Parallel Computing with Python SSH.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parallel Computing with Python using a cluster\n",
    "================================\n",
    "\n",
    "**[Rodrigo Nemmen](http://rodrigonemmen.com), IAG USP**\n",
    "\n",
    "This IPython notebook illustrates a few simple ways of doing parallel computing. It assumes you have a parallel IPython cluster running over SSH as described in this [tutorial](http://astropython.blogspot.com.br/2016/02/how-to-setup-ipython-parallel-cluster.html). Launch the cluster:\n",
    "\n",
    "    ipcluster start --profile='ssh'\n",
    "\n",
    "Practical examples included in this notebook:\n",
    "\n",
    "1. Parallel function mapping to a list of arguments (multiprocessing module)\n",
    "2. Parallel execution of array function (scatter/gather) + parallel execution of scripts\n",
    "4. Easy parallel Monte Carlo (parallel magics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy\n",
    "import nemmen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Mapping a model to a grid of parameters \n",
    "\n",
    "<!---\n",
    "Inspired on \"useful parallel\".\n",
    "-->\n",
    "\n",
    "Uses the *multiprocessing* module that comes by default with python, i.e. method independent of IPython.\n",
    "\n",
    "Idea: you have a function $f(\\mathbf{x},\\mathbf{y})$ of two parameters (e.g., $f$ may represent your model) stored in the arrays $(\\mathbf{x},\\mathbf{y})$. Given the arrays $\\mathbf{x}$ and $\\mathbf{y}$, you want to compute the values of $f(\\mathbf{x},\\mathbf{y})$. Let's assume for simplicity that there is no dependence on the neighbours. This is an embarassingly parallel problem.\n",
    "\n",
    "<!---\n",
    "### TODO\n",
    "\n",
    "* Random sampling of parameter space if desired\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import multiprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time wasting function that depends on two parameters. Here, I generate a lot of random numbers based on the normal distribution. The two parameters are $\\mu$ and $\\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(z):\n",
    "    x=nemmen.random_normal(z[0], z[1], 100000)\n",
    "    return x.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arrays of input parameters. You could easily modify this to take as input a matrix, not two arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n=3000\n",
    "X=numpy.linspace(-1,1,n) # mean\n",
    "Y=numpy.linspace(0.1,1,n) # std. dev."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# creates list of arguments [Xi, Yi]\n",
    "pargs=[]\t# this is a list of lists!\n",
    "for i in range(X.size):\n",
    "\tpargs.append([X[i],Y[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parallel execution. Check out all the cores being used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ncores=multiprocessing.cpu_count() # number of cores\n",
    "pool = multiprocessing.Pool(processes=ncores) # initializes parallel engine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 43.6 ms, sys: 1.88 ms, total: 45.5 ms\n",
      "Wall time: 3.94 s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "t=pool.map(f, pargs)\t# parallel function map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pool.close()\t# close the parallel engine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Serial execution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.88 s, sys: 19 ms, total: 9.89 s\n",
      "Wall time: 9.94 s\n"
     ]
    }
   ],
   "source": [
    "%time t=map(f, pargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# if you want to convert list to matrix \n",
    "#y=array(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that there is a similar map method for IPython parallel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Parallel execution of array function\n",
    "\n",
    "Uses IPython parallel. Consider a function $f(x)$ which takes an array $x$ containing the grid of input parameters. We want to split the function calls (\"split the array\") to the different cores in our machine:\n",
    "\n",
    "![test](http://computing.llnl.gov/tutorials/parallel_comp/images/array_proc1.gif)\n",
    "![test](http://computing.llnl.gov/tutorials/parallel_comp/images/array_proc2.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our time-waster function $f(x)$ that can be applied to an array of integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# test if n is prime\n",
    "def isprime(n):\n",
    "    for i in range(3, n):\n",
    "        if n % i == 0:\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "# tests each element of an array if it is prime\n",
    "def f(x):\n",
    "    return map(isprime,x) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generates big array of integers (in this case, 10k elements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = scipy.random.randint(0,100000, (10000,)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Serial execution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 19.8 s, sys: 236 ms, total: 20 s\n",
      "Wall time: 20.1 s\n"
     ]
    }
   ],
   "source": [
    "%time y=f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now explain how IPython parallel works **(slides)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import ipyparallel\n",
    "client = ipyparallel.Client(profile='ssh')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to use the direct view, which means that commands always run on all nodes. This as opposed to a balanced view, which asynchronously executes code on nodes which are idle. In addition, we are going to turn blocking on. This means that jobs will block further execution until all nodes have finished."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "direct = client[:]\n",
    "direct.block = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Splits the input array $x$ between the cores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "direct.scatter('x',x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify that the array was indeed divided equally among the 24 engines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   "source": [
    "direct['x.size']"
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       "        52790, 11785, 96408, 75751, 84511,  7621, 49029, 80483, 79332,\n",
       "        10895, 82197, 71232,  1086, 20668, 67705, 28667, 93329, 11430,\n",
       "        64770, 61354, 41449, 23493, 60306, 75633, 26663, 57794, 87212,\n",
       "        34775, 61697, 74176, 22076, 24136, 50504, 47742, 13462, 31583,\n",
       "        27084, 11568,  6259, 41361,  9438, 55368, 70874, 74120, 29222,\n",
       "        45444, 75561, 56979, 50068, 66488, 81005, 14737, 43887, 56425,\n",
       "        53931, 17516, 81944, 99544, 47542,  1167, 72530, 20767, 82284,\n",
       "        79104, 13849, 71920,  7619, 91330, 30525, 48759, 16593, 83123,\n",
       "        88915, 17950,  4929, 86258, 26765, 31225, 85472, 45471, 30827,\n",
       "        89774, 26886, 83798, 68838, 26626, 16584, 53991, 15571,  7569,\n",
       "        39182, 52834, 81432, 30715, 73621, 76099, 88035, 72906, 65534,\n",
       "        24258, 50605, 20958, 84656, 81591, 76731, 70452,  2475,  3550,\n",
       "        66020, 29092, 42771, 56215, 58129, 93219,  3832, 70634, 75648,\n",
       "        39123, 81547, 15472, 19206, 82034, 13850, 82948, 60829, 49282,\n",
       "        83044, 92399, 74513, 84701, 61674, 21378, 32306, 92383, 22161,\n",
       "        33111, 74849, 32124, 18208, 92565, 15454, 30163, 12852, 41060,\n",
       "        60378, 74069, 48410, 97662, 28770,  9240, 60302, 85919, 66308,\n",
       "        84746,  2519, 45694, 39024,  5314, 94743, 25236, 27728, 50782,\n",
       "        82193, 88715, 96275, 93308, 73825, 33561, 84667, 35667, 61101,\n",
       "        56402,  2397, 52968, 18126, 70894, 28240, 72661, 19817, 45316,\n",
       "        95650, 26123, 65693, 26943, 90406, 63483, 66367, 86754, 48489,\n",
       "        16534, 39784, 73973, 91953, 28860, 59100, 79220, 60104, 95368,\n",
       "        61311,   958, 24451, 89015,  7456,  4171, 58871, 78417,  7813,\n",
       "          959, 22746, 38182,  7274, 11410, 89856, 74933, 94030, 52558,\n",
       "         9898, 96335, 90594, 72564, 93442, 49752, 56296, 93271, 62138,\n",
       "        37589, 18946, 38389, 59972, 49677, 61386,  2915, 81477, 78217,\n",
       "        30247, 26235, 47617]),\n",
       " array([30305, 29514, 14839, 98275,  7855, 63525, 58813, 51271, 31045,\n",
       "        93693, 20965, 31478, 19035, 97871, 70745, 58274,  2612, 29461,\n",
       "        60376, 51915,  9579, 34191, 91020,  8031, 40797, 30852, 17052,\n",
       "        48265, 22666, 42818, 72508, 85007, 23574, 36418, 72434, 59610,\n",
       "         8880, 94362, 25401, 20728, 26034, 90812, 61593,  1611, 39125,\n",
       "        70278, 26485, 28319, 52910, 97571, 48558, 74939, 17170, 30988,\n",
       "        52030, 49722, 67254, 24349, 37506, 46760, 50205, 57361, 27118,\n",
       "        61237,  1434, 69370, 31457, 16249, 15703, 96804, 60063, 67559,\n",
       "        97797, 57589, 62905, 47653, 33484,  1596, 89952, 79482, 19040,\n",
       "        50617, 97060,  7105, 58943, 49348, 19892, 16127, 91153, 34576,\n",
       "        77595, 45824, 47805, 21552, 83796, 48272, 98467,  2851, 47311,\n",
       "        92284, 15614, 73005, 92858,  5684, 55272, 58710, 48821, 94610,\n",
       "         9219, 46431,   644, 16146, 12333, 24379, 95872, 27580, 94972,\n",
       "        43300, 95011, 11124, 91131, 50203, 57614, 23689, 18602, 55811,\n",
       "        47995, 68302, 77706, 55046, 66570, 44928, 61577, 69568, 20645,\n",
       "        14477, 75022, 88169, 26034, 42439, 45483, 44681, 74735, 33031,\n",
       "        25795, 66922, 62816, 80289, 26234, 50081, 30541, 30514, 68523,\n",
       "        14747, 87417, 38761, 68204, 45191,  4620,  4365, 78572, 27398,\n",
       "        34719, 75940,   690, 66384,  7349, 15560, 97873, 81258, 13434,\n",
       "         5379, 75449, 74401, 38453, 67770, 90130,  8250, 80511,  7184,\n",
       "        53803, 11889, 87504, 71280,  3688, 53484, 75481, 85704, 71452,\n",
       "         5587, 95241, 72911, 33505,  4937, 99078, 37025, 84535, 22022,\n",
       "        62312, 67505, 77566, 23864, 66804, 51580, 36055, 69170,  3031,\n",
       "        69081, 27870,  9655, 24716, 86309, 44064, 55733,   299, 32513,\n",
       "        19841, 23670, 44686, 75527, 63759, 87065, 30211, 25920, 72873,\n",
       "        34840, 19066, 81535, 45508, 51769, 33473, 15041, 38148, 79528,\n",
       "        62692, 26664, 91410, 68114, 97625, 30358,  7019, 39404,  5710,\n",
       "        88383, 17491, 46242,  4653,  2967,  2015, 70988, 14995, 19232,\n",
       "        20323, 14250,  3776, 29628, 44875, 85994, 11484, 84250, 36378,\n",
       "        36184, 23481, 29933, 82059, 65049, 30207, 43165, 63672, 85482,\n",
       "        63409, 11364, 84862,  9730, 96595,  4408, 32054, 25170, 48451,\n",
       "        88285, 15860,  1818, 30473, 93394, 12610, 38565, 85650, 20761,\n",
       "        75907, 59981, 83744,  8508, 84666, 18523, 68173, 63054, 61759,\n",
       "        11562, 22876, 74119, 93149, 49320, 32998, 63474, 20364, 64352,\n",
       "        12250, 88698, 17076, 65765, 52087, 69546, 91264, 90190,  9703,\n",
       "        97348, 65367, 75632, 43596, 86180, 24341, 59968, 50800, 31129,\n",
       "        49946, 19943, 24690, 82736, 82672, 57414, 16102, 99751, 69911,\n",
       "        25732, 99189, 31787,  8850, 50945, 95480, 53560, 84322,  5898,\n",
       "        87040, 50227, 34041, 45186,  6615, 33966, 91468, 87099, 83301,\n",
       "        83021, 19016, 20990, 39658, 68918, 17715, 83317,  6990, 29842,\n",
       "        83122, 28725, 59390, 90843, 64156, 37320, 25954, 77401, 72616,\n",
       "        83565,  8522, 40382, 99025, 30542, 70651, 23230, 73661, 33476,\n",
       "        20389, 82947, 65541, 85303, 31380, 62428, 70239,  6426, 55599,\n",
       "        39981, 55293, 13540, 47674, 37351, 99919, 90437, 37626, 68146,\n",
       "        27311, 41303, 24259, 59647, 81310, 74091, 98515, 46938, 45826,\n",
       "        15093, 69216, 44737, 75841, 80298, 15480, 81746, 47408, 54433,\n",
       "        18865, 16147, 58524]),\n",
       " array([76010,  3962, 57266, 29450, 58694, 39138,  6985, 82260, 39120,\n",
       "        35056, 19984,  7999, 61671, 48764, 51275, 37039, 93465, 11870,\n",
       "        64441, 15906, 25663, 93116, 14831, 83833, 82542, 31646, 98293,\n",
       "        22741,  5332, 97621, 73733, 18550, 84145, 73713, 18019, 48039,\n",
       "        95285, 80840, 50691, 57117,  9873, 43097, 60282, 81589, 82006,\n",
       "        12202, 98839, 73862, 26339, 32242, 25839,  9521, 72143, 57507,\n",
       "        32975, 90800, 40770, 86857, 46950, 47033, 33694, 99865, 41588,\n",
       "        50627, 53800, 58895, 78861, 16760, 77508, 41163, 49268, 19254,\n",
       "        45942, 98296, 60801, 58620,  3754, 30032, 56396, 38932, 15924,\n",
       "        33948, 51320, 96805, 28497, 26404, 73680, 19793, 94114, 20030,\n",
       "        86934, 59696, 74509, 10247, 44825, 26423, 63763, 62868, 19429,\n",
       "        45896, 64502, 74373, 31434, 72958, 93639, 20901,  8938, 18296,\n",
       "        14876, 58273, 72102, 16564, 74271,  8308, 50239, 72627, 88559,\n",
       "        28412, 33296,  6547, 35991, 13410, 76762, 93441, 72331, 44510,\n",
       "        73458, 25087, 12954, 25865,  6582, 36042,  3444, 27227, 25529,\n",
       "        67978,  6393, 77230, 43528, 36522,  4755, 54381, 81870, 60067,\n",
       "        73022, 58593, 75875,   731, 49432, 62970, 84534, 80457, 90031,\n",
       "        15661, 51479, 49461, 28926, 34979, 89990, 67709, 40638, 70450,\n",
       "        21806, 48168, 81285, 36747,  1449, 24814, 90761, 25879, 60052,\n",
       "        48920, 14297, 94653, 59837, 21498, 40165, 99070,  8066, 65458,\n",
       "        27707, 55506, 66896,  8311, 98219, 29750,   703, 99029, 30612,\n",
       "        48768,  2617, 74146, 48566, 10702, 34478, 46985, 41647, 25995,\n",
       "        10658, 74918, 92063, 11972, 31827, 16903,   235, 63419, 34992,\n",
       "        77303,  7806, 85385, 71643, 64423, 44502, 39084, 50227, 46802,\n",
       "        18341, 18940, 83286, 80848, 70880,  6111, 28609, 65949, 12322,\n",
       "        58719, 49789, 11054, 61354, 95301,  7563, 44414, 82627, 60785,\n",
       "        16802, 34059, 38999, 11943,  1977, 99237, 14683,  8716, 41667,\n",
       "        88878, 21542, 64377, 15943, 49386, 76988, 28212, 25096, 98251,\n",
       "        32650, 66450, 67548,   934, 93067, 75674, 80984, 64271,  6494,\n",
       "        65023,  7346, 60003, 62668, 12619,  4603, 67571, 65237, 83269,\n",
       "        21010, 57791, 74645, 57095, 74063, 51506, 82303, 78903, 44542,\n",
       "        16709, 59642, 93888, 94145, 57190, 90433, 69386, 91333, 66777,\n",
       "        26844, 51046, 59704, 55673, 73822, 55351, 90339, 12575,  9401,\n",
       "        98012, 52054, 81712, 56270, 45006, 31556, 29524, 38831, 15084,\n",
       "        49885, 83004, 95765, 90462, 96117, 24847, 31101, 76226, 52480,\n",
       "        16186, 52410, 68593,  1563, 14930, 70907, 49828, 75148, 64324,\n",
       "        19987, 49303, 24520, 64678, 57107, 33261, 18636, 64298, 12767,\n",
       "        11269,  1335, 75097, 59812, 17982, 76345, 24570, 35350, 81101,\n",
       "        75328, 10755, 37711, 41671, 36311, 55542, 94652, 34702, 45423,\n",
       "        59022, 72646, 45325, 16616, 55731, 24018, 53198, 59783, 42151,\n",
       "        22582, 27903,  1121,  2902, 61236, 84211, 67545, 41922, 11726,\n",
       "        93568, 68072, 93400, 34465, 47996, 54011, 44540, 62974, 51916,\n",
       "        16719, 37436, 89685, 25371, 56284, 84134,  4840, 85427, 97958,\n",
       "        82415, 15342, 96551, 38229, 23263, 79063, 97081,  6597, 10214,\n",
       "        66956, 70799, 71885, 86962, 68038, 40237, 98682,  8787, 88535,\n",
       "        96258, 40032, 66839, 49630, 68655, 80196, 67186, 10253, 52071,\n",
       "        21897, 61474, 83577]),\n",
       " array([62857, 82364, 49782, 18952, 21084, 66153,  7379, 99586, 49313,\n",
       "        46766, 11667, 41873, 87085, 43175, 70157, 69525, 88440, 32596,\n",
       "        12719, 86560, 36215, 99649, 68119, 85959, 57975,  5924, 61644,\n",
       "        51625, 79852, 25422, 61873, 67070,  4344, 53526, 84004, 46678,\n",
       "        56790, 83195, 10041, 29879, 81769, 54668, 38283, 51119, 48075,\n",
       "        21463, 57169, 42738, 84961, 33117, 52140, 79230, 92807, 68515,\n",
       "        44772, 48421, 60042, 29460, 56355, 17777, 92717,  1601, 31114,\n",
       "        12277,  6625, 69744, 51064, 20423, 23425,  6776, 56294, 53122,\n",
       "        57603, 39381, 20463, 51926, 89731, 31035,  1914, 16853, 84051,\n",
       "        29441, 98973, 64224, 88781, 92732, 31703, 20519, 30587, 44788,\n",
       "        22746, 45631, 10283, 46872, 89572, 86461, 51829, 51459, 97336,\n",
       "         3545, 94508, 76135, 58293, 85329, 13360, 72601, 48404, 43852,\n",
       "        28618, 64582,  9805, 38879, 87046, 10808, 56905, 55239, 44603,\n",
       "        35687, 21067,  2481,  1895, 23235, 51162, 84880,   870, 76371,\n",
       "        54332, 99517, 60492, 15942, 22090, 19480, 29774, 26597, 22234,\n",
       "        65430, 40836, 46889, 61677, 68756, 33819, 15198, 77517,  1977,\n",
       "        90526,  8548, 72762, 61067, 10311, 72067, 18171, 98926,  8642,\n",
       "        40639, 85205, 91447, 68599,  2395, 58963, 32624, 72554, 74144,\n",
       "        71314, 78629, 47400, 65366, 72995, 36337, 95812, 80948, 13083,\n",
       "        93644, 60042, 99889, 69463, 24965, 39943, 47158, 63866, 20696,\n",
       "        10944, 66866, 90391, 61612, 23489, 97230, 70423, 68438, 31394,\n",
       "        26147, 19393, 13931, 73113, 31746, 88157, 45457, 22493, 65489,\n",
       "        20961, 96352,  9293, 11640, 74873, 27979, 78997, 96825, 29492,\n",
       "        48103, 86522,  8909, 40119, 10221, 25030, 40642, 85299, 35159,\n",
       "        41352, 57015, 94624, 12094, 54993, 16013, 28982, 54064, 69448,\n",
       "        28465, 69669, 76242, 40070, 71044, 86354, 45685,  8033, 61141,\n",
       "        32518,  4242, 35617, 35515, 85189, 78030, 69171,  1191, 90991,\n",
       "        97781, 84405, 63267,  1897, 46625, 47311, 85372, 38709, 70421,\n",
       "        21195, 56493,  8816, 79536, 94258, 28680, 92712, 65100, 40699,\n",
       "        60485, 54543, 92520, 38256, 50213, 22287, 55159, 46929, 10779,\n",
       "        86755, 42511, 35870, 46138, 27073,  7389, 14325, 44152, 78282,\n",
       "        16121, 80934,  2527, 98529, 95211, 17306, 55909,   110, 60007,\n",
       "        65453, 58044, 58558, 86670, 91886,  6369, 36272, 85722, 81271,\n",
       "        76439, 54719, 83419, 27387,  6786, 17109, 82362, 65541, 51304,\n",
       "        65760,  2453, 21494, 35729, 20010,   960, 31722, 55764, 57357,\n",
       "        43308, 62551, 69334, 13082,  6403, 80360, 50046, 97214, 11787,\n",
       "        25288, 90711, 74014, 88998, 94973, 69588, 94001, 10413, 29992,\n",
       "        46137, 39504, 28394, 31401,  1574, 45173, 83105, 46351, 99129,\n",
       "        61392, 12113, 64629,  6914, 32189,  9777, 94026, 10033, 38601,\n",
       "        27120, 86990,  9734, 35722, 22860, 82496, 96158, 92398, 49585,\n",
       "        64439, 74490, 32612, 68634, 55896, 38083, 72568, 77150, 52674,\n",
       "        38992, 23238, 57118, 48032, 53825,  7544, 17008, 65361, 58526,\n",
       "        81648, 34092,  6935, 55584, 53222, 84729, 41398, 29516,  4368,\n",
       "        54888, 40967, 81690,  1001,  8272, 51485, 36015, 67405, 17131,\n",
       "        33982, 57968, 40245, 20268, 11788,  1502, 86506, 70761, 60145,\n",
       "        46760, 11538, 30544,  6180,  7949,   642, 85305, 41685, 40623,\n",
       "        44059, 51495,  8452]),\n",
       " array([81255,   653, 55991, 57766, 71210, 24048, 73268, 93112, 23883,\n",
       "        87968, 78747, 69310, 58867, 53708, 40020, 51856,  9604, 27010,\n",
       "        41207, 42246, 33472, 51081, 68965, 53505, 11267, 53801,  7957,\n",
       "        43910, 47240, 38857, 81340,  3450, 44303, 43305, 88354, 48168,\n",
       "        31800, 22343, 34576, 96899, 68233,  1754, 35731, 36382, 56348,\n",
       "        90296, 46135, 96400,  4589,  2026, 51573, 75202, 50182, 40970,\n",
       "        16836, 16431, 92220, 85368,  8388,   677,  2031, 54431,  7086,\n",
       "        78749,  4045,  5893, 53105, 78176, 70667, 94123, 40362, 47289,\n",
       "        88870, 57541, 48268, 79232, 96204, 94420, 20252, 13153, 18714,\n",
       "        28058, 58725, 32368, 93018, 43721, 86017, 90779, 56853, 52069,\n",
       "        80337, 58153, 52745, 96980, 15460,   293, 69047, 61436, 50174,\n",
       "         5433, 92478, 86277, 24279, 67954, 98146, 17748, 80547, 80171,\n",
       "         1583, 56878, 48854, 82547, 42724, 26154, 81669, 78382, 31223,\n",
       "        96048, 91281, 99389, 30853, 62017, 46697, 90968, 84198, 16803,\n",
       "        79752, 27440, 23198, 64858, 14211, 79865, 89715, 52302,  8933,\n",
       "        65987, 17978, 95268, 78101, 28978, 20334, 77060, 55120, 20724,\n",
       "        66115, 89662, 46451, 86026, 89116, 84701,  9029, 23892, 22685,\n",
       "        25549, 13755, 42702, 70954, 86522, 72562, 49426, 82675, 50195,\n",
       "        83289,   930, 84257, 24538, 67730, 47536, 18570, 75316, 21428,\n",
       "        11040, 26898, 32135, 63621, 93521, 16976, 16064, 24558, 56511,\n",
       "        19578, 20608, 73927, 46585, 33341, 17568, 27360, 28065, 78779,\n",
       "        55129, 76419, 51485, 56219,  1600, 29687, 73205, 56222, 80974,\n",
       "        88259, 23148, 11327, 94439, 52548, 25989, 20178,  6802, 94005,\n",
       "        57168, 78061, 83027, 99221,  3028, 35579,  7332, 97021, 38208,\n",
       "        10907,  5759, 15304, 34001, 74659, 12692, 48297, 56920, 83546,\n",
       "        82744, 13897,   886, 73034, 51662, 67243, 91055, 16567, 47378,\n",
       "        59599, 14990, 66114, 92358, 70646, 65308, 28820, 57982, 44248,\n",
       "        27471, 54108, 81517, 20666, 83701, 83923, 14423, 32200, 56036,\n",
       "        50827, 29821, 37360, 90741, 33408, 69241, 48978, 98750, 39209,\n",
       "        87890, 70132, 78077, 73751, 26649, 56190, 29660, 98584, 22134,\n",
       "        33950, 56492, 50347, 32851, 88212, 43827, 82461, 53251,  6066,\n",
       "        92408, 61986, 61289, 27890, 34577,  6984, 88496, 10399, 25321,\n",
       "        22096, 78141, 27375, 47723, 28484, 65606, 53239, 94435, 26139,\n",
       "        14401, 96889, 39140,  1039, 24235, 55313, 95077, 47560, 49556,\n",
       "        97061, 57409, 72669, 38621, 43081, 54041, 83406, 10724, 24916,\n",
       "        24437, 28583, 90791, 24616, 67673, 91520, 21130, 39589, 69546,\n",
       "        66219, 51795, 58386, 99526, 16243, 55573, 58060, 54075, 11433,\n",
       "         1229, 28499, 70499, 37178,  8994, 63986, 99254, 86619, 25422,\n",
       "        10477, 83550, 20942, 52265, 89314, 59268, 36860, 47005, 11734,\n",
       "        86179, 78526, 81586,  7464, 28540,  5373, 92314, 78850, 66948,\n",
       "        90951, 54460, 33892, 93558, 28591, 97769, 60391, 91357, 82148,\n",
       "        70123, 64257,  8287,  6434, 25726, 71100, 49692, 62314, 90811,\n",
       "        71705, 62867, 64567, 94610, 27200, 54041, 66802, 38364, 14782,\n",
       "          409, 91292, 65686, 23088, 50234, 97590, 86786, 55415, 52034,\n",
       "        46084, 97716, 59868, 54734, 68164, 57125, 29588, 81155, 66763,\n",
       "        46476, 66237, 83359, 64964, 96868, 40285, 56117, 34129, 24322,\n",
       "        97352, 23357, 89565]),\n",
       " array([87162, 32041, 26908, 78852, 20859, 18843, 27894, 60702, 46379,\n",
       "        71414, 59979, 54757, 84101, 29511, 75766, 27945, 23215, 31779,\n",
       "        96070, 35968,  3411, 49105, 62409, 45275, 25951, 43160, 20371,\n",
       "         4095, 70901, 83999, 48707, 84267, 27984, 58012, 51297, 27734,\n",
       "        52375, 80973, 58742, 84425, 41674, 57402,  4873,  4853, 34065,\n",
       "        33264, 85692, 62731, 15335, 41189, 40898, 35218, 51491, 25716,\n",
       "        36745, 90755, 58225, 13785, 19346, 55606, 92352, 63404, 61810,\n",
       "         5825, 62581, 70866, 68386, 32101, 42150, 47701, 18990, 85147,\n",
       "        42660, 69020, 63683, 14463, 13675, 81211,  3503, 30852, 57718,\n",
       "        79022, 32222, 50122, 45410, 67720, 13091, 86279, 21430, 79453,\n",
       "        50606, 70345, 47849,  6009, 88401, 22315, 74645, 63000,  3038,\n",
       "        82015,  3891, 47149, 38566, 95553, 42988, 81606, 25593, 95768,\n",
       "        29821,  4468, 43278, 69420, 66347, 87437, 61981, 68507, 90002,\n",
       "        20865, 78379, 17912,  8461, 64027, 12497, 52681, 14262, 95855,\n",
       "        52045, 79976,  6177, 17248,  6500, 25518, 69038, 22617, 75302,\n",
       "        27634,  5161, 71043, 34759, 86817, 49808, 81673, 46534, 45353,\n",
       "        74927, 57047, 27025, 57984, 44768, 61832, 39503, 22752, 36130,\n",
       "         3772, 42701, 34654, 60427, 56186, 40566, 31006, 11393, 32562,\n",
       "        92197, 66983, 29228, 59732, 94760, 48373, 78271, 16212, 21796,\n",
       "        91322, 38247,  8279, 91529, 98593, 71448, 38777, 65260, 43266,\n",
       "        90438, 97401, 53681, 86264, 35364, 26601,  4180, 29582,  9352,\n",
       "        38747, 91891, 98236, 23127, 78441, 58235, 16819, 93293, 88872,\n",
       "        94867, 79036, 44899, 41072, 91604, 24994, 45728, 86074,  2306,\n",
       "        45757, 81963, 70548, 16513,  9523, 58120, 52037,  3968, 68506,\n",
       "        46025, 28255, 20249, 26184, 54521, 12704, 71713, 68418, 73474,\n",
       "        17688, 54624, 78835, 54829, 78705,  7023, 65071, 45352, 16835,\n",
       "        58317, 95543,  8694, 22221, 17028, 38258, 23625, 70295, 94214,\n",
       "        12674, 63905, 36770, 66887, 54139, 51271, 65389, 54953, 43558,\n",
       "        42878, 71388, 82801, 41376, 88315, 43449, 46481, 70024, 22370,\n",
       "        70097, 89811, 86880, 78325, 69936, 49290, 10188, 56657, 71438,\n",
       "        62288, 44261, 57590, 38227, 65601, 38698,   211, 60227, 13841,\n",
       "        51208, 64585, 85356, 12797, 87300, 48443, 82426, 85063, 97687,\n",
       "        36410, 47324, 89715, 91598, 26988,  4284, 27955, 90136, 69167,\n",
       "        76286, 73639, 81024, 72464, 17590, 15302, 89432, 79767, 74067,\n",
       "        86874, 33798, 88422, 26279, 71856, 36670, 12465, 49582, 42626,\n",
       "        86777, 31329, 19305, 49196, 76372, 28529, 71708, 71503, 81982,\n",
       "        26906,  5085, 64482, 82663, 17204, 18623, 66522,  9105, 68754,\n",
       "         9544, 17800, 90180, 71604, 34473, 23941, 11319, 71111, 36410,\n",
       "        67864, 75092, 67255,  1382, 11740, 32883, 85500,   796, 47360,\n",
       "        38298, 77267, 41127, 51309, 25294,    32, 37188, 91343,  6417,\n",
       "         5578, 91250,  3290, 21118, 78448, 70170, 16013, 48941, 81028,\n",
       "        85729, 23514, 51648, 13104, 73425, 51634,  9905, 38646, 22927,\n",
       "        63213,  7314, 70425,  3215, 18404, 42932, 70938, 18053, 22072,\n",
       "        58433, 86247, 43090, 97662, 53374, 20936, 58592, 21944,  5271,\n",
       "        96175, 93353, 18656, 21745, 46608, 24045, 69558, 61490, 83838,\n",
       "        71081, 12103, 27749, 31281, 37919, 79546, 10264, 53490, 45181,\n",
       "        62874, 13570, 55983]),\n",
       " array([75955, 44853, 79770, 57813, 63421, 70202, 58859, 13704, 41173,\n",
       "        31085, 19346, 91833, 27969, 25266, 53841, 80051, 81514,  2481,\n",
       "          745, 51423, 29742, 68166,  7860, 57871, 37620, 52655,  3903,\n",
       "        71321, 78810, 45627, 70616, 54378, 63437, 54918, 88978, 25892,\n",
       "        17156, 12804,   544, 47985, 67487, 42472, 21504, 44701, 95115,\n",
       "        63893, 15492, 97411, 26697, 98095, 69507, 40953, 93871, 74404,\n",
       "         1970, 95325,  9788, 70545, 79845, 23583, 56984, 82183, 64806,\n",
       "        68432,  3366, 95626, 12110, 65779, 29582, 10238, 56640, 66135,\n",
       "        91769, 81998, 98955, 74263, 93463, 24821, 12390, 65078, 91128,\n",
       "        91104, 77806, 47431, 30924, 84386, 90186, 20398, 68515, 93022,\n",
       "        72099, 67645, 15861, 79973, 82280, 72081, 14484, 94591, 69592,\n",
       "        45486, 29473, 96072, 87033, 13871, 69900, 52977, 16086, 79162,\n",
       "        55339, 83056, 43213, 85198, 42156, 77878,  6706, 75479, 54437,\n",
       "        34898, 33621, 74660, 84259, 86558, 84049,   936, 15237, 73355,\n",
       "        22261, 25086, 72388, 47085, 26267, 77149, 64465, 56735, 15799,\n",
       "        90704,  3489, 62547, 45715, 43205, 74579, 18095, 17309, 40432,\n",
       "        46680, 92269, 28653, 91010, 77969, 46336, 85538,  6154, 68080,\n",
       "        30595, 49120, 85498, 61600, 13416, 82342, 14722, 90939, 13094,\n",
       "        91723, 50799, 58907,  2313, 50689, 64922,  5016, 50850, 49657,\n",
       "        70821,  4541, 67800, 42171, 12888, 45028, 20912, 94196,   100,\n",
       "        77469, 58368, 25150, 16854, 47221, 13889, 27173, 23667, 76902,\n",
       "        15584, 61750, 89589, 77578, 20231, 71309, 55242, 91723, 55252,\n",
       "        60665, 79471, 59622, 90587, 46810,  5039, 28382, 44465,  6790,\n",
       "        90288, 53269, 31032, 70005, 59898, 29333, 63730, 75417, 49733,\n",
       "        17105, 61022, 92388, 66861, 45238, 41430, 99049, 94797, 59975,\n",
       "        80082, 15327, 88324, 32583, 50453, 62968, 37987, 75155, 19962,\n",
       "        69433, 37697, 42974, 79036, 36658, 45862, 37298, 92362, 36113,\n",
       "        41712, 13910, 51766, 65057, 55872, 48070, 14099, 34071, 93921,\n",
       "        37523, 35841, 35372, 53041, 96553, 18318, 64199, 21291, 76679,\n",
       "        31006, 18326,  6522, 11831, 50255, 94213, 72165, 48980, 89331,\n",
       "        29480,  1393, 15881, 26264, 70400, 33134, 32651, 48601, 89004,\n",
       "        29178, 46057, 95701, 31751, 91872, 34239, 88787, 71525, 55937,\n",
       "        93737, 39412, 13553, 10090, 76989, 45785, 43910, 63377, 50172,\n",
       "         2925, 50464, 82263, 40486, 51168, 84626, 37181, 94599, 41823,\n",
       "         4873, 49330, 87038, 80615, 17457, 99469,   543, 74852, 47622,\n",
       "        21318, 25221, 94264, 51556, 26459,  7026, 76412, 87846, 30483,\n",
       "        30823,  9136, 99768, 27159, 46432, 30818,  4711, 99370, 17306,\n",
       "        72737, 40307,  1687, 46618, 97308, 10268, 25591, 95540,   911,\n",
       "        18604, 86222, 67800, 91641, 49773, 20258, 74750, 57993, 84511,\n",
       "        89412, 60205, 91423, 11836, 69861, 75104, 70299, 11354, 18921,\n",
       "        42102, 24161,  4004,    87, 87287, 13832, 55879, 68976, 35182,\n",
       "        16555, 83606, 43796, 85122, 63315, 92526, 82861, 20352, 84931,\n",
       "        59174, 98447, 51917, 88928, 91392, 62769, 83204, 97468, 80010,\n",
       "        38897, 92965, 23557,  5005, 15732,  1087, 35937, 34726, 82532,\n",
       "        27924, 32217, 61595, 16148, 81127, 63653, 63462, 42611, 11906,\n",
       "        12534,  4053, 91854, 71422, 41237, 39792, 85703, 43539, 77852,\n",
       "        43711, 78650, 56651]),\n",
       " array([83000, 88240,  5054, 39180, 94059,  4567, 34864,  8822, 41161,\n",
       "        76368, 45790, 10835, 25608, 40562, 45748, 68732, 76507, 28377,\n",
       "        96997, 40272, 51342, 14137, 68977, 30161, 21923, 23305, 32911,\n",
       "        42223, 63535, 32111, 66385, 20146, 78708, 33962, 49419, 89290,\n",
       "        86303, 59840,  2398, 97956, 69755, 43682, 71755, 57964, 97345,\n",
       "        46758, 41628, 18390, 58294, 39025, 25986, 27295, 33566, 11511,\n",
       "          213, 43474, 70558, 19364, 17661, 54172, 55881,  1952, 98730,\n",
       "        93432, 17383, 40874, 52338, 49542, 31513,  5449, 83357, 79429,\n",
       "        31774, 11272, 15336, 45875, 39523, 82141, 13626, 87252, 83391,\n",
       "        30626, 38881, 82286, 49620, 52898, 41482, 81209, 74182, 44438,\n",
       "          249, 80736, 91425, 44851, 73441, 32194, 53509, 60811, 93752,\n",
       "        12302, 86817, 86740, 78375, 28950, 80638,  7526, 62674, 12948,\n",
       "        57584, 14757, 44051, 82935, 21705, 62865, 18430, 27269, 88753,\n",
       "        71523, 21326, 18660, 44631, 55348, 58798, 48201, 59891, 81844,\n",
       "        63583, 44165, 83049,  1834, 85902, 98271, 30569, 75924, 62888,\n",
       "         9161, 60911, 10577, 40692, 29876, 69541, 50390,  1203, 21762,\n",
       "        85158, 62267, 20864, 44306, 46173, 92685, 80259, 78026, 16365,\n",
       "         5182, 94407, 44734, 79334, 47731, 75662, 59021, 63742, 81537,\n",
       "        73135,  2887, 83679, 34862, 65538, 66044, 54943, 97337, 61781,\n",
       "        23737, 55551, 93238, 57556, 95187, 95562, 93983, 52737,  5620,\n",
       "        94209, 59906, 92105, 39309, 76300, 88420, 13596, 23413, 53726,\n",
       "        15386, 88615, 92910, 28285, 15208, 75427, 81143, 46071, 72585,\n",
       "        80919, 93458, 62497, 12199, 25458, 68333, 70734, 28102, 37839,\n",
       "        28348, 97531, 64488, 80693, 29161, 60962, 89906, 88871, 96104,\n",
       "        24931, 46523, 50296, 11364, 92515,  2961, 49170, 49797, 27314,\n",
       "        98504, 70069, 31317, 85666, 65751, 94463, 66563, 50431,  3747,\n",
       "        77507, 89696, 14465, 61028, 73629, 85673, 45674, 59442, 29228,\n",
       "        56396,  3173, 77178, 63034, 46393, 77810, 22166, 63771, 23869,\n",
       "        31907,  9390, 35572, 47941, 97572, 41451, 23936, 40077, 21160,\n",
       "        46012, 40300, 21262, 56045, 25450, 92004, 56301, 96141, 32281,\n",
       "        96724, 19557, 54076, 71674, 59530,  6328, 31543, 53628, 86629,\n",
       "        44166, 47974, 72514, 57895, 14381,   225, 73022, 23871, 43821,\n",
       "        24111, 80545,  3925, 19303, 29003, 27548, 22004, 82883, 87566,\n",
       "        45414, 91530, 40738, 62572, 90718, 90563, 63722, 87032, 80690,\n",
       "        84699, 35724, 72914,   535, 30787, 42262, 35664, 31967, 67651,\n",
       "        36084, 15736, 55885, 83529, 98818, 71250, 91565, 34666, 57259,\n",
       "        29954,  9097, 43915, 81454, 77125, 10177, 83231, 55931, 43846,\n",
       "        10193,  6004,  9122, 95273, 71363, 51797, 71363, 48069, 19510,\n",
       "        84916, 81685, 39148, 23013, 84932, 36040, 96841, 51261, 16135,\n",
       "        38155,  3631, 84214, 14346,  6003, 66067,  2623, 62188, 26700,\n",
       "         3795, 92809, 17903, 25131, 78194, 41891, 33024, 84035,  5051,\n",
       "         4904, 67312, 21922, 54967, 50307, 28352, 85776, 36423, 29343,\n",
       "        53177, 18733, 77774, 63823, 95876,  9197, 89624, 42121, 18661,\n",
       "        72960, 81611, 86901, 60185, 27292,   929,  7446, 11512, 21221,\n",
       "        73920, 57029, 24419,  5835, 17203, 70755, 25861, 62307, 10777,\n",
       "        63192, 29042, 49844, 93016, 19661,  8367, 70824,  6397, 12646,\n",
       "        43453, 27864, 62349]),\n",
       " array([96170, 61940, 26406, 50869, 20094, 59707, 71138, 40298, 15568,\n",
       "        13044, 42090, 74881, 13337, 78290,  8314, 13279, 56075, 68561,\n",
       "        60772, 76804, 80411, 49687, 63305, 46551, 91847, 73284, 21209,\n",
       "        78287, 61209, 91256, 21998, 22196, 17085, 12951, 92193, 36379,\n",
       "         7997, 89301, 82457, 72897,    45, 49765, 24464, 32777, 39331,\n",
       "         2750, 30886, 94497, 74942, 94612, 84139,  9552, 50971, 76520,\n",
       "        53887, 69960, 98065, 38163, 75135, 99032, 29394,   416, 34369,\n",
       "        68728, 86580, 43773, 14584, 15809, 81616, 99423, 91616,  4838,\n",
       "        26474, 87053,  4769, 26261, 63925, 97048, 42140, 96340, 88831,\n",
       "        25243, 22741, 46909, 49366, 71871, 42025, 18971, 88500, 48656,\n",
       "        59986, 95275,  3585, 28674, 99309, 83286, 86341, 99111, 28662,\n",
       "        70938, 80324, 43209,  8593, 80990, 46150, 17479, 44142,  2013,\n",
       "        98223, 21699, 44061, 41140, 53678, 38843, 98350, 67633, 17065,\n",
       "        21393,  3189, 75662, 48612, 32843, 76756,  2511, 71611, 40923,\n",
       "        16425, 37663, 28240, 73759, 23668, 32333, 84261, 82357, 29225,\n",
       "        55295, 54880, 67685, 30803, 19963, 19711, 49212, 85139, 21224,\n",
       "        64688, 62670, 53619, 92288, 65825, 67226, 19517, 78055, 59141,\n",
       "        34008,  6693, 88747, 95244, 75612, 76635, 71129, 63378, 23808,\n",
       "        29169,  2266, 85683, 58923, 76619, 55288, 66041, 96229, 39395,\n",
       "        77487, 74027, 93392, 14082,  1337, 73264, 20565, 13509, 65022,\n",
       "         6746, 38441, 24857, 92749, 85819, 31520, 88864, 56802, 20426,\n",
       "        21389, 22536, 81432, 90283, 21809, 38879, 86162, 35070, 13774,\n",
       "        21360, 41928, 73129, 12110, 81922, 86034, 36062, 69415,  2848,\n",
       "        39465, 81249, 13478,  5673, 36954, 20910, 30932, 18605,  3215,\n",
       "        87593,  6539, 24398, 37400, 99884, 74750, 62423, 81236, 54252,\n",
       "        15262, 29942, 92804, 37368, 26715, 28092, 58144, 44844, 46386,\n",
       "         4266,  1326, 23702, 99277, 27722, 93748, 97955, 64050, 35208,\n",
       "        27059, 98344, 98460, 26636, 11242, 50886, 77539, 31058, 33912,\n",
       "        26302, 77479,  3915, 42747, 24731, 93794, 67834, 27527, 99656,\n",
       "         4289, 46717, 41495, 44348, 18967,  1833,  9415, 52834, 48563,\n",
       "        21302, 99740, 59911, 25234, 61170, 83681, 49662, 49406, 81831,\n",
       "        87469, 80986, 70500, 59740, 19624, 39211, 87713, 97940, 41245,\n",
       "        41288, 33625, 59089, 35484, 14294, 76373, 89186, 18720,  2310,\n",
       "        68130, 92034, 58746, 58992, 34696, 19387, 78621, 21088, 57996,\n",
       "        79680, 48607, 75994, 62888, 29042, 85891, 15877,   283, 30023,\n",
       "        56334, 23065, 53354, 77770, 29145, 79093, 40923, 43189, 39134,\n",
       "        14228, 85427, 66985, 59608, 81779, 70377, 10383, 52090, 93411,\n",
       "        33960, 55789, 12827,  5804, 78735, 61664,  7137, 36943, 18691,\n",
       "        61830, 48380, 70387, 25482, 71045, 53496, 20944, 13350, 97607,\n",
       "        80580, 29904, 16916,  7939, 48862, 78959, 37866, 54940, 45799,\n",
       "        28971, 81255, 26263, 52747, 88254, 35892, 10821, 95903, 66606,\n",
       "        45996, 51426, 74304,  2855, 68601, 32561, 17838,  1936, 75575,\n",
       "        45016, 46603, 33276, 95948, 47483,  9289, 28321, 15167, 25766,\n",
       "        69705, 94566, 91229, 33168, 42517, 13518, 78885, 21248, 99876,\n",
       "        40163,   807, 83350, 54649, 67108, 23091, 64179, 35091, 91696,\n",
       "        74908, 44914, 14823, 14175, 62397, 18934, 19451, 85350, 51714,\n",
       "        92929, 86023,  1118]),\n",
       " array([ 3890, 26945, 91921, 79693, 21686, 62383, 54679, 54462, 75670,\n",
       "        15897, 91422, 90455, 69738,  5857, 90421,  8527, 49470, 39608,\n",
       "        51684, 68337, 74644,  9257, 89760, 92811, 84175, 18346, 13263,\n",
       "        82318, 65596, 65534, 24503, 52924, 39835, 90913, 23896, 55706,\n",
       "        15173, 52119, 93882, 70957, 28311,  1671, 85820,  8930, 43300,\n",
       "        43476, 86083, 10338, 52099, 32190,  5119, 96790, 74524, 95359,\n",
       "        13596, 49841, 25382, 92184, 64353,  7048, 88464,  1050, 51512,\n",
       "        30909, 55902,  2086, 49196, 16006, 90376, 17453, 48427, 98358,\n",
       "        55608,  6998, 40261, 44853, 25490, 87535, 73382, 39939, 36609,\n",
       "        46691, 48238, 54535, 58550, 49504, 60630,  8461, 55570, 39184,\n",
       "        91709, 20464, 69871, 91952, 57076, 77956, 82462, 13891, 35986,\n",
       "        30668, 35834, 73921, 20407, 25683, 25241,  8421, 81697, 41691,\n",
       "        13639, 11494, 49498, 45566, 46890, 32609, 28635, 93360, 58052,\n",
       "         8234, 41373, 73000, 38597, 21441, 87209, 55912, 20398,  7209,\n",
       "        71035, 48441, 10804, 61099, 43249, 68549, 72044, 21675, 35709,\n",
       "         6063, 38987, 65045, 55220, 64648, 72513, 72508, 11029, 94326,\n",
       "        85990, 60940, 58982, 69298, 46922, 81939,  4896, 65748, 34927,\n",
       "        94404, 36085, 65416, 26295, 45385, 31442,  5622, 29280, 46146,\n",
       "        11775, 21376, 54086, 25949, 81923, 38680, 55923, 83608, 47609,\n",
       "        67334, 23507, 22104, 96410, 20976, 67233, 75462,  6203, 25264,\n",
       "        25561, 49549, 20521, 76895, 69750, 13603, 78172, 44599,   393,\n",
       "        14560, 48689, 38556, 49531, 19756, 22092, 84998, 23180,  4895,\n",
       "        30240, 83784, 89030, 84831, 65184, 13542,  7129, 64765, 98332,\n",
       "        18162, 58562, 66296, 28299, 18291, 54898, 93809, 59467, 20526,\n",
       "        43018, 18724, 44198, 59463, 61355, 68796, 67264, 67356,  4063,\n",
       "        38522, 92338,  3681,  1072, 66327, 27997, 65130, 76298, 28391,\n",
       "        92530, 72999, 74749, 25708, 82768, 38833, 41999, 97592, 90245,\n",
       "        73353, 18020, 46005, 58609, 72188, 20393, 34221,  9192, 14673,\n",
       "         3003,  4984, 92495, 28560, 76738, 97217, 76803, 87400, 63945,\n",
       "        96109, 56450, 23449,  9155, 37980, 95030, 78751, 31385, 79576,\n",
       "        16597, 45533, 63231, 23420, 94254, 60827,  7907, 98658, 95479,\n",
       "        70196,   581, 67097, 90120, 30603, 51406, 29957,  9132, 59676,\n",
       "         7432, 30816, 46304, 70341, 67769, 12485, 81101, 88834, 55755,\n",
       "        75431, 42435, 66541, 87626, 76943, 23041, 22416, 74454, 82099,\n",
       "        60177, 13157, 64817, 48396, 83220, 24382, 82011, 95579, 96537,\n",
       "        90138, 71554, 30163, 80710, 20104,  1543, 88771, 22980, 84732,\n",
       "        44346, 32042, 53594, 19536, 85971, 81203, 27003, 28684, 50878,\n",
       "        15497, 76927, 12919,  4376, 17917, 26409, 13988, 53063, 13881,\n",
       "        90779, 31740, 42129, 18712, 38019, 65247, 44431, 46330, 43849,\n",
       "        30749, 98460,   724,  5549, 47951, 14671, 60504, 41010, 37331,\n",
       "        52617,  3431, 23293, 91734, 95166, 46492, 58333, 57933, 46193,\n",
       "        62646, 98217, 45642, 28519, 45921,  6873, 52730, 37400, 23764,\n",
       "        19828, 97223, 20473, 39390, 46517, 72837, 53990, 63594, 77092,\n",
       "        59442, 20571, 49604, 34988, 62303, 27007, 79759, 93455, 52209,\n",
       "        47287, 61007,  2689, 44448, 81192, 24406, 21368,  1780, 38316,\n",
       "        45627, 53379,  8064,  9118, 52544, 13842,   922,  5864, 27646,\n",
       "        12588, 22954, 21430]),\n",
       " array([29587, 98409, 33432, 51619, 49234, 15729, 87069, 31063, 72340,\n",
       "        97852, 38175, 43272, 11242, 19556, 82213, 41895, 27685, 75030,\n",
       "        50912,  6617, 67714,  5593, 31292, 13440, 56813, 11241, 77122,\n",
       "        30094, 79209, 35180, 94420, 71795, 43718, 70393, 68950, 47838,\n",
       "         5005, 69007,  2466, 33835, 83875, 47684, 62835, 56031, 37803,\n",
       "        63354, 61176, 60993, 44444, 81522, 50356, 37675, 28583, 33483,\n",
       "        52045, 89157, 18245, 21209, 72520, 22081,  3160, 75489, 94143,\n",
       "        90272, 10159, 61584, 68557, 11415, 56301, 33562, 63597, 50513,\n",
       "        60328, 69781, 39359, 88608, 94299, 72661, 13761, 33834, 55666,\n",
       "        66888, 31499, 45995, 38223, 24985, 92186, 17871, 29127, 18006,\n",
       "          818, 87426, 94570, 49552, 46785,  6204, 70642, 15850,  6605,\n",
       "        35878, 89829, 72303, 42556, 25610, 85375, 60368, 60084, 53110,\n",
       "        54300, 32295, 57385, 90556, 52500, 76205, 50327, 50585, 98810,\n",
       "         5933, 10585, 22320, 60446, 95023, 39610, 94859, 45235, 52290,\n",
       "        16129, 16620, 62188, 89837, 86406, 14949,  6938, 53191, 41856,\n",
       "        29953, 89445, 73704, 76210, 46652, 74781, 39420, 95656, 82702,\n",
       "        19385, 31092, 14353, 84478, 12703, 21037, 28170, 92953, 85021,\n",
       "        75706,  7784, 91290, 28146, 77703, 33809,  8213, 33821, 86827,\n",
       "         4731, 51929, 26674, 98673, 74097,  7290, 32453, 40558, 39777,\n",
       "        73939,  7948, 72853, 50767, 13306, 47431, 67854, 49633, 44869,\n",
       "        50377, 60224, 63944, 48593, 87141, 20878, 49258, 18263, 14791,\n",
       "        16738, 66223, 96558,  7334, 69048, 54110, 73763, 58894, 49942,\n",
       "        10763, 20774, 10427, 63534, 58330, 81663, 31976, 80344, 42970,\n",
       "        26212, 35867, 17059, 60041, 41359, 92344, 31416, 90444,  8036,\n",
       "        30932, 23235, 53691, 20768, 41955, 81264, 64688, 51244, 22671,\n",
       "        77078,  6804, 53514, 19145, 21910, 55552, 78095, 74658, 12657,\n",
       "        98195, 76770, 35429, 79029,  9654, 89770, 24935, 50594, 53552,\n",
       "        78694, 98122,  9528,  9147, 85170, 52759, 16286, 78797, 48692,\n",
       "        55073, 68378, 70135, 60789, 64679,   916, 54524, 49872, 22826,\n",
       "        74217, 53384, 66301, 46408, 51737, 65268, 14681, 82641, 97934,\n",
       "        36009, 13775, 50415,  1775,  2076, 77831,  5772, 44219, 74834,\n",
       "        57786, 54874, 40758, 42295, 70732, 36106,  5808, 27274, 28266,\n",
       "        80908, 35503,  2764, 11151, 72591, 44063, 38906, 50336, 20688,\n",
       "        78852, 32415, 32559, 23157, 24746, 13063, 80088,  8948, 35334,\n",
       "        43113,  7445, 45907, 58432, 48696, 83431, 42338,  4822, 67776,\n",
       "        70277, 27211, 53715, 49908, 59792, 29273, 98220,  7054, 28174,\n",
       "        11820, 95532, 61822, 18910, 15764, 51191, 44429, 58187, 56297,\n",
       "        36420, 44796, 84758, 38415, 71829, 42773, 82644,  7442, 58753,\n",
       "        59087, 37800, 91887, 80273, 13864, 87063, 55268, 66779, 15383,\n",
       "        61887, 52822, 87487, 86248, 41368, 84686, 41477, 72813, 80838,\n",
       "        52355, 42310, 87159, 32601, 47615, 64526, 88720, 53210, 61102,\n",
       "        74015, 69731, 97727, 21986, 55799, 38487, 94294, 14707, 75840,\n",
       "        27965, 12900, 94375, 31248, 11278, 74509, 78735, 48348, 50949,\n",
       "        48117, 11389, 32536, 72213, 40766, 95278, 99898, 85413, 12414,\n",
       "        47311, 44110, 30456, 67356,  1061, 89182, 53403, 82748, 16598,\n",
       "        95032, 63428, 78111, 91399, 53417, 88588, 51465, 98179, 41693,\n",
       "        55983, 74568,  5023]),\n",
       " array([96278, 27088, 89134,  8772, 57396, 60463, 60320, 92181, 88741,\n",
       "        75918, 52503, 23649, 27809, 26579, 40598, 89310, 49825, 78485,\n",
       "        94075, 69279, 97600,  5472, 21448, 68806, 91746, 53339, 51468,\n",
       "        57114, 94548, 19068, 83933, 40290,  7937, 33308, 52788, 22767,\n",
       "         6326, 81108, 41049, 91158, 20798, 64237, 76355, 75399, 98897,\n",
       "        24396, 71443, 36416, 68685,   621, 34213, 68873, 12149, 54438,\n",
       "        47644, 31747, 36472, 54728, 70691, 38565, 68102, 16896,  5825,\n",
       "        58321, 42746, 64016, 80342, 79161, 47538, 73322,  9371, 80952,\n",
       "        83769, 40599, 89868, 78144, 61668, 82809, 74000, 61957, 45493,\n",
       "        84625,  3584, 76685, 24722, 90930, 86571, 84811, 52670, 32551,\n",
       "        86382, 75729, 84689, 63508, 66825, 90945, 92475, 83372, 62505,\n",
       "        73610, 61014,  1121, 35580, 98900, 99412, 96283,  5182, 52880,\n",
       "        10720, 24403, 82054, 61586, 36286,  7645, 31440,  6983, 52850,\n",
       "        72442, 50992, 60050,  6081,  8015, 68424, 25192, 32078, 96055,\n",
       "          518,  7524, 98181, 56683, 28627,  6735, 54531, 64685, 67351,\n",
       "        60466, 57969, 58138, 95539, 50809, 86551, 66593, 84998,  7276,\n",
       "        57854, 33398, 59665, 25548, 85768, 98678,  8565, 26439, 26995,\n",
       "         1936, 13953, 85412,  7144, 25356, 64013, 72127, 18524, 31814,\n",
       "         5028, 59860, 25638, 84977, 69567, 37826, 50465, 48917, 37245,\n",
       "        78345, 13951, 62210, 85171, 64299, 51407,  8003,  1137, 75586,\n",
       "        60918, 87722, 97933, 44347, 31177, 61090, 28771, 57978, 77925,\n",
       "        77248, 49556, 96502, 44632, 39217, 40736, 45771,  8749,  7174,\n",
       "        52328, 22880, 42563, 73319,   574, 72064,  5710, 59626, 85305,\n",
       "        56521, 58003, 77945,  6913,  5768, 88471, 38587, 96042,  3563,\n",
       "        31014, 76647, 64157, 59903, 52653, 10519, 52446,  2948, 73419,\n",
       "        24550, 24010, 42244, 67363, 79739, 66596, 49770, 21142, 59568,\n",
       "        71668, 33223, 42534, 55689, 24046, 27766, 88901, 78684, 60893,\n",
       "        32546, 67349, 51509, 38517,  5751, 31085, 90136,   756, 95702,\n",
       "        45759, 74120,  8452, 37522, 69721, 93678, 29736, 77791, 76764,\n",
       "        99954, 24840,  6800, 72877,  1283, 63763, 97287, 73656, 21810,\n",
       "        10449, 23572,  9206, 36090, 49762, 25171, 90762, 41043, 67259,\n",
       "        83309, 31949, 75204, 38119, 40911, 28289, 74594, 87658,   303,\n",
       "        16293,  4645, 15139, 43387, 76533, 37365,   743, 96457, 29978,\n",
       "        42363, 95419, 25927, 21618, 22057, 32695, 28373, 65920, 88834,\n",
       "        68595, 79869, 83130, 76004, 63412, 30555, 52657, 90481, 96503,\n",
       "        10042, 90889, 31919, 65669, 18057, 21865, 99395, 59742, 64080,\n",
       "        57902, 88484, 26941, 32094, 43572, 77331, 81402, 50366, 47996,\n",
       "        85033, 43375,  1284, 21075, 50905, 62588, 90239, 12071, 37019,\n",
       "        14278, 65347, 36868, 91048, 77156, 23991, 38762, 79492, 31468,\n",
       "         6272, 39508, 21066, 17380, 65998, 17203, 54934, 45631, 24895,\n",
       "        41278, 96794, 88862, 15354, 25855, 83401, 21562, 56389, 93441,\n",
       "        86738, 28266, 44333, 23415, 81578, 14367,  5873, 44760, 30004,\n",
       "        13222, 76550, 65114, 23541, 41341,  8988, 20849,  3433, 60659,\n",
       "        91377, 43393, 15184, 63783, 73357,  6684, 74319, 95726, 23910,\n",
       "        93584, 64574, 39037, 31151, 94640, 16015, 10462,  8213, 20098,\n",
       "        54995, 30766, 10949, 69577, 57165, 47222, 99273, 18934, 45068,\n",
       "        94559, 25717, 24963]),\n",
       " array([30246, 75734, 53772, 25180, 53339, 88337, 96452, 50906, 38709,\n",
       "        51332,    16, 59303, 80768, 61806, 77893,  6377,  4054, 81162,\n",
       "        73804, 22252, 93761, 84574, 38955, 79220, 45585, 86292, 80268,\n",
       "        97802, 65521, 28748, 68134, 84287, 89651, 78371, 61999, 93546,\n",
       "        60148, 85623, 75980,  1700, 85124, 44074,  8552, 75488, 95770,\n",
       "        46658, 61378, 56303, 75070, 92031, 93586, 16374, 13552, 91420,\n",
       "        82934, 92206, 93587, 23949, 77571, 84743, 16552, 68189, 25216,\n",
       "        44322, 40463, 77413,  3774, 90630, 72355, 67236, 35545, 31831,\n",
       "        71633, 42852, 97606, 52664, 43026, 96226, 71669, 66843, 24868,\n",
       "         7301, 60513, 21315, 33683, 38091, 42571, 90938, 79758, 37378,\n",
       "        57145, 10511, 30897,  4486, 14218, 85360, 34350, 84935, 89468,\n",
       "        31486, 35180, 54876, 55799,  3456, 52296, 56811, 31934,  4571,\n",
       "         9971, 98258, 45044, 34922, 50679, 22039, 55429, 42175, 22950,\n",
       "        30392, 49041, 58950, 78901, 97588, 18236, 32403, 91288, 90284,\n",
       "        27877, 82077, 68796,  5634, 57835, 96383, 47175, 48581, 68394,\n",
       "        90723, 25469, 72890, 81877, 75021, 19170, 31321, 61163, 70077,\n",
       "        82231, 20842, 75018, 15109, 54933, 31818, 44332, 68800, 49762,\n",
       "        81163, 39347, 67378, 50073, 27079, 10676, 33919, 79733, 48593,\n",
       "        82101, 57965, 10446, 30641, 25926, 47363, 93165, 92096, 24444,\n",
       "         1829,   969, 71306, 39046, 55829,  2004, 13478, 45364, 75692,\n",
       "        40134, 91474, 18799, 88641, 83912,  6107, 87769, 85931, 35540,\n",
       "        54399, 91978, 30073, 94001, 55051, 76457,  4175, 78116, 19575,\n",
       "        42305, 64779, 67569, 87086, 22129,  7747, 67355, 29076, 33173,\n",
       "        83677, 73920, 21276, 23078, 76931, 60930, 72591, 18863, 19073,\n",
       "        98193, 26330, 79550,  9455, 35727, 49715, 71965, 97461, 45591,\n",
       "        46822, 72995, 73525, 25340, 50839, 63392,  6538,  3464, 89622,\n",
       "        71577, 95785, 24498,   442, 20356, 60680, 42917, 26349, 28195,\n",
       "        59173, 63814, 23287, 62058, 24538, 87210, 95339, 23553, 38160,\n",
       "         3683, 53586, 92567, 89361, 68059, 88094, 20328, 73104,  8683,\n",
       "        31353, 26609, 78961, 58654, 75538, 35855, 35968, 46877, 54283,\n",
       "        30738, 27868, 56827,  3798, 13948, 49420, 44753, 88560, 62534,\n",
       "        84001, 24168, 25629, 45672, 36023, 84138, 88076, 99237, 67835,\n",
       "        87891, 12592, 61364, 29950,   862, 86554, 66546, 32404, 60548,\n",
       "        71577, 22372, 72272, 83117, 44463, 13363, 99290, 91775, 57841,\n",
       "        69428, 38149, 67811, 37013, 10059,  5435, 75747, 36694, 20795,\n",
       "        81518, 45123, 19426, 77000, 94457, 85878, 41896, 21871, 32200,\n",
       "        37522, 16807, 75146, 72821, 34409, 94020, 13098, 22292, 69607,\n",
       "        11611, 47561, 68139, 96622, 93455, 73304, 90478, 19405, 37250,\n",
       "        39582, 94505,  7662,  3269, 46799,  3500, 16648, 31973, 86954,\n",
       "        47951, 19881, 63628, 83840, 52012, 99437, 96824, 47795, 18016,\n",
       "        32469, 47432, 54184, 82239, 63579, 61397, 96463, 66254,  8313,\n",
       "        70161, 80103, 35496, 29393, 20130, 61181, 20699, 63458, 17926,\n",
       "        81779, 24007, 76794,  6317, 82301, 15389, 29882,   328, 80187,\n",
       "        43290, 78028, 10981, 89258, 26338, 36687, 47497, 54330, 83416,\n",
       "        24405, 62041, 67157, 99561, 90258, 87867, 80602, 65972, 49819,\n",
       "        88423, 22991, 66217, 21610, 12940, 22204, 44900, 65755, 88029,\n",
       "        99654, 32712, 35669]),\n",
       " array([29031, 84556, 45873, 29408, 63772, 12078, 79579, 32045, 11484,\n",
       "        37766,  3270, 42040, 16211, 34281, 31101, 40064, 49321, 74013,\n",
       "        10796,  7144, 86393, 14940, 88732, 26964, 14838, 59644, 53322,\n",
       "         7736,  8505, 11961, 59952,  4396, 37413, 29779, 86888, 46387,\n",
       "        54889, 34147, 28879, 60353, 92201, 48571, 81031, 19044, 77150,\n",
       "        96964, 45868, 42787, 54455, 56161, 98902, 99632, 62179, 13393,\n",
       "        34505, 33273, 92146, 16025, 35437, 88879, 80486, 21450, 30030,\n",
       "        64556,  9076, 68915, 50423, 11498,  1597, 89125,  7789, 95130,\n",
       "        74578, 21905, 23158, 45553,  4688, 68018, 21753, 17108, 64505,\n",
       "        37940, 22010, 52356, 32114, 90359, 49197, 36686, 90334, 74031,\n",
       "        90947, 23960, 23147, 48225,  2668, 71077, 17893, 71064, 57952,\n",
       "        42984, 14773,  9144, 21883, 99362, 57095, 27355,  8737, 88955,\n",
       "        45094, 45513, 65831, 58884, 58359, 36338, 62295, 80120, 13105,\n",
       "         7273,  2898, 36442, 12018, 35094, 34614,  3262, 55965, 31330,\n",
       "        47867,  4456, 53424, 21078,  4689, 62204, 60321, 88606,  6263,\n",
       "        16973, 19682, 52227, 34003, 59741, 40286, 45061, 60442, 70179,\n",
       "        12255, 67366,  5523, 82311, 10750, 85492, 53846, 38817, 10809,\n",
       "        39892, 85055, 88561, 98888, 58553, 58145, 64897, 92170, 28288,\n",
       "        56124, 93676, 67986, 42473,  5336, 99459,  5722, 98929,  9647,\n",
       "        63238, 43617, 92165, 13062, 15391, 29654, 35765, 62780, 54095,\n",
       "         3229, 28261, 12616, 95602,  7385, 67855, 78443, 88156,  8728,\n",
       "        89269, 48821, 62901, 91815, 68897, 45312,   963,  7484, 47573,\n",
       "        49522, 86897, 57859, 19348, 46731, 19546, 86560, 96221, 51515,\n",
       "        75366, 77377, 25086, 87260, 62681, 11539, 71990, 76771, 80569,\n",
       "        58301, 77278, 80627, 63474, 65642, 85911, 69316, 68667, 49187,\n",
       "        59879, 68680,  9631, 49630,  3639, 26848, 49797,  2652, 73262,\n",
       "        19050, 40260, 44296, 70200, 56951, 15357, 85089, 70851, 15985,\n",
       "        18458, 33589, 21622, 97770, 46361, 19933, 40003,   743, 88731,\n",
       "        74108, 56564, 68636, 37908, 86171,  4366, 75247, 92806, 36180,\n",
       "        29514, 45281, 53648, 75648, 57401, 78388, 19504,  3588, 63800,\n",
       "        97698, 42631,  5620, 88187, 32033,   986, 28358, 41308, 90176,\n",
       "        76285, 35756, 52173, 83679, 66167, 37994, 19494, 82371, 97750,\n",
       "        68581, 61373, 33948, 41460, 95296, 83794, 32125, 70786, 28127,\n",
       "        97115, 49386, 42203, 86245, 62425, 58713, 45366, 41238, 47225,\n",
       "        98023, 62169, 36322,  5670, 47814, 35193, 30525, 97370, 87838,\n",
       "         7191,  5495, 73226, 42094, 78613, 54706, 75888, 89590, 28830,\n",
       "        38191,  9580, 22396, 34771,  6197,  4923,  2479, 10228, 99071,\n",
       "        58839, 22512, 17735, 62973, 89480, 12358,  4907, 35893, 58008,\n",
       "        73382, 53819, 37498, 34126, 36318, 17412, 37071, 98458, 27857,\n",
       "        79496, 30501, 44976, 53887, 32596, 76585, 21614, 66370, 46883,\n",
       "        31181, 61119,  5946, 74694, 84172, 33217, 47022,  7489, 25586,\n",
       "        14200, 37734, 95704,  9914, 26024, 90860, 31746, 20759, 45178,\n",
       "        41365, 91613, 93704,  5013, 64874, 41416, 19503, 94341, 89583,\n",
       "        58771, 67932, 33353, 16017, 67978, 10492, 24098, 78279, 95458,\n",
       "        56365, 65372, 55267, 12566, 89110, 89264, 17085, 87649, 58466,\n",
       "        21682, 87474, 36022, 55878, 57295,  3440, 67630, 99198,  8323,\n",
       "        32708, 83397, 87392]),\n",
       " array([25400, 36298, 94292, 84887,  3705, 76236, 58734, 74514, 87981,\n",
       "        12497, 42710, 23401, 84495, 40894, 75424,   589, 98431, 34876,\n",
       "        78571, 85550,  2062, 16194, 44916, 92125, 41075,  7021, 35554,\n",
       "         2793, 26774, 13837, 45015, 25549, 79660, 64067, 53602, 35399,\n",
       "        96060, 13544,  8071, 46587, 72523, 60862, 41407, 82528, 49987,\n",
       "        88722, 86667,  3238, 37431, 81169, 92877, 47830, 90696, 93704,\n",
       "         6613, 41065, 64986, 31942, 41566, 38759, 39500, 83248, 73325,\n",
       "        39364, 38499, 71570, 14440, 10465, 54787, 36385, 44637, 26679,\n",
       "        61641, 45343, 70641, 14202,  2229,   308, 23389, 86463, 10880,\n",
       "        87820, 42102, 28602, 57929, 97673, 66201, 25057, 58386, 20578,\n",
       "        24336, 65517, 62818, 32132, 73298, 35105, 14967,  2454, 63327,\n",
       "        48062,  2709, 93308, 84910, 89311, 21029, 81236, 64737, 15982,\n",
       "        62480, 41749, 88966, 80861, 73593, 78283, 92297, 15887, 32400,\n",
       "        71647, 48039, 40302, 67795, 16447, 91121, 36719,  1385,  6017,\n",
       "        42708,  7641,  4593, 10755,  2995, 24070, 56825, 14085, 36856,\n",
       "        82848, 45375, 17846, 25851,  1624, 48574, 11946, 41103, 36881,\n",
       "        82162, 89171, 57612, 19035, 11051, 25457, 51625, 27902, 22832,\n",
       "        50314, 71266, 76677, 66356, 43486, 18417, 38709, 62556, 57694,\n",
       "        26578, 32691, 74103, 94351, 78015, 45719, 80590, 83525,  1667,\n",
       "        42600, 85216, 42517,  9888, 96230, 16518, 76401, 32161, 15466,\n",
       "            5, 23941, 40969, 23497, 34093, 13515, 78846, 15069, 78917,\n",
       "        51991, 80720, 88464, 91368, 87835, 47344,  2075, 27998, 62452,\n",
       "        69878, 34124, 13291, 86575, 50723, 43001, 52938, 26000, 49598,\n",
       "        14217, 80892, 41711, 23557, 44111, 78297, 25116, 57170, 48343,\n",
       "        53157, 55663,  3043,  4479, 74356,  1724, 76306, 78801, 43212,\n",
       "        47671, 20462, 75911, 88820, 14921, 59123, 28397, 15236, 29042,\n",
       "        60071, 79820, 95356, 98589, 59422, 11930, 10439,  2814, 52364,\n",
       "        23324, 87694,  3289, 94448, 70810, 58488, 22778, 89104, 23902,\n",
       "        62216, 29026, 68327, 20062, 58442, 73111, 16245, 21839, 50546,\n",
       "        64660, 46821, 38607, 79654, 84933, 21384, 53044, 77428, 23171,\n",
       "        60840, 79774, 43444, 32109, 18098, 95380, 90501, 29386, 69636,\n",
       "        68731, 42523, 25602, 43476, 76929, 71447, 49490, 47633, 10464,\n",
       "        15619, 70572, 34954, 68016, 83454, 80490, 65249, 63559, 51530,\n",
       "        18710, 16123, 10112, 86148,  3594, 59777, 36462, 81483, 75670,\n",
       "        85846, 90936, 76932, 41640, 20434, 37533, 47698, 53770, 40192,\n",
       "        78776, 80695, 78143, 12447, 20837,  4994,  5422, 66951, 39296,\n",
       "        41633,  2102, 29283, 10247,  5345, 95112, 79700, 64451, 11002,\n",
       "        37851, 81178, 39581, 75269,  4286, 62967, 98029,  7320, 15297,\n",
       "        23959, 61962, 25309, 56233,  5924, 59077, 12860, 62811, 71344,\n",
       "        95496, 43302, 84415, 77193, 74949, 84909, 95769, 65649, 96436,\n",
       "        57355,  4809, 57896,  1293, 67039, 23425, 29146, 79452, 86569,\n",
       "        64779,  2773, 40936, 95892, 21133, 89643, 11961, 24258, 38802,\n",
       "        16276, 82581, 24340, 29070, 70740, 50579, 19197,  8352, 34144,\n",
       "        63465, 57903, 71955, 90357, 27016, 78667, 38133, 13429, 24178,\n",
       "        56715, 21192, 79494, 26023, 71360, 70046,  7077, 60266, 83854,\n",
       "        49834, 60318, 85960, 31341, 64542, 23849, 51053, 54636, 34707,\n",
       "        89036, 27973]),\n",
       " array([55089, 48859, 86135, 27653, 81541, 80197, 22512, 26423, 54537,\n",
       "         7518, 24290, 85654, 80545,  5112, 45812, 12044, 41597, 35685,\n",
       "        16032,  2741, 54642, 33612, 94832, 33207, 68159, 41798, 15808,\n",
       "        59913, 25826, 18166, 71249,  8424, 94061, 71926, 13228, 36046,\n",
       "        14423, 26980, 75877, 40157, 89439,  8090, 51872, 81827, 70472,\n",
       "        53799,  9424, 11884, 15717, 56196, 52248, 61942, 20652, 77076,\n",
       "        83380, 58855, 57131, 92718, 54343, 19661, 71022, 80664, 48051,\n",
       "        76430, 35479, 85177, 29000, 20264, 51798, 68382, 42273, 16680,\n",
       "        11628, 38143, 78236, 93117,  8649, 34576, 58137, 90135, 99448,\n",
       "        62063, 32905, 40185, 90514, 26795, 38915, 38280, 83440, 30568,\n",
       "        34965, 57007, 15077, 78842, 50520, 96982, 60997, 91272, 63469,\n",
       "         1198, 92660, 32578, 94702, 76701, 35201, 45857, 49287, 48551,\n",
       "        29060,  6736, 24987, 59797, 90929, 86664,   377, 83519, 31149,\n",
       "          539, 12039, 44008, 92403, 61183, 43114, 28716, 73391,  1442,\n",
       "         1801, 79123, 46931, 71298, 17915, 15487,  5458, 51334, 51673,\n",
       "        26561, 13454, 60627, 49509,  4084, 19322, 97816, 59448, 99700,\n",
       "        61200, 86912, 73743, 37732, 75161, 17840, 37762, 27219, 25396,\n",
       "        50594, 23421, 48939, 84351, 81068, 59203, 98133, 21306, 15292,\n",
       "        99536, 67752, 38458, 23990, 69528, 76746, 36025, 17960, 35314,\n",
       "        62136,  7895, 77468,  5936,  3208, 98849, 87998, 27117, 65528,\n",
       "        17118, 49575,   792, 10529, 26681, 97939,  6155, 55264,  7548,\n",
       "        80267, 61637, 75130,  8348, 41164, 78440, 96324, 23910, 54688,\n",
       "        38082, 34135, 81759,  6720, 46610, 86681, 85199,  3811, 63877,\n",
       "        26215, 43199, 69799, 93347, 22261, 17349, 37919, 93912, 69426,\n",
       "        22243, 22017,  4743, 54493, 84930, 25247, 31514,  4355, 50730,\n",
       "        73811, 41227, 17028,  5331, 91508, 24122, 51200, 11138, 44127,\n",
       "        90806, 77022, 64562, 10898, 14174, 57913, 99828, 57706, 42772,\n",
       "        54179, 68862, 76345, 88100, 72139, 30147, 45699, 93063, 11577,\n",
       "        94785,  1717, 96386, 26568, 25113,  6798, 19647,  2788, 62534,\n",
       "        91619, 12402, 30850,  7600, 46501, 85409, 38677, 68801, 36002,\n",
       "        55182, 65801, 85868, 96940, 44912, 77689,  3985, 51174, 32874,\n",
       "        53751,  3903, 74851, 21809, 97624, 84626, 67521, 64527, 60793,\n",
       "        11559, 71589, 42158, 11201, 23790, 31542, 53567, 76873, 43710,\n",
       "        63793, 22247, 21891, 58106, 11862, 13876, 65170, 67826, 37654,\n",
       "        82869, 27342, 71249, 76014, 78362, 90595, 87212, 47904, 63778,\n",
       "        46775, 17269, 78978, 74667, 20049, 98112,  9934,  1577, 12606,\n",
       "          200, 19884,  4397, 22854, 14313, 74765, 23727, 26694, 58000,\n",
       "        91095, 94519, 67833, 47448, 61996,  8433, 96791, 94240, 63468,\n",
       "        37776, 96938, 64397, 70325,  3465, 45726, 24296, 78209, 98297,\n",
       "        59382, 78362, 50303, 48305, 53011, 56718, 16154, 11122, 52286,\n",
       "        61757, 10110, 37164, 40601, 65825, 36576, 34943, 64910, 74708,\n",
       "        48105, 89720, 82707, 30607, 45693,  5616, 76611, 71829, 58655,\n",
       "           49, 28841, 96414, 45350, 77407, 96970,  2763, 78034, 29117,\n",
       "        34884, 28101, 70907, 97462, 47138, 80405, 60233, 88443, 90548,\n",
       "        20092, 48496,  6044, 53731, 59364, 88567, 81135, 43713, 74604,\n",
       "        95751, 84810, 90817, 80139, 76085, 63316, 16613, 84413, 84048,\n",
       "        24994, 27104]),\n",
       " array([33629, 52925,  1612, 68572, 19643, 28450, 29381, 58091, 67925,\n",
       "        24570, 80341, 62258, 68138, 35566,  7720, 11147, 77200, 26219,\n",
       "        38666, 54037, 84103, 42013, 77278,   382, 37611, 20500, 39904,\n",
       "        93788, 90500, 74245, 56705, 25521, 22059, 40351, 63133,  4421,\n",
       "        95238,  8037,  7385, 69054, 31272, 38738, 96539, 98408, 46165,\n",
       "        98376, 55733,  7455, 15620, 70403, 44502, 44869, 83228, 67642,\n",
       "        86760, 61364,  4051, 21647, 78853, 22601, 78600, 26946, 84746,\n",
       "        74347, 64246, 30552, 21960, 20803, 33696, 24709, 56727, 49360,\n",
       "        89432, 64282, 95093, 64036, 96100, 75730, 19912, 40296,  5576,\n",
       "        74665, 76835, 74765, 29160, 45511, 97921, 61411, 65662, 76829,\n",
       "        37528, 85487, 12267,  4315, 41632, 66377, 55330, 39209, 64830,\n",
       "        63232, 36191, 84189, 51336, 71310, 47439, 72667, 61905, 93717,\n",
       "        30230, 92124, 77418,  9741, 65484, 33601, 14730, 32388, 71917,\n",
       "        65947, 12240, 66876, 34033, 63522, 70475, 15571, 22147, 72689,\n",
       "        22581, 39724, 48563,  2466, 23414,    44, 58384, 65412, 30379,\n",
       "        47102, 14197, 80069, 65916,  4810, 66280, 71394, 77604, 31238,\n",
       "         9509, 80019, 59997, 71770, 65305, 64450, 43156, 56013, 85957,\n",
       "        85503, 44973, 72255, 42333, 61782, 64236, 55454, 32738, 36878,\n",
       "        11154, 64859, 55458, 73886, 54085, 72637,  9663, 28550, 25753,\n",
       "        34285, 50093, 23964,  6750, 38056, 19822, 92321, 68399, 49920,\n",
       "        35424,  7928, 30282, 28379, 26424, 90600, 61804, 28984, 41985,\n",
       "        58993, 16527, 58494, 95192, 66992, 53001, 13340, 20606, 24993,\n",
       "        83724, 84847, 90092, 38104, 92373, 85010, 16604, 14771, 38182,\n",
       "        22055,  4187, 54083, 71764, 69130,  3460, 79384, 56945, 39851,\n",
       "        96667, 89715, 11301, 11581, 62738, 47171, 39821, 55295, 23686,\n",
       "        68069, 55072, 87276, 93634, 71456, 17147, 70730, 95517,  5926,\n",
       "        62997, 17967, 78427, 99549,  1617, 52819, 14809, 63507, 43635,\n",
       "        73718, 79137, 80335, 17584, 53603, 66886, 46503, 34993, 54154,\n",
       "        89025, 57031, 42187, 96996,  6837, 99192, 57984, 85881, 11362,\n",
       "        89583, 60030,  9650, 25546, 32900, 51589, 65190, 65193, 87397,\n",
       "         6144, 92220, 93340, 52426, 45850, 41512, 64485, 54493, 39624,\n",
       "        13912, 23964,  8115, 16021, 83886, 26330, 93189, 55651, 44196,\n",
       "        53259, 11779, 58389, 91055, 66093, 15360, 61597, 95118, 63363,\n",
       "        44215,  1878,  1135, 91371, 20310, 88206, 16760,  2627, 50337,\n",
       "        86546, 80038, 64418, 96787, 31432, 13694, 14568, 46860, 81106,\n",
       "        71548,  9010, 20427, 18951, 41138, 33346, 92090, 10819, 55635,\n",
       "        32228, 59676,  5272, 30084, 86267, 16851, 16231, 25470,  2912,\n",
       "        87496,  3113, 31952, 59259, 75495, 73256, 72880, 86759, 88311,\n",
       "        72869, 71744, 86575, 54920, 39005, 52644, 46337, 10495, 32532,\n",
       "        59922, 13881, 70599,  2007, 15150, 69579, 70124, 42661, 60176,\n",
       "        26534, 72274, 49878, 66443, 62875, 17056, 56283,  3394, 99832,\n",
       "        78251, 87728, 77820, 56774, 29531, 19059, 94748, 98742,  9413,\n",
       "        93437, 17061, 65602, 40084, 48354, 57277, 47140, 55565, 41015,\n",
       "        16030, 66510, 22110,  7553, 32201, 74986, 55981, 24145,  6370,\n",
       "        28240, 42626, 34479, 37064,  5746, 39714, 72299, 17147, 41181,\n",
       "        42116, 42427, 81107, 14180,  6630, 85127, 53502, 75895, 68420,\n",
       "        61545, 97250]),\n",
       " array([13154, 43591, 84672, 89591, 88342,  3063,   955,  7336, 78982,\n",
       "        27765, 57155,  8589, 52505, 51577, 11604, 44879, 59125, 65705,\n",
       "        95423, 32669, 49061, 31116, 42568, 70052, 84958, 25409,  6996,\n",
       "        85809, 72239, 22757, 95010, 67410, 49207,  3816, 69137, 83347,\n",
       "        54194,  7712, 95074, 55194, 25821, 82519, 86014, 94139, 23811,\n",
       "        98424, 61195, 52113, 48201, 97578, 82559, 43594, 27216, 96322,\n",
       "        65878, 23162, 31540, 97590, 30230, 92388, 35981, 97826, 76204,\n",
       "        13485, 77130,  7643,  6655, 34813,  7703, 60837, 44787, 83427,\n",
       "        30447, 20009, 81114,  2829, 83331, 17679, 65132, 16773, 81935,\n",
       "        15126, 27465, 54036, 44603, 55671, 52899, 59387, 64427, 68132,\n",
       "        72274, 32046, 98588, 81288, 52503, 71776, 67107, 97268, 11771,\n",
       "        95036, 13171, 40494, 62764, 39567, 91870, 55411, 10093, 22041,\n",
       "        40054, 37320, 21971, 78670, 78502, 99771, 22538, 29936, 25677,\n",
       "        85732, 13648, 78728,  6353, 20590, 85049, 43792, 65441, 31932,\n",
       "        16005, 76186, 76938, 91701, 30193, 99235, 15045, 71002, 91123,\n",
       "        77174, 59359, 36413, 71801, 82702, 27976, 44913, 74784, 28152,\n",
       "        13105, 45235,    67, 13960, 11700, 20921, 11061, 97555,  4344,\n",
       "         8608, 11730, 61819, 61335, 83702, 35189, 22776, 20745, 66866,\n",
       "        52345, 66262, 53241, 53036, 50949, 16982, 83017, 19775, 88012,\n",
       "         1099, 53865, 61129, 78751, 32147,  4043, 39637, 46232, 11144,\n",
       "        63432, 89940, 36944,  5852, 94568, 96349, 31460, 13508,  6484,\n",
       "        56395, 81480,  4313, 47195, 66409, 61364, 99007, 18956, 60436,\n",
       "        50841, 50278, 96908, 17698, 11447, 65535, 90915, 55088, 98787,\n",
       "        17462, 90451, 24785, 44966,  2636, 75919,  3676, 30036, 81168,\n",
       "        66497, 70013, 39814, 37211, 98045, 84475, 70435, 54565, 49542,\n",
       "         1554, 57569, 33777, 42768, 85198, 38463, 53719, 52088, 52595,\n",
       "        63403, 96178, 35636, 37974, 67134, 71100,  1062, 67291, 99084,\n",
       "         5827, 20789, 44013, 10274, 78931, 30865, 11512, 16905, 43749,\n",
       "        94892, 16231, 18088, 78225, 73614, 16070, 65747, 37528, 22746,\n",
       "        34346, 71573, 33372, 74518, 12662, 38224, 89691,  2300,  6537,\n",
       "        82204, 60876, 71601, 37375, 92312,   501, 89107, 95390, 28295,\n",
       "        64993,  6625, 36105, 88471,  4110, 97276, 51990, 33526, 87517,\n",
       "        12064, 43773, 92006, 86137, 93698, 12989, 27519, 34935, 49407,\n",
       "        18004, 94940,  3532, 21540,  5336, 43164, 99381,  2575, 24386,\n",
       "        64880, 92132, 50735, 33456, 91941, 60241, 99046, 15350, 30285,\n",
       "        98377, 90383, 18086,  4635, 39578, 94724, 84584,  8333, 23463,\n",
       "        88473, 34472, 75498, 94604, 63958, 18814, 11417, 22566, 80804,\n",
       "        88207, 80187, 95787, 94912, 45672, 91999, 38648, 30372, 82686,\n",
       "        34776, 35739, 13579, 34750, 51413, 50645, 32835,  7299, 17571,\n",
       "        33367, 48884, 64365, 43636, 79549, 85208, 30239, 41824, 68758,\n",
       "        86751, 71032, 59923,   521,  8761, 91270, 12407, 62751,  6579,\n",
       "        89920, 12824, 72102, 13998, 12828, 47580, 22189, 69277, 90147,\n",
       "        95471, 19312, 28939, 29738, 96186, 51350, 56697,  6409, 38194,\n",
       "        60620, 99253, 66947, 39109, 76224, 75865, 77481, 73441, 67298,\n",
       "        38891,  1615, 94340, 14687, 19239, 21798, 75329, 42060, 47113,\n",
       "        28541, 62359, 18114, 36425, 56730, 69905, 58090, 17623, 89828,\n",
       "        46154, 35581]),\n",
       " array([ 3257, 43931, 46586, 73550, 16041, 14279, 86904, 86605, 61399,\n",
       "        85142, 80352, 16371, 43718, 26687, 84560,  5236, 80662, 89849,\n",
       "        94941, 28098, 99462, 22152, 95866, 18175, 13554, 91012, 71420,\n",
       "        99147, 41764, 48875, 64269, 68024, 31448, 80631, 72210, 76149,\n",
       "        98729, 88605, 68340,  2337, 41799, 86025, 74139, 66282, 71394,\n",
       "        56470, 32343, 22482, 11122, 43367, 43249, 83505, 66189, 49238,\n",
       "        43613, 21679, 54304, 72380,  2058, 86370, 95048, 93870, 18009,\n",
       "        33804, 65908, 72997, 54317, 50893, 79401, 55429, 65965, 14637,\n",
       "        70124, 93732, 19275, 41585, 37657, 79443,  2385, 27860, 10152,\n",
       "        14695, 30039, 27594, 16402,  9006, 25161, 17680, 57388, 72438,\n",
       "        30191, 44726, 76781, 61655, 35181,  7642, 48288, 66547, 54359,\n",
       "        22892, 86814, 14750, 18934, 62982, 89772, 83242, 37602, 71139,\n",
       "        56435, 60115, 28696, 28986, 91454, 16532,  7786,  2797, 53722,\n",
       "        85972, 37547, 17747, 25622, 92305, 14336, 30579, 72788,  6688,\n",
       "        64296, 66448, 81243, 46632, 69467, 76234, 68085, 71374, 38000,\n",
       "        90033, 36007,  4047, 18408,  6919, 78352, 21213, 73782, 46146,\n",
       "        18146, 44640, 45363, 54692, 34480, 33579, 58923, 79625,  4349,\n",
       "        42410, 44897, 39439, 14461, 54375, 59070,  1973, 46173, 10378,\n",
       "        54890, 17152, 39333,  2441, 24929, 68310, 81005, 31053, 37061,\n",
       "        96504, 32906, 72046, 65555,  4846, 42690, 43953, 65116, 72373,\n",
       "        11465, 83077,  3606, 34353, 55670, 76872, 27613,  1237, 23252,\n",
       "        73910, 54384, 84331,  1391, 39376, 50905, 40066, 77824,  6222,\n",
       "        31445, 64723, 29303, 37630, 66275, 46081, 91529, 49006,   973,\n",
       "        83516, 70606, 74182, 16098, 74579, 83414, 36486, 86053, 34293,\n",
       "        38234, 54919, 74105, 79224, 17509, 60860, 68278, 40873, 77604,\n",
       "        58946, 59871, 29630, 42846, 60026, 61476, 84460, 19661, 76839,\n",
       "        77505, 24295, 38253, 63182, 22355, 43689,  3845, 75718, 73988,\n",
       "        48796, 67237, 92393, 78231, 77653, 42007, 62472, 68943, 94234,\n",
       "        48010, 74564, 30316, 18924, 28770, 86568, 78445, 98967, 54795,\n",
       "        25728, 25599, 11495, 68848, 96465, 45649, 23576, 20186, 42827,\n",
       "        72614, 10201, 59377,  5334, 83379, 86906, 46904, 38457, 30048,\n",
       "        87937, 42841, 71125, 90687, 86513, 36190, 84288, 58406,  7740,\n",
       "        52088, 36518, 69888, 13598, 50772, 78762,   567,   393, 33052,\n",
       "        15874, 65367, 36327, 86642, 80928, 65287, 64228, 76184, 47267,\n",
       "        53479, 49592, 25247, 84249, 65048, 69030, 97180, 44397, 65856,\n",
       "        63622, 58823, 53697, 68175, 44592, 79072, 35156, 79662, 86520,\n",
       "        79029, 50566, 67635, 31994, 22887, 98299, 71062, 40747, 71813,\n",
       "        41706, 69122, 65067, 32064, 58836, 30316, 36277, 54882, 97271,\n",
       "        72625, 51234, 22900, 26593, 98085, 97197, 31398,  2399, 30360,\n",
       "        65787, 73515, 15089, 44732, 24221, 85115,  5061, 14345, 82884,\n",
       "        89591, 15890, 26748, 79375, 98985, 11395, 70733, 76442, 79224,\n",
       "        88085, 43111, 20287, 69338, 35308, 33131,  3000, 44686, 74351,\n",
       "         5412, 61113, 19817, 15671, 91089,  6355, 14040, 57761, 91676,\n",
       "        64168, 79216, 20481, 96205, 55180,  9519, 17773, 72417, 78934,\n",
       "        80269, 33117, 79454,  3803, 92342, 94155, 76071, 75911, 16876,\n",
       "        58506, 53357, 60567, 45067, 80154,  9633, 73803, 88035, 85474,\n",
       "        75956, 67376]),\n",
       " array([21764, 22830, 63741,  2602,  5413, 79943, 11688, 39510, 81818,\n",
       "        29482, 94772, 43678, 73933, 98800, 31426, 97286, 56089, 44459,\n",
       "        37546, 93065, 62811, 85626, 65049, 99458, 71210, 57250, 86631,\n",
       "         7522, 46642, 89353, 24502, 55591, 47981, 64810, 74338, 35014,\n",
       "        92603, 55495, 11266, 68703, 42298, 77902, 87702, 26111, 23713,\n",
       "        45154, 75644, 78027, 41026, 40511, 89349, 41567, 98734, 95145,\n",
       "        86380, 55678, 16295, 74099, 70327, 79317, 71553,  6317, 23566,\n",
       "        30750, 21959, 16524, 80541, 82701,  7735, 79801, 98006, 57461,\n",
       "        37445, 38387, 90774, 17656,  3379, 73724, 98984, 51901, 39645,\n",
       "        62279,  1805, 80025, 90873, 87247, 72462, 81763,  6326,  2157,\n",
       "        73865, 83781, 55276, 28101, 99301, 61167, 25378, 64555, 66485,\n",
       "        17671,  7079, 68771, 66567, 99485, 85177, 38460,  7553, 98133,\n",
       "        36636,  7327,  1489, 65956, 73224, 28978, 50080, 94363, 31424,\n",
       "        64798,   966, 83643, 46204, 92936, 16985, 55509, 76419, 99395,\n",
       "        73757, 57749, 36771, 30917, 17746, 67176, 60193, 85089,  8907,\n",
       "        38671, 82835, 78691, 84258, 90516, 68760, 67981, 60871, 42161,\n",
       "        37609,  3322, 37582, 99969, 97551, 84379, 68095, 43550, 43130,\n",
       "        27492, 18602, 30634, 22905, 67805, 85947, 30261, 24767, 26835,\n",
       "        99988, 59557, 47943,  1194, 82760, 87763, 16116, 10037, 45383,\n",
       "        13355,  7159, 89613,    46, 80661, 79245, 82235, 91688, 65744,\n",
       "        43095, 60707, 23932, 15222, 12477, 57174, 73766,   160, 22445,\n",
       "        52765, 20855, 48772,  5378, 62436,  4120, 50860, 64672, 36971,\n",
       "        61424, 16315, 21645, 31294, 85889, 30245, 33859, 94112, 77452,\n",
       "        71038, 83103, 22182, 85894, 68729, 71809, 25970, 67566, 18113,\n",
       "        56203, 50024, 11760, 59153, 39800, 38920, 16366, 35960, 94569,\n",
       "        84339, 80938, 44056, 16821, 44471, 94291, 75171, 84599, 56283,\n",
       "        14443, 31605, 30128, 24767, 95238, 37085, 92883, 45780, 61553,\n",
       "        70490,  5802, 80471, 19288, 45241, 44341, 55644, 81594, 51471,\n",
       "         6988, 39793, 24615, 68832, 34833, 14533, 81511, 70058, 92946,\n",
       "        72401, 37463, 44407, 42829,  1202,  2491, 58585, 99129, 77743,\n",
       "        35742, 40411, 87487,   757, 77917, 59654, 54751, 23754, 61338,\n",
       "        22035, 34306, 51319, 44620, 75966, 54855, 49528, 18973, 39280,\n",
       "        14186, 76812, 24172, 42998, 96212, 94752, 43300, 85846, 40078,\n",
       "        22552, 82945, 31385, 20668, 88844, 54275,  9693, 72026, 82356,\n",
       "        94336, 96489, 75096, 13419, 79158, 80797, 54584, 30363, 15408,\n",
       "        94247, 98904, 49417, 57522, 51937, 45696, 12700, 50050, 98086,\n",
       "        67413, 40739, 99188, 82360, 58728, 56769, 53241, 63839, 28757,\n",
       "        47873, 19423, 64252, 17911, 47461,  6050, 54271, 79498, 18871,\n",
       "        52636,  8893, 52370, 53142, 32065, 31413, 72646, 76906, 53666,\n",
       "        74060, 29467, 27333, 94825, 85863, 77458, 60410, 97424, 35349,\n",
       "        34587, 58351, 82695, 42477, 58805, 27443, 83834, 34347, 82872,\n",
       "        14439, 38346, 84410, 51051, 90622, 97798, 85952, 24388,  3872,\n",
       "        26469, 80116, 95397, 25230, 84192, 55362, 27505,  3287, 97277,\n",
       "        77903,  3513, 18302, 52612, 13160, 68836, 79735, 52406, 31450,\n",
       "        76394, 49328, 65211,  3577, 30451, 96647, 19633, 65679, 19614,\n",
       "        44075, 18036, 48383, 48486, 75594, 19071, 78317, 85360, 25723,\n",
       "        44353, 23378]),\n",
       " array([ 6698, 79667, 15751,  8469,  4086, 99613, 84107, 40560, 27216,\n",
       "         4676, 79370, 57691, 28076, 61546, 34436, 28436, 47515, 73272,\n",
       "        57573, 88934, 91683, 30812, 98134, 49121, 36447, 73997, 40153,\n",
       "        68218,  8086, 13015, 61960,  6946, 90796, 92122, 47202, 16092,\n",
       "        89921, 94515, 88956, 23263, 80729, 21684, 21861, 87976, 68714,\n",
       "        57240, 68238,  8143, 16563, 68969, 93127, 63240, 70817, 32947,\n",
       "        10054, 68423, 80477, 98134,  2352, 57762,    72, 72233, 72918,\n",
       "        57166, 88860, 22321, 91243, 57140, 63112,   969,  8613, 88774,\n",
       "        61351, 17117, 29183, 76836, 56495, 72580, 40866, 93511, 31254,\n",
       "        63804,  8303, 48498, 19565, 52185, 69200, 24468, 61439, 64828,\n",
       "        35736, 86408, 48116, 33605, 74164, 18967, 79439, 70828, 81264,\n",
       "        86024, 35485, 66252, 87065, 38554, 60857, 15861, 26645, 21947,\n",
       "        69259, 65022, 50957, 81911,  5835, 54102, 83163, 56962, 57566,\n",
       "        89966, 16543, 44967, 91896,   920, 77213,  6428, 88005, 64978,\n",
       "         4242, 49648, 11515, 56484,  5574, 68369, 61212,   530, 91062,\n",
       "        93241,   118, 97957, 25097, 90055, 81267, 62881, 50990, 70124,\n",
       "        47463, 73581,  3861, 89387, 70044, 68814, 18871, 12194, 22418,\n",
       "        80675, 21068, 45391, 75989, 99696, 36585, 29901, 93484, 53417,\n",
       "        85943, 90746, 73005, 60712, 96331, 55508, 32828, 76207,  1704,\n",
       "        23777, 74910, 44959, 64653,  7506, 47412, 83302, 50736,  9055,\n",
       "        67391, 41992, 21278, 41099, 68601, 89034, 82496, 52495, 19431,\n",
       "        25568, 32529, 42421, 27744, 20029, 11681, 67981, 24135, 17489,\n",
       "        42368, 49982, 65388, 28815, 90921, 39227, 43549, 67493,  8501,\n",
       "         1609, 28041,  4480, 56727, 57170, 90447, 53563, 21631, 61584,\n",
       "        35926, 66809, 26529, 80236, 59504, 61776,  7151, 18808,  2580,\n",
       "        35876, 81463, 66490, 17475,   291, 98903, 25492, 13507, 80106,\n",
       "        60621, 69393, 26314, 68888, 95160, 48003, 16630, 86440, 84208,\n",
       "        74688, 50983,  7432, 25152, 52807, 76904, 64184, 38567, 83234,\n",
       "        97801, 53251, 45947, 45652, 49775, 84615, 18912, 80017, 89578,\n",
       "         6114, 87399, 24419, 32076,  3842, 71435,  3416, 36686, 75104,\n",
       "        44290, 94142, 92780, 85724, 70738, 55916, 97492,  2514, 81394,\n",
       "        51706, 62745, 88247, 86918, 11208, 26296,  4156, 62529,  1487,\n",
       "         3056, 17428, 93888, 87787, 82586, 81182, 29909, 50217, 69028,\n",
       "        85661, 89330,   913, 18066, 49540, 33520, 45775, 45265, 51567,\n",
       "        15882, 54559, 12252, 51886, 58753, 65763, 54903, 35952, 63251,\n",
       "        54861, 41481, 31733, 13265, 54875, 71453, 31541, 94725, 23092,\n",
       "        51266, 40385, 56764, 61850, 93976, 24211,  1366, 67052, 21462,\n",
       "        88034, 91363, 94051, 70348,  7955, 25676, 77876, 82717, 90330,\n",
       "        48735, 70877, 67445, 32384, 45867, 86842, 43531, 20926, 28109,\n",
       "        73627, 69509, 90412, 39480, 52798, 38707, 38366, 50231, 88334,\n",
       "        54251, 18447, 92356, 29415, 33675, 94487, 93785, 55512, 29399,\n",
       "        60232, 96020, 69256, 92131, 94292, 40196, 83998, 55511, 59575,\n",
       "        88665, 43833, 69388, 36135, 52302, 92631, 35077, 61439,  4468,\n",
       "        21545, 41620,   725, 14242, 11230, 56081, 37778, 43384, 83860,\n",
       "         8504, 56406, 94951, 57166, 97160, 81698, 51315, 20267, 40616,\n",
       "        11524, 57040, 11149, 53617, 24049, 11951, 53578, 68150,  4527,\n",
       "        91666, 20896]),\n",
       " array([86037, 35819, 33142, 48620, 96111, 43315, 97334, 77796, 53245,\n",
       "        66059, 83328, 57600, 85940,  6341, 18674, 33186, 71332, 43797,\n",
       "        17841, 84775, 34533, 79057, 11887, 38909, 75789, 74122, 44361,\n",
       "        51493, 61367, 24637, 70567, 99337, 49871, 82942, 95035, 77295,\n",
       "        70325, 90400, 25181, 61816, 69658, 25327,  5864, 99074, 12277,\n",
       "         9312,   177, 15549,  8361,  6066, 36048, 24997, 37844,  7156,\n",
       "        46788, 47055, 99397, 80949, 57971, 27956, 81406, 28842, 53279,\n",
       "        13422, 90577, 46477, 66372, 84000, 52971,   236, 26529, 85168,\n",
       "        32306, 61355, 58169, 84585,  3620, 63419, 37462, 89595, 96920,\n",
       "        15534, 99683, 25343, 67843, 49095, 27388, 94484, 92334, 28582,\n",
       "        68598, 80836, 81103, 87249,  1536, 26365, 55749, 63016, 42639,\n",
       "        76909, 63340, 92013, 59746, 52692,  9547, 48932, 61493, 68713,\n",
       "        54693, 52298,  3154, 34975, 99426, 18745, 22474, 54249, 83291,\n",
       "        83709, 38768, 23384, 23489, 29262, 95169,  9123, 24139, 25254,\n",
       "        48637, 31634, 56664, 16136, 51954, 74527, 36370, 73475, 14211,\n",
       "        93612, 48444, 84676, 37165, 38055, 50979, 81635, 14813, 57192,\n",
       "        28211, 12679, 61949,  6419, 34476, 67730, 49025, 11655, 56409,\n",
       "        18641, 43443, 97466, 64230, 10771, 86572,  1908, 20166, 42031,\n",
       "        87102, 81972,   146, 31959,  2910, 99521, 57691, 91148,  9266,\n",
       "        63105, 48432, 72876, 28766, 35361, 47234, 28564, 14067, 38040,\n",
       "        93319, 51772, 22603, 14741, 11196, 54638, 87459, 65985, 44385,\n",
       "        10642, 90377, 15812, 47031, 58834, 23261, 58313,  9508, 83819,\n",
       "        99757, 84803, 54511, 74276, 47860, 38208, 65839, 76233, 48317,\n",
       "        96260, 52310, 57984, 15273, 30068, 18152, 91890, 60929, 87115,\n",
       "        17420, 77629, 89650, 53648, 30539, 62048, 73991,  5800, 48309,\n",
       "        69740, 48852, 43104, 88830, 16448, 28141, 44014, 69182, 59845,\n",
       "        89815, 67556, 60168, 46392, 88039, 14809, 29414, 40725, 31683,\n",
       "        21249, 65617, 10497, 35513, 37825, 65874, 98256, 82835, 73005,\n",
       "        12530, 20970, 17618, 65878, 87353, 47560, 55130, 32010, 38831,\n",
       "         1902, 73896,   942, 12654, 42744, 24548, 89002, 54842, 14121,\n",
       "        60523, 71120, 89794, 76679, 11931, 46141, 95399,  9375, 82506,\n",
       "        71172,  4311, 96596, 85316, 79479, 51370, 38371,  3148, 40131,\n",
       "         5901, 87089, 21866,  8373, 55592,  8772, 98900, 44267, 40872,\n",
       "        44585, 19991, 18929, 32129, 39798, 90359, 63856, 62002, 78133,\n",
       "        11886, 12668, 94016, 65447, 53755, 13497, 26850, 74424, 79539,\n",
       "        95781, 62313, 62779, 49178, 39161, 39170, 98792, 77824, 15788,\n",
       "        56300, 83364, 10356, 66585, 92831, 86808, 71520,  3422, 47937,\n",
       "        53743, 41406,  3059, 75600, 59865,  5741, 71362,  1774, 15570,\n",
       "        45585,  3148, 42751, 98906, 74084, 34939, 33455, 44482, 87165,\n",
       "        64418, 99191, 87161,  9295, 73117, 22104, 63882, 72983, 83798,\n",
       "        66479, 91455, 21720, 13399, 89367, 82404, 32646,  3910, 99879,\n",
       "        66873, 15561,  1275,  8955, 31440, 42478, 77283,   127, 62076,\n",
       "        69051, 87512, 17120, 51049, 36762, 46848, 86135, 75463,  9459,\n",
       "        74106, 27883, 28840, 41011, 76645, 10471, 48157, 23425, 61119,\n",
       "        87758, 65364, 67109, 13040, 83785, 64908, 43599, 76322, 81990,\n",
       "        33510, 15076, 55381, 25983,  3117, 46002, 77705, 23559, 83227,\n",
       "        80361, 28847])]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "direct['x']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to apply the function in each different core"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "CompositeError",
     "evalue": "one or more exceptions from call to method: execute\n[0:execute]: NameError: name 'f' is not defined\n[1:execute]: NameError: name 'f' is not defined\n[2:execute]: NameError: name 'f' is not defined\n[3:execute]: NameError: name 'f' is not defined\n.... 20 more exceptions ...",
     "output_type": "error",
     "traceback": [
      "[0:execute]: ",
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<ipython-input-1-c679c6b49964>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
      "\u001b[0;32m----> 1\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m",
      "\u001b[0m\u001b[0;31mNameError\u001b[0m: name 'f' is not defined",
      "",
      "[1:execute]: ",
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<ipython-input-1-c679c6b49964>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
      "\u001b[0;32m----> 1\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m",
      "\u001b[0m\u001b[0;31mNameError\u001b[0m: name 'f' is not defined",
      "",
      "[2:execute]: ",
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<ipython-input-1-c679c6b49964>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
      "\u001b[0;32m----> 1\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m",
      "\u001b[0m\u001b[0;31mNameError\u001b[0m: name 'f' is not defined",
      "",
      "[3:execute]: ",
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<ipython-input-1-c679c6b49964>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
      "\u001b[0;32m----> 1\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m",
      "\u001b[0m\u001b[0;31mNameError\u001b[0m: name 'f' is not defined",
      "",
      "... 20 more exceptions ..."
     ]
    }
   ],
   "source": [
    "%%px\n",
    "y=f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why the errors above? Because each core does not see the local engine. They work as separate machines and you have to load all variables and modules in each engine. That's easy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting myscript.py\n"
     ]
    }
   ],
   "source": [
    "%%file myscript.py\n",
    "# test if n is prime\n",
    "def isprime(n):\n",
    "    for i in range(3, n):\n",
    "        if n % i == 0:\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "# tests each element of an array if it is prime\n",
    "def f(x):\n",
    "    return map(isprime,x) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Execute code which defines the methods on the different engines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AsyncResult: finished>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "direct.run(\"myscript.py\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compute the \"model grid\" correctly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 55 ms, sys: 6.79 ms, total: 61.8 ms\n",
      "Wall time: 2.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%px y=f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively to the command above, you could use\n",
    "\n",
    "    direct.apply(f,x)\n",
    "or\n",
    "\n",
    "    direct.execute('y=f(x)')\n",
    "You should time this in your watch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have the separate arrays $y$ containing the results on each engine. How to get it back to the local engine?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[0:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[1:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[2:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[3:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[4:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[5:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[6:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[7:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[8:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[9:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[10:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[11:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[12:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[13:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[14:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[15:3]: \u001b[0m417"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[16:3]: \u001b[0m416"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[17:3]: \u001b[0m416"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[18:3]: \u001b[0m416"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "\u001b[0;31mOut[19:3]: \u001b[0m416"
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     "metadata": {},
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    {
     "data": {
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       "\u001b[0;31mOut[20:3]: \u001b[0m416"
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     "metadata": {},
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    },
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mOut[21:3]: \u001b[0m416"
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     "metadata": {},
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    {
     "data": {
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       "\u001b[0;31mOut[22:3]: \u001b[0m416"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%px \n",
    "import numpy\n",
    "numpy.size(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y=direct.gather('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have it back in the local engine.  :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Easy parallel Monte Carlo\n",
    "\n",
    "Suppose you need to do 100k Monte Carlo simulations. Wouldn't it be great if you could easily split them among your (hopefully many) cores?\n",
    "\n",
    "In this example, I have a dataset and I will just do bootstrapping resamples on the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import astropy.io.ascii as ascii"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load dataset ([available in the repository](https://github.com/rsnemmen/parallel-python-tutorial/blob/master/allrb.dat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data=ascii.read('/Users/nemmen/work/projects/finished/jetpower/data/allrb.dat')\n",
    "\n",
    "xdata=data['pb']\n",
    "ydata=data['pj']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# number of desired bootstraps\n",
    "nboot=400000\n",
    "\n",
    "# number of bootstraps that will go to each core\n",
    "n=nboot/size(client.ids)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Passes variables to the engines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First make sure all of them see the path to any custom modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%px\n",
    "import sys, os\n",
    "home=os.environ['HOME']\n",
    "sys.path.append(home+'/work/software/python') # make sure pythonpath is updated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "importing numpy on engine(s)\n",
      "importing nemmen on engine(s)\n",
      "importing scipy on engine(s)\n"
     ]
    }
   ],
   "source": [
    "direct.push(dict(n=n,xdata=xdata,ydata=ydata))\n",
    "\n",
    "with direct.sync_imports():\n",
    "    import numpy, nemmen, scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now everything below is executed in parallel! (IPython magic)\n",
    "\n",
    "<!---\n",
    "Have a look also at the %autopx command.\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 65.9 ms, sys: 6.92 ms, total: 72.8 ms\n",
      "Wall time: 8 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%%px\n",
    "r=numpy.zeros(n)\n",
    "\n",
    "for i in range(n):\n",
    "    [xsim,ysim]=nemmen.bootstrap([xdata,ydata]) # data bootstrapping\n",
    "    r[i]=scipy.stats.pearsonr(xsim,ysim)[0]\t # just compute simple Pearson coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assemble result from cores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r=direct.gather('r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison, how long does it take to do the same simulation in serial mode?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 33s, sys: 742 ms, total: 1min 34s\n",
      "Wall time: 1min 35s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "for i in range(nboot):\n",
    "    [xsim,ysim]=nemmen.bootstrap([xdata,ydata])\n",
    "    t=scipy.stats.pearsonr(xsim,ysim)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Useful documentation\n",
    "\n",
    "## IPython video tutorials\n",
    "\n",
    "* [IPython in depth: high productivity interactive and parallel python - PyCon 2014](http://youtu.be/XFw1JVXKJss)\n",
    "* [The IPython Notebook Revolution](http://youtu.be/t_TzRaK9kpU)\n",
    "\n",
    "## Parallel computing\n",
    "\n",
    "### General\n",
    "\n",
    "* [Introduction to parallel programming](https://computing.llnl.gov/tutorials/parallel_comp)\n",
    "\n",
    "### Python\n",
    "\n",
    "* [AstroPython blog](http://astropython.blogspot.com.br), maintained (not so often anymore) by the speaker\n",
    "* [Using IPython for parallel computing](http://ipython.org/ipython-doc/stable/parallel/index.html)\n",
    "* [Parallel computing with IPython](http://www.astro.washington.edu/users/vanderplas/Astr599/notebooks/21_IPythonParallel)\n",
    "* [Simple python parallelism](http://scottsievert.github.io/blog/2014/07/30/simple-python-parallelism/) and [easily distributing a parallel IPy Notebook on a cluster](http://twiecki.github.io/blog/2014/02/24/ipython-nb-cluster/). Some ideas on making a function parallel easily\n",
    "\n",
    "### Executing general (non-python) jobs in parallel\n",
    "\n",
    "* [Submit non-python commands to a running IPython cluster](https://gist.github.com/zonca/8994544)\n",
    "* [GNU Parallel](http://www.gnu.org/software/parallel/)\n",
    "* [xjobs](http://www.maier-komor.de/xjobs.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       " 23]"
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "client.ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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