{
"cells": [
{
"cell_type": "markdown",
"id": "7261a9c7-b0d7-4ed8-bf53-37c97c5cbded",
"metadata": {},
"source": [
"# 2025-10-08 Low Rank\n",
"\n",
"* Reflection on algorithm choices\n",
"\n",
"* Low-rank structure\n",
"\n",
"* Primer on interpolation"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "74e962e7-4a7d-4365-94b3-28c1553c4235",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Aplot (generic function with 1 method)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using LinearAlgebra\n",
"using Plots\n",
"using Polynomials\n",
"default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n",
"default(aspect_ratio=:equal)\n",
"\n",
"# Here's our Vandermonde matrix again\n",
"function vander(x, k=nothing)\n",
" if isnothing(k)\n",
" k = length(x)\n",
" end\n",
" m = length(x)\n",
" V = ones(m, k)\n",
" for j in 2:k\n",
" V[:, j] = V[:, j-1] .* x\n",
" end\n",
" V\n",
"end\n",
"\n",
"# Our modifiend Gram Schmidt for QR\n",
"function gram_schmidt_modified(A)\n",
" m, n = size(A)\n",
" Q = copy(A)\n",
" R = zeros(n, n)\n",
" for j in 1:n\n",
" # First we normalize our column\n",
" R[j, j] = norm(Q[:, j])\n",
" Q[:, j] /= R[j, j]\n",
" # Then we make all following columns orthogonal to the current\n",
" R[j, j+1:end] = Q[:, j]' * Q[:, j+1:end]\n",
" Q[:, j+1:end] -= Q[:, j] * R[j, j+1:end]'\n",
" end\n",
" Q, R\n",
"end\n",
"\n",
"# Householder for QR\n",
"function qr_householder(A)\n",
" m, n = size(A)\n",
" R = copy(A)\n",
" V = [] # list of reflectors\n",
" for j in 1:n\n",
" # Build v for the current column\n",
" v = copy(R[j:end, j])\n",
" v[1] += sign(v[1]) * norm(v) # Here's the fix!\n",
" v = normalize(v)\n",
" # Build and apply F\n",
" R[j:end, j:end] -= 2 * v * (v' * R[j:end,j:end])\n",
" # Keep track of the reflectors\n",
" push!(V, v)\n",
" end\n",
" V, R\n",
"end\n",
"\n",
"# Here's a function to apply the reflectors V to a vector x\n",
"function reflectors_mult(V, x)\n",
" y = copy(x)\n",
" for v in reverse(V)\n",
" n = length(v) - 1\n",
" # This is applying F as we did to form R\n",
" y[end-n:end] -= 2 * v * (v' * y[end-n:end])\n",
" end\n",
" y\n",
"end\n",
"\n",
"# Create a dense matrix Q from reflectors V\n",
"function reflectors_to_dense(V)\n",
" m = length(V[1])\n",
" Q = diagm(ones(m))\n",
" # Apply the reflectors to the identity matrix to build Q\n",
" for j in 1:m\n",
" Q[:, j] = reflectors_mult(V, Q[:,j])\n",
" end\n",
" Q\n",
"end\n",
"\n",
"# And Cholesky QR\n",
"function qr_chol(A)\n",
" # First find R\n",
" R = cholesky(A' * A).U\n",
" Q = A / R # Triangular solves are easy\n",
" Q, R\n",
"end\n",
"\n",
"# Also Cholesky QR with actual orthogonality retained\n",
"function qr_chol2(A)\n",
" # First one had loss of orthogonality\n",
" R = cholesky(A' * A).U\n",
" Q = A / R # Triangular solves are easy\n",
" # So we Cholesky decompose twice\n",
" R2 = cholesky(Q' * Q).U\n",
" Q = Q / R2\n",
" # Note, triangular * triangular = triangular\n",
" R = R2 * R\n",
" Q, R\n",
"end\n",
"\n",
"# Finally our visualization aids\n",
"# Let's use the peanut blob again\n",
"function peanut()\n",
" theta = LinRange(0, 2*pi, 50)\n",
" r = 1 .+ .4*sin.(3*theta) + .6*sin.(2*theta)\n",
" r' .* [cos.(theta) sin.(theta)]'\n",
"end\n",
"\n",
"# and a perfect circle\n",
"function circle()\n",
" theta = LinRange(0, 2*pi, 50)\n",
" [cos.(theta) sin.(theta)]'\n",
"end\n",
"\n",
"function Aplot(A)\n",
" \"Plot a transformation from X to Y\"\n",
" X = peanut()\n",
" Y = A * X\n",
" p = scatter(X[1,:], X[2,:], label=\"in\")\n",
" scatter!(p, Y[1,:], Y[2,:], label=\"out\")\n",
" X = circle()\n",
" Y = A * X\n",
" q = scatter(X[1,:], X[2,:], label=\"in\")\n",
" scatter!(q, Y[1,:], Y[2,:], label=\"out\")\n",
" plot(p, q, layout=2)\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "9a890985-34d2-4600-9c9b-0b0016d9db6c",
"metadata": {},
"source": [
"## Condition number via SVD\n",
"\n",
"Recall that we can compute the condition number of a matrix from its singular values.\n",
"\n",
"$$ \\begin{split} U \\overbrace{\\begin{bmatrix} \\sigma_{\\max} && \\\\ & \\ddots & \\\\ && \\sigma_{\\min} \\end{bmatrix}}^{\\Sigma} V^T = A \\end{split} $$\n",
"\n",
"$$ \\begin{align}\n",
"\\lVert A \\rVert &= \\sigma_{\\max} &\n",
"\\kappa(A) &= \\frac{\\sigma_{\\max}}{\\sigma_{\\min}} = \\texttt{cond}(A)\n",
"\\end{align} $$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "7b4bf715-9123-45f9-86ac-f86802efb34f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2×2 Matrix{Float64}:\n",
" -4.66531 -0.518554\n",
" -0.518554 0.287251"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make a random symmetric matrix\n",
"A = randn(2, 2)\n",
"A = A + A'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2018ed95-425b-486c-8824-7fef7bd21e91",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"svdvals(A) = [4.7190242617009615, 0.3409628088748754]\n",
"cond_A = maximum(S) / minimum(S) = 13.840290315747376\n",
"norm(U * U' - I) = 2.220446049250313e-16\n",
"norm(V * V' - I) = 0.0\n"
]
},
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The condition number is the ratio of the largest and smallest singular value\n",
"@show svdvals(A)\n",
"U, S, V = svd(A)\n",
"@show cond_A = maximum(S) / minimum(S);\n",
"\n",
"# U and V are in fact orthogonal\n",
"@show norm(U * U' - I)\n",
"@show norm(V * V' - I)\n",
"\n",
"# Let's see what this matrix does to the peanut\n",
"Aplot(A)"
]
},
{
"cell_type": "markdown",
"id": "d6c47fd4-fca6-44f3-bb1f-227dd2079f4b",
"metadata": {},
"source": [
"## Least squares\n",
"\n",
"Consider autonomous vehicles.\n",
"\n",
"* Need to solve least squares problems in real time\n",
"\n",
"* Weight/size/cost increase with computational needs\n",
"\n",
"* What algorithm to choose?\n",
"\n",
"* What precision to use?\n",
"\n",
"### Factors\n",
"\n",
"* How many objects to track?\n",
"\n",
"* Speed (of robot and objects)\n",
"\n",
"* Movement mode - aerial, wheeled, walking?\n",
"\n",
"* Environment - fog, lighting, etc - longer memory needed?\n",
"\n",
"* Tolerances (how accurate does the solution need to be?)\n",
"\n",
"* Consequences of errors, and who is responsible?"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "17bccb2a-fef4-4eff-b311-d96e8943212f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cond(A) = 56.089149554120844\n",
"\n",
"Housholder, from Julia\n",
" 0.042941 seconds (16.12 k allocations: 22.086 MiB, 14.73% gc time, 26.93% compilation time)\n",
"norm(Q * R - A) = 5.419947033929591e-13\n",
"norm(Q' * Q - I) = 3.4228183349535124e-14\n",
"\n",
"Cholesky\n",
" 0.083962 seconds (159.33 k allocations: 31.155 MiB, 6.38% gc time, 78.06% compilation time)\n",
"norm(Q * R - A) = 4.7598648681881803e-14\n",
"norm(Q' * Q - I) = 1.0712375374007724e-12\n",
"\n",
"Housholder, single precision\n",
" 0.087600 seconds (198.00 k allocations: 20.700 MiB, 84.27% compilation time)\n",
"norm(Q * R - A) = 0.0002855807790455134\n",
"norm(Q' * Q - I) = 1.7505894f-5\n",
"\n",
"Cholesky, single precision\n",
" 0.409190 seconds (4.42 M allocations: 231.161 MiB, 7.47% gc time, 98.44% compilation time)\n",
"norm(Q * R - A) = 3.9128822133829075e-5\n",
"norm(Q' * Q - I) = 0.00057106407f0\n"
]
}
],
"source": [
"# Let's look at the raw time to solve with our methods above\n",
"A = rand(5000, 500)\n",
"A_32 = Float32.(A)\n",
"@show cond(A)\n",
"\n",
"println(\"\\nHousholder, from Julia\")\n",
"@time Q, R = qr(A); # Householder; backward stable\n",
"@show norm(Q * R - A)\n",
"@show norm(Q' * Q - I)\n",
"\n",
"println(\"\\nCholesky\")\n",
"@time Q, R = qr_chol(A) # Unstable\n",
"@show norm(Q * R - A)\n",
"@show norm(Q' * Q - I)\n",
"\n",
"println(\"\\nHousholder, single precision\")\n",
"@time Q, R = qr(A_32); # Lower precision\n",
"@show norm(Q * R - A)\n",
"@show norm(Q' * Q - I);\n",
"\n",
"println(\"\\nCholesky, single precision\")\n",
"@time Q, R = qr_chol(A_32); # Lower precision\n",
"@show norm(Q * R - A)\n",
"@show norm(Q' * Q - I);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "fc9766a3-b09f-4c48-99b3-f0ff444aa614",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cond(V) = 2.4996629598602743e9\n",
"\n",
"Housholder, from Julia\n",
" 0.000067 seconds (16 allocations: 15.688 KiB)\n",
"norm(Q * R - V) = 3.5159362514746e-15\n",
"norm(Q' * Q - I) = 3.254229278676633e-15\n",
"\n",
"Cholesky\n",
" 0.000036 seconds (16 allocations: 11.883 KiB)\n",
"norm(Q * R - V) = 3.0243458890798737e-16\n",
"norm(Q' * Q - I) = 1.0000208696450787\n",
"\n",
"Housholder, single precision\n",
" 0.000057 seconds (12 allocations: 8.219 KiB)\n",
"norm(Q * R - V) = 1.8764177333132612e-6\n",
"norm(Q' * Q - I) = 1.8709579f-6\n"
]
}
],
"source": [
"# And lets check with a particularly ill conditioned matrix\n",
"V = vander(LinRange(-1, 1, 22))\n",
"V_32 = Float32.(V)\n",
"@show cond(V)\n",
"\n",
"println(\"\\nHousholder, from Julia\")\n",
"@time Q, R = qr(V); # Householder; backward stable\n",
"@show norm(Q * R - V)\n",
"@show norm(Q' * Q - I)\n",
"\n",
"println(\"\\nCholesky\")\n",
"@time Q, R = qr_chol(V) # Unstable\n",
"@show norm(Q * R - V)\n",
"@show norm(Q' * Q - I)\n",
"\n",
"println(\"\\nHousholder, single precision\")\n",
"@time Q, R = qr(V_32); # Lower precision\n",
"@show norm(Q * R - V)\n",
"@show norm(Q' * Q - I);"
]
},
{
"cell_type": "markdown",
"id": "7c10af3b-cb7b-48c3-a55a-4c36638d1044",
"metadata": {},
"source": [
"## Low rank approximation\n",
"\n",
"The SVD can be truncated to yield the best rank-$k$ approximation of a matrix."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "a5e9d06e-7190-4874-a361-e1a0f9632742",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make a random rank 2 matrix\n",
"n, k = 2, 1\n",
"\n",
"A = randn(n, n)\n",
"Aplot(A)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "bd6ee4a5-cdf8-49d3-a47c-18c355f65200",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"S[1:k + 1] = [1.283712670445647, 0.41954590250072576]\n",
"norm(Â) = 1.283712670445647\n"
]
},
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make the SVD\n",
"U, S, V = svd(A)\n",
"\n",
"# Let's truncate out the last singular value\n",
"@show S[1:k+1]\n",
"Û = U[:, 1:k]\n",
"Ŝ = S[1:k]\n",
"Ṽ = V[:, 1:k]\n",
"Â = Û * diagm(Ŝ) * Ṽ'\n",
"@show norm(Â)\n",
"# Here's our reduced A\n",
"Aplot(Â)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c5bcd4fe-ace5-4588-96df-f79dd39bebee",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# And the part left out\n",
"Aplot(A - Â)"
]
},
{
"cell_type": "markdown",
"id": "1cd92015-1ffc-44ec-b8fa-6f32f96c8fb7",
"metadata": {},
"source": [
"## Example: Galaxies\n",
"\n",
"Suppose we have two galaxies of size $n_1 = 100$ and $n_2 = 200$, each randomly distributed around their respective centers."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "eb2f71e0-96ef-446b-8be3-189b1a234faf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"galaxy(center, sigma, n) = reshape(center, 1, 3) .+ sigma*randn(n, 3)\n",
"g1 = galaxy([0 0 0], 1, 100)\n",
"g2 = galaxy([10 0 0], 1, 100)\n",
"\n",
"scatter(g1[:, 1], g1[:, 2], aspect_ratio=:equal, label=\"galaxy 1\")\n",
"scatter!(g2[:, 1], g2[:, 2], label=\"galaxy 2\")"
]
},
{
"cell_type": "markdown",
"id": "f03e1e8a-1267-4e2a-8b6d-3bcd3499052f",
"metadata": {},
"source": [
"### Force between stars\n",
"\n",
"Consider the gravitational force from a star at position $x_2$ acting on a start at position $x_1$.\n",
"\n",
"$$ F_{1, 2} = G \\frac{m_1 m_2}{\\left\\lvert \\left\\lvert x_2 - x_1 \\right\\rvert \\right\\rvert^3} \\left( x_2 - x_1 \\right) $$\n",
"\n",
"where $m_1$ and $m_2$ are the masses of each star, respectively."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "16ad8fac-1c35-4855-8ad0-218e9cb279cf",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"300×100 Matrix{Float64}:\n",
" 0.0092555 0.00659191 0.0109241 … 0.00924183 0.00902314\n",
" 0.00205554 0.0011782 0.00171437 0.000804196 0.00143314\n",
" 0.000161345 -0.00102562 -0.00111365 0.000713908 0.000338838\n",
" 0.00891627 0.00661779 0.010422 0.00812364 0.0083581\n",
" 0.000134426 2.41079e-5 -0.000645886 -0.000886846 -0.00033312\n",
" 0.00112317 -0.000375582 0.000205911 … 0.00146679 0.00118899\n",
" 0.00888392 0.00603805 0.00973773 0.00858864 0.00851904\n",
" 0.000703421 0.000352533 6.72438e-5 -0.000398637 0.000192527\n",
" -0.000847777 -0.00148159 -0.00211502 -0.000303389 -0.000622363\n",
" 0.00818796 0.00583 0.00913395 0.00768037 0.007762\n",
" 0.000218858 8.26747e-5 -0.000412912 … -0.000702157 -0.000199458\n",
" -4.68933e-5 -0.000942961 -0.00104933 0.000378266 0.00010238\n",
" 0.00767546 0.00563559 0.0088714 0.00750916 0.00742524\n",
" ⋮ ⋱ \n",
" 0.00896992 0.00633828 0.0100622 0.00827117 0.00843467\n",
" 3.88403e-6 -5.56722e-5 -0.000774142 -0.00101226 -0.000452355\n",
" 0.000147973 -0.000943928 -0.000970932 … 0.000607043 0.000300734\n",
" 0.0100196 0.00673199 0.0110054 0.00933815 0.0094457\n",
" 0.000106889 -3.88533e-6 -0.000779955 -0.00111612 -0.000442161\n",
" -0.000577707 -0.00148147 -0.00201912 4.214e-5 -0.000332865\n",
" 0.00639916 0.00515134 0.00776259 0.00642084 0.00629253\n",
" 0.00185955 0.00125154 0.00185531 … 0.00110014 0.00147084\n",
" 0.00105506 -4.25808e-5 0.000557162 0.00137125 0.00112444\n",
" 0.0100633 0.00691262 0.0114197 0.00946221 0.00953241\n",
" 0.000594516 0.000279234 -0.000216889 -0.00068787 6.02512e-7\n",
" -5.58421e-5 -0.00121833 -0.00145847 0.000523819 0.000146799"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make a matrix of all gravitational forces\n",
"function gravity(g1, g2)\n",
" m = size(g1, 1)\n",
" n = size(g2, 1)\n",
" F = zeros(3*m, n)\n",
" for i in 0:m-1\n",
" for j in 1:n\n",
" r = g2[j, :] - g1[1+i, :]\n",
" F[1+3*i:3*(i+1), j] = r / norm(r)^3\n",
" end\n",
" end\n",
" F\n",
"end\n",
"\n",
"gravity(g1, g2)"
]
},
{
"cell_type": "markdown",
"id": "f963f463-2df1-46d1-af15-15b36222604d",
"metadata": {},
"source": [
"### Spectrum (Singular values)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "6c32ab17-bb2c-471b-a960-a9a668450cec",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# A new pair of galaxies\n",
"g1 = galaxy([0 0 0], 1, 500)\n",
"g2 = galaxy([10 0 0], 1, 500)\n",
"F = gravity(g1, g2)\n",
"\n",
"# Let's plot the singular values\n",
"U, S, V = svd(F)\n",
"default(aspect_ratio=:auto)\n",
"scatter(S, yscale=:log10, ylims=(1e-16, 1e1), xlims=(0, 200), label=\"singular values\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "2b57b731-8ebd-4c00-a362-00711b1d533f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(F - F́) = 0.004289146304990904\n"
]
},
{
"data": {
"text/plain": [
"0.004289146304990904"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make a minimal model\n",
"k = 10\n",
"Û = U[:, 1:k]\n",
"Ŝ = S[1:k]\n",
"Ṽ = V[:, 1:k]\n",
"F́ = Û * diagm(Ŝ) * Ṽ'\n",
"\n",
"# And how good does it do?\n",
"@show norm(F - F́)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "d4bd26ea-db6a-4b4e-97ca-ad33aa01a397",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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s2fInFvv1vRZycnJqamqSiyx5fn5+vXr1Er8BUSgUent7A1BQUFBRUSkfo6io+PXH6ldXzhGW09HRCfW9M37Wwuh7a2HQls0rFiZFj3Tov/vEZVblbvohhJBKYrFYw4cPHz58OIDs7GyBQKCjo/OLyzx79mz510pKSkePHv3FBVap5OTkUaNGARg1atS9e/fEl48aGBh8/aJEW1tbZh/7XOeKEIC+vv7j21c5HM6bN28iIyNfxjT5EJfg/IfLoL49evfuzXQ6Qoh0ktRd82w2+zsfa5pdu3aJv1i+fPnX02vUVtTFIhQTCATzV657y9bPbT0U7Ry9M+NObz7TZvte7xsXlZSUmE5HCCGkmtTdIhw1eeZL07Hcjo5ln/Va5LTt/yz41PgZ86+fozvrCSGkrqjR+9RVJz4+/sXnzL9b8P+VWk4JfP0xJSWFkVSEEEKqXx0twpCQkIJmfSqcVfxbr9DQ0GrOQwghhCl1tAiLiou5csoVzuLLqkj2bdGEEEJqsjp6jrCpiUn9K1f+fqKaSIjYYCS+BpejGPvIyGgtg9kIIYRUpzq6R9itWzfl+KfITwOA9I/Y1hMhFyCnBA2DgnrGY6bPf+znz3RGQggh1aGO7hHKycmdPug6Zt7wrGG7cX4+fj+ORm0BoLRQqKqVHGcwZMLUayfdbW1tmU5KCCGkatXRIgTQp3cvX48jDmN/T+42WSRuwdCL8N6J1vbQb1nQZarD/A225mcunXBn9tk/hJCa4MmTJ9u2bWM6RZ0WERHRpUuXqlhy3S1CAObm5jq6ukmdRgFAxF2EXICTHxRUkRSFmIdcLvde4Esd03YLp09Z77xMWbnii2sIIVJv6NChPB4vJ+cH3tTG4/Hk5OSqLlIdZGtr26tXr6pYcp0uQgD5eXllb6u/64IFnlBQRcQd3NsGx11o0lkEcHgc18Dj1637hPjeldQTkgghtYuFhYWFhcUPfUtRUZGysjI9wbhWqKMXy5TT1zdA5mfkpkBNB2o6KMrGrU1YdBtNOkPIh88e7LTjBV/8kF5obNb1zHkPpvMSQgiRsLq+Rzh1zNCI6ycLOjhCVRsAXnrCaiKU1SHg4eBINO2CZd6QVwZQUJi54Pga/6fPjh/czXBoQgghklPX9wgnTRhnmvNS/t0j5CQCQOo7GJoBgN9hNOmIgashrwwBD6EeuL4uPyX+7J1HS1c4c7lcZmMTQgiRlLpehDIyMgFenmPqfZZJf4+MT2DLQMAHgOdXYLsYAIpz4NoPyTHoOQtzr/CmnNgXI2pr2TMjI4PZ5IQQQiSirhchABUVlTPu+/w8PdRPTYCmIT4EAYCAC0U1ADg9G3ZLMGwTjMyhVA+G7QRDN3/suX6Q42RmYxNCCJEIKsIy1tbWd07uNY44w356ChlxEL8uOTsBpYUwc/h7HI+DL+FCOcXYAlZMTAxTaQkhhEhKXb9Y5mvdrKziosLu3bs3cd7QHBkVUcYnJL6GqXXZbG4xrq5C3DMYtYe8clZWloPjFF/Pi02aNGE0NSGEkF9CRfitAQMGfHjRddFyp4tnZvJtpkNWHgBEQriNhsVwjNsrHiYC4uKeW/cfHvb4np6eHpOJCSGE/AI6NFoBTU3NsyeObpoxor7fbsSFAcCLG9BvBZupXw8TNemUar9hyZpNzKQkhBAiCVSE/2rV0oXBN89rZLxGylu8uoVuFVwdI2wzwP9pSPVnI4QQIilUhN/TsmXLgLvXGp6biLQP0DKqYASLJWDLCcVX1hBCCKmFqAj/Q5s2bcIe3dWW5aIgs8IBbCGPzaY/RkIIqa3oN/h/MzAwWLt4tlLE9Qrmxb9oadqs2hMRQgiRGCrCSpk5dUqD6Gus2P89HZibrH194f6/NjAUihBCiATQ7ROVoqSkFHDvusOYyckh+rkN2/PfBrBT3oDFEqooTlmwcvv6lb179WQ6IyGEkJ9BRVhZhoaGEU8fPXr0yHH6vKyeS4VzLoEtkw1kZ8SNWjZ/46yPC2ZNZzojIYSQH0aHRn+M2ymP7AGbhFZTwJYpm6TTJHvm9U17jyYkJDAajRBCyM+gIvwBXC73yfOXAvOh384QCnKsZp3xuMxEKEIIIb+EDo3+gOTkZJb2V08W/fgUd7eiMANySgJOvttT2WmTxjds2JC5gIQQQn4YFeEPkJeXB6+k7MPzy/A/iknu0G0qnpASedeiZ/+g+zeMjY2ZSkgIIeRH0aHRH6Cnp8fOSQSvBEXZuL8LCzzLWjA7Ad67RGFXk5Ub9xgwLC0tjemkhBBCKouK8AewWKwFM6eo3d2AiDvoOhYKKgAQfA7ujqivh/5OGLw+wWJmGxv7m3fuMh2WEEJIpVAR/hjnpYsG6ZUq+h2EfisAiHuOoNNY8RBdx6F+A4RdFYWcz+SyR0yZM2LCtKSkJKbzEkII+Q9UhD+GxWKdP3pwRM9O4HIA4IErxuyCnCKyvmCXPRr8hqVeWBsqmHXxRopii47d3NzcOBwO06kJIYT8KyrCnzHJcYR67CMAyIiDYTsAODsH4/fDcjyKcuDaD48OivRbFzr8ueDqaxPzrrfveTEbmBBCyL+hIvwZffv2bZARwYp7XvY5Mx6y8jDpAj4XbqPgsAbTTqHHDNRvIGSxU1kaI6YtnD53UXp6OqOpCSGEVICK8Gew2ewHNzxM7ixh8zgoykbyGxh1AIBnF9GuP36zgUiEc/MQcBydRmPeVd6ieyc4bdrZ2D0JDGI6OyGEkP9BRfiTjIyM3jx/4mhnJeu9A2w2hAIAiHmEDsMA4LEbFFQx8xyaWaG0CI/cRIGn00pYvYeNc1r3R3FxMbPhCSGElKMi/Hny8vKnj7p35r1Vin2C2KcAUJwLVS0ACDqNoRsBID4M+4bgNxss9cK6Z/x1Ya6xqmZWvTMyMhhMTgghpBwV4S+RlZX19/JcYamtmB2PV7dRXw9Zn1GcAxUtyCmBX4qzczH/OswHQU4RAPilfL02sU0dRkyawXR2QgghABXhr5OVlf1j9cqkmBctQnYpCDkIOAEBDzJyAPDGF636QtMQAHJTcGA4jk3Bm4ei4vygtwmWtg6pqanMhieEEELPGpUMTU3NiKeP3Y+f3LDVNS/ojCg3CSIhkt/AuCMAcPJxYBhGbUPzHuLxQmwJffvI0nbQ6+DHqqqqTEYnhJC6jfYIJUZeXn7hnFmp7yOnG2Qr8gpZAccAFkRCAHi4Hz1mlregmKhF7xSLKdv2HGAmLiGEEABUhBKnoKBwZO+OpDdhTV+fkcv4iNhgAIh6gM5jykYI+Qg+hxO/Y2v30kgf9xOnCwoKGAxMCCF1HBVhldDU1IwKDVjR20T25XWkf4SAW/aE7pIC7B6A1Pfo74QVDzFmZ1aXma269Pj48SPTkQkhpI6iIqwqCgoKWzaseennpXdmHLgc8EsBwGMJbKZh2CbotYCMHLQai/rMTxx9rP+oiQKBgOnIhBBSF1ERVq22bdtGBvqYNWnIenEdRdlI+/D3MdJyjdpm6ZoFBAQwEZAQQuo6KsIqp62t7XPjYsMnuxFxFyZdKhyTY9Qt9MWrag5GCCEEVITVQ0dH55GnR6NAV5b4AOk/ycjy+PzqDUUIIQSgIqw2LVq0CHnsrZ71poJ5vJJ6KeEd2raq9lCEEELohvpqZGBg0KKBWsj7J6LfbAAg8i589qKkEGzZorykW01EPXr0oJvrCSGkmlERVqsrJ92t7AYnZ8/j5yQj/gWmn0Z9PQACoeBU6NnH3W2fPfJSV1dnOiYhhNQhdGi0WhkYGEQ+feSIZzIvrmGWh7gFAYAtw7WcEtdpzuLVG5nMRwghdQ8VYXWrX7++to6ucOBasGX+Z0Z+Gr/tIC/fxyKRiKFohBBSF1ERMiAy5oPIoHXZh6JsnJ2LPzvj9CzsH5qVk7dj9z7qQkIIqTZUhAxQVFQAjwMAhVnYMxCt7bDuGeZfh90SQYdha/afbmvZy9/fn+mYhBBSJ1ARMsDepovCu4cAcPtP9FuBDkNRlI1d9njnhzb9+NPORjcd1n+mc2uLriEhIbR3SAghVYqKkAG/T5qg+eIcsj7jQyA6DAOA47/DfilG74BWY5yZjU/POB1Gv2k+ttfinb91sIqKimI6MiGESC0qQgaoqand9jihd3w4S04RLBYSIqGgjLb9UZwLd0eM3Y1pp9B9GnglJfm5H7M45j0HOE6dlZCQwHRwQgiRQjW9CD9//tz0fx07dozpUBJg0aHD6+DHKkIOAHwKQau+APDwAPougKFZ2ZFStgxmX8D654JVQZdzG7Xt0v38hQtCoZDZ5IQQImVq+g31PB7v06dPrq6ujRo1Ek9p164ds5EkRUtLy0C7/ru8FHA5qKcLAG8eYvFtALi4FP1WwHwQeBycX4iECFEzqzzL6ZO2n3fevPPsoT09e3RnNjwhhEiNml6EYvb29q1aSeGjOLetd/p98/ycjhMR/xIA+CVQUEVxLjLjYT4IAI5NQcteGL8PAOJfCItyEhO4do7TJg7tt3n9aj09ve8tnRBCSCXU9EOjYtHR0T4+Ph8/fpSySyiHDHJYPb6f1sPteHENxTlQUEVRNtLeo1E7AHgfAAUV9JwNADf/wM2NaNUH00/xFt49yW1v1rP//Qc+zOYnhBApUDuKcPLkySNHjjQ1Ne3QocOnT5+YjiNJyxfOffng2rRhdvKudmjSBcHnABYgAoDX99FlLACEXUVmHBbeQqu+yM/AVWfRI7cMocrA8TN6DhwRGxvL7CYQQkitxuSh0fj4+AsXLlQ4y9DQcOLEiQB0dXVfvnzZvn17AGFhYSNHjhw5cuTLly+rNWgVMzIyOnbowIxnz+auXBcR+lrguBufXwJAfhrU9QHg4UHMvQwWC+8DcMUJE91g1B6AsCjb/9mljj3tLx53s7ezY3QjCCGktmKyCHNycv7t+SmtW7cWF2G9evXELQigY8eOmzdvnjhxYkpKivSdHuvSufMLP++MjIyRk2eGluSUhpyHmg7yUqDfCvxSqOlAwMOl5Vh4C/UboigbFxYhNxlNOuW2GTZwztr2hruunDpsbGzM9HYQQkgtU31FKBQKo6Ki8vLymjdvrqurC6B9+/be3t4/tBDxtaOZmZnSV4RiOjo6/vduxMXF9R0yOlHtN26oB1r0BIsNAB8CYWqD+g3B52L/MPRfATMH8XcJgBdxz6wHDH8V8EBbW5vJDSCEkNpGAucIz5496+jo2KxZMxaLxWKxUlNT/znmyZMnTZs2NTMz6969u76+/uzZs3k83k+sy9PTU0FB4bfffvvl1DVakyZN3r54umNC93pfQlhPTkDAA78U6bEwaAUAQafQbkBZCwr58D8Kt5Gi8wuTi1k2/YcnJiYymp0QQmoZCewRHjt2LDIy0sLCgsViffz48Z8DPn/+7ODgoKWlde/evcaNGx87dmz37t3Kysqurq7/uXBnZ+fMzExzc3MFBYWHDx9evnx57dq1CgoKvx67hpOTk1s4Z9a0SRMmzV50X1TCebBHpK4PTh4ARNzFJHcAKC3EgREwtcbYvdAwEJUUvI15ZNFn0LUTB627WTGbnxBCagsJ7BFevnw5Ozvb19e3a9euFQ7YunVrfn7+mTNn+vfv36pVK1dX1z59+hw4cCA5Ofk/F96rV6/CwsLTp0+7ubnx+XwPD49Nmzb9eubaQkVF5drZY2+eeDWLuyOXEI43DwGgIB31GwLA1dWwHI/B66BhAACKamg/JH3GzdHT5hUVFTGZmxBCag8J7BE2aNDg+wNu3LhhaGjYrVu38imOjo4PHz68c+fOzJkzv/+99vb29vb2lUxSWFgYHx/v4uJSPmXo0KGmpqaV/PYaS19f/1XQox17Dmzde7vk1S0oqaMwE4qqiHtWdq+9mFCAjE/IT8ttbn/t+o2xjmOqOSePxxOJRGx27bgnR4rxeLyfO/VAJEj8U2CxWEwHqdOEQmFl7j6v8otlUlNT09LSRowY8fVfCPG+Y0REhGTXxefzeTxeTk5O+ZTi4mLpeDinjIyM87JFs6ZOshs25j1btouYTQQAACAASURBVPT5ZTTvCYM2ZbNFQjzYjVAP6LeCmi4nIWLR2hvNfzM1NzevzpDiv3PS8QdeqwmFQvopME78U6AiZFYl/yFURxEC+OZSRvHHCi+r+RXq6uqmpqY7duyQ7GJrjoYNG4YHPvK4eGn2irVFqlp/z7i8EmwZrAmGjJx4Qm76x0FTJvpcPG5mZlZt8VgslkgkqgtncGs4LpdLPwXG8fl8BQUFKkJmCYVCDofzn8Oq/ChWSUkJAFVV1a8nqqmpASguLq7qtUsfGRmZCePHRQc/bvP6GDv2KQAkRSP1HUZtK29BANBtljHu5JQFy5nKSQghtUWVF6GSkhKA/Pz8ryfm5uYCUFZWruq1S6vGjRu/Dva379ZRJvgsIm6j2+QKBum1SM7niv+oCSGE/JsqPzSqr68PIDMz8+uJWVlZAAwMDKp67dLt0qkj1vaDo3NEgpZ9/p6a+g7PLyP5DeSUiku40dHRX1+mRAgh5BtVvkeoo6NjaGj49OnTr09aBgYGAih/dhr5OWpqamH+D7oa1UPh//8/4+F+nJmDRu0w4i/0W1HUedLQKXO96CUVhBDy76rjSveRI0empaU9fPhQ/FEkEl24cEFRUdHBwaEa1i7d5OTkNjkt1oj2BIDoB4h5hOU+aD8E2sbQbynqPj1znvfkBSvpcTOEEPJvJFCEPj4+zs7Ozs7O4eHhALZs2eLs7Lx+/fryAStWrNDR0Zk4ceKZM2f8/f0nTZoUFBS0cuVKHR2dX1876d27t6kwRTb8Bnz2YuxesGX+Z7aqVmYf5x373RlKRwghNZ0EzhGGhYUdOXJE/LWGhsb58+cBKCsrlz8CRk9Pz9fXd9q0aZMnTwagpqa2bt26DRs2/PqqidiDGxeHjPv9SUasUMvo76lfwvH+CTLjRfUaeAX77t22mbmAhBBSc7Gq853vqampeXl5TZo0kZeXr4rl+/j47Nix48GDB1Wx8JpPy9Q82+k5APC5OD0TpUWwGA6txsj6LBN4oldznbuXz1fRn7wYl8ul+whrgoKCAvEdSoRBRUVFysrKdB8hs8T3EaqoqHx/WLU+Dathw4bNmzev0t/FdVk9JQVwiwHg0nIYW2DuFXQeg88v4btPIMLDmNT6jVtOX7CssLCQ6aSEEFKD0GMhpceUsSOV/A8gPw2JkeizAABOzUBuMlY+wnIfkd3Skt96nfD00W3e3nn9n9/c0EIIIXUWFaH0cF66sFWqv8J1Z7S2A4AobwAY4QIZORwZj4i76D5DtDqQs9BrR2y9lp1tngYHMxuYEEJqAipC6aGgoBDse9e+IZeloAIAzy6V7Rfe/QuN2mLSITTugJc34e4oDL+dqWNuM3xyx572b9++ZTY2IYQwi4pQqsjJyS1dME8jPw4AMuOh1xxCAcJvot9yAPDehYg7WHofS70wdrfQfsULXoMOvR22bd9O7y8khNRZVITSxsrKSiEuCIVZkFdGSQFyEqHTFGxZZCci/Bamn4ZSfYTfhGs/lBai2xTO2IOr/TKNW3e4e8+L6eyEEMIAKkJpIycnd9j1L81jI2DQGlEPIOBDRhYAXt1Ct0lgy+DLKzzYjZWP0Gc+hHx4bhB+Ds9s3H3w/A2NWra/5nmT6S0ghJBqRUUohQYN6O/pvu23zBD2zQ0AC2kfASD7C3SaAsD9HXB0haIaXnvh9mbMuYwl99B/pbBl7ySW5piZSyx69X/0+DGzm0AIIdWGilA62Vhbv3vx1M/zgu6JkTJKqnh2EQqq4OQDQNpHNO4AoQCeGzD3CtT18Oo2joxHk86YeV7wx6uXZnOHLtw4dMwELpfL9HYQQkiVoyKUZjbW1p8iQvYvHl/faxOrMB2RdwFA/KiL+DAYd4SKJrITcWcLlnjBfBBykrB7IB66Fehb3PpUot3MbMmq9Xw+n9mtIISQKkVFKOVUVFTmzJ6V8j7S2cZA4Z0vIu+CLYvSIuQkQacJAASeQL8VUKqH5BicmoFJ7lh0C6O2iaYcK5hw9JD/e/shI6kLCSFSjIqwTlBSUnLZuDYpJtwiwk1JXhb+h6GohqIcAPgSjmZWAHBtNaYcQcPfIBLizhbs6IPg86UNWj1OhV5zM89bt5ndBEIIqSJV/oZ6UnNoaWmF+T/w8fGZMHtRpuxM4ZuHGCaAUAg2GzwOCjNhaAYA11YDLKwOEr/RScQvzfwUOsVp9Ulg2OBBDG8DIYRIGu0R1jm2trafIp9P1U5U5uWyrjqhYXN8CUdBJtT1ACAjDp9fYuRfYMugKBsnp2FbT4RcyNNsPnL6ojFTZ+fn5zO9BYQQIklUhHWRiorK0X07CxI/jjfmq8cH4tafUFBBQSYARHuj8xgAKC3C3sFoPxRrgjHJHb8fF7q8uyFnZWXrQFeTEkKkCRVh3cVms88eOfji/qWRli0Vj4wGrwQ5SchLg7o+ADw8AMvxMP//Y6FCPlLe8uTrxdZvu+cgve+eECI9qAjrOhMTkyvnT3u7b27XUIV9aBQUVJGXBgCR92A1sWzQS09stoTXdnwJL+Fw1vzl+teuvQxmJoQQCaKLZQgAdLexiQj2u3jl2vwVa7LltUXWUyDgQkEVAF7ewJMTWOELpfriwXw+d+u1xfmFLn9tWM1kaEIIkQTaIyR/cxw1Ij4qrHtTLTkvF4hEEAogFOCOC2aeK2vB0iI8PYurq/KLufuPnAymNxoSQmo/KkLyP1RVVX1uXZ3YMFeBV4A3PkiIQOP2ZS2YEIHtvZCfik4jYbekaMAGu8kLN/61k+nIhBDyS6gIybfk5OSOH9wddMuj/k1nJEVDwxAASgpwchpmX0K/FWhqCYPW6DKmcPmTvXdCL1+7znRkQgj5eVSEpGIWFhb3L57QfbyNlRkLAMHn0G1K2VPZyuWn5w5yWeOyi5GEhBAiEVSE5F917dLlU9TL+kkvwOMgNgStbctmFGTg9Ez82QXn5uLUjLjPCfvcDjOalBBCfh5dNUq+R0VFZdOqZesuzM4rLYK8MgAUpGPPIAxej8lHxGMEJQVrrztFv/+4f/sWJrMSQshPoT1C8h8WzJ6xdmQ3xbQoJL8BAM+NGLwOZgP/HqGoVjDm4LWnb8LDw5kKSQghP42KkPy35QvneV88We/xbgiFiHsOM4dvR7BYWVZzjl24wkQ6Qgj5JXRolFRK9+7dJ9t3PX1mcr6a9t9T02PhtQ2JUYAIItxR5G9yXqanp8dcTEII+WG0R0gqa9/2LTt+7yeTm1T2+UMgDo+D5QSsDsKaYMw4nWbYo02nbv7+/ozGJISQH0NFSH7AzGlTmjTQQEE6+KXwWIKFnvitO7ITsHsArq4SqWlnd5rSd+5Gc+u+cXFxTIclhJBKoSIkP2brupUal+cjyhtt7FFfD5w8uI3CkA2Ydw39nWBkzjcwi8jkt7a227P/YElJCdN5CSHkP1ARkh8zYthQp9G9lW84lb3O3nc/es2BSRfwS3FoNMJvov0QTD3B6Tplmft1rabtVq5Z/+HDB6ZTE0LIv6IiJD/MacmCRVMngM8FgDe+6DQKAK6vRYuemOQONV24jQKvVNjfqXja+R1R7A69HUY4jv/06ROzsQkhpEJUhORn9LPtrZkQCAD8UiiooLQI75+g11zwSnB0IqaewOB1kFXA6VnISSzsPu8Gp5n5sBk9Bw7PyspiOjshhPwPKkLyM6ytrXWyYvD5JWTkUVqI5GiYdAGLhedX0GEo9FshKRqXlmPBDUw6hM5jRBAV8Fj+Ee8btem80WVbUVER01tACCFlqAjJz2Cz2fevnW98Y56smhaeXQKvFLLyABAbjNZ2AHBzIya6QV0fqe+xyx7aJpjtgY3hJdPPb77/zqSVeWBgILObQAghYlSE5CcZGxtHh/pvdOyueP8vcHKRFA0A3GIoqEAkQtZnGJlDJMTJaZh2CpbjwS3G3sG4vVmgZZzecXLvOZtad+nx7t07preDEFLXURGSn6eiorLGacW7508sXh+Wy4pD3DNoN0HqO/A4UFQDgE+hMGgDg9YoLcLBERiwEvNvoNdsFGbzinLfpOS27mbXzX4IPaSUEMIgKkLyq4yMjML8vH0uHdc8P42lpo1HByGniOJcAEh8DZPOAOB3GJYTYWqN3BTs6gej9lj1BOvDBPNvPFUwsx7k6Lx6dW5uLrMbQgipm6gIiWT06NEjMujhaMW3agWJrEOj0MAUH58CgEgEAFHe6OIIABeXYNRWdHFEcS72D8Pdv1C/QfGgTdtf8U079Thy8gyT20AIqZOoCInE6OjonD60Nz/xw4kljoZFn9jHJ0OxHuKeA0BJPlQ0UZyD/HS06AWRCIfHo/s0zLqAHjOhVE+Un54pVJrr/EfvQSPevn3L9KYQQuoQKkIieVMmjvsSE/7s/rWmzw/KxPggOQaK9VCYhfRP0G8JAG980MAUZg4QieCxBIGn0HseVjwUrHv+2HS6zcipp855ML0RhJC6goqQVBULC4uPr0K8LhzTPDmGraGPUA/Iypc9jybmMToMAYCQ8+CXYuY5GJmjOAd3XHDrz8zC0ulLnCdMn5OZmcnsJhBC6gIqQlK1bG1t34cFzrUylPfZhdxkfHkFkRDFuVDRAoCAYxi+GQBS3mKPA5p0wnIfrA0R/Bl9gW1lZmP78eNHZvMTQqQeFSGpclpaWvt3/hX/+rnlm8NKLD7r/i6o6yMzHiIR+KVQ0YRIhNMzMf0MLIZDVh7xYTi/UPTILblIZN5z4J07d5neAkKINKM31JNqoqen9/TB7Y8fP46cNON9qQrnUwjaDymb9/kFGvxWdvrQzx0vPTFsE4zagy1TlPp+3La/Bt/yOnt4P4vFYjA/IURa0R4hqVbNmjV79fTxlU1zjWXy2JeWgMVGSQGSY9C4AwAkRCLsGhbdRpPOYLERdAY3NxYkvr94x7fv4JGJiYlMxyeESCEqQsKAgQMHxIYHr+llpFqSyfLcABYbIgEABBzD4HWQkQOPg32DkfEJI7diTbBgVdAjI0eLPoMCntATSgkhEkZFSJjBZrM3rXHKin9rLftZKcYL7wMBICkKTToBwI31aD8UwzZB2xgiERIikB6bbtB18OjxMTExzCYnhEgZKkLCJHl5eX+vm26zByknh+NDUNljaPhcvPNH9+kAUJAB134IuQCtxrAYkdd7WedB49f+uZXZ2IQQaUIXyxCGsVisKZMm2PbpZd1v6Bd5NeGnZ1DXh14LsFgQiXBkPPqtQGvbstHNexT2mHnAY5ZBwxNzZkxlNDghRErQHiGpEQwMDKJC/Ob1s5C96gQ+F2ABwNtHaPDb3y0oxpbJG7ln8679IvHuIyGE/BraIyQ1hYqKyr5dO4wau7kcX5KTlQmRCO8D0W7A3yOEfMSGIPkNZORLFDU+f/5sbGzMWFxCiLSgPUJSsyxfONf72PZG9eVZgSfByYdy/bIZcc+wpRvCrkJGDvzSXJl6tkMd4+PjmcxKCJEKtEdIapxOnTrFhPp3sxsUw1HhpX9Es25Ij8W5BZh3DZqNxGOEPWd9jA/rMXBEdKi/qqoqs4EJIbUa7RGSmkhVVTXM/8GKQZ1kffdBKMC9rRizo7wFyxh3TOswae+hIwxlJIRICSpCUkPJyclt2bRhxTTH+uen48srmNr8z+y8VMQGl5p0u37Ph6GAhBApQUVIajSXDat3TrFjl+Sj/EGjr72wuSvOzMHzK7j5R2Tka4/LVxjNSAip3agISU03/fdJetoaEPIB4KUnfPZh0W0suIFm3VBSwFfTnbB4nbZJ6zWbXLhcLtNhCSG1DxUhqQXseveQeXUTAh7ubMacS1DTwfW1iLyDWRewNlQ4wS2rme3Wk9d0TM3/2uman5/PdF5CSG1CRUhqgW0bVun5bWc9OQ5TGyjVQ2wIkqPx+wmoauHcPDx2Q7sBwvme+b0Wr70Q0LBFh+VOq96+fct0akJI7UBFSGoBHR2doPueTSNOsjT0ASDkPPotB4sF331Qqo9ZHmjUFscm4fNLoeUEzqRjuyL5FnbDbfr2DwgIEAqFTMcnhNRoVISkdjAyMtq7bbMqLx8A0j7AoA1EIgSfx5ANEIlwZCL6Lcf4/VDXg8dS8LnFdk6B+oPtlu7UN2lx6dKl4uJipreAEFJDURGSWsPKykrhnQ9EQsgqgMtBXio0G0FWAR+DoGWI1nbI+lx23/2YnQDg516q0iCt45Rxrp6NWnWYNX9RXl4e0xtBCKlxqAhJraGurj5h2EDVO+th3BFv/SDgQkYeAD4Eom1/APDageGbodkIIRfw8jqc/DB2D4rzhCkxOfqdjobn6lv06dpnYFxcHLMbQgipUagISW2ya8vG8U1Emh8fsO5showcMuMBoLQYCqoAEB+GVn0g4OGBK6adhoIqjk6EqhbWhWKSu0i/ZTFLMfRDommnHpZ2g4NDQhjdFEJITUFFSGoTNpvtvmf7S69LK6eOUt5jy1LVwItr0DJC2gcAYLHAYiP+BZpaQkEFUd5Q0YDdEnA52DMQABbfwbpngrH7Qkob9hjxe79hY0KoDgmp86gISe3TuHHjrVs2x4cHrRndS9lzFaskD8HnwOeCxQaPg/x0qOsBQPhN2EwFgDtb0HkM7JeBW4ydtnjnB4thvFmXvBuOsJu12nbQ8JKSEma3iBDCICpCUlvp6Oj8uWFt2ofX8xrnqwsL2Hsd0LwHQi9CTQt5aQCQmwytxhAJEf2grBGPTcbAVRi9A006wXcf7m0tUDF4mALNZmaOU+fQnfiE1E1UhKR2U1VV3b/DJefz20sui5okBcjc3oSiXHwIBI8DpfoozEJhFurrg8XGp1DUb4BWfcErwd7BaNkb60Ix9YRo6CZOzwVXXiWZmnUOCAhgeoMIIdWNipBIiZHDhn6KDP0U/tT640lVNo91dAJMrRHuCRlZCHgAEBuC1nYA4OcOi2HoNAoiES6vxIVFkFUQ2i1Nt1vXf7lr5552BQUFzG4LIaQ6URESqWJkZPTE62ZK9PMldm01gw6yn55BUgwKM8HjgFsMeWUAeHUb1r8DwL2tkJHFEi9YT0HqB/jsLc7LCcsQaZuaDZ8wLSMjg9ltIYRUDypCIoVUVVV3bd3yOTL0stv2RrcWKSgp4fo66JggJQYAuMVQqg9eCV5cx7BNYLFwbTU+hWLpfazwFc26wB3q4hlb+pt5F09PT5FIxPTWEEKqFhUhkVqqqqojRoxIiHn16OSu9iVRCi8uIfQiSgsBQMhHQgSaWoItiy+vkBSNiW5QVMPzK9hpi/SPoo4jcwf8MWbntdadu3/+/JnpTSGEVCFZpgMQUuWsrKxePnn4wMdn3V+uL3b2FRi0RZQ3ZBWgXB8Anl9B7zlgsfA+AE+Ow+lx2e35xTncerox759Y9u4X9TxIU1OT2a0ghFQR2iMkdYWdrW3oIy/fU7tblH5geyyGjDxS3wNAZhwaNAeAOy6YfBgKqhAJcWsT9jjgzUPU00016m5sbrXf/Siz+QkhVYT2CEnd0rNH95jnQU+Dg0dNmZ2aVyzM+gwFFZTkQ8gHJx9ajQHgxnqIhFj1BCw2ABFQwCtZf3aarKzsnOm/M7wBhBBJoz1CUhdZWVrGvX6+w2mestsQ6JggyhulRVBUA4DcZHwIxPAt4hYsI6eYO/7oHzv28Hg8pjITQqoIFSGpo+Tl5ZcuWRx083zbtMcyjw8hKwGFmQAQ8wgdhoHFKhsXdhWu/bDFEjv6ZBaUbNi0ha4jJUTK0KFRUqeZm5tHPn0cFRXVb+SEVAUlQfQDFGRAXb9stsdicDmYfhr1GgAQFGbtuftH9LgpnhdOscqbkhBSy9EeISFo06bNp8hnh5ymq1xaCE4ucpIA4LUXinIw+bC4BZGbjGgfjpL2g9dfNrtsZTYwIUSCqAgJAQB5efkZM2bEhPp1KQpnB56ASIjAU3BYUzbbazsOjUFBOpp0KrEYs8njUS+HEfQkNkKkAx0aJeRvhoaGIY+8lq5ef+TyoqKsL2j4GwD4H0H6Rzj5gS0jHsa3mRb0/OIgx8l+d68zGZcQIgm0R0jIt3Zt+WN576bsglSIhBAK4H8E4/aWtWBuCm5twr4hvIeHgqNjd+5yZTosIeRXURES8i0Wi7Vx1YoBtn0QG4yUt2jUDnJKAPD+CfYPgX4r/H4Uy324U06uuxlhP9yRz+czHZkQ8vOoCAmp2J/OSzTvrkVBBpQ1AKA4FxeXYOEtdBwJNV3EP8eTEyUZCb7hH7rZOXz58oXpvISQn0RFSEjFzM3NXZbM0LzlhNS3APD8MrpNQf2GAHB1Fbxd0XEE5l4RzvR4pmHd1qrXrt17SktLmc1MCPkJVISE/KtZUyeH3L2kXvAFmfFIiEAzKwAI9UBRFuZdg6k1np6B+xhkJ+Z3nb7SI6hR647ux08ynZoQ8mPoqlFCvsfU1NTr8ulBU8Zl1mta9tA1v8OYfx0AvF2R+harAiErj5IC4UvPzC8NF/6577Gf//5d23V1dZlNTgipJNojJOQ/dO3SxevsId2MCFZ8GERC8LlQ0URxDsKuYKIbZOXxIRDbe6EgAx2G8cYfuMJr06JLT/djJ5gOTgipFCpCQv5bx44dXwU90go9ipL8sv3Ct/4wcwBbFrkp8FiCRXdgvxRqOri5SRR2PUfPYp7LoYa/tTt28gzT2Qkh/4GKkJBK0dPT27tpldbhoeAWg1eC/LSyR5I+OgiH1ajfEEnRODYJI1zg7I8hG4XNrNNQf5bThkZtOrsdOSYQCJjeAkJIxWpEEcbHx58+fXrhwoWjR48ODg7+Zu6bN29Gjx5tZmY2YMCAx48fM5KQEADjxox6eN7NVFeV5bUNqtrISwWA2GC0tgWAyysw7RQM2+GtHw6NRoueWHRbuMw3qYn9wh3HdUzN9h5wy8vLY3YTCCH/VCOK0MXFZdmyZZGRkVeuXElISPh6VkJCgo2NTV5enpOTU4MGDezt7YOCgpjKSYiZmVlUiL8l55Vy4nO8ugWRELwSyCujIAMiIfRbgZOHy8ux6BbaDcCzSzg8DrpNBeMP5jgeWnontknr9idPnaaXGhJSo9SIIty5c2dmZua1a9cqnKWkpOTp6Tlu3LgTJ05YW1uvX7+++hMSUk5eXj7g/s1NdiaaKGadmQMNQ6R9QE4StJsAwIsb6Doearp4548X17HyESzH48srnJsvLMjM6TB++r7rBq06HD5xiuHNIIT8vxpRhPXq1fu3Wb6+voMGDVJSUgLAYrFGjRrl7+/P5XKrMR0h35KRkVm2cF7mp+hVfZvVS3/Nur8DimoozgGApCiYdAaA+7swbi9k5fHkBCLvwjkAvx9DMyuhSJTBk5+7arN+i/aHjh6n1/wSwrgaUYTfkZiYaGJiUv7RxMREIBCkpqYyGIkQMRaLtWXD6vjIUAuZZIWQU0j7gNIilBdbQTp0m4JbjMeHMO0U5JVxbxv83DFqO9aGCEfvSNFqN3/DDk2TNms3uWRmZjK6KYTUaVV+Q314eHhubm6Fs8zMzDQ1Nb/zvaWlpfn5+fXr1y+foq6uDiA9Pd3IyEiyOQn5ORoaGiGP7m/ZsXt3OCf/1HRhq7749AzNupXN/hCI1raQU0T8C7wPwMJbgAhHxkOxHnrPFTZwzQ0+73LDZ8ehE2MG2S+YMaVTp06Mbg0hdVGVF6Gzs/M/LwQVu3HjRp8+fb7zvQoKCsrKyoWFheVTxF9raGhINiQhv0JGRma98/L1zstXrtt0/PLx7Lw8WE4AiwVeCfLSoGEAAEGnMHAV2DK4/ScatcUAZ2QnwnUAWvUV2S7m1mt49o3vjbGz2hvrHj+039TUlOFNIqQukXwRCgQCGRmZ8o/e3t6/srSGDRumpKSUf0xOTgagp6f3K8skpIps/3P9gpm/u+7Z5+7au7RxV5HfETRoivSPAJDyFkbmEAoQfhNrQyAU4Mh4jHVFk85IjsGpGdA2Lmw/JpBb3H7k3JYabM/zJwwMDJjeIELqhEqdIywoKLh8+bKTk1Pfvn07duy4ZcuWCoedPHmyZcuWsrKyqqqqY8aMSUpK+vV8Xbp0+bpKvb2927Ztq6ys/OtLJqQqGBoa7t61I+bJ/fEtVRUe7WUlReP1fQgFYMtAwEdOInSagi2LN74wtkCTzshNwbFJmHwY00+jw1BR6rui/JywhLzG7a2t+w99/fo10xtEiPSrVBGGhYWNGTNm+/bt7969e/HiRYWvXnN3d586daqOjs6xY8eWL19+586dXr165efnV2b5nz59unLlys2bNwGEhIRcuXIlJCREPGvJkiUxMTGrV6/+/Pnz0aNHL168uGLFikpvHSHMMDY2Pnv0QM6XdwuacdQEBayzc2DYDh+CIOBDRhYAPoWiVR8A8NqGoRuh1wJfwuHuiF5zsCYYS+4JBqwOylXpaD9i6qx5nz59YnZzCJFyokpISkry9fXNycn5+PEjgJkzZ34zIC8vT11dvXXr1qWlpeIpHh4eAP7444/KLP/ChQsm/2v+/Pnlcy9fvtyoUSMAGhoa27Zt+85yHjx4YGtrW5k1kqpQWlpaUlLCdIoaRygULlu9QcOkLcugFfakwKg9jnJhvwzLvHGUi8YdcJiDo1yYdIHLWxzlYnUQDM0wahtWPcGGFxjrWq9xy4XLVnI4nEquMT8/v0q3iFRGYWGhUChkOkVdJxAICgsL/3NYpc4R6uvr6+vrA8jKyqpwwL1793Jzc52dneXl5cVTRowYoaGhcf78+crc/z527NixY8f+29xRo0aNGjUqPz//O7cbivH5/OzsbF9fX/FHNpvdsWPH//wuQqoUi8XauWXjqqULtu/a47bXvlC9EZ5dgo4JkmPQohdYLLBlkPgaOibQMUFRNs7OwXxPaDYS34YPVc38loP2B8SdbmkxYeSQ3S5/yMnJMb1NhEgVyVwsExYWBqB3797lU+Tk5GxsbG7dupWXl/f1/Q8/rTJ9lpGRERcX5+LiUj5l8eLFvXr1+vW1k8rgcrkikYged1AheXn5tatWjncconaIAAAAIABJREFU5XrwyMXrq7lWv4si7sBmKoRCCPlIj4V+KwAIPIlec6HZCEnRODMbM89Dtyn4XNGLa3mx2oeu+d728nHbtrF79+7fWdfXF1oTphQXFwsEAhaLxXSQOk0oFFbmRyCZIhSfNdTR0fl6ovjFpAkJCRIpwsrQ09OzsLB48OBB9ayOfENchAoKCkwHqbnatWt36vCBQ3t2/Lnd9VhUSdYuW2Hj9nh1B7Ly4JUAQGwIHF0B4PoaTDkK3abIScKh0WjTD13HCfst/5L6bqzLKeuTF256nPrOrqGamlp1bROpGJvNVlZWpiJkllAo5HA4/zlMMk+WKSoqwj9u7xN/pP+cEvINJSUllw1r0mOj77tvaVnynn1pCeSV8NYPALgcyCuBx0FhFhq1hUiIIxPg6IrB62DSBYmR8D9akBx7Pyisibmlj48vw1tCiFSQzB6h+NRgcXHx1zt/4nZUVFSUyCoIkT62ffu86dvn3bt3wyfNiC3JLn1youzcobYx1PUA4F0ADFrBpAsAXFqOggyM2ALdZiIg6a3/8MWbRve4dezgXtrtIORXSGaPUHxQNDs7++uJ4o/a2toSWQUh0qp58+bRoQEv7l9pEX1aKe8LvHdBWR0FmQAQ/xwtegNA+C0UZWH6aeg2wxtfbLHEw32FBhannrzVNmlF77Ig5FdIZo+wdevWACIiIsRfiEVERKirq9PTMQipjNatW795HuTldX/phi0fLywUiATITgCvBPKKAPDkOMbvB4Co+/DaiQWeqNcAgBDILv2/9u47oKmr7wP492YBYYPsjSAIgqKCuLeoiOtxPGqte9Q9Wq2ry05t62jrqtuq1IEDwYHIUIYDJ0vZU3Zkk3nfP0J5eNU6WjQKv89fuSeH5Hcy+OYm95xbvXLfR6Wi8tXLF6t0BIS8r5pmj3Do0KEMwwQEBDS0JCYmJiUl+fr60pc2hLwihmGGDh2SfPPabzMHmKGCs30s9MyRlwAAlUUwtAarwKnP8ZG/MgWR+wAH5+LnweU5KV9s3Lr1120sndSJkNf3qnuEx48fB1BYWIi/FoIB4Obm5uzsDMDR0XHcuHHHjh379ddfZ86cmZ2dPWXKFD6fv2LFijdWOSHN1pzpU+dMn3r02InFqz8vqRSzfebWn90p9wEs20GrFQBc90f4TvznG9h5gsuXluWsDNx0+sKYi6f8VVs8Ie8d5hU/Qj53x+77779fuXKl8nJFRcXo0aNDQ0OVm1paWrt37x4/fnxTFfoqQkJCNm7cSNMnVIWmTzS5mpqab3/YuOnIuRqBHiZuQVEqMm5i+GcozcaO/+KTyxD8v3V3hee//qST5vKFH9H0CZWrrq6m6RMqp5w+oamp+eJur7pHmJaW9mxj47MJ6ujoXL58+datWwkJCbq6un369FGeO5AQ8o8JhcKvv/x82NDBUz9anHJkocLvs/qDaKIPYtDS/6VgjQiJoXicVKOm9duuPcsWzFVhzYS8d141CBufJv4FOnfu3Llz539RDyHkad5duiTfjl3x2frd578X5WVCJkF+Arp+UH/1dX9c/AmeY2HTEbUVZaYdvfoODjn9p5WVlUqrJuS98cZPzEsIaRIbvlo3widq9vI1yQdmK8CAVQBAUihiDuHTiIa9Q0WXCY/SYvr5jU28eZVWJSXkVTTNUaOEkLege/fuCbHhnw5pp5F/F2mxAHDuO0zZVZ+ClUU4/Tl+8mH9l6WL6iZMnfEqi0sRQigICXnPfPPZquig4zqhP6KqBDIx9C0AIC8em3xh0Q7zjmNNjGLh6VPF+s4dvfPz81VdLyHvOgpCQt4/HTp02LXxS4MdfuBrAIBChv2zMPcoPMcCLA7OxS+jFbUV2fputp37jJo0XSQSqbpkQt5dFISEvJfGjxl97dQh9YocAEgOR+tuMHaATIytI9C2P9Zdx5RdGLZG2n/JmYdP2nh0CQsLU3XJhLyjKAgJeV+1bdu2X4+uTHIY8uJh7wUAEbvQwQ+eY8GyOLkGBz8Ch8v2W1Di87nvqt+6DvCtqKhQddWEvHMoCAl5j+346VvTcyuZ0uz6pWfunEXP6QBw6WfIxFh+CT2nQ1qHa/trCzNjUx4bt2m/4JPVdHI0QhqjICTkPWZlZRVz8bRLeRyTfAUAxFUQ6kMmwfWjGPMdGAahvyBsG6bswpoYjNsgbuuz7c9gI8f285atzMnJUXX5hLwTKAgJeb/Z2NjcjYm0KruPolQwHMgkyIuHrSe4fBSl4VYAPjoGfQv4L0fYdnhPYleE1vl+tv1qmoNX3+H//TA8PFzVIyBExSgICXnv8Xi8c/77TQ9OZPTNcT8IdZXQ0AGAG/7ovwBcPqIPQibGXH+YOWPbOGTcRM8ZknkBgazb0DmrnNp7hoSEyGQyVY+DENWgICSkOXBzc7sXeXGatw3v+CdgOChKBYDCFFi2A4CI3/GfbwBg3wz0m48Jm2BgjQNzUPCo1nvqow6zfFdvN7Nz+n33bjqahrRAFISENBPGxsZ7ftsSe/GU1bmPOQXJKE4HTw2SWihkYBho6CI/CQyDDn6oEWHXJEzejsnboGuKsG1SNZ0Sz2lz91+17dhzyqx5YrFY1aMh5O2hICSkWenUseO9qNCt65Zo7hgFfUskh0EhB8MBgPTrcBkAAFe2YcBCWLgiIQQhm7HsAqb+Dh1jRW68SM340K1cPQePnj4j0tPTVTsWQt4OCkJCmhsejzd/3rzoQH/3kmuc0K0oL4C0FjIxJDX1q5ImXUHHUQBw5gvMOgQtQ5z+Ammx+CQUC0+xNh3reJrXHuU7dh1k38H74OGjqh0OIW8aBSEhzZO7u/u96CtRwSeNfh/FNbJByBYY2yM/CQAkNVDXRmkW9MygY4KCh0iPxYc7wOFgix80dLAyHJ9GKIZ/lqHlPH3lenuPboeP+tPRNKS5oiAkpDnz7tIl9XbUd5P66t86xHkYhoRLqCqFpiHKH6OiEHoWABAXgF4zwTC4tBnth6H/QtRV4sdBePwQfT+SL72Q4TBy2tc7TRzdd/3+e3l5uarHREgToyAkpJnT0dH5ZOni4vSEDYPtrbS4nI19Yd8F1/ZDqxXKHwNAWQ6MWwPA3bPoMwcA9s+E76cY+QUYDraOQO0Taf/FZaN//ig4v7VH1yP+x1Q5HkKaGgUhIS0Cl8tdvnhBdtKd2DOHOlfe5EXuZDJuoDQbVSVQ00JNOVgWYMBTQ8EjgEE7H1SVYv9MzP0TI7+ERTuE71LcPVeq12byJ19btvU4THFImgsKQkJaFs/OnW+GnS9JTxz65KIuapjt42DTEfeDwTBQyAEgKw5OvQEgfAcGLIaRHYrS8NsYDFyMNdGY668Y+WWedZ9pn37bz3dUYmKiaodDyL9HQUhIS6Srq3vu2B95Cbe+muZncPk77v1APIqEUA9luZBJwBMAQEoU3IcCwLGP8eF2OHSDKA8b+iLlGlwGSqfsDrP4T48JC+Yt+5RVLvlNyPuJgpCQlktTU3Ptpyvykm6f+n2T+ZklGupq+GMejFsj9wEA1FVCqIvactSUw7YzFHLsmoSxP2DM92jbDynXELZdVF6x42iAubOH//ETqh4NIf8QBSEhLZ26urqfn19u8v2zG5f3tdZQO7EcKVEozYKBFQpTUZYLIzsASLgEm05o3RUKGbaNRVUplpzD2hh2/qmC9hOnrN7Yo79PfHy8qkdDyGujICSEAADDMAMGDLhyLuBu0JEpvr34m3xg7oLwHVDXQm0FAKTFot0gAIj4HVbtMfwz8DVweCH8l0FDRzL8qyjLkT0+XD5q0jSJRKLasRDyWigICSH/j7Oz8/7fdyRHh/gJs9UeBDLRh1CcAXE1xNVQ1wKA6/4YtBQAAtZCzwxLzqHnDBjaoCi9XMKeibjp0LlnGJ3dibw/KAgJIc9hb29/9ui+yry0ZW4cbXklc+gjtLLB42QAkEugoYPqMjyKxNBVABAXgN1T4Ngdsw6xa6Jz/H4e/emWWYs+Vu0QCHlFFISEkL/F5/N//Przivz0OV0tdeOOIGwH5FIoFACQFgvXQWAYlGTiwo9YfgHuvtDQxXV/BP/wpDBn77Ez3Qf5paWlqXoQhLwEBSEh5OW2b9p4K9jfr4uL4LcR0NRDSWb9MaUAru7B0E+hpgVpHX4ZieIMTNiCNTGKz+OiXeZ6DxsffOGiqssn5EUoCAkhr8TBweHs8SNH1y+0kBVzDsyGnjmK0gAg+y4cuwFA4NdwG4xRX8HAEjIxbp/Gg+ASdYsx0+edO3dOtcUT8gIUhISQ1zB6xPDcRw/WTh5qcP4LJIejuqz+fIcKOeIvou9HAFCWgw39UJSKLhPw359qx28d/9XvIydOlcvlqi6fkOegICSEvLYvV38SfuS3Id08eJsHw9Aa2Xfw5DFa2YLhgFVg1weYsBl+62DfBYY2MHWq6TLtQo78oyV0+Ax5F1EQEkL+CTc3t+CTRy/u3WRdEscJWANWBrAAkBgKGw/YeQJAcQZ+HoyjS5F9R6xrvScoqvsgv4KCAtVWTshTeKougBDyHuvXt09W4t11X3+/1X9+RVEeWAUyb8K5HwBUFmP7OEzZCZuOys6KkV/EJF/p7jP8QUy4UChUZd2ENEJ7hISQf2v92k/PbllrriNgLm2GVAyBOgBc/BlDV9anoEyCyN3YNYkNWJdZzRkxfnJlZaVqayakAQUhIaQJ9O7VK+1OTBdRpFr+feTGA8DDCHiMAIDqMvw0CJVFGLUeq64qZh8J1ezWzrtPRkaGamsmRImCkBDSNNTV1a9dPPvtFB/+1V0QVwEsuHwAODQPQz6B72oY2SPjJk6uZq/7Z1fKXLr2/23n7wrl9HxCVIeCkBDSZLhc7rLFC/f8/K3BzpGQSaGQ4clj1DyBuy8ARO7G6S8w+BOsicaSoLr+i5ds/sOuXafz589THBIVoiAkhDSxyRPHn93xXSuBHHfOIvc+7L0BoDAFMX9g0WlYuePqHvwyEgq5bOjq7N6fjvr6kL2rx/3791VdOGmhKAgJIU2ve7duD6Ium4V9j+IMcLgAEH0Qgz8GTw33gnDvHFaGo/9CiPIQ9K24tibLxLvjyOmOHl2vRUWpunbS4lAQEkLeCFNT0yunj7Z+cJDzMBwA8hPrjyA9vwFTdoKnhpDNSLiElRGYdxweI+St7FPL6nqPmNCx9+CQkMsqrZ20LBSEhJA3xdnZOfX+TWc9MGmx4HAhl0FcDQ4X2saoKMTNE5ixD2qaCFiLa3vhtw5rYhUTf7kjNx06dYFj5557Dxykc/ySt4CCkBDyZgUfO2RxZjGHw0NqNOoqoaELAPEX4TUOHB7iL6A4HbOPoJUtto/FvXPoPkW2LCR14Lcf7b9q79KBfjskbxoFISHkzbKxsbkfFTqlsxn37Bfg8vAkDwBEuWhlBwARv2PUV2AYnPgUroMweRvsvHD5FxxZJJEr8mwHdBo1w6mjd0xMjGpHQZoxCkJCyBunr6+/d/vWY7s2tdo5HFqtkBwGDV1UlQLAk3wYO6C2Auk30Hs2AOydBi0DrL2OUV+hpkwmkz+CaY+JC03buH+94SeWZVU7FtL8UBASQt6S0SOGXw/6c1JXR/6BmVDXxt0zAKAMtrwHaN0VDIPkcPDU4LMcVcXY7Aev8Vh3HcNWK3TNCiX8z7Yd0bRsM3jMJFqVhjQhCkJCyNtjb2//x+5tabej+hSfFzyOZyJ2wdAa+UmQisFXA4C7gegxFQDOfAm/tWg3GPEXcXgRRn+DtbHsxC219j0v3kx09OzVy/c/4RERKh0NaSYoCAkhb5uVlVVY4ImS1Ac9Sy7p1DzGsU9g3Bp5CQBQng8DawBIv472wyCtRcBaLDoD87a4+DMCv0avmVh1Tb7mxlXdnr7Tl/iOGkN7h+RfoiAkhKiGtrZ2xPkzMSf3DnbUVf9jNmqeIPsOhPqoLEZtBTQNwTBIvAK3IdA0QFoMkq5g4WnYeSJqPzYPRVVpTb+l59Guvc/4voPpNIfkn6MgJISokouLy/lTx0K2f9XfxYK77T8Q6uH2KagJUVcJAMVpMG8LAOE7MXo9OFzEHkFyGFZdxbA1KMlk405VGjiE15nZ9vBz79Y3ISFBtcMh7yMKQkKI6vXo0ePy2eM5D26MMS7n3ziKhFAINCDKA08NkhoAKHgEqw5gFbi0CVN2gaeGwwshrcPa65ixH/beYo1WD3JF7r0Gdx88MjY2VtUDIu8TCkJCyLvCzMzs+IFdecl3usRv0xUw2DsNNh5IDAUAsADw+CHMXaCujcxbqCzGyC8BFjsnIPcBpu7EZzcV8wOiOU59xs8YPf4D2jskr4iCkBDybjEyMooNDb565NcPurXR/GM2U5SKhEswdkDufdSUQasVANw5ix7TACBsO0ydMW4DNA2w+0Oc+wamTuLxW0/xPL1HTes3dHhRUZFqh0PefRSEhJB3kZub26E9O1Ovh/60dKreyaV8VoKANdAxQVk2ADzJQytbAIg9iqErAODwIjh0w7zj6OCHqAO4/meVlVdYqdCifTeD1m4fzl106vRpmUymwhGRdxYFISHk3WVqarp0yeKSjKQjKz9w15HxDs9HSSaePIaGHqpKoJCD4UAgRFkOSjLRZy7kUvwyCu6+WBkOLh/VItmI9aLJBw5p+Hyw5ay9a4f4+HhVj4m8cygICSHvOi6XO+Y/o+9FhYZs+7yTnTFnyzBYt8ft02AYsAoASLkGt8EAEHUA7Qai02hc3gqwWHIOnUYj4RJOrq6prc2x6O0xfFpbzx537txR7YjIO4WCkBDy3ujTu/etiEshB7bY3NjOexCEBxfA4aLmCeoqIdQDgHvn0G0KFHLEHMLorwHg2ApUFGFNDGYehNdYmU2nZJHcy2f02A9npqSkqHY45B1BQUgIec/069c3M/7WjQsn28ZsFHJZnFwFAysUpgJARSH0zFGcDrO24KkhLwEFDzH2B3D5OLUOF3+G9yQsPS9bE3tCz6/r8EkHDvurejRE9SgICSHvJQ8Pj8Sb1679ucOLyVGP2oP7QfUnO6wuhaQGapoAcC8Q3acAwK2TEOVi3gm09kZZDv6Yj8D1pTLBtPlLLJ3bT/to0YkTJyorK1U7IqIqFISEkPeYh4fH9fCLp76e59HagvOzD+y7IC4ABlYoTAEAUT4MbQAgfAfGfA+GQVosdk+Bz3JM2wuZmO0yMa/v6v38fpOPPGjdwfvEqdOqHQ5RCQpCQsh7b/Bgn9uRl4J3fGufE8oJ/g4lmVDXQcYNCPVQVQIA4iromIBV4OgSzD8JE0fs/hDT92LsD3Doilsn6+ICi4VW4+d/atOu8/GAU6oeEHmrKAgJIc2Ez6CBafeu3w0/3/rsIj0NHvZMg1Aft08Df531MOMmbDrCwBKRu9F7NsycUZaDLcPR5b9Ydx2LzijGfJ9t0XPS0i8G+I2mhWlaDp6qCyCEkKbk5uaWeu96XFzclbDwfcfPpKSmy2+dYHkC1Jaj6K8lvB9dxYfbAeD4Cvz3Z7TpifLH2DEBdp5wGSDtMjG04GHPSQvH9O60c/MGhmFUOyLyptEeISGkGerUqdMnHy9PvB5Zkp7gnX5Yk5Hh7NfgqUFcAwA15RDqQVwNUR7a9ASrwK4PMGo9xm1EOx/IxEiNFtXJ95wM9uw3JCkpSdWjIW8WBSEhpDnT1dWNvnQu+uQel/JbgoRgJIUCgIElitLxJL9+nbakKzB3RZueAHDuG5z7Fl7jsPC0YkVYXIeFPcfO3LFnv+pGQN44CkJCSPPn7u4ef/3qL9P6aVfmMrFH0Ok/iNgFvgbqqgAgLQbtfADgfjByH2DhaTh0h0ATGTeRHFGqZrLk8+83b92qUChUOwryhlAQEkJaBIZhZk+fmpd0u3PaUd30MOQl4KY/SrMhrob4r3mHYdsxdgMYBpIa/Doat0/DpT+GrRG3HbR88yEdm7aLVqx+8OCBXC5PSUkJDw/Py8tT9bBIE6CDZQghLYi2tnZsaHBQUPDpSxoXLx8vqimR/TGfbe2Ngodw7oOqEhhaA8DRpeg4Et2nIOUa9s1A71mKzmOrb/j/ciTw1z2Hwcp5Vm48Hk9W8EghqdPRUNPW1rK2se3q4WZtZmRvb+/i4gLA2NhYKBSqeMDkFVAQEkJaFg6H4+c3zM9vGACWZWfMX3Iy7HBFVS16TKufZVFZhIJHmLITlcU4ugSLz4Gvhi3D0WMaNA3ZJ/mYuFn65ydSaS0WnsP5DaInj0WdRmc/OH/tj7OMuSuKDjGVRYy6DkdarZBJ1XhcBThcDvgcMAIhH3J1dXWumoYal1ETCPjqGupc8AV8hqsm5Co4AnU+n6/GyOV8oZDLcrgc8NTVWQmrJhRwGC6jkHPVNBgFw+OzDIfHylieuhoXHIaRgsNjZQxPwOUwrFym4PJ5rBwMh2U4HFYuB1ddwAXL1skUPChYhsuABauQgcODAgxHpmAZhUzB4fEZAKxEwXAUUobHZ1kWcpmM4QkYBQtGxoKRS+UMl88BWFbCcjhyCYcnkCsUjEIm4/AFjEKhYGXgcOQSOcPjcRlGIa9VcNQgA5cvkys4CqmU4QsYBQAJy+EpJFJweRwwCnkdyxVABg5PqlBw5VIZRyBgFCwgUTA8hUTO4TMAh5VJGB5fIQOHK5WzPFYqYfhqHCgUcjHLUWOlMobPgOWwMilHjScXKxjOjOkzXJwcXvySoCAkhLRcDMPs3bbl48TE5Wu/DP3FT8pXR2UxMuPg3AcAru7FgMXQNcXhRRiwCK274vcPsOIK7pyBtBZTf8epz6BvgQ9+w6+j0d4XE7ewW/zgu4rV0MXJVfLJB3D/fE1+AgZ/goC1sO8C6w4I+g7dZ6A4E2nR6PEBovbBxBH6Trh2AF0mICcFhYnoOApXj8PcBTomuBeITqOR8wC1TxjHHuzd07DtDC4XqdGM+1A2PRx8dcbMmY2/xDj1ZiuLUZLBOPVmH0YwRvYQ6rOPrjKuA9jHyZBLGMt2bGIY49CVratGQTLTtg/7KJoxsIC2MfswknEdwBY8grSWserAJl1h7L1YaR3yEhjXAWxKFKNjAn0LNimMcRvEFqSitoKx7cQmhTJ2nqxCjqzbTDsfNjUa2kaMoQ2bGMK4DmRLMlFZyjh0YxMuwqYTwCDzJuM+lE2NhlAPRg5IuABXH5RlobyQcerFPrgA6w7g8ZEaw3TwY1OvQl0Lpk64fx5ug1GWg7Jcpm0f9v45WLcHXwOPIpmOI9nUqxAIYe6Ce+fgNgRPMlGczrgOYh8EwtIdzn0tHpW5OL3kZUC/ERJCWjoXF5fzAX8e+36ZiVzEnFoLaR346gCQeRPOfaGQIT0WnmPx4Dy6TADDwdV9GP45xFWIvwjfVXhwHgaW6DUTZ76E7yq088GxT7DoDOoqkRePuX8icjd6TMXgjxH0LRacgrYxStLx8WXcO4v+CzD8M8QexbILUNeGQAOfXMGdsxjzHfp+hNQorLoKcTXsPbHgFHs/GLMOwn0IKoux9jqbn4zeszFhM5sSheUXWX1zGFpjZTibcg0Tt7I9Z7ClWVgbw1aVotN/MOMAmxqLxYGsuSuEulh9jU27gbHfswMWs4UpWBPF1lWhvS/mHGFTrmFBAGvbGTw1rI1h029ixBfs0JVsXgJWX2VlUjj3xoIT7KNIfPQn26YnFDKsjWWz78B3FYavY7PisDKC5fBg54nFZ9mkUMz6A64DIa7E2lg25x4GLcXob5AegxVhUBPCwg1Lg9mEEEzfiw7DUVGMtdfZvAT0mYtxP+LRVXwcAg1dtLLDx5fYhMuYshOdx6A0G+uuswWP0H0qJm1F0hUsvwgdY+gYY8UVNjEEk37BtN3oOknfzuWlLwAKQkIIAYCRfsPyU+N9zaSad04gLx4ApGLw1VBRBAMrACh/XP8LYlUxDCyRdQdteoLh4H4wun4AlkV6LDxGIDEUbkOgbYyI3zFqPeoqkJ+ILhNwwx/dp8DAEiFbMHELilIhl6HjKFz+BcPWQNsI1/Zi3EbEX4CdJ5x6I+hbfPAbpHVIv4EhKxGxC71nw6Idzm/AlF3IioOmPrzGI/h7jP8Ralq4fQZjvkf0IXQeg9beOPcNpu9BcTpkYvSehfMbMWo9dE0RcwgTNuPmCbQbBKfeOPsVpu1BeQEqi9FvPi5tht9aGFoj8nd88CvuBsKhG1wH4ux6TN2F2goUPILPclz+FT7LYeKIy1sxeTsSQ2HhBvehCPwak7dBLkHGLfiuRvgO9JsHC1dc/BlTdiI1GoY28BiBoG8xcQsYDpKuYPhnuLoX3afCqj2Cf8CUXci+Aw1deI5F8A8YuwFqmrgbiNFfI+YPeI6DbScEfY+pu/D4IVgWXSfhwo8YvR6aBrjxJ8b+gJvH4T4U9l2UTyvD4b70qacgJISQehwOJ/DPQ798NFyQEY3idBi3Rl4CuHxIxQCgoYvKEuCvBdvEVVDXBoCKAuhboroMOiYAUPAQlm4AUJoFM2fkJ8K2MwBkxqFNbyjkkNZB2xipMXAdCACp0Wjng8IUmLuCr46HkWjvCwBlObBwRUoU3IeAYZAcjo4jIMqDrik0DZB0BR1HAUDuAzh0R1oM2g0Ch4ukUHT6D2pE4KlB1wyJoeg4GgAybsBlADJuok1v8AT13aS1kElgaI2kK+g4EgBSrsF9KHLuw9YTfHUkXUGnUVDIUV0KYwckh8NjOAAkh8FjOB4nw6Id1DSRHFb/52U5sGiHR1frh5Acjo4jUZKJVjbQ0EVyGDxGAEBhCmw7Iy0G7Qb/NbSRKC+AVitoGSI5HB4j64fm2APp1+HSHxwuksPhMQK15eAJoGuKh+H1t5Z5C237I+s2HLuDy8fDcHQY/nrP+z94rRBCSDM27cMPoi+cNt7/X1i549ImaLVCRSEkNWjbD7dPAYC+BQoewtAWBQ8BQNMAFYVQE9bPSuTxIRMDf+Ulq4Byp0QuAU8AuRQ8AQBIaqCm9Ve7Wv05pADUVUBDF6wCHB4A1JZOCgEwAAAW4ElEQVRD0wAAap5A0wA1ImgaAkD1E2gZAgCHC4ZBtah+s+YJtAwbbYqg3QoAGAYcLqpF0G7UTXmbAKrLoNUKABRycPmoLqv/qxoRtFpBXAV1nf9tKmsWCP9XTI0IWoaQS+u/Um6499pyaOg16tao5vrNRkOrLYem/l9D1gcADgcMg9qK/9deW1F/EuaGduUNNjxQDRdeGQUhIYQ8rVPHjlFBxweUh2uWPGS2j4PnOASsg6Ub1LURsQv95uPEpzBzQmk2SrPgOgg3j4OvAbCoLIZNRzyKBADj1sh9AJM2yL4LACaOyL0PvjrEVVDI0coWj5MBQNcMpVkwsEJRKgAYWKEoDQwHcikUcuiZozgDAPTNUZIFXVOUZQOAnhlKswBAoYBCBj0zlGYDgK4pSrOhbYQn+QCgY1LfznAgrYOe6f/rpmmIigIA0DOvvzW+Ouoq/7epa1Z/Ko/q0v9tAlDXQVUJdM1Rmln/5yWZ4PIhqQHLQt8CJVkAoGOKspz6ASprVv65Qg6F/H+b+uYoyYSuKcpy/ndrAMBAJv7fpvKhaBhawyPDFaCuEnoWKE4HAH1LFKe91tNNQUgIIc/h4OAQcupoVX7aniVjnHMuaiQEcX72gdd4PIzEhY1guPjJBz2nYvs4mLRBxk3cC8KgZTi8EHZeKExFxg30mYOAtdA0gJYBEi/DawJCf4VMgnaDEXUAbfsi4SJqRPAch9BfoWsKVoF85SGje8CycOqNuAA49UJiCMTV8BiJq3uh1QpgUPAI7Ych6iAAOPdBXABad8XDCIir0GE4og5AXRtqWshPhLsvYo+AZeEyEDePwaYTMm+h5gk6+CHqAHgC6FsgMw7tBuPGn2AVcB+KmD9g7oLHD1FZhA7DEX0ADANzVzyKhMsA3D4FuRQew3FtH4zsUFEEUR46DMe1fQBg54X4C3DqjftBkNbBYwSu7YOuKWQSFKWhwwhEHQAAp964fQqOPZB0BeKq+qFp6EIgRF482g9D9EGwLFwHIfYo7Doj/TpqROg4Elf3gK8OPTNk3IT7UFw/CoUcHYYh+iAs3ZCfhIpCdByFyN2v9Vxzv/jii6Z+/ahMenp6dHT05MmTVV1ICyWXywHweDQnR8UkEomampqqq2g+PNq7L5g1bfXyRX3c7ASPrnArHjsaCbvZ6Ho5mGnm3WFqKyXXDnGl1ZyEEOQ9AE+AS5vReTSCvoO6DtQ0EfoLes/GmS8g1IOpE4K+xcAlCP4ODAfth+HIYvSZjVsnUJqFPnOwbwbch6JGhNsBGPIJjiyBcWvYdkLAOgxagvAdkNWh62QcmIXOY/EkDw8uYPDHOLwIFq6wbo9Tn8NnKSJ2QVqHbpNxYBY6jUZVCe4GYvDH8F8KE0fYd8XJVei/EDeOoqoUPWdi/0y4DwGrQMwhDFmBE6ugbw6XATi6FH3mIP4iitPQbx72zYJTbwj1EPobhqxA4NfQ0IHHCByah+5TkRmHjFsYuBgH58LOE63sEPwdhnyMS5vAMOgyAftnwWs8ijOQeBk+y3F4IczbwtqjfmhX96KuAj2mY98MtPeDpBo3j2HIJzj2MQys4NQHfy5Hv/mIO4myHPT7CPtmwqU/eAJE/o4hK3FqHYR6aD8Mhxei50w8jEDOfTh2B8MZpF/uaaH54qeYYZXfYjcLISEhGzduvHTpkqoLaaEkEgnLsvQvWOUqKyu1tbVVXUXLIpfL8/Lyqqur4+PjU1LT8guLMgtKy8tKaiTyclFprQxySZ1YLJYpwIFCLFNwOAwLyCRSnrqGTCIGh8sVqEurKziaepDUKMDhCnXl5YWMditGJlFIxYyOEfskH1pGDFi2qgyGVhDlQ6jHCDTYshwY2qCqFAwH2oYozoChDaS1qH4CQ2uUZkLbGDwBW5LFGDugohAMw+oYM4UpaGULmRgVxTCyR0kmNPUhEKIkA0Z2qBZBLmN1TZniNOhZgJWjvBBG9hDlQiCEhg5KMmFog9pKSKqhb4GSTOgaMwyPFeXC0BaVReDyoGmA4gwYWkFah2oRDK1RmgOhHiNQZ8tyYWjFVItYhQI6xijJgK4pwyrYyhIYWjNP8lmBJqOuzZZmwdCaqa1gJbX139ZqGTEcDltRCD0LVJWAx2eEemxpNvTMGWktW1cFPTOI8iHUZXhq7JN8xthh50/rZwzp/uKnjz68E0LIv8Xlcq2trQG0bdtW2VJdXS0UCl96LsPa2lqBQMAwTHFxsYmJSVlZmVwu19PTy8zMNDU1raurKy4utrGxycrK0tDQEAqFmZmZ1tbWpaWlYrHYxMQkMzPTyMhIoVAUFxdbWFgUFRUJBAKhUFhQUGBsbFxTUyMWi/X19QsLC3V1dblcbmlpqYmJSXl5OY/H09TULCgoMDU1FYvFNTU1xsbGBQUFOjo6AoFAWUxFRQXDMDo6OgUFBSYmJmKxuKqqytTUtLCwUEtLS01NrbCw0NzcvKKiQqFQGBgY5OXlmZiYyOVykUhkYWFRUFCgqampoaHx+PFjS0vL8vJyqVRqamqanZ1tZGQEQDm0goICDQ0NbW3t3NxcS0vLysrK2tpaCwuL7OzsVq1aMQxTVFRka2v7+PFjNTU1PT29rKwsKyur2traiooKKyur7OxsAwMDPp9fUFBga2tbWFjI5XJbtWqVmZlpaWlZU1PzKh8KaY+QNBnaI3xH0B7hu+AVg5C8UQqFora2VlPzJV+N0sEyhBBCWjQKQkIIIS0aBSEhhJAWjYKQEEJIi0ZBSAghpEWjICSEENKiURASQghp0SgICSGEtGgUhIQQQlo0CkJCCCEtGgUhIYSQFo2CkBBCSIv2rpx9orCw8NatW0lJSc7OzsOGDWtoF4lEu3btatyzb9++Xl5eb71AQgghzdM7EYTBwcG+vr58Pp/D4YwdO7ZxEJaWln766addu3ZtWD7c3t6egpAQQkhTeSeCsEOHDtevX2/fvn3//v2f22H37t0uLi5vuSpCCCEtwTsRhObm5ubm5qqughBCSEv0fhwsM3XqVBcXFz8/vwMHDqi6FkIIIc3KG98jlMlkUqn0+ffN4/H5/Bf/uUAgmDx5cvfu3QUCweXLl6dNm/bo0aNvvvnmDVRKCCGkJXrjQfjzzz+vXLnyuVfNmzfvt99+e/GfW1tbHzx4UHl52rRpJiYmP/7447p169TV1Zu4UEIIIS3SG/9qdMaMGQl/Y926da97a8OHD5dIJI8ePXoTpZJ/KSgo6MyZM6quoqWrra1dvny5qqsg2Lx5c1JSkqqraOni4+N/+eWXl3Z71T3CioqKuLi4uLi41NRUHR2dDRs2PNvnyZMnGzdujIyMVCgUnp6eK1asMDc3NzQ0NDQ0fL3a/15OTg4AExOTprpB0oTu3bsnlUrHjRun6kJatPLy8rNnzz41+5a8fVFRUe7u7nS4u2qlpaVFR0e/tNurBqGlpWVlZaXyspmZ2bNBWFpa2rVr16ysrBEjRggEgj179vj7+8fGxtra2r70xuVyeVZWFoC6urrKysr09HSGYezs7ABcunTJ3Nzc1dWVYZjY2Ni1a9d27tyZgpAQQkhTedUgXLx4saura6dOnUaOHCkSiZ7t8Nlnn6WkpJw5c2b48OEAbt682b1798WLF7/Kd2VFRUWtW7dWXo6Liztz5oy6unptbS2A0NDQDRs2qKmpcbncmpoab2/vI0eOvOrgCCGEkJd51SBcv3698gLDMM9eKxaLDx065OrqqkxBAJ6engMGDDh37tzjx4/NzMxefOMmJiZlZWWNWxru5Ycffli0aFF6ejrLsnZ2dlZWVq9YMCGEEPJK2Nfk6upqZmb2VOP169cBLFu2rHHj1q1bAZw4ceJ17+IfU94jIYQQouTm5vbS7Gia6RNpaWkALC0tGzcqN5VXvR0LFy5cuHDhW7s7QgghzUDTTJ9QHkdjYGDQuFF5sGhFRUWT3AUhhBDyJjRNEHI4HAAymaxxo3JBGS6X2yR3QQghhLwJTROEenp6AJ464EW5qa+v3yR3QQghhLwJTROEbdq0AZCamtq4UbmpvIoQQgh5NzVNELZr187U1DQoKIhl2YbGwMBAdXX1nj17NsldEEIIIW/CqwZhQUFBenp6enq6RCKRy+XKy/n5+fW3wuEsWLAgLy/vu+++U7YcOnQoJiZm6tSp2trab6RwQgghpCkwjffhXmDEiBFnz559qrF79+7Xrl1TXpZIJKNGjQoODrazsxMIBA8fPuzSpUtISAgFYTMTExMTGRn5VOOgQYM8PDwat9y9e3fv3r3Z2dkmJiYTJ07s3bv3W6yxGVIoFA8fPoyLi8vLy9PX1589e/azfWpqanbt2hUdHc2ybNeuXefMmaOpqflUn8DAwICAAJFI1KZNm9mzZzs4OLyV8puP4uLiuLi4hIQEmUw2YcIEa2vrxtc+fPjw9OnTT/2Jp6dnv379GrdkZGTs3LkzOTlZT09vxIgRo0aNeuN1Ny8JCQmBgYHJyclVVVX29vY+Pj79+/d/qo9MJtu3b19YWFhdXV2nTp3mzp377KrX4eHhR44cKSoqetUJ9RcuXNj5jDNnzjTuI5fLAwICFi9evHDhwkOHDkkkkteeEk/eec89GeS2bdsa9/H39+fxeMbGxsOGDbOxsWEYZuPGjaoquHlo/IHSwcHh2Q5Pnjxxd3fncDi9evXq06cPh8NxdXUtKytr3Gfx4sUAnJychg0bpqurKxQKIyIi3tYImoNly5Y1ftmHhYU91eH48ePPvjuWLl3auE90dLSWlpa2tvawYcPatm0LYM6cOW9vDO+/X3/9VfnA2tjYeHh4CIVCALNnz27cRywW9+3bF0CXLl0GDRokEAgsLS2zsrIa99mwYQPDMDY2NsOGDXvtlWVIC6cMwrS0tL/rUFxcrKOj4+LiIhKJWJatq6vr378/l8tNSEh4i2U2N5MnT960aVNkZKSFhcVzg3D+/PkA/P39lZsnT5586j9sSEgIgIkTJ8rlcpZlc3NzzczMbGxs6urq3s4QmoHt27evWbMmICBg0aJFLwjC8+fP/90tSCQSBweHVq1aZWZmsiyrUChmzJgB4OzZs2+08ubk4MGD69evLyoqUm4WFBR4eXk99Rgqf6Rr+PwdFRXF5/N9fX0bOsTHx3O53P79+ytf/xSE5PW8NAg3bdoEYP/+/Q0tyq9SFy9e/FYKbOZsbGyeDcKamhpNTU13d/fGjZ07d1ZXV6+oqFBuKr9/a/zEKRcQDggIeNM1Nz/Kh+4fBGFQUBCA1atXN7QUFBRwOJwhQ4a8oVJbgtDQUAALFixoaLG1tTU0NJTJZA0tI0eOBKBctpplWeUaZJGRkcrNN35iXtJciUQi5RlCnhIREQFg6NChDS3dunXT19cPDw9/a7W1NLdu3aqurm78mAMYNmxYXV3djRs3lJsRERFt27a1t7dv3AFAWFjY2yy1haioqKiqqnq2/dl3h4mJSceOHSMiIhQKxdurr3nR0dFBo8VbMjIyMjMzhwwZ0ng5F+WrveH4hoiICH19/W7duik3KQjJP+Hh4WFgYKCpqdmpU6cTJ040violJUUoFBoZGTW0cLlcKyurlJSUt15mS6F8bJ8696dyUzmdt6ysrKys7Lkd6HlpcuPHj9fV1dXW1nZycvrtt9/YRgckKh9tGxubxv1tbW1ramoaDsInr2vv3r1o9PHipW8HZR9LS8uGpGyaRbdJy6Gurj5ixAgvLy9dXd2UlJR9+/aNHTt2y5Ytyl9NAJSXlz97dJahoeH9+/elUimfz3/rJTd/5eXl+Gt13wbKTeVVz+2gq6vL5/OVV5EmweVy+/Xr16tXL2Nj4+zs7AMHDixYsCApKanh+I4XPFO0LPM/c/78+R07dowZM2bQoEHKlpe+HaRSaW1tbeMOFITk9SxbtqzxsXNLly7t2LHj6tWrP/zwQ+VKe8+l/FDMvtpcHfK6nvvwNm78u8df+QPJW6qyBRg1alTjuRCrVq3y8vLatm3b3Llz27Vr93d/Re+Of+zmzZsTJkxo06bNtm3bGhr/wduBvhol/4qNjc2MGTOqq6tjY2OVLbq6uqWlpU91E4lEQqFQIBC89QJbhBcs9qu86rkdysvLZTLZCz6+kH9JR0fn448/Zln2ypUryhZdXV38zTOlvIq8unv37g0ePFhfXz8kJKTxbzEvfTsIBAINDY3GHSgIyb9lZmaGv75zAODo6FhTU1NcXNzQQS6X5+Tk0NztN8fR0RFAZmZm40blpvJhNzAwMDAwyMrKeraD8m/JG/LsuwPPPFNZWVlCodDc3PytV/ceS0hIGDhwoKam5pUrV6ysrBpfpXzNP/fV3vBfyMHBITc3Vy6XKzcpCMm/FRMTg0Y/Tffp0wdAcHBwQ4fo6OiysrKnFtcgTahz586ampqNH3MAQUFBGhoa3t7eys0+ffokJiZmZGQ0dDh37hwAel7eqJe+OwoLC+Pi4pRrIKigvvfTo0ePBg4cyOFwLl26ZGdn99S19vb2dnZ2wcHBDTkHQDlxpVevXsrNvn37ikSi6Ojo+qvfzLwO0jxJpdI9e/ZUVlYqN2Uy2ebNmxmGcXZ2bpiyU1RUpK2t7erq2jChfsCAAVwuNz4+XmV1NyPPnUfIsuy8efMA/Pnnn8rNgIAAhmFmzZrV0OHixYsAJk2a1DCh3tzc3NramibU/wN/N4/wwIEDxcXFDZvHjx9XV1fX19dvWOJHIpG0bt3ayMioYUL9zJkzATy1Shd5gZSUFHNzc2Nj4xes0fHtt98C+PHHH5Wbygn1jSdrPnjwgMPhDBgwgCbUk9cmFosBqKmpOTk5eXl5KQ+7srCwuHfvXuNuR48eVS6x5ufnp1xibcOGDaqquXl47n6bj49PQweRSPTsEmulpaWNb0R5ZG/jJdae/VdOXuDw4cPP3UHJzs5WdrC1teXz+fb29l26dFF+Kaqjo3PhwoXGNxIVFfXUEmuNP6+Ql1q5cuVzn4URI0Y09Kmrq1Musebl5dWwxJryw0eDH374QbnEmp+f36suuk0IAJZlg4KCoqKisrOzRSKRkZGRt7f3pEmTlBNaG1Muup2ZmWlqajpp0iRadPtf8vf3f+o3DwB2dnbjxo1r2FQuuh0VFcWybLdu3V6w6HZpaamTk9OcOXPoh9vXkpiYGBgY+Gz7vHnzlIvBRkZGhoWFpaamlpaW6uvre3h4fPDBB6ampk/1Vy66nZiYaGBgQItuv67w8PDr168/2+7o6Dh69OiGTeWi21euXKmtrfX09HzBotsFBQUUhIQQQlo0+nmWEEJIi0ZBSAghpEWjICSEENKiURASQghp0SgICSGEtGgUhIQQQlo0CkJCCCEtGgUhIc1Hbm7urFmzvL29ExMTVV0LIe8NmlBPSLOSk5Pj5OQkEonU1NRUXQsh7wfaIySkWbl27Zq3tzelICGvjoKQkGYlPDycVnYl5LVQEBLSrISHhytPunb37t2DBw+eOnVK1RUR8q6jICSk+cjLy8vKyvL29r506VJlZWV+fv6KFStUXRQh7zqeqgsghDSZ8PBwLy+viIgIQ0NDT09PCwuLkSNHqrooQt51tEdISPMRHh6ek5MTHh5uaWkJwN7e3tnZWdVFEfKuo+kThDQfjo6Oe/bsMTQ09PX1DQwMdHNzU3VFhLwHaI+QkGYiNzc3Pz+/S5curq6uzs7ON27cYFn2xIkTqq6LkHcdBSEhzUR4eHjXrl0bZhBaWFhERkY6OjqqtipC3n0UhIQ0EwqFYvr06crL69evj42NLS0tbd++vWqrIuTdR78REkIIadFoj5AQQkiLRkFICCGkRaMgJIQQ0qJREBJCCGnRKAgJIYS0aBSEhBBCWrT/A0fivcInY+zVAAAAAElFTkSuQmCC",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's make a minimal model\n",
"n = 200\n",
"norm_err = zeros(n)\n",
"for k in 1:n\n",
" Û = U[:, 1:k]\n",
" Ŝ = S[1:k]\n",
" Ṽ = V[:, 1:k]\n",
" F́ = Û * diagm(Ŝ) * Ṽ'\n",
" norm_err[k] = norm(F - F́)\n",
"end\n",
"\n",
"scatter(norm_err, yscale=:log10, ylims=(1e-15, 1e0), xlims=(1, n), label=\"\\$\\\\vert \\\\vert F - F_k \\\\vert \\\\vert\\$\", xlabel=\"\\$k\\$\")"
]
},
{
"cell_type": "markdown",
"id": "678f2e73-fe67-4929-9d02-f7a6ec3ac11a",
"metadata": {},
"source": [
"## What is interpolation?\n",
"\n",
"Given data $\\left( x_i, y_i \\right)$, find a (smooth?) function $f \\left( x \\right)$ such that $f \\left( x_i \\right) = y_i$.\n",
"\n",
"### Data in\n",
"\n",
"* Direct field observations/measurements of physical or social system\n",
"\n",
"* Numerically processed observations, perhaps by applying physical principles\n",
"\n",
"* Output from an expensive \"exact\" numerical computation\n",
"\n",
"* Output from an approximate numerical computation\n",
"\n",
"### Function out\n",
"\n",
"* Polynomials\n",
"\n",
"* Piecewise polynomials (includes nearest-neighbor)\n",
"\n",
"* Powers and exponentials\n",
"\n",
"* Trigonometric functions (sine and cosine)\n",
"\n",
"* Neural networks\n",
"\n",
"Interpolation fits the data **exactly**!"
]
},
{
"cell_type": "markdown",
"id": "63ef7ada-fc4b-499a-a6d4-9db4bb066e30",
"metadata": {},
"source": [
"## Polynomial interpolation\n",
"\n",
"We've seen how we can fit a polynomial using Vandermonde matrices, with one column per basis function and one row per observation.\n",
"\n",
"$$ \\underbrace{\\Bigg[ 1 \\Bigg| x \\Bigg| x^2 \\Bigg| x^3 \\Bigg]}_{A \\in \\mathbb R^{m\\times n}} \\Bigg[ \\mathbf p \\Bigg] = \\Bigg[ \\mathbf y \\Bigg] $$\n",
"\n",
"It's possible to find a unique polynomial **$p$** when which of the following are true?\n",
"\n",
"1) $m \\leq n$\n",
"\n",
"2) $m = n$\n",
"\n",
"3) $m \\geq n$"
]
},
{
"cell_type": "markdown",
"id": "227d8c78-0579-42a5-8ccc-6385f1be4149",
"metadata": {},
"source": [
"### Polynomial interpolation with Vandermonde"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "4f6f2b58-d966-4526-9cfc-55c62e74cdcd",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's build some data\n",
"x = LinRange(-1.5, 2, 4)\n",
"y = sin.(x)\n",
"\n",
"# And find coefficients so that A p = y\n",
"A = vander(x)\n",
"p = A \\ y\n",
"\n",
"# How well did we match?\n",
"scatter(x, y, label=\"data\")\n",
"s = LinRange(-3, 3, 50)\n",
"plot!(s, [sin.(s) vander(s, length(p)) * p], label=[\"fit\" \"true\"])"
]
},
{
"cell_type": "markdown",
"id": "c2c13b2a-a1c4-479e-ab09-14e86ae298e2",
"metadata": {},
"source": [
"Recall that Vandermonde matrices can be ill-conditioned."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "71fbde33-440e-4a1a-956d-7b31af7f0466",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"k = 1, cond(A) = 4626.449923375609\n",
"k = 2, cond(A) = 2.7224082423906505e8\n",
"k = 3, cond(A) = 1.8388423738279527e13\n",
"k = 4, cond(A) = 9.028174036334257e17\n",
"k = 5, cond(A) = 5.645434903563094e18\n"
]
}
],
"source": [
"for i in 1:5\n",
" A = vander(LinRange(-1, 1, 10 * i))\n",
" println(\"k = $i, cond(A) = $(cond(A))\")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "87d9eaa9-e94e-4da7-9bb7-674609c8bad4",
"metadata": {},
"source": [
"Is this due to the points $x$?\n",
"\n",
"Or is this because of the basis functions $\\lbrace 1, x, x^2, x^3, \\dots \\rbrace$?\n",
"\n",
"Or something else?"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.6",
"language": "julia",
"name": "julia-1.11"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}