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Useful to convert (x; y) coordinates to chain-coded coordinates.

Usage

pix2chc(coo)

chc2pix(chc)

Arguments

coo

(x; y) coordinates passed as a matrix

chc

chain coordinates

Value

a matrix or a numeric

Note

Note this function will be deprecated from Momocs when Momacs and Momit will be fully operationnal.

References

Kuhl, F. P., & Giardina, C. R. (1982). Elliptic Fourier features of a closed contour. Computer Graphics and Image Processing, 18(3), 236-258.

See also

Examples

pix2chc(shapes[1]) %T>% print %>% # from pix to chc
chc2pix()                         # and back
#>   [1] 5 4 3 2 4 4 3 4 4 3 4 4 3 4 3 3 4 3 4 3 3 4 3 3 3 4 3 3 3 3 3 3 3 3 3 2 3
#>  [38] 3 3 2 3 3 2 3 3 2 3 2 3 2 3 3 2 3 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 3 2 2 2 2
#>  [75] 2 3 2 1 2 3 2 2 2 2 3 2 2 2 3 2 3 2 3 4 3 4 4 4 4 3 4 4 5 4 4 4 5 4 5 5 5
#> [112] 5 5 5 6 5 5 6 5 5 6 5 6 5 6 5 5 5 6 5 5 5 5 5 5 5 5 4 5 4 5 4 5 4 5 4 5 4
#> [149] 4 4 5 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
#> [186] 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
#> [223] 2 2 2 2 2 2 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [260] 1 0 1 1 1 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 1 1 2 1 1 1 1 1 0 1 1 0 1 0 1 0
#> [297] 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [334] 0 7 0 0 0 7 0 0 0 7 0 7 0 7 0 7 0 7 0 7 7 7 7 0 7 7 6 7 7 7 7 6 7 7 6 7 7
#> [371] 6 7 6 6 7 6 7 6 6 7 6 6 7 6 6 7 6 6 6 7 6 6 7 6 6 6 7 6 6 6 7 6 6 6 7 6 6
#> [408] 6 7 6 6 7 6 7 6 7 6 7 7 7 7 7 0 0 7 0 0 1 0 0 1 0 1 1 1 2 1 2 1 2 1 2 1 2
#> [445] 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 1 1 2 1 1 1 1 1 1 0 1 1 0
#> [482] 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [519] 0 0 1 7 1 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2 2
#> [556] 2 2 1 2 1 1 0 0 0 0 1 7 0 7 0 7 0 7 7 0 7 7 0 7 7 7 0 7 7 0 7 7 7 0 7 7 0
#> [593] 7 7 0 7 7 7 0 7 7 0 7 7 7 0 7 7 0 7 7 0 7 7 7 0 7 7 0 7 7 7 0 7 7 0 7 7 0
#> [630] 7 7 7 0 7 7 0 7 7 7 0 7 7 0 7 7 0 7 7 7 0 7 7 0 7 5 5 5 4 5 5 4 5 5 5 4 5
#> [667] 5 4 5 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5
#> [704] 5 4 5 5 5 4 5 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 4 5
#> [741] 4 4 4 5 3 4 3 3 3 3 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1
#> [778] 2 2 2 1 2 2 1 3 4 4 3 4 4 4 4 4 4 4 4 5 4 4 4 5 4 5 5 6 6 5 6 6 5 6 5 6 6
#> [815] 5 6 5 6 6 5 6 5 6 6 5 6 5 6 5 6 5 6 5 5 6 5 6 5 5 5 6 5 5 5 5 5 5 5 5 5 5
#> [852] 4 5 4 5 5 4 5 4 5 4 4 5 4 4 4 5 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
#>        [,1] [,2]
#>   [1,]   -1   -1
#>   [2,]   -2   -1
#>   [3,]   -3    0
#>   [4,]   -3    1
#>   [5,]   -4    1
#>   [6,]   -5    1
#>   [7,]   -6    2
#>   [8,]   -7    2
#>   [9,]   -8    2
#>  [10,]   -9    3
#>  [11,]  -10    3
#>  [12,]  -11    3
#>  [13,]  -12    4
#>  [14,]  -13    4
#>  [15,]  -14    5
#>  [16,]  -15    6
#>  [17,]  -16    6
#>  [18,]  -17    7
#>  [19,]  -18    7
#>  [20,]  -19    8
#>  [21,]  -20    9
#>  [22,]  -21    9
#>  [23,]  -22   10
#>  [24,]  -23   11
#>  [25,]  -24   12
#>  [26,]  -25   12
#>  [27,]  -26   13
#>  [28,]  -27   14
#>  [29,]  -28   15
#>  [30,]  -29   16
#>  [31,]  -30   17
#>  [32,]  -31   18
#>  [33,]  -32   19
#>  [34,]  -33   20
#>  [35,]  -34   21
#>  [36,]  -34   22
#>  [37,]  -35   23
#>  [38,]  -36   24
#>  [39,]  -37   25
#>  [40,]  -37   26
#>  [41,]  -38   27
#>  [42,]  -39   28
#>  [43,]  -39   29
#>  [44,]  -40   30
#>  [45,]  -41   31
#>  [46,]  -41   32
#>  [47,]  -42   33
#>  [48,]  -42   34
#>  [49,]  -43   35
#>  [50,]  -43   36
#>  [51,]  -44   37
#>  [52,]  -45   38
#>  [53,]  -45   39
#>  [54,]  -46   40
#>  [55,]  -46   41
#>  [56,]  -46   42
#>  [57,]  -47   43
#>  [58,]  -47   44
#>  [59,]  -47   45
#>  [60,]  -48   46
#>  [61,]  -48   47
#>  [62,]  -48   48
#>  [63,]  -48   49
#>  [64,]  -48   50
#>  [65,]  -49   51
#>  [66,]  -49   52
#>  [67,]  -49   53
#>  [68,]  -49   54
#>  [69,]  -49   55
#>  [70,]  -50   56
#>  [71,]  -50   57
#>  [72,]  -50   58
#>  [73,]  -50   59
#>  [74,]  -50   60
#>  [75,]  -50   61
#>  [76,]  -51   62
#>  [77,]  -51   63
#>  [78,]  -50   64
#>  [79,]  -50   65
#>  [80,]  -51   66
#>  [81,]  -51   67
#>  [82,]  -51   68
#>  [83,]  -51   69
#>  [84,]  -51   70
#>  [85,]  -52   71
#>  [86,]  -52   72
#>  [87,]  -52   73
#>  [88,]  -52   74
#>  [89,]  -53   75
#>  [90,]  -53   76
#>  [91,]  -54   77
#>  [92,]  -54   78
#>  [93,]  -55   79
#>  [94,]  -56   79
#>  [95,]  -57   80
#>  [96,]  -58   80
#>  [97,]  -59   80
#>  [98,]  -60   80
#>  [99,]  -61   80
#> [100,]  -62   81
#> [101,]  -63   81
#> [102,]  -64   81
#> [103,]  -65   80
#> [104,]  -66   80
#> [105,]  -67   80
#> [106,]  -68   80
#> [107,]  -69   79
#> [108,]  -70   79
#> [109,]  -71   78
#> [110,]  -72   77
#> [111,]  -73   76
#> [112,]  -74   75
#> [113,]  -75   74
#> [114,]  -76   73
#> [115,]  -76   72
#> [116,]  -77   71
#> [117,]  -78   70
#> [118,]  -78   69
#> [119,]  -79   68
#> [120,]  -80   67
#> [121,]  -80   66
#> [122,]  -81   65
#> [123,]  -81   64
#> [124,]  -82   63
#> [125,]  -82   62
#> [126,]  -83   61
#> [127,]  -84   60
#> [128,]  -85   59
#> [129,]  -85   58
#> [130,]  -86   57
#> [131,]  -87   56
#> [132,]  -88   55
#> [133,]  -89   54
#> [134,]  -90   53
#> [135,]  -91   52
#> [136,]  -92   51
#> [137,]  -93   50
#> [138,]  -94   50
#> [139,]  -95   49
#> [140,]  -96   49
#> [141,]  -97   48
#> [142,]  -98   48
#> [143,]  -99   47
#> [144,] -100   47
#> [145,] -101   46
#> [146,] -102   46
#> [147,] -103   45
#> [148,] -104   45
#> [149,] -105   45
#> [150,] -106   45
#> [151,] -107   44
#> [152,] -108   44
#> [153,] -109   44
#> [154,] -110   44
#> [155,] -111   44
#> [156,] -112   44
#> [157,] -113   43
#> [158,] -114   43
#> [159,] -115   43
#> [160,] -116   43
#> [161,] -117   43
#> [162,] -118   43
#> [163,] -119   43
#> [164,] -120   43
#> [165,] -121   43
#> [166,] -122   43
#> [167,] -123   43
#> [168,] -124   43
#> [169,] -125   43
#> [170,] -126   43
#> [171,] -127   43
#> [172,] -128   43
#> [173,] -129   43
#> [174,] -130   43
#> [175,] -131   43
#> [176,] -132   43
#> [177,] -133   43
#> [178,] -134   43
#> [179,] -135   43
#> [180,] -136   43
#> [181,] -137   43
#> [182,] -138   43
#> [183,] -139   43
#> [184,] -140   43
#> [185,] -141   43
#> [186,] -142   43
#> [187,] -143   43
#> [188,] -144   43
#> [189,] -145   43
#> [190,] -146   44
#> [191,] -146   45
#> [192,] -146   46
#> [193,] -146   47
#> [194,] -146   48
#> [195,] -146   49
#> [196,] -146   50
#> [197,] -146   51
#> [198,] -146   52
#> [199,] -146   53
#> [200,] -146   54
#> [201,] -146   55
#> [202,] -146   56
#> [203,] -146   57
#> [204,] -146   58
#> [205,] -146   59
#> [206,] -146   60
#> [207,] -146   61
#> [208,] -146   62
#> [209,] -146   63
#> [210,] -146   64
#> [211,] -146   65
#> [212,] -146   66
#> [213,] -146   67
#> [214,] -146   68
#> [215,] -146   69
#> [216,] -146   70
#> [217,] -146   71
#> [218,] -146   72
#> [219,] -146   73
#> [220,] -146   74
#> [221,] -146   75
#> [222,] -146   76
#> [223,] -146   77
#> [224,] -146   78
#> [225,] -146   79
#> [226,] -146   80
#> [227,] -146   81
#> [228,] -146   82
#> [229,] -146   83
#> [230,] -146   84
#> [231,] -146   85
#> [232,] -146   86
#> [233,] -145   87
#> [234,] -144   87
#> [235,] -143   87
#> [236,] -142   87
#> [237,] -141   87
#> [238,] -140   87
#> [239,] -139   87
#> [240,] -138   87
#> [241,] -137   87
#> [242,] -136   87
#> [243,] -135   87
#> [244,] -134   87
#> [245,] -133   87
#> [246,] -132   87
#> [247,] -131   87
#> [248,] -130   87
#> [249,] -129   87
#> [250,] -128   87
#> [251,] -127   87
#> [252,] -126   87
#> [253,] -125   87
#> [254,] -124   87
#> [255,] -123   87
#> [256,] -122   87
#> [257,] -121   87
#> [258,] -120   87
#> [259,] -119   87
#> [260,] -118   88
#> [261,] -117   88
#> [262,] -116   89
#> [263,] -115   90
#> [264,] -114   91
#> [265,] -113   92
#> [266,] -112   93
#> [267,] -112   94
#> [268,] -111   95
#> [269,] -111   96
#> [270,] -110   97
#> [271,] -110   98
#> [272,] -109   99
#> [273,] -108  100
#> [274,] -108  101
#> [275,] -107  102
#> [276,] -107  103
#> [277,] -106  104
#> [278,] -105  105
#> [279,] -105  106
#> [280,] -104  107
#> [281,] -103  108
#> [282,] -102  109
#> [283,] -102  110
#> [284,] -101  111
#> [285,] -100  112
#> [286,]  -99  113
#> [287,]  -98  114
#> [288,]  -97  115
#> [289,]  -96  115
#> [290,]  -95  116
#> [291,]  -94  117
#> [292,]  -93  117
#> [293,]  -92  118
#> [294,]  -91  118
#> [295,]  -90  119
#> [296,]  -89  119
#> [297,]  -88  120
#> [298,]  -87  120
#> [299,]  -86  121
#> [300,]  -85  121
#> [301,]  -84  122
#> [302,]  -83  122
#> [303,]  -82  122
#> [304,]  -81  122
#> [305,]  -80  123
#> [306,]  -79  123
#> [307,]  -78  123
#> [308,]  -77  123
#> [309,]  -76  123
#> [310,]  -75  124
#> [311,]  -74  124
#> [312,]  -73  124
#> [313,]  -72  124
#> [314,]  -71  124
#> [315,]  -70  124
#> [316,]  -69  124
#> [317,]  -68  124
#> [318,]  -67  124
#> [319,]  -66  124
#> [320,]  -65  124
#> [321,]  -64  124
#> [322,]  -63  124
#> [323,]  -62  124
#> [324,]  -61  124
#> [325,]  -60  124
#> [326,]  -59  124
#> [327,]  -58  124
#> [328,]  -57  124
#> [329,]  -56  124
#> [330,]  -55  124
#> [331,]  -54  124
#> [332,]  -53  124
#> [333,]  -52  124
#> [334,]  -51  124
#> [335,]  -50  123
#> [336,]  -49  123
#> [337,]  -48  123
#> [338,]  -47  123
#> [339,]  -46  122
#> [340,]  -45  122
#> [341,]  -44  122
#> [342,]  -43  122
#> [343,]  -42  121
#> [344,]  -41  121
#> [345,]  -40  120
#> [346,]  -39  120
#> [347,]  -38  119
#> [348,]  -37  119
#> [349,]  -36  118
#> [350,]  -35  118
#> [351,]  -34  117
#> [352,]  -33  117
#> [353,]  -32  116
#> [354,]  -31  115
#> [355,]  -30  114
#> [356,]  -29  113
#> [357,]  -28  113
#> [358,]  -27  112
#> [359,]  -26  111
#> [360,]  -26  110
#> [361,]  -25  109
#> [362,]  -24  108
#> [363,]  -23  107
#> [364,]  -22  106
#> [365,]  -22  105
#> [366,]  -21  104
#> [367,]  -20  103
#> [368,]  -20  102
#> [369,]  -19  101
#> [370,]  -18  100
#> [371,]  -18   99
#> [372,]  -17   98
#> [373,]  -17   97
#> [374,]  -17   96
#> [375,]  -16   95
#> [376,]  -16   94
#> [377,]  -15   93
#> [378,]  -15   92
#> [379,]  -15   91
#> [380,]  -14   90
#> [381,]  -14   89
#> [382,]  -14   88
#> [383,]  -13   87
#> [384,]  -13   86
#> [385,]  -13   85
#> [386,]  -12   84
#> [387,]  -12   83
#> [388,]  -12   82
#> [389,]  -12   81
#> [390,]  -11   80
#> [391,]  -11   79
#> [392,]  -11   78
#> [393,]  -10   77
#> [394,]  -10   76
#> [395,]  -10   75
#> [396,]  -10   74
#> [397,]   -9   73
#> [398,]   -9   72
#> [399,]   -9   71
#> [400,]   -9   70
#> [401,]   -8   69
#> [402,]   -8   68
#> [403,]   -8   67
#> [404,]   -8   66
#> [405,]   -7   65
#> [406,]   -7   64
#> [407,]   -7   63
#> [408,]   -7   62
#> [409,]   -6   61
#> [410,]   -6   60
#> [411,]   -6   59
#> [412,]   -5   58
#> [413,]   -5   57
#> [414,]   -4   56
#> [415,]   -4   55
#> [416,]   -3   54
#> [417,]   -3   53
#> [418,]   -2   52
#> [419,]   -1   51
#> [420,]    0   50
#> [421,]    1   49
#> [422,]    2   48
#> [423,]    3   48
#> [424,]    4   48
#> [425,]    5   47
#> [426,]    6   47
#> [427,]    7   47
#> [428,]    8   48
#> [429,]    9   48
#> [430,]   10   48
#> [431,]   11   49
#> [432,]   12   49
#> [433,]   13   50
#> [434,]   14   51
#> [435,]   15   52
#> [436,]   15   53
#> [437,]   16   54
#> [438,]   16   55
#> [439,]   17   56
#> [440,]   17   57
#> [441,]   18   58
#> [442,]   18   59
#> [443,]   19   60
#> [444,]   19   61
#> [445,]   19   62
#> [446,]   20   63
#> [447,]   20   64
#> [448,]   20   65
#> [449,]   21   66
#> [450,]   21   67
#> [451,]   21   68
#> [452,]   22   69
#> [453,]   22   70
#> [454,]   22   71
#> [455,]   23   72
#> [456,]   23   73
#> [457,]   24   74
#> [458,]   24   75
#> [459,]   24   76
#> [460,]   25   77
#> [461,]   25   78
#> [462,]   26   79
#> [463,]   26   80
#> [464,]   27   81
#> [465,]   27   82
#> [466,]   28   83
#> [467,]   28   84
#> [468,]   29   85
#> [469,]   30   86
#> [470,]   31   87
#> [471,]   31   88
#> [472,]   32   89
#> [473,]   33   90
#> [474,]   34   91
#> [475,]   35   92
#> [476,]   36   93
#> [477,]   37   94
#> [478,]   38   94
#> [479,]   39   95
#> [480,]   40   96
#> [481,]   41   96
#> [482,]   42   97
#> [483,]   43   97
#> [484,]   44   98
#> [485,]   45   98
#> [486,]   46   99
#> [487,]   47   99
#> [488,]   48   99
#> [489,]   49  100
#> [490,]   50  100
#> [491,]   51  100
#> [492,]   52  100
#> [493,]   53  101
#> [494,]   54  101
#> [495,]   55  101
#> [496,]   56  101
#> [497,]   57  101
#> [498,]   58  101
#> [499,]   59  101
#> [500,]   60  101
#> [501,]   61  101
#> [502,]   62  101
#> [503,]   63  101
#> [504,]   64  101
#> [505,]   65  101
#> [506,]   66  101
#> [507,]   67  101
#> [508,]   68  101
#> [509,]   69  101
#> [510,]   70  101
#> [511,]   71  101
#> [512,]   72  101
#> [513,]   73  101
#> [514,]   74  101
#> [515,]   75  101
#> [516,]   76  101
#> [517,]   77  101
#> [518,]   78  101
#> [519,]   79  101
#> [520,]   80  101
#> [521,]   81  102
#> [522,]   82  101
#> [523,]   83  102
#> [524,]   82  103
#> [525,]   82  104
#> [526,]   82  105
#> [527,]   82  106
#> [528,]   81  107
#> [529,]   81  108
#> [530,]   81  109
#> [531,]   81  110
#> [532,]   80  111
#> [533,]   80  112
#> [534,]   80  113
#> [535,]   80  114
#> [536,]   79  115
#> [537,]   79  116
#> [538,]   79  117
#> [539,]   78  118
#> [540,]   78  119
#> [541,]   78  120
#> [542,]   78  121
#> [543,]   77  122
#> [544,]   77  123
#> [545,]   77  124
#> [546,]   77  125
#> [547,]   76  126
#> [548,]   76  127
#> [549,]   76  128
#> [550,]   76  129
#> [551,]   76  130
#> [552,]   75  131
#> [553,]   75  132
#> [554,]   75  133
#> [555,]   75  134
#> [556,]   75  135
#> [557,]   75  136
#> [558,]   76  137
#> [559,]   76  138
#> [560,]   77  139
#> [561,]   78  140
#> [562,]   79  140
#> [563,]   80  140
#> [564,]   81  140
#> [565,]   82  140
#> [566,]   83  141
#> [567,]   84  140
#> [568,]   85  140
#> [569,]   86  139
#> [570,]   87  139
#> [571,]   88  138
#> [572,]   89  138
#> [573,]   90  137
#> [574,]   91  136
#> [575,]   92  136
#> [576,]   93  135
#> [577,]   94  134
#> [578,]   95  134
#> [579,]   96  133
#> [580,]   97  132
#> [581,]   98  131
#> [582,]   99  131
#> [583,]  100  130
#> [584,]  101  129
#> [585,]  102  129
#> [586,]  103  128
#> [587,]  104  127
#> [588,]  105  126
#> [589,]  106  126
#> [590,]  107  125
#> [591,]  108  124
#> [592,]  109  124
#> [593,]  110  123
#> [594,]  111  122
#> [595,]  112  122
#> [596,]  113  121
#> [597,]  114  120
#> [598,]  115  119
#> [599,]  116  119
#> [600,]  117  118
#> [601,]  118  117
#> [602,]  119  117
#> [603,]  120  116
#> [604,]  121  115
#> [605,]  122  114
#> [606,]  123  114
#> [607,]  124  113
#> [608,]  125  112
#> [609,]  126  112
#> [610,]  127  111
#> [611,]  128  110
#> [612,]  129  110
#> [613,]  130  109
#> [614,]  131  108
#> [615,]  132  107
#> [616,]  133  107
#> [617,]  134  106
#> [618,]  135  105
#> [619,]  136  105
#> [620,]  137  104
#> [621,]  138  103
#> [622,]  139  102
#> [623,]  140  102
#> [624,]  141  101
#> [625,]  142  100
#> [626,]  143  100
#> [627,]  144   99
#> [628,]  145   98
#> [629,]  146   98
#> [630,]  147   97
#> [631,]  148   96
#> [632,]  149   95
#> [633,]  150   95
#> [634,]  151   94
#> [635,]  152   93
#> [636,]  153   93
#> [637,]  154   92
#> [638,]  155   91
#> [639,]  156   90
#> [640,]  157   90
#> [641,]  158   89
#> [642,]  159   88
#> [643,]  160   88
#> [644,]  161   87
#> [645,]  162   86
#> [646,]  163   86
#> [647,]  164   85
#> [648,]  165   84
#> [649,]  166   83
#> [650,]  167   83
#> [651,]  168   82
#> [652,]  169   81
#> [653,]  170   81
#> [654,]  171   80
#> [655,]  170   79
#> [656,]  169   78
#> [657,]  168   77
#> [658,]  167   77
#> [659,]  166   76
#> [660,]  165   75
#> [661,]  164   75
#> [662,]  163   74
#> [663,]  162   73
#> [664,]  161   72
#> [665,]  160   72
#> [666,]  159   71
#> [667,]  158   70
#> [668,]  157   70
#> [669,]  156   69
#> [670,]  155   68
#> [671,]  154   67
#> [672,]  153   67
#> [673,]  152   66
#> [674,]  151   65
#> [675,]  150   65
#> [676,]  149   64
#> [677,]  148   63
#> [678,]  147   63
#> [679,]  146   62
#> [680,]  145   61
#> [681,]  144   60
#> [682,]  143   60
#> [683,]  142   59
#> [684,]  141   58
#> [685,]  140   58
#> [686,]  139   57
#> [687,]  138   56
#> [688,]  137   55
#> [689,]  136   55
#> [690,]  135   54
#> [691,]  134   53
#> [692,]  133   53
#> [693,]  132   52
#> [694,]  131   51
#> [695,]  130   51
#> [696,]  129   50
#> [697,]  128   49
#> [698,]  127   48
#> [699,]  126   48
#> [700,]  125   47
#> [701,]  124   46
#> [702,]  123   46
#> [703,]  122   45
#> [704,]  121   44
#> [705,]  120   44
#> [706,]  119   43
#> [707,]  118   42
#> [708,]  117   41
#> [709,]  116   41
#> [710,]  115   40
#> [711,]  114   39
#> [712,]  113   38
#> [713,]  112   38
#> [714,]  111   37
#> [715,]  110   36
#> [716,]  109   36
#> [717,]  108   35
#> [718,]  107   34
#> [719,]  106   34
#> [720,]  105   33
#> [721,]  104   32
#> [722,]  103   31
#> [723,]  102   31
#> [724,]  101   30
#> [725,]  100   29
#> [726,]   99   29
#> [727,]   98   28
#> [728,]   97   27
#> [729,]   96   27
#> [730,]   95   26
#> [731,]   94   25
#> [732,]   93   24
#> [733,]   92   24
#> [734,]   91   23
#> [735,]   90   22
#> [736,]   89   22
#> [737,]   88   21
#> [738,]   87   20
#> [739,]   86   20
#> [740,]   85   19
#> [741,]   84   19
#> [742,]   83   19
#> [743,]   82   19
#> [744,]   81   18
#> [745,]   80   19
#> [746,]   79   19
#> [747,]   78   20
#> [748,]   77   21
#> [749,]   76   22
#> [750,]   75   23
#> [751,]   75   24
#> [752,]   75   25
#> [753,]   75   26
#> [754,]   75   27
#> [755,]   75   28
#> [756,]   75   29
#> [757,]   75   30
#> [758,]   76   31
#> [759,]   76   32
#> [760,]   76   33
#> [761,]   77   34
#> [762,]   77   35
#> [763,]   77   36
#> [764,]   77   37
#> [765,]   78   38
#> [766,]   78   39
#> [767,]   78   40
#> [768,]   78   41
#> [769,]   79   42
#> [770,]   79   43
#> [771,]   79   44
#> [772,]   79   45
#> [773,]   80   46
#> [774,]   80   47
#> [775,]   80   48
#> [776,]   80   49
#> [777,]   81   50
#> [778,]   81   51
#> [779,]   81   52
#> [780,]   81   53
#> [781,]   82   54
#> [782,]   82   55
#> [783,]   82   56
#> [784,]   83   57
#> [785,]   82   58
#> [786,]   81   58
#> [787,]   80   58
#> [788,]   79   59
#> [789,]   78   59
#> [790,]   77   59
#> [791,]   76   59
#> [792,]   75   59
#> [793,]   74   59
#> [794,]   73   59
#> [795,]   72   59
#> [796,]   71   59
#> [797,]   70   58
#> [798,]   69   58
#> [799,]   68   58
#> [800,]   67   58
#> [801,]   66   57
#> [802,]   65   57
#> [803,]   64   56
#> [804,]   63   55
#> [805,]   63   54
#> [806,]   63   53
#> [807,]   62   52
#> [808,]   62   51
#> [809,]   62   50
#> [810,]   61   49
#> [811,]   61   48
#> [812,]   60   47
#> [813,]   60   46
#> [814,]   60   45
#> [815,]   59   44
#> [816,]   59   43
#> [817,]   58   42
#> [818,]   58   41
#> [819,]   58   40
#> [820,]   57   39
#> [821,]   57   38
#> [822,]   56   37
#> [823,]   56   36
#> [824,]   56   35
#> [825,]   55   34
#> [826,]   55   33
#> [827,]   54   32
#> [828,]   54   31
#> [829,]   53   30
#> [830,]   53   29
#> [831,]   52   28
#> [832,]   52   27
#> [833,]   51   26
#> [834,]   50   25
#> [835,]   50   24
#> [836,]   49   23
#> [837,]   49   22
#> [838,]   48   21
#> [839,]   47   20
#> [840,]   46   19
#> [841,]   46   18
#> [842,]   45   17
#> [843,]   44   16
#> [844,]   43   15
#> [845,]   42   14
#> [846,]   41   13
#> [847,]   40   12
#> [848,]   39   11
#> [849,]   38   10
#> [850,]   37    9
#> [851,]   36    8
#> [852,]   35    8
#> [853,]   34    7
#> [854,]   33    7
#> [855,]   32    6
#> [856,]   31    5
#> [857,]   30    5
#> [858,]   29    4
#> [859,]   28    4
#> [860,]   27    3
#> [861,]   26    3
#> [862,]   25    3
#> [863,]   24    2
#> [864,]   23    2
#> [865,]   22    2
#> [866,]   21    2
#> [867,]   20    1
#> [868,]   19    1
#> [869,]   18    1
#> [870,]   17    1
#> [871,]   16    1
#> [872,]   15    0
#> [873,]   14    0
#> [874,]   13    0
#> [875,]   12    0
#> [876,]   11    0
#> [877,]   10    0
#> [878,]    9    0
#> [879,]    8    0
#> [880,]    7    0
#> [881,]    6    0
#> [882,]    5    0
#> [883,]    4    0
#> [884,]    3    0
#> [885,]    2    0
#> [886,]    1    0
#> [887,]    0    0