import numpy as np

NUM_HILL_PROBLEMS = 1000
NUM_HILL_COEFF = 14

aHill = np.array([[0.980773, -0.794122, -0.203711, 0.394696, -0.0102847, 0.53679, -0.609485, 0.870846, 0.726005,
                   0.00979644, -0.601245, -0.853633, 0.25248, 0.608936],
                  [-0.649525, 0.188513, 0.000946074, 0.0400708, -0.875057, 0.367962, -0.167455, 0.798761, -0.00143437,
                   0.567858, -0.0378735, 0.647816, 0.461043, 0.983886],
                  [-0.192114, 0.317728, 0.364544, 0.927793, -0.170324, 0.242714, -0.0334788, -0.0517899, -0.582263,
                   -0.856807, -0.569628, -0.42027, 0.89526, 0.270119],
                  [-0.655202, 0.0336619, 0.695791, 0.120029, -0.174108, -0.857601, -0.220069, -0.562914, 0.763359,
                   -0.129368, 0.352336, -0.688223, 0.773858, -0.294839],
                  [0.941893, 0.18955, -0.575976, 0.236183, 0.907834, 0.602893, 0.285379, 0.242531, 0.434309, -0.561937,
                   -0.616382, 0.593188, -0.924802, 0.549791],
                  [0.605274, 0.277932, 0.913144, -0.464705, 0.623768, -0.120701, -0.607044, -0.517502, 0.907224,
                   -0.20188, -0.105075, -0.498215, -0.62859, -0.453841],
                  [-0.892453, 0.856563, -0.760857, -0.582995, -0.735405, 0.503098, -0.330607, 0.848506, 0.306925,
                   0.853938, -0.28135, 0.789605, 0.0334178, -0.424177],
                  [0.196509, 0.382916, -0.697562, 0.235267, 0.978271, -0.723563, 0.346538, -0.395245, 0.337626,
                   -0.122959, -0.73748, 0.441084, -0.139439, 0.857356],
                  [0.74102, -0.450911, -0.49559, 0.229041, 0.0950041, -0.0567949, 0.363689, -0.704459, 0.653554,
                   0.918943, -0.294534, -0.204138, -0.420209, 0.846797],
                  [-0.163244, -0.448103, 0.17832, 0.501999, -0.633473, 0.933042, -0.247719, -0.258644, 0.424848,
                   -0.551256, -0.92523, -0.659719, 0.400983, 0.78338],
                  [0.535569, 0.802789, -0.23545, -0.415937, -0.974364, -0.043611, 0.530015, 0.31608, 0.623585,
                   -0.855403, 0.929258, -0.504379, -0.855831, -0.169836],
                  [0.853023, -0.384198, -0.386273, 0.419782, -0.375591, 0.0748619, 0.73278, -0.87463, 0.667776,
                   -0.578173, -0.610034, 0.671987, 0.632984, 0.230934],
                  [-0.710074, 0.666189, -0.45909, 0.917051, 0.755425, 0.437361, -0.489731, -0.194861, -0.231117,
                   0.16361, 0.628407, -0.233192, -0.68511, -0.903989],
                  [-0.469955, 0.734611, -0.915159, 0.692373, -0.754753, 0.40849, 0.608448, -0.52617, -0.120884,
                   0.466292, -0.127049, -0.582934, 0.686514, 0.590075],
                  [0.493515, 0.693594, -0.896908, -0.37846, -0.503769, 0.569262, -0.702994, 0.159337, 0.778008,
                   -0.723258, -0.198584, -0.0903653, 0.303323, 0.673269],
                  [0.79223, 0.103244, 0.103122, 0.495163, 0.572863, 0.292093, -0.863948, 0.0235908, -0.171911,
                   -0.163549, 0.0760826, -0.0276193, -0.7893, -0.60332],
                  [0.0878018, 0.410932, 0.821711, 0.740837, 0.653066, -0.464766, -0.851741, 0.181555, 0.510666,
                   -0.901242, 0.0212104, -0.0457472, 0.771844, -0.684256],
                  [-0.846065, 0.849239, 0.273843, -0.949767, 0.826716, 0.409833, 0.234718, 0.102268, 0.276833,
                   0.0104678, 0.271035, -0.595569, 0.359844, -0.875118],
                  [0.841365, -0.0588092, 0.0414747, 0.0989715, 0.178442, 0.202979, -0.715262, -0.260048, 0.771538,
                   0.988525, -0.105991, -0.965453, -0.537461, -0.633351],
                  [0.87817, -0.691946, 0.217872, 0.611499, -0.103305, 0.137974, -0.36198, -0.0779748, -0.650624,
                   -0.666433, 0.268838, 0.740165, 0.673757, 0.294595],
                  [-0.224708, -0.52208, -0.588794, -0.938719, -0.958495, -0.531358, 0.606372, 0.368511, -0.741325,
                   -0.0480667, -0.900327, -0.984375, -0.935789, 0.907285],
                  [0.278176, -0.133457, -0.206153, -0.452864, -0.155187, 0.789666, -0.0904263, -0.716544, 0.170568,
                   -0.147313, 0.665944, 0.978576, -0.209387, -0.916135],
                  [0.0771203, -0.706046, -0.392193, 0.111667, -0.752861, -0.050325, 0.365581, -0.00418104, 0.126255,
                   0.705741, 0.952696, 0.563158, 0.754875, -0.120884],
                  [0.102878, -0.441389, -0.941038, -0.791925, -0.948607, 0.926145, -0.741142, 0.877132, -0.289163,
                   0.53032, -0.0471511, -0.486068, -0.0707114, 0.632496],
                  [-0.0599689, 0.972289, 0.393048, -0.567186, 0.843562, 0.711539, 0.735893, 0.991455, 0.597156,
                   -0.412336, -0.581286, -0.15891, 0.857784, -0.134251],
                  [0.940367, -0.396588, 0.405622, -0.731986, 0.943297, -0.0779138, -0.40379, -0.130039, 0.776605,
                   -0.975768, -0.0753502, -0.344157, 0.0782189, 0.223914],
                  [-0.233741, -0.452498, 0.938963, -0.321024, 0.355327, -0.281961, 0.211707, -0.285257, -0.935362,
                   0.00308237, -0.472884, -0.973754, 0.0484939, 0.222571],
                  [-0.421064, 0.0721152, -0.689322, -0.775445, 0.241676, 0.972228, 0.262368, 0.465011, -0.917783,
                   0.221778, 0.828669, 0.934446, -0.170751, -0.465499],
                  [0.170446, -0.754875, -0.638539, -0.873226, 0.0806604, -0.308756, 0.778191, 0.756401, -0.880673,
                   0.0933561, -0.885617, 0.826777, 0.54973, 0.241432],
                  [-0.736808, 0.870968, 0.136753, 0.747368, 0.667043, -0.273415, 0.872433, -0.879391, 0.341533,
                   0.714896, 0.688772, 0.878719, 0.793756, 0.135899],
                  [0.221656, 0.505417, 0.397382, 0.392865, 0.688223, 0.0693686, 0.787713, 0.0578326, 0.939573, 0.314798,
                   0.838069, 0.191321, -0.24778, 0.0381787],
                  [-0.218726, -0.771783, 0.420148, 0.561754, -0.961547, -0.257302, -0.289895, -0.882382, -0.683706,
                   -0.595447, 0.24247, -0.0452589, 0.537278, -0.560595],
                  [0.361126, 0.980346, -0.835871, 0.905271, 0.553087, 0.749504, 0.481491, 0.0979339, 0.482284,
                   -0.384747, 0.396466, -0.601611, -0.301187, -0.149693],
                  [0.322184, 0.872982, 0.0863369, 0.554979, -0.294961, 0.94116, -0.889889, 0.16184, -0.240394,
                   -0.578661, -0.0708335, 0.351543, 0.972594, -0.731376],
                  [-0.56682, 0.190344, -0.0611896, 0.316141, 0.268227, 0.303507, 0.0925016, -0.667104, -0.0868252,
                   -0.104343, -0.105502, -0.289285, 0.869686, 0.432234],
                  [-0.960265, -0.907773, -0.972961, 0.792474, 0.246681, 0.253029, 0.266701, -0.291421, -0.809198,
                   -0.449995, 0.366192, 0.30192, 0.145909, 0.249184],
                  [0.26719, 0.529527, -0.10593, -0.956175, -0.230811, 0.353313, -0.531541, -0.922056, -0.288736,
                   -0.555589, 0.290139, -0.215308, -0.295083, 0.235389],
                  [0.26194, 0.854793, -0.520371, 0.131993, 0.382183, 0.645802, 0.905148, -0.301737, -0.559801, 0.345561,
                   0.750969, 0.626576, -0.643727, 0.201819],
                  [-0.752617, 0.304788, 0.729057, -0.869076, 0.50969, 0.794671, -0.848384, 0.0179144, -0.112339,
                   -0.968078, -0.13889, 0.0203558, 0.304178, 0.061861],
                  [-0.719047, 0.188879, 0.643544, 0.122715, -0.978271, -0.283914, 0.25425, -0.611072, 0.900815,
                   -0.872127, 0.626576, -0.812555, 0.54387, -0.272744],
                  [0.309, -0.501267, 0.131687, -0.394024, 0.12534, -0.44438, -0.146764, -0.466048, 0.754875, -0.647389,
                   0.628651, -0.959166, -0.261574, 0.877194],
                  [-0.335856, 0.00125126, -0.0269478, 0.87701, -0.598498, 0.0360424, 0.75689, -0.0259102, -0.575488,
                   -0.956725, -0.552293, -0.0600909, -0.114902, -0.830195],
                  [0.797235, -0.0578326, 0.0112003, -0.46263, 0.0234077, -0.422346, 0.25956, 0.0345164, 0.684194,
                   -0.497726, -0.324747, -0.512009, -0.586657, -0.528672],
                  [-0.979247, 0.525315, 0.583666, 0.602405, -0.762627, 0.440962, 0.956786, -0.326579, -0.199377,
                   0.379559, -0.614734, 0.268593, 0.533189, 0.147313],
                  [-0.373028, 0.584155, -0.562853, 0.965575, -0.664418, 0.706961, 0.108432, -0.522568, -0.710807,
                   -0.821833, -0.704764, -0.678152, -0.0796228, -0.345012],
                  [0.164403, -0.414655, -0.791681, -0.518479, -0.163549, 0.446333, 0.997986, 0.98352, 0.753227,
                   -0.677541, -0.193457, -0.702567, 0.439741, -0.165014],
                  [-0.818415, -0.452376, -0.776788, 0.90173, -0.328471, -0.816584, 0.471603, 0.271279, -0.52739,
                   0.288919, 0.914121, -0.188269, -0.186071, -0.322184],
                  [-0.393719, 0.865047, 0.143101, -0.413556, -0.897702, 0.980895, -0.824641, 0.776177, -0.603626,
                   0.341594, 0.868648, 0.858821, 0.196509, -0.808893],
                  [-0.613819, -0.342326, 0.0928068, 0.580737, 0.111118, 0.415326, 0.182592, -0.257485, 0.773186,
                   0.662221, 0.715384, 0.405988, -0.248146, -0.442244],
                  [0.319315, -0.633168, -0.382427, -0.483505, 0.372967, -0.376568, 0.973937, 0.932005, 0.083285,
                   -0.608325, 0.66277, -0.189245, 0.833918, -0.688955],
                  [-0.604663, -0.870785, -0.635426, -0.845088, 0.871944, -0.274636, 0.346232, 0.357402, -0.548265,
                   -0.461898, -0.088168, -0.331645, 0.436384, -0.992798],
                  [0.70806, 0.250954, 0.0291452, -0.554369, 0.0277413, -0.468123, -0.967406, 0.196631, -0.412152,
                   0.119175, -0.653127, -0.610767, 0.514084, -0.90228],
                  [-0.669057, 0.103488, 0.09476, 0.0174261, -0.909726, 0.758232, -0.132664, 0.884274, -0.247414,
                   -0.465865, -0.401105, 0.468184, -0.206275, -0.355022],
                  [0.723991, 0.24015, 0.47795, -0.732231, -0.198279, 0.250038, -0.527024, 0.947142, -0.444563, 0.258644,
                   0.704215, 0.283181, 0.0561846, 0.436567],
                  [-0.49144, 0.718619, -0.386151, 0.941221, -0.846797, 0.234901, -0.0626545, 0.685781, -0.221717,
                   0.771538, -0.87286, 0.611988, -0.170629, 0.180273],
                  [-0.937681, -0.221107, -0.960082, -0.472579, 0.744377, -0.4185, -0.972716, -0.444258, 0.160924,
                   0.409528, 0.564379, -0.880673, 0.231056, 0.0611896],
                  [-0.410321, -0.596484, -0.604358, 0.222633, -0.981872, 0.742729, 0.414411, 0.326945, 0.415143,
                   -0.152013, -0.0675985, -0.896298, 0.596423, 0.257546],
                  [0.378887, -0.866573, -0.783929, -0.177587, 0.76043, 0.717765, 0.405744, 0.0395215, -0.0889004,
                   0.37846, 0.526353, -0.954588, 0.762688, 0.298379],
                  [-0.903317, -0.918088, -0.804376, 0.0162053, 0.959227, 0.247719, 0.0364086, 0.686941, 0.747124,
                   -0.653127, -0.240028, -0.777886, -0.285073, -0.351604],
                  [0.46324, 0.621326, -0.00558489, 0.367229, 0.669851, -0.193274, 0.33903, -0.318278, -0.470504,
                   -0.724601, 0.418867, 0.0977508, -0.0252998, -0.120579],
                  [-0.270486, -0.0263985, -0.603504, -0.952147, 0.175939, 0.0170598, -0.597095, -0.237159, 0.395184,
                   0.568102, -0.778924, 0.601306, 0.879574, 0.478927],
                  [0.307291, 0.156713, -0.0368358, -0.595874, 0.7257, 0.151219, -0.265481, 0.313944, 0.85992, 0.552171,
                   -0.0631428, 0.0419019, -0.981445, -0.994873],
                  [0.919797, 0.681143, 0.498032, -0.104404, -0.296365, -0.360454, 0.664602, -0.648122, 0.220618,
                   -0.830744, -0.381085, -0.497238, -0.207251, -0.820368],
                  [-0.995056, 0.300333, 0.912107, 0.148961, 0.525559, 0.222877, 0.383099, -0.0541704, 0.728019,
                   0.168432, 0.891476, -0.626514, -0.378521, -0.147374],
                  [-0.939024, 0.249245, -0.310892, -0.977355, -0.938841, 0.83105, 0.856685, 0.80047, -0.17185, 0.405194,
                   -0.0186468, -0.53325, 0.961608, -0.15421],
                  [0.422346, 0.000152593, -0.640675, -0.0401318, 0.255654, -0.319132, -0.346294, 0.429853, 0.696585,
                   -0.924619, 0.510239, -0.833552, -0.709037, 0.710685],
                  [-0.147618, 0.884396, -0.560595, 0.753594, -0.924924, 0.712271, 0.814997, 0.00619526, -0.691519,
                   -0.348369, 0.238563, -0.470016, -0.205054, -0.305216],
                  [-0.426069, -0.788629, -0.557665, -0.583789, 0.204199, 0.581652, -0.384991, -0.151402, 0.65331,
                   0.202551, -0.773858, -0.54326, 0.914548, 0.931639],
                  [0.192785, 0.0216987, 0.0480056, -0.622059, 0.316996, 0.247353, 0.611133, 0.862972, -0.344523,
                   0.902341, 0.48265, 0.196509, -0.560472, 0.309366],
                  [-0.355754, -0.41728, -0.391583, -0.00485244, 0.481857, -0.0329905, 0.018891, -0.687368, -0.831904,
                   -0.863643, -0.607715, 0.848323, 0.690664, 0.887265],
                  [-0.936644, -0.572497, -0.913877, 0.571215, -0.408673, 0.529588, -0.555223, -0.667165, -0.702506,
                   0.925901, -0.753655, 0.351054, 0.790948, -0.647023],
                  [-0.409101, -0.60332, 0.544603, 0.0331736, -0.113315, -0.980224, -0.414533, 0.855647, 0.557115,
                   0.677541, 0.3596, -0.970275, -0.66979, 0.116062],
                  [-0.163793, 0.0240181, -0.327189, 0.319437, -0.0879849, 0.602344, 0.930723, -0.663442, -0.820856,
                   -0.229408, 0.739677, -0.699454, -0.881344, 0.445845],
                  [-0.732475, -0.0491653, 0.782708, -0.339518, -0.148656, 0.972594, -0.973449, 0.114658, -0.408673,
                   0.464705, 0.355449, 0.888058, 0.464278, -0.15067],
                  [-0.554491, 0.124607, 0.519211, 0.534837, 0.404279, -0.496994, -0.28251, 0.646107, -0.168859,
                   -0.696036, -0.0200507, -0.867489, -0.258217, -0.112156],
                  [0.00344859, -0.431379, -0.582324, 0.39555, 0.409528, 0.957762, 0.244484, 0.483566, -0.212134,
                   -0.147618, 0.600757, -0.0921964, -0.803827, -0.896542],
                  [0.860286, -0.233436, -0.319559, -0.448836, -0.429975, 0.216895, 0.37608, -0.0306101, 0.866451,
                   0.475448, -0.245155, -0.423322, 0.192358, -0.0823084],
                  [-0.421918, 0.426252, 0.377422, 0.0870083, 0.119358, -0.0128483, -0.85577, 0.425886, 0.219703,
                   -0.770318, 0.102634, -0.456648, 0.736808, 0.52678],
                  [0.294961, 0.829096, 0.951842, 0.684622, 0.35435, 0.228248, 0.495163, -0.585559, 0.339152, 0.988708,
                   0.354472, 0.558824, -0.694754, -0.806452],
                  [-0.472396, 0.383221, -0.320353, 0.891293, 0.881954, 0.247536, 0.496689, 0.635975, 0.78338,
                   -0.0312815, 0.560533, 0.250282, 0.0578936, -0.812983],
                  [-0.404035, -0.376446, 0.847163, -0.950987, 0.449568, 0.357524, 0.92114, -0.48088, 0.404584,
                   0.0722373, 0.0104068, 0.633106, 0.671316, 0.184668],
                  [-0.279458, -0.995178, 0.115818, 0.972411, -0.409101, -0.0998871, 0.289712, 0.734977, 0.860591,
                   0.188696, -0.177282, 0.865474, 0.503586, 0.488449],
                  [-0.758782, -0.355388, -0.903562, -0.187231, 0.275613, 0.570421, -0.919675, -0.965209, 0.717399,
                   0.0346385, 0.979675, 0.480636, 0.890378, 0.160436],
                  [0.140843, -0.0366527, 0.797418, -0.388043, -0.447127, 0.571581, 0.00558489, 0.189367, -0.687551,
                   0.5244, -0.668386, 0.0214545, 0.295877, 0.404523],
                  [0.391156, -0.831599, 0.60094, 0.0838954, 0.0737022, 0.447249, 0.320353, 0.652211, 0.00546281,
                   -0.707511, -0.789789, -0.337565, 0.0636921, -0.535691],
                  [0.815302, -0.994873, 0.00350963, 0.417096, -0.386578, -0.275979, 0.261025, -0.859859, 0.742607,
                   -0.914304, -0.00540178, 0.284463, 0.872433, 0.215491],
                  [-0.573107, -0.613941, -0.217933, -0.387677, 0.550218, -0.999573, -0.791375, 0.855281, -0.742607,
                   0.559069, 0.526841, -0.186682, 0.961791, -0.238868],
                  [-0.176672, -0.327433, 0.766472, 0.313272, -0.0713828, -0.908872, 0.248512, -0.170934, -0.0322581,
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