DifferentialPCA.ipynb

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    "<a href=\"https://colab.research.google.com/github/differential-machine-learning/notebooks/blob/master/DifferentialPCA.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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   "cell_type": "markdown",
   "metadata": {
    "id": "ry17s9WGAn18"
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   "source": [
    "# Differential PCA\n",
    "\n",
    "---\n",
    "Brian Huge & Antoine Savine, August 2021\n",
    "---\n",
    "\n",
    "This notebook presents an implementation of <b> differential PCA</b>, introduced in our Risk article <b> Axes that matter: PCA with a difference. </b> The Risk article is published in the October 2021 issue of [Risk Magazine](https://www.risk.net/risk-magazine). It is also available on [Risk.net](https://www.risk.net/cutting-edge/banking/7877231/axes-that-matter-pca-with-a-difference), behind Risk paywall. \n",
    "\n",
    "The article is also presented in a recording publicly available on [YouTube](https://www.youtube.com/watch?v=eHZZa6fpL20), with closed-captions:"
   ]
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   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "from IPython.display import HTML\n",
    "\n",
    "# Youtube\n",
    "HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/eHZZa6fpL20\" \\\n",
    "    title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; \\\n",
    "    autoplay; clipboard-write; encrypted-media; gyroscope; \\\n",
    "    picture-in-picture\" allowfullscreen></iframe>')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differential PCA is an application of <b> differential machine learning </b> to dimension reduction. Differential ML was introduced in our October 2020 Risk article [Differential Machine Learning: the Shape of Things to Come](https://www.risk.net/cutting-edge/banking/7688441/differential-machine-learning-the-shape-of-things-to-come). Its main promise is the design of novel, more effective, ML algorithms based on the availability of <b> differential labels </b>. Classic datasets in machine learning include inputs $X\\in\\mathbb{R}^n$ and labels $Y \\in \\mathbb{R}$. Differential labels are defined as the gradients of labels $Y$ wrt inputs $X$:\n",
    "    \n",
    "        \n",
    "$$Z^{\\left(i\\right)} \\equiv \\frac{\\partial Y^{\\left(i\\right)}}{\\partial X^{\\left(i\\right)}} \\in \\mathbb{R}^n$$\n",
    "    \n",
    "Differential labels are easily and efficiently computed with [algorithmic adjoint differentiation (AAD)](https://sites.google.com/view/antoinesavine-aad) in some situations, like simulated datasets in finance.\n",
    "\n",
    "Differential PCA leverages differential labels to perform dimension reduction in a safer and more effective manner than classic PCA or other classic dimension reduction algorithms. Classic PCA projects data on axes of orthogonal variation and truncates coordinates on axes of insignificant variation. We demonstrate in the article that classic PCA is unsafe and ineffective in financial applications, because variation is not the correct metric. Small variations in the input space may have large repercutions on a given Derivatives transaction or trading book, so PCA may unwillingly truncate critical information from the data. Conversely, directions of large variation may be irrelevant for the target, preventing PCA to reduce dimension as much as would be otherwise possible. \n",
    "\n",
    "By contrast, differential PCA projects data on axes of principal <b> relevance</b>, defined as the magnitude of directional derivative sensitivities, and revealed by singular value decomposition (SVD) of the differential data $Z$. We demonstrate in the paper that differential PCA is safe, in the sense that it guarantees that no information meaningful for the target may be lost in dimension reduction. It is also effective, in the sense that further (linear) dimension reduction cannot be performed without deletion of meaningful information. \n",
    "\n",
    "Differential PCA is discussed in detail in the article. This notebook provides an implementation, along with basic application examples. The follow-up notebook [Bermudan5F.ipynb](/~https://github.com/differential-machine-learning/notebooks/blob/master/Bermudan5F.ipynb) applies differential PCA to the practical problem of Bermudan swaptions, illustrating the shortcomings of classic PCA in a context of practical relevance where we also illustrate the properties and benefits of the differential counterpart, and demonstrate its application to identify Derivatives risks from simulated data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5iVi2n9nAn1-"
   },
   "source": [
    "# Imports"
   ]
  },
  {
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   "execution_count": 2,
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     "base_uri": "https://localhost:8080/",
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    "id": "Xc6xxocRAn1_",
    "outputId": "cfad62d6-3867-4e20-b5d8-9d4ca0afb91a"
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     "text": [
      "Not running on CoLab\n"
     ]
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   "source": [
    "if 'google.colab' in str(get_ipython()):\n",
    "    colab = True\n",
    "    print('Running on CoLab')\n",
    "else:\n",
    "    colab = False\n",
    "    # enable full width for wide figures\n",
    "    from IPython.core.display import display, HTML\n",
    "    display(HTML(\"<style>.container { width:100% !important; }</style>\"))\n",
    "    display(HTML(\"<style>.output_result { max-width:100% !important; }</style>\"))\n",
    "    print('Not running on CoLab')\n",
    "\n",
    "if colab:\n",
    "  %matplotlib inline\n",
    "else:\n",
    "  %matplotlib notebook\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation, PillowWriter\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "if colab == True: mpl.rc('animation', html='jshtml')\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression, Ridge, RidgeCV  \n",
    "from sklearn.preprocessing import PolynomialFeatures \n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "from scipy.stats import norm # cumulative normal distribution\n",
    "\n",
    "# enable full width for wide figures\n",
    "from IPython.core.display import display, HTML\n",
    "display(HTML(\"<style>.container { width:100% !important; }</style>\"))\n",
    "display(HTML(\"<style>.output_result { max-width:100% !important; }</style>\"))\n",
    "\n",
    "# constants\n",
    "epsilon = 1.0e-08"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2qQsm3BpAn2A"
   },
   "source": [
    "# Implementation of differential PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mcYbXS9lAn2B"
   },
   "source": [
    "The <b> DiffPCA </b> class defined below implements differential PCA with an API similar to [scikit-learn's PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) to project data on axes of principal relevance revealed by eigenvalue decomposition of the covariance matrix of differential data. \n",
    "\n",
    "The constructor takes 2 parameters: <i> n_components </i> and <i> central </i>. \n",
    "The parameter <i> n_components </i> is identical to scikit-learn's PCA: if omitted, data is re-paramterized in terms of coordinates on axes othogonal and decreasing relevance, but no dimension reduction is performed. If <i> n_components </i> is a positive integer, the data is projected on the <i> n_components </i> principal axes of relevance, truncating coordinates on the remaining <i> n_features - n_components </i> axes, where <i> n_features </i> is the original dimension of the data. If <i> n_components </i> is a real number between 0 and 1, dimension reduction is set to explain at least the proportion <i> n_components </i> of the total relevance, in other terms, the (squared) error of projected gradients (denoted $\\epsilon$ in the article) is smaller than  <i> 1 - n_components </i>.\n",
    "The parameter <i> central </i> may be set to perform central differential PCA, as discussed in the article. Default is non-central DPCA, the correct alternative for most applications.\n",
    "\n",
    "The <i> fit </i> method performs differential PCA, i.e. eigenvalue decomposition of gradient covariance. It takes input data $X$ and differential data $Z$ for compulsory arguments. For consistency with scikit-learn's PCA, it also takes labels $y$ as an optional argument, which is ignored.\n",
    "Results are available after fitting in the following attributes:\n",
    "- <i> n_samples_ </i> (integer) the number of training examples\n",
    "- <i> n_features_ </i> (integer) the dimension of original data\n",
    "- <i> mean_ </i> (vector of dimension n_features_) the means of the original data columns\n",
    "- <i> n_components_ </i> (integer) the reduced dimension\n",
    "- <i> components_ </i> (matrix of dimension n_components_ x n_features_) the n_components_ axes of relevance, represented by (othogonal) unit vectors and sorted by decreasing relevance\n",
    "- <i> explained_variance_ </i> (vector of dimension n_components_) the relevance (gradient magnitude) of the n_components_ principal axes\n",
    "- <i> explained_variance_ratio_ </i> (vector of dimension n_components_) = explained_variance_ / total_relevance (sum of relevances of the n_features_ axes)\n",
    "- <i> singular_values_ </i> (vector of dimension n_components_) = sqrt (explained_variance_)\n",
    "- <i> noise_variance_ </i> (vector of dimension n_components_) = total_relevance - sum (explained_variance_)\n",
    "\n",
    "The <i> transform </i> method performs dimension reduction by projecting some data $X$ onto the principal components computed by <i> fit </i>. This method can also project derivatives $Z=\\partial V / \\partial X$. If $Z$ is passed, the derivatives wrt reduced data $L$ (for 'latent'),  $S=\\partial V / \\partial L$, is returned along with reduced data $L$.\n",
    "\n",
    "As customary in scikit-learn, <i> fit_transform </i> combines  <i> fit </i> and <i> transform </i> and <i> inverse_transform </i> reconstructs $X$ (and optionally $Z$) from $L$ (and optionally $S$). Reconstruction is performed in the least-square sense, the information lost in truncation cannot be recovered."
   ]
  },
  {
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   "execution_count": 3,
   "metadata": {
    "id": "7dxtBHHiAn2C"
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   "source": [
    "class DiffPCA:\n",
    "    \n",
    "    def __init__(self, n_components=None, central=False):\n",
    "        \"\"\"\n",
    "        The API is consistent with sklearn.decomposition.PCA \n",
    "        (see https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html)\n",
    "        \n",
    "        n_components = number of components to keep. If n_components is None all components are kept:\n",
    "        n_components == n_features\n",
    "        \n",
    "        If 0 < n_components < 1, select the number of components such that \n",
    "        the amount of 'variance' (squared magnitude) that needs to be explained is greater than the percentage specified by n_components\n",
    "        \n",
    "        Default = squared error magnitude (epsilon*total_variance in the article) of 10^(-8), i.e. error norm is 0.01% of total norm\n",
    "                        \n",
    "        central = specific to differential PCA, standard scikit-learn PCA is always central. By contrast, \n",
    "        differential PCA is noncentral by default, see article\n",
    "        \"\"\"\n",
    "        \n",
    "        self.n_components = n_components\n",
    "        self.central = central\n",
    "        \n",
    "    def fit(self, X, Z, y=None): # note y is ignored, just like in scikit-learn PCA\n",
    "        \"\"\"\n",
    "        X: input data\n",
    "        Z: differential data = dy/dZ, see article\n",
    "        (y: labels)\n",
    "        \"\"\"\n",
    "        \n",
    "        # data shape\n",
    "        self.n_samples_, self.n_features_ = X.shape\n",
    "        \n",
    "        # central?\n",
    "        self.mean_ = Z.mean(axis=0) # average differentials\n",
    "            \n",
    "        # compute covariance matrix of differentials\n",
    "        z = Z - self.mean_ if self.central else Z\n",
    "        self.cov_ = z.T @ z / self.n_samples_\n",
    "        \n",
    "        # eigenvalue decomposition\n",
    "        d, P = np.linalg.eigh(self.cov_)\n",
    "                \n",
    "        # reverse order so largest eigenvalues come first\n",
    "        d = d[::-1]\n",
    "        P = P[:, ::-1]\n",
    "        \n",
    "        sumd = np.cumsum(d)\n",
    "        total_variance = sumd[-1]\n",
    "\n",
    "        # find the number of principal components\n",
    "        if self.n_components is not None: \n",
    "            # n_components is larger than 1 = number of components\n",
    "            if self.n_components >= 1:\n",
    "                self.n_components_ = self.n_components\n",
    "            # n_components is smaller than 1 = square magnitude explained\n",
    "            else:\n",
    "                sumd /= total_variance\n",
    "                self.n_components_ = np.searchsorted(sumd, self.n_components) + 1\n",
    "            \n",
    "        else:\n",
    "            self.n_components_ = min(self.n_samples_, self.n_features_)\n",
    "            \n",
    "        explained = sumd[self.n_components_-1]\n",
    "        unexplained = total_variance - explained\n",
    "\n",
    "        # filter irrelevant components\n",
    "        d = d[:self.n_components_]\n",
    "        P = P[:, :self.n_components_]\n",
    "            \n",
    "        # results, attributes as in sklearn.decomposition.PCA\n",
    "        self.components_ = P.T\n",
    "        self.explained_variance_ = d\n",
    "        self.explained_variance_ratio_ = d / total_variance\n",
    "        self.singular_values_ = np.sqrt(d)\n",
    "        self.noise_variance_ = unexplained\n",
    "        \n",
    "    def transform(self, X, Z=None): \n",
    "        \n",
    "        # transformed dataset\n",
    "        L = X @ self.components_.T\n",
    "        \n",
    "        if Z is None:\n",
    "            return L\n",
    "        \n",
    "        else:\n",
    "            # transformed derivatives\n",
    "            S = Z @ self.components_.T\n",
    "            return L, S\n",
    "        \n",
    "    def fit_transform(self, X, Z, y=None):\n",
    "        self.fit(X, Z, y)\n",
    "        return self.transform(X, Z)\n",
    "    \n",
    "    def inverse_transform(self, L, S=None):\n",
    "        \n",
    "        # L to X\n",
    "        X = L @ self.components_\n",
    "        \n",
    "        if S is None:\n",
    "            return X\n",
    "        \n",
    "        else:\n",
    "            # S to Z\n",
    "            Z = S @ self.components_\n",
    "            return X, Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kxUqa1AOAn2E"
   },
   "source": [
    "# Bachelier basket dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "heVfZEPzAn2F"
   },
   "source": [
    "We demonstrate differential PCA with a basic Bachelier basket simulator, similar to the ones implemented in [DifferentialML.ipynb](/~https://github.com/differential-machine-learning/notebooks/blob/master/DifferentialML.ipynb) for the demonstration of differential neural networks, and [DifferentialRegression.ipynb](/~https://github.com/differential-machine-learning/notebooks/blob/master/DifferentialRegression.ipynb) for the demonstration of differential regression. We start with an implementation of Bachelier analytics, so we can compare results with correct prices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "-lTw2LZ1An2H"
   },
   "outputs": [],
   "source": [
    "# Bachelier analytics \n",
    "\n",
    "def Bachelier(S, K, sigma, T):\n",
    "    d = (S - K) / sigma / np.sqrt(T)\n",
    "    return  sigma * np.sqrt(T) * (d * norm.cdf(d) + norm.pdf(d))\n",
    "\n",
    "def BachelierDelta(S, K, sigma, T):\n",
    "    d = (S - K) / sigma / np.sqrt(T)\n",
    "    return norm.cdf(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xZ_UdtQJAn2H"
   },
   "source": [
    "Next, we have some helper functions to randomly generate model configurations: stock volatility and correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "ZVMlTJwiAn2I"
   },
   "outputs": [],
   "source": [
    "# Helpers to generate random volatilities and correlations for the stock market\n",
    "\n",
    "# generates random stock volatilities\n",
    "def genVols(num_stocks, lower=5, upper=50):\n",
    "    vols = np.random.uniform(low=lower, high=upper, size=(num_stocks, 1))\n",
    "    return vols\n",
    "\n",
    "# generates a random correlation matrix\n",
    "def genCorrel(num_stocks):\n",
    "    randoms = np.random.uniform(low=-1., high=1., size=(2*num_stocks, num_stocks))\n",
    "    cov = randoms.T @ randoms\n",
    "    invvols = np.diag(1. / np.sqrt(np.diagonal(cov)))\n",
    "    return np.linalg.multi_dot([invvols, cov, invvols])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1IvAw8mlAn2I"
   },
   "source": [
    "Next, we have more helper functions to conveniently generate basket options with random basket weights, strike and notional. We also have functions to randomly set basket volatility and scale basket weights accordingly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "04D4cY4dAn2J"
   },
   "outputs": [],
   "source": [
    "# Helpers to generate random basket options\n",
    "\n",
    "# generates random notional\n",
    "def genNotional(lower=1, upper=10):\n",
    "    notional = np.random.uniform(low=lower, high=upper)\n",
    "    return notional\n",
    "\n",
    "# generates random strike\n",
    "def genStrike(lower=50, upper=150):\n",
    "    strike = np.random.uniform(low=lower, high=upper)\n",
    "    return strike\n",
    "\n",
    "# generates random positive weights summing to 1\n",
    "def genWeights(num_stocks):\n",
    "    w = np.random.uniform(size=(num_stocks, 1))\n",
    "    return w / w.sum()\n",
    "\n",
    "# generates a random basket volatility\n",
    "def genBktVol(lower=10, upper=30):\n",
    "    bkt_vol = np.random.uniform(low=lower, high=upper)\n",
    "    return bkt_vol\n",
    "\n",
    "# compute basket volatility\n",
    "def basketVol(weights, stock_vols, stock_correl):\n",
    "    weighted_vols = weights * stock_vols\n",
    "    bkt_vol = np.sqrt(np.linalg.multi_dot([weighted_vols.T, stock_correl, weighted_vols])).item()\n",
    "    return bkt_vol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_gDEVpc6An2K"
   },
   "source": [
    "Next, we have a basic structure to hold the parameters of a basket option, and functions to create basket options, either randomly or with given parameters, and update weights to match given basket volatility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "Ei1m276HAn2K"
   },
   "outputs": [],
   "source": [
    "# basket structure\n",
    "\n",
    "from collections import namedtuple\n",
    "Basket = namedtuple(\"Basket\", \"notional strike weights\")\n",
    "\n",
    "# create a basket option\n",
    "def makeBasket(num_stocks, notional=None, strike=None, weights=None): # None = generate randomly\n",
    "    \n",
    "    n = genNotional() if notional is None else notional\n",
    "    k = genStrike() if strike is None else strike    \n",
    "    w = genWeights(num_stocks) if weights is None else np.array(weights).reshape(num_stocks, 1)\n",
    "    \n",
    "    return Basket(n, k, w)\n",
    "\n",
    "# update weights and strike to match some target basket volatility\n",
    "def updateBasket(basket, stock_vols, stock_correl, tgt_bkt_vol=None):\n",
    "    \n",
    "    bkt_vol = basketVol(basket.weights, stock_vols, stock_correl)\n",
    "    tgt = genBktVol() if tgt_bkt_vol is None else tgt_bkt_vol\n",
    "    ratio = tgt / bkt_vol\n",
    "    \n",
    "    return Basket(basket.notional, ratio * basket.strike, ratio * basket.weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b2Ws4gNgAn2L"
   },
   "source": [
    "Finally, we have the simulator class.\n",
    "\n",
    "The constructor takes the following arguments:\n",
    "- <i> num_stocks </i> (integer) the number of stocks in the universe\n",
    "- <i> num_baskets </i> (integer) the number of basket options in the book\n",
    "- <i> maturity </i> (real number) the maturity of basket options in years (same for all basket options for simplicity)\n",
    "- <i> stock_vols </i> (vector of dimension num_stocks) the normal stock volatilities, randomly generated if omitted\n",
    "- <i> stock_correl </i> (squared matrix of dimension num_stocks) the stock correlation, randomly generated if omitted\n",
    "- <i> baskets </i> (collection of num_baskets Basket objects) the parameters of the basket options, randomly generated if omitted\n",
    "- <i> tgt_bkt_vols </i> (vector of dimension num_baskets) the target volatilities for the baskets (weights are rescaled accordingly), randomly generated if omitted\n",
    "- <i> seed </i> (integer) the seed for random generations, 0 if omitted\n",
    "\n",
    "The method <b> trainSet </b> generates a (differential) training set. It takes the following arguments:\n",
    "- <i> num_examples </i> (integer) the number of training examples\n",
    "- <i> lower, upper </i> (two real numbers) the lower and upper bounds for initial stock prices\n",
    "- <i> seed </i> (integer) the seed for the Monte-Carlo simulations\n",
    "\n",
    "It returns a (differential) training set $X$, $y$, $Z$ where:\n",
    "- <i> $X$ </i> (matrix of dimension num_examples x num_stocks) are the initial stock prices\n",
    "- <i> $y$ </i> (vector of dimension num_examples) are the corresponding subsequent combined payoffs of all the basket options in the portfolio, picked on one MC path with initial state $X$\n",
    "- <i> $Z$ </i> (matrix of dimension num_examples x num_stocks) are the differential labels $\\partial y / \\partial X$\n",
    "\n",
    "The method <b> testSet </b> generates a test set $X$, $y$, $Z$ where $X$ is an independent set of initial stock prices, $y$ are the corresponding <b> correct </b> basket option prices (actually, the sum of basket option prices in the book, i.e. correct book value) computed analytically with Bachelier's formula, and $Z$ are the deltas $\\partial y / \\partial X$.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "Pa9EipvEAn2L"
   },
   "outputs": [],
   "source": [
    "class BachelierSimulator():\n",
    "    \n",
    "    # None = generate randomly\n",
    "    def __init__(self, num_stocks, num_baskets, maturity, stock_vols=None, stock_correl=None, baskets=None, tgt_bkt_vols=None, seed=0):\n",
    "        self.num_stocks = num_stocks\n",
    "        self.num_baskets = num_baskets\n",
    "        self.maturity = maturity\n",
    "        self.sqrtT = np.sqrt(maturity)\n",
    "        \n",
    "        np.random.seed(seed)\n",
    "        \n",
    "        self.vols = genVols(num_stocks) if stock_vols is None else np.array(stock_vols).reshape(num_stocks, 1)\n",
    "        self.correl = genCorrel(num_stocks) if stock_correl is None else np.array(stock_correl).reshape(num_stocks, num_stocks)\n",
    "        \n",
    "        baskets = [makeBasket(num_stocks) for _ in range(num_baskets)] if baskets is None else baskets\n",
    "        self.bkt_vol = np.array([genBktVol() for _ in baskets])\n",
    "        self.baskets = [updateBasket(basket, self.vols, self.correl, bkt_vol) for basket, bkt_vol in zip (baskets, self.bkt_vol)]\n",
    "        \n",
    "        vT = np.diag(self.vols.ravel()) * self.sqrtT\n",
    "        self.cov = np.linalg.multi_dot([vT, self.correl, vT])\n",
    "        self.chol = np.linalg.cholesky(self.cov) \n",
    "                \n",
    "    # simulate (differential) training set, returns X, Y, Z where\n",
    "    # X = initial state in dimension num_stocks = initial stock prices\n",
    "    # Y = payoff of the basket option(s)\n",
    "    # Z = dY / dX in dimension num_stocks, i.e. pathwise derivatives\n",
    "    def trainSet(self, num_examples, lower=25, upper=175, seed=0):\n",
    "        np.random.seed(seed)\n",
    "\n",
    "        s0 = np.random.uniform(low=lower, high=upper, size=(num_examples, self.num_stocks))\n",
    "        wT = np.random.normal(size=(num_examples, self.num_stocks))\n",
    "        sT = s0 + wT @ self.chol.T\n",
    "        \n",
    "        pay, deriv = np.zeros((num_examples, 1)), np.zeros((num_examples, self.num_stocks))\n",
    "        for basket in self.baskets:\n",
    "            bT = np.dot(sT, basket.weights)\n",
    "            pay += np.maximum(0, bT - basket.strike)\n",
    "            deriv += np.where(bT > basket.strike, 1, 0).reshape(-1, 1) * basket.weights.reshape(1, -1)\n",
    "        \n",
    "        return s0, pay, deriv\n",
    "    \n",
    "    # simulate (independent) test set, returns X, Y, Z where\n",
    "    # X = initial state in dimension num_stocks = initial stock prices\n",
    "    # Y = price of the basket option(s)\n",
    "    # Z = dY / dX in dimension num_stocks, i.e. deltas    \n",
    "    def testSet(self, num_examples, lower=40, upper=160, seed=1024): # must be a different seed\n",
    "        np.random.seed(seed)\n",
    "        \n",
    "        s0 = np.random.uniform(low=lower, high=upper, size = (num_examples, self.num_stocks))\n",
    "        \n",
    "        prices, deltas = np.zeros((num_examples, 1)), np.zeros((num_examples, self.num_stocks))\n",
    "        for basket, vol in zip(self.baskets, self.bkt_vol):\n",
    "            b0 = np.dot(s0, basket.weights)\n",
    "            prices += Bachelier(b0, basket.strike, vol, self.maturity)\n",
    "            deltas += BachelierDelta(b0, basket.strike, vol, self.maturity) @ basket.weights.reshape(1, -1)\n",
    "        \n",
    "        return s0, prices, deltas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "v9JKMkRmAn2L"
   },
   "source": [
    "# Differential PCA on Bachelier basket dataset: one basket option"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1YD9JBz2An2L"
   },
   "source": [
    "As a first demonstration example, we simulate a training set for one basket option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QJiC8cu7An2M",
    "outputId": "4620440a-0b7f-48ea-c6bc-1e530302b4df"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using training seed 7030\n",
      "using test seed 129525\n"
     ]
    }
   ],
   "source": [
    "# test for 1 basket\n",
    "\n",
    "num_stocks = 20\n",
    "num_baskets = 1\n",
    "\n",
    "seed = np.random.randint(131072)\n",
    "print(\"using training seed\", seed)\n",
    "\n",
    "bach = BachelierSimulator(num_stocks, num_baskets, 3, seed=seed)\n",
    "\n",
    "# enough examples so we don't worry about overfitting in low dimension\n",
    "num_examples = 131072\n",
    "\n",
    "x_train, y_train, z_train = bach.trainSet(num_examples, seed=seed)\n",
    "\n",
    "num_test = 1024\n",
    "test_seed = np.random.randint(131072)\n",
    "print(\"using test seed\", test_seed)\n",
    "\n",
    "x_test, y_test, z_test = bach.testSet(num_test, seed=test_seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nkRmLAAhAn2M"
   },
   "source": [
    "Perform differential PCA on the training set, with error tolerance $\\epsilon = 10^{-8}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "DuUlVvQ_An2N"
   },
   "outputs": [],
   "source": [
    "# differential PCA\n",
    "\n",
    "dpca = DiffPCA(1.0-epsilon)\n",
    "\n",
    "# L = latent representation in low dimension, S = dY / dL\n",
    "L, S = dpca.fit_transform(x_train, z_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5SJc7kkhAn2N"
   },
   "source": [
    "Check that dimension was correctly reduced to one, as we know that basket option values only depend on the basket in the Gaussian model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PMlgkrEFAn2O",
    "outputId": "1f1b3787-27f3-456b-b515-f2a3050010f5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(131072, 20) (131072, 20)\n",
      "(131072, 1) (131072, 1)\n"
     ]
    }
   ],
   "source": [
    "# dimension reduction\n",
    "\n",
    "# initial\n",
    "print(x_train.shape, z_train.shape) # 131072 x 20\n",
    "\n",
    "# reduced\n",
    "print(L.shape, S.shape) # 131072 x 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tn14ApgkAn2O"
   },
   "source": [
    "Next, we check that no relevant information was lost in dimension reduction. We check this simply by learning the pricing function by polynomial regression in the reduced space, and compare with the correct pricing function on the test set. The code for polynomial regression uses scikit-learn's [PolynomialFeatures](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html) and [LinearRegression](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) in a [Pipeline](https://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html) and is copied from [DifferentialRegression.ipynb](/~https://github.com/differential-machine-learning/notebooks/blob/master/DifferentialRegression.ipynb). \n",
    "\n",
    "Note that the original dimension is too high to perform regression, more sophisticated learning algorithms like neural networks would be necessary for the task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "IbT41dX_An2O"
   },
   "outputs": [],
   "source": [
    "# polynomial regression, for tests\n",
    "\n",
    "def make_polynomial(degree=5):\n",
    "    return make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(normalize=True))\n",
    "\n",
    "poly_reg = make_polynomial()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 268
    },
    "id": "N25WDfmiAn2O",
    "outputId": "e1b75d90-731e-466b-a75c-33b10240a466"
   },
   "outputs": [
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       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# polynomial regression in the reduced dimension space\n",
    "poly_reg.fit(L, y_train)\n",
    "\n",
    "# predict test set \n",
    "pred = poly_reg.predict(dpca.transform(x_test))\n",
    "\n",
    "# plot results\n",
    "plt.figure()\n",
    "plt.plot(y_test, pred, 'co', markerfacecolor=\"white\", label=\"predicted\")\n",
    "plt.plot(y_test, y_test, 'r--', label=\"ground truth\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z-lUapdLAn2P"
   },
   "source": [
    "We see that the predictions match correct values, demonstrating that a correct pricing function was learned from the reduced data, hence confirming that no relevant information was truncated. Finally, we check that the one relevant axis exactly corresponds to the (scaled) basket weights. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "w5X4zGDXAn2P",
    "outputId": "d5d60182-bed8-4e07-bbc7-6e3b1c11037e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# compare principal axis to normalized basket weights\n",
    "\n",
    "print(dpca.n_components_) #1\n",
    "\n",
    "axis = dpca.components_[0]\n",
    "weights = bach.baskets[0].weights\n",
    "normalized = (weights / np.linalg.norm(weights)).ravel()\n",
    "\n",
    "print(np.allclose(axis, normalized)) # True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_3xltdoaAn2P"
   },
   "source": [
    "As mathematically demonstrated in the article, differential PCA correctly identified that the financial product only depends on the initial basket, and correctly estimated its weights, from simulated data, without knowing anything about the product being a basket option. Differential PCA performed a drastic dimension reduction, transforming multi-dimensional stock data into one-dimensional basket data, without loss of relevant information. The polynomial regression simply approximated Bachelier's pricing function with polynomials. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J4n27QvuAn2P"
   },
   "source": [
    "# Differential PCA on Bachelier basket dataset: multiple basket options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AAXWOx_wAn2P"
   },
   "source": [
    "We easily generalize to a portoflio of multiple basket options below. Simulate training and test sets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "56_OcTIVAn2Q",
    "outputId": "2d7b3387-94f2-4d13-f9ad-64aa7cbcf65c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using training seed 69409\n",
      "using test seed 11050\n"
     ]
    }
   ],
   "source": [
    "# test for 3 baskets\n",
    "\n",
    "num_stocks = 20\n",
    "num_baskets = 3\n",
    "\n",
    "seed = np.random.randint(131072)\n",
    "print(\"using training seed\", seed)\n",
    "\n",
    "bach3 = BachelierSimulator(num_stocks, num_baskets, 3, seed=seed)\n",
    "\n",
    "# enough so we don't worry about overfitting in low dimension\n",
    "num_examples = 131072\n",
    "\n",
    "x_train, y_train, z_train = bach3.trainSet(num_examples, seed=seed)\n",
    "\n",
    "num_test = 1024\n",
    "test_seed = np.random.randint(131072)\n",
    "print(\"using test seed\", test_seed)\n",
    "\n",
    "x_test, y_test, z_test = bach3.testSet(num_test, seed=test_seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OSMcuzMcAn2Q"
   },
   "source": [
    "Perform differential PCA and check that dimension was reduced to the number of baskets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TzcyMTSUAn2Q",
    "outputId": "56e796cf-18b2-4c97-d08c-2964c35a60b1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(131072, 20) (131072, 20)\n",
      "(131072, 3) (131072, 3)\n"
     ]
    }
   ],
   "source": [
    "# differential PCA\n",
    "\n",
    "# L = latent representation in low dimension, S = dY / dL\n",
    "L, S = dpca.fit_transform(x_train, z_train)\n",
    "\n",
    "# dimension reduction\n",
    "\n",
    "# initial\n",
    "print(x_train.shape, z_train.shape) # 131072 x 20\n",
    "\n",
    "# reduced\n",
    "print(L.shape, S.shape) # 131072 x 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1N00x9WJAn2Q"
   },
   "source": [
    "Perform regression on reduced data and check that no relevant information was truncated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 268
    },
    "id": "nkFge6b6An2Q",
    "outputId": "09ef90fd-2297-44ca-d385-f12b32016553"
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "<img 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kBKwIhHBX331FUaMGKEMYJcuXfDll1+qfYgMAtH4MrAqCZAACZQjgZwVK+AyeLC644G330bjkSO1U7+YN49LwFwC1pJrRRpAwwQWzoYe6ulZrr8FFWcAZU9fbm6uMlmyZ0+Mnxg1Iw1M4RlAuY+kf5F9gVFRUZD9f7JXcPDgwZg0aZJ6jMwQSvoYidoVUydpYCSS93ppYGJjYyFLwWIks7Oz0bx5cxW9K7OIspwsM48y65iUlKSijSUNjJg/aceqVatUNLJED4spFBMpEcRSpC9i+mSp/sEHH1Tt+fHHHzkDqPWNYGUSIAES0CSQlwfccQfw++8FNzp4EGjSRPPGltVpAGkAtQRV0QZQGnczTgKRPICyRCppX1gqloDOXtGKbRnvTgIkQAI3gcDs2cD48QUP3r0baNmy3BtCA0gDqCWqyjCAWg0sY2UawDKCK0M1GsAyQGMVEiAB+yOQng54eclSEdCuHRAeDvz4I2CWNaI8O00DSAOopScaQC18rAyoJWgJcgkNDVVJrFlIgARIwKEI5OQAPXsChw8D27YBtWsDhhmsQBA0gDSAWvKyVwOoBYWVS0WABrBUuHgxCZCAPRGQ5V2zIzoxa5bl8m8F9pUGkAZQS140gFr4WJkzgNQACZCAnRAo9X512ecn+/2M0rUrIEn/nZwqhQgNIA2gltBoALXwsTINIDVAAiRgBwSMvH0xGRmm3jTw9MTcovL2Xb58da+feVmxAhg4sFJJ0ADSAGoJjgZQCx8r0wBSAyRAAjZOwDxn7SSzkztmFHVyx/HjQMOGlj2OjweKOOu9orHQANIAammMBlALHyvTAFIDJEACNkyg1KdWrVkD3Hvv1R4PHQosXXrTek8DSAOoJT4aQC18rEwDSA2QAAnYMIGSnFvfY/Nm7N61C43HjgXkHHg5gvOee4BijuqsLBw0gDSAWlqjAdTCx8o0gNQACZCADRNYdu4cHtq/HyldusDH1fWanlxevhxVZKZPyn/+A4webTW9pQGkAdQSIw2gFr5yq/zJJ5+o4+TkOLibWeQYOmnDt99+W+JmMA1MiVHxQhIgASsjUOwMoBzn1r791bx+Rlm//mq+PyspNIA0gFpSpAHUwldulW9kAGNiYlSi5R07dqgj7nRLcfejAdQly/okQAK2RKDIPYCxsdcs7+bs2gWXW26xqq7RANIAagmSBvAqvszMTLi7u2ux1KlcXgawpP2gAdR5W6xLAiRgTwTMo4Dnr1uH0HHjTN075++PP/btQ3853cPKCg0gDaCWJO3RAKakpOBf//qXWsb09fXFuHHjsHr1ajVz9tZbbyleDRo0wBNPPIEjR47gv//9L/r164dPP/0Uq1atwpQpU9TnderUwahRozBmzBgTYycnJ9P1xofVqlVT95XZM8NYyX0WLlyILVu2oHHjxnj33XfRqVMn033E8MlzLl68iLvvvhtdunTBa6+9VuwSsDzXvNxxxx2IjIxUz5Ql2w4dOqjniYmVNtyonTe6n7Rn7ty5yhgPGTJE9c/Nza1IrXEJWOsryMokQAJWQEBM4H+XLcPnzz1nas20F17ALRMmoH+NGlbQwmubQANIA6glzDIbwLS04p8rB1+bnwl7vWsloqpKlYJ7FXWtt3ep+vjkk09i/fr1+PDDD1GrVi1ltH7++Wc8/vjjFgYwMTERL7/8sjJ/UpKTk9G+fXtMmzYNgwcPxqZNmzBy5Ei88847ymhJuZGxMgxg06ZNMWfOHGX+Jk+ejK1btypT6erqqkyhmMEZM2agf//+WLduHaZOnYq8vLxiDaDUl7ZJP1q0aKGMXkBAgGqXmM0HHngA48ePV/eIiIi4YTuvdz8xxA899BCee+451WZhIQZQuBZVaABLJU9eTAIkUMEESn2iR1YW4OaGnPR0XG7XDh6xsdgWFYX2ERFwqaRTPcqChAaQBrAsujHVKbMBvN6XQsLjJVeSUcTAycHYRZU77gAiIwt+Ir9pXbxoeaVsxi1hkdm/wMBALF26FAMGDDAZu7p16yoDYz4D2KZNGzWbZ5Rhw4bhwoUL+Omnn0yfyezhmjVrsHfv3lIZwA8++AD/+Mc/VJ19+/Yp07Z//36IMRRzJeZz7dq1pufILJsYweKCQK63ZCv14uLiLJawS2pUC+8pFEMpM4tHjx6Fixh5AIMGDYKzszOWL19OA1hCHfIyEiCBm0OgVCd6SBNffx1YsgT4v/+7eqZvYiJQrVqlHeemQ4kGkAZQRz+wNwO4a9cutdQbGxuL4OBgE5u2bdvi9ttvtzCAYghlds4ock3fvn3VbJxRZOl44MCBuHz5sjJEJTVWf/75J9q1a6duI2ZPZut+/fVX1QYxnjJjJzOTRpk/f756blkM4KlTp9SMp3kpaTuLMoBigsX0GkVmAvfs2YNffvmFBlDr28bKJEACFUmgVCd6FD7OrX9/YNWqimxeud+bBpAGUEtUZTaAVroEvHPnTmWwZEYsKCjIxEY+k31z5jOAknZF/jNKUcZM9hHKDJhhAGUmzFhyNep5e3tj0aJFFnsAzY2VmDp/f39s2LAB3bp1UwZVln7LywAWlbalLO2U/hQVBSyMhKvMDBZVuASs9RVkZRIggXIgUKoTPX79Feje3fKpskplvh2pHNpU0begAaQB1NJYmQ2g1lMrrrKxBLxs2TI8+OCD6kHSR1kClqCP6xnA4paAf/jhB0RHR6t7yZ5CmamTvYFSDh8+jCZNmuDjjz8usQGUJWAxbXJfowwdOlQtCRc3A3j69GnUq1cP27Ztw6233mqqV1zalhu1szT3owGsOL3yziRAAuVDoCQnenTesQPn5s9HTfM8p0OGAMuWlU8jKvkuNIA0gFqSszcDKDBkafd///ufCgKpWbOmMmyyr0/25M2bN0/xkijgwjOA27dvV8u2RhBIVFQUnn76aYsgEDFqssz8xRdfIDc3VwVe/P7771iyZEmJDeDmzZvRuXNnzJo1SwWgSNskGOV6QSDZ2dkqolmWrMXIenp6ws/Pr8gZO+nfjdpZmvvRAGp9xViZBEigEgjc6ESPlEuXkNi4MYLPny9ojaxqyD50Gy00gDSAWtK1RwNYVBoYCWDo0aMHZs6cWawBlB8YaWBkZs9IAzNWzn/MLzJz9thjj+GPP/5Qs4qyd0/MVuE0MNdbApZbffTRR8qYxsfHo2fPnmp5+nppYKSOBJa8+uqrkD1/Xbt2tUgDU/jkjhu1szT3owHU+oqxMgmQQCUQuNEM4M7Nm9G8a1e4Z2dfbY0NLvkWxkgDSAOo9dWyRwNYGEhaWppaPpW8dkZkrhY0VrYgwD2AFAQJkMDNJmDsAWzh5YXvWraEs2SqkAwSX32F3PvvR7+jR1Fn+XJkVK+Oj55/3qrTu5SUJQ2gDRhAmZGS2R3ZSC8zQ5L8V2Z/ZKnRKDk5OWo2SZYDZb9ZQkICQkJCVFTqhAkTIMmGCxdJ/CvBB8ePH1ezUbIfbNKkScUm7C1KVPZoAIXxgQMHVN48ye0ns2YSwCA57apXr17S7xavKyEBGsASguJlJEACFUrg1ePHMTU2FvcGBmKakxNubdlSPW/twIHoM3IkpoeGYtLx49jQqhW6+ftXaFsq4+Y0gDZgACWHm0R+tmrVSgUMyFJeYQOYmpqqTJwsJ/bq1UsZFdmT9vrrr6ulSNn8X8UsQmn69Olq35iYw7vuukslGn7ppZcwYsQItR+tpMVeDaDskzt48KDKjSdBE//5z3/QMv8fg5Ky4XUlI0ADWDJOvIoESKBiCRj7AKeuXo1p+ac+yRNnP/00Gk2bhl4BAfDduBFLmzXD0Fq1KrYxlXB3GkAbMICyuV+K5GaT2b8aNWoUOQMoEaCSxNi8rFy5UuWh+/zzz/Hwww+rH8m+sfr162P48OF47733TJfLyRJiAmUGsXnz5iWSnz0awBJ1nBeVGwEawHJDyRuRAAloEIi8eBEtGjVCjeRk010Oz5qFhuPGqSXfqORkSCQwZwA1IFtZVac8w2FZWcOKak5xBrC4pks+O1kKFnM3ceJEddmXX36pzKBEqXbs2NFU9cyZM2oWUWYHZSm4JIUGsCSUeM31CNAAUh8kQAI3ncCePcAtt1g2IzYWyD8QIDcvD/2ioxGdlobDHTpwD+BNf2Hl0wC7NoCffPKJijqVEynuv/9+RUyMoKQQkWVjSUJsXmR2UZaQ5Si0khQawJJQ4jU0gNQACZCA1RIQo9eggal5Uc2bY+ayZZgYEoIIb29l+mbGxeH7+HisbNEC/eXIUTsoXAK2gSVgc52VZgZQ0n3I/jU50WLLli3qPFYpTz31FD777DPIzEvhEh4ernLc/fjjj0XK+8qVK5D/jCICkvtLsITkmTMvxsyO3M98/6EdfG/YhXIkIKekGGcVS35CFhIgARKoFAK5uYCMi7LNSiZIvv8eWLEC33TrhjFHjyLGbIwM9fTEnLAwuzF/wpcG0E4NoEQBd+/eHWfPnlVLvQ0bNjR9n8QAyp5AGXiLMoChoaFYt25dkd8/iTx+5ZVXrvlZUQZQIpMPHTqkkikX3ptYKV9uPsQmCMie1PPnz6sAJzkvmYUESIAEKpyAJHEeNQqYPv2q+UtMBOQX0PxgSUkL83tSEs5kZqKOuzu6VqtmF8u+5lxpAO3QACYmJqrkwLGxsfjll19wS6F9DcYSsOS38/Lysvie3WgJuDQzgHJj2VcowSliAuVZEsjCQgJCQLbepqenK/MnaYokWp2FBEiABCqcgBzf9tVXVx8TFgYcOAC4ulb4Y63tATSAdmYADfMnuf3kOLM2bdpcoznZ3yfn1sqRYh06dDD9XGYLZRAuryAQY5CX+xZ3Rq21fSHYnsonIOavdu3a/OWg8tHziSTgWAQSEoBCmTIg57S3aOFYHPJ7SwNoRwbQMH/Hjh3D+vXr8be//a1IUcvysJxsIYmfFy9ebLpGAkMk+re80sCYP1yWg7OyshzyS8ZOF0/Azc2Ny74UCAmQQMUT+PprYNAgy+fYwXFuOuBoAG3EAK5duxayZCungjz++OMqt9+gfDHfc889avZEzoOVhM9yrqycYmFeZGk3TKa684uRCFqWg80TQUtuwPJKBK0jTNYlARIgARIgAW0CEuAxZQrw+usFtxo/Hpg1S/vWtn4DGkAbMYASSSt7+ooqstwrRYI3iitywoekhDEvCxYsUEfBSQSmLMFJupjJkyeX21Fwtv7lYPtJgARIgARsnEBSEtC0KXDu3NWO7N4N8FQnhYIG0EYMoLV+BSkga30zbBcJkAAJODCBLVuuJnGW4LL16wH5uxyGwEwDJlFw/KYB1PoXggLSwsfKJEACJEAC5UkgOxuQc3ol4KNnT0By2ubnwC3Px9jDvTh+0wBq6ZgC0sLHyiRAAiRAAuVFQJZ3W7UquNvttwNr1wKF0p2V1+Ns/T4cv2kAtTRMAWnhY2USIAESIIHyICCBHbNnF9xJzrnftAlg7tli6XL8pgHU+upRQFr4WJkESIAESECHgJxoVXiGb8UKYOBAnbs6RF2O3zSAWkKngLTwsTIJkAAJkEBZCWRmAu3aXY3sNUp8PBAQUNY7OlQ9jt80gFqCp4C08LEyCZAACZDAdQgUeyav5PeT5d0XXgDmzQPkeLdly8iyFAQ4ftMAlkIu115KAWnhY2USIAESIIFiCHxz4QLGHD2KmIwM0xWtrlzBD/Pno+6ddwJjxgAyC3j27NWULyylIsDxmwawVIIpfDEFpIWPlUmABEiABIogIOZvwN69uDcwEJOCgxHh7Y3TX36JJo8+qq7OdXGB84kTV/P8sZSJAMdvGsAyCceoRAFp4WNlEiABEiCBQgRk2bfRli1o6e2NbyMi4Cw/l6jeP/80XTll7FhMnT0bLozyLbN+OH7TAJZZPFKRAtLCx8okQAIkQAKFCEQmJqL7rl2IatMGHeUotwYNLK7Y9ccfaJ2ZiQ2tWqGbvz/5lZEAx28awDJK52o1CkgLHyuTAAmQAAkUIrDs3Dk8tH8/0gB4de9e8NMaNYAzZ5CSlwffjRuxtFkzDJVTP1jKRIDjNw3kg9hhAAAgAElEQVRgmYRjVKKAtPCxMgmQAAk4JIFio3sBqBnAnTuRMmYMfHbsuMpnwQJg1Cj1x6jkZHTesYMzgJrK4fhNA6glIQpICx8rkwAJkIDDESgqureBpyfmhoWhf24uchIS0Cg5Gb3Pn8c7q1bBafp0oH59xSk3Lw/9oqMRnZaGwx06cA+ghno4ftMAasiHS8Ba8FiZBEiABByMQFHRvWLmZsTFocuMGRi3fDkQHo7V69bhgZgYFQU8MT8KWK6bGReH7+PjsbJFC/SXJWGWMhOgAaQBLLN4pCIFpIWPlUmABEjAYQhcE91rRPAWdZzb8eP4xtv7mjyAoZ6emCMzhTR/2rrh+E0DqCUiCkgLHyuTAAmQgMMQsIju9fO72u/ISMA80APAxqNH0aVhQ/Xj6+0VdBhwFdRRjt80gFrSooC08LEyCZAACdg0gdIYNCO6N6VLF/i4ul49vu2rr0z9zxo8GO7/+hejeytJERy/aQC1pEYBaeFjZRIgARKwWQLXDeYoYonWYgZw6lRg/vyCvkdGIqp1a0b3VqIaOH7TAGrJjQLSwsfKJEACJGCTBK4XzFFckIbFHsA//oDz009f7Xt6OnI9PRndW8lK4PhNA6glOQpICx8rkwAJkIDNESg2mON6aVry8oAZM3AkLg5Nhg7FvQEBeC05GQ07dVIpXRjdW/ky4PhNA6ilOgpICx8rkwAJkIDNESgymMOsF9ckao6NtTjO7bdvvsGIOnUQk5FhqsXo3sqXAcdvGkAt1VFAWvhYmQRIgARsjsA1wRyFepCSnV1wVJsEeTz3XMEVXbuqyN8cJyf8npSEM5mZqOPujq7VqjGpcyUrgeM3DaCW5CggLXysTAIkQAI2R6AkM4Bdt23D5YED4ZaYWNA/s+PcbK7Tdthgjt80gFqypoC08LEyCZAACdgcgRvtARweGYkvevSw7JcsAwcH21xf7bnBHL9pALX0TQFp4WNlEiABErBJAhIF/ODevehYtSp6BwSgXdWq8HV1xRsnTqD/uHF4bN26q/3q2BHYtAkwTv2wyd7aZ6M5ftMAaimbAtLCx8okQAIkYJMEVp4/j2H79yNTonsBuGZno8WJEzjTpAneDwxEvSeewNyhQ/H5yJHc22elb5jjNw2gljQpIC18rEwCJEACNkfAyAHYJzAQk4OD0WrbNlTp2ROX/PwQsWQJ3ureXQV2dN6xAxtatUI3f3+b66MjNJjjNw2gls4pIC18rEwCJEACNkXA2P8X4e2N1RERcB461OI4t5fefx9LIyKw/dZb4f/HHzzWzYrfLsdvGkAteVJAWvhYmQRIgARsgoBx5u//EhPxelwcNoeEoEPDhpZtNzvO7e1GjfDMkSOcAbTit8vxmwZQS54UkBY+ViYBEiABqydQ+MzfAZGR+PqVVyzbnZ4OVKkCIwdgWx8fJGZn43CHDtwDaKVvmOM3DaCWNCkgLXysTAIkQAJWTaDwmb+tv/sOnsOHm9p88JlnEL5woenvxikg8sGqFi3Qv0YNq+6fIzeO4zcNoJb+KSAtfKxMAiRAAlZLoMh8fz//DPTqpdo8auVKrKlXzzTLl5uXh/v37IEsE3/WrBkG1qxptX1jwwCO3zSAWt8DCkgLHyuTAAmQgNUSME782JeUhGbffQe8/z7g4gL89hvQpQuiUlJUpO+aiAj4u7lhRlwc1sTHY0Xz5hhA82e179VoGMdvGkAtkVJAWvhYmQRIgASslsDyU6fQq3lzBF66dLWN8+cDzz5raq+x38/4INTTE3PCwrjsa7Vv1LJhHL9pALWkSgFp4WNlEiABErBOArt3A61aWbYtKQnw8zN9Zuz3eyk4GHf6+6NrtWoM+LDOt1lkqzh+0wBqyZUC0sLHyiRAAiRQKQSMNC5nMjNVkubrmrXx44HZs03tOtiyJRrv3AlnZ2fTZ7Lfr190NKLT0hjpWylvsPwfwvGbBlBLVRSQFj5WJgESIIEKJ1A4jYs8sIGnJ+aGhaFv9er4PSkJYgzrOjnh9tBQOElKl/yy5YMP0CksDPcGBmJicDAkAbSYvplxcfg+Ph4rGelb4e+voh7A8ZsGUEtbFJAWPlYmARIggQolYJ7GZXxQEC5lZ2NrSgrWJSYi6tIl1HBzw4WsLNWGZ1euxPxFiwraEx8PBASgKAPJ/X4V+toq5eYcv2kAtYRGAWnhY2USIAESKHcCxnLvqcxMjDp0CJ39/PBo7dp48dgxxGRkmJ7n4+yMbAAbfXwQfsst2JuYCPe+fbG0VSt0evVVi2COUi0hl3uPeMOKIMDx2wYMYEpKCl577TXs3LkTO3bswMWLFzF16lRMmzbtGk1s374d48aNw+bNm+Hq6ooePXpgzpw5aFj4yB4ACxcuxKJFi3D8+HHUrVsXjz76KCZNmgQ3N7cSa40CKjEqXkgCJEACFU6gqNm6QFdXxGdn477AQEwyW8adv2cPlnXtijwnJzht2QK0a4fc3Fz027uXe/sq/E3d/Adw/LYBAxgTE4PWrVujVatWaNKkCT744IMiDeCBAwfQvn17de2ECROQkZGBKVOmIDExUZnHGmYZ2adPn46XX35ZXXfXXXdh69ateOmllzBixAgsWbKkxMqkgEqMiheSAAmQQIUSKHxqh7Ff7/XYWPyQkGCZn+/rr4FBg0ztyf3Pf+A8erT6uxHdu6FVK3Tz96/QNvPmN48Ax28bMIB5eXlKIU5OTmr2T4xcUTOAgwYNwoYNG3D06FH4+vqqOrGxsWjcuDFGjx6NN954Q30WHx+P+vXrY/jw4XjvvfdM6psxY4YygdHR0WjevHmJVEkBlQgTLyIBEiCBCiVQ5Kkd+U+UiN2+0dHYKxG77dvDpWNHYOtWU3tmDR2KjosWmcyekd9vabNmGFqrVoW2mze/eQQ4ftuAATSXR3EGMDs7W5k+MXXvvvuuhaLuvvtutcx76NAh9fmXX36Jhx9+GFFRUego/xDklzNnzqilYJkdlKXgkhQKqCSUeA0JkAAJVCwB49SOqDZt0NEsV5/xVJnVG7xuHeKGDLFoSNr27fBJToa52eMMYMW+K2u5O8dvOzGABw8eRNOmTdWevpEjR1ro68UXX8TcuXORnp4OT09PTJw4EbNmzUJqaiq8vb0trpXZxV69emHp0qUl0igFVCJMvIgESIAEKpTAsnPn8ND+/Ujp0gU+rq7XPCvtzz/h3aFDwedyVNvp04hKTVXHuRnLvczvV6GvyapuzvHbTgzgpk2bcNttt2HZsmUYUug3vJkzZ6oZvdOnT6NOnTp46qmn8Nlnn6k9goVLeHg4GjRogB9//LFIoV65cgXyn1FEQEFBQUhOTjYtO1uVwtkYEiABErBxAiWJwL3RDOCOrVsR3rUrvOTf7wULgFGjYCwN70hJQXS7dtifns78fjauldI0nwbQzgzg8uXLMXjwYAsNGAZQlnhr166tDODnn3+Oy5cvF2kAQ0NDsW7duiJ1JJHHr7zyyjU/owEszdeO15IACZBAyQhcL4lzf7PAvszcXNTZtAmdfH3xXcuWcHZykk3gwIwZyJ0zB/cfP46cX37BlAceQES9eirKd0Z+MmfzljC/X8neiz1cRQNoJwawLEvAaWlp8PLystDxjZaAOQNoD1979oEESKAiCZRkxq4kzy8uqtcwbsYpHCvPn8eow4dxPisLEjIop3Ys/vBD1Js/Xz3mxwcfxN+feQZOAHLNHixmb3bDhqju5qZOArnhEXElaTSvsRkCNIB2YgCNIBBJ47J48WILAfbu3RvHjh0zBYHI/r5hw4apXIEdzPaEnD17Vi0RMwjEZr6/bCgJkICVESjpjN2Nmn2jqF7jHN4Hq1fHnJMn0dHXF5svXcKbdepgbNOmFre/a+lSdO/cGZOOH0f/wEB8Ex+PeWFhGFW/PlxkppDFIQnQANqJART1ytJvZGQkjhw5gqpVqypBx8XFmdLASOCHlISEBNSrV08lfjY3i/Jz2SvINDAO+W8BO00CJKBJoKQzdiV5zI329BmRuq5OTugdEIAhNWvi/WXLEJmfy894xsajR9EpNBTpOTnw3bgRH4aH4x8HD1pE/ZakPbzG/gjQANqIAVy7di1kyVZOBXn88ccxcOBASN4/Kffcc49aypVE0O3atUPbtm0tEkGL4SsuEbREBJsngpY0MkwEbX9fdPaIBEigYgmUdMbucIcOJZp1u1FUb3xmJmps2qSWfBc1aoT7pk1D0IcfFnRy6FDALJuDYRjfbtQIzxw5Yor6rVgqvLs1E6ABtBEDKJG5ktS5qCI5/uTnUv766y+MHz9e5fgzPwouLCzsmqoLFixQaWPkpBEJDnnssccwefJkHgVnzd9Yto0ESMAqCZR0xq6kp2tc734y0/jPgwdxMVtO8gW67tqF355/3sQld8MGOHfrVvD3vDwYS8YtvLywNz0dJTWiVgmbjSoXAjSANmIAy+VtV8BNKKAKgMpbkgAJ2ByBG83YlfZ0jeJmFI1l5j6BgZjm7o7wsDBEp6Yic+hQXEhLw8OTJ6NX3bqYaHbmrwSNrImPx60+PvgrNRVG8IjNQWaDy5UAx28aQC1BUUBa+FiZBEjATgiU9wygYDHfUyiGrpmXFxpt2XI11cvIkXD64w/gq6/Umb65OTnot28ftl66BA9nZ8Sa5WuVfYLZeXlgihc7EVs5dYPjNw2glpQoIC18rEwCJGAnBMp7D6CRSmb1xYtYfv48zmZlKVLBZ88iVvb3GUX2gosJBGDs81sQFoalFy6oqOARtWqhl78/6nl4oGu1aiXaf2gnr4TduAEBjt80gFpfEgpICx8rkwAJ2BGBwjN2Ed7eKuHyzPyEyyVdei2cSsY5P3/fqFWrsODttwuI5R/nBhcX9ZmxzCx/llm/0fXrY3YR+7/tCDm7okGA4zcNoIZ8AApICx8rkwAJ2BmBovIAmi+93ihJtGEiZb/e8YwMxGdnwyUnB+f690fgpUsFtBYuBJ55xoKeMQPo4+yMj5o2xUAxiCwkUAwBjt80gFpfDgpICx8rkwAJ2CGB4kzejZJEG8vI1V1dVbCGBHpM9fLCra1bwyk11UTq8R9/xAe9el097i2/GOf6rktIwJqICNwVGGiHZNml8iTA8ZsGUEtPFJAWPlYmARJwEAIlSRId4OqK7rt2oa67O26tWhXfRkTAOSEBaN0aOHkSeR07ov2CBdiWlqaOe5tkFulrLDPXcHPD6c6dudfPQXSl002O3zSAOvrhErAWPVYmARKwZwLGTOCpzEyMOXIE7apWxeqWLYucuduekoJZoaEYfvAgPDIzceSXX1B/5EggOBjYsgXw8QFatDAFetR2czMFhgjDqi4uSMnJwaoWLdC/Rg17xsq+lRMBGkAaQC0pUUBa+FiZBEjATgkUtdwrM3sLGze+xqAZe/dkBrDltm0Fx7l16QL8+ivgLGEgV4sR6DElOBivxsWZPm/g4YG5jRrR/NmpniqiWxy/aQC1dEUBaeFjZRIgATskYJ6seXKhhMzfx8dfk4jZMHXrZszA3evXFxD58kvgoYcsCBlmUXIBxmZkYHbDhkzxYocaqowucfymAdTSGQWkhY+VSYAE7IyAEcghKWBWyx6+QoEaxpFs5kexbY2JQbvQUAsSEz/6CNMffbTI5eJfk5K43GtnurkZ3eH4TQOopTsKSAsfK5MACdgZgdKeCJL7ww9w7tPHgkKVdeuQ4eGBPgEBmBwSAiOf4PTYWKxJSEBNNzcsbtKEy712pp3K7g7HbxpALc1RQFr4WJkESMDOCJT0TOAPw8PRMi0NbZs2VXn+pOS9+CL6PvII1iYk4Om6dbHywgWcycw0Earl5oaRdeticoMGjPK1M93cjO5w/KYB1NIdBaSFj5VJgATsjEBJZgDv3rgRaZ6eyHVxwcJPP0W/9evx5KxZ+H7YMPx56RI679iBeWFhGFW/Pn5PSlImsI67O49yszOt3OzucPymAdTSIAWkhY+VSYAE7IyA7AEMiopCWx8ffFdEypf3J03CP2fNws7x45E0fjy6+vjgz9RUdN61CxtatVL5/3w3bsQXzZphWK1adkaH3bEmAhy/aQC19EgBaeFjZRIgATsksPL8eQzct88yWfOlS2gRFgbfpKSrPQ4JAQ4cADw9TaldljZrhgaenmoGUMxgN39/O6TDLlkLAY7fNIBaWqSAtPCxMgmQgJ0SGHf0KOadPInsvDxEHDuGPf/4h2VPT54E6tVTnxmpXf7XqpWqszctDeZRwnaKiN26yQQ4ftMAakmQAtLCx8okQAJ2TOCrc+cQ9/zzeHH5clMv5Tg3p02bgPz0MHKGr6SGkZNA2vj4qCjflTzNw45VYT1d4/hNA6ilRgpICx8rkwAJ2AEB48g3i2CN7Gyceewx1JFkzvll0NSpyHjwQUw0Sw5tpHaRS0I9PTEnLIzpXexAE7bQBY7fNIBaOqWAtPCxMgmQgA0QKGzwOvv5YVNysorOPZiejsWnTuF8drapJ5Ku5e2QEHS/7z4E7tx59fP4eHyTk4MxR48iJiPDdK2rk5NaJjaifl3MEkfbABo20YYJcPymAdSSLwWkhY+VSYAErJxAUWf6ejg54Upe3jUmTj4Y/OuvOFazJnY0b46nL1/GqS1b8OLzz6Ojn5+63txMJmRl4ZkjR1DbzQ0nO3dmbj8r14K9NY/jNw2glqYpIC18rEwCJGDFBIwzfe8NDMT4oCD8EB+PGSdOoKOvL+Y0bIhWPj6ITkvD9Lg4bDp+HPF9+6reHKtTB48tXYrfANRwc0MHX98ij4XrGx2NdQkJkOjfgTVrWjEJNs0eCXD8pgHU0jUFpIWPlUmABKyUgHGmb0tvbwyvVQsvHjtmsXQr6Vrm5u/Xy12xAs6DB5t68lvv3nhi8mQ0rloVW1JSEJ+dbZkSRkxj/rFuLwYFYXZYmJVSYLPsmQDHbxpALX1TQFr4WJkESMBKCRgneswMDcWk48evMXAz4uLw/cWLuDhmDAJ27DD1Iu6553DqlVdULr+3GzVSS7yvNGiAj8+etTCQdd3dMb9RIwzgzJ+VKsD+m8XxmwZQS+UUkBY+ViYBErBSAsaZviEeHrjFxwffRkTA2SxAI/fMGTjXrWvR+pYffohJffoosyinech5v/84eFAt8Q6qWZPHulnpu3bUZnH8pgHU0j4FpIWPlUmABKyUgDEDKM2LatPGFMShmpuTA7RuDURHq79mVq+Ovw4eROfdu9UJHh7OzhYzgDzVw0pfsoM3i+M3DaDWV4AC0sLHyiRAAlZKQPYA1t60CRezspDSpQt8XF2B3FwgM1Md34ZPP0XeqFEY9dhj6DRpEr46f14FhBxs3x4P7t2r/tzcywv70tN5qoeVvmNHbxbHbxpAre8ABaSFj5VJgASsjIB5mpYlp08jMjn56gxgbCxw553APfco84e8PGw5exYdDx5UUcFbLl3C9NBQRF26hO/j49HWxwfbU1N5qoeVvV82p4AAx28aQK3vAwWkhY+VSYAEKpFAkSd2mO3rKyrnn4+LCz7++GMM+PjjgpYeOYLchg1x/549+DExEXl5ecjJ/6mR2JmnelTii+WjykSA4zcNYJmEY1SigLTwsTIJkEAlESjK3JmncjHP+dexalVMjY3F/V5eWNW+vUUL07/5Brt69FBpXH5ISMCUkBB09fPD2awsXMjMVHn/6nl4oGu1akzsXEnvlo8pGwGO3zSAZVNOfi0KSAsfK5MACVQCAXNzNyn/HN5dqakqt58s2U4LCVFpWiTad1WLFgiKikLTrVsROXq0ResCVq9Goq+v+kxm+l4ODsaU0NBK6AEfQQLlT4DjNw2glqooIC18rEwCJFDBBMwTOhupXIqaDRRD91qDBmo/3+J58/DVa68VtGzIEOQsXWpK4+Ln4oI+0dEqvcvQWrUquAe8PQlUDAGO3zSAWsqigLTwsTIJkEAFEzDSuRipXIqbDRx79Cg2p6TgwerVMXDUKAyOjLzaMvn/HXdYtDIqOVmleWF6lwp+ebx9hRLg+E0DqCUwCkgLHyuTAAlUMAEjobOkcqni4oJGW7ZAjncrPBvotX8/Qs6dw9qOHRGQloZR33+PXU8+iVVt2lgmgM7LU8EfO1JTEdepE/f5VfD74+0rjgDHbxpALXVRQFr4WJkESKCCCZjPAGbk5qL7rl2mxM5qNjA6GgdHjULjvXuR5+uLnb/9hpednLAmIUG17L7AQEzM3zcouf3UEXDx8fi6eXMe41bB7463r1gCHL9pALUURgFp4WNlEiCBciRQVJoXMXkP7d+P3gEBGFKzJh7ev18ldpbZwDu+/RYb+/e3bMHZs8itWVPN8m1ISoLs9zuTlWW6RvYKjq5fH7PDwsqx5bwVCVQ+AY7fNIBaqqOAtPCxMgmQQDkRKC7NS1pODoI9PFRS5g6+vth86ZKaAQxcvBiNJ04seHrNmsDp04CLi/rM2Odn3rzabm5Y0LgxBsq1LCRg4wQ4ftMAakmYAtLCx8okQALlQKCowA5Zrp2ev1zr7+qKxOxsiLVzzsvDhQcfhF9iYsGTFywARo2yaElKdjZ8N26EkTamjrs7c/uVw7viLayHAMdvGkAtNVJAWvhYmQRIQJNAUWlejFvm5gds/JacjLUtWyLC2xvRQ4bgtm++MT11+549aBsRcU0rGOmr+WJY3eoJcPy2MwO4Y8cOvPLKK/jzzz+RlJSE4OBgPPTQQxg7diy8vLwK/tHbvh3jxo3D5s2b4erqih49emDOnDlo2LBhqURLAZUKFy8mARIoZwKF07wUvr1h5CKbN8cdsnT7++/I6dlTpXD5++zZuDsgAN+1bFlkpO++9HQc7tCBkb7l/M54O+sgwPHbjgzgvn37cOuttyI8PByTJk1C9erV8dtvv+H1119Hnz59sHr1aqW6AwcOoH379mjdujUmTJiAjIwMTJkyBYmJidi5cydq1KhRYnVSQCVGxQtJgAQqgIB5mhcfV9drnpCSkoIt3brhFnd31Pz9d0CuSUzERicndN25U11/b2CgaalXLR3nH/O2skUL9C/Fv4cV0D3ekgQqjADHbzsygC+99BKmT5+OI0eOIMwsQu2f//wnlixZgoSEBPj7+2PQoEHYsGEDjh49Ct/8Y41iY2PRuHFjjB49Gm+88UaJBUcBlRgVLyQBEqgAAtedAZQkzt27FzxVfgm+/371d2OPn6ezM7Lz8tR/RpFgj0VNmtD8VcD74i2thwDHbzsygLL0O23aNFy4cEHN/hll/PjxanlXXraHh4cyfcOHD8e7775rocS7774bx48fx6FDh0qsUAqoxKh4IQmQQAUQyMzNRYPNm3Fr1apYHRFRsJQ7eDCwYoXpiblPPAHn9983/d1YGv65VSsgLw+RSUnqZ938/dGtWjUu+1bAu+ItrYsAx287MoAxMTFo06YNevbsqWbxZCn3119/xcMPP6wM34IFC3Dw4EE0bdoUixYtwsiRIy3U+OKLL2Lu3LlIT0+Hp6dniZRKAZUIEy8iARKoAAKFU7/0CQjAVF9ftAsNtXjaHfPm4blhw0wzehIc0i86GrLcyz1+FfBieEubIMDx244MoChO9vc98MAD6v9GefbZZ/HWW2/ByckJmzZtwm233YZly5ZhyJAhFiKdOXOm2jt4+vRp1KlTp0gBX7lyBfKfUURAQUFBSE5ONi0n24Ty2UgSIAGrJ1BUYmcXJyfVbiP1y60+PtiWmqpSvLSIicGuxx6z6Nc3MTH4+NIl7EhJQXS7dtifno6Z+elhuMfP6iXABlYgARpAOzKAMgPYq1cv1KpVS+3lkxnALVu2qCCQAQMG4MMPPzQZwOXLl2OwLJGYFcMAnjlzBrVr1y5SdrLELEvNhQsNYAV+S3lrEnBAAsUldp4bFqaCNoKjolDX3R3HMjKQnJOjPlv0xRcInj1b0fp8xAgMf/RRrGrRApLDr/OOHSaKoZ6emBMWxj1+DqgrdrmAAA2gHRlAmdGT4I5jx47B29vb9JY//vhjPP7444iMjFTGTmcJmDOA/OeDBEigogkUl9hZzuH9v/h4BLi6IiE7WzXDLzUV9+zahf5PPokBAQHA5MnAc88ht04d0zLv9ltvhf8ff+CZunXxYI0aTOhc0S+Q97cJAjSAdmQAxdjJ0q2YQPMSHR2Nli1b4u2334ZEBEsQyIgRI7B48WKL63r37q3MI4NAbOK7y0aSgF0SuF5i55Xnz2PQvn3oExiIycHBaPPRR/B44QXFoeuCBRg9ZIjFrJ4R6PF2o0Z45sgRlftPgjxYSIAEoAJD/fz8HHoLl1Nenln8vw2rQpI5i9kTE+fj42Pqyfvvv4+nnnoK3377Lfr27auWfmU2UNLFVK1aVV0XFxdnSgMza9asElOggEqMiheSAAmUgEBxaV0sjGHTpnCWbSoJCaY7vrB0Kb4NDbUI6jBSvbTx8UFSdjYDPkrAn5c4DgGO33Y0A/jdd9+hX79+6NChg9oDKKlg5KQP2dsnJ4LIKSHu7u4qQKRdu3Zo27atRSJoyRPIRNCO8+VnT0nAGgkUl9jZMIa73NxwS5culk2PjUWUn5/a52c+y2fMAMrFsheQSZ2t8Y2zTTeLAA2gHRlAEZEs/8oM3u7du9W0rkTo3nfffZg4cSICAwNNOvvrr78g+QGjoqIsjoIzTyBdElFSQCWhxGtIgARKSuB/iYnouWsXotq0QUc/PxiRwKsuXEDQlCkY99VXBbfq2BHYtAlwcjIldl7arBmG1qoF4xzgnxMT8XmzZhgox8CxkAAJmAhw/LYzA1jZ2qaAKps4n0cC9kvg6/Pn8cyhQ0jIycHd/v54tHZtvHjsGGIyMvDUd9/hvXnzCjovSZ4HDjT93ZjtWxMRAX83N9NxbiuaN8cAmj/7FQ17VmYCHL9pAMssHqlIAWnhY2USIIF8AuOOHsW8kyctjmSTjH/3+ftjYoMGaHnuHDzatYNTaipq/ve/eL9TJ4vEzvfv2YMfExNN9ZnqhdIigesT4PxzXx0AACAASURBVPhNA6j1HaGAtPCxMgmQAACJ7h24b5/K5TchKAgP7duHi9nZWLJ8OR7avBlOktnAzw84fVqld+kbHW2R2Hl6bCx+SEjAtJAQNPbyUnn/uvI4N2qLBK5LgOM3DaDWV4QC0sLHyiTg8ARkj19QVBTa+vjghaAgbEhMxKLoaCT07VvAZsoUwCwBvXlwh1zk6eSk9vlxqdfh5UQApSDA8ZsGsBRyufZSCkgLHyuTgMMSMII71ickYMaJE/B3cUFiTg4GbtiAFa++WsDFxQW4fBlwczN9ZqR3aeDhgZgrVyD7/Bjk4bBSYsfLSIDjNw1gGaVztRoFpIWPlUnAIQkUdcybj7MzDj77LOru2mVicur551HPPPAj/yfGDGBtNzcsatKE6V0cUkXstC4Bjt80gFoaooC08LEyCTgcAeOYN+M0jwhvb+w/fRrtQkIsWPT+/HO4tWqF1RERcHaScJCrxUjvsj01FTEdO8Ld2dnhGLLDJFAeBDh+0wBq6YgC0sLHyiTgEASM5d5TV66otC63Vq1qaewkt9+QIYrFRX9/+J8/j9WJiRiwdy/uCQjA5JAQiFGMTkszpXdZycTODqEddrLiCHD8pgHUUhcFpIWPlUnA7gnIjN8LR44g9soVU19Vkmc5hvKHH4B77736+cSJ2NulizJ6xmkeX549i0cPHrRIDcNlX7uXDDtYSQQ4ftMAakmNAtLCx8okYNcExPw9uHcvfFxckJqTY+prmq8vvG699erfP/0UGD5c/dEI7jBO8zD2+j1csyYaeHqim78/ujG9i11rhp2rPAIcv2kAtdRGAWnhY2USsBsCxjLvmcxMlYevs58f6kdF4WJWlsrvNyk4GIlZWdg9ahTGL19e0O9PPgFGjFB/NwyfzADeXq2ayve3Ny0Nhzt0gIvZPkC7gcaOkMBNJMDxmwZQS34UkBY+ViYBuyBQVFRvLVdXXMjORliVKhhYowZ6enige/36lv01O85NgjvE8EWnpqqcfrPi4lRyZ+71swuJsBNWSIDjNw2gliwpIC18rEwCNk/AiOo1ZvlkD9+CkyfxamwsruTlqf7dsXMnIkePtujr0N9/x7MtW1oEd6xJSDBd4+7khC+Z3Nnm9cEOWC8Bjt80gFrqpIC08LEyCdg0AVn2bbRlC1p6e+Pb/HQtcqbvmydOqGXfycHBuGXXLnjdcYepn8t69MCOJUuw4vx5i8AQVycnFezhAkB2CzK5s01Lg423AQIcv2kAtWRKAWnhY2USsGkCkYmJ6L5rF1RUr58fvj5/Hg/t34/eAQFY3aIFnCVHX3Iy0KYNcPw4Jn70ERY1aoRAV1d80rQpuu3apfYGpmZnY8Hp04pFDVdXvBsezuTONq0MNt4WCHD8pgHU0ikFpIWPlUnAJgkYAR9i+N45cwYfhYcj2MND5e1LysnB/gsX0PStt4DPPwcaNgRiYoB69RCVno7OO3aoPnfy9cXZzEwcbN8eD0RH4+fEREwICsLLoaEM+LBJVbDRtkaA4zcNoJZmKSAtfKxMAjZFQIzf9NhYLDx1SkX3Gsu2pk7k5WHLyJFof+DA1Y/uuw/47jvTj400L8YHM0JDsenSJayJj1dLvgNq1rQpHmwsCdgyAY7fNIBa+qWAtPCxMglYLYHCaV0uZGVh1OHDOJeVZWqzsc9PAj8+2LwZz3ftatmfs2eBWrVMnxlpXswvCvX0xJywMC75Wq0S2DB7JcDxmwZQS9sUkBY+ViYBqyRQVFoXOXE3xMMDo+vXx5wTJ9CqalVT4AcWLACee87Ul6SAAPieOwdnV1fTZ8YZvhuSklDFyQnzGzdGPQ8PdGViZ6vUABtl/wQ4ftMAaqmcAtLCx8okYHUECqd1OXr5MsYdO4bTmZmmtsrS72sNGqg9e+jTB1i3zvSzN8eOxfg+fVQU8MTgYFOalxlxcfg+Pl5d9zWXe63uvbNBjkeA4zcNoJbqKSAtfKxMAlZFoHBal28vXlSBHeY5/qLT0vB6bKxK0rw+Lw939uhh6sPa7dvRJzkZbXx8VIBHYdMo9x9Tvz7ebNTIqvrNxpCAIxLg+E0DqKV7CkgLHyuTgFURME/r0s7X95ocf0Zjc//4Aw94eWHPlSs48ttvcHZxAV54AXBywszYWEyJiVE5/YwiSZ0z8/Iwul49/KdxY6vqMxtDAo5KgOM3DaCW9ikgLXysTAJWRWDZuXMqj19Kly7YkpKCnmY5/lRDL18GvLzUH0+OHYugPn0g5/Z28/dXnxnHuW2/dAnvhYfjr5QUrEtIwOaUFDXzN4czf1b1vtkYxybA8ZsGUOsbQAFp4WNlErAqAsYM4MzQUMievZScHGUGfSSYIzIS6N7d1N7MJ56Ax0MPYVqDBnghKAiyNCwpYsyPc5OLJenzu02aMMWLVb1pNoYEAI7fNIBa3wMKSAsfK5OA1RCQ/XmRSUkqKbMYP6OoUz6eegpYsaKgrUOHImrxYlNSZ+MHtdzc8K+6dSH3kiIzg90Y5Ws175gNIQFzAhy/aQC1vhEUkBY+ViYBqyBgnvZFzuKt4uKCbn5+OHHmDHb27m3Zxl9/RW7XrugXHa1m/eaHheH+vXvRrmpVRLVty1M8rOKNshEkcGMCHL9pAG+skutcQQFp4WNlErjpBIy0L30CA3F3tWoYdfSoatPHVatieKdOcDZL/Jxy6RKic3PVUq9EAa9s0QJ13N3VTOC8sDA8L2lhWEiABGyCAMdvGkAtoVJAWvhYmQQqlYD56R413dwgC70P79uHMC8vdKhaFZ+dO4fE7GzVJpecHESNGYN2u3Zh8SOPYOTjj5vaKnkA+wUG4qsWLdBXzvFNSEBy165wd5Z00SwkQAK2QIDjNw2glk4pIC18rEwClUag8Okexjm+suRr7Pjrl5aG9997D16jR2N327Z4d+tWrLt0CQu7dEENNzecycxEQlYWnjlyBCNq1UJ8drZK7vxiUBBmh4VVWl/4IBIgAX0CHL9pALVURAFp4WNlEqgUAuane3T29cWk48fR0NMTRzMy4OPsjNTcXIxatQoL3n5btSctOBjeR44g19XVtNfvcIcOcAJw/549+DExUeX583BywrP169P8Vcpb5ENIoHwJcPymAdRSFAWkhY+VSaDCCZif7rGqRQs03rJFGbfDGRnq2ff5+WHlnXfCLTHR1Jaec+Zg5PDh6F+jBqKSk9Uev7cbNcLahASV5kVO+BXjePq221TACAsJkIDtEeD4TQOopVoKSAsfK5NAhRMwP93jp4QEvBYXp2bvZAn4XxcvYuGAARZtyI2JQT8J9khLg8z6pefkwHfjRnWNl7Mz0nNz1Z/FTIpBZCEBErBNAhy/aQC1lEsBaeFjZRKoEAJGsMepzEysvXgRX164gH/XrYt3Tp+GRPv+3d8fWxcuxMezZxc8v2NHYNMmdZybMesnp3x4ODub8v3JXF+gmxsWN2lC81chb443JYHKI8DxmwZQS20UkBY+ViaBciFgMnxXruDnxEQVmHExP5pXHiDGzcnJCb0DArA6IgLfHDmCO9u2hX9q6tXnS5LngQNNbUnJzlazfl80awY5Hu6nxER1lFtPSezs789cf+Xy1ngTEri5BDh+0wBqKZAC0sLHyiSgTcA8uteI7DVuGuLhoU7mWB0fj82XLmF7QADaBAcjMi8P77z1Ft7Ztw/V33sPCAiwaIcxA9jR11fV4zm+2q+JNyABqyPA8ZsGUEuUFJAWPlYmAS0CRnTvrT4++Cs1FfcGBmJScDAivL2vns0bF4c18fG4y98fj44ejSEbNqiZvpzly9Hozz/R0tsb30ZEwNlJ4nuvlty8PFOkb15enloyXt2ypVY7WZkESMD6CHD8pgHUUiUFpIWPlUmgzASM6N4ILy9Ep6cXa+Ye2rgRy2+/3fSc1JAQ+OzZg28yMjBg715lGieam8bYWBXpK5ZwdL16mNu4cZnbyIokQALWS4DjNw2gljopIC18rEwCZSIg5m/hyZMYffQoFjVqhH8fOYKoNm3Q0c/P8n5ffw0MGmTxmde6dfiibVsVxFE4ObRcKMvIkibm46ZNMbBmzTK1j5VIgASsnwDHbxpALZVSQFr4WJkESk2gsGn7KDwcjx88iJQuXeDjKhn6AOTlARLV++efpvvv+/e/0XThQnV0246UFES3a4f96emYERuL7xMS8Hz9+uhVrRr6REer4I9htWqVum2sQAIkYDsEOH7boQHcuHEjZsyYgaioKGRkZKB+/foYPnw4Xn75ZZMyt2/fjnHjxmHz5s1wdXVFjx49MGfOHDRs2LBU6qWASoWLF5OAFgFjz5+RykVm/q6ZAczKAvr2BdauNT2r5YcfYmCPHpjSoIEpxYvxw1BPT8wJC7NI+izpXyTal4UESMB+CXD8tjMDuHTpUjzyyCMYNGgQHnroIfj4+ODo0aM4ffo0pkyZopR84MABtG/fHq1bt8aECROUSZSfJSYmYufOnahRiuSuFJD9/uPAnlkXAdOeP29vlcpFkjmHREUhxNMTxzMy0K5qVXzXsuXVgI4RI4DPPkNe9ep4YP16/JKSgkBXVxzp2NGU2Hlk3boYWKMGularptK6SPBHv+hoUwJo+YyFBEjAfglw/LYjA3jq1CmEh4er2b533nmnWNWKOdywYYMyhr6+vuq62NhYNG7cGKNHj8Ybb7xRYsVTQCVGxQtJoMwEzPf8yV6/05mZ+NehQ0jMzlZG0DknB1M//RTe4eHo/MwziMjLw/EdO/BS9eoqJ+D00FB1/q95YueOVaviP40amSKGZ8bFqWtX8oSPMr8nViQBWyLA8duODOArr7yCadOmISYmBiEhIUXqMFsSvPr6KpP47rvvWlxz99134/jx4zh06FCJNUwBlRgVLySBMhGQZd8XjhxB7JUrqn6/wEB8Gx+vonRlKfj1lBS0uu029bM0T0+Ef/YZTuXP4hvLu738/S0SO6+Xc3/z8pBp1iLzpeAyNZSVSIAEbIoAx287MoB33nmnWsKVZeDx48cjOjoaAQEB6N+/P2bPnq2M38GDB9G0aVMsWrQII0eOtBDriy++iLlz5yI9PR2enp4lEjIFVCJMvIgEykRg5fnzGLhvH6o4O+Ny/hm8cqpHFRcXdK9WDas//xxOb75punfOs8+i6/DhOJKRgWXNm6Nb/vKuKbFz1arYnJKirl/RvDlquLnhTGYm6ri7m5aCy9RQViIBErA5Ahy/7cgAirGTpVw3NzdMnDgRnTp1wtatWzF16lS0bdsWv//+uwoMue2227Bs2TIMGTLEQrAzZ87EpEmT1H7BOnXqFCnmK1euQP4ziggoKCgIycnJpuVkm/sWsMEkYCUEjCPdxJQdTE/H9NhYZAMqV9+EoCBMOnYMv126BM8rV3C5d2/LVucf52Z+jq8EchRO7Bzg6op3w8N5lq+VvHM2gwRuFgEaQDsygE2aNMHhw4chRk6CO4wyf/58PP/881i/fj28vLyUAVy+fDkGDx5cpAE8c+YMateuXaQmZYlZlpoLFxrAm/UV5nPthUBxOfnu9vdXAR5vnzqlzvdtdPIkDj/yiGW34+NNx7kZ5/h+GB6OZl5eykRKYmcpU4OD8XJoKM/ytRfRsB8koEGABtCODKDM+ElaF0nx0qZNG5MsZE+fBIdIcEffvn21loA5A6jxbWNVEiiGgJHeRWb6Ovv64t3Tp017/iR6Nz5b5gGv5vfb/fTTaHnwoPrrsh494LF8ucVsnjEDaDxKEjvLrN/iJk0460cFkgAJmAjQANqRAfznP/+JJUuWXGMAjX1/b775ppoJlL2AI0aMwOLFiy2+Cr1798axY8cYBMJ/IEigEgkY6V3kXN7htWph0L59asnXy9kZX124oP78Uo0aiMjMxB4/P3y9Zg36z5iBzJkzMa9BA4u0LebLvXLfDr6+eL1BA5XTj2ldKvGl8lEkYAMEaADtyAD+9NNPkEje6dOnq718Rpk3bx5eeOEFtQewS5cuauk3MjISR44cQdWqVdVlcXFxpjQws2bNKrF0KaASo+KFJFAkgf8lJqLnrl1YEBaGl2Ji1LLtS8HBGLJ/P7r7+2P1/v1wlu0af/sb8McfyHVzQ789e9T5v581bYquO3diTUQE/N3cTMu93s7OPMqNeiMBErguAY7fdmQA5U3ff//9ECP40ksvoWPHjti2bZvas9ezZ0/83//9nxKDJIJu166dCgwxTwSdkJDARND8B4MEKpGALP0+euCAivCVfH5SnPOfL7N5KWPHwmf79oIW7dsHNGtmOs1DjJ8c3WYUWe71cXLCuS5d4O5s3KkSO8RHkQAJ2AwBGkA7M4CXL19Whk9SwUgwR926dTFs2DAVCezh4WES5l9//aVSxUhUsPlRcGFhYaUSLwVUKly82AEJmEf2GulWBIMEZ0yNiVFEZJn3Nl9fTDx+XOX3+3tqKtbcd58lrd27gZYt1WdGoMe0kBBMi41FXXd3lRxayiomcnZAlbHLJFB6Ahy/7cwAll4CejUoID1+rG3fBIqK7K3l5oZcABeysiAzdr0DAvBNixZovGWLCvaYu2YNnjI/jadmTeD0acBFMgBeLeZ5/balpiIvLw9q2bdZMwZ62Lek2DsSKDcCHL9pALXERAFp4WNlOyZgHtk7KTgYTapUwasxMeoUDznVY0SNGvj0wgW8EhICX1dXjD56FC+sWIG5ZsFZ702YgCdnzLh6vm9+kaXhvtHR+DUpCSk5OerTyUFBeKVhQwZ62LGe2DUSKG8CHL9pALU0RQFp4WNlOyVgHtn7bUQEJhw7hgUnT+JK/j4/6bbM5121bwVl0hdfYPqHH6oP1m7fjj7JyWp5eGJwsOnMXiOvn7HD74X69fFmo0Z2SpLdIgESqCgCHL9pALW0RQFp4WNlOyUQmZiI7rt2YWPr1lh46pRK59KhalUV4ZuYlYXVCQnwcXZGam4u7t20CeEnTmCeRPrm5GDf+fMIl1N6nJxQXHJoCRiROUExf3No/uxURewWCVQsAY7fNIBaCqOAtPCxsp0SWHbuHB7avx9Bbm44lZWlInLFtBmRvtLtB728sLJDBxOBcR9+iHlhYWpP4OqICNOyr8wmynLvmCNHsDstTe0frO3mhgWNG2Og7A9kIQESIIEyEOD4TQNYBtkUVKGAtPCxsp0SePX4cUyNjUV9d3eczMxUs3V98s/zHbZ/P4bt24fpTzxR0Hs/P+SePo12+/Zhe2qqWvaVfYMR3t4q0bOx7Hurjw/mhIWha7Vq3O9np9pht0igsghw/KYB1NIaBaSFj5XtkICx/6+Flxd+SUyEHOJ2d/6s3m9JSTjXvz8GR0YW9HzoUGDpUvV3I7pXooPNZwvdnJzwXL163Otnh3phl0jgZhHg+E0DqKU9CkgLHyvbIQFj/1+ohweOX7ly1di1aYOO7u6Al5dlj3/9Fbj9dtNnRn4/4wOZORxSvTo+ad6ciZ3tUCvsEgncTAIcv2kAtfRHAWnhY2UbJyCzfZFJSRDTJ6Wrnx/ePX0a/42PVyd63OLtjZ1paUjp0gU+Tz8NfPBBQY/T04EqVSwIGDOAYZ6eOJqRgTEM8rBxhbD5JGC9BDh+0wBqqZMC0sLHyjZMQCJ0Rx46hHNZWaZeFF66re7qCtdz5/Dfnj3R8dIl5P3973j9zjux9YknIOlhCuf3u3/PHvyYmAiXvDw8GxSE2aU8mceGcbLpJEAClUyA4zcNoJbkKCAtfKxsowTE/D24dy86+vri7mrVcPjyZSy7cEEFekzOD944dOAA2rZsiZPVq+PRZcvw0513wjkvD9/Ex2PA3r3F5vd7rFYtvBseziVfG9UGm00CtkKA4zcNoJZWKSAtfKxsgwRk2bfOpk24nJuL1JwctdQrM3kW6VsWLACee87Uuwdfew2Z99+PSSEhKrL37VOnMCM2VuUBNIoEeixt1gwDmNrFBlXBJpOA7RHg+E0DqKVaCkgLHyvbIAEjxYukZPkrNRWezs7IyM29Gujh7Q3UqgUkJJh6dnz2bDRs1w5yBrDFcjGgIoTF+GXl5WFF8+bM62eDemCTScBWCXD8pgHU0i4FpIWPlW2IgBHwcf/u3bjFxweH09MRn5ODEA8PdbZvmq8vvG691bJHsbFIqVsXvhs34v0mTXAlNxcfnDmjAkMkwjcPQC1XV7wTHo7+NWrYEA02lQRIwNYJcPymAdTSMAWkhY+VbYCAGD9JxCxHul0sJuCjx19/4X9jxxb0plMn4I8/1HFuRmSv8UMjUOSBgAD8OygI3ZjU2QZUwCaSgP0R4PhNA6ilagpICx8rWykBMX2/JyVh9cWL+OzcOSRky2Lt1SJ7/mTnnpzWIQEfcr7vuDfewHsvv3z1gq+/BgYMUH/MzctDv+horE1IgHteHtLz7/F83bqY16SJlfaezSIBEnAEAhy/aQC1dE4BaeFjZSskIBG+Y44eRUxGhmqdYfQkeGNXaip6796Nbv7+WF2lCpy/+AKYOhXfXLyIVfPnI6NvX4xt0sR0hNvMuDh8Hx+vlnqbeHri2JUraOXlhW3t2llhz9kkEiABRyLA8ZsGUEvvFJAWPla2MgJfnz+PQfv2oYG7O05lZZmOcDPy9RmnfFxYuBDVv/nmauuXLAGefBJiHEcdPozTmZmmXoV6esLf1RUH0tORnpsLCRzZ9re/WVmv2RwSIAFHJMDxmwZQS/cUkBY+VrYiAl+dO4dH9u9HQVpn4JWQENxerRq65u/TW3XgAB5s1syy1cePAw0aqM+SsrLg/8cfeKpOHXUKyA/x8fghMVEtG8tZvv9p3NiKesymkAAJODIBjt80gFr6p4C08LGylRAYd/Qo5p08iew8WawFCp/o0cDTE8ujo9HhySctW1zoOLeiAj5cAHzerBlTvFjJu2YzSIAErhLg+E0DqPVdoIC08LGyFRCQmb8h+/ejjY8P/ubjg/fPnrXY9xedmgqvu+7CLVu3mlq78vHH0f+DD4o9yk2MpDuA8cHBmBoaChcnSfrCQgIkQALWQ4DjNw2glhopIC18rHwTCUik72sxMZBAjcz8mT9pjo+LCz4ODy84kePdd4Gnnza1dN2GDbgHwD0BAZicf7JHdFqaShWzJiEBvs7OGBMUhMkNGtD43cT3y0eTAAlcnwDHbxpAre8IBaSFj5VvEgEJ2PjXoUO4kJVlOdsnRi4uDmvi47G6fn3c16gRkJoKdOqEhJAQ1Bg9Gh38/RF16dK1J3s4Oam0MC/T+N2kt8rHkgAJlIYAx28awNLo5ZprKSAtfKx8EwiI+Xtw7154ODmhV0AAVkdEWC7lZmXh+C23oOaJE/DauhUuEvSRlYUUJyd1okd1V1e8EBSEP5KT1YyfUXiU2014mf/f3nmAR1llffyfSSEhBUIIPSSBBEIIAkovirgq6CIuIoSyoH6f7i6r7seqSG8WRIG1Iai4ukoXsKJYlqJIooIgEAglQAIBEkhCKun5nnPJO8wE0AnvZOr/Pg+PZubet/zued/7n3vvOYenJAESuG4CHL8pAK/beKQhDUgXPja2MQFZ9m2bmKgyehRWVmJxVBSCvb3R3Mfnkqfvvn1A587Gq0p94gmEL1ig/q7p4CFLxUUVFSoo9PqOHZnKzcZ9ydORAAnoI8DxmwJQlwXRgHThY2MbEhDx99DBg3g/M1Pl4RXHDM3rVy5j6bJl+MuKFcYr+qFjR6R9+y1GNWumMnoM3b8fu/Lz8XCzZvg6JweJ+fno5uuLxJ49udfPhv3IU5EACViHAMdvCkBdlkQD0oWPjW1EQJZ9H0pOVrN+mugzZvjw8EBAgwZmV3LovfcQEx6OjXFxaoZQc/DQKkmYmEHBwfjshhtsdAc8DQmQAAlYlwDHbwpAXRZFA9KFj43rkICWz/fj8+fxSnq6OlOUjw9OlJVhkLb3LzUViIw0u4qumzahhczyXbhgFhewqbc3zlRn+fijtKf4q8Pe46FJgATqmgDHbwpAXTZGA9KFj43riEDNfL6y5OtdveQre/YSunZFL5n1k9h+PXsCEgYmPh4JS5eiz+7d6qruCg5WWTw61K+PtOJiNXvo4+GB92NiMLJp0zq6ch6WBEiABGxDgOM3BaAuS6MB6cLHxnVAQPPy7RUUhPB69fD5+fMorI7zJ7N4efn5yNm5E/UmTQJ8fIA1ay6JwIgI5JeXK09ff4MBAxo2xLbcXBRUVECyedwXGoqVsbHc71cHfcZDkgAJ2J4Ax28KQF1WRwPShY+NrUxAln1Dtm9HBaCEm1a01G7Dt27Fh3PmXPr4n/8EFi40uwLN01eEYkZZmcrh29zLC8f69IGPQf5iIQESIAHXIMDxmwJQlyXTgHThY2MrE4hPSsKac+cwJCQEU1u3RsrFi/hzcjLubtQIa0aMQP1Dh4xnrPz6axhuv/3y31VVuGffPnyVkwMRkpIVONRgQObNN1v5Knk4EiABErA/AY7fFIC6rJAGpAsfG1uRwMWKCgR9/z26BQbituBgVFVV4d9nz+L+s2fx6vDhZme64Z13ENG9O6a0bo04f39IKrfnqzOAyDyfzB3KLODZvn2teIU8FAmQAAk4DgGO3xSAuqyRBqQLHxtbgUBpZSX+99AhrMjIUBk9TGP7vTd/PsZv2mR2lg1nzuC+5GSV89d0mVj7WwTgYy1b4uXoaCtcHQ9BAiRAAo5JgOM3BaAuy6QB6cLHxjoJTEpJwcKTJ1U2DinG2H5+figdNgyNNm68fIaxY4EPPlB/i6PIxCNHkFYd1kU+E0cP8fjd1a0b9/vp7Bc2JwEScHwCHL8pAHVZKQ1IFz42vk4CskdvzIEDar+fFBWY2TS23yOPAN98Yzz64A8+wOdjxph58G6/cAH99+xRdSRMzAft22NM8+bXeUVsRgIkQALORYDjNwWgLoulAenCx8bXQWBNRgb+dvgwcqq9fGXJ1hjbT/L2PvvspaP6+QEvvICEcePQZ88ebOncGQOCg9VXktpNHD4kpVtZVRWeaNUKC6KiOEfW/AAAIABJREFUruNq2IQESIAEnJMAx28KQF2WSwPShY+Na0ng3n37sDE722yfX9eAABzMysLFQYPMj5aUBMTGGmP7zQ4Pxz/DwpTDh5bazQvAxLAwvNi2bS2vhNVJgARIwLkJcPymANRlwTQgXfjY2EICsuQ7OikJa8+fR7SvL7LKypBXWamWfed/9x1iH33U/EgFBYC/v/pMi+1nWkGygoxt0gRL27fnfj8L+4DVSIAEXIsAx28XF4DLli3Dww8/DH9/fxTIoGhSfvnlF0yaNAmJiYnw8vLCwIEDsWDBArRp08ZiK6cBWYyKFa+TwNrMTEw4fBhZ5eXGI9Q3GFBUWYnKP/wBHiYBn6vi4+GxapWxnrbUu/nCBRRXVqrYfr0CArD9ppuY0eM6+4PNSIAEXIMAx28XFoDp6eno2LGjEn+5ktLKRAAmJyejR48e6NKlCyZPnozi4mLMnDkTOTk52LNnD0JDQy2ycBqQRZhY6ToJDN23D59mZV327q2O2ffKvn1Y1b+/2VHHT56MnNGjr4jt93lWlrFefr9+CPCShV8WEiABEnBvAhy/XVgADhkyBB4eHmjUqBHWrVtnJgBHjBiBLVu2ICUlBUFBQeopSE1NRXR0NCZOnIj58+db9GTQgCzCxEq1JCCx/br89BOOlJRc9u71EF9dAElJqOrXDx4XLlw+al4eNhQX44mUFJwoLjabKZSZP3ESWd+xI4ZZ+MOmlpfL6iRAAiTgdAQ4fruoAFy+fDkmTJiAAwcOYPr06WYCsFwS3gcFYdy4cVi6dKmZ0d555504fvw4Dh8+bJEx04AswsRKtSAw8fBhvHr6tDG2X0LXrujVoAFQVQUMGAB8953xaPPj49H9jTcwsNq7V/YKbrtwAU+mpOBgUZFa9g0A8B+Kv1r0AKuSAAm4AwGO3y4oADMzMxEbG4u5c+cqEfjAAw+YCcBDhw4hJiYGixcvVt+blqeeegoLFy5EUVERfH19f/cZoAH9LiJWsJCAiLfWO3Ygs7zczMtXLdumpwMREZePdMcdKPj3vxF45AhuDAjA69HRxpRumoevhIeZER6OGRER3O9nYR+wGgmQgPsQ4PjtggJw+PDhOHPmDLZv366WgGsKwB07dqBv375YtWoV4uPjzax93rx5mDp1Kk6fPo3mVwmKW1JSAvmnFTGgsLAwtcdQW0p2n8eHd2otApKZY1RSEkpNsnnklJXhrv37cWL7doTPmHH5VJ07A7t2IaGgAH1271Y5ezPKyozf+xkMKs5fXv/+9PC1VgfxOCRAAi5HgALQxQTg+vXrMXr0aOzevVvNAkq5lgBcvXo1Ro4ceVUBKAKyWbNmVxj87NmzMWfOnCs+pwB0uXeDzW5odUYGRh08CJmx6xEYiLmRkThfVoamAAbWtMFXXwUee0wJvKH792N/QQHei4nB5OPHkZiXp0LEHCku5n4/m/UeT0QCJOCsBCgAXUgAipdvVFQUxo4dq/b9aUWWeT/99FOcOnUK3t7e6r/XuwTMGUBnfdQd87rv2bsXX+bkmC35Slq3/rt2YfMTT5hd9K59+9AuJsYskLNWQdqUV1Uh2MsLy9q3p7OHY3Y3r4oESMCBCFAAupAAPHHiBCIjI3/TvIYOHar2A8py7fjx47FkyRKz+oMGDcKxY8foBOJAD6krXop4+UYlJuJkaekVIV6+e/NNTHr6abPbbvr992pvYE3BJ3/LzKGUmeHhmM79fq5oLrwnEiCBOiBAAehCAlBi+UlQ55rlhRdewLZt2/Dll1+icePGiIuLU0u/W7duxdGjRxEYGKiapKWlGcPASBtLCg3IEkqsY0rgyaNHsejUKeWYIZk8PomLg0FCvFy8CMyZg6oXX4SHePwCqJg9G38aNgy78vJw2mSfXz0PD5RUVUECwwwLCcGauDg6etDMSIAESKAWBDh+u5AAvFa/19wDKPUkEHT37t1x4403mgWCzs7OZiDoWjxArFo7AjVz+RpDvGzdCtx6q/FgmaNGISY+Hhv690c9g0E5e8hMn8Tzk+Ip4hDA6g4dMLKp7BZkIQESIAESqA0BCkA3FYBiJLt27cLTTz+NhIQEs1Rwbdu2tdiGaEAWo3L7ipLSbeSBAxjcsCG+vnBBCTgV4mXMGGDt2st8PvgA+fHxCNq+HSs7dFBLxPL/UjQR6O/hgfdjY7nXz+2tigBIgASulwDHbzcQgNdrHJa0owFZQsm960h8v605ORi0dy+aeXurvXylVVVoee4cTo0YYQ7n55+Bbt2QkJurZv22dO5snAGszgOCz+PicGdICJd83dusePckQAI6CXD8pgDUZUI0IF34XL7xh5mZ+NvBg8iqqoLmqSs3PfvddzHr/ffN77+oCPDzUyFe7pUQL4WFONSjB/60fz++qvYUZjo3lzcZ3iAJkICNCHD8pgDUZWo0IF34XLaxzPpJYOcPz5833qMs5U4LC0OPrl1hOHHC+HlSbCzyduwwZvJ4Pi0NG7Oy8FxkJH7IzcXG7GxIcOflHTpwyddlLYY3RgIkYGsCHL8pAHXZHA1IFz6XayzCb87x43jx5EnlpStFZv6Ut2+rVjCMHw989pnxvqe9/TYWRkcb62r1Jaaf9v9DGzWil6/LWQpviARIwN4EOH5TAOqyQRqQLnwu1VjSuY09eBAXKyuNsf20dG7Hf/wREZMnX77f0FAgPR0JRUVqr9+8iAglAjdlZyMxP99Y74lWrbAgKsqlOPFmSIAESMARCHD8pgDUZYc0IF34XKaxiL/7kpIuz/ZVx/ZbnZ6O22NjEZKXd+leJb/0xx8DPXqoP/PLy40evtqMn8wiisPHmthYDG/SxGUY8UZIgARIwJEIcPymANRljzQgXficvrGItW+zs3HXvn2QRVv5Z4ztt2cP0LWr+T2ePAm0amX8TPP29TcYUFh5KcpfdL16ONirF718nd46eAMkQAKOTIDjNwWgLvukAenC59SNZdbvf5KTcaGiwszDV8X2694dEAFYXZJvuAHtJJizQUvcBuXtO1Q8fLOzUVZVpYI7f9ChA0YxsLNT2wUvngRIwDkIcPymANRlqTQgXfictrG25Ovj4aFi+omH7+DgYEz+9Vfk/fGPZveV+M476NOmDe4OCcHU1q3NvH0/z8pSy733hYZidWwsZ/2c1iJ44SRAAs5GgOM3BaAum6UB6cLndI1LKyuxMDUVU1NT1bXLfN4N/v5YGBWFfllZ8ImONr+nU6eAli2xLjMTDyYno6B6mVcqiXdwA4MBp/v2hY/JzKDTQeEFkwAJkIATEuD4TQGoy2xpQLrwOU1jEX537NmD7/PyYPDwgIRpMQ3sfP+WLVi2aBGCCgrUPZX6+GBXZuYVs32mN/yfdu0wrkULp2HACyUBEiABVyLA8ZsCUJc904B04XOKxpNSUrDw5EmIi4Ys194UEIBdBQVq2XdGYCC6R0Ya7yMhNha7Zs/GwrAwnCguNn4uYlH2/EmR4zwVFoYXa5Fz2ilA8SJJgARIwIkIcPymANRlrjQgXfgcvvGTR49i4alTykHDz9MTAxo0wP6iInTy98fHBw/CMHKk8R6q7rsPw6ZOxa+lpUju0QNvnz6NR48ehbZPUCoGGAx4NyaG4V0cvud5gSRAAq5OgOM3BaAuG6cB6cLn0I3XZmZi9IEDasbu0twdsDgqCn8/cgRVAweaX/vzzwNTpkAL6/Lfzp2x6ORJlcNXZv5k5nB4aChW0NHDofucF0cCJOA+BDh+UwDqsnYakC58DttY8/Jt4+2NE2VlSgRK+aiyEvfedpv5de/dC3TqpD7TAjt38ffHnsJC9VlHPz/80r07HT0ctrd5YSRAAu5IgOM3BaAuu6cB6cLncI0lsPPmnBwM3rsX9QwGFJl47T6+bh1eWbzY/JrLywFPWSC+VLQZQPEOlllDSeX2ElO5OVw/84JIgARIgOM3BaCup4AGpAufwzQW4ffciRNYdOoUcisqjNfV1NsbmSUleHb9ekx94w3j51v++Efc8umnyiNYK7LUe8++fWrZF1VVKLz5Zs76OUwP80JIgARIwJwAx28KQF3PBA1IFz6HaCwx+h4+fBgXysvRKygItzdsiHlpabizUSMMP3sW9wwfjkb5+cZrHbZuHT4OCVFewFNMAjs/l5qKjdnZ8AVwccAAh7g3XgQJkAAJkMDVCXD8pgDU9WzQgHThs3tjCfHy0smTKqBzfU9PFJjM/r2+bBn+vmKF8Rp3LlqEu7p3R05FxRVxAKWShHoJ9vREZr9+dr8vXgAJkAAJkMBvE+D4TQGo6xmhAenCZ9fGq86exejkZOM1yIzeNJnR8/BAQIMGZtd2z7PPonLIEExu3Ro5ZWVYf/48tl+4gJSSElVPBGRrHx8c79PHrvfEk5MACZAACVhGgOM3BaBllnKNWjQgXfjs1nji4cN45fRpdX5PDw8MatQIn8TFwfCf/wAPPmh2XV03bcJtbdvi9fR0lFQHc9Zm/CQjSFd/f+wuLMSWzp0xIDjYbvfEE5MACZAACVhOgOM3BaDl1nKVmjQgXfhs3lhSurVJSEBGeblaxtVKQteu6BUSApgsASM+HglLl6LP7t1K3PVp0ECJwFdPnUJaSYny8l3VoQNWZmZif2EhjvTsqcQkCwmQAAmQgOMT4PhNAajLSmlAuvDZtPETR47gX+npSriJs8fg4GAUVlTg1ZQUXBw0yPxaZCZw3DhjXL932rdHh/r18XxaGj7PyoIXgLmRkUjIy1N/r+vYEcNCQ216PzwZCZAACZDA9RPg+E0BeP3WA4AGpAufTRpfrKhAeEICzpWXX+HsEXv8ONbMnYu4EycuX0teHhAYqP7W4vppX4qjh+nMYaSvLxa0bUvxZ5Oe5ElIgARIwHoEOH5TAOqyJhqQLnx13njovn34NCtLnUcWZ2X2b0hICKaGhaHbQw/B66OP1Hc5ISFoMHcuDBMmGK9Ji+v3TU4OSquXi59o3hyDmzRBZmkpmvv4oH/Dhlz2rfNe5AlIgARIwPoEOH5TAOqyKhqQLnx12rj7zp3YWVBgPIefwYDbgoPxSVAQDBERZudutn49ukVFYVp4OOL8/dWePi2un1Rs5+uLA9zjV6f9xYOTAAmQgC0JcPymANRlbzQgXfjqrPFjhw7h9TNn1PFl2bZbYCAS8/KQuWQJQteuvXze2Fhg717MO3UKM0+cMFvelXYyC7i8QweMatq0zq6VByYBEiABErA9AY7fFIC6rI4GpAuf1RtLSre+O3fix8JCtd+vsvoMc1q0wMz27c3P99prwKOPqs/yy8sRtH27cu4oN6lVwnRuVu8jHpAESIAEHIEAx28KQF12SAPShc+qjVecPYs/JyerfX6mzhqdUlKw93//1/xcR48CbdsaP9OcPWSfoPwT4bienr1W7R8ejARIgAQciQDHbwpAXfZIA9KFzyqNZdavxfffI7NSm+8D7m7UCNPDw9E5IQF+gwebnaeyogIGg8wPXiqas8dXOTlqCbgegJUUf1bpGx6EBEiABByVAMdvCkBdtkkD0oVPd+MN587hvqQksxk/Oags9n4/bRpCd+wwnuOZ6dMx87bblBfwFEn5dhVnjxciI/Fk69b07NXdMzwACZAACTg2AY7fFIC6LJQGpAufrsZrMjIQf/CgOoYxj6+/P9I2bULskCGXj/3XvwKLFiGhtFRl9Wjm7Y2zZWXG72W5OMzHB/DwYDYPXT3CxiRAAiTgPAQ4flMA6rJWGpAufNfVWJZ8h+/di49zctTMnzGPr6Rhi48H1qwxHnfNkCEY/sknakZPc/TQvpRFYE8AN/j745fCQmbzuK7eYCMSIAEScE4CHL8pAHVZLg1IF75aN16bmYn4AweUoNMycqg8vhLvr1Urs+Mlff65WuaVPL4DgoONWT20gNBaZWbzqHU3sAEJkAAJOD0Bjt8UgLqMmAakC5/FjWXWr/+uXUioDuwsS77dAwIwKzUVJZs3w+eZZ8yPVVSEfG9vFdplZYcOGNmkCe7Ztw+ao0dPf3/8o3VrZvOwuAdYkQRIgARciwDHbwpAXRZNA9KFz6LGH1bP+omPryzZdg8KwqMtW+JscTE6DR+OO3buvHycbt2An39Wf2uhXV6PisKX2dnYmJ2tQryIE8gnnTpZdG5WIgESIAEScE0CHL8pAHVZNg1IF77fbCyzfiP378f66ly+Ullbvm1QUIC3FyzA/du2XT7Gt98Ct92m/q4Z2kWLC7haZgOZ1aPuOo1HJgESIAEnIcDxmwJQl6nSgHThu2bjdZmZGHXggMrKYRrUWRqM2rIFK+fOVW0rvLyw+pZbsOallzClTRtjaJfn09KwMStLBYWW4ifZPm65heFd6qa7eFQSIAEScDoCHL8pAHUZLQ1IF74rGsus3+ikJKw9f94429crKAgL2rRBZ19f1GvRAt45OZfbJSZiQ5s2mHD4MDJqhHaRWUApjb28kNGvn3UvlEcjARIgARJwagIcv11IAG7evBnLly/Hjh07cPLkSTRs2BDdunXDzJkzcdNNN5kZ6i+//IJJkyYhMTERXl5eGDhwIBYsWIA2bdrUyqBpQLXC9ZuVJajz/yQn40JFhdrrV2FSe/TevVjxj3+Yte/30UfYNnSomtUT4bj1wgUsP3sW72VkqHqyXPxYixZ4pV07610kj0QCJEACJOASBDh+u5AAvP/++5GVlQX5b2xsLM6dO4eFCxdi586d+Oqrr5TIk5KcnIwePXqgS5cumDx5MoqLi5VIzMnJwZ49exAaGmqxcdOALEb1mxVlyXfEgQPoGhCAXwoKEODpiYKKSxJw1yOP4MYjRy63790bCV98gT579hhDvGhfarH+JMZfQf/+8PMUKclCAiRAAiRAAuYEOH67kADMzMxEkyZNzHq4oKAAUVFRiIuLw7fiJABgxIgR2LJlC1JSUhAUFKQ+S01NRXR0NCZOnIj58+db/JzQgCxGdc2KK86cwQOHD+PO4GD8kJeH3PLyS5k9QkPRs3lzs3bTH38cc15+GUUVFcYQL6NMnDo0z9/Z4eGYFRmp/+J4BBIgARIgAZckwPHbhQTgtSxUZv7S09Nx6NAhlJeXK9E3btw4LF261KzJnXfeiePHj+Pw4cMWGzsNyGJUV63YfedO7KyO7fda27aYeOwYBjdqhI8DAmCosRw//ptvsNLbG5s6dUJ9T0+V1k0L8iwH1zx/d+Tl4VzfvnT40Nc1bE0CJEACLk2A47eLC8Dc3FyEh4er5d8NGzYoERgTE4PFixdjwoQJZsb91FNPqSXjoqIi+Pr6WmT4NCCLMF1R6WJFBZps346Cqiqjs8eksDC8ePIkTn7xBVq99RaQm3up3a23Aps3G+P6TW3dGr8WFOC73Fx80akTOgcEYH9hIZ5LTcUX2dlM6XZ9XcJWJEACJOBWBDh+u7gAHDt2LNasWaOcPcQRRBxE+vbti1WrViFe8saalHnz5mHq1Kk4ffo0mtdYetSqlZSUQP5pRQwoLCwMIjS15WS3eoJqebPirHHL7t1qqVeKqbPHBB8fLO7b9/IRe/cGVq4EIiLUZ9r+vihfX6QUF6OehweKqz195XumdKtlZ7A6CZAACbgxAQpAFxaAM2bMwLPPPovXXnsNjz76qDJzTQCuXr0aI0eOvKoAPHPmDJo1a3bVx2L27NmYM2fOFd9RAP7+W0QcPcYePIiSqiqIk4bBJJ/v/Vu2YG11bD91JC8voKgI8PY2Hljb3ydttawgfYOC8NeWLZnS7ffxswYJkAAJkIAJAQpAFxWAItJErD333HNqVk8repeAOQN4fe+PJ44cwaL0dLPGytEjLAy9goPNPn9v3DiMe+89JRC1ou3v23zhApZER2PpmTM4W1KCo716ca/f9XUJW5EACZCAWxOgAHRBAaiJPxGAs2bNMjNwzQlk/PjxWLJkidl3gwYNwrFjx+gEYsVXgiz59t21Cz8XFBhn7Tw8PDCoUSN8UlkJQ5cuZmf7+7p1eKtxY9zRsCGmR0QYM3vI/j7J5ft8ZCTEyUOyfKzr2BHDahGyx4q3xUORAAmQAAk4OQEKQBcTgM8884yK6Td9+nTI/1+tyNLv1q1bcfToUQQGBqoqaWlpxjAwL7zwgsVmTQO6OioRfs8cP45n0tKMwk+i+klWj8S8PKTs3Ys2NQI7o7QUCUVFyrtXW+bVjm6aDo57/Sw2T1YkARIgARK4BgGO3y4kAMWD98knn4TM5NWc+ZP+79WrlzIDCQTdvXt33HjjjWaBoLOzsxkI2gqvijUZGfjzwYMoMzmWBHa+tWFDjGzcGHtnz8Z88fLVytixwAcfqL80R4+pYWGAhwfWZmbiWHHxpawerVphaEgI+jdsyGVfK/QTD0ECJEAC7kyAAtCFBOCAAQOwbdu2a9pzlYnH6K5du/D0008jISHBLBVc27Zta/U80IDMcQ3ZuxebcnJQbsLa12BAcWUlfmnQAF1vvPFyg+hoQIJzt25t/Exz9Hg9Kkod5/OsLLT28cGx3r0p+mplmaxMAiRAAiTwWwQ4fruQALSHqdOALlEvraxE28REnCotvZTFo3Vr4/69CUeOIH7BAkxas8bYRa/Nno2/z5gBg0EWey8VzdHjq2oBGejpCYkXWHjzzfAxqWePfuY5SYAESIAEXIsAx28KQF0WTQMCJqWkYNHJkzA6d8TFXfbglXh/DRqYMf5h9Wr0b9pUCcUpJkJRc/SQ0C6yX1D2Cj4lwaFrOSurq0PZmARIgARIwC0IcPymANRl6O5sQOLoMebAAaw5d87o3JHQtSt6aYLv3XeBhx4y41t5/jwMISHYcO4cnkhJwYniYuP3po4eEuT58VatKP50WScbkwAJkAAJXIuAO4/fGhOPKtPNcbSVWhFwVwMSATfxyBGcLitTIV3imzRRQZ7z+/VDgARxDg8X12ojy8IWLRCwYoWa9ZNUbnH+/iqd21MpKUjMz0c9AI29vJBeXo7xTZvirfbtuexbK0tkZRIgARIggdoQcNfx25QRBWBtLKZGXXc0IBF/w5OS0LM6pIvM+omTx62//orEmBj0vO8+SblymdR77yHh3ntVeJdm3t44W3bZP5jhXXQYH5uSAAmQAAlcNwF3HL9rwqIAvG7zAdzNgArKy9Fo+3aE+/mhY/36+CQrS836+Xl64pGFCzFr6VK0Tkm5TDQ3F5WBgbhn3z5ozh3ypRbnzwvA31u2xL2NGzO8iw47ZFMSIAESIIHaEXC38ftqdCgAa2czZrXdwYBkr99/s7Px0KFDyCgrMwvxIjN4z4SHY3J8PPDjj4pNTkgIzrzzDsLuvhv7CwvxfFqaytwxOzwc0fXrI7usDI8ePQpfDw/k9u/PpV4d9semJEACJEAC10fAHcbv3yNDAfh7hH7je1c3IFnuHXfgAAqr4/rVDPHyZkIC3h082IxQ940bsbN+feNnppk7TEO9rOzQAfc3aaKDPpuSAAmQAAmQwPURcPXx2xIqFICWULpGHVc2IMnoEX/woLpzmelT+XtNQ7yMHg2sWmUkUxoaipKTJ/HrxYtG545oX1/8OyYGnQMC1GygFuqF4V10GB2bkgAJkAAJ6CbgyuO3pXAoAC0ldZV6rmpA/zh8GK+fPq3y+GplcVQUgr290cLDA7c0bWpG47HHHsPrw4YZPxPBGF6vHs6UlqKo8vJRWvj44JWoKAznzJ8Oq2NTEiABEiABvQRcdfyuDRcKwNrQqlHXFQ1IMnqklZRcsddP0rvFpKbi4AMPmFEo3L0bARcuGD9r5+uLlOJidAsIwI8FBWjl7Y28igps6NQJA5jHV4e1sSkJkAAJkIC1CLji+F1bNhSAtSVmUt+VDEjSrjX6/ntIaGZtr1/KxYv4c3Iy7g4JwYspKYgZPx4ekt2jumzIyEDzevVUiBcpI0ND8Y9WrdTfgQaDcvrYXVCAdR07YlhoqA7SbEoCJEACJEAC1iPgSuP39VKhALxecnCdMDBD9+1TnrqSzu3O4GD8MywMZ0pK8NSxY+jp64sNvXvDo7T0EikfH1QuX457Y2LUvr7Y+vVViBcJ6dLMxwe7u3VD8A8/qKpNvb3xRrt2FH86bIxNSYAESIAErE+AApCp4HRZlbMbUGllJaISE3GytBQd6tfHwaIiyD6909ViL/zsWexbtAiBP/98idP//A/w2muAnx8ScnONM38S129uRASmnziB16OiVJiXMaGh+E9sLDw9PHQxZmMSIAESIAESsDYBZx+/rcGDM4A6KDqzAU1KScHLp06hrDrEi4ZhSHW6No9XX0X7+fPRsLAQkPy+Tz0FTJtmpJVfXo6g7dvV3+LVOyM8XP3dxd8f+4uKsKlTJ9zWqJEOumxKAiRAAiRAAnVDwJnHb2sRoQDUQdJZDejJo0ex8NQp414/mf2L+ukn9AoKwictWsDQuPFlodejBwLXrAEiIsxIaTOAEuB5VmSk2YxgE29vnO7Th7N/OmyLTUmABEiABOqOgLOO39YkQgGog6YzGtDqjAzl2GEa129rTo7K5ZuUl4fYoUONRHIDA/HA1q1Y37UrDCZLuRLQeej+/UgqLMSRnj0hi7yS7u3rnBw1o7ieTh86rIpNSYAESIAE6pqAM47f1mZCAaiDqDMZkKR0i09Kwrrz59UdJ3Ttil6ytAtg1dmz2LxgAd567bXLzh5PP40NTzyB4UlJaqZwSuvWiJPl3eqAzl9kZ+ODmBi08fMzBngO9fLC0vbt6fShw6bYlARIgARIoO4JONP4XVc0KAB1kHUGAxLhN/vYMTx38qRakpV4flLy+/VDgJcXkJqK83/9Kxpv2nSJRJcuwPvvA506qT8lHdxjR44YHUPkM28PD7O9g+LtO6FFC0yLiOCyrw57YlMSIAESIAHbEHCG8buuSVAA6iDsyAYkwk9Srz1z4oTK6CH/ZCZvcHAw/n706KUZQEn11ru3IlDm6YkP/vEPPPDiizB4ehqpqOXeffuwMz9fhXlJvngRxZWVmBMRgWg/PzT38UEsMAXzAAAXP0lEQVR/BnjWYUVsSgIkQAIkYGsCjjx+24oFBaAO0o5qQDJr97fDh5FZVqburr7BgIHBwSqXr8z/RSckYOaHH2L866/Do7xc1dm+di1uDg1VQZ+nmiz3zktLw+dZWegaEIBfCgogDh5LGNtPh9WwKQmQAAmQgL0JOOr4bUsuFIA6aDuiAYn4k317MtP3XW4uSqqq1HLt9i5d0LdhQ2DvXqBzZ+Ndnx82DPXeegv7vbzw+JEj2FNYeNU0cLLsK8JwBpd5dVgMm5IACZAACTgCAUccv23NhQJQB3FHMyBZ9m24fTva+/nheHExsqtn9+QWG3t54ePly9H3zTeNd/z0lCl48fbbgWoP35Y+PpgXGaly9y47c0aJQQnyLMvHa2NjcX+TJjposSkJkAAJkAAJOAYBRxu/7UGFAlAHdUczoM/Pn8eQ/ftVWBZZyu0bFISlp08jvbAQi954A4999NHlu/3wQ1Tcdx+WpqerzB3Bnp7Iqagwfi/LxkWVlVzy1WEfbEoCJEACJOCYBBxt/LYHJQpAHdQdwYBk1u/7CxdUYGfZq+fl4aFi/I1v2hQjDhzAQ8XF+NfMmZfTuQEI+eQTvN27N+5t3FjF75Ncvpp3sDbj18BgUDmB6dmrw0DYlARIgARIwCEJOML4bW8wFIA6esDeBiT7/Z5IScGJ4mJ1F14AxKVD9vuNTU7GkoULMWjdukt3KDH/3nkHlcOGqSDOu/Pz0SUgABLPTxxDZNZQ/itLxY+1aoVp4eEM6aLDNtiUBEiABEjAcQnYe/x2BDIUgDp6wZ4GpDl73N2oEbbn5qKoogKl1fcyJiAA/ebOxV8/++zSJ+HhwNatxnRuWhq3EC8vRPj64lfJ91tVhU2dO2MAQ7rosAg2JQESIAEScAYC9hy/HYUPBaCOnrCXAcmyb9vERLSoVw9VVVX4KT9fpWqTZdz+v/6KN15+GXES/8/DA+cGDEDTjRsBPz/jneaXlyNo+3Z0rl8fvxYVqc+Zvk2HIbApCZAACZCAUxGw1/jtSJAoAHX0hr0MaO7x43gmLc24b0+Wb//YqBFWPvAAAnbvVneU3bgxRkyejP/edNMV4k6bAfQ3GFBYHdR5ZkSEDhJsSgIkQAIkQALOQ8Be47cjEaIA1NEbtjag0spK/OXQIbyXkYGegYE4WlSEEgD3AFhx881md1J59izuychQsQBlqfdor15qT59k9hDHj8S8PHWMgxcv4kjPntzvp8MO2JQESIAESMC5CNh6/HZEOhSAOnrFVgYkS75jDhzAR+fPo7Q6l6922T0PHMDW+fPhm5Z26aOmTYH0dMDTE9pMn3y8MS4Owd7eKj2cOH5IZo/dBQVY17EjhoWG6qDApiRAAiRAAiTgXARsNX47MhUKQB29U5cGpIV3+SQrC2+fPq2WaiWX77TqNG3/On4chjlzMGn1anhL/L5mzYCZM4G//c14R9peP9NblDAxsldQ/jujdWvMjIzUQYBNSYAESIAESMD5CNTl+O0sNCgAdfRUXRlQzfAucokBnp54t317DJdsHBkZlwRfdZF0bo3//e9LoV5MiukMoDeAeW3aoImPD5acPo0zJSXGZWEdCNiUBEiABEiABJyOQF2N384EggJQR2/VhQFp4V1ktk9y78b5+2N/YSGeS0vDxqwsfHfuHPo99tglEQhg6bBh+GLWLHzcqZPyBNaKttdvW24uLlZUKPEYVb8+5qWlqYDRXPrV0fFsSgIkQAIk4NQE6mL8djYgFIA6eszaBiTLvlE//ohO/v74OC7OXNBJXt6AgMtXGxeHb5YswR3l5cbUb2aCMTUVG7Ozr7i7SF9fLGjblvv+dPQ7m5IACZAACTg3AWuP385IgwJQR69Z24C25uTg1l9/RULXruhlupy7ZQswcKDxStMffBAtFy9Wsf3mpaZiuuwHrN7bp1WSPX6ybPxmu3Yqn++Z0lI09/FBfwZ61tHjbEoCJEACJOAKBKw9fjsjEwpAHb1mbQOaePQoXj51Cvn9+iHASxK7AfjwQ2DECONVrhw4EB4rV2JU06bGkC6bsrPh6+GBbhIaprgY6aWlmBUejhkREQzvoqN/2ZQESIAESMA1CVh7/HZGShSAOnrNmgYky78td+xARlnZpRlAHx9g4kTgzTeNV5j0+edqT6AW0uX56v18Wh5fqcglXh0dyqYkQAIkQAJuQcCa47ezAqMA1NFz1jQgbfm3hY8Pbr94Ee/94Q+XrkwcO6ZMQeWsWbgnORlf5eQYM4AEenqisKICPQIC8HhYGJd4dfQlm5IACZAACbgPAWuO385KzW0FYEFBAaZPn461a9ciOzsbMTExmDx5MuLj4y3uS2sa0KqMDIw+eBDLY2Lw3Usv4c1Fi9R1FG3ahF979YLM9okX8JSwMPgYDJBl38T8fLT19VXhXFhIgARIgARIgAQsI2DN8duyMzpeLbcVgHfccQd+/vlnvPDCC2jXrh1WrlyJZcuWYcWKFRg9erRFPWVNAzJ1ADmbl4dv//MfbIqMRErLlupavD08UGaSBUT+frRFCyyKjrboWlmJBEiABEiABEjgEgFrjt/OytQtBeAXX3yBu+++W4m+UaNGGftORGFSUhLS0tLg6en5u31qTQOqGQKmCsD3Fy4o792mPj5YmJqKhPx85fwR7eeHCS1bqplAFhIgARIgARIggdoRsOb4XbszO05ttxSADz/8MFavXo2cnBx4ad62AFatWqVm/3744Qf06dPnd3vJ2gZkGgR6ikkQaAZv/t2uYAUSIAESIAESsJiAtcdvi0/sQBXdUgD27t0bFRUV+Omnn8y6Qmb/4uLi8Oabb+KRRx753W6qCwO6Who4evb+blewAgmQAAmQAAlYTKAuxm+LT+4gFd1SAMqevzZt2mDTpk1m3XDmzBm0aNECzz//PKZMmXJFF5WUlED+aUUMKCwsDLm5uQgKCrJal8pysLb8y+DNVsPKA5EACZAACZCAIkABCLitAGzbti2+/PLLqwrAefPmKY/gmmX27NmYM2fOFZ9bWwDy+SQBEiABEiABEqg7AhSAbioAr3cJ2FYzgHVn8jwyCZAACZAACZAABaCbCkDZ3ycOHzWdQMQxRLyC7eUEwkeSBEiABEiABEig7glQALqpAJSl37vuukt5Ao8cOdJoaYMHD8bevXvtEgam7s2dZyABEiABEiABEhACFIBuKgCl8yXm386dOzF//nxERUWpGcG3334by5cvx5gxYyx6QmhAFmFiJRIgARIgARJwKAIcv91YAEoquGnTppmlghPPX3ulgnOoJ4MXQwIkQAIkQAIuTIAC0I0FoDXsmgZkDYo8BgmQAAmQAAnYlgDHbwpAXRZHA9KFj41JgARIgARIwC4EOH5TAOoyPBqQLnxsTAIkQAIkQAJ2IcDxmwJQl+HRgHThY2MSIAESIAESsAsBjt8UgLoMTzKANGzYECdPnrRqKjhdF8XGJEACJEACJEACv0lAS+V64cIFNGjQwC1puWUqOGv19KlTp1QuYBYSIAESIAESIAHnIyATOK1atXK+C7fCFVMA6oBYWVmJ06dPIzAwEB4eHhYfSfvlwZlDc2TkcnUTIhdysfTlQluhrVhqK1LPne2lqqoK+fn5aNGiBQwGQ22wuUxdCkA7dCX3Hlz7JS1T8bK0HhQUZIeeccxT0l5oL5ZaJm2FtmKprWgCkO/c2hBzrboUgHboT76k+ZKujdnRXmgvltoLbYW2YqmtUADWhpRr1qUAtEO/8iXNl3RtzI72Qnux1F5oK7QVS22FArA2pFyzLgWgHfq1pKQE8+bNg6Seq1evnh2uwDFPSS5X7xdyIRdLn1jaCm3FUluRerSX2tByvboUgK7Xp7wjEiABEiABEiABEvhNAhSANBASIAESIAESIAEScDMCFIBu1uG8XRIgARIgARIgARKgAKQNkAAJkAAJkAAJkICbEaAAtGGHFxQUYPr06Vi7di2ys7MRExODyZMnIz4+3oZXYb9Tbd68GcuXL8eOHTtU+jxJo9etWzfMnDkTN910k9mF/fLLL5g0aRISExPh5eWFgQMHYsGCBWjTpo39bsBGZ162bBkefvhh+Pv7Q2zGtLgbl+3bt+P5559HQkICiouLVcT+cePGYcaMGUYs7sZk9+7dmDNnDn766SdIGqvWrVtj9OjRePLJJ1G/fn2X5yLBe5955hns2bMHwuL8+fOYNWsWZs+efcUTWhvbeO2117B48WIcP35cBQd+4IEHMHXqVHh7e9voydd3Gku4VFRU4JVXXsHXX3+N/fv3q3EoPDwcQ4cOVWORvJNrFmfnoo+qa7emALRh/95xxx34+eef8cILL6Bdu3ZYuXIlZLBfsWKFeoG7ern//vuRlZUF+W9sbCzOnTuHhQsXYufOnfjqq6+UyJOSnJyMHj16oEuXLuqlJAO/iMScnBz10g8NDXVZVOnp6ejYsaMSfxIQ21QAuhsXeT7+/Oc/Y8SIEer5CAgIQEpKisq+I/bgjrZy4MAB9WOpffv2Spw0btwY3333HZ599lncfffd+OSTT1yey4kTJ9S7oXPnzuo9Ku/QqwnA2jwvzz33nPpRIe8b7T0tP9bHjx+Pt956yyneN5ZwkfeJiNtRo0bh9ttvV/YjIlnsp3nz5upd7OfnZ7xfV+DiFJ1np4ukALQR+C+++EK9oGVQk4dPK/KySUpKQlpaGjw9PW10NfY5TWZmJpo0aWJ2cnkhRUVFIS4uDt9++636Tgb8LVu2qMFeywiSmpqK6OhoTJw4EfPnz7fPDdjgrEOGDFFpBRs1aoR169aZCUB34iJCWESOzPa98cYb1yTvTkwEgogSGZSPHj2Ktm3bGrn85S9/UUJFZnSCg4Nd+hmSFF5S5DmR2T/5QXg1AWipbciPUm1m+c033zQylZln4S0zZfKD1dGLJVxkBlBmjUNCQsxuR9418sP8gw8+wNixY9V3rsLF0fvNntdHAWgj+rKkt3r1ajWLJUuaWlm1apWa3fjhhx/Qp08fG12NY51GZv5kwD906BDKy8uV6JOBf+nSpWYXeuedd6rlmcOHDzvWDVjpamR5fMKECZBZHhl4TAWgu3GRJU5Z0pNZDVmiulpxNybCQOMis+cye6OVp59+Wm2RkEDQElvUXZ6hawnA2tiGrMCI6JFtBr169TIyPXPmjJotE8Ets63OVH5LGF/tPmQCQp4zEb0Sn1aKK3Jxpj60xbVSANqCMoDevXtDfn3Jvh3TIrN/MvslvzwfeeQRG12N45xGljnlxSMicMOGDUoEyt5I2YsjYsi0PPXUU2rJuKioCL6+vo5zE1a4EpkdlVmGuXPnqvuW/UemAtDduNx2221quV9mzEXcyCyMzIoOGzYML774ohI47sZEzEwEcdeuXfGHP/xBzYTL7Ne2bduUgJEfTa+++qpbcbmW0KmNbYjgkW05shohWy9Mi/CVpVKxQ2cqtRWA7733Hh588EG1heCee+5Rt+qKXJypD21xrRSAtqAMqL0q4sCwadMmszNqvzJNf3nZ6JIc4jQycK1Zs0Y5e8jeJnEQ6du3L2RmtKZzjGRPkV/isgdM9qu4Uhk+fDjEFsTpQZa2agpAd+MiPwJk2V824MtAJD+gZP+sLPXdeOON+P7779WMjTvaiuxt+9Of/qT2ymrl8ccfx8svv6xsx51s5VpCpzYM5If3+++/r/Ya1yyyDSEiIkLtUXamUhsBKKsv8u4NCwvDjz/+CIPBoG7VFbk4Ux/a4lopAG1BuVoAyp6dL7/88qoCUMSNbEB2pyKbrmXzsXiZPfroo+rWtRe3LJePHDnSDIcmAEUoNWvWzGVQrV+/Xm0DEI9Gba/RtQSgu3CRH0xHjhxRKRNNnwvxYPy///s/fPPNN8rjVQSguzARg5cZQJmRatq0qdoPKzNUMmjLcyQ/It555x23eoZ+TwBaYhsidGTv28WLF68qACMjI6/44e7oLx9LBaDsGb311ltx9uxZ9YPKNMqCK3Jx9H6z9fVRANqIOJeAzUFre5lq7q+pzdKNjbquTk+jOcHITKjs+9OKLAN/+umnOHXqlJoFk/+609K4PC8yKyweirLkqRXZ/ymzMrL8KaEr3ImJMJBZcXGQOnbsmNly5bvvvouHHnoIW7duVT+O3IWLNZeACwsLzcLoCG9XXgKW/eiylUBm2iVE1w033GD2rtOWgF2JS52+zJ3w4BSANuo0+TUly5o1nUDkF6p4BbuTE4gm/mSTvyzpmRZt87aEX1iyZInZd4MGDVIDnys5gciMjsww/FYRoSP7AWXfm7tw0bxaawpA7QfCSy+9pGYC3YmJ2IgIO9n+ICLQtMgeyU6dOuH111+HsHMXLr/nBGLJ8yL7+8aMGaN+cPTs2dOIVWbFhLUrOoFo4k+c6v773/+a/cjSALgiFxsN905zGgpAG3WVLP3eddddVyxXDR48GHv37nWLMDCCWgK4Sgw3me2S/79akaVfmcmQUBeBgYGqinipaWFgZMO2qxTZdyQDT80i9yib+8VuxNtTHIXciYsEqhWv75qD77/+9S/885//VHsA+/Xr51ZMxEbEWUrEnvwQkriIWnn77bfVnq2PP/5YzYy6i6381lKnpQxkGbRly5Zq363pj055BmXPsbOEgTF9h/wWF038iQ3JVgoJxn+14opcXGXcsNZ9UABai6QFx5GYfxJoU5avJPadzAjKi1vCf8gvUFcv4sEr2QpkJq/mzJ/cuxaCQTa3d+/eXW32Nw0ELS8kVw8ErdlAzT2A8rm7cRFvRBGC8mNBbEOeHZk9lmWrzz77TKFyNyayLeDee+9VM1WyB1B+HMgPCNkrKRlBZB+pj4+Py3ORH0ayNCnZL2TpW2LYSdw/KfJDW/aH1sY2tIDHsuxpGghaPKudJRC03PvvcREnoVtuuUU9S+I0JAH3TYsseZvGl3QVLq4+tl7v/VEAXi+562gn+72mTZtmlgpOXjjukgpuwIABalbrWkULZCrf79q1S4X/kI3JpqngTF9O19EFTtPkagLQ3bjIpnwRfLIUpXnLyw8l+fEgse604m62Isu/MjslKwcSRkm8NyWAuLxLTAP8ujIX8cyVvWtXK7KsKd/X9nmREDoSfkq2Zcg+SgmLIu9rZ0kFJ/f7e1ykzm9tOZElcwkJY1pcgYvTvPhtfKEUgDYGztORAAmQAAmQAAmQgL0JUADauwd4fhIgARIgARIgARKwMQEKQBsD5+lIgARIgARIgARIwN4EKADt3QM8PwmQAAmQAAmQAAnYmAAFoI2B83QkQAIkQAIkQAIkYG8CFID27gGenwRIgARIgARIgARsTIAC0MbAeToSIAESIAESIAESsDcBCkB79wDPTwIkQAIkQAIkQAI2JkABaGPgPB0JkAAJkAAJkAAJ2JsABaC9e4DnJwESIAESIAESIAEbE6AAtDFwno4ESIAESIAESIAE7E2AAtDePcDzkwAJkAAJkAAJkICNCVAA2hg4T0cCJEACJEACJEAC9iZAAWjvHuD5SYAESIAESIAESMDGBCgAbQycpyMBEiABEiABEiABexOgALR3D/D8JEACJEACJEACJGBjAhSANgbO05EACZAACZAACZCAvQlQANq7B3h+EiABEiABEiABErAxAQpAGwPn6UiABEiABEiABEjA3gQoAO3dAzw/CZAACZAACZAACdiYAAWgjYHzdCRAAiRAAiRAAiRgbwIUgPbuAZ6fBEiABEiABEiABGxMgALQxsB5OhIgARIgARIgARKwNwEKQHv3AM9PAiRAAiRAAiRAAjYmQAFoY+A8HQmQAAmQAAmQAAnYmwAFoL17gOcnARIgARIgARIgARsToAC0MXCejgRIgARIgARIgATsTYAC0N49wPOTAAmQAAmQAAmQgI0JUADaGDhPRwIkQAIkQAIkQAL2JkABaO8e4PlJgARIgARIgARIwMYEKABtDJynIwESIAESIAESIAF7E/h/RvJ7XHYZPokAAAAASUVORK5CYII=\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# polynomial regression in the reduced dimension space\n",
    "poly_reg.fit(L, y_train)\n",
    "\n",
    "# predict test set \n",
    "pred = poly_reg.predict(dpca.transform(x_test))\n",
    "\n",
    "# compute error and plot\n",
    "plt.figure()\n",
    "plt.plot(y_test, pred, 'co', markerfacecolor=\"white\", label=\"predicted\")\n",
    "plt.plot(y_test, y_test, 'r--', label=\"ground truth\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nFXwwE8UAn2R"
   },
   "source": [
    "And, finally, check that differential PCA correctly estimated the basket weights from data. Note that the principal components cannot correspond to the baskets, because the components are orthonormal by construction. What this means is that the principal components and the basket weights are meant to <b> span the same subspace </b>, which is easily verified below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "xh1i4PAbAn2R",
    "outputId": "d4ef7ccd-dc0e-4a2b-c30d-812c4612ccb5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# compare principal axes to basket weights\n",
    "\n",
    "print(dpca.n_components_) # 3\n",
    "\n",
    "axes = dpca.components_.T # 3 principal components in columns\n",
    "weights = np.array([basket.weights.ravel() for basket in bach3.baskets]).T # 3 vectors of basket weights in columns\n",
    "\n",
    "# check that weights and axes span the same 3-dimensional subspace\n",
    "# since axes are orthonormal, it is sufficient to check that weights belong to their spanned space\n",
    "\n",
    "# project weights onto axes\n",
    "projected_weights = axes @ axes.T @ weights \n",
    "# check that projection error is zero\n",
    "print(np.allclose(weights, projected_weights)) # True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zX-bx4hzAn2R"
   },
   "source": [
    "This concludes the implementation and basic demonstration of differential PCA. The notebook [Bermudan5F.ipynb](/~https://github.com/differential-machine-learning/notebooks/blob/master/Bermudan5F.ipynb) further demonstrates it in the context of Bermudan options, highliting further properties and benefits of differential PCA in an example of practical relevance. The notebooks also highlights critical differences between classic and differential PCA, and shows how differential PCA identifies the risk factors of exotic Derivatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "bea4_BXAAn2S"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "DifferentialPCA.ipynb",
   "provenance": []
  },
  "kernelspec": {
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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