// Copyright (c) 2009-2010 Satoshi Nakamoto
// Copyright (c) 2009-2016 The Bitcoin Core developers
// Distributed under the MIT software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.

#include "pow.h"
#include "validation.h"
#include "arith_uint256.h"
#include "chain.h"
#include "primitives/block.h"
#include "consensus/consensus.h"
#include "uint256.h"
#include <iostream>
#include "util.h"
#include "chainparams.h"
#include "bitcoin_bignum/bignum.h"
#include "utilstrencodings.h"
#include "crypto/MerkleTreeProof/mtp.h"
#include "mtpstate.h"
#include "fixed.h"

static CBigNum bnProofOfWorkLimit(~arith_uint256(0) >> 8);
static CBigNum bnProofOfWorkProgPowLimit(~arith_uint256(0) >> 28);

double GetDifficultyHelper(unsigned int nBits) {
    int nShift = (nBits >> 24) & 0xff;
    double dDiff = (double) 0x0000ffff / (double) (nBits & 0x00ffffff);

    while (nShift < 29) {
        dDiff *= 256.0;
        nShift++;
    }
    while (nShift > 29) {
        dDiff /= 256.0;
        nShift--;
    }

    return dDiff;
}

unsigned int GetNextWorkRequired(const CBlockIndex* pindexLast, const CBlockHeader *pblock, const Consensus::Params& params)
{
    if (!pindexLast || pindexLast->nHeight < params.nDifficultyAdjustStartBlock)
        return params.nFixedDifficulty;

    if (params.IsTestnet() || params.IsDevnet()) {
        // If the new block's timestamp is more than nTargetSpacing*6
        // then allow mining of a min-difficulty block
        if (pblock->nTime > pindexLast->nTime + params.nPowTargetTimespan * 1) {
            return params.nFixedDifficulty;
        }
    }

    // 9/29/2016 - Reset to Lyra2(2,block_height,256) due to ASIC KnC Miner Scrypt
    // 36 block look back, reset to mininmum diff
    if (params.IsMain() && pindexLast->nHeight + 1 >= HF_LYRA2VAR_HEIGHT && pindexLast->nHeight + 1 <= HF_LYRA2VAR_HEIGHT + 36 - 1) {
        return params.nFixedDifficulty;
    }
    // 02/11/2017 - Increase diff to match with new hashrates of Lyra2Z algo
    if (params.IsMain() && pindexLast->nHeight + 1 == HF_LYRA2Z_HEIGHT) {
        CBigNum bnNew;
        bnNew.SetCompact(pindexLast->nBits);
        bnNew /= 20000; // increase the diff by 20000x since the new hashrate is approx. 20000 times higher
        LogPrintf("Lyra2Z HF - Before: %08x %.8f\n", pindexLast->nBits, GetDifficultyHelper(pindexLast->nBits));
        LogPrintf("Lyra2Z HF - After: %08x %.8f\n", bnNew.GetCompact(), GetDifficultyHelper(bnNew.GetCompact()));
        if (bnNew > bnProofOfWorkLimit) { bnNew = bnProofOfWorkLimit; } // safe threshold
        return bnNew.GetCompact();
    }

    int nFirstMTPBlock = MTPState::GetMTPState()->GetFirstMTPBlockNumber(params, pindexLast);
    bool fMTP = nFirstMTPBlock > 0;

    if (pblock->IsProgPow()) {
        if (pindexLast->nTime < params.nPPSwitchTime) {
            // first ProgPOW block ever
            return params.nInitialPPDifficulty;
        }
    }
    else if (pblock->IsMTP() && !fMTP) {
        // first MTP block ever
        return params.nInitialMTPDifficulty;
    }

    uint32_t BlocksTargetSpacing =
        (params.nMTPFiveMinutesStartBlock == 0 && fMTP) || (params.nMTPFiveMinutesStartBlock > 0 && pindexLast->nHeight >= params.nMTPFiveMinutesStartBlock) ?
            params.nPowTargetSpacingMTP : params.nPowTargetSpacing;
    if (cmp::greater_equal(pindexLast->nTime, params.stage3StartTime))
        BlocksTargetSpacing /= 2;

    unsigned int TimeDaySeconds = 60 * 60 * 24;
    int64_t PastSecondsMin = TimeDaySeconds * 0.25; // 21600
    int64_t PastSecondsMax = TimeDaySeconds * 7;// 604800
    uint32_t PastBlocksMin = PastSecondsMin / BlocksTargetSpacing; // 36 blocks
    uint32_t PastBlocksMax = PastSecondsMax / BlocksTargetSpacing; // 1008 blocks
    uint32_t StartingPoWBlock = 0;

    if (pblock->IsShorterBlocksSpacing()) {
        if (cmp::less(pindexLast->nTime, params.stage3StartTime)) {
            // first time we see a block with shorter interval
            // Normally we should take difficulty and halve it. But to give some leeway to the miners
            // we divide it by 4
            uint32_t base = (pindexLast->nBits & 0x007fffff) << 2;
            uint32_t exponent = pindexLast->nBits >> 24;

            if (base > 0x007fffff) {
                base >>= 8;
                exponent++;
            }
            return (exponent << 24) | base;
        }

        uint32_t  numberOfStage3Blocks = pindexLast->nHeight;

        if (params.stage3StartBlock != 0) {
            // we know the first stage3 block
            numberOfStage3Blocks = pindexLast->nHeight - params.stage3StartBlock + 1;
        }
        else if (pblock->nTime < params.stage3StartTime + BlocksTargetSpacing*PastBlocksMax*3) {
            // transition to stage3 happened recently, look for the last block before the transition
            const CBlockIndex *pindex = pindexLast;
            while (pindex && cmp::greater_equal(pindex->nTime, params.stage3StartTime))
                pindex = pindex->pprev;

            if (pindex)
                numberOfStage3Blocks = pindexLast->nHeight - pindex->nHeight;
        }

        if (numberOfStage3Blocks < params.DifficultyAdjustmentInterval(true)/2)
            // do not retarget if too few stage3 blocks
            return pindexLast->nBits;
            
        PastBlocksMin = std::min(PastBlocksMin, numberOfStage3Blocks);
        PastBlocksMax = std::min(PastBlocksMax, numberOfStage3Blocks);
    }
    else if (pblock->IsProgPow()) {
        uint32_t numberOfPPBlocks = pindexLast->nHeight;

        if (params.nPPBlockNumber != 0) {
            // we know the first ProgPow block
            numberOfPPBlocks = pindexLast->nHeight - params.nPPBlockNumber + 1;
        }
        else if (pblock->nTime < params.nPPSwitchTime + BlocksTargetSpacing*PastBlocksMax*3) {
            // transition to progpow happened recently, look for the first PP block
            const CBlockIndex *pindex = pindexLast;
            while (pindex && pindex->nTime >= params.nPPSwitchTime)
                pindex = pindex->pprev;

            if (pindex)
                numberOfPPBlocks = pindexLast->nHeight - pindex->nHeight;
        }

        if (numberOfPPBlocks < params.DifficultyAdjustmentInterval(true)/2)
            // do not retarget if too few PP blocks
            return params.nInitialPPDifficulty;

        PastBlocksMin = std::min(PastBlocksMin, numberOfPPBlocks);
        PastBlocksMax = std::min(PastBlocksMax, numberOfPPBlocks);
    }
    else if (nFirstMTPBlock > 1) {
        // There are both legacy and MTP blocks in the chain. Limit PoW calculation scope to MTP blocks only
        uint32_t numberOfMTPBlocks = pindexLast->nHeight - nFirstMTPBlock + 1;
        PastBlocksMin = std::min(PastBlocksMin, numberOfMTPBlocks);
        PastBlocksMax = std::min(PastBlocksMax, numberOfMTPBlocks);
        StartingPoWBlock = nFirstMTPBlock;
    }

    if ((pindexLast->nHeight + 1 - StartingPoWBlock) % params.DifficultyAdjustmentInterval(fMTP) != 0) // Retarget every nInterval blocks
    {
        return pindexLast->nBits;
    }

    return BorisRidiculouslyNamedDifficultyFunction(pindexLast, BlocksTargetSpacing, PastBlocksMin, PastBlocksMax);
}

unsigned int CalculateNextWorkRequired(const CBlockIndex* pindexLast, int64_t nFirstBlockTime, const Consensus::Params& params)
{
    if (params.fPowNoRetargeting)
        return pindexLast->nBits;

    // Limit adjustment step
    int64_t nActualTimespan = pindexLast->GetBlockTime() - nFirstBlockTime;
    if (nActualTimespan < params.nPowTargetTimespan/4)
        nActualTimespan = params.nPowTargetTimespan/4;
    if (nActualTimespan > params.nPowTargetTimespan*4)
        nActualTimespan = params.nPowTargetTimespan*4;

    // Retarget
    const arith_uint256 bnPowLimit = UintToArith256(params.powLimit);
    arith_uint256 bnNew;
    bnNew.SetCompact(pindexLast->nBits);
    bnNew *= nActualTimespan;
    bnNew /= params.nPowTargetTimespan;

    if (bnNew > bnPowLimit)
        bnNew = bnPowLimit;

    return bnNew.GetCompact();
}

// Firo - MTP
bool CheckMerkleTreeProof(const CBlockHeader &block, const Consensus::Params &params) {
    if (!block.IsMTP() || block.IsProgPow())
	    return true;

    if (!block.mtpHashData || block.mtpHashData->IsMTPDataStripped())
        // MTP data was stripped from the block, can't verify. Return true
        return true;

    uint256 calculatedMtpHashValue;
    bool isVerified = mtp::verify(block.nNonce, block, Params().GetConsensus().powLimit, &calculatedMtpHashValue) &&
        block.mtpHashValue == calculatedMtpHashValue;

    if(!isVerified)
        return false;

    return true;
}

bool CheckProofOfWork(uint256 hash, unsigned int nBits, const Consensus::Params& params)
{
    bool fNegative;
    bool fOverflow;
    arith_uint256 bnTarget;

    bnTarget.SetCompact(nBits, &fNegative, &fOverflow);
    // Check range
    if (fNegative || bnTarget == 0 || fOverflow || bnTarget > UintToArith256(params.powLimit))
        return false;

    // Check proof of work matches boundary
    if (UintToArith256(hash) > bnTarget)
        return false;
    return true;
}

unsigned int BorisRidiculouslyNamedDifficultyFunction(const CBlockIndex *pindexLast, uint32_t TargetBlocksSpacingSeconds,
                                         uint32_t PastBlocksMin, uint32_t PastBlocksMax) {

    const CBlockIndex *BlockLastSolved = pindexLast;
    const CBlockIndex *BlockReading = pindexLast;

    typedef numeric::Fixed<32, 32> fixed;

    uint32_t nPastBlocks = 0;
    int32_t nActualSeconds = 0;
    int32_t nTargetSeconds = 0;
    fixed nBlockTimeRatio = 1;
    CBigNum bnPastTargetAverage;
    CBigNum bnPastTargetAveragePrev;

    float FastBlocksLimit[5040] = {317.772675, 136.233047, 83.194504, 58.732189, 44.894745, 36.089561, 30.038040,
                                   25.646383, 22.327398, 19.739056, 17.669304, 15.980045, 14.577670, 13.396597,
                                   12.389578, 11.521759, 10.766892, 10.104856, 9.519974, 8.999868, 8.534638, 8.116274,
                                   7.738231, 7.395114, 7.082433, 6.796428, 6.533921, 6.292217, 6.069008, 5.862312,
                                   5.670416, 5.491832, 5.325264, 5.169573, 5.023761, 4.886943, 4.758339, 4.637252,
                                   4.523063, 4.415215, 4.313211, 4.216604, 4.124989, 4.038000, 3.955308, 3.876611,
                                   3.801635, 3.730131, 3.661870, 3.596645, 3.534262, 3.474546, 3.417336, 3.362480,
                                   3.309842, 3.259294, 3.210718, 3.164004, 3.119051, 3.075764, 3.034055, 2.993842,
                                   2.955048, 2.917603, 2.881439, 2.846493, 2.812708, 2.780028, 2.748401, 2.717779,
                                   2.688117, 2.659371, 2.631500, 2.604468, 2.578238, 2.552775, 2.528048, 2.504027,
                                   2.480681, 2.457985, 2.435913, 2.414439, 2.393541, 2.373197, 2.353385, 2.334085,
                                   2.315279, 2.296949, 2.279077, 2.261647, 2.244643, 2.228050, 2.211855, 2.196043,
                                   2.180601, 2.165517, 2.150779, 2.136376, 2.122297, 2.108531, 2.095068, 2.081899,
                                   2.069015, 2.056406, 2.044064, 2.031982, 2.020151, 2.008564, 1.997213, 1.986092,
                                   1.975194, 1.964513, 1.954042, 1.943775, 1.933707, 1.923833, 1.914146, 1.904642,
                                   1.895315, 1.886162, 1.877177, 1.868356, 1.859695, 1.851189, 1.842834, 1.834627,
                                   1.826564, 1.818642, 1.810856, 1.803203, 1.795680, 1.788284, 1.781012, 1.773861,
                                   1.766828, 1.759910, 1.753104, 1.746408, 1.739819, 1.733335, 1.726954, 1.720672,
                                   1.714488, 1.708400, 1.702405, 1.696502, 1.690688, 1.684962, 1.679321, 1.673764,
                                   1.668288, 1.662894, 1.657577, 1.652337, 1.647173, 1.642082, 1.637064, 1.632116,
                                   1.627238, 1.622427, 1.617683, 1.613004, 1.608389, 1.603837, 1.599346, 1.594915,
                                   1.590544, 1.586230, 1.581973, 1.577772, 1.573626, 1.569533, 1.565493, 1.561504,
                                   1.557567, 1.553679, 1.549840, 1.546049, 1.542306, 1.538608, 1.534956, 1.531349,
                                   1.527786, 1.524266, 1.520788, 1.517352, 1.513956, 1.510601, 1.507286, 1.504009,
                                   1.500770, 1.497570, 1.494406, 1.491278, 1.488186, 1.485129, 1.482107, 1.479118,
                                   1.476164, 1.473242, 1.470352, 1.467494, 1.464668, 1.461872, 1.459107, 1.456372,
                                   1.453666, 1.450989, 1.448341, 1.445720, 1.443128, 1.440562, 1.438024, 1.435511,
                                   1.433025, 1.430565, 1.428129, 1.425719, 1.423333, 1.420971, 1.418633, 1.416319,
                                   1.414028, 1.411759, 1.409513, 1.407289, 1.405087, 1.402906, 1.400746, 1.398608,
                                   1.396490, 1.394392, 1.392315, 1.390257, 1.388219, 1.386200, 1.384199, 1.382218,
                                   1.380255, 1.378310, 1.376384, 1.374475, 1.372583, 1.370709, 1.368852, 1.367011,
                                   1.365187, 1.363380, 1.361589, 1.359813, 1.358054, 1.356310, 1.354581, 1.352868,
                                   1.351169, 1.349485, 1.347816, 1.346161, 1.344521, 1.342894, 1.341282, 1.339683,
                                   1.338098, 1.336526, 1.334967, 1.333421, 1.331888, 1.330368, 1.328861, 1.327366,
                                   1.325883, 1.324412, 1.322953, 1.321507, 1.320072, 1.318648, 1.317236, 1.315835,
                                   1.314446, 1.313067, 1.311700, 1.310343, 1.308997, 1.307661, 1.306336, 1.305021,
                                   1.303717, 1.302422, 1.301138, 1.299863, 1.298598, 1.297343, 1.296097, 1.294861,
                                   1.293634, 1.292416, 1.291208, 1.290008, 1.288818, 1.287636, 1.286463, 1.285298,
                                   1.284142, 1.282995, 1.281856, 1.280725, 1.279603, 1.278489, 1.277382, 1.276284,
                                   1.275193, 1.274111, 1.273036, 1.271968, 1.270908, 1.269856, 1.268811, 1.267773,
                                   1.266743, 1.265720, 1.264703, 1.263694, 1.262692, 1.261697, 1.260708, 1.259727,
                                   1.258752, 1.257783, 1.256821, 1.255866, 1.254917, 1.253975, 1.253038, 1.252108,
                                   1.251184, 1.250267, 1.249355, 1.248449, 1.247550, 1.246656, 1.245768, 1.244886,
                                   1.244009, 1.243139, 1.242273, 1.241414, 1.240560, 1.239711, 1.238868, 1.238030,
                                   1.237198, 1.236371, 1.235548, 1.234732, 1.233920, 1.233113, 1.232312, 1.231515,
                                   1.230723, 1.229937, 1.229155, 1.228378, 1.227605, 1.226838, 1.226075, 1.225316,
                                   1.224563, 1.223814, 1.223069, 1.222329, 1.221593, 1.220862, 1.220135, 1.219412,
                                   1.218694, 1.217980, 1.217270, 1.216565, 1.215863, 1.215166, 1.214473, 1.213783,
                                   1.213098, 1.212417, 1.211740, 1.211066, 1.210397, 1.209731, 1.209069, 1.208411,
                                   1.207757, 1.207106, 1.206459, 1.205816, 1.205176, 1.204540, 1.203907, 1.203278,
                                   1.202653, 1.202031, 1.201412, 1.200797, 1.200186, 1.199577, 1.198972, 1.198371,
                                   1.197772, 1.197177, 1.196586, 1.195997, 1.195411, 1.194829, 1.194250, 1.193674,
                                   1.193101, 1.192531, 1.191964, 1.191401, 1.190840, 1.190282, 1.189727, 1.189175,
                                   1.188626, 1.188080, 1.187537, 1.186996, 1.186459, 1.185924, 1.185392, 1.184862,
                                   1.184336, 1.183812, 1.183291, 1.182772, 1.182256, 1.181743, 1.181233, 1.180725,
                                   1.180219, 1.179716, 1.179216, 1.178718, 1.178223, 1.177730, 1.177240, 1.176752,
                                   1.176267, 1.175784, 1.175303, 1.174825, 1.174349, 1.173875, 1.173404, 1.172935,
                                   1.172468, 1.172004, 1.171542, 1.171082, 1.170625, 1.170169, 1.169716, 1.169265,
                                   1.168816, 1.168370, 1.167925, 1.167483, 1.167042, 1.166604, 1.166168, 1.165734,
                                   1.165302, 1.164872, 1.164444, 1.164018, 1.163594, 1.163172, 1.162752, 1.162334,
                                   1.161918, 1.161504, 1.161092, 1.160681, 1.160273, 1.159867, 1.159462, 1.159059,
                                   1.158658, 1.158259, 1.157862, 1.157466, 1.157072, 1.156680, 1.156290, 1.155902,
                                   1.155515, 1.155130, 1.154747, 1.154365, 1.153986, 1.153607, 1.153231, 1.152856,
                                   1.152483, 1.152112, 1.151742, 1.151374, 1.151007, 1.150642, 1.150279, 1.149917,
                                   1.149557, 1.149198, 1.148841, 1.148486, 1.148132, 1.147779, 1.147428, 1.147079,
                                   1.146731, 1.146385, 1.146040, 1.145696, 1.145354, 1.145014, 1.144675, 1.144337,
                                   1.144001, 1.143666, 1.143332, 1.143000, 1.142670, 1.142340, 1.142012, 1.141686,
                                   1.141361, 1.141037, 1.140715, 1.140393, 1.140074, 1.139755, 1.139438, 1.139122,
                                   1.138808, 1.138494, 1.138182, 1.137872, 1.137562, 1.137254, 1.136947, 1.136641,
                                   1.136337, 1.136034, 1.135732, 1.135431, 1.135131, 1.134833, 1.134536, 1.134240,
                                   1.133945, 1.133651, 1.133359, 1.133067, 1.132777, 1.132488, 1.132200, 1.131913,
                                   1.131628, 1.131343, 1.131060, 1.130778, 1.130496, 1.130216, 1.129937, 1.129659,
                                   1.129382, 1.129107, 1.128832, 1.128558, 1.128286, 1.128014, 1.127744, 1.127474,
                                   1.127206, 1.126938, 1.126672, 1.126407, 1.126142, 1.125879, 1.125616, 1.125355,
                                   1.125095, 1.124835, 1.124577, 1.124319, 1.124063, 1.123807, 1.123552, 1.123299,
                                   1.123046, 1.122794, 1.122543, 1.122293, 1.122044, 1.121796, 1.121549, 1.121303,
                                   1.121058, 1.120813, 1.120570, 1.120327, 1.120085, 1.119844, 1.119604, 1.119365,
                                   1.119127, 1.118889, 1.118653, 1.118417, 1.118182, 1.117948, 1.117715, 1.117482,
                                   1.117251, 1.117020, 1.116790, 1.116561, 1.116333, 1.116106, 1.115879, 1.115653,
                                   1.115428, 1.115204, 1.114980, 1.114758, 1.114536, 1.114315, 1.114094, 1.113875,
                                   1.113656, 1.113438, 1.113221, 1.113004, 1.112788, 1.112573, 1.112359, 1.112146,
                                   1.111933, 1.111721, 1.111509, 1.111299, 1.111089, 1.110880, 1.110671, 1.110463,
                                   1.110256, 1.110050, 1.109844, 1.109639, 1.109435, 1.109231, 1.109029, 1.108826,
                                   1.108625, 1.108424, 1.108224, 1.108024, 1.107825, 1.107627, 1.107430, 1.107233,
                                   1.107037, 1.106841, 1.106646, 1.106452, 1.106258, 1.106065, 1.105873, 1.105681,
                                   1.105490, 1.105300, 1.105110, 1.104921, 1.104732, 1.104544, 1.104357, 1.104170,
                                   1.103984, 1.103798, 1.103613, 1.103429, 1.103245, 1.103062, 1.102879, 1.102697,
                                   1.102516, 1.102335, 1.102155, 1.101975, 1.101796, 1.101617, 1.101439, 1.101262,
                                   1.101085, 1.100909, 1.100733, 1.100558, 1.100383, 1.100209, 1.100036, 1.099862,
                                   1.099690, 1.099518, 1.099347, 1.099176, 1.099006, 1.098836, 1.098667, 1.098498,
                                   1.098330, 1.098162, 1.097995, 1.097828, 1.097662, 1.097496, 1.097331, 1.097167,
                                   1.097003, 1.096839, 1.096676, 1.096513, 1.096351, 1.096190, 1.096028, 1.095868,
                                   1.095708, 1.095548, 1.095389, 1.095230, 1.095072, 1.094914, 1.094757, 1.094600,
                                   1.094444, 1.094288, 1.094133, 1.093978, 1.093823, 1.093669, 1.093516, 1.093362,
                                   1.093210, 1.093058, 1.092906, 1.092755, 1.092604, 1.092453, 1.092303, 1.092154,
                                   1.092005, 1.091856, 1.091708, 1.091560, 1.091413, 1.091266, 1.091120, 1.090973,
                                   1.090828, 1.090683, 1.090538, 1.090393, 1.090250, 1.090106, 1.089963, 1.089820,
                                   1.089678, 1.089536, 1.089394, 1.089253, 1.089113, 1.088972, 1.088833, 1.088693,
                                   1.088554, 1.088415, 1.088277, 1.088139, 1.088002, 1.087865, 1.087728, 1.087591,
                                   1.087456, 1.087320, 1.087185, 1.087050, 1.086915, 1.086781, 1.086648, 1.086514,
                                   1.086381, 1.086249, 1.086117, 1.085985, 1.085853, 1.085722, 1.085591, 1.085461,
                                   1.085331, 1.085201, 1.085072, 1.084943, 1.084815, 1.084686, 1.084558, 1.084431,
                                   1.084304, 1.084177, 1.084050, 1.083924, 1.083798, 1.083673, 1.083548, 1.083423,
                                   1.083298, 1.083174, 1.083050, 1.082927, 1.082804, 1.082681, 1.082559, 1.082437,
                                   1.082315, 1.082193, 1.082072, 1.081951, 1.081831, 1.081711, 1.081591, 1.081471,
                                   1.081352, 1.081233, 1.081114, 1.080996, 1.080878, 1.080760, 1.080643, 1.080526,
                                   1.080409, 1.080293, 1.080177, 1.080061, 1.079946, 1.079830, 1.079715, 1.079601,
                                   1.079486, 1.079373, 1.079259, 1.079145, 1.079032, 1.078919, 1.078807, 1.078695,
                                   1.078583, 1.078471, 1.078360, 1.078249, 1.078138, 1.078027, 1.077917, 1.077807,
                                   1.077697, 1.077588, 1.077479, 1.077370, 1.077261, 1.077153, 1.077045, 1.076937,
                                   1.076830, 1.076723, 1.076616, 1.076509, 1.076403, 1.076296, 1.076191, 1.076085,
                                   1.075980, 1.075875, 1.075770, 1.075665, 1.075561, 1.075457, 1.075353, 1.075250,
                                   1.075147, 1.075044, 1.074941, 1.074838, 1.074736, 1.074634, 1.074533, 1.074431,
                                   1.074330, 1.074229, 1.074128, 1.074028, 1.073928, 1.073828, 1.073728, 1.073628,
                                   1.073529, 1.073430, 1.073331, 1.073233, 1.073135, 1.073037, 1.072939, 1.072841,
                                   1.072744, 1.072647, 1.072550, 1.072453, 1.072357, 1.072261, 1.072165, 1.072069,
                                   1.071974, 1.071878, 1.071783, 1.071689, 1.071594, 1.071500, 1.071406, 1.071312,
                                   1.071218, 1.071125, 1.071032, 1.070939, 1.070846, 1.070753, 1.070661, 1.070569,
                                   1.070477, 1.070385, 1.070294, 1.070203, 1.070112, 1.070021, 1.069930, 1.069840,
                                   1.069750, 1.069660, 1.069570, 1.069480, 1.069391, 1.069302, 1.069213, 1.069124,
                                   1.069036, 1.068948, 1.068859, 1.068771, 1.068684, 1.068596, 1.068509, 1.068422,
                                   1.068335, 1.068248, 1.068162, 1.068076, 1.067990, 1.067904, 1.067818, 1.067733,
                                   1.067647, 1.067562, 1.067477, 1.067392, 1.067308, 1.067224, 1.067140, 1.067056,
                                   1.066972, 1.066888, 1.066805, 1.066722, 1.066639, 1.066556, 1.066473, 1.066391,
                                   1.066308, 1.066226, 1.066145, 1.066063, 1.065981, 1.065900, 1.065819, 1.065738,
                                   1.065657, 1.065576, 1.065496, 1.065416, 1.065336, 1.065256, 1.065176, 1.065096,
                                   1.065017, 1.064938, 1.064859, 1.064780, 1.064701, 1.064623, 1.064545, 1.064466,
                                   1.064388, 1.064311, 1.064233, 1.064155, 1.064078, 1.064001, 1.063924, 1.063847,
                                   1.063771, 1.063694, 1.063618, 1.063542, 1.063466, 1.063390, 1.063314, 1.063239,
                                   1.063164, 1.063088, 1.063013, 1.062939, 1.062864, 1.062789, 1.062715, 1.062641,
                                   1.062567, 1.062493, 1.062419, 1.062346, 1.062272, 1.062199, 1.062126, 1.062053,
                                   1.061980, 1.061908, 1.061835, 1.061763, 1.061691, 1.061619, 1.061547, 1.061475,
                                   1.061404, 1.061332, 1.061261, 1.061190, 1.061119, 1.061048, 1.060977, 1.060907,
                                   1.060837, 1.060766, 1.060696, 1.060626, 1.060557, 1.060487, 1.060418, 1.060348,
                                   1.060279, 1.060210, 1.060141, 1.060072, 1.060004, 1.059935, 1.059867, 1.059799,
                                   1.059731, 1.059663, 1.059595, 1.059527, 1.059460, 1.059393, 1.059325, 1.059258,
                                   1.059191, 1.059124, 1.059058, 1.058991, 1.058925, 1.058859, 1.058792, 1.058727,
                                   1.058661, 1.058595, 1.058529, 1.058464, 1.058399, 1.058333, 1.058268, 1.058203,
                                   1.058139, 1.058074, 1.058010, 1.057945, 1.057881, 1.057817, 1.057753, 1.057689,
                                   1.057625, 1.057561, 1.057498, 1.057434, 1.057371, 1.057308, 1.057245, 1.057182,
                                   1.057119, 1.057057, 1.056994, 1.056932, 1.056870, 1.056808, 1.056746, 1.056684,
                                   1.056622, 1.056560, 1.056499, 1.056437, 1.056376, 1.056315, 1.056254, 1.056193,
                                   1.056132, 1.056072, 1.056011, 1.055951, 1.055890, 1.055830, 1.055770, 1.055710,
                                   1.055650, 1.055591, 1.055531, 1.055471, 1.055412, 1.055353, 1.055294, 1.055235,
                                   1.055176, 1.055117, 1.055058, 1.054999, 1.054941, 1.054883, 1.054824, 1.054766,
                                   1.054708, 1.054650, 1.054593, 1.054535, 1.054477, 1.054420, 1.054363, 1.054305,
                                   1.054248, 1.054191, 1.054134, 1.054077, 1.054021, 1.053964, 1.053908, 1.053851,
                                   1.053795, 1.053739, 1.053683, 1.053627, 1.053571, 1.053515, 1.053460, 1.053404,
                                   1.053349, 1.053293, 1.053238, 1.053183, 1.053128, 1.053073, 1.053018, 1.052963,
                                   1.052909, 1.052854, 1.052800, 1.052746, 1.052691, 1.052637, 1.052583, 1.052529,
                                   1.052476, 1.052422, 1.052368, 1.052315, 1.052261, 1.052208, 1.052155, 1.052102,
                                   1.052049, 1.051996, 1.051943, 1.051890, 1.051838, 1.051785, 1.051733, 1.051681,
                                   1.051628, 1.051576, 1.051524, 1.051472, 1.051420, 1.051369, 1.051317, 1.051265,
                                   1.051214, 1.051163, 1.051111, 1.051060, 1.051009, 1.050958, 1.050907, 1.050856,
                                   1.050805, 1.050755, 1.050704, 1.050654, 1.050604, 1.050553, 1.050503, 1.050453,
                                   1.050403, 1.050353, 1.050303, 1.050254, 1.050204, 1.050154, 1.050105, 1.050056,
                                   1.050006, 1.049957, 1.049908, 1.049859, 1.049810, 1.049761, 1.049712, 1.049664,
                                   1.049615, 1.049567, 1.049518, 1.049470, 1.049422, 1.049373, 1.049325, 1.049277,
                                   1.049229, 1.049182, 1.049134, 1.049086, 1.049039, 1.048991, 1.048944, 1.048896,
                                   1.048849, 1.048802, 1.048755, 1.048708, 1.048661, 1.048614, 1.048567, 1.048521,
                                   1.048474, 1.048428, 1.048381, 1.048335, 1.048289, 1.048242, 1.048196, 1.048150,
                                   1.048104, 1.048059, 1.048013, 1.047967, 1.047922, 1.047876, 1.047830, 1.047785,
                                   1.047740, 1.047695, 1.047649, 1.047604, 1.047559, 1.047514, 1.047469, 1.047425,
                                   1.047380, 1.047336, 1.047291, 1.047246, 1.047202, 1.047158, 1.047114, 1.047069,
                                   1.047025, 1.046981, 1.046937, 1.046893, 1.046850, 1.046806, 1.046762, 1.046719,
                                   1.046675, 1.046632, 1.046589, 1.046545, 1.046502, 1.046459, 1.046416, 1.046373,
                                   1.046330, 1.046287, 1.046244, 1.046202, 1.046159, 1.046116, 1.046074, 1.046032,
                                   1.045989, 1.045947, 1.045905, 1.045863, 1.045821, 1.045779, 1.045737, 1.045695,
                                   1.045653, 1.045611, 1.045570, 1.045528, 1.045487, 1.045445, 1.045404, 1.045363,
                                   1.045321, 1.045280, 1.045239, 1.045198, 1.045157, 1.045116, 1.045075, 1.045035,
                                   1.044994, 1.044953, 1.044913, 1.044872, 1.044832, 1.044791, 1.044751, 1.044711,
                                   1.044671, 1.044631, 1.044591, 1.044551, 1.044511, 1.044471, 1.044431, 1.044392,
                                   1.044352, 1.044312, 1.044273, 1.044233, 1.044194, 1.044155, 1.044115, 1.044076,
                                   1.044037, 1.043998, 1.043959, 1.043920, 1.043881, 1.043842, 1.043804, 1.043765,
                                   1.043726, 1.043688, 1.043649, 1.043611, 1.043572, 1.043534, 1.043496, 1.043458,
                                   1.043419, 1.043381, 1.043343, 1.043305, 1.043267, 1.043230, 1.043192, 1.043154,
                                   1.043116, 1.043079, 1.043041, 1.043004, 1.042966, 1.042929, 1.042892, 1.042854,
                                   1.042817, 1.042780, 1.042743, 1.042706, 1.042669, 1.042632, 1.042595, 1.042559,
                                   1.042522, 1.042485, 1.042449, 1.042412, 1.042376, 1.042339, 1.042303, 1.042266,
                                   1.042230, 1.042194, 1.042158, 1.042122, 1.042086, 1.042050, 1.042014, 1.041978,
                                   1.041942, 1.041906, 1.041870, 1.041835, 1.041799, 1.041764, 1.041728, 1.041693,
                                   1.041657, 1.041622, 1.041587, 1.041552, 1.041516, 1.041481, 1.041446, 1.041411,
                                   1.041376, 1.041341, 1.041307, 1.041272, 1.041237, 1.041202, 1.041168, 1.041133,
                                   1.041099, 1.041064, 1.041030, 1.040995, 1.040961, 1.040927, 1.040893, 1.040859,
                                   1.040824, 1.040790, 1.040756, 1.040722, 1.040688, 1.040655, 1.040621, 1.040587,
                                   1.040553, 1.040520, 1.040486, 1.040453, 1.040419, 1.040386, 1.040352, 1.040319,
                                   1.040286, 1.040252, 1.040219, 1.040186, 1.040153, 1.040120, 1.040087, 1.040054,
                                   1.040021, 1.039988, 1.039955, 1.039923, 1.039890, 1.039857, 1.039825, 1.039792,
                                   1.039760, 1.039727, 1.039695, 1.039662, 1.039630, 1.039598, 1.039566, 1.039533,
                                   1.039501, 1.039469, 1.039437, 1.039405, 1.039373, 1.039341, 1.039310, 1.039278,
                                   1.039246, 1.039214, 1.039183, 1.039151, 1.039119, 1.039088, 1.039056, 1.039025,
                                   1.038994, 1.038962, 1.038931, 1.038900, 1.038869, 1.038837, 1.038806, 1.038775,
                                   1.038744, 1.038713, 1.038682, 1.038651, 1.038621, 1.038590, 1.038559, 1.038528,
                                   1.038498, 1.038467, 1.038436, 1.038406, 1.038375, 1.038345, 1.038315, 1.038284,
                                   1.038254, 1.038224, 1.038193, 1.038163, 1.038133, 1.038103, 1.038073, 1.038043,
                                   1.038013, 1.037983, 1.037953, 1.037923, 1.037894, 1.037864, 1.037834, 1.037804,
                                   1.037775, 1.037745, 1.037716, 1.037686, 1.037657, 1.037627, 1.037598, 1.037569,
                                   1.037539, 1.037510, 1.037481, 1.037452, 1.037423, 1.037394, 1.037364, 1.037336,
                                   1.037307, 1.037278, 1.037249, 1.037220, 1.037191, 1.037162, 1.037134, 1.037105,
                                   1.037076, 1.037048, 1.037019, 1.036991, 1.036962, 1.036934, 1.036905, 1.036877,
                                   1.036849, 1.036820, 1.036792, 1.036764, 1.036736, 1.036708, 1.036680, 1.036651,
                                   1.036623, 1.036596, 1.036568, 1.036540, 1.036512, 1.036484, 1.036456, 1.036429,
                                   1.036401, 1.036373, 1.036346, 1.036318, 1.036291, 1.036263, 1.036235, 1.036208,
                                   1.036181, 1.036153, 1.036126, 1.036099, 1.036071, 1.036044, 1.036017, 1.035990,
                                   1.035963, 1.035936, 1.035909, 1.035882, 1.035855, 1.035828, 1.035801, 1.035774,
                                   1.035747, 1.035721, 1.035694, 1.035667, 1.035641, 1.035614, 1.035587, 1.035561,
                                   1.035534, 1.035508, 1.035481, 1.035455, 1.035429, 1.035402, 1.035376, 1.035350,
                                   1.035324, 1.035297, 1.035271, 1.035245, 1.035219, 1.035193, 1.035167, 1.035141,
                                   1.035115, 1.035089, 1.035063, 1.035037, 1.035012, 1.034986, 1.034960, 1.034934,
                                   1.034909, 1.034883, 1.034857, 1.034832, 1.034806, 1.034781, 1.034755, 1.034730,
                                   1.034704, 1.034679, 1.034654, 1.034629, 1.034603, 1.034578, 1.034553, 1.034528,
                                   1.034503, 1.034477, 1.034452, 1.034427, 1.034402, 1.034377, 1.034352, 1.034328,
                                   1.034303, 1.034278, 1.034253, 1.034228, 1.034204, 1.034179, 1.034154, 1.034130,
                                   1.034105, 1.034080, 1.034056, 1.034031, 1.034007, 1.033982, 1.033958, 1.033934,
                                   1.033909, 1.033885, 1.033861, 1.033836, 1.033812, 1.033788, 1.033764, 1.033740,
                                   1.033715, 1.033691, 1.033667, 1.033643, 1.033619, 1.033595, 1.033571, 1.033548,
                                   1.033524, 1.033500, 1.033476, 1.033452, 1.033429, 1.033405, 1.033381, 1.033358,
                                   1.033334, 1.033310, 1.033287, 1.033263, 1.033240, 1.033216, 1.033193, 1.033170,
                                   1.033146, 1.033123, 1.033100, 1.033076, 1.033053, 1.033030, 1.033007, 1.032984,
                                   1.032960, 1.032937, 1.032914, 1.032891, 1.032868, 1.032845, 1.032822, 1.032799,
                                   1.032776, 1.032754, 1.032731, 1.032708, 1.032685, 1.032662, 1.032640, 1.032617,
                                   1.032594, 1.032572, 1.032549, 1.032526, 1.032504, 1.032481, 1.032459, 1.032436,
                                   1.032414, 1.032392, 1.032369, 1.032347, 1.032324, 1.032302, 1.032280, 1.032258,
                                   1.032236, 1.032213, 1.032191, 1.032169, 1.032147, 1.032125, 1.032103, 1.032081,
                                   1.032059, 1.032037, 1.032015, 1.031993, 1.031971, 1.031949, 1.031927, 1.031906,
                                   1.031884, 1.031862, 1.031840, 1.031819, 1.031797, 1.031775, 1.031754, 1.031732,
                                   1.031711, 1.031689, 1.031667, 1.031646, 1.031625, 1.031603, 1.031582, 1.031560,
                                   1.031539, 1.031518, 1.031496, 1.031475, 1.031454, 1.031433, 1.031411, 1.031390,
                                   1.031369, 1.031348, 1.031327, 1.031306, 1.031285, 1.031264, 1.031243, 1.031222,
                                   1.031201, 1.031180, 1.031159, 1.031138, 1.031117, 1.031097, 1.031076, 1.031055,
                                   1.031034, 1.031013, 1.030993, 1.030972, 1.030952, 1.030931, 1.030910, 1.030890,
                                   1.030869, 1.030849, 1.030828, 1.030808, 1.030787, 1.030767, 1.030747, 1.030726,
                                   1.030706, 1.030686, 1.030665, 1.030645, 1.030625, 1.030604, 1.030584, 1.030564,
                                   1.030544, 1.030524, 1.030504, 1.030484, 1.030464, 1.030444, 1.030424, 1.030404,
                                   1.030384, 1.030364, 1.030344, 1.030324, 1.030304, 1.030284, 1.030264, 1.030245,
                                   1.030225, 1.030205, 1.030185, 1.030166, 1.030146, 1.030126, 1.030107, 1.030087,
                                   1.030068, 1.030048, 1.030029, 1.030009, 1.029990, 1.029970, 1.029951, 1.029931,
                                   1.029912, 1.029892, 1.029873, 1.029854, 1.029835, 1.029815, 1.029796, 1.029777,
                                   1.029757, 1.029738, 1.029719, 1.029700, 1.029681, 1.029662, 1.029643, 1.029624,
                                   1.029605, 1.029586, 1.029567, 1.029548, 1.029529, 1.029510, 1.029491, 1.029472,
                                   1.029453, 1.029434, 1.029415, 1.029397, 1.029378, 1.029359, 1.029341, 1.029322,
                                   1.029303, 1.029284, 1.029266, 1.029247, 1.029229, 1.029210, 1.029191, 1.029173,
                                   1.029154, 1.029136, 1.029117, 1.029099, 1.029081, 1.029062, 1.029044, 1.029025,
                                   1.029007, 1.028989, 1.028970, 1.028952, 1.028934, 1.028916, 1.028897, 1.028879,
                                   1.028861, 1.028843, 1.028825, 1.028807, 1.028789, 1.028770, 1.028752, 1.028734,
                                   1.028716, 1.028698, 1.028680, 1.028662, 1.028645, 1.028627, 1.028609, 1.028591,
                                   1.028573, 1.028555, 1.028537, 1.028520, 1.028502, 1.028484, 1.028466, 1.028449,
                                   1.028431, 1.028413, 1.028396, 1.028378, 1.028360, 1.028343, 1.028325, 1.028308,
                                   1.028290, 1.028273, 1.028255, 1.028238, 1.028220, 1.028203, 1.028185, 1.028168,
                                   1.028151, 1.028133, 1.028116, 1.028099, 1.028081, 1.028064, 1.028047, 1.028030,
                                   1.028012, 1.027995, 1.027978, 1.027961, 1.027944, 1.027927, 1.027909, 1.027892,
                                   1.027875, 1.027858, 1.027841, 1.027824, 1.027807, 1.027790, 1.027773, 1.027756,
                                   1.027739, 1.027723, 1.027706, 1.027689, 1.027672, 1.027655, 1.027638, 1.027622,
                                   1.027605, 1.027588, 1.027571, 1.027555, 1.027538, 1.027521, 1.027505, 1.027488,
                                   1.027471, 1.027455, 1.027438, 1.027422, 1.027405, 1.027389, 1.027372, 1.027356,
                                   1.027339, 1.027323, 1.027306, 1.027290, 1.027273, 1.027257, 1.027241, 1.027224,
                                   1.027208, 1.027192, 1.027175, 1.027159, 1.027143, 1.027127, 1.027110, 1.027094,
                                   1.027078, 1.027062, 1.027046, 1.027029, 1.027013, 1.026997, 1.026981, 1.026965,
                                   1.026949, 1.026933, 1.026917, 1.026901, 1.026885, 1.026869, 1.026853, 1.026837,
                                   1.026821, 1.026805, 1.026789, 1.026774, 1.026758, 1.026742, 1.026726, 1.026710,
                                   1.026695, 1.026679, 1.026663, 1.026647, 1.026632, 1.026616, 1.026600, 1.026585,
                                   1.026569, 1.026553, 1.026538, 1.026522, 1.026507, 1.026491, 1.026475, 1.026460,
                                   1.026444, 1.026429, 1.026413, 1.026398, 1.026383, 1.026367, 1.026352, 1.026336,
                                   1.026321, 1.026306, 1.026290, 1.026275, 1.026260, 1.026244, 1.026229, 1.026214,
                                   1.026199, 1.026183, 1.026168, 1.026153, 1.026138, 1.026122, 1.026107, 1.026092,
                                   1.026077, 1.026062, 1.026047, 1.026032, 1.026017, 1.026002, 1.025987, 1.025972,
                                   1.025957, 1.025942, 1.025927, 1.025912, 1.025897, 1.025882, 1.025867, 1.025852,
                                   1.025837, 1.025822, 1.025808, 1.025793, 1.025778, 1.025763, 1.025748, 1.025734,
                                   1.025719, 1.025704, 1.025689, 1.025675, 1.025660, 1.025645, 1.025631, 1.025616,
                                   1.025602, 1.025587, 1.025572, 1.025558, 1.025543, 1.025529, 1.025514, 1.025500,
                                   1.025485, 1.025471, 1.025456, 1.025442, 1.025427, 1.025413, 1.025398, 1.025384,
                                   1.025370, 1.025355, 1.025341, 1.025326, 1.025312, 1.025298, 1.025284, 1.025269,
                                   1.025255, 1.025241, 1.025226, 1.025212, 1.025198, 1.025184, 1.025170, 1.025156,
                                   1.025141, 1.025127, 1.025113, 1.025099, 1.025085, 1.025071, 1.025057, 1.025043,
                                   1.025029, 1.025015, 1.025001, 1.024987, 1.024973, 1.024959, 1.024945, 1.024931,
                                   1.024917, 1.024903, 1.024889, 1.024875, 1.024861, 1.024848, 1.024834, 1.024820,
                                   1.024806, 1.024792, 1.024778, 1.024765, 1.024751, 1.024737, 1.024724, 1.024710,
                                   1.024696, 1.024682, 1.024669, 1.024655, 1.024642, 1.024628, 1.024614, 1.024601,
                                   1.024587, 1.024573, 1.024560, 1.024546, 1.024533, 1.024519, 1.024506, 1.024492,
                                   1.024479, 1.024465, 1.024452, 1.024439, 1.024425, 1.024412, 1.024398, 1.024385,
                                   1.024371, 1.024358, 1.024345, 1.024331, 1.024318, 1.024305, 1.024292, 1.024278,
                                   1.024265, 1.024252, 1.024238, 1.024225, 1.024212, 1.024199, 1.024186, 1.024172,
                                   1.024159, 1.024146, 1.024133, 1.024120, 1.024107, 1.024094, 1.024081, 1.024068,
                                   1.024054, 1.024041, 1.024028, 1.024015, 1.024002, 1.023989, 1.023976, 1.023963,
                                   1.023950, 1.023937, 1.023925, 1.023912, 1.023899, 1.023886, 1.023873, 1.023860,
                                   1.023847, 1.023834, 1.023822, 1.023809, 1.023796, 1.023783, 1.023770, 1.023758,
                                   1.023745, 1.023732, 1.023719, 1.023707, 1.023694, 1.023681, 1.023669, 1.023656,
                                   1.023643, 1.023631, 1.023618, 1.023605, 1.023593, 1.023580, 1.023568, 1.023555,
                                   1.023542, 1.023530, 1.023517, 1.023505, 1.023492, 1.023480, 1.023467, 1.023455,
                                   1.023442, 1.023430, 1.023417, 1.023405, 1.023393, 1.023380, 1.023368, 1.023355,
                                   1.023343, 1.023331, 1.023318, 1.023306, 1.023294, 1.023281, 1.023269, 1.023257,
                                   1.023245, 1.023232, 1.023220, 1.023208, 1.023196, 1.023183, 1.023171, 1.023159,
                                   1.023147, 1.023135, 1.023123, 1.023110, 1.023098, 1.023086, 1.023074, 1.023062,
                                   1.023050, 1.023038, 1.023026, 1.023014, 1.023002, 1.022990, 1.022977, 1.022966,
                                   1.022954, 1.022942, 1.022930, 1.022918, 1.022906, 1.022894, 1.022882, 1.022870,
                                   1.022858, 1.022846, 1.022834, 1.022822, 1.022810, 1.022799, 1.022787, 1.022775,
                                   1.022763, 1.022751, 1.022740, 1.022728, 1.022716, 1.022704, 1.022692, 1.022681,
                                   1.022669, 1.022657, 1.022646, 1.022634, 1.022622, 1.022611, 1.022599, 1.022587,
                                   1.022576, 1.022564, 1.022552, 1.022541, 1.022529, 1.022518, 1.022506, 1.022494,
                                   1.022483, 1.022471, 1.022460, 1.022448, 1.022437, 1.022425, 1.022414, 1.022402,
                                   1.022391, 1.022379, 1.022368, 1.022357, 1.022345, 1.022334, 1.022322, 1.022311,
                                   1.022300, 1.022288, 1.022277, 1.022265, 1.022254, 1.022243, 1.022231, 1.022220,
                                   1.022209, 1.022197, 1.022186, 1.022175, 1.022164, 1.022153, 1.022141, 1.022130,
                                   1.022119, 1.022108, 1.022096, 1.022085, 1.022074, 1.022063, 1.022052, 1.022041,
                                   1.022029, 1.022018, 1.022007, 1.021996, 1.021985, 1.021974, 1.021963, 1.021952,
                                   1.021941, 1.021930, 1.021919, 1.021908, 1.021897, 1.021886, 1.021875, 1.021864,
                                   1.021853, 1.021842, 1.021831, 1.021820, 1.021809, 1.021798, 1.021787, 1.021776,
                                   1.021765, 1.021754, 1.021744, 1.021733, 1.021722, 1.021711, 1.021700, 1.021689,
                                   1.021679, 1.021668, 1.021657, 1.021646, 1.021635, 1.021625, 1.021614, 1.021603,
                                   1.021592, 1.021582, 1.021571, 1.021560, 1.021549, 1.021539, 1.021528, 1.021518,
                                   1.021507, 1.021496, 1.021486, 1.021475, 1.021464, 1.021454, 1.021443, 1.021433,
                                   1.021422, 1.021411, 1.021401, 1.021390, 1.021380, 1.021369, 1.021359, 1.021348,
                                   1.021338, 1.021327, 1.021317, 1.021306, 1.021296, 1.021285, 1.021275, 1.021264,
                                   1.021254, 1.021243, 1.021233, 1.021223, 1.021212, 1.021202, 1.021191, 1.021181,
                                   1.021171, 1.021160, 1.021150, 1.021140, 1.021129, 1.021119, 1.021109, 1.021098,
                                   1.021088, 1.021078, 1.021068, 1.021057, 1.021047, 1.021037, 1.021027, 1.021016,
                                   1.021006, 1.020996, 1.020986, 1.020976, 1.020965, 1.020955, 1.020945, 1.020935,
                                   1.020925, 1.020915, 1.020905, 1.020895, 1.020884, 1.020874, 1.020864, 1.020854,
                                   1.020844, 1.020834, 1.020824, 1.020814, 1.020804, 1.020794, 1.020784, 1.020774,
                                   1.020764, 1.020754, 1.020744, 1.020734, 1.020724, 1.020714, 1.020704, 1.020694,
                                   1.020684, 1.020674, 1.020664, 1.020654, 1.020645, 1.020635, 1.020625, 1.020615,
                                   1.020605, 1.020595, 1.020585, 1.020576, 1.020566, 1.020556, 1.020546, 1.020536,
                                   1.020526, 1.020517, 1.020507, 1.020497, 1.020487, 1.020478, 1.020468, 1.020458,
                                   1.020448, 1.020439, 1.020429, 1.020419, 1.020410, 1.020400, 1.020390, 1.020380,
                                   1.020371, 1.020361, 1.020352, 1.020342, 1.020332, 1.020323, 1.020313, 1.020303,
                                   1.020294, 1.020284, 1.020275, 1.020265, 1.020256, 1.020246, 1.020236, 1.020227,
                                   1.020217, 1.020208, 1.020198, 1.020189, 1.020179, 1.020170, 1.020160, 1.020151,
                                   1.020141, 1.020132, 1.020123, 1.020113, 1.020104, 1.020094, 1.020085, 1.020076,
                                   1.020066, 1.020057, 1.020047, 1.020038, 1.020029, 1.020019, 1.020010, 1.020001,
                                   1.019991, 1.019982, 1.019973, 1.019963, 1.019954, 1.019945, 1.019935, 1.019926,
                                   1.019917, 1.019908, 1.019898, 1.019889, 1.019880, 1.019871, 1.019861, 1.019852,
                                   1.019843, 1.019834, 1.019825, 1.019815, 1.019806, 1.019797, 1.019788, 1.019779,
                                   1.019770, 1.019760, 1.019751, 1.019742, 1.019733, 1.019724, 1.019715, 1.019706,
                                   1.019697, 1.019688, 1.019678, 1.019669, 1.019660, 1.019651, 1.019642, 1.019633,
                                   1.019624, 1.019615, 1.019606, 1.019597, 1.019588, 1.019579, 1.019570, 1.019561,
                                   1.019552, 1.019543, 1.019534, 1.019525, 1.019516, 1.019508, 1.019499, 1.019490,
                                   1.019481, 1.019472, 1.019463, 1.019454, 1.019445, 1.019436, 1.019428, 1.019419,
                                   1.019410, 1.019401, 1.019392, 1.019383, 1.019374, 1.019366, 1.019357, 1.019348,
                                   1.019339, 1.019331, 1.019322, 1.019313, 1.019304, 1.019295, 1.019287, 1.019278,
                                   1.019269, 1.019261, 1.019252, 1.019243, 1.019234, 1.019226, 1.019217, 1.019208,
                                   1.019200, 1.019191, 1.019182, 1.019174, 1.019165, 1.019156, 1.019148, 1.019139,
                                   1.019130, 1.019122, 1.019113, 1.019105, 1.019096, 1.019088, 1.019079, 1.019070,
                                   1.019062, 1.019053, 1.019045, 1.019036, 1.019028, 1.019019, 1.019011, 1.019002,
                                   1.018994, 1.018985, 1.018977, 1.018968, 1.018960, 1.018951, 1.018943, 1.018934,
                                   1.018926, 1.018917, 1.018909, 1.018900, 1.018892, 1.018884, 1.018875, 1.018867,
                                   1.018858, 1.018850, 1.018842, 1.018833, 1.018825, 1.018816, 1.018808, 1.018800,
                                   1.018791, 1.018783, 1.018775, 1.018767, 1.018758, 1.018750, 1.018741, 1.018733,
                                   1.018725, 1.018717, 1.018708, 1.018700, 1.018692, 1.018684, 1.018675, 1.018667,
                                   1.018659, 1.018651, 1.018642, 1.018634, 1.018626, 1.018618, 1.018610, 1.018601,
                                   1.018593, 1.018585, 1.018577, 1.018569, 1.018561, 1.018552, 1.018544, 1.018536,
                                   1.018528, 1.018520, 1.018512, 1.018504, 1.018496, 1.018487, 1.018479, 1.018471,
                                   1.018463, 1.018455, 1.018447, 1.018439, 1.018431, 1.018423, 1.018415, 1.018407,
                                   1.018399, 1.018391, 1.018383, 1.018375, 1.018367, 1.018359, 1.018351, 1.018343,
                                   1.018335, 1.018327, 1.018319, 1.018311, 1.018303, 1.018295, 1.018287, 1.018279,
                                   1.018271, 1.018263, 1.018255, 1.018247, 1.018239, 1.018232, 1.018224, 1.018216,
                                   1.018208, 1.018200, 1.018192, 1.018184, 1.018176, 1.018169, 1.018161, 1.018153,
                                   1.018145, 1.018137, 1.018129, 1.018122, 1.018114, 1.018106, 1.018098, 1.018090,
                                   1.018083, 1.018075, 1.018067, 1.018059, 1.018052, 1.018044, 1.018036, 1.018028,
                                   1.018021, 1.018013, 1.018005, 1.017998, 1.017990, 1.017982, 1.017974, 1.017967,
                                   1.017959, 1.017951, 1.017944, 1.017936, 1.017928, 1.017921, 1.017913, 1.017905,
                                   1.017898, 1.017890, 1.017882, 1.017875, 1.017867, 1.017860, 1.017852, 1.017844,
                                   1.017837, 1.017829, 1.017822, 1.017814, 1.017807, 1.017799, 1.017792, 1.017784,
                                   1.017776, 1.017769, 1.017761, 1.017754, 1.017746, 1.017739, 1.017731, 1.017724,
                                   1.017716, 1.017709, 1.017701, 1.017694, 1.017686, 1.017679, 1.017671, 1.017664,
                                   1.017656, 1.017649, 1.017642, 1.017634, 1.017627, 1.017619, 1.017612, 1.017604,
                                   1.017597, 1.017590, 1.017582, 1.017575, 1.017568, 1.017560, 1.017553, 1.017545,
                                   1.017538, 1.017531, 1.017523, 1.017516, 1.017509, 1.017501, 1.017494, 1.017487,
                                   1.017479, 1.017472, 1.017465, 1.017457, 1.017450, 1.017443, 1.017436, 1.017428,
                                   1.017421, 1.017414, 1.017406, 1.017399, 1.017392, 1.017385, 1.017377, 1.017370,
                                   1.017363, 1.017356, 1.017349, 1.017341, 1.017334, 1.017327, 1.017320, 1.017313,
                                   1.017305, 1.017298, 1.017291, 1.017284, 1.017277, 1.017270, 1.017262, 1.017255,
                                   1.017248, 1.017241, 1.017234, 1.017227, 1.017220, 1.017213, 1.017205, 1.017198,
                                   1.017191, 1.017184, 1.017177, 1.017170, 1.017163, 1.017156, 1.017149, 1.017142,
                                   1.017135, 1.017128, 1.017120, 1.017113, 1.017106, 1.017099, 1.017092, 1.017085,
                                   1.017078, 1.017071, 1.017064, 1.017057, 1.017050, 1.017043, 1.017036, 1.017029,
                                   1.017022, 1.017015, 1.017008, 1.017002, 1.016995, 1.016988, 1.016981, 1.016974,
                                   1.016967, 1.016960, 1.016953, 1.016946, 1.016939, 1.016932, 1.016925, 1.016918,
                                   1.016912, 1.016905, 1.016898, 1.016891, 1.016884, 1.016877, 1.016870, 1.016863,
                                   1.016857, 1.016850, 1.016843, 1.016836, 1.016829, 1.016822, 1.016816, 1.016809,
                                   1.016802, 1.016795, 1.016788, 1.016782, 1.016775, 1.016768, 1.016761, 1.016754,
                                   1.016748, 1.016741, 1.016734, 1.016727, 1.016721, 1.016714, 1.016707, 1.016700,
                                   1.016694, 1.016687, 1.016680, 1.016674, 1.016667, 1.016660, 1.016653, 1.016647,
                                   1.016640, 1.016633, 1.016627, 1.016620, 1.016613, 1.016607, 1.016600, 1.016593,
                                   1.016587, 1.016580, 1.016573, 1.016567, 1.016560, 1.016554, 1.016547, 1.016540,
                                   1.016534, 1.016527, 1.016520, 1.016514, 1.016507, 1.016501, 1.016494, 1.016487,
                                   1.016481, 1.016474, 1.016468, 1.016461, 1.016455, 1.016448, 1.016442, 1.016435,
                                   1.016428, 1.016422, 1.016415, 1.016409, 1.016402, 1.016396, 1.016389, 1.016383,
                                   1.016376, 1.016370, 1.016363, 1.016357, 1.016350, 1.016344, 1.016337, 1.016331,
                                   1.016325, 1.016318, 1.016312, 1.016305, 1.016299, 1.016292, 1.016286, 1.016279,
                                   1.016273, 1.016267, 1.016260, 1.016254, 1.016247, 1.016241, 1.016235, 1.016228,
                                   1.016222, 1.016215, 1.016209, 1.016203, 1.016196, 1.016190, 1.016183, 1.016177,
                                   1.016171, 1.016164, 1.016158, 1.016152, 1.016145, 1.016139, 1.016133, 1.016126,
                                   1.016120, 1.016114, 1.016107, 1.016101, 1.016095, 1.016089, 1.016082, 1.016076,
                                   1.016070, 1.016063, 1.016057, 1.016051, 1.016045, 1.016038, 1.016032, 1.016026,
                                   1.016020, 1.016013, 1.016007, 1.016001, 1.015995, 1.015988, 1.015982, 1.015976,
                                   1.015970, 1.015964, 1.015957, 1.015951, 1.015945, 1.015939, 1.015933, 1.015926,
                                   1.015920, 1.015914, 1.015908, 1.015902, 1.015896, 1.015890, 1.015883, 1.015877,
                                   1.015871, 1.015865, 1.015859, 1.015853, 1.015847, 1.015840, 1.015834, 1.015828,
                                   1.015822, 1.015816, 1.015810, 1.015804, 1.015798, 1.015792, 1.015786, 1.015779,
                                   1.015773, 1.015767, 1.015761, 1.015755, 1.015749, 1.015743, 1.015737, 1.015731,
                                   1.015725, 1.015719, 1.015713, 1.015707, 1.015701, 1.015695, 1.015689, 1.015683,
                                   1.015677, 1.015671, 1.015665, 1.015659, 1.015653, 1.015647, 1.015641, 1.015635,
                                   1.015629, 1.015623, 1.015617, 1.015611, 1.015605, 1.015599, 1.015593, 1.015587,
                                   1.015581, 1.015575, 1.015569, 1.015563, 1.015558, 1.015552, 1.015546, 1.015540,
                                   1.015534, 1.015528, 1.015522, 1.015516, 1.015510, 1.015504, 1.015499, 1.015493,
                                   1.015487, 1.015481, 1.015475, 1.015469, 1.015463, 1.015458, 1.015452, 1.015446,
                                   1.015440, 1.015434, 1.015428, 1.015422, 1.015417, 1.015411, 1.015405, 1.015399,
                                   1.015393, 1.015388, 1.015382, 1.015376, 1.015370, 1.015364, 1.015359, 1.015353,
                                   1.015347, 1.015341, 1.015336, 1.015330, 1.015324, 1.015318, 1.015313, 1.015307,
                                   1.015301, 1.015295, 1.015290, 1.015284, 1.015278, 1.015272, 1.015267, 1.015261,
                                   1.015255, 1.015249, 1.015244, 1.015238, 1.015232, 1.015227, 1.015221, 1.015215,
                                   1.015210, 1.015204, 1.015198, 1.015193, 1.015187, 1.015181, 1.015176, 1.015170,
                                   1.015164, 1.015159, 1.015153, 1.015147, 1.015142, 1.015136, 1.015130, 1.015125,
                                   1.015119, 1.015114, 1.015108, 1.015102, 1.015097, 1.015091, 1.015085, 1.015080,
                                   1.015074, 1.015069, 1.015063, 1.015058, 1.015052, 1.015046, 1.015041, 1.015035,
                                   1.015030, 1.015024, 1.015019, 1.015013, 1.015007, 1.015002, 1.014996, 1.014991,
                                   1.014985, 1.014980, 1.014974, 1.014969, 1.014963, 1.014958, 1.014952, 1.014947,
                                   1.014941, 1.014936, 1.014930, 1.014925, 1.014919, 1.014914, 1.014908, 1.014903,
                                   1.014897, 1.014892, 1.014886, 1.014881, 1.014875, 1.014870, 1.014865, 1.014859,
                                   1.014854, 1.014848, 1.014843, 1.014837, 1.014832, 1.014827, 1.014821, 1.014816,
                                   1.014810, 1.014805, 1.014799, 1.014794, 1.014789, 1.014783, 1.014778, 1.014772,
                                   1.014767, 1.014762, 1.014756, 1.014751, 1.014745, 1.014740, 1.014735, 1.014729,
                                   1.014724, 1.014719, 1.014713, 1.014708, 1.014703, 1.014697, 1.014692, 1.014687,
                                   1.014681, 1.014676, 1.014671, 1.014665, 1.014660, 1.014655, 1.014649, 1.014644,
                                   1.014639, 1.014634, 1.014628, 1.014623, 1.014618, 1.014612, 1.014607, 1.014602,
                                   1.014596, 1.014591, 1.014586, 1.014581, 1.014575, 1.014570, 1.014565, 1.014560,
                                   1.014554, 1.014549, 1.014544, 1.014539, 1.014533, 1.014528, 1.014523, 1.014518,
                                   1.014513, 1.014507, 1.014502, 1.014497, 1.014492, 1.014487, 1.014481, 1.014476,
                                   1.014471, 1.014466, 1.014461, 1.014455, 1.014450, 1.014445, 1.014440, 1.014435,
                                   1.014429, 1.014424, 1.014419, 1.014414, 1.014409, 1.014404, 1.014399, 1.014393,
                                   1.014388, 1.014383, 1.014378, 1.014373, 1.014368, 1.014363, 1.014358, 1.014352,
                                   1.014347, 1.014342, 1.014337, 1.014332, 1.014327, 1.014322, 1.014317, 1.014312,
                                   1.014307, 1.014301, 1.014296, 1.014291, 1.014286, 1.014281, 1.014276, 1.014271,
                                   1.014266, 1.014261, 1.014256, 1.014251, 1.014246, 1.014241, 1.014236, 1.014231,
                                   1.014226, 1.014220, 1.014215, 1.014210, 1.014205, 1.014200, 1.014195, 1.014190,
                                   1.014185, 1.014180, 1.014175, 1.014170, 1.014165, 1.014160, 1.014155, 1.014150,
                                   1.014145, 1.014140, 1.014135, 1.014130, 1.014126, 1.014121, 1.014116, 1.014111,
                                   1.014106, 1.014101, 1.014096, 1.014091, 1.014086, 1.014081, 1.014076, 1.014071,
                                   1.014066, 1.014061, 1.014056, 1.014051, 1.014046, 1.014042, 1.014037, 1.014032,
                                   1.014027, 1.014022, 1.014017, 1.014012, 1.014007, 1.014002, 1.013997, 1.013993,
                                   1.013988, 1.013983, 1.013978, 1.013973, 1.013968, 1.013963, 1.013958, 1.013954,
                                   1.013949, 1.013944, 1.013939, 1.013934, 1.013929, 1.013924, 1.013920, 1.013915,
                                   1.013910, 1.013905, 1.013900, 1.013896, 1.013891, 1.013886, 1.013881, 1.013876,
                                   1.013871, 1.013867, 1.013862, 1.013857, 1.013852, 1.013847, 1.013843, 1.013838,
                                   1.013833, 1.013828, 1.013824, 1.013819, 1.013814, 1.013809, 1.013804, 1.013800,
                                   1.013795, 1.013790, 1.013785, 1.013781, 1.013776, 1.013771, 1.013766, 1.013762,
                                   1.013757, 1.013752, 1.013747, 1.013743, 1.013738, 1.013733, 1.013728, 1.013724,
                                   1.013719, 1.013714, 1.013710, 1.013705, 1.013700, 1.013696, 1.013691, 1.013686,
                                   1.013681, 1.013677, 1.013672, 1.013667, 1.013663, 1.013658, 1.013653, 1.013649,
                                   1.013644, 1.013639, 1.013635, 1.013630, 1.013625, 1.013621, 1.013616, 1.013611,
                                   1.013607, 1.013602, 1.013597, 1.013593, 1.013588, 1.013584, 1.013579, 1.013574,
                                   1.013570, 1.013565, 1.013561, 1.013556, 1.013551, 1.013547, 1.013542, 1.013538,
                                   1.013533, 1.013528, 1.013524, 1.013519, 1.013515, 1.013510, 1.013505, 1.013501,
                                   1.013496, 1.013492, 1.013487, 1.013482, 1.013478, 1.013473, 1.013469, 1.013464,
                                   1.013460, 1.013455, 1.013451, 1.013446, 1.013442, 1.013437, 1.013432, 1.013428,
                                   1.013423, 1.013419, 1.013414, 1.013410, 1.013405, 1.013401, 1.013396, 1.013392,
                                   1.013387, 1.013383, 1.013378, 1.013374, 1.013369, 1.013365, 1.013360, 1.013356,
                                   1.013351, 1.013347, 1.013342, 1.013338, 1.013333, 1.013329, 1.013324, 1.013320,
                                   1.013315, 1.013311, 1.013306, 1.013302, 1.013298, 1.013293, 1.013289, 1.013284,
                                   1.013280, 1.013275, 1.013271, 1.013267, 1.013262, 1.013258, 1.013253, 1.013249,
                                   1.013244, 1.013240, 1.013236, 1.013231, 1.013227, 1.013222, 1.013218, 1.013214,
                                   1.013209, 1.013205, 1.013200, 1.013196, 1.013191, 1.013187, 1.013183, 1.013178,
                                   1.013174, 1.013170, 1.013165, 1.013161, 1.013157, 1.013152, 1.013148, 1.013143,
                                   1.013139, 1.013135, 1.013130, 1.013126, 1.013122, 1.013117, 1.013113, 1.013109,
                                   1.013104, 1.013100, 1.013096, 1.013091, 1.013087, 1.013083, 1.013078, 1.013074,
                                   1.013070, 1.013065, 1.013061, 1.013057, 1.013052, 1.013048, 1.013044, 1.013039,
                                   1.013035, 1.013031, 1.013027, 1.013022, 1.013018, 1.013014, 1.013010, 1.013005,
                                   1.013001, 1.012997, 1.012992, 1.012988, 1.012984, 1.012980, 1.012975, 1.012971,
                                   1.012967, 1.012963, 1.012958, 1.012954, 1.012950, 1.012946, 1.012941, 1.012937,
                                   1.012933, 1.012929, 1.012924, 1.012920, 1.012916, 1.012912, 1.012908, 1.012903,
                                   1.012899, 1.012895, 1.012891, 1.012886, 1.012882, 1.012878, 1.012874, 1.012870,
                                   1.012865, 1.012861, 1.012857, 1.012853, 1.012849, 1.012845, 1.012840, 1.012836,
                                   1.012832, 1.012828, 1.012824, 1.012819, 1.012815, 1.012811, 1.012807, 1.012803,
                                   1.012799, 1.012794, 1.012790, 1.012786, 1.012782, 1.012778, 1.012774, 1.012770,
                                   1.012766, 1.012761, 1.012757, 1.012753, 1.012749, 1.012745, 1.012741, 1.012737,
                                   1.012733, 1.012728, 1.012724, 1.012720, 1.012716, 1.012712, 1.012708, 1.012704,
                                   1.012700, 1.012696, 1.012691, 1.012687, 1.012683, 1.012679, 1.012675, 1.012671,
                                   1.012667, 1.012663, 1.012659, 1.012655, 1.012651, 1.012647, 1.012643, 1.012638,
                                   1.012634, 1.012630, 1.012626, 1.012622, 1.012618, 1.012614, 1.012610, 1.012606,
                                   1.012602, 1.012598, 1.012594, 1.012590, 1.012586, 1.012582, 1.012578, 1.012574,
                                   1.012570, 1.012566, 1.012562, 1.012558, 1.012554, 1.012550, 1.012546, 1.012542,
                                   1.012538, 1.012534, 1.012530, 1.012526, 1.012522, 1.012518, 1.012514, 1.012510,
                                   1.012506, 1.012502, 1.012498, 1.012494, 1.012490, 1.012486, 1.012482, 1.012478,
                                   1.012474, 1.012470, 1.012466, 1.012462, 1.012458, 1.012454, 1.012450, 1.012446,
                                   1.012442, 1.012438, 1.012434, 1.012430, 1.012426, 1.012423, 1.012419, 1.012415,
                                   1.012411, 1.012407, 1.012403, 1.012399, 1.012395, 1.012391, 1.012387, 1.012383,
                                   1.012379, 1.012375, 1.012372, 1.012368, 1.012364, 1.012360, 1.012356, 1.012352,
                                   1.012348, 1.012344, 1.012340, 1.012337, 1.012333, 1.012329, 1.012325, 1.012321,
                                   1.012317, 1.012313, 1.012309, 1.012305, 1.012302, 1.012298, 1.012294, 1.012290,
                                   1.012286, 1.012282, 1.012279, 1.012275, 1.012271, 1.012267, 1.012263, 1.012259,
                                   1.012255, 1.012252, 1.012248, 1.012244, 1.012240, 1.012236, 1.012232, 1.012229,
                                   1.012225, 1.012221, 1.012217, 1.012213, 1.012210, 1.012206, 1.012202, 1.012198,
                                   1.012194, 1.012190, 1.012187, 1.012183, 1.012179, 1.012175, 1.012172, 1.012168,
                                   1.012164, 1.012160, 1.012156, 1.012153, 1.012149, 1.012145, 1.012141, 1.012137,
                                   1.012134, 1.012130, 1.012126, 1.012122, 1.012119, 1.012115, 1.012111, 1.012107,
                                   1.012104, 1.012100, 1.012096, 1.012092, 1.012089, 1.012085, 1.012081, 1.012077,
                                   1.012074, 1.012070, 1.012066, 1.012062, 1.012059, 1.012055, 1.012051, 1.012048,
                                   1.012044, 1.012040, 1.012036, 1.012033, 1.012029, 1.012025, 1.012021, 1.012018,
                                   1.012014, 1.012010, 1.012007, 1.012003, 1.011999, 1.011996, 1.011992, 1.011988,
                                   1.011984, 1.011981, 1.011977, 1.011973, 1.011970, 1.011966, 1.011962, 1.011959,
                                   1.011955, 1.011951, 1.011948, 1.011944, 1.011940, 1.011937, 1.011933, 1.011929,
                                   1.011926, 1.011922, 1.011918, 1.011915, 1.011911, 1.011907, 1.011904, 1.011900,
                                   1.011897, 1.011893, 1.011889, 1.011886, 1.011882, 1.011878, 1.011875, 1.011871,
                                   1.011868, 1.011864, 1.011860, 1.011857, 1.011853, 1.011849, 1.011846, 1.011842,
                                   1.011839, 1.011835, 1.011831, 1.011828, 1.011824, 1.011821, 1.011817, 1.011813,
                                   1.011810, 1.011806, 1.011803, 1.011799, 1.011796, 1.011792, 1.011788, 1.011785,
                                   1.011781, 1.011778, 1.011774, 1.011770, 1.011767, 1.011763, 1.011760, 1.011756,
                                   1.011753, 1.011749, 1.011745, 1.011742, 1.011738, 1.011735, 1.011731, 1.011728,
                                   1.011724, 1.011721, 1.011717, 1.011714, 1.011710, 1.011706, 1.011703, 1.011699,
                                   1.011696, 1.011692, 1.011689, 1.011685, 1.011682, 1.011678, 1.011675, 1.011671,
                                   1.011668, 1.011664, 1.011661, 1.011657, 1.011654, 1.011650, 1.011647, 1.011643,
                                   1.011640, 1.011636, 1.011633, 1.011629, 1.011626, 1.011622, 1.011619, 1.011615,
                                   1.011612, 1.011608, 1.011605, 1.011601, 1.011598, 1.011594, 1.011591, 1.011588,
                                   1.011584, 1.011581, 1.011577, 1.011574, 1.011570, 1.011567, 1.011563, 1.011560,
                                   1.011556, 1.011553, 1.011549, 1.011546, 1.011543, 1.011539, 1.011536, 1.011532,
                                   1.011529, 1.011525, 1.011522, 1.011518, 1.011515, 1.011512, 1.011508, 1.011505,
                                   1.011501, 1.011498, 1.011495, 1.011491, 1.011488, 1.011484, 1.011481, 1.011477,
                                   1.011474, 1.011471, 1.011467, 1.011464, 1.011460, 1.011457, 1.011454, 1.011450,
                                   1.011447, 1.011443, 1.011440, 1.011437, 1.011433, 1.011430, 1.011426, 1.011423,
                                   1.011420, 1.011416, 1.011413, 1.011410, 1.011406, 1.011403, 1.011400, 1.011396,
                                   1.011393, 1.011389, 1.011386, 1.011383, 1.011379, 1.011376, 1.011373, 1.011369,
                                   1.011366, 1.011363, 1.011359, 1.011356, 1.011353, 1.011349, 1.011346, 1.011343,
                                   1.011339, 1.011336, 1.011333, 1.011329, 1.011326, 1.011322, 1.011319, 1.011316,
                                   1.011313, 1.011309, 1.011306, 1.011303, 1.011299, 1.011296, 1.011293, 1.011289,
                                   1.011286, 1.011283, 1.011279, 1.011276, 1.011273, 1.011270, 1.011266, 1.011263,
                                   1.011260, 1.011256, 1.011253, 1.011250, 1.011246, 1.011243, 1.011240, 1.011237,
                                   1.011233, 1.011230, 1.011227, 1.011224, 1.011220, 1.011217, 1.011214, 1.011210,
                                   1.011207, 1.011204, 1.011201, 1.011197, 1.011194, 1.011191, 1.011188, 1.011184,
                                   1.011181, 1.011178, 1.011175, 1.011171, 1.011168, 1.011165, 1.011162, 1.011158,
                                   1.011155, 1.011152, 1.011149, 1.011145, 1.011142, 1.011139, 1.011136, 1.011132,
                                   1.011129, 1.011126, 1.011123, 1.011120, 1.011116, 1.011113, 1.011110, 1.011107,
                                   1.011104, 1.011100, 1.011097, 1.011094, 1.011091, 1.011088, 1.011084, 1.011081,
                                   1.011078, 1.011075, 1.011072, 1.011068, 1.011065, 1.011062, 1.011059, 1.011056,
                                   1.011052, 1.011049, 1.011046, 1.011043, 1.011040, 1.011037, 1.011033, 1.011030,
                                   1.011027, 1.011024, 1.011021, 1.011017, 1.011014, 1.011011, 1.011008, 1.011005,
                                   1.011002, 1.010998, 1.010995, 1.010992, 1.010989, 1.010986, 1.010983, 1.010980,
                                   1.010976, 1.010973, 1.010970, 1.010967, 1.010964, 1.010961, 1.010958, 1.010954,
                                   1.010951, 1.010948, 1.010945, 1.010942, 1.010939, 1.010936, 1.010933, 1.010929,
                                   1.010926, 1.010923, 1.010920, 1.010917, 1.010914, 1.010911, 1.010908, 1.010905,
                                   1.010901, 1.010898, 1.010895, 1.010892, 1.010889, 1.010886, 1.010883, 1.010880,
                                   1.010877, 1.010874, 1.010871, 1.010867, 1.010864, 1.010861, 1.010858, 1.010855,
                                   1.010852, 1.010849, 1.010846, 1.010843, 1.010840, 1.010837, 1.010834, 1.010831,
                                   1.010827, 1.010824, 1.010821, 1.010818, 1.010815, 1.010812, 1.010809, 1.010806,
                                   1.010803, 1.010800, 1.010797, 1.010794, 1.010791, 1.010788, 1.010785, 1.010782,
                                   1.010779, 1.010776, 1.010772, 1.010769, 1.010766, 1.010763, 1.010760, 1.010757,
                                   1.010754, 1.010751, 1.010748, 1.010745, 1.010742, 1.010739, 1.010736, 1.010733,
                                   1.010730, 1.010727, 1.010724, 1.010721, 1.010718, 1.010715, 1.010712, 1.010709,
                                   1.010706, 1.010703, 1.010700, 1.010697, 1.010694, 1.010691, 1.010688, 1.010685,
                                   1.010682, 1.010679, 1.010676, 1.010673, 1.010670, 1.010667, 1.010664, 1.010661,
                                   1.010658, 1.010655, 1.010652, 1.010649, 1.010646, 1.010643, 1.010640, 1.010637,
                                   1.010634, 1.010631, 1.010628, 1.010625, 1.010622, 1.010620, 1.010617, 1.010614,
                                   1.010611, 1.010608, 1.010605, 1.010602, 1.010599, 1.010596, 1.010593, 1.010590,
                                   1.010587, 1.010584, 1.010581, 1.010578, 1.010575, 1.010572, 1.010569, 1.010566,
                                   1.010563, 1.010561, 1.010558, 1.010555, 1.010552, 1.010549, 1.010546, 1.010543,
                                   1.010540, 1.010537, 1.010534, 1.010531, 1.010528, 1.010525, 1.010523, 1.010520,
                                   1.010517, 1.010514, 1.010511, 1.010508, 1.010505, 1.010502, 1.010499, 1.010496,
                                   1.010494, 1.010491, 1.010488, 1.010485, 1.010482, 1.010479, 1.010476, 1.010473,
                                   1.010470, 1.010468, 1.010465, 1.010462, 1.010459, 1.010456, 1.010453, 1.010450,
                                   1.010447, 1.010445, 1.010442, 1.010439, 1.010436, 1.010433, 1.010430, 1.010427,
                                   1.010424, 1.010422, 1.010419, 1.010416, 1.010413, 1.010410, 1.010407, 1.010404,
                                   1.010401, 1.010399, 1.010396, 1.010393, 1.010390, 1.010387, 1.010384, 1.010382,
                                   1.010379, 1.010376, 1.010373, 1.010370, 1.010367, 1.010365, 1.010362, 1.010359,
                                   1.010356, 1.010353, 1.010350, 1.010348, 1.010345, 1.010342, 1.010339, 1.010336,
                                   1.010334, 1.010331, 1.010328, 1.010325, 1.010322, 1.010319, 1.010317, 1.010314,
                                   1.010311, 1.010308, 1.010305, 1.010303, 1.010300, 1.010297, 1.010294, 1.010291,
                                   1.010289, 1.010286, 1.010283, 1.010280, 1.010277, 1.010275, 1.010272, 1.010269,
                                   1.010266, 1.010263, 1.010261, 1.010258, 1.010255, 1.010252, 1.010250, 1.010247,
                                   1.010244, 1.010241, 1.010239, 1.010236, 1.010233, 1.010230, 1.010227, 1.010225,
                                   1.010222, 1.010219, 1.010216, 1.010214, 1.010211, 1.010208, 1.010205, 1.010203,
                                   1.010200, 1.010197, 1.010194, 1.010192, 1.010189, 1.010186, 1.010183, 1.010181,
                                   1.010178, 1.010175, 1.010172, 1.010170, 1.010167, 1.010164, 1.010161, 1.010159,
                                   1.010156, 1.010153, 1.010151, 1.010148, 1.010145, 1.010142, 1.010140, 1.010137,
                                   1.010134, 1.010131, 1.010129, 1.010126, 1.010123, 1.010121, 1.010118, 1.010115,
                                   1.010112, 1.010110, 1.010107, 1.010104, 1.010102, 1.010099, 1.010096, 1.010093,
                                   1.010091, 1.010088, 1.010085, 1.010083, 1.010080, 1.010077, 1.010075, 1.010072,
                                   1.010069, 1.010067, 1.010064, 1.010061, 1.010059, 1.010056, 1.010053, 1.010050,
                                   1.010048, 1.010045, 1.010042, 1.010040, 1.010037, 1.010034, 1.010032, 1.010029,
                                   1.010026, 1.010024, 1.010021, 1.010018, 1.010016, 1.010013, 1.010010, 1.010008,
                                   1.010005, 1.010002, 1.010000, 1.009997, 1.009995, 1.009992, 1.009989, 1.009987,
                                   1.009984, 1.009981, 1.009979, 1.009976, 1.009973, 1.009971, 1.009968, 1.009965,
                                   1.009963, 1.009960, 1.009957, 1.009955, 1.009952, 1.009950, 1.009947, 1.009944,
                                   1.009942, 1.009939, 1.009936, 1.009934, 1.009931, 1.009929, 1.009926, 1.009923,
                                   1.009921, 1.009918, 1.009915, 1.009913, 1.009910, 1.009908, 1.009905, 1.009902,
                                   1.009900, 1.009897, 1.009895, 1.009892, 1.009889, 1.009887, 1.009884, 1.009882,
                                   1.009879, 1.009876, 1.009874, 1.009871, 1.009869, 1.009866, 1.009863, 1.009861,
                                   1.009858, 1.009856, 1.009853, 1.009851, 1.009848, 1.009845, 1.009843, 1.009840,
                                   1.009838, 1.009835, 1.009832, 1.009830, 1.009827, 1.009825, 1.009822, 1.009820,
                                   1.009817, 1.009815, 1.009812, 1.009809, 1.009807, 1.009804, 1.009802, 1.009799,
                                   1.009797, 1.009794, 1.009791, 1.009789, 1.009786, 1.009784, 1.009781, 1.009779,
                                   1.009776, 1.009773, 1.009771, 1.009768, 1.009766, 1.009763, 1.009761, 1.009758,
                                   1.009756, 1.009753, 1.009751, 1.009748, 1.009746, 1.009743, 1.009740, 1.009738,
                                   1.009735, 1.009733, 1.009730, 1.009728, 1.009725, 1.009723, 1.009720, 1.009718,
                                   1.009715, 1.009713, 1.009710, 1.009708, 1.009705, 1.009703, 1.009700, 1.009698,
                                   1.009695, 1.009693, 1.009690, 1.009688, 1.009685, 1.009683, 1.009680, 1.009678,
                                   1.009675, 1.009673, 1.009670, 1.009668, 1.009665, 1.009663, 1.009660, 1.009658,
                                   1.009655, 1.009653, 1.009650, 1.009648, 1.009645, 1.009643, 1.009640, 1.009638,
                                   1.009635, 1.009633, 1.009630, 1.009628, 1.009625, 1.009623, 1.009620, 1.009618,
                                   1.009615, 1.009613, 1.009611, 1.009608, 1.009606, 1.009603, 1.009601, 1.009598,
                                   1.009596, 1.009593, 1.009591, 1.009588, 1.009586, 1.009583, 1.009581, 1.009578,
                                   1.009576, 1.009574, 1.009571, 1.009569, 1.009566, 1.009564, 1.009561, 1.009559,
                                   1.009556, 1.009554, 1.009552, 1.009549, 1.009547, 1.009544, 1.009542, 1.009539,
                                   1.009537, 1.009534, 1.009532, 1.009530, 1.009527, 1.009525, 1.009522, 1.009520,
                                   1.009517, 1.009515, 1.009513, 1.009510, 1.009508, 1.009505, 1.009503, 1.009501,
                                   1.009498, 1.009496, 1.009493, 1.009491, 1.009488, 1.009486, 1.009484, 1.009481,
                                   1.009479, 1.009476, 1.009474, 1.009472, 1.009469, 1.009467, 1.009464, 1.009462,
                                   1.009459, 1.009457, 1.009455, 1.009452, 1.009450, 1.009447, 1.009445, 1.009443,
                                   1.009440, 1.009438, 1.009436, 1.009433, 1.009431, 1.009428, 1.009426, 1.009424,
                                   1.009421, 1.009419, 1.009416, 1.009414, 1.009412, 1.009409, 1.009407, 1.009405,
                                   1.009402, 1.009400, 1.009398, 1.009395, 1.009393, 1.009390, 1.009388, 1.009386,
                                   1.009383, 1.009381, 1.009379, 1.009376, 1.009374, 1.009371, 1.009369, 1.009367,
                                   1.009364, 1.009362, 1.009360, 1.009357, 1.009355, 1.009353, 1.009350, 1.009348,
                                   1.009346, 1.009343, 1.009341, 1.009338, 1.009336, 1.009334, 1.009331, 1.009329,
                                   1.009327, 1.009324, 1.009322, 1.009320, 1.009317, 1.009315, 1.009313, 1.009310,
                                   1.009308, 1.009306, 1.009303, 1.009301, 1.009299, 1.009296, 1.009294, 1.009292,
                                   1.009290, 1.009287, 1.009285, 1.009282, 1.009280, 1.009278, 1.009276, 1.009273,
                                   1.009271, 1.009269, 1.009266, 1.009264, 1.009262, 1.009259, 1.009257, 1.009255,
                                   1.009252, 1.009250, 1.009248, 1.009246, 1.009243, 1.009241, 1.009239, 1.009236,
                                   1.009234, 1.009232, 1.009229, 1.009227, 1.009225, 1.009223, 1.009220, 1.009218,
                                   1.009216, 1.009213, 1.009211, 1.009209, 1.009207, 1.009204, 1.009202, 1.009200,
                                   1.009197, 1.009195, 1.009193, 1.009191, 1.009188, 1.009186, 1.009184, 1.009181,
                                   1.009179, 1.009177, 1.009175, 1.009172, 1.009170, 1.009168, 1.009166, 1.009163,
                                   1.009161, 1.009159, 1.009156, 1.009154, 1.009152, 1.009150, 1.009147, 1.009145,
                                   1.009143, 1.009141, 1.009138, 1.009136, 1.009134, 1.009132, 1.009129, 1.009127,
                                   1.009125, 1.009123, 1.009120, 1.009118, 1.009116, 1.009114, 1.009111, 1.009109,
                                   1.009107, 1.009105, 1.009102, 1.009100, 1.009098, 1.009096, 1.009094, 1.009091,
                                   1.009089, 1.009087, 1.009085, 1.009082, 1.009080, 1.009078, 1.009076, 1.009073,
                                   1.009071, 1.009069, 1.009067, 1.009065, 1.009062, 1.009060, 1.009058, 1.009056,
                                   1.009053, 1.009051, 1.009049, 1.009047, 1.009045, 1.009042, 1.009040, 1.009038,
                                   1.009036, 1.009034, 1.009031, 1.009029, 1.009027, 1.009025, 1.009022, 1.009020,
                                   1.009018, 1.009016, 1.009014, 1.009012, 1.009009, 1.009007, 1.009005, 1.009003,
                                   1.009001, 1.008998};
    float SlowBlocksLimit[5040] = {0.003147, 0.007340, 0.012020, 0.017026, 0.022274, 0.027709, 0.033291, 0.038992,
                                   0.044788, 0.050661, 0.056595, 0.062578, 0.068598, 0.074646, 0.080713, 0.086792,
                                   0.092877, 0.098962, 0.105042, 0.111113, 0.117170, 0.123209, 0.129229, 0.135224,
                                   0.141194, 0.147136, 0.153047, 0.158927, 0.164772, 0.170581, 0.176354, 0.182089,
                                   0.187784, 0.193440, 0.199054, 0.204627, 0.210157, 0.215645, 0.221089, 0.226490,
                                   0.231846, 0.237158, 0.242425, 0.247647, 0.252825, 0.257957, 0.263045, 0.268087,
                                   0.273084, 0.278037, 0.282945, 0.287807, 0.292626, 0.297400, 0.302129, 0.306815,
                                   0.311457, 0.316055, 0.320610, 0.325122, 0.329592, 0.334019, 0.338404, 0.342747,
                                   0.347049, 0.351309, 0.355529, 0.359709, 0.363848, 0.367947, 0.372008, 0.376029,
                                   0.380011, 0.383956, 0.387862, 0.391731, 0.395562, 0.399357, 0.403115, 0.406837,
                                   0.410524, 0.414175, 0.417791, 0.421373, 0.424920, 0.428433, 0.431913, 0.435360,
                                   0.438774, 0.442156, 0.445505, 0.448823, 0.452109, 0.455365, 0.458589, 0.461783,
                                   0.464948, 0.468082, 0.471188, 0.474264, 0.477311, 0.480331, 0.483322, 0.486285,
                                   0.489221, 0.492130, 0.495013, 0.497868, 0.500698, 0.503501, 0.506279, 0.509032,
                                   0.511760, 0.514463, 0.517141, 0.519796, 0.522426, 0.525033, 0.527617, 0.530177,
                                   0.532715, 0.535230, 0.537723, 0.540193, 0.542642, 0.545070, 0.547476, 0.549861,
                                   0.552225, 0.554569, 0.556892, 0.559195, 0.561478, 0.563742, 0.565986, 0.568211,
                                   0.570417, 0.572604, 0.574772, 0.576922, 0.579054, 0.581168, 0.583264, 0.585343,
                                   0.587404, 0.589448, 0.591475, 0.593485, 0.595479, 0.597456, 0.599417, 0.601361,
                                   0.603290, 0.605203, 0.607101, 0.608983, 0.610850, 0.612702, 0.614538, 0.616361,
                                   0.618168, 0.619961, 0.621740, 0.623505, 0.625256, 0.626993, 0.628716, 0.630426,
                                   0.632122, 0.633805, 0.635475, 0.637132, 0.638777, 0.640408, 0.642027, 0.643634,
                                   0.645228, 0.646810, 0.648380, 0.649938, 0.651484, 0.653019, 0.654542, 0.656054,
                                   0.657554, 0.659043, 0.660521, 0.661988, 0.663444, 0.664890, 0.666324, 0.667749,
                                   0.669162, 0.670566, 0.671959, 0.673342, 0.674715, 0.676078, 0.677432, 0.678775,
                                   0.680109, 0.681434, 0.682749, 0.684054, 0.685351, 0.686638, 0.687916, 0.689185,
                                   0.690445, 0.691697, 0.692939, 0.694173, 0.695399, 0.696616, 0.697824, 0.699025,
                                   0.700217, 0.701400, 0.702576, 0.703744, 0.704904, 0.706056, 0.707200, 0.708336,
                                   0.709465, 0.710586, 0.711700, 0.712806, 0.713905, 0.714997, 0.716081, 0.717158,
                                   0.718228, 0.719292, 0.720348, 0.721397, 0.722439, 0.723475, 0.724504, 0.725526,
                                   0.726542, 0.727551, 0.728553, 0.729550, 0.730539, 0.731523, 0.732500, 0.733471,
                                   0.734436, 0.735395, 0.736348, 0.737295, 0.738236, 0.739171, 0.740100, 0.741023,
                                   0.741941, 0.742853, 0.743759, 0.744660, 0.745556, 0.746445, 0.747330, 0.748209,
                                   0.749082, 0.749951, 0.750814, 0.751672, 0.752524, 0.753372, 0.754214, 0.755052,
                                   0.755884, 0.756712, 0.757535, 0.758352, 0.759165, 0.759974, 0.760777, 0.761576,
                                   0.762370, 0.763159, 0.763944, 0.764724, 0.765500, 0.766271, 0.767038, 0.767800,
                                   0.768558, 0.769312, 0.770061, 0.770806, 0.771547, 0.772284, 0.773016, 0.773745,
                                   0.774469, 0.775189, 0.775905, 0.776617, 0.777325, 0.778030, 0.778730, 0.779426,
                                   0.780119, 0.780807, 0.781492, 0.782174, 0.782851, 0.783525, 0.784195, 0.784861,
                                   0.785524, 0.786183, 0.786839, 0.787491, 0.788140, 0.788785, 0.789426, 0.790064,
                                   0.790699, 0.791331, 0.791959, 0.792583, 0.793205, 0.793823, 0.794438, 0.795050,
                                   0.795658, 0.796263, 0.796865, 0.797464, 0.798060, 0.798653, 0.799243, 0.799829,
                                   0.800413, 0.800994, 0.801571, 0.802146, 0.802718, 0.803287, 0.803852, 0.804416,
                                   0.804976, 0.805533, 0.806088, 0.806639, 0.807189, 0.807735, 0.808278, 0.808819,
                                   0.809357, 0.809893, 0.810425, 0.810956, 0.811483, 0.812008, 0.812530, 0.813050,
                                   0.813567, 0.814082, 0.814594, 0.815104, 0.815611, 0.816116, 0.816618, 0.817118,
                                   0.817615, 0.818110, 0.818603, 0.819093, 0.819581, 0.820067, 0.820550, 0.821031,
                                   0.821510, 0.821987, 0.822461, 0.822933, 0.823403, 0.823870, 0.824336, 0.824799,
                                   0.825260, 0.825719, 0.826176, 0.826630, 0.827083, 0.827533, 0.827981, 0.828428,
                                   0.828872, 0.829314, 0.829754, 0.830193, 0.830629, 0.831063, 0.831495, 0.831925,
                                   0.832354, 0.832780, 0.833204, 0.833627, 0.834047, 0.834466, 0.834883, 0.835298,
                                   0.835711, 0.836123, 0.836532, 0.836940, 0.837346, 0.837750, 0.838152, 0.838552,
                                   0.838951, 0.839348, 0.839744, 0.840137, 0.840529, 0.840919, 0.841307, 0.841694,
                                   0.842079, 0.842463, 0.842844, 0.843225, 0.843603, 0.843980, 0.844355, 0.844729,
                                   0.845101, 0.845471, 0.845840, 0.846207, 0.846573, 0.846937, 0.847300, 0.847661,
                                   0.848021, 0.848379, 0.848736, 0.849091, 0.849445, 0.849797, 0.850147, 0.850497,
                                   0.850844, 0.851191, 0.851536, 0.851879, 0.852221, 0.852562, 0.852901, 0.853239,
                                   0.853576, 0.853911, 0.854245, 0.854577, 0.854908, 0.855238, 0.855567, 0.855894,
                                   0.856219, 0.856544, 0.856867, 0.857189, 0.857509, 0.857829, 0.858147, 0.858463,
                                   0.858779, 0.859093, 0.859406, 0.859718, 0.860028, 0.860338, 0.860646, 0.860953,
                                   0.861258, 0.861563, 0.861866, 0.862168, 0.862469, 0.862769, 0.863067, 0.863365,
                                   0.863661, 0.863956, 0.864250, 0.864543, 0.864835, 0.865125, 0.865415, 0.865703,
                                   0.865991, 0.866277, 0.866562, 0.866846, 0.867129, 0.867411, 0.867692, 0.867971,
                                   0.868250, 0.868528, 0.868804, 0.869080, 0.869354, 0.869628, 0.869900, 0.870172,
                                   0.870442, 0.870712, 0.870980, 0.871248, 0.871514, 0.871780, 0.872044, 0.872308,
                                   0.872570, 0.872832, 0.873092, 0.873352, 0.873611, 0.873869, 0.874125, 0.874381,
                                   0.874636, 0.874890, 0.875144, 0.875396, 0.875647, 0.875898, 0.876147, 0.876396,
                                   0.876643, 0.876890, 0.877136, 0.877381, 0.877626, 0.877869, 0.878111, 0.878353,
                                   0.878594, 0.878834, 0.879073, 0.879311, 0.879548, 0.879785, 0.880021, 0.880256,
                                   0.880490, 0.880723, 0.880955, 0.881187, 0.881418, 0.881648, 0.881877, 0.882106,
                                   0.882333, 0.882560, 0.882786, 0.883011, 0.883236, 0.883460, 0.883683, 0.883905,
                                   0.884126, 0.884347, 0.884567, 0.884786, 0.885005, 0.885223, 0.885440, 0.885656,
                                   0.885871, 0.886086, 0.886300, 0.886514, 0.886726, 0.886938, 0.887150, 0.887360,
                                   0.887570, 0.887779, 0.887987, 0.888195, 0.888402, 0.888609, 0.888814, 0.889019,
                                   0.889224, 0.889427, 0.889630, 0.889832, 0.890034, 0.890235, 0.890435, 0.890635,
                                   0.890834, 0.891033, 0.891230, 0.891427, 0.891624, 0.891820, 0.892015, 0.892209,
                                   0.892403, 0.892597, 0.892789, 0.892981, 0.893173, 0.893364, 0.893554, 0.893744,
                                   0.893933, 0.894121, 0.894309, 0.894496, 0.894683, 0.894869, 0.895054, 0.895239,
                                   0.895423, 0.895607, 0.895790, 0.895972, 0.896155, 0.896336, 0.896517, 0.896697,
                                   0.896877, 0.897056, 0.897234, 0.897412, 0.897590, 0.897767, 0.897943, 0.898119,
                                   0.898294, 0.898469, 0.898643, 0.898817, 0.898990, 0.899163, 0.899335, 0.899507,
                                   0.899678, 0.899848, 0.900018, 0.900188, 0.900356, 0.900525, 0.900693, 0.900860,
                                   0.901027, 0.901194, 0.901360, 0.901525, 0.901690, 0.901854, 0.902018, 0.902182,
                                   0.902345, 0.902507, 0.902669, 0.902831, 0.902992, 0.903152, 0.903313, 0.903472,
                                   0.903631, 0.903790, 0.903948, 0.904106, 0.904263, 0.904420, 0.904576, 0.904732,
                                   0.904887, 0.905042, 0.905197, 0.905351, 0.905505, 0.905658, 0.905811, 0.905963,
                                   0.906115, 0.906266, 0.906417, 0.906568, 0.906718, 0.906867, 0.907017, 0.907165,
                                   0.907314, 0.907462, 0.907609, 0.907756, 0.907903, 0.908049, 0.908195, 0.908341,
                                   0.908486, 0.908630, 0.908774, 0.908918, 0.909062, 0.909205, 0.909347, 0.909489,
                                   0.909631, 0.909772, 0.909913, 0.910054, 0.910194, 0.910334, 0.910473, 0.910612,
                                   0.910751, 0.910889, 0.911027, 0.911165, 0.911302, 0.911439, 0.911575, 0.911711,
                                   0.911846, 0.911982, 0.912117, 0.912251, 0.912385, 0.912519, 0.912652, 0.912785,
                                   0.912918, 0.913050, 0.913182, 0.913314, 0.913445, 0.913576, 0.913706, 0.913836,
                                   0.913966, 0.914096, 0.914225, 0.914353, 0.914482, 0.914610, 0.914737, 0.914865,
                                   0.914992, 0.915119, 0.915245, 0.915371, 0.915497, 0.915622, 0.915747, 0.915872,
                                   0.915996, 0.916120, 0.916243, 0.916367, 0.916490, 0.916613, 0.916735, 0.916857,
                                   0.916979, 0.917100, 0.917221, 0.917342, 0.917462, 0.917583, 0.917702, 0.917822,
                                   0.917941, 0.918060, 0.918179, 0.918297, 0.918415, 0.918532, 0.918650, 0.918767,
                                   0.918884, 0.919000, 0.919116, 0.919232, 0.919348, 0.919463, 0.919578, 0.919693,
                                   0.919807, 0.919921, 0.920035, 0.920148, 0.920262, 0.920374, 0.920487, 0.920599,
                                   0.920711, 0.920823, 0.920935, 0.921046, 0.921157, 0.921268, 0.921378, 0.921488,
                                   0.921598, 0.921707, 0.921817, 0.921926, 0.922034, 0.922143, 0.922251, 0.922359,
                                   0.922466, 0.922574, 0.922681, 0.922788, 0.922894, 0.923001, 0.923107, 0.923213,
                                   0.923318, 0.923423, 0.923528, 0.923633, 0.923737, 0.923842, 0.923946, 0.924049,
                                   0.924153, 0.924256, 0.924359, 0.924462, 0.924564, 0.924666, 0.924768, 0.924870,
                                   0.924971, 0.925073, 0.925174, 0.925274, 0.925375, 0.925475, 0.925575, 0.925675,
                                   0.925774, 0.925874, 0.925973, 0.926071, 0.926170, 0.926268, 0.926366, 0.926464,
                                   0.926562, 0.926659, 0.926756, 0.926853, 0.926950, 0.927046, 0.927143, 0.927239,
                                   0.927334, 0.927430, 0.927525, 0.927620, 0.927715, 0.927810, 0.927904, 0.927999,
                                   0.928093, 0.928186, 0.928280, 0.928373, 0.928466, 0.928559, 0.928652, 0.928744,
                                   0.928837, 0.928929, 0.929020, 0.929112, 0.929203, 0.929295, 0.929386, 0.929476,
                                   0.929567, 0.929657, 0.929747, 0.929837, 0.929927, 0.930016, 0.930106, 0.930195,
                                   0.930284, 0.930372, 0.930461, 0.930549, 0.930637, 0.930725, 0.930813, 0.930900,
                                   0.930988, 0.931075, 0.931162, 0.931248, 0.931335, 0.931421, 0.931507, 0.931593,
                                   0.931679, 0.931764, 0.931850, 0.931935, 0.932020, 0.932104, 0.932189, 0.932273,
                                   0.932357, 0.932442, 0.932525, 0.932609, 0.932692, 0.932776, 0.932859, 0.932942,
                                   0.933024, 0.933107, 0.933189, 0.933271, 0.933353, 0.933435, 0.933517, 0.933598,
                                   0.933679, 0.933760, 0.933841, 0.933922, 0.934003, 0.934083, 0.934163, 0.934243,
                                   0.934323, 0.934403, 0.934482, 0.934561, 0.934640, 0.934719, 0.934798, 0.934877,
                                   0.934955, 0.935034, 0.935112, 0.935190, 0.935267, 0.935345, 0.935422, 0.935500,
                                   0.935577, 0.935654, 0.935730, 0.935807, 0.935883, 0.935960, 0.936036, 0.936112,
                                   0.936188, 0.936263, 0.936339, 0.936414, 0.936489, 0.936564, 0.936639, 0.936714,
                                   0.936788, 0.936863, 0.936937, 0.937011, 0.937085, 0.937158, 0.937232, 0.937305,
                                   0.937379, 0.937452, 0.937525, 0.937597, 0.937670, 0.937743, 0.937815, 0.937887,
                                   0.937959, 0.938031, 0.938103, 0.938174, 0.938246, 0.938317, 0.938388, 0.938459,
                                   0.938530, 0.938601, 0.938671, 0.938742, 0.938812, 0.938882, 0.938952, 0.939022,
                                   0.939092, 0.939161, 0.939231, 0.939300, 0.939369, 0.939438, 0.939507, 0.939575,
                                   0.939644, 0.939712, 0.939781, 0.939849, 0.939917, 0.939985, 0.940052, 0.940120,
                                   0.940187, 0.940255, 0.940322, 0.940389, 0.940456, 0.940523, 0.940589, 0.940656,
                                   0.940722, 0.940788, 0.940854, 0.940920, 0.940986, 0.941052, 0.941117, 0.941183,
                                   0.941248, 0.941313, 0.941378, 0.941443, 0.941508, 0.941573, 0.941637, 0.941701,
                                   0.941766, 0.941830, 0.941894, 0.941958, 0.942022, 0.942085, 0.942149, 0.942212,
                                   0.942275, 0.942338, 0.942402, 0.942464, 0.942527, 0.942590, 0.942652, 0.942715,
                                   0.942777, 0.942839, 0.942901, 0.942963, 0.943025, 0.943086, 0.943148, 0.943209,
                                   0.943271, 0.943332, 0.943393, 0.943454, 0.943515, 0.943575, 0.943636, 0.943696,
                                   0.943757, 0.943817, 0.943877, 0.943937, 0.943997, 0.944057, 0.944116, 0.944176,
                                   0.944236, 0.944295, 0.944354, 0.944413, 0.944472, 0.944531, 0.944590, 0.944648,
                                   0.944707, 0.944765, 0.944824, 0.944882, 0.944940, 0.944998, 0.945056, 0.945113,
                                   0.945171, 0.945229, 0.945286, 0.945343, 0.945401, 0.945458, 0.945515, 0.945572,
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                                   0.950238, 0.950286, 0.950334, 0.950382, 0.950430, 0.950478, 0.950526, 0.950574,
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                                   0.957604, 0.957640, 0.957676, 0.957713, 0.957749, 0.957784, 0.957820, 0.957856,
                                   0.957892, 0.957928, 0.957963, 0.957999, 0.958035, 0.958070, 0.958106, 0.958141,
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                                   0.958735, 0.958769, 0.958804, 0.958838, 0.958872, 0.958907, 0.958941, 0.958975,
                                   0.959009, 0.959043, 0.959077, 0.959111, 0.959145, 0.959179, 0.959213, 0.959246,
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                                   0.959548, 0.959581, 0.959614, 0.959647, 0.959680, 0.959713, 0.959746, 0.959779,
                                   0.959812, 0.959845, 0.959878, 0.959911, 0.959943, 0.959976, 0.960009, 0.960041,
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                                   0.960332, 0.960364, 0.960396, 0.960428, 0.960460, 0.960492, 0.960524, 0.960556,
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                                   0.961336, 0.961366, 0.961397, 0.961428, 0.961458, 0.961489, 0.961519, 0.961549,
                                   0.961580, 0.961610, 0.961640, 0.961670, 0.961701, 0.961731, 0.961761, 0.961791,
                                   0.961821, 0.961851, 0.961881, 0.961910, 0.961940, 0.961970, 0.962000, 0.962030,
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                                   0.990909, 0.990911, 0.990913, 0.990915, 0.990918, 0.990920, 0.990922, 0.990924,
                                   0.990927, 0.990929, 0.990931, 0.990933, 0.990936, 0.990938, 0.990940, 0.990942,
                                   0.990944, 0.990947, 0.990949, 0.990951, 0.990953, 0.990955, 0.990958, 0.990960,
                                   0.990962, 0.990964, 0.990966, 0.990969, 0.990971, 0.990973, 0.990975, 0.990977,
                                   0.990980, 0.990982, 0.990984, 0.990986, 0.990988, 0.990991, 0.990993, 0.990995,
                                   0.990997, 0.990999, 0.991002, 0.991004, 0.991006, 0.991008, 0.991010, 0.991013,
                                   0.991015, 0.991017, 0.991019, 0.991021, 0.991023, 0.991026, 0.991028, 0.991030,
                                   0.991032, 0.991034, 0.991036, 0.991039, 0.991041, 0.991043, 0.991045, 0.991047,
                                   0.991050, 0.991052, 0.991054, 0.991056, 0.991058, 0.991060, 0.991062, 0.991065,
                                   0.991067, 0.991069, 0.991071, 0.991073, 0.991075, 0.991078, 0.991080, 0.991082};

    if (BlockLastSolved == NULL || BlockLastSolved->nHeight == 0 ||
        (uint64_t) BlockLastSolved->nHeight < PastBlocksMin) { return pindexLast->nBits; }


    for (unsigned int i = 1; BlockReading && BlockReading->nHeight > 0; i++) {

        if (PastBlocksMax > 0 && i > PastBlocksMax) { break; }
        nPastBlocks++;

        if (i == 1) { bnPastTargetAverage.SetCompact(BlockReading->nBits); }

        else {
            bnPastTargetAverage = ((CBigNum().SetCompact(BlockReading->nBits) - bnPastTargetAveragePrev) / i) +
                                  bnPastTargetAveragePrev;
        }
        bnPastTargetAveragePrev = bnPastTargetAverage;

        nActualSeconds = BlockLastSolved->GetBlockTime() - BlockReading->GetBlockTime();
        nTargetSeconds = TargetBlocksSpacingSeconds * nPastBlocks;
        nBlockTimeRatio = 1;
        if (nActualSeconds < 1) { nActualSeconds = 1; }

        if (nActualSeconds != 0 && nTargetSeconds != 0) {
            nBlockTimeRatio = double(nTargetSeconds) / nActualSeconds;
        }


        if (nPastBlocks >= PastBlocksMin) {
            if ((nBlockTimeRatio <= SlowBlocksLimit[nPastBlocks - 1]) ||
                (nBlockTimeRatio >= FastBlocksLimit[nPastBlocks - 1])) {
                assert(BlockReading);
                break;
            }
        }


        if (BlockReading->pprev == NULL) {
            assert(BlockReading);
            break;
        }
        BlockReading = BlockReading->pprev;
    }

    // Limit range of bnPastTargetAverage to a halving or doubling from most recent block target
    if (bnPastTargetAverage < (CBigNum().SetCompact(BlockLastSolved->nBits) / 2)) {
        bnPastTargetAverage = CBigNum().SetCompact(BlockLastSolved->nBits) / 2;
    }
    if (bnPastTargetAverage > (CBigNum().SetCompact(BlockLastSolved->nBits) * 2)) {
        bnPastTargetAverage = CBigNum().SetCompact(BlockLastSolved->nBits) * 2;
    }

    CBigNum bnNew(bnPastTargetAverage);

    if (nActualSeconds != 0 && nTargetSeconds != 0) {

        if (nActualSeconds > 3 * nTargetSeconds) {
            nActualSeconds = 3 * nTargetSeconds;
        } // Maximal difficulty decrease of /3 from constrained past average
        if (nActualSeconds < nTargetSeconds / 3) {
            nActualSeconds = nTargetSeconds / 3;
        } // Maximal difficulty increase of x3 from constrained past average

        bnNew *= nActualSeconds;
        bnNew /= nTargetSeconds;
    }


    if (bnNew > bnProofOfWorkLimit) { bnNew = bnProofOfWorkLimit; }


    // debug print
//    printf("*********************************************************************************\n");
//    printf("Difficulty Retarget - Boris's Ridiculously Named Difficulty Function\n");
//    printf("nHeight = %i\n", pindexLast->nHeight);
//    printf("nPastBlocks = %u\n", nPastBlocks);
//    printf("nBlockTimeRatio Target/Actual = %.4f\n", nBlockTimeRatio.to_float());
//    printf("Mean blocktime = %.1fs\n", TargetBlocksSpacingSeconds / nBlockTimeRatio.to_float());
//    printf("SlowBlocksLimit = %.4f\n", SlowBlocksLimit[nPastBlocks - 1]);
//    printf("FastBlocksLimit = %.4f\n", FastBlocksLimit[nPastBlocks - 1]);
//    printf("Before: %08x %.8f\n", BlockLastSolved->nBits, GetDifficultyHelper(BlockLastSolved->nBits));
//    printf("After: %08x %.8f\n", bnNew.GetCompact(), GetDifficultyHelper(bnNew.GetCompact()));
//    printf("Ratio After/Before: %.8f\n", GetDifficultyHelper(bnNew.GetCompact()) / GetDifficultyHelper(BlockLastSolved->nBits));
//    printf("*********************************************************************************\n");

    return bnNew.GetCompact();
}