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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Thresholding with random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can read this notebook without knowing any Python programming, by skipping over the code, but reading the code will often help understand the ideas.\n",
      "\n",
      "I based the notebook on my understanding of the 1992 paper by Keith Worsley (see refs below). For me, this paper is the most comprehensible paper on random fields in neuroimaging. Please refer to this paper and the Worsley 1996 paper for more detail.\n",
      "\n",
      "An earlier version of this notebook became the [Random fields introduction](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch14.pdf) chapter in the book [Human Brain Function second edition](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Most statistics packages for functional imaging data create statistical parametric maps. These maps have a value for a certain statistic at each voxel in the brain, which is the result of the statistical test done on the scan data for that voxel, across scans.  $t$ values and $F$ values are the most common.\n",
      "\n",
      "For the sake of simplicity, I'll assume that we have $Z$ values instead of $t$ or $F$ values.  $Z$ values are values from the standard normal distribution.  The same sort of arguments apply to $t$ and $F$ values, just with slightly different formulae.\n",
      "\n",
      "The null hypothesis for a particular statistical comparison probably will be that there is no change anywhere in the brain. For example, in a comparison of activation against rest, the null hypothesis would be that there are no differences between the scans in the activation condition, and the scans in the rest condition. This null hypothesis implies that the whole brain volume full of statistic values for the comparison will be similar to a equivalent set of values from a random distribution."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The multiple comparison problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given we have a brain full of $Z$ values, how do we decide whether some of the $Z$ values are larger (more positive) than we would expect in a similar volume of random numbers?  So, in a typical brain volume, we have, say, 200000 voxels and therefore 200000 $Z$ scores. Because we have so many $Z$ scores, even if the null hypothesis is true, we can be confident that some of these $Z$ scores will appear to be significant at standard statistical thresholds for the the individual $Z$ scores. For example, $p$ value thresholds such as $p<0.05 $ or $p<0.01 $ correspond to $Z = 1.64 $ and $Z = 2.33 $ respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats\n",
      "normal_distribution = scipy.stats.norm()\n",
      "# The inverse normal CDF\n",
      "inv_n_cdf = normal_distribution.ppf\n",
      "inv_n_cdf([0.95, 0.99])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "array([ 1.64485363,  2.32634787])"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, if we threshold our brain $Z$ scores at $2.33 $ or above, we would expect a number of false positives, even if the null hypothesis is true. So, how high should we set our $Z$ threshold, so that we can be confident that the remaining peak $Z$ scores are indeed too high to be expected by chance? This is the multiple comparison problem.\n",
      "\n",
      "We could call all the $Z$ scores in the brain a \"family\" of tests.  We want to find a threshold so that we can correct for a whole \"family\" of tests.  For this reason, these multiple comparison correction methods are often known as *family-wise* correction methods."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Why not a Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem of false positives with multiple statistical tests is an old one. One standard method for dealing with this problem is to use the Bonferroni correction. For the Bonferroni correction, you set your p value threshold for accepting a test as being significant as $alpha$ / (number of tests), where $alpha$ is the false positive rate you are prepared to accept. $alpha$ is often 0.05, or one false positive in 20 repeats of your experiment. Thus, for a statistical map with 200000 voxels, the Bonferroni corrected p value would be 0.05 / 200000 = [equivalent Z] 5.03. We could then threshold our Z map to show us only Z scores higher than 5.03, and be confident that all the remaining Z scores are unlikely to have occurred by chance. For some functional imaging data this is a perfectly reasonable approach, but in most cases the Bonferroni threshold will be considerably too conservative. This is because, for most stastistic maps, the Z scores at each voxel are highly correlated with their neighbours."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Functional imaging data usually have some spatial correlation. By this, we mean that data in one voxel are correlated with the data from the neighbouring voxels. This correlation is caused by several factors: \n",
      "\n",
      "* With low resolution imaging such as PET, data from an individual voxel will contain some signal from the tissue around that voxel;\n",
      "* Unmodeled brain activation signal, which is very common, will tend to cover several voxels and induce correlations between them;\n",
      "* Resampling of the images during preprocessing causes some smoothing across voxels;\n",
      "* Most neuromaging statistical analyses work on smoothed images, and this creates strong spatial correlation. Smoothing is often used to improve signal to noise according to the matched filter theorem (the signal we are looking for is almost invariably spread across several voxels).\n",
      "\n",
      "The reason this spatial correlation is a problem for the Bonferroni correction is that the Bonferroni correction assumes that you have performed some number of *independent* tests. If the voxels are spatially correlated, then the $Z$ scores at each voxel are not independent. This will make the correction too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An example can show why the Bonferroni correction is too conservative with non-independent tests. Let us first make an example image out of random numbers. We generate 16384 random numbers, and then put them into a 128 by 128 array. This results in a 2D image of spatially independent random numbers. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Constants for image simulations etc\n",
      "shape = [128, 128] # No of pixels in X, Y\n",
      "n_voxels = np.prod(shape) # Total pixels\n",
      "s_fwhm = 8 # Smoothing in number of pixels in x, y\n",
      "seed = 1939 # Seed for random no generator\n",
      "alpha = 0.05 # Default alpha level\n",
      "\n",
      "# Image of independent random nos\n",
      "np.random.seed(seed) # Seed the generator to get same numbers each time\n",
      "test_img = np.random.standard_normal(shape)\n",
      "plt.figure()\n",
      "plt.imshow(test_img)\n",
      "plt.set_cmap('bone')\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - array of independent random numbers')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x107179a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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7tsvh9V1if83Z/THLsyWyqpDGCaZtsX1tm7qqKfJC8JHqGlVTKNKM6fEZUNMg\nnNNlUZIlKY7bodsfEfsxsiIhSzK6ZWBYBjTg9hw0U8ewDWzPRkIi8iPCVcBiPMPqCBNrOV7iz9Yt\npaRCAuH0z0tURUOWVIJ5IAIQdYNm6nR6nY3v6Tx8X1fCP3juXzkXYkWZsV4ssB2HTk/8SYEGUHUZ\nRRWLschLiizHsl3sjovtOOiGwf4TV9BMERHNklTwqHSTWqlJo4TVdInVscjTHMPUKQsZwzRwuy6G\nq2M4OmVeMTk9RZIVnI4DjQSSiLRG65AsEYumzCvyPKVuKvIsY+fqHv2dPlki/H55kkMDy/GSYBmQ\nxRmKpKHKJlEQYhgVmmFgnmuvmo6EgiTLGLa5ibhG64jZ6RiUGtPs4LoDLNsmXIeE/hqkXXRLJ40z\nJBQGwy1oZNbTNWkW0VAQ+oKWIQFFXjK9PwVJQlFkgrlP2VKFVE3F9iwcTwSqlpMVmqnjjTwMS0fT\nDaqyxJ/5aKbGaH8LyzOwO8JPqigKg90hSRhR1zWT+xOaphLPbmThDzNSmqbBtB3SOOLs+IhgvaLT\nHWCYQntsmkZQdCbrDTft3Nm/nq1RZF0EBqqaxekCTTcY7myTRhnT+1MSP6ZpQNEUTNtso9Uquqmz\ndbiFrMgkYcIzH3mWm09f4/Tu/LWW5HsS7z/BVtSspmtuPHWVa7cOuPP8Hc7uTQU9goaqzHF7LrvX\nd4mDmGgdCoGiKximQRj4rOZz0jQmz1KauqaqS8qyYLi1i2V1aGhQVQXN0DFt4cPTTR134GK5Ijxv\nWLqgergmaRIzH49xBy6mbTG7PyVYBkLIyMInlsUZ0SpEkRUUWWU5XiLLIhhhuRadQQdZkTeBjzzJ\nkSQJwzKocmHSlmUpHMpSRRguMV0dp+dQpAVVVbdam/AuF3lBEiZ4wx5u10U3DExb+N/qUgjKJEqI\n1iGO5yFJEAUBwdJHOxL8KdOxqMoKwzawXJuBO+TKjUO+/Kuf5+zubfYOr2LZLtE6QlFkrI6Fv1wT\n+QGWZSLLCpEfkqUJSRIy3B9guSbROiRaCx9n1fIL/ZlPEiZoqo1i6WRpgiRJuD1vo0HohoGq6aia\nht212TrcIlyKYMNiPCFLE/qjLTq9LrKiCNO1SJFkUHWN2k+QkOkPH2gss9kJUbgiWiaMtnfp7w0o\nsoLVZIU37AjaUOvHrOuaTkvQPo/A65aO5ViMrgxxPAdN1zi9fcpyMmPrUBBmB/WQuqyJ/QRFVRgd\njFhNVIIgugBbAAAgAElEQVSFz/Rogm7o9EYDyqIkXIQompgXbtejrguOXngFQ3MYDHO2DrboWl3q\nuqHMK9azNXUlIu+arqEowq/rdDLcvkuwCJjcn+ANOng7PcJVRBavqUrBwXT7wt9m2iZlWWG65iYK\n35w2HD5zncGgy6f+z/dXRar3nWCLojWmbXH3xSMWkyXLqY/tusiyjKar6LaO47kUeYGsyNgdG80Q\nTnfDNiiKITvxLrPjCcvxgiQVRF1ZllFkndAPuHXjSQa7fV7+3Mus50tUXW21NIe6rPHna8KVj2po\n7F7bI0nX3L79OUbX+mjmIUWZ0UgV29f2UDWNIs1ZzRcc371DFgnNq6pKeqMBo8Nd9q/vMtwZcPTy\nCeEyRFEVNFOjyisR5csLdFPHdm2yJENRlDZCq2PaJoZlboiaaZyQRBFO1+Xg6QOcrouiKizPlpvg\ngu3ZeEMPfy4WbG+rKzQi/YCqrClSQSA1LJ0syZDbKG4SxpR5iaFb7BwcouviuQBO32Xvxi7afQ1D\n0/n2b/sobsfmF37hM5yNZyLirFlkSb6h0ZR5iWpoKIpMVZXUdYVpmyDplOscwzYY7PbRDOGvypIM\nRVfYv7VHd9QTfjpZRjM0OiMHf7liOZ2xWk7RDR1F0ekNRqRhzuTeBEmSUDUFwzaQVaH1qaZElgxx\nvC6WZ6MoCpqhYbS+wSRI6A49Sq9kfGdM0zr756dzZsdTyryirkqOXrqHoigYpkWwXOOvVgThFLvr\ncPDEDQzDosgKuiOP/k5f+PEsfRPxLLMSWVFE8Gerhzfy6HRdFuOe2Dg0nf5ogGEZrVArN75RwzLw\nOh5NU+F6Hroh5oQ/9fEXa/I0JYt1VFVFN3SMlpuWZwX+3Mf2bCzXQi4rJEkiWkcUacH8eE4RZUw9\nB7v7Zv9MxLuL951gMxxdOOH9kNnpDM0QC14zNHTLwLSN1iRNhfYiSciKJAiVpri2t9WnLqHKQfYV\nylKYiJIkURYFVZ1RNTkNdavaL+mOegx2h2RJRhpXrOdrZFWmO+qTpSlpFlGVBZIkoRkqda2jGUK1\n1wyN1XLOarqkzEugdUjbOnbHQtVUqqIk9qNNBFfTVDRNpSxK8jRHNwTPq6lrdMNg68ouvVEfvXWS\nC0a9RlkU1HWNbun0dwe47YSM1zFlISKIZV4gwrcSumngjbp4Qw9FkdsgSSyyF+oGzrMY6poir8ii\nFMfr4A16RKuQNMqE5mLqIl3Lc1BROHzigK7n8Pkv3yEphKA0bZuyKEnilDiKaUoRPZYUWVArdBFE\naBCO+boqSdIASQFNM6irCkWV8UYevW3BYZNauoYsy8iyTBIHlGVKUeQYpkN/MKLMK5bjJd2hh2GL\nyHSW5CRBjOt1sR1BJlYUBUmW0Np2xEFMkZWYroUsS/jzANXQqJuGYCk0IduxQYY4iCizkqaWkOQG\nRZOJ4xCUBkWR0XSNLM5QdQ3Ls1taj4qiiWyGdJUgK8KqQGlopApVV7AcB6833GRzNA1kSYYkSS0R\nuxVsLR9NllXqqqRBZDnUtfCZKZqwHkzHxLQNdMvAn6+JVmEbOBPZG2WZsTwTG9ribM56vsKwDbYP\ntt+lFf/W8L4TbE9+6AO4nQ7+3Gc9XSMrYucd7IrMgDRMyVuOkazIwt8xXyJJMp2+SEvxhh0MU29T\nTmSyNKMq63YCqnzx05+lbFKuHIpc08V4hqorjA62sD0bzdRI44wkiJnem9KkKk/e/E3YZp88ydk6\nEGbw2d1TTNtkuLdNf2uEqmqc3T+iqWuuPf0EttshCVNe+uxLpHFCFgunsm5qdAYd+rvCLEojYTJH\n65RgGdAZdHj2mz5AU0MSpKwmS9I4Y+/Gnkj/ck1BHUBC1UXe4zXzGtE6YjVdMbk/JliuyZMS3TTo\njroYtsHxC8eoukp35LVaQbFx0NdVTVOLoMTwyhBv6HHvS/coihLN0iiLkpMXj9EMnc5Why/fvY8i\ny9SqxPCKyCaQFZmqqojDgHC9xrQcQcPpOsiy1JKJBXWlqWE+mXL3zpe49cEP8OxHPopm6IK7lgu/\no27pRH7E8nRJXdXIispTH/4gkiy1rHwJRVFZnC1Io5Tedk/kYzomk/tTTl5aopsGqi6EmJZpr9KI\nFFVBUUV8TTcNbnzdddI44+z2GVVR0Rv1if2Yhpqt/R1C3+fkzhFb+zvsHOxRlgW6pTPY3dpEIdMw\nZXJ3IjI2ThdUZUGWpiRxSHcgNLLbX3qBJA7Z2rmCrglahiSJrJk8EX7WwW4f0zGp60ZE0DsiuJFF\nCbPJGFVTObx1A7fvMtgdijQ2WcbxbOyug9N1MCy9zX8tWU6WTMdH1HVFtI6QkAnXIWWZI6sSjme9\n5pp8L+J9J9gcV6Qgye3uU2SFIMLGGYoiU+St1qRrhGufKAjFTqlqaHqGbsaobVjf6lhkcRvNHPWQ\nJImqKFmuz/AXIbu7NZoq0zRQVTVVUbG/N8IyDJJ5SLSKhOmoGFy9dQvTtMnjnL2rO+T9nNV40Zoq\ndUsCdtm7fgVFlekO+tiug6nrnN47ZX42pypqZFlBkkQazvmuLEkSyNLmN0VVMSyR/lIVFbKqYDoG\nTtduaRc5SQiKotI0DU7mbBKs5Xl7X1kWqUqS4E1lacbk6JTuVo+da9sEi4DIjzcUiKqsUNooreVa\nKKrS9rvIZQVoKlANicCXmU+nyLIKtdRmPWgUWUmeZHjDriC06lZLY1AwbBNvCIEU0NBg2Dq6oyCt\ny00E9JyUnITCN6jqGuEqJFgGGyKt1Chomo7qGcRBhL9cUWQihzZahSiqLDRCRaYz7AjFtWGT51rX\nIkG/Kktsz8HuWJtk9aZugzhJLsbTcyjyEmjojvpolkbkB9gdkeWRLCOquqCuK6glQZ4tK/IsFxkU\nEmJ+JglVVSLLEoZtomkaSS2RBCmlJmhLkiw06HMStmbqIDdMT05IYg8kEQjobvdYzudUpaBnbIRz\new9JkdE0lX7fo0py4ZfTVFRdhjE0dS02GklkLIS+oCutppc8trcVeSoY7pouTE9RCSEiWkXopo7p\nmoKk6NlMz05YjCd0vAGmJXhKeZKznq6xOzampVOWBZ1Bhw9+yweoior56Zww9JEbgyqXKCixLBdV\n0cnijIOtEQd7W9z5wl3yNKfICnpbXXau7xCtIvIkY3t7gKqpnN0ZE8cPaCdN0/DkR57Fci0md6e4\nrs2zH7qFaekkseBC1W24XVYUIl+YN2VRYjomakdMNpqG2f2ZMFOTHLfrCt9Zx2YxmTM5OkNVdbIo\nZzleYns2B09dQWv7RzM0hntD5qcLonXE/GRO0kbfVEtG1VWCRcDseM7OjR10R8ef+1imxXZb5cOf\nrfEXa9azBU3ToKgaumawPp4RhAs0zcC0HDpun+HeCMs1RUGCJOPa09fp7fSo8opwFbEYL1BUBW/o\nQYPwZ3ZsNOMaSMJJHswD8lSklEXriLpqkGSJYBEQ+zG2ZyMrMuO7EzRDxRt6LCdz7r10G6/bx7Qc\nZidTVrMl/e0B3qjL9a+7wfJ0SbAIcDwHRZUpinKjWTldF7ffYT1ds5wsWZ4tMW2D4ZVRyx0TQkBR\nFRFU8CxkFOq6IfIj7rzwAmWZ0x310VWLYBGg6qqYe46JJHXxVyKH1jAsLNeh03NR1BukUUqRlaRR\nSuzHohCApYtMhDYrJo59nv/cr2FZHtEy5caHbnDtA9eJ1hH+PBBJ/3VC09QYloGqa2RRRmkauKZJ\nbJg0gDf0MGydYL2iaWpufvgWEjInL5+gHKuspkvmx8s3WprvKbzvBFsaJqRRhmYI2kXdVJRlgWE7\nyKpCnhZISFgdG8txUbUVYbhC1hsG+31BZIwSmkYsDN0Q0c3JvemmFIxl2Xi9HoZlICEL1nrLezub\nLcjKkqQQfi8ASRYazXkI/u7LRximgdN3UVtmuqqJro7XCUUqfGJFUTKdLiibRphJPYc0SgSZMkvx\nBr1NXqjQrkS0s0EkPq/nS+aTKV6/T78e4vZEtZPB7oiqEKk4uqVvshiahgd+tqIkCROSKGaxOEOS\nGrb2t3E7HuvpmjwrQIJoFVGYIhc1iRJOXjqhrppNVG33xhUURaauG6q8Jisi0lRQCzq9HrpmYtim\n4EhVNWVZcef5l1BvK3Q6fZpGmFjneZFhsCZaByjqLpJk0dQ1WRtskGVJVOXYH6LqGv7cF+9TVtgd\nC9tzmB1NyZOCpoHuqMdN8ynCVUQeZ1gd4duqyoo0SIRPLhBcLs3QqBvBf1RUhcGeoKWc3T7FaqOg\n6+l6U6FEkWQkVUGWJBHNPCdumwZVJYoPDLd3RSGCRiSudwadTW6y23eFv81xMEwLb9ClaSruvvAy\nmmaiyFpLPBZkbE3XsByTcOWTxinL8ZIsS1Akg8H2iOsfvIYkScxP58KXZpvtGEfEYUSn52G5Yn5F\ny4CmqIjDhDIvmJ2MycuMYLVG1XWmR1N0wwRJwuk6Iqofpe/Wkn9LeN8JtizJqcsKtS35IiuAVGO6\nJjQS4Sqgrit0U8fpdLBsl/n8mLzUsDxLRCXnhXC0Kgq6ZVJXcP/5+9gdm06/g2YYuF0PzRC+I2Dj\nQD8ez5gs1yRFIaJrinBa50kuShmVFS998Q6mY7B/cx/d1llN15sqCaJqR4Pbc0nSjLuvHKMoCv3t\nPoqm4C9XjI+OoZFwvM7G3APh3yra6JkkScRxyPT0lKYCwxDcM1XVGGyPNju+6QhTb3Y0I41SNEPb\nZEPIikxRZpwe38XpOTzxwWewbIdgGbbmvkS4ClFVBcsTtbyCebAx9Xs7XUbDLRzPIU8ywcFKI8qy\nZO/qIYOd0YaLV1VVmx9b8coXnycOQw6v38Lr9VDb1CUaCFYrlpMZpm0LAVpUFFlOkReoqorbdRns\nD6GB9XS12VBM18Ltu8yOZ1SFCCoMdkYcPnWNFz/zZcbhWGgmpiC0plFKVVbEfkweZxSmjtQmnHvD\nDqODEeM7Y2ZHPk98+Ak6g84mX7Kphb9KkUXgosxLgmUgAkWmhqaI5PO9w6vCz6mJzcUbeazGosCB\n3bWFsLJFYvv21W1O7tzj7guv0B9s0+n2BH1HEVFfwzbaIIBMWRQsTudUVYWpu2xf2ePGh57g7hfv\nCv5dmw51nvy+mEw2WTjnm8Fyutr4D2fjM5bzGaoq3CVnt8+wOy6GZbT0JovF6SWP7W2F1bHQdJWt\nw22GV4bEfgTI0EhEgc9kfITV0xld2WoFxoDR1SGqppL4KXkqSvs4XUG2TeOUJIiJ/JCqLIWJa+ib\nQIQkS4wORiiqMGO1PR1v2CFYCda/ZqiouoZqaG16T8Fieobqq3RHHUxH+Ldsz0ZRFV767AukUUJ/\np0eWpJzePuLw6WscPn2N9XRNkZR0ur1NGtV8PmZ6csy1J59isLWNoqkbnp4zsBntb+MNeui6gT/3\nWU7nzMcTDMOi0+21RGAhUDRdbf04YpGURYlWqtx4+lkcz8YwDHrDLv1hly9++guc3hUk4KqUWC1m\nGJZFd6u3qdc2OT3B9+c8981fj+ValEXJYGeEbhgYpkj+dj13UxCxzITpbOgOiquh6WLBq6pCVVTE\nQYIsKSiyTrAMoJFw+8J/VJXCl1hVNZO7E9I44fjlezQ1mLaFP/eJViHROtikJZVFSRxE9HeG2B2H\nuhJCSJZFPTpv1N3kBzeAaRlsHWyJKHUpOGuWK5zmG61SEYRW3dJQFFHhRDf1TQpWFmc4rXM+WIi+\n90YeTd0QzAP6u312buygKApJGDM7nhD5KfMTBRmV/atXoVFQdZW9J/bQDOFHlCQJWVHwBj0URRXm\nciLKccV+zMlLx8iyxOjKSGhzcYama7hdESAb7g1FsExRCNchRVaQp8ISsCwX88BmsD/Adh3KvBY1\nARcBTk8EW6qyeJdW/FvD+06wSbK0CZcrikJn4Ik6VFFKnmVkSUyWJGRJ1kb4enhDjzzNmR1NN9E0\n3RL5fOcO3SzJUFSVpE2pMV2x8JuqTflJEvzZmu62h9NzUHUNw9bJU8FOP6cdNA1UdUWdlfhLn7IQ\naVqma6IpKk0jchrTOCFch0yPJwz3R9AIMztLckHMbMmrWZKQJBGKJuN4wpRQNFlUcLBstvb0TVvD\nVcjybIG/WNHfEs70aBWRpzm2Z6O3CfhFXpBnOZqiYcqC2a+bOk0tiRJMh1vc/pLIJZVkCUmCsiyx\nVBlv6IkUr7wgWK3wVxXB8iadXhfbc0SeoaQgIQveXEs1MCSDcBVSFhWGYWNZDm7PQzdEJYss9cmL\nDJCx3Q5NLTJChMajivpwirwREJEfEC59DMvCdjoPaCwSbUqbyB4BE90w0A1jU4yzbCvCGI7IICny\ngixJKYtCpLDpKnmW0xgPgjg0YDkWiiY4hpIk0vIUTUVWZSzXJItzgjTAG4oqMkUm+lmWZdI0xV+u\nGewORdmiMCVai3zeqhBZIqqm4fUFUVc3Bfla1VTBeyyFxut4LqqqchadkqdZmxOaMz9Z4PZEpFPT\nVCpVRHV1U7hTdNN8QKlRVcpMBD0AVE1H01V6gyG2ZxP7MatkRbgSgs3pOthd+91c9m8a77tc0a97\n7ltRNVUkns/WmG16k3DcF8iSijfo43gumqGJdJFW+1qNl4LMORR0hiwRJVnKohK1ydrJ2hl0Wl6X\nQlWJyhFn9484uvMSddlQF+ccIonYjyjLClmSN+lTjtfBtGyiZcR8PGN2OiYJEvK4FNqdpjI5OmM1\nWUIti0qpWcnibEmRimCGLMsi7N7IdLw+V5+6jjfsEq4iluMFJy8fsTxbEK4i1tM1q8lKUA9q0A2T\n4d4W2wfb1LXISBhdGTE6HDG6MiKNIu69cBu74+CNhMlzXkLHdi1Ge0P8ZUieVRtzZLg3YrAzEuWh\nGsiSlPl4Qrj08ecBTQM7h7sUWUHkCzJtGqWCqkLTluuON6at2/c4eFJU/pjcm3J2fJ/x8V06vS6D\nnW0M00BRVeo2CV5UTmlaWodMU0NdgaqKMlH9HVFnT26jtcvpAlmW6A77rGdrwlXI1sGW0KSWYRuE\nAUkRZaSW0xnB0t8k3Q/3hixOF4zvTuhud+kM2oyUVjjEfsxqut60R1FEGe04iDel0s8rhQTLgPG9\nU45fuUNVVNDITO8LukcWZ5iOxXBv0Loa8ra6jNOWT18yvT8lT/KW2mSg6QrL6ZwkjJFlBdu1sVyb\nMi9FhWVVQdU0QfzNhY+2yApiPyZcBiIY5Zotp80kT1PCtQjO5GmOool0u+Vkzva1Ha4+cxXTsfj7\nf/dvwWWu6NsDwzJo6mYzWKYj8tzqqkaWFEzLpSklgrlP3YgUpN5ogOkYDPYGgtdlm2i6iDDOjmfI\nkoTdcTaMc0mWNuRGVVdxPIflQiL0fWbHY+RGpTvsixQfXdtoa27fRVUVgmVIEsY0lkSWZQRLXxAt\n+w2arrdVSGR0w8DpGFBzgZNn0FQ1tCWs68qmKnQkZPI0J1z7+Mu1KPIoSW09LZFdIWgLQpNtKoQQ\n0VQRDc4yohU0VbPRqlRVRVUVirzcaDPBMmQ2XhIHidCCaqHd9LeHotzTOgaEn8m2XYqkJPZTkqAN\nyEjSphgijTAh0yhl1axQNZWdqztEfiQWX1sUtMxLkjAmWK85fEIR/sdAVPU9FySC6iCyNizHRDc0\nBjtD4WOra2RZQpIlvL5HVeRMTk4wHWPDzj/PpCiLkjgMkRUFy7HQTQ3TNuhtDyjSvA1A5QSLQNAn\ntrpISJvy6SJ6ILIFZFneUCnCVbhJ4YvWLvFa/N2NeB2L9K11TJlVRKuI+fGMIhdBD80Q2lJVVC2B\n1tpsNOdzXG3dD4PdPpIskUQi3cy0TbqjAb2R+HsJSZiS/3/svcmPZWu63vVbfb/7vaPLyMzTVZ3q\nblc2F+QBSPbATBAjRkgI8QcgRsB/AIwQQyQGwAgkLIuJZTwwg2tzbWNX3brVnDYzI6Pbsfu9+n4x\neFfsY3MNVza3XBypPimV58Q5KUXG2uv73u99n+f3xBneUJBb/3Qughe42K7FMpWft27oYlWzTKqq\npCwqtL46ff57mZZJ1x94TdX8Jl/7f+H1rdvYJhcTwm0o1hdDro4ng7gizKsiK9jclxz2T2imwg//\n8A+YX5311YrQPs5fnWHoGtEuIk8L/JHfV2oBh/WR3cOOjg43cFl8Z0FRx7z/6iuSKObp7oE8KRjP\np0wuJoKzKWvmL+b4I59f/h+/pCpq5lcLDEvjuNvjDjzGi/FJ/Di/PJMGtKZJoz+vmF/PJXjlfkPX\ndgwmgcAo40zItHHKZrmScI3RmDSJOe526MYZtueg9gEhFRDuQnbLLS++c4039Lj94oYiKfCHQQ+V\nnGFaNk1vsC+yQjyS2yPvv7jl8WbZN4xlw7Ack+SYSmO5x1kPx1NM3aUsKnTNJO/9lKZjMlqI5Sna\nRuxXe1Y3K17/8DUf/s4H3PzyPdE+EjF1Wp6qJk2TDdG0DLI4Ew/lYiRDi11EtI/kRe/lFeP+upfF\nKUUu2rDJ5YSydKmbgiKXz4bj2xh93zTdp+w3WxzPZXY5B0WcBh98/0NQFbIwI9pH3PzyhhffvebV\nD16zfLtk+yDPhB5tbtqSadHRkSc5++WeaB+SJgmmLc6RcBeSRVKxKmgMhhO6pmP/tMcfB/hDn6Zt\npcJ82hNMxVER72PSMOuR7g7D2ZD5ixnnr85Y3a6JjwmKojEYj/jgBx8ymAwwHYvHN4+kYYo/7vuo\nvgMKpFHKi48vOXshHtnV/RpVFex3MA5Eo6iK3Mb2bKE92xaDyYgiqbj/4v50oH1b1rduYwv3e959\n+RXBcMR4OpPqow8GaeuG8LlZ3rW0jEHpqIqG/VOP99bFWlXmJbUmY3hdFyuN1v83pxf+HtZ7mroW\nf998yvf/0u/RVh0KKt4gEFSSZQg7K8pY3645ro8UaUHXdqInOhyJox1t+wLd0nlmo9muLfBI0xBD\nepxSFTKMMGwTWqHdotBzxlayAagaiqlR5gWmZbK4uuD6k5fYrs2Xf/orsqRgOJr2lqSW9f2S8CBE\nCNtxZKIKmA4YtnEyzddlRRKFoMhVrK1bLMc+nfoPbx6pcnEgxMdYsNaFCITbFuJDwsPXD6fGedIn\nZemGfuKvxfuYxzePct0fBfhjH8M2BIBodgSTAdOzBbbncFgdKevylJLUNo1cNVWF5JgSbiNxIdQN\nZVZg2CaKpYg0RtU5u7rE9jyBiQbynJY3S8LtES/wGUzEH1vlpVQkvbNCbFQVumlA11FmBdEuIosy\nRmdj1B4EGe+jE0iyzEt26zW6oXP54aUkXy3GIoa1UgxTJ08KjuvDacJZZAXh7oCiyjBifj2nbSUT\nI95HVGXJYDLEtA1UTWHzsGZ190hTy+c5GA2g6zg8HcjjAtuXZzWcDcl6TJTpmL2YWCU8xGiGznAx\noqFl97QBtWUwHZAmEZunJahdz/oT2VSZVYzmBuOzcU+o/vasb9/GdjjwePeOqrjEtiQqzBt6XLw+\np6MD5bGPTeswTEOCUtKCeJ8Q9elCs6sZ+82+b+TXoIrjQCQJghGyHJMizcjTjGg/wA18vvt7P5Lw\njqI+kXDbtqWuhOn2dPMk0ztF0ODH9YFwuyfLY5quj0zrOtpGmvKmbco1d7kjz/ITgtmwdLpG5CVd\n19EB4f4AdAwnU7oOkjBmNBuxuD7j9aevUbSWn/zx3yfep8zOZOpWlxWbxxUoLR/96FOC0ZAizWnb\n7tSUf/Ybtm3TEzXAtHsN08DHsOTKvrpZ9TIPnTRJydMUyRVRURSN5JiQpzkvv/uS4XzI5m5DFmfM\nrmYYpnFKxTqsD0zOJ0zOJ7gDQWLTSmWcpwXjxQxNU3uVv5BsRalfM16cYXk2b3765jTZ6+izJ2xT\nqvUkh05hcXnVO0kalB4R//jmgSzKWFyfMepf1kMmIS/dIenJualUo3PREO6f9oTrI03T4gbuKUjl\nuDmwf9phmCZN2xCFO+ZXZ1x9/ILJxRR/6NE0IkuyPZvkkJAcY/yxz3A+5Pbz9xy3Ryxb/LXz6wX7\npz2b+w1pHPeSoEBM8m3H5n7F/dtbRtMJg8mYwUSAprvHLboZn/R93tDj9rNbkmNy2ux0Q+ewOZJn\nBbMXMxQD3n/1NZ3ScN5cEodH1stHNM2ATjRwZSFVvOlYzF/MeofFt2d96za219/7iOF8SFuB0sqL\nadgG4T4iDROW7x6kf2VbvX2lYLXc4wYul5+8oi4kzmy1uiGK9vj2FMNwQOmIDkfiXST+yKJC0w3K\nIuPzn/4MxwsYjefMXsyYXExOVp7kEOMNPV7/6LXonu43NJ2YiquqwvUGfPy9HzE7OxdBaJyxeVhx\nf5Nz/vKc7/z+93EGLoPJQBhvqiLUkTg/2cauPr4StFJVU2U1dVkTDAO8oWiN4iiFrmW+eMHZhcaH\nP/qYLMpErFqlxFEkw4VDRppIyIfjeqfIvK7tcAOfwXQgTo5dhNU3lm3PwnJtLj+5It5HrG/XjBdj\n3OEVwdinrhoev15KZaCLW4L3QCfm7/XtCt3ScX2XJAzZrTY0TU2RSHLVYDZgcjFGtwyUTUgei1ND\nM3SUqpYKJjwQRyJa9vyBDDkGLmevz9BN+Qg/N8rTMKEqaxHO1oJ7uvnqC8oqRcdlsliIvtAR32ka\nZsT7BG/o0bYV66c7ZpcLXi9e83T7wOruCaXVcQO/B5bG3L+56UXA3cmTPBxNsSyXaBfTtRDtIh6+\nviPchbieh6brJ4qygBEsbFfkM5ZrsX8SQMJwNsQfeyiqQjAOTkOJ6eWMs9fnrN6vSKOE2dUMb+gx\nuZgwGHjM52NWTzs2633vapDqVbOkZ9n1Osg8Fn3jcCw906ebJ9pKZTSa0zVCgzb7Q+LZzZElOcf1\nb+P3fq1rNJswnsvEave4QzPlqnRcH0mOMVmcCYlWUXv8tEJ0OKJqAooMNzHhNhTy7m7JdJrjuUPx\nVbagqUJhaPo8BEVROGwPJMeMKunwRm7fqBVMeHJIsF0xnQunzZJKoW4gAycYMF5MsF2bJJQ0KqFD\nHDB7Tt4AACAASURBVHE8W0gaKDi+i6YLzSM5Jr2YVnpMi5eLHksekYZbCR+ZDvGHPrqpk4QpTdPg\nDySiz7TNUyrSeDERyYWqUWSFVGxWh64JMqfMC7I0kSHJcEaZVSRxAmqHaeno5jfhN00vk3B8l+F0\nxGgxEvrJk6C87dMV/nAisIa7sO+biX2tqkrauqbI+0qp6xifjXpxc02RNSKwVaWSFHdERpFn7JYb\nEivDMAyCid9rEY0+klH6aVVZ90bxTrytjsVumxCGe168mjCajwQTXjfy/EL5WVuOKT7buqSuxboV\nH2P2qx2D0UQGJ1FKGkllp2gqVp8CpRs6mm7g9DkCaSjT3yITaclxc8SwRCDeIeJe0zaxPQfTMk+Z\nrs8UEDcIsFy7z3QoSY4Jjj9gfr0g2kZkUXoKxTFdAy9wGI4C7m4eOWz2ol3r0fFFlqNZ4HheD2+Q\n2D7LdkQJoKrouo5hWuiGAXRkqQA1/bF/Ak5mUfabe+n/Jda3bmNL+l7BcXNkfbcW9IumnfIqx2fT\nZ3kOo8WIrmsI9zuUTifaSxq7puvMFy/lhI12tG3NbHaNPxwwOhsR7WLyOJfJpOVw+eI1WZIShXse\n3hiE2+jUQ3I8mzIvufnFDbqps3i1wHZt2qYl2kfYns34fMzy7SPbhzXzF2cE0wHOO4e26bj5xfv+\nxZBouLqqQVHxBn7fNJZ+zfpuxe2X7zgedkwWE15973U/0hd1edVboOJDxObvrXoJi8KHP3zN9HzM\n+mEnzew46KeXqsgvjkc26zugY7a4omsVyiKj2RdUlcAKy7xkfbumaRq8gStX3LsN0S7s8yVaRmcj\nLj64YPluebq2to1IKvIk5+n9UjDbi3OuPr7C9hzW79ekYcr7X93KRPGQ4ASSRFWXNW0t4c+D0ZjR\nbEx0OJLnMYY1om074kN8mpYCpzBkmd4mXLw84/t/6VNu312x3+0ZL+bQKTx89XDCYj/rGIV5pnJx\n/RpQ+Pqnb+joWFxeAnKljfcxju/w3R//oA/QqfAGLqqqEh9iCQZ6dcZhdeCwOnD9nZeousbbn73l\nsN71odz1CfrZ1A3RLqIupPpDkUyG8w8usH27JxjXZIm0D9q+/+UPA7Z3G5ZvHsjzlMFoyOJiwd27\nW6JjJAQa06Sua9bLNeEv1/zwD/+A1xefsHq/OiHl5y/mfPDD1/z8j/+Ep4c7ZlcfYdoWt1+/xR8G\nvP7eJxJZ2Pfrvk3rW7exvfviC86urk9ooqYSwuv4YiKN/Ko+5S0GYwFO+oMhWZJxeNphOdKoNSwN\nwzD6D5DF/OySYDjoQ0Uk8CNLU4mOG4/Eexr3OKCeAlLXDaZlCDpns+Ps1TnD+VAU9oVYrABJmqoa\nyqJG1TWhiUzGp0lu10sIbNdG0ZQ+1bs+ae2SY8zT/R3L+xtUVSpLkR7INDaLMopUpm9ZnHLYbFEU\nHccRGchgNiJNSzoF/FFwcjXoa42Ohk6f99YxIYcE44EkyPcDjme6haIouAOH5BCRZ3nvMjD7pPWC\n4+bQR8QplLmY/t2h29NEwHJtHM/F62PfLNeiqZqTPk02QuktpnHc56Uq2J4QRYq86CPv9JMkQrDu\norJ/ngqXeUEUHimreZ+7aaIi5F3JUlWlMj4kFKWQNbrOE+2cKQE7WXQkmAT4o+CEmE+jhKap0Ay1\n32BMhovRaVCj9RmebSMbsulYJ4+wqqrYvktTP0cutifZUtfnPjzb9vbbDWWdMLs8PwX9BIHHYjrm\nPsk5ZgV5UlDkBVVZSIZtU/cB2yLjUXX1RAOJDxHRNpRNtL86G6bRE54l48N23d4M77Bb+5i2yKgk\nMKjEH3m/uZf+X2J96za2P/1H/wDblg+bZVuiZXMsPv69j1FUhXe/es9gPmBxvQA64n2MPxiQxyWb\nhw3X373mgx++5uaXkiz+YvqSYDwgGAcU/QSsKmvKoiBL5YSeXkyZDCdiKNc0qj7hSHDWOWWRkSYR\n0yuxbi3fLgnXoViKCh/N0EBR8AeBJMj/UyRb0zbl2pIWTC4mgh/3bNZ3Gzb3m9N09ubNFzw93fHy\n+ntoisXh6SAaOlUhjyUzMk8zsjQhS2NMw0bXdJIoIeqvfK7v4gSik0IBb+gxjsdY3qcUaSFsua7D\n7qUCtmujGz0gsUf6NFVDeDySRCEXH14QjIYkRwkhvv3iBn8U4Hgux41shGevz/HHPqYlwE1Nlwog\ni1Isx0QfGoJBMnrumWVQVSXR4UBdNnj+QDyVvoPtODRlcwpYfrZOabomyCJFITkIqmi/e2K19Ll9\nv+Tmizt2yy1d2zE6GzO/nveZrHvSOKIoUpk2KypVlNK2Te8HlVBiw9TJ0ozdasNhs2V1+8jZywvO\nXl1K1qkhf6cizdk97gSn7ljkSX563m7gs3i1IDkkbO43p8GNgoIdSFVPJ62BN5//kuSziB/9a3+Z\n8XxGMAl49eELPv3+B2wfN2yXW1RVbiqu5zNaTDl/fU7bdoTbENuxe/2eUFdcd8BxHXHLe2lhjHzK\nQgqDxzdLulplfnZBMJZJ8avvfkyVl2RxTryPyaJv0FTflvWt29hm8xf4w4BCL6jrmok/YTAZ0LQt\n6TEV9E8r4smmp8+6A4+ZopDHKW7g9Var4UmImCUp68cHbMclGI2YXc0Yn4+pq4KyKDnuDpLUbs9O\nurfhdMhwKnauLE6xQ2H5v//8LV2j4ASOWJeykt3DTnpYI5f9ekNHx3g2PQ0TnnVsXdf2qv4CTVeZ\nX8+hb1CfnV/jeUPm8yuGkwleT8Ztm1b8s7aB3/jU5ZCiyFFQ0VSDeB9z/+X9CaOdpzl5mpJEUc8d\na/F8X4z/I/8UGWha5mkqB5yiA4/bA7puMF0ssGyZuvljn7Zr4diLaAupRG3P6X2lCmVWUKTCEhP0\nuYlSVJi2If27Pt+zLquTg8SyTRzfYTAdMD4fkyUpmqYxv5r3xJBKohcDCbo2TAN/5ONPXRStg1bj\n6d0Tmq6J62Dk0dRN35/dUOQZjucSTAYMRuNTXoDpSLj1sxBX0b4JybE9h2AsGbTHzfFkGTusBD/k\njwOh1SLk4TzNiMJ9L5i9IM8TNutHrj54yWgmIFHLMRnMhmL3qmsWV1eURUYRlxy7I5Zj8fD+kcPT\nluMhYjAZnrh8pm2Spymf/ZOfs1/tRNJkqpimJIdN5lNmlxNopILruhbd0v+Zw6YqKombDLM+m0Na\nNlVZYbs2k/MJWfJbHduft66B/wGQkgr+W+C/ASbA/wS8At4B/x7wZ0YxV9cf4/queDgdi9nVFH/s\nk8YZu+e0o6wgT7KTyXd8NsYNHNJI2O5NLZsBSkcW5Rx3e959/gVnLy6ZLOb449783HWs71f86h/9\nQk77xYTjWtKnPvzdDwmmAWmYiY0m9FndPbK+W3L5wTXeKKDMhKIRbkJGZyMsz2a7WlGkmWQVWI5c\nKZKctuvERF/VfUqWxvkHC5JDzGF94PL6Q0BYZZb7TY+mKiosLMFjaypdPx2s+6tyckyJdjHji7FY\n0aKM1cOS5e0tqiZQRscJmJzNuPrkqr/6Jn3qlYAqn0NL2l3LcXtgcjZlcj7DsHqj+1gyJzRNrD7x\nMWQ4GfcVn3bCBGWJ+DEXL89wB65sGv3hImEkOkWaU5U1mmrKpjf0CKYB47ORYIOajvH5GEUVW5Km\na7i+jW7J8GI4E/tTkVTkcc72fsv0aio/f1u4css3j4T7I2VZMFnMGM0mOAPnJK8JxgEXH5yzX+0J\ne5qJbugYpsTdLa7PCDchx5VsOrqhcVgJQntyIVU7irgz6rqkKBMUrUWhoywzkmSPHXzM7MWMMi1Q\nNBXbtcTr2sLFy2sAHt8+UmZHJucT7pYbVndPDGcjvJGPogjt2XIs1o9L3n/5hqJIJefD8/GDEdAx\nnI6YXEyJtqEMa3oK8nA2PMlByrzoZU1RL3avKHOxGwbfecHsxZQ3P/v6170v/IWu38TGVgH/CfBT\nwAf+MfB3gP+w//2/Av5T4D/rf/0zyxlafP6TX/Q9tobV8h7Hs5nMF6iqzuRsQnQ48nhzR1PVvWVF\nw3IdmromOaZUZc3T3T3HzQ5VMXB8lx/9Gz+mrTqWb5dcqCqaIQEo0S5kPJ8yvZyxeLmQKkGVdPbk\nmBLvIhRNZbQY0TQVqqqyX2+o65JPf/971FXL0/s1x/2Ox/c3wpPLUn7+j/8ho8mMi6sPCGbfBCQr\nisSoWZbBeDGiqWrapcAFu06EtM89EnfgYrs2+9Wew3rPYb3tjdE6htHTMwwdy5XUKV3XmFxMSNIj\n1ZuSq+uXjGcz4q1YnNzAOWFy9su95FICTdX0EzaZphmWhWZofV9MqmPdkpfsObi6rTuyOMfvNX+6\nZZCu1hw2WyaXYwxzSNIk7Jc7lm8fyVOZavojATaGhx1qa+OPPUnqqhri44HNco3lmv3zFIFuU0ku\nQVVUPN08iUC6aUUP2EFT1cS7iKdjQpbkaIaONwwwclP6Yv2Qgw66nrT7+HbZE0VULMfE9mxml3Oi\nw5G3v/oSXTMxdJt97z+eXMj0WUGq2+fJOUrHJz/6PqqqYjk2l69fMpyNufrgGjdwiHcRx+2RLBVf\nsKpJf0w2UiGICHh0gmbqvH/zBW/f7Hj14aeMxjOyOmM0m7J4edb3CjtMwyY5xCzvV7RKxfRqJgOr\nwCHcRUTbCKsXqeum0GnGZ2PuvrglPkQ4vos/khuB5di0TYfj/1ag++etZf8LIAZ+BVwB/w7wb/Zf\n/++B/51/zsamGRqbh41E09kWVZLT1BWW5eEPBrhDlyKXPolYdZSeAyb8tWcG13G9Z/u0wTQcbNfl\n/OULjqsD29v3zF/WwgbbRRRpyXgxJRgPpMfUVJSVmIZVRRWdUiDMeX84oGvh/u0NaZQIIsgxsQOb\nw05S603LoqNju91hWo6Eh/Qe1bZtqdKSNEmAhiovqXIJDTb6NKe6zyfNYrHc2J59mqrmaSaWLUVj\nMB72/S7pXz27ISzXwh8FjM8mzK/OGM/m1PljXzUZGI04D6JdRBZnvReyo8yF3z+9nPUp7RVp2J68\nt6qqopkSWWgY1glm+TxMUPpQHVWX37tOCBxiO0qpa6FN6MYYzVBpu4ZO6YNIdLWf+nYoGgLBRD3R\nV8quEwmH2rBf7iRkeSYQg67rqOuGfHNkdfdEVQo9xegpF0KWlaBqpVNO6U3VqncJeOJN1g0VfxSQ\nxDH7py3BcIQxtAi3B7najV6AgtjnhpI7+nyNt2y7f44V/mDAeDHFtEyKrDwNJbbLNY7rMZiOqMuK\npq6pyoKuD/QxLIPRfMzNm5o4PEofsM9RGPkOi6tzOVD6z3pVlJRFQdPWGLZBWzXUldjP2qbF8UWE\nK+JmAwUBAuiWVOeqqvTfgxj7nz2335b1m+6xvQZ+H/gHwBnw1H/9qf/3P7PKuCIYjPFHHuOzMcHU\nR9U0Dk8hbSM9qvFiymg+PjX761I+BM/2oLquhW2mmD0+WSHZi5Ld7FllzxBJw5bTOIsyfvn3fsnD\n7VuO+x2L82ss0yGJQhzfo6nlCjO5mJLFQlH4kz/6GY7v4vg+4/mM8WJKWzdUVc2L4pV4I02TNEx7\nvFBFXZcs379HQSWPi54QUTOaD3ECl2gbkobindw/7TFMg4uPLrj88BKgp3xkLF6e8+oHr+ialjIr\n2a8OJ9LraDrhL/+1v4KqaN+4KHTBGT1vfkUqOQFePw2LdhHTiymvf/iKh68eeHyzpCxzTMdkcX2O\npmnQChiyqb6hmOSxGKh1U2d+ccbVRy9wPI/kGLO+W9K1HfPrM5Q+hs72bMqyRNdlmqkoqgxz2pLZ\n1TmTszmGKb7UbJmd6Bq2Z+MOXbIoE6HrfICu63R0bO63bJdbdtsldVlSlQXBaMRgNMTvc0LbVjYD\ny7XoEAS91gon7rgJ+8PHwrIsLNtDVWXDSdOINmlls69LdpsnOqVhfDY9ZUR0bUcWZRzWB6nMcXm6\neSJPchzflljFYIA39BnNRpRFSRJGrB8f6DrIE8mJCCYBVy8/ZjK5YLKYo6BRFSWHp8OJ4qEoCpOL\nCYZhMRxOGY4mBOOA289uuf/qjjg8Yjkmo8WQJErYPm4AyXw4e3nO2csLsihj97RmeXuPPxjiBQP2\n69WvcRv4i1+/yY3NB/4X4D8Gov/bf+svBn92/d2/9TeoK2G4f/L9H/K7Z/+6TMjMjKZpTk1k3RDh\nZFkWbJ8e6NqO8XxK3V+rFhcLzs7n3L15oOuvf4Yl6dnPOO3npPE8zUnCRAz3WUVdNqJzc1QURe3l\nHEIS8QYek/MZqqoRHULK4kgSJUzOZ4xmY+l9FRWFYYkP8XCkLhsUVIbzIZZrSy5qLoy5uuqT4DNp\nyG9WT6THlK4WEsSzc6DrwLQsDMOg6xKKNCfahSdrlmEKxeKZqKuospE1NLgDV3ySYUqZF4KObuUk\nB2jquhfP5oIKL+tvksd7IKHt2BJK7Zi0tUNVVdRVhWZoQo8ocxbXZ4wHU3nJNwfypBD6cF4ymA7w\nhnKN7Y4xhmGgqRpdK7juPM0ZL0SAHO/jEyDUdCQfAeR7aeqGMi84rHdSyWrGKXHKdlyKHi/Vti2a\nqZ+qXWrRiJm2RZEX5KkMEUzb7NX6VR8h6LB4cSbX1hbcgWz8ju+SRA1FVhLvY/ZPe5SezyfcNo1g\nHJykKv7Aw+gn7IqqMlqM6bqO6HikLp75gEbfu5Qe3GASkBxjqqwWvHwruHWlx7wDfchOTVO36Loc\n3OvbFfunLfEx6p9bx+ZpRVt3kvGaZ6DA9EIGWnVZkyUptzdfkqZHDMOiKotfwxbw61u/qY3NQDa1\n/xH4m/3XnoBz5Jp6Afxzj4jR4ALXHeK4Hkbn8fT2SaqKrsNxxXf3PJquSskEffPLz9A0Hcu2KRKR\naXznr77m7GpOGmWEUXLCvDhBv1l0HaP5iOPmyNPbJ4H8jTxG+QxNMdE16X94A+/kOJBsU5Pp5VRY\nV08268cl9+/eoZnqybjc1A3JISbcH4iOB3Tdwh8MGUzEXqS0EB8TuqYj3IXyoqwO1G3Buy9+RVN1\nTCaXTM4nXHx4TlO37J/25LH4KvM05eFNzvpujeVY+EOfs9fnTC9njBcjDqsD918/oBuSYBSMfcqe\nGxZujhzWB4ZTqRCzKCNPUtI4JYtT9ss93tAnGAdYrkWZlYTrkHpQM72Y9MniFk/vl+Q9dTZPEx5v\nb9FNDX80YPu4JdwcURHg4dPNEjdwmF5OZTMvq14FL/q/JEw5ro8MZ8P+mhyye9wQHY7M/QXjc4k9\nDLch4TYk2h9J4gOaZmI7HsPZkEnv/kjDhCSMBSCpKjRNc0o203QNLOjahuh4YLgY4o080QkmBaZj\nigZxPhIkUR8iYzoW47Mxh/VeYJp5y9O7peRvqAqD6YDhfMj5B2d9WHTBiw8uaKuGn/39X9BUDfPr\nOau7Je8/v8E0bSzbYbo4xw1EdjO7mjG/nvPw9o7t4xrLdgWbZemn5HgncPqDRUi+bdexX+7YPq5P\nqPfBZETdVNy/ucGyHeZnV1RVQZrKxLupRCKVRim+P2IyPseyXFRV4+uvf/rr3hf+wtZvYmNTgP8O\n+CXwX/9TX/9fgf8A+C/73//mn/2j8OEPvkOVSXJ2VVYoKmiaSpYVZElOuItOGqc8yTnuDlRFjWLp\np97L4nrO4RCy2+zpVNFzPYtWVVWlKRuSKmF1J9cFdyhYbznNql4mYqDrGpquA/KC3H71lqJMUXup\nhWHYOJ7H9OyMLE74+pe/kni9ToNGwTAtZhdnTPqrsySZb3v6bMl+vcUfDnj1g9fkccZxV2GaHmZg\ncvnRJcEk6ENylVOFalgGtiPqfdtzBIDZ1Nx8+RVP97dMZnPaVrIj3MBFVxTSOCMLU5JQtGfzq5k0\nnMcB0T4mTzLquqZIS/I4x7CFUOGPfYqsYHWzosxK4kMCdL3X08DpsxkM02Iyn2NaFlVeYTkWwTg4\nHUCmI/SRNBSyRtt1uIHXB1hL7J839EgOMXXP4PNGHrvVmvgYSXqUL18zbRMnsFndtuiG0fc9u5NT\nRFGkQa/rxqla000dpx8+rN+vMSyTj37nE3RdEujLojx9NmzfZnw2PgUvS1UtZnlVU/nOjz+Va3kH\nu6cN4f7A8k7BG/pM5nOaWoi50VZyZp/puPEhpsyq/sAUGcdgOmAwkZxYFHh6v4JWYTgbY7vuSdJU\nlxVRDwpoKok0HM2HTM8nLN/f8/XPv8SyXVzPx7JtfMfHn7i0VUdbyjRbQSUNMyzLZX49x5+6uEOn\nl4CUNM1vTfB/3vorwL8P/Az4Sf+1/xz4L4D/GfiP+Ebu8WfWJ7/7fda3aw7rA1mUovUgxboSe0p8\niE/i1yIpSOMETTHkQ5QVBK8vuP7uNT/5uz/h7ss7Fi/P8If+KRAYRXRkVVmxfPsIdLz+4UdYtikc\n/PFADNp9Unpd1XS9cPX+zTsebm9wPZ/xZMb59Su8wMcfDrh98zXLr26xbEFZD0dTBtMRw9mQyw8v\nGC+G/IP/7Y95unni6qOX5FnO9mnN+HzC9afXPH79SBIlDIYTBtMh1999RVM3vdDVQtUUFE3BsEz8\nkUxZg7HwysLDkdsv3lKkOaPRGcPpmOFsJOwtIAtTwm1IFmcMZgNmL+acvT5nOBty3AiG6Tnqbvu4\nRdf1U+ScXdjsl8LYT47JacLo+LK5NnUjf2dfMiaqosLxxC4ksX0aw/kIaNktN6iaTlu3OK4jKfRt\nh2mZmJbBYXOgbRouP3pBMA1AkwT23cOWsw/PGc1HGAthmFV5haapeGOP/fJAfEh6w7zSo8LN/qqq\nnSaPdB1pmBBMB3z0ux/y+HbJ8u3yBHtEkZCUwWxw6tc+k4ejnQi0P/7970gOZ58itV4+EkcHTNNm\nMhUnQdt1HFZH/GFwCqPePe2pshLLkmGPbul4A5dgGuANPHbLHcs3S5q2YzSf4A3k2h4fxN6XhmmP\ncWqxXJG9LF7MadqCz376cxzNx3KESzecDlm8nBPtIm4/u0M3TEzTPsE0Z1czFHVOMBzydLNkfbei\naX+7sf1564+A/ycZ81/78/5w01tCRvMRw/mwP+0SBjOxQ2WJoIbKPr5uMVrgjz2SKOTu3VuaVozS\nmmEwu5px3O6JDiHj+YSqqKUEH/m9IFMlS1K+/JNfYlk2tu0xOZ9w9upMTPeHhKrXyimqwnRxwXAy\n4erDK7xBQBaXPWnEJEvPUDqV2dWc8XyCO/BRVZnSPr594OuffUldNMwuF1iOXG1N6xNUNG5+cUNZ\nlKLbu1gwOhsxOhtxWB6IdhHL+J48TWkbGM7GvPrBy28SrXQNr21YnF+SxTmWJc3saBeKuHUg4lbb\ntwkPB3arjYSE9M38aBeJh7WsewyPTnKM2S2l76gb+sl4r6gKel8B2b4jPaNNKFq4vhdYZEWPSpLK\nripr2BzYrB7ZbZa8/u6njMczyrzEdCwGswFZnHFYHXh8f0OWJeiWhuN6XH3wkqZqUTqFLEx56ntp\nMoRw2K4e+fLznzKdXTGcz06ASHcgw4IyK4n2EcfNkdWtdD5s32G8GOFPAni7FKhCb4s6rg5Yjsn4\nfCyIobuNHCCT4JTxevvZ7WloMb+6QDcMnm4fcDyX608+YHX/yOPNHf70A6aLKXdf3nLY7CnLDEO3\nMA2HODqSlzGDqY/l2qiKIgOmMBGkES26eclgPMAfy1X5uA1P6VzQg0YfZWgyGE7RNEMsakNOuCwR\nd9uYzoK2m1IVYm97+Prh5BKRvqLL/HoGf/sv4vX/V7N+01PRf+FVV2JXMWy5Smzvt+Rxzmgx6v2O\n3cnkbTkmwXiAP/bZrzXC457oELF52OIGLt7IZ7fa0ja5uBmSgmgboet9v8K2KbKc43qHYZj4fsvZ\nqzMm55NTr6SuajRNRdN1/GAojoGLC0zHoi63vQhVQdcNbMdlspgzfzHH9iQuL9pGHHchm/sVk8UM\n1/dPdAvH94h2Ieu7NY7vYjk2ju/iBt7pZ6DpGsfdgeN2hz8YMDVmDGZD8iTjuD1iuzbBeADdtaQ4\nRUkfINKckorkSqai6SppLJYkbyA9nOfsgudA6sF0wGG9Y7/eoSgqru+hAJ3S0TQ1mi6VI3R0bSuM\nvNOzEw+soign4KcE8RQcNntW90suXr5CnWsYloGiQZHn5ElGFmeEhwNpEhEdIkzTYTAekUYx0T6k\nbmr0rEA3jJMMpu1adusNjjMgGI1wXB9v4OOPfUEcqSllJqDJw/ogE8XzCYqmUmYyNCrzArfvu2aR\nIL4PTwc51IqqD8kxZXMrapJDjOVKnsBkMcXxXLoGdNNgMBlx2O6ADm/oM5gPUd/c0zQ1bVujqPJM\nG3Q6peGw3aEZWh+U3ImPtmloaUABy7MZTgdkfoaiqRxW+/5nlZKnOdE2lJaDG5ClMXF8xJ94sqkX\nAvAE8EaCv0qO4jhIw/QUJqOooqlzff838br/S69v3cbW1A3BNEA3RBWvGd+EaCRhQp5lDGcj5i8W\nMrmiYzAVfZs78Oga5LrTm5AH45FQPEyTxmpP/ZtgHPQ9K9E60YFuPOc7WgxnAxRFEDUookU7ro8c\nenySbuhopnGy1qweHgkPwh+zHJsiK3sSa4xpmsyvzsSXmRWEuyNVUdDRUeS5kGrrEW3dUpfy0qZh\nihu4vPz+S8Ljjiovuf7OayaLGfEuZvn+nruvbvjoR9/l8sMXTC4mbB/WfPZ//gpN0xn2ORCargvD\nrKgYTifUbc1u+8Rhu8MfDnAHHrZrc1wdcQKHyeWEzfKJpq3xxx626/D0fkkSRhRlhmlYGJbo2nRD\nBjaaIXFxZVpQFhVt2xKMfObXc6qiYvuwYzicoWEyGE7wem7ZfrXhV//oZ+i6iesGOLaPqohbom1a\n8jJjt1qzvLtjfn7J9Gxx6rPRwXS+4OPv/A7Hw5abLz/jkx/9EPDZPmwJxgFXn1wJfSTNufnFzek6\n/vT2if1yz/phRdNWBNOAYDyQqXFWcvOLdwSTAYtXixNVeHY1AwRC+RyVZ/s2tm9T5gXpMWV1dluc\nCwAAIABJREFUs6JKW8bjBa7vY7s2/mgghnnbQFFVFFQs75yqynnzq8/Ii4jLj68IJgF5nOFPfCGe\njAdYjonpWjSNqASKPGO7XJEnObYnPmSzg6LJiaIdcXIkmPiEW/eExor3EXPLwJpKL9KwDFRFcPDK\nM125rlndPv2/vJX//1vfuo3tuDn2I+tvrENaH3Tb1g3uQBKChjPx0zVNw3G3BwWGkzFJmBJtQzEh\nqyLVaDtIo0y0VtfiKdR6K1BTN2iaCGjdwJUX8X57Qkg/9128gSeY7KalSHPiLKauSwzLxPUC4a2Z\n4tc7bo50Xdur5lvhuU1csjg7iTGrUqgMdSVIHlVX++ueKid33dK0NUVaYJo2/miI7UjI8HFzpCrq\nk1q8zEsMU14cb+CJXCXLRM6gqycctDfyaJWaskgZTIYng3fbCpuubkoe3t3gBzaf/uhj6q4jSxLc\n3p7Wha04E0yTaH8UGogv1SUgYuI+G1TVJZOzrkXjNhiPcH0f1/NP19u6kgGHqoiGbHZ5Rl1Vp5+x\n6ViYto0XBGiaTtsINdkwxf84nE0YTse8+/xLDtvt6UpZ99KcwXTA/mlLtD9iWDrD+VAqvbolTwX0\n6foSgmLapvQaFUUQQk1L14gFq6ma/llVFGkOqFI52pKSNpgO6RoJ7HFcB3/oQ399FluUc/qstnXV\nR0saElps2xJujfQ0y7yS/6/HYgnqqjmRUIw+MlDtp7ziZOlEJFwJzKCuao7rQ99LFjeOYZki3m1b\nvMA7icCzHqVVFb+Ve/xa1/r2qWdpZRRZzuR8hht4VGWFqmksrhZ4IzH4DhdD8jTl5//wH9O1HT/4\ny79PmZVytfMcDFsSo6pSYscuPrzg5afXUkkdYo4b6WFpuqQEza7nbB+23H1x328GYm2yHKnydEvH\nG3qkYcLm8Yl3X7zDHwyYLObMXkwxbZPj6shxc+h59+Lre7ZTxYeYtm6ZXy2IDhbRQSxNklIUMFyM\nqItKsgo0hd3qyOObJaAyHE/Em5rIFdkbeZy/vKDMS7b3WwETKjC/OmO33LB8/yjwQ885vQz+yMfx\nbQajEYvrBYPJgMPmiFLWTK+m3L15y0/+/k/5t//dv84f/OEf8Lf+xt9htdzw6Y9/gNKpbJc73MDF\nsHS+/vnnZEmG5YvcRFEU5i/mjM/HbO42bB+2rG7XgJjYg0lwQhmBUDWmFzMh7x5T0ihjejWlrmpu\nv3hPVdRcTAcs3AtGswnxPqHquWyKIpvX+GzE+QcX6JbO6maF7fhyEFmCfrdck4e393z9J19y9eFL\nzl6dMz4bk8UZ24dNnx5VC9usxyOpmiqtiLxk/yRk5rqqeP/ZA/ExpKpKDN3C9fvnGrinjaJICyzP\nwht6lFlBFqai22tbjj0jranrE9vt1cffwbQtwk2E7dp4Q5+mCXtgaEEaJezXOyzLIhgPMQ2L+eW5\nHGJ9BquqSeU8nV/g+2OCoWCWsiSXTbiTgzBPMqJjiKopnF3L52Zzv6JtO+jEvfNtWt+6XNHf+/G/\nhW4YhIc9+80K07bQVePU5J1c9LTTMEVVpRppa4mbSyMhaaiacKiqsuCw3xAedr2DwGY0n/SBwhVZ\nLNcKx7cZX0xYXM8l9EXT+olfzXG3R9UU/FFAHudkcXZq4ErqvAF9WvnzSyoJ8gaWLVigPE3Yb9YU\nifSInskjVVEzvZhz+eEVjuehPCcyo9DU0rvzBi5VWYsA+XyMZgh1IksSkiikaVoMw8QNhGkmYb9K\nr8GTA+CZciJctZIiLek6+f6TYwLAYCKMNgWF4WhCWTTcvX2kaTqm53OapiXchqdIwOdqzfXkKusP\nfdq2JdpG7B538jLFuXDl4BSzd9hsCfdHHE+q4/XthjIrhDrrSBJ7mRUYlkkwkmDlMpNQYpH56Gi6\nRMs1VcNuuePp5oH4GPVVPDzdPXLc7nuTe4iq6BiGeYJmxoeYY++TVVSFw3bL6v6R7XIFihjL8z45\nq227Ph9CWh2WbRGMhgTjQS/uzXi6fZT2hGkwv5xx+eq8j1JMiI4RTSXVtaZpvSWqpkMoyYZpUKYi\nztZ07RSF5w09/LHoCf1R0E88jZ4aLQfE+FxkKW3b0jXS69R0Xb7nnjCs6zrBVLBdz/1P23Olb9rH\nRCqKiuM7/OJP/x78Nlf017NsVxq5dVMQRjuCcISuSsq31avQj+ujZA/UjdhQXr9i+7jhi598huN7\nTC/mkveYxBz3G9IkQkElOo6J9pEkN/XgR6OHVvojXxrCZ2MczxEhZl2SRCG6qcrE6ihNW2/g4fo+\n8/NLkmNMuDviDT0hi1RNn2Af9Pytkqf7J7ZPS6bzC+xLGfe7gSeDhus5i5cL1rdrwu2RthXxZZkX\nLF7MmX90SZmXhNuIYBxQZuIJ3W92pGnI5euXuL6PPw4wbenhdW3Xb2TSP3n+5zIre3R0TlVWMt3r\nOvyRIMhn52dCHd6G/Ok/+Zyq7PD8AU3dksc5aSg+RIDBWGgiTdOcDPbbxx3r23XvcCh76rFG1mWo\nuoqqK2weV9R1xfhMUDtPN09YrsVwNhSRqabiDQPZQHWVJhOVvtOn2ddVg1G3uFOX7f2W9796T3jc\n0SkNHVc0bcf2aUWeZBhfmSxeXDKeT0nDhN1yR5HmFGnBcRPijzwMW2d5+8BuvaapaxS144Xykrpq\nyPp0q8F0wOVHlyiqQnyI+yhBjTRMWC03LG/u0S2D85dX+AOX+fmUcBcKaiuUDW9yMTvZ+JJQrrV1\nVZ2cBMApx0BYeu7puZRZeTq0n3NaLcdi/mJOGqWSY+D2QNC8lMPac7HdjrqsGc2G+GOfpmlPB/Oz\nNzWLJWQomAS/ydf+X3h96zY2wxLm1nAy7ZPPFaqiwO0dB+u7NckhPok9w+2RwVQkA5pq4Poew+mA\npqwxIpPx+IxgIL4+zx+SJznBOBCsET1No88fPTztsX0H3dAJtyF0Cq8//YiqrLn/4pbhbMTkYtIb\nwjoWr87I4oB4H5ElKTefv8WybHTTOBGAq7xCxcDzxqhodE2HaRnS8xp6J5iiNxQk9+O7B7pWsOee\n7zKdjoheLOi6TqLt6obRYoRh60QHF8sSCkYWZ7RNQwccNltuvngDgKrqOI6PPwwYzkaneDijD4KO\n9hHhLqT807KfdsJ2+USWxPzgxz/EHwx5uFly3IYncixAepQp6vTFDFVV2T5sT5tA3YcFWz1uuipr\nNg9LyjpncXXGeDHDMEw0R+eTH39CcoiJ9vJMNUPDH3koikpySE49IUUVKVBVClUZRaqtiw8vmBRj\n6roij8V0PppMGXwy4PyDC6JtzHEtIdS6oTFaDOk6+bNxGKNEHYPRBM8fSMpUMEbTRdD7jP4xTIPd\ncidX+/5z09aSXNZULcFoRJYlvP38M8o8IdxFhLuIru24+OCKupK0qWAy4OX3X8r0Okw4rHZ0KNi2\nTZ5Kf9nx5fPz8PUjTV33spIZVx+/YPlOyCaWIyHMZV6yW25499lXTM/mfXrYmjwtoOuwPLtPuBd8\n+/RSrvr75R5UsfiNzyfousZsMf5X95L/Baxv3cam6aqgZCwb1w0wTVNOe005sevlVIIsEu+j5Vio\nqpz0hiX+0bIsQFWYXZ6j6TIoeA7WUFSl752ZaH326HMVODob4/gOh/UOVVO5+PCS5JBwWB7whj6a\nqqL11yohOMhV7PHdPeH2yPxS0rfzJD+5J7R+c+k6kTekUXqydYmiP5bEczhVRKqqUuUl8S5ENzTc\ngUd8SFA1lfmLGV7kYVpWj8GuOGz2WLaJG3hkScZxuxcSrWVDk6LrBv64kb+3bZ2ItoZpUKQ5y/Ve\nhKyuQ7g/Ulc5ru8QDD3yND/1n0xbmGVpJXj0PEuoy4bDk0hPLNeWn41tYvZDBUVVSeIDcRjy3d/7\nHtcfvyTcR9BBMPZPWsU0SnsSsINuqqdrrNo/o7YRH3DXthRZzmA6ZHY1O/XHjusjbdXh+gHTszkX\nr65oijsOqyO6qZ0iFXVTxw1cikwcF64rG6naGViWS9t2feCwcfLe5lFGoyqnahhdpEld2zGcjVEP\nsNss2a126LrkmUorQXBaaZjKoWnqJ4jmfr0T7qAt7L08zU8T+uQQk2cFmq4QjEVgnoQR+/WG0Wx8\n8rhmseg6VU0R2YotZJbniWfbNWRxSa4oLHwH03KIzOibyW7vL3Z951/9y/7/YX3remw//sO/2jf3\nI4osY3oxJxgHHHdH6qrCG8iV0R24ItEwdWYv5gymAbbvEB9D3n/xhnB3RDNUPvrdj5m/WND00zmz\nDzEGwTQ/vzxiJxKMT1WVLO9uybKYwXgkAELXpkxLon3M6GzE+GyM6RiSv2AZQhipO4LJsL8yCTtL\n6dk2HVCWGXmaEB8kSSuLcrJIejnH9ZE8yfFH/ukqtr5/4ss//YK2E13UcD5k8XIhWZ7WN6z9Is14\nfH9HfAwFr10JXfb6k9e8+PgaXTdp244qk9jBthWNW1M1whhTO3arFUVWQKfS1i2aatChEYcZRVai\nabIxjM/GTM4nPZk45suf/4KHt7dkoQAEqrxGN3RsX5j6hm0ymAYYpoltOXz0g4+ZnU9JIwEf7h53\ntE0nfLMkI08yyUXVVLyhNOXDbdgLSlWi7VH8tccQx3c4e/0NzsdyLAErZkJNyVN58TVD5/z1OaPZ\n+BR7OD4b4Y98XN8hi/Je1kOfFaAK3jzO+s3e7gGTGseVJFJ5Q49wE1KXNeevxd2iaxaj2bTvx2bi\neX3akIQxeg9FWN+vCLchZVph9lRjN+ilG/1n87nPO16MefX912i6zuObJW8/+5yHmxuaooNWhgaq\npkorYijTZtOW6b7l2ORpyur2kfgQkSXZKfzaDRy6rifFRILCWt2u+eM/+tvw2x7br2d1bYeiKViO\nxWAyIhgPxCqzhKqopHdimWi6ijcSg/r0fEJVVWyXa7IkpSkbDFOaz7PzCbphsrnbnCY/h82Opqkx\nDAvTNNH6BPeqlBdfbRS6VqGtOuJ9Iibriwnr92vivYSQZEl2Ql3XpQSv2J4r17BKNstnpHUa9lyy\nNKQsC/TMFEGvK17CcB+SpxG2b/HdP/gBtuuKpKNqSJOc+JhgmBZOH5EX7yPypDgFBheZTNA0Ta7U\niqIxGI1QkJ6N9GoKDqsD1bEApUFVhXQxvzqTqDjXoUhLqqIkGEkGatO0JHGK5YmwtCoqyqIkPsZS\n9Qw9dN0gr3LSPEZBRdekyjFtg6ZPijdss2flteyetn3UnQTUhNsQo0eE04nO6lkV/5yEVRUVg6HP\neD7Etk12qz3HrWCahKknfSfd7L20vkNT1eyfDictpGFKWn2VVzQ9QFMgpQZZXNDBKcgn3scoqnwG\nRd4BtmtRZCVhDx7VejlL27Y9x6+hKkssxxYvKVLRZWnWux18mebWFVmUU6Ypuq2jqM+bqXZK4Gqq\nmixNaNoKP/VJDrHkt5omixdnOJZ7ujVonYZTt5SZYOpHC6nmiqwkjWOSMMYNfBzPQdU0uq49+aaf\nQ4YkoPu3aPBf6+oAxxNld9e2Peq7wbJt0ijjsDoKU98yuPrOFeevz5mejXl4d8+7z76CVmPSUxMm\nZ2MGw4HgkNOCpm3RdI3Hm3ui/YGLVy+ZLGbYhjTX8yyXHpRmEwRj6rohXIc4nsvlhyMZHiQ5yTGR\n697mSJWXtK3EwummTrSTKZg39AjOxpx/eM76dk1VlhwPMq1yA4/x2ZThbMjmfsPuacPq6QZvbPN/\nsfcmsZbseX7XJ+bxRJz53CnnN9Wr6urqrsbGbSTjQV60gCULJMSCLRIIgbBYIiExLGDDClggWABi\nwcpCAlu2Jbu7TFfXXPWGejne8cxDzCOLX5zzmm67bbe7XH5Wh5R6mambmffdG/GP3/D9fr6/MfwN\nemGfeBcRDELcnk8eZyzeLXECBwWBD6q6SFHiXSJ4IDTaWrhqTs/D6TnMb24o8oyP/8yvYvsOy9sl\n68WCw2GFYVj4PRHo+kHAaDrlsDlwWO8ZX405f3bB/O2cPMtPqvv9as/mTqxGj7/2mOFsjNJ+zMO7\nO25fvwVEL6eqSreJ1TugYU1yiFg+zIn3EX7YY3g+hlZeVkdLlajhfdn+dnGFRVaiAOeXU97/lWfs\nk5S7d3Ne/vgVWZxx89lNJ3VRJHnesQhGAfEuZjeXZYyqqxzsg6S0j0OiTcTi3YJgHOD1fXrDHr1R\nj3ASsl/uuf7ZOwYXQ8JJyO3Pb9gttzRVTVWJnq1pmpNjo6kbdss9h+2G65cvmT26wg8Djolgpmnj\n9XyGZ4MTMeXlD19x98UN0WHXQT1HuD1XNHZ1Q57lLG7vKIuS7Vxw6Xma8+LXXnD29Iz9cg8ohOOQ\n5CA+YAFwlkweTRmej4h3MdvFCmjFr/zsCs3QT+Ocpmnwwi9Dtf8UNPkLvizHpMwKWVEPezJn2saS\nyajI3CBLE6KoYBD1ibYR24cN0W7PaDalKVsURac36GH7Ljdf3MoKvWlO3H1dM1AxqAvxztmejWaq\nFHlGGmuoqsZgNqTIM25evyH5dMv+sMTzu1zS7Q7Xsvi1b37IarHhh9//ROLsPFvmZkWJ1tl1mkoE\nuv1pnyTq7EG5WKqGZ4OurXbQP4eqLNjOD8SbgtXtiqqQyLXjDEUSxFWqMqbJZT53VKWPL2aScTod\nUuUV0S5GQUdBDj+ANJa5luuEzB6fMb6cEgz64sWMdEzHwuv7uD0P25coQq2LE9zlW3brTRfEIlvi\nqqpYz1cCVHR9hmdjRudTso7CoqBQlBlJciCPRf+lKBptqwhgsiw47Ldoqo7luoBs9fbLHWZX5Q1m\nfSZXY/b7iJ989zNUS2O73rNbbijzCl03RCqhaScLHIh0YnQ5OjHoyqIki6X6aluBbaaR+GGzJD2N\nKVRNJZyKHCfdJ1+a6Q0NzdAFcGobGJZJ6UrmxWF9QDV0Pvj1r2PoFlVRnaQ3VVlhuRaKqlJ0tOSq\nq/SyNKGqdBzXl5CfjoJc1xWO66NpOfF+JwSZixEKyul72TQN63tJzJIQZpc8zZi/nQsCK5fQnPNn\nEo5UVw11XdBUUq02VU1e1KctavOnB9sv9jIdCeQwbZPR+YjlzbIjbLSnG7hKCqJoS7TdoWka8zdz\ndFPn4tkFWZITbQ44PRfd1Hn707cyuxr4YlGxTVzPp0gqjl59yzHRDJWqLigyXTyfZ0OyPOLzn215\nuNtz8/o1v/Ivf5vH74+5e32DFcK3vvUBb17f8r3f/RFKJwzVDQ1FEbx1FstbXdM1gmFAvBnQFAJ2\nVEA4XuOQ/iSkqRqWtysW71bUdc1hdaCumu5Glzg//fe1aHVZUtQdYNITAXA4kWH68mbJ5mGLrpko\npka0iamqgrKSfE7P6PPkg/d49NGjDlgpEhiza80s1zrxv/QuUKSpa/brDbSy2JHN3pGSC14vZHgm\n8pXrT6+J1pHo2vYblosber0h/f60W7qI7KGupeXygwA/9MmTjCLJKdMC27cJxiFBNwb44vtfsHg7\nl5ddUXTOBw3V0056xqqsKMuSMisJxwHhJBAHSOdhlc2x5EuYjsn2Yct2uSXPUixX7g3HF+JGekiJ\ntnH3+51vt3NviI2uoczNkxZweD7kg29/wGFzYHW7wu7Zp80zyEGURjLnqopKKtmmhC7gp6naboEk\ny4lgNKAsMh7e3Yh4/HIsC4eHDY5nS35p95xIPqrEQD68uSeNMnRdpz8bcP706sSka6rmVN3WdUMW\nJRR5RVM3BKOvltzjK7c8+PN/8bfQDQPHt1FUlfmbOYt3c6LdgaajT7g9l/5kQBLHHDZb/FDQL3Ul\nN+2Rc18WMo+SBcNY0DUoaIaOG3gEw173e4i3LsrxOlnE1XuXhKMABQ3TcFAaHVXpjNL7BFAp25b1\nIQJD0DxS7Th4oY/tWCfihUALY5GyDHr4Ax838FBURXA1rx9Y36/Yr9csHq5pqXj0/lNQ4LDd4Q96\nhKM+uikEhyzpDqjAQ9VFLKuqClVRE29jNndr9usDqqqg6Sp5mqFbOk8+eobtOhzWe8k47fts5zui\nTXQSBB/JwgLW1FG7pPDDuqu6TAkmLvKCojOle0EPP5QhuG5oFJkkn7dNQ1WJ9MPxfDy/d4oJLPMS\ngGAY8uTDp7z4+jPBXxcl/lACl3eLzSlwuG0kTWu/3mEYOl//9kdMrqZoplBwRbDaZzgb0J8NSJOE\nlz/+lN1yS5bktM0xVarisNmzuHsQe1v3/9M0DevFnM18wX69o20k6IQWVE3iFsUKpZEeErbzrQQH\n5cUpIEdRZC43nA2INhHRNpKEL00l3sWyhLgYAi2KquJ4Do7nY5iShGVYBpqhYTkWg1kfy7GoihrL\ndbAcB6fn4vZckn3S8d0KURB0yK2j+0HXdUYXI7zQ60JmrNNIp23lUM/TlOXtXGRQgY+m63z3O38D\n/nR58Iu5kiihpSFNpBWJtoKJ1rpkH9MxCSd9/IHP5z/4CfvVlsFkjKprxLsYL/QIJ4GU/mnRDUiV\nLo28FhR3U4FS0yKp4GVe0NYwPp+ehs2KAo7r8vj955iGh9re0pQ1u8UOUMiKis9+/hbHd3D8L2cV\nxzxI3dBPWO2m8xw6vnPa3DVNw/JmITapNKdtGxRNoaxyUFq8vk/TtmRZQi8MsD2HKq9k0xcLesnr\nex1nrqGuRdi7X+0l37Nt0buhdNOK1GUwGaGpOrv5lqoo2S13IiuIM5rmOFBuSPZfplq1bUu0jWhb\nGF9OqXKReSSHqNOYibXIcmU+FO+Szn8rsgrbsemFfRxPvkZ1XUuISF6KE2Q2ZDAZEAx68vVTFYFC\nFiW7VcVutaXIc4JhiGHpRPsDhqly8fySsqxoVZVoG1EWpUQXOhZ1VVNVJdvVBr8X4vkSBVgVsrGt\nm5o8zej1+/hBIPmgWcJ2lVBVJW2uEI60bhRSnuaZuqnT1pLuftgcTgleti+i8jzLMWwN3TrST9qT\n4LatG+paAlxUXbDvmq5192PHCmxbmkbpIKI2iqIwSArofKbHF1iRCbGkrmr0QvRsRymOpuvopkI4\n6cvLPRfvaat0bgRNYv1UTaVuBLUfjgJMw/glP/n/ZNdX7mC7ffmOON5x/uTRKX/R7/cIOuKHgPIm\nDC+GLG7vSfYZeVxQpkIp7Q18xhdjUIVxtbheSKJ7nEpYh2tx++41+/WKfn+G64tWLpz2efTRI26/\nuGXdwRaH50OCUcDooiKL004cKsZ8VZWglKgQDVq/kw+s79cUaYHT+xJbdDyEjgnpwTgkS1IW13Om\nj6Y8+fgJq9slwT7gqfUUFJXdfEdv1OP82bfYPGy7qqom2u1ZPtyjmefMbElhN0yD7XwjzK6qRjc0\nTKcnkEVDI5yEANy/vkfTVB59+IRkl/D2p29xei4oCvE+Ik8lF/SwOeD4G7F+aSr75Z5wEvLoo0cs\nrhfM38xPS4Fj4jkgJv+iIo2l5XM6uoXtuR3TzWL7sCGNU0zbAkWhKisWXeu8vF1RZMLTs1ybyxdX\nLG4fePv5F0wvzrEchyQ6YNoq2+0ORZUHNEsyonXUQR5rVncLVF3jxdc/YvpohtvzeP2jV+RpwfBs\nQL8J6fV7XRCP2/mCFQznA6q8JNknBCPZyEfb6EsQ5R+4ji9ayXOQTNv7dzfcf+eGxx+8YPJo0sFM\nYXg+YrNY8Mnv/RA/6GNZbmfJ03ADhyItToRjTROQgOPZjC5GlHnVidHl+1tmQnmukRnZYRMxuhjR\nG0k1fpy76qYOLazulxw2uw5gKXpKy5Hkq/50wOR8zNnZ+J/NA/4ndH3lDra6aigziccznY6DVVSn\nGYduyizisDqgogktwjTQdV2qnKZlfb/BH/pSNXQkiWN1kx5S2koWDFUh8EBaeTAlHFenbVr2K0mc\nr7qDzPFdHGTwfPTzAad1fx7n0ArmqMxkOKwbeocxEgFxVVanoJHjlcYp2+UaRQEv9DEsyQiNdzF1\n2VCXQnDN4lRyRDUNWoUyK4n3sczeTJ2qkji/PMlO+HBVVTtBqrRaZKW0nEpNckhIowzDNk+Hk8gU\n2pP8QMTQOZvlEvSaWTajyETiYrlSUVRFKWTXOhWrGnQoaqmSVUVkJZZjd9GAPqqmyAwySVEUiPmS\nVqx04S+WYxFO+kI4yeQg1A2d8eWU3qBHWTUoSgUKlFlBGiW4oUvTSIi0F/p4vR7RYcduu6BuRQ6S\nxqJNsxxHkEZRRtNIwPZgPOyCcfayPOhsTG0j442yKDmsDsT7mLIssWwL3RQ3wtGxIuOARBwCVkne\nWcvapqEqavKkQFczlFbvWlvxDJuObIQV9fiSOIrPbYmZNDSi7Z74EGNadidrsU8AzGPivKpr2I7F\n7GxEnuWsb1dURYmmiwzH9kQMLNgpkyqvOWwj+v3gn+lz/k97feVmbN/+M38FFY2zJ+dcvLjAcu3T\nQ1YVFaZtsl/vuf3ituPrOwTdur4/HZDsE9598g6j0zQl+4TeMOC9X38PVVVZ367xej0G4zGGIbyy\no83ItARdU1c1VV6R7BI2DxvKrMTxHby+16WiK90NqEh2pSubsGQvbVhd16SHFC/0ePbNZ6iq2kkX\nxOzs+m5nUDbYLFa8/ewllmPLUqOzYh1pwcubJduHrYQND3roukGVN9CqlFl50rLtl3uijaDTj2la\nxxyHIitoEU9okRUs3szFdoMkz+umjtYF/nqhVLzhJOSwPrC4feDh7h15mtGWKuu7NfEupjcUrVuZ\nlYJo3ycYtkFv2BPjvaZ2liPxf1q21X0NfUxX8jrjfUyRVsJxywpMR2ZlRwzT6HJEf9RnfDHDtMXR\ncfX+Y6aPzlA1TV4UZcXmfk28jwmnffkexoKTslyLH/793+H7v/PbjKYz/F7I/M0DySFBNwwOKxn0\n75c76qISE72qnOIMH14/sFvuaKqG/qxPnua8+/Qdh/WOIsvRTQPXdwgnfUzbFE1hUlAXdIHSkix1\nXCK0DVimTVNJ6tj4aoxhmazuVgxmQz78lz5kfDnG8W2uP3/H6m6JqmqonTh6s1ixW0o/l+VCAAAg\nAElEQVSAsx/6jDs7W7SJQOHUTYwnA3711z+ijHN+8t1PcXous8cz+pPONF/XZHFOvI3Zr/ds7jeU\nZcVv/53/C/50xvaLubRuGJ4lIig9zjJG58MTjqWuRLQpK3qjSyZvUCwZfhumeDFBRJJFFvPw+oG2\nbZk9mVLkJUWaU+Y1TVWf8kqVzjJTF8JpUxSk2nBNCZnVJFxju1xT5AWj2YSyqNgtNhz2W7IkwfND\nXL/H8EwSncpc7E6Lmwd6/RDDMjlsDifkjGXb9IIQRdFkIJ8V5ElKksQoqGjo5FlK2zYUWY7tOpw9\nPTtVknVZkUWp0F57LtMn0xOLzvZkM1dkxckJ4QbyMfObB+Ldgabuoar2qa1yu9Y079T7bQuaquMF\nHuOrMU0tdIwyK3B8h8mjCZv5ivUnc+xASCJJKof40YER7yMMS8drPWGEZcWpDXR7HmrXyiqqQpHn\nbFcL4miHokI47uMGLofNjjRKGJ4P0U2jU/3LYsELfVqU00zV9u3TLPPy6TPC0YD+eIRlWfSn/Q4A\neqDIJc5PQbyUN5/fSCp7Z0xvO1pzkQvCqCqqLrVdpa5KNF2nyAvuX991wmKTZJ9KAI/2peC2qWoO\nmwjd0PBCH0WVzbbTc2jr9iQMzpNcxNKew+OPHrO8mbO8m9MrA6ZXF2ia0eWx6qck+SyLuHn3BYNk\nTC8YUGQ5pqFxeztnudpS5AWmZdAbBuiGiIqjbUx6OM5CNTRL/cphi75yB5vEpsmNtr5bs7iZY1g6\nTz9+gmGZ3L2663I225O2qKpknW1YBoapf0lZVZT/H9d/cjnm7NkZqzuZgx3DOmpFtkVHam9VySEg\nhnwRuxqmAW1LnmZsV2vatuHqvUe0h5Rod2A5fyCKNpydPaXX7zM4FwV4sotZPyxZ3c8ZzIQe+/aT\nd0ImGfRwPR8/CASzlMtKPk0SlncPuJ5PEA6o65KqKimyHD/06V+NSKOU3XLfQRlzyrxkMBvw4W98\nRFWWbB62XVSefSIQH1YHvEA0UYf9lu1ycUonOiY5BeNAUuIPqbRlhoFlOfT6odAk9gnru/VpWzm+\nHFG3OeVPUupaNp1FWlDkBV4g5vXtMqXIXKrOM1lmpSwdeo4Y3jXlFDqczzN227VsuBtxK+imzm61\n5bDdc5U9EnTTYgeII8Af+Bi2yfpuTdWJo4/t/9P3P8CwjdP4wHKG7BY7Ht480CKH6RHOePvyDjdw\nGcwkA9QwjS51vWR1u5JNdOhJpkLdkMcZSZSwvFug6zrBMCRLcoqipG/pUtHmJekhJT2kOD0bp+fg\ntJxYf8cQ6bqu2TxsZFbXc7h87xGqBq9+9hlt2zA+Pzvh503r6PVtiQ57bm9eUpcNbaVTVyWqqfLm\n3b3k0wJ615GIcycj2kSkUQZNi9VtlFX9q9XcfeUONsu16etDuTldi6atWM83/Ojv/oBg1MfxXOq6\nknQqQz1FrLUtNE0r3kRDhLjHMJOyKEn3Mi9JY/EFJt0bixbxRhraqdUUkioYtik0VIWTh7Gpa84e\nX6JpKm0reJjn33wP7TOFh3cKXiBAxeX1sgvLUKFW8IO+zL00lbouKLKSLDEYng3pT0LJiWxELBxO\nA4JRKBkInkv7edOFs6jUXbhykRZiD9Jq2qYhOUR4oYOhqaiKbPCyOJPgZzp8kaZh2CKPGM7GlJnI\nAyLtwNkTyXGQbVuDYcnnZjo6eZ4QrWI++38/Qzd1Lj+4JE9y8kRePrQyqLdd2fqOr8YnaYFmalx9\n8IgyLVleL0/ZrIZtiJfx5u60XTQtkVcMhhNM2+LsySWmYxJtI7xej7Zt+enf/758v3CYPjpj8njC\nbrGjzCS276jTEpuZ+D2PcY1tpyUrilKgAvs9WZJhT0Y4riNIJNOg6ba6im1w2Ow7G5+F4znouoYT\niLdz/nYufltH7EpN3VIWOXmedIliRscHVOlP+xx2W159csvV8yf0hgEPb+6IOxw5Ssv8+pZWEU/z\nYDyhrWE4mUGrsng77xhuAcG4h6ZrLK+XJNuUnj8QOnHPxQ0c8U27Fk3dCL+waVm8ncuGOSswbRu/\nM9bXpQTuOF3V/FW5vnIHm6oJ3tp2v2yP0kTjsI3QdAOv56MbGropMMhTlVWUxPsGVVPQNJW4807q\nhrQE8VZsUNv5RrDfWSEEEEXBsmzKPGe7WpFnovLXO6Gq5crQuCoqilz0WcPZEMMyiA8xCgqO5xAO\nh9RFzWA6RNcN1vcrANyOrqooKlmaUdeVSDtUsceLd0+qEqWDKUqauE7bNjRt1WULODieI+2lbZ44\nWtBS1zVVVXVyFvk8jzPJpj7+3Yq0SLpKXUtknh+GbJcb6lIeprZtiXdCfVVVFcM1UHWFLJmQxzmL\n6wXnz88ZX4zZzuUhKfMSzdAZziYyNzR0PN2jrir2y32niwtZ367Y3G/QHYEkukibnsYJTdUACkqg\nYVoWrhfgBRKEnEQxq/sVliUztpefvKVIC84vn1JkGWkUyzBcV9FaDaVWBAffHXBHmYekW9Ud0key\nZuN4T56lNE0lEozOfSDY8pqqkwKVRXkSFSudNvCIMKq7UUbbCuhRxiP6iUaTRhGKqjIYjjjsN+zX\nW9rnjzuKR0vboaCapqaoK9aLuWRgPIde2Mf1ZHlWZAVOlxXh+HIIp4cUaoX+cMJgMmJ4NsTre+Le\nycWzbFrSDmdJxmFzoC7rU1Ri27Snav8Ia/iqXF+5gy2PM4yBkFPrqmZyccbZ43P8QYBuGLR103HF\nTNkYKQL/i3YHou1O5mWKtBeWYxMMJRtBN3Tifcxht8c0LRQN9rsVqq7SGzxmfnvHz37wu7h2H9cJ\ncUNfFO299hRcEncAxeHZEFVXxU6z2ZMcYrzQ5+nXXtAbBKRJKhSGqsVybJIk5rDbkqYHLMfGNCy8\nkYvTczls9syvb3n0wVN6/YDl7VK2wJbB8uGO+c0NnjtgMB4zeTJleDbE9V2J9Xt5R5bGNE2NHwbo\npsl6sWNzv+bNJ2+wbAvTEW3X8WA7tmXJQQ4wv9vElnlFmSXsVntMS6q6pq4xLIP3vvUB0Tri4fXD\nyaQejCUcxHJtCahZ7vEHIms5BqgcBdNtI4JURVO4ffuKLE84O3vK+PyM519/v3sxVVLx5OUJoV1m\nBav7Oa9+9jmzy0ss20ZBwe15zJ6ckec53/vbv8uTj54znI55eH1PnhQn+qwbuKf7KItlDqkoCqZj\n4vQcNiuDuirZr3fQKgzPRoSTkP5swM1nNyyvl1TdQTC+mogDo5HBe54WzB7PuHr/isX1giySit7t\nOTTNEFXV2C02zO/ucHyXydUUPwjpD2bUhWz/v/btj6ibhsXtSraZnsWPv/M9lrdzxhdjbNdj/uYB\nzdAZT/siuNY0ms6RYvds+soIy3G4fP+K6dX0hL1f381JY5HfTB5NCCd9mo5GrB8dEaooD3RLMlW/\nStdX7mCzXAtVVcjTgqosKcoUw9JwfFfoup6gj8u8Ot1oSRwR7w9dFF6HwW4k8UrTNWxPJA3b5ZbN\nwwrFkyg6wzRxei6Tqwnblcpqfo8b+AyGQ1RNpBJtR/042mGOmO1jdVJkGYvbOzTjiv54QLQ7kOeZ\nhAQ3CpZpsd81FHnW8dEsppcz/IHIQK4/f8vyLj1VVse5S1VWeJ7HxZMLVGyJyouFOZYeUvIkx3Yt\nNANQodeXcJZjBddUIkZWVcFBK6psT48VRnpIydMc27dlyN9VpE0tYt+6qmVG2bSUmXhWj5GC2/kW\nr++jWSrxLuqqNu0UUNy27QmvDqL3sjupR6PPyLMETdFp6wZV1U4b4mj3pdC2peHh+pZ4d8B2bBzP\nwQ8Crl48RVEVbN+ljZJTKvuxnVUUKPOCPNFQdfWENGpbUHXt9D2tqxo/8GmvzqhLTu4BTZe/z3It\nwknYUUAM3MBFN3Sauu6WMbLAOtI4NEPH9x1aZFmwnW+JdpFsNRVNZmyey+MPnwqKabnDsSWF6uhC\nUVWFoN+nLuQ+rrrlhhtI3m2e5hRpLpkIaU6036NqGuF4IC95VZG8jA4gkB4kP9awDIJRQFPVRLtY\nKjlbhLl69/+bxOkv9bn/J72+cgdbfzoQdf02YrvYcH//irot+eDjb/LkoxdcffCINBbOluVa1E3N\nZiEK/vHZmXDpO9xM24o2zA3ck13lsDrIBhWFwXDK+GrMk689ZbQbY1neKeRks9h2rV63yLjfSJJV\n6Am/35DhsGoqRNGGaOezXTgs7u4wLJ2v/cavoOsG28WO7XoJCvTHQ65ePOHq/cvOaiM34OpmjaLI\nImR8Ne4w1huef/wezz56zBc/ec27L265+fxGsEqqght6BJOwY3iJUNXxHZyeQ28YMLoYn1Ttiqqc\neP9VVaHkCmkkh6PjO+K/7czjZke9rZsGU9cos5K7l3cyHB8H7Fc7ltdL3v/2+6iaydtP32CYBo8+\nfCKZmZ0WTdVUbF8q6iOXX9VU3r98H1VVeP2jN6RRxna+6cSkIr/I05zp4ylpcuCLH39KMBjw7KMP\n6U8GeKHP+YsLySmdb/F8n+F0RN0lOhmWcOeizUHwTap6gooe8wHKQrykeZITjgecPbtkfbc+tW3H\nhCd/4ItfOJaWv20FPmmYFqomkZDzt/OT/zQci++3aQWjnqX3pFHCYDRG03XWdxsu3r/g8UeP+fn3\nfs7dF7c8vHkgGIdcfXhFEYv537I9Zlcu6S4Ta1o3d+1P+2znW7IoJd4l7NYblg/3DCZDhmdjirRg\nfbeh31mxZMwh3YbtWgTDXoedKtntt4SjHk8/eozr2qgtvHtz98t65P9Y11fuYMs6gWnTNuRZimP3\nUHWVplZID4IMunn9ip99/we8+OhjhpMpo7Npp3T3ZDbVtOw2a9I4pm1rqrJ/Sop68a0XtE3TxZLF\n5EnB3cu7LrrOpypr9ivZCka7A9FB2hTHF4GpZqjcvnpLnksuQdu2fPhr38D1e1i2i6KBZqid3ETB\ntCVT1PYd6qJmefeA41knRXuZl4yvJqRRyt0Xt5LD0A3uUVXmtysUTRVt2Vi0ZcvrJVkkb+PxxejU\nclVlzeLdgqqoO1aaTlWVPLy9RdU0Hr3/BNOWQ6Yq5OE++kOPlBPLtURLV4muqyoqDpvDabunmwaG\nbbKZSwCx7TrkecKnP/ghw8mEyflZhy53iHdx14ZKNQJQ5zWtpmK5tuS1mgb9cZ9wHJ5SlcbnI9LE\n4f7NHX7YF0Jtp8eT4b4sULTO6pRG6SlABxBybyuwymOq1n6zpWka/KCHrosNabta83B7i9JouJ53\nWkQ1dYNpSbu6vl+T7GKCcXCa5x7ndlks+QnGcYbZSOstlOOJoMVdhyov2a9lvrV5WHN/847V+oFH\nL14QjALyWGxW/dng5JLRdB1Vr0i2EWnsCyF4uWUzX5/Ycm2HT4o20ellK5kWKUkU09JimCbL2yVp\nkpLHOfFeArNNTycvZEZaJBmru/Uv76H/Y1y/zINNA34XuAb+dWAI/G/AE+A18G8C2z/4h/I4x/Vd\nVA0aagajKbbrnm7Gw/rA3du3fP7TH+D7Ib4/YHw+E7lEVnYZiSXbtZjKLcsRjVhaMDgbcPHigrKQ\n4fr1p9fE20jEr32fYNTrDruMumzYbdZcv35FfzTg2YcfSshMVXH76pr1fAGKwuP3n/Lhr32DppY5\nUTgOO11dS9UUgs85mzKYjvjiR58yf3eHrhloukG6Twg6Isftz2+Ybw4Ew4Dx1YSLqzHxPuHtz2/o\nDXr0Z31sz2Z9vxb5SpSQL8UiZDkWRV6SbCLWd2ts35aPdy2KLCPa7zBsk8njMY7vkcUZm/s1u6Uo\n7BVN+Glu4BKOQ/kapDm9oRz0vYHPfi0U1nAS4gYuD68fqMua8xfnLB9SPvvuj7l68gzb8hiejzqe\nXnvSiR1/Hu9jVO3LxY9u6gxmfWaPpqf5YjgOcHKH4XgmhnxX6LNllFKZHTUlycThoCokHS5eZD4i\nBFY6Jlx/2kc3Na6/eEOWZASDEMMVTeLdu7fcv7tmdnaF47gomtrBGJH8BwX2qz2H1f5kZq+6dv4I\n3ayqCtsTLFGZl7IUUmByNT1ZAONdTFUJEPT25S33129J4j3Dy28zGA1ZXi/x+z7D2ZDdfEe8jQkn\nIaqmkCYx8SEiizJ2yx3bxYbJ1eyk0yuzUvJMO0lSvItJo4Q8y7qYPoXl7ZLblzcorfhDiyImOgTs\ndxF5nHNY7Vnf/+nB9o97/fvAT4EjD+WvAf838F8B/0n367/2B//Q6HJEckjwwh4vvvEBuiFiWwUZ\n+uqmzuXjZ7S/qdDzh6SH9JRj0HQYH8d3GE/PGAxHfPzrX0fVNF598hZlLiv4qqhOUgDbs3n2K8/E\n7L2J2K+27FZbTNOmKVs8J8Bxeqia3ER5VuB6AfZT7/RGXt2uT3jnw+Yg1IUuou5IlKjKCsfxMHSL\numzQdOjP+jg9cSEoXXJWVVRUhVifLFugick+YbeQIOm6qvH7PlVdsltt0E2tkx4sRPZQCOJIU1Xe\nfPoFq/s5ba2gKxZvfvyWqizYbba0lYLtWdSV8MGcnst+tef282sM20QzdO7f3KBqiohbPZukO5TK\nTOxE5sBk9mSK6epsHjbYjtelKaVAy2G9B8ANHPI0P329RaVfnSqqoqi4fzenrmtUXePmi1sA/L5H\nGid89r2fMnt0TjCQQzfaSEV9THVq2wbLldQm07FIdjHRLma/3RNvI1pa8qigbQSHbbtiQLctj+Fw\nJtm1gUuyi6mKEtt3WN0IZ+7odtk8bMlTSXMyuuUKHVjBdI7pUzF6N39VNaE937+5J4tSVEUjS1Pi\n6IChuoxGAdRi2zpWnMkhZvOwYr/bECcSSG3bLrYjflaJOQzEp1xWaJpJU4vUx3IMzMA7Gej3qx3x\nYc/27ZzHHzzn2dUzHl490DYNT772DUzHYv56LjPVqvqFHwZ/0tcv62C7An4L+M+B/7D7vX8D+Avd\nz/8n4G/xDzjYbNdidbsULtawd5oPVUUpg9+mJRyMMd5zqLpB+ClfoNt42a5NOBqiqSrTyylVVaEb\nGllnUWoqEV02dY3l+PTHIdEu4rDdE+2kMrFsW5LWFfGQlrlUg1VRYdkOtmszeTShbVpZo3ce0DKX\nFk/VujCNo6K7Bd20aFuIDns8RTIMvMCTCEBLUuDrWtrko/K96SLToo20rqZtEowDyjInS+JTUM1u\nuWW32mG7jrRqecnqbsH9mzum51domsn6bkOeJcTRgV6/j+c7p7ZK1VTyJJO5zyjE6Tms7pbols74\nYia5nLTkscgDwmGP3rCH4zmkkSPE4bIi2h5Y36+wXEtCa7pliGZIdoDW+VLFm6p2GOuczcOmW9BU\n7NeHjt9vCZxzvafXFwhCtIuI9yLXUQ0NvRG9oqZrpxlj27SkkbSJaZTSNk1nSzJpahn2K4oi7adm\n4Hgeavd1lMR12K9kTmfa5skSV9c1KO1JtKvq6ml0oChC3ahUVQbyiItifbeiLCoGE/GhFlmBY4uP\nVVP1k9cTRLJU5IX4j4sK07Lwgh62I0ErTs9FUdQOiKnguK4AGbqcUS9wTwRq17U5bA0264pw2CMY\nhuzmUqFfvfeYNEq5ffk5umF0rpp/cQS6T5GW8Bdx/TfAfwz8fmftDHjofv7Q/foPXYdNxL6DLAqU\nUOYmySHtmPEC6kOV6s4wDTYPG4pUUoFM28R0TezMpqlqVssNumVw/vyc+fWcd5+9QVN1dMPADSWT\nYH69YHm34M2nL9E0k14YMnt6ju3ZJ67W8maJ01UbTcfML9ICN3A4f3bWiWFTdEPDckyyjuba1A2D\nswHBsMe7T9+yvJ+z2y0ZzsaMzsd4gUt/ErK8WbBb7aDbsuWpkFlXd6uTtk0yQxt0Q2N4NiIYydt7\ndbfisN1RFJlUQFnB+nZNUyo4bg/dEICAQAl9Lr0rqqLu5kTijZX0Jb0DdBpoumjTdEMqtLoUrdmR\nAPvkGy8IRwHX7+65f3XHbr05Vc5pHGE5FqYlSemqqjK+HGO9Z7Fd7LrM1hpFU7vDMGJ1uyLZS3U1\ne3yG6ciszwuEhLyZL7l9fYNteihonefWoT8bEG8jyrwi3idoHSDTjd2TDe4olD5axuqq6eCjPUC0\neyKLGJMnOXdf3IEixvMsOYZqO6RRxN2bN9Aq6IZ52m4f7wetWyok+4RelymgGya26zJ5NCFPhCgi\nwdmSViUb2xbLMQnGobg9LJNg2BOtWd2eyMx+hzG3PZt0n3SibsHnjy7G9IY9Dqs9hu/y6FtnWJZB\n01S8+uyatz97KxvWnstuve+es/0pivI4A/2qXH/Uwfb/AP8j8F8Df5K16L8GzIHvAf/qP+Rj2u7H\nH7r++v/xv1Blop96+t7X+OAb3zyB+mhbqg6VYzmiBDcs4zSIb9u2K+tzBsMQ27WJo5Q2zk7+Qcu2\nTnBBWjkwy7Jiu9iSHGKmlyHD2YgiTymKlLZS0FQV0/7STpPsk9Mnn0YJ++2WtgZaFdM00H0dRVO7\n9XwhLcSwh9Nz8QIP3ZEU9WN8mtuTmZBUbSLL2NyvSQ6ppKKbBoYtZnvHdzpChlR3yT4h3kVdwI2G\nbgmOOj0kOK6HFwik0jDNDr9jYFo2qiroJVXVKMuch+sb6rLpmF7aqc2qVeVUCR+H62VaUJYlm8WW\nzf2GLM6xXZEbqJqkXFVljaLIFq4sKqqyRjeb30eikGi+o3k/T3KaugW1JTnE5FlOldcdoMDG7/fQ\ndJWmVFAVDS90sT0havSGAdBS5SXR+oDpWtR1fYrZE7CiYNoldDgj2h0wLbkX1M4loGpaxzxTZbOr\nqyc6b9O9UJu6xeiEvGkWUy4yqqLB9hwG05HcD6udVNOGjuPZJxJKU8vs1bBMVBUWt7LUcXs2bujj\nD3zaphUhdsd403SNLEmZv7ujNwzxAp88lkq0rqQNDkYhmqaeDrq2ack6CkuZ50TbmCzO8EJpVZe3\nK8qiZB8v+PnL757E2V+l64862H4d+M+A3wP+PeDv/An9m7+JtJ2/BdhI1fY/I1XaGXAPnCOH3x+6\nLM3n8bNnWLaDaZqnDM5oG0nbVNWE4xCn58pDVDcn1XSVVxy2e5JDxLPf+vM8fu8R3/27P2S7O9Bv\nB9iew9UHj2XGU9Vcf3YtB0D3FtVUnfHFiNHlmB9/5/fYLbaMxmcEwz7TqynhVP7dY4WomzqL2zu+\n+MmnTM7OObu6QvO6Q7fnkkYp+/X+ZGMaTAfdQ+qR7lPmb+fMjQVlWVFk5akyK/OS+1f36F3ikm7I\n3KY3kPavPxt0ASkSLpPsU/oT0d6VWUmSxaRRxvTJhPHVmHDSp8or7l7dddih6vQ5+QOf9XzO57/3\nYyzL5fGz96W9rRu2yy2GpTN7MqM/6XeKd9kGXn96zfZhQ6uI2n766Lyr0iSNPt4LGSXaRieqCG1L\n1rXpfl+WGLc/v+kOQQXHF+zQ4nre5cDauIEHCly9/wTHs3n3yTvKvGIwG5za9MmjCW7gcP/qns3D\nBt3UTwlZvWEPN3C5+fxGSC15QZrEJMleglb8HpfvPSIYh5RFCYrC8Hwoi4EunrCpalY3K9pGYXpx\nLkHXtsFnP/oxi5s7LNPl/KlQR+q6Zrtck+cJlmvx4hsf4XqeZHPMN+yXOwazIajwyfd+iNvz+NU/\n92cJRhJmrRs6eZKdUsiCccD+51s+/8GnPPrgKU3dslsI9Tg5xAzPR1iOJQToOBNvMAWL2yXb5YrV\nwwN+2CcYCjEZ4OH1A17f48/91b948o/WZc3f+5t//U/oCPjFX3/UwbYH/gPgN5Dq7QY4Wvxb4Jt/\nzH/zP+1+gMzU/iPg30aWBv8O8F92//0//0F/2A/6JMkOw9Zx/PC0fi8L2TA6PXmTNXXN7at3ZHGK\nqhjCVFPEa6obGklWcHN9z83bd0RRItWEIpsrw+oCQLq5jKB7pCqry4bN/Qa1NXAcHxR5Yx/fZ6qq\n4IceiSa4mHib0FTQG/SYPZt1TK6KzcOG7XLNdrlhv1tx+8bGNFz8IMALfWgVmal18XlVWZ3akrqq\nyLOMppW2U/VsCXVerTlsd0S76ITCWT3M2S03hMWItqnZrOdURY3S6IybIaCwvl1jGDqPn1+SRCmr\nxVE7pnUU3YTx7FxIFTfvmJyf4YUBeZ6QFy1pnJIcko4mUp+cC1mXliVRiQGGJZvOcNrvmG0WbdOg\ndR+jGRqbxZp4H1HXEsTihR5+6NEb9Fjfb9iv94TjfmdTUvD7sqRxey6mZeIFHqv7Ba8+/QRNNbEt\nv0Md5WzmG6q8pD8bYnXEW60T6R4H/nVZYdl2l8uqoBsGiipVZnJIOGy37DYrLMvD6wVC81AUtosd\nbWeNy5OCNMqoixbH8RmdzQgG4vc1LZPZozMO2x2KpmJaBq0iG3O/7xOORPSbZRmD0RRFVVjeLNEN\ng7Nn5xKvWJSs7ueyfKKFRmF8PsUPfHRdRwHqqiTLErLEli1+l48r9jIN23fwqoA8LyjyjM1yzvTx\niN6gL4SazYrv//bf4/zxYybnFyzeLv6Yj/sv5/pHLQ/+MvDfAv8D8N/xD2kP/ymv49/5XwD/O/Dv\n8qXc4w9dw8mMu3dvCLWBaLFMXfA0NOimgCeN7vC4e3XDZrFmenGB6/soqmRDmnbI/pCwWKy4vb6W\nm8rvoaB1FYPS/RARqe056LqPoihdePES03Aw+y4AiqKidZak41u8rmvmr0UHZ9sOwShkdDGEFvZr\ngRFu5mvWiwVZGlO3FU/f/wDX809zH1VVO01ZdcojVVVVWsCmRikEr0RfFsubxZosyljfbugNAry+\nx3a1YrtaQa1QlDn396/QNAPfH1A3ArZc3iwJ+j0+/JUX7HcRu90By5Wh+G4hobmziyvWizmvPv2U\ncBQydMa0imRlZnEqhFpFtran6LmmQW3VU/DLUWIxmPbRTB3N0AXs2TTd19mmyDOWt3PqsmUwHTKY\n9jl/csb0asIn1ackUUJvFEggTioynP4k7FT/DaZjUVY5L3/2Ca4TcH75HKWrGiZ+z10AACAASURB\nVPfrnbSJXeVTdtvlIheEkhcKbNRWnA6pJAJYRVEk1T7JWM+XvH35OZPZJZbpnpLNVK1rSeuWJIpI\nowSl1RmMp1w+f4JlW2SHFMM2mD05w3LsLtdBoeoWT+EkZHwx7mINC8ZnF+RpxvJmgRt4XL53KR7Q\nKGGzWJ2AkLbrcvbkEqdDJmm6hqoroNaURU60i9B0Ha2rVFVdwx/4YpUC7t+9Y79boxoK4VhQ6Mvl\nDT/8ne9guzbPvvYBdz//F0eg+78Cj4B/C/jRL+jf/9vdD4A18Ff+UX/ANGzG0wssy5NgCkPHsEyG\nsxFe4DGcDTumVITfC1EVnd4goCpLFrcP9MdDvPCc3XJHtD3gewO0UEM3zFMe6cPtDZvlnLIqCIdD\nnn/0Eb3hgGDU4/qzG9JI4tgURaEqa0bTPh9+6z2W8w2b1V42fU1DMA4xHIM0Dlnfr/ju3/wdPv72\n1xmOQuJHExSVbuuXUdc1rtcjjVJe/uALikw2YFrnOZXDIqXMChRNIRiEpEnCbrvBCYVdpmsGft9k\nfD6Rw9jUmV6c4wchXq+HqimcvTgTPV/W0Atl6+p9LMyz69d37NcHok0kQSJ9h/60T9u2rB+WtC08\n/+gjzp5cMTob8QEfUxZFV40UbO43J5BmFiXohs7oatwN1tOTobrMxK+p6xqWa5F1G8qqqDAtm/H5\njOnjM/y+j2HqpGnG/dsH9uvDiZ7rD3wmj6a0tczFDusDeVpInkOjc3b+FN0QSkh8iFE1hcv3rugN\nBIm+ma+5e32LaVq4PZ/Zk5kkTHXG+OPMUFVVOQCLStT5xYj9attV67C5W1MUOffXb1DQGGpTksOe\n6LBjfH7GcDbCdmzKvOKwiTBtA8uzTwb/3adrmVEatlRj3QtCVRUOW5HDDM/GFEnBT/7uTzjsdpRF\nwezJOW3dsnlYk0YpvUH/BDKtiopw1Of5rz5nt9py/flrJhdn9MfDjrYseafLhztef/YZ54+vePrx\nt0j3Ba9/8gZVUxmMpvzZv/SXuXr+ROgjs/4v6Aj4xVx/1MH2N4D//p/VJ/KPe7m+j+t5J9YabYui\ngB9KupPj2zS1yDx6XaCwbunsVhmH7Q6vJ/KJeB+xX+0IRiJsPfL/NV1D0aCscuqmpG4EwqgZGr1R\ngGbcU9cVtul0a/uiGyJDtNtz//ZGyB+2het7OIorXPmHOdtlwrMPnuP3elJFGBqWbWOaNoqioioq\nySEmjQRP7fgOKEd7UyYCT1uWCLZrU9cleQYonTXG89ANDb/vnwSaVTnAMG1QW7yey+jsWZdYvheI\no6rQn/apypr5mwd26303lxPskxd6lEXFfr3F9hxmj87xw0DsXRczCRmhlfSrezFra7pAMTVTUE9t\n27C8faDMapRWwTB1UBS80MUwDUpDUOl1VmNZNkqoSYvWNmRJzn6zo8hSsoPMuISGohAMRTC9nW/Z\nrrZdyIzRzd+cDgJqEe131FXFs/5zwlHIbrUn3ssQ3/V9dMOkrio0U8gdUhmLr1I3ZNtc5gWNUqHq\nGv3xBD/s4fiOBGQfDjRNje1ZeKFHq5TUSo5uqyg66JZOlqSs5nNs16FXSbuJqpBnOQoKhmaxX+/I\nkpRw3MdyZCNqWibBMCTaHLh/eUdZF5iuweV7j1GA9f3yFOQiENIcTVOxvT6XLx51RJaf4nhON+O0\nUFAp84Iiy6mbAi/sMZrOuHt5R7KPcUMPL/B4+t6H8mLYxif1wVfl+qMOtn/uDjWA4fkQtZNtaIbO\nfrUni3PxZapqx8qXyqA/66MZGuvbtQRjdDIO3dSoqpyiSvH657g9nyyWtb2qqcwuLhlOJjiBEEyj\ndcp+tWcwGxAfDsSHPcE4xPFFjf5w88D1F69ZLuZsN2tUVSXoD3j83guasmUzX+MGHpPLGWla8vqz\nt7z55BWHzYGqrOiFAV7Q47A90LYNg+mQYBzSG/RY3ix5ePMgociqQm/U60zpNb1+QG8Q4PcFty2z\nFUHvaIaO3XPQDhpFnrO8v2V8PuLDb72HZphEUcL2YcNhfcDry2Hvhh5plLFf7rl/fcfydsHjj54w\nvhgRb2MMU8f2rG7TGguo0pHQlaatiZMD4bCP3+9RloW0zGXNbrPk0x98n8FoyuzysUAQFSFYqJo4\nGupKPtbybPK84N1nb0SDpehstw9sd3NefPh1xrMLoq1IEcJJyGETsZlvWNzdER8iBqMJdV2xuLth\nOJswuZyyvK+I4x375YY6r1nerIj3CZ4fMHsyIxgF3L25oSpKBpNxp/uLMB3r5A+N9nvmn76Ttu/y\nsXhTA4/l9YKWlsFsQH86YHw1pSpLou2eH33nd1ncX/Ptv/CvUJPz7t0nBP4IpX0qft3BiMnlWBh6\nSUl0/Y6H+zeUVc5gNGEwGeJ0wm62UNc1jufiBh5FKgEy06tzDNPstqS6BObkMmI4bCLqUnSd26VQ\nnP/sX/pNhpMx1y9vuXSf8vTj51R5w/J6QbyLulBp+V4oisLqdkUapwym/+JUbP9cXlUpiOumaSk7\nL17d4XNQ4LDes11s2S23WJ6Jo7rkaQ6tQn80xDBN4l2Moqq4votx5FHFWYddtsmymDxPmT05o61g\n8W7Fdr7GCz0BB3rdbE1V8EOfZRJz8+aOlhrbcU/J2YvbO3TdQjN0vNAnGPYp8pI0SmgaEVTano3r\neVi2haLKzXvMcWibBl3XcTyHpq5AUU6Cz7bJKYuauqw6kSn4AxEsS0J8y2F9wLAMBrMBRZnghz1c\n3yVNcjYP61PeQNS9kQ1LAj1MxyTfZuT7hM18jelYIi3QVLI4P6HEJdH8S7mC23PpDQPCUUhZ5J0o\nGsq8JD7E+L0SOqabbHnFBeKGHvBl8A1tK9KKLsC3zCuyQ07RiWN7Ax/LtYVGmxW0gO066Kbkt1Zl\nQRLvqKuSxf0teZZDq7J+2JAeBMIp6U8ehtlxx+KcNE7RdQlAdgOpZunmcyIFstE18aLqhhCFj9X5\n8GxEb9AlpZU1qqIzmIy6LFUdWgVDt3B8WYQURUq1zeiPJfKwrjLcnsfFiyuKWIg0k0cTTNs8bSVN\n28S0bXTd6ECixe9jAeYkUUyZF1iWQ1kU3HzxlsPmQJ6Lo8MNHLIkY7vYyDOhKKiYKJQoao0/6GE5\nNkUuG32n53zpigncX9Yj/8e6vnIH2/p+hWHoxLuE/eqAoionvyDA+m7D8vaBzXIlEoh+SLyN0TWd\n0ZNLyrxk8W6Jadh4U/+EjNkttgTjkP60z/WbL5jf3TC5muI6AWl8oEhT2kbBtA3GF7OTQX3wqE+a\nRJ05+4zhVGLK9tsNrz77hHAw4MXH36DX72GYEh7TNpJRGox6jK/GpzSs/nRwshbF24jDao9pW0wf\nT1ndqBRZ2WnFdHSz5rDdsX5YY9k24bjP8GJIMAyoq5qHNw/cv7zn2TefcfHiguFsiO2Y6KbJ/NN3\n/OBvfY/n33yPydWUzcMGTdOYPJ5g+3aX5tQQ72PeffZWxLjTEXULm4cNiiJkiMNqj2EZjC5GqKrG\n9PKc/lQqNiGvCvdf03Qcx0dTDcmAWIq1SzcMhmcDzl9cAHQpWgJ6nD46g7YlOaSgtCitTp0rZHHG\n828+FxvTfCNVjO8QjgIs18QNfIo0x7Jsbt684ZPvf58wmOB5/x93bxYrWZ7nd33OvkWc2CPunpmV\nlVVd0z3dTPfYY8aDjS3ZkkFIICQLCSHggQckdgkZxIsfeLGfELwijBEggZBfEEICg23QzHim3dMz\nvVRlVeV+99jjnDj7xsPv3GhP2zQ1bdo9NUcqZd/svHnj3ow48f///t/v59OXnqwXM5xNWpQ7h5+3\nqhpoasnyZsn0fMqTX7w4bO2ausHpOvTGfcJ1yOZuS3fo05/2D5Yv6b7WrK9XbBdb9ruI9772Eb1J\nj2AZomJyfPSU2eMjTt474Xt/99ssbu559PQZpukS7SJmT445efZNfu///g6Lq3sahGC7vl3T1HVr\nqVIFANEiioLNlqKQjGaahKA2XDx9nyZrePvZ50RhSJHnfOPXfplHX3nKy999QbB8idsVzV6e5oxO\nRgyPhyJgLkrWt2s832NyJqHeLMnof8lWbF+0J/EngT+FZNv+CeAbwO/9rB7UT7j+8j/9F/55vF6H\nPBUG2oPwd728J01i/EGPqqzI41zmaW0wVdU0irw4CDqauqauHlAzAkZUVQhWO4aTPk+ePcG2fcpC\nHIy266I0EkZVdQ2/tTDVVc12uWEzX7VSkCG63lJ7s5Jur89wNpYVWFW32rQCGnB7HqPjUTur40Cc\nVVBFYNJAHMVslxtoJH6SpRL9kBWq1I7qSo7ye+PeAay5W0qWKc8ywvWWzXxDXUN32GW3DFhey2wm\ni1NMy8SwTem6Jhl1VTM7HjM7HrNbb0miBLfT0i1aq/1g2m91gfUB/dMddDEdS+z2YXwAN2ZxRhrl\nTM+OOHp0LKsgXaMz6GK36fqqqA5kXlVTRXtX1T/yAuxjRkcjRsdjWUnkZTuGSA+S5jTKiHeRbMU1\nTcr+kyGu26Uqa9bLG2ql5PzpY2GctaedZVEyPB5id0zW84V0ig2hKsc7+T4Mw2B2MRNPgyLxlIeg\n9MPz8KG6JE0GIWls7tZs78T7mieiA8yzjHSfoKk6pu6g6/ohcFvlUtuyXYfeoI+my9rD63n44x6a\nrqJpMkc1bYOyqNrDlC7+qEe37x9+Xqoiz400jQ96x06/y+hkQqcvKPV4Fx8OSbIkO3RTnY7D6Eye\nt4qiEK5C/s//5W/AHyFL1X8LvAf8LlD9fb//3/xMHtH/x9WbiELNsOK2UmWS5QmXr18xnI05f/aE\nqqxJwgxF1WiaGn8op4337+bQSjjKskJRysOwffZ4xs3La949f8uv/TO/yuOvPOL7v/UJYRBx8vic\nNE7ZzbdyQlaUh7Lz8nJBuk8PRArD1NuCusNocixbR1N4+nlRyRYiL2gao6X50kIrNYqsJE/E//hg\n41rezZlf3TI7P8XpeGzv1xjt4YHbdbFsi9XtQnJLUUpd1gSrgDiIAZi/vSNLU0Dh6EnK9GKGoqr0\nxwM28xXbxZoPv/URuqlLoLYR8ODJ4yP6gy43767YhxF1XaO1p5ijkxFe36MsBJhYlwI+7A674mqI\nUpqqgVqaHnUJfm/I6GjC9GKK0h6IdIddmQWtw8MbzMM2fHW9Qjd1/JEw5XRDpzMQjWKZy/Y7aqkd\ndVkfWhxFLgb58cmY6ekx3dGH3Ly44erFW+J0h+pU2F0Lx/UOrgpFgdHxkCxPefPp54SbgLvX9wfR\ns2aIi3Mw6VM3glmKdjG7xba1WeVC/lBV/JEvsznX4sV3P2NxNW8JMhIHibYhcRDi+R26/kAUie3n\npVHK7ctbYb1Nx4emgz8S6KjTcdgutmRxSnfQOfRIdVOcubZrU5YFn/7OD4l2e0ZTaSVGYcj86o40\njvkn/8Kf5ujRGeFawKvrVlwUrsMDZPSBy0fDAXe0vFr+PF7uP/X1RW5s3wJ+gZ9Nhu0PfL364afM\nTk9FdeZYuL7LyBty+sExui4BWlVV6Qw67FYrwl3Dow+foJs6eZayD3cURcrJowtG05mcTLbvsqqm\no2kGi9s1aBo18iKPdhEAXt87yDXmb++lsL7Zoygap08vGIwHrdBYEOFpLN1QVVXFNaooKC1rbHox\nQTcNbj67OWwr8kxmSGq7CouDhLoC2+ngdFwRxzTCVRO8j/y9tuccSBZ1O5fyRz6TszFZmhGHkZij\nkpLl1ZLesMvX/+TXePPJG+6v5iyuVphW2JrBG7IkY3G/pqgq+rMxtapT5dUhsBwFEXEQY3s2p89O\n5Web5Kxv1+x3Mud59MEFjmdzf70gVpXD3725W7O539DUDdNHUzmcaa1IYbHHdi1AOZzyXb+4RtNV\nZhfHpPuUu1d3zB7PqOuK1d09iqLR6foHm/32fktVSr+0rhvyVEYG3X6Pr3zjm6A03Ly8oeP7+MMe\nvYnEWXargGQf4/dHVHkFTSP+hrMx+82esqi4fnlDvE9Y364PJ+iu76GlOtEuRFHlJigrpgTdMJhd\nHGO7DkVWEK4DxmcTjt6bUReST8za7W4cxESBaO+8voduGqiqdG+TfSI0YU0l2uzZrQRPVFc1aZTR\nG/XoTfQ26lHhdXwxeBU1mmoyGM54/AsXHD2aEW0SPrn5WOxsm5A0FjuW1xePiKoqh8O3T37rEzGl\ndSXX92W6vsiN7QdIxenmZ/xYvtC1ma/p+kMUJOxpeTaD6UCEtXHG3es7QJL+cRSQZ7K1ggbTNtAS\nhbwo8foeg6NBq5FrqFu9ntvxCDZ7qlocm4ZtEG2iHw1T2xOjYBWSxkJP7U16HD06OpjPi7ykqWus\ntgIlW0XtAE5UNRXdkBVbFEQHIKGs4BryXE5oFVo8uStDbsMy6Ay65ImERbNW/uJ4HlaL7y4pBeFk\nC67adm0Mw2S/kS3V+m6N13EYPO6znvcIN7J1K7MS13cODLT53Zz1ZomumnQHvhz5OxJi3S12xGEs\ndaxxD9uzWV4v2Xy+aXFBksNyOg6dngcoh5VVtIvIolQw3Kp6cHOqqtoy9YofZeHihM1iyfBoxPTs\niHAdtDawupX6JhimddgK64ZG1ta6Hpylm/sNIIcL49MJaZTw7tM3FFmJ53cOFN/7t/dyU+l0BTRQ\nVvhjn9HxiLKohHW22rFdbFlc3uGP+gymQ7ojHzsruH93S7oXjV6wEZKKP2hPztUarVFa14JHdyDz\nraoVrjzcxGmL8Q9Yeems7tktNziefF/Bekew2lFVZftG46IZGgoc5r5CBjFI4xRV07HdDpPjY44v\nTvj4t5+zbMEJTdPg9d2DFNuwDfR2Sx2sAlY36xZw0Gt1fl+e64vc2CYIN+23gaz9vQbpe/5jvzpe\n/1B9KrKcQUtZyGOhXWznW7yex2A2oDvqkKcZu3lAVdYcv3fGpJhS5jmn75/jeB6rmxVREEm/zzIO\nvLdgHdAddTE0g2ARgMJhiPygrsuSlDzLMKzhITG+ul6iqCqWZzG9mFFXAhJUVbWtsthUZcXbj9/i\n+R6zJzPpbwYx67s12+Wa3W5JfzzgyUcforf5obqShLztSlnf7tjML2+ZX99w8uQCz3dJo+yAUUr2\n4ofU263xQytivw65v5xT1TXhLsKwTbxWtRbvRDpz/N4Rv/sbv8mbz17y+OlXGIyn6KZOp99hMBuQ\n7JMDNbfMS/AgTzO2C3kBur7Hm+dvca8XnH14jmro3Ly4OQSgLbflk20jMWi1M67B8YC7V3csrxbk\naUYUBgTBGqtjUGQjOgOJujR1Q1XUuB0fVRX8034Ttn1Sm+7IZ3w6ZnG54PX3X2O7Fk6Lfy/LnKou\nyBMBDIitCvbbgDwtcDoOdgtPKIuK29e33L66I08FRKpoFdvdHKtjoBtTRicjAOJQ5lhO12F+e8Xd\n9RtU7TFlWXB3/Y5Or8PTjz4iWO24evGWiw8f4w/77LeyzZ9cTLA9W9yh/Q6aobF6teb+8orV8hbP\n8xkMj0iiiFzCi3SGQ5589T0RMye5RD2KUt7QOjbBMiAKBAo6v15Qi92a0fHoUBU0bYP9Zk+4kcMq\nVVXbr6+3o4KS7XyDP+79PF7uP/X1RW5sf/ln/SD+INf0/Aiv57XEjpw4TNDmO2zPEoP1PqGuKhpq\n4aU1yiHFX1ZiSu+PRli2DK2jUMgRlmPSHXQ5ff+E+7dz9lvJ9DyoyX5UcarIs5wsTduIg9Mm81eC\nrlYUOfEzRQ2owIF/9gCBrIrygMUeZUOSKG47ngFJHEOtYHsuo+MhVVGyKopDCHizXEi3UbcxHYvJ\n+VQ4W03DPthRlzVuV4rd/sgnS3LyVEQchimrOBRFiA6x1J4kQiKkCVXXWqCAgmlYMjPbp+IlaKGD\npi14n3AbkKcpdT05mLMeZCdFXpIXElEBqVrVtcwUpe8qxnhALGFtpEI39cN/lm3h1h51VbFbSU1M\n01SBDKQ5tmOLt0BRDvOhByafaUvr4IAcL0rCdUCR5zgdD8eVihdwWCUZpqwci6IgiSPJDiqqzABb\nZ0S/HjA5neEPe5i2ceDqWbbVHsZk6IbJYDKkPxlgmCaruYmqSIWsyAp28x131g3b5ZrNYo3nd3g8\nfioEEVWVLaoiuCjdMPAHfVy3I/8+hoJdWoJMnwzpDLqk+7SlJotqUEgk7c/BMjEdkyIvWN6uZHWn\nQLjbgdIVEowqisOqrKmV+iC7bpqm5RI2h9TBl+X6Ije2v/2zfhB/kOv8wzOU1t+YJSLtCJZBm54v\nWwb/juvXl/KE6MiQOIkirl7dMTk94uKD92T7lRdEQSirj7Tkg29+wKOPLgCFpmkELxNlB6ltnuaE\nux3JPkLTDNyOR3/aJ08znv/Wx4yOx/hjn9X1ijgQC1Bn0GF0NmZzvyHaRcJra0+h0ihldbNifb9k\nebsgzzN0XWc0nXF8ccbodMTyZsl+GzB7NMVwdN5+93PSMGM0OuH8Kxd89CtfJVyFrG4XbJYLsiin\n62cMZs94/1vPuP7s6hDutT2boyfHAKJey0qKTCCG3WEXf9zj9tUtn377M7qjIV/75RNh7O+FeBsH\nEduFgAcHxwOe/70fkuxjqqpGU3WGs7GISvYp3ZFPd9QlT3OSUFYSaiUvtgf5SV3Xhy1kmcsM6oEE\ni6JIeb6UUPT8+lbov65LtNuj6Rq9Ue/wAn6AIewWO+pavp+6qsV8Vcnhwvp+haapDKcjnI53aGdA\nQ7fvy4xTUdgt1txf3dAbDun4vlTA+p22cO/j+T5NJTyIB4quqskuYnu/odvtc3RxxmA2aA1ZTRvp\nKaBRsWyPm1dXhPsN+3DL8eNzTp6cy2l+lhOsAvGXOhYnT85xuw6GZaLrBkmUUJWldJ4dExqEV3e7\nIo1jGqoWqy5/tjvoMrmYsLmTMLbtWeR5xuL6lv5kiKbppK3bwuk6bU2wPIw7Hug4+23083rJ/1TX\nT7qx/ToS89jzDx4cNPx+SOQ/tuv21Q2GLRiWqqgYHg2lbxilFHnRei17KFoP25HTqP1uT5VX2E6H\nju/T6XkSDQgj/GEf23XRVClJ/+A3fiArvzBpqyocQquOJyFQtyOsr47fwR/7Qj3tugee1/GTIxSF\nNgayxrRMLNemO+i2kEgRizwQU+sKDEO4Wd1Bl9HRhLLK+PX/9W8Sb8TMXWalBIK7Azy3YTgeYnsO\nVVEJoiZIGEwmMG7QVJNot+fz73wq29PWxqUbGuEmRDcENZ4liZBALAPDMukMugwmfZ790vuij8sL\nOv3mYEJqmpr52znH7x3TH/fojwaoaDRVQxxFbJdrdF1kLlUlJ8B1tz5sY+MwJg5jdL2NF7S2eJBg\nct3I1zJdaTOoXZkRxvuIcLujSEui3f4wk6vaFZqma61tSz2w6K5fXtFUDaquYTomZm0eoixlXgs1\nV1dJo+TQn9QNHW/kkWXJ4eZ4/PiUfbtiK3LxZVRZeRDbPISE0zhF10V1F+8jltf36LpQeYtUgKJN\nLSIX0zJxm678b9Om3x9juaJQ1A2d/SakKWvee3aO6ViEUdzq/8x2VVgf8oGKIi0cf+ijW7IaO396\niqKovI7eHiCXyX5PsFmjakNMx2J6foxhGtLgGPeYnk8wTYMkTHj32SXRTlwfru/h9bzDCfGX5fpJ\nN7Y/2f7a+cfxQL7odfX5FY7ntY5QhdHJiO6oy5vvv6EqK7GId108X0KmSZSwmcvNozcY0h3IsHu7\n2BHtYvpj4ZTlScZuteXy80sMw0A3pDdoOSaGZeL6Ll7Pw/IsirSg0/faWYbcXLx+h9uXt+w3Ie99\n7QmarnL54h3BKkTTdc4/OGcw7REHSWtzEouQEBo0HM9jcjJhfDpicDTk5ccf89v/x99hODzl4tFX\nyNOSpob+YILlmPTGPTRDJ1yFbO+3xEHC9GKK5Zjkac5mvubd8zf0xgO6Ax+359JUNcFih93Oocqy\nIN7v0ZeC2e6OuvTHPuOTZ1y9uGZ+Ocd0pJHQ6XfZzrcsrpaMT8a4HYfBZITSqC2QM2IzX9EfD8Vu\nnxVkatrSXy36056cDK5CdF+AlHIqKD3MBlA1rZ37yAmc5VoMpgPypIvX63D94pIo3OJ1O6jtCq1p\n5CSyLCt0XWF4MiKLU1794CWmZTI8GgtaSFWlJB9J2b4q6xbpnbCdyyltpy+02E7ewfVc+tMB00cT\n7PaNM2mzeWmUYnccnK7MNfMkJ92n+CMR7bz7dM/86h7DsnA9lySIUTT1QOMQIbMNzYgszRlMB9iu\n0Je7gy6vv59SRCmnZzOJjbx4S9OeLDdNTZEX1GX1I9y9bdIZeBiWeGfPnpxSlSWXn11RFqUg0OOY\nJI7wqx5ux6U7nJFGGeu7NdNHM06fnWJpOuvbNa8/fiOrtbKS59rIP6gmvyzXl6554HY9mgY5Tasb\nokCWyFmSoeka/siHphFZx1qot3Uh2xvP94iDmJe/9+rwD9W0q4Q8K5icTvngmx9w+fyKzf0Wz3fx\n+p3DzOLhFOtBNJvGGWl82wZr5cld5iXP/94nmLbcDHojiYAk+4jPf/dT/EEfTdPbk1p5MT/MacJ1\neHiiTk+O+fN/8V8g3uakQUlVlgcH6IP7YLdasl1sqPKGum5YXM9bLI91IAY/iJ3LXFZ8bk++J3/k\nM82OsF0HGoV9EPK9X/8Ofr/HeDbl+s0V8+sb8jxldDzmm3/qVyjzDmrLByuynLD1LAh9tsHvyzhg\nfb/E7cgbgWmZdPoek5MRZhuWzlOR2Rw9OZIxQRhT1w1VITFJVVGgbkj3Kct8QZGXpHFKFO6Jo4A4\nCfD7PY7Oz1uir3pYNT2IpccnE1n9Ho+ENJzmnH1wRlVWBMvgAG0si5wsSxlMhri+y24poIRf/Wd/\njbvLW779v/8GamOgoIKitK4Fk91yR7pP2cw3bfg2P1jWhzOpV23nAYurhaxGi4L7y1s8X1wWDznI\neBeht96HaBcdqMn7dchv/q3fpqpLVqsljtelPxqzni/J0wxVPxO0ua4SzkDh7QAAIABJREFUbNZ8\n9r1POHl8QW/c482n76RPuxH7WLJP8Ad96RX7XWxP4Ap1JaHoYLnj3fNLsjAh2kmLZno+pTvyD+Fd\npfhyCV2+dDc207YOy3pBXCfQ0IL0GsoiP7QS4jCmzAsM05bYRVORR9I5fLBVeV3pdmaJyIEHsyGb\n++0BTaS1wUsaqGoZUBdFwfLuTt4xawESPghDFBQ2d2t0S2d2cSzH8brGbrlmdbdC103cbqfdSlUS\nR6nrQzI8jQXS2Ol3OH38lOX1kkW6QFXESymnsBquZxMsN2zu11i2g24YZEkOjYXtSIfxQTRSFSVF\nnmPYJv3pAMMy2myXj+04BKuA9XzJ4vaO7f2WcLUnDHbE+4hguxHN2z5B01R64x5VVbFbBZimgeLZ\nRLsITdfxR32yJCHP8sMN9bCDaYO/bruSVjW1zZ4JYjyLc6qywnEsbNc6eF2D1Q4amX1UD1IeGlRd\nOcQUaBpJ5LeKO1VVcTxhpeV5QrzfU2QVXt/D811MwyCOIjbLBWmaHBoDtmdD3dAd+Jy/f8rNmyuu\nXlzh+31xwj6ASk25IUVbOXGsqqrdesvJ/ORszOR8Srj+lDiMURTZahd5gaKC4Wp0lc7BjwHIyfg+\nZr/ei8vV1Ll8fUMaR5R1znCq0vH7ZHEqkNGqatV9e9HvJTGqKr3W1c2acBMc0OV5i4lyffeAl3/o\nE2u6etAtJvtEvp+6xm75dA8U6v0u/Pm84H/K68sVToG//M0/9mdwfFeeKGmO2RqAmroh2u+5efOO\n7XJDGqeMjkZMzmYYhkGWpqzu5pi2weR0Rqfv0R/3OH96ij/sUjfyjnnz4hqtTbknQUy4DoUfX1Xi\nFrAMGqXkk+99m/XqlscfPuPsgwtOPxDWl+VaqKqKpulomka6T9kuthSZEGE1XUdVldY6nrO6XUjm\nzbFxfVfkJorCbrHj3fO3JEEsq55BB82Aq9dvsGyNb/zK14XmO99Rt7PA4WzI6GTM4GgoaCCEo5+E\nMbuN3KCOLo5kjvLJO9l6TvoEq4AsyjAtW473l0sG0xHHj85QG4OmUIm2Cbpt8vgXn+D6HrZrcfxE\nZm1ZWqAZGm7XpT/rMzoeoSA3YsM22C0CXn3vNbtVcFh1PiTpw+2ey8/etQcDDo+fnTM9HbMPYnbr\nHZv7FQC2K0wzQzc5eXLO7PwE15cpSVWWMh88GsqLUVWJg5ibt2/5+LvfZTvfkgQp4XqPpmg8/egR\n68Udv/6//U1M02I8O5KYQ9fj/a8+wes6bJZb1rcbirRieDSmP5UtvdMRXNVDZmx0PKQz6LDfCakF\n5JDG6TjEQUwWp0T7kLqqcLsdtpslb19+RrxNSYOcLM0Ooer9Zi83xvNJK3fJ0Q2TydkRjz96wntf\nf4+6bKBRGR6NKPOSt8/f0DRw9vQRrif5ONMyWg+utDbKrGwL9OaBrPwQ5lY0tW0XGAyPh619bEWw\nCthv9tiuTXfY4eb1Fb/zW38b/ghVqv5QXaZjYTky80BRMF0Lu/ug2pOtotP12n9Ui7puSJKEqipb\ncKHRauo8LNc8BEHX8wVJKDhnqyWRyuopQddlJqSPNIyOg2qC15UTPxniSn/P63mHnFWwDojDiLKo\nqEup4RiWJd2/9kasKCIJ8Xod/IF/sK4/HM/ncY5uGuiGIUo4VZ7Q/rBH3h6UjE7GVKWIeLt9/4BG\ndzyHelATbvaURUFv1BPfaCnv9A9ba/ke92RJim6YmKYl4U9Vh1qF1hdR1zVlVpJFP6ouxfuk7bCq\nmIq8aDRDJMViUJIIQbgNuH13jT/s0Z8OqPKSvEHILGXVFtIb0ihhfb+WYO58JbbyBmh1fHVdUVVF\nq8irKVKJ1bi+R5HnJFEMNRRZeTiFTIOczpG4NLMolZhQUcr2dp/R1Ep74ij/xo0CSZSyuF5S5BW2\n67YxlwJ34IvkBw7+WbvFsg9nQ5oG3K4rkuZABv7doY/lGTSNgq6bqGaNZonchaYhizOiICDJQgzN\nwrbkUEHXdSGPuLS4+C6u79Eb98UgVoiU+SHwTaVQ5hVNoxxIukUu/15ZklGUGXEUMjqaYLuOHFw4\nJno7l9MN7SB6Nm1TwJjrULJ7iiK4+i/R9UVubP8igu2e8fAs/zmeino9gUyqbeSjN+nRG/faSIKK\nZbnMzo45/+CC5c2KxeWczXJJd9jl/a9/KKyx1/ecPjulqj3uruYsru/5/Psf0x8NuXj/qWTCtnvS\nKCVPM2rjoblg4vgubs/lw69+i/12T5U1rG83BKuQ4fGQ7qBDlghCZnEt26iO78sp30NJ2tBaSa7K\n5GRGb9Kn0/faqlGNP/R/hOVpZzdFluP6Lr/wx76Bpmtcvr5FUeDk6XEbWYAsyWWrnIpjtTPokGcF\nmq5y+sEZuqGxvtugqionz04o85L7t/es50vSKMX1RP/Wn4po+v7tHdvNCqfjMLmYoKDw4rsvpBWh\nKizezYX75loHbFQURFLi9mysjiPYojwnifd0R10s22S/Dn+fMGZ2ccR2vmU33/HDzXPquiJO9ui6\nTsfvtZnDhjSN2G3XVJWIavxhn8nZhOHxkBe/+zl3r28xTQujXZ10un20U5OTpyd0h11uX96SJhm3\nV3PSuGI8OceyPMnydWxUQ+X2at7CKzeUeYWua2wXK+LQkKZC38ZyxPEqJXLJjp08PZWDj1acEix3\nNHVDfzJgePQedV2zWwbMnswwbUEfpfuU5dWKu6srXn72ezx6+gFf/aU/LtvN1ih1yAVmBUmYYLsW\n3UGH9e0GRVU4/+CC9f2aq+eX9CZ9euO+9FJrgX/uN3viXUwQrqjJhVp8enwYU6CC7VgoisK7Ty6J\ndhH+WG7gy6vlIYR9+vTs5/Fy/6mvL3Jj+6uIMu+Tn/Fj+UJXXdWHbWF30GW/3lPmJZ7voV7MxL84\n6qFbhgRSuy5O95TuyKc37lMVNU4nkLxOVshKrwZNtVAVoXIMpgN0TSMJY+J9TLQPUG5rqqrk5P1T\n+pMB/fEAy7JRdZnrhJuQLE5RdZU4iEiTjE5PUEW267SrtJo0TiVg2yrNkjCRWlLHQVsGxHHM/HIh\nxN5Bl02+JliH+KMeqqYxf3svodda5j22rpG1bK5oJyscy7UItmvWi3sM3aM3kC2a6ZikUYbpmPgj\nn5sXNyRBTH8ypBmJFCSO96zf3TEYS2Hd7dvyRqJqNLWEfBsaVEVWZbohvP+6bqizQsgWrkoSxpJk\n11RpfTyWEn9dN3j9DrquySqHhv0m5Ohixvl7J7z44QsWt2scz6XT6+IP+62jNcOyXXxfKMq2KyvT\ncBMQbgPSfYrX9dqKkRzO+CMff+TTHXSoqpLPv/8xyT6hM/Qo0opOp9f2iyuSMCZPMqqqlse+DWnq\nGkVRmJxND82UdJ9IHqzVNVZlRVWKxBpFkeDxZi9SZ12Xg56yEhKLrmEYBoZhspjPCdchmqlx/Ogc\nb2Axmh0xmA0oWyGOyLVTkjhCM4VmLLEmITrrreZvdDzCsq22Qyo9Vsu2ZDVmGWiGyuRkiukaGKbF\ndrUh2GyFzjsYch/vybME1/OlSdEuXybnE6qy4vbVHcPj4c/3hf8HvL7Ije2OPyQ3NUDAd3l5cIdu\nF1uUpcLjrz3G60voUkCMEtr0eh16456UfNs8mt2xaJqaLJGgqKqodLo9dENsRoNxj/6ox/3lnNXd\nkiTZiyF9F4nebtJva0EKqqYJTWMXs9rHpEkKTY3l2YxPWveAobXp+Jr4ekGRFdhuXwCMu4iykO9H\nUQXxE6xCusMuR0+O2C43REHEYDZEURWuX16hoDA8EvqDqirEYUIcSEZM1VQ6tcfi5pZXnz3n9Owp\nvcGwNUFJLMDpOPQmfe5e31GVNZOzCbqls9/s2W4XXL15xXA25OjJMXk6okgLilburFvaYeDtdIVc\nkqfFQf7sdqVvur5bs5vvZIs88jl+fHaowXV6Hl6/Q3ckqfmqqBlfjDh9cszd9RV31zmd/ozeaIDT\nsQ8BX9fp4DpdLM9qHao267sV9+/uGExH9CcDUcg1DeFmT2/S4/HXHqEoKtvFiiTdsVlt2C1n6JpF\nt9dDM+RwZb8t2oF8TZ5mJHFyOCyYns/ojweEW5mBhesQL5V810PjoSyKA4E53OyJdlELopQArKqq\nLSpLkv2buzW71Y7p+YzjR2e87394aG6Em5BqJ5m5KNiTZaLNm5xOSKKULMnapob0PXvjPidPT/nB\nr3+P1c0CpyM0aZEuS/5yeDLEH/nstxGruznvXr7E9TooT3Ru371jt13zy3/2V5mcTURRaGj0Z33m\nb+csrhYSmv4SXV/kxvb3gP8B0eE9hFka4G/8rB7UT7o0XSPaRcLMMvXDNu36sys6gy6uL0X1JNwd\ntHUPw1DLtbi7vOLy5SsmsxM6fp80lpvB+HRMEsXcvLni6MkRnZEQI4aboTggbZvBZIyqaqzv1ly/\negcNXHzwROzm+xjN0Oh7fUzHpK4rlrf38q7Y72N3HCzPlgFw1bBbbFsCrSOkhXVweLwPUZTOoIPj\nOaiKxuZujd1xGM6G6KZsI/IkIwlikiihaRrGpwK53G9ChpMZw6MxVQZZnPLid17gj32Gx0MaINyE\nDGYDLNeSeMFmL8BFDHr+hLpUiYMEf9glNwo2L65ZL5eE4UqqS6pKbzDCcTtomoE/lHd7TZcVmuXa\nGE5MGiVkSXrwKERBRN4Sdd88fyEECqR8naU5imoyPT3BH/aI45AXz7+HhoVry8jB9YW2a3s2/shv\nYxLifhVcvHbION68uuTyxUuGsymO53L66Cn9fkRVNHT7DhcfXRCsduwWO3brDWVeYLselit90cHR\ngO6wS7SNiHY3hw7y9GLK6mbF/O19G51o2G9D6rrBNE3qqmlBBCa2J6HbIhM0EICqawxnIzqDDoub\nO3arNYPxGKfjYlg6y5s52+WWOpe6maKIXW18MiaNMoI0QNNV9lnB+nZDf9pn+miK1+seJC+7xU74\na4MOT77xHpv7NZfPBRqqKhrT41MGkwGn759LTevWo6kUkjA5dF4HR4PWIi8k4C/T9UVubD0gAf78\nj/3+z+XGJo74RkgICEXiYfD88C4m2JiUopCTn4f+XRqnpHGCojZUdSVF6yDCcixGxxPSOCHY7Nit\ndvSnQ0zXoj8ZCEWilWpUZc12vmV1u0JVFcbHM+pSaiyqpqIZmiTvy4KmqSTfFmd0eh36Q5/OsEtZ\nVMRBhKppaKYQLYJVINb5vERtjelN06AbchDQNDVVUWJYJoZptp5RqSUpKCiagqpDmRfEYYTruwwm\nI8J1RBwmhJu9vKCOR3Ij24Y4HSE77Df7Q/peVXUGoym6ahzyZhIMhTLP29qOrHJ3qy1pkGNatvRN\nbeOA7KlKwRzZHdnKZnHaUk+a1jtasV0taWpwHEm2p0lGnoqpStU0IXgkMaauoDgKo+mA0dGIMIxQ\nDQ3Pd9lvbVntKhws5xIJgd1yy93lFY8+rDm6OKXT6aNhsb3foukao9MRVQspqOuauqlbv6iFpsnW\nz+26hOv9IUZieRIA39xvxBNqS3zi4ZQ0U/JDHapp1Yl5KhGjPC2Io4iiyDl7/5xet8f86oYoiKgL\ncDuyq9jv9hRZhmk6GJaL3ZWvqapqS/6QmWpdyptgHEpMxLRMBrMhu4WY5vNEyDPD4yHr2xXb+bYN\nlbuMj2Yt7bjDYDyiLqDMKvbbPWbbWVUQIonj2VRV/ZNelX/ori9yY/vXftYP4g9y5WmO7dnt7EAI\nBF6vQ3fYoakbtvdbVF0VZ+U+kaL5o5Gw/Td7zp8+5sNvfUS6z4l3ySEqkoQJZVZhGg7b+x2GcYNu\n6hLhcB6TZwVlVh6O8DXFpClrbj6Xd/Lj945Z3SzZzFdoKw3Xdzl79pi6bNiv90yORjx+dsH15T3r\nxbbFe+tEu4gIASYG6y11XTM6HmM6Jot3C6qyYnI+xbB06lpuqnVVY3ccuv0OnWM5jYv3e969eMV+\nE0KtsdusmV/f0O338QcDepMeru9SFiX372559+lrOt0ejvejrFKe5hiGSW/Yw2jT/1EQH24C3VGH\nPLs43HS3dzviUGaGeZITbSN2ix2b+zVZKsX5i48eURUVy8slXr/TYs5XJPuc8dFRu5IJiII9ddOw\nXS4p8pwyL+gOff74n/lTZFFBHhU8+8pjjs+mvHx1xT6RVoO8Oe2FwlvKTExrH5+m6pimVN+cjsPt\nq1uCVUDVAj+jraz8LcfGH/Zp6obu0BdkeJxx/eKKhlpuQuMTmromizI2txvKvBTLuivYJLN9gwgW\nOznZdk3CzZ7dYiduBVs6tov7G27fvcW0daanJxw/OidY7VjcLOQEvW7oDQeMjifUpXhS/XEXVdW4\n/OxKlIanY6JthO3ZzB4Lpj5YBTgtN+3hJlh2JOaR7oUGYtrCutN1jcG0j2EbbOdbaew4FkmQkO5T\netMe5XLH8loO3R6gll+m64vc2M6B/xz4tfbj/wv4d4Grn9WD+kmX05GwbRxGhMsAGqE7BJsNmq5j\nOJYQVVtYHkg48gGZ44/6jE5GzN/NSfcZXq9zmJMURU5Z5pSFpOnjUFoNcjKloOk6dZWJ0MVx0NpT\nTkVVDyRUy7FRVDGIq2igyKyvKiv2wZ7rV29Z3q/o9vqCJtdVsiQl3u+h4VCtMVtTuWkbMJRp7gO6\neR+ErOdzyjJHUVWZHdqWtDKqBmqx1pueCaXaEhpq4jAiDves79dkUY5GAo18fkMjpfFxh/MPzoha\nDeBuuRNxtGfjj3rY7ozdakuw3MnP25TYQ5EXrdszo2loT+Zq4kAIHqqm0ul7DE9GpGFCmRdoqgam\n2ebiHJyOg2aNqcoSVTGwHYfhdCop+nJHWVVi11ptqZqG0WSAbZnUlcQUCkO+T9M28fod+dmbcvAR\n7SJ0Q5opmqZiWAbr2zUg0Q3Tslp5jgYoNE5DVZfUdYVhmZhttzeLM9K23/rgljVMXea7tkldyEFB\nmRWy8jYNoGkJwB3se5umEndDnuR0B10UFIJNiN/3mZxOaeQHKB3X9oQ3CWP2mz2NUrcOCBXbk1pX\nlmxY362YWuJGFby6wuZ+w261Jc8yyqKgM+i0UR+JFGm6RlbmaIZ8nOyTw+lrmZeyva4q4dwlf/Qq\nVX8N+O/4kZn9X25/78/9rB7UT7oGs6Eo9eYL3j5/SbfXR1U1VstbJqdTvv6rv8xuHrC+u6UuK1Rd\nI1gGuL6L49mtH7ERYm0qJvGmbgg3IXmesY+2aOYFlmvy7vkt+22EZUtBfXA0QI/FP2p3HIFVzgZs\n51suP3lHZ9BldnGEqmlURcV2sTtUpFarLZvtlh9+9/cI1lsuHn+A5/vYjsUm2hPudszOjvGHQoTQ\nTZ3J2VhOFSs5aavKivHZhPIy482L52wWK8LlnvGpBEjf+4UPxAWw3DE4HjJ7fMSnv/Wc2xe3Qo7I\nU5Z3tximTW84kvySpR9WbIqiMJj2+PCX3ufN83e820as7lY07SrS9V2GR0Nu3lzy5vlLOn4fwxTC\nRNlKWmzPZngscZH9LuTF9z7F7XocnZ+27/5depMeeZYTroUXNzmd4foObtfFH0ue7+7NvaB0WrBn\nWVW8u7zj8uqet5+8Zjwb8o1vfcSu76OqYoF6wA+5XVe24rM+k2TK7as77l7fcf7hGf1pH83Q2dxv\nuHt1hz/yBTaJQlnK1vHBCt+f9ttOb0MUxALifKhiPRTiqwrdlBum49k0dcPmfkO43TM5HQumqqpx\nOja9aZ9gPWV7F6I0stV/MJgNJiPO3j/l/V98jzfP37JbBQyPpMe8nW/EVFVV3Ly5JApDzt57hOXa\nBzn48nbO4Eg6p67vUtUlu483beWwYXZxTH86JNrsUTUFUCSq01JJUETe/QBVyBKZiTqeg9NxD4ip\nL8v1RUGTf+3v+/i/Bv79n8mj+QJXsA4YzgZS4I5CmgYcz2U0mzCYjIUO4Zj0p31Wt3OCzY4sS2gY\n4Y+67XC5ETpHX/qTTSP0im7PJ4tHhyDt+HSC03FJwxSnYzOcDVAVpWW0ZUTbCKvNcB2/fyI3ClM/\nVLwUVaEqqpbiUUjy//yc40fnzE5O6PhdLMvk7tJjebvk+MkJvbHYgMqiZHG5EOqDY7K6XbLf7mXA\nrFvMTs9QGll5jI6GDGcD1vMtRVHij/tUecW7j9+xuLknDLeohiIoIMtFUVQZlLcJedM22xCmR1VV\n/ODv/oDtKmwN491DbjBYSqwi3qU4rken59Hp+Qe5SrTbt2FPiRl4vofdMeSwQ9NI9inb+ZayqDAd\ni+4QaBsKm/ma5e0d58pjDMvg7eef0jQKj569T7gNWd8t2e8CNE2jQaGq4ertHcFu30IT5XvRdO1g\nnqpKgViGmx3Bekv+SYh/32M4mVGkIl1GkQhRHMmcsSpFeGK5FvEuIomkvmS7NpPziST7bZPJbIjX\ncVncrwiDiHefvGmDtTIiMS2T8fGI/qTH6n5DluQsLhfE21j8GK0kJYtT6rrBsORGN79asL7biMkr\nK3C6LpZjHrqkuqbT7fVwOk7bLhEAalMjoekWMR6sAlRNp65LdtsVpmu2zRcNmoa7Nzc8INijSBR9\nHa/XRoJERSk0GxmXPKxSvyzXF7mxrYB/BfjvkYTLvwT8o5od+sB/CXwVOQ7414HPkdPXR8AbZIW4\n/fFP3M639Ma+fJpSU1YpiuZw/Oj84O3UTZ3B0YDV/J4oFDy405U0dt0ID+zhXfkB+Oh0HMqiR5nV\nGLrMTabnM9Jhwv2be/Ey9hzyTJLcURBT5iXxLsYfC7E1z/IWpVwdXKdZnBIHseCqVZNHH7yPP/Jx\nuw6Oa+PY0j3ULYvx2YTuoAM0LC6X3Ly4xR/79KY91ncrdosd/ckAx3M5e/JEtphFyeR0TG/oc/np\nFUVZMpj2mV8uePPD1+zDLVVV4FVdbMel2+uTpxL6VZQfVZtMR5oD83d3fP83f4Cq6nKS+MEptic0\n1nAdEgcxiqLQ7fXx/A79WZ+jxzP22z2Xn2ZAQ1UJn6zT6widt65Jw/Sw1ZETbeOge8uilPXdks1y\nie25WK7J608/RdN0BqMJ4Tpkfb8U+odt0p8MKauaV5++FdJKryMKRk8iCXEQi4w6L8UdsY9I04i7\nT15jOg6Pnxa4HYEbKChtRzchCiKqQpyh3WGH3WrH6nolkZVhl+7IP3RKZ6cTprMhWZazvFtx9/YG\n27U5ee+sHUVo9EY+g+mA3TpktwqItzFRGLc3ftkKJnu5YWiaSrjdE+1iNvdr9ts9m/sN/emAR79w\nQYOw3yzHPRBQGmqKPKeua3TDoMwrgk3A/O2cdJ9imNIsKKqEaBdg6S6DowFN0zC/nlNkBZqqs9nM\nSbM9z776VXpDlyRKMB0hq2RJ1kZyqh9/Kf6hvr4IZOkx8F8Af6L9+DeAfxt494/wdf868HeA/wq5\nuXrAf4LcMP8q8JeAAfAf/djnNf/mf/BXOHl6QhJHRGGI53uYtk1dNJS5gPoe5Cnzy3sR9T6Y0hU5\n6UEFtbUGPfDxe6Meu+WO+bv5IfOjtqiZdJ8S7Xfswy0dv0+3Nzjo9wzLkN5qIgVnRZFGRBqlLK+X\n5O3M6QGnNDodoeka87dzykw8oUpL90jjpMXLBJRZRVPqTM6mjE/HbBcb2S4nstIaHg3F71k3h7nR\n/dt7ylIQSjev3/Hq48/wvC7+YMD04uggi073wiAzLAO7Pc63PZu6rGl4OFEMKLKCsw/P0A2dm5c3\nGKbBYNbn7vU9y+sltmvhj3yOnhyxvLvn+Xd+QFWV6IbB0fkZ/mAo6XYFaWAM5Aa0vFoS7aIDYUPT\nNTbzFZv7Nf3xAFVXub++pshzLNuRClFWMToZY3sWq7s5eSq2+9FswvT0GLsjJOO7N7fkSSZh4NZe\n5fg2qg53b24o8pLBaHzAf1dtxUxR5A0vXO/bE/CuGMnKCq/n0Rv3GJ9NsFxLDi3ClDRIiJOUaB8T\nrgMhqCgKu82aOAr5yi99ldGReFsbOKgE8zTH6TioqtqegBYo0J6c5u3PRWZ9tic/46qS+V68i9kH\nAdudzFht28Xr9PC6vfbF/CNicRzGeEOH8fmA3V1IuIoP2TbXd1spd8PiZs5uuaE3GqDpBsF6J1au\noxGOJ296TVXzn/6H/8aPvsAf8uuLrNjeAP/c/49fswf8U8C/2n5cAjvEofCn29/76wi598dvbGRJ\ncohoTE+7DGcDNENjcbUkiwPy+GF4rWC7Lrbr4nQcirwgWO4kY6QqrYNAlX6jJv1GiUyIXzHchAdQ\noNfziOOA9XyFrln0BiNZSY17rX0+ZLfYYbWD3rquKYuSIs3JW7emXuqHBH1ZVixvlsS7mKZp8Idd\nvH5HxM3rLfc31+i6wXh6fDitNG0Lz28o0q1ESJLoALx8sAo9HMnnad4OvTXcrkfH9wUZZOhS6dI0\nLNcm3AQE6x29sU9tyfC4N+4xfTRFN+/YLrbttjshCvb4Q0FJe72Q/c5GbTHowSpgt9wS7gLqupIh\nel0fkDeaIXNJwzIOAdU8zdubXkNVywp6MG3l0WmO3xuTpQlRGECjYDk2g+kQp2Mzv74ljWO8XkeQ\n5l23RZdXWJaBCofZqZ2JAFpRIFztD0BJQJhmrcvUsA1QVGBPkUtcyLAM3K7dmprcAyq7oWFxu2J9\ns2JwPMQfdNFUjWAdsFvsCDc7wv2a23e3FGktM7auOAYeEOu6IVYpJRB/rKIqh3jIQzWraRrKsmI9\nX2JaFpbjoOpiMNvvAqJ9iK5aHJ1pjGazQ/fW9kRhWOQFw+mYZ1//kJf1S8L1OzHFuybDo9Fh+wtg\nWbbg3JPsUJmry6qFGziH2t6X5fpJN7a/BPwVZLX241cD/Ds/5dd8AiyQud03gO8A/x7SRb1v/8x9\n+/E/cM1vb1EU9VA+lzqVSxImFJmgb9IoJW/JC07HYb8VfdqDDMR05Ai8qRt60x66oR8yW51+h/0u\nIFhv6I0HDD37IIaZXRxR5TVNLfSNNEqxXVtO7Za7toxdsr3fkqd9b2i7AAAgAElEQVT5gRMftN3I\ndJ+yuF60J2kGTteR1WDrx3z8tcecf3SG9luiThsejVAUhe1cIiw0ImoJdxuuv/OSo/MzLp49pSqq\nw/ZYN8Qxefz4nMF0RBYVZHHO/ds7ia8MxXbv9Tw+/e7HBLdrqupY5oBJ3pbSJQ+oaRo3L24INjtW\n93dsl13ypMQfdXnv6+9RZgVpnEpSPlc4Pn2EYUkjxHIkcjC5mEimq6m5fSlD/KaW02D52Wy5u7pk\nenLC8cU528VWCuSqSqfXbUvfJVVe0ul1sFybXm/IcDLh6S+9T102RNuYqihxPJuvfPNDQCHY7VE0\nFdM2uXtzx/3bW+6vrlBUBX/oyyFLEDF7fIQ/6nLz8obdYidgTNts3a7iuUjjjCzJKd/NWzt8evAR\nDMZ9/LHP/dt7oeia4jZQ0Nhv9hiaI2+ANaxuVhgtTqoqRfFn2sahmWK5Np1BRbIXZ2lZVCTxniBc\n0en2GI1nQp7p+7zf/6r8ufmOplBZXi4YHA3ojXukUULTKAyOBpiOKfj81Y44iESxpwkyqwgF/Gm5\nFtOLKfdv7ilzlenZFMOSuWtVVMRhguf/0Qnoftz++h1+Pxpc+bGPf5qv+U3g3wK+Dfxn/EO2nP9v\nX+PTT77N55/+Dpqmc3r+FEUTVruqapRFSRTIFqffk5xOQ9OqxUwhPCQJu5Vw0RzPExyQph1EJdE+\noGlqkTIbxkFA/CBx6fZ9EXTcroh2EcPjobzwigrXsen2O6zeLYiDSHR/LZhQbbluZSr0hPHpmDIv\nWN+uhb6QFQSbLbZn0e37aLrBYCozwyzJsNqiMg3kuY3X7aDrusz0ykpAi1GKaRs0VY3X7dAb9bn6\n/C1xFGI7Yo/q9Dx0U28xQTa9Ue/wJAZZ7QWr4LDSbOqGpqpbxHrIm/hzpuczRkdjFFSqom5jKg6O\n57ZyY40okApaJ5SIgTDhpJxfNTLUDzZbkens25BpEGJYOv1pr5W0SBYbaMv0JUW2p9PzUQ2VOIzI\nk5J4m9C05JY8LVp+WHSoKInBSdDxDTW7zZpurydNDaVmu1yTRonk58oCw5LVZZ7lpEmKVdqHyE6Z\nF20FzpDteyNS6N16S1WXjE5GKLpgx23HpWlqkn1MWRTohoGu66BAkeaHbbDgy62WYFLTNGIVa+oc\n3dDbaJGgklRdw7RtvN6QalThOB2qokJR1QPGuypLaGuHcRCxW21Y368ocuGyabpGFovLNlgHeKWH\n6RgkcdzCCUaYtsnrzz7h7ctPaRqZQX+Zrp90Y/uf219j4H/8sf/vL/LTX1ftf99uP/6fgP8Y6aQe\ntb8eA/N/2Cd/61f+LDdv3uL3h/SHY+7e3KAZKqfvXwgAcbnh/CsXvP+N97l7c8d+u2+P9GWm8uoH\ndzz/zvd59MEzuoMeli20DTFPxdy+veT0ySMmJ0cYbc/v5uUN8X5PnsX8sT/3K5y+d8LNi2uiMKY/\n6R1M7rPjEUenU25e3LBZbtt5iRTONV2TFWZZ4fkeFx+dyzC9KNF2MUkY8dl3P0HR4NEH7zM6HtPp\ndciz/DCTETFIjWGNOXt2TpkLoFE4/iVZklLXsnpzex6u77APd+zWC87+xDeZnh2haiq7+Y77N/e4\n3Q7D2QTHtdu/VyeNU25e3kqWCoT0ahuoms785orLN5+xXt7j+wP8wQh/0Bf7eXvzfvAPrO83bOdb\nilzoImVW0h11OX12KgKbuyXr5Zy6bPC8AUmQ8e75a55+/RmziyMAkjBhu9jh9ly6wy5vf/iGYBVw\n8vSUNIn4nb/12xi6Ra8/xnIssjRnfilvKkVW4nQdusOuoNh1Hdv+f7h7k1/b0jS967f6fvf77NPe\nNtqMbEsuUxamVEiWMJYQIAsxQAjJniEQjJgh8j+AERIDGNCMGCAzsbEt2VXOEtW6Kiu7aG/c5vS7\n32vt1TcM3u/swFS6KqiqdFbGl7q6uicz8q7Ye61vfe/7Ps/v8Un3MTevXtP7pa/x9b/+db7/vX/O\nZ9//mKg/xLB0ttstpitui91aMjyHszHhIFLgxUhkJYYEJifbhLvXMa8++pzBdMDTv/pMeomhwETL\nomJ1J/3I2aNTQQXZJkkqoTdN3eCFLuFA3BdN0xKNeriBJwSTroftPjpszoZhKJCm6B3DQaDAq+AE\nci87uUtHTl1WLO8W3L6+QusEmyUnRFMADzvRxj1kwW5WK/muKun9nj95i154RBZnnL19xq//g7/3\n53js/9WuL1M4/6/A//AlfvZlV4KgkH4Tmbj+HWT6+THwjvr5f4b09v7x/+ef/e5f+ZW/ocJuI8JB\nDy90cXyXumyIVzt26w2GZaHr5r+gE7Jsi6ZsSLZ7iqTAslzoxLqUJxnL6xWruyXxdkfY6+G47sEk\n3xv3pNFcNUTDHnQay5vVoT8hm4KcDvKsIC9K2q5ht97QNDV+FJBsd6zu7knj9EAnyeKM7WKnCLDS\nRBeqRQ9DnUDXd0vmV3eqTGxxXIe2a1nfif91v01EpOs5hxKzqRuSTczi+p77y1vqqmZ2cYLn+5R5\nSVMpwbJro2sy6Nitd2xVT80LJbm8yIsDOl1T0gBdNxiMxgwmI4bTMaHKwHR8h2gYEW923L2+Ybfc\nomkwOZvgqre9aQvaqMxKDFNndDxidDwhGvbkBWOaRMMeHR2L63v28R7bsUmThNs316zvJf18fDqR\nE1VWYlkOpmUfrHbhKMINvQMhtmu+OLFnaUbbdPhRRBD10DWDqpB7JE3EbB72I6anM6ZnR7ihjx95\nFJmEzhiWaNoe+oBVUco0WWW/RsMegyOR69B1LOf3bBZLHNcVzl0t/cW6kBO+iKZTqlzi7vbb9ICH\nfwAiVLkEcLfKVYEm/WPbk16dTNxlYjm/vuX++gbX93FcYRYahk5/3KOqSoosYzgbM5gILMC0FVvO\ntjAdi/6kT38yxDQtXF9aMA+CXcMy+J3f/IfwFQBN/tvA3wLOEOfBwzQkAqo/59/7nyOiXxv4DJF7\nGMjJ8O/yhdzjj1+wZTMYyVTL9R3swKapa+avFmxXW4pCpANN0TI+mzCaDQ9etyzJMA2b8eyEuqhI\n1jGWbdI0DYtrARs6tiPlnirtwmHIyfMT9tseWqeRJwW3r+7UxKxmrmwno+MRi/s19zdLwkFAOAq4\n+vwVTimhJ/Fmy+2bK2zLpcgKXN9FQ6fYK1KD70r8ma5Bp5HGKV3bMr+6ZX5zT38wZHxyxNnbZ5RF\nLtO/vEDTDWamwWDS5+jxjDIvufrkivnVPcu7e9q2wVNpVnmSkafSFO8f9SWEZJ+zW0oEYbLbKZP9\nRDDR+4LGFj2ebmoSZxhI4Inf8wn7IZquSSC0oeP3fS4/S7l5eY2mweBoRH/ax3YcdoZxiHUzTJ3B\ndMjx02M0XWe32rHf7FXosEG82vHqo8+xHJun7z9nd7Ph5Uef4Tg+/dGIrpMs1OOL8wPOOktS6DrO\n37tQWQY12S6jKiv6fUkyX88XtHVLfzykrTRe/vAlk7MJp88uWN7fkecZp08eMT07Jhr3GMyGlFnJ\nj3/7B2xXGyXRkBdmXVRoGkTjiGjUR9cNNZTQsB3Bzie7Nevlkufvfw3b9IhXO7I4w3KtA5CyKkqK\ntFVUkZIiLTh6fEQ4CCU4Rp3qHN/Bi7yDYPkhwnC32IlgPHC5/vwN2/WK/miIHwRiERv2mJxOqMqS\nfSwJZV7Po6+qGDrJ+6DrGMyG6LrO4mqBYRoMj4cSHr7YUaTFT3sc/9KuP2lju0b6a/+u+v1hY9vx\n5xfofh/45Z/y87/xp/2D2T6hPx1QZCX3l3fc3H1K3eQ8ffYNBtMhTSNht0WR8vzrj3j2ziOKpmZx\ns2J5vZSpk+cwezIjVKeb9f2KItvjeNL7CvsRjifxapqmsb5do2mSgPRAqUi2O9IkoVZ9uf02Fh6+\naTK/vqEsCjn5+TKRDft9LiwhqfaGPc7fOpc8TtMQH2pVE68l8kzTdQmf6Qf4Uci4FRGyYQkiqeta\nzp6fc3d5zf31LUfaEZqus7icHzR5k9Mj3MBTVF6dIq1YZEvauhFCb1GJCV+hof2ej9/zFG1ETQod\nQaGn+5jrV6/ww4jTR4/RdY1OoXrapiNexQdZRNgLuXj7MYah40W+CHP3imEWuITDkKAnsXqarpGn\nYlF7CCQOByF5plPVOUWesZ1v8fyQt77xPhoCULz+/I3w+AaDg0/VDV3cyDuIS/vjHl4gJ88HiUYQ\nRdSF8Pt13cAyLFa3K3mxWCHepHcgxcZq4JMlGVXeYltiti+Lgs1iSZrEdHrL2funGKbB5n6DFwmQ\nc5vmJOuE6eyU8dExk5MZhi7TxaqqD+JtwzI4fX5KUzdkiQiBS11TRA/t8L1YjqVyX3uSSBanh1Od\nG7oH8vL5W0+YlSeUac0yW0h2a9OSbBP64xGO5xL0I+qiZreMSZWQ92FdfXJ16PvJZF2gApPzyVdq\nY/u++vW/8ec/of2FrbZtiIYhppVTFBn7ZEe633J2nuHakrXoeA6Wr9MfR/SGEff3K5n2WSa6pqEr\nz2Bv3JNSbqHRNDWeI0QMW00EHxLGy7zEC1zCYUSZFYcMUwklgaaplXVFo3O6g41lcjyjA7arFbbt\nEPUHaLpONAxxA080d6ZBs8/JkpRkE1MWFa4nnLOmFk+q7bhUZUGaJCS7DV4YMJ5NSHY7tFtEMlFL\nmAiIx1D6XTq2K6LV7XItmQGWfSjNH8rMruuwVDNcN3XKQnqDji+wgaYt2McJhmGKvkqhdLpO6LjJ\nNqZtG3qxlDya2REOQhxP+kRlJjKEupaH+kFQu13KZLnY5zS1SolvW9qmUf5P+VwH0xHD2ZgiLUi2\nMcltjKbrWLZHpbRfpmPQ1BVFlqPrglx/6Ek+/Hv6kbzI9rsYDQ3DNlQUX0NvMMQNXbzAP+QPNE0j\nea4o769uHBr84iOtSeMYx3Ep80J8zJbQWpJ1Qm88IlAG+LqqxUiuI2w2OkzTJBr1lEOiOfiOHyAP\nui6lf6jCmr3Qo9ir8B81VRYbVE2RFfSGA2zHZnW7okyLQ/tkv9njuC5hL5LM1g7i5Y50l1JmUk6b\nlkmWxKIOMA3SXUqe5kL3iCRP9xdp/Ukb2/8O/AfAP/8p/10HfPNnckV/ygp7fWzfZXQ64ck3njB9\nNOLm1SWruwVNucQ2A5598zlvf+dtgijk7m7F1WfXGLrON37la2yWW27e3JPFmXgRmwY6DctyMQ3p\nOTRlQ6M1ArS0xbwsQRiC72nqBs/36Y9l1C/s+lI+FU3j/PkjbM/BdmxuXr/h848/pN8bM5rMxP9n\niph2v0tZ367ZJzH5PqVrOxzfY3o+xbBMwXX3BBvz4icfc/vmDWWZMT05oT/qE/b6nJw9glZM3n4k\nfP7tYsv89pr7myt6vRGW5bBa3kKnMRzMCHo+4TAUIOJmL3Fuyhhd5+KBPH56zORsImVV5HL/ek7b\ndOyW8RdpT65Nmeckuw11UzLYDXj58SdcvnzB+9/6DoPhlMX1vQT0nh+zW+5Y367wQpdOg818y26+\nlRyCQjaY3XJHXVXoCAigqdpDTFy82hGvY7wghE5jN99SVzKpXNxsiXc24Ujoulmckmz2JJvkEMLj\nheJHLfMhINGHtYopPASfVCJsTTYJg6OBqO/TgjROQQMvDASaWR5RlSU3n9+yuFowuzhjcCTxg+lu\nT7yOGZ2OCQYBaZyynW9ZXM0lLDn0sZTMo8gKmqqGDjU0cIlGEQDL6wV13RAhXtV4nRyyR5umkcmp\nKQTi5fWC07fO8E498eJmJWVaiBumqLE9myCSqqNtWu5e3lLmFU7gCOeuH9Cf9gVflebst4JC2q22\nBwLvL9L6kza2/0L9/hcpzv1zr3AguG3hUlnYlodjh3h+TqVX6JjYtovturx58ZLtaoNt+ERRRJ5K\n9qgkM23ZLjYE/VCasY6DFwVEI6EtNE3DvkqoilIatMocrWmasiCJrcVSKVmO57FdrNlvUzQtEjuL\nJRmftu3ieDLFytKUdB+TZxm6buJ4PqER4vhySrRdBzf0qApJjHc8SUU3TRPTtCmLEpAprGU7uF6A\nYcjXqJu6pHHd3VHmBdGghx8EmKZN1PTQDZPheIhpWwI91KSUqUppXgOk+4TFzR2TiyGOZzG/uWNx\nu8D1fYq0YLNYgd5JiIhpYFgm/ckAyxLMket59IdDbFcoLH7kgyYAw91KPJuru4mQUuoWP/QIQ5/V\n/ZrFzYo0SWiaGsf1sCyxXWkqqrBWZZxruxLAYpsHX6jRgmkbFPuCmPggNO2NeyKnKSvRplkSDl1X\n0sA3lPNBQn1yOVmVUqB4oWjQltdLme6qSahhGPRGfUzL4PrlJXVd4aj/z/vX9yQb6Tm6voMXuFLG\nSSoNeZpRlQXD2RjPFm1YU4ugW6jAHsv7W+LtjiJvcD0f0xERedM0SrRbH67DMA28yCccRTieo/yq\nBq1pUBu6OlVLP7htWobFSETXe9n0NF2jVbRpS8UBPkzhvcgjXu/I4j3F/qvjFb1Wv8+BHGiAd9Wv\nv/8zvq5/6YqGIYaps9/uWV4vePPJK/bbhOPHF3QNrG5kc3nz0Rt+/3u/znaz4lf/1t8EQ+cnv/8R\nk/Mpp2+fcvfmhtuXN1y8/QjdkKlZbxRxdDEFJBgl3+fE92uWVyt5k44jNF1jOBsdpo/L6yWWazGY\nDri/vOH+6prtwmMwGXH+zgVB1OfRs7dVQIvDqw8/4/7qmixPOH3yiK+/90Q2BTXtqqua/eYL8KNp\nm5iORW8wwjRc4nVMNIywHFukHm138F1qaKT7hPubS6anxzz72jclFauDPD3FtE36oz6rmxWvP3zD\nkw+eML4Q9HeRFcKs2214+elPePzBI/J0xh/8xm+zuJ5z8fhtNKNjPV+ocsqgQ/p5T95/LuzPuuXJ\nu+/w+J23D0ij6fkRq9sVL3/4knizoawyVrdLLNsmGoSML46YnUz4+I8+Y7PYst3sqKqSo9MTwl5P\ncfeEliINeou27fAij/N3zonXMfev7/ECAVpmu5z9OsWwTSZnE06enXDz4obVzYo8K9ALOVln+5z9\nZs/wWHJW52/mhwfacqwDJSMYSClWpAWGJRakqigZn44Zn42xlVneMEw2d1uW10vQIOiHuKGHrXyd\nXuQzmDbMr29YXC0IhyGWM5LmvQrscX1XIAS/+3tcvnzJB9/615gcSxK9F/rYns39q3t2y53g6QP5\nzt3QZXIxEZtgK0nxkmGqMnHpSHcZ6S4jGkVC9FVoriqvcNRLulYlbZGVDGYDHn/wmJvPbrj6+JI0\nzn5ej/yfaX2Zwvm3gf8ZOAL+CTBBTnE/D4Lud7/+nX+doCcTo2wvuh7H82gbkRHUZa1OUXD9+jVZ\nsmcyPaFrNHbLWPo4Xcfici4lUCkJ4o1yJgyOZDCRblO2yy112SgbkjDXAJE3BM6BmmsqGUCeZLRN\nq6Qoonvq2o4yr9QoXRTveZaxuL/C8RzOnjxRdNoax5X+x+pWMDWGZZBnCevFnHDQoz8aiKBTF4pq\nlQun/0HJbHv2wT/aH48lCKV+wBGNpAxTSVYPuQFd20oKe9uQbHbUZYUfhUTRgKZUb+8gJIx6VGVF\nstnRHw/oT4aHfMpsl1GmgjVPtgnxaqeuTbHo1CRvMO0zPT+iazWSTcJ2sZKIwrIh2e1puk7QSLMR\ns4tjTNsSHpym4ypbj2Zo7OP4IHitcvnOV4s7tpsFo9kY1/eJVzG6aeAFHsurBdvlDsexKcucq5ef\nU5YF0WBwsDbl+5y2bjFMnaoolYezJI8lMUqCeAqVNG9hOxKzuJ1v2W8S0jg7mPwf8gbcUPy3mzvh\n18XrWDHh+ri+h4ZY+wQ9tKc/6XP69FhOb45Hvz/Csmy5P6qauqgPm+5+uxeMtyGBx9v7LWUqp9fV\nzYI0ThUN2MYLPZpGsksH0wHRMGSk8iEkIjASiIAnmbhpnMpENs2JlWd4eDzit37jH8BXQO7xsDRE\npPt3gf8eMal//2d5UX/SWlzfMzmZit8wKxkejenajqtPrkgTob22yjBsWw6u4xMvE5pMHsLdaic3\nbFLQNR2ru6XYkML+YYqUxZlselmFaUqoRb4v2M4lnMRqpClruDpB35fTXSK5nP3RUPpioSeNZsU5\ne8gPnZ4fk+4TXr74MXmeUmQ5tJo0j1U4RxqnVGVFNIzYXs6Z314ye3RMb9oj2SaUWcF+uz+w3krl\nvQTJOz199ETwTLWkYhmmQTiUad/6ZoXpWJydnrFbSCiu47vSL3q5wg8Dnr//AVmScfdyzujo+EAp\nyRQi3Y98wkFAlgi5ZL/do+s6buCwma+IN1ui4ZD+eKBIFyajkxHDmTxMH/3uR1x+8ook3uIGHqu7\nLdGwR2/Sw3ZFbOtFHourOfFSEsWGsxFmzwStY35dkO33aJqO5wtaZzW/I89j3v72+3huxN3rO5J1\nzHa+Eez6bk84CCnLgpvLV4yOZlw8e6bkFvIZ6aaOpuvkScr6XpwlQW/DYNoXEoeSVtieTZqkZEnG\n+m7FfiuDI0F36wcUltCWCxbXCxkMZTmTsylHFzN2q5hkkxAOIyWwbXE8m+HRkHe/+U2mR2ds59vD\ny9qwTCzX4uztM7zQEwRSnKpUtJTFm4Vg2E2N5e0Cw/wCRBn0A+qqVr5YjaDnMz0ek2wTLl/cYKoY\nxAfMOcBusWN1vZLISM9hqiqZX5T1ZQOT/xoCmPy76s/6z+Zy/vSlY7K937JeLNkslpy0F4S93sFk\nbLkyDWuahifvvkvbNbSF2HE0XZO+hGUerFbTR1Nsx6bMamVSdglqMZPrhhzjJSjEOaB9oGN5syBe\nb0nTHdFwwOxM9GXb5fpglq7LmrYVy9FDkEfbtAzGY977+neoy4Y3H78i7PeI+j3JRtXEy1iVopMa\nTaeE/QhDt9ncrdkt1+iGrtwMplxf5AnjS+m36rqmyAt5sLICDTD0LzJNdUP0cw+5CUK30AiiSNhm\nnnhcy6wkXssE0bQNomFPwSLFaVBkgmkfTAcUWUGyjvHCACfw8KNAmuTq1GDZFsNJn14/ZHw8JEtS\nnMClLiu2S8Fpu4FLvIyJtZig5xOvdpRlQZFJ0HGWpCr/NKSySuLNBjewmV6cML34VTS9w/Eimqrl\n9PmZnJaLSm3GAXVZ4wchf+XX/g1oBXYgnk+T87fOsF2bzXJL09ZwD4OjPkfnM5WXUYgTJcu4frHB\n9X1s22Fxd0vXtZw+vqBtYXO/xvFdlXnQUWQ5y/tbLNvi6Tef0zUCohT/skpcsy2ikfQCX/zgc3lR\nZTL9bBpxkgxnI4lDjITKMZwNDz3fBzqvbooNbXgkUXniTMkPlOO6rNmthGGYrPfohkzQ87QgWSeY\nlkGWZGzmKyzHluxdNc3dLXZ//GH8S7y+zMb2XyKWp/8D+BHwHClJfy7L9eSElCWpcLb2GY4r1APT\nlsTvuqrRSo3eeITlWGzvN4pA2h6U4rZjSTjxsI9pWezqnTrRbWnKRgWpiHi3yGVzsBwLxxMDc7JO\nuHt9x36/QUPn9PGFlEq6djgx7rd7DMPAC8Xs3rbiQXVcjyfvvMtmsebuzQ2mYeF6PnpaYLnWoeEd\nL3fYloPjetBoZFlGkRfYjsg5LMeSfAfF+M9TpWLvukN4TV3UQAc3HLyEVVEdFO9N1VCV4lt0XBfX\nE8nHAyFidbMS0MBAiLKj2Yi6qlQQs/EFGUOHpq5xWlciDXWR0GT7FE0T5HlVlMRreUCCfkjQD8mS\nlN1qczjlFFl+eLDTZI+mgaUQ6duF9KKOzqc0dc3tm2uapqauS44vjvHDgNtXdxKeMwzlM9jnKipR\nNHC243L06Ih4FXPz4pq27XA8CV/xI58szfFDn/50QDSUjT6NU0zLkL5qW7PbrNE1Ax1Dseck86DO\na8o8x7Stg1SoKkuapsK1HMJ+SJGWInxu5DRdFAJSiIY9oQqvY5I4Jk8z9E5gCGUuoub+WIANbdMK\nzr1tAY3akvBpDUDT8EL531RlRV0pzZwhCP1CbZjxJpbBjRICZ3EmmQ5ZrmRMGprRYmg6XSfkkl+k\n9WU2tl9XvyIgRJwCf1ayx597jU/HtE1Dvx5hmja27VDl5WFqU1f14SZtmga91jl6MqOpGnZL4fSL\nQHWgTgAFbS39kWQbc/XpK7wwxFH6r6osSeO9BHS4wkETommDZdkMhlOCsH8ol4J+SJVX5PsC0zJl\nMurZdHSKPpvi93xO3zrF7wdKztCy3+0xTIk96437xKuY+Zs5eSoWrPHJRLRlro+u7DamwhDRdaTJ\nnjeffg5oHF+c01QGTdmAJo3+tu2oS+mbZHEmn4VhCMAwk7+7NxgcsOZ+5OOGLtvF9jA980KPyfmY\n289vhWaiSpw3H70iGkU8eu8Ju+WO1e2KzXxNGu9pu4beeMDxo1NefbhmO19h2R698YDH7z8CYHm7\nUOgeCeHpsvIQH+dHESdPTnn69aciNl3FvPfNt0ADy7WZ39zxh9/7PZ68+xbDyZjF5YK262QooEga\nDy+oSuUQxKuYzf2a7WIt+bOWyWedbPwPjf/pxZRks2dxtcTxHRkGBC7hSACVji8nWycUsXOZipG/\nqgQZ1XWdErV2zE7PaduOq0+uGc6GnL51hvna5O6y5P7mUrSZywFPP3iL2ZMLXv2Tj3j10WccTR/h\ne70DEeIBqZXvc4o0p+vAD+VFXhUVlm2i6xqVOp094JEOk2Flou/alnSfKw1gpe5tW7U3dI4fnbDb\nbvjh7/4Bvd6QqD/8Sgl0H9Y3kOHBWP15jrDUfvizuqg/aYUDScxxA4/xyZjuwf6UFhiGLuEYumJc\naRp1VbG8v5MbmAeZiEmgKBdN1VCkhcI0iwhW14SoYLkWTVOTbCWqrj8equRzQ9KMNI26qNE1QdSY\ntsg7dF0ggU3V0HUyyjcs43DC0TQOSd+WygjVTZ1kt6Mo00PykRd5GLZB29aHcb0XeqpEfuCuyeig\nKkscTxrSbd1iWAbhKKRVQTVt27GP9yRxTFM2yl+ooSulu5PgObgAACAASURBVKEmww/wQd2UE2HY\nD0QBH/l0bcv6bs391R3zyzum3bHINtqOthFoZ6M0Z3XZKDmFTls37BUdNt0XuK1xYLIJGqdVcpPm\nIJjtQOUODAlHEUUmUXd+L6BuGiVRMAGdumjIkgzb2pPvc9msk4zWa7+gcih5R1M3pDvRpJ08O5US\nN87YKqLJ8HgEGqRxSq7sWg+fd1XK4CUc9KjKgv1uJ9PTQDZ413cZnUyIhn16w/6BFuwGHrvVhutX\nr2ipJEjZsYiGEUU5kIpAV3M8TWL4+qMhXuirHqJFmRe8+skL9R2LKuAhKb6uhNZcVzWtcq5YjnWQ\nRcXrWOUaaDR1jaZLtGC83XD54084Pr9gMjvGMA2F3E/I9ilN0bJbb8n2kjf7i7S+zFT07wH/FaJr\n+28Rs/p/B/yPP8Pr+pet7/5bf/s/xPEdhsdDjh7PDranQolZz989p+s6kk0i5U9Z8Ee/9TvcX90Q\n9Yc4rqM2IJkuWY4ksDdNo/A6LcPjMePTsVBqDY3VzZz+pM+zb751oFhIspIrhuiiIovTAz75gG7u\nOhply3E8RyCNvQBd11hcLtgtdnRtK0LQ4wGvPvmU29dXEtrrCiBxOBsymA7ZzDfE6x2DaZ+gp3I4\n9znbxY4yK9B1g5Mnp4T9HvFShJzj0zGWY4LatOPNlsXdLXQd/eEQy5IIQC8MCHrCOhM4pHbQ6RmW\nlNJ+zyeNU958dMnlp5+zuL1B00RbF/YE/RSvJCehrVuassZ2HMYnExzXFauTymbVNVH8p7uU1e2a\n1c1aekp1e8gqcH2Xo8cz3vql55R5xesP36Abkr61mm9Y3C5J4wyt0/G8QOGkLOqqOZBJ2qaRIJxN\nQrJOKNNS6eliJmcTvvVr30bTdIq0JN9n6KbO8ZMZ+92eT/75hzSVlOdNI1CB688vKfOC/mTI4uaO\nm5dv6I+Ucdwy8Xsh45Mp04sjRscjTOsLy9p6OeezD39AXTbonX2IdhyMR/QGI5XNKlTdqD/g+EJ6\nx+EglMCg+YKf/M4fyQvIcljfbdjcrVlcC6V/OBuSrBPildz30ThifDKSuMUXt+RprojCJbZjc/bO\nGYvFFd/7R3+fsN/n5PwRaJDtU9589jllWjA+OibZbbi7foOum7x48X34Ck1Fff7Fnto/RVDeP5cl\nvrpMva0KmXht98pILp7AeLPl+uVr+qMRhqnjBwMpS2yxCUWqr/Cg9XkQOga9AC+QWL18L3YS0zQx\nDIsszrn57FqFNMsE0PZsjp+dkCUZ+01CkUvat2EZ+KHHUAXSlllJkcu1SmSfy/HjGVVZsV1syWJB\ndUe9gSKLOIdIOwnqkN6cH/msF0vFURvRnw7oT2F1uyKNMwZHrYJw6oeJrGGaeCoLIBh4nFontDU0\nZUey2VLkOWGvp7RSHmVeslFloO05ZIrRLynvsiGNZlNGJ2N0TagabiAi2rqsuLuas5rPGQwmeGFI\nVdQHSUm5TynLQpwOmo6mD7EsW0TCamKtaRqmLS+dNEn40W99H00zMEwJFTlwzWwpsW7fvOHNqxcc\nledMjmb0JvLvYrk2WZwRr1X6uqGTxgm6oTM5Gwv8EVQOp0e83lJkObvFjkpJXizHPrhK2kbILmFf\nXCh+EBL1CwZHgpGXkGKRW5iWoUp5TzRjZc1wOubxW29jK1EuHVRFxXa5oipqDMM65J0WmURAPmDm\nm6ZB001GsyNsx6FtJfWq6zqMvbx4HkJ5TFteVhqachAk7NY7vNCTjVOFemdJhqm7XDx6l+FoiuVa\nWK4lJ+y2pi4bbMtlenrM4GjA7PyUf/yPfh5P/J9tfZmN7XPgvwb+F0T68R8BL36WF/UnrTIv2S62\nkthjm+wWwprvT/tYtimb3WrN/OaGqqiJogGj0TFeJDFiXiAUDVGxt4d0bcPQcfoi09hvRWndNq3y\nJNrkccHlx5eqHyEnxuHxkNHZiCzJ0HWN/PIhScoliHx6E2G11VXN7Ysb1rdrmrphOBvwzi+9RVmU\n7HcJ27mkP82ezIhGwvvKEiHTCpCwZTgbYDomrz6+oyhcxidHDI+GeKFHvI6JV7uDdukhTu9BC2c5\nFoYthurp+ZTtfMv1Z9cs73K26zWmZUkuhGcfXhZVUWE7FvvdHi/0GB6Lbq3rWianR/TGfRbXCxpl\nqjdMg9oy2Mdbrl+/JOxFWM6A/TZVG6xOmuxFpFvKqSHs9/ACE8c22S13ZPsMPxSrluM7bJYLPvmj\nn3Dy+Iyn77/D8lo+38nZBL/viy7vZcbl60/ROwPPDZk+mjI6lqHR4lrSzw3DoLM7qrKQIJbHR4SD\nQIJpVO9QcioyNvONyjzoi7i1g7qU3tTR+Qw3ENN52IswDYvh0Ri/5x8ABvutnJb9fnDIdNCzkuF0\ngqHZQgapZEIvWPU1ddUSDYYHpHy8ks/CCzzpOXYdlmUze3SGpf78MBB52EQFJ24fwAXQkWz2Qmcu\nShxfhkKWKfdHvIqxdJ933vslJsdinbMcSzIOHId0tyfdpQSDY4K+z8nz05/XI/9nWl9mY/s7yPHz\nQZD7z9TPfi5ru9iKkn6f02xqIWRYUlGnccZuGWNZLu/+0texTAdajSxOsWxJ0K6KijcfXh6mc08/\neErUDwWbHHiMTsf0JqJpczxpzI9PJ4KPaRq6lsNmUZUVNy9uJPVJWXhs1ybfF8TrBDcSOOR+K6nd\np2+dMn8zZ7vY8oPf/AHpPubu6grXCQnDwWHTTuOMfRyzj2M50bgyyXRDj6fvv6VEl/5Bc9fWLXVZ\ncfXZa9E7GQ5t29C0tZjoXVHla0hJqqteZLTqU2U1ddFI6R56dG0rkXumIRNJV2xcn//wxUF20dQ1\nyWYvIlTfVUHSEpwShANmx4/YLjcUWcHkaEZdwXq+JOyHjI+fM7++l76QUrtvl1uiUcTx02PVg5Re\nUNu2ymiesb7bUGSlnGI00W7NL+/QW5tv/fJfw/OkFL3+7Jrblzcq18JQrQbpYQ4mI0zbosgrVndr\n2lqmi17kgdbQNJUS6BZsVxtOnp4xOZmgvRab0tN3Ltitd/zkDz6kPxHsUlPV7Dd7hXESOu3ies5H\nv/cTeqOBWMqQSsNQwdNowkALfJdvfP05ZVHy5nqJbhmSyL7PKbKC7WpNNOrx+P0nJJs989dz/EgU\nAKv7hejvdJnAhkOZMOdpysgaYlgmyWaPHwVMz6csbhYsru+JRsIa7FqZ+k8vpoJDahqyZa58rRvq\nqlZi3T2b+Yoi/+oND1YIP62PDGd+rnPfYl/IxLOWKZdpC275AbdSlxWW4wg+WpVH+T6TEGJlLN9v\n9+rBNGSSZMjD8kCBeMinfGi4BoMQP/LRNZ00SalKiZer8orNfKPsPpLGZNqmenPviZJIhWB0gmS2\nTLYLobJef7YnL/ekaYznR/i9gLbtyOKM/TYRKUuW4o5dwkFIkWc0XcX0bIYXymS0a1sKhds2bYuy\nFGFvbXRouoonrGo0TRwKZVYoqYHo1izLxrZd2k56L8k6VuSJlqqqAXA8W8KQlxvSJCFLU9XrchmM\n+4SDEAyRapi2xWA8RtdMVvNb6qo8kEDapiHohxw/OqVWxAld02Xzalr8yGf2aCbY7EKCd0zLojcS\nYoVglnRR/HcSeJ2sY/xeyPH52SG7dbtYq++opDfqMzmZ0lT1IaLOMOVU/7ARj45HOL6NaVtY7hfQ\nSElvF2S3G7jYlokfeux3CUWaYVoTgkFIso4p8hLT0hkeDTl5ckK2T7n89BLDsNRpVXydpm1RlSVV\nWdJ1LWHgMTud0dKRAaX6zN3AJd9n7NYb6kqyRfNEpqGGKaVkU1cYhkYYBUDH6m7BfpccBhZN1ZDv\nM/xegN8L0BUavGu7g/xDBlq6ZOW2HfleJuZtKzrOroOqqqmrSoCov0DrywwPfhn4vxA923+KQCF/\njy+8pP8q13d/5Vf/JsOT4WHiYzsWaJrgV1yb2eMZRVZw9/IOQyG7y0x0Q7W6cfy+j2EYamzvkqcF\nu1XMfrNnebM8lKf7rUzZAEazEU/feywZmep0VmYlyTo50FofKLMPN5euC2NsenGEF/kSzHK7IY0z\nEVUOeszOTzl+dMrwaKQmhdJDshyRsly885hH7z/i1WefcPniBbbtYdkPuZIcCCWiDp/hBT7pLqU3\n7nP+7iOCvgTYPCQh6cpnu73fHOirpm2JZayoSbY7tsuV9JzyjMnZ0cE+lecp6+UdRxcnPP3ac56/\n95jxdMh+nx2yXAUMINmffhSRbQVJFA16TM+m9KcDmrqVKWrZYNomo5MxvVEk2GrbUv0wwXlPTo7o\nj4fYnnMo7dpGRM9+FOBFvkL8GErT9yBnSNB1A9txiDcxu+WWQtnJHtwpbdOiaxptLYHDfhAIUikK\nGEyHgM5+sweQnIC8pCwrgkFI0Avpmk7lfy558+nn6Bo8f+epgAwU/YROUxYroQwvbu959eGnMiHe\nZWy3MWlZEoxCNF1XIE4VIrMv0NCxHOkXPkguTMvk9Nkpb33zbT741rsUecoPfuf7VFmFYVjohkGR\n5uwU2DJe7gCNaNhTuRcho2Oh415+colpW/i9QKWhWZy9cy694bzEDTyiYUQQ+fzfv/734Ss0PPif\nkA3tn6k//3X1s58LtsiwhLCapxlZkmJaNl0jA4OWiHE3ErlBVRNvYoUa6sizlNefLBgfH3H86FRC\nlzV52DV0BkcDNncbVrerA575QZFvO7YCUq5FLGmIZEPTtS8Sh5A3rWEZyr8oIlhbiT+zNGG/S2hp\nCAfhQfFuWy5VURM32wNr3nItJfK1KYqM26s36r+zKbMSmo7hqMd2tWO52NK1ndBdDVM14z21oVcq\nfEQmha0SFnfq4fb7gTS41akVII0T6qbCMB2hYJQ1hVagaTpBFDI9nTGYDPBCl7puVPhIJ4JTZdyv\n8pK6bugaMEyZOosSX1NOCA3bdQ4RfQ+Ms6qsDuE18TIWOGTfFxmKZRAvYzJESFqWJek+xiws6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6bA+DoiqvyLM9aRZj+xa25zCajfGj4HDNuvLkur7Hk/eesV2suH51xeTkiOnpTMTb9QNFRVdM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\nJMPT63uYjo4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Xb+B1b9i2U93bWI5JliQi6i1rEXK6NoaiQtNyCCKRSmgG/mTI05cvsDpm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\npmP9CltKaUWN6lFYmmcZeVpQuRVNXR+Hu4ZpYOgWru/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ar16zi+a8eV/T7085O3+M7ciM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V534lnfr7vA5TzNeLx5aG9mU6gkSUGRlWi6zuR4TlPX1G2qVJZKz1VBwlgcxZENOi9Y3a5E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\ncQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10715eed0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this picture, whiter pixels are more positive, darker pixels more negative. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Bonferroni correction is the right one for this image, because the image is made up of 128*128 = 16384 random numbers from a normal distribution. Therefore, from the Bonferroni correction ($\\alpha / N = 0.05 / 16384$ = [Z equivalent] 4.52), we would expect only 5 out of 100 such images to have one or more random numbers in the whole image larger than 4.52."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Bonferroni threshold for this image\n",
      "bonf_thresh = inv_n_cdf(1 - (alpha / n_voxels))\n",
      "bonf_thresh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "4.5227713755927113"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The situation changes if we add some spatial correlation to this image. We can take our image above, and perform the following procedure:\n",
      "\n",
      "* Break up the image into 8 by 8 squares;\n",
      "* For each square, calculate the mean of all 64 random numbers in the square;\n",
      "* Replace the 64 random numbers in the square by the mean value.\n",
      "\n",
      "(In fact, we have one more thing to do to our new image values. When we take the mean of 64 random numbers, the mean and variance will tend to zero. We have therefore to multiply our mean numbers by 8 to restore a variance of 1. This will make the numbers correspond to the normal distribution again.  Why 8?  Because the variance of the mean of 64 numbers with variance 1 is 1/64, and so we need to multiply the numbers by $\\sqrt{64}$ to restore a variance of 1.  See: [Sum of uncorrelated variables](http://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9_formula.29)).\n",
      "\n",
      "The following is the image that results from the procedure above applied to our first set of random numbers:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Divide into FWHM chunks and fill square from mean value\n",
      "sqmean_img = test_img.copy()\n",
      "for i in range(0, shape[0], s_fwhm):\n",
      "    i_slice = slice(i, i+s_fwhm)\n",
      "    for j in range(0, shape[1], s_fwhm):\n",
      "        j_slice = slice(j, j+s_fwhm)\n",
      "        vals = sqmean_img[i_slice, j_slice]\n",
      "        sqmean_img[i_slice, j_slice] = vals.mean()\n",
      "# Multiply up to unit variance again\n",
      "sqmean_img *= s_fwhm\n",
      "# Show as image\n",
      "plt.figure()\n",
      "plt.imshow(sqmean_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Taking means over %s by %s elements from image 1' % (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x107424590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IGl8cx4SNkDgRZj1JEsIgJBFmS7Edm2wxJ85jFvohpdESoS9L8eO4Dpl8how0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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107176590>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We still have 16384 numbers in our image. However, it is clear that we now have only (128 / 8) * (128 / 8) = 256 independent numbers. The appropriate Bonferroni correction would then be ($\\alpha / N$ = 0.05 / 256 = [$Z$ equivalent] 3.55). We would expect that if we took 100 such mean-by-square-processed random number images, then only 5 of the 100 would have a square of values greater than 3.55 by chance. However, if we took the original Bonferroni correction for the number of pixels rather than the number of independent pixels, then our $Z$ threshold would be far too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Smoothed images and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The mean-by-square process we have used above is a form of smoothing. In the mean-by-square case, the averaging takes place only within the squares, but in the case of smoothing with a smoothing kernel, the averaging takes place in a continuous way across the image. We can smooth our first random number image with a Gaussian kernel of FWHM 8 by 8 pixels.  (As for the mean-by-square example, the smoothing reduces the variance of the numbers in the image, because an average of random numbers tends to zero. In order to return the variance of the numbers in the image to one, to match the normal distribution, the image must be multiplied by a scale factor. The derivation of this scaling factor is rather technical, and not relevant to the discussion here)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# smooth random number image\n",
      "import scipy.ndimage as spn\n",
      "sd = s_fwhm / np.sqrt(8.*np.log(2)) # sigma for this FWHM\n",
      "stest_img = spn.filters.gaussian_filter(test_img, sd, mode='wrap')\n",
      "\n",
      "def gauss_2d_varscale(sigma):\n",
      "    \"\"\" Return variance scaling for smoothing with 2D Gaussian of sigma `sigma`\n",
      "\n",
      "    The code in this function isn't important for understanding the rest of the tutorial\n",
      "    \"\"\"\n",
      "    # Make a single 2D Gaussian using given sigma\n",
      "    limit = sigma * 5 # go to limits where Gaussian will be at or near 0\n",
      "    x_inds = np.arange(-limit, limit+1)\n",
      "    y_inds = x_inds # Symmetrical Gaussian (sd same in X and Y)\n",
      "    [x,y] = np.meshgrid(y_inds, x_inds)\n",
      "    # http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function\n",
      "    gf    = np.exp(-(x*x + y*y) / (2 * sigma ** 2))\n",
      "    gf    = gf/np.sum(gf)\n",
      "    # Expectation of variance for this kernel\n",
      "    AG    = np.fft.fft2(gf)\n",
      "    Pag   = AG * np.conj(AG) # Power of the noise\n",
      "    COV   = np.real(np.fft.ifft2(Pag))\n",
      "    return COV[0, 0]\n",
      "\n",
      "# Restore smoothed image to unit variance\n",
      "svar = gauss_2d_varscale(sd)\n",
      "scf = np.sqrt(1 / svar)\n",
      "stest_img = stest_img * scf\n",
      "\n",
      "# display smoothed image\n",
      "plt.figure()\n",
      "plt.imshow(stest_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - smoothed with Gaussian kernel of FWHM %s by %s pixels' %\n",
      "          (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x107d0b0d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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slMI4Vf6jJ6pibDjxrKxMmwyMMWkW3T/gkdEct0gWO6tSlu2HKiDNYlLF1Fky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\nzJgxY8aMGTNmzJgxY8aMGTNm/OGI/wfnXRGn/Y0XTgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10741aed0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In our smoothed image, as for the mean-by-square image, we no longer have 16384 independent observations, but some smaller number, because of the averaging across pixels. If we knew how many independent observations there were, we could use a Bonferroni correction as we did for the mean-by-square example. Unfortunately it is not easy to work out how many independent observations there are in a smoothed image. So, we must take a different approach to determine our $Z$ score threshold. One approach used by ``SPM`` and other packages is to use Random Field Theory (RFT)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can think of the application of RFT as proceeding in three steps. First, you determine how many resels there are in your image. Then you use the resel count and some sophisticated maths to work out the expected *Euler characteristic* (EC) of your image, when it is thresholded at various levels. These expected ECs can be used to give the correct threshold for the required control of false positives ($\\alpha$)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is a resel?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is a \"resolution element\". The number of resels in an image is similar to the number of independent observations in the image. However, they are not the same, as we will see below. A resel is defined as a block of pixels of the same size as the FWHM of the smoothness of the image. In our smoothed image above, the smoothness of the image is 8 pixels by 8 pixels (the smoothing that we applied). A resel is therefore a 8 by 8 pixel block, and the number of resels in our image is (128 / 8) * (128 / 8) = 256. Note that the number of resels depends only on the number of pixels, and the FWHM."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# No of resels\n",
      "resels = np.prod(np.divide(shape, s_fwhm))\n",
      "resels"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "256"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is the Euler characteristic?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Euler characteristic of an image is a property of the image after it has been thresholded. For our purposes, the EC can be thought of as the number of blobs in an image after it has been thresholded. This is best explained by example. Let us take our smoothed image, and threshold it at $Z > 2.75$. This means we set to zero all the pixels with $Z$ scores less than or equal to 2.75, and set to one all the pixels with $Z$ scores greater than 2.75."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We make a function to show the thresholded image:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def show_threshed(img, th):\n",
      "    thimg = (img > th)\n",
      "    plt.figure()\n",
      "    plt.imshow(thimg)\n",
      "    plt.set_cmap('bone')\n",
      "    # axis xy\n",
      "    plt.xlabel('Pixel position in X')\n",
      "    plt.ylabel('Pixel position in Y')\n",
      "    plt.title('Smoothed image thresholded at Z > %s' % th)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 2.75 and display\n",
      "show_threshed(stest_img, 2.75)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAR8AAAEZCAYAAACuDiFQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+YiIiIiIiIiIiIiIiIiIiIiIFL7/B0g6VU5XR4b+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1074a5690>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Zero in the image displays as black and one as white.  In this picture, there are some blobs, corresponding to areas with $Z$ scores higher than 2.75. The EC of this image is just the number of blobs. If we increase the threshold to $3.25$, we find that some of the blobs disappear (the highest $Z$ values at the blob peaks were less than 3.25)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 3.25 and display\n",
      "show_threshed(stest_img, 3.25)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAR8AAAEZCAYAAACuDiFQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA/QZL2Ytvc8TAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107f57390>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One blob remains; the EC of the image above is therefore 1. It turns out that if we know the number of resels in our image, it is possible to estimate the most likely value of the EC at any given threshold. The formula for this estimate, for two dimensions, is on page 906 of Worsley 1992, implemented below. The graph shows the expected EC of our smoothed image, of 256 resels, when thresholded at different $Z$ values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# expected EC at various Z thresholds, for two dimensions\n",
      "plt.figure()\n",
      "Z = np.linspace(0, 5, 1000)\n",
      "\n",
      "def expected_ec_2d(z, resel_count):\n",
      "    # From Worsley 1992\n",
      "    z = np.asarray(z)\n",
      "    return (resel_count * (4 * np.log(2)) * ((2*np.pi)**(-3./2)) * z) * np.exp((z ** 2)*(-0.5))\n",
      "\n",
      "expEC = expected_ec_2d(Z, resels)\n",
      "plt.plot(Z, expEC)\n",
      "plt.xlabel('Z score threshold')\n",
      "plt.ylabel('Expected EC for thresholded image')\n",
      "plt.title('Expected EC for smoothed image with %s resels' % resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x107f31d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RI6zBM26cDUUiEgtJnfRV2pFM1aEDfPYZDBwI99xjA7hNmKDkL+WX\n1ElfB3Elk2Vl2TAO8+ZZnb9fPzjmGHjrLU3NKGWnpC+S5LKz4bzzrN7frx88+SS0amV/dcBXSitp\nz8jdtStE7drw/few996uwxFJLjNnWtL/6CPbIFx5JRx9tO0dSOZK6TNylyyxg1pK+CJ76tQJRo+G\nRYugRQu47DI4+GAbx//HH11HJ8ksaZO+SjsiJWvYEO66C5YuhaFD7eSuQw6Brl1h8GD47jvXEUqy\nSdadwVCfPiEOOABuv911KCKpZccOmDzZDvi+9x60bGkTuZxyipWAKiZ0YHRJpCDlnaRN+sceG+Kh\nh6BbN9ehiKSunTth6lSr/X/0EaxdCyecAN2721SOhxyiUT7TSUon/WrVQqxbZ9MkikhsrFsHEyfC\np5/C9Omwfj0ce6xtAI4+Gtq317SkqSyZk/6pwFPY7FwvAg8XejzUtm2Ib75JeFwiGSUvz2b0mj7d\njqPNmwdVq1ryP+IIOOwwGxKiVSuoXt11tFKSZE36FYClwInAD8As4GLAn+JDvXqFGDXKQXRJJjc3\nl5ycHNdhJAWti4h4rYtQCL79FubPt8vChXaQeOVKqFsXWre2S6tW0LQpNGlil/r17XwCF/S9iAiS\n9F0c0ukErADWeLdfB86iYNJXzx2PvtARWhcR8VoXWVnQrJldzjorcv/u3dYTaNkyuyxfbkNCf/ed\nXTZutC7WTZtaj6J69SKX/fYreLt27dgeTNb3onRcJP1GgL8j2ffA0YWfpKQvkjwqVIDmze1y8sl7\nPr5jB/zwg20AfvzRykZ5ebBgAfz0U+R2Xh789htUqWLn4NSqteffWrWgWjUrM5V0qVIFfv7Z9kQq\nVbKNSaVKkUv4tqu9kGTkIukHGjKqfft4hyEisVK5sp0k1qJFyc8NhWDrVhtCYtOmov9u22aXTZsi\n14u6bN9uB6c//NB6KoUvu3YVvJ2dvedGITvbLllZkevRLiU9Lysrcka0/8zoRN4XhIua/jHAQOxg\nLsDdQD4FD+auAFomNiwRkZS3EjjQdRCFVcQCaw7sBcwH2rkMSERE4qsH1oNnBdbSFxERERGRdHcq\nsARYDvR3HItLLwMbgK9cB5IEmgBTgMXAIuAWt+E4VQWYgZVFvwYechtOUqgAzAPGuQ7EsTXAQmxd\nzHQbSnAVsJJPc6ASmV3v7wocgZI+QH0g3J+rBlYazNTvBUA1729F4Eugi8NYksHtwKvA+64DcWw1\nsE9JT0q23qv+E7d2EjlxKxNNBTa6DiJJrMcaAABbsBP5GroLx7k/vL97YQ2lXx3G4lpj4DRsOJdk\nHUsskUpcB8mW9Is6cauRo1gkOTXH9oBmOI7DpWxsI7gBK3t97TYcp54E7sS6fWe6EPAxMBu4prgn\nJVvSD3TilmSsGsBbwK1Yiz9T5WPlrsbA8UCO02jcOQP4Cathq5UPnbEGUQ/gJqxEvIdkS/o/YAft\nwppgrX2RSsDbwCjgXcexJItNwAdApg5achzwV6yWPRo4ARjpNCK31nl/84B3sHJ50tOJWwU1Rwdy\nwVpxI7Fd+UxXF6jtXa8KfAZ0dxdO0uhGZvfeqQbU9K5XB6YDRYySlJx04pYZDfwI7MCOc1zhNhyn\numAljfnYrvw8IsN4ZJpDgbnYuliI1bPFkn4m9945APtOzMe6NWdy7hQRERERERERERERERERERER\nERERERFzNpE++OHLbuAUl0H5NAMu9t3uDTwTh+XkAh1K8fwcij8paQ0BRl2UzJJswzBI5noHGzck\nfHkOO9v0ozgvt2LA5x0AXOK7HXScqNL+xmI5/pTGspI9KOlLMmoN/BO4tIjHqmPjzczHhqi4wLu/\nI3bq+XxsBM7q2IQjw7AzV+cSGZisN3b25mRgEnYK+8ve6+Zi47kU9h9sAKt5wN+9+xoCHwLLgId9\nz90CPObFcizwN++95wH/h/3uKgDDvc+wEBtELux87/lLiYyVX9xn8dsXmIidkfkCGoRMRFJAJWxo\n2POLefxcYKjvdi1snKaVRMoiNbCk2hcbZx2gDbAWqIwl/e+IjGHzINDLu14bS7bhiUrCCo/t0ttb\nZk3vPdcQGQY8HzjPu94O28BU8G4PwTZmR2IJ2v85wIZKftS73gPbKBHls+T44noauMe7fpoXh8o7\nUoBa+pJs7sdav2OKeXwhcBLW8u4C/I4lwXXAHO85W7DjAZ2xUTnBEvlabC8ihCXT37zHTgbuwlri\nU7Bk6h/tFfZsNYewPYXN2PhIX2N1f7xlv+1d745tjGZ7798dKxWtAlpgifoU733Cxnp/52KD7hHl\ns/h19T1nApqER4oQtJ4pkgg52AHdI6M8ZzlW8z8deABLvO9EeX5xJY6thW6f4713aezwXd9N5Pe0\nnYL19BHAgCJefxg2cNz1WJnqqkLv639PKHrDU5hKOhKVWvqSLOpgNevL2DMh+zXAkuqrWN38CKzl\n24DIuPI1sXLKVCJlm9ZAU2AJeybGjyg42foRRSz3dyJD11LEexRnMlbqqefd3seLY18soY/Fjl8U\ntUy/oj7L0kLP+YzIweYe2DoVKUAtfUkW12OJ8f8K3f8gBUs9h2I173xsHuXrvb8XYl0oq2JzyJ4I\n/D+sF9BCYBdwuffcEAVbyfcDT3nPy8ZKL4UP5i7EWt7zsQOwGym+d4z//m+wOvtE7713AjdiG65h\nRBped5XwXkE+yyBsSO6Lgc+xEpCIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiU1/8Hg8MWuPjD\nos4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1080a37d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the graph does a reasonable job of predicting the EC in our image; at $Z = 2.75$ threshold it predicted an EC of 2.8, and at a $Z = 3.25 $ it predicted an EC of 0.74"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expected_ec_2d([2.75, 3.25], resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([ 2.82495998,  0.74493991])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the Euler characteristic give a Z threshold?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The useful feature of the expected EC is this: when the $Z$ thresholds become high and the predicted EC drops towards zero, the expected EC is a good approximation of the probability of observing one or more blobs at that threshold. So, in the graph above, when the $Z$ threshold is set to 4, the expected EC is 0.06. This can be rephrased thus: the probability of getting one or more regions where $Z$ is greater than 4, in a 2D image with 256 resels, is 0.06. So, we can use this for thresholding. If $x$ is the $Z$ score threshold that gives an expected EC of 0.05, then, if we threshold our image at $x$, we can expect that any blobs that remain have a probability of less than or equal to 0.05 that they have occurred by chance.  The threshold $x$ depends only on the number of resels in our image."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Is the threshold accurate?  Show me!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can test the treshold with a simulation:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simulation to test the RFT threshold.\n",
      "# find approx threshold from the vector above. We're trying to find the Z value for which the expected EC is 0.05\n",
      "tmp = (Z > 3) & (expEC<=alpha)\n",
      "alphaTH = Z[tmp][0]\n",
      "print('Using Z threshold of %f' % alphaTH)\n",
      "\n",
      "# Make lots of smoothed images and find how many have one or more blobs above threshold\n",
      "repeats = 1000\n",
      "falsepos = np.zeros((repeats,))\n",
      "maxes = np.zeros((repeats,))\n",
      "edgepix = s_fwhm  # to add edges to image - see below\n",
      "big_size = [s + edgepix * 2 for s in shape]\n",
      "i_slice = slice(edgepix + 1, shape[0] + edgepix + 1)\n",
      "j_slice = slice(edgepix + 1, shape[1] + edgepix + 1)\n",
      "for i in range(repeats):\n",
      "    timg = np.random.standard_normal(size=big_size) # gives extra edges to throw away\n",
      "    stimg = spn.filters.gaussian_filter(timg, sd, mode='wrap')\n",
      "    # throw away edges to avoid artefactually high values\n",
      "    # at image edges generated by the smoothing\n",
      "    stimg = stimg[i_slice, j_slice]\n",
      "    # Reset variance using scale factor from calculation above\n",
      "    stimg *= scf\n",
      "    falsepos[i] = np.any(stimg >= alphaTH)\n",
      "    maxes[i] = stimg.max()\n",
      "print('False positive rate in simulation was %s (%s expected)' %\n",
      "      (sum(falsepos) / float(repeats), alpha))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using Z threshold of 4.054054\n",
        "False positive rate in simulation was 0.049 (0.05 expected)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the random field correction compare to the Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I stated above that the resel count in an image is not exactly the same as the number of independent observations. If it was the same, then instead of using RFT for the expected EC, we could use a Bonferroni correction for the number of resels. However, these two corrections give different answers. Thus, for an alpha of 0.05, the $Z$ threshold according to RFT, for our 256 resel image, is $Z=4.05$. However, the Bonferroni threshold, for 256 independent tests, is 0.05/256 = [$Z$ equivalent] 3.55. So, although the RFT maths gives us a Bonferroni-like correction, it is not the same as a Bonferroni correction. As you can see from the simulation above, the random field correction gives a threshold very close the the observed value for a sequence of smoothed images. A Bonferroni correction with the resel count gives a much lower threshold and would therefore be way off the correct threshold for 0.05 false positive rate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "To three dimensions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Exactly the same principles apply to a smoothed random number image in three dimensions. In this case, the EC is the number of 3D blobs - perhaps \"globules\" - of $Z$ scores above a certain threshold. Pixels might better be described as voxels (pixels with volume). The resels are now in 3D, and one resel is a cube of voxels that is of size (FWHM in x) by (FWHM in y) by (FWHM in z). The formula for the expected EC is different in the 3D case, but still depends only on the resels in the image. If we find the threshold giving an expected EC of 0.05, in 3D, we have a threshold above which we can expect that any remaining $Z$ scores are unlikely to have occurred by chance, with a $p<0.05$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More sophisticated random fielding"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Random fields and search volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I oversimplified when I said above that the expected EC depends only on the number of resels in the image. In fact, this is an approximation, which works well when the volume that we are looking at has a reasonable number of resels. This is true for our two dimensional example, where the FWHM was 8 and our image was 128 by 128. However, the precise EC depends not only on the number of resels, but the shape of the volume in which the resels are contained. It is possible to derive a formula for the expected EC, based on the number of resels in the area we are thresholding, and the shape of the area (see Worsley 1996). This formula is more precise than the formula taking account of the number of resels alone. When the area to be thresholded is large, compared to the FWHM, as is the case when we are thresholding the whole brain, the two formulae give very similar results. However, when the volume for thresholding is small, the formulae give different results, and the shape of the area must be taken into account. This is the case when you require a threshold for a small volume, such as a region of interest."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "t and F statistic volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Keith Worsley's 1996 paper gives the random field formulae for $t$ and $F$ statistics.   ``SPM`` and other imaging packages generate $t$ and $F$ statistics maps. They use the random fields formulae for $t$, $F$ to work out the corrected (family-wise) error rate at each $t$, $F$ value."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Estimated instead of assumed smoothness"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`SPM` and other packages also *estimate* how smooth the images are, rather than assuming the smoothness as we have done here. `SPM` in particular looks at the the residuals from the statistical analysis to calculate the smoothness of the image, in terms of FWHM. From these calculations it derives estimates for the FWHM in x, y and z. Other than this, the corrected statistics are calculated just as described above."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A brain activation example in SPM"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is an `SPM8` results printout for a first level FMRI analysis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Display some saved SPM results output\n",
      "from IPython.core.display import SVG\n",
      "SVG(filename='spm_t_results.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
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        "<text id=\"text3078\" transform=\"matrix(1,0,0,-1,306.4168,570.25)\"><tspan id=\"tspan3080\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0\" y=\"0\">}</tspan><tspan id=\"tspan3082\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"-40.8336 -31.9376 -26.6096 -22.1616 -7.9376 0.9584 10.7344 16.9584\" y=\"-179.084\">stim_hrf</tspan></text>\n",
        "</g><g id=\"g3084\" transform=\"scale(10,10)\"><text id=\"text3086\" transform=\"matrix(1,0,0,-1,68.4168,479.75)\"><tspan id=\"tspan3088\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 10.672 21.344 34.672 40.896 49.792 58.688 68.464 72.912 78.24 87.136\" y=\"0\">SPMresults:</tspan></text>\n",
        "<text id=\"text3090\" transform=\"matrix(1,0,0,-1,155.5,479.75)\"><tspan id=\"tspan3092\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 2.78 5.56 10.56 16.12 21.12 26.12 31.68 34.46 41.13 47.8 56.13 61.69 67.25 72.81 78.37\" y=\"0\">./sess1/SPM8_ana</tspan><tspan id=\"tspan3094\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -79.8632 -74.3032 -72.0832 -66.5232 -60.9632 -58.1832 -55.4032 -52.6232 -47.0632 -43.7332 -38.1732 -33.1732 -27.6132 -22.0532 -19.8332 -14.2732 -11.4932 -5.3832 -2.6032 3.2368 6.0168 11.5768 14.3568 19.9168 25.4768 31.0368 36.5968 42.1568 47.7168 53.2768 56.6168 62.1768 68.0168 73.5768 76.3568 81.9168 87.4768 93.0368 95.8168 99.1468 104.7068 110.2668 115.2668 118.0468 121.3768\" y=\"11.6664\">Height threshold T = 3.162616 {p&lt;0.001 (unc.)}</tspan><tspan id=\"tspan3096\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -80.4132 -75.4132 -72.6332 -67.0732 -61.5132 -58.7332 -55.9532 -53.1732 -47.6132 -44.2832 -38.7232 -33.7232 -28.1632 -22.6032 -20.3832 -14.8232 -12.0432 -7.0432 -4.2632 1.5768 4.3568 9.9168 12.6968 17.6968 23.2568 28.2568 33.8168 36.0368\" y=\"23.4164\">Extent threshold k = 0 voxels</tspan></text>\n",
        "</g><path d=\"m 3734.17,4563.33 1270.83,0 0,1831.67 -1270.83,0 0,-1831.67 z\" id=\"path3098\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6395 0,-1831.67 1270.83,0 0,1831.67 -1270.83,0\" id=\"path3100\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3102\"><g clip-path=\"url(#clipPath3106)\" id=\"g3104\"><g id=\"g3110\" transform=\"matrix(1270.83,0,0,1831.67,3734.17,4563.33)\"><image height=\"1\" id=\"image3112\" transform=\"matrix(1,0,0,-1,0,1)\" width=\"1\" xlink:href=\"data:image/png;base64,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\"/></g></g></g><g id=\"g3114\"><g clip-path=\"url(#clipPath3118)\" id=\"g3116\"><g id=\"g3122\" transform=\"scale(10,10)\"><text id=\"text3124\" transform=\"matrix(1,0,0,-1,406.167,432.334)\"><tspan id=\"tspan3126\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 7.22 12.78 17.78 20 25.56 31.12 33.9 42.23 47.79 50.57 53.9 56.12\" y=\"0\">Design matrix</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3128\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3130\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3132\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3134\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3136\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3138\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,4563.34 0,18.33\" id=\"path3140\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6395 0,-17.5\" id=\"path3142\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3144\" transform=\"scale(10,10)\"><text id=\"text3146\" transform=\"matrix(1,0,0,-1,391.833,444.25)\"><tspan id=\"tspan3148\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 4369.17,4563.34 0,18.33\" id=\"path3150\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6395 0,-17.5\" id=\"path3152\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3154\" transform=\"scale(10,10)\"><text id=\"text3156\" transform=\"matrix(1,0,0,-1,434.167,444.25)\"><tspan id=\"tspan3158\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">2</tspan></text>\n",
        "</g><path d=\"m 4792.5,4563.34 0,18.33\" id=\"path3160\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6395 0,-17.5\" id=\"path3162\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3164\" transform=\"scale(10,10)\"><text id=\"text3166\" transform=\"matrix(1,0,0,-1,476.5,444.25)\"><tspan id=\"tspan3168\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">3</tspan></text>\n",
        "</g><path d=\"m 3734.17,6111.67 17.5,0\" id=\"path3170\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6111.67 -18.33,0\" id=\"path3172\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3174\" transform=\"scale(10,10)\"><text id=\"text3176\" transform=\"matrix(1,0,0,-1,359.417,607.5)\"><tspan id=\"tspan3178\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">20</tspan></text>\n",
        "</g><path d=\"m 3734.17,5820.84 17.5,0\" id=\"path3180\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5820.84 -18.33,0\" id=\"path3182\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3184\" transform=\"scale(10,10)\"><text id=\"text3186\" transform=\"matrix(1,0,0,-1,359.417,578.417)\"><tspan id=\"tspan3188\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">40</tspan></text>\n",
        "</g><path d=\"m 3734.17,5530.84 17.5,0\" id=\"path3190\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5530.84 -18.33,0\" id=\"path3192\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3194\" transform=\"scale(10,10)\"><text id=\"text3196\" transform=\"matrix(1,0,0,-1,359.417,549.417)\"><tspan id=\"tspan3198\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">60</tspan></text>\n",
        "</g><path d=\"m 3734.17,5240 17.5,0\" id=\"path3200\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5240 -18.33,0\" id=\"path3202\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3204\" transform=\"scale(10,10)\"><text id=\"text3206\" transform=\"matrix(1,0,0,-1,359.417,520.334)\"><tspan id=\"tspan3208\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">80</tspan></text>\n",
        "</g><path d=\"m 3734.17,4949.17 17.5,0\" id=\"path3210\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4949.17 -18.33,0\" id=\"path3212\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3214\" transform=\"scale(10,10)\"><text id=\"text3216\" transform=\"matrix(1,0,0,-1,353.833,491.25)\"><tspan id=\"tspan3218\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 3734.17,4658.34 17.5,0\" id=\"path3220\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4658.34 -18.33,0\" id=\"path3222\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3224\" transform=\"scale(10,10)\"><text id=\"text3226\" transform=\"matrix(1,0,0,-1,353.833,462.167)\"><tspan id=\"tspan3228\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">120</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3230\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3232\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3234\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3236\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3238\" transform=\"scale(10,10)\"><text id=\"text3240\" transform=\"matrix(1,0,0,-1,413.333,702.334)\"><tspan id=\"tspan3242\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 16.12 18.9 22.23 27.79 32.79 35.57 38.9 43.9\" y=\"0\">contrast(s)</tspan></text>\n",
        "</g><path d=\"m 3734.17,6450 1270.83,0 0,494.168 -1270.83,0 0,-494.168 z\" id=\"path3244\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6450 0,494.17 1270.83,0 0,-494.17 -1270.83,0\" id=\"path3246\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"M 3734.17,6450 5005,6450\" id=\"path3248\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6450 0,494.17\" id=\"path3250\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6450 0,-12.5\" id=\"path3252\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6450 0,-12.5\" id=\"path3254\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6450 0,-12.5\" id=\"path3256\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6491.67 -13.34,0\" id=\"path3258\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6903.34 -13.34,0\" id=\"path3260\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3262\"><g clip-path=\"url(#clipPath3266)\" id=\"g3264\"><path d=\"m 3734.17,6491.67 423.332,0 0,411.664 -423.332,0 0,-411.664 z\" id=\"path3270\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6491.67 0,411.66 423.33,0 0,-411.66 -423.33,0\" id=\"path3272\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4157.5,6491.67 423.332,0 0,0 -423.332,0 z\" id=\"path3274\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4157.5,6491.67 423.33,0 -423.33,0\" id=\"path3276\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4580.83,6491.67 424.168,0 0,0 -424.168,0 z\" id=\"path3278\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4580.83,6491.67 424.17,0 -424.17,0\" id=\"path3280\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3282\"><g clip-path=\"url(#clipPath3286)\" id=\"g3284\"><g id=\"g3290\" transform=\"scale(10,10)\"><text id=\"text3292\" transform=\"matrix(0,1,1,0,362.417,666.917)\"><tspan id=\"tspan3294\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 4574.17,0 0,2930 -4574.17,0 0,-2930 z\" id=\"path3296\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 557.5,1267.5 0,2930 4574.17,0 0,-2930 -4574.17,0\" id=\"path3298\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3300\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,2930\" id=\"path3302\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,45.83\" id=\"path3304\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3306\" transform=\"scale(10,10)\"><text id=\"text3308\" transform=\"matrix(1,0,0,-1,53,114.667)\"><tspan id=\"tspan3310\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 1014.17,1267.5 0,45.83\" id=\"path3312\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3314\" transform=\"scale(10,10)\"><text id=\"text3316\" transform=\"matrix(1,0,0,-1,94.5,114.667)\"><tspan id=\"tspan3318\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.1</tspan></text>\n",
        "</g><path d=\"m 1471.67,1267.5 0,45.83\" id=\"path3320\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3322\" transform=\"scale(10,10)\"><text id=\"text3324\" transform=\"matrix(1,0,0,-1,140.25,114.667)\"><tspan id=\"tspan3326\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.2</tspan></text>\n",
        "</g><path d=\"m 1929.17,1267.5 0,45.83\" id=\"path3328\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3330\" transform=\"scale(10,10)\"><text id=\"text3332\" transform=\"matrix(1,0,0,-1,186,114.667)\"><tspan id=\"tspan3334\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.3</tspan></text>\n",
        "</g><path d=\"m 2386.67,1267.5 0,45.83\" id=\"path3336\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3338\" transform=\"scale(10,10)\"><text id=\"text3340\" transform=\"matrix(1,0,0,-1,231.75,114.667)\"><tspan id=\"tspan3342\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.4</tspan></text>\n",
        "</g><path d=\"m 2844.17,1267.5 0,45.83\" id=\"path3344\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3346\" transform=\"scale(10,10)\"><text id=\"text3348\" transform=\"matrix(1,0,0,-1,277.5,114.667)\"><tspan id=\"tspan3350\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.5</tspan></text>\n",
        "</g><path d=\"m 3301.67,1267.5 0,45.83\" id=\"path3352\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3354\" transform=\"scale(10,10)\"><text id=\"text3356\" transform=\"matrix(1,0,0,-1,323.25,114.667)\"><tspan id=\"tspan3358\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.6</tspan></text>\n",
        "</g><path d=\"m 3759.17,1267.5 0,45.83\" id=\"path3360\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3362\" transform=\"scale(10,10)\"><text id=\"text3364\" transform=\"matrix(1,0,0,-1,369,114.667)\"><tspan id=\"tspan3366\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.7</tspan></text>\n",
        "</g><path d=\"m 4216.67,1267.5 0,45.83\" id=\"path3368\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3370\" transform=\"scale(10,10)\"><text id=\"text3372\" transform=\"matrix(1,0,0,-1,414.75,114.667)\"><tspan id=\"tspan3374\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.8</tspan></text>\n",
        "</g><path d=\"m 4674.17,1267.5 0,45.83\" id=\"path3376\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3378\" transform=\"scale(10,10)\"><text id=\"text3380\" transform=\"matrix(1,0,0,-1,460.5,114.667)\"><tspan id=\"tspan3382\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.9</tspan></text>\n",
        "</g><path d=\"m 5131.67,1267.5 0,45.83\" id=\"path3384\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3386\" transform=\"scale(10,10)\"><text id=\"text3388\" transform=\"matrix(1,0,0,-1,510.417,114.667)\"><tspan id=\"tspan3390\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 45,0\" id=\"path3392\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3394\" transform=\"scale(10,10)\"><text id=\"text3396\" transform=\"matrix(1,0,0,-1,47.3332,123.083)\"><tspan id=\"tspan3398\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 557.5,1754.17 45,0\" id=\"path3400\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3402\" transform=\"scale(10,10)\"><text id=\"text3404\" transform=\"matrix(1,0,0,-1,41.75,171.75)\"><tspan id=\"tspan3406\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">50</tspan></text>\n",
        "</g><path d=\"m 557.5,2240.83 45,0\" id=\"path3408\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3410\" transform=\"scale(10,10)\"><text id=\"text3412\" transform=\"matrix(1,0,0,-1,36.1668,220.417)\"><tspan id=\"tspan3414\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 557.5,2727.5 45,0\" id=\"path3416\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3418\" transform=\"scale(10,10)\"><text id=\"text3420\" transform=\"matrix(1,0,0,-1,36.1668,269.083)\"><tspan id=\"tspan3422\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">150</tspan></text>\n",
        "</g><path d=\"m 557.5,3214.17 45,0\" id=\"path3424\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3426\" transform=\"scale(10,10)\"><text id=\"text3428\" transform=\"matrix(1,0,0,-1,36.1668,317.75)\"><tspan id=\"tspan3430\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">200</tspan></text>\n",
        "</g><path d=\"m 557.5,3700.83 45,0\" id=\"path3432\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3434\" transform=\"scale(10,10)\"><text id=\"text3436\" transform=\"matrix(1,0,0,-1,36.1668,366.417)\"><tspan id=\"tspan3438\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">250</tspan></text>\n",
        "</g><path d=\"m 557.5,4186.67 45,0\" id=\"path3440\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3442\" transform=\"scale(10,10)\"><text id=\"text3444\" transform=\"matrix(1,0,0,-1,36.1668,415)\"><tspan id=\"tspan3446\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">300</tspan></text>\n",
        "</g><g id=\"g3448\" transform=\"scale(10,10)\"><text id=\"text3450\" transform=\"matrix(1,0,0,-1,55.75,409.917)\"><tspan id=\"tspan3452\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:12;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 8.004 12 18.672 22.668 26.004 32.676 36.672 40.008 46.68 53.352 57.348\" y=\"0\">Statistics: </tspan></text>\n",
        "<text id=\"text3454\" transform=\"matrix(1,0,0,-1,119.25,409.917)\"><tspan id=\"tspan3456\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-weight:bold;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica-BoldOblique\" x=\"0 6.11 11.95 17.51 23.07 25.85 31.96 37.52 43.08 45.86 51.42 57.53 60.31 66.42 71.98 75.31 80.87 86.98 89.76 93.09 99.2 103.09 105.87 111.43 116.99 122.55 126.44 132 138.11 140.89 146.45 152.56 155.34 161.45 170.34\" y=\"0\">p\u2212values adjusted for search volume</tspan></text>\n",
        "</g></g></g><g id=\"g3458\"><g clip-path=\"url(#clipPath3462)\" id=\"g3460\"><path d=\"m 557.5,4050.83 4574.17,0\" id=\"path3466\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:30;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3468\"><g clip-path=\"url(#clipPath3472)\" id=\"g3470\"><g id=\"g3476\" transform=\"scale(10,10)\"><text id=\"text3478\" transform=\"matrix(1,0,0,-1,60.25,394.167)\"><tspan id=\"tspan3480\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 13.34 19.18 21.4 26.96 31.96 37.52\" y=\"0\">set\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3482\"><g clip-path=\"url(#clipPath3486)\" id=\"g3484\"><path d=\"m 557.5,3916.67 502.5,0\" id=\"path3490\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3492\"><g clip-path=\"url(#clipPath3496)\" id=\"g3494\"><g id=\"g3500\" transform=\"scale(10,10)\"><text id=\"text3502\" transform=\"matrix(1,0,0,-1,92.3332,383.167)\"><tspan id=\"tspan3504\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 4.5 -27.5 -22.496\" y=\"0\">c p </tspan></text>\n",
        "<text id=\"text3506\" transform=\"matrix(1,0,0,-1,156.3332,394.167)\"><tspan id=\"tspan3508\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 7.22 12.78 17.78 20.56 26.12 29.45 35.29 37.51 43.07 48.07 53.63\" y=\"0\">cluster\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3510\"><g clip-path=\"url(#clipPath3514)\" id=\"g3512\"><path d=\"m 1197.5,3916.67 1372.5,0\" id=\"path3518\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3520\"><g clip-path=\"url(#clipPath3524)\" id=\"g3522\"><g id=\"g3528\" transform=\"scale(10,10)\"><text id=\"text3530\" transform=\"matrix(1,0,0,-1,124.333,383.167)\"><tspan id=\"tspan3532\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3534\" transform=\"matrix(1,0,0,-1,129.333,378.667)\"><tspan id=\"tspan3536\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3538\" transform=\"matrix(1,0,0,-1,165.4998,383.167)\"><tspan id=\"tspan3540\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3542\" transform=\"matrix(1,0,0,-1,170.4998,378.667)\"><tspan id=\"tspan3544\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3546\" transform=\"matrix(1,0,0,-1,234.083,383.167)\"><tspan id=\"tspan3548\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3550\" transform=\"matrix(1,0,0,-1,239.083,378.667)\"><tspan id=\"tspan3552\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3554\" transform=\"matrix(1,0,0,-1,211.2498,383.167)\"><tspan id=\"tspan3556\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">k</tspan></text>\n",
        "<text id=\"text3558\" transform=\"matrix(1,0,0,-1,215.7498,378.667)\"><tspan id=\"tspan3560\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">E</tspan></text>\n",
        "<text id=\"text3562\" transform=\"matrix(1,0,0,-1,348.4168,394.167)\"><tspan id=\"tspan3564\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12 16.68 21.68 27.52 29.74 35.3 40.3 45.86\" y=\"0\">peak\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3566\"><g clip-path=\"url(#clipPath3570)\" id=\"g3568\"><path d=\"m 2752.5,3916.67 1830,0\" id=\"path3574\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3576\"><g clip-path=\"url(#clipPath3580)\" id=\"g3578\"><g id=\"g3584\" transform=\"scale(10,10)\"><text id=\"text3586\" transform=\"matrix(1,0,0,-1,279.833,383.167)\"><tspan id=\"tspan3588\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3590\" transform=\"matrix(1,0,0,-1,284.833,378.667)\"><tspan id=\"tspan3592\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3594\" transform=\"matrix(1,0,0,-1,320.9998,383.167)\"><tspan id=\"tspan3596\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3598\" transform=\"matrix(1,0,0,-1,325.9998,378.667)\"><tspan id=\"tspan3600\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3602\" transform=\"matrix(1,0,0,-1,430.7498,383.167)\"><tspan id=\"tspan3604\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3606\" transform=\"matrix(1,0,0,-1,435.7498,378.667)\"><tspan id=\"tspan3608\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3610\" transform=\"matrix(1,0,0,-1,362.1666,383.167)\"><tspan id=\"tspan3612\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">T</tspan></text>\n",
        "<text id=\"text3614\" transform=\"matrix(1,0,0,-1,398.7498,383.167)\"><tspan id=\"tspan3616\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">(</tspan></text>\n",
        "<text id=\"text3618\" transform=\"matrix(1,0,0,-1,401.6666,383.167)\"><tspan id=\"tspan3620\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">Z</tspan></text>\n",
        "<text id=\"text3622\" transform=\"matrix(1,0,0,-1,407.08301,378.667)\"><tspan id=\"tspan3624\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Symbol;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Symbol\" x=\"0\" y=\"0\">\u2261</tspan></text>\n",
        "<text id=\"text3626\" transform=\"matrix(1,0,0,-1,410.9166,383.167)\"><tspan id=\"tspan3628\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">)</tspan><tspan id=\"tspan3630\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"65.5832 73.0802 80.5772 83.0792 90.5762 98.0732 100.5752 108.0722\" y=\"-6.0832\">mm mm mm</tspan></text>\n",
        "</g></g></g><g id=\"g3632\"><g clip-path=\"url(#clipPath3636)\" id=\"g3634\"><path d=\"m 557.5,3770.83 4574.17,0\" id=\"path3640\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3642\"><g clip-path=\"url(#clipPath3646)\" id=\"g3644\"><g id=\"g3650\" transform=\"scale(10,10)\"><text id=\"text3652\" transform=\"matrix(1,0,0,-1,181.333,130.667)\"><tspan id=\"tspan3654\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 2.502 7.506 12.51 14.508 19.512 22.014 26.514 31.518 36.522 43.02 47.52 50.022 55.026 57.528 59.526 64.53 69.03 74.034 76.032 78.534 86.031 91.035 95.535 97.533 105.03 110.034 112.536 120.033 125.037 128.034 133.038 135.54 138.042 143.046 148.05 153.054 155.556 160.56 163.062 168.066 175.563 183.06 185.562 190.566 195.57 200.574 203.571\" y=\"0\">table shows 3 local maxima more than 8.0mm apart</tspan></text>\n",
        "</g></g></g><g id=\"g3656\"><g clip-path=\"url(#clipPath3660)\" id=\"g3658\"><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3664\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3666\"><g clip-path=\"url(#clipPath3670)\" id=\"g3668\"><g id=\"g3674\" transform=\"scale(10,10)\"><text id=\"text3676\" transform=\"matrix(1,0,0,-1,55.75,117.083)\"><tspan id=\"tspan3678\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.498 11.502 13.5 18.504 23.508 26.01 28.512 31.014 36.018 39.015 44.019 48.519 53.523 58.527 60.525 65.529 68.031 70.533 76.032 78.534 83.79 86.292 91.296 93.798 98.802 103.806 106.308 108.81 113.814 116.316 121.572 124.074 129.078 131.58 136.584 141.588 146.592 149.094 152.091 157.095 159.597 164.601 169.605 174.609\" y=\"0\">Height threshold: T = 3.16, p = 0.001 (0.999)</tspan><tspan id=\"tspan3680\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 13.005 18.009 23.013 25.515 28.017 30.519 35.523 38.52 43.524 48.024 53.028 58.032 60.03 65.034 67.536 70.038 74.538 77.04 82.296 84.798 89.802 92.304 96.804 101.808 106.308 111.312 113.31 117.81 120.312 122.814 127.818 130.32 135.576 138.078 143.082 145.584 150.588 155.592 160.596 163.098 166.095 171.099 173.601 178.605 183.609 188.613\" y=\"9.75\">Extent threshold: k = 0 voxels, p = 1.000 (0.999)</tspan><tspan id=\"tspan3682\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 44.523 49.527 54.027 59.031 61.029 65.529 68.031 73.035 78.039 81.036 83.538 88.038 90.036 95.04 99.54 102.042 107.046 110.043 112.545 115.047 120.303 124.803 130.059 132.561 137.817 140.319 145.323 147.825 152.829 157.833\" y=\"19.5\">Expected voxels per cluster, &lt;k&gt; = 7.463</tspan><tspan id=\"tspan3684\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 45.027 50.031 57.528 62.532 67.536 70.533 73.035 78.039 80.541 83.043 87.543 89.541 94.545 99.045 101.547 106.551 109.548 114.048 116.55 119.052 124.308 128.808 134.064 136.566 141.822 144.324 149.328 151.83 156.834\" y=\"29.25\">Expected number of clusters, &lt;c&gt; = 6.75</tspan><tspan id=\"tspan3686\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.499 13.995 19.998 25.002 27.504 30.006 35.01 37.512 42.516 47.52 52.524 55.026 57.528 63.027 69.525 76.023 81.027 83.529 86.031 91.035 93.537 98.541 103.545 108.549 111.051 113.553 119.052 127.548 133.551 138.051 140.553 143.055 148.059 153.063 155.565 158.067 163.566 170.064 176.562 181.062 183.564 186.066 191.07\" y=\"38.91641\">FWEp: 4.810, FDRp: 4.894, FWEc: 69, FDRc: 69</tspan><tspan id=\"tspan3688\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 235.165 240.169 245.173 248.17 253.174 258.178 262.678 265.18 270.184 272.686 275.188 277.69 280.687 285.691 290.695 295.699 300.703 308.2 310.702 315.958 318.46 320.962 325.966 328.468 333.472 335.974 338.476 343.48 348.484 353.488 355.99 360.994\" y=\"1e-05\">Degrees of freedom = [1.0, 115.0]</tspan><tspan id=\"tspan3690\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.166 242.662 249.16 256.657 259.159 264.415 266.917 271.921 276.925 279.427 284.431 286.933 291.937 296.941 299.443 304.447 306.949 311.953 316.957 319.459 324.463 326.965 334.462 341.959 344.461 351.958 359.455 361.957 369.454 376.951 379.453 381.955 386.959 389.461 394.465 396.967 401.971 404.473 409.477 411.979 416.983 419.485 424.489 426.991 429.997 434.497 439.501 444.001 449.005 451.003 455.503\" y=\"9.75001\">FWHM = 12.2 12.1 12.4 mm mm mm; 4.1 4.0 4.1 {voxels}</tspan><tspan id=\"tspan3692\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 241.672 246.676 254.173 259.177 261.679 264.181 269.185 274.189 279.193 284.197 289.201 294.205 299.209 301.711 306.967 309.469 314.473 319.477 324.481 329.485 334.489 336.991 341.491 346.495 350.995 355.999 357.997 362.497 364.999 370.255 372.757 377.761 382.765 387.769 390.271 395.275 397.777 400.774 405.778 410.278 415.282 417.28\" y=\"19.50001\">Volume: 1202364 = 44532 voxels = 592.9 resels</tspan><tspan id=\"tspan3694\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 244.174 249.178 251.176 253.678 258.178 260.176 264.676 269.68 272.182 274.684 279.688 282.19 287.194 289.696 294.7 297.202 302.206 304.708 309.712 312.214 317.218 319.72 327.217 334.714 337.216 344.713 352.21 354.712 362.209 369.706 372.208 374.71 377.707 380.704 385.708 390.208 395.212 397.21 399.712 404.968 407.47 412.474 417.478 419.98 424.984 429.988 432.49 436.99 441.994 446.494 451.498 453.496 457.996\" y=\"29.25001\">Voxel size: 3.0 3.0 3.0 mm mm mm; (resel = 67.06 voxels)</tspan></text>\n",
        "<text id=\"text3696\" transform=\"matrix(1,0,0,-1,60.25,364.91699)\"><tspan id=\"tspan3698\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 32.0832 36.8832 64.0832 68.8832 73.6832 78.4832 83.2832 105.25 110.05 114.85 119.65 124.45 146.4168 151.2168 156.0168 173.8332 178.6332 183.4332 188.2332 193.0332 219.5832 224.3832 229.1832 233.9832 238.7832 260.75 265.55 270.35 275.15 279.95 292.75 302.35 307.15 311.95 316.75 333.9168 338.7168 343.5168 348.3168 353.1168 375.0832 379.8832 384.6832 389.4832 394.2832 416.25 421.05 425.85 430.65 435.45 440.25 445.05 449.85 454.65 459.45 464.25\" y=\"0\">0.000370.0000.0009030.0000.0000.000 7.14 6.480.000 36 \u221278 \u221218</tspan></text>\n",
        "<text id=\"text3700\" transform=\"matrix(1,0,0,-1,279.833,355.25019)\"><tspan id=\"tspan3702\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"0\">0.0000.000 6.39 5.900.000 33 \u221287 \u221221</tspan><tspan id=\"tspan3704\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"9.75\">0.0000.000 6.20 5.740.000 21 \u221296 \u221218</tspan></text>\n",
        "<text id=\"text3706\" transform=\"matrix(1,0,0,-1,124.333,335.75019)\"><tspan id=\"tspan3708\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 82.3336 87.1336 109.75 114.55 119.35 124.15 128.95 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 228.6668 238.2668 243.0668 247.8668 252.6668 269.8336 274.6336 279.4336 284.2336 289.0336 311 315.8 320.6 325.4 330.2 352.1668 356.9668 361.7668 366.5668 380.9668 385.7668 395.3668 400.1668\" y=\"0\">0.1100.106460.0170.0060.010 5.40 5.090.000\u221218 0 72</tspan></text>\n",
        "<text id=\"text3710\" transform=\"matrix(1,0,0,-1,279.833,326.00019)\"><tspan id=\"tspan3712\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 225.4668 230.2668 239.8668 244.6668\" y=\"0\">0.2880.180 4.25 4.090.000\u221224 3 66</tspan><tspan id=\"tspan3714\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 220.6668 225.4668 230.2668 239.8668 244.6668\" y=\"9.75\">0.8610.509 3.66 3.550.000 \u22126 \u22126 69</tspan></text>\n",
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        "<IPython.core.display.SVG at 0x1071a1550>"
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     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You will see the FWHM values at the bottom of the page - here they are 4.1 voxels in x, 4.0 voxels in y, and 4.1 voxels in z. These values are rounded; I can get the exact values from MATLAB by looking at ``xSPM.FWHM``.  These are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FWHM = [4.0528, 4.0172, 4.1192]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is therefore a block of volume approx:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resel_volume = np.prod(FWHM)\n",
      "resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "67.064316892672011"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's the value you see at the bottom the SPM printout after ``resel =``.  The resel count of 592.9 in the printout comes from a calculation based on this estimated FWHM smoothness and the shape of the brain. In other words it applies the search volume correction I mentioned above.  If it did not apply this correction then the resel count would simply be the number of voxels divided by the resel volume:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "44532 / resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "664.0192886966679"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The table gives statistics for each detected cluster in the analysis, ordered by significance level.  Each line in bold in the table is the peak voxel for a particular cluster.  Lines in standard type are sub-clusters within the same cluster.\n",
      "\n",
      "Look at the peak voxel for the third-most significant cluster.  This is the third bold line in the table, and the seventh line overall. On the left-hand side of the table, you see the values for the \"peak-level\" statistics.  The extreme left gives the voxel location in millimeters.  Our voxel of interest is at location x=-42, y=18, z=3.\n",
      "\n",
      "The value in the \"T\" column for this voxel is 4.89.  This is the raw $t$ statistic. The column $P_{FWE-corr}$ gives the random field corrected $p$ value. In this case the value is 0.037. 0.037 is the expected EC, in a 3D image of 592.9 resels when thresholded at $t = 4.89$. This is equivalent to saying that the probability of getting one or more blobs of $t$ value 4.89 or greater, is 0.037.\n",
      "\n",
      "There are other corrected $p$ values here, based on cluster size, and based on the false discovery rate, but I didn't cover those corrections here.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Worsley, K.J., Marrett, S., Neelin, P., and Evans, A.C. (1992). [A three-dimensional statistical analysis for CBF activation studies in human brain](http://www.math.mcgill.ca/~keith/jcbf/jcbf.abstract.html) Journal of Cerebral Blood Flow and Metabolism, 12:900-918.\n",
      "\n",
      "Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., and Evans, A.C. (1996). [A unified statistical approach for determining significant signals in images of cerebral activation](http://www.math.mcgill.ca/~keith/unified/unified.abstract.html) Human Brain Mapping, 4:58-73."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}