Quantum Optimal Control with SciML and Julia

Quantum Optimal Control with SciML.ipynb

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    "# Quantum Optimal Control with SciML\n",
    "\n",
    "As an exercise with SciML let's use `ModelingToolkit.jl` to generate the the equations of motion for unitary evolution and then use `DiffEqFlux.jl`'s ability to differentiate and then optimize the parameters of a differential equation to implement quantum optimal control. We will define a toy problem Hamiltonian with time dependent controls. The unitary at any given time is the solution to the differential equations of motion. Then we can parameterize the time dependent controls as the coefficients of some set of basis functions and ask `DiffEqFlux` to optimize the control parameters such that the final state of the differential equation solution is as close to the target unitary as possible. In essense we get the GOAT algorithm [1] for quantum optimal control for free.\n",
    "\n",
    "# DRAG as a Quantum Optimal Control Toy Problem\n",
    "\n",
    "We will to work through the classic quantum optimal control problem of rediscovering the DRAG pulse shape [2]. Starting from the transmon qubit, the model is a three-level, weakly anharmonic oscilator, with the levels enumerated as $|0\\rangle$, $|1\\rangle$ and $|2\\rangle$. We would like to drive a unitary on the qubit subspace $|0\\rangle$, $|1\\rangle$. The nearby third level leads to two delterious effects from off-resonance driving of the $|1\\rangle \\leftrightarrow |2\\rangle$ transition: (1) population leakage to the $|2\\rangle$ state and (2) the Stark shift leads to a dynamic shift of the qubit frequency during the pulse.\n",
    "\n",
    "If we take the anharmonicity to be $\\Delta$ and work in the qubit rotating frame then the drift or natural Hamiltonian is:\n",
    "$$\n",
    "\\mathcal{H}_{drift} = \\begin{bmatrix}\n",
    "0 & 0 & 0 \\\\\n",
    "0 & 0 & 0 \\\\\n",
    "0 & 0 & \\Delta\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We are then looking for the quadrature controls that will implement an X90 whilst minimizing leakage and the off-resonance effect from the third level. With control over the amplitude and phase of the pulse the quadrature control Hamiltonians are $X = a + a^\\dagger$ and $Y = i(a - a^\\dagger)$. In matrix form these are\n",
    "$$\n",
    "\\mathcal{H}_{X} = \\begin{bmatrix}\n",
    "0 & 1 & 0 \\\\\n",
    "1 & 0 & \\lambda \\\\\n",
    "0 & \\lambda & 0\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "and\n",
    "$$\n",
    "\\mathcal{H}_{Y} = \\begin{bmatrix}\n",
    "0 & -i & 0 \\\\\n",
    "i & 0 & -i\\lambda \\\\\n",
    "0 & i\\lambda & 0\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "where in the harmonic approximation $\\lambda = \\sqrt{2}$.\n",
    "\n",
    "The analytical solutions come from the DRAG papers which tell us that quadrature controls the solution is to put the derivative of the $X$ control on the $Y$ channel. Now let's see if we end up finding something similar to that from numerical optimal control.\n",
    "\n",
    "[1]: Machnes, S., Assémat, E., Tannor, D., & Wilhelm, F. K. (2018). Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits. [Physical Review Letters, 120, 150401](https://doi.org/10.1103/PhysRevLett.120.150401).\n",
    "[2]: Motzoi, F., Gambetta, J. M., Rebentrost, P., & Wilhelm, F. K. (2009). Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits. [Physical Review Letters, 103 (11), 110501](https://doi.org/10.1103/PhysRevLett.103.110501)."
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      "Julia Version 1.4.0\n",
      "Commit b8e9a9ecc6 (2020-03-21 16:36 UTC)\n",
      "Platform Info:\n",
      "  OS: Linux (x86_64-linux-gnu)\n",
      "  CPU: Intel(R) Core(TM) i7-8565U CPU @ 1.80GHz\n",
      "  WORD_SIZE: 64\n",
      "  LIBM: libopenlibm\n",
      "  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)\n"
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      "\u001b[32m\u001b[1mStatus\u001b[22m\u001b[39m `~/.julia/environments/v1.4/Project.toml`\n",
      " \u001b[90m [6e4b80f9]\u001b[39m\u001b[37m BenchmarkTools v0.5.0\u001b[39m\n",
      " \u001b[90m [0f7d4b38]\u001b[39m\u001b[37m CoherentControl v0.1.0 [`~/repos/CoherentControl`]\u001b[39m\n",
      " \u001b[90m [aae7a2af]\u001b[39m\u001b[37m DiffEqFlux v1.12.0\u001b[39m\n",
      " \u001b[90m [41bf760c]\u001b[39m\u001b[37m DiffEqSensitivity v6.19.1\u001b[39m\n",
      " \u001b[90m [0c46a032]\u001b[39m\u001b[37m DifferentialEquations v6.14.0\u001b[39m\n",
      " \u001b[90m [587475ba]\u001b[39m\u001b[37m Flux v0.10.4\u001b[39m\n",
      " \u001b[90m [7073ff75]\u001b[39m\u001b[37m IJulia v1.21.2\u001b[39m\n",
      " \u001b[90m [961ee093]\u001b[39m\u001b[37m ModelingToolkit v3.7.1\u001b[39m\n",
      " \u001b[90m [429524aa]\u001b[39m\u001b[37m Optim v0.21.0\u001b[39m\n",
      " \u001b[90m [91a5bcdd]\u001b[39m\u001b[37m Plots v1.3.7\u001b[39m\n",
      " \u001b[90m [e88e6eb3]\u001b[39m\u001b[37m Zygote v0.4.20\u001b[39m\n"
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     "text": [
      "┌ Info: For saving to png with the Plotly backend ORCA has to be installed.\n",
      "└ @ Plots /home/cryan/.julia/packages/Plots/Xnzc7/src/backends.jl:375\n"
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   "source": [
    "using LinearAlgebra: I\n",
    "using SparseArrays: sparse\n",
    "\n",
    "using DifferentialEquations\n",
    "using DiffEqFlux: sciml_train\n",
    "using DiffEqSensitivity: ForwardDiffSensitivity\n",
    "using ModelingToolkit\n",
    "using Optim\n",
    "using Zygote\n",
    "\n",
    "using Plots\n",
    "plotly()"
   ]
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    "# Analytical DRAG Solution\n",
    "\n",
    "For reference let's take a look at the analytical solution from [1,2]. If we fix the pulse time to $T_{gate}$ and start with a Gaussian pulse shape on the X quadrature:\n",
    "\n",
    "$$\n",
    "\\Omega_x(t) = A_x \\left( \\exp\\left[ -\\frac{\\left(t-\\frac{T_{gate}}{2}\\right)^2}{2\\sigma^2} \\right] - \\exp\\left[-\\frac{T_{gate}^2}{8\\sigma^2}\\right] \\right)\n",
    "$$\n",
    "\n",
    "then the analytical solution for the Y quadrature is:\n",
    "\n",
    "$$\n",
    "\\Omega_y(t) = -\\frac{\\lambda^2 \\frac{d\\Omega_x(t)}{dt}}{4\\Delta}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "[1]: Motzoi, F., Gambetta, J. M., Rebentrost, P., & Wilhelm, F. K. (2009). Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits. [Physical Review Letters, 103 (11), 110501](https://doi.org/10.1103/PhysRevLett.103.110501).\n",
    "\n",
    "[2]: Gambetta, J., Motzoi, F., Merkel, S., & Wilhelm, F. (2011). Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator. [Physical Review A, 83(1), 012308](https://doi.org/10.1103/PhysRevA.83.012308)."
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       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
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       "    <script>\n",
       "    PLOT = document.getElementById('2cf48ee1-f1e7-4870-8908-62217483336e');\n",
       "    Plotly.plot(PLOT, [\n",
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   "source": [
    "# natural units of GHz and ns\n",
    "Tgate = 30\n",
    "σ = Tgate/4\n",
    "Ωx(t) = exp(-(t-Tgate/2)^2/(2σ^2)) - exp(-Tgate^2/8σ^2)\n",
    "\n",
    "Ωy(t, λ, Δ) = -(λ^2/4Δ)*Ωx'(t)\n",
    "\n",
    "p = plot()\n",
    "times = range(0, Tgate; length=51)\n",
    "plot!(times, Ωx.(times), label=\"Ωx\")\n",
    "plot!(times, Ωy.(times, √2, -0.2), label=\"Ωy\")\n",
    "xlabel!(p, \"Time (ns)\")\n",
    "ylabel!(p, \"Pulse Amplitude\")\n",
    "display(p)"
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    "# Equations of Motion\n",
    "\n",
    "Under some Hamiltonian $H(t)$ the unitary $U$ evolves under the equation of motion\n",
    "\n",
    "$$\n",
    "\\frac{dU}{dt} = -iHU\n",
    "$$\n",
    "\n",
    "so for a $D$ dimensional system we have $D^2$ complex equations or $2D^2$ real equations to solve. I had trouble with complex equations and `DiffEqFlux.jl` even though the inputs and loss functions are real (see [this issue](https://github.com/SciML/DiffEqFlux.jl/issues/74)) so we'll use the usual trick of splitting a complex matrix into real and imaginary components and stacking appropriately so that the $D \\times D$ matrix of complex equations of motion becomes a $2D \\times 2D$ matrix of real equations of motion.\n",
    "\n",
    "$$\n",
    "U = U_r + iU_i \\rightarrow\n",
    "\\begin{bmatrix}\n",
    "U_r & -U_i \\\\\n",
    "U_i & U_r\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Since there left half of the stacked form aleady has both the real and imaginary components we care only about the first $D$ columns of the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "3-element Array{Equation,1}:\n",
       " Equation(derivative(Uᵣ₁ˏ₁(t), t), Uᵢ₂ˏ₁(t) * Ax + -1.0 * Uᵣ₂ˏ₁(t) * Ay)\n",
       " Equation(derivative(Uᵣ₂ˏ₁(t), t), Uᵢ₁ˏ₁(t) * Ax + Uᵣ₁ˏ₁(t) * Ay + 1.4142135623730951 * Uᵢ₃ˏ₁(t) * Ax + -1.4142135623730951 * Uᵣ₃ˏ₁(t) * Ay)\n",
       " Equation(derivative(Uᵣ₃ˏ₁(t), t), Uᵢ₃ˏ₁(t) * Δ + 1.4142135623730951 * Uᵢ₂ˏ₁(t) * Ax + 1.4142135623730951 * Uᵣ₂ˏ₁(t) * Ay)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# TODO: explore variables that are functions i.e. Ax(..)\n",
    "# TODO: figure out how to make λ a variable but still work with complex2real\n",
    "@parameters t Δ Ax Ay \n",
    "@variables Uᵣ[1:3,1:3](t) Uᵢ[1:3,1:3](t)\n",
    "@derivatives D'~t\n",
    "\n",
    "# quadrature control Hamiltonians\n",
    "Hx = ComplexF64[[0 1 0];[1 0 √2]; [0 √2 0]]\n",
    "Hy = ComplexF64[[0 -1im 0];[1im 0 -1im*√2]; [0 1im*√2 0]]\n",
    "\n",
    "# DiffEqFlux does not seem to handle complex so we use the usual trick to turn a complex matrix M = Mr + Mi into a real matrix [Mr -Mi;Mi Mr]\n",
    "complex2real(A) = vcat(hcat(real(A), -imag(A)), hcat(imag(A), real(A)))\n",
    "\n",
    "Hdrift = zeros(3,3)\n",
    "Hdrift[3,3] = 1\n",
    "\n",
    "# bring the -1im in here before we separate real and complex\n",
    "Htot = Δ * sparse(complex2real(-1im*Hdrift))\n",
    "Htot += Ax * sparse(complex2real(-1im*Hx))\n",
    "Htot += Ay * sparse(complex2real(-1im*Hy))\n",
    "\n",
    "# equation of motion dU/dt = -iHU\n",
    "U = vcat(hcat(Uᵣ, -Uᵢ), hcat(Uᵢ, Uᵣ))\n",
    "\n",
    "rhs = (Htot * U)[:, 1:3]\n",
    "rhs = simplify.(rhs)\n",
    "lhs = D.(vcat(Uᵣ, Uᵢ))\n",
    "\n",
    "eqs = lhs .~ rhs\n",
    "\n",
    "# loook at some of the equations\n",
    "eqs[1:3,1]"
   ]
  },
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   "cell_type": "code",
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       ":((var\"##MTIIPVar#410\", var\"##MTKArg#406\", var\"##MTKArg#407\", var\"##MTKArg#408\")->begin\n",
       "          @inbounds begin\n",
       "                  let (Uᵣ₁ˏ₁, Uᵣ₂ˏ₁, Uᵣ₃ˏ₁, Uᵢ₁ˏ₁, Uᵢ₂ˏ₁, Uᵢ₃ˏ₁, Uᵣ₁ˏ₂, Uᵣ₂ˏ₂, Uᵣ₃ˏ₂, Uᵢ₁ˏ₂, Uᵢ₂ˏ₂, Uᵢ₃ˏ₂, Uᵣ₁ˏ₃, Uᵣ₂ˏ₃, Uᵣ₃ˏ₃, Uᵢ₁ˏ₃, Uᵢ₂ˏ₃, Uᵢ₃ˏ₃, Δ, Ax, Ay, t) = (var\"##MTKArg#406\"[1], var\"##MTKArg#406\"[2], var\"##MTKArg#406\"[3], var\"##MTKArg#406\"[4], var\"##MTKArg#406\"[5], var\"##MTKArg#406\"[6], var\"##MTKArg#406\"[7], var\"##MTKArg#406\"[8], var\"##MTKArg#406\"[9], var\"##MTKArg#406\"[10], var\"##MTKArg#406\"[11], var\"##MTKArg#406\"[12], var\"##MTKArg#406\"[13], var\"##MTKArg#406\"[14], var\"##MTKArg#406\"[15], var\"##MTKArg#406\"[16], var\"##MTKArg#406\"[17], var\"##MTKArg#406\"[18], var\"##MTKArg#407\"[1], var\"##MTKArg#407\"[2], var\"##MTKArg#407\"[3], var\"##MTKArg#408\")\n",
       "                      var\"##MTIIPVar#410\"[1] = Uᵢ₂ˏ₁ * Ax + -1.0 * Uᵣ₂ˏ₁ * Ay\n",
       "                      var\"##MTIIPVar#410\"[2] = Uᵢ₁ˏ₁ * Ax + Uᵣ₁ˏ₁ * Ay + 1.4142135623730951 * Uᵢ₃ˏ₁ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₁ * Ay\n",
       "                      var\"##MTIIPVar#410\"[3] = Uᵢ₃ˏ₁ * Δ + 1.4142135623730951 * Uᵢ₂ˏ₁ * Ax + 1.4142135623730951 * Uᵣ₂ˏ₁ * Ay\n",
       "                      var\"##MTIIPVar#410\"[4] = -1.0 * Uᵢ₂ˏ₁ * Ay + -1.0 * Uᵣ₂ˏ₁ * Ax\n",
       "                      var\"##MTIIPVar#410\"[5] = Uᵢ₁ˏ₁ * Ay + -1.4142135623730951 * Uᵢ₃ˏ₁ * Ay + -1.0 * Uᵣ₁ˏ₁ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₁ * Ax\n",
       "                      var\"##MTIIPVar#410\"[6] = 1.4142135623730951 * Uᵢ₂ˏ₁ * Ay + -1.4142135623730951 * Uᵣ₂ˏ₁ * Ax + -1.0 * Uᵣ₃ˏ₁ * Δ\n",
       "                      var\"##MTIIPVar#410\"[7] = Uᵢ₂ˏ₂ * Ax + -1.0 * Uᵣ₂ˏ₂ * Ay\n",
       "                      var\"##MTIIPVar#410\"[8] = Uᵢ₁ˏ₂ * Ax + Uᵣ₁ˏ₂ * Ay + 1.4142135623730951 * Uᵢ₃ˏ₂ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₂ * Ay\n",
       "                      var\"##MTIIPVar#410\"[9] = Uᵢ₃ˏ₂ * Δ + 1.4142135623730951 * Uᵢ₂ˏ₂ * Ax + 1.4142135623730951 * Uᵣ₂ˏ₂ * Ay\n",
       "                      var\"##MTIIPVar#410\"[10] = -1.0 * Uᵢ₂ˏ₂ * Ay + -1.0 * Uᵣ₂ˏ₂ * Ax\n",
       "                      var\"##MTIIPVar#410\"[11] = Uᵢ₁ˏ₂ * Ay + -1.4142135623730951 * Uᵢ₃ˏ₂ * Ay + -1.0 * Uᵣ₁ˏ₂ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₂ * Ax\n",
       "                      var\"##MTIIPVar#410\"[12] = 1.4142135623730951 * Uᵢ₂ˏ₂ * Ay + -1.4142135623730951 * Uᵣ₂ˏ₂ * Ax + -1.0 * Uᵣ₃ˏ₂ * Δ\n",
       "                      var\"##MTIIPVar#410\"[13] = Uᵢ₂ˏ₃ * Ax + -1.0 * Uᵣ₂ˏ₃ * Ay\n",
       "                      var\"##MTIIPVar#410\"[14] = Uᵢ₁ˏ₃ * Ax + Uᵣ₁ˏ₃ * Ay + 1.4142135623730951 * Uᵢ₃ˏ₃ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₃ * Ay\n",
       "                      var\"##MTIIPVar#410\"[15] = Uᵢ₃ˏ₃ * Δ + 1.4142135623730951 * Uᵢ₂ˏ₃ * Ax + 1.4142135623730951 * Uᵣ₂ˏ₃ * Ay\n",
       "                      var\"##MTIIPVar#410\"[16] = -1.0 * Uᵢ₂ˏ₃ * Ay + -1.0 * Uᵣ₂ˏ₃ * Ax\n",
       "                      var\"##MTIIPVar#410\"[17] = Uᵢ₁ˏ₃ * Ay + -1.4142135623730951 * Uᵢ₃ˏ₃ * Ay + -1.0 * Uᵣ₁ˏ₃ * Ax + -1.4142135623730951 * Uᵣ₃ˏ₃ * Ax\n",
       "                      var\"##MTIIPVar#410\"[18] = 1.4142135623730951 * Uᵢ₂ˏ₃ * Ay + -1.4142135623730951 * Uᵣ₂ˏ₃ * Ax + -1.0 * Uᵣ₃ˏ₃ * Δ\n",
       "                  end\n",
       "              end\n",
       "          nothing\n",
       "      end)"
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    "# now use ModelingToolkit to build a specialized function for these equations\n",
    "# ODESystem expects 1D arrays so vec both sides\n",
    "# use explicit form to get consistent order of parameters\n",
    "# sys = ODESystem(vec(eqs))\n",
    "sys = ODESystem(vec(eqs), t, vec(vcat(Uᵣ, Uᵢ)), [Δ, Ax, Ay])\n",
    "\n",
    "# second return value is in-place version and we'll go head and evaluate the expression\n",
    "display(generate_function(sys; expression=Val{true})[2])\n",
    "dudt = generate_function(sys; expression=Val{false})[2]\n",
    "nothing"
   ]
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   "cell_type": "code",
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   "source": [
    "# build the DE function with time dependent controls\n",
    "\n",
    "# basis of sinusoids to ensure the pulse goes to zero and the start and finish\n",
    "# the parameters `p` give the N basis coefficients: with 1:N for the X controls and N+1:2N for the Y controls\n",
    "function controls(t, p)\n",
    "    num_controls = length(p) ÷ 2\n",
    "    Ax = sum(a*sinpi(ct*t/Tgate) for (ct,a) in enumerate(p[1:num_controls]))\n",
    "    Ay = sum(a*sinpi(ct*t/Tgate) for (ct,a) in enumerate(p[(num_controls+1):end]))\n",
    "    Ax, Ay\n",
    "end\n",
    "\n",
    "# wrapper function evaluates the time dependent controls and then passes them on\n",
    "function dudt_wrapped(du, u, p, t)\n",
    "    (Ax, Ay) = controls(t, p[2:end])\n",
    "    dudt(du, u, [p[1], Ax, Ay], t)\n",
    "end\n",
    "\n",
    "UId = complex2real(Matrix{ComplexF64}(I, 3, 3))\n",
    "U₀ = vec(UId[:, 1:3])\n",
    "nothing"
   ]
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       "    <head>\n",
       "        <title>Plots.jl</title>\n",
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    "# plot the first three basis functions\n",
    "ts = range(0, Tgate; length=51)\n",
    "ax = plot()\n",
    "for order in 1:3\n",
    "    p = Float64.(order .== 1:2order)\n",
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",
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
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   ],
   "source": [
    "# look at the populations under something a little over a π pulse as a sanity check\n",
    "prob = ODEProblem{true}(dudt_wrapped, U₀, (0.0,Tgate), vcat(2pi*-0.2, [0.1, 0.0]))\n",
    "sol = solve(prob, Tsit5(), abstol=1e-8, reltol=1e-8)\n",
    "pops = []\n",
    "ts = range(0, Tgate; length=51)\n",
    "for t = ts\n",
    "    # the solution is a column stacked version of [Uᵣ; Uᵢ]\n",
    "    u_tot = reshape(sol(t), 6, 3)\n",
    "    U = u_tot[1:3, 1:3] + 1im*u_tot[4:6,1:3]\n",
    "    state = U*[1;0;0]\n",
    "    push!(pops, abs2.(state))\n",
    "end\n",
    "p = plot()\n",
    "for ct = 1:3\n",
    "    plot!(p, ts, [ps[ct] for ps in pops], label=\"|$ct⟩\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization\n",
    "\n",
    "Now for some target $U_{goal}$ let's build a loss function that solves the differential equation to the endpoint at Tgate and then calculates the overlap with the goal unitary using $|tr\\left(U_{goal}^\\dagger U_{solved}\\right)|^2/D^2$ defined only on the qubit subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "loss_adjoint (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lock Δ to -200 MHz for now\n",
    "# docs say ForwardDiffSensitivity is best for small systems\n",
    "prob = ODEProblem{true}(dudt_wrapped, U₀, (0.0,Tgate), vcat(2pi*-0.2, [0.08, 0.0]))\n",
    "function predict_adjoint(p)\n",
    "    Array(solve(prob, Tsit5(), p=vcat(2π*-0.2, p), saveat=Tgate, save_start=false, abstol=1e-8, reltol=1e-8, sensealg=ForwardDiffSensitivity()))\n",
    "end\n",
    "\n",
    "Ugoal = zeros(ComplexF64, 3, 3)\n",
    "Ugoal[1:2, 1:2] = [[0 1];[1 0]]  # X180\n",
    "# Ugoal[1:2, 1:2] = [[1/√2 -1im/√2];[-1im/√2 1/√2]]  # X90\n",
    "Ugoal_adjoint = complex2real(Ugoal')\n",
    "\n",
    "function loss_adjoint(p)\n",
    "    U = reshape(predict_adjoint(p), 6, 3)\n",
    "    Utot = hcat(U, vcat(-U[4:6, :], U[1:3, :]))\n",
    "    m = Ugoal_adjoint*Utot\n",
    "    # manually take the trace of the real and imaginary parts\n",
    "    1 - abs2(m[1,1] + m[2,2])/4 - abs2(m[4,1] + m[5,2])/4\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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   "source": [
    "# as we scan the amplitude we should see the loss function oscillate\n",
    "As = range(0,0.2; length=51)\n",
    "plot(As, [loss_adjoint([A, 0.0]) for A in As])"
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    "# double check that we can take a gradient on either side of the minimum\n",
    "display(gradient(loss_adjoint, [0.05, 0.0]))\n",
    "display(gradient(loss_adjoint, [0.11, 0.0]))"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "# Optimized Pulse Shapes\n",
    "\n",
    "Wonderfully the optimal control finds the exact solution we expect (up to a sign for X180). \n",
    "\n",
    "1. With a single sinusoid basis function it optimizes the area under the curve to perform a π (or -π) X pulse and puts zero amplitude in the Y quadrature as expected.\n",
    "2. With the second basis function the optimization has something that starts to look like the derivative of the first basis function and so the optimization gives that component to the Y quadrature.\n",
    "3. With the third basis function the optimization can smooth out the turn-on and off sections of the pulse and it almost starts to look like the analytical Gaussian solution.\n",
    "4. With the fourth basis function there is little change."
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
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   "source": [
    "# lets look at the optimized controls for varying numbers of basis functions\n",
    "opts = []\n",
    "for ct in 1:4\n",
    "    p = 0.01*randn(2ct)\n",
    "    res = sciml_train(loss_adjoint, p, BFGS(initial_stepnorm=1e-6))\n",
    "    push!(opts, res)\n",
    "end"
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",
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
       "    </head>\n",
       "    <body>\n",
       "            <div id=\"c7217056-4c6f-46db-81a5-e3780f18650d\" style=\"width:600px;height:400px;\"></div>\n",
       "    <script>\n",
       "    PLOT = document.getElementById('c7217056-4c6f-46db-81a5-e3780f18650d');\n",
       "    Plotly.plot(PLOT, [\n",
       "    {\n",
       "        \"xaxis\": \"x1\",\n",
       "        \"colorbar\": {\n",
       "            \"title\": \"\"\n",
       "        },\n",
       "        \"yaxis\": \"y1\",\n",
       "        \"x\": [\n",
       "            0.0,\n",
       "            0.6,\n",
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       "            8.4,\n",
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       "            11.4,\n",
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       "            13.2,\n",
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       "            18.6,\n",
       "            19.2,\n",
       "            19.8,\n",
       "            20.4,\n",
       "            21.0,\n",
       "            21.6,\n",
       "            22.2,\n",
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       "            25.2,\n",
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       "            27.0,\n",
       "            27.6,\n",
       "            28.2,\n",
       "            28.8,\n",
       "            29.4,\n",
       "            30.0\n",
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       "        \"showlegend\": true,\n",
       "        \"mode\": \"lines\",\n",
       "        \"name\": \"Ωx\",\n",
       "        \"zmin\": null,\n",
       "        \"legendgroup\": \"Ωx\",\n",
       "        \"zmax\": null,\n",
       "        \"line\": {\n",
       "            \"color\": \"rgba(0, 154, 250, 1.000)\",\n",
       "            \"shape\": \"linear\",\n",
       "            \"dash\": \"solid\",\n",
       "            \"width\": 1\n",
       "        },\n",
       "        \"y\": [\n",
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          "font": {
           "color": "rgba(0, 0, 0, 1)",
           "family": "sans-serif",
           "size": 15
          },
          "text": "Pulse Amplitude (MHz)"
         },
         "type": "linear",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1)"
        }
       }
      },
      "image/png": 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       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
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       "    <body>\n",
       "            <div id=\"b7276208-856c-4bc9-b7bf-ce08d8be262c\" style=\"width:600px;height:400px;\"></div>\n",
       "    <script>\n",
       "    PLOT = document.getElementById('b7276208-856c-4bc9-b7bf-ce08d8be262c');\n",
       "    Plotly.plot(PLOT, [\n",
       "    {\n",
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       "    <head>\n",
       "        <title>Plots.jl</title>\n",
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y5gvZlCK5EUjWjzMD+FnFWTGU3OzkzM6h/PP9mZ0c4eZNNd5IzE7sL+w3/NxyEtdMs5+y7zupEO/92njnyiNzo0ryYP/PvNlXiliqTBEIGoGgCDX/f3HWIa/ReH3FZSdcasaZM24T2xyzmIuSCIiACIScANe6cuSOF4/OB6YboeaF1RtvvGE/9sV5HExdyLhmldN6OeWTIsLkRqi58yxHSCgVFPjsHXUpnLz447pujl5yiiVHjzITp5zyorU2oa5t9C/XMllGoYSa65w5LTgzcaSMI2b1Jf7T47TquhLXC/OGAEfO3CSWzRsTvPmSOXrPPDjizJFnZ8q5I2ecps2RrMzkCK0j33ytPqHmhTtHjZ3krEuuS4g5Ak9hY4yZsoWaN3Q4dZx9h2JAoeD0dY4gOo+uqo8LRZd9xxlNJxeOVnPGAKe5OyOVTj25BIFLEdwKNW9MkFFD7GqrqyPUHLllu+pKXLfrrN11YlZbv3OEOvu94TYWFGpeqHHNcalSrgLp1K8hoWb/5Prs2pZQcOYBP4M4ZZ83HLMTOfCmEvsS+w9vQHHGB2+KUbB5A8VZFuPmvc/4Z5fHz/PsG2GsT648eLORLDgNnX2ayxy4nIHvHSUREIHcCARBqDkYwScO8MY8P9tYZ864c2ZhcUDETZJQu6GlY0VABAJLgCN5HPHj3UhuROUkN0LtrMulVHPNcH3JGdXi5k3OFMhchZof9Nw8ihegnILJD3x+uHM9KdcjcgqiI9ScmsiRSsoOR1azE6WQF7COGDnSwPMynx/tpkyWUSih5tppXhhnJl6cc1p19tTRzGPY5rrWcvI4ZwMtt88fZtm8scCv7MTROQogR6p5s6O+Zym7FWpetGc+n/qvf/0rzj77bPtueW03DnhDiH2aN1ooyLVtSsZ1n1y3StnniDsTBYHywn5fX6Lcc3ouRxZ5U4JTjp0RY97F52gjN3Lj+mlOEWdZ3LzNrVDXFv/a2NVW13ymfNcXs7reG25jwfcVb3SwrFxSoTYlyywrV4F0znE22GNc+RmTnTjLgX3euXGS+bpzo4nn8fzsxKnvvAlV2+g2bwryc4uzadin3bz3nXhlllfXlHS3PJgnP4O4ppw3LbnfRkM3UXOJtY4RgSgQCIJQc1YZ983IvnnPpU0chOAX/wdz1g1vzvP6kf/rOEhSW5JQR6Fnq40iEHECnITDESyOGnEDLG6M5CSuceSoBEeluHFT5lrVbGzOhb4jVPVh5WZnnDKb+SiWuoTa2ZHaOZYbWHFjrNpG75wLW0eoHUGobYSao0Bcf13bCHW2ULspk+12K9S8A8xRLmf9eX1iw5EuilljdtblNFJKKmWIa2PrSuwbXBPsrH/m6Ban69Y3Qs22c4pzMYXaWUvKxwxxU6/sxJsJvODn6CBTQ4/N4ogb775T0Bl7rqPnnfi6EtdeU0IoKJwCzgsPxoMj/5Rgtp03ljiiSIF0bn6EUajdxsKNUPtlUzLemOE6eI72c5+J7MSYc5kINzLkDIXMxKUn3MOB6/3ZP7ITZ0hQmLlUIXsDNmdTPmfDskK892vr0/kINfPhzUtuCMhNGLknhZIIiEDDBOoS6tiDtT+7vuEcG3eEdfb2T/ngjWbeDMyeIcfrMC4V4zUcbwZyDxb+n+VnV33LpyTUjYuRzhYBEQgAAU45zHVjqsyNk7Kbxo2GKDJc18sRi7oem8XyuGEYRzYoL87IBndM5ppKPnooM/FijRuCOULNTYG4cVT2plw8hyPjlFJHqHlBzrWsHEHMXkPNdeK8kZCLULspk/WoTaidNdu88GSbMhN3uObU3lyE2tl4LXuzKubHf3SMZUPTlikFHF3iaCrrlb0W26kbL+Q5DZUbfXHjIWdDLMaIF/eZiRLNJQPOSG0xhdphSW7cECwz8UYJ+xJH9DgTgqkhoXbOpxxzh3AKRn0zAPg+YBkczWY7ubu48xgtbibFEW7KM3fj5kg2N/hjCqNQu42FG6H2y6ZkjB0/K9hWijE/U5zE0RlKNC8ouYQgM1HEuZ6fM0LYR2pLfI0zJLgRWfazprlem32Ha7R5A7IQ7/3a6lCfUHPjSC7j4Xsp+3PFqV/2kowA/NtTFUWgZASCMELNWXucYcXPvMzEv/GRnrwu4CP8uHcOPxd4A7m+6w4Jdcm6mwoWARHwigAvCDk6V1viKCanHHJ3Z+4azSna2WtnM89zpi9y4x1KLR+Rk5k4isep4RwJ5y7YXB/oJH5Ic4SH02OdUXJeUFN4OULuCDXrynpwAyjeJXUSpxtxtIRSyXWdzvOYOZrNEWauJ+RUcSfxkVQ8LhehdltmbWsqnUcrZT/WixLHGxEcocpFqHnnmJtxMR9ydB5XwzhyR3PKLjcyy7zory22zmOQOOWdHDKniDMvSj8ZUzA5fZqj+c4O17zIpyg6iRLL+HEqONcus2y3Qs1zKFuZ/8CdacvZU77ZLzj6y5sybGvmzAlnpkTm7IdsoWYfpMRwWlvmjAzGiDd1OKro7D5f1/uQz8rmNG7eFCJ3Z7MqsqLMU6pZl8wN3GoTaq5X5iwM9nvnMVxu2dVWR6+mfLuNhRuhLtZnYEMjshRjTufnc9Kd9xE3/OPFJEdhuHbfSc4Nv9pmSzhLW3gDkKPNtSVn93S+zuMyk/OcZz4HmkJfqPd+dj3q4+FMHc++gcmbSqwTN83L5ckOxYql8hWBoBEIglDzc53TuHmT3Nkjgf9veQ3Fm4PcA4fLnXhjnsfy+qq+gRkJddB6qeorAiJQUAJu1lCzYN6x5AUYH3fE0RbKAkejKeGUCU4fonRx7Q1H8jLl3JFxii5HcSlpvFjlyA/l3NmAiiM5vChnPtxIjaNDfDYs1y9SZDlqyQtR3kHl6AplmPWgEHI3Zo5Wcwom13HygpfrjRtaQ+22TGc9MWWV9eFdXP7MC1CWxXXqrCMv3Nkutoc3LjhyzGPrEyrnWbSUMEodZZFt4ZRTjrpnimR9nYFt4hp0bn5Exhzdp0DwnyQfMcabGxyF5sZIfNQRE9eS858refNcTqWneFA2ODWcU8gdKXArhZRQ3gzgqC/XxLPv1SXUrAunWzOulGnGmuew/exXjCn/6TsylC3UTr6cys6bEzyXMs1+S0FmP6Uk15c4C4Fx5IwLig43X2NifPh4L45OUpDJ0Um1CTVvAnHqLOvI9Wecas4p9bwZVYg11LxhxM1l6kvkyLjms4babSxKIdScPcNZFk5ivDjqyvX3zjRr7sXAjeqYansEIOPJ9ywvHLknA28aMp6cIcF+ROnNvonF1xjX+naTZz342cD3HWPPOvDmGj/zeCMwcyf7Qr333fDgUiDWiX2D73dOUWef5w0n5kNu/AxREgERyI1AEISaLeHyLufzizfcuQcE94pwBJufV9yMljfXuFkhb3zXlSTUufUNHSUCwSLAfftjwapyqWrrVqidevJii2JDyeJaVooYJYPSRlnmhVl2ohTy8TK82OU5FCUKMKWYo5GUZ8oiE0WYdeN3jhIyP8o0R1M5LZmyRZHgBSkTL2wpPxzN5PRmXhBzvSwvhClT/GfAVNfGS27L5MU3R0Ep81w3ydFcPvKGd3h5Ec/pUbwhwOmeHNni37mumSPOlOT6xIZ14Y0L1p8jxtwwiTcvOELMqfG8IeEmUR45pZ0syZ18KNaUOf4D5drRzMR/npRJjmpTFrk7N+WCG9plSqhboea6ZN5o4QwDXrRPnTq1XqFmnSj+/AdPkeYNAvYZxp99xRnt5XG1Tfnm1HSKLPsobwrwjrvTjsyZDHWxdHZ+5uuUjswlDuyzvBHB/pR5kVGbUPOmCmWcyyR4s4d9gBvsFUqoc+kLzk2YfIXaTSxKIdS8idXQc6ozZ0HUJtRsI/sY5ZifJ3yvsM/wfc33MKd2Zydn9Lq25SmZx1JMGQM+c54zPCj5vJnF9x/f0+wPTirEe98tD7aV0875eebcIOJ+CpzlwkeJNbTEJJc+qGNEICoEgiDUXO7FvUT4mcf/h7wpy88o53Gn/NzjDEH+v+KNPl7bcVCkrhvREuqo9G61UwREoGgEKJOU3+wp3kUrUBmLgAiIgAiIgAiIgA8JBEGoC41NQp0DUe6w2tDubjlk0+AhnGLEXYCVREAEgkWAj2bitGyOonI0kKNwfkj6TPFDFFQHEQgPAU7Vzp7REZ7WqSUiIAKFIBBYoW7E7E4JdQ49R0KdA6RCHNKIjlyI4pWHCDSGAKflcjMfTsnmJjzcCIq7RmdOy21M/vmcK6HOh5rOEQERqIuAhFp9QwREoCECgRXqhhpWz+sS6hzgSahzgKRDRCDiBLjGhusJuRMyn/nLnZS5uQ+/lypJqEtFXuWKQDgJSKjDGVe1SgQKSUBCXUiaIcpLQh2iYKopIhAhAhLqCAVbTRUBDwhIqD2ArCJEIOAEJNQBD2Cxqi+hLhZZ5SsCIlBMAhLqYtJV3iIQPQIS6ujFXC0WAbcEJNRuiUXkeAl1RAKtZopAyAhIqEMWUDVHBEpMQEJd4gCoeBEIAAEJdQCCVIoqSqhLQT2PMrWpWR7QdEqYCUiowxxdtU0EvCfgG6HW/3vvg68SRSBHAhLqHEFF7TAJddQirvaKQDgISKjDEUe1QgT8QsA3Qu0XIKqHCIjAdgQk1OoUtRKQUAe0Y+gOdkADp2oXioCEulAklY8I+JOAldoKq2ILzIrNsKq++HPFFx+gvOcAwLLSX7DAJxFk/l79s2XxVR5S6+v2efbrFrZWVKC8rKz698zX0vmRU/rYypVLUdalO2JlTRArK6/6nvFzufO37b/7k7ZqJQIikAsBCXUulCJ4jIQ6gkFXk0UgBAQk1CEIopoQagJWZQWM9Wtgrl8NY/1qmOvXoHLJPMSS5VWSvMUWZVuYt6aleZs8bwFiMcSaNEO8STP7u/OzlapEvEVr+3XnK4ZtP9t/y/i95mtEnnFexrEpw0DSFur067xwzjyWf3Z+N75bikTbTrAqt4LtrPF9a9bvWa/bEl5ejrLOPWBWbEK8WUvEm7dCvHlLxOyfq353fm6Wfs15PZZIhrrfqHEi4GcCEmo/R6eEdZNQlxC+ihYBEcibgIQ6b3Q6UQTyJlCbJKdleTWMdTXl2TIqEW/VDolWbau/U6YT7Ttvk+Ty7YU5Lc9N4bU4ejPl24K1NS3hqZVL7dFtc9N6mJs3wNzEr/WwMn7O/LvzM4XcEexMGXd+3iblLRF3ZLxK2hGP5x17nSgCIsB7bbH0jBifp2XLluHyyy/HrFmz7Pr27NkTf/jDH7Dbbru5rjnbHLOC0GrXTSvcCRLqwrFUTiIgAt4RkFB7x1olhZuAtZUjyekR5Go5rh5ZrluSE63abSfMaYHm39vaI69BSt4IdeOJWFs21RDwaunevN6WcotiXvWzLekZP3O03x7p5oh3s1bgTY/yHXqn49WqbTp2Lfk9fRMk3rR54yusHEQgRASCINSmaWL//ffHD3/4Q1xxxRX2TYBXXnkFZ5xxBj7++GN06tTJVUQk1DngklDnAEmHiIAI+I6AhNp3IVGFfEjAWLMSqVXfwli1DJv+NxXJDjtsJ8+WkaoW4+0lOS3Hzt/jzVr4sJWFqVJQhLoxrTW3bKwh3Vs+mYVEh67pmykbnJsn/M6bK2sA06iS66pZBi0zxJv9omVbe5p+kz7fs6etK4lA2AkEQajffvtt/PSnP8UXX3xRIxynnnoq9ttvP3D0ury8HNddd539+i233ILVq1fj1ltvrTV8EuocerWEOgdIOkQERMB3BCTUvguJKlQCAhSf1KplaWn+7lv7Z2MVv1Oiv7XXGifad0GyfRdbfJoO2LNajqtHIUMsyW5CEgWhdsODx1bPXtjgzF5Ii7aZ8bu5cS2Mtatgbd2SvjHTmrMU2iNuf29X9b29/XfndU5bVxKBIBKoS6gX/d8RJWlO9zsmblfuP//5Tzz22GMYP358jdd++9vf2uJ8ySWX4NBDD7WFm+3Za6+98NRTT2HAgAES6nyjKKHOl5zOE7R7WT4AACAASURBVAERKCUBCXUp6atsLwmkli9CxdzZ4OjiNllehtR33yJW3sSW5UT7runvHdLynJborvYaXaXcCEioc+NU11Hcld1cl96AzljHJQSr7O81fubSgnWr7X7pCHdatNPCnSngzuuNq5XOFoHCEgjCCPXMmTNx7i/OxYcffFij8eeeey4GDhxoC/Xo0aNx5ZVXolu3bjjzzDPxn//8p05QGqHOoQ9JqHOApENEQAR8R0BC7buQqEKNIMCRwMrlC5H6Nv3l/Fz57UJbkJNddrIFOdlph23y3L6L1rg2gnn2qRLqAsJsICtuvmav168ScHPdqgwRp4Snfzc3rK2S7Pb29xryXT3i3V7rvb0LXeRLCoJQc/uwPffcE7fddhsOO+wwO2aLFy/GAQccgHfeeQedO3fGCy+8gBdffBE777yzLdU/+9nPJNSN6d0S6sbQ07kiIAKlIiChLhV5ldsYAhQESnJq+cL096qfjbXf2dJc1nmntDxn/BxL8lFOSsUmIKEuNuE88jfNKtFeVbWTvLOjfJVwV4+Ir7KfD17XaHfmdHOOhscSiTwqo1NEIDi7fM+dOxcnnXQSbrjhBvTp0wennXYabrzxxmrBNgwDQ4YMQcuWLfH666+jefO6NyDUCHUOPV9CnQMkHSICIuA7AhJq34VEFcogYK9rrh5tXpQedf52ob3Jky3LlObOVd/5c8cdxa/EBCTUJQ5AI4vnc8ztKeb2yHemcKennqcf7cbXV9kbqGWPeNe6/pvPO1cSgQwCQRihvvPOO/Hwww9j48aN9qg0d/zm+mnu7r333nvjr3/9q90i7gC+bt063H///fXGWEKdw1tAQp0DJB0SPgJ8hGAsfM2KUosk1FGKtk/bahrVo8zZ07XjLdpUSXP39PcqgU60bu/TxqhaEuro9AF7U7V6pps78m1t3Zy1vjs99Xzb+u/0dHOOgGujtWj0nyAIdS6RqKiowNChQ/HEE0/Y66rrSxLqHIhKqHOApENEQAR8R0BC7buQhLZC5uaN9hRtZ5S5err2isW1TtGmQMeaNAstj7A2TEId1sjm3y4rVVk92r1tlLvm6LezDpxLM+rbXC1zOnr+NdKZpSYQBqGeMGECrr76apxzzjk4//zzG0QqoW4QESChzgGSDhEBEfAdAQm170IS+ApxHXP2hmCUZwr1dlO0q6ZrI6apLoEPfFUDJNRhiWRp2mFu2lA1rbz+6ebbNlpLP14sc303H33XZOC+iDdvaU9Lj7dohXjT8D77vTSRalypYRBqtwQk1FXE+IDviy++GLwA7du3L5588kl7ETqThNptt9LxIiACfiAgofZDFIJZh9SKxTU2BHM2B+MIU/aGYBTpRLvOwWyoau2KgITaFS4dnC8By6xjrfdqVC78EihrAmvTenAndPtra8U2waZkO1+U7czf7Z9bAvEE+Iz5WHnT9Jc2Ncw3UrWeJ6EuKM7gZMat0/v3729vj8458uPGjUOrVq1wzTXXSKiDE0bVVAREIIuAhFpdol4CponKZfNRufQb8DnOzs7aHIFOtOtUc0OwqtHmuDYginSnklBHOvz+bbxhbJPrTNHmiHjm7xurBHzLJlhbt1R/wTK3yTUFu0lTxB3Zrvqd4l39tyZpEc/+3f5b1WtRlnUJtX/fKkWt2Zw5c+wHdnOUmunjjz/GWWedVf27RqiLil+Zi4AIFImAhLpIYAOYrT1Nm/K8bD5S9vcF9s/2NO2uPRFv2QZN+gyqnrYdKysPYCtV5WITkFAXm7DyLwUBy0htE+yKtGibjnDX8Xttx1gVGefx/IotdnOq5boOEa9VzDNE3jm/hqwnyxEr9+fntIS6FL3YB2VOmjQJ9957L5577jm7NitXrrSfO7Zo0SL7dwr1N998g5/85Cfb1faII44oWAumvP4mOrVqhtZNE2jTNIHm5Ql7WkosngAS/B63f6/tb/YxmcfF4gWrlzISAREIJgEJdTDj1phap75bWi3MqaXzUfktBXoBEm072eJc1rUnkjv0QFmX9M/836IkArkSkFDnSkrHiUCaQLWsV4m5MzJuC3uNv1WkRT7ruO0kveq8WJMmMNauQiyRBBLJjO+JWv7mHFPzNY7eJ1p3AGy/iAOxeNo16BDxrJ+r/pbLca0O+gE4+zdKSWuoAUyePBl33303nn/+eTv2y5cvt59BtmDBgmqhfuONN9C0adMafYPPLLvqqqsK1l/G3/8Amq5dCtMwYBkm4paBpjED5TEDTWCgDCbKYCDJL4tf6WPSX6b97M7qL9bKkfEqEU9Ld7xKzqsE3H7DbPt5u3N4sVV1Xr3HVQt9zfwaPMfOP6sOlmXv/soREvsRC2VNqn+2f9cFYMH6nDLyiECJHkEmofYovl4XYxowViyBsXIxjJVLsPXTd+2LNuPbBYi1aIVk5x5IcF1zlx72emd+1+NqvA5SOMuTUIczrmpVQAlYlv3Zj6ovy6AHpKr+RpdwXqv6OeM1nlP59Rwkd+oPmCYs00SFYWJrykRFykSlYdk/86vSqPpKmUhV/WwY6Z/5ZZgm+Lv93TRx9uUXS6gD2qUaVe1PP/0Up512GmbNmmXn89577+HCCy/EW2+9VS3UZWVluPbaaxtVTkMnZ1/8bk4BKyssrNwC++u7Lc7P2/6W/XoyDnRsGkOnpha6lBvoVG6iU9X3DuUmOpQbaF9mon2ZgXZlJtolDSRgApT4KiGv/m5sk/Tsvzm/U+DTb2C+GdNCb3/P/pv9u1NGOt/0edv+5pxnVVYA/JCo5N26ihrfufGEfReIkl1O0c78nhZwfvGuW9kOvRBv1gKxpi3s7/FmLRGzv6d/5q6Q/F2bUTTUM/V6UAlIqIMauXS97R21VyxCavni9BrnFenvqZVLkOzUDcnO3VHWqRuM9WvQ8oCj0lO3m2m322BH3d+1l1D7Oz6qnQiQwMYUsGKzheVb+B1YscXCii3A8s3p785rLcuA2assbEoBdI4WZUCLJL9iaF79c/p3vtbcfq3qqyy27ffM85LAgTvEJdRR7Yq77rornnnmGQwaNMje7btnz54YO3ZsSYU6n1isr6R8Z0l4Rc2/bXvdwndbAL6hKOEdmwIcSNuvcwz92zhfQM+W/nrkSXr6TE3RzpbvLV+8b09n5KNcrM0bYW7ZsO3nzemf7de2bABiibR4O6JdJd2xpi2r5DtLxm0R3/Ya17YoiYAfCUio/RiVmnXiZxmluZKiTHF2BHrFIsSS5Uh27oZkp+62PFOiy/i9c7f0lDwlEfCYgITaY+AqTgQyCPAa/+v1lv311rcce6oSZArzZlQJtGVfy3fm4FozoFNToFOzGDpXfbd/bxpD52ZAhWFhQNu4LcmU5UIlraEuFMkA5jN9+nT7wd2pVAq77747Hn300eop3mHflGy1I9wVwMSFFtqWA1+staq+gO8qrBqCvU22Y2jfJIDBzqoyL2hNSvaWKvm2ZXtDWsS3k/GM17akf+ZofKaMZ46I1xD1qpHyGsdS3vX8xOB3Ip+2QELtn8CkVn2bHl3mV9VIM0eczXWrqmU5PeKcFmb+zMe9KImAnwhIqP0UDdUljATSwpwW53n8ed02id5QCfRuFUPv1jF0bQb0be1Ic1qQHVnmQFkpE4U6iilmRW3luMsoh12oG8LBN3CmYG/72ULTBKplu589qg0kYsAxPaMzemKPmGeMeqdHxdOCXv2zI+cU9aq/V0t7xeZtU9Kzpqcbq5ajSf8hSLRsY+/CG2/RJuPn1g2FTq9HnICE2tsOwPd0WprTI82VGSPO8Zat7ZHmsswRZ/7cYQdvK6nSRKARBCTUjYCnU0WgisCc1RbeWGrBGXGet26bRHdvEUPvVtvEmT/3oUS3imGH5uFDuHnzZjRr1iwUDZNQNxDGqAt1fXiWbsqUbY5qAws3Wliy0cKwLnEM6xKr/grFu6UYjbCs9Ah51vR0/l7xySwkOu0Ic8NamBvXwtywDobz86b1tmQnWlTJdo2fW1fLt5WqRNmOfcDnx+pROMUIoH/zlFAXJzbpUeYqYc4YceburLYwV03Ptr9XrXPmRotKIhB0AhLqoEdQ9feSADe6fv87y/76gN9Xpn+mNHOZ5QFd0qLMEWdHosujMx5lh0JC7WWPLHFZEmr3AVi4wcJby7nGI/310XcUbEeu06LdLgTTxd2TKeAZlpmWa1uw19nfq2W76u8GJXz9GpibNtjHcId0inWiBYU784uj31V/b+n8Pf03bdpWwJh5nJWEOn/gfN9U2uuZa65t5t+S7btWr2121jRz9DnRtmP+BepMEQgAAQl1AIKkKpaEwGYD+KBKmG15rhLoge1i2KNDDEM6xLBHx/R3Lq1UShOQUEeoJ0ioGx9sTmtJy7Vpf//vtxb6ttk2ek3B5pQWpeISsCo2w5bsDevSEp7xZdg/V8l5xt/5fMP0KHi2hFPA09KdLeexZAF3tyguklDnLqGuP7wm3w8Za5urd9Fesdg+0RlddkaanZ217ed+KolABAlIqCMYdDV5OwJc4zx/Q3rE2ZHnT1ZbtjBXy3OVQHNppFLdBCTUEeodEuriBPudFdtGsCnZyRiqR7G/1w4YsWPE5r0UB3OjczW3bMoQ75rCnZZwjo7XlHFOLU9LdpZwt3RGx7cXcUlKo0O1XQZRF2pj3SoYq1fAWLPc/p5as6Lq9/T3RKdusDaurdpF25mqzXXO3e3lFEoiIAI1CUio1SOiSmDqEgtTlph4fYkF5+rUGXGmRPNnDQu57x0SavfMAnuGhNqb0HGzM4r1+AUW3lluoWtz4PhecRzXO4YBbfQx5U0UClOKvTt61gg4R7+rBbzGa2lJ5+PH6pyGXj0Kvm2knNPWEdet3/oiFmah5q7Z9owLW5hXILV6uf3d+Z3fuUt2ol0nJNp2qv6erP69MxJtOhSmwysXEYgIAQl1RAKtZuKjVRRoC1MWW3h9iYnd28cwcscYRnaL45AddU1aqC4ioS4UyQDkI6EuTZB4F/C5r038+xsLPVsCx/eO4/heMezcWh9kpYlIcUu1N2ardRp6en14ba/FmzSrKeH2CHjt09CddeOIR2fmQ1CE2ty0vnofAMa59hsvzt/TfSHerCUSrdvXEOZkhjhTpPkcZyUREIHCEZBQF46lcvIXgSWbLLy+OC3RvP7kVG1boHeM4ZAd4+jQ1F/1DUttJNRhiWQO7ZBQ5wCpyIe8tsjCc99Qrk30ax2rluteWnddZPL+zt7ZbC1z7XdNGdsm4vbfN1DEmteYir5tg7YqEc9YK+7IOQL6TMVSCHW1HFetyTdqWa+/TZq3yXHm7IR0TLaPx7YN9dogqDHx9ztKtROB+glIqNVDwkKgwkCVPJv2KDTXRI/cMV41Cq2ZkV7FWULtFWkflCOh9kEQMqrwysJtcj2oXQzH9UqPXO/UUiPX/oqUP2tTU/g46lnXJm3bZJyjofaO54kk4q3aIlbeBLGypojze3nT9O9Vf0v/nP6b/XqZ83pTsOxk+y5pGbQlvep71e/2CizntazXY9W/87Sa59uvZR5fhb5eobYsWJUVsCq31vy+Nev37Ncrt6Jy8VxbeJ1ZA5kb2jmsHEGuIccU5Ro3LNIb2iEWnVkD/nxXqFYikBsBCXVunHSUPwks3mjh/k8tzFxu2jJ90A4cgU5LNDfHVfKegITae+YlK1FCXTL0DRbM9db2yPXXJvbsWCXXvWPYsbk+GBuEpwNyJuCIY+XSb+x1udbWLbC2VsCsTH9Pf1X9TEl1Xud3+/eqv1FOjRTAh1PyC1Xfq363Mn+3f+Yh6WNqvJZ1rpWdV7WY07NrEfdkuf3s81gZhb+85vfyrN+rX992rLHuO5Tv1L/GdPtElShLjnPuVjpQBAJHQEIduJBFvsIbU8A/55l4Zp6JGcss/KhPHLu0jeGCgXE01wMbSt4/JNQlD4F3FZBQe8e6MSW9MJ9inRbswR1iuGRQHCf01shXY5jq3IASqJLwDRvWo0WLFtvJO0el7ZFhJREQARFwQUBC7QKWDi0pAV4LPjPPskX6mF5x/Lh3zJbpuMZbShqX7MIl1L4KR3ErI6EuLt9i5D52poFZKyys2QqcPzCOX+wqsS4GZ+XpbwKlWEPtbyKqnQiIQGMISKgbQ0/nFpvAtKVW9Wg0d+WmQP+4TxztmxS7ZOWfLwEJdb7kAniehDqAQauq8uTFFu79xLTXy5w/MGHLtT5YgxtP1dwdAQm1O146WgREoH4CEmr1EL8R+OA7R6IttC5HWqJ7x9BHT4TxW6hqrY+EOhBhKkwlJdSF4VjKXPiBS7F+9AsT5w2M22LdX8+2LmVIVLYHBCTUHkBWESIQIQIS6ggF28dN/WY9p3Jb+OfXJlZtoUSnR6P36qj53D4Om4Q6aMEpdH0l1IUmWrr8Fm20cM8npi3Xx/RIi/VQ7exYuoCo5KISkFAXFa8yF4HIEagh1Nw0Uf4SuT5Qygb/Y56J2z80MXe9ZU/lpkQfsqM6YSlj0tiyNULdWIIBOl9CHaBg5VjVzQZw75y0WPdvC5y/axxH99Q66xzx6bCAEJBQByRQqqYIBISARqgDEqgQVXOrCdz/iYn7PjXRtRnsJ7r8Yf9EiFoY7aZIqCMUfwl1uIPNaeActWbidPAz+kuswx3x6LROQh2dWKulIuAFAQm1F5RVBgks5DOjq0T68O5xnLdr3H5utFK4CEiowxXPelsjoY5GsPlM63s/MfDZmvTO4D/tF0eXZtFou1oZTgIS6nDG1det0jRgX4ensZWTUDeWoM5viMC7Kyzc/6mJx79M73nDp7TwudFK4SQgoQ5nXGttlYQ6QsEGMHN5egOzd5Zb+L/d9MitaEU/XK2VUIcrnmqNCJSagIS61BEIb/kvL7Bw36cGPloFezSaMt22PLztVcvSBCTUEeoJEuoIBTujqf9dbuG6dw1wvfX1eyUwUhtfRLMjBLjVEuoAB09VFwEfEpBQ+zAoAa/Sw5+n10czUaTPHKBldwEPqavqS6hd4Qr2wRLqYMevsbXnGuvr/mfi0G4x/GavOLq30NSjxjLV+d4QkFB7w1mliEBUCEiooxLp4rZzdQXsad0U6cHtgV/smsBRPXRtVVzq/sxdQu3PuBSlVhLqomANVKYpE/j1/wz86WPTHq2+YrDuoAYqgBGtrIQ6ooEPY7O1NtsXUZVQ+yIMga3ESwtMTF6c3myM+9RwWreeHR3YcBak4hLqgmAMRiYS6mDEyYtazllt2aPVX661cP1ecfygl8TaC+4qIz8CEur8uOksERCB2glIqNUz8iGwYgtw0/sGJi6y8MNeMVukNdsvH5LhO0dCHb6Y1tkiCXWEgp1jU5/7Jj0NnDtPUqx31Q6UOZLTYV4SkFB7SVtliUD4CUiowx/jQrfwdx+Y+N37Bs7eJY5r9kigY9NCl6D8gkxAQh3k6Lmsu4TaJbAIHX7Lh6a9cdnlg+P2VPCElgBFKPr+b6qE2v8xUg1FIEgEJNRBilZp6/rQ5yZuet/E0C4xXDMkjoHtdIFU2oj4s3QJtT/jUpRaSaiLgjU0mS7cyN3ATUxdauGGvdLPr1YSAT8QkFD7IQqqgwiEh4CEOjyxLFZLXppv4qYPTLQqA64eksAIPSGlWKhDka+EOhRhzK0REurcOEX9qNcXW/bGZfwnwtHq/TrrbmzU+0Sp2y+hLnUEVL4IhIuAhDpc8Sxka95ebtkiPX+9hav3iOPEPhpcKCTfsOYloQ5rZGtpl4Q6QsEuQFPv/YTrqw38ZOc4rhycQLcWBchUWYhAHgQiI9TaATqP3qFTRMA9AQm1e2a+P6ORn59fr7fsqd0vLzBx9R4JXPQ9ibTvY+6jCkqofRSMYldFQl1swuHLf+1W4NjXUliyEbhneAKHddNodfii7P8WRUao/R8K1VAEQkFAQh2KMBakERtT6Z27uZcM10hzw7GmiYJkrUwiREBCHaFgS6gjFOwCN/WZeSYueNPAhd9L4Nd76q5tgfEquwYISKjVRURABApJQEJdSJrBzeuO2emdu4/rRZGOo0dLDRoEN5qlrbmEurT8PS1dQu0p7tAVtmijhQveNLHVsOzR6j6t9I8ndEH2aYMk1D4NjKolAgElIKEOaOAKVO2/z03v3N2vTXrn7r076XqmQGgjm42EOkKhl1BHKNhFbCqnRd38gYF7D0jglL4arS4iamVdRUBCra4gAiJQSAIS6kLSDE5en62xcPnbBhZsAH63TwJH9ZBIByd6/q6phNrf8Slo7STUBcUZ6czeWMrRagMH7xDD3QdosVGkO4MHjZdQewBZRYhAhAhIqCMU7Kqm/vFj05bpm/dJ4IrBGgyIXg8obosl1MXl66vcJdS+CkfgK1NpAue/aeC9lRbuOSCB/fV4rcDH1K8NkFD7NTKqlwgEk4CEOphxy6fW769Mj0qXJ4Df75fA99ppVDofjjqnfgIS6gj1EAl1hILtYVMf/jy9YRmnT126m+76eog+MkVFVqgb+RiYyHQQNVQEXBKQULsEFtDDb3yfa6UNW6Qv1GOwAhrFYFRbQh2MOBWklhLqgmBUJrUQ4LokjlZ3bBqzR6s7NRUmESgcgcgKdeEQKicREIEMAhLqcHeHN79Nj0rv0DyG3+8X1yaq4Q63L1onofZFGLyphITaG85RLuWaWQYe/dLCvQfEcUxPjVZHuS8Usu0S6kLSVF4iIAKREeoIznLhdch9n5q4fb8Ezhyg6xC9270hIKH2hrMvSpFQ+yIMoa/EywvSo9Un7xzDzftqw7LQB9yDBkqoPYCsIkQgQgQiI9QRiunkxRYue9vAbu1i+P3+CXRtFqHGq6klJyChLnkIvKuAhNo71lEvaVVFesOyZZvSG5Y1ehOQCN5lj3ofymy/hFq9ITAE9FkViFBJqAMRppwqaViwRfqZeZY9vfsnO2tUOidwOqigBCTUBcXp78wk1P6OTxhr9+fZ6cdU3LJPAr/cXf/kwhhjL9okofaCssoQgegQkFCHI9Yvzuc1homDdojZU7xbl4ejXWpF8AhIqIMXs7xrLKHOG51ObASBWSssnDPdwOHdY7hVU8AbQTK6p0qooxt7tVwEikEg8EId8ZkQGyrTo9JTFlv4/f5xHKs9W4rxNlGeLghIqF3ACvqhEuqgRzC49V+3FTh5agptymN4coTWVQc3kqWpuYS6NNxVqgiElUDghTqsgcmhXX+fa+KKt038sDd38E6gTJPfcqCmQ4pNQEJdbMI+yl9C7aNgRLQq580wMGe1hadGJtC9RSyiFNRstwQk1G6J6XgREIH6CEiog9k/Ln7LwPsrLfx6zwQO665riGBGMZy1llCHM661tkpCHaFg+7ipN71v4qHPTTw5MoGhnfUP0ceh8k3VJNS+CYUqIgKhICChDlYYP1mdXjrWt3UMDxyYQBNNdAtWACNQWwl1BILsNFFCHaFg+7ypj31p4qz/GPb07x/10Xwtn4er5NWTUJc8BKqACISKgIQ6OOF84ivTlmlubnrxIF0vBCdy0aqphDpC8ZZQRyjYAWjqlCUWTpmSwuWDE/jlbvonGYCQlayKEuqSoVfBIhBKAhLqYIT1lzMNTFxo4S8HJjC8q2a0BSNq0aylhDpCcZdQRyjYAWnqF2stnDLVwIFdY/jj/prDFZCweV5NCbXnyFWgCISagITa3+H9fK2Fc6cb9l4rlOnmSX/XV7UTAQl1hPqAhDpCwQ5QUzenYEt1Mg57Crh27AxQ8DyqqoTaI9AqRgQiQkBC7d9AcxdvTvG+fi/NXvNvlFSzbAIS6gj1CQl1hIIdwKZy904+s5o7gPdupaldAQxh0aosoS4aWmUsApEkIKH2Z9gvf9vAi/Mte+Oxg3fQdYA/o6Ra1UZAQh2hfiGhjlCwA9rU2z40cdcc0x6p/r7+mQY0ioWvtoS68EyVowhEmYCE2l/R/2pdeop352bpKd6tyvxVP9VGBBoiIKFuiFCIXpdQhyiYIW4Kp3udMsXAEyMSOLmvNisLcahzbpqEOmdUOlAERCAHAhLqHCB5dMg/55m2TF+9RwKX767/+R5hVzEFJiChdgl0xowZmDhxImbPno0VK1bYZ3fu3BmDBg3CkUceiWHDhrnM0bvDJdTesYYFQLOV8gY+fRl3ADdwwffiuHKw/sHmDTIkJ0qoQxJINUMEfEJAQu2PQIx7x8CzX6eneB+yoy6a/BEV1SIfAhLqHKlNmTIFl19+Od5//31bngcPHoyOHTvaZ69YvgIffvShLdn77LMPbr31VowYMSLHnL07TELtHWuV1HgC36y3cPJUA3t1jOGuYdoBvPFEg5uDhDq4sVPNRcCPBCTUpY3K1+vTU7zbNonhgeEJtGtS2vqodBFoLAEJdQ4Er7/+evzpT3/CBRdcgIsuughdu3at9awlS5bgrrvuwn333YdLL70U1113XQ65e3eIhNo71iqpMARSZnoH8AoDuH94Al2bFyZf5RIsAhLqYMVLtRUBvxOQUJcuQv/6Oj3F+7LdExg3RDPQShcJlVxIAtEUapfTcYcPH46nn34a3bt3z4n9okWLcNJJJ4HTw/2UJNR+iobq4obA6dMMzFljYeIRSXRo6uZMHRsGAhLqMERRbRAB/xCQUJcmFkdNTGHOatgbjx3eXVO8SxMFlVoMAtEUapckU6kUkkl3T5XP5xyX1XJ9uITaNTKd4CMCv37XwMRFFl4clUTXZj6qmKpSdAIS6qIjVgEiECkCEmrvw/2zaQa+3WzhrgOS6Nfa+/JVoggUk4CE2iXdXXfdFWeccYa9njoW23Z3jQJdVlYGy+Lwtz+ThNqfcVGtcidww3smnvvGxEujEujeQne3cycX7CMl1MGOn2ovAn4jIKH2LiLLNgEnT01h59YxPHig9kPxjrxK8pJAtITa5VTv2gJBiW7Tpg2GDh2Kxx57DJ06dbIPk1Bvo6WLXy/fwtEr6+YPTDz1lYkXRyXQu5WkOgo9QJ8pUYiy2igC3hGQUHvDetYKxvoR1gAAIABJREFUCydPMfDTfnH8ek+tl/aGukopBYFoCXUBCFOo586da6+R5lrpJ5980t7RW0ItoS5A91IWORL4/UcmHvrcxEuHJ9CvjaQ6R2yBPUxCHdjQqeIi4EsCEurih+XfX5v2kzruG57AGf0l08UnrhJKSUBC7ZI+hZrTuisrK3HllVfizjvvxK9+9StcddVVaNq0qaZ8A9DFr8tOpcPzInDHbBN3zzHx4uEJDGwnqc4LYkBO0mdKQAKlaopAQAhIqIsbKP5/vvkDA0+OSOLQbvr/XFzayt0PBCTULqPgCLVz2vjx43H66adj4MCBmD59uoRaQu2yR+nwxhCgUN/+UXr69+7t9U+7MSz9fK6E2s/RUd1EIHgEJNTFi9nYmQbeWGrhyZEJDNAMsuKBVs6+IiChdhkOPjqLU70z0+LFi/GTn/xEQl0FRRe/LjuVDm8UgQc+NcHNyijVe3WUVDcKph9PtoANGzegZcuWfqyd6iQCIhBAAhLqwget0gROmWqA358ckUBzdw/HKXyFlKMIeEhAQl0g2IZh4Ouvv0bfvn0LlGPhs9Eu34Vnqhz9QYDrqa+eZeDFw5PYr7Ok2h9RKVwtdJOucCyVkwiIACChLmwvmLfewilTDOzTKYY7h2kn78LSVW5BICChzjFK2aPSdZ3GEexSpl69eqFJkybVj/QaO3Yszj77bLtKEupSRkZlF5vAY1+a+L//pqV6eFdJdbF5e5m/hNpL2ipLBMJPQEJduBhzejdHpi8ZFMflu2vzscKRVU5BIiChzjFamc+cru+UUj+HukOHDli+fDkSie3vEEqocwy2DgssAT5O6xczDLxweBIjdpRUBzaQWRWXUIclkmqHCPiDgIS6MHF44isTP5vGzccSOGlnyXRhqCqXIBKQUOcYNW4+lpmOPfZY3HXXXejRo0eNv48ZMybHHItzGJ+RvXbt2lozl1AXh7ly9ReBZ+aZOG2agRdHJXGYdhf1V3DyrI2EOk9wOk0ERKBWAhLqxneMmz8wwT1MuPnYAV10A7vxRJVDkAk0SqgtAD56C8UsD4eHk8kkPvjgAwwaNMg38d+4cSO6dOmCI444AgsWLLDXc//pT3+y/8ZEoaZsn3feedvVeZdddilYO3TxWzCUyihPAs99Y+LHkw28MCqJ0Tv56FMqz/ZE/TR9pkS9B6j9IlBYAhLqxvE8f4aBj1db9sh0j5b6H9s4mjo7DAQaJdQ+AxB5od6yZQsefvhhHH/88ejatStuvPFGfPjhh3jmmWeqhfqNN97AsmXLaoTuxBNPxLhx4woWTl38FgylMmoEgVcWx/CjaUn84yADR3U3G5GTTi01AX2mlDoCKl8EwkVAQp1fPNdVAme+mUSrMgsPH2D4aVAtvwbpLBEoEAEvhJrLj5s1a1agGtedTeSEmjuLDxgwwCZy5JFH2lPQM9PcuXMxatQofPXVV9VCXVZWhmuvvbaowdDFb1HxKnMXBCYusnDMqyk8PTKB43trfZcLdL46VJ8pvgqHKiMCgScgoXYfwpfmm7j2XROjdorh1n21k7d7gjojzAS8EGqv+EVOqLPBzps3Dz/72c8wceJEtGjRAnfeeaf9bOzMEWoJtVfdUeX4hcDriy0c81oKDx+UwIl9JNV+iYubekio3dDSsSIgAg0RkFA3RKjm6++utHD8a4a92eejB0um3dHT0VEgIKHOMcrffPNNjSO5PnnChAno379/jb/zsVV1Jg8Wnd966614/PHH7Udnce30gw8+iG7dutlV0qZkOQZbh4WOAB/rMXamgSsGx/FjSXXg4iuhDlzIVGER8DUBCXXu4eH/z+MmpXD7fgmcOUA3pXMnpyOjREBCnWO0g/LYrPqaI6HOMdg6LJQEXltsYfQrKbx8RBKjumsTlSAFWUIdpGipriLgfwIS6txiNGGhheNeS+GxEXXM8PJgoCi3muooEcggUIJ+KaHOsQdOnjw5pyMPPfTQnI4rxUES6lJQV5l+IvDCfBOnTDUwaXQSQztLqv0Um/rqIqEOSqRUTxEIBgEJdcNx4iMo+f/y34clMaaH/l82TExHlJxACUTaabOEuuTR964CEmrvWKsk/xJ47EsTV71jYtLoBAa200WCfyO1rWYS6iBESXUUAQ8IFOiCWUJdf6z+9oWJX/7XwHOHJXHwjvo/6UHPLnwRBXqvFL5i4cxRQp1jXDVCnSMoALr4zZ2VjiwNgbvnmLjnk7RUd2+hi4XSRCH3UvWZkjsrHSkCItAwAQl13Yz4//HWD038+7AE9umk/48N9yYdIQKAhDrHXsA11M2bNwcfVVVRUVHnWZbFW0L+TBqh9mdcVKvSEPjdByZe+IZSnUTr8tLUQaXmRkBCnRsnHSUCIpAbAQl17Zwo0n/7PC3TmsGVW1/SUSJAAhLqHPvB4YcfjpkzZ9rPdeajqfjc50QiWI8OkFDnGGwdFhkC494x8L+Vli3VSv4lIKH2b2xUMxEIIgEJ9fZR+/W7Bl5eaOG5wxLo0VIj00Hs16pz6QhIqF2wnz9/Pv72t7/ZX6lUCqeffjp+/vOfo0+fPi5yKd2hEurSsVfJ/iVw/gwDy7cAzx4arBtk/iVa+JpJqAvPVDmKQJQJSKhrRv+XMw28u4IynUSHplHuGWq7CORHQEKdBzfTNME11X/961/x0ksvYdiwYTjrrLNw/PHH289/9muSUPs1MqpXqQlwJ9MmceDhgyTVpY5FbeVLqP0YFdVJBIJLQEK9LXbnTjewYGNappvqX2BwO7VqXlICEupG4v/uu+/sEeubb77Zzom/+zVJqP0aGdXLDwSOfjWFnVvHcMdQXVH4IR6ZdZBQ+y0iqo8IBJuAhDodv1OnGqgwgGc0Q6t0HVq7cZeOfQFLllA3Aub0GdPxlwf+gueeew59+/bF2WefjQsuuKARORb3VAl1cfkq92AT2GoCh01I4eAdYrh+L0m1n6IpofZTNFQXEQg+gagLNR3u+EkG2pQDj2hmVvA7tFpQcgISapchWLlyJR577DE8+OCDWLRoEU488UScc8452HfffV3m5P3hEmrvmavEYBFYuSUt1af2jWPs7vFgVT7EtZVQhzi4apoIlIBAlIV6QyVw3KQU+reJ4Z4DdPO4BN1PRYaQgIQ6x6BOmTLFluh///vf2G233ezR6JNPPhmtWrXKMYfSHyahLn0MVAP/E5i3zsKhEwxcNSSOs3eRVPshYhJqP0RBdRCBKgIhmKIaVaFetpkj0ykc2DWGW/eVTOs9LQKFIiChzpEkn0PdpUsXjBkzBv369UNdz5seN25cjjl6f5iE2nvmKjGYBN7/zrJHqnn3/sQ+kupSR1FCXeoIqHwRCBeBKAr13HWWPc37h73j+PWe+r8Wrh6t1pSagIQ6xwgMHz48pyNnzJiR03GlOEhCXQrqKjOoBN5YmpbqFw9P4oid9EzOUsZRQl1K+lllh2B00kc0VZUSEYiaUH+1zsI50w0c1SOOsbtJpkvU7VRsiAlIqEMc3OymSagjFGw1tSAEXlpg4sTXDUwencSwLpLqgkDNIxMJdR7QdIoIiECdBKIk1Is2WjjiFQNnDojjl5Lp+t8VumGoT408CUiocwB31VVX4cYbb0Qikdt6E8MwcO211+J3v/tdDrl7d4iE2jvWKik8BJ78ysRlMw1MOiqJQe0k1aWIrIS6FNRVpgiEl0BUhPq7LcCoV1I4vnccVw/RyHR4e7RaVmoCEuocInDIIYeAH7433XQTRo4cWe8Z06ZNAwW8RYsWmDx5cg65e3eIhNo71iopXATu+8TEHbNNTBqdQI+Wkmqvoyuh9pq4yhOBcBOIglBvTAFHvJLCiB1iuGHv3AaEwh11tU4EikdAQp0DW444X3/99bj99tvRp08fHH744Rg8eDA6d+5sb07GR2l99NFHeO211zB37lxcfvnl9gh1riPaOVShIIdIqAuCUZlElMAtH5p4baGJiUcmUa5rE097gYTaU9wqTARCTyDsQm1a6ZHpIR1i+P1+If+HpWnaoX+/BqGBEmoXUVq6dKn96KxXX30Vs2fPxrp16+yzW7dubT9Ka9SoUfbjtLp27eoiV+8OlVB7x1olhZPA//3XwJJNwD8PCfkFis/CJ6H2WUCKUR1dFBeDqvKsg0DYhfroV1Po1SqGu4bpf5XeBCLgBQEJdSMob9261T67vLy8Ebl4d6qE2jvWKim8BH7wmoH+bYDbwn7X30chlFD7KBiqigiEgECYhfrHrxtoUwY8+H3JdAi6qpoQEAIS6oAEqhDVlFAXgqLyiDqBDZXA8BdTOGfXOM4fqE1evOgPEmovKKsMEYgOgbAK9WnTDHC69xMjJNPR6c1qqR8ISKj9EAWP6iCh9gi0igk9gdmrLBzwUgp/H5nEaD2juujxllAXHbEKEIFIEQijUPM506sqgGcPlUxHqjOrsb4gIKH2RRi8qYSE2hvOKiUaBMYvMPGzaQamH53EQD1Oq6hBl1AXFa8yF4HIEQibUF/yXwNz11kYPyoZuViqwSLgBwISaj9EoZh1yNjoRUJdTNDKO4oE7ppj4pEvTFuqm+s6pmhdQEJdNLTKWAQiSSBMQn3lOwbeXWHh1SOTSGoVUiT7sxpdegIS6jxjwEdpLVq0CD179swzB+9Pk1B7z1wlhp/A2JkGvlkP/OswTbMrVrQl1MUiq3xFIJoEwiLUv/mfgUmLLftxjq3KohlLtVoE/EBAQu0yCvwQHjt2LB566CFUVlbaz6FetWoVTjnlFDz11FNo166dyxy9O1xC7R1rlRQtAj+cbKBXS+AP+0uqixF5CXUxqCpPEYgugTAI9S0fmHjma9OW6U5NoxtLtVwE/EBAQu0yCpdeeimmT58Oyumxxx5rC/WaNWtw8skno3PnznjkkUdc5ujd4RJq71irpGgR2Gykd/4+vX8cF31Pc+4KHX0JdaGJKj8RiDaBnITax89Gv2O2ib98auLVIxPYqWUs2sFU60XABwQk1C6D0KtXL0ydOhW9e/dGLBazhZppyZIlGDJkCJYvX+4yR+8Ol1B7x1olRY/Ap2ssW6ofOSiBo3tKqgvZAyTUhaSpvERABHISap9ieuBTE7d+yJHpBPq3kUz7NEyqVsQISKhdBrxZs2ZYv349kslkDaEmyPbt24Pf/Zok1H6NjOoVFgKvLLRw0pQUZhydxG7tfXyh4+ORl9r6goQ6LO8QtUME/EEgqEL96Bcmxs0y7A3Idvfz/xh/hFm1EAHPCEioXaIeNGgQbrnlFowZM6aGUN9111148MEH8dFHH7nM0bvDJdTesVZJ0SVw3ycm7v/UxIxjtElMoXqBhLpQJJWPCIgACQRRqP8xz8Qvphv2mun9Ovv4hq26mAhEkICE2mXQ//73v+PMM8/ECSecgCeeeAIXXXQR3n//fcyYMQNPP/00TjzxRJc5ene4hNo71iop2gT4GJPP1gAvHK5NygrREyTUhaCoPERABBwCQRPqF+ebOPH1tEwftINkWj1ZBPxGQEKdR0RmzpyJO++8E1988QXi8Tj69euHiy++GPvtt18euXl3ioTaO9ahKylgU4T9wP/HrxvYoTnw56GS6sbGQ0LdWII6XwREIJNAkIT6tUUWjnglhVeOTGJUd8m0erII+JGAhNqPUSlSnSTURQKrbEWgFgKVZnrn75N2juPS3bRJWWM6iYS6MfR0rgiIQDaBoAj19GUWRr2SwlMjEvhBL/0fUU8WAb8SkFDnEJkLL7wwh6NgP5f6gQceyOnYUhwkoS4FdZUZZQJfrLVw4Esp3D88geN0MZR3V5BQ541OJ4qACNRCIAhCPWtFWqbvPSBh35hVEgER8C8BCXUOsTn00EOrj+Kjsjjlm7t99+3bF6lUCl9++aX9+siRI/Gvf/0rhxxLc4iEujTcVWq0CXC63nGTUvYmZXt00HS9fHqDhDofajpHBESgLgJ+F+qPV3Gat4Gb9onj9P6SafVkEfA7AQm1ywjdeOON9kg05TSRSK+NrKiowBVXXIEuXbrg6quvdpmjd4dLqL1jrZJEIJPAXz4z8efZpv04rXZNxMYtAQm1W2I6XgREoD4Cfhbqr9ZZGDXBwGWD4zhvV8m0erIIBIGAhNpllLp27Yq5c+eiRYsWNc5cuXIl+EitZcuWuczRu8Ml1N6xVkkikE3g6lkGPlplYfyopOC4JCChdglMh4uACNRLwK9CvWgjp3kbOGuA9t5QFxaBIBGQULuMVrt27fDee++hd+/eNc787LPPMHToUKxevdpljt4dLqH2jrVKEoHaCJw8xUD7JsDdB2jnbzc9RELthpaOFQERaIiAH4X6uy2w10z/sHccVw3RyHRDMdTrIuAnAhJql9Hgc6Y/+ugjnHfeebZUW5aFefPm4Z577sHuu++uNdQAdPHrslPp8MgQMC1g+EspHN8rjst21wVTroHXZ0qupHScCIhALgT8JtQbU8CoCSmM7BbDDXvphmsuMdQxIuAnAhJql9FYs2YNLrvsMjz99NPYuHGjfXZ5eTlGjx6NBx98EB07dnSZo3eHa4TaO9YqSQTqIjBvnWVL9Z3DEjiht6Q6l54ioc6Fko4RARHIlYCfhNqwYD9nmptW3rafZDrXGOo4EfATAQl1I6Lx3Xff2RuSde7cGcmk/9dFSqgbEWydKgIFJDBliYXRE1P2JmV7d9LO3w2hlVA3REivi4AIuCHgJ6E++tUUereK2TdZlURABIJJQELtMm68sKsr8RFabdu2dZmjd4dLqL1jrZJEoCECD39u4rYPTftxWh2bNnR0tF+XUEc7/mq9CBSagF+E+keTDbRtAjx4oGS60DFWfiLgJQEJtUvafA51fYlrqv2aJNR+jYzqFVUCv37XwDsrLEw80v8zXEoZIwl1KemrbBEIHwE/CPVp0wzwkvHxEZLp8PUwtShqBCTULiM+efLkGmeYpon58+fjoYcewpVXXonjjjvOZY7eHS6h9o61SgLAe0uazdxgV+BFVfMkcP9wXVTVBUtC3WA30gEiIAIuCJRaqM+ZbmBVBfDsofrcdxE2HSoCviUgoS5QaPj86Z/+9KeYNGlSgXIsfDZFE+oscdLFb+FjpxzDTeD7L6Uweqc4xulRKbUGWp8p4e7/ap0IeE2glEJ9yVsG5q63MH6UZiZ5HXeVJwLFIiChLiDZfv364csvvyxgjoXNqmhCnVVNXfwWNm7KLfwE5m+wcOCLBm7bL46TdtbO39kR12dK+N8DaqEIeEmgVEJ95TsG/sdlPqOTSGoGl5chV1kiUFQCEmqXeGvblGzr1q144YUXQGFduHChyxy9O1xC7R1rlSQCbgm8sdTCIS+n7E3K9u+sK61MfhJqt71Jx4uACNRHoBRCfd3/DExebOHVI5NoWab4iIAIhImAhNplNOvalIyPzfrzn/+M888/32WO3h0uofaOtUqqIqB11K66wqNfmPjt++mdv7s2c3VqqA+WUIc6vGqcCHhOwGuhvuUDE898bdoyrac6eB5uFSgCRScgoXaJeOLEidud0axZMwwYMABdu3Z1mZu3h0uoveWt0kQgHwLXv2di+jITk0drfZ3DT0KdT0/SOSIgAnUR8FKo7/nExDPzTHs3751aaPaReqUIhJGAhNplVLnx2OOPP77dWatXr8Ypp5yCCRMmuMzRu8Ml1N6xVkki0BgCZ7xhIBED/vp97QBLjhLqxvQmnSsCIpBNwCuh/uc8Exe9ZeD1o5IY1C4HmdasLnVWEXBHwCfvGQl1jmFbtGgR+DVy5EhMmTJlu7M+++wze7o3P6T9miTUfo2M6iUC2xMY8XIKh+wYx6/20CZlEmq9Q0RABApJwAuhnrokvS/GlDFJHLxDDjJdyAYWIy+fiEsxmqY8RaCxBCTUORJ87LHHcOmll2LVqlV1nnHqqafWOnqdYxFFP0xCXXTEKkAECkZg8UYLB75k4Ld7x3FK32hLtYS6YN1KGYmACAD24Efz5s2LxuLjVRZ4U/S+4Qn8qHe0P7+LBlkZi4CPCEioXQTDNE20atUKn3/++XZn8YO5ffv2LnLz/lAJtffMVaIINIbAm8so1SlMPyaJA7qEYIQjTxgS6jzB6TQREIFaCRRTqJdtgi3TF38vjvMGSqbVBUUgCgQk1C6jbBgGEolgrmuUULsMtg4XAR8QePIrE9fMMvHmMQl0i+iGNhJqH3REVUEEQkSgWEKdsoCR41M4rFsc1+4pmQ5Rl1FTRKBeAhLqHDrIhRdeiEsuuQT9+vUDf64v3X333TnkWJpDJNSl4a5SRaCxBG5638TkxSamjonmzt8S6sb2IJ0vAiKQSaBYQn38JAPdWwB3DgvmwIt6iQiIQH4EJNQ5cDv44INxxx13YMiQIeDP9aVp06blkGNpDpFQl4a7ShWBQhA4e7qBlAn87aDoXahJqAvRg5SHCIiAQ6AYQn3udAPrK4GnRkbvM1o9SwSiTkBCHaEeIKGOULDV1FASOGxCCsO7xnFdxKYSSqhD2Z3VKIeAdk/2vC8UWqivmWXgnRUWJo2O5iwizwOoAkXAZwQk1DkE5Nlnn83hqPQhJ5xwQs7Hen2ghNpr4ipPBApLYNlm4KTXUzh7l2jt/C2hLmw/Um4iEHUChRTqO2abePQL037WdPsmUSer9otANAlIqHOIezKZ+x3HVCqVQ46lOURCXRruKlUECklg+jILh76cwn+PTWLPjtHY+VtCXcgepLxEQAQKJdRPfGVi3DsmphyVQP820fg8Vu8RARHYnoCEOkK9wvdCrWlvEeqNampjCDz4mYm755i2VDfP/X5fY4os6bkS6pLiV+EiEDoChRDqVxdZOPa1FKYclcSwCD/WMHSdQw0SgTwISKjzgLZq1Sq8/vrrWLhwIZo1a4YePXrgkEMOQdOmTfPIzbtTfC/U3qFQSSIQeAK/nGlg8UbgH4eEfwMcCXXgu6saIAK+ItBYof7fSst+PNZjIxI4tqcej+Wr4KoyIlACAhJql9DfeOMNjBkzBrzAa9GiBfhc6i1btqBjx44YP3489ttvP5c5ene4hNo71ipJBLwgMHpiCvt2iuE3e4VbqiXUXvQmlSEC0SHQGKFesMHCiJcNXD0kjp8PkExHp9eopSJQNwEJtcvewUdnHX300bj00kvRvn17++wlS5bghhtuwLvvvmt/+TVJqP0aGdVLBPIj8O1mYP8XUrh5nzhO2jm8F3YS6vz6h84SARGonUC+Qr05BYx4OYUf9Ipj3ODwfuaq34iACLgjIKF2xwvdunXD4sWLtzuLIDt37oz169e7zDG/w5ctW4ZTTz3VPnny5MnVmbz99tu4+OKL7RH0vn374sknn0TLli3t1yXU+bHWWSLgZwLTllo48pUUZh6bxOAO4dwUR0Lt5x6ouolA8AjkK9RjXk1hlzYx3L5/uGcFBS+iqrEIlJaAhNol/7322gtvvvnmduulOUo9atQofPzxxy5zzO/wESNG2CPlEyZMqBZqy7LQv39/vPDCCxg4cCDGjRuHVq1a4ZprrpFQ54dZZ4lAIAjc/6mJv3ya3qSsSQiv8yTUgeiGqqQIBIZAPkJ9xhsGTAt49OAQfsgGJnKqqAj4k4CE2mVcKKuPPPIILrnkEvTr1w98TNbnn3+OP/7xjzjnnHPw/e9/vzpHrqsuVuJI+Icffojf/OY31UI9Z84cnHnmmeAoNRPl/qyzzqr+XSPUxYqG8hWB0hO45L8GVmwGnhoZvos9CXXp+5dqIAJhIuBWqK9428Cc1RZePiICj1UIU6DVFhHwiICE2iXoWCz3KZUcMS5mmjFjRg2hnjRpEu69914899xzdrErV64E13wvWrTI/p1CzXTVVVdtVy3uVl6opIvfQpFUPiLgjsCoV1IY3iWOa/cM19o+faa46wc6WgREoH4CboT6/BkG3l1p2Y/HalkmsiIgAiKwPQEJtcteMXXqVJSV5faJOnz4cJe5uzs8W6i5lvruu+/G888/b2e0fPly7L333liwYEG1UHOX8lmzZtUoaOzYsbjyyivdFV7P0br4LRhKZSQCrggs3RzDyNfK8Ls9Ujiuh+nqXD8frM8UP0dHdROB4BHIVaifmJfAzbMT+OvQFIZ2Cs9navAiphqLgL8JeCHUiUTCflxzsVPMKvaQcLFbUEf+fDTXgAED7FePPPJI3HXXXfbP2UL96aef4rTTTqsW5vfeew8XXngh3nrrrWqh5s2Aa6+9tqgt0cVvUfEqcxGol8CUJRaOeTW9Sdmg9rnPqPEzVn2m+Dk6qpsIBI9ALkI9YaGFH01OYeqYpP14QiUREAERqIuAF0LtFX1PhJqjvVwvzXXThJedpk2b5lV7txNqFrzrrrvimWeewaBBg+zdvnv27AmOQDNpDbVnoVFBIlBSAvd8YuJvn5u2VCdDMPtbQl3S7qTCRSB0BBoS6ndX8FnTKfx9ZBJjekimQ9cB1CARKDABCbVLoMOGDUNFRQWGDh263U7fzOr22293maP7w7/++mt7h2/+Q+C07l69euHkk0/G1VdfjenTp+P888+3N0vbfffd8eijj1bXU0LtnrXOEIGgErjoLQNrKoDHRwR/kzIJdVB7oeotAv4kUJ9QL9hAmTZwzZA4zhwQgjuS/gyBaiUCoSIgoXYZzq5du9prksvLy12eWfrDJdSlj4FqIAJeEjh0Qgojdojjmj2CfVEoofay16gsEQg/gbqEeosBjBifwrE94xg3JNifm+GPolooAv4hIKF2GYt9993XHgVu0qSJyzNLf7iEuvQxUA1EwEsCCzdaGPqCgTuHxXF8r+BeHEqovew1KksEwk+gLqE+9jUDO7cG/rh/8Gf2hD+KaqEI+IeAhNplLLhG+v7778fpp5+Obt26IfsxWly77NckofZrZFQvESgegUmLLPxwcgozf5DEwLbBXAsooS5e/1DOIhBFArUJ9dnTDWxOAU+EYJlMFGOqNotAKQlIqF3S5xrpcePGgTtv15b8vNG4hNplsHW4CISEwJ2SsYEEAAAgAElEQVRzTDz5pWlLdRCVWkIdko6oZoiATwhkC/U1swzMWmHhtdFJn9RQ1RABEQgSAQm1y2h17NgRN954Iw4++OBaNyXjBmF+TRJqv0ZG9RKBRhKwgIZM+fw3DWyqBB45OHhTGSXUjewffj49h77r5+qrbsEkkCnUf56dfioCH4/VLnir+YIZANVaBEJGQELtMqB9+/bFV1995fIsfxwuofZHHFQLESgVgZEvp3B49zjGDQ7WemoJdal6jMoVgXAScIT673NNjJ1pYOpRSQwI6JKYcEZIrRKBYBGQULuM189//nOcd9552HvvvV2eWfrDJdSlj4FqIAKlJPDNegtDX0zh+r0SOGeX4Ei1hLqUvabEZWsEu8QBCGfxFOr/rmmGwyekMG1MEgd2DeJimHDGRq0SgSASkFC7jNqVV16Jhx56CPvvv3+tm5JxwzK/Jgm1XyOjeomAdwR+976JP89Jj8gMbBeMi0gJtXf9I1AlSbb9Gy6fx2bWks0Y/XoS9w1P4ITewbm56N+Aq2YiEG0CEmqX8T/iiCOQTNa9acX48eNd5ujd4RJq71irJBHwM4E7Z5t44isTbx6TRFkAriUl1H7uTaqbCASLwLebgYNf2oqLBiVx/sAAfAAGC69qKwKRJCChLmDY161dh9ZtWhcwx8JmJaEuLE/lJgJBJnDRWwZWVQBPBuARMRLqIPc01V0E/EOAA+cjx6cwrKOBm/bXDmT+iYxqIgLBJiChLkD8PvroI9x777144oknwAs/vyYJtV8jo3qJQGkIjHolhWFd4rhuT3+P0kioS9M/SlKqz6cKl4SJCi0YgRNfN9ChKXD7HhVo3rx5wfJVRiIgAtEmIKHOM/5bt27Fs88+a4v0m2++icGDB+Pcc8+1Nyzza5JQ+zUyqpcIlIbAss3AsBdSuHHvOE7u61+pllCXpn+oVBEIEwHOylm6CXj20ASyn0MdpnaqLSIgAt4TkFC7ZD5//nw88MAD9sZkvMirqKjA888/jzFjxrjMyfvDJdTeM1eJIuB3AtOXWTjk5ZS9nnqfTv7cpExC7fdepPqJgL8J/PY9E5MWp581nYhBQu3vcKl2IhA4AhLqHEM2ceJEezT65ZdftkejzzrrLJxyyino2bMnPvjgA/Tq1SvHnEp3mIS6dOxVsgj4mcBDn5v448fpTcralvuvphJq/8VENRKBoBB44FMTf/o4LdM7VM3y1gh1UKKneopAMAhIqHOMUywWswX6sssuw5AhQ6rPatu2rYQ6i6EufnPsVDpMBHxEYNw7Bj5bAzx/eMJHtUpXRZ8pvguJKiQCgSDw3Dcmfv6f9GMCB3fYNgOnUUKtdf6BiL0qKQJeEpBQ50j78MMPx5QpUzBy5EiceeaZOO6449CkSRNIqLcHqIvfHDuVDhMBnxE4fpKBnVsDv9/PX1Id2s8UXZj77B2g6oSJwJvfWhgxPoWXj0jisG41l7M0SqjDBEltEQERKAgBCbULjF988QXuuecePProo/azqE899VQ8+OCDmDNnjqZ8Z3AM7cWvi76iQ0UgiATWV6Y3Kbt4UBxn7+KfTcr0mRLE3qQ6i0DpCHy51sKIlw3cum8cp9Sy4aKEunSxUckiEEYCEuo8orpx40Y89thj9prq2bNnY9iwYbjgggtwwgknoLzchwsQq9qoNdR5BNsvp2gkyy+RCH093ltpYdiLKUw8MomDd/DHJmUS6tB3OzVQBApGYO1W2CPTP+0Xx6W71X5jUEJdMNzKSAREAICEupHdYNq0afaoNXf6bt++Pb799ttG5li80yXUxWOrnEUgTASenmti3DvcpCyBbi1KL9US6jD1LrVFBIpL4IhXUtijQww371v30hUJdXFjoNxFIGoEJNQFivjixYtx//3347e//W2Bcix8NhLqwjNVjiIQVgJ8zMx/lpmYNDpZ8iZKqEseAlVABAJB4LRpBsriwEPfr38fCAl1IMKpSopAYAhIqAMTqsZXVELdeIbKQQSiRIAXpy3LgHsPKO0mZaEQai3biNJbR20tAYHL3jbw+RoLL41q+CaghLoEAVKRIhBiAhLqEAc3u2kSap8FWxfYPguIqpNNwLRgr6c+sU/daxG9oBYKofYClMoQgYgSuO1DE//6Ov2s6eYN+zQk1BHtKGq2CBSJgIS6SGD9mK2E2o9RUZ1EwN8EPl9r2Tt/P3ZwEkf1KM16agm1v/uIaicCpSTwyBcmrv8fZTqBXq1y+4ySUJcyYipbBMJHQEIdvpjW2aLICLVGfiPUq9VULwiMX2Dh9DdSeOuYJPq3ye2CtZD1klAXkqbyEoHwEJiw0MIJk1OYdlQS+3bO/bNJQh2ePqCWiIAfCEio84yCYRhYtGgRevbsmWcO3p8WGaH2Hq1KFIHQE/jjxyaenWfizWOTyP2ytTBYJNSF4ahcRCBMBN5daWHk+BSeGpnAmB61Px6rrvZKqMPUE9QWESg9AQm1yxjwQ3js2LF46KGHUFlZCcuysGrVKpxyyil46qmn0K5dO5c5ene4hNo71ipJBMJI4LwZBjalgEcP9naTMgl1GHuT2iQC+RNYsMHCyJcNXDUkjp8PcCfTLFVCnT97nSkCIrA9AQm1y15x6aWXYvr06aCcHnvssbZQr1mzBieffDI6d+6MRx55xGWO3h0uofaOtUoSgbASOPTlFA7eMY5f7eH+IjZfJhLqfMnpPBEIH4EtBuyR6aN7xv+/vTuBkqK63z7+dPcgO0Q2QXYEEYKILBo2BYKyKW4ohr+CoIAQoxIkojER44ZGYw6gr8a4EUAMroiCiiKyK7vKqiKL7CCKRNCp7vfcamcEZJju6eruWr59Dgdlqm7d+/ldmn66qm7ZgbooLwJ1UdTYBwEEChIgUCc5N+rUqaNZs2apbt26CoVCdqA2r61bt6pZs2bauXNnki1mbnMCdeasORICfhXYciCmNlMt/f3ssL36dyZeBOpMKHMMBLwhcPHbluqWlR5pXfQrZQjU3qg1vUTAKwIE6iQrVbJkSe3fv185OTlHBGoDWaFCBZnf3foiULu1MvTLFmAxOc9MhFlbY+o+I75I2ZmV0n9HNYHaM1ODjiKQVoFBcywdyJUmdix6mDYdJFCntUw0jkDgBAjUSZa8SZMmGj16tC644IIjAvXYsWP15JNPauXKlUm2mLnNCdSZs+ZICPhd4InVUT26KmqH6jLF0jtaAnV6fWkdAS8I3LHY0qKdMb3TPYEHTRcyIAK1FypOHxHwjgCBOslaPf/88xowYIB69eqlCRMm6A9/+IOWLVumuXPnavLkyerdu3eSLWZucwJ15qw5EgKuEkjT2f9bFln6cr/0YufUzhYVZkWgLkyInyPgb4Exn0T11FrzrOkcVSie+lgJ1Kkb0gICCPwsQKAuwmxYuHChxowZo3Xr1ikcDqtBgwa68cYbdfbZZxehtcztQqDOnDVHQiAoAhe9banxidL9rdIXqgnUQZlNjBOBXwpM/jyqYQstzeqRo9N+5cwtJgRqZhoCCDgpQKB2UtPlbRGoXV4guoeABwX2HZLaTM3VLU3DGlCEx9ckMmQCdSJKbIOA/wTe2xrTeW/m2mH6nGrOhGmjRKD231xhRAhkU4BAnaT+7t27ddttt9n3S5vXfffdp0cffVSnnnqqnnvuOdWqVSvJFjO3OYE6c9YcCYEgCXy4K6Y2r+Xq/Qty1K6qcx968wwJ1EGaTYwVgbjAJ3tj6vhGrv5fu4h61XX2iQIEah/NsjTd0uQjIYaSAQECdZLI5h5ps8r3tGnT7HunW7durQceeECLFy/WoUOH9OKLLybZYuY2J1BnzpojIRA0gYmfRfXXxVHNvyhHJ5V0dvQEamc9aQ0Btwvs/F52mP5947CGNnY2TJuxE6jdPgPoHwLeEiBQJ1mvihUravXq1apSpYpGjhypDRs26IUXXtDevXt12mmn8RxqSXz4TXJSsTkCPhG4c0l8Fd4Z3VJfhfdwEt5TfDJBGAYCCQp0nJarc6uFNKpFetZmIFAnWAg2QwCBhAQI1Akx/byReQ61+XAXiUTUsmVLDR061F71Ozc3V2XLluU51ATqJGcUmyPgL4E+71mqVEIa08a5D8IEan/NEUaDwPEEer9rqWJx6bF2zr2HHH08AjVzMKsCXKaeVf50HJxAnaRq48aN7Uu8S5curS5dumjTpk2qVq2aFixYoL59+2r9+vVJtpi5zbnkO3PWHAmBoAr8GI0vUta3QVh/+LUzl2oSqIM6mxh30AT+MN/Stv+l/1F8BOqgzSzGi0B6BQjUSfqOHz9e/fv3VzQa1fDhw/XQQw/Zl3mfccYZ9qOzzIJlbn0RqN1aGfqFgL8EPv06prZTczX5tznqWiP1RcoI1P6aH4wGgWMJ3L0sqne2xJ81HUn9beO4yARq5iACCDgpQKAugubGjRtlVvtu0aKFvbe53HvixIn2GepQKM3/ChShv3m7EKhTwGNXBBBISuDVL6O6fq6l+T1zVK9cau+LBOqk6NkYAc8JPLE6qkc+jofpaqXS330CdfqNOQICQRIgUCdQbROeE31VqlQp0U0zvh2BOuPkHBCBQAv8fWVUUzdGNefC1BYpI1AHehoxeJ8LvPJlVAM+sPR+jxydUTG1L98SpSJQJyrFdgggkIgAgToBpWTOOsdiZqUBd74I1O6sC71CwM8CA+dYsmLS0+cUfYEhArWfZwhjS1rARwsazdsRU6dpuZrWNUfnVc9MmDbeBOqkZx07IIDAcQQI1AlMj7lz5yawVXyTdu3aJbxtpjc8bqB28B9oPvxmurIcDwF3C3SYlquuNcIa2axoi5TxnuLu+tI7BIoisP6bmDq9YWn0WWH9X/2ivTcU5bgE6qKqsR8CCBQkQKAO0NzgDHWAis1QEXCRwMbvYmrzmqUxbcK6rG7yH5wJ1C4qJl1BwAGBb36QOr2RawfpP56e/HtCql3gDHWqguyPAAKHCxCok5wP5tnTBb3M4mTLly9PssXMbU6gzpw1R0IAgSMF3vkqpkvfydW8njlqWiG5SzsJ1MwmBPwl0G16rn2/9Oizin4rSCoiBOpU9NgXAQSOFiBQJzkn7rjjjiP2MI/PMqt+z5w5U8OGDdPIkSOTbDFzmxOoM2fNkRBA4JcCj62K6t9ropp/UY5KJPE5mkDNbELAPwL93rcUCae2rkKqGgTqVAXZHwEEDhcgUDs0HxYuXKgnnnhCzzzzjEMtOt8Mgdp5U1pEAIHkBIYtsLT1f9ILv008UROokzNmawTcKjBikaXV+2Ka1iW1lf9THR+BOlVB9kcAAQJ1mubAaaedpjVr1qSp9dSbJVCnbkgLCCCQukCPGblqVimke1smFqoJ1Kmb0wIC2RYwj9Gb8kX8WdOls5unWeU725OB4yPgMwHOUDtUUBOkO3TooO3btzvUovPNEKidN6VFBBBIXmDV11KfWbka0iiswY0KX5CIQJ28MXv4WMDBp3JkSum5dVHducSE6Yjqlk1uDYV09JEz1OlQpU0EgitAoM6rfYL/QB1rUbIffvhBa9eu1dVXX61///vfrp1NBGrXloaOIRA4geV7Yuo4LVfPdojootrHD9UE6sBNDwbsI4Hpm2O6bGauZvXI0dlVsh+mDS2B2kcTjKEg4AIBAnWSRTjWomMlS5bUr3/9a11yySWKRBK7hDHJwzqyOYHaEUYaQQABhwRmbInpkrdzNfuCHJ11nA/aBGqHwGkGgQwLLNkd/+JsYqeILqxV+NUomeoegTpT0hwHgWAIEKiDUWd7lATqABWboSLgEYFn10X1t6VRvX9BRLXKHPvsFYHaI8WkmwgcJrDq65h6vm3ptmZhXdvQPWHadJFAzVRFAAEnBQjUSWhOnz5dU6ZMkWVZ9tnoiy++OIm9s78pgTr7NaAHCCDwS4HRy6OausmE6hydcIzP3QRqZg0C3hLY94PUbmquetYO675W7grTBGpvzSV6i4AXBAjUCVbpv//9r3r37q0WLVqoRIkSWrBggcaNG6chQ4Yk2EL2NyNQZ78G9AABBI4tcPMCS5u+k14+75e3zRComTUIeEfgkCV1nZ6r1ieFdF8rd94Gxxlq78wneopAVgQSXFsrr28E6gSr1KpVK3Xu3Fn333+/vcdzzz2nESNGaOfOnQm2kP3NCNTZrwE9QACBggWufNdShRLSY22P/BBOoGbWIOAdge4zctWwfEiPtHZnmDaSBGrvzCd6ioAXBAjUCVapXLlymjdvnk4//XR7D7OytzlTbR6TVaVKlQRbye5mBOrs+nN0BBA4voD5QrjDtFx1PjmsvzT/+TJRAjUzBwFvCPSaaalicemJ9u4N0wRqb8wleomAlwQI1AlWKxQKafPmzapRo0b+HmXKlNHy5ctVv379BFvJ7mYE6uz6c3QEEChcYNv/4qH6lqZhDTwtHqoJ1IW7sQUC2Ra4epalUEga38HdYZpAne2ZwvER8J8AgTrBmhKoE4Tiw2/iUGyJAALHFFi2O2aH6gk/PWqHQM1EQcDdAoPnWNpzSHqxs/vDNIHa3XOJ3iHgRQECdYJVM4HaLERWtWrV/D3Ms6fffPNN1a5dO//P6tSpk2CLmd+MM9SZN+eICCBQNIE3N8d0+cxce+XvRiUPyFwRxAsBBNwnYBYUXP9NTG90zXFf5wroEfdQe6ZUdBQBTwgQqBMskwnUibxiMXMXoDtfBGp31oVeIYDAsQWeXhvVfcujeqPjITWsUhomBBBwmcDtH1lasCOmt7of+5F3LutufncI1G6tDP1CwJsCBOoE6zZz5syEtjQrgbv1RaB2a2XoFwIIFCRgAvXrX/6oOT2LK8d9j7OlcAgEVuDuZVG9sSmqGd1y9KsTvMVAoPZWvegtAm4XIFC7vUIO9o9A7SAmTSGAQMYEhsw+qF0/FvPM/ZkZg+FACGRJ4OGVUT23Pqq3uuWoWqksdSKFwxKoU8BjVwQQ+IUAgTpAk4JAHaBiM1QEfCRgFiUbsLCkqpSSxrXxxqJHPuJnKF4SMHedJXaHWpFH9diqqB752JyZjuiUcmk+WJF7efwdCdRpgqVZBAIqQKD2aOHN86+vuuoqu/eHX45uFkUrXry48u75Hj58uAYOHGhvR6D2aLHpNgIBFzCBumTpMvbK311rhPXnM7n2O+BTguFnSeDZdVH9+aOo3uoeUZMTvRmmDR2BOksTiMMi4FMBArVHC9uxY0ddeOGF9irjhwfqihUraufOnYpEfnkWh0Dt0WLTbQQCLpD32KyvDpjHaVka2SysaxsSqgM+LRh+hgVe+CKqIXMt+57psyp7N0wTqDM8cTgcAgEQIFB7tMj79+/XihUrNGrUqCMCdfny5fXNN98cc1QEao8Wm24jEHCBw59DveSnZ1RP7pSjHrW8/aE+4GVl+B4SeH1jVJe/a9n3TJ9bzft/7/LPUGfgEnkPlZmuIoBAEQUI1EWEc8Nuc+fOPSJQHzhwQCeddJK6du2qTZs2qX79+nrkkUfsPzMvArUbqkYfEEAgWYHDA7XZd9qmmH73Xq7+1T6i353CmepkPdkegWQEZn4VU5fpuZrWJUfdano/TJuxc8l3MjOAbRFAoDABAnVhQi7++dGB+uDBg3r66ad16aWXqmrVqrrnnnvss9hTpkzJD9SzZ8/W2rVrjxjVoEGDdOuttzo20qM//DrWMA0hgEAgBY71njJiSUTTtoT1asdcNSxnTjPxQgABpwUW7grpolnF9K/WubqoZtTp5rPWHoE6a/QcGAFfCmQiUIfDYZUsWTLtfqFYLObLT1WWZalhw4Y2YLdu3TR27Fj7v48O1EcLf/755+rSpYs+++yz/EB96NAhDRs27BfFMAHcqReB2ilJ2kEAASNQ0HvKmE+jevTT+GrDdcv648wZFUfALQLL9sTU5c1c/aN1RFfV99eVIARqt8wy+oGAPwQyEagzJeXbQF0Q4NGB+osvvlC/fv00Y8YMlS5dWmPGjNGcOXOOOENdrFgx/eUvf0lrTQjUaeWlcQQCJ3C895S/r4xqwnoTqr35PNzAFZMBe0Lgzc1RDZ0btVfUH3iav8K0KQCBugjTkPvNi4DGLkERIFB7sNIbNmywV/g2/yCYFb3No7L69Omj22+/XQ888ID+85//2I/OMvdOP/nkk6pevXr+GWoCtQcLTpcRCLhAYV/S3b0sqmkbo5reLUcVigcci+EjkKLAyr0x9XzLUteaIT3ezp/PfSdQpzhJ2B0BBI4QIFAHaEKwKFmAis1QEfCRQGGB2gz1jsWWPtgWs89Ul8rx0eAZCgIZFFi8K6aeb1u6s3lYgxv578x0HiWBOoOTikMhEAABAnUAipw3RAJ1gIrNUBHwkUAigdoMd8QiSyv2xOwz1RFuqfbRDGAomRBYsMOE6Vw9eHZE/U/1b5g2lgTqTMwojoFAcAQI1MGpNY/NClCtGSoCfhJINFCbMf9hvqUv98f0ehdOU/tpDjCW9ArM3hYP04+29d8CZMeSI1Cndz7ROgJBEyBQB6jirjpDzeIWAZp5DBWB1ASSCdTmSIPmWPr6kDSlsz/v/zxCk/fS1CYXe8s8Z9qE6WfPjeiKev4+M51XbgI1Ex8BBJwUIFA7qenytlwVqF1uRfcQQMA9AskGatPzvu9bisakCR0DEKrdUyp64jGBNzebBchy7S+fLqkTjDBtSkSg9thEpbsIuFyAQO3yAjnZPQK1k5q0hQACmRIoSqA2fbviXUvlikn/PodQnalacRzvCLy2MapL37E09fwc9agVrEUHCNTemaf0FAEvCBCovVAlh/pIoHYIkmYQQCCjAkUN1KaTF71tqUZp2feG8kIAgbjAlC+i9lUcr52fo/NrBCtMm/ETqPmbgAACTgoQqJ3UdHlbBGqXF4juIYDAMQVSCdTmFuOu03PV5MSQHv4NoZophsCkz6K6fq6lqV1y1KFa8MI0gZq/Awgg4LQAgdppURe3R6B2cXHoGgIIFCiQSqA2jR604qG6zUkh3deKUM1UC67As+uiGr4wHqbbnhTMME2gDu78Z+QIpEuAQJ0uWRe2S6B2YVHoEgIIFCqQaqA2B9j3QzxUd68Z1l+bB2fxpUJx2SAwAk+uieqvi+NhulXl4IZpAnVgpjwDRSBjAgTqjFFn/0AE6uzXgB4ggEDyAk4EanPUHd/HQ/WVp4R16xmE6uQrwR5eFXh0VVQPrIhq6vkRNasY7DBNoPbqLKbfCLhXgEDt3to43jMCteOkNIgAAhkQcCpQm65u+i6mLtMtXd8orJuaEKozUD4OkWWBf34c1bhV8TDd+ETCNIE6yxOSwyPgQwECtQ+LWtCQCNQBKjZDRcBHAk4GasOy7puYuk637LPUgxsRqn00VRjKUQIProjqmXXxMN2gPGE6j4dVvvmrggACTgoQqJ3UdHlbBGqXF4juIYDAMQWcDtTmICv3xjRojqV+DcIa0phQzdTzn8C9y6L67xdRTe0SUe0yhOnDK0yg9t98Z0QIZFOAQJ1N/Qwfm0CdYXAOhwACjgikI1Cbjn28N6ZeMy1dc2pYtzUjVDtSLBpxhcDguZaW7IrZYfrkUoTpo4tCoHbFNKUTCPhGgEDtm1IWPhACdeFGbIEAAu4TSChQmwdOFyE3bD4QU693LHU4OaQHzuKRWu6rPj1KVmCICdO7Y/pPxxw1LJ/s3j7e/rD3CAK1j+vM0BDIggCBOgvo2TokgTpb8hwXAQRSEUgoUKdwgO9+lC6bmas6ZUJ6oj2hOgVKds2iwP4fpT7v5apcsZAmdmIeH68UBOosTlQOjYAPBQjUPixqQUMiUAeo2AwVAR8JpDtQ51H1ftey//OF3xJGfDR9AjGUNfti6vOepc7VQ3rwbOZvYUUnUBcmxM8RQCAZAQJ1Mloe35ZA7fEC0n0EAiqQqUBteK+fa+mLb2N68bwclSsWUHCG7SmBd7eaMJ2r25tFeBRcgpUjUCcIxWYIIJCQAIE6ISZ/bESg9kcdGQUCQRPIZKA2tiM/tPTe1phe7BxRLVZHDtp089R4x6+P6roPLE3qFFGvuiysl2jxCNSJSrEdAggkIkCgTkTJzdsksRAPgdrNhaRvCCBQkECmA7Xpx+jlUT29LmqH6qYVirDaGeVEIM0C9y+P6l9ronaYbl2FOZoMN4E6GS22RQCBwgQI1IUJ+ejnBGofFZOhIBAggWwEasP7+Oqo/rrY0oudc3RONQJLgKac64d6wzxLy/fGNKkjV1EUpVgE6qKosQ8CCBQkQKAO0NwgUAeo2AwVAR8JZCtQG8LJn0fV930TqiPqWZtLan00rTw5lP/lSv/3nqUTItLznSIK8z1PkepIoC4SGzshgEABAgTqAE0NAnWAis1QEUiXQBK3mTjVhWwGajOGGVtiunxmrsa1jahfA0K1U3WlneQE1n8TU59Zls6pGtLDv2El7+T0jtyaQJ2KHvsigMDRAgTqAM0JAnWAis1QEfCRQLYDtaFctDOmXjMt3dI0zErKPppbXhnK+9viK3nf0jSiP57Olzqp1o1Anaog+yOAwOECBOoAzQcCtQ+KnYWzgz5QYwgeF3BDoDaEa/fFQ3WvemHd2ZxQ4/Fp5ZnuT/wsftuBWXysdz3mnROFI1A7oUgbCCCQJ0CgDtBcIFAHqNgMFQEfCbglUBvSHd9LvWbmqmWlkB5pzWW3PppmrhzKgyuiGrcqai8+1q4qN0w7VSQCtVOSAW2HkxsBLXzBwyZQB2hKEKgDVGyGioCPBNwUqA3rISseqiuVCOmZcwnVPppqrhrKTfMtfbgrZi8+VqcsYdrJ4hCondSkLQQQIFAHaA4QqANUbIaKgI8E3Bao82ivft/Sl9/G9PL5OapcwkfgDCWrAt/nSmZumQhtLvMuxlXejteDQO04qXca5Oyyd2rloZ4SqD1UrFS7SqBOVZD9EUAgGwJuDdTG4o7Fliasj+lf7SM6vwZnEbMxP/x0zHk7Yho8x1Krylz9kM66EqjTqUvbCARPgEAdoJoTqANUbAUXuZgAABmZSURBVIaKgI8E3ByoDfNLG6IaNMfSn86I6NYzOJ3oo6mX0aE8tDKqUUssPdYuor48ni2t9gTqtPLSOAKBEyBQB6jkBOoAFZuhIuAjAbcHakP9xf6YHaorFQ/ZZ6vLneCjAjCUtAqYhe6GzrP07Q8xPdY2ogbludIhreCSCNTpFqZ9BIIlQKAOUL0J1AEqNkNFwEcCXgjUedwjFlmaujF+Cfi51QhGPpqGaRnKaxujGjrX0oCGYd3dkgXu0oJ8jEYJ1JmS5jgIBEOAQB2MOtujJFAHqNgMFQEfCXgpUBv2SZ9FNWiupXtaRnRzEy4B99FUdHQoIz+0NPnzmH2Jd/eaKX75wkJLSdWGQJ0UFxsjgEAhAgTqAE0RAnWAis1QEfCRgNcCtaFfvS9+CXi9svFLwItz8tFHMzK1oXy6L2aflT65VEiPto2oQvHU2mPv5AUI1MmbsQcCCBQsQKAO0OwgUAeo2AwVAR8JeDFQ5/HfON/SrG0xPdk+ot9USfEspI9qGtSh/HtN1L5f+qGzI7qRqxeyNg0I1Fmj58AI+FKAQO3Lsh57UATqABWboSLgIwEvB2pThmfXxVcB/2friIY25hJwH03NhIdyyJJ+P8/S8j3xS7zPqsyXKwnjpWFDAnUaUGkSgQALEKgDVHzPB2ruEQvQbGWoCPws4PVAbUayYk/8EvCmFeOXgBOngjPDZ2+L2WelO50c0tg2XPvvhsoTqN1QBfqAgH8ECNT+qWWhI/F8oC50hGyAAAJ+FPBDoM6ry/VzLS3eFV8FvHklYrUf5+vhYxq9PKrRKyz7Xun/q8/VCW6pN4HaLZWgHwj4Q4BA7Y86JjQKAnVCTGyEAAIuE/BToDa0T6yO30drQvW1DQlZLptujnTnqwPmrHRUP1gxO0zXK8eXJ47AOtQIgdohSJpBAAFbgEAdoIlAoA5QsRkqAj4S8FugNqX5cFf8EvB2J4U0ri2XAftouurFDVH7fumhjSO6szlfmLixtgRqN1aFPiHgXQECtXdrl3TPCdRJk7EDAgi4QMCPgdqw/hiVrnjX0rpvYrqrRVi96hK+XDDdityFz7+N6W9Lo9r4XUy3NYuoSw3OShcZM807EqjTDEzzCARMgEAdoIITqANUbIaKgI8E/Bqo80r0+qaoRi2JqmbpkEa1CKtZRYKYl6av+WLkb0st3bc8qr82j+gvzcPiqxF3V5BA7e760DsEvCZAoPZaxVLoL4E6BTx2RQCBrAn4PVDnwT7ycVR3LrE0qFFYd7WIqHRO1sg5cIICT66J2melz68R0l+bh1W7DF+GJEiX1c0I1Fnl5+AI+E6AQO27khY8IAJ1gIrNUBHwkUBQArUp2a6DskP1KxuiGtUiosGNONfpxqn81hZzebelUjmyz0q3r0qQdmOdCuoTgdpL1aKvnhUI0ONuCdSenaXJd5xAnbwZeyCAQPYFghSo87Tn74jZwfqgJftstXmGMa/sC6zeF79PeunumH1GmkdhZb8mRekBgbooauyDAAIFCRCoAzQ3CNQBKjZDRcBHAkEM1Hnle25dVKOWRtWxWvz+6lpcUpyVmX0gN36f9JhP4vdJ39aMKweyUgiHDkqgdggym80E6OxnNpk5dmICBOrEnHyxFYHaF2VkEAgETiDIgdoU24pJo5ZYemBF/DLw2wlzGf078Ogqc5+0pUvrhO0Fx04uxdUCGS1AGg52zEBNQEuDNE0iEAwBAnUw6myPkkAdoGIzVAR8JBD0QJ1XyjX7YvZq4B/vjdlnqy+vx1nSdE5zs/q6uby7SgnpL80j+k0VgnQ6vTPZNmeoM6nNsRDwvwCB2v81zh8hgTpAxWaoCPhIgEB9ZDGnbYrfX12jdMh+fjWP2XJ2sq/cG79P2nyBYe6TvoIvLpwFdkFrBGoXFIEuIOAjAQK1j4pZ2FAI1IUJ8XMEEHCjAIH62FUxj9kyl4JfWDusu1uGVbcsZ1BTmb9Ldsd0wzxLn35tgnREtzTlCoBUPN28L4HazdWhbwh4T4BA7b2aFbnHBOoi07EjAghkUYBAXTC+eczWVbNytWhnTOdWC6tvg5Auq0sQTHS6mlXUx6+P6j/ro/rqgHRVg5Bu/HVElUok2gLbeVGAQO3FqtFnBNwrQKB2b20c7xmB2nFSGkQAgQwIEKgLR47G4sHQ/Fr/jexgfXWDsE77FWetj6U3b3tM4z+LB+keNcO6ukFIPWvzRUThM80fWxCo/VFHRoGAWwQI1G6pRAb6QaDOADKHQAABxwUI1MmRmnuA8866Nq8Y0tWnhtXnFMLi14dkB2hj870lXV0/HqSrl+ZLh+RmmPe3JlB7v4aMAAE3CRCo3VSNNPeFQJ1mYJpHAIG0CBCoi876/OdRjV8X1dI9MfuMdd8GYTWtEKwAOfOrWH6QNgbm13nVg2VQ9Bnkzz0J1P6sK6NCIFsCBOpsyWfhuATqLKBzSAQQSFmAQJ0yodbui5+1Hr8+pgblzSXh8XAd9mmu3Po/E6LjQbp4JD5eE6QrFE/dkha8L5BUoOb51N4vOCNAIM0CBOo0A7upeQK1m6pBXxBAIFEBAnWiUolt99KGeLCevS2aH6xbVvZHsjbPjjZB+vWNUTtAm1/tq/pjbIlVl60SEUgqUCfSINsggECgBQjUASo/gTpAxWaoCPhIgECdnmJu2G/OWsfP4paMSK0qh9SsUkhnVoz/KlMsPcd1qtVPvo7JPOpq6a747+ZXkwohXdcwHqRL5Th1JNrxmwCB2m8VZTwIZFeAQJ1d/4wenUCdUW4OhgACDgkQqB2CPE4zH+2KadmemJbvjv9ufp1S7udwfWalkJpVDGXtkmlzyXpeaM77vXqpkJpXCqlF5ZBamN8rhVTW5V8CpL+SHCERAQJ1IkpsgwACiQoQqBOV8sF2BGofFJEhIBBAAQJ1doq+4qdgbQfsn4J21ZIhmXCddxbb/PdJJZ3t3+ff/hyel/505vnEE44MziY8n8j90M7CB6g1AnWAis1QEciAAIE6A8huOQSB2i2V8GE/WLTFh0V1z5AI1O6pxep9P4frvKBdtlhI9cuHVKu0FJUUi/38++H/nfcz83Zhnpttfv/55zHtPiiZMF0y5+czzvaZ58ohVS7hHgN64n0BArX3a8gIEHCTAIHaTdVIc18I1GkGpnkEEEiLgO8Dtce/kDIheNqmmMqdIJmnXYdCklkGzKwgnv976Ng/M9vG9wnJXHY+uFFIJ5diEbG0/EWi0XwBAjWTAQEEnBQgUB9P0+Mfco4eGoHayb86tIUAApkS8H2gzhQkx0EAAVuAQM1EQAABJwUI1E5qurwtArXLC0T3EEDgmAIEaiYGAgg4KUCgdlKTthBAgEDt0TkwevRojR8/3u5927Zt9fjjjysSiWjRokW68cYbZT6A1q9fXxMnTlSZMmXs7TIRqPfs2aP3339fl112mUdl6TYCCLhN4KWXXlL37t1VsqTDq1+5baD0BwEEMiLw8ssvq0mTJjr11FMzcjwOggAC/hZ45ZVXVL58eXXq1MnzAw3FYmZ5E/+/5s2bpyFDhujDDz9UsWLF1LlzZ91www269NJL7X8cXnvtNTVu3FgjR45U2bJl9ec//zmjgdr0wQRrXggggIATAqVKlbLfUwjUTmjSBgIINGjQQG+88QaBmqmAAAKOCHTo0ME+cUmgdoQzM40cPHhQBw4cUMWKFe0DXn311XaobtmypQYMGGCfpTavjz/+WNddd13+/2fqDDWBOjPzgKMgEBQBAnVQKs04EciMAIE6M84cBYGgCBCoPV7p1atX66KLLrJD8+LFi/XYY4/JXHZgXrt371azZs20ZcsW+/9NoJ49e7YOHTp0xKi7dOlin8124rV3716dfvrp+uqrr5xojjYQQAABVahQwX5P4Qw1kwEBBJwQMJ9TzGXfJljzQgABBFIVMFnq9ttv17nnnptqU8fdPxOfgwJzyXeetAnQffv2te+lNmenZ86cqXHjxunVV1+1N9m5c6f955s2bcoP1Nu3b1f//v1/UazWrVs7MgHMZZmcoXaEkkYQQOAnAc5QMxUQQMBJAc5QO6lJWwggwBlqD8wBy7LUsGFDu6fdunXT2LFjNX/+fF177bX2/dJ5i2qYs9UmYH/00Uf2tkuXLrXvrTbbmtfvfvc75eTk6Morr0zbqPfv36+HHnpId911V9qOQcMIIBAsgTvvvNNeC+KEE04I1sAZLQIIpEXAvKcMGjRI1atXT0v7NIoAAsESMO8pZkHmpk2bpnXgPXr0SGv7pvHAnKHet2+fzjrrLL311luqW7fuEbCNGjXSlClT7NUrzWrftWvX1vDhw+1tzCXfJmTzQgABBBD4ScAsZRlCAwEEEEAAAQQQcK+AeZqTOZGa7ldygdrDH6LMZd3mbE3NmjXzTc3CZLfeeqvmzJmjoUOHKjc31/6W5LnnnlOJEiXSY+9hw/SA0CoCCCCAAAIIIIAAAggg4E2B5AK1N8dIrxFAAAEEEEAAAQQQQAABBBBwXIBA7TgpDSKAAAIIIIAAAggggAACCARBgEAdhCozRgQQQAABBBBAAAEEEEAAAccFCNSOk9IgAggggAACCCCAAAIIIIBAEAQI1Fmu8qJFi+yVxb/77jvVr19fEydOVJkyZbLcKw6PAAJeE3j22WftR/7NmDFD7dq1s7u/c+dOXXPNNdq6dauKFStmL7jYuHFjrw2N/iKAQIYFPvvsM1133XUyT0gJhUIaM2aM2rdvby/eevPNN2vevHk6ePCg7rnnHvuxN7wQQACB4wmYzyP9+vXTtm3bdOjQIfv9xTxRyS/vKQTqLM7/WCxmPw/bLOduPuSOHDlSZcuWtVcj54UAAggkKjB+/HgtWbJEy5cv17333psfqM0/Xm3atNHgwYPtoP3www/rnXfeSbRZtkMAgYAKnHfeeerfv7/69Omj9957TzfddJM+/vhjPfPMM/Z7yKRJk+wPxq1bt9aqVatUqlSpgEoxbAQQSETAfPl24okn6ve//72+/fZb+yTiypUrNX36dF+8pxCoE5kFadrm008/1YABA2TOUpuX+cfKfGOT9/9pOizNIoCAzwT2799vfxnXuXNnjRo1Kj9QV6lSRRs2bFDp0qXtER/9/z5jYDgIIOCQwPbt21W5cmWZZ7h+/vnn9nuLeS+5/PLL7c8t3bp1s49kzk6bzy15/+/Q4WkGAQR8LLB+/XqZL+0++eQT+4s7P7ynEKizOGHNt7yPPfaYXnnlFbsXu3fvVrNmzbRly5Ys9opDI4CAVwUOD9Q//vijTjrpJO3duzd/OE2aNNGrr75qfzPMCwEEEEhEwARm855hrqJr27at/bnljDPOsHc1t5mYzy1mG14IIIDA8QQsy7LfS8ytJBMmTFCPHj18855CoM7i3J85c6bGjRtnf8A1L3N/QcuWLbVp06Ys9opDI4CAVwWODtTmjPTXX3+dPxxza8m0adNUr149rw6RfiOAQDoEYpJCRzZsPvwOHTpUP/zwg5566imFw2H76hfzucWEaPMyPzefW8wZJl4uEzhGTV3WQ7oTUIG1a9eqa9eumjVrlq666ipfvKcQqLM4mVevXq2+ffvqo48+snuxdOlS+9ve+fPnZ7FXHBoBBLwqcPQl39WqVZO5tMosdBiNRu1Lvjdv3qySJUt6dYj0GwEEMiBg3i+uuOIK+2zS6NGj84/Yu3dv+3OLObNkXj179rQ/t5x//vkZ6BWHQCBAAj77QsRclWuubDGfQ8zLvL9ccskl9klFP7ynEKiz/HezUaNGmjJlisylmGa179q1a9ur3vFCAAEEkhU4OlAPHDhQzZs315AhQ/Tyyy/bCwq9/vrryTbL9gggEDCB++67T+Y+arO69+Ev8yQS8x4yefJk+2q6c845R+ZsU/HixQMmxHARQCAZgeuvv14VK1a0F041i5KZq1zM5xKznpQf3lMI1MnMhjRsO2fOHPuSKbNsfNOmTe3H2pQoUSINR6JJBBDwq8CIESPslTK//PJL+9tfs+Lu3Llz9f3339ur9O7YsUPly5e371k65ZRT/MrAuBBAwCGBSpUq2SvyHh6UFyxYYF/dYj4Ym88uZsGyhx56SN27d3foqDSDAAJ+FdizZ499a4hZ3NDcTmLWXRg2bJidf/zwnkKg9uvMZVwIIIAAAggggAACCCCAAAJpFSBQp5WXxhFAAAEEPC3gs/vYPF0LOo8AAggggIALBQjULiwKXUI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       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
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       "    <script>\n",
       "    PLOT = document.getElementById('7a43d78d-f8d2-4d5a-88b4-c4c90e4a11d7');\n",
       "    Plotly.plot(PLOT, [\n",
       "    {\n",
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       "    {\n",
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     "metadata": {},
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    }
   ],
   "source": [
    "# plot the resulting optimized controls\n",
    "using Printf: @sprintf\n",
    "ts = range(0, Tgate; length=51)\n",
    "for ct in 1:4\n",
    "    opt_p = Optim.minimizer(opts[ct])\n",
    "    ax = plot()\n",
    "    plot!(ax, ts, [controls(t, opt_p)[1]/2π/1e-3 for t in ts], label=\"Ωx\")\n",
    "    plot!(ax, ts, [controls(t, opt_p)[2]/2π/1e-3 for t in ts], label=\"Ωy\")\n",
    "    xlabel!(ax, \"Time (ns)\")\n",
    "    ylabel!(ax, \"Pulse Amplitude (MHz)\")\n",
    "    title!(ax, @sprintf(\"%d Quadrature Controls with Error = %.3e\", ct, Optim.minimum(opts[ct])))\n",
    "    display(ax)\n",
    "end"
   ]
  }
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