{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Hybrid Controlled Invariant Set\n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "This example considers the hybrid constrained linear control system:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x}_1(t) & = x_2(t)\\\\\n",
    "\\dot{x}_2(t) & = u(t)\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^2$ and input constraint $u \\in [-1, 1]$\n",
    "and the jump:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1^+ & = -x_1 + u/8\\\\\n",
    "x_2^+ & = x_2 - u/8\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^2$ and input constraint $u \\in [-1, 1]$\n",
    "that can occur anytime.\n",
    "\n",
    "In order to compute controlled invariant sets for this system, we consider\n",
    "the projection onto the first two dimensions of controlled invariant sets of the\n",
    "following lifted system:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x}_1(t) & = x_2(t)\\\\\n",
    "\\dot{x}_2(t) & = x_3(t)\\\\\n",
    "\\dot{x}_3(t) & = u(t)\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^3$;\n",
    "with a first jump to a temporary mode:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1^+ & = x_1\\\\\n",
    "x_2^+ & = x_2\\\\\n",
    "x_3^+ & = u\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^3$ and unconstrained input;\n",
    "and a second jump back to the original mode:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1^+ & = -x_1 + x_3/8\\\\\n",
    "x_2^+ & = x_2 - x_3/8\\\\\n",
    "x_3^+ & = u.\n",
    "\\end{aligned}\n",
    "$$\n",
    "Note that the input `u` chosen in the first jump is the input that will be used for\n",
    "the reset map and the input `u` chosen for the second jump is the input that will be used\n",
    "for the state `x_3` of the continuous-time system.\n",
    "\n",
    "The matricial form of this system is given by $\\dot{x}(t) = Ax(t) + Bu(t)$ where `A` and `B` are as defined below.\n",
    "As shown in Proposition 5 of [LJ21], a set is controlled invariant for this system if and only if it is weakly invariant for the algebraic system\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x}_1(t) & = x_2(t)\\\\\n",
    "\\dot{x}_2(t) & = x_3(t)\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^3$;\n",
    "with a first jump to a temporary mode:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1^+ & = x_1\\\\\n",
    "x_2^+ & = x_2\n",
    "\\end{aligned}\n",
    "$$\n",
    "with state constraint $x \\in [-1, 1]^3$\n",
    "and a second jump back to the original mode:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "x_1^+ & = -x_1 + x_3/8\\\\\n",
    "x_2^+ & = x_2 - x_3/8.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The matricial form of this system is given by $E\\dot{x}(t) = Cx(t)$ with a first jump\n",
    "$Ex^+ = Ex$ and a second jump $Ex^+ = Ux$ where:\n",
    "\n",
    "[LJ21] B. Legat and R. M. Jungers.\n",
    "*Continuous-time controlled invariant sets, a geometric approach*.\n",
    "7th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2021, **2021**."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Polyhedron DefaultPolyhedron{Float64, Polyhedra.Intersection{Float64, Vector{Float64}, Int64}, Polyhedra.Hull{Float64, Vector{Float64}, Int64}}:\n6-element iterator of HalfSpace{Float64, Vector{Float64}}:\n HalfSpace([0.7320508075688772, 0.7320508075688772], 1.0)\n HalfSpace([-0.5, 1.0], 1.0)\n HalfSpace([-1.0, 0.375], 1.0)\n HalfSpace([-0.7320508075688772, -0.7320508075688772], 1.0)\n HalfSpace([0.5, -1.0], 1.0)\n HalfSpace([1.0, -0.375], 1.0)"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "cell_type": "code",
   "source": [
    "A = [0.0 1.0 0.0\n",
    "     0.0 0.0 1.0\n",
    "     0.0 0.0 0.0]\n",
    "B = reshape([0.0, 0.0, 1.0], 3, 1)\n",
    "E = [1.0 0.0 0.0\n",
    "     0.0 1.0 0.0]\n",
    "C = A[1:2, :]\n",
    "U = [-1.0  0.0  1/4\n",
    "      0.0  1.0 -1/4]\n",
    "\n",
    "using SetProg\n",
    "function maximal_invariant(family, γ = nothing; dirs=dirs)\n",
    "    model = Model(sdp_solver)\n",
    "    @variable(model, S, family)\n",
    "    @constraint(model, S ⊆ □_3)\n",
    "    @variable(model, T, family)\n",
    "    @constraint(model, T ⊆ □_3)\n",
    "    x = boundary_point(S, :x)\n",
    "    @constraint(model, C * x in E * tangent_cone(S, x))\n",
    "    @constraint(model, E * S ⊆ E * T)\n",
    "    @constraint(model, U * T ⊆ E * S)\n",
    "    S_2 = project(S, 1:2)\n",
    "    if γ === nothing\n",
    "        @variable(model, γ)\n",
    "    end\n",
    "    @constraint(model, [point in dirs], γ * point in S_2)\n",
    "    @objective(model, Max, γ)\n",
    "    JuMP.optimize!(model)\n",
    "    @show solve_time(model)\n",
    "    @show JuMP.termination_status(model)\n",
    "    @show JuMP.objective_value(model)\n",
    "    if JuMP.termination_status(model) == MOI.OPTIMAL\n",
    "        return JuMP.value(S), JuMP.objective_value(model)\n",
    "    else\n",
    "        return\n",
    "    end\n",
    "end\n",
    "\n",
    "import GLPK\n",
    "lp_solver = optimizer_with_attributes(GLPK.Optimizer, MOI.Silent() => true, \"presolve\" => GLPK.GLP_ON)\n",
    "import CSDP\n",
    "sdp_solver = optimizer_with_attributes(CSDP.Optimizer, MOI.Silent() => true)\n",
    "using Polyhedra\n",
    "interval = HalfSpace([1.0], 1.0) ∩ HalfSpace([-1.0], 1.0)\n",
    "lib = Polyhedra.DefaultLibrary{Float64}(lp_solver)\n",
    "□_2 = polyhedron(interval * interval, lib)\n",
    "□_3 = □_2 * interval\n",
    "u_max = 1/8\n",
    "x2l0 = √(2u_max) - u_max\n",
    "dirs = [[-1 + √3, -1 + √3], [-1/2, 1.0], [-1.0, x2l0]]\n",
    "all_dirs = [dirs; (-).(dirs)]\n",
    "inner = polyhedron(vrep(all_dirs), lib)\n",
    "outer = polar(inner)"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Ellipsoidal template\n",
    "\n",
    "We start with the ellipsoidal template. The objective consider is to maximize `γ`\n",
    "such that `γ * inner` is included in the set."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solve_time(model) = 0.015919923782348633\n",
      "JuMP.termination_status(model) = MathOptInterface.OPTIMAL\n",
      "JuMP.objective_value(model) = 0.8944271817461347\n",
      "h(S, x) = x[2]^2 + x[1]^2\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "sol_ell, γ_ell = maximal_invariant(Ellipsoid(symmetric=true))\n",
    "\n",
    "using Plots\n",
    "function hexcolor(rgb::UInt32)\n",
    "    r = ((0xff0000 & rgb) >> 16) / 255\n",
    "    g = ((0x00ff00 & rgb) >>  8) / 255\n",
    "    b = ((0x0000ff & rgb)      ) / 255\n",
    "    Plots.RGBA(r, g, b)\n",
    "end # Values taken from http://www.toutes-les-couleurs.com/code-couleur-rvb.php\n",
    "lichen = hexcolor(0x85c17e)\n",
    "canard = hexcolor(0x048b9a)\n",
    "aurore = hexcolor(0xffcb60)\n",
    "frambo = hexcolor(0xc72c48)\n",
    "cols = [canard, frambo]\n",
    "\n",
    "x2 = range(0, stop=1, length=20)\n",
    "x1 = 1 .- x2.^2 / 2\n",
    "x2l = range(x2l0, stop=1.0 - u_max, length=20)\n",
    "x1l = -(1 .- (x2l .+ u_max).^2 / 2 .+ u_max)\n",
    "upper = [[[-1/2, 1.0]]; [[x1l[i], x2l[i]] for i in eachindex(x2l)]; [[x1[i], x2[i]] for i in eachindex(x2)]]\n",
    "mci = polyhedron(vrep([upper; (-).(upper)]), lib)\n",
    "polar_mci = polar(mci)\n",
    "\n",
    "SetProg.Sets.print_support_function(project(sol_ell, 1:2))"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can plot the primal solution as follows:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "cell_type": "code",
   "source": [
    "function primal_plot(set, γ=nothing; npoints=256, xlim=(-1.05, 1.05), ylim=(-1.05, 1.05), args...)\n",
    "    plot(ratio=:equal, tickfont=Plots.font(12); xlim=xlim, ylim=ylim, args...)\n",
    "    plot!(□_2, color=lichen)\n",
    "    plot!(mci, color=aurore)\n",
    "    plot!(set, color=canard, npoints=npoints)\n",
    "    γ === nothing || plot!(γ * inner, color=frambo)\n",
    "    plot!()\n",
    "end\n",
    "primal_plot(project(sol_ell, 1:2), γ_ell)"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "and the dual plot as follows:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "function polar_plot(set, γ; npoints=256, xlim=(-1.5, 1.5), ylim=(-1.5, 1.5), args...)\n",
    "    plot(ratio=:equal, tickfont=Plots.font(12); xlim=xlim, ylim=ylim, args...)\n",
    "    γ === nothing || plot!(inv(γ) * outer, color=frambo)\n",
    "    plot!(polar(set), color=canard, npoints=npoints)\n",
    "    plot!(polar_mci, color=aurore)\n",
    "    plot!(polar(□_2), color=lichen)\n",
    "end\n",
    "polar_plot(project(sol_ell, 1:2), γ_ell)"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Polyset template"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We start with quartic polynomials:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solve_time(model) = 0.012025117874145508\n",
      "JuMP.termination_status(model) = MathOptInterface.OPTIMAL\n",
      "JuMP.objective_value(model) = 0.896\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.896"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "p4, γ4 = maximal_invariant(PolySet(symmetric=true, degree=4, convex=true), 0.896)\n",
    "γ4"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "Below is the primal plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "cell_type": "code",
   "source": [
    "primal_plot(project(p4, 1:2), γ4)"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "and here is the polar plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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5eiIR19Lywyyhn0BgoYIUOi0ExnOo1cKxA/x9//TyCZkR0jJcaMtsidNbyLmnMYaQDgwhJ2EI2SaVSj/+6KPvli/X8fgwcjzRuRvYfRsKqxIIrFWQQrOFwHgOlUre/n94xw+OC4yZEhJvw6e1ObeF3HoaA4aQHgwhJ2EI2SOVSr9buOizefNUOh2/Zz/9gOEgtPfvEWsTCCxXkEK/hcB4DqsrhX9tFuVcnRPWeoC/5Z/egBNbyJWnsQGGkA4MISdhCNlAfUbo5/M+05KELixSM/5pIszqv6MbsCGB4JAKUqxqITA+aJF3U7xpfbxa+7+wtnGNblBsnrNa6PpP4wYwhHRgCDkJQ8gsw50i/EFQqFHqR4yFbj3sfC3UtgSCAytIsbaFwPQYPhw/yN+5fVxQ84yQFlbd/tApLXTlp7FJGEI6MISchCFkiiGBbYQ+eSpFTfPmmvFTwM/fnmPanEBweAUpNrQQmM1hTbXwj1/88/PmRrTv5G3FPTgd30LXfBqbgSGkA0PISRhC+xnfMjcChFtqi7Qjx0G3HvYc054EgpMqSLGthcDsZ5ZePCvcvH6Yb/iroQli2hfROLiFrvY0tghDSAeGkJMwhPYwTuAYn6hlVXk3fb1UT08ngkIsP7gJdiYQnFpBis0tBAZzKJcJNq8PuH1rfkR7+tP3jmyh6zyNacIQ0oEh5CQMoW2ME/h8QFypRvlu8RVVr376AcOBZ+MNE+xPILhABSn2tBCYyyF57rTwjw0TA5o9F9KCR++dWoe10BWexlbBENKBIeQkDKG1GiSwudh7Zfnt3+qKNJOnEQltbTsmIwkEl6kgxc4WAlM5rKkW/ryyRXXt/MgONEfvHdNCDKFbwhByEoaQvgYJjBX7SHWat4uvXPHz1kx50bbrYphKILhYBSn2txAYySFJEvv+ER/aMzeyQ5pvKJ1HOKCFGEK3hCHkJAwhHY0TCAC3VdIZ9y7UpXTVjRxnw8uhDCYQXLKCFEZaCEzkkLydI1z3/TjfyOmhLXhg+WVStluIIXRLGEJOwhCaZzKBAHC8ruyD4ivqxydA1+7WHpPZBIILV5DCVAvB/hxK6wRrl7evkS2I7ODHF1rcndUWYgjdEoaQkzCETWkqgQCwsbLg+5o7mikvEfEJVh2T8QSCy1eQwmALwc4c6vX8Pzf5ZZ9e1CyJzs0r2GshhtAtYQg5CUPYmJkE6oH8tjTnH61U9cJsq2Yk2EggcKSCFGZbCPblkDx7UrR149yI9j38wizuzFILMYRuCUPISRhCY2YSCAAaUv9O8ZWzvhLN1FfAy5vmMVlKIHCqghTGWwh25JDMzxX+uHRaQMyTwbEWd2ajhRhCt4Qh5CQMIcV8AgFAode9VnTxWkSY9pkXQGD57SVgM4HAwQpS2Ggh2JzDmmrhym8HgtebYa0tThky3kIMoVvCEHIShtBiAgGgVqd58e65wnbttWMm0blAlNUEAmcrSGGphWBbDhVy4ZolnWsVC6I6Ci19TjezLcQQuiUMISd5cgjpJBAAqrTqaXezy1K66kaMsXgfCbYTCByvIIW9FoINOdRpBb+sblFw97voJF++wPy+DLYQQ+iWMISc5JkhpJlAAKjUqqfeyarq3ks36DHzx3RAAsEtKkhhtYVgbQ5JUrDll4grl1Y07xzIt/B3PVMtxBC6JQwhJ3laCOknEACqtOqMO2cruvfSDRppZjfHJBDcqIIUtlsIVuaQv++foCMHVjZPCbP0SWyMtBBD6JYwhJzkOSG0KoEAUK1TT71ztrx7b/3AEU3tQyVQXHrn06mdpo5kMYHgdhWkOKCFYE0OeXv/CTi6/4fmXRzQQgyhW8IQcpInhFCj0cz/bN53337bwyfkGb/mzUSWJx9kem3GnbNFXR/SDR1tcgdHJhDctIIUx7QQaOeQOLQ74MDuNTRamKuUzi6+sGjliglPPmnDejCEbsnCm8wIOcvGjRs3LV7+fWQynQQCgEqve+neuaJOSSYrWD+BqWwnENy6ggDQulvCqPdHP/YW6y3k8Yix/eOfeCRuy/78Ocs2VB/+x2QOyT4Da/T6jEN718SkhgjEZg7YUuL7bWTSzGkvAIBtLUTuh/W/DhCyzQ9Llz3lG02zgnqSfLv4yp24eN2ohn+1kXm3vNctCt68/IsRAYXbH58+qg1WkBH/tfDQobPFbP8sKod5m0f+kBEXvXeD14r55JXzDfYh+w2u7tl32t3sGp3G/NFaSny/i0qeNf3F9T//zNqSEZdgCJErys/Pv3DxUi8an6RF+bjk6vlgf81TU+tNSijk4vVLw7d+v2h0sMMSCJ5RQYojWwj/5fD25pHLpsRE7f3Va+UC8tZ14x30A4ZXpKa9dO+cQq8zf6g4sc+iyKTXX34VW4gAQ4hc009rfhwYGGVxVpqyqjz3iECnmfIS8PmGjeS9AvHiT55up8vbPHLK8ATHJBA8qYIUB7cQAPg8YtLglnmbRyx7uln4nz9I1i0my0sN39UNf6KwY+Kr985rSL3542ALkQGGELkckiR/WrV6sBet08GdNYUb5GWaabNB/OCdIfLiWcmP3655LXnZ611FQsc9yT2tghTHtxD+y+HtTSPeThdLls8T7NoKWi31Le3jE3KbRb1ffMXidYDYQkTBECKXc+TIEYFK3c7L8r3jL8mrF5Td1EybZXyjed6xvYH//nJk6aPj+sexucyGPLOCFKe0EADEIv57Uzrl/DbiEe11yeKPybv5AAA8nmbytNPewkVlNy0eAVuIAEOIXNCPK1cOlYRa3K1Eo3yt8KJm4lQiIsqwUbDvz/Aze86uGZzSNpjNNTbkyRWkOKuFABAV6vX3l+mrXmnvs24hf+920OtBINRkzPhTXb2l6q7Fh2MLEYYQuRaZTLZ127aB/hauyFeT+tlFF5SPDCbaJRo2CvZsj75+IuuHQbGRFubumYUVpDixhQAwYUD89V+Hdy47J/nxG5DWgbePevrsxVW3z8gqLD4WW+jhMITItWzZsqWzX6j5UTAAmFtyrTg2juw70LCFf/CfqBsnT34/IDzYwkg1s7CCxpzbwsgQr2PL+7/4sJdo8Sdkfi4REqZ9+oW3iy7fVcstPhZb6MkwhMi1rFm2fJDIwqua26ruHgWV5snnDMMSxOljwWcPHlvePywIK+hkzm0hn0d88XLKb+939fp5MXnxLJHQVjV01KzCCxYHKgBb6MEwhMiF0BkfvKWsW1RxS/3sSyC6f9ZI3rjivWfLoaWPRIV6OWSZ92EFm+LcFgLA8N4xR5Y9GvjPL7yje6F7n4q2Hd4rukznwySxhZ4JQ4hciMXxQYVeN7vwonb0JCL8/gUyZHmp+PfVO77o3TrG8lWmDMIKmuf0FnZuE5z90+DmF/YJdm7Rjpl4TszbWFlA54HYQg+EIUSugs744LySa9L2nSCl2/2v1SrJz4u/fimpV+cIRyzxP1hBOpzewpgIn1OrBsbmnxXs3qaZ+srKqvxL8mo6D8QWehoMIXIVFscHd9UUHSOVmtEPPk1UvG398JSAF0a3ccgC78MK0uf0FoYEiE983z/+3nnhsb2acU+/VXxZqtPSeSC20KNgCJGrMD8+WKZRflF6Q/30dMNbg3DuVGhpzpq3H3LQ+gAAK2g9p7cw2F98fHn/uMILwpI7sqQun5Reo/lAbKHnwNswsaW8vHz//v1yubxTp05du3Y1v/Pdu3dLSkoabGzZsmVQUBBrC3Qt1PjgLzGmq0YCvF9yVdtnINEs9v6m6krRX79uX/Got8Rxz2GsoG0cds+mpgT5iw4tfiTl2Z1lDw87c/Pa39WFwwKj6TyQauHMl18FAHvua49cHJ4RsuKnn36KjY0dP378s88+261bt6FDh8pkMjP7f/PNN10b2b9/v8MW7HTmxwe3Vt296S3SPzrk/tckKfnjp7cmtUtu7biPj8EK2sPp54XhwZLDSx/1Pbhd3bvfN+U5JRolzQfieaEnwBAyLzMzMyMjIzU19fbt2wqF4ptvvvn3339nzJhh8YHr1q373UhaWpoDVusizIwPlmmUSypuqZ6aCrz/nq7Zmc10le8+3dFhy8MK2s/pLUxo7rd7YV/Jvj/VXbq/V3KVzjQFBVvo9jCEzPv888/1ev1PP/0UHx8vkUhmz549bNiwtWvX3rlzx/wDR40aNdZI8+bNHbNgpzM/Pvhh6TVtn4FExH+vZcllon9/3/BBGt5ZiXOc3sKu7UNXvdlNnHM+VyLcSuNjSA0MLfzt143sLQ85C4aQYRqNZteuXcnJyQkJCYaNTzzxhE6n+/fff524MFdmZnxwT03xNT5J9hts2CLcs+2p/rFd2oU4Zm1YQWY5vYVPDmoxpX8U30e0pOJWKe0XSOG/Fr7/+ht4Xuh+MIQMo14OTU5ONt5IfXn58mXzj83IyEhPTx8+fPiCBQsqKytZXKUrIUnyp1WrTI4PSnXaL8tuqCc8a7jjLllSKLx0ZsGLyY13ZgNWkA1Ob+HCmV3a+SrJmJjPym5Y9UB8jdRdYQgZVlZWBgChofXGAEJCQgCgvLzczAP9/Pzu3LkjEonOnz//9ttvJyUlXbvW5HXeJEnK5fKsrKysrKycnByG1u4cR44cEag0JscHl1XkahJTiLiWhi1eOzd9+FynYH8LH8nNCKwge5zbQgGft+OL3uLye+e18iN1pZYfYARb6JZwfIJhGo0GACSSeh/97O3tDQBKZZOvw7zyyivz5s2jHqXT6RYuXPj6669Pnjz59OnTJvcvKyvLy8t7/vnnASAiImLTpk0M/hZYIpPJiP8+I9vYqqXLTI4P5qqk/9QV64a9YthC3s7xKb/7ypjHWFzlf7CCbHPuTEVEsNfa99Imzj/7Wen1rT4hXjw+/ccaZiqUStWEJyewt0hG6HQ6kUjk7FW4Ogwhw6jmVVfX+ySnqqoqAPD19W3qUS1bPjjp4fP5c+bM2bNnz65du3Jyclq3bt14//Dw8A4dOpw6dYqxdbOPJMnG/wVkMtlfO3b8EmtifPCzshu6IaPA58FDvPduXfBCkkjI+ssYWEHHcG4LH+sT+/jBe9vPVK2pyHs5LMHyA4zcb+Gc1yUSsYvPF6rVamcvgQPwpVGGxcbGAkBpab3XW6hh+bi4OPrHSU1NBQCLF5py3ZYtWzr7mxgfPFxbcpsPkNbbsIXMveEnq5g0pCWwDCvoSM59jXT5G119QPV7ZX6RWmHtY/E1UneCIWRYZGRkTEzMoUOH9Hq9YeOBAwcAwOLnyxgrKCgAALf/ZJk1S02MD2pI/ZcVt9Sjn3owOAjgdXDHJ8924PNMvLjKIKyg4zmxhX7ewvUfpAm8BF+U37Th4dhCt4EhZN5TTz1VWlr6119/UV8qlcr169eHh4cPGDCA2lJcXLxkyRKqjgCgUqkaXCOamZn5+++/R0dHJyYmOnLlDpafn3/hkonxwa1Vd+WR0USbDoYtZOFdUdm9yUOte/3KWlhBZ3FiC/s/FN2/W9QFZeVlBa0bUzSALXQPGELmvfHGG/Hx8ZMmTfroo49WrlzZt2/fnJycr776ysvr/m1jc3NzX3311Q0bNlBflpeXR0dHjx49+p133pk7d+5TTz3Vq1cvnU63dOlSgcCd38Q1OT6o0OtWVeapRowx3ig5vnvO+LasvjuIFXQuJ7bw+ze6Ejxybql1oxQG2EI3gCFkXkhIyKFDh4YMGfL111+/9NJLCoVi48aNk43eUffz83vooYcMF8j4+/tPmDDh4sWLCxcu/OCDD3bt2jV8+PCjR48+/vjjTvodOEJT44MbKgv0rds/+HBtAJDV6S+de2G0iYuGmIIVdAXOamFkiNcn05IrCeWxujLbjoAt5DqCJOl/5B6yGkmSJmcG7Nz/5MmTM2bM4NZVo3V1dX5+foYvDx8+PHXUmJ+jU433kem1I24dU898hwgzuobw4K4n4NLGj7qztDCsoEvJOX1r61xHX0eq1elbjvlTVaHbltDT5neh81WymcUXvlq62KWuI1Wr1Tg+YRGeEbLLqgrasD93mZBkOQ4AACAASURBVLz74C+V+dA+sV4FSVJy5uDsMa1YWgZW0NU45bxQwOctmtlFKdAcrm14NzT68LyQuzCEyAlkMtnWrdsG+tf7J79cr91YdUc9aKTxRvL2zRAJpHUy/XncdsIKuiantHBU39j45gFfldn1OU3YQo7CECInMDk+uLnqLtGmIxEabrxRfPboS4+1YGMNWEFX5pQWLpndRUmobX6nkIIt5CIMIXKCxuODGlL/c1WBasCwevupVfpL555mYWoCK+j6HN/C3ikRyR3CvrLyk7gbwxZyDoYQOZrJ8cGdNUX65nFEVL1bMJIXz6YlRUSGeDG7AKwgVzi+hXMzEmWE6rKixs7jYAu5BUOIHK3x+CAJ8FPNXdWjQxrs6ZN99JXH4pn96VhBbnFwC/umRsY1D/jK1plCY9hCDsEQIocyOT54SlpeIxETreqXqapCX3R3RO8YBn86VpCLHNzCj57rdE9fZ9U9e5uCLeQKDCFyKJN3H/y5tlDZZ2CDPYmzx8cPaCEWWXF/HPOwgtzlyBaO6hvr5ytaWmbLp482hi3kBAwhcqg13zccHyxUKy7Jq4gu9e/ERJLi7OMvPMbYvSawglznsBbyeMS7z3Q6qSrTkHrLe9OALXR9GELkODKZbNu2huODf9Tcg9QeIKz34RfU+GDX9iZu2GsDrKB7cFgLJw1pqdHpdlYXMXVAbKGLwxAix9m8eXOD8UEdSf5ZU6Ttnt5gTwbHB7GC7sQxLQzwFY3sG7+upoDBY2ILXRmGEDnOmmUNxwePS8v0IaFERFS9/dQq/aXsyUMYGB/ECrofx7Rwxtg2NaSihIlLZgywhS4LQ4gc5M6dOxcvXW4wPviHtETZvU+DPcmLZ9OSIqNC7R0fxAq6Kwe0sEdSeHCg5MfyXGYPiy10TRhC5CDr161rMD5Yp9OcrS0nkro02NPn3DH7xwexgu7NAS18dWzbIyq7Pm7NJGyhC8IQIkcgSXLD2nUNxgf31ZYI2nQAL+96u1ZV6Avv2Dk+iBX0BGy3cPyAeIVGk6OoY/zI2EJXgyFEjnD48GFho/HB7fIyVbeGdxkkso5PGGjX+CBW0HOw2sLm4T4tYwPXV+YxfmTAFroYDCFyhJ9Wrhpa/3SwUqvOlVUTbTvW248kxdnHp4+0fXwQK+hpWG3hc8NanNFWMn5YSpzY552Q1h+89TZLx0f0YQgR62Qy2dZG44MH60oE7RJBIDTeSN6+GeJl+/ggVtAzsdfCcQPiFWrNbaWU2cMaXFLVDX/sMZYOjujDECLWNR4fBICdikpV564N9pRk2z4+iBX0ZCy1sHm4T4uYgN8r8xk8pgEJsFtR9uzzGWwcHFkFQ4hY13h8UKrTXq+rJNrUf11UrdJdtHF8ECuIWGrhmH6xJ9RVDB7QIFtW6RMc1KVLw6umkeNhCBG78vPzG48PnpKVi2JbgLjeOaLN44NYQURho4VDukcrQa3Q65g6oMFOZfnUl15k/LDIBhhCxK4ff1jTYHwQAA4oKhWJKQ32tO3ug1hBZIzxFnbrGKrVkwdrSxg5moFCrztcXTxx4kRmD4tsgyFELCJJcu3q1Q3GB0mAzLpyaNep3q423X0QK4gaY7aFfB7Rs0v0P7WMfQA3ZX9Nca+ePSMjIy3vitiHIUQsOnz4cOO7D95WSnViMRFSr442jA9iBVFTmG3h6N7ReaTM/uMY26Wteu7FF5g9JrIZhhCx6MeVqxrcfRAAzsgryVbt620iSfE568YHsYLIPAZb2P+haIVWU6vTMLIwAChSK27Ja4cNG8bUAZGdMISILSbvPggAR1U16rYdjLdYe/dBrCCig6kWJjT34/GII3WlTC3sn7ripyZOFNe/WAw5EYYQscXk+CAJcFlaSbRsbbzRqrsPYgURfUy1sHP7sCN1zHwAN44PuiAMIWJL4/FBAChQyUAshoCgB5usufsgVhBZi5EWPpoafk3HzNuEOD7ogjCEiBUmxwcB4KK8moir1zz644NYQWQb+1vYvVOYilCTTCwGxwddEIYQscLk+CAAnFPXKRLqvS5Kc3wQK4jsYWcL0zqFypXaOyp7TwpxfNA1YQgR80yOD1LOq+qI5vEPvqY3PogVRPazp4UBvqKgAEmmrMLONeD4oGvCECLmmRwfBAANqS+W1xDRD7JHZ3wQK4iYYk8L28QHnpdX27kAHB90TRhCxDyT44MAkKeSif2DQPjfrZdo3H0QK4iYZXMLU9sG3dLK7fnROD7osjCEiGFNjQ8CwE1lLRidDlq8+yBWELHBthYmJQTUEWp7fi6OD7osDCFimMnxQcpNtVzZPNbwpfnxQawgYo8NLWwfH6gjtXqw8dJRHB90ZRhCxDCT44OUazolhP93pmh2fBAriNhmbQvbxQfIVbpyjcq2H4fjg64MQ4iY1NT4IOWOSgbhUdSvyYvZDyVGmBwfxAoix7CqhYF+IrGIf0NRa9vPwvFBV4YhRExqanwQAPQkWamoI0LuvyPok33k1cdNvC6KFUSOZFULQ4O8bqrqbPgpOD7o4jCEiDFmxgcBoEyrEkq8QSAEaHJ8ECuIHI9+C6MjfO6qbLlwFMcHXRyGEDGmqfFBSpFaLgy8/96hyfFBrCByFpotjI/yvauz5T1CHB90cRhCxJimxgcpxRqlPjgUwPT4IFYQORedFraK8q7UW31XQhwfdH0YQsQMM+ODlHKtShMUDKbGB7GCyBVYbGFMhI+Gr7P2sDg+6PowhIgZZsYHKYV6jTYwCAAk2ceMxwexgsh1mG9heLBER+itOiCOD3IChhAxw8z4IKVUryF8/UGt0l08axgfxAoiV2Omhf4+Qj1YF0IcH+QEDCFbtFptQUFBcbEVn+Gk0Wjy8/NLS0vZWxVLzI8PUir1GvDxNb77IFYQuaamWujnLdTprAshjg9yAoaQFYsWLYqMjIyLi4uKikpOTs7MzDS/P0mSCxYsiIiIiI+Pj4iI6Nq1a3Z2tmOWyggz44MGtVoNePsY7j6IFUSuzGQL/X2EOj1J/zPWcHyQKzCEzFu+fPmsWbPS0tL+/fff9evX19TUDBo06NatW2Ye8u2337799tt9+vTZuXPnunXrioqKBgwYcOfOHYet2R7mxwcNFDoNqNXU+CBWELm+xi308xFqdaSOdgpxfJArBM5egLtRKBTvv/9+mzZttm3bJhQKAaB9+/apqamffPLJ2rVrTT6ktrb2448/TkxM3Lx5M5/PB4AWLVr07t173rx5y5cvd+jqbXJ/fDDE9PiggVKr4V27MGFgiyu3a7CCiBP+a+Ef2xf06dMl0t9HpNHqNaReQJi7g6bBLm3V2y9+xPIaEQPwjJBh+/fvr6ysHDdunPC/u+516dKlY8eO27Zt02hMTyDt2rWrtrb2ySefpCoIAL169WrRosXmzZtJK16GcRrz44MGaq1GfPl0n6QQrCDiEOPzQi8xX68nFaSWzgNxfJBDMIQMo97b6927t/HGXr161dbWNvXqaFMPKS8vLygoYG2lzLA4Pmig0+v8+LpZi7Kwgohb6r1GSgBJ73IZHB/kEAwhw+7duwcAYWH13jCjviwsLGTqIa7D4vggRUuSYiFPKlVhBREXGVpIc38cH+QWfI+QYQqFAgD8/eu9YRYYGAgAMpnMzEP8/PzoP6S0tDQ7OzsoKAgA4uLijh49ysDSbbJ68dKhZscHKVpSrwOi19iHsYKIo1p3S+g5sffulft4hOWds2WV3oEBbdq0kUql7C/NHJ1OJxKJnLsG14chZBj1SkhdXb17tdTW1gKAl5eJe+8ZHtLgD4z5h4SHhyclJe3duxcAfHx8nPVEz8/Pv3z16rwWPSzuSQLotLozWzPjk2NbdI5nf2kIMazwRtHR9UdEAp6QxpUyO5XlGXNe9vX1dcDCzFOr1c5eAgfgS6MMoy6VrqioMN5IfRkREWHtQ8xceM3n84OCgoKCgpz4zz0644MGBAGb5/be8tHm2+fyWF4XQgwrvFH069sbwoK9lSq9kLBwSojjg5yDIWRYUlISAJw6dcp4Y2ZmppeXV+vWra16iL+/f3x8PFsLtRvN8UEKAUAA0bNzxLYFfbCFiFuoCs6fnlxYoSRJvcV/+eH4IOdgCBk2YMAAHx+fTZs2GSYfbt68mZWVNWTIEIlEQm0pLCy8dOmSXH7/Dp9DhgwRi8W///674SCXLl26cuXKyJEjDQMVLsj83QcbEBI8AZ+QKbTpKdhCxCVUBde8k1ZQqoCkVD6Pz7N0Roh3H+QcDCHD/P3933jjjezs7GnTpl2+fPnIkSNjxowRCoXvv/++YZ+PPvooMTHR8CFqoaGhs2bNOn78+Kuvvnr16tWDBw+OHz/ey8vrnXfecdJvghaa44MUPkEI+IRUrgEAbCHiCkMFR6bHrtqRq+6QKhYIzT8Exwe5CC+WYd4HH3xQU1OzZMmS1atXA0B4ePjmzZtTUlLMPGTu3Ll1dXUrVqxYsmQJAERFRW3btq1Dhw4OWrH1qPHBX2Ifov8QPp9XK7v/kQJUCx9/a/MTH43Ba2eQazJU8LE+sQfOFCv4XhAYJBFYeEsexwe5CM8Imcfj8b755pvCwsJDhw5lZmbevXt3xIgRxjssW7ZMoVD06PHgYkuBQLB06dJ79+4dOnTo1KlTBQUFAwcOdPjCrUBzfNAYn8erkz/4bB08L0SuzLiCALD8z1xFl94gk/oLzT3ncXyQo/CMkC2hoaHp6ekmvyUQCAQCE//lw8PDw8PDWV4XM9YsWz6YxvigMR5BGM4IKXheiFxTgwrKFNodhwtgzjQoyA3im3tpFO8+yFF4RoisRufug43xgNcghIDnhcj1NKggAGzalydIaAV+/qRMGswzF0K8+yBHYQiR1awaHzQQkLzSSkXj7dhC5DoaVxAAvtt2W57SGwCI6qoYoslX0XB8kLswhMg6Vo0PGpPo+fklcpPfwhYiV2CygnlF0qu5VUS7RAAQV1WGN/2+OI4PcheGEFnHqvFBY6E80a1C0yEEbCFyNpMVBIDVf94iuqSBQAAA/KqKMKGkqSPg+CB3YQiRdawaHzQWIxAXFJv7AGJsIXKWpipIkrBqR646pSf1pb6yPEpk+uN/cXyQ0zCEyAr07z7YWIzYp6jU9M00DLCFyPGaqiAAHMwqVvC9iGaxAAAkqaytjhKaDiGOD3IahhBZwYbxQYNWEr+KahMXyzSALUSOZKaCYBgfpNRWewvFXjwTn3qI44NchyFEVlizbPkgK8cHDRLEfjyCKK1UWtwTW4gcw3wFpXLNjsMF0OVh6kuypKiZl1/j3QDHB7kPQ4josm180CBQIBKL+Nfya+jsjC1EbDNfQQDYtC9PmNAafO/HjywrSRCYfl0Uxwe5DkOI6LJtfNCYAPhXb1fT3BlbiNhjsYIAsHh7niyll+FL0b2CdqbeIMTxQTeAIUS02Dw+aMyfFJ+7SeuMkIItRGygU0Hj8UGK8G5Ba4mJl0ZxfNANYAgRLTaPDxprJ/DOvlFl1UOwhYhZdCoI9ccHAQBIUllekiD2bbwnjg+6AQwhosXm8UFjyT5BN/OtCyFgCxFzaFaQJGHVXw/GBwGALCv2E0l8G33iNo4PugcMIbLMnvFBYw/5hkrlmrIqyxeONoAtRPajWUEAOHS2WCn0vj8+SLmT18EroPGeOD7oHjCEyDJ7xgeNRQol3mLBqcvlNjwWW4jsQb+CALBse67c6DIZABDm5XYRNnxdFMcH3QaGEFlmz/hgAxJSdPximW2PxRYi21hVwft3H0xJM94ouHU9ybvhGSGOD7oNDCGywM7xwQY6Cvz2nS21+eHYQmQtqyoIAL/vvS1MaA1+RteFKZWqqoo2koZXiuH4oNvAECIL7B8fNJbuG3bhWpleT9p+BGwhos3aCkKj8UEAIPNvtfALbvBHAMcH3QmGEJnDyPigse5+YXwecT2/1p6DYAsRHTZU8Hah9NrtaqJ9ovFG/o0rvUQNTwdxfNCdYAiROYyMDxrz5QskfOH+M0V2Hic9JeK3T3tt+nATthCZZEMFAeCHv25BykPAr3cbetG1y2k+Dd8jx/FBd4IhROYwMj7YQEvCd+uRe/YfZ0Ba9Ka5vbGFqDHbKtjg7oP3yaSaqooOXoHG23B80M1gCFGTmBofbGB4QNTxs0Uard7+Q2ELUWO2VRAa3H3wP+SNK4n+oQKCMN6I44NuBkOImsTU+GADvf3CRUKebdOEjWELkTGbKwgN7j74H/Glc4+K650O4vig+8EQoiYxOD5oTMLjS0jRzpOFTB0QW4go9lTQ5Pgg6PW6G5d71J8dwvFB94MhRKYxOz7YQE9J8Ob9BQweEFuI7KkgAGzalydIaFVvfBCAvJ0TIfYJF0qMN+L4oPvBECLTmB0fbGBCSFxBYW1+kZTBY2ILPZmdFQSA77bdlqc0fF1UcOHsIK96L4rg+KBbwhAi035bv76bkLGpiQZiRD4SgWjT/nxmD4st9Ez2V7Dx3QcBAEiSOJ/1qF+E8bYDtcU9u/fA8UE3gyFEps16681vqm7dU8tZOn43YdCPO24zflhsoaexv4LQ+O6DAABA5t0M4QnixD7GG/9VV059GV8XdTcYQmTa9OnTP/76yxnFF+6y08LJofG371Yz++ooBVvoORipoOnxQQBhVuYwn3rvkRepFbkKHB90QxhC1KSMjIyPv/5yJjstTBD7ebPw6igFW+gJGKkgmLz7IADodOT5M4PqD9H+U1c8dtx4HB90PxhCZA6rLewtCl266Qbjh6VgC90bUxUE6u6DnXs12EhevRgv8YsWeT3YArBbUTZpyjN2/jjkgjCEyAL2WvhcWMvKasUJW29PaBG20F0xWEHT44MA4pOHx/iEG2+hxgeTk5Pt/InIBWEIkWUstTBMKPEDySLWTgoBW+iOGKwgmLz7IADU1epu5zwSUO96URwfdGMYQkQLSy2cEhT354Hb1XVqBo/ZALbQnTBbQTB190EAIE4dfSQgypv34CJSHB90bxhCRBcbLRwUECXi8zfsymXqgCZhC90D4xXMvVfX+O6DoNcLjh0c5x9tvA3vPujeMITICoy3UEjw0kSh89Zetuee9XRgC7mO8QoCwJodudC54d0HyasXo3iCBvfgxLsPujcMIbIO4y18Kbx1bZ1q++E7jBzNDGwhd7FRwfvjg10ajg9KDu2Z7FfvdBDvPuj2MITIasy2MEIoiSZ83/v+gv2HsghbyEVsVBCauvtg0T1e0d1HAxqOD+LdB90bhhDZgtkWvhnR9l5R7eHsEvsPZRG2kFtYqiA0cfdB4YGdE4JijD9rHu8+6AkwhMhGDLawg1eAFyl+f9VFRhZmEbaQK9iroFSu2XGkALo8XG9rTRVcPj8msLnxNrz7oCfAECLbMdjC10JbZ18pO5hVzMjCLMIWuj72KggAm/blCVu2Bl8/4438AzuHBzXz5wuNN+L4oCfAECK7MNXC3v7hYr3wlW+zSHavHn0AW+jKWK0gmBwflEnhzIlngur9OBwf9BAYQmQvRlpIALwW1rqgsG7HUdYvHzXAFromtit4805t4/FB/oGdA/wjQwX1rojB8UEPgSFEDGCkhf38I8QawYyFZ3UszxQawxa6GrYrCABL/sghu/asNz4okxInjzwfHN9gTxwf9BAYQlbU1NTMmTOnY8eOMTExw4cPP3r0qPn9165dO66RzMxMx6yWEfa3kAB4K6JNZbVyxR/XmV2bedhC1+GACirVujV/3dJ0SzfeyN/798CAyHChxHgjjg96Dgwh8+Ryed++fb/77ru0tLQpU6Zcu3atb9++u3btMvOQ8+fPb9q06ebNm7lGZDKZw9bMCPtb2MsvPEgveWfZudJKJbNrMw9b6AocUEEAWP9vLsS0IEKN7ixRU807fXxao9NBHB/0HALLuyArLVy48Ny5c6tXr546dSoAzJ49OzEx8YUXXrhx44ZQKDTzwMOHD/v6+jpqmazIyMgAgJlz3lgUmdRc5G3DEd4Nb/NayYWXv83a9GnDj/xgFdXCse9vGvvx2Bad4x35oxE4qoIkCfN+uS4fMJkw2ij454/RQc1D6r87SI0PbsXxQc+AZ4TM++mnnwICAp5++mnqy+Dg4MmTJ+fl5R08eNCp63IQO88Lk7yDOogCd54oPHDGQaMUBnhe6CyOqSAA/H30TrlWRLRqZ9hCFt7lX7kwJSiuwZ44PuhRMIQMq6ioyMnJ6devn/HJ38CBAwHgxIkT5h+bm5u7d+/eU6dOKZUOfWGQcXa28K2w1iq55unPMuVKLeNrMw9b6HgOqyAAvPfDFXmf4UA8OCEUb9v4QnALX37D18ZwfNCjYAgZdvv2bQBocL11dHQ0AOTl5Zl/bHJy8oABA9LS0iIiIubPn086bKSOBfa0sJnI+4ngmGqNYMbCs2yszTxsoSM5soK7TtzLrdITSamGLeTl8/5lpaOCmjfYE8cHPQ2+R0iLTqfTaDRmduDz+dQpoFQqBYDg4GDj71Jf1tbWNvXwNm3afP755ykpKb6+vpcvX16wYMG7776r0Wj+97//mdy/oqLixo0bjzzyCABER0evWLHC+t8T6yZMmKBSKme8+8F3UVa/XzgtpOU/ucc27leO6dNscPdmLK2wKfh+oWM4soIkCa8tu6B49HHCcDqo1Yj+2PBeaGs+QTTYeX9NcfeHH/b19aX+OBuTyWREo/1dmU6nE4lEzl6Fq8MQ0rJw4cLXX3/dzA6jR4/esmULAAgEAgBQq+vdcp16qdPMlTIvvPBgVqlHjx6jRo1KSkr6/PPP58yZ4+Pj03j/gICAyMjId955BwB8fX29vW25LMUBXnzpJZFYPPP1N629dsaLx387vO3HNXkTPzl5Y+PwkABHX7mHLWSbIysIAJv35d1RiIjEB+/58fbv7Czw7uob0njnXdqqt17+0OQfK51O57J/3Ewy/y94RMEQ0tKvX79vvvnGzA6tW7emfkGd/FVUVBh/t7KyEhqdJpoRGho6atSoZcuWnT9/vkePHo13EAgE/v7+AwYMoHlAJ3r++ecJgrDhOtJ+/hGb6oquBYWOfu/Yge/68XiO/mc4tpA9Dq6gSq2b8d05+WNTDSdzZHkp7/Det+LTGu9MjQ8OHz6cxzPxzhGPxzO53WVx6/zVWTCEtHTp0oXm9WMJCQlCofDatWvGG6kv27Vr18SDTKD+1eke/5qjZipmvPaGta+RfhjebkJe5lky+u0V5794qTNrC2wStpANDq4gACxYf0UWEUcktDVsEf++9rmQ+Ij6E/QUHB/0QFz6pw0niMXivn37ZmZmFhc/uPp/27ZtADBo0CCaB9FoNLt27SIIom3btpb35oKMjIx3531q7bUzEULJ9JAWOoVm2Z952w457jNIjeG1M8xyfAXziqRf/HJVPnTCg01nToSWV0wIMrEAvPugZ8IQMm/OnDl6vf7FF1+k3mnfsmXL5s2bH3vssTZt2lA7nD59OiQkZPbs2dSXZWVlr7/+enZ2tkKh0Ov1165dGz9+/MWLF8eNG+dOn/b7zDPP2HAd6bjgmDipQtU+dfKnJy/dqmJveWZgC5ni+AoCwJR5pzS9BxJB/70XWFcr2P7bJ+HtGl8jAzg+6KkwhMwbNGjQp59++ueff4aHh0dFRY0ZMyYpKWnVqlWGHTQaTWVlpeGCNLVa/fXXX3fp0sXb29vLy6t9+/Zbt24dMWLEypUrnfQ7YIsNMxU8IOZGtBeePq7oM7TfqwfulDjnY+ewhfZzSgXX/X0r655W3/vBizHC39eODWzW1svf5P44PuiZCE4Pq7myy5cv79q1q66uLjk5eejQocZXMFdXV2dmZsbExHTo0IHaUlBQcPz48YKCgtra2sjIyPT09KSkJDMHP3ny5IwZM06dOsXu74FRdXV1fn5+ALB69eoPrbx2ZmvV3cXaSt1DPaIvHDi7ZlCQv3MuB9+TWTj2/SP4fqENnFLBu6WyDhP/kT/7GhEdc3/TmRORf2/bENdNSJg4B1DodaNuH7uWe8vMKzGGpzFXqNVqHJ+wCEPISZwOIdjUwtn3Lpzr2J4Q8tqVXzqy9FEfL+dc54UttIFTKqjXkw9P33s+upu+39D7m6orBV9/sqp5SiuJ6ZL9XXUvu33kjj27zRwWQ+iW8KVR5AQ2vEb6UWR7cdZJdUKH674t0l/ZL5U753pafI3UWk6pIAB8sOrCVbm3vu+Q+1/r9aJ13z8bFNtUBQHvPujBMITIOaxtYQBf+FVUouCX1ep+w6/5JvR+eX8dttDlOauCO0/cW7jllnLCdMPHihJ7d8TVSicFN/xwbQO8+6AnwxAip7G2hZ28A58JjBGuW6Ue8eT1gNY9XthbVuWcTyfHFtLhrAreKKgd97/jqqdeAL/7V8SQt3PER/Z/EdWJ1/R0+T+1RU899RSOD3omDCFyJmtbOCUkPlGmFG7/TfPYxJyYrslTdt4oaPITXFmFLTTPWRUsr1b2m7FfOWgMEd/q/iZpnXDd93MjO4QKmowcCbBbWf7stOcdtErkYjCEyMmsaiEB8FlkR7+L5+Bspm7AY2W9HuuWsetIdokD1tkYtrApzqqgVK7pN+NAZYceZNf/7uqs1wvXfT/GNyLNN9TMA3F80MNhCJHzWdVCX75gYXSicNuvZH4udOspGztt8BtHvlh/xSmXP2MLG3NWBRUq3YDZh3IDW2kHPGbYyPt7S6uqmhdDWpp/7E5F+VS8TMaDYQiRS7CqhS3EvnMjOgh/XArVlUTr9uqX3/tke/HQNw7VSNUWH8s4bKExJ1Zw4OyDF/lR6scnGy6QIc+f8Tlz8kuzbw0CdffBmuKJkyY5ZKXIFWEIkauwqoU9/MKmBjQXrlwISiUEhaimv31IH9d6/I49mYUOWGoD2EKKsypYI1X3fnnfWYhSjZkK/90agrxXINq8flF0YgC/ydufUfbXFPfq0cOdPs4QWQtDiFyIVS2cFBw3kPAS/PAd6LQgEGhGPlX5+NRRH52ewdrIIwAAIABJREFU8llmrczRkxXYQmdV8G6prMtzu64EtFWPfVBBqKsV/rD4nfA2rSWmP0rN2C5t1XP4sWqeDUOIXItVLXwzrE2nGplw41ogSQAgWrdXzfx4U1lI7KjtP2zP0esd+rahJ7fQWRU8ebEs6el/73bqpxnxpOEVUVCrhCsXTvSJGOBv+SQPxwcRYAiRC6LfQh5BfBXVKfZ2Ln/rr/c3SSTqx5+WPj1z9q+FHSf/6+BXSj2zhU6pIEnCwt+uPTrrYO1jz+rTBz74hl4v/HllLy0vI9TCBTIUHB9EgCFErol+C8U8/uLopNCL53j7/jFsJJrHKaa/nfPQ40/MO9/52V2OzKGntdApFTyYVdw1Y/cHmwtVL71LtE80/pZgy/rWxaX/i2hP5zg4PogoGELkoui30I8vXNW8S9CRA8TBXQ+2EgSR3FUx65NL3UY/seBS0jM7/zrioFv7ek4LHV/Bo+dKur+wd/gHmedbP6J88V0iJMz4u7yd2yKvXv02OlFg9jJRAxwfRBQMIXJdGRkZ/1swf2bRhXuWWhgkEH3fPMV3/y7ixKF63yAIokOy4tUPr6Q9MfHbqw7LoSe00MEVpBI4+N2Tp+P7ql6fTzyc/uDSGAAAII7sCzx5dFmzZG8erTuTSHWaX2vv4d0HEWAIkYub/sIL//vy8xnFllsYIZSsiU312/kncWx/w+85I4fu3UJHVtBiAgEAzhz32fP3imYpQQLLtxyS6jRrKm6PL8hsNajvtGnTWFk04hQMIXJ106dP//jrL2fQeI00Uui1snmKz64dxLEDJr7t8By6awsdVkFaCQSAs6e8tm9aGdMlSuRl/oByvXZ9Vf6EglPyXskns8/++Mt6bt1cELHEOXc3RcgqGRkZADCTxr18m4m8f4hJnbZ7R51are83yMQeVA7bJ125emHit1vjV1/+LKPjiN4xJvZkAtXCse9vcpt7+TqmgkfPlbyx4uLFApkyfRgxrhdhsn+Us6e8tm74PqZLjNknhlyv/aPm3sbqu4OHDjnx2fbWrVszv2jEWRhCxA30Wxgt8voxJvX5Q3urlAr9kMdN7+TAHLpTCx1QQSsSCABZJ722bfw+pksLsW9Tu2ACkUUYQsQZ9FsYJpT8FJP64umTxXU12jGTTb+eBo7LoXu0kO0KWpdAADh52PufbStjUuPEPia/jwlENBGkUz60H9nn5MmTM2bMOHXqlLMXYoW6ujpG3o9ZvXr1hzRaCAAKvW5W4YWcyHDN09NBaOkaCpIkr17w3rs13k/PUg73ZBaOff8IR1vIagXrJfChXk3+w8UIcXCX34HdK5unNDP1NDBO4IefzWUwgUw9jR1GrVaLRJYvIPJwGEJO8uQQgjUt1JD6j0qunhARmudngi+Nn85yDjnaQvYqaEMCgSR5f20Ozj79fbPO4UJJg2+yl0AKhtAtYQg5ycNDCNa0kARYUZ67SVGmzphBRDajdXQ2c8i5FrJUQVsSCAA6reDXn2Ju5y5pluxf/7YSbCeQgiF0SxhCTsIQgjUtBIBdNUULynI0Tz4HHZLo/gDWcsihFrJRQRsTCAAKuXDNkqQa+edRHSU8vmGzYxJIwRC6JQwhJ2EIKVa18LKi+rXCi8re/fX9hwK9j+ACYCuHnGgh4xW0PYEAZEWZaNWiwXzf18Nb8+D+/z5HJpCCIXRLGEJOwhAaWNXCcq3qtcKLd6OjNBOfB0nDt5fMYSGHLt5CZitoTwIBgLx1XbB2xcvB8WOD7v+Xd3wCKRhCt4Qh5CQMoTGrWqgh9V+W5uzV1KqffYmItrJnTOfQZVvIYAXtTCAAEEf2iXb/9XlUx64+IeC8BFIwhG4JQ8hJGMIGrGohAOypLZ5fel0zdDR072P1D2M0hy7YQqYqaH8CQaMW/rY2LPfmwqikKJGXcxNIwRC6JQwhJ2EIG7O2hQUq2RvFl8uaN9dMeBa8TU9km8NcDl2qhYxUkIEEApClxaIfl3YH0f/C2+mAdHoCKRhCt4Qh5CQMoUnWtlBD6r8ru7lDXq558jmiTQdbfiRDOXSRFtpfQUYSCACQdVKw7dfZoa36+0e4SAIpGEK3hCHkJAxhU6xtIQCcllb8r+SqMjlVO3Ks5Q+gMYmJHDq9hXZWkLEEKhWCTT8H5t6cG9EuW1njOgmkYAjdEoaQkzCEZtjQQqlOM68s56RGqn7yWSKhrY0/2O4cOrGF9lSQsQQCkLeuizb80FcUECvy2lxzz6USSMEQuiUMISdhCM2zoYUAcKyu7NPSa6pOnbUjxoKXFQ+sx74cOqWFNleQwQSCRs3/a7Mo+3Qfn+ATymoXTCAFQ+iWMISchCG0yLYWSnXaReU398rKNY9PIFIesv3H25FDB7fQtgoymUAA8uY14cafmpFElVY1ZNhQ10wgBUPoljCEnIQhpMO2FgLAJXn1x6XXK0NDVGMmExFRtq/A1hw6rIU2VJDZBIJcJtj+G3HlggDIkSNGuHICKRhCt4Qh5CQMIU02t1BPkluq7qyouK1LfVg3aKQt8xUGNuXQAS20toIMJ5AkyVPHiB2bBQAjhwyeu+BzF08gBUPoljCEnIQhpM/mFgJAtU69tDx3r7RU238Y9OwHfDtuZG19DlltoVUVZDiBAGR+Ln/zz/rqykd69FiyYjknEkjBELolDCEnYQitYk8LAeC2SvpV+a2rOoV66GiiS5oVH9jdmJU5ZKmF9CvIfAKrKvh//q65caVHSsqadWujoqK41RUMoVvCEHIShtBadrYQAM7Jqr6pzL0n4KmGPk4kdnFYDhlvIc0KMp5AkEmJ3X9pzxzr1Kbt+l/WJyUlgbOfFTbg3IIxhHRgCDkJQ2gD+1sIACfqyhZX5ZWIhapBI4jEVLvyQDuHDLaQTgWZT6BCDgd26o4dSIiP/3ntTw8//LDhO05/VliLcwvGENKBIeQkDKFtGGkhAByvK1teXXCP0Kv7DyVSu4OA9fcOGWmhxQqycBZYBwd3644fjI+N+XH16j59Gn7EuSs8K6zCuQVjCOnAEHIShtBmTLUQAM7JKr+vvnNNVavr2Y/s2Q987Pj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      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "polar_plot(project(p4, 1:2), γ4)"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "We now try it with sextic polynomials:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solve_time(model) = 0.02682185173034668\n",
      "JuMP.termination_status(model) = MathOptInterface.OPTIMAL\n",
      "JuMP.objective_value(model) = 0.93\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.93"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "p6, γ6 = maximal_invariant(PolySet(symmetric=true, degree=6, convex=true), 0.93)\n",
    "γ6"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "Below is the primal plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "cell_type": "code",
   "source": [
    "primal_plot(project(p6, 1:2), γ6)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "and here is the polar plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "cell_type": "code",
   "source": [
    "polar_plot(project(p6, 1:2), γ6)"
   ],
   "metadata": {},
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "source": [
    "We now try it with octic polynomials:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solve_time(model) = 0.08796405792236328\n",
      "JuMP.termination_status(model) = MathOptInterface.OPTIMAL\n",
      "JuMP.objective_value(model) = 0.96\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.96"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "cell_type": "code",
   "source": [
    "p8, γ8 = maximal_invariant(PolySet(symmetric=true, degree=8, convex=true), 0.96)\n",
    "γ8"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "Below is the primal plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "cell_type": "code",
   "source": [
    "primal_plot(project(p8, 1:2), γ8)"
   ],
   "metadata": {},
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "source": [
    "and here is the polar plot:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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XHpVrt1B0mzFCaA2EUJQQQgFYGcK9e/dOmfr8ldRUWYcuxn4JTGCw+bN2JJAEqSDHphaSLTlk01KUG75vrDXMCWkeo/S2bVQu3ELRbcYIoTUQQlFCCAVQawh37do19YUXrqVdl3V9kH1oMPndc88s+xJIAlaQY2sLyfocGo10ZK90+x9DfSOmBsd42XLjX5dtoeg2Y4TQGgihKCGEArAQwu3btz//wovXb96QPdCb7TPQdI8Ijt0JJMEryLGjhWR9DkvU0q0b5RfOzgqOHegXaf03rq7ZQtFtxgihNRBCUUIIBVBtCLds2fLCyzNu3r4t7dmX4vuTxz33J6pLAslJFeTY10KyOofs9VTlhu+jy7VzQprHqqzdDFywhaLbjBFCayCEooQQCqBSCDdv3vzijJm3szKlvQZSj75075226phAcmoFOXa3kKzMIcvS0f3SbZse9gl/PqiJt9SqI6Wu1kLRbcYIoTUQQlFCCAVgCuHmzZtfeHlGRna29KHB1L0PKZXmq9U9geQCFeTUpYVkZQ5LS2RbNsqTz8wMiR1k3ZFSl2qh6DZjhNAaCKEoIYQCKCkp2b17N5dASd8hzIN9SH7PLxReEkguU0FOHVtI1uWQvXFNuf77KE3FnJDmTa04Uuo6LRTdZowQWgMhFCWE0NH+/PPP56a94OgEkotVkFP3FpI1OTQ7UjotuEmt55S6SAvFtRkTQmgdhFCUEELH2bVr1+Spz6ffuiXtM4h69iUF/wdCTVywghxeWkjW5LC0RLZlgzz57CshzQb41fJZrtBCsWzGJgihNRBCUUIIHeHgwYPPTJqccu2atEdf6jOQVB7mz/KbQHLhCnL4aiFZkUP2eqpyw9qYCv2ckOaNLc6+d3oLXX8zrgQhtAZCKEoIIb9OnTr1zMSJZ/+9KOt0PztwGPn4mj/LewLJ5SvI4bGFVGsOjUY6sk+6/fdH/SInB8Woar5OqXNb6MqbcbUQQmsghKKEEPLl/PnzUydNPnI6SRbT3DB8DBMcav6sIxJIIqkgh98WUq05VBfLN/+sSrn4Vsh9D/qE1Dgq57XQNTdjCxBCayCEooQQ1l1ycvIrL8/YffiwxNffMGoc07ip+bMOSiCJqoIc3ltIteWQTbkoX7+2vUT5ZnCzULmq2ndwVgtdbTOuFUJoDYRQlBDCukhOTn7nzbe27tqlJ4YdOorp0t2Ou8bbR3QV5DiihWQ5h3q95O+/pAf+nhoUMyowSkLVTDh0SgtdZzO2EkJoDYRQlBBC+yQnJ89/590tW/+sYI1MxzjDkBHm10hzaAJJtBXkOKiFZDGHbE6m8uc1EYXF74W2aKKq5iQa4VvoCpuxTRBCayCEooQQ2opL4Pa/tqkYaaGXZ8XjzzANG5medXQCSeQV5DiuhWQhhyxLiQelf/46xr/hpKDGcqbyX43ALUQI3RJCKEoIofW4BO7avqO1zOuoptDw0GC29wCS3Pl9KkACyS0qyHFoC8lCDosL5Ru+D7h5Y15Yy5YefpVHJWALEUK3hBCKEkJoDVMCE7xCT1aoUzwUFeMmMaER3LPCJJDcqIIcR7eQas4hm3RMvumnR30jpgQ3qbRrKFgLEUK3hBCKEkJomSmBj/lERsk95mVf0nbvbRw4jNsR5BKozL7x/rNtnh3mwASS21WQI0ALqaYcqovl678LvHnzw/BWlS5SKkwLEUK3hBCKEkJYE/MEjvBv+HX+tc1lubrxzzExzUjYBJKbVpAjTAupphyeOCL7/ZdnAqOfDGxkfkKpAC1ECN0SQihKCGFV5gkcFRClMRpmZZxLCw7UjZ9CXt4CJ5DcuoIcwVpI1eWQLchTrF3VpKT0w/DWwbK714N1dAsRQrfk8F8HAI6WnJz85OjH+tzfPeDQufXRceOCGt/Qlo27fiy1U1fdlP+xOVmea5cGbly5aKjf7d8fmTKiOSrIi2ZdY0fMGTn89X37TmU6+rMkEmZ0v8ZpG4d9M6lR5O4fPb5YQBk3dS+9frnb/WPTjh1W59wdlcr3k/A2zz01YfOmTY4eFbgN7BGKEvYIOZX2ArkLVB5Q58zN+lf76JPMfa2Vv37rm3N9/uS24wbHCNA/Tn2ooImQ+4Ucg5H9aee1N1adL1IFlPV9hCRS+fdfPuIZ/FJwU8l/F0Zw3H4h9gjdEvYIQZSq7gVyFfyt4Ob/5VzSPjeDQsKUy997qoUhbeOwCQmxqKCDCLlfyJFKmHGDmqRtHPr5Uw1C//jG48A23TMv/u4tn3wrKV+vvTMq7BeCLRBCEJmaEkhEX+amrijN0E1/gwrzVd9+uvp/7T9/pYtCLtxGXt8qyBG+hfRfDq9tGDo7Xqn69lM2JialY+cnrif+qym6Myq0EKyGEIKYfLdmTd8HHgw7krzh3gQS0dKcK+sNxbqX35RePOO/7YcDn/V9rF8jC2/Fu/pZQY5TWkhESoX0rQltrvwy9CH9JcWlU+q+g6fdOrO96PadUal8F4W1mfzUhN83bxZyVCA6CCGIyZKFi94Mav5YQLTy3vvVfZJ9+XemQvvi67LEf0JP7Dq1elDH+wKFHFh9riDHWS0koohgjz8/iv/qxZbeh7axXbouKr6xMjeVO/ehhYfvR2FtJo1/Ci0ECxBCEI3k5OTMW7e7eFUu3IqclL+Yct20V2SHdkdeOnLym4HR4V5CDgwV5DixhUQ0tn/jSz8ldChLkYYGrmfK3sxI1rFGImrh4bs4vO3k8U/jGCnUBCEE0Vi9atUQ7zAJc88deb7Nu/abQa19/hVp4t6Iy0ePftk/NLD6O9g5CCpozrktDA/yOLSy3/MPeksq1Ee8lS/dOqMxGgjfF0JtEEIQB71e/8P36wZ6h5k/+FfR7e9Ls3TPz2IunAk8tffQyn4hAaigkzm3hVIJs+iFjr/M6SIvzLgQHDDp5qlig47QQrAIIQRx2LZtWwO5R7Ty7jHPE6V5H+Ve1U6ZyWbe9tz1677PHooI9hBySKhgTZzbQiJK6Bl14PO+voW3bocFT7pxqtCgJbQQaoYQgjisXvnlQHmAafGWtmx2RrJuwvMkkSrXf711Uc9mUb5CjgcVtMzpLezQPDBpzaBIfW5uaOCzN04V6NFCqBFCCCKQn5+/Z+8/D/neOS5aZtS/eOtMxZARTMNGqu+XfzKtXY8OYZbfgV+ooDWc3sKoMK9jXw2IkhQXhAY+dzNJjWOkUAOEEETgh3XreviHe0vl3OLczIuFLVvTA72Um9cldPSbOrK5kINBBa3n9BYG+SmPfNmvkawkP8hv6q3TZUY9oYVQBUIIIrB65ReDlEHcn9cX3DgpM+offZJOHwvOvrJ6djchR4IK2srpLQz0VR5e2S9aWZbp7/W/2+f0LEtoIdxL5uwBuK3c3Nw9e/aUlZW1adOmS5culle+efNmVlZWpQebNGkSEBBQ7fr1Cjd9sHP0/UR0tVy9Mu+absZbTIlaseWn37/o66kSbhtGBe3zXwsFvTa3uQBfxb7lD3WcuP2SyuvdrH/fC2/FmLWQ1pKj72sPLg57hA6xZs2a6OjoMWPGTJw4sWvXrkOGDCktLbWw/uLFi7tUsWfPHsEG7MpM0we1rPG1zGT98DFMYLDqtzWvj2vRvplwl49BBevC6fuFoYGq/Z/19dAWHTCWrc67dmdU2C8EIkIIHSExMXHSpEmdO3e+du2aRqNZvHjxtm3bpk+fXusL165du95MXFycAKN1cebTB5fnXC1oFENdHqCkxAaG/Defai3YMFDBunN6C2Mb+uxc0lumK/u+6OZ+dfadUaGFgBA6wocffmg0GtesWdO4cWOVSjVz5syHH374u+++u3HjhuUXjhgxYrSZhg0bCjNgV2aaPni+rHBrSZZu9HgqK1VsW//j23G4s5LoOL2FXVoGf/V6V5mHfG7mhesVdw7SoIWAEPJMp9Pt2LGjffv2sbGxpgcfffRRg8Gwbds2Jw5MpLjpgzrWOCfrX93IJ8jLW75r8xP9oju1CBJmAKggv5zewscHxkwY0FAWEjDz9jnuAmyEFtZ7CCHPuMOh7du3N3+QW0xOTrb82kmTJsXHxyckJCxcuDA/P9+BoxQJ0/TB7/LSiqOimfZd2Kzb8vMnFj7fvvYX8wEVdASnt3DJy51aBDFF/t4fZF+6Oyq0sB5DCHmWk5NDRMHBweYPBgUFEVFubq6FF/r4+Ny4cUOhUJw5c2b27Nnt2rW7ePFiTSuzLFtWVnby5MmTJ09euXKFp7G7HG76YJFB90PBDd2jTxKRx/YNc59pE+irFODTUUHHcW4LZVLJ1kU95WUFByuKdhXfHQBaWG9h+gTPdDodEalU91z62dPTk4jKy8tretWLL744f/587lUGg2HJkiWvvPLK+PHjjx8/Xu36OTk5aWlpkydPJqKwsLANGzbw+CM4SGlpKXPvjSNq9fVnn09SBn2Ye8Xw0GDyD2SvXfHKvfniqOEOGqE5VNDRnDunIizQ47u34p5ccOrDrEvtPfxD5Xf+wXItnPzU0+WryhOGDq36Qjs2Y+cyGAwKhcLZo3B1CCHPuOYVFhaaP1hQUEBE3t7eNb2qSZMmpj9LpdJZs2bt2rVrx44dV65cadasWdX1Q0NDW7VqdezYMd7G7Xgsy1r4L1BVcnJydkamIdAn2ahle/UjIs/dmxZObaeQO/wwBiooDOe2cHiv6Ef23tqcXPFO9sXPG3S4OyqV7+LwttOfm6paq6o6v9DWzdjptFqts4cgAjg0yrPo6Ggiys7ONn+QmyzfqFEj69+nc+fORFTriaZubPWqVYO9wxblpWgfGUtSGZt62ac0b9zgJrW/sm5QQSE59xjpyle7eGsKLrC6Pwtv3TMqHCOtZxBCnoWHh0dFRe3bt89oNJoe/Oeff4io1uvLmEtPTyeientlGW76oNxIRUFBTOv2ROSxd+t7E1tJJY49KoUKCs+JLfTxlK97O07K6D7NvVqov2fPCS2sVxBC/j3xxBPZ2dlbtmzhFsvLy9etWxcaGtq/f3/ukczMzBUrVnB1JKKKiopK54gmJiauX78+MjKybdu2Qo7cdWzbti1Cpvq5+FbFI2OJiL19U5Fza/yQ2FpfWBeooLM4sYX9ukX26xxqDA9bnHe18qjQwnoDIeTfq6++2rhx43Hjxr3zzjurVq3q3bv3lStXPv74Yw+PO7eNTU1Nfemll3788UduMTc3NzIycuTIkW+88ca8efOeeOKJHj16GAyGzz77TCarp1/irl75pZ+O1TdpzjRsRESqwztnjbnPod8OooLO5cQWfvlKZ0l+1v6S3PNlhZWeQgvrCYSQf0FBQfv27Rs8ePAnn3wybdo0jUbz888/jx8/3rSCj49Pt27dTCfI+Pr6jh079ty5c0uWLHn77bd37NiRkJBw8ODBRx55xEk/gZPl5+f/vXfPcU1hxZARRESlauP501NHVnPSEF9QQVfgrBaGB3m8N6mtPNhvQe4Vtuqo0MJ6gGHZqn/1wBuWZW062drK9Y8ePTp9+nRxnTWqVqt9fHysWXP5smXL337/ZpMmuicnERHt3fEonf/5nQccNDBU0KVcOX510zyhzyPVG4xNHtuarZa85d2wv181n3ulvHhW5vlVa9f07dfPys3YRWi1WkyfqBX2CB3L1ilH4pqi5CBff/Z5ekWJduAwIiKWVZ3YO3NUUwd9FiroapyyXyiTSpa+1EGuYpbkXdWxxqormPYLt/733T+4E4QQXEtycvK1GzekzVszwaFExF5LCVJRXJsQR3wWKuianNLCEb2jmwTKSn18ttw7leLuqFS+n4S3mT5lKo6Ruh+EEFzLqpUrK4zGioF3LuqhPHVw2vAYR3wQKujKnNLCFS93kOlKV+Vfr3ankP6ba4/vC90PQgguRK/Xr1mzRhrdhAmLJCLSVhjPn37KAbMmUEHXJ3wLe3YM6xDrV+7r+0fBzRpHhXNn3BFCCC7kzz//1BiM2gEJ3CJ77lRcu7DwIA9+PwUVFAvhWzjv2VZyo2Z14Q1DzWcRooXuByEEF7LgvfclASFSLPQAACAASURBVEFM4zunxnglHXxxeGN+PwIVFBeBW9i7c3jjEGWpp+fuYksfhxa6GYQQXEV+fv6Jfy/o+w65s1yQZ8y4ObRnFI8fgQqKkcAtfOfplgoF+21RjUdH74wKLXQjCCG4ioUffkhSGdO2E7fInDo8pn+MUiHl6/1RQfESsoUjekf7kC7LqD9X5UIzlUeFFroLhBBcxVerv2V69iWJhIiIZZVJh6cO5+1eE6ig2AnWQomEeXPcfbJgv7W17RQSWuguEEJwCYcOHSosLqa4eG6Rmz7YpWUwL2+OCroHwVo4bnATQ072seKcQkPtN/NDC90AQggu4Y3Zs2Wt2pHXnVue8jh9EBV0J8K00M9bMaxXtCQ8fGthhlWjQgtFDiEE59PpdIdOnDT27HdnWVthPJ80fjAP0wdRQfcjTAunP9pUVl68UW1VCAktFDmEEJxv0aJFjLcP0+jON4LsuVNx7cIjgus6fRAVdFcCtLB7u9AgT0kRa7yoKbZ2VGihaCGE4HyffbmKevQ1LXqdPlT36YOooHsToIUvjYyVBvtvUdvw/mihSCGE4GSpqamZmRlMp7g7ywV5xts36jh9EBWsDxzdwjH9GhnycnYVZxrJhnvVoYVihBCCk82ePVvavDV5eHKLzMnDYwfUafogKlh/OLSFDUO9YqP9dSrV2dJaJhRWHhVaKDYIITjZlh072Qd63VlgWWXS4SnD7J8+iArWNw5t4TMDGsoCfbeXZts8KrRQVBBCcKatW7dW6HRMs5bcInstJcjD/umDqGD95LgWPta/sSEna686x4Zjo6ZRoYXigRCCM733/vuyzvffuZoMkSrJ/umDqGB95qAWNgz1imnoVy5hUsqtPXf0nlGpfBeFtZkwbnxqaiqPowLeIYTgNDqd7uTZs8Yu3e8saysM5+ycPogKgoNaOKpnpCQocH9Jrn0vD5erWKKQkBAehwS8QwjBaZYuXcp4eDINorlFu6cPooLAcUQLB98fodCW7i237XwZk+3FGcMTEnx8fPgaDzgCQghOs3LlF0znB0yL9t19EBUEc7y3sGvrYH1p6fWSglKj3o6X76jInzh1Ci8jAcdBCME58vLyrt26yXbodmfZrrsPooJQFb8tlEqYBztFSP0DTpcW2Pray+XFpVLq1atX7auCUyGE4BwL5s+XevkwYRHcoh3TB1FBqAm/LRzZPUzupTyhsfno6LaS7InPTZZI8GvW1eFvCJxj7fffk2l3kGWVp22bPogKgmU8trBft0hjUcGxCttOHNWz7C511lMTJtTx00EACCE4QXJycr66hG3bkVu09e6DqCBYg68Wxjb0kbDG9NICHWu0/lWH1NktW7aIjeXhJirgaAghOMEnCxcyUqnpfFGb7j6ICoL1+Gphh5ahMk+fK+Vq61+yvSL/meen1uVDQTAIIQhNr9dv/PVXaesOxDBEtt19EBUEW/HSwr7tAxhfrwuaIivXL9BrT6lzR40ebfcngpAQQhDatm3bDBKZvk0HbtH66YOoINin7i18oE2IkvRndKVWrr8D0wdFBSEEoX214vOKcg0Tex+3aOX0QVQQ6qKOLYxrE1yWm3+posTK9TF9UFwQQhBUfn7+33v/UTVoRAolkbXTB1FBqLu6tNDPWxHg73m7tNDI1n79bUwfFB2EEAT1w7p1wSqv8tbtuEVrpg+igsCXurSweYy/VKHM0GlqXRPTB0UHf1UgqNUrv1Ab9MTdd8mKuw+igsAvu1vYOdZH4uF5U1tmeTVMHxQjhBCEk5ycfOvmrVJdBRMZRVbcfRAVBEewr4XtmvgqPOQ3KmoJIaYPihFCCMJZvWpVG7m3IroJdwNCy9MHUUFwHDta2LKxP2PQXjeUW14N0wfFCCEEgej1+h++XyeXSDXNWhDVMn0QFQRHs7WFLRr7aQqLbxq1FtbB9EGRQghBILt27YqUe1zSa6hxUyJizyV1axtW7fRBVBCEYVML/X0UCrnsltbSyTKYPihSCCEIZN03q/vJ/G+VFjFRjYnIK+nAS49Uc1wUFQQh2dTCkGCvQq2lQ6OYPihSCCEIIT8/f9+BA42VnqqAIJLLa5o+iAqC8KxvYWSol0ZXUdOzmD4oXgghCOGHdese9AtLrygzRjWmGqYPooLgLFa2sHGYh5E1VhgN1T6L6YPihb8zEMLqlV8MUgWf15WWRzeudvogKgjOZU0Lm4apZDJZiVFf9SlMHxQ1hBAcLjk5OePW7S5egf/qypiIhlWnD6KC4ApqbWFUmJdKKdNUt0eI6YOihhCCw61etWqId5iEYW6VFjHhDVRJh8ynD6KC4DostzA0UCWTMZrq9ggxfVDUEEJwLG764EDvsFx9BUmlJJMZzp0yTR9EBcHVWGihr5ecIdJVue42pg+KHULoKHq9Pj09PTPThms46XS669evZ2dnO25Uwtu2bVuk3KOR0utmRakiMMT87oOoILimmlro4yk3GllDlRBi+qDYIYQOsXTp0vDw8EaNGkVERLRv3z4xMdHy+izLLly4MCwsrHHjxmFhYV26dElKShJmqI62euWXA+UBRHRTW2YICTPdfRAVBFdWbQt9veQGo9HAGiutjOmDYocQ8m/lypUzZsyIi4vbtm3bunXrioqKBg4cePXqVQsv+fTTT2fPnt2rV6/t27evXbs2IyOjf//+N27cEGzMDpKfn79n7z99fcOI6Ja+vMLXl5s+iAqC66vaQh8vuV5vkDL3/NrE9EE3IHP2ANyNRqOZM2dO8+bNN2/eLJfLiahly5adO3d+7733vvvuu2pfUlxc/O6777Zt23bjxo1SqZSIYmJievbsOX/+/JUrVwo6er79sG5dD/9wb6mciK4bdExh7tgBMReuFaGCIAr/tfC33xf26tUp3NdLodUZZAxjvg6mD7oB/OXxbM+ePfn5+Y899hhXQSLq1KlT69atN2/erNPpqn3Jjh07iouLH3/8ca6CRNSjR4+YmJiNGzeyVtwO25WtXvnFQGUQ9+cMY4Xq9rVe7YJQQRAR8/1CD6XUaGAlZh3E9EH3gBDyjPtur2fPnuYP9ujRo7i4uKajozW9JDc3Nz093WEjdTjT9EFuMau81EdOM5aeRAVBXO45RsqQirl7IA3TB90DQsizW7duEVFISIj5g9zi7du3+XqJKJimD3KLFYaKktIKVBDEyNRCIvKU3A0hpg+6B3xHyDONRkNEvr6+5g/6+/sTUWlpqYWXVDr32vJLsrOzk5KSAgICiKhRo0YHDx7kYei80uv169Z+vyykDbfIEulYY/fR3VFBEKlmXWMffLLnzlV/e/33FUaBXnuqOOenIUNKSkqcOzYLDAaDQqFw9ihcHULIM6VSSURqtdr8weLiYiLy8Kjm3numl1T6t2T5JaGhoe3atdu9ezcReXl5ueCGvmXLlgYKz0ZKL26x3Ggw6A0nNiU2bh8d06GxU4cGYI/blzMOrjugkDKmPcIdxRnDhw4NDw937sAs02ot3UkYODg0yjPuX0VeXp75g9xiWFiYrS+x8G9MKpUGBAQEBAS4YAXJbPogp9SoZxjaOK/nr+9svHY6zXnjArDH7csZP83+MSTAg2HlpgcxfdBtIIQ8a9euHREdO3bM/MHExEQPD49mzZrZ9BJfX9/GjRs7aqCOZD59kKMxGhhiHuwQtnlhL7QQxIWr4IIp7W/nagJVdw5yYPqgO0EIeda/f38vL68NGzaYZj6kpKScPHly8ODBKpWKe+T27dvnz58vKyvjFgcPHqxUKtevX296k/Pnz1+4cGHYsGGmCRXiYj59kKNjjTKZpFSjj++IFoKYcBVc/UZceraGGsdGyu/8K8b0QXeCv0We+fr6vvrqq0lJSc8991xycvKBAwdGjRoll8vnzJljWuedd95p27at6SJqwcHBM2bMOHz48EsvvfTvv//u3bt3zJgxHh4eb7zxhpN+iLoynz7IMbBGuUxSUqYjIrQQxMJUwWHx0V9tTa0IiGgoURCmD7odnCzDv7fffruoqGjFihVff/01EYWGhm7cuLFjx44WXjJv3jy1Wv3FF1+sWLGCiCIiIjZv3tyqVSuBRsyrO9MHo+83f9DAklQqKS69c0kBroWPvL7x0XdG4dwZcE2mCg7vFf3PiUyN1EOu10VJFYTpg24He4T8k0gkixcvvn379r59+xITE2/evDl06FDzFT7//HONRtO9e3fTIzKZ7LPPPrt169a+ffuOHTuWnp4+YMAAwQfOj0rTBzlShiQSibrs7rV1sF8Irsy8gkS08o9UTaee8qyMhgovwvRBt4MQOkpwcHB8fHy3bt1M11ozkclkKpWKuTcVRBQaGhofH9+1a1eZTKx76qa7D1Z6XEoSYhjTHiEHLQTXVKmCpRr91v3p1DHOmJcdpfDE3QfdD0IIfDLdfbDS4zKGYY1UKYSEFoLrqVRBItrwd5ostil5eGpL1JEKT9x90P0ghMCnStMHTTwkUp3ekJ2vqfoUWgiuo2oFiWjZ5mtlHXuy2RnBnj4yhsH0QfeDEAJvqk4fNPGQyDQV+uvZ1YSQ0EJwDdVWMC2j5N/UAqZFW8q41VTpjemDbgkhBN5UnT5o4imRGg2Gq5nlNb0WLQTnqraCRPT1H1eZTnEkk0lvpreVefyF6YPuCH+dwJuq0wdNJAyjkMrTs6q/hjgHLQRnqamCLEtfbU3VdnyQiJRpKS1UfrvVmZg+6H4QQuBHpbsPVuWlUGZkl1l+E7QQhFdTBYlo78lMjdSDaRBNLFuedTtfX3Ff8/swfdD9IITAj2qnD5oLUHjk5dd+txq0EIRkoYL03/RBImIzb/kpPPbpisZNekbwMYLDIYTAg5qmD5prIFdJpNLs/Bq/JjRBC0EYlitYUqbbuj+dOt1PRGza1dYevqfUuY+MGCH4MMHhEELgQU3TB81FM3Klr/fF60XWvCFaCI5muYJEtOHvNHlsM/L2ISJVyiWZXj88IcHb21vYYYIQEELgQU3TB801kKkMjOzfa4VWvidaCI5TawWJaPnvaaUde3B/ZlMvXyMdpg+6K4QQ6srC9EFzDZWe2jLt6atq698ZLQRHsKaCd6cPErF5OYxer1NIMX3QXSGEUFcWpg+ai1Z4sRpNUmqxTW+OFgK/rKkgmU0fJCI25VKgQoXpg24Mf69QVxamD5oLkatYg/5KWoGt748WAl+srCDL0ldb7kwfJCKPC2cLK8owfdCNIYRQJ7VOHzRhiKK8/UtLtTkFtZ84WglaCHVnZQWJaN+pzHK5J9MgmojIaKy4erFVC9x90J0hhFAntU4fNNdC7qUKDjyWnGvHB6GFUBfWV5CIPv89tcx0msyNNJlUNnX6Sw4eIDgTQgj2s2b6oLm2cq8Kg+TweXtCSGgh2MumCpruPsgtSpJPGw163H3QvSGEYD9rpg+aa+XpR+qSv8/k2/2JaCHYyqYKEtH63dfksc3Ix5dblJw9+dCDD+Lug+4NIQT7WTN90FwTpY9BU3b23yyjkbX7Q9FCsJ6tFaRK0wfzc3Xq4lfefMNhAwSXgBCCnaycPmhOxjCNvQOkSuWl67ZNoqgELQRr2FHBa7dLLl4rZFq2vbN8LkmlVPbp08dRQwTXgBCCnaycPljJA0pf8vbbczKzjp8e3zHsl/d7bJi7AS2EatlRQSL6ZstV6tiNpDJuUZqUOPzhIZg+6PbwFwx2snL6YCWdPPz1JeWbDtU1hETUPy5yw7yeaCFUZV8Fze8+SERUXKTLzvi/uXMdMkRwJQgh2MP66YOVtPcMMKiLDp+6rdMb6z4MtBCqsq+CZH73QSIiYs+cCAoMatGihQPGCK4FIQR72DR90JxKIo31DlD4+dg3m7AqtBDM2V1BMrv7IIc5cXjc2DG8jg5cFEIINtPr9evWfj/I6umDlfRW+lfIPLcfvc3XeNBC4NSlgpWmD7IFeYaczLf/7//4HiO4IoQQbHb9+vVSTZmR7JwC0cM7mM3L23iAh68JTdBCqEsFiWjD32my2Kam6YN0KrFJ45jAQJsP/oMYIYRgs9jY2G/WrHk582xqeYk9L1f5eJAkPaP4eoY9L68JWlif1bGCRLRs87WyjnePi9KxAy+/9CI/gwOXhxCCPcaMHbts1Zczs+xsYW/vYAoK3bDnOr+jQgvrp7pX0Pzug0TE3rxOmrJp06bxN0ZwaQgh2KkuLRzkHWrML/52xw3eR4UW1jd1ryDde/dBImKOHXywWzepVMrTGMHVIYRgP7tb2NbTX15Rce0mz0dHOWhh/cFLBStPH9TrDacS33/vPX6GCGKAEEKd2NdCCTH9fMIkQSEb9qQ7YlRoYX3ASwWp0t0HidjkJG9v7/j4eD7GCOKAEEJd2dfCYb7hhpyCFZuvOmhUaKF746uCxN19sEMP0yKz/+9xo0fV8T1BXBBC4IEdLWzh4evHSPLL2CPnchw0KrTQXfFYwcrTB3OyDBk33583r85jBDFBCIEfdrRwtE+4VuGz9NcUx40KLXQ/PFaQqt598PDeFs2aBgXZfBFdEDWEEHhjawsf9o9kszN/35tWqNY6blRooTvht4J0790HSaczHD805623eHlnEBGEEPhkUwv9pYpuPiGykLAfd6Q6dFRooXvgvYKpt9Tmdx9kkxLlcvnYsWN5eXMQEYQQeGZTC5/ya6jPLZz/w6W63LPeGmih2PFeQSJavTWVOty9+6Bk785RQxNw98F6CH/lwD/rW9jW0z9MIi9mlb/v539yfSVooXg5ooJ3pg92ujN9kL16yaAuegfTB+slhBAcwvoWPuPbUKult75OFmBUaKEYOaKCVOXug7I925qEhzVt2pTHjwCxQAjBUaxsYV+/cM/S0psFuv1JWQKMCi0UFwdVkO69+yCbk2lIu/rK66/z+xEgFgghOJA1LZQyzET/KK3EY843QuwUElooHo6rYEmZbuuBdOp0P7co/3ublGGeePJJfj8FxAIhBMeypoXDAxoqiwqTUor3nuTzJoUWoIWuz3EVJKINf6fJmzQjbx8iouJC/blTwwcP9vHx4f2DQBQQQnC4Oy2s+f6FCkYyOaCxTu754tLTrGPPHr0LLXRlDq0g3Tt9ULpnu7dCOXX6S474IBAFhBCEMGbs2IXLllrYLxwe0MCzWH29QL/1oMNPHzVBC12ToyuYcqP47vTBEjV7/LCnStmrVy9HfBaIAkIIAnl01KMWjpHKGcn0oCY6LU1fdtrg4DmF5tBCV+PoChLRit+usF0e5KYPSvdsj1J5TZo6BdMH6zP83TtEUVHRrFmzWrduHRUVlZCQcPDgQcvrf/fdd49VkZiYKMxoBWP5+8KBfhHhOjZXr/jit0tCjgotdB0CVLBca1i95aquazwRkbqYjh3I11c8NWGCgz4ORAEh5F9ZWVnv3r2XLVsWFxc3YcKEixcv9u7de8eOHRZecubMmQ0bNqSkpKSaKS0tFWzMgrHQQoZodnBTXb76jS/OZueXCzkqtNAVCFBBIlq3LZWiYpjgUCKS7tra0SOgdauWsbGxjvtEcH0yZw/ADS1ZsuT06dNff/31s88+S0QzZ85s27bt1KlTL1++LJfLLbxw//793t7eQg3TacaMHUtE05+b8mlYuyaqe37eDl4BD3oEHPWVvfDpqQ3vdxdyVFwLR8/ZMPrd0TEdGgv50UBCVZBlaf4Pl8r6j2eI2PxcyalEqW/QM89Pddwngihgj5B/a9as8fPze+qpp7jFwMDA8ePHp6Wl7d2716njciEW9gv/F9KUvZ257VjWPycEmkphgv1CZxGmgkT058EbuXoF07QFESm3/jrCP/JcacGo0aMd+qHg+hBCnuXl5V25cqVPnz7mO38DBgwgoiNHjlh+bWpq6u7du48dO1ZeLuiBQaeoqYVBMuXLwbF6Vv7UB4ll5XqBR4UWCk+wChLRW99cKOuVQAzD3kiTXrnoL5ENT0jA9EFACHl27do1IgoPDzd/MDIykojS0tIsv7Z9+/b9+/ePi4sLCwtbsGABK9iUOiepqYXDAho2Y6UFMt/pS04JPyq0UEhCVnDHkVupBUamXWdiWeWvP0wPbrJHWzhx6hRHfy64PnxHaBWDwaDT6SysIJVKuV3AkpISIgoMDDR/llssLi6u6eXNmzf/8MMPO3bs6O3tnZycvHDhwjfffFOn0/3f//1ftevn5eVdvnz5oYceIqLIyMgvvvjC9p9JaKWlpQzDVHrw4YSE8mVLZ7708qfhd78vZIjeDW3x5PXEn/9RjOrVYNADDQQeKr4vFIaQFWRZ+t/nZzV9H2EYhj15NFRd0iy0QUlFVufOnbl/s1aqdjN2ZQaDQaFQOHsUrg4htMqSJUteeeUVCyuMHDny119/JSKZTEZEWu09t1znDnVaOFNm6tS7X9d37959xIgR7dq1+/DDD2fNmuXl5VV1fT8/v/Dw8DfeeIOIvL29PT09bft5nMFgMFQ7zvFPPaVUKF+eMtW8hZEKj1dCmn2kvvnke0cv/5wQ5KcUdrBoocMJWUEi2vh32g2NgmnbiTRl8j82vB3RZntJ9sTnJtt6elpNm7HLsvx/8MBBCK3Sp0+fxYsXW1ihWbNm3B+4nb+8vDzzZ/Pz86nKbqIFwcHBI0aM+Pzzz8+cOdO9ezUnT8pkMl9f3/79+1v5hq5AIpHUNGd57BOPMxKm0nmkD/s32KspSPJgRr516J9lfSQSof83HC10HIErWKE1TF92umz4swzDyP78ra9XUHOV72uZ5+dNnGjrPHoLm7FrEtf+q7MghFbp1KlTp06drFkzNjZWLpdfvHjR/EFusUWLFtZ/Ivd/nfXn/+aqnVPxTliLx68fO8X4zv7izKJpHYQfFVroCAJXkIgWrrtQGtaIib2PTUuRnzk5I+b+Q+rsli1bYPogcMT0vzaioFQqe/funZiYmJl59+z/zZs3E9HAgQOtfBOdTrdjxw6GYe677z6HjNIlVT13xksiWxzRVpeV+/nvqZv3CXcNUnM4d4ZfwlcwLaNk0Q//lg0ZSzqd4sfVc0Kbe0vl2yvyMX0QTBBC/s2aNctoND7//PPcl/C//vrrxo0bhw8f3rx5c26F48ePBwUFzZw5k1vMycl55ZVXkpKSNBqN0Wi8ePHimDFjzp0799hjj1U6+9TtVW1hU5XPm6H36Spo/HtHzl8tcMqo0EK+CF9BIpow/5iu5wAmIEj6129dJKp437ACvfaUOhfTB8EEIeTfwIED33///T/++CM0NDQiImLUqFHt2rX76quvTCvodLr8/HzTuWparfaTTz7p1KmTp6enh4dHy5YtN23aNHTo0FWrVjnpJ3Cmqi0c4Bcx2idMp/Tp89KeG1nOuewcWlh3Tqng2j+vnrylN/YcyF65qDp59K3Q+4hoR3EGpg+COcbtJ6s5S3Jy8o4dO9Rqdfv27YcMGWJ+BnNhYWFiYmJUVFSrVq24R9LT0w8fPpyenl5cXBweHh4fH9+uXTsLb3706NHp06cfO3bMsT8Dr9RqtfW/en75+Wfz7wuNxL52+/wpD0mYrOzU6oEBvs45HXxX4u3Rcw7g+0I7OKWCN7NLWz35V9nE/zH+gbKP5i4Kvq+rdxARTcxI+nzDT3369LHjPW3ajF2BVqvF9IlaIYSi5PYhpCot1LLGKTeT0v097/PVHvisr5eHc87zQgvt4JQKGo3s/VN2n4nsauw9WL5qydBi7czQZkR0ubx4TvHVtIzb9p38iRC6JRwaBRdV6RipgpEsi2wXmFd0uVgR/+KekjLnnE+LY6S2ckoFiejtr87+W+Zp7D2Y2f1ndE7u9JCm3OPbSrInPjdZXFMgwNGwNYDrqtRCH6n8y4advHILLpaoer6wR40WujxnVXD7kVtLfr1aPnYKe+m8av/fH0e0kTIMEelZdpc6C3cfhEoQQnBplVoYKFN81bCTZ2bu5TKP7lN35xQ45+rkaKE1nFXBy+nFj/3f4YonprKaUvkP3yyObBssu3NlIkwfhGohhODqKrUwVK5aHdXJOys3xRDQfsL2y+k1XsHVodBCy5xVwdzC8j7T95QPHMUEhSpWLX0luGkbT3/Ts5g+CNVCCEEEKrUwRK5aHdU58HZmnndk10k7DiRlOWVUaGFNnFXBkjJdn+n/5LfqzrbtIl/16ViP4If9I03PYvog1AQhBHGo1MIgmXJNVOdGmdnlQVGDXj2waN0Fp5z+jBZW5awKaioM/WfuS/Vvqu8zRP7N8t4G2XPBTcxXwPRBqAlCCKJR9dyZVQ07tssrMvqFvLc5Y8ir+4pKtLW+Ce/QQnNOrOCAmXvPSSO0Qx+Xr1nZpbhsTmjlS/vuqMjH3QehWgghiEmlFqok0qWR7QaVk7GkYl9ZWLMxW3cl3hZ+VGghx1kVLCrR9nzh71MUUfHI0/K1X7bPLVgQ3lpy710XLpcXl0qpV69eQg4MxAIhBJEZM3bsJ5+tmJl5Nq2ihIgkDPN66H3PK4PZ8+fyug0Y8c7xCR8kFpcKPbMCLXRWBW9ml3Z6ZscFv/u0j4yXr17RKTv/o4i2UrMKskT7i7Pez7s85YUXMH0QqoXNAsRn3Pjxy7768uXMu9cjHR0Y/XF4a4/df2m79d6QExQ94vdvfr9iNAr6tWF9bqGzKnj0XE67p7bdbNNH13eY/IvFDxSVLopoIzOr4PGSvMkZSWsVJfO//PzNt+cIOTYQEYQQRKnqtbk7ewV+H921wYF9VFRW8vi0mT/dbj1+m8BHSutnC51SQZalJb9c7Dtjb/Hwica2neXLFiRUSOaZHRE9XpI3KSPpS1nh3JXLz12+NHr0aNyiFmqCEIJYVW1hhMLju+gu8Zl5ip+/LRs+/kq3Rx6df6bDxB1C5rC+tdApFdx7MrPLpJ1vb7xdMe1N8vSSLZ0/WRn8v9BmXOiQQLAVLrotSvXhottWqnRtbs6OooyF2Zf1Qx5hH+jN/nvWc/emxj7GDya1HtozivcBVKueXJtb+AoePJ316hfnzqWXlsc/zHTrbUXh2gAAIABJREFUwZ5KVPz+y7ywlt19QojoeEnel+p0CvCdO/+DUaNGOaJ/uOi2W0IIRQkhNFdtC29oy17LOJ8VGal7fCJ5egufQ7dvocAVrJRAMhplv/3oe+Hs0sh2jZXeAiSQgxC6JYRQlBDCSqptoZ5lP8+9uqkkSzdmAtOyLbGswDl04xYKWcHKCZRI2LwcxZrPO2np3fCWF8qKhEkgByF0SwihKCGEVVXbQiI6XZo/J/PfspatdSOeIJVK4By6ZQsFq2DVBBIRe+Kw7Pf104JiYuSeQiaQgxC6JYRQlBDCatXUwjKj/uPslH8qCnRjJzLNWxGRkDl0sxYKU8FqE0glavmGtYHp6U/5NfijPEfgBHIQQreEEIoSQliTmlpIRMdK8t7J/re8RVvdI2PIw5NIuBy6TQsFqGD1CSRiTx+Xb/qpu8o/k7RMoJ/wCeQghG4JIRQlhNACCy0sM+qX5FzdVZarGzWOadPxzqOC5NANWujoCtaUQCrMl2/43uNmur9c7hES5KwEchBCt4QQihJCaJmFFhLRmbKCuVkXi6OidaPGk99/N6tzfA5F3UKHVrDGBBoMzIHdzO4//eSKkLDQdxbMd2ICOQihW0IIRQkhrJXlFupY4ze5134puqUfNJy69ybT71YH51CkLXRcBWtMIBF79ZJsw/fS8rIGwcEffLTI6QnkIIRuCSEUJYTQGpZbSETXK0rfzb543VNZMWYC08DsV7wjcyi6FjqogpYSmJcj+/0Xw7UrEf7+nyxb6iIJ5CCEbgkhFCWE0Eq1tpAl+rPw1pLcq/qO3QxDRpJKZfaco3IoohY6ooIWEkiaMmbnVsOx/cG+fp8uXfL444+7TgI5CKFbQghFCSG0Xq0tJKJig25xTso+Tb7ukbFMh673POeYHIqihbxX0FIC9To6uMf491++np6LPlwwadIkV0sgByF0SwihKCGENrGmhUR0vqzwvexLeSHBFaPHMyHh9zzngBy6eAv5raClBBqN7PHD7PZNnjLZ+3P/7+WXX3bNBHIQQreEEIoSQmgrK1toZNn1BTdW5V0z3h9vGJBACuU9T/OdQ5dtIY8VtJRAlmVPH2f//FXJGue8/tobb7zhygnkIIRuCSEUJYTQDla2kIjy9BUf56QcrSjWjRjLtOtc+Wlec+iCLeSrgrUk8Nwp+vNXmU772oyX3333XddPIMfpm7GtEEJrIISihBDax/oWEtHp0vz3cy4XhoRWjB5X+Ugp8ZlDl2ohLxWsJYHnk+jP32QVmv+99OLs2bN9fX15GLdQXGEztglCaA2EUJQQQrvZ1EIDy/5SkP51Xlr1R0qJtxy6SAvrXsFa9wLZv36Ta8tnTJu2YMEChmFcZKuwnugGjBBaAyEUJYSwLmxqIRHl6Ss+yb16pLxQN+Lxao6UEj85dHoL61jBWk6HOXOC3bZJrtf978UXPvjgA9OBUNfZKqwkugEjhNZACEUJIawjW1tIRKdLC+blXC4ICa4YNZ4JrXKklHjIoRNbWJcKWkqgwcAmJbLbf1ewhlkvvfT+++9X+i7QpbYKa4huwAihNRBCUUII686OFhpYdgN3TmlcD8OAYaSscqSU6ppDp7TQ7gpanBeoZ48fYndtUTLMazNnzJ07t9rTYVxtq6iV6AaMEFoDIRQlhJAXdrSQiPL12sW5KYfKC3XDx1SefW9ShxwK3EL7KmgpgTote2Q/+/dfHnLZm6+9anlShAtuFZaJbsAIoTUQQlFCCPliXwuJ6GxZwbycy3lBQRWjxjNhEdWvZG8OBWuhHRW0lMDycjq8x7h3p6dS+fYbs1999dVaJ0W45lZhgegGjBBaAyEUJYSQR3a30MiyGwtufJF3zdi1u2HQcFKqql/PrhwK0EJbK2gpgWWlzP5dhoN7vD0933l7zowZM6ycF+iyW0VNRDdghNAaCKEoIYT8sruFRFSg136am3JAU6AbOprpFEc1BcD2HDq0hTZV0FIC1cXMnu2GYwd8vL3nvfvOCy+8YNPUeFfeKqolugEjhNZACEUJIeRdXVpIRBc0Re/nXM729akYPZ6JrDlyNubQQS20voKWEliYL9n9lz7pqJ+P7/x570+ZMsWOq8O4+FZRlegGjBBaAyEUJYTQEerYQiOxWwpuLc9LNbTrrH94JHl61biqLTnkvYVWVtDS/QJzs2W7turOnwrw8f3wwwXPPvus3RdIc/2tohLRDRghtAZCKEoIoYPUsYVEpDboVuSl7lBnGQYOpwd63bMLVYnVOeSxhdZU0FICM2/Jdm7RXUoO8vVd9NGip59+uo7XCBXFVmFOdANGCK2BEIoSQug4dW8hEV0tVy/IvXJNxlSMfIJp1tLSqtblkJcW1lpBSwlMvybf8YcuLSXYz/ejTz4ZN24cL5fJFstWYSK6ASOE1kAIRQkhdCheWkhE+4qzPspNKWsYrX1kTDWX7TZnRQ7r2ELLFbSUwMsX5Du36LNuh/j4fLzkU37vGi+irYIjugEjhNZACEUJIXS0X37+efrkKZ+G17WFOtb4c376t/nX2Y7d9IOGk5fFd6sth3a30EIFa0wgy7LnTsl3bjEUF4b6+n685NMxY8bwfrMkcW0VJMIBI4TWQAhFCSEUwHdr1rw2/eW67xcSUZFBtzIvdXtxpjG+P9urfzV3sTBnMYd2tLCmCtaYQJ2OThyR/v0Xo9OG+vl+tOTT0aNHO+h+gaLbKkQ3YITQGgihKCGEAigpKdm6ZevLU3g4Rsq5pS1bmnftuKZA3+9heqAXyWSW1q45hza1sNoK1pjAUjVz8B86tEchkYYG+C1cvHjUqFEOvWWu6LYK0Q0YIbQGQugQOTk5J06cuHDhgsFgeO2116x5SV5e3jfffHP+/HlPT88hQ4YMGzbMwsoIoQBKSkq8vLzW//ILL98XmlwpVy/Lv3ZeW6Lvn0DdHiSZ3NLaNeTQyhZWrWBNCWRv31Ts26k/n+QlVwYHBcz/+CNHJ5Ajuq1CdANGCK2BEPKvR48ehw4d4v4skUgMBkOtL7l69Wp8fHx2dnZcXFxWVlZKSsrTTz/97bff1vSbCCE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     "metadata": {},
     "execution_count": 13
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    "polar_plot(project(p8, 1:2), γ8)"
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   "metadata": {},
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