{ "cells": [ { "cell_type": "markdown", "id": "a77c1997-ce07-4d7f-96a3-a8a7811aa511", "metadata": {}, "source": [ "# Difference Finite Scheme of Diffusive Equation derived from Lattice Boltzmann" ] }, { "cell_type": "markdown", "id": "b23f99a1-bc9b-4657-9fe8-a46c34b89270", "metadata": {}, "source": [ "Due to the similarities in the grid structure between the Lattice Boltzmann method and finite difference schemes, several studies have been conducted over the years to investigate how these methods can be directly related and interpreted {cite:p}`ancona1994fully,junk2001finite,suga2010accurate,dubois2017lattice,bellotti2022finite,chen2023fourth`. In this section, we develop a finite-difference interpretation for different Lattice Boltzmann formulations." ] }, { "cell_type": "markdown", "id": "88580bae-c33c-41ef-b735-ff704777543f", "metadata": {}, "source": [ "## Interpretation for Diffusive Equation\n", "\n", "In the remainder of this section, we develop a FDM interpretation of the diffusive LBM, following the approach proposed by {cite:t}`suga2010accurate`." ] }, { "cell_type": "markdown", "id": "ce1deef2-8ab2-48f3-bde8-cdd328bac60e", "metadata": {}, "source": [ "Given the LBM formulation for the diffusive equation:\n", "\n", "$$\n", "f_i( x_{\\alpha} + e_{i,\\alpha} \\delta t, t+\\delta t) = f_i(x_{\\alpha}, t) -\\left( \\frac{ f_{i} - f_{i}^{eq} }{ \\tau } \\right) \\qquad \\rightarrow \\qquad f_i( x_{\\alpha} + e_{i,\\alpha} \\delta t, t+\\delta t) = f_i(x_{\\alpha}, t) - \\omega\\left( f_{i} - f_{i}^{eq} \\right), \n", "$$(LB-df-Eq)\n", "\n", "where the equilibrium distribution function is defined by\n", "\n", "$$\n", "f^{eq}_{i} = w_{i}\\phi(x_{\\alpha}, t),\n", "$$(df-feq-Eq)\n", "\n", "and the equilibrium moments are given by \n", "\n", "$$\n", "\\displaystyle\\sum_{i=0} f_{i}^{eq}=\\phi, \\quad \\quad \\displaystyle\\sum_{i}f_{i}^{eq} e_{i,\\alpha} =0 \\quad \\quad \\textrm{and} \\quad \\quad \\displaystyle\\sum_{i}f_{i}^{eq} e_{i,\\alpha} e_{i,\\beta} =c_{s}^{2} \\phi \\delta_{\\alpha\\beta}.\n", "$$(moments-fi-df)\n", "\n", "Through Chapman–Enskog analysis, it is demonstrated that the first-order non-equilibrium moment describes the pressure gradient and, consequently, the average velocity:\n", "\n", "$$\n", "m^{neq}_{\\alpha} = \\displaystyle\\sum_{i} e_{i,\\alpha}\\left( f_i-f_i^{eq}\\right) = -(c_{s}^{2} \\tau \\delta_{t})\\partial_{\\alpha}\\phi \\quad \\quad \\textrm{and} \\quad\\quad \\tau = \\displaystyle\\frac{\\nu}{c_{s}^{2} \\delta_{t}} +\\frac{1}{2}.\n", "$$" ] }, { "cell_type": "markdown", "id": "3d9b571d-73ec-425b-be09-0803e063c767", "metadata": {}, "source": [ "### FDM Interpretation" ] }, { "cell_type": "markdown", "id": "d5097838-71ff-49e1-9c00-8cafe3875003", "metadata": {}, "source": [ "For simplification we redefine the notation for $f_i( x_{\\alpha} + e_{i,\\alpha} \\delta t, t+\\delta t)=f_{i,x+c_{i}}^{t+1}$. Reinterpreting the Eq. {eq}`LB-df-Eq` in pre-streaming moment:\n", "\n", "$$\n", "f_{i,x}^{t+1} = f_{i,x-c_{i}}^{t} - \\omega \\left( f_{i,x-c_{i}}^{t} - f_{i,x-c_{i}}^{eq,t} \\right).\n", "$$(pre-LB-df-Eq)" ] }, { "cell_type": "markdown", "id": "103de3bc-ca42-4725-bef7-55c4b0ceb6ea", "metadata": {}, "source": [ "Summing the Eq. {eq}`pre-LB-df-Eq` over all lattice direction and replacing $f_{i}^{eq}$ by Eq. {eq}`df-feq-Eq`, we have:\n", "\n", "$$\n", "\\displaystyle\\sum_{i}\\Big( f_{i,x}^{t+1} \\Big) = \\displaystyle\\sum_{i}\\Big( f_{i,x-c_{i}}^{t} - \\omega \\left( f_{i,x-c_{i}}^{t} - f_{i,x-c_{i}}^{eq,t} \\right) \\Big) \\qquad \\rightarrow \\qquad \\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega) f_{i,x-c_{i}}^{t} + \\omega w_{i}\\phi_{x-c_{i}}^{t} \\Big),\n", "$$" ] }, { "cell_type": "markdown", "id": "574205ff-b109-44f4-acf4-2f2a6e3c99cc", "metadata": {}, "source": [ "using the Eq. {eq}`moments-fi-df` to replace $f_{i,x-c_{i}}^{t}$ in the above equation:\n", "\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega) f_{i,x-c_{i}}^{t} + \\omega w_{i}\\phi_{x-c_{i}}^{t} \\Big) \\qquad \\rightarrow \\qquad \\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t} - (1-\\omega) \\displaystyle\\sum_{k\\neq i} f_{k,x-c_{i}}^{t} \\Big).\n", "$$" ] }, { "cell_type": "markdown", "id": "2e9545e3-b512-4c17-8374-856526667c12", "metadata": {}, "source": [ "Spliting the terms in the above equation and using Eq. {eq}`pre-LB-df-Eq` for $f_{i,x-c_{i}}^{t}$:\n", "\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega)\\displaystyle\\sum_{i}\\left( \\displaystyle\\sum_{k\\neq i} f_{k,x-c_{i}}^{t} \\right),\n", "$$\n", "\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega)\\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left( f_{k,x-c_{i}-c_{k}}^{t-1} - \\omega \\left( f_{k,x-c_{i}-c_{k}}^{t-1} - f_{k,x-c_{i}-c_{k}}^{eq,t-1} \\right) \\right) \\Bigg),\n", "$$" ] }, { "cell_type": "markdown", "id": "f24c0d79-d948-4abe-b7ca-f5fd064bb1e5", "metadata": {}, "source": [ "doing the same initial procedure to the terms $f_{k,x-c_{i}}^{t-1}$:\n", "\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) -(1-\\omega)\\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left( f_{k,x-c_{i}-c_{k}}^{t-1} - \\omega \\left( f_{k,x-c_{i}-c_{k}}^{t-1} - f_{k,x-c_{i}-c_{k}}^{eq,t-1} \\right) \\right) \\Bigg)\n", "$$\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega) \\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left( \\omega w_{k} \\phi_{x-c_{i}-c_{k}}^{t-1} + (1-\\omega) f_{k,x-c_{i}-c_{j}}^{t-1} \\right) \\Bigg),\n", "$$" ] }, { "cell_type": "markdown", "id": "5a8a7372-a10a-4565-aac4-fdcf800eac5c", "metadata": {}, "source": [ "notice that $\\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left( \\omega w_{k} \\phi_{x-c_{i}-c_{k}}^{t-1} \\right) \\Bigg)=\\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left(w_{k}\\right) \\omega \\phi_{x+c_{i}}^{t-1} \\Bigg)$ and using Eq. {eq}`moments-fi-df` we have $\\displaystyle\\sum_{i}\\Bigg( \\displaystyle\\sum_{k\\neq i} \\left( f_{k,x-c_{i}-c_{j}}^{t-1} \\right) \\Bigg)= \\displaystyle\\sum_{i}\\left(\\phi_{x+c_{i}}^{t-1} - f_{i,x+c_{i}}^{t-1}\\right) $. So rewriting the above equation base in the observations:" ] }, { "cell_type": "markdown", "id": "ed10935a-4798-4a88-bde4-572514fd2ebb", "metadata": {}, "source": [ "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega)\\displaystyle\\sum_{i}\\Bigg( \\left(1-\\omega + \\omega \\displaystyle\\sum_{k\\neq i} \\left(w_{k}\\right) \\right) \\phi_{x+c_{i}}^{t-1} \\Bigg) + (1-\\omega)^{2}\\displaystyle\\sum_{i}\\Bigg( f_{i,x+c_{i}}^{t-1} \\Bigg).\n", "$$(last-fdm-form)" ] }, { "cell_type": "markdown", "id": "f4fdbea3-8961-4fe9-8276-a468b34adca6", "metadata": {}, "source": [ "Interpreting $f_{i,x+c_{i}}^{t-1}$ with Eq. {eq}`pre-LB-df-Eq`:\n", "\n", "$$\n", "f_{i,x+c_{i}}^{t-1} = f_{i,x}^{t-2} - \\omega \\left( f_{i,x}^{t-2} - f_{i,x}^{eq,t-2} \\right) ,\n", "$$\n", "\n", "and replaing it in Eq. {eq}`last-fdm-form`, we obtained a four-level explicity scheme:\n", "\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega)\\displaystyle\\sum_{i}\\Bigg( \\left(1-\\omega + \\omega \\displaystyle\\sum_{k\\neq i} \\left(w_{k}\\right) \\right) \\phi_{x+c_{i}}^{t-1} \\Bigg) + (1-\\omega)^{2}\\displaystyle\\sum_{i}\\Bigg(f_{i,x}^{t-2} - \\omega \\left( f_{i,x}^{t-2} - f_{i,x}^{eq,t-2} \\right) \\Bigg),\n", "$$\n", "$$\n", "\\phi_{x}^{t+1} = \\displaystyle\\sum_{i}\\Big( (1-\\omega + \\omega w_{i}) \\phi_{x-c_{i}}^{t}\\Big) - (1-\\omega)\\displaystyle\\sum_{i}\\Bigg( \\left(1-\\omega + \\omega \\displaystyle\\sum_{k\\neq i} \\left(w_{k}\\right) \\right) \\phi_{x+c_{i}}^{t-1} \\Bigg) + (1-\\omega)^{2} \\phi_{x}^{t-2}\n", "$$(df-final-form-fdm)" ] }, { "cell_type": "markdown", "id": "492f1111-7d38-46d7-8174-228899f02346", "metadata": {}, "source": [ "Expanding the sums:\n", "\n", "$$\n", "\\begin{array}{c}\n", "\\phi_{x}^{t+1} = (1-\\omega + \\omega w_{0}) \\phi_{x}^{t} + (1-\\omega + \\omega w_{1}) \\phi_{x-1}^{t} + (1-\\omega + \\omega w_{2}) \\phi_{x+1}^{t} - (1-\\omega)^{2} \\Big( \\phi_{x}^{t-1} + \\phi_{x-1}^{t-1} + \\phi_{x+1}^{t-1} \\Big) \\\\\n", "-(1-\\omega)\\omega \\Big( (w_{1}+w_{2})\\phi_{x}^{t-1} + (w_{0}+w_{1})\\phi_{x-1}^{t-1} + (w_{0}+w_{2})\\phi_{x+1}^{t-1} \\Big) + (1-\\omega)^{2} \\phi_{x}^{t-2}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "4f1cf231-0fa8-4fc3-aba1-eda210dd17a8", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## 1st Benchmark: Decay of Sinoidal Wave\n", "\n", "Considering a 1D **convection–diffusion equation** with constant coefficients\n", "$$\n", "\\frac{\\partial u}{\\partial t}+c\\frac{\\partial u}{\\partial x} = \\nu\\frac{\\partial^2 u}{\\partial x^2} \\qquad x\\in\\mathbb{R},\\ t\\ge 0,\n", "$$\n", "\n", "with **sinusoidal initial condition**\n", "\n", "$$\n", "u(x,0)=A\\sin(kx+\\phi),\n", "$$\n", "\n", "where $A$ is the initial amplitude, $k$ the wavenumber, $\\phi$ a phase shift.\n", "\n", "Then the analytical solution is\n", "$$\n", "\\boxed{u(x,t)=Ae^{-\\nu k^{2}t}\\sin\\big(k(x-ct)+\\phi\\big) }\n", "$$\n", "\n", "So:\n", "\n", "* **Convection** shifts the wave: $x \\mapsto x-ct$ (wave travels at speed $c$).\n", "* **Diffusion** damps the amplitude exponentially: $A(t)=Ae^{-\\nu k^{2}t}$.\n", "\n", "If you use a cosine initial condition $u(x,0)=A\\cos(kx+\\phi)$, the solution is the same form:\n", "$$\n", "u(x,t)=Ae^{-\\nu k^{2}t}\\cos\\big(k(x-ct)+\\phi\\big).\n", "$$\n" ] }, { "cell_type": "markdown", "id": "9eb935eb-77bf-4b26-8724-1c35e0ff6f4a", "metadata": {}, "source": [ "### LBM D1Q3 Code - FDM Code (Only Diffusive Case $c=0$)" ] }, { "cell_type": "code", "execution_count": 159, "id": "8af67b35-07fb-4bfa-8f3b-202b0afe3f2d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dx=2.5133e-01\t dt=1.2566e-01\t nt=382\n", "c_lbm=0.000, tau=0.6250\t omega=1.6000\n", "nt=382.000, nue=0.0417\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "A = 1.0 # Amplitude\n", "phi = 0.0 # Wave initial shift\n", "k_w = 1.0 # Wave number\n", "c = 0.0 # wave speed\n", "nu = 0.0066666666666666666*np.pi # Diffusive coefficient\n", "m_waves = 1 # Wave Period\n", "L = m_waves * (2.0*np.pi / k_w) # Domain Lentgh\n", "t_end = 48.0 # Final time\n", "#--------------------------------------- Lattice-Properties-D1Q3 ----------------------------------------------\n", "w = np.array([4.0/6.0, 1.0/6.0, 1.0/6.0],dtype=\"float64\")\n", "cx = np.array([0, 1, -1],dtype=\"int16\") \n", "cs=1.0/np.sqrt(3.0);\n", "#------------------------------------- Parameters (numerical units) -------------------------------------------\n", "Nx = 25 # Numerical Length\n", "x = np.linspace(0.0, L, Nx, endpoint=False,dtype=\"float64\") # Numerical Domain\n", "dx = L / Nx # Grid size\n", "r=2**(1) # dx/dt relation\n", "dt = dx/r\n", "ce = c/r\n", "nue = nu * dt / (dx*dx)\n", "tau = 0.5 + nue / cs**2\n", "omg=1.0/tau\n", "nt = int(np.ceil(t_end / dt))\n", "print(f\"dx={dx:.4e}\\t dt={dt:.4e}\\t nt={nt:d}\") # Print values for check\n", "print(f\"c_lbm={ce:.3f}, tau={tau:.4f}\\t omega={omg:.4f}\")\n", "print(f\"nt={nt:.3f}, nue={nue:.4f}\")\n", "#--------------------------------- Initialization - LBM - Numerical Arrays -----------------------------------------\n", "u=np.zeros((Nx),dtype=\"float64\")\n", "u = A * np.sin(k_w*(x+dx/2) + phi)\n", "f=np.zeros((3,Nx),dtype=\"float64\")\n", "fp=np.zeros((3,Nx),dtype=\"float64\")\n", "for k in range(0,3):\n", " f[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", " fp[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", "#--------------------------------- Initialization - FDM - Numerical Arrays -----------------------------------------\n", "ufm2=np.zeros((Nx),dtype=\"float64\") # u field at the step t-2\n", "ufm=np.zeros((Nx),dtype=\"float64\") # u field at the step t-1\n", "uf=np.zeros((Nx),dtype=\"float64\") # u field at the step t\n", "ufp=np.zeros((Nx),dtype=\"float64\") # u field at the step t+1\n", "ufm2 = A * np.sin(k_w*(x+dx/2) + phi)\n", "ufm = A * np.sin(k_w*(x+dx/2) + phi)\n", "uf = A * np.sin(k_w*(x+dx/2) + phi)\n", "ufp = A * np.sin(k_w*(x+dx/2) + phi)\n", "#--------------------------------- Initialization - Save Data Arrays -----------------------------------------------\n", "snaps=5 # number of states saved over time including 0 and t_end\n", "u_snaps = np.empty(snaps, dtype=object) # array field used to same data over time\n", "uf_snaps = np.empty(snaps, dtype=object) # array field used to same data over time\n", "snaps_id = np.linspace(0, nt, snaps, dtype=\"int16\") # timesteps to take the field\n", "snap_index = {sid: i for i, sid in enumerate(snaps_id)}\n", "for i in range(snaps):\n", " u_snaps[i] = np.zeros((Nx), dtype=\"float64\")\n", " uf_snaps[i] = np.zeros((Nx), dtype=\"float64\")\n", "u_snaps[0][:]=u[:]\n", "uf_snaps[0][:]=uf[:]\n", "#----------------------------------------- Maind Loop --------------------------------------------------------\n", "for t in range(nt):\n", " #========================================= LBM - Solution =============================================\n", " #--------------------Collision----------------\n", " for k in range(0,3):\n", " fp[k,:]= f[k,:] - (f[k,:] - w[k]*(u[:]+cx[k]*(ce*u[:])/cs**2))/tau\n", " #-----------------streaming-------------------\n", " for k in range(0,3):\n", " f[k,:]=np.roll(fp[k,:], cx[k], axis=0)\n", " #----------------------Macro------------------\n", " u[:]=f[0,:]+f[1,:]+f[2,:]\n", " #---------------------save-snaps--------------\n", " if t+1 in snaps_id:\n", " i = snap_index[t+1]\n", " u_snaps[i][:]=u[:]\n", " #========================================= FDM - Solution =============================================\n", " if (t<2) :\n", " ufm2[:]=ufm[:] # Swap for update t-1 to t-2\n", " ufm[:]=uf[:] # Swap for update t to t-1\n", " uf[:]=u[:] # Swap for update t to t-1\n", " else :\n", " ufp[:]=( ( (1-omg+omg*w[1])*np.roll(uf[:],1,axis=0) + (1-omg+omg*w[0])*uf[:] + (1-omg+omg*w[2])*np.roll(uf[:],-1,axis=0) )\n", " - (1-omg)**(2)*( np.roll(ufm[:], 1, axis=0) + ufm[:] + np.roll(ufm[:], -1, axis=0) )\n", " - (1-omg)*omg*( (w[0]+w[1])*np.roll(ufm[:], 1, axis=0) + (w[2]+w[1])*ufm[:] + (w[2]+w[0])*np.roll(ufm[:], -1, axis=0) )\n", " + (1.0-omg)**(2)*ufm2[:] )\n", " ufm2[:]=ufm[:] # Swap for update t-1 to t-2\n", " ufm[:]=uf[:] # Swap for update t to t-1\n", " uf[:]=ufp[:] # Swap for update t+1 to t\n", " if t+1 in snaps_id:\n", " i = snap_index[t+1]\n", " uf_snaps[i][:]=ufp[:]" ] }, { "cell_type": "code", "execution_count": 160, "id": "9a6cee11-d08e-45e3-be3e-c09dc87d7020", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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VilgsZoGBgUwsFpf4NXERQtZTewTryBlY5KOn9ggWFyEss362adOGAZB72NraysrU1NSYtrY209bWZpaWlmzGjBmyYwoLC2MAWHJystK2AbAXL16UqB+JiYmsdevWTE9PjwkEglIfh0gkYkOHDmU6OjrM2NiYLV68WK68a9eubNmyZSWuX1x5VRMjFLEOw9axFv1XF/noMGwdixGKymR/NSVuRo8erXAco0eP/uRxent7y8q1tbXZ7du3GWOMZWRksHr16jFtbW1mYGDAxo0bV+QxFrS9bt26Uve5In1IFbHaf6xn9hvWFPmo/cd69iGV4qrArVu3GACmoaEh66u2trbc+edj3t7erE+fPnLbPo4rxhh79eoVa968OdPQ0GBOTk7s9OnTcvWLK69qErIS2IQnU9j/Ho0r8jHhyRSWkJVQJvurCXEVHh7OWrZsyQQCAdPV1WWurq5s6dKlTCKRMMbyY8DT05Npa2szgUDAGjVqxM6ePSvXRu3atdn+/ftlzzt27Mh0dXUZn89nAwYMYO/fvy9y/6NHj2azZs0qVZ8rmjQvikliPZgkxrnoR6wHk+ZFlcn+akJcFebj48M8PT3ltp05c4Z5eXkxPp/PTExM2IgRI1h8fLysvHBcffjwgXXt2pVpaWkxKysr9tdff8m1V1x5cT7n+zUhZYnDWKFpKEmlysrKQlhYGOzt7Uu03FABYWQ8RAlFTyghMNKtsDW6SfUSG58KUZq4yHKBrmaFrNFNapaotFQki4uOK31NzQpZo5vULInZiUjLSy+yXFdFp0LW6CY1C5NE56/DXRSuPjgVsEY3KT+f+/2akLJCSXcVQycFQgghhBBCyg59vyaVjSZSI4QQQgghhBBCygkl3YQQQgghhBBCSDmhpJsQQgghhBBCCCknlHQTQgghhBBCCCHlhJJuQgghhBBCCCGknFDSTQghhBBCCCGElBNKugkhhBBCCCGEkHKiUtkdIGVLIpEg4M5rJMYkw9BcH3Vb1QKPx6vsbpFqQCKRwjfoAxKTM2Corw1PNyvwePS7HPkyEqkUT6KjIMxIh4m2DhpZWILHpbgiX0bKpAhOe4OUXBH0VAVw1XUBl0NxRb4MYxIg5ykgjQe4xoBaQ3A49B2KEPLl6F+oGuTOyUcY4zwDc9ovwooRGzCn/SKMcZ6BOycflfm+2rZtC3V1dejo6MgeW7ZsAQCMGTMGampq0NXVhUAggIuLC6ZMmYKwsDC5NjgcDrS1tZGamiq3vUePHuBwODh9+nSJ+rJ7927Uq1fvs48lNzcX06dPh76+PgwMDDBjxgzk5eV9dv3StlcV/PPwDYZO34GZ3kexeP0FzPQ+iqHTd+Cfh2/KdD81KW42b96Mhg0bQl1dHX379lUo//nnn+Hu7g4VFRV8++23xbZ39epV1K9fH7q6uqhduzYuXbqktN6VK1fA4XBK1GZluxTyFu327sTwk0fx7eWLGH7yKNrt3YlLIW/LdD81Ja6ys7MxceJE2NvbQ1dXF7Vq1cKuXbuU1o2Li4OBgUGx+4qOjkb37t2hra0NGxsbbN++vVTlVdHTpGf4wXcefnu9GttC/8Jvr1fjB995eJr0rEz3U1PiCgBmzJgBa2tr8Pl8WFpa4ttvv0VOTs4njzU6OrrI9p49e4aWLVuCz+fDwcEBe/fuVVovICAAampqSs+RVQ3LugyW0AkseRSYaHb+fxM6gWVdLtP91KS4KiAWi+Hk5AQ9PT257YGBgejQoQP09fVhZmaGSZMmITMzs8h2UlNTMXz4cPD5fJiamuLXX38tVTkhVRkl3TXEnZOP8Oug32HnboMN95fhbOpebLi/DHbuNvh10O/lknivXLkS6enpssfUqVNlZVOnTkVaWhpEIhEuX74MNTU1eHl5ISgoSK4Na2trHDlyRPY8JiYGjx49gqmpaZn3tyhLly7F3bt3ERgYiFevXuHOnTtYvnz5Z9cvbXuV7Z+Hb7BwzVk42Bhj24rhuLJ/JratGA4HG2MsXHO2zBPvmhI3FhYWWLhwISZOnKi03MnJCatWrULv3r2Lbevdu3fo168flixZApFIhFWrVmHAgAF49+6dXL2MjAzMnDkTzZs3L5NjKE+XQt5i2sWzcDU0wolBw+A/ZQZODBoGV0MjTLt4tswT75oQV3l5eTA3N8e1a9eQmpqK3bt34/vvv8eVK1cU6k6fPh1eXl7Ftjls2DCYmZlBKBTi2LFj+OGHH/DPP/+UuLyqeZr0DJtDtsJKyxI/156PPxv8gZ9rz4eVliU2h2wt88S7JsRVQV9fv36N1NRU+Pr6wtfXF6tWrZKrU/hYLSwslLaVkpKC7t27Y+TIkUhOTsahQ4cwY8YM3L17V66eVCrFxIkT0aJFi3I7rrLCsi6DpcwEVFzAMTgKjskLcAyOAiouYCkzyzzxrilxVeCXX36Bra2twvbhw4fD1dUVcXFx8Pf3h6+v7ycT5RkzZiApKQmRkZG4c+cOtm/fLveDTnHlhFRllHTXABKJBH/N2YMmPetj8akfUbupCzR1NFG7qQsWn/oRTXrWx18/7IVEIqmU/tnb22Pjxo1o2rQpvL295crGjh0LHx8f2fO9e/di8ODB0NDQKFHbL168wJQpU+Dv7y/7xTgyMrJU/du1axcWLlwIc3NzmJubY8GCBdi5c+dn1y9te5VJIpFi855baN7AESt+6ou6LhbQ0lRDXRcLrPipL5o3cMTmPf9AIpFWeN+qetz0798fffv2hZGRkdLy0aNHo1u3buDz+cW2denSJdSvXx89e/YEl8tFz5490bhxY4UvEwsWLMDw4cPh7Oxcqr5WNIlUiuV3b6G9vQP+7NkXXuYW0FZTg5e5Bf7s2Rft7R2w4u4/kEgprj6mra2NJUuWwNHRERwOB02bNkW7du0UkpkzZ84gKSkJo0aN+mR7oaGhuHv3LlasWAFtbW00adIEI0aMkF09L668qpEyKQ5FHoWnngdmOU+Hk44jNHgacNJxxCzn6fDU88Dh90chZRRXhbm5uUFbWxsAwBgDl8vF27ef98PX/fv3oa6ujilTpoDH46FJkybo378/duzYIVdv48aNcHNzQ5s2bT5rPxWFMQlY2kpAvR04elvAUasHDlc7/796WwD1dmBpK/NvPa9gVT2ugPy7Hi5duoSffvpJoezdu3cYOXIk1NTUYGxsjN69e8Pf319pO5mZmTh8+DCWLl0KPT09uLi4YMaMGbLvT8WVE1LVUdJdAwTceY3Y8HgMm9cf3EJjJblcLobN7YfYMCEC7ryupB7mGzhwoMIVlE6dOuH9+/d4/Tq/bz4+Phg7dmyJ2/Ty8sK2bdvg7u4u+8XYxsYGd+/ehZ6eXpGPgl+Vk5OT8eHDB7nbq+rVq4fIyEiIRCKF/RVXv7TtVTbfoA+IEaZi1IAm4HI5cmVcLgej+jdBjFAE36APldTDqhk3ZU0qlYIxprDNz89P9vzRo0e4du0a5s6dWy59KEtPoqPwITUVUxs2AZdTKK44HHzTsAnep4rwJDqqknpYPeIqKysLjx8/hoeHh2ybSCTC7NmzsW3btmL74+fnB3Nzc7krX/Xq1ZPFVXHlVU1w2hsk5CSgl0UPhfHbXA4Xvcy7Iz47AcFpZXt3TmlU5bj67bffoKOjAxMTE/j6+mLGjBly5UuXLoWBgQG8vLw+efWwJOeriIgIbNiwAatXry7xcVaanKeA5AM42lPAKRRXHA4XHO3JgORDfr1KUlXjKi8vDxMnTsQff/wBNTU1hX3MmTMHe/fuhVgsRmxsLE6dOoVevXop7U9wcDBycnIUvj8VxFVx5YRUdZR01wCJMckAAPu61krL7erayNUrK/PmzZM7EWdkZHyyvqWlJZKSkuS2cblc/O9//4OPjw/u378PFRUVNGrU6Iv71rJlS6SkpBT5KBg/lZ6eDgBy45AK/j8tLU2h3eLql7a9ypaYnP83c7BWfrXWwcZIrl5ZqAlxU9Y6deqEJ0+e4PTp08jLy8Pp06dx79492Xi93NxcTJw4EVu2bFH6xaaqEWbkfw5cDJXHVcH2gnploabFFWMMEyZMgLOzM/r37y/b/uOPP2LMmDElutshPT1dYYylnp6e7FxUXHlVk5Kb/8Ollaal0nJLLUu5emWhJsXV3LlzkZ6ejsDAQEyZMgVmZmayshUrViA0NBRxcXH47bffMGPGDJw6dUrpfps1a4aMjAxs3rwZubm5uHfvHk6dOiU3vnjy5MlYsmQJDA0Nv/g4y500Pv+/KkV8pgq2F9QrAzUlrlavXg0vLy+0bt1aaVvdunXD3bt3oaurC3Nzc1hbW2PcuHFK66anp0NbWxsqKv/N8Vz4fPWpckKqOkq6awBDc30AQFjAe6Xl4QGRcvXKyooVK+ROxAW3rhUlKioKBgYGCtvHjBmD/fv3Y/v27aX6lbYs6OjoAIDcVeiC/9fV1S11/dK2V9kM9fP/Zu/eJygtfxeZIFevLNSEuClrrq6uOHLkCBYvXgwTExPs3LkTQ4cOlX1hXblyJRo3blzkF5uqxkQ7/3PwJlF5XBVsL6hXFmpSXDHGMHXqVAQHB+P06dOyO5ju3LmDe/fuKb2NUxkdHR2FO2xEIpHsXFRceVWjpyoAAHwQK79DIiozSq5eWahJcVXAzc0Nnp6eGDNmjGxbs2bNIBAIoKqqii5dumDy5Mly44U/ZmhoiHPnzuHgwYMwMzPD3LlzMXbsWNn5av/+/cjLyyt2+EOVwTXO/29eEbfbF2wvqFcGakJchYSEYNu2bUXezZCcnIyOHTti4sSJyMzMRFJSErS1tTFy5Eil9XV0dJCZmSk38Wzh89Wnygmp6ijprgHqtqoFMztjHFpxEtJCYySlUikO/XYKZvYmqNuqViX1MN/x48fRtm1bhe3Ozs5wcHDAwYMHizwZf0rhW+qB/C+nH88MWvgxZcoUAIC+vj6srKzw8uVL2WtfvnwJa2trCASKX9yKq1/a9iqbp5sVzE342HfiEaTSwrcLMuw7+QjmJgJ4ullVUg+rZtyUhz59+uDFixdISkrCuXPn8PbtW9lYyGvXruHYsWMwMjKCkZERDh8+jD///BONGzcut/58iUYWlrDi87Hl6SNIC9+Gyhi2Pn0Ea74AjSyUX7GsCFU1rhhjmDZtGh49eoQrV67InTeuX7+Od+/ewcLCAkZGRpgxYwYCAgJgZGSEmJgYhf16eHggOjoaQqFQtu3ly5dwd3cvUXlV46rrAiM1I5yLvqAwblvKpDgXcxHG6kZw1XWppB5W3bgqLDc395NjupXt72MtWrTA/fv3kZiYiDt37iA2NlbufPXo0SPZ+WrVqlX4+++/5a6sVylqDQGeFVjGNrBCccWYFCzjT4BnlV+vklTFuLp79y7i4uLg4uICIyMj9OnTB6mpqTAyMsKjR48QGhoKsViMmTNnQk1NDfr6+pg8eTIuXLigtC+urq5QVVWFr6+vbNvH56Piygmp6mid7hqAx+Nh0prR+HXQ7/DutwrD5vaDXV0bhAdE4tBvp/Do/HP8fOz7SluvOyIiAuvXr8fDhw/x4MEDpXV2796N+Pj4z5p109TUFDExMRCLxdDU1AQAtGrVSnard3HGjh2LZcuWyWZYXb58OSZMmPDZ9UvbXmXi8biYProtFq45i3krT2NU/yZwsDHCu8gE7Dv5CPefhWLpnN6Vsl53VY+bvLw82UMqlSIrKwtcLld2+3dubi4kEonskZWVBR6PB1VVVaXtPX36FPXq1YNYLMa6deuQlJSE0aNHAwCOHTuG7OxsWd3Zs2eDz+dj6dKlpT7uisDjcjG/ZVtMu3gWk8+fxjcNm8DF0AhvEhOw9ekj3Ah7hz+6966U9bqrelxNnz4d9+7dw40bN6CvL3930uzZs+XOJceOHcOOHTtw+fJlmJiYKLTl6OiIFi1aYP78+di4cSMCAgJw4MAB2XJCxZVXNVwOF8NsBmNzyFZseLsZvcy7w1LLElGZUTgXcxG+KX6Y7vRNpazXXZXjKj09HceOHUO/fv0gEAgQEBCApUuXokuXLgDyZyO/f/++bCmrW7duYdu2bZ9cPu7FixeoXbs2pFIp9u/fj1u3buHFixcAgHXr1smdm9auXYvAwMAqO+EVh8MDdH/Kn6U8ZSqgPTn/lvK8t/kJd/ZNcPQ2Vsp63VU5rgYPHoyOHTvKnj948AATJkzAy5cvYWJigpycHNlyaJMnT4ZYLMb27duLXHVBS0sLQ4YMwc8//4xDhw5BKBRi06ZNstnOiysnpMpjpEoRi8UsMDCQicXiUr/29omHbKT9N6wjZ6DsMdJhKrt94mGZ97NNmzZs3bp1SstGjx7NVFVVmY6ODtPV1WWOjo5s4sSJLDQ0VK4eAPbixQulbdja2rJTp06VqC85OTmsd+/eTF9fnwkEAhYREVGKI8l//dSpU5menh7T09Nj06dPZ7m5ubLyyZMns8mTJ5e4fnHlVdGtB8Fs4JQ/WYv+q2WPgVP+YrceBJfpfmpS3Hh7ezMAco82bdrIHU/h8tGjR8vKa9euzfbv3y973rFjR6arq8v4fD4bMGAAe//+fZH7Hj16NJs1a1ap+lsZ/n77hrXy+YvZb1gje7T22c7+fvumTPdTU+IqPDycAWDq6upMW1tb9vj4/PMxHx8f5unpKbetcFx9+PCBde3alWlpaTErKyv2119/ydUvrrwqepL4lM1+8SP736Nxssf3L39kTxKflul+akpcpaens44dOzIDAwOmra3N7O3t2Zw5c1hGRgZjjDGhUMgaN27MdHV1ma6uLnN3d2c7d+6Ua6Nr165s2bJlsudjxoxhAoGAaWtrs06dOrGAgIAi9+/t7c369OlT4v5WFqn4EpMI2zFJjPN/D2E7JhVfKtP91JS4KuzmzZtMIBDIbbt79y5r0aIFEwgEzMDAgPXq1UvuWArHlUgkYkOHDmU6OjrM2NiYLV68WK694so/5Uu+XxNSFjiMFbr3j1SqrKwshIWFwd7evsTLPnxMIpEg4M5rJMYkw9BcH3Vb1aq0K9ykepFIpPAN+oDE5AwY6mvD082qUq5wk5pFIpXiSXQUhBnpMNHWQSMLy0q5wk1qFimTIjjtDVJyRdBTFcBV16VSrnCTmoUxSf4s5dL4/DHcag0r5Qo3KXtf+v2akC9FSXcVQycFQgghhBBCyg59vyaVjX4WJoQQQgghhBBCygkl3YQQQgghhBBCSDmhpJsQQgghhBBCCCknlHQTQgghhBBCCCHlhJJuQgghhBBCCCGknFDSTQghhBBCCCGElBNKugkhhBBCCCGEkHJCSTchhBBCCCGEEFJOKOkmhBBCCCGEEELKCSXd5LO0bdsW6urq0NHRkT2MjIzKfb92dnY4ffr0J+twOBy8fPnys/dx+vRpODs7Q0tLCy1btsTr16+/qH5p26vJamrcBAQEoEuXLjAyMgKHw0FKSopc+c2bN9GuXTsIBALo6ekV255QKMTQoUNhbGwMY2NjzJkzBxKJRKGeWCyGk5NTidqsyWpqXO3ZsweNGzeGQCCAubk5xo8frxBbBYYPH16ifS1evBimpqbg8/kYMWIE0tPTS1X+NampcfX333/D3d0d+vr6MDAwQKdOneDv7y8r3717N3g8ntxxr1q1qsj20tPTMWXKFJibm0NPTw9jx45FZmamQj3GGFq2bKn0HPk1qalx9bH58+eDw+HI7S8vLw/ffvstLCwsIBAI0LJlSzx79uyT7fz555+wsbGBtrY2evTogZiYmFKVE1KVUNJNPtvKlSuRnp4ueyQkJFR2l75YcHAwRowYgXXr1iEpKQnt27dHnz59kJeX91n1S9ve16Amxo2qqioGDx6M3bt3Ky3X1tbGuHHjsHbt2hK1N2rUKKirqyMiIgK+vr64fv06Vq5cqVDvl19+ga2t7Zd0vcaoiXGVmZmJVatWIS4uDq9evUJMTAymTp2qUO/ChQuIi4srtj0fHx/s3LkTd+7cQWRkJBITEzFz5swSl3+NamJc1atXD1euXEFycjKEQiF69OiBfv36ydVxd3eXO+4ff/yxyPa+//57vHv3DoGBgQgPD0d0dDS+/fZbhXpbtmyBurp6WR9OtVQT46qAr68vzp07B3Nzc7ntmzdvxrlz5/DgwQMkJSWha9eu6N27NxhjStu5ceMGfvrpJxw7dgxCoRCmpqYYMWJEicsJqXIYqVLEYjELDAxkYrG4srvySW3atGHr1q1TWvbs2TPG5/OZv78/Y4yxpKQkZm1tzXbv3s0YY+zy5cusQYMGjM/nMzMzM/bNN9+wzMxM2etFIhGbNm0as7GxYbq6uqxhw4YsMjKSDRw4kHE4HKahocG0tbXZ5MmTFfbdqFEjBoBpamoybW1ttmzZslId18KFC1mPHj1kz3Nycpienh67cePGZ9UvbXs1XU2NmwJhYWEMAEtOTlZafvPmTSYQCD7ZRnp6OuNwOCw0NFS2bffu3czW1lau3tOnT1ndunXZ5cuXi22zpqvpcVXgzJkzzNraWm5bamoqc3Z2Zm/evGEA2IsXL4p8fcuWLdnq1atlzx8/fsw0NDRkx1tc+dfma4irnJwctnHjRsbj8VhOTg5jjDEfHx/m6elZ4jaMjY3Z9evXZc9v3bqlEDeRkZHMwcGBPX369JPnyK9BTY6rvLw81rBhQ3br1i1ma2vLTp06JSubMWMGmzhxouz5hw8fGAAWHx+vtK2RI0eyadOmyZ7HxsYyLpcr+7exuPLCqsv3a1JzqVRatk9KLCszG+9fR1XIvqxrWUJD68t+ia5fvz68vb0xdOhQPHnyBOPHj0erVq0wevRoAICmpia2b98ODw8PREREoEePHli7di0WLFgAABgzZgwyMzPx4MEDmJmZwdfXF5qamjh27Bjs7Oywfv169O3bV+m+Hz9+DA6Hg/v376NevXqy7R4eHoiMjCyyzwW3uvn5+cm9TlVVFbVr14afnx/atWun8Lri6pe2vbKUlZ2LiKikct1HAVtLA2ioq35RG9U5bsoSY0z2KCCVShEREYHU1FTw+Xzk5eVh4sSJ+OOPPyCVSsu8D58izs1FaHLFxJWjvgE0VSmuCvzzzz/w8PCQ2zZv3jyMGjUKzs7Oxb4Xfn5+8Pb2lj2vV68esrKy8ObNG3h6ehZbXp6yJdmIyYot130UMNcwgzrv6/13DgAiIyPh4eGBtLQ0MMawYMECqH70WQsODoaJiQm0tbXRrVs3LF++vMhhLFKpVOF8lZWVhbdv38ri9ZtvvsGiRYtgaGj4qbe1zDEmBvLeVczOVBzA4Wh+URPVPa7WrVsHDw8PtGnTRqHe+PHjMW7cOISGhsLGxgY7duxAs2bNiry13s/PDzNmzJA9NzU1hZmZGfz9/eHg4FBsOSFVDSXd1cD711GY2vCnCtnXlqcr4Vy/ZCerefPmYdGiRbLnjRo1wtWrVwEA3333Ha5evYqmTZsiPT0dL168kNVr1aqV7P8dHBwwefJkXLhwAQsWLEBcXBxOnTqFiIgIWFhYAAC8vLy++Lj8/PxKVC89PV3hi4Wenh7S0tI+q35p2ytLEVFJGP/DvnLfDwDsXD0Krg6mJapbE+OmLOno6KB169bw9vbGtm3bkJSUhA0bNgCALOlevXo1vLy80Lp1a9y6datC+xeanITeh/dXyL7ODh2JuiYUV0D+ONwdO3bg7t27sm3379/HrVu38Pz58xK1Ufh8pKqqCi0trSLPV4XLy1NMViy8Xy0p9/0AwOI6v8BOu2TDMmpqXNnY2CAlJQVpaWnYs2cPrK2tZWWtW7eWJS4RERGYOHEiRo8ejTNnzihtq0ePHlixYoXsh5nly5cDyD9fAcChQ4eQlZWFUaNGITw8/DOP7jPlvQNL7Fd8vTLAMTwFqNYpUd2aGFfv3r3D5s2bizwfOTg4oF69enBycgKPx4OpqSn+/vvvIturyt+vCPkclHRXA9a1LLHlqeJ4zvLaV0mtWLFC6bgtIH8yjilTpqBv375Ys2YN+Hy+rOzJkyeYN28e/P39IRaLkZeXB1dXVwBAREQE1NXVYWNj80XH8bl0dHQgEonktolEIujq6n5W/dK2V5ZsLQ2wc/Woct9Pwb5KqibGTVk7cOAAZs2aBScnJ/D5fEyYMAF+fn7Q19dHSEgItm3bJvdFrCI56hvg7NCRFbavkqrJcXXjxg2MHDkSJ0+ehLu7OwAgJycHkyZNwtatW6Gmplaidgqfj/Ly8pCZmVnk+apweXky1zDD4jq/lPt+CvZVUjU5rgBAV1cXU6dOhZGREZ49ewZ7e3u5q4T29vbYuHEj3N3dkZmZCS0tLYU21q9fj++//x6enp5QUVHBnDlzcO3aNRgaGiIpKQlz587FtWvXKvKw/qPikJ8MV9C+SqomxtWkSZOwdOlSGBgoP29PnToVMTExiI6OhrGxMU6fPo327dvDz89P9iPBx6ry9ytCPkul3txOFFSXMSefGpPE2H/jkCZNmsQMDAxYRESErMzR0ZEtXbqUpaenM8YYW7dunWz8WGxsLAPAIiMjlbZrb28vN0ZIGQ6HozCusXbt2kxbW7vIR4GFCxeynj17yp7n5OQwfX19ufFqHyuufmnbq+lqatwUKIsx3cps2bKFNWrUiDGWP95SXV2dGRoaMkNDQ8bn8xmHw2GGhobs4cOHpW67JqjJcXX9+nWmr6/PLl26JLc9LCyMcblcWRwYGhoyAExPT4/9/vvvSvvSsmVLtmbNGtnzJ0+eMHV1dbkx3Z8q/9rU5Lj6WF5eHtPU1CxyrpGgoCDG5XJlx1KcixcvMjMzMyaRSNjNmzeZioqKLEb19fUZAGZgYMCOHTtWovZqmpoaVwDkzkdcLpfp6uqyb7/9ljHGWJ06ddi+ffvk2nZwcCgyDkaOHMmmT58uex4XF6cwpvtT5YVVl+/XpOaipLuKqS4nheL+0ejfvz8bMWIEY4yx77//nrVs2ZLl5eUxxvInXdm8eTNjjLHAwEDm4uIiN2lLnz59WPfu3Vl0dDSTSCTs+fPnLCEhgTHGWNOmTeW+FCpjZmbGjh8//lnH9fr1a6alpcUuXLjAsrKymLe3N3N2dma5ubmfVb+07dV0NTVupFIpE4vF7PXr1wwAi42NZWKxmEmlUsYYYxKJhInFYtmkZ2Kx+JOf8aCgIJacnMzy8vLYzZs3mYWFBfv7778ZY4xlZGSw9+/fyx5Hjx5lfD6fvX//nmVnZ39W/6u7mhpXN2/eZHp6euz8+fMKZXl5eXJx8P79ewaAXb58maWmpiptb+fOnczGxoa9efOGpaSksG7durGxY8eWuPxrU1Pj6tChQ+zt27dMIpGw5ORkNm3aNGZkZMRSUlIYY4xduHCBRUdHM8YYe//+PevcuTPr3r17ke29e/eOxcbGMqlUyp4/f85cXV3Zn3/+yRhjLCsrSy5GHzx4wACwV69esYyMjM/qf3VXU+Oq8PnIysqK7dixgyUlJTHGGJswYQLr1KkTEwqFTCKRsJMnTzI1NTX2+vVrpe1dv36d6enpsUePHrGMjAw2fvx41q5duxKXF1Zdvl+TmouS7iqmupwU2rRpw9TU1BR+8UxISGDbtm1j9vb2TCQSMcbyr+42bNiQLVq0iDHG2MmTJ5mdnR3T1tZmrVu3Zr/88ovcPxopKSls8uTJzMLCgunq6rLGjRuz9+/fM8YYO3v2LLOzs2MCgYB98803Svu2fft2ZmFhwfT09NiKFStKfWwnT55kTk5OTENDgzVv3pwFBQXJym7fvq1wxeBT9UtS/jWpqXFTcIW78CMsLIwxlp88KSsvsGzZMta1a1fZ8y1btjATExOmqanJPDw82OnTp4vc9+dePa9JampctW3blnG53BJfsUSh2csLxxVjjHl7ezNjY2Omo6PDhg0bppCgF1f+NampcbVixQpmZ2fHtLS0mLGxMevRo4dc3MyZM4eZmpoyTU1NZmVlxaZMmcISExNl5fv372e1a9eWPT916hSztLRkmpqazNnZmW3fvr3IfRd3N9DXoKbGVWGFZy9PSUlh48aNY2ZmZkxXV5e5u7uzw4cPy8oLxxVjjG3dupVZWloyLS0t1q1bN9mPQSUt/1h1+X5Nai4OY0UskEcqRVZWFsLCwmBvbw8NDY3K7g4hhBBCCCHVGn2/JpWNW9kdIIQQQgghhBBCaipKugkhhBBCCCGEkHJCSTchhBBCCCGEEFJOKOmuomioPSGEEEIIIV+OvleTykZJdxXD4/EAADk5OZXcE0IIIYQQQqq/zMxMAICqqmol94R8rVQquwNEnoqKCrS0tBAfHw9VVVVwufS7CCGEEEIIIaXFGENmZiaEQiH09PRkF7cIqWi0ZFgVlJOTg7CwMEil0sruCiGEEEIIIdWanp4ezMzMwOFwKrsr5CtFSXcVJZVK6RZzQgghhBBCvoCqqipd4SaVjpJuQgghhBBCCCGknNCAYUIIIYQQQgghpJxQ0k0IIYQQQgghhJQTSroJIYQQQgghhJByQkk3IYQQQgghhBBSTijpJoQQQgghhBBCygkl3YQQQgghhBBCSDmhpJsQQgghhBBCCCknlHQTQgipEtq2bYu2bdtWdjdKTFl/4+LiMHDgQBgaGoLD4WD9+vUAgLdv36Jz584QCATgcDg4ffp0mfYlPDwcHA4Hu3fvLtN2SfVVHp+n8v6M2tnZYcyYMeXWflF2794NDoeD8PDwMm23up3TCCHlh5JuQggBkJ6eDm9vb3Tt2hUGBgafTGDatm0LDocDDocDLpcLPp8PV1dXjBo1ClevXi31vm/duoX+/fvDzMwMampqMDExQa9evXDy5MkvPKqqJzAwEIsWLSrzL7dfasyYMbK/KYfDgY6ODhwcHDBw4ECcOHECUqm0RO189913uHz5MubNm4d9+/aha9euAIDRo0fD398fy5Ytw759+9CwYcPyPJwqwc7ODj179vxkncLvu4qKCqytrTF06FAEBgbK1b1165as3v79+5W216JFC3A4HNStW7fMjqMsNG7cGBwOB1u3bq3srhSrqn5GP1Zwvq5bty60tbVhaGiIevXqYdasWYiOjq7QvlSH94sQUvlUKrsDhBBSFSQkJGDJkiWwsbGBp6cnbt269cn6VlZWWLFiBQAgIyMDISEhOHnyJPbv34/Bgwdj//79UFVVLXa/3t7eWLJkCZydnTF58mTY2toiMTERFy9exIABA3DgwAEMHz68LA6xSggMDMTixYvRtm1b2NnZyZVduXKlcjr1L3V1dezYsQMAIBaLERERgXPnzmHgwIFo27Ytzpw5Az6fL6uvrL83btxAnz59MGfOHNk2sViMBw8eYMGCBZg+fXq59N3W1hZisbhEMVfVfPy+5+XlITQ0FNu2bcOlS5cQGBgICwsLufoaGho4ePAgRo4cKbc9PDwc9+/fh4aGRoX1vSTevn2LJ0+ewM7ODgcOHMA333xT2V36pKr8GQWA3NxctG7dGq9fv8bo0aMxY8YMpKen49WrVzh48CD69eunEDPlqaq/X4SQqoGSbkIIAWBubo6YmBiYmZnh6dOnaNSo0SfrCwQChS/9v/32G2bOnIktW7bAzs4OK1eu/GQbx48fx5IlSzBw4EAcPHhQLmH64YcfcPnyZeTm5n7+QVUzampqlbp/FRUVhb/p0qVL8dtvv2HevHmYOHEijhw5IitT1l+hUAg9PT25bfHx8QCgsL0scTicKpdslpSy971p06bo2bMnLly4gIkTJ8qVde/eHWfPnkVCQgKMjIxk2w8ePAhTU1M4OzsjOTm5QvpeEvv374eJiQl+//13DBw4EOHh4QrJWXVR2Z9RADh9+jRevHih9AfJrKws5OTkVFLPFFWF94sQUjXQ7eWEEIL8q21mZmZf1AaPx8PGjRtRu3ZtbN68GSKR6JP1f/75ZxgYGGDXrl1Kr1B26dJF7vZcoVCI8ePHw9TUFBoaGvD09MSePXvkXlMwtnfNmjX466+/4OjoCHV1dTRq1AhPnjyR1VuzZg04HA4iIiIU9jtv3jyoqanJJS6PHj1C165dIRAIoKWlhTZt2uDevXsKr42KisL48eNhYWEBdXV12Nvb45tvvkFOTg52796NQYMGAQDatWsnu1W44K4CZeMfy/KYP9fcuXPRuXNnHDt2DG/evJFt/7i/BWNCGWP4448/ZMe2aNEi2NraAsj/IYXD4cgSrjFjxihNvhYtWgQOhyO37erVq2jZsiX09PSgo6MDV1dXzJ8/X+E9KDwk4saNG2jVqhW0tbWhp6eHPn36ICgoSOn+QkJCMGbMGOjp6UEgEGDs2LHIzMyUq5uQkIDXr18rbC9rBZ9FFRXFawN9+vSBuro6jh07Jrf94MGDGDx4MHg8XrHtT58+HTo6OkqPY9iwYTAzM4NEIgEAPH36FF26dIGRkRE0NTVhb2+PcePGlfhYDh48iIEDB6Jnz54QCAQ4ePCgQp3S/A18fHzQvn17mJiYQF1dHbVr1y72tvX09HRoa2tj1qxZCmUfPnwAj8fDihUrPuszmpWVhUWLFsHFxQUaGhowNzdH//79ERoaKquzZs0aNG/eHIaGhtDU1ESDBg1w/Pjxkrx9CgrabdGihUKZhoaG3N0oQMk+A8oUfH4L+3jceXU9pxFCKh4l3YQQUoZ4PB6GDRuGzMxM3L17t8h6b9++xevXr9G3b1/o6uoW265YLEbbtm2xb98+jBgxAqtXr4ZAIMCYMWOwYcMGhfoHDx7E6tWrMXnyZCxduhTh4eHo37+/7Mr54MGDweFwcPToUYXXHj16FJ07d4a+vj6A/C+trVu3RmpqKry9vbF8+XKkpKSgffv2ePz4sex10dHRaNy4MQ4fPowhQ4Zg48aNGDVqFP755x9kZmaidevWmDlzJgBg/vz52LdvH/bt2wc3N7cKOeYvMWrUKDDGihyz37p1a+zbtw8A0KlTJ9mx9e/fH+vWrQOQn8zt27dPNrlaSb169Qo9e/ZEdnY2lixZgt9//x29e/dW+qPHx65du4YuXbpAKBRi0aJFmD17Nu7fv48WLVooHX86ePBgpKWlYcWKFRg8eDB2796NxYsXy9XZvHkz3Nzc5P7uZSEhIQEJCQmIi4vDgwcP8N1338HQ0FDpmHAtLS306dMHhw4dkm3z9fXFq1evSjwUY8iQIcjIyMCFCxfktmdmZsqGFPB4PAiFQnTu3Bnh4eGYO3cuNm3ahBEjRuDhw4cl2s+jR48QEhKCYcOGQU1NDf3798eBAweKrF+Sv8HWrVtha2uL+fPn4/fff4e1tTWmTp2KP/74o8h2dXR00K9fPxw5ckT2Y0KBQ4cOgTGGESNGlPozKpFI0LNnTyxevBgNGjTA77//jlmzZkEkEiEgIEBWb8OGDfDy8sKSJUuwfPlyqKioYNCgQQrvf0kU/Ii1d+9eMMY+Wbe0n4HSqs7nNEJIBWOEEELkPHnyhAFgPj4+SsvbtGnD6tSpU+TrT506xQCwDRs2FFnnzJkzDABbt25difq0fv16BoDt379fti0nJ4c1a9aM6ejosNTUVMYYY2FhYQwAMzQ0ZElJSQr7O3funGxbs2bNWIMGDeT28/jxYwaA7d27lzHGmFQqZc7OzqxLly5MKpXK6mVmZjJ7e3vWqVMn2bb//e9/jMvlsidPnij0v+C1x44dYwDYzZs3Feq0adOGtWnTplyPuSijR49m2traRZa/ePGCAWDfffddkf1ljDEAbNq0aXLbCvq3evVqhX3a2toq7Mvb25t9/M/zunXrGAAWHx9fZP8K9vFxzNarV4+ZmJiwxMRE2TZfX1/G5XLZ//73P4X9jRs3Tq7Nfv36MUNDQ6V9U/b3K8zW1pb16NHjk3VGjx7NACg8LC0t2bNnz+Tq3rx5kwFgx44dY+fPn2ccDodFRkYyxhj74YcfmIODA2Os+M8nY/nxaGlpyQYMGCC3/ejRowwAu337NmPsv8+yspguienTpzNra2tZ/F+5coUBYC9evJCrV5q/QWZmpsJ+unTpIjv+AoXj8/LlywwA+/vvv+XqeXh4yNUrzWd0165dDABbu3atQt3C54uP5eTksLp167L27dvLbbe1tWWjR49WaOtjmZmZzNXVlQFgtra2bMyYMWznzp0sLi5OoW5JPwM+Pj4MAAsLC5NtA8C8vb0V2izcx6p6TiOEVC10pZsQQsqYjo4OACAtLa3IOqmpqQBQoqvcAHDx4kWYmZlh2LBhsm2qqqqYOXMm0tPT8c8//8jVHzJkiOxKNQC0atUKAPDu3Tu5Os+ePZO7DfTIkSNQV1dHnz59AAAvX77E27dvMXz4cCQmJsquSGZkZKBDhw64ffs2pFIppFIpTp8+jV69eimdmbvw7dKVdcyfqyR/0/JSMBb8zJkzJZ5FPSYmBi9fvsSYMWNgYGAg2+7h4YFOnTrh4sWLCq+ZMmWK3PNWrVohMTFRFqtA/m3QjLEyXQZJQ0MDV69exdWrV3H58mX8+eef0NHRQffu3eVu5/9Y586dYWBggMOHD4MxhsOHD8vFSXE4HA4GDRqEixcvIj09Xbb9yJEjsLS0RMuWLQH8996fP3++1FcX8/LycOTIEQwZMkQW/wW3hRd1tbskfwNNTU3Z/4tEIiQkJKBNmzZ49+7dJ4e0dOzYERYWFnL7DggIgJ+fn8KY+pI6ceIEjIyMMGPGDIWyjz/zH/c5OTkZIpEIrVq1wvPnz0u9T01NTTx69Ag//PADgPxbvMePHw9zc3PMmDED2dnZAD7vM1DeqtI5jRBSsSjpJoSQMlbwJf5TCXXBuMOSJnERERFwdnYGlyt/2i64jbHw2GwbGxu55wVf3D4epz1o0CBwuVzZ5GCMMRw7dgzdunWT9e/t27cA8pe8MjY2lnvs2LED2dnZEIlEiI+PR2pqapku1VTWxywWixEbGyv3KKmS/E3Ly5AhQ9CiRQtMmDABpqamGDp0KI4ePfrJBLzgvXF1dVUoc3Nzk/1w8rGSxEx54PF46NixIzp27IjOnTtj0qRJuHbtGkQiEebNm6f0Naqqqhg0aBAOHjyI27dv4/3796We5X/IkCEQi8U4e/YsgPy/8cWLFzFo0CBZwtimTRsMGDAAixcvhpGREfr06QMfHx9ZYvcpV65cQXx8PBo3boyQkBCEhIQgLCwM7dq1w6FDh5T+/UryN7h37x46duwoG6NsbGwsG9//qaSby+VixIgROH36tGyc+IEDB6ChoSEbl1xaoaGhcHV1VTr2/mPnz59H06ZNoaGhAQMDAxgbG2Pr1q3FzntRFIFAgFWrViE8PBzh4eHYuXMnXF1dsXnzZvz6668APu8zUN7K4zxOCKkeKOkmhJAyVjCW0cnJqcg6tWrVAgD4+/uXSx+KmkyKfTQG0sLCAq1atZKN63748CEiIyMxZMgQWZ2CxGD16tWyq5GFHwVXgStbccd85MgRmJubyz1KqiR/09Iq6up/4TG3mpqauH37Nq5du4ZRo0bBz88PQ4YMQadOnRTqfomSxExFsbKygqurK27fvl1kneHDh+Ply5dYtGgRPD09Ubt27VLto2nTprCzs5PF/7lz5yAWi+Xin8Ph4Pjx43jw4AGmT5+OqKgojBs3Dg0aNJC7Qq5MwRXlwYMHw9nZWfY4cuQIoqKiFK5qAsX/DUJDQ9GhQwckJCRg7dq1uHDhAq5evYrvvvsOAIq9E+J///sf0tPTcfr0aTDGcPDgQdkEb+Xlzp076N27NzQ0NLBlyxZcvHgRV69exfDhw8sktmxtbTFu3Djcu3cPenp6nxwzXxbK8jNXnKr0mSSEfBlaMowQQsqQRCLBwYMHoaWlJbtFVRkXFxe4urrizJkz2LBhQ7GJq62tLfz8/CCVSuWukrx+/VpW/jmGDBmCqVOnIjg4GEeOHIGWlhZ69eolK3d0dASQf2W+Y8eORbZjbGwMPp8vN3mSMqW5zbysj7lLly5FToRWnH379oHD4aBTp06f9Xpl9PX1kZKSorBd2YzyXC4XHTp0QIcOHbB27VosX74cCxYswM2bN5X+XQrem+DgYIWy169fw8jICNra2l9+EOUoLy/vk4lty5YtYWNjg1u3bhW7PF9RBg8ejA0bNiA1NRVHjhyBnZ0dmjZtqlCvadOmaNq0KZYtW4aDBw9ixIgROHz4MCZMmKC03YyMDJw5cwZDhgzBwIEDFcpnzpyJAwcOoF27dqXq77lz55CdnY2zZ8/KXQW9efNmiV5ft25deHl54cCBA7CyskJkZCQ2bdokV6c0n1FHR0c8evQIubm5Ra4Rf+LECWhoaODy5ctQV1eXbffx8SnxfkpCX18fjo6OsnPQl34GlH0+c3JyEBMTI7etMs9phJDqg650E0JIGZFIJJg5cyaCgoIwc+ZMhaVrClu8eDESExMxYcIE5OXlKZRfuXIF58+fB5C/NnFsbKzcOtF5eXnYtGkTdHR00KZNm8/q84ABA8Dj8XDo0CEcO3YMPXv2lPsi2qBBAzg6OmLNmjVKE6CCNai5XC769u2Lc+fO4enTpwr1Cq7MFLStLNksrKyP2dzcXHYbc8GjJH777TdcuXIFQ4YMgbOzc6n2+SmOjo4QiUTw8/OTbYuJicGpU6fk6iUlJSm8tl69egBQ5G3O5ubmqFevHvbs2SP3XgcEBODKlSvo3r37Z/W5opYMe/PmDYKDg+Hp6VlkHQ6Hg40bN8Lb2xujRo36rP0MGTIE2dnZ2LNnDy5duoTBgwfLlScnJytcVSzuvQeAU6dOISMjA9OmTcPAgQMVHj179sSJEydKdJv6xwqufH7cJ5FIVKoEdtSoUbhy5QrWr18PQ0NDdOvWTa68NJ/RAQMGICEhAZs3b1YoK+gjj8cDh8ORu0IcHh6O06dPl7jPH/P19UVCQoLC9oiICAQGBspuJ//Sz4Cjo6PCnRZ//fWXwpXuyjynEUKqD7rSTQgh/9q8eTNSUlIQHR0NIP+q0ocPHwAAM2bMkLsFUyQSYf/+/QDylxkKCQnByZMnERoaiqFDh8rGFX7KkCFD4O/vj2XLluHFixcYNmwYbG1tkZiYiEuXLuH69euyNX0nTZqEP//8E2PGjMGzZ89gZ2eH48eP4969e1i/fv1njzU2MTFBu3btsHbtWqSlpcndWgvkJ9M7duxAt27dUKdOHYwdOxaWlpaIiorCzZs3wefzce7cOQDA8uXLceXKFbRp0waTJk2Cm5sbYmJicOzYMdy9exd6enqoV68eeDweVq5cCZFIBHV1ddnkUoWV1zEXJS8vT/Y3zcrKQkREBM6ePQs/Pz+0a9cOf/31V5nub+jQofjpp5/Qr18/zJw5E5mZmdi6dStcXFzkJphasmQJbt++jR49esDW1hZCoRBbtmyBlZXVJ++mWL16Nbp164ZmzZph/PjxEIvF2LRpEwQCgdL1h0ti8+bNWLx4MW7evFmiydRCQkKwdOlShe1eXl7o0aMHAPn3XSqVIjw8HNu2bYNUKoW3t/cn2+/Tp49s0r/PUb9+fTg5OWHBggXIzs5WiP89e/Zgy5Yt6NevHxwdHZGWlobt27eDz+d/Mmk7cOAADA0N0bx5c6XlvXv3xvbt23HhwgX079+/xP3t3Lkz1NTU0KtXL0yePBnp6enYvn07TExMFK7AFmX48OH48ccfcerUKXzzzTcKV6hL8xn93//+h71792L27Nl4/PgxWrVqhYyMDFy7dg1Tp05Fnz590KNHD6xduxZdu3bF8OHDIRQK8ccff8DJyUnuB6eSunr1Kry9vdG7d280bdoUOjo6ePfuHXbt2oXs7Gy52P6Sz8CECRMwZcoUDBgwAJ06dYKvry8uX74MIyOjz36/KvqcRgipQipjynRCCKmKbG1tlS5fhEJLybRp00auTEdHhzk7O7ORI0eyK1eulHq/169fZ3369GEmJiZMRUWFGRsbs169erEzZ87I1YuLi2Njx45lRkZGTE1Njbm7uyssa1bU8lSMFb0Ezvbt2xkApqury8RisdI+vnjxgvXv358ZGhoydXV1ZmtrywYPHsyuX78uVy8iIoL973//Y8bGxkxdXZ05ODiwadOmsezsbLn9OTg4MB6PJ7fUjrIluMrrmAsrvHSVlpYWs7OzYwMGDGDHjx9nEolE4TVfumQYY/lLSNWtW5epqakxV1dXtn//foUlwwriw8LCgqmpqTELCws2bNgw9ubNG4V9FH5vrl27xlq0aME0NTUZn89nvXr1YoGBgXJ1CvZXeEkyZcsolXbJsKI+T+PHj2eMKV8yjM/nsw4dOrBr167JtffxkmGfUpIlwz62YMECBoA5OTkplD1//pwNGzaM2djYMHV1dWZiYsJ69uzJnj59WmR7cXFxTEVFhY0aNarIOpmZmUxLS4v169ePMVa6v8HZs2eZh4cH09DQYHZ2dmzlypWypbsKn6cKx2eB7t27MwDs/v37SstL8xnNzMxkCxYsYPb29kxVVZWZmZmxgQMHstDQUFmdnTt3MmdnZ6aurs5q1arFfHx8FOKcsZItGfbu3Tv2yy+/sKZNm8qdM3v06MFu3LihUL8knwFl77NEImE//fQTMzIyYlpaWqxLly4sJCREaR+r4jmNEFK1cBij2RgIIYQQQr4W/fr1g7+/P0JCQiq7K4QQ8lWgMd2EEEIIIV+JmJgYXLhw4bPHwRNCCCk9GtNNCCGEEFLDhYWF4d69e9ixYwdUVVUxefLkyu4SIYR8NehKNyGEEEJIDffPP/9g1KhRCAsLw549e2BmZlbZXSKEkK8GjekmhBBCCCGEEELKCV3pJoQQQgghhBBCygkl3YQQQgghhBBCSDmhidQqiVQqRXR0NHR1dcHhcCq7O4QQQgghhBBCSoExhrS0NFhYWIDLLfp6NiXdlSQ6OhrW1taV3Q1CCCGEEEIIIV/g/fv3sLKyKrKcku5KoqurCyD/D8Tn8yu5N4qkUini4+NhbGz8yV9tyNeDYoIoQ3FBCqOYIMpQXJDCKCaIMtUtLlJTU2FtbS3L7YpCSXclKbilnM/nV9mkOysrC3w+v1oEPCl/FBNEGYoLUhjFBFGG4oIURjFBlKmucVHccOHqcySEEEIIIYQQQkg1Q0k3IYQQQgghhBBSTijpJoQQQgghhBBCygkl3YQQQgghhBBCSDmhpJsQQgghhBBCCCknlHQTQgghhBBCCCHlhJYMI4SQEhJGxkOUkAapRIqQF2EQJaRBYKQLJy97cHlcCIx0YWJjXNndJIQQQgghVUiNT7pv376N1atX49mzZ4iJicGpU6fQt2/fT77m1q1bmD17Nl69egVra2ssXLgQY8aMkavzxx9/YPXq1YiNjYWnpyc2bdqExo0bl9+BEEIqlTAyHuNrf4eszOwi62hoqWNn4DpKvAkhhBBCiEyNT7ozMjLg6emJcePGoX///sXWDwsLQ48ePTBlyhQcOHAA169fx4QJE2Bubo4uXboAAI4cOYLZs2dj27ZtaNKkCdavX48uXbogODgYJiYm5X1IhHyVKvsqsyghLT/h5gDuLd3QdVw7mDuaISY0Fpd23YT/3SBkZWZDlJBGSTchhBBCCJGp8Ul3t27d0K1btxLX37ZtG+zt7fH7778DANzc3HD37l2sW7dOlnSvXbsWEydOxNixY2WvuXDhAnbt2oW5c+eW/UEQ8pWrCleZpRIpgPyEe83NReByubLnHUe1wZx2i+B/J0hWjxBCCCGEEOArSLpL68GDB+jYsaPcti5duuDbb78FAOTk5ODZs2eYN2+erJzL5aJjx4548OBBke1mZ2cjO/u/hCE1NRUAIJVKIZVWvS/pUqkUjLEq2TdSOSozJpKFItlV5rot3dBlTFtYOJoiOjQOl3ffQsC/V5mThSIYWRl+0b7ycvOQnpKJ9OR0pCdnIC05A2nJ6Xh4/hkAQE1TDb9P2Ir05AyoaajCycsezvUd0GpQU/jfCcKb5+/g3MChLA67WqBzBSmMYoIoQ3FBCqOYIMpUt7goaT8p6S4kNjYWpqamcttMTU2RmpoKsViM5ORkSCQSpXVev35dZLsrVqzA4sWLFbbHx8cjKyurbDpfhqRSKUQiERhjsit65OtWmTGRGJ8IAHBt7IgfDk2R7d/ExRAeXWph+YCNCH4UisT4RAiEOpDkSZApEiNDlPnvQ4yMlExkpGT89/+iTGTKleVvy8pQfjWdw+UAAMICIpGSIIK2QBNZMdl4cO4psjNzZPVObjgPYZQQdh7WsHO3hrZAq5zfncpF5wpSGMUEUYbighRGMUGUqW5xkZaWVqJ6lHRXkHnz5mH27Nmy56mpqbC2toaxsTH4fH4l9kw5qVQKDocDY2PjahHwpPxVZkw8ifQDAPSc1Bk5yXl4/PcLJMeKkJ6SjrTkDGSKxACANaO2QZIrQWaaWGk7XB4Xuvra0NHXgY6eNnQNdGBqYwJdT23o6GlDR18buvo60NHXlpUXbLt+8A42Td2Bsb8ORefRbWVtSiRSRL2Jxon1F3Bp5w1Ic6U4ve6SLHk3dzSFc30HONfPvyLuVN8euvo65fuGVSA6V5DCKCaIMhQXpDCKCaJMdYsLDQ2NEtWjpLsQMzMzxMXFyW2Li4sDn8+HpqYmeDweeDye0jpmZmZFtquurg51dXWF7Vwut8oGFIfDqdL9IxWvMmKCMYbIwA8AgP2/HkdceDw0tNRhaGnwbwKtDSMLQ7x/HQ17dxs07dEgP1E20JEl0AWJtqaOBjgczmf1w7WBIwDgyu5b6Dy6rew94HK5sHGzQtSbGADA/IPfwqm+PT68icHbZ+/yH8/f4eCykxCn59/VYu5gCucGDnCu7wCXBg5wbuBQqkS8sieVK4zOFaQwigmiDMUFKYxigihTneKipH2kpLuQZs2a4eLFi3Lbrl69imbNmgEA1NTU0KBBA1y/fl229JhUKsX169cxffr0iu4uITUSYwyhvuG4c/wh7px4iPfB0QAAQwt9TF0/Fg07e0JNQ01W//Lum3hxwx/th7VEj0mdyqVPXF7+SdX/bhDmtFuELmPbwcLRDNGhsbjskz97eUE9Ho8HWzcr2LpZoePI1gAAiUSCqLexePM09KNE/ESRibhTfXvwDXQV+lEVJpUjhBBCCCElV+OT7vT0dISEhMieh4WF4eXLlzAwMICNjQ3mzZuHqKgo7N27FwAwZcoUbN68GT/++CPGjRuHGzdu4OjRo7hw4YKsjdmzZ2P06NFo2LAhGjdujPXr1yMjI0M2mzkhpPQYY3j7/B3uHH+I2yceIjokFjp62mjetxF6Tu6ErbP3gMfjoWnPBnK/KkqlUlz2uQkAcPKyL7f+CYx0oaGljqzMbPjfCYL/nSCFOhpa6hAYKSbKAMDj8WBTyxI2tSxlibhUKv3oingo3hRKxM3sTeDcwAEu9fOvhjs3cKClywghhBBCqpkan3Q/ffoU7dq1kz0vGFc9evRo7N69GzExMYiMjJSV29vb48KFC/juu++wYcMGWFlZYceOHbLlwgBgyJAhiI+Pxy+//ILY2FjUq1cPly5dUphcjRDyaYwxBD8JkSXasWFC6BrooEXfxpi+aTzqtasDVTVVvH3+DkDJrjKXFxMbY+wMXFemt3VzuVxZIt5hRCsA+Yl41Nv8RPzN0/xE/NCKU7Jx6obm+gAAU1tjDJvfH64NHcE31KWlywghhBBCqigOY4xVdie+RqmpqRAIBBCJRFV2IjWhUAgTE5NqMZ6ClL+yigmpVIrXj97i9r+3jgsjE6BnzEeLfk3QemBTeLSpDRVV+d8Dv/Zbqj9OxC/vvonn1/yhpqGKnKxcAEDj7l4Y9H1veLatgyt7bmHNuC34dtukcrvVvnDf6FxBPkYxQZShuCCFUUwQZapbXJQ0p6vxV7oJIZVPKpUi8H4wbh9/iLsnHyH+QyL0TQVo2b8pWg9sCvdWbuCp8Ip8fXlcZa5OuFwurF0tYe1qidjweDy/5o/llxbA0EwffreDcHrTRfzQYTGcGzigaY8GAABRQsmWsCCEEEIIIeWLkm5CyCcVzJSdl5uHl7f9Ic1h0DMWFJvsSiQSBNx9jdvHHuDuqcdIikmGoYU+WvVvilYDm6JOC1fweEUn2oWZ2BjL9uPayKnMjq+6KRgzHhcmhGfrOrBysUC38e3x7Kofjv1+FvuWHAMAhPqGIzNNDC1dzcrsLiGEEELIV4+SbkJIkUp7W7ckTwK/24GyRDtFKIKxlSHaDm6OVgObonYzl2pxq1BVVjBZ3KVdN9FxVBtwuVxwOBw07OyJ+h3dMa3RXIS8CMPdk4/w/Kofek7uhD4zusHIwqCSe04IIYQQ8nWipJsQUqSPZ8qu29INzfs3gKuXE2LDhHIzZT84/wzvXobj3unHECWkwdTWGB1HtkargU1Rq7ETJdplqLily0JehgEAfj37E3xvvsLZrZdxfO05tB/RCgNn94J9XZvK7D4hhBBCyFeHkm5CSJEKZsB2b+mGVdd/QUJCAkxMTODW1AUCIz4+vIlGcpwIm6fvhLmDKbqMbY/Wg5rBpYEDOBxOJfe+Zirp0mV2dazRuFt9DF/QHxd33MCpDRdwZfctNOpaDwO/7w2v9nXpb0QIIYQQUgEo6SaEFCnkRf5V067j2oHL5eLN43fYe/I4Hpx9ivSUDOiZCAAAw+f3x5hfh1ISVwFKO6mctkAbg77vhX4zu+Gfow9w7Pez+KnTEjh52WPQ973QelAzhdniCSGEEEJI2aFvWoSQIhXMgK2mqY6lQ9fhzvGHsHIxR5/pXdF6YDOkp2Tg+7beUNdSp4S7An3OpHIqqiroMKIV2g9viRc3AnD897NYMXIjdsw7gP6zeqDbhA7Q5muVZ7cJIYQQQr5KlHQTQoqkqaMOAPht5EYIjPmYvGEk+n7TAyoq+aeOy7tvAvhvRm1S9XE4HNTv4I76HdwR5h+BY2vPYee8A9i35Bh6TuqEvjO7w9jKsLK7SQghhBBSY9DsRoQQBVKpFJd8bmL/rycAAIbm+tjxai1aDmoimxRNKpXisk9+0l0wozapXuzdbfGjz3Tse/cHek3pjAvbr2GUwzSsHL0Job7hld09QgghhJAaga50E0Lk+N0OxNbvdiPkRRgadvbE0yu+EH5IwC99VqFZv/pw9XJGbJgQl33yZy8H/ptRm1RPRpaGmPDbSAxfMACXdt7AifXncW3fbTTo7IlB3/dC/Y4eNHyAEEIIIeQzUdJNCAEAxITFYftP+3Hn+EO4NnLE+rtLYWxlIFunO+BOEAKKmCmbbi+vGbR0NdH/2x7oM70r/jn2AMd/P4u5XZbCwcMWA7/vhbZDmkNVTRVA/hruooQ05OXm4eVtf0hzGPSMBUoncyOEEEII+ZpR0k3IVy4zTYxDy0/ixPoL4Bvq4Mc909FhRCvZbeQFM2VTcvX14Knw0H5YS7Qb2gK+t17h2O9nsWr0ZuyafxD9Z/VAo671MKPp/Pw13IugoaWOnYHrKDYIIYQQ8tWjpJuQr5REIsHVPf9g14KDyBBlYsiPfTD4xz7Q1NaQq1cwU7ZUKoW+LR8mJiayhJzUbBwOB/Xa1UW9dnUR/uo9Tqw9B5+Fh7B38VFZwl23lRua928AVy8nxIYJcWlX/rCDrMxsiBLSKOkmhBBCyFePvjkT8hXyux2I6Y3n4fcJW+HVwR0+rzdg9OIhCgk3IQXs6ljj+51TsS9sC1oPbJa/kQMYWxnAurYF6rZ0Q+fR7bDm5iK4t3QDAEgl0krsMSGEEEJI1UBJNyFfkZh3cVgyaA2+b+sNFVUeNtxbinn7Z9HVSFJihub6qN3MBQDQflhLBD54g5+7rMLCnisQFxEPLpeLLmPbAQBCXoRVZlcJIYQQQqoEur2ckK9ARmomDq84hRPrzkNgzMdPe2eg/fCWdJs4+SyihDQAQM8pnTFn11Rc8LmCo8vPYZLH9/hm3RhYOJnJ1SOEEEII+ZpR0k1IDSaRSHBl9y34LDyEzFQxhs7th0E/9KbbyMkXKZitPiY0FnWau6JpnwboMLgN/vx+L36fsBX2HjZy9QghhBBCvmaUdBNSQ/n+8wpbv9uN0Jfh6DCiFcYtHw4Ta6PK7hapAZy87AEAl3bdRPsRrQAA2gItzNk1Fc37NsKvg34HAKQIRWCM0RrfhBBCCPmqUdJNSA0T8y4Of/24D3dPPkKtJs7YcH8Zajd1qexukRqEy8sfluB/Nwg/dFiCZv3qw9XLGbFhQlz2uYm8XAkAYPcvRxDqF4GZf0yAnrGgMrtMCCGEEFJpKOkmpIbISM3EoeUncXL9BQiM+Zi7bybaDWtB47ZJmRMY6UJDSx1ZmdkIuBOEgDtBCnU0tNQxcdVI7PE+ionu3+PbbZPQom/jSugtIYQQQkjloqSbkCpMGBkPUUIapBIpQl6EQZSQBoGRLpy87MHlcSEw0oWhpQEu++SP2xaniTFsXn8MnNOLxm2Xg9j4VIjSxJBKpXgTJoQoVQwBXxMu9vlrlwt0NWFmzK/sbpY7Extj7AxcB1FCGvJy8/Dytj+kOQx6xgK52DSxMUbL/k2wfspfWNR/NTqOao1pG8ZBR0+7sg+BEEIIIaTCUNJNSBUljIzH+NrfISszu8g6quqqsHA0RUTgB3QY2Qrjl4+AsZVhBfby6xEbn4qRs3YhKzuvyDoa6irYv2HcV5N4m9gYQyqVQt+WDxMTE6V3VRiY6WPxqR9xde8/+GPWLry8EYDvd05Fw86eldBrQgghhJCKR0k3IVWUKCEtP+HmAO4t3dB1XDuYO5ohJjQWZ/+4jOCnocjNzgWXx8XGB8vh1sS5srtcrir7KrMoTSxLuD1rW6FH+7qwNNNDVGwKLtwIgG/gB2Rl50GUJv4qku7S4HA46Dy6Leq1r4vfJ2zFvK5L0XNyJ0xaPQqaOpqV3T1CCCGEkHJFSTchVZRUIgWQn3CvubkIXC4XGamZeHjuGd75RUBVTQW5OXmYvX0KajWu+Ql3ZV9lzs3N37ebsxm+G98BWdm5UFHhom1TF3RtUwczvI/AN/ADpFJpuey/JjCxNsJvlxbi/J9X8dcPe/H0ii9+8JkGj9a1K7trhBBCCCHl5qtIuv/44w+sXr0asbGx8PT0xKZNm9C4sfIJfdq2bYt//vlHYXv37t1x4cIFAMCYMWOwZ88eufIuXbrg0qVLZd958tUKeREGAOg6rh0A4OKO6/BZeAhZ6VkYNr8/9E0F2PDNdoS+DK/xSffnXmXOzZUgMysHGZnZyBTnfvT/ORCLc5Ehzv//DHEOMpU8Pt6enZO//6C3sRjzvfzn39hAB9pa6gCAw+eeomd7D9hY6sPEUJeWyyqEw+Gg15TOaNDJA2vGbcGcdovQf1Z3jF02DOqa6pXdPUIIIYSQMlfjk+4jR45g9uzZ2LZtG5o0aYL169ejS5cuCA4OhomJiUL9kydPIicnR/Y8MTERnp6eGDRokFy9rl27wsfHR/ZcXZ2+LJKyJUpIAwDomQiwqP9qPDj7VG7ctv+/M0YX1KvJCq4eu9eyxNhBzfDqTQxCw+ORmZUDQz1t6OpoIC09C95rz0MikUKclYOMzBzk5kk+2a6mhiq0NNVkD+1//2tipFtouzpevnqPfx69xfTRbVDX1RJammrIzslFZFQyIqKS4Bf0AQBw8/4bXL8bLGvf2sIAtpb5D2sLfdhaGsLaXA/q6qqf/X5U9q32ZcHC0Qyrb3jj1IaL2LXgEB7//QI/7ple439AIoQQQsjXp8Yn3WvXrsXEiRMxduxYAMC2bdtw4cIF7Nq1C3PnzlWob2BgIPf88OHD0NLSUki61dXVYWZmVn4dJ189gZEuAGD12D+QlyPB0nNz0aRHA1l5dGisXL2aKC9PgqCQWBw4/RgAEPg2Bt8uPgYdbXUY6mnLkmJzYz7S0rNgbKCDOi7m0NZSh1ZBQq2lDi2Nf5NnrX8TaQ01aGqogscr+XJqamo8/PPoLfi6mqjraiHb7uZkDgC4cCMALwM/4LsJ7dHIww6R0UmIiEpCZFT+f5/4hiMlVQwA4HAAM2MBbC0NYPPvoyAx1xdoffLqeFW41b6s8Hg8DJzdC426eWHV6M2Y1XwBhs7th5G/DISq2uf/KEEIIYQQUpXU6KQ7JycHz549w7x582TbuFwuOnbsiAcPHpSojZ07d2Lo0KHQ1pZf4ubWrVswMTGBvr4+2rdvj6VLl8LQsOhZo7Ozs5Gd/d8s1KmpqQDyr+BVxTGgUqkUjLEq2bevRUJUEgAgKyMbW56thKWTuezvIZVKccnnJgDAwdO2Qv5OFRETEokUIeHxeB4QiecB7+EXFAVxdi5UVXkAgN6d3NGrgwccbIzA5f6XmPoGfcCMX46igYcN/te/SYn3V5pjcbI1AgBcuO6Pzq3c5PYvlTJcvOEPAHCxN4GFqQAWpgI09bKXa0OUJkZkdDIiP0rGHzx7hxMXn0MiZQAAHW112Fjow8biv2TcxtIAlqYCqKjwkCzK+O9WezdLdGtXF5ZmAkTFivD3zQD4BkUhKzsPyaIMmBjqlPj4PldZxIW1qwXW3/0VR1aexv5fT+DB+af4wWcaHD3tyq6jpMLQvx9EGYoLUhjFBFGmusVFSftZo5PuhIQESCQSmJqaym03NTXF69evi33948ePERAQgJ07d8pt79q1K/r37w97e3uEhoZi/vz56NatGx48eAAej6e0rRUrVmDx4sUK2+Pj45GVlVWKo6oYUqkUIpEIjDGlywCR8pObnYv93idxY+9dAPlJ98rRm9B6SFOY2hkhLjwBt488RPDjUACASCSCUCgs936VR0xIpQzvY1IQ8CYOAW9iEfhWiAxxDtRUeXBzMkH/rnVR18UU7yITsf3IE1gYaYKvxZCQEC/Xzus3kQAAHnLL7b0QpaQAAHyDovDNggNo39QBpka6iEtIw42H7xAUIpTVEwqVnwcAwFRfBab6JmhU97/hLbl5EsQlpCMqVoSouFRExaUiNEKI24/eIjMrN//YuByYGulAwM+f7dvcRBeDutWBlTkfOlpqMDc0Rn23tvDecBVBIUIkJiRCqFP+48nLMi46TmwF52b2+HPWPsxoOh/9ZndDz2kdwVMp+v0kVQ/9+0GUobgghVFMEGWqW1ykpZVsmGeNTrq/1M6dO+Hu7q4w6drQoUNl/+/u7g4PDw84Ojri1q1b6NChg9K25s2bh9mzZ8uep6amwtraGsbGxuDzq94toFKpFBwOB8bGxtUi4GsKYWQCVg7Zgnd+ERi/Yjj2/3oC2ZnZCH4UiuBHoQr11bXUYediCxMTo3LvW1nEBGMMH2JSZFeyX7x6j5RUMVRVeKjrao4hvRqgfl0buDmZya5uA4CBQQy2H3mCu8/eY1CvZgpXme8+y7/qX9/DUelcDWWBcTSgoa6CrOw8BIUIZUn2xzTUVWBvawmTz7it29ICqO9RaJ+MISklE5HR+VfGI6OT8cQvAgAQI0zDwrVXAAC1nc3QqZUb2jd3RZ/O9RAUcgUJojw0L6f34mNlfa4waW8Cz6fuOPDrCRxddRp+14Pww+5psKllWQa9JRWB/v0gylBckMIoJogy1S0uNDQ0SlSvRifdRkZG4PF4iIuLk9seFxdX7HjsjIwMHD58GEuWLCl2Pw4ODjAyMkJISEiRSbe6urrSyda4XG6VDSgOh1Ol+1fTPL3iixUjNkBTRwPr7vwK14aOaD+sJUQJaZBKpAh5EQZRQhoERrpw8rIHl8eFwEgXJjbG5dqvgkm78vLy8NwvFBKEQ1+gVeJJu2KEIjzzj8SLgPd4FhCJhKR08LgcuDmbo3cnT9Svaw13V4tPTiymopJ/qvINisKsxcfQvd1/s5df/PeW6oJ65RWv5qZ62L9hXIVPYGZsqAtjQ100cLcFAOw98RB/HbyLdb8MhJ5ACyHh8bj14A027/kHm3ffgotD/p09CcnpFfbZLetzhYamOsYvH47mfRph1ehNmNbwJ4xbNhz9ZnWn81E1Qf9+EGUoLkhhFBNEmeoUFyXtY41OutXU1NCgQQNcv34dffv2BZD/68n169cxffr0T7722LFjyM7OxsiRI4vdz4cPH5CYmAhzc/Oy6Db5ykilUhxafgp7vI+gYRdPzN03E3zD/MnRTGyMZUm1ayOnCu/b50zalZCUjucBkXjmn381O0YoAocDuDiYolPLWqjvbgNPNytoaaqVuB8CXU3ZVWbfwA/wDfygtB8CXc3SH2QpmBnzZcdZMIFaRSu4vTw+KR2NPO3gbGeCbm3rQJQmxs0Hb3Dk7FMAwP6TjxEZlYzOrd3QpJ693J0D1YVbE2dsfb4aPgsOYdv3e3DvzGP8sGsazB1Mi38xIYQQQkgVUaOTbgCYPXs2Ro8ejYYNG6Jx48ZYv349MjIyZLOZ/+9//4OlpSVWrFgh97qdO3eib9++CpOjpaenY/HixRgwYADMzMwQGhqKH3/8EU5OTujSpUuFHRepGdKS07Fq9GY8uvAcI38eiBE/DyhyXoDKILc+tpslWjawRi0XG8QIU+XWx75+7zVihCI893+PyOj8CeAcbIzQoqEj6te1Rr061uDrlOz2G2XMjPmVcpW5KnKxz79l/MKNAHRtU0d2q71AVxO9O3rg6p0gvI9JRu/OHvANjMLc305DV0cDbZu6oHNrN3i6Wcndnl/VaWip45t1Y9C8TyOsGfcHJnl+j8lrRqPHpI60BjohhBBCqoUan3QPGTIE8fHx+OWXXxAbG4t69erh0qVLssnVIiMjFW4LCA4Oxt27d3HlyhWF9ng8Hvz8/LBnzx6kpKTAwsICnTt3xq+//kprdZNSCXkRhsUD1yAjJQNLz89D425eld0lBQUzMnrWtsIG70FISIiHpjYfGZk5cLYzQXBoHLKyc7F1321YmeujgbsNxg9tjvp1raEv0C6m9dKpCleZq4KC85Vv4AfM8D6ieKv9v3cB9GjvjtkTOuJdZDyu3nmNq3eCcO6aH0wMddGxZS10auUGJzvjapO4eratgz99f8dfP+zDhm/+wt1Tj/D9jm/ApNJKH4JBCCGEEPIpHMYYq+xOfI1SU1MhEAggEomq7ERqQqEQJiYm1WI8RXVzyecmNk3bDtvaVvjl+ByY2ZX/hFef48xVX6zedhXzpnWBvkAL+08+REBwLKSMwdRIF6ZGfPi9jsKUka0wsl/Jl+oin+9z1+lmjME/OBpX7wThxr1giNLEsLMyRKdWbujUqhYsTPU+qz+Vca54cukF1k7chsxUMXKzc5Gb84n3QksdOwPXUeJdgejfD6IMxQUpjGKCKFPd4qKkOV2Nv9JNSFWSk5WDP2buwsUd19FtfAdM3zQOaholH9tc0RKT0gEAu44+QFx8KhxtDDB7Ygc08rSDhakAvkFRmP7zYUil9NtdRfncW+05HA48alnCo5YlZo1thye+EbhyJwj7Tj7E9kN3UdfV4t8Z0F3K/C6Fstaoqxf+8vsdv43ahMcXnwMAajVxRq8pnWDuaIaY0Fhc2nUT/neDkJWZDVFCGiXdhBBCCKk0lHQTUkFiw4VYMuh3hAe8x/c7vkHXce0ru0tFSkzOwKlLL3Dk/DMAgJ6uJn6e0Q2mBiowNTWV/fIYFZsC4L/JvUjF+NJb7VVUeGjWwAHNGjhAnJWDu09CcfVOEDb63MTGXTfQ0NMWnVvVRqvGTqWa8K4i6err4H/eg/D44nPwVHmIDomFhrYG3Fu6wb2lGzqOaoM57RbB/04QpBJpZXeXEEIIIV8xSroJqQBPLr3AipEboc3XxIZ7S+Fc36Gyu6RUSHg8jp5/iqt3XkNFhYvmDRxw/V4wNDRUUdfVAgkJ8bK6UinDxZsBAP6b3ItUP5oaav/eYu6GlNRM3Lz/BlfvBuHXjRehrqaClo2c0KmVG5rUs5ObAV1xKbmwUi0lVxZCXoQBAKas+R/8bgfi18Fr0eubLpi2YSx4Kjx0GdsO/neCEPIirFJm/yeEEEIIASjpJqRcSaVSHFh6AvsWH0OjbvXw094Z4BvoVna35EilDI9ehuHIuWd46hcBE0NdTBzWAr06eSA6ToTr94LhG/gBsxYd/Xf28hxEx6XKTdpVHcbckOLp8bXQr2s99OtaDzFCEa7dzZ+Abe5vp8DX0UC75q7o3MoNxoa6+N93PqUeV17WRAlpAABHL3v0md4Nf++4jg1TtyM2XIiFh7+DhaOZXD1CCCGEkMpASTch5SQ1KQ2/jdqEp5de4n+LBmP4gv5VKjnNzs7F5dtBOHr+KcI/JKGWoym8v+2Bds1coKKSf0VToJvz3/rYQVHwDYoC8FCunYpYH5tUPHMTAUb1b4JR/ZsgNCIeV24H4drdIJy54gsDPa0SLSUnShOXa9ItMMr/ASsmNBbuLd3QfWJHmNoZY8mg3/Fd65/RaVQbuXqEEEIIIZWBkm5CysHb5++wZOAaZKSKsezifDTqUq+yuyRTMF779BVfiNLEaNXYGT9M6QyPWpYKy0d9PGnXf7cRq1b4bcSkcjnaGuObUcaYPKIV/IOjcPT8M/zz8C0AIDU9C8mpWTAz4sOrjg26tqmDGd5H4Bv4QbbkXHlx8rIHAFzadRMdR7UBl8tFg06eWH93KRb2XIGd8w/K1SOEEEIIqQyUdBNSxv7eeR2bpu+EvbsN1txcDFPbqjFrcmhEPI6cf4art4OgosJFj/buGNSjPizN9D75uoJJu6RSKQz5vGqzhAMpe1wuB55uVgj/kIh/Hr7FoB71kZySgROX/HHkgh96d/LA6IFN0b1dXfgGfsCbMGG5rqnO5eXHof/dIMxptwhdxraDhaMZokNjYWCuB2FkAgAg8MEbGtNNCCGEkEpDSTchZSRbnI3N03fiks9N9JjUCVM3jIWaumql9ulT47V1tTUqtW+k+hKligEAbZu5wN3VAhGRUbj3IhoHTj/BxRsBaN3EWa5eeREY6UJDSx1ZmdnwvxME/ztBCnW4PC62zt4NngoPvad2Kdf+EEIIIYQoQ0k3IWUgJiwOSwb+jsigD5izayq6jGlXqf0pyXhtQj5XwRJxUbEpcHe1gKaGKob3aYQ+nT1x8PQTHD77FADwOjQWWdm50CinH59MbIyxM3AdRAlpkEqkCHkRBlFCGgRGunDysgeXx4WuvjZObfwbm6bvQHRoLCauGgkejz4DhBBCCKk4lHQT8oUeXXyOlaM2QkdfBxvuL4NTvcobP5qUkoFTl17i1OWXxY7XJuRzFSwRd+FGADq3cpNt19XWwMRhLfEsIBKBb2Jw7+k7DJm2A2MGNkOvju7l8oOPiY0xTGzyh3AUdQv5N+vGwNzRFFu/9UFsuBBz982EhpZ6mfeFEEIIIUQZSroJ+UwSiQT7lxzH/l+Po2nPBvhxz3To6uuU6T4K1kKWSqV4EyaEKFUMAV9TYRKzzx2vTUonKi0VyWIxJFIpAuOFSMoSw0BDE7WNTcDjcqGvqQlL3Zo/qVzBmP6ilpILfBMDAFj2Y2/cvP8Ga3dcw6GzTzBhWEt0bFELXG7F/wDUd3o3mNoaY/mw9ZjTzhtLzvwEAzP9Cu8HIYQQQr4+lHQTooQwMv6Tt6xyeRzsmHsAz6/6YezSYRg6t2+ZTy4WG5+KkbN2fXItZFUVLtyczeEXFFXjx2tXdsIblZaKzvt8IM4r+u+hqaKCK6PG1vjEW6CrWaKl5JxsTdCyoROG92mE7YfuYsn6Czhw6jEmj2iJZvUdKvzui2a9GmLt7SVY2Os3zGy2AEvPz4NdHesK7QMhhBBCvj6UdBNSiDAyHuNrf4eszOyiK3EAXX0drLi0EPU7epRLP0Rp4v/WQq5thR7t68LSTA/hHxJx6MwTfIhJQW6eFKlpWTV+vHZVSHiTxWKI8/LAAdDIwhIDa9eFrUAPEaIUHA8MwJPoKIjz8pAsFtf4pLu0S8k52hrjt7n9EBAcjW0HbuPH5afgXssSU0a0gmdtqwrtu3N9B2x6uBwLe67Aty0X4pfjc1C/g3uF9oEQQgghXxdKugkpRJSQlp9wcwD3lm7oOq4dzB3NEB0Sg0PLTyEqJBZgwE97p5dbwg1AtsaxZ20rbFo8BCmpmXLjtQW6GhClZWH+9C6o7WxRbv2oCioi4ZVIpRDn5UGcl4us3Dxk5uUiKzcX4rw8ZObm4nVCPADARiBAe3tHRKWlQpiRAQtdPmY3a4kVd2/BNy4OknJem7qq+Jyl5Oq6WmDT4iF4/DIcfx64g2k/H0az+vaYNLwVnP8dJ14RTKyNsO7Or1g6ZC3md1uGb7dNQtdx7Sts/4QQQgj5ulDSTUghUkl+0uTe0g1rbi4Cl8tFtjgbl3bdQFRI/vq/STEp0DMWlGs/3oQJAQCdW7th15F7OHjmCXg8Lnq0r4tBPRrgZeAHrPjjEt6Gx9f4pLsgkW1kYYl9/QYhOi0NqTnZsBHoYUrDJki6cwshyUn4++0bPIr6gKy8XGT+mzBn5eb+m0DnJ9SZubnI+jeRzsr7L6nOkUhK1JcPqan448kjaKqqIEciQUpWllz5uLMn4WJoBEtdPiz5fFjo8mGhq5v/XJcPdZUvP+1W9q32X4LD4aCJlz0aedrh5oNgbD90D2Pn7EXHlrUwYWgLWJlXzDhrbb4Wfj07F5un78TvE7YiOjQWY34dSmvQE0IIIaTMUdJNSCEhL8IAAF3HtQOXy0XMuzgsHrgGH4Kj8eOe6ZBKpFgzbgtCXoQVOVtyWShY43jX4ftITc/CsD6NMLR3Q/B18sdrxyely9WriSRSKd4lJ+OAvy8AQJiZAa+//kBmbq7S+tuePYamqio0VVShqaoCLRVVaKiqQlNFBZqqqtBRU4exlva/dVTk6ub/t/D2f5+rqOKA/0tsfvIIB/sPRiPL/26JzsjJQVRaKm6GvcPK+3fgZGAIY21tRIhScP99JOIy0sE+6qORlpYsAbfk82X/b6GrC0s+H3z1T4/Hrwq32pcFLpeDDi1qoU0TZ1y8+Qo+R+9jxCwf9OzgjrGDmsHIoGwnJVRGRVUFs7ZNgoWTGbb/tB8xYUL8sGsq1DTUyn3fhBBCCPl6UNJNSCGihDQAgLmjGd4+f4f53ZZBi6+JjQ+Ww8HDFv53guTqlYfouBRcv/caAMDX1cDmX4fC2kL+CmBUbAqA/9ZMru4kUilCk5MQIIxDgDAO/sI4BCXEyyXY5jq6GFLHHbWNTKCvqSlLkIPi4zHx/Gl817Q5pjduVi79M9fRBQBEiFLkkm5tNTW4GBrBLy4WANDX1Q3D3D1l5TkSCWLT0xCVmoqotI8eqWl4FS9ETFoacqT/XWXXUVNTmpQX/H9iZmaNGluuosJD704e6NLaDScuvcT+k49w6dYrDOjuhZF9G4OvW77xzeFwMPiHPjCzN8HK/23Cj+8TsPjUjxAYVf33jhBCCCHVAyXdhBQiMMpPrp78/Rxn/rgMa1cLLL+4AHzD/O3RobFy9cpSTm4eDp55gr0nHkFbM/9qm66OhsLSX1Ipw8WbAQD+WzO5OskrlGAHCOMQGC+UXb21FejB3cQUnRycUNfEFK/jhVh69x/0q1UbA2vXVWjv/vtIAIChpla59bm2cf77fDwwAP3d6oD70czbUsZwPDBArl4BNR4PNgI92Aj0lLYrZQzxGRmyZDw6LfXfBD0Nj6I+IDo1Fem5ObL6qv/e/qyrpg4bPT3EpKfBXFcXvVxqob9bHQw/cQSPo6Oq3dhydXVVDO/TCL07euDw2Sc4cv4Zzl7xw/C+jTCoR31olvPV59YDm8HIyhDefVZiZvMFWHZhPqyczct1n4QQQgj5OlDSTUghTl72AIDDK8/Ao3VtLDnzE7T+vdomlUpx2eemXL2y8uhFGNbtuI6Y+FQM6dUALRo6YtrCw/ALisIM7yPo3i5/9vKo2BRcvBkA38APAFDuY1ALxg/n5uXhcdg75EaGwVBTq8Tjh/OkUoQkJcon2AnxyPo3wbbX00ddE1N0cXRGXRNT1DY2AV9dXa4NbVVVAKVPeMsS79/3+Ul0FIafOIKBtevCRqCHyI+uMH9cr6S4HA5MdXRgqqOD+uaKY/MZY0jNzv736ngqzr4JwoW3b2Crp4fghARcDQ3Fuof3oaGigiaW1jDVyb8t+5UwDp5m1S9p1NFWx4RhLdG/mxf2nngEn6MPcPzic4we0BS9O3lCVbX8Zuiv3dQFGx8sx4KeKzCz2XwsPvUj3Fu5ldv+CCGEEPJ1oKSbkEKeX/cHADApQ15uHu6ceAgLRzNEh8biss9N+N/Nv72cyyubZDcuIRWbfG7i1sO38KpjjRVz+8Le2gix8an/rYUc+EGWZH9MQ10FgnK8/ba044fzpFK8LZRgB/2bYHMA2OvnJ9hdnVzg/m+CrVsowVamvBLe0ii4nV2cl4fH0VF4/O8+P6apogJ9zbL9e3A4HAg0NCDQ0EBtYxO8SUrAhbdvsLBVWzSytIKUMQQnxONOZARuR4bj75C3AIDf7t+BrzAOrWxs0cLatsz7Vd4M9LTx7fj2GNKrAXYduY8NPjdx+NwzjB/SHJ1auYFXRp+/wswdTLHh3lIsHrAGP3Vagjm7pqL98Fblsi9CCCGEfB0o6SbkIxf+ugqfBYfA5XEhlUjx6l4wXt0LVqinoaX+xbeX5+ZKcPTCM+w+9gBaGmr45dse6NSyFjj/XsX9eC1kqVSKN2FCiFLFEPA1la6FXB4+XqqroYUlulhao46VNd6npeLoK388jYmGOC8PK+78g+i0NAQlxCNbkl/fQd8AdU1M0d3ZVZZg66h93i3ClZXwfsxSl48ro8ZW+qzhBhr5x1gwtpzL4cDN2ARuxiaY1KARDvr7YuHNa/A0McPL2BgcCwwAB4C7qRla2diilY0d6pmZQ41XPdZ0NzcRYMGMbhjetxG2H7qHpZv+xsEzTzBpeEu0aOiIuIS0Mv+M6OrrYMWlBVg36U+sGLkRMe+EGL6gv+yzSQghhBBSGpR0E/KvwytPY+e8A+g7vRsGzO6BtKQMSCVShLwIgyghDQIjXTh52YPL40JgpAsTG+PP3tdz/0is3XEN76OTMaB7fYwf0hzaWopXfAvWQgYAN6eKv1X446W6tvfsi7P+vjj3NhgB8ULZutUA4CeMRUNzS/R0cZXdIv65CbYyVSXhLZjUDECl3bpd3Njys8H5d2LMad4SnmbmiElLw933EbgTGY6D/r7448kjaKuqopmVDVra2KKVrR3sBHpVPqG0tzbC8h/74NWbGPx54Dbm/nYaLg6mCH+fgJzcopd701BXwf4N40qdeKuqqeIHn2kwdzDF7l8OI/pdLL7dNgmqaqpfeiiEEEII+cpQ0k2+eowx7Jx3AEdWncHInwfif4sGg8PhwMwuv7wslwVLSE7H5t23cO3ua7jXssSO1T3hbFd1J0IrmJE7RyJBM5+/kJmbC0d9A3iYmqGPqxsSMjOw9eljfNOgsdyM3eWhKiS8VUFpb7U319XFoNp1Mah2XUikUryKF+JOZATuRoZj6Z1byPtHCis+H61s7NDKxg7Nra2LXbasMtVxMceGRYPx1C8C63fdkCXczvYmGNSjvmzegws38uc9yMrOgyhN/Fl3hHA4HIz6ZRDMHUyxdsJWCCMT4H18DnT0tMv6sAghhBBSg1HSTb5qEokEm6btxIW/ruKbtWPQ/9se5bKfPIkUJ/9+gR2H70FNlYf507qia9s64HKr3tVFiVSKBx/e4/yb1zjz71XTRLEYUxo0QlN9I9R3dJRN3vY46gO2Pn2MpKyau1Z4VfMlt9rzuFx4mJrBw9QM0xo1QXpODh59eI87keG4ExmBQwF+4HE4qGdmnn8V3MYOHqZmUFEyVv5LJ9j7EhwOB4087bBgeldMmnsQ6moqeBsmxMPnYZg6qjU83azQtU0dzPA+At/AD5B+4UzuHUe2homNERb1W4VZLRZg6fl5MLc3LaOjIYQQQkhNR0k3+Wrl5uRi1ejNuH3sAb7fORVdx7Yrl/34vY7C739dw7vIePTp7IlJw1uBr1O1riRKGcOL2GicC36NiyFvkJCZCRu+AM2srHErIhwzGjdF/1q1IRQK5V4XKUoB8N84Y1L+yvJWex01NXRwcEQHB0cAwIdUEe5ERuBORDh2vXiODY8egK+ujuZWNmhla4dWNraw4gtKPcFeeXkbnj/E4bsJ7QFwsPPwPYz6bjemj26L3p080L1dXfgGfsCbMOEXD8/waF0bG+4vw4IeKzCz2QIsOfMT3Jo4l8FREEIIIaSm+yqS7j/++AOrV69GbGwsPD09sWnTJjRu3Fhp3d27d2Ps2LFy29TV1ZGVlSV7zhiDt7c3tm/fjpSUFLRo0QJbt26FszN9AasusjKzsWTQ73h53R8Lj36PVv2blPk+kkUZ2LrvNi7efAU3JzNs/20kajmZlfl+PhdjDIHxQpx78xrn3wYjOi0NZto66OPqhp4uteBhYgq/uFjcigjH8cAA9HWVXzqpopbqIorK61Z7K74Aw+p6YFhdD+RJpfCPi8XtyHDcjYzALzevQcIY7PT0UcfYRJZwNyo0wV7BLe7ivDwki8XlmnSLUvPvsLC2MICnmxXaNXPB5j3/YPWfV3Hr4Rv07uQhV+9LWbtaYuODZfDutxpz2nlj7v5Z5XLuIIQQQkjNUuOT7iNHjmD27NnYtm0bmjRpgvXr16NLly4IDg6GiYnyRIHP5yM4+L8ZqwtPMLRq1Sps3LgRe/bsgb29PX7++Wd06dIFgYGB0NCoWlcwiaIMUQZ+7r0Sb5+/w9Lz81C/o0eZti+RSHHmqi/+OngXHA4HP0zuhJ4d3MttiaPSCk1KxNk3r3H+TTDCUpJhoKGJbs4u6OVSCw0tLOUm5vp4/PCIU8fQ2dIadXNz5JKrj+uRmkOFy4WXuQW8zC0wq0lzpGZn4cGH97gTGYHr70IAAAWREi8WQ1ddHQOt66K/Wx0MP3EEj6OjZBPxlRcBP/8Oi6jYFHi6WUFbSx0/fdMZbZs647ctl7F0498AAL5u2Z2X9YwFWH3tF6wasxm/DvodE1eNwsDZPav8RHSEEEIIqTw1Puleu3YtJk6cKLt6vW3bNly4cAG7du3C3Llzlb6Gw+HAzEz5FUnGGNavX4+FCxeiT58+AIC9e/fC1NQUp0+fxtChQ8vnQEiZSBaKML/bMsSGCbHy6i+o3dSlTNsPfBuD37dfQ3BoHHp2cMeUka2gx9cq0318jg+pIpx/E4xzb14jKCEeOmpq6OLoDO827dHMyhqqRSwf9fH44SfRUflJ9pOHcnXKe6kuUjXw1TXQxdEZXRydUdvQCAtvXUcfVzek5+Rg3+tX+DPAF/VMzTHCwxN9XN3wODoKgfHCcp30zsU+/4fTCzcC0LXNf3MkNPGyx+61ozHyWx9k5+Th0q1AtGjgCGPDL1vmr4CahhrmH/wW5g6H8dcPexH6Mgx9Z3QDh8Mpl9UOCCGEEFK91eikOycnB8+ePcO8efNk27hcLjp27IgHDx4U+br09HTY2tpCKpWifv36WL58OerUqQMACAsLQ2xsLDp27CirLxAI0KRJEzx48KDIpDs7OxvZ2dmy56mpqQAAqVT6xZP8lAepVArGWJXs2+cSRiZgXtelyEwVY83NRbB3tymz4xOlifHXwbs4f90fTrbG2LJ0KOq6WgBApb2H8RkZuBjyBuffBuNFbAw0VFTQ3s4BMxo1RRtbO6ir/PfxL6qP5to6uDxiNJLEYuRJJXj87h3yVFWgr6mF2kbG4HG5MNDUhLm2To2KFfJpBRPnDaldFw3MLRATF4eAjHQceuWPH65ego5q/nJxIcmJFRIXvoEfMOOXw+jWro5s9vK/b75CckomAOB9dDJGfbsbM8a2Rdc2tcvsqvTYpUOhLdDEznkHcf3AnSLrqWupY0fAWpjYGJXJfqu6mvjvB/lyFBekMIoJokx1i4uS9rNGJ90JCQmQSCQwNZWfZdbU1BSvX79W+hpXV1fs2rULHh4eEIlEWLNmDZo3b45Xr17BysoKsbGxsjYKt1lQpsyKFSuwePFihe3x8fFy48WrCqlUCpFIBMaYbKbq6iwmVIiVQzaDw+Ng/omZ0DbVUJgU7HNIpQw3H4Zi/+kXkEikGDuwIbq0cgGPxy2T9mMzMiDKyYaUMbxJTkJKdjb01NXhom8ALocDgZo6zLT/W74oNTsbNz+8x7X34XgRLwSXw0FTM3MsatIcLS2soKWav8awKCmpxH1QAWACDqTgoo2hMQQCgXxMiLMgFFe9GC4PyXkpyJRmQMqkiM6JQYY0E9pcLViomYPL4UKLqw19Fb3K7ma5U83NH8/96sN7WPNUkJ6aCk+BAF7NWuJ9XQ+sff4Uj+Ji4PPyBQJiYtDf0QUtLCyVzoL+JfJyMqGuxkN2jgS+QVHwDVKcyV1djYefZ7THuetBWPHHZVz5JwBThjeBvqBs7kCx87L6b19aahjwQw841LOFMDwB/xx+gODHocjOzEb4mwhAo3p8gfhSNe3fD1I2KC5IYRQTRJnqFhdpaWklqlejk+7P0axZMzRr1kz2vHnz5nBzc8Off/6JX3/99bPbnTdvHmbPni17npqaCmtraxgbG4PPL7+Jhj6XVCoFh8OBsbFxtQj4Twl5EYZl/TdAYMzHir8XwMjSoNjXxMWnIiVNDKlUirdh8UhJE0NPVxPO9vnvh56uJkTpWVi3/QZevY1B51Zu+GZUaxjql936vdFpqRhx8kixM0SfGjwMAfHxuPAmGHfeR0DKGJpZWWNpu47o7OAEvTKaZ6CyYyIxOxFpeemQMikiMyORlpcOXRUd2GjZgMvhQldFB4bqhuW6/7WvNiBHmlNkHTWuGpbXWVKu/agKGkslwLPHuBz1HiMbNpaLCyNjY0h9nwMAZjRqgjuRkZh3/zZMtXUwpE5dDKntDlMdnTLph4kJsH/92GI/q6bGfDT2csXdJ6FY8+dVzF52AbPGt0enlrW++Kp3siD/riWn+vYQxafi8vZbWHLmJ7Tq1Qz9pvXADx2WIOBOEAQCQZHziNQ0lX2uIFUTxQUpjGKCKFPd4qKk83nV6KTbyMgIPB4PcXFxctvj4uKKHLNdmKqqKry8vBASkj9xUMHr4uLiYG7+31jFuLg41KtXr8h21NXVoa6urrCdy+VW2YDicDhVun8lEXA3CAt6roC1qwWWX1wAfgnGdMbGp2LUd7uRlV10ssvjcsAYYGtlgE1LhsCrjnVZdhsAkJKdDXFeHjjInyF6YO26sBXoIUKUgqOv/PE0JhrivDz0PnIQORIJGphbYGGrtujm5AJj7bJL/j9WWTGRmJ2I+a9+KTbh/c19abklvBnSTNn+XXVd0MqoJUzUTSDMFv6fvbsOb+p6Azj+vfG0qbsgxSlS3N1tyGBjsI2NuQ/YBoPhMHQMfnM3ZGMbDIa7uw0rTpFSd0vSJPf+/kgplBYvfj7Pw9M2ObnWQ5r3nnPel01JmzmWeZxcOZdsOQc/1cO9flebtzRhd8wFnl04z5lgz27LT7C3Oy/BXtuy5RnYsAmHE+KZfXA/3+/dzZe7dtC2TDmerh5Bo9CStx30BgV4EhTgCUCVCiHXbNusfnkiwkOZ8eNaxn+2jA3bT/DBq23x9rz1/y+n958FoMfbHandrgYjuk7i/ZajmbDsI6o2rkSH/i05tOkIp/efpXL94s0hcT97GP5+CMVP9AvhSqJPCEV5kPrFjR7jQx1063Q6ateuzZo1a+jevTvgvHuyZs0a3nrrrRvahsPh4ODBg3Tq1AmAsLAwAgMDWbNmTX6QnZGRwY4dO3j99dfvxGkIt2jnsn2M7fUJlRuUZ8yCIbi43Viyr/RMc37AHREeSudWVQkJ9CQ6NpVZ/+zkfEwqDlnhic61eLNfczSaopOQ3a6LmZ/rBocwp2dvHLLMlvPn2B59niNJSfntnqpSjZdr1SXkPpwxUVwy7Vk3FPBm2rNuKuhWFAWH4sCm2LDJdmyyLe97W4Hvc2UbF3KcgWSA3p/aXrXIsGeQZc/CQ+tB1+Au/HV+HmdyzuKQHXfkGlzu8lH/sznnyLJnYdKYKHWXRv1vNsFeFf8AJrRux4dNmrPgaCSzD+7n2X/+JszTi77VIuhVuQoed6nyg4ebkVEDOtOiQXmmfruKZwf8wsCXWtO6ccVbugGQnuScVhZUNhCfIC+mrRvN8McmMbTDeCYs/YjgsoEF2gmCIAiC8Oh5qINugEGDBvHcc89Rp04d6tWrx4wZM8jOzs7PZt6vXz9CQkKYOHEiAGPHjqVBgwaUK1eOtLQ0pk6dytmzZ3nppZcA552XAQMGMH78eMqXL59fMiw4ODg/sBfuvfVztzDp2c+p16kmw/8YiM6gu+HXXkyIEBEeyudjeqNSSZw+l8iydYc5H5OKh7uR9Awz7ZpVvmMBN0BkonNNeMdyFfjfjq3MPrCfFIuZMl5evFSrNlqVmk+2baaij+9DHXADyIrzd1LGNYzHgjqTmJvEqexT2GQb5U3lSLAkkmpLZcGFfzGoDdjk3PygObeoYPqynxWUmzqWeGsCf0fPRytpcSh2LLK1wPPjj0zEU+eJh9YDD607HloPPK/8XueBu8Ydvbrw7JfrSbYm8+HB4fd01D/EzZ2Vz/Yn1WzGZrezM+o0Nq0GH6ML4X7+qFUqvIzGQjW63fV6+kXU5NnqNdgVc4FZB/5jypaNTNu2mS4VKvJ0tRpEBNydWvbNG1SgeuVQpv+whtHTF7N+2zHee6UNXh43N+rt4eucPRN7Ko5qTSpjNBkZv3goIx6bxLBOH9PtrY4F2gmCIAiC8Oh56IPu3r17k5iYyMiRI4mLi6NGjRosX748PxHauXPnCkwLSE1N5eWXXyYuLg4vLy9q167N1q1bCQ8Pz28zePBgsrOzeeWVV0hLS6NJkyYsX75c1Oi+Tyz9fjUzXvuOVk834f0f30CjvblufjzKGex2blUVh0Pmuzlb+H3hLoIDPZk+8gkSkjOZ+OVyjkclULncnSuHdCY9DYBJWzaikiSerFKNJ8KrUtnXD0mS2HkhGriUSfphkSvnEmeJJ9YcR6wlljhLHMczTwBwOjuKT45PR4UKg1qPVqVFK+mQcQbl0eZofHQ+zsdVWgySMf97rZT3VaVBJ2nRqnRFPnfpe21eO+e/1fFrWRiziKEVh1DJ49I0YYvDQrotg4Nph5h5bjbVPatR0qUE6bZ00m0ZnMs5x8G87x1KwVFwo9qYH4xfHqRf/OeZ99Vd64ZKcr5P3alR/5sV4uZOiJs7siwTpFLj7+9/w1OsJEmiXkgo9UJCSczJ5s/Dh/j90H7+jjxMVf8Anq4WQdcKlTDmJf67U7w8XBj73mO0aFiBT79fzbMDfuG9V9rQsmHFG95GuZphACz/aR1tnm2OSqXC6GrID7z/nLqwQDtBEARBEB49D33QDfDWW29ddTr5+vXrC/w8ffp0pk+ffs3tSZLE2LFjGTt2bHEdolBM5k5ZyA8fzqLbmx1443/9b2ktSHqGM4jVatW8/tEcTpxJpH/vRvTtVhedVsN/kdEF2hW3kynJfLtnF/8cjQSgacnSTGrTDm9jwWzL5/KCcm/Dna2RfXEqs91h53DmYbBLuOvcb2sqs6IopNsyiLXEEmuJyw+wY81xJOcm548+u2lMBBmCcNe6k5ybwhOhvajrXQtfvS9q6dIsg2MZx5lwdDLN/ZrxWHDnYj3/i7x0XgAk5iZSiUtBt0FtwKA2cFztnE1RwzOClv7NC71eVmSy7dn5wXiaLT3ve+fP6bZ0LpgvkG5zTlu/nISEu9YND60HWskZiHrrvKjlWROdSoub1pXybg1p7NuQSUencizzeP7sgPudn4srb9atz2u167L+bBSzD+5n2JqVTNi0gZ6Vw3m6WgRlve9sYrpWjSpSs0oon3y7mhGfLKJ14+MMfKk1nu7Xz3CuUjvfYw5uPsL7LUfTvn9LgssGEnMqDpvVhiI7+/KJvaepWLfcHT0PQRAEQRDuT49E0C08/BRF4adhc/hj8gKeHt6T58b0vuUETR7uziB24hfL8fNx45sJfQqMaF+ISyvQrrj8FxfLN7t3svL0SQJdTTxXvSY/799LhtWC5xWBtawo/B15CIBwvzuXEbnIqcypBdtcayqzXbYTb00g1nxFcG2Jw+xw3rRQocLf4EeQIYh6PnUIMgQSZAgiyBCISevMcr0uYQNR2Wfw0LoTYAgotJ8Eq3N2gklTPFmxi1LKpSQAm5I209i3Yf7IMzgD6k1JWwq0u5JKUuGmdcNN60ZokS0usck2MmyZlwXllwLzk1mn8trYmXfhn/zfjVFtJMy1NAaVc8bNkYxjlDE9OKOrapWK1mFlaR1WlvPp6cw5tJ+/Dh/il/37aBhagqerRdC2TDm06juzpMPLw5XxH3RlzZZj+aPe77/alub1y1/zdR6+bhhc9FhyrBzcdISDm44UaqNSSXw14BeCywZSq031O3L8giAIgiDcv0TQLTzwHA4HX7z1I4u/XcVr056j58Aut7ytHHMum3c6M9W7uOj5YfIzuJkuLRuQZYWl65zBboWw2w92FUVh87mzfLNnJ9uizxPm6cWk1u3oVrEyJ1KS+Xn/XnbFXKDvvLn0Cq9KSQ9PzqWn8XfkIWfyKpzByp1y+VTmCqbyROiqUc6vHIm5SQWmMsdZEkjOTckLrC8F2InWxPyp3y5qF4IMgQQbg6ntVYsgozO49tf7oVFd+63odgPe4nBxn8cyjzPp6FSa+ja+bFr3Fo5lHi/Q7nZoVVp89N746AuXt1sUs4SzOed4u9ybVHArR44jhzPZZzmdHcWprNP5U/H/jP6LNQlrKGMqQ1nXMpQxhVHapdQtrSO/20p4eDCkcTMG1G/E8lMnmH1wP28tW4yfiyu9q1TjqarVCM5bL34hM4NUsxmHLBOZmECKxYy3wXjNteVXI0kSbZpUomaVEnzy7So+mrKQds0qM+CFVrhfJRGjf0k/foycTnpSJrJD5uS+KNKTMvHwdaNczTBUahVGk4GvBvzMiK6TGLtwCLXbRhTbtRIEQRAE4f4ngm7hgWa32Zn83Bds/HMr7/3wOh1eaHXL2zp6Ko7Rny4mMcU5tTctPYcPJy+gU0tn9vILcWksXXeI/XnTy2+njIFDlll+8gTf7NnJ4cQEqvoH8GWnx2hXplx+EH15huidMRfYmRdkX+7yDNF3wsUpyhXdKjC4wnucjj1NliObTHsm/no/zuWcw+ywMOXYJ4BzGrSv3pdgQyA1PKsTZHSOWAcZA3HXuN/y7IO7GfBejZvGhE6lI1fO5Vjm8fx9Xk6n0uF2B0fb4dJofoI1gYru5XHVuFLFI5wqHs68ExsTNvHjmV9o4dcMg9rA6ewo5l9YQK6ciwoVoS4h+UF4GdcyBBuD7uh1ux16jYZuFSvTrWJljiYlMufgfn7+bw9f7d5B67AytC9XnuFrVmFxXD1jvFGjYeWz/W848Abw8XJlwpBurNx4hOk/rmHPgXN88Fpbmlxlerh/ST/8SzrLxF1tCvno+R8wuucnjOg6mTELBlO3fY0bPh5BEARBEB5sIugWHliWHCvjnpzG3lUHGD53EE17Nril7ciywtzFu/l29ibKlPTjk9fb88GEeVisdvZHRucH2Zcz6DV43GAJsstZ7Xb+ORrJt3t2cTY9jUYlSjKzR68i6xVfniG6OEbxbsXFqcwaScOIw6OJscQCYFDpCTQEEmwI5lT2aVr4NadNQCsCDAHoVMWf/Op+CHh99D5Mqjb+npbqguuP+m9O3gpAc79m+dPLHYqD6JwLnM4+zemsKI5nnWB94kYUFAwqA2GupZ0j4qYwyrqWwVPned3juBNr/a+lkq8fY1u2YXDjZiw8doTZB/fz/srl+c/XDAikT7WI/Fr2F2eDmO12Us3mm/5/IkkS7ZuHU7taSaZ8s5IPJy2gQ4tw3unfCnfTzSfN1Bl0jJ7/AWN7fcKo7lMYPf8D6nWsedPbEQRBEAThwSMpinJz9XKEYpGRkYGHhwfp6em434flnmRZJiEh4aYyEt9N2enZjOg6mRN7TjNq/gfUaXdr0zVT0rL5+Itl7Nh3hqe61uHVvk3RatXEJWaQnmlGlmWORyWQnmHGw91IhTDn9fBwMxLod+O/t6zcXH4/tJ8f9+0hMTub9mXL82qdenetPNKNcigOorLPcDg9kkMZhzmReRIFBXeNOxGe1SmhhFA7pBY+eh8kScpPYNYr9PE7lsDsontdm/p+cSb7LKMOO5M4OrOXFz3qP6bKSEq7lrrqdswOM2eyz3Iq6zSnsk9zOus0abZ0wJmkrYxrGcqaylDGNYzSrqUwqC8FmvdD2TJFUfjz8EGGrl2FBGjVajqVq8ArtetSydcPWVHoO28uO2Mu8M+TfYkIvPVKA4qisGzdYT77eR0Gg5Yhr7WjYe0yt7StXKuNcU9OY8+K/Yya9z71O9e+5eO6X93vfz+Ee0P0C+FKok8IRXnQ+sWNxnRipFt44KQlpjOs48fEnk5g8qoRhN9EeZ/L7fzvDOM/X4qiwLThPal/WUmfQD/3/KD6dsqCJefk8Mv+vcw88B9mm43ulcJ5tXZdyngVXqt7LyiKQrw1gcPphzmUEcnRjKPkOMwY1UYqu1eivnddtqfs5InQnjTxbURCQgLeOu/8Ufm7kcDsIh+9T34A9yAlCCtuxTXqf/F3XNm9EuDsC6m2VE5lOUfDT2dHseDCv1hlKxISocYQyuQF4Ua14YbW+t/JsmWSJCHn3TMe0awlVoed2Qf3s3DOEbpUqMSABo3oFV6VnTEXiExMuK2gW5IkOrWqSp2IUkz+egUfTJhPp1ZVeef5lphcb26NvE6vZeRf7zG+93RGPz6VkX+/T8PH6tzysQmCIAiCcP8TQbfwQEk4n8SH7caRlZbNtPVjKFP96iN5V2OzOfj+983MWbiLehGl+ejtjvh4uRbrcUZnpPPD3t38GXkIlSTRp2p1XqhRmyA3t2Ldz63ItGUSmXGUwxmHOZweSVJuMmpJTVlTGdoHtqOqezhhpjDUkprTWVFsT9nJ5uQtNPIpOH3/biUwEwq6U9PcJUnCW+eNt7c3db2dQaBDcXDBHMPprNP5ido2Jm7KL+lmVBsp4xqGwWEgwOBPJY+Kd7Vs2cUa9VX8/KkbEsoLNWrz95HDfL5jG+1m/kzzUmEF2t0ufx83PvmoJ0vWHOKzX9axe/9ZhrzejlKhPjc1M0ar0zJ87kA+7jODsb0+YcSf79GoW91iOUZBEARBEO4/IugW7isJ5xKvmgU4MTqZL975CY1GzfRN4wi5hRHo6NhURk9fzIkzibzRrzlPPVYHlerWknsV5VhyEt/u3smi40dx1+t5rXY9+kXUKFTy627KlW2cyDzB4YxIDqVHci7nHAoKwYYganrVoKp7FSq6V8CoLnyMlycwm3zsEyJ01ShrKEuSLemuJTATCrtbo/5qSU1JlxKUdClBC5y1xy0OC/OjF7IifiUBen92pOwk1ZbGzKQ5lDOVpbZXLSI8qnEs8zhnc87d0eO7WKP+bHoadUNC0arV9KlanR6VKjP74AFmbHfeFNp2/hy9q1TH1+X6dbevR5IkurSpRp2IUkz6agXvjZ+HWiXhkK++Usug1zDrfy8UDrz/GMiEvjMY+8Q0hs8dSJMe9W/7+ARBEARBuP+IoFu4byScS+TF8IFYcqxXbSNJEp9t+/iWAu6VGyOZ+u0qvD1dC9Xevl17Yi/wze6drIk6TZDJjY+atuDJKtVw0d5eUrFbWccsKzLnc6I5nBHJ4fRIjmUex6bY8NC6E+4eTruA1oR7VMZbd/0p7pdPZT6edYLjnICUgm3uRsbu+4XiiAE5FUVxgP0IyKmg8gJNZSRJDSovJHXwvT7MO8qgNuCWVz+9b8k+lDeV5UTMCeJ1iexL28f86AXYFBsAO1N2Ud5UlhBjyC1nrr+WizXq/448xOOVq6DK24dBo6V/jVosP3GMPXGx/BcfR4tff+D5iFq8XKsOHoabT4R2pUA/d6aP7MV3czYzc/4OAMqU9OWprnXyqx0sWeusdmCx2knPNBfKA6HRahg2ZwATn/mM8b2n89EfA2n6uAi8BUEQBOFhI4Ju4b6RnpTpDLglqNakMh1eaElQ2UB2Ld/H3MkLkR0yiqKg1qhvars55lw+/WE1y9dH0r5ZOO+90gYXo+6ar7mR2r/BJjc2nD3DN7t3sjMmmnJe3kxt24GuFSqhVd/cMRblZpJVSZLEoXRnkH04I5JMeyY6lY6KbhXoGdqDKh7hlDCG3nTgc/lUZrvDzuH4w2C8s1mqr+ZeB7yKIwYlqSMoRU9VVgAkI/gue+gD78vLlpU3lcVD40F53/I082+CxWHhz/N/syZhHScyT/LRoVEE6AOo7V2TOl61CXMtXWwzIy6W17taLfu9cc5s+9936c6mc2f56b89zDr4Hy/XqsvzETVx1V37feB6JEmiWf1yzJy/A5OLntPnkog8HkuLBhWIqBxKh+ZVeHvUXPZHRiPLRU+112g1DJv9LpOe/YzxvT/lo98H0KxXw9s6LkEQBEEQ7i8i6BbuG7LD+aG0WpPKfLJuNCqVil3L9zF/+hKqNq6E3WYnctvx/HY34mLt7eS0bIa/3ZEOLapc9zUXMjNoN/NnzHb7VdtoVSpKeXpyMiWFGgFBfNu5G63LlM0faSsOmfas/IDbmaW6SX6W6vWJGziZdYpcOZcJRyaTlJuMhERp11I092tKVY8qlDOVRVsM5bsuTmWWZRlTjus9ySZ5XwS8cmre/iXQ1gFjT9CUBPs5MM8D227n83Iq3OGg+17fgLi8bFlD74IjszqVjmizs6b84IrvYZbN7E7dy6bEzSyNXY6X1ovaXjWp412bCm7lUUu3foPqRmvZl/T0ZHCJkvSvUYuvdu/gsx1b+eW/vbxRtz59q1ZHr7n1P4XHo5zJBN/u3wJrrp2vftvAzv1nGPd+VyqWCaBTy6rsj4zmeFTCVWfXqDVqPpz5DpJK4uM+M1BkheZPNrrlYxIEQRAE4f4igm7hvnFyXxQAHV5oiUqlYuu/uxj3xDTqdKjB8D8Gsn7uViK3Hefkvigq1i13zW1dXnu7bCk/pn7UkxLBXjd0HKlmM2a7HQmoGxxCr/CqlPLw5GRKMt/v3c2Z9DRssoybTs+cx5+kfsjNjyDfiItJqCq6VWBwxfc4k32Gg3nJz05nReW3K+lSkt4lnyDcrTIm7UM6zbsYAl5FsQM2UPL+kXvZ14vfX/ncxfa5KPa8a64KAV1jcJxHkmNA8kAx9gY5HRzHUewxoC4Fkusd6Rf3ww2IG13rr1PrqOBengjP6jhKP8vxzBPsSd3LntS9rE5Yi0ljopZnDWp716KKe/hN3yS62Vr2fq6ujGreipdq1uGzndv4eNN6fti7m3fqNaBneFU0t3AzKT3D+XsIDfIionIo9WuEMfLTRbw+bA4DX2pNaJBXgXZXo9aoGfLr26hUKiY8/T9kWaHlU41v+ngEQRAEQbj/iKBbuG+kJ2UCEFQ2kJ3L9jHuiWk07FaXYbPfRaPVEFw2sEC7q7m89nafrnV4Ja/29o1y5E0DrRscwpyevcnKzWXOwf389N8eUszOD/QpFjMjm7W8rTJE13M25xwARpWRIQeGkZSbjIvahXD3Sjxb+mnM9hz+jJ5Hdc9q1PN+ODMfK4oCchKK7YjzAVUIaCqAdTVYLIANsDuDTCUHJfVNFEmVHyhfCqJtwO1m0s4LyOQkMP8G6FCwO4NtbJeapb+Zl9tbg6LyAMkTVJf9kzyRVJ6g8nCOTuc/7/xZkq5Tguo+GHG/lbX+akmdX6Ls6ZJ9iMo+w+7UvexO2cPGpM0YVAYiPKtTx7sW1T2qFagLfi0hbu75QfWN/n8McXdncpv2vFq7LjO2b2Xo2lV8u3c3A+o3pEuFSjc1Y8XD3ZnM7UJcGhGVQwkJ9OSr8X347Od1TP56JdUrhRRody1qjZoPfnkTSSUx6Zn/ocgyrfo2veFjEQRBEATh/iSCbuG+4eHrLKe1fdFuFny+jLoda+YH3AAxp+IKtCvKtWpv36jIROd00R6Vwpl14D/+t2Mr2bk2eoZX4aVaddgTc4HBq1fcdu3fq8myZbE9ZSeLY5YCcCTzKA19GtDItwHlTeUujTJmOEcTs+xZxX4Ml7s4lRmHDQM7IduOrPYplqnMimIDRxw4YkC+AI4Y5/4u/8dla9rlBLDtBFUgSCaQtM5/aJ2Pa8JAWxVJ0jkfu/icpAN0l7XXXfZcUY/p8l5zaRtK9veQ9Sl4/4RKV+eyc1BAyUaxboL0d8HQE0nfGJR0kNNQ5DSQ00BJA/vJvMfSnc9TOOO1IhlB8rgsUPfK/1lSeaLIeb9vdUVwH4Ok9gbJC0lXB8XYHSXlWbDtQlEcFP84u9PtrvWXJIkypjDKmMJ4IvRxLphj2JO6l92pe/jy5DdoJQ1VPapS26smNT1r3LEZHGW8vPmsYxdeq1OPT7dtYcCKpXyzZxeDGjSidVjZG5qpUCHMmcxtydpDdGheBZVKQq/T8MGrbalSIYiJX64AwNPtxioYqNVq3v/pDSSVxOR+nyPLCm2eaXbrJykIgiAIwj0ngm7hvlEuL0D+a9oiareNYPjcQfkBtyzLrPh5XYF2lyvO2tvJ5hwAvti1g5jMDHqFV2Vgg0YEmpzBfmJ2NlB8tX8BbLKN/WkH2JK8jf1pBwAINgSRakulT4netAxoXug1CVbnzQHTHcwcfuVUZneA7Mueh2tOZVbkHJBjwHExoL5QMKCWEygwAq3yAVUQqENA3xJJHQLqYBTrVjDPAq+fUekLj+rLubshpS/o6qMyvVacl+DSuajylifYz8FlQbckSSCZUBRnv0FXA8nY5dLzV9ue4gAlwzlSLqfljWCngZxeMFCX00A+63xcSQMl7xfgOArJnfJ+B+4omnKgKQcqZxBI7g4UbbU7MsUdim+tvyRJhLqEEOoSQreQx0iwJOZPQf8x6hckJCq5V6SOVy1qedXES1dwmcitZPi/UrifPz907cHe2Bg+2bqZVxYvpEZAEO81akzjEqWu+dqL57w/Mpq3R82lU8uq+dnLl6475LwpA4z/fBkqlYqm9a69NAacgfd7P7yOSlIx5bkvkB0y7Z5rcd3XCYIgCIJwfxJBt3DfOBt5HgBFVjBnmln3+2aCywYScyqOFT+v4+Bm5xRjlbrgB/virL19LDmJf48dBUCvUfPvU89QxT+gQJtz6WnApRrBt0pRFE5lnWJz8jZ2Ju8k25FDmGtpnirxJA186pFkTWZM5Hi2pWynuX/TAhmfZUVmU5KzBvHFpFZ3RIGpzLVJt7XBw7MqyNGQ8zfYnVOZFfNSkNR5o9QXwBHr/KqkXbYxtXOEWh0M6lDQ1XcG6nmBNepgJKnoKcWKnAxmwHEeKGIqvf2s86vqxtbt3xJNZedX8zwUY3eky34fiiKDeX7BdtchSWqQvIo85mv1XjnzC8j+DNynIGlCQE4BexSK/STYDoH9hLNh1lSU7G/yg3FJUw405fMC84A7FozfLn+DHx2D2tMxqD1puWnsTfuP3Sl7mH3uD347Ozu/Fnhtr1poJPUNZ/i/kQz7tYKCmf34E2w5f45p2zbz7D9/0zC0BO81bEKtoKJnc3i4GTHoNVisdvZHRrM/MrpQG71OTbVKIQydvIC+3evySt+maNTXvkGhVqsZ9MNrqNQqPnnhK2RZoUP/ltc9B0EQBEEQ7j8i6BbuCyf2nubLd35GUkkossLhrcc4vPVYoXYGF32B6eXFVXs7KSeH6du3MPfwQQJcnSPHPgYjlfPqAF8kKwp/Rx4CLtUIvlmJ1kS2JG1ja9I24q0JeOu8aOHfgsa+DQkxXvpgn5KbCjiTVU06OpWmvo3zs5dfnqyquMovFUVRHM5vNFXB8CRa2y7I2Zw3Uh17qWHWFBQMecFziHOKt6FdfjCNOgRU/kjSLb7lFHPAeyskSe0cVbbtRkl5FsX4OGhKOQN+83znWuq8dneU2i/vGxlJd+kGxMUQWs7+CzI/AmNfJHUQiv0E2CJRzIsAS15j01WC8cAbDsbv5LKDizx1nrTyb0Er/xZk2bP4L+0Ae1L2MD96AXPP/0WAPiA/4K5gKk8zv6aX/R/ZzLHM4+TKuWTas264rJ0kSTQpWYrGJUqyJuoUn2zbQq+/fqdV6TK817BxofeEQD93Zv3vBdIzzciyzPGoBNIzzHi4G6kQ5hz993AzEuDrxu//7ubbWRs5ciKO0QO7XHc2jkqlYsC3r6BSSXz60tcoskzHF1vf2sUUBEEQBOGeEUG3cM9FHTzLkHbjKFk5hPd+fB2b1Y7skDm5L4r0pEw8fN0oVzMMlVqFh68b/iX9yDHnMu371azYEEn75uG89/L1a28XxWq38/N/e/lq1w5UKolhTZpTMzCInn/9zu7YmCJr/+7KK0ukvomptNn2HHal7GJL8jaOZ57AoNJTx7s2z4f1o5JbxSID58uTVR3LPJ4fZF/uymRVxUFxJIDtIIrtAFhWOR+0H4TMwegJBiqDvimSOhjFfg7Ms8H0IZJr/zs2enpfBLwqr7yEbWaw7XL+K3Sgxjs72g7XvwFhWeD8wfg4kq56fjCuKA7n7AP7SbCfzAvGj6JYllzKhC65XhGM5wXkqqACv9vbXXZwK0waE018G9HEtxEWh4WD6YdYn7CReGs8AGm2dGIsMYS5lqKpe2Ma+zZk0tGpHMs8nl8J4GZIkkSbMuVoFVaWxcePMn37Vjr/PpMu5SsyoEEjynh557cN9HMn0M+ZzO1aN/76dqtLeLlARn26mBc++I2x7z1GROXQax6HSqXina9fRlJJfPryNyiyQqeX29z0+QiCIAiCcO+IoFu4p84eiWZwm7EElPJjwrKPcPO6FEBerSzY0ZNxjJ5+c7W3r6QoCktPHGfy1o3EZWXxTLUI3q7XEC+jkQuZGTdU+9fLeO3p5XbZzqH0w2xJ3sa+1H3YFQdV3MN5tczL1PaqiV597SzVlyerup31qte8DnIm2A5eCrJtB0F2JqxD5QuSM5DANAQM3UlOsuHveWntrpK72xl0k3tnpyvfBwGvpA4G32X3tD423PoNCElSO7Oca0oCrS4LxuUigvFjKJalVwTjZfOC8fIoaC89p61TcNnBXcigblAbqOtdhyx7NocyDtM+oC0W2ZJfC7yCqTwt/VvQ0Ls+xzKPczbnHGVMN59UEUAlSXStWJmO5Sow/8hhPtu5jfazfqFn5Sq8Xb8hIW7uXMjMuOGyZTWqlODHT55l9KeLeWfkXF5/tjm9H6t9zf8/KpWKd756GUmlYvqr3yLLCl1ebXtL5yMIgiAIwt0ngm7hnrlwMpbBbcbiGeDBpBXDcfMyEZeYcdVpmiCxaedJ5izcSblSfnwyvGd+DdybsT8ulvGb1rMnNobWYWX4pVvPAqNWN1v793KKonA25xxbkrayLXkHmfZMQo0hPB7ag4Y+9Qslgboeb40Vb1UWiuKgtCrusiDPKy/Iu/G6xopiBdsRsB24FGA78mpPS66grQbGx5C01UFbHVSBKOY/IWOEc58qLyCh4Ebvxlpq7qOA9+LacwBd9Tu6r6sq5hsQkqQCTQnnP1peEYzHgONiMH4S7CdQLMvhYtI4VKBY0fGfs3Kbvj6K4RdIff6OZ1CHS5n7a3vVpqJ7efqVeoY9qftYl7Ceb09/j1HtvDEWa4677X1p1Wp6V61O90rhzDl0gK92bWfB0SN0rViJxcePYnE4rvpao0bDymf7579n+HqZmDH6Sb6bvYkvfl3PoWMXGPpmB1xdrn4jTpIk3v7iRVQqif+9/h2KLPPY6+1v+7wEQRAEQbjzRNAt3BNxZxL4oPUYXN2NTFk1Eg9fd+ISM3jm3Z+wWO3XfG3XttUZ+GLrm6q9DRCTmcHUrZtZeOwIlXz9mNmj11UzExt0NkwqC7IiE6hKw5Q3wuzm4o5KUmHQFPyvk5Kbwrak7WxO3kaMOQYPrTuNfRvSyKchJV1K3NIo8JVTeAs9D1edwusMTE/lBdgHwXYA7McAO6AFbWXQN0bSvuYMsNVhBaYp52/nsqnM6LtesY+7s5b6ovsi4L0P3K0bEM5gPNT5T9+iQDDuLJ82DfQdQDKgsR+BrHUoWVaQ3Jxr+AGsq1G0Ve7YtP+LmfsTrAlUpDwalYb6PnWp71OXGHMss8/+zqGMw6yIX0m0OZqW/s2p6VkDjerW//TpNRr616jFk+FV+WX/Pr7ZvSM/4K4VGMRTVatTysOTs5ctRzHb7aSazQVu1GnUKt7o15wqFYOZ8MUyXhw8i48/6ErZUn5X2zWSJPHmZy+gUqv47M0fkGWFbm92uOVzEQRBEATh7hBBt3DXJUYn80HrMWh1GqasHolXgCcA6Znm/IA7IjyUzq2cpXc27TjB30v3YXc412V2axdxUwF3dm4u3+7Zxfd7d+Om1zGxVVt6hVe96prsZGvyDWVEHhM+gtM5Z9iStJUjGUfRSBpqe9WiT4knqeIRjvp2A40CmcPrgLGnc2qw/VyBKbyKIwUUR8Ep4vbDeaORknNdrrYakssTztFsTcW8OtbXd/lUZtL6YaAN5FZFls/f3eRhQgH38gaEJKlQLtYXd30GNLVItSTg7+eJ5DgIubtQLuYCyP4GJWcWiq4Okq4e6OqBJvzWE+pd4WLm/k1Jm2ns27BAboRAQwA2xQZA9+CuHMqI5IuTX+Oh9aC5X1Na+DW7raUZrjodb9atT42AQJ5d8DcqSeJESgrx2Vl0LFeBuiGhPF65Cn3nzWVnzAUcctHrypvXL0+ZEr4M/+RfXvlwNh+82vaaS2YkSeL16c+jUkl88faPyA6ZHu90uuXzEARBEAThzhNBt3BXJcem8kHrMSiywtR1o/ENufShV877UBoRHsrnY3ojyzLfzt7EH4v2UC+iNFlmK5HHY/PbXY9Dlpl/NJJp2zaTZrHwUs06vFanHibdtQPOTHtWfsBd0a0CTX2b5GdE3pi4ieNZJ8iVcxl5eCw2xUYlt4q8EPY8db1r509nLQ75mcO1dZC8Z+aPRCvqMBSVJ2RccNbATn0eRclwtlWFgK46kuEt5wi2JhxJdRuJ1gpMZd6NO7sh7Yo2dyN5mHB/ubxmuaaW83tJ58ymrquLogqAjKHg8hKSyg0ldydK1ufOfiS5omhrI+nqO4NwbZVbDsIvBtnXy/Bf06sGPUK7cS7nPOsTNrAybjWLYpYQ4Vmdlv7Nqe5R7ZarAFwsIfhRk+acz8zg8x3b+eW/fQxt0owelcLpFV6VnTEXiExMICKw6CRrJYK9+HZiXz75bhXjP1/GoWMxvPNCS3Taoq+LJEm8Ou05JJWKrwb8jCIrPD6g8y0dvyAIgiAId54IuoW7Ji0xnSFtx2LNsTJt/Rj8SxacRnk8yrleuHOrqqRn5jB86iIOHY/Jr729bP1hIo/Hcjwq4bqlwbadP8fHm9YTmZTIYxUqMbhRU0LcC6/BLsrFTMcV3SrwYaUPUEkqonOiiUmLIcGamN+uiW9jugR3xFfvexNX4SbYnXXJ0bcG81/IuVsh9wDIeYndpLxyQ9raSC5PgbY6kvrWR+6KUmAqs8NGRtpO3F3tUMyloYQHzI0uOzB0yMug/jqKkuusI5670xmEZ38JWVPzgvBaeSPh9fOC8BvLVXCzGf5LupSgX+lneLJEL7Yn72BtwnqmH/8MH503Lfyb08y3CZ46z5u6FCkW5/KPqv4B9K9Zmxdr1mbylo28v2o5vx86wJPhVQu0uxqDXstHb3WkWsUQZvy4lmOn4xn33mME+nsU2V6SJF6Z+iwqtYqvB/2CLMv0GvTYTR27IAiCIAh3hwi6hbsiIyWTIe3GkZGcybT1YwguG1ioTXqG80Op3SHz4gezsDscfD62N9UrOdeHhgR6FmhXlKi0VCZt3sCq06eoGRjEvCf6UDPo5gLCsznnAGjs04gdyTtZEb+aqOwoTBoTDbzr4aJx4d+YxZRyLXlHAm5FyYXcPWBe4HwgaxIKKtBGOIMYbTXQVkdxxELq06CriWRoWezHcdHFqcyKWsZCIO6ul7KXC4+mW1l2IEk60NUCXS0kXkNRbGA7DLk78oLwb5zrxCWXy4Lwes6a71dZDuGj92Fylbcw22JRZDuZlp0ocgqSyhs3Qz0klQajNgjvK6aRG9QGWvg3p7lfM6Kyz7AuYT2LYpaw4MK/1PKsQUv/FlR2r3RDo9/eBufslrPpadQNCSXEzZ3POnShT5XqjFq/hg/XrATAqL7+n1tJkujWLoKKZQMY8cm/vPDBTEYO6EyDmkVnXpckiZcmPY1KJfHt+7+RmZJJk8cbXLfkoiAIgiAId9cjEXR/+eWXTJ06lbi4OCIiIvj888+pV69ekW2///57fvvtNw4dOgRA7dq1mTBhQoH2zz//PL/++muB17Vv357ly5ffuZN4gGWnZzO0w8ckX0jhk3VjKFExpMh2Hu7OD6/TvltNhTL+TPigG34+bvnPX4hLK9DucukWC5/t3MbMA//h7+rK/zp0pkv5ireUwCzZmgzAn9F/k2XPoop7OO+Uf5MIj+poVBqOZRzn35jF+ZmTi4PiuADWjSjWjZC7zbkeW8o7d2NfJLeBSKqCI15K7g7nN2Jqt3C3FcOyA0nSgq4G6Gog8WpeEB6ZNxK+AyX7W8j6FCTjFUF4tfwgXHHE4JnRF8/Lkw1ejJMts/KPQ9EVXS9ckiTKmMIoYwrjqZK92Zq0jbWJ65lybBoB+gBa+jeniW8j3LRuhV57UbifPwB/Rx7i8cpVUOW95zQsUZJFfZ6l3ayfOZ+Rwee7duBhNNKjUnh+m6upVDaQH6c8y7jPlvLBx/N4vldDnn+iIWp14ZsAkiTxwoS+mLMtzJnwD3Mm/HPV7Rpc9PwYOV0E3oIgCIJwlz30QffcuXMZNGgQ33zzDfXr12fGjBm0b9+eY8eO4e/vX6j9+vXr6dOnD40aNcJgMDB58mTatWvH4cOHCQm5FCx26NCBn3/+Of9nvf7aNZcfVTmZZoZ1mkDsqTimrh1N6SolimxntzvYe9A5wuzuZuCz0b0xGi5NMZVlhaXrnDdCnOXDnGwOB3MO7ed/O7ZhczgYUL8RL9SshUFz46W0Looxx7IybhUbkzYDEGwI5rnSTxPqElqgXYLVOQ3+YubkW+Eczd6FYt0A1k3gOAWoQVsLyfU10DdDkW2Q+gTYT1wKwPNff3czhwvC5e7EsgNnEB4BuggkXkZR7GCPvGw6+veQNR0woOhqIunqo6j8bijZ4I3UC3fVuNA2sDVtAlpxPOsE6xLW83f0fOZFz6eudx1a+regvKlcoRt5FxMy7oq5QN95c+kVXpWSHp6cy8teHp3hzLcQERDIB6uW88ehA4xp0To/WL8adzcjk4c+zsz5O/jhj80cPh7LyAGd8HR3KeLaSbR7rgULv3De+A0o7Ue/UU8QVDaQ2FNxLP9pHQc3H8GSYyU9KVME3YIgCIJwlz30Qfenn37Kyy+/TP/+/QH45ptvWLJkCT/99BMffvhhofazZ88u8PMPP/zAvHnzWLNmDf369ct/XK/XExhYeIq0cIklx8rwxyZy5vB5pqwaSdmI0kW2S03PYdSni9gfGe38OS2H9z+eR6eWzuzlF+LSWLruUP7zKpUKRVFYe+Y0Ezdv4ExaGk+GV2Vgw8b4ubje1DEqisKhjMOsjFvNgfSDeGjdaerbhPWJG5AkCDYW/KAuKzKbkrYAlzIn3/C+7Oeco9m5myB3uzMYUAWAvimSfgDoGiGpLguubYfzp/AqKc+iGB8HTSlnbWyROVy4x+70sgNJ0jiTAWqrI7m+lBeEH7ksCP8BlLzZJpIJdA2QNCWc7XV1UIzdUVKevel64ZIkUdGtAhXdKtC3ZCabk7awLmEDW5O3E2oMoaV/Cxr5NMBF4wx+vYxGPFxk7Fg5nHaCs/sPotU6sNnUZGUbcHGR0KDn49ZtOZ+ezqj1a+j6xyyeqRbBoIaNcdcbrnosKpXEc70aEF4+iDEzFvPCBzMZ915XqlQonNNCkZ0Z5f1L+hJ/JpHE8ym0e64l1ZpUps2zzXm/5WgObjqC7LixRJSCIAiCIBSfhzrozs3NZc+ePQwdOjT/MZVKRZs2bdi2bdsNbSMnJwebzYa3t3eBx9evX4+/vz9eXl60atWK8ePH4+Nz9SRWVqsVq9Wa/3NG3uiHLMs3nI37bpJlGUVRbvnYci25jOw2hRN7TjNh2UeUr12myG0dj0pg+NR/sVhtjHinE+N/XE6O4mDnuWi2zItG0YJkA22W83O1i6QmwZbNuH/+Ymv0eRqFluCz9p2p5OuXf9w3dHxyLtuSt7MyfjUxllhKGkvwUun+1POuywVzDOsTN3As8zgTj0yhiU9j/PV+JFgT2Zy8heNZJ5wbUa6zP8UCubsgdxPkbgTHGUAD2lrg8ibom4K6AkjSxQJMKAW25wEYATPYdjn/FWJEweOK190Zt9snhIfT3esXKlBXAWMVMPZ3lsnL+gzM34IqFHJ+Rcn+HCQ3FF0L0LcBfWfn/5vcw8iaqje9R5PalQ4B7Wjn34YjGUdZl7iB2Wd/Z+75v2jgXZ+Wfs1x05ioHXEam3L1EoNaSYdOY6VecAj/9n6a3w78x2c7t7H4xDGGNGp63SnntauV4IcpzzDq08W8Ofx33u7fgu7tIgqMuh/fexqAZ0c9QcK5JH4Z+QdI0GdoDwDaPtecg5uOcHzvacrXLnPT1+JmiPcKoSiiXwhXEn1CKMqD1i9u9Dgf6qA7KSkJh8NBQEBAgccDAgI4evToDW1jyJAhBAcH06ZNm/zHOnTowOOPP05YWBinTp1i2LBhdOzYkW3btqFWFz3qOHHiRMaMGVPo8cTERCwWy02c1d0hyzLp6ekoinLTo1f2XDszXvyeI1tO8P7s1/Er50VCQkKhdpt3R/HVrO2EBnkw6p3WOPQQX0fCKl/9w6cKhf4r/iHUzZ2pTZrTKCgESVaK3H5RMhwZbMvcwY6sneTIZiobK/GYf2fC9KWRZInUpFSsdisBGgcGyUyudS+nkjYSr7KRJWvJzTVRSithUYxY060kZBfcr5podOxAx3Z0/IeEFQf+5FIfKy9jozaKzQVsQDZAYlGHmUeDit9QkQbIaDiBijRkPLFTHlAh44mcrAFu7Pxvx+30CeHhdS/7hQsOTECK4w3sVEXDSfTKFvTWjWisi1DQIgGWrDVkZtVEwfOW9+WHL0+696SDS1t2Zu9mZ+puNiZtwl/jlx9wh+lLU8e1Fj4aH5LtyezO3kuU9Qw2JZdziedw6JxlAB8LKUGDDj58uX8fQ9asZOZ/e3mvVl0qenlf6xAY/mYLZv6zl+k/rGXXf6d5rW8DDHrnn/HYM7EAGL31tOvYjKzMLH4Z8QcO7LR7sTku3vr8djf6fnmrxHuFUBTRL4QriT4hFOVB6xeZmZk31O6hDrpv16RJk/jjjz9Yv349BsOlKYBPPfVU/vfVqlWjevXqlC1blvXr19O6desitzV06FAGDRqU/3NGRgYlSpTAz88P9xssZXU3ybKMJEn4+fndVIe32+xM6DODyM0nGLNgMLXbVi/cxiHzXV797XZNK/PBq23Q67UcSojHKjungdYJDqFX5SqUdPfgVGoKX+/ZxYXMDGQUXqpZm/caNEZ7lRscRTmTfZZVCavZkbILraShiW8T2vq3wt9QeF2lv8PORM1eJK5+M0TBgORjApUb5O50jmTnbgLHOUDrXF+qfxd0zVCry2KUJG6tgvflx9f8lrZQXG61TwgPt3vaL3JKQBZ4u2WBMQgIApoCH4L9LFL2DLAuw8AmDGwGbW3Qt3WW4VMXndDxevzxpxzleEp5kgPpB1kau5wEeyIqVIS5l6a6f3VCjc5td1DaM/nYJxzPOoGHpyf+Jv/LtgNflSrN9ujzjNm4jhdXL6dv1eoMrN8ID8PVp5x/+GZn6tYoy5SvVzH801WMe/8xSoV4E1TaOeXcnGLF39+fVyc/hySrmDnib/yD/VAU53yaoNJBReYzKU7ivUIoiugXwpVEnxCK8qD1C8M1/mZf7qEOun19fVGr1cTHxxd4PD4+/rrrsT/55BMmTZrE6tWrqV69cOB4uTJlyuDr68vJkyevGnTr9foik62pVKr7tkNJknRTx+dwOJj6/JfsWLKXUfM+oG77GoXaZGSaGTV9MXsPnuOd/i15onOt/CmSF6dY1w0OYU7P3kjA4hPH+HrPLuKzswhwdSU+O5vO5Sui114/UZqsyOxL+48Vcas4lnkcX50PT4b2pJlf0/z1mEVRHOmAhSKTM+X8DfbdzoA8Y5Az2zK5oA4FXTMkfTPQ1UdS3dza8gfFzfYJ4dFwr/qFrKvi/MYyH8mlB9JlJb4UbSkUOcn5g+d3SHIsimW1szZ41gTQVEEytHVOQ9eUv+lKBypU1PKuSbo9gxPZJ6nuUY09aXtZm7ieCm7l6RTYgQjP6jTza8LxrBOct0RTzr1soe00KlmKxX2e5bcD//G/7VtZdvI4gxs3o+dlmdCv1LZpOOXDAhg+dSGvfDiboW92oEIt55Txlb+sp91zLVCr1bw27TksWRamv/wNoRWc+Skq1CpzV35P4r1CKIroF8KVRJ8QivIg9YsbPcaHOujW6XTUrl2bNWvW0L17d8B592TNmjW89dZbV33dlClT+Pjjj1mxYgV16tS57n6io6NJTk4mKKhwcptHhSzLTHvxazb+vZ3hcwfRoEvtQm1Onklk6OQF5JhzmTaiF3WqlyrwfGSic8pjr/CqnElLZcS61WyLPk+7MuX4rUcv9sRcYPDqFUQmJhARePVrbXaY2ZS4mZXxa0i0JlLeVI63yr1OLa+aqG8g6ZiiOKeAoq2D5D0zb232dhT7AVDiLm+I5PYe6JuBuswtlScTBOHWXV4v/JrJBtW+SIbmSC5PochZYF2PYl2VlxF9BqhLoRjaIunbgjaiQPB+PRdLB3YK6khZUxh70/axIm41M058TogxmFqeNQu0K4pWrebFmrV5rEJFJm7eyJDVK/KznFf1DyjyNaVDffhu0jNM/nolI6ctol29cjhcdOw/eJbX2oyldLNwNG5GbEFe6Ev6cSY2FYw6VEWUHRMEQRAE4c56qINugEGDBvHcc89Rp04d6tWrx4wZM8jOzs7PZt6vXz9CQkKYOHEiAJMnT2bkyJHMmTOH0qVLExfnDLJMJhMmk4msrCzGjBlDz549CQwM5NSpUwwePJhy5crRvn37e3ae95KiKPzvte9YM2sjH856l6aP1y/UZu3WY0z4YhmhQV58NuZJgvw9CrVJsThr7e68EM3wtasJcnPj1+49aVqyNACJ2dkF2l0p0ZrIqrg1bEzaTK6cSz3vOrxR9lXKmMJu7oTsR5xfNRVR0geCdb0z07i6BOibg6IB86/g0gvJpffNbVsQhOJToF74VZINXlEvXFKZwNgFydgFRbFC7jYUyyowz3dmRFf5oehbO0fBdfXza4JfzcXSgQnWBCq6l6eed13qedfleOYJlsQuY1HsEgDO5ZzH6rCiV1+9vKS/q4np7TvxVJVqjNqwlu5zZ9O3anXea9ikyCnnLkYdowd2plqlYD7/eR2OdjVAkogEIvNKMAJQM+890O4gcv8Zyte6s4nUBEEQBEEo6KEPunv37k1iYiIjR44kLi6OGjVqsHz58vzkaufOnSswLeDrr78mNzeXXr16FdjOqFGjGD16NGq1mgMHDvDrr7+SlpZGcHAw7dq1Y9y4cY9krW5FUfjq3Z9Z+sMaPvj5TVo+1bjA8w6HzPe/b2bWPztp3bgSQ99sj0Ff9NTwNLMzmP7naCSv16nPG3XrFai3fS49DQBvw6XV0YqicCLrJCviVrIndR8uahda+7ekdUArvHVe3AxFyQXrFsiZ43zAPMtZc9j1DTC0Q9I4P7jKubudQbecelPbFwSheBWoF644nDfM5FRnkH0D9cIlSQ/6Fkj6FijKWLDtcwbg1lUo5j9AMqHoW+QF4M2KXDZSyqUk3moLx1MX0NjdFRzHQE6lnNqLd0s141vHKY7nJLErZTeH0yNpG+CsBe6mdSviiJzqh5Zg0VPPMPPAf8zYvpWlJ44zuHFTeoVXLTTlXJIkenWqhYtRx4S8Ot2hfu5EBLijsznI1ao5kW7m+Plk0Kj5dvgfVKxSgkr1yt/GlRcEQRAE4WZIysXsKsJdlZGRgYeHB+np6fdtIrWEhAT8/a9ee1dRFL4fPJO/pi1iwDev0PmVtgWez8iyMGbGYnbtP8trTzelT7e6RU7BTjHnMHHzRuYdOYxeZ6OynztT2nXgvPk8WfYsTBoTJYwlGLF2Nf/FpvBH9+eo4u/HzpTdrIxfRVT2GYIMQbQPbEMjn4bXHEkqfA52yN2BYlkCllWgpIPKD+REcH0Pldurha9NzjzIGAru41A9QiPdN9InhEfPw9gvFEUB+1GwrnYG4fajgA70jZH0bcDQGknlzDR+PnMXvpnPolddvWSIVVZx2vAF+zIT2JC4CYDmfk3pENgOX73vNY8lITuLSZs3suDYEWoGBl11yvmRk7G8PGQ2Jlc9OTm5vNy3CU93r4dKJSHLCm+Pmsv+yGgqJWWQcugc09aPIaxaqSL2ePsexj4h3D7RL4QriT4hFOVB6xc3GtMV20h3YmIi+/fv58yZM6Snp2O1WjGZTISEhFCxYkWqVr35GqnC/e3XUXP5a9oi3vzfC4UC7tPnkhg2eQHpWRY++agn9WqULvR6RVGYd+QwEzdvQFbglbpVOcRfqNUK447sKdReFwS1/WFT2gp+ij1Imi2Nqu5VeK/CAKp6VEF1g+swFUUG2568QHs5yCmgLgkufZAMnVFkC6Q+AbkbUZSXCyZnUmTnWlEATeUbv1iCIDwwJEkCbWXQVkYyvY1iP5cXgK9GyRgOGSNQtLWRDG1xxwu9SkZR4LjVnU1ZgSTYDfhrLDQ1xVFBn4FeJROid6GKd1+6BT/G6vi1rIpfw5r4dTTwqU/noA6EuoQWeSz+riY+bd+Jp6pWZ9T6NXT7YxZ9q0XwXsPGeF426+d4lDMnxlvPtSAuIZ1vZ28i8kQsI97phItRR6eWVdkfGU27QV1YO+YvhrQbx6cbxxFa/tHNRSIIgiAId8ttBd1RUVH88MMP/PPPPxw7diy/npqnpyd6vZ6UlBSsVisAHh4edOrUiX79+j2ya58fJrM/nsfs8fN4ZcqzdH+7Y4HnNuw4wfjPlhLk78EPk58hJNCz0OtPpSQzfN1qdlyIpnvFygxr2oLTWVEcOaOgKJCe6UJcggcWiw6DIZfgwFTcXC2o1bA3cytNfBvTLqANoS43VvZHURSwHcgLtJeBHA+qIDD0QDJ2dmYyvjgKbzt8Y8mZbiApmyAIDz5JUxI0LyC5voDiSAbrGmcitsypuGEDwK7yx+Q1mvJGDUGObEwaE3pjKFbLYAyOg7hrnWu/3bRu9AjtRqegDmxI3MiyuJVsTd5GDc8IOgd1pIJb0dO+64WEsqjPs8w88B/Tt29h2YnjfNC4KU/kTTlPz3AuzykR7EWX1tWoVC6IMTMW8/qwOUwa2iP/fdhil5m4fDjvNR/JkLZjmb5pHP4lrj3aLgiCIAjC7bmloDsxMZH333+fRYsW0apVK1577TWaNWtG6dKl8fT0LNA2JyeH+Ph4tm3bxsaNG3njjTcwmUx89tlnNG9+b+sOC7fmr2mL+GXEHzw/9imeeL9r/uOyrPDT3C388vd2WjQoz7C3OuJiLJiEyGq389XuHXy7exdBbm781r0XTUo6pzhmyM4yXiUMpRlU8gUi/RM5YzlJsiqSJNmCCjUyDgaWf4dqntefOeGcInrkUqDtiHZOHTd0RDJ0Am2NorMU30JyJkEQHg2S2gdcnkRyeRJFzkLJnATmP9Eq6YSY3yBEXRJc2iEZHkPSlkVW93UuR7EfAd2l8pN6tZ52gW1p5d+S7Sk7WRq7jI+PTKKcqRxdgjoS4Vm90OwdjUpF/xq16FK+IpO2bGTompXMPXSQMS1b4+FuxK6H7VHnwEvNeUMWzZ+vxuq1R3h69K80q1ceux483I14+XswedVIBjYdwZC2Y/l0w1i8Ajzv8pUUBEEQhEfHTQfdK1as4L333qNPnz6cPn26UJB9JRcXF8LCwggLC6Nv374oisJff/3FoEGDaN26NZMnTxallh4gC79czncf/EbfYY/z9PCe+Y9nZVsZ+78lbNt7mlf6NuHZx+sX+r1uPX+O4etWcyEjndfq1OONOvXRay51wbM5zmy77YNaYtfEcVS1mLOco5ShJI8HvohNtvHzmd9Iyk2+5jEqthMolqVgWQKOMyB5gqEDkqEz6Opcd4T6dpMzCYLwaJBUJhR13rRwr++QsDnXgOfMQ8n+AUVTEbS1nM9fJfGiRqWhiW8jGvk0YH/aARbHLmPGic8JNgbTOagjDbzroVEV/FPt5+rKtHYd6V2lGqPWr6H7H7NoEVyahLow+eQ2OLntUuMg578zGZFIdcEz0JkMzi/UhymrRzKw2UiGtBvHJ+tG4+599eRugiAIgiDcupsKupcsWcLXX3/Npk2b8PK6tVE+SZJ48sknefLJJ5k0aRIvvvgiP/300y1tS7i7lv6whi/e/pFegx7j+XFP5T9+NjqZoZMXkpKWzZShj9OwdsFyNMk5OUzcvIH5RyOpGxzCd126Uc7bp9D2M22ZeKst7E6YSbotlQYeJt4MCsPPUB60Js7lROOtthRZ71axnwHLUmewbT8Okpsz47hhBOgaIElFZ0y/GkkdDOpgJCgwOiUIglDAxRkvjlgkl8eR9M1Q3EeCdTOKZQGY/3I+b16AovYHfTtn2bIrNyOpqOlVg5peNfLLjX1/+kfmRf9Dx8B2NPdrVihJ5OVTzqdu2QRqCRQFT5uOLmEVqRTox9G4RJZEHSdVa0VRS/y5ah+Nw8ugUasILhvI5JUjGNR8JB91nsjklSNwcTMWOjZBEARBEG7PTWUv/+STTxg0aFCxZpJbsWIFISEhj1yitfsxe3nCuUTSkzKRHTLH954m9kwsQaWDqFCrDLuW/8dvo//ksdfb8dbnL+aPYm/edYqx/1uCv4+JCUO6UzLYO397iqLwV+QhJm3ZCMCHjZsVWfLGLtvZlrydVTEzGeq34bpZgPepJ9Ao4HEUxwWwLEMxLwH7YZBcQd/aOXVc3+S69XWFm/OgZZMU7o5HvV/IuQcgpRdo6yJ5zyyUeFFJ7gP2faCp4nyfwgCGtkjGbqBrhCRd/d53dE40S2KXsz15B0a1kTYBrWgb0LrIcmML9h9m0AZnyTBthoLHCdDl3Z9UgOQIyPWU8N8L9UuXYNx7j+GeF2Af232Kwa3HUKFOGcYvHoreeHvlLx/1PiEUTfQL4UqiTwhFedD6xY3GdKJk2D1yvwXdCecSeTF8IJYc61XbqNUqfjnxGYGlA5Blhd/mbeeHP7bQtG45hr/TEVeXSx/UTqYkM3ztanbGRPN4pXCGNmmOj4tLge3ZZBubk7awOGYZSblJNPf04Xn3BSgKSLo6YOwFmpJgPwfmv1FydyNJkK7tiQenwbYP0IO+pTMZmr45kmS4U5fokfegvQkKd8ej3i8U22GU5B6ABNo6UGTiRQXJ5x/nqLj5XxTzQnCcApUvGLo4A3BN+FWXWiVZk1get/Ka5cZ+P7ifj9atpnfZcHYmxHAmM406roE8HlKJ6uWCWXPhNJ/u386rFWux8fdI3Fz1TBrag9KhzllHBzcdYWiH8dRoVZXR8z9Ao731PKuPep8Qiib6hXAl0SeEojxo/eKulwzbtWsXdevWLa7NCXdZelKmM+CWoFqTyrR7vgVGbz0HVh/l3y+doycOh0xmSjbuAbmM+2wpm3ae5IXejXi+V0NUKueHxYuJ0r7ZvZMQdw9m9XiCRiVKFtiX1WFlQ+ImlsYuJ82WRj3vugwIfhuVLRLMCzhudeeftOo09fXHX+9OisVAWqaWpkY1LpIDd9sC0LdA8pjmDLiLmKopCIJwV9xE4kVJHQym18D1VbAfdgbflkUoOb+AphwYuoKxa6F8Eb56X54pVVS5sXp0CupICZdQUixm9DobTcJ9eKFpBf48vpW15yL5Oec0/R0tCCupR3/EhsnbyHeTnmbo5AW88uFsxgzsQsPaZajWtDKj5n/AyK6TmNzvcz6c9Q5qtajQIAiCIAjFodiC7jfffJOdO3cWenzGjBmcPXuW0aNH4+HhUVy7E4qZ7HBO6a7WpDKfrBsNwMrf17H0u1U0e6IhKbGpHNp8lNjEDMb8OpuE5EwmfdidJnXL5W9j87mzjFi3mpjMjCITpZkdZtYlbGBZ7Aqy7Fk08m1Al6DOBBkDAchMXwHApqxAosxH8XZswcM1njqGNHCBGJsLLroccgxv4eb55t25MIIgCNdwK4kXnXXAqyJpq6K4DYHcLSjmhShZX0HWdBRdPSRDN2cCyMtuKhZdbmw7ER7VkTSh1I44yZ+JJyDR2T40L8fb0vRfAKgdIWHUNSEk0JNvJvRl7P+WMHjifF5/phl9utWlbvsaDPt9IOOfnIbBRc/A7197IEYZBEEQBOF+d0tB98aNG/n6669p3LgxzZo1o3r16lxtlvqAAQOIioritddeY9y4cZQrV67IdsK9dXJfFLJRR8Tj9Tl2Op5Vi/ew8PvVlO5Ykx5jnmT38v3sO5vEmJ/W4u/vwfeTnqZU3rTEpJwcJmxaz4JjR6gXHMoPj3Wn7GWJ0rLtOayOX8OKuFVYZAtNfZvQOagj/ga/AsfgqsoFoG+AFy84/kNFDslKWU6pumBweQydfAHMg3DViNEXQRDuH7eTeFGSNM6lMfrmKHIWWFc6A/CMjyBjDIqhtTMA1zfJTwhZVLmxC7YDqNWgKFDBVI7m/s3w1/sTb4lnwflVJNmjUasVLmQnoSgKLkYdEwZ35/vfN/PVzI2cOpfE4Nfa0fTx+rz/05tMef4LjG5GXp/+vKgwIgiCIAi36ZaCbr1ez/r165k7dy6SJOHh4YFWq+WTTz6hWbNm1KlTp8Dd8bCwML799lvefvttfv3112I7eKH4RMekYm1Tne83HuH7jUecD1YK5Rjw2kd/OH+uXYYAo47vJz2DyVWPrCj8dfggk7ZsQpJgSpv29KxcJf8DWqYtk5Xxq1kVvwa7bKeFfzM6BnbAR+9dYN+KIw7MC8D8GwAu8jFw7Y9k7IGfpiQXQ3M55zSYEfWxBUF4KEkqExgfRzI+nve+uAjFshAl7VVQeaMYOuet/66GJEkFyo39emI+BzL/wU1lx5pzBHNKMnqTDy5mPfoEEz5udjDa+fPAQY7G2fi4VRtKe3rx6tNNKVPSl4lfreB8TCoThnSjbb/m5GSa+eLtH3H1cOG5Mb3v9aURBEEQhAfaLQXd9evXJzY2lqNHj7J582Y2btzI7NmzGTx4MJIk4erqSuPGjWnevDnNmzenbt26uLu7Y7PZivv4hWKiMekhbwQ5IjyU5rVK4+muJcum4se5W0nPMIMk0bZKKCZXPSeSk/lo3Sp2x1ygZ+UqfNi4WX6itLTcdJbHrWBtwnoAWvm3oENgezx1l5YXKIoVLKtRzPMhdwugA109yN0I6nJIprcLZQHGPD/vYCvflWsiCIJwr0jqQDC9DK4vgf1o3vrvxSg5M0EdBsZuYOiKpAlFJakI0ufylGlPoeoPJU1Qq6bze6usooq+CTN3p9Nx9m8MaNCQF2vWoW3TyoQGeTJ08kJeHjyLiUO60+3NDpgzzfw4bA4ubkaeeL/rPbgKgiAIgvBwuK013ZUqVaJSpUq89NJLHDlyhPnz57Nu3TrWr1/Phg0bWLFiBZIkoVar8fT0pGbNmsV13EIxCykfDNtO4JZr53+jnkClkjgYeYpZP27BarVjsDmwaNX4lwtk2rbNfLdnF6HuHszu8QQN8xKlpeSmsDR2OesTNqJRaWgX2Ib2AW3zy9soigL2g85A27wElHTQ1kJyHwOGTuA4h5K8Eex7UFKeRSkyCzDONZKCIAiPAOf678pI2soobh9A7jYU8wKU7G8hawaKtg6SsRtu2gT0KhlFgWwpgt3pERw0x2PURNHCLYmyuhT0Kpny3hLLnn6OGdu3MHXrZhYdO8rENu2pVi6IH6Y8w9DJC3hjxB8Me7MDT33Yg5xMM98NnomLu5HOr7S915dDEARBEB5IxZZIDaBEiRL069ePfv36AXD+/HnWrVvH7t278fb25t133y3O3QnF6HxiOnY9pJ+P5eWe49A2DWNvXBJ6VJQ0Z3I2LgVL7VBGR+8i54KD1+vU5/U69dBrNCRaE1kcs4xNSZsxqAw8FtyZNgGtcdU4R74VRxJYFjqDbfsJUPmDS28k4+NImjL5x6AoN54FWBAE4VEjSWrn2m59ExQ5G6yr89Z/j6J+XgWJHCkYk/9MWgUaaIWz1vfCmEU4lB+paMggwZqATi0xrGkLulSoxLA1K+kxdzYv1qzNgPqN+GLsU0z5eiWjpy/m1NlEXhr7FDkZZv73+vcYXA20frrpvb0IgiAIgvAAKrag+/333y/02JVBuHD/SlZsJNYFpUFJ4gBIgpIAMrFhroArAEGShr+ffpoyXt7EmeNYdG4JW5O2Y9KY6Bnag1b+LTCqjShKLoplpTPQtm4AVGBog+Q2BHSNixytvpUswIIgCI8iSeUKxm5Ixm4ojgRyUj7E5NiMKzGQ2AzZ2AnJ0IMQY3VeL/sqC05so6JhO5k52xl8YCiPBXemqV8T/un9ND/u28P/dmxj+ckTjG/VhuHvdKRMKV++mbWRM+eT+WjS0+RkmZ3J1UwGGnUT5UEFQRAE4WYUW9Ddu7dItPIgMwWY0DnsaDR2yrl6EIIZcrNJ0es4nKUgA3a7hqeCqqDT5/DVyb/YmbILD60HfUo+SXO/ZujVehTbEeTs+WD+F5RU0FRFch8Ohs5IKs/rHsftZAEWBEF4FElqf2zq8uDYzPdJFahm0lNTWYY+Zw7ZhLItJ4Qocya4Qxu/WlgySvDrmVn8G7OEx4I782KtxnQoV56P1q7iuQXz6Fm5CsPaN6d0qA9jZizhjeF/MOHjvliyLIzv/SnjFw+lVhvx/iwIgiAIN6pYp5cLDy6fIDW1/U6iVjtLv2XmPa4FauR973DAeXUuHx36FV+dD/1KP0NT38ZoyATzXGTzPOfotMoHjD2c08e1Fe7B2QiCIDxadGp/ACTg2wRPJDyoakilqSmOFsadtDQ62/lqFF4v+xLdQh7j3wuL+e3MLBbFLKZLUGd+7tadBUePMWHzBtafOc2IZi35+uM+DJ28gFeH/c7oj3piybYyqvsUJq0cQZVGFe/dCQuCIAjCA0QE3QIAUTkJ+JnMmFR21OmueKhsuEoO/Ize/GfORDZZyFJrSLEl8WLZ/jTyroPatg0lfSCKdR2ggL4lkuld0DfNrycrCIIg3HmuxrpghmcC9LQxDOOsOZosexY5GhMxBhNB5oGolTgMuX+hJG4hyNiD10r3pFtIF/6NWczMs7NZHLuELkGdWNb3GSZs3sSAFUtpUTqMsSO68dU363h/wj+8/UYHLDlWPuo8gU/WjqZczbB7feqCIAiCcN8TQbcAgF6TzISgvHIzQQWf65b31Sqr+CP6OZrot0DyYBQ5CTQVkdw+AGNXJJV3oe0KgiAId54kqVEAg+MQpXNHUtp0efWH70CJdzZ0nwS2PZDzC0r2VwTqGvFqcC+6Bo3g39iVzDw7B0/tUrrV6sRjFbowZsN6ei34g0HdGlEyxJsZP6/jsScaYcnJ5cP245i2YSylKofe03MXBEEQhPudCLoFALzdU/LLzeQ4qrMk2YWTSg6lVBo6eKXirYlCr5J5ruTPYPYE42NIxp5I2vB7feiCIAiC6saqP0j6Bkguj6O4DQPLchTzXyjpAwmUPHnFrys9A/ozPz6SWWfn4KH14MN2bdl5UsXHmzcQERDE08835I+ZO6jatjpui/cwpO1Ypm8aR1BYwN0/Z0EQBEF4QNy1oPuvv/5i48aN6HQ6atSoQffu3XFzc7tbuxeuw93gLDdzNDOEyuXm4qtZRyXrMaq5H0eyHkJxLvVmh7kNDUrPQJJ09/BoBUEQhMvdbPUHSeUKLj2RXHqi2E+hmOeB+R985N942aMqvX3aMz/ZzryYv/Hw8GBY+0bM3ZXK9LM76f5MZQ7+cwrXBhXQbjnK4DZjmb5xLL4hPvf4KgiCIAjC/emuBN2zZs3iueeeIzQ0lAMHDrB7924GDhxIs2bNRDmx+0SINgWAv88Hc+TAX3xR/1e89afIyA5l8fkWxNviGVhhP5LkKQJuQRCE+9CtVn+QNGWR3AajmAaCdT2K+W/cLdN53lVHb8/mrMkwMT9xKZWqeFA3txLzdkcS2MwD3TGF9OqlMR08y5B24/h0w1g8fN3v2PkJgiAIwoNKdTd2EhwcjCRJlC5dGg8PD1q3bs0PP/yAWq3mv//+uxuHIFxHkMEZSOcYJHbGRDN8ZxkeX92DWvM7MXJXaRLV+gLtBEEQhIeLJGmRDG1ReX2L5LcByfQGRvkoXYy/813pKJ72ySBHs5nWDc4TGJTE4ZA0qO1CQngwMQYdH3YYT3Z69r0+DUEQBEG479yVke5WrVqRnJxcaDr5008/fTd2L9wAF70/WKGsRxpPNTfj6WiMfwY0Coc09SlKq9MutRMEQRAeapI6AEyvgeurYNuFJucv6sorqBNi47yjNP/qzuLhHczJ895kGX2wePiTeziNoYOGUeeJ0lhyzUjGoxj1WZhzTejlGqjVGvw9ytC2Tpd7fXqCIAiCcFfdtTXdHh4ed2tXhXz55ZdMnTqVuLg4IiIi+Pzzz6lXr95V2//111+MGDGCM2fOUL58eSZPnkynTp3yn1cUhVGjRvH999+TlpZG48aN+frrrylfvvzdOJ07QqutDlZoaopja0IUFzgDLoAdJLvCs/5xl9oJgiAIjwRJkkBXD0lXD0UeiWRZTMmcv3jL7xA5yhk2eHqxsVQJtvqGoIuAyT1WOKtgFLIdcFbBWLUbEXgLgiAIj5SHPnv53LlzGTRoEN988w3169dnxowZtG/fnmPHjuHvX3jUduvWrfTp04eJEyfSpUsX5syZQ/fu3dm7dy9Vq1YFYMqUKXz22Wf8+uuvhIWFMWLECNq3b09kZCQGg+Fun2Kx8NB7oWRBBUMGX5VOI0quzYVMNSFuDsJUe9DLGfntBEEQhEePpHIDlz5ILn1QbEdxMf9Ne9UCOrpv44SvOwdzvPKrYERmebHtdBXUShkc0mkaljlMuCkVvUomIf30vT4VQRAEQbirJEW5mJf69hw5coSvv/6aPn360LBhw+LYZLGoX78+devW5YsvvgBAlmVKlCjB22+/zYcffliofe/evcnOzmbx4sX5jzVo0IAaNWrwzTffoCgKwcHBvPfee7z//vsApKenExAQwC+//MJTTz11Q8eVkZGBh4cH6enpuLvf+8QziiMGJamjs9zM1UhGJN9l+dlvhUeLLMskJCTg7++PSnVX0kEIDwDRLx5timIFy2qs2XPQ2nYhSZBm1zJ8TyNyFlfgp2/fQ6VSYbFaOHGuOVXcUpl14DX6tRt0rw9duMvEe4VwJdEnhKI8aP3iRmO6Yhvp/vjjj/nzzz9Zu3Ythw4dyn/8xx9/ZNu2bYwePZrQ0NDi2t0Nyc3NZc+ePQwdOjT/MZVKRZs2bdi2bVuRr9m2bRuDBhX8MNC+fXsWLFgAQFRUFHFxcbRp0yb/eQ8PD+rXr8+2bduuGnRbrVasVmv+zxkZzpFjWZaR5aKm4t1lUiB4L3GWmFEcyLZIsrOicTWFotKGQ165GUUKRLkfjle462RZRlGU+6O/CvcN0S8edVrQd0Sn78jcjU/Ru9J/qIEv6m/gfM1d/LxuBz3rT8PdpQTbosKpUn0LVuk/0V8eQeK9QriS6BNCUR60fnGjx1lsQbeXlxdLlizB4XAUePzFF1+kW7duvPPOOwwbNix/ivbdkJSUhMPhICAgoMDjAQEBHD16tMjXxMXFFdk+Li4u//mLj12tTVEmTpzImDFjCj2emJiIxWK5/sncFRrADwBZ9ic9PR0PxeOKu0wJ9+TIhHtPlmXS09NRFOWBuPMo3B2iXwgX2SUbAH/s7k6DiiXIdMzlmfCDSJntOJFQnqC8RJwGXSYJCeJvyaNGvFcIVxJ9QijKg9YvMjMzb6hdsQXdkiRRoUIFSpUqVeg5X19fvv/+e15//XV+++234trlA2Xo0KEFRtAzMjIoUaIEfn5+98X08ivJsowkSfj5+T0QHV6480SfEIoi+oVwkeWgs0KJZIzF3/Mtqvi9xJgvvyC47gY6hUbRueJxAMK9UvH3yQX13Z39Jtxb4r1CuJLoE0JRHrR+caP5vIot6J46dSpPPfUUYWFhdOjQgcaNG+Pq6pr/vKurKzrd3a3x7Ovri1qtJj4+vsDj8fHxBAYGFvmawMDAa7a/+DU+Pp6goKACbWrUqHHVY9Hr9ej1+kKPq1Sq+7ZDSZJ0Xx+fcPeJPiEURfQLAUCv1AC207DMYaw2KyqVinHvDmDGMD+esJ7g97cXEmbIprJvHCS3QdbWR+3SGwxtkaTCfx+Fh494rxCuJPqEUBS1lIDKkQSyAvYjzuWvKi/QVEbKW/J6v+SYutG+W2xB95w5c/j3339RFIUZM2ag1WqpVasWLVq0oF69emRlZXH27Nni2t0N0el01K5dmzVr1tC9e3fAefdkzZo1vPXWW0W+pmHDhqxZs4YBAwbkP7Zq1ar85HBhYWEEBgayZs2a/CA7IyODHTt28Prrr9/J0xEEQRCE+5Za7fxIEW5KJTKrNz+sDkcjl8GlRRQ/hh2mtD4bgOEn6lHRJ5WWbscpZxuEkuGOZOyKZOyFpA2/l6cgCIIg3GuOGHx4FlKLXn6rAEhGeMCSOxdb0P3nn38SFRWFwWBg9+7drF27lnXr1jF16lRkWSYkJIT58+cX1+5u2KBBg3juueeoU6cO9erVY8aMGWRnZ9O/f38A+vXrR0hICBMnTgTg3XffpXnz5kybNo3OnTvzxx9/sHv3br777jvAeUduwIABjB8/nvLly+eXDAsODs4P7AVBEAThUePvUQarrEKvkqnilkqV6luALQXaWGUVxzaXYI1PVRaVTKZKYDQt3ZJoJi/EkDMLRVMFyaUXGB5DUt1/S68EQRCEO0xORcKCAlhVVTkj1yFZNuGjyqK0ajd6+RCSYnaOfj+KQXe5cuUoWbIkAJ06daJTp04ApKamsnz5cv788897sna5d+/eJCYmMnLkSOLi4qhRowbLly/PT4R27ty5AtMCGjVqxJw5cxg+fDjDhg2jfPnyLFiwoEACuMGDB5Odnc0rr7xCWloaTZo0Yfny5Q9sjW5BEARBuF1t63Rh1W5ISDtFdk42kvEoRn0W5lwTerkGaknNkRVxWBamY6rjTVqtUiw850VcRSt/m85T2yWLbt5WAjLGI2VMQjG0RzL2Al09JElMPRUEQXgUpOWm4gkct7gzOcETOIkKBQcqJDwZ4u9ORUMG6dZUPLX39lhvRrHV6R44cCBDhgy56lppi8XCa6+9xi+//FIcu3vg3W91uq/0oNXIE+480SeEooh+IVzpWn3CbrMz9olp7Nh1CqlFFeQgLekVVVjJpGNNDQnKUfw0Cs8EuFJJexCV4xyoSziDb2MPJHXRnzGE+594rxCuJPqEUJSE5C/wtX3GHylh+OvcqG04x7b01hzOrU6q6iSl1Tt4yfc4yfoB+Hm9ca8P94ZjumLr4aNGjWLQoEFs2bKl0HMjRoxgypQpmEym4tqdIAiCIAgPGI1Ww/A/BhIRHop61X68sjSYNlpo4FGOP7fKJJ+pS5CxHjMu5PDOuUpscbyJQ1MDJfsblMQWyKkvo1hWoCi59/pUBEEQhGKmyDlg2wnAU95R1NMfYdV5f77eJ/P1phj+2GDkdLonADnWB6v0ZLEF3Z6envz666/s3buX33//vcBzK1asYPTo0eTmij+SgiAIgvAo0xl0jPnnA8qVD8I6fztVS/pz+M9TvOQXgSVXwxerMihj60E97wb8GhPJO6dzWWr/CJtpGMipKGlvoyQ2Q86YhGI/WeQ+FEcMiu0wcu4B5Jy5yFnfOL/mHkCxHUZxxNzlsxYEQRCKoigKSu4e5PRhKImN8WU7AP/GlGbAsV6sUJegS51aTGnTnnrBoRitzknasZYHK64stjXdAFqtlrfffrvQ40uXLmXDhg106NChOHcnCIIgCMIDyGgy8vGSYbzfajQxP62l+/Be/PP3f7RqWokO9cvzzZ5dBLu781Hzd4hlPwti1rAkTke7wGdp7xOGIXcxmOej5PyEoq3pnH5u6ISkcnUG3EkdQTEXue8HNfOtIAjCw0RxxIH5HxTzP+A4A6oQcOnPktgYOrvPp4J3Kmp7HKWs1VAd8UNrcjAiogmy/A0AF2ze9/YEbtJdWUDh6+tLz549C9TtFgRBEATh0WXydGXi8uG4eZnYO3Uhg/o1Y8uOkxxeEMXMTj3xc3Hh5YXLOXzSl5GVxtDEtxFLYpbx3uHvWJhRBbP3SiTP/4FkQskYjpLY2DlSYt2WF3BLoK0L7pPAe47zq7au8/GLmW8FQRCEu0ZRrCjmxcgpL6AkNkfJ+hq0EUhev5Lm8RdzUnzZlX0GgIr6dF63R5IdtZ8dB5ZwcN8XWOP6Eu7unKmUlGG/h2dy825qpDs+Ph6TyVTswfOxY8eoWLFisW5TEARBEIT7m5e/B5NXjmBQsxH8O3gWk2a9w8Tv1zB+wmI+HtyNAxUTmbRlI2uiTjG6eWumVu/A0rgVLIldxsr4VbQNaEP7wM9wkdLzRr7ngflv58ZVIeA5A5Xaz/mzrg6KsTtKyrNg24WiOJDu3akLgiA8EhRFAdsBFPN8sCwBJQO0tZDcx4GhE0k2M4tjlrEp6WcMKj3e1jJY5f/Qq2RqlImnRpn4Qtu0yipSs7zuwdncupsKulUqFS+88AIzZswgKCioWA5g5syZbNu2ja+++qpYticIgiAIwoPDL9SHyatGMrDZSL5/6Ws+XTCYid+t5p2Rc/nwjfasfOZ5Rm9Yy1vLFtG2TFnGtOhM56COLItbzrK4FayMX027gDa0D+yPi+sbKJmTIOcXFDkWEpsRT3XOyLUwq+tQ0rUMJlVzfNkF9iOgq36vT18QBOGhpDgSwbLQGWzbT4IqAFz6Ihl7IGnCiDPHsejMXLYmbcdV40rPkO60CmjJqNULGRZ7FpPKjsbuTvfgEIIMatLsKjalpXAmJ5osWYOP4n+vT/Gm3FTQ7efnx+TJk3nyySfp378/zz///C2n+D979ixjx45FlmV++OGHW9qGIAiCIAgPvuCygUxeOYL3WoxiWp8ZTF4yjC/mbGLs/5byTI96fNW3KytPn2T0hjW0m/kLgxs3pW+1J+kU1IGlsZeC77YBrWnlosIDmB5fEX+thWam49TV7SPT/is7Yv2IznXleR/Iyb2AyeVen7kgCMLDQ1FywbrOGWhbNwJqMLRFchsKukZIkpronGj+PfMtO1N24aH1oE/JJ2nu1wwUNd/s3smSqDPUdDeSolYAmU8vnL9iLyYcDomQTP09OMNbd9OJ1EqXLs2yZcsYNGgQkyZNon///nTq1Inq1asjSdeeqJWRkcHmzZv5/fffWbFiBePHj+eVV1655YMXBEEQBOHhULpKCSYu/4gPWo1h/BPTGL/4Q8qW8uPrmRuJOp/MyHc7sfKZ55m8ZRMj169h4bEjTGzdjj4le9MpqAPLYlewPG4lWS7RPOsN7mo70VJLzhuboGiz0VgXU991I23cYp07tO1HsZ9H0pS4tycuCIJwn1AcMc4qEYrDORtITgWVF2gqI0lqUHkVmYBSsUU6A23zv6CkgbY6kvsIMHRGUnkAcCb7LP/GLGZP6l58dT70K/0MTXwbo1Np2R59no/WruJ8RjqVJH/27AeNxoY21YGXOhd9Whr2DBspnj5YQ12x27WUVTnu8tW5PZKiKMqtvnjfvn1MnTqVf/75B61WS926dQkJCcHT0xMPDw9yc3NJSUkhJSWFqKgoDh48iJ+fHy+++CLvvvsuvr6+xXkuD5QbLaR+r8iyTEJCAv7+/rc8m0F4uIg+IRRF9AvhSrfbJw5uOsLQDuOp0aoqo+a9z+5D5xk9fTH+Pm5M+rAHIYGe7Ig+z7C1q7iQkcEbdevzWp166NRqMmwZrIyewePGWRyzeHBIPZiOgR0xaU3OY3NYiY9tRoAmFRkdKnKdawuN3cHQMf/DoVD8xHuFcCXRJ+4v16v8AIBkRMqr/KDIKWBehGKeB/ajoPIFQzck4+NI2vL5LzmZdYp/Lyxif/pBAvT+dAnuTCOfBmhUGlLMOUzcvJF5Rw5TOyiYj1u1ZeHfO/gm5wiK+uqDuZJD4XXXcN5/pVNxXoJbcqMx3W0F3RdlZmayatUqtm3bxpEjR7hw4QJZWVmo1Wo8PT0pXbo01atXp1mzZjRu3Pi6I+KPAhF0Cw8a0SeEooh+IVypOPrE7pX7Gdl1Eo2612Xo7Hc5H5vGhxP/ISPLwvj3u1KrWkmsdjtf7NrOt3t2UcbTiwmt21ErKJhd8b9RWxmPosCJXE+2ZQdRwq0xDTyCcLEtR7HtQgL2MZhaHv4o5oWQuwVQg74lkrEb6JsjSbpivS6POvFeIVxJ9In7i2I7jJLcA2flhzpg7AmakmA/B+Z5YNsNKOA2DHJ3gXW984X6lkjGnqBviiQ5J1ErisKxzOMsjFlEZMYRgo3BdA3qTD2fuqglNYqiMO/IYSZu3oCswIeNm/JElWqoJIlpMxbz186joFYYN6QrSYqFFIsZb4ORij6+vPf+TMxoGN27OR261b1XlyvfXQ26hZsngm7hQSP6hFAU0S+EKxVXn9j8zw7GPfkp7fo1Z+D3r5GVk8vIaYvYd/g8A15oRY8ONQA4kpTI0DUrORgfR7+ImtQJO0crzST0Kvmq27bKKjYznLbBzwAXE/4sdgbg9kiQPJ0j38ZuoK0pBguKgXivEK4k+sT9Rc49ACm9QFsXyXsmknTpdyLbjkHqSyDnZRLXVHYG2sYuSKpL9bIVReFQxmH+vbCY41knKOlSgq7BXajtVQtV3vZOpSQzfN1qdlyIpnvFygxr2gJfFxccDpkf/tjCzPk78rcXUTkEQ1wqLTrVQuVpYum6Q+yPjAagf8PyvPh+t7twZa7tRmO6m17TfbOys7NFfW5BEARBEG5Kkx71ef+nN5jy3BcY3Yy8Pv15Phneky9+Wc+071dz6mwiA15sRWVfP+Y90Ydf9+/j0+1b2JqcxupStUm64ElGmolwryS8jWZkvYN0g4Rao5Ala6jmcekDpaT2A9f+SK79UWwnUCwL8qZN/g7qEiiGrkjG7kiaUvfuggiCINxJ9iPOr8aeSJIKRU4Fy1LnWm3bQZDy4jnXN1C5DSjwUkVR+C9tP//GLOZ0dhRlXMMYWP4dIjwv5fyy2u18tXsH3+7eRZCbG79170WTks731MxsC2OmL2Hn/jPUDPBg34UU0KjZf+QCADtmb77iWB3Ys6x37FLcCXc86F62bBnz58+nVKlSDBs2DDc3tzu9S0EQBEEQHgJtn22OOdPC52/9gIu7kefHPsWAF1tRpqQvn/6wmrMXUhj3/mN4urvwQs3atCtbjkHrfifFcZYMFxUaczVql61BKQ9Pzqan8Xfkfzj8tuBizGVDyhoSj8bQJagT4e6V8z8YStrySNoPUEzvQe5OFMtCZwmy7C9RtDWco9+GTkiqB6tGrCAIwjXJqc6vjjPIKS9B7lZAcS638fwCRXKH1H4gGS69RJHZk7qXf2MWcy7nPBXcyvNBxUFUcQ8vMENo6/lzDF+3mgsZ6bxaux5v1K2HQaMFIOp8EkMnLyQtI4epwx4nYecJIn9dT8UmlTi68yRt3u1MaLWSeLgbqRDmz47Fe5n50RxCO9e6m1fnthVb0F2vXj1ycnJo1aoVLVq0oEWLFnh7e9OrVy969erFqVOneOedd/j555+La5eCIAiCIDzkur7RHnOWhR8+nIWLm5EnP+hG17bVKRXizUdTF/LykNlMHtqdMiX9CHX34MUadZgTvwsPtxyypZ2cy9VQ1VSTAF0a1cKjOZaZC0ATz3aczz3GlGPTKOVSii7BHanjVTt/CqQkqUDfAEnfAMV9JFjWolgWomSMh4wJKPpmeeu/WyJJhUvX3GoWYEEQhLtJkXPAuhYsS50PZH+DRVWV89KTnHFUQmcLopS2JCbbKnwBVF44FAc7knexKGYxMZZYqriHM7TSYCq5Vyyw7eScHCZu3sD8o5HUDQ7huy7dKOftk//8xh0nGPfZUoL8PfhxyrOEBHoSac1FZc7lxKoDDPzqJR57rX1+e1mW+f6fHajMuZSrGXYXrk7xKbag++mnn+aHH37gyy+/5IsvvkClUlG1alVatWpFkyZNCAoKIjo6urh2JwiCIAjCI6L34G7kZOTw/ZBZuLi70OXVtkSEh/L95Gf4cNICXh06h1EDOtOkbjkupFlwOCTUagWTWzb7c1ex/9iq/G1JEs7nzSGMqf4kkRlHWBy7lC9PfkOA3p+OQR1o7NsInUp72WuMYOyMZOyM4kgGyxIU8wKUtHdAckcxdMhb/13bOS3zOlmAFQDJCHlZgAVBEO4mRbGAdQOKZSlY1gEW7KoyaIBTFhMfJ3iicB5w1siWUBjifwBfA2xNS+PfE8OJtyZQwzOCF8v0p5yp7BXbV/g7L1GaosCk1u3oFV4VVd7otywr/PznVn7+axstGpRn2FsdcTE6k1cu/2lt/nbW/b4FnUFHcNlAYk7FseLndRzc7JwGr1I/WHkAij2RWkpKChs3bmTDhg1s2rSJ//77D1mWkSSJIUOGMGHChOLc3QNLJFITHjSiTwhFEf1CuNKd6hOKovDVuz+z8MvlDPntbVo/3RSAHHMu4z9fxqadJ3ilb1MyQhW+2LueT9q3orKfH6uj97L05CGSsu20CImgRkAwI9Zs5K3aLXizboP87UdlnWFJ7FJ2p+7FXetGu4C2tPJvgYvG5erHZD+FYv7XWZtWvgDqUDA8BtoqkPYW18sCLPn8g6StUmzX6H4m3iuEK4k+cXcpSi5Yt6BYloB1DSjZzpk3hs5g6EhMzjGCct5AUeC8PRCLrhNGXUXMucfQ5y6hpCYeSYLRsTXxMzWna3BnSrkWznNxMiWZ4WtXszMmmh6VwhnapDm+LpfeR7NzrIz7bClbdp/i5T5NePbx+vlT0edMmM/Pw39HrVHjsF+9DrfBRc+PkdPxL+lX/BfqJt2zRGre3t50796d7t27A85yYmvWrOHzzz/nww8/LO7dCYIgCILwCJAkiddnPE9Olpkpz3+B0WSgUbe6uBh1jH+/Kz/N3cK3szdRskkgVrWWqHM2yjgMBJwvR1dLEPvkRObtj2KhFIPVrsVLbyiw/TBTad4q/wZx5jiWxq3gnwsLWRy7lJb+zWkf0BZPnWfhY9KURXIbiGJ6F2x7UMwLIGcWKJnOBqoS4DkDlTrvg6GuDoqxO0rKs2DbhaI4EHnRBUG4UxTFDrk7nIG2ZRUo6aAui+T6ojM3haZMfls7MVhlFXqVTEltHCg/wcVcZXkTf6yyiu6hz1HLr3B97IuJ0r7ZvZMQdw9m9XiCRiVKFmhz7kIKQycvIDk1m8lDe9Co9qUR8r8/XcTPw3+n3+gnqdmpClp0oMDJfVGkJ2Xi4etGuZphqNQqPHzd7ouA+2bctZJh58+fZ9q0acyYMeNu7O6+J0a6hQeN6BNCUUS/EK50p/uEw+7g474z2P7vbsYt+pDabSPyn1uz5SgjflpCXATo0hR89lMgqLXrIbEWKDqJil4+zOjUhYo+vkXuJy03jZXxq1mbsB6bbKOxbyM6BXUg0BBwzeNTFKtz3bd5LqACJGf9WkNX0LdAUpmQc+ZBxlBwH4fKpfftX5QHgHivEK4k+sSdoSiOvJuAS8G6HOQUUJcEQ2ckQyfQVCiyDOK6hA38e/47ni3RiQqmspxI/Zdz2QdIsYOnsQE+el/+id1E1xKv0NK/eYHXbjl/lhHr1nAhI53X6tTjjTr10WsKju1u2X2Ksf9bgp+3iQlDulMy+FKpsYVfLueLt3+kz9AePDe2N4mJiQ9Mv7jrI91ZWVn8+uuv+Pv706VLF4xGY4HnS5QogdX6YKV2FwRBEATh/qLWqBk66x1G9ZjK6B5TmbhiOFUbVwKgdeNKRGWmMuH4VnI9IKe+lsfKVqJSkB9HYxNZEnUcRev8LJJqsdBlzm88F1GLd+s3xE1fMBmap86TJ0v0oktQJ9YlrGdF/Co2Jm6ijlctOgd1IsxUusjjkyQ9ijokbyNfITliUCz/oqQPAnQo+kagKe98/mK2YEEQhNugKArY/stbo70M5ARQBYPx8bxAu0qRgfblsuxZpDgMrE9N4quzG5EkFU18e9OlVEf89L4cyzhOimMXWfas/Nck5+QwYfMG/jkaSb3gUL7v0o2ylyVKA+f67d/mb+fHP7bQpE45hr/TEVeXS++3y35cwxdv/0jPgV3oP74Pd2k8+K4rtqC7R48erFmzBgAPDw969+5Nr169aNq0KXq9noyMDKKiooprd4IgCIIgPKK0Oi2j/n6PYZ0m8FHnCXyydjTlazmnSZYP8UM6oqCoJdINdmZdOAQX8l6oA5CQHArj67XkhC2NL3ZuZ9Hxowxt0pxuFSsV+mDqonGhc3An2ga2ZUvSVpbGLmd05DjC3SsXKjeW72I5MTkNyfUZJNdnUOznwboaxbIKsn9wPm+ehyLpQd8GSVPijl0vQRDufzdb8UBRFLBHOqeOm5c580qo/MHQwblOWxvhrMJwHbIiczD9EFuTtgFwIusk3UO60cKvGSatKb9dgjUBAJPGhKwo/BV5iMlbNgIwpU17elYuHNjnmHP5+PNlbNhxghd6N+L5Xg1RqS61WT1rI9Nf+ZbHXm/Pq5/0Q5IkEXRfj7+/P1lZWWzZsoXffvuN2bNn8/3336NWq/Hz8yMlJYX333+/uHYnCIIgCMIjTG/UM3bhEIa0HcvQDuOZtmEspSqHkhaXjd8ueLZPfU5ExbP+WBTVqofQoUFlqgYEsG1PFL/M3kp2VQuvt61Pt4qV+XjTBgatXMofhw4wukUrKvkWXiuoU2lp6d+c5n5N2Z26h8Uxy/LLjXUO6khd70vlxtBUBsCSPZs4RwRnzdFk2bMwacpQyjiOQMcgDPIRUPmgZH4CmRNRNJWQDG1B3xY0Fa87KiUIwsPjZioeIGflrdFeCo6zIHnlBdqdQFfHGaDfAKvDyuakrayKX02sJY5gQxAAXmo/QqUIFh09RYrFjLfBSGVfX5YnrANAsrnTZ95cdsVcoGflKnzYuBk+LoUTTkbHpjJ08gLikzKZOKQ7TeuVK/D8hr+2MfX5L2jfvyVvff7CQ/+eV2xBt7e3N7GxsbRt25a2bdtisVhYvnw5u3fvJj09nQYNGvD0008X1+4EQRAEQXjEubq7MGHpR7zXchRD2o5l+qZxpGeY0VihSbnSvNGlMX8t2cuXv21g63mJ9u+Vo0FYSWZZt5Ke4fxwG+zmzpedHmPTuTOM2bCWx36fSb+ImrxbvxHu+sL1t1WSinredanrVSe/3NhXp74hINqfjkHtaezbmBxbFu6A3n4Qa3JvTmQFkmA34K+xEGiKQ6/PAAkyDO/g4VUdcjehWFahZP8MWZ+DugSKvo0zCNfWvOEP0YIgPKDk1LyA+2oVD3aBYnYmYXScB8kdDG2RDKNA1wBJuvGQLiU3hdXx61ifsJ4ch5k6XrV4Iex5UnOsfHV2OtHWs4w6PIn4BA/MFh1GQy4B/ul4uOUgSTBwxTK8NYHM7vEEDa9IlHbR9n1RjJ6+GE93F76b9DSlQwtOOd+6cBcTn/4fLfs2YcC3rzwQa7dvV7EF3VOmTGHcuHHk5ubywgsvEB4eXiCLuSAIgiAIQnFz93Fj8soRDGw2ksFtxtJhYl8ALsSlEVE5lCe71KZi2QBGTlvEC+//RscWVQHwcC+Ye6ZpydIs7fscP/+3h8/zppwPa9KcbhWLmD6OM5t6FY9wqniEO8uNxS3j1zOz+OfCQpp7laeTzpkFuKIhg4qGjEKvt8oqMmUtnioTGDoiGTo6S/rk7nBOQbcsRsn52Tkarm+NZGgDukZIku4OXEVBEO4lRckrj6Wtg+Q9E0lSodijQd6LomRfaqgujeT2Eeib3PR7wams06yMW82u1N3oVDqa+zWlTUBr/PTOZJJbM4/hcEio1Qqe7jl4uucU2obDIdEuLJyxTbsUSpTmPA+F2Qt28u3sTTSsVYYR73bCzbVgpYidy/Yx7slpNO5Rjw9+ehO1+tG4qVjs2cuTkpK4cOECERER12/8CBPZy4UHjegTQlFEvxCudK/6RPzZRAY2GwE+bpwLCyAiPJTPx/TOXz+YkpbNqE8Xs+/weQC+m9SX8PLBRW4rNjOTCZvXs+TEceoGhzC6RWsqFzHl/EpxlniWxa5gU9JmPFTZhOiNvFz6edxUFy6tz1RX5OezszmUGcPbFcdTxhRW5LYURXYmRrKudpb6cZwFyRX0zZH0bZ1fVaYiX3s/Eu8VwpVEn7hEzpkLGSPA9U1nwG3dALYDgAEMLUHyBvPsm6544FAc7E3dx/K4VZzMOomf3o92AW1o6tcYo7rgjcf9cbE8teBXagR5M65VG86bzxOfk8KGqAtsPpWKq1ZHulnhj+7PEREYVGhfZksuE79cwdqtx+jXswEvPdW4wPptgL1rDjK8y0TqdqjBiD8HodEWDtwftH5xz+p0+/r64utbdPkNQRAEQRCEOyGglB9TVo3krY4fA7A/MpqXBv1CeQ8j2lwHNp2arPRLIzdfz9zExCHdMbkWnkIe5ObG5x0fo3eVs4zZsJauv8/k2YiaDLjKlPOLAg0B9A/rh7/ejz+j/ybTrGHQkZl55cZ65Jcbq+CVxca0nzmbc+6qQbckqUBXC0lXC8X0AelGdtQAAIG9SURBVNhPgHUVimU1imUgoEXRNcxbB94aSV30Z6+bTc4kCMLdo8gpYN0EObOdD2R/iSK5ga4xksfzoG+JpHJFzt3tDLpvsOJBtj2HjYmbWB2/hqTcZCq5VeTd8m9RwzPiUu6JK0QmJmDN1dKzfCNKu5ZmW1QGn247hEqSGNP0cRyyzJA1K4lMTCgUdMfEpzF08kJi4tMY/35XWjSsUGj7BzZGMrLrJGq0rMJHfwwsMuB+mD3UZ5uSksLbb7/NokWLUKlU9OzZk//973+YTEXfGU5JSWHUqFGsXLmSc+fO4efnR/fu3Rk3bhweHh757YqaZvb777/z1FNP3bFzEQRBEATh2kIrBPPmlGcY89tG0Kg5fj6Z4+eLaOhwcPRkHC8Nnsm4D7pSvrR/kdtrUrIUS/r2y59yvvj4UYY2bk73SkVPOb9IRgbg7XJvEm0+z4r4VWxI3Eg1j6q09G+Or84ZIF9eeudaJEkCbQXQVkAyvYniuAAWZyZ0JWMUMBJFWzM/EZukca6zvJnkTCLwFoQ7z1lD+wCKdSPkbgTbIUABVV4Q6/Iqkts7SJK24AvtZ51fL1ZGuIp4Szyr4tewKXEzNsVOA+/6vBPYhlKupa57bCkW5/tEitlMp9m/cio1hV7hVRnSuCneRhd2Xogu0O6iXfvPMurTRbiZDHw7sS9lShaeFRS5/TjDu0ykcsMKjJr3Pjq9tlCbh91DHXQ//fTTxMbGsmrVKmw2G/379+eVV15hzpw5RbaPiYkhJiaGTz75hPDwcM6ePctrr71GTEwMf//9d4G2P//8Mx06dMj/2dPT806eiiAIgiAIN6B0WAD61QdAp8HgZqTR8y3QerjiyDITtSGSU/9F8f/27ju8yaqN4/g3adK9N6Wb2dKyV9l7ioqgoqiIir4IDkAZorIEHKCAeyAOQFEQFQdLkL03tOxCoXvvleZ5/0gbKBQo0JAW7891IW3yNDmppyW/5zznvinUMfX3CXz51wGem7SUV5/tQd+uYRU+nqWFBc+1aM299UOYtfVfxq37mx+OHWZa526EeFQc1u01hpP7WbosY7uxnam7+DdpEwtOfYythaHSr4pbq9arsqgNdsNQ2Q0zrJQVbEQpXIeS/QFkv4OiaQBWPUBT5wbFmfYa7teng4RuIUxCKUmBos0ohVugcBsoGYZCaFbtUdkMBasOKCUJkDYYivcD5fc4K4oe8n8xfFLaGaH8/QrHs0+wJmEdBzMOYa+xo7d3L7p5dsXZ0umq46+lWGfYV/72ts20re3HB7370cjTy3h/TGYGAK7WNsbnXbZqH598v4mWjQOYOuYeHO2tr3rck/vO8FrfmdRtFsT03yZgZXPtq4XuZndt6I6KimL16tXs2bOHli1bAvDhhx/Sr18/5syZg4/P1f+4hIWFsWLFCuPnderUYebMmTz22GPodDo0lxUMcHZ2xtvb2/QvRAghhBCVpi/Ro84vIqiuN7Gn4ik+GsPEn8ZhobFAr9fzStepHNkShbujLZ/PepT3v/qHmR+t5siJOF56qhtWlhW/NSq75HxI2Hmm/buBAT8u5onGTXm5bTscrcq/0QywNaw0b0nZSnv3CCzVWjp5dKCTRweic87xwakFUALLL/7CmZwzdPXsQphTo2te9nk9KrUr2A5CZTsIRZ8LRVsNhdjyvgMl23CQ2hPsX0RV1k7IsiWKzf2GSsjFe1CUkluM/0KIKymKrrQewxYo3Ay6Y4Y7NGFg+ygqq06gbVy+4rg+GQVQivdQkDyYc/qWpOntcVXnEKjei5X+KCoo18mgWF/MrtTdrElcR0zeBWrb+DA8aBgRbm2wVFe+yFpKXh7zdm3nx6OHAajn4sr3Awdjcdl+ar2isDzyKAChHp4UFBbz7mdrWbs5iqH3t+bZRztgYXH176+zh88zsfdb+IfU5q0/JmFjd3Uo/6+4a0P3jh07cHZ2NgZugB49eqBWq9m1axcDBw6s1OOUbYrXXFGhb9SoUTzzzDMEBwfzv//9j+HDh1/3UrPCwkIKCwuNn2dlGSqZ6vV69Hr9zby0O0Kv16MoSrUcmzAPmROiIjIvxJXMPSdO7j8LwAMv98fJ3ZFpg+bw9uMLGP/taCw0FvQc1pkjW6I4uf8s9VoEM2FkLxrVr8W8hRs4fjqB6eMG4ON17dWhiNp+/D7kMb49dIAP9+xk1ckTTGzfkfsvr3JeWqL2RPZJZke9Swe39nhaeZBUmMzW1G1kFmcC0M+7D4czjzD35Dw8LN3p7NGJDu7tcdLeaoFVG7DsafijFEH2HCj4DpQ8SH8cReWKYtkBLFuDtjVY3W9oRVR0DL2m4pX+qmLueSGqn2ozJ0rrHlBW90BJN/S+1oRAad2DG14JUpIERVtK/2wHJQtUTmDZAWyeAKsOoDa0zVJK/6Mol153epEeW72h44G1/igNOQplGbb0sEK9mrwiPRb6DDYmb2JD0r9k6bJo7BTOQ/UHE+pw6XdQZb6nhTod3x4+wCd7d6NWqXiySTO+Prif0+lpPPrLTwxqGEqAkzPnMzNYcTySvXGxAKSl5zJyzjpiYtOY8nJ/urdvUOFzxkRdZHzP6XgFevDWH5OwtrOq1LiqzbyopMqO864N3QkJCXh6lr/sS6PR4OrqSkJCQqUeIyUlhRkzZvDss8+Wu3369Ol069YNW1tb1q5dy/PPP09OTg4vvvjiNR9r9uzZTJs27arbk5OTKSgoqNR47iS9Xk9mZiaKotSIyoHC9GROiIrIvBBXMveciD8XD4CNqxVBrXwZ9emTfDxyEfn5BYz86AlsXa2MxyUlJQHQOtyLt8b1Zs6Xm3lm/Pe8MKwdLcJ8r/s89/n6E+HqzoeH9vPq+jV8f3A/45q3op6zC4W6QjRo0VHMyZxTnMw5ddXXa9ASrg6jo3t7YoousCtnN7/G/c7K2N9oZBtKW/vWBFsFXfeE/o3YYok9kKa8BVhhpWzGsnAfmsI/UKFHjzNqoCBnHbk5dSnBF0y05m3ueSGqn+owJ9Qk4sbjqLj2e3EFa1L5Hj1el92qQ8tRLNmFJbvQchoFFToaUsQDFNIWndIACi2gEMguAZKu+RyxRUUsTm6Bg1pHbUtv2trZ42ShkFmiYmduDrFFCWTrNXinruZk/mlUKhUt7JrR3qEdnloPKIDkguRKvWZFUdh4MYZPDh8kMS+XgXXq83SjcPJ1OpYcPkShvoQ9cbHsKQ3Zl9Oq1Mya+xcOai0zx/Um0NfF+Hv0cglnk5g5aD6O7vaM/e458opyyUvKveq4ilSHeXEzsrOzK3VcjQvdEydO5J133rnuMVFRUbf9PFlZWfTv35/Q0FCmTp1a7r433njD+HGzZs3Izc3lvffeu27onjRpEmPHji33+H5+fnh4eFTblmEqlQoPD48aMeGF6cmcEBWReSGuZO45USvQUJAoP60QT09P+g/vhbOLMzOHzGPh2B9p3iPceNzlJ+c9PT1Z1CCQmR+tZvan//L4A2146qGICi+ZNH4N8HlgIDsuxjB100aGr/ubx8Kb8HCjMPYfroOOQkDB3q4ArbaE4mILcnKtARUarHBo4I2XgyNeeNGKluToctmeuoONyZv4Imkh3tbedPXoTDu3COw1djf/zcjzgxxwdcgDm95AF8Pt+mwo3oc6bwkUb8GabViz1XAZurY1WLYy/G0RCLcR+i9n7nkhqp9qMSeKkyG9AEPdgxZgPQgs/KDkAhSsgOJ9qCjA3UUNan3pSvZmKNoBSo6hlZdlB7B6DpVle7RqV7TAzf605uTkkpZgjbtNPZ5u8Ipxq4le0aPLPMLB6IXkleRTXBzL/bXvpbNHp1v6nXA4MYGZWzexLz6OboHBLGrfkTourgAkJmfhtVchT1FQgGJ7ULSgKgZtjuF0nLq4hLqBXsyacB9ODjYVPkdCdBLvDPkEBxd75vwzFWfPyu8rh2oyL26CtXXlLpmvcaF73LhxPPnkk9c9Jjg4GG9v76vOvOh0OtLS0m64Fzs7O5s+ffrg4ODAypUr0WqvX2GvTZs2zJgxg8LCQqyu0UrEysqqwvvUanW1nVAqlapaj0/ceTInREVkXogrmXNO1G8eDMDab/6l17AuqNVqOj7Qljd/HseMh+ZyaOMx43FXjs/J0Za3Jw5kya+7+fKHrUSeimfqmHtwcbK97nO29w/kz0ef4NtD+5m/awe/nThOZqEasKG1T20Gh4YZL9NcHnmUPXGxKEBGYSG+TpfG4GjpQJ9avejt3ZPj2SfYmPQvP11czvKLv9DGrRVdPTpTx75OpVe/9ZaNDB8U/ILKdqChDRmA2gnFogtK3kLD5y7foqIApWgPFO2C7L+BElB7gGVrVJZtDJekW9zeyrv8rhBXMvec0KtK94JoW6Jy/f7Szwit0dv0h9QHoeQEZI2BkhhADdomqOyeBquOoAm77Gtu3YUCQ2XwTh4d0VhoKCwpZGvKNtYmriehIBEPS3fySvIZWPs+unt1venHj8vOYs72rfx6IoqG7h58d/9gOviXr2ielVuILrsES6BJqC/9u4VR29uZ8xdT+fKHbaSXtlx8YXhXXJwqDvxJF1KY0GsGltZa3l0/BVfv61dbvxZzz4ubUdkx1rjQ7eHhgYfH1aXorxQREUFGRgb79u2jRYsWAGzYsAG9Xk+bNm2u+XVZWVn07t0bKysrfv/990qdvTh48CAuLi7XDNxCCCGEuDPUpSvTR7ZG8UrXqfQe3hWfOt5kp+dQu14tzkca3txeax+eWq3i8QfaEFqvFlPeX8VTr3zHjFfuJazB9fd0WlpYMKJ5KwbUb8j4dWvYeuE89lpLXu/UlbDSCsCtavvyQEgjHl2xjN1xsZRcYwwqlYoQx4aEODYksziTLcnb2Ji0ia0p2/Gz8aWrZxfaubfFxqLilaZLj2Nh2D9avBcl7XEUmwdAE2BoP5T/i6F6OaBSO6DStkVl1QUARZ8DxftRinZB0R6UrGkYQrg7imVrVJatS0N45U4AKCVxoEtFQwrkbURPpvQKF9WDrvTqWJtBACi6s1C0u7Sl1w5QSi+JVruisn/ZUHH8Bm27bkVZ+8DCkkK+jv6WPWl7yC8poKVrC54JeooSfQmzT7xLXkneTT1ublERX+zfw5f792Jvacnsbj0ZHBpWrkhambLfiU1Cfflw2sOo1SqSUrP56Jt/yc0rwt/HhZi49Gte/JIan874HtNBUXjvnym4+7je3DfhLlfjQndlhYSE0KdPH0aMGMFnn31GcXExo0ePZsiQIcbK5bGxsXTv3p3vvvuO1q1bk5WVRa9evcjLy2Px4sVkZWUZC555eHhgYWHBqlWrSExMpG3btlhbW7Nu3TpmzZrFK6+8Ys6XK4QQQgjAyd0Ba1srCvIKObIliiNbKt5y9u2by5ixaiJay4qvZmsR7s+iOU/w5txVjHrjR0YP68Lgfs1uGDK97R3oW7ceWy+cx85Sy/3LlvBYeBPGRrTH0coatUrF4NAwdsfFEpmcRBPvWtd/PVon7vHpR79afTiaeYyNSf/y/fkl/HThZyLc2tLVs/O1e/CqXQx9uJV8Q8G04j1XH6Oyuar3r0ptD1adDFWWKQvhB1CKdhsCSdZbgA7UbpeF8DYVhvDLe4W7AlzRmlx6hQtzUUoSoGi34ZO871GyZ5ZW/FeDtikqu2dR1O6QNRmsuqGyucck40gsSORU9mkAvo9ZgrulG929utHFoxPuVu4AbEneClxqR3gjekVhRdQx5u7YSkZBAU83a8HIlm2wt7x2VfOT0YYrhPt3C0OtVnHg2AXenLsKrdaCT2c9wulzycz+eDUno5MIqVv+91Z6Uibje0yjKL+IuZum4ennftPfh7vdXRu6AZYsWcLo0aPp3r07arWaQYMGsWDBAuP9xcXFnDhxgrw8w1mj/fv3s2vXLgDq1q1b7rGio6MJDAxEq9Xy8ccfM2bMGBRFoW7durz//vuMGDHizr0wIYQQQlTI09+DhZEfkJmSjb5Ez+kD0WSmZOPk7kDdZkGoLdREHznPvP99yfQH5/LGT+OwtKo4eHu4OfDh9If55PvNzP96A0dPxDJhZG9sba7fjietIB+A93v141hyEvN3beePkyd4vlUbhoY3wd/JudxxlaFWqWnsHE5j53DSitLYlLSFf5M3szF5E8F2QXT17EIb11ZYWVy66k5l4UO641Lyi+NR9DqyC3aj6NNQqV1xsG6NSq3BRlsL1xuEXUMI74jKqiMAij6vNITvKg3hs4BiULuiaFujsmxlCOGauqVVoQ29wotojKXDENAGSK9wcUcp+kwoPgLFR1CKDxs+1l++DVVBZfcMaBuDNhyV2lBvSckrbSVcxavbObocdqftZVvKdk7nnDG2+PKz8WVqozfQqC9FNL2iZ0vKNuBSO8Lr2XnxAjO3/Mux5CTuqd+ACe06UbsS9aMyswy/j7w9HPnqh618u2InzRr5MW3sPbg42ZFfUFzuuDJZadlM7DWDnPRc5v47jVpBXlc9trjLQ7erqytLly695v2BgYEoimL8vEuXLuU+r0ifPn3o06dPlY1RCCGEEFXL098DT3/DVrQGrepedX+95sG4eDkzZeB7TB88hzd/HoeldcVBWqOx4MXhXWlUvxZvf7KGERMW89ar9xJ0nZUcV2vDZd+x2Vk807wlA+o35P2d25i1dRMLD+ylnZ9/ueNulqulKwN97+Pe2vdwMOMQG5M2sTB6ET/E/Eh793Z09exCbRsfUgtTmXjsI4r0RVc8QjZwHgBLtSVvh7+Fm5VbpZ9fpbY1XGZr1R64PIQb9oQr2W8DxaVtl+obvkgTQobuAzxtfAx7IKVXuMBQPZziZMPeal2U4eTLbW49UJQCKI6E4sMoxUeg+DCUGOY7KgfQhoHNQFTacBS0kPEcqOzA7rly+7MVRW/YhgGG9mG3SafXcTjzCNtStnMw4zB6RU+4UyNG1nkWN0s33oqazYX8i7x7Yi4d3dvjaeVJUmESW1K2cSL7pOH7dZ3949EZ6byzdTNrz56mmXctlj/4CM1rVf575+Ro+H307qdriU/K5JkhHXhsYGtjMcnYhIxyxwHkZuYysfdbpMalMfffafjWlxNn13JXh24hhBBCiIq06tOM6b9NYMr97zB10BymrnjlmsEboHv7htQN8GDye7/z7MQlTBjZmx4dGlZ4bKiHoSr68sijPBDSCC97e97p0ZvnWrTig53bWREVCUBKXh56RUF9i8XJLFQWtHBpTguX5iQVJPNv8iY2J29lXeI/NHCoT7hTmDFwN3CoT0f3Dpe9kd/KieyTFOmLyNbl3FTovtJVIVzJh6KDhsvRC/4wHKSLxJ37IbMNimUr0DQATT2wHmi47F0XBZaNb3kMogYqicONx0urh1+tMlsPFEUHulPlV7B1J4ESwBK0oYatEqUr2FgEli98VnyscnUPVBa39BIVReFsbjTbUnawK203ObocAmz9edBvEG1d2+BsaajsnVqYiqXakiJ9ESeyTxpD9uUs1ZY4VHB5eWZBAR/u3sn3hw/gYWfHvN79GFC/4U0XPczONvx/SEzNZsH0h2kScqltol6v8NfGowDUDzL8fsvLzmdS35kknE3kvQ1TCQj1u6nn+69RKTda2hUmkZWVhZOTE5mZmdW2ZVhSUhKenp41onKgMD2ZE6IiMi/ElWranNi//jBv3Ps2jTuHMm3l+OsGb4C8/CLe+3wd67ZEMbhfM0Y90QWttvwb8qNJidz742JUQKvS6uX+Ts7ElFYv331Z/9sGbu6MbdueHsGVr0p+PcX6Yval72dj0iaOZ58AwNXShQkNXsHb5lL3Fr2i5+3j73Ei+yRTQl8n2D7otp+7IvqczyDnfbB7jdzcOOy0x6D4EFC6+q6yN7Re0jRGZXOv4ZJ0TT1Qu1fJ9+NySkkc6NNRlJIqW1UVt05feATSB2Fo19XSUMxM419+6wEKKreVqLSNDFejllwoXcE+bFjBLo4ECgC1Yd5owy8FbE09VKrr/zxfXnPgmlQ2qG6y5kBKYQrbU3eyPWUH8QUJOGudaefWlnbuEfjZ+lb4NamFqWTrctAres7nxZCjy8FeY0+ArT9qlRoHjX25k2PFJSUsPXqI+bt2UFxSwv9atuHpZs2x1ly/69KVCgqLWbBoI7+vO2y8rUmoL/26GqqXxyZk8NfGoxwqLUK58L3H8fdyYnK/WZw5dI5310+hQcs6N/Wc11PT/g2pbKaT0G0mErpFTSNzQlRE5oW4Uk2cE/v/OcKb975Now4Nmf7reKxsrt+NRFEUVq45yIJFG2kQ7MWMV+7F083BeH9sdha9vl9Evk53zcew0Wh4v3c/vj14gJ2xF2ji5c0r7TrQ3u8aRdFuwcqLv/Fr3O/GFbQwx0Z08GhPU+fG2FjYsCV5K19FL+LJwCfo6tm5yp73cvq8ZZD1BjjMJim7PZ6enqhUekP7Jd1plPzfoHAdqL1AnwYY9o2icgJNHUNw0tQtDeN1Qe15S2HcVOFK3Dp9wUHIeKi0Xdfiqy7tVlKHgO6goXe2Psmwiq1kGA6w8AVtY1TacMM+bE0oKvUt9LKn6k7G5JfksydtL9tSdnA8+wSWaktaujSnvXs7Qh1Drntp+E2NV1HYcO4ss7duIjo9nYcahTO2bXs87G7+9Z8+l8zUD1YRn5TF8IfaseinbRQWlVzzeGsrDV+/8xgfPfUJx3ed4u01rxMa0eB2Xs5Vatq/IZXNdHJ5uRBCCCH+05p3D+etPybxxoC3efO+d5j26wSsba8dvFUqFQ/0aUaDYG/emPs7T73yHVNevodWTQyBubaDI2sfH056fj4lej2RyUmkFeTjam1DqIcnFmo1LjY21HZwpFdwXbZdiGHujq08vnI5Eb5+jIvocFN7Ma+lrBjTS3VfIKM4nQ1J//LZmS/QqDQ0cgyhtk1t4FK7IpMo2wtbsAKIAECl0oAmGMUiEHK/Ndzv/DEqbahhJVN32hDIdacNq5r5K7m0Mu6IUhrAVWWr4po6oPa6fhi/rKDbNVdV/0MF3arFqn9Zuy6r+6DkIkrJBcPl3sZCZ/GG+wtXg2UrVHZPGFawteGo1FXXjkpl4QMWPoaaAje5xaFEKeFoZiTbU3awL30/OkVHiGNDRgQ/TUuX5lhb3Lj1cJnY7Kwb/s7IKixk1pZ/2XYhhnZ+/nzY5x5CSrez3AxFUfhl9UE+/vZf/HxcWfje4wT6utGjQ0Mys/PR6/WcjE4iMysfJ0cb6gcZArCtlYbPnvucyO0nmPX35CoP3HczWek2E1npFjWNzAlREZkX4ko1eU4c2nSM1/vPpmHbekz/bQI2djd+w5yRlcf0eX+x5/A5nh7SniceaItafQsrsYrCP9FnmLNjGydTU+gWGMy4iPa39Ia6zMakTXxz7jueCXqKjh6G/dYphSnsSz/AvvT9xn2j3tZe9PDsTnOXZrhZVW1vXaX4GErqQC5VL38YtIFX7Jm9dAlxhY+hlEDJRcPe3bIwrjsNujNAoeEglYNxNfxSGK9rDOP6osOQNhi0rVC5fn/1qmppQTdcl6M28d5ycwfeO73qr+hzoCQWSuJAH2d4/SWxULQf9AmAitId3IaCZtoww+q1yhZy5oPdGNQOI297HNdys5d1A8TkXWBbynZ2pO4kszgLHxsfOrhFEOHeFlfLm/8ZqszVMRYqFQoQ4OTMax060y0o+Jau+sjMzmf2x6vZuucMg/o24/knOmNleeN1WF2xjrcefp/dfx/krVUTad7DND8nNe3fEFnpFkIIIYS4CU06N2LmX68xuf8s3hjwNjNWTbxh8HZ2tOW9yQ/wzc87WPjjNo6diOONF/uRV1B83RUjJwcbvD0uvUFTqVT0CK5Lt6A6/HHyOB/s3E7/H77nnnoNeLltO4Jdbv6NfFl7oS0pW2nvHoFapcbdyp3e3j3p6dWdtyJncyb3LPYW9vxwYRmLY5YSbBdEy9LibJfvAb9ll/UKt+QQZB+6+pgKeoWXu1tlYShupQkAehirnBvCeOxlYfwUFEei5K/CsM8XUNkbVsYpffOuDQN9Iora2xhYVCq1oYDWHSjodqPAe0f6llfhqr+iKKBPNfx/0MdBSVmojrsUtJWsy75CAxbeYFEb1N6G0G01EJXtAMMl4xa+xqJl+rJ2XRZVeyLocqmFqUw88noFFf4vKavwr1ap2ZG6i20pO7iYfxEHjQMRbm1o796OAFv/26pBkJ6fT75OV64ORICTM6fTUvl0724uZmdRoiiMaN6SVyI6oLW4tcJu+4/GMGP+XxQW6Xh74v10uKK7Q1JMcoXtFoPC/fl26k8c+vcY01aON1ngvptJ6BZCCCGEKNW4Uyiz/57Ma/1mMbn/LGb+MQkb++u39rKwUPP0kPY0auDD9Hl/Mmzst2Rm51NUfP29kYvnP1UueAOoVSrubRBC37r1+SXqGAt276DX4m8YFNKIF1tHVKrf7qXHMgTNE9knefv4e1e1ITqTexaAxwOH4mHlwaGMw+xL38evcav46eIKfG1qG6uj+9v63VKoUFn4gPvfKLpU0tJTcLVPADKrZGXXEMb9DX/oXkEYP30pjBftNNyZtwglbxGo7FAsfEHtbNg/XraXvGAtChaG29VOpScNDB+rVDdXoKpC1eAyd0UpnZfaluVX/Sto44ZSDCWJpYE6tjRUl4bpknjD32VXG4BhddrCB9Q+oG2Gyrq/IWCXXsKN2uNSqC7b062PAcsIk7brupZsXU6lKvx/fPozzuZGo1FZ0MylGQ/6PUCYY6Ny/bRvR4leDxgC99JBD6MC/jh1gk/27iYxNwcvOzsSc3PpV7f+LQVuXYmeRT9t57sVO2ka6sebL/XD47I6FGAI3E+HjqEgr/AajwJaSw1BYVKl/FZI6BZCCCGEuExYhxBmr36d1/rO5LV+s5j552vYOty4p3bbZkF8/d7jvDLzF5LTDPukG4fU5p7u4cYqwH9uMFQBLijUkZmdf1XoLqO1sODhsMbc3zCUpUcP88menfx2PIpHwhvzfMs2lSqa5KCxr3QbIjuNLe3c29LOvS2FJYUcyTzGvvR9rEtcz29xq/CwcqeFS3NaurSgjn3wTRWFUln4oKi80ZEEtp1Nfslo+TDeDRWXFXSzH49KUwd0p1D0CaDPAH0m6AwnICjajVK0pcLHVVR25UK4IZg7g8oZVdnHpZ9f+tjhijBZ+cBbFbXbDbtIS4BiUIoMIbrsBIRlB9AdR1GKQcm8FKiV0lXf9KdQlBxAf+kB1a6GQG1RG6zqozIG6tK/VU6VPzlT1oareJ9J2nVVhl4xvLYGDvWZ2PBV1Co1ekVPCTrcLd04iQoFhWKlmCcDn6CVa0vsNLZVPo7I5CQABoU04t9z0Xy0eycHE+PpGVyHb+8fxP74OMavX0NkchJNvGvd1GMnJGUybd6fRJ6Kv6r39uUyU7INgVsF4R1C6PNUV7yCPPnuzWUc3mzYf19cpCMzJRtPf4/bf9H/MRK6hRBCCCGu0KhdA2avnsykPjN5rd9MZv01uVLB29vTifEje/L85B8B8PF0plu7BlhbaWkS4kufzo14YcoyDkVeRK/X3+DRwEqjYXjT5jwUGsY3hw7wxb49/HTsCMOaNOfZFi1xtr72mNys3Hg7/K2b3q9qZWFFS9fmtHRtjk6vIyr7OPvS9rM9ZSerE9bipHWihUszWrq0oIFD/Ruu9qUWppJZlEVqYQqRSVHk6vNuOIYqV7ZaWrgR7J5CZd31spXx0j3d+lhwXYJKGwL6LFDSDYFcn2H4o2SglH2szzRcVq07DfoMFH0mxkvay1GjqBwNYV3tDEqu4WaVFeR+ZrgPPcZQrCo9CZPzPnpNsCEkK0Wl9xcDpcG57HPjfZf9bby/9DauUb4p9wOU3A8uu8HCUEVe7Wj8nqls7rm0Sm3hg0p145+BSlO7oGCNigLDpf3Fe64+5gZbD27X+bwYANq4tuFQxmGOZUWyL/0AaUVpeFl50ty5KfsyDtDNsytdPDuZbBwp+XkAfLxnFzFZmTT3rsXigQ/Szs+wRSQlz3B/WsF19uFXYMP2E7z76Vrs7az4aMYQwhvWvuax+hLD76PwDiHM2TgVlUrFxy9+zZEtx3n1m1GsXriBI1uijMeJmyOhWwghhBCiAqERDXh77RtM7D2DSX3eYtbfk7FzvPEqV/SFVAAG9Ahn7eYoTp1L4q1X7sXPxwW1WkW/rmEcirzIyegkQupWbtXKztKSUa3a8Fh4E77cv5dFB/ex+MhBnm3eiiebNsfesuJ+xG5WbsZAeyu9uDVqDeFOYYQ7hfFE4GOczjnD3rR97Evfz4akf7GzsKWpc1NaujYnzKkRlury47iZPbOmDN4qlYUhehbvveGqqkqlBQs34OrxXG8NV1EKLgX00pBe9rFS9nlR6Z523VkUXZQh3KMGlSWotJfycfFxQ6hHW3qfZenHWkOxsbLjy27j0ueqcvdZXrqv9DalaAfkfQe2/0Nl08Nwv9qhtOicxrCXOmsS2NyDyvbhW/+m34iFD6l8j7uLGlTKHS0qV6KUcDYnmt1phqC/+PwS9Ohxt3SnmXMT2rm1pY59HU5mn2JfxgGTVfgv0BXzc+Qxvjm4HwBbrZYfBz1MK5/a5a4YiMnMAMD1OifZyj1uYTHzv97IqvWH6RpRn/Eje+Fwg/oUpw9EA9Dnqa4AfPzi1/z28WrGfP4cvZ7ogqJXOLIlitMHomlwxV5wcWMSuoUQQgghriGkTT3eWfsGE3u/xaQ+bzH778nYOV3/0u7MLMNqVJ8ujRjcrzmT3/udp8d/z4vDu9K/Wxi1vZ3LHXcznKyteaVdB4Y1bcane3fz0e6dfHNwPyNLA7mVxnRv7dQqNfUd6lHfoR6P+D/M+bwY9qbvY1/afralbsdKbUVjpzBauLYw9gK/fM9skFUg3Wp1wcva+6o9s9m6HNOudl9W0M1Uq6oqlXVpkbCrC9CVxadLl7m/iNr2gauOMwZehzGoTRR4FbWHIXQX7wOHl82yl7qMHi/QllapNmUBO0UhsSCRo1mRHMs8RlT2CfJL8tGW7tNv69aG+2sPwNOqfB/4pELDZd/2GvsqHU9WYQHfHz7ENwf3kV5QQHs/f7bEnMfRyoqWVwRuvaKwPPIoAKGV6GZwee/tCSN7cU/38Epd8p+Zkg2AZ4AH7w3/mH8Wb+Hlz56l34geAPjU8S53nLg5ErqFEEIIIa6jYet6vLPuTSb2msHE3m8xe/Xr2DtfO3g7ORpWo2ITMujXNYyF7z7G/K838PYna/h3x0laNg4od9yt8LC1481OXXm6WQs+2r2Tt7du4usDexndOoLBIY2MxZYq0/u3tsPNty5VqVQE2gUQaBfAYN8HiMuPZ1/6fval7y/XC9y/tIJ6fft6DHd5Am93b9RqNQ2oR3v3CN4+/h4nsk8a99aaSllBN7P3pi4LsvkrUGzuN0vgvZlV/5osqzibyKxIjmVGciwrktSiNCxUFtS1r0Nf796EOTVCURRmRM0itSgVDyuPK8Kuni0p24BLnQBuV1JuDl8f3M/Sw4co0pcwODSMEc1akl1UyJaY8+yJi+XRFcsYHBqGv5MzMZkZLI88yp64WAAsrlMP4Vq9tyvLyd1QWO3zcd8RfSSG15a+RJeH2xvvjzuTUO44cXMkdAshhBBC3ECDlnV4d/2bTOg5nQm9ZvD2mtdxcKl49at+kGE16s8NR+nTuRF2tla8NrovndvW593P1rL70DkA6gXefjGi2g6OzO7ei2dbtGLezu1M3rCOL/bt4aU27WheqxZ9l3x73d6/NhoNax8ffkvB+3I+NrXwsenPAJ/+pBSmsD/9AHvT97Mq/k8AsnXZ7MjZRSeXjnhYuwOGlfOO7u05kX2S83kxt3T5+81Qle1LBpOuql53DNUh8N6BVf/KStdlkJebDyoqXXPgWor0RZzKPs3RrGMcy4w07teubeNDC5fmNHIKpaFDA6wtLl1mfS73PHDtCv9lxQdvpnBgRc5lpPPl/r2siDyGpcaCxxo3ZXjT5saCiLHZWdhoNOTrdOyOi2V3aci+nI1Gg4tNxSfqLu+9PbhfM0Y+Xrne25fzrW844XTm0Dlm/DaBNv1bGO/T6/WsWbQRgLrNTPtzereS0C2EEEIIUQn1mgfz7vopjL8seDu6Xr3qU1ad+1DkRV6Ysox+XQ2XlGdk5ePt6URquqGY1sffbWba2Htwv0Z4vxlBzi7M79Of/7VszQc7tjF27V8EODkbA3fry3r/nr9s9SxfpyM9P/+2Q/fl3K3c6eXdk17ePfn5wgr+iP8LGwsb/kz/m9/T/yDILpB69vUItg9CqzLsATfVntlqpxoE3uqy6p9amMrc+HkUxxVf85jr7ffXK3ou5F0ovWQ8kpPZpyhWinHSOtHIMYRe3j1p5BiCi+W1v5c3U+H/VhxLSuTzfXv46/RJXKxteKltBEPDm+JoZVXuuNoOjqx9fPgtXZVS1nu7qLiEtycOpEOrOjc9zqzUbD4c/RUAil5h2bu/kZGchU8db+LOJLBm0UaObDVUMFdXUPlc3JiEbiGEEEKISqrbLIj3/pnC+B7TmdBzBu+se+Oq4O3kYIO1lYaCQh2HIi9yKPLiVY+j1ag5fzGVx1/+hjFPd6Nnx5Bb6oN9pRB3D74YcD8H4uOYtmkDAHZaLc+3aktH/wBUKhWtavvyQEgjHl2xjN1xscYewabgbmVY1e7q0Rk/F1/itPEczjzKgYyDrE1cZzxuZ+ouSpQS6tgFE2wfhJ3mxi3RaqLqEnirw6p/ti6HYsUQuK/XI/vy/f6phanGkB2ZFUW2LhtLtSUNHRow2O8BGjmG4mtTu9I/S7da4f96FEVhV+xFPtu7m80x5/BzdGJq524MDm2Etebavd5rOzgaQ3Vl2oJVpvd2ZaTEpjKx91ukJ2Zgaa2lqKCYI1uiOLIl6qpjrW2t5PLyWyShWwghhBDiJtRpElgavKcxvsd03l33Jo6Xvdn19nBk8fynyMzOR6/XczI6icysfJwcbagfZCga5eRgg421lg+++ofp8/9i446TvPpcT1yvs1f8ZjSr5cPDjcI5nJSIm60tT/62gja1fRndui3tfP1Rq1QMDg1jd1zsLfX+rayyvbBbUrYx3OUJItza0t6jHQAZRZm8e2IOsflxWKmtWJuwjtwSQ2skb2svgu2CCLYPpo5dMP62fjdsTVZTVIfAWx2U7eOvb1/P2CMbuGq/f2RWFJuTt3Is6xgJBYmoUBFoF0gXj040cgqlrn0dtOprh9kbud0K/5dej8I/Z8/w2b7dHEiIp6G7B/N696NfvQZoqrg3fXxp7+2oG/TevpG4MwlM6DWDEl0J87a+hZWNJZkp2ehL9Jw+EE1mSjZO7g7UbRaE2kKNk7uD9Oi+RXfHby8hhBBCiDsouHGAccX71e7TeHf9mzi5X7r009vDEW8Pw+fXaws2dcw9dGlbnzlfrOPxl79h7IjudGvXoEpWvct6+r7bvTfZxUW8v2Mbj69cTrCLC0PDmxLo5FzuOFMoC1Inc07xRfFCuqq74G3jZdwzG5sfB8ATgY8RYOtPYkEiZ3KjOZtzljO50exK20OJUoJGpSHA1p9g+yDjaviVlaZvJLUwtUpXNMXtiSndc93Rvb1xnuj0Os7mRnM08xjpRRkALLvwMx5WHoQ5hjLY9wFCHBtWeTXx21FcUsKqk8f5fN8eTqWl0sqnNgvvHUiXgKAq+Tm+0s303r6e6KMxTOw1A1tHG+ZunGoM02V/S1uwqiWhWwghhBDiFgSFB/Dehqm82n2aMXg7ezjd9ON0iahPk1Bf3v9yPVPe/4ONO04ybkQPXJxu3BP8esp6+sZkZTI4NIxugcHsjr3IkiOHmL11k7GNVV7RtffU3q7L98xGF54j+vw3Vx1TtmdWpVLhbeONt4037d0jACjWFxOTd4EzOWc5m3uWwxlHWJf4D2Bo42RYDQ8i2C6YOnZB2GsrDmPVpV+4uCS1KA2AhIJEll34mdi8WE5kn6JAX4CdhS1+tn4kFSbRx7s3j/g/ZObRXi2/uJhlx47w1YG9xGVn0y0wmJndetLS59ZCcEJy1nWvjrGy1LBs1V5WrT9S6d7b1xK16xST+83EM8CD2atfx8Xz5n9viZujUhRFMfcg/ouysrJwcnIiMzMTR8eqK15SVfR6PUlJSXh6ehoLwoj/NpkToiIyL8SV/otz4nzkBV7tPg0nD0feXT/ltt7A/rPtOO9/+Q8qFbzybE+6RNS/5cc6lBDPwJ+W0tqnNksHPYz6slW3xJwcHvz5By5mZwEQ7unF0PAmDKjfEBvtrV+qW5HUwlQyi7JITUsh2yqHXH3eba0w5xTnGFfDz+ZGcybnLLklhuJ0Xlael0K4veGydK1ay7nc80w5Nh249v5hgGmN3iTQLqBKX391dKdW/UuUElIKU4gvSCA+P4H4gvjSvxPI1l3q9+xu6U4tG28aONSnkWMogXYBbEvZzlfRi3gy8Am6ena+7bFcy8221csoyOf7wwf59uABMgsLGFC/Ic+2aEVD91u/7DohOYvHXvqagsJrdxpQqUCrsWDsMz3o3z3sllfR968/zJSB71K3WRAzfp943faH5lDT/g2pbKaTlW4hhBBCiNsQEOrHnI3TeLXbVF7tNpX3/pmCi5fzLT1W9/YNadbIjzlfrOf1Ob/TvX1Dxo7ojpPDzff0Luvpe63ev7Glgfv1jl3YEnOeSf+sZdbWTQwKacTQ8CYEu7je0mu4kpuVGy5aF2xzbarkjbS91p4mzuE0cQ4HDIWrkgqTOJsTzZncs5zNiWZP2j50ig4LlQX+tv64WxoCZJBdIBMavIKF2tCS6073CwfzX+ZuilX//JL8K0J1PPEFCSQWJKFTdMbHrGVdCx8bbxo5haJSVPwS9yt17eowOXRiubZcpuiRXZHY7Cx6fb+oUm31LFQqFh7Yxw9HD1OiV3ioURjPNGuJn9PtrxJnZucbA3eTUF/6dzN0PLgYn853K3YRm5CBosAbL/Wn622ciNu6chezHplH025hvLn8FaxtrW78RaJKSOgWQgghhLhN/g1rM2fjVF7pNo1XuhmCt6v3rbV9cnW2Y+ar97J+63He/+ofHn95Ea8825NOberd1OO42NhUqvdv77r1eKpZC2IyM1h69DDLjx1l0cH9RPj6MzS8CT2D66C1MGHf6NukUqnwsvbCy9qLCPe2gOGy9At5F0tD+FmOZkYCEJ17jhcOvEywfTC1bXxw0jrhpHUkyC7Q2DIq0C7gtvsyX0t1uMw9W5djfP7KVg0HQxBOK0ozhuq4ggQSSj/OKM40Hudq6YK3tTcNHRrS1bMLPta18Lb2xsXSudz39Wx2NL/E/crp3DMm7ZF9Pen5+eTrdKiAVtdpqzd90wb+PReNtUbLk02a82TT5rjb3t72j8vpSzsINAn15cNpD6NWq8jIymPpr3uITcjA3dWelLQcvD1uvXL4mm828v4zn9LpwQjGfzsarWXVXtEirk9CtxBCCCFEFfBrUJu5G6fySrepvNzhDV785BkcXOxvqQqwSqWiZ8cQmoX58d5n63jt3d/o1SmEl5/qhmMlV71vtvevv5MzE9t3Ykybdvx9+hRLjhxk9N+r8LSz4+FG4Qxp1JhaDjWjXZBWrTVcZm4fBF7dWRX3J8sv/sIQ34coUoo4k3OWQxmHySzOJK/kUiG5Hy/8xM8XV+CoccRJ62gI5ZZOxo+dtU7GoO6kdcLa4ub21N5q4K1KZav5DRzqV1g1fFbUO5zKOc2hjMMcSD9oXLVOKEg0jl2r0uBl7U0tG286O3SilrVhL763tRc2FpWbnw4ae7QqLcVKsUl6ZFdGWbu8VldswWhV25d6rm489fsvpBcUsDculnERHXgkrDEOVlW/OnwyOgmA/t3CUKtV7D8Sw/QFf1Fc2ns7Mzuf2R+v5mR00nULM17LL/P/5NMx39B/RA9e+OQZLKrxSbS7lYRuIYQQQogq4lvfh9eWvMS4blOZ1GfmNY+ztrViYeQHN2y/4+5iz9sT72fNpkjmfb2BfYdjGD+yF+1b1qnUeG629y+AlUbD/Q1DuL9hCFEpySw9coivD+zjkz276B5Uh6HhTWjvH1Buj3h1V1bt2l5rT0eP9uXuK9IXsT7hH5ZdXE5Xjy742fqSWZxJZnEWmcWZXMy7yLHSz8sulS5jrbYqDeFOV4T0yz7XOuGocUCj1tww8N7qZe56RY9O0VGsL6ZIX0SxXkexUkyxvvTPZR8fyjgMgJulG2sT1lGs6MgsziQu3xCu00oLnP0S+ytOWkdqWdeijl0w7d3bGS8Pd7N0u+0VaDcrN8bVehkrJytQYZZL7SOTDWF3cGgYapUKRVHYfjGGz/buZtuFGNxsDCcQXmodwRNNm5tsHJlZhhM/jg7WzP54NX9uOEqzRpd6bx+MvFjuuMpSFIXvp/3M99N/5uHx9/H07KEmqagubkxCtxBCCCFEFbJxsIHSMrWW1lqemvkI9VvVJf5MAqu/3siRrVEU5BWSmZJdqZ63KpWKPl0a0bJxAO98uoYJs1fSt0sjXnyq6y1XL66sEHcPZnTtwYT2nfj1eCRLjhxi2G8rCHBy5tHwxgwOCcPF5ub3m99pl/qFb6W9e0S5wKhRaTiYaQiinTw6XLNXs6Io5JXkGQN5RlHGpY+LM8ksziS+IJHM4sxyRcIAVKiw19ijURlWGEuUEn6+sAIHrQN6RW8MxhqV4a354vM/4GblWmFovvTxpWB95cmAytiVtpsDGQfRqrTYa+yoZVOLCLe2qIA/4v/iXp97GOQ78KYf92a4aJzxtDPs87+dHtm3qqxdnlZtwYJdO1h18jhn0tNo5OHJh33uwc3Whkd/+Zns4mtvB6gKDvaGn+Op7/+JRqNm3Ige3NuzsbH3dmxCBgBOjpX/WdPr9Xw65ht+/fBvnp71KEMmmvb/pbg+Cd1CCCGEEFVIX1K6mtmyDulJmfz+yRre2xBBeIcQejzemVe6TuXIlijjcZXl7mrPu689wN8bjzF/0Qb2HD7PhJG9iGgebIqXUY69pSWPNW7K0PAm7IuPY8mRQ8zdvo25O7ZxT70GDA1vQlPvWhWuosVmZ5Gam0tqWhr/JCWQUVhw3erQplAWsk9kn7zl/cMqlQo7jR12Gjt8bHyu+3w6vY5sXbZxtbwslB9MP0R6cQYFJYXsS99Pti4bC5UFWrUWrUqLHsOcyCjOwNrCCq1ai42FNY5qB7RqSyxLj9OqS/+oNJd9fNntVx2nRas2HLsjZReLY5YyPHDYVav+AFuStwLgalk1hfSqq9jsLI4lJQIwZu1f2Gst6VmnLm927koHvwBUKhXLI48Cl9rvmcLx0wks/2s/ADbWWr6ZOww3l0sVxfV6hb82GsZRP8izUo9Zoith7ohPWf/dZl78ZAQD/ter6gcubspdHbrT0tJ44YUXWLVqFWq1mkGDBjF//nzs7a+9N6RLly5s2rSp3G3PPfccn332mfHzmJgYRo4cycaNG7G3t2fYsGHMnj0bjeau/nYKIYQQohJOH4gG4N5RvQnvFMqr3aYxrssUZq9+Hd96teg9vCtHtkRx+kA0DVrVvanHVqlU9OsWRssmAbz9yRpenfkL93QPZ/SwLtjbmb4SsUqloqVPbVr61Ob1jl34OfIoPxw9zC/HIwl192Bo46bcW78hdpaWwM1VhzZl8L68X/id2D+sUWtwsXTBxbJ8MT0HjQNncs/Sx7vXNQPvV9GLGODT32RtsurYG07SVLTqf6eqhptLcl4uf586yaqTx9kXH4dl6d7mui6u/DpkKLZaS+OxekUxhu5Qj8qF3ZuRlZ3PF0u38tu6Q9QuLbqYnpnHm++vol9XQ/Xy2IQM/tp4lEOll5dXpvJ/UUERsx6dx84/9jNx8Yt0e6RDlY9d3Ly7OiUOHTqU+Ph41q1bR3FxMcOHD+fZZ59l6dKl1/26ESNGMH36dOPntpdVJywpKaF///54e3uzfft24uPjeeKJJ9BqtcyaNctkr0UIIYQQNUNmiuHS4lp1vKkV5MWcjVOZ1OctXmo3mWkrX8Wnjne5426Fp5sDc18fxB//HOHDb/5l98FzTHy+N62bBlbFS6gUN1tb/teyNc+2aMXm8+dYcuQgb2xcz+ytmxjYMJSh4U0oKikxVodu4u7JI02aEujsclV16PT8fJOGbjcrN94Of8usrbrg+pe536nAWxWr/jVJZkEBa86cYtXJ4+y4eAG1SkVH/0De79UXHwcHhqz4iTPpaTz12y9XtdXbU1rx36IK+0Xr9Qp//3uUT7/fTFFxCS882ZX2LeswbOw3FBTqOBR50RiyL2dtpblh68C87HymDHyXyO0nmLbyVdr0b1Fl4xa3564N3VFRUaxevZo9e/bQsmVLAD788EP69evHnDlz8PG59mVBtra2eHt7V3jf2rVriYyMZP369Xh5edG0aVNmzJjBhAkTmDp1KpaWlhV+nRBCCCH+G5zcDRW+488kEN4hBO9AT+Zvn8nUB95jfI/p9B7etdxxt0qlUjGgR2NaNQnk7U/WMHbGcu7t2ZjRw7pga3Pn3o+oVSq6BAbRJTCI2Kwsfjh6mGXHjvD94YPGFcLmtXyY36EL3l5eqNVqWtX25YGQRjy6Yhm742KNVaRNyc3KzRiqzbF/GKpH4L3Tq/7mkFtUxD/RZ1h18jibz59Dp9fT1tePt7r2oHedesY6BLHZWZVqq1dVdQtORSfx/pfrOXIijp4dQxg1rDPuLobv8+L5T5GZnY9er+dkdBKZWfk4OdpQP8iw593JwQZvj2ufmMpKy2Zyv1nEHI/l7TVvEN4xpErGLKrGXRu6d+zYgbOzszFwA/To0QO1Ws2uXbsYOPDaxQSWLFnC4sWL8fb2ZsCAAbzxxhvG1e4dO3YQHh6Ol5eX8fjevXszcuRIjh07RrNmzSp8zMLCQgoLC42fZ2VlAYYiB/o78A/NzdLr9SiKUi3HJsxD5oSoiMwLcSWZExDcJACAv7/eSLehHVGr1dg72zHr78l8MOIz/vh8HQBBjf2r5Pvk6WbP3Ncf4Pf1R/jk203sPniOCSN70SLcn8TkLDJK38ifik4mIzsfZwcb6gV5oFarcXawwes6b+RvVi17e8a2bcfoVm1Yd/Y0H+zcDsCJlBQ+P3KQp6zb4OfkbDz+gYah7I6L5WhSIuGeXtd41LuHndq2UoHXTm1rsp8hF60LsxpNN676x+TFkK3LwUFjj/9lq/4uWheT/hxX9e+KQp2OzTHnWHXyBBvOnaVAp6OpVy0mtu9E37r18LS7dBKh7Dlr2dmzZugw0sra6qUkk16Qj4u1DaHuHlio1bja2FDLzv62xpmTW8jCZdtZufogfj4uzJsymOZh/uXG4ulmj6ebYYwNgiv+WbjWGFLj0pjUdyYZiZm8u/5N6jUPrrG/g2vavyGVHeddG7oTEhLw9Cy//0Kj0eDq6kpCQsI1v+7RRx8lICAAHx8fDh8+zIQJEzhx4gS//PKL8XEvD9yA8fPrPe7s2bOZNm3aVbcnJydTUFBQ6dd1p+j1ejIzM1EUpVL7R8TdT+aEqIjMC3ElmROQmZkJwNGtUbzc8XU6PdwWr0B3Es+lcPF0nPG4b6cu44Uvn0ajrZqeuRFNvAl+rT+fLtnBmOnL6dQ6iJ0HzlNUfO03hVaWFsx74148XO2uecytauXkQm+/AD7PzKCFpycrTp9k8fFI2tbyoaOPL228a+FYWuX9YkoKSUlJVT6G6mis90vk6XPRK3riiuLJ1edhp7bFx7IWapUaW7UdJZklJGHa74cthtXbUEIuJYI8w18lmP75q+J3hU6vZ29SAutjzrMp9gK5xcXUc3bhyZAwevgF4FNWxyk3j6TcvAofQwN4ogK1BbU8K7jSNb+ApPxbe6+uKApb9pzju5X7KCjQMfS+pvTr2hCtxqLK5nvS+RTeGfIxuiIdr614ESdf+xr9s1TT/g3Jzq7cNqEaF7onTpzIO++8c91joqKibvnxn332WePH4eHh1KpVi+7du3PmzBnq1KlcT8yKTJo0ibFjxxo/z8rKws/PDw8PDxwdTVux81bo9XpUKhUeHh41YsIL05M5ISoi80JcSeYEUF+Nla0VhXmFnNh1hhO7zlx1iMZSw6GNkcwf/hVv/DQWe+eqCb2enp58NCOIX9ce4pPvNhkDd5OQ2vTtGkZtbydiEzL5e+NRDkXFUlhUgsbS9qqFiqrim+QOQN8GIbzRuh070lP59UQUc/fvoURRcC+9kjAHBVtnZ+z/A9v0PLn0vf4v77jV6/Uk5udRpAK9vuSaq8w+V+z11ysKe+Ni+ePUCf4+fYr0gnwCnZwZ3rQ599RrQF1X0+7Lr6xzF1L5YOE/HDh2kS5t6zH6yS54ut3elpKrnuNoDDMfWICNvTVzNkzFK+DGLQiru5r2b4i1deXaNta40D1u3DiefPLJ6x4THByMt7f3VWd5dDodaWlp19yvXZE2bdoAcPr0aerUqYO3tze7d+8ud0xioqHdwPUe18rKCiurq6uKqtXqajuhVCpVtR6fuPNkToiKyLwQV/qvzwnvQE++jvyAzJRs9CV6Th+IJjMlGyd3B+o2C0JtocbJ3YH4s0lMfeA9xnZ6k7f+mIR3YNUEX7UaBvdrjoebPZPf/R2AuoGedG/fABtrS5o1gn5dw3hhyrKbqop8K8JKLxlfcTySDu0780hYY4Y2bkpWYQHbL8Qw5d9/AFhy9DDLIo/S3NuHjgGBdPQPIMzTC3UFLcjE3SEuO4uhq/+goKTkmseUVbb3sXfgSFIiq04e58+TJ0jIzaGWvQMPhjbinvoNaeThWWG7OnPIyy/im593sOyPfdTydOL9NwabpMBh1K5TTO43Ew9/d95e/TouXs5V/hzmUpP+DansGGtc6Pbw8MDD48ZncSIiIsjIyGDfvn20aGE4j7hhwwb0er0xSFfGwYMHAahVq5bxcWfOnElSUpLxrPC6detwdHQkNDT0Jl+NEEIIIe5Gnv4eePob3q9cqy2Yp78H87fPZHL/WbwY8Rozfp940y3EricjKx+Anh0b8sc/R9h5IJpXn+tJy8YBqNUq+nUN41DkRU5GJxFSt1aVPe/lyqo+742LZfTG9Qxp3IRAF1djdeiUPMMlv5/1v4/E3By2xpzj8727mbtjKy7W1rT3C6BjQCAd/AKo5VC1q4TCvNLy8ykoKUEFtPKpzeDQMAKcnK+qbP/hrh3sir3I+cwM3Gxs6VevPgPqN6R5LZ9qdVJGURQ27jjJh4s2kpVTwFMPteOR+1piqa36uLX/nyNMuf8d6jQN5K1Vk6rsShlhOjUudFdWSEgIffr0YcSIEXz22WcUFxczevRohgwZYqxcHhsbS/fu3fnuu+9o3bo1Z86cYenSpfTr1w83NzcOHz7MmDFj6NSpE40bNwagV69ehIaG8vjjj/Puu++SkJDA66+/zqhRoypcyRZCCCGEuBb/hrVZsGMWU+5/h3FdpjBx8Yt0GFj5xYHrySwN3ff3bspTD7Xn7U/W8PK0n2nVJIDnHu1IbW/ncseZgouNjbE69MGUJA5uWHfVMTYaDY08PenlUJfHGzeluKSEAwnxbI05z5aYc0xcvwYFqOfqRgf/ADr6B9Kmti82Wq3Jxi1Mr6xifUuf2iwd9LAxQHva2ZOQk8ORpETydTr+PHWCfvUaMKNrD9r6+qGphqufMXFpfPDVP+w5dJ4Orerw0lPdqOXpZJLn2vbrbmYO+YCm3cJ4c/krWNtK/qgJ7trQDYYq5KNHj6Z79+6o1WoGDRrEggULjPcXFxdz4sQJ8krPslpaWrJ+/XrmzZtHbm4ufn5+DBo0iNdff934NRYWFvzxxx+MHDmSiIgI7OzsGDZsWLm+3kIIIYQQleXi6cR7/0zhnWEfMX3wXJ5973EGjbnnti+XdXIsbYuUkEGTEF8+mvEwW3af5oulW3lmwmIa1PEqd5wp1HZwZO3jw0nNzSU1LY04XTEZhQW4WtsQ6uGJhVqNi41NuR7dWgsLWtf2pXVtX8ZGtCc9P5/tF2LYEnOO1adPsujgfizVFrSsXZuOpSG8obvHDVc9Y7OzSC+rUp2cRFpB/nXHIUwrMiUZgAH1GrAvPpYD8fH8ffokhxITsNFoaODmzsHEBMa368jjTSruDmRuBYXFfLdiFz/8tgd3V3vemTSQ9i1vvQbUjaz7bhNznv6EDg+0YeL3L6C1lBNPNYVKURTF3IP4L8rKysLJyYnMzMxqW0it7BL6mrCfQpiezAlREZkX4koyJ26dXq9n4aSl/PTebwwY2ZtR84djobn1yuZRp+MZMWEJTUJ9+XDaw6jVhlBaUqJnzeZI3vt8HcXFJbRvWYcxz3S/bg/g21VV80JRFM6kp7GldBV818UL5Ot0uNva0sHPEMA7+AfgYVf+ctvY7Cx6fb+IfJ3umo9dtn9Ygrfp5BYVcSw5iaNJiayIOkZUSjIqQAEsLSzoEhDEPfUb0C2oDkeTEhmyYhnjItozqlVbcw+9HEVR2LrnDPO/3kBaRi5D72/NYwNbY2VluhC8csFffPLyIvo+3Z2XPhuBhUXVdD2obmravyGVzXR39Uq3EEIIIURNoVarGfHOY/jU8WLBqK9IPJ/E5B/GYOtwayvRZW9YD0Ve5IUpy+jXNYza3s7EJmTw18ajFBcbClgdjrrII6MX8kCfpjz2QBtcnGyr7DVVNZVKRV1XN+q6ujG8aXMKdTr2x8exOeYcW2PO8+sJQwebEHcPOvoH0ME/kFY+tUnPzydfp7vh/uH0/Pz/ROi+E6v+OUVFRCYncSQpkaOlf86mpxkDtqet4cTIAyGhDG/agnqubmgvC5IxmRkAuFqb7kqMWxGbkMH8rzewfd9Z2jQLZN6UB/Gt5XLbj5sUk1xh8cU6TQNZ/fUG/vxiPQ+9ci/PvPNYtSkaJypPQrcQQgghRDXS/9meeAZ48NZD7zO285u8tWoi7rVvvg2Sk4MN1lYaCgp1HIq8aKxUfjlrKw2fzHyUTbtO8sNve/h9/WGG3NuSIQNaYlcD9opaaTRE+PkT4efPhPaQkpfHtgvnjQH8i/17sdZoCHE3FLVr5OHJkgceMhZ4a1XblwdCGvHoimXsjos17jO+m5li1T+7sPBSwE42BOzo9HQUwMrC8P2P8PVjRPOWhHt6UdfVjaOJCQxa/iMxmZlXbQ/QKwrLI48CEOphmnZ2ZRKSs8jMzkev13MyOonMrHycHG2oH2RYaXVysMHbw5HCIh1Lf93N9yt34+xow8xX76VTm3pVEoCTYpJ5OnQMBXmF1zxGo7Xg3lG9JXDXUBK6hRBCCCGqmVa9m/LBlhm8fs9sXmj7Gm/9MYk6TQJv6jG8PRxZPP+pSgWKIL8IBvZuyuJfdrHk1z2sXH2Qxx9ow/29m2JlWXPeLrrb2nJfgxDuaxCCoiicSE1ha8x5fjp2BICjyUl0XPQlHQICaOpVi9oOjtR2dOTeBiHsjoslMjmJJt6mqeRextx7y2931T+rNGAfTUo0rmJHZ6QDYK3REOruQQe/AJ5r0ZowTy/qubpVWPzs8sr2j65YxuDQMPydnI2V7ffExZY7zhQSkrN47KWvKSi89gkIaysN457tyTc/7yAhOYshA1ry5INtsbGuup7ymSnZhsCtgvAOIfR5qiueAR58++Yyjm49DoCuuISs1By8Akx7EkKYRs35LSqEEEII8R8S3DiABTtn8caAtxnT8Q0m/ziGNv2a39RjeHs4Gvdq36gtmJODDaOGdeHBe1qw6KcdfPLdJpb9sY+nHmpHny6N0FhU//2Vl1OpVDR096ChuweFJTrm7tjGax06k5Sbw+aY8/wSFYn+itJGC3bvYHPMeWMYr+3ggI+DI7UdHHG2tr7tVcbqsLe8bDW/1RVVwyta9c8qLOBYUhJHk8sCdhLnSgO2jUZDqIcnnQICeb5VG8I8vajj4lrp6uKuNjZYW1hQUFLC7rhYdpeG7MvZaDS42Jju8vLM7Hxj4G4S6kv/bpe2YPy54SiHIi9SUKhj5od/0yLcn3cmDSTQ9+avOrkRfYnh/0l4hxDmbJyKrkjHrKHzidp5iomLX+TPz9dxZEuU8ThR80joFkIIIYSoptx9XHl/0zRmDZ3Pm/e+zegPn2bAyN4mfU5PNwcmjOzFI/e15KsftvH2J2v44bc9jHikA53bVs3ltHda2b5gZ2trnmnekteA4pISEnNziM3K4tfjkSyLPIqfoxO5RUVsPHeWuOxsCksuhWM7rRYfB0dDCC8N5JfCuSOedvY3rKBeHfaWRyYnATA4NKzceDMLCjianIh76V7rp1etJC3f0E6uLGB3CQgk7LKAfTur0D4OjiztMwC1nS1K6bju9Kq/vvQExJXFBkPr1iIlLYcjUbHoFYURj7TniUFtTTb3Tx+IBqDPU13JychlxkPvE7n9BNNWvkqb/i3QFek4siWK0weiadCqrknGIExLQrcQQgghRDVmY2/D1F9e5bMx37Jg1FfEnUlkxLuPmbyyr7+PK9PHDWDowNZ8sXQLr8/5nYZ1vHhuaCdaNQkw6XNXtbJ9wcsjj/JASCPUKhVaCwt8HZ3wcXDkg53bAJjcsYvx8nJFUUjJzyMuK4vYbMOfuOxsYrOyOBAfxx8ns8gqvLQHV6tWU8vegdqOjsbVccPHhnBey97hplaZb6RErydfpyNfV0x+cbHh4+IrPtYVk1dcTMFlx+2ONeztX3k8ktWnT5GvKyY2K4uYrEzAsAcbINDJmckduhDm6UWwi4tJLvP2trMzVqk29WX9FTkZbTgB0b9bmDFw7zsSw/tfrudifDotGvuz59B5nJ1sTXqyKTMlGwCdTs/zLSaQn1PArL8n06RzIwB86niXO07UPBK6hRBCCCGqOQsLC0YteAqfut58OuYbEs4lMeG7F7C+A8XOGgR7Mff1wRw4doHPl2xhzPSfaRHuz3NDOxJa784HpVtRFhj33MT+YZVKhYetHR62dtcMhNmFhcZAHpuVRVxpMD+bnsaWmHMk5eZeejzA3tKwD7iwpIR3t2/B286eEkUxBmTL0urdUzdtwNPOjvziCkJ1aYAuKimp1GvXqtVYa7TYarVYazTG1fvkvFwCnVxws7WlobsH4Z5ehHl6sT8+jon/rGVQSCMGhoTe3De6hsnMMqzk+3g5sffweZat2suO/dE0CfFl+rgBZOcWsufQeeNxpuLk7gDAgpFfUrdZIHP/nYZXgIfx/rgzCeWOEzWPhG4hhBBCiBpi4Iv98Ar0YPaj83m121Sm/zYBFy/nO/LczRr58enMR9i29wxfLN3KsxOX0KlNPUY80p4gP/c7MoZb5WJjg41GQ75OV6X7hx2srGhoZdg3XpFCnY74nGxjKP/1RBQ7L15Ap9ez+tRJEnJzyoViBcMe87T8PFxsbHC0ssLL3h5rjcYYmm0uC9C2Wi02Gi3WWg22Gi3WWi22Gi02Wg3WGi02Gk25NlwAhxLiGfjTUlytbfjsnvuuqhr++oZ1gOmrhlcHdnaGk1bT5/1FUmo2dQI8ePPl/vTs0BCVSsWfGwwV1J0cTbevvDC/kF1/7jc8j7sDc/6dhrXNpZNper2eNYs2AlC3WZDJxiFMS0K3EEIIIUQN0u7eVszdNI03BrzNixGGyuYBoX535LlVKhUdWtUlonkw67ce56sftzJs7Lf06RzKUw+1w9vT6Y6M42bVdnBk7ePD73jVcCuNhkBnFwKdDX2cS/R6dl68wLAmzRgcGnbV8csjjzJ+/Rr+16I1j4Q3qdKxlLmVVf+7TUZWHr+tPcxPf+wFIL+wmA/eHEzLxgHGy8j1eoW/NhpCd/0g05yAiI9OZPrguZyPvABAWmIGr/WZSe/hXfGp403cmQTWLNrIka2G/vPqGlbMUFwioVsIIYQQooap36IOH+6cxeR7ZvNS+9eZsuIVmnULv2PPb2GhpnfnULq1a8Dv6w/z7fIdrNtynPt6NWHY4Da4ONkZj01IziI9M5fUlFR2HkogK6egwrZlpla7dJ81YJb9w1Dx3vIyd6o3talW/WuC8xdT+enP/az+9xgKENEsiE27TpGdU8A3y3eSlJpjrF7+18ajxt72pqifsOuv/bzz+AIcXO2ZtnI80wfPpSCvkCNbojiyJeqq461treTy8hpMQrcQQgghRA3k6e/BvK1vMeOh95nUZyZjvniO3k92vaNj0GotGNS3Gf26NuLnP/ez9Nc9/LnhCA/f04Ih97YiJ6+wUn2QF89/6o4Eb3OrDqvM5lr1NxdFUdh/9ALLVu1l+76zuDrb8vigNtzfqwkFhTp2HYymoFDHociLxpB9OWsrDU4OVXcCoqSkhO+n/cySt1bQdkALJnz7AvbOdiyM/IDMlGz0JXpOH4gmMyUbJ3cH6jYLQm2hxsndAU//ircxiOpPQrcQQgghRA1l52jLW6sm8uGor5jz1CfEn0lk2PSH73hbLxtrS54Y1Jb7ezVh8a+7Wfr7XlauOUTvzqHGwB1S15P7ejXDz8flqj7Imdn5/4nQXV1WmavDqr+pFReXsH7bcZat2svpc8nU8XfntVF96NGxIZbaSxFo8fynyMzOR6/XczI6icysfJNdiZGVms2sofM5sP4ww996hCET7zeuonv6exhDtbQFu/tI6BZCCCGEqME0Wg0vf/4cPnVr8dXExcRHJzJu4fNYWmnv+FgcHWx4/vHOPNivOd8s38nyvwwFony9nXlzdHdq165laA8V4kufzo14YcoyDkVeNPZLvtv911aZzSEzO59f1xzil78PkJqRS0TzIEY90YWWjf0rPBnl7eFoDNUhdU13AuLEntNMf3AuhXmFzF79Os17NDbZc4nqR0K3EEIIIUQNp1KpeHj8fXgHefLOEx+SFJPCtJXjcXQzzx5QDzcHXn2uJx5u9nz1wzYuJmQwbtYfPDu0E93aNUStVqFWq+jXNYxDkRc5GZ1k0sBTnfwXVpnNISY2jZ/+2Mffpfu1+3QO5aF7WhDo62bWcSmKwl9frufjF7+mTrMg3vhpLJ7VvNq/qHoSuoUQQggh7hKdH4zAw9eVKfe/y4vtJjP2y+ewsbcx2z7RskJhE0b2ZN3mY0z94E+W/LqHe3s0pmu7+tT2dgYweR9kcXeqcL/2A224r1cTXJxszT08CvMLmf/8l6z7dhMDRvbmf+8PM8sVKML8JHQLIYQQQtxFQiMasGDHLCb0msG4LlOve6y1rRULIz8wWfAu62+sUql57fluxKcWsWTlHuYt/Id5X28wrkLa2Fia5PnF3amy+7XNKe5MAtMGzyH2ZDwTvnuBHo91MveQhBlVj1kphBBCCCGqTK1gL8Z++T9e7T4NAL8GPgyZeD+16ngTfyaB1V8bev8W5BWSmZJtstBd1t/4741HaR7ShSYhvjRr5E96Zi7/bDvBF0u3AvDpd5uIPBlPr44htGoSgEZjYZLxiOolOS2X9JxEgEoVMcvMzue3tYdY8fcBUtNzadvs+vu1zWXnH/t4+/EFOHk4smDHLIIbB5h7SMLMJHQLIYQQQtyFbOytAXD2dOLCiThSYtPp+UQXwjuE0OPxzrzSdSpHtkShLzFdEbOyysyHomKZMn8d9/Vqim8tV2ITMti44yR5+UUA9O8ezoGjMazbEoWzow1d2zWgZ8cQwhv4VKswJapOYnIWL8/4ncKikmseU9ZOrqhIVy33a1+ppKSE76b8xNJZv9D+/la8umgUdpf1rBf/XRK6hRBCCCHuQqcPRAPwzNuPknQ+lUWv/0D00Rhe/PgZHFzs6T28K0e2RHH6QLTJWhQ5OdhgbaWhoFBH1Okkok6vveoYaysNQ+9vzdhnunP6XDLrtkSxfutxVq4+SC1PR3p0CKFnxxCC/aX41N0kIzvfGLibhPrSv1sYtb2dr2onN2P+nxyKisXFqXrt175SRnIms4fO5+CGozw9eygPj79PThgJIwndQgghhBB3ocyUbAB86tai95Pd8Gvow/yRXzIifCxjvxyJTx3vcseZgreHI4vnP0V6Zi6pKamkZOrIyim45iXE9YI8qRfkyf8e68ShqIus2xLFr2sP8f0vu6gT4EHPjg3p0SHkP9HT+25X1iauSUhtPpz2MGq1IaCGllaxP3EmkYLCYlLSc5k0qjc9OoRgZVk9o8vx3aeY/uBciguKeXvtGzTrFm7uIYlqpnrOXCGEEEIIcVuc3A3twuLPJBDeIYQuD7cnrEND3h/xGZP7zyK8U0i540zF28MRTzd7kuxVtPP0NF5yfj1qtYpmjfxo1siPl5/uxu6D51i7OYqvf9rBZ4u30CTEl56dQugaUR8nBxuTjl+YxqnoZAD6dg1DrVZdtV872N+dszEpPHJfS/pX0xCrKAp/fLaWT15eRL0Wwbzx0zg8qtkl76J6kNAthBBCCHEXqtssCIDVX2+kx+OdUavVuNd2Y+afr/Hnl+v5cNRXACbd010VLLUaOrSqS4dWdcnLL2LTrlOs2xLF+1+uZ97Cf2jTNIieHUPo0KoO1tdpx5SQnEVmdj56vb5SRbuEaaVm5AJwKOoiq/89xrGT8ahU0LtzIx66pzmZ2QWMfuNHsrILzDzSihXkFTJ/5Bes/34z94/uy7NzHkdrKe3ARMUkdAshhBBC3IXUFoYV5SNbo3il61R6D++KTx1v4s4ksGHJFmPYXjDqK2KOx/L07KFY21qZc8g3ZGtjSd8ujejbpRFpGbls2H6CtZujmPrBH9hYa+nUuh49OjakVePyFdATkrN47KWvKSjUXfOxy4p2SfA2DV2JnhNnEtl/NIb9R2M4cPQCABu2n6B1k0BGDetM9/YNjfu1/9xwFLjUdq46iT0dz7RBc4g/k8ikxS/S7dGO5h6SqOYkdAshhBBC3IWc3B2wtrWiIK+QI1uiOLIl6qpjrGwseejVe1n27m/sWX2Q8d+MIjSigRlGe/Ncne0Y3K85g/s1JzYhg3Vbo1i3OYo1myNxdrShW7sG9OoUSqP6tcjMzjcG7usV7crMzpfQXUX0eoUz55PZd8QQsg9GXiQvvwgbay1NQ325r1djVvx9kAZBnsx89T7jnu6yr/1royF0l7Wdqy62/7aHd4Z9iKu3Mwt2ziIozN/cQxI1wF0dutPS0njhhRdYtWoVarWaQYMGMX/+fOzt7Ss8/ty5cwQFBVV4308//cSDDz4IUGElwh9++IEhQ4ZU3eCFEEIIIW6Dp78HCyM/IDMlG32JntMHoslMycbJ3YG6zYJQW6hxcnfA09+Dro904N0nP2ZMxzd48JV7eWLaw1he51Lt6qa2tzNPDo5g2KC2nIpOYm1pBfRfVh+klqcTzcJ8AUPgvrxoV5MQX/p0bsQLU5ZxKPKisbiXuHmKonDuYir7j8Sw/+gFDhy7QFZOAZaWGsIb+PDYwNY0D/OnYR0vNBoLok7Hs+Lvgxw+HscLU5bRr+ulEyF/bTScCAEqVQPgTijRlfDNGz/y4zu/0uGBNrzy9fPYOVa/KuqierqrQ/fQoUOJj49n3bp1FBcXM3z4cJ599lmWLl1a4fF+fn7Ex8eXu+2LL77gvffeo2/fvuVuX7RoEX369DF+7uzsXOXjF0IIIYS4HZ7+Hnj6ewBcty2YX4PazNsyg5/n/M63U5ax66/9jP9mNPWaB9+poVYJlUpF/WAv6gd7MfKyCuhrNxtW+eOTMvnx9z1079AQL3fDirZaraJf1zAORV7kZHQSIaXVs+9mVbG/XVEU4hIz2Xckhn1HYjhwLIa0jDw0GjWN6vkwqG8zmof7E1qvVoVVx50dbLCytKCwqIRDkReNIfty1laaalEoLz0pk1mPzuPwv8cY8c5jPPjKvdIOTNyUuzZ0R0VFsXr1avbs2UPLli0B+PDDD+nXrx9z5szBx8fnqq+xsLDA29u73G0rV67koYceump13NnZ+apjhRBCCCFqKguNBUMmDqR1v+a8++RHvND2NYa+PohHJg1Eo615bxktLNQ0D/OneZg/nm4OLFy2ndrezny1bDufLt5MsJ87Ab5uBNR2RSn9mpS0HJOPy9wF3W5nf3tiShb7j15g/5EY9h2NISklG7VaRYM6XvTrGkbzMH/CG/pgY215w3F4eTgy74170VgaVovNVdwuKSb5uleDJMWk8NELC9EVl/Du+ik06dLIpOMRd6ea9xu0knbs2IGzs7MxcAP06NEDtVrNrl27GDhw4A0fY9++fRw8eJCPP/74qvtGjRrFM888Q3BwMP/73/8YPnz4dc94FRYWUlhYaPw8KysLMPQorI6XMun1ehRFqZZjE+Yhc0JUROaFuJLMiZovMMyP+dtnsnTmLyyesZwdq/byytfPE9jI75Yf09zzoqw4V+9Oocx69V427z7NsZPxXIhL42DkRdJKK2kv+mkHf/5zFP/argTUdsHPx5WA2q74+7jg7mp/26ubiclZPD7mmxsG3u8/eBIvE4XN9MzcS/vbQ2rTt2sYtb2diE3I5O+NRzkUFUtBoY70zFw0FioOHLvA/iMX2H/sArEJGQDUDfCgS5t6NA/3p3HD2tjblS/AV5n/z3q9HncXWzw8PFCr1TQI9rrmcaaSFJPCM2FjKcwrvO5x9VsEM3Xlq7j5uMrvNhMz9++Km1XZcd61oTshIQFPz/KFFzQaDa6uriQkJFTqMRYuXEhISAjt2rUrd/v06dPp1q0btra2rF27lueff56cnBxefPHFaz7W7NmzmTZt2lW3JycnU1BQ/Voh6PV6MjMzURSl2uylEeYlc0JUROaFuJLMibtH31FdaNA+iM9fWsyoVhMZPL4/fZ/rZqyKfjPMPS/cnQxveX9be4DmIe60CPWgRahH6dgUXn9/DSejU3iwbzi6Ej2xiVnsOhDNr2sOUaI3rINbW2mo7eWIj5cjtb2cqO3lSG1vJ7w9HLDUWlzzuS8XHZNqDLwhdT3p1jYYbw8HEpKz2bDzLFGnkygo1BF9PhaVYpr3h6kpqcbnn/x8F+P+9lpuHtT3j+CNeeuITchk8ru/kZRqWPn39XYivL4Xj9zTmNB6njjaWxsfLy83k7zcmx+HuecEwLmTFwyBWwUNWteh85AIPAPdiT2RwPL3/iC79PU/Om0gJRodSUlJZhnnf0l1mBc3Izs7u1LH1bjQPXHiRN55553rHhMVdXV1zpuVn5/P0qVLeeONN6667/LbmjVrRm5uLu+99951Q/ekSZMYO3as8fOsrCz8/Pzw8PDA0bH6VcnU6/WoVCrj2UchZE6Iisi8EFeSOXF38ezlSfMDTfj2zZ9YNvN3Dv8TxSuLRlG77s1tsTP3vEjPMQTnqNNJzPzkX/p2bWQs2vX3xmOcjE4BoFeXxuVWXHW6EuKTsjgfm8aFuDTOx6YRE5fOwcjjZOcaVkfVKhXeno74+7hetULu7GhTbnU8NasEMKwwz5/6ULmK3Q8OiOClqT9xKCoWJ2fnqxaPbkdxcQm5+UXk5RcRdTYdgLAGvkSezSAvv4jzsWnsP3qB0+eSUEqvtffycOR/j3WiaSNf3F0qLkJ8O8w9JwDSnQxXnoZ1COG9f95ErVZz8WQci99YQXFBMb4NfLh4Ig5XN9cq/f8hrq06zIubYW1tfeODqIGhe9y4cTz55JPXPSY4OBhvb++rzkbpdDrS0tIqtRd7+fLl5OXl8cQTT9zw2DZt2jBjxgwKCwuxsqq4v6WVlVWF96nV6mo7oVQqVbUen7jzZE6Iisi8EFeSOXF3sba15rk5T9D+/la8++THPN98PM+88xgDRva6qf/H5pwXLk52WFtpKCjUcSgqlkNRsVcdY22lwcXJrtz4LC3Vhn3fvm7ljlUUhYysfGLi0oiJLQ3jsWls23uG5X9loi9dHXewtzZcnl56iXpCsiHk9enSqFwfcQC1Gvp1C+dQVCynziVTN8CTvIIicvMMYTkvv8gYnMs+zr/G7XlX/CnWlVz1en/+cz8//2n42NPNgWZhfjzYrznW1lrenLuKiObB9OoUelvf9xsx9++Ks4fOA9D3qa6o1WrWf7+Zj1/8GjcfFz7aNZvju08z56lPOHvoPCFt6ptljP9F5p4XN6OyY6xxodvDwwMPD48bHhcREUFGRgb79u2jRYsWAGzYsAG9Xk+bNm1u+PULFy7k3nvvrdRzHTx4EBcXl2sGbiGEEEKImi6sQwifH3yPLycs4aMXFrLt1928snCksTp6debt4cji+U9VWQEzlUqFi5MtLk62NAnxLXdfUbGOi/EZ5cJ4dEwK/+44SV5+EQDvfb6OH3/fS21vZ3Q6fWm4LiQjKx+AuV+sZ87n66/z/GBrY4mttSV2tpbYGD+2wtnJxvix4RgttsaPLdl35DyLV+5m9JNdGNA9HGsrLRaXbRn4c4OhP7aTo/mrhptaZorh0uCCvCJejHiNE3vO0H1oR174+BnsHG3JKr28vOw4IW5VjQvdlRUSEkKfPn0YMWIEn332GcXFxYwePZohQ4YYK5fHxsbSvXt3vvvuO1q3bm382tOnT7N582b++uuvqx531apVJCYm0rZtW6ytrVm3bh2zZs3ilVdeuWOvTQghhBDCHGzsbXjx42dof38r5j79KSPCxzHygyfpPbxrtW+h5O3haAzVpmwLZqnVEOzvTrC/e7nbFUVh6W+7+fT7LfTsGIKDnTVxiRnY2mhxd7PH1tqSuMQMtu87S/cODYloFoydrSEo29pYYmtraQzONtbaW/5+29tZsnjlbrbsPs1D/VuUu8Rdr1f4a6MhdNcPuvsvpy77Fn446ivqtQjm/U3TCe8YYrw/7oyhDpSTu4M5hifuIndt6AZYsmQJo0ePpnv37qjVagYNGsSCBQuM9xcXF3PixAny8vLKfd3XX3+Nr68vvXr1uuoxtVotH3/8MWPGjEFRFOrWrcv777/PiBEjTP56hBBCCCGqgxY9m/DF4bl8OvYb5j7zKVtX7mLMF//DrZaLuYdWbalUKpqH+QOGtl2TR/e9KvC+MGUZAA/f08JkJwbKLoc9FHmRF6Yso1/XMOP+9r82HjX2y64Jl/beqvycfJa98xs/zfkNAN/6tViwYyYazaVopNfrWbNoIwB1mwWZZZzi7nFXh25XV1eWLl16zfsDAwNRyqpFXGbWrFnMmjWrwq/p06cPffr0qbIxCiGEEELURPbOdrz69Sja39+aec99zoiwMbzw8Qi6PNyu2q96m0t1CLxODjaX9rdHXjQ+5+WsrTQ4Odx9l5fr9XrWf7+Zha8tJTsth+5DO7H66w1cPBXP+O7T6T28Kz51vIk7k8CaRRs5stVQnPlWKvYLcbm7OnQLIYQQQgjTandvKxq1a8CHo79i1qPz2LpyFy9+/AxO7tWvO4u5VYfAW9X722uKo9uO8+mYbzi59wxdHm7H07OHolar+PfHbRTkFXJkSxRHtlzdAcna1kouLxe3TUK3EEIIIYS4LU7ujrz+41g6DNzGglFf8UzYWMZ8/hzt7mtl7qFVK9Ul8N6p/e3VQeL5ZL6auJh/l22nXotgPtg8nbAOl/ZtL4z8gMyUbPQlek4fiCYzJRsndwfqNgtCbaHGyd2hRhQLFNWbhG4hhBBCCFElujzcnsadQ/ng2c+ZMvBdej7RmQfHDaCosJjU5FT2xBwmOzXnPx1q/kuB15zyc/L58e1f+XnuKhxc7Xl10Sh6PN7pqkv3Pf09jPOvQau65hiq+A+Q0C2EEEIIIaqMq7cL03+bwNpv/+Xjl75m3feb4OoSOkbWtlYsjPzgPxW8heno9XrWfbeJryf/QE56Dg+9ci8PT7gPG/u7b4+6qDkkdAshhBBCiCqlUqno/WRXnD0def2etwFw8nTkiSkPERTuT/yZBFZ/bShUVZBXSGZKtoRucduObo3ikzHfcGrfWbo83I5n3n4MrwCZV8L8pBSfEEIIIYQwCWcPJwBq1fEiP7uAn+f8jqJX6DWsK3M2TiW8dG+tvkRvzmGKGi7hXBJvDXmfMZ3eRKVS8cGWGUz+YYwEblFtyEq3EEIIIYQwidMHogF49LUHqNXQg0Xjf2Jclym06tuMB8cNoNeTXTiyJYrTB6JlP624aXnZ+fz49kqWv/8HDq72jP9mNN0f63hX9xgXNZOEbiGEEEIIYRKZKdkA+NTxwjPIjfc2TOHfH7exfO4qxveYjm99QyGx9MRMcw5T1DB6vZ61325i0eSl5GTkyr5tUe1J6BZCCCGEECZR1t847kwinvXdsLBQ0/PxzvR4rBP71x/ms7HfAvDL/D+xsbem7zPdsTVhj2pR8x3ZEsWnYxZxan80XYa055nZQ+UyclHtybUXQgghhBDCJOo2CwJgzTf/otdf2retUqlo1j0cB1d7AELa1uPLCYt51P9/fDVxMSmxqWYZr6i+4qMTmfHw+4zt/CZqC7Vh3/bSlyVwixpBVrqFEEIIIYRJqC0M6ztHt0Yxa9AC+o/oiW89H+LOJLBmkaF6OcCT04fw8mfP8euCv1j12VpWfPAHXR/twINjBxAUHmDOlyBMKOViGpkXc0Ax7P/PTMm+qoe7vYs9P8xeyYoP/sDRzZ7x346m+1DZty1qFgndQgghhBDCJJzcHbC2taIgr5ATu85wYteZq46xtrXCyd0BD183Rrz7OI++Poi/v/qHX+b/ybpvN9GydxMeHHcvzbqHo1KpzPAqhCkkxaQwofNMivKLrnmMxlKDnaMt+Tn5PPTqvTw8XvZti5pJQrcQQgghhDAJT38PFkZ+QHpSJqnJqaTGZJKdmnPVaublPbrtHG0ZPHYA97/Ql80/7+CnOb8zodcM6jQN5MFx99L5oQg0WnkLW9NlpmQZArcKwjuE0OeprtSq4038mQRWfPAnZw+fR1eko16LYMZ8/qz0cRc1mvzGEkIIIYQQJuPp74G7rxtOSfa07e1Z6cuCNVoN3R7tSNdHOnBw41F+nvM7bz++gIWTljDwpf70G9EdO0dbE49emEpZb/awDiHM2TgVtVpNfHQiKxf8xdnD57GxtyY/p4Anpz8sgVvUeLIZQgghhBBCVFsqlYpm3cKZ9ddkvjg8l2Y9wvn6tSU86v8/vnj1O5IupJh7iOIWnD54DoDeT3bh4sl4vhz/PU+HvEzk9hOM/3Y0z88bbjiutNe7EDWZrHQLIYQQQogaISjMn1e/HsXwtx7htw//ZtVna/ll/l90GdKOB8fdS50mgeYeoqgERVE4f+wCAEtmLCfhXDI29tY8POF+Hhp/HzZ21hzZYiiyV9brXYiaTEK3EEIIIYSoUdx9XHl69lAeee0BVn+9gV/m/ck/i7fQvGdjHhx3Ly16Npaia9WMoihEH4lh8/IdbF6+kwvHYwFw8XZh5AfDadm7CZbWlsbj484kAJd6vQtRk0noFkIIIYQQNZKtgw0PvNSf+0b1YfPynfw85zcm9XmLoHB/Hhx3L12GtENrqQUgKSaZzJRs9CX6a7ankr3DVUtRFM4cPMemn3ewZcVOYk/FY+9sR8R9Len7dDe+ePV7LLQWtB3Qotxef71ez5pFG4FLvd6FqMkkdAshhBBCiBrNQmNB1yHt6fJwOw5viuTnub/z7pMfsfC1JQx8sT+t+zblxYjJFOQVXvMxrG2tWBj5gQTv26QoCif3nWVzadCOP5uIg6s97e9rxaj5w2naLQytpZYTe08Dhh7ur3SdSu/hXfGp431VD/eyXu9C1GQSuoUQQgghxF1BpVLRpEsjmnRpxPnICyyfu4pv3/yRxTN+Ngbu8I7l21Ot/toQ8AryCslMyZbQfQsURSFq1ym2LN/JlhU7STyfjJO7A+3vb81Ln46gSZdGV7V5c3J3xNLGkqL8Io5siTLu4b5cWQ93IWo6Cd1CCCGEEOKuExDqx7iFz/PkW4/w9eSlrP3mXwDcfV0JbhxI3WZBhHcIocfjnXml61SObIkytrESN6bX64nccdIQtH/ZSfKFVJw9negwsDWdHoygcadQLDQW1/x6T3933tk0GS2WoCCX/Iu7moRuIYQQQghx13Kr5UJo2/qs/eZfug/twLFtJxjZYjzBjQOo37IO9VsE07hzKEe2RHH6QDQNWtU195BN7lb3t5eUlHBs2wlj0E6NS8e1lgsdH2hDx8FtCevQEAuLawftK7n7uuLpaejd/l/4vov/LgndQgghhBDirlbWdqr/c714ddFotv26m71rDnFq/1nWfbeJEl0JAN9N/Ynju05Rr0Ud6rUIpk6TgHIVte8GSTHJPB06ptL720t0JRzZEsXm5TvZtnIXaQkZuNd2pdPgCDoNbktouwbliqAJIa4moVsIIYQQQtzVyvYFx59JILxDSGlgjACgqLCYH2b9wuIZy/Gp483pg+dYv3gzuuIS1BZqAsP8qN882BjEgxv7Y2VjdctjMXcV9cyUbEPgVkF4h2vvb9/1537OHDrPtpW7yEjOwtPfna6PdKDT4LY0bFNPgrYQN0FCtxBCCCGEuKuVtZ1a/fVGejzeuVxg1GgtOPTvMQD+9/4wGrSqS1FhMdFHYji17yyn9p3h1P6z5YN4Iz/qNQ+mXotg44p4ZYL4za4ym0LZvvXwDiHM2TjV+L0IaVMPZ08nLj4VR3piJgtGfYV3oAe9hnWh4+C2NGhVV3qfC3GL7urQPXPmTP78808OHjyIpaUlGRkZN/waRVGYMmUKX375JRkZGbRv355PP/2UevXqGY9JS0vjhRdeYNWqVajVagYNGsT8+fOxt7c34asRQgghhBC3oqzt1JFKtqeytNLSoGUdGrSsA/QEqDCI/7Pk5oJ4ZVeZTVFFvaSkhNyMPPauOQhAg9Z12PzzDrLTczmx+zTbf9tNdnouzp6OADwyaSDD33pEgrYQVeCuDt1FRUU8+OCDREREsHDhwkp9zbvvvsuCBQv49ttvCQoK4o033qB3795ERkZibW0NwNChQ4mPj2fdunUUFxczfPhwnn32WZYuXWrKlyOEEEIIIW6Bk7sD1rZWFOQV3nJ7qmsF8XNHy4L4WU5eEcQDQn0NIbx5MPVbBBv3jl+5ylzZKuolJSXkZuaRk55LdnouOek55KTnkpVm+DsnPcdwe0bp36W3ZaXlkJeVX+6xls/9AzCcaKhdrxYDRvam04MR5GbmMa7LFKztrCVwC1FF7urQPW3aNAC++eabSh2vKArz5s3j9ddf57777gPgu+++w8vLi19//ZUhQ4YQFRXF6tWr2bNnDy1btgTgww8/pF+/fsyZMwcfHx+TvBYhhBBCCHFrPP09WBj5QZXvpba00lK/RR3qt6hjvK2iIL5hyRZ0xSWo1IYQqygKv3+yhqBwf3RFOmOIdvZ0AuCzcd/i4u1suD0txxim87LyURTlqnGo1SrsXeyxd7HDwcUOexd7nD0c8a1XC3sXexxdDffZu9hzbNtxVnzwB8++9zj9RvTA1sGmXLhe881GAOmPLUQVuqtD982Kjo4mISGBHj16GG9zcnKiTZs27NixgyFDhrBjxw6cnZ2NgRugR48eqNVqdu3axcCBAyt87MLCQgoLL+3fycrKAgw9DvX66tcTUq/XoyhKtRybMA+ZE6IiMi/ElWROiIpUh3nh7uuGu68bAPVaBFd4TFWMT6O1oG6zIOo2C6LvM90BKC7Sce5oDEtnrmD7b3vJSMrki1e+o7hIZ/w6tVqFtb3hqsr46EQsrS1xdLPHp6439s5lYdoQnB2cyz62w8HV/qrgfD3utV1Y8cEfbP99LwNf6oeiKMYgr9frWb3IELqDmwSY9P9XdZgTovqpafOisuOU0H2ZhIQEALy8vMrd7uXlZbwvISEBT0/PcvdrNBpcXV2Nx1Rk9uzZxpX3yyUnJ1NQUHC7Q69yer2ezMxMFEWR6pQCkDkhKibzQlxJ5oSoiMwLcPK1p2G7umz/bS/9RnYnYmALEs+nYGmtxc7JFmt7K7b+tJsvxy7hvhd70/Xx9pV63NyCHHILcio9jszMTACObo3i5Y6v0+nhtngFupN4LoXNy3ZyYvcZ43FJSUk3/0IrSeaEqEhNmxfZ2dmVOq7Ghe6JEyfyzjvvXPeYqKgoGjZseIdGVDmTJk1i7Nixxs+zsrLw8/PDw8MDR0dHM46sYnq9HpVKhYeHR42Y8ML0ZE6Iisi8EFeSOSEqIvPCoGmncOBHtv+yj4Gj+uPje2lbol6vZ8fK/cbjrlzkqTL11VjZWlGYV8iJXWc4sevMVYdY2VoRWD8AT09304wBmROiYjVtXpTV/LqRGhe6x40bx5NPPnndY4KDK75k6Ea8vb0BSExMpFatWsbbExMTadq0qfGYK8/66XQ60tLSjF9fESsrK6ysrm4loVarq+2EUqlU1Xp84s6TOSEqIvNCXEnmhKiIzAvQaA1vvY9ujWJ89+lXVVE/WlpFXaPVmOz75B3oydcm2N9+K2ROiIrUpHlR2THWuNDt4eGBh4dpfgkEBQXh7e3NP//8YwzZWVlZ7Nq1i5EjRwIQERFBRkYG+/bto0WLFgBs2LABvV5PmzZtTDIuIYQQQghR81VFFfWq4OnvYQzVDVrVNelzCSFqYOi+GTExMaSlpRETE0NJSQkHDx4EoG7dusae2g0bNmT27NkMHDgQlUrFyy+/zFtvvUW9evWMLcN8fHy4//77AQgJCaFPnz6MGDGCzz77jOLiYkaPHs2QIUOkcrkQQgghhLgmU1VRF0JUb3d16H7zzTf59ttvjZ83a9YMgI0bN9KlSxcATpw4YSwoATB+/Hhyc3N59tlnycjIoEOHDqxevbrc9fpLlixh9OjRdO/eHbVazaBBg1iwYMGdeVFCCCGEEKLGklVmIf57VEpFzf6EyWVlZeHk5ERmZma1LaSWlJSEp6dnjdhPIUxP5oSoiMwLcSWZE6IiMi/ElWROiIrUtHlR2UxX/V+JEEIIIYQQQghRQ0noFkIIIYQQQgghTERCtxBCCCGEEEIIYSISuoUQQgghhBBCCBOR0C2EEEIIIYQQQpiIhG4hhBBCCCGEEMJE7uo+3dVZWae2rKwsM4+kYnq9nuzsbKytrWtEuX5hejInREVkXogryZwQFZF5Ia4kc0JUpKbNi7Isd6Mu3BK6zSQ7OxsAPz8/M49ECCGEEEIIIcStys7OxsnJ6Zr3q5QbxXJhEnq9nri4OBwcHFCpVOYezlWysrLw8/PjwoUL1230Lv47ZE6Iisi8EFeSOSEqIvNCXEnmhKhITZsXiqKQnZ2Nj4/PdVfmZaXbTNRqNb6+vuYexg05OjrWiAkv7hyZE6IiMi/ElWROiIrIvBBXkjkhKlKT5sX1VrjLVP8L5YUQQgghhBBCiBpKQrcQQgghhBBCCGEiErpFhaysrJgyZQpWVlbmHoqoJmROiIrIvBBXkjkhKiLzQlxJ5oSoyN06L6SQmhBCCCGEEEIIYSKy0i2EEEIIIYQQQpiIhG4hhBBCCCGEEMJEJHQLIYQQQgghhBAmIqFbCCGEEEIIIYQwEQnd4ioff/wxgYGBWFtb06ZNG3bv3m3uIQkz2rx5MwMGDMDHxweVSsWvv/5q7iEJM5s9ezatWrXCwcEBT09P7r//fk6cOGHuYQkz+/TTT2ncuDGOjo44OjoSERHB33//be5hiWrk7bffRqVS8fLLL5t7KMKMpk6dikqlKvenYcOG5h6WMLPY2Fgee+wx3NzcsLGxITw8nL1795p7WFVGQrcoZ9myZYwdO5YpU6awf/9+mjRpQu/evUlKSjL30ISZ5Obm0qRJEz7++GNzD0VUE5s2bWLUqFHs3LmTdevWUVxcTK9evcjNzTX30IQZ+fr68vbbb7Nv3z727t1Lt27duO+++zh27Ji5hyaqgT179vD555/TuHFjcw9FVAONGjUiPj7e+Gfr1q3mHpIwo/T0dNq3b49Wq+Xvv/8mMjKSuXPn4uLiYu6hVRlpGSbKadOmDa1ateKjjz4CQK/X4+fnxwsvvMDEiRPNPDphbiqVipUrV3L//febeyiiGklOTsbT05NNmzbRqVMncw9HVCOurq689957PP300+YeijCjnJwcmjdvzieffMJbb71F06ZNmTdvnrmHJcxk6tSp/Prrrxw8eNDcQxHVxMSJE9m2bRtbtmwx91BMRla6hVFRURH79u2jR48extvUajU9evRgx44dZhyZEKI6y8zMBAwBSwiAkpISfvzxR3Jzc4mIiDD3cISZjRo1iv79+5d7fyH+206dOoWPjw/BwcEMHTqUmJgYcw9JmNHvv/9Oy5YtefDBB/H09KRZs2Z8+eWX5h5WlZLQLYxSUlIoKSnBy8ur3O1eXl4kJCSYaVRCiOpMr9fz8ssv0759e8LCwsw9HGFmR44cwd7eHisrK/73v/+xcuVKQkNDzT0sYUY//vgj+/fvZ/bs2eYeiqgm2rRpwzfffMPq1av59NNPiY6OpmPHjmRnZ5t7aMJMzp49y6effkq9evVYs2YNI0eO5MUXX+Tbb78199CqjMbcAxBCCFFzjRo1iqNHj8p+PAFAgwYNOHjwIJmZmSxfvpxhw4axadMmCd7/URcuXOCll15i3bp1WFtbm3s4opro27ev8ePGjRvTpk0bAgIC+Omnn2Qryn+UXq+nZcuWzJo1C4BmzZpx9OhRPvvsM4YNG2bm0VUNWekWRu7u7lhYWJCYmFju9sTERLy9vc00KiFEdTV69Gj++OMPNm7ciK+vr7mHI6oBS0tL6tatS4sWLZg9ezZNmjRh/vz55h6WMJN9+/aRlJRE8+bN0Wg0aDQaNm3axIIFC9BoNJSUlJh7iKIacHZ2pn79+pw+fdrcQxFmUqtWratOzoaEhNxV2w4kdAsjS0tLWrRowT///GO8Ta/X888//8iePCGEkaIojB49mpUrV7JhwwaCgoLMPSRRTen1egoLC809DGEm3bt358iRIxw8eND4p2XLlgwdOpSDBw9iYWFh7iGKaiAnJ4czZ85Qq1Ytcw9FmEn79u2vaj168uRJAgICzDSiqieXl4tyxo4dy7Bhw2jZsiWtW7dm3rx55ObmMnz4cHMPTZhJTk5OubPP0dHRHDx4EFdXV/z9/c04MmEuo0aNYunSpfz22284ODgYaz44OTlhY2Nj5tEJc5k0aRJ9+/bF39+f7Oxsli5dyr///suaNWvMPTRhJg4ODlfVerCzs8PNzU1qQPyHvfLKKwwYMICAgADi4uKYMmUKFhYWPPLII+YemjCTMWPG0K5dO2bNmsVDDz3E7t27+eKLL/jiiy/MPbQqI6FblPPwww+TnJzMm2++SUJCAk2bNmX16tVXFVcT/x179+6la9euxs/Hjh0LwLBhw/jmm2/MNCphTp9++ikAXbp0KXf7okWLePLJJ+/8gES1kJSUxBNPPEF8fDxOTk40btyYNWvW0LNnT3MPTQhRjVy8eJFHHnmE1NRUPDw86NChAzt37sTDw8PcQxNm0qpVK1auXMmkSZOYPn06QUFBzJs3j6FDh5p7aFVG+nQLIYQQQgghhBAmInu6hRBCCCGEEEIIE5HQLYQQQgghhBBCmIiEbiGEEEIIIYQQwkQkdAshhBBCCCGEECYioVsIIYQQQgghhDARCd1CCCGEEEIIIYSJSOgWQgghhBBCCCFMREK3EEIIIYQQQghhIhK6hRBCCCGEEEIIE5HQLYQQQgghhBBCmIiEbiGEEEIIIYQQwkQkdAshhBBCCCGEECYioVsIIYQQQgghhDARCd1CCCGEEEIIIYSJaMw9ACGEEELcPdLT05k2bRo6nY7Tp0/z0EMP8eijj/Lqq6+iKArp6elMnjyZ0NBQcw9VCCGEuCMkdAshhBCiShQVFfH8888zd+5cfHx8OH/+PEFBQfz222/MmzePU6dO0b9/f1xcXPjoo4/MPVwhhBDijpDLy4UQQghRJT777DOef/55fHx8ALC2tkZRFAIDAwkKCqKkpIR69erxyCOPmHmkQgghxJ0jK91CCCGEqBJubm507NjR+PnevXsB6NOnDwB9+/alb9++ZhmbEEIIYS6y0i2EEEKIKjF06NByn2/cuBGNRkOHDh3MNCIhhBDC/FSKoijmHoQQQggh7j7NmzdHq9Wya9cucw9FCCGEMBtZ6RZCCCFElUtLS+PQoUN06dKl3O1fffWVeQYkhBBCmImEbiGEEELctuTkZFq3bs3kyZMBWLNmDXq9ntatW5c7Zvv27eYaohBCCGEWErqFEEIIcds2bdrEnj170Gq15Ofns2zZMnx8fMjJyQEgNzeXF198kalTp5p3oEIIIcQdJnu6hRBCCHHbcnJyePnll7G0tCQnJ4dJkyaRlZXFa6+9RkBAAEVFRYwfP57GjRube6hCCCHEHSWhWwghhBBCCCGEMBG5vFwIIYQQQgghhDARCd1CCCGEEEIIIYSJSOgWQgghhBBCCCFMREK3EEIIIYQQQghhIhK6hRBCCCGEEEIIE5HQLYQQQgghhBBCmIiEbiGEEEIIIYQQwkQkdAshhBBCCCGEECYioVsIIYQQQgghhDARCd1CCCGEEEIIIYSJSOgWQgghhBBCCCFMREK3EEIIIYQQQghhIv8HnKvqDn8LNUcAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#****************************************Data-Analysis*********************************************\n", "# ---------------- exact solution ----------------\n", "def u_exact(x, t, A, k_w, phi, c, nu):\n", " return A * np.exp(-nu * k_w**2 * t) * np.sin(k_w * ((x+dx/2) - c*t) + phi)\n", "u_ana = np.empty(snaps, dtype=object) # array field used to same data over time\n", "for i in range(snaps):\n", " u_ana[i] = np.zeros((Nx), dtype=\"float64\")\n", "# -----------------Plot Results --------------------\n", "plt.figure(figsize=(10,5))\n", "colors = plt.cm.viridis(np.linspace(0, 1, snaps))\n", "for i in range(snaps):\n", " plt.plot(x, u_snaps[i], \"s\", color=colors[i], lw=1, label=f\"LBM t={(snaps_id[i]/nt)*t_end:.2f}\",fillstyle='none')\n", " plt.plot(x, uf_snaps[i], \"o\", color=colors[i], lw=1, label=f\"FDM t={(snaps_id[i]/nt)*t_end:.2f}\",fillstyle='none')\n", " u_ana[i] = u_exact(x, (snaps_id[i]/nt)*t_end , A, k_w, phi, c, nu)\n", " plt.plot(x, u_ana[i], color=colors[i], lw=1, label=f\"Exact t={(snaps_id[i]/nt)*t_end:.2f}\")\n", "\n", "plt.xlabel(\"$x$\",fontsize=16)\n", "plt.ylabel(\"$u(x,t)$\",fontsize=16)\n", "plt.title(\"1D Convection-Diffusion: LBM vs Analytical Solution\")\n", "plt.grid(True, alpha=0.3)\n", "plt.legend(ncol=5,fontsize=9,loc=\"center left\",bbox_to_anchor=(0.0, 1.2))\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a8cd98fa-1ac0-412c-a58d-dbbe2b4c1dcb", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## 2nd Benchmark: Temperature ramp\n", "\n", "Analyzing the accuracy of diffusive equation solver, we apply it to a one-dimensional analytical case. The geometry is described by a domain of length $L$ initialized with a constant temperatura $T(x,t=0)=0$. The boundary conditions are given $T(x=0,t)=1$ and $T(x=L,t)=0$.\n", "\n", "### Steady-State Analytical Solution\n", "\n", "The analytical solution of this problem is given by:\n", "\n", "$$\n", "T(x,t\\rightarrow \\infty)= -\\frac{x}{L} + 1.\n", "$$\n", "\n", "### Transient Analytical Solution\n", "\n", "For the 1D heat equation $\\partial_t T=\\nu\\,\\partial_{xx}T$ on $0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# ---- Modes and series -------------------------------------------------------\n", "def modes_dirichlet_dirichlet(L, N):\n", " n = np.arange(1, N+1) # n = 1,2,...,N\n", " k = n * np.pi / L # eigenvalues mu_n\n", " return n, k\n", "\n", "def project_coeffs_dirichlet(T0_func, L, N, grid_pts=4000):\n", " \"\"\"\n", " B_n = (2/L) ∫( T0(x) - T_ss(x) ) sin(nπx/L) dx, with T_ss = 1 - x/L.\n", " \"\"\"\n", " x = np.linspace(0.0, L, grid_pts, endpoint=True)\n", " Tss = 1.0 - x / L\n", " u0 = T0_func(x) - Tss\n", " n, k = modes_dirichlet_dirichlet(L, N) # (N,), (N,)\n", " S = np.sin(k[:, None] * x[None, :]) # (N, M)\n", " B = (2.0 / L) * np.trapz(u0[None, :] * S, x, axis=1)\n", " return B, n, k\n", "\n", "def T_series_dirichlet(x, t, L, nu, B, k):\n", " \"\"\"\n", " T(x,t) = T_ss(x) + sum_n B_n e^{-nu k_n^2 t} sin(k_n x), T_ss = 1 - x/L.\n", " \"\"\"\n", " x = np.asarray(x)\n", " Tss = 1.0 - x / L\n", " coeff = B * np.exp(-nu * (k**2) * t) # (N,)\n", " add = np.sum(coeff[:, None] * np.sin(k[:, None] * x[None, :]), axis=0)\n", " return Tss + add\n", "\n", "# ---- Parameters -------------------------------------------------------------\n", "L = 1.0\n", "nu = 0.1/2.0 \n", "N = 200\n", "x = np.linspace(0, L, 600)\n", "\n", "# ---- Case A: initially cold rod T0(x)=0 (closed-form coefficients) ----------\n", "n, k = modes_dirichlet_dirichlet(L, N)\n", "B_cold = -2.0 / (n * np.pi) # exact coefficients for T0 ≡ 0\n", "\n", "times = [0.0, 2.0, 4.0, 6.0, 8.0]\n", "\n", "#--------------------------------------- Plot Results -------------------------------------------------------\n", "xl = np.linspace(0, L, Nx)\n", "times = np.linspace(0, t_end, snaps, dtype=\"float64\") # timesteps to take the field\n", "plt.figure(figsize=(7, 5))\n", "colors = plt.cm.viridis(np.linspace(0, 1, snaps))\n", "for i in range(snaps):\n", " T_xt = T_series_dirichlet(x, times[i], L, nu, B_cold, k)\n", " plt.plot(x, T_xt, \"--\", color=colors[i], label=f\"Exact $t = {t:.2f}$\")\n", " plt.plot(xl, T_snaps[i], \"s:\", color=colors[i], lw=1, label=f\"LBM $t={(snaps_id[i]/nt)*t_end :.2f}$\",fillstyle='none')\n", " plt.plot(xl, Tf_snaps[i], \"o:\", color=colors[i], lw=1, label=f\"FDM $t={(snaps_id[i]/nt)*t_end :.2f}$\",fillstyle='none')\n", "plt.xlabel(r\"$x$\",fontsize=18)\n", "plt.ylabel(r\"$\\phi(x,t)$\",fontsize=18)\n", "plt.legend(ncol=3,fontsize=8)\n", "plt.xlim(-0.05,1)\n", "plt.ylim(-0.2,1.01)\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "041b2452-96a8-4067-9c87-9713b5118ff5", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Fourth-order Diffusive Equation" ] }, { "cell_type": "markdown", "id": "283ebf80-415a-449b-be96-0f37684c9c56", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Expanding the sums:\n", "\n", "$$\n", "\\begin{array}{c}\n", "\\phi_{x}^{t+1} = (1-\\omega + \\omega w_{0}) \\phi_{x}^{t} + (1-\\omega + \\omega w_{1}) \\phi_{x-1}^{t} + (1-\\omega + \\omega w_{2}) \\phi_{x+1}^{t} - (1-\\omega)^{2} \\Big( \\phi_{x}^{t-1} + \\phi_{x-1}^{t-1} + \\phi_{x+1}^{t-1} \\Big) \\\\\n", "-(1-\\omega)\\omega \\Big( (w_{1}+w_{2})\\phi_{x}^{t-1} + (w_{0}+w_{1})\\phi_{x-1}^{t-1} + (w_{0}+w_{2})\\phi_{x+1}^{t-1} \\Big) + (1-\\omega)^{2} \\phi_{x}^{t-2}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "3091481d-1e33-41cb-9bc4-2ff2ed0c7da0", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Considering \n", "$$\n", "\\alpha_{1}=\\Omega + a\\omega, \\quad \\alpha_{2}=\\Omega + (1-2a)\\omega, \\quad \\beta_{1}=-\\Omega(\\Omega + (1-a)\\omega), \\quad \\textrm{and} \\quad \\beta_{2}=-\\Omega(\\Omega + 2a\\omega),\n", "$$\n", "\n", "where $\\Omega=(1-\\omega)$ and $a=w_{1}=w_{2}$. Replacing in the Eq. {eq}`df-final-form-fdm`:\n", "\n", "$$\n", "\\begin{array}{c}\n", "\\phi_{x}^{t+1} = \\alpha_{1} \\phi_{x-1}^{t} + \\alpha_{2} \\phi_{x}^{t} + \\alpha_{1} \\phi_{x+1}^{t} + \\beta_{1}\\phi_{x-1}^{t-1} + \\beta_{2}\\phi_{x}^{t-1} + \\beta_{1}\\phi_{x+1}^{t-1} + (1-\\omega)^{2} \\phi_{x}^{t-2}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "b4be3801-f5a4-4e44-8532-25f3833d0e67", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "To recover the partial differetial equation described by the above equation, we expand each $\\phi$ term in Taylor series:\n", "\n", "$$\n", "\\phi_{x}^{t\\pm 1} = \\phi \\pm \\Delta_{t}\\frac{\\partial\\phi}{\\partial t} + \\frac{\\Delta_{t}^{2}}{2}\\frac{\\partial^{2}\\phi}{\\partial t^{2}} \\pm \\frac{\\Delta_{t}^{3}}{6}\\frac{\\partial^{3}\\phi}{\\partial t^{3}} + \\frac{\\Delta_{t}^{4}}{24}\\frac{\\partial^{4}\\phi}{\\partial t^{4}} \\pm \\mathcal{O}(\\Delta t)^{4},\n", "$$\n", "\n", "$$\n", "\\phi_{x\\pm 1}^{t} = \\phi \\pm \\Delta_{x}\\frac{\\partial\\phi}{\\partial x} + \\frac{\\Delta_{x}^{2}}{2}\\frac{\\partial^{2}\\phi}{\\partial x^{2}} \\pm \\frac{\\Delta_{x}^{3}}{6}\\frac{\\partial^{3}\\phi}{\\partial x^{3}} + \\frac{\\Delta_{x}^{4}}{24}\\frac{\\partial^{4}\\phi}{\\partial x^{4}} \\pm \\mathcal{O}(\\Delta x)^{4},\n", "$$\n", "\n", "$$\n", "\\phi_{x}^{t - 2} = \\phi - 2\\Delta_{t}\\frac{\\partial\\phi}{\\partial t} + \\frac{4\\Delta_{t}^{2}}{2}\\frac{\\partial^{2}\\phi}{\\partial t^{2}} - \\frac{8\\Delta_{t}^{3}}{6}\\frac{\\partial^{3}\\phi}{\\partial t^{3}} + \\frac{16\\Delta_{t}^{4}}{24}\\frac{\\partial^{4}\\phi}{\\partial t^{4}} \\pm \\mathcal{O}(\\Delta t)^{4},\n", "$$\n", "\n", "$$\n", "\\phi_{x\\pm 1}^{t-1} = \\phi \\pm \\Delta_{x}\\frac{\\partial\\phi}{\\partial x} - \\Delta_{t}\\frac{\\partial\\phi}{\\partial t} + \\frac{\\Delta_{x}^{2}}{2}\\frac{\\partial^{2}\\phi}{\\partial x^{2}} \\mp \\Delta_{t}\\Delta_{x} \\frac{\\partial^{2}\\phi}{\\partial x\\partial t} + \\frac{\\Delta_{t}^{2}}{2}\\frac{\\partial^{2}\\phi}{\\partial t^{2}} \\pm \\frac{\\Delta_{x}^{3}}{6}\\frac{\\partial^{3}\\phi}{\\partial x^{3}} \\mp \\frac{\\Delta_{x}^{2}\\Delta_{t}}{2}\\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} \\pm \\frac{\\Delta_{x}\\Delta_{t}^{2}}{2}\\frac{\\partial^{3}\\phi}{\\partial x\\partial t^{2}} - \\frac{\\Delta_{t}^{3}}{6}\\frac{\\partial^{3}\\phi}{\\partial t^{3}} + \\mathcal{O}(\\Delta x \\Delta t)^{3}.\n", "$$" ] }, { "cell_type": "markdown", "id": "3d2a86e1-5a3b-49fe-aec8-2d2ad78be37d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Replacing the expanded terms and simplifying the term (this link provide a sympy code that reach the above equation {doc}`appendix/sympy-code-fdm-diffusive-expansion`), we have:\n", "\n", "$$\n", "0=\\Delta_{t} \\omega^{2} \\frac{\\partial\\phi}{\\partial t} + \\Delta_{x}^{2} a \\omega \\left(\\omega - 2\\right) \\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\Delta_{t}^{2} \\omega \\left(4 - 3 \\omega\\right) }{2} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} - \\Delta_{t} \\Delta_{x}^{2} \\left(a \\omega^{2} - a \\omega - \\omega + 1\\right) \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} + \\frac{\\Delta_{x}^{4} a \\omega \\left(\\omega - 2\\right) }{12}\\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$\n", "\n", "$$\n", "\\Delta_{t} \\omega^{2} \\frac{\\partial\\phi}{\\partial t} = - \\Delta_{x}^{2} a \\omega \\left(\\omega - 2\\right) \\frac{\\partial^{2}\\phi}{\\partial x^{2}} - \\frac{\\Delta_{t}^{2} \\omega \\left(4 - 3 \\omega\\right) }{2} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} + \\Delta_{t} \\Delta_{x}^{2} \\left(a \\omega^{2} - a \\omega - \\omega + 1\\right) \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} - \\frac{\\Delta_{x}^{4} a \\omega \\left(\\omega - 2\\right) }{12}\\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\frac{a \\left(2 - \\omega \\right)}{\\omega} \\frac{\\Delta_{x}^{2}}{\\Delta_{t}} \\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{ \\left(3 \\omega - 4\\right) \\Delta_{t}}{2\\omega} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} + \\frac{\\left(a \\omega^{2} - a \\omega - \\omega + 1\\right)\\Delta_{x}^{2}}{\\omega^{2}} \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} + \\frac{ a \\left(2 - \\omega\\right) }{12\\omega} \\frac{\\Delta_{x}^{4}}{\\Delta_{t}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "9ec53d04-487d-4ec6-8006-f4827d3081ca", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "where $\\nu=\\frac{a \\left(2 - \\omega \\right)}{\\omega} \\frac{\\Delta_{x}^{2}}{\\Delta_{t}}$ is the same term recovered in the Chapman-Enskog Analysis. To enforce fourth-order $\\Delta_{x}$ convergence rate, employ the relations\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu \\frac{\\partial^{2}\\phi}{\\partial x^{2}}, \\qquad \\frac{\\partial^{2}\\phi}{\\partial t^{2}} = \\nu^{2} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}, \\qquad \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} = \\nu \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{a \\left(2 - \\omega \\right)}{\\omega} \\frac{ \\left(3 \\omega - 4\\right) \\nu\\Delta_{x}^{2}}{2\\omega} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\left(a \\omega^{2} - a \\omega - \\omega + 1\\right)\\nu\\Delta_{x}^{2}}{\\omega^{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\nu\\Delta_{x}^{2}}{12} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{ a\\left(6 \\omega - 8 - 3\\omega^{2} + 4 \\omega \\right) \\nu\\Delta_{x}^{2}}{2\\omega^{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\left(a \\omega^{2} - a \\omega - \\omega + 1\\right)\\nu\\Delta_{x}^{2}}{\\omega^{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\omega^{2}\\nu\\Delta_{x}^{2}}{12\\omega^{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\nu\\Delta_{x}^{2}}{2\\omega^{2}}\\left( a\\left(10 \\omega - 8 - 3\\omega^{2} \\right) + 2\\left(a \\omega^{2} - a \\omega - \\omega + 1\\right) + \\frac{\\omega^{2}}{6} \\right) \\frac{\\partial^{4}\\phi}{\\partial x^{4}} \n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\nu\\Delta_{x}^{2}}{2\\omega^{2}}\\left( a\\left(8 \\omega - 8 - \\omega^{2} \\right) + 2\\left(1 - \\omega \\right) + \\frac{\\omega^{2}}{6} \\right) \\frac{\\partial^{4}\\phi}{\\partial x^{4}} \n", "$$\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} - \\frac{\\nu\\Delta_{x}^{2}}{2\\omega^{2}}\\left( a\\left(\\omega^{2} - 8 \\omega + 8 \\right) - \\frac{\\omega^{2} - 12\\omega + 12 }{6} \\right) \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\mathcal{O}(\\Delta x)^{4}\n", "$$" ] }, { "cell_type": "code", "execution_count": 92, "id": "ba5c4a8d-93ca-4083-9a95-17c61667b73f", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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Ht4D7d2RVKlWtziEIgloR+88//6BTp044evSoRjISEVHtiaKI/Px8WV6iKMr99vH6669j7ty5Gj/v1atX8fnnn+Pq1asAgICAABQWFuL48eMavxbVHO/IyqT8juyVK1dQVlYmjUWtKx07doSVlRWysrJw+fJleHt7P/Y558yZg5iYGEybNg1///03TEz4exERkVwKCgpgY2Mjy7Xz8vJgbW1drX0vXbqEffv2YePGjWjevDkcHR0RHh6OixcvAgDu3r2LRYsWPbQ4trS0REhIiEayP0r79u1x/PhxeHp6AoA0bKF8BqKSkhLMmzcPjRs3RlFREXbv3o3Nmzejfv36Wsln7FjIysTd3R3m5uYoKipCcnJynU9xZWpqCj8/Pxw6dAjHjx/XSCG7bNkymJiY4MMPP2QRS0RE1ZKQkIBp06bh888/xxdffIGePXsiLS1N+n79+vWlj/F1gSAI0qeaAPD5559j+vTpeOKJJwAA48ePR5cuXTBx4kTEx8fj008/rfNpNelfLGRlolAo0KJFC8TGxiI+Pl4rc7V2794dhw4dwokTJzB+/PjHPp+1tTV++OEHtbYTJ06gXbt2sLW1fezzExFR9VlZWSEvL0/aVqlUyMnJga2tbZ3fbLCysqr2vs8++ywuX74Me3t79O3bFwDQpEmTuopWwfLlyx+60E+vXr3w/PPPV/q9tWvXwtnZGV9++SUAICYmBtu2bcOqVasAAOfOnUPfvn357IgWsZCVUatWrRAbG4u4uDgEBATU+fXKf6Os7QNfjxIdHY3+/fvD09MTBw4cQKNGjerkOkREVJEgCGof76tUKpSVlcHa2lrnPjU7cOAA+vXrV+n37ty5g8WLF9fZ0ILJkyfX6rjQ0FCUlZVh0aJFuHfvHtLS0nDw4EH06NEDSqUSAHDw4EH069cPWVlZsLe3r9V1qGZYyMpIjpkLgPtTft2+fRsNGzbU6PlVKhVsbW3h7OzMj1WIiKhKYWFhGD16dKXfa9CggU4NLQCAI0eO4J9//kFgYCDS0tJw8uRJODk5wd7eHk5OTgCAzMxM/Pnnn5g2bRo2bdqESZMmyZzaOLCQlZG2C1kHBwd4e3sjNjYWERERVX50UludO3fGqVOnYGdnBzMzM42em4iIDMf169fRp08fjZ5z06ZNOHLkCABgxowZ6NWrF956663HPm9CQgKee+455ObmqrVnZ2fDx8cHR48exaZNm1BcXIxXX30VO3fuRNeuXR/7ulQ9LGRlpO1FEYD7wwtiY2Nx4sQJjReyANC0aVO17aVLl0KhUGDq1KkavxYREemn6OhojZ/z1Vdfxauvvorvv/9eo+dt3rz5Q5d3/+mnnzR6PaoZ3Ro0Y2TKC9kbN24gPz9fK9es63GyD4qJiUFwcDDefvtthIeH1/n1iIiIyLjoZCF75MgRBAYGwtXVFYIgYMeOHY88Jjw8HJ06dYJSqUSLFi2wbt26Os/5uBo0aCDNM3flyhWtXLO8kD19+jSKi4vr9FodO3bEggULMHXqVDz99NN1ei0iIiIyPjpZyObn56Njx45Yvnx5tfZPTEzEs88+iz59+iAmJgbTp0/HuHHjsHfv3jpO+vi0PU62VatWaNCgAe7du4czZ87U6bUEQcCsWbOwbNkyaSqS0tJSFBYW1ul1iYiIyDjoZCE7cOBAfPLJJ3jhhReqtf/KlSvh4eGBr776Cm3atMGUKVPw8ssv4+uvv67jpI9P24XsgxM7a2N4Qfk1gfvLJ7711lsICAhAVlaWVq5NREREhksnC9maioiIgL+/v1pbQEAAIiIiZEpUfXI98AVA6+tEJyUl4bfffsPx48dx8uRJrV6biIiIDI9BzFqQlpYmzeNWzsnJCTk5OSgsLISlpWWFY4qKilBUVCRtl0+rUVJSgpKSkroN/IDmzZsDAC5fvqy165ZPC3L8+HEUFxdrbQWSxo0bIywsDGfPnkW/fv008n7Lz6HNPqPHwz7TP+wz3VRaWgpRFFFWVgaVSlXh++ULCoiiWOn3SR5lZWUQRRGlpaUVfqb4M1ZzBlHI1sbChQsxb968Cu1HjhxBbGys1nKkp6cDAGJjY7F7926tFJVFRUVQKBRIS0vDunXrKvwSUNcaNGiA0NBQAEBhYSFycnIeO8P+/fs1EY20iH2mf9hnusXExAQuLi7Izs5+aAH03/lPSV65ubnIz8/HwYMHK6xelpGRIVMq/WUQhayzs7NUEJZLT0+Hra1tpXdjAWDmzJkIDg6Wtm/evAlvb2/06tUL7u7udRlXTVFREaZPn47CwkJ06tQJLi4uWrlup06dcPr0aVhYWGDQoEFaueZ/FRQUIDAwEFevXsVff/0Fb2/vGp+jpKQE+/fvR//+/bkIg55gn+kf9pluEkURN2/eRH5+PmxtbSssQyuKIvLz82Ftba21T96oaqIooqCgALm5uXBxcYGPj0+FfZKSkrSeS98ZRCHbrVs36Q5fuf3790tLslZGqVRKayMDkCY7NjMz0+pf1GZmZnB3d0dCQgISExMrLChQV5566imcPn0ap06dwpgxY7Ryzf8qLi5GVlYW8vPzUVpa+lj/37Xdb/T42Gf6h32me9zc3JCYmIgbN25U+J4oitLwOhayusPBwQHOzs6V9gl/vmpOJwvZvLw8XL16VdpOTExETEwM6tevj6ZNm2LmzJm4efMmNmzYAACYOHEivvvuO3zwwQd4/fXXcfDgQfz222/YvXu3XG+hRry8vJCQkIC4uDitzbfavXt3LF26VGszF1SmYcOGOHToEBITE+Hr6ytbDiIifWVubo6WLVtWOi94SUkJjhw5gl69erFA0hFmZmZQKBRyxzAoOlnI/v3332prMJcPARg7dizWrVuH1NRUJCcnS9/38PDA7t278c4772DZsmVo3LgxfvzxRwQEBGg9e220atUKf/31l9am4ALu35EFgHPnziE3Nxf16tXT2rUf1KBBAzRo0EDaLr+z0KtXL1nyEBHpGxMTE1hYWFRoVygUKC0thYWFBQtZMlg6Wcj27t27wgDoB1W2alfv3r3rfIL/uqLtuWQBwNXVFc2aNcP169dx6tSpCtOXySE1NRX9+vVDeno69u7dix49esgdiYiIiHSYQcwjq+/kKGQB+eaTrYqDgwO8vLzg6uoKDw8PueMQERGRjmMhqwPKC9nExMRKxznVlfLhBbpSyFpYWGD79u04evQo3Nzc5I5DREREOo6FrA5wdXWFtbU1ysrKkJCQoLXrln90HxERgdLSUq1d92EsLCzg7OwsbR87dgxHjhyRMREREZFuW758Odzd3WFhYQE/Pz9ERkZWuW/v3r0hCEKF17PPPivt89prr1X4/oABA7TxVmqMhawOEAQBrVq1AqDd4QXt2rWDnZ0d8vLycPbsWa1dt7piYmIwcOBADBo0CNHR0XLHISIi0jlbtmxBcHAwQkJCEB0djY4dOyIgIAC3bt2qdP9t27YhNTVVel24cAEKhQKvvPKK2n4DBgxQ22/Tpk3aeDs1xkJWR8gxTlahUEjDC44ePaq161aXl5cXunXrhm7duqF169ZyxyEiItI5S5Yswfjx4xEUFARvb2+sXLkSVlZWWLt2baX7169fH87OztJr//79sLKyqlDIKpVKtf0cHBy08XZqjIWsjigvZOPj47V63fLhBceOHdPqdavD0tISO3fuxM6dO2FlZSV3HCIiIq3Izc1FTk6O9CoqKqp0v+LiYkRFRanNPGRiYgJ/f39ERERU61pr1qzB8OHDYW1trdYeHh6ORo0awcvLC5MmTcKdO3dq/4bqEAtZHSHXzAU9e/YEcP+O7MOmPJOLpaWlWhG7ceNGDjMgIiKD5u3tDTs7O+m1cOHCSvfLyMhAWVkZnJyc1NqdnJyQlpb2yOtERkbiwoULGDdunFr7gAEDsGHDBoSFheGLL77A4cOHMXDgQJSVldX+TdURnZxH1hjJMUYWALp06QKlUolbt27hypUrUg5dtH37dowePRoNGjRAdHS01pbzJSIi0qbY2Fi12XuUSmWdXGfNmjVo3749unbtqtY+fPhw6ev27dujQ4cO8PT0RHh4OPr161cnWWqLd2R1RHkBefv2bWRmZmrtukqlUvoDrIvjZB/Ur18/dO3aFSNHjkTjxo3ljkNERFQn6tWrB1tbW+lVVSHr6OgIhUKB9PR0tfb09HS1GYAqk5+fj82bN+ONN954ZJ7mzZvD0dERV69erf6b0BIWsjqiXr16cHV1BaD9u7K6PE72Qba2tjh48CCWLl0KExP+0SUiIuNmbm4OX19fhIWFSW0qlQphYWHo1q3bQ4/9/fffUVRUhFGjRj3yOikpKbhz5w5cXFweO7OmsRrQIXI98PXgOFldZ21tDUEQAACiKGLRokW4e/euzKmIiIjkERwcjNWrV2P9+vW4dOkSJk2ahPz8fAQFBQEAxowZg5kzZ1Y4bs2aNRgyZAgaNGig1p6Xl4f3338fJ0+eRFJSEsLCwjB48GC0aNECAQEBWnlPNcExsjrEy8sLhw4dkmWpWkEQcO3aNaSmpurkb1yVmT9/PubOnYumTZvilVdegZmZmdyRiIiItGrYsGG4ffs25syZg7S0NPj4+GDPnj3SA2DJyckVPsWMi4vDsWPHsG/fvgrnUygUOHfuHNavX4+srCy4urrimWeewYIFC+psrO7jYCGrQ+R64MvOzg4dOnTA2bNncezYsQpzyemqMWPGYO3atQgMDNTJHy4iIiJtmDJlCqZMmVLp98LDwyu0eXl5VTlTkaWlJfbu3avJeHWKQwt0iFxTcAH6NbygnIeHB86dO4f+/fvLHYWIiIhkwEJWh5QXsleuXIFKpdLqtfWxkAWgNsdsYWEhPvnkExQXF8uYiIiIiLSFhawOcXd3h5mZGYqKipCcnKzVa5fPXHDu3DlkZ2dr9dqaIIoiXn75ZXz88cd488035Y5DREREWsBCVocoFAq0aNECgPaHF7i6uqJ58+ZQqVTVXtZOlwiCgLfffhuOjo7Sk5pERERk2FjI6hiOk629gIAAJCYmolevXnJHISIiIi1gIatjdKGQ1fWFER7GxsZG+vqff/7Br7/+KmMaIiIiqkucfkvHyLUoAvBvIXvq1CkUFRXp9ZRWd+7cQY8ePZCYmAgzMzO9mVKMiIiIqo93ZHWMnHdkW7ZsiUaNGqGoqAh///231q+vSfXr18ezzz4LT09P+Pr6yh2HiIiI6gALWR1TvijCjRs3kJ+fr9VrC4IgzV5w5MgRrV5b0wRBwLJly3Dq1Ck0b95c7jhERERUB1jI6hhHR0fUr18fwP35ZLXt6aefBgAcPnxY69fWNBMTE7U1pKOionD+/HkZExEREZEmsZDVQXKOky0vZI8fP47S0lKtX7+unDp1Cn369EFAQACSkpLkjkNEREQawEJWB8k5TrZ9+/ZwcHBAXl4eoqOjtX79utKqVSs0a9YMrVu3hoODg9xxiIiISANYyOqg8nGychSyJiYm0jys4eHhWr9+XXFwcEBYWBj++usv2NnZyR2HiIiINICFrA6S844sYFjjZB/UqFEjtSnFDG34BBERkbFhIauDHixkRVHU+vV79+4N4P7CCIZa6K1atQo9e/bElClTZPl/TERERI+PhawOatGiBUxMTJCbm4v09HStX79Dhw6ws7NDTk4OYmJitH59bWjYsCEAQBRFqFQqmdMQERFRbbCQ1UFKpRLu7u4A5BleoFAopFW+DG14QbkXX3wRp06dwsqVK6FQKOSOQ0RERLXAQlZHyfnAF2C442Qf1KVLFwiCAOD+ndlr167JnIiIiIhqgoWsjpL7ga/ycbJHjhxBWVmZLBm0paysDJMnT0bHjh0RFRUldxwiIiKqJhayOkrORREAwMfHB/Xq1UN2djbOnTsnSwZtKSsrw5UrV1BQUIAzZ87IHYeIiIiqiYWsjpL7jqypqSl69OgBwLCHFwCAubk5/vjjD+zevRvjxo2TOw4RERFVEwtZHVU+RjYhIQHFxcWyZCgfXmBICyNUxdbWFgMHDpS2i4uLUVBQIGMiIiIiehQWsjrKzc0N1tbWKCsrQ0JCgiwZyh/4Onr0qFFNUZWTk4Nnn30Ww4cPN9h5dImIiAwBC1kdJQiC7DMXdOrUCdbW1rh79y4uXLggSwY5xMXF4dixYzh48CAuXbokdxwiIiKqAgtZHSb3A19mZmbSOFljGF5QrkuXLvjtt99w+PBhtG/fXu44REREVAUWsjpM7ge+AOOYT7YygYGB8PX1lbY5xICIiEj3sJDVYXIPLQDUC1ljGif7oMTERPj4+OCvv/6SOwoRERE9QKcL2eXLl8Pd3R0WFhbw8/NDZGRklfuWlJRg/vz58PT0hIWFBTp27Ig9e/ZoMa3m6cId2c6dO8Pa2hp37twxqnGyD1q2bBkuXryI9957z+AXhyAiItInOlvIbtmyBcHBwQgJCUF0dDQ6duyIgIAA3Lp1q9L9Z8+ejVWrVuHbb79FbGwsJk6ciBdeeEGvJ7gvvyN7+/ZtZGZmypLB3NwcPXv2BAAcPHhQlgxy+/LLLzF16lTs378fCoVC7jhERET0/3S2kF2yZAnGjx+PoKAgeHt7Y+XKlbCyssLatWsr3f/nn3/GRx99hEGDBqF58+aYNGkSBg0ahK+++krLyTWnXr16cHV1BSDfA18A0K9fPwBAWFiYbBnkZG5ujm+++UbqCyIiItINOlnIFhcXIyoqCv7+/lKbiYkJ/P39ERERUekxRUVFsLCwUGuztLTEsWPH6jRrXdOFcbJ9+/YFcH+cLB96Ao4dO4aBAwciPz9f7ihERERGzVTuAJXJyMhAWVkZnJyc1NqdnJxw+fLlSo8JCAjAkiVL0KtXL3h6eiIsLAzbtm2rckxjUVERioqKpO3c3FwA98falpSUaOidPL6WLVsiPDwcsbGxsuXy9vaGg4MDMjMzcerUKXTt2lWWHJUp/3+irf839+7dw/Dhw3Hz5k3MmzcPn376qVaua0i03Wf0+Nhn+on9pn/YVzWnk4VsbSxbtgzjx49H69atIQgCPD09ERQUVOVQhIULF2LevHkV2o8cOYLY2Ni6jltt5YX4kSNHEBoaKlsOLy8vnDx5EitXrkRGRoZsOaqyf/9+rV1r6tSp+PPPP9G5c2dZ+0TfabPPSDPYZ/qJ/aY/dPHfV12nk4Wso6MjFAoF0tPT1drT09Ph7Oxc6TENGzbEjh07cO/ePdy5cweurq6YMWMGmjdvXun+M2fORHBwsLR98+ZNeHt7o1evXnB3d9fYe3lcgiBg7dq1yM3NxaBBg2TLkZSUhJMnTyI1NVXWHP9VUlKC/fv3o3///jAzM9PKNQcNGqT2Z4dqRo4+o8fDPtNP7Df9k5SUJHcEvaOThay5uTl8fX0RFhaGIUOGAABUKhXCwsIwZcqUhx5rYWEBNzc3lJSU4I8//sDQoUMr3U+pVEKpVErbOTk5AO6vZqVLP/Bt27YFAFy9ehUKhQImJvIMa+7fvz8A4Pjx41CpVGr/73SBnP22bt06qFQqvP7667JcX1/p2s8aPRr7TD+x3/QH+6nmdPJhLwAIDg7G6tWrsX79ely6dAmTJk1Cfn4+goKCAABjxozBzJkzpf1PnTqFbdu2ISEhAUePHsWAAQOgUqnwwQcfyPUWNKJZs2YwMzPDvXv3kJycLFuONm3awMnJCffu3cPJkydly6FrDh06hKCgIEyYMAHR0dFyxyEiIjIqOnlHFgCGDRuG27dvY86cOUhLS4OPjw/27NkjPQCWnJysdnfy3r17mD17NhISEmBjY4NBgwbh559/hr29vUzvQDNMTU3RokULXLp0CXFxcbINexAEAX379sWmTZsQFhYmrfhl7Hr37o2xY8fCxcUFTzzxhNxxiIiIjIrOFrIAMGXKlCqHEoSHh6ttP/300zr1kJYmeXl54dKlS4iPj0dAQIBsOcoL2YMHD2L+/Pmy5dAl5WOY5RryQUREZMz4r68e0IWlaoF/F0Y4deoU8vLyZM2iSx4sYlUqFb744osqV6AjIiIizWEhqwd0YVEEAPDw8IC7uztKS0v1fqGJuvLhhx9ixowZCAwM5OIRREREdYyFrB7QlTuywL+rfB08eFDmJLpp3LhxcHZ2xuTJk2FqqtMjd4iIiPQeC1k9UF7I3rhxQ/ZlUVnIPpyXlxeuXr2KMWPGyB2FiIjI4LGQ1QOOjo6oX78+gPvzycqpT58+AIDo6GhkZmbKmkVXWVtbS1/n5+dj06ZNMqYhIiIyXCxk9YSuDC9wdXVF69atIYoi78o+QlFREfr164cRI0Zg9erVcschIiIyOCxk9YSuPPAF/LvKF9fvfjilUolnnnkG9evXh7e3t9xxiIiIDA4LWT2hK3dkARayNTFv3jycO3cOTz31lNxRiIiIDA4LWT1RXsjGx8fLnOT+alampqZISEjAtWvX5I6j0wRBgJubm7R98+ZN2cc5ExERGQoWsnriwTuyoijKmqVevXro1q0bAN6VrYnLly+jW7dueOaZZ5Ceni53HCIiIr3HQlZPeHp6QhAE5OTk6EQR9MwzzwBgIVsT9evXh5mZGczNzXHv3j254xAREek9FrJ6wsLCAu7u7gB0a5xsWFgYV7CqpkaNGmH//v04fvw4mjVrJnccIiIivcdCVo/o0gNfnTt3hr29PbKzs/H333/LHUdvNG/eHA0aNJC2r127JvtQESIiIn3FQlaP6NIDXwqFAv369QMA7Nu3T+Y0+ik0NBQdOnTAxx9/LHcUIiIivcRCVo/o0h1ZgNNwPa5//vkHBQUFOH36NIdnEBER1QILWT2iS4siAP8+8HXy5Enk5OTInEb/jBs3Dtu3b8f//vc/mJqayh2HiIj01PLly+Hu7g4LCwv4+fkhMjKyyn179+4NQRAqvJ599llpH1EUMWfOHLi4uMDS0hL+/v64cuWKNt5KjbGQ1SPld2QTEhJQXFwscxrAw8MDnp6eKC0tRXh4uNxx9NKQIUNgbm4ubd+5c0fGNEREpG+2bNmC4OBghISEIDo6Gh07dkRAQABu3bpV6f7btm1Damqq9Lpw4QIUCgVeeeUVaZ8vv/wS33zzDVauXIlTp07B2toaAQEBOjnjDgtZPeLm5gZra2uUlZUhMTFR7jgAOA2XJi1duhQtWrTAuXPn5I5CRER6YsmSJRg/fjyCgoLg7e2NlStXwsrKCmvXrq10//r168PZ2Vl67d+/H1ZWVlIhK4oili5ditmzZ2Pw4MHo0KEDNmzYgH/++Qc7duzQ4jurHhayekQQBJ0bXlA+TpYPfD2e0tJSbNu2DVlZWdi+fbvccYiISEa5ubnIycmRXkVFRZXuV1xcjKioKPj7+0ttJiYm8Pf3R0RERLWutWbNGgwfPhzW1tYAgMTERKSlpamd087ODn5+ftU+pzaxkNUzulbI9unTBwqFAvHx8bh+/brccfSWqakpdu3ahVWrVmHOnDlyxyEiIhl5e3vDzs5Oei1cuLDS/TIyMlBWVgYnJye1dicnJ6SlpT3yOpGRkbhw4QLGjRsntZUfV9tzahsLWT2jazMX2Nvbo2vXrgA4vOBx2dvbY8KECRAEAcD9j3cKCwtlTkVERNoWGxuL7Oxs6TVz5sw6uc6aNWvQvn176d9xfcRCVs/oWiELcBquulBaWorx48cjMDCwyo+UiIjIMNWrVw+2trbSS6lUVrqfo6MjFApFhaXr09PT4ezs/NBr5OfnY/PmzXjjjTfU2suPq8055cBCVs/o0qII5cof+Dpw4ADKyspkTmMYrl69ii1btuDQoUM4evSo3HGIiEgHmZubw9fXF2FhYVKbSqVCWFgYunXr9tBjf//9dxQVFWHUqFFq7R4eHnB2dlY7Z05ODk6dOvXIc8qBk1fqmfIxsrdu3UJWVhbs7e3lDQSga9eusLW1xd27dxEVFaXXH1HoitatW2P79u3Iy8tTG3BPRET0oODgYIwdOxadO3dG165dsXTpUuTn5yMoKAgAMGbMGLi5uVUYZ7tmzRoMGTJEbdl04P6D5dOnT8cnn3yCli1bwsPDAx9//DFcXV0xZMgQbb2tamMhq2fq1asHFxcXpKamIi4uDn5+fnJHgpmZGfz9/bFt2zb89ddfLGQ15L8FbFlZGRQKhUxpiIhIFw0bNgy3b9/GnDlzkJaWBh8fH+zZs0d6WCs5ORkmJuofwMfFxeHYsWNVzjj0wQcfID8/HxMmTEBWVhZ69OiBPXv2wMLCos7fT01xaIEe0sVxsgMHDgQA/PXXXzInMUxZWVno27cvVq1aJXcUIiLSMVOmTMH169dRVFSEU6dOqd3kCg8Px7p169T29/LygiiK0jMu/yUIAubPn4+0tDTcu3cPBw4ckD4R1jUsZPWQLo6TLS9kIyMjcfv2bZnTGJ6NGzfiyJEjmDlzJjIzM+WOQ0REpBNYyOohXbwj6+bmhg4dOkAURS6OUAcmT56MDz/8EAcPHoSDg4PccYiIiHQCC1k9pIuFLMDhBXVJEAR8/vnn8PHxkdpEUZQvEBERkQ5gIauHysepXLlyBSqVSuY0/xo0aBAAYM+ePZyGq45dvXoVfn5+uHz5stxRiIiIZMNCVg+5u7vDzMwM9+7dw40bN+SOI+nWrRtsbW1x584d/P3333LHMWjvvPMOTp8+jbfeekvuKERERLJhIauHTE1N0aJFCwC6NbzAzMxMegKSwwvq1k8//YShQ4di06ZNckchIiKSDQtZPaWr42TLhxeEhobKnMSwOTo6YsuWLdI8gQDHzBIRkfFhIaunysfJ6lohO2DAAADA33//zWm4tOjgwYMYMGAA8vPz5Y5CRESkNSxk9ZSu3pF1dXVFx44dIYoi9u7dK3cco1BYWIhRo0Zh3759+Pzzz+WOQ0REpDUsZPWULi6KUI7DC7TL0tIS27dvx6hRozBr1iy54xAREWkNC1k9VV7IJicno6CgQOY06srnk927dy+n4dISPz8//Pzzzzq5DjYREVFdYSGrpxwdHVG/fn0A9+eT1SXdunWDnZ0d7t69i9OnT8sdxyh9//33eO+99/gAGBERGTQWsnpMVx/4MjU1xTPPPAOAwwvkcOHCBbz11lv46quvsGfPHrnjEBER1RkWsnpMl8fJlg8vYCGrfe3atcOyZcswe/ZsaRYJIiIiQ6TThezy5cvh7u4OCwsL+Pn5ITIy8qH7L126FF5eXrC0tESTJk3wzjvv4N69e1pKq326OnMBcP+BL0EQEBUVhZs3b8odx+i8/fbbWLBgAQRBkDsKERFRndHZQnbLli0IDg5GSEgIoqOj0bFjRwQEBODWrVuV7v/rr79ixowZCAkJwaVLl7BmzRps2bIFH330kZaTa48uF7JOTk7w8/MDAPz5558ypzFuKpUKb731FjZs2CB3FCIiIo3S2UJ2yZIlGD9+PIKCguDt7Y2VK1fCysoKa9eurXT/EydO4KmnnsKIESPg7u6OZ555Bq+++uoj7+LqswfHyOriQz2BgYEAgP/9738yJzFumzZtwvfff49x48bh+vXrcschIiLSGJ0sZIuLixEVFQV/f3+pzcTEBP7+/oiIiKj0mO7duyMqKkoqXBMSEhAaGirNaWqIWrRoAUEQkJOTg/T0dLnjVPD8888DAA4cOMAVp2T06quvYuLEiVi/fj2aNWsmdxwiIiKNMZU7QGUyMjJQVlamto48cP/j6suXL1d6zIgRI5CRkYEePXpAFEWUlpZi4sSJVQ4tKCoqQlFRkbSdm5sLACgpKUFJSYmG3kndUigUcHd3R2JiImJjY9GgQQO5I6lp1aoV3N3dkZSUhD179kiFrSaV95W+9JlcvvnmGwD//n8SRVG28bPsM/3DPtNP7Df9w76qOZ0sZGsjPDwcn332GVasWAE/Pz9cvXoV06ZNw4IFC/Dxxx9X2H/hwoWYN29ehfYjR44gNjZWG5E1wsHBAYmJifjjjz+kYlyXtGvXDklJSfj+++9halp3f9z2799fZ+c2NIWFhVi0aBFeeOEFtG/fXrYc7DP9wz7TT+w3/ZGRkSF3BL2jk4Wso6MjFApFhY/L09PT4ezsXOkxH3/8MUaPHo1x48YBANq3b4/8/HxMmDABs2bNgomJ+iiKmTNnIjg4WNq+efMmvL290atXL7i7u2v2DdWhsLAwREdHQ6lU6uQwCgsLC/z55584f/48BgwYUKEfHldJSQn279+P/v37w8zMTKPnNlSzZ89GdHQ00tLScPnyZa2vBsY+0z/sM/3EftM/SUlJckfQOzpZyJqbm8PX1xdhYWEYMmQIgPtPXoeFhWHKlCmVHlNQUFChSFIoFABQ6YNQSqUSSqVS2s7JyQEAmJmZ6dUPfOvWrQHcX91LF3P36dMHtra2uHXrFs6cOYMnn3yyTq6jb/0mp3nz5uH69et47733UK9ePdlysM/0D/tMP7Hf9Af7qeZ08mEvAAgODsbq1auxfv16XLp0CZMmTUJ+fj6CgoIAAGPGjMHMmTOl/QMDA/H9999j8+bNSExMxP79+/Hxxx8jMDBQKmgNkS4vigDc/6WkfHGEXbt2yZyGgPt3yTdv3ozOnTtLbbo46wUREdGj6GwhO2zYMCxevBhz5syBj48PYmJisGfPHukBsOTkZKSmpkr7z549G++++y5mz54Nb29vvPHGGwgICMCqVavkegtaUV7IJiQk6OwgcU7DpduSkpLQvXt3vRobTkREBOjo0IJyU6ZMqXIoQXh4uNq2qakpQkJCEBISooVkusPNzQ1WVlYoKChAQkKCVNjqkoEDB0KhUODChQtITEyEh4eH3JHoAdOnT8fJkycxceJEHD58mKuBERGR3tDZO7JUPYIgqC2MoIvq16+PHj16AOBdWV20du1aDB06FJs3b2YRS0REeoWFrAHQ5aVqy5XPIctxsrqnfv362LJlC1xdXaW20tJSGRMRERFVDwtZA6DrD3wB/46TPXz4MLKzs2VOQw9z5MgReHt76/QvRkRERAALWYOgD3dkW7ZsiTZt2qC0tBShoaFyx6EqiKKIGTNm4MqVK/j000/ljkNERPRQLGQNgD4UsgDwwgsvAAC2bdsmcxKqiiAI2LlzJ6ZMmWLwM34QEZH+YyFrAFq2bAkAuHXrFrKysuQN8xAvvvgiACA0NBSFhYUyp6GqNGzYEN9++y0sLS2ltvz8fBkTERERVY6FrAGwtbWFi4sLAN0eJ9upUyc0bdoUBQUF2Ldvn9xxqJpWr16NNm3a4OrVq3JHISIiUsNC1kDow/ACQRCku7IcXqAfiouLsWzZMty4cQO//PKL3HGIiIjUsJA1EPpQyAL/Di/YtWuXzq5ERv8yNzdHWFgYvvjiC8yZM0fuOERERGpYyBoIXV8UoVz37t3RqFEjZGVlVVidjXSTk5MTPvjgA2mxBFEUkZKSInMqIiIiFrIGQ1/uyCoUCgwZMgQAhxfoI1EU8fbbb+OJJ57A2bNn5Y5DRERGjoWsgSgvZK9cuQKVSiVzmocrH16wfft2lJWVyZyGaqKgoAAnT57EnTt3cOHCBbnjEBGRkWMhayDc3d1hZmaGe/fu4caNG3LHeag+ffrAzs4O6enpiIiIkDsO1YC1tTUOHDiAP/74AyNHjpQ7DhERGTkWsgbC1NQULVq0AKD7wwvMzc2lJWs5vED/2NnZSYtbAPfv0kZFRcmYiIiIjBULWQOiLw98AVCbhksURZnTUG0VFhZi8ODB6NWrFw4ePCh3HCIiMjIsZA1I+ThZXV4UoVxAQAAsLS1x/fp1nDlzRu449BgUCgVMTExgYWEhdxQiIjIyLGQNiL7MXAAAVlZWGDhwIABg69atMqeh2rK0tMSOHTtw9OhRdO/eXe44RERkZFjIGhB9KmQB4JVXXgEA/PbbbxxeoMcsLCzg4+MjbScnJ3PsMxERaQULWQNSPkY2OTkZBQUFMqd5tOeeew6Wlpa4du0aoqOj5Y5DGnD37l34+/vj5ZdfxubNm+WOQ0REBo6FrAFxdHSEg4MDgPvzyeo6GxsbPPvsswCALVu2yJyGNMHe3h79+vVD06ZN0aNHD7njEBGRgWMha0AEQdCrB74AYNiwYQA4vMBQmJiYYMWKFTh9+jQaN24sdxwiIjJwLGQNjL6Nkx00aBCsra1x/fp1nDp1Su44pAGCIKBhw4bS9vHjx/Hee+/p/IpzRESkf1jIGhh9K2StrKzw/PPPA+DwAkOUmZmJwMBAfPXVV1i2bJnccYiIyMCwkDUw+rQoQrny4QW///4779oZGAcHB3zzzTfo06cP3nzzTbnjEBGRgWEha2AeHCOrL2NOBwwYAFtbW9y8eRPHjx+XOw5p2KhRo3DgwAFYWVlJbWVlZTImIiIiQ8FC1sC0aNECgiAgOzsbt27dkjtOtSiVSgwZMgQAhxcYKhOTf/+q2bBhA2bNmoW7d+/KmIiIiAwBC1kDY2FhAXd3dwD6Obxg69atvFtnwHJycjBjxgxcvnwZ69evlzsOERHpORayBkgfx8n6+/vDwcEB6enpOHz4sNxxqI7Y2tpi3759GDJkCKZPny53HCIig7B8+XK4u7vDwsICfn5+iIyMfOj+WVlZmDx5MlxcXKBUKtGqVSuEhoZK3587dy4EQVB7tW7duq7fRq2wkDVA+jZzAQCYm5vjxRdfBACuCGXg2rVrh9deew2CIAAAVCqVXv1ZJSLSJVu2bEFwcDBCQkIQHR2Njh07IiAgoMrhhcXFxejfvz+SkpKwdetWxMXFYfXq1XBzc1Pbr23btkhNTZVex44d08bbqTEWsgZI3xZFKPfqq68CuD+8oKioSOY0pC0ffPABnnjiCezevVvuKEREemfJkiUYP348goKC4O3tjZUrV8LKygpr166tdP+1a9fi7t272LFjB5566im4u7vj6aefRseOHdX2MzU1hbOzs/RydHTUxtupMRayBkgf78gCQO/eveHq6orMzEy1jzjIcJWUlCA2NhaFhYW4c+eO3HGIiPRKcXExoqKi4O/vL7WZmJjA398fERERlR6za9cudOvWDZMnT4aTkxPatWuHzz77rMLzKVeuXIGrqyuaN2+OkSNHIjk5uU7fS22xkDVA5YVsQkICSkpKZE5TfQqFAiNGjAAAbNy4UeY0pA1mZmbYuXMndu/ejTFjxsgdh4hIJ+Tm5iInJ0d6VfUpZUZGBsrKyuDk5KTW7uTkhLS0tEqPSUhIkB6sDg0Nxccff4yvvvoKn3zyibSPn58f1q1bhz179uD7779HYmIievbsidzcXM29SQ1hIWuAXF1dYWVlhdLSUiQkJMgdp0ZGjx4NAPjzzz+RmZkpcxrSBjMzMwwaNEjaLigowDfffMPFMYjIaHl7e8POzk56LVy4UGPnVqlUaNSoEX744Qf4+vpi2LBhmDVrFlauXCntM3DgQLzyyivo0KEDAgICEBoaiqysLPz2228ay6EpLGQNkImJiTRzgb6Nk+3QoQPat2+P4uJibN26Ve44pGWiKGLYsGGYNm0apk6dKnccIiJZxMbGIjs7W3rNnDmz0v0cHR2hUCiQnp6u1p6eng5nZ+dKj3FxcUGrVq2gUCiktjZt2iAtLQ3FxcWVHmNvb49WrVrh6tWrtXxHdYeFrIHS13GywP2VoAAOLzBGgiBg2LBhsLW1xciRI+WOQ0Qki3r16sHW1lZ6KZXKSvczNzeHr68vwsLCpDaVSoWwsDB069at0mOeeuopXL16Ve1Tr/j4eLi4uMDc3LzSY/Ly8nDt2jW4uLg8xruqGyxkDZQ+F7KvvvoqBEHAkSNHcP36dbnjkJaNGjUKiYmJ6N69u9SmL8stExFpW3BwMFavXo3169fj0qVLmDRpEvLz8xEUFAQAGDNmjNod3UmTJuHu3buYNm0a4uPjsXv3bnz22WeYPHmytM97772Hw4cPIykpCSdOnMALL7wAhUIhzS6kS1jIGih9XBShXJMmTdC7d28AwK+//ipvGJJF/fr1pa9TUlLw5JNPIiYmRr5AREQ6atiwYVi8eDHmzJkDHx8fxMTEYM+ePdIDYMnJyUhNTZX2b9KkCfbu3YvTp0+jQ4cOePvttzFt2jTMmDFD2iclJQWvvvoqvLy8MHToUDRo0AAnT55Ew4YNtf7+HsVU7gBUN/T5jixw/6GvQ4cO4eeff8aMGTOkyfPJ+Lz33nuIjIzExIkTERERwT8LRET/MWXKFEyZMqXS74WHh1do69atG06ePFnl+fRpYaLHuiMbHR2NJUuWYOXKlYiIiKhykDBpX/kd2Vu3biErK0veMLXw4osvwsLCApcuXcKZM2fkjkMyWrlyJYYPH47NmzeziCUiIjWPVcj6+/vj/fffx48//oitW7diwoQJeP3113H48GFN5aNasrW1lQZl69vMBQBgZ2eH559/HgDw888/y5yG5GRvb49NmzbB3d1dart06RLHzRIR0eMVsqtXr8aSJUsQGRmJr776CuvWrcOXX36J7777DkOHDkV2dvZjhVu+fDnc3d1hYWEBPz8/REZGVrlv7969IQhChdezzz77WBn0mSEMLwCAX375hXf7SfL333+jc+fOGDt2LP9cEBHpsHPnzmHatGlqsypo2mMVsi+99BKmTZsGE5N/T+Po6Ijff/8dCoUCffr0QU5OTq3OvWXLFgQHByMkJATR0dHo2LEjAgICcOvWrUr337ZtG1JTU6XXhQsXoFAo8Morr9Tq+oZAnx/4AoABAwbA2dkZt2/fxu7du+WOQzoiLi4ORUVFuHXrFocaEBHpsLlz52LlypUYNmxYnV2jzmYtWLFiBeLj4zF79uxaHb9kyRKMHz8eQUFB8Pb2xsqVK2FlZYW1a9dWun/9+vXh7Owsvfbv3w8rKyujLmTL78jq49ACADA1NcXYsWMBoMp+J+MzcuRIHDhwAL///jvMzMzkjkNERFVwdnbG3r17sWrVqjq7Rp0Vsg4ODvD19cW2bdtqfGxxcTGioqLg7+8vtZmYmMDf3x8RERHVOseaNWswfPhwWFtb1/j6hkLfhxYAkObBCw0NxT///CNzGtIVvXv3Rr169aTtb7/9FkePHpUxERER/ZdSqYSXlxdeeumlOruGxqbf+vrrr1FaWorBgwejVatWyMzMRHx8fK0eyMjIyEBZWZk0B1o5JycnXL58+ZHHR0ZG4sKFC1izZk2V+xQVFaGoqEjazs3NBQCUlJSgpKSkxpl1UfPmzQEAV65cQVFRkdoQEH3RvHlzdOvWDREREVi3bh3ef/99te+X95Wh9Jkx0HSfHThwAG+//TbMzMwQHR0t/QJHmsOfM/3EftM/htZXISEhmDBhAmbNmoWOHTvWyTU0Vsg2aNAAS5cuxcyZM+Hr64uEhASUlpZixYoVmrpEta1Zswbt27dH165dq9xn4cKFmDdvXoX2I0eOIDY2ti7jaU1ZWRlMTU1RWFiIDRs2oFGjRnJHqpVOnTohIiICy5cvh7e3d6XjIvfv3y9DMnocmuqzoqIidO/eHfb29rh27RquXbumkfNSRfw500/sN/2RkZEhdwSNOn78OMLDw7Fjxw489dRT6N27N3r37o1u3bpVuRxuTQmihuewyc3NxZkzZzBy5EiMGjUKCxcurPE5iouLYWVlha1bt2LIkCFS+9ixY5GVlYWdO3dWeWx+fj5cXV0xf/58TJs2rcr9/ntH9ubNm/D29kZ8fLzaND/6rn379oiLi8Pu3bvRv39/uePUSm5uLpo0aYKCggIcPnxYbf3okpIS7N+/H/379+d4ST1RF32mUqmgUqlganr/d/Pi4mKUlJQY9dAiTeLPmX5iv+mfpKQktGrVCjdu3EDjxo3ljvPYevbsiQEDBuDmzZs4fvw4Lly4AOD+kAM/Pz/06dMHQ4cORevWrWt9DY2v7FWvXj306tUL27dvx5NPPgl3d3e8+eabNTqHubk5fH19ERYWJhWyKpUKYWFhVa5cUe73339HUVERRo0a9dD9lEollEqltF0+u4KZmZlB/cC3bt0acXFxSEhI0Nv3Vb9+fQwdOhTr1q3Dhg0b0KtXrwr7GFq/GYO66jNRFPHmm2/i7Nmz2LVrF9zc3DR+DWPFnzP9xH7TH4bWTx4eHpg5c6Y0tPHOnTs4ePAgDh06hPDwcGlWg8d5BuaxBk2mp6dX+b3OnTvD19cXixYtqtW5g4ODsXr1aqxfvx6XLl3CpEmTkJ+fLz38M2bMGMycObPCcWvWrMGQIUPQoEGDWl3X0BjCA1/Avw99bdmyBXl5eTKnIV128+ZN/Pnnn4iJicHFixfljkNEZLSmT5+OkSNHYs6cOTh79iwaNGiAV155BStWrEBsbCxSU1OxZ8+ex7rGY92RXbx4MSwtLfHhhx9W+hFednY2MjMza3XuYcOG4fbt25gzZw7S0tLg4+ODPXv2SA+AJScnV3h4KS4uDseOHcO+fftqdU1DZCiFbM+ePdGiRQtcvXoVv//+u1TYEv1X48aNERkZiePHj+OZZ56ROw4RkdHq1KkTNm3ahISEhEpvfjo5OVV4sL+mHquQXbRoEWJiYvDBBx+gXr166NevH5o1a4a7d+/iu+++Q3x8PKZPn17r80+ZMqXKoQTh4eEV2ry8vLhs5X/o+6II5QRBwOuvv46PPvoIq1evZiFLD+Xu7q421j0jIwMbNmzA9OnT9XL2DiIifda8eXNpJiVNe+wxsj4+Pli+fDmysrJw8OBBbNy4Ebdv34arqyt2796NgQMHaiIn1VL5Hdnk5GQUFhbC0tJS5kS1FxQUhDlz5iAiIgJnz56ts6k8yLCoVCoMHToUhw4dwvXr17Fs2TK5IxERkYZo7GEve3t7vPjii3jxxRc1dUrSAEdHRzg4OCAzMxNXrlxBhw4d5I5Ua87OzhgyZAi2bt2KVatWyTK1G+kfExMTjB49GufOncP48ePljkNERBrEz9gMnCAIBjNOFgAmTpwIANi4cSMf+qJqCwoKQmJiItq1aye1ZWdny5iIiIg0gYWsETCkQrZPnz5o2bIlcnNzsWnTJrnjkB55cEnb+Ph4eHp64uuvv+a4eiIiPcZC1ggYygNfwP2PicvnJf7+++9ZhFCt/PLLL7hz5w62bt2K0tJSueMQEVEtsZA1AuV3ZOPj42VOohljx46Fubk5zpw5g6ioKLnjkB4qn4T7jz/+MLgJyImIjAkLWSPw4NACQ7iD6ejoiFdeeQUA8MMPP8ichvSRIAh488034ezsLLX99NNPOHr0qIypiIiopljIGoEWLVpAEARkZ2fj1q1bcsfRiPKHvn777Tc+9EWPLTIyEhMmTECfPn0QHR0tdxwiIqomFrJGwMLCAs2aNQNgGONkAeCpp55C27ZtUVBQgEOHDskdh/Rc27Zt8corr+Cll17CE088IXccIiKqJhayRsLQxskKgoDJkycDAEJDQ6FSqWRORPrM2toav/zyCzZs2ABBEAAApaWlSExMlDkZERE9DAtZI2FIU3CVGz16NOzs7JCamoq9e/fKHYf0nCAIUCqV0vbMmTPRsWNH7Ny5U8ZURET0MCxkjYQhFrI2NjYICgoCAHz33XcypyFDUlxcjMjISOTm5qKkpETuOEREVAUWskbCEAtZ4P5DX4IgYP/+/bh06ZLccchAmJub48CBA9i1axdefvllueMQEVEVWMgaifJFERISEgzqDlPz5s3RpUsXALwrS5plZmaGwMBAaTsvLw8DBw7EqVOnZExFREQPYiFrJNzc3GBlZWWQD7A899xzAID169cjKytL3jBksObOnYs9e/bg1VdfNahfBomI9BkLWSNhYmJiUEvVPqh9+/bw9vZGfn4+fvrpJ7njkIGaM2cORowYgZ9//pmrgRER6QgWskbEUMfJCoKAKVOmAAC+/fZblJWVyZyIDJGtrS1++eUXPPXUU1LbsWPHEBkZKWMqIiLjxkLWiBjqHVkAGDFiBOrXr4/ExEROl0RakZ6ejldeeQU9evTAvn375I5DRGSUWMgaEUNbFOFBVlZWmDRpEgBg0aJFEEVR5kRk6CwsLNCjRw+0bNlS7S4tERFpDwtZI2KoQwvKTZ06FUqlEidPnsTx48fljkMGzs7ODr/99huOHDkCa2trqT05OVnGVERExoWFrBEpH1qQnp6O7OxsmdNonpOTE8aMGQPg/l1ZoromCAIaNGggbW/ZsgUtW7bE8uXLZUxFRGQ8WMgaEVtbW7i4uAAw3Luy7777LgRBwK5du3D58mW545CR+euvv1BcXIy0tDS5oxARGQUWskbGkB/4Au4Pn3j++ecBAF999ZXMacjY/PTTT/j1118REhIitalUKhkTEREZNhayRsaQH/gq9/777wMANmzYwDtjpFWCIODVV1+FqakpAEAURbz00kuYOXMmF1EgIqoDLGSNjKE/8AUATz31FLp164bi4mJ8++23cschIxYeHo4dO3ZgyZIluHLlitxxiIgMDgtZI2MMhSwAfPDBBwCA5cuXG+SDbaQf+vTpg99//x3ffvstvL295Y5DRGRwWMgamfIxsleuXDHosXvPP/88vL29kZ2dje+++07uOGTEXn75ZUyYMEHaTk5OxsSJE5GTkyNjKiIiw8BC1sh4eHjAzMwMhYWFSElJkTtOnTExMcGsWbMAAF9//TXy8vJkTkR0f8zs2LFjsWrVKrz55ptyxyEi0nssZI2MqakpPD09ARj+8IKhQ4eiRYsWuHPnDlatWiV3HCIIgoBPPvkE7du3x6effip3HCIivcdC1ggZyzhZU1NTfPTRRwDuL5BQWFgocyKi+w8jxsTEoHnz5lLb1q1b+TAYEVEtsJA1QsZSyALAqFGj0LRpU6Snp2PNmjVyxyECcH/oS7lLly5h9OjR8PHxwcWLF2VMRUSkf1jIGiFDXxThQWZmZpgxYwYA4IsvvkBRUZHMiYjU2djY4Mknn0TPnj05swERUQ2xkDVCxrAowoOCgoLg6uqKlJQUrFu3Tu44RGqaNGmCsLAwbNmyBYIgAABKS0tx4MABmZMREek+FrJGqLyQTU5ONopxoxYWFvjwww8BAJ988gnu3bsncyIidSYmJrCzs5O2P//8c/Tv3x/Tp0+XLxQRkR5gIWuEHB0d4eDgAFEUjeYBkwkTJqBx48ZISUnBDz/8IHccoocqKiqCIAjo3Lmz3FGIiHQaC1kjJAiCUY2TBe7flf34448BAJ999hny8/NlTkRUtQULFuDChQsYOXKk1JaYmIiCggIZUxER6R4WskbK2MbJAvfHyjZv3hzp6elYvny53HGIHsrb21saM1tcXIzBgwejY8eOOH/+vMzJiIh0BwtZI2VMU3CVMzMzQ0hICID7MxhwiVDSFwkJCcjMzER2djacnZ3ljkNEpDNYyBopYyxkAWDkyJFo3bo17t69i6VLl8odh6haWrdujQsXLuDPP/9Ew4YNpfbk5GQZUxERyY+FrJF6sJAVRVHmNNqjUCgwb948AMBXX32FjIwMmRMRVY+dnR26du0qbUdERMDT0xPBwcFQqVQyJiMiko9OF7LLly+Hu7s7LCws4Ofnh8jIyIfun5WVhcmTJ8PFxQVKpRKtWrVCaGioltLqF09PTwiCgOzsbNy6dUvuOFr18ssvw8fHBzk5Ofjkk0/kjkNUK/v27UNpaSnu3LmjtlIYERmfuqiXanpOuejs335btmxBcHAwQkJCEB0djY4dOyIgIKDKoqu4uBj9+/dHUlIStm7diri4OKxevRpubm5aTq4fLC0t0axZMwDG9cAXcH/OzkWLFgEAVqxYgWvXrsmciKjmQkJCEBoaqjZEJi8vjzNyEBmZuqiXanpOWYk6qmvXruLkyZOl7bKyMtHV1VVcuHBhpft///33YvPmzcXi4uJaXe/GjRsiADExMbFWx+ujgIAAEYC4evVquaPUWnFxsbhjx45a9fuAAQNEAOLQoUPrIBlV5XH6jB5u8uTJoru7uxgeHq7R87LP9BP7Tf8kJiaKAMQbN25U+5i6qJdqek456eQd2eLiYkRFRcHf319qMzExgb+/PyIiIio9ZteuXejWrRsmT54MJycntGvXDp999hnKysq0FVvvGOsDX+W++OILCIKA3377DadOnZI7DtFjycvLw59//omkpCT+vUdkJOqiXqrNOeVkKneAymRkZKCsrAxOTk5q7U5OTrh8+XKlxyQkJODgwYMYOXIkQkNDcfXqVbz11lsoKSmRplx6UFFREYqKiqTt3NxcAEBJSQlKSko0+G50l6enJwDg0qVLevuey3PXJn+bNm0wevRobNiwAe+99x7CwsKkeTup7jxOn1HVlEoloqOj8eeff6Jnz57S/9/U1FQ4Ozs/1p9t9pl+Yr/pn/K+ys3NVZsiUqlUQqlUVti/Luql2pxTTjpZyNaGSqVCo0aN8MMPP0ChUMDX1xc3b97EokWLKi1kFy5cKD29/qAjR44gNjZWG5Fll5WVBQCIiYnR+4fi9u/fX6vjevXqhc2bN+PYsWOYO3cu/Pz8NJyMqlLbPqOHs7Ozk36eCwoKMHXqVHh4eGDq1Kmws7N7rHOzz/QT+01/lM+k4+3trdYeEhKCuXPnauQaNa2XdJ1OFrKOjo5QKBRIT09Xa09PT69yMnAXFxeYmZlBoVBIbW3atEFaWhqKi4thbm6utv/MmTMRHBwsbd+8eRPe3t7o1asX3N3dNfdmdFj79u0REhKC9PR09O/fH2ZmZnJHqrGSkhLs37//sfLHx8fjyy+/xG+//YaPPvqo0t96SXM00WdUPX/99RdycnKQmZmJwYMHw8rKqlbnYZ/pJ/ab/klKSgIAxMbGqj18VdW/S3VRL9XmnHLSyULW3Nwcvr6+CAsLw5AhQwDc/w0iLCwMU6ZMqfSYp556Cr/++itUKpU0FU18fDxcXFwqFLFAxdv05bfwzczMjOYH3t3dHVZWVigoKEBKSgpatWold6Rae5x+mz17NjZs2IBr167hu+++w4wZMzScjipjTD9rcnn++edx5swZ5OXlqd2NvXnzZq1mdGGf6Sf2m/4o76d69erB1tb2kfvXVb1U03PKSScf9gKA4OBgrF69GuvXr8elS5cwadIk5OfnIygoCAAwZswYzJw5U9p/0qRJuHv3LqZNm4b4+Hjs3r0bn332GSZPnizXW9B5JiYmUvFqrA98Aff/wvjyyy8BAJ988glu3rwpcyIizWnbtq3akJmdO3eiefPmnEOZyEDURb30qHPqEp28IwsAw4YNw+3btzFnzhykpaXBx8cHe/bskQYfJycnq00C3qRJE+zduxfvvPMOOnToADc3N0ybNg0ffvihXG9BL7Rq1QoxMTGIi4tDYGCg3HFkM3LkSHz//feIiIjAhx9+iI0bN8odiahO/PnnnyguLkZhYaHcUYhIA+qiXnrUOXWJIIpGtD7pQ6SkpKBJkyZITEw0mjGyADBnzhwsWLAA48ePxw8//CB3nBorKSlBaGgoBg0a9Ngfnf3999/o2rUrRFHEsWPH8NRTT2koJT1Ik31GNSeKInbt2oX+/ftLY2ZTU1MB3B87Vxn2mX5iv+mfpKQkeHh44MaNG2jcuLHccfSCzg4tIO0w9rlkH9S5c2e88cYbAICpU6dyLk4ySIIgVHjwa8qUKWjdujW2bdsmYzIioppjIWvkWMiq+/TTT2FnZ4czZ87gxx9/lDsOUZ3Ly8tDSkoK8vPz0aJFC7njEBHVCAtZI1f+sFd6ejqys7NlTiO/Ro0aSfMLz5w5UzfXlSbSIBsbG5w4cQJHjx5Fhw4dpPYjR47w7wQi0nksZI2cra2tNC9cfHy8zGl0w+TJk+Hj44PMzEy88847cschqnMKhQLdunWTtlNTUxEYGIjWrVvjypUrMiYjIno4FrLE4QX/YWpqih9++AEmJib49ddfsXfvXrkjEWlV+cTnTZo0QfPmzeWOQ0RUJRayxEK2El26dJEmfp40aRIKCgpkTkSkPT4+Pjh37hz++OMPafWfsrIyLFq0CJmZmTKnIyL6FwtZYiFbhU8++QSNGzdGYmIi5s+fL3ccIq1SKpVo0qSJtB0WFoZZs2aha9eunNGDiHQGC1ni6l5VqFevHpYvXw4AWLx4Mc6dOydzIiL5uLi4oHXr1pg8ebLaGu1ERHJiIUvSHdkrV65ApVLJnEa3PP/883jxxRdRVlaGcePGobS0VO5IRLJo3749oqKi1NZaP3fuHMaNG8fZPYhINixkCR4eHjAzM0NhYSFSUlLkjqNzvvnmG9jZ2eH06dNYtGiR3HGIZGNmZgZT039XNp82bRrWrFmD999/X8ZURGTMWMgSTE1N4enpCYDDCyrj5uaGZcuWAQBCQkJw/vx5mRMR6YZPP/0UPXr0wIIFC6Q2jp8lIm1iIUsA+MDXo4wZMwaBgYEoKSnB2LFjUVJSInckItl1794dR48eRdOmTaW2WbNm4dlnn+XfJUSkFSxkCcC/D3xxUYTKCYKAH374AfXr18eZM2fw6aefyh2JSOdkZ2dj+fLlCA0N5d8lRKQVLGQJAO/IVoezs7M0i8Gnn36K6OhomRMR6RY7OztERUUhJCQEzz33nNR+5coVFBcXy5iMiAwVC1kCwEK2uoYNG4aXX34ZpaWlGDNmDAoLC+WORKRTWrVqhblz50IQBABAUVERBgwYgPbt2yM2NlbmdERkaFjIEoB/C9nk5GQWZw8hCAJWrFgBJycnXLx4Ee+9957ckYh0WlxcHPLy8pCbm6s2lpaISBNYyBIAwNHREfb29hBFEVevXpU7jk5r2LAh1q9fDwBYsWIFdu7cKXMiIt3VoUMHXLlyBbt27YKNjY3U/t133+HmzZsyJiMiQ8BClgDcv9PI4QXVFxAQIN2Nff311zn/LtFD2NraonPnztL20aNHMXXqVLRp0waZmZkyJiMifcdCliQsZGvm008/ha+vL+7evYtRo0Zx/kyiarK2tkb37t0xYsQIODg4SO2iKMqYioj0EQtZkrCQrRlzc3Ns2rQJNjY2OHz4MD7//HO5IxHphU6dOuHYsWP4+uuvpbb09HQ88cQT+O2331jQElG1sZAlCQvZmmvZsiVWrFgB4P6qX+Hh4fIGItITgiDA0tJS2v7qq69w9uxZLF68mIUsEVWb6aN3IWPx4KIIoihK0+fQw40ePRphYWFYv349hg0bhujoaLi5uckdi0ivzJkzBzY2NujduzdMTO7fYykrK0N8fDzatGkjczoi0lW8I0uSFi1aQBAEZGVl4fbt23LH0SsrVqxAx44dcevWLbzyyiuc/J2ohmxsbDBnzhz06tVLalu/fj3atWuHd999V8ZkRKTLWMiSxNLSEs2aNQPA4QU1ZWVlhT/++AN2dnaIiIjgP7xEGnDmzBmoVCp+wkFEVWIhS2o4Trb2PD09sXHjRgD358j85ZdfZE5EpN++/fZbnDp1CpMmTZLaTp8+jZkzZ+Lu3bsyJiMiXcFCltQ8OE6Wau65557Dxx9/DAAYP348zpw5I3MiIv3WtWtXtYfCZs2ahc8//xwzZsyQMRUR6QoWsqSGd2QfX0hICAYMGIDCwkI8//zzSE1NlTsSkUEQRRFvv/02OnfujJkzZ0rtubm5uHfvnozJiEguLGRJDQvZx6dQKLBp0ya0bt0aKSkpGDJkCAoLC+WORaT3BEHAc889h8jISHh4eEjtCxYsQMuWLblcNJERYiFLasoL2WvXrqGkpETmNPrL3t4e//vf/1C/fn1ERkbi9ddf59yYRBry4NSApaWl2LlzJ1JSUmBmZiZjKiKSAwtZUuPm5gYrKyuUlpYiMTFR7jh6rUWLFti2bRtMTU2xefNmLFiwQO5IRAbH1NQUZ8+exS+//IKBAwdK7Tt37sTPP/+M0tJSGdMRUV1jIUtqTExM0LJlSwB84EsTnn76aaxcuRLA/bGznMmASPMsLCwwYsQI6U5taWkp3n33XYwZMwY//PCDzOmIqC6xkKUKOE5Ws9544w1pXtnXXnsN+/btkzkRkWErKyvD+PHj0aZNG4wdO1Zqz8jI4B1aIgPDQpYqYCGreV9++SWGDx+O0tJSvPTSS4iKipI7EpHBUiqV+PDDD3HhwgVYW1tL7UFBQWjbti2OHTsmYzoi0iQWslQBC1nNMzExwbp169CvXz/k5eVh0KBBuHbtmtyxiAyaicm//8RlZGQgIiICV69eRaNGjWRMRUSaxEKWKuCiCHVDqVRi27ZteOKJJ3Dr1i0EBAQgPT1d7lhERsHR0RGJiYnYvn279HccACxbtgzr1q3jLC1EeoqFLFVQfkc2LS0NOTk5MqcxLLa2tggNDYWHhweuXbuG/v37486dO3LHIjIK9erVw/PPPy9t3717F7Nnz0ZQUBDCwsJkTEZEtcVCliqwtbWFs7MzAA4vqAvOzs7Yt28fXFxccP78eQQEBCA7O1vuWERGR6lUSivxBQQESO0XLlxAbm6ujMmIqLpYyFKlOE62brVo0QIHDhyAo6MjoqKiMGjQIOTl5ckdi8ioWFtb47333sNff/0lTd1VVlaGl156Cc2aNcPx48dlTkhEj8JClirFQrbueXt748CBA3BwcMCJEycQGBiIgoICuWMRGbWUlBTp6w4dOkhfc2U+It3EQpYqxQe+tKNjx47Yu3cvbG1tER4ejsDAQOTn58sdi8hoNWvWDLGxsTh27Bjq1asntQ8fPhxTpkzBP//8I2M6IvovnS5kly9fDnd3d1hYWMDPzw+RkZFV7rtu3ToIgqD2srCw0GJaw8I7strTpUsXhIaGwsbGBgcPHsSAAQP4kB2RjBQKBby9vaXtuLg4/Pbbb1ixYgXHzhLpGJ0tZLds2YLg4GCEhIQgOjoaHTt2REBAAG7dulXlMba2tkhNTZVe169f12Jiw1JeyMbHx0OlUsmcxvA99dRT2L9/P+zs7HDs2DH0798fmZmZcsciItz/hOrgwYP49NNPpb8bAeCnn37CoUOHOOyASEY6W8guWbIE48ePR1BQELy9vbFy5UpYWVlh7dq1VR4jCAKcnZ2ll5OTkxYTGxYPDw+YmpqisLBQbcwY1Z0nn3wSBw8eRIMGDRAZGYm+ffsiIyND7lhERk8QBPTp0wczZ86U2rKysjBt2jT07dsXhw8fljEdkXHTyUK2uLgYUVFR8Pf3l9pMTEzg7++PiIiIKo/Ly8tDs2bN0KRJEwwePBgXL17URlyDZGpqCk9PTwAcJ6tNnTp1Qnh4OBo1aoSYmBj06tULycnJcsciov8oKSnB6NGj0aVLFzz99NNSe2xsLB/aJNIiU7kDVCYjIwNlZWUV7qg6OTnh8uXLlR7j5eWFtWvXokOHDsjOzsbixYvRvXt3XLx4EY0bN66wf1FREYqKiqTt8nFPJSUlXOHl/7Vs2RJxcXGIjY1V+4tal5T3lSH1mZeXF8LCwjBgwABcunQJ3bt3x//+9z+0a9dO7mgaYYh9ZujYZxXZ29tj6dKlUKlUKC0tBQCoVCq88MILuHPnDrZt24Zu3brJmpH9pn/YVzWnk4VsbXTr1k3tL43u3bujTZs2WLVqFRYsWFBh/4ULF2LevHkV2o8cOYLY2Ng6zaovTE3v//HYt28fmjVrJnOah9u/f7/cETRu7ty5mDdvHlJSUtCzZ0989NFHaNu2rdyxNMYQ+8zQsc8e7vbt28jOzkZhYSH++ecfhIaGArg/N61CoZAtF/tNf3A4Wc3pZCHr6OgIhUJRYR369PR0acWpRzEzM8MTTzyBq1evVvr9mTNnIjg4WNq+efMmvL290atXL7i7u9c6uyFJT0/Hjh07UFxcjEGDBskdp1IlJSXYv38/+vfvDzMzM7njaFxgYCBefPFFnDhxAvPnz8eGDRvwwgsvyB3rsRh6nxki9ln1jRw5EpcuXUL79u2ltldeeQWCIGDBggVqD4vVNfab/klKSpI7gt7RyULW3Nwcvr6+CAsLw5AhQwDc/8gmLCwMU6ZMqdY5ysrKcP78+SoLMKVSCaVSKW2XT3dkZmbGH/j/Vz79THx8vM7/PzHUfnNycsKBAwcwfPhw7Nq1C8OHD8fnn3+O999/X1qJSF8Zap8ZMvbZo5mZmaFTp07S9o0bN7Br1y6IoogvvvhClv9/7Df9wX6qOZ182AsAgoODsXr1aqxfvx6XLl3CpEmTkJ+fj6CgIADAmDFj1J4gnT9/Pvbt24eEhARER0dj1KhRuH79OsaNGyfXW9B75YsiJCcno7CwUOY0xsvS0hJ//PEHJk6cCFEU8eGHH+L1119XG+NNRLqpSZMmOH/+PL755hvp71QA+OKLL/Dpp5/yo2Six6STd2QBYNiwYbh9+zbmzJmDtLQ0+Pj4YM+ePdIDYMnJyTAx+bcOz8zMxPjx45GWlgYHBwf4+vrixIkTapNaU800bNgQ9vb2yMrKwtWrV9U+KiPtMjU1xYoVK+Dt7Y3p06dj3bp1uHr1KrZt24aGDRvKHY+IHqJt27Zq49tzc3Px2WefIScnB0888YTODt0i0gc6W8gCwJQpU6ocShAeHq62/fXXX+Prr7/WQirjIQgCvLy8cOrUKcTFxbGQlZkgCJg6dSpatWqFYcOG4dixY+jSpQv+97//sW+I9IhSqcTy5cuxc+dODBgwQGrfs2cPACAgIEDvhw4RaYvODi0g3cClanVPQEAAIiIi4OnpievXr6Nbt27YvHmz3LGIqJrMzc0xatQo/P7779Ini6Io4t1338XAgQPx448/ypyQSH+wkKWHKh/TxUURdEubNm1w6tQp9O3bF/n5+Xj11VcxdepUFBcXyx2NiGqhsLAQzzzzDNzc3DB06FCp/dKlS7yRQPQQLGTpoXhHVnc1aNAAe/fulR56/O677/D000/jxo0bMicjopqysrLC119/jaSkJNjZ2UntH330EVq3bo1vv/1WxnSk65YvXw53d3dYWFjAz88PkZGRVe67bt06CIKg9rKwsFDb57XXXquwz4PDYHQJC1l6qAcLWVEUZU5D/2VqaorPPvsMu3btgr29PU6ePIlOnTph3759ckcjolooX4gGuD+NJHB/ifZ+/fpJ7RkZGbhz547Ws5Fu2rJlC4KDgxESEoLo6Gh07NgRAQEBuHXrVpXH2NraIjU1VXpdv369wj4DBgxQ22fTpk11+TZqjYUsPVSLFi0gCAKysrJw+/ZtueNQFQIDAxEVFYUnnngCGRkZCAgIwHvvvccpuoj0mEKhwPbt25GSkqI2A8/ixYvRuHFjLF26VL5wpDOWLFmC8ePHIygoCN7e3li5ciWsrKywdu3aKo8RBAHOzs7Sq3xGqAcplUq1fRwcHOrybdQaC1l6KEtLS2l5Wg4v0G3NmzfHiRMn8OabbwIAvvrqK/j5+XHJZSI95+LiorYdHR2Ne/fuoXnz5lJbUVERf3E1ILm5ucjJyZFeVfVtcXExoqKi4O/vL7WZmJjA398fERERVZ4/Ly8PzZo1Q5MmTTB48GBcvHixwj7h4eFo1KgRvLy8MGnSJJ39FICFLD0SH/jSHxYWFli5ciV27NgBR0dHnD17Fr6+vlixYgWHhhAZiL179yIiIgLPPvus1Pbzzz/Dzc0NS5YskTEZaYq3tzfs7Oyk18KFCyvdLyMjA2VlZRXuqDo5OSEtLa3SY7y8vLB27Vrs3LkTGzduhEqlQvfu3ZGSkiLtM2DAAGzYsAFhYWH44osvcPjwYQwcOFAa7qJLdHoeWdINXl5e2LdvH+/I6pHBgweja9euCAoKwt69ezF58mTs3r0bP/zwA9zc3OSOR0SPQRAEPPnkk2ptO3fuxJ07d9QKDVEUUVpaqu14pAGxsbFqf1crlUqNnbtbt27o1q2btN29e3e0adMGq1atwoIFCwAAw4cPl77fvn17dOjQAZ6enggPD1cbr60LeEeWHokzF+gnFxcXhIaGYtmyZVAqlQgNDYW3tzfWrFnDu7NEBmb79u3YuXOntIw7ABw9ehTjxo2r8m4e6a569erB1tZWelVVyDo6OkKhUCA9PV2tPT09Hc7OztW6lpmZGZ544glcvXq1yn2aN28OR0fHh+4jFxay9EgsZPWXiYkJ3n77bURFRaFr167IycnBuHHj8MwzzyApKUnueESkIaampnj++efh6OgotW3ZsgVZWVlITk5W21elUmk7HtURc3Nz+Pr6IiwsTGpTqVQICwtTu+v6MGVlZTh//nyFsdgPSklJwZ07dx66j1xYyNIjlY+RvXbtGj+m0lNt27bFiRMnsHjxYlhYWODAgQNo164dvvvuO50c80REj2/p0qX48MMP8fbbb0ttN27cgIeHB+bOncuC1kAEBwdj9erVWL9+PS5duoRJkyYhPz9fujs/ZswYab5xAJg/fz727duHhIQEREdHY9SoUbh+/TrGjRsH4P6DYO+//z5OnjyJpKQkhIWFYfDgwWjRogUCAgJkeY8Pw0KWHqlx48awtLREaWkpEhMT5Y5DtaRQKPDuu+/i3Llz6NWrF/Lz8zF16lT4+fnh9OnTcscjIg0zMzNDt27d0KZNG6ltw4YNSE5OxuHDh6XlcQFwuJEeGzZsGBYvXow5c+bAx8cHMTEx2LNnj/QAWHJyMlJTU6X9MzMzMX78eLRp0waDBg1CTk4OTpw4IU3xplAocO7cOTz//PNo1aoV3njjDfj6+uLo0aMaHaurKXzYix7JxMQErVq1wtmzZxEXF4eWLVvKHYkeQ8uWLXHo0CGsWrUKM2fORFRUFPz8/DBhwgR89tlnqF+/vtwRiaiOvPfee/D09ESjRo2ktnv37sHHxwfPPfcc5s6dCxsbGxkTUm1MmTIFU6ZMqfR74eHhattff/01vv766yrPZWlpib1792oyXp3iHVmqFo6TNSwmJiaYNGkS4uLiMHr0aIiiiFWrVknTsvAjRyLDpFQqMXz4cPTt21dq27VrF+Li4vDbb7/B0tJSauddWtIHLGSpWljIGiYnJyds2LABhw8fRtu2bZGRkYE33ngDXbp0qfBbPBEZphdffBG7du3CokWLoFAoANwvYnv27InXX38dN2/elDkhUdVYyFK1cFEEw9arVy+cOXMGixcvhq2tLaKjo9GnTx8MHjyYv7wQGThTU1MEBgZi2LBhUtvZs2dx/Phx/Prrr7CyspLaeZeWdA0LWaoW3pE1fGZmZnj33Xdx9epVvPXWW1AoFNi1axfatWuHqVOn4vbt23JHJCIt6dixI44ePYply5bBwcFBah85ciReeOEFnDt3TsZ0RP9iIUvVUl7IpqWlIScnR+Y0VJcaNmyI5cuX4/z583juuedQWlqK7777Dh4eHpg1axYyMzPljkhEdUwQBPTo0QNvvvmm1JaZmYmtW7dix44davsWFRXxTi3JhoUsVYutra20SgjvyhqHNm3a4H//+x/CwsLg6+uL/Px8fPbZZ/Dw8MD8+fP5Cw2RkXFwcMCZM2ewaNEidOjQQWoPCQlBu3btsH37dhnTkbFiIUvVxnGyxqlv3744ffo0tm/fjvbt2yM7OxshISHw8PDAF198gfz8fLkjEpGWtG3bFu+99560LYoi/vjjD8TGxqrNdnLv3j0UFBTIEZGMDAtZqjaOkzVegiBgyJAhiImJwebNm+Hl5YW7d+9ixowZaNasGebPn4+7d+/KHZOItEwQBPz9999Ys2YNnnvuOan9119/hbOzM+bNmydjOjIGLGSp2ljIkomJCYYNG4YLFy5g/fr18PT0xJ07dxASEoKmTZsiODgYKSkpcsckIi2ys7PD66+/rrbq0/79+5Gbm6vWplKpcOXKFTkikgFjIUvVxkKWypmammLMmDGIi4vD5s2b4ePjg/z8fHz99ddo3rw53njjDVy+fFnumEQkk19//RVHjhzBa6+9JrUdP34crVq1gr+/Px8OI41hIUvVVl7IxsfHc+UnAnB/Te5hw4YhOjoae/bsQe/evVFSUoK1a9eiTZs2GDBgAEJDQ/nnhcjICIKAnj17Sg8JA0BMTAwUCgWaNm0KQRCk9tDQUGRnZ8sRkwwAC1mqNnd3d5iamqKwsJArvZAaQRAQEBCAQ4cOISIiAkOGDIEgCNi7dy+effZZeHl54ZtvvuFMB0RGbOrUqUhNTcXcuXOltn/++QfPPfccnJ2dkZGRIV840lssZKnazMzM4OnpCYDDC6hqTz75JLZv346rV6/i3XffhZ2dHa5evYpp06bBzc0N06dPx/Xr1+WOSUQyaNiwIZo2bSptp6SkoE2bNvD19YWjo6PUvnHjRhw4cABlZWVyxCQ9wkKWaoTjZKm6mjdvjsWLFyMlJQXff/892rRpg7y8PKxYsQLTpk1Dz549sXbtWuTl5ckdlYhk0rVrV1y4cAG7d++W2kpKSjB9+nT0798fhw4dkjEd6QMWslQjLGSppmxsbDBx4kRcvHgR+/btw5AhQ6BQKHDq1Cm88cYbcHV1xZtvvonTp0/zARAiIyQIAuzs7KTt3NxcvPzyy/D29kbv3r2l9vXr12PmzJl8kJTUmModgPTLgw98EdWEIAjo378/evfujV9//RX//PMPfvrpJ1y5cgU//PADfvjhB7Rr1w6jRo3CiBEj0KRJE7kjE5EM6tevj5UrV0IURbWHwlasWIHIyEg0bdoUrVu3BgDpl98H9yPjwjuyVCPlq3vxjiw9Dnt7e7z33nuIi4vDoUOHMHLkSCiVSly4cEFaZKF379748ccfkZWVJXdcIpLBg8WpKIp499138eKLL+LFF1+U2nfv3g1vb2988803ckQkHcBClmqk/I7s9evXUVhYKHMa0neCIKB3797YuHEjUlNTsXr1ajz99NMQRRGHDx/G+PHj4eTkhJdeegnbtm3jnzkiIyUIAoYOHYo//vgDTk5OUvvWrVtx+fJlXLt2TW3/hIQEbUckmbCQpRpp2LAh7O3tIYoirl69KnccMiAODg4YN24cwsPDcf36dXz++edo164diouLsW3bNrz00kto2LAhhg4dii1btiA3N1fuyEQks2+++QY///wzxo8fL7XFx8fD09MTvr6+KC0tlTEdaQMLWaoRQRD4wBfVuaZNm+LDDz/E+fPncfbsWbz//vto1qwZ8vPz8fvvv2P48OFo2LAhnn/+eaxfvx6ZmZlyRyYiGdja2mLUqFFo166d1Pb333/D1NQUjRo1gqnpv48C/f7774iNjeVDpQaGhSzVWPk4WT7wRdrQoUMHfPnll0hMTMTp06cxY8YMtGzZEkVFRfjf//6H1157DY0aNUL//v2xdOlSflJAZORGjBiB9PR0tXGzBQUFeO2119C2bVucP39exnSkaSxkqcZ4R5bkIAgCOnfujIULFyIuLg7nzp1DSEgI2rVrh9LSUhw4cADvvPMOWrZsCS8vLwQHByMsLAzFxcVyRyciLatfvz5atmwpbWdkZKBPnz5o1aoV2rdvL7UvW7YM77zzDi5cuCBHTNIATr9FNcZCluQmCALat2+P9u3bY+7cuYiPj8eff/6J3bt348iRI4iPj0d8fDy+/vpr1KtXD/3798fAgQPh7+8Pd3d3ueMTkZY1bdoUf/75J0pLS9VmQ1i1ahUuXbqELl26SMMTioqKIAgCzM3N5YpLNcA7slRjDxayHGtEuqBVq1bSHdiMjAz8/vvv0pCD3NxcbNu2DePHj4eHhwdatGiBiRMn4o8//sDdu3fljk5EWvTgmFlRFLFw4UKMHTsWzz77rNT++++/w8nJCXPmzJEjItUQ78hSjbVo0QKCICArKwsZGRlo2LCh3JGIJHZ2dnj55Zfx8ssvQ6VSISoqCrt378aBAwdw8uRJXLt2DdeuXcOqVasgCAJ8fX3Rr18/9OvXD926dYONjY3cb4GItEAQBAwePBiDBw9Wa9+/f3+F+atVKhV+//13PPPMM3BwcNBiSnoUFrJUY5aWlmjatCmuX7+OuLg4FrKks0xMTNClSxd06dIFc+fORU5ODg4fPowDBw4gLCwMFy9exN9//42///4bX3zxBRQKBTp16oSePXuiZ8+e6NGjBxwdHeV+G0SkRWvXrsX48ePVVheMjo7G8OHDYW9vj9u3b6vd2SV5sSeoVry8vKRCtkePHnLHIaoWW1tbBAYGIjAwEADwzz//4ODBg9i/fz8OHz6M69ev4/Tp0zh9+jSWLFkCAGjTpg169uyJXr16oWfPnmjSpAmXwyQyYAqFosK/a1lZWWjXrh28vLzUitg333wTDRo0wOTJk+Hm5qbtqAQdHyO7fPlyuLu7w8LCAn5+foiMjKzWcZs3b4YgCBgyZEjdBjRifOCLDIGrqytGjRqF9evXIykpCdevX8fGjRvx5ptvok2bNgCAS5cu4YcffsCoUaPQrFkzuLm54YUXXsDnn3+OQ4cOcWEGIiPg7++P8+fPY+PGjVJbVlYW1q5di4ULF+LevXtS++3bt1FQUCBHTKOks3dkt2zZguDgYKxcuRJ+fn5YunQpAgICEBcXh0aNGlV5XFJSEt577z307NlTi2mNDwtZMkRNmzbFyJEjMXLkSAD3p+w5duwYjh49iqNHjyI6OhqpqanYsWMHduzYAeD+OLu2bdvCz88Pfn5+6Nq1K9q2bcuPHokMkIWFhfS1ubk51q9fj9OnT8PT01Nqnz9/PtasWYMvv/wSU6ZMkSOmUdHZv2mXLFmC8ePHIygoCACwcuVK7N69G2vXrsWMGTMqPaasrAwjR47EvHnzcPTo0QqDtUlzuCgCGQNHR0cMGTJE+nQnPz8f0dHROHXqlPS6ceMGLly4gAsXLmDNmjUAACsrK3To0AFPPPGE9GrXrp3aP4JEpN+srKwwYsQIjBgxQq09JiYGhYWFalP93bx5Exs2bMDgwYPh7e2t5aSGTScL2eLiYkRFRWHmzJlSm4mJCfz9/REREVHlcfPnz0ejRo3wxhtv4OjRo9qIarTK78heu3YNpaWlvPtERsHa2lp6EKxcamoqIiMjpcL29OnTyM3NxcmTJ3Hy5ElpP1NTU7Rp00atuPXx8YGdnZ0cb4WI6siRI0dw7tw56YYPAOzcuRMfffQRQkND1eqTsrIyKBQKOWIaDJ2sPjIyMlBWVgYnJye1dicnJ1y+fLnSY44dO4Y1a9YgJiamWtcoKipCUVGRtF0+zq2kpAQlJSW1C25EnJycYGlpicLCQsTHx6utoKJN5X3FPtMfhtZnjo6OGDRoEAYNGgTg/j9MV65cQUxMDGJiYnD27FnExMTgzp07OH/+PM6fP48NGzZIxzdt2hTe3t7w9vZG27Zt0a5dO7Ru3RqWlpZyvaUKDK3PjAX7TT7ld13L/983btwYAwYMQL9+/dT6pUWLFvDx8cGPP/6Ihg0bsq9qQScL2ZrKzc3F6NGjsXr16mpPlbNw4ULMmzevQvuRI0cQGxur6YgGycnJCUlJSfj111/RpUsXWbPs379f1utTzRl6n9na2qJXr17o1asXRFFERkYGEhMTkZCQIL0yMjKQnJyM5ORk7NmzRzpWEAQ4OzujadOmai9XV1eYmZnJ9p4Mvc8MFftNN0ycOBEAEBoaCuD+g6SpqanIz8/HyZMnoVAokJGRIWdEvaSThayjoyMUCgXS09PV2tPT0+Hs7Fxh/2vXriEpKUmaUge4P3kxcP/jvLi4OLWB2AAwc+ZMBAcHS9s3b96Et7c3evXqxSUsq2njxo1ISkqCnZ2ddDdK20pKSrB//370799f1n/gqfrYZ//KzMxEbGwsLl68KP33woULuHPnDlJTU5GamopTp05J+5uYmMDDwwOtWrVCy5Yt0apVK+lrV1fXOpsWjH2mn9hvum3gwIEICAhAUlISnnvuOQD3H1inmtHJQtbc3By+vr4ICwuTHrJQqVQICwur9AnA1q1b4/z582pts2fPRm5uLpYtW6Y2qXE5pVIJpVIpbefk5AAAzMzM+ANfTa1btwYAXL16Vfb/Z+w3/cM+Axo1aoRGjRqhd+/eUpsoirh165ZU1F64cEH6OicnR1qZ7K+//lI7l42NjVTYenl5wcvLCy1atICnpyccHBw0UuSyz/QT+013lY+XL8fxsjWnk4UsAAQHB2Ps2LHo3LkzunbtiqVLlyI/P1+axWDMmDFwc3PDwoULYWFhgXbt2qkdb29vDwAV2klzOAUXkeYJggAnJyc4OTmhb9++UrsoikhLS0N8fDzi4uKkV3x8PBISEpCXl4fo6GhER0dXOKednR2aN29e6atp06YwNzfX5lskoiqYmOj09P46SWcL2WHDhuH27duYM2cO0tLS4OPjgz179kgPgCUnJ7PDZcZClkh7BEGAi4sLXFxc8PTTT6t9r7i4GAkJCRWK3ISEBPzzzz/Izs7GmTNncObMmQrnNTExQZMmTaTC1sPDA+7u7mjSpAmaNm3K1YqISKfpbCELAFOmTKlyMuHw8PCHHrtu3TrNByI15VOLpKWlIScnB7a2tjInIjJO5ubmaN26tTTc50GFhYVISkpCQkICrl27pvawWUJCAgoLC3H9+nVcv34dhw4dqnC8IAhwdXWFjY0NNm7cCHd3d7UH0Jo0aYIGDRpw2V4ikoVOF7Kk2+zs7ODk5IT09HTEx8ejc+fOckciov+wtLREmzZtpCV3HySKItLT0ysUtzdu3JBmUyguLsbNmzcBVP3pi6WlpVTUurq6wsXFBa6urmovFxcXtecSiIg0gYUsPRYvLy+kp6cjLi6OhSyRnimf5svZ2Rndu3ev8H2VSoXbt28jISEBO3fuRMOGDXHz5k2pyL1x4wbS0tJQWFgoDWd4mAYNGlRa5D5Y/Do5ObHgJaJqYyFLj8XLywtHjhzhOFkiA2RiYgInJyfUr18ft27dwqBBgyo8/V5UVISUlBSpsC2fNuyff/5RexUVFeHOnTu4c+cOLly48NDr2tnZSTM6ODk5Vfp1+ba9vT2HNRAZMRay9Fj4wBeRcVMqlfD09KwwV/eDRFFEZmYm/vnnn0qL3PJXamoqSkpKkJ2djezsbFy5cuWR1zc1Na200G3QoEGVL97xJTIcLGTpsZQXsvHx8TInISJdJQgC6tevj/r16z90SkRRFJGVlYVbt24hPT0dt27dkl6VbWdnZ6O0tFQqhKvL2tq6QnHr6Oj40OLX1taWd36JdBALWXos5TMXxMfHQ6VScUo0Iqo1QRDg4OAABwcH6ZfkhykqKsLt27crLXbLhzE8+Lp79y7KysqQn5+P/Px8JCcnVzubiYkJ7OzsYG9vDwcHB9jb26u9HtVmZWXFQpioDrCQpcfi4eEBU1NTFBQU4ObNm5WuokZEVBeUSiUaN26Mxo0bV2t/lUqFnJwcZGRkVFroVvbKyMhAYWEhVCoVMjMzkZmZicTExBpnNTU1rbTAtbW1Rb169dT+W9XX9erV47AIov9gIUuPxczMDJ6entITyyxkiUhXmZiYSAVkixYtqn1cYWEhsrKyKn1lZmY+sr20tBSlpaXIyMhARkbGY70Hc3PzRxa/5f+1trbGlStXIAgC7OzsYGNjA2tra1hbW0tfc1U30ncsZOmxeXl5SYWsv7+/3HGIiDTK0tISlpaWcHFxqfGxoiiioKCgysI3JycHubm5av+trC0/Px/A/VXcaloQL168uMrvmZqaqhW4Dxa5tfna2toalpaWsLKygpmZGYdTUJ1jIUuP7cFxskRE9C9BEKQC73GW+y0rK0NeXt4jC94Hv87OzkZSUhKUSiUKCgqQl5cnjQ8uLi4GAJSWlkpFtaaZmJhIRW35LwOP8/WjvsdnNIwTC1l6bJyCi4iobikUCtjZ2cHOzq7ax5SUlCA0NLTS+X9LSkqkovbBAre2Xz/YJooigPtjksvbtEGpVMLS0hIWFhZQKpWwsLBQ+1obbQqFQivvlf7FQpYeGwtZIiL9YmZmJo0X1iRRFFFcXIzCwkIUFhaioKBA418/uF1+Zxm4P4tFUVGRRt9PTSkUCrXiVqlUwtzcvNqve/fuyZpfH7GQpcdWXshev34dhYWFsLS0lDkRERHJQRAEqYDTdJFcmbKysgoFbnlBe+/ePem/D36t6baysjK1PNq8C00sZEkDGjZsCHt7e2RlZeHatWsPnfCciIhIUxQKBWxsbGBjYyNbhtLS0gqFblFREQoLC1FSUoLi4mIUFRWhuLj4ka+0tDR8++23sr0XfcRClh6bIAho1aoVIiMjERcXx0KWiIiMhqmpKUxNTWFtbf3Y50pKSmIhW0N8xI80guNkiYiI5LF8+XK4u7vDwsICfn5+iIyMrHLfdevWQRAEtZeFhYXaPqIoYs6cOXBxcYGlpSX8/f1x5cqVun4btcJCljSChSwREZH2bdmyBcHBwQgJCUF0dDQ6duyIgIAA3Lp1q8pjbG1tkZqaKr2uX7+u9v0vv/wS33zzDVauXIlTp07B2toaAQEBOvkwGgtZ0ggWskRERNq3ZMkSjB8/HkFBQfD29sbKlSthZWWFtWvXVnmMIAhwdnaWXk5OTtL3RFHE0qVLMXv2bAwePBgdOnTAhg0b8M8//2DHjh1aeEc1w0KWNKJ8UYS4uDhpDkEiIiKquQcXuMjJyalyWrHi4mJERUWprappYmICf39/REREVHn+vLw8NGvWDE2aNMHgwYNx8eJF6XuJiYlIS0tTO6ednR38/Pweek65sJAljWjZsiUEQUBWVtZjryVORERkzLy9vaUFMOzs7LBw4cJK98vIyEBZWZnaHVUAcHJyQlpaWqXHeHl5Ye3atdi5cyc2btwIlUqF7t27IyUlBQCk42pyTjlx1gLSCEtLSzRt2hTXr19HXFwcGjZsKHckIiIivRQbG6u2pLFSqdTYubt164Zu3bpJ2927d0ebNm2watUqLFiwQGPX0RbekSWN4ThZIiKix1evXj3Y2tpKr6oKWUdHRygUCqSnp6u1p6enw9nZuVrXMjMzwxNPPIGrV68CgHTc45xTm1jIksaUF7Lx8fEyJyEiIjJ85ubm8PX1RVhYmNSmUqkQFhamdtf1YcrKynD+/Hm4uLgAADw8PODs7Kx2zpycHJw6dara59QmDi0gjXnwgS8iIiKqe8HBwRg7diw6d+6Mrl27YunSpcjPz0dQUBAAYMyYMXBzc5PG2c6fPx9PPvkkWrRogaysLCxatAjXr1/HuHHjANyf0WD69On45JNP0LJlS3h4eODjjz+Gq6srhgwZItfbrBILWdIYDi0gIiLSrmHDhuH27duYM2cO0tLS4OPjgz179kgPayUnJ8PE5N8P4DMzMzF+/HikpaXBwcEBvr6+OHHiBLy9vaV9PvjgA+Tn52PChAnIyspCjx49sGfPngoLJ+gCFrKkMeWF7LVr11BaWgpTU/7xIiIiqmtTpkzBlClTKv1eeHi42vbXX3+Nr7/++qHnEwQB8+fPx/z58zUVsc5wjCxpTOPGjWFpaYmSkhIkJibKHYeIiIgMHAtZ0hgTExO0bNkSAB/4IiIiorrHQpY0iuNkiYiISFtYyJJGsZAlIiIibWEhSxrFQpaIiIi0hYUsaRQXRSAiIiJtYSFLGlW+KEJqaipycnJkTkNERESGjIUsaZSdnZ00CTPvyhIREVFdYiFLGsdxskRERKQNLGRJ41jIEhERkTawkCWNKx8ny6EFREREVJdYyJLG8Y4sERERaQMLWdK4B6fgUqlUMqchIiIiQ8VCljTOw8MDpqamKCgowM2bN+WOQ0RERAZKpwvZ5cuXw93dHRYWFvDz80NkZGSV+27btg2dO3eGvb09rK2t4ePjg59//lmLaamcmZkZPD09AXCcLBEREdUdnS1kt2zZguDgYISEhCA6OhodO3ZEQEAAbt26Ven+9evXx6xZsxAREYFz584hKCgIQUFB2Lt3r5aTE/DvA18cJ0tERER1RWcL2SVLlmD8+PEICgqCt7c3Vq5cCSsrK6xdu7bS/Xv37o0XXngBbdq0gaenJ6ZNm4YOHTrg2LFjWk5OAB/4IiIiorqnk4VscXExoqKi4O/vL7WZmJjA398fERERjzxeFEWEhYUhLi4OvXr1qsuoVAUWskRERFTXTOUOUJmMjAyUlZVJS52Wc3JywuXLl6s8Ljs7G25ubigqKoJCocCKFSvQv3//SvctKipCUVGR2rEAcOPGDQ28A7K1tQUAXLx4EUlJSXV2nZKSEmRkZCApKQlmZmZ1dh3SHPaZ/mGf6Sf2m/4pr0E440/16WQhW1v16tVDTEwM8vLyEBYWhuDgYDRv3hy9e/eusO/ChQsxb968Cu28g6tZKSkp8PDwkDsGERGR3rhx4waaNm0qdwy9IIiiKMod4r+Ki4thZWWFrVu3YsiQIVL72LFjkZWVhZ07d1brPOPGjcONGzcqfeDrv3dk7969Cw8PD1y4cAF2dnaP/R5IO3Jzc+Ht7Y3Y2FjUq1dP7jhUDewz/cM+00/sN/2TnZ2Ndu3a4c6dO6hfv77ccfSCTt6RNTc3h6+vL8LCwqRCVqVSISwsDFOmTKn2eVQqlVqx+iClUgmlUlmhvUmTJtLH4qT7cnJyAABubm7sNz3BPtM/7DP9xH7TP+X9ZGqqk+WZTtLZ/1PBwcEYO3YsOnfujK5du2Lp0qXIz89HUFAQAGDMmDFwc3PDwoULAdwfKtC5c2d4enqiqKgIoaGh+Pnnn/H999/L+TaIiIiIqI7obCE7bNgw3L59G3PmzEFaWhp8fHywZ88e6QGw5ORkmJj8O+lCfn4+3nrrLaSkpMDS0hKtW7fGxo0bMWzYMLneAhERERHVIZ0tZAFgypQpVQ4lCA8PV9v+5JNP8Mknn9T6WkqlEiEhIZUONyDdxX7TP+wz/cM+00/sN/3DPqs5nXzYi4iIiIjoUXRyQQQiIiIiokdhIUtEREREeomFLBERERHpJaMqZJcvXw53d3dYWFjAz88PkZGRD93/999/R+vWrWFhYYH27dsjNDRUS0npQTXpt9WrV6Nnz55wcHCAg4MD/P39H9nPpHk1/Vkrt3nzZgiCoLYQCmlHTfssKysLkydPhouLC5RKJVq1asW/I2VQ035bunQpvLy8YGlpiSZNmuCdd97BvXv3tJSWjhw5gsDAQLi6ukIQBOzYseORx4SHh6NTp05QKpVo0aIF1q1bV+c59YpoJDZv3iyam5uLa9euFS9evCiOHz9etLe3F9PT0yvd//jx46JCoRC//PJLMTY2Vpw9e7ZoZmYmnj9/XsvJjVtN+23EiBHi8uXLxTNnzoiXLl0SX3vtNdHOzk5MSUnRcnLjVdM+K5eYmCi6ubmJPXv2FAcPHqydsCSKYs37rKioSOzcubM4aNAg8dixY2JiYqIYHh4uxsTEaDm5catpv/3yyy+iUqkUf/nlFzExMVHcu3ev6OLiIr7zzjtaTm68QkNDxVmzZonbtm0TAYjbt29/6P4JCQmilZWVGBwcLMbGxorffvutqFAoxD179mgnsB4wmkK2a9eu4uTJk6XtsrIy0dXVVVy4cGGl+w8dOlR89tln1dr8/PzEN998s05zkrqa9tt/lZaWivXq1RPXr19fVxHpP2rTZ6WlpWL37t3FH3/8URw7diwLWS2raZ99//33YvPmzcXi4mJtRaRK1LTfJk+eLPbt21etLTg4WHzqqafqNCdVrjqF7AcffCC2bdtWrW3YsGFiQEBAHSbTL0YxtKC4uBhRUVHw9/eX2kxMTODv74+IiIhKj4mIiFDbHwACAgKq3J80rzb99l8FBQUoKSnhmtVaUts+mz9/Pho1aoQ33nhDGzHpAbXps127dqFbt26YPHkynJyc0K5dO3z22WcoKyvTVmyjV5t+6969O6KioqThBwkJCQgNDcWgQYO0kplqjrXIo+n0ggiakpGRgbKyMmlVsHJOTk64fPlypcekpaVVun9aWlqd5SR1tem3//rwww/h6upa4S8Cqhu16bNjx45hzZo1iImJ0UJC+q/a9FlCQgIOHjyIkSNHIjQ0FFevXsVbb72FkpIShISEaCO20atNv40YMQIZGRno0aMHRFFEaWkpJk6ciI8++kgbkakWqqpFcnJyUFhYCEtLS5mS6Q6juCNLxunzzz/H5s2bsX37dlhYWMgdhyqRm5uL0aNHY/Xq1XB0dJQ7DlWTSqVCo0aN8MMPP8DX1xfDhg3DrFmzsHLlSrmj0UOEh4fjs88+w4oVKxAdHY1t27Zh9+7dWLBggdzRiGrNKO7IOjo6QqFQID09Xa09PT0dzs7OlR7j7Oxco/1J82rTb+UWL16Mzz//HAcOHECHDh3qMiY9oKZ9du3aNSQlJSEwMFBqU6lUAABTU1PExcXB09OzbkMbudr8nLm4uMDMzAwKhUJqa9OmDdLS0lBcXAxzc/M6zUy167ePP/4Yo0ePxrhx4wAA7du3R35+PiZMmIBZs2bBxIT3tnRNVbWIra0t78b+P6P4U2tubg5fX1+EhYVJbSqVCmFhYejWrVulx3Tr1k1tfwDYv39/lfuT5tWm3wDgyy+/xIIFC7Bnzx507txZG1Hp/9W0z1q3bo3z588jJiZGej3//PPo06cPYmJi0KRJE23GN0q1+Tl76qmncPXqVemXDgCIj4+Hi4sLi1gtqU2/FRQUVChWy38ZEblavU5iLVINcj9tpi2bN28WlUqluG7dOjE2NlacMGGCaG9vL6alpYmiKIqjR48WZ8yYIe1//Phx0dTUVFy8eLF46dIlMSQkhNNvyaCm/fb555+L5ubm4tatW8XU1FTplZubK9dbMDo17bP/4qwF2lfTPktOThbr1asnTpkyRYyLixP//PNPsVGjRuInn3wi11swSjXtt5CQELFevXripk2bxISEBHHfvn2ip6enOHToULnegtHJzc0Vz5w5I545c0YEIC5ZskQ8c+aMeP36dVEURXHG/7V39zFNXX0cwL+lWMnQrWDUCTJZdYAv8yVo1USobv4xdZqZrDFbnQRfJqJGhpjAX2CUKFMT2TBDxREksIIiI46MbYSXzAAhvsYJoi7TLJM5V3C1AkL1PH/42Mc+bXm9bb3j+0n6zzn3nPu9adBfbs89NzlZfPLJJ7bjn2+/tWvXLtHc3CyOHDnC7bf+z7ApZIUQ4ssvvxRvvPGGUKlUQqvVioaGBlufTqcTMTExdscXFxeLsLAwoVKpxPTp00V5ebmHE5MQA/veJk2aJAA4fFJTUz0ffBgb6N/ai1jIesdAv7O6ujoxf/58MXLkSKHRaER6erqwWq0eTk0D+d56enpEWlqamDx5svDz8xMhISEiPj5etLe3ez74MFVdXe30/6jn31NMTIzQ6XQOY2bPni1UKpXQaDQiNzfX47lfZgoh+HsCEREREcnPsFgjS0RERET/PixkiYiIiEiWWMgSERERkSyxkCUiIiIiWWIhS0RERESyxEKWiIiIiGSJhSwRERERyRILWSIiIiKSJRayRERERCRLLGSJiIiISJZYyBIR/ddff/2F1tZWb8eQ1IEDB/Ddd98NaY5Tp05JlIaISFosZImIANy+fRtbt27FqFGjvB1FUomJifjqq69QUVExqPF1dXXIy8uTOBURkTR8vR2AiMjbHj58iLVr18JoNGL06NG2dpPJhLS0NLS0tODvv/+G1WrF2rVrkZCQAJVK5cXE/adUKpGfn4+oqCjMmTMH48ePH9D4goICGAwGN6UjIhoahRBCeDsEEZE3bdq0CVqtFps2bbK1mUwmrFq1CpmZmZg7dy4A4OzZs9Dr9Zg1axaqqqrg7+/vrcgDtmfPHty8eRMnT57s9xir1Yq33noL165dwyuvvOLGdEREg8OlBUQ0rF26dAnV1dWIjY21a9+7dy8SEhJsRSwArFy5Etu2bUNjYyN2797t6ahDsm3bNpw9exa//vprv8dUVFRg0aJFLGKJ6KXFQpaIhrXPP/8csbGx8PW1X2lVWVmJ9evXo7Ky0q599erVAIDi4mKPZZRCQEAA3nnnHeTk5PR7DJcVENHLjoUsEQ1bZrMZpaWlWL58uUNfeHg4LBYL2tvb7drHjh0LAPjzzz89klFK0dHRKC0t7dexFosFDQ0NWLp0qZtTERENHgtZIpJETk4O9Ho9Nm/ejLi4OGRlZXklx8OHD5GUlIRVq1bh008/RXJyMo4dO4b33nvP4djKykr4+vpi5syZDn1FRUW4e/cu9Hq9XfudO3cAAFOmTHHPBfQiKSmpz+3BSkpKEBAQgPPnzzv0RUdHo6WlBffu3evzXGfOnMHKlSsd7lRLkYOISCosZIloyNLS0lBVVYXCwkIcPXoUu3btwhdffIGmpiaP5jCZTIiKikJrayvKyspw7NgxhIWFYefOnU4Lr7q6OsybNw9KpdKhT6lUYsKECQ7tBQUFAGD3YJgnXLp0CX5+fk4zvej333/HgwcPUFNT49AXGhoKALhy5Uqf53O1rECKHEREUuH2W0Q0JN3d3cjIyMDp06cxYsQIAEBDQwO6urpcbvW0f//+Qe1rOmbMGJSUlLjs1+v1MJvNOHr0KBQKBYBnD2ht2LABOp3O4fjm5mYEBwf3+/w3b95EQUEBdDodtm7dOuD8Q3H8+HFkZGT0edz27duRn5/v9AEttVoNHx8f3L59u9c57t27hzt37mD+/PluyUFEJBUWskQ0JBaLBV1dXUhJSUFnZycWLlwIg8HQ60NCycnJSE5OljSH0WhEdXU1Dhw4YPdSg+d3HxcvXuww5o8//sCbb77Zr/l7enpgMBgQGRmJsrIypz+5u0t7eztGjRplt8ctAOTl5cFkMiExMdHWplQqodPpMGvWLId5FAoF1Go1/vnnn17PZzQasWbNGrflICKSCpcWENGQBAYGwmAw4OrVq9Dr9QgJCcGHH36Ijo4Oj+bIzs4GAHzwwQd27bW1tVAoFE7vyFosFrz22mv9mn/Lli1Qq9WorKzsc8yDBw8QERGB0NDQAX2qqqqczldVVYV3333Xof3w4cPo6elxaDeZTIiMjHQ618iRI/H48eNe87taViBlDiIiKfCOLBENWX5+Pj766CPU1NSguLgYJSUlCA4ORmZmpkfOb7Vace7cOYSEhDg8hFVTU4O3334bY8aMcRinVCrR3d3d5/xpaWno6upCeXm5bflER0eHy5/N1Wo1rl+/Pogrce7y5csOhaXZbMaVK1dQWFho137//n0oFAr4+fk5nautra3X1/DeuHEDQgiEhYW5NQcRkRRYyBLRoB06dAgZGRmoq6vDihUrsGLFCqSnp0Or1eLWrVsux+3btw8//PDDgM8XGBiIM2fOOLSbTCY8efIEc+bMsWvv7OxEY2Mj4uLiAACnTp3CsmXLbIWcWq1GW1tbr+c8ceIEWltbcfLkSfj4/O9HrNjYWBQVFQ34Ggbj/v37DjkvX76MyMhITJ061dYmhMCWLVtcrt999OgRHj9+3Ou64N72jpUqBxGRVFjIEtGg5ebmYsSIEQgMDLS1qVQqBAcHIyoqyuW4lJQUpKSkSJZj3Lhx8Pf3d7jrWlRUhO7ubixatAgAUFZWZredVmhoaK+F7Pfff4+mpiZkZ2fbHh4Dnq2X7ezslCx/X0aPHo0jR45g4cKFUCgUOH/+PD7++GN0dnaira0NgYGBaG9vR3x8PABgyZIlTud5vu1WeHi4y3MZjUbU1ta6NQcRkVS4RpaIBm3evHkoLi62K2S//fZbtLa2YseOHR7LoVAosHHjRly8eBFCCADATz/9ZHv7VlBQEFpaWqDRaOzGzZw5E7/99pvTOS9cuIA1a9agvLwcU6dORUREhO2j0Wjw+uuvu/eiXrBkyRIUFhYiIiICWq0WWq0WBoMBVqsV06ZNQ3R0NCZOnIimpiYcP37c5Tz19fV49dVXMWPGDKf9DQ0NmDRpkstrkyoHEZFUFOL5v/pERANksViQmpqKjo4O+Pj4wGw2Q6PRIDExsd8PUUmlo6MDcXFxaGtrw4QJExAeHo7ExESkpqaivr4e48ePR1ZWFgICAmxjfv75ZyxevBgmkwlqtdpuvhkzZuDatWsuz3fw4EHs3LnTXZdjRwiBzz77DHl5eQgICEBSUhLi4+NRWFiIhIQE+Pr6YvXq1UhPT3e4jhdt3rwZZrMZ33zzjdP+7du3Y+7cuYiJiXFrDiIiqbCQJaJh6+nTpwgKCkJOTg7ef/99b8dxq6dPn2LKlCnIyspy+kpeq9WKyZMn45dffnHYXouI6GXFpQVENGz5+Phg48aNMBqN3o7idqdPn4a/vz+WLVvmtP/HH3/EggULWMQSkaywkCWiYW3Hjh2oqKhwuVb232L//v3IzMy0e2jtRb3tVkBE9LLi0gIiGvays7PR2NiIr7/+2ttR3GLfvn0wmUw4ePCg0/5Hjx5h2rRpuHXrlm2fXCIiOeAdWSIa9uLi4vDkyRPk5eV5O4rkKioq0NLSgoyMDJfHlJaWYvny5SxiiUh2WMgSEeHZiw/q6+vR3Nzs7SiSCgoKQm5uLpRKpctjamtrsW7dOg+mIiKSBpcWEBEREZEs8Y4sEREREckSC1kiIiIikiUWskREREQkSyxkiYiIiEiWWMgSERERkSyxkCUiIiIiWWIhS0RERESyxEKWiIiIiGSJhSwRERERyRILWSIiIiKSJRayRERERCRL/wHD5w5JaiWErwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "\n", "# ---- data ----\n", "om = np.linspace(0.2, 1.5, 1000)\n", "a = (om**2 - 12*om + 12) / (6*(om**2 - 8*om + 8))\n", "r = 1.0 - 2.0*a\n", "s = a * (2.0 - om) / om\n", "\n", "# ---- figure and axes ----\n", "fig, ax1 = plt.subplots(figsize=(7, 5))\n", "\n", "# Left y-axis: omega\n", "ax1.plot(s, om, 'k:', label=r'$\\omega$')\n", "ax1.set_xlabel(r'$s = a(2-\\omega)/\\omega$',fontsize=16)\n", "ax1.set_ylabel(r'$\\omega$',fontsize=16)\n", "ax1.set_ylim(0.3, 1.1)\n", "ax1.set_xlim(0.0, 1.0)\n", "ax1.grid(True)\n", "\n", "# Right y-axis: r\n", "ax2 = ax1.twinx()\n", "ax2.plot(s, r, 'k-', label=r'$r = 1 - 2a$')\n", "ax2.set_ylabel(r'$r$',fontsize=16)\n", "ax2.set_ylim(0.48, 0.8)\n", "ax2.set_xlim(0.0, 1.0)\n", "\n", "# ---- combined legend ----\n", "lines1, labels1 = ax1.get_legend_handles_labels()\n", "lines2, labels2 = ax2.get_legend_handles_labels()\n", "ax1.legend(lines1 + lines2, labels1 + labels2, loc='best')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 106, "id": "80434587-6592-4256-9df8-9ce569d6fa4e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dx=6.2832e-01\t dt=3.1416e-01\t nt=39\t tn=12.25\n", "c_lbm=0.000, tau=1.0000\t omega=1.00\n", "nt=39.000, nue=0.1667\n", "dx=3.1416e-01\t dt=7.8540e-02\t nt=153\t tn=12.02\n", "c_lbm=0.000, tau=1.0000\t omega=1.00\n", "nt=153.000, nue=0.1667\n", "dx=1.5708e-01\t dt=1.9635e-02\t nt=612\t tn=12.02\n", "c_lbm=0.000, tau=1.0000\t omega=1.00\n", "nt=612.000, nue=0.1667\n", "dx=7.8540e-02\t dt=4.9087e-03\t nt=2445\t tn=12.00\n", "c_lbm=0.000, tau=1.0000\t omega=1.00\n", "nt=2445.000, nue=0.1667\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "A = 1.0 # Amplitude\n", "phi = 0.0 # Wave initial shift\n", "k_w = 1.0 # Wave number\n", "c = 0.0 # wave speed\n", "nu = 0.066666666666666666*np.pi # Diffusive coefficient\n", "m_waves = 1 # Wave Period\n", "L = m_waves * (2.0*np.pi / k_w) # Domain Lentgh\n", "t_end = 12.0 # Final time\n", "#--------------------------------------- Lattice-Properties-D1Q3 ----------------------------------------------\n", "w = np.array([4.0/6.0, 1.0/6.0, 1.0/6.0],dtype=\"float64\")\n", "cx = np.array([0, 1, -1],dtype=\"int16\") \n", "cs=1.0/np.sqrt(3.0);\n", "#--------------------------------- Initialization - Save Data Arrays -----------------------------------------------\n", "cases=4\n", "Nx0 = np.array([10, 20, 40, 80],dtype=\"int64\")\n", "r0 = 2**(0)*np.array([2.0**(1), 2.0**(2), 2.0**(3), 2.0**(4)],dtype=\"float64\")\n", "u_cases = np.empty(cases, dtype=object) # array field used to same data over time\n", "for i in range(cases):\n", " u_cases[i] = np.zeros((Nx0[i]), dtype=\"float64\")\n", "for case in range(0,cases):\n", " #------------------------------------- Parameters (numerical units) -------------------------------------------\n", " Nx=Nx0[case] # Numerical Length\n", " x = np.linspace(0.0, L, Nx, endpoint=False,dtype=\"float64\") # Numerical Domain\n", " dx = L / Nx # Grid size\n", " r = 1*r0[case] # dx/dt relation\n", " dt = dx/r\n", " ce = c/r\n", " nue = nu * dt / (dx*dx)\n", " tau = 0.5 + nue / cs**2\n", " omg=1.0/tau\n", " nt = int(np.ceil(t_end / dt))\n", " print(f\"dx={dx:.4e}\\t dt={dt:.4e}\\t nt={nt:d}\\t tn={nt*dt:.2f}\") # Print values for check\n", " print(f\"c_lbm={ce:.3f}, tau={tau:.4f}\\t omega={omg:.2f}\")\n", " print(f\"nt={nt:.3f}, nue={nue:.4f}\")\n", " #--------------------------------- Initialization - LBM - Numerical Arrays -----------------------------------------\n", " u=np.zeros((Nx),dtype=\"float64\")\n", " u = A * np.sin(k_w*(x+dx/2) + phi)\n", " f=np.zeros((3,Nx),dtype=\"float64\")\n", " fp=np.zeros((3,Nx),dtype=\"float64\")\n", " for k in range(0,3):\n", " f[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", " fp[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", " #----------------------------------------- Maind Loop --------------------------------------------------------\n", " for t in range(nt):\n", " #========================================= LBM - Solution =============================================\n", " #--------------------Collision----------------\n", " for k in range(0,3):\n", " fp[k,:]= f[k,:] - (f[k,:] - w[k]*(u[:]+cx[k]*(ce*u[:])/cs**2))/tau\n", " #-----------------streaming-------------------\n", " for k in range(0,3):\n", " f[k,:]=np.roll(fp[k,:], cx[k], axis=0)\n", " #----------------------Macro------------------\n", " u[:]=f[0,:]+f[1,:]+f[2,:]\n", " #---------------------save-field-cases--------------\n", " u_cases[case][:]=u[:]" ] }, { "cell_type": "code", "execution_count": 156, "id": "88da6481-ee3f-4bdc-bbaa-03857553c9c4", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#****************************************Data-Analysis*********************************************\n", "# ---------------- exact solution ----------------\n", "def u_exact(x, t, A, k_w, phi, c, nu):\n", " return A * np.exp(-nu * k_w**2 * t) * np.sin(k_w * ((x+dx/2) - c*t) + phi)\n", "u_ana = np.empty(cases, dtype=object) # array field used to same data over time\n", "xl = np.empty(cases, dtype=object) # array field used to same data over time\n", "for i in range(cases):\n", " Nx=Nx0[i] # Numerical Length\n", " x = np.linspace(0.0, L, Nx, endpoint=False,dtype=\"float64\") # Numerical Domain\n", " dx = L / Nx # Grid size\n", " r = r0[i] # dx/dt relation\n", " dt = dx/r\n", " nt = int(np.ceil(t_end / dt))\n", " xl[i] = np.linspace(0.0, L, Nx0[i], endpoint=False,dtype=\"float64\")\n", " u_ana[i] = np.zeros((Nx0[i]), dtype=\"float64\")\n", " u_ana[i] = u_exact(xl[i], nt*dt , A, k_w, phi, c, nu)\n", "# -----------------Plot Results --------------------\n", "plt.figure(figsize=(10,5))\n", "colors = plt.cm.viridis(np.linspace(0, 1, cases))\n", "for i in range(cases):\n", " plt.plot(xl[i], u_cases[i], \"s\", color=colors[i], lw=1, label=f\"LBM $Nx={Nx0[i]:.0f}$\",fillstyle='none')\n", " plt.plot(xl[i], u_ana[i], color=colors[i], lw=1, label=f\"Exact $t={t_end:.2f}$\")\n", "\n", "plt.xlabel(\"$x$\",fontsize=16)\n", "plt.ylabel(\"$u(x,t)$\",fontsize=16)\n", "plt.title(\"1D Convection-Diffusion: LBM vs Analytical Solution\")\n", "plt.grid(True, alpha=0.3)\n", "plt.legend(ncol=5,fontsize=9,loc=\"center left\",bbox_to_anchor=(0.0, 1.2))\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 108, "id": "a99b2836-bcf8-47c9-9c0f-b01b3572b4a4", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Erro0= 0.0007675056151646606\n", "Erro1= 4.5801886601000255e-05\n", "Erro2= 2.843695561303167e-06\n", "Erro3= 1.772197264107726e-07\n", "[-4.02508353 2.08310237]\n", "ltests[i] = np.array([1.00,0.33,4.03,0.0007675056151646606,4.5801886601000255e-05,2.843695561303167e-06,1.772197264107726e-07],dtype=\"float64\")\n" ] } ], "source": [ "Erro= np.zeros((cases), dtype=\"float64\")\n", "for i in range(cases):\n", " Erro[i]=np.sqrt(np.sum((u_cases[i]-u_ana[i])**2))/np.sqrt(np.sum((u_ana[i])**2))\n", " print(f'Erro{i}=',Erro[i])\n", "TEp=np.polyfit(np.log(Nx0), np.log(Erro), 1)\n", "print(TEp)\n", "print(f'ltests[i] = np.array([{1/tau:.2f},{cs**2:.2f},{-TEp[0]:.2f},{Erro[0]},{Erro[1]},{Erro[2]},{Erro[3]}],dtype=\"float64\")')" ] }, { "cell_type": "code", "execution_count": 104, "id": "1a5c5b3a-a578-4fb1-8d0b-9426b63dfd0e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "#------------------ List of teste cases ---------------------------\n", "ntests=7\n", "ltests = np.empty(ntests, dtype=object) # list [omega, cs**2, a, erro1, erro2, erro3]\n", "ltests[0] = np.array([1.00,0.33,4.03,0.0007675056151646606,4.5801886601000255e-05,2.843695561303167e-06,1.772197264107726e-07],dtype=\"float64\")\n", "ltests[1] = np.array([1.33,0.33,1.98,0.14172076082874474,0.03676563394470728,0.00926664086838909,0.0023217597555758216],dtype=\"float64\")\n", "ltests[2] = np.array([1.60,0.33,1.97,0.173048134806591,0.045658664282350235,0.011566406970317222,0.002901017675903232],dtype=\"float64\")\n", "ltests[3] = np.array([1.78,0.33,1.96,0.1806210735638166,0.04785433656697225,0.012139180249442527,0.003045785275804],dtype=\"float64\")\n", "ltests[4] = np.array([0.67,0.33,2.12,0.4515322151274699,0.09291589762687379,0.022049149483031594,0.005442330222168221],dtype=\"float64\")\n", "ltests[5] = np.array([0.40,0.33,2.19,2.5815332944176905,0.5537880973820454,0.11602188228229841,0.02759320543861061],dtype=\"float64\")\n", "ltests[6] = np.array([0.22,0.33,1.80,4.667938739917,2.687002267460583,0.5746533215752334,0.1219574567471747],dtype=\"float64\")" ] }, { "cell_type": "code", "execution_count": 154, "id": "11fcd4b0-141b-44b3-ad92-7580131f24b3", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "plt.figure(figsize=(7,4))\n", "plt.title(\"$Grid$ $Convergence$ $Test$\",fontsize=14)\n", "colors = plt.cm.viridis(np.linspace(0, 1, ntests-1))\n", "plt.loglog(1/Nx0,ltests[0][3:],'r--',fillstyle='none', label=f'$\\\\omega={ltests[0][0]}$ - $Slope={ltests[0][2]}$')\n", "for i in range(7)[1:]:\n", " plt.loglog(1/Nx0,ltests[i][3:],'--',color=colors[i],fillstyle='none', label=f'$\\\\omega={ltests[i][0]}$ - $Slope={ltests[i][2]}$')\n", " \n", "plt.loglog(1/Nx0,2.*1.0/(Nx0**2),'k-',fillstyle='none')\n", "plt.text(0.02, 0.001, \"$2nd-order$ $Slope$\", rotation=8,fontsize=12)\n", "plt.loglog(1/Nx0,1.*1.0/(Nx0**4),'k-',fillstyle='none')\n", "plt.text(0.02, 0.00000025, \"$4th-order$ $Slope$\", rotation=15,fontsize=12)\n", "# plt.ylim(0,0.01)\n", "plt.grid(True, alpha=0.3)\n", "# plt.legend(loc=2,ncol=3,fontsize=8.5)\n", "plt.legend(ncol=3,fontsize=9,loc=\"center left\",bbox_to_anchor=(0.0, 1.2))\n", "plt.ylabel('$E_{T}$',fontsize=16,rotation=0,horizontalalignment='right')\n", "plt.xlabel('$\\Delta x$',fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d255eb5d-0dba-4648-95e6-328b26ae26d9", "metadata": {}, "source": [ "## Extension for Higher-Dimensions and Anisotropy\n", "\n", "{cite:t}`suga2014accurate` also extend the approach for 2 and 3D cases considering anisotropic scenarios. Notice that different second order errors will appear with other dimensions:\n", "\n", "$$\n", "\\begin{array}{ll}\n", "1D-Isotropic: \\qquad & \\displaystyle\\frac{\\partial\\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} - \\textcolor{red} {\\frac{\\nu\\Delta_{x}^{2}}{2\\omega^{2}}\\left( a\\left(\\omega^{2} - 8 \\omega + 8 \\right) - \\frac{\\omega^{2} - 12\\omega + 12 }{6} \\right) \\frac{\\partial^{4}\\phi}{\\partial x^{4}} } + \\mathcal{O}(\\Delta x)^{4}\\\\\n", "2D-Isotropic: \\qquad & \\displaystyle\\frac{\\partial\\phi}{\\partial t} = \\nu\\left(\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\partial^{2}\\phi}{\\partial y^{2}}\\right) - \\textcolor{red} { \\Delta_{x}^{2} R1 \\left( \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\partial^{4}\\phi}{\\partial y^{4}} \\right) } - \\textcolor{red} { \\Delta_{x}^{2} R12 \\left( \\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial y^{2}} \\right) } + \\mathcal{O}(\\Delta x)^{4}\\\\\n", "2D-Anisotropic: \\qquad & \\displaystyle\\frac{\\partial\\phi}{\\partial t} = \\nu_{x}\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\nu_{y}\\frac{\\partial^{2}\\phi}{\\partial y^{2}} - \\textcolor{red} { \\Delta_{x}^{2} R1 \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\Delta_{x}^{2} R2\\frac{\\partial^{4}\\phi}{\\partial y^{4}} } - \\textcolor{red} { \\Delta_{x}^{2} R12 \\left( \\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial y^{2}} \\right) } + \\mathcal{O}(\\Delta x)^{4}\\\\\n", "3D-Isotropic: \\qquad & \\displaystyle\\frac{\\partial\\phi}{\\partial t} = \\nu\\left(\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\partial^{2}\\phi}{\\partial y^{2}} + \\frac{\\partial^{2}\\phi}{\\partial z^{2}}\\right) - \\textcolor{red} { \\Delta_{x}^{2} R1 \\left( \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\partial^{4}\\phi}{\\partial y^{4}} \\right) } - \\textcolor{red} { \\Delta_{x}^{2} R12 \\left( \\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial y^{2}} + \\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial z^{2}} + \\frac{\\partial^{4}\\phi}{\\partial y^{2}\\partial z^{2}} \\right) } + \\mathcal{O}(\\Delta x)^{4}\\\\\n", "3D-Anisotropic: \\qquad & \\displaystyle\\frac{\\partial\\phi}{\\partial t} = \\nu_{x}\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\nu_{y}\\frac{\\partial^{2}\\phi}{\\partial y^{2}} + \\nu_{z}\\frac{\\partial^{2}\\phi}{\\partial z^{2}} - \\textcolor{red} { \\Delta_{x}^{2} \\left( R1\\frac{\\partial^{4}\\phi}{\\partial x^{4}} + R2\\frac{\\partial^{4}\\phi}{\\partial y^{4}} + R3\\frac{\\partial^{4}\\phi}{\\partial y^{4}} \\right) } - \\textcolor{red} { \\Delta_{x}^{2} \\left( R12\\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial y^{2}} + R13\\frac{\\partial^{4}\\phi}{\\partial x^{2}\\partial z^{2}} + R23\\frac{\\partial^{4}\\phi}{\\partial y^{2}\\partial z^{2}} \\right) } + \\mathcal{O}(\\Delta x)^{4}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "id": "8d1d47c2-6390-4f6c-bb0e-69080c5cfec7", "metadata": {}, "source": [ "## Interpretation for Diffusive Equation in a MRT-Framework\n", "\n", "Extending the approach Developed above for now considering a sistems of multiple relaxatio time. The present development follow sequence presente in {cite:t}`lin2021multiple`." ] }, { "cell_type": "code", "execution_count": 3, "id": "149b4d11-4be7-4f5e-a871-a1e1f4b88e8e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "from pylab import *\n", "from sympy import *\n", "import numpy as np\n", "\n", "fic, f0c, f1c, f2c = symbols(['f_{i\\,x+c_{i}}^t','f_{0\\,x+c_{i}}^t','f_{1\\,x+c_{i}}^t','f_{2\\,x+c_{i}}^t'])\n", "f0tp1, f1tp1, f2tp1 = symbols(['f_{0\\,x}^{t+1}','f_{1\\,x}^{t+1}','f_{2\\,x}^{t+1}'])\n", "f0, f1, f2 = symbols(['f_{0\\,x}^t','f_{1\\,x}^t','f_{2\\,x}^t'])\n", "f0m1, f1m1, f2m1, f0p1, f1p1, f2p1 = symbols(['f_{0\\,x-1}^t','f_{1\\,x-1}^t','f_{2\\,x-1}^t','f_{0\\,x+1}^t','f_{1\\,x+1}^t','f_{2\\,x+1}^t'])\n", "f0m1t1, f1m1t1, f2m1t1, f0p1t1, f1p1t1, f2p1t1 = symbols(['f_{0\\,x-1}^{t-1}','f_{1\\,x-1}^{t-1}','f_{2\\,x-1}^{t-1}','f_{0\\,x+1}^{t-1}','f_{1\\,x+1}^{t-1}','f_{2\\,x+1}^{t-1}'])\n", "f0t1 = symbols('f_{0\\,x}^{t-1}')\n", "w0, w1, w2 = symbols(['w_0','w_1','w_2'])\n", "s0, s1, s2 = symbols(['s_0','s_1','s_2'])\n", "phi, phic, phim1, phip1 = symbols(['\\\\phi_{x}^{t}','\\\\phi_{x-c_{i}}^{t}','\\\\phi_{x-1}^{t}','\\\\phi_{x+1}^{t}'])\n", "phitp1, phit1, phit2= symbols(['\\\\phi_{x}^{t+1}','\\\\phi_{x}^{t-1}','\\\\phi_{x}^{t-2}'])\n", "phim1t1,phip1t1= symbols(['\\\\phi_{x-1}^{t-1}','\\\\phi_{x+1}^{t-1}'])\n", "cx=np.array([0,1,-1])\n", "wi=np.array([w0,w1,w2])\n", "wiM=Matrix([w0,w1,w2])\n", "fi=np.array([f0,f1,f2])\n", "fM = Matrix([f0,f1,f2])\n", "ficM = Matrix([f0c,f1c,f2c])\n", "feq=phi*wi\n", "feqM=Matrix([feq[0],feq[1],feq[2]])\n", "feqc=wiM*phic" ] }, { "cell_type": "code", "execution_count": 4, "id": "b6afef1d-1d5a-4d34-b61a-0d1c4213d67d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}1 & 1 & 1\\\\0 & 1 & -1\\\\-2 & 1 & 1\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ 1, 1, 1],\n", "[ 0, 1, -1],\n", "[-2, 1, 1]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m0=np.array([1,1,1])\n", "m1=cx\n", "m2=3*cx*cx - 2\n", "M=np.array([m0,m1,m2])\n", "MM=Matrix([m0,m1,m2])\n", "MM" ] }, { "cell_type": "code", "execution_count": 5, "id": "0b9787bf-cb37-4901-98bb-81024cef3171", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\phi_{x}^{t} \\left(w_{0} + w_{1} + w_{2}\\right)\\\\\\phi_{x}^{t} \\left(w_{1} - w_{2}\\right)\\\\\\phi_{x}^{t} \\left(- 2 w_{0} + w_{1} + w_{2}\\right)\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ \\phi_{x}^{t}*(w_0 + w_1 + w_2)],\n", "[ \\phi_{x}^{t}*(w_1 - w_2)],\n", "[\\phi_{x}^{t}*(-2*w_0 + w_1 + w_2)]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Meq=np.array([simplify(sum(feq*M[0])), simplify(sum(feq*M[1])), simplify(sum(feq*M[2]))])\n", "MeqM=Matrix([simplify(sum(feq*M[0])), simplify(sum(feq*M[1])), simplify(sum(feq*M[2]))])\n", "MeqM" ] }, { "cell_type": "code", "execution_count": 6, "id": "5992655c-6259-40fb-9dfa-68940c7ba2f0", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}s_{0} & 0 & 0\\\\0 & s_{1} & 0\\\\0 & 0 & s_{2}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[s_0, 0, 0],\n", "[ 0, s_1, 0],\n", "[ 0, 0, s_2]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "I=eye(3)\n", "S=np.array([I[0,:]*s0,I[1,:]*s1,I[2,:]*s2])\n", "SM=Matrix([I[0,:]*s0,I[1,:]*s1,I[2,:]*s2])\n", "SM" ] }, { "cell_type": "code", "execution_count": 7, "id": "a33d1281-add3-40f2-84e5-a6f5e583938b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{3} & 0 & - \\frac{1}{3}\\\\\\frac{1}{3} & \\frac{1}{2} & \\frac{1}{6}\\\\\\frac{1}{3} & - \\frac{1}{2} & \\frac{1}{6}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[1/3, 0, -1/3],\n", "[1/3, 1/2, 1/6],\n", "[1/3, -1/2, 1/6]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "MMinv=MM.inv()\n", "MMinv" ] }, { "cell_type": "code", "execution_count": 8, "id": "b350b626-5259-47ec-8452-ce6f79d588df", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{s_{0} \\left(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} - \\frac{s_{2} \\left(- 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3}\\\\\\frac{s_{0} \\left(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} + \\frac{s_{1} \\left(f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t\\right)}{2} + \\frac{s_{2} \\left(- 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{6}\\\\\\frac{s_{0} \\left(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} - \\frac{s_{1} \\left(f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t\\right)}{2} + \\frac{s_{2} \\left(- 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{6}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ s_0*(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 - s_2*(-2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3],\n", "[s_0*(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 + s_1*(f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t)/2 + s_2*(-2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/6],\n", "[s_0*(f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 - s_1*(f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t)/2 + s_2*(-2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/6]])" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(MMinv*(SM*(MM*(ficM))))" ] }, { "cell_type": "code", "execution_count": 9, "id": "577abd11-4499-4209-b4ca-ea531f1a0d1e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}f_{0,x+c_{i}}^t\\\\f_{1,x+c_{i}}^t\\\\f_{2,x+c_{i}}^t\\end{matrix}\\right] = \\left[\\begin{matrix}f_{0,x+c_{i}}^t - \\frac{s_{0} \\left(- \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} + \\frac{s_{2} \\left(2 \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} - 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3}\\\\f_{1,x+c_{i}}^t - \\frac{s_{0} \\left(- \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} - \\frac{s_{1} \\left(- \\phi_{x-c_{i}}^{t} w_{1} + \\phi_{x-c_{i}}^{t} w_{2} + f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t\\right)}{2} - \\frac{s_{2} \\left(2 \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} - 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{6}\\\\f_{2,x+c_{i}}^t - \\frac{s_{0} \\left(- \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{3} + \\frac{s_{1} \\left(- \\phi_{x-c_{i}}^{t} w_{1} + \\phi_{x-c_{i}}^{t} w_{2} + f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t\\right)}{2} - \\frac{s_{2} \\left(2 \\phi_{x-c_{i}}^{t} w_{0} - \\phi_{x-c_{i}}^{t} w_{1} - \\phi_{x-c_{i}}^{t} w_{2} - 2 f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t\\right)}{6}\\end{matrix}\\right]$" ], "text/plain": [ "Eq(Matrix([\n", "[f_{0,x+c_{i}}^t],\n", "[f_{1,x+c_{i}}^t],\n", "[f_{2,x+c_{i}}^t]]), Matrix([\n", "[ f_{0,x+c_{i}}^t - s_0*(-\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 + s_2*(2*\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 - 2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3],\n", "[f_{1,x+c_{i}}^t - s_0*(-\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 - s_1*(-\\phi_{x-c_{i}}^{t}*w_1 + \\phi_{x-c_{i}}^{t}*w_2 + f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t)/2 - s_2*(2*\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 - 2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/6],\n", "[f_{2,x+c_{i}}^t - s_0*(-\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 + f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/3 + s_1*(-\\phi_{x-c_{i}}^{t}*w_1 + \\phi_{x-c_{i}}^{t}*w_2 + f_{1,x+c_{i}}^t - f_{2,x+c_{i}}^t)/2 - s_2*(2*\\phi_{x-c_{i}}^{t}*w_0 - \\phi_{x-c_{i}}^{t}*w_1 - \\phi_{x-c_{i}}^{t}*w_2 - 2*f_{0,x+c_{i}}^t + f_{1,x+c_{i}}^t + f_{2,x+c_{i}}^t)/6]]))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PM=ficM-MMinv*(SM*(MM*(ficM-feqc)))\n", "display(Eq(ficM,PM))" ] }, { "cell_type": "code", "execution_count": 10, "id": "f1b59ed7-a7ce-4e42-9312-a9465010508d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x}^{t+1} = \\phi_{x}^{t} s_{2} w_{0} - f_{0,x}^t s_{2} + f_{0,x}^t$" ], "text/plain": [ "Eq(f_{0,x}^{t+1}, \\phi_{x}^{t}*s_2*w_0 - f_{0,x}^t*s_2 + f_{0,x}^t)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fp0=simplify(collect(PM[0].subs(phic,phi),phi).subs({f0c:f0,f1c:f1,f2c:f2}).subs({-w0-w1-w2:-1,f0+f1+f2:phi,f1+f2:-f0+phi,-w1-w2:-1+w0}))\n", "Eq(f0tp1,fp0)" ] }, { "cell_type": "code", "execution_count": 11, "id": "099a7744-170b-4785-9b6b-3076ffd4b291", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{1,x}^{t+1} = - \\frac{\\phi_{x-1}^{t} s_{2} w_{0}}{2} + \\frac{f_{0,x-1}^t s_{2}}{2} - \\frac{f_{1,x-1}^t s_{1}}{2} + f_{1,x-1}^t + \\frac{f_{2,x-1}^t s_{1}}{2}$" ], "text/plain": [ "Eq(f_{1,x}^{t+1}, -\\phi_{x-1}^{t}*s_2*w_0/2 + f_{0,x-1}^t*s_2/2 - f_{1,x-1}^t*s_1/2 + f_{1,x-1}^t + f_{2,x-1}^t*s_1/2)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fp1=simplify(collect(PM[1].subs(phic,phim1),phim1).subs({f0c:f0m1,f1c:f1m1,f2c:f2m1}).subs({-w0-w1-w2:-1,f0m1+f1m1+f2m1:phim1,-w1-w2:-1+w0}) \n", " .subs({f1m1+f2m1:phim1-f0m1,w1-w2:0}) )\n", "Eq(f1tp1,fp1)" ] }, { "cell_type": "code", "execution_count": 12, "id": "68a9f239-5c26-4f72-bbcd-87596968e68d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{2,x}^{t+1} = - \\frac{\\phi_{x+1}^{t} s_{2} w_{0}}{2} + \\frac{f_{0,x+1}^t s_{2}}{2} + \\frac{f_{1,x+1}^t s_{1}}{2} - \\frac{f_{2,x+1}^t s_{1}}{2} + f_{2,x+1}^t$" ], "text/plain": [ "Eq(f_{2,x}^{t+1}, -\\phi_{x+1}^{t}*s_2*w_0/2 + f_{0,x+1}^t*s_2/2 + f_{1,x+1}^t*s_1/2 - f_{2,x+1}^t*s_1/2 + f_{2,x+1}^t)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fp2=simplify(collect(PM[2].subs(phic,phip1),phip1).subs({f0c:f0p1,f1c:f1p1,f2c:f2p1}).subs({-w0-w1-w2:-1,f0p1+f1p1+f2p1:phip1,-w1-w2:-1+w0}) \n", " .subs({f1p1+f2p1:phip1-f0p1,w1-w2:0}) )\n", "Eq(f2tp1,fp2)" ] }, { "cell_type": "code", "execution_count": 13, "id": "1a4b349f-ff29-4e27-b788-29288e57b473", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x}^{t+1} = f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t + \\frac{s_{1} \\left(f_{1,x+1}^t - f_{1,x-1}^t - f_{2,x+1}^t + f_{2,x-1}^t\\right)}{2} + s_{2} w_{0} \\left(- \\frac{\\phi_{x+1}^{t}}{2} - \\frac{\\phi_{x-1}^{t}}{2} + \\phi_{x}^{t}\\right) + s_{2} \\left(\\frac{f_{0,x+1}^t}{2} + \\frac{f_{0,x-1}^t}{2} - f_{0,x}^t\\right)$" ], "text/plain": [ "Eq(\\phi_{x}^{t+1}, f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t + s_1*(f_{1,x+1}^t - f_{1,x-1}^t - f_{2,x+1}^t + f_{2,x-1}^t)/2 + s_2*w_0*(-\\phi_{x+1}^{t}/2 - \\phi_{x-1}^{t}/2 + \\phi_{x}^{t}) + s_2*(f_{0,x+1}^t/2 + f_{0,x-1}^t/2 - f_{0,x}^t))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "term1=collect(fp0+fp1+fp2,[w0*s2,s2,s1/2])\n", "Eq(phitp1,term1)" ] }, { "cell_type": "markdown", "id": "46cec5be-ad43-4aa8-a64f-ff94b281cd5e", "metadata": {}, "source": [ "Reinterpreting the above equation, we can derive\n", "\n", "$$\n", "f_{0,x}^{t}+f_{1,x+1}^{t}+f_{2,x-1}^{t}=\\phi^{t-1}_{x}\n", "$$(rel-f-1)" ] }, { "cell_type": "code", "execution_count": 14, "id": "334ed131-d105-4adb-9d30-fe8cb5bc2a5e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x}^{t+1} = f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t + \\frac{s_{1} \\left(\\phi_{x}^{t-1} - f_{0,x}^t - f_{1,x-1}^t - f_{2,x+1}^t\\right)}{2} + s_{2} w_{0} \\left(- \\frac{\\phi_{x+1}^{t}}{2} - \\frac{\\phi_{x-1}^{t}}{2} + \\phi_{x}^{t}\\right) + s_{2} \\left(\\frac{f_{0,x+1}^t}{2} + \\frac{f_{0,x-1}^t}{2} - f_{0,x}^t\\right)$" ], "text/plain": [ "Eq(\\phi_{x}^{t+1}, f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t + s_1*(\\phi_{x}^{t-1} - f_{0,x}^t - f_{1,x-1}^t - f_{2,x+1}^t)/2 + s_2*w_0*(-\\phi_{x+1}^{t}/2 - \\phi_{x-1}^{t}/2 + \\phi_{x}^{t}) + s_2*(f_{0,x+1}^t/2 + f_{0,x-1}^t/2 - f_{0,x}^t))" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "term2=collect(fp0+fp1+fp2,[w0*s2,s2,s1/2]).subs(f1p1,phit1-f0-f2m1).subs(f1p1,phit1-f0-f2m1)\n", "Eq(phitp1,term2)" ] }, { "cell_type": "markdown", "id": "7edc314d-bfea-4c15-96a1-f6d776850660", "metadata": {}, "source": [ "To repalce the term $f_{0,x}^{t}+f_{1,x-1}^{t}+f_{2,x+1}^{t}$, in the above equation we use the $\\sum_{i}f_{i,x}^{t}=\\phi_{x}^{t}$:" ] }, { "cell_type": "code", "execution_count": 15, "id": "e575a688-c042-4999-b367-7480e57d3dd5", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t = \\phi_{x+1}^{t} + \\phi_{x-1}^{t} - \\phi_{x}^{t-1} - f_{0,x+1}^t - f_{0,x-1}^t + 2 f_{0,x}^t$" ], "text/plain": [ "Eq(f_{0,x}^t + f_{1,x-1}^t + f_{2,x+1}^t, \\phi_{x+1}^{t} + \\phi_{x-1}^{t} - \\phi_{x}^{t-1} - f_{0,x+1}^t - f_{0,x-1}^t + 2*f_{0,x}^t)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rel2=(f0+f1m1+f2p1).subs(f1m1,phim1-f0m1-f2m1).subs(f2p1,phip1-f0p1-f1p1).subs(-f1p1-f2m1,f0-phit1)\n", "Eq(f0+f1m1+f2p1,rel2)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a7017119-893f-454d-85c2-2b24c78f5507", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x}^{t+1} = \\phi_{x+1}^{t} \\left(- \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + 1\\right) + \\phi_{x-1}^{t} \\left(- \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + 1\\right) + \\phi_{x}^{t-1} \\left(s_{1} - 1\\right) + \\phi_{x}^{t} s_{2} w_{0} + \\left(f_{0,x+1}^t + f_{0,x-1}^t - 2 f_{0,x}^t\\right) \\left(\\frac{s_{1}}{2} + \\frac{s_{2}}{2} - 1\\right)$" ], "text/plain": [ "Eq(\\phi_{x}^{t+1}, \\phi_{x+1}^{t}*(-s_1/2 - s_2*w_0/2 + 1) + \\phi_{x-1}^{t}*(-s_1/2 - s_2*w_0/2 + 1) + \\phi_{x}^{t-1}*(s_1 - 1) + \\phi_{x}^{t}*s_2*w_0 + (f_{0,x+1}^t + f_{0,x-1}^t - 2*f_{0,x}^t)*(s_1/2 + s_2/2 - 1))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "term3=collect(fp0+fp1+fp2,[w0*s2,s2,s1/2]).subs(f1p1,phit1-f0-f2m1).subs(f1p1,phit1-f0-f2m1).subs(-f0-f1m1-f2p1,-rel2)\n", "term4=collect(collect(expand(term3),[f0m1,f0,f0p1,phip1,phim1,phit1]).subs(f0*(-s1-s2+2),-2*f0*(s1/2+s2/2-1)),(s1/2+s2/2-1))\n", "Eq(phitp1,term4)" ] }, { "cell_type": "code", "execution_count": 17, "id": "31abf5fd-0469-461e-ab81-5ef87b278ccf", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x+1}^t + f_{0,x-1}^t - 2 f_{0,x}^t = - 2 \\phi_{x}^{t} + f_{0,x+1}^t + f_{0,x-1}^t + 2 f_{1,x}^t + 2 f_{2,x}^t$" ], "text/plain": [ "Eq(f_{0,x+1}^t + f_{0,x-1}^t - 2*f_{0,x}^t, -2*\\phi_{x}^{t} + f_{0,x+1}^t + f_{0,x-1}^t + 2*f_{1,x}^t + 2*f_{2,x}^t)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rel3=(-2*f0+f0m1+f0p1).subs(-2*f0,-2*phi + 2*f1+ 2*f2)\n", "Eq(-2*f0+f0m1+f0p1,rel3)" ] }, { "cell_type": "markdown", "id": "9e7c9c94-c3b9-457b-8f33-59c93fe18a5b", "metadata": {}, "source": [ "Replace the distribution functions in above relation by your collisional form" ] }, { "cell_type": "code", "execution_count": 18, "id": "97e2084c-de35-4c41-af9c-7b69be8afb66", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x+1}^t + f_{0,x-1}^t - 2 f_{0,x}^t = - 2 \\phi_{x}^{t} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} + 2 f_{1,x-1}^{t-1} + 2 f_{2,x+1}^{t-1} + s_{1} \\left(f_{1,x+1}^{t-1} - f_{1,x-1}^{t-1} - f_{2,x+1}^{t-1} + f_{2,x-1}^{t-1}\\right)$" ], "text/plain": [ "Eq(f_{0,x+1}^t + f_{0,x-1}^t - 2*f_{0,x}^t, -2*\\phi_{x}^{t} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} + 2*f_{1,x-1}^{t-1} + 2*f_{2,x+1}^{t-1} + s_1*(f_{1,x+1}^{t-1} - f_{1,x-1}^{t-1} - f_{2,x+1}^{t-1} + f_{2,x-1}^{t-1}))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rel3s1=collect(rel3.subs(f0p1,phip1t1*s2*w0-f0p1t1*s2+f0p1t1).subs(f0m1,phim1t1*s2*w0-f0m1t1*s2+f0m1t1).subs(f1,-phim1t1*s2*w0/2+f0m1t1*s2/2+f1m1t1+s1/2*(f2m1t1-f1m1t1)) \n", " .subs(f2,-phip1t1*s2*w0/2+f0p1t1*s2/2+f2p1t1+s1/2*(f1p1t1-f2p1t1)),s1)\n", "Eq(-2*f0+f0m1+f0p1,rel3s1)" ] }, { "cell_type": "markdown", "id": "58087138-b7ad-4b8e-a7e1-b7ab3e7dd4a7", "metadata": {}, "source": [ "Replacing in the above relation the terms $f_{1,x-1}^{t-1}$ and $f_{2,x+1}^{t-1}$ usgin Eq. {eq}`rel-f-1`:" ] }, { "cell_type": "code", "execution_count": 19, "id": "99e40163-494a-4300-9272-38fa61b12af2", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x+1}^t + f_{0,x-1}^t - 2 f_{0,x}^t = 2 \\phi_{x+1}^{t-1} + 2 \\phi_{x-1}^{t-1} - 2 \\phi_{x}^{t} - f_{0,x+1}^{t-1} - f_{0,x-1}^{t-1} - 2 f_{1,x+1}^{t-1} - 2 f_{2,x-1}^{t-1} + s_{1} \\left(- \\phi_{x+1}^{t-1} - \\phi_{x-1}^{t-1} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} + 2 f_{1,x+1}^{t-1} + 2 f_{2,x-1}^{t-1}\\right)$" ], "text/plain": [ "Eq(f_{0,x+1}^t + f_{0,x-1}^t - 2*f_{0,x}^t, 2*\\phi_{x+1}^{t-1} + 2*\\phi_{x-1}^{t-1} - 2*\\phi_{x}^{t} - f_{0,x+1}^{t-1} - f_{0,x-1}^{t-1} - 2*f_{1,x+1}^{t-1} - 2*f_{2,x-1}^{t-1} + s_1*(-\\phi_{x+1}^{t-1} - \\phi_{x-1}^{t-1} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} + 2*f_{1,x+1}^{t-1} + 2*f_{2,x-1}^{t-1}))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rel3s2=(rel3s1.subs(f1m1t1,phim1t1-f0m1t1-f2m1t1).subs(f2p1t1,phip1t1-f0p1t1-f1p1t1))\n", "display(Eq(-2*f0+f0m1+f0p1,rel3s2))" ] }, { "cell_type": "code", "execution_count": 20, "id": "ed9aa113-d5d9-4826-8551-5377db155a76", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle f_{0,x+1}^t + f_{0,x-1}^t - 2 f_{0,x}^t = - \\phi_{x+1}^{t-1} \\left(s_{1} - 2\\right) - \\phi_{x-1}^{t-1} \\left(s_{1} - 2\\right) - 2 \\phi_{x}^{t} + \\left(s_{1} - 1\\right) \\left(2 \\phi_{x}^{t-2} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} - 2 f_{0,x}^{t-1}\\right)$" ], "text/plain": [ "Eq(f_{0,x+1}^t + f_{0,x-1}^t - 2*f_{0,x}^t, -\\phi_{x+1}^{t-1}*(s_1 - 2) - \\phi_{x-1}^{t-1}*(s_1 - 2) - 2*\\phi_{x}^{t} + (s_1 - 1)*(2*\\phi_{x}^{t-2} + f_{0,x+1}^{t-1} + f_{0,x-1}^{t-1} - 2*f_{0,x}^{t-1}))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rel3s3=collect(simplify(collect(expand(rel3s2.subs(f2m1t1,phit2-f0t1-f1p1t1)),[f0p1t1,f0m1t1,2*f0t1,phim1t1,phip1t1,phit2])),[s1-1])\n", "display(Eq(-2*f0+f0m1+f0p1,rel3s3))" ] }, { "cell_type": "markdown", "id": "ab013b3f-596d-4d65-90fa-3bb050fe3b89", "metadata": {}, "source": [ "Replacing the above relation in $\\phi_{x}^{t+1}$ term:" ] }, { "cell_type": "code", "execution_count": 21, "id": "909f097e-bb79-466e-b11c-02a0f16f4822", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x}^{t+1} = \\phi_{x}^{t-1} \\left(s_{1} - 1\\right) - \\phi_{x}^{t} \\left(s_{1} - s_{2} w_{0} + s_{2} - 2\\right) + \\left(- \\frac{\\phi_{x+1}^{t-1}}{2} - \\frac{\\phi_{x-1}^{t-1}}{2}\\right) \\left(s_{1}^{2} + s_{1} s_{2} - 4 s_{1} - 2 s_{2} + 4\\right) + \\left(- \\frac{\\phi_{x+1}^{t}}{2} - \\frac{\\phi_{x-1}^{t}}{2}\\right) \\left(s_{1} + s_{2} w_{0} - 2\\right) + \\left(s_{1} - 1\\right) \\left(s_{1} + s_{2} - 2\\right) \\left(\\phi_{x}^{t-2} + \\frac{f_{0,x+1}^{t-1}}{2} + \\frac{f_{0,x-1}^{t-1}}{2} - f_{0,x}^{t-1}\\right)$" ], "text/plain": [ "Eq(\\phi_{x}^{t+1}, \\phi_{x}^{t-1}*(s_1 - 1) - \\phi_{x}^{t}*(s_1 - s_2*w_0 + s_2 - 2) + (-\\phi_{x+1}^{t-1}/2 - \\phi_{x-1}^{t-1}/2)*(s_1**2 + s_1*s_2 - 4*s_1 - 2*s_2 + 4) + (-\\phi_{x+1}^{t}/2 - \\phi_{x-1}^{t}/2)*(s_1 + s_2*w_0 - 2) + (s_1 - 1)*(s_1 + s_2 - 2)*(\\phi_{x}^{t-2} + f_{0,x+1}^{t-1}/2 + f_{0,x-1}^{t-1}/2 - f_{0,x}^{t-1}))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "term5=simplify(collect(expand(term4.subs(-2*f0+f0m1+f0p1,rel3s3)),[phim1,phip1,phim1t1,phip1t1,phit1,phit2,phi,f0p1t1,f0m1t1,f0t1]))\n", "term5s1=collect(term5,[s1*s1+s1*s2-3*s1-s2+2,s1+w0*s2-2,s1*s1+s1*s2-4*s1-2*s2+4]).subs(s1*s1+s1*s2-3*s1-s2+2,(s1-1)*(s1+s2-2))\n", "Eq(phitp1,term5s1)" ] }, { "cell_type": "markdown", "id": "af732d92-fb07-4ef7-9a01-c91b4e0baadc", "metadata": {}, "source": [ "Applying a shift in time for the Eq. XX." ] }, { "cell_type": "code", "execution_count": 32, "id": "30ee9264-bc08-49e6-a338-a6edc330f2c0", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x}^{t+1} = \\frac{\\phi_{x+1}^{t-1} s_{1} s_{2} w_{0}}{2} - \\frac{\\phi_{x+1}^{t-1} s_{1} s_{2}}{2} + \\frac{\\phi_{x+1}^{t-1} s_{1}}{2} - \\frac{\\phi_{x+1}^{t-1} s_{2} w_{0}}{2} + \\phi_{x+1}^{t-1} s_{2} - \\phi_{x+1}^{t-1} - \\frac{\\phi_{x+1}^{t} s_{1}}{2} - \\frac{\\phi_{x+1}^{t} s_{2} w_{0}}{2} + \\phi_{x+1}^{t} + \\frac{\\phi_{x-1}^{t-1} s_{1} s_{2} w_{0}}{2} - \\frac{\\phi_{x-1}^{t-1} s_{1} s_{2}}{2} + \\frac{\\phi_{x-1}^{t-1} s_{1}}{2} - \\frac{\\phi_{x-1}^{t-1} s_{2} w_{0}}{2} + \\phi_{x-1}^{t-1} s_{2} - \\phi_{x-1}^{t-1} - \\frac{\\phi_{x-1}^{t} s_{1}}{2} - \\frac{\\phi_{x-1}^{t} s_{2} w_{0}}{2} + \\phi_{x-1}^{t} - \\phi_{x}^{t-1} s_{1} s_{2} w_{0} + \\phi_{x}^{t-1} s_{1} + \\phi_{x}^{t-1} s_{2} w_{0} - \\phi_{x}^{t-1} + \\phi_{x}^{t-2} s_{1} s_{2} - \\phi_{x}^{t-2} s_{1} - \\phi_{x}^{t-2} s_{2} + \\phi_{x}^{t-2} + \\phi_{x}^{t} s_{2} w_{0} - \\phi_{x}^{t} s_{2} + \\phi_{x}^{t}$" ], "text/plain": [ "Eq(\\phi_{x}^{t+1}, \\phi_{x+1}^{t-1}*s_1*s_2*w_0/2 - \\phi_{x+1}^{t-1}*s_1*s_2/2 + \\phi_{x+1}^{t-1}*s_1/2 - \\phi_{x+1}^{t-1}*s_2*w_0/2 + \\phi_{x+1}^{t-1}*s_2 - \\phi_{x+1}^{t-1} - \\phi_{x+1}^{t}*s_1/2 - \\phi_{x+1}^{t}*s_2*w_0/2 + \\phi_{x+1}^{t} + \\phi_{x-1}^{t-1}*s_1*s_2*w_0/2 - \\phi_{x-1}^{t-1}*s_1*s_2/2 + \\phi_{x-1}^{t-1}*s_1/2 - \\phi_{x-1}^{t-1}*s_2*w_0/2 + \\phi_{x-1}^{t-1}*s_2 - \\phi_{x-1}^{t-1} - \\phi_{x-1}^{t}*s_1/2 - \\phi_{x-1}^{t}*s_2*w_0/2 + \\phi_{x-1}^{t} - \\phi_{x}^{t-1}*s_1*s_2*w_0 + \\phi_{x}^{t-1}*s_1 + \\phi_{x}^{t-1}*s_2*w_0 - \\phi_{x}^{t-1} + \\phi_{x}^{t-2}*s_1*s_2 - \\phi_{x}^{t-2}*s_1 - \\phi_{x}^{t-2}*s_2 + \\phi_{x}^{t-2} + \\phi_{x}^{t}*s_2*w_0 - \\phi_{x}^{t}*s_2 + \\phi_{x}^{t})" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "term6=simplify(expand(term5s1.subs( -f0t1+f0m1t1/2+f0p1t1/2, (phi-(phip1t1+phim1t1)*(1-s1/2-s2*w0/2) - phit2*(s1-1) - phit1*s2*w0)/(s1+s2-2) ) ))\n", "Eq(phitp1,term6)" ] }, { "cell_type": "code", "execution_count": 33, "id": "9e5c1272-ba84-46b9-9bf6-76ce12da63e1", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\phi_{x+1}^{t-1} \\left(\\frac{s_{1} s_{2} w_{0}}{2} - \\frac{s_{1} s_{2}}{2} + \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + s_{2} - 1\\right) + \\phi_{x+1}^{t} \\left(- \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + 1\\right) + \\phi_{x-1}^{t-1} \\left(\\frac{s_{1} s_{2} w_{0}}{2} - \\frac{s_{1} s_{2}}{2} + \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + s_{2} - 1\\right) + \\phi_{x-1}^{t} \\left(- \\frac{s_{1}}{2} - \\frac{s_{2} w_{0}}{2} + 1\\right) + \\phi_{x}^{t-1} \\left(- s_{1} s_{2} w_{0} + s_{1} + s_{2} w_{0} - 1\\right) + \\phi_{x}^{t-2} \\left(s_{1} s_{2} - s_{1} - s_{2} + 1\\right) + \\phi_{x}^{t} \\left(s_{2} w_{0} - s_{2} + 1\\right)$" ], "text/plain": [ "\\phi_{x+1}^{t-1}*(s_1*s_2*w_0/2 - s_1*s_2/2 + s_1/2 - s_2*w_0/2 + s_2 - 1) + \\phi_{x+1}^{t}*(-s_1/2 - s_2*w_0/2 + 1) + \\phi_{x-1}^{t-1}*(s_1*s_2*w_0/2 - s_1*s_2/2 + s_1/2 - s_2*w_0/2 + s_2 - 1) + \\phi_{x-1}^{t}*(-s_1/2 - s_2*w_0/2 + 1) + \\phi_{x}^{t-1}*(-s_1*s_2*w_0 + s_1 + s_2*w_0 - 1) + \\phi_{x}^{t-2}*(s_1*s_2 - s_1 - s_2 + 1) + \\phi_{x}^{t}*(s_2*w_0 - s_2 + 1)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "collect(term6,[phim1,phip1,phi,phim1t1,phip1t1,phit1,phit2])" ] }, { "cell_type": "markdown", "id": "630e1118-ae3e-4049-a1a4-75a408877f65", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Fourth-order MRT Diffusive Equation\n", "\n", "To recover the partial differetial equation with Fourth-order of convergence error, we expand each $\\phi$ term in Taylor series (this link provide a sympy code that reach the above equation {doc}`appendix/sympy-code-mrt-fdm-diffusive-expansion-4th`):\n", "\n", "$$\n", "0=\\frac{\\Delta_{t}^{2} \\left(- 3 s_{1} s_{2} + 2 s_{1} + 2 s_{2}\\right)}{2} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} + \\frac{\\Delta_{t} \\Delta_{x}^{2} \\left(s_{1} s_{2} w_{0} - s_{1} s_{2} + s_{1} - s_{2} w_{0} + 2 s_{2} - 2\\right)}{2} \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} + \\Delta_{t} s_{1} s_{2} \\frac{\\partial \\phi}{\\partial t} + \\frac{\\Delta_{x}^{4} s_{2} \\left(- s_{1} w_{0} + s_{1} + 2 w_{0} - 2\\right)}{24} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\Delta_{x}^{2} s_{2} \\left(- s_{1} w_{0} + s_{1} + 2 w_{0} - 2\\right)}{2} \\frac{\\partial^{2}\\phi}{\\partial x^{2}}\n", "$$" ] }, { "cell_type": "markdown", "id": "e0891eee-0d50-46e0-999f-b21ebc3a5ef1", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "$$\n", "\\Delta_{t} s_{1} s_{2} \\frac{\\partial \\phi}{\\partial t} = - \\frac{\\Delta_{x}^{2} s_{2} \\left(- s_{1} w_{0} + s_{1} + 2 w_{0} - 2\\right)}{2} \\frac{\\partial^{2}\\phi}{\\partial x^{2}} -\\frac{\\Delta_{t}^{2} \\left(- 3 s_{1} s_{2} + 2 s_{1} + 2 s_{2}\\right)}{2} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} - \\frac{\\Delta_{t} \\Delta_{x}^{2} \\left(s_{1} s_{2} w_{0} - s_{1} s_{2} + s_{1} - s_{2} w_{0} + 2 s_{2} - 2\\right)}{2} \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} - \\frac{\\Delta_{x}^{4} s_{2} \\left(- s_{1} w_{0} + s_{1} + 2 w_{0} - 2\\right)}{24} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "2134af24-6280-48dd-937c-452ac800905c", "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\phi}{\\partial t} = \\frac{\\Delta_{x}^{2} (1-w_{0})\\left(2 - s_{1}\\right)}{2\\Delta_{t} s_{1} } \\frac{\\partial^{2}\\phi}{\\partial x^{2}} - \\frac{\\Delta_{t} \\left(- 3 s_{1} s_{2} + 2 s_{1} + 2 s_{2}\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} - \\frac{\\Delta_{x}^{2} \\left(s_{1} s_{2} w_{0} - s_{1} s_{2} + s_{1} - s_{2} w_{0} + 2 s_{2} - 2\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} + \\frac{\\Delta_{x}^{4} (1-w_{0})\\left(2 - s_{1}\\right)}{24\\Delta_{t} s_{1}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "26823591-8eb9-4a1a-a7e2-5dca215f7565", "metadata": {}, "source": [ "Considering diffusive coeficient $\\nu=(1-w_{0})\\left(\\frac{1}{s_{1}} - \\frac{1}{2}\\right)\\frac{\\Delta_{x}^{2}}{\\Delta_{t}}$, we can rewrite the equation" ] }, { "cell_type": "markdown", "id": "823cb3fa-8be2-4020-96d8-e401317e5730", "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} -\\frac{\\Delta_{t} \\left(- 3 s_{1} s_{2} + 2 s_{1} + 2 s_{2}\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{2}\\phi}{\\partial t^{2}} - \\frac{ \\Delta_{x}^{2} \\left(s_{1} s_{2} w_{0} - s_{1} s_{2} + s_{1} - s_{2} w_{0} + 2 s_{2} - 2\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} + \\frac{\\nu\\Delta_{x}^{2}}{12} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "dbe5d967-dd10-4e3d-92fb-c53227b8e0a2", "metadata": {}, "source": [ "Using the relations:\n", "\n", "$$\n", "\\frac{\\partial\\phi}{\\partial t} = \\nu \\frac{\\partial^{2}\\phi}{\\partial x^{2}}, \\qquad \\frac{\\partial^{2}\\phi}{\\partial t^{2}} = \\nu^{2} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}, \\qquad \\frac{\\partial^{3}\\phi}{\\partial x^{2}\\partial t} = \\nu \\frac{\\partial^{4}\\phi}{\\partial x^{4}},\n", "$$" ] }, { "cell_type": "markdown", "id": "f023f08c-5bcd-41db-a9d8-c0bf21f0333b", "metadata": {}, "source": [ "we can reduce the equation in terms of $\\frac{\\partial^{4}\\phi}{\\partial x^{4}}$:\n", "\n", "$$\n", "\\frac{\\partial \\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} - \\frac{\\Delta_{x}^{2} (1-w_{0})\\left(2 - s_{1}\\right)}{2 s_{1} }\\frac{\\nu \\left(- 3 s_{1} s_{2} + 2 s_{1} + 2 s_{2}\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} - \\frac{ \\Delta_{x}^{2} \\nu \\left(s_{1} s_{2} w_{0} - s_{1} s_{2} + s_{1} - s_{2} w_{0} + 2 s_{2} - 2\\right)}{2 s_{1} s_{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} + \\frac{\\nu\\Delta_{x}^{2}}{12} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "be5882ae-4483-4da4-9db9-32f92823573a", "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\phi}{\\partial t} = \\nu\\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\Delta_{x}^{2} \\nu \\left(3 s_{1}^{2} s_{2} w_{0} - 2 s_{1}^{2} s_{2} - 6 s_{1}^{2} w_{0} - 18 s_{1} s_{2} w_{0} + 12 s_{1} s_{2} + 12 s_{1} w_{0} + 12 s_{2} w_{0} - 12 s_{2}\\right)}{12 s_{1}^{2} s_{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}}\n", "$$" ] }, { "cell_type": "markdown", "id": "c962db21-aadf-457d-99d7-006c9ad69c9a", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Making the term $\\left(3 s_{1}^{2} s_{2} w_{0} - 2 s_{1}^{2} s_{2} - 6 s_{1}^{2} w_{0} - 18 s_{1} s_{2} w_{0} + 12 s_{1} s_{2} + 12 s_{1} w_{0} + 12 s_{2} w_{0} - 12 s_{2}\\right)$ equal to zero e can reach fourth order approximation. For $w_{0}=2/3$ (weight specific from the lattice D1Q3) the relation reduce to $4s_{1}^{2} -8s_{1}+4s_{2}$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "d1a67854-570f-4ba9-9f1a-ccb1ff07db79", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "\n", "# ---- data ----\n", "s1r = np.linspace(0, 2.0, 1000)\n", "s2r = s1r*(2-s1r)\n", "\n", "plt.plot(s1r,s2r,'k--')\n", "plt.xlabel(r'$s_{1}$',fontsize=16)\n", "plt.ylabel(r'$s_{2}$',fontsize=16)\n", "plt.xlim(0,2)\n", "plt.ylim(0,1.05)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 72, "id": "d7c3fdcc-376f-403d-8f70-b427ef722068", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dx=6.2832e-01,\t dt=3.1416e-01\t nt=39,\t tn=12.25\n", "c_lbm=0.000,\t tau1=1.0000,\t tau2=1.0000\n", "s1=1.0000,\t s2=1.0000\n", "nt=39.000\t, nue=0.1667\n", "dx=3.1416e-01,\t dt=7.8540e-02\t nt=153,\t tn=12.02\n", "c_lbm=0.000,\t tau1=1.0000,\t tau2=1.0000\n", "s1=1.0000,\t s2=1.0000\n", "nt=153.000\t, nue=0.1667\n", "dx=1.5708e-01,\t dt=1.9635e-02\t nt=612,\t tn=12.02\n", "c_lbm=0.000,\t tau1=1.0000,\t tau2=1.0000\n", "s1=1.0000,\t s2=1.0000\n", "nt=612.000\t, nue=0.1667\n", "dx=7.8540e-02,\t dt=4.9087e-03\t nt=2445,\t tn=12.00\n", "c_lbm=0.000,\t tau1=1.0000,\t tau2=1.0000\n", "s1=1.0000,\t s2=1.0000\n", "nt=2445.000\t, nue=0.1667\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "A = 1.0 # Amplitude\n", "phi = 0.0 # Wave initial shift\n", "k_w = 1.0 # Wave number\n", "c = 0.0 # wave speed\n", "nu = 0.066666666666666666*np.pi # Diffusive coefficient\n", "m_waves = 1 # Wave Period\n", "L = m_waves * (2.0*np.pi / k_w) # Domain Lentgh\n", "t_end = 12.0 # Final time\n", "#--------------------------------------- Lattice-Properties-D1Q3 ----------------------------------------------\n", "w = np.array([4.0/6.0, 1.0/6.0, 1.0/6.0],dtype=\"float64\")\n", "cx = np.array([0, 1, -1],dtype=\"int16\") \n", "cs=1.0/np.sqrt(3.0);\n", "#--------------------------------- Initialization - Save Data Arrays -----------------------------------------------\n", "cases=4\n", "Nx0 = np.array([10, 20, 40, 80],dtype=\"int64\")\n", "r0 = 2**(0)*np.array([2.0**(1), 2.0**(2), 2.0**(3), 2.0**(4)],dtype=\"float64\")\n", "u_cases = np.empty(cases, dtype=object) # array field used to same data over time\n", "for i in range(cases):\n", " u_cases[i] = np.zeros((Nx0[i]), dtype=\"float64\")\n", "for case in range(0,cases):\n", " #------------------------------------- Parameters (numerical units) -------------------------------------------\n", " Nx=Nx0[case] # Numerical Length\n", " x = np.linspace(0.0, L, Nx, endpoint=False,dtype=\"float64\") # Numerical Domain\n", " dx = L / Nx # Grid size\n", " r = 1*r0[case] # dx/dt relation\n", " dt = dx/r\n", " ce = c/r\n", " nue = nu * dt / (dx*dx)\n", " tau1 = 0.5 + nue / cs**2\n", " tau2=1.0/((1.0/tau1)*(2.0-(1.0/tau1)))\n", " nt = int(np.ceil(t_end / dt))\n", " print(f\"dx={dx:.4e},\\t dt={dt:.4e}\\t nt={nt:d},\\t tn={nt*dt:.2f}\") # Print values for check\n", " print(f\"c_lbm={ce:.3f},\\t tau1={tau1:.4f},\\t tau2={tau2:.4f}\")\n", " print(f\"s1={1.0/tau1:.4f},\\t s2={1.0/tau2:.4f}\")\n", " print(f\"nt={nt:.3f}\\t, nue={nue:.4f}\")\n", " #--------------------------------- Initialization - LBM - Numerical Arrays -----------------------------------------\n", " u=np.zeros((Nx),dtype=\"float64\")\n", " u = A * np.sin(k_w*(x+dx/2) + phi)\n", " mx=np.zeros((Nx),dtype=\"float64\")\n", " mxx=np.zeros((Nx),dtype=\"float64\")\n", " f=np.zeros((3,Nx),dtype=\"float64\")\n", " feq=np.zeros((3,Nx),dtype=\"float64\")\n", " fp=np.zeros((3,Nx),dtype=\"float64\")\n", " for k in range(0,3):\n", " f[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", " fp[k,:]=w[k]*(u[:]+cx[k]*ce*u[:]/cs**2)\n", " #----------------------------------------- Init Loop --------------------------------------------------------\n", " for t in range(nt*10):\n", " #========================================= LBM - Solution =============================================\n", " #--------------------Collision----------------\n", " for k in range(0,3):\n", " feq[k,:]= w[k]*(u[:]+cx[k]*(ce*u[:])/cs**2)\n", " mx = np.einsum('i,ix->x', cx, f-feq)\n", " mxx = np.einsum('i,ix->x', 3.0*cx*cx-2.0, f-feq)\n", " for k in range(0,3):\n", " # fp[k,:]= f[k,:] - w[k]*( cx[k]*mx[:]/(tau1*cs**2) + (cx[k]**2-cs**2)*mxx[:]/(2.0*cs**2*tau2) )\n", " fp[k,:]= feq[k,:] + w[k]*( (1.0-1.0/tau1)*cx[k]*mx[:]/cs**2 + (1.0-1.0/tau2)*(cx[k]**2-cs**2)*mxx[:]/(2.0*cs**2) )\n", " #-----------------streaming-------------------\n", " for k in range(0,3):\n", " f[k,:]=np.roll(fp[k,:], cx[k], axis=0)\n", " #----------------------------------------- Maind Loop --------------------------------------------------------\n", " for t in range(nt):\n", " #========================================= LBM - Solution =============================================\n", " #--------------------Collision----------------\n", " for k in range(0,3):\n", " feq[k,:]= w[k]*(u[:]+cx[k]*(ce*u[:])/cs**2)\n", " mx = np.einsum('i,ix->x', cx, f-feq)\n", " mxx = np.einsum('i,ix->x', 3.0*cx*cx-2.0, f-feq)\n", " for k in range(0,3):\n", " # fp[k,:]= f[k,:] - w[k]*( cx[k]*mx[:]/(tau1*cs**2) + (cx[k]**2-cs**2)*mxx[:]/(2.0*cs**2*tau2) )\n", " fp[k,:]= feq[k,:] + w[k]*( (1.0-1.0/tau1)*cx[k]*mx[:]/cs**2 + (1.0-1.0/tau2)*(cx[k]**2-cs**2)*mxx[:]/(2.0*cs**2) )\n", " #-----------------streaming-------------------\n", " for k in range(0,3):\n", " f[k,:]=np.roll(fp[k,:], cx[k], axis=0)\n", " #----------------------Macro------------------\n", " # u[:]=f[0,:]+f[1,:]+f[2,:]\n", " u=np.einsum('ix->x', f)\n", " #---------------------save-field-cases--------------\n", " u_cases[case][:]=u[:]" ] }, { "cell_type": "code", "execution_count": 73, "id": "3a991843-a271-4b83-80a8-e1c2d8e84654", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#****************************************Data-Analysis*********************************************\n", "# ---------------- exact solution ----------------\n", "def u_exact(x, t, A, k_w, phi, c, nu):\n", " return A * np.exp(-nu * k_w**2 * t) * np.sin(k_w * ((x+dx/2) - c*t) + phi)\n", "u_ana = np.empty(cases, dtype=object) # array field used to same data over time\n", "xl = np.empty(cases, dtype=object) # array field used to same data over time\n", "for i in range(cases):\n", " Nx=Nx0[i] # Numerical Length\n", " x = np.linspace(0.0, L, Nx, endpoint=False,dtype=\"float64\") # Numerical Domain\n", " dx = L / Nx # Grid size\n", " r = r0[i] # dx/dt relation\n", " dt = dx/r\n", " nt = int(np.ceil(t_end / dt))\n", " xl[i] = np.linspace(0.0, L, Nx0[i], endpoint=False,dtype=\"float64\")\n", " u_ana[i] = np.zeros((Nx0[i]), dtype=\"float64\")\n", " u_ana[i] = u_exact(xl[i], nt*dt , A, k_w, phi, c, nu)\n", "# -----------------Plot Results --------------------\n", "plt.figure(figsize=(10,5))\n", "colors = plt.cm.viridis(np.linspace(0, 1, cases))\n", "for i in range(cases):\n", " plt.plot(xl[i], u_cases[i], \"s\", color=colors[i], lw=1, label=f\"LBM $Nx={Nx0[i]:.0f}$\",fillstyle='none')\n", " plt.plot(xl[i], u_ana[i], color=colors[i], lw=1, label=f\"Exact $t={t_end:.2f}$\")\n", "\n", "plt.xlabel(\"$x$\",fontsize=16)\n", "plt.ylabel(\"$u(x,t)$\",fontsize=16)\n", "plt.title(\"1D Convection-Diffusion: LBM vs Analytical Solution\")\n", "plt.grid(True, alpha=0.3)\n", "plt.legend(ncol=5,fontsize=9,loc=\"center left\",bbox_to_anchor=(0.0, 1.2))\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 74, "id": "15d4fbdf-e31e-41b1-b478-18ccb2c6ae41", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Erro0= 0.0007675056151644276\n", "Erro1= 4.580188660075553e-05\n", "Erro2= 2.84369556091393e-06\n", "Erro3= 1.7721972578567817e-07\n", "[-4.02508353 2.08310237]\n", "ltests[i] = np.array([1.00,0.33,4.03,0.0007675056151644276,4.580188660075553e-05,2.84369556091393e-06,1.7721972578567817e-07],dtype=\"float64\")\n" ] } ], "source": [ "Erro= np.zeros((cases), dtype=\"float64\")\n", "for i in range(cases):\n", " Erro[i]=np.sqrt(np.sum((u_cases[i]-u_ana[i])**2))/np.sqrt(np.sum((u_ana[i])**2))\n", " print(f'Erro{i}=',Erro[i])\n", "TEp=np.polyfit(np.log(Nx0), np.log(Erro), 1)\n", "print(TEp)\n", "print(f'ltests[i] = np.array([{1/tau1:.2f},{cs**2:.2f},{-TEp[0]:.2f},{Erro[0]},{Erro[1]},{Erro[2]},{Erro[3]}],dtype=\"float64\")')" ] }, { "cell_type": "code", "execution_count": 71, "id": "5488c916-018e-4f49-bc9d-6ced0f0bbd89", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "#------------------ List of teste cases ---------------------------\n", "ntests=7\n", "ltests = np.empty(ntests, dtype=object) # list [omega, cs**2, a, erro1, erro2, erro3]\n", "ltests[0] = np.array([1.00,0.33,4.03,0.0007675056151646606,4.5801886601000255e-05,2.843695561303167e-06,1.772197264107726e-07],dtype=\"float64\")\n", "ltests[1] = np.array([1.33,0.33,4.00,0.0005319361354470807,3.3129765953764316e-05,2.0679546121974942e-06,1.2921092318928152e-07],dtype=\"float64\")\n", "ltests[2] = np.array([1.60,0.33,4.08,5.860129798788711e-05,3.189703761917948e-06,1.931515584995748e-07,1.196493783881998e-08],dtype=\"float64\")\n", "ltests[3] = np.array([1.78,0.33,3.99,0.0002483413735518823,1.579458417941352e-05,9.910176963429327e-07,6.199383613392777e-08],dtype=\"float64\")\n", "ltests[4] = np.array([0.67,0.33,4.02,0.03555687087757651,0.002131864590352776,0.00013235766481817078,8.263390671807474e-06],dtype=\"float64\")\n", "ltests[5] = np.array([0.40,0.33,4.05,0.5815809299211789,0.03474238662797822,0.0020727393050372516,0.00012853963043932504],dtype=\"float64\")\n", "ltests[6] = np.array([0.22,0.33,3.64,3.3399608313842446,0.5520470158617199,0.031960605145718385,0.0019041931043053725],dtype=\"float64\")" ] }, { "cell_type": "code", "execution_count": 87, "id": "8e1d9d14-cdc0-4c93-ba1d-fca1e3f16f23", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "plt.figure(figsize=(7,4))\n", "plt.title(\"$Grid$ $Convergence$ $Test$\",fontsize=14)\n", "colors = plt.cm.viridis(np.linspace(0, 1, ntests))\n", "# plt.loglog(1/Nx0,ltests[0][3:],'r--',fillstyle='none', label=f'$\\\\omega={ltests[0][0]}$ - $Slope={ltests[0][2]}$')\n", "for i in range(7):\n", " plt.loglog(1/Nx0,ltests[i][3:],'--',color=colors[i],fillstyle='none', label=f'$\\\\omega_{1}={ltests[i][0]}$ - $Slope={ltests[i][2]}$')\n", " \n", "plt.loglog(1/Nx0,1.*200000.0/(Nx0**4),'k-',fillstyle='none')\n", "plt.text(0.02, 0.05, \"$4th-order$ $Slope$\", rotation=15,fontsize=12)\n", "# plt.ylim(0,0.01)\n", "plt.grid(True, alpha=0.3)\n", "# plt.legend(loc=2,ncol=3,fontsize=8.5)\n", "plt.legend(ncol=3,fontsize=9,loc=\"center left\",bbox_to_anchor=(0.0, 1.2))\n", "plt.ylabel('$E_{T}$',fontsize=16,rotation=0,horizontalalignment='right')\n", "plt.xlabel('$\\Delta x$',fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "13482706-a7bd-4b39-a862-67fb68664044", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Sixth-order MRT Diffusive Equation\n", "\n", "Extending up to Sixth-order of convergence error (this link provide a sympy code that reach the above equation {doc}`appendix/sympy-code-mrt-fdm-diffusive-expansion-6th`):\n", "\n", "$$\n", "\\frac{\\partial \\phi}{\\partial t} = \\nu \\frac{\\partial^{2}\\phi}{\\partial x^{2}} + \\frac{\\Delta_{x}^{2} \\nu R^{4th}}{12 s_{1}^{2} s_{2}} \\frac{\\partial^{4}\\phi}{\\partial x^{4}} - \\frac{\\Delta_{x}^{4} \\nu R^{6th} }{24 s_{1}^{3} s_{2}} \\frac{\\partial^{6}\\phi}{\\partial x^{6}},\n", "$$" ] }, { "cell_type": "markdown", "id": "21843987-e622-4ef9-ac48-c32d02a5ae57", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "where $R^{4th}$ and $R^{6th}$ are the terms in fouth and sixth-order error, respectively, given by:\n", "\n", "$$\n", "R^{4th}=\\left(3 s_{1}^{2} s_{2} w_{0} - 2 s_{1}^{2} s_{2} - 6 s_{1}^{2} w_{0} - 18 s_{1} s_{2} w_{0} + 12 s_{1} s_{2} + 12 s_{1} w_{0} + 12 s_{2} w_{0} - 12 s_{2}\\right)\n", "$$\n", "\n", "$$\n", "R^{6th}=\\left(7 s_{1}^{3} s_{2} w_{0}^{2} - 13 s_{1}^{3} s_{2} w_{0} + 6 s_{1}^{3} s_{2} - 6 s_{1}^{3} w_{0}^{2} + 12 s_{1}^{3} w_{0} - 5 s_{1}^{3} - 34 s_{1}^{2} s_{2} w_{0}^{2} + 67 s_{1}^{2} s_{2} w_{0} - 32 s_{1}^{2} s_{2} + 30 s_{1}^{2} w_{0}^{2} - 60 s_{1}^{2} w_{0} + 28 s_{1}^{2} + 52 s_{1} s_{2} w_{0}^{2} - 104 s_{1} s_{2} w_{0} + 52 s_{1} s_{2} - 48 s_{1} w_{0}^{2} + 96 s_{1} w_{0} - 48 s_{1} - 24 s_{2} w_{0}^{2} + 48 s_{2} w_{0} - 24 s_{2} + 24 w_{0}^{2} - 48 w_{0} + 24\\right)\n", "$$" ] }, { "cell_type": "markdown", "id": "d436a1eb-4929-41d0-b946-79a9af58d5c8", "metadata": {}, "source": [ "Making the term $\\left(3 s_{1}^{2} s_{2} w_{0} - 2 s_{1}^{2} s_{2} - 6 s_{1}^{2} w_{0} - 18 s_{1} s_{2} w_{0} + 12 s_{1} s_{2} + 12 s_{1} w_{0} + 12 s_{2} w_{0} - 12 s_{2}\\right)$ equal to zero e can reach fourth order approximation. For $w_{0}=2/3$ (weight specific from the lattice D1Q3) the relation reduce to $4s_{1}^{2} -8s_{1}+4s_{2}$:\n", "\n", "Trying to make both $R^{4th}$ and $R^{6th}$ null for lattice D1Q3 ($w_{0}=2/3$), we have the relation:\n", "\n", "$$\n", "R^{4th}=4s_{1}^{2} -8s_{1}+4s_{2}=0 \\qquad \\rightarrow \\qquad s_{2}=s_{1}(2-s_{1})\n", "$$\n", "\n", "$$\n", "R^{6th} = \\frac{s_{1}^{3}}{3} + \\frac{4 s_{1}^{2}}{3} - \\frac{16 s_{1}}{3} + s_{2} \\left(\\frac{4 s_{1}^{3}}{9} - \\frac{22 s_{1}^{2}}{9} + \\frac{52 s_{1}}{9} - \\frac{8}{3}\\right) + \\frac{8}{3}=0 \\qquad \\rightarrow \\qquad s_{2} = \\displaystyle\\frac{-\\left( \\frac{s_{1}^{3}}{3} + \\frac{4 s_{1}^{2}}{3} - \\frac{16 s_{1}}{3} + \\frac{8}{3}\\right) }{\\left(\\frac{4 s_{1}^{3}}{9} - \\frac{22 s_{1}^{2}}{9} + \\frac{52 s_{1}}{9} - \\frac{8}{3}\\right)} = \\frac{3(2-s_{1})(s_{1}^{2} +6s_{1} -4)}{2(2s_{1}^{3} - 11s_{1}^{2} + 26s_{1} - 12)}\n", "$$" ] }, { "cell_type": "code", "execution_count": 91, "id": "ae766c35-1fc3-4a00-96f7-1a40024d82c9", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "\n", "# ---- data ----\n", "s1r = np.linspace(0, 2.0, 1000)\n", "s2r4 = s1r*(2.0-s1r)\n", "\n", "s2r6 = (3.0*(2.0-s1r)*(s1r**2.0 + 6.0*s1r - 4.0))/(2.0*(2.0*s1r**3 - 11.0*s1r**2 + 26.0*s1r - 12.0))\n", "\n", "plt.plot(s1r,s2r4,'k--')\n", "plt.plot(s1r,s2r6,'r--')\n", "plt.xlabel(r'$s_{1}$',fontsize=16)\n", "plt.ylabel(r'$s_{2}$',fontsize=16)\n", "plt.xlim(0,2)\n", "plt.ylim(0,1.05)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "219a512d-d131-4065-8740-2e2e159bd3fc", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }