Modeling/JuMP.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimizing a newsvendor problem with JuMP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using JuMP, CairoMakie\n",
    "import HiGHS"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a simple newspaper example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our Profit for one day with supply 42 is: $ 70\n"
     ]
    }
   ],
   "source": [
    "newspaper_cost = 5\n",
    "customer_price = 7\n",
    "\n",
    "supply = 42\n",
    "demand = 40\n",
    "\n",
    "# Daily Profit is equal to the newspapers sold less the cost we paid for it\n",
    "function profit(demand, supply, customer_price, newspaper_cost) \n",
    "    return (min.(demand, supply) .* customer_price) .- (newspaper_cost .* supply)\n",
    "end\n",
    "\n",
    "# one day\n",
    "single_profit = profit(demand, supply, customer_price, newspaper_cost)\n",
    "println(\"Our Profit for one day with supply $supply is: \\$ $single_profit\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on this model, we set a constant daily `supply` level and calculate the profit given uncertain, fluctuating demand. How will our strategy perform over 3 days, where one day we have demand that exceeds our supply and another day in which our demand is much less than supply?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our Profit for three days with supply 42 is: $ sum(multi_day_profit)\n"
     ]
    }
   ],
   "source": [
    "# two days\n",
    "three_day_demand = [40, 60, 25]\n",
    "multi_day_profit = profit(three_day_demand, supply, customer_price, newspaper_cost)\n",
    "\n",
    "println(\"Our Profit for three days with supply $supply is: \\$ $sum(multi_day_profit)\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that with the cost and sales price assumptions in this model, there's a profit hit on day 3 that brings down the 3-day profit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Plot Demand vs Profits\"\"\"\n",
    "function plot_profit(demand, supply, profit; bar_labels=true)\n",
    "        N = length(demand)\n",
    "        fig = Figure(resolution=(800,400))\n",
    "\n",
    "        ax1 = Axis(fig[1,1], title=\"$N-day Newspaper Demand\")\n",
    "        ax2 = Axis(fig[1,2], title=\"$N-day Newspaper Profit with Supply $supply\")\n",
    "\n",
    "        colors = [i >= 0 ? :grey : :crimson for i in profit]\n",
    "\n",
    "        if bar_labels\n",
    "                demand_labels = demand\n",
    "                profit_labels = profit\n",
    "        else\n",
    "                demand_labels = [\"\" for i in demand]\n",
    "                profit_labels = [\"\" for i in profit]\n",
    "        end\n",
    "        barplot!(ax1, demand, \n",
    "                bar_labels=demand_labels, \n",
    "                label_size=16,\n",
    "                label_offset=-30,\n",
    "                color=colors)\n",
    "        barplot!(ax2, profit, \n",
    "                bar_labels=profit_labels, \n",
    "                label_size=16,\n",
    "                label_offset=-30,\n",
    "                color=colors)\n",
    "        return fig\n",
    "end\n",
    "\n",
    "plot_profit(three_day_demand, supply, multi_day_profit)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding the optimal supply level\n",
    "\n",
    "For this example I'll use the Julia `JuMP` optimization library to find the optimal daily supply level $s$ that maximizes the total daily profit. Our first step is to convert this word problem into an optimization problem:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let:\n",
    "\n",
    "* $p$ = the customer price\n",
    "* $d$ = demand\n",
    "* $s$ = daily supply strategy\n",
    "* $c$ = our newspaper cost\n",
    "\n",
    "Then we want to maximize the sum of daily profits over $N$ days. If we have both price and cost as fixed, then we have: \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\max \\sum_i^N p* (\\min(d,s)) - cs \\\\\n",
    "&= \\max \\sum_i^N 7(\\min(d,s)) - 5s\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because $\\min(d,s)$ is nonlinear, this can make finding an optimal solution a little difficult. Luckily, we have techniques to convert this problem into a linear one. [See this article on the Operations Research Stackexchange for more info.](https://or.stackexchange.com/questions/711/how-to-formulate-linearize-a-maximum-function-in-a-constraint/712#712)\n",
    "\n",
    "First, let $x = \\min(d,s)$. Then we can add some additional constraints and variables to convert this nonlinear optimization problem to a linear one:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\max & \\sum_i^N 7x - 5s \\\\\n",
    "\\text{s.t.} & \\\\\n",
    "x & \\le d \\\\\n",
    "x & \\le i \\\\\n",
    "x & \\ge d - M(1-y) \\\\\n",
    "x & \\ge s - My \\\\\n",
    "s & \\ge 0 \\\\\n",
    "y & \\in \\{0,1\\}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $M$ is some reasonable solution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ 7 x - 5 s $$"
      ],
      "text/plain": [
       "7 x - 5 s"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 0. Params\n",
    "demand = 40\n",
    "M = 100\n",
    "\n",
    "# 1. Establish model\n",
    "model = Model(HiGHS.Optimizer)\n",
    "# Option: To Suppress all the printing, use `set_silent(model)`\n",
    "set_silent(model)\n",
    "\n",
    "# 2. Variables\n",
    "@variable(model, s >= 0, Int)\n",
    "@variable(model, x >= 0)\n",
    "@variable(model, y, Bin)\n",
    "\n",
    "# 3. Constraints\n",
    "# convert the min(d,i) nonlinear constraint to linear\n",
    "@constraint(model, x <= demand)\n",
    "@constraint(model, x <= s)\n",
    "@constraint(model, x >= demand - M*(1-y))\n",
    "@constraint(model, x >= s - M * y)\n",
    "\n",
    "# 4. Objective Function\n",
    "@objective(model, Max, (customer_price * x) - (newspaper_cost * s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Optimize the model and print the value of $s$\n",
    "optimize!(model)\n",
    "value(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# What was the profit at this optimal value?\n",
    "objective_value(model)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vectorizing in `JuMP` for multiple demand days\n",
    "\n",
    "This code is starting to get a little messy, because of that $\\min(d,s)$ constraint needs to be applied to each value of demand $d$ in an array.\n",
    "\n",
    "To implement this in JuMP we'll need to *vectorize* the constraints and the variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "optimize_problem"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\"\"\"Wrap the optimization problem within a function\"\"\"\n",
    "function optimize_problem(demand)\n",
    "    # 0. Params\n",
    "    M = 100\n",
    "    n = length(demand)\n",
    "\n",
    "    # 1. Establish model\n",
    "    model = Model(HiGHS.Optimizer)\n",
    "    # Option: To Suppress all the printing, use `set_silent(model)`\n",
    "    set_silent(model)\n",
    "\n",
    "    # 2. Variables\n",
    "    @variable(model, s >= 0, Int)\n",
    "    @variable(model, x[i=1:n] >= 0) # Vectorize x \n",
    "    @variable(model, y[i=1:n], Bin) # Vectorize y too\n",
    "\n",
    "    # 3. Constraints\n",
    "    # convert the min(d,i) nonlinear constraint to linear\n",
    "    @constraint(model, x .<= demand) \n",
    "    @constraint(model, x .<= s)\n",
    "    @constraint(model, x .>= demand .- M .* (1 .- y))\n",
    "    @constraint(model, x .>= s .- M .* y)\n",
    "\n",
    "    # # 4. Objective Function\n",
    "    @objective(model, Max, sum((customer_price .* x) .- (newspaper_cost .* s)))\n",
    "    optimize!(model)\n",
    "\n",
    "    return value(s)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "demand = [30, 30, 60, 25, 100]\n",
    "\n",
    "optimal_supply = optimize_problem(demand)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again we can plot the daily profit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimal_profits = profit(demand, optimal_supply, customer_price, newspaper_cost)\n",
    "\n",
    "plot_profit(demand, optimal_supply, optimal_profits)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What if demand is uncertain?\n",
    "\n",
    "Optimizing over known demand is trivial - how would you set an optimal strategy when demand is unknown? \n",
    "\n",
    "We'll continue the example by randomly drawing from a demand model where demand $\\sim \\text{TruncatedNormal}(40, 10)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random, Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set seed for reproducibility\n",
    "Random.seed!(42)\n",
    "\n",
    "# Specify the truncated distribution with truncated(dist, lower=0)\n",
    "dist = truncated(Normal(40, 20), lower=0)\n",
    "# Randomly sample 1000\n",
    "sample_demand = rand(dist, 100)\n",
    "# Plot\n",
    "hist(sample_demand, \n",
    "     figure=(resolution=(500,300),),\n",
    "     axis=(title=L\"\\text{100 Random Samples from Truncated Normal}(40,20)\",))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_sample_supply = optimize_problem(sample_demand)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here our optimization problem selected a daily supply strategy of 29 newspapers. We again show the results below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimal_profits = profit(sample_demand, random_sample_supply, customer_price, newspaper_cost)\n",
    "\n",
    "plot_profit(sample_demand, random_sample_supply, optimal_profits, bar_labels=false)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Statistics\n",
    "\n",
    "How could we improve upon our assumption that demand is drawn from a $\\text{TruncatedNormal}(40,20)$ distribution? If we had a few days of data we could improve upon our inventory strategy using Bayesian stats. \n",
    "\n",
    "Here we'll use `Turing`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: [Turing]: progress logging is disabled globally\n",
      "└ @ Turing /Users/nelsontang/.julia/packages/Turing/FlV8f/src/Turing.jl:23\n",
      "┌ Info: [AdvancedVI]: global PROGRESS is set as false\n",
      "└ @ AdvancedVI /Users/nelsontang/.julia/packages/AdvancedVI/hVQ2g/src/AdvancedVI.jl:15\n"
     ]
    }
   ],
   "source": [
    "# Disable progress bars and such\n",
    "using Turing; Turing.setprogress!(false);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need to first specify our priors here. Before, we assumed the distribution had a mean $\\mu=40$ and standard deviation $\\sigma=20$, but with uncertain demand we don't know these parameters for certain. We'll need to specify distributions for these parameters and then sample from the posterior distribution after we get some data."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's say we get 5 days of observed data $d$ with an empirical mean of $\\bar{d}$. We have priors as such:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sigma & \\sim \\text{HalfStudentT}(\\mu=10, \\nu=20) \\\\\n",
    "\\mu & \\sim \\mathcal{N}(\\bar{d}, 20) \\\\\n",
    "\\text{Demand} & \\sim \\text{TruncatedNormal}(\\mu, \\sigma, 0)\\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "demand_seen = sample_demand[1:5]\n",
    "demand_unseen = sample_demand[6:15];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "newspaper (generic function with 2 methods)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@model function newspaper(demand)\n",
    "    σ ~ Truncated(TDist(20), 10, 100)\n",
    "    μ ~ Normal(mean(demand_seen), 20)\n",
    "    for i in 1:length(demand)\n",
    "        demand[i] ~ Truncated(Normal(μ, σ), 0, 100)\n",
    "    end\n",
    "    return demand\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Found initial step size\n",
      "│   ϵ = 1.6\n",
      "└ @ Turing.Inference /Users/nelsontang/.julia/packages/Turing/FlV8f/src/inference/hmc.jl:190\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n",
      "┌ Warning: The current proposal will be rejected due to numerical error(s).\n",
      "│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)\n",
      "└ @ AdvancedHMC /Users/nelsontang/.julia/packages/AdvancedHMC/iWHPQ/src/hamiltonian.jl:47\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Chains MCMC chain (1000×14×1 Array{Float64, 3}):\n",
       "\n",
       "Iterations        = 501:1:1500\n",
       "Number of chains  = 1\n",
       "Samples per chain = 1000\n",
       "Wall duration     = 7.06 seconds\n",
       "Compute duration  = 7.06 seconds\n",
       "parameters        = σ, μ\n",
       "internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size\n",
       "\n",
       "Summary Statistics\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    mean \u001b[0m \u001b[1m     std \u001b[0m \u001b[1m naive_se \u001b[0m \u001b[1m    mcse \u001b[0m \u001b[1m      ess \u001b[0m \u001b[1m    rhat \u001b[0m \u001b[1m e\u001b[0m ⋯\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  \u001b[0m ⋯\n",
       "\n",
       "           σ   10.7138    0.7466     0.0236    0.0283   741.2224    1.0009     ⋯\n",
       "           μ   30.0993    4.7900     0.1515    0.1848   729.7710    1.0012     ⋯\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m\n",
       "\n",
       "Quantiles\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    2.5% \u001b[0m \u001b[1m   25.0% \u001b[0m \u001b[1m   50.0% \u001b[0m \u001b[1m   75.0% \u001b[0m \u001b[1m   97.5% \u001b[0m\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
       "\n",
       "           σ   10.0100   10.1814   10.4606   10.9982   12.8911\n",
       "           μ   19.8593   26.9420   30.2833   33.3436   39.1081\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idata = sample(newspaper(demand_seen), NUTS(), 1000; progress=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chains{Float64, AxisArrays.AxisArray{Float64, 3, Array{Float64, 3}, Tuple{AxisArrays.Axis{:iter, StepRange{Int64, Int64}}, AxisArrays.Axis{:var, Vector{Symbol}}, AxisArrays.Axis{:chain, UnitRange{Int64}}}}, Missing, NamedTuple{(:parameters, :internals), Tuple{Vector{Symbol}, Vector{Symbol}}}, NamedTuple{(:start_time, :stop_time), Tuple{Float64, Float64}}}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import Plots\n",
    "Plots.histogram(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You can also access the data like so:\n",
    "samples = idata[:μ].data\n",
    "hist(samples[1:end], figure=(resolution=(400,200),),)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14-element Vector{Symbol}:\n",
       " :σ\n",
       " :μ\n",
       " :lp\n",
       " :n_steps\n",
       " :is_accept\n",
       " :acceptance_rate\n",
       " :log_density\n",
       " :hamiltonian_energy\n",
       " :hamiltonian_energy_error\n",
       " :max_hamiltonian_energy_error\n",
       " :tree_depth\n",
       " :numerical_error\n",
       " :step_size\n",
       " :nom_step_size"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "keys(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{ChainDataFrame}:\n",
       " Summary Statistics (2 x 8)\n",
       " Quantiles (2 x 6)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "describe(idata)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way of inspecting the output is to convert it to a `DataFrame`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×16 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">iteration</th><th style = \"text-align: left;\">chain</th><th style = \"text-align: left;\">σ</th><th style = \"text-align: left;\">μ</th><th style = \"text-align: left;\">lp</th><th style = \"text-align: left;\">n_steps</th><th style = \"text-align: left;\">is_accept</th><th style = \"text-align: left;\">acceptance_rate</th><th style = \"text-align: left;\">log_density</th><th style = \"text-align: left;\">hamiltonian_energy</th><th style = \"text-align: left;\">hamiltonian_energy_error</th><th style = \"text-align: left;\">max_hamiltonian_energy_error</th><th style = \"text-align: left;\">tree_depth</th><th style = \"text-align: left;\">numerical_error</th><th style = \"text-align: left;\">step_size</th><th style = \"text-align: left;\">nom_step_size</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">501</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.2875</td><td style = \"text-align: right;\">29.3936</td><td style = \"text-align: right;\">-25.2256</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">1.87558e-6</td><td style = \"text-align: right;\">-25.2256</td><td style = \"text-align: right;\">31.6603</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">30.1024</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">502</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">12.8347</td><td style = \"text-align: right;\">34.7469</td><td style = \"text-align: right;\">-27.0374</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.398906</td><td style = \"text-align: right;\">-27.0374</td><td style = \"text-align: right;\">27.5185</td><td style = \"text-align: right;\">1.02739</td><td style = \"text-align: right;\">1.40166</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">503</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6082</td><td style = \"text-align: right;\">23.9739</td><td style = \"text-align: right;\">-25.8737</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.964192</td><td style = \"text-align: right;\">-25.8737</td><td style = \"text-align: right;\">27.9632</td><td style = \"text-align: right;\">-0.696942</td><td style = \"text-align: right;\">-0.696942</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">504</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3797</td><td style = \"text-align: right;\">33.5923</td><td style = \"text-align: right;\">-25.3461</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.912656</td><td style = \"text-align: right;\">-25.3461</td><td style = \"text-align: right;\">26.5635</td><td style = \"text-align: right;\">-0.224364</td><td style = \"text-align: right;\">0.303854</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">505</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3797</td><td style = \"text-align: right;\">33.5923</td><td style = \"text-align: right;\">-25.3461</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.590583</td><td style = \"text-align: right;\">-25.3461</td><td style = \"text-align: right;\">27.0681</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">0.748131</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">506</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.1618</td><td style = \"text-align: right;\">27.5725</td><td style = \"text-align: right;\">-25.2787</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">-25.2787</td><td style = \"text-align: right;\">25.4022</td><td style = \"text-align: right;\">-0.0195941</td><td style = \"text-align: right;\">-0.0810465</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">507</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3686</td><td style = \"text-align: right;\">32.9134</td><td style = \"text-align: right;\">-25.2642</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">-25.2642</td><td style = \"text-align: right;\">25.3413</td><td style = \"text-align: right;\">-0.00163741</td><td style = \"text-align: right;\">-0.0819738</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">508</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.9088</td><td style = \"text-align: right;\">23.5613</td><td style = \"text-align: right;\">-25.973</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.743265</td><td style = \"text-align: right;\">-25.973</td><td style = \"text-align: right;\">26.9938</td><td style = \"text-align: right;\">0.276306</td><td style = \"text-align: right;\">0.588385</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">509</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3761</td><td style = \"text-align: right;\">23.5702</td><td style = \"text-align: right;\">-26.1859</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.917502</td><td style = \"text-align: right;\">-26.1859</td><td style = \"text-align: right;\">26.6893</td><td style = \"text-align: right;\">0.141407</td><td style = \"text-align: right;\">-0.184401</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">510</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.2422</td><td style = \"text-align: right;\">34.1285</td><td style = \"text-align: right;\">-25.6943</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">0.890245</td><td style = \"text-align: right;\">-25.6943</td><td style = \"text-align: right;\">27.0689</td><td style = \"text-align: right;\">-0.249144</td><td style = \"text-align: right;\">0.292641</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.11051</td><td style = \"text-align: right;\">1.11051</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& iteration & chain & σ & μ & lp & n\\_steps & is\\_accept & acceptance\\_rate & \\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 501 & 1 & 11.2875 & 29.3936 & -25.2256 & 3.0 & 1.0 & 1.87558e-6 & $\\dots$ \\\\\n",
       "\t2 & 502 & 1 & 12.8347 & 34.7469 & -27.0374 & 3.0 & 1.0 & 0.398906 & $\\dots$ \\\\\n",
       "\t3 & 503 & 1 & 10.6082 & 23.9739 & -25.8737 & 3.0 & 1.0 & 0.964192 & $\\dots$ \\\\\n",
       "\t4 & 504 & 1 & 10.3797 & 33.5923 & -25.3461 & 3.0 & 1.0 & 0.912656 & $\\dots$ \\\\\n",
       "\t5 & 505 & 1 & 10.3797 & 33.5923 & -25.3461 & 3.0 & 1.0 & 0.590583 & $\\dots$ \\\\\n",
       "\t6 & 506 & 1 & 11.1618 & 27.5725 & -25.2787 & 3.0 & 1.0 & 1.0 & $\\dots$ \\\\\n",
       "\t7 & 507 & 1 & 10.3686 & 32.9134 & -25.2642 & 3.0 & 1.0 & 1.0 & $\\dots$ \\\\\n",
       "\t8 & 508 & 1 & 10.9088 & 23.5613 & -25.973 & 3.0 & 1.0 & 0.743265 & $\\dots$ \\\\\n",
       "\t9 & 509 & 1 & 10.3761 & 23.5702 & -26.1859 & 3.0 & 1.0 & 0.917502 & $\\dots$ \\\\\n",
       "\t10 & 510 & 1 & 10.2422 & 34.1285 & -25.6943 & 3.0 & 1.0 & 0.890245 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×16 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m iteration \u001b[0m\u001b[1m chain \u001b[0m\u001b[1m σ       \u001b[0m\u001b[1m μ       \u001b[0m\u001b[1m lp       \u001b[0m\u001b[1m n_steps \u001b[0m\u001b[1m is_accept \u001b[0m\u001b[1m accep\u001b[0m ⋯\n",
       "     │\u001b[90m Int64     \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │       501      1  11.2875  29.3936  -25.2256      3.0        1.0        ⋯\n",
       "   2 │       502      1  12.8347  34.7469  -27.0374      3.0        1.0\n",
       "   3 │       503      1  10.6082  23.9739  -25.8737      3.0        1.0\n",
       "   4 │       504      1  10.3797  33.5923  -25.3461      3.0        1.0\n",
       "   5 │       505      1  10.3797  33.5923  -25.3461      3.0        1.0        ⋯\n",
       "   6 │       506      1  11.1618  27.5725  -25.2787      3.0        1.0\n",
       "   7 │       507      1  10.3686  32.9134  -25.2642      3.0        1.0\n",
       "   8 │       508      1  10.9088  23.5613  -25.973       3.0        1.0\n",
       "   9 │       509      1  10.3761  23.5702  -26.1859      3.0        1.0        ⋯\n",
       "  10 │       510      1  10.2422  34.1285  -25.6943      3.0        1.0\n",
       "\u001b[36m                                                               9 columns omitted\u001b[0m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DataFramesMeta\n",
    "first(DataFrame(idata), 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Vector{Float64}\u001b[90m (alias for \u001b[39m\u001b[90mArray{Float64, 1}\u001b[39m\u001b[90m)\u001b[39m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "typeof(demand_seen)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we really want to get is a posterior predictive sample, though. It looks like `Turing` doesn't quite have that functionality fleshed out, but there *is* an undocumented function (see [this link](https://github.com/TuringLang/Turing.jl/blob/5990fae9f176e84d83bd119fa4a6b0e68f028493/src/inference/Inference.jl#L463))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Found initial step size\n",
      "│   ϵ = 0.003125\n",
      "└ @ Turing.Inference /Users/nelsontang/.julia/packages/Turing/FlV8f/src/inference/hmc.jl:190\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Chains MCMC chain (200×2×1 Array{Float64, 3}):\n",
       "\n",
       "Iterations        = 1:1:200\n",
       "Number of chains  = 1\n",
       "Samples per chain = 200\n",
       "parameters        = y[1], y[2]\n",
       "internals         = \n",
       "\n",
       "Summary Statistics\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    mean \u001b[0m \u001b[1m     std \u001b[0m \u001b[1m naive_se \u001b[0m \u001b[1m    mcse \u001b[0m \u001b[1m      ess \u001b[0m \u001b[1m    rhat \u001b[0m\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
       "\n",
       "        y[1]   20.2274    0.0954     0.0067    0.0087   153.2982    0.9958\n",
       "        y[2]   20.4225    0.1048     0.0074    0.0079   153.6657    0.9953\n",
       "\n",
       "Quantiles\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    2.5% \u001b[0m \u001b[1m   25.0% \u001b[0m \u001b[1m   50.0% \u001b[0m \u001b[1m   75.0% \u001b[0m \u001b[1m   97.5% \u001b[0m\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
       "\n",
       "        y[1]   20.0531   20.1593   20.2187   20.2850   20.4118\n",
       "        y[2]   20.2046   20.3618   20.4250   20.4954   20.6124\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@model function linear_reg(x, y, σ = 0.1)\n",
    "    β ~ Normal(0, 1)\n",
    "    for i ∈ eachindex(y)\n",
    "        y[i] ~ Normal(β * x[i], σ)\n",
    "    end\n",
    "end;\n",
    "σ = 0.1; \n",
    "f(x) = 2 * x + 0.1 * randn();\n",
    "# Create x/y data\n",
    "Δ = 0.1; \n",
    "xs_train = 0:Δ:10; ys_train = f.(xs_train);\n",
    "xs_test = [10 + Δ, 10 + 2 * Δ]; ys_test = f.(xs_test);\n",
    "\n",
    "# add observations\n",
    "m_train = linear_reg(xs_train, ys_train, σ);\n",
    "chain_lin_reg = sample(m_train, NUTS(100, 0.65), 200);\n",
    "\n",
    "# Set a function parameter to `Missing` to predict it\n",
    "m_test = linear_reg(xs_test, Vector{Union{Missing, Float64}}(undef, length(ys_test)), σ);\n",
    "predictions = predict(m_test, chain_lin_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ys_pred = vec(mean(Array(group(predictions, :y)); dims = 1));\n",
    "sum(abs2, ys_test - ys_pred) ≤ 0.1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking from the above example, we can then call `predict` on our earlier model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chains MCMC chain (1000×1×1 Array{Float64, 3}):\n",
       "\n",
       "Iterations        = 1:1:1000\n",
       "Number of chains  = 1\n",
       "Samples per chain = 1000\n",
       "parameters        = demand[1]\n",
       "internals         = \n",
       "\n",
       "Summary Statistics\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    mean \u001b[0m \u001b[1m     std \u001b[0m \u001b[1m naive_se \u001b[0m \u001b[1m    mcse \u001b[0m \u001b[1m       ess \u001b[0m \u001b[1m    rhat \u001b[0m\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m   Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
       "\n",
       "   demand[1]   30.6618   11.6674     0.3690    0.4921   1026.1315    1.0023\n",
       "\n",
       "Quantiles\n",
       " \u001b[1m parameters \u001b[0m \u001b[1m    2.5% \u001b[0m \u001b[1m   25.0% \u001b[0m \u001b[1m   50.0% \u001b[0m \u001b[1m   75.0% \u001b[0m \u001b[1m   97.5% \u001b[0m\n",
       " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
       "\n",
       "   demand[1]    8.1583   23.0186   30.5773   38.6348   53.3413\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# See predictions for 1 additional day of demand:\n",
    "demand_preds = predict(newspaper(Vector{Union{Missing, Float64}}(undef, 1)), idata)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the demand for this day here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can plot the histogram directly with Plots, too\n",
    "Plots.histogram(demand_preds)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can extract the values and optimize over this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Then the posterior predictive samples would be:\n",
    "demand_samples = demand_preds[:\"demand[1]\"].data |> vec\n",
    "\n",
    "bayesian_optimum_supply = optimize_problem(demand_samples)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we'll visualize 1000 imaginary draws from this posterior demand distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ndwVpQE3H6sXzzz//wAMP1NXV3XXXXQ6HY/bs2bNnz545c+aXvvSleDwueeilGGsqlcptJO+54DhO4dusFtRfsZ2dnWeeeeaBAweWLl366KOPkh9UT08PQoiMApFYt27dxIkTSeaihMIPcJQeUkSD1wvICgeQk4cQ2rNnD8b4F7/4BUJozpw5mr/KgoxrQAiReh5dXV3klYjEAkgNQCl358tf/jKSxQIwxiSNdMqUKQihn/70p6MdlBQOIB/JWwLhiiuuuPfeexFCM2bMIGmG8Xj8jjvu2LRpEykQQjqE3DXuu+++aDRKURR5Jfp//+//YYwfe+yxjo6Oiy++mKRA7d69m7yk/vWvf5Uctueeey75lmRxkhC7wtEpb6hsMNnwH//4R96ukIcIRVHct28feUn1er09PT3KjUshwl27dmFZzjv5KI0Q3rVrl/KJy7KQrEwyA5SvB8AUckOENrgtKN8TcKFfWWXdFpTvCThfknsWWS3s27ePxB8fe+wxjLEgCOQ2snjxYrKCmhBh3npjBTs2t8Hc1rJ2Jw/tySGBToTQo48+Ki0kiUpNTU3pdJoc469//WuMcV9fX319PcoJEeY9F8rf5lqo5orleZ4IryVLlsjLdD355JM/PMJ1110nXcPvvfcexviJJ554/PHHyUhD9T9ANYDA0kLuzfTf//3fEUKBQGDOnDkkDHTfffeV8lUWZECvx+M5+eSTpaqy5E569913k49LliyZP38+udwnTpwobUtSAhFCFEUdOHBgtIPKuplijM855xzpQsxkMu3t7QihhQsXfvvb3z7uuOMQQvPnzyfDVURRlKqcf/TRRxhjsgJCiJQofOutt8gBzp8//6KLLpo7dy5CqLa2dmhoSPqZ0TQ9bdo06b3kd7/7nfLRKW+obLDyzTRvoVF55yg0rl5gKZ+4LAvlAkv5egBMIfeegCv/tqB8T8CFfmWVdVtQvifg4gUWPqIYnE7nGWecQZzfCCGpXrGywCKF8idMmHDbbbdl7ahgx+Y2mNuaSoHFcdzSpUtJ49OnTz/ttNOkvAVSXeJzn/sc+Thz5kyn00kkcpbAynsulL/NtVDNFSt/B5BDbr+E3BwschFu2rSJfFT/AywICCwt5N5Mk8nk1772NXKP8/v9//M//0NuMZq/yiIUCp1zzjkk2eKUU075xje+gY7cSRmGOffcc8llt3TpUhKlpml69+7dZFuGYUg04ZRTTlE4qNyb6ccff0zc3eRmun///tNPP51ccG63++KLLx4ZGZFWXrlyJZINb7700ksRQmPGjCGvJhjjJ554QroLIITmzJlDat5Il/tvf/tbYkN9ff2vfvUryfjRjk55Q2WDlW+mWQKrra1t6dKlUiqrcuPqBZbyicuyMEtgKVwPgCnkFViVflsoeE/ANrotKN8TsCaBlclkbrjhBuLUoSjquOOOe/7556VvlQXWa6+9RsJVWWUaVHZsVoO5rakUWBjjkZGRa6+91u/3S6epvb39t7/9Lfn27bffnjZtGkLI5XJ94xvfIJZkCay856LgmcqyUM0V+7Of/QzloyiBpf4HWBAQWHoiCMKhQ4fyngxtX2WRTCZDoVDer0KhUDgcHm3DM844Q34BlUI6ne7u7tY8SUI8Hv/kk0/kNevkl7soir29vbldkffo1GxYusHKlN648olTRuF6AKwD3BYKYrPbQi59fX1y5a2eaDSqo5GltEY6c8+ePXmvqMOHD5Ohf3KUz4XKMyVHxyu2IOp/gApQGCZAsDU9PT0vvfTSqlWrKIo6ePAgmZ3KUgwPDxN39969e0ldGaM3BIAqB24LQBlQPhdFnSnrX7F5gTINNmfDhg2XXHIJx3FXXnllpVyUAAAYCtwWgMqiQq9YKNNgc1asWHHCCSfMnTuXFCG0IDU1NT/84Q/RkVHNZdgQAKocuC0AZUD5XBR1pqx/xeYFQoQAAAAAAAA6AyFCAAAAAAAAnTE/RPjLX/5y9+7dpHoYAAC2p6ura+7cuVmTrlQccOMCgKpCw43LfA/W7t27u7q6VK7McVw6nTbSHKBMyGtyApUOGWCvcuWurq7du3cbak8ZgBtXdQI3Ljth9I3LfA/WlClTpkyZctNNN6lZOZlMZjIZUpQMqGg4jhsaGmprazPbEEAHDh061NbWJp+jVwGVP3aLAzeu6gRuXHbC6BuX+R4sAAAAAAAAmwECCwAAAAAAQGdAYAEAAAAAAOiM+TlYAAAARsOy7MjIiHxJTU0Nmc+VsH///n379s2bN6+C6kQDAGBlwIMFAID9eeqpp8YdzbXXXku+Yhhm2bJl06ZNW758eWtr64YNG8w1FQAAewAeLAAA7E9nZ+fEiRPvvPNOacmkSZPIPxs3btyxY8fOnTsXLVr0wAMPrFq1av78+cuWLTPJUgAAbAIILAAA7E9nZ+eJJ574la98JWu5IAj333//mjVrFi9ejBC67LLLHnjggS1btoDAAgCgRCBECACA/dm3b9/06dP/8pe/bNq06dlnn5XKfnZ3d/f19XV0dEhrdnR07Ny50yQzAQCwD+DBAgDA/nR2dr799tv33ntvW1tbZ2fnpEmTtm7detxxx/X39yOE5Intra2toVCI53mn87Pb4/PPP//cc8/JGwyHwxMmTAiHw2r2nkqlMpmMynqGgJXhOC4ajfp8PrMNAXSAnEqVP8xMJuP1eotqHwQWAAA2J5PJ1NfXX3DBBbfddpvD4Thw4EBHR8eqVat27twZiUQQQoFAQFo5EAhgjMPhcFNTk7SwsbFx+vTp8jbfffddmqblIkwB5xF0OiDANDDGDocDTqU9IKdSpcDS8IIEVwkAADbH6/Xu3btX+tje3r5+/fq1a9eGw2EyfY18drloNEpRVH19vbyFhQsXLly4UL6EzJshV2YKECmmcmXAynAcl8lk4FTaA7/fHwgEVCont9tdbPvgsgYAoOpob29HCA0PD7e2tiKESKCQ0N/f39TU5HK5TDMOAABbAB6sowiHww0NDWZbAQCAnmzfvv0b3/jG1q1b58+fT5a8++67Xq/3mGOOoWm6vb19+/btX/7yl6WVlyxZorsNPT09JByZTCZramqSyaTf729oaHA4HIcPH+Y4LhAIxGKxGTNm7Nu3r7a2NhAIHD58mKKoYDBYV1cXjUYRQrW1tYcPH/b7/TRNi6KYSCQCgUAymfR4PCRoFQwGyZo0TUejUa/X6/V6Y7FYXV1dOp1mGIam6Zqamng8HgwGE4lEbW0tMSkYDDIMk06naZoOBoNutzudTlMUFYvFKIpqa2vr7+8XBGH8+PHxeLyuru7QoUPEjEAgkMlkRFGMRCJkw6GhoWAwKAhCTU1NKBQKBAIcx9E0TVEUadDn87nd7kgk0tTUxHFcXV1dKBQiHZJIJPx+P8a4vr7+8OHDGGOv1+vxeBBCXq83mUyS46IoCmNMuqWpqSkcDvv9foRQOp1uampKJBI+ny8SibAsO27cOITQoUOHyMper1cQhHHjxo2MjCQSifHjxyeTSZ7nEUKpVAoh5Pf7Y7HYhAkTent7yRmpq6uLxWJTp07t7u4WBIHn+Vgslk6nk8mkw+Egsz6Hw+F4PE5MJfaLojg4ODhu3LhoNJpIJEiHIIQoimpoaCD/x+PxRCKBMQ4EAolEoq2tjeyUoqiJEye+//77ZH3i/iTnrrm5ORwOcxzX1tYWiUQEQWAYpra2lrhgKYoiJzSRSCCEHA7HmDFjXC7X2LFjP/nkE6k1ckk0NTUJgpDJZHier6ur8/v9Bw8eJOvEYjGv18txnN/vj0ajgUCgrq6OnA7S7aIosizb1tY2MjJCTkdtba3D4WhoaOjv73e5XOT65HmeZdlAICCdO1EUyYFPmjSpt7fX7XY7nc5EIuFwONrb2zs7O+vq6qSfTCAQICclHA7X1tYSw+rq6gRB8Pl84XC4ra2N5/nDhw+TisGZTIZcJ/F4nJw7ssdAIBAMBh0ORywWy2QyLMuSnxI5QN1/6XJAYB1FLBYDgQUANuPUU091Op1r16697bbb5s2bt2PHjp/85CdXX321w+FACK1evfrHP/7x8uXLTz755Pvuu+/VV1/dvn277jYMDQ2Rxx65+0cikfr6eofDQQRWJpMZM2ZMKBSaPHlyb29vMBjkeb6np4em6bFjx1IUNTg4iBCqq6vr6empr693Op2CIJAXwng8XlNT43A4KIoSRXFgYEAURZfLNTw87PP5AoHAyMhIJpNJJBKpVMrhcASDwZGRkcbGRiKJEEKxWGzs2LGpVCoejzudTpLMG4vFnE7n0NAQQsjn8x06dIg82EKhEMa4p6enoaGBpmlBEOLxuCAIQ0NDZMOenp6mpiaWZevr63t7e8eMGUMS/InGIpLL5/ORllmWpSiqv7+fdAjRfOS5eOjQIYxxbW1tTU0NQqi2tjYSidA0TSryY4wzmczw8DBFUX19fQ0NDRRFkUd1JBIJBAIDAwOZTMbn84mi2NPTk06nR0ZGvF4vz/M1NTX9/f0kwTkajTIMQ1EUEQperzeVSvn9fnIWwuEw2bC1tfXQoUOiKJIQodPpjMfjNE2TJ/Tg4GAoFCKmEhEmCEJvb6/X6x0YGIhEImPHjiUyDiHkcDjIHoeGhmKxmCAIDQ0NkUiktrb24MGDRHO3trb29PQghEi/ud3uVCpF0vj6+/sZhqmpqenr6xMEIZ1OkxNKVq6rq8MYRyIRcj0IguD1eseMGdPf348xpijK5XL5/f6hoSGPx8NxXDwe5ziOHHhfXx/G2OVyDQ0N1dbWkjM4PDxM2iSHjxBKp9MY41QqRTp5eHgYIVRfX+9yuRwOR29vL5H7giCwLMswzJgxY6RzR6RnJBKpq6sjAsvtdpPfRXNzc09PD8Mw0k9GEATyTjIwMECEVzgcJoowEAj09/f7/f5MJnPo0CHyi4jH4xRF1dTUhMPhuro6aY/19fWCIJDjSiaTRBkT3X/sscfq/kuXAwILAACb4/F4nnnmmZUrVy5duhQhRNP0VVddRZKoEELr1q3r6upaunSpw+GgafqOO+44/fTTzTS3QuA4jviW7IRUvwPQF0EQdB9FizGOxWL6tqkvILAAALA/8+bN27NnT2dnZzwenzlzJomkEGia3rx5889//vP9+/fPmjXLfqLBIBKJhDX7CmNczt2RmKxlIVE204nFYmRAib7IPV4WBAQWAOgMwzDWfPBUOTRNZ5VakBMMBufNm1dOe6xMMpmUfyQBykohHA7Lp/HWAMnmMWLl8pN1KoFyAqMIAUBn5EPSAKAiyPIEWCpSRlJ/yonFA09VgkV8b6UAAgsAAMAcQqGQ2SZ8ipX9HCTT2VKAAisDJPk9Lxa8JPICAgsAAMAcpJFlgBzry5fyO9UAOaTOhfUBgQUAAABYCIs8Po1OrgKVZntAYAEAAABANkYLLOs76ioRhcBi+QGBBQAAAABVRCqVsoibUHc3Hsdx+jZYCiCwAAAAAKDySCaTagQKmQNHjiiKpSibcDisedss7O3GA4EFAIZj75sIYATaxqhbxC0BlAcyOaDyOpYKmSlApggsJ+l02mh3FwgsADAcHV/4gCpBW90E69R9UE9lVTGtOCplpCqZ07CclOjGUwMILAAAAEAHtPnPyjyzDQCUDRBYAAAA1qJCI30Wn5XPslh8sh1AMyCwAAAArAUk7VUVILCysM4gxxIBgQUAAAAAxmKp8gEWh+d5ewSOQWABAAAAgIFgjK0826MpiKJoe9EJAgsAAAAAygeEgBEILAAAAAAwiDKMk7cmkHSlFxbvSRBYAAAAgAmk0+nyl5cE7AQILAAAAMAORCIRs00A9AcqIRsECCwAAABAFeBwsiVwWg0CBBYAAABQBBaPy5QNjLE9yjUBBgECCwAAACiCyh0EJ4qijgWWeJ6H4gvaGBoaKriODfrWabYBAAAAAFAOWJatiHGLZY7ZGe2SzE3dU3MWbBC4BA8WAAAAAFiIgYGBcu4ulUoZ2j7P84a2b1lAYAEAAACAHajc6G0WMFUOAAAAUCbs8UtXbQQAACAASURBVMgBDMU2Sfe6FwQZHBzUt0E1gMACAACwNERaQbEiANAAyfcy5f0EBBYAAIBpYIwLJvya8vINAPaAhE1NSZkHgQUAAGAa6XSaYRizrQAAm2NK0QcQWAAAAABgMuCntB8gsAAAAMyB4zizTbA/MDjAICApsCAgsAAAAMwhHo+XZ0ccx0mBSH2TUaxft1NN0XCrURE1NiG0XRAQWAAAADZHPmuevskow8PDOrYGEKLRqNkmADoAAgsAAAAAdCMUCpltAmAJQGABAAAARoExzk01M3puFnNRDptaP6gK6AUILAAAAMAoMMbpdDprodGzC1uZSswJ0wbLsuUZYaAyZS2RSBhtSRYgsAAAAABACUiK0gDLsuVx16l0iJZ/6AAILAAAAEB/RkZGzDZBN+wd0wQMAgRWxcPzfNkGewMAAKjEyslGcM8EygAIrIqH53l4uwIAwPbk5nJpRipaAdgSi4h7EFgAAACAKiKRiIl7t2BqvF0rMqRSKZ7ndWlKFMXyzwNIJng2HRBYAAAAAKAFmIenIBhji/iTyg8ILAAAAMBawCyNgA0AgQUAAABYC5hIGLABGgVWLBZ78cUX33jjjVzX3/79+7dt2zYwMFCybQAAADbHIskiJWJublYZgIFEgAa0CKxbb721oaHhq1/96qJFi0455RTpp8UwzLJly6ZNm7Z8+fLW1tYNGzboaqrOdHd3m20CAADVzmiJ2xqGuZFU4vInFCPLDNoyDh0HMOpCmUOo5S/RqYwgCBVxyRUtsB577LEbbrjh4YcfTiaTO3fufP/996+//nry1caNG3fs2LFz585kMrlly5Zbbrnl6aef1ttgAAAA+6PBs0WegnmfhfbwkwESZQ6hmuihzPvCwDBMRRTaKFpgbdq06ZJLLrnwwgsdDsfixYs3bdrk9/sRQoIg3H///WvWrFm8eDFN05dddtmSJUu2bNligM0AAABAEVTE0wgAcmEYxrjGjdapzqLWDoVCr7766vr16xFCoijSNH3ppZeSr7q7u/v6+jo6OqSVOzo6fv3rX+tnKgAAAAAAQDbaqnYZHWktTmD19vYihOLx+Be+8IW33nqroaHh4osvvvnmm71eb39/P0KopaVFWrm1tTUUCvE873R+tpdYLJY1aybDMG63W+ULlnCEoszOiyiKue3kXWhxSDS6Es3W61RajdzTUYknqCjIqVRZEwhjTFGU0SYBAFA9xGIxl8tlthXZFCewiIq68sor169ff8stt+zatevGG2+Mx+ObN28mMdpAICCtHAgEMMbhcLipqUlaeO+99952223yNmfPnj179mzSckFSqRTDMLqozpGREbfbrWahxWFZNpFIVETGnxye50OhEE3bsFBI7lUkX2JLeTE0NETTtMqzmUgk5DcKAACQwbEwhJAgCHJnh75kMhnjGq9ciusR8pC4/vrrr7vuOoTQ0qVL0+n0jTfeePvttzc2NqKjZ9CMRqMURdXX18tbuOaaa6655hr5kptuugkhNH78eDUGJJPJTCZD9lUiPM/n7jTvQouTyWSi0ajcd1gRcBzncrna2trMNkR/cq8i+ZLu7u7JkyebYZeBYIzb2tpUCixQVyUSiUTGjh1rthV2xpSiDEbvNB6PNzQ0GNR4JpMh2diAnOL8B+PGjUMILVy4UFpy0kkniaLY3d3d2tqKjri4CP39/U1NTRb02gEAAACVSHlC7UY7k4AqoTiB1d7e3tjY+N5770lL9u7d63A4pkyZMmnSpPb29u3bt0tfbd++fcmSJbpZCgAAAFQ3UG8CqCCKE1hut3vVqlUbN258/vnnE4nEtm3bbr755ksvvdTr9VIUtXr16rvuuuuVV17hef7uu+9+9dVXL7/8coPsNoWs9HxrwvO81fKxGIaxWp06AAB0RxAEqHhefhKJhNkmAPkpOivt5ptv7u/vP+ecc8iIoYsvvvj2228nX61bt66rq2vp0qUOh4Om6TvuuOP000/X2V5TiUQidXV15d/v4OBgc3OzypUjkYjP56utrTXUpKJIp9MURVXc6AEA0BdBEBwOh16tWfClBWOsbbQ8UAowMbZlKXoMl9vtfuCBByKRyFtvvTUyMvLggw9KKas0TW/evDkcDr/++uvRaNRm7isTsdosDQAAaEA+Bqh0TJkSB7ATBS8h208xaTQax1UGg8GTTjpptK/mzZtXgkkAAAAAUBIgQAuSTCZ9Pp/CCior2wGjYcMqRFUCjHMBADsx2qzPCCGO4yD0ViwgDgDTAYFVqagszQoAQEWgkAnAsqy9ZwIAAFsCAstMyjwjOgAAAAAA5QEElkb6+vpKbwRqugAAAABWRt/BGVUFCCyNWHCMNAAUhdXqpQHVCSRLWRwIT2sGBBYAVCk9PT1mmwBUBoY+YvXKlGBZFsqcmoiaclzVFrQBgQUAAAAoURFBIvCEEcwqXqWmLka1OcNAYAEAANgEqN4CANahigRWiS9hIyMjelkCAABgBOWPkZVnKDTGuKiUQShBrp5UKgXOP4OoIoFVokKqCCc5UD309vaabQIA5EehaKo2RFGMRqPq17f+9HxlrtGj0CEwYMs4qkhgAYCdgNLegGWB6VMLok0CJhIJbbvTvCFQCiCwqgXwwAFAJQLhG0BCd9cgYCggsKoFyCHTABQyAEwH5nuwPuUfHGf9GKguYIwr+gUDBBYAjAqU4gQAoCCjlXcyTgZZM+Sn+yDWdDpd0SliILDsiS4z+QAAANiPsgXaqm0wI3hbswCBZU8qWvUDAAAYR1EDEgFAM9UisGBUCwAAgNFoe7UrfQaVyvKd2GBKn2Irk1Un1SKwBgcHzTYBqEgwxpXu54dUfTXs379/27ZtAwMDZhtS2WiTDgqP6nQ6bb8HuWUjDOqDpwzDWG3aAI7jrNax1SKwlKk4j7FBBmsu5XD48GF9LTGUYh+ilT5Bqf2eT/rCMMyyZcumTZu2fPny1tbWDRs2mG1RfjDGFXenKh1BECp6HFllUdFlICzoVAOBhVAFpiLqYnBuI5pLOVTWmOGCNxGrvQYBhrJx48YdO3bs3LkzmUxu2bLllltuefrpp802Kg8URcGVCZSI1SSIvQGBVb1U4duwSmAMZvUgCML999+/Zs2axYsX0zR92WWXLVmyZMuWLWbb9RmiKFotFlNBVNzLs9GM1iEa0pSTyWTe5eWvCmZZQGDZBHi1BQANdHd39/X1dXR0SEs6Ojp27txpoklZiKII0yJpRnKuV5aXvQxkyaDh4eFiWxitS2HWEAmn2QYA+tDX1zd58mSzrQCACqO/vx8h1NLSIi1pbW0NhUI8zzudn90ed+/evWvXrqwNGxsbR3uJzyKZTLIsy/M8y7IkFZf8T/6SNCOapkVRTKVSPM9LiUdkIUJIvgnGmPxDgoZkOU3TZCuMMcdxoigKgiDtizxNybfkf7KcrMnzPE3THMdJjZNnJ2kEY0xRlHxDsrLUCMMwHMeRNUVRJCuT1sguCBRFkQ0lk1iWJXuX75dsSP4KgkBRFDlMcjgOh0Oq7s0wDNk72ZxsQj6S/6UNeZ6PRCL4CMQAhFAmk5EOluM4qbdpmiaHL61MDpA0RT5ijMk/0uGQ/0mbxAxygNI6DMOQzpG6xeFwEDvJHkkjgiCQbiFXhcPhoChK6nDyFWmW2Cx1iGQ/ORE0TZOjy2Qy8quFnK/+/n7SPtkjWShdkHmvFnmHkG8ZhiHWkuMiu5OOjnxF/s+6hrM2lF/J5FwQg6VekjqcYRjSJkVR0nGRY5euFoqiiNnS1ZLJZEhfkeMlLZDWkskk6fyCcBzncrnUrCkBAguoYJLJJM/zdXV1ZhtiFcitSvdmY7FYMBjUvVkrQCImgUBAWhIIBDDG4XC4qalJWtjd3f3yyy/LN8xkMnV1dSqTghmGaW9vr6urQx8coBcsED/4BC1YgD844Jh/nLhnP5o/k5w1jLH4u+dOuugs7HSQU0kePxhj6qNuau5M8cMDaMECiqLQBwfwggUIIfTBAXrOCWJPH06z9Pz5pBH8wSeUSFMLFuDeQap3iFowDx95jFEU9WkWzvufUPPni3v2UxSi5h+HUhlxMETPnk1RlPjGB6ilCcVTlEihhQtzN0QUNXXhQoqixPc/oRcswC/9a9IJ06jG+k9NpSgKY/HjbiroRQ1BdLD/mIULyVYI46kLF1L7D1HTx2GXU9yzn3Y50QnTkdOBMf60Q97fjxYs+LSjRBEhRFEUfv8TjGl60SLSn59e5x8cQAsX4h1vjp83kw76xX3daMEMces/xv7b58XuXrRgZoENMUZb/zH2mAnI7UOcQJEjOrJHaWX8/ifUggWobxh53dSYOpZlR0ZGWlpayKlBXYfxUOSYBSdhjNEnvSiSFN97Lzh1vGPX/tYzFokfdWHsoBctwh8coMge3/+EEumpixbh9z+hFi5ER/9mRVFEew/QFC0iTC1Y8OkFEInjeJKa04IEEX9yCDmd1JQGVOsT9+ynFy6UH9dnV4u04a4Px39xkbj15QVfORUhhD844JhzgrDjzZYzF+P3P0EIob7hScdPpcbWC0+/3HBMGzF1Ws5Jxx8coOfPl3fIZz155H+KosR/7kETWqnxzeiDA6LoIoeA9+yXXy3i+5/QCxdmbYjDMfzOxxOWLkTvfIw5Dk2YQLU2IoTE9z8h5w7v2Y8RIhuKCH96sp75x6J/PzXLVPm5kzpHfOYfTecuRbGkGIlTxx9PURS5zEL/eCuTyagUWDzPg8ACqgjyhm22FUVgtLUHDx40wpEZDoftKrAaGxvR0UGNaDRKUVR9fb18tWXLli1btky+5KabbpI2L4jX662pqWlsbEx3D/laW9Ndg77x49PdQ75x49IHBnzjx0trRsbU10+amNtCpnfE09qaOThEViYtIITS3UPe5mZ2JCnSjK+tjayc7h5CCPna2rgUz4USNa3jkCP7EZLuHvK1taW7BsmaYizJZQRPWxtCKOn5xFVXL4g0+Sp3Q4TQZ2a0tcU97/saxzrHfaZHkSBmDoXooN/R1MiGEuRgyTe+8eOZwZi7uZnyedNdg5TL6WltpdyuT0060iHk/892esTOoyzpGvS1tcWc3trmZro+yBwe8Y4fH6GddS0tzFDce8TC0TZECEUcLrfXR3vdmBdyj1S+MpcRqRqvs3UscWO0HVmZjaS5BFvb1oYQYkJJnhU5h9PjD3D0SKC5OXMoRPYu7VE6NdKS7N0dHJY66tO+dHkFh8fd1oY5numP0DVeZ3MLXecfrYXPToLLm3QcCLa1RShnvexqiVPO4JFTz8cz5NxFaIfHHxjNMHK1ZPVe1v8IoaRnn7u+wSVdV1nXateg1H7WhoLDk3J2BdraUp2HcYpxjxnjIt0l9duR8yhvOUI76hV7QCLicNaPGyd4ogJ2uEmDBwZ848cLvg8aGxtVCiyfz6dmNTmQgwXk5+DBg2abYEMOHTpktgnAUbS2tqIjgUJCf39/U1NTsa+qQIXimthqtgnFQblduXIZUINjTJ17xpRy7rEaz1Nl+TzMAmrPANXApEmT2tvbt2/fLi3Zvn37kiVLTDQJKCfOCS2FV7ISrmMn0/4as62oWAzIoFCgGgUWeBEkwuGwNWdlB4DyQFHU6tWr77rrrldeeYXn+bvvvvvVV1+9/PLLy2aAs3Vs2fYFGA0dqDXbBMBCQA6WCVgnNVsafgIAVcu6deu6urqWLl3qcDhomr7jjjtOP/30su3ddcyEsu0LMBrPrKnM7o/MtqJ80D6P2SZYGlt5sCqlFlTFpWZXJ729vWabYAhQVCkLmqY3b94cDodff/31aDRaTvcVAFQ0nnnHmW2CpbGVwIIC3JYlmUzK84grAn2FSDKZtEjp/NKFY6VPzpiXYDA4b948jwfeyAEA0AdbCSwbU+kTPkQikSqf7sNObstwOGy2CYAd8JwwXa+mKKcDvCnWwT0dql4jBAKrUrCI80MDGmZgACxFMpmECWIBI9B3NBzlgpTiknC1jy+8kjocYxv0akqiEs8vCCwzEQTBXP2h8sHZ3d2teRcF5xIRRfHw4cOa2weMJhqNgsACANtzVKlYTbhntOtiSV68C443rnGDAIFlICMjI8orkMmbymNMXiyStWbl2NnAwEDZ9pVKpWBKWqAoXJNVVbIGgDJAB6FKxVGAwDIQaf6NVCplriWAZlRONqcLqVSqUkbCAhbBOb6Z/KP5/d4900CvAwBUMyCwVFFisaihoSG9LAGMg8zWbrYVAKAFzRkqjjHmF+QDAFsCAksVeSfmKxgBBCoLlmUrLiW/4opfAAAA6IJ75hSzTSgACKyjSKVS6sfrSRHAMlDOfQFI1w431CtW5cUvgII4JrQiuqzzrwFWwz3Fnol6lNPq4wpBYB2FZaeOKTGLy+LONgvKRx17zK4V4YGKwNk8pswT3AJWg4LJoU3CngIrk8mk0+ky7Mj69QVITUjNCoYUaDC6sGRuKQeIfAEAUDY8s6eVeY++U+YqfOua2Fo2S4yG9lbv7Aj2FFgMw5QndFL6oHrlCkOl1xfVZVYT9UPb9CpqYOXIVywWg1x4ANCMa/oUyuM224qjoOv8ZptwFE4bCSzP56q3wr49BVYFoaxIKm6GnNyiBhYM/5VIOp0um8Ayt8KnKIp5PcG2nIsQKBt0rQ/Rnz56XMdMoJwOc+0BAIMAgaUn9hMTBWFZNpFIKKygew2w0To5FArpuyMr0NPTY+LeeZ7PK/HLE38HqgFHY70ktgB7Y8T8ORYHruzCqA9XmZJLLpVBL2VCG83wPF/mx+1onays8wB9gSApYBFon5tyWyvgCOSlCmeArlKBVdRQQYsnXFs/0R6wHzA0ErAI3gXHwwwtgDWpUoGVt3BoUWQymXImYuvoJSrbCABlFEp6gmQsllAoVHBSbcBOSDPkAKVPUWxXKLeb9oFvz0yqVGCVTjgc1ivVd3BwUCHgcujQIaSrwEqn0+WcX280pNys3EPTa8Jja06cbEShNWsWbwOMA+Z4BgpCB2sLpj3RNd7yGFOdgMAyH57nFR6QUoqVXVGeqLGUzKqCnjBTBmkODg5q2EoXB5UpWXoAAFgWmOrbUOwssAx6rbdstXdbYujYwNLLjJUNoydJhEsa0IyjIWi2CQBgRewssKREK71GPBFvyvDwsJqAnV5PLIyxucWQbEyuwLL4gAbjyM1KhKsOUImrfbzZJgCAFalggaVewRQ14klhWpiiwjSl59ETMpkMFCAg6B7hys1Fs44jp1h9I69Yq/6CV7i0zC3BBQAFscgcLJBlD4xGBQssvRRMFroXxiSwLGvXcV5V6/XRTF9fX8F15PpGTba+fB31LltbVmcFqgSLzMFip3kDAX2pYIFVWXAcJwUWy1aZc2hoKHcaQd2dNJKvRY1uAFC+uR2VZT3UrQAAwFDKVgXU2Tq2PDuyAiCwTKBsboO8+fjGPa0V5oSuoHRyU1AeSgkAgI5oKHJBuZxFzZlI1weQo5LmWKTcrvLsyHXMhPLsyAo4zTbAEmQyGZ7nnU7oDR3gOM7lyv6tKmgvg4CSBAAA5EVDmVZnkXFAR/MYygUPlGoHPFgIIZROp2FuNb0o6CGrlIAXz/O2L0IGAACAECrKPweoBAQWUG6sWWA9l1QqZbTjDQQcYFlof43ubTrG1OneJqAL3oVzzDbBhlSkwOI4Tv5kqp6RUIIglOhpkw/mB0yHzIMEABbEc8J0fRt0tY+3X91w58RWqtZnthWARiiD5/SsSIEVi8XkA/E0l4nSnFmsUCtLfQsavCPJZDIej5ey37yzEOo1qSJgHFaYnxsAioLyuClZorct60XRgVrItapcqNZGQ9uvSIGlF5pLXpVe+VN5/sEyI9eLts8NL10cm4Ip0yYCNsYze5rRu3AdM4Gu8xu9F2viaKw32wTgM1wTW0zZb1ULrMrCiEoHFRFd1XfOFsldN1oqGNTNl5NKpQwqvVuduKdONNuET6la6VMe3DOmmG0C8Bl0XcCc/ZqyV1ti9HOoFB9GJpPJqiMvxVjLX0ChWArO2aKtRP5ogxkrQnSWjsqZcARBUBC4GGPQo0XhaDE2JAEAgHUAgXUUpWQ46VgrcmRkRK+mCLmPycHBQY7jUqnU4OCgvvtSCcZYrzF0w8PD8o88z2d1YN7MMwtSzvmVddkXxrhCQ64AAABGAwLrKIpKJcYYG/RELDGTXQG5Fslb590gcnPOWJY1KLleFMWs81gpYyetM6ujmnh0lq4FAKAgznEVP1GMb9EJZptQMZQksN59991//vOfWQv379+/bdu2SnmklQLLstaMjygEucwqvJRKpcrpnpGjJm2/DDPVGFrJVpoFUkONsbzuPRKPVv4VJ5NJ6wzUAICKwNVeeKIYrzUmsR4VB/hl1KK9p/r6+s4444zf/OY30hKGYZYtWzZt2rTly5e3trZu2LBBDwtLQsc4VAVRtsmkDUUQBF30q5oMrTLkcRvqnZKEjobg8uDg4Gg6CWpDAOXENWmc2SZYAsrrMdsEQB80CiyM8SWXXJL13r9x48YdO3bs3LkzmUxu2bLllltuefrpp/UwUjssy+ronIDpdHQhkUio8XwIgqBLqLQolabNzYYx1rE8vSmV7kVR1LxfmMkb0AXnBHPG0gOmQ/k8tB3rtWoUWLfeemtXV9fxxx8vLREE4f7771+zZs3ixYtpmr7sssuWLFmyZcsWnezMz8GDB/VqSs3YMSjIqQupVMqyoSVtKdssy+o49rDEuRoFQcAYK4ievLl3DMNovryhRle1YctnIWAidKCWrg+abYX+aBFYb7311saNGx9++OHa2lppYXd3d19fX0dHh7Sko6Nj586dOtg4Ojo+p6HYj4709vaabYIWKmUWamVCoRDLsgqiJx6PWzN3ENARQ+fu9Zw4w7jGAcA2FF3jP5FIXHTRRRs2bFiwYIF8OUkxaWn5zMfb2toaCoV4nnc6P9vLgw8++OCDD8o39Pv9U6dOVVksIJVKMQxDUZTb7Y5EIhhjt9sdDod9Ph9CSPqHBKHi8bjD4YjFYlKpJ2k1qUGyJBaLcRw3ODiYSCRcLleWMdL66XR6cHAwHA5Ho9FEIkGyu6SVyWqkwayP5P9MJkMiUNFolKbpoaGhSCQSj8c9Hg9CSN5L8iNiGIbjuHQ6HQ6Hw+Gw3+/nOE7eeCQS4XmepMv4fD5iXjqd9vl8IyMj8Xh8cHAwGo1ijAcHB+PxOM/zPp+PHHIqlSK78Pl8DMNk2Uxa8/l8pJG8ZySTycTjcYwxWVla7nK5yD/xeDwUCmUymUgkQhqRTBJFkfRnVvukHafTGYlESNwq1ySyZjKZ5Hk+mUzKl3McJ98wHo+73e7c8xIOh0dGRsh+ybahUIh0CFmTXAzpdJqmaa/XK5k3MjLCsqzL5aLpT99PyIhI6aPcQvnZdzqdZLIjyZ6sSzcWiw0PD8sPU/ordVEoFKqvr3c4HPIVYrGY2+0m55ecdJfLJQiC3+8fbS+Si4uiKI/HQ65JKWGR2MzzvCiKFEXRNN3f38/zvNvtJmeQ/EN+feSqdjqdUg8ok0wm5e9mgBHA3L0AYDpFC6wrr7xywoQJ69aty1pO3pgDgc/qpQYCAVImp6npsymoTjnlFLkIQwg9++yzHo8nGFTlHnQ4HOTO7vF4OI4jkqW2tpZsHo1GpXZIDYVAICAftC+tJjVIlvh8vpqammAw6PF4fD5fljHS+m63OxgMsizLcRzDMIIg+Hw+lmXHjh0rrSZtK/8YjUYDgYDT6SQfa2pqaJoOBAKJRILneb/fHwgEJEUiPxDy2HM6nW63u7a2NpVK+f3+YDAob7ympqa2tpbos2AwyHEcy7JerzcYDBIjg8FgTU2NKIoul8vr9dbU1Pj9fkEQiEpgWbaxsTEYDPb09JDHnrwzyV/SWta5wBhTFEXaJKcgt2MRQl6v1+/3E6VCFpLWfD4fxjgYDEYikUwmI2+ftBMIBHieJ+I41ySyJk3TREjJl7MsK99QMi/rvESjUdI5Uss1NTWkn8mapMc8Hg9N03LzMplMIBAYGhqaOPHTqtwMw4iiKN9F7uHQNE3kDpEXWVcs+cfn8wUCAZZlpcMhf0dGRqRTkEqlWJZtaWmRr+Dz+cjFSQ5WEAS32511dOQfjuPIXqSEQoqiSAvk0pLbTAQWMV5+IsheyEcyPpR0kUqBRd4oAAAA7E1xAuvxxx/funXrO++8k3snbWxsREcXcIpGoxRF1dcfNSXT1KlTp06dKl9CwohyD4EC0hu2x+Nxu92iKHo8Hp7nyeZut5v8wzAMcW55vd50Oi1FEqXVpAbJEpfLRVZ2uVxEMch3Kq3vcDi8Xq/H4yGr0TRN/ATyZqVtycdkMtnY2Oh2uz0ejyiK0u6IU8TlchHxRP6X71FqUxAEiqKIsuQ4zuPxeL1e+b5I4+QYiXlut5u0QEwljYuiGIvFiOVkHWKJZIB0mPLOlGzLPUHd3d2TJ08mKiSrBXk/kN05HA7JD+RyuUKhkNvtxhiTrZxOp7x96ehyTYpEIlLnIIQ4jiPPfslUhBBN0/INJfNyGycnVH6wpDcky8m2WR4s6RRICymKSqfT8l3kHg7P8x6Ph4ha+fmV/yOdGql98pecOGlNsq+sEyRvgXzMOpXkH57n5RcAMZ60Q45LbnM8Hiei0OFwMAxDBBw68nuRulEURdKTKgWW3FkLAABgV4rLwXr11VfD4fCUKVOcTqfT6Xz99dcffvhhp9P5zDPPtLa2oqPHovf39zc1Ncl1g77oMqZPKiA0GiVWb6qIZBddKkYWlQ+n+dwVLByg0PLBgwfJtxqqD0QikSqsWVCFhwwANsflcjSPMduIaqE4gbV27drnnnvuz0eYOXPmaaed9uc///nkk0+eNGlSe3v79u3bpZW3b9++ZMkSvQ3+jGLHbeUdIFZwJj6VU7aVglmT1UhklQorWEuJZdncdbSN6NS9ZJeUXy8vbcqyLBk6R77VMOqN4zhzC6qVrbYZxtj6BJRc8AAAIABJREFU01MCAKANyukwa+bjKqQ4X/3MmTNnzpwpfbzpppvGjRt39tlnk4+rV6/+8Y9/vHz58pNPPvm+++579dVX5XrLdJQfG0NDQ8cee2zZjJFjtVKo8Xh8zBilV5xSaiZJxGIxv99vnLhMpVJSro+krQcGBrJSACsFvQSWKIq5PwS54hQEIat0HIkAIoRI9qFxPmkAAAA7oWcyxLp167q6upYuXUoSbu64447TTz9dx/aLpaigVSkVHzDGUjClt7d3/Pjx0lc8z1tNP2lDEIRUKiUNYhgYGKirq0MllDYgtaPkoyKsA8Mwdk3E5nk+d24c5UqhoVCIJACk0+lMJgMCy1AcDVb8RQAAoIGSJhX65z//+dBDD33WFk1v3rw5HA6//vrr0Wj08ssvL9m8khjNO6KmoKLyBHZZiT48z0shs6yvkslk3rne1GORmpxZE9dIB2XWDIOGUs2VMzOZjHXmnK5CnOMr0sMKVBDuqRPNNqFa0H/WxmAwOG/ePCs7ANRHW0abzlZbvW9tjJaBzjBMJpMZ7Vgwxobm1482iQ0pI27cfiuIMmTvGYGGoK09fLQAUCU4WhrNNqFagGmxlQiHw8pyQY2rY2hoSJvmUBaCpBZX7uOwlHl/SycWiyk8oU2s8C7l4BsqjuW6U/LtjTawsSJGmKpBl1GoAGBNnG1NhVcCgHyAwCoJ6dnJsuxoSfSax2RpSwAvWHjCaBTy302cLVvSnYYOkcsVtbFYbLThrpqnLwRBA1gdClF2ma/QNWV84ZUAIB/2FFjJZFLH1tSkGSkIrCwKelBMCbGVEuVR74kRRbHgnI/JZNJO80LKT3c0GlUvMfNeBvF4XF5+Qg3KCewAUDqOsQ2O+qNz82nac7w5g7IBwDrYUGDF43E1kTtpGpCCZI1a10wsFmMYpmCKvbaCUiVy6NAhzduqL0fJ8/xoyVsSgiCUntNDZsspsZESyVVIpByXys3z+i8FQSh2VEE1J+wD5YEO1FI+VVNxAEBVUcECKzcck0gkOI5TmXuUSCTKXFCR4zjLjrnjOE5ft5+5ZDKZ0it1lUixEV5BEEwXhXkBH1i14WiBSt8AoAMVLLBy0aXcNsuypcsgzWUhS6zpgBBKJBIaZjgRBMF0RaKM7QcnsiybNzaaTCbLVsY9L6Io2r7zATmuyW1mmwAAdsBWAks9DMOM5rBJpVKaHQlS2rLmAuUDAwMlpjBnMplYLGazJ2ImkzGu5juZRcegxtUwPDysoOlFUSy/4zMWi8l/BXpFyQGEEKIoR7DWbCOAasQ5AaqslRWbCCzlAVm5QUODnqnKykxlNkwZqgqRB7ZtygQUi9whRPRoMpks2BtGlN8kF6EGt6VmT6fKsDjP8wV/IDCYUTPu2dNG+8pzwvRyWgLojtPCVaZck8aZbUJ1YROBpfx0tEjwS18zpOefhufc0NAQz/PlGaxnQV+aXGANDAyQfwoWTTDiKirKLSfPhZLMLhYdc96hvqgR0P4as02obByNdSYb0NRgrgGAdbCJwKo2eJ6Xxv8XjB/pHmDK8ggyDKPgFyln1ftKgWVZDS6oorSRmiELukzaDQCWwjkO6oJWNo7GOttkAdpNYJUnW0V5XJWGHPMsdBElkktG9zlbsh7epiQJWQHNHctxnHqBpa0iv5r4L8uyGoaOml7JFgDU4ztlrtkmAHlwtY9evpWiEEWV0RYDsZvA+vjjj8uwF+Wwl3Kyjhr5pUv9CNs7JwqW1DIaNbKy9BoHRkRySxmWWObiJgBgAxwNQbNNsBaaHY3OiorA2k1g6VjMKbf2JsY4N1NnNG/TaCIsb6Dn8OHDxRtYVoVher3K3H42ZbLFYim97oYRkMu4qNGy1qzRBQAVgfu4Y8w2wSa4jp1stglFYDeBVZCspzLGeDTpQHJ45Zm8FEXlCrjRXuiLyl/W9vQqWBReR3TZV7GOEzK+j/xvTaViLppT3cPhsCiKRUWiK0LOAgCgEu9Js8w2wf7YXGDlxuOyvD4YY+VsFX3Holf5U0rfwhAYY83hM/WRu1JifDzPG+r40Sw6dcyZ0zxlNQAAJkJ53GabYH9sLrCMq06pDTtNR2MFcr2PKr0y6iOeBUWMgoRiGIZsjjE2VFubOJuN7VP9AAAAtGFzgWU0WdMLGj2YrmpLg6qn/CnYvb29BdfJm5BHAqbE4BInw1GjckhYsKhmyxmDBgBAGYqmHWNMrvIFFAUIrM/IyjRXMwccwzDyh5bmTHCVcRZtISGLpycXNM/oiuF51Q/P86XPAJj3ehBFMR6PMwxD3E6k6oEuUkbZe5dOp6VrNe9Q1nQ6neUJs/iVAwDVhYN2TZ1othEViVnVOkBgfYbkBiDPlazyTronWctHKcpT6Uspo5V3CiCLZ8mMZp5Ub8noiuF5h3AKgqDGGaZcsCOvxxFjzHGc8vyDCihMC6hepeXVjuFw2PSxogAAALYBBFYe8j5xdU9zGe3ZXEqeVjqdLt3vohKGYUqcBodhGIXYloL7JG8XmVLs9ODBg9o2zOttyhqBUfoREYUnCILVkhEBALA3vkUnmG2C+VS2wKrCd27rHG80Gi1FYImiyPN8Xu9UluMnV4vkBg0zmYyCa6f8aPO6ZW1Vegl+4h3EGBsU7APdZnEczY10sNZsK4CqxFHZ6kIXKrsLCs5YTAop2an2tLJ/y9CZlVOpFNm7LiJPIZ6VFY1Vc1DKFaHi8XiZ55zu7e3VtsfKmoimbO5SQBt0sJbyesy2AgCqlEoVWGqeQ+l0OpPJCIJgdBKPdcitPl8iPM9LOWGCIBBHSKUIVkmM8jxfUO5om/9R9yIFyteqpCMtMvmjRcwAAACwIJUqsPJmc2dR5tdrDcPgFbBISVKWZY2YC0938mbIFVXVQptqLPNpkiJ9psdDiSVGD/AEAACoXCpVYJUHDQ/d3CeuNteIKTMZlz5uzlAU0upJstHg4KAgCKUMw8wiEomYeLzlQVuFCIsPTQUAACHkGFtJUyPbDxsKLFEUR3vE8jxf1Ku/hmSj3JhRBZW6VqMFNY+bKx2FtHpyxgVBwBjnzbxWPwiUZVlpL2piixoweqRCUX61ivBQAgCgAff0Spoa2X44zTagVEi1Kpqm5UuyMsFFUSSPyd7eXitkjWQymZqaGn3bTKfTPp9Pr9ZGUwDDw8NOZ9HXjOY5iXVEfRmzWCym5iIZHh4eO3ZsaUaVBMMwNE27XK7cr3ied7v1n2hMLsVYlnU4HBRF6b4Xg2BZNkt31tTUBINB6eP+/fv37ds3b968lpaWslsH2BPnuLF8H4TRi4CiaVf7eLOt0I2K92CpGSSYTCYN1VXFppbLc4PU5wlJ6c95/RP6zmoymr9HffQtHo9LKs1OBcGliXHUjJxQiPOq8agp+5aUq4gZgfy9heO4yjqtTz311Lijufbaa8lXDMMsW7Zs2rRpy5cvb21t3bBhg7mmArbB1T7BM3em2VZUFDTtaKw32wjdqDwPViaT8Xq9ZltxFKWoN/VpXlJCsYb0rGQyqb7TBgYGtL3EDwwMSI6TTCajwdelhqJcR+l0Wk13jYyMeDx5RrMzDJPla+R5Xs1xEYeZ5DbLvUJyI4+5V0I8Htfd01m1dHZ2Tpw48c4775SWTJo0ifyzcePGHTt27Ny5c9GiRQ888MCqVavmz5+/bNkykywFbAVdY62nFVBOKk9gjYyMtLW1mW1FAdSPrlIzHFIDZBZqac6fUChUW1srD4gYzfDwsCAIDQ36p1gaUXRjNImcTqe1SZysGKuazL+8gdSRkRGrvU5UKJ2dnSeeeOJXvvKVrOWCINx///1r1qxZvHgxQuiyyy574IEHtmzZUs0Ci/bXUO48oWcAAIqi4kOEpWBcPadcETBaSIhl2dJHveW2EA6HOY4rqk5BOTG9ykBBlPPE9QrICoKgPLBAOQiYTqdLV+dqRjboG4A2hX379k2fPv0vf/nLpk2bnn32WamGS3d3d19fX0dHh7RmR0fHzp07TTLTElBuF+0H1ykAlErlebB0JBqN+v1+bdsmEonRksrj8XhWynleFSUIgjzYFIvF1HiY8u5X5agx3RPRNGevGz3UIFd2FDvDo7KfTE0GFcY4lUo5nc5oNBoIBBBCg4OD48aNy1qnFIWUSqWM8BHmYoNSvZ2dnW+//fa9997b1tbW2dk5adKkrVu3Hnfccf39/QgheUy8tbU1FAplxYL7+/vJmhLkl6jyJY09gnwhx3EO1e94HMdRLJt3E8yy5NvPljTWqTRMalBkWf7oRkazUL5QzSGQddQfbN71yZuGmhY4jqNZlvwtaCTP8+zRK6tpn+O4/N07dQLvdBQ0Vbkrcr8VOU7gOKR4IgranHdNjuMwx1EUJR7d1conXQGR40SOw5o8F6Odd/Ix71VX1C9otN2xLCsfJKeAIAgOh6OovdhHYJUn4XdwcHDy5Mlkd+pH7YXD4fr67MS9UCgkv62Hw2E1AosUDtA2ekt3v5H6oXmEUuaxLorcEK0R3spMJqPcLMMwTqfTCHViUGQ5FyuMui2dTCZTX19/wQUX3HbbbQ6H48CBAx0dHatWrdq5cycJ5hIFTAgEAhjjcDjc1NQkLXzqqac2b94sb3PChAkzZ85U+W6TSqUYhsn62QrxeEp1QQ0xHqdGRsS8m2QYMRaj5cvrfEhdy5INOJ7CWY2MYqF8oZpDIOuoP9i86wvxOEJITQtCPJ4Kh4VYzKHCSC6V4kZGcDyeVH0iOI4Lh8N5UzZVmqrcFbnf4nAURxO04olQZrQ1hXicirgot5vy0Morq9wXDkdQLElpKr882nknH/NedUX9gvLuLhKJeDwelQIrnU4X65GpVIGVleOCMc56vzSIUp43iUSiublZL0tSqVRjY6NeralEwW+nBmU5wrKs+uICZdNqCKFMJpP3qKVZmIaGhtRn9Be0XE3IWBAEDWE7DR7HCq3V/re//e3MM88k/69fv/6WW27Zu3ev9G17e/v69evXrl0bDofJj0g+EiIajVIUlfVGtHbt2rVr18qX3HTTTQih1tZWNfYkk8lMJpP1g02P6fep2xwhlBkz5GltzYwZyt0EpzNsOOVR3VReG8SaJMcIWY3ktVC+UM0hkHXUH2ze9dNj+hFCalpIj+n3trQwQ3GvCiMjwWBdayvTF/aq7j2O4xwOh8J5L2iqclfkfis4PYLT61Y8EcqMtmZ6TL+zqYlyu52tTcorq9yX4HCL7rirhEsx97yTj3mvuqJ+QXl3x/N8a2urSoGlId5VeQKLeKosNR0ecVRkLcwdY6+vj82U+qXyIpwENUJHpa+lr6+PeAfVMNqDn3R7NBqtq6tT2VRuCxRFyZ0NkUhEORKXyWTU//YKXrrGlSGNRCKau6WyWLRo0e7du8n/ckeURHt7O0JoeHiYPCnlr2f9/f1NTU15C4wBAGAPPCfOKMNeKi/JXX1J7rLR1dUltypriL42BEEo6C2zQo14SWCNNvOjKIrqFUPppZWI+ydv16lsPJPJmJ7TbboBlU5tbe3xR2hpadm+ffu4cePeeustaYV3333X6/Uec8wxkyZNam9v3759u/TV9u3blyxZYobVAACUCbpWt7rcSnspwz6qAXlYR5exe4lEQo2rQ68ITlYqCZlzpqgWdNEEUhlPI8iaPk9lOTH1KlavqCXGOK8kHW24n3SmSOaQLjbYjFNPPdXpdK5du/bll1+Ox+PPPPPMT37yk6uvvpoUo1+9evVdd931yiuv8Dx/9913v/rqq5dffrnZJgMAUPFUXogwl3Q6rZByaG8EQYhEIrW1tSW2MzIyIi/4FIvFLFjiUt+0bpVz8Kmv0Wp0uhLLsnnjVvLZIUfrokgkkjvMQpnRXJKViMfjeeaZZ1auXLl06VKEEE3TV111FUmiQgitW7euq6tr6dKlDoeDpuk77rjj9NNPN9NcoFy4JuiWFAsAudhBYCUSiWIfHnIGBgaUx15W1pQg2ijPkLQSIQO7SN1Uv99vxHR7monH45ayJ4t0Ol3sb0TDhAFWZt68eXv27Ons7IzH4zNnzpS/k9A0vXnz5p///Of79++fNWtW1b6tVSF0fZCiKTqosVgPYAqUx7p32iwgRPjZiPfRQjxlS4iRuyIUsMfIec3wPJ9KpaymCC1b01U9Upfm9V2Vc9imQdA0PX369JNOOimvxzcYDM6bNw/UVdVB0+6Z7WYbARSB96RZZpugFhBYCB3JQDL9GalSNFTQyPnRtCnJMSpxHECx6BXzGhwc1KUdqxGPx0kqYd6OssKICqB6cB87yWwTAKBUQGAVjcrcnWIRRdE6WS8lVsEgIwd5nh+tDCORkvLYq+baBNFoVOWzX6/uHa1wqEGh5ILXm+TRzDprpr8wAIBmHE1jzDYBAEoFBFZ+BEEY7XlsUJmivHssc/qX9EhWfjYX9DxhjEVRTCQS6u0ndS4wxsXOzMhxXFHhwhIDvqlUarRgWdYoRV0QRbFgb3/00Ufkn6wrM5lM2tXZBgAAYH0qUmCVoRSWKIqleHFyH/nSEuVcluHhYfm2ujyz1U/VwrKsmul0jAvtiaJ46NAhfdtkGEau80rXrFZL/1JAs6kQEAQqF8rpdE0eV3g9ADCYihRYGvJty/xQjMfj8j1ijKXEKWUPTYl25vU8FaVHTZ/WV/cIrCiKub2ayWSsE5AlWMoeqHQKVDAO2jG2HJOgA4AyFSmwNJAbK8n1ZEhPOCMGqJdn0Hs5H9IGpfiQR3tuHDaZTOroVhFF0WqDMXXsz/JElosN5gIAUBD31IlmmwDohg0FlsqX71zFI6kTvWSKXCXIn3kqg48WHxivcBTEY6Q+xirvKKJ7ch/eFRSYKwVdrr28Wi1rNvTR9KV6cUYixTzPg9IqG+4ZU8w2ATAWR0tj4ZWACsFWAos8V8o8+F+BvA8ejLHKh2gpwbKCmfiGOjlIItdo9udK24LOJGmFvMdlqeAaysn6Koqi/FhFuUWzFGreZDuWZUcb+DkagiBUQyVei+Bo1F5RGQBshrPZ6kNNbSWwJEGj7x0fY2wd0UYomPxe0N+j/jk6MDCgck2VyCN9Kr1c0hyFeTWr1WqOMwyTm8pmREQ1ay+lBz0NGiELGIvDQfstN7GVhGvKeHMN8Bx/rLkGAAbhmmb1Ymm2ElgS+j7MFEo2mEWJqehFhdvkalX3wWV6DQgVRbHEpozO7i/DuLzyy6MyjOcFCkK5Xa5jJ5ttxag425rMNYAOljpVq11xjKkz2wSbY0+BBSijuRa8ZWtXUhSlbUNRFIlXTEErWPaoTcdqAwUAAFAPzBFkNJUnsARBkCf3lFhzXCVyl49BldyNoESXxuHDh4tan2GYErVI+TPZRVGUDyYgJVKz1jH0GpMup6wxDel02oK5TSzLVsloAwAh5Gwda7YJAFDBVJ7AwhjLoy3lGWonz1gqW7iw9CmNlcNSREkoPMUlgSU//HA4XHC/mpWBmjKnBIMibgzDqGlZxwrp0uWUJeN4ni/KPzTapaK+S9Wc2VAoBAKrenAdM8FsEwCggqk8gaWN0TwrmUwGY2zNZ4bRzjlSz0LB55T3AV/QKo7jiipTqW0AQa5zTs1+86afq0GSmJYNio0W9rWswQAAAPbGbgJrNPfSaG6JaDTKsqzVBglaimITtohPUb2O0SvkKopiQVOVJy5UcPaQK0QQhIJR13Q6DWXQgUqBojUmLwIAUBC7CSyr1TzMCpblVXKWfR6X0pmkdEJRsULT+0HZkak+GG2oQ9SImhQY42LLXwH2wHvyiWabAAC2xSYCyzr1e7IGo2UZlldDGFcgIEshFatgSs9vK/jYlgcorVYLIwuLDG7QkN+m4NiT5Jrpc1ACAADYDJsILOs4riz1oMrSBGaNSlOogKCLSaU7dVT6nHIDzRzHlZLkpOPVotCUgoUKGXVQnAIAAKAUbCKwFNAWeDI9XKUByz4RjR5DULpMSSaTBRtJJBJ9fX1ZCzVnzRN0vMwklamXN1f9OM10Ol2GMqpAReOdN9NsE6yCZy50RbVgc4GVSqW0ObfMTXtXM2A+F4tPDl0GDJWYFqxKlRe525JhmDKMIhRFEcYqAspQPq/ZJlgFuqa4rqCDfuf4ZoOMAQzF5gLLOqHDoijW5WPZShO6gzGWe2iyNGWlaCB9EQRhtPcB9QLLUqFtAAAkKLeLrvWZbQWgBZsLLMuir69Fs6Ou0rGa086UyHLe6vPFYrUJswEAACodEFjmQOI4oVDIbEM0wvO8jj4PnucNkkpl9mkZLVNyc9LVZFxZZPwjAABAVVGNAss60RDrWFIs+gosjLFBXZGblq4SbS5Goz1Yue0X9FxmMhl9vZtW8xoCAABYEy0CSxCE3bt3b9269b333suNTezfv3/b/2/v3mPjuOo9gJ9zZmZ3Hl7bieN4Y1ITN7m9Te9VSUBQIoHDjSX+qhxFqlAlBFIUSAgqCEGbgkQgkUgRCPEHKCilqomqSoV/EClCFGQIiMSiCBWooCHFpnac1Ov4sV7b633NzLl/HDzd+LHeXZ/dmdn9fv5onXn+Zs545udzzpx55ZWpqSkZ4VWgUChs+iqTGBCoxKgB0ACk1Fo1zGtxEkcXE+ld/X+1G1VkX4/fIWxVZO99focAEFwVJ1hvvfXW+9///oMHD37yk598+OGHDx06NDY2JmblcrmjR4/u27fv2LFj8Xj87NmzkoPd2NLSUqFQ2PTJuvVqEsdxvEev3G8F1vrLg1sX2GEgVike3TT4Z5WEp6VY/DUVilMaCsrO7X6HsFVKV4ffIQAEV8UJ1mc/+9n5+fmRkZFkMvnGG2/MzMx84hOfELPOnz9/9erV4eHhdDo9ODh44cKFK1euyA54fXW76RcnWHLbSjbtTMM5X1utUs/Rz+vflad05lHOUBqhqK3ctLasbq+Ilrmj8DZtQ8OL/Pcev0MA+I/KEqxMJvPrX//6qaee2rt3LyFk//79Z8+evXbt2uzsrOM4ly9fPnXq1KFDhxhjx48f7+vrGxwcrE3YzUVUHXHO16ZTvn9eptL2uBIfVF6r9MtxoUiepChnHFQpyjylzXPmIXSUjna/Q6gTtbvT7xBgE5UlWAsLC5/+9Kf7+/u9KaIWx7bt8fHxycnJ4ln9/f3Dw8OyAm0wFdV+SR/1VOIDstJ2w40SsjAOnV+OfD4vKzdyXbf+49+GpV0YoNloe97ldwiwCbWipbu6ui5duuT98/bt29/73vc+9KEPdXV1iVyqq6vLmxuPx2dnZ23bVtV39vKPf/zj73//e/E2p6en29vby2x+Wl5eLhQKYoO2bYunl+h9tbi4KJ5k+Xzetu1MJiPedBNzGWNeM6Jt29lsVsxyXddxHG+xfD6vKApjTLSViAE8xVyxWbFHbzohRKxYKBQ452JHhUJBLJPP5wuFAqV01cKO49i2bRgGpVQsIGJTFEUcIGMsl8uJzYqteT+LuWJFb2tiGbFrsaT4r+M4U1NTtm27rusdoKqq+XxeHI44TO/QxFoiThFANpsVK+ZyOW8LYkXOuViGEJLL5cTBitNLKRWVT2IV13XF2bBte3l5WUyxV4iTk06nTdMUcYqznc1mvTi9vXv/JSttpiIGxpg4w6KgvXMidiSmi/PmBSz2LrYszqpXuIwx74xxzkUBibMhSkqUqVg3l8t5ZS0uPHExEEJEAN6xi92tOiGKoogfxML5fJ5zLk67uA7FLLH88vKyd7WIQxMxu65LKRWXt1ea4vx7vxSiaLwy8s5S8Tn0DsQ7n2J5Mcs7ZHEyxWGKXWSz2eXlZcbK+oOtUChomlbOkgAA4VVZglXsxz/+8Re/+EXDMF588UWy0oUoFot5C8RiMc55Mpns7HynJvPGjRs//elPi7fDObcsq8wEK5PJiBRBPHiKH7pzc3Pi2Sn+KR5RjuMkk0nveSY24mVLXoLlpS+Koriuu7i42NraurCw0NLSoqqqmC4ePAsLC+Jp530eREz3EixKKWPMe3B6qYAXm/d54Hw+Tyn1HmPiuZ5KpUTC4T0mvQeh9wOlVKzopV/5fF48Yr0T4hGJpngQio2oquotIxIF7ykrFiArCZb4Z/FckSWIFUWFSnGCJY5InATxPBari5/FiqKYxD+9BEtkM+IoxHEpiuKlL8V7906LCMBxHJEciH+K0+LFrCiKKFxCiMiuCCFij94yiURCnEMvySYrw0asTbBEGGI7rutqmiYCKL4MRIosEizvVHjlInYn5haKUn+vb5/4r5fHeNeniKH4avFOaWGlC1dxqF45irn5fD6dTnvTvd8aUUElvqhY/PeJuJbISq8sEQml1FtSFLR38czPz3d2diLBAgDwVJNgjY6Onjhx4o9//OMTTzxx7ty5lpYWQkhHRwe5d6DFVCpFKW1vv6dF/LHHHnvssceKp5w7d44QsmPHjnJ2nU6nLcsyDIMQ4rquZVmFQsE0TcdxDMMQz13LsrLZ7LZt2wzDEMkQIYQxJuIkhOTz+dbW1ugK8UgWGzFNU1GUQqFgWVYulzNNU9O0TCZjGEZLS4t4iIr6M/HwFtmhiIEQIqqRdF13HEdVVbHHSCSiqqpoExR78VaklIpGH8uyOOeGYWQyGfH0isViyWTSsixN00S6ZllWJpMxTVPkCtls1jRNkVJYluU4jq7rIkJRFWSapvhZPAjFii0tLZZl6bouDpCsJLiZTCYWiy0tLYmoCCGtra2GYbS2tmYyGcZYa2urGC/eNE0Rs+u6bW1tuq5TSltbW0X1xqoES8QgElyxoq7rogpHURRCiK7r4kyapmlZluu6Yhemaba1tS0vL8diMS+MfD4vCteyLEKIpmmiKHVdFzUuIvJIJKLruihKUSdEVmqwIpEIIURV1Vgslk6nGWOGYUQiEZFXeedE5BOmaYoaTUppS0uLruttbW3pdFrkB5qmiYmtra2EEJGR5PP5jo4O0zQ555qmpdNpEZI4w4ZhiMRRZNhid9FotKWlRVR9iYMSx26aZjQaVVVV5HCMMXEEuVPiAAAW40lEQVTs3tUiDk1sWVzY4soUUYlrT5xPEb84D+LUiRW9Ci3x6+AloKJuVWRL3q+P+EGcbUppNBrlnCuKIs4SY2zHjh1lJljilwUAoLFV/BbhX/7yl/e+9726rt+4ceM73/mOl7XE43FCSCKR8JZMJBKdnZ1B/lM1yJ8HqfXXc+szXGQ544xLV/WhlXnOa9otyfdR1/HZZgAAKSpLsFzX/djHPtbf3//LX/6yt7e3eFZPT09vb+/Q0JA3ZWhoqK+vT06Y95KbHASwG6/XdlM75Q9s0Tzv5Ffd93/TC9L3tAkA6oNGI36HAEFRWRPhtWvXRkZGBgYGnn/++eLpH//4xw3DOHny5De+8Y1jx4598IMf/NGPfnT9+vXifEuiQslxg0q8j5bJZETLVPlbg0wm43WghnWl02nRbL2R5vwUN0gU2X8/VZrxy2aho7/voczwX/2OQjJmlbq/eahlsjVP2GZWWYL1z3/+kxDy3e9+d9X0Rx991DCMM2fOjI2NHT58WLyId/HixSNHjkiLtGwlalxc1y2zm0iN1LT9RfS22fp2vDfvmpz04T1TqdT27ZsP3l1OlaHowi8jKAgHFrP8DgGaV/Q9/13OYszUianXOpgQqSzbOHnyJF+P6IDFGLt06VIymXz11VdTqdTp06drE3M91GgAzxK1a1uv5Cin5bSczyp77xKSGgzBJV3tRjmvtMVw06rQMkMtp2tgANu1AQCgmPzqnNbW1oMHD0ajUelb3qKKamXqn1is200nmUzK3YvruhUN6Rnk9wCEioaG91Q9rmmJbvvpdLpu37QB8Evkwd7NFwKAWiRYgdWoY4X7SHrXoo3SF+l5nldFV+l7jvVJoaR/i8YbIhVgi5TtbX6HABAOTZRgFQt+H6Pq3pQs8WAWQ4RvZQtrSR+FYaMIN6pQ3HriVaOEqfxsprhB1iO9hVoMRVbmwt7orAAAULUmSrDEqNPiZ+lNb9JV925jiYeoGCd90y1stIzX6SdQrWA+DiGx0QkR08sfl0F8JmjdWX7VOSHBAgDYuoZNsNzZeXJvriBGbPcrnrDz6lR8GTt0lfqMklqady2t6gRWRe6+Uf1coEfPClKeDQAQQI2TYNHMPf2B3MkZjjGp66hwK7H5QuUrmQpLGbpMTcxy1NNURVnK2LOSe4kBADSYxkmwlHGpD/hwcWSmktyupt2NS22t42M1L02WKxA3MNUwctNTgNAyHnnY7xAA5GicBGurwtzkwf41IW1bjuskZqRtrSmxOxWPHMFz99bYpVaGuRqRV7Ir6HTQOyBCU8OA9bJp9+/2O4QmhUt5xcht8X/ndpV1CXRiSl40EGJ0aavvAPKpOSmRrIvOrhmvJIMv+QA0LDW+w+8QmhQSrNV4Yf2mLnVscpNaLjylCOH5un/YseRpr665cyOF0VsStxYc/J9jfocAANBokGCViy4H7qMxkfEEWen5pEzPB6GVk9+5W+c9uiUbNAtS43Gzfn4XXP3HW+IHud3dAACgFpo9weLZMA/cULDJSk6lzC1sscs2vfHW6p5AQAghhLpcbk3YFtnoEQ9NRt2FRi4In2ZPsEigOk75WknmTiUD9FZdkLClZWdmk9G/lJU+fAAgndaLbtoQPk2fYAWJbw/pYIxppFT+8l2AeMlxkOq6AADAL0iwgPC5ahOsyYoHdGCLyzy//vCedG6dr3HTt6dJqAaM5W/8uz47csfers+OAACgCkiwao5Kf+V+flG5Xe++5OviSxV/y0VJZ/l647CzhTRZr+82TaWD0Hm/fLxueU+g8k5v4C4AACCEhDfBosl1ajt8oW06yOfCVj+cp03cvaf7+fQ8Tfn/MT651PmldV+Oo6FrN3TClA5Wyvn3Bq3Yd2s4cBcAQBiFNcEiM4HoNkQIIbnav7rPOWnkp3ZJ6fUH7VSmy/jm9AbrBkUIR8x3MdgbwGa0Pe/yOwQIhNAmWI2hNh8bdoLRgFhTyt0yvvfydrBrvxYrbmDdFM3mecDTSoBGp3Z3+h1Cg9Dui/sdwpYgwdqEXXk/7vLV6pPGtcnbIPiUXMFNy8/bAADqT0WC1eByaBOBdVDbsafR8QgAANbXsAmW2wTNZOAj6rru1KzfUQAAND61c5vfIVSjcROs1KLfIVTOcde+e+8G7xuIVQp4j6jK2cEYoBUAoLFp//Vuv0OoRsMmWEHgVDg4EE0urEqnqMvduTJelwsFdL4GgCBhRpRQ6ncU0LDCnWDZdzdso+GbfTyuDpyqR0gPAN8//Mxr+XrBFjlvh6QBOlRjtALUWfTAg36HAI0szAkW5252wyTArcE78E3FHr1nSEle/wa+9UbA54VAvCAZkDAIIWTj4SrYTMpd3HhAWr8TaACAxhbmBAvqKR2IrmDOnSm/Q1jjjp+1Wbzavob8Vm2GCAEAAEIIEixoQtTljsRPLS030UAefD6E744AAPgBCVZZWDoboFYh2Bruuu5yaHrcK/++43cI73CRYAEAlAcJVlmU1BIv1P6bgxBYa4bPqJ86fOwSAABkQ4IFIUBnUtTXTmCFieD1/SqJutxZrGyUEIAgiz78gN8hAFQGCVYN0Tw+DFeVNYMLsLtzDEPzV4I7jrsQmmZQgE2xFtPvEAAqgwSrlK1+bydv8wxehq9YZCzhokE2LDDUFgDAepBglcJtdGwvj49dlMBX/K0A9cEHAAgOJFiNzqlH6kNfHyGc4xWzcHHm5Y1VAQAA90KC1ei29pI/d5xyF3W5u4QOZ2HiLmw8zjsAAGxNsyZY+E5IGWjBdtb7Xk0o8Aq/tA0AACBRkyZYfN3e647rpoP74pUy7fPnq1moki1X4ljtmwr5ILR2/T80WWNvvvnmX//617XTR0dHX3nllampdQbdKDELAKAKTZpgrYs5jrtQm15EcxIe9vSuz/kNTaKL1fr4eLi/68fzjVah+9RTT7344ovFU3K53NGjR/ft23fs2LF4PH727NlyZgFAfSg7tvkdgnxIsORgJZMPPpuqWyQATWt5eXl4ePhzn/vcyy+/vGrW+fPnr169Ojw8nE6nBwcHL1y4cOXKlU1nAUB9RB54t98hyIcESw5Wr+olijf1VvBKGwE5x3ASje3ll18eGBh46aWXGLvnzuY4zuXLl0+dOnXo0CHG2PHjx/v6+gYHB0vPAgDYCiRYIUPvJv0OITBmKqsXVBaXHaSnDe3xxx+fmZmZmZnp7e0tnj4+Pj45Odnf3+9N6e/vHx4eLj0LoOGpuzqVHe33TInv8CuYxtMICZYb/vfFGuAQAAIrkUgQQrq6urwp8Xh8dnbWtu0Ss+ofp59UhRm630FAvdFohEa04ina/bv9CqbxqH4HIIGbXCAdMb+j2BJnLkXaDL+juIfz9l1y33a/o6gHNrdIFL+DgFqan58nhMRi79wlYrEY5zyZTJaY1dnZ6U08f/78uXPnirf5kY985MCBA7du3SongOXl5Vwul04He+AxjZDyDqeZ2bbdjPl3vbhTU6yOF+Hk5KRt26t6FGwklUq1tbVVtP1GSLCgFni+We4g7O4c2dW++XIQML/97W8/+tGPip+ffvrpCxcubLRkR0cHIWRx8Z0G4lQqRSltb28vMat4C1//+te/9rWvFU85f/48IaSnp6ecUNPpdDabFfuCUCsUCrqud3d3+x1IY8rcnjPK+52SgjHW3d1dZoJVaXZFmjDBYovLDdEu2vichSXSFe6KybV4mR+xdlwe8rG16uCRRx7xBrsqrm1aKx6Pk5WGQiGRSHR2dmqaVmLWqo1QSmVFDgDNoOlyDfXONHG531EQQghDv6uSnHqOFFov9p2yhvRky1m+FOzmpACwLOt/VxR3olqrp6ent7d3aGjImzI0NNTX11d6FgDAVjRdghUcysR6o8kDgGyU0pMnTz777LPXrl2zbfu55567fv366dOnS88CANiKpmsibCLJBeTPcnHHQXf4kDpz5szY2Njhw4cVRWGMXbx48ciRI5vOAgCoGhKshsWTi6Sjxe8oGoo9kSB70E85BEZGRlZNYYxdunTp29/+9ujo6EMPPRSNRsuZBQBQNVRxNBc+gW/ZQvNqbW09ePDguilUiVkAAFVAgtVkso32WV8AAIAAQoIFwcXHJ/0OoVHM4XPjAAB1hQQLgos7+DazHHz+P2OCKIk6fZUcAKDJIcECGcZQ1RQOdK4BRxcDAAggJFggg+0QEojhWwEAAIIACVbTUf/9tt8hAAAANDgkWE2H58v7HB4AAABUCwkWQGPJIYEGAPAfEiwAGXIFXrCLJ/Bszp9IJhL+7BcAAIogwZKMZfPOLMYcajp0aZnn7hnE1Z6a9SsYAADwHRIs2VxOXMfvIAAAAMBPSLAAAAAAJEOCBQAAACAZEiwAAAAAyeQnWKOjo6+88srU1JT0LQMAAACEgswEK5fLHT16dN++fceOHYvH42fPnpW4cQAAAICwkJlgnT9//urVq8PDw+l0enBw8MKFC1euXJG4fQAAAIBQkJZgOY5z+fLlU6dOHTp0iDF2/Pjxvr6+wcFBWdsHAAAACAtpCdb4+Pjk5GR/f783pb+/f3h4WNb2AaB86tik3yEAADQ1aQlWIpEghHR1dXlT4vH47OysbdsbrwQAtZHO+B0BAEBTU2VtaH5+nhASi8W8KbFYjHOeTCY7Ozu9ic8888wzzzxTvOIjjzzynve8Z2Jiopy9LC8vU0oty1JdZphm1GXEjES5QgxD2bndsgzOOWPMdd3M3l2maXLGOOfFW6A7ma5H1e2tpqkTQlSqmYZGKVVdJWpFVSWicu6aUUop51wnKmXU1DWVacS0dF2PcC5mKYriOA4hhO9kpmnSHVyl1DAMJRJVCg7TNUpppMMluqbqOqXUsqLeirZtU0r5TqaoimlGCCERqppm1Nndaba0uBHVdV2xMKNUJ4xwYkYVqkRMM6J0MEIpIcQ0o7RTMcyoS6m6k3GXG4bhEM4YixLFjUYj29ssS9dcxTQN13UJIZRShSvU5aYZZUVnRiWqaUbIrg6zxSIqi1KFGBEa365blsY0YmhiReK4LS1G8clUqWZZUc55/t1dkTZLpYQ43DAiogjEHiml4nAUoplmVGWapTJXUzVNc13XNE0RiUJUErMNw+Cc0w6qcuLqRqQlWlCjumGwnYwSbpp6hGmWEeGcky7KNNUytAjR1t1jlGqME4MRYkbFVcEUjXGuRFSF0ghVaQs3jQhXGO3khmGIFVddLZxzSqnCVE2JmKZJd7qmaVJKI0QlRkTp4KZpqtsVTokTjZhWixtV7d07lJhhWVGN5S0jsupqiVDNNaJiLwpXTTPqnUnT/M/ClFLStU03o0pEVajmFmzLMgghZCcTy4urJeIyy9JF2XkrKm2MKpppmqRLUR3XMDU1olJKte1UFDrbSRijYkWdENqiu65b2LXdsqz/XHJFZ9I7Cd7VQnd1GIbBFFVxuRJRGWPaNmJZem45PzExwVhZf7AtLCy0traWsyQANBX1XTv9DkEmaQlWR0cHIWRxcdGbkkqlKKXt7e3Fiz355JOf//zni6d861vfYozt3r27nL2k0+mOjg6xr038H9lbzhbBJ4VCYXp6uru72+9AKvM/fgdQI1s8rtu3b3d3d5eZYBX/GQYA4NHeHbInQmnSEqx4PE5WGgqFRCLR2dmpaVrxYpFIJBKJFE9RFIUU/blcGl0hIWLwFYqykVRUmih0AGgG0vpg9fT09Pb2Dg0NeVOGhob6+vpkbR8AAAAgLKQlWJTSkydPPvvss9euXbNt+7nnnrt+/frp06dlbR8AAAAgLKQ1ERJCzpw5MzY2dvjwYUVRGGMXL148cuSIxO0DAAAAhILMkdwZY5cuXUomk6+++moqlUL1FQAAADQnmTVYQmtr68GDB6VvFgAAACAsZNZgAQAAAABBggUAAAAgHRIsAAAAAMmQYAEAAABIhgQLAAAAQDIkWAAAAACSyR+moVJjY2NjY2Pnzp0rZ+FCoWDbtmEYNQ4Kas513XQ6je/+NoaFhYVYLFbmRwZ/97vf7dmzp8YR1RxuXM0JN65GUusbl/81WAcOHCg/6Lm5ufHx8VqGA3WSy+Vu3LjhdxQgx+uvv+66bpkL79mz58CBAzWNpw5w42pOuHE1klrfuCjnvPKofPPCCy8MDQ298MILfgcCW3Xz5s2BgYGbN2/6HQhI0NbWduvWrba2Nr8DCSjcuBoGblyNpNY3Lv9rsAAAAAAaDBIsAAAAAMmQYAEAAABIhgQLAAAAQDKlzNeMgyMej+/fv9/vKGCrKKWmaX7gAx/wOxCQgFL64Q9/WFX9H/YlsHDjagy4cTWSWt+4QvYWIQAAAEDwoYkQAAAAQDIkWAAAAACSIcECAAAAkAwJFgAAAIBkIXuLcHR09E9/+lMsFmtpafE7Figln89PT08vFXFdNxqNeguUKEqUcnC8+eabExMT8Xh81fQqiq+Zi7WZjz1ccONqDEG5cfGQyGazAwMDhBBd1wkhX/3qV/2OCEr5yU9+supKO3HihJhVoihRykEzMDDwpS99qXhKFcXXzMXazMceRrhxNYaA3LhCk2B95StficViw8PDjuMMDg5SSn/2s5/5HRRs6MKFC/fdd9/Pi/ztb38Ts0oUJUo5INLp9PXr15944glCyKr7VBXF18zF2szHHka4cYVa0G5c4UiwbNvetWvXk08+6U05fPjwwMCAjyFBacePH3/00UfXTi9RlCjl4HjppZc6Ojo6OjoYY8X3qSqKr5mLtZmPPaRw4wq1oN24wtHJfXx8fHJysr+/35vS398/PDzsY0hQ2r/+9a8HHnjgV7/61fe///1f/OIXmUxGTC9RlCjl4Hj88cdnZmZmZmZ6e3uLp1dRfM1crM187CGFG1eoBe3GFY5PWyQSCUJIV1eXNyUej8/Oztq2ja9zBNPIyMhrr732/PPPd3d3j4yM9PT0/PznP9+/f3+JokQpB18VxXfnzp2NVmn4YsUlHTq4cTUkv25c4ajBmp+fJ4TEYjFvSiwW45wnk0n/goINZbPZ9vb2T33qU7Ozs2+88cbNmzdd1z1x4gQpWZQo5eCrovhu37690Sr1i9snuKTDBTeuRuXXjSsc+XVHRwchZHFx0ZuSSqUope3t7f4FBRvSdf3GjRveP3t7e59++unPfOYzyWSyRFGilIOviuLr6enZaJX6xe0TXNLhghtXo/LrxhWOGiwxmoWoyhMSiURnZ6emaf4FBRUQLeIzMzMlihKlHHxVFN/u3bs3WqV+cfsEl3TY4cbVGPy6cYUjwerp6ent7R0aGvKmDA0N9fX1+RgSlDA0NLRr164///nP3pTXX39d1/X777+/RFGilIOviuJr5mJt5mMPI9y4GpVvN67KXoL0zze/+U3Lsv7whz8UCoUf/vCHlNLf/OY3fgcF68tms7t3737f+973+9//fmFh4cqVK9u2bfvyl78s5pYoSpRy0Ozdu3fVcDJVFF8zF2szH3vo4MbVMAJy4wpNguU4zqlTpxhjmqZFo9Ef/OAHfkcEpbz22mv79+8XSTxj7Atf+EI2mxWzShQlSjlo1t6nqii+Zi7WZj72MMKNqzEE5MZFOefV1rr5YGFhYXR09KGHHir+OBQEk+u6IyMji4uLDz74oGVZq+aWKEqUcvBVUXzNXKzNfOyhgxtXA6vzjStkCRYAAABA8IWjkzsAAABAiCDBAgAAAJAMCRYAAACAZEiwAAAAACRDggUAAAAgGRIsAAAAAMmQYAEAAABIhgQLAAAAQDIkWAAAAACSIcECAAAAkAwJFgAAAIBkSLAAAAAAJEOCBQAAACAZEiwAAAAAyZBgAQAAAEiGBAsAAABAMiRYAAAAAJL9PwKH5I6Aw9hDAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bayesian_optimal_profits = profit(demand_samples, bayesian_optimum_supply, customer_price, newspaper_cost)\n",
    "\n",
    "plot_profit(demand_samples, bayesian_optimum_supply, bayesian_optimal_profits, bar_labels=false)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The title may be misleading as it's not 1000 days, rather it's 1000 possible realizations of 1 day of demand from our posterior predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.8.3",
   "language": "julia",
   "name": "julia-1.8"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.8.3"
  },
  "orig_nbformat": 4
 },
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 "nbformat_minor": 2
}