tutorial_python/python_distance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# MVPA MEG Tutorial (Python): Distance measures and cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "[Tutorial starting page](https://github.com/m-guggenmos/megmvpa/).\n",
    "\n",
    "**Goal of this tutorial:** comparison of Euclidean and Pearson distance measures + cross-validation.\n",
    "\n",
    "## Tutorial\n",
    "\n",
    "We start with some imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "import numpy as np\n",
    "import scipy\n",
    "from sklearn.discriminant_analysis import _cov\n",
    "\n",
    "from cv import ShuffleBinLeaveOneOut, ShuffleBin\n",
    "from dissimilarity import Euclidean2, CvEuclidean2, Pearson, CvPearson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We set a seed, in order to make analyses reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's load some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "root = '' # This is the /path/to the directory containing the data.\n",
    "          # We leave it empty here, because the data is located in the current directory.\n",
    "\n",
    "# Load data and trial labels for the two sessions of participant 01\n",
    "sessions = [\n",
    "    # Session 1\n",
    "    dict(\n",
    "        data=np.load(os.path.join(root, 'data01_sess1.npy')),\n",
    "        # data has shape n_trials x n_sensors x n_timepoints\n",
    "        labels=np.load(os.path.join(root, 'labels01_sess1.npy'))\n",
    "        # labels has shape 1 x n_trials (i.e., one condition label [object category] per trial)\n",
    "    ),\n",
    "    # Session 2\n",
    "    dict(\n",
    "        data=np.load(os.path.join(root, 'data01_sess2.npy')),\n",
    "        labels=np.load(os.path.join(root, 'labels01_sess2.npy'))\n",
    "    )\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we set some parameters. Only the number of permutations and the number of pseudo-trials are free parameters. The number of conditions, sensors, time points and sessions are derived from the data (i.e., from the `sessions` variable above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Parameters\n",
    "n_perm = 20  # number of permutations\n",
    "n_pseudo = 5  # number of pseudo-trials\n",
    "n_conditions = len(np.unique(sessions[0]['labels']))\n",
    "n_sensors = sessions[0]['data'].shape[1]\n",
    "n_time = sessions[0]['data'].shape[2]\n",
    "n_sessions = len(sessions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define our distance measures: non-cross and cross-validated variants of the (squared) Euclidean and the Pearson distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ec = Euclidean2()\n",
    "ec_cv = CvEuclidean2()\n",
    "ps = Pearson()\n",
    "ps_cv = CvPearson()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-cross-validated distances\n",
    "\n",
    "We start with computing non-cross-validated distances (`ec` and `ps`). For this, the analytic logic is contained in a nested for loop, with loops for the number of sessions, number of permutations, number of timepoints, number of conditions, and number of conditions again. Overall, the logic contains 3 crucial steps:\n",
    "1. Compute pseudo-trials for the training and test data\n",
    "2. Whiten the training data (here using the Epoch method, which is recommended in our manuscript)\n",
    "3. Apply distance measure to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pre-load mechanism, for convenience\n",
    "preload_result = True\n",
    "if preload_result:\n",
    "    result = np.load(os.path.join(root, 'result_distance.npy'))\n",
    "else:\n",
    "    result = np.full((n_sessions, n_perm, n_conditions, n_conditions, n_time), np.nan,\n",
    "                     dtype={'names': ['ec', 'ps'], 'formats': 2*['f8']})\n",
    "    for s, session in enumerate(sessions):\n",
    "\n",
    "        print('Session %g / %g' % (s + 1, n_sessions))\n",
    "\n",
    "        X = session['data']\n",
    "        y = session['labels']\n",
    "\n",
    "        cv = ShuffleBin(y, n_iter=n_perm, n_pseudo=n_pseudo)\n",
    "\n",
    "        for f, (train_indices, test_indices) in enumerate(cv.split(X)):\n",
    "            print('\\tPermutation %g / %g' % (f + 1, n_perm))\n",
    "\n",
    "            # 1. Compute pseudo-trials\n",
    "            Xpseudo = np.full((len(test_indices), n_sensors, n_time), np.nan)\n",
    "            for i, ind in enumerate(test_indices):\n",
    "                Xpseudo[i, :, :] = np.mean(X[ind, :, :], axis=0)\n",
    "\n",
    "            # 2. Whitening using the Epoch method\n",
    "            sigma_conditions = cv.labels_pseudo_test[0, :, n_pseudo:].flatten()\n",
    "            sigma_ = np.empty((n_conditions, n_sensors, n_sensors))\n",
    "            for c in range(n_conditions):\n",
    "                # compute sigma for each time point, then average across time\n",
    "                sigma_[c] = np.mean([_cov(Xpseudo[sigma_conditions==c, :, t], shrinkage='auto')\n",
    "                                     for t in range(n_time)], axis=0)\n",
    "            sigma = sigma_.mean(axis=0)  # average across conditions\n",
    "            sigma_inv = scipy.linalg.fractional_matrix_power(sigma, -0.5)\n",
    "            Xpseudo = (Xpseudo.swapaxes(1, 2) @ sigma_inv).swapaxes(1, 2)\n",
    "\n",
    "            for t in range(n_time):\n",
    "                for c1 in range(n_conditions-1):\n",
    "                    for c2 in range(min(c1 + 1, n_conditions-1), n_conditions):\n",
    "                            # 3. Apply distance measure to the data\n",
    "                            data = Xpseudo[cv.ind_pseudo_test[c1, c2], :, t]\n",
    "                            result['ec'][s, f, c1, c2, t] = ec.predict(data, y=cv.labels_pseudo_test[c1, c2])\n",
    "                            result['ps'][s, f, c1, c2, t] = ps.predict(data, y=cv.labels_pseudo_test[c1, c2])\n",
    "    # average across permutations\n",
    "    result_ = np.full((n_sessions, n_conditions, n_conditions, n_time), np.nan,\n",
    "                      dtype={'names': ['ec', 'ps'], 'formats': 2*['f8']})\n",
    "    result_['ec'] = np.nanmean(result['ec'], axis=1)\n",
    "    result_['ps'] = np.nanmean(result['ps'], axis=1)\n",
    "    result = result_\n",
    "    np.save(os.path.join(root, 'result_distance.npy'), result_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To take a look at the results, we use matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f910fb597f0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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oiqIotVLrkoiU0qyal0EPN0gp/yOl9JFS+gF3A/9IKWehG8Bxjn6zOcD62sbW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\niDHGGK9ZEDHGGOO1/wNOVtLMnc6hLwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f911257a320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(211)\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result['ec'], axis=(0, 1, 2)), label='Euclidean')\n",
    "plt.xlim((-100, 1000))\n",
    "plt.ylabel('Euclidean distance', fontsize=12)\n",
    "plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result['ps'], axis=(0, 1, 2)), label='Pearson')\n",
    "plt.xlim((-100, 1000))\n",
    "plt.xlabel('Time [ms]', fontsize=12)\n",
    "plt.ylabel('Pearson distance', fontsize=12)\n",
    "plt.legend(loc='lower right')\n",
    "\n",
    "# plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Euclidean distance:** the Euclidean distance rises shortly after stimulus onset (at 0ms) and until it reaches a maximum. Interestingly, the distance remains at this maximum after stimulus offset (at 500ms) until the end of the epoch, although the condition-specific information content [drops to zero](https://github.com/m-guggenmos/megmvpa/blob/master/tutorial_python/python_decoding.ipynb) towards the end of the trial. This indicates that the non-cross-validated Euclidean distance is not only influenced by condition-specific differences in activation patterns, but also by noise.\n",
    "\n",
    "**Pearson distance:** the Pearson distance _decreases_ after stimulus onset, corresponding to an increase of the correlation between condition-specific activation patterns (note that the Pearson distance is defined as 1−r). Thus, activation patterns in fact get more similar after stimulus onset, which intuitively seems surprising, since the [decoding analysis](https://github.com/m-guggenmos/megmvpa/blob/master/tutorial_python/python_decoding.ipynb) shows that they also get more distinct. In contrast to the Euclidean distance, the Pearson approaches its baseline value towards the end of the trial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Cross-validated distances\n",
    "\n",
    "We now turn to cross-validated measures. Here too, the analytic logic is contained in a nested for loop, with loops for the number of sessions, number of permutations, number of timepoints, number of conditions, and number of conditions again. Overall, the logic contains 4 crucial steps:\n",
    "1. Compute pseudo-trials for the training and test data\n",
    "2. Whiten the training data (here using the Epoch method, which is recommended in our manuscript)\n",
    "3. Apply distance measure to training data\n",
    "4. Validate distance measure on testing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pre-load mechanism, for convenience\n",
    "preload_result = True # for recomputing the decoding analyses, set to False\n",
    "if preload_result:\n",
    "    result_cv = np.load(os.path.join(root, 'result_distance_cv.npy'))\n",
    "else:\n",
    "    result_cv = np.full((n_sessions, n_perm, n_conditions, n_conditions, n_time), np.nan,\n",
    "                        dtype={'names': ['ec_cv', 'ps_cv'], 'formats': 2*['f8']})\n",
    "    for s, session in enumerate(sessions):\n",
    "\n",
    "        print('Session %g / %g' % (s + 1, n_sessions))\n",
    "\n",
    "        X = session['data']\n",
    "        y = session['labels']\n",
    "\n",
    "        cv = ShuffleBinLeaveOneOut(y, n_iter=n_perm, n_pseudo=n_pseudo)\n",
    "\n",
    "        for f, (train_indices, test_indices) in enumerate(cv.split(X)):\n",
    "            print('\\tPermutation %g / %g' % (f + 1, n_perm))\n",
    "\n",
    "            # 1. Compute pseudo-trials for training and test\n",
    "            Xpseudo_train = np.full((len(train_indices), n_sensors, n_time), np.nan)\n",
    "            Xpseudo_test = np.full((len(test_indices), n_sensors, n_time), np.nan)\n",
    "            for i, ind in enumerate(train_indices):\n",
    "                Xpseudo_train[i, :, :] = np.mean(X[ind, :, :], axis=0)\n",
    "            for i, ind in enumerate(test_indices):\n",
    "                Xpseudo_test[i, :, :] = np.mean(X[ind, :, :], axis=0)\n",
    "\n",
    "\n",
    "            # 2. Whitening using the Epoch method\n",
    "            sigma_conditions = cv.labels_pseudo_train[0, :, n_pseudo-1:].flatten()\n",
    "            sigma_ = np.empty((n_conditions, n_sensors, n_sensors))\n",
    "            for c in range(n_conditions):\n",
    "                # compute sigma for each time point, then average across time\n",
    "                sigma_[c] = np.mean([_cov(Xpseudo_train[sigma_conditions==c, :, t], shrinkage='auto')\n",
    "                                     for t in range(n_time)], axis=0)\n",
    "            sigma = sigma_.mean(axis=0)  # average across conditions\n",
    "            sigma_inv = scipy.linalg.fractional_matrix_power(sigma, -0.5)\n",
    "            Xpseudo_train = (Xpseudo_train.swapaxes(1, 2) @ sigma_inv).swapaxes(1, 2)\n",
    "            Xpseudo_test = (Xpseudo_test.swapaxes(1, 2) @ sigma_inv).swapaxes(1, 2)\n",
    "\n",
    "            for t in range(n_time):\n",
    "                for c1 in range(n_conditions-1):\n",
    "                    for c2 in range(min(c1 + 1, n_conditions-1), n_conditions):\n",
    "                            # 3. Apply distance measure to training data\n",
    "                            data_train = Xpseudo_train[cv.ind_pseudo_train[c1, c2], :, t]\n",
    "                            ec_cv.fit(data_train, cv.labels_pseudo_train[c1, c2])                            \n",
    "                            ps_cv.fit(data_train, cv.labels_pseudo_train[c1, c2])\n",
    "\n",
    "                            # 4. Validate distance measure on testing data\n",
    "                            data_test = Xpseudo_test[cv.ind_pseudo_test[c1, c2], :, t]\n",
    "                            result_cv['ec_cv'][s, f, c1, c2, t] = ec_cv.predict(data_test, y=cv.labels_pseudo_test[c1, c2])\n",
    "                            result_cv['ps_cv'][s, f, c1, c2, t] = ps_cv.predict(data_test, y=cv.labels_pseudo_test[c1, c2])\n",
    "    # average across permutations\n",
    "    result_cv_ = np.full((n_sessions, n_conditions, n_conditions, n_time), np.nan,\n",
    "                      dtype={'names': ['ec_cv', 'ps_cv'], 'formats': 2*['f8']})\n",
    "    result_cv_['ec_cv'] = np.nanmean(result_cv['ec_cv'], axis=1)\n",
    "    result_cv_['ps_cv'] = np.nanmean(result_cv['ps_cv'], axis=1)\n",
    "    result_cv = result_cv_\n",
    "    np.save(os.path.join(root, 'result_distance_cv.npy'), result_cv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we plot the cross-validated distances on top of the non-cross-validated distances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f910fa45a20>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yjaECRgjxP1Stlh1AbIpDxdNVLR84eSOKXedCebtnbZ0aRqPRFGmM1mCGAo2k\nlNcM7veRYfauizjZWTOsRdWHPRWNRqPJE0Y/IocCEQb3+cgQFBnHuqM3GNS8Cq5O+VsrW6Mp6hS3\nejBxcXF07NiR5ORkw/o8fvw4o0aNMqy/nGK0BvMVsEgI8RmQKqObpVqlJhPm/3MZs5SMaZu/dbI1\nmuJAcasHM3fuXAYMGJAq+0BeadCgAYGBgVy9ehVPT0/D+s0uRmswPwFPAP8A51O8zhk8TrEjOt7E\n4v1XebyBO1XKOD3s6Wg0RZaiWg9m0aJF9OvX797nzz//nAYNGtCoUaMHUvybzWa8vLyIiLi/YVSz\nZs10MzX36dMnVRbpgsRQDUZKqa3SuSAxycxH608SnZDE+A66urSmiLFpEtw8bmyfFRtAr8y3vO7m\nIrvLu+++y6BBgzI8P2U9GFDJLjMiZT2YW7du4ePjw5gxY+7Vg1m7di3lypVj6dKlvP/++/e0j3Hj\nxgEq79mcOXOYOHEicL8ezOnTp+nbty8DBw5MNV5iYiIXL17Ey8sLgE2bNrF27Vr279+Pk5MTt2/f\nTnW+lZUV/fr1Y/Xq1YwePZr9+/dTtWpVKlSo8MBafH19mTZtGm+//XYm32b+UKhKJgshqgALgAoo\nz7OZUsrvhBBTgHFAiOXU96SUGx/OLI3l2u1YXl58iKOBkTzfoRoNK5fKfWdmM5xap16d3we36sZN\nVKMpZBSnejChoaGUKnX/b3/r1q2MHj0aJye1m1GmzIPlOgYNGsTUqVMZPXo0S5YsyVC4li9fnhs3\nbmS41vzEaDdlG+AloCNQFriXY15K2SEbXSQBb0opDwkhSgL+QogtlmPfSCm/NHK+D5OEpGRW+l9n\n2qZTSGDG8Gb0rF8xd51JCSfXwN//heCTqu3yPzDydyhXy7A5azTpkoWmUdAUxXowjo6OOZ5r69at\nOX/+PCEhIaxZs4YPPvgg3fPi4+NxdHTMUd9GYfSW1jfA88BOoBmwEigPbM/OxVLKICnlIcv7aOAU\nRbxYmZSS88ExbDt1i93nQjl4+TYz/r5A+8938N7q49Qo78yGie1zL1wADi2A5aPAnARPzYEX/gFp\nhvmPw62Thq0lX4m9DafWw+FFsO8nOLPpYc9IU0S5Ww8GSLcezF0y2yLr0KEDS5cuJTk5maCgoHup\n/VPWgwFVQvnEiRMAD9SDyQmlS5cmOTn5npDp1q0b8+bNu2fHSbtFBiCEoH///rzxxhvUrVsXNze3\ndPs+e/asUIcNAAAgAElEQVQs9evXz9F8jMLoLbIBQGsp5VUhxH8s21t/Aj8DU3LSkRDCC2iCqifT\nFpgohHgW8ENpORn/OgoBF0NiWHLwGltO3uJS6J0HjrerUZavn2lM2xpuCJGHYmLxUbD9I/BsDaM2\ngJXFA2XUBvilD/zyBIzbDqW9cj9GQbBuIpxen7rtyRnQeMjDmY+m0JPWBtOzZ0+mTZvG5MmTGTt2\nLB9++OE9Az8ou8iECROoX78+1tbWTJ48mQEDBqTbd//+/dm+fTs+Pj54eno+UA/mlVdeITIykqSk\nJF577TXq1at3rx5MuXLlaNmyJdHR0TlaT/fu3dm9ezddu3alZ8+eHDlyBF9fX+zs7Hj88cf59NNP\nmTFjBgAvvKBKbA0aNIjmzZszf/78e/2sW7cOPz8/pk6dCsCOHTvo3bt3juZiFIbWgxFChANlpJRS\nCBEEVJdSxgohoqSULjnoxxn4G/hESrlKCFEBFWMjgY8AdynlmHSuGw+MB/D09Gx25coVA1aVc07f\njGLwzH3cSUiidfWydPOpQAMPV0zJZhJMZsq72FOrQkljBts6BXZ/A+N2gEfT1MdCz8OMdlDvSeg/\nw5jx8oPwy/B9E2g+Dlq/BHbOsGIMXNkDz64FL10Pp7Ch68EYz6FDh/jmm2/49ddfDeszISGBjh07\nsnv3bmxsUusTBVEPxmgN5hTQHDiA0jSmCCGigOvZ7UAIYYvaWlskpVwFIKW8leL4LGB9etdKKWcC\nM0EVHMvlGvLEhZAYhs/ej4ONNesmtMPTLR9djsOvwN4fodGQB4ULQNka0Hws7PsR2v9LfS6MHJwN\nCGj7KrhadkSf+QXmdIelw+C5bdphQVPsadq0KZ07dyY5OdmwWJirV68ybdq0B4RLQWG0DeZVlKEe\n4A2gKdAHi1aRFULtFc0BTkkpv07R7p7itP5AgCGzNZhrt2MZNms/AIvGtcxf4QKwdbLaEnsskzyi\nbV8FGwf4+/P8nUtuSYyFQ79C3T73hQuAY2kYuhSEFfw2GJKTMu5DoykmjBkzxtBAy5o1a6baJixo\nDBUwUsqDKYz056SUXaWULaWUu7LZRVtgBNBFCHHE8noc+K8Q4rgQ4hjQGXjdyHkbgZSSlxcfIs6U\nzK9jW1K9nHPWF+WFq/vhxGolQFwyKUrmXB6aPwcBKyDkTPrnJEQrF+eHwfFlEB8BLZ9/8FiZatD7\nawg9C+c2Gztu7G1lvyqmJcMLguJabv1RoKD+7/IjXX83YDBQXkrZRwjhC7hIKbP0JJNS7iaFa3MK\nCn3My99nQzgaGMnnTzWgrnu2zU25Q0rYNhWcK0CbiVmf3/ZVODhHaTED56Y+FnYBfmoLto7g3R68\n2qv38ZGWG7AZrGyUplS1LXi2grw4JaRdx/6foUID5aSQHnV6Q0l38JsLdR7P+5hmM/z1Gez8r/ps\n4wCuVaDfdPBsmff+HxEcHBwICwvDzS2PTiqaAkdKSVhYGA4ODvk+ltFxMBNR22SzgbuhqnHA90D6\nWeSKAVJKfth+Ho9SjvRvUgBFwi7ugCu7odcXYFci6/NLlIWW42H3t9D2NXBveP/Yln8r4VGrB1za\nCSfXZt5XxYbQ6kWo/xTY2Gd+blZc3q3idvr+L2OhZW0LTUbAzi+Uzal0HrJMx0fB6ufhzEZo8AxU\nrA93QuDEWuVU8OJutTWnyZLKlSsTGBhISEhI1idrCh0ODg5Urpz/9yqjvcguAI9JKS8LIcKllKWF\nENZAsJQyfSftfMLX11f6+fkVyFh7LoQydNZ+PupXjxGtvfJ3MClhVme4EwYT/bJ/k4+9DdNbgmMp\n5XFm76xu8PN7Q5cPoMNbqu+Iq4AEh1JgX1IJH7MZEmPUNtv+nyHkNJQoB81Gge+YzLfoMsJsVm7U\nwSfgjVNKa8qIiGvwXUNo93rm9qbMiAmGX/qq7baen0GL8feF2vVDMKeb0pae/sU4DS0rooKUhuha\npEO9NMUIo73IjDbylwTu1oK5K7lsgUSDxylU/LDtPOVL2vO0b5X8H+z0BrhxGDq9kzMNwqkMPDUb\nQs/BhjfVDf7P98HFA1pNUOcIoTSE0l5KEN2NqbGyAgcXJUxe2gcj1oCHL+z8Er5tADs+zbkt48DP\nSgvrOiVz4QJQqgrU7KGcAZJNORsH1NzWTYTwSzBilbL3pBQiHk2hy4dKeztsnItolnNaOEAFw+Zm\nTRpNEcBoAbMTmJSm7RVUhctiid/l2+y9GMb4DtVwsDXO+yNdzMmw/WNwqwkNB+f8+mododMkOLYE\nlo2AoCPw2GSwy4G3mxBQvTMMXQKvHIZ6/ZVtZ+cX2e8j5KyK36nZA5qOzN41vqPhTrASsKY4JWz+\nfF9pN1lxZBGc/UOttVqn9M9p8wp4d4BN78B1/2wuJA+c36q2B8Mvw9GHk+lWo8lvjN4icwd+R+Uh\n8wAuAtHAE1LKm4YNlA0aN20mjxwy7kZhSjZjSjbjaGuNEILzwdFsOHaTZX7XiDcls+udzjjZ5bOv\necBKZSsYOA/qpx+BnCXmZPi1P1z6Gyo1gee2Kw0lt5jNsHYCHF0M3T+BNi9nfn5yktqOCr+stKGS\nD2Z/zXDe3zUCBCRGQ1y4em/rqIRmq5eUvSYtEVfhxzZQqTE8uy7ztUYFweyuSpD1+FR53wmh0u0c\nW6qcHUpXhdLeytkhvfGyyy99lTbpXA7iImCif97602gMoFAHWkopg4QQzYEWgCdqu+yAlLLAfWAv\nBMdw9lZ0qoj54Oh4EpPM2NtY42hnjbN91suPjDXxy97LzPvnEuGxJoQABxtr4kzJCAHNq5Zh4mM1\n8l+4gLJ/lKkGPk/mvg8ra7VVtuENaP9m3oQLqOv7/gCmO7D5fYi6Dg0GgnuT9Pve8THcOKRsHdkV\nLnfn3fIF5ZRQ9wllQ3GtAn9MUm3HlsHwlVAyRU43sxnWvKTe95ue9Vpd3OH5ncoRYOO/4OJf6uZ/\nZTdY2Sp7ibRUG6z+GAxZAjZ22V/DXYKOKgHfbSqUrQ2/DVJaTNMROe9LoynEGKrBFCZKeNSS3s/9\nwBcDGxJnSmbpwWvsv5Q6Ydzg5lWY2q8+djbqxiOlZPvpYM4HxxAZZyI0JoGNx28Sk5DEY3XK4+tV\nhrjEJGITk6lSxome9StSwSX/Xf0ACDoGP7dXT9atJxTMmDkhKVFpMgEr1I24pDs0GQ7t3lBbcFLC\ntv+otDZNR0Lf73M+hpRgin3Qc+7Uelg1Hsp4qxxsjqWUprT+VTi8UAnAps9mfxyzGf75Vm1HunqA\n71jlyebgClGBarzN70ODp6H/zJwL6ZXjlCfb6ydUn7M6KycMrcVoHjJGazB5FjBCiGvcN+hniJSy\nQOt1NmrSVFYZ8x0B16MAqOrmxMCmlang6kBCkplzt6JZsPcKLbzLMGN4MyLjTLy/+jh7LoQBYG0l\ncHW0pXV1NyZ0qoFPpXyObcmKdRPh2HJ481ThdqWNva2CIk+uVTfRUlXh8S/h/BY4MBOajVbBk3nV\nnNJyYQcsehoqN4fBi2DNi8ru0uEtVRsnN55hCdFg63Tf2SElO79USUZbvaSEfnb7jwyEbxsqbazn\np6rt7J+w+JmcC0KNxmAKo4DpmOJjc2AkKu7lClAVeBlYIKX8Kk8D5RBfX1+5a89+lvtfo2b5krT0\nLoOVVeqbwNoj13lrxTHKONlxOzYRe2sr3u5Vh/5NPChhZ114AsjiwuGrutDwaXUTKipc2gXrX4cw\nS8Xs1i9D94/zzw04YJWyUdmVgMQ70PtLZUfJD6RU23P7Z6hccJ0mZS9j9aZJStC+egRKed7va/Zj\ncOOIsq21flnZjDSaAqbQCZhUnQkRAPSQUl5P0VYZ+ENKWaAFCbIbB3P4ajgTfztMoyqlmPyED+UL\nassrJ+z5n9qSeX5X6iDJokBSgqrvYuuYOvYkvzg4R2kWfb4Hn775O5bZrLb99v2kbDONh6rttIoN\n09fQji2DVePUdlu//6U+FhMM/3wH/vNVzJFXe+UWXueJ3Nl5NJpcUNgFzG3AW0oZmaKtFHBJSlmg\n+zoFGWiZr5jN8ENTlRZm7J8PezZFAykLLlgSIOqGypLgPx+SE8CprHKH9ukHtR8Haxs4t0Ul7fRs\nDcNWgG0GDzJxEXDoFzgwGyKvQonyKsC09UsFtx7NI0thFzDzAW/gYyAQqAK8C1yVUmYz4MEYio2A\nObcVFj2lKlU2GJj1+ZqHx51QOL8NLmyHC9tUGpqS7lBvgMqlVq4WjFyvglazwpys+tnzg/I4G7pM\npfPJ6Nz4SBVMq9HkgcIuYBxQlSufBioBQcAy4D9SyjjDBsoGxUbA/NJHxUu8ekxvlRQlzMnK2eHg\nbCV0ynjDmM0q7iUnJCXAzM4QG6rihtIKkehbsHykyu4wbgdU8DFuDZpHjkItYAoTxULABPrD7C7K\nMJ6drMmawklkoHI8yK33X9Ax5crs8yQMnHO//doBWDpCaS829kqIjd2qtuQ0mlxQ6AIthRAdpJQ7\nLe+7ZHRedtL1a9Kw+2uVdLLZqIc9E01ecM1j1lr3htBxkgpS9WimMgoEHoATa1Tfw1cqT73lo1T8\nTod/GTLtHJNsUnPLzP6VEKOEoY73eSQw4lHnR+Cuh9icDM6RQDUDxnp0CDkDp9dDh7dVVmPNo027\n1+HMBvjzXfXZuSI0HAQ9PlaaUcX6Kvbor2lQuxdUqJf6+uDTKp3P3cSaVtbgUlmlvilXW2WIyCmm\nONg7HQIPqgzb4Veg49vQ+b0Hz711QmWiOLZMbeMNX1m447k0hqC3yAora15ScR2vB6h6LhpN9E11\nM6/URGXBTqsp3AlVJRlKlFM3+uqdAaGSke7/WZWftrF4ryUnKo83UOcMXfqgE0HUDeW9mF6gafAp\nFXMUfBLK1YXydSAmBK7tg/F/K4EHKsPDitHqYcnGUQm/0+uVUBuxRv+2CxnaBpNNirSAiQxUiR19\nx8Lj/33Ys9EUJc5uhtXjVXCusALbEiquptkoVffn7g1dSiWQIq7A6hfUuS/uuW+/Ob8NFj6lhJVP\nPxVTZFsC4sOVNrLjU6VZPzkDanZV18Tehv/5qmSgYzerPte8pDSnjpNUmQSnMiqT9JJhKjD12XXZ\ny0knpapEevuiyiuX12J3mnQpdAKmsKaKKdIC5o/3VL2UVw7fj/bWaLJLcpJKKHpui8om3folcG+U\n8fmn1sPSYdDnOyWI4qPgx9YqVqdCPZXKJik+9TXVH4P+M8C5fOr2u8Gkvb5QWa+3TYVO76n6RSm5\ntBMWD1YZC0ZtyNxuI6VKaLrHkr+u3gDltm90uqFHhbALygXed+wD32GhM/IDww3oQ3OXuHAVsFd/\noBYumtxhbQNVWqhXdqjTG6q0VFpJg6fVzTz6BozdApV9VU62S7uURuJYCpzcwK1G+kKhwdNw9DfY\n8qESSg0Hqe26tHh3gG7/UVmrz22BWt3Tn5uUKjPDnu9V2h/XKrB1stq66/lZwQbU5pW4cKUt1u2j\nEsGmh5RwfLnaAvVqa/wcIq+r0Ieo60rQ5PN3mGcBI6X824iJZIUQoifwHWANzJZSTiuIcQucg3NU\n6vu2rzzsmWgeFYSAbh/B3O7KrnL2D+UWX9nyIGtfEuo8nv2+en8NP7WBKq1U7ryMbmBNR8Le/6l0\nOzW6pq+R7J0Ou75S5/b6QvUVfRP2/6Ru2Na2EHNLaVJ9vk/fXpQWsxnMSQUbVxYfpbYcr/sr7c27\no6rUmpKYEJWR/NyfYFcSXtydvfx22SUuAhYNVHOpP1B9hy6V8vVeY6iOKYRYJYRon6atvRBiRR77\ntQamA70AH2CIECL3EWWmODi+Qv1Q05J4RwW3pURK9cO4GZDz0sA5ndf+GVCj24NeQBpNfuLZUuU9\nO/uH0k46v5/7vsp4q9IDI9dlbiuxsVOlqm8FqDIPaYm9rewutXrCE98qASSEyl7deJh60j+3WVU1\nPbxQ/e1kRNBR+HUAfN8EPqkAn3spW1BKbh5XGkZkYK6WnSGJd1S27KCjKrM4qESpKTm3FX5qrWoQ\ndX5faYurxqvtTiNISlB2r9BzMHghDJilqtFu+RCOLDZunDQYHZHVERXFn5K9wJo89tsCOC+lvAgg\nhFgC9ANO5qiXxDvgN0+p2zG3lBo6bPn9m/mR32D9a2DnDM1GqtTywSfVE9S1/eqcMtWh3pMqYWEZ\n79T9X90Hl3dDQpTaVnCrCS3GZd/n/+hvKr1I21dztCyNxhC6TVVJN3t+ppKT5gWXStk7r94Alcdt\n+8cqkDSlVrHvJ+Wg8Ni/U2s3Vlbw5I/Q93/qvZSweBBs+0gJI7fqqceIC1c316R48GqntqjOb4Ml\nw5W7tFdb9be76BlIiFRZrcf8obYD0xJ+Ga7sgbp9wd456/UFHYNNb6v7x8C56qaeGKNKhp/5Q3nu\n7fpKrb+8j3J6qOCj3MZXjlXH0tqvckpcOCwbqQrnDZh9v2x4/5+Vo8eaF2HdK8pl3WCMThVzHagr\npYxK0VYKOC2lrJjxlVn2OxDoKaV8zvJ5BNBSSplhfd4HjPxn/lA1Ve4Eq/3fRkOVap54RxkMz22G\ng7OgalsV3Hh2kyqcBeDqqdRIa1s4sVrtR1vbKn//VhOUy+fWKcowD2Btp4RU3G2o0AD6/aBcSzPD\nnKw8cBxKwbjtRWtvWaPJC+e2qK2bnp9DqxdUW1yEqptTrQMMWph1H1E3YHor5R49cv19gSSlEi7n\nNqtksR7NVHtMCMzvrWwRHd9R9idXD2j/L3WfqNISRqxSGljEVVUy++Q6uHlMXV+7t5pXRo4GNwOU\n9nV6Pdi7whNf388lmJSoigeaYsHDF06sUltWfX9Qxfnusmq82mkZ80f27WlpCT2vKqaGX1FF/hoP\nTX08IQZOroGw83D7EmLQgsLlRZaqMyHmAo7A81LKKCGECyoQM0lKOSoP/WZLwAghxgPjAWpVLtvs\nzPFDyiC5+QPwm6Nu9r2/VPXUQanCi56B4BPqc+uXoet/lJE04iocXaoipRsMTK2FRN2AjW+pH497\nY/VEEnYeWr4IXd6/Hxh5aj1seFNpJS2fV9Ud0+aiklIFqR36FfZNV6WE6+WhJLJGU9SQEn59Umn/\nA+cqt+i//ws7PslZiYpDv8K6l9UWWquX1EPavhnwxzvpV4KNCoJ5vSD8kiqxMHyV+vs8thxWPafs\nQskmZTNBKqFTt496KP3rM+j8AXR868F53DgMc7qruJ/WL6nicmm1ocu7lYBDQNfJ0Pa1Bx8q4yNh\nRjuIDYde09S2YHoPnn7z1IOvg6sKXrUroWxM5iQVS2dlDYMWQdXWWX6Fhc5NOVVnQpQGFgI9gNtA\nGWATMEJKGZGHflsDU6SUPSyf3wWQUn6W0TW+layl33hnpUkkxiijZZcPH9wTjo9U2ke1TuqHnV2k\nVP+pG99S2wn9pkO1jg+eFxehvF4OLQBre2g+VqnxwafUnuyV3UrtBqjZA4b8lj1DpUZTnIiPVBVJ\nA/3UQ+DW/0DVNurvIbtIqQzpF7YpI3mFesp2WrMbDF6c/s054hocWQStXlQ36Lvs/lb93ZbyhMbD\nofGQ1AXiVo1XNqBhy1X/99YRBT93ULsa4//OPLnp4YVqm75654zPibgKq19U94navZUreco+/efD\n769avPqsIT4CEmPVPcTKRm0X9v/5we38DCjUAuZep0K4A5WBa1LKdCzpOe7PBjgLPAZcBw4CQ6WU\nJzK6xrdRfek34yV1E2885P6+o9EkxloC2rIoVBZ6HnZ+AceX3d96c3JTJX5r9VQvF/f8maNGUxRI\niFE1cy7vUp/H7QCPpjnsIxoCViqD/c0A9RQ/bHnuShncvqRKfqe3DZYYq7zuIq6qrTLvDvcFT8AK\nFdtTtU3Ox0wPs1ntbmybqrSi9m8orejsJlg+Wmlagxcb4hVXqAWMECJDrzQp795Vc93348C3KDfl\nuVLKTzI7v9AGWt6+qDw5KtRXhlBta9Fo7pMYC2tfUts8/aY/7NlkTvhlmNcbogKVgKncAnZ9qbzA\n0ov9ySshZ9R2/7nNKo9czC1lUxqxOrXtJg8UdgFjJoOofillge77FFoBo9Foig+mOGUD2f21srV6\ntYdn1+bvNvfFv9W2vhDKbpSet1suKewCJq2fmzswCfhdSplRpuV8QQsYjUZTYCTegVO/qxi2Em4F\nM2Y+lAYvjKli7iGlvJKm6YoQYiTKZlKgAkaj0WgKDLsS0GhwwY5ZBLbXCyJbnAuQwzqxGo1Goynq\nGKrBCCF+JbUNxgnogHJd1mg0Gs0jhNE2mMlpmu4AR6SUW9M7Pz8RQoQAabfsCoKyQOhDGPdhotf8\naKDXXPypLaU0rIRusS049rAQQvgZaSQrCug1PxroNRd/jF6vITYYIcT3aT6PTfN5pRHjaDQajabo\nYJSRf1Saz1+k+dwNjUaj0TxSGCVg0vrLFX7/ufxj5sOewENAr/nRQK+5+GPoeg2xwQghoqSULik+\n35ZSlsnouEaj0WiKP0a5KdsIITpzX3NJ+1mnB9ZoNJpHDKO2yIKBuaho/TlAWJrPwQaNU2gRQvQU\nQpwRQpwXQkzK+oqigRCiihBihxDipBDihBDiVUt7GSHEFiHEOcu/pVNc867lezgjhOjx8GafN4QQ\n1kKIw0KI9ZbPxXrNQohSQogVQojTQohTQojWj8CaX7f8rgOEEL8JIRyK25qFEHOFEMFCiIAUbTle\noxCimRDiuOXY90JkI5WAlFK/8vhCaWgXgGqAHXAU8HnY8zJobe5AU8v7kqiyCT7Af4FJlvZJwOeW\n9z6W9dsD3pbvxfphryOXa38DWAyst3wu1msGfgGes7y3A0oV5zUDHsAlwNHyeRnKYalYrRkV7N4U\nCEjRluM1AgeAVqidqU1Ar6zGLohUMY8CLYDzUsqLUspEYAmQg+plhRcpZZCU8pDlfTRwCvWH2Q91\nQ8Ly790ynP2AJVLKBCnlJeA86vspUgghKgO9gdkpmovtmoUQrqgb0RwAKWWiVEUCi+2aLdgAjpaa\nU07ADYrZmqWUO1EFIFOSozVaany5SCn3SSVtFqS4JkMMTRVTrJjiagt8DkQDPzMl8kYmZ3sA11J8\nDgRa5uPsHgpCCC+gCbAfqCClDLIcuglUsLz3APaluCzQ0lbU+BZ4G6W13aU4r9kbCAHmCSEaAf7A\nqxTjNUsprwshvgSuAnHAZinlZiFEsV1zCnK6RpPlfdr2TNEaTHoo4bIUeB34ELjCFNelTHGt+XAn\n9vAQQjgDK4HXpJRRKY9ZnmiKTUoIIcQTQLCU0j+jc4rbmlEPm02Bn6SUTVBpnlLZEovbmi12h34o\n4VoJKCGEGJ7ynOK25vTIzzVqAZOW+8KlP+oJribwHdATWMwU1/QMW9eBKik+V7a0FQuEELYo4bJI\nSrnK0nzLojbfLZF915GjOHwXbYG+QojLqO3OLkKIhRTvNQcCgVLK/ZbPK1ACpzivuStwSUoZIqU0\nAauANhTvNd8lp2u8bnmftj1TtIB5kF+5K1ymRH7PlMgLTIn8F/AW4At0TnX2FFfRzN3qIFBTCOEt\nhLADBgPrCnje+YLFU2QOcEpK+XWKQ+uAkZb3I4G1KdoHCyHshRDeKAF9oKDmawRSynellJWllF6o\n/8vtUsrhFO813wSuCSFqW5oeA05SjNeM2hprJYRwsvzOH0PZGIvzmu+SozVattOihBCtLN/Vsymu\nyZiH7eFQ4K/JLiXkZJfucrLLv+VkF680x+rLyS5STnaZms51DnKyy0052eXPFG22crLLZjnZZQHw\nOMrD6gLwvpzs0ktOdhn10NebxxfQDqU+HwOOWF6PA27ANuAcsBUok+Ka9y3fwxmy4WlSmF9AJ+57\nkRXrNQONAT/L//UaoPQjsOb/AKeBANTDpX1xWzPwGxDEfTvK2NysEfWAHWA59j8sgfqZvR6dbMrK\nfjIddcOwtbQuZUrk4BTnfAG8BlTyil9cA5iHcmN84/K03qeY4joJ+AxoypTIw0xx/RxlCAboxJTI\nvy39uKP+c0pyVxPSaDSaR4wC2SJLL9AnzXFhCdw5L4Q4JoRomuJY3gMYp7g+jfKKaQZ8jbKnTAcG\nMsW1suUcG2C4WbLBK37xC8AulNtia+CY16QNX/+U1Gcxyqvsbaa49kAJl3mop4IvUthnpqGehLYC\n3zHFdUSu5q3RaDRFmIKywcxH3dQzohdqr68mMB74CVQkNUoQ9EIFAA0RQvhke9QprlZMcf0WWBYv\nbS/0TJj2p1f84jpe8Ytf6pkwrYaUCOBFy9ndgIrvJI2vAUxFGXcbWOY0D3jt86Qhm0Ok62/AM8Ai\nk7Q+7RM/13uaaXAI0Bx4mimurVH7k18DfVBq6DymuPbN9rw1Go2mGFBgW2SWGIr1Usr66Rz7GfhL\nSvmb5fMZ1FaWFzBFStnD0v4ugJTys2wNqjSHBQfMtXcNS3yvqQlbgQocMgMVZtp+VbGj1bE79sJU\nPkY6LEnGqrdvwoxkEzbjLk/rvSBlV16TNnQA1lYiNP4f+1fKSkTS44mfRpyWVV2tMNtusXsr2VME\n37IVySFJ0sqjecKPq8NxcagjrizdZPfuR0JQF2jIlMhLOf/2NBqNpuiRbQ1GCFFHCPGhEGJ6is8N\nDZpHeoGKHpm0Z80U1xImaf3lWbNHzKDED9ubsN0F+Fye1rvR5Wm9mwB1VyR3OGwvTM6LkrpstCWp\nz9rktmYTNr3SCheAy9N67wTa36Cs+VXThMRnTZPEaVk1EWhjxqrHJ0nDTLYi2RNo9obpxQrhuDwH\nDDwtq/7RMfGbMgnS1vamLL2x9qTVbbwmbXDNzZek0Wg0RYlsaTBCiKdRW1WrgKFSShchhC8wTUrZ\nNVsDZa7BrLf0tdvyeRvwDkqD6SmlfM7SPgJoKaV8OYMxxgPjhX0JK2frpCa1XE1cFh6Uci1FKSe7\nB86XEpJuncTGnIhAklCqJvZOzpmuw5Rs5nJoLNZWAk83J2yslNklwWQmMfQCSMmdEp64OdtjbQWR\ncS+PSqAAACAASURBVCZu30nEPjGCyiKEIOlGGK6UdLCllJMtDrbWxCQkEROfBEBVN6fsfJ0ajUZj\nOP7+/qFSynJG9ZfdVDFTgW5SyqNCiEGWtqNAI4PmkVFwj20G7ekipZzpNWnDgUqEboxf8Bxz3+pD\nlfHLKF3iQeFy7xr/XxC/v0JimdrYTdwP2UwQml4i0fjEJKQER/sHv9YEUxJJi4bgcPUvZtb9ljln\n7AmNScBkOV6lhB237yTy5ejmdKpdPss5aDQajdEIIa4Y2V92BUx5lG883E8pYGR6gXXAy0KIJagc\nXpFSyiAhRAiWAEaUYBkMDM2irwsf2c5LfkdAw5HfQCbCBUA0fAb2/Yhd6wnZEi5AusIFwMEu46/T\n3tYG+4HT4cdWvHjpFZ73bkagbVXCzCXxto+ipCmUJadMLNxXXgsYjUZTLMiugPEHRqAyaN5lMNmM\nYhVC/IYy2pcVQgQCk7HEokgpZwAbUcF754FYYLTlWJIQ4mXgT1RK/LlSyhOZjXXZYWhNoDIlykEZ\n76wnZ+sIE/ZnfZ4ROJeHIUtg73SsQs/iGbodT7MJbJ3A1pFhMoxvTvcmMLwelUvrrTKNRlO0ya6A\neQXYLIQYi0oI9ydQC+ienYullEOyOC6BCRkc24gSQNnlDPAeJSt8moNrCo4qLdQLIDkJTHfA3gUu\n74ZfnqCeuMxvB67yVo86D3eeGo1Gk0ey5UUmpTwN1EEZ+j9AxYU0kFKey8e55Y4pkXeYEvkZoghU\naba2AQdXtTVXsQEAfSuEsfTgNRKTzA95chqNRpM3siVghBAegL2UcpmU8gsp5RLAVghRKX+n9wjh\nWApKVaV9yRuExiTyx4mbD3tGGo1GkyeyGwezhtSpmrF8Xm3sdB5x3BtSLub0/9s77/CoirWB/950\nEgKBNAih9wCBQGgCKlUEFSwICGLD3vW791qvvV299oJeRESkWhBFBKQIogJBeg89AZKQQAqQtjvf\nH7OBEFJOwm7q/J5nn5w9OzPnnU1y3jPzNpoG+jL9T6c6cxgMBkO5Y1XBtFFKbcl/wvHeGAqcScPO\nSMo+xkYGsPZACqmnc0ruYzAYDJUUqwomSURa5T/heJ/sfJFqMA10WFH3WjrUJzYpvSKlMRgMNYjM\nHBtuterUc+aYVhXMFOBbEblKRCJE5Gp0xbvJzhSmxtNQZ95pkbsPgD0JGRUpjcFgqCEs3ZHAkHdW\n4lE3pEWzJxY4K4Despvy6+hiNW+hI+sPo5XL28V1MpQS/wbgF0JA6nZ8PFuzJ9EoGEPZmbxqH5+u\n3MfgiFBGdQunS+OAIoOEDdbIzLGxeHsCHcPq0CK4+LRSlZW/9iXz+e/78ff2ILC2F7GJGSzflUSr\nkNrknDi6+8Drwzc561qWFIxSyg686XgZXEnDzsixLbQKGWcUjKFMKKV445ddTPptLxEN6/Dd33HM\nWHOItqH+vDkqksjwgIoWsUqy81gaD8/cyK4EvXXdu0Ug43o14YoODfB0d17lk5W7k/B0d6N3y0Cn\njZnHrmPpTPwyBm8PN3w83TmekYWXuxtPDWvHrZc0x/vxU07dl7e6gsFRq7szcJ7aVkpNcaZANZ6G\nkbBvOe1be/HHQaNgDCWTmWNjd0I6giACX/15kNkxhxnXswkvjujI6excFmw+ygfLYrnhkz95/poO\njO3R+LzVTFJ6FrPWHuKXbceo5elOsL83oXV8uKFbOB0bFZ3822ZXuEnR6ZOqA0oppqw+wBsLd1Kn\nlicf3hTFweTTzFhziAdmbCCsrg939GvBmO6N8SskD6FV7HbFO7/u5oNlsQAMjgjlmeHtaRroR2Ja\nJusOnMCuFD2b1yekjk+px09My+T2qevw83Zn3v19aFi3lqO0Mbi5ueb3ZzWb8lPAv9EJLk/n+0gp\npQa4RLKLJDo6WsXExFS0GKVn2zyYewtzun7FP/9wZ+sLV1D7Iv5oDdWX2MQMZq49xDfr40g9c77H\n4UMDWvHo4Dbn3fhTTmXz8KwNrNpznOGRDWkZXJsz2bnEnTjDrzsSyLEpujerh4ebG0kZWcSfOMOZ\nHBvDOjXgscFtaBXiD0Cuzc7KPUl8uz6eJTsSCK7tTb/WQfRtHcSg9qH4eFaBIOdS8MmKvbzxy04G\ntQ/h9esjCartDWjlunxnIp+t2sfa/SnU8fHggQGtuK1P80JXNAlpmTz9/VbO5OTSMawuEWF1aB7k\nR2gdH2p5ufOPuZtYtC2BG6PDaRbkx4fLYsm1KRoG+HAw+fR5Y7UI9qNlcG2UUtjsCg93N+r7ehHg\n50nT+n5c1jaYRgG1zrY/eTqbCVPWsichg7n39C7yoUFE1iulop313VlVMInAIKXU5hIbVxKqrIJJ\n2QfvR7Gt20sMX92SH+7vQ+fGZkvDcI71B0/wwbI9rNiVhKe7MKRDA4Z3aoiXuxs2pQiq7UW3pvUL\n7WuzK977dTcfrdiLza6o5elO3VqeDOvUkPG9mpxnV0jLzGHyyn18/vt+TmXb8PJww8NNsNkVWbl2\n6vl6cmWnhiRnZPHH3mTSM3Pp1aI+U2/rUSFKJtdm58PlsayOPU7/diFc0zms0Jx+6Zk57DyWfnbu\n9fy8inyIW7ojgYnTYhjeqSEfjI0qcqW24dAJ3l+6h+W7kmgb6s8r13Ykutm538Gmwye566sY0jNz\naRHsx+5jGWTbzs/W4Sbw9PAIbu/TDBEhIS2Td3/dQ3JGFj2a16d7s/qIaBvKX/tSOHLyDG4iuLsJ\n2bl2TpzO5sTpbHJs+p7eroE/zYP82HE0jQPJpxGB/90czaCI0CK/w4pSMAeB1kqpbGdd2NVUWQVj\nt8MbTUltPZLOMUN5a1RnbuhWMMbVUBPZdPgkby7axe+xx6nn68ntfZozpkcTgv29Sz1Wdq4dDzex\ntDWSnJHFnBi9Ssq12bEr6NmiPv3bhuDloZ/Uc212vvs7nn99t5n+bUOYNL7b2c/yyLHZ2Z2QTniA\nL3V9PUstc3HEnzzDI7M2sO7ACVoG+7E36RQAkeF1aRVSm2aBfnh5uLFydxJr96eQaz//vtekvi+R\n4XXpHB5A39ZBtGvgT2xiBtd+/AfNgnyZe/cl1PIqXmkqpVi8PYEX5m/jSGom7Rr40zk8gAZ1fZj0\n216Cansz+ZZo2jesQ3aundjEDOJPniEhLZOk9CwuaRlIzxYXZ3dRSrE36RTLdyaydGcCR05mEtGw\nDh0b1aFPqyCimhTvhVxRCmYC0Ad4HkjI/5nDAaDSUWUVDMAXw1G5mbQ98H/c1rcZT17ZvqIlMriA\n1DM52O3qvHpFSimm/XmQTXEnGd6pIZe2CeZUVi5v/LKLWesOEejnxV2XtmBcz6YXtd/vKr5ec5Cn\nv9/KVZENeXhga7YfTWPbkTQ2HjrJ5viTZObolc9r13ViaMeGTrnm0h0JPDZnEza74pVrOzKiSyMO\np5xm/qYj/L7nOAeST3E0NROANqG16d8uhJ7N65Odq0jLzCEpPYut8alsjksl/uQZAEIcStuuYP4D\nfQjLt91UEqezc5n6xwHW7EthU9xJTp7OoXuzekwa343A2qV/GChPKkrB5CmR/I0FbYOplBuuVVrB\n/PIkxHzBlX6zaFTfj8m3dK9oiQxOJik9i2s/Xk3q6RxeHNmBkV0aYbMrnv1hKzPXHqaWpztncmwE\n+nlhV4q0zFxu6d2MRwe3xt/HuU//zubT3/by2sKdZ997ubsREVaHrk3qERFWh6l/7GdrfBrXdw3n\nuWsiqFPG+Sil+HTlPt74ZScRDevw0U1daRbkV2jbzBwbGVm5Z+0nRXEsNZOVe5JYuTuJ7UfTePOG\nznRrWvbYQ6UUielZBNf2dpkh3Zk4W8FYfQSyUFjF4DQCmkLuGToFKdYcM55k1Y0z2TYmfrmO5Ixs\n2jTw59HZm/h1RyKnsnJZsSuJB/q34qGBrVm5O4nvNsSRlWPn8SFtiQirU9GiW+Luy1rSPMiPtMxc\nOoTVoVVI7fOM3td0DuODZXv4aHks246kMvPOXsVWnS2MzBwbT323he82xHNVZEPevKFzsVtYPp7u\nluxCDer6cGN0Y26MblxiWyuICKFl8PiqLliNgzGZF8sTvyAAOtTNZu72XDJzbNXOM6emYrMrHp61\ngc3xqXw6vhsD24cy6be9vLNkNwp49dpO3NSzCQCDIkKLNchWZoZ0aFDkZ14ebjw+pC3dm9Vn4rQY\nxn++hhkTe1m2y2Tm2Jj4ZQy/xx7nscFteHBAq2rtJl2VKU0czDXAZUAQensMAKXUBIv9hwLvoStT\nTlZKvV7g838A4/LJ1R4IVkqliMgBIB2wAbnOXMJVSny1oa9N7SyUcmdvUgYdwoqORTBUDWITM3j3\n190s3p7Ac1dHnL0J39+/FYPah3Imx0aXGuQxeGmbYD67uRt3TVvPzVPW8NUdPalbq3glk2Oz88CM\nDfwee5w3b4hklJNWGgbXYLUezHPAp472o9BJLq8ATlrs744uVnYlEAGMFZGI/G0cdWa6KKW6AE8C\nvymlUvI16e/4vHorFzi7gmnqo33fY01Ef5Vm/cEUJkxZy6C3f2PxtgQeGtia2/qcv+vctoF/jVIu\neVzeNoRJN3dlx9E0JkxZe0E8T35sdsXjczbx644EXhzRwSiXKoDVFcztwGCl1FYRuU0p9aiIzERX\nt7RCDyBWKbUPQERmASOA7UW0HwvMtDh29cNXK5gQ93Tc3eoYBVOFOZxymps/X0ttbw8eH9yGsT2b\nlGhormkMaBfKx+O6cd/X6xk3+S+m39GTAF9tk9kSl8rvscfZdSyNrUfSiE3M4J9D2zKhd7OKFbo6\nohS1vbgwcOgisKpgApRSWx3H2SLiqZRaKyKXWezfCJ0gM484oGdhDUXEFxgKPJDvtAJ+FREb8KlS\n6jOL162aOLbIPM6k0DSwtcmqXEVRSvHU91sQ4Lv7Lik06M+gGRwRymc3R3P39PWM/d8aJvZtztdr\nDvL3Ib1JElbXhzYN/LmtTzPG9WxawdJWU359jraBbu15vm4Xnk/d6IwhrSqYvSLSQSm1DdgK3Csi\nJ4ATzhCiAFcDqwtsj/VVSsWLSAiwRER2KqVWFuwoIncBdwE0adLEBaKVEx5e4F0XTh+ndUht9iRW\nTF2YLXGphNTxrtZeMEopNselYlOK4NreBNX2LjGgzipzYg6zas9xXhrZ0SgXC/RvF8LkCdHcOS2G\nx+duolmgL89dHcHILo1K7WVmKCV/fgyr3yPljEpCpwRzClYVzDNAXojpE8AMdNLL+y32j0en+c8j\n3HGuMMZQYHtMKRXv+JkoIt+jt9wuUDCOlc1noONgLMpWOfELhFPHaR3iz687EsnOtV8QGe1Klu1M\n4I4vY3ATYVD7EG7q2ZR+rYKqhC+/VZRSvLV4Fx8t33v2nAiM6BzGP4a2o1FALWx2xbwN8Xy2ch/J\np7LPtukYVocrOzZkcEQo9fy8UEqnT/Fyd8PNTTiaeoaXf9pBrxb1GdejAh92lNICVxEubRPMt/de\nQsqpbPpWs7+3SoMtB47vhrrh4FMXtnwDi56E9tew/+T0Qzyf6rR7p1U35Z/zHa8FWhXTvDDWAa1F\npDlasYwBbirYSETqoj3Vxuc75we4KaXSHcdDgBdLef2qh2+QXsG0ro3Nrth//BRtG/iXy6X3JKTz\n0MyNdAirQ99WwcyJOcyibQk8OqgNDw9qXS4yuBqlFG8v2c1Hy/dyY3Q4Qzs24Hh6NjuPpTN9zUEW\nbj3G2B5NWB17nD2JGXQIq8OQDtplOCfXzh97k1m+azPu3ws+Hm6cybFhV+DuJtTz9QIUOXY7b1wf\nWXE3yZ0L4KdHYeQn0GpgxchQBorL3mxwAqvfg2Uv6WO/EDiTAk37wnX/A6Y79VKWFIyIpCilLsie\nJyKJSqmQkvorpXJF5AFgEdpNeYpSapuI3OP4fJKj6bXAYqXUqXzdQ4HvHX7uHsAMpdQvVuSu0vgF\nwYmDZ5XKroT0clEwJ09nM3FaDD6e7nx2czRhAbV4dHBr7pgaw8y1h3hwQKtq8VT57q97+GBZLKOj\nG/PadZ3Om9PtfZvx5qJdTP3jAC2C/fh4XFeGdmhwXhulFFvj01iyI4FTWbn4eulAvjPZNpJPZZGc\nkc313cJpGlh4ZLnLsdth6UuQkQAzRsP1k6HDyIqRxVC52PY9hHaCTtfD8Vi9wr3iFfB0/la41S2y\nC5zTRcQTrSws4VgF/Vzg3KQC76cCUwuc24euQ1Oz8A2E+PW0CKqNh5uw61gadA5z6SUzc2zcP+Nv\njp7MZOZdvc7mX/L2cGd098Y8OHMDf+1P5pKWQS6Vw9X8svUY7y3dw6hu4RcoF4Dwer68NyaKf18V\nQd1anngUknpdROgUXpdO4ZX0aXv3L5C0A4a9BVvmwje3QVYadLUUtmYoipOH4ed/wGX/gEbdKlqa\n0pO8FxK2whWvQe/7XH65YhWMiKxCe3D5iEhBm0c48IerBKvx+AXB6WS83IXmQX7scnHKmNPZudz9\n1XpWxybz31EX5l8a1D6U2t4ezNsQX6UVzJlsGy/9tJ12DfwLVS75qeyJCYtEKVj1X51yqNtt0OUm\nmDMB5j8IQW2gSa+KlrBqkn0KZo6FhC36Jn33SvAtvCxCpWXHfP2z/dXlcrmSrMaTgSlALvB5vtdk\n4F7gOpdKV5PxDQJ7LmSepE0Df3YnFO1Jdiorl5lrD5GZYyvTpdIyc7hlylpWxx7nrVGdub6Q8gC1\nvNwZ2rEBC7ccK/N1KgMfr4gl/uQZXhzRsdCVSbXgwCqIj4E+D4O7B3j5wY3ToHYoLHlOK6CisBUd\n6Fijsdvh+3sgcRsM/DekH4MfHij+uywrK9+C9VOdPy7Ajh8hrCsElE+QarH/YUqpLx3bVlGO47zX\nNKXUIqWU+Wt0FY5ofk4l0y7Un0MppzmdnVto04+Wx/Lkd1t4eUFRcatFk5GVy82T17Dh0Ek+GNu1\n2Noz10Y1Ij0rl6U7Ekt9ncrAgeOn+PS3fYzsEkaP5lXsybM40o/B31/p7Q+AVW9rZdJl3Lk2Xn5w\n2b/g8F+we1Hh42yaBa80hC+GwcaZkH268HY1kd9e10//g1+Cfo/D4Bdg1wJY86lzr5OwTRvgFzwO\niTtLbl8aUuMgfn25rV7AYqoYIEpE2gOISFsR+U1ElotIOxfKVrNxRPNz+jhtHMb93YUEXKaeyeGr\nPw9Sx8eD6X8dYuGWo5YvYbMrHpq5ga1H0pg0vhvDI4uvz9GrRSChdbz5fkNRHuaVmxd/2o6nu/DU\nsGpUX+fMCZg2AuY/AB90hXc7wb7l0Pv+C422XSdA/Raw9AWwF1iFbpiun9AbdIT0ozDvHvhvO20Q\nrukc2Qi/vaEVdm9HZEav+6DNUFj8DGye67yVzG//AS9/8PbXSsaZK6QdP+mf7a9x3pglYFXBvAzk\nBT6+hXY7/g342BVCGdBxMACnjtM21KFgjl24TTbtjwOkZ+UyfWJPOjcO4J/fbuZwirUnz1cW7GDZ\nzkReuKaDpay97m7CiC6NWLErkZRTVaa4KQC/7U5i2c5EHhnUhpDqEjiamwWzxuuVy/Wfw5VvQkgE\nNIrWtpeCuHvCgGcgcbs2/Oexfir8cD+07A+3LYQH/4ZbF0BwW5h7G6wpInFG3Hptk9j6nUumV2nY\nMhfcPOGKV8/FFIlo9+/QCPhuInw+GA6vK36c7NMwqR/MGgdphTwIJu6A7T9Az7tg4HNw8HfYPKf4\nMe027Yr+biTMvhlWv69XQYWxY77++wgqbZRJ2bGqYIKVUgki4gP0BZ5Gx6J0cZlkNZ18K5jG9X3x\n8XRjVwE7zKmsXD5fvZ+B7UKIDA/ggzFRoOChWRvIsRVfaHT6XweZsno/t/dpzvhe1lNvjOzSiFy7\nYsHmI6WeUkWhlOKtRbsIr1eLWy5pVtHiOAe7Hebdp29CIz+GTjfoG9NNs+HOpeBTRO2YiGuhYWf4\n9Xn4ehS81QZ+fBhaD4ExM8Gzlr55NusLt8yHtsNg4T9g6YuQGq9XTKnx+tqTB+jttm9uh3WTy3X6\nxVJwdXZRY9m1Am01CGoVSEbqWx/uXA4jPoKTh+DzQTrGpChW/ReObYY9S+CjnvD3tPNXKCvf1FuZ\nvR+ArrdoL7XFT0PaER0MOftmbfdJTzg3z+/vgZgpUL85HN0ES56FSX21i3p+e1pGIhz8o1xXL2Dd\nTTlJRFoBnYB1SqksR86wqh8QUVk5a4M5jrub0DrkQkP/jDWHOHk6h/sH6CeSJoG+vHZ9Jx6YsYF3\nf93NP644fwfTblesij3O1NX7Wb4riQHtQnh6eOm2i9o39KdDWB2mrD7A2B5NqoShfPH2BLbEp/Lm\nDZHlmg3Bpax+B7Z+ow3OkTda7+fmBkNe1rExqfHQcoC+kXWdAB4FvOY8a2nngAWP6Zvjqv/mG8dT\nOxH0flB7py14XCuffv9XsZkDlr+qV2S3/uycJ/XDayD9CAwuIrbbzR2ixkPESL1NueTfOsQgavz5\n7ZL3wh/vQ6cb4fIn9Hc2/0FY9zlc8iCEtNeKrO8j5zzThr8N/+sPbzv+R2s30EGRO+bDoBe0wtgy\nR69KL/2HbpOeoB8GVr0Fe5fC5U9CcizsWQyocrW/gHUF8xKwHl2PZbTj3CCcmLPGUADPWuDpB6eT\nAZ3O/bfdSWc/zsyx8dmqfVzSMpCuTc65FF8VGcbK3Ul8vGIv/VoH06uF3mrbeSyNB2dsYE9iBkG1\nvXloYGvuuawF7qUMmhQRHhzQmnumr2f+piNc17Vop4DKgN2ueHvxbloE+XFtVKOKFsc5JO6A5a/p\nm1rfx0rfv/ml8LRFW527B1z9HrS7St9os0+DLVu/z7uBj/5Kb7Etexl8AqDHnaWXyRkc3aw9sJQN\nZo6Gib9CrbKXOwZg67fgUQvaXll8O+/acO1ncOYkzH9IK5m8PkrBL0+AuzcMeQn8G8AtP8GmGfD7\nO/DtHeDmAZ6+WmHnEdYFhr4ByXv077pJb0jZBz89ol9wvnIB8A+FkR9B68F6ZTrD8fBRt7FWZKEd\nLu77KCVWU8VMFZE5juO8Df6/0ClfDK7CkY8MoG2oP9+sjyPlVDb1/byYE3OYpPQs3ht94S7lc1d3\nYN2BEzw6eyMLH+7H1vg07p2+Hl9vd94Z3ZlhnRri7VH2hI5DIkJp37AOHyyL5ZrOYZV6FfPTlqPs\nSkjn/bFRlVpOy9ht+mbuUweG/7d8Vgsi0GZI0Z+7e8LISXorZ+Vbha+GXI3dBj8+pJ/+r35fx/3M\nuQXGf6vlu6C9Xa/misOWC9vnQZsrtAIpCQ8vrWy/vBrm3qqVf/N+entqz2Jtw/F3VPp0c9OrnM43\n6aDYdZO1UsizvebR867z3we1glt+1HYhW/aFK6U8OoyEppdopdug47nrljNFKhgREaX0BqGIuAGZ\n+Y4BjrtevBqOIx8ZkM+TLJ0ujQP4aHks3ZvVo3fLwAu6+Xl78N6YLlz38R+M/3wNO4+m0yqkNlNu\n7X42Ov9icHMTHh6oVzE/bj7CtVHOXcVM+m0vCzYfJbpZPS5rE0zP5oFlynCca7Pz7pLdtA3156pO\nxXvIVSpOHIRTSRBeSG29vz7WrqbXf35uG7Uy4OYG/R6Dr66FzbOLzhiQZ3NwtmJc+z84skF/L+2G\n6VXXD/fp1UT/JyHAkXA0fj2s/C/sXqhXJrUCtN3DlqOdJjx9tOJuOUDHE51Kgo7XW5fD2x/GOewl\nK16DFa/q88HtocddF7Z3c9Pythtm/Roi1rZFa4dA60HWx3UBxa1gUoE8S2EuOqI/P+I4Z4rFuwq/\nIB3jAOc8yRLS2XE0jYS0LN65sUuRtcgjwwP4vyva8vrCnfRtFcTH47tSx8dazXMrnF3FLI3l6kjn\nrWI+WbGXN37ZSeuQ2sxYc4gvVh/A18udazqHMaZHEzqH1yUxPYstcansO55BRmYu6Vk6Pqhb03r0\nbhGIn7cH3/0dz+RV+9h3/BSf3dytcuZPm/8gZCTB2Jnnbri2HPj6Br1vfsMU6HDtufbHY/U2VJsr\nS3fTKy9a9IcGkdrQ3WWctk/k53QKTLsGmvaBK99w3nVT43TsSMuB576XqHGQslfbjTbN0Dd430Dt\nFOETAD3u1vJlnoSsDL3K8fCGuBjt/HD1e9r+4uWvVxalwS8Ibl+o53voT4hbp+UqbCVVzSlOweTf\nrGteZCuD6/ANOutyGFrHmzo+Hmw8fJJVe47Ts3n9Qlcv+bmrXwu6NqlHl8YBTjduu2IV8+UfB3jj\nl51c0zmMd0Z3IcdmZ83+FBZsPsIPG48wa91h/L09zioU0Pfl2l4e5NoVX6w+AICflzunsm10alSX\nT8Z1ZUiHitkeKJbs09oFNTdTP/F3duw2x0zRqdTrNYdvJ4K7l/bk2vKN9uby8Iar3q6cKfhFoO+j\nOu/ZzgUQkc9jKTdLu+ce26L/prvdBiFOCqNb9LTeIiv4vQz8N3Qeq7endi/Snl6DXoDud+iVRmFk\npunttR/u144MHa/T9tCy4Fsf2g3XrxqKKFekOqgEREdHq5iYmIoW4+JY/IyOQXgmAUS4cdKfxBxM\nwa5g1l29zhrwKwq7XXHle6vw8nDjxwf7XtRYP2yM5+FZGxkcEcrH47riWWBFlJ6Zw/xNR9gan0rb\nUH86NqpLmwb++Ht7ICLk2uxsiU/lj73JHEw+xcgujejdMrDIFV6Fs/NnmDVWp0tXdnjAEUPxfpR2\nIx49XW83Hd2k99L3/wbh3WHExxDcpmJlLw67DT7opo3rdy7TN3yl4Ls7td1g2Fvw6ws65mb0Vxd/\nvQOrYeowuPwpuPxfFz8e6FXkj4/Axukw/rsqVergYhGR9UqpQvZmy0ZxNpivuHBb7AKUUiY9q6vw\nDQJbFmRngLc/bRrUZu2BFC5pGVjhygX0Kuamnk14bv42tsanlrmOR8qpbP79wza6Na3HhzdFXaBc\nAPx9PIstlevh7kZUk3pENblIr6HyYtfPumrpTbNh8iAdXe/hozMeX/GqNuKP/1ZvKR36S7vJTHo7\npwAAIABJREFU9n7gwm2nyoabO/R5SAf/LXlWF7RK2qWVy4BntYfZqeM69cqRDRAWVfZr2W3aO6tO\nuPaQchbunjDiQ50xuV4z541bAylu3yQW2Ot4pQIj0faWOEe/EcBJVwtYo8kXCwPQMUzfwB8dXHme\nYEd2aYS3hxuz1x0u8xhvLtpFRlYur17b6aK826oMdpv2HGo9CBp1hV736tiNtf/TAXYNOup2tQLg\n9sXwyBYdc1LZlUsenW/SRvU/PtA2oy1ztYG73+P689736xXOspcv7jobv9aBi4NfAC8nl6QWMcrF\nCRS5glFKvZB3LCKLgOFKqVX5zvUFnnWteDWcs9H8yVC/Odd1DadTeF06hFWeGiR1fT0Z1qkh8zbG\n89Sw9qX29tocd5JZ6w5xe5/m5Vaxs8KJX6+9k9o6PIcufxK2zdOrl/5Pn9/W08clhaBciqePTjdj\ny9Y2JDeP820jPnW0C++SZ/UWV7M+pb9GZpoOKGzcs3I6PBgA66lieqHjXvKzBuht9UIiMlREdolI\nrIg8Ucjnl4tIqohsdLz+bbVvtaXACsbLw61SKZc8RndvTHpmLgtKkWgTtA3n2R+2EVTbm0eqSSlm\nS+z6Wd90WzlcSL1rw60/6TxgtYMrVjZn4e6p3X/dPQt3SOhxp45M/62M3mSr39NKeuhrldPhwQBY\nVzAbgFdFpBaA4+crwEYrnUXEHfgIuBKIAMaKSEQhTVcppbo4Xi+Wsm/1w9dhZzlduUOOejavT4sg\nP2avO1SqfnPXH2bT4ZM8Nawd/k50oa707PxZu+rmz21Vv/m5rbGagGct6Hm3dl5IKGWZiezTOjCx\n/dVVs6pkDcKqgrkV6AOkikgC2ibTF7Bq4O8BxCql9imlsoFZaBuOq/tWbQqsYCorIsLo7o1Zd+AE\nsYlFF0bLT3pmDm8u2kV003qM7FJNUrhYIXkvHN91bnusJtPtVu3YsLaUNVU2z9bxKz3vdYlYBudh\nScEopQ4opS4BWgLXAK2UUpcopQ5YvE4jIL8VOM5xriCXiMhmEVkoInlxOFb7IiJ3iUiMiMQkJSUV\n1qRq4VVb5y+q5CsYgOu6huPhJnz150FL7T9ZsZfjGdk8e1VE5XUldgW7FuqfJeW2qgn41tcR6Ztm\n66BEKyili3w16KTdtw2VmlJF3ymlDiul1iilSrcXYo2/gSZKqUjgA2BeaQdQSn2mlIpWSkUHB1eD\nvWwRvYo5lVzRkpRIsL83o6LD+eqvg8QcKP5mcTjlNJN/3891UY3o3Dig2LbVgs1zYdpIeK+zzrYb\n2hHqWS+RUK3pcTfknoENFmNi9v8GSTv06qUmPZhUUcor+188kL8IdLjj3FmUUmlKqQzH8c+Ap4gE\nWelbrfENrLgVTMI2Hf1skaeGtScsoBaPztlIembR1bT/s2gXbgL/GNrWGVJWbs6c1GncU/bpWuh9\nH9X1QwyaBh2hWT/tom0rvCT4efw1SXtXGs+xKkF5KZh1QGsRaS4iXugszPPzNxCRBuLYKxGRHg7Z\nkq30rdb4BVWMDWb/Sl246N1O8GF3WPiEzgpbDP4+nrwzugvxJ87w4o+FG27XHzzBj5uOcNelLWlY\n9+ITb1Z6tszV6WBu/BJGfQEDn9Vp2A3n6Hk3pB7WCSiLI2Wfjh+Kvr3quW7XUMpFwSilcoEHgEXA\nDmCOUmqbiNwjIvc4mt0AbBWRTcD7wBilKbRvechdKciXUbncSDuiqxQGtoIrXtNBc+sm69Q1JdC9\nWX3uvbwlc9fHMXnVPo6lZgKQlJ7Fawt3MOHzNYT4e3P3pS1cPQtr2O06T1VWhmvG3/AVhHaChkap\nFEnbYfpvbOWbRa9istLhlyd1sGn3O8pXPkOZsVpwDBGpC7QFziuMoJRaZqW/Y9vr5wLnJuU7/hD4\n0GrfGoNVG4yV+hZWyM3WdTRyzpyry977PvjubtizSEehlxBR/vDANvy1L4WXF+zg5QU7aBRQi+MZ\nWeTY7FwVGcYjg1rj5235T8+1rPyPTqveoBOMnQ11S/BoU+ps6p4SObpZ5xK78j/GXlAcbu46CeU3\nt+lyBH0eOv/zo5tg7m1wYr+uxllBtU0MpcfSf7mI3IqORckATuf7SAGV5FG0muIbCDmntO9/Uekw\nDqzWKd5vmqMLHJUVpWDRkxC3FkZN1coljzZXwOZZOvV4k17FDuPl4cbsu3qx/Wga6w6cIOZACgG+\nntzZrwUtgi0Ubiovdv6slUuLyyFuPfxvANw068L8WDmZurZIXIwun2DL0tmAr3qneMWx4SvtBdhp\nlCtnUT3ocK3OGL38VZ19OLCl/ntc+5leOfsG6SqQZYn6N1QYVh95XwFuUEqFKqWa53sZ5eJqAhze\nRicOFN3m72mQc1pnrC2rvebEAZ1Ycd1knVQxfx0S0AWY3Dz0HrgFPNzdiAwP4I6+zflkfDdeuy6y\ncimX43vg+7v11tXYWXDHYh11/sUwOPD7+W1X/VeXzg2L0hUGO4+F9V/A728XPX5Opk7H3/7qczXW\nDUUjogt9uXvpUr+njsPMMbDwn/pv757fjXKpglhVMB7AYlcKYiiCvNTsx3cV/nnOGdj5k44MP50C\n8+49VzXQKjFT4ONLIH4DXPWu3oYoSK0AXRN896LSjV0ZyT4Fs27SCmX0dB1VHhoBE5dC3XC9RZga\np9sm7tB10yPHaEP9kJdh5Cd6VbL0Rf3UXRg7f9LBgF1vLr95VXXqNNQ16w+s0i7de5fp7cWxsy4s\nJWyoEljdCH8DeEZEXlJK2V0pkKEAga0B0SnPC2P3Im0TuPQfugriz/+n97F7329t/CMbdGr1FpfD\nNR9CQOOi27YZCouf1iV9q3Icx+bZuqjX+G/Pn69/KIz+Wm+Vzb4ZbvtZP017+8MVr5xrJ6JdjVPj\nYd59uvKhmyPnVnaGVvRxMXr12ezS8p9fVabrBF2s7OQhuO4zaBhZ0RIZLgKrCuZRoAHwTxE5z+Ks\nlGridKkM5/Dy1TfzohTM1m900arml2olsW8FLHlOH4d2KLxPfmKmgKcv3DhN1+4ojjwFs2exTlZY\nVVn/JYR00CV2CxLcBq6dBLPHwWf9dVDfyE/Ope3Jw8MbxnwNM0bDpll61ajs+vdVq77+nfW82zmO\nFzUJEb1iETGOEdUAqwpmvEulMBRPUNvCFUxmKuxerHM65Xl2XfMBfNAVFj0FN88r/p80M1Vv8XS8\nvmTlAhDUSrsu7/6l6iqYIxvh6Ea48s2iv5v2V0G//4NVb2nF3Xls4e1868PEJa6TtaZilHK1wZKC\nUUr95mpBDMUQ3Bb2LdcxAu75fmU7F2iPpk43nDvnWx8uewJ++RfsWQJthhQ97qbZ2jmgNHEFbYZq\nz56sDJ1mvqrx95c6wWJkCZ5d/Z/S22dthpon6TKSk5NDXFwcmZmZFS2KoQA+Pj6Eh4fj6enaLOZW\n3ZQ9gWeAm4Ew4AjwFfCKI8OxwZUEt9PFm04e1O6beWz9VgeohXc/v333O2Dd//R2Vsv+2phdEKX0\n9lhYVOnK1ra5Av78UG/Ftb+qTNOpMLJP6bxgHa7VFRWLw81drwwNZSYuLg5/f3+aNWtWsxKaVnKU\nUiQnJxMXF0fz5s1dei2ra9H/AIOAe4DOjp8D0MZ/g6vJi0dJ2nnu3KnjsHe53t4q+M/r7gmDX9KG\n7PVTCx/z0F/avhBdyqjoJr11Lflt35euX2Vg63eQna7LEhtcTmZmJoGBgUa5VDJEhMDAwHJZWVpV\nMKOAa5RSi5VSu5RSi4FrgRtdJ5rhLEEOV+X8CmbnT6BsRSf9a3ulTiK44jVt1N6/Unt/ZWU4Vi+f\na0XR8brSyeLuCVHjYPs87UVVlfj7S23PKiFQ1OA8jHKpnJTX78Wqkb8oacxfT3ngUwf8wyBp97lz\nu37R22OhRVRBFIGhr8PU4fBjgdQb4q6VU4+7dVnb0tLzblgzSReKGvxi6fuXROJO7T7deYzz7B8J\n23QWgiteNTaVGoS7uzudOnUiNzeX9u3b8+WXX+LrW0RGDIPTsapg5gI/isgLwCGgKdomM8dVghkK\nENz23Aom54y2gXSdUPzNskFH+Oc+HTR4Yr9ewWSe1N5jOZlwyYNlk6VeM2h/DcRMhUv/6Vxjf2Ya\nfD0KUg9BWjxc+n/OGXfd5zptS1EeYYZqSa1atdi4UVd2HzduHJMmTeKxxx67qDFtNhvu7sXn4zNo\nrG6R/RP4FZ2PbD06KeVy4F8ukstQkOB2Or2J3Q77V+kiTW2uKLmfm7uOyWhxOXS7Bfo8DAP/DUNf\n1ZHTZaX3A5CVChu/LvsYhbHoKUiLg+aXwbKXIOaLix8zM00HV3a83qRtqcH069eP2NhYAKZPn06P\nHj3o0qULd999NzabDYB7772X6OhoOnTowHPPPXe2b7NmzfjXv/5F165dmTt3Lu+//z4RERFERkYy\nZswYAFJSUhg5ciSRkZH06tWLzZs3A/D8889z++23c/nll9OiRQvef//9cp55xWHVTTkb+LfjZagI\ngtvopJdpcbpuhldtaNa34uRp3B3Ce+isAd0nlphh2RK7F+kEkX0fhf5P63QuPz2qPb46jCz7uJtn\n6wj7HhMvXkZDmXjhx21sP5Lm1DEjwurw3NUWgomB3NxcFi5cyNChQ9mxYwezZ89m9erVeHp6ct99\n9/H1118zYcIEXnnlFerXr4/NZmPgwIFs3ryZyEidTSAwMJC///4bgLCwMPbv34+3tzcnT54E4Lnn\nniMqKop58+axbNkyJkyYcHb1tHPnTpYvX056ejpt27bl3nvvdbmLcGXA0gpGRPqLSHPHcQMR+VJE\nvhARkze7vAhup38m7tQ34pb9dTR5RXLJAzpJ5s4FFz/W6RSY/6C2KV3+pHYmGPUlNO6hk1Lm5QYr\nLUrpBJ5hUdCo28XLaahSnDlzhi5duhAdHU2TJk244447WLp0KevXr6d79+506dKFpUuXsm/fPgDm\nzJlD165diYqKYtu2bWzffq5w3ujRo88eR0ZGMm7cOKZPn46Hh35O//3337n5Zp17bsCAASQnJ5OW\nppXq8OHD8fb2JigoiJCQEBISEsrrK6hQrNpgPgby9mPyUsieAT4DrrEygIgMBd4D3IHJSqnXC3w+\nDr3lJkA6cK9SapPjswOOczYgVykVbVHu6kOegtn2nbZN9H+qYuUBaHeVzre1ZhJEWPozKJrFz2ol\nM/7bc4rTyxeu+x98GK294cpSavjA79p2ZcoUVyhWVxrOJr8NJg+lFLfccguvvfbaeef379/PW2+9\nxbp166hXrx633nrrea68fn7nHGIWLFjAypUr+fHHH3nllVfYsmVLsXJ4e597GHR3dyc310J56GqA\nVRtMI6XUIRHxQCuau4B7gUusdBYRd7T95kogAhgrIhEFmu0HLlNKdQJeQiuv/PRXSnWpkcoFtO3A\nN0iX4EWgdTER+uVFXnXBg6u1l1ZZSdoFm2Zo77QGnc7/rF5T6HEXbJyhMxuXlnWTwSfA1HA3nGXg\nwIF88803JCbqEuApKSkcPHiQtLQ0/Pz8qFu3LgkJCSxcWHgJZ7vdzuHDh+nfvz9vvPEGqampZGRk\n0K9fP77+WtskV6xYQVBQEHXq1Cm3eVVGrCqYNBEJBS4Dtiul8urLWt1E7AHEKqX2Oew5s4AR+Rso\npf5QSp1wvP0LCLc4ds0huB3Yc/VWT+2QipZGE3Wz9s5a93nZx1j+ik642bcI755+j2ub09J8LtE5\nZ3Sw6NFNkLK/8JLHJw/peKGo8Tolv8EARERE8PLLLzNkyBAiIyMZPHgwR48epXPnzkRFRdGuXTtu\nuukm+vQpvP6MzWZj/PjxdOrUiaioKB566CECAgJ4/vnnWb9+PZGRkTzxxBN8+eWX5TyzyofVLbIP\ngHWAF/CI41wfYGeRPc6nEXA43/s4oGcx7e8A8j8+KOBXEbEBnyqlCq5uagbBbeDg7zo/VmXBt75e\nHWyeDYOe1zE7peHIRtj+A1z2r6JrfvjWh76PaAVzYLVWHMte1g4PeXj46Noh3RxR+icOwLQRWvl1\nN8b9mkpGRiEPHmh7Sn6bSh5Tp04ttP2BAwfOHnt6evL7779f0KZ+/frMmzfvgvPPP//8ee+3bt1a\ntMDVDKsK5k3ge8CmlNrrOBcPOP0/V0T6oxVMfhepvkqpeBEJAZaIyE6l1MpC+t6F3r6jSZNqWEUg\nxLGr2LYSKRjQ3lmbZui09T3vKl3fZS9rL7GS6tf0vBfWfKarbtpztdH+ild0lc3MVL11+ONDutxz\n9zth5lidyPOW+VDftfmWDAZD4ZSoYBz2kwwgQCmVlXdeKbW76F4XEA/kr2QV7jhX8FqRwGTgSqXU\n2bozSql4x89EEfkeveV2gYJxrGw+A4iOji5lWccqQNR4nS6/oJ2iomnUDcK6antHjzutR8of/BNi\nl+hsACWVC/DyhStfh1Vv61ieDtedn9a98xhY8Tqs/A9smK5r5Ny6QAebGgyGCqFEG4xSygbsBi6m\nZuk6oLWINBcRL2AMMD9/AxFpAnwH3JxfeYmIn4j45x0DQ4Cas8bMj2ct7Z5cGek+UZd1PrDKWntb\nDvzyBNRuoFccVuhwLdyzSpcnKFgzxM0dBjwNN82BNlfC7b8Y5WIwVDBWt8i+Bn4SkffQ9pOzqwOl\n1LKSOiulckXkAWAR2k15ilJqm4jc4/h8EjqIMxD42JGILc8dORT43nHOA5ihlPrFotyG8qLjdbD4\nGfj1Bb0tVVKOs9Xv6cJfN07TqxNn0eYKaxkODAaDy7GqYO51/Hy+wHkFtLAygFLqZ+DnAucm5Tue\nSCE2HaXUPnSJAENlxrMWXP0uzL1VR+CPnQ2ePoW3TdwBv72hVyQRIwpvYzAYqjyW3JSVUs2LeFlS\nLoYaQsQIHdC4bwV8c5veBiuILRfm3Qfe/jDsrXIX0WAwlB+m+LXBuXS5SSuOXT/Dl9fA7sU6QSfo\ngMofH4Yjf+s2fkEVK6uh2uPu7k6XLl3o2LEjo0aN4vTp0xUtUpEopRgwYMDZ9DLOICkpiaFDK87r\n1Gousjoi8raIrBeRgyJyKO/lagENVZAed8LV7+sSATNGwUfd4bP+8FEP2DRTR+Z3uLaipTTUAPJS\nxWzduhUvLy8mTZpUcqcSyMu87Gx+/vlnOnfu7NTo/+DgYBo2bMjq1audNmZpsLqC+RjoCrwI1Ace\nRNeFecdFchmqOt1ugUe2wPWfg28gKLsu9vXYDhj2pin6ZSh3Knu6/q+//poRI87ZJKdNm0ZkZCSd\nO3c+m0QzP7169WLbtnMpmi6//HJiYmIuaDdy5MizKWzKG6tG/iFAe6VUsojYlFI/iEgM8CNGyRiK\nwt1TuxR3uqGiJTFUNAufgGPFJ4QsNQ066dgoC1SFdP2rV6/m008/BWDbtm28/PLL/PHHHwQFBZGS\nknLBnEaPHs2cOXN44YUXOHr0KEePHiU6+sJUjdHR0TzzzDMWv1TnYnUF4wakOo4zRKQucBRo5RKp\nDAaDwQlUpXT9KSkp+Pv7A7Bs2TJGjRpFUJC2U9avf2GhvBtvvJFvvvnmrNw33FD4g1xISAhHjhwp\n3RfnJKyuYDahE10uBVaht8wy0AGYBoPBUDwWVxrOpiql6/fw8MBut+NWMIi4CBo1akRgYCCbN29m\n9uzZRdqXMjMzqVWrYpK9Wl3B3AkccBw/jK4FEwBMcIFMBoPB4DIqa7r+tm3bnl1JDRgwgLlz55Kc\nnHxWxsIYPXo0//nPf0hNTT27lVeQ3bt307FjxWS1sFoyeV++40RckOTSYDAYyoP86frtdjuenp58\n9NFH9OrV62y6/saNG5eYrj81NRWl1Hnp+m+//XYiIyPx9fUtdbr+4cOHs2LFClq1akWHDh14+umn\nueyyy3B3dycqKoqpU6cyf/58YmJiePFFXbrihhtu4OGHH+bZZ589O05MTAyTJk1i8uTJACxfvpzh\nw4eX8du6OESpknNCis7TMhEYCwQppSJF5FKggVJqjotlLBPR0dGqMI8Kg8FQPuzYsYP27dtXtBhV\nhqNHjzJhwgSWLFni1HEvvfRSfvjhB+rVq3fe+cJ+PyKy3plFHa1ukb2ITqH/GZCXBz8OXeLYYDAY\nDBdJw4YNufPOO50eaPnYY49doFzKC6tG/luBKKXUcRH5xHFuPxbzkBkMBoOhZG688UanjhccHMzI\nkSOdOmZpsLqCyasJA+cyKdfOd85gMBgMhvOwqmB+Bt4WEW84a5N5CR1oaTAYDIVixcZrKH/K6/di\nVcE8BjREB1vWRa9cmmJsMAaDoQh8fHxITk42SqaSoZQiOTkZH58iymk4EatuymnAtSISglYsh5VS\nx1wqmcFgqNKEh4cTFxdHUlJSRYtiKICPjw/h4eEuv06xCkZEfIFngI7A38BrSql1ZbmQiAwF3kPb\ncyYrpV4v8Lk4Ph8GnAZuVUr9baWvwWCofHh6etK8efOKFsNQgZS0RfYRcDWwE7gBKFOFKBFxd4x1\nJRABjBWRiALNrgRaO153AZ+Uoq/BYDAYKhklKZihwBCl1D/RN/irynidHkCsUmqfUiobmAUUrJU7\nApimNH8BASLS0GJfg8FgMFQySlIwfkqpowBKqcNoA39ZaAQczvc+znHOShsrfQ0Gg8FQySjJyO8h\nIv0BKeI9SqllrhKutIjIXejtNdBlBXZVgBhBwPEKuG5FYuZcMzBzrv60deZgJSmYRGBKvvfJBd4r\nrEXzxwON870Pd5yz0sbTQl8tjFKfodPZVBgiEuPMXD5VATPnmoGZc/XHUUjSaRSrYJRSzZx0nXVA\naxFpjlYOY4CbCrSZDzwgIrOAnkCqUuqoiCRZ6GswGAyGSobVXGQXhVIqV0QeABahXY2nKKW2icg9\njs8nobMFDANi0W7KtxXXtzzkNhgMBkPZKRcFA6CU+hmtRPKfm5TvWAH3W+1bianQLboKwsy5ZmDm\nXP1x6nwt1YMxGAwGg6G0WM1FZjAYDAZDqTAKxkmIyFAR2SUisSLyREXL4yxEpLGILBeR7SKyTUQe\ndpyvLyJLRGSP42e9fH2edHwPu0TkioqT/uIQEXcR2SAiPzneV+s5i0iAiHwjIjtFZIeI9K4Bc37U\n8Xe9VURmiohPdZuziEwRkUQR2ZrvXKnnKCLdRGSL47P3Hem9ikcpZV4X+UI7H+xFu2x7AZuAiIqW\ny0lzawh0dRz7A7vRKXv+AzzhOP8E8IbjOMIxf2+gueN7ca/oeZRx7o8BM4CfHO+r9ZyBL4GJjmMv\nIKA6zxkdsL0fqOV4PwddXLFazRm4FOgKbM13rtRzBNYCvdBxkAuBK0u6tlnBOIdqm85GKXVUOZKO\nKqXSgR3of8wR6BsSjp95ZfNGALOUUllKqf1or8Ae5Sv1xSMi4cBwYHK+09V2ziJSF30j+hxAKZWt\nlDpJNZ6zAw+gloh4AL7AEarZnJVSK4GUAqdLNUdH2q46Sqm/lNY20/L1KRKjYJxDjUhnIyLNgChg\nDRCqHGmEgGNAqOO4unwX7wL/BOz5zlXnOTcHkoAvHNuCk0XEj2o8Z6VUPDqB7yHgKDr2bjHVeM75\nKO0cGzmOC54vFqNgDJYQkdrAt8AjStcHOovjiabauCOKyFVAolJqfVFtqtuc0U/yXYFPlFJRwCn0\n1slZqtucHXaHEWjlGgb4icj4/G2q25wLw5VzNArGOVhJhVNlERFPtHL5Win1neN0gmPZjONnouN8\ndfgu+gDXiMgB9HbnABGZTvWecxwQp5Ra43j/DVrhVOc5DwL2K6WSlFI5wHfAJVTvOedR2jnGO44L\nni8Wo2Ccw9lUOCLihU5nM7+CZXIKDk+Rz4EdSqm38300H7jFcXwL8EO+82NExNuR3qc12jhYZVBK\nPamUClc6VdIYYJlSajzVe87HgMMikpfscCCwnWo8Z/TWWC8R8XX8nQ9E2xir85zzKNUcHdtpaSLS\ny/FdTcjXp2gq2sOhurzQaW52o70unq5oeZw4r77o5fNmYKPjNQwIBJYCe4Bfgfr5+jzt+B52YcHT\npDK/gMs550VWrecMdAFiHL/reUC9GjDnF9AFFbcCX6G9p6rVnIGZaBtTDnqlekdZ5ghEO76nvcCH\nOAL1i3uZSH6DwWAwuASzRWYwGAwGl2AUjMFgMBhcglEwBoPBYHAJRsEYDAaDwSUYBWMwGAwGl2AU\njMFgMBhcglEwBkMhiMhTIjK55JYXfZ3LRcQuIhkiMtTJY7dxjGsTkYnOHNtgsEK5lUw2GCoTIpKR\n760vkAXYHO/vVkq9Wo7iHFFKhZfcrHQopXYDtUVkhbPHNhisYBSMoUailKqdd+zIOTZRKfVrxUlk\nMFQ/zBaZwVAIIvK8I8ElItJMRJSI3CYih0XkhIjcIyLdRWSziJwUkQ8L9L/dURXyhIgsEpGmpbj2\nrSKyWkTecYy9T0QucZw/7KhOeEu+9sNEVxxNF5F4Efk/530TBkPZMQrGYLBOT3Tyv9HoejFPozPy\ndgBuFJHLAERkBPAUcB0QDKxC54Mq7bU2o3NGzUBnde4OtALGAx86SiiATkZ6t1LKH+gILCvj/AwG\np2IUjMFgnZeUUplKF6U6BcxUSiUqXbhqFboYG8A9wGtKqR1KqVzgVaBLaVYx6DTyXyilbMBsdAr1\nF5WuNLgYyEYrG9BJDCNEpI5S6oRyVCA1GCoao2AMBusk5Ds+U8j7vBVFU+A9x/bWSXS5WqF01Q8L\njo1SqqjrXY/OcH1QRH4Tkd6luI7B4DKMgjEYnM9h9JZVQL5XLaXUH664mFJqnVJqBBCCTrM/xxXX\nMRhKi1EwBoPzmQQ8KSIdAESkroiMcsWFRMRLRMaJSF2lqzKmAXZXXMtgKC3GTdlgcDJKqe8dBvhZ\nDrtLKrAEmOuiS96MNvq7o4tEjXPRdQyGUmEKjhkMFYiIXAosQgd6jlZKLXLi2K3R5by9gPuUUlOd\nNbbBYAWjYAwGg8HgEowNxmAwGAwuwSgYg8FgMLgEo2AMBoPB4BKMgjEYDAaDSzAKxmAkvayaAAAA\nG0lEQVQwGAwuwSgYg8FgMLgEo2AMBoPB4BL+H+TJWfJzL3UEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f910fae71d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(211)\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result['ec'], axis=(0, 1, 2)), label='Euclidean')\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result_cv['ec_cv'], axis=(0, 1, 2)), label='Euclidean (c.v.)')\n",
    "plt.xlim((-100, 1000))\n",
    "plt.ylabel('Euclidean distance', fontsize=12)\n",
    "plt.legend(loc='center right')\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result['ps'], axis=(0, 1, 2)), label='Pearson', clip_on=False)\n",
    "plt.plot(np.arange(-100, 1001, 10), np.nanmean(result_cv['ps_cv'], axis=(0, 1, 2)), label='Pearson (c.v.)', clip_on=False)\n",
    "plt.xlim((-100, 1000))\n",
    "plt.ylim((0, 1))\n",
    "plt.xlabel('Time [ms]', fontsize=12)\n",
    "plt.ylabel('Pearson distance', fontsize=12)\n",
    "plt.legend(loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Euclidean distance:** with cross-validation, the Euclidean differences now approaches zero towards the end of an epoch. Thus, cross-validation removes the noise bias, which previously led to high Euclidean distances at the end of a trial despite the absence of true activation pattern differences (as indicated by decoding analyses).\n",
    "\n",
    "**Pearson distance:** with cross-validation, correlation coefficients increase and thus the Pearson distance (1−r) shows a stronger negative deflection from 1. This result is expected, as 1) cross-validation corrects for effects of noise and 2) noise generally decreases correlation coefficients."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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