\n",
+ "plt.plot(speeds, entrance_lengths, label='Entrance Length', color='b', linewidth=2)\n",
+ "plt.xlabel('Water Speed (m/s)', fontsize=12, fontweight='bold')\n",
+ "plt.ylabel('Entrance Length (m)', fontsize=12, fontweight='bold')\n",
+ "plt.xticks(fontsize=10)\n",
+ "plt.yticks(fontsize=10)\n",
+ "plt.title('Entrance Length vs. Water Speed', fontsize=14, fontweight='bold')\n",
+ "plt.legend(fontsize=10)\n",
+ "\n",
+ "# Remove grid lines\n",
+ "plt.grid(False)\n",
+ "\n",
+ "# Customize plot layout\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Save the plot as a high-quality image (e.g., PNG)\n",
+ "plt.savefig('entrance_length_vs_water_speed.png', dpi=300)\n",
+ "\n",
+ "# Show the plot\n",
+ "plt.show()"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 607
+ },
+ "id": "p0m77gJIRcFP",
+ "outputId": "03700698-b37a-411d-9914-6b35ac2eb247"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "#### Find the entrance length when the velocity is $0.01 m^2/s$"
+ ],
+ "metadata": {
+ "id": "czOJt9o9caOy"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Find and print the entrance length and Reynolds number at water speed equal to 0.01 m/s\n",
+ "water_speed = .01 # m/s\n",
+ "index_2m_s = int(water_speed * 100) # Index corresponding to 0.01 m/s in the speeds array\n",
+ "Re_2m_s = (water_speed * pipe_diameter) / water_kinematic_viscosity\n",
+ "entrance_length_2m_s = entrance_lengths[index_2m_s]\n",
+ "print(f\"At water speed of {water_speed} m/s:\")\n",
+ "print(f\"Reynolds number: {Re_2m_s:.2f}\")\n",
+ "print(f\"Entrance Length: {entrance_length_2m_s:.2f} meters\")"
+ ],
+ "metadata": {
+ "id": "JeD0ensSJ0Gb",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "04429bee-3272-46a8-874d-38af3a4eaaec"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "At water speed of 0.01 m/s:\n",
+ "Reynolds number: 4980.08\n",
+ "Entrance Length: 9.09 meters\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "As the speed of the water flow increases, the entrance length also exhibits a proportional increase, highlighting the direct relationship between flow velocity and the extent of the entrance region in the pipe. This observation underscores the significance of controlling the entrance length in understanding and optimizing fluid dynamics within the system."
+ ],
+ "metadata": {
+ "id": "LT-kZxoERozY"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## 3-More Accurate/Rigorous Method"
+ ],
+ "metadata": {
+ "id": "DpBGU7XFV2v8"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### 3-1-Normalize the expression on paper\n",
+ "\n",
+ "The analysis in Question 1 assumes that $U(x) = U_o = 〈v〉$. But in fact, the free-stream velocity changes as the boundary layer grows in the channel. Therefore, assuming a linear velocity profile, $v_x=\\frac{U_xy}{δ}$, in the boundary layer, and utilizing the von Karman momentum integral equation,\n",
+ "\n",
+ "\\begin{equation}\n",
+ "τ_w=ρ \\frac{∂}{∂x} ∫_0^∞v_x (U-v_x )dy+ρ\\frac{∂U}{∂x} ∫_0^∞(U-v_x )dy\n",
+ "\\end{equation}\n",
+ "\n",
+ "and the fact that the flow rate $Q$ is constant, the following expression for the growth of the boundary layer can be derived:\n",
+ "\n",
+ "\\begin{equation}\n",
+ "\\frac{dδ_{(x)}}{dx}=\\frac{6μW}{ρδ_{(x)}Q}\\frac{[H-δ_{(x)}]^2}{H+4δ_{(x)}}\n",
+ "\\end{equation}\n",
+ "\n",
+ "Manipulate this expression so that it can be integrated numerically. Hint: normalize it and keep symmetry in mind."
+ ],
+ "metadata": {
+ "id": "RP1zfP1KV9uG"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Duscussion**\n",
+ "Discuss the boundary conditions and assumptions employed to derive the equation above. What limitations does this equation possess? Is it universally applicable across all Reynolds numbers?"
+ ],
+ "metadata": {
+ "id": "Ff0a8uFLT_kG"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "Submit your answer and written work via **Gradescope**."
+ ],
+ "metadata": {
+ "id": "f-U-p9JZWHfy"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "lZcAJ3QiPKJ3"
+ },
+ "source": [
+ "### 3-2-Numerically integrate the normalized expression\n",
+ "\n",
+ "Using the normalized form of the differential equation, use `scipy.integrate.solve_ivp` to numerically integrate the expression and find the value of x where $δ$ is fully developed.\n",
+ "\n",
+ "For more information on how to use `scipy.integrate`, click [here](https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html#scipy) to go to the relevant section of the class website."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "7iAzmaKEp-P0"
+ },
+ "outputs": [],
+ "source": [
+ "def entrance(d, x, Re = 1):\n",
+ " '''Solving for the entrance length of the tube with non constant velocity\n",
+ " Args:\n",
+ " d: δ_star; Normalized δ; partial derivative wrt x or y (numpy array)\n",
+ " x: x_star; Normalized x; position along channel (numpy array)\n",
+ " Re: Reynolds number, constant dimensionless quantity used to show\n",
+ " turbulence or roughness of flow. Set to unity as default value (float)\n",
+ " Returns:\n",
+ " dxdy: Normalized expression for the entrance length\n",
+ " '''\n",
+ "\n",
+ " # assume Re is at unity for the example\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ " dxdy = (Re*d/6)*((1+(2*d))/(2-d)**2)\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ " return dxdy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "BGKBtOjYsBc6"
+ },
+ "outputs": [],
+ "source": [
+ "# Integrate the solution in scipy using defined function\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ "dspan = [0, 1] # since del is dimensionless it will range from 0 to 1\n",
+ " # where del of 0 is at the entrance of the tube and at a del of 1 is the\n",
+ " # begining of fully developed flow\n",
+ "\n",
+ "n = 300 # number of steps in linspace\n",
+ "tspan = np.linspace(0, 1, n)\n",
+ "xo = [0] # we're starting at the entrance of the tube\n",
+ "\n",
+ "# Solve using scipy.integrate.solve_ivp\n",
+ "soln = integrate.solve_ivp(entrance, dspan, xo, t_eval= tspan)\n",
+ "d = soln.t\n",
+ "x = soln.y[0]\n",
+ "### END SOLUTION ###"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "ufUkZqZNHuVN"
+ },
+ "source": [
+ "### 3-3-Plot the results\n",
+ "Plot the resulting data to show the behavior of the integrated expression.\n",
+ "\n",
+ "For more information on how to use `matplotlib` to make publication quality plots, click [here](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html#preparing-publication-quality-figures-in-python) to go to the relevant section of the class website."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "0h4ys3UGHL6L",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 597
+ },
+ "outputId": "09edcec3-d16b-44b0-d5d6-4390f5aa5a5e"
+ },
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "fig = plt.figure(figsize=(5, 3), dpi=200) # formats the plotted figure\n",
+ "\n",
+ "# Plot the integrated expression\n",
+ "plt.plot(x, d, linewidth=2)\n",
+ "\n",
+ "# Format for publication quality\n",
+ "plt.xlabel('x*/Re [dimensionless]', fontsize=10, fontweight='bold')\n",
+ "plt.ylabel('δ* [dimensionless]', fontsize=10, fontweight='bold')\n",
+ "plt.xticks(fontsize=8)\n",
+ "plt.yticks(fontsize=8)\n",
+ "plt.grid(False) # Remove grid lines\n",
+ "\n",
+ "# Customize plot layout\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Show the plot\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "QK8RXm8ZboYw"
+ },
+ "source": [
+ "### 3-4-Define the entrance length\n",
+ "\n",
+ "At what value of x does the boundary layer become fully developed?\n",
+ "\n",
+ "Hint: What is the coordinate where $δ$ = 1?\n",
+ "\n",
+ "Store your solution as a numpy array labelled `Le`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "EYKTX9Qfc20I",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "e54962a0-a928-473c-b68b-a118dde977b3"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Le (x @ δ*=1) = 7955615.397\n"
+ ]
+ }
+ ],
+ "source": [
+ "### BEGIN SOLUTION ###\n",
+ "Le = np.array(x[-1])\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ "# Print Value\n",
+ "print(\"Le (x @ δ*=1) =\",np.round(Le,3)) # we want to know the dimensionless\n",
+ " # length at which del is 1 since this will give us our entrance length where\n",
+ " # flow is stil developing"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "###3-4-Compare the result of approximation with the integral method\n",
+ "Let's first find the entrance lenght for the formula one wind tunnel"
+ ],
+ "metadata": {
+ "id": "Hx9-mqmWPs3u"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "def entrance(d, x, Re = 62666667):\n",
+ " '''Solving for the entrance length of the tube with non constant velocity\n",
+ " Args:\n",
+ " d: δ_star; Normalized δ; partial derivative wrt x or y (numpy array)\n",
+ " x: x_star; Normalized x; position along channel (numpy array)\n",
+ " Re: Reynolds number, constant dimensionless quantity used to show\n",
+ " turbulence or roughness of flow. Set to unity as default value (float)\n",
+ " Returns:\n",
+ " dxdy: Normalized expression for the entrance length\n",
+ " '''\n",
+ "\n",
+ " # assume Re is at unity for the example\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ " dxdy = (Re*d/6)*((1+(2*d))/(2-d)**2)\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ " return dxdy\n",
+ "\n",
+ "# Integrate the solution in scipy using defined function\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ "dspan = [0, 1] # since del is dimensionless it will range from 0 to 1\n",
+ " # where del of 0 is at the entrance of the tube and at a del of 1 is the\n",
+ " # begining of fully developed flow\n",
+ "\n",
+ "n = 300 # number of steps in linspace\n",
+ "tspan = np.linspace(0, 1, n)\n",
+ "xo = [0] # we're starting at the entrance of the tube\n",
+ "\n",
+ "# Solve using scipy.integrate.solve_ivp\n",
+ "soln = integrate.solve_ivp(entrance, dspan, xo, t_eval= tspan)\n",
+ "d = soln.t\n",
+ "x = soln.y[0]\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ "\n",
+ "fig = plt.figure(figsize=(5, 3), dpi=200) # formats the plotted figure\n",
+ "\n",
+ "# Plot the integrated expression\n",
+ "plt.plot(x, d, linewidth=2)\n",
+ "\n",
+ "# Format for publication quality\n",
+ "plt.xlabel('x*/Re [dimensionless]', fontsize=10, fontweight='bold')\n",
+ "plt.ylabel('δ* [dimensionless]', fontsize=10, fontweight='bold')\n",
+ "plt.xticks(fontsize=8)\n",
+ "plt.yticks(fontsize=8)\n",
+ "plt.grid(False) # Remove grid lines\n",
+ "\n",
+ "# Customize plot layout\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Show the plot\n",
+ "plt.show()"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 597
+ },
+ "id": "ZerxXUKptP6G",
+ "outputId": "8899dd70-2dc6-45e9-b135-2ec64fc2cad9"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "### BEGIN SOLUTION ###\n",
+ "Le = np.array(x[-1])\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ "# Print Value\n",
+ "print(\"Le (x @ δ*=1) =\",np.round(Le,3)) # we want to know the dimensionless\n",
+ " # length at which del is 1 since this will give us our entrance length where\n",
+ " # flow is stil developing"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "0BI6oQ8qwhUu",
+ "outputId": "11bdd4bf-0ca8-4e24-92af-0c5fbc77f5c1"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Le (x @ δ*=1) = 7955615.397\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Activity** Let's reassess the entrance length approximation. For turbulent flow, we initially employed one approximation method. Now, let's verify this by employing the alternative approximation method and compare the 3 different results."
+ ],
+ "metadata": {
+ "id": "vJrY3IfcDXTX"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Given values\n",
+ "wind_speed = 100 # m/s\n",
+ "tube_diameter = 9.4 # meters\n",
+ "air_viscosity = 1.5e-5 # m^2/s\n",
+ "\n",
+ "# Calculate Reynolds number\n",
+ "Re = (wind_speed * tube_diameter) / air_viscosity\n",
+ "\n",
+ "# Determine the flow regime and calculate the entrance length (Le)\n",
+ "if Re < 2000:\n",
+ " flow_regime = \"Laminar\"\n",
+ " Le = 0.005 * Re * tube_diameter\n",
+ " equation_used = \"Le = 0.005 * Re * D\"\n",
+ "elif Re > 3500:\n",
+ " flow_regime = \"Turbulent\"\n",
+ " Le = 10 * Re * tube_diameter\n",
+ " equation_used = \"Le = 10 * Re * D\"\n",
+ "else:\n",
+ " flow_regime = \"Transition\"\n",
+ " # For transition, use the average of laminar and turbulent equations\n",
+ " Le_laminar = 0.005 * Re * tube_diameter\n",
+ " Le_turbulent = 4.4 * (Re ** (1/6)) * tube_diameter\n",
+ " Le = (Le_laminar + Le_turbulent) / 2\n",
+ " equation_used = \"Average of laminar and turbulent equations\"\n",
+ "\n",
+ "# Output the results\n",
+ "print(f\"Reynolds number (Re) is {Re:.0f}, the flow is in the {flow_regime} regime.\")\n",
+ "print(f\"Entrance Length (Le) is {Le:.2f} meters, calculated using the equation: {equation_used}\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "zuxr6D8iDwjT",
+ "outputId": "0f096c97-b289-4f71-a3ea-032743e37a50"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Reynolds number (Re) is 62666667, the flow is in the Turbulent regime.\n",
+ "Entrance Length (Le) is 5890666666.67 meters, calculated using the equation: Le = 10 * Re * D\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Note:** The demonstration reveals that both the model and one of the approximations yield irrational numbers. This emphasizes the critical importance of thoroughly verifying the limitations of equations and models before their application."
+ ],
+ "metadata": {
+ "id": "tC_agxz2DyUn"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Discussion** The model's entrance length behaves illogically at high Reynolds numbers, yielding irrational results. Explore reasons behind this anomaly.\n",
+ "\n",
+ "The model's entrance length fails at high Reynolds numbers, yielding irrational results. This occurs due to increased turbulence impeding laminar flow, disrupting the boundary layer's development."
+ ],
+ "metadata": {
+ "id": "RRs7UP5rBDYj"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "SbcoTuHbtDak"
+ },
+ "source": [
+ "### 3-6-Define An Equation For Le Using New Value\n",
+ "\n",
+ "Using the obtained value of `Le`, make a general expression for the entrance length similar to the expression derived in part 1.\n",
+ "\n",
+ "*Hint*: The value obtained for Le is dimensionless."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "z3iuGDfTvYyr"
+ },
+ "source": [
+ "Submit your answer and written work via **Gradescope**."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "W_TIpO1s6Mjl"
+ },
+ "source": [
+ "### 3-7-Comparing Integration Methods\n",
+ "\n",
+ "Compare your previous results using the `RK45` integration method with alternative methods.\n",
+ "\n",
+ "Define your equation as `methods`.\n",
+ "\n",
+ "For more information on other integration methods for `scipy.integrate`, click [here](https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html) to go to the relevant section of the class website. Further detail into integration methods for `scipy.integrate`, is also provided in the documentation [here](https://docs.scipy.org/doc/scipy/reference/integrate.html)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "eepM5dJK8emB",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "6c0366f7-990c-4a7d-af01-ae243c97ffab"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Using method RK23\n",
+ "Number of RHS function evaluations: 83\n",
+ "Le (x @ δ*=1) = 7954490.72986\n",
+ "\n",
+ "\n",
+ "Using method RK45\n",
+ "Number of RHS function evaluations: 38\n",
+ "Le (x @ δ*=1) = 7955615.39722\n",
+ "\n",
+ "\n",
+ "Using method DOP853\n",
+ "Number of RHS function evaluations: 89\n",
+ "Le (x @ δ*=1) = 7955285.42507\n",
+ "\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# make a list of methods\n",
+ "methods = [\"RK23\", \"RK45\", \"DOP853\"]\n",
+ "\n",
+ "# loop through methods for best\n",
+ "for i in methods:\n",
+ " print(\"Using method\",i)\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ " other_methods = integrate.solve_ivp(entrance, dspan, xo, method=i, t_eval= tspan)\n",
+ " d1 = other_methods.t\n",
+ " x1 = other_methods.y[0]\n",
+ " Le = np.array(x1[-1])\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ "# print values for each method within loop\n",
+ "# some solver statistics\n",
+ " print(\"Number of RHS function evaluations:\",other_methods.nfev)\n",
+ "# calculated length from each method\n",
+ " print(\"Le (x @ δ*=1) =\", np.round(Le,5)) # dimensionless\n",
+ " print(\"\\n\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Note** All the various numerical methods demonstrated above exhibit consistent accuracy up to the fourth significant digit in solving the integral."
+ ],
+ "metadata": {
+ "id": "_GHddIDwSer0"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "_45mKgasR0Y6"
+ },
+ "source": [
+ "## 4-Discussion and Analysis"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "OXqzw7jWR0Y6"
+ },
+ "source": [
+ "### 4-1-Explain why the equation derived in Question 3d differs from the one obtained in Question 1.\n",
+ "**Discuss** in 1-3 sentences.\n",
+ "\n",
+ "**Answer**:in that part of the notebook it shifts away from the assumption of a constant and uniform fluid velocity upon entering the channel. Instead, it considers the variable nature of this velocity across the entrance, influencing the way flow is analyzed. As a consequence, the initial flow condition changes over the developing region, leading to an extended entrance length."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "N93m2GRF90ci"
+ },
+ "source": [
+ "### 4-2-Describe the integration methods used in 3g and how they differ in performance. Was the best method used originally in 3b? Why or why not?\n",
+ "\n",
+ "\n",
+ "**Discuss** in 3-5 sentences.\n",
+ "\n",
+ "**Answer**:at 3-7 , we compared three numerical integration methods: RK23, RK45, and DOP853, ranked by their error levels. RK45 provides similar precision to DOP853 but with fewer iterations. Thus, our choice to use the default scipy.integrate_ivp method was valid."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### 4-3- A Reynolds number of 1 was used as a starting point to simulate laminar flow. If the Reynolds number were increased, what would happen to the entrance length? Does it get larger or smaller? Why does this occur?\n",
+ "\n",
+ "**Explain** your reasoning using the derived equations for `Le` and the nature of turbulence.\n",
+ "**Discuss** in 3-5 sentences.\n",
+ "\n",
+ "**Answer**:As the Reynolds number increases, the entrance length also grows due to the increased turbulence in the flow. The relationship between entrance length and Reynolds number is directly proportional, meaning that as one increases, the other follows suit. This relationship is substantiated by the derived expressions in both Question 1 and Question 2e."
+ ],
+ "metadata": {
+ "id": "Dh09_QLSLs7i"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "Ga1hxJLNs1H0"
+ },
+ "source": [
+ "To visualize, plot the curve above with the following values of Re:\n",
+ "\n",
+ "1, 10, 100, 500, 1000, 5000.\n",
+ "\n",
+ "*Hints*:\n",
+ "\n",
+ "1. Use a [lambda function](https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-as-Arguments.html#lambda-functions) to allow redefinition of Re.\n",
+ "\n",
+ "2. Make a semi-log plot for easier viewing of trend in results.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "id": "iMNgZLshYyWg",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 625
+ },
+ "outputId": "a7ac6dcc-683e-4d68-db06-98490da76e13"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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JMiOEiOlqcyeK6tqZuGL7v4uMjB+MnCVtHhKh/m/q/7YGKsAJMdHWrVuxc+dO7mPHjh3DsWMDR3ZRAU6IMvBuvwRGYP93hDIv4KH+b+r/tgZqQSGEEEIGkVZoZP73SNoBdw+j/m8rov7vXkrp/waoACfEZDt27IAgCCb/IYQoA28CSpC7A0K95POSvcU0lQP17E2LSt39pv7vXtT/LT0qwAkhhBAjqls6kV/TxsRTorwV04s6APV/A6D+b2saCf3fABXghBBCiFEnjY0fjFRq//dhflyhO+DU/03939ZCBTghhBBixIl8/gHMadEjqP/bIxzwCJM+F5FR/3cv6v+2DirACSGEECOM9X+HeTlZIRuRNZYCDUVsPEKZ7SfU/92L+r+tgwpwQgghhONqcycKatn+76nU/60I1P9N/d/WRAU4IYQQwmGs/WSqYttPjMz/Dp8hbR4Sof5v6v+2JirACSGEEA5jF/BMixpBBbhnBOARKnkqYjPW/50cYF5bh9iM93+nmLWO0f7vuOHR/x02ZrzEmYiPCnBCCCGE4wSnAA/2cESoEvu/G4qBxhI2Tv3fVmW0/ztlBPV/e/vA3T/ACtmIiwpwQggh5BoVjR0ormtn4iNq+gmg2AJ8WPd/BwXCNjjYrHV4O+BuPg5w86b+b2uhApwQQgi5xshrPzFWgI+c+d8hLiEIdJHPpA2j/d9JyRbp/w6S2fhBY/3foQrs/waoACeEEEIYI+oApiDw+7+9ogB383ZahwOa/91Lbgcwjc7/pgKcEEIIGRlOFrIFeJiXE4I95POSvcU0FgNNpWxcoe0n1P/di/q/rYsKcEIIIaSfsoZ2lNazL9krtv2k0Mj4QYUW4NT/Tf3fckAFOCGEENKP8fYTL4kzkQj1f1P/t5WNtP5vgApwQgghZICTBfXc+FQl7oALAr8A944B3ORTkFoK9X/3ov5v66MCnBBCCPmRIAjcCSgR3k4IdJfPS/YW01AINLMFqVLbT6j/uxf1f1sfFeCEEELIj0rrO1DeyOn/VuL0E2DEtZ+kV7F91YAM+7/T0pjYjfR/l1H/t2xRAU4IIYT8yNj8b0W2nwB0ABNAsEuwvPq/r15Fd1ERE3dOSjKrIG2p70Qzr/9bZrvfJRfPceMho8dKnIm0qAAnhBBCfsS7fh5Q6AQUY/3fPrGAq7/0+YisrKUM5a3lTDwlMMUK2RjH2/0GAKeUqWatU36Z334SEiezA5gXznLjYWMnSJyJtKgAJ4QQQtDb/82bgBLl6ww/NwcrZCSy+gKgpYKNj7D2k+QA8/qqxdZ2kl+AO5vZ/11mpAAPllkBztsBd/P1g7uf8p4E9kcFOCEmqq6uxt69e7FhwwYsWLAAPj4+UKlUUKlUWLlypdnr7d+/H0uXLkVISAjs7e0REhKCpUuXYv/+/ZZPnhByXcV17ahq7mTiitz9Bvi3XwKKbT9Jq+QXtnIqwAVBQNvJE0zcNizMrP5vQRC4O+Ae/k5w8ZTPk8mm6qtoulrFxEPHjFd0/zcA2Fg7AUKGC39/yzwb1+v1eOSRR7Bt27YB8fLycpSXl2P37t1YtWoV3n77bajV9ByZEKkYaz8Zef3fytsBFwSBuwMe5R4FXydfK2TE11NWBm1FJRN3TjGvTaapugOtDV1MXG6736VG+r+V3n4C0A44ITckLCwMt9xyyw197DPPPGMovidOnIgPP/wQ6enp+PDDDzFx4kQAwNatW/Hss89aLF9CyPUZvYBHiQW4sf5v33jAxU/6fERW2FSI2o5aJi6n3W8AaDt5kht3mmpeAW6s/URu/d/GDmCGjlHu/O8+tANOiIk2bNiApKQkJCUlwd/fH0VFRYiMjDRrjdzcXLzyyisAgClTpuDw4cNwdOwdB5WUlIRFixZhzpw5yMzMxMaNG/Hggw8iJibG4p8LIWQgY/O/R/m5wNfV3goZiawuD2hlX/pX4u43AKRV8dtPZHcA02j/t3l5GjuAKacLeARB4B7A9AwKgauXjxUykhbtgBNioj/96U9YuHDhkFpRXnvtNWi1WgDApk2bDMV3HycnJ2zatAkAoNVq8eqrr954woQQkxXUtqG6hX3JXpG73wBQeJgfV2j/d3ol236igkpW878FQUAbZwKK/agY2PiYXpAKegHlnAt4vINd4OhqN6QcLamhshytDeyts2FjxlshG+lRAU6IRARBwOeffw4AiI+Px9Sp/JFSU6dORVxcHADg888/hyAIkuVIyEhlrP1EsRfwFB7ixxW4A64X9Nz+73iveHg4eEifkBHd+fnQ1bJtMuaOH6yvbENHSw8Tl137yQVj/d9UgBNCLKiwsBAVFb0jv+bMmTPo+/Y9Xl5ejiLOhQyEEMsydgFPSqSXxJlIQK/nH8D0Hwc4K++l/8v1l9Hc3czE5df/baT9xNz+7xwj7Sfx8irAjc3/DklQfv83QAU4IZK5dOmS4e34+PhB37f/49nZ2aLlRAjp6/9mXwqP83eFt4sC+7+vXgA62M8XkbOlz0UCRud/B8qrAG9P4xzAVKnglJRk1jq8A5gqlbxuwBT0epRcOs/EfcMj4eTmboWMpEeHMJXsizVA9Qgq3vxGA4s2WTsLo8rKygxvh4SEDPq+oaGhhrdLS0tFy4kQAuRVt6K2le3/Vm77iZH+b4UW4Lz53xqVBpP9J1shGz5Bp0NbegYTd0hIgMbd9IJUr9OjgtP/7RvuBntH+ZR8NSVF6GxhX5UYKe0nABXgyladDZSx39DEOlpaWgxvu7i4DPq+zs7OhrdbW1tFy4kQMtj8bwW2nwD8AlylAcKnS5+LyHr0PTh19RQTH+szFs62zpyPsI7OnBzom5qYuLnjB2tKW9HdqWPicuv/Njb/O3SM8ud/96EWFEIk0tn50w17dnaDn0S3t//pZe+Ojg7RciKEAMfz2AJcpQJSIhW4A67rAYqPsfHgSYCDm/T5iOxi7UW0a9uZuNz6v0UfPxjnYW5Koirh9H+r1GqEjB5rhWysgwpwQiTi4PDT9b/d3d2Dvm9X108vh187qpAQYjk6vcDdAU8IdIOns3xGtllMRRbQzXlVTaHtJxlV/FeB5Tb/u43X/21jA8dJ5rXJ8Pq/1RoVAqM9bjAzy9PrdCjLvsDEA6JGwd7JyQoZWQcV4IRIxNXV1fD29dpK2traDG9fr12FEHLjLlU0o6mDHdk2XbH930bGD0YOPplpuOJdwGOntsMEX/m0Ogg9PWjPZNtkHMeNg8bF9DYZnVaPyiuNTNw/0g229pqhpGhRVwvy0M15ZTd0BPV/A9QDrmx+o62dgbRk/vn2P3jZ/0AmT/+Dl/0PZBJCLOt4Pjt3GQCmxyhvHB8AoIBTgGvsgVB5tWRYQpeuC2eqzzDxRL9EONg4sB9gJR3nL0BoZ9tkzO3/vlrYDG2PnonLrf+b134CAGEjqP8boAJc2WQ8EWQkSkhIMLydk5Mz6Pv2f3z0aHk/sSBkODvGuYDHRq1CcoQCD2D2dAClnJF8YSmArfJa3c7VnEOXjp1uI7v+b177CQBnMy/g4bWfAECIzOZ/l3AOYGpsbBAUN/h4XqWhFhRCJBIZGYmgoCAAwKFDRl4G/tHhw71TCoKDgxERESF2aoSMSN1aPTIK2XnYiaEecLZX4P5UaTrAKUiV2v/NGz8IyLD/m3MAU2VnB8eJiWatwzuAaWOrhn+EfOZqa3t6UJFziYkHxsbD1l4+r0pIgQpwQiSiUqmwePFiAL073CdP8nc9Tp48adgBX7x4MVQqlWQ5EjKSnCltREcPO7JNse0nI6z/m3cBj6ONI8b4jLFCNnz6zk50ZGUxccdJk6C2N/0SqJ5uHaoK2DGGgTHu0NjKp9SrvJIDbQ87hGCktZ8AVIATIqm1a9dCo+k9DLNmzRpmxGBHRwfWrFkDALCxscHatWulTpGQEeNYHr//e4ZiD2By5n/buQJBk6TPRWTtPe04X8PetDjZfzJs1bZWyIiv48wZCJypWOZeP1+V1wS9TmDiwbLr/zYy/3uEHcAEqAecEJMdPXoUeXl5hr/X1v70yzsvLw87duwY8P4rV65k1oiNjcW6devw17/+FZmZmZgxYwaeeuopREdHIz8/Hy+99BKyftwNWbduHUaNGiXK50II4R/AdLBVIzHMQ/pkxNbZDJSfZuPh0wGN8kqB09WnoRW0TDwlQG7tJ/xXQp3MnP9ttP87Tl5nGUovsgcwbeztERgTa4VsrEt533WEiGTr1q3YuXMn97Fjx47h2LGBl1vwCnAAePHFF1FdXY133nkHWVlZuPfee5n3eeihh/DCCy8MOWdCCF97txZZJY1MPCnCC/Y28hnZZjHFxwGBbbdRav93eiXnsCmA5ECZHcDk9H+rnZzgONa8C2l4Bbidgwa+YfIZY9vT2YnKK5eZeEj8GGhs5POqhFSoBYUQianVamzbtg1ffvklFi9ejKCgINjZ2SEoKAiLFy/Gvn37sHXrVqjV9O1JiFjSC+uh1bMv2c9QbP83p/0EAKKU2f/Nm//tZueGOM84K2TDp2ttQ8d5tk3GMWkKVLamF6RdHVrUFDcz8aBYT6g18vk9Up5zEXod+yQwdMzIaz8BaAecEJPt2LGDaTMZitTUVKSmplpsPUKI6Y5zxg8CI+wCHidvwE8+BxItpamrCdl12Uw8KSAJGrV8Xt3oOJUJcApSc8cPVlxphMA+l5Tf/G/O+EEACBs78g5gArQDTgghZATi9X+7OdhgTJB8RrZZTFstcJW9+hsRswAFvtKWeTUTAtiKVG7zv3njBwHzD2CW5/D7v4fDAUx7J2f4RUZZIRvrU953HiGEEDKIxvZuXKxgX7KfFu0NjVqBYz+LjvDjI6z/W3bzvzkX8Kjd3WEfb96FNLz+bwcXW3gHmX6Nvdg6W1tRXZjPxEMSxkEto1clpEQFOCGEkBHlRH4d9yX76dEK7f/mXT8PjKj5394O3ohyl89Oq7ahAV3Z7I3IzsnJUJnxqkRHSzfqyluZeHCsJ1QyejJZln0BgqBn4mEjcPxgHyrACSGEjCjHOO0nADAjRqn935wDmG7BgHe09LmIrLajFnmNeUw8OTBZVpeatWdkgPcs0Mnc9pPcRm5cftfPs+MHASBshB7ABKgAJ4QQMsLwDmD6udoj2lc+I9sspqkMqGdf+kfkbEBGBamlZFRlcONym//NGz8IAM5TzTuAaXz+t7wK8FJO/7ejmzu8Q8OtkI08UAFOCCFkxKhq6kRBTRsTnx7tLasdUosxNn5Qof3fJypOcOOyO4B5/DgT0/j6wC7KvDaZ0ux6JubsYQ93P8cbzs3S2hobUFtazMRDx4xX5veciagAJ4QQMmIYu35++kib/63AAlwQBJyoZAvwYJdghLqFWiEjvp6KCnQXFTFx52nTzCpIm2s70FzTwcRD4z1lVdgWnz/DjYePS5Q0D7mhApwQQsiIMaLmfwsCvwD3igbcQ6TPR2QlLSWoaqti4lMDzWvrEFvbCf71887Tppu1TpmR8YMho+V1/XwJFeBcVIATQggZEQRB4M7/Dvd2QoinkxUyElldPtBczsYVevvlyQp+YTs1SG4FOL9NxnmaeXmW5rDtJ4C8DmAKgsDdAffwD4S7n7/0CcmIIgvwrq4uPPXUUwgKCoKjoyNSUlLw7bffmvSx3333HW666Sb4+PjAw8MDycnJeO+990TOmBBCiNgKa9tQ2dTJxBU7fpB3+yWgyPYTADhZyS/A5XQAUxAEbgFuFxUF24AA09fRC9wdcK8gZzi72w8pR0uqryhDaz37qlPYuJF5+2V/iizAV65cib///e+4//778frrr0Oj0SA1NRVHjx4d9OO++OIL3HLLLeju7sZzzz2HF198EY6OjnjggQfw6quvSpQ9IYQQMRhrP1Hs+MGCg/x4xCxJ05CCTq9DWhU7WWS012h4OshnR7gr9wp0dezXofO0aWatU1veis7WHiYup91vgNpPBmNj7QQsLT09Hf/5z3+wceNGPPnkkwCABx54AGPHjsX69etxnHPyuM/mzZsRGBiIH374Afb2vc8gV69ejfj4eOzYsQO//e1vJfkcCCGEWB6v/QQApkUpsADX6/j93/7jAGfl7fhn12ejpbuFicuv/5tfgzhPN68AL8vm93+Hxsur/7v4PGf+t0qF0BE8/7uP4grwTz75BBqNBo888ogh5uDggIceegi///3vUVpaitBQ/mno5uZmeHp6GopvALCxsYGPz439sCorKxv08crKyhtalxBCiHn0egEnODvg8QGu8HaRz0v2FlN5BuhsZOPRcyVORBrG2k/kV4Bz+r/VajglmzcmsYzT/61SqxAU63GDmVmeXqdD6UV2/rd/ZDQcXd2skJG8KK4Az8rKQmxsLNzcBv7PTf7xi/vMmTNGC/C5c+fipZdewh/+8AesWLECKpUKH3zwATIzM/HRRx+ZnYuxf4cQQoi0squa0dDOvmQ/Q6njB/MP8ONRcyVNQyq8A5i2altM9J9ohWz4hO5utGdkMnHHceOgcXU1eR1djx4VVxqZeECkG+wc5FPWVeVfQXdHOxMPo/YTAAoswCsrKxEYGMjE+2IVFRVGP/YPf/gDCgsL8eKLL+KFF14AADg5OWHXrl1YvHixOAkTQggRndH530ocPwjw+781dkCYeaPuhoMObQdOV59m4hP9JsLRRj4X0nScOwehnS1InWeY9/+kqqAJ2h49Ex824wfHJkqah1wprgDv6OgY0ELSx8HBwfC4Mfb29oiNjcXy5ctx5513QqfTYcuWLfjFL36Bb7/9FlPNvCK2tLR00McrKysNO/OEEELEc+QKW4Br1CokR8qraLGI7naglHPVeWgKYKe8cYtZ1Vno0bOvbsiu/eS4sfGD5vV/Gxs/GCqzA5jFF84wMY2tLYLiR0ufjAwprgB3dHREV1cXE+/s7DQ8bszjjz+OkydP4vTp01CrewfE3H333RgzZgx+85vfIC2N8wNtECEhyrvogBBChpvOHh3SC9miZWKoB1wdbK2QkciKjwO6bjYefZP0uUjA6Pxv2RXg7AFMlaMjHCeYN5KvlHMA09ZeA79I+fRV93R2ouJyDhMPjkuArZ0Cz1zcAMWNIQwMDOQebuyLBQUFcT+uu7sb27Ztw+23324ovgHA1tYWCxYsQGZmJrq7OT/QCCGEyFpmUQO6tOxL9jNHKbT/u2CE9X9zDmC62roiwTvBCtnw6Vpa0HH+PBN3SpoClZ2dyet0tvWgpriZiQfHekCjkU9JV5ZzEXqdlolT//dP5PN/y0ISExORm5uL5uaBX6B9u9eJiYncj6urq4NWq4VOp2Me6+npgV6v5z5GCCFE3o7k1XDjsxRbgB9kYw4eQGCixImIr6GzAdn12Uw8OTAZGrXGChnxtWdkAJwawtzr5ytyGyEIbDxEduMHz3DjNP/7J4orwJcvX27o3e7T1dWF7du3IyUlxTCZpKSkBDk5P7084ufnBw8PD3z22WcDdrpbW1uxZ88exMfHD9q+QgghRJ6Ocvq/Xe1tMCHEQ/pkxNZaDVy9wMYjZwMyKkgthXf5DiDH9hMj/d9mzv82ev38aHn1f/MOYDo4u8AvMkr6ZGRKcQV4SkoK7rrrLjz99NNYv349tmzZgnnz5qGoqAgvv/yy4f0eeOABjB7900EAjUaDJ598Erm5uZg6dSpee+01/O1vf0NycjLKysrw7LPPWuPTITJSXV2NvXv3YsOGDViwYAF8fHygUqmgUqmwcuVKs9fbv38/li5dipCQENjb2yMkJARLly7F/v37TV5Dq9Xin//8J2bNmgVfX184OjoiOjoaq1evxsWLF83OiRClqWvtwsUK9iX7qdHesJHRS/YWU2Dk+nnq/7Yq3vxvjbc37EeNMmsd3vXzTm528Ap0vuHcLK29qRE1xYVMPHTseKgV+CTwRinuECYAvPvuu/jDH/6A9957Dw0NDRg/fjz27t2L2bNnD/pxzzzzDCIjI/H666/jT3/6E7q6ujB+/Hh88sknWLZsmUTZE7ny9/e3yDp6vR6PPPIItm3bNiBeXl6O8vJy7N69G6tWrcLbb7894DzCtWpra5GamoqMjIwB8YKCAmzZsgU7d+7E5s2bsWrVKovkTchwdMzI9fMjqv0EGFH934HOgQh3C7dCNnw9V6+iOz+fiTtPnQrVID/jr9VS34nGq+wYw5DRnlCpVEPK0ZJKLnBuvwQQPk4+M9nlQIFP/3tHDm7cuBGVlZXo7OxEeno6br311gHvc/DgQQicRqqf//znSEtLQ0NDA9rb23Hy5EkqvgkjLCwMt9xyyw197DPPPGMovidOnIgPP/wQ6enp+PDDDzFxYu8PqK1btw76qotOp8PSpUsNxfedd96J/fv3Iy0tDW+88Qb8/PzQ1dWF1atXm7WjTojSHL3C7/+eqcQLeASBfwDTIxzwUt5L/6UtpShvLWfiUwOnyqog5d5+iRu4ft7o+EG59X8bK8ATpU1E5hS5A06IGDZs2ICkpCQkJSXB398fRUVFiIyMNGuN3NxcvPLKKwCAKVOm4PDhw4azBUlJSVi0aBHmzJmDzMxMbNy4EQ8++CBiYmKYdXbu3ImjR48CAB577DG8+eabhseSk5OxYMECTJ48Gc3NzXjiiSeQnZ0NGxv6dicjiyAI3P7vYA9HRPrI5yV7i6nLA5rZgnQk7X4D8ms/aTdWgJs7/5szfhAAQmQ0/1sQBBSfz2Libr7+cPcPsEJG8qXIHXBCxPCnP/0JCxcuHFIrymuvvQattnc006ZNm5iDvU5OTti0aROA3v7uV199lbtOXxHv5eWFjRs3Mo/HxMTg6aefBgDk5eXhs88+u+GcCRmuCmrbUNHUycRnjfKR1Q6pxRi7fn6E9X8nB8rngjtBELgHMO3Cw2FrZCyysXV4O+CeAU5w8XQYUo6W1Hi1Ei217KtO4eMmKPN7bgioACdEIoIg4PPPPwcAxMfHG71ZderUqYiLiwMAfP7550yrVG5uLrKze8du3X333XBy4t9s1/9gKBXgZCTi7X4DSp7/fZATVAGRc6TORHR6Qc+dgBLrGQsfR/n8/+3Oz4e2hi1Izb1+vr6iDR0t7G2fw+X6eZr/zbL4a9LvvvuuxdaKiIi47sFJQoaLwsJCVFRUAADmzBn8F+KcOXNw+fJllJeXM60ufa0n11snICAAsbGxyM3NxbFjx4aYPSHDD+/6eZUKmBEtnwLNYnRaoOgIGw+cADjJq0izhJz6HDR1NTFxubWfGBs/6GR2+8kwuX7eWAE+1rzbPkcCixfgK1eutNjLDMuWLaMCfAieO/4crjResXYakhnlMQrPTX/O2mkYdenSJcPb8fHxg75v/8ezs7MHFODmrpObm4vS0lK0tbXB2VmBfa+EcPTo9DhZwE5AGRvkDk9n028eHDYqTgNd7LhF6v+2Lu4BTLUazsnmtcnwxg+q1CoExcqnANfrdSi9cI6J+0ZEwcnN3QoZyZtop7J4E0aItK40XsG5GvabgVhHWVmZ4e2QkJBB37fvwigAKC0tHfI6giCgrKzM0NpCiNKdLW1Eaxd7FbZi209GWP/3iQq2sLVR22Cy/2QrZMMn9PSgPT2diTuMHQuNu+kFqU6rR/mVRibuH+EKe0f5HK6vLshHZ1srE6fpJ3yy7QGnZn2iNC0tLYa3XVxcBn3f/jvVra0Df6BZah1ClIzXfgIAs5Q4fhDg93/bOACh8toRtoRObSeyqtlJGxN8J8DJln8mxho6zp+Hvq2NiZs7/eRqYRO0Xew19sPm+nlqP+ES7alTUlISHnvsMbM/ThAEPPjggyJkRIh1dXb+NI3Bzm7wl8Dt7e0Nb3d0dIiyDiFKdjSPLcAdbNWYHCGfl+wtpqsFKGN3WhE2DbCVz4QMSzl99TS6dF1MPCUwxQrZGNfW77xOf87TzHtSVHLRyPXzMuv/Ljp3molpbGwQHD/GCtnIn2gFeHh4OFasWHFDH0sFOFEiB4effhF2d3cP+r5dXT/9crl2VOG16/T/uznrEKJUzZ09OFPayMSTI71hb6PAq7CLjwN6tt1Gqf3fxyuOc+MzgmZInMngWjmH31WOjnCcNMmsdXgHMG3tNQiIkk9fdXdHOyou5zDx4PgE2A7yO2okE6UAt0T/N/WQD90oj1HWTkFScv98XV1dDW9frx2krd/Llte2mVy7zmAF+GDrEKJUJ/ProNOzv0MU234ywvq/j1Wwha2bnRvGeMtnp1XX2IjO8xeYuFNyEtTXeeWyv47WblSXtDDx4DhPaGzk00Vceuk89Dr2SWD4ePOebIwkFi/A+y4OGTXqxoshS6xBIOuJICNR/wOT/Q9S8vQ/eNn/QCZvHR8f40VF3zoqleq6BzYJUQpe+wmg4AOYvOvnnbwB/3HS5yKy6vZq5DXmMfGpgVOhUcvn1Y22kycBvZ6Ju8wwb5e+LLsB4OxHhsps/nfRWbYnHwAiJlABbozFC/Df/OY3sliDELlJSEgwvJ2Tw75U11//x0ePHj3oOomJidddJzQ0lEYQkhGDdwGPj4s94gNcOe89zDWVAzWcnyeRcwC1fHZILcVY+8n0IPMuthFbq7H+75kzzVqn5BI7ShMAwhLkVYAXc/q/ndw94BsWIX0yw4TyvjsJkanIyEgE/Xj18KFDhwZ938OHDwMAgoODERERMeCxmf1+gA+2TlVVFXJzcwEAM8zcdSFkuCpv7EBBLTt5YmaMtzKna+X/wI8rtP1kOBTggiCg7Ribp01gIOz63elgyjqll9j+b1dvB7j7yedMT1N1FRoqK5h4+LhEqBT4JNBSRP8v09bWhkuXLuHSpUuorq42xDdv3oyoqCg4OTlhypQp1y1ICBnuVCoVFi9eDKB3Z/rkSf5FEidPnjTsXC9evJgpGmJjYw274h999BHa29u56+zYscPw9tKlS4eaPiHDwpFc9tpvAJg5ylfiTCSS/z0/Hn2ztHlIQC/ocbKC/bkZ6R6JQJdAK2TE111YCG1lJRN3mTnDrCeB9ZVtaGtiD+yHJXjJ6slk8bkz3Di1nwxO9AJ827ZtGDduHMaNG4c9e/YAAPbu3YsnnngCxcXF6OzsxOnTp3H77bejsLBQ7HQIsaq1a9dCo+ntU1yzZg0zGrCjowNr1qwBANjY2GDt2rXcdZ588kkAQH19PdavX888np+fj7/85S8AgJiYGCrAyYhx+IqRAlyJBzD1Ov4BTN94wD1Y+nxEll2fjYYu9kZIOe1+A4OMHzTzlUje7jcAhMqs/aToLNt+AgDh4ydKnMnwIvoVSpmZmRAEASqVCrfccgsAYMuWLYbHVSoVBEFAR0cH3nzzTbzyyitip0TIDTl69Cjy8n46/FNb+1OfaV5e3oAdZwBYuXIls0ZsbCzWrVuHv/71r8jMzMSMGTPw1FNPITo6Gvn5+XjppZeQldV7mGXdunVGDyKvWLEC77zzDo4dO4Y333wTVVVVePjhh+Hp6Yn09HQ8//zzaG5uhlqtxhtvvAEbG/nclkaIWLQ6PfcCnjh/VwS4K3AUWkUW0NnIxhW4+w3wb78E5FeA88YPQq2G81Tz5n/zCnCVWoWQOPnM/9brdCi5cJaJ+4ZHwtlDPnnKkei/lc+e7f0fExISYpjmcPjwYahUKjg7O8PPzw8FBQUAgAMHjIxSIkQGtm7dip07d3IfO3bsGI5d80OXV4ADwIsvvojq6mq88847yMrKwr333su8z0MPPYQXXnjBaC4ajQa7d+9GamoqMjIysGvXLuzatWvA+9jb22Pz5s1YsGDBdT4zQpThbFkjWjrZUWhz4hTafpJnpP0kZp60eUjkWDlb2NqqbTHFf4oVsuHTd3ejPT2DiTuMGwuNh4fJ62i7dUaun3eDvZPtEDK0rMq8XHS1s2cuaPf7+kRvQamurh4wAq2kpATNzc0AevvAL126hMDAQAiCQC0oZERQq9XYtm0bvvzySyxevBhBQUGws7NDUFAQFi9ejH379mHr1q1QX+fwio+PD44fP4633noLM2fOhLe3NxwcHBAVFYWHH34Yp06dwqpVqyT6rAixvkOX+e0ns0dS/7eNAxCuvEPXbT1tOFNzholP8pskr+vnT5+GwLl12GWGedNPKvOaoOthxxiGjZFX+wlv+glA/d+mEH0HvL6+9yUUPz8/AMCVK1cMj02fPh12dnaYOHEiKisrr3s5CSHWtGPHDqbNZChSU1ORmpo6pDVsbGzw6KOP4tFHH7VQVoQMX4c4BzAdbTWYosTr5zsagbJMNh4+HbCVz4QMS8moyoCWc9vntKBpVsjGOKP93zPNe1JkbPyg/OZ/swW4jZ09guMSOO9N+hN9B7yv97ShoffgRF8PrUqlMrSk9L2Pk5N8nsUSQggZPurbunGuvImJT4v2hoOtfC5osZjCQ4CgY+MK7f82ev18sLx2+1s54wfVLi5wHGfepUi86+ftnWzgFy6fWfadra2oyrvCxEMTxsLGjNs+RyrRC/CAgAAIgoC0tDS8//772L59OwAgLCwM9vb2AIC6ut5net7e3mKnQwghRIGOXKmBwLkxcE6sQttPjPZ/j5wC3MvBC7GesVbIhk9bW4uu7Gwm7jxtKlS2pvdttzV2oa6c7asOifeEWiOfudolF85AENg2Gbp+3jSit6BMmTIFhYWF6O7uxgMPPACgd/e7/2UiOTk5A3bECSGEEHPw2k8AYLYSC3BB4F/A4xrUO4JQYcpaylDcXMzEpwdNh1oln4K07Th/l97s8YOc3W9Ahu0n5+j6+aEQ/Sv3wQcfHPB34cctir54RkaGYQd8qpkjegghhBC9XsDhXHb8YJiXEyK8FdjaWHsFaCpl4zHzABld0GIpw+H2S8CS18/Lf/63IAjc/m8Xbx94BYdYIaPhR/QC/NZbb8XLL78MZ2dnCIIAZ2dn/OUvf8HcuXMBAN999x3c3d3h5uaGWbNmiZ0OIYQQhcmuakZtaxcTnxPrK6sbAy1mBN1+CRif/y2nA5iCXo+242yetuFhsAsxvSAV9AJ3B9zD3wlu3vI5XNtQWY6WWvZVp4jxk5T5PScCSW7nePLJJ7F27VrU1NTAx8cHtv16oZ5++mk8/fTTUqRBCCFEgXi734BC208Afv+3Sg1EzZU8FbFp9VqkVaYx8TjPOPg4yud2067Ll6GrZb8OzR0/WFPags7WHiYeJqPdb8D47ZcRE2j+t6kkux7PxsYGgYGBUv1zhBBCRohDudVMzFajwrRoBR7s7+kEijitDkGTACd5FWmWcKH2Alp6Wpj49GB5tZ+08W6/hPnjB432f8usAC/m9X+rVAgblyh5LsOV1U4vZGZm4sEHH0Rqaip+97vf4erVq9ZKhRBCyDDV2qVFZlEDE58S7gUXe8n2mKRTcgLQshe9IFqht19W8Atb+fV/c/K0sYFTcopZ65RcZAtwtUaF4Fj5zLLX9vSg5OI5Jh4QPQqOLvIZkyh3ohfg77//Pvz8/ODn54d//vOfAIDz589j1qxZ2LlzJ77++mu89tprmDFjBlpa2Ge5hBBCiDEn8uug1bPzBxXbfmKs/3sEjR900Dhgkp98Jm3o29vRceoUE3dKTITGxdnkdbo7tagqYGfZB8a4w9ZePrPsKy5nQ9vFnrmg6SfmEb0AP378OGpra1FXV4dp03oPTLz66qvo6vc/r+8a+r4CnRBCCDEFr/0EUPL8b874QXt3IHiK9LmIrKmrCRdqLzDxKQFTYKeRz0Uv7RkZEHrYvm1z20/Kcxuh17FPJuU3fpDf/x0+nvq/zSF6AX76dO//KC8vL0yYMAEA8M0330ClUkEQBMNYQgDYu3ev2OkQQghRCEEQuPO/fV3tMTpQgS+FN1cC1RfZeNRsQKO8dpsTlSeg51z0MiNIZrdfHjEyftDMA5glF/nXz4clyOssQ9EZdrffztEJgTFxVshm+BK9AC8vL4dKpUJ4eDgAoKamBhUVFQCADRs2IDc3Fy4uLhAEAZcvXxY7HUIIIQpRVNeO0nq2H1q54wc5u9+AYscPHi3jF7ZyO4DZeuQwE9N4esIhYbTJawiCgOILbAHu6GoLnxCXIeVnSS31tagpLmTiYWMnQGOjvCeBYhK9AK/9cSxPUFAQAODKlSuGx+68807ExMQgJaX3kEJDA3uQhhBCCOE5dJnffkL938OfXtDjaDlbgAe7BCPSLdIKGfF1FxWhp7iEiTvPnAmVxvS+7car7Wip62TiYWO8oVLL58lk0Rl++0nkxMkSZzL8iV6A6/W9Lx/1/NgflZ+fb3gsMrL3m8jVtfelQht69kQIIcREvPYTlQqYFSOf+dAWo9fxd8C9RwEeYdLnI7Kc+hzUdbI7wjODZ8rq1Y3Ww0e4cZfZ5l0syNv9BoDwMfJqPyk8k8mNRyYq7wyC2EQvwL28vCAIAjIyMlBeXo59+/YBAHx8fAyFd3NzMwDA21teX2iEEELkqbNHhxMFbNEyIcQDns7yOaBnMeWngA7Oq8QxP5M+Fwnwdr8BYFawvG7Mbj3CKcBVKvOvn+f0f6tU8pr/rdNqUXzuDBP3CYuAq7cCn/SKTPQt57Fjx6KqqgoNDQ0IC+t9lq5SqZCcnGx4n7y8PKhUKgQEBIidDiGEEAU4UVCHzh72gJ5i20+ufMOPj5ovbR4SOVLGFra2alskBSRZIRs+fUcH2tPYWzodxo+Djafpc7u7O7Uov9LIxP0j3eHgbMt+gJVU5Gaju6OdiUcmUvvJjRB9B3z58uWGt/tPPbnrrrsAAIWFhSgp6e2fmjyZ/icSQgi5voM5/P7vefF+EmciEV4BbusEhMtrIoglNHU14Vwte9HLFP8pcLJ1skJGfO3p6RC6u5m4y6zZZq1TntsIvZYdPxg+Vj673wBQyJl+AlABfqNEL8AfeughLFy4cMC4wdtuuw2//OUvAQCff/45gN7ifPp0eZ1sJoQQIj+CIOAHzgFMb2c7jA92t0JGImu5ClSeZeORcwBbB+nzEdmJCv74wZnB5rV1iM1o//cc8wrwEiP932Ey6/8uymL7v+0cHREUl2CFbIY/0VtQNBoNvvjiC5w8eRKFhYUIDw8fUGgvW7YMN910EwBg1KhRYqdDCCFkmMuvaeOPH4zzhVpGEyMsJu87flyp7Sfl/MJ2Voh8+r8FQUDrYc74QS8vOIwZY9Y6xZz+b0c3O/iGymeWfUt9LWpKiph4+LiJNH7wBkn2X23q1KmYOnUqEw8NDUVoaKhUaRBCCBnmDhhpP7kpbgS1nwCKLMAHGz8Y4RYhfUJGdBcVoae0lIk7z5wBldr05oKGKv74wfAEL1mNHyzM4refRFD7yQ0TvQWlP61Wi8OHD2Pnzp146623pPynCRkylUpl0p+5c+ded639+/dj6dKlCAkJgb29PUJCQrB06VLs37/f5Hy0Wi3++c9/YtasWfD19YWjoyOio6OxevVqXLzIuS2PEIX4gVOAa9QqZR7A1GmB/ANs3DdekeMHs+uzUd9Zz8TlNn6wjTf9BIDL7DlmrWP09suxMms/of5vi5NsB3zLli149tlnUVfX+8WmUqnw2GOP4f7778eJEydga2uL9PR0uLsrsH+PkB/p9Xo88sgj2LZt24B4eXk5ysvLsXv3bqxatQpvv/021IPsotTW1iI1NRUZGRkD4gUFBdiyZQt27tyJzZs3Y9WqVaJ8HoRYS0tnDzKK2AJtcrgn3B3lMzHCYsrSga4mNq7A3W/A+O2Xshs/yOv/VqvhPMO8s2y8+d8qFRA6Wj4HMHVaLYrPn2HiNH5waCQpwP/4xz/ihRdeGHAQs8/8+fPx4YcfQqVSYffu3VixYoUUKRFywx599FE89thjRh93dnY2+tgzzzxjKL4nTpyI9evXIzo6Gvn5+Xj55ZeRlZWFrVu3wtfXF//3f//HXUOn02Hp0qWG4vvOO+/Eww8/DC8vL6SlpeGFF15AdXU1Vq9ejeDgYCxYsGAIny0h8nL0Si20evZ3ychrP7lF2jwkwms/sVPbyW/8YHo6E3ccZ/74wYq8RiYeEDVMxg9OpMt3hkL0AjwzMxMvvPACABhePupfiN9xxx1Qq9W9p9p/+IEKcCJ7fn5+GDt2rNkfl5ubi1deeQUAMGXKFBw+fBiOjo4AgKSkJCxatAhz5sxBZmYmNm7ciAcffBAxMTHMOjt37sTRo72/pB577DG8+eabhseSk5OxYMECTJ48Gc3NzXjiiSeQnZ1Nt8wSxeC1nwBKHj/4LRuzcwFC2TNVw53R8YMB8ho/2JaWxh0/6Gzm9JPyyw3c8YNym35SyJl+AlD7yVCJ3gO+efNmQ8EdEhKC4ODgAY97e3sjJiYGgiDgzJkzYqdDiNW89tpr0Gq1AIBNmzYZiu8+Tk5O2LRpE4De/u5XX32Vu05fEe/l5YWNGzcyj8fExODpp58G0HvJ1WeffWaxz4EQa9LrBRzkXD8f5O6AWH8XK2QksqZy4OoFNh41F7BR3m2fxyuOD4vxg23Gxg+aOf+7+CLbSgUA4TLr/+bN/7ZzdEJQ7GgrZKMcohfgh38c0+Pi4oLMzEykpKQw7xMREQEAhgt5CFEaQRAMM+/j4+O5E4GA3mlBcXFxAHpn5F/btpWbm4vs7GwAwN133w0nJ/6u0MqVKw1vUwFOlOJiRTNqWrqY+E3xfrI6oGcxRscPjpz2E0BeBbggCNzr5zXe3nAYY/o8bEEQuPO/Hd3s4BMinyeTLXW1qOWOH0yk8YNDJHoBXllZCZVKhenTp8PXl39C3d7eHgDQ1tYmdjqEWEVhYSEqKioAAHPmDH5Kvu/x8vJyFBUVDXisr/XkeusEBAQgNjYWAHDs2LEbSZkQ2THWfjLy+r+VdwDT2PjBEJcQeY0fLOSPH3SZOdO88YOV7Wip54wfHCOz8YNnjLSfUP/3kIn+9MXGxgbd3d3Q69mXlfr07Xxf+5I8GZrKP/wBXblXrJ2GZOxjRyHw+edF/3c+/vhjfPTRRygqKoJGo0FAQACmT5+OlStXGi6VutalS5cMb8fHxw+6fv/Hs7OzERkZecPr5ObmorS0FG1tbYMeDiVkODjAuf3SzkaN6THyesneIrTdQMFBNu4/FnALkjwdsWXXDZfxg+zlOwDgPNu8KS28y3cAOfZ/G5v/PUniTJRH9AI8MDAQeXl5SEtLQ2trK/N4VlYWzp49C5VKRRfyWFhX7hV0nOVcX0yGpH8RDPT2Wefl5eHdd9/FkiVLsGPHDmacZllZmeHtkJCQQdfv/31Qes1Oy42sIwgCysrKDK0thAxHda1dOFvWyMSnRXnDyU6BL4WXngS62d+ZStz9BobH7ZeA8fGDLjNmmLUOb/63/MYP9qDkwhkm7hsWAVcvGj84VKK3oPRdO9/S0oL58+ejoKDA8NjGjRsHjEibNm2a2OkQcsOcnJxw77334l//+heOHDmCrKwsfPPNN3jmmWfg7d27a7F7924sXrwYPT09Az62paXF8LaLy+D9ff13qq990mqpdQgZbg5ergFnki1uilPg5TvAiBs/yCvAZTd+sL0d7dfcvQAAjuPHQ+PhYfI6RscPRstr/GB5Tja6OzqYOLWfWIbo2warVq3Cu+++CwBI7zc3UxAE/L//9/8GHDJ78MEHxU6HkBtWXl4OD84P2fnz52PNmjVYsGABsrKycOjQIfzjH//AE088YXifzs6fev3s7AafXtB3JgIAOq754WepdQgZbnjtJwAwL95f4kwkwhs/aO8OhCRLn4vI6jrqcL7mPBNPCkiCo418WlPbTpzgjx80s/2kNLt+WIwfLDjNzjoHgMhEKsAtQfQd8JkzZ2LlypUDCu2+K7v73gaABx54gHbAiazxiu8+/v7++OSTT2Br27t70TdOsI+Dg4Ph7W7OD/D+urp+mvJw7bkIS61DyHCi1elxmDN+MMrXGWHe8pkPbTENRUBNDhuPmQdolNduc6T8CASwBans2k8OHuTGXefONWudovP8/u+IcXIrwNndfntnZwTGDn7+iJhGku/kf/3rX3B0dMTbb7/NHMZUqVR4+OGHB1wmQizDPnaUtVOQlLU/36ioKMyfPx/79u1DXl4eKioqEBTUe1jK1dXV8H7XawfpPw3o2jaTa9fpX5Cbsw4hw8mp4gY0d2qZ+DylTj+5/BU/HqPM/u/DZfyDjXNCBp8YJSVBr0cLpwC38feH/WjT52ELegHF52uZuIunPbyD5fNzur6iHA2V5Uw8YsJkGj9oIZL8V9RoNHjzzTexdu1afPHFFygsLAQAREZGYuHChXQ4TCRSTAQhAyUkJGDfvn0AeltW+grw/gcm+x+k5Ol/8PLag8nXruPjY/wgTN86KpXqugc2CZGz77KvcuM3KfX2y9z9nKBKkf3f3bpuHCtnR6XGeMQgxFU+P7c6L16CroZTOM+da9aUlqvFzeho6WHiEeN8ZDXtxVj7SfRk5bVAWYukT2NGjRqF3/3ud1L+k4RIytgP0ISEny5oyMnhvLTcT//HR1+zs3LtOomJidddJzQ0lEYQkmFLEAR8e4ktwF3tbZAUIZ+JERbT2QwUcWb3hyQBLso7cJp5NRPt2nYmPjvEvFslxdZ64AA37jLXvF36onNsEQ8A4XJrPznFFuAqtRoRdP28xYjeA07ISNJ/RGHf7jfQ+2pP398PHTo06Bp9t8cGBwcbbontM3PmTzfCDbZOVVUVcnNzAQAzzByPRYic5Ne0oaiOLdDmxPnCzkaBv8Lyvwf07A4p4m6TPhcJHCrl/xybGzpX2kSug9f/rXJwgLOZZ9d4/d82dmqExHveaGoW19nWirKci0w8OC4Bji6unI8gN8LiO+B//vOfh/TxGzZssFAmhEirsLAQ337bO7kgOjoawcHBhsdUKhUWL16Mf/zjH8jJycHJkye519GfPHnSsHO9ePFiZkc9NjYWo0ePRnZ2Nj766CP87W9/415Hv2PHDsPbS5cutcSnR4hVfG+k/WR+gkKnnxjr/45dwI8PY4Ig4FAZW4C727tjvM94K2TE13P1Kjqvuf8BAJynToV6kHM412qp70RdGXsGKCTeCza2miHlaElFZ05B4FyeGDVJPiMhlcDiBfhzzz03pD4mKsCJHO3ZswcLFiyAjZHDJ1evXsWyZcsMk0kee+wx5n3Wrl2LLVu2QKfTYc2aNTh8+PCA6SQdHR1Ys2YNgN4bZNeuXcv9t5588kk89NBDqK+vx/r167F58+YBj+fn5+Mvf/kLACAmJoYKcDKs8fq/NWoV5sYqsP9br+PP//YIA/xMP+g3XOQ35qO8lT3oNyt4FjRq+RSkrQf5u/QuZk4/4R2+BIDI8fK61IY3/QQAoqj/26Jkc5RVEARZHUAgpL81a9agp6cHy5Ytw7Rp0xAREQFHR0fU1tbi4MGDePvtt1Fb2/vDdebMmfj1r3/NrBEbG4t169bhr3/9KzIzMzFjxgw89dRTiI6ORn5+Pl566SVkZWUBANatW4dRo/hTXVasWIF33nkHx44dw5tvvomqqio8/PDD8PT0RHp6Op5//nk0NzdDrVbjjTfeMPqkgRC5q2vtwqniBiaeHOEFdyf5XFhiMaXpQAd7HTtiF/Rek6gwvN1vAJgTKp/pJ4Dx8YMuN801ax1j4wfDx8qn/1uv06HwDHv9vId/ILyC5HMoVglE+c0s8K4rI2SYq6iowKZNm5gZ3/0tW7YMW7duHXAJTn8vvvgiqqur8c477yArKwv33nsv8z4PPfQQXnjhBaP/hkajwe7du5GamoqMjAzs2rULu3btGvA+9vb22Lx584CbZgkZbg5croGe8+vk5tEK3P0GjEw/gWL7v3njB21UNpgRJJ9zK/rOTrSdOMHE7RNGw9bf9Daoni4dynLYJ5O+Ya5w9uD/vrCGitxsdLa2MPGoSUm0SWphFi/At2/fbuklCbG6nTt34tChQzhx4gQKCgpQW1uL5uZmuLi4IDQ0FNOnT8eKFSuue5mUWq3Gtm3bsGzZMmzZsgUZGRmora2Fj48PkpKSsHr1apOKZh8fHxw/fhz/+te/8MEHHyA7OxttbW0ICgrCzTffjN/85jcYM2aMpT59QqziO870E2CE9X/buQLhM9n4MNfY2YgzNWeY+GT/yXC1k89Bv7aTJyH0u4G4j+vcm8xapyynHjot21cdQe0nI5bFC/AVK1ZYeklCrG7OnDmYM8dyL4umpqYiNTV1SGvY2Njg0UcfxaOPPmqhrAiRj84eHQ5fYW+/HOXngnBvBY7VrC8Aai+z8Zh5gI2d9PmI7Ej5EegFtiCV3/jBg9y42e0nRsYPyu32y3zO+EE7RyeEjKYNHUtT4AwnQgghw93Jgjq0d+uY+M9G0u43AMQqs/3EWP+3nMYPCoLA7f/W+PrAwYxXGAW9gKILbP+3s7sdfMPks9vfWFWJ+vJSJh4xYRI0Ngo8c2FlVIATQgiRHWO3X/5stEIL8BF0+2WPvod7+2WEWwTC3MKskBFfV3Y2tFfZr0OXOXOgUptePtWUtqC9qZuJhw+T2y9p/KA4JCnAS0pK8D//8z+IiYmBo6MjNBoN9w9NayCEECIIAr7Prmbi3s52SAz1kD4hsXU2AcXH2XhoMuAsrx5hSzh99TRae9h52HNC5DX9pMXI9BNXM8cPGm0/kVn/dz6v/1ulQuTEKdInMwKIXvFevnwZ06dPR2NjI01HIYQQcl0XK5pR2cQefJsX7weNWj47hhaT9z2g17LxEdZ+Ir/xg2yeKjs7i9x+qbGV1+2XXe3tKLt0gYkHjYqHk5u7FTJSPtEL8GeffRYNDb2jdwZ7qYWKc0IIIcAg7SdK7f/ONdL/Hae8MaKCIOBg6UEm7mrnikS/RKnTMaqnuhqd584xcaeUFKidTT8E3NrQhZoSdqxfSLwnbO3kc9lQ0dnT0OvYJ4E0/UQ8ohfgBw8eNBTegiDA1dUV7u7u0Gjk84VHCCFEPngFuJ2NGrNGyesle4vQaY3cfhkO+MZLn4/I8hvzUdrCHvSbGTQTtmr5HPQzOv1krnm79EXn2Ek+ABAxTl5fy/mZJ7nxaOr/Fo3oBXhra2+fl4ODA/bt22fRUW6EEEKUpbKpAxfKm5n4zBgfONkp8JxQyQmgg72gBXHKvP3yh9IfuPF5YfMkzmRwLd9/x427zjMvz4KzxsYPyqcA12m13Pnf7v4B8A4Nt0JGI4PohzAjIiIAANOnT6fimxBCyKC+4xy+BBR8+2XOl/y4Qvu/fyhhC3AbtQ1mBsvnsiFdayvaT7A7wg5jxsA2MNDkdbrae1DOuf3SL8INLp7yuf2y7NIFdLW3MfGYKVNlNaVFaUQvwJcvXw5BEFBRUSH2P0UIIWSYM3b75c3xCuz/FgQgZy8bd/AAIuRTkFpKVVsVLtZdZOIpASlwsXOxQkZ8bUeOQOjpYeKuP7vZrHWKL9ZBr2fPt0Ulymf3GwDyMk9w4zFTpkqcycgiegG+fv16REZGIicnB88//zz0evbmK0vr6urCU089haCgIDg6OiIlJQXffvutyR//3//+F9OmTYOzszM8PDwwffp0/PAD/2UzQgghltHc2YPj+exL9uND3BHg7mCFjERWdQ5oYvuhEXsboJFPP7SlHCg9wI3Lrv3ku++5cZebzSvAC8/w208iJ/ianZNYBEFAXga72+/o6oaguNFWyGjkEL2h7je/+Q1CQkJQWFiI5557Dv/6178wceJEeHuz16+qVCps27ZtyP/mypUr8cknn2Dt2rUYNWoUduzYgdTUVBw4cAAzZw6+q/Dcc8/hz3/+M5YvX46VK1eip6cHFy5cQHl5+ZDzIoQQYtyBnGr06Ngdw/lKvXwnm7P7DQDxt0ubh0R47SeAzG6/7O5G6yF2/KBtWBjsR40yeR1djx7FnNsvPfyd4BngNKQcLelqQR5a69k8oyYnQ03DMkQlegG+Y8cOqFQqqFQqCIKAsrIybjErCIJFCvD09HT85z//wcaNG/Hkk08CAB544AGMHTsW69evx/HjnMsOfnTy5En8+c9/xt/+9jf89re/HVIehBBCzPPNRX77ya1jAyTORCK8/m8bByDGvJ3W4aCpqwmZVZlMfLzPePg5yae/vy09A/pW9pIg15tvNqsfuiy3AT1dOiYeOV5et1/ydr8BICbJvFnnxHySHimX4ovuk08+gUajwSOPPGKIOTg44KGHHsLvf/97lJaWIjQ0lPuxr732GgICAvCb3/wGgiCgra0NLi433pdWVlY26OOVlZU3vDYhhChJZ48OBy+zBzAjfZwxyk8+/cEWU18AVLP90IieB9iZPmd6uDhSfgRagZ0zfVPYTVbIxjij00/M7P8uPMMfPxiZKJ/2EwDIy2D7v23s7RE+PlH6ZEYYSa6iFwThun8sJSsrC7GxsXBzcxsQT07uHSZ/5swZox/7/fffIykpCW+88QZ8fX3h6uqKwMBAbN68+YZyCQ0NHfRPX06EEDLSHcurRVs3u2N4yxh/We0YWoyx6SfxC6XNQyLG2k/k1P8t6PVo/Z7NU+PlBcfERDPWEVDIGT/o6GYH/0g3zkdYR0NlOerKSph4xPhJsLWTz5QWpRJ9B/zAAf6hC7FUVlYikDMmqC9mbBpLQ0MDamtrcezYMfzwww/44x//iLCwMGzfvh1r1qyBra0tVq9eLWruhBAyUn19sYobv3WMQttPeP3fKrUixw926bpwtPwoE49wi0CUe5QVMuLrvHAB2mr2VRiXeTdBZUY/9NWiZrQ3dzPxyPE+UKvl82QyLzONG49JouknUhC9AJd69ndHRwfs7dlnbg4ODobHefouDKqrq8N//vMf3HPPPQB6xyiOGzcOL7zwgtkFeGkp53R7P5WVlbQLTggZ8bQ6PXf+t5+rPRJDPKRPSGyt1UApp/gJnwE4swMKhru0yjR0aNnfvXLa/QaMTz9xnWdm+8lZI+0nE2Q2fpDT/61SqxFFt19KQnHXijk6OqKrq4uJd3Z2Gh439nEAYGtri+XLlxviarUa99xzD/74xz+ipKQEYWFhJucSEhJiTuqEEDIiZRY3oL6N3TG8ZYy/rHYMLebyfgCc1ssRNv1EdgX4D2wBrnJ0hPN08w4kFnDGD9raaxAS73nDuVlae1MjKnKzmXhI/Bg4usqnTUbJJCvAtVottm/fjj179qCwsBAAEBkZiTvuuAMrV66Era1lZp4GBgZyp6z0HXgMCgrifpyXlxccHBzg4eEBzTUvNfn59Z7QbmhoMKsAJ4QQcn0jrv2Ed/kOAMSlSpuHBHR6HXf+t4+jD8b5jLNCRnxdhYXozstn4i4zZ0LtYPoM+oaqNjRebWfiYWO8YWMrn7F++afSey+Cuga1n0hHkgK8tLQUqampuHTpEgAYDl1eunQJX375JV5//XXs27fPIsVtYmIiDhw4gObm5gEHMdPS0gyP86jVaiQmJiIjIwPd3d2ws7MzPNbXN+7rK6/Ty4QQMtwJgsAdP+jmYIOpUcprx0BXC1BwkI0HjAc8wyVPR2zna8+jvrOeid8UehPUKknmQJik1chle2ZPP+EcvgRkePslZ/oJAETT7ZeSEf2rv6enB4sWLcLFixcNhXffXHCg94fvpUuXsGjRIvRwrn411/Lly6HT6bBlyxZDrKurC9u3b0dKSophBGFJSQlycnIGfOw999wDnU6HnTt3GmKdnZ14//33kZCQYHT3nBBCyI25WNGM8ka2P/jm0f6w1cinQLOYK98COrbdhqafWBe3/1ujgYuZ59gKOOMH1WoVwsfK58lkd2cHis+fYeK+EVFw91PopVcyJPpPt/fffx9nz54dcBlP/z99hfj58+fx73//e8j/XkpKCu666y48/fTTWL9+PbZs2YJ58+ahqKgIL7/8suH9HnjgAYwePfCa1dWrV2PMmDH49a9/jXXr1mHTpk2YPXs2iouL8corrww5NzK8VVdXY+/evdiwYQMWLFgAHx8fw9f1ypUrzV5v//79WLp0KUJCQmBvb4+QkBAsXboU+/fvN3kNrVaLf/7zn5g1axZ8fX3h6OiI6OhorF69GhcvcmYMG1FbW4sNGzZg/PjxcHNzg5ubG8aPH48NGzagro69JY0QSzHefqLQQsDY+MHRyivABUHAt8XfMnFnW2ckB8hnAEHP1avoyMpi4k5JSdB4eJi8TmtDJ64WNjPx4DgP2DtZps3WEgqzMqHjbHjG0O63pERvQfn4448Nb4eHh2PdunWYMGECAODs2bN45ZVXDD3hH3/8MX71q18N+d9899138Yc//AHvvfceGhoaMH78eOzduxezZ88e9OMcHR3xww8/YP369XjnnXfQ1taGxMREfPnll7j11luHnBcZ3vz9LVMQ6PV6PPLII8ytr+Xl5SgvL8fu3buxatUqvP3221CrjT9Hrq2tRWpqKjIyMgbECwoKsGXLFuzcuRObN2/GqlWrBs0nLS0NS5YsQVXVwELo/PnzOH/+PLZu3Yrdu3fTxB4iCl4Bbm+jxuxYBbb8abuAK9+wcc8IwC9B8nTEllOfg7JW9kK6WcGzYKex43yEdbR8a+TynZvNaz/JzzI2/UReX8u5J49x49T/LS3RC/CsH59Vurq64siRIwgODjY8Nn36dCxatAhjxoxBc3PzoJfkmMPBwQEbN27Exo0bjb7PwYMHuXE/Pz/s2LHDInkQ5QoLC0N8fDy++Ybzy/Q6nnnmGUPxPXHiRKxfvx7R0dHIz8/Hyy+/jKysLGzduhW+vr74v//7P+4aOp0OS5cuNRTfd955Jx5++GF4eXkhLS0NL7zwAqqrq7F69WoEBwdjwYIF3HVKS0txxx13oKamBjY2Nvjf//1fLFzYuxO3d+9e/P3vf0dlZSXuuOMOnDp1iib7EIsqrG1D7lX22u/Zsb5wslPckC4g/wDQxe6QIn4hoMDLhni73wAwP3y+xJkMruXrr7lx11vMyzP/NDtKEyogaqJ8CvCerk4UZGUwcY+AQPiGR1oho5FL9J9wdXV1UKlUSE5OHlB89wkODkZSUhK+//571NezBzUIkYsNGzYgKSkJSUlJ8Pf3R1FRESIjzfuBlZuba2hnmjJlCg4fPmwYgZmUlIRFixZhzpw5yMzMxMaNG/Hggw8iJiaGWWfnzp04erT3YovHHnsMb775puGx5ORkLFiwAJMnT0ZzczOeeOIJZGdnw8aG/XZ/5plnUFPTu2vzwQcf4K677jI8NmvWLEyePBn33HMPqqur8eyzz9KTU2JRI276yaXd/HjCYknTkIIgCPimmN2gcNA4YGbwTCtkxKetrUV7ZiYTd5w4EbZmvOrZ1tSFyvwmJh4Y7Q5nd/ncKll05jS0nFHNsSkzlHnjrIyJ3gPedynOYMV1Q0MDAAyYPEKI3PzpT3/CwoULh9SK8tprr0Gr1QIANm3axMyld3JywqZNmwD09ne/+uqr3HX6ingvLy/uKz0xMTF4+umnAQB5eXn47LPPmPepqqrC+++/DwC49dZbBxTffe6++25D+9V7773HtKkQMhS8AlyjVuFno/2skI3ItN1Azj427hoEBE+RPh+RXWm8guLmYiY+K2QWnGydrJARX8t333PH8bneeotZ6xRk1XBHu0dPlNfXcm4av/0kdqp8nhSNFKIX4MHBwRAEAVlZWfjoo4+Yxz/++GOcPn0aKpWKu0NOiFIIgoDPP/8cABAfH4+pU/n9dlOnTkVcXBwA4PPPPzdMD+qTm5uL7OzeCxTuvvtuODnxf5n1PxjKK8C/+OIL6PV6ABj07EXfOnq9Hl988YXR9yPEHFVNncgqaWTiKZFe8HBS4GZM4SGgi90hRcIiYJCzHsPVd8X8vuqfhf1M4kwG1/INv/3Ebb6Z7SdG+r/l1H6i7e5Gwel0Ju7m6w+/yGgrZDSyif5dP3Nm77MqQRBw3333Yfr06Vi9ejX+53/+BzNmzMC9997LvC8hSlRYWGiYKT/nOqOt+h4vLy9HUVHRgMf6Wk+ut05AQABiY2MBAMeOsbsepq7T/zHeOoTciP0XKrnxkdd+skTKLCTD6/+2U9thdsjgwxCkpG1oQFsaW5A6jBsHWzM2BDtaulGR28DE/SPd4Opl+iU+Yis+n4XuDnbk56iU6dR+YgWi94CvXr0a27ZtM4wgTEtLM1yKA2DA7t7DDz8sdjojyoH3slFX0WbtNCTjHeSMm345+vrvaCV9F1EBvTvgg+n/eHZ29oBec3PXyc3NRWlpKdra2uDs7Mys4+7ujoAA40VPYGAg3Nzc0NzcbNh5J2So9p8fQf3fuh7++EGXACA0Rfp8RFbQWIC8xjwmPj14OlzsXKyQEV/r998DOh0TdzO3/eRMDa+LBdGTZNZ+YmT6SWzKDIkzIYAEBfiUKVOwdu1avPbaa9xnWH2F+eOPP05jziysrqKNO5OUWEdZ2U/juK43TaTvwiigd1LJUNcRBAFlZWWG1pb+65gy2SQ0NBQXL15kciHkRlQ3dyKjmD0XNCXcEwHu8tkxtJjCw0AHu0OK0Xcosv3E2PSTW8LNK2zF1mxkipXrLeblaaz9JFpG7Sc6bQ/yT6UxcRdvHwTGxFohIyLJd/7f//53/PnPf4aDgwNzEY+DgwP++Mc/4vXXX5ciFUKspqWlxfC2i8vgu0D9d6pbWweOabP0Otdbo/86165ByI3Yf6GKu2OYOi5Q+mSkcOlzflyB008AfgFuo7bBnFDzbpUUk66pCW0nTjJx+4TRsAsLM3mdztYelOWwT658w1zh5uPI+QjrKLlwDl1t7CviscnToVLgk8DhQLJBq88++ywef/xxfPfddygqKoIgCIiMjMTNN98MT09PqdIgxGo6OzsNb19v4k/f9CAA6LimZ8/S65gyfahvnWvXIORGfHme3/+9YJwS20+0QM5eNu7sC4RPlz4fkZU0l+Byw2UmPjVwKtzs3KyQEV/LgQMA5zZINzN3vwvP1UDQs88moyfJZ/cbMN5+MipFeV+Dw4WkNx14eHhg+fLlUv6ThMiGg8NPL613d3cP+r5d/ea0Xjuq8Np1+v/d3HXa29uvm0v/da5dgxBzVTd3IqOIbT+ZHO6JQHcFfn0VHwXa69j46DsAtUb6fEQ2XNpPWr421n5i3q3XxttP5NP/rdfpkJfJ7vY7e3giKE6+56aUToFXjZE+3kHO138nBZH75+vq6mp4+3qtHG39Xiq8tkXk2nUGK8Cvt057e7tJbSV965jSrkLIYL6+yG8/WTBWgbvfALWfANCoNLgp9CYrZMOna21FG2eik/2oUbCPMv1yta4OLUovsU8mvYNd4OEvn1nnpZfOo7OFPQ8WkzwdagU+CRwuLF6AP/jggwB6b/V79NFHDX83hUqlMlzRTYZOzhNBRqL+hx37H6Tk6X/Ysf+BTN46Pj4+111HpVIxhy1DQkJw9erV6+bSf51rcyHEXMbaTxTZ/63XAdl72LiTNxCuvLG75a3luFh3kYknByTDw8FD+oSMaD14CALnlT/XW83b/S46Vwu9Tv7tJ1eMXb5D00+syuIF+I4dO6BSqdDa2opHH33U8PfrEQSBCnCiaAkJCYa3c3JyBn3f/o+PHj3widS16yQmJl53ndDQ0AEHMvvWOXXqFJqamlBVVWV0FGFlZSWam5u5uRBijpqWLqQXsjuGE8M8EOShwPaTkhNAG6dFIX4hoFHeC9DGLt+ZH2HepTZia/nayOU7Zo4fzD9dzY3LafygXq/DlfQTTNzRzR0ho8dYISPSh46+EiKRyMhIBAUFAQAOHTo06PsePnwYQO9NshEREQMe639h1WDrVFVVITc3FwAwYwa702HqOv0f461DiKm+ulgFznk13K7E3W8AuLibH1do+8k3RWxftVqlxrzQeVbIhk/X2obWI0eYuF1kJOxiYkxep7tDi5KL7JNJz0BneAXKpx2yPPsi2psamXhM0lSoNdR+Yk2iFODXXp197ehB3h9ClE6lUmHx4t5fvDk5OTh5kj0UAwAnT5407FwvXryYeQUpNjbWsBP90Ucfob29nbvOjh07DG8vXbqUeXzRokVQ/zh+avv27Ubz7ltHrVZj0aJFRt+PkOvZd47ffnKbEvu/jbWfOHoCkfK5DdJSylrKcK72HBOf5DcJ3o7eVsiIr/XAAQj9Jkn1cb3lFrNugyw8WwOdVs/E5TT7GwByjh/mxmOTafqJtVn8NbADBw4AAHx9fQf8nRACrF27Flu2bIFOp8OaNWtw+PDhAZNFOjo6sGbNGgCAjY0N1q5dy13nySefxEMPPYT6+nqsX78emzdvHvB4fn4+/vKXvwAAYmJiuAV4QEAA7r//frz33nv4+uuv8cknnzBTij7++GN8/ePLtb/85S8HvTGTkMHUtnYhrZCdBjIh1AMhnvI5sGYxxceBVs5tn/G3Axpb6fMR2VdFX3HjCyIXSJzJ4Jr37ePG3VJTzVrnSia//SRminzaT3RaLXLTjjNxR1c3hI6dYIWMSH8WL8DnzJkz6N8JGa6OHj2KvLyfrleura01vJ2XlzdgxxkAVq5cyawRGxuLdevW4a9//SsyMzMxY8YMPPXUU4iOjkZ+fj5eeuklZGVlAQDWrVuHUaNGcXNZsWIF3nnnHRw7dgxvvvkmqqqq8PDDD8PT0xPp6el4/vnn0dzcDLVajTfeeAM2Nvxv9RdffBFfffUVampqcN999yEzMxMLFy4EAOzduxd/+9vfAPQ+oX7hhRdM/m9FyLW+Ntp+otAndRd28eMJSyRNQypfFbIFuEalwc/Cf2aFbPh0TU1oPXqUidvFRMM+lv+zlqeztYc7/cQryBneQfKZFFVy4Sx3+kns1BnQGPmdQKRD/wcIMdHWrVuxc+dO7mPHjh3DsWvGWvEKcKC36K2ursY777yDrKws3Hvvvcz7PPTQQ4MWvBqNBrt370ZqaioyMjKwa9cu7No18Be+vb09Nm/ejAULjO9AhYaGYs+ePViyZAmqqqrw0ksv4aWXXhrwPgEBAdi9e7dJV9YTYsw+Y5fvjFVg/7euhz9+0NELiJoreTpiK2gsMHr5jpeDlxUy4mv57jv+5TupqWa1n+RnVUPPeTY5aor/kPKztMtG2k/ipiuvBWo4Ev0QpiAIaG9vR3t7O7RarSH+xRdfYN68eUhISMDy5cuRnZ0tdiqEyIJarca2bdvw5ZdfYvHixQgKCoKdnR2CgoKwePFi7Nu3D1u3bjX0Zxvj4+OD48eP46233sLMmTPh7e0NBwcHREVF4eGHH8apU6ewatWq6+aTkpKC8+fP49lnn8XYsWPh4uICFxcXjBs3Ds8++ywuXLiAlJQUS336ZASqa+3CyQJ2x3BCiDtCvRTYflJwEOhgP18kLB5R7Se3Rd4mcSaDa/7SSPvJIJsUPMOh/UTb3c2dfuLi6YXg+ATORxCpib4DvmXLFjz22GMAgNdffx2PP/44jh49auhJFQQBOTk5OHLkCM6fPw8/P/l8ARPS344dO5g2k6FITU1Fqpl9h9eysbHBo48+ikcffXRI6/j4+OD555/H888/P6R1COHZd6EKOs6O4QKlTj8x1n4ydpm0eUhAEATsL9zPxG3VtpgXJp/pJ9raWrRxDr47JCTAPtL0y3famrpQntvAxP3CXeHhJ58nk4VnMtHdwR7Qj502iy7fkQnRd8AzMzMNU05uuaV3xubmzZsNsb6XfWpra/Hmm2+KnQ4hhBCJ7TlbwY0rcvxgTyeQvZeNuwQA4cqbPHG54TKKmouY+MzgmXCzc5M+ISOav/4a0LNTS9xuN28TJO9UNcA5yxAjs/aTnOPsqEUAiKf2E9kQvQDvO1Dm5+eH2NhYAMAPP/wAlUoFtVoNJ6efnjF+8w07Q5QQQsjwVdnUgYwith0jMdRDme0ned8C3S1sfOydgAJ3Hnm734Acp5/w83S7zbw2mbzMq9x4zGT5vHrf3dmBglPpTNzN1x8BMbFWyIjwiF6AV1ZWQqVSISwszPD3vukRr776KkpLS+Hl5QVBEAZMmCCEEDL87T1bCd5VD4smBEmfjBRGWPsJb/qJo40j5oTIZwJaT2UlOk6dYuKOEyfCNjjY5HWaaztQVcBOFQmMcYerl8OQcrSk/FPp0HZ3MfH46bPMOmxKxCV6AV5X1zv3NTCw96XGK1euGB67+eab4eHhgaSkJAAwXHdNCCFEGfacY9tPVCrg9vEKbD/pagUucw4keoQBwZOlz0dk52rPoaKN/f87J2QOnGzl8+pG837+IVFzZ3/nneIfvqTpJ+RGiF6A9z3bamtrA4ABu9x9V2w7OPQ+c7S3txc7HUIIIRIprG3DubImJj410hv+bvLZMbSYy/sBbQcbH7us91mHwvB2vwEZTj/hXb6jVsPttlvNWucKp/1EpQKiJ8mn/aSztRWFWexuv1dQCHzDTT9sSsQnegHu6+sLQRCQlpaGY8eO4aOPPgLQuyPedwNgY2MjAMDbWz7X1RJCCBkaY4cvFyVS+8lwp9Pr8HXR10zcxdYFM4NnWiEjvu7iYnReuMDEnZKTYeNr+rXxDVVtqC1tZeLBcZ5wcrMbUo6WlJdxAnqdlonHTZ9N7ScyI/oYwsTERJSVlaGtrQ2zZ/e+/KFSqTBt2jTD+1y+fBkqlQpBQQr9oUwIISOMIAj4glOA26hVuG2MAm+/7GgA8r5j4z6xgP9Y6fMR2enq06jpqGHi88LmwV4jn1ezm/cbOXyZat4hUaPtJ0nyaj/JMdp+MkviTMj1iL4D/vOf/9zwtiAIhvGD999/PwDg4sWLqKqqAgBDLzghhJDhLaeqBXnV7I7h7FhfeDrLZ8fQYrL3Anr2lkWltp8Mm+knvMt3bGzgOn++yWsIgoArGWz7iVqjQlSi6bvoYmtvakTJhbNM3DciCt7BoVbIiAxG9AL83nvvNVzE02f16tVYsmQJAODzz3uv6xUEAdOnK29GKiGEjES83W+App8oQY++B98Wf8vEPew9kBIon1tzO3Nz0dVv8EMf5xnTYePpafI6deWtaKhiL7UJS/CCg7N8bjbNPXkMAmfWOc3+lifRW1CA3ot3nnnmGRQVFSE8PHxAq8lvf/tb/PrXvwYAuLq6SpEOIYQQEQmCwO3/trdR42cJ8nrJ3iJaa4DCQ2w8YDzgM0r6fER2vPw4Grsamfj88PmwVcunIG3ew7kQCYC7mdNPctP4s7/l1n6SffQgNx43jdpP5EiSAhzoPXTZN4qwP0dHR8NhTEIIIcNfVmkjyhrYaSA/G+0PF3vJfu1I5+KngMDuPCpx9xsA9hbwC1s5tZ8Iej2a9rJ5quzt4XLzzSavo9cLyOW0n9jYqhEx3mdIOVpS49UqVORmM/HAUXFw95PXEwXSS/QWFEIIISPLF2f47Sd3KLX95Nx/+fExS6XNQwKt3a04UHqAiQc4B2Cyv3xmnbdnZkJbWcnEXebdBI2Li8nrVOQ2oK2RvdQmMtEXdg7yeTKZfZT9fwIAo2fdJHEmxFSSfPU0NzfjrbfewnfffYfy8nJ0dbFfzEDvdJT8/HwpUiKEECICnV7Al+fZwsfV3gZz4+RzYM1i6vKBcnbuMsKmAZ7h0ucjsu9KvkOXjv0dfnvk7VCr5LOn17xnDzfufscis9a5nM5vP4lNls+usiAIyD5ykImrNRpqP5Ex0QvwiooKzJw5E8XFxQBgmILCQzMqCSFkeDuWV4uaFrZAu2VMABxsNVbISGTnPuLHx98tbR4SMdZ+sjBqocSZGKfv6kLzV+yMco2HB1xmzjB5HW23Dvmn2fGDjq62CE3wGlKOlnQ1/woaKsuZeETiZDi5uVshI2IK0QvwZ599FkVFRQB6C2xjRfZghTkhhJDh4bMsthAAFHr5jiDw20/UtkDCEsnTEdvVtqtIr0xn4vFe8YjxjLFCRnytBw9B39LCxN1SF0BlZ/oIzMJztejp1DHxmCn+0Gjks9t/6Qi//SSB2k9kTfQCfP/+/Yaim4psQghRrrYuLb66UMXEfVzsMSNagTcdl2UCDYVsPPZWwEk+O6SWsr9wPwSwv8fltPsNAE17vuDG3e64w6x1co20n8Qly+ciKZ1Wy718x87REVGTk62QETGV6E/hGhoaAAAajQbbt29HXV0dtFot9Ho980enY59pEkIIGR6+uVSFjh725/jixCDYyGjH0GKMHb4cd5e0eUiE136igkpW0090jY1oPcQWpLZhYXBMTDR5nY7WbpRcqGPiHv5O8IuQz8jk4vNZ6GhuYuKjUmbA1k4+N5ISlug/Eftmfk+fPh0rVqyAp6cn1GoF/iAmhJAR7tPT/PaTpRODJc5EAroe/uU79m5A7G3S5yOy3IZcXG64zMRTAlPg5+RnhYz4mr/6GuhhbyR1v+MOs86Z5WVWQ69nd/tjk/1ldV6Nd/gSoPaT4UD0SviOO+6AIAhobWWvJCaEEKIM1c2dOJZXy8Rj/V0wJsjNChmJLO97oKOejScsBmwdpM9HZF8WfMmNy6/9xNj0E/PyzE1nW6kAIFZG7SfdHe3IyzjJxF28vBGSMNYKGRFziF6A//73v4e3tzeysrLw3nvvif3PESKavkPE1/szd+7c6661f/9+LF26FCEhIbC3t0dISAiWLl2K/fv3m5yPVqvFP//5T8yaNQu+vr5wdHREdHQ0Vq9ejYsXL5q8Tm1tLTZs2IDx48fDzc0Nbm5uGD9+PDZs2IC6OvYlWEJ4Pj9TAc6GIZZODJHVjqHFnDc2/eQeafOQgF7QcwtwB40Dbg4z/VIbsXWXlaHjFDsS0mHCeNhFRJi8TlNNO6oKmpl4QJQ73H3lc3HglfQT0HazE4fiZ8yBWq3AiUMKI/ohzLfffhspKSnYt28fVq5ciX/84x9ISkqCtzf/QM6GDRvETokQq9Hr9XjkkUewbdu2AfHy8nKUl5dj9+7dWLVqFd5+++1BW7Vqa2uRmpqKjIyMAfGCggJs2bIFO3fuxObNm7Fq1apB80lLS8OSJUtQVTVwt+f8+fM4f/48tm7dit27dyM5mQ7zkMF9ypl+olIBSyYqcPpJZzOQw9kRdgsGwk0fczdcZFZl4mo7eyDxptCb4GJn+qU2YrPY7G8jV8/Hpchn9jdg/Op5aj8ZHkQvwJ977jnDzqAgCEhLS0NaWprR96cCnMjdo48+iscee8zo487OzkYfe+aZZwzF98SJE7F+/XpER0cjPz8fL7/8MrKysrB161b4+vri//7v/7hr6HQ6LF261FB833nnnXj44Yfh5eWFtLQ0vPDCC6iursbq1asRHByMBQv4B6RKS0txxx13oKamBjY2Nvjf//1fLFzY+zLt3r178fe//x2VlZW44447cOrUKYSEhJj034eMPDlVzciuZHcMp0V5I9BdPjuGFpOzF9B2svFxdwEKPONkdPZ3tHzaTwRBQNMXnAJco4FbqumHRAVBQG4a236iVqsQM1k+BXhrfR1Kzp9l4r5hEfANj7RCRsRckt6jOtjLkIIgKPNlSqI4fn5+GDvW/P663NxcvPLKKwCAKVOm4PDhw3B07C1OkpKSsGjRIsyZMweZmZnYuHEjHnzwQcTEsLN1d+7ciaNHjwIAHnvsMbz55puGx5KTk7FgwQJMnjwZzc3NeOKJJ5CdnQ0bG/Zb/ZlnnkFNTQ0A4IMPPsBdd/00uWHWrFmYPHky7rnnHlRXV+PZZ5/Fjh07zP6cycjwmZHDl0uUePgSMD79RIHtJ53aTnxb/C0T97T3xLSgaVbIiK/zwkV0F7IjIV1mzoSNl+kjIa8WNaOppoOJh431hoOL7ZBytKScY4cgCHomTlfPDx+SPFUXBOG6fwhRutdeew1arRYAsGnTJkPx3cfJyQmbNm0C0Nvf/eqrr3LX6Svivby8sHHjRubxmJgYPP300wCAvLw8fPbZZ8z7VFVV4f333wcA3HrrrQOK7z533303br31VgDAe++9x7SpEAL0Xj2/+wxbgNvbqLFgrHwOrFlMcyVQcIiN+48F/BOkz0dkh8oOobWHHaJwW+RtsFXLpyA1Ovt7kZmzv422n8jra/kSr/1EpUL8jDmS50JujOg74Nu3bxf7nyBE9gRBwOeffw4AiI+Px9SpU7nvN3XqVMTFxeHy5cv4/PPPsXnz5gGvDOXm5iI7OxtAb4Hs5OTEXWflypWGIvyzzz5jCuwvvvgCen3v7smvfvUro3mvXLkSX3/9NfR6Pb744gs88sgjJn7GZKQ4kV+Hq838q+ddHeRToFnM+Y8AzmU0Sr16fk8+v69aTtNPhJ4eNO9le/LVTk5wnTfP5HV0Wj2uZLAFuJ2DBhHj5HORVE1xIWqKCph42JhxcPX2sUJG5EaIXoCvWLFC7H+CENkrLCxERUUFAGDOnMF3KObMmYPLly+jvLwcRUVFiIz8qZ+vr/XkeusEBAQgNjYWubm5OHbsGPO4qev0f+zYsWNUgBOGsavn71Ri+4kgAFnvcx5QAWOXS56O2Go7anG0/CgTD3MNwzifcVbIiK/18GHo6tmRkK7z50PtaPoZhKLztehsY2eIR03yg42dfKaKXDz0HTceP3OutImQIVHeaRFCRPbxxx8jISEBTk5OcHV1xahRo7BixQocOHDA6MdcunTJ8HZ8fPyg6/d/vG+3eyjrlJaWoq2tjbuOu7s7AgKMv7QaGBgINzc3bi6EtHdr8dWFSibu42KHWaMUuBNXfhqoZS+jQdRcwF15Tzj25u+FTmBvNl0UvUhWZ7YaOW12AOC+dKlZ6+Sc4LfZjZ4mn/YTnVaLS0cOMnEbe3vETZ0peT7kxkl6CDMrKwt79uxBYWEh2tvb8d///hcVFRXQarXQaDQIDlbeDzBr+ubtN1BbWmztNCTjExqOW1Y/Ifq/078IBnr7rPPy8vDuu+9iyZIl2LFjB9zd3Qe8T1lZmeHt600TCQ0NNbxdWlo65HUEQUBZWRni4uKYdUyZbBIaGoqLFy8yuRDy1YUqtHWzBdodExR69fwZ3u43gMT7pc1DAoIg4PP8z5m4CiosijZvrJ+YtPX1aD3I9uTbBgfDKTnJ5HXam7tRzLl63s3HAYExHkNJ0aIKz5ziXj0fmzwddo78lkQiT5IU4J2dnXjwwQfx3//2nhzvP/Hkt7/9LT755BOoVCrk5+cjPDxcipRGhNrSYlRe4ezWkBvi5OSERYsW4eabb0Z8fDxcXFxQU1ODQ4cO4Z///Cfq6uqwe/duLF68GN9++y1sbX/qf21paTG87eIy+Nzc/mMMr71B1tLrXG+N/uvQbbbkWh9l8p+U3TlRgSMrezqBC5+wcXs3YLR8+qEt5WLdReQ15jHxlMAUBLoEWiEjvuY9e4AfD7f3575kCVRmjIS8nFYFgXOTVPy0QFnt9l88yG8/GTP3ZxJnQoZKki2KZcuW4b///S934smKFSsM8U8//VSKdAi5IeXl5fjwww+xatUqzJw5E4mJiZg/fz5eeOEFXLx4ERMnTgQAHDp0CP/4xz8GfGxn508zg+3s7Ab9d+zt7Q1vd3QMHIdl6XWut0b/da5dg4xsJXXtOFnA9t3G+btibLACr56//CXQye48YuydgK3yZp3vztvNjS+OWSxtItfR+Nlubtx9iel5CoKAnBNsKxUAxE2VT/tJe3MTCk6nM3E3Xz+EJsinJ5+YRvQCfNeuXYNer33zzTcbfsEfPnxY7HQIuWEeHh5GH/P398cnn3xi2PXuGyfYx8HBwfB2d3f3oP9OV9dPEyWuHVVo6XWut0b/da5dg4xsn5wu48bvmqLQq+e5hy+hyPaTLl0X9heyv7ddbF1kdfV8Z3Y2unJymLhTUhLs+rXyXU9NSQvqK9qYeHCcJ9y85fNzL+foQeh1bMtXwuybzdrtJ/Ig+v+x/pd33H777YZdwj729vYYPXo0BEHAxYsXxU6HENFERUVh/vz5AHr7wvumngCAq6ur4e3rtXL0PzB5bYuIpdcxpa2kbx1T2lXIyKDXC9h1ii3AbdQqLFXi9JPmCqCAc8jaexQQYnqf8XBxoPQAmrvZm01vjbgVjjbyKUgbPzVy+PLOO81aJ+c4f/d79HT5tNoAwIVD33PjY+bI50kRMZ3oPeCZmZkAgODgYOzevRv33nsvsrKyBrxPUFAQzpw5g8pK/jcBuTE+oSOrn14On29CQgL27dsHoLdlJSgoCMDAw479D1Ly9D/sGHrNLs616/j4GJ800beOSqViDluGhITg6tWr182l/zrX5kJGruP5dShvZFuS5sX7wdvFnvMRw9zZ/wCcWweR+HNAgbv9n+exhy8BYEnMEmkTGYTQ3d3b/30NlZMT3G6Zb/I6uh49cjmzv20dNIhK9B1SjpZUXVTAnf0dkjAWHv7yaZMhphO9AK+vr4dKpUJiYiI0Gv4czb4LQfq/ZE6GToqJIGQgYy+9JyT8dENeDucl0/76Pz569OhB10lMTLzuOqGhoQMOZPatc+rUKTQ1NaGqqsroKMLKyko0NzdzcyEj18en+Icv756iwCdpgsCffqJSAxPulT4fkVW3V+N4xXEmHuEWgQm+E6yQEV/LoUPQNTYycbdbb4X6mp93gyk8V4uudvYQZ8xkP9jay2j2t7HDl3Po8OVwJXoLSt9NfQ0NDUbfp69Q6Js3TMhw1X9EYd/uNwBERkYa/n7oEOca6376zkIEBwcjIiJiwGMzZ/4053WwdaqqqpCbmwsAmDFjBvO4qev0f4y3Dhl5mjp68NUFdl6yj4s95sbJZ8fQYsoygDp2Ggii5wFuQWx8mNuTvwd6zm7/4pjFsurtbzLSfuJxp7mzv420n0yTT/uJTtuDbM7V87b2DoidSj+XhyvRC/DIyEgIgoC0tDRcvsyOxHvvvfdQVFQElUqFmJgYsdMhRDSFhYX49ttvAQDR0dED5tqrVCosXtx7Kj8nJwcnT57krnHy5EnDE9LFi9lfeLGxsYad6I8++gjt7e3cdfqfvVjKuYxi0aJFUP94aGf79u1GP6e+ddRqNRYtks/sX2I9e85WoEvLFmjLJgWPsNnfP5c2DwkMNvtbTlfPa2tr0coZ2mAbGgrHyZNNXqetqQslF9nZ3+6+jgiIdud8hHUUZGWio4XtyY+dOgN2DvLpySfmEf2n5c039x4O0Ol0mDFjBtLS0gyP3X777XjwwQcNf583b57Y6RByQ/bs2QMtZ9Zsn6tXr2LZsmWGqSKPPfYY8z5r1641tGGtWbOGGevX0dGBNWvWAABsbGywdu1a7r/15JNPAuht71q/fj3zeH5+Pv7yl78AAGJiYrgFeEBAAO6/v3d6w9dff41PPmHnG3/88cf4+uuvAQC//OUvB70xk4wcH3MOXwK9008Up7sduMAZj+vgDsTdLn0+IjtXew6FTYVMfFrQNAQ4y+f7v+mLPQBnGoj7ksXmzf4+WQWBHf1Ns7+JJETvAX/00UexadMm9PT0oL6+3tCKIggCvvrqK8NccDs7OzzyyCNip0PIDVmzZg16enqwbNkyTJs2DREREXB0dERtbS0OHjyIt99+G7W1tQB62zt+/etfM2vExsZi3bp1+Otf/4rMzEzMmDEDTz31FKKjo5Gfn4+XXnrJcEB53bp1GDVqFDeXFStW4J133sGxY8fw5ptvoqqqCg8//DA8PT2Rnp6O559/Hs3NzVCr1XjjjTdgY8P/Nn/xxRfx1VdfoaamBvfddx8yMzOxcGHvLtfevXvxt7/9DQDg6+uLF154Ycj/Dcnwl3u1BWdLG5l4YqgHYvxc2Q8Y7i7tBrrYnUeMXQ7YOrDxYW5X7i5uXFaHLwUBjR9/zH3MY8kSs9a5dKyCfUAlr9nfrfV1KDidwcTd/fwREj/GChkRSxG9AI+KisLf//53PP7444ZnlLxnlq+88grT70qInFRUVGDTpk3MjO/+li1bhq1btw64BKe/F198EdXV1XjnnXeQlZWFe+9lD3E99NBDgxa8Go0Gu3fvRmpqKjIyMrBr1y7s2jXwF6e9vT02b96MBQsWGF0nNDQUe/bswZIlS1BVVYWXXnoJL7300oD3CQgIwO7du026sp4o38dGbr5U5OFLADi1kx9X4Ozv1u5WfFX0FRN3tXXFTaE3WSEjvo5Tp9BdyO7SO02dCttg00dgVuQ2oqmaneQTGu8JVy/5PLm6cPA7CHq25Ytmfw9/klxF/9hjj8HX1xfr1q1DSUnJgMeCg4Px8ssv47777pMiFUJuyM6dO3Ho0CGcOHECBQUFqK2tRXNzM1xcXBAaGorp06djxYoVmDZt2qDrqNVqbNu2DcuWLcOWLVuQkZGB2tpa+Pj4ICkpCatXrx60aO7j4+OD48eP41//+hc++OADZGdno62tDUFBQbj55pvxm9/8BmPGXH93JCUlBefPn8frr7+O3bt3o6ioCEDv2Y3Fixdj7dq18Pb2Num/EVG2bq0en2WVM3EHWzUWTpDPgTWLqc4GSjlnNfzHAsGTpM9HZPsK96FDyxakC6MXwsFGPgWp0d3vu5abtc7Fo5zdbwAJM+Uzx17Q63H+h2+YuEqlxtibTB+1SORJkgIcAO666y4sX74cp0+fRuGPz14jIyMxadIkWfVaEcIzZ84czJkzx2LrpaamIjU1dUhr2NjY4NFHH8Wjjz46pHV8fHzw/PPP4/nnnx/SOkTZvsu+itpW9ubU28YEwM3B1goZiez0u/z4pBWKnP296wq//WTZqGUSZ2KcrqkJzV99zcQ1Hh5wnW96QdrZ2oOCrBom7uhqi8gJxu9WkFrx+TNormFnlEckToKbjwInDo0wkhXgQG/ryeTJkzHZjFPKhBBCrO/D9BJuXJHtJz2dwNkP2biNAzD+bunzEdmluku4VHeJiY/zGYc4rzgrZMTX9MUeCJz7QtwXL4bazs7kdS6nVUHHmeQTNzUQGhv5tHWc/559sgEA42++TeJMiBjk85VGCCFElkrq2nHkSi0Tj/B2wrRoBbYo5ewFOjh3V4xZCjh6SJ6O2Iwdvlwea15bh5gGPXx5911mrWOs/WTMTPnMdW9rbEBeJtsC5ezphahJSVbIiFiaJDvgLS0teOutt/Dtt9+ivLzc6I2XKpUK+fn5UqRECCHERB9m8He/70sOU2YL4akd/PikFZKmIYX2nnZ8WfglE3eyccJtEfLZae08dw5dP14u1p/j5Mmwj442eZ2qgmY0VLYx8aBRHvDwdxpSjpZ08dD30HNGLY6d+zOojdwqToYX0QvwqqoqzJo1CwUFBQBgGDvIo8gf5IQQMox1a/Xc6Se2GhWWTVbgdJy6fKDoCBv3iQPCpkqfj8i+LvoabT1sQZoalQonW/kUpA0WOnx56Sh7kBgAEmS0+y0IAi4cYA9fAsC4ebdInA0Ri+gF+DPPPGPY1VapVEaL7MEKc0IIIdbxvZHDl7eMCYCPC3/c5rB22sjowckj6/Dl8lHyaT/Rtbaied9+Jq52dYXbrbeavE5XhxZ5mdVM3N7JBtGT5HOosezSeTRUsm0y4eMnwt1PPjPKydCIXoDv37/fUHRTkU0IIcPLB0YOX96fHCZxJhLQdgNnPmDjGjtgPDuzf7i70nAFZ2vOMvHRXqOR4J1ghYz4mvd+CaG9nYm7L1oEtaPpV7HnplVB28M7fBkAG1v5tHWcM3L4ctw8059sEPkT/RBm382XTk5O+Oyzz9Dc3Ay9Xs/9o+P0OxFCCLGOwQ5fTo1S4OHLy/uANnY8HUYvApyV9/kONnpQTi2hljp8yb35EvJqP+loacaVtGNM3NHNHTFJKVbIiIhF9AK873bLGTNmYPHixXBxcRH7nySEEGIB/zFy+PLe5DCo1fIp0CxmsPYThenSdWFP/h4m7mjjiNSood1RYEmdly6h8+JFJu4wfjwc4kwfkVhT0oLa0lYmHhDlBu8g+dQllw4fgE6rZeJj5twMjY0C5+2PYKIX4L/85S8hCAJycnLQ09Mj9j9HCCHEAnp0enyUWcbEbTUqLFfi4cv6QiD/ABv3igIiZkmfj8i+KfoGzd3NTPyW8FvgaudqhYz4Gv77ETdu9s2Xh4fH4ctz33/FfYzaT5RH9AJ83bp1mDZtGkpLS7Fo0SIcO3YMTU1NYv+zhBBChqD38CU7MvaWBIUevszcBoBzTkmhN1/+J+c/3LicZn/rWlrQtIfdpVc7OcHdjJuEO9t6kJvO3ihp56BBzGT/IeVoSaUXz6G+nJ04FJowDl5BwVbIiIhJ9ALc1tYW27dvh6OjI7755hvMnj0bXl5e0Gg0zB8bG8ucCe3q6sJTTz2FoKAgODo6IiUlBd9++63Z68yfPx8qlQqPP/64RfIihJDh4v0047O/FaenA8j6NxtX2wKJP5c+H5FdrLuIc7XnmHiMRwwm+E6wQkZ8Tbs/5x6+dLvjDqidnU1e5/JJ/uHL2JQA2NrL5/DlmW/YeewAMO5n8pnHTixH9AK8sLAQM2fOREdHBwRBuO4fS1i5ciX+/ve/4/7778frr78OjUaD1NRUHD161OQ1Pv30U5w4ccIi+YhBre79X6fT6Wi6DJEtQRAMh6s1dHnEsFFU28Y9fBnm5YTpSrz58sKnRm6+XAK4+Emejtj+m/Nfbvy++Ptkc/hSEAQ0fPgh9zHPn99n+jp6AecPsa1UADB2jnx2lVvqapGXwd586eTugdiU6VbIiIhN9AL82WefRW1t7w/yvjngvD+Wkp6ejv/85z/4y1/+go0bN+KRRx7BDz/8gPDwcKxfv96kNTo7O/G73/0OTz31lMXysjQ7OzsAvT+kjN0sSoi1tbe3G54g9n3NEvn798libvw+pR6+zNjKjyetkjYPCTR1NWFf4T4m7mzrjNujbrdCRnztaWno/vECv/4cJ0826/BlWU4Dmqo7mHjQKA9ZHb489/3XEPTsLv24ebfS4UuFEn0O+LfffguVSmX4Jezh4QFXV1fDDq6lffLJJ9BoNHjkkUcMMQcHBzz00EP4/e9/j9LSUoSGhg66xssvvwy9Xo8nn3wSGzZsuOFcysr4z7r7VFZW3vDazs7OaG3tPdHd3NwMBweHG16LEDEIgoD6+nrD393c3KyYDTFVR7cOH3FuvrTTqHHXFAUeviw/BVScZuP+44BQ5Y192523G106dtNmUfQiONua3tYhtob3OfPYYd7uNwCju9/j5srna1mn7cF5zuFLlUqN8dR+oliiF+DtP/Zv+fj44NChQxg9erSo/15WVhZiY2OZX/bJyckAgDNnzgxagJeUlOCvf/0r3nnnHTiaMeCf53qF/lC4uLjg6tXeQyV1dXXQaDTw8PCgl/mJ1QmCgPb2dtTX1xueJKpUKhpBOkx8fqYczZ3sGLTbxwcq8/BlxjZ+POkhxR2+1At6fHSZP1Xknrh7JM7GuJ6qKrT88AMT1/j4wG3+fJPXaanvRNE5tpXKyd0OkYk+Q8rRkvIyTqKtkW2Bip6SDDcf+dzQSSxL9AJ87NixyMjIwOTJk0UvvoHeXeXAwEAm3herqOAP4u/zu9/9DhMnTsS998r71jM7Ozv4+vqipqb30ojq6mpUV1dDo9HIpoePjEzXnktQqVQIDg4W7VUvYjmCIGDnCX77yS+nhUucjQTa64ELnMto7N2B8XdLn4/ITlScQEkLe7g2OSAZ0R7RVsiIr/GjjwDOxXwedy2HyoxWtouHy8E7IjVmZhA0Gvn8PDrzNf/wZeItCyXOhEhJ9AL88ccfxwMPPICsrCy0tLTA1VXc+aIdHR2wt2d3afpaNDo62F6wPgcOHMCuXbuQlpZmkVxKS9mXcfurrKw07MzfCG9vb3R3dw8Y60i3iRI56Su+xf6+J5ZxqrgB2ZXsbOhxwe6YGOohfUJiy3oP0Hay8cSfA3byacewFGOjB++Nl8+Gk9DdjYaPODdfajTwvMf0XXpdj55786VKrcKYWfI5fFlTUoSy7AtM3DMoBGHj5DORhlie6AX47NmzsWTJEuzevRuzZ8/Gk08+iXHjxsHDw4P7/mFhQxtx5ejoyD2U2NnZaXicR6vV4oknnsAvf/lLJCUlDSmHPiEh4vaYqVQqBAUFwcvLC42NjWhvb6cCnFidRqOBnZ0d3Nzc4OLiQjvfw8i7g+x+K+6VNb1+8PYThSlvLcehskNM3M/RD3ND50qfkBEt330HXS3bNuI67ybYBgSYvE5+VjU6WtjL/6ISfeDsIZ9WqrPfsAdiASBx/gLlfc+RAUQvwCMiIgxfRGfPnsUDDzxg9H1VKhW0nCtYzREYGIjycvbGq74Dj0FB/Fuv3n33XVy+fBlvv/02ioqKBjzW0tKCoqIi+Pn5wcnJaUj5icHBwQEBZvxgIoSQa1W3dGL/BfZguIeTLRZNkM9tgRaT9x3QyHnCETUX8BkleTpi+/jyxxA4Fw0tj1sOW7V8pmzUf2Ds8KV589jPH+TffDlujnwOX3a1t+PSEfb2VRt7eyTMudkKGREpSbY11TduUOw54ImJicjNzUVz88CXUfvaShITE7kfV1JSgp6eHsyYMQORkZGGP0BvcR4ZGYlvvvlmyPkRQogc/Se9FD069mfwPVNC4WCrwMPd6Vv4cQWOHuzSdeHTK58ycRuVDZaPks/Nl52XL6Mj8xQTt4uMhNPUqSavU1PSgqoC9sZtz0BnBMV6DCVFi7p46Hv0dLJtsaNnzoWDMx1aVzrRd8D7DFZc9x9TOFTLly/HK6+8gi1btuDJJ58E0Hsz5vbt25GSkmKYTFJSUoL29nbEx8cDAO69915ucb506VKkpqbi4YcfRkqK8kZSEUJIj06P99PY3WCVCvjFVAUevqy9AuRxbkd2CwZiF0ifj8j2FexDQxc7ZePm8Jvh6ySfKRv1777LjXveZ94FQed+4J+/GjcnWDZtHYJej6yvvuA+lniLfOaxE/FI0gMu5Rd8SkoK7rrrLjz99NOorq5GTEwMdu7ciaKiImzb9lO/3wMPPIBDhw4ZCv/4+HhDMX6tyMhILFmyRIr0CSFEct9euoqrzezZmXlxfgj1kl/b3ZCl/ZMfn/wrQCPZvpQkBEHAe9nvcR+T0+hBbV0dmvfsZeIqJye4L1ls8jptTV3IzbzKxG3tNYhLkU+rZkFWJhqr2JavoNjR8IuIskJGRGqi/6Q5ePCg2P8E491338Uf/vAHvPfee2hoaMD48eOxd+9ezJ49W/JcCCFE7nYcK+LGH5geIWkekuhoAM5w+ow19sCUX0mfj8jSq9JxpeEKE4/3iscU/ylWyIiv4T//gdDdzcQ9li6FxoxLvC4cLodey76iPnpGIOwc5fPk6vS+z7nxSammP9kgw5t8vhotyMHBARs3bsTGjRuNvo+pTwws1RpDCCFydL6sCelF9Uw8wtsJs2Lkc1mJxZx+F+hpZ+MT7gGclff5vneJv/v9y4RfyqYdQ9/djYYP+SMSvX75C5PX0fbocPEw5/ClChh/k3wOX9YUF6Lkwlkm7urji1HJ06yQEbEGmg9GCCEj2LajBdz4A9MioFbLo0CzGJ0WSDNy+DLlUWlzkUBxczF39KC3gzdui5DPFefN+/ZxRw+6zJ0Lu4gIk9e5knGVO3owcrwP3H3l00p1ej+/93vibXdATbdZjxgW3wH/85//DABISEjA8uXLDX831YYNGyydEiGEEI6qpk7sPcf2obra2+DupFArZCSynD1Acxkbj5oL+CdIno7Y3s9+nxu/J/4e2GlMv1FSTIIgGD186bXC+Nhi3jpnv+f8vwUwYZ58vpbbmxqRffQgE7e1d8C4m26RPiFiNRYvwJ977jmoVCosW7YMy5cvN/zdVFSAE0KINN49UQStnjN6MCkULvYK7FA8+Q9+fOpj0uYhgebuZuzO283EbdW2uDv2bukTMqI9IwNdl7KZuH1srFmjB8svN6CuvJWJ+4S6yGr04Nnv9kPXw+7Sj5l7MxxcaPTgSCKbFhTqtSaEEOm0d2vxQXoJE1ergBVKPHxZdgooTWPjXtFAzHzp8xHZZ1c+Q4eWnTF9e9Tt8Hb0tkJGfIPtfpuzeXf2B+O733Lpddf29Bi9+XLibYskzoZYmyhbHNcW01RcE0KIvOw6XY7GdnYn7raxAQodPWhs9/tRQC2bvSiL0Oq1+CCbf6PkL0abfqhRbN2lpWj9/gcmrvH0hNvChSav03i1HUXn2R5yR1dbjJriP6QcLSn3xBG0NbLz2KMmJcErKNgKGRFrsngBvn37dgC9V9D3/zshhBB50OsFbD9ayH3soZmREmcjgeYK4OJnbNzeHZhwn/T5iOxA6QFUtFUw8ZSAFMR5xVkhI76Gf/8b4GzQed53L9T29iavc+5gGcDZ5xs7JwQaW3k8uRIEAae+pNGD5CcWL8BXrFgx6N8JIYRY18HcahTUtjHxCaEemBTmaYWMRJb+L0CvZeOTHwDsldd3a2z04C8S5LP7rWtpQeMnu9gHbG3heZ/pT4o623qQfZw9SKy2UWHsbPnsKpdnX0R1UT4T9wkNR9jYCVbIiFibPJ4aEkIIkcy2QXa/5dIvazFdLUDGNjauUgPJj0ifj8iyqrOQVZ3FxENdQzE7RD6X0TX+97/Qt7FPAt1TU2Hj62vyOhePlEPbpWPisckBcHKTx6QXAMjYw3mygd7db8V9zxGTUAFOCCEjSHZlM47l1THxQHcHLBgrn6u6LebUTqCriY2PvgPwCJM+H5Ftv8Bv+7x/9P1Qq+TxK1/f3Y36nfzDl54P/NLkdbQ9ukEOX8rn4p3akiIUnM5g4o6uboifOccKGRE5sHgLSlRU1A1/rEqlQn4++xINIYQQy9h6hL/7vWJ6BGw18ijQLEbbDZx4k//Y9CekzUUCBY0FOFB6gIm727tjacxSK2TE17xnD7Q1NUzcadpUOI4ZY/I6l09WoaOZvb4+NMELPiGuQ8rRkjL2fMqNT7ztDtjamd7rTpTF4gV4UVERVCrVDU0+oZdhCCFEPBWNHfj8DHtVt6OtBvclKW83GBc+AVrYw4gInwmETJE+H5HtuLiDG7837l442cpjso2g16Nu2zvcx7wfWmXyOnq9gDPflXIfm3iLfL6Wm2trkHOMvY3Uxt4eibfeboWMiFyIdtOCucU0jSokhBBxbTtayL14564pIXB3srVCRiLS64Fjb/Afm/EbaXORQHV7NfYU7GHi9hp73Bcvn0kvrQcOoLuggInbjx4N5xnTTV6n8GwNGq+2M3HfMFeExMnnIPHpfZ9Dr2N71MfddAscXd2skBGRC0nmgAMYdFe8r1inIpwQQsTR2N6NDzkX72jUKjw868ZbB2Ur71ughr1hEX4JwCjlXbzz7+x/Q8uZ9LIkZomsLt6p28o5EAvA+6GHTN64EwQBp79mv5aB3t1vubya3tnainPff83EVWo1Jt++RPqEiKxYvOFPr9czf5588kkIgoB58+bh6NGjaGxsRGNjI44dO4abb74ZAPDQQw9Br9dbOh1CCCEA3jtRjPZudifu9nGByrx45+hr/PiM3wAyKdAspaW7BR9f/piJq1VqrEiQzyjg9tOn0ZHFTmixDQqC2223mrxOZV4jqouambibjwOiJ5o+QUVsZ7/dh55O9jbSuGmz4O4nnwuCiHWI1oLS59NPP8Urr7yCoKAg7N27Fw4ODobHpk2bhj179iAmJgbvvPMO5syZg1/8Qj5zSgkhRAk6unXYfryI+9jqOQrc/S5NB0qOs3G3EGDsMunzEdnHuR+jtaeVic8Pn49Qt1ArZMRnbPfb61e/gsrG9HLk9Df83e/En4VBLZODxNrubpze/wX3saRFyvsaJOYT/Sv1tddeAwCMHz9+QPHdx8HBAePGjYMgCHjrrbfETocQQkacj0+Vor6NnRYxJ9YXY4LcrZCRyI69zo9P+zWgUVave7euG/++9G/uY78a+yuJszGuKz8frT9wrp338IDHsjtNXqeuvBXF59kxmg4utoifHjikHC3p0uEf0N7UyMTDx0+EX4QCn/QSs4legJ89exYqlQqXLl2CjnMQQavVIju7t0/vwoULYqdDCCEjilanx5bD7KE3APifOdESZyOBmlwg50s27uABTHpA8nTEtid/D2o62JF+KYEpGONt+kg/sRnb/fa8/36onUxvgcoysvs9/qYQ2Nppbig3S9PrdEYv3klevFzibIhciV6A9x2sLC0txX333YcrV64YHsvLy8P999+PkhL+NxQhhJCh+fJ8Jcoa2D7UCaEemBrlZYWMRHbkFQCcA/1JqxR37bxWr8XW81u5jz045kGJszGuu6wMTV+w7RgqBwd43v9zk9dpqmlHbsZVJm5jp8a4OfK5eOfy8cNorKpk4v5RMQgdM94KGRE5Er0HfPLkyTh8+DAAYNeuXdi1axfs7Hqvh+3u/uklUZVKhUmTJomdDiGEjBiCIOCfh/i734/OiZbNtAiLqS8AzrOHEWHjAKSslj4fke0r3IeyVvYmyDjPOEwLmmaFjPjqtvwL4LwC7nHnnbDxMv1J4KmviiFwxmgmzAiCg4s8WosEvR4nP/uI+1jSomXK+54jN0z0HfDf/e53A8YLCoKArq4udHV1MWMHn3zySbHTIYSQEePg5RpkV7LTIqJ8nXFLggKnMBz5OyBwpmlNWgG4+Emfj4h0eh3+de5f3MceHv+wbAq9nspKNH72GfuAjQ28HzJ9l765rgOXT1QxcbVGhcT58rl4JzftOOrL2QuCPINCMCrF9DnnRPlEL8AXLlyIF198EUBv8a1SqQb86Yv96U9/wsKFC8VOhxBCRgRBEPD691e4j62eHQW1Wh4FmsU0lgBnP2TjaltghvKunf+2+FsUNRcx8Sj3KMwPl8+c87qt24CeHibuvmQxbIODTV4n6+sS6Dm73/HTA+HqxQ54sAZBEJD26X+4j6UsuQtqtTx61Ik8SDKv5+mnn8bBgwdx++23w9HREYIgQBAEODo6IjU1FQcOHMCzzz4rRSqEEDIiHLlSizOljUzc380eSyaaXvgMG8deBzgX0WDi/YC7fPqDLUEv6PH2ube5jz08/mGoVfIYxddTXY3GjzktQRoNfB55xOR1Whu6cOl4BRNXqVWYfGv4UFK0qPxT6agpKWLi7v4BGD1zruT5EHkTvQe8z6xZszBr1izo9XrU1tYCAHx8fKBWy+MHBSGEKMVgu9+PzomGvY3CduKaK4HT77FxlQaY+Vvp8xHZgZIDyGvMY+JhrmG4LeI2K2TEV//Odgjd7PhL94W3wy7M9LaRrG+Lodeyu99xKf5w83EcUo6WIggCTu7i734nL74Lao3CvufIkElWgPdRq9Xw81NWLx4hhMjJifw6nCpuYOK+rva4N1k+/bIWc3wToOti4+PvATwjJE9HTIIgGN39XjVuFWzUkv9a59LW16Phv/9lH1Cp4L3a9AOx7c3duHSEs/utAibfFjGEDC2r6OxpXC1gn/S6+vhizJx5VsiIyJ3Fv1PfffddAEBERARmz55ttTUIIWSkGqz328FWYTtxrTVA5jtsXKUGZv1O+nxEdqT8CLLrs5l4sEswFkbL5xxV/Y6dEDrY8Zeut90K+yjTL6I5810JtD3swdqYKf7w8Dd9friYBt39XrQcGht5TGgh8mLxAnzlypVQqVRYtmzZDRfPlliDEEJGopMFdUgrrGfiPi52uD9FPv2yFnNiM6BlCz2MuRPwiZE+HxENtvv94NgHYauWR6Gna2xEw/vvcx/z+Z9HTV6ns7UH5w+Vcx+bvEA+X8ulF8+jIpd9UuTs6YWxN8nnQCyRF2rAJoQQBdn0A3/3++FZUXCUyU2BFtNWC2TwL6JR4u738YrjOFdzjon7OflhScwS6RMyom7nTujb2pi4y89uhkNcrMnrZH1XAm0XOz88eqIvvIPkcamSIAg48ckH3MeS7rgTNj/ee0LItURrFisuLja0khBCCBFfZlE9juXVMXFPJ1v8Yqp8dgwt5thrQHcrGx99B+CfIHk6YhIEAZuzNnMfe3Dsg7DTyKPQ0zY0oGEn/3e/Obvf7c3dOHeAvWQIACanRtxIaqIoOX8WZdkXmLijmzvG/0w+B2KJ/IhWgGdmZuJXv/qVWMsTQgi5xhs/sJMxAGDVrCg428vjcJ7FtFQB6fyLaDBLeZe6HSw9iAt1bKHn7eCNZaOWSZ+QEXVbt0Lf3s7EnefMhuPYMSavc/qbYu7ud8R4H/iGug4pR0sRBAHH/suZvgNgysKlsLWXx3xyIk+i/kS+9qZLU8nlBi9CCBkuMovqcTi3hom7O9rigWkK3P0+8ndA28nGR98BBCVKno6Y9IIem8/wd78fHv8wHGzkUej1VFej4X1+O4bvGtMvQ2pt6MIFI73fyQsjbyg3MRSczkBl3mUm7uTugYm3yudALJEnUQrwGy28LfXxhBAykgiCgJe/ZgsBAHhoZiRcHeRxOM9iGkuBU9s5D6iAub+XPB2xfVP8DXIbcpm4v5M/lscut0JGfHVb/gWhk31S5Dr/Z2btfp/6qgg6zuST6Em+8A2Tye63Xo9jH/2b+1jy4rtg6yCPJ0VEvixegG/fzvuheGMiIiIsthYhhCjVkSu1SOdMPnFzsMGK6RHSJyS2I68AOvaCF4xdprjeb51eh7fOvMV9bPWE1bDX2EucEV9PZSUajcz99nl8zf9v777jm6j/B46/krRN9y5dFFqg7I0s2VMZggPFhQjixIXiFvf6yVcQB27BLYiiggMF2Ruh7A2lG7p30zS53x+FSsmltJDRhvfz8Qhp7nN3eSfX0HfuPp/3p9b7KcguZd86y7rfaKDH6NqXL7S3w1s3kpl4zGK5b3AInYaNcEJEoqGxeQI+ceJEW+9SCCGEFYqi8L+/1M9+3z2gOQFeLnb2O+cY7FA586jRwsCnHB+Pnf1+/HeO5x+3WN7Yt3G9qnyS9cGHKEajxXL/ESPqVPlk2++JmE2WV8Fbdg8nOMrnomK0FbPZxIaF6mUWe107XiqfiFqRMoRCCNGA/bXvJLtS8i2Wh/p6MKlPrOMDsrfVb4K5wnJ5p5tcru630Wy0evb7nk731Ju63+XJyeT99JNlg1ZL6P3313o/eadKOLAxw2K5Rquh+6j60/f74Po1ZKckWSz3DwuXut+i1iQBF0KIBspkVpj1l2XfYID7BrbA28PFKp9kHoRdKt0ctG4w4HHHx2NnPx/5mZQiy1J8sf6xjGo2ygkRqct67z2osPxSFDB2LPpmtU+ctyw5jmK2PPvdundEvZn10lRRwQYrdb97X3ejzHopak0ScCGEaKCW7krj4MlCi+VRAZ7c3LOJEyKys+UvgmI5OI+ut0FQrMPDsacSYwkfJHyg2ja181TctPXjy1XZgQPk/7rEssHNjdCp99V6P5lJhRzeetJiuVan4bJ6VPd794pl5GWkWywPioyibf/BTohINFSSgAshRANkNJmZ9bf62e8Hh8Tj6e5is14mbYKDv1ku1+ldsu731/u/JrPUsqxkfFA8w2OHOyEidafemgUqlcsCr7sOj8aNa72fjYvVa9i37RuFf4jXBcdnS+WlJWz88TvVtt7jbkarc7HPnLArScCFEKIBWrgtmRPZlhOexIZ4c1232ic+DYKiwF8z1Nt63AkB0Y6Nx85yynL4fM/nqm0PdnkQraZ+/Oku3rSJ4rVrLZZrPD0Jva/2s14m78sheX+uxXI3D229Ovu9dcliSvLzLJaHNYml1eX9HB+QaNDqx6dYCCFErRUZKpj992HVtmnDWuKuc7H/2g8shZQtlsv1AdDvUcfHY2cf7fyIYmOxxfKujboyoPEAJ0RkSTGbOTXzf6ptwbfdhnt4eC33o7DBytnvzkOb4BNQP8osFufl8u/Sxapt/W6ZhFYrZ79F3bjY/9JCCOH6Pl5zjKwig8XyVuF+XNUxygkR2ZHJCMtfUG/rNw28gx0ajr0lFySz8NBC1bZHL3u03swUXfDHH5Tt3WuxXBcYSMidU2q9n0NbT5KVXGSx3NPXnS7D6s84ho2LvsVosJxkqEn7TsR26uqEiERDJwm4EEI0ICcLyvhkjeUEIABPjGiFVls/EjSb2f4lZKucIfWPhp73OD4eO3tnxztUqJRZHNZ0GB3DOjohIkvm8nIyZ7+t2hZ67z3o/Go3W2WF0cTmX9R/l7uPisXDq34MNM1JS2HXimWqbf1vmVRvvhSJhsVuCfiuXbvYe9a34/3795OQkGCvpxNCiEvC7L8PUWo0WSzv3SyEQa0aOSEiOzIUwao31NsGPQPu9WNwnq3sydrDn4l/Wix307jxUNeHnBCRurzvv8eYYlke0T06msCbbqr1fvasTqUwx/Kssn+YF+361Z9+/eu++xLFbFl9p3WfAYQ3c63a88Jx7JKAp6WlcdlllzF9+n8j06dPn06PHj1IUfnQCiGEOL9DJwtZuC1Zte3pkW1c70zcxveh+JTl8kbtoNONjo/HjhRFYda/s1Tbrmt5HU39mzo4InWmwkKy5qqXRwx7+GG0tZwF0lBiZNsfiaptvcY2Q+dWPy7Qpx3az+EtGyyWa3Vu9L1xghMiEq7CLtd3oqKiuPHGG/nmm2/YtGkTAH/88Qe33HILjetQlkgIIcR/Xv99PyrzlHBNl2g6NA5wfED2VJAG6+eotw19AVxs0NvK5JVszdhqsdzbzZt7OtWfrjZZH36IKS/PYrln27b4jxpZ6/1s/T0RQ7FlV5tGTf1o0bV+XMlRzGZWffGpalvn4SMJaBTh4IiEK7FbB6uXXnqJhQsXMmPGDDQaDR4eHrz88sv2ejohhHBpG45ksfKgZV1oDzctjw5v6YSI7Gz5i6BSCYTYfhDvWtN9l5vKmbl1pmrb7e1uJ9Qr1MERqStPTCTny69U2xpNfxSNtnZnrXMzitn9j/rV8N7XtkBTT8Yx7F+3ivQjBy2We3h50/Pa8U6ISLgSmyfgSUlJAGi1Wq655hoWLFiARqNh/PjxaLXaqvYmTerP6GYhhKjPzGaF1/7Yr9o2qU8sjYPqxzTdNpOyDXZ9r9427EVwsa42X+37SnXK+VCvUCa2m+iEiNSd/L83wWi0WO7Tty8+l19e6/2sX3QEs8qlnKbtQ2jcKuiiYrSV8rJS1nw7X7Wtx9hxePu72BUn4XA2T8BjY2Mt+iEqisKCBQtYsGABABqNhooKy0tPQgghLP3wbzJ7Ugsslgd5u3PfQBcbBGY2wx9PqLd1ugmiuzk2HjvLKs3i410fq7Y91PUhvN3rx5erorXrKFq50rJBpyP8SSvHS0Xi7ixO7Mm2WK7Vaugzrv78Lm/5eRHFuTkWy/3Dwuk26mrHByRcjs0T8P79+1cl4CkpKRw9ehSNRkOzZs2k/7cQQtRRQZmRmcssL4MDPDA4ngAvdwdHZGe7F0LqNsvl7j4w5HnHx2Nnc7bPoaTCckbTdiHtGNN8jBMisqQYjZx8Q70aTdDNN6NvUbvE2WQys36R+qQ7HQY1JijC54JjtKX8UxlsW/qTatvACXfgVsuBpkLUxOYJ+KpVq6p+7tevHxkZGQCEh4ezUu3bsxBCCKveWX6YrKJyi+WxId7c2qt+VMawGUNRDZPuPAL+kQ4Nx972Zu3l5yM/q7Y92ePJejPlfO73Cyg/etRiuS4wkLD7p9Z6P3tWpZJ30vLLhqevO91HxV5MiDa1+uvPMal0tYlp24EWPXo7ISLhiuz26V66dCkbNmzgvvvu4/7772fjxo0sXbrUXk8nhBAu58ipQuZvSFRtmzG6LR71pFSbzaybDYXplssDm0Dv+x0fjx0pisIbW9TPKo+MG0nnRp0dG5AVFbm5ZL77rmpb6IMPoAuoXV/o0sJytiw9rtrWc0wz9N7140pO8t5dHN5sWXZQo9EycOKdrlfqUziNXf73VhSFZ555Bh8fHx5//HGmT5+Oj48PTz/9NIqiUkNLCCFENYqi8NLS/VSoDFYb2CqMwa3rR6k2m8k9ARvUEz2GvwLuno6Nx87+OP4HCZkJFsu93LyY1m2a4wOyIuvddzEXWI4/0MfHE3TDDbXez+Zfj1Feajn2KyTal7Z9oy4qRlsxm02snK/eH7/j0CtoFNvMwREJV2aXBPzkyZNotVruu+8+QkJCCAkJ4f7770er1VZ1SRFCCGHdiv2nWHPIsuygm1bDjNFtXe9M3LKnwWSwXN60L7SpH32hbaXYWMxb/76l2jap/SQifOpHfemy/fvJ/X6Balv400+hcatdL9bMpEL2rUtTbet3QzzaelJ2cNfff5KZlGixXO/tw+U33Or4gIRLs0sd8IiICLZv347B8N9/ps899xyvvvqq6/3REEIIGyszmnj5t32qbZP6xNI8zNfBEdnZoWVwQKWLokYLV77ucmUH5ybM5VSJ5QyfkT6R3N7udscHpEIxm8l44cXKqjTn8Bs2FJ/etesLbTYrrPrmAGoXv5t3DSO6npQdLM7LZd33X6q29R53s5QdFDZnt4l4NBoNnp7/XTI883NWVhZbtmyhqKiIqKgoevbsibt7/ej7JYQQ9cEHq45yIttysFqorwcPDIl3QkR2VF4Cvz+m3tb1Nojs6Nh47OxgzkG+2f+Natsj3R7By83LwRGpy1u0iNKdOy2Wa9zdafT447Xez751aZw6UWixXOem5fJr60/ZwdVff46hxHLip6CoxnS+YpQTIhKuzm4J+LmMRiP3338/n3/+OeazvlEHBgby0ksvMXVq7UdSCyGEqzqWWcQHqywrTgA8fmVr/D1d7ITF2rcg74Tlcq8gGPyc4+OxI7Ni5pVNr2BSTBZtPSJ6cEXsFU6IylJFTg6n3pql2hY85Q48YmJqtZ+SgnI2/az+u9z1iib4h9aPLxtJe3axf616lbbBk+5GV8uuNkLUhc1/qxISEvj8888BmDZtGnFxcQBMnDiRBQsWWAzCzM3N5cEHHyQzM5MXXnjB1uEIIUSDoSgKM37ZQ7nJ8rJ/p5hAxnV1sbkUsg7D+jnqbUNfBJ8Qx8ZjZz8f+Vl14KWb1o1nej1Tb7ponvrfW5jz8y2Wu8fEEHr33bXez4afjmAosRx4GRDmRdcr60cJTVOFkRWfzVVta9W7H7Eduzg4InGpsPkgzLlz5/Lee+/x6aefEnP6W/KqVav4/vvKaYXP/g9Go9Gg0WhQFIVXX32V3bt32zocIYRoMH7dmcb6IyqzBGrg1avb15vBajahKPDbI2C2rLdM4x7QZYLjY7Kj3LJcZv2rflZ5UrtJNAuoHxU2Sv79l/yf1CehiZjxLFrP2lWjST2Uy8FN6kUX+t/UEjd33QXHaEvbliwmJy3FYrmHlxcDb5vihIjEpcLmCfimTZsAaNmyJW6nL9t8/HFlWR9FUQgPD2fYsGEMGDCA4ODgqjPiZrOZDz/80NbhCCFEg5BfYuTlpeoDL2+/PI720S42CGzPj3B8jeVyjQ5GzwKta9U4f3v72+QbLM8qR/tGc2fHO50QkSXFaKwceKnCb9gwfPv3r9V+TBVmVn93SLWteddGNGlbP65s5J/KYNOP36u29Rk/Ad/g+hGncE02/x8uOTkZjUZDRMR/ZZT+/vtvNBoNDz30ECdOnGDZsmWsXLmS5ORkHn744ar11qxR+c9YCCEuATP/OqA642WEvyePDG/phIjsqCQH/nxKva3nPRDRwbHx2Nm2jG38dFj9rPJTPZ6qNwMvs+fPx3D4sMVyjbc34U9bOV4qdvydRG665YBGd72OvtfXj0HEiqKw4rMPqDBafubCYpvRebgMvBT2ZfMEvKioCAAvr8r/UFJTU8nOzqZZs2bMnj27WsUTT09PZs2aRXx8PIqikJSUZOtwhBCi3tuelMs3m9X//3vuqrb46l1sENiyZ6DYsgwffpEwqPaJXkNQVlHGCxtfUG0bHDOYATEDHBuQFYZjx8l69z3VtrD778c9MrJW+8lJL2brb9ZnvPQN0l9wjLa0f+1Kjif8a9mg0TBsylS0uvrRRUa4Lpsn4Ge6nZypdLJt2zYABg8ebHWb2NhYAMrKymwdjhBC1GuGChOPL9qlWid5YKswRrSvH5Oy2MyR5bDzW/W2K18HvZ9j47GzuTvncqLAssqLl5sXT/Z40gkRWVLMZtJnzEAptzwbrI+PJ3hC7SahMZsVVn61H3OF5S9zSGNfOgyMvuhYbaE4L5eVX3yi2tZxyBVExrdycETiUmTzBDwkJARFUdi2bRsnT56s6v+dnW05sAggMzOTrVu3ApUlCYUQ4lLy3j9HOHKqyGK53k3LS2Pa15vKGDZhKIQlD6u3xQ+Htlc7Mhq725u1ly/2fqHaNrXzVCJ9a3dW2d5yv/+e0n/VzwZHvPQimlrO1bFndQoZxyynrddoYOAtrdDq6ke//n/mf0xZkWVtcp/AIPrddLvjAxKXJJt/Gtq1awdARkYGUVFR/Pnnn2g0GhYvXsy4ceNYt24dmZmZJCcns3jxYoYOHUpeXh4ajYb27dvbOhwhhKi39qTmM9dKze8Hh8TTJMTbwRHZ2YqXID/ZcrmHH4ye7VIzXhrNRp7b8BxmxbKkZIfQDtzapn5MbW5MTSXzf2+ptgVNuBXvLrUrw1eQVcrGn4+ptnUcEkNEXP0YRHx460YObVyr2jbkjnvx9HWxWWZFvWXzjoVjxozh77//BioHOZw5e6MoCosXL2bx4sU1biuEEJcCo8nM44t2YTJbXq5vF+XPXf3rR1k6mzmxEbaoX/Zn2IsQ4Fo1zuftmcehXMtKIG5aN168/EV0Wuf3MVYUhfQXXsRcYjnrqnt0NI0eeqjW+1n1zQEqDJYTDPmHetJzTP34XS4rKmLFp+o1v1v27EN8j8sdHJG4lNn8DPiUKVPo3r17VXlBjUbDxx9/TPv27VEUxeJ2RuPGjbnjjjtsHY4QQtRLH60+yr50y8v1bloNb47riHs9uVxvE8Yy+PUBQKWje9O+0G2Sw0Oyp2N5x/hwp3pZ3bs63EV8UP2oBFLw668Ur1U/Gxz58ktofXxqtZ8DGzNI3p+r2jZoQhvcPZz/ZQMqp5svzrOM09PHl8GT73FCROJSZvMz4Hq9njVr1rBo0SJSU1MZOHAgPXr0oHfv3gwePJhTp05V69OoKApBQUH8+OOP+MqlHyHEJeDQyULeWXFEte2+gc1pF1U/LtfbzMpXIduyvB1unjDmHZeq+V1hruDZ9c9iVJlgqEVgC6Z0qB+TuxhPniTjtddV2wKuuxafy2t3Nrgwp4z1i1SOLdC2bxSNWwVdcIy2dDzhX/as/Eu1beDEO/EJrB9xikuHXWpb6fV6brnllmrL2rZtS0JCAs8++yxLly4lPz+f6OhoRo0axRNPPEFUVJQ9QhFCiHqlwmTmsUW7VKebbxnuy9TBLZwQlR0lrocN76q3DXoaQpo7Nh47+2T3J+zOspzVWavR8tLlL+Guq92ARntSFIX0p59RnW5eFxZK+OOP124/ZoV/vtyvOt28T4AHl19XP36XSwsLWPbB26ptsZ270ba/9SptQtiLQ4vLRkRE8OmnnzryKYUQol55f+VRdibnWSzXauDNcZ3Qu9WPy/U2UVYAi+9BtetJVBfoNdXhIdnT3qy9fLTzI9W2CW0m0CGsfkwwlPvttxSvX6/aFvn88+gCancFZteqFFIOqHc9GXBLa/Rezq9frygKyz+dq9r1xN3Ti2FTprpWpSHRYLjOdT8hhKjnEpLzeOcf9cv1d/ZrRueYQMcGZG9/PgX5KhMM6Txg7Pugc36CZiulFaU8te4pTIrlQMRY/1imdqkfXzYMx45zaub/VNv8R47Eb+jQWu0nJ72YjYvVK/i07BFOXMfQC47Rlg6sW8WhTetU2wbcOgn/sEYOjkiISpKACyGEA5SUVzBtQYJq1ZNmoT5MG+Zi080f+A0SvlZvG/IchLdzbDx29va/b3M833IGSJ1Gx2t9X6sX080rRiNpTzyBojLpnVt4OBHPzajVfkwmM8vn7cNktOxG5Rukp/+N9eN3uSArkxWfqw+GjevcjY5DRzg4IiH+45IJuMFgqOpX7uXlRc+ePatKI9bkp59+Yvz48TRr1gxvb29atWrFo48+Sl5env2DFkK4tNd+38/xrGKL5TqthlnjO+Pp7kJdT4pOwa8Pqrc17etyXU82pG3g2wPqs3ve3fHuetP1JOujjynbbdk/HSDytVfR1XIyvG2/JZKZZDmRDcDgiW3Qe9eDfu5mM8s+mI2hxPIz5+nnz/B7HpKuJ8KpXDIBv/3225k1axa33HILc+bMQafTMXLkSNatU78MdcZdd93F/v37ufXWW3nnnXe48soree+99+jduzelpaUOil4I4WpWHjjF15tUumIADw6Od62uJ4pSmXyXZFm2efjBNR+4VNWTfEM+M9arnzluH9KeKR3rR9WT0l27yPrgA9W2oFtvxbdPn1rtJ+NYPv/+kaja1mlwDDGtgy80RJva/scSkvbsUm0bdudUfIPqR5zi0uU6HfBO27JlC99//z0zZ85k+vTpANx22220b9+exx9/nA0bNljddtGiRQwcOLDasm7dujFx4kS++eYbpkypH/+RCiEajlOFZTy2aKdqW+eYQKYOcq0qIGz7HA79od428k0IbOLYeOxIURRe3Pgip0pOWbR56jx5rd9ruGudfzbYVFRM6mOPgcmyf7pHXByNHn2kVvsxlFbw9+d7UVTG1AZFeNPr6vox4c6pxGOs/W6+alvbfoNo2bN2XzaEsCeXS8AXLVqETqfjrrvuqlrm6enJHXfcwdNPP01ycjIxMTGq256bfANcc801TJw4kf3799c5lpSUlBrb09PT67xPIUTDYTIrTFuQQFZRuUWbl7uO2eM74+ZKE+5k7K4ceKmmzVXQ6SbHxmNnCw8u5O8T6t0bH7nsEeIC4hwckSVFUch44QWMJ1SuwLi5EfXmm2i9zt8//cxslwVZlv3HtVoNwya3w60eTLhTXlbK0jlvYjJa1mH3Cw2TCXdEveFyCfiOHTto2bIl/v7+1Zb36NEDgISEBKsJuJqMjAwAQkPrPqK7Ls8jhHA9H6w6wvoj2aptM0a3JS60djMNNgiGIvhhEpgMlm0+jWD0HHChPrcHcw7y5tY3Vdv6RPXhxlY3Ojgidfk//UTB0qWqbaH33oNXh/a12s++dWkc2WZ5ph+g++g4wpr4XXCMtvTP5x+Sm6Z+8uvKe6eh93ahz5xo0Fzo1Eul9PR0IiMjLZafWZaWllan/f3f//0fOp2OcePG2SQ+IcSlYWtiDrP+PqTaNrRNODf1cLEv6L8/pj7bJcDVc8EnxLHx2FGJsYTpq6dTbra8shGkD+KlPi/ViwF+hiNHyHj5FdU2r86dCb377lrtJzu1iLUL1Y9tZPMAul5RP7oV7VvzD3tXr1Btu+yqa2nSvqODIxLCOpc7A15aWoper7dY7unpWdVeW99++y2fffYZjz/+OPHx8XWOJTk5ucb29PT0qjPzQgjXkVtczoPf7UCl4iBRAZ787/qO9SJBs5md38NO9SogXP4AxA9zbDx29urmV0ksSFRv6/sqjbydX1vaXFZG6rRHVEsOav39iX7rf2jczp8CGMtNLPt0r2rJQb2PG8PuaIe2HnSjyklLYfmnc1XbIlq0pO+NExwckRA1c7kE3MvLC4PB8hJo2en/hLxq0dcNYO3atdxxxx1cccUVvPrqqxcUS+PGjS9oOyFEw2U2K0z/YSfp+ZaJj06r4Z2buhDo7eGEyOwk8xAstTKIL7obDH7OsfHY2a9Hf+XXo7+qtt3e7nb6Ne7n4IjUnXz1NQyH1c9aR732Ku7R0bXaz9rvD5GbblnKD2DIbW3wC/a84BhtxVhuYOnb/4fRYPmZ03v7MPqhx9G5OX8wrBBnc/7XVhuLjIxUHdx4ZllUVNR597Fz507GjBlD+/btWbRoEW61OEsghBAAc1cdYcUB9b6yjwxryWWxLlT+zFAIC24Fo0qCpveH6z4DN9f5snEw5yAvb3xZta1DaAce7GKl9rmD5f34E3k//KDaFnTLLbWe7XLfujT2b1AvFtBxcGPiOoVdcIy2oigKKz79gMwTlpMgAQy/+wECGkU4OCohzs/lEvDOnTtz6NAhCgoKqi3fvHlzVXtNjh49ypVXXkmjRo34/fff8fX1tVeoQggXs+rgKd6y0u+7X3wo9w5woZKDigK/TIWsg+rtY96BYOdXAbGVfEM+D698mDKT5VlWX3df/q///+Guc/5Z1tI9e8l48UXVNn2bNjR6/LFa7edkYgGrv1c/tmFN/Lj8mhYXHKMt7Vr+B3tXL1dt6zRsBC179XVwRELUjssl4OPGjcNkMvHxxx9XLTMYDMybN4+ePXtWVSZJSkriwIED1bbNyMhg+PDhaLVali1bRliY87/dCyEahqTsEh76PkG1RnKor55ZN3RGq3Whft8b3oV9v6i3dZsE7a5xbDx2ZFbMPLX2KVKK1KtrvHD5C8T4OX9QbUVuLqkPPohSbjk4VOPtTfSst9CqjJE6V2lhOX9+tBtzheUvs7tex/Ap7dC5Oz99SDt0gH/mfazaFtoklgG3ydwdov5yub4VPXv25Prrr+epp57i1KlTtGjRgi+++ILExEQ+++yzqvVuu+02Vq9ejXLWX8srr7ySY8eO8fjjj7Nu3bpqM2eGh4czbJhrDSQSQthGabmJu7/+l/xSy9rDOq2G927uQpjf+ROfBuP4Glj+vHpbZCe48nXHxmNnH+78kLWpa1Xbbm59M1fEXuHgiCwpJhNpj07HaKXSV9Srr6CPO/8VCbPJzF+f7aUoV6WcJDD4tjYENvK+qFhtoTgvlyWzX8dsqrBo8/Dy5qppT+Hu4UKfOeFyXC4BB/jyyy+ZMWMGX331Fbm5uXTs2JGlS5fSv3//GrfbubNytro337Ss7TpgwABJwIUQFhRF4ZnFu9mfXqDa/tSI1vRq5jol+MhPqaz3rVhWxcArGMZ/De61G+zeEKxJWcMHO9WncO/SqAvTL5vu4IjUZb7zLsVWZnoOvv12/EeMqNV+Nv96jJQDuaptXYY1oUW3elDhxWTitzlvUpSjXmN/xNRHCI6q3SBTIZzFJRNwT09PZs6cycyZM62us2rVKotlitq1YyGEqMFn647z045U1barOkVxR1/X6QdNeUnloMuSLMs2jRbGfeZSU80fyz/Gk2ueVG0L9QrlrQFv1Yt+3wV/LiP7o49U27y7d6fR9EdrtZ/D206yfZnKjJlAdKvAejPV/KqvPiV5327Vtp7X3ECL7r0cHJEQdef8TlxCCNFALd93kld/36/a1ircj/+7roPr1Ps2m+HneyFth3r74Geh+WDHxmRHeWV53L/ifgqNhRZtbho33hrwFmHezh8nVLp7D2lPqn9JcAsPJ3r2rFrV+z55vIAVX6j/LvsG6Rl+R/t6Ue9759+/s+OPJaptTTt24fIbbnFwREJcGOd/moQQogHal1bAg9/vUB106efpxocTuuHt4UIXGVe9Dvt+Vm9rPRr6WqkF3gAZTUamrZpGcqH6ZGrTu0+na3hXB0dlyZiRQcp996lOtoO7O43nvI1baOh591OYU8ZvH+xSnWxH66bhyrs64O3v/HKSJ3YlsOLzD1Xb/MMaMerBx9BqdQ6OSogLIwm4EELU0anCMqZ8sZWScpNFm0YDb4/vTFyojxMis5NdP8Aay7ExAITEw9UfVL5wF6AoCq9sfoVtJ7epto9qNoqbW9/s4KgsmUtKSLlvKhWZmartEc88jdd5yu4ClJdV8NvcXZQWWFZOAeg/viXhcf4XE6pN5KSlsOTt11HMll8S3Nw9GPPI03j5OT9OIWpLEnAhhKiDMqOJO7/8lzSVmS6hctDlkDbhDo7KjpK3VNb7VuMZCDcvAE/XSXy+3PclPx3+SbWtY2hHXuj9gtO7FSlmM2lPPEnZvn2q7UE330zQjTfWYj8Ky+ftIzulSLW946DGtOvn/MGMpYUFLP6/FzEUq8/IeeXUaYQ3qx91yYWoLUnAhRCilsxmhUd/2MnO5DzV9vGXxXBnv/oxUM0m8pLg+5vBpFKSTutWWfEkxHUmF1qVvIq3tr2l2hbhE8GcwXPwdHP+1OuZc96h8O+/Vdt8+vQh/OmnarWfTb8c5fhOlQG1QJN2wfQZ5/yk1lRhZMms18nLUJ+R8/Lrb6FV734OjkqIiycJuBBC1IKiKLzy235+26WeCPSMC+blq9s7/eyozRRnw1fXQrF6FwdGzYI410l8Ek4l8Njqx1Cw7NTv5ebFe4PfI9Tr/P2p7S33u++sVjzxaNas1oMud61MtlrxJCjSh+FTnD/oUjGb+XPu21YrnrTuM4Be153/TL8Q9ZEk4EIIUQsfrD7K5+uPq7bFhnjz4a3d8HBzkf9Sy4vh2xsg+7B6e+/7odtEx8ZkR8fyjnH/P/erTjOvQcOb/d+kVXArJ0RWXcGyv8h46WXVNl1gIDEffoDO//zdgQ5vO8naherH1tPXndFTO6L3cu4AYkVRWPXVZxxYv1q1PbJFK4bf86DrfOEVlxwX+WshhBD2s3BbMm/+eVC1zd/Tjc9u706Qj/OrRNiEyQgLJ0Kq+iBEWl4Jw15ybEx2dLL4JHcvv5t8Q75q+yPdHmFgzEDHBqWieMsW0qZPR7Xsjrs7jd99B48m56/BnnIwl+Xz96Fyoh+tm4YR93TAP9T5Eylt/fVHtv/+i2qbX0gYYx97Vma6FA2aJOBCCFGD5ftO8tRP6pfAPXRaPpzQjeZhvg6Oyk4UBX59AI6o9y8mogNc9ym4SKm3fEM+9yy/h4ziDNX2cS3HMbGd88/0lx08SMp9U1GMRtX2yJdfwrt79/PuJzO5kN8/2IW5Qn3SucET2hDVIvBiQrWJvatXsPbb+aptHl7eXP34DHwCgxwblBA2Jgm4EEJYsTUxh6nfbsdktkxYNBp4+8bOXN7c+f2CbWb587DzO/W2oFi45UfQ+zk0JHspqyjjwX8e5EjeEdX2QTGDeKbnM07v4lCekkrylDsxF6lXKgl79BECr776vPspyCpl6bs7MZZZls4EuPzaFrTqGXExodrE8R3bWPbhHNU2nZsbVz/2LI1iXWigs7hkSQIuhBAq9qTmc8f8rRgqLOsOA7w0tj0jO0Q6OCo7Wj+n8qbGJwxu/Qn8XKO8otFs5LE1j7H91HbV9q6NuvJm/zdx0zq3H3RFZibJd9xhtdZ30G0TCJky5bz7Kc438OucBEqs1PruNDSGLsPP333F3lIO7OXX2eq1vtFoGPnAdGLadXR8YELYgSTgQghxjgMZBUz4bDMFZRWq7Q8NiWdCr6YOjsqONn8Efz+n3ubhC7f84DLlBivMFTy55klWJa9SbW8R2IJ3Br/j9HKDFTk5nJg0ifITJ1Tb/UeOJPzJJ897hr6koJxfZu8gP7NUtb1lj3D6XOv8coPpRw6y+I0XqDColLwEhky6h5a9+jo4KiHsRxJwIYQ4y5FThdzyyWZyS9T7297SswkPD413cFR2tG0e/PG4epvWHcZ/BVFdHBuTnZjMJp5d/yx/nfhLtT3CJ4IPhn5AgD7AwZFVZ8rLI2nyHZQfOara7t27F5FvvI5GW/Of8LIiI7/O2UFuRolqe0zbYAbf1gaN1rndbE4eP8qPrz1Hean6l4Re146n8xWjHByVEPYlCbgQQpx2LLOImz7ZTHax+qX6Ee0jeGmsC9X6TvgWlk6z3n7Nh9B8sOPisSOzYualTS/x27HfVNv9Pfz5aOhHRPg4tx+0qbCQpCl3YjhwQLVd37YNjd99F61HzVV3DCVGfn0ngexU9dkjw5r4ceVd7dE5uXRmVlIii16dYXWWyw6Dh3P5Dbc6OCoh7E8ScCGEAI5nFXPzJ5vJLFS/BD6gZRhv39gZnZPPFtrMrh9OTzGvXhGDUW9Bh3EODclezIqZVze9anWKeR93Hz4c+iHNAp07uM9UWEjynXdRtmePartHs2Y0+eQTdL41V90xlBhZ8u5OMpMKVduDIn246oFOeHg6t497dkoSP7zyLGWFBartLXv1ZeiUqa7zhVeIszj30yeEEPXAoZOF3PKp9eS7T4sQPprQDb2ba5TfY/tXleUGrSXfV7wO3c8/uK8hMJlNvLTpJavJt5ebF3OHzKVDWAcHR1adKT+fpCl3UrZbveSle9MmNJk3D7eQkBr3U1Zs5Nc5CVaT78Bwb8Y+3BkvP+fWrT+VeIxFrzxLqZXku/llvRj5wHS0Ohf5zAlxDknAhRCXtD2p+dz2+RZyrHQ76REXzKe3dcfT3UUSga2fwW+PWG8f8jz0vs9x8dhRhbmCGetnsPTYUtV2vU7Pu4PfpWt4VwdHVl1Fbi5Jk+/AsH+/art7dDRN58/HPbxRjfspLSznl7cTyE5VL1noH+rJ2Ic74xPg3AlsMo4e5sdXZ1BWrB5nbOdujH74CXRukqII1yW/3UKIS9aOpFwmfr7FarWTbk2D+Pz27nh5uEjyvXEuLHvKevuAJ6FfDcl5A2I0G3lyzZNWB1y6a915e9Db9Izs6eDIqqvIyiJp0iQMh9XrkbuFh9Pki/m4R9Zc8rI438AvbyeQm67el9o3SM/Yh7vgG+Tc6i5ph/bz42vPU16qPjC0SfuOjHn0adzc3R0cmRCOJQm4EOKStPFoNlO+2EpxufrEJF2bBDJvUnd89S7w36SiwLpZsKKGKeT7PQoDn3RcTHZkMBmYvnq61VKD7lp3Zg+cTd9o55a1M6anV1Y7OX5ctd0tPJwm8+fh0bhxjfspzCnj1zkJ5J1UT2p9g/SMndbF6VPMJ+/dxeI3X8ZYpl7tpHHb9lz92HMyxby4JLjAXxYhhKib33en8/D3CZSb1CfZ6dUsmM8mdsfHFZJvsxmWPQ2bP7C+zqBnYICVUoQNTEF5AQ+seMDqJDt6nZ45g+bQJ7qPgyOrznDkCElT7qQiI0O13T0qiiZfzMcjJqbG/WSnFrHk3Z0U56mPX/AL8eTqepB8H9q8nt/fmYmpQv1qU9OOXRg7/Rnc9c49Qy+Eo7jAXxchhKi9Lzcm8vyve1GsjD8c0DKMjyZ0c40+3xXl8PO9sGeR9XWGvgh9H3ZYSPZ0quQU9yy/h8O5h1Xbvdy8eG/we/SI7OHgyKor2b6D5HvvxZyfr9ru3qQJTed9jnt0dI37STuSx+9zd2EoUU9qA8K8GDutC37Bzk1qd/79O8s/+wBrH7pmXbtz1bSncDtPaUUhXIkk4EKIS4KiKLz11yHeW6ne1xZgWNtw3ru5i2tUOzEUwoJb4dgq6+tc+X/Q6x6HhWRPx/OPc8/f95BWnKba7uPuw9whc50+4LLwn5WkPvIISlmZartHs2Y0mfc57uHhNe7n+M5Mln26F5NR/SpOUIQ3Y6d1ceqAS0VR2LjoWzYu+s7qOi2692b0w4+jc5M+3+LSIgm4EMLlGU1mnlm8m4XbUqyuM6ZTFG/d0Al3nQtMj1B0Cr65HtITrKyggdGz4bJJjozKbnZl7mLqiqnkGfJU2/09/Plg6Ad0DOvo2MDOkffjj6Q/9zyY1Mcd6Fu2pMnnn+EWGlrjfvauTWX1twetXsUJaezLmAc74+3vvDPKZpOJFZ9/wK7lf1pdp3WfAVx53zSpdiIuSfJbL4RwaXkl5dz3zXY2HM22us7kPnE8O6oNWleYZCdjD3w7HgqsfNnQecB1n0LbsY6Ny07+PP4nz65/FoNJvQ90uHc4Hw37iOaBzR0c2X8Us5nM2bPJ/uRTq+t4X3YZjee+j87f3+o6ZrPCxsVHSfg7yeo60S0DGXFvR/RezvvzbigpZsnsNzixa4fVdbqMuIpBt92JRusCX3iFuACSgAshXNaxzCLu+GIbx7PUS7MBPDWiNXf1b+Yas+0d/AMW3QFGK69X7w83fgtx/Rwblx0oisKHOz9k7s65VtdpHtCcD4d96NTp5c3FxaQ+8QRFy1dYXcdv2FCi/vc/tHrr3UXKyyr4+/N9JO7KsrpO865hDJ3UFjcnjl/Iy0hn8ZsvkZOabHWdvjdNpMfYca7xmRPiAkkCLoRwSeuPZHHv1/9arfHtptXw5riOXNu15hJvDYKiwMb34K8ZWJ3d0jccbv0RIpw746MtlFWU8dyG5/jj+B9W1+kc1pn3hrxHgD7AgZFVZ8zIIPne+6xOsAMQeMMNRDz/HJoaZnwszCnjt7m7yE5Rn7gGoH3/aPrd2NKpV3FS9u/hl7deszq1vEarZfhdD9B+0DAHRyZE/SMJuBDC5Xyz+QTP/bIXk1k9GfVy1/HBrV0Z2KrmmQUbhIryypktd3xlfZ3g5jDhJwiKdVhY9pJVmsVD/zzErqxdVtcZ0HgAMwfMxMvNeaX3SnfvJuW+qVRkZlpdJ/S++wh94P4azwRnHM/n9w92U1qgPlMrQI+r4rhsZKxTzyjvWbWcvz9+D7PJyhdeDz2jH36C5t2cW4FGiPpCEnAhhMsoM5p4/pe9LNhm/fJ3ZIAnn068jHZRzjszajP5KfDD7ZCy1fo6TfvC+K/AO9hhYdnL9pPbmb56Opml1pPaW9vcyqOXPYqb1jl/3hRFIe+HHzj58isoRqP6Su7uRL70EoHXXF3jfvauTWPtwkOYK9S/SGrdNAy+tTWtetU8S6Y9VRiNrPryU3b+9ZvVdXyCgrn6sRlENI93YGRC1G+SgAshXEJSdgn3fvMve9PUL38DdIoJ5JMJ3Wjk7wKTfRxbBYsmQ4n1waV0mQCjZoFbw66vrCgKX+37iln/zsKkqFcQ0Wl0PN3zaW5odYODo/uPuayMjBdfIn/xYqvr6AIDafzeu3hfdpnVdYzlJlZ/e5CDm9Qn6QHw8nNnxN0diGwReDEhX5SCrFMsmf0GGUcOWV2nUWxzrn58Bn4hNVd2EeJSIwm4EKLB++fASR7+PsFqf2+A0R0j+d/1nRr+BDtmc+W08itfBUW9BjRoYPjL0Pt+aOAD3YqNxTy/4XmWJS6zuo6fhx+zBs6iV2QvB0ZWXXlSEikPPoThwAGr63i0aE7MBx/UOLtl3qkS/vxoD9mp1vt7B0f5MOq+jk6d3TJx1w5+e2em1f7eAPE9LmfE1Edw93SBL7xC2Jgk4EKIBstkVpiz/BDv/GN9ch2Ah4fG89CQ+IZfdaE0DxbfA4esDz7E3QfGfQatRjgsLHs5mneUaaumcTz/uNV1mvg14b0h7xEXEOfAyKor/GclaU88gbmw0Oo6Pn37Ej17Fjo/P6vrHEvIZMX8fZSXqZ/lB2jSLoQrprTDw0llBhWzmc0//8D6hV9bndkSoMfV19N3/AQpMyiEFZKACyEapNS8Uh5ZkMDm4zlW1/HVuzFzXEdGdHBeH1mbSVwPi++GfOv92wluXtnfO7yd4+KyA0VRWHR4ETO3zqS0otTqen2j+/JGvzecVunEXFbGqbdmkftVDQNggeA7JtNo2jQ0ViacqSg3seGno+xeZX2iKICuVzSh55hmaJ00WVRhThZ/zn2bpN0JVtdx0+sZftcDtOk70GFxCdEQSQIuhGhwfklI5dmf91BYQ5eTluG+fHBrN5qH+TowMjuoKIdVr8O62VgtMQjQejRcPRc8G/bg0pyyHJ7f8DyrkldZXUeDhvs638ddHe9Cq3FOMlp28CBp06djOGz96ovWx4fIN17Hf5j1snuZyYX8/fk+ctOt16r38NQx5Pa2NOscdlExX4xDm9fz98fvUVZk/Sx/UGQ0Yx59mtCYpg6MTIiGSRJwIUSDkV9q5Llf9vBLQlqN643tHMXr13bA26OB/xeXdRh+nFLDlPKARgtDX4DLH2zw/b3XpqxlxvoZZJdZH1gaoA/g//r9H32i+zgwsv8oZjM5X3xJ5qxZ1qucAPr4eKLfmYM+Tr1rjGJWSFiezKZfjmI2Wf9iFRLty5V3tyewkfdFx34hyktL+Gfex+xdvbzG9eJ7Xs4V9zyM3ts5cQrR0DTwv05CiEvF5mPZPLJwJ6l51rskuOs0zBjdlgm9mjbs/t6KAts+h2XPQA1dMPBpBOM+b/AzW5ZVlDHr31l8d+C7GtdrH9Ketwa+RZRvlIMiq8548iRpTz5JycZNNa7nP+YqIl94Aa2VZLQwp4wVX+wj9WBejftp1SuCATe3wt3DOQOH0w7t5/f33iL/pPVqLBqtlv63TKLbqKsb9mdOCAeTBFwIUa+VlFfw1l+H+Hz98ZrGfNE4yIt3bupC1yZBjgvOHvKSYek0OPJ3zevF9oNrPwH/ht2/fcepHTy3/jkSCxJrXO/GVjfyWPfH8NA5vqSioijk//wLJ994A3N+vtX1NHo94U89SeD48arJqKIoHNiYzvpFRzCUWO8+5eaupe8N8bTtG+WUpNZYbmDjou/YtuQnFLO1SjvgGxLKqAem07hNewdGJ4RrkARcCFFvbTiSxZM/7SYpp6TG9a7tGs2LY9rh5+nuoMjswGyGbZ/B8heg3HoJOrTuMGQG9H4AGnCFiRJjCXO2z+G7A9+h1NC3PcQzhJf6vET/xv0dGN1/ylNSyXj+eYrXr69xPX3bNkTPnIm+eXPV9oKsUlZ+fYCUA7k17iesiR/DJrclKMLngmO+GCn79/DXR++Sm55a43qtLu/P0Dvuw9O3gY+xEMJJJAEXQtQ7+aVGXv99P99vraHiB+Dv6cZr13ZgdEfndEmwmawj8OsDkLSh5vVCW8F1n0BkJ8fEZScbUjfw4sYXSSuuuS//wMYDeeHyFwjxCnFQZP9RTCZyv/ueU7NmoZTU8AVQoyFkyh2EPfAAGg/Ls/Nms8LuVSls+vkoFeXWzyajga5XNKXH6Dh0bo7/YlVeWsKab7+ocUZLAA8vb4bccS9t+g6ULidCXARJwIUQ9YaiKCzekcprvx8gq8hQ47q9m4Xw1g2diAp03mQkF628pHJSnfVzwFRe87rd74RhL4FHwx3kdrL4JDO3zaxxUh0AT50nj3V/jOtbXu+UJK90924yXnyJsj17alzPLSKCqP/7P3x69lBtP3m8gNXfHSQzyXrlEADfYD3DJrUlKt7x3acUReHghjWs/uozinKtl/QEiG7dlhFTHyWgUbiDohPCdUkCLoSoFw5kFDDj5z1sTaz5Er2HTsujw1tyZ79maLUN9AycosDB3+GPJyE/qeZ1fRrB2Peh5XDHxGYHRrORb/Z9w9ydc2us6w3QLqQdr/d73SkT61Tk5pL59hzyFi6scZIZAP+RI4l4/jl0AZZlH8uKjGz8+Sj71qfVWDkSIL57OANuaone2/Hdp7JTkvln3gck7dlV43panRu9x91Ej6vHodU28JlkhagnJAEXQjhVfqmRd1YcZv6GREzmmrOVbk2D+L/rOtKiUQPud5p9FP58Cg7XfBYYgM63whWvgFfDHVi6OX0zr29+naP5R2tcT6/TM7XzVCa0nYCb1rF/mhSTibyffiLzrVmY8vJqXNctLIyI55/Db+hQizazWWH/+jQ2/nwUQ7H1QZYAPgEeDLi5FXGdHF/b21BSwubFC/j3t58xm6zPugkQ0Tye4fc8RFiTWMcEJ8QlQhJwIYRTlFeY+WbzCeasOExeifV6ygDeHjqeuLI1E3o1bbhnvUtyYPWbsPUTMNecnBHYBK6aA80HOyY2OziWd4xZ/85idcrq867bLbwbL17+Ik39HT+BS9G69Zx6800Mhw6dd93A68fR6LHH0Pn7W7Sd2JvNhh+PkJNmfUKdM9r2i+Lya1ugd/B08maTiV0rlrHhh28oLbBezQXAzUNPnxtuoeuosXLWWwg7kARcCOFQiqKwbO9J/u/PAxzPOn+yMqBlGK9c3Z6Y4Aba97nCAJs/gjX/A0PNSQ8aLfS4GwY/C/qGeZY/uzSbuQlz+fHwj5iUms+u+rn78XC3hxnXcpzDZ7QsO3SIU2/OpHjduvOu6960CZEvvIBP794WbVkpRWz46QjJ+2ruPw0Q0MiLgbe0pnErx17RUBSFY9u3subrz8lJq3m6e4Am7Tsx9M6pBEU08MHNQtRjkoALIRxmy/EcZi47cN5+3gDRgV48d1VbhrcNb5jVFswm2P0DrHwV8s7TzxsgpieMegsiOtg/NjsoKi/i6/1fM3/vfIqN5/9iNab5GB7p9ojDK5wYU1PJ/OAD8n9aXFn6sQYavZ7Qe+4mePJktHp9tbaCrFK2/p7IgY3p5+3n7eaupdvIWLoMbYLO3bFfNNIO7Wfd91+RvLfmft4AvkHBDJx4Jy179W2YnzkhGhBJwIUQdvfviVxm/32IdUeyzruuu07DXf2bMXVQi4Y5lbzZBHsXw6o3IPvw+df3Dq2sbtLppgZZ17vEWMK3B75l/t755J/vDD/QMqglz/R8hq7hXR0Q3X+MGRlkffQReYt+hBqmkD/Dd/Bgwp9+Go/G0dWWF+aU8e8fiexfn475PGMWAOI6hdL3hnj8QxxbrSfjyCE2/PANxxP+Pe+6Wp2OriPH0vu6G/HwaqBXmoRoYBrgXzchREORkJzH7L8PsfpQZq3WH9QqjGdHt6V5WAPsfmE2w/5fKhPvzAPnX1/rBpfdAYOeapCDLEsrSllwYAGf7/mcXMP5r2gE6AO4t9O9jG813qGDLI0nT5H9ySfkLViAUovE2yMujkaPP4bfoEHVlhflGtj+ZyJ716dhrjh/4h0U4c3l17UgtkPoBcd+IU4eP8qGH77h2L9barV+kw6dGXTbFEJlkKUQDiUJuBDCphRFYeOxbD5afazWiXebSH+eHdWGPi0cm6zYREU57PkRNrwDp/bVbpvWo2HoixDawr6x2UG+IZ+FBxfy9f6vySk7f79nd607N7e+mTs73kmA3rJkn72UJyWRM38+eT/+hGKouaY8gC4oiND7pxJ0ww1o3P8rCZh3qoSdy5PZvyEdU0XNXVYAvPzc6TE6jrZ9o9DqHHNFQ1EUUg/uY+uvP9Y68Q5p3IQBE+4gtlNX6W4ihBNIAi6EsAmTWeHPPRl8tOYou1LO3xUBIMLfk+lXtOKaLtHoGlp1E0Mh/PsFbJoLBTVP210lqgsMfxVi+9g3NjtIL0rny31f8uPhH89by/uMK2Ov5MGuDxLjF2Pn6P5Tuns32Z99TuFff523jzeAxsOD4Im3EXLXXej8/KqWnzxewI6/T3B0R+Z5+3gD6Ny1dBoSQ7crmuLhoOomZrOJo9s2s/XXH0k/fLBW23gHBNJn/K20HzgMrU6qmwjhLJKACyEuSmm5iUX/JvPJ2uMk5dQwZfdZAr3dubNfMyb3icPLo4ElAYUZlVVNtn52/qomZ4TEw8Anod21Da6f98Gcg8zfO58/jv9x3qomZ/SK7MX9Xe6nU1gnO0dXSTGbKV63juzPPqdk8+babaTTEXD1WMLuuw/36OjT+1E4sTebHX8lkXY4r1a70Wg1tOkdwWWj4vAL9rzAV1A3FeXl7FvzD9uWLiY3vXZf/vTePnQbfTXdRl2Nh2cDnj1WCBchCbgQ4oIczSzim01JLPo3mYKy89S1Ps3f0407+zXj9j6x+Hk6fua/C6YocGJ9ZdK9/9fz1/E+I7gZDHgSOoyDBlRLudxUzvITy1lwcAHbT22v9XbdI7oztfNUuoV3s2N0/zHl55O3eDF5331P+YkTtdtIqyXgqqsIve9ePJpW1h0vKzZyYGM6e1ankp9Zu7P7Gg206hXBZSNjCQhzzMDFvIx0di7/gz2rllNWWFCrbTy8vOg68mq6jRqLp08DHFshhIuSBFwIUWtGk5nl+07y9eYTrD+SXevt/PRuTO4bx+S+cQR4NaDEuywfdn4P2z6v3cDKMwKbwoAnoON40DWc/2ZTi1JZdGgRPx3+qVb9u8/o2qgrUztPpUdkDztG95/S3bvJ/fY7Cn7/vVb9uwHQaPAfPZrQe+9F3ywORVHIOJ7P3tWpHP73FCbj+burnN4N8T3C6T4yjsBw+yfeZpOJY9u3svPv30ncWfsvQ+56T7qOHEO30dfg5et3/g2EEA7VcP4yCCGcJjmnhEX/pvD91iROFtQy4QFCfT24/fJYbu3VlEBvDztGaEOKAmnbK/t37/4BjLXrVgNAWBvo8yB0uB50DeOLhtFsZEPqBn449ANrUtag1KbD82l9ovowqf0kekT0sPtAPlNREYV//knud99TtndvrbfTuLvjP3YMIZMno2/WDENpBfvWpbFnTSqZSYW13o/WTUPrnhF0HtaEoAifC3kJdVKQlcm+1SvYueJPirLPX77zDE8/f7pcMYrOV4zG299xg16FEHUjCbgQQlV+qZHfd6ezeHsqWxJrfzYUIC7Uhyn94riua2M83RtI14vcE7BrIexaULv63Wdr2hf6PATxwypPkdZziqKwJ2sPS48t5c/EP+t0tlun0TEibgS3t7udVsGt7BglKEYjRevXU/DrrxSu+Kf2Z7sBrZ8fQTeOJ+jWCWhDQ0nem8PBT/ZwfFdWrc92A3h4udF+QDQdBzXGJ0B//g0ugqGkhEOb17F/7SqS9+2u/DJYSwGNwuk2+hraDxyKu94xfdGFEBdOEnAhRJXyCjOrDp5i8Y5UVuw/Rbmp9okKQKeYQO4d0IxhbSMaRlWT0lzY+3Nl4p20oY4ba6DtGLj8IWjsmD7PFyulMIXfjv3G0mNLSSxIrNO2Xm5eXBd/HRPaTiDK135TlCuKQtmePeT/8isFv/+OKaduX/7cwsMJnjiRgOvHkZ2lsHFlBoe3HaSs6Pw1wM/mG6Sn05AY2vaNwsPTfn8qTRUVJO7czr61Kzm2bTMVxvI6bR/erAWXXXUtLXv2kaomQjQgkoALcYkrrzCz+Xg2f+7J4Lfd6eSV1C1R8XDTMrpjJLf2akqXmMD6X1O4LB8O/w37foZDy8BUt4QH7xDoeht0ux2CYu0QoG1lFGfwT9I/LEtcVqcBlWfEBcQxvtV4rmp+Ff4e/naIsDLpNhw8SOHyFRT89hvlx4/XeR/ePXoQeNNNlLfqwdG9eRz+317yTtah+9Bp0a2CaN8/mrjOoejsVMfbVFFB6oG9HN6ygYMb1lJaywGVZ+jc3Ijv2YdOw0cS3apt/f/MCSEsSAIuxCWoyFDB6oOZ/LUvg38OnKKwllVMztY0xJtbezZlXLfGBPnU8/7dBWlw8Hc48BscXwvmun3JAKBJ78qZK9uOATf7dkW4GIqicDjvMCuTVvJP8j/sy67l5EBncdO4MaTpEMa3Gs9l4ZfZJcFTKioo2b6dohUrKFy+AmNqLWupn0Xr54ff2Ksx9BlLUqY7q9dmUfhLQp334+HlRuveEbTvH223/t3lZaUk7tzO0a2bOLZ9K2XFRXXeh39YOJ2GjaD9oGHSv1uIBk4ScCEuEacKy1i+7xR/7ctgw5HsOncvAdBpNQxu3YgJvZrSt0Uo2vrazURRIPMgHFhamXin/nth+/Hwg443QPc7ILydbWO0IZPZREJmAv8k/cM/Sf+QUpRyQfuJ8IlgXPw4ro2/ljDvMBtHCebSUorXr6dw+QqKVq3ClJd3Qftxa9uR0iE3c1Ifx4n9eRgWnLyg/YQ18aP9gGjiLwvHXW/77hsl+Xkc/XcLR7Zu5MTuBEzGun/x02i0xHXpRqfhI4nt1BVtAypnKYSwThJwIVxUhcnMzpQ81hzKYs3hTBKS8+oypquajo0DuKZLNKM7RhHmV0/P/hqKKmt1H/2nsotJztEL249GBy2GVJYQbDUSPBxT47muskqz2Ji2kY1pG1mftr5OAynP5uPuw7Cmw7iq2VVcFnEZWo3tul0oikJ5YiLF6zdQvG4dxZs2oZSV1X0/QHmTdhT3vIps33jSUsox7TYDta8OcoZvkJ6WPSJo2TOckCjb1sU2m02cPHqExF3bSUzYTtrhA3UaSHm2RrHNadNvIK37DMA3KNimcQohnE8ScCFchKIoHMsqZuPRbNYdzmL90awL6lpyRnSgF9d0iebqLtG0aFQPJ/AwVUD6Tji+ujLpTtp0YV1LzojqAh1vhPbXga/tz/5erBJjCQmnEtiUsYmNaRs5kFOHuuTn0Gl09Inuw1XNrmJgzEA83WxXNaMiO5uSrVsrk+716zGmpV3Qfsrd/cgPb09hu0FkujWmuFiBTCCz7gm8u6eOFl0b0bJnBNHxgWhsdOVGURTyTqaTvHcXJ3buIGnPzgvqWnKGb0gobfoOpG2/QYTGNLVJjEKI+kkScCEaqDMJ96Zj2Ww6lsOmY9lkFta+TJuaIG93rmgXwTVdoukeG1y/upiYjJUJd+JaSFxXmXCXX3iyA1TOVNnu2sqz3WEtbROnjZxJuLee3MrWjK3szdpLhXLhX6gAOoZ1ZGTcSK6MvZIQrxCbxHkm4S7ZsoXiLVsoP3JhVx7K3f3IDYwnL7gV+ZEdKeL0gE8DYKj7WWSdm5aYNkG07BlBXMdQ3DwuvuuGoijkZaSRvG83yXt3k7JvN0W5F3bl4QxPH1+ad+9F236DiWnbHo3WPgM/hRD1iyTgQjQQJeUV7ErJZ3tSLttP5LEjKZfs4jpW8FARE+zFFW0jGNY2nG5Ng3CzU+WHOivOgpStkLyl8j7137pNimNNVFdoPQpaj4awVvWibreiKKQUpbAzcyc7T+1kZ+ZODuUewqSYLmq/7lp3ekb2ZHCTwQxsPPCi+3UrJhOGw4cpTUigdMcOShISMJ5IqvN+zBotxT5R5PvHUeAfR35gc0o9Qy8qNgC9txtNO4TQrFMYMW2DL7p8oLHcwMmjh0k7dID0wwdIO3SAkvy8i47TP6wRLS7rRYvuvYhu3U7KBwpxCZIEXIh6yGgyc+hkIXtTC9idms+O5Fz2pxdiMl9gJ+5ztI/2Z3jbCIa3C6dVuJ/zy5gZiiBjN6QnQFoCpGyBnGO22bfWDeL6VybdrUaCv/1qWNdWdmk2+3P2sy97H3uy9rAzc+cF9+E+l5+7H30b92Vwk8H0jeqLr8eFdR9SFAVjaiple/ZStncvpbt3U7ZrF+aSun0JUoAyzxAK/ZpQ6BtDvn8shf6xmHS2GUvgG6QnrnMYzTqFEhkfeMGlA80mE9kpSZw8fpSTx46QfvggmSeOYTZd3JegM8Jim9Hisp606N6bsKZxzv/MCSGcShJwIZyszGji8Mki9qTlsye18rY/o5DyirpXKbHG011Lz7gQBrUKY1i7CKIDvWy27zoryYFT+/9LttN3QtYhqMMU6OflHQLNBkGrEdBiKHgF2m7fdaAoCidLTnIo9xD7svdV3U6WXFjVDmua+DXh8qjLGdRkEN3Du+Ouc69bnCYT5UlJGA4cqEy29+6lbN9+zPn5ddqPWaOl1DOUIt/GlQm3XwyFvjFUuNuwtJ8GGjX1p0nbYJp1DiM0xrfOyayx3EBOagqnjh/l5PGjnDp2hMwTx+s8CU5N3Nw9iG7TjrjOl9Giey8CGoXbbN9CiIZPEnAhHMRoMnM8q5iDGYUcOllYdX8ip+SCq5PUpE2kP/1bhtI/PoxuTYMcPyW8oaiyFGDm/sqE+9S+yvvCdNs/l9YdmvSC5oMrbxEdwcF9aXPLcjmSd4TDuYc5knek8pZ7hEJjoc2fy8/dj56RPekd1ZveUb2J8Yup1XaKolCRno7h8OGqW9nhw5QfPVanad4VoEwfTLFPJMU+URT5RFHsE0mJTwRmbd2S/9rwDdIT0zaYmDbBxLQOxtO3ds9hqqggLyOdrOQTZCWfIPv0fV5GOopiuy+4Z4Q2iaVpxy7EduxCdJt2uHvU04pBQginkwRcCBtSFIXMQgPHs4pJzC7mWFYxiVnFHD99M5rskGmf1ircj17NgunVLIQeccGE+Drgj7/ZBHlJlSX/sk/fco5C1mHIO2G/59W6Q+PLILYvNO0DMT3Awz4TqJzNYDKQXJDMicITnCg4QVJBEicKTnA8/zjZZdl2e15fd1+6hnele3h3ukd0p1VwK9y01v/7NhUWUp54gvITJyg/kfjfz0ePYi4urvXzVug8KfFuRIlXGKVe4ZR4h1Hq1Yhi73BMbva7iuIT4EF0qyCiWwYR1TKQgDAvq2e5FUWhJD+P3PRUcjPSyEtPIzc9rfJxeiqmiosbuFqTkMZNaNy2AzFtO9C4TTt8AoPs9lxCCNciCbgQdWSoMJGeV0ZqXimpeaUkZZdwPLsy0U7MKqa43DZ9RmvirtPQPjqArk2CuKxpkH0TbkMh5CVDfgrkJ0HO8f8S7ZzjF1f6r7b0/pUJd+Me0LR35b0d6nMrikKeIY+04jTSi9JJK0ojqTCpKtlOL05HsWVXGSsaeTWiU6NOdArrxGURl9E6qDW6syZgUUwmjCdPYkxNw5iWhjE1tTLBTkyk/MQJTNm1+zKgoMGgD8CgD6LUM5gyz9DKZPt00m2009Tz5wqK8Ca8WQCRzQJUE25ThZHCrCwKsk5RkJVJ/qkMctNOJ9wZaZSXlto9Rq1OR6O45kTFtyaqVVtJuIUQF0UScCHOoigKBWUVpOZWJtdpp5PsM49T80ovutTfhYgM8KRzTCBdmwTRtWkg7aICbNOlxGyG4sz/kuuqRDv59M/JUJZ38c9TJxoIja9MsmO6V96HtbZJlxKj2UhmSSZpRWmkF6eTXlyZZGcUZ5BWXHlfWmH/ZO5sHloPWgW3olNYp6pbI10gFRkZlcn1vn3kpK/4L9lOT8eYkQG1OLNr0rpTpg/C4BlMmWcwZfpgyjyDqn426INQHDyzooeXG42a+hHRLICIZgE0ivVDqzVSkHmKgqwUju/YTkHmKQqzMqsS7uK83Aue0OZC+QYFE9GiFVEtWxPZsjXhzVpIlxIhhM1IAi4uCaXlJrKKDJwqNJBZaCCrqPI+s+icx4UGDDYc/HghogO9aB/tT4foANqfvoXW5ey2ooChAIpOQdHJ0/dn/Vx8zvKLLHV3UTRaCG0FUZ0hshNEdoaIDqCvfeUOs2Imz5BHVmkW2aXZ1e/LKu/PLMsz5DnkDLYanUkhrMyDjm5NaaNE0MwUTKTBi4BiBfP2HEyZe6jIWkVBdjZ5hdb7jZs1Wozufhh8/Sn3OPfmV/WzwcPfrt1EzkdRjHjoywkIU/AJqEDvbcTNvYyK8iJK8nM5uiWX3X/nUZyXR0W547/Uns0vJIzwZs1pFNec8GYtCI9rIWe3hRB2JQm4aFDMZoVCQwUFpUbya7jllZSTVVhelWAXGezXD/RCeXvoaBnuR6twP1pG+NEy3Jd2UQEE+3j8t5KpAsryITsFSvOgLPf0fV71+5Kc6gl2Rd1nC7Q771AIbwuN2kKjNpX34e2rdSUxmAwUGAooyDtJYXkhBeUF5BvyKSgvqLwZKu9zynLILs2uvJVlX3S97DpRFPRG8C0D77LKe58yBZ9zfm5U4UUjgyeBReBdYEBXUAyUAgeAAyhAhU7PSTcvKty8Mbp5U+Huj9EngooA78pl7pX35R5+lLtXJtdGDz/HvVYqrwqhGFAUAyhlZ92XVS3XKAbc9OVotWUo5mKMhkIqDKUYgELbFny5KG56PaGNmxAS05TQ07dGcc3x9g9wdmhCiEuMJODCIRRFwWhSKDWaKDOaKC03UVZReV9sMKkm0WpJdkGZ0dFXoi+Qgh4jnpQT5mmiRZCOZgEamgfqaO5vIsarnCBtCdqy/MokOisPUvJgXV7l47L8ysS63PYVNOzBDJRpNJRpNBh8wygNbEJZYGNKA5tQ6NeIAu8gCjTKf4l0ySEKDm2jYM9/SXVBeQEGk33PhGrMlcmzvgI8jFT+bAS98ewEujKJ/u9ny8daRYtZ645Z64FJ54FJ64FZ545Jp/8vmXbzptzdizQvbyr8vDE29abidEJd2e6FUsNASltQFBNQAYoRRakAjKBUoCjlp5Pnsspk2nxucn12kl1ObUpEVjj3JHY1Hl7eBEVGERQZTWhM06qEOyCskcw0KYSoF1wyATcYDDz33HN89dVX5Obm0rFjR1555RWGDRt23m1TU1OZNm0af/31F2azmUGDBjF79myaNWvmgMido8JkPp0YmyuT49MJcunpn8vO+rm03HTWOpXbGYxW2k+vc+axrSaRuTgK7pjwwoAn5XhpDHhRXvlYU3nvRXlVm+fpNq/Tbda28daU46sz4q0xolcMuJvL0JydtOSevjn81UK5Bso0WkpPJ8hl2sr7Uo2GMq22KnEurWr7b1n1dc9q07lRqnOr3B4Fg8UZ6JOVpz4L/61VnBpFwcMIfhX/JcUeVUmyYpEwe1ScXm48vfz0du5GDXqTO24md9zMHrifvtcpHujM7mg0Z5LlynuT7r8kuvq9e+V6nh4Yvd3J1npw6qw25SJL7VWWwKsAc3G1xBjFiHI6YUapOP2z2nL19aEC5ayfK78auSY3Dz1BEZEEnk60gyKiKn+OiMI7IFAmuhFC1GsumYDffvvtLFq0iIcffpj4+Hjmz5/PyJEjWblyJX379rW6XVFREYMGDSI/P5+nn34ad3d3Zs+ezYABA0hISCAkJMRuMX9y3/0Eetu+qoO9uAF+p2+XAgNgwI3KV95wjtOF0gBep28OcaHfzTSVlTxKdRpK3TTgVduky3j6Vou4TKdvF1XsxXQ60T6dUOPEfvcNhN7bB7/QMPxDw/ALbYR/aBj+YafvQxvhExgkZ7OFEA2WyyXgW7Zs4fvvv2fmzJlMnz4dgNtuu4327dvz+OOPs2HDBqvbzp07l8OHD7Nlyxa6d+8OwIgRI2jfvj1vvfUWr732mt3iNiuFmJX6109ZiHpNsfKzqLc0Wi3eAYH4BAThExiId2AQPgGB+IaE4n9Woq33tn9ddyGEcBaXS8AXLVqETqfjrrvuqlrm6enJHXfcwdNPP01ycjIxMeqzxi1atIju3btXJd8ArVu3ZsiQISxcuLDOCXhKSkqN7enpdpgRUAghHEyr06H38cUnILAyuQ4MqkysT9/OLPMJDMLL10/OXAshLnkul4Dv2LGDli1b4u9ffQKJHj16AJCQkKCagJvNZnbt2sXkyZMt2nr06MFff/1FYWEhfn6173RhLdEXQoj6Rufmht7HF08fX/S+lfeePr6nl/lYb/P1xV3vKX2uhRCiDlwuAU9PTycyMtJi+ZllaWlpqtvl5ORgMBjOu22rVq1sGK0QQtSNm7sHbno9bno97h5n3Xt4VF+m1+Pmcc59Vbsnnj4+1RJqNw+9JNFCCOEgLpeAl5aWotdbTlri6elZ1W5tO+CCtrUmOTm5xvb09PSqM/NummDcNE7o8yh/b3G1N0FT9U+1H855lRr1ZRq1de1Eo/nvOc/+GU1lInjmhWj+W0eD5XKNVoNGq0GrqbzXnLVMo+W/5ee0ac9eT4Ndk0+NVlvLxPjsBNrTol3n4Y7WwTNXCiGEsD2XS8C9vLwwGCwL0paVlVW1W9sOuKBtrWncuHGt171j7uw6rS+EEEIIIRomlxsJExkZqTq48cyyqKgo1e2Cg4PR6/UXtK0QQgghhBC15XIJeOfOnTl06BAFBQXVlm/evLmqXY1Wq6VDhw5s27bNom3z5s00a9asTgMwhRBCCCGEUONyCfi4ceMwmUx8/PHHVcsMBgPz5s2jZ8+eVZVJkpKSOHDggMW2W7durZaEHzx4kH/++Yfrr7/eMS9ACCGEEEK4NI2iKC43fcUNN9zA4sWLmTZtGi1atOCLL75gy5YtrFixgv79+wMwcOBAVq9ezdkvv7CwkC5dulBYWMj06dNxd3dn1qxZmEwmEhISCAsLs2mcKSkpVV8IkpOTpQ+4EEIIIUQ9Y498zeUGYQJ8+eWXzJgxg6+++orc3Fw6duzI0qVLq5Jva/z8/Fi1ahXTpk3jlVdewWw2M3DgQGbPnm3z5FsIIYQQQlyaXPIMeEMhZ8CFEEIIIeo3e+RrLtcHXAghhBBCiPpMEnAhhBBCCCEcSBJwIYQQQgghHEgScCGEEEIIIRxIEnAhhBBCCCEcSBJwIYQQQgghHEgScCGEEEIIIRxIEnAhhBBCCCEcSBJwIYQQQgghHEgScCGEEEIIIRzIzdkBXMoqKiqqfk5PT3diJEIIIYQQQs3ZOdrZudvFkATciTIzM6t+7tGjhxMjEUIIIYQQ55OZmUlsbOxF70e6oAghhBBCCOFAGkVRFGcHcakqKytj9+7dAISFheHmdmlekEhPT6+6ArBlyxYiIyOdHJGwFTm2rk2Or+uSY+va5PjWTUVFRVWvhQ4dOuDp6XnR+7w0M756wtPTk+7duzs7jHolMjKSxo0bOzsMYQdybF2bHF/XJcfWtcnxrR1bdDs5m3RBEUIIIYQQwoEkARdCCCGEEMKBJAEXQgghhBDCgSQBF0IIIYQQwoEkARdCCCGEEMKBJAEXQgghhBDCgSQBF0IIIYQQwoFkIh4hhBBCCCEcSM6ACyGEEEII4UCSgAshhBBCCOFAkoALIYQQQgjhQJKACyGEEEII4UCSgAshhBBCCOFAkoALIYQQQgjhQJKACyGEEEII4UCSgAshhBBCCOFAkoALIYQQQgjhQJKAiwbvzTffJCYmBj8/P7p06UJhYaGzQxI2tHHjRrRaLa+88oqzQxE2YjAYmDx5Mk2aNMHf359evXqxceNGZ4clLkBmZiajRo3Cx8eHVq1asWLFCmeHJGxEPqf25ebsAIS4GO+//z5//vkn69evJyYmht27d+Ph4eHssISNmM1mpk2bRvfu3Z0dirChiooKYmNjWbduHY0bN2bhwoVcddVVJCYm4uvr6+zwRB1MnTqViIgIMjMzWb58OTfccAOHDx8mODjY2aGJiySfU/vSKIqiODsIIS6EyWQiJiaGtWvX0rx5c2eHI+zgww8/ZP/+/eTn59OiRQueffZZZ4ck7CQqKoolS5bQrVs3Z4ciaqmoqIjg4GCOHTtG48aNARg4cCATJ05k0qRJTo5O2IN8Tm1HuqCIi1ZUVMTzzz/PlVdeSXBwMBqNhvnz56uuazAYeOKJJ4iKisLLy4uePXvy999/X9DzpqSkUFJSwqJFiwgPD6dVq1Z88sknF/FKxLmcdWwBsrOzefvtt3nxxRcveB+iZs48vmc7fPgwOTk5tGjRwib7E+psfbwPHz6Mr69vVfIN0KFDB/bu3WvPlyGssPfnWT6ntiUJuLhoWVlZvPTSS+zfv59OnTrVuO7tt9/OrFmzuOWWW5gzZw46nY6RI0eybt26Oj9vamoq+fn5HDp0iMTERH744Qeefvpp1q5de6EvRZzDWccW4JlnnuHhhx8mMDDwgrYX5+fM43tGaWkpt956K0899RQBAQEXtS9RM1sf76KiIvz9/att5+/vT1FRkV3iFzWz5+dZPqd2oAhxkcrKypT09HRFURRl69atCqDMmzfPYr3NmzcrgDJz5syqZaWlpUrz5s2V3r17V1u3T58+CqB6e+aZZxRFUZTt27crgJKYmFi13f333688+eSTdniVlyZnHtuuXbsqFRUViqIoysSJE5WXX37ZTq/y0uWs43tGeXm5MmrUKOXmm29WzGaz7V+gqMbWx3v79u1KUFBQtW3vv/9+5dFHH7XPCxA1ssfnWVHkc2ovMghTXDS9Xk9ERMR511u0aBE6nY677rqrapmnpyd33HEHTz/9NMnJycTExADU6qxay5Yt8fDwQKPRVC07+2dx8Zx1bFevXs3BgweJjo4GID8/Hzc3N44ePcq8efMu8NWIcznr+ELlANsJEyag0Wj44osv5LPrALY+3vHx8RQVFZGamlr1Wd2zZw+33Xab3V6DsM4en2f5nNqPdEERDrNjxw5atmxpccmyR48eACQkJNRpfz4+PowbN45XX30Vg8HA/v37WbBgASNHjrRVyKKWbH1s77rrLo4cOUJCQgIJCQmMGTOGqVOnMnv2bFuFLOrA1scX4O677yY9PZ0ffvgBNzc5F1Sf1PZ4+/r6MnbsWJ5//nlKS0tZunQpu3btYuzYsY4OWdRBXT7P8jm1H3k3hcOkp6cTGRlpsfzMsrS0tDrv8/333+eOO+4gNDSU0NBQXn75Zfr163fRsYq6sfWx9fb2xtvbu+qxl5cXvr6+0h/cSWx9fE+cOMGnn36Kp6cnoaGhVcv/+OMP+fzWA3U53nPnzmXixImEhITQuHFjFixYICUI67naHl/5nNqXJODCYUpLS9Hr9RbLPT09q9rrKjAwkB9//PGiYxMXxx7H9mzWRvILx7D18W3atCmKVMCtt+pyvMPCwvj9998dFpu4eLU9vvI5tS/pgiIcxsvLC4PBYLG8rKysql00THJsXZsc30uLHG/XJse3fpAEXDhMZGQk6enpFsvPLIuKinJ0SMJG5Ni6Njm+lxY53q5Njm/9IAm4cJjOnTtz6NAhCgoKqi3fvHlzVbtomOTYujY5vpcWOd6uTY5v/SAJuHCYcePGYTKZ+Pjjj6uWGQwG5s2bR8+ePavKHomGR46ta5Pje2mR4+3a5PjWDzIIU9jEe++9R15eXtXo6SVLlpCSkgLAAw88QEBAAD179uT666/nqaee4tSpU7Ro0YIvvviCxMREPvvsM2eGL2ogx9a1yfG9tMjxdm1yfBsQZ88EJFxD06ZNrc5+d/z48ar1SktLlenTpysRERGKXq9Xunfvrvz555/OC1yclxxb1ybH99Iix9u1yfFtODSKIjVmhBBCCCGEcBTpAy6EEEIIIYQDSQIuhBBCCCGEA0kCLoQQQgghhANJAi6EEEIIIYQDSQIuhBBCCCGEA0kCLoQQQgghhANJAi6EEEIIIYQDSQIuhBBCCCGEA0kCLoQQQgghhANJAi6EEEIIIYQDSQIuhBBCCCGEA0kCLoQQQgghhANJAi6EEEIIIYQDSQIuhBBCCCGEA0kCLoQQQgghhANJAi6EqJOMjAzCwsLQaDRVt6+//lp13TVr1qDT6arW0+v17Nq1S3VdjUZDbGxsreMYM2YMGo2GkSNHApCYmFgtprNvbm5uBAUF0bVrVx5++GEOHjxY59d9sebPn281vvnz59dpX2dve+57du7zvPDCCzZ7Da5m1apV1d6r22+/3dkhVXGF4/j222/b7HdeCFcjCbgQok4iIiL48MMPqy174IEHSElJqbassLCQiRMnYjabq5a98sordOzYEYDU1NTzPpe1dQoLC/nrr78AGDdu3Hn3YzKZyMvLY8eOHcyZM4cOHTqwaNGi824nhBBC2IObswMQQjQ81113HRMmTOCrr74CIC8vj8mTJ7Ns2TI0Gg0ADz/8MImJiVXb9OvXj0cffRSAlJQUWrVqxZAhQ3j11Vfp0KFDtf2vW7eOJ598ksTERA4fPoyXl1e19qVLl2IwGHBzc+Pqq6+uMU6AU6dOsWnTJoxGIwBGo5E777yTkSNH4u3tfVHvxYW67LLLaNq0KUCdzvyfT2xsbNXrBmjbtq3N9u1qwsLCqr1X3bt3d2I0ric+Pr7q/T1x4gTbtm1zckRC1COKEEJcgLy8PCUmJkYBqm7vvvuuoiiK8uuvv1Zb7ufnpxw/frxq2+PHjyvXX3+9otFoFK1Wq9x6660KoAQHBysjR45UAMXd3V258847lezsbIvnvvbaaxVAGTp0aLV9nv2c5/73tn37dsXNza1a+99//22fN0fFvHnzqj33vHnzLnhfZ++nadOmNotR1B/n/r48//zzzg7potjy918IVyBdUIQQFyQgIKCqn+oZTzzxBBs2bODOO++stu6cOXOqneWNjY1l4cKF7N69m+uuu45vvvkGgJycHP766y8mT57MoUOH+PjjjwkODq62r+LiYv7880+gdt1PzujSpYvF2eCsrCzVdfPy8pg5cyYDBgwgNDQUd3d3goOD6du3L7Nnz6a4uLjWz3uhli5dysCBA/Hz88Pf359+/frVqtvM+foODxw4sFp7YmIiX3/9NT179sTHx4ewsDBuvvlmjh07BkB5eTmvvfYarVu3xtPTk8jISCZPnkx6errVGI4ePcr06dPp0qULgYGBeHh4EBERwejRo1m0aBGKotQq7oyMDB566CHi4uLQ6/VEREQwadIkq12Tvv/+e6666ipiYmLw9PREr9cTFRVFt27dmDJlCh9++CEmk6lq/dr2Ad+6dStTpkyhdevW+Pn54eHhQWRkJCNHjmTevHmUl5dbbKO274KCAmbMmFH1XoaGhjJu3DgOHDhg9b08n7Vr1zJx4kTi4+Px9fXF09OTuLg4Jk6cyNatW1W3qaio4OOPP2bYsGFERkai1+vx8vIiJiaGXr16cd9996mO61i2bBk33HADzZo1w9vbu+q4duzYkQkTJjBnzhwKCwsv+LUIcUlx9jcAIUTD9tBDD1U7s3XuWeaxY8da3Xbv3r3K+PHjFY1GU237KVOmKImJiarb/PDDDwqgaLVa5eTJk1XLz3cGXFEUpUOHDtXaV69ebbHO2rVrlYiICIt9nX2Lj49XDh48WKf3qS5nAF977TWrzz19+vQaz4Cf78zpgAEDqrVfffXVqs8TEhKiHDhwQLn88stV25s1a6bk5eVZxP7+++8rHh4eNb5/I0aMUIqLi2uMe+TIkUpISIjq9k2bNlVyc3OrbT916tQan/PMrbCwsGqblStXVmubOHFitX2azWZl2rRp591np06dlBMnTlTb9tx99+vXT4mLi1PdPjAwsNoVotocR6PRqEyaNKnGuDQajTJjxgyL13TVVVed9zWFhIRU227mzJm1en93795t8Tuh9nrkDLi41EkCLoS4KKWlpUqbNm1U/xg3atRIOXXqlMU2iYmJyk033aRotVpFo9Eot9xyiwKVXVBGjBihAIqHh4dy3333KTk5OdW2HT9+vAIoAwYMqLb8fAn41q1bq305iIqKUsrKyqqtc+TIEcXf37/aPtq3b6+MHj1aadeunUUCem4SWZPaJiBr1qyp9oUEUGJiYpQrrrhCiYyMVE1Ga3qe8yXggBIWFqYMHz7cIuH19vauev5hw4ZVPT5ze+2116rte+HChdXadTqdcvnllyujRo1SoqOjq7WNHz++xrjP3Lp06aL069dP0el01Za/+uqrVdumpqZWe898fHyUwYMHK1dddZVy2WWXKY0aNbqgBPzll19WjWfIkCGKn59fteVt27ZVDAaD1X2fubVu3VoZPHiw4unpWW35nXfeWafjeN9991Vr9/PzU4YOHaoMHz5c8fX1rdb2wQcfVG23YcOGam1BQUHK8OHDlVGjRildunRRgoODLRLw8vLyavv08PBQ+vXrp4wZM0bp1auX0rhxY0nAhagjScCFEBdt69atqsnGokWLVNdPSkpSvLy8lBEjRigJCQmKoijVksnVq1crvXv3ViIjoJf4wgAADHhJREFUI6sluaWlpVWJwJn+5meoJeDXXXedct111yn9+vWrlnx7e3sry5Yts4jrTF/0M7fvvvuuWvu5Z6b/97//1fo9qm0CMnr06GrrXXvttUp5ebmiKIpSXFysDB482KYJeMeOHavOJu/du9fiPRw2bFjVF5XFixdXaxs0aFDVfk0mk9KkSZNqid2+ffuq2o1GozJq1Khq22/bts1q3Oe+R+e2n/3c69evr9a2Zs0ai/d1//79ypw5c2pMks9OwHNychQvL69q7d9++21Ve1JSkhIbG1ut/cMPP7S673OPxbntcXFxtT6OBw8eVLRabVVbjx49lPz8/Kr2kydPVhufERISUvW6v/nmm2r7TUpKqva8ZrNZ2b59u/L+++9XLUtNTa22zZdffmnx/iYmJioff/yxkp6ebtGm9nokAReXOqmCIoS4aJs3b7a6/OwqE2fExMRw4MABmjRporpd//792bBhA8nJydWqlCxbtoyioiI0Gg3XXnvteeP68ccfLZZ1796d77//nmbNmlVbbjab+fXXX6see3h4sGjRomr9rs/t37pkyZKqyi62YDKZ+Oeff6ote+2113B3dwfA29ubl156yWKdizF9+nQCAwOByoopgYGB5OXlVbXPmDEDvV4PwJAhQ6pte3Zf7O3bt5OUlFT12NvbmxkzZlRbPy0trdrjJUuW0K1bN9W4evbsWa1P9pgxY6w+95lqMme88sor3HDDDbRo0YL4+HiioqJo3bo1rVu3Vn0uNcuXL6e0tLRaPDfddFPV45iYGB577DGmTp1a7fXcfffdqvuLjo7m2WefrXp8pn//md+p2pTlPOPXX3+tVt6zvLycyZMnV1tHOauffXZ2Nhs2bGDgwIEW79Vjjz3GyJEjad68OfHx8TRq1IguXbrQpUuXqnVCQ0Px8fGpGvvw3nvvUVxcXPX+NmnShKZNm1qM/RBCWCcJuBDiohw+fJjHH39cte2tt95izJgx9O3b16LNWvJ9tpiYmGqPzyTDvXv3Jioq6gKirRxQ9+CDD/LTTz/h4eFRtTw7O5uCgoKqx+Xl5aoJ/NmOHz9+QTFYk5WVRUlJSdVjDw8PWrZsWW2d9u3b2/Q5zy0B6efnVy0BP/v5/Pz8qq1rMBiqfj73vUhNTb2o9+/ckoABAQFWnzs6Opp77rmnqj79X3/9VVUnHioTyMGDB3P//ffTr1+/GmM64+wSmmD5PgF06tSp2uOaXk+XLl1wc6v+JzcgIKAqAVcbyGnNuc+TkJBAQkLCebcZOHAgffr0YcSIEfzxxx8ALFiwgAULFlStFxUVxfDhw5k2bVpVzX4PDw9mzJjBk08+CcCWLVvYsmVL1Tb+/v7079+fu+66i6uuuqrWr0OIS5lUQRFCXDCTycRtt91WLWk8O2E0m81MnDiRoqKi8+5LURSLpOds5eXlLFmyBKh99RNFUSguLmbJkiXVqqn89ttvPPbYY7XaR00cUQ3F3s6c/T5Dq63+ZyEoKMhuz13T+xcSElLtsU6nq3FfH3zwAT/++CPXXnstkZGR1dqysrJYuHAhAwYM4Oeff65VbGefQQaqVfu5EOe+Hjj/a7Kls9/rJUuWMG/ePEaOHEloaGi19dLS0pg/fz49evSolmQ/8cQTrFixgltuuYWmTZtWez8KCgpYunQpY8aM4Z133rH/ixHCBUgCLoS4YG+88QabNm2qehwfH8+///5L//79q5YdO3aMRx555KKfa/ny5eTn5wOodmuxxtvbm9GjRzNv3rxqy99//3327dtX9TgkJKTaGV5/f38MBgNK5VgZ1Zu1MoYXKjQ0tFqXm/Lycg4fPlxtnb1799r0OW0lLi6u2uMrr7yyxvdOURSbz0Z67bXX8uOPP5KWlkZRURF79uxhzpw5VYmuoii8/fbbF/R6du/ebbHOrl27atzGXs59njfeeOO87/X9999ftb5Op+P222/nt99+IzMzs2qW2LO7DBkMBubOnVvteQYPHszXX39NYmIixcXFHDx4kHnz5uHr61u1zqxZs+z0qoVwLZKACyEuyI4dO3jxxRerHut0Or788kt8fX354osvqiWzn3zyCb/99ttFPd+ZZK179+616r5yrjFjxjBgwICqxyaTqVqNbK1Wy+jRo6seFxQU8Mgjj1Tr6gCVSdzmzZt5+OGHWbx4cZ3jqIlOp2PgwIHVlj3zzDNVM3iWlpby/PPP2/Q5baVr165ER0dXPf7rr7/48ssvLdYrKyvj999/54YbbiAlJcUmz11SUsKrr77Knj17qpb5+PjQrl07JkyYgKenZ9XyjIyMWu1zyJAh1WZg3bRpEwsXLqx6nJqaysyZM6ttc/bvjz2NHj262hnot956i+3bt1usl5WVxfz587n55purliUlJTF79uyqOu9Q2RWmc+fOTJgwodr2Z79Xr732Glu2bKm6MuDl5UXLli256aabaNSokeo2QgjrJAEXQtSZwWBgwoQJVYkhwJNPPkmvXr2Ayol25syZU22bKVOmkJ2dfUHPV1FRwS+//ALUbfKdc539hQEqk/qzz2y+8MIL1c7mvf/++0RFRTF48GDGjh1Lnz59CAoKolevXsyZM6fqjLwtPf7449WSq0WLFtGiRQuuvPJKWrRowfLly23+nLag1Wp58803qx6f6X4UFxfHiBEjGDVqVNXEPKNGjeKHH36goqLCJs9dXl7Os88+S4cOHYiMjGTgwIFcffXVVe/Z2d0v2rRpU6t9BgcHW4xtGD9+PN26dWPo0KG0bdu2Wl/s1q1bM2nSJJu8nvNp3bo1U6ZMqXqcmZlJt27d6Ny5M2PGjOGKK66gVatWhIeHM2nSJDZs2FC1bk5ODo888gjNmzenadOmDBkyhGuuuYahQ4fStWvXas9z9nv15ptv0rNnT8LCwujbty9jx45l1KhRxMXFVUvma/v+CnGpk0GYQog6e+aZZ6p1hejSpYvFmdlJkyaxZMmSqrPEGRkZ3HvvvdXOItbWypUrycnJAS4uAR8wYACDBg1i5cqVQOXZ7BdeeKFqsGDLli1ZunQpN954Y9WZvJycnKr1z3XuoDpbGDBgAC+++CLPPfdc1bKkpKSqCiOTJ0/m888/t/nz2sLNN99MdnY206dPrxpUmJiYaLVvvz36QGdkZFg9CxsSEsIrr7xS6309//zzZGdn895771UtUzvT3L59e5YsWVJVLcYR3n//fQwGQ7WrDDt37mTnzp0W61r7PT379+pcsbGxqoOrs7OzWb9+veo2Xl5evPXWW7UJX4hLnpwBF0LUyZo1a5g9e3bVY71ez1dffVVVKu9sH3/8MeHh4VWPf/jhh6pp5+viTPeTzp07W5QPrKtzz4IvXry4WgWJAQMGcODAAWbPns2QIUNo1KgR7u7u6PV6oqOjGTRoEM888wybNm3i1ltvvahYrJkxYwa//PIL/fr1w8fHBx8fH3r27Mn8+fP57LPP7PKctvLAAw+wf/9+nnjiCbp3705QUBA6nQ5vb2+aN2/OmDFj+N///sexY8csqtxcKD8/P7777jseeOABevXqRZMmTfDx8cHNzY3g4GB69OjBM888w549e2jXrl2t96vRaHj33XfZuHEjkydPpmXLlvj4+ODu7k54eDhXXHEFn3zyCdu2bSM2NtYmr6W23N3d+eKLL1i3bh2TJ0+mTZs2+Pr6otPp8Pf3p3379tx66618/vnn1aakj4+PZ/78+dx1111069aN6OhoPD09cXNzqzq7/frrr5OQkFBtMOtXX33FY489Rr9+/YiNjcXPzw+dTlfVfeXhhx9m9+7dDB482KHvgxANlUY5d6i3EELUIyaTiaioKE6dOsUrr7zCM8884+yQLsj8+fOrdVGYN29etTrXQrgy+f0Xojo5Ay6EqNdycnK49957ef755y0GiTVkkyZNQqPRoNFomD9/vrPDEcLm3n777arfcUf1jxeioZA+4EKIei0sLKxatRIhhBCioZMEXAghHCA2NtZq/XJH9x8WwhHi4+Pld14IK6QPuBBCCCGEEA4kfcCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHAgScCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHAgScCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHAgScCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHAgScCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHAgScCFEEIIIYRwIEnAhRBCCCGEcCBJwIUQQgghhHCg/wcIW3gkhUR7sAAAAABJRU5ErkJggg==\n"
+ },
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "# Redefine Re in the same function from before within a for loop.\n",
+ "\n",
+ "### BEGIN SOLUTION ###\n",
+ "D_values = [0, 1] # Range of normalized d*\n",
+ "Re_values = np.array([1, 10, 100, 500, 1000, 5000]) # Values from above in an array\n",
+ "num_steps = 300 # Number of steps in linspace below\n",
+ "time_span = np.linspace(0, 1, num_steps)\n",
+ "initial_condition = [0] # Starting at the entrance of the tube\n",
+ "### END SOLUTION ###\n",
+ "\n",
+ "fig = plt.figure(figsize=(4, 3), dpi=200) # Format the plotted figure to be larger and clearer\n",
+ "\n",
+ "# Loop the integration for different values of Re and plot each iteration inside the loop\n",
+ "for i in range(len(Re_values)):\n",
+ " ### BEGIN SOLUTION ###\n",
+ " Re = Re_values[i]\n",
+ " e_re_lambda = lambda X, D: entrance(X, D, Re=Re)\n",
+ " solution = integrate.solve_ivp(e_re_lambda, D_values, initial_condition, t_eval=time_span) # Solve the ODE\n",
+ " D = solution.t # D = independent variable\n",
+ " X = solution.y[0] # X = dependent variable solution\n",
+ " # Use semilogx\n",
+ " plt.semilogx(X, D, linewidth=2, label=Re_values[i]) # Normalized x-axis to see where D crosses 1\n",
+ " Le_value = np.array(X[num_steps - 1])\n",
+ " ### END SOLUTION ###\n",
+ "\n",
+ " # Print values for Le\n",
+ "print(\"\\n\")\n",
+ "\n",
+ "# Labels and publication-quality details\n",
+ "plt.xlabel('X*/Re [dimensionless]', fontsize=8, fontweight='bold')\n",
+ "plt.ylabel('δ* [dimensionless]', fontsize=8, fontweight='bold')\n",
+ "plt.xticks(fontsize=6)\n",
+ "plt.yticks(fontsize=6)\n",
+ "plt.grid(False) # Remove grid lines\n",
+ "plt.legend();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Class Activity**\n",
+ "Now, reconsider the pipe question (3-2). Is the result consistent or closely aligned with the graph above when the velocity of water is 0.01 m²/s?\n"
+ ],
+ "metadata": {
+ "id": "kljFh_UJXjcH"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### 4-4-Discuss the limitations encountered in applying the integral method for wind tunnel practicality, as observed in the notebook. Highlight the reasons behind its ineffectiveness in real-life wind tunnel applications for finding the entrance length.\n",
+ "**Discuss** in 3-5 sentences.\n",
+ "\n",
+ "**Answer**:As the Reynolds number escalates, turbulence augments, consequently elongating the entrance length. This direct proportionality between the entrance length and Reynolds number implies their simultaneous increase. However, this model's validity diminishes at a certain threshold, wherein errors become notably significant, rendering it unsuitable for accurate entrance length calculations."
+ ],
+ "metadata": {
+ "id": "x395KMl-E3Iu"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [],
+ "metadata": {
+ "id": "rlSwfeYbpgEV"
+ }
+ }
+ ],
+ "metadata": {
+ "colab": {
+ "provenance": []
+ },
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
\ No newline at end of file