/**
Module implements FAST<sup>[1]</sup> corner detector algorithm - Features from accelerated segment test (FAST) algorithm
discovered and developed by Edward Rosten and Tom Drummond.

This package offers D class interface to machine generated C code, adopted
to D, which is located originally on $(LINK3 https://github.com/edrosten/fast-C-src, Edward Rosten's github).

Copyright: Copyright (c) 2006, 2008 Edward Rosten, Relja Ljubobratovic 2016

Authors: Edward Rosten, Relja Ljubobratovic

License: $(LINK3 http://www.boost.org/LICENSE_1_0.txt, Boost Software License - Version 1.0).

1. Edward Rosten, Tom Drummond (2005). "Fusing points and lines for high performance tracking", IEEE International Conference on Computer Vision 2: 1508–1511.
*/
module dcv.features.corner.fast;

import mir.ndslice;


import dcv.core.image : BitDepth;
import dcv.features.utils : Feature;
import dcv.features.corner.fast.base : xy;
import dcv.features.corner.fast.fast_9;
import dcv.features.corner.fast.fast_10;
import dcv.features.corner.fast.fast_11;
import dcv.features.corner.fast.fast_12;
import dcv.features.corner.fast.nonmax;

public import dcv.features.detector;

/**
FAST corner detector utility.
*/
class FASTDetector : Detector
{
    public
    {
        /// Should the non-maximum suppression be performed with the detection.
        static immutable PERFORM_NON_MAX_SUPRESSION = 0x0100;
        /// Should the features be sorted by score at the output.
        static immutable SORT_OUT_FEATURES_BY_SCORE = 0x0200;
    }

    /// Pixel neighborhood type, described in the paper.
    public enum Type
    {
        FAST_9,
        FAST_10,
        FAST_11,
        FAST_12,
    }

    private
    {
        uint _threshold;
        Type _type;
        int _flags;
    }

    /**
    Default constructor.

    Params:
    threshold = Threshold on pixel intensity difference between central and border pixels.
    type = Pixel neighborhood type.
    flags = Flag value where <i>PERFORM_NON_MAX_SUPRESSION</i> and/or <i>SORT_OUT_FEATURES_BY_SCORE</i> flags can be passed.
    */
    @safe pure nothrow this(uint threshold = 100, Type type = Type.FAST_9, int flags = 0)
    {
        assert(threshold > 0);
        this._threshold = threshold;
        this._type = type;
        this._flags = flags;
    }

    /// Threshold for corner detection.
    auto threshold() const @property @safe pure nothrow @nogc
    {
        return _threshold;
    }
    /// Threshold value setter.
    auto threshold(uint value) @property @safe pure nothrow @nogc
    {
        assert(value > 0);
        _threshold = value;
    }

    /// Type of the detector.
    auto type() const @property @safe pure nothrow @nogc
    {
        return _type;
    }
    /// ditto
    auto type(Type type) @property @safe pure nothrow @nogc
    {
        _type = type;
    }
    /// Algorithm flags.
    auto flags() const @property @safe pure nothrow @nogc
    {
        return _flags;
    }

    /**
    Detect features for given image.

    Params:
    image = Input image where corners are to be found. Only 8-bit mono image is supported as this time.
    count = How many corners are to be found. 

    Returns:
    Array of found feature points.
    */
    override Feature[] detect(in Image image, size_t count = 0) const
    {
        import core.stdc.stdlib : free;
        import std.exception : enforce;
        import std.algorithm : min;

        enforce(image.depth == BitDepth.BD_8, "Invalid bit depth - FAST is supported so " ~ "far only for 8-bit images");
        enforce(image.channels == 1, "Invalid image format - has to be mono");

        Feature[] features; // output features
        int featureCount = 0; // feature count - internal use
        int* featureScore = null; // feature score intenal use
        xy* xyFeatures = null; // xy (feature coordinate) array - internal use

        scope (exit)
        {
            free(featureScore);
            free(xyFeatures);
        }

        xy* function(const ubyte*, int, int, int, int, int*) detectFunc;
        int* function(const ubyte* i, int stride, xy* corners, int num_corners, int b) scoreFunc;

        final switch (_type)
        {
        case Type.FAST_9:
            detectFunc = &fast9_detect;
            scoreFunc = &fast9_score;
            break;
        case Type.FAST_10:
            detectFunc = &fast10_detect;
            scoreFunc = &fast10_score;
            break;
        case Type.FAST_11:
            detectFunc = &fast11_detect;
            scoreFunc = &fast11_score;
            break;
        case Type.FAST_12:
            detectFunc = &fast12_detect;
            scoreFunc = &fast12_score;
        }

        xyFeatures = detectFunc(cast(const ubyte*)image.data.ptr, cast(int)image.width,
                cast(int)image.height, cast(int)image.rowStride, cast(int)threshold, &featureCount);

        if (flags & FASTDetector.PERFORM_NON_MAX_SUPRESSION)
        {
            int nonMaxFeatureCount = 0;
            xy* xySuppressed = null;

            featureScore = scoreFunc(cast(ubyte*)image.data.ptr, cast(int)image.rowStride,
                    xyFeatures, featureCount, cast(int)threshold);

            xySuppressed = nonmax_suppression(xyFeatures, featureScore, featureCount, &nonMaxFeatureCount);

            // free the score before the suppresion
            free(featureScore);
            featureScore = null;

            // assign new feature count after the suppression
            featureCount = nonMaxFeatureCount;

            // free previous features and assign new ones.
            free(xyFeatures);
            xyFeatures = xySuppressed;
        }

        featureScore = scoreFunc(cast(ubyte*)image.data.ptr, cast(int)image.rowStride, xyFeatures,
                featureCount, cast(int)threshold);

        features.reserve(featureCount);
        foreach (i; 0 .. featureCount)
        {
            Feature f;
            f.x = xyFeatures[i].x;
            f.y = xyFeatures[i].y;
            f.width = 16.;
            f.height = 16.;
            f.octave = 0;
            f.score = featureScore[i];
            features ~= f;
        }

        // TODO: sort raw results. (before creating Feature objects)
        if (flags & FASTDetector.SORT_OUT_FEATURES_BY_SCORE)
        {
            import std.algorithm : sort;

            features.sort!((a, b) => a.score > b.score);
        }

        // TODO: if not sorted, taking first N features does not make any sense.
        if (count && count < featureCount)
        {
            import std.range : take;
            import std.array : array;

            features = features.take(count).array;
        }

        return features;
    }
}

version (unittest)
{
    import std.algorithm : map;
    import std.array : array;
    import std.algorithm.sorting : isSorted;
    import dcv.core.image;

    // lena image resized to 128x128 in grayscale
    immutable lena_128x128 = [155, 154, 156, 148, 149, 146, 147, 147, 146, 152, 158, 165, 165, 160,
        139, 115, 87, 82, 91, 95, 99, 96, 97, 99, 99, 95, 100, 106, 108, 113, 118, 115, 119, 120,
        127, 122, 116, 122, 122, 124, 124, 123, 124, 122, 123, 123, 125, 121, 126, 126, 124, 126,
        122, 121, 119, 120, 121, 124, 122, 121, 123, 125, 122, 121, 129, 119, 121, 121, 120, 124,
        117, 124, 121, 120, 116, 117, 115, 112, 103, 93, 105, 125, 136, 144, 155, 148, 145, 142,
        146, 146, 147, 144, 145, 145, 144, 145, 147, 147, 152, 147, 158, 204, 212, 216, 205, 130,
        93, 99, 109, 113, 108, 109, 117, 110, 111, 112, 111, 116, 114, 108, 117, 116, 115, 113,
        109, 113, 162, 119, 155, 154, 156, 148, 149, 146, 147, 147, 146, 152, 158, 165, 164, 160,
        139, 115, 87, 81, 91, 95, 99, 96, 97, 99, 99, 95, 100, 106, 108, 113, 118, 115, 119, 120,
        127, 122, 116, 122, 122, 124, 124, 124, 124, 122, 123, 123, 125, 121, 126, 126, 124, 126,
        122, 121, 119, 120, 121, 124, 122, 121, 123, 125, 122, 121, 129, 119, 121, 121, 120, 124,
        117, 123, 121, 120, 116, 117, 114, 112, 103, 93, 105, 125, 136, 144, 155, 148, 145, 142,
        146, 145, 147, 144, 145, 145, 144, 145, 147, 147, 151, 147, 158, 204, 212, 216, 205, 130,
        92, 99, 109, 113, 108, 109, 117, 110, 111, 112, 111, 116, 114, 108, 116, 116, 115, 113,
        109, 113, 162, 117, 147, 151, 155, 151, 147, 149, 149, 143, 146, 153, 163, 164, 165, 156,
        138, 111, 85, 79, 87, 93, 97, 91, 92, 95, 95, 96, 102, 102, 109, 110, 116, 115, 115, 116,
        120, 120, 118, 120, 119, 123, 122, 123, 123, 120, 121, 121, 118, 118, 121, 122, 121, 124,
        114, 123, 118, 117, 125, 123, 118, 122, 122, 120, 120, 124, 124, 120, 115, 119, 119, 119,
        118, 118, 120, 117, 118, 117, 113, 112, 103, 101, 97, 110, 130, 140, 148, 150, 147, 143,
        149, 146, 147, 150, 149, 144, 145, 147, 148, 146, 147, 147, 143, 185, 209, 214, 216, 185,
        98, 98, 104, 111, 111, 111, 110, 114, 111, 114, 109, 112, 114, 112, 115, 118, 116, 116,
        116, 98, 41, 40, 149, 149, 152, 147, 148, 149, 144, 145, 148, 155, 162, 161, 159, 158,
        132, 111, 87, 77, 80, 91, 92, 97, 97, 89, 90, 89, 103, 103, 109, 111, 116, 113, 118, 117,
        118, 122, 124, 117, 121, 121, 117, 125, 121, 122, 121, 122, 121, 121, 124, 118, 117, 119,
        124, 124, 119, 118, 122, 121, 118, 122, 126, 123, 121, 119, 118, 122, 124, 119, 117, 120,
        118, 121, 114, 118, 117, 117, 115, 112, 102, 102, 96, 100, 123, 136, 144, 152, 151, 147,
        150, 151, 152, 150, 147, 148, 148, 146, 145, 144, 147, 147, 140, 150, 200, 213, 216, 212,
        149, 95, 100, 106, 111, 112, 113, 111, 109, 111, 112, 109, 112, 112, 115, 116, 118, 128,
        100, 43, 36, 42, 148, 150, 147, 149, 144, 148, 145, 143, 154, 163, 159, 159, 160, 149,
        133, 115, 85, 78, 82, 92, 98, 95, 92, 93, 93, 89, 100, 104, 108, 115, 116, 115, 118, 119,
        116, 120, 121, 124, 123, 117, 123, 121, 121, 125, 127, 124, 120, 120, 120, 125, 120, 121,
        123, 119, 121, 118, 119, 123, 120, 120, 125, 128, 123, 121, 122, 121, 120, 116, 121, 116,
        112, 118, 121, 118, 117, 117, 114, 112, 108, 113, 100, 92, 110, 134, 143, 146, 158, 151,
        153, 155, 153, 154, 150, 152, 147, 144, 146, 141, 140, 143, 142, 141, 178, 207, 215, 217,
        198, 110, 94, 102, 105, 110, 110, 110, 113, 111, 113, 112, 119, 120, 118, 122, 125, 86, 41,
        38, 40, 45, 148, 147, 150, 150, 150, 145, 145, 151, 155, 158, 160, 155, 153, 148, 135,
        119, 89, 78, 85, 92, 97, 96, 92, 92, 97, 92, 101, 104, 108, 109, 113, 114, 116, 119, 119,
        119, 118, 118, 120, 120, 119, 121, 121, 121, 124, 121, 119, 121, 117, 123, 121, 116, 118,
        118, 120, 125, 121, 120, 117, 121, 121, 124, 126, 121, 118, 117, 119, 115, 118, 119, 115,
        116, 117, 120, 116, 116, 112, 113, 111, 105, 96, 91, 107, 129, 138, 148, 156, 154, 151,
        157, 158, 153, 148, 150, 155, 149, 148, 145, 144, 146, 142, 142, 139, 196, 213, 217, 214,
        169, 97, 100, 100, 109, 111, 114, 114, 115, 112, 121, 116, 121, 124, 126, 88, 41, 57, 38,
        41, 43, 147, 143, 151, 150, 152, 149, 146, 154, 159, 162, 156, 157, 151, 150, 138, 114,
        86, 76, 84, 90, 95, 94, 96, 92, 91, 95, 97, 99, 109, 112, 112, 120, 118, 111, 118, 119,
        116, 121, 116, 118, 117, 119, 117, 123, 119, 120, 120, 122, 120, 117, 118, 118, 115, 119,
        116, 117, 116, 117, 117, 117, 121, 121, 126, 121, 118, 122, 121, 118, 120, 118, 117, 115,
        119, 117, 115, 118, 111, 111, 109, 100, 98, 97, 109, 124, 140, 150, 154, 156, 159, 148,
        152, 151, 153, 147, 150, 146, 147, 143, 143, 143, 142, 141, 137, 166, 205, 215, 218, 205,
        125, 97, 103, 114, 113, 110, 111, 110, 112, 119, 120, 127, 124, 82, 58, 37, 31, 36, 43,
        46, 150, 153, 148, 151, 150, 151, 150, 158, 162, 159, 151, 151, 152, 150, 136, 111, 82,
        74, 87, 91, 90, 96, 97, 96, 93, 94, 98, 106, 109, 110, 112, 115, 117, 117, 119, 117, 116,
        117, 119, 117, 119, 121, 120, 117, 116, 116, 118, 122, 127, 122, 114, 116, 113, 110, 114,
        119, 113, 113, 115, 117, 118, 117, 122, 124, 122, 124, 120, 115, 117, 118, 116, 116, 115,
        117, 116, 116, 112, 114, 112, 106, 100, 97, 109, 124, 136, 146, 151, 155, 151, 150, 149,
        146, 150, 149, 147, 148, 147, 146, 149, 143, 143, 142, 139, 135, 194, 214, 217, 219, 186,
        92, 99, 106, 111, 113, 111, 111, 113, 120, 124, 126, 78, 30, 39, 37, 39, 38, 45, 68, 148,
        151, 150, 150, 152, 150, 160, 162, 162, 160, 151, 150, 153, 153, 142, 117, 86, 78, 86, 90,
        93, 98, 98, 90, 93, 93, 96, 103, 107, 110, 114, 114, 116, 119, 119, 120, 114, 114, 120,
        120, 120, 120, 117, 118, 117, 126, 116, 122, 124, 123, 117, 114, 109, 112, 113, 115, 113,
        116, 116, 114, 114, 119, 119, 115, 123, 120, 115, 117, 119, 115, 118, 116, 114, 115, 115,
        120, 117, 110, 110, 99, 99, 96, 106, 120, 134, 142, 149, 152, 154, 151, 149, 152, 153,
        145, 149, 149, 147, 147, 148, 148, 147, 144, 142, 131, 147, 196, 212, 219, 217, 164, 101,
        103, 109, 108, 113, 114, 113, 121, 123, 96, 37, 33, 37, 35, 43, 41, 42, 49, 151, 149, 151,
        154, 158, 158, 159, 160, 158, 154, 147, 151, 152, 151, 135, 116, 83, 77, 89, 90, 93, 92,
        92, 92, 92, 95, 98, 103, 109, 111, 109, 116, 109, 116, 115, 122, 117, 114, 111, 114, 119,
        120, 118, 118, 116, 121, 119, 116, 118, 116, 114, 115, 113, 111, 116, 121, 115, 111, 111,
        112, 110, 119, 119, 121, 122, 117, 118, 117, 117, 116, 117, 113, 115, 117, 116, 116, 112,
        113, 107, 105, 104, 96, 107, 121, 129, 139, 146, 144, 153, 149, 150, 152, 148, 145, 148,
        152, 148, 145, 147, 146, 144, 141, 141, 136, 134, 185, 212, 219, 221, 201, 106, 92, 105,
        106, 113, 117, 123, 123, 80, 33, 32, 43, 47, 44, 46, 38, 46, 35, 156, 156, 152, 153, 157,
        163, 157, 153, 156, 153, 151, 153, 153, 149, 135, 109, 82, 72, 80, 95, 92, 91, 92, 91, 90,
        93, 96, 104, 109, 108, 111, 112, 117, 111, 114, 116, 115, 114, 113, 117, 117, 119, 115,
        120, 119, 120, 120, 116, 119, 116, 116, 116, 114, 111, 113, 106, 111, 111, 109, 109, 110,
        118, 117, 120, 120, 118, 116, 114, 118, 118, 113, 118, 116, 118, 113, 117, 112, 109, 105,
        108, 105, 98, 102, 118, 129, 138, 140, 145, 151, 152, 145, 147, 145, 146, 146, 144, 148,
        148, 145, 144, 144, 140, 138, 135, 132, 146, 205, 217, 221, 218, 172, 90, 98, 101, 107,
        112, 121, 83, 36, 36, 41, 41, 45, 42, 41, 38, 36, 40, 154, 154, 152, 155, 165, 157, 147,
        147, 146, 150, 154, 150, 155, 152, 138, 111, 84, 75, 83, 90, 92, 93, 90, 93, 91, 91, 98,
        103, 106, 110, 111, 116, 116, 113, 114, 114, 114, 118, 116, 120, 118, 113, 117, 117, 118,
        116, 116, 116, 123, 115, 113, 117, 115, 111, 109, 121, 126, 121, 114, 107, 109, 115, 109,
        119, 114, 115, 118, 117, 118, 119, 116, 116, 116, 117, 115, 116, 113, 113, 110, 104, 102,
        96, 102, 118, 129, 135, 140, 143, 143, 147, 149, 145, 147, 144, 145, 148, 146, 147, 144,
        142, 138, 134, 133, 135, 134, 133, 182, 211, 221, 222, 206, 112, 95, 101, 105, 118, 85,
        37, 37, 39, 42, 51, 50, 48, 44, 33, 39, 38, 155, 154, 150, 162, 165, 150, 140, 137, 138,
        154, 154, 152, 157, 152, 138, 117, 83, 73, 84, 88, 93, 94, 91, 93, 92, 94, 101, 101, 106,
        112, 113, 116, 116, 114, 116, 115, 114, 119, 118, 113, 117, 120, 117, 117, 120, 117, 119,
        115, 117, 129, 129, 133, 136, 141, 159, 157, 167, 168, 172, 175, 182, 164, 121, 107, 108,
        115, 113, 114, 122, 118, 121, 115, 114, 117, 118, 114, 114, 108, 109, 102, 103, 97, 101,
        113, 126, 134, 137, 136, 140, 146, 146, 146, 144, 144, 145, 146, 148, 142, 143, 139, 135,
        135, 134, 134, 134, 131, 139, 200, 216, 220, 220, 183, 98, 106, 115, 86, 31, 33, 35, 41,
        51, 51, 50, 44, 32, 35, 39, 42, 152, 150, 151, 163, 157, 144, 131, 133, 137, 154, 157,
        154, 158, 154, 136, 113, 81, 72, 83, 91, 93, 92, 90, 91, 95, 96, 95, 104, 107, 113, 108,
        112, 117, 114, 112, 115, 118, 117, 114, 119, 120, 122, 117, 116, 117, 114, 115, 126, 138,
        138, 134, 141, 141, 162, 162, 165, 177, 174, 176, 169, 180, 178, 186, 186, 152, 106, 105,
        109, 115, 115, 117, 115, 118, 119, 113, 114, 107, 110, 110, 101, 102, 97, 100, 118, 131,
        143, 134, 137, 141, 144, 146, 145, 141, 142, 143, 143, 144, 142, 138, 136, 131, 134, 131,
        133, 134, 131, 133, 167, 209, 219, 225, 215, 146, 109, 90, 36, 32, 34, 39, 41, 45, 43, 40,
        42, 38, 42, 34, 35, 152, 151, 160, 163, 149, 133, 115, 117, 140, 154, 158, 155, 159, 153,
        137, 115, 78, 69, 77, 86, 89, 91, 91, 92, 93, 95, 97, 106, 108, 109, 113, 116, 117, 115,
        115, 121, 117, 117, 119, 121, 118, 113, 117, 120, 127, 122, 118, 142, 142, 135, 138, 139,
        134, 148, 156, 161, 166, 171, 179, 169, 168, 180, 182, 184, 195, 190, 136, 104, 105, 114,
        119, 113, 113, 116, 111, 110, 111, 104, 104, 100, 97, 97, 99, 116, 130, 135, 138, 136,
        139, 139, 141, 143, 145, 139, 140, 138, 140, 137, 134, 136, 132, 128, 129, 132, 133, 131,
        132, 129, 193, 218, 222, 226, 207, 95, 33, 35, 36, 39, 46, 43, 41, 43, 36, 47, 39, 33, 38,
        36, 153, 163, 164, 154, 142, 114, 96, 117, 142, 155, 157, 156, 154, 152, 138, 115, 77, 70,
        82, 84, 91, 89, 89, 88, 92, 97, 98, 101, 106, 107, 110, 110, 108, 113, 111, 113, 113, 114,
        119, 113, 108, 172, 150, 134, 119, 115, 116, 126, 124, 124, 141, 131, 141, 143, 148, 156,
        169, 154, 174, 178, 177, 180, 187, 185, 194, 189, 196, 178, 102, 103, 106, 112, 113, 114,
        108, 110, 106, 104, 106, 100, 96, 89, 100, 115, 130, 136, 138, 134, 136, 138, 139, 144,
        144, 140, 133, 134, 135, 137, 138, 135, 133, 132, 128, 132, 131, 133, 133, 129, 146, 205,
        219, 227, 223, 57, 31, 34, 39, 39, 46, 43, 46, 36, 40, 47, 37, 45, 36, 45, 158, 168, 161,
        148, 130, 92, 79, 118, 145, 158, 160, 157, 157, 157, 140, 112, 77, 66, 71, 82, 85, 83, 88,
        89, 93, 93, 95, 95, 107, 105, 109, 110, 113, 114, 113, 118, 115, 114, 113, 131, 96, 115,
        116, 108, 114, 114, 115, 123, 122, 127, 132, 129, 141, 135, 148, 144, 157, 173, 165, 184,
        184, 176, 185, 187, 180, 190, 190, 194, 193, 127, 97, 100, 107, 107, 109, 107, 104, 105,
        103, 100, 97, 91, 99, 117, 127, 139, 137, 137, 136, 136, 134, 136, 141, 142, 133, 132,
        132, 134, 137, 133, 135, 132, 128, 131, 133, 134, 136, 132, 130, 180, 220, 226, 174, 28,
        28, 35, 40, 48, 41, 46, 32, 35, 45, 42, 34, 35, 46, 36, 162, 164, 154, 140, 114, 68, 78,
        120, 141, 156, 160, 157, 156, 151, 133, 111, 74, 62, 75, 82, 84, 89, 88, 88, 93, 90, 94,
        100, 102, 102, 107, 109, 111, 108, 113, 110, 114, 115, 116, 148, 96, 108, 115, 109, 120,
        112, 119, 124, 119, 118, 128, 120, 131, 134, 148, 158, 163, 168, 175, 172, 181, 183, 181,
        191, 182, 192, 191, 196, 190, 196, 176, 92, 97, 96, 102, 104, 102, 105, 100, 96, 95, 92,
        98, 116, 133, 142, 143, 139, 136, 136, 136, 131, 132, 141, 136, 134, 132, 135, 137, 133,
        133, 134, 131, 132, 135, 136, 136, 137, 140, 140, 208, 178, 35, 36, 34, 35, 43, 40, 46,
        39, 40, 43, 37, 35, 37, 53, 29, 22, 164, 162, 150, 125, 87, 65, 87, 119, 143, 159, 163,
        158, 154, 152, 134, 109, 69, 62, 75, 82, 90, 87, 89, 85, 88, 87, 94, 99, 102, 108, 106,
        108, 111, 107, 111, 113, 114, 109, 139, 102, 108, 103, 98, 108, 116, 119, 119, 118, 129,
        131, 124, 124, 129, 134, 138, 153, 164, 162, 163, 182, 176, 189, 183, 190, 190, 189, 194,
        191, 192, 196, 197, 189, 84, 87, 90, 96, 98, 98, 95, 98, 95, 91, 95, 115, 134, 143, 144,
        141, 138, 133, 124, 124, 120, 132, 141, 135, 133, 134, 138, 133, 133, 132, 134, 135, 135,
        138, 137, 141, 139, 146, 132, 39, 37, 32, 40, 41, 43, 43, 41, 33, 52, 38, 38, 45, 60, 41,
        23, 103, 162, 152, 139, 107, 72, 66, 87, 120, 142, 157, 158, 158, 154, 151, 138, 111, 70,
        64, 74, 86, 92, 86, 87, 89, 90, 91, 94, 99, 101, 107, 105, 106, 107, 109, 111, 109, 117,
        109, 117, 105, 96, 98, 108, 110, 116, 119, 113, 121, 116, 123, 131, 130, 127, 126, 138,
        142, 154, 173, 167, 179, 181, 182, 188, 184, 189, 190, 193, 187, 192, 177, 196, 213, 219,
        207, 77, 87, 97, 100, 93, 94, 95, 91, 98, 119, 134, 143, 147, 146, 143, 132, 117, 105,
        107, 123, 136, 138, 136, 136, 139, 133, 133, 134, 135, 135, 135, 134, 137, 141, 146, 139,
        43, 36, 36, 32, 44, 44, 47, 38, 37, 45, 44, 39, 40, 53, 48, 27, 77, 160, 152, 142, 123, 82,
        73, 74, 88, 122, 142, 155, 160, 160, 157, 151, 135, 107, 76, 60, 74, 83, 85, 87, 91, 87,
        93, 91, 96, 100, 99, 106, 102, 109, 111, 114, 115, 108, 116, 129, 102, 96, 97, 101, 115,
        105, 114, 113, 117, 123, 118, 125, 126, 136, 126, 139, 133, 141, 144, 171, 173, 181, 180,
        176, 191, 182, 192, 183, 179, 186, 209, 207, 211, 212, 215, 226, 182, 70, 88, 93, 92, 92,
        90, 87, 98, 119, 134, 145, 146, 144, 144, 136, 116, 88, 82, 106, 127, 142, 138, 134, 137,
        134, 132, 133, 138, 137, 134, 136, 139, 141, 143, 66, 42, 38, 39, 39, 49, 46, 42, 35, 48,
        48, 41, 35, 48, 77, 42, 67, 139, 163, 145, 132, 98, 68, 76, 76, 87, 117, 143, 157, 161,
        159, 158, 147, 132, 103, 76, 65, 76, 85, 86, 88, 90, 97, 89, 88, 90, 101, 105, 104, 105,
        105, 109, 108, 114, 115, 119, 101, 99, 98, 103, 108, 108, 112, 112, 113, 110, 116, 119,
        127, 127, 135, 133, 136, 128, 133, 145, 167, 173, 178, 182, 189, 187, 173, 168, 193, 209,
        208, 206, 207, 206, 204, 209, 219, 223, 110, 75, 85, 91, 88, 88, 87, 97, 115, 130, 144,
        144, 143, 144, 136, 119, 81, 55, 83, 119, 135, 137, 133, 139, 136, 135, 131, 135, 133, 134,
        137, 140, 147, 97, 33, 30, 35, 42, 45, 40, 41, 33, 39, 44, 36, 37, 43, 67, 56, 71, 131,
        142, 152, 134, 112, 76, 76, 80, 73, 88, 120, 140, 155, 160, 158, 160, 149, 133, 107, 76,
        63, 74, 82, 84, 87, 91, 94, 91, 91, 98, 99, 103, 104, 106, 109, 108, 111, 113, 118, 103,
        94, 102, 102, 99, 107, 110, 104, 106, 104, 111, 119, 121, 127, 120, 131, 138, 132, 136,
        134, 144, 163, 164, 176, 179, 166, 156, 193, 208, 206, 203, 198, 204, 204, 203, 205, 206,
        210, 221, 218, 86, 71, 79, 86, 84, 84, 92, 111, 131, 145, 146, 144, 138, 137, 120, 91, 40,
        54, 103, 126, 139, 138, 134, 136, 133, 134, 134, 137, 135, 136, 144, 130, 39, 34, 35, 40,
        47, 48, 45, 40, 39, 51, 37, 38, 53, 58, 74, 74, 124, 145, 134, 134, 115, 88, 75, 83, 81,
        80, 81, 116, 141, 156, 159, 156, 157, 151, 132, 107, 78, 65, 78, 86, 88, 86, 86, 90, 88,
        92, 95, 97, 104, 106, 105, 108, 108, 108, 113, 112, 98, 99, 105, 103, 108, 109, 107, 110,
        102, 116, 122, 124, 127, 129, 132, 138, 141, 138, 129, 132, 136, 165, 166, 171, 149, 185,
        202, 199, 196, 205, 206, 199, 199, 199, 199, 208, 209, 212, 219, 224, 208, 64, 71, 77, 77,
        80, 93, 114, 134, 145, 145, 144, 145, 136, 127, 92, 38, 40, 88, 110, 132, 140, 134, 134,
        135, 132, 132, 135, 134, 139, 147, 52, 34, 38, 35, 42, 44, 43, 39, 38, 50, 37, 46, 41, 54,
        63, 75, 118, 138, 144, 129, 155, 92, 71, 76, 82, 81, 73, 82, 118, 138, 153, 157, 160, 156,
        150, 132, 107, 75, 71, 81, 88, 90, 86, 88, 90, 89, 92, 93, 97, 101, 111, 105, 106, 109,
        109, 121, 111, 100, 95, 103, 108, 108, 101, 102, 109, 110, 117, 120, 127, 131, 122, 125,
        134, 138, 135, 128, 131, 143, 165, 149, 141, 190, 200, 199, 200, 203, 196, 193, 192, 201,
        200, 198, 198, 202, 204, 207, 210, 218, 186, 89, 66, 72, 76, 85, 113, 131, 145, 145, 141,
        145, 139, 125, 87, 37, 39, 64, 94, 123, 137, 138, 132, 131, 131, 135, 136, 140, 144, 100,
        37, 29, 34, 47, 51, 42, 36, 32, 48, 43, 38, 46, 49, 54, 71, 117, 140, 142, 133, 151, 159,
        79, 73, 79, 78, 82, 75, 85, 115, 136, 151, 156, 159, 159, 152, 134, 107, 77, 65, 77, 84,
        86, 89, 89, 87, 89, 94, 94, 99, 101, 105, 107, 107, 107, 110, 111, 97, 99, 100, 100, 100,
        106, 100, 112, 110, 123, 117, 116, 127, 134, 123, 131, 132, 130, 127, 127, 132, 143, 136,
        164, 194, 191, 195, 192, 200, 195, 195, 195, 187, 192, 202, 200, 203, 204, 209, 207, 208,
        213, 217, 222, 110, 61, 71, 85, 111, 133, 144, 145, 144, 146, 152, 125, 92, 41, 33, 38,
        71, 108, 126, 137, 136, 131, 135, 132, 138, 142, 129, 34, 30, 34, 37, 47, 49, 44, 37, 39,
        46, 38, 37, 47, 49, 54, 106, 137, 139, 133, 156, 159, 158, 74, 75, 84, 81, 81, 77, 87,
        119, 137, 150, 158, 157, 155, 149, 135, 107, 83, 66, 77, 84, 87, 85, 95, 87, 89, 90, 92,
        99, 101, 105, 109, 107, 103, 150, 94, 91, 90, 105, 107, 104, 105, 99, 109, 108, 123, 128,
        125, 134, 131, 131, 128, 131, 129, 129, 131, 122, 124, 171, 190, 197, 192, 193, 184, 189,
        194, 188, 203, 201, 206, 195, 203, 203, 204, 198, 206, 205, 213, 210, 214, 220, 49, 60,
        82, 111, 128, 142, 145, 144, 144, 143, 125, 93, 44, 33, 30, 41, 83, 115, 132, 136, 131,
        129, 137, 138, 142, 62, 34, 38, 38, 44, 46, 46, 42, 38, 51, 35, 42, 45, 40, 46, 101, 141,
        133, 128, 144, 161, 160, 158, 80, 79, 81, 79, 79, 77, 87, 115, 140, 152, 160, 156, 156,
        154, 135, 107, 82, 65, 74, 82, 88, 88, 89, 92, 88, 90, 94, 97, 105, 106, 103, 102, 110,
        141, 88, 101, 103, 98, 101, 104, 102, 111, 112, 112, 116, 127, 133, 119, 134, 129, 126,
        122, 121, 119, 113, 153, 177, 180, 179, 181, 185, 190, 193, 181, 190, 198, 202, 202, 199,
        206, 205, 204, 206, 204, 202, 201, 204, 212, 217, 223, 148, 52, 73, 106, 131, 144, 144,
        145, 147, 141, 123, 93, 47, 37, 35, 30, 51, 93, 116, 133, 128, 127, 134, 140, 104, 33, 34,
        37, 41, 41, 46, 46, 36, 46, 43, 42, 50, 41, 37, 84, 139, 140, 127, 144, 154, 158, 155,
        157, 84, 78, 83, 81, 79, 72, 83, 119, 140, 152, 157, 157, 156, 155, 135, 108, 76, 64, 76,
        84, 81, 84, 88, 95, 90, 93, 97, 99, 100, 105, 99, 95, 196, 113, 98, 91, 94, 97, 102, 102,
        102, 108, 114, 118, 123, 131, 124, 117, 127, 126, 131, 116, 115, 103, 173, 181, 187, 190,
        182, 179, 178, 170, 192, 195, 196, 188, 198, 203, 200, 200, 202, 204, 190, 200, 204, 208,
        205, 209, 212, 221, 224, 77, 64, 103, 125, 143, 140, 143, 143, 148, 122, 93, 50, 36, 34,
        35, 27, 58, 173, 211, 212, 176, 203, 131, 38, 33, 40, 40, 43, 46, 51, 48, 45, 43, 38, 48,
        40, 37, 58, 130, 143, 130, 138, 154, 155, 153, 152, 154, 76, 78, 81, 78, 80, 72, 79, 112,
        137, 153, 157, 157, 155, 151, 133, 107, 79, 60, 72, 77, 82, 85, 85, 85, 89, 92, 92, 94, 98,
        99, 96, 89, 201, 101, 97, 93, 98, 107, 100, 105, 106, 102, 116, 125, 136, 119, 136, 115,
        127, 119, 110, 103, 125, 168, 166, 188, 175, 168, 190, 172, 184, 185, 189, 192, 195, 198,
        191, 193, 202, 191, 190, 205, 205, 197, 202, 204, 205, 208, 208, 212, 221, 188, 61, 100,
        125, 144, 145, 145, 147, 141, 125, 96, 47, 34, 32, 30, 43, 202, 211, 184, 205, 218, 221,
        202, 30, 35, 39, 45, 45, 56, 39, 44, 45, 43, 44, 55, 36, 38, 118, 145, 134, 134, 153, 158,
        153, 153, 151, 150, 76, 76, 82, 82, 84, 78, 81, 114, 136, 152, 157, 156, 156, 151, 134,
        111, 72, 61, 71, 80, 83, 86, 86, 87, 88, 88, 94, 95, 99, 101, 97, 134, 174, 106, 89, 94,
        102, 106, 99, 107, 108, 103, 114, 124, 113, 110, 122, 122, 115, 116, 97, 144, 167, 179,
        157, 172, 172, 169, 168, 181, 183, 185, 184, 188, 190, 191, 192, 187, 184, 200, 198, 199,
        198, 197, 197, 202, 202, 203, 199, 205, 218, 219, 66, 96, 126, 141, 145, 145, 144, 144,
        123, 91, 39, 30, 29, 88, 209, 193, 193, 217, 221, 219, 224, 230, 38, 35, 38, 42, 45, 42,
        38, 41, 40, 40, 50, 43, 39, 95, 145, 139, 135, 150, 155, 155, 154, 153, 151, 151, 85, 78,
        83, 83, 85, 78, 80, 111, 139, 153, 160, 160, 159, 151, 136, 106, 69, 65, 65, 80, 87, 92,
        88, 88, 89, 87, 93, 97, 99, 107, 94, 203, 168, 92, 91, 92, 95, 98, 87, 108, 117, 124, 112,
        122, 105, 121, 120, 118, 98, 92, 158, 173, 179, 158, 158, 175, 160, 179, 174, 164, 192,
        190, 182, 183, 181, 187, 176, 197, 196, 196, 193, 200, 195, 198, 196, 199, 207, 207, 209,
        205, 208, 219, 201, 79, 126, 146, 147, 149, 145, 142, 121, 86, 34, 29, 147, 213, 160, 197,
        218, 211, 209, 209, 211, 231, 87, 35, 39, 44, 44, 41, 43, 38, 37, 44, 49, 42, 62, 136,
        142, 133, 146, 151, 152, 153, 154, 152, 153, 150, 82, 89, 82, 91, 86, 88, 87, 114, 137,
        154, 160, 163, 159, 155, 136, 108, 77, 67, 71, 79, 86, 88, 91, 90, 88, 95, 94, 98, 101,
        106, 87, 212, 163, 93, 94, 93, 94, 83, 103, 113, 116, 110, 107, 115, 120, 115, 122, 116,
        91, 160, 159, 163, 161, 152, 160, 172, 177, 169, 174, 181, 172, 179, 185, 182, 161, 188,
        185, 196, 195, 194, 195, 189, 199, 194, 205, 194, 192, 200, 202, 202, 204, 207, 214, 146,
        119, 140, 147, 148, 147, 135, 106, 73, 49, 188, 207, 161, 205, 211, 209, 203, 199, 203,
        215, 228, 92, 33, 41, 45, 37, 33, 43, 39, 39, 44, 33, 41, 117, 148, 138, 144, 154, 151,
        149, 149, 148, 149, 149, 150, 87, 88, 88, 88, 86, 89, 87, 116, 136, 155, 157, 158, 162,
        159, 140, 107, 76, 68, 76, 85, 91, 88, 94, 91, 93, 92, 98, 98, 106, 102, 88, 203, 139,
        98, 85, 91, 93, 103, 103, 100, 117, 100, 109, 120, 120, 108, 108, 90, 159, 148, 158, 138,
        173, 142, 167, 168, 169, 184, 163, 176, 171, 176, 177, 162, 182, 186, 176, 187, 195, 191,
        194, 197, 196, 198, 148, 196, 199, 200, 197, 197, 200, 198, 207, 211, 182, 135, 143, 143,
        143, 128, 101, 140, 215, 181, 177, 212, 209, 204, 201, 195, 200, 210, 216, 224, 72, 37,
        42, 45, 39, 38, 42, 46, 45, 42, 23, 80, 142, 141, 136, 154, 153, 150, 149, 148, 147, 149,
        149, 150, 92, 88, 95, 89, 88, 88, 88, 112, 139, 150, 158, 163, 159, 158, 143, 109, 75, 65,
        76, 82, 92, 92, 91, 85, 91, 88, 95, 96, 99, 95, 91, 203, 125, 101, 86, 96, 97, 96, 90,
        107, 109, 111, 117, 117, 113, 106, 104, 144, 146, 143, 129, 162, 138, 168, 166, 174, 163,
        166, 178, 171, 171, 163, 164, 186, 177, 181, 184, 182, 185, 188, 197, 198, 197, 153, 192,
        189, 195, 197, 201, 197, 195, 192, 194, 201, 204, 136, 147, 138, 136, 144, 204, 196, 189,
        193, 210, 206, 199, 200, 198, 200, 205, 212, 216, 221, 34, 42, 45, 41, 41, 34, 35, 42, 41,
        35, 46, 126, 147, 136, 148, 155, 156, 151, 151, 151, 150, 148, 147, 149, 91, 88, 88, 91,
        93, 88, 92, 117, 141, 152, 159, 165, 162, 160, 143, 111, 75, 64, 79, 80, 90, 88, 91, 92,
        92, 87, 92, 96, 94, 88, 133, 194, 129, 109, 95, 98, 96, 96, 85, 92, 111, 109, 103, 111,
        106, 117, 137, 143, 135, 136, 127, 150, 158, 149, 175, 164, 157, 161, 184, 184, 142, 178,
        166, 170, 184, 171, 172, 183, 170, 189, 174, 174, 174, 186, 183, 180, 188, 194, 186, 188,
        192, 194, 179, 186, 196, 168, 138, 142, 189, 210, 180, 176, 208, 206, 199, 199, 197, 200,
        203, 203, 207, 211, 220, 221, 33, 43, 45, 44, 39, 34, 40, 44, 50, 52, 100, 142, 140, 142,
        154, 155, 150, 150, 154, 152, 145, 151, 147, 144, 89, 89, 89, 93, 92, 87, 91, 113, 140,
        155, 161, 166, 164, 163, 145, 110, 77, 68, 77, 79, 87, 91, 88, 88, 86, 91, 92, 95, 93, 82,
        187, 184, 135, 116, 91, 93, 97, 98, 90, 98, 117, 97, 110, 114, 106, 136, 142, 125, 144,
        111, 138, 156, 150, 154, 146, 162, 173, 163, 158, 146, 178, 161, 171, 172, 174, 172, 166,
        177, 185, 171, 173, 183, 181, 170, 186, 190, 194, 187, 181, 181, 184, 186, 183, 189, 181,
        195, 167, 210, 177, 182, 197, 204, 201, 200, 199, 198, 199, 204, 200, 195, 207, 210, 221,
        215, 32, 41, 45, 42, 37, 34, 41, 44, 50, 76, 137, 141, 137, 149, 154, 152, 153, 149, 147,
        147, 150, 147, 144, 146, 95, 91, 89, 87, 91, 91, 94, 113, 138, 156, 167, 169, 166, 163,
        144, 109, 77, 63, 75, 86, 86, 89, 87, 85, 88, 91, 90, 97, 90, 79, 217, 175, 135, 114, 108,
        99, 100, 99, 101, 102, 112, 111, 111, 102, 134, 133, 125, 148, 111, 132, 135, 147, 154,
        144, 158, 169, 167, 161, 156, 178, 164, 171, 163, 171, 171, 163, 170, 172, 178, 177, 178,
        172, 180, 192, 180, 187, 178, 182, 170, 182, 175, 178, 174, 160, 175, 200, 178, 196, 191,
        207, 204, 192, 198, 197, 196, 199, 203, 200, 190, 189, 205, 209, 218, 159, 29, 37, 35, 40,
        35, 44, 46, 47, 62, 119, 144, 134, 145, 151, 154, 152, 152, 149, 150, 146, 148, 148, 146,
        147, 89, 88, 84, 86, 88, 81, 88, 115, 137, 156, 166, 168, 166, 164, 140, 116, 75, 64, 74,
        86, 84, 87, 87, 90, 87, 87, 92, 91, 91, 80, 217, 177, 130, 128, 109, 107, 89, 92, 95, 96,
        105, 96, 109, 135, 139, 121, 143, 100, 135, 139, 145, 128, 135, 158, 161, 158, 140, 168,
        170, 163, 162, 166, 173, 163, 172, 164, 156, 162, 177, 173, 175, 181, 168, 185, 187, 169,
        178, 179, 168, 173, 179, 170, 156, 199, 182, 178, 193, 200, 203, 201, 192, 198, 198, 196,
        196, 199, 199, 204, 159, 169, 203, 202, 212, 49, 30, 37, 42, 54, 32, 39, 50, 35, 77, 147,
        139, 141, 153, 152, 155, 152, 153, 153, 149, 151, 151, 150, 151, 147, 86, 89, 81, 85, 82,
        83, 93, 115, 143, 158, 166, 165, 160, 162, 144, 113, 74, 66, 79, 85, 86, 93, 87, 88, 86,
        86, 89, 91, 90, 77, 215, 170, 145, 125, 122, 115, 105, 72, 97, 109, 109, 103, 134, 129,
        126, 154, 101, 143, 143, 140, 127, 137, 150, 128, 160, 131, 167, 166, 156, 166, 162, 151,
        170, 150, 161, 151, 168, 153, 160, 169, 169, 175, 183, 169, 171, 171, 167, 174, 174, 159,
        161, 174, 194, 175, 186, 201, 200, 197, 184, 188, 194, 197, 197, 200, 197, 201, 198, 165,
        150, 176, 136, 189, 209, 34, 48, 41, 50, 38, 35, 35, 41, 69, 121, 143, 134, 148, 151, 155,
        151, 153, 155, 151, 148, 151, 152, 152, 150, 148, 87, 80, 83, 81, 77, 81, 89, 120, 140,
        156, 163, 164, 163, 161, 143, 112, 79, 69, 72, 83, 87, 89, 87, 84, 89, 85, 92, 92, 87, 76,
        203, 168, 147, 141, 116, 126, 90, 80, 94, 97, 105, 132, 125, 119, 131, 110, 138, 129, 143,
        138, 136, 120, 145, 146, 128, 165, 148, 147, 165, 153, 159, 156, 146, 170, 156, 156, 144,
        165, 168, 161, 171, 167, 177, 171, 161, 168, 166, 173, 156, 158, 198, 172, 182, 193, 203,
        197, 192, 189, 187, 192, 194, 198, 198, 201, 203, 202, 196, 150, 173, 118, 157, 185, 130,
        31, 33, 55, 38, 34, 44, 35, 54, 97, 143, 141, 141, 151, 154, 158, 150, 150, 154, 154, 151,
        149, 148, 153, 147, 152, 83, 88, 84, 80, 81, 81, 90, 122, 143, 159, 163, 165, 164, 164,
        142, 116, 83, 70, 81, 82, 87, 87, 88, 87, 87, 92, 89, 91, 83, 72, 195, 177, 160, 146, 121,
        131, 104, 100, 92, 112, 136, 130, 122, 130, 114, 133, 128, 144, 130, 136, 126, 149, 142,
        128, 154, 143, 147, 141, 150, 151, 155, 158, 163, 141, 140, 165, 154, 167, 154, 168, 169,
        160, 161, 154, 163, 149, 146, 151, 186, 169, 184, 191, 202, 196, 191, 192, 191, 193, 194,
        196, 200, 201, 201, 200, 207, 207, 147, 167, 132, 162, 144, 209, 37, 39, 40, 46, 55, 36,
        40, 40, 63, 134, 145, 139, 147, 151, 152, 150, 152, 150, 151, 153, 150, 151, 151, 148,
        151, 152, 84, 88, 92, 83, 87, 89, 92, 117, 142, 157, 164, 166, 165, 161, 146, 116, 83, 67,
        74, 85, 82, 84, 82, 85, 90, 87, 85, 85, 81, 72, 201, 184, 175, 163, 140, 145, 122, 96, 94,
        132, 111, 116, 129, 118, 131, 125, 137, 126, 110, 126, 146, 127, 131, 157, 146, 148, 141,
        148, 151, 135, 113, 89, 121, 149, 157, 154, 153, 151, 157, 149, 158, 156, 156, 164, 141,
        145, 177, 189, 171, 189, 200, 193, 184, 181, 187, 189, 194, 196, 196, 201, 201, 200, 200,
        203, 208, 184, 163, 136, 141, 100, 171, 211, 29, 38, 48, 48, 42, 60, 39, 40, 97, 145, 138,
        142, 149, 152, 150, 151, 148, 147, 152, 151, 149, 149, 152, 149, 150, 147, 87, 90, 82,
        90, 85, 95, 97, 116, 139, 156, 164, 169, 165, 163, 145, 115, 78, 63, 75, 79, 91, 86, 85,
        87, 88, 86, 87, 85, 80, 67, 201, 197, 184, 172, 161, 152, 146, 105, 121, 115, 121, 137,
        112, 120, 135, 126, 131, 107, 125, 140, 124, 123, 141, 139, 91, 114, 106, 84, 94, 105, 138,
        151, 90, 120, 154, 162, 133, 130, 151, 155, 120, 55, 144, 139, 135, 186, 165, 179, 195,
        197, 194, 186, 189, 192, 189, 196, 196, 195, 198, 202, 199, 201, 205, 209, 207, 160, 143,
        72, 90, 136, 213, 102, 26, 36, 43, 31, 43, 45, 44, 56, 132, 143, 137, 148, 155, 152, 154,
        149, 151, 147, 151, 150, 149, 149, 151, 150, 147, 146, 89, 86, 89, 85, 93, 88, 104, 122,
        141, 158, 165, 170, 166, 164, 149, 117, 76, 63, 69, 83, 88, 86, 90, 89, 84, 87, 89, 85, 77,
        70, 206, 196, 195, 178, 149, 153, 147, 108, 111, 104, 125, 99, 118, 133, 125, 130, 109,
        117, 125, 129, 119, 133, 138, 110, 136, 117, 99, 83, 80, 53, 153, 153, 113, 126, 122, 68,
        80, 98, 87, 56, 59, 82, 33, 147, 186, 154, 177, 189, 194, 187, 195, 192, 192, 188, 194,
        198, 198, 199, 199, 203, 201, 201, 204, 200, 149, 79, 77, 83, 116, 193, 210, 36, 35, 41,
        42, 33, 42, 41, 40, 103, 145, 136, 143, 153, 153, 152, 150, 152, 148, 149, 148, 149, 145,
        144, 147, 147, 146, 145, 88, 88, 91, 89, 92, 96, 98, 123, 145, 160, 164, 165, 167, 162,
        147, 119, 72, 60, 72, 85, 84, 89, 89, 90, 86, 89, 90, 86, 84, 67, 214, 202, 211, 171, 137,
        118, 115, 99, 105, 115, 88, 110, 132, 123, 129, 119, 121, 126, 126, 110, 135, 133, 93, 131,
        124, 92, 104, 106, 97, 88, 98, 126, 87, 65, 48, 111, 52, 77, 38, 33, 43, 38, 122, 151,
        155, 196, 197, 191, 192, 190, 193, 193, 189, 191, 196, 197, 198, 197, 206, 202, 204, 192,
        111, 75, 86, 80, 88, 113, 178, 208, 48, 35, 43, 44, 41, 35, 47, 38, 47, 132, 139, 134,
        149, 157, 156, 153, 153, 154, 153, 150, 145, 143, 148, 150, 146, 147, 148, 146, 90, 93, 92,
        92, 86, 99, 104, 123, 144, 162, 163, 164, 167, 164, 150, 118, 75, 61, 75, 84, 84, 90, 90,
        90, 90, 91, 89, 87, 81, 68, 214, 209, 201, 181, 119, 106, 129, 108, 106, 86, 103, 131,
        128, 130, 114, 114, 129, 127, 106, 132, 128, 115, 122, 117, 91, 110, 106, 70, 54, 50, 66,
        90, 85, 89, 77, 88, 44, 91, 42, 25, 30, 161, 126, 167, 188, 194, 195, 190, 192, 187, 191,
        192, 188, 188, 193, 191, 202, 198, 207, 197, 82, 73, 75, 78, 83, 99, 148, 183, 194, 40,
        30, 39, 41, 35, 36, 42, 45, 34, 93, 142, 135, 146, 156, 156, 153, 156, 153, 151, 152, 151,
        148, 150, 144, 148, 150, 145, 147, 147, 97, 92, 92, 86, 88, 93, 95, 121, 142, 158, 164,
        164, 165, 163, 150, 120, 78, 63, 74, 83, 88, 84, 85, 89, 90, 86, 91, 86, 87, 76, 171, 204,
        201, 183, 123, 130, 147, 136, 84, 103, 124, 130, 120, 104, 120, 126, 124, 112, 135, 126,
        111, 123, 124, 115, 86, 53, 69, 53, 50, 53, 107, 92, 49, 83, 100, 79, 51, 115, 25, 48,
        181, 109, 169, 193, 172, 177, 190, 185, 189, 184, 185, 188, 193, 192, 193, 195, 197, 195,
        96, 122, 86, 76, 84, 106, 143, 157, 178, 199, 35, 40, 42, 44, 42, 34, 38, 53, 57, 42, 123,
        142, 131, 154, 159, 156, 155, 156, 152, 153, 152, 150, 149, 153, 149, 150, 148, 148, 145,
        144, 99, 95, 90, 95, 90, 88, 101, 120, 142, 158, 162, 164, 166, 162, 147, 121, 77, 64, 73,
        82, 84, 85, 87, 89, 87, 89, 90, 92, 89, 80, 79, 209, 196, 197, 159, 116, 118, 112, 97,
        125, 124, 129, 100, 110, 117, 118, 109, 131, 121, 127, 119, 130, 85, 46, 80, 57, 40, 44,
        46, 110, 103, 37, 33, 107, 83, 48, 29, 96, 54, 170, 118, 184, 188, 175, 176, 182, 179,
        181, 181, 182, 186, 185, 186, 190, 192, 194, 126, 72, 96, 137, 136, 140, 156, 160, 161,
        169, 200, 33, 36, 38, 54, 44, 39, 39, 34, 46, 42, 78, 139, 140, 141, 159, 159, 157, 159,
        156, 154, 152, 150, 150, 150, 147, 143, 148, 149, 149, 144, 145, 96, 96, 94, 95, 89, 89,
        97, 120, 140, 159, 164, 161, 165, 163, 148, 122, 80, 63, 77, 81, 84, 82, 90, 91, 88, 89,
        87, 92, 90, 82, 72, 218, 203, 197, 158, 172, 158, 91, 121, 126, 128, 89, 115, 122, 110,
        114, 122, 118, 82, 113, 115, 70, 72, 83, 49, 36, 60, 29, 50, 92, 52, 41, 118, 94, 52, 72,
        21, 86, 157, 117, 179, 196, 177, 172, 180, 177, 176, 173, 176, 180, 188, 189, 191, 193,
        162, 73, 59, 112, 112, 141, 158, 158, 162, 160, 179, 202, 35, 30, 38, 40, 46, 48, 38, 37,
        46, 49, 44, 114, 138, 136, 152, 161, 159, 161, 156, 156, 157, 151, 151, 153, 150, 150,
        148, 150, 146, 145, 147, 144, 96, 95, 97, 90, 94, 90, 93, 118, 141, 161, 166, 166, 165,
        166, 149, 124, 77, 58, 70, 79, 84, 82, 89, 86, 86, 87, 85, 90, 93, 92, 77, 134, 210, 192,
        147, 176, 107, 115, 125, 119, 96, 121, 111, 110, 110, 112, 124, 126, 71, 78, 64, 71, 90,
        55, 34, 95, 32, 31, 82, 35, 34, 71, 63, 79, 53, 71, 80, 137, 118, 189, 193, 187, 181, 176,
        173, 176, 170, 171, 168, 185, 189, 187, 188, 105, 61, 62, 102, 130, 110, 97, 138, 161, 167,
        177, 188, 39, 26, 33, 42, 44, 50, 45, 44, 36, 41, 42, 63, 130, 137, 140, 161, 160, 162,
        157, 157, 157, 158, 155, 152, 152, 152, 151, 151, 150, 149, 145, 141, 145, 98, 94, 95,
        96, 89, 84, 87, 116, 141, 159, 168, 166, 168, 164, 151, 121, 73, 63, 76, 78, 81, 85, 88,
        85, 89, 84, 87, 95, 95, 98, 91, 74, 198, 199, 185, 181, 99, 113, 122, 110, 112, 122, 122,
        111, 101, 123, 112, 111, 88, 80, 52, 83, 44, 29, 58, 115, 32, 37, 69, 33, 44, 47, 46, 47,
        101, 91, 95, 100, 187, 189, 190, 181, 177, 174, 179, 171, 164, 179, 181, 182, 182, 178,
        190, 164, 75, 95, 76, 91, 126, 101, 140, 166, 192, 153, 35, 36, 30, 43, 45, 47, 50, 40,
        36, 37, 48, 55, 95, 126, 119, 152, 162, 159, 156, 158, 155, 157, 157, 156, 154, 151, 152,
        151, 154, 151, 149, 150, 149, 143, 97, 98, 91, 91, 88, 85, 83, 112, 136, 160, 163, 166,
        167, 167, 148, 123, 77, 59, 69, 79, 82, 86, 87, 87, 84, 90, 90, 94, 99, 100, 96, 82, 93,
        200, 189, 190, 151, 105, 110, 99, 116, 120, 109, 103, 123, 114, 98, 74, 64, 76, 83, 72,
        47, 34, 60, 88, 44, 63, 40, 50, 75, 78, 75, 70, 110, 107, 109, 161, 183, 179, 183, 177,
        172, 173, 172, 169, 164, 175, 176, 182, 187, 188, 199, 184, 117, 80, 102, 80, 91, 126,
        135, 169, 74, 34, 36, 42, 37, 47, 47, 49, 47, 34, 38, 44, 38, 62, 117, 118, 125, 161, 163,
        160, 156, 158, 157, 158, 156, 157, 156, 153, 154, 151, 151, 149, 147, 147, 147, 144, 94,
        99, 94, 92, 92, 86, 79, 110, 140, 158, 164, 165, 168, 165, 150, 125, 79, 58, 70, 81, 84,
        89, 88, 87, 85, 85, 90, 93, 96, 104, 99, 89, 80, 210, 198, 186, 119, 113, 90, 107, 115,
        105, 118, 119, 115, 113, 104, 57, 57, 44, 81, 66, 59, 45, 67, 89, 79, 40, 40, 41, 42, 40,
        39, 89, 78, 105, 138, 164, 171, 178, 171, 166, 172, 171, 172, 172, 170, 169, 191, 187,
        189, 192, 191, 191, 145, 85, 59, 90, 68, 125, 140, 130, 66, 29, 32, 38, 50, 46, 52, 48,
        39, 35, 39, 41, 46, 82, 129, 112, 136, 160, 160, 159, 159, 157, 156, 162, 157, 156, 155,
        156, 155, 152, 150, 151, 150, 146, 147, 143, 96, 92, 96, 95, 89, 82, 80, 109, 137, 155,
        164, 167, 168, 166, 149, 125, 78, 59, 75, 83, 89, 88, 92, 89, 87, 87, 88, 93, 100, 102, 98,
        93, 77, 214, 212, 155, 95, 113, 108, 116, 94, 124, 118, 115, 101, 57, 38, 73, 42, 39, 46,
        55, 77, 34, 66, 56, 115, 35, 42, 33, 32, 28, 96, 80, 125, 157, 176, 176, 181, 177, 163,
        157, 160, 177, 157, 159, 178, 190, 192, 195, 190, 193, 192, 188, 160, 89, 52, 36, 75,
        102, 125, 142, 41, 36, 39, 38, 45, 53, 53, 48, 37, 39, 41, 39, 43, 117, 125, 119, 148,
        155, 160, 158, 158, 160, 154, 157, 154, 157, 154, 153, 153, 153, 150, 152, 154, 146, 145,
        141, 94, 98, 92, 92, 90, 85, 82, 112, 136, 156, 165, 166, 166, 167, 150, 126, 83, 60, 71,
        85, 87, 89, 90, 94, 87, 87, 94, 94, 98, 103, 101, 99, 85, 218, 210, 100, 95, 103, 106, 96,
        121, 116, 119, 103, 110, 33, 64, 36, 40, 35, 36, 73, 54, 57, 90, 43, 103, 66, 77, 28, 24,
        107, 105, 143, 156, 124, 175, 183, 187, 166, 157, 153, 176, 168, 155, 166, 180, 192, 191,
        197, 195, 198, 203, 202, 175, 98, 64, 37, 67, 62, 141, 144, 38, 39, 37, 41, 42, 48, 51,
        45, 40, 36, 44, 43, 73, 133, 123, 139, 146, 143, 148, 154, 160, 160, 156, 154, 154, 156,
        161, 154, 153, 153, 151, 151, 154, 150, 146, 142, 88, 95, 97, 93, 88, 87, 81, 109, 139,
        155, 163, 165, 169, 168, 150, 126, 84, 64, 69, 83, 87, 91, 91, 91, 90, 90, 91, 89, 153,
        103, 101, 100, 88, 182, 212, 105, 113, 103, 89, 126, 116, 90, 50, 71, 78, 42, 96, 33, 42,
        43, 34, 43, 61, 44, 84, 79, 65, 37, 29, 24, 86, 115, 144, 165, 158, 129, 158, 185, 176,
        164, 164, 165, 151, 150, 164, 178, 187, 192, 196, 197, 195, 204, 206, 206, 191, 125, 77,
        32, 35, 69, 151, 150, 47, 41, 42, 45, 47, 49, 56, 42, 37, 44, 45, 37, 107, 134, 120, 151,
        149, 143, 143, 142, 146, 149, 153, 155, 154, 154, 153, 155, 153, 154, 153, 150, 150, 147,
        145, 141, 94, 96, 94, 90, 88, 86, 79, 109, 137, 157, 163, 166, 166, 168, 151, 123, 86, 60,
        74, 83, 91, 92, 96, 91, 90, 88, 92, 115, 102, 104, 106, 104, 100, 102, 220, 104, 100, 106,
        115, 119, 123, 94, 74, 45, 44, 37, 95, 33, 64, 56, 39, 42, 54, 46, 71, 101, 52, 97, 21,
        68, 127, 133, 164, 175, 167, 136, 161, 188, 179, 166, 160, 138, 148, 161, 165, 185, 187,
        191, 197, 198, 200, 206, 205, 207, 197, 146, 75, 35, 26, 65, 148, 155, 47, 58, 48, 48, 52,
        54, 52, 39, 38, 43, 39, 51, 126, 131, 139, 161, 153, 149, 146, 145, 143, 139, 142, 143,
        143, 151, 154, 154, 152, 151, 150, 148, 148, 144, 140, 139, 93, 93, 90, 91, 85, 83, 77,
        107, 135, 157, 167, 170, 169, 167, 149, 126, 84, 68, 81, 87, 87, 90, 91, 93, 90, 91, 92,
        102, 101, 105, 109, 108, 106, 103, 190, 111, 96, 124, 118, 124, 106, 61, 39, 85, 31, 32,
        78, 48, 52, 41, 48, 36, 48, 33, 70, 66, 26, 128, 41, 138, 115, 159, 168, 187, 179, 135,
        165, 194, 163, 155, 146, 152, 160, 164, 166, 178, 187, 194, 194, 199, 199, 203, 204, 208,
        205, 161, 93, 46, 32, 38, 79, 164, 59, 41, 47, 48, 48, 50, 49, 41, 40, 47, 37, 86, 138,
        123, 148, 161, 158, 156, 151, 151, 149, 147, 145, 142, 139, 137, 140, 141, 147, 149, 148,
        145, 145, 151, 145, 142, 90, 88, 92, 88, 88, 86, 80, 107, 135, 158, 166, 168, 170, 167,
        151, 126, 80, 67, 75, 84, 89, 92, 93, 95, 93, 90, 97, 101, 107, 101, 100, 97, 90, 127, 92,
        97, 116, 132, 115, 113, 66, 66, 25, 112, 39, 38, 29, 59, 86, 30, 47, 40, 33, 46, 45, 110,
        24, 51, 139, 103, 164, 152, 164, 183, 182, 148, 178, 164, 149, 150, 149, 155, 165, 166,
        172, 176, 186, 192, 194, 193, 198, 200, 203, 207, 205, 181, 104, 69, 33, 33, 70, 167, 63,
        35, 52, 52, 57, 58, 42, 40, 44, 41, 48, 118, 131, 131, 157, 158, 155, 154, 156, 158, 155,
        156, 148, 150, 143, 138, 143, 139, 137, 135, 137, 144, 146, 147, 142, 143, 90, 91, 93,
        88, 84, 84, 79, 108, 139, 156, 165, 169, 170, 168, 150, 126, 84, 63, 73, 83, 90, 89, 92,
        93, 92, 93, 95, 99, 104, 108, 108, 107, 106, 152, 123, 183, 105, 121, 104, 105, 38, 113,
        24, 128, 29, 38, 65, 95, 57, 34, 49, 71, 31, 93, 45, 33, 31, 126, 80, 178, 162, 162, 158,
        186, 183, 172, 170, 134, 147, 155, 156, 160, 168, 169, 171, 172, 178, 189, 189, 190, 194,
        200, 203, 208, 204, 192, 115, 62, 29, 36, 63, 172, 71, 44, 63, 52, 56, 55, 40, 44, 49, 38,
        68, 131, 124, 140, 155, 157, 156, 153, 155, 159, 160, 160, 154, 150, 147, 144, 144, 138,
        136, 134, 135, 139, 135, 138, 142, 144, 90, 91, 90, 89, 90, 87, 79, 106, 136, 156, 167,
        170, 170, 166, 151, 125, 84, 63, 77, 81, 89, 94, 92, 91, 90, 92, 94, 102, 106, 108, 109,
        113, 171, 64, 28, 52, 140, 117, 104, 51, 90, 47, 32, 123, 27, 39, 43, 44, 39, 45, 45, 61,
        35, 87, 82, 30, 89, 95, 170, 165, 184, 151, 155, 190, 191, 159, 67, 88, 96, 101, 125, 155,
        171, 174, 169, 169, 177, 188, 187, 185, 187, 195, 196, 200, 197, 162, 95, 44, 29, 31, 81,
        180, 90, 49, 51, 50, 63, 48, 41, 41, 44, 40, 96, 131, 120, 148, 154, 153, 152, 155, 152,
        152, 154, 156, 157, 150, 148, 150, 146, 143, 139, 142, 139, 137, 134, 134, 131, 130, 92,
        90, 92, 91, 89, 86, 76, 107, 137, 157, 168, 170, 172, 168, 153, 128, 81, 63, 76, 84, 84,
        97, 90, 91, 91, 90, 92, 99, 104, 106, 114, 125, 150, 49, 30, 108, 118, 93, 80, 49, 90,
        34, 83, 138, 26, 39, 60, 34, 43, 34, 31, 62, 51, 63, 53, 44, 134, 141, 157, 180, 189, 145,
        176, 193, 140, 128, 143, 145, 126, 80, 58, 62, 110, 163, 168, 165, 168, 180, 188, 180,
        185, 190, 186, 160, 100, 75, 71, 65, 33, 35, 56, 169, 124, 41, 63, 54, 54, 40, 40, 40, 45,
        42, 122, 127, 127, 156, 157, 152, 151, 152, 152, 149, 149, 151, 154, 148, 148, 149, 145,
        150, 152, 148, 141, 138, 137, 132, 126, 125, 88, 92, 94, 92, 90, 87, 76, 105, 138, 153,
        169, 166, 171, 173, 152, 127, 85, 64, 78, 88, 91, 91, 91, 90, 84, 88, 89, 97, 100, 105,
        147, 135, 157, 69, 83, 116, 123, 74, 43, 71, 58, 55, 61, 67, 35, 49, 32, 36, 92, 28, 34,
        31, 54, 42, 23, 135, 116, 167, 170, 193, 167, 163, 196, 105, 107, 116, 120, 78, 139, 118,
        97, 84, 81, 106, 150, 158, 164, 178, 188, 182, 179, 170, 99, 94, 90, 102, 92, 75, 57, 36,
        60, 156, 119, 41, 55, 56, 55, 46, 42, 42, 42, 60, 129, 122, 140, 153, 153, 151, 149, 151,
        150, 148, 148, 151, 152, 149, 148, 148, 149, 149, 149, 149, 144, 146, 143, 132, 128, 123,
        90, 93, 90, 87, 93, 83, 71, 108, 135, 155, 168, 169, 169, 170, 154, 131, 85, 65, 71, 82,
        88, 89, 90, 89, 86, 88, 87, 95, 130, 135, 144, 145, 145, 114, 140, 46, 32, 64, 73, 114,
        55, 67, 34, 48, 66, 45, 31, 31, 80, 44, 36, 37, 32, 30, 71, 100, 182, 168, 189, 196, 177,
        193, 71, 72, 57, 51, 44, 40, 41, 35, 76, 125, 110, 110, 132, 149, 156, 185, 190, 191,
        180, 118, 79, 45, 40, 41, 50, 58, 38, 29, 65, 152, 109, 62, 57, 55, 47, 40, 39, 44, 31,
        90, 134, 123, 148, 154, 153, 148, 149, 151, 147, 147, 148, 151, 152, 147, 146, 148, 148,
        148, 147, 147, 142, 141, 139, 138, 131, 125, 82, 88, 83, 84, 82, 75, 67, 99, 135, 158,
        167, 169, 170, 169, 150, 129, 82, 61, 72, 76, 84, 89, 86, 85, 87, 80, 75, 181, 200, 131,
        138, 147, 130, 63, 62, 26, 79, 79, 103, 52, 78, 114, 31, 50, 37, 44, 33, 31, 31, 109, 73,
        29, 27, 27, 148, 163, 162, 175, 197, 190, 189, 67, 54, 39, 39, 41, 36, 56, 129, 49, 34,
        57, 125, 116, 128, 138, 154, 183, 200, 199, 79, 41, 41, 68, 68, 36, 46, 48, 39, 30, 64,
        143, 125, 60, 55, 50, 38, 41, 43, 46, 36, 114, 132, 132, 153, 152, 148, 146, 146, 148,
        146, 152, 146, 152, 148, 146, 145, 149, 144, 142, 144, 143, 138, 134, 132, 133, 132, 126,
        87, 89, 88, 81, 80, 70, 61, 100, 132, 157, 168, 170, 170, 171, 150, 126, 82, 65, 75, 85,
        87, 87, 85, 87, 83, 79, 68, 178, 152, 133, 140, 126, 138, 57, 30, 60, 54, 54, 42, 38,
        112, 117, 40, 37, 31, 35, 60, 33, 35, 45, 33, 47, 48, 105, 93, 173, 175, 181, 198, 195,
        81, 67, 42, 41, 82, 78, 30, 51, 199, 187, 62, 95, 111, 105, 122, 131, 155, 192, 213, 124,
        41, 44, 49, 65, 147, 48, 52, 49, 39, 30, 77, 133, 130, 89, 62, 51, 37, 44, 45, 37, 59,
        132, 132, 145, 151, 148, 150, 144, 146, 147, 146, 147, 147, 145, 147, 148, 144, 145, 142,
        142, 143, 139, 135, 132, 127, 127, 123, 124, 92, 90, 88, 93, 81, 70, 58, 95, 134, 156,
        170, 171, 175, 172, 154, 125, 85, 67, 74, 86, 93, 89, 94, 93, 103, 70, 35, 161, 120, 200,
        162, 53, 39, 29, 69, 58, 45, 61, 77, 58, 106, 150, 32, 42, 52, 33, 111, 42, 35, 46, 32, 31,
        37, 92, 157, 152, 177, 196, 193, 108, 110, 101, 82, 41, 104, 59, 59, 111, 205, 198, 128,
        106, 94, 105, 116, 130, 158, 204, 211, 90, 100, 92, 76, 135, 146, 59, 41, 37, 40, 32, 88,
        111, 144, 84, 77, 45, 47, 42, 44, 38, 85, 136, 127, 147, 150, 150, 150, 145, 148, 145,
        144, 148, 149, 145, 144, 145, 144, 138, 142, 142, 139, 133, 132, 121, 119, 125, 144, 162,
        88, 92, 86, 87, 81, 74, 63, 96, 133, 157, 168, 174, 174, 174, 154, 125, 88, 74, 80, 88,
        96, 96, 99, 60, 38, 93, 124, 171, 163, 215, 51, 78, 34, 61, 107, 46, 32, 60, 73, 62, 110,
        156, 54, 34, 37, 30, 43, 56, 39, 46, 29, 33, 135, 117, 151, 176, 197, 191, 101, 113, 115,
        134, 128, 93, 76, 128, 142, 176, 194, 170, 133, 103, 116, 108, 117, 128, 162, 215, 200,
        88, 111, 123, 146, 171, 122, 48, 53, 43, 40, 42, 74, 92, 159, 75, 66, 41, 37, 40, 44, 38,
        111, 129, 135, 152, 148, 147, 146, 146, 146, 147, 150, 147, 146, 147, 144, 143, 140, 138,
        137, 131, 135, 132, 128, 129, 152, 167, 177, 185, 92, 92, 90, 82, 79, 68, 58, 93, 135,
        158, 166, 172, 176, 176, 159, 128, 90, 72, 82, 93, 102, 101, 116, 34, 99, 165, 125, 122,
        137, 55, 43, 75, 88, 44, 81, 31, 48, 46, 77, 78, 106, 147, 76, 37, 32, 37, 35, 35, 45,
        30, 25, 62, 88, 186, 166, 188, 195, 94, 105, 122, 126, 132, 132, 128, 125, 109, 98, 124,
        112, 151, 162, 134, 109, 118, 117, 124, 155, 211, 204, 156, 137, 120, 108, 81, 49, 65, 73,
        42, 30, 48, 68, 80, 177, 73, 68, 36, 43, 44, 44, 64, 125, 125, 142, 153, 150, 147, 145,
        143, 142, 146, 145, 146, 143, 148, 144, 140, 140, 133, 132, 132, 129, 129, 152, 169, 179,
        184, 182, 185, 90, 88, 86, 84, 73, 70, 55, 91, 134, 160, 168, 173, 176, 174, 159, 131, 90,
        65, 80, 89, 97, 96, 95, 135, 149, 145, 75, 57, 87, 38, 43, 41, 102, 133, 110, 44, 32, 66,
        107, 96, 91, 124, 111, 49, 34, 38, 36, 37, 39, 31, 25, 147, 121, 156, 177, 198, 98, 88,
        114, 126, 137, 142, 140, 135, 137, 135, 129, 136, 141, 152, 145, 146, 115, 125, 118, 116,
        154, 203, 208, 168, 146, 128, 122, 114, 93, 88, 80, 53, 31, 42, 61, 76, 180, 81, 60, 45,
        36, 59, 35, 80, 129, 122, 151, 152, 143, 146, 143, 143, 144, 145, 143, 141, 144, 145, 139,
        139, 136, 134, 131, 129, 135, 166, 182, 187, 186, 186, 186, 186, 91, 83, 83, 73, 70, 63,
        50, 82, 132, 155, 170, 175, 176, 176, 158, 131, 87, 66, 81, 89, 99, 96, 97, 114, 108, 102,
        58, 94, 43, 33, 76, 82, 108, 50, 94, 32, 49, 80, 41, 132, 115, 103, 129, 33, 39, 38, 30,
        44, 40, 33, 95, 88, 173, 181, 199, 129, 78, 102, 116, 123, 139, 146, 155, 153, 160, 152,
        153, 164, 168, 161, 162, 132, 128, 125, 115, 116, 153, 200, 213, 179, 152, 144, 129, 120,
        106, 102, 85, 56, 41, 54, 57, 64, 179, 83, 69, 43, 31, 46, 33, 103, 127, 131, 150, 148,
        147, 146, 145, 145, 146, 143, 142, 143, 139, 140, 141, 134, 135, 131, 125, 146, 175, 192,
        193, 188, 188, 184, 185, 188, 77, 80, 73, 73, 72, 56, 49, 80, 127, 156, 169, 172, 175, 174,
        159, 130, 89, 68, 80, 88, 93, 98, 110, 115, 150, 149, 130, 67, 55, 51, 92, 113, 84, 104,
        47, 32, 37, 67, 78, 82, 92, 151, 57, 69, 50, 44, 32, 35, 40, 38, 140, 115, 172, 187, 178,
        52, 91, 105, 118, 126, 139, 147, 156, 160, 166, 166, 165, 165, 165, 168, 149, 137, 131,
        125, 116, 111, 141, 194, 220, 178, 165, 141, 132, 127, 114, 112, 95, 42, 39, 41, 51, 56,
        168, 100, 50, 54, 35, 38, 40, 124, 127, 143, 150, 148, 145, 146, 148, 144, 144, 145, 143,
        139, 139, 139, 137, 135, 129, 125, 142, 178, 194, 195, 192, 189, 185, 184, 187, 189, 78,
        79, 73, 69, 67, 62, 47, 86, 133, 156, 168, 171, 173, 176, 157, 134, 87, 66, 75, 90, 126,
        123, 124, 120, 78, 48, 70, 54, 57, 69, 71, 96, 122, 52, 45, 37, 41, 38, 80, 70, 81, 31,
        89, 119, 48, 38, 36, 35, 34, 101, 106, 178, 189, 206, 27, 63, 97, 110, 115, 126, 137, 144,
        156, 164, 169, 169, 172, 168, 170, 164, 154, 142, 137, 129, 122, 118, 131, 195, 217, 179,
        156, 152, 134, 122, 120, 110, 94, 54, 42, 46, 46, 46, 166, 135, 40, 39, 42, 34, 62, 130,
        126, 148, 152, 150, 147, 145, 146, 144, 145, 142, 143, 139, 141, 136, 136, 128, 125, 130,
        175, 189, 193, 193, 191, 191, 188, 188, 194, 196, 75, 71, 68, 66, 63, 57, 47, 81, 127,
        154, 168, 172, 174, 172, 157, 132, 89, 67, 81, 89, 95, 102, 118, 82, 78, 91, 76, 42, 80,
        68, 83, 99, 57, 55, 37, 37, 40, 43, 43, 56, 72, 24, 97, 125, 61, 35, 33, 30, 29, 139,
        113, 180, 186, 50, 35, 68, 105, 111, 113, 122, 129, 138, 150, 161, 168, 171, 179, 166,
        163, 162, 148, 138, 137, 129, 122, 120, 132, 186, 220, 179, 155, 150, 140, 124, 117, 114,
        85, 50, 53, 49, 40, 41, 166, 156, 37, 34, 44, 36, 88, 133, 133, 155, 150, 144, 147, 146,
        142, 145, 143, 140, 140, 138, 137, 137, 135, 129, 123, 163, 188, 192, 190, 191, 192, 193,
        191, 196, 199, 200, 65, 66, 63, 63, 58, 55, 46, 76, 133, 150, 164, 170, 169, 169, 159,
        132, 88, 71, 82, 85, 93, 100, 98, 124, 129, 65, 94, 94, 60, 49, 44, 120, 76, 55, 42, 48,
        45, 38, 41, 88, 48, 30, 98, 70, 159, 34, 26, 25, 103, 104, 189, 195, 159, 30, 39, 68, 98,
        110, 118, 120, 131, 140, 143, 149, 160, 170, 171, 164, 164, 157, 148, 132, 127, 126, 116,
        116, 132, 169, 219, 188, 157, 148, 137, 127, 122, 109, 68, 36, 37, 48, 37, 30, 171, 147,
        33, 30, 49, 39, 116, 131, 145, 164, 150, 149, 146, 146, 141, 142, 142, 141, 138, 135, 139,
        136, 129, 126, 144, 185, 193, 191, 189, 193, 191, 196, 202, 202, 202, 200, 73, 62, 64,
        64, 59, 49, 40, 84, 131, 151, 165, 166, 169, 173, 153, 132, 92, 65, 97, 82, 93, 152, 138,
        39, 58, 147, 94, 48, 45, 67, 66, 133, 129, 44, 66, 50, 37, 30, 32, 66, 64, 57, 108, 123,
        76, 140, 26, 25, 139, 110, 195, 203, 28, 32, 45, 68, 92, 109, 119, 121, 128, 135, 144,
        151, 153, 168, 162, 165, 159, 156, 144, 124, 121, 122, 112, 111, 120, 164, 217, 204, 156,
        148, 137, 122, 117, 110, 56, 31, 45, 54, 37, 33, 156, 142, 60, 40, 44, 46, 128, 130, 153,
        156, 148, 149, 147, 146, 143, 142, 141, 139, 137, 138, 133, 132, 126, 124, 173, 191, 192,
        188, 190, 192, 197, 203, 206, 205, 198, 200, 69, 65, 65, 65, 60, 50, 37, 76, 130, 153,
        161, 166, 164, 171, 154, 129, 83, 60, 73, 139, 125, 105, 110, 54, 124, 66, 83, 47, 89, 122,
        115, 106, 82, 52, 47, 48, 27, 31, 47, 119, 46, 89, 111, 176, 31, 73, 22, 72, 102, 160,
        203, 46, 28, 30, 56, 63, 92, 110, 112, 116, 126, 137, 141, 147, 152, 152, 158, 160, 158,
        153, 138, 127, 119, 118, 110, 111, 124, 154, 205, 218, 151, 141, 135, 129, 118, 97, 41,
        36, 49, 67, 38, 29, 149, 132, 69, 39, 37, 76, 134, 130, 153, 152, 148, 147, 148, 147, 146,
        141, 140, 141, 139, 134, 132, 133, 124, 149, 188, 192, 189, 190, 191, 200, 204, 206, 206,
        202, 203, 204, 73, 71, 65, 68, 56, 45, 35, 77, 126, 153, 165, 170, 167, 172, 156, 134,
        87, 64, 73, 87, 109, 125, 111, 50, 78, 96, 74, 89, 63, 65, 102, 121, 63, 59, 39, 37, 39,
        40, 75, 60, 87, 89, 42, 64, 30, 37, 39, 125, 113, 199, 146, 24, 29, 30, 75, 67, 90, 106,
        113, 121, 121, 126, 141, 140, 140, 148, 150, 152, 150, 144, 133, 115, 111, 127, 114, 110,
        122, 150, 197, 222, 143, 142, 136, 124, 115, 93, 32, 36, 51, 70, 54, 26, 132, 131, 106, 37,
        31, 102, 137, 135, 153, 150, 147, 144, 144, 147, 145, 140, 141, 142, 139, 137, 133, 127,
        127, 174, 194, 192, 189, 190, 199, 206, 207, 202, 203, 204, 206, 203, 76, 71, 70, 64, 55,
        44, 33, 72, 125, 153, 164, 168, 169, 172, 160, 134, 85, 57, 108, 111, 97, 104, 80, 54,
        68, 112, 83, 67, 128, 32, 127, 107, 90, 117, 39, 50, 31, 24, 55, 139, 48, 102, 44, 31, 29,
        24, 154, 140, 107, 166, 83, 28, 30, 29, 86, 62, 95, 109, 113, 119, 124, 131, 134, 140,
        141, 147, 148, 151, 148, 141, 131, 96, 119, 130, 130, 120, 114, 145, 193, 219, 132, 136,
        127, 118, 113, 55, 32, 37, 54, 63, 38, 28, 117, 151, 123, 39, 30, 122, 137, 144, 152, 150,
        147, 144, 143, 142, 142, 142, 140, 142, 139, 137, 130, 122, 148, 189, 194, 190, 191, 194,
        204, 205, 203, 201, 203, 205, 206, 203, 77, 70, 71, 67, 57, 49, 40, 84, 131, 154, 162,
        165, 169, 172, 158, 131, 96, 71, 75, 84, 91, 111, 76, 60, 87, 99, 56, 68, 93, 52, 112,
        76, 154, 93, 36, 41, 44, 24, 39, 52, 40, 109, 29, 34, 23, 52, 170, 173, 175, 86, 26, 30,
        35, 30, 81, 68, 91, 109, 110, 115, 124, 128, 132, 140, 139, 140, 146, 148, 148, 146, 132,
        107, 121, 88, 63, 104, 110, 121, 180, 189, 140, 137, 127, 116, 104, 31, 40, 50, 56, 46, 38,
        27, 88, 160, 129, 34, 47, 137, 136, 151, 151, 148, 148, 140, 143, 144, 142, 137, 144, 139,
        135, 133, 130, 119, 166, 191, 193, 194, 195, 203, 204, 203, 203, 204, 206, 206, 207, 203,
        69, 70, 67, 67, 55, 59, 56, 100, 138, 157, 162, 164, 169, 170, 162, 131, 90, 64, 76, 88,
        97, 105, 79, 72, 73, 72, 27, 133, 48, 82, 98, 83, 151, 58, 36, 27, 44, 87, 35, 26, 93,
        48, 53, 37, 35, 135, 157, 179, 166, 29, 37, 37, 38, 39, 99, 74, 98, 105, 110, 119, 122,
        128, 134, 136, 140, 143, 144, 148, 148, 148, 138, 122, 111, 115, 115, 108, 86, 109, 166,
        165, 143, 130, 134, 121, 57, 40, 34, 41, 60, 48, 36, 51, 50, 162, 144, 36, 85, 140, 139,
        152, 151, 147, 142, 144, 142, 144, 139, 141, 139, 135, 133, 136, 127, 131, 176, 194, 193,
        193, 200, 204, 205, 205, 203, 211, 207, 208, 205, 206, 63, 73, 64, 73, 57, 63, 74, 113,
        140, 155, 160, 163, 169, 174, 161, 133, 94, 63, 76, 86, 100, 105, 46, 57, 70, 44, 103, 51,
        82, 69, 92, 77, 81, 94, 97, 35, 37, 163, 25, 23, 48, 39, 85, 109, 167, 107, 107, 211, 31,
        30, 48, 39, 37, 31, 105, 75, 103, 105, 113, 118, 120, 125, 130, 134, 136, 138, 142, 146,
        148, 144, 146, 136, 131, 125, 122, 133, 146, 193, 185, 157, 141, 136, 124, 110, 39, 43,
        36, 46, 73, 67, 48, 34, 32, 166, 133, 47, 121, 138, 141, 151, 151, 146, 146, 145, 143,
        141, 146, 141, 139, 139, 137, 133, 128, 140, 186, 192, 194, 198, 204, 203, 204, 204, 205,
        206, 207, 206, 205, 209, 72, 66, 70, 67, 58, 52, 79, 113, 139, 154, 161, 163, 170, 174,
        163, 136, 94, 65, 78, 87, 96, 141, 65, 59, 64, 95, 66, 44, 66, 61, 103, 104, 72, 112,
        125, 56, 66, 102, 57, 52, 40, 132, 140, 173, 73, 89, 192, 49, 47, 47, 48, 47, 37, 36, 99,
        77, 101, 110, 111, 116, 119, 127, 129, 130, 134, 142, 142, 144, 148, 147, 139, 142, 141,
        135, 150, 192, 157, 195, 188, 154, 134, 133, 126, 60, 43, 45, 43, 63, 86, 63, 52, 45, 28,
        158, 135, 76, 132, 137, 142, 149, 149, 146, 143, 145, 142, 142, 137, 141, 141, 137, 133,
        133, 125, 153, 189, 192, 193, 201, 206, 204, 203, 204, 205, 207, 209, 209, 210, 210, 68,
        60, 60, 67, 56, 47, 80, 119, 142, 154, 162, 160, 167, 175, 163, 137, 95, 59, 75, 85, 135,
        103, 55, 64, 121, 38, 62, 45, 63, 59, 73, 88, 63, 117, 150, 57, 117, 51, 24, 46, 103, 143,
        175, 184, 84, 105, 82, 34, 38, 42, 39, 55, 40, 32, 91, 77, 99, 110, 114, 119, 117, 124,
        127, 127, 130, 132, 138, 140, 141, 147, 139, 140, 136, 145, 160, 202, 167, 201, 190, 153,
        134, 128, 120, 40, 46, 45, 46, 61, 70, 58, 60, 42, 26, 144, 125, 99, 135, 137, 148, 148,
        147, 142, 144, 141, 142, 142, 135, 138, 141, 138, 136, 133, 125, 159, 190, 192, 200, 206,
        207, 203, 205, 204, 204, 208, 209, 208, 208, 210, 67, 60, 57, 57, 54, 56, 73, 110, 141,
        155, 162, 165, 171, 174, 163, 137, 98, 58, 74, 112, 92, 122, 48, 93, 114, 41, 50, 58, 61,
        79, 58, 62, 67, 65, 113, 127, 121, 53, 69, 98, 102, 153, 194, 90, 83, 171, 30, 58, 47, 39,
        39, 67, 44, 33, 95, 85, 91, 110, 117, 114, 120, 124, 130, 130, 125, 128, 128, 134, 136,
        137, 135, 133, 140, 146, 167, 203, 169, 207, 188, 146, 133, 128, 71, 37, 50, 40, 59, 50,
        67, 63, 56, 34, 29, 126, 113, 109, 131, 140, 150, 149, 151, 147, 142, 142, 142, 141, 140,
        138, 136, 136, 134, 124, 123, 166, 194, 195, 203, 206, 205, 205, 207, 204, 205, 208, 209,
        208, 209, 209, 60, 50, 56, 58, 57, 55, 73, 116, 142, 155, 164, 161, 171, 173, 166, 140,
        93, 63, 82, 98, 85, 121, 55, 43, 109, 56, 59, 47, 54, 88, 81, 72, 61, 61, 73, 121, 93, 31,
        90, 169, 185, 187, 78, 70, 167, 32, 31, 87, 34, 36, 45, 62, 41, 30, 88, 86, 84, 106, 111,
        120, 118, 122, 125, 130, 125, 130, 122, 118, 125, 130, 132, 135, 134, 127, 123, 134, 152,
        135, 142, 117, 124, 130, 39, 41, 43, 43, 43, 60, 68, 62, 55, 43, 28, 124, 108, 120, 141,
        139, 151, 149, 146, 145, 141, 138, 146, 140, 142, 139, 139, 136, 132, 129, 120, 165, 192,
        201, 208, 205, 204, 207, 208, 205, 208, 210, 212, 210, 210, 211, 48, 48, 51, 62, 50, 58,
        73, 117, 144, 156, 168, 168, 171, 170, 165, 135, 94, 59, 132, 74, 115, 133, 44, 82, 53, 54,
        67, 54, 47, 128, 100, 95, 71, 77, 111, 60, 67, 142, 108, 187, 206, 114, 96, 123, 49, 40,
        41, 47, 38, 34, 47, 58, 59, 31, 90, 94, 73, 103, 111, 121, 116, 117, 126, 129, 133, 134,
        89, 70, 70, 91, 93, 94, 83, 70, 84, 104, 105, 74, 99, 103, 134, 89, 39, 38, 37, 38, 51,
        46, 54, 75, 34, 60, 32, 97, 120, 125, 135, 141, 146, 147, 145, 145, 145, 142, 142, 138,
        142, 139, 135, 138, 134, 124, 124, 175, 197, 207, 209, 208, 207, 204, 207, 208, 208, 209,
        213, 210, 212, 211, 46, 46, 49, 56, 50, 59, 85, 116, 144, 160, 170, 168, 171, 172, 159,
        135, 89, 147, 67, 81, 136, 103, 56, 59, 44, 49, 70, 60, 43, 148, 69, 88, 91, 89, 79, 61,
        92, 143, 122, 198, 190, 96, 108, 174, 40, 43, 37, 48, 50, 40, 54, 42, 68, 31, 85, 79, 71,
        93, 108, 114, 113, 115, 123, 125, 137, 136, 127, 116, 112, 106, 111, 122, 125, 131, 142,
        159, 173, 126, 131, 134, 130, 36, 38, 46, 40, 42, 70, 49, 59, 74, 38, 83, 40, 75, 140,
        133, 137, 143, 148, 146, 148, 143, 144, 140, 140, 138, 140, 139, 140, 137, 132, 125, 127,
        180, 202, 211, 209, 209, 209, 206, 205, 207, 210, 212, 211, 209, 210, 209, 44, 45, 49,
        48, 53, 61, 83, 111, 146, 156, 167, 173, 175, 172, 161, 138, 135, 62, 66, 109, 95, 91,
        65, 130, 33, 33, 92, 49, 44, 157, 51, 77, 108, 86, 70, 86, 123, 145, 108, 187, 77, 123,
        164, 39, 40, 44, 39, 37, 45, 35, 49, 54, 64, 32, 69, 73, 63, 91, 102, 107, 107, 110, 120,
        122, 129, 134, 135, 128, 111, 114, 118, 113, 134, 144, 152, 145, 152, 125, 141, 134, 54,
        31, 36, 37, 35, 36, 36, 50, 58, 76, 49, 81, 39, 74, 148, 144, 137, 142, 152, 148, 150,
        148, 145, 148, 145, 145, 137, 139, 138, 140, 133, 122, 128, 188, 209, 211, 208, 207, 209,
        211, 210, 211, 211, 211, 206, 209, 204, 205, 43, 42, 45, 49, 45, 65, 87, 107, 140, 154,
        170, 172, 175, 178, 161, 139, 89, 60, 78, 133, 93, 79, 42, 106, 34, 43, 79, 80, 72, 113,
        136, 84, 57, 106, 83, 120, 138, 131, 98, 193, 130, 200, 44, 47, 44, 45, 46, 45, 44, 47,
        45, 52, 58, 43, 73, 73, 54, 73, 93, 96, 106, 112, 116, 122, 125, 128, 132, 128, 121, 117,
        114, 111, 114, 120, 130, 122, 116, 141, 136, 114, 31, 37, 41, 44, 38, 39, 45, 62, 51, 76,
        57, 83, 45, 65, 154, 148, 142, 152, 151, 150, 147, 149, 146, 145, 144, 142, 139, 137, 136,
        133, 131, 121, 126, 193, 213, 213, 210, 209, 210, 214, 213, 212, 209, 204, 202, 201, 203,
        203, 41, 41, 39, 42, 40, 74, 82, 103, 137, 149, 169, 171, 174, 178, 161, 136, 91, 52, 105,
        86, 99, 38, 67, 79, 41, 52, 53, 35, 117, 139, 74, 109, 74, 58, 125, 104, 59, 81, 110,
        169, 157, 52, 40, 41, 45, 50, 46, 42, 44, 44, 58, 55, 49, 43, 57, 68, 49, 68, 83, 92, 93,
        106, 114, 119, 121, 127, 132, 127, 124, 117, 117, 120, 114, 111, 116, 132, 145, 129, 129,
        46, 35, 33, 37, 47, 59, 45, 55, 68, 63, 90, 52, 72, 53, 58, 167, 153, 141, 149, 150, 153,
        148, 149, 147, 150, 148, 145, 141, 138, 137, 134, 126, 117, 120, 198, 217, 213, 215, 213,
        214, 215, 211, 207, 203, 204, 207, 206, 208, 208, 44, 38, 38, 38, 35, 91, 91, 107, 129,
        147, 166, 171, 171, 172, 161, 139, 93, 56, 91, 92, 83, 54, 67, 43, 38, 66, 45, 47, 132,
        127, 118, 152, 100, 103, 80, 134, 50, 92, 123, 202, 113, 33, 45, 42, 38, 44, 43, 44, 38,
        41, 44, 52, 51, 52, 45, 50, 51, 60, 70, 80, 93, 101, 114, 113, 124, 127, 126, 128, 129,
        128, 132, 143, 150, 155, 148, 148, 140, 135, 82, 70, 29, 39, 43, 60, 54, 45, 51, 75, 66,
        78, 58, 72, 41, 39, 165, 155, 138, 148, 150, 150, 144, 146, 145, 146, 147, 145, 143, 139,
        135, 134, 125, 118, 116, 201, 217, 215, 214, 214, 212, 211, 209, 208, 211, 210, 209, 208,
        207, 206, 35, 40, 47, 40, 46, 93, 90, 112, 131, 149, 168, 169, 171, 173, 160, 137, 93, 53,
        77, 94, 77, 69, 88, 50, 32, 81, 36, 53, 101, 93, 108, 104, 108, 102, 67, 137, 117, 50,
        101, 195, 45, 42, 43, 42, 34, 48, 39, 47, 38, 50, 41, 46, 45, 50, 41, 51, 54, 54, 44, 60,
        80, 91, 104, 117, 119, 124, 127, 134, 137, 145, 148, 149, 162, 160, 152, 155, 140, 139,
        33, 66, 40, 38, 46, 49, 39, 62, 42, 85, 70, 75, 59, 78, 57, 44, 165, 157, 142, 156, 152,
        151, 150, 146, 148, 147, 146, 146, 142, 136, 134, 133, 128, 115, 126, 207, 217, 216, 212,
        210, 209, 211, 211, 210, 209, 207, 204, 205, 204, 201, 38, 42, 37, 37, 48, 79, 87, 113,
        127, 148, 167, 169, 170, 175, 162, 136, 95, 58, 76, 93, 55, 51, 118, 49, 41, 70, 39, 39,
        110, 96, 48, 73, 131, 104, 118, 134, 118, 97, 106, 69, 61, 47, 50, 42, 39, 52, 35, 48, 43,
        43, 37, 40, 47, 45, 48, 52, 57, 46, 62, 36, 49, 74, 87, 106, 119, 124, 126, 134, 137, 145,
        165, 159, 159, 156, 165, 156, 136, 124, 35, 48, 49, 44, 44, 66, 34, 47, 42, 86, 70, 67, 73,
        73, 73, 38, 170, 156, 141, 152, 152, 148, 143, 146, 146, 143, 144, 145, 141, 135, 132,
        133, 122, 112, 141, 213, 220, 214, 208, 209, 211, 213, 213, 207, 202, 204, 201, 201, 195,
        182, 43, 37, 36, 37, 43, 71, 91, 119, 131, 151, 165, 165, 168, 172, 165, 138, 90, 51, 67,
        73, 38, 55, 81, 40, 60, 63, 39, 40, 107, 127, 43, 71, 108, 112, 146, 130, 133, 135, 82,
        75, 44, 41, 45, 43, 48, 62, 43, 49, 39, 44, 43, 44, 40, 49, 56, 47, 53, 45, 62, 48, 40, 47,
        71, 87, 97, 111, 115, 125, 135, 139, 146, 157, 162, 154, 156, 145, 135, 101, 38, 47, 52,
        53, 50, 68, 49, 43, 46, 92, 78, 66, 71, 76, 82, 42, 163, 152, 134, 137, 141, 140, 145,
        144, 145, 141, 144, 140, 135, 133, 134, 130, 123, 111, 164, 214, 218, 211, 209, 210, 211,
        212, 209, 204, 202, 198, 184, 152, 95, 48, 39, 37, 35, 38, 32, 59, 86, 105, 130, 150, 165,
        166, 167, 173, 158, 134, 85, 65, 182, 100, 37, 50, 60, 55, 47, 42, 39, 40, 73, 138, 80, 75,
        78, 130, 85, 99, 138, 131, 158, 152, 49, 42, 41, 42, 56, 72, 36, 57, 42, 40, 47, 41, 41,
        43, 52, 50, 57, 45, 60, 75, 50, 57, 63, 72, 86, 95, 103, 110, 121, 129, 138, 145, 156, 144,
        146, 127, 123, 85, 43, 47, 50, 53, 46, 58, 48, 45, 57, 85, 75, 75, 67, 81, 66, 50, 165,
        139, 116, 110, 123, 125, 130, 133, 139, 140, 144, 140, 139, 134, 128, 128, 117, 110, 187,
        217, 213, 209, 209, 209, 208, 207, 205, 195, 177, 137, 62, 34, 34, 38, 43, 46, 38, 34,
        35, 59, 70, 95, 129, 151, 164, 167, 164, 168, 159, 127, 99, 203, 87, 116, 49, 34, 74, 56,
        66, 46, 38, 41, 83, 114, 129, 75, 42, 91, 106, 118, 110, 144, 66, 96, 167, 42, 39, 41, 52,
        77, 30, 69, 40, 38, 48, 41, 40, 43, 49, 49, 55, 41, 41, 66, 76, 99, 111, 118, 122, 128,
        126, 130, 130, 142, 148, 143, 147, 149, 150, 165, 184, 191, 152, 71, 49, 52, 42, 50, 43,
        52, 60, 81, 73, 72, 73, 84, 69, 64, 146, 119, 111, 97, 101, 109, 112, 114, 117, 123, 129,
        135, 134, 134, 133, 121, 115, 114, 198, 216, 206, 208, 206, 206, 205, 201, 193, 166, 110,
        38, 36, 32, 56, 61, 59, 61, 49, 42, 35, 52, 59, 82, 122, 147, 163, 165, 163, 167, 156, 141,
        172, 52, 53, 134, 32, 29, 84, 49, 55, 48, 70, 45, 57, 119, 96, 123, 52, 99, 153, 66, 80,
        120, 84, 59, 151, 157, 37, 39, 58, 68, 35, 59, 44, 45, 39, 50, 42, 49, 40, 54, 48, 47, 41,
        74, 88, 110, 116, 111, 117, 122, 123, 127, 130, 137, 137, 134, 134, 136, 151, 167, 186,
        194, 195, 200, 180, 81, 47, 46, 40, 48, 53, 82, 66, 75, 72, 77, 73, 73, 141, 118, 126,
        122, 114, 106, 103, 103, 101, 101, 102, 110, 113, 119, 122, 118, 114, 116, 200, 211, 202,
        205, 208, 207, 205, 190, 177, 136, 46, 37, 47, 61, 70, 68, 118, 96, 73, 58, 43, 50, 43,
        57, 108, 146, 161, 165, 164, 165, 184, 151, 88, 62, 115, 56, 36, 32, 55, 54, 29, 40, 97,
        66, 74, 41, 120, 63, 85, 130, 78, 89, 80, 98, 96, 118, 141, 57, 156, 38, 46, 63, 35, 77,
        39, 39, 38, 48, 40, 41, 44, 55, 51, 47, 39, 68, 91, 112, 112, 115, 115, 117, 128, 124,
        128, 132, 130, 130, 133, 139, 158, 173, 185, 191, 194, 198, 198, 203, 187, 68, 31, 27, 41,
        73, 57, 70, 68, 64, 61, 87, 144, 120, 132, 128, 122, 119, 115, 105, 100, 92, 92, 85, 96,
        92, 93, 103, 87, 106, 195, 206, 199, 205, 206, 206, 203, 178, 110, 37, 41, 58, 61, 75, 73,
        81, 133, 127, 111, 83, 66, 62, 41, 56, 103, 146, 159, 161, 164, 168, 163, 137, 90, 123,
        160, 37, 34, 37, 40, 97, 25, 35, 123, 67, 72, 31, 70, 120, 94, 132, 63, 118, 105, 91, 109,
        131, 125, 44, 103, 59, 46, 46, 30, 82, 42, 44, 40, 52, 57, 43, 44, 44, 57, 51, 42, 60, 91,
        102, 108, 115, 118, 116, 125, 129, 131, 128, 131, 133, 138, 149, 162, 176, 185, 185, 188,
        193, 198, 199, 203, 207, 151, 34, 45, 71, 57, 65, 64, 58, 54, 107, 139, 133, 140, 136,
        135, 128, 127, 124, 117, 110, 103, 92, 89, 81, 100, 111, 82, 83, 197, 204, 203, 209, 203,
        202, 176, 116, 41, 56, 71, 64, 74, 78, 77, 77, 130, 135, 141, 121, 90, 76, 40, 48, 106,
        142, 160, 164, 166, 168, 159, 132, 148, 88, 66, 37, 36, 28, 40, 116, 110, 119, 72, 64,
        73, 59, 75, 58, 114, 67, 68, 68, 110, 118, 142, 126, 50, 138, 38, 151, 44, 50, 40, 83, 45,
        45, 39, 46, 56, 47, 41, 55, 49, 68, 47, 64, 89, 106, 108, 118, 113, 120, 126, 134, 131,
        127, 127, 134, 142, 153, 161, 172, 183, 183, 186, 188, 194, 199, 201, 203, 209, 186, 41,
        41, 55, 62, 61, 59, 40, 133, 136, 145, 140, 139, 136, 135, 132, 128, 126, 121, 114, 111,
        102, 87, 111, 123, 84, 115, 201, 208, 208, 210, 205, 195, 101, 38, 54, 76, 67, 70, 82, 85,
        76, 78, 119, 131, 147, 145, 123, 92, 51, 48, 103, 148, 166, 168, 167, 170, 159, 133, 213,
        97, 45, 44, 42, 38, 53, 37, 56, 57, 49, 55, 85, 75, 28, 114, 40, 56, 56, 95, 82, 107, 130,
        149, 107, 44, 145, 77, 51, 37, 36, 76, 43, 41, 44, 44, 59, 40, 47, 68, 56, 87, 43, 48, 90,
        104, 115, 102, 117, 127, 126, 127, 129, 129, 131, 138, 145, 154, 159, 167, 174, 178, 181,
        185, 191, 194, 199, 202, 207, 212, 192, 42, 55, 55, 70, 65, 36, 149, 139, 142, 145, 139,
        137, 135, 135, 134, 130, 129, 122, 119, 117, 106, 119, 122, 96, 157, 206, 209, 210, 210,
        198, 167, 54, 46, 81, 80, 76, 87, 94, 83, 77, 89, 89, 117, 138, 150, 145, 120, 55, 45,
        105, 145, 168, 169, 170, 173, 160, 135, 191, 85, 30, 37, 42, 37, 64, 59, 41, 36, 76, 55,
        32, 36, 44, 53, 94, 45, 59, 62, 101, 79, 135, 122, 134, 88, 97, 40, 178, 39, 39, 85, 53,
        44, 41, 46, 58, 48, 43, 60, 56, 102, 59, 40, 94, 112, 100, 118, 122, 128, 127, 129, 126,
        130, 132, 139, 148, 153, 157, 161, 166, 171, 174, 177, 188, 193, 199, 201, 206, 211, 215,
        173, 48, 38, 66, 58, 34, 164, 132, 144, 142, 139, 135, 134, 136, 135, 132, 127, 127, 124,
        121, 117, 121, 125, 110, 185, 212, 211, 212, 208, 186, 125, 49, 79, 81, 82, 84, 105, 96,
        87, 83, 92, 37, 83, 126, 160, 161, 133, 74, 45, 105, 148, 170, 169, 171, 172, 161, 141,
        173, 68, 34, 35, 33, 38, 53, 49, 43, 34, 99, 36, 49, 30, 92, 33, 73, 77, 64, 66, 71, 82,
        101, 113, 144, 123, 32, 177, 201, 28, 29, 78, 44, 44, 39, 44, 55, 52, 38, 62, 66, 111, 78,
        35, 81, 100, 118, 121, 121, 125, 127, 128, 128, 131, 133, 138, 142, 150, 152, 158, 167,
        168, 174, 184, 186, 190, 193, 199, 204, 208, 214, 218, 93, 35, 53, 47, 34, 157, 131, 141,
        140, 138, 137, 139, 136, 136, 134, 131, 132, 123, 119, 118, 129, 130, 124, 197, 216, 210,
        209, 204, 167, 78, 66, 86, 85, 86, 99, 104, 83, 82, 96, 93, 26, 42, 107, 164, 167, 144, 82,
        35, 105, 148, 169, 169, 173, 172, 161, 140, 109, 86, 27, 41, 37, 65, 39, 42, 39, 38, 117,
        35, 60, 30, 49, 57, 81, 62, 75, 95, 83, 83, 74, 124, 132, 130, 38, 67, 185, 29, 27, 69,
        50, 41, 36, 42, 69, 46, 43, 50, 84, 105, 80, 30, 89, 104, 119, 119, 122, 123, 128, 128,
        132, 135, 136, 139, 141, 147, 152, 159, 161, 166, 172, 176, 186, 189, 192, 201, 205, 207,
        210, 220, 213, 41, 41, 44, 33, 144, 132, 143, 141, 138, 135, 134, 133, 132, 130, 131, 130,
        124, 120, 116, 122, 150, 169, 202, 213, 212, 208, 202, 133, 67, 80, 79, 94, 99, 101, 85,
        80, 94, 95, 92, 27, 34, 100, 161, 169, 153, 71, 31, 103, 146, 171, 172, 170, 173, 165,
        144, 96, 128, 34, 38, 40, 45, 39, 40, 40, 38, 136, 32, 74, 29, 41, 55, 86, 42, 67, 93, 91,
        74, 68, 145, 136, 131, 43, 46, 180, 25, 25, 64, 71, 39, 36, 44, 62, 37, 50, 47, 94, 92, 91,
        34, 85, 108, 118, 114, 122, 125, 126, 129, 129, 131, 136, 134, 139, 145, 148, 152, 159,
        164, 173, 177, 183, 185, 193, 200, 205, 210, 209, 216, 219, 104, 35, 31, 40, 146, 136,
        144, 142, 140, 139, 137, 134, 132, 128, 129, 126, 121, 118, 115, 157, 187, 195, 209, 214,
        212, 205, 183, 92, 80, 86, 87, 95, 103, 92, 80, 84, 91, 89, 95, 23, 32, 87, 152, 170, 148,
        72, 26, 104, 149, 170, 171, 171, 176, 166, 143, 158, 83, 47, 35, 53, 36, 33, 43, 36, 54,
        124, 31, 61, 29, 49, 61, 31, 43, 59, 89, 101, 72, 77, 135, 115, 101, 34, 40, 175, 40, 30,
        74, 68, 40, 42, 41, 58, 36, 42, 58, 88, 102, 98, 36, 84, 114, 118, 120, 127, 127, 130,
        126, 130, 129, 135, 136, 140, 145, 146, 151, 158, 164, 168, 174, 181, 185, 191, 197, 202,
        207, 209, 213, 218, 209, 34, 27, 58, 141, 137, 142, 144, 140, 139, 135, 133, 129, 126,
        127, 123, 117, 116, 145, 197, 201, 200, 213, 213, 213, 201, 148, 80, 83, 78, 95, 103, 104,
        81, 78, 96, 90, 90, 95, 22, 23, 74, 149, 170, 153, 78, 28, 101, 151, 170, 172, 171, 177,
        163, 143, 138, 33, 47, 51, 38, 35, 36, 37, 27, 134, 109, 32, 35, 39, 43, 34, 38, 39, 59,
        60, 122, 45, 58, 136, 147, 60, 128, 134, 114, 158, 32, 58, 60, 47, 57, 41, 42, 49, 47, 77,
        107, 115, 102, 39, 88, 114, 123, 127, 126, 124, 126, 128, 124, 129, 132, 134, 137, 142,
        143, 153, 156, 157, 171, 172, 181, 183, 191, 199, 202, 206, 209, 211, 215, 219, 34, 22,
        90, 137, 152, 143, 139, 136, 137, 134, 132, 133, 127, 126, 120, 118, 114, 185, 215, 212,
        205, 214, 215, 211, 182, 107, 87, 80, 82, 98, 103, 92, 80, 88, 93, 93, 98, 81, 21, 23, 67,
        149, 172, 155, 93, 29, 97, 147, 169, 172, 172, 174, 167, 145, 117, 47, 55, 38, 38, 38,
        37, 36, 113, 43, 76, 38, 41, 70, 32, 31, 39, 47, 66, 49, 105, 104, 92, 131, 122, 134,
        143, 171, 34, 30, 38, 41, 53, 56, 52, 44, 44, 46, 58, 104, 114, 110, 87, 49, 87, 114, 119,
        123, 127, 128, 128, 126, 128, 126, 132, 133, 134, 139, 145, 150, 153, 156, 166, 172, 176,
        186, 192, 196, 205, 204, 207, 209, 211, 217, 146, 22, 119, 134, 149, 139, 139, 138, 136,
        132, 134, 131, 127, 125, 119, 116, 116, 197, 216, 208, 206, 215, 213, 203, 150, 99, 93,
        85, 87, 106, 96, 86, 82, 96, 94, 86, 84, 76, 24, 24, 62, 145, 169, 157, 109, 30, 93, 146,
        168, 165, 166, 165, 162, 144, 121, 57, 45, 39, 35, 47, 39, 83, 39, 48, 77, 36, 35, 45, 37,
        40, 42, 34, 68, 53, 37, 82, 137, 107, 123, 67, 99, 117, 151, 141, 88, 50, 39, 77, 49, 51,
        39, 47, 67, 106, 112, 114, 78, 58, 96, 113, 122, 121, 129, 133, 126, 127, 123, 126, 130,
        133, 132, 139, 145, 149, 150, 155, 162, 163, 178, 186, 188, 196, 202, 203, 207, 209, 211,
        214, 205, 20, 121, 134, 144, 138, 138, 132, 134, 131, 132, 133, 129, 122, 120, 117, 126,
        201, 213, 201, 207, 216, 211, 185, 121, 110, 93, 88, 94, 101, 97, 84, 82, 95, 99, 93, 79,
        72, 25, 21, 55, 143, 171, 166, 105, 33, 93, 149, 167, 172, 172, 173, 166, 144, 132, 49,
        42, 37, 38, 43, 39, 38, 50, 42, 67, 45, 57, 37, 47, 37, 38, 46, 101, 33, 34, 76, 110,
        139, 122, 116, 31, 51, 41, 24, 62, 58, 78, 81, 43, 48, 44, 61, 80, 114, 115, 118, 66, 72,
        100, 119, 123, 124, 129, 129, 126, 128, 122, 125, 125, 132, 132, 135, 144, 145, 149, 152,
        159, 165, 172, 179, 187, 193, 199, 202, 205, 207, 210, 213, 214, 20, 124, 133, 143, 148,
        139, 137, 134, 134, 132, 133, 131, 127, 121, 121, 128, 198, 213, 199, 208, 217, 204, 157,
        108, 109, 93, 83, 93, 94, 84, 76, 90, 97, 80, 85, 87, 83, 30, 27, 42, 133, 166, 162, 111,
        37, 91, 144, 166, 171, 172, 173, 168, 141, 141, 46, 39, 34, 33, 45, 40, 62, 36, 42, 54,
        55, 34, 39, 77, 32, 49, 31, 64, 70, 82, 77, 89, 96, 81, 134, 64, 109, 41, 40, 45, 46, 53,
        42, 55, 34, 41, 73, 93, 114, 119, 114, 56, 85, 116, 121, 129, 129, 129, 133, 130, 125,
        126, 126, 129, 130, 132, 135, 141, 144, 147, 154, 159, 161, 170, 179, 188, 190, 196, 200,
        202, 206, 209, 209, 211, 73, 117, 139, 144, 140, 137, 135, 134, 135, 134, 132, 129, 123,
        125, 124, 126, 177, 197, 197, 211, 215, 199, 136, 106, 102, 97, 85, 90, 79, 68, 92, 97,
        92, 88, 88, 80, 90, 36, 31, 37, 128, 164, 161, 121, 44, 86, 140, 167, 169, 170, 172, 164,
        142, 153, 50, 41, 30, 31, 59, 68, 36, 34, 56, 56, 44, 56, 49, 50, 38, 38, 65, 52, 77, 32,
        132, 103, 124, 83, 59, 120, 115, 122, 41, 45, 54, 46, 43, 45, 36, 57, 74, 103, 113, 115,
        105, 45, 89, 120, 125, 130, 126, 134, 127, 125, 126, 125, 128, 124, 128, 130, 135, 143,
        141, 147, 151, 154, 161, 165, 170, 180, 187, 193, 199, 204, 208, 208, 208, 211, 184, 127,
        131, 127, 131, 136, 141, 139, 137, 136, 136, 131, 125, 129, 132, 131, 133, 152, 183, 212,
        211, 193, 122, 101, 92, 82, 86, 85, 67, 80, 101, 89, 83, 80, 91, 89, 69, 29, 29, 30, 119,
        158, 160, 126, 47, 84, 140, 163, 169, 169, 172, 166, 145, 145, 54, 49, 37, 42, 43, 42, 35,
        36, 48, 57, 49, 51, 48, 51, 37, 34, 71, 31, 72, 77, 32, 43, 86, 83, 48, 95, 166, 27, 41,
        35, 45, 38, 38, 37, 41, 67, 94, 105, 115, 112, 76, 65, 103, 122, 124, 127, 130, 132, 134,
        129, 132, 128, 123, 130, 130, 128, 135, 140, 141, 142, 148, 151, 158, 167, 173, 180, 188,
        192, 198, 201, 207, 209, 211, 210, 212, 132, 101, 94, 101, 114, 123, 131, 135, 140, 135,
        136, 131, 138, 143, 136, 132, 136, 191, 220, 210, 171, 110, 98, 88, 81, 90, 67, 72, 88,
        91, 86, 83, 87, 84, 82, 51, 27, 25, 32, 107, 163, 170, 131, 53, 81, 140, 165, 168, 170,
        174, 164, 148, 117, 70, 58, 33, 45, 41, 44, 38, 55, 55, 44, 61, 56, 37, 47, 33, 44, 34,
        63, 64, 107, 50, 47, 47, 62, 55, 92, 124, 33, 47, 34, 36, 44, 29, 36, 58, 71, 103, 107,
        114, 111, 42, 79, 124, 124, 124, 129, 132, 132, 133, 131, 131, 127, 127, 124, 126, 128,
        135, 136, 140, 146, 145, 153, 157, 163, 165, 176, 184, 190, 195, 201, 206, 211, 213, 212,
        215, 114, 70, 67, 72, 83, 83, 95, 110, 116, 122, 128, 136, 146, 150, 130, 122, 143, 203,
        220, 201, 146, 102, 80, 72, 85, 80, 62, 85, 92, 89, 86, 84, 96, 85, 69, 49, 25, 26, 32,
        103, 163, 172, 138, 49, 77, 135, 161, 166, 171, 172, 167, 145, 109, 74, 71, 35, 44, 37,
        37, 45, 42, 60, 44, 62, 53, 44, 38, 44, 40, 59, 30, 93, 121, 147, 50, 61, 81, 92, 34, 57,
        43, 32, 53, 36, 35, 34, 49, 72, 91, 106, 105, 107, 73, 44, 96, 124, 124, 121, 126, 128,
        132, 128, 130, 127, 133, 126, 124, 125, 127, 131, 135, 137, 142, 146, 153, 154, 162, 163,
        171, 178, 184, 196, 200, 203, 207, 211, 212, 214, 159, 76, 84, 73, 70, 67, 66, 70, 75, 79,
        92, 113, 138, 149, 146, 143, 157, 212, 215, 181, 117, 79, 61, 74, 80, 65, 81, 94, 85, 85,
        82, 95, 92, 79, 55, 45, 33, 31, 31, 97, 165, 178, 152, 61, 82, 135, 159, 171, 170, 174,
        170, 150, 67, 81, 64, 42, 32, 32, 44, 46, 36, 64, 38, 60, 60, 54, 45, 50, 51, 36, 47, 38,
        90, 131, 142, 128, 77, 80, 39, 39, 41, 34, 36, 32, 30, 35, 57, 79, 100, 104, 109, 100, 28,
        79, 119, 123, 123, 128, 129, 128, 128, 133, 133, 128, 128, 130, 125, 127, 128, 128, 135,
        135, 140, 141, 149, 149, 155, 160, 171, 178, 182, 196, 196, 201, 205, 209, 210, 214, 206,
        74, 86, 88, 86, 77, 67, 55, 46, 41, 43, 55, 93, 150, 188, 151, 183, 214, 206, 151, 82,
        53, 55, 75, 68, 82, 100, 85, 77, 81, 81, 93, 90, 68, 47, 43, 47, 66, 58, 97, 167, 180, 166,
        77, 83, 134, 161, 172, 167, 173, 171, 150, 86, 83, 46, 47, 41, 56, 38, 42, 36, 44, 39, 56,
        47, 51, 44, 32, 30, 63, 43, 38, 35, 119, 136, 109, 102, 129, 32, 47, 32, 32, 36, 31, 36,
        43, 62, 90, 104, 107, 108, 37, 49, 109, 117, 127, 127, 128, 126, 130, 131, 133, 132, 129,
        130, 130, 127, 126, 134, 129, 132, 132, 137, 141, 144, 147, 150, 162, 173, 175, 183, 191,
        193, 201, 206, 207, 210, 213, 213, 75, 90, 96, 95, 90, 83, 71, 52, 39, 35, 35, 79, 194,
        201, 145, 198, 214, 191, 99, 51, 50, 69, 67, 62, 97, 93, 77, 76, 72, 91, 104, 83, 57, 45,
        51, 82, 83, 90, 112, 162, 180, 166, 99, 87, 136, 160, 171, 170, 176, 172, 144, 93, 86, 34,
        40, 42, 39, 41, 40, 41, 41, 53, 38, 57, 53, 36, 35, 47, 32, 59, 48, 37, 57, 109, 153, 69,
        120, 36, 41, 35, 36, 28, 28, 37, 67, 73, 106, 113, 111, 35, 47, 92, 116, 119, 123, 126,
        130, 128, 129, 130, 132, 131, 133, 133, 130, 131, 127, 126, 129, 127, 132, 139, 139, 143,
        147, 152, 159, 161, 168, 182, 189, 194, 200, 205, 206, 209, 209, 214, 115, 83, 101, 100,
        94, 92, 83, 69, 56, 38, 33, 80, 191, 194, 167, 198, 195, 127, 46, 47, 58, 55, 63, 88,
        101, 75, 71, 70, 84, 104, 90, 78, 74, 49, 58, 74, 86, 97, 127, 166, 179, 169, 112, 87,
        131, 160, 170, 171, 177, 171, 147, 109, 79, 34, 36, 39, 38, 42, 40, 49, 42, 41, 60, 52,
        43, 79, 47, 32, 84, 38, 67, 39, 68, 91, 75, 116, 54, 40, 41, 42, 35, 33, 35, 50, 67, 90,
        110, 101, 33, 44, 88, 114, 115, 118, 124, 128, 128, 126, 125, 127, 128, 135, 129, 134,
        133, 133, 127, 127, 131, 132, 129, 137, 137, 139, 143, 151, 157, 157, 170, 171, 183, 188,
        197, 202, 206, 208, 208, 211, 191, 75, 89, 101, 97, 85, 86, 83, 65, 62, 60, 76, 185, 202,
        193, 168, 121, 57, 43, 54, 57, 56, 84, 95, 81, 70, 67, 71, 97, 105, 85, 79, 60, 52, 61, 48,
        85, 108, 112, 159, 174, 165, 110, 87, 131, 163, 167, 171, 177, 171, 150, 98, 84, 33, 36,
        43, 33, 49, 44, 58, 31, 37, 67, 61, 55, 83, 34, 36, 81, 60, 62, 49, 43, 60, 142, 64, 83,
        33, 37, 37, 28, 28, 37, 72, 87, 79, 42, 36, 74, 94, 108, 115, 118, 125, 123, 125, 127,
        129, 133, 129, 131, 132, 136, 136, 133, 131, 135, 132, 131, 129, 128, 132, 136, 138, 140,
        148, 153, 160, 162, 169, 179, 186, 193, 196, 202, 207, 208, 214, 209, 71, 88, 93, 96, 91,
        89, 89, 79, 84, 81, 94, 184, 207, 169, 89, 56, 46, 60, 64, 62, 82, 99, 88, 68, 60, 71,
        84, 106, 92, 87, 65, 54, 65, 49, 36, 66, 83, 102, 146, 175, 166, 120, 87, 127, 160, 170,
        174, 178, 172, 157, 69, 55, 41, 40, 46, 35, 53, 43, 77, 41, 41, 51, 56, 57, 109, 83, 42,
        64, 33, 57, 103, 47, 90, 107, 96, 40, 27, 40, 43, 36, 38, 41, 38, 29, 53, 79, 97, 101,
        112, 114, 112, 115, 118, 125, 126, 125, 127, 128, 126, 130, 133, 132, 135, 138, 134, 134,
        133, 128, 133, 131, 131, 133, 141, 144, 148, 150, 156, 161, 171, 173, 183, 187, 196, 199,
        202, 208, 211, 211, 82, 80, 89, 91, 97, 97, 92, 90, 99, 98, 93, 152, 155, 85, 70, 66, 66,
        72, 61, 78, 102, 91, 73, 64, 58, 83, 100, 108, 94, 80, 56, 61, 60, 38, 40, 46, 72, 81, 138,
        171, 166, 122, 89, 125, 160, 170, 173, 174, 171, 154, 50, 36, 38, 65, 34, 51, 49, 52, 93,
        36, 41, 63, 46, 42, 93, 111, 35, 82, 103, 29, 60, 45, 63, 115, 90, 68, 37, 50, 48, 31,
        30, 51, 64, 74, 83, 103, 110, 110, 113, 117, 119, 118, 116, 126, 123, 126, 122, 127, 132,
        130, 131, 130, 138, 137, 129, 134, 134, 131, 134, 130, 131, 133, 137, 141, 145, 147, 160,
        162, 168, 178, 183, 183, 193, 196, 202, 209, 209, 212, 150, 71, 83, 88, 101, 104, 95, 101,
        108, 106, 103, 103, 94, 78, 83, 89, 81, 63, 68, 93, 90, 78, 66, 56, 69, 96, 105, 105, 95,
        70, 55, 50, 45, 47, 45, 60, 57, 67, 138, 186, 189, 142, 90, 127, 158, 173, 179, 179, 174,
        133, 44, 55, 37, 40, 37, 46, 47, 51, 44, 42, 33, 89, 31, 33, 105, 123, 47, 39, 122, 38,
        47, 119, 36, 97, 81, 47, 37, 40, 41, 43, 45, 72, 89, 103, 103, 107, 113, 114, 114, 120,
        118, 120, 118, 121, 128, 127, 127, 125, 128, 128, 132, 131, 133, 137, 133, 137, 131, 141,
        134, 138, 133, 139, 141, 143, 143, 147, 153, 158, 166, 173, 173, 181, 191, 195, 200, 207,
        204, 209, 196, 60, 81, 91, 99, 105, 106, 111, 113, 103, 100, 94, 91, 89, 98, 97, 79, 69,
        85, 88, 70, 62, 65, 63, 87, 109, 111, 96, 82, 60, 51, 46, 39, 44, 41, 48, 46, 54, 144, 199,
        199, 178, 98, 124, 157, 170, 175, 174, 170, 133, 64, 38, 60, 41, 39, 45, 49, 54, 39, 85,
        37, 130, 36, 34, 117, 72, 115, 32, 83, 51, 32, 61, 81, 77, 107, 81, 35, 30, 39, 53, 76, 90,
        98, 102, 108, 107, 112, 115, 114, 113, 122, 121, 116, 121, 123, 123, 127, 125, 130, 128,
        130, 129, 134, 131, 134, 140, 134, 135, 139, 140, 140, 137, 142, 144, 144, 147, 156, 162,
        159, 173, 172, 179, 187, 193, 198, 201, 205, 209, 210, 57, 76, 88, 97, 100, 113, 114, 110,
        108, 105, 100, 99, 110, 108, 96, 86, 87, 85, 75, 67, 66, 62, 78, 107, 117, 102, 83, 69,
        49, 52, 44, 54, 82, 45, 46, 48, 48, 157, 192, 197, 184, 98, 128, 155, 170, 175, 175, 169,
        104, 65, 44, 36, 49, 48, 51, 53, 70, 66, 51, 44, 93, 42, 53, 112, 83, 130, 40, 69, 97, 43,
        67, 57, 43, 74, 71, 116, 32, 50, 64, 79, 99, 100, 106, 109, 111, 117, 117, 113, 123, 120,
        119, 122, 121, 123, 127, 125, 122, 129, 129, 130, 131, 135, 137, 138, 133, 134, 136, 142,
        137, 137, 137, 142, 145, 146, 150, 153, 155, 158, 169, 172, 184, 186, 191, 197, 201, 204,
        204, 209, 88, 78, 84, 91, 97, 108, 106, 119, 114, 106, 110, 114, 119, 106, 92, 85, 85,
        72, 73, 76, 71, 79, 107, 122, 117, 97, 74, 41, 44, 44, 55, 80, 79, 37, 45, 50, 44, 143,
        194, 196, 179, 97, 127, 156, 169, 175, 175, 170, 100, 56, 38, 30, 58, 55, 64, 52, 54, 69,
        46, 73, 62, 62, 49, 106, 64, 62, 116, 53, 80, 44, 41, 74, 40, 43, 38, 92, 80, 72, 74, 80,
        96, 98, 110, 114, 115, 114, 120, 115, 118, 118, 122, 122, 121, 120, 127, 123, 121, 124,
        127, 130, 129, 134, 135, 135, 132, 135, 135, 139, 141, 139, 140, 141, 140, 155, 147, 155,
        159, 156, 162, 169, 180, 188, 190, 193, 198, 204, 204, 207, 138, 91, 85, 86, 94, 96, 119,
        125, 117, 115, 116, 129, 122, 102, 80, 73, 66, 68, 82, 82, 72, 85, 116, 122, 113, 78, 51,
        43, 40, 50, 74, 95, 98];

}

@safe pure nothrow unittest
{
    FASTDetector detector = new FASTDetector;
    assert(detector.threshold == 100);
    assert(detector.type == FASTDetector.Type.FAST_9);
    assert(detector.flags == 0);
}

@safe pure nothrow unittest
{
    FASTDetector detector = new FASTDetector(3, FASTDetector.Type.FAST_10, FASTDetector.PERFORM_NON_MAX_SUPRESSION);
    assert(detector.threshold == 3);
    assert(detector.type == FASTDetector.Type.FAST_10);
    assert(detector.flags == FASTDetector.PERFORM_NON_MAX_SUPRESSION);
}

unittest
{
    auto lslice = lena_128x128.map!(v => cast(ubyte)v).array.sliced(128, 128).asImage(ImageFormat.IF_MONO);

    uint threshold = 50;
    int flags = FASTDetector.PERFORM_NON_MAX_SUPRESSION | FASTDetector.SORT_OUT_FEATURES_BY_SCORE;
    size_t cornerCount = 10;

    foreach (type; [FASTDetector.Type.FAST_9, FASTDetector.Type.FAST_10, FASTDetector.Type.FAST_11,
            FASTDetector.Type.FAST_12])
    {
        FASTDetector detector = new FASTDetector(threshold, type, flags);
        Feature[] features = detector.detect(lslice, cornerCount);

        assert(features.length == cornerCount);
        assert(features.isSorted!"a.score > b.score");
    }
}

unittest
{
    auto lslice = lena_128x128.map!(v => cast(ubyte)v).array.sliced(128, 128).asImage(ImageFormat.IF_MONO);

    uint threshold = 50;
    int flags = 0;
    size_t cornerCount = 10;

    foreach (type; [FASTDetector.Type.FAST_9, FASTDetector.Type.FAST_10, FASTDetector.Type.FAST_11,
            FASTDetector.Type.FAST_12])
    {
        FASTDetector detector = new FASTDetector(threshold, type, flags);
        Feature[] features = detector.detect(lslice, 0);

        assert(features.length != cornerCount); // real count should be around 23 with 43 without suppression
        assert(!features.isSorted!"a.score > b.score");
    }
}