{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Aproximação\n", "\n", "Como aproximar um conjunto de dados usando uma sequência de funções simples?\n", "\n", " * Polinômios\n", " * Interpolação - Introdução\n", " * Interpolação de Lagrange\n", " * Método dos mínimos quadrados\n", " * Códigos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introdução\n", "\n", "Qual o objetivo?\n", "\n", " 1. Modelar dados experimentais\n", " 2. Aproximar uma função complexa usando funções mais simples\n", "\n", "Dada uma função $u(x)$ queremos aproximá-la usando um conjunto de funções que são, de alguma, forma convenientes:\n", "\n", "$$\n", "u \\approx u^\\delta (x) = \\sum_{i=1}^N \\hat{u}_i \\phi_i(x)\n", "$$\n", "\n", "\n", "Porque queremos fazer isso? \n", "\n", " * Funções muito complexas \n", " * Funções que não são conhecidas explicitamente (algumas funções especiais)\n", " * Queremos desempenho na hora de calcular as funções: praticamente todas as funções básicas são aproximadas utilizando polinômios (muitas vezes polinômios racionais)\n", " * Quando conhecemos apenas alguns pontos da função: sempre que você tiver um experimento ou estiver processando dados de uma sequência de simulações numéricas.\n", " \n", " \n", " \n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "# 12 methods for generic function sin:

sin(x::BigFloat) in Base.MPFR at mpfr.jl:744
sin(::Missing) in Base.Math at math.jl:1167
sin(a::Complex{Float16}) in Base.Math at math.jl:1115
sin(a::Float16) in Base.Math at math.jl:1114
sin(z::Complex{T}) where T in Base at complex.jl:805
sin(x::T) where T<:Union{Float32, Float64} in Base.Math at special/trig.jl:30
sin(x::Real) in Base.Math at special/trig.jl:53
sin(A::LinearAlgebra.Hermitian{#s663,S} where S<:(AbstractArray{#s664,2} where #s664<:#s663) where #s663<:Complex) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/symmetric.jl:907
sin(A::Union{LinearAlgebra.Hermitian{#s664,S}, LinearAlgebra.Symmetric{#s664,S}} where S where #s664<:Real) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/symmetric.jl:903
sin(D::LinearAlgebra.Diagonal) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/diagonal.jl:561
sin(A::AbstractArray{#s664,2} where #s664<:Real) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/dense.jl:826
sin(A::AbstractArray{#s664,2} where #s664<:Complex) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/dense.jl:833

" ], "text/plain": [ "# 12 methods for generic function \"sin\":\n", "[1] sin(x::BigFloat) in Base.MPFR at mpfr.jl:744\n", "[2] sin(::Missing) in Base.Math at math.jl:1167\n", "[3] sin(a::Complex{Float16}) in Base.Math at math.jl:1115\n", "[4] sin(a::Float16) in Base.Math at math.jl:1114\n", "[5] sin(z::Complex{T}) where T in Base at complex.jl:805\n", "[6] sin(x::T) where T<:Union{Float32, Float64} in Base.Math at special/trig.jl:30\n", "[7] sin(x::Real) in Base.Math at special/trig.jl:53\n", "[8] sin(A::LinearAlgebra.Hermitian{#s663,S} where S<:(AbstractArray{#s664,2} where #s664<:#s663) where #s663<:Complex) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/symmetric.jl:907\n", "[9] sin(A::Union{LinearAlgebra.Hermitian{#s664,S}, LinearAlgebra.Symmetric{#s664,S}} where S where #s664<:Real) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/symmetric.jl:903\n", "[10] sin(D::LinearAlgebra.Diagonal) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/diagonal.jl:561\n", "[11] sin(A::AbstractArray{#s664,2} where #s664<:Real) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/dense.jl:826\n", "[12] sin(A::AbstractArray{#s664,2} where #s664<:Complex) in LinearAlgebra at /opt/julia-1.4.1/share/julia/stdlib/v1.4/LinearAlgebra/src/dense.jl:833" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "methods(sin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpolação\n", "\n", "É lógico que, em geral, a aproximação é apenas uma aproximação! Então existe um erro:\n", "\n", "$$\n", "u(x) - u^\\delta(x) = \\varepsilon(x)\n", "$$\n", "\n", "A idéia é minimizar este erro de alguma forma.\n", "\n", "Uma possibilidade é escolher $N$ pontos $x_i$ e impor que o erro é zero nestes pontos:\n", "\n", "$$\n", "\\varepsilon(x_i) = 0 \\qquad i=1, \\ldots, N\n", "$$\n", "\n", "Esta abordagem é conhecida na literatura como colocação. Se a função $u(x)$ é conhecida apenas por alguns pontos $(x_i, u_i)$ isto é chamado de *interpolação*.\n", "\n", "Isto resulta num sistema de equações lineares:\n", "\n", "$$\n", "\\left(\\begin{matrix}\n", "\\phi_1(x_1) & \\phi_2(x_1) & \\cdots & \\phi_N(x_1) \\\\\n", "\\phi_1(x_2) & \\phi_2(x_2) & \\cdots & \\phi_N(x_2) \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "\\phi_1(x_N) & \\phi_2(x_N) & \\cdots & \\phi_N(x_N) \\\\\n", "\\end{matrix}\\right)\n", "\\cdot\\left(\\begin{matrix} \\hat{u}_1 \\\\ \\hat{u}_2 \\\\ \\vdots \\\\ \\hat{u}_N \\end{matrix}\n", "\\right)\n", "= \\left(\\begin{matrix} u(x_1) \\\\ u(x_2) \\\\ \\vdots \\\\ u(x_N) \\end{matrix}\n", "\\right)\n", "$$\n", "Esta é a matriz de Vandermonde.\n", "\n", "A escolha de funções $\\phi_i(x)$ adequadas simplificam a solução do problema. Se, por exemplo, $\\phi_i(x_k) = \\delta_{ik}$ onde $\\delta$, neste caso, é o delta de Kronecker, a matriz é diagonal.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mínimos quadrados\n", "Por outro lado, podemos, para uma sequência de pontos minimizar o erro quadrático total:\n", "\n", "$$\n", "R(\\hat{u}_1, \\ldots, \\hat{u}_N) = \\sum_{i=1}^Q \\left[ u(x_i) - u^\\delta(x_i)\\right]^2\n", "$$\n", "onde $Q$ é o número de pontos. Esta operação se chama método dos mínimos quadrados.\n", "\n", "Chamando $u(x_i) = u_i$, para minimizar este resíduo (erro quadrático total), basta derivar e igualar a zero, assim, chega-se ao seguinte sistema de equações lineares:\n", "\n", "$$\n", "\\left(\n", "\\begin{matrix}\n", "\\sum_{i=1}^Q \\phi_1(x_i)\\cdot\\phi_1(x_i) & \n", "\\cdots &\n", "\\sum_{i=1}^Q \\phi_1(x_i)\\cdot\\phi_N(x_i) \\\\\n", "\\sum_{i=1}^Q \\phi_2(x_i)\\cdot\\phi_1(x_i) & \n", "\\cdots &\n", "\\sum_{i=1}^Q \\phi_2(x_i)\\cdot\\phi_N(x_i) \\\\\n", "\\vdots & \\ddots & \\vdots \\\\\n", "\\sum_{i=1}^Q \\phi_N(x_i)\\cdot\\phi_1(x_i) & \n", "\\cdots &\n", "\\sum_{i=1}^Q \\phi_N(x_i)\\cdot\\phi_N(x_i) \\\\\n", "\\end{matrix}\\right)\n", "\\cdot\n", "\\left(\\begin{matrix} \\hat{u}_1 \\\\ \\hat{u}_2 \\\\ \\vdots \\\\ \\hat{u}_N \\end{matrix}\\right)\n", "= \n", "\\left(\\begin{matrix} \\sum_{i=1}^Q u_i \\phi_1(x_i) \\\\ \\sum_{i=1}^Q u_i \\phi_1(x_i) \\\\ \\vdots \\\\ \\sum_{i=1}^Q u_i \\phi_1(x_i)\\end{matrix}\\right)\n", "$$\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Uma formulação mais geral\n", "\n", "Uma formulação mais geral é escolher funções peso $w_k(x)$ de modo que\n", "$$\n", "\\int_a^b u(x)w_k(x)\\:dx = \\int_a^b u^\\delta (x) w_k(x) \\:dx\n", "$$\n", "\n", "Escolhendo $w_k(x)$ = $\\delta(x_k)$ (*Delta* de Dirac), recuperamos a interpolação. Escolhendo $w_k(x) = \\phi_k(x)$ temos o método de Galerkin, muito usado no método de elementos finitos.\n", "\n", "Com o método de elementos finitos, a função não necessariamente vai passar pelos pontos, mas o erro será minimizado e pode-se obter uma aproximação melhor.\n", "\n", "Outro ponto a ser considerador é o que ocorre quando as medidas possuem erro e como isso afeta a aproximação." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Polinômios\n", "\n", "$$\n", "p_n(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\ldots a_n x^n = \\sum_{i=0}^n a_i x^i\n", "$$\n", "Um polinômio é dado por seus coeficientes $a_i$.\n", "Em Julia, a indexação começa em 1, portanto é conveniente reescrever a definição acima como:\n", "\n", "$$\n", "p_n(x) = a_1 + a_2 x + a_3 x^2 + a_4 x^3 + \\ldots a_n x^{n-1} + a_{n+1} x^n = \\sum_{i=1}^{n+1} a_i x^{i-1}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "polyval1 (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function polyval1(a, x)\n", " n = length(a)\n", " \n", " y = 0.0\n", " for i in 1:n\n", " y += a[i] * x^(i-1)\n", " end\n", " \n", " return y\n", "end\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Método de Horner\n", "\n", "Maneira mais eficiente e mais precisa de calcular o valor de um polinômio:\n", "\n", "$$\n", "p_n(x) = a_1 + x\\left(a_2 + x\\left(a_3 + x\\left(\\ldots + a_{n+1} x\\right) \\right) \\right)\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "polyval2 (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function polyval2(a, x)\n", " \n", " y = a[end]\n", " \n", " for i = (lastindex(a)-1):-1:1\n", " y = a[i] + x * y\n", " end\n", " \n", " return y\n", " \n", "end\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "a1 = rand(3)\n", "a2 = rand(6)\n", "a3 = rand(15)\n", "a4 = rand(30);\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "using PyPlot" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "using BenchmarkTools" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = 0.5\n", "y1 = polyval1(a3, x)\n", "y2 = polyval2(a3, x)\n", "y1≈y2" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 53.656 ns (1 allocation: 16 bytes)\n", " 24.466 ns (1 allocation: 16 bytes)\n" ] }, { "data": { "text/plain": [ "1.3341605163233816" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@btime polyval1(a1, x)\n", "@btime polyval2(a1, x)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 103.634 ns (1 allocation: 16 bytes)\n", " 27.227 ns (1 allocation: 16 bytes)\n" ] }, { "data": { "text/plain": [ "0.7279395452223381" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@btime polyval1(a2, x)\n", "@btime polyval2(a2, x)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 244.759 ns (1 allocation: 16 bytes)\n", " 42.393 ns (1 allocation: 16 bytes)\n" ] }, { "data": { "text/plain": [ "0.8797525846941783" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@btime polyval1(a3, x)\n", "@btime polyval2(a3, x)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 476.799 ns (1 allocation: 16 bytes)\n", " 74.871 ns (1 allocation: 16 bytes)\n" ] }, { "data": { "text/plain": [ "0.1460046630356562" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "typeof(a3)\n", "@btime polyval1(a4, x)\n", "@btime polyval2(a4, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### E os tipos dos dados???" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7-element Array{Int64,1}:\n", " -3\n", " -1\n", " 5\n", " 4\n", " -3\n", " -4\n", " -4" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a5 = rand(-5:5, 7)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-385.0" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "polyval1(a5, 2)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-385.0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "polyval1(a5, 2.0)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-385.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "polyval2(a5, 2.0)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-385" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "polyval2(a5, 2)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4-element Array{Rational{Int64},1}:\n", " 1//2\n", " 2//3\n", " 3//4\n", " 4//5" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a6 = [1//2, 2//3, 3//4, 4//5]" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Variables\n", " #self#\u001b[36m::Core.Compiler.Const(polyval2, false)\u001b[39m\n", " a\u001b[36m::Array{Rational{Int64},1}\u001b[39m\n", " x\u001b[36m::Float64\u001b[39m\n", " y\u001b[91m\u001b[1m::Union{Rational{Int64}, Float64}\u001b[22m\u001b[39m\n", " @_5\u001b[33m\u001b[1m::Union{Nothing, Tuple{Int64,Int64}}\u001b[22m\u001b[39m\n", " i\u001b[36m::Int64\u001b[39m\n", "\n", "Body\u001b[91m\u001b[1m::Union{Rational{Int64}, Float64}\u001b[22m\u001b[39m\n", "\u001b[90m1 ─\u001b[39m %1 = Base.lastindex(a)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m (y = Base.getindex(a, %1))\n", "\u001b[90m│ \u001b[39m %3 = Main.lastindex(a)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %4 = (%3 - 1)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %5 = (%4:-1:1)\u001b[36m::Core.Compiler.PartialStruct(StepRange{Int64,Int64}, Any[Int64, Core.Compiler.Const(-1, false), Int64])\u001b[39m\n", "\u001b[90m│ \u001b[39m (@_5 = Base.iterate(%5))\n", "\u001b[90m│ \u001b[39m %7 = (@_5 === nothing)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m│ \u001b[39m %8 = Base.not_int(%7)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m└──\u001b[39m goto #4 if not %8\n", "\u001b[90m2 ┄\u001b[39m %10 = @_5::Tuple{Int64,Int64}\u001b[36m::Tuple{Int64,Int64}\u001b[39m\n", "\u001b[90m│ \u001b[39m (i = Core.getfield(%10, 1))\n", "\u001b[90m│ \u001b[39m %12 = Core.getfield(%10, 2)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %13 = Base.getindex(a, i)\u001b[36m::Rational{Int64}\u001b[39m\n", "\u001b[90m│ \u001b[39m %14 = (x * y)\u001b[36m::Float64\u001b[39m\n", "\u001b[90m│ \u001b[39m (y = %13 + %14)\n", "\u001b[90m│ \u001b[39m (@_5 = Base.iterate(%5, %12))\n", "\u001b[90m│ \u001b[39m %17 = (@_5 === nothing)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m│ \u001b[39m %18 = Base.not_int(%17)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m└──\u001b[39m goto #4 if not %18\n", "\u001b[90m3 ─\u001b[39m goto #2\n", "\u001b[90m4 ┄\u001b[39m return y\n" ] } ], "source": [ "@code_warntype polyval2(a6, 0.5)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "polyval3 (generic function with 1 method)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function polyval3(a::Vector{T}, x::S) where {T,S}\n", " R = promote_type(T,S)\n", " \n", " y = convert(R, a[end])\n", " \n", " for i = (lastindex(a)-1):-1:1\n", " y = a[i] + x * y\n", " end\n", " \n", " return y\n", " \n", "end\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Variables\n", " #self#\u001b[36m::Core.Compiler.Const(polyval3, false)\u001b[39m\n", " a\u001b[36m::Array{Rational{Int64},1}\u001b[39m\n", " x\u001b[36m::Float64\u001b[39m\n", " R\u001b[36m::Type{Float64}\u001b[39m\n", " y\u001b[36m::Float64\u001b[39m\n", " @_6\u001b[33m\u001b[1m::Union{Nothing, Tuple{Int64,Int64}}\u001b[22m\u001b[39m\n", " i\u001b[36m::Int64\u001b[39m\n", "\n", "Body\u001b[36m::Float64\u001b[39m\n", "\u001b[90m1 ─\u001b[39m (R = Main.promote_type($(Expr(:static_parameter, 1)), $(Expr(:static_parameter, 2))))\n", "\u001b[90m│ \u001b[39m %2 = R::Core.Compiler.Const(Float64, false)\u001b[36m::Core.Compiler.Const(Float64, false)\u001b[39m\n", "\u001b[90m│ \u001b[39m %3 = Base.lastindex(a)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %4 = Base.getindex(a, %3)\u001b[36m::Rational{Int64}\u001b[39m\n", "\u001b[90m│ \u001b[39m (y = Main.convert(%2, %4))\n", "\u001b[90m│ \u001b[39m %6 = Main.lastindex(a)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %7 = (%6 - 1)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %8 = (%7:-1:1)\u001b[36m::Core.Compiler.PartialStruct(StepRange{Int64,Int64}, Any[Int64, Core.Compiler.Const(-1, false), Int64])\u001b[39m\n", "\u001b[90m│ \u001b[39m (@_6 = Base.iterate(%8))\n", "\u001b[90m│ \u001b[39m %10 = (@_6 === nothing)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m│ \u001b[39m %11 = Base.not_int(%10)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m└──\u001b[39m goto #4 if not %11\n", "\u001b[90m2 ┄\u001b[39m %13 = @_6::Tuple{Int64,Int64}\u001b[36m::Tuple{Int64,Int64}\u001b[39m\n", "\u001b[90m│ \u001b[39m (i = Core.getfield(%13, 1))\n", "\u001b[90m│ \u001b[39m %15 = Core.getfield(%13, 2)\u001b[36m::Int64\u001b[39m\n", "\u001b[90m│ \u001b[39m %16 = Base.getindex(a, i)\u001b[36m::Rational{Int64}\u001b[39m\n", "\u001b[90m│ \u001b[39m %17 = (x * y)\u001b[36m::Float64\u001b[39m\n", "\u001b[90m│ \u001b[39m (y = %16 + %17)\n", "\u001b[90m│ \u001b[39m (@_6 = Base.iterate(%8, %15))\n", "\u001b[90m│ \u001b[39m %20 = (@_6 === nothing)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m│ \u001b[39m %21 = Base.not_int(%20)\u001b[36m::Bool\u001b[39m\n", "\u001b[90m└──\u001b[39m goto #4 if not %21\n", "\u001b[90m3 ─\u001b[39m goto #2\n", "\u001b[90m4 ┄\u001b[39m return y\n" ] } ], "source": [ "@code_warntype polyval3(a6, 0.5)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 30.833 ns (1 allocation: 32 bytes)\n" ] }, { "data": { "text/plain": [ "1.0428333333333333 + 0.39693333333333336im" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@btime polyval2(a6, 0.5+0.2im)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 28.239 ns (1 allocation: 32 bytes)\n" ] }, { "data": { "text/plain": [ "1.0428333333333333 + 0.39693333333333336im" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@btime polyval3(a6, 0.5+0.2im)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomials.jl" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "using Polynomials" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1 + 2∙z + 3∙z²" ], "text/latex": [ "$1 + 2\\cdot z + 3\\cdot z^{2}$" ], "text/plain": [ "Polynomial(1 + 2*z + 3*z^2)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = Polynomial([1,2,3], :z)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Polynomial{Int64}" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "typeof(p)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17//16 - 15//4*im" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p(1//2 + 3//4im)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2-element Array{Complex{Float64},1}:\n", " -0.3333333333333333 - 0.4714045207910317im\n", " -0.3333333333333333 + 0.4714045207910317im" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roots(p)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1 + 2∙x" ], "text/latex": [ "$1 + 2\\cdot x$" ], "text/plain": [ "Polynomial(1 + 2*x)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p2 = Polynomial([1,2]) # Raízes" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1-element Array{Float64,1}:\n", " -0.5" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roots(p2)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1.0∙z + 1.0∙z² + 1.0∙z³" ], "text/latex": [ "$1.0\\cdot z + 1.0\\cdot z^{2} + 1.0\\cdot z^{3}$" ], "text/plain": [ "Polynomial(1.0*z + 1.0*z^2 + 1.0*z^3)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(p)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "2.0 + 6.0∙z" ], "text/latex": [ "$2.0 + 6.0\\cdot z$" ], "text/plain": [ "Polynomial(2.0 + 6.0*z)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "derivative(p)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "degree(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Macro quando os coeficientes são conhecidos" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.75" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@evalpoly(0.5, 1, 2, 3)\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ ":(Base.Math.evalpoly(0.5, (1, 2, 3)))" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@macroexpand @evalpoly(0.5, 1, 2, 3)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.75" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "evalpoly(0.5, [1,2,3])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Interpolação\n", "\n", "Dado um conjunto de n pontos $(x_i, y_i)$, qual o poliômio que passa por todos?\n", "\n", "$$\n", "y_i = a_0 + a_1 x_i + a_2 x_i^2 + \\ldots a_n x_i^n \\qquad i=1, \\ldots, m\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Vandermonde\n", "\n", "Com n+1 pontos distintos, se o polinômio for de grau n, pode-se montar o seguinte sistema linear:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "1 & x_0 & x_0^2 & \\cdots & x_0^n \\\\\n", "1 & x_1 & x_1^2 & \\cdots & x_1^n \\\\\n", "\\vdots & \\vdots & \\vdots & \\ddots & \\vdots\\\\\n", "1 & x_n & x_n^2 & \\cdots & x_n^n\\\\\n", "\\end{bmatrix}\\cdot\n", "\\left\\{ \\begin{matrix} a_0 \\\\ a_1 \\\\ \\vdots \\\\ a_n\\\\ \\end{matrix}\\right\\}\n", "= \\left\\{\\begin{matrix} y_0 \\\\ y_1 \\\\ \\vdots \\\\ y_n\\\\\\end{matrix}\\right\\}\n", "$$\n", "\n", "Mas esta é uma operação cara, $\\mathcal{O}(n^3)$!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outra possibilidade\n", "\n", "$$\n", "y = f(x) \\approx a_0 + a_1(x-x_0) + a_2(x-x_0)(x-x_1) + \\cdots + a_n(x-x_0)(x-x_1)\\cdots(x - x_{n-1})\n", "$$\n", "\n", "Com isso chegamos ao seguinte sistema linear triangular:\n", "$$\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 &\\cdots & 0\\\\\n", "1 & (x_1-x_0) & 0 & 0 & \\cdots & 0\\\\\n", "1 & (x_2 - x_0) & (x_2 - x_0)(x_2 - x_1) & 0 & \\cdots & 0\\\\\n", "\\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots\\\\\n", "1 & (x_n - x_0) & (x_n - x_0)(x_n - x_1) & (x_n - x_0)(x_n - x_1)(x_n-x_2) & \\cdots &(x_n-x_0)(x_n-x_1)\\cdots(x_n-x_{n-1})\\\\\n", "\\end{bmatrix}\\cdot\\left\\{\\begin{matrix} a_0\\\\ a_1 \\\\ a_2 \\\\ \\vdots \\\\ a_n\\end{matrix}\\right\\} = \n", "\\left\\{\\begin{matrix} y_0\\\\ y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n\\end{matrix}\\right\\}\n", "$$\n", "\n", "Resolver este sistema é muito mais barato: $\\mathcal{O}(n^2)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpolação de Lagrange:\n", "\n", "$$\n", "y(x) = \\sum_{i=1}^n y_i h_i(x)\n", "$$\n", "\n", "onde $h_i(x)$ é o interpolador de Lagrange:\n", "\n", "$$\n", "h_k(x) = \\prod_{i=1\\ldots n,}^n \\frac{x - x_i}{x_k - x_i} \\qquad i\\ne k\n", "$$\n", "\n", "Propriedade:\n", "$$\n", "h_i(x_i) = \\delta_{ij} \\quad \\text{onde} \\quad \\delta_{ij} = \\left\\{\\begin{matrix}1, \\: i=j \\\\ 0, i\\ne j\\\\ \\end{matrix}\\right.\n", "$$" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lagrange1 (generic function with 1 method)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function lagrange1(k, z, x)\n", " \n", " h = 1.0\n", " \n", " n = length(z)\n", " \n", " for i = 1:n\n", " if i != k\n", " h *= (x - z[i]) / (z[k] - z[i])\n", " end\n", " end\n", " \n", " return h\n", "end\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lagrange2 (generic function with 1 method)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function lagrange2(k, z, x)\n", " \n", " h = 1.0\n", " n = length(z)\n", " for i = 1:(k-1)\n", " h *= (x - z[i]) / (z[k] - z[i])\n", " end\n", " \n", " for i = (k+1):n\n", " h *= (x - z[i]) / (z[k] - z[i])\n", " end\n", " return h\n", "end" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.0:0.005:1.0" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N = 10\n", "x = range(-1.0, 1.0, step=0.2)\n", "#x = [cos(k*π/N) for k in 0:N]\n", "xx = range(-1.0, 1.0, step=0.005)\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "hh = [lagrange2.(k, Ref(x), xx) for k in 1:length(x)];" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "image/png": 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Q35/SWy8LIYRIXYkVM8Ul9PT00Nvbi6IolJWVnfK1ubm5AHi9Xkw2ByCrZs4I/QMzIrX6tsvWGaeOPAHsZ+mBSP+2DzCazGQW6GkxWTkjhBBiLOJdVbOKSzh69CigL821Wq2nfK3NZiM9Xe/E6lf1zLz0ETkD+PuOdVUdc0Zkzx7UQCCxJ4AUrAohhBgLd2xqJruoNDEtM23atBG/Pp4V6Q+FAAj2+4hGwuM7yHEggcgA/fFVM0YTam8vKAqWEX7TzWVlGPNyIRwmsGfPoDoRIYQQYjTCwQB9nR2AnhGpr9c3Uh1LINLr6Tu230wKZkUkEBkg6PMCYPLpG9iZi4sH7bh7Moqi4Fh2FgD9H2wnO1ZcFE+tCSGEECMV7x9iS3eimC10den1hqWlpSM+RzwQ6ezqwhqbpgnEPudSiQQiAwS8fQAYevWI0TKCyuSBHLE6Ef+2bYkNiuLFRkIIIcRIuRMrZkpoaorVimRlnbDb7snEA5Guri7s8UAk9jmXSiQQGSAeKRpjq2fMZSOPPAHs8YzI9u1kFurFql53F6GAfxxHKYQQ4sOuO7HHTGkiEBlNNgT0wAWgp6cHS1o8I+Ibx1GODwlEBkhkRLq6AbDEOtONlG1uJYrDgerxYGhtS+x42NPaMr4DFUII8aE2MCMS30W3ZJSfSa5YI7NwOIw5Te/EKhmRFKaqUYKxSFFpawf0GpHRUEwm7IsWAeDfvmPA9EzjOI5UCCHEh11i6W5RcSIQGW1GxGQyJZbwKja93lECkRQW7O9P/FlpaQXAPMroE8C+UN+pN7B3byIQkYJVIYQQI6VpWqK+0OTMxO/3D9rIbjQyMzMBUC1675HgVC5Wve+++1AUhW984xsTdclRiUeJFpsdta0NGFsgYqvSd+oN7NlDVnE8EGkep1EKIYT4sPN1uwkH/CgGA55YD5DCwkJMJtOozxUPRKJG/bV+7xQNRLZs2cJvfvMbFsWmLVJRPBCx2uygaShWK8acnFGfx161QD9fTQ2ZufnAsf0ChBBCiFOJZ0Nc+QW0xDL0o52WiYsHImFNAabo1IzX6+Wmm27it7/9baKCNxUFY1GixWwG9PoQRVFGfR5TcTHGrCwIh0kP6R3suluaZfM7IYQQI9LdEuuoWlw65kLVuHggEoyq+n+n4tTM2rVrueqqq7j00ktPeWwwGMTj8Qz6mij+2DfHEgs+xjItA3pjs/j0jKW5FRSFYL+P/t7U3GxICCFEaklkRAqLaW0dn4yIP3ZjPOUyIk888QQffPAB995774iOv/fee3G5XImvkewwOF7iGRFzVM9cjHbFzEC22PRMuLqajPj0jBSsCiGEGIH4dL7JlU00GsVms415RiG+hNfn1/tZTanOqg0NDXz961/n0UcfxWazjeg1d999N729vYmvhoaJ26clHiWaIxEATIUFYz6XPVGwupdsKVgVQggxCu7YjWvIpJcKFBUVjalUACAjQ+9nFY5E0AwGAilYrDr6EtwR2rZtG+3t7SyL7UoLEI1GWb9+Pb/85S8JBoMYjcZBr7FarSPa3jgZAj49EDEFgvp/8/LGfK741Ezw0CEyP3YZIL1EhBBCnFokHMbTrvey8oX1G+OioqIxn89qtWKxWAiFQmgmMwGfF01VUQyp070jaYHIJZdcwu7duwc99vnPf565c+fy3e9+94QgZLIFvHozM1O/nr4y5+eP+Vym/HyMeblEOzpxKvr7lIyIEEKIU+lpbUbTVCx2Bx1dbuD0AhEAp9NJV1cXqsmMIRQk6O/HFmv5ngqSFog4nU6qYpmBuLS0NHJyck54PBXEMyJGTywzchqBiKIo2BdU4X3rLewePQ0mNSJCCCFOJb7HTFZxCUdjPa3G0shsoHggYrA5oN9LwOtNqUAkdXIzkyw+b5YIRE5jagbAtkAvWLU16vvM9LS2oEajp3VOIYQQH27xaXx7fpG+R4zZTM4YeloNFG/zbnCk5g68ScuIDOWtt96ayMuNSrA/NjUTiYLRiDE7+7TOZ5s/DwBDbS2mNAuRcAhPR3tiV14hhBDiePFAREl3QU8/hYWFGE6znsPp1De8U6w2NI593qUKyYjEhPz6XjPmqIopL++0C3mslXMBCB86nAg+3C1SsCqEEGJ48amZgStmTlc8ENFMFv3c/v6THT7hJBCJSWREVPW06kPizCXFGJxOtHAYl1Nfx93dLAWrQgghhqZpWuKGtS+g7zEznoGIGlskMnCT11QggQj6Nz8UWy1jimVETpeiKNgqKwFIV/S/ZilYFUIIMRy/p5egz4emKHT16N24T7dQFY4FIpHYZ1FIpmZSTzjgR9P0PvzmqIop//QDEQDrXH16xuHVo89umZoRQggxjHh9SFp+EYFAAKPRSN443BjHA5FwbMszyYikoGBsvkwBDJo2LhkRANtcPSNia9Wb07ill4gQQohhxPeYsebrWZD8/HxMptNfU5KYmtE0NIMh8ZmXKiQQAUKx6NCsGFAAU27uuJzXOldfOWM5fAQAb1cn4UBgXM4thBDiwyUxfZ+mt2UvKBj7ViMDWSwWzLGd5TWjWaZmUlGiUFXT81am01y6G2edPUtfCtzlTjSP6W6VrIgQQogTxadmwkY9CzJegQjoDUUBNJNJpmZSUTwjYoroDcdOt4dInMFqxTK9AgCXU49wpWBVCCHEUOJLd71BfcXMeBSqxjkcDgA0o0mW76ai+HyZKRTW/ztOgQiALTY9k46+bEo2vxNCCHG8aCRCb3srmsFAn0//TMofh1YScfGMiGoyS0OzVJSYmontdDheGRE4VrCa5ouvnJGpGSGEEIP1treiRqN6R1X0AtN48DAeElMzRpmaSUnxb4pJVcFsxhCrMB4P8YJVW1sHIFMzQgghTpRYMZOnT8eMZ30IHDc1IxmR1BOfLzNFVUxZWSiKMm7njmdErA36D1l3cxNarChWCCGEAOiO7zET68Q93oHIsWJVM0G/f1zPfbokEOHY1Iw5qo7rtAzoS4GNubk4gmFAIdjvo7+3Z1yvIYQQ4swWz4gkY8UMDJ6aCQf8qGrq7AYvgQgDVs1EVUzZWeN+ftvcuRg1jXSH/oMg0zNCCCEGcjc3ogHeoL5oImlTM7EGafFtTVKBBCIMrhExZueM+/nj0zNOg6ycEUIIcaLu5kY0s4VINIrRaCR3nBprxg2cmoHU2oFXAhEg5I+tmomqGJOQEbFW6nvOpHn1CDSeghNCCCH83j78fR6iVj1rkZeXhzG2U+54OTY1Y0aDlFrCK4EIxzIi5qg6rj1E4mzz9EDE1h5bOSMZESGEEDHxzwRTlp6RH+9pGTg2NYOigMEggUiqSfQRUce/WBXAUlGBYrHg6NOvIzUiQggh4uJZckN6clbMwIn7zaRSLxEJRIBQbCmTKapizBr/qRnFZMI6axbpAb1tb09bK9FIeNyvI4QQ4swTz4iEYvUbyQhEYPB+M1IjkmJCgVggoqqYMjOTcg3r3LlYI1FMRiOaqtLT1pqU6wghhDizuJub0BQDgdh+Z8kKROx2OwCawZRSO8FP+UBEVaNEgkEAjFEVg8uVlOvYKuegAE5FL0DqloJVIYQQ6NP1qlUPEtLS0khPT0/KdRKBiNGYuAFPBVM+EAkHgok/m1QNoytJGZFKfQmvo1+PQmUJrxBCCFWN0tPaTNSmBwnjuePu8Y4FIqZESUIqkEAkFhUqmoZB0zBmJicjkghE3HpXVSlYFUII4WlvJxqJgF3PgiRrWgYGByLhoEzNpIx4esqoqhjsdgxWa1KuY8rKwpSfT1qsa570EhFCCOFuSe4eMwMNmpqRYtXUES/YMUU1jEmqD4mzVlaSFtRXzkgvESGEEN3NTWhA2JjcFTNwXEZEilVTRzwqNKpq0gMR29zKREbE3+fB7+1L6vWEEEKkNndzI5rJQhQwGAzj3tp9oEE1IhKIpI74N8M0AYGIdU4lJlXDjgJIVkQIIaa67uYm1Fiham5uLqbYpnTJMHBqJhyQqZmUkeghMgFTM/HN79ISK2ekTkQIIaYyd0tTYo+ZZE7LwOA+IpIRSSHhAcWqyVoxE2epqEAxmxOBiGREhBBi6gr2+/B1uxMZkYkKRDAaZfluKkm0d5+AqRnFbMYya1aiYFV6iQghxNQV/wzQHMlfugtSI5Ky4pXDRjV5XVUHslVWkhaQJbxCCDHVuZsa0RQD0dgeM8lsZgZgs9n0PygKQekjkjomskYE9CW86bGVMz2tLajRaNKvKYQQIvW4mxpQrTZAweFwJK21e5zZbE4Uw4YjETRNS+r1RmrKByKDakSS1N59IFvlHGzhCEZNQ41G6O1oS/o1hRBCpB53cyNRm16oWlhYiKIoSb9mfHomiqJ3dE0BUz4QmcgaEdB34VUARyDe2EymZ4QQYipyNzUmNrtLdn1InMMxcL+Z1FjCK4HIoM6qGUm/nik7G2Ne7oBW71KwKoQQU000EqGnrQV1gpbuxtnt+vVSqbvqlA9EBk7NGJzJD0QAbJVzSQ9KRkQIIaaqnrYWotEo6oCpmYlgje2nphmMiRrJyTblA5FQv56aMqkqRmdyC4XirJVzjq2caZGMiBBCTDXx1u6a0Zj01u4DxVfO6N1VJRBJCSG/DwBTVMWQ5IrlOFvlsT1nJCMihBBTj7uxYcJauw+UWMJrSJ2mZhKI9OvfCLPVimI0Tsg1rZVzE03NfD3dBPtTo2BICCHExHA3NyZau0/UtAwMmJoxGqVGJFWEY01dzI60CbumdXoFZqMJa1hfOiWt3oUQYmpxNzdOWGv3gRJTM1Ijkho0TSMcCgJgdTgm7LqKxYJ15sxjK2daZHpGCCGmCk3TcDc1TthmdwMNrBGRQCQFRCMRVFUFwJzmnNBr2yrnkJboJSIZESGEmCp83W6CgQCaRZ8mmcipmYE1IlNiaubee+9lxYoVOJ1O8vPzufbaazlw4EAyLzkq4QG99q3OiQ1ErHOOtXrvamqY0GsLIYSYPO7mWCMzRSEtLS3prd0HGrh8N5wi+80kNRB5++23Wbt2LZs3b+Yf//gH4XCYNWvW4PP5knnZEYsE9WkZRdUwZUxMD5E469zKRC8Rd5NkRIQQYqpwNzUSnYT6EBg4NZM6Dc2Sul7o5ZdfHvT/Dz/8MPn5+Wzbto0LLrggmZcekXg0aNRUDCfpIRKJRHjvvffYv38/oVCIiooKVq5cSWbm2PemsVVWkh6fmmlpIhqJYJyg5VtCCCEmj54RGZ8VM1o0Su+zz+J56e9EOjuxzplD7le+jHXmzCGPH1isGonVSE62Cf3k6+3tBSA7O3siLzuseDRoVDWMw3RVDQQCPPLII7S0tCQea2trY/v27Xz84x9nwYIFY7q2KTeXtIxMjFGVKPpOvDmlZWM6lxBCiDNHV1PDuKyYiXR303jH1/Bv25Z4LHjwIJ5XXqHkZz8j46NrTnhNfGoG4xTsI6KqKt/4xjdYvXo1VVVVQx4TDAbxeDyDvpIpvmJGb+9+YkZEVVWeeuopWlpasNvtXHnlldxwww2Ul5cTCoV4+umn2bVr15ivbx+QFelqqh/zeYQQQpw5upobiZ7mZneR7m7qP/tZ/Nu2YUhLI++b36T0wV+Tdv75EA7T/O1v4x/i8ylRrAoEgqmREZmwQGTt2rXs2bOHJ554Ythj7r33XlwuV+KrrCy5GYLIKTIiO3bsoLa2FrPZzC233MLZZ5/N/Pnz+dznPseyZcvQNI3nnnuOhoaxFZtaK4/ViXQ1SiAihBAfdiF/P30eDxhNY27trkUiNH3zmwRrDmHKz6fiqSfJvf02nBddRNmDvyb94ovRQiFa/vXf0KLRQa81mfTrAgRDoXF5T6drQgKRO+64gxdeeIE333yT0tLSYY+7++676e3tTXyN9QN+pMKxaNA0REYkGAzy+uuvA3DxxRdTXFyceM5gMHD11Vczd+5cotEof/nLXwiMoejHNrcSZ2zPma5GWTkjhBAfdt0tzfqKGSAvL29Mrd07H/wN/Zs2ozgclP3ut4PqQRSjkaKf3oPB5SK4fz89Tz9zwustZv2awamQEdE0jTvuuINnn32WN954g+nTp5/0eKvVSkZGxqCvZDo2NaNhPG757o4dO/D5fGRnZ3P22Wef8FqDwcAnPvEJsrOz8Xg8JxTmjum6b8MAACAASURBVIR14NSMZESEEOJDr6uxnqht7I3M/Hv30vnggwAU/fjH2ObMOeEYU1YWeWu/ql/vd79Di/XLirOYzQCEQuFRXz8ZkhqIrF27lj//+c889thjOJ1OWltbaW1txZ8iBTIDi1UNAwIRTdPYsmULAOeee+6wEavVauXaa68F9MClvn50wYRlxgzSI/oPiLupEfW4FJoQQogPl87G+kRGZLQrZjRNo+3HP4FIBOfll+O6+qphj828/noMTifhhgZ8GzYMes4aa6QWjkRGOfrkSGog8utf/5re3l4uuugiioqKEl9PPvlkMi87Yonlu6o6KCNSV1dHZ2cnFouFRYsWnfQc5bnpLJ2RB8Arz/wRde9foXdkfUEMFguZZWUYVBU1GqGnrXWM70QIIcSZoKvh6Khbu/ujKpt7vPz25bd4JLeEly+8DPdd30LTtGFfY7DbcX1Cv1HufnxwbWZ85Uw4RW5+k7p892R/SakgXiNyfEZk7969AFRVVQ2qMB6k6zC8eQ/se45LVAt7+RxNvbD7L/exmGooWgIr74CqT4Jh+F19bZVzSd+/HY/DSldTPdnFJeP3BoUQQqSU9oZ6tBy9VvJUgcg+r58HG9p5saMXX1QFWxZcdwsA99d2MLvVw9emFXB9QRaKopzw+qzrr6f7j3/C+847RPv6Ejfc8c+1SIoEIlN6r5mw1wvEMiKxFruqqrJ//34A5s2bN/QLtz0Mv1oJe54BNUJ6bikX5Ovnes1wMSEs0LID1n0R/t85sP+lYcdgq5yTqBNxS8GqEEJ8aIX8/fT2eU/Z2r0zFOGb++v5yJYDPNXajS+qkhsOce7uD7hs9wesznBgNyjU9Ae5s7qeG3cexh0+cZrFOns2lunTIRzG+/b6xOM2eywQUVMjWTClA5GQrw/QMyJKbPfdxsZGvF4vVqt16OLaN/4dnv86RIMw4yL40nq4Ywvn3PZzMjMz6VOtbLnwUfjID8CeBV018MRn4Nkvg7/nhNNZ586TJbxCCDEFdDU2JApVh6sP+Vt7D6vfq+axFjcAH8vL5K9zS3n6+3dw76/+g1/OLOCZs+awa3UV359RhN1gYH23l6u2HaQ1eGLxqfOyywDoe+21xGO2WDM1VdNQ1cnPikzpQCTs6wf0ddXxtNbBgwcBmD179olFqhv+G9b/h/7ni38At/wVihYDYDabufDCCwHYuHUnoXO/Dt/YDavuBBTY+Tg8eD60DG4wY5s/D2csI9J5tC4J71IIIUQq6Gw8ihoLRAa2hAAIqip3H2zk9r119EaiVKXb+dvSWfy2qoLZL7+A1teHZfp0Mq64AgCnycjXphXw0lmzKbWZOeIPcf2OQ/QelxlxXnYpAL7169HCeqBij914a0ZjYs+1yTSlA5GQPxaImC2Jx44cOQLArFmzBh9c+za89m/6ny/7MVz4bThuTm7RokVkZmbi8/nYunUrWJ2w5ifwhVcgqwJ66+EPH4V9zyVeY8rOxpWh71njbpGVM0II8WHV1XCUqF0PAoqKihKPu8MRrt9xmIeaOgG4szyfl8+aw9mZ6WihEO5HHgEg59YvoBgGf2zPS7ezbsksiqxmavqDfGN/w6D6TNuCBRhdLtT+fgKx+kebXc+I6DvwSiAyqcKxQMQcW8oUDAZpbm4GoKKi4tiB/h5YdztoKiy5GVZ/fcjzGY1Gzj//fAA2bNhAOBZ9Un4O3P4WzLgYwv3w1Gfhvd8kXpdTOVffcyYSobu1eVzfoxBCiNTQXn9s6W48EKnzB7l6Ww3v9/rIMBn486IZ/PPMYkwG/Ua396WXiLS2YszLJeOaa4Y8b7ndykNV07EoCn/v7OXPLV2J5xSDAcfZKwDwvfc+MGC/GYNBApHJFk9JmWPflKNHj6JpGpmZmYN31n39R+BtheyZcOV/nPScixcvxuVy4fP52DZgIyLsWXDT03D2l/T///t3YP3P9KcWLEgUrHbWHx2ndyeEECKVtLe2gGLAarGQmZnJAV+Aaz6oodYfpMRq5vllc7g051gjT03TcP/+9wBkf/azGCyW4U7NkgwH/zxDD25+criZtgH1Io6zzwGg/733gGOBiJ4RGX1X8PE2pQOR+DfAFPum1NXVAQwuUm3dA1sf0v/8sf8Ci+Ok5zSZTJx33nkAbN68mejAqRajCa64Hy78nv7/b/wEXvsh9vnzj9WJNNSd3psSQgiRcgJeL32x+o2ioiL2+wJ8avsh2kMR5qfZeOmsOVSmDW4X4Vu/nmDNIQwOB1k33njKa9xWlsdipx1PROW+I8d2jHeco3cH79++HS0UGhyIjGF7kvE2tQOR2IY/lgErZgDKy8uPHfT6jwANFnwCpp8/ovMuWbIEh8NBT08P1dXVg59UFLj4brjsJ/r/v/uf2Nr/lghEOmoPjf0NCSGESEkDC1XV0ml8aschOsMRFqbbeXrpLAqs5hNe0/U7PRuSeeONGEew5YlRUbhntt6j5MkWNwd8epBhnTULg8uF5vcTqKnBEsusaAYjkZBMzUyqSKyGw2xzoKoqLS16BFlSEmsq1rgVal4Fgwk+8i8jPq/ZbE7sT7Nhw4ahG7utvhOu+jkApn2/JyvW86zjyOExvhshhBCpqqvhKFFbGm6Hk/vM2bjDURY57Ty1ZCbZ5hN7i/p37aJ/yxYwmcj+P58d8XWWu9K4IteFCvy8Tu/WrRgM2BcsACCwe89xNSKSEZlUkUgsEHE46OzsJBwOYzabj23LvOG/9P8uvAFyZg5zlqGtWLECk8lES0tLYsrnxINuhSv0mpM8k14t7enpJhRIjb14hBBCjI+2o3X0uHJ4YdEqPBoscTr4y+KZZA0RhAB0/f4PALiuvhrzKPek+dZ0/fjn23s46tczHraFCwHw79ktUzOpJN7e1uJ00tTUBOhruw0GA7hrofp5/cDVd4763GlpaSxZsgSAjRs3Dn/gObfDJf+KKzOANTZ/KAWrQgjx4bK/pY0XFp9Hv9XO3DQbjy+egWuYICR09Ch9r74KQPYXPj/qay1It3NRlhMV+N+GDgBsVccyIvGpGYxGQimQEUnqXjOpTNM0IrGOcpZ0Z2LZbqLJzLaHAQ1mXQr5w7R6P4WVK1eydetWampqaG9vJz8/f+gDz/8nbFsO4HztEEGzic6NT1M85wdjuubpiKgRDnQfoLGvkTZfGxEtgt1kJ9OayezM2VS4KjAZpuyPjBDiDBAMtuP1HSQYaCEUdmNQTBiMdhyO6TjTF2A2n7rWYrz1hML8tup8PI50skIBnli1YNhMCEDXQw+BppF+4YXY5swZ0zW/XJ7HW919PNXq5vszi7HHMiLBQ4cwq2riOL9v8jPwU/ZTJRqJEK/cMDudifqQ4uJiiIRg+6P6k8u/MOZr5OTkMG/ePKqrq9m4cSPXXnvtsMfaPvMjnM9fT6fTQcemZ+HcZTD3yjFf+3iaptHZ6KWr0UskrJKeaaVwhgtrmomNzRt59tCzbGrehCfkGfYcVqOVswvP5qKyi7hs2mVk2bLGbXxCCDEWmqbS07uNtrbncbs34PfXnfT49PT5FBV9ksKCj2E25RBu8hJu86FFNUyZVizTMjDYxu+jsT+qctMHB+nIzMUeCvA9zUPhEIWpcZHOTnrXPQtAzhdvHfN1L8hyUm6zUB8I8bf2bm4sLMCYl0u0o5Po4cMogAYEYv20JtOUDUQGtrW1ZGTQfuAAENsN8eDfob8TnEUw+6OndZ1Vq1ZRXV3N7t27ueSSS3AO2OV3IFNhIS6T/sPZ7nPAXz4HNz8z4pU6w9E0jcMfdPD+87V0tx73A2eAjvxa3sx/CneaHog5LU5mZc6iwFGAxWjBH/HT3t9OTXcN/ZF+3ml6h3ea3uH+9+9nTcUabpp3E1W5Vac1RiGEGK1IxEtz85M0NP6RQKBxwDMKDsdM7LZiLJZcVC1CNOrD6z1IINCA17uPmpp9HKr5v+Q0XUHW/ssxRO3HXm024DirANeaaRgcwwcMIxFWNW7fW8c2fxhLOMTVuzay9KOXnvQ17kcfRQuFsC1ehH358jFf26Ao3Fycw09rW3i02c2ni3KwzanE19FJ8NAhjAaFiKoRkKmZyROvFFZUDb/FQigUwmAwkJOTA288pR+0+NN674/TUFZWRllZGQ0NDbz//vtccsklQx6nKAq5ZRXg66ArkoEWCaI8/hn43AtQvGRM146Eo7zxx/3UbGkDwGQxUDDdhWJWOVLfhNmTTl7rDK5r/Q6RhW1c+In5LC5chNFgPOFcqqZyqOcQ6xvX82rdq1S7q3mh9gVeqH2B80vOZ+2StSzIXTCmcQohxEhFo37q639PfcPviERiG5ca08nPv4L8vDW4XMuHnX4Jhbporl5HU/1TBNJq6Sx5ju68tyjr+hquyNmE2/uJdgXwbW7Bv7eTnFvmYy0f21SOqml8fX89r3V5sGgqV+zeSI7PM6i1+wmv8fnofuxxAHK+cGtiD7SxuqEwm3trW9ji8VHvD2KdNQvfhg0Ea2owGgxE1ChB/+QHIlO2WDXe1taoqXTH5styc3Mxhvqg5h/6QQuvH5drrVq1CoAtW7YQivUuGUp+VRWKphHUFLxF50OoD/78KegcfW+RSDjKC7/cSc2WNgwGheVXVfD5+89j9i0WfpH/LX6/4Pv8ZfH9RCt6MGDAsruIhqcgEhx6W2iDYmBO1hy+uPCLPPWxp3j8qse5ZuY1GBUj7zS9w6df/DQ/ePcHdPm7hny9EEKcDk1TaWn9K5s2X0rtkf8kEunD4ZjB3Lk/5fzz3mP+vPvIzf3ISWtAQtuCmJ6cS/mGf6Hs4D9hM5QStfRSV/Tv9J73MgX/tJTcLy7ElG9H7QvT8b+7CRw+cdf0U49V419qmljX1o1Jgc8dfJ+ivh6M8ZvdYfQ8sw61txfztHKclw590zoahVYzqzPTAXiuvQfrnNkAhA4dwmTUbziDkhGZPPEmLkZVoyvWTyQ/Px/2vwjRIOTNg4LxucOvrKwkOzsbt9vN9u3bOeecc4Y8Lq1qIWlvvYLXbqFjybdx7vRAy07407XwhZfBVTqi62maxmsP7aPpQA9mm5Erv7KI0sos1jeu51tvfwt/xM8M1wzuueoeqnKrOLy9ndcerqZxfzfP/mwbV9+xhPQs60mvUZVbxT3n3cOXFn2JB3c+yPO1z/Pc4ed4o/4N1i5dy42VN05aYasWDhPYf4DA/moirW1EOjvRohEURcHgzMBckI+5rAzbggWYCwomZYxCpIJwOExraysdHR14PB68Xm+iG7TNZiMjI4Ps7GxKS0tJS0ubtHF6vQeo3v/PeDw79LFZi5k589sUFFyNoozsftrzZj2eV/QViY4l+ZRcezuzLLdSc+heGhv/RN3RX+H1HWRh1X+Tv3YJ7sf2EzjQTdcf95H/1cWYC0b+/n9W18rvmzpRgP+ZN436539PtzOH3OwsfVXmELRwmK6H9S7eOZ//AorxxMz0WHyiIIt3e7ysa+vmi7P1QCRQU4N5XiUEIRQOn+IMySeBiKrR2a/XTuTn50P1r/QDqj45btcyGAyce+65vPTSS2zevJkVK1YM+cNoX7AAlz+I126htb6BGTc9Aw9dDl2H4E+fgM+/DGnDR9Nxu95s5PAHHRhMCld9ZREllVm8UvcK31n/HVRNZVXxKh648AHSLXqkPHNpPhk5dl745U66mnw894vtfPLby7CnD7+vQVx5Rjk/Pf+n3Dj3Ru7ZfA/V7mrue/8+Xqx9kXvOu4fprumnPMd4iHo89L32Op6XXqJ/yxa0EW7kZMrPJ+2880i/8ELSzz8Pg+PkLfyFOJNpmkZbWxsHDhygpqaG5uZm1AErKE4mXnxfVVVFQUHBaU8bjISqhjl69DccqfslmhbGaEynYtpXKCv7HEaj7dQniBkYhGRcWo7zkvLY+E1UzvkhroxlVO//Hp2dr7Fr91oWLfx/5Nw8n44/7CZ0xEPXo/vJv2MJBsupg4PfNXbwQJ0+HX7P7BKuSDPzQKw1Q1n5tOHH+PIrRJpbMObk4Lr24yN+b6dyZZ6L7x5soNoXoGWmfv1oRyfmWAAXjo1tMk3ZQMTr04MPg6rR4dFXiuRlZcD6N/UD5l41rtdbsmQJb775Jt3d3ezfv5/58+efcIypuJhMDDQBrXt2wQ03wy1/hT98FDoPwqPXwf/5G1iHLngF6G71sXGdPpWz+lOzKanMYnPLZr73zvdQNZVrZl7DD1f9ELNhcBFWXrmTT33nLJ79+Qf0tPXzwi93ce1dSzFbRxaVL85bzONXPc4zNc/wi22/YHfnbq5//nruOusuPjP3MxhGeNcyWuGmJroeepiep59GG9CYx+ByYa+qwlxSgikvD8VsBk0l2tNLuK2NUG0twUOHiLS307tuHb3r1mFwOHBecTlZ11+PfcnY6nLGWyQUpafdT29HP76eIOFglEhIxWg2YLYaSXNZyci1kVngwDKOlf5ieJqqEe0OEHEHiHQH0PxR1FAURQHFYsTgMGPKtmHKtWPMOHUwPxH8fj/bt29nx44dtLe3D3rO4XBQVFSEy+XC6XRijN2J+/1+PB4P7e3tdHR00NXVxbvvvsu7775LaWkpq1evprKyctg7/NPl8x1i795v0ufVt67PzfkIlXN/gs06uuZe3s3Nx4KQNdPI+Ej5CccUFl6DxZLDzl230dX1Jrt338HChb8m56Z5tP3XdiLt/XheriPzmpM3tny61c0PavSeVN+ZXsgXSvNo2LebqE3PppSWn3ht0APErvjmdrfcjME28iDrVLLMJs51pfNuj5d/9Ie5pKSEcFMTxljmqzs09HT8RJqSv7k2HurkF49v4RzAoKl09uhzgHn+QxAJQGY55J8YKJwOi8XCihUrWL9+PRs3bhwyEFEUhbyycvB10V5fpz+YWQa3PAt/uByaP4AnboKb/gKmE6dONE3j7ccOoEY0yhfksPCiEvZ17ePrb3ydiBphzbQ1/HjVj4csRgXIyLVzzZ1LeOY/ttFe5+GV3+7hyq8uwmAY2Z2P0WDkhsobuKD0Av51w7+yqWUT971/H282vMl9599Hrj13xH9fpxLt66Pzl7/E/ehjENEjesusmbiuugrnZZdhmTnzlHdsan8//h078L69nr7XXyfc2EjvM+vofWYd9uVnkXPrraRfeCFKkn7RDkVTNdrqPNTu6KC5poeO+j7U6Ah+USiQXZRG4UwX0xbkUDo3K2UCE7+3j9ZDB2k7XEN3azOejnb8fR7CwQBqNIrZasVid+DMycWVX0Bu+XSKZs0hu7h0Qv/uh6NpGuEWH4H9boJHegk19KEFoqd+IWB0WbFUZGCbk4V9fg4G+8R+T3p7e9m0aRPbtm0jHEvBG41GZs2axZw5c5g5cyYul+uU/1b8fj+HDx9m7969HDx4kMbGRp588kkKCwu54oormDZt+Dv9sWht/Rv7D3yfaLQfkymTyjn/SkHBNaPOwgRquun5m75tRsal5UMGIXHZ2atZvOh37Nx1G51db3Do8P3Mmf19sm+YQ+fv9+Dd1IxjWT6W0qFvBF/t7OXr++sBuK00l7um6dO+bUcOJ/aYKS0denrdt2Ejwf37URwOsj796VG9x5G4PM/Fuz1eXu7s5YpZMwk3NWEOh+lW7fwpMB/3X/fwbx+bj8k4Of/eUuM31QQzGhQCsSyIZjQTjuj1A1nNsWxI5VX65nTj7Oyzz2bDhg00NjZSX18/eHO9mMLFS2Hja/j8/fR7enFkuCCvUl/K+8jH4Mjb8MytcN3DJ6zoqd3RQdPBHkxmAxd+Zg6ekIe73ryL/kg/5xSew73n3ztsEBKXVZjG1Xcs5rmfb+foni62vHCEc66ZMar3WZhWyG8u+w1PHXiKB7Y9wHst73Hd367jvgvu49yic0d1rqF4/v53Wv/9HqJdemGsY+W55N52G46VK0f1i8rgcJC2ahVpq1aR/73v4t+2jZ6nn6H3xRfxb91G49ZtWGfPJu+ub5B+8cVJTUV7uwPsfaeZ6o0t+HoGTytZHSZc+Q6cWVbMdhMms4FoWCUUiOLrCdDb4cffF8bd7MPd7GPfO80YTArTF+ZSeW4h5VU5GCf4F0xHfR01722g9oMttI1wI8fjj7M7M5i+5CxmLj+HGcvOxnSSLdCTIdIToH9rG75tbUS7j5vqMxn0rEe2DYPdhGLR/361YJSoL0ykK0C0O0C0N4h/Zwf+nR10GxVsc7JIX1mMdVYmyggD/LHweDy89dZb7NixIzH1UlBQwIoVK1iwYAF2u/0UZxjMbrdTVVVFVVUVfX19vPfee2zZsoXW1lYeeughFi9ezOWXXz7q8x4vGg1Sc+jfaWp6DICsrJUsmP+fWK15oz5XuKOfrkf3gwqOpfk4Lxk+CInLzl7F/Pk/Y8+eO2ho+APpaZUUz74O+5I8/Ds66Hm+lrwvLzrhd8GmHi+3760jqsF1BVn8aFZJ4pi6w4fAYMBkMJCdnT3kdd1/0LMhWddfhzEzc9Tv9VTW5GTwg5om3uvx4Z85C95ej8EfYLM6iygGOvqCkxaEwBQNRM6ZkcM5hVbohqhVj1QzMzMx1j6pHzD75Ou8xyo9PZ1Fixaxfft2Nm7cOGQg4lq2HMebL9FvtdBeV0vFoqX6EyXL4NOP6dMz1c/DC9+Aa/4nETCpUZX3nqsFYMll5ThzbNz55ndo9jVTml7Kzy/+ORbjyH6RF053cdHNc3ntoX1sfamOgooMKhaNLpuhKAo3zr2RFUUr+Nbb36Kmu4bbX72dLy3+El9e9OVTBkRDiXp9tN1zD73P6s1+LNOnU/D975N+3upRn2uo8TqWL8exfDl5d92F+4+P0PPEkwRramj86locy5eT/93vJLoTjpfuVh9bXqzj0LZ2NFXPfJhtRqYvyqV8fjZFszJx5thOGQT5eoO0HfHQdKCbut2deDoDHN7eweHtHaRlWln8kTLmn1+MNYl35OFAgD1vv8aeN/5Be93gzRuzioopmDGbnNJyXAWFpLkyMVttGIxGwsEAwX4fno52elpbaDtymLYjh/D3edj3zpvse+dNrI40Kleez9LLrya3vCJp70HTNIKHeuh7p4lgTTfxroeK2YB1Via2OVlYpmVgLkhDMZ4i4xaMEmroI1jbg39vF5G2fgLVbgLVbkx5dpwfKcexOG9cA5JgMMiGDRvYuHEjkVimsKKigtWrVzNr1qxxCaadTieXXnopK1eu5PXXX+eDDz5g586d1NXV8clPfnLM2RG/v4Hde9bS17cXUKioWMuM6XeiKKP/XaGFo3T9uRotEMEyLYOsT80e8XsvyL8CX8WdHKn7b/Yf+BecznlkXjEL/54uQkc9BA50Y597LKDY3dfPZ3fVElA11uRk8J9zyzEMuFZraztYHOQNU6jq37sX38ZNYDSS/dmRb243GuV2K3McNg72B/hg5lyWAHuDGbSZMjAR5V8+Nr4zAKM1JQMRgAvK03i/GsI2PYLPcdqgvgmMVph2+h9sw1m5ciXbt29n//79dHV1nbCUy75oIS5/iH6rhdZ9e44FIgAzLoTr/gBPfRa2/wnsWbDmJwDUbG2nu7UfW5qZJZeV8+fqP/NWw1uYDWYeuOgBMiyjWwtfeU4hbUc87H6rkX88tI8bv7+CjNzR3+3McM3gsSsf47737+OZmmd4cOeDbGvbxv3n30+eY+R3OaGjR2n4ylcJ1daCopDzpdvJ++pXUZJwl2wuyKfg298m90tfout3v8f9yCP0b91K3fU34Pr4x8n/7ncwDXNnM1L9nhCb/nqYA5taiG/OXDw7k4UXlTJ9US5G8+juTtJcVmYsyWPGkjzOu2E2XU1eDmxu5cB7rfh6gmxcd4gtLx1hwfklLPto+YgKkUfK3+dh+8svsP2VFwj06ZlGg9HE9KXLmbX8HKYvXU5a5ui68EYjEZoPVlP7wRYObHqHvs4Odr3+Mrtef5kZy1aw4uPXUTp3/PrWaJpGoNqN5416wo3exOPWGS7SVhRiW5AzokLFgQxWI7ZZmdhmZeJaU0G4zYfvvVZ829qIdPjpfvIAfW/U47pqxqAPtrGOf/fu3bzyyiv4fD5A72F02WWXDXnDMx7S0tK45pprWLp0KevWraO7u5uHH36YNWvWcO65544q6OnoeI191d8mEvFgNmexYP4D5ORcOOax9TxfS6StH0O6mZyb56GYRvfvafr0r9Hn3Udn52vs3fdPrFj+HOmri/G+3YjnH0exVWahKAr7vH5u3HmYvqjKua40frOgAvOAwDISCtEbCIDFwbSKoQv33bHN7TKuvBJzfOf3JLgo28nB/gCbcwqpsKTzkkFfQXOWUk9J5ullsk6X8Yc//OEPJ3UEJxEMBrnvvvu4++67j21bPE6a399Ew5FDqOlZhJwZlKWFmdf3Lky/AJbdMq7XGigtLY2mpibcbjeapjHnuH0EDDYbjX95ig6zgjkcYd4lx3V2zauEjBI48BI0vAeqijbtPF57eB/+vjBnXVFBtKSXu966C1VTufvsu7m4/OIxjbV0bhYN1W48HX46G7xUnls4pjsqk8HERWUXMS1jGhubN3LUc5QXal9gQe4CStJP/Q/P9/77NHzhViKtrZgKCij79a/I/NSnxm1523AMVitpK1fiuvbjRHt6CB48SHD/fnqfWYcxOwfr3Lmj/vtQVY1dbzby8oO7aTuif2hXLMplza0LOOuKCrKL0zCc4k77VBRFwZFhpXx+DosuLsOZa6O3w4+vJ0hrbS971zehaXqBsnGUv6AHCgX8bF73FM//4j7qd+8gEgriKihk1fX/H1esvYuFF19G/vSZWGyj/yVnMBhw5RVQsWgpy664htL5C4kEA3Q1N9Ld0sTet16jYd8u8sorSM86vQ/xYG0vXY9W4323CdUTQjEbSF9ZRPanK3GeX4q5KA1lHNLWxnQLtsps0lcVoVhNhJq9qL0h/Ds6CDV5sZRnjKmGxO1288wzz7Bx40bC4TDZ2dl87GMfY82addmi9wAAIABJREFUNWQmIc1/PJfLxZIlS/B4PLS1tXH48GF8Ph8zZ848ZSGrqoY5dPg/OFjzI1Q1SEbGUpYt/SMZGWPPPPbv7MDzSh0okHPLfCxF6aM+h6IoZGetorX1WQKBRlQtSGHV5fg2NRPtCWKdnkGNBa7bcQh3OMoSp4PHFs8k3TT4d1Jb7SG27N4LJhMXXHTRCTeeoaNHaf3Rj0DTKP6/92PKHb86uuOpwLq2bnpNZuoaDRx2lZKl9HOxVs0Fl1427tcbzef3lA1Ejrz7Ns2NR4lm5hO228nrr2G+dgCW3wrlQ/f5GC9Op5OdO3fS3t7O8uXLMZsHr2DxbNpEna+HiN/PWZ8Yoqla0WKwZsDh1+HoBhqa09mxJwuz1cilX5jHdzZ+m0ZvI6tLVvPdFd8dczrWYFAoqcxk38YWetv9WKwmima6xnQugDlZc7hs2mVsbdtKo7eR52ufx2wwsyR/ybBj9PzjHzSuvQOtvx/bwoWUP/zQmDeBGiuj04nzsktJP281/l27CTc14X39dfq3bsW+ZDGmrJHd7fe09/PSr3az791mohGNvHInV3xpIcvWTCPNNb4/33EGo0JeuZOqC0rIr8igu9VHnztI04Fuqje14HCaySlJH9XPiKaq7H37dZ772T0c+WALajRKfsVMLvo/t3HprV+leM48zOP471VRFFz5BVT+/+ydd3gc1fm275nZri3qxeqyZVnuNrjiQnWJAdv0EkoCIaGlk0AS0iBffgmBQIDgEHovBmPAYLBxwb3KNpYsWbJ6l3a12l1tnfL9sbIsWe6WMdcVHl9r7cxOOXPOmXPe85bnnTKdYVNnosgRnHU1dLY0s2fVZ3haW0gdPBSD+eRCr2VngI73yulcXo3qDSMYJGzT04m/YRiWUUmnTe991OfRiRhzHVgnp6GpEK7zIrcF6NrWjGjRoz/B9lAUhQ0bNrB48WKcTieSJHHBBRdwxRVXfG3htQeh0+kYNmwYRqORAwcO0NjYSFNTE4WFhT1ROIcjGGpm9547aG39GIDMzO8xcsRj6PWnLjwpnhDtL+4FWcN2QSbWiUdnMT0eJMmCxZJHS8tHdHYWEZ8yDX0kkUi9j7JgiO+G3LgiCmNsZt4ZM/iImXRLNq2nvLUdgLlz5/Yb61sffYxgcTExM2eQ8L2Tz7J7Mkgx6lhU20Znk58GvwNRU7nYUI5N7mL6JbMG/H4nM3+ffZf0swQ5EM04qHQ7V+XL+6I/5M444/fOyckhNTUVWZbZunVrv9/Txo0HwBv0E/J3HfkiU+6G2f8PgK+2Rp+lcGoanzYtY3vLdsw6Mw9OfvC0ByNHkoXpV0dVeJs/PEB7L7X1qSDHkcPr33md+YPno2oqT+x8gntX3UtnqLPfsZ3LltHw059BJILtkkvIfvUV9EfLYPw1wDx2LLnvLSb5l79AMJnwb9lC1fwFOF98Ce04XAwlGxp5++GtNFd2ojdJzLyhgKvuP5fUvFMX7E4GgiiQMyqRax6YwCXfH44twYS/M8zKl/bxwWNFuBqP0s8OQ3tdDW8+eB+fPfM4XR0uHMkpXPaz+/nu/z3OsKkzEM+wlip+UDqz7riX7z/xLMPOmwmaRvHaL3jhpz9k56cfHrcdADRZxfNFLc2P7SBQ7AQBYialkvqrc3HMyUUaQLPVsSCadMR+J5eUn47HkGtHC6u4l1TgfKkYpevYJFMtLS3897//5YsvvkCWZXJzc7nrrruYMWMGOt3ZsbgLgsDUqVO57rrr0Ol0lJeX8+abbx6RTdrl2sDWrZfR2bkdSbIyauTTDM3/HaJ46nWvaRodHxxACyroM6zYLz79SJ6kxItIS7sa0Nhf9ges01KptIrclizjjMiMtpp5+yhCCEBV+X4ALAY9lsM4iiItLbg/+ACAxB/+8LTLejzESBKj9Hr0xdEo0Ytbd5Ag+jkxFpkzi/9ZQSQSDKABYUNUUssUWvBoFnZHMs/4vQVBYNq0aQBs3ryZYLAvxW7chEmYwtGBqKXyQL/zezDlbjzTHqU6dA4AmcIb/GP7PwC4e+zd/cweakhG8YRQgzKaduKx44XnpZEzOhFV1lj5YjFK5PS6rlln5uFpD/PnqX/GKBn5sv5LrvnoGva27+05pnPZMhrv+xUoCo75l5P+z8cGNLb+VCHo9STcfjt5H31IzHnnoYXDtP7tb9TefAvh+vp+x8sRhVWv7mP1q6XIYZX0gjiue3AiI2ekn3BY9ICWXxQYOjGVG/84mckL8tDpRRrL3bz98FY2fXDgqG2ryDKb3nuTV3/9E5oqyjCYzUy/4VZuffQZhk6e9rWuvgHsicnM+/F93PDwo6TlFxAJBVn90rO89Ydf42yoO+p5oVoPLU8W4VlRA4qGMT+WlJ+MJ25h/tcmgBwOfbKFpB+MxjEvD3QCwbIOWp8sIlzv7Xesqqps3LiRZ599lubmZsxmMwsXLuTmm28+JnX414lhw4Zx4403otfrqays5I033ugJHdY0lcqqJynadQuRiAurtZCJE5aSnDzntO8b2NNOsMQJkkD8VUOP60zcG4qs0tUZwu8Jo6p9x8b8Ib9Gp4vF11XGevcn3Dk5BpdRZLgq8vbYwcQeRQgBaGptAyAlqb8/nOuFFyASwTJhApbx40+4rKcKWVFxbW9DiKhYjSqX1W8CQBWEk5oPzgT+Z51V5VAITadHE0UEwIGXNeoYHnxjFx/dO40E65lRlR/E8OHDSUxMpL29na1btzJjxiFNjKlgKI6QTNCgp2H7FrJGjj7qdfYFLgSqSTfs4Y3ml/A6bBTGD+PGwhvRVI3g/g78Ra2EKt2o3kOrLNGqx5BlxzTYgXlsMlLM0dXQgiBwwXeH8dZDW3A2dLH140qmLBxy2nWwMH8hhQmF/HzNz6nz1nHzpzfzqwm/Yl5LGo2/vh9Uldirryb1T3/8RvBJ9IYhM5PM5/6L+513afnb3/Bv307V5fNJ+c0DOK68EkEQ8LQHWP7sXtpqvQgCTLw8j3NmZ5/RsM0ThaQXOWdODvkTUlj3djnVe9rZubyG6j3tXHRLIcnZh5ybnfW1LPvXI7TVVAGQN34CF99+N7aEM2fPPlGk5Rdw/Z8fYffK5Xz5+os07t/Hq7/+MdOuvYlz5i3o6TdqSMHzeTW+jY2ggRijI/aywZjHJH3tQtSRIIgCtunpGIfE4nqtBNkZpPWZ3cRePpiYiVHfLLfbzZIlS6ipiZJz5efnc/nllx81o/fZRG5uLjfddBOvvfYa1dXVLF68mAULLqa07D5crnUADEq7hqFD/3BSDKlHg+IL4/4wGv5tvyATfeqx6dhVRaWxopPKojbq9rlwt/p7IqQknUhippW8sUkMm5KGxR7H4MG/4OOyV3mkNp0uCYZ6FJ4qDhA78+jjUjgYwBeRwQh5h5mTZZeLjnfeBSDha9CGAPxrVQVNTT40SUAcE0fM6ugCWBNEVEVG0p0ZU+SJ4H9YEAmi6aMrILsugiSrVJhH09gZ5MdvFfHy9yae0bhqURSZMWMG77//Pps2bWLSpEk9djRBryfJHkuLFqLxq91HvYamaZRvjVIJJ020864cdcr6pV9DqXTjXFZLpOkwlbsIqKD6IgRLnARLnLg/rcIyOgnbBZnok45sZ7fYDZx/4zA+XfQVRSvqGHJOCklZpz8ADosfxtuXvs3vN/yelbUreee9hxnxloZOVrHPm/eNFEIOQhAE4q69hpipU2i8/wECO3bQ9LsH8a5YiXDH/Xz2Rh3Brggmq55Zt40gs/D0nCrPBOwJZubdNZrKojbWvFGKq7GLxX/bwTlzsjlnbjYlX65k9UvPIodDmGx2Lrz1DoadN/MbMXkfhCCKjJ31HfLGn8uK/z5N9a4drH3tBar3FDH37p+j80i43ipDcUUHXsv4ZBzz8o4pfJ8tGNJiSL53HK539kffzSUVhJt81GT5+HT5p4TDYfR6PXPmzGH8+PHfqHY4HFlZWdxwww28+uqrNDauZ/2GRxDFTkTRxLCCP5OWduWA3cv9USVql4w+1YLt/KNrtZWISunmJnZ+VoOnva8mWhBA06LakZYqDy1VHrZ9XMXYWVn4Js7lr8IQQhgYoW/n6VIbVo9MsNSFeeSRBfKWAxUo5qhAlDckv89vrldfRQsEMI0YQcx5U0/z6Y+Pz4qbeXJVOQDqiFha4yy4rd3jtygSCYW+FUTOBuRwBFUfnfhj1Sgx1nfmXcET7wXZUOHk4WX7+MNlw8/oiz5y5EjWrl2L0+lk27ZtPeYagNT8Yezdv5vW5oajnt9W66WzLYBOL/Jecglyk8CMrhAF+5NpKyoBBASjRMy5KZhHJqIfFINo1KGGFSJNXYSrO/HvaiPS1IV/Zyv+XW3ETErFfnH2EQfpvLFJDDknmYodrax6dR9X338u4gAIazaDjcfOf4y31zxFzhP/RheB0gILI3992zdWCOkNQ2Ym2a+8jOull2l7/HEqizsp+U8ZqqgnOdvGnB+OwhZ/9s1Kx0LeuCTS8h2se2s/5dtb2basjB0fLSLgKQEge/Q45t7985MOw/06YU9M5or7/8ielctZ88pz1O7Zxabfv0hBzAQEDaRYI3FX5GMa+s19Boj6jiTcVIh3bT0ty/ezYsfn1OyKqvgzMzNZuHDhUYmxvmnIzs5izhyBTs9nCIIGpDLh3BewWgsG7B6BEieB3W0gQNyVQ48aqlu5q4117+zH54qS0xktOnK7Q95TcuyYrXo0wOsMUF/aQcn6RlprvLy0p5EPLZ0oooHRWhE/jTxG7OhnkNdCV1HrUQWRiuKvQNIhAqmph2jpFZ+PjtdeByDhh3eccWFyb0MnP31rF5oGN0/JZkeGgR0eP/szo+HEmigih8Nw9nIa/u8KIpFIGLVbI+JQXSAZyRwxlUdFJ3e+vpOXNlaT6jDxo5nHzi1wOhBFkenTp/PBBx+wceNGJk6ciKGbFyNz2gwo24VfjuB1tWOL79/Zy7dFtSGOAh0rmj5Dj45fCY/gVaI9ymLdjuO2K5HS+vIIiAYJY7YdY7Yd64wMwnVevKvqCJa66NrUROCrduIWDDniCzb92qHU7XPRXudj18o6xs8eGGpnLRBg4hOrCPmhLk3PXy4NIa64hQcnP8hlgy8bkHucSQiSRMJt36cqZgx7V7tBEEhs38MkexsW/TDgmy2IAJitBmbdPpK41C2sf+N5VKUTEBkyaT6X/eTWM+6IOhAQBIExl8xlUPpQWl7eQ6yQCBp0xXUx+N6J6Cxn1uQ6UBAEgaY0P0sd2/GHAoiawARrIRdffTl6+ze/LwGEw05K9t2Hx7sWQYDW1hwqyieTmiIzYoAoYNSATMeSqEnGOj0DQ2Z/LW1XZ4g1r5dRvScavRLjMDBuVjbDpw9Cfxg3jEDUQd+RZKHwvDQe3FzFklDUV2dUY4Tf560lFPDTlvwucVxFsNSF6o8cMcKqqjpqyoyzWvpEDrlefhnV68UweDC2i88MeeZBNLoD/OCV7QQiCtPzE/n9pcN5qKqJHR4/Fek5ZKheECUiJ5gk9Ezhm7/cPENQ5HCPaSYWTzQkVmdg7qg0fjevEID/+7SUxTv6OyAOJEaNGkVcXBx+v5/t27f37HdMmoQtGPU2b9i5o995mqpRsSOavGqndRWiJvBY52+QamJAhLiYZ4mX/4j0+sVQt+2o9xcEAWOWncRbR5B4+yh0yRZUXwTna/twvV2GGuqbU8NiNzCtO4pm68dVuFv8p10HmqrSeP8DhEpLkRISGPfCW4zPnkpADvCb9b/hz5v+TEg5uy/K8aBpGps/OMCWNZ0gCAx2tDOq5Dm6Pnyfyvnz6drSPzrqm4i9q1ew4c2/oiqd6I1xGGzXUr8/l2X/3ovf0z/64ZsGTdPoKmol/HYLsUIiiqiwufUjPt75FEsf/wuBbsK1bzJCoRAffvghb775Jv5QgKTYBBaIkxnlTMP57F5k9zf7XQDocG9j69bLcDrXIopGhhX8hbjYX6IoepYsWUJTU9OA3Me9rBLVG0aXaMZxSX/itppiJ28/vJXqPe2IksA5c7K58aEpjLkos58Q0htBReXe0jqe7xZCLmhQuHy9l8rPLwSgtXMZcpYLFI1gWccRr9HeEY0EzMg4ZCqSOzpwvfAiAEn33H1GNb6t3iA3PreFps4gg5NieOqG8egkkXPs0YVqWXZ36g5BIBQ4/XH8dPA/K4jIsnLINIMHMib0/Hb79Dx+MD2qtvrV4t1nVBiRJInp06cDsH79+p4IGik2loTuxHZ1mzf0O6+pshNfRwjJKPC5toRb2xYwpDEVJIGEm0cQc89D0cR9vhZ46Tuw643jlsU0JJaUH4+L2lgF8Be10vp0EZHWvp20YHIqmcPjUSIqq18r7aEmP1W0P/MM3s8/B72ejCf/RVLucJ65+BnuGnMXAgLv7n+Xmz65iTrv0aMhziY0TWP9O+XsWB51IpyycDCz/+9qcl57BX1mJnJjE7W33krL3/6OepZXHkeDIsusevE/fLboCRRZZvC5k7njmWc4/7szkfQitcVO3npoCzV7nWe7qEeFGpBxvVVGx9tlaCEFQ7ad9F9OZvj35qIzGKnevZPXHvjZCee+ORuora1l0aJF7Ny5E4gyMd9x948ovGs6UpwRuT1A26LdyM7AWS7pkaFpKlXVT7Nz5w2Ewi1YLIOZcO4S0tOvY9as2QwZMgRZlnnnnXf6RQueLILlHfi3R7XCcVfmI+gPCRaKrLLhvQo+fnI3AW+EhHQr1/x2ApMXDD6mAALQGAxz1a4K3mvpQCfAPwoyefmqMaTl2PE2ZRBoOQfQcA2Nht4GSvq/EwGfl0B3GothvdJCuJ5/HrWrC+OwYdhmz+533kDB1RXmu89toaq9i/RYM6/eNgmHOaq1GW+P+gFWpmcS6S5j0P+tIHJWoChyX41Ixrl9fn9gbiHXT8xC1eC+xbt5a2vtGSvLmDFjiI+Px+/3s3Hjxp79qd05NZqPMHAeNMu40mqY7BvJ1c4oM178VUOjdNFxOXDb5zDsUlDC8MGdsOwXEDn2yy/oRBxzckj64WhEmwG5NUDrU0X4d7cdOkYQOP+GAnSGaOhnyYbGU3523/oNtD/5FABpf/xDTxibJErcOfZOFl28iDhjHPtc+7jmo2tYUr7krIea9Yaqaqx5rZQ9q6PC6szrhzJ+dnaU3XT8eHKXLCH26qtB03C9+CLVV11NcN++s1zqvvB7OnnvLw9StPwjAKZcdQPzf/EbTDFWRp2fwdX3n0v8oBgC3ggfP7WbdW/vR46cWPbZrwuhyk5antgZ9RUQwX5JNkl3jEYXb2L49Au4/qFHcKSk4mlr4c3f38feNSvPdpH7QJZlvvjiC1588UU6OjpwOBzccsstzJ49G71ejz7JQtIPx6BLNKO4Q7Qu2tNvgXC2EQjUsbPou1RWPgaopKYuZMK5S3r8QURR5MorryQ2NpaOjg6WLl16yu+yGlLoeD/qfBkzJQ1j7iE+Hr8nzNJ/FrFrRXTMHnV+Blfdfw4Jg47PsLrG5eHi7WVs9/hx6CTeHD2Y7w5KwGDScek9Y4hNsdC861IAOsQvCVkaCZa50A4Ley8v2ommN4Km9TiqRlpbcXX7hiT99CdnTBvS4A5w9aKN7G/xkWI38sYPJjGoF4V7ulFPikGHIuloj4lGxwXOsiDyP8usuvXdN/AmDwJBZAabscz6HZgOdWZBELiwIJkOf5jddZ2s3NeKpsHkvPgBdy4SRRGbzUZxcTGNjY2MGzcOo9GI1u6kZH8xwXCICQuv6aFL1rTo5BcJKexI+pBftV6PUTNgnZGBbUavNNM6IwxfGHUFr9kAjTth/3LImQYxxw691MWasIxLJtLgQ24PEtjbjiarGPNio+Ycix69QaK2xEVjuZuCSWkYTpKeWm5ro/b229ECAWKvvZaku+7qd0yaOZVJwnCcByqR6jyUFm2iaPdaTB0yalcQEDBaYs5K9ICmaqx6ZR+lm5oRBLjolkKGT+vL3SIaDNguvADT8BF0bd5MpL4e9/vvI+h1mMeOPevOuC1VB1j88G9pq6lCbzJz2U/vZ8wlc/vUp8VuoHBqGpGgQku1h5ZqD9V72knLj8ViOzvcGwehKSqeFTV0vF+OFlSQEkwk3jqCmHHJfcKkY2LjGD79Qpz1Nbga6jiwfTPBLi9ZI8cel4b8TKO1tZXXX3+dkpKoY/CYMWO4/vrrSTqMe0I06TCPSiS4vwPFFSSwpx1TQdxZ4z8JBwM0V5RTX1pMxb5FVDb8jmCoFjQDyfYfkZ11NyaLo09f0uv1ZGZmsmvXLtra2jCbzWRkZBzjLkdG5ydVhMrdSLFGEm46lEvG2eBj6eNFOBu6MJh1zLp9BGMvzjquU72iafyjuplfltUTUDVGWc28O3Ywo+2Hogh1BonMwjiK1/rRW2sw2pvBpBLTMCaaCLFXLq61n35Mm89PjEHHjAu6zTmPPEJw127MY8eS/ItfnJExq7zFy/X/3UytK0Caw8Rrt08mL6mvACYIAts6uyj3h4j3dZLqdTMkM4O07JwBLcu3FO8ngC3vv4M/MQ00jVnmYsSLHuzJZHsQgiBwfkESIVlle00HW6pc1Di7OL8gecBDexMTEzlw4ABut5twOExBQQGWhER2LluKIokMHjUWa1KUVdTZ4KNoRR2qJDPVGENuOB19hpWE6wr6c1QIQpQtNn0CHFgF7mrY9XpUEEkb0++Ze0M0SljGJoOqEq72EK72IDd3YSqMR5BEknPs1JW48LQH8bQHGHJu8gm/XJqq0vDjnxDavx9jfj4Z/3oCoZsR0utq56svPmPtqy+w+sVFlK9dS2xNhIw2M4OcZsz1Aep372bf+jUULf+Ios+X0bR/H0GfD1tC4inlNjlZaJrGmjfKKN3YhCAKXHLbCAompR71eGNuLo6FCwjX1BCuqMC/aRNdW7ZgmTgByfH1sKsejn0b1rL0kYcJeD3EpqZxzYN/IaPwyF6EoiSSPTKB5Gwb9aXRNt+3sQmjRUdytu2sCIKR9gDtLxUT6HZCtJyTQuLNw9EnHLn9dQYDw6bOAAHqS/bSXLGf+tK95I2fgN749TuAKorCxo0bWbx4MV6vF7PZzBVXXHFMdlTRKGEenUTogBvFGV0gmArjv5ZQZEWWqd27m6LlH7PmledY++rzlG35hIj9XcT4XSAo+BotVHyczv41texY9gHFa7+go7EeUafHkRSlnbfb7ZhMJioqKqisrCQvLw/HSbwDoepO3B9EtcQJNxSiT4n6PFR/1c7HT0VNMfYkMwt+No5BQ45PF1/hD3LzV1W83xJlHL15UAL/HZFDoqF/nZqtBmJijezfqBCbt4GQpR5H/Qx0Ygzm4YcI5T7/aCkhQSJnUBqjx59DsGw/zb//PWga6Y/8HcMZSG63oqSF7720DVdXmMFJMbx5xxRyEo4cClMdCLPe7cMcDpHnbCZnUAqZg/OPeOyp4ltB5ASwcen7BOOSMKsBZmSLMPaGIx4nCALT8hNJsZtYU9bGviYvK/e1MDkvgfiYgVuJCIJAQkICu3btorm5mcLCQhxpaZS/9TpdkohDkMiYEM2Bs29jE/WlHRgdTcyMDEWTIOm2UUjHWp0m5MHoa6H5K3BWRDUjtZsga3I0i+/RyiUKmIbEISWYCZa6oqnM90fTYEtmHSm5dko2NNLR5CcuLeaE1J8Azueew/3OOwgmE1kvPI8+OZmWygpWvbCIFf99iprdO/E629FUFbPNTkreENLyhxGTlcYBXTPthi5UQcOk6FCCIVyN9VQVbWPHsqXUlxajNxqJS0s/IxoHTdNY9045xV82IAhwyW0jyD835bjniWYz9rlz0aen49+8mUhNDe7FixFMRswjR35t2hFVVVj3xsusfeU5VEUhZ+w5XPnAn7EnHj8bcmyKhYLJabgafbib/dTsddJa4yW9IA6D6esJwtM0ja6tzbheLUFxhxDMOuKvGYr9wqzjZlkVBIHMEaNJysmlcud23E2NlG1aR0bhyNNOnncyaG5u5s0332TPnj1omsaQIUO46aabTkg7IBokLL01I8VOzIUJZyw3jquxni0fvMtnzzzOnhWf0lReRsDXSUJhB7mzGzDHh9BUCbVtGoLzEmLsaYBAyN9FqMtHS2UF+9atpnTjWjRNIyk7l8ysLNra2mhtbaWqqoqxY8eeEDW9FlFpf6kYtUvGck4KthkZaJrGnlX1rHp5H4qskT40lvk/GXfckHlF03i2ro07iqupC0awSSL/HJbJT3JS0R2DdDAh3UrzfgNhtqOPcSKoOozVg7FOS0cQBORwmC+++AJNp2fK5EkMysik8b77iNTVYZs9m4TbbjvJFjg2ZEXlnyv387sP9hJWVCbmxPPKbZNIOUZ0VUBRea+lA1UQGdlURWZyEjkFwwa0XCczfwvaN8ngfhg8Hg8Oh4POzk7s9pNLY388PPL9G+nKyicp0sbdM2Jh9l+Oe87GinZ+/FYR7b4wZr3E7y4t5PoJWQNK1f3222+zb98+srOzufXWW/nsh9+juLOdvKQ0Fj71XwCWPLqT5nI30+LDxKkx2C7KwnHJCYbRqipsegpW/wXkIOjMcOFvYdKPQDr2QBaq7sT5aglql4xoN5B4ywgM6Va2flTJtmXVmKx6bvjDJMzHUdcH9uyh+oYbQZZJe/ghxJkzWP3ys1Rs29xzzKCC4RSeN5OcMeNxpPTN+htRIzy751me2/McqiIzyGfjcv0MbLVBWg4c8qexxicw4bIrGHXxHPSGgRFkNU1j05IDFH0etT9fdEshw6acfGKtcH0DTQ88gH9bNKLJNGIEaQ8/hKmwcEDKeTQEfT6W/evvVO+OOkNOmH8V0667CVE8udBcrTuL8KYlB1BkFVOMnvO/W8DgcWc2F5DiDdOxeH9PpIIxz0HcNQXoYk++fZ31tSz9x8N0NDWi0xuY9cN7KZx+apmqTxSyLPPll1+yfv16VFXFZDIxe/Zsxo49euIxPA/3AAAgAElEQVTHo0HpitD27B7kFj+Sw0jSD6M+MQOFpooyti19j/Jtm6LmXcBsdzB4ai6W3C2E1UoA7PYxDC/8OzExfdmWI6EgdcVfcWDHFko3fEm4OzLDnpTMtOtvIfecSSxatAi32824ceOYP3/+ccvUubwK75p6RJue1J+dg2aU+PKt/ZSsi/qpDT8vjRnXFxw3q/ROTxe/3d9AkTdapvPjbDw6LJN004ktLn0dQZb+59+kTnwaMWJh8JePkvKDSRhzHBzYXcSrS5YC8Mtf/hJt6zbq77oLwWAg75NlGE7BFHU0VLb5+Nk7u9ldF9Xm3Do1h9/OK0R/HI19e1hm5IZoSo3vr/+YmcOGMPvq6wasXHBy8/f/rEZk3ScfIdtiSVFaGTt5GqSOPO45mfEWFoxNp7jRQ1V7F6tKW9lc6WR8dtyAaUcyMjLYvn07HR0dJCQk4AgEOFBbScjfxblXXU84qPDlW2Xk6kWydUYiMRrJN4488TTlghDNLjziCmgtAdeBqMmmeAk4MiBhyFHNNbpYE+aRiQQr3CiuIP6iVvTJFjKnpFG1uw2vM4ivI8jg8UefjNRgkLrbf4DicmGbO4faobl8+M+/0l5bgyCIFE6byaU/+RUT519F6pChmKz91f6SIDExdSIXZ13Mfnc5ZXIN2/TlNA8WufTy28lJyMPV2IDf3UH17p3sXb0CQZRIyslFkk5v1b7t46qe6JiZNxQwfNqgU7qOZLfjWDAfXUoK/u07or4jixejBfxR3xH9wK9u2+tqePeh39J8oBydwcjcu38epUEXTl4TIwgCqXkOcscm0lzZiac9SMWOVrzOABkFcUj6gdfuBPa20/7iXiLNftAJOObmEbtgCNJJ+iYdhMXuoHD6BbTXVuNqqKN86ybCAT9ZI8ecEe1URUUFb775JqWlpWiaRmFhITfeeCPZ2dmnZNoSDVL0fSx1RTUjJU7MIxMQT1Mz1VRRxvKnH2P9W6/i6s7bkzd+AufdcCXZM934de+gaC4kyUp+/m8YVvAQBkN/nzNJpyMuLZ3B50xk3JxLscUn0lZThdfZTvmWjbRWljNlzjyK95XS3NxMamoqiYlH910L13vpWLwfNIi/dhhqrJFP/v0VlTujZGbnXTWEyQsGH9MfpC0c4bf7G3igvIHmcASrJPKXoen8eUg69mPkjDkcBrOOYGcSvuDniGY3umACMRRgGhzL+s8+ocntwSjCBdOmU3/33ageDwm33YZ9gCJlQrLCf9ZW8pO3imjoCGAz6XjkqtH8aOZgpBNYGFskkddrmvAhkOlqYYhRR8HosQNStp4yfmuaOTYUWWb9is9QLDay5XoKL74OrMdXSwPEGHUsGJeOw6xnW5WLaqefN7bU4uoKMyYjFvNxQsOOB5PJhCAIVFVVUVtby8zZc9m9+nMiAhROmEpLnUL19lbOtQroBJG4eYMxZZ+Cj4ElHsZcD470KM+Ipx72vhd1ak3Ij+4/AkSLHsu4ZMINPuS2AIE97Yh6iYyZ6ezb2IyzoYvEDCtxR8n10PrIP/CtWYOSmkJRYS57vliOqiikDxvBwvv/wJhLvoPFfmLPE2+OZ/6Q+QyKGURRaxFNXU183ryK9mSF6264j9zMYbTXVuNzOanevZOSL1cTExdPQkbWKQ38Oz+rYcuHUZKiaVfnM/qC01vZCIKAecQIHAvmE2lqJlxeTmBnEZ0fLEWXEI8xP3/AfC/Kt25kyd/+jL+zA1tiElf99iFyRo877etabFFHVlXVaD7QSXudj/JtLSRlWbEdxVfjZKEGo6RVns+q0SIq+rQYkr4/EvOIhNOuH53BQMHU6WiqRkNpMU3lpTSW7ev2GxmYMcflcvHBBx+wevVqAoEAMTExLFy4kAsuuOC0xzXRKGEemUCwxIniChHY58IyMvGUhBF3SzMrn3uaNS//l87WFkRJYviMC5lzzz0kDG+k3vlXPN5dgEZy8jzGjnmO+PipJyTISjo9qUOGMuaSuej0Bpr2l9LR1EDtji1kjT2XdncnlZWVjBkzpofUsTc0WcX5UgmqN4J5dCLqyEQ++GcRbbVe9EaJuXeMYtiUtKP2h46IzOM1LdxVUtOjBbk6NY6XR+UxNe7UfJySsux8taYOc9JXRExOHDXnY52Qxucff0hAhcykBNI3bsK3Zg261FTSH30U8QjPdjLQNI3Pilu487WdLPuqCVnVOG9IAq98fxITck7OtLixxcWBiEqCz8NwLcTwceecVtkOx7eCyHEQ9vvZsGY1qsnCMK2a3Hn3wEmopkVBYHxWHPPHDqLG6edAWxe76ty8vqUWdyBCfrIN62msStLT0ykuLqazs5OI0YhWtJ2AJGBXNFo7Uolr85Oql+iyhRl07ehTT6ImCFGH1XNujW43FEFHJRS9AjUbwZYWDQM+3IlXJ2IZk4waiBCp9xE64MakaOiHxNJU2UnjfjeFU9PQHSaU+bdvp/mPf8RtNrJ1eA7tjfXoDEYu+v6dXPi9H54SfbggCBQmFHJl/pWomkqxs5haby2LK97DE6sx/6q7yM0spK26Cq+zjfItG6jdu4eknLyT8gnY/UUdG9+Lmn0mL8hj3KyBYZQFkGJisM+Zg2n4CAK7diE3NeFdsRLf+vWY8vPRpx7dCfZ40FSVje++wRfPP4Mqy2SOGM1Vv3uYuNSTNycdDaIokDksnvRhcTTu78DrDFK6qRm/J0zakFh0p6EdCRS343ypmHC1BwSwnZ9B/HXDkOwDNx4IgkjWyDEkZmZRVbSdjqYGyjatJ3P4qNOitA+FQnz55Ze89957tLW1IYoikydP5pprriEtbQDr36jDNCKRQIkTxRUkWObCPCoR0XhiY1okFGTjO6/xyZP/oL22GgSBETMv4tKf/gx7Xi0Hah/E6VyNpkWw28cwcsS/yM66DZ3u5DnBJZ2OjOEjyZ80leaK/XS2NuM5UIohPYeuYBCn08nIkSP7CQaelTUEvmpHtOgITh7ER898hb8zjDXeyPyfjmNQ/pGdUtvCEZ6qaeVHJTWs6/AR0TTG2Mw8PzKX2zOSsOpOfeEo6UQivjS65MWo5g6MVUOIHT+SFau+QJMkxmdmIjzxJGgagx75O6aCoce/6FGgqBorSlr42du7eWFDFW5/hCSbkf+3cBS/+U4hdvPJa1APBMJs9Pgxh0OM87QxauLkUy7fkfCtj8hx4G1q5PFH/4FitXO5tZjxv3z3tK63vrydv3yyj31NUdZGvSRw+Zh0bpiUyfisuFOStqurq3nppZcAKOhop7G5mty4ZDrtN3O+IKIXBEzXZJE4fuAmRNy1sOZvsOctUOXovrQxcO73YeSVYOxPn+zb3Ij7wwOggj7TypetQVpbAhRMTuXiW4f3HKd2dVG5YCH1nU525Q1C0TTi0zO57Gf3k5g5cM9Q763nX0X/YnnVcrTudJozM2Zy89AbkbdUsW3pe8jhEAgCoy6cxbTrbj6uBqZ4XQNrXi8D4Nx5OUy6LO+Ix2mahhaQkV1B5I4gqi+CGpRRAwpauBfvhhCdPESzDtGiQ7Tq0cWZkOJMgIzr5VdwLlqE2h3bb//OXBLvuQdj3pHvezSE/H4+ffpRDmzfAsD4uZcz47vfRzoBp8BTRTgos2FxBSXrozb7GIeBGdcVkDfuxDSOB6F4QriXHiBQHCWLkhJMxF89FGPOmY0waq+t5oN/PExnSzM6g5HZd/4kGmlzEohEImzfvp1169bh727DvLw85s6dS0J8Ar6OED53iK6OEF2dISIhhUhQIRJS0DQNURIRJQGdXsRsM2Cy6rHYDNiTTNgSzEf1SZNdQdr+swelM4Q+1ULiD0YfN5rmwI6trHpxEZ62KEtz9uhxTL1uISFxI3X1LxGJRH1xTKZMhgz+JcnJ8wZMS6cqCuvefJntH72PYjQTyBuBBlxxxRWMHn0o43i4zkvrM7tAhc6Riazd0ISmQWqeg7k/GoXF3l/LsNPTxQv17XzY6ibcPcWNsJr4ZU4qcxIdA/YMiqyy7M3biUlfi61pMglJv+DVjR+CpnFtcTHsLcY2dw4Z//znKV3f7Q/z9rY6XtlUQ4M7SmJnMUh8/7xc7piZh9106ibc5W2d3Lq3igSvm/tKN3Hrrx445WsdCSczf/9PCiLOslKefulFVKOZm/I6GHzzEz2/KZpGsS9AsS9AaVeQplCEtnCELllFBVRNQxDAJkk49BJ2nUSyQU+aQY/L6Wf1riZKDnRAREUAshOifiXzRqeRn2w9qRdg+fLlbN68GZMootu3A7OikZv6M0ZbdHTE+Bj52znH1YaoaghFCaKoAVQliCCICIIeUdQjCHokyYQoHiatuuuiDq07Xga5m8HRYI0KI6OuhuypfTRIwYoOnK+XogVkiNGztiWAW9aYd/dockZFbb7Nf36I3cs/Ym9GEggCuWPP4dKf/hqDuX+2X1VV6erqIhAIEAqFCAaDKEp0Itc0DUEQMBgMfT4xMTHoe/lVVHRU8OxXz/YRSAriCrg67TJMGxqp2BRlqzVZbUy/4RZGXTDriH4BpZub+OLlfaDBuEuymHLFYARBQNM05LYA4VovkUYf4UYfkeYutODpEX2JVj361Bgkh0Bg5xp8K99H9TaDKGCfN4/EO+/EmJd73Os46+v48NG/4GqsR9LrueQH9zBi5kWnVbaTQUNZB6tfL6WzNdp/csckMv3aoceNZNDUaERM56dVaCEFRLDNyMB+UVYf5swziYDPy7In/k7NniLgxB16I5EIu3btYt26dXg80UWJ3epg6KDxGAIJuJr8dDR3ocqnPuSKOgFHopn4QTEk59hJybGTlGXriViS2wO0/mcPqjeMPt1K0u2jEI/gQ+Npb2X1S4ccxG2JSZx38ywE205aWj9GVaN0/mZzDjk5d5KaMh9RjL5fmqaher0objeK243qD6DJMigymiyjKQqiyYRoNiOYzEhxseiSkhCPsiouWbeaz//zL/z2RMLJ6ZjNZu655x5iYmLQIiotT+5Ebg3QaTOwpi6aTbzwvDRmXlfQxxepIRjmg1Y3S1o62Os7xDw7zmbh3uxk5iQ6EHuNv5qm4Zf9RJQIEfXQRyfqMOvMmCQTJp0J8Timp6K1q3ApPwBVIrz352xxN2MMBVmwZCmiw8Hgjz9Cl3TigrgnGGFlSQvL9jSxrrydsBIlS4s1S1w/TM/tWS0kBGvA3w5d7eB3QsQPSuTQAtJgjfJiOTIgLhtSRkVJO82HNEc1gRCTNu9DVBUe3PgRdz74xxMu4wk9xzdNEHn66ad55JFHaG5uZsyYMTz55JNMnDjxuOedKUGkedtWFn34EUgSd09PIu6Cu/jM2cmHrW7Wury45dNnjdSpoPkjaH4ZIaAgBGQSBJHJaQ4uyUnkvJx40hzHtqFHIhEWLVqE0+lE53Fhbqji0qxfECNJeC7SM/ySyd3HefD5SvH59uHzlRII1hMKtRAKtaAovuOWVZIs6PVx6PWx6PXxGA1JGE1pmAQ7xvoSTPtWYWqpRqd0d5WYJBg2D4bOhZzzwGgj0h7A+XIxclsATYA9XQqtJonrHpyEVr6XL++9k+KM6Ms46sJZXHz73fgDAVpaWmhpaaG1tRWXy0VnZycej+eUGBeNRiM2mw2r1YrdbicuLg7FpLDOtY6VbSvxEFXvW/VWZusmk7KxE39TdCWYNqSAi26/i5TcQ0kOy7e3sOL5YjQNRl2QwZRZWYTKOggdcBOq6kT1RY5YDtGqRxdvQrQZoloPkw6ht5pc1dBCCmpARvVHULxh5I5QVJA7AjQtjNJShuLcj+yqIGZ8HvE334T53HOPKNgWr/2Clc//GzkUwhqfwPxf/JbUIaeuFlZVFVVVEQQBURRPWJiWwwrbP6mm6PNaVFVDpxcZNyuLcbOy0R/BbBA84Kbz40oiTdHJRp9hJe6KfAwnGBIOUVOUJstRoVKSTnnlq6oK6996lW1LFwOQM2Y88378K0zW/mXx+/1s27aNzZu3EOiODNFhwtSZiSmQisBhztY6kZhYA9Y4EzEOAwazDr1RQm+UEEQBVdFQFZVIWCXoDeP3RvB7wnjaAiiy2u/+giiQkmMnszCOzOEJxFsknM99hdolY8iykXjbqB4zjSLL7Pz0Qza++zpyKITRrjDi0kzMKXV0+ff3XNNqLiRNmo29JZNIdT3h2lrCNTVEGhpQ3G5QTn6MFO129CkpGHJzMeTlYszLwzR8OIa8PBr27+P9//sT7tQcVJOFwmHDuPa663B/UoXvy3rCAqx0R5AFgWlX5zPq/KgPW7EvwGqXl5VOD1s6u3ruZRAEZieYmRMbIk5ro8XfQktXS/Rvr+/Hy2GlE3QkmBNIsaSQEpNCniOPgvgCCuIKyLBlIAoikbDC6o/nIMVW0nHgPPY25JFafYCZm7eT/sQT2GfPOuY9wrLKnno3G/e3sLG8iZ0NAcK9mnm4volbxU+5nLWYhCOPOSeMtDEwYiGMvBLVkUnOim2E9Qbu3LycPzxw/+ld+zB8owSRt99+m5tvvplFixYxadIkHn/8cd59913KyspITj52qN+ZEkQOrFjOqxs2I4siCZfO4pWgjabQoQZ26CRGWc0UWk1kmYwkGXRYdRISUf8QVdPwKioeWcEdkWkJR2gMRWgIRmgMhWkNH3lC6YOwgiGskihKZBgNDLGaGBkXw4QUO0PtZozdq/OGhgaef/55VFUlqSPAfPOl+CU/cT824fZuwuXagM9XctzbRbUgRkBFVWU07eQTmEmahCkgYwpEMIUUTCEVUwhMtnxMg6agS5iGe2cGwf3RAaE+rOLKsaNf9SB7jKDqDKRPnYl5UBa1tbV0dBw5WVS0vAJGoxGTyYTJZELqnlQEQUBVVSKRCKFQiHA4TCgUQlX7D9D9rikJ+PQ+3KIbn96HT+clw20kt0JDDIYRBYGxsy/lvGu/S8N+P589uxe7ACNzbaTqxZ4Jsgc6AUOGDUO6Ff2g6EeXYEI8RYdlNSAjOwNEGrsIN/mINHYRafKhhfs+myYHUdrLQGjHduEoYhfMQrLZiASDfPHCMxSv/QKArFFj+c49v8Bsd+D3+/F4PHi9XrxeLz6fj0AgQDAY7PcJh8MoioKqqiiK0k8olCSpz+dgG5nNZsxmMyaTCYvFgt1ux2azoQZ17F7eTOsBPwICMbFGJs/PY+jEFERJJNLmx7O8uscMI5gkYs51oE/xo7S1EWlpRW5vQ+nsRO30oHiiH7WzEzUQQItEoivxSKT/BKnXI+j1CDodgtGAFGNFtNuRrFZEmw3JbkOKjUWXmIiUkIguMaH7ewJSbCxlG7/ks0X/Qg6HcKSkMu/H95E2pABN06iuqmHDl5uprClH1aL3FRUjlq4MTP40BERiUywkZdmIHxRDQrqVhEEx2OJNp+TXpaka3o4g7hY/7XU+Wqo9tFZ78HX0nUwNJon8wQ4Gt3YhRFSMeQ4Sbh1BU2UZK59/Gp+vDHuWj8QCBYOjA4Tu9lUFrBVxmFeq6PZ29ROgDodgsSDFOhAtFgRJF61jnQ5EETUURAsEUf1+lI4OtPDRxxvRasU0aiSB/CEsry7DnZYLgsDC6d8hfkUIAdjik2kzS+TclE91rMjGjg62e4K4Dhtq49R6YgJbiXSuQpU7T7huJUFCL+rRiTpkVSaoHD8PTqwxlklpk5iSNoXY4ipwPEPA72D79suYsH4948+bTtqf/thzfCQcprG+mur6Bmqa2ylpCbC3Q6LMbyNC3zFjiFDPPHEL86TNDBUbojsFERyZUb+9uGywpoAlMUpOaYgBUX9IUx32QaAjqt12VUZZtV2Vve4gwIiFTBSvozY+hfm7N/Cfn959wvV1IvhGCSKTJk1iwoQJPPVUNJ+IqqpkZmZy7733cv/9x5bAzpQgsuSpZ3hREyiJG4rfaEGTBBxGHfNS47goycFomwWDTkASBERBQBQFJDG6LQhR84yqRR2INE1DUaPbmqahaBpBRaUhEKYhEKY+GKYxFKHeH6LSG6QtLBMSNNCAgzV/sAm0aBpqVA1J1jCrYEXAEvEjedqIEb1kGrvQWeoxCj6MWhgJBVGT0Us2DPo0jMZUDIZE9HoHkmRH1FkRBQOCIB28BQLRZ0BTu003fhTVjyL7UVQfsuxBld0ocieK0hn9qwXREFARUZGifwWh57uGiKoJCLKAoFhR5SSQLQRkPa5IF0EMyKIJWdV1nyOgiSKC3oCoNyLqjaDXI4o6RCk6mNFrIDxWJ9XQQNVQVQUUGVVV0BS5+xNBlWVUOdLnagIgCBqCoCKgIggqoiojaDI6EYyCGbMkoUNAFFVAAUFFkyJoUhhNigAygqB1X+9gg0aFBoGoaU4T1D7DuXDY34Ntfmi/0PM/iNE5QtUhqjoERY8o60DTgSYidNe5rISJaBG6tAhhVUFDRDHoUAUJVBE0Ee3gBwE0AVWLCroH//aUqldhtSNMRP3aQej95WAHPlgnROtXiNaPIKhESy0iICAJKmZRxYQBXbTjo8qdaCE3GlGzTPSjRf8KRCfNg997/a6Jh3478vSp9a93FbrtrQgHt7ubUJBBUAA12sd9gg5FFVE1HZrOQkQ0oSCgqhKqJoFiRIrYQBLQDEEUgx/ZEESVZFSir7giRPuq2v36q8Kh7xoavW7fsw/EbnNCrz7Rq48IgF7VYQqb0YcsGEJmRFVC0MAEDNJpoO8irG/BL9VjsgQwGMLokNGhICFjbFMwVyqYqzUMARlR7e67FiPYLGA1IVjNYDNDjBFMetDrEHQCgtZ7IANBO/guwMF3AU2FiIoWVND8YfAG0bxBNI8fXD7opYH2mozsHDkCnyMRRWfCYUij0SDRbNHoMkhogtj3JVIj6OQ6dOEq9OEDiKqnT1vH6GKw6R1Y9bHYjLE4DLHY9LHYDbHYDXHY9HZ0og5JFLv7q9BjelWIEJK78EbceGQXnSEnLcEGmv01tPjrkLUIGiKoRqyhWK5JDBPUJCqqxpGxz0l4TCbuiIArrKNFttCoxqFw5EVKPB6miMVM0VdwjsNLZoKViCMH2ZGF4shBjc1FsaUj6PTROUkQEIWD5aXPtti9LQgQkTXCikpEUVG8LRgrPiVm/1JimjYBsDDnCTZlj2V6/Q7evWlgida+MYJIOBzGYrGwePFiFixY0LP/lltuwe12s3Tp0j7Hh0IhQr2yk3o8HjIzMwdcELn+2WfZVDnwFLvf4lt8i2/xLb7F0WAkTJrgJA4vDvwYhTCKJuHUbNSSghM7RxOlBxLDhFru1n3A50Mu4d2sixkd3svnF18Hp8mz1BsnI4icUU7m9vZ2FEUhJaUv/XVKSgqlpaX9jv/rX//Kn/70pzNZJADGOkNsTRCwK26SjSmEFYlAWMEflgnKKqoa1WycjIjWWyo9KLFKYlQqlUShjxTbR3oV6dG8CEJ05RRRNUKqjKz6ULQQmiCgChIKEkr3WkYWdN2rwO5O22+p3Y1TETNP9JyDC2C07u8aYrfeROjWEkRXwtH9HL6/Z819aPtkcPjxR1rBH+s3rV+lCWhazxN1P5bQ79hov+h1XJ9rHrssPcf3+Vno9e1Yg1CvlafQ985Cj66r152F3udoRylxXwzUMX3Qq74OtVrfej68NfvUn9brKbq1Coc0Bgf/nkjv6V+3h+8Ruv+JmtBLQdSrDoXepevus73ULH2v13f78BL229Z6P+ghi8kR207QQBDQosv447xRIqgSGhKqJqJoEprQrZERNDThoHrpmwFR09CrGqgyOlXB7O/C3tWFMRJGkBQEE0j6I7/PWq+tg6POwbpQj1A/aq960jShT731Paf/Pg0BCQUzYQzBMJEYI47YNoxChH2REKrOg13TSAono1dSCQgxdAp2/KKNLqAe+swxAhqJ3fs0ujXvanQeOqiF79GodW+rJzhPGSQRvSRg0InoJRGvVMBjugeYI39CnlZOeqh9QIWQk8XZu/MR8MADD/Dzn/+8Z/ugRmSgcel5FzGl9ddE4kvIH/IbsrKOrJLSeplg1B4TjNZHsIh+Z+DCwZQAtXUvUFPzbI+jqdmcg2n7dKxNk1n8/9k77/A4ynNv31O2S7vqXbIkS7bcbdzAYLCppjkmkAokEJKQnITzEUhPziHJSQIphJqEkhwChBB6780GbLCxjbtlW7Jk9bqStu/Ozsz3x6xWNm6SLFk6eO7r2kvS7sz7vrs7mvnNU1lNzCqRnp7OV77yFdxpaUQ0jbCqE9Y0goqKT4mjaP0n635Tr540EWuALIAsisgCWAQh+bskCMiJhySQ/F0WB563CAKyYHw+dXV1fPzxx+zcuTOZ2SKKItZAH0J3G9mdXjIqf8g0ScIhCmhiDLkshH1aJ7q9A1XxocYDxkMNoWoRVBRU4vtdbgwXmOFVEEAQEUQZUTAyfwTRgihakz9FyYEkOZHkFETZhSy7ES2pSJZUBDUFpR6i1Qrx+hiCakHAOKF3KjpNURVrVQYLLs3hnQfvpW7TRjSrHTXVRaA8jYBVJR5RkWISDtWBXbUfRTwMDx0dQRYQbSJWpxW7y47L5cLtduN2puDfWUvjB2vQw2FsdjtLr/omU05bQuiD7QTerUbp0BFseQj7ZXro8Shq125UXx1IXkRPHCkvHcHtQnBZERx2BFlG11V0XTOCarU4WjCIGvSjB4OowSBqbw9qhxfdH+r3WBkH1X6/Cyog2rBPWoylaAGCvQT6zdISOGZkkbq4GDLs7FjdwqZVe+nt7UGVIqhyGDk1juiKEYkHiUTDB39A+yEIAg6nA7vLjt1px+6wI1tlJFlClmUsVguSKCH0i0xNJx6LE41EiUVi+Hr99PX0EVUOHRcg6Xay3HlUVlYw//TZaBEfr99zJ007jRLZuaUTWHz2WTiIEPM2E/O1EQt0ooS7iUd7iat+VCGM5gTNoaM7QHOC7tDRHKCPQN03IS5gibiQVDe+gERXc4Sw10Y86Gb+BVczpfRUeh7ZBZpOmyCwrieWvGhb7BKFMz1kz77VNcsAACAASURBVHRhKREJalH6lAgBJYpfjeJXYgTjCiE1TjCuEFEVIppKRI2j6KAiouoCKgKqLiZ/Gu5sETnxkETjp0UQcVsspFmsZFjtpAl2lN0aPev85PlUzrFLSILAO9k7qPW3IhDhlKYdFO/Yk3y/cm4unhUrSPvsJVgnTDj0h6JpRhaJlsgm0dSBzJLDPdT9fkcHyQaS1Wh/0f9TlI2sFFsqumSh/bc30/zq47zwmeXMn/YsdnuQ2vZl/Fl5n6iu0QQsKljEDXNvYHLG5GP/sg/B/sKkX5xouo5FEpFF4ZDXp5AS4qVH7uN/eAq77+xRWddgGVeumU8yWjEiDZsb6Xv/fjqmPEKqezYL5j01YmMPF13XaWt7htq9txKNtgGQmjqNstLv0ljtIOcliKgKz7b8mciEScStNlJSUrj88stHtDjSYPB6vWzatInNmzfT1zcQEJaTk8Ps2bNpevNlGrdvwhFVWHHBpWinX8bLd2yi0iZS4ZCSd3qOaZmkLinGWnxwfZKRRA3EiFR7CW3pIlrTk3RdA1gnuInmunjznSZCikbpzCyWfXN6slfF3o0f8fYD99DX0Q5A0dTpnPq5K8iaVEFvtBdfxIfX76Uv2Ic/7EeJKMSVOEpMQYtrxrlMkBARkZCMoDjZgtPmxGlzkmpPxWF1YLFYksGe/QGfn2xPr+s6u9a8y6pHHiDQbXScLZ09l3O/eR2pmQeXxo73+PG/s43Ijg5UvwOEA694uhpD7alD66lH7WtE62tEC7QbPv1B0p8JIeflYSkqQ84uB0suWsiB0qGAOnB6kTPtOOfl4pqfd1Drel3T2be9m+3vNtOw3YumDeznypJInyDjyNbRLRFCMT89PT14vV4CgaNnhQ0FQZOR4y7SUjIpKilkxtzJlE4uOPi70DS2vPUq7z7yALFwGEEQmX7mOZz6+SsOWQRNi8VQOzuNINtQCC0YTPwMoYb8qISJE0YVjEdcCKNLcQSLFcFiQ7RajN+tNmRXOlZPLra0fGR7OhaLm3hUZuNLz7L+xWeNOjnA5FMWc8ZXriE1wzg2wtu66P5XtRETU+6hLs1O7cedBwS72l0Wyk/KpnJeLgWVaSPaR+uTREMK295tZsvbTYR8MWwCLEmzYNcNoer8bCm333or0Xgca1crnz3nXNK2VuN74QXU/c47znnzSPvcZaSeey6iY/Q7b/ejx2K0/c+v6X3iCbZMrmTnnJOoLN5BXtkG6JtB1Tl/5sHtD/LE7ieIa3EEBJZPXM71c68ny3H4UvbHi9frXyf03r2kFm4itfkyFlz5uxEdf9zEiIARrLpgwQLuuusuwAhWLSkp4bvf/e6YBat663rp+8e77D39BhB0Fp3yDg5HyYiNP1RCoTqqq39OT6+R02+3FTBx4g/Izb0IQRB599anKO/MYU84xMa2u9AkGceCJXT19mK1Wlm+fDnTpx+9V86xEIvF2LFjB5s2baK+vj75vN1uZ8aMGcyePZuCggLWPv0Yqx//J6KmcYZmZ85jjyPIMh+/0cCap2pIlQXOnJEJ9X1JS7OlMAXXgjwc0zIPukANB13TUVqDRKq9RKq9xJr8B1i1LYUpOGdl45iZRUOdn9f+vg0trjNhRibnf3PGQX1SlFiUdc8+wUfPPYkaN8L0S6bP4pTLvkRh1bQRs4Yd9v3oOrUb1vHhU/+mfa9xV+jOzmXJV66hYv4pg5pf13WUthCR3d1EdnagtIQ5ZOKUrgFhEMIgRBCEOIJNRHRYEJ02BJsDyelEcLpBtKFHjOJjSnvokOnMUprNuKjMysZSOLg6OpGgQu3GDvas76B1T+8BogSM9Nf0fCeeLAe2VBnZoaLLcaJKOPGIGBlV0RhKTCEajRGLKChRDU0FQRcQdBkhEQQsYiUrO5OSiXlMqMoZUidhf3cX7zx4H3vWrgHAYrMz7+JLmHP+chwpoyuwAUJ9vWx46Vk2vf4SsbBhOSqYPJUzrvgaBZMO7qYa3t5N9792gqpjn5JBxheraGv0U/NROzUbOwj7B75Dp9tK2exsiqekUzgpHftRiqMNBl3TaanppfrDNmo2dBCPGlZUT4aNxWlWJG8EOctBzndnI9pltm/fzhNPPAG6hqeljq/+8hbSsrIJvP02vU8/TfD91YblAyP7xn3xRaRdehn2aVNH9f9S6eig+frvEd64EQSBNz73WbyizBS7jawFfwNdYPa0lWTmFdHoa+SOj+/gtfrXAEi1pnLj3Bu5pPKSo9YoGU3+8+3/5LyOWuw51XiarmHeV346ouOPKyHy2GOP8dWvfpV7772XBQsWcPvtt/P4449TXV19UOzIJxm1yqqdIfpu3UDjSX8glLWdstLrKC+/fsTGHyyaptDQcD919XehaTFE0U5Z6XUUF1+NJBnFfwJ9Prpu3oiMxAdWjd5dt+JDY9G809idk09dXR0AM2fO5Pzzz8cxgncEmqZRX1/Pli1b2LFjB7H9UvDKy8uZM2cOVVVVyUJi9Zs28NTNNwEwo6mL0+//X+xTjeqquq7z+t+3U7O+A5tTZsXVUxF3dBPa0jlw1yyCrdSDrdyDtcxjFPY6yslP13TU3ijxrjCxRj+xBh/RBv9BNTksBS4cUzNxzMrGkm0UUav+oJW3H9qJrsPEk7I552vTjti109fVybpnn2Dr26+jqcb4OaUTmb3sQqpOPWPEOvz2E1cUatatYd2zT9DZUA+AbLWxYMVlzLv4s8c0X7IgW73viKnCQ0XKsGMtSsE2MQ37xDSkTPsxXRBikTitNX007eqhZU8v3pYA8WNZowCebAdZRalkFaeQW+omr9xzyLomQ6G5egerHv47rTVGBV7ZZmP6knOYe8FnSBvBcvpgfHfte2vY+tZr7HjvnaQFJKt4Aos+dzkVC44sTiO7vHQ9vBPiGraKNDKvnIJok9FUjebdvexZ387ejzuJhgb+hwQBsktSyUkUUMuZ4CYtx3FQG4dPoqkaPW0hOvb5ad7VQ8OO7gPETmahi9lnF5O9z0d4UyeCXSbnO7OS/6O6rvPoo4+ye/duxFCAYjXEFb/5Exa7URhPaWuj75ln6H3yKZTm5uS4tqoq0i67DM/FFyF5Rq4ar67r+F56mfabb0bt7kZMTSXnlpu5c9UqdFHkgtIFKJ7biHj2Yo9dx6nLBq4rmzs389u1v2VHt1FuYW7uXG465SbKPGUjtr7B0h3u5uwnzuZmVwaW9Hoymm5gzlc+xem7AHfffXeyoNns2bO58847Wbhw4VH3Gy0hEvJH6fr1WgL5a2mdeQ92eyGLTnknmeJ6PAiF6tm+4wZ8vs0AZKSfRlXV/xxkmfnwhdcpWu2gN67TdVIO0Y/vYVtDDSUWJ5998FFWrVrFe++9h67rOBwOFi9ezPz58w+oMjoUNE2jtbWVbdu2sW3bNvx+f/K19PR0Zs+ezaxZs0hLO7C3Q19HO//88f8jEgxQ3NXHGectJ/eHPzhgm3hM5bnbN9G2t4+UDBuX/WgedkkgtKGD0JZOlOaDzeyiy4LktiKmWIzKmkbusVEMLKgQ90YOMP/3I1hFbBXp2KvScUzOQPIMXLR1XWfzW42sftLoHTNlUT5LrqgatBna19nB2mceZ8e7bxNXDHFmT0ll0smnMvmUxRRNmY4oDe9Y0jWN1ppd7P5wNTvefZuwP9E2wO5gznkXMvfCFTg9h+6rcazomo7qj6F6I8S9EdTeqPE5h+NokThoRoCkIAKyiJRiRUq1IKZYseQ4kXOcg+5vcixr9HWH6W4OEuiJEvbHCPliREMKumZ8t7oOFpuEzSljc8o43VbcmQ7cWQ5Ss+xYjrEx5WHXpuvs/vB91j7zOJ37jBsEQRApmTGLKactoWL+KdicB1cSHix9He3Urv+QbSvfTI4PkDexkoWXfIGJcxcMumtwpLaX7ge3o8eMJoJZV087oH+PGtdo3OmlYbuXpmovPW2hQ45jT7GQkm7DmWpFsoiIokBc0YhF4gR7owR6omif+P+02iUmzs2h6uR88ia68b1aT+DdZhAh6+rp2CsPdG35fD7uvvsuYjEFW9s+Zk6dygXXff8AsaVrGqG1a+l94kn8b7xh1JQBBKsV12mn4T7vXFKWLkU6hutIaOPHdN19F8E1RuqrrbKCorvuYktjAy++9TZCPM4PvnkjNS/eSmfVo0R7J3P+JS8dsM64FueRnY/w501/JhwPY5fs3DjvRr4w+Qujblndn4e2P8Qf1v+B2zJSEVzt5DT/ihlXXj6ic4w7ITJcRkuIKFGVxv9ajSwr7D77/yEQZuaMe8nOHv2AHV3XaW17it27f4WqBpFlN5Mm3URe7mcOeSCu/t1TTOjJYVtYZcIXJmMLbOaZv9+NJa7yHw8+gZySQkNDA88//zxdXUbcgMPhYPr06cyYMYOCggLkI/QW0XWd3t5eGhsbqampoba2lmBwoHCX3W5n6tSpzJw5k5KSkoN85QDxWIxH//sHdNTV4glFWBwWqHz+OcRDnHTDgRhP/X4DfR1h0vNdrPjenGSviHh3mMieHqJ7+4g1+FF7j1z1MIksIGc4sOS7sJakYpvgxpLvQjhEO3A1rvHuv3cne6HMOquYUy+rGNZJIOz3se2dN9j0+sv4OtuTz1sdToqnzaSoaio5ZRPJLCrB6fYc8iIRCQTwtjTRuW8vTTu307hjK8Eeb/L1lPQMZpy1jDnnX3xcTP0mx46u6zRs3cz6l56hftOG5POCKFIwqYqS6bPIKasgZ0IZKRmZhxStSiRCT1sLXY37aNldTfPObXQ17ku+LlksVC5YxMyzzqNo6oxhHb+xRj9dD25HCyhIHitZV0/Hcpiu2YGeCC01vXTu89PZ4KezMUDsMJWAP4nFJpFdkkpeuZuSqZnkTfQkLY++dxrwvWa8r/RLK3HNP3SDx3Xr1vHyyy+DpuKq3cZZV1zNSecvP+S28Z4efC+8SO+TTxLdPVAtFosF59y5OBfMx7VgAfaZM4/aDVdpacG/ciW+554nvNm4aRSsVrK+/S0yrrkG0Wrlb7ffSlOvn0yrxHd//HP23fwStSdfD4JOVelrFJZXHDRuc6CZX675JR8k6nksLlzMr0791XGJHdF0jYufuZgGfwO354pgDVDYdhdVX75gROcxhchR0DWdPT9+D6cosOWsB7BJq0hPO5mTTnpkxOY4FIrSR/Wun9PR8TIAaWkLmDb1Vuz2gkNu7+vpoed3W5AQed2nsOLnC/Hk2Pjzlz6DIgpccM5ypnz9mwCoqsqWLVtYuXLlAQGksiyTn5+Px+PB5XIlK5MGg0F8Ph9dXV2EwwdmJVgsFiorK5kxYwaVlZVHFDIAr91zJ9veeR1rXOXU3U1M+stfSVl82mG37+sM88ytGwn2Rg8SI/ujRVXiXWHUQAwtoKAngj8RMUqnOyzImXYkj21QlSojAYVX79tK8+5eEODUSyuYdVbxMd+JaJpK47at7PrgXfas+4BIwH/QNqIk40xLQ7ZYEEUJJRolEgygRA7OCLE6HJTNmU/VqWdQPmfesK0rJmNPT2szO99fRfWad+lpaTrodUEQcXo8WGx2RFlGVWJEg0EiwYOtg4IgUlg1lUknn0rVaUtGRJjGvRG6HthGvDOMYJPI+FIVjqqjd6XWdZ1YOI7fGyXQEyESVFAVDU3Vka0islUiJc1GSoadlLSD/z91Xce/sgnfa/UAeC4sI3Vx0WHn0zSNBx54gMbGRiR/L67WOr7w3zdTWDX1sPvouk509278r72O7/XXiNXUHriBLGMtLsZaVoaUkY6U6gZNRQtHUFpbidXWorS0JDcXLBbcn1lO1je/ibXEsFyrqspvf/kLVFFi8eyZnLXis3T+fSt7PD8inLELa/SbLD7/R4d+T7rGo9WP8qf1fyKmxciwZ/DLRb9kSfGSI3zyx87KxpVc9/Z1uK0p/CqnEwSdCV0PU/H5RSM6jylEBsH2H6zCI4msXriJ7LS70HWV+fOewe2eefSdh0FPzzq277iBaLQVQZAoL7ueCROuPaI7aM1Lr1HynpPeuMaaOHz9T6cjigLPXXctNR3NlFtdXPLwYwfso2kae/fuZdOmTdTW1h4kMg6FKIrk5uZSXl5ORUUFxcXFRxUf/Wx561XeuO9u0GHB3hbKzzybwt///qj79XaEePZPHxPsjZKW6+TC78wkLWf4Zuuj0bHPx2t/246vM4zFJnHu16clG/KNJJqm0lG3l31bN9G+dw+d9XX0drRxpGT/lIxMMgqLKZw8hcLJ0yicMg15mK41k/FLX0cb9Zs30rK7mo76vXibG9GO0LPFnpJKekEhBZWTya+cQsn0mThSR/Y8CKCFFLoe3kGsznADpp5VYjQZHKWMGV3X6Xu5jsB7RkyH++wS3GcfJgV3Pzo6OrjnnnvQNA17Uy1pssCVt9xxyCylQxHdW0do7YcE160j9NF61IQF+YiIIo7Zs0lZuoS0FSsOal63ae2HPPvKqwhqnB/+6Ec4UlLpe2MfDbv+QcfUh1D85Sz7zBtHnGJPzx5+/N6P2d1jWG8+P+nzfH/+93HII58BpOs6V716FRs7NvL1qV9kuv9/Aaj0vUTJioODm48FU4gMgs0/WEWmJPL2tF3MnVtNW9szZGQsZs7sf4zoPJqmUFd/F/X1fwU0HI4Spk27HY971lH3ffcPj1Penc+OsEqo1M2K750EGL1ynv2b4Z755l8fxH6Ynj26rtPd3U1rayuBQCCZ6iiKIg6HA4/HQ3p6Ojk5OYMWHvvTVrObf9/0Q9R4nMmt3UxSBMpffgk5fXAnht6OEM/d/jEBbxS7y8L535pBQeXIxj/oms7mtxv54JlaNFUnNdPOhf8xk8zCwTdSO1bUeJxgr5dQby/xuIKuqlhsdmwpKbjS0rHaj1/Kocn4Qdc0Qr4+At5u4oqCFleQLFZsLhdOT9pxdcXpcY3eF/cS/LAVAFu5h/TLJiEfpVvyUNGicXqe3EN4qyECPBeWk7p48FWu33nnHVatWoWoqTj3bKG4agqf+/lvhmw11HWdeHs70dpalIYG1L4+VJ8fQZIQ7Dbk7GxsEydiq6g4YrDr/XfcRnNPH5kSXJfoXhvZ3UPbP9dQe/r1IGpMnfgi+ROmHHE9MTXGnRvv5MEdDwJQ7inn96f/fsTrjrzf/D7ffvPbWEUrz5z/F/Zs+TKi4qRKf4H8ZaUjOte4qaw6nlETxSziIYXysv+kvf0FvN738HpXk5Fx6ojMEQrVsX3HjcmA1Py8S5k06b+R5aNfBH19vZR0GwKjRdGYXDrwRZaddQ72++8mIktUP/wPZt/4w0OOIQgCWVlZZGWN/J1/yNfH83+6GTUeJ9cforyjl9zf/27QIgQgLcfJZT+ax8t/2ULHPj/P3fYx8y8q46TzShAPEd8xVLpbAqx6ZBettYarqnx2NkuvrBqRNMShIMky7qwc3FlHbvJocmIhiCKutPRB39GP6lpkkfQVFdgmuOl5eg/RvX20374RzwWluBbkj4h1RGkL0v3ITuKdYZAE0i+pxDXvyJmTn2Tx4sVs376drq4ulIJSmnZsY/VjD7P4y1cNaRxBELDk5WHJy4NTh3e+VxSFFm8PCOIB5ROsRSnIMTdO71RCWduorX6K/Ak/P+JYVsnK9+d/n0WFi/jZ+z9jb99evvTSl7hh7g1cPuXyEQlkjWtx7th4BwBfqvoSqYk4HSmWiuweW/fv+Knre5yJJ75XPaLicJRQWPhlAKp3/RfqIDovHgld12lpeZx1Hy3H59uMLLuZPu1Opk79/aBECMDWD9YiI9GjKwQ1yNlPiIiixMSySgB2rVtzTGsdDpqm8tKdf8Df3UkKIjPr20k57TTcF1885LFcHhsrbjyJynk5aJrO2uf38vQfN9Kxzzfs9QX7orz3+G4e/81HtNb2YbFJnPHlySy7dvpxFyEmJv+XcM7JIff6k7CWutFjKr3P1tJx18dEanoP6sI8WLSYSt+rdbTf+THxzjCSx0r2tTOHLELAiHm7OHGeiaamE3emsu65J6ndsHZYazsW1q9+H10QEZQYC88+N/m86LQgZdhxtxmZocHYm4Mec1HBIp5a/hRLipagaAq/++h3fPutb9MVHoQb6Sg8svMRqr3VuK1urplxDUrMCIqXlFRkx9ieF09YIaIlFL6YKI0xsfwGbLY8wuF97Km5edjjxmJetm77D3ZW/wRVDZGWtpCFC14iN/fCIY0T3d4DQFvUWGdu6YGmrRmXfQmAFi1GoKZm2OsdDmsef4SGrZuQJZk5u/ZhtdnI+8Uvhq3aLVaJc66ZxtlXTcFql2iv8/HEzet57f5tdOzzDfoE2N0c4L3HdvPPn3/Alreb0FSd0plZfOmmhUw/vfC4pseZmPxfRc50kP3NmXguLkewyyitQbr+tpXOv2wmtKXTCBofBFo4jn9VI21/XI9/ZRNoOvapmeRcNwdbyfBd7RMmTGDevHnGHxOnogsCr/z5T/R1tA17zOGwYZ0hfnJcdpyfiN2xFqaQ0nESuiojuxppa9w26HEz7Bnceead/Gzhz7BJNlY3r+bS5y/l3aZ3h73WXd5d3P3x3QDcOO9G0u3pRCKGuJFjqciOsXWOnLCuGV0SIQ5izLg4yXIqU6p+y6bNX6O5+Z+4U6dRUPD5wY+n67S1Pcuemt+iKF4EwcLE8u9RUvL1Idcn8Yd8FHcb7pQ2RcfpseJKO7B4VcG8+aQIEgERtv3jfk7+9ciW5z0cNR99yNpnHgdgRks3qZEY2T/6EdaiY+tmLAgCk0/Op2BSOh8+V8vude3UbOigZkMH6fkuymZlkTvBTXq+E6tdRhAFQr4ovq4IrbV9NFV76WocyDTIKXWzcHkZxVMyTAFiYjJEBFEg9dRCnLNz8L25j+C6NmKNfrz/qkawSdirMrCVebDkOY2sNVlEj2uoPRGU9hCRXT1Ea3vRFUO0SGk20pZPxDE1c0TWd/bZZ7Nr1y78fj8ZldOJ7t7K83+6mS/96g/IR0nJHQn6envoCoZBEJh/ysHZJpbCFKStLmy9U4llbqG+5gXyigdf/VoQBL5Y9UXm5c7jh+/9kD09e/jOW9/hovKL+P6875PpGPzn2BXu4nsrv0dEjXBq4alcUnEJAJFQNwBSLAWL0xQiY4MsQlxDjosomoJFtJCZeQalpd+lvv5udlYb5W4HI0b6+jZSU/tHensNhexyVTJ1yh9wu2cMa2kb1q+mQkvBL0bxqSJlpe6DLqaCIFA1Zx7rN65lx7bNLIjFjpoTf6x4W5p55c9/AqDS4iK/rRb7jBlkXHnFiM2RmmHnnKunMeecCWx8bR97N3XS0xqkpzV41H1FUaB0VhbTTiugeKopQExMjhXJZSH9MxW4zywh8EELwY/a0fwxwps7CW/uPOr+cq6T1MVFOGdnIxyhavFQsdvtXHDBBTz22GP0Whx4MrLoqKtl5UP3c/bXR7ZC6KF444XnQRCwxCLMWbzkoNetiWB4j3c+nZlb8IfeAX4y5Hkq0it49MJHuX3D7Tyy8xFe3Psi7za9yzdmfIMvVn0Ru3zkYOK2YBvffvPbNPobKXAVcMtptyTPi9GoYRGRYh7EUSryN1hOXCFikSCi4dDs9ER6yHEagYTlZdejxLppbnmUndU/oadnLRMnfh+7/cAyzZoWpavrHVpaHqPba5jMRNFGWel1lJRcgygOXxT0bG8GJtNt0QCRnAmHjp6fe8232LDhQ3psMnX/+icTr/rasOc8GkokwvO3/oZYOERuZjYT3/4QwWaj4He3IAwj4+ZoZBWlcO4104iG4+z9uJO22l7a9/nxd4VRoiq6Do5UC640GzkT3BROSqN4SgaO1NG/GzIxOdGQUq14zi3FffYEYk1+Iju9KC0BlLYgajAOcQ0kASnNhpxhN0r8T0o3CguO0g3BlClTmDJlCjt37kSYNBN97Uo2v/EKBZOnMnXx0lGZEyAej1NduxcQqCqbgHSI85+lwBAi7uaZdFQIiI5aAr5GUtxD7yZvk2z8aMGPuLD8Qn71wa/Y6d3JrRtu5aEdD/GFyV/gookXUZhyoEU6rsV5ae9L3Lr+VnqiPWQ7srnv3PtIsw9kJUajhpCUY24Ey9hGaZywQkSQJUDBrlnpDncnhYggCEye/Custlzq6u6grf1Z2tqfJ80zF5erAgSRSKSJvr6NxOP+xD4S+XmXUlZ23WGLkw2WcDxMfqtxsPSpdiBO1mG606ZkZVOaW0hdRwsbX35+1ISIruu8es8ddDc14Ex1M33dVkQg58YbsJWXj8qc/dgcMlMW5TNl0YAQ1HUdXdNHJLPGxMRk8AiigK3EfVCMh67roDNqtUcOxwUXXEB9fT3ePh+lp55F9/tv8Mb9d5MzoYysktJRmXPtu6uIIyDEFc5a8dlDbiO5LEjpNujxoPVWIqXvprb6BWYt+I9hzzs9azr/uvBfvFD7AvdsvoeWYAt3b7qbuzfdzZSMKVSmV+KyuOgOd7O+fT3eiBGMWpVRxW1LbqMo9cCCcbFYv0Vk7IXIiXsmtximKIdupTvSfcBLgiBSXnYd8+Y+SVraQkCjt+8jmlsepbn5Ebq7VxGP+7HZ8phQci0nL3ydKVNuPmYRArChei1FsVziqDR3GyWUsw8jRAAWXPUNABpR6Hhv+MFMR+LDp//N7g/eQ5Rk5gfi2AJBnAsXkn7FyLlkhoIgCKYIMTEZRwiCcNxFCEBqairLlxul3uu7e8icPod4NMrzt91CNHTo/jjHyprVqwHIT3GSln34zJ9+90xq+GQAur2Dz545HLIoc0nlJbx4yYv85rTfsDB/IQICO707eb72eR6tfpTX972ON+Ilw57B9+Z+j0cueOQgEQIQVw2hIkc9Yy5ETliLCIkP3q5ZaT9MapTHM5u5J/2LUGgfvb0fEYk0o6Nis+aS6p6OO3X6iDfKa9lcQymT6fKEUHrtOFItOD2HdzcUzZ1Prt1FeyTIhw/cx/LFp4/oevasW8Oax43SV+yrUAAAIABJREFU9wsrpuJ6/BlEl4uC3/5m0A22TExMTEaLKVOmcNJJJ7Fx40a6HR6cWTn0tDTx0h2/Y8UP/3tEWyTs3PQxQVUDXeOc5Z854raWwlTC27rJCZ9MPQ+hyVuJxbxYrUcvoX80LJKF5ROXs3zicjpDnWzs2Eijv5GQEsJj8zA5YzJzc+diEQ+flhtXB2JERjJ+ZzicsEJEsBofvE230B1uPeK2TucEnM6jlyA+VjRdw7XPuKuIp6fAvjhZRSlH9bGe/PkreO6he6n199C5fh3Z8xaMyHo699Xxyt1GcOr02QtIT5STz/2vn2MpPLYsGRMTE5ORYtmyZYaLxusle95pRN9+ibpNG1j1z/9l6Ve/MWLzvPriCwCkyyJlU4+cBdNvEXH2ZBDpLcae1kjD3lepqPryiK0HINuZzXml5w1pH02LomNkGcpR0zUzZgg2Q4PZsRzkmhkrdrRvp8pfCoBqNaotZhUdvcxzxYUXk2uxo4kCq+6+bUTW4u/u4pnf/wolGqG4ahoTXn4DNA3PJZeQtmLFiMxhYmJiMhJYrVYuvfRSRFFk774Gyi+8FICNLz/HxldeGJE5Nq/9gL64BrrOBZ+55KjbWxJCRPVGEMOnANDa/OqIrOVYicUS1zxNQoy7jCzSMeQEFiKGuc6myyNStW4k2LZpAzbdSsAWpq3TqO6aVTK4SqynX/Mt0HX2hf3UPPf0Ma0j5Ovjyd/8F/6uTtLy8plT24ze2YWtsoK8//6vYxrbxMTEZDQoLCzknHPOAeDjXXuYcqERSPrOP+5l53vvHNPYqhrnlZdeAiDbbqVy5tF7hUkuC5LHqP+UZzsDgKj+Eao6OrErQ6E/UFWOedAFYcxLHZywQkS0J4QIMj2hnjFejUG4xggeihaJdLUYB+tgLCIAJUvPpsJjFEF765EHiAWPXnfjUESCAZ655Rd4mxtJycjkdGsa8fUbEF0uCm+/HdFhNmgzMTEZn5x88snMmDEDXdfZ1tbFlHPOB+CVv9xGzUcfDnvcF/75EBFRBk3jsiu/Muj9LPkuAHIdlcQC2QhijM7OlcNex0iRzJiJutHHIMj4k5y4QmS/2vrBoH8MV2LQFmyjuMsQEukTiolHVWSLSFquc9BjnPmzX2CLqwQEnVf/+0dD7g0R6PHy+C9+TFvtHuypbs6aPIv4Cy+CKFJ4+23YJk4c0ngmJiYmxxNBELj44ovJy8sjFApRG9aoOPUMdE3j+T/9lu2r3hrymHXbt7J5z14AppZNILdo8LVALHmGELFHNcLtRvf0pn2vDXkNI83+FhHGQQbi2K9gjJDtEvHEhTocGJ71YCR5v/ZdKiNGQGzMbhy8GYUpiENQq6mlZZy5ZBnoOnua6vnwgfsGvW93UyP/vumHdDbU4/Skcd7cU1HuuR+A3J/+lJTFi4fwbkxMTEzGBqvVype//GU8Hg/d3d202dxMPm0puqbx6l9uY+2zT6Brg+uX09fZzr8ffghdlrGL8NkrvzqktVjyjRvJeHsIp804h/oC76Hr6tDe1AgTjSWKmUXdIJsWkTFDsojEEwYDNaKgaMqYrmff9l1IiARTY3R6owBkFQ8uPmR/pnznOmbZjGJDa157gQ8f++cRLSO6rrP5jZf550+up6+9DU9uHufPX4xyh9EgKfMbXyfjisuH8Y5MTExMxga3282VV16J0+mktbWVVrubGcuMrr3vP/ogT9/yCwI93iOO4W1p4u+/v5mo3QW6zhcvvwJ5iFWk+y0iSluQgqKTUWNOdKGPPt+m4b2xEWKgmNnYp+7CCSxEZIuIkrg+p6hOusNjlzkTUkI4Gg1Vap+Ylmzell00dCEiiCJLbr+byoAhZlY//W+eufkXeFuaDthO13Uad2zlif/5GW/+7S/EY1EmzJjNOQUVhG+9HYCMa75G9g03HMtbMzExMRkTsrKyuPzyy3E4HDQ3N7MrEOPky69Btlip37yRB7//Hda/8DTR0IEW8XgsxsZXnufvv74Jn9MDwJlnnEHpxIohr0HOcoAkoEdVCgs9BFqNlN+O9qG7iEaSWLK8+/gQIidsHRHZIhHRdUDAqdnpCHWQ58obk7V80PIBM4OVAGRPLaH7X7sByBxkoOonkTMzOfcPd2D97rfYmZlK3eYN1N2wkdyyiWQUFBGPxWir3YO/2zgYJYuFRcsvI/eVtwh98IEx97XXkn39/xvzaGoTExOT4VJYWMjXvvY1Hn74Ybq7u3k/FGLptddT/cITdO6rY9U//5f3H3uY/MrJpGZmEw0GaNq1g4DVSTS3BASBk2bPZvHS4fWuESQRS44TpTWII64R7zsJWEd725tMmvTDkX2zQyAabQNAjqQhjHHDOziBhYhkHXDNpKhOOkNH7yQ5WqytWcNXokuMP/JdBHsNa0ZmgWvYY9qnTuX0P9xG5n9eR3WqjQ6Pi/a9NbTvrUluY7HZmTz/ZCarEtE/3EHI70dwOCj4za9xX3DBsbwlExMTk3FBdnY2X//613n00UdpbW3l5bfepmLmQuaecgZ177+Nt6mBph3bAFBtdqLZRaipRr+vk046iYsuuuiYbsgs+S6U1iDxthAZGaeja/cRi9cSDjfhcBxcev14EI11ACBH0xE9pkVkzNjfNePSHLSH2sdkHaqm0rvHUKexLIHevhgAKek2rI5j+3qcc+cy88GHyPzeDfRt34s3xUE0xYk9vwC3KxWPt5f4Pf8grBqBU/Zp08i/+bfYJ006tjdlYmJiMo5wu91cc801rFy5kjVr1lBTU0MN4C6sIHPqXGLhEL5AgFDEuAkURZGzzjqLRYsWHbNVeP84kaLKEvbsq8CZs5uu7ncoLrryWN/akNF1jWg0IUQi6Ug5pkVkzJAt0oAQUR10hDrGZB1bu7ZS2me4hDwVObS2GP7KjIKhx4ccCltFBaVPPkHPI/8i5YEHiDd1QJPxXuOJbexTp5Jx1VdxX3ghwgj2ZTAxMTEZL8iyzNlnn83s2bN5//332b59Oz6fD5/Pl9xGEASqqqpYunQpOTk5IzLvAQGr55Xy8YczcebsprPjrTERIoriRdcVdF1AjnkQbWMvA8Z+BWOEbBVREtkkhkVkbITIqqZVzA4Z9Tkc5el4dxjF1TKOwS3zSUSbjcyvXU3GV79CZNs2ojU1aJEIckYG9unTsRYPPi/exMTE5P8yWVlZrFixggsuuICmpia8Xi+apuHxeCguLsbpHHztpsHQX9Qs3hUmxW1BC8wDnqS390Pi8SCyPHLn+sEQjSas/9FUBF1GspmumTFj//Rdp2anI9w8JutYW/cBl0S/DYCt1IP3rUbg2OJDDocgSThmzcIx6+jliU1MTEw+zVitVsrLyykvLx/VecQUC6LLghZUiHeEyS6YQsyfjTW1k56e1WRnnzuq83+SfrcMEaOfmWAZeyv42EuhMcJilQ5I3x0L10xzoBlbm46IiJBhRXJb8SZdM8dXJZuYmJiYjDyCIGDJM6wsSluQgsp0Aq0zAejsevu4r6c/Y0aIGAG5/Z3ox5KxX8EYIdukAdfMGMWIrGxcybSQkZvuKEsn5IsR9isgQHq+KURMTExMPg1YchNxIh1hCirTCLQYVumurnfQ9cFVeR0p+l0zYr8QMS0iY4cRI2L8nqK6CCpBgsrxLfW+qnEV0xNCxFbqxttqzO/OcmAZB7ndJiYmJibHjpyTKPXeESI9z4kWnooac6AoXfj8W4/rWpJCJGq4ZkTTIjJ2SJKImsjKStUMtXo8rSKBWIBNrR8zOdFfxlrmwdtiVFTNMK0hJiYmJp8aLAkhonSEEASBgoosgu1TAeg6zu6ZaMwQIpJpERkf6InStim6cZC0BluP29yrW1ZTHirEolsQUyzImfZkfMhoBKqamJiYmIwNcqKLutoTQYupFFSkEWgx4kS6u945rmuJRFoAkCIZAAiWsZcBY7+CMURPfAEO1QpAa+D4CZED3DJlHgRBGAhULTSFiImJicmnBcllZM6gQ7zTiBMJts1A1wX8ge1EIsfn2qPrelKIWMKZgBmsOuboiTgMWZewaDItwZbjMq+qqbzX/F4yUNVa6kbX9WSMSEb+yBQzMzExMTEZH8j7uWcyC10IpBHuNlKHu7qPj1UkHu9DVY3rjDWSECKma2ZsEa0ieiJzJkV1HjeLyObOzfgifUwLG4XMbKUeQn0xoqE4giiQnjuyBXVMTExMTMYWS44DgHh7CFESyS1NPe7umUjEqJelxz3Iug0wLSJjjmyTk5kzqZrzuFlEVjatpCxaiFOzI9gkLPkuetpDALiz7EjjwGdnYmJiYjJy7B+wCpBX7kmm8Xp7VqOq4VFfQ78Q0WLZ9NtBTIvIGCNbRWL9QkR10RZsOy7z7l8/xDrBjSAK9LYZ5rL0PDM+xMTExOTTRn/Aanw/IRLzFaBGstC0KN6eNaO+hv74EDWciZTIGjWDVccY2TpQ1CxFddIebEfV1FGds8HXQF1f3YBbZoIbgJ424+BMM90yJiYmJp86LDmJnjPdYfS4Rl65BxDoazTcM12db476GvqFSCyYMSBExkHNqhNbiFikpEUkTUslrsfpDHeO6pwrG1cCMDM2GTAsIkDSNZOeZwoRExMTk08bYqoFwS4bmTNdYewuC+l5TgLNiSqr3aNfZTWccM1EfRlJ14xoWkTGFottwDWTL+UC0BIY3TiRVU2rSFfcpEVSQABrsZEh05uwiJiBqiYmJiafPgRBSAasKu0D7plQ1yTQncRinaNeZbU/RiTcm4YoGCYR0yIyxuzvmskTcwBoCjSN2ny+mI+N7RupipQBYMl1ItpklJiK3xsBIM20iJiYmJh8KpEPEbCKJqP0Jqwio+yeiUSM65sWyko+Z8aIjDGydcA1ky0YOdWN/sZRm29182riepyTtdkAWEsMt0xvQh3bXRYcKdZRm9/ExMTEZOywHCJgFaC7djoAXV1vjdrcitKHovQAoAeyjSdFSAaLjCEnuBARURIuuXTdOCAafA2jNt87jUau+GzF6DFgLU4FBoSIGR9iYmJi8ulFzk4IkU4jVTc9z4nNKeNrmgZIBIK7CIdHxyofDu8z1iBlIWqJGiIWCUH4FAuR+vp6rrnmGsrKynA4HEycOJGbbrqJWCw2WlMOGYtVIpZwzbhVI6J5tCwiiqbwfvP7iLpIdo8hQKwlxk8zY8bExMTk04+clShq1h1G13QEUSC3zI0Wc2FhdK0ioX4hIhbtV0NkfNgiRm0V1dXVaJrGvffey/bt27ntttu45557+OlPfzpaUw4ZI0bE+N0eN1wiDf7RsYhsaN+AP+Znll6FEAfBJiXVcX8NETM+xMTExOTTi5xuB1FAVzRUXxQYcM9Eu+cCoydEwiFDiIh6IdI4ClQFkEdr4GXLlrFs2bLk3+Xl5ezatYu//vWv/PGPfxytaYfE/gXNLFFDk/VF++iL9uGxeUZ0rrf2GQfXBbazAMMaIojGwTCQumsWMzMxMTH5tCJIAnKmnXhnmHhnGDnNTt5E41rTUT2FvFOhp3ct8bgfWU4d0bn7XTPE88dVMTM4zjEifX19ZGRkHPb1aDSKz+c74DGaWPbLmtHDKjkOI3NmpONEdF3n7ca3AZgVqwIG4kN0TR+IETFdMyYmJiafapLumS4jTiS31I0gQG9zGg57Oboep7t71YjPGwrXA6BF8wZcM+PEInLchEhNTQ133XUX11577WG3ufnmm/F4PMlHcXHxqK5pf4uIHlGZkFICjLx7Znv3djpCHThlJ2ldxkHYnzET6I0Sj2mIkkBqln1E5zUxMTExGV/I2QkhkghYtdplMgqNelIWbREAnaPgngklXDPxUG7SIjIeipnBMITIj3/8YwRBOOKjurr6gH2am5tZtmwZn/vc5/jGN75x2LF/8pOf0NfXl3w0No5eKi0cGCMCUOEwyq7X++pHdJ63GwxryFnZS1G7jHoh/RaRnkR8iCfbgSSNj4PCxMTExGR0sGQlaol0DTS5yyszbkwjXScB0N29Ek1TRmxORfGhKN0AxPzZyOPMNTPkGJEbb7yRq6666ojblJeXJ39vaWlh6dKlLFq0iPvuu++I+9lsNmw221CXNGxkq4QOxDE+iEq7se7a3toRnadfiCyzLjXmzXIguSyAmTFjYmJiciKRtIjsL0TKPWx/r4XOmgKyFmagKF76+jaQnn7yiMwZDO4GwGbLpzdgReL/eLBqdnY22dnZg9q2ubmZpUuXMnfuXB544AFEcXyor34sNmM9MR1kAcoshmumprdmxOao76untq8WWZCpipQRoz2Ztgv71xAxA1VNTExMPu30x4ioPRF0RUOwiOQmLCId+4JMPn8Jbe1P09n15ggKkT0AuFwVtAYU3OPMIjJqq2hubmbJkiWUlJTwxz/+kc7OTtra2mhraxutKYeMbDHUYH8tkQIxDzCCVRV1ZMxi/UGqC/IXIDQb6Vr7C5F+i4hZzMzExMTk04+YYkGwS0bzO69hFUnLMQqbqYqGVTgNgM6O19B1/UhDDZpAQoikuCYRCcTGVeddGEUh8sYbb1BTU8Nbb71FUVER+fn5ycd4QU58CVE1UdQs7iLFkoKqqyMWJ/JWgxF0dGbRmcQa/QBYi93J15M1REzXjImJicmnHkEQBjJnEgGr/YXNAEJt05EkF5FoCz7f5hGZc8AiUknIr5w4Bc2uuuoqdF0/5GO8IFuNtx9JlHnXggoT04yA1ZGIE+kMdbKlcwsAS5yL0CMqgkXEknDDxCJxgn1GpVlTiJiYmJicGFiyDw5YzS1L1BOpj5CVacQTdnS8PCLz9QsRu20i8ah6YtcRGW9YrAe6ZrSAQkVaBTAycSJvNhidFGdmzSSl0whOtRSlICSOgv74EIfbij0RvGpiYmJi8unmkxYRGMicaavzkZNzAQAdna8e8827ovQSi3UCIGoTjPnF8RWsekILEVEWEEWBaOJ71oIKlemVAFR7q4+w5+B4pe4VAM4rPY9YQ8ItUzLglknGh5jWEBMTE5MThkNlzuSUGtcGX2cYp+0UJMlJJNKM37/1mOby+7cDYLcXEQsZN7y2hCVENIXI2CMIAha7REwzlIgaVJiWOQ2AHd07jmns1kArH3d8jIDAsrJlSSFiKz44Y8Z0y5iYmJicOAxYRELJ5+wuSzJpoWtfjMyEe6b9GN0zfv82ANzumYT9RhKGJVGzyrSIjBMsNmnAIhJQmJwxGVEQ6Qx30hHqGPa4r9Qb1pB5efPIkjJQ2o2g1P0zZvo6jIPQk+MY9jwmJiYmJv+36BciWiiOGhzI0MxNNMBrq+sjJ+d8wIgT0XVt2HP5EkIkNXU64YARk2hJhAcItvEhAcbHKsYQi01KlnnXggoO2UG5xyhstr1r+7DH7XfLnF92PrGmAOggpdmQ3AMF23o7BlK3TExMTExODESrhOQxOr7HD1Fhtb3OR1bmEiQphUikmd7e9cOey+9LWERSpxP2JSwi/SXeTYvI+MBik4ju55rRdT3pntnePTwhsrd3L9XeamRB5pySc/aLDxmwhui6Tl8iUMmTbVpETExMTE4k5ETmTPwQmTPtdT4EwU5uImi1te3pYc2hKL2EI0bvtP0tIsn0XZspRMYF+7tmUHX0qMq0LEOIbO0aXpDQS3UvAXBq4amk2dOINRhdhPevHxIJKMTCccAUIiYmJiYnGofKnMkocCHbJJSoSk9rkLz8zwLQ0fEKqho65DhHwuczykc4HCVYLB7CfkOIiIlMHDNGZJwg2yQ0QE/4zLSAwpycOQBs6tiEMsTGQ3EtzrM1zwJwUflF6Lo+UMhs//iQxMGXkm5LFlYzMTExMTkxSAqRrgGBIYoCuaXGdaJtbx9pnnk47CWoaoCOzteHPEdP7zoA0jzzAAgHjOuZqJlCZFxhSZimtMQXogYVJqVPwm11E4qH2Nm9c0jjvdv0Lh2hDtJt6ZxZciaqN4IWUEASsBakJLfrNQNVTUxMTE5YLAlLuLKfRQQg7wD3jEBe/iUAtLUO3T3T2/MhAGnpCwGSWTPEDSFixoiME/qFiCobH4UWiCEKInNz5wKwvn1oQUJP7H4CgBUVK7BK1qQ1xFKQckAVu75EoKrHDFQ1MTExOeFIWkS6w+jaQNGygcwZw6Wfn2cIEW/PGiKRlkGPr6ohfIkaJOlpRvO8sD+GCIneu2bWzLihX4jEE0JETSjG+XnzAVjXtm7QYzUHmlndvBqAyyZdBkB0n3Ew2fZzy8B+qbtmfIiJiYnJCYeUbgdJgLiO2hdNPp+bKGzW0xokGlJwOIoTQkKnuflfgx6/t28juh7Hbi/E4ShC13VCfTFkYWAbwWJaRMYFSSGSiBFRfcYBsTDfMGWtb1tPSBlckNBTu59CR2dh/kJK3CUAh6yoCmbqromJicmJjCAKyBl24MDMGafbijvLeL6j3rh+FBV9BYDmlsdQ1SiDoavL6Pyenn4KANFQHDWuJYWIYBERROFwux9XTCGSECIxIRGsmrCIVKZVUpRSRFSNsrpl9VHHicQjPLXnKQA+N+lzxlgxFaU1UchswmFSd80YERMTE5MTkv3dM/vTn8bbVtcHQFbWWdhs+SiKl/b25446rq7rdHW+AUB21jkABBNWF4dDBsZP6i6YQgSLzfhS+lN4+y0igiBwVslZALzV8NZRx3mm5hm8ES8FrgLOLDkTAKUpAJqOmGpF8gwUMjsgdTfLFCImJiYmJyJyZn/mTOSA5/PKEw3w9hqufVGUKS6+CoD6ffei6+oRx/X7txGJtiBJTjIyTgMg1Guk7qakGP1mxkvGDJhCJGkRiSTyqtVEnjXAWRMMIbKqcdUR3TMxNcY/tv0DgKunX41FNL7oaMNAfIggDJjAzNRdExMTE5OBFN5DW0Ta6/qS3XcLC76ILHsIh+uP2n+mveNFADIyTkeSDDdPMHGT7XIZN9/jJWMGTCGSFCJhNSFEfANCZFb2LEpSSwgoAV7c++Jhx3i0+lFagi3kOHJYUbEi+XwyPmTCJ+NDzNRdExMTkxMdOREL8knXTFZRCpJFJBqKJzMsZTmFkuKrAdhb+yc07dCxIqoapqXFyN7sz7gBCPYa2ztN18z4o1+IhBSjqZAWVNATokQURL5Y9UXAEBv9ynR/usJd3LvlXgC+O+e72GXjwNJ1faCi6kEZM2bqromJicmJTtIi4o0krzsAkiySk7hu9MeJAJSUXIPVmkM40kBDwwOHHLO9/QXi8T7s9iKyspYmnw/1GTfZ9kQ4gmAdP5f/8bOSMSIpRGKq8WnoRi2Rfj5T8RmcspOa3hpe2PvCAfvqus4v1vwCf8zPlIwpLJ+4PPma2hMdKGRWmHLAfv2pu2nZphAxMTExOVGR3DaQRVB11N4D40Ry+xvgJeJEACTJScXE7wOwt+4OAoFdB+wTjwfZW3cHAEVFVyAIA1aP/mBVe6J2iBkjMo7oFyJKTENKMboh7u+ecVvdXDvrWgBuXX8rrYHW5Gt3fXwXq5pWYREt/Pq0XyOJA19svzXEku86KFe7t8PMmDExMTE50RFEATmz3z3zSSFyYOZMP3l5nyUzcym6HmPLlm8RjXYAxo1xTe3viEbbsNuLKSq88oD9golgVWviemTGiIwjknVEoiqiOyFE9gtYBbhyypVUpFXgjXi5+rWreWTnI9yw8gbu33o/AD9Z+BMmpU86YJ+BQmYHxoeYqbsmJiYmJv0MZM58otR7InOmuzmIEh3IkhEEgSlTbsFuLyYcaeCj9ZfQ0PgAO3bcSHPzIwBMnnRTMki1n1AiWNWaKCRixoiMIyz2hEUkqiL1CxHfgUFAFsnCX8/+K8WpxTQHmrll3S288f/bu/fgKOt7f+DvZ++7STabkJALhGC4BLkJyiGVY8WjHMXS1o5OK+rPQutgtbbaSlWo90srFsbO1LGt4yB6Om2pWm9TQalVfq0e1IqoSAAJdwkJkMvuJtls9vI5f+w+T7Jk79lkd8P7NZMZ2P3u7vPNk81+8vl+Pt/n8N+hV/T42byfafuGDNRfqBpZH8LWXSIiUsXqnCkssaDAYYYEBScOuyLuM5vKcO7c/4HVWguvtwX79j2ClvD+IvVTH4yoDQFCfwCrGRFjeBOzXFqaMWT7ALJNzYiIADp1aaazb9C4yoJK/Olrf8ILX7yA7Se2o6qgCt+Z+h2cPebsQWMjNjKLsaMqW3eJiChW5wwAVJ5lx/4dJ9F60IVxU0si7rNaJ6Bh/us4+uX/wOn8GAZDEcZVL4XDMW/Q83jcPgT8QUABDArQB0CXQ8WqZ3wgEhEMhDd68Z9WNKRyWBxYMXsFVmBF3Of0HRuwkZnDHHGf86TaustCVSKiM12spRkgdAG8/TtOouWAc9B9AKDXWzGx9gcJX8PdHvpMK7CbgHCHKJdmcohOp8AQjgylIBSIBDqS28s/loFtuwM3MgMGtu5yWYaI6ExnVJdmOnohgWDEfZVq58xBV9TtI5LlDhfCFo2xINgXDkRyKCN/xgciQP/yTMASShAFOqJnRJLlPRQuVD1tIzOArbtERNRPZzdBMeqAIOA/7Y/g8glF0OkV9Lj64IqSMUmWmhEpGmOF9IUKX9k1k2OM4QDEHz4xAXcfxB+M95CYJCj9gUi4/Wogtu4SEZFKUZSYyzMGkx5jw3/QNu+LvjyTDC0jUmpBMNyBw6WZHGNSO2cUhDaXESDgTG95xn+iB+LxQzHpYKwuiLhPRLSMCAMRIiICBhSsRsl6VE9xAACamzrTfv7+jIgF0hvq2tRZGIjkFFM4I9LXG4ChJFRcenqKLFne8OYzplo7FH3kt7e3y4e+3gCgAMXlDESIiGhAC2+UzhktENk3hEAkakYkd3pVGIgAMIUvAuTrDUBfEopMT99uN1lqIGKeGHtZptBhhsGYO9EoERFlT7zOmapJxVAUwHXSg640/0COzIiEa0SYEckt6tJMX68fBkf6GRERgTfcZhWtPoStu0REdLpYm5oBoT+Uy2pCG2M2N3Wk/Nzenv4e99/fAAAgAElEQVRNNAsdZq1YlTUiOUZbmvH4oS8NZ0SipMgS8Z/yhC50Z1BgqikadL/auutgfQgREYWpgUig0xu1UaJ/eSb1glX1kiLWIiMMA3aT0Fm4NJNTTFY1IxKAMVy74UujVarvYHj/kJqiUDvWabRCVbbuEhFRmK7QGNrXQwB/++CygKHUiXS2hj53SioLEAwvy0CvQDHkzsd/7hxJFhm1YlU/DOEgwX/Ck/IGMlp9SJRlGYCtu0RENJiiKHE7Z6omhz5TOo53w+MefAmSeDpawntXVdgg3tzrmAEYiAAYuDQTgKHUAugA6QsgmMIJT1QfwtZdIiKKJV6diLXQhNLwdhDHvkgtK6JmRBwVNi0jkksdMwADEQD9SzO+Xj8Ugw6G0vDyzInkl2f8J3pCe48YdDBPHLyjKlt3iYgoFq1zJkZ9Ys20UgDA0ca2lJ5XzYiUVNog4dZdXQ4VqgIMRAAM3EcklLbqj0x7kn6O3i9C1czmumIoUVpz1YIhtu4SEdHp4mVEAGDCjFAgcqSxPemyAQn2Z+JDGZHQZ5zCpZncY7T0F6sCgCGcsfCfTD4jogYiltMu1azqPMHWXSIiiq4/EIm+h1X1FAf0Rh26OrxoP96d1HO6O3rh9wWh0yuwj7EMyIhwaSbnDGzfBQBjuGDV15pcRiTYF9DqQ2IFIrzqLhERxWIYE946wumF+AKD7zfpMW5qqHvmyK72pJ6zvTkUsBSPtUGn1w2oEWFGJOdo15oJR4vqNWL6jnUllQLzHnACAYHeYdayKafjVXeJiCgWXYFRWzLxt0XPikyYPgYAcGRXcnUiJ4+4AQDlNYUAwK6ZXKZu8d7n8UNEYKwsAPQKxONHIIkdVr3qskx9CRRFiTpGrRFhRoSIiE4XauFNrk6kualT+8M5Hi0QmRDaYDMXrzMDMBAB0L80IwL4+4JQDLpQMAKg75g74eMT1YeICPcQISKiuBJ1zjgqbKEL1/kFx75IvN27GoiMrQ11crJrJocZTDqoiQy1c8Y0LpTK8h3rivtY38meUPSqU2Ce5Ig6pre7f6//4jIGIkRENFiiglVFUbSsyKGd8Zdnelx9oYvkKUBZeGnmjO6a8Xq9mDNnDhRFwSeffDISL5kSRVEilmcAwBgORPq+jB+IeHaeAgCYJzti7t2vFqoWlphhMOXWDwAREeUGNRCJd4mRujnlAIADO04gGBh8XRqVmg0pqbD1Z/3P5K6ZO++8E9XV1SPxUmk7vYXXNCGUyuo74op6ESKV57NQIGKbXRZzDHdUJSKiRNTOmVhLMwAwbloJLAVGeNy+uNeeUZduKgZssKl2zZxxxaqbN2/Gli1bsG7duuF+qSE5fVMzY4UNukIjpC8I72FX1Mf4TvTA19IN6BVYw9XM0XSqharsmCEiohiM4YxI0NWHYF/0YlS9Xoe6uaGsyL5/t8Z8rqO7Qy2+NdNLtdvUrpkzqn23tbUVK1aswB/+8AfYbIk/hL1eL1wuV8TXSDl9LxFFp8AyJVR86o0RdXZ/2AIgVKSqsxljPjf3ECEiokR0NiN0ttBnUazOGQCY+h8VAIB9H53Q/ngeqMfVh1NHQ2UF46f1ByL9GZEzZGlGRLB8+XLcdNNNmDdvXlKPefTRR1FcXKx91dTUDNfhDWIOn3xvT/9JNYcvvdy7b3B1sviC6Pk4FI0WNFTFfW7uIUJERMlI1DkDANVTHXBU2ODzBqJmRdRsSFlNIWx2k3Z70DNKilVXrVoFRVHifu3ZswdPPPEE3G43Vq9enfRzr169Gk6nU/s6evRoqoeXtmiBiGVKCaALdc74WiO31O355ASCPX7oHeaYbbtA+Kq73EOEiIiSkKhzBgg1WEy/IFR3+dk7X0KCkRtvfvFBKFtfO7O/ZECC0l+sas2tjEjKR7Ny5UosX7487pi6ujq8/fbb2LZtG8xmc8R98+bNw3XXXYfnnntu0OPMZvOg8SPFHF5aUZdmAEBfZIJl2hj0Nrah6/3jKLliMgBA/EG43joCACj8z2oouuibmAGAt9uvBTd2XnWXiIji0ApW4yzNAMDZC6rw0aZDaG/uxr7trZj6H5UAQtc1O9LYDijA2Qv6m0SCAz7b8j4QKS8vR3l5ecJxv/nNb/DII49o/29ubsZll12Gv/zlL2hoaEj1ZYedlhHp9kXcXnh+FXob29Dz8QnY/6sGersZ7q1HEXB6obebUPiV+MsynSdDyzKFJWYY2bpLRERxaBmROEszAGApMGLuf0/AB68dwPsvH8CE6WNgKTBix5bQH8kTpo9B8YA/fkXdQ8Skg6LPrS3Ehi0smjBhQsT/CwtD+3JMmjQJ48ePH66XTZsaiPT2RBb+mCc5YBxXCN+xLrT9cQ+s08fA9Y/QibZffhYUY/zgQitUZTaEiIgSSLTN+0CzLx6Pxvea4W7rxebf78SEGaVofLcZADD30sjPYDUjkmvZEIA7q2rUQGTg0gwQ6p4pXVoPxaRH32EXnJsPAgIUNFSiYO7YhM+r7SHCQISIiBJQA5Fgl0/bCTUWk8WAy2+aBYNRh+Z9nXj/lQMAQkHI+PrI2sVcDkRG7IgmTpyY1JVss8VsDdWIeHt8g+4zlttQvmIW3P//KPydXhScV5GwU0bVf40ZdswQEVF8OosBugIjgt0++Nt6tcuNxFJeU4Sr7joPH71+CF2dXkw+byxm/9fgVQetY+ZMDkRyXbSumYFMNUUY8/+mp/y87JghIqJUGMqs6Ov2wX/KkzAQAYCy8UVY/INZccdoGZEc20ME4NKMxpQgEEmXtocIMyJERJSEZDtnUpHLSzMMRMISZUTS0dvtY+suERGlJNnOmVQIA5HcZwnvIxLwB+GPscd/qtSOmQIHW3eJiCg5qXTOJEstfGUgksOMZj2U8L5kXk9msiKd7JghIqIUJbPNe6pyuViVgUiYolP660S6MxOIqIWqDhaqEhFRkgxloRqRYLc/YkfUoWCNSJ4wW9U6kcEtvOnQ9hBhoSoRESVJZzZAVxQqF8jU8gy7ZvKEer2ZTC3NaK27XJohIqIUZHp5RitWtTEQyWmZ7pzpZEaEiIjSkOmCVS7N5In+QGToSzO93T6t1oQZESIiSkUmAxER6e+a4dJMbrMUhJZmeruGHoioyzIFxSYYzWzdJSKi5KlLM7623iE/l/QGgGDo31yayXGWwgwGIlyWISKiNGUyIxLsDn2mKSZdwivGZwMDkQGshSYAgKd76IGIdrE7LssQEVGK1G3exeNHYIifSYFwuYEunPXPNQxEBshkRqSzNXyNmUpmRIiIKDU6kx764tAfx0PtnFEzIgxE8oA1HIh43EMPRDpaugEAJRUMRIiIKHVaC+8Ql2eC3WrrLgORnNefEekb0vNIULSMSEllwZCPi4iIzjyZqhNRMyJ6ZkRyn7Wov0ZERNJ+nq5OL/x9Qeh0CorCW/USERGlIlOBCGtE8oiaEQn6Bb7e9K/Aq2ZDisdaodfzW0xERKnr3111aC28/TUiude6CzAQiWA06WEwhr4lniEUrHa0hAtVWR9CRERpUi9+5z/lGVKWXgtEWCOSHzLROdNfH8JAhIiI0mMotQIKIN4AgkP4TAqGL1vCGpE8odWJDKFgVe2YYUaEiIjSpRh10BebAQythZftu3kmsxkRdswQEVH6MlGwGmAgkl/U682kWyPi8wbQ1eEFwIwIERENTX8gkl7BqgQEol55NwevMwMwEBnEOsSMiJoNsRYZtaCGiIgoHf2dM+llRIKe8GeZwmLVvKHWiPS406sR6WhlfQgREWXGwM6ZdKhFrjqbAYpOydhxZRIDkdPYwnv79zi9aT2+k627RESUIdrSTFt6LbwBV+iPan34j+xcxEDkNAXhCuXuznQzIuFC1QoWqhIR0dAYSiyhFt6+IIJpZOrVQETHQCR/FDjCGRFXehmRjuPhi91xDxEiIhoixaCDoTS0POM70ZPy4wNuZkTyjs0eyoh43D4EAsGUHhsIBLVdVUvHMSNCRERDZwhvBeFrST0QUbMoejsDkbxhLTRCFy7o8bhSS4N1tvQgGBCYLHoUlfJid0RENHTGcM2hL7xZZirUjAiXZvKIolNgDUeO3c7UApH25tAPSWl1IRQlN6uTiYgovxjVjEhrGkszLmZE8lJBmp0zbce6AHBZhoiIMkcNRPyt3ZBgap0zrBHJUza1cybFjEhbOCMyprow48dERERnJsMYK2BQIH1BBDqS32FVRPprRBiI5Bc1I9KdYkakvTmUERnDjAgREWWIoldgLFfrRJJfnpHeAMQXarrg0kyeUTMiPSlkRPp6/XCFrwXAjAgREWWSVieSQsGquiyjWPRQjPphOa5MYCASRToZEbVQ1VZs0q7gS0RElAnG8N5UvtYUApHwfli5vCwDMBCJSm29dbclvxbXrtWHcFmGiIgyK529RALhK8HrS3J7OwkGIlHYw3v7u9t6k97bv79jhssyRESUWVrnzKkeiD+5zTb94cJWQ4l52I4rExiIRFFYGjppPm8Avd2+pB7Tphaqsj6EiIgyTG83QbEYgGDyW70zI5LHDEa9dhXeZJZnRKR/aYYdM0RElGGKogyoE0kuEOnPiDAQyUv2MaETp3bCxNPd6YXH7YOiU1BSxUCEiIgyzxj+fPGFSwESUfccMeT4JUcYiMRQNKa/TiSRE4fdAIDSqgIYTbnbIkVERPnLNK4IANCXRCAi/mD/9u5nco3I66+/joaGBlitVpSUlOBb3/rWcL5cRqkZEXebJ+HYk0dCgcjY2qJhPSYiIjpzmcaHahB9x7oSbvUecHoBARSjDrqC3N5SwjBcT/zXv/4VK1aswC9/+UtcfPHF8Pv9+Pzzz4fr5TKuSF2aSSoj4gLAQISIiIaPodwGxaiD9AXgP+WBcawt5lh/e+izS19iyfmLsA5LIOL3+3Hbbbdh7dq1uOGGG7Tbp0+fPhwvNyzs4aUZ58n4GRER0ZZmymvtw35cRER0ZlL0CozVheg77ELfsa6kApFcb90Fhmlp5uOPP8axY8eg0+kwd+5cVFVV4fLLL0+YEfF6vXC5XBFf2VJSFTrBzpMeBHyxe7bdbb3o7fJBp1PYMUNERMNKW5456o47zh/urDHECVZyxbAEIgcOHAAAPPDAA7jnnnvwt7/9DSUlJbjooovQ3t4e83GPPvooiouLta+amprhOLykFDjMMFkNkKCgM07P9vH9TgBAeW0RDDm8lz8REeU/04RQ5t17OP4f6upeI8aK3P8DOaVAZNWqVVAUJe7Xnj17EAyGMgh33303rrrqKpx33nnYsGEDFEXBCy+8EPP5V69eDafTqX0dPXp0aLMbAkVRUBpulVI3K4vmeFMnAKBqUvGIHBcREZ25TBNDgYivuQtBrz/mOPXieMaK3M+IpFQjsnLlSixfvjzumLq6Ohw/fhxAZE2I2WxGXV0djhw5EvOxZrMZZnPurGeVVheg5YBT26wsGjUjUjXZMVKHRUREZyhDsRn6EjMCHV70HXHDMqVk0JhAtw/BrtCu4PmwNJNSIFJeXo7y8vKE48477zyYzWbs3bsXF1xwAQDA5/Ph0KFDqK2tTe9Is6A0fAG7WIFIb7dPu48ZESIiGgnmicXo6TgB7yFX1EDEH75Cr77UAp0590sGhqVGxG6346abbsL999+PLVu2YO/evbj55psBAN/+9reH4yWHhRqItMUIRJq/CC3LOCpssOb4ZZaJiGh0UJdnvPs7o96vbgEfr6smlwzbPiJr166FwWDA9ddfD4/Hg4aGBrz99tsoKRkcveWqsnB1suukB71dPlgKIzeFObyrDQAwYXrpiB8bERGdmdQsSN8RF4IeP3TWyI/yvnBHjTFPLjkybDurGo1GrFu3Dq2trXC5XPj73/+OGTNmDNfLDQtroQkl4YsMNe+LjDxFBEfUQGTmmBE/NiIiOjMZSi0wlFuBINDb1DHofu+BUO2i+az8KBngtWYSqJ4aijyP7Ys82e3N3ejq8EJv1GHcFBaqEhHRyLHUhzLxvXsiP5v8Hb0IdHoBHWDKk002GYgkoAYZp2dEmrafAACMry+BgRe6IyKiEWSZFvojuXd3G8Tfv+mmmg0xjSvKi0JVgIFIQtVTQ4HIqS+70O30AgCCQcGebaEW5fqvVGbt2IiI6MxkrnNAbzch2OOHp7FNu703nL031eXHsgzAQCShgmIzKuvsgACN7zYDAI42tqOrwwuzzYCzzinL8hESEdGZRtEpsJ1XAQDo/ncLgND+IZ7PTwEArDPyp3aRgUgSZi4cDwDY9a9m9PX68b8vNQEIZUO4rTsREWVDwbwKQAG8+zrh2duO7g9bAL/AOK4Qppr8uRo8A5EkTD53LKxFRnR3evH0T/6J9uZuWAqNmPe1idk+NCIiOkMZxlhR+J/jAABtG3bB9eYhAEDh+VVQFCWLR5YaBiJJ0Bt1+O8bZsAQLvxRdAouurYe1kJuYkZERNljv7QWhgHXk7HOKYft3IosHlHqFBGRbB9ELC6XC8XFxXA6nbDbs9+G1HasC0d3t6NuTjnsZdZsHw4RERHEH4SnsQ3iDcB2XgUUXfazIal8fg/bzqqj0ZhxhRgzrjDbh0FERKRRDDrYZie+Dlyu4tIMERERZQ0DESIiIsoaBiJERESUNQxEiIiIKGsYiBAREVHWMBAhIiKirGEgQkRERFnDQISIiIiyhoEIERERZQ0DESIiIsoaBiJERESUNQxEiIiIKGsYiBAREVHW5PTVd0UEQOhywkRERJQf1M9t9XM8npwORNxuNwCgpqYmy0dCREREqXK73SguLo47RpFkwpUsCQaDaG5uRlFRERRFyehzu1wu1NTU4OjRo7Db7Rl97lzA+eW/0T7H0T4/YPTPkfPLf8M1RxGB2+1GdXU1dLr4VSA5nRHR6XQYP378sL6G3W4ftT9gAOc3Goz2OY72+QGjf46cX/4bjjkmyoSoWKxKREREWcNAhIiIiLJG/8ADDzyQ7YPIFr1ej4suuggGQ06vUKWN88t/o32Oo31+wOifI+eX/7I9x5wuViUiIqLRjUszRERElDUMRIiIiChrGIgQERFR1jAQISIioqwZtYHIL37xCyxYsAA2mw0OhyOpx4gI7rvvPlRVVcFqtWLRokXYt29fxJj29nZcd911sNvtcDgcuOGGG9DV1TUcU4gr1eM4dOgQFEWJ+vXCCy9o46Ldv3HjxpGY0iDpfK8vuuiiQcd/0003RYw5cuQIlixZApvNhrFjx+KOO+6A3+8fzqlEler82tvb8eMf/xj19fWwWq2YMGECbr31Vjidzohx2TyHTz75JCZOnAiLxYKGhgZ8+OGHcce/8MILmDZtGiwWC2bNmoVNmzZF3J/Me3IkpTK/p59+Gl/96ldRUlKCkpISLFq0aND45cuXDzpXixcvHu5pxJXKHJ999tlBx2+xWCLG5PM5jPb7RFEULFmyRBuTS+fwn//8J77xjW+guroaiqLglVdeSfiYrVu34txzz4XZbMbkyZPx7LPPDhqT6vs6ZTJK3XffffL444/L7bffLsXFxUk9Zs2aNVJcXCyvvPKKfPrpp/LNb35TzjrrLPF4PNqYxYsXyznnnCPvv/++/Otf/5LJkyfLNddcM1zTiCnV4/D7/XL8+PGIrwcffFAKCwvF7XZr4wDIhg0bIsYNnP9ISud7vXDhQlmxYkXE8TudTu1+v98vM2fOlEWLFsmOHTtk06ZNUlZWJqtXrx7u6QyS6vx27twpV155pbz22mvS1NQk//jHP2TKlCly1VVXRYzL1jncuHGjmEwmeeaZZ2TXrl2yYsUKcTgc0traGnX8e++9J3q9Xn71q19JY2Oj3HPPPWI0GmXnzp3amGTekyMl1flde+218uSTT8qOHTtk9+7dsnz5cikuLpYvv/xSG7Ns2TJZvHhxxLlqb28fqSkNkuocN2zYIHa7PeL4W1paIsbk8zlsa2uLmNvnn38uer1eNmzYoI3JpXO4adMmufvuu+Wll14SAPLyyy/HHX/gwAGx2Wxy++23S2NjozzxxBOi1+vljTfe0Mak+j1Lx6gNRFQbNmxIKhAJBoNSWVkpa9eu1W7r7OwUs9ksf/7zn0VEpLGxUQDIv//9b23M5s2bRVEUOXbsWOYPPoZMHcecOXPk+9//fsRtyfzwjoR057hw4UK57bbbYt6/adMm0el0Eb8sf/e734ndbhev15uZg09Cps7h888/LyaTSXw+n3Zbts7h/Pnz5ZZbbtH+HwgEpLq6Wh599NGo47/zne/IkiVLIm5raGiQH/zgByKS3HtyJKU6v9P5/X4pKiqS5557Trtt2bJlcsUVV2T8WNOV6hwT/X4dbefw17/+tRQVFUlXV5d2W66dQ1UyvwfuvPNOmTFjRsRtV199tVx22WXa/4f6PUvGqF2aSdXBgwfR0tKCRYsWabcVFxejoaEB27ZtAwBs27YNDocD8+bN08YsWrQIOp0OH3zwwYgdayaOY/v27fjkk09www03DLrvlltuQVlZGebPn49nnnkmqcs4Z9pQ5vjHP/4RZWVlmDlzJlavXo2enp6I5501axYqKiq02y677DK4XC7s2rUr8xOJIVM/S06nE3a7fdBGRCN9Dvv6+rB9+/aI949Op8OiRYu098/ptm3bFjEeCJ0LdXwy78mRks78TtfT0wOfz4fS0tKI27du3YqxY8eivr4eN998M9ra2jJ67MlKd45dXV2ora1FTU0Nrrjiioj30Wg7h+vXr8fSpUtRUFAQcXuunMNUJXoPZuJ7lozRu1VcilpaWgAg4gNK/b96X0tLC8aOHRtxv8FgQGlpqTZmJGTiONavX4+zzz4bCxYsiLj9oYcewsUXXwybzYYtW7bghz/8Ibq6unDrrbdm7PiTke4cr732WtTW1qK6uhqfffYZ7rrrLuzduxcvvfSS9rzRzrF630jJxDk8deoUHn74Ydx4440Rt2fjHJ46dQqBQCDq93bPnj1RHxPrXAx8v6m3xRozUtKZ3+nuuusuVFdXR/xSX7x4Ma688kqcddZZ2L9/P37+85/j8ssvx7Zt26DX6zM6h0TSmWN9fT2eeeYZzJ49G06nE+vWrcOCBQuwa9cujB8/flSdww8//BCff/451q9fH3F7Lp3DVMV6D7pcLng8HnR0dAz55z4ZeRWIrFq1Co899ljcMbt378a0adNG6IgyK9n5DZXH48Gf/vQn3HvvvYPuG3jb3Llz0d3djbVr12bsQ2y45zjwQ3nWrFmoqqrCJZdcgv3792PSpElpP2+yRuoculwuLFmyBNOnT8fpV2kY7nNIqVuzZg02btyIrVu3RhRzLl26VPv3rFmzMHv2bEyaNAlbt27FJZdcko1DTcn555+P888/X/v/ggULcPbZZ+Opp57Cww8/nMUjy7z169dj1qxZmD9/fsTt+X4Oc0FeBSIrV67E8uXL446pq6tL67krKysBAK2traiqqtJub21txZw5c7QxJ06ciHic3+9He3u79vihSHZ+Qz2OF198ET09Pfjud7+bcGxDQwMefvhheL1emM3mhOMTGak5qhoaGgAATU1NmDRpEiorKwdVfLe2tgJA3pxDt9uNxYsXo6ioCC+//DKMRmPc8Zk+h9GUlZVBr9dr30tVa2trzPlUVlbGHZ/Me3KkpDM/1bp167BmzRq89dZbmD17dtyxdXV1KCsrQ1NT04h/iA1ljiqj0Yi5c+eiqakJwOg5h93d3di4cSMeeuihhK+TzXOYqljvQbvdDqvVCr1eP+SfiaRkrNokR6VarLpu3TrtNqfTGbVY9aOPPtLGvPnmm1krVk33OBYuXDio0yKWRx55REpKStI+1nRl6nv97rvvCgD59NNPRaS/WHVgxfdTTz0ldrtdent7MzeBBNKdn9PplK985SuycOFC6e7uTuq1Ruoczp8/X370ox9p/w8EAjJu3Li4xapf//rXI247//zzBxWrxntPjqRU5yci8thjj4ndbpdt27Yl9RpHjx4VRVHk1VdfHfLxpiOdOQ7k9/ulvr5efvrTn4rI6DiHIqHPEbPZLKdOnUr4Gtk+hyokWaw6c+bMiNuuueaaQcWqQ/mZSOpYM/ZMOebw4cOyY8cOrUV1x44dsmPHjohW1fr6ennppZe0/69Zs0YcDoe8+uqr8tlnn8kVV1wRtX137ty58sEHH8i7774rU6ZMyVr7brzj+PLLL6W+vl4++OCDiMft27dPFEWRzZs3D3rO1157TZ5++mnZuXOn7Nu3T37729+KzWaT++67b9jnE02qc2xqapKHHnpIPvroIzl48KC8+uqrUldXJxdeeKH2GLV999JLL5VPPvlE3njjDSkvL89a+24q83M6ndLQ0CCzZs2SpqamiHZBv98vItk9hxs3bhSz2SzPPvusNDY2yo033igOh0PrULr++utl1apV2vj33ntPDAaDrFu3Tnbv3i33339/1PbdRO/JkZLq/NasWSMmk0lefPHFiHOl/g5yu93ys5/9TLZt2yYHDx6Ut956S84991yZMmXKiAbFQ5njgw8+KG+++abs379ftm/fLkuXLhWLxSK7du3SxuTzOVRdcMEFcvXVVw+6PdfOodvt1j7rAMjjjz8uO3bskMOHD4uIyKpVq+T666/Xxqvtu3fccYfs3r1bnnzyyajtu/G+Z5kwagORZcuWCYBBX++88442BuH9FlTBYFDuvfdeqaioELPZLJdccons3bs34nnb2trkmmuukcLCQrHb7fK9730vIrgZKYmO4+DBg4PmKyKyevVqqampkUAgMOg5N2/eLHPmzJHCwkIpKCiQc845R37/+99HHTsSUp3jkSNH5MILL5TS0lIxm80yefJkueOOOyL2EREROXTokFx++eVitVqlrKxMVq5cGdH+OlJSnd8777wT9WcagBw8eFBEsn8On3jiCZkwYYKYTCaZP3++vP/++9p9CxculGXLlkWMf/7552Xq1KliMplkxowZ8vrrr1Y6GCYAAADjSURBVEfcn8x7ciSlMr/a2tqo5+r+++8XEZGenh659NJLpby8XIxGo9TW1sqKFSsy+gs+HanM8Sc/+Yk2tqKiQr72ta/Jxx9/HPF8+XwORUT27NkjAGTLli2DnivXzmGs3xHqnJYtWyYLFy4c9Jg5c+aIyWSSurq6iM9EVbzvWSYoIlnozSQiIiLCKN7inYiIiHIfAxEiIiLKGgYiRERElDUMRIiIiChrGIgQERFR1jAQISIioqxhIEJERERZw0CEiIiIsoaBCBEREWUNAxEiIiLKGgYiRERElDUMRIiIiChr/g/jsQRD2qH/8QAAAABJRU5ErkJggg==", "text/plain": [ "Figure(PyObject

)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in 1:length(x)\n", " plot(xx, hh[i])\n", "end\n" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject

)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(xx, hh[5])\n", "axhline(y=0, color=\"black\", linestyle = \"--\")\n", "axhline(y=1, color=\"black\", linestyle = \"--\")\n", "\n", "for xv in x\n", " axvline(x=xv, color=\"red\", linestyle=\"--\")\n", "end\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vamos organizar a interpolação de Lagrange" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "struct Lagrange\n", " x::Vector{Float64}\n", " y::Vector{Float64}\n", " Lagrange(x, y) = new(copy(x), copy(y))\n", "end\n", "Base.Broadcast.broadcastable(lgr::Lagrange) = Ref(lgr)\n", "\n", "function lagrange(k, z, x)\n", " h = 1.0\n", " n = length(z)\n", " for i = 1:(k-1)\n", " h *= (x - z[i]) / (z[k] - z[i])\n", " end\n", " \n", " for i = (k+1):n\n", " h *= (x - z[i]) / (z[k] - z[i])\n", " end\n", " return h\n", "end\n", "\n", "function interp(lgr::Lagrange, x)\n", " \n", " y = lgr.y[1] * lagrange(1, lgr.x, x)\n", " \n", " for i = 2:length(lgr.x)\n", " y += lgr.y[i] * lagrange(i, lgr.x, x)\n", " end\n", " \n", " return y\n", "end\n", "\n", " \n", "(lgr::Lagrange)(x) = interp(lgr, x) " ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.0:0.005:1.0" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = range(-1, 1, step=0.2)\n", "y1 = sin.(π.*x1);\n", "xx = range(-1, 1, step=0.005)\n" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "lgr = Lagrange(x1, y1)\n", "yy = sin.(π.*xx);\n", "yy1 = lgr.(xx);" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject

)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "plot(x1, y1, \"ro\")\n", "plot(xx, yy, \"r-\")\n", "plot(xx, yy1, \"b--\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpolação Linear\n", "\n" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject

)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x2 = range(-1, 1, step=0.2)\n", "y2 = sin.(π.*x2);\n", "\n", "plot(x2, y2, \"ro\")\n", "plot(x2, y2, \"b-\")" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [], "source": [ "struct LinearInterp\n", " x::Vector{Float64}\n", " y::Vector{Float64}\n", " LinearInterp(x, y) = new(copy(x), copy(y))\n", "end\n", "Base.Broadcast.broadcastable(lin::LinearInterp) = Ref(lin)\n", "\n", "function interp1(lin::LinearInterp, x)\n", " \n", " if x < lin.x[1] || x > lin.x[end]\n", " error(\"Fora do Range\")\n", " end\n", " \n", " index = 2\n", " n = length(lin.x)\n", " for i = 2:n\n", " if lin.x[i] >= x\n", " index = i\n", " break\n", " end\n", " end\n", " i1 = index-1\n", " return lin.y[i1] + (lin.y[index] - lin.y[i1]) * (x - lin.x[i1]) / (lin.x[index] - lin.x[i1])\n", " \n", "end\n", "\n", "(lin::LinearInterp)(x) = interp1(lin, x)\n" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Figure(PyObject

)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin = LinearInterp(x2, y2)\n", "yy2 = interp1.(lin, xx);\n", "plot(x2, y2, \"ro\")\n", "plot(xx, yy2, \"b-\")" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 3.953 μs (3 allocations: 96 bytes)\n" ] } ], "source": [ "@btime yy2 .= interp1.(lin, xx);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Mínimos quadrados\n" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "linfit (generic function with 1 method)" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function linfit(x,y)\n", " sx = sum(x)\n", " sx2 = sum(x->x^2, x)\n", " N = length(x)\n", "\n", " sy = sum(y)\n", " syx = sum(x[i]*y[i] for i in 1:N)\n", " \n", " return [N sx; sx sx2] \\ [sy; syx]\n", "end" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.0:2.0:43.0" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = 1.0:20\n", "y = 2 .*x .+ 3.0" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2-element Array{Float64,1}:\n", " 3.0\n", " 2.0" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "linfit(x,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Pacotes\n", "\n", " * [Interpolations](https://github.com/JuliaMath/Interpolations.jl)\n", " * [Dierckx](https://github.com/kbarbary/Dierckx.jl)\n", " * [GridInterpolations](https://github.com/sisl/GridInterpolations.jl)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercícios\n", "\n", "### Problema 1\n", "\n", "Interpole a função de Runge com $-1 \\le x \\le 1$:\n", "$$\n", "f(x) = \\frac{1}{1 + 25x^2}\n", "$$\n", "\n", " 1. Use 11 pontos uniformemente distribuídos\n", " 2. Aumente o número de pontos\n", " 3. Tente usar os pontos $x_k = \\cos\\left(\\frac{k\\pi}{N}\\right)$ para $k = 0\\ldots N$.\n", " 4. Brinque com o número de pontos\n", "\n", "### Problema 2\n", "\n", "Procure na Net o método de diferenças divididas de Newton a interpole a função anterior nos mesmos pontos. Este método é simplesmente um jeito inteligente de resolver a matriz apresentada lá em cima.\n", "\n", "### Problema 3\n", "\n", "Use a biblioteca Interpolations.jl e Dierckx.jl para fazer as interpolações. Compare a interpolação linear com os splines.\n", "\n", "### Problema 4\n", "\n", "Crie funções para fazer os seguintes problemas de mínimos quadrados:\n", " * $y = a_0 x^ a_1$\n", " * $y = a_0 \\exp \\left( a_1 \\cdot x\\right)$\n", " * Polinômio genérico de ordem n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "f(x) = 1.0 / (1.0 + 25x^2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "@webio": { "lastCommId": "29381185e1ea4e088b6d502855c75c92", "lastKernelId": "27064174-b830-4bb2-b21b-58da93beea16" }, "kernelspec": { "display_name": "Julia 1.4.1", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.1" } }, "nbformat": 4, "nbformat_minor": 2 }