import numpy as np

### 1: IH
### 2: EH
### 3: AE
### 4: AO
### 6: AH
### 7: UH
###
### 11: iyC beat
### 12: iyF be
### 21: eyC bait
### 22: eyF bay
### 41: ayV buy
### 47: ayO bite
### 61: oy boy
### 42: aw bough
### 62: owC boat
### 63: owF bow
### 72: uwC boot
### 73: uwF too
### 82: iw suit
### 43: ah father
### 53: oh bought


MEANS = {'1':   [525.2877,   1941.229,   4.429892,   4.79822],
        '2':    [663.079,    1847.689,   4.542639,    4.867548],
        '3':    [728.7752,   1893.15,    4.615404,    4.989836],
        '5':    [810.9155,   1336.642,   4.839556,    4.933221],
        '6':    [714.8795,   1448.528,   4.671836,    4.831577],
        '7':    [543.7372,   1288.546,   4.424041,    4.69879],
        '11':   [411.3944,   2275.093,   4.39259, 4.796765],
        '12':   [440.3333,   2197.091,   4.476098,    4.667141],
        '14':   [441.1307,   2233.011,   4.403062,    4.860253],
        '21':   [599.2163,   1978.542,   4.40423, 4.894037],
        '22':   [592.5507,   1959.899,   4.087865,    4.802181],
        '24':   [569.8613,   1991.994,   4.516866,    4.941955],
        '33':   [620.1378,   2059.224,   4.347911,    5.027536],
        '39':   [766.087,    1829.261,   4.693657,    5.013284],
        '41':   [808.0645,   1449.711,   4.8443,  4.95776],
        '42':   [782.8331,   1672.451,   4.788051,    5.007045],
        '43':   [780.8631,   1326.295,   4.705,   4.908504],
        '44':   [718.2819,   1273.59,    4.702502,    4.840136],
        '47':   [777.8737,   1478.317,   4.718795,    4.919554],
        '53':   [740.2186,   1167.617,   4.744859,    4.794929],
        '54':   [557.1122,   975.9273,   4.660808,    4.762645],
        '61':   [539.7747,   982.9505,   4.592872,    4.76811],
        '62':   [628.9169,   1342.568,   4.514038,    4.772455],
        '63':   [620.0192,   1332.923,   4.057321,    4.700364],
        '64':   [528.9181,   953.4962,   4.608001,    4.762555],
        '72':   [452.4824,   1282.609,   4.364288,    4.775122],
        '73':   [445.9345,   1819.35,    4.312133,    4.828277],
        '74':   [467.2353,   1204.176,   4.356453,   4.634414],
        '82':   [416.0622,   1873.91,    4.364174,   4.858582],
        '94':   [553.9443,   1486.107,   4.564759,   4.965292]}

COVS = {'1':    np.matrix([[8156.961,4075.974,13.05440,6.823964],
                            [4075.974,85957.07,23.81249,31.39354],
                            [13.05440,23.81249,0.425308,0.02637788],
                            [6.823964,31.39354,0.02637788,0.2685742]]),
        '2':    np.matrix([[12610.98,   4598.212,   15.72022,   10.93343],
                            [4598.212,  76695.1,    35.53953,   32.24821],
                            [15.72022,  35.53953,   0.3856857,  0.04138077],
                            [10.93343,  32.24821,   0.04138077, 0.2402458]]),
        '3':    np.matrix([[20287.03,   -945.841,   23.69788,   19.12778],
                            [-945.841,  85500.7,    32.35261,   42.61164],
                            [23.69788,  32.35261,   0.408185,   0.05798509],
                            [19.12778,  42.61164,   0.05798509, 0.2402007]]),
        '5':    np.matrix([[14899.38,   14764.41,   31.29953,   25.64715],
                            [14764.41,  33089.55,   30.80144,   35.65717],
                            [31.29953,  30.80144,   0.3399745,  0.1391051],
                            [25.64715,  35.65717,   0.1391051,  0.2939521]]),
        '6':    np.matrix([[10963.32,   11881.45,   24.02174,   14.15601],
                            [11881.45,  50941.8,    30.80307,   29.26477],
                            [24.02174,  30.80307,   0.356582,   0.08377454],
                            [14.15601,  29.26477,   0.08377454, 0.2798376]]),
        '7':    np.matrix([[7374.7, 6907.065,   14.77475,   6.575189],
                            [6907.065,  103775.4,   -6.194884,  33.8729],
                            [14.77475,  -6.194884,  0.3619565,  0.08537324],
                            [6.575189,  33.8729,    0.08537324, 0.3309069]]),
        '11':   np.matrix([[7398.308,   111.3878,   14.47063,   5.261133],
                            [111.3878,  112484.4,   4.204222,   27.97763],
                            [14.47063,  4.204222,   0.439087,   0.01820014],
                            [5.261133,  27.97763,    0.01820014, 0.2864814]]),
        '12':   np.matrix([[8980.604,   16.4375,    12.43177,   6.508381],
                            [16.4375,   68185.02,   -41.39826,  43.07926],
                            [12.43177,  -41.39826,  0.4922286,  0.04943888],
                            [6.508381,  43.07926,   0.04943888, 0.2746969]]),
        '14':   np.matrix([[5766.88,    1678.53,    13.6561,    6.172833],
                            [1678.53,   97981.07,   -18.30658,  5.520951],
                            [13.6561,   -18.30658,  0.391424,   0.02907505],
                            [6.172833,  5.520951,   0.02907505, 0.2467823]]),
        '21':   np.matrix([[11345.63,   902.1107,   15.79774,   8.412416],
                            [902.1107,  94016.08,   21.16553,   52.47692],
                            [15.79774,  21.16553,   0.3749903,  0.04202547],
                            [8.412416,  52.47692,   0.04202547, 0.2549386]]),
        '22':   np.matrix([[7981.016,   7101.174,   15.52651,   7.784475],
                            [7101.174,  67936.53,   30.4288,    81.06186],
                            [15.52651,  30.4288,    0.4057237,  0.07124884],
                            [7.784475,  81.06186,   0.07124884, 0.4493804]]),
        '24':   np.matrix([[7187.811,   4778.768,   11.81843,   8.616023],
                            [4778.768,  97292.62,   24.02699,   46.71447],
                            [11.81843,  24.02699,   0.3862976,  0.05487306],
                            [8.616023,  46.71447,   0.05487306, 0.2361443]]),
        '33':   np.matrix([[13020.63,   -808.1123,  24.56315,   8.443287],
                            [-808.1123, 86325.97,   40.21192,   34.7022],
                            [24.56315,  40.21192,   0.4743995,  0.04472998],
                            [8.443287,  34.7022,    0.04472998, 0.2473551]]),
        '39':   np.matrix([[9703.72,    5470.067,   24.62053,   27.96038],
                            [5470.067,  24951.84,   1.931964,   29.95240],
                            [24.62053,  1.931964,   0.2513445,  0.06440874],
                            [27.96038,  29.95240,   0.06440874, 0.1886862]]),
        '41':   np.matrix([[15762.87,   13486.23,   34.61164,   22.15451],
                            [13486.23,  36003.67,   33.8431,    30.52712],
                            [34.61164,  33.8431,    0.4143354,  0.1125765],
                            [22.15451,  30.52712,   0.1125765,  0.2592451]]),
        '42':   np.matrix([[17034.35,   8582.368,   28.08871,   21.32564],
                            [8582.368,  83324.55,   22.75919,   38.33975],
                            [28.08871,  22.75919,   0.3619946,  0.06974927],
                            [21.32564,  38.33975,   0.06974927, 0.2425371]]),
        '43':   np.matrix([[12651.21,   14322.93,   32.66122,   27.76152],
                            [14322.93,  31322.54,   35.98834,   42.55531],
                            [32.66122,  35.98834,   0.3651260,  0.1821268],
                            [27.76152,  42.55531,   0.1821268,  0.3104338]]),
        '44':   np.matrix([[11222.69,   12217.39,   25.91937,   20.97844],
                            [12217.39,  42712.38,   31.49909,   51.63623],
                            [25.91937,  31.49909,   0.3007976,  0.1284959],
                            [20.97844,  51.63623,   0.1284959,  0.3128419]]),
        '47':   np.matrix([[14093.57,   9982.23,    34.45142,   19.68046],
                            [9982.23,   45110.74,   35.51612,   32.38417],
                            [34.45142,  35.51612,   0.3875129,  0.1126590],
                            [19.68046,  32.38417,   0.1126590,  0.2684052]]),
        '53':   np.matrix([[13901.81,   14774.98,   29.65039,   23.37561],
                            [14774.98,  28293.08,   26.55524,   28.10525],
                            [29.65039,  26.55524,   0.3192664,  0.1368551],
                            [23.37561,  28.10525,   0.1368551,  0.3102375]]),
        '54':   np.matrix([[9024.312,   11004.40,   14.01676,   6.774474],
                            [11004.40,  31347.50,   0.5099728,  1.338353],
                            [14.01676,  0.5099728,  0.3226124,  0.1001887],
                            [6.774474,  1.338353,   0.1001887,  0.3517336]]),
        '61':   np.matrix([[8717.966,   8360.663,   9.581423,   -3.629271],
                            [8360.663,  32997.70,   -18.37126,  -13.78926],
                            [9.581423,  -18.37126,  0.31812,    0.09862598],
                            [-3.629271, -13.78926,  0.09862598, 0.3626406]]),
        '62':   np.matrix([[11036.78,   18957.63,   21.16886,   10.91295],
                            [18957.63,  86701.64,   15.58485,   35.06782],
                            [21.16886,  15.58485,   0.3620286,  0.08347947],
                            [10.91295,  35.06782,   0.08347947, 0.2859568]]),
        '63':   np.matrix([[11190.96,   16442.24,   34.42818,   9.032116],
                            [16442.24,  53108.15,   44.34654,   47.59889],
                            [34.42818,  44.34654,   0.2837371,  -0.000626268],
        '72':   np.matrix([[5302.16,    8112.09,    11.229, -1.767770],
                            [8112.09,   142019.8,   -1.869954,  25.76638],
                            [11.229,    -1.869954,  0.4222974,  0.03546093],
                            [-1.767770, 25.76638,   0.03546093, 0.3773977]]),
        '73':   np.matrix([[5441.397,   6032.27,    6.348957,   0.7710968],
                            [6032.27,   89482.47,   -10.52576,  19.44117],
                            [6.348957,  -10.52576,  0.418909,   0.01018179],
                            [0.7710968, 19.44117,   0.01018179, 0.2577171]]),
        '74':   np.matrix([[3658.316,   -3584.357,  6.224247,   9.464968],
                            [-3584.357, 51303.03,   -78.23124,  26.34888],
                            [6.224247,  -78.23124,  0.3590685,  0.04111837],
                            [9.464968,  26.34888,   0.04111837, 0.2657895]]),
        '82':   np.matrix([[5067.216,   3725.284,   8.112584,   -2.087986],
                            [3725.284,  95441.09,   4.191305,   8.484181],
                            [8.112584,  4.191305,   0.4392269,  0.02049446],
                            [-2.087986, 8.484181,   0.02049446, 0.284428]]),
        '94':   np.matrix([[7035.538,   4075.101,   14.86012,   4.748889],
                            [4075.101,  41818.21,   26.42395,   26.1902],
                            [14.86012,  26.42395,   0.3585293,  0.03962729],
                            [4.748889,  26.1902,    0.03962729, 0.2598092]])}
                            [9.032116,  47.59889,   -0.000626268,   0.4513407]]),
        '64':   np.matrix([[7020.379,   9304.635,   11.09179,   2.643800],
                            [9304.635,  34884.03,   -2.304886,  -0.4383724],
                            [11.09179,  -2.304886,  0.3025123,  0.09179999],
                            [2.643800,  -0.4383724, 0.09179999, 0.3638192]]),