ST4_2020_Cosmology_TD2.ipynb

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        "<a href=\"https://colab.research.google.com/github/jchamilton75/CS-ST4-Cosmo-2020/blob/master/ST4_2020_Cosmology_TD2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Centrale-Supélec - ST4 - Cosmology - TD2\n",
        "\n",
        "Welcome this this second practicle work in cosmology. Today we'll start analyzing real cosmology data: Type Ia supernovae. The aim of this notebook is to reproduce by yourself the discivery of a non-zero cosmological constant that was made in 1998 and lead to the Nobel Prize in Physics for Saul Perlmutter, Brian Schmidt and Adam G. Riess.\n",
        "\n",
        "We will address the following topics:\n",
        "1.   Downloading, plotting type Ia Supernovae data (real data) and testing it against emblematic cosmological models.\n",
        "2.   Fitting the best cosmological parameters to the data using direct fitting.\n",
        "3.   Exploring the parameters space ussing Monte-Carlo-Markov-Chains in order to calculate accurate statistically meaningful constraints on cosmological parameters from the same data.\n",
        "\n",
        "You will learn about:\n",
        "*   Supernovae physics, Magnitudes and distance modulus that are observational quantities very commonly used in astrophysics.\n",
        "*   Bayesian statistics and Monte-Carlo Markov-Chains that have become key tools in modern data analysis, especially in cosmology.\n",
        "\n",
        "\n",
        "\n",
        "Before doing anything, we will first run the required few lines of code + the loading of the cosmolib library:"
      ]
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      "source": [
        "import sys\n",
        "print(\"Using Python {}\".format(sys.version_info[0]))\n",
        "\n",
        "from pylab import *\n",
        "import numpy as np\n",
        "%matplotlib inline\n",
        "from matplotlib import rc\n",
        "rc('figure',figsize=(10,5))\n",
        "rc('font',size=12)\n",
        "rc('text',usetex=False)\n",
        "!pip install emcee\n",
        "!pip install iminuit\n",
        "!rm -rf cosmolib.py*\n",
        "!wget --no-check-certificate https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/cosmolib.py\n",
        "import cosmolib as cs"
      ],
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          "text": [
            "Using Python 3\n",
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: emcee in /usr/local/lib/python3.10/dist-packages (3.1.4)\n",
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            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: iminuit in /usr/local/lib/python3.10/dist-packages (2.21.3)\n",
            "Requirement already satisfied: numpy>=1.21 in /usr/local/lib/python3.10/dist-packages (from iminuit) (1.22.4)\n",
            "--2023-05-10 16:33:40--  https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/cosmolib.py\n",
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            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.109.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 15812 (15K) [text/plain]\n",
            "Saving to: ‘cosmolib.py’\n",
            "\n",
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            "\n",
            "2023-05-10 16:33:40 (14.4 MB/s) - ‘cosmolib.py’ saved [15812/15812]\n",
            "\n"
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        "# Cosmological Analysis with type Ia Supernovae\n",
        "We will not detail everything related to supernovae here, but just recall a few basic elements.\n",
        "\n",
        "## What are Supernovae ?\n",
        "Supernovae are stars that \"appear\" in the sky suddenly and remain very bright for a few weeks up to a few months. Some historical supernovae were even visible during the day. Astronomers gradually understood that these were stars terminating their lives in a gigantic explosion. Their luminosity is typically 1 billion times larger than that of the initial star so that they are visible over cosmological distances (up to z=1 typically although a few ones are even further thanks to Hubble Space Telescope).\n",
        "\n",
        "With the development os spectroscopic astronomy, astronomer realized that all supernovae were not spectroscopically indentical, they had different emission and absorption lines indicating very different chemical composition. Nowadays, two different mechanisms for Supernovae explosions have been recognized and the Supernova Classification is made on these mechanisms rather than on spectral features:\n",
        "- The **Core Collapse** correspond to the gravitational collapse of a very massive star (therefore young as the lifetime of a star scales as the inverse of its mass to the 2.5 power). The external layers of gaz fall on the internal ones provoking a bounce and nuclear burning of the material. This is the explosion. These Supernovae are spectroscopically classified as type II, Ib or Ic depending on their spectral features.\n",
        "- The **Type Ia Supernovae** correspond to the explosion of a white dwarf in a binary system in which the companion is significantly less dense and is being eaten gradually by the white dwarf's gravitational potential well. Beyond a mass of 1.44 $M_\\bigodot$ (the Chandrasekhar mass) the white dwarf no longer has enough *quantum pressure* to hold the external layers. As a consequence, the external layers collapse and provoque bouncing and nuclear explosion.\n",
        "\n",
        "## Standard Candles\n",
        "Concerning type Ia supernovae, the same type of simple object explodes (a white dwarf at the Chandrasekhar Mass). One therefore expects the explosion to be very reproductible from a type Ia supernovae to another. In practice, type Ia supernovae at their maximum luminosity are indeed the best standard candles known in cosmology with a dispersion of their absolute luminosity typically 12% (after some corrections). They can therefore be used to measure distances throughout the Universe.\n",
        "\n",
        "Using type Ia supernovae in 1997, two tems have discovered the acceleration of the expansion of the Universe, theat is usually interpreted within Friedman-Lemaître-Robertson-Walker models as the effect of a cosmological constant.\n",
        "\n",
        "## The Union Sample 2.1\n",
        "We will redo this analysis with a modern sample comprising 580 supernovae discovered and followed with 19 different telescopes. The light curves of these supernovae were deeply analysed in order to uniformize photometrically the measurements (correct for the effects of the different telescopes, filters, ...) so that the luminosity at maximum is expected to be as clean as possible. This uniformization represents a tremendous analysis effort that we will completely ignore in the following notebook.\n",
        "\n",
        "We will be using the sample called \"Union Sample 2.1\" from the article by N. Suzuki et al., ApJ 746, 85 (2012), http://arxiv.org/abs/1105.3470\n",
        "\n",
        "An even more modern and large sample is available and is called JLA (Betoule et al. 2014): http://supernovae.in2p3.fr/sdss_snls_jla/ReadMe.html, you may be interested in downloading it and trying it if you want (but this is not expected for this course).\n",
        "\n",
        "## Which observable ?\n",
        "When observing a supernova, one measures its light-curve: the time evolution of its apparent luminosity, as in the following curve:\n",
        "<img src=\"https://weareallinthegutter.files.wordpress.com/2010/12/supernova3b.jpg\">\n",
        "It is the luminosity at maximum that consitutes a standard candle with an absolute magnitude of $M_v=-19.3 \\pm 0.12$ \n",
        "\n",
        "The absolute magnitude is defined by the magnitude of the object if it was located 10 parsec away:\n",
        "$$ M = -2.5 \\log_{10} L(10\\mathrm{pc})$$\n",
        "\n",
        "The apparent magnitude on the other hand is measured at the actual distance *d* (in parsecs):\n",
        "$$ m = -2.5 \\log_{10} L(d [\\mathrm{pc}])$$\n",
        "and the luinsoty at distance *d* is of course:\n",
        "$$ L(d) = \\frac{L(10)}{(d/10)^2}$$\n",
        "\n",
        "Because we are measuring luminosities, the cosmological distance we need to use here are **luminosity distances**.\n",
        "On can therefore define the **distance modulus** as:\n",
        "$$\\mu \\equiv m-M=5\\log_{10} D_L - 5$$\n",
        "(with $D_L$ assumed to be in parsecs in this formula).\n",
        "Which is therefore a direct logarithmic measure of the luminosity distance. This is the quantity that is used in cosmology.\n",
        "\n",
        "For each supernova, one measures the apparent magnitude at maximum, deduce its distance modulus (which requires a lot of efforts that will be ignored here). On the other hand a measurement of the redshift of the supernova is performed using a spectrum of the object (this is the easy part - note that we have not discussed the way of **finding** supernovae which is in itlsef really difficult for they are rare objects: typically one per galaxy and per century).\n",
        "\n",
        "The SNIa Hubble diagram is therefore the simple representation of $\\mu$ as a function od $z$ and we know that this quatity directly depends upon cosmological parameters because:\n",
        "$$D_L(z) = c\\times(1+z)\\times\\int_0^z \\frac{1}{H(z')}dz'$$\n",
        "with\n",
        "$$ H(z) = H_0\\times\\sqrt{\\Omega_k\\times(1+z)^2+\\Omega_m\\times(1+z)^3+\\Omega_\\Lambda}$$\n",
        "\n",
        "## Important remark\n",
        "The absolute luminosity of supernovae depends on the inferred distance of the supernovae used to calibrate it. It therefore depends on the Hubble constant and finally, the luminosity distance depends on the Hublle constant in the same manner, so that finally the Hubble constant value disappears in the distance modulus $m-M$. This means that supernovae are insensitive to the Hubble constant and canot be used to constrain it alone.\n",
        "\n",
        "## Download the file from GitHub:\n"
      ]
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      "source": [
        "!rm -f union2.1.txt\n",
        "!wget --no-check-certificate https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/Data/union2.1.txt\n",
        "! ls -lrt"
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          "text": [
            "--2023-05-10 16:35:26--  https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/Data/union2.1.txt\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 33899 (33K) [text/plain]\n",
            "Saving to: ‘union2.1.txt’\n",
            "\n",
            "\runion2.1.txt          0%[                    ]       0  --.-KB/s               \runion2.1.txt        100%[===================>]  33.10K  --.-KB/s    in 0.003s  \n",
            "\n",
            "2023-05-10 16:35:27 (10.2 MB/s) - ‘union2.1.txt’ saved [33899/33899]\n",
            "\n",
            "total 60\n",
            "drwxr-xr-x 1 root root  4096 May  8 13:37 sample_data\n",
            "drwxr-xr-x 2 root root  4096 May 10 16:23 __pycache__\n",
            "-rw-r--r-- 1 root root 15812 May 10 16:33 cosmolib.py\n",
            "-rw-r--r-- 1 root root 33899 May 10 16:35 union2.1.txt\n"
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      "source": [
        "### Reading the file\n",
        "The file, in ASCII format, is found in the Data directory. It contains 5 columns for each supernova:\n",
        "- the name of the supernova\n",
        "- its redshift\n",
        "- its distance modulus\n",
        "- the uncertainty on the distance modulus\n",
        "- a quantity irrelevant here (the probablity for the SNIa to have exploded in a low mass galaxy) related to systematics.\n",
        "\n",
        "One reads the file using the numpy \"loadtxt\" command which is very convenient and returns the columns we are interested in in the form of tables:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k_tsMT4SvqPW"
      },
      "source": [
        "filename='union2.1.txt'\n",
        "zsn,musn,dmusn=np.loadtxt(filename,usecols=(1,2,3),unpack=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
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      "cell_type": "markdown",
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      "source": [
        "Looking at the first 10 gives:"
      ]
    },
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      "cell_type": "code",
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          "base_uri": "https://localhost:8080/"
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        "outputId": "b1ba16b6-922f-4858-f11f-ab7d794c3819"
      },
      "source": [
        "for i in range(10):\n",
        "    print('z={0:5.3f} mu={1:6.3f} +/- {2:6.3f}'.format(zsn[i], \n",
        "                                                       musn[i], dmusn[i]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "z=0.028 mu=35.347 +/-  0.224\n",
            "z=0.050 mu=36.682 +/-  0.167\n",
            "z=0.053 mu=36.818 +/-  0.156\n",
            "z=0.070 mu=37.447 +/-  0.158\n",
            "z=0.063 mu=37.483 +/-  0.156\n",
            "z=0.088 mu=38.229 +/-  0.188\n",
            "z=0.079 mu=37.488 +/-  0.156\n",
            "z=0.017 mu=34.654 +/-  0.199\n",
            "z=0.042 mu=36.336 +/-  0.167\n",
            "z=0.045 mu=36.640 +/-  0.165\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87acHX4gyrYV"
      },
      "source": [
        "Let's now plot the supernovae's distance modulus as a function of redshift including error-bars, you will use the function 'errorbar' instead of 'plot' in order to plot the error-bars as well. Also, we plot the data in Log-Log which is better in this case."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JU332_tsymSy",
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          "height": 730
        },
        "outputId": "7f63841b-23ab-45f6-98ab-04a58220b7eb"
      },
      "source": [
        "rc('figure',figsize=(10,8))\n",
        "errorbar(zsn, musn, yerr=dmusn, fmt='ko')   \n",
        "xscale('log') \n",
        "xlim(1e-2,2) \n",
        "ylim(33,46) \n",
        "xlabel('Redshift') \n",
        "ylabel('Distance Modulus')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Distance Modulus')"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MYxlOzcizIqX"
      },
      "source": [
        "### $\\chi^2$ of each model\n",
        "The most common manner to compare data and a model is to use the least-square method: one measures the value of a statistical quantity named $\\chi^2$ which depends upon data, their uncertainties and the model that is tested against the data.\n",
        "\n",
        "In fact, one can easily demonstrate that for a dataset whith Gaussian error-bars, and a model depending on a set of parameters $f(\\vec{\\theta})$, minimizing the $\\chi^2$ with respect ot the parameters $\\vec{\\theta}$ allows finding the parameters which maximize the probability that the data is taken from the model with the given error-bars. This means doing a \"fit\" to the data, the minimum of the $\\chi^2$ corresponds to the best-fit and is an unbiased and optimal estimator of $\\vec{\\theta}$ if the error-bars are Gaussian.\n",
        "\n",
        "Let's assume that we have the data $\\mu_i(z_i)$ with uncertainties $\\sigma_i$ for $i$ going from $0$ to $N-1$, and a model $\\mu_{th}(\\vec{\\theta}), z)$, then the $\\chi^2$ writes:\n",
        "$$\\chi^2(\\vec{\\theta}) = \\sum_{i=0}^{N-1} \\frac{\\left( \\mu_i - \\mu_{th}(\\vec{\\theta}, z_i)\\right)^2}{\\sigma_i^2}$$\n",
        "\n",
        "A natural and simple interpretation of the $\\chi^2$ (we will see a more rigourous one later) is the following: for each measurement, we calculate the distance of this measurement to the theoretical curve for a given set of paramters, and we take this distance in units of error-bars (therefore dividing the distance on the y-axis by the error-bar). We then take the square of this quantity because being above or under the curve makes no statistical difference (Gaussian errors). One then sums all of these quantities for each data point in order to have a global estimate of the distance of the curve to the points. It is then expected that the smaller the $\\chi^2$, the better the agreement of the curve to the points. Furthermore, if the error-bars were correctly estimated and if the model does not overfit the data, each individual $\\chi^2$ should be of the order 1 in average, so that the global $\\chi^2$ should be of order $N$ on average (over all possible realizations). As a consequence, on top of the $\\chi^2$ information, one usually gives the *number of degrees of freedom* (*ndf*) which is the number of data points minus the number of parameters that have been adjusted for this curve. If $\\chi^2/ndf$ is too large this means that the model is bad or that the uncertainties were underestimated. If $\\chi^2/ndf$ is too low, then it can mean that the error bars are overestimated or that the model overfits the data. The ideal value 1 is of course an average and each realisazation fluctuates around this average (with a probability distribution given by the $\\chi^2$ distribution at N degrees of freedom https://en.wikipedia.org/wiki/Chi-squared_distribution).\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mMFZG0zbzOTm"
      },
      "source": [
        "***Question 1:*** You are now expected to overplot on the supernovae Hubble diagram the three different canonical cosmological models in three different colours, and for each model calculate the $\\chi^2$ and number of degrees of freedom of the supernova data sample, which you will dispay in the legend of the plot.\n",
        "\n",
        "The three cosmological models are of course:\n",
        "- flat: $h=0.7$, $\\Omega_m=1$, $\\Omega_\\Lambda=0$, $w=-1$\n",
        "- open: $h=0.7$, $\\Omega_m=0.3$, $\\Omega_\\Lambda=0$, $w=-1$\n",
        "- lcdm: $h=0.7$, $\\Omega_m=0.3$, $\\Omega_\\Lambda=0.7$, $w=-1$\n",
        "\n",
        "Remember that the SNIa data is NOT luminosity ditance but distance modulus that is defined as:\n",
        "$$\\mu \\equiv m-M=5\\log_{10} D_L - 5$$\n",
        "(with $D_L$ assumed to be in parsecs in this formula).\n",
        "So you need to apply this formula to your luminosity distance, you can alternatively use the cs.musn1a() function that does this for you (same arguments as cs.lumdist())."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sW9MpkiXywe6"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oAHkxCnAziZ4"
      },
      "source": [
        "You should see that the $\\Lambda$CDM models gives a significantly better $\\chi^2$ and has $\\chi^2/ndf$ close to 1, which is the sign of a good fit. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vn2scfVF0jUc"
      },
      "source": [
        "### Brute Force Exploration of the Parameter space\n",
        "We can explore the parameter space $(\\Omega_m,\\Omega_\\Lambda)$ in a brute force manner to fit the best combination and calculate the confidence intervals.\n",
        "\n",
        "***Question 2:*** Take 100 values for $\\Omega_m$ between 0 and 1, 100 values of $\\Omega_\\Lambda$ between 0 and 1.5 and calculate the $\\chi^2$ for each of these in a 2d-array. You will the display this array adjusting the colorbar to see the shape of the confidence intervals between $Min(\\chi^2)$ and $Min(\\chi^2)+11.83$ (corresponding to 3$\\sigma$)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mZ9GLpmtzT7j"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "122gJjSHz1rP"
      },
      "source": [
        "***Question 3:*** Now display the same $\\chi^2$ map but with contours at 1, 2 and 3 sigmas (corresponding in 2D to $Min(\\chi^2)$ + 2.3, 6.18 adn 11.83. Do not forget to use *np.meshgrid()* to transform your 1D X and Y coordinates to 2D arrays. We suggest you to use the following colors for the filling the contours: \n",
        "- *blue* for the $1\\sigma$ contour\n",
        "- *dodgerblue* for the $2\\sigma$ contour\n",
        "- *deepskyblue* for the $3\\sigma$ contour\n",
        "\n",
        "\n",
        "You should also display the best fit value in a legend, as well as the *Flat Universe* locations in the parameter space (witlh a dotted black line for instance)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lCFQGcQgztCe"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTEshma800II"
      },
      "source": [
        "### Fitting with Minuit\n",
        "Instead of looking at $\\chi^2$ values for individual models, we want to find the best-fit model, which means minimizing the $\\chi^2$. For this, we will be using the MINUIT library (initially developped at CERN in the 70's) that does this in a very efficient manner using  a set of methods (including the simple conjugate gradient) to find the minimum of the N-dimensional surface (N is the number of parameters to be adjusted). In order to simplify, I have implemented in the cosmolib library a simple wrapper tom Minuit that will avoid you to get into the insides of Minuit..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MKu9TeoQ1YSy"
      },
      "source": [
        "#### First try with a straight line\n",
        "Before trying with the SNIa data, let us first try to fit a straight line with Minuit. We generate points following some straight line and add Gaussian errors:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PdSwQbthz5g0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "2f84d9f9-1951-4010-86e1-998a50c5863b"
      },
      "source": [
        "rc('figure',figsize=(10,5))\n",
        "x = linspace(0,1,10)\n",
        "sy = 0.2\n",
        "y = 3*x + 2 + np.random.randn(10)*sy\n",
        "sigma_y = np.zeros(10) + sy\n",
        "errorbar(x,y,yerr=sigma_y,fmt='ro', label='Sample Data')\n",
        "xlim(-0.1,1.1)\n",
        "xlabel('x')\n",
        "ylabel('y')\n",
        "legend(loc='upper left')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2e2cbe3280>"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SwQ0DjJs1h3B"
      },
      "source": [
        "Minuit needs a specific format for the function to be fitted (this is called a *signature* - le names and order of the arguments of the function). We will fit a linear function defined in the follwing way:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cN_gLHK61BYT"
      },
      "source": [
        "def line_to_fit(x, pars):\n",
        "  values = pars[0] + pars[1]*x\n",
        "  return values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v6sAlHlL1opm"
      },
      "source": [
        "Now let's perform the Minuit fitting that requires an initial guess. Finding the initial guess is sometimes tricky (and can be most of the work actually...) but in the present case (0,0) will work fine. Here is below to the wrapper to Minuit implemented in the cosmolib library."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yGWBh5BC1koy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ef539b85-8b9f-45d8-edac-794bdb976de9"
      },
      "source": [
        "guess = np.array([0., 0.])\n",
        "result = cs.do_minuit(x,y,sigma_y,guess,functname=line_to_fit)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Fitting with Minuit\n",
            "Chi2 = 5.826354767750129\n",
            "ndf = 8\n",
            "Fitted values:\n",
            "[1.8481543  3.10789557]\n",
            "Errors:\n",
            "[0.11755076 0.19817347]\n",
            "Covariance:\n",
            "[[ 0.01381818 -0.01963636]\n",
            " [-0.01963636  0.03927273]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6-pBD3az10Q5"
      },
      "source": [
        "Let's analyse the results. The output of minuit can be understood as the following:  returns in a list the fitting object, the value of the fitted parameters, their error bars and the covariance matrix, then the chi-square and the number of degrees of freedom. So here they are:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qODKeidd1rZX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ef2c7a79-ce46-43dd-92d8-4c1558da9e5b"
      },
      "source": [
        "print(result[0])\n",
        "print(result[1])\n",
        "print(result[2])\n",
        "print(result[3])\n",
        "print(result[4])\n",
        "print(result[5])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "┌─────────────────────────────────────────────────────────────────────────┐\n",
            "│                                Migrad                                   │\n",
            "├──────────────────────────────────┬──────────────────────────────────────┤\n",
            "│ FCN = 5.826 (χ²/ndof = 0.7)      │              Nfcn = 42               │\n",
            "│ EDM = 4.88e-20 (Goal: 0.0002)    │                                      │\n",
            "├──────────────────────────────────┼──────────────────────────────────────┤\n",
            "│          Valid Minimum           │        No Parameters at limit        │\n",
            "├──────────────────────────────────┼──────────────────────────────────────┤\n",
            "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
            "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
            "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
            "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
            "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
            "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
            "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
            "│ 0 │ x0   │   1.85    │   0.12    │            │            │         │         │       │\n",
            "│ 1 │ x1   │   3.11    │   0.20    │            │            │         │         │       │\n",
            "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
            "┌────┬───────────────┐\n",
            "│    │     x0     x1 │\n",
            "├────┼───────────────┤\n",
            "│ x0 │ 0.0138 -0.020 │\n",
            "│ x1 │ -0.020 0.0393 │\n",
            "└────┴───────────────┘\n",
            "[1.8481543  3.10789557]\n",
            "[0.11755076 0.19817347]\n",
            "[[ 0.01381818 -0.01963636]\n",
            " [-0.01963636  0.03927273]]\n",
            "5.826354767750129\n",
            "8\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PKTkqklT2RmI"
      },
      "source": [
        "So finally we can write the result and error bars as:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yldKx59J2Md7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "595a12eb-be36-4254-ea81-4b01dfbd7739"
      },
      "source": [
        "for i in range(len(result[1])):\n",
        "  print('Parameter {0:d} = {1:5.2f} +/- {2:5.2f}'.format(i, result[1][i], result[2][i]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Parameter 0 =  1.85 +/-  0.12\n",
            "Parameter 1 =  3.11 +/-  0.20\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FV58xaca2Ycj"
      },
      "source": [
        "Which is very consistent with the input values. You can rerun the above lines changing the amount of noise, run it many times to generate multiple realizations...\n",
        "\n",
        "We show below the initial data along with the fitted straight-line:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RXpTouzJ2U_Y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "cd8108db-7298-49e8-b821-edd4c511a4be"
      },
      "source": [
        "errorbar(x,y,yerr=sigma_y,fmt='ro', label='Sample Data')\n",
        "plot(x, line_to_fit(x, result[1]),'k', label='Fitted with Minuit')\n",
        "xlim(-0.1,1.1)\n",
        "xlabel('x')\n",
        "ylabel('y')\n",
        "legend(loc='upper left')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2e2ca339d0>"
            ]
          },
          "metadata": {},
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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a0q5dO0qVKpWJ71za6tatS926dbP8uPd75ZVXmDt3Lp06dWLo0KFcvXqV5cuXU7NmTcLDwx/aN+n/97vvvku/fv2wsbGhW7du+XK0VkRExBIYhsG2bdvw8vJK/nxUrFgx3n77bUaOHKnf0TlEI1aSae7u7owePZqvv/6al19+mf79+ydv+89//kPZsmV544036N+/P5s2bQISV9E7ePAgXbt2ZfXq1YwcOZLly5djZWWFt7d3cn8XFxd27dpFnTp1mD59OvPnz2fgwIGMHTs23fUljVJVr16d4sWLp2pPz30annjiCZYvX87Vq1cZOnQo/fv359ixY+muwdI89dRTfPjhh4SFhfHmm2+ydetW1q5dS4MGDR7Zt3HjxgQEBHDkyBEGDx5M//79U4x8iYiISM4wDINvv/2Wpk2b0qNHD44ePYqTkxN+fn6EhIQwceJEhaocZDIe9+r6fCA8PBxnZ2fCwsJwcnJKtT0mJoaQkBAqVaqEnZ2dGSoUyR30syIiIhYtFy9esXv3bjw9PdmzZw+QeAnG2LFjmTBhAsWKFcuaF8nF35+s9KhskERTAUVEREREcon9+/fj5eXF//73PwBsbW0ZMWIE77zzDqVLlzZzdfmbgpWIiIiIiIU7cuQIXl5ebNu2DYACBQrw6quv8u6771KuXDkzVyegYCUiIiIiYrGOHz+Or68vn376KQBWVlYMHDgQb29vKlWqZObq5H4KViIiIiIiFiY4OBg/Pz8++ugjEhISAOjXrx++vr5Uq1bNzNVJWhSsREREREQsxPnz5wkMDOSDDz7g3r17ALzwwgv4+flRp04dM1cnD6NgJSIiIiJiZpcvX2batGksX76cu3fvAtC5c2f8/f1p3LixmauT9FCwEhERERExkxs3bjBr1iwWLVpEVFQUAK1btyYwMJBnnnnGzNXJ41CwEhERERHJYWFhYcybN4+5c+cSEREBQNOmTQkMDKR9+/aYTCYzVyiPS8FKRERERCSH3Llzh0WLFjFz5kxu3boFQN26dQkMDKRr166WFaji4//5evdu6NgRrK3NV4+FszJ3ASIiIiIieV1MTAzz58/Hzc2NSZMmcevWLZ566ik2btzIoUOHeP755y0rVG3ZAjVq/PP8ueegYsXEdkmTgpWIiIiISDa5e/cuy5cvp3LlyrzxxhtcvXoVNzc31q5dy++//46HhwdWVhb2kXzLFvDwgNDQlO2hoYntCldpsrD/i/ncnTtgMiU+7twxdzW5kslkwtfX19xliIiISG7w76lu9z/PpHv37rF69WqqVavGiBEjCA0NpVy5cqxcuZKgoCAGDBiAtSVOq4uPh7FjwTBSb0tqGzcuS79XeYWClaSS9NeTChUqYGdnR9myZXn22WdZtGiRuUvLcRUrVsRkMmEymbCysqJIkSLUrl2bYcOGsX///kwde+rUqXz++edZU6iIiIg8nmya6paQkMCGDRuoVasWQ4YM4ezZs5QuXZqFCxdy6tQpXnvtNWxsbDJXe3baswcuXHjwdsOA8+cT95MUFKwkhb1799KoUSOOHDnCa6+9xuLFi3n11VexsrJiwYIF5i7PLOrVq8fatWv58MMPmTZtGm3btmXbtm00a9aMN998M8PHVbASERExk2yY6mYYBl988QX16tWjX79+nDhxgmLFijFz5kyCg4MZPXo0dnZ2WfQGstGlS1m7Xz6iVQEtiQWsvDJlyhScnZ05cOAARYoUSbHt6tWrOVqLpShbtiwDBgxI0TZjxgxefPFF5s2bR5UqVRgxYoSZqhMREZHH8qipbiZT4lS3Hj3S9TnMMAy+/fZbPD09OXjwIABOTk5MmDCBsWPH4uTklMVvIJu5uGTtfvmIRqwshYWsvHLmzBlq1qyZKlQBlCpVKsXzVatW0a5dO0qVKoWtrS01atRg2bJlqfpVrFiR559/nu+//55GjRphb29P7dq1+f777wHYsmULtWvXxs7OjoYNG3L48OEU/QcPHkyhQoUIDg6mU6dOODo6UqZMGfz9/THS+kfxX0JDQ3nllVcoXbo0tra21KxZkw8++CD935Q02Nvbs3btWooVK8aUKVNS1DF79mxatGhB8eLFsbe3p2HDhmzatClFf5PJxJ07d1izZk3yVMPBgwcDcO7cOV5//XWqVauGvb09xYsXp3fv3pw9ezZTNYuIiAhZOtVt9+7dtG7dms6dO3Pw4EEcHR2ZPHkyISEheHl55b5QBdCyJZQrlxgw02Iygatr4n6SgoKVJbCglVcqVKjAr7/+yh9//PHIfZctW0aFChWYPHkyc+bMwdXVlddff50lS5ak2vf06dO8+OKLdOvWjWnTpnHr1i26devGunXreOONNxgwYAB+fn6cOXOGPn36kJCQkKJ/fHw8nTt3pnTp0sycOZOGDRvi4+ODj4/PQ2u8cuUKzZo1Y8eOHYwaNYoFCxZQuXJlhg4dyvz58x/re/NvhQoVomfPnoSGhnLs2LHk9gULFlC/fn38/f2ZOnUqBQoUoHfv3nz11VfJ+6xduxZbW1tatmzJ2rVrWbt2LcOHDwfgwIED7N27l379+rFw4UL+7//+j++++442bdok35FdREREMigLprrt37+fjh070rp1a/bs2YOtrS1vvPEGwcHBTJkyhWLFimVRsWZgbQ1Jl3/8O1wlPZ8/X/ezSoshqYSFhRmAERYWlub26Oho49ixY0Z0dHTmX+zePcMoV84wEv8+kvphMhmGq2vifjng22+/NaytrQ1ra2ujefPmxsSJE41vvvnGuHv3bqp9o6KiUrV16tTJcHNzS9FWoUIFAzD27t2b3PbNN98YgGFvb2+cO3cuuX3FihUGYOzatSu5bdCgQQZgjB49OrktISHB6Nq1q1GwYEHj2rVrye2A4ePjk/x86NChhouLi3H9+vUUNfXr189wdnZO8z38u/auXbs+cPu8efMMwPjiiy+S2/59zLt37xq1atUy2rVrl6Ld0dHRGDRoUKpjplXTvn37DMD48MMPH1qvpcnSnxUREZGssGvXgz933f+477NIksOHDxvdunUzAAMwbGxsjBEjRhgXLlzI8beR7TZvNoyyZVN+T1xdE9vzmUdlgyQasTI3C1t55dlnn2Xfvn10796dI0eOMHPmTDp16kTZsmXZunVrin3t7e2Tvw4LC+P69eu0bt2a4OBgwsLCUuxbo0YNmjdvnvy8adOmALRr147y5cunag8ODk5V26hRo5K/NplMjBo1irt377Jjx44034thGGzevJlu3bphGAbXr19PfnTq1ImwsDAOHTqU3m9NmgoVKgRAREREctv935dbt24RFhZGy5Yt0/1a9/ePi4vjxo0bVK5cmSJFimS6XhERkXwvA1Pdjh8/Tp8+fahfvz7btm3DysqKIUOGcOLECZYuXUrZsmVzqPgc5O4O983IYft2CAlJbJc0KViZmwWuvNK4cWO2bNnCrVu3+OWXX5g0aRIRERF4eHikmPL2008/0aFDBxwdHSlSpAglS5Zk8uTJAKmC1f3hCcDZ2RkAV1fXNNtv3bqVot3Kygo3N7cUbVWrVgV44LVH165d4/bt26xcuZKSJUumeAwZMgTI/IIckZGRABQuXDi57csvv6RZs2bY2dlRrFgxSpYsybJly1J9Tx4kOjoab29vXF1dsbW1pUSJEpQsWZLbt2+n+xgiIiLyAI8x1e3MmTMMHDiQWrVqsXHjRkwmE/379+fYsWN88MEHVKpUKUdLz3H3T/dr1UrT/x5BqwKamwWvvFKwYEEaN25M48aNqVq1KkOGDGHjxo34+Phw5swZ2rdvT/Xq1Zk7dy6urq4ULFiQ7du3M2/evFTXSD3oBngPajfSsSjFoyTVMGDAAAYNGpTmPnXq1MnUayRdi1a5cmUA9uzZQ/fu3WnVqhVLly7FxcUFGxsbVq1axfr169N1zNGjR7Nq1SrGjRtH8+bNcXZ2xmQy0a9fv1TfVxEREckAd3fYtAnGjEl5jXu5cjB/Pn81akTgsGGsWrWKe/fuAfDCCy/g7+9P7dq1zVS0WDoFK3NLGo4ODU172U+TKXG7mVdeadSoEQCX/h4527ZtG7GxsWzdujXFaNSuXbuy5fUTEhIIDg5OHqUCOHnyJJC46mBaSpYsSeHChYmPj6dDhw5ZXlNkZCSfffYZrq6uPPXUUwBs3rwZOzs7vvnmG2xtbZP3XbVqVar+pgdMQdi0aRODBg1izpw5yW0xMTHcvn07a9+AiIhIfubuDh06wN+zZdi+nct16jB1xgxW9O/P3bt3AejcuTMBAQHJn4VEHkRTAc3NwlZe2bVrV5qjRdu3bwegWrVqwD8jTffvGxYWlmaAyCqLFy9O/towDBYvXoyNjQ3t27dPc39ra2t69erF5s2b01zl8Nq1axmuJTo6mpdffpmbN2/y7rvvJocka2trTCYT8ffdk+zs2bNp3gjY0dExzbBkbW2d6v/BokWLUhxTREREssDfn2duAG//73+4VanCokWLuHv3bvKKf//9738VqiRdNGJlCR4xHJ2TFwmOHj2aqKgoevbsSfXq1bl79y579+5lw4YNVKxYMfnapI4dO1KwYEG6devG8OHDiYyM5L333qNUqVLJo1pZyc7Ojq+//ppBgwbRtGlT/vvf//LVV18xefJkSpYs+cB+06dPZ9euXTRt2pTXXnuNGjVqcPPmTQ4dOsSOHTu4efPmI187NDSUjz76CEgcpTp27BgbN27k8uXLjB8/PnmZdICuXbsyd+5cOnfuzIsvvsjVq1dZsmQJlStX5ujRoymO27BhQ3bs2MHcuXMpU6YMlSpVomnTpjz//POsXbsWZ2dnatSowb59+9ixYwfFixfP4HdPRERE0hIWFsZcYB4QMW8ekLiQ1pQpU2jXrt0DZ5eIpCm7lyfMjXJ0ufWUL/zPcpbbt+fYEuv3++9//2u88sorRvXq1Y1ChQoZBQsWNCpXrmyMHj3auHLlSop9t27datSpU8ews7MzKlasaMyYMcP44IMPDMAICQlJ3u9BS5YDxsiRI1O0hYSEGIAxa9as5LZBgwYZjo6OxpkzZ4yOHTsaDg4ORunSpQ0fHx8jPj4+1THvX27dMAzjypUrxsiRIw1XV1fDxsbGeOKJJ4z27dsbK1eufOT3I2mpeMAwmUyGk5OTUbNmTeO1114z9u/fn2af999/36hSpYpha2trVK9e3Vi1apXh4+Nj/PvHLSgoyGjVqpVhb29vAMlLr9+6dcsYMmSIUaJECaNQoUJGp06djKCgIKNChQppLs9uybTcuoiIBYiM/OfzRWSkuauxCBEREcbUqVONokWLJv+er1enjvHll18aCQkJ5i7PcujcMQwj/cutmwwjC1YJyGPCw8NxdnYmLCwszTtmx8TEEBISQqVKlbCzs8u6F75zB/5evpvISHB0zLpj52KDBw9m06ZNySvwSe6RbT8rIiKSfvp8kSwmJoZly5Yxbdq05EsCngL8gF7h4Vjdt8qvoHPnb4/KBkl0jZWIiIiI5Gl3795l+fLlVK5cmTfffJNr167x5JNPsvY//+F3oDeJt3YRyQydQSIiIiKSJ927d4/Vq1dTrVo1RowYQWhoKK6urrz33nscP36cAf36oTszSVbR4hWWxNEx7SXXRURERCTdEhIS+PTTT/Hx8Um+PcsTTzzBu+++y2uvvfbPLVH+XlJdJCtoxEos3urVq3V9lYiIiDySYRh8/vnn1KtXj/79+3Py5EmKFy/OrFmzOHPmDKNGjUpxn0mRrGTRwWrKlCmYTCZq1ar1yH19fX0xmUypHrpgXkRERCRvMwyDb775hiZNmtCzZ09+//13nJ2dCQgIICQkhAkTJuDg4GDuMiWPs9ipgBcuXGDq1Kk4PubqI8uWLaNQ0uol/HMjWxERERHJe3744Qc8PT358ccfAXB0dGTs2LGMHz+eYsWKmbk6yU8sNlhNmDCBZs2aER8fz/Xr19Pdz8PDgxIlSmRjZf/QSvUiD6efERERyS4///wzXl5e7NixAwBbW1tGjhzJ22+/TalSpcxcneRHFjkVcPfu3WzatIn58+c/dl/DMAgPD8/WD3QFCiTm0Xv37mXba4jkBUk/I0k/MyIiIpn122+/0a1bN5o3b86OHTuwsbHh9ddf58yZM8yZM0ehSszG4oJVfHw8o0eP5tVXX6V27dqP3d/NzQ1nZ2cKFy7MgAEDuHLlSpbXaG1tjbW1NeHh4Vl+bJG8JDw8PPnnRUREJDOOHz9Onz59qF+/Pl9++SVWVlYMGTKEkydPsmTJEsqWLWvuEiWfs7g/Iy9fvpxz584lD+umV9GiRRk1ahTNmzfH1taWPXv2sGTJEn755RcOHjz40Lskx8bGEhsbm/z8UYHJZDJRqlQpLl26hK2tLY6OjphMpseqVyQvMwyDO3fuEB4ejouLi34+REQkw86cOYOfnx/r1q0jISEBk8lEv3798PX1pWrVquYuL2/TrYAei0UFqxs3buDt7Y2XlxclS5Z8rL5jx45N8bxXr140adKEl156iaVLl/LOO+88sO+0adPw8/N7rNdzdnYmOjqa69evc+3atcfqK5IfmEwmihQpgrOzs7lLERGRXOivv/4iMDCQDz74gPj4eAB69uyJn59fhmY1iWQ3k2FBV5ePGDGCHTt28Oeff1KwYEEA2rRpw/Xr1/njjz8ydEwXFxdq1qz50BGwtEasXF1dCQsLe+hIFyROXYyLi8tQbSJ5mY2NjaYAiohYgjt3IGnF5MjIxFEIC3b58mWmTp3KihUruPv3DXy7dOmCv78/jRo1MnN1kh+Fh4fj7Oz8yGxgMSNWp06dYuXKlcyfP5+LFy8mt8fExBAXF8fZs2dxcnJ67GUzXV1duXnz5kP3sbW1zfDN4nT9iIiIiEjm3bhxg5kzZ7Jo0SKio6OBxD+wBwYG8vTTT5u5OpFHs5hgFRoaSkJCAmPGjGHMmDGptleqVImxY8c+1kqBhmFw9uxZ6tevn4WVioiIiEhWCQsLY+7cucybN4+IiAgAmjVrRmBgIO3atdN1upJrWEywqlWrFp999lmqdk9PTyIiIliwYAFPPvkkkDjnNioqiurVqyfvd+3atVTXZS1btoxr167RuXPn7C1eRERERB5LZGQkixYtYtasWdy6dQuAevXqERgYyHPPPadAJbmORV1jlZa0rrFq06YNP/zwQ4p7VTk4ONC3b19q166NnZ0dP/74I5988gl169blp59+wsHBId2vmd55lCIiIiIWLzwckhYS2r4dOnYEM17GEBMTw7Jly5g2bVryAmA1atTA39+fnj17YmVlcXcDknwu111jlVkvvfQSe/fuZfPmzcTExFChQgUmTpzIu++++1ihSkRERCTP2LIF7r/E4rnnoFw5WLAA3N1ztJS7d+/ywQcfEBgYSGhoKABPPvkkfn5+9OvXT9esS65n8SNW5qARKxEREcn1tmwBD4/U9yFKmmK3aVOOhKt79+7x0Ucf4efnx9mzZ4HExcW8vb0ZNGgQNjY22V6DSGakNxtorFVEREQkr4mPh7Fj0765a1LbuHGJ+2WThIQEPvnkE2rWrMmQIUM4e/YsTzzxBIsWLeLUqVO8+uqrClWSpyhYiYiIiOQ1e/bAhQsP3m4YcP584n5ZzDAMPv/8c+rVq0f//v05efIkxYsXZ9asWZw5c4ZRo0Zl+DY3IpYsz1xjJSIiIiJ/u3Qpa/dLB8Mw+Pbbb/H09OTgwYMAODs7M2HCBMaOHUvhwoWz7LVELJGClYiIiORud+5AoUKJX0dGgqOjeeuxBC4uWbvfI/zwww94enry448/AuDo6MjYsWMZP348xYoVy5LXELF0ClYiIiIieU3Llomr/4WGpn2dlcmUuL1ly0y9zM8//4yXlxc7duwAwNbWlpEjR/L2229TqlSpTB1bJLfRNVYiIiIieY21deKS6vDPKoBJkp7Pn5/h+1n99ttvdOvWjebNm7Njxw5sbGx4/fXXOXPmDHPmzFGoknxJwUpEREQkL3J3T1xSvUyZlO3lymV4qfXjx4/Tp08f6tevz5dffomVlRVDhgzh5MmTLFmyhLJly2ZR8SK5j6YCioiIiORV7u7QoQM4Oyc+374dOnZ87JGqM2fO4Ofnx7p160hISMBkMtG/f398fHyoWrVqNhQukvsoWImIiIjkZfeHqFatHitU/fXXXwQGBvLBBx8Q//c9r3r27Im/vz+1atXK6kpFcjUFKxERERFJ4fLly0ydOpUVK1Zw9+5dALp06UJAQAANGzY0c3UilknBSkREREQAuHHjBjNnzmTRokVER0cD0KZNGwIDA3n66afNXJ2IZVOwEhEREcnnwsLCmDt3LvPmzSMiIgKAZs2aMWXKFNq1a2fm6kRyBwUrERERkXwqMjKSRYsWMWvWLG7dugVA/fr1CQwMpEuXLpj+vVS7iDyQgpWIiIhIPhMTE8OyZcuYNm0a165dA6BGjRr4+/vTs2dPrKx0Rx6Rx6VgJSIiIpJP3L17lw/WriUwMJDQ0FAAnnzySfz8/OjXrx/WGbxhsIgoWImIiIjkefeAjwC/+vU5e+4cAOXLl8fb25uBAwdiY2Nj1vpE8gIFKxEREZE8KiEhgU83bsQHOAlw7hxPPPEEnp6evPrqq9ja2pq5QpG8Q8FKREREJI8xDIMvvvgCb29vfv/9dwCKA+9MmcLr48bh4OBg3gJF8iAFKxEREZE8wjAMvvnmG7y8vDh48CAAzs7OTAgLYyxQeOxYUKgSyRZa8kVERERyt/j4f77evTvl83zk+++/p2XLlnTp0oWDBw/i6OjIu+++S8gff+AJFDZ3gSJ5nIKViIiI5F5btkCNGv88f+45qFgxsT2f+Pnnn3n22Wdp27YtP/30E3Z2dowfP56QkBACAwMpWrSouUsUyRcUrERERCR32rIFPDzg72XDk4WGJrbn8XB1+PBhunXrRvPmzdmxYwc2Nja8/vrrnD59mtmzZ1OyZElzlyiSryhYiYiISO4THw9jx4JhpN6W1DZuXJ6cFnjs2DF69+5NgwYN+PLLL7G2tuaVV17h5MmTLFmyhLJly5q7RJF8ScFKREREcp89e+DChQdvNww4fz5xvzzizJkzvPzyy9SqVYtNmzZhMpl48cUXOXbsGO+//z4VK1ZMu6OjY+L3wzASvxaRbKFVAUVERCT3uXQpa/ezYH/99ReBgYF88MEHxP89AtezZ0/8/f2pVauWmasTkSQKViIiIpL7uLhk7X4W6NKlS0ybNo0VK1Zw9+5dALp06UJAQAANGzY0c3Ui8m8KViIiIpL7tGwJ5colLlSR1nVWJlPi9pYtc762TLp+/TozZ85k8eLFREdHA9C2bVsCAgJ4+umnzVydiDyIrrESERGR3MfaGhYsSPzaZEq5Len5/PmJ++USt2/fxtvbm0qVKjFr1iyio6Np3rw53333HTt37lSoErFwClYiIiKSO7m7w6ZNUKZMyvZy5RLb3d3NU9djioyMZOrUqbi5uREQEEBkZCT169fnq6++4qeffqJdu3bmLlFE0kFTAUVERCT3cneHDh3A2Tnx+fbt0LFjrhipio6OZtmyZUyfPp1r164BUKNGDQICAujZsyemf4/EiYhFU7ASERGR3O3+ENWqlcWHqrt37/L+++8TGBjIxYsXAahcuTJ+fn707dsXawuvX0TSpmAlIiIikgPu3bvH2rVr8fPz49y5cwCUL18eb29vBg4ciI2NjZkrFJHMULASERERyUYJCQls2LABHx8fTp06BcATTzyBp6cnr776Kra2tmauUESygoKViIiISDYwDIPPP/8cb29v/vjjDwBKlCjBO++8w4gRI3BwcDBzhSKSlRSsRERERLKQYRh88803eHp68uuvvwLg7OzMW2+9xZgxYyhcuLCZKxSR7KBgJSIiIpJFvv/+ezw9Pfnpp58AcHR0ZNy4cYwfP56iRYuauToRyU4KViIiIiKZ9PPPP+Pp6cl3330HgJ2dHSNHjuTtt9+mZMmSZq5ORHKCgpWIiIhIBh0+fBgvLy+++uorAGxsbBg2bBiTJ0+mzL9vXCwieZqClYiIiMhjOnbsGD4+PmzatAkAa2trBg8ejJeXFxUqVDBzdSJiDgpWIiIiIul0+vRp/Pz8WLduHYZhYDKZ6N+/Pz4+PlStWtXc5YmIGVmZu4CHmTJlCiaTiVq1aqVr/9DQUPr06UORIkVwcnKiR48eBAcHZ3OVIiIiktf99ddfvPbaa1SvXp2PPvoIwzBwd3fn6NGjrFu3TqFKRCx3xOrChQtMnToVR0fHdO0fGRlJ27ZtCQsLY/LkydjY2DBv3jxat27Nb7/9RvHixbO5YhEREclrLl26xNSpU1m5ciV3794F4LnnnsPf35+GDRuauToRsSQWG6wmTJhAs2bNiI+P5/r164/cf+nSpZw6dYpffvmFxo0bA9ClSxdq1arFnDlzmDp1anaXLCIiInnE9evXmTFjBosXLyYmJgaAdu3aERAQQIsWLcxcnYhYIoucCrh79242bdrE/Pnz091n06ZNNG7cODlUAVSvXp327dvz6aefZkOVIiIiktfcvn0bLy8vKlWqxOzZs4mJiaF58+Z89913fPfddwpVIvJAFhes4uPjGT16NK+++iq1a9dOV5+EhASOHj1Ko0aNUm1r0qQJZ86cISIiIqtLFRERkTwiMjKSqVOnUqlSJQIDA4mMjKRBgwZs376dn376iXbt2pm7RBGxcBY3FXD58uWcO3eOHTt2pLvPzZs3iY2NxcXFJdW2pLaLFy9SrVq1NPvHxsYSGxub/Dw8PPwxqxYREZHcKDo6mmXLljFt2rTkSw9q1qyJv78/PXv2xGQymblCEcktLGrE6saNG3h7e+Pl5fVYdymPjo4GwNbWNtU2Ozu7FPukZdq0aTg7Oyc/XF1dH7NyERERMRtHRzCMxEc6F726e/cuS5cu5cknn2T8+PFcv36dypUrs27dOo4cOYK7u7tClYg8FosKVp6enhQrVozRo0c/Vj97e3uAFKNOSZIuOE3aJy2TJk0iLCws+XH+/PnHen0RERHJHe7du8cHH3xA1apVGTlyJJcuXaJ8+fK8//77HD9+nBdffBFra2tzlykiuZDFTAU8deoUK1euZP78+Vy8eDG5PSYmhri4OM6ePYuTkxPFihVL1bdYsWLY2tpy6dKlVNuS2sqUKfPA17a1tU1ztEtERETyhoSEBDZs2ICPjw+nTp0CEi8X8PT0ZOjQofocICKZZjHBKjQ0lISEBMaMGcOYMWNSba9UqRJjx45Nc6VAKysrateuzcGDB1Nt279/P25ubhQuXDg7yhYRERELZhgGn3/+Od7e3vzxxx8AlChRgnfeeYcRI0bg4OBg5gpFJK+wmGBVq1YtPvvss1Ttnp6eREREsGDBAp588kkg8e7nUVFRVK9ePXk/Dw8P3nnnHQ4ePJi8OuCJEyfYuXMnEyZMyJk3ISIiIhbBMAy+/vprvLy8+PXXXwFwdnbmrbfeYsyYMfqDq4hkOZNhGIa5i3iYNm3acP369eS/MiW1/fDDD9xfekREBPXr1yciIoIJEyZgY2PD3LlziY+P57fffnusxTDCw8NxdnYmLCwMJyenLH0/IiIikr127dqFp6cne/fuBaBQoUKMGzeON998k6JFi5q5OhHJbdKbDSxmxCqzChcuzPfff88bb7xBYGAgCQkJtGnThnnz5j1WqBIREZHcad++fXh6erJz504gcWXgUaNGMXHiRH0WEJFsZ/EjVuagESsREZHc49ChQ3h5ebF9+3YAbGxsGDZsGJMnT37o4lUiIumR70asREREJH/5888/8fHxYfPmzQBYW1szePBgvLy8qFChgpmrE5H8RsFKREREcpVTp07h5+fH+vXrMQwDk8nEiy++iI+PD1WqVDF3eSKSTylYiYiISK5w7tw5AgICWL16NfHx8QD06tULPz8/atasaebqRCS/U7ASERERi3bx4kWmTp3KypUriYuLA+C5557D39+fhg0bmrk6EZFEClYiIiJika5du8bMmTNZvHgxMTExALRr146AgABatGhh5upERFJSsBIRERGLcvv2bebMmcP8+fOJjIwEoEWLFgQEBNCuXTszVycikjYFKxEREbEIERERLFy4kNmzZ3P79m0AGjRoQGBgIJ07d8ZkMpm3QBGRh1CwEhEREbOKjo5m6dKlTJ8+nevXrwNQs2ZNAgICeOGFFxSoRCRXULASERERs4iNjeX9998nMDCQS5cuAVClShX8/Pzo06cP1tbWZq5QRCT9FKxEREQkR927d48PP/wQf39/zp07B0D58uXx8fFh4MCBFCigjycikvvoXy4RERHJEfHx8WzYsAFfX19OnToFgIuLC56engwdOhRbW1szVygiknEKViIiIpKtDMPgs88+w9vbmz///BOAEiVKMGnSJEaMGIG9vb2ZKxQRyTwFKxEREckWhmHw9ddf4+npyaFDhwAoUqQIb731FqNHj6Zw4cJmrlBEJOsoWImIiEiW27VrF56enuzduxeAQoUKMW7cOMaPH0+RIkXMW5yISDZQsBIREZEss2/fPjw9Pdm5cycAdnZ2jBo1iokTJ1KyZEkzVycikn0UrERERCTTDh06hJeXF9u3bwfAxsaG4cOHM3nyZFxcXMxcnYhI9lOwEhERkQz7888/8fHxYfPmzQBYW1szZMgQPD09qVChgpmrExHJOQpWIiIi8thOnTqFn58f69evxzAMTCYTL774Ij4+PlSpUsXc5YmI5DgFKxEREUm3c+fOERAQwOrVq4mPjwegV69e+Pn5UbNmTTNXJyJiPgpWIiIilu7OHShUKPHryEhwdMzxEi5evMjUqVNZuXIlcXFxAHTt2hV/f38aNGiQ4/WIiFgaBSsRERF5oGvXrjFz5kwWL15MTEwMAO3btycgIIDmzZubuToREcuhYCUiIiKp3L59mzlz5jB//nwiIyMBaNGiBYGBgbRt29bM1YmIWB4FKxEREUkWERHBwoULmT17Nrdv3wagQYMGBAYG0rlzZ0wmk3kLFBGxUApWIiIiQnR0NEuXLmX69Olcv34dgJo1axIQEMALL7ygQCUi8ggKViIiIvlYbGws77//PoGBgVy6dAmAKlWq4OfnR58+fbC2tjZzhSIiuYOClYiISD507949PvzwQ/z9/Tl37hwA5cuXx8fHh4EDB1KggD4iiIg8Dv2rKSIiko/Ex8ezYcMGfH19OXXqFAAuLi54enoydOhQbG1tzVyhiEjupGAlIiKSDxiGwWeffYa3tzd//vknACVKlGDSpEmMGDECe3t7M1coIpK7KViJiIjkYYZh8PXXX+Pp6cmhQ4cAKFKkCG+99RajR4+mcOHCZq5QRCRvULASERHJo3bt2oWnpyd79+4FoFChQowbN47x48dTpEgR8xYnIpLHKFiJiIjkMfv27cPT05OdO3cCYGdnx6hRo5g4cSIlS5Y0c3UiInmTgpWIiEgecejQIby8vNi+fTsANjY2DB8+nMmTJ+Pi4mLm6kRE8jYFKxERkVzuzz//xMfHh82bNwNgbW3NkCFD8PT0pEKFCmauTkQkf1CwEhERyaVOnTqFn58f69evxzAMTCYTL774Ij4+PlSpUsXc5YmI5CsKViIiIrnMuXPnCAgIYPXq1cTHxwPQq1cv/Pz8qFmzppmrExHJnxSsRERELN3f4ekW8GG/frz99dfE3rsHQNeuXfH396dBgwZmLFBERKzMXYCIiIg8xJYtxFerBkBRYOyXX3Lq3j18atdm7969fPnllwpVIiIWQCNWIiIiFurO2rU4DByI6V/t5QDfP/6AS5fMUZaIiKRBI1YiIiIWJiIigqkBAdweNAiD1L+sk4PWuHHJ0wRFRMS8FKxEREQsRHR0NHPmzMHNzY1vvb0paxgP/kVtGHD+POzZk5MliojIA1hUsPrzzz/p3bs3bm5uODg4UKJECVq1asW2bdse2Xf16tWYTKY0H5cvX86B6kVERDImNjaWJUuW8OSTTzJhwgSuX79O/SeeSF9nTQcUEbEIFnWN1blz54iIiGDQoEGUKVOGqKgoNm/eTPfu3VmxYgXDhg175DH8/f2pVKlSirYiRYpkU8UiIiIZd+/ePdasWYO/vz9//fUXAOXLl8fHx4dBFSpAhw6PPoiLSzZXKSIi6WEyDMMwdxEPEx8fT8OGDYmJiSEoKOiB+61evZohQ4Zw4MABGjVqlKnXDA8Px9nZmbCwMJycnDJ1LBERkX+Lj49nw4YN+Pj4cPr0aQBcXFzw9PRk6NCh2NraJl47VbEihIYmTvv7N5MJypWDkBCwts7ZNyAiko+kNxtY1FTAtFhbW+Pq6srt27fT3SciIiL5hokiIiKWwjAMtmzZQt26dXnppZc4ffo0JUqUYM6cOZw5c4bXX389MVRBYlhasCDxa9O/1gVMej5/vkKViIiFsMhgdefOHa5fv86ZM2eYN28e//3vf2nfvn26+rZt2xYnJyccHBzo3r07p06demSf2NhYwsPDUzxERESyimEYbN++nUaNGtGrVy/+/PNPihQpwpQpUwgJCeHNN9/E3t4+dUd3d9i0CcqUSdlerlxiu7t7zrwBERF5JIu6xirJ+PHjWbFiBQBWVla4u7uzePHih/ZxcHBg8ODBycHq119/Ze7cubRo0YJDhw7h6ur6wL7Tpk3Dz88vS9+DiIgIwM6dO/H09GTfvn0AFCpUiDfeeIM333wzfdcAu7snXmvl7Jz4fPt26NhRI1UiIhbGIq+xCgoK4sKFC1y8eJFPP/2UggULsmzZMkqXLv1Yx/nxxx9p1aoVw4YNY/ny5Q/cLzY2ltjY2OTn4eHhuLq66horERHJsL179+Ll5cXOnTsBsLe3Z9SoUUycOJESJUo83sHu3IFChRK/jowER8csrlZERB4kvddYWWSw+reOHTty+/Zt9u/fj+nf88wfoXnz5ly7di354uD00OIVIiKSUYcOHcLLy4vt27cDYGNjw/Dhw5k8eTIuGV3BT8FKRMRs8sziFQAeHh4cOHCAkydPPnZfV1dXbt68mQ1ViYiI/OOPP/6gV69eNGzYkO3bt2Ntbc2rr77KqVOnWLRoUcZDlYiI5AoWeY3Vv0VHRwMQFhb22H2Dg4MpWbJkVpckIiICwKlTp/D19eXjjz/GMAxMJhMvvfQSPj4+VK5c2dzliYhIDrGoEaurV6+maouLi+PDDz/E3t6eGjVqAHDp0iWCgoKIi4tL3u/atWup+m7fvp1ff/2Vzp07Z1/RIiKSL507d45XX32Vp556ivXr12MYBh4eHvz++++sXbtWoUpEJJ+xqBGr4cOHEx4eTqtWrShbtiyXL19m3bp1BAUFMWfOHAr9Pb980qRJrFmzhpCQECpWrAhAixYtqF+/Po0aNcLZ2ZlDhw7xwQcf4OrqyuTJk834rkREJC+5ePEiU6dOZeXKlcl/4OvatSv+/v40aNDAzNWJiIi5WFSw6tu3L++//z7Lli3jxo0bFC5cmIYNGzJjxgy6d+/+yL5fffUV3377LVFRUbi4uPDaa6/h4+Pz2KsJioiI/Nu1a9eYMWMGS5YsISYmBoD27dsTEBBA8+bNzVydiIiYW65YFTCnaVVAERFJcuvWLebMmcP8+fO5c+cOkDhLIjAwkLZt2+ZMEVoVUETEbNKbDSxqxEpERMRSREREsGDBAmbPnp28eFLDhg0JDAykU6dOj337DxERydsUrERERO4TFRXF0qVLmT59Ojdu3ACgVq1aBAQE0KNHDwUqERFJk4KViIgIEBsby3/+8x+mTJnCpUuXAKhatSp+fn706dMHKyuLWkhXREQsjIKViIjka0m39fD39+evv/4CoEKFCvj4+PDyyy9ToIB+VYqIyKPpt4WIiORL8fHxfPLJJ/j6+nL69GkAypQpg6enJ0OHDqVgwYJmrlBERHITBSsREclXDMNgy5YteHt7c+zYMQBKlizJpEmT+L//+z/s7e3NXKGIiORGGZ4wvn///qysQ0REJFsZhsH27dtp2LAhHh4eHDt2jCJFijB16lSCg4N54403FKpERCTDMhysmjdvTtWqVQkICCA4ODgraxIRkfzmzh0wmRIff98rKivt3LmTp59+mq5du3L48GEKFSqEl5cXISEhTJo0iUJJ94gSERHJoAwHq48++ogqVaoQEBBAlSpVePrpp1m+fDk3b97MyvpEREQybO/evbRr14727duzb98+7O3teeuttwgJCcHf358iRYqYu8T0cXQEw0h86ObAIiIWKcPB6sUXX+Srr77i4sWLLFiwAMMweP311ylTpgwvvPACmzZt4u7du1lZq4iISLr8+uuvPPfcczz99NPs2rWLggULMnr0aM6cOcPMmTMpUaKEuUsUEZE8xmQYhpFVBztz5gzr169n3bp1nDp1CmdnZzw8PBg4cCDPPPNMVr1MtgsPD8fZ2ZmwsDCcnJzMXY6ISN535w4kTceLjMzwqMwff/yBj48PW7ZsAcDa2ppXXnkFT09Pypcvn1XViohIPpLebJCldzu0t7fHwcEBOzs7DMPAZDLxxRdf0Lp1axo3bpy8+pKIiEhWOnXqFC+99BJ16tRhy5YtmEwmXn75ZYKCgli5cqVClYiIZLtMB6uIiAhWrVpFhw4dqFChApMnT6ZixYps2rSJy5cvc/HiRTZs2MDVq1cZMmRIVtQsIiICwNmzZxk6dChPPfUU69evxzAMevfuzR9//MGHH35I5cqVzV2iiIjkExm+j9UXX3zBunXr+PLLL4mJiaFx48bMnz+ffv36Ubx48RT7enh4cOvWLUaOHJnpgkVERC5evMiUKVN47733iIuLA+D555/H39+f+vXrm7k6ERHJjzIcrHr27ImrqytvvPEGAwcOpFq1ag/dv27durz00ksZfTkRERGuXr3KjBkzWLp0KTExMQB06NCBgIAAmjVrZubqREQkP8twsNq5cydt2rRJ9/5NmjShSZMmGX05ERHJx27dusXs2bNZsGABd/6+z9XTTz9NYGDgY/0uEhERyS4ZDlb6RSYiItktIiKCBQsWMHv2bMLCwgBo1KgRgYGBdOzYEZPJZOYKRUREEmU4WImIiGSXqKgoli5dyvTp07lx4wYAtWrVIiAggB49eihQiYiIxVGwEhERixELvLd8OVNmz+by5csAVK1aFT8/P/r06YOVVZbeJURERCTLKFiJiIjZxcXF8SHgD/w1YQIAFStWxMfHhwEDBlCggH5diYiIZdOf/kRExGzi4+NZt24dNRo14lXgL6CMiwvLli3jxIkTDB48WKFKRERyBf22EhGRHJeQkMBnn32Gt7c3x44dA6AkMAn4v6NHsS9Rwqz1iYiIPC6NWImISI4xDIOvvvqKRo0a4eHhwbFjxyhatCjT/PwIBt4A7O3tzV2miIjIY1OwEhGRHPHdd9/RokULnn/+eQ4fPkzhwoXx9vYmJCSEd8aNo1DSjrt3Q3y8OUsVERF5bApWIiKSrX766SfatWtHhw4d+Pnnn7G3t2fixIkEBwfj5+eH83ffQY0a/3R47jmoWBG2bDFbzSIiIo9LwUpERLLFr7/+ynPPPcczzzzDrl27KFiwIGPGjCE4OJgZM2ZQokSJxPDk4QGhoSk7h4YmtitciYhILqFgJSIiWeqPP/7A3d2dRo0a8d///pcCBQowbNgwTp8+zYIFC3jiiScSd4yPh7FjwTBSHySpbdw4TQsUEZFcQcFKRESyxMmTJ3nxxRepU6cOn332GSaTiZdffpmgoCBWrFiBq6tryg579sCFCw8+oGHA+fOJ+4mIiFg4LbcuIiKZcvbsWQICAlizZg3xf48u9e7dG19fX2rcf+3Uv126lL4XSO9+IiIiZqRgJSIiGXLx4kWmTJnCe++9R1xcHADdunXD39+fevXqPfoALi7pe6H07iciImJGClYiIvJYrl69yowZM1i6dCkxMTEAPPvsswQEBNC0adP0H6hlSyhXLnGhirSuszKZEre3bJlFlYuIiGQfXWMlIiLpcuvWLd59913c3NyYO3cuMTExPPPMM3z//fd8++23jxeqAKytYcGCxK9NppTbkp7Pn5+4n4iIiIVTsBIRkYeKiIggMDCQSpUqMXXqVO7cuUOjRo34+uuv2b17N61bt874wd3dYdMmKFMmZXu5cont7u6ZK15ERCSHaCqgiIikKSoqiqVLlzJ9+nRu3LgBQO3atQkICKB79+6Y/j3KlFHu7tChAzg7Jz7fvh06dtRIlYiI5CoKViIikkJsbCzvvfceU6ZM4fLlywBUrVoVf39/evfujZVVNkx2uD9EtWqlUCUiIrmOgpWIiAAQFxfHmjVr8Pf35/z58wBUrFgRHx8fBgwYQIEC+pUhIiLyIPotKSKSz8XHx/Pxxx/j6+vLmTNnAChTpgxeXl688sorFCxY0MwVioiIWD4FKxGRfCohIYEtW7bg7e3N8ePHAShZsiSTJ09m+PDh2Nvbm7lCERGR3EPBSkQknzEMg+3bt+Pl5cXhw4cBKFq0KBMnTmTUqFEUKlTIzBWKiIjkPha13Pqff/5J7969cXNzw8HBgRIlStCqVSu2bduWrv63b99m2LBhlCxZEkdHR9q2bcuhQ4eyuWoRkdzBMAy+++47WrRowfPPP8/hw4cpXLgw3t7ehISE8M477yhUiYiIZJBFjVidO3eOiIgIBg0aRJkyZYiKimLz5s10796dFStWMGzYsAf2TUhIoGvXrhw5coS33nqLEiVKsHTpUtq0acOvv/5KlSpVcvCdiIhYlp9++glPT0++//57AOzt7Rk9enTyv5ciIiKSOSbDMAxzF/Ew8fHxNGzYkJiYGIKCgh6436effkrfvn3ZuHEjHh4eAFy7do2qVavSpUsX1q9fn+7XDA8Px9nZmbCwMJycnDL9HkREzOXgwYN4eXnx9ddfA1CwYEH+7//+j0mTJvHEE0+Yubr73LkDSaNlkZHg6GjeekRERP6W3mxgUVMB02JtbY2rqyu3b99+6H6bNm2idOnSuLu7J7eVLFmSPn368MUXXxAbG5vNlYqIWI7ff/8dd3d3GjduzNdff02BAgUYNmwYp0+fZsGCBZYVqkRERPIAiwxWd+7c4fr165w5c4Z58+bx3//+l/bt2z+0z+HDh2nQoEGqG1c2adKEqKgoTp48mZ0li4hYhJMnT/Liiy9St25dPvvsM0wmEy+//DJBQUGsWLECV1dXc5coIiKSJ1nUNVZJxo8fz4oVKwCwsrLC3d2dxYsXP7TPpUuXaNWqVap2FxcXAC5evEjt2rXT7BsbG5tiRCs8PDyjpYuImMXZs2fx9/dnzZo1JCQkANC7d298fX2pUaOGmasTERHJ+ywyWI0bNw4PDw8uXrzIp59+Snx8PHfv3n1on+joaGxtbVO129nZJW9/kGnTpuHn55e5okVEzCA0NJQpU6bwn//8h7i4OAC6deuGv78/9erVM29xIiIi+YhFTgWsXr06HTp0YODAgXz55ZdERkbSrVs3HrbOhr29fZrXUcXExCRvf5BJkyYRFhaW/Dh//nzm34SISDa6evUq48ePp3Llyixbtoy4uDieffZZfv75Z7Zu3apQJSIiksMscsTq3zw8PBg+fDgnT56kWrVqae7j4uLCpUuXUrUntZUpU+aBx7e1tU1ztEtExNLcunWL2bNns2DBAu7cuQPAM888Q2BgIK1btzZzdSIiIvlXrghWSdP4wsLCHrhPvXr12LNnDwkJCSkWsNi/fz8ODg5UrVo12+sUEcku4eHhLFiwgDlz5iT/W9ioUSMCAwPp2LEjJpPJzBWKiIjkbxY1FfDq1aup2uLi4vjwww+xt7dPvgD70qVLBAUFJV9PAImjWleuXGHLli3JbdevX2fjxo1069ZNI1IikitFRUUxa9Ys3Nzc8Pb2JiwsjNq1a/P555/zyy+/0KlTJ4UqERERC2BRI1bDhw8nPDycVq1aUbZsWS5fvsy6desICgpizpw5FPr75pGTJk1izZo1hISEULFiRSAxWDVr1owhQ4Zw7NgxSpQowdKlS4mPj9fCFCKS68TGxvLee+8xZcoULl++DEDVqlXx9/end+/eqW4tkes5OoJl369eRETkoSwqWPXt25f333+fZcuWcePGDQoXLkzDhg2ZMWMG3bt3f2hfa2trtm/fzltvvcXChQuJjo6mcePGrF69+oHXZYmIWJq4uDjWrFmDv79/8kI6FStWxMfHhwEDBlCggEX9sy0iIiJ/MxkPW2ovnwoPD8fZ2ZmwsDCcnJzMXY6I5APx8fF8/PHH+Pr6cubMGSBx0R0vLy9eeeUVChYsaOYKRURE8qf0ZgP96VNExIwSEhLYsmUL3t7eHD9+HICSJUsyefJkhg8f/tBbRYiIiIjlULASETEDwzDYvn07Xl5eHD58GICiRYsyceJERo0alXxNqYiIiOQOClYiIjnIMAx27tyJp6cnP//8MwCFCxfmjTfe4M0338TZ2dnMFYqIiEhGKFiJiOSQn3bswPPZZ/n+7+f29vaMHj2at956ixIlSpizNBEREcmkPLZer4iI5Tl48CBdunThmb9DVUFgzIgRBAcHM2PGDIUqERGRPEAjViIi2eT333/H29ubzz//HIACBQow5N49vADXWbMS790kIiIieYJGrEREstiJEyfo378/devW5fPPP8dkMvHyyy8TdOgQKwFXcxcoIiIiWU4jViIiWeTs2bP4+/uzZs0aEhISAOjduze+vr7UqFED7twxc4UiIiKSXRSsREQyKTQ0lClTpvCf//yHuLg4ALp164a/vz/16tUzb3EiIiKSIxSsREQy6OrVq0yfPp2lS5cSGxsLwLPPPktAQABNmzY1c3UiIiKSkxSsREQe082bN5k9ezYLFy7kzt/T+5555hkCAwNp3bq1masTERERc1CwEhFJp/DwcBYsWMDs2bMJDw8HoHHjxgQGBvLss89iMpnMXKGIiIiYi4KViMgjREVFsWTJEmbMmMGNGzcAqF27NgEBAXTv3l2BSkRERBSsREQeJDY2lpUrVzJlyhSuXLkCQLVq1fDz86N3795YWemOFSIiIpJIwUpE5F/i4uJYvXo1AQEBnD9/HoCKFSvi6+vLSy+9RIEC+qdTREREUtKnAxGRv8XHx/Pxxx/j6+vLmTNnAChbtixeXl4MGTKEggULmrlCERERsVQKViKS7yUkJLBlyxa8vb05fvw4AKVKlWLSpEn83//9H3Z2dmauUERERCydgpWI5FuGYfDVV1/h5eXFb7/9BkDRokWZOHEio0aNolChQuYtUERERHINBSsRyXcMw+C7777D09OT/fv3A1C4cGHefPNN3njjDZydnc1coYiIiOQ2ClYikq/8+OOPeHp68sMPPwBgb2/PmDFjeOuttyhevLiZqxMREZHcSmsFi0i+cODAATp37kzLli354YcfKFiwIGPHjiU4OJjp06fnTKiKj//n6927Uz4XERGRXE3BSkTytN9//50XXniBJk2a8M0331CgQAGGDx/O6dOnmT9/Pk888UTOFLJlC9So8c/z556DihUT20VERCTXU7ASkTzpxIkT9O/fn7p16/LFF19gZWXFwIEDOXHiBMuXL8fV1TXnitmyBTw8IDQ0ZXtoaGK7wpWIiEiup2AlInlKSEgIQ4YMoUaNGnzyyScYhkGfPn34448/WLNmDW5ubjlbUHw8jB0LhpF6W1LbuHGaFigiIpLLKViJSJ5w4cIFRowYQdWqVVm9ejUJCQl0796d3377jQ0bNvDUU0+Zp7A9e+DChQdvNww4fz5xPxEREcm1tCqgiORqV69eZfr06SxdupTY2FgAOnbsSEBAAE2aNDFzdcClS1m7n4iIiFgkBSsRyZVu3rzJ7NmzWbBgAVFRUQC0bNmSwMBAWrVqZebq7uPikrX7iYiIiEVSsBKRXCU8PJz58+czZ84cwsPDAWjcuDGBgYE8++yzmEwmM1f4Ly1bQrlyiQtVpHWdlcmUuL1ly5yvTURERLKMrrESkVzhzp07zJw5k0qVKuHj40N4eDh16tThiy++YP/+/XTs2NHyQhWAtTUsWJD49b/rS3o+f37ifiIiIpJrKViJiEWLjY1l0aJFPPnkk7z99tvcvHmTatWqsWHDBg4fPkz37t0tM1Ddz90dNm2CMmVStpcrl9ju7m6eukRERCTLaCqgiFikuLg4Vq9eTUBAAOfPnwdIHq166aWXKFAgl/3z5e4OHTqAs3Pi8+3boWNHjVSJiIjkEbnsk4mI5HXx8fGsX78eX19fgoODAShXrhyenp4MGTKEggULmrnCTLg/RLVqpVAlIiKShyhYiYhFSEhIYPPmzfj4+HD8+HEASpUqxeTJkxk+fDh2dnZmrlBERETkwRSsRCTr3LkDhQolfh0ZCY6Oj+xiGAZfffUVXl5e/PbbbwAULVqUt99+m1GjRuGYjmOIiIiImJuClYiYhWEY7NixAy8vL/bv3w9A4cKFGT9+POPGjcM56VokERERkVxAwUpEctyePXvw9PRk9+7dADg4ODBmzBgmTJhA8eLFzVydiIiIyONTsBKRHHPgwAG8vLz45ptvAChYsCAjRoxg0qRJlC5d2szViYiIiGScgpWIZLujR4/i7e3NF198AUCBAgUYOnQo7777Lq6urmauTkRERCTzFKxEJNsEBQXh6+vLhg0bALCysuLll1/G29sbNzc3M1cnIiIiknUUrEQky4UAfsOHs/bjj0lISACgb9+++Pr6Ur16dfMWJyIiIpINrMxdwP0OHDjAqFGjqFmzJo6OjpQvX54+ffpw8uTJR/ZdvXo1JpMpzcfly5dzoHoRuRAaygigKrBm3ToSEhLo3r07v/32G5988olClYiIiORZFjViNWPGDH766Sd69+5NnTp1uHz5MosXL6ZBgwb8/PPP1KpV65HH8Pf3p1KlSinaihQpkk0ViwjAlStXmD59OsuWLSP277ZOHTrgP2UKTZo0MWttIiIiIjnBooLVm2++yfr16ylYsGByW9++falduzbTp0/no48+euQxunTpQqNGjbKzTBH5282bN5k1axYLFy4kKioKgJZAINDq88/TdYNgERERkbzAoqYCtmjRIkWoAqhSpQo1a9bk+PHj6T5OREQE8fHxWV2eiPwtPDw8eXR4+vTpREVF0aRJE77dupUfgFbmLlBEREQkh1lUsEqLYRhcuXKFEiVKpGv/tm3b4uTkhIODA927d+fUqVPZXKFI/nHnzh1mzpxJpUqV8PHxITw8nLp167J161Z+/vlnnm3XDpO5ixQRERExA4uaCpiWdevWERoair+//0P3c3BwYPDgwcnB6tdff2Xu3Lm0aNGCQ4cOPfReObGxscTGxiY/Dw8Pz7L6RfKCmJgYVq5cydSpU7ly5QoA1atXx9/fn169emFlZfF/oxERERHJVibDMAxzF/EgQUFBNG3alJo1a7Jnzx6sra0fq/+PP/5Iq1atGDZsGMuXL3/gfr6+vvj5+aVqDwsLw8nJ6bHrljzszh0oVCjx68jIPH8NUVxcHKtWrSIgIIALFy4AUKlSJXx9fXnppZdS/0zms++PiIiI5H3h4eE4Ozs/MhtYbLC6fPkyTz/9NHFxcfz888+UKVMmQ8dp3rw5165d4/Tp0w/cJ60RK1dXVwUrSS2fBIf4+HjWr1+Pr68vwcHBAJQrVw4vLy+GDBmCjY1N2h3zyfdHRERE8o/0BiuLnAoYFhZGly5duH37Nnv27MlwqAJwdXXlxIkTD93H1tYWW1vbDL+GSF6RkJDA5s2b8fb2JigoCIDSpUszefJkhg0bhp2dnZkrFBEREbFMFhesYmJi6NatGydPnmTHjh3UqFEjU8cLDg6mZMmSWVSdSN5kGAZffvklXl5eHDlyBIBixYrx9ttvM3LkSBzTO/J0/2qcu3dDx47wmFN4RURERHIji7riPD4+nr59+7Jv3z42btxI8+bN09zv0qVLBAUFERcXl9x27dq1VPtt376dX3/9lc6dO2dbzSK5mWEY/O9//6NZs2Z0796dI0eO4OTkhK+vLyEhIUycODH9oWrLFrj/DyHPPQcVKya2i4iIiORxFnWN1bhx41iwYAHdunWjT58+qbYPGDAAgMGDB7NmzRpCQkKoWLEikHi/q/r169OoUSOcnZ05dOgQH3zwAS4uLhw4cIDSpUunu470zqOUfCgPXUO0Z88ePD092b17N5C4suaYMWOYMGECxYsXf7yDbdkCHh7w739OTH8vvr5pE7i7Z0HVIiIiIjkrV15j9dtvvwGwbds2tm3blmp7UrBKS9++ffnqq6/49ttviYqKwsXFhddeew0fH5/HClUied2BAwfw8vLim2++ARKvMRwxYgTvvPNOxn5W4uNh7NjUoQoS20wmGDcOevTQtEARERHJsyxqxMpSaMRKHigXj1gdPXoUb29vvvjiCwAKFCjAq6++yrvvvku5cuUyfuDvv4e2bR+9365d0KZNxl9HRERExAxy5YiViGS9oKAgfH192bBhAwBWVla8/PLLeHt74+bmlvkXuHQpa/cTERERyYUUrETyqJCQEPz8/Fi7di0JCQlA4pRZX19fqlevnnUv5OKStfuJiIiI5EIWtSqgiGTehQsXGDFiBFWrVmXNmjUkJCTQo0cPjhw5wieffJK1oQqgZUsoV+6fhSr+zWQCV9fE/URERETyKAUrkTziypUrvPHGG1SuXJnly5dz7949OnXqxP79+/n888+pU6dO9rywtTUsWJD49b/DVdLz+fO1cIWIiIjkaQpWIrnczZs3mTRpEm5ubsyfP5/Y2FhatWrF7t27+frrr2nSpEn2F+HunrikepkyKdvLldNS6yIiIpIv6BorkVwqPDyc+fPnM2fOHMLDwwFo0qQJgYGBdOjQAdODpuZlF3d36NABnJ0Tn2/fDh07aqRKRERE8gUFK5Fc5s6dOyxZsoQZM2Zw8+ZNAOrWrUtAQADPP/98zgeq+90folq1UqgSERGRfEPBSiSXiImJYeXKlUydOpUrV64AUL16dfz9/enVqxdWVprZKyIiImIu+iQm8jji4//5evfulM+zSVxcHCtXrqRKlSqMHTuWK1euUKlSJdasWcMff/xB7969FapEREREzEyfxkTSa8sWqFHjn+fPPQcVKya2Z4P4+HjWrl1L9erVGT58OBcuXKBcuXKsWLGCEydOMHDgQKw11U5ERETEIihYiaTHli3g4QGhoSnbQ0MT27MwXCUkJLBx40Zq1arFwIEDCQ4OpnTp0ixYsIBTp04xbNgwbGxssuz1RERERCTzFKxEHiU+HsaOBcNIvS2pbdy4TE8LNAyDbdu20aBBA/r06UNQUBDFihVjxowZnDlzhjFjxmBnZ5ep1xARERGR7KHFK0QeZc8euHDhwdsNA86fT9yvTZvHPrxhGOzYsQNPT09++eUXAJycnHjzzTd54403cHJyymDhIiIiIpJTFKxEHuXSpazd7z579uzB09OT3bt3A+Dg4MCYMWOYMGECxYsXf+zjiYiIiIh5KFiJPIqLS9buBxw4cAAvLy+++eYbAGxtbRkxYgTvvPMOpUuXzkiVIiIiImJGClYij9KyJZQrl7hQRVrXWZlMidtbtnzkoY4ePYq3tzdffPEFAAUKFODVV1/l3XffpVy5cllduYiIiIjkEC1eIfIo1tawYEHi1yZTym1Jz+fPT9zvAYKCgujXrx9169bliy++wMrKikGDBnHixAmWLVumUCUiIiKSyylYiaSHuzts2gRlyqRsL1cusd3dPc1uISEhDB48mJo1a7JhwwYA+vbty59//snq1atxc3PL7spFREREJAdoKqBIerm7Q4cO4Oyc+Hz7dujYMc2RqgsXLjBlyhT+85//cO/ePQB69OiBv78/derUycmqRURERCQHKFiJPI77Q1SrVqlC1ZUrV5g+fTrLli0jNjYWgE6dOuHv70+TJk1yslIRERERyUEKViJZ4ObNm8yaNYuFCxcSFRUFQKtWrQgMDKRlOha1EBEREZHcTcFKJBPCw8OZP38+c+bMITw8HIAmTZoQGBhIhw4dMP17sYu8ztEx7ZUTRURERPI4BSuRDLgDLJk3jxnz5nHz5k0A6tatS0BAAM8//3z+C1QiIiIi+ZyClchjiImJYSUwFbji5QVA9erV8ff3p1evXlhZaaFNERERkfxInwJF0iEuLo6VK1dSpW5dxgJXgEoVK7JmzRr++OMPevfurVAlIiIiko9pxErkIeLj41m3bh1+fn4EBwcDUA7wBF45fBibIkXMWZ6IiIiIWAj9iV0kDQkJCXz66afUqlWLQYMGERwcTOnSpVkwcyangOGAjY2NucsUEREREQuhYCVyH8Mw2LZtGw0aNKBv374EBQVRrFgxZsyYwZkzZxjz+uvYmbtIEREREbE4mgooQmKg2rFjB56envzyyy8AODk58eabb/LGG2/g5OSUuOOdO2asUkREREQslYKV5Ht79uzB09OT3bt3A+Dg4MCYMWOYMGECxYsXN3N1IiIiIpIbKFhJvvXLL7/g5eXFt99+C4CtrS0jRozgnXfeoXTp0mauTkRERERyEwUryXeOHj2Kl5cXW7duBaBAgQK8+uqrvPvuu5QrV87M1YmIiIhIbqRgJflGUFAQvr6+bNiwAQArKytefvllvL29cXNzM3N1IiIiIpKbKVhJnhccHIy/vz9r164lISEBgL59++Lr60v16tXNXJ2IiIiI5AUKVpJnXbhwgcDAQN5//33u3bsHQI8ePfD396dOnTpmrk5ERERE8hIFK0npzh0oVCjx68hIcHQ0bz0ZcOXKFaZNm8by5cuJjY0FoFOnTvj7+9OkSZPMHdzREQwjC6oUERERkbxEwUryjJs3bzJr1iwWLlxIVFQUAK1atSIwMJCWLVuauToRERERycsUrCTXCw8PZ968ecydO5fw8HAAmjRpQmBgIB06dMBkMpm5QhERERHJ6xSsJNe6c+cOixcvZubMmdy8eROAunXrEhgYSNeuXRWoRERERCTHKFhJrhMTE8PKlSuZOnUqV65cAaB69er4+/vTq1cvrKyszFyhiIiIiOQ3FvUJ9MCBA4waNYqaNWvi6OhI+fLl6dOnDydPnkxX/9u3bzNs2DBKliyJo6Mjbdu25dChQ9lcteSUu3fvsmLFCqpUqcLYsWO5cuUKbm5ufPjhh/zxxx/07t1boUpEREREzMKiRqxmzJjBTz/9RO/evalTpw6XL19m8eLFNGjQgJ9//platWo9sG9CQgJdu3blyJEjvPXWW5QoUYKlS5fSpk0bfv31V6pUqZKD70SyUnx8POvWrcPX15eQkBAAypUrh7e3N4MHD8bGxsbMFYqIiIhIfmcyDMtZO3rv3r00atSIggULJredOnWK2rVr4+HhwUcfffTAvp9++il9+/Zl48aNeHh4AHDt2jWqVq1Kly5dWL9+fbrrCA8Px9nZmbCwMJycnDL+hnIjC1puPSEhgU2bNuHj40NQUBAApUuXZvLkyQwbNgw7Ozuz1SYiIiIi+UN6s4FFjVi1aNEiVVuVKlWoWbMmx48ff2jfTZs2Ubp0adzd3ZPbSpYsSZ8+ffjoo4+IjY3F1tY2y2uWrGcYBtu2bcPLy4ujR48CUKxYMd5++21GjhyJYy68t5aIiIiI5G0Wf0GKYRhcuXKFEiVKPHS/w4cP06BBg1TX2DRp0oSoqKiHXqcVGxtLeHh4iofkPMMw+Pbbb2natCk9evTg6NGjODk54efnR0hICBMnTlSoEhERERGLZPHBat26dYSGhtK3b9+H7nfp0iVcXFxStSe1Xbx48YF9p02bhrOzc/LD1dU1c0XLY9u9ezetW7emU6dOHDhwAAcHByZNmkRISAje3t75b0qmiIiIiOQqFh2sgoKCGDlyJM2bN2fQoEEP3Tc6OjrNqX5J1+FER0c/sO+kSZMICwtLfpw/fz5zhUu6/fLLL3Tq1InWrVuzZ88ebG1tGTduHMHBwUydOpVixYqZu0QRERERkUeyqGus7nf58mW6du2Ks7MzmzZtwtra+qH729vbExsbm6o9JiYmefuD2Nra6vqrHHbkyBG8vb3ZunUrAAUKFODVV1/l3XffpVy5cmauTkRERETk8VhksAoLC6NLly7cvn2bPXv2UKZMmUf2cXFx4dKlS6nak9rScwzJfkFBQfj4+PDpp58CYGVlxcCBA/H29qZSpUpmrk5EREREJGMsLljFxMTQrVs3Tp48yY4dO6hRo0a6+tWrV489e/aQkJCQYgGL/fv34+DgQNWqVbOrZEmH4OBg/Pz8+Oijj0hISACgX79++Pr6Uq1aNTNXJyIiIiKSORZ1jVV8fDx9+/Zl3759bNy4kebNm6e536VLlwgKCiIuLi65zcPDgytXrrBly5bktuvXr7Nx40a6deumqX5mcuHCBf7v//6PatWq8eGHH5KQkECPHj04cuQIH3/8sUKViIiIiOQJFjViNX78eLZu3Uq3bt24efNmqhsCDxgwAEhcbGLNmjWEhIRQsWJFIDFYNWvWjCFDhnDs2DFKlCjB0qVLiY+Px8/PL6ffSr535coVpk2bxvLly5OvfevUqRMBAQE0btzYzNWJiIiIiGQtiwpWv/32GwDbtm1j27ZtqbYnBau0WFtbs337dt566y0WLlxIdHQ0jRs3ZvXq1RoVeRzx8f98vXs3dOwIj1g45H43btxg1qxZLFq0iKioKABatWpFYGAgLVu2zOpqRUREREQsgskwDMPcRVia8PBwnJ2dCQsLy1/3T9qyBcaMgdDQf9rKlYMFC8Dd/aFdw8LCmDdvHnPnziUiIgJIvDnzlClTaN++PSaTKTsrFxERERHJFunNBhY1YiVmtGULeHjAv3N2aGhi+6ZNaYarO3fusHjxYmbOnMnNmzcBqFu3LoGBgXTt2lWBSkRERETyBYtavELMJD4exo5NHargn7Zx41JME4yJiWHBggW4ubnxzjvvcPPmTapXr86nn37KoUOHeP755xWqRERERCTfULAS2LMHLlx48HbDgPPnYc8e7t69y4oVK6hcuTLjxo3j6tWruLm58eGHH/LHH3/Qu3fvFMvdi4iIiIjkB5oKKJDGjZXTsnvDBga/8gohISEAlCtXDm9vbwYPHoyNjU12VigiIiIiYtEUrARcXNK1m/fy5YQApUuXZvLkyQwbNgw7O7vsrU1EREREJBdQsBJo2TJx9b/Q0DSvs0oALgB/Fi3KjHfeYeTIkTg6OuZ4mSIiIiIilkrBShLvU7VgAXh4YJhMmO4LVwl///fnvn05s3Jl/lp+XkREREQknbTKgCRyd4dNmzD+NS0wvHBh7qxeTZ9PPlGoEhERERF5AAUr+Ye7O1bHj7MV+BC4uW4dRW7dovCgQeauTERERETEomkqoKRkbU33pK979EicJigiIiIiIg+lESsREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREREREckkBSsREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREREREckkBSsREREREZFMUrASERERERHJpALmLkAsjKMjGIa5qxARERERyVU0YiUiIiIiIpJJClYiIiIiIiKZpGAlIiIiIiKSSQpWIiIiIiIimaRgJSIiIiIikkkKViIiIiIiIpmkYCUiIiIiIpJJClYiIiIiIiKZpGAlIiIiIiKSSQpWIiIiIiIimaRgJSIiIiIikkkKViIiIiIiIpmkYCUiIiIiIpJJClYiIiIiIiKZpGAlIiIiIiKSSQpWIiIiIiIimVTA3AVYIsMwAAgPDzdzJSIiIiIiYk5JmSApIzyIglUaIiIiAHB1dTVzJSIiIiIiYgkiIiJwdnZ+4HaT8ajolQ8lJCRw8eJFChcujMlkMnc5OS48PBxXV1fOnz+Pk5OTucsRM9A5IKDzQHQOiM4B0TkAiSNVERERlClTBiurB19JpRGrNFhZWVGuXDlzl2F2Tk5O+fYHSBLpHBDQeSA6B0TngOgceNhIVRItXiEiIiIiIpJJClYiIiIiIiKZpGAlqdja2uLj44Otra25SxEz0TkgoPNAdA6IzgHROfA4tHiFiIiIiIhIJmnESkREREREJJMUrERERERERDJJwUpERERERCSTFKxEREREREQyScEqH4mNjeXtt9+mTJky2Nvb07RpU/73v/+lq29oaCh9+vShSJEiODk50aNHD4KDg7O5YslqGT0HtmzZQt++fXFzc8PBwYFq1aoxfvx4bt++nf1FS5bLzL8F93v22WcxmUyMGjUqG6qU7JTZc2DDhg00b94cR0dHihQpQosWLdi5c2c2VixZLTPnwI4dO2jbti0lSpSgSJEiNGnShLVr12ZzxZLVIiMj8fHxoXPnzhQrVgyTycTq1avT3f/27dsMGzaMkiVL4ujoSNu2bTl06FD2FZwLKFjlI4MHD2bu3Lm89NJLLFiwAGtra5577jl+/PHHh/aLjIykbdu2/PDDD0yePBk/Pz8OHz5M69atuXHjRg5VL1kho+fAsGHDOH78OAMGDGDhwoV07tyZxYsX07x5c6Kjo3OoeskqGT0P7rdlyxb27duXjVVKdsrMOeDr60v//v1xdXVl7ty5BAYGUqdOHUJDQ3OgcskqGT0Htm7dSseOHbl79y6+vr5MmTIFe3t7Bg4cyLx583KoeskK169fx9/fn+PHj1O3bt3H6puQkEDXrl1Zv349o0aNYubMmVy9epU2bdpw6tSpbKo4FzAkX9i/f78BGLNmzUpui46ONp588kmjefPmD+07Y8YMAzB++eWX5Lbjx48b1tbWxqRJk7KtZslamTkHdu3alaptzZo1BmC89957WV2qZKPMnAf371+xYkXD39/fAIyRI0dmV7mSDTJzDuzbt88wmUzG3Llzs7tMyUaZOQeeffZZo0yZMkZMTExyW1xcnPHkk08aderUybaaJevFxMQYly5dMgzDMA4cOGAAxqpVq9LVd8OGDQZgbNy4Mbnt6tWrRpEiRYz+/ftnR7m5gkas8olNmzZhbW3NsGHDktvs7OwYOnQo+/bt4/z58w/t27hxYxo3bpzcVr16ddq3b8+nn36arXVL1snMOdCmTZtUbT179gTg+PHjWV6rZJ/MnAdJZs6cSUJCAhMmTMjOUiWbZOYcmD9/Pk888QRjx47FMAwiIyNzomTJYpk5B8LDwylatGiKm8UWKFCAEiVKYG9vn611S9aytbXliSeeyFDfTZs2Ubp0adzd3ZPbSpYsSZ8+ffjiiy+IjY3NqjJzFQWrfOLw4cNUrVoVJyenFO1NmjQB4LfffkuzX0JCAkePHqVRo0aptjVp0oQzZ84QERGR5fVK1svoOfAgly9fBqBEiRJZUp/kjMyeB3/99RfTp09nxowZ+hCVS2XmHPjuu+9o3LgxCxcupGTJkhQuXBgXFxcWL16cnSVLFsvMOdCmTRv+/PNPvLy8OH36NGfOnCEgIICDBw8yceLE7CxbLMjhw4dp0KABVlYpo0STJk2Iiori5MmTZqrMvAqYuwDJGZcuXcLFxSVVe1LbxYsX0+x38+ZNYmNjH9m3WrVqWVitZIeMngMPMmPGDKytrfHw8MiS+iRnZPY8GD9+PPXr16dfv37ZUp9kv4yeA7du3eL69ev89NNP7Ny5Ex8fH8qXL8+qVasYPXo0NjY2DB8+PFtrl6yRmX8HvLy8CAkJYcqUKQQGBgLg4ODA5s2b6dGjR/YULBbn0qVLtGrVKlX7/edQ7dq1c7oss1Owyieio6NTDNsnsbOzS97+oH5AhvqKZcnoOZCW9evX8/777zNx4kSqVKmSZTVK9svMebBr1y42b97M/v37s60+yX4ZPQeSpv3duHGDTz75hL59+wLg4eFB7dq1CQwMVLDKJTLz74CtrS1Vq1bFw8MDd3d34uPjWblyJQMGDOB///sfzZo1y7a6xXJk5WeKvETBKp+wt7dPc75rTExM8vYH9QMy1FcsS0bPgX/bs2cPQ4cOpVOnTkyZMiVLa5Tsl9Hz4N69e4wZM4aXX345xfWWkvtk9veBjY1NipFqKysr+vbti4+PD3/99Rfly5fPhqolK2Xm98GoUaP4+eefOXToUPI0sD59+lCzZk3Gjh2rP7zkE1n1mSKv0TVW+YSLiwuXLl1K1Z7UVqZMmTT7FStWDFtb2wz1FcuS0XPgfkeOHKF79+7UqlWLTZs2UaCA/jaT22T0PPjwww85ceIEw4cP5+zZs8kPgIiICM6ePUtUVFS21S1ZJzO/D+zs7ChevDjW1tYptpUqVQpInC4oli+j58Ddu3d5//336dq1a4pra2xsbOjSpQsHDx7k7t272VO0WJSs+EyRFylY5RP16tXj5MmThIeHp2hP+stSvXr10uxnZWVF7dq1OXjwYKpt+/fvx83NjcKFC2d5vZL1MnoOJDlz5gydO3emVKlSbN++nUKFCmVXqZKNMnoe/PXXX8TFxfH0009TqVKl5Ackhq5KlSrx7bffZmvtkjUy8/ugXr16XLt2LdWH56RrckqWLJn1BUuWy+g5cOPGDe7du0d8fHyqbXFxcSQkJKS5TfKeevXqcejQIRISElK079+/HwcHB6pWrWqmysxLwSqf8PDwSJ4HnSQ2NpZVq1bRtGlTXF1dgcQPT0FBQan6HjhwIEW4OnHiBDt37qR379458wYk0zJzDly+fJmOHTtiZWXFN998ow9PuVhGz4N+/frx2WefpXoAPPfcc3z22Wc0bdo0Z9+MZEhm/i3o27cv8fHxrFmzJrktJiaGdevWUaNGjXz7V+rcJqPnQKlSpShSpAifffZZinAdGRnJtm3bqF69er6dApaXXbp0iaCgIOLi4pLbPDw8uHLlClu2bEluu379Ohs3bqRbt25pXn+VL5j7RlqSc3r37m0UKFDAeOutt4wVK1YYLVq0MAoUKGD88MMPyfu0bt3a+PdpER4ebjz55JNGqVKljJkzZxrz5s0zXF1djTJlyhhXr17N6bchmZDRc6Bu3boGYEycONFYu3Ztise3336b029DMimj50Fa0A2Cc6WMngNRUVFGzZo1DRsbG2PChAnGwoULjcaNGxvW1tbG9u3bc/ptSCZk9BwIDAw0AKN+/frGvHnzjNmzZxtPPfWUARgfffRRTr8NyaRFixYZAQEBxogRIwzAcHd3NwICAoyAgADj9u3bhmEYxqBBgwzACAkJSe537949o1mzZkahQoUMPz8/Y8mSJUbNmjWNwoULG0FBQWZ6N+anYJWPREdHGxMmTDCeeOIJw9bW1mjcuLHx9ddfp9jnQR+mzp8/b3h4eBhOTk5GoUKFjOeff944depUTpUuWSSj5wDwwEfr1q1z8B1IVsjMvwX/pmCVO2XmHLhy5YoxaNAgo1ixYoatra3RtGnTVH3F8mXmHFi3bp3RpEkTo0iRIoa9vb3RtGlTY9OmTTlVumShChUqPPD3e1KQSitYGYZh3Lx50xg6dKhRvHhxw8HBwWjdurVx4MCBnH8TFsRkGIaRAwNjIiIiIiIieZausRIREREREckkBSsREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREREREckkBSsREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREflbdHQ01atXp3r16kRHRye337x5ExcXF1q0aEF8fLwZKxQREUulYCUiIvI3e3t71qxZw+nTp3n33XeT20eOHElYWBirV6/G2trajBWKiIilKmDuAkRERCxJ06ZNmThxIjNmzKBnz55cuXKFTz75hPnz51O1alVzlyciIhbKZBiGYe4iRERELMndu3dp1KgRkZGRREZGUqNGDXbt2oXJZDJ3aSIiYqEUrERERNJw8OBBGjdujJ2dHceOHaNSpUrmLklERCyYrrESERFJwzfffANATEwMp06dMnM1IiJi6TRiJSIi8i9Hjx6lcePGvPTSS/z2229cv36d33//HWdnZ3OXJiIiFkrBSkRE5D5xcXE0bdqUW7ducfToUUJCQpJD1gcffGDu8kRExEJpKqCIiMh9AgMD+e233/jggw8oXLgwderUwdvbm1WrVrF9+3ZzlyciIhZKI1YiIiJ/O3ToEE2bNmXEiBEsXLgwuT0+Pp7mzZsTGhrKn3/+SZEiRcxXpIiIWCQFKxERERERkUzSVEAREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREREREckkBSsREREREZFMUrASERERERHJJAUrERERERGRTFKwEhERERERySQFKxERERERkUxSsBIREREREckkBSsREREREZFM+n+v8ha4D3jkHQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6QM8zqfs2vtP"
      },
      "source": [
        "#### SNIa fitting with Minuit\n",
        "So let's go back to the SNIa. As before, in order to be able to use minuit, the fitting function (the model) nees to be given with a specific *signature* (meaning the name and order of the arguments) in the folowing manner:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z2BwnwyM2q0P"
      },
      "source": [
        "def newmusn(x, pars):\n",
        "    cosmo = {'h':pars[0], 'omega_M_0':pars[1], \n",
        "             'omega_lambda_0':pars[2], 'w0':pars[3]}\n",
        "    val = cs.musn1a(x, cosmo)\n",
        "    val[isnan(val)] = -1e30\n",
        "    return val"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qsh6UJnz2-lO"
      },
      "source": [
        "where pars is therefore an array with the cosmological parameters. Note that in the eventuality that the function cs.musn1a() should return a undefined value (*nan* = \"Not a Number\") which can happen for some combinations of paramters for which the integral of proper distance does not converge, we replace this *nan* with a stupidly high negative value that will show minuit thiss set of parameters is really bad, but will not generate an error due to the presence of *nan*.\n",
        "\n",
        "The fitting will need some initial guess, we will choose $$(h=0.7 ; \\Omega_m=0.3 ; \\Omega_\\Lambda=0.7 ; w=-1)$$\n",
        "We also choose to fix some of the parameters (with the fixpars keyword added in the muniuit call):\n",
        "- $H_0$ is not constrained at all by SNIa so we fix it\n",
        "- $w$ can be constrained by SNIa but we choose here not to include it in the analysis as it makes things more complicated. We fix it to -1\n",
        "So we will fix variables 0 and 3 adding to the minuit call the following *fixpars = [0, 3]*\n",
        "\n",
        "***Question 4:*** Perform the fit and print the fitted values as above."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0Aaw8hzR25JA"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R_Qm5oQs32tr"
      },
      "source": [
        "We are happy to find the expected 0.28 and 0.72 for $\\Omega_m$ and $\\Omega_\\Lambda$ with a satisfying $\\chi^2/ndf$\n",
        "\n",
        "Have a look at the covariance matrix as well using the index 3 of the returned result from Minuit.\n",
        "\n",
        "The error bars and covariance matrices are a useful measurement of the confidence intervals, but in the case these are complicated and non gaussian, and particularly when there are a large number of dimensions, this simple fitting approach is a bit limited. It only gives the best-fit value, but we would like to visualize the shape of the confidence intervals in multi-dimensions...\n",
        "\n",
        "This is where Monte-Carlo-Markov-Chain become useful..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7oAczCe64ANn"
      },
      "source": [
        "### Fitting with Monte-Carlo-Markov-Chains\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u7iAyZmq4Pms"
      },
      "source": [
        "#### The Likelihood and the $\\chi^2$ (a more rigourous version than above)\n",
        "We have spoken about the $\\chi^2$ and explained in a simple manner its statistical meaning. Actually the $\\chi^2$ has a deeper rigourous meaning that we will explain here.\n",
        "\n",
        "Assume again that we have data $x_i$, $y_i$ for $i$ going from 0 to $N-1$, each with an uncertainty $\\sigma_i$. We have a physical model for describing our measurements $y=f(x,\\vec{\\theta})$ where $\\vec{\\theta})$ are the parameters of the model (which we want to determine). Each $y_i$ should therefore be randomly drawn from $f(x_i,\\vec{\\theta})$ with a noise whose statistical distribution will be assumed to be a Gaussian (this is the important hypothesis here).\n",
        "\n",
        "One can therefore write the following equation for all values of $i$:\n",
        "$$y_i = f(x_i,\\vec{\\theta}) - n_i$$\n",
        "where $n_i$ is a random number with a Gaussian distribution centered on 0 and a variance $\\sigma_i$, therefore:\n",
        "$$P(n_i) = \\frac{1}{\\sqrt{2\\pi\\sigma_i^2}} \\exp\\left( -\\frac{n_i^2}{2\\sigma_i^2}\\right)$$\n",
        "which can be rewritten as the probability of measuring our data $d_i=(x_i,y_i)$ given a set of parameters $\\vec{\\theta}$:\n",
        "$$P(d_i \\mid \\vec{\\theta}) = \\frac{1}{\\sqrt{2\\pi\\sigma_i^2}}\\exp\\left( -\\frac{\\left(y_i-f(x_i,\\vec{\\theta})\\right)^2}{2\\sigma_i^2}\\right)$$\n",
        "\n",
        "The overall probability of the measurement dataset is the product of all individual probabilities:\n",
        "$$P(\\vec{d} \\mid \\vec{\\theta}) = \\prod_{i=0}^{N-1} \\frac{1}{\\sqrt{2\\pi\\sigma_i^2}} \\exp\\left( -\\frac{\\left(y_i-f(x_i,\\vec{\\theta})\\right)^2}{2\\sigma_i^2}\\right)$$\n",
        "It is then easy to exchange product and exponential, and we rename this probability expressed this way as the **likelihood** of the data and the model:\n",
        "$$\\cal{L}(\\vec{d} \\mid \\vec{\\theta}) =  \\frac{1}{\\prod_{i=0}^{N-1}\\sqrt{2\\pi\\sigma_i^2}} \\exp\\left( \\sum_{i=0}^{N-1}-\\frac{\\left(y_i-f(x_i,\\vec{\\theta})\\right)^2}{2\\sigma_i^2}\\right)$$\n",
        "\n",
        "The best-fit set of parameters $\\hat{\\vec{\\theta}}$ is the one that maximizes this Likelihood $\\cal{L}$. It is therefore also the one than minimizes the following quantity:\n",
        "$$\n",
        "\\begin{eqnarray}\n",
        "A(\\vec{d} \\mid \\vec{\\theta}) &=& -2\\log\\left(\\cal{L(\\vec{d} \\mid \\vec{\\theta})}\\right)\\\\\n",
        "&=& -2\\log\\left( \\frac{1}{\\prod_{i=0}^{N-1}\\sqrt{2\\pi\\sigma_i^2}}\\right) +\\sum_{i=0}^{N-1}\\frac{\\left(y_i-f(x_i,\\vec{\\theta})\\right)^2}{\\sigma_i^2}\n",
        "\\end{eqnarray}$$\n",
        "The first terms does not depend on the parameters $\\vec{\\theta}$ and therefore does not play any role in the minimization. The second term is exactly the $\\chi^2$ we have used so far. It is therefore perfectly legitimate and rigourous to use the $\\chi^2$ method when the error bars are Gaussian:\n",
        "$$\\chi^2(\\vec{d} \\mid \\vec{\\theta}) = \\sum_{i=0}^{N-1}\\frac{\\left(y_i-f(x_i,\\vec{\\theta})\\right)^2}{\\sigma_i^2}$$\n",
        "\n",
        "### The Bayes Theorem and the *Posterior Probability*\n",
        "So far, we have discussed the probability of measuring $\\vec{d},\\vec{\\sigma}_i$ if the parameters are $\\vec{\\theta}$, this is what is called a Likelihood. Obviously, as a physicist, the quantity we are more interested in is rather the probability that the parameters be $\\vec{\\theta}$ if the data is $\\vec{d},\\vec{\\sigma}_i$. This latter quantity is known as the **posterior**. The difference between both quantities is expressed through the Bayes Theorem (https://en.wikipedia.org/wiki/Bayes%27_theorem) which states that for two interdependent statistical proposals A and B one has:\n",
        "$$P(A \\mid B) = \\frac{P(B\\mid A)P(A)}{P(B)}$$\n",
        "In our case this writes:\n",
        "$$P(\\vec{\\theta} \\mid \\vec{d}) = \\frac{P(\\vec{d}\\mid \\vec{\\theta})P(\\vec{\\theta})}{P(\\vec{d})}$$\n",
        "A few important quantities appear here:\n",
        "- The posterior $P(\\vec{\\theta} \\mid \\vec{d})$\n",
        "- The likelihood $P(\\vec{d}\\mid \\vec{\\theta})$\n",
        "- The probability of the parameters **independently** of any knowledge of the data, which is called the **bayesian prior** $P(\\vec{\\theta})$\n",
        "- The probability of the data independently of the model. This one has no particular interest (it does not depend upon the parameters) and simply associated to the global normalisation of our posterior (whose integral needs to be 1).\n",
        "\n",
        "We therefore have:\n",
        "$$P(\\vec{\\theta} \\mid \\vec{d}) \\propto P(\\vec{d}\\mid \\vec{\\theta})\\times P(\\vec{\\theta})$$\n",
        "If the bayesian prior is uniform, then the posterior and the likelihood are equal, otherwise they are different... Note that if one takes a uniform prior for a parameter $a$, this does not correspond to a uniform prior for $a^2$, $\\sqrt(a)$ or any function of $a$. As we have no particular reason to think that $a$ is a better parameter than any function of $a$, the bayesian prior seems to be an unavoidable quantity if one wants to talk about the probability of the parameters given the data...\n",
        "\n",
        "There we dangerously step into the eternal debate between **frequentists** and **bayesians**:\n",
        "- Frequentists think that there is no scientific legitimity to use a prior, and that it is therefore impossible to write a posterior. They limit themselves to speaking only about the likelihood: the probability of making such a measurement if the parameters are $\\vec{\\theta}$. They will therefore never talk about the *proabbility of a parameter* which is meanlingless to them. This appraoch is very legitimate in the sense that the physical parameters of our Universe do not seem to have a probability (unless you believe in Muliverse, String Landscape...): they are what they are. The random variables are not the parameters but the measurements.\n",
        "- Bayesians are undoubtedly less rigourous but think that the target of science is is to answer the question $P(\\vec{\\theta} \\mid \\vec{d})$ and not $P(\\vec{d}\\mid \\vec{\\theta})$. It is therefore a necessity to chose a prior and talk about posteriors. A scientist therefore needs to manage in such a manner that choice of the prior affects the final result in a minimal manner...\n",
        "\n",
        "Beyond this deep and legitimate epistemological debate, in most concrete cases it changes nothing: Bayesians will often take results from other experiements as a prior while Frequentists will incorporate these results in their likelihood. Finally they will often find the same confidence intervals which will be directly interpret by Bayesians as the probability density of the parameters. Frequentists will say instead that these confidence intervals are such that they contain the *true value* of the parameters in X% of the experiments one could have done.\n",
        "\n",
        "This is subtle yet persitant difference and there are sometimes cases where one approach performs better than the other.\n",
        "\n",
        "In practice, frequentist methods are usually rather complicated to implement when there are many parameters and we want to calculate/visualize the exact shape of the confidence intervals and we want to propagate uncertainties. Monte-Carlo-Markov-Chains methods are fundamentally Bayesian and are easy to implement and make the error propagation straightforward. In most cases, this simplicity argument often turns frequentist physicists into usual bayesians...\n",
        "\n",
        "### Monte-Carlo-Markov-Chain Methods (MCMC)\n",
        "A MCMC method aims at directly determining the posterior, in order to do so, one will directly sample the parameter space in order to calculate the posterior on each point.\n",
        "\n",
        "If one samples the parameter space uniformaly, efficiency is going to be very low: there will be many points sampled in the region where the probability is low (which we care little of) and comparatively few samples in the high posterior regions which we would like to sample well.\n",
        "\n",
        "The solution is therefore to sample the parameter space in a non-uniform manner and drawing more samples where the posterior is high and less where it is low. Ideally, one would directly sample the parameter space using the posterior, which is equivalent to knowing the solution beforehand...\n",
        "\n",
        "In fact there exists a magic algorithm known as **Metropolis-Hastings** (from the names of a subset of its inventors in the 50') which directly allows to draw random numbers and end-up with a series of points (a Markov Chain) whose distribution converges asymptotically towards the posterior. It souds like magic but actually works. \n",
        "\n",
        "The most amazing thing is maybe thet this algorithm is very simple. here it is:\n",
        "- start with a random point in parameter space $\\vec{\\theta}_0$\n",
        "- draw a new point randomly in parameter space $\\vec{\\theta}_i$\n",
        "    - calculate the posterior ratio $a=\\frac{P(\\vec{\\theta}_i \\mid \\vec{d})}{P(\\vec{\\theta}_0 \\mid \\vec{d})}$\n",
        "        - if $a\\geq 1$ then keep the new point $\\vec{\\theta}_1=\\vec{\\theta}_i$\n",
        "        - if $a\\lt 1$ then draw a random number uniformly between 0 and 1\n",
        "            - if this number is smaller than $1-a$ then don;t keep the new point but keep the former one $\\vec{\\theta}_1=\\vec{\\theta}_0$\n",
        "            - otherwise keep the the new point $\\vec{\\theta}_1=\\vec{\\theta}_i$\n",
        "- then start over with drawing a new $\\vec{\\theta}_i$\n",
        "\n",
        "This way one constructs a series of parameters sets  $\\vec{\\theta}_i$ for $i$ between 0 and $N_{samples}$ which will have the following properties:\n",
        "- it is a Markov Chain: ($\\vec{\\theta}_i$ only depends upon its predecessor $\\vec{\\theta}_{i-1}$)\n",
        "- it samples the posterior $P$, meaning that the density of points in the chain in the parameter space is porportional to $P(\\vec{\\theta} \\mid \\vec{d})$. We therefore directly obtain the shape and statistics of the posterior by looking at the spatial distribution of the points in the chain.\n",
        "\n",
        "Let's show how it works on a simple example with a simplistic (although correct) implementation of Metropolis-Hastings. We define a Gaussian posterior which we chose to be centered on 2 with a variance equal to 3. We then use our Metropolis-Hastings algorithm with a 10000 elements chain. Ideally we should reject the first part of the chain that takes some time to \"start\" (this is called the \"Burn out\") but we will not do it here in order to remain simple."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gV7GKGdk3nhA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "09ed4d68-d840-4aca-94ea-fc2fcb3eace9"
      },
      "source": [
        "#### Define the posterior (we cheat here, in general its shape \n",
        "#### is not known, we need to calculate it at each step in a \n",
        "#### complicated and CPU consuming manner)\n",
        "def like(x):\n",
        "    return 1./(np.sqrt(2*np.pi)*3) * exp(-0.5*(x-2.)**2/3.**2)\n",
        "\n",
        "#### IInitialize the chain\n",
        "nbtot = 10000\n",
        "chain = np.zeros(nbtot)\n",
        "init = 10.\n",
        "\n",
        "#### Run the Metropolis Hastings just as a python \n",
        "#### transcription of the above\n",
        "#### The jump to the next element is made in a wide manner with a random\n",
        "#### number uniformly between -15 and 15\n",
        "nok = 0\n",
        "while nok < nbtot:\n",
        "    pini = like(init)\n",
        "    new = init + np.random.rand(1)*30-15\n",
        "    pnew = like(new)\n",
        "    a = pnew/pini\n",
        "    #print(a)\n",
        "    if (a>=1):\n",
        "        chain[nok] = new\n",
        "        init = new\n",
        "        nok += 1\n",
        "    else:\n",
        "        rd = np.random.rand(1)\n",
        "        if (rd < (1-a)):\n",
        "            #print('ok')\n",
        "            chain[nok] = init\n",
        "            init = init\n",
        "            nok += 1  \n",
        "        else:\n",
        "            chain[nok] = new\n",
        "            init = new\n",
        "            nok += 1\n",
        "        \n",
        "print(chain)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[10.          4.55294323  4.55294323 ...  2.19916649 -5.61254389\n",
            " -5.61254389]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_GQjcwHE4icC"
      },
      "source": [
        "Now let's just plot the histogram of the sampled values along with the shape of the posterior that we assumed at the beginning:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RJJFCcZb4ePP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "a81621f3-8dc9-49e1-c45d-3895df72298b"
      },
      "source": [
        "bla=hist(chain, bins=100,range=[-20,20], density=True, label='MCMC samples')\n",
        "xx=linspace(-10,10,100)\n",
        "plot(xx,like(xx),'r-',lw=3, label='Input Likelihood')\n",
        "legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2e2ca47430>"
            ]
          },
          "metadata": {},
          "execution_count": 38
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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XcBg2bBgSExPx448/4uHDh6hduzaCgoKwcOFCODs7V8v7qQyJSl+zswxUZmYmnJ2dkZGRoV7ZhIiIqLLK2peoVm4GTq4JhbM8Rx2L9fDFy28sg0pSPMxOL19Gs7OBdu2AW7fUofsOrugVugb51lKt5ub8BZieys/Px+3bt9G4cWNIpdqfE6LK2rBhA958801ER0ejU6dOYqfzTJX57Fe2NuCcJCIiIh1NP7tVUCABwKd931YXSHrj4ACsXi0I1ct+jInn9+r3dYiISIBFEhERkQ58HiZhbMwhQezXFkG4WL9F9bxg//7Fj1Le/SMMtXIzyrmAiIiqikUSERGRDv5z/AdYqZ7uQ5JvZYMlvSo3cfy5LVkiOHQqyMXUc9ur9zWJiMwYiyQiIqJKCki+gl63Lwhiazq/jHtOdar3hdu3B8aOFYTGxRyE15P71fu6RGTWQkJCoFKpjGI+kr6xSCIiIqqkd/8IExw/cHDF/7qMqpkXX7SoeLPZf9goi/Cv01XbsJKIiMrGIomIiKgSmv+diD4J5wWxVV1GI9dGVjMJeHsD778vCL107RTqZ6TVzOsTEZkRFklERESVEBr5i+D4scwJO1r3L6d1NfnoI+SUWvrbSqXEhAv7ajYHIiIzwCKJiIjoGTwz0zDs2ilBbFOHIcizqeE9aNzcsKONsDAbc+l3OMhzazYPIiITxyKJiIjoGSZG/wprpUJ9nGdli40dhoqSy/qOw6DE013unQpy8erlw6LkQkRkqlgkERERVcA5LwuvXfpdENvepj/S7ZxFySeplgcO+3YRxN48vxeWpYo4IiKqGiuxEyAiIjJk42IOwr4wX32skFhgXecRz7zOe86Bcs8lfjGkSjmt6zwCA+Mi1McNMtMwIC4CwLAqPS8RERVjTxIREVF5iorwRoyw2Dng1x13XeqJlFCx8/VbItbDVxB7K3q3SNkQkb5JJBIsWLBAfbxgwQJIJBI8fPiwWp5/w4YNkEgkSExMVMe8vb0xdKg4w4rLkpiYCIlEgg0bNtTI67FIIiIiKs9vv6Fe9mNB6PuAV0RKphSJRKs3q8O9G0BERNntUdyzVd6DyFiUfJk/f/78sxvXgNzcXCxYsAAnT56sVPuTJ09CIpEgLCzs2Y1JVBxuR0REVJ61awWHsR7N8Fc9H5GSETrUvBvuOrmjQebfT4Nr1wIvvCBeUkRmJjc3FwsXLgQA9OrVS2/Pm5eXByurmvua/sYbb2DMmDGwtbWtsdc0dOxJIiIiKsu9e8ABYS/L9jYDREpGm8LCElvaDxYGd+wAsrLESYiI9EYqldZokWRpaQmpVAqJRPLsxmaCRRIREVFZNmwAFE9XjMuxlmJvi57i5VOGMP++KJKU+lWekwPs3CleQkQiCAkJgYODA1JSUjBixAg4ODjA3d0dM2fOhKLU/8Mlc1qWLVuGlStXolGjRpDJZAgKCsKVK1cEz9mrV68ye4ZCQkLg7e2tfj53d3cAwMKFCyGRSLTm+jyvyjzPnTt34OPjA39/fzx48AAA8OTJE0yfPh1eXl6wtbWFj48PlixZAqVSWeFzlTUnqcSZM2cQEBAAqVSKJk2aYNOmTVptEhISMHr0aLi6usLOzg5dunTBgQPaQ3nT0tIwadIk1K1bF1KpFG3btsXGjRu12j158gQhISFwdnaGi4sLJkyYgCdPnlT4HvSNw+2IiIg0KZXAunWC0L4WPZFjaydSQmX728EVJ5t0RL9b0U+DP/4ITJwoXlJkeJRK4NEjsbMom5sbYFH1v9krFAoMGDAAgYGBWLZsGY4ePYrly5ejadOmmDx5sqDtpk2bkJWVhffffx/5+fn4+uuv0adPH/z555+oW7dupV/T3d0dq1evxuTJk/Hyyy/jlVeK5yu2adOmyu/nWW7duoU+ffrA1dUVR44cQe3atZGbm4ugoCCkpKTgnXfeQcOGDXHu3DnMnTsXqamp+Oqrr3R+nZs3b2LUqFGYNGkSJkyYgB9//BEhISHo2LEjWrVqBQB48OABunbtitzcXEybNg1ubm7YuHEjhg0bhrCwMLz88ssAiocQ9urVCzdv3sSUKVPQuHFj7Ny5EyEhIXjy5Ak++OADAIBKpcLw4cNx5swZvPvuu2jRogV2796NCRMm6O3+VQaLJCIiIk3HjwO3bwtC29rWzFA7XRdS2Nmmv7BIOnsWuHEDaN5cz5mR0Xr0CKhTR+wsypaWBvzTG1MV+fn5ePXVVzF//nwAwLvvvosOHTrghx9+0CqSbt68ifj4eNSvXx8AMHDgQAQGBmLJkiVYsWJFpV/T3t4eo0aNwuTJk9GmTRuMGzeuyu+jMq5fv46+ffuifv36+P3331GrVi0AwIoVK3Dr1i3ExMSgWbNmAIB33nkHnp6eWLp0Kf7973/Dy8tLp9e6ceMGTp06hR49egAAgoOD4eXlhfXr12PZsmUAgC+++AIPHjzA6dOn0b17dwDA22+/jTZt2uBf//oXhg8fDgsLC6xZswbXrl3DTz/9hLFjxwIo/u8UFBSE//znP5g4cSIcHR2xd+9enDp1Cl9++SU+/PBDAMDkyZPRu3fvqt88HXC4HRERkSaNBRuuuXtrLbltKI437YyHmhvbrl8vTjJEInr33XcFxz169EBCQoJWuxEjRqgLJAAICAhAYGAgDh48WO05VtWVK1cQFBQEb29vHD16VF0gAcDOnTvRo0cP1KpVCw8fPlQ/+vXrB4VCgVOnTun8ei1btlQXSEBx71nz5s0F9/XgwYMICAhQF0gA4ODggNDQUCQmJuLq1avqdvXq1cNrr72mbmdtbY1p06YhOzsb4eHh6nZWVlaC4tbS0hJTp07VOf+q0LlIksvlmD17Njw9PSGTyRAYGIgjR44887obN25gxowZ6Nq1q3piWFnjHh89eoSlS5eiZ8+ecHd3h4uLC7p06YLt27frmioREZkZvSxz/fAhsFu459C2tgMAA53QXGhpjd2tNP7CunEjUFQkTkJEIpBKper5QSVq1aqF9PR0rbYlvSyl+fr6lvm91NC89NJLcHR0xO+//w4nJyfBufj4ePz2229wd3cXPPr16wegeD6Qrho2bKgV07yvd+7cQfMyeq5btGihPl/yz2bNmsFCY3hlWe08PDzg4OAgaFfWa1QnnYukkJAQrFixAmPHjsXXX38NS0tLDB48GGfOnKnwuoiICHzzzTfIyspS34zy2n300UdwdXXFf/7zH3z22Wews7PDmDFj8Mknn+iaLhERkW5+/hkoLFQfyi2tsadlL/HyqYSdrfsJA/fvA7/9Jk4yRCKwtLTU6/OVt8pb6YUgxDBy5EjcunULW7Zs0TqnVCrRv39/HDlypMzHyJEjdX698u6rSqXS+bmMjU5zkqKiorBt2zYsXboUM2fOBACMHz8e/v7+mDVrFs6dO1futcOGDcOTJ0/g6OiIZcuWITY2tsx2rVq1Qnx8PBo1aqSOvffee+jXrx+WLFmCWbNmwd7eXpe0iYiIKu/nnwWHv/l2RYbMUaRkKifun+GA7VLjngZ//BEYOlS8pMhwuLkVz/0xRG5uNf6S8fHxWrG4uDj1qnVAcW9JWUP1Sno7StT0ktlLly6FlZUV3nvvPTg6OuL1119Xn2vatCmys7PVPUc1pVGjRrhx44ZW/Pr16+rzJf+8fPkylEqloDeprHbHjh1Ddna2oDeprNeoTjoVSWFhYbC0tERoaKg6JpVKMWnSJMybNw/JycnlTghzdXWt1Gs0btxYKyaRSDBixAgcP34cCQkJaN26tS5pExERVU5iIhARIQjtadVL7y+j6+IMlbGjTX9hkbRvH5CeDpSas0BmysJCL4sjmIo9e/YgJSVFPS8pKioKkZGRmD59urpN06ZNcfDgQfz999/qYXyXLl3C2bNnBd917eyKV7ysqeWpJRIJ1qxZg6ysLEyYMAEODg4YNmwYgOJFFRYsWIDff/8dAwYIF5p58uQJHBwcqmXvpcGDB+Orr75CREQEXvhnM+ucnBysWbMG3t7eaNmypbrd4cOHsX37dvW8pKKiInz77bdwcHBAUFCQut2aNWuwevVq9cINCoUC3377rd5zr4hOdyomJga+vr5aYyADAgIAALGxsTqvmlFZ9+/fBwDUrl27wnZyuRxyuVx9nJmZWS35EBGRCdKc/+rqijPe7URJRVf7WvTE5yfXASW/A4uKiudWcTlwIgEfHx90794dkydPhlwux1dffQU3NzfMmjVL3WbixIlYsWIFBgwYgEmTJiEtLQ3/+9//0KpVK8F3S5lMhpYtW2L79u3w9fWFq6sr/P394e/vX2EOv/zyi7oHpbQJEyY887u0hYUFfvrpJ4wYMQLBwcE4ePAg+vTpgw8//BB79+7F0KFD1ct05+Tk4M8//0RYWBgSExOf+T36ecyZMwc///wzBg0ahGnTpsHV1RUbN27E7du38csvv6h7jUJDQ/H9998jJCQEFy5cgLe3N8LCwnD27Fl89dVXcHQs7rF/6aWX0K1bN8yZMweJiYlo2bIldu3ahYyMDL3nXhGdiqTU1FR4eHhoxUti9+7d009WGh4/fox169ahR48eZb5+aYsXL8bChQurJQ8iIjJx27YJj0eNQqGltTi56CjL1h4YNAjYs+dpcPt2FklEGsaPHw8LCwt89dVXSEtLQ0BAAL777jvBd8wWLVpg06ZN+Pjjj/Gvf/0LLVu2xObNm7F161acPHlS8Hzr1q3D1KlTMWPGDBQUFOCTTz55ZpG0TfNnzT969epVqQ4Ha2trhIWFYdCgQRg+fDiOHj2KwMBAhIeH4/PPP8fOnTuxadMmODk5wdfXFwsXLoSzs/Mzn/d51K1bF+fOncPs2bPx7bffIj8/H23atMG+ffswZMgQdTuZTIaTJ09izpw52LhxIzIzM9G8eXOsX78eISEh6nYWFhbYu3cvpk+fjp9++gkSiQTDhg3D8uXL0b59+2p5D2WRqHSYedW0aVM0b95ca4nEhIQENG3aFCtXrhR0VZZn2bJl+PDDD3H79m3B+M+yKJVKDBkyBMePH0dUVBTatm1bYfuyepK8vLyQkZGh1QNGRESmpaJhbIlfDCn3HADg+nVAc2Gh48fh/XuuHjKrGYntsoBSy+vC0rJ4EYfatat2b8io5Ofn4/bt22jcuDGkUqnY6RiMxMRENG7cWDC3nkxLZT77mZmZcHZ2fmZtoNPqdjKZTFCAlE6o5Ly+TZ06Fb/99hvWrVv3zAIJAGxtbeHk5CR4EBERPZPGgg3w8AB69hQnl+c1dChQ+nexQgHs2iVePkRERkqn4XYeHh5ISUnRiqempgIAPD099ZPVPxYuXIhVq1bhiy++wBtvvKHX5yYiIvNSYU/K4sHaQ+2Cg4t7YoyJg0NxobRz59PY9u1AqQWXiIjo2XTqSWrXrh3i4uK0FkOIjIxUn9eX//u//8OCBQswffp0zJ49W2/PS0REpCUmBoiLE8ZKD1szJsHBwuOTJ4EHD0RJhYjIWOlUJI0aNQoKhQJr1qxRx+RyOdavX4/AwED1RLOkpKQyV+yorO3bt2PatGkYO3YsVqxY8dzPQ0REVCmaQ+0aNwb+WbnV6AweDJTeT1CpBH75Rbx8iAyEt7c3VCoV5yNRpeg03C4wMBCjR4/G3LlzkZaWBh8fH2zcuBGJiYn44Ycf1O3Gjx+P8PBwwW68GRkZ6vXNz549CwD47rvv4OLiAhcXF0yZMgVA8Vr148ePh5ubG/r27au1o3DXrl3RpEmT53u3REREmlQqYMcOYWzMGKCGN4nUGzs7YNgwYeG3fTvwwqzyryEiIgGdd5TatGkT5s+fj82bNyM9PR1t2rTB/v370fMZk1vT09Mxf/58QWz58uUAinfWLSmSrl69ioKCAvz999+YWMaypevXr2eRREREeuP/4BaQlCQMjhkjTjL68uqrwiLp9GnU8Z+ENEc38XIiIjIiOhdJUqkUS5cuxdKlS8tto7l+PPC0i/NZQkJCBGulExERVacX4yKEAR8foHVrcZLRlwEDACcnoGQOsUqFITfOYH2n4eLmRTVKh11eiEyCPj/zOs1JIiIiMjUvxv8hDIwYYbxD7UpIpcBwYUHUPz5SpGSopllbF2+AnJtrPHt8EelDyWe+5P+BqtC5J4mIiMhUNEq/B7+Hd4TBESNEyUXvRo4ENm9WHwYkX4FzXhYyZI4iJkU1wdLSEi4uLkhLSwMA2NnZQWLshT9RBVQqFXJzc5GWlgYXFxdY6mH7BhZJRERktvpr9iLVqQN06SJOMvrWr19xj9I/G75bqZTonXAee1r1Fjkxqgn16tUDAHWhRGQOXFxc1J/9qmKRREREZmtAnEaRNHy48W0gWx57e6B/f2DfPnWoX3wkiyQzIZFI4OHhgTp16qCwsFDsdIiqnbW1tV56kEqwSCIiIrNUOycdHVOuCYOmMtSuxPDhgiKp1+0LsCkqRIFV1cfrk3GwtLTU6xdHInPBhRuIiMgs9b0ZBQuUWgnJwQHo00e8hKrD0KGCRSgcCvLQJemyiAkRERkHFklERGSWtFa1GzSoeA6PKalbV2uOVf+bXOWOiOhZWCQREZHZsZfnontirDBoakPtSmgsBd4vPhLg/jlERBVikURERGan5+2LsFWUmsxuZQUMHixeQtVp2DDBoUf2I/g/uCVSMkRExoFFEhERmZ2+t6KFgd69ARcXUXKpdn5+QLNmgpDW0udERCTAIomIiMyKRKVEUMIFYfCll8RJpiZIJFpD7rTmYxERkQCLJCIiMiv+92/BPfeJMGiqQ+1KaAy5a/F3IupncJNRIqLysEgiIiKz0jvhvOD4lmt9oGlTkbKpIV274rHMSRAKun2hnMZERMQiiYiIzErvW8Ii6WSTTiJlUoMsLXHau70g1EtzyCEREalZiZ0AERFRTamVm4G2qXGC2IkmnfDfOQdEyqjmnGzSEcOvhauPu965BGtFIQotrUXMiojIMLEniYiIzEbP2xdhgad7BOVa2yLKy1/EjGrOqcYdBMcOBXnodPeaSNkQERk2FklERGQ2NOcjnW3UDgVW5tGT8sjeBZfqCZcCD9K4H0REVIxFEhERmQULpQJBCRcFsZNNOoqUjTg03y/nJRERlY1FEhERmYW2qfGolZ8liJnFog2lhDcWFkl+D+/AI/NvkbIhIjJcLJKIiMgs9NIYWnajdkOkONcRKRtxxHr64onUQRDT2liXiIhYJBERkXnQnI90wsx6kQBAaaG9FHjQ7YvltCYiMl8skoiIyOS55TxBm/s3BbGTTc2vSAK0hxh2S4wFCgvFSYaIyECxSCIiIpPX7U6s4DjbRoYL9VuIk4zINJcCdyrIBc6dEykbIiLDxCKJiIhMXo/bsYLjiIatzXYT1b8dauFK3abC4KFD4iRDRGSgWCQREZFpU6nQI1E47+aMxrwcc6O19Pnhw+IkQkRkoFgkERGRSfN5lIx62Y8FMc3FC8yN5pA7xMQADx+KkwwRkQFikURERCatR2KM4DjF0R0JrvVFysYwxHg2R461VBg8dkycZIiIDBCLJCIiMmk9bguLpDPe7QCJRJxkDEShpTUivfyFwaNHxUmGiMgAsUgiIiKTZa0oRGDyFUHsjHc7cZIxMGc178ORI4BKJUouRESGhkUSERGZrA4p12FfmK8+VkLCIukfpzXvw507wK1bouRCRGRoWCQREZHJ6p4YKzj+q24TpNs5i5OMgYmr3Qhp9rWEwSNHxEmGiMjAsEgiIiKTxaW/KyApo1eN85KIiACwSCIiIhPlnJeFNqk3BbFTjVkklXa2UTth4PhxQKEQJRciIkPCIomIiExS1zuXYIGnCxHkWdniQv2WImZkeM54txUGnjwBzp8XJRciIkPCIomIiExSD435SFFerVBgZS1OMgbqgWNtxLt5CYMcckdEBCuxEyAiItKF95wDlWr3QtIlwbHWam4EoHhJ9GaPkp8GjhwBPvpIvISIiAwAe5KIiMjkeGamoXF6qiB2TnP+DQEoY9+oc+eAnBxRciEiMhQskoiIyOS8cOdPwXG61BHX6niLk4yB+8OrNWBp+TRQWAicPi1eQkREBoBFEhERmZyuGkPtIhq2hkrCX3llybG1AwIDhcETJ8RJhojIQPA3BhERmRaVCi/cuSwIRTRqI1IyRqJPH+ExiyQiMnMskoiIyKR4p9+DZ9ZDQexcw7bltCYAQO/ewuMLF4CMDHFyISIyADoXSXK5HLNnz4anpydkMhkCAwNx5MiRZ15348YNzJgxA127doVUKoVEIkFiYmK57ffu3YsOHTpAKpWiYcOG+OSTT1BUVKRrukREZGa6Jgl7kdLsa+GWWwORsqlZ3nMOlPuo0AsvALa2T4+VSuDUqepNlojIgOlcJIWEhGDFihUYO3Ysvv76a1haWmLw4ME4c+ZMhddFRETgm2++QVZWFlq0aFFh20OHDmHEiBFwcXHBt99+ixEjRmDRokWYOnWqrukSEZGZ6aox1O5cozaARCJSNkZCJisulEo7flycXIiIDIBO+yRFRUVh27ZtWLp0KWbOnAkAGD9+PPz9/TFr1iycO3eu3GuHDRuGJ0+ewNHREcuWLUNsbGy5bWfOnIk2bdrg8OHDsLIqTtHJyQmff/45PvjgA/j5+emSNhERmQmJSokuGj1JHGpXSX36ACdPPj3mvCQiMmM69SSFhYXB0tISoaGh6phUKsWkSZMQERGB5OTkcq91dXWFo6PjM1/j6tWruHr1KkJDQ9UFEgC89957UKlUCAsL0yVlIiIyI74Pk1A7VziX5hwXbagczXlJly4Bjx6JkwsRkch0KpJiYmLg6+sLJycnQTwgIAAAKuwd0uU1AKBTp06CuKenJxo0aKA+Xx65XI7MzEzBg4iIzEPXO8Klv5Od6+KuSz2RsjEyAQGAnZ0wVrpniYjIjOhUJKWmpsLDw0MrXhK7d+9elRNKTU0VPKfm6zzrNRYvXgxnZ2f1w8vLq8o5ERGRcdCaj9SQvUiVZmMDdO8ujHHIHRGZKZ2KpLy8PNiWXv3mH1KpVH2+qkqeo7zXedZrzJ07FxkZGepHRUMAiYjIdFgqFQhM+lMQ41A7HWnul8TFG4jITOm0cINMJoNcLteK5+fnq89XVclzlPc6z3oNW1vbMgssIiIyba0e3IJTQa4gFsGeJN1ozku6dg24fx+oxyGLRGRedOpJ8vDwUA+HK60k5unpWeWESobZlfc6+ngNIiIyPYFJVwTHt1zrI83RTaRsjFSHDoDmIkscckdEZkinIqldu3aIi4vTWgwhMjJSfb6qSp7j/Pnzgvi9e/dw9+5dvbwGERGZni7JwqF2fzRsLVImRszKCggKEsZYJBGRGdKpSBo1ahQUCgXWrFmjjsnlcqxfvx6BgYHqRRKSkpJw/fr150qoVatW8PPzw5o1a6BQKNTx1atXQyKRYNSoUc/1vEREZLoslAp0Tv5LEIv0YpH0XDSH3LFIIiIzpNOcpMDAQIwePRpz585FWloafHx8sHHjRiQmJuKHH35Qtxs/fjzCw8OhUqnUsYyMDHz77bcAgLNnzwIAvvvuO7i4uMDFxQVTpkxRt126dCmGDRuGF198EWPGjMGVK1fw3Xff4a233kKLFi2q9IaJiMj0tEy7rTUf6Q8vf5GyMXKaRdLNm8C9ewCHuxORGdGpSAKATZs2Yf78+di8eTPS09PRpk0b7N+/Hz179qzwuvT0dMyfP18QW758OQCgUaNGgiJp6NCh2LVrFxYuXIipU6fC3d0d8+bNw8cff6xrukREZAa6JAmX/uZ8pCpo0wZwdgYySm3KGx4OvPaaeDkREdUwnYskqVSKpUuXYunSpeW2OVnG5nPe3t6CnqVnGTFiBEaMGKFrekREZIYCk4WLNkSyF+n5WVoCPXoA+/c/jZVTJHnPOVDu0yR+MaQ6siMiqhE6zUkiIiIyNBZKBQI15iNx0YYq6tVLeFzGHz+JiEwZiyQiIjJqLf5OhJM8RxBjT1IVaa5wd+NG8X5JRERmgkUSEREZtS5JwqW/b9fywAPH2iJlYyLatdPeL+nUKVFSISISA4skIiIyaprzkf7g0t9VZ2UFdO8ujIWHi5MLEZEIWCQREZHRkqiUCNBctIHzkfSD85KIyIyxSCIiIqPVIi0RLvnZghjnI+mJ5rykq1eBv/8WJxciohrGIomIiIxWYLJwPlKiiwdSndxFysbEdOgA2NsLY5yXRERmgkUSEREZLc1FG9iLpEfW1kC3bsIYh9wRkZlgkUREREZJolKi892rglhkQxZJeqU5L4mLNxCRmWCRRERERsnnYTJc8zIFsUiubKdfmvOS/vwTePRInFyIiGoQiyQiIjJKgXf/EhzfdXJHinMdkbIxUZ06ATKZMHb6tDi5EBHVIBZJRERklDSX/o7ifCT9s7EBunYVxrh4AxGZARZJRERkfFQq7f2RWCRVj549hccskojIDLBIIiIio9PwyX3Uy34siLEnqZpoFkkxMUBmZtltiYhMBIskIiIyOpr7I/1t74LbtTxFysbEBQYWLwdeQqkEIiLEy4eIqAawSCIiIqMTmCxctCGygT8gkYiUjYmTyYCAAGGMQ+6IyMSxSCIiIqOjvWhDK5EyMROcl0REZoZFEhERGRWPzL/RMOOBIMb5SNVMs0iKigLy8sTJhYioBrBIIiIio9JZY3+kDFt73HBvJFI2ZqJrV8Ci1FeGgoLiQomIyERZiZ0AERGRLgLLGGqnkvBvflXhPedAuecSvxgCODkB7doBFy8+PXHqFIAO1Z4bEZEY+FuFiIiMSoDmog0calczNIfcnT4tTh5ERDWARRIRERmPtDQ0e5QsCHE+Ug3RLJLOnYOVokicXIiIqhmLJCIiMh5nzggOc6yl+KtuU5GSMTPduwuPc3LQ6sEtcXIhIqpmnJNERETGQ2Pp6Qv1W0BhYSlSMuah9HylI25egp68gOS/cMmzuRhpERFVK/YkERGR8dCYB8P9kWqW5v0OuHulnJZERMaNRRIRERmHzEwgNlYQim7AIqkmaS6SEZD8FyQqpUjZEBFVHxZJRERkHM6dA5RPv5AXWFgh1sNXxITMj2ZR6izPge/DJJGyISKqPiySiIjIOGgMtbvs0Qxya1uRkjFPqU7uSHauK4h11liSnYjIFLBIIiIi48D5SAYhqkFLwXHAXRZJRGR6WCQREZHhk8uBqChBKIrzkUShOeSuc/JfgEolUjZERNWDRRIRERm+6OjiQukfSkhwsX4LERMyX9EaPXge2Y/QIOOBSNkQEVUPFklERGT4NPZHul7HG5lSB5GSMW+3XBvgoZ2zIBbIeUlEZGJYJBERkeHTmI+kuRQ11SCJBOc15iV15rwkIjIxLJKIiMiwKRTFy3+Xwv2RxBXVQFikskgiIlNjJXYCREREmrznHFD/e6sHt3AgM1NwnkWSuDRXFmz6OAW1c9Lx0L6WSBkREekXe5KIiMigae7Dc7uWB/524JdxMV2r0xjZNjJBrNPdqyJlQ0SkfyySiIjIoAUkXxEcaw71opqnsLDERU8/QSyAizcQkQlhkURERIZLpULnFGEPheYS1CQOzSF3nJdERKaERRIRERmsxun34J7zRBDjJrKGQXNeWMu023CQ54qUDRGRfrFIIiIig6U5H+mBgyuSXOqJlA2VFuvhC7nl0/WfLFVKdEi5JmJGRET6w9XtiIhIFKVXsCtPgMYQrugGrQCJpLpSIh3IrW1xuZ6vYDhkwN2/cKpJRxGzIiLSD517kuRyOWbPng1PT0/IZDIEBgbiyJEjlbo2JSUFwcHBcHFxgZOTE4YPH46EhAStdhkZGZg1axaaNWsGmUyGRo0aYdKkSUhKStI1XSIiMmKa81yiNDYxJXFFe2lsKsvFG4jIROjckxQSEoKwsDBMnz4dzZo1w4YNGzB48GCcOHEC3bt3L/e67Oxs9O7dGxkZGZg3bx6sra2xcuVKBAUFITY2Fm5ubgAApVKJ/v374+rVq3jvvffg6+uLmzdvYtWqVfj9999x7do1ODo6Pv87JiIio1An6xEaPbkviJ3nfCSDEtWgFd5DmPq4XWocbIoKUWBlLWJWRERVp1ORFBUVhW3btmHp0qWYOXMmAGD8+PHw9/fHrFmzcE5jR/TSVq1ahfj4eERFRaFz584AgEGDBsHf3x/Lly/H559/DgD4448/EB0dje+++w7vv/+++vrmzZtj4sSJOHr0KF5++WWd3ygRERkXzaF2mTZ2uO7eSKRsqCwX67eAEhJYQAUAsFUUos39OBazRGT0dBpuFxYWBktLS4SGhqpjUqkUkyZNQkREBJKTkyu8tnPnzuoCCQD8/PzQt29f7NixQx3L/GdX9bp16wqu9/DwAADIZMLN64iIyDRpDrW70KAFlBaWImVDZcmUOuB6HW9BjPslEZEp0KlIiomJga+vL5ycnATxgIAAAEBsbGyZ1ymVSly+fBmdOnXSOhcQEIBbt24hKysLANCpUyfY29tj/vz5OH78OFJSUhAeHo5Zs2ahc+fO6NevX4U5yuVyZGZmCh5ERGR8NL9say45TYZBc0l27pdERKZApyIpNTVV3aNTWkns3r17ZV73+PFjyOXySl1bu3ZtbN++HRkZGejbty8aNGiAXr16wdPTE8ePH4eVVcUjBBcvXgxnZ2f1w8vLS5e3SEREBsApPxvN/74jiGluXkqGQbN47Xj3GiyUCpGyISLSD52KpLy8PNja2mrFpVKp+nx51wGo9LXu7u5o3749PvvsM+zZswcLFizA6dOn8eabbz4zx7lz5yIjI0P9qGgIIBERGaaOKdfU81wAQG5pjcv1fEXMiMqjWbw6FeTCT6PAJSIyNjot3CCTySCXy7Xi+fn56vPlXQegUtcmJCSgd+/e2LRpE0aOHAkAGD58OLy9vRESEoJDhw5h0KBB5eZoa2tbZjFGRETGQ3OoXayHL1dMM1B/O7gi0cUD3k9S1TEOuSMiY6dTT5KHhwdSU1O14iUxT0/PMq9zdXWFra1tpa7dsGED8vPzMXToUEG7YcOGAQDOnj2rS8pERGSENL9kR3OonUHTHHLH/ZKIyNjpVCS1a9cOcXFxWoshREZGqs+X+SIWFmjdujXOnz+vdS4yMhJNmjRR73304MEDqFQqKBTC8cyFhYUAgKKiIl1SJiIiI2NbKEeb1HhBjIs2GLYojU1lA+7+BahU5bQmIjJ8OhVJo0aNgkKhwJo1a9QxuVyO9evXIzAwUL1IQlJSEq5fv651bXR0tKBQunHjBo4fP47Ro0erY76+vlCpVIJlwQHg559/BgC0b99el5SJiMjItL0fDxvl0z+IKSQWuFC/hYgZ0bNoFrF1ctKBW7dEyoaIqOp0mpMUGBiI0aNHY+7cuUhLS4OPjw82btyIxMRE/PDDD+p248ePR3h4OFSl/or03nvvYe3atRgyZAhmzpwJa2trrFixAnXr1sW///1vdbuQkBAsW7YM77zzDmJiYtCqVStcvHgR69atQ6tWrbiRLBGRidMcqnWtTmNk29qJlA1VRmItT/xt7wL3nCdPg6dPAz4+ouVERFQVOvUkAcCmTZswffp0bN68GdOmTUNhYSH279+Pnj17Vnido6MjTp48iZ49e2LRokWYP38+2rZti/DwcLi7u6vbubm54fz58xg3bhz27duHqVOnYu/evZg4cSJOnjwJGxsb3d8lEREZjcDkK4Lj6AYty2lJBkMi0dovCadPi5MLEZEeSFQq0x40nJmZCWdnZ2RkZGhtgktEROLxnnNAK2apVODS12PgUPB0W4jJw+fgkF/3mkyNnkPI+b1YcOzpcHz4+ADx8eVfQEQkgsrWBjr3JBEREVWXFmm3BQUSwJXtjIXWf6ebN4EyVrUlIjIGLJKIiMhgaA61u+VaHw/ta4mUDenimrs3Mm005o6dOSNOMkREVcQiiYiIDIbW/khc+ttoKC0scVFzFULOSyIiI8UiiYiIDINKhU53rwpCLJKMS5TmkLtTp8RJhIioilgkERGRQWj6+C5q52YIYpGcj2RUtIqky5eBJ09EyYWIqCpYJBERkUEI0NgfKdXBDXed64qUDT2Py/V8Ibe0fhpQqYCzZ8VLiIjoObFIIiIig6A1H8mrFSCRiJQNPY8CK2vEejYXBjkviYiMEIskIiIyCJo9SVFe/iJlQlXBTWWJyBSwSCIiItF5ZqahQWaaIBbVoKVI2VBVaM1Lio4G8vLKbkxEZKBYJBERkeg6a/QiPZE6IL52Q5Gyoaq46OkHhaTU14vCQiAyUryEiIieA4skIiISXUAZ+yOpJPwVZYxybO3wV90mwiCXAiciI8PfQEREJDqt+UjcH8mocV4SERk7FklERCQq19wMNHuULIhFc38ko6b13y8ionjYHRGRkWCRREREotJc+jvX2hZX6jYVKRvSh2jNnqScHCAmRpxkiIieA4skIiISleZQuwueLVBkaSVSNqQPj+2cgRYthEHOSyIiI8IiiYiIRBWQfEVwrLWENBmnHj2Ex5yXRERGhEUSERGJxlGeg5ZptwWxyIatRcqG9KpnT+Hx6dOAUilOLkREOmKRREREoul49xosVU+/OMstrXDJw1fEjEhvNIuk9HTgypWy2xIRGRgWSUREJJqAu8IvzbEezSG3shEpG9IrLy+gcWNhjPOSiMhIsEgiIiLRaO2P5OUvUiZULTR7k1gkEZGRYJFERESikBbmo01qvCDGRRtMTFCQ8Dg8HFCpxMmFiEgHLJKIiEgU7e/dgI2ySH1cJLHARU8/ETMivdPsSUpLA+LixMmFiEgHLJKIiEgUgRpLf1+p1xQ5tnYiZUPVokkTwNNTGOOQOyIyAiySiIhIFFrzkRpwPpLJkUjKHnJHRGTgWCQREVHNKyhAh3vXBSEu2mCiNIfccV4SERkBK7ETICIiM3T+PKRFBYJQdIOWIiVD1UqzJ+nuXXR/bz3uOtcts3niF0NqICkiooqxJ4mIiGqexryUa+7eyJA5ipQMVSs/P6B2bUEoIJmbyhKRYWORRERENe/kScEhl/42YRKJ1pC7wCQWSURk2FgkERFRzSoqAs6eFYQivVqLlAzVCI0hdwF3WSQRkWFjkURERDXr4kUgO1sQiuSiDaZNoyepcXoq6mQ9EikZIqJnY5FEREQ1S2OoXbybFx7Zu4iSCtWQ1q0BFxdBqAvnJRGRAWORRERENUtjn5w/GnKoncmztAR69BCEuiT9KVIyRETPxiKJiIhqTlERcPq0IMShdmaiVy/BYWAyiyQiMlwskoiIqObExgJZWYIQF20wExqLNzR9nAL37MciJUNEVDFuJktERDVHY6jdLdcG+NuhlkjJUHXynnNAcGyhVCDWxg5OBbnqWJekP7GvZZDmpUREomNPEhER1RyNRRv+aMihduZCaWGptR9WFw65IyIDxSKJiIhqhkJRxnwkDrUzJ5qLdHThprJEZKBYJBERUc24dAnIyBCE/uCiDWZFsyhu+vgu3LPTRcqGiKh8LJKIiKhmaMxHSqjliTRHN5GSITFcrdsEmTZ2ghhXuSMiQ8QiiYiIaoZGkcSlv82PwsIS0ZrzkrhfEhEZIBZJRERU/ZRK4NQpQYibyJonzeKYRRIRGSKdiyS5XI7Zs2fD09MTMpkMgYGBOHLkSKWuTUlJQXBwMFxcXODk5IThw4cjISGhzLYPHjzAO++8g/r160MqlcLb2xuTJk3SNV0iIjIEly8D6cK5J1y0wTxpFsc+j++idg7nJRGRYdF5n6SQkBCEhYVh+vTpaNasGTZs2IDBgwfjxIkT6N69e7nXZWdno3fv3sjIyMC8efNgbW2NlStXIigoCLGxsXBzezouPTk5Gd26dQMAvPvuu6hfvz7u3buHqKio53iLREQkuuPHhcc+PrjvVFucXEhUf9VtiiwbGRwL8tSxwKQrONCih4hZEREJ6VQkRUVFYdu2bVi6dClmzpwJABg/fjz8/f0xa9YsnDt3rtxrV61ahfj4eERFRaFz584AgEGDBsHf3x/Lly/H559/rm77zjvvwMrKCtHR0YLiiYiIjNSJE8Lj3r3FyYNEp7CwxPkGLdE74YI69kLSZRZJRGRQdBpuFxYWBktLS4SGhqpjUqkUkyZNQkREBJKTkyu8tnPnzuoCCQD8/PzQt29f7NixQx27fv06Dh06hA8//BBubm7Iz89HYWGhLmkSEZEhKSrSmo/EIsm8ae+XxHlJRGRYdCqSYmJi4OvrCycnJ0E8ICAAABAbG1vmdUqlEpcvX0anTp20zgUEBODWrVvIysoCABw9ehQAULduXfTt2xcymQwymQyDBg1CYmLiM3OUy+XIzMwUPIiISEQXLwKaP4tZJJm1iIZtBMc+j++iTtYjkbIhItKmU5GUmpoKDw8PrXhJ7N69e2Ve9/jxY8jl8kpdGx8fDwAIDQ2FjY0Ntm/fji+++AJnzpxBv379kJubW2GOixcvhrOzs/rh5eVV+TdIRET6pznUrkULoF49cXIhg/BX3abItLUXxF5IuixSNkRE2nQqkvLy8mBra6sVl0ql6vPlXQegUtdmZ2cDAOrVq4cDBw4gODgYM2fOxNq1a3Hr1i1s3bq1whznzp2LjIwM9aOiIYBERFQDOB+JNCgsLLWWAn+BQ+6IyIDoVCTJZDLI5XKteH5+vvp8edcBqNS1Jf8MDg6GhcXT9EaPHg0rK6sKF4cAigsxJycnwYOIiERSUACcPi2MsUgiAOcaCYfcdb1zSaRMiIi06VQkeXh4IDU1VSteEvP09CzzOldXV9ja2lbq2pJ/1q1bV9DO0tISbm5uSE/nXgpEREYjOhrQHCbdq5coqZBh0ZyX1DDjARo8uS9SNkREQjoVSe3atUNcXJzWYgiRkZHq82W+iIUFWrdujfPnz2udi4yMRJMmTeDo6AgA6NixI4DijWdLKygowMOHD+Hu7q5LykREJCbNoXZt2gC1uT8SATfcG+GRTDjag/OSiMhQ6FQkjRo1CgqFAmvWrFHH5HI51q9fj8DAQPUiCUlJSbh+/brWtdHR0YJC6caNGzh+/DhGjx6tjvXq1Qt16tTBli1b1EPxAGDDhg1QKBTo37+/bu+QiIjEo7mJLIfa0T9UEgut3iTOSyIiQyFRqVQqXS4IDg7G7t27MWPGDPj4+GDjxo2IiorCsWPH0LNnTwDFhU54eDhKP3VWVhbat2+PrKwszJw5E9bW1lixYgUUCgViY2MFPUSbNm3ChAkT0LlzZ7zxxhtISkrC119/jS5duuDEiROwtLSsdL6ZmZlwdnZGRkYG5ycREdWk/HzAxQUoPR/111+BYcMAAN5zDoiTFxmMsTEH8dnhVerj+w6uqJf5EJBIRMyKiExZZWsDK12feNOmTZg/fz42b96M9PR0tGnTBvv371cXSOVxdHTEyZMnMWPGDCxatAhKpRK9evXCypUrtYbQjR8/HjY2Nvjiiy/w4YcfwsXFBe+88w4+//xznQokIiIS0R9/CAskCwvgGb8ryLxo9iTVy34MxMUBzZuLlBERUTGde5KMDXuSiIhE8vHHwH//+/S4Y0eg1JBr9iQRVCr8sWpCcXFUYtUqYPJk8XIiIpNW2dpApzlJRERElcb5SPQsEgnONWorjGku9kFEJAIWSUREpH+ZmcXD7Urr10+cXMigaQ65w4kTgFIpTjJERP/QeU4SERHRM506BSgUT4+trYHu3cXLhwxWhMamsnj4EIPe+j9cq9NEq23iF0NqKCsiMnfsSSIiIv07dkx43LUrYG8vTi5k0O4610WSs3AD+a6Jl0TKhoioGIskIiLSv6NHhcccakcVOOPdTnDc/U6sKHkQEZVgkURERPp1/z5w5Yow1revOLmQUTjbqJ3gODD5CmyKCsVJhogILJKIiEjfNIfaOToCnTuLkwsZhXON2kCJpxvI2hXK0f7edREzIiJzxyKJiIj0S7NI6t0bsOI6QVS+dDtn/FVXuFBDt8RYcZIhIgKLJCIi0ieVSns+EofaUSWc1ZiX1INFEhGJiEUSERHpT3w8kJwsjHHRBqqE097tBcdt7sfDKT9bpGyIyNyxSCIiIv3R7EXy8ABatBAnFzIq5+u3gNzSWn1sqVKiS9KfImZEROaMRRIREemP5nykfv0AiaTstkSlyK1tEd2gpSDWnUPuiEgkLJKIiEg/FArg+HFhjPORSAdnNIbcdeN+SUQkEhZJRESkHxcuAE+eCGMskkgHmpvKNn2cAs/MNHGSISKzxiKJiIj04/Bh4bGfH9CggTi5kFG6Wqcx0qWOghiXAiciMbBIIiIi/fj9d+HxgAHi5EFGS2lhibON2gpiXAqciMTAIomIiKouIwOIiBDGXnxRnFzIqGnul9QtMRYSlVKcZIjIbLFIIiKiqjt+vHjhhhI2NkBQkHj5kNE6rVEkueVlotWDBHGSISKzxSKJiIiqTnM+Uo8egL29OLmQUbvrUg+3XOsLYkEJF0TKhojMFYskIiKqGpWK85FIr0417iA47nn7okiZEJG5YpFERERVc/MmcPu2MMb5SFQF4RpFUseUa3CU54iUDRGZIxZJRERUJfPfXyE4TrOvBe+tyfCec0CkjMjYRXq1htzSSn1spVKi651LImZEROaGRRIREVWJ5lCo043bAxKJSNmQKcizkSK6QStBjEPuiKgmsUgiIqLnV1CAF5L+FIQ0h0oRPY/wxh0Fx0EJF4vnvxER1QAWSURE9PwiIuBQkCcInW3UTpxcyKScaiIsthtkpgFxcSJlQ0TmhkUSERE9P41V7f6s2xSP7F3EyYVMyo3ajXDfwVUY/O03cZIhIrPDIomIiJ6fxpdWzaWbiZ6bRKL9edJcap6IqJqwSCIioudz7x4QEyMIsUgifdL6PJ08CeTni5ILEZkXFklERPR8Dh0SHGba2uNC/RYiJUOm6Ix3OyhRaqXEvDzg9GnxEiIis8EiiYiIns/Bg4LDU97tUVRqbxuiqnoic8IlD19hUONzR0RUHVgkERGR7goKgCNHBKETTTuLlAyZshNNOwkD+/eLkwgRmRUWSUREpLszZ4CsLEEovAnnI5H+Hdcsvm/e5FLgRFTtWCQREZHuDhwQHMZ6NMND+1oiJUOm7K+6TZCm+dnS+PwREekbiyQiItKdxryQk006ldOQqGpUEgvt3iQWSURUzVgkERGRbhISgOvXBaETLJKoGmnNSwoPBzIzxUmGiMwCiyQiItKNRi/SQztnXPZoJlIyZA7ONGqHAotSKycWFWktHEJEpE8skoiISDcaRVJ4k45QSfjrhKpPjq0dIr38hUEOuSOiasTfakREVHm5ucCJE4IQh9pRTTjuozEv6eBBQKkUJxkiMnkskoiIqPKOHwfy858eW1riVGMu/U3VT2vxhgcPgIsXxUmGiEweiyQiIqq8vXuFx127IlPqIE4uZFbu1PIEfH2FQW4sS0TVhEUSERFVjlIJ7NsnjA0bJk4uZJ6GDBEec14SEVUTnYskuVyO2bNnw9PTEzKZDIGBgThSyRVmUlJSEBwcDBcXFzg5OWH48OFISEio8JozZ85AIpFAIpHg4cOHuqZLRET6EhUF3L8vjA0fLk4uZJ6GDhUenz8PpKSIkwsRmTSrZzcRCgkJQVhYGKZPn45mzZphw4YNGDx4ME6cOIHu3buXe112djZ69+6NjIwMzJs3D9bW1li5ciWCgoIQGxsLNzc3rWuUSiWmTp0Ke3t75OTk6JoqERHpk+ZQuxYtgGbNAMSVe4n3HP6ln/SoRw/A2RnIyHga27sXmDxZvJyIyCTp1JMUFRWFbdu2YfHixVi6dClCQ0Nx/PhxNGrUCLNmzarw2lWrViE+Ph779+/HrFmzMGPGDBw+fBipqalYvnx5mdesWbMGycnJeOutt3RJk4iIqsOvvwqPOdSOapq1tfaQuz17REmFiEybTkVSWFgYLC0tERoaqo5JpVJMmjQJERERSE5OrvDazp07o3Pnp6vT+Pn5oW/fvtixY4dW+8ePH+M///kPPv30U7i4uOiSJhER6dvNm8DVq8IYh9qRGEaMEB6fOCHsWSIi0gOdiqSYmBj4+vrCyclJEA8ICAAAxMbGlnmdUqnE5cuX0amT9l4aAQEBuHXrFrKysgTx+fPno169enjnnXd0SRFyuRyZmZmCBxERVZFmL1KdOkBgoDi5kHkbOBCwsXl6XFgIHDokXj5EZJJ0KpJSU1Ph4eGhFS+J3bt3r8zrHj9+DLlcXulrL1++jO+//x4rVqyApaWlLili8eLFcHZ2Vj+8vLx0up6IiMqgOR/ppZcACy6QSiJwdAT69hXGOOSOiPRMp99weXl5sLW11YpLpVL1+fKuA1Dpa6dNm4ZBgwbhxRdf1CU9AMDcuXORkZGhflQ0BJCIiCrh4UPgzBlhjEPtSEyaQ+4OHgTkclFSISLTpNPqdjKZDPIyfgjl/7P7ukwmK/c6AJW6dvv27Th37hyuXLmiS2pqtra2ZRZjRET0nA4cKN4jqYRMBvTrJ14+RC+9BJQejp+VBZw8CQwYIFpKRGRadOpJ8vDwQGpqqla8JObp6Vnmda6urrC1ta3UtR9++CFGjx4NGxsbJCYmIjExEU+ePAEAJCcnlzukj4iIqonmULsXXywulIjE4uEBdOkijHHIHRHpkU5FUrt27RAXF6e1GEJkZKT6fJkvYmGB1q1b4/z581rnIiMj0aRJEzg6OgIoLoS2bt2Kxo0bqx9ff/01AKBDhw4YPHiwLikTEVFV5OQAv/0mjHGoHRkCzSF3e/cKezyJiKpApyJp1KhRUCgUWLNmjToml8uxfv16BAYGqhdJSEpKwvXr17WujY6OFhRKN27cwPHjxzF69Gh1bPfu3VqPV199FQCwadMmrFy5Uvd3SUREz+e334Dc3KfHlpbA0KHi5UNUQrNYv3cPKOOPsUREz0OnOUmBgYEYPXo05s6di7S0NPj4+GDjxo1ITEzEDz/8oG43fvx4hIeHQ6VSqWPvvfce1q5diyFDhmDmzJmwtrbGihUrULduXfz73/9Wtxuh+ZchPF1afNCgQahdu7aOb5GIiJ5bWJjwOCgIcHcXJxei0vz8gObNgRs3nsZ27QL+2ZaEiKgqdF6/ddOmTZg+fTo2b96MadOmobCwEPv370fPnj0rvM7R0REnT55Ez549sWjRIsyfPx9t27ZFeHg43PkLl4jI8OTnA/v3C2OjRomTC1FZNP+wunMnUOoPtEREz0uiUpn2T5PMzEw4OzsjIyNDaxNcIiKqwN69wiFNEknxkKZ69QTNvOccqOHEyFwlfjFEGLhwAdDcqP7CBaBDh5pLioiMSmVrA+4ESEREZdMcatejh1aBRCSqDh2Axo2FsZ07xcmFiEwKiyQiItIml2sv/c2hdmRoJBKg1OJPADjkjoj0gkUSERFpO3YMyMgQxl55RZxciCqiWSTdugX8s+ATEdHzYpFERETaNIfade0K1K8vTi5EFenYEfD2FsY45I6IqohFEhERCRUWAnv2CGMcakeGikPuiKgasEgiIiIAxavUec85gDfGfQGkpwtPcqgdGTLNIunmTeDSJXFyISKTwCKJiIgEXrp2SnAc69EMaNRIpGyIKqFTJ+0hd5pDRomIdMAiiYiI1GyLCjDwxjlB7EDzHiJlQ1RJEon2kNAdOzjkjoieG4skIiJS63XrPJwKctXHSkiwr0VPETMiqiTNIXfx8cDFi+LkQkRGj0USERGpDb96UnAc2dAf951qi5MMkS46d9beWHbLFnFyISKjZyV2AkREZBgc5TnoeytaEPu1RZBI2RBp855zoNxziV8MAcaOBRYtehr8+Wdg6VLA0rIGsiMiU8KeJCIiAgAMiIuAraJQfVxgYYVDzbuJmBGRjsaOFR7fvw8cPy5OLkRk1FgkERERAGDY1XDBcXiTDsiQOYqUDdFz8PMDOnQQxjjkjoieA4fbERERcP8+ut0R7iuzt9RQu4qGOREZlLFjhQs27NoFrF4NyGTi5URERoc9SUREBOzYAUuVUn2YYy3FUZ9AERMiek5jxgAWpb7eZGUB+/aJlw8RGSUWSUREBGzdKjg83KwL8mykIiVDVAWenkCfPsLYTz+JkwsRGS0WSURE5u76dSAyUhD6tSVXtSMjprmAw6FDwKNH4uRCREaJc5KIiMzdhg2Cw4d2zjjj3V6cXIieU+l5cw5ye5y3soG0qKA4UFQE7NgBTJ4sUnZEZGzYk0REZM6KioBNmwShPS17ociSf0Mj45Vta6c9p07jjwFERBVhkUREZM4OHwZSUwWhnW36i5QMkf784q8xLykqCrhyRZxkiMjosEgiIjJn69cLDi/X88ENd29xciHSo1ONO+CBg6sw+OOP4iRDREaH4ymIiMzVo0fA3r2C0M7W/URKhki/FBaW+MW/D977I+xpcPNm4IsvABsbdaiiPcASvxhSnSkSkQFjTxIRkbnauhUoKFAfyi2tBBvIEhm7Ha01ho4+fMg9k4ioUlgkERGZK42hdkeavYAMmaNIyRDpX6JrfUQ2aCUM/vCDOMkQkVFhkUREZI4uXQJiYgQhDrUjU7SjzYvCwO+/A3fvipMMERkNFklEROZo3Trhcf36OO3dTpRUiKrTwebdAMdSPaRKJbBxo3gJEZFRYJFERGRusrO19kbC+PFQWliKkw9RNcqzkQJjxgiDP/5YXCwREZWDRRIRkbn5+WcgM/PpsUQChIaKlw9RdZs4UXickAAcOyZOLkRkFFgkERGZE5UKWL1aGBs8GPD2FiUdohoRGAi00ljA4f/+T5xciMgosEgiIjInUVFaCzZg8mRxciGqKRIJ8N57wti+fUBSkjj5EJHBY5FERGRGfnlrnuD4rlMdNAlXVLihJpFJeOMN7QUc/vc/8fIhIoPGIomIyFw8eoSh104LQlvbDeSCDWQeHB2B8eOFsXXrYFNUKE4+RGTQWCQREZmLDRtgq3j6hbDAwgrbNfeQITJlmkPu/v4bg2+cEScXIjJoLJKIiMxBGUOLDjXvhkf2LuLkQySGli2B3r0FofEX94uUDBEZMhZJRETm4MAB4OZNQein9oNESoZIRO+/LzjscO8GWt2/WU5jIjJXLJKIiMzB8uWCw2vu3ohu0KqcxkQmbPhwoEEDQSjkAnuTiEiIRRIRkam7cAEIDxeEfug8onhZZCJzY2UFvPOOIDT86knUyXokUkJEZIhYJBERmTqNXqQ0+1rY2yJIpGSIDEBoKCCVqg9tlEWYeGGviAkRkaFhkUREZMqSkoAdOwShDR1fQoGVtUgJERmAOnWACRMEoddjDsFBnitSQkRkaKzEToCIiKrRN98ACoX6MNfaFlvaccEGMi9lbZbsreyA45DAAioAgFNBLsZc+g3rAl6p6fSIyACxJ4mIyFRlZgJr1wpCO1v3Q4bMUaSEiAxHomt9HPbtIohNPL8XVooikTIiIkOic5Ekl8sxe/ZseHp6QiaTITAwEEeOHKnUtSkpKQgODoaLiwucnJwwfPhwJCQkCNokJydj4cKFCAgIQK1atVC7dm306tULR48e1TVVIiLztm5dcaFUQiLBD51GiJYOkaFZo9Fr5Jn1EC9dOyVSNkRkSHQukkJCQrBixQqMHTsWX3/9NSwtLTF48GCcOVPxjtXZ2dno3bs3wsPDMW/ePCxcuBAxMTEICgrCo0dPV5T59ddfsWTJEvj4+GDRokWYP38+srKy0L9/f6xfv173d0hEZI7y8oClS4Wxl19GUi0PcfIhMkAX67dAdP2Wglho1C5ApRIpIyIyFBKVqvI/CaKiohAYGIilS5di5syZAID8/Hz4+/ujTp06OHfuXLnXfvnll5g9ezaioqLQuXNnAMD169fh7++PWbNm4fPPPwcA/PXXX6hbty5q166tvlYul6Ndu3bIzs5GcnKyTm8wMzMTzs7OyMjIgJOTk07XEhEZI+85BzD+wj58evR7QfyVcUtxsX4LkbIiMkz94//A2l2LBLFJI+fjmE8gEr8YIlJWRFRdKlsb6NSTFBYWBktLS4SGhqpjUqkUkyZNQkRERIUFTFhYGDp37qwukADAz88Pffv2xY5SKy+1atVKUCABgK2tLQYPHoy7d+8iKytLl5SJiMyOTVEhJv8RJoidbtSOBRJRGY76BOCWq3Bz2Q/O/szeJCIzp1ORFBMTA19fX62qKyAgAAAQGxtb5nVKpRKXL19Gp06dtM4FBATg1q1bzyx+7t+/Dzs7O9jZ2VXYTi6XIzMzU/AgIjInwX8egUe2cGPMr7u/JlI2RIZNJbHAdy8EC2Jt7t9E31tRImVERIZApyIpNTUVHh7a49lLYvfu3SvzusePH0Mulz/XtQBw8+ZN7Nq1CyNHjoSlpWWFOS5evBjOzs7qh5eXV4XtiYhMSkEBJkfsFITONWyD8w1aiZQQkeHb2zIICbU8BbHpZ7ayN4nIjOlUJOXl5cHW1lYrLv1n1+q8vLxyrwPwXNfm5uZi9OjRkMlk+OKLL56Z49y5c5GRkaF+6DqHiYjIqG3ciPpZfwtC33QbI1IyRMZBYWGJb7oJe1tbP7gF7NsnUkZEJDadiiSZTAa5XK4Vz8/PV58v7zoAOl+rUCgwZswYXL16FWFhYfD09NRqo8nW1hZOTk6CBxGRWSgsBP5ZBKdEZINW+MOrtUgJERmPfS164pZrfWFwwQL2JhGZKZ2KJA8PD6SmpmrFS2LlFTGurq6wtbXV+dq3334b+/fvx4YNG9CnTx9dUiUiMj9r1gCJiYLQN91eAyQScfIhMiIKC0t801Wj1zUmBti7V5yEiEhUOhVJ7dq1Q1xcnNZiCJGRkerzZb6IhQVat26N8+fPa52LjIxEkyZN4Ogo3AH+ww8/xPr167Fy5Uq89honHBMRVSgzE1i4UBC64OmHs43aipQQkfEp7k0SrnSH//wHUCjESYiIRKNTkTRq1CgoFAqsWbNGHZPL5Vi/fj0CAwPViyQkJSXh+vXrWtdGR0cLCqUbN27g+PHjGD16tKDt0qVLsWzZMsybNw8ffPCBzm+KiMjsLFsG/C2ci/RFrxD2IhHpQGlhia815/BduQJwM3sis6PTZrIAEBwcjN27d2PGjBnw8fHBxo0bERUVhWPHjqFnz54AgF69eiE8PBylnzorKwvt27dHVlYWZs6cCWtra6xYsQIKhQKxsbFwd3cHAOzevRuvvPIKmjVrho8//ljr9fv374+6detWOl9uJktEJi81FfDxAXJz1aEjPgF4e6T2z1AiqpiFUoEDGz5Ai78Tnwbr1QPi4wEHB9HyIiL9qGxtYKXrE2/atAnz58/H5s2bkZ6ejjZt2mD//v3qAqk8jo6OOHnyJGbMmIFFixZBqVSiV69eWLlypbpAAoBLly4BAOLj4/HGG29oPc+JEyd0KpKIiEzeggWCAkkhscCSoBDR0iEyZkoLS3zWexJ+2jH/afD+/eLe2gULRMuLiGqWzj1JxoY9SURk0q5fB/z9BXMmfm7zIuYOmiZiUkTGb/3OT9A74cLTgJ1dcW9SJVbaJSLDVdnaQKc5SUREZEBUKmDmTOGkcpkMK7uPFS8nIhOxuNebgEWpr0m5ucD8+eVfQEQmhUUSEZGx2rsXOHBAGJsxA2mObuLkQ2RC4ty9gUmThMH164uXBScik8ciiYjIGOXmApqrf9atC8yaJU4+RKZo4ULA3v7psUoFvPsulwQnMgMskoiIjNHnnwN37ghjy5YBzs7i5ENkijw8gDlzhLGoKGDtWnHyIaIawyKJiMjYxMUBS5cKY0FBwFjORSLSuw8/BHx9hbE5c4AHD8TJh4hqBIskIiJjolIBU6YABQVPY1ZWwP/9HzeOJaoOtrbAqlXCWEYG8O9/i5MPEdUIFklERMbkp5+AI0eEsenTgVatREmHyCz07avdU7tlC3DsmDj5EFG103kzWSIiEklKCjB1qjBWvz7wySfi5ENk4rznPF09snatgThmuwfO8pynDUJDgUuXAAcHEbIjourEniQiImOgUgFvvVU8zKe0b7/lFzSiGvDQvhaW9AoRBhMSOOyOyESxSCIiMgY//AD89pswNnYs8PLL4uRDZIZ+bjsA0fVbCoNr1mjvV0ZERo9FEhGRobtzB/jXv4QxDw/gm2/EyYfITKkkFvj3kBnIsZYKT0yaBDx8KE5SRFQtWCQRERmyoiJg/HggK0sYX7sWcHUVJyciM5ZUywOL+rwlDD54ULzJrEolTlJEpHdcuIGIyJB98glw6pQw9uab8D4N4DSH+BCJ4ee2A7DY6rZwmN0vvwDr1gFvvy1eYkSkN+xJIiIyVIcOAZ9/Low1bAisXClOPkRUTCIpLojc3ITxqVOBCxfEyYmI9IpFEhGRIUpOBsaNE8asrIDt2wFnZ3FyIqKn6tUrXrShNLkcGDkSePxYnJyISG9YJBERGZqCAuDVV7W/aC1dCnTpIk5ORKTtlVeKN3Mu7c6d4j9wKJWipERE+sEiiYjIkKhUwDvvABERwvjLLwMffCBOTkRUvi+/BLp1E8YOHQIWLhQnHyLSCxZJRESGZPFiYMMGYaxJE+DHH4vnQRCRYbG2BnbsAOrWFcY//RT46SdxciKiKmORRERkKLZvBz76SBizswPCwgAXF1FSIqJK8PQs/v/X0lIYnzgROH5cnJyIqEq4BDgRkYi85xQvIdzh7jX8vG0ebEuflEiArVuB9u1FyY2Iylfy/25pE3q/hYVHv38aKCwsHip75gzQunUNZkdEVcWeJCIikbV6cAvrwxbAVlEoPLF8OTB8uDhJEZHONnZ8Ces6afw/m5kJDB4MJCWJkxQRPRcWSUREImr+dyI2b58PZ3mOIL65/WDtVbOIyOB91mdS8TLgpd29C/TuXby0PxEZBYlKpVKJnUR1yszMhLOzMzIyMuDk5CR2OkRET12/jr87vgD33CeC8IkmHfHWyI+hsLAs+zoiMmiJn/QB+vUDzp0TnmjSBDh5EvDyEiUvIqp8bcCeJCIiMVy9CvTpo1UgnWvYBu+OmMcCiciYyWTA3r1Ay5bCeEICe5SIjASLJCKimnbuHNC9O5CaKghHNWiJSSM/htzatpwLichouLkVr2ynWSjdugX06AFcvy5OXkRUKSySiIhq0t69QN++QHq6IBzj0RwTRy1Ano1UpMSISO/q1i0ulFq0EMbv3AG6dgVOnxYnLyJ6JhZJREQ1QaUC/ve/4uWA8/MFpy56NseE4IXItrUTKTkiqjblFUrp6cXzlnbsECcvIqoQiyQiouqWnw+89RYweTKgVApOHWvaGWNf/QyZUgeRkiOialevXvGCDZ07C+MFBcCrrwLz5wMKhSipEVHZuLodEVF1unMHGDUKOH9e+9ybb8LHbTiKLLmvN5E5kBXk49rNjcC+fdon+/Yt3jy6Tp2aT4zIjFS2NuBvZiKiSvCec6DC84lfDNEO7toFhIYCjx5pn5s3D1i0CEVzD+opQyIydHk2UmD3bmDqVGD1auHJY8eA9u2Bn38GevYUJ0EiUuNwOyIifUtPB954o3hDSc0Cyd4e2LYN+OwzQCIRJz8iEo33R7/B23EwPu3zNgo1l/q/dw/o1at4I+mcnLIuJ6IawiKJiEif9u0D/P2Bn37SPtesGRAZWTwHgYjMl0SCHzsPx5jXFiPVwU14TqUCvv4aaNsWCA8XJz8iYpFERKQXcXHAkCHAsGHFfw3W9MorQHQ00KpVzedGRAbpQoOWGPLmNzjl3V775K1bxb1Kb7wB3L1b47kRmTsu3EBEVAnlzUlyzsvC5D924t2YfUBhYRkNnDG9x1vY07IXh9cRUZkslApMPP8r/hOxVWuLAACAnR0waxbw4YfF/05Ez62ytQF7koiInoNTfjZmnP4Jp/83Ce9G7Sq7QBowALhyBXta9WaBRETlUlpYYl3AK8ClS0C3btoNcnOBBQuA5s2LV8Az7b9vExkErm5HRKSDepkP8UbMAbwRcxBO8nImVterB3z5JTBu3D/F0aUazZGIjJP3j/Gw6DoLE6T7MeP0FjgV5Aob3L0LzJwJDB9evAgMEVUbFklERP8od5lvlQodU67hzQv7MPDGWViplGW3s7YuXpVq/nzA0bHa8iQi06W0sMT6TsOxt0UQ/nXmJ4y5dBiWpX/mLF7MAomoBrBIIiIqR4Mn9/HyXyfw8l8n0CS9jMUY/qGEBBavjSkeDuPrW3MJEpHJemTvgo8GTMHm9kMw//hadLtzGejYsXghByKqdiySiIhKqFRo9jAJ/W9Gon98JNqn3qiwuRISHPDrjq+7vYaj6ybXUJJEZE6u12mMsa9+hsRuSqBuXcBCezp5RZtdl7nRNRE9E4skIjJvf/8NnDgBHDuG8B170ejJ/Wdekmtti1/8+2JDh5dwq7ZXDSRJRGZNIoH3OUsAD4Hd5RdERKQ/LJKIyHzI5cDVq0BUFPDHH8Ubu167pj7d6BmXJ9TyxJZ2g7CzTX9kSh2qN1ciIj1gLxPR89G5SJLL5fj444+xefNmpKeno02bNli0aBH69+//zGtTUlIwY8YMHD58GEqlEr1798bKlSvRpEkTrbY//PADli1bhtu3b8PLywvTpk3D1KlTdU2XiMxRbi4QH1+8wWtcXHFhdOkScOMGUFSk01OlSx2xr0VP7PLvg1gPXy7lTUQmo6ICCmARReZN5yIpJCQEYWFhmD59Opo1a4YNGzZg8ODBOHHiBLp3717uddnZ2ejduzcyMjIwb948WFtbY+XKlQgKCkJsbCzc3NzUbb///nu8++67GDlyJP71r3/h9OnTmDZtGnJzczF79uzne6dEZPwUCuDx4+IhcmlpQGoqcO9e8SM5GbhzB0hMLD5XBSmO7jjaLABHfLogsqE/Ci2t9ZM/ERERGQWJSlX5HcmioqIQGBiIpUuXYubMmQCA/Px8+Pv7o06dOjh37ly513755ZeYPXs2oqKi0LlzZwDA9evX4e/vj1mzZuHzzz8HAOTl5cHLywtdunTB/v371dePGzcOe/bsQXJyMmrVqlXpN1jZXXWJqAqUyuIempJHYWHxo6Cg+J9yufCRnw/k5RU/cnOBnJynj+xsIDPz6SM9Xfiojk0UHRyAnj2xKK8ezjVqh6t1GrPHiIjMHnuSyBRVtjbQqScpLCwMlpaWCA0NVcekUikmTZqEefPmITk5GV5eZU9iDgsLQ+fOndUFEgD4+fmhb9++2LFjh7pIOnHiBB49eoT33ntPcP3777+PLVu24MCBAxg3bpwuaRNRVRQVAZ6exb04CkVxQVTy7wqFzsPXDELTpkCXLkBgYPGjfXvA2hrrnjH0hIiIilXHXCfOnyJDolORFBMTA19fX62qKyAgAAAQGxtbZpGkVCpx+fJlTJw4UetcQEAADh8+jKysLDg6OiImJgYA0KlTJ0G7jh07wsLCAjExMRUWSXK5HHK5XH2ckZEBoLhqJKLnoFQWD28zQvcc3HCnlgfu1PJAfO1GuF67EbYsDwE0/3L0T6+WUp5b5vMQEZmjir47VfTz8nm/c1XHcxJpKvksPWswnU5FUmpqKjw8PLTiJbF798rebPHx48eQy+XPvLZ58+ZITU2FpaUl6tSpI2hnY2MDNze3cl+jxOLFi7Fw4UKteHk9XERkwrIfFT+Sr6hDzjvmi5gQEZHxcP6qZq+r6eck85aVlQVnZ+dyz+tUJOXl5cHW1lYrLpVK1efLuw5Apa7Ny8uDjY1Nmc8jlUrLfY0Sc+fOxb/+9S/1sVKpxOPHj+Hm5gaJyHMMMjMz4eXlheTkZM6Pqga8v9WL97d68f5WL97f6sX7W714f6sX72/1MrT7q1KpkJWVBU9Pzwrb6VQkyWQywVC2Evn5+erz5V0HoFLXymQyFBQUlPk8+fn55b5GCVtbW61izMXFpcJrapqTk5NBfEhMFe9v9eL9rV68v9WL97d68f5WL97f6sX7W70M6f5W1INUwkKXJ/Tw8EBqaqpWvCRWXkXm6uoKW1vbSl3r4eEBhUKBNI0lfAsKCvDo0aNnVn1ERERERERVoVOR1K5dO8TFxWlNnouMjFSfL/NFLCzQunVrnD9/XutcZGQkmjRpAkdHR8FzaLY9f/48lEplua9BRERERESkDzoVSaNGjYJCocCaNWvUMblcjvXr1yMwMFC9OEJSUhKuX7+udW10dLSg+Llx4waOHz+O0aNHq2N9+vSBq6srVq9eLbh+9erVsLOzw5AhxrsEpK2tLT755JMy52ZR1fH+Vi/e3+rF+1u9eH+rF+9v9eL9rV68v9XLWO+vTpvJAkBwcDB2796NGTNmwMfHBxs3bkRUVBSOHTuGnj17AgB69eqF8PBwwdJ6WVlZaN++PbKysjBz5kxYW1tjxYoVUCgUiI2Nhbu7u7rtqlWr8P7772PUqFEYMGAATp8+jU2bNuGzzz7DvHnz9PTWiYiIiIiItOlcJOXn52P+/Pn46aefkJ6ejjZt2uC///0vBgwYoG5TVpEEAHfv3sWMGTNw+PBhKJVK9OrVCytXroSPj4/W66xduxbLly/H7du34eXlhSlTpuCDDz4QfYU6IiIiIiIybToXSURERERERKZMpzlJREREREREpo5FEhERERERUSkskoiIiIiIiEphkVQDjh07hokTJ8LX1xd2dnZo0qQJ3nrrrTI31wWAc+fOoXv37rCzs0O9evUwbdo0ZGdn13DWxiM1NRVz5sxB79694ejoCIlEgpMnT5bZtlevXpBIJFqPgQMH1mzSRkSX+wvw86svGzZsKPOzKpFIcP/+fbHTMxpyuRyzZ8+Gp6cnZDIZAgMDceTIEbHTMgknT54s9zP6xx9/iJ2e0cnOzsYnn3yCgQMHwtXVFRKJBBs2bCiz7bVr1zBw4EA4ODjA1dUVb7zxBv7++++aTdjIVPb+hoSElPmZ9vPzq/mkjUR0dDSmTJmCVq1awd7eHg0bNkRwcDDi4uK02hrTZ9dK7ATMwezZs/H48WOMHj0azZo1Q0JCAr777jvs378fsbGxqFevnrptbGws+vbtixYtWmDFihW4e/culi1bhvj4eBw6dEjEd2G4bty4gSVLlqBZs2Zo3bo1IiIiKmzfoEEDLF68WBDz9PSszhSNmi73l59f/fv000/RuHFjQczFxUWcZIxQSEgIwsLCMH36dDRr1gwbNmzA4MGDceLECXTv3l3s9EzCtGnT0LlzZ0GsrFVrqWIPHz7Ep59+ioYNG6Jt27bl/jHq7t276NmzJ5ydnfH5558jOzsby5Ytw59//omoqCjY2NjUbOJGorL3Fyje12fdunWCmLOzczVnaLyWLFmCs2fPYvTo0WjTpg3u37+P7777Dh06dMAff/wBf39/AEb42VVRtQsPD1cpFAqtGADVRx99JIgPGjRI5eHhocrIyFDH1q5dqwKg+v3332skX2OTmZmpevTokUqlUql27typAqA6ceJEmW2DgoJUrVq1qsHsjJ8u95efX/1Zv369CoAqOjpa7FSMVmRkpAqAaunSpepYXl6eqmnTpqoXXnhBxMxMw4kTJ1QAVDt37hQ7FZOQn5+vSk1NValUKlV0dLQKgGr9+vVa7SZPnqySyWSqO3fuqGNHjhxRAVB9//33NZWu0ans/Z0wYYLK3t6+hrMzbmfPnlXJ5XJBLC4uTmVra6saO3asOmZsn10Ot6sBPXv2hIWFhVbM1dUV165dU8cyMzNx5MgRjBs3Dk5OTur4+PHj4eDggB07dtRYzsbE0dERrq6uOl1TVFTEIWCVVNn7y89v9cnKyoJCoRA7DaMTFhYGS0tLhIaGqmNSqRSTJk1CREQEkpOTRczOtGRlZaGoqEjsNIyara2tYGRJeX755RcMHToUDRs2VMf69esHX19f/pytQGXvbwmFQoHMzMxqzMh0dO3aVasXqFmzZmjVqpXge66xfXZZJIkkOzsb2dnZqF27tjr2559/oqioCJ06dRK0tbGxQbt27RATE1PTaZqkuLg42Nvbw9HREfXq1cP8+fNRWFgodlpGj5/f6tG7d284OTnBzs4Ow4YNQ3x8vNgpGY2YmBj4+voKinYACAgIAFA8PJSq7s0334STkxOkUil69+6N8+fPi52SyUpJSUFaWprWz1mg+HPNn7P6kZubCycnJzg7O8PV1RXvv/8+/7CqI5VKhQcPHqi/5xrjZ5dzkkTy1VdfoaCgAK+++qo6VrKQg4eHh1Z7Dw8PnD59usbyM1VNmzZF79690bp1a+Tk5CAsLAyLFi1CXFwctm/fLnZ6Ro2fX/2ys7NDSEiIuki6cOECVqxYga5du+LixYvw8vISO0WDl5qaWu7nEQDu3btX0ymZFBsbG4wcORKDBw9G7dq1cfXqVSxbtgw9evTAuXPn0L59e7FTNDnP+jn7+PFjyOVy2Nra1nRqJsPDwwOzZs1Chw4doFQq8dtvv2HVqlW4dOkSTp48CSsrfnWujC1btiAlJQWffvopAOP87PK/tI6USiUKCgoq1dbW1hYSiUQrfurUKSxcuBDBwcHo06ePOp6Xl6e+TpNUKlWfN2X6uL8V+eGHHwTHb7zxBkJDQ7F27VrMmDEDXbp00en5jE113l9+fsv3PPc9ODgYwcHB6viIESMwYMAA9OzZE5999hn+97//VVe6JiMvL6/cz2PJeXp+Xbt2RdeuXdXHw4YNw6hRo9CmTRvMnTsXv/32m4jZmaZn/ZwtaWNIXzSNjebCTmPGjIGvry8++ugjhIWFYcyYMSJlZjyuX7+O999/Hy+88AImTJgAwDg/uxxup6NTp05BJpNV6nHjxg2t669fv46XX34Z/v7+WiunyGQyAMVL1mrKz89XnzdlVb2/z+Pf//43AODo0aN6eT5DVp33l5/f8unrvnfv3h2BgYFm8VnVB5lMVu7nseQ86ZePjw+GDx+OEydOcB5dNXjWz9nSbUh/ZsyYAQsLC/7srYT79+9jyJAhcHZ2Vs8LBYzzs8ueJB35+flh/fr1lWqr2aWYnJyMF198Ec7Ozjh48CAcHR3LbF/W/kmpqalmsUx1Ve7v8yoZtvT48WO9PJ8hq877y89v+fR53728vPT2BwJT5+HhgZSUFK14yWfUnD+T1cnLywsFBQXIycnRmg9GVfOsn7Ourq4G9Zd4UyGTyeDm5mYW3xOqIiMjA4MGDcKTJ09w+vRpwc9YY/zsskjSUb169RASEqLzdY8ePcKLL74IuVyOY8eOlflFyN/fH1ZWVjh//rxgmE1BQQFiY2MFMVP1vPe3KhISEgAA7u7uNfq6YqjO+8vPb/n0ed8TEhLM4rOqD+3atcOJEyeQmZkp+LIeGRmpPk/6l5CQAKlUCgcHB7FTMTn169eHu7t7mYtjREVF8TNdTbKysvDw4UP+7K1Afn4+XnrpJcTFxeHo0aNo2bKl4LwxfnY53K4G5OTkYPDgwUhJScHBgwfRrFmzMts5OzujX79++Omnn5CVlaWOb968GdnZ2Rg9enRNpWySMjMztbp5VSoVFi1aBAAYMGCAGGmZDH5+9ausHcgPHjyICxcuYODAgSJkZHxGjRoFhUKBNWvWqGNyuRzr169HYGAgF7+oorI+o5cuXcLevXvx4osvam19QfoxcuRI7N+/X7CE/bFjxxAXF8efs1WUn58v+P1V4r///S9UKhV/9pZDoVDg1VdfRUREBHbu3IkXXnihzHbG9tmVqFQqldhJmLoRI0bg119/xcSJE9G7d2/BOQcHB4wYMUJ9fPHiRXTt2hUtW7ZEaGgo7t69i+XLl6Nnz574/fffazhz41FS6Pz111/Ytm0bJk6ciMaNGwMA/vOf/wAATp48iddeew2vvfYafHx8kJeXh927d+Ps2bMIDQ3F999/L1r+hq4y9xfg51efmjVrhvbt26NTp05wdnbGxYsX8eOPP8LDwwPR0dGoW7eu2CkaheDgYOzevRszZsyAj48PNm7ciKioKBw7dgw9e/YUOz2j1qdPH8hkMnTt2hV16tTB1atXsWbNGlhbWyMiIgItWrQQO0Wj89133+HJkye4d+8eVq9ejVdeeUW9SuDUqVPh7OyM5ORktG/fHi4uLvjggw+QnZ2NpUuXokGDBoiOjja4IUuG5Fn3Nz09He3bt8drr70GPz8/AMDvv/+OgwcPYuDAgThw4ACL/zJMnz4dX3/9NV566aUyR42MGzcOAIzvsyvqVrZmolGjRioAZT4aNWqk1f706dOqrl27qqRSqcrd3V31/vvvqzIzM2s+cSNS3v0t/RFPSEhQjR49WuXt7a2SSqUqOzs7VceOHVX/+9//VEqlUsTsDV9l7m8Jfn7146OPPlK1a9dO5ezsrLK2tlY1bNhQNXnyZNX9+/fFTs2o5OXlqWbOnKmqV6+eytbWVtW5c2fVb7/9JnZaJuHrr79WBQQEqFxdXVVWVlYqDw8P1bhx41Tx8fFip2a0Kvq+cPv2bXW7K1euqF588UWVnZ2dysXFRTV27Fj+bKiEZ93f9PR01bhx41Q+Pj4qOzs7la2trapVq1aqzz//XFVQUCB2+gYrKCio0t8TjOmzy54kIiIiIiKiUthnSEREREREVAqLJCIiIiIiolJYJBEREREREZXCIomIiIiIiKgUFklERERERESlsEgiIiIiIiIqhUUSERERERFRKSySiIiIiIiISmGRREREREREVAqLJCIiIiIiolJYJBEREREREZXCIomIiIiIiKiU/wchCyfulx5RJQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EUYQjtHh5QHw"
      },
      "source": [
        "not bad eh !!!\n",
        "\n",
        "You can try to run it with more elements to see the convergence improving.\n",
        "\n",
        "The above example may seem a bit stupid in the sens that we knew the formula of the posterior beforehand... Here the Gaussian. However in most realistic cases, the value of the posterior in one point of the parameter space has no analysitcal expression and we need to calculate it in a complicated manner than is usally very greedy in terms of CPU. The Metropolis-Hastings allow to very efficiently sample the parameter space with a minimum number of calls to the posterior function."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SVusMo3g5Tg5"
      },
      "source": [
        "#### Example of a straight-line fit\n",
        "Let's take the example of a fit of a straight-line in order to go further in our understanding of the method. It will also be the occasion of using a more efficient and robust version of the Metropolis-Hastings algorithm that I have prepared in the library cosmoOUlib.py relying the pymc library (https://pymc-devs.github.io/pymc/).\n",
        "\n",
        "We draw the following points according to a linear law which we will want ot fit:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9vWfdYd14k_I",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "9bd1e80e-3696-4f1f-fa66-6aa48de079b7"
      },
      "source": [
        "rc('figure',figsize=(10,5))\n",
        "x = linspace(0,1,10)\n",
        "sy = 0.2\n",
        "y = 3*x + 2 + np.random.randn(10)*sy\n",
        "sigma_y = np.zeros(10) + sy\n",
        "errorbar(x,y,yerr=sigma_y,fmt='ro', label='Sample Data')\n",
        "xlim(-0.1,1.1)\n",
        "xlabel('x')\n",
        "ylabel('y')\n",
        "legend(loc='upper left')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2e2c840910>"
            ]
          },
          "metadata": {},
          "execution_count": 39
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yWsmUeKc5lPn"
      },
      "source": [
        "The function we will adjust is given below. We also prepare a variable called 'data' that contains the data x,y and errors as well as the model we want to fit. This is done using a class called Data() defined in cosmolib.py (have a look at the code !):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HmYXf6VW4yOS"
      },
      "source": [
        "def fonction(x, par):\n",
        "    return par[0] + par[1]*x\n",
        "\n",
        "data = cs.Data(x, y, sigma_y, fonction)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lIEOeGhu5vbS"
      },
      "source": [
        "We now run the MCMC exploration using again a function from the class `Data` in cosmolib.py called run_mcmc() that is part of the `data` Class. We will be drawing 1000 MCMC samples. A first drawing called the \"burn\" is done with a fraction of the total number of samples (here 1/3) and then the real drawing is done. This is necessayr to have the MCMC start from a good position. The burn sampes are not kept:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n82f0vzy5q5O",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c5819025-3a93-4e1d-c977-4fad75ca32f1"
      },
      "source": [
        "guess = np.array([0., 0.])\n",
        "chain = data.run_mcmc(guess, nbmc=1000, allvariables=['p0', 'p1'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "None\n",
            "None\n",
            "Ndim init: 2\n",
            "New ndim: 2\n",
            "Burning\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 333/333 [00:00<00:00, 589.37it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sampling\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1000/1000 [00:01<00:00, 630.55it/s]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5noIQHSd56Vz"
      },
      "source": [
        "And we now plot the elements of the chain:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fAcbxfuA5zBU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "f151213b-1a50-4c07-f392-e1ec41288a8d"
      },
      "source": [
        "plot(chain['p0'], chain['p1'], ',', alpha=0.1)\n",
        "plot(2,3,'g*', label='True Value',ms=20)\n",
        "xlabel('p0')\n",
        "ylabel('p1')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'p1')"
            ]
          },
          "metadata": {},
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H_75zbA86Bz6"
      },
      "source": [
        "We see that the distribution of the points nicely contains the true value. Now we want to interpret the MCMC chain in terms of confidence intervals.\n",
        "\n",
        "First important thing here: the notion of marginalization. One says that he marginalizes over a variable when one has a probability that depends upon many variables and we look at the probability reduced to a subset of the variables by integrating over the marginalized ones. Here we marginalize over $b$:\n",
        "$$P(a) = \\int P(a,b) \\mathrm{d}b$$\n",
        "With a frequentist approach to probabilities (typically when using Minuit) such a marginalization involves a very complex procedure in order to explicitly calculate this integral.\n",
        "\n",
        "On the contrary, with a Bayesian MCMC approach, integrating over dimension $b$ reduces to just tracing the histogram of all dimensions of the chain except $b$. We can easly show the individual probabilities of all of our variables when marginalized over all the other ones, and we can calculate confidence intervals for each individual variable marginalized over the others.\n",
        "\n",
        "In our straight-line fitting example:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oFoSAC15587r",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "9d2997e0-2f1c-4c1f-a861-6aac92b0c45e"
      },
      "source": [
        "mp0 = np.mean(chain['p0'])\n",
        "mp1 = np.mean(chain['p1'])\n",
        "sp0 = np.std(chain['p0'])\n",
        "sp1 = np.std(chain['p1'])\n",
        "aa=hist(chain['p0'], bins=100, range=[1,4], alpha=0.5, label='p0 = {0:3.2f} +/- {1:3.2f}'.format(mp0, sp0))\n",
        "bb=hist(chain['p1'], bins=100, range=[1,4], alpha=0.5, label='p1 = {0:3.2f} +/- {1:3.2f}'.format(mp1, sp1))\n",
        "plot(2,100,'bv',ms=20)\n",
        "plot(3,100,'gv',ms=20)\n",
        "legend(fontsize=13)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2e2c7718a0>"
            ]
          },
          "metadata": {},
          "execution_count": 43
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MMLFgnnb6Imx"
      },
      "source": [
        "The blue and green triangles show the True Values.\n",
        "\n",
        "Now regarding the N-dimensional confidence intervals, they are for sure impossible to draw on a screen, we therefore usually show 2-D plots af all pairs of variables, marginalizing over the others. In our example there is only one 2-D plot which we show through a 2-D histogram (we overplot in red the true input values):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ob156siQ6E8I",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "52f233de-aead-45f4-ead5-ff22786e6544"
      },
      "source": [
        "im2d = hist2d(chain['p0'], chain['p1'], bins=100, \n",
        "              range=[[1,4],[1,4]])\n",
        "imshow(im2d[0].T, interpolation='nearest', origin='lower', \n",
        "       extent = (0,5,0,5))\n",
        "colorbar()\n",
        "xlabel('p0')\n",
        "ylabel('p1')\n",
        "plot(2,3,'r*', label='True Value',ms=10)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f2e2adafcd0>]"
            ]
          },
          "metadata": {},
          "execution_count": 44
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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OtnsM3BohSfc6WSNtS0CTOTZ2c2aIiLyZVRRgdcWieS6ow1N4ZFh2+fJllJeX4+eff8YLL7yATz75BLfeeqtD106YMAEajQZBQUGYNm0aTp061cmtJSIiInfyyJ6ZpUuXYuvWrQAAlUqFGTNmYNOmTa1eExQUhLlz59qCmaNHj2Ljxo1ITEzEsWPHEBUV1eK1JpMJJtPVjQ6rqviXPhEReSari4aZuGheJ1u8eDFSUlJQWlqKnTt3wmKxoL6+vtVr0tLSkJaWZkvfdddduOOOO5CUlITVq1djy5YtLV67du1aPPPMMy5rPxERUWexiipYXfAkkivq8BSK2DX79ttvR2VlJQ4ePAhBcG6Mb8yYMbh48SJ++umnFss01zMTFRXl9btmt8l+mwA7vn2kWxCYB/aTpM/HX10bpr6n9FrTNa0vBhN8VjqfJ7RAWj7gwtU1cFTHfpScs18vR7Rw4Rkicpyn75q95tAEBIR0vC/CWNOAFQlfetx9tociwrKUlBQcPnwYhYWFTl8bFRWFioqKVsuo1WpoNBrJQURE5IksEFx2eAuPHGayV1dXBwAwGAxOX3v69GmEhYW5uklERERuwWEmOY+6kwsXLsjyzGYz3nzzTQQGBuLGG28EAOj1ehQUFMBsvjqccPHiRdm1e/bswdGjR5GcnNx5jSYiIiK38qiemYceeghVVVVISkpC3759UVZWhh07dqCgoABZWVkICbmyX09GRga2bduGM2fOIDo6GgCQmJiIESNGYPTo0dBqtTh27Bhef/11REVFYcWKFW68KwUTpYvBCL5284dUdrGw3Xwm/yYPhdWF29XtL61bFdAgSVsTpPNeyrTSob/I/f62n4PC+0jOiRWV0rqMJul5uzk1RERKYgFcMkTkTbMJPSqYSU9Px2uvvYaXX34Zly5dQo8ePTBq1CisX78e06ZNa/Pajz/+GJ9//jlqa2uh0+kwb948ZGZmIjzc/puUiIhImTjMJKeIp5m6WuOM8W7/NJMd+54Zn969JGlzbF9J+tfYq7tsG2KkdTWESXtH7Htm1AHS8w0/2vfMXD0f9L1eco49M0TUEZ7+NNOfvr0dASEd/24y1pjxl1s+97j7bA+P6pkhIiKi1rlqx2vumk3dkn2PhvXXSknar6yHJN1TdXVMt14bIDlXfY20Q/Ca0GpJWl8i7fUJjJWer/n56u8KLJH+XrG39C8M1alfpO2uk87X4To0RKQkIgRYXTBnRvSiR7O9JywjIiKibok9M0RERArCYSY5BjNEREQKYhUFWMWODxG5og5PwWCG2s9Hun+SePGSJO0XcHW2/TXHpJde7quWpLUD6iTph3/3lST9D328JF0wPNj2c+j3/pJzvpW1krTVbk6M/RwZ+6e0+LQTEZGyMJghIiJSEAtUsLhgyqsr6vAUDGaIiIgUhMNMct4TlhEREVG3xJ4ZajfRLF21V9VTKy1QVm770aKLlpzyrZX+RRDbQ7pR6E9G6RYUUUGVknTxtT1tP19I6Ck5F3ZMWrefQdou+3ZznRkiUhIrVLC6oC/CFXV4CgYzRERECmIRBVhcMETkijo8hfeEZURERNQtsWeG2s1+eMZi92i2ShNi+9m3Tlo2pEha155TN0rSsboLkvS66Pcl6eqGSbafD+t6Ss4FRkm3TujRIB2yUlUa0BqxwdrqeSIid+IEYDkGM0RERAoiiipYXbB6r+hFKwB7z50QERFRt8RghoiISEEsEFx2OOP7779HamoqrrvuOgQFBaFPnz5ISkrCrl27ZGVPnjyJ5ORkhISEIDQ0FH/4wx9w8eJFWTmr1YrnnnsOAwYMQEBAAIYPH4533nnH6deEw0zUfqJ0bolo/4SzVbT96Fsp3a5AbZBuZ+BbGCRJ3xBTLkmH+0grHxhy3vbzdZOkZXeEjpGkzUHBkvQ1pb2lzbSb68PtDIjIk1lF18x3afK/aIecO3cO1dXVmDNnDiIjI1FbW4v33nsP06ZNw9atWzF//nwAQHFxMZKSkqDVarFmzRrU1NTg+eefx3fffYdDhw7B3//qFjQrV67EunXrMG/ePMTHxyMvLw+zZs2CIAiYOXOmw21jMENERERtmjx5MiZPnizJe/TRRzFq1Chs3LjRFsysWbMGly9fxtGjR9G/f38AQEJCAm677TZkZ2fbypWUlCArKwsLFizApk2bAAAPPvggxo0bh+XLlyM1NRU+dnsAtoTDTERERApi/W0CsCuOjvLx8UFUVBQqKyttee+99x7uvPNOWyADABMnTkRsbCx27txpy8vLy4PZbMYjjzxiyxMEAQ8//DCKi4tx4MABh9vBnhkiIiIFsUKA1cn5Li3VAwBVVVWSfLVaDbVa3dwlAIDLly+jrq4OBoMBH330ET755BOkp6cDuNLbcuHCBYwePVp2XUJCAvbs2WNL5+fnIzg4GIMHD5aVazw/duxYh+6FwQy5jv0cmtpa289CyXnJOf/+Gmn6V+lfCJ+dHiRJ3xTyiyT9VJ+Ttp8fLU2QtsNP2g7BfmDY/h+pYPc/BcHurxWR684QkfeKioqSpDMzM/H000+3WH7p0qXYunUrAEClUmHGjBm2YSK9Xg8A0Ol0sut0Oh0qKipgMpmgVquh1+sRHh4Owe7/wY3XlpaWOnwPDGaIiIgUxNXbGRQVFUGjufoHZmu9MgCwePFipKSkoLS0FDt37oTFYkF9fT0AoK6ursU6AgICbGXUarXtv62VcxSDGSIiIgVx1XyXxjo0Go0kmGnLoEGDMGjQld7z++67D7fffjumTp2KgwcPIjAwEABgMplk1xmNRgCwlQkMDHSonCM4AZiIiIjaLSUlBYcPH0ZhYaFtiKhxuKkpvV6P0NBQW2+MTqdDWVkZRFGUlQOAyMhIh9vAnhnqPL5NPl710rVbAoprJOkwozQCPzNAuu5Mdk/p2jHqa/9t+3mi9nvJuf2h10vStRE9JWlTf2laXWvflVkpSYlN2s41aIjI3axw0d5MLphEDFwdDjIYDBg4cCDCwsJw5MgRWblDhw4hLi7Olo6Li8Orr76KkydP4sYbr+7Pd/DgQdt5R7FnhoiISEHE355m6ughOhnMXLhwQZZnNpvx5ptvIjAw0BaQ3H333di9ezeKiq7uKPzPf/4ThYWFSE1NteVNnz4dfn5+2Lx589V7E0Vs2bIFffv2RWJiosNtY88MERERtemhhx5CVVUVkpKS0LdvX5SVlWHHjh0oKChAVlYWQkJCAAArVqxATk4OJkyYgMceeww1NTXYsGEDhg0bhvvvv99WX79+/bB48WJs2LABZrMZ8fHx+PDDD7F//37s2LHD4QXzAAYzREREimIVXTTM5GQd6enpeO211/Dyyy/j0qVL6NGjB0aNGoX169dj2rRptnJRUVH46quvsGTJEjz55JPw9/fHlClTkJWVJXt6ad26dejVqxe2bt2K7OxsxMTEYPv27Zg1a5ZTbRNE+5k3hKqqKmi1WozHdPgKfu5ujnewW7vFRyudOS8OkE70atAGSNKnH5BWNyiqzPbzI/2+lJz7tuYGSfrdT38nSWtPSesK+1a6t5NwoUKSthquLihlNTdIL+YaNERep0E0Yx/yYDAYnHrKp7M1fjf93xf3wy/Yv+0L2mC+XI8PbnvD4+6zPThnhoiIiBSNw0xEREQK4q5hJk/GYIaIiEhBXL03kzdgMEMeQWiQzj0x9ZTOVfI/LZ3VXh1+dRLZV9XSTcpGBp+VpFXXS9e0uXw5RJLuGSZN+1+Wrkgp1Bmv1mXXbutvS3gTEZH7MJghIiJSEA4zyTGYISIiUhAGM3J8momIiIgUjT0z1DXs1mOxVFZK0r7B0r2YQqzS8nW9+0jSl8w6288fDNFKzp2P7iFJ11+Wzr9R9ZbWXR0lXcSplyFYkhYqDVd/hh27OTMqf+naD5xTQ0Suxp4ZOfbMEBERkaKxZ4aIiEhB2DMjx2CG3EKllm5XIP62hXwjwUfaadgn3yBJF4VdHVqymKSPbZ+u6i1J9+gprbuuTDqsVBcmbVuPHtLzfk12/LAapY9tc1iJiLqaCNesEeNNexlxmImIiIgUjT0zRERECsJhJjkGM0RERArCYEaOwQy5hWxuickoSfrUmyVpwe7R7Wvyr57/tVY6x6VksHQSTOA1lyXphgjp7zaZpfNeGnrYbaWgvfqot8rukXHRrp1ERNT1GMwQEREpCHtm5BjMEBERKQiDGTk+zURERESKxp4Zcg+77Q3s152Rredy/qIk7RN2dcsB9a/Sj3HEfmmMbrhb+qt9LkrnxAjSpkC0C/HFHlfn64gXL0lPqqR/2Qg+0jVvRItFWl6wr9zulxMRtUEUBYgu6FVxRR2egsEMERGRglghuGTRPFfU4Sk4zERkZ2jFWbz8779haMVZdzeFiIgc4FHBzPfff4/U1FRcd911CAoKQp8+fZCUlIRdu3Y5dH1lZSXmz5+PsLAwBAcHY8KECTh27Fgnt5q8zYwzX2NIZRH+78w37m4KEZFM4wRgVxzewqOGmc6dO4fq6mrMmTMHkZGRqK2txXvvvYdp06Zh69atmD9/fovXWq1WTJkyBSdOnMDy5cvRp08fbN68GePHj8fRo0cRExPThXdCzrLarTMjm1tile4i4vffM7afexqjJOeM4YGSdOBnGmlddnsxBZderVtrrMH40u8AABNK/4sNif+Hhl5X58z4qqVr2oh26+UIvtL5OLI5M/ZzZDiHhoicxDkzch4VzEyePBmTJ0+W5D366KMYNWoUNm7c2Gowk5ubi2+++QY5OTlISUkBAKSlpSE2NhaZmZl4++23O7Xt5B3uPHUEqt82llSJIiafPordQQlubhUREbXGo4KZ5vj4+CAqKgqHDx9utVxubi7Cw8MxY8YMW15YWBjS0tKwfft2mEwmqO3+qqbu7ZqqSvS5XIOA8qs9M6kFX+PqXrIiUn78Dwpi+tnO+zaU41dVIC6pgkFE5A5cZ0bOI4OZy5cvo66uDgaDAR999BE++eQTpKent3pNfn4+Ro4cCZVK2m2fkJCAV155BYWFhRg2bFhnNpsUJuuDtzC66IwkTwRs8/tVAPrWVGBL/mZJmf/6RuCJHnd2SRuJiOxxmEnOI4OZpUuXYuvWrQAAlUqFGTNmYNOmTa1eo9frkZSUJMvX6XQAgNLS0haDGZPJBJPp6romVVVV7W06uUpbc0earO/ic7ZMckrt21eSrguVrv3ib7hy7QcDb8Gw0iL4WRpsM+Ht/2k3TVsBNAg++LzPKAia3leaWaKXNrvByb2aOEeGiKjDPDKYWbx4MVJSUlBaWoqdO3fCYrGg3n5jQjt1dXXNDiMFBATYzrdk7dq1eOaZZzrWaFKc3YPj8UN4FF7c9Qb6VZfDRxRbLGuBgFJ1KP4ScRd+UffpwlYSEUmJLhpm8qaeGY96NLvRoEGDMHHiRNx3333YvXs3ampqMHXqVIitfNkEBgZKelcaGY1G2/mWZGRkwGAw2I6ioqKO3wQpwunQCMye9jj2Rt/Uarl/97oRCwbPZyBDRG4nAhBFFxzuvhEX8shgxl5KSgoOHz6MwsLCFsvodDro9XpZfmNeZGRki9eq1WpoNBrJQd2H0U+N/Ijr0dKAjxXAdyHXwqTya6EEERG5k0cOM9lrHCIyGAwtlomLi8P+/fthtVolk4APHjyIoKAgxMbGdno7qfNYKislaVXTnja7/ZB8L1ZL0lofaVeqOVj6sRd9BQwt+QVWQQWVaIUVV6J8238FFQaoylHbvwcCS6S/SyiRtlO0Ww9Htu6Ms3NqiIjsWCFA4HYGEh7VM3PhwgVZntlsxptvvonAwEDceOONAK70thQUFMBsvvrFkJKSgvPnz+P999+35ZWXlyMnJwdTp07lY9nUqht//QW+ohUNggpmlS/eGZgEs8oXDYIKvqIVQyrOubuJREQArj7N5IrDW3hUz8xDDz2EqqoqJCUloW/fvigrK8OOHTtQUFCArKwshISEALgyx2Xbtm04c+YMoqOjAVwJZm655Rbcf//9+OGHH2wrAFssFk7upVb5W8y4tuZKIF0S1Bt/HD8HZ7URyLshAev/vQ3XVl/EtTUX4G9hrwoRkSfyqGAmPT0dr732Gl5++WVcunQJPXr0wKhRo7B+/XpMmzat1Wt9fHywZ88eLF++HC+99BLq6uoQHx+P7OxsDBw4sIvugLqK1Xh1srePpof0pEH6aL39TBehd4gkrQ5qwJmQCBRq+uKvN06HyeKPgAoLyhCGh25ehIWFeYgxlMLf0gAYaqWV9dRK6/b3l6TFOuk2DRxmIqKOsooCBC6aJyGIrT0i1E1VVVVBq9ViPKbDV+CkT4/UZE8j+2BGUEsDCmilE7ob7IIZs9YfgmiFaL9P0m8sASrb+ZAfyqUnL0uDG7FWugSAfTAj24OKiDxOg2jGPuTBYDB41AMhjd9NQ95dDp+gjk+dsNSa8H36Bofv8/Dhw9i2bRu+/PJLnD17Fr1798Ytt9yCv/zlL5J5qXPnzsW2bdtk1w8cOBAFBQWSPKvViueffx4vv/wy9Ho9YmNjkZGRgXvuucepe/Gonhkid2kpkHH0PBGRt1u/fj2+/vprpKamYvjw4SgrK8OmTZswcuRIfPvttxg6dKitrFqtxquvviq5XqvV2leJlStXYt26dZg3bx7i4+ORl5eHWbNmQRAEzJw50+G2MZghIiJSEHdtZ7BkyRK8/fbb8G8ynJ6eno5hw4Zh3bp12L59uy3f19cXs2fPbrW+kpISZGVlYcGCBbZV/h988EGMGzcOy5cvR2pqKnzsnlZtCYMZUjzRbnVna02NJK2yG+oRQqWbRPoZpKtL+9RK06Jw9R+8GCgdwhLsRmnFS79K22I/rGTfw8PtDIjISe4KZhITE2V5MTExGDJkCE6ePCk7Z7FYcPny5RaHsPLy8mA2m/HII4/Y8gRBwMMPP4xZs2bhwIEDGDt2rENtY985ERERtYsoijh//jz69JGujl5bWwuNRgOtVovQ0FAsWLAANXZ/aObn5yM4OBiDBw+W5CckJNjOO4o9M0RERAri6qeZ7DdXVqvVDq/NtmPHDpSUlGDVqlW2PJ1OhyeeeAIjR46E1WrFp59+is2bN+PEiRPYt28ffH2vhB56vR7h4eEQBOm9NN0g2lEMZoiIiBSkcW8lV9QDAFFRUZL8zMxMPP30021eX1BQgAULFmDMmDGYM2eOLX/t2rWScjNnzkRsbCxWrlyJ3Nxc28TejmwQbY/BDClTk7kmVrsd1WVbCFgskrTPL3YrTdv9VYAA6T8uob7J2jAqu7J283Hs58BwOwMi8nRFRUWSeS2O9MqUlZVhypQp0Gq1yM3NbXOi7uOPP44///nP2Lt3ry2Y6cgG0fYYzBARESnIlZ4ZV0wAvvJfZzdYNhgMmDRpEiorK7F///5WN3JuFBgYiN69e6OiosKWp9Pp8OWXX0IURclQkyMbRNvjBGAiIiIFcefeTEajEVOnTkVhYSF2795t2zOxLdXV1SgvL0dYWJgtLy4uDrW1tbInoQ4ePGg77ygGM0RERNQmi8WC9PR0HDhwADk5ORgzZoysjNFoRHV1tSz/2WefhSiKSE5OtuVNnz4dfn5+2Lx5sy1PFEVs2bIFffv2bfZR8JZwmIm8jv28FPu0KjhIekHvXtJ0bSuTzoLsxnAvS8uqevWUpBsu2G1/QETUQeJvhyvqccbSpUvx0UcfYerUqaioqJAskgcAs2fPRllZGUaMGIF77rkHgwYNAgB89tln2LNnD5KTkzF9+nRb+X79+mHx4sXYsGEDzGYz4uPj8eGHH2L//v3YsWOHwwvmAQxmiIiIFMVdi+YdP34cALBr1y7s2rVLdn727Nno2bMn7rzzTnzxxRfYtm0bLBYLbrjhBqxZswbLli2DSiUdEFq3bh169eqFrVu3Ijs7GzExMdi+fTtmzZrlVNsYzBAREVGb9u3b12aZnj174q233nK4TpVKhYyMDGRkZHSgZQxmiIiIlMVd40wejMEMeR3BbpzVfp0Zy68GSdrHavcvOsRuTk3TtWOqpMtx29cN+zVvZG2xayz3ZiIiZ7lomAmuqMND8GkmIiIiUjT2zBARESmIq7cz8AYMZoiIiBTEXU8zeTIGM+R1ZPNY7Aj+0v2SLAbpjrGorJQkVdomy3ybG6R19QiRpK2V0vk4qsAA6e9qZjEpIiLqGAYzRERESiIKrpm8y54ZIiIicgfOmZHj00xERESkaOyZoW7HWlvb6nkfrVaSFpvsvyTYz4E5f0GSlq8rY7eOjGD39wPXmSEiZ3HRPBkGM0RERArCp5nkOMxEREREisaeGSI7Yl2dNN30UW/pKQi+0se87VlNRlc1i4joKi8aInIFBjNEREQKwmEmOQ4zERERkaKxZ4aIiEhJ+DSTDIMZIjvW+npJuunj1rJzqta7aVX+/q3WTUTkPOG3wxX1eAcOMxEREZGisWeGiIhISTjMJMNghoiISEkYzMgwmCFqg2gVmyYk5wQf/5bLopk5Nnbr0ogNZhe0kIioe2MwQ0REpCSicOVwRT1egsEMERGRgojilcMV9XgLPs1EREREisaeGaK2NJ0nI7Qe/0v2cSIi6gycACzDYIaIiEhJOGdGhsNMREREpGjsmSEiIlIQQbxyuKIeb8FghsgZduvMWM0NrZ6XXc51ZYioozhnRobDTERERKRo7JkhIiJSEk4AlmEwQ0REpCQcZpJhMEPUEW3MkSEios7HYIaIiEhJ2DMjw2CGiIhISRjMyPBpJiIiImrT4cOH8eijj2LIkCEIDg5G//79kZaWhsLCQlnZkydPIjk5GSEhIQgNDcUf/vAHXLx4UVbOarXiueeew4ABAxAQEIDhw4fjnXfecbpt7Jkh6kSCr58kzXVmiKjD3PQ00/r16/H1118jNTUVw4cPR1lZGTZt2oSRI0fi22+/xdChQwEAxcXFSEpKglarxZo1a1BTU4Pnn38e3333HQ4dOgR/f39bnStXrsS6deswb948xMfHIy8vD7NmzYIgCJg5c6bDbeu0npndu3fj//2//+fUNc5Effays7MhCEKzR1lZWXtvg4iIyKM0rgDsisMZS5Yswblz5/DSSy/hwQcfxJ/+9Cfs378fDQ0NWLduna3cmjVrcPnyZfzrX//CokWLsGLFCuzcuRMnTpxAdna2rVxJSQmysrKwYMECvPLKK5g3bx527dqF3/3ud1i+fDksTmzc22k9MydOnMC2bdvw+uuvO3yNo1Ffa1atWoUBAwZI8nr27Ols84mIiKiJxMREWV5MTAyGDBmCkydP2vLee+893Hnnnejfv78tb+LEiYiNjcXOnTsxf/58AEBeXh7MZjMeeeQRWzlBEPDwww9j1qxZOHDgAMaOHetQ2zxqmGnJkiV4++23JV1Q6enpGDZsGNatW4ft27e3WcekSZMwevTozmwmdWMqdYAkbTUZWy3PYSUicjkPmgAsiiLOnz+PIUOGALjS23LhwoVmv4cTEhKwZ88eWzo/Px/BwcEYPHiwrFzj+U4JZq677jqHyxoMBmeqBuB41NeW6upqBAUFwcfHx+k2EBERdSdVVVWStFqthlqtdujaHTt2oKSkBKtWrQIA6PV6AIBOp5OV1el0qKiogMlkglqthl6vR3h4OARBkJUDgNLSUofvwalg5pdffkHfvn0xfPjwNsv+9NNPqKysdKb6ZtlHfW2ZMGECampq4O/vjzvuuANZWVmIiYnpcDuIiIi8UVRUlCSdmZmJp59+us3rCgoKsGDBAowZMwZz5swBANTV1QFAs8FQQECArYxarbb9t7VyjnIqmBk8eDB69uyJXbt2tVl29erVeOqpp5ypvln2UV9LgoKCMHfuXEyYMAEajQZHjx7Fxo0bkZiYiGPHjsnerKZMJhNMJpMtbR+lEhEReQoBzk/ebakeACgqKoJGo7HlO9IrU1ZWhilTpkCr1SI3N9c2EhIYGAgAku/URkajUVImMDDQoXKOcCqYSUhIwD/+8Q9YLJYuGcJpLuprSVpaGtLS0mzpu+66C3fccQeSkpKwevVqbNmypcVr165di2eeecZl7Sbv1dYcGSKiTufiR7M1Go0kmGmLwWDApEmTUFlZif379yMyMtJ2rnGIqHG4qSm9Xo/Q0FBbsKTT6fDll19CFEXJUFPjtU3rbYtTj2bPnDkTaWlpzS58Y2/atGlOPclkr6Wozxljx47FzTffjL1797ZaLiMjAwaDwXYUFRW1t9lERERey2g0YurUqSgsLMTu3btx4403Ss737dsXYWFhOHLkiOzaQ4cOIS4uzpaOi4tDbW2tbE7swYMHbecd5VQwc9ttt+GNN95AREREm2WHDRvWZm9KS5pGfZ9++qlT0Zm9qKgoVFRUtFpGrVbbIlNnI1QiIqIuJbrwcILFYkF6ejoOHDiAnJwcjBkzptlyd999N3bv3i3pGPjnP/+JwsJCpKam2vKmT58OPz8/bN68+eqtiSK2bNmCvn37NvtQUEs6/Gj2//73P+zZswdnz54FAERHR2PSpEkYNmxYu+prGvXt3btXFvU56/Tp0wgLC+tQHURERB7DTY9mL126FB999BGmTp2KiooK2XIps2fPBgCsWLECOTk5mDBhAh577DHU1NRgw4YNGDZsGO6//35b+X79+mHx4sXYsGEDzGYz4uPj8eGHH2L//v3YsWOHUyMy7Q5mTCYTHnroIbz11lsQRREq1ZVOHqvVioyMDNx777149dVXJWvGtKVp1JeXl9di1KfX62EwGHD99dfDz+/KcvEXL16UBS179uzB0aNHsWjRonbeJREREQHA8ePHAQC7du1q9kGgxmAmKioKX331FZYsWYInn3wS/v7+mDJlCrKysmSTi9etW4devXph69atyM7ORkxMDLZv345Zs2Y51bZ2BzN//OMf8eabb+KRRx7BwoULcf3110MQBPz000946aWX8PLLLyM0NBQvvviiw3U6GvVlZGRg27ZtOHPmDKKjowFcWaNmxIgRGD16NLRaLY4dO4bXX38dUVFRWLFiRXtvk4iIyKO0ZyuClupxxr59+xwuO2TIEHz22WdtllOpVMjIyEBGRoZzjbHT7mBm+/bt+MMf/oBNmzZJ8gcOHIi///3vqKqqwvbt250KZhyN+pqTnp6Ojz/+GJ9//jlqa2uh0+kwb948ZGZmIjw83OE2EBEReTQPWgHYU7R7o0mz2YxbbrmlxfOJiYloaGhwqs59+/ZBFMUWj0bZ2dkQRdHWKwMAf/nLX5Cfn4/KykrU19fj3Llz2Lx5MwMZIiIiL9fuYOaOO+5otQvp008/xe23397e6omIiKg5bnqayZO1e5jp2WefRVpaGmbMmIEFCxbghhtuAACcOnUKf//733Hu3Dm8++67sseiQ0NDO9ZiIiKibsxdc2Y8WbuDmcZdLr/77jvk5eVJzjUOCTX3WLXFYmnvryQiIiKSaXcw89RTT8l2uiQiIqJO5uLtDLxBu4MZR3bUJCIiIhfj00wy7Z4ATEREROQJOrydAREREXUdTgCWYzBDRESkJBxmkuEwExERESkae2aIiIiUxEXDTN7UM8NghoiISEk4zCTDYSYiIiJSNPbMEBERKQl7ZmQYzBARESkIH82W4zATERERKRqDGSIiIlI0DjMREREpCefMyLBnhoiIiBSNPTNEREQKwgnAcgxmiIiIlMaLAhFX4DATERERKRp7ZoiIiJSEE4BlGMwQEREpCOfMyHGYiYiIiBSNPTNERERKwmEmGQYzRERECsJhJjkOMxEREZGisWeGiIhISTjMJMNghoiISEkYzMhwmImIiIgUjT0zRERECsIJwHIMZoiIiJSEw0wyHGYiIiIiRWMwQ0REpCSiCw8n1NTUIDMzE8nJyQgNDYUgCMjOzpaVmzt3LgRBkB2DBg2SlbVarXjuuecwYMAABAQEYPjw4XjnnXecaxg4zERERKQo7pozU15ejlWrVqF///646aabsG/fvhbLqtVqvPrqq5I8rVYrK7dy5UqsW7cO8+bNQ3x8PPLy8jBr1iwIgoCZM2c63DYGM0RERNQmnU4HvV6PiIgIHDlyBPHx8S2W9fX1xezZs1utr6SkBFlZWViwYAE2bdoEAHjwwQcxbtw4LF++HKmpqfDx8XGobRxmIiIiUhI3DTOp1WpEREQ4XN5isaCqqqrF83l5eTCbzXjkkUdseYIg4OGHH0ZxcTEOHDjg8O9iMENERKQgjcNMrjg6S21tLTQaDbRaLUJDQ7FgwQLU1NRIyuTn5yM4OBiDBw+W5CckJNjOO4rDTERERN2Yfe+JWq2GWq1ud306nQ5PPPEERo4cCavVik8//RSbN2/GiRMnsG/fPvj6Xgk99Ho9wsPDIQiC7HoAKC0tdfh3MpghIiJSEhevMxMVFSXJzszMxNNPP93uateuXStJz5w5E7GxsVi5ciVyc3NtE3vr6uqaDZoCAgJs5x3FYSYiIiIlcfGcmaKiIhgMBtuRkZHh8iY//vjjUKlU2Lt3ry0vMDAQJpNJVtZoNNrOO4rBDBERUTem0WgkR0eGmFoSGBiI3r17o6Kiwpan0+lQVlYGUZR2M+n1egBAZGSkw/UzmCEiIlIQwYVHV6murkZ5eTnCwsJseXFxcaitrcXJkyclZQ8ePGg77ygGM0REREripkezHWE0GlFdXS3Lf/bZZyGKIpKTk21506dPh5+fHzZv3nz11kQRW7ZsQd++fZGYmOjw7+UEYCIiInLIpk2bUFlZaXvSaNeuXSguLgYALFy4EL/++itGjBiBe+65x7Z9wWeffYY9e/YgOTkZ06dPt9XVr18/LF68GBs2bIDZbEZ8fDw+/PBD7N+/Hzt27HB4wTwAEET7wSpCVVUVtFotxmM6fAU/dzeHiIi6UINoxj7kwWAwQKPRuLs5No3fTUP+f2vgow7ocH0WkxHfb1nh1H1GR0fj3LlzzZ47c+YMevbsiYULF+Lbb79FaWkpLBYLbrjhBtx7771YtmwZ/Pyk36lWqxXr16/H1q1bodfrERMTg4yMDNx7771O3Qt7ZoiIiJTExY9mO+Ps2bNtlnnrrbccrk+lUiEjI6PDT1BxzgwREREpGntmiIiIlIYTRCQYzBARESmIq/ZV6sy9mboah5mIiIhI0TwqmDl8+DAeffRRDBkyBMHBwejfvz/S0tJQWFjo0PWVlZWYP38+wsLCEBwcjAkTJuDYsWOd3GoiIqIu5MHrzLiLRw0zrV+/Hl9//TVSU1MxfPhwlJWVYdOmTRg5ciS+/fZbDB06tMVrrVYrpkyZghMnTmD58uXo06cPNm/ejPHjx+Po0aOIiYnpwjshIiLqHBxmkvOoYGbJkiV4++234e/vb8tLT0/HsGHDsG7dOmzfvr3Fa3Nzc/HNN98gJycHKSkpAIC0tDTExsYiMzMTb7/9dqe3n4iIiLqeRw0zJSYmSgIZAIiJicGQIUNkezfYy83NRXh4OGbMmGHLCwsLQ1paGvLy8prdmZOIiEhxOMwk41HBTHNEUcT58+fRp0+fVsvl5+dj5MiRUKmkt5SQkIDa2tpW592YTCZUVVVJDiIiIk/UOMzkisNbeHwws2PHDpSUlCA9Pb3Vcnq9HjqdTpbfmNe4j0Rz1q5dC61WazuioqI61mgiIiLqMh4dzBQUFGDBggUYM2YM5syZ02rZuro6qNVqWX5AQIDtfEsyMjJgMBhsR1FRUccaTkRE1Fk4zCTjUROAmyorK8OUKVOg1WqRm5vb5u6ZgYGBzc6LMRqNtvMtUavVzQZCREREHseNezN5Ko8MZgwGAyZNmoTKykrs378fkZGRbV6j0+mg1+tl+Y15jtRBREREyuNxwYzRaMTUqVNRWFiIvXv34sYbb3Touri4OOzfvx9Wq1UyCfjgwYMICgpCbGxsZzWZiIioy3CdGTmPmjNjsViQnp6OAwcOICcnB2PGjGm2nF6vR0FBAcxmsy0vJSUF58+fx/vvv2/LKy8vR05ODqZOncphJCIi8g6cMyPjUT0zS5cuxUcffYSpU6eioqJCtkje7NmzAVyZsLtt2zacOXMG0dHRAK4EM7fccgvuv/9+/PDDD7YVgC0WC5555pmuvhUiIiLqIh4VzBw/fhwAsGvXLuzatUt2vjGYaY6Pjw/27NmD5cuX46WXXkJdXR3i4+ORnZ2NgQMHdlaTiYiIupQgihDEjneruKIOTyGIohfdjYtUVVVBq9ViPKbDV/Bzd3OIiKgLNYhm7EMeDAYDNBqNu5tj0/jdFDd7NXz8Azpcn6XeiOPbV3rcfbaHR82ZISIiInKWRw0zERERUev4NJMcgxkiIiIl4aJ5MhxmIiIiIkVjzwwREZGCcJhJjsEMERGRknCYSYbDTERERKRo7JkhIiJSEA4zyTGYISIiUhIOM8lwmImIiIgUjT0zRERECuNNQ0SuwGCGiIhISUTxyuGKerwEh5mIiIhI0dgzQ0REpCB8mkmOwQwREZGS8GkmGQ4zERERkaKxZ4aIiEhBBOuVwxX1eAv2zBARESmJ6MLDCTU1NcjMzERycjJCQ0MhCAKys7ObLXvy5EkkJycjJCQEoaGh+MMf/oCLFy/KylmtVjz33HMYMGAAAgICMHz4cLzzzjvONQwMZoiIiMgB5eXlWLVqFU6ePImbbrqpxXLFxcVISkrCTz/9hDVr1mDZsmX4+OOPcdttt6G+vl5SduXKlfjjH/+I2267DX/729/Qv39/zJo1C//4xz+cahuHmYiIiBTEXU8z6XQ66PV6RERE4MiRI4iPj2+23Jo1a3D58mUcPXoU/fv3BwAkJCTgtttuQ3Z2NubPnw8AKCkpQVZWFhYsWIBNmzYBAB588EGMGzcOy5cvR2pqKnx8fBxqG3tmiIiIlKRx0TxXHE5Qq9WIiIhos9x7772HO++80xbIAMDEiRMRGxuLnTt32vLy8vJgNpvxyCOP2PIEQcDDDz+M4uJiHDhwwOG2MZghIiLqxqqqqiSHyWRqd10lJSW4cOECRo8eLTuXkJCA/Px8Wzo/Px/BwcEYPHiwrFzjeUcxmCEiIlKQxmEmVxwAEBUVBa1WazvWrl3b7rbp9XoAV4ak7Ol0OlRUVNiCJb1ej/DwcAiCICsHAKWlpQ7/Xs6ZISIiUhIXL5pXVFQEjUZjy1ar1e2usq6ursU6AgICbGXUarXtv62VcxSDGSIiom5Mo9FIgpmOCAwMBIBmh6qMRqOkTGBgoEPlHMFhJiIiIgVx9TCTKzUOETUONzWl1+sRGhpq643R6XQoKyuDaDcRufHayMhIh38vgxkiIiIlcdPTTI7o27cvwsLCcOTIEdm5Q4cOIS4uzpaOi4tDbW0tTp48KSl38OBB23lHMZghIiIil7n77ruxe/duFBUV2fL++c9/orCwEKmpqba86dOnw8/PD5s3b7bliaKILVu2oG/fvkhMTHT4d3LODBERkYK4a9E8ANi0aRMqKyttTxrt2rULxcXFAICFCxdCq9VixYoVyMnJwYQJE/DYY4+hpqYGGzZswLBhw3D//ffb6urXrx8WL16MDRs2wGw2Iz4+Hh9++CH279+PHTt2OLxg3pV7sR+sIlRVVUGr1WI8psNX8HN3c4iIqAs1iGbsQx4MBoPLJsa6QuN305jkVfD1C+hwfQ1mIw58+pRT9xkdHY1z5841e+7MmTOIjo4GAHz//fdYsmQJ/vOf/8Df3x9TpkxBVlYWwsPDJddYrVasX78eW7duhV6vR0xMDDIyMnDvvfc6dS/smSEiIiKHnD171qFyQ4YMwWeffdZmOZVKhYyMDGRkZHSoXQxmiIiIFMSdw0yeisEMERGRkljFK4cr6vESfJqJiIiIFI09M0REREri4u0MvAF7ZoiIiEjR2DNDRESkIAJcNAG441V4DAYzRERESuKqrQi8aJk5DjMRERGRorFnhoiISEG4zowcgxkiIiIl4dNMMhxmIiIiIkVjzwwREZGCCKIIwQWTd11Rh6dgMENERKQk1t8OV9TjJTjMRERERIrGnhkiIiIF4TCTHIMZIiIiJeHTTDIcZiIiIiJFY88MERGRknA7AxkGM0RERArCFYDlPGqYqaamBpmZmUhOTkZoaCgEQUB2drZD12ZnZ0MQhGaPsrKyzm04ERERuY1H9cyUl5dj1apV6N+/P2666Sbs27fP6TpWrVqFAQMGSPJ69uzpmgYSERG5G4eZZDwqmNHpdNDr9YiIiMCRI0cQHx/vdB2TJk3C6NGjO6F1RERE7idYrxyuqMdbeNQwk1qtRkRERIfrqa6uhsVicUGLiIiIyNN5VDDjChMmTIBGo0FQUBCmTZuGU6dOubtJRERErtM4zOSKw0t41DBTRwQFBWHu3Lm2YObo0aPYuHEjEhMTcezYMURFRbV4rclkgslksqWrqqq6oslERETO46J5Ml4TzKSlpSEtLc2Wvuuuu3DHHXcgKSkJq1evxpYtW1q8du3atXjmmWe6oplERETkYl43zNTU2LFjcfPNN2Pv3r2tlsvIyIDBYLAdRUVFXdRCIiIi5zTuzeSKw1t4Tc9MS6KiovDjjz+2WkatVkOtVndRi4iIiDqAj2bLeHXPDACcPn0aYWFh7m4GERERdRJFBjN6vR4FBQUwm822vIsXL8rK7dmzB0ePHkVycnJXNo+IiKjziACsLji8p2PG84aZNm3ahMrKSpSWlgIAdu3aheLiYgDAwoULodVqkZGRgW3btuHMmTOIjo4GACQmJmLEiBEYPXo0tFotjh07htdffx1RUVFYsWKFu26HiIjIpVw134VzZjrR888/j3PnztnS77//Pt5//30AwOzZs6HVapu9Lj09HR9//DE+//xz1NbWQqfTYd68ecjMzER4eHiXtJ2IiIi6niCKXhSauUhVVRW0Wi3GYzp8BT93N4eIiLpQg2jGPuTBYDBAo9G4uzk2jd9Nv497Er4+HX9opcFiwr+Or/O4+2wPj+uZISIiolbwaSYZRU4AJiIioq61b98+CILQ7PHtt99Kyn7zzTcYO3YsgoKCEBERgUWLFqGmpqbT2saeGSIiIiWxAhBcVE87LFq0CPHx8ZK8G264wfbz8ePHceutt2Lw4MHYuHEjiouL8fzzz+PUqVP45JNPOtLiFjGYISIiUhB3P830u9/9DikpKS2eX7FiBXr16oV9+/bZ5uJER0dj3rx5+Pzzz3H77be36/e2hsNMRERE5JTq6mo0NDTI8quqqvDFF19g9uzZkknF9913H0JCQrBz585OaQ+DGSIiIiVpnADsiqMd7r//fmg0GgQEBGDChAk4cuSI7dx3332HhoYGjB49WnKNv78/4uLikJ+f36FbbwmHmYiIiJTExU8zVVVVSbJb2q/Q398fd999NyZPnow+ffrghx9+wPPPP4/f/e53+OabbzBixAjo9XoAgE6nk12v0+mwf//+jre7GQxmiIiIurGoqChJOjMzE08//bSsXGJiIhITE23padOmISUlBcOHD0dGRgY+/fRT1NXVAUCzwVBAQIDtvKsxmCEiIlISF/fMFBUVSea3NBeItOSGG27A9OnT8f7778NisSAwMBAAYDKZZGWNRqPtvKsxmCEiIlISFz+ardFoOrQCcFRUFOrr63H58mXb8FLjcFNTer0ekZGR7f49reEEYCIiImq306dPIyAgACEhIRg6dCh8fX0lk4IBoL6+HsePH0dcXFyntIHBDBERkYI0rjPjisMZFy9elOWdOHECH330EW6//XaoVCpotVpMnDgR27dvR3V1ta3cW2+9hZqaGqSmpnb4/pvDYSYiIiIlcdPeTOnp6QgMDERiYiKuueYa/PDDD3jllVcQFBSEdevW2cqtXr0aiYmJGDduHObPn4/i4mJkZWXh9ttvR3Jycsfb3Qz2zBAREVGb7rrrLpSXl2Pjxo145JFH8O6772LGjBk4cuQIBg8ebCs3cuRI7N27F4GBgXj88cfxyiuv4IEHHkBubm6ntY09M0REREpiFQHBBT0zVufqWLRoERYtWuRQ2bFjx+Lrr79uT6vahcEMERGRkrhpmMmTcZiJiIiIFI09M0RERIriop4ZeE/PDIMZIiIiJeEwkwyHmYiIiEjR2DNDRESkJFYRLhkicvJpJk/GYIaIiEhJROuVwxX1eAkOMxEREZGisWeGiIhISTgBWIbBDBERkZJwzowMh5mIiIhI0dgzQ0REpCQcZpJhMENERKQkIlwUzHS8Ck/BYSYiIiJSNPbMEBERKQmHmWQYzBARESmJ1QrABQveWbloHhEREZFHYM8MERGRknCYSYbBDBERkZIwmJHhMBMREREpGntmiIiIlITbGcgwmCEiIlIQUbRCFDv+JJIr6vAUHGYiIiIiRWPPDBERkZKIomuGiLxoAjCDGSIiIiURXTRnxouCGQ4zERERkaKxZ4aIiEhJrFZAcMHkXS+aAMxghoiISEk4zCTDYSYiIiJSNPbMEBERKYhotUJ0wTCTN60zw2CGiIhISTjMJMNhJiIiIlI09swQEREpiVUEBPbMNMVghoiISElEEYArHs32nmCGw0xERESkaB4VzNTU1CAzMxPJyckIDQ2FIAjIzs52+PrKykrMnz8fYWFhCA4OxoQJE3Ds2LHOazAREVEXE62iyw5nmUwm/PGPf0RkZCQCAwNx880344svvuiEu3SORwUz5eXlWLVqFU6ePImbbrrJqWutViumTJmCt99+G48++iiee+45XLhwAePHj8epU6c6qcVERERdTLS67nDS3LlzsXHjRtx7773461//Ch8fH0yePBn/+c9/OuFGHedRc2Z0Oh30ej0iIiJw5MgRxMfHO3xtbm4uvvnmG+Tk5CAlJQUAkJaWhtjYWGRmZuLtt9/urGYTERF5vUOHDuEf//gHNmzYgGXLlgEA7rvvPgwdOhRPPPEEvvnmG7e1zaN6ZtRqNSIiItp1bW5uLsLDwzFjxgxbXlhYGNLS0pCXlweTyeSqZhIREbmNu4aZcnNz4ePjg/nz59vyAgIC8MADD+DAgQMoKipy9a06zKOCmY7Iz8/HyJEjoVJJbykhIQG1tbUoLCx0U8uIiIhcyE3DTPn5+YiNjYVGo5HkJyQkAACOHz/uqjt0mkcNM3WEXq9HUlKSLF+n0wEASktLMWzYsGavNZlMkp4bg8EAAGiA2SWLLBIRkXI0wAwAED300WVXfTc13mdVVZUkX61WQ61Wy8rr9Xrbd2pTTb9n3cVrgpm6urpmX/yAgADb+ZasXbsWzzzzjCz/P9jjugYSEZGiXLp0CVqt1t3NsPH390dERAT+U+a676aQkBBERUVJ8jIzM/H000/Lynbke7azeU0wExgY2Oy8GKPRaDvfkoyMDCxZssSWrqysxLXXXotffvnFoz7IXaWqqgpRUVEoKiqSdSd2B7x/3j/vv/veP3Cld75///4IDQ11d1MkAgICcObMGdTX17usTlEUIQiCJK+5gAXo2PdsZ/OaYKbxSSh7jXmRkZEtXttSl5pWq+22/5gBQKPR8P55/+5uhtvw/rv3/QOQzcH0BAEBAbaekK6m0+lQUlIiy3fke7azed471U5xcXE4duwYrFbphKaDBw8iKCgIsbGxbmoZERGR8sXFxaGwsFA2x+bgwYO28+6iyGBGr9ejoKAAZrPZlpeSkoLz58/j/ffft+WVl5cjJycHU6dObbHbjIiIiNqWkpICi8WCV155xZZnMpnwxhtv4Oabb5bNvelKHjfMtGnTJlRWVtpmRe/atQvFxcUAgIULF0Kr1SIjIwPbtm3DmTNnEB0dDeDKi3zLLbfg/vvvxw8//IA+ffpg8+bNsFgszU7ubY1arUZmZma3DYB4/7x/3j/vv7veP8DXoCU333wzUlNTkZGRgQsXLuCGG27Atm3bcPbsWbz22mtubZsgetizZ9HR0Th37lyz5xqDl7lz58qCGQD49ddfsXz5cnz44Yeoq6tDfHw8nn/+eYwePbqLWk9EROS9jEYj/vznP2P79u349ddfMXz4cDz77LO444473NoujwtmiIiIiJyhyDkzRERERI0YzBAREZGiMZghIiIiRes2wUxNTQ0yMzORnJyM0NBQCIKA7Oxsh6+vrKzE/PnzERYWhuDgYEyYMAHHjh3rvAZ3go68BtnZ2RAEodmjrKyscxvuAocPH8ajjz6KIUOGIDg4GP3790daWprDG5Aq/f3vyP0r/b0HgO+//x6pqam47rrrEBQUhD59+iApKQm7du1y6Hqlv/9Ax14Db/gM2Fu9ejUEQcDQoUMdKl9SUoK0tDT07NkTGo0G06dPx+nTpzu5leQoj3s0u7OUl5dj1apV6N+/P2666Sbs27fP4WutViumTJmCEydOYPny5bbHvsePH4+jR48iJiam8xruQh15DRqtWrUKAwYMkOT17NnTNQ3sROvXr8fXX3+N1NRUDB8+HGVlZdi0aRNGjhyJb7/9ttX/oXnD+9+R+2+k1PceAM6dO4fq6mrMmTMHkZGRqK2txXvvvYdp06Zh69atmD9/fovXesP7D3TsNWik5M9AU8XFxVizZg2Cg4MdKl9TU4MJEybAYDBgxYoV8PPzwwsvvIBx48bh+PHj6N27dye3mNokdhNGo1HU6/WiKIri4cOHRQDiG2+84dC17777rghAzMnJseVduHBB7Nmzp3jPPfd0RnM7RUdegzfeeEMEIB4+fLgTW9h5vv76a9FkMknyCgsLRbVaLd57772tXusN739H7l/p731LGhoaxJtuukkcOHBgq+W84f1viaOvgbd9BtLT08Xf//734rhx48QhQ4a0WX79+vUiAPHQoUO2vJMnT4o+Pj5iRkZGZzaVHNRthpnUajUiIiLadW1ubi7Cw8MxY8YMW15YWBjS0tKQl5fX7MZbnqgjr0FT1dXVsFgsLmhR10lMTIS/v78kLyYmBkOGDMHJkydbvdYb3v+O3H9TSnzvW+Lj44OoqChUVla2Ws4b3v+WOPoaNKX0z8C///1v5Obm4sUXX3T4mtzcXMTHxyM+Pt6WN2jQINx6663YuXNnJ7SSnNVtgpmOyM/Px8iRI2WbjiUkJKC2ttbheRfeYMKECdBoNAgKCsK0adNw6tQpdzep3URRxPnz59GnT59Wy3nr++/o/Tfyhvf+8uXLKC8vx88//4wXXngBn3zyCW699dZWr/G29789r0EjpX8GLBYLFi5ciAcffBDDhg1z6Bqr1Yr//ve/zS6+mpCQgJ9//hnV1dWubio5qdvMmekIvV6PpKQkWb5OpwMAlJaWOvwPQ6mCgoIwd+5c2//Mjh49io0bNyIxMRHHjh1z654c7bVjxw6UlJRg1apVrZbz1vff0fv3pvd+6dKl2Lp1K4ArOyLPmDEDmzZtavUab3v/2/MaeMtnYMuWLTh37hz27t3r8DUVFRUwmUy297uppp+BgQMHuqyd5DwGMw6oq6trdo+Oxm3Y6+rqurpJXS4tLQ1paWm29F133YU77rgDSUlJWL16NbZs2eLG1jmvoKAACxYswJgxYzBnzpxWy3rj++/M/XvTe7948WKkpKSgtLQUO3fuhMViQX19favXeNv7357XwBs+A5cuXcJTTz2FP//5zwgLC3P4usb315s+A96Iw0wOCAwMbHZc3Gg02s53R2PHjsXNN9/s1F85nqCsrAxTpkyBVqtFbm4ufHx8Wi3vbe+/s/ffHKW+94MGDcLEiRNx3333Yffu3aipqcHUqVMhtrKri7e9/+15DZqjtM/An/70J4SGhmLhwoVOXdf4/nrTZ8AbMZhxgE6ng16vl+U35kVGRnZ1kzxGVFQUKioq3N0MhxkMBkyaNAmVlZX49NNPHXrvvOn9b8/9t0Rp731zUlJScPjw4VbnvXjT+98cR16DlijlM3Dq1Cm88sorWLRoEUpLS3H27FmcPXsWRqMRZrMZZ8+ebfE+QkNDoVarvfoz4A0YzDggLi4Ox44dg9VqleQfPHgQQUFBiI2NdVPL3O/06dNOddm6k9FoxNSpU1FYWIjdu3fjxhtvdOg6b3n/23v/LVHSe9+SxuEBg8HQYhlvef9b4shr0BKlfAZKSkpgtVqxaNEiDBgwwHYcPHgQhYWFGDBgQItzx1QqFYYNG4YjR47Izh08eBDXXXcdevTo0dm3QG1gMGNHr9ejoKAAZrPZlpeSkoLz58/j/ffft+WVl5cjJycHU6dObXYsVcmaew0uXrwoK7dnzx4cPXoUycnJXdm8drFYLEhPT8eBAweQk5ODMWPGNFvOW9//jty/0t97ALhw4YIsz2w2480330RgYKAtsPPW9x/o2Gug9M/A0KFD8cEHH8iOIUOGoH///vjggw/wwAMPAAB++eUXFBQUSK5v7L1qGtD8+OOP+Ne//oXU1NQuvRdqniA6O1CqYJs2bUJlZSVKS0vx8ssvY8aMGRgxYgQAYOHChdBqtZg7dy62bduGM2fOIDo6GsCVL4KxY8fif//7n2QF0F9++QWHDx9W1Cz29r4GMTExGDFiBEaPHg2tVotjx47h9ddfh06nw+HDhxEeHu7Gu2rb4sWL8de//hVTp06VTGRsNHv2bADw2ve/I/ev9PceAP7v//4PVVVVSEpKQt++fVFWVoYdO3agoKAAWVlZWLJkCQDvff+Bjr0G3vAZaM748eNRXl6O//3vf5K8r776SjKHqLq6GiNGjEB1dTWWLVsGPz8/bNy4ERaLBcePH1dE75TXc+OCfV3u2muvFQE0e5w5c0YURVGcM2eOJN2ooqJCfOCBB8TevXuLQUFB4rhx4xS5GmZ7X4OVK1eKcXFxolarFf38/MT+/fuLDz/8sFhWVuaeG3HSuHHjWrzvpv8MvPX978j9K/29F0VRfOedd8SJEyeK4eHhoq+vr9irVy9x4sSJYl5enqSct77/otix18AbPgPNaW4F4MZ/K/aKiorElJQUUaPRiCEhIeKdd94pnjp1qquaSm3oVj0zRERE5H04Z4aIiIgUjcEMERERKRqDGSIiIlI0BjNERESkaAxmiIiISNEYzBAREZGiMZghIiIiRWMwQ0RERIrGYIaIiIgUjcEMEbXom2++wdixYxEUFISIiAgsWrQINTU17m4WEZGEr7sbQESe6fjx47j11lsxePBgbNy4EcXFxXj++edx6tQpfPLJJ+5uHhGRDYMZImrWihUr0KtXL+zbtw8ajQYAEB0djXnz5uHzzz/H7bff7uYWEhFdwWEmom7m6aefhiAIKCgoQFpaGjQaDXr37o3HHnsMRqMRAFBVVYUvvvgCs2fPtgUyAHDfffchJCQEO3fudFfziYhkGMwQdVNpaWkwGo1Yu3YtJk+ejJdeegnz588HAHz33XdoaGjA6NGjJdf4+/sjLi4O+fn57mgyEVGzOMxE1E0NGDAAeXl5AIAFCxZAo9Fg8+bNWLZsGfR6PQBAp9PJrtPpdNi/f3+XtpWIqDXsmSHqphYsWCBJL1y4EACwZ88e1NXVAQDUarXsuoCAANt5IiJPwGCGqJuKiYmRpK+//nqoVCqcPXsWgYGBAACTySS7zmg02s4TEXkCBjNEBAAQBMH2c+PwUuNwU1N6vR6RkZFd1i4iorYwmCHqpk6dOiVJ//TTT7BarYiOjsbQoUPh6+uLI0eOSMrU19fj+PHjiIuL68KWEhG1jsEMUTf197//XZL+29/+BgCYNGkStFotJk6ciO3bt6O6utpW5q233kJNTQ1SU1O7tK1ERK3h00xE3dSZM2cwbdo0JCcn48CBA9i+fTtmzZqFm266CQCwevVqJCYmYty4cZg/fz6Ki4uRlZWF22+/HcnJyW5uPRHRVeyZIeqm3n33XajVajz55JP4+OOP8eijj+K1116znR85ciT27t2LwMBAPP7443jllVfwwAMPIDc3142tJiKSY88MUTcVFhaGnJycVsuMHTsWX3/9dRe1iIiofdgzQ0RERIrGYIaIiIgUjcEMERERKZogiqLo7kYQERERtRd7ZoiIiEjRGMwQERGRojGYISIiIkVjMENERESKxmCGiIiIFI3BDBERESkagxkiIiJSNAYzREREpGgMZoiIiEjR/j8nV9zEmYaD1gAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t3uOVwVt6fcc"
      },
      "source": [
        "Finally MCMC results are often represented as a kind of matrix of plots with all the 2-D and 1-D posteriors smoothed for a nice appearence. The 2-D histograms are also replaced by 2-D contours that show various confidence intervals (exemple 68 and 95% Confidence Levels). The function matrixplot() in the cosmolib.py does that for you !"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a21hJYWj6OLo",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 871
        },
        "outputId": "432af4ea-bdc1-4bc0-b695-f025a69e2a14"
      },
      "source": [
        "rc('figure',figsize=(10,10))\n",
        "sm = 1.5   #smoothing parameter - to be adjusted not to change the shape\n",
        "cs.matrixplot(chain, ['p0', 'p1'], 'blue', sm, \n",
        "              limits = [[1,4], [1,4]], labels=['p0','p1'])\n",
        "\n",
        "#### Overplot the True Values\n",
        "subplot(2,2,1)\n",
        "plot([2,2], [0,2], 'k--')\n",
        "subplot(2,2,4)\n",
        "plot([3,3], [0,2], 'k--')\n",
        "subplot(2,2,3)\n",
        "plot(2,3,'g*', label='True Value',ms=20)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f2e2aaf8a30>]"
            ]
          },
          "metadata": {},
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9sW7ltDZ6wKL"
      },
      "source": [
        "By rerunning the drawing of the noise for the straight-line, and rerunning the rest, you will see how different realizations move with respect to the True points.\n",
        "\n",
        "#### A bit more advanced:\n",
        "We could have specified a more general model for fitting, for instance a 4th order polynomial, and fit only the first two parameters. This can be easily done with the provided MCMC functions using the `fixpars` parameter:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mqv4bKqS6mEO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "1d180036-6445-4b2e-baf6-b2b092b087c0"
      },
      "source": [
        "def fonction(x, par):\n",
        "    return par[0] + par[1]*x + par[2]*x**2 + par[3]*x**3 + par[4]*x**4\n",
        "\n",
        "data = cs.Data(x, y, sigma_y, fonction)\n",
        "guess = np.zeros(6)\n",
        "chain = data.run_mcmc(guess, nbmc=1000, allvariables=['p0', 'p1', 'p2', 'p3', 'p4', 'p5'],\n",
        "                   fixpars=[2,3,4,5])\n",
        "\n",
        "sm = 1.5   #smoothing parameter - to be adjusted not to change the shape\n",
        "cs.matrixplot(chain, ['p0', 'p1'], 'blue', sm, \n",
        "              limits = [[1,4], [1,4]], labels=['p0','p1'])\n",
        "\n",
        "#### Overplot the True Values\n",
        "subplot(2,2,1)\n",
        "plot([2,2], [0,2], 'k--')\n",
        "subplot(2,2,4)\n",
        "plot([3,3], [0,2], 'k--')\n",
        "subplot(2,2,3)\n",
        "plot(2,3,'g*', label='True Value',ms=20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[2, 3, 4, 5]\n",
            "[2, 3, 4, 5]\n",
            "Ndim init: 6\n",
            "New ndim: 2\n",
            "Len(pos): (32, 6)\n",
            "len(fixepars): 4\n",
            "New len(pos): (32, 2)\n",
            "Burning\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 333/333 [00:00<00:00, 575.03it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sampling\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1000/1000 [00:01<00:00, 604.02it/s]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f2e2aa42d70>]"
            ]
          },
          "metadata": {},
          "execution_count": 46
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HeF3psIM7DnL"
      },
      "source": [
        "Here we have not specified anything regarding the value of the unfitted parameters, so the code automatically sets them to zero. We could have decided to fix them to another value through the *fidvalue* keyword which should have therefore contained a nympy.array with the fiduciual values for all the parameters listed in the allvariables."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vCnuAgOx7LIU"
      },
      "source": [
        "#### MCMC on SNIa data\n",
        "***Question 5:*** Now perform the MCMC fitting on the supernovae data for the $\\Lambda CDM$ model with variables $\\Omega_m$ and $\\Omega_\\Lambda$ (we won't look at $w$ and remember that supernovae do not constrain the Hubble constant so these two should not be fitted but fixed to respectively -1 and 0.7 as fiducial values).\n",
        "You should then display the matrix plot of the contours."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P8lB7QFo65a3"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PH3ZHbM87a9O"
      },
      "source": [
        "# You have just won the Nobel Prize in Physics 2011\n",
        "https://www.nobelprize.org/prizes/physics/2011/summary/\n",
        "\n",
        "just a bit too late..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MsapwMDB7ePc"
      },
      "source": [
        "# Going further\n",
        "For those of you willing to go further it is interesting to investigate the constraints imposed by SNIa data on the Dark Energy equation of state $w_0$. In order to do so, you may first explore with a MCMC the three parameters jointly ($\\Omega_m, \\Omega_\\Lambda,w_0$) but you will soon realize how degenerate they are with each other using only SNIa data. This is why adding other probes like Baryonic Acoustic Oscillations and the Cosmic Microwave Background is so powerful: it breaks these degeneracies as these probes are differently sensitive to cosmological parameters with respect to SNIa. A simpler way of investigating this is to explore only $(\\Omega_m, w_0$) while forcing the curvature to be zero (as observationnally suggested by the CMB alone as well as prefferred from a theoretical point of view) through $\\Omega_\\Lambda = 1-\\Omega_m$. You will therefore see that the SNIa data is consistent with $w_0=-1$, that is to say a simple cosmological constant.\n",
        "\n",
        "You will go much further during the Integration Week by combining different cosmological probes and breaking these degeneracies in a rigourous manner."
      ]
    }
  ]
}