module crypto.rsa;

import std.bigint;
import std.bitmanip;
import std.datetime;
import std.base64;
import std.typecons;

import crypto.utils;

struct RSAKeyPair
{
    string privateKey;
    string publicKey;

    this(string privateKey, string publicKey)
    {
        this.privateKey = privateKey;
        this.publicKey = publicKey;
    }
}

struct RSAKeyInfo
{
    @property BigInt modulus()
    {
        return _modulus;
    }

    @property ubyte[] modulus_bytes()
    {
        return _modulus_bytes;
    }

    @property BigInt exponent()
    {
        return _exponent;
    }

    @property ubyte[] exponent_bytes()
    {
        return _exponent_bytes;
    }

    this(BigInt modulus, ubyte[] modulus_bytes, BigInt exponent, ubyte[] exponent_bytes)
    {
        _modulus = modulus;
        _modulus_bytes = modulus_bytes;
        _exponent = exponent;
        _exponent_bytes = exponent_bytes;
    }

private:

    BigInt _modulus;
    ubyte[] _modulus_bytes;
    BigInt _exponent;
    ubyte[] _exponent_bytes;
}

class RSA
{
public:

    static RSAKeyPair generateKeyPair(uint bitLength = 1024)
    {
        assert((bitLength >= 128) && (bitLength % 8 == 0), "Bitlength is required to be a multiple of 8 and not less than 128.");

        BigInt x, y;

        BigInt ex_gcd(BigInt a, BigInt b)
        {
            if (b == 0)
            {
                x = BigInt("1");
                y = BigInt("0");
                return a;
            }
            BigInt ans = ex_gcd(b, a % b);
            BigInt temp = x;
            x = y;
            y = temp - (a / b * y);
            return ans;
        }

        BigInt cal(BigInt a, BigInt k)
        {
            BigInt gcd = ex_gcd(a, k);
            if (gcd % 1 != 0)
            {
                return BigInt("-1");
            }
            x = x * (1 / gcd);
            if (k < 0)
                k *= -1;
            BigInt ans = x % k;
            if (ans < 0)
                ans = ans += k;
            return ans;
        }

        BigInt p, q, n, t, e;

        while (true)
        {
            p = generateRandomBigInt(bitLength / 2, 1, 1);
            if (isProbablePrime(p))
                break;
        }
        while (true)
        {
            q = generateRandomBigInt(bitLength / 2, 1, 1);
            if (isProbablePrime(q))
                break;
        }
        n = p * q;
        t = (p - 1) * (q - 1);
        e = PRIMES[(rnd.next % 42) + 6500];

        BigInt d = cal(e, t);

        return RSAKeyPair(encodeKey(n, d), encodeKey(n, e));
    }

    static string encodeKey(T : iPKCS = SimpleFormat)(BigInt modulus, BigInt exponent)
    {
        return T.encodeKey(modulus, exponent);
    }

    static RSAKeyInfo decodeKey(T : iPKCS = SimpleFormat)(string key)
    {
        return T.decodeKey(key);
    }

    static ubyte[] encrypt(T : iPKCS = SimpleFormat)(string key, ubyte[] data, bool mixinXteaMode = false)
    {
        return encrypt_decrypt!("encrypt", T)(key, data, mixinXteaMode);
    }

    static ubyte[] encrypt(RSAKeyInfo key, ubyte[] data, bool mixinXteaMode = false)
    {
        return encrypt_decrypt!"encrypt"(key, data, mixinXteaMode);
    }

    static ubyte[] decrypt(T : iPKCS = SimpleFormat)(string key, ubyte[] data, bool mixinXteaMode = false)
    {
        return encrypt_decrypt!("decrypt", T)(key, data, mixinXteaMode);
    }

    static ubyte[] decrypt(RSAKeyInfo key, ubyte[] data, bool mixinXteaMode = false)
    {
        return encrypt_decrypt!"decrypt"(key, data, mixinXteaMode);
    }

private:
    static InsecureRandomGenerator rnd;

    static BigInt generateRandomBigInt(uint bitLength, int highBit = -1, int lowBit = -1)
    {
        ubyte[] buffer = new ubyte[bitLength / 8];

        uint pos = 0;
        uint current = 0;
        foreach (ref a; buffer)
        {
            if (pos == 0)
                current = rnd.next;
            a = cast(ubyte)(current >> 8 * pos);
            pos = (pos + 1) % uint.sizeof;
        }

        if (highBit == 0)
            buffer[0] &= (0xFF >> 1);
        else if (highBit == 1)
            buffer[0] |= (0x01 << 7);

        if (lowBit == 0)
            buffer[$ - 1] &= (0xFF << 1);
        else if (lowBit == 1)
            buffer[$ - 1] |= 0x01;

        return BigIntHelper.bigIntFromUByteArray(buffer);
    }

    static bool isProbablePrime(BigInt n)
    {
        if (n == 2)
            return true;

        foreach (prime; PRIMES)
        {
            if (n % prime == 0)
                return false;
        }

        return millerRabinPrimeTest(n);
    }

    static bool millerRabinPrimeTest(BigInt n)
    {
        int s = 40;
        BigInt a;

        for (int i = 0; i < s; i++)
        {
            a = rnd.next % (n - 2) + 2;
            if (BigIntHelper.powMod(a, n, n - 1) != 1)
                return false;
        }

        return true;
    }

    static ubyte[] encrypt_decrypt(string T1, T2 : iPKCS = SimpleFormat)(string key, ubyte[] data, bool mixinXteaMode)
    if (T1 == "encrypt" || T1 == "decrypt")
    {
        RSAKeyInfo ki = decodeKey!T2(key);
        return encrypt_decrypt!(T1)(ki, data, mixinXteaMode);
    }

    static ubyte[] encrypt_decrypt(string T)(RSAKeyInfo key, ubyte[] data, bool mixinXteaMode)
    if (T == "encrypt" || T == "decrypt")
    {
        if (mixinXteaMode)
        {
            return encrypt_decrypt_mixinXteaMode!T(key, data);
        }
        
        size_t keySize = key.modulus_bytes.length;

        BigInt getNextBlock(out size_t blockSize)
        {
            if (data.length == 0)
            {
                blockSize = 0;
                return BigInt("0");
            }

            if (T == "decrypt")
            {
                ubyte[] block = data[0 .. ($ >= keySize) ? keySize : $];
                blockSize = block.length;
                return BigIntHelper.bigIntFromUByteArray(block);
            }
            else
            {
                // Prevent preamble 0, and make the encrypto results random
                ubyte preamble = rnd.next!ubyte(0x01, 0xFF);
                blockSize = (keySize <= data.length) ? keySize : data.length;

                while (true)
                {
                    ubyte[] block = [preamble] ~ data[0 .. blockSize];
                    BigInt t = BigIntHelper.bigIntFromUByteArray(block);
                    if (t >= key.modulus)
                    {
                        blockSize--;
                        assert(blockSize > 0, "Key bits is too small.");
                        continue;
                    }
                    return t;
                }
            }
        }

        ubyte[] ret;

        while (data.length > 0)
        {
            size_t blockSize;
            BigInt block = getNextBlock(blockSize);
            if (blockSize == 0)
            {
                break;
            }

            block = BigIntHelper.powMod(block, key.modulus, key.exponent);
            ubyte[] block_buf = BigIntHelper.bigIntToUByteArray(block);
            if (T == "encrypt")
            {
                for (size_t i; i < keySize - block_buf.length; i++)
                {
                    ret ~= cast(ubyte)0;
                }
            }
            else
            {
                block_buf = block_buf[1 .. $];
            }

            ret ~= block_buf;
            data = data[blockSize .. $];
        }

        return ret;
    }
    
    static ubyte[] encrypt_decrypt_mixinXteaMode(string T)(RSAKeyInfo key, ubyte[] data)
    if (T == "encrypt" || T == "decrypt")
    {
        import crypto.tea;

        int[4] xteaKey;
        int rounds = 64;
        size_t keySize = key.modulus_bytes.length;

        void generateXteaKey(in ubyte[] buf)
        {
            ubyte[] data = new ubyte[int.sizeof * 4];
            for (int i = 0; i < int.sizeof * 4; i++)
            {
                data[i] = buf[i % buf.length];
            }

            for (int i = 0; i < 4; i++)
            {
                xteaKey[i] = data.peek!int(i * int.sizeof);
            } 
        }

        BigInt getNextBlock(out size_t blockSize)
        {
            if (data.length == 0)
            {
                blockSize = 0;
                return BigInt("0");
            }

            if (T == "decrypt")
            {
                ubyte[] block = data[0 .. ($ >= keySize) ? keySize : $];
                blockSize = block.length;
                return BigIntHelper.bigIntFromUByteArray(block);
            }
            else
            {
                // Prevent preamble 0, and make the encrypto results random
                ubyte preamble = rnd.next!ubyte(0x01, 0xFF);
                blockSize = (keySize <= data.length) ? keySize : data.length;

                while (true)
                {
                    ubyte[] block = [preamble] ~ data[0 .. blockSize];
                    BigInt t = BigIntHelper.bigIntFromUByteArray(block);
                    if (t >= key.modulus)
                    {
                        blockSize--;
                        assert(blockSize > 0, "Key bits is too small.");
                        continue;
                    }

                    generateXteaKey(block);
                    return t;
                }
            }
        }

        ubyte[] ret;

        size_t blockSize;
        BigInt block = getNextBlock(blockSize);
        if (blockSize == 0)
        {
            return ret;
        }

        block = BigIntHelper.powMod(block, key.modulus, key.exponent);
        ubyte[] block_buf = BigIntHelper.bigIntToUByteArray(block);
        if (T == "encrypt")
        {
            for (size_t i; i < keySize - block_buf.length; i++)
            {
                ret ~= cast(ubyte)0;
            }
        }
        else
        {
            generateXteaKey(block_buf);
            block_buf = block_buf[1 .. $];
        }

        ret ~= block_buf;

        if (blockSize >= data.length)
        {
            return ret;
        }

        data = data[blockSize .. $];

        if (T == "encrypt")
        {
            ret ~= Xtea.encrypt(data, xteaKey, rounds);
        }
        else
        {
            ret ~= Xtea.decrypt(data, xteaKey, rounds);
        }

        return ret;
    }

    immutable static size_t PRIME_TABLE_SIZE = 6543;
    immutable static uint[PRIME_TABLE_SIZE] PRIMES = [
        2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
        67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137,
        139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211,
        223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
        293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
        383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461,
        463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
        569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643,
        647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
        743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
        839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937,
        941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021,
        1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097,
        1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193,
        1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283,
        1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
        1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459,
        1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549,
        1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619,
        1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721,
        1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
        1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
        1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003,
        2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,
        2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203,
        2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
        2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377,
        2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459,
        2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579,
        2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677,
        2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
        2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837,
        2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
        2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041,
        3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167,
        3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
        3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347,
        3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461,
        3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541,
        3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,
        3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
        3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833,
        3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923,
        3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
        4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129,
        4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
        4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337,
        4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447,
        4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547,
        4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,
        4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
        4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871,
        4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967,
        4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051,
        5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
        5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
        5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399,
        5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479,
        5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573,
        5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683,
        5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
        5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867,
        5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007,
        6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101,
        6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211,
        6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
        6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379,
        6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529,
        6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637,
        6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733,
        6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
        6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949,
        6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027,
        7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159,
        7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253,
        7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
        7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
        7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589,
        7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691,
        7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817,
        7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
        7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053,
        8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161,
        8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263,
        8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369,
        8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501,
        8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609,
        8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699,
        8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803,
        8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893,
        8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
        9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133,
        9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227,
        9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341,
        9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433,
        9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533,
        9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649,
        9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767,
        9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857,
        9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967,
        9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091,
        10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163,
        10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259,
        10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333,
        10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453,
        10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531,
        10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639,
        10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729,
        10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847,
        10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937,
        10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047,
        11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119,
        11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239,
        11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317,
        11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423,
        11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503,
        11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621,
        11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731,
        11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827,
        11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923,
        11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987,
        12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101,
        12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197,
        12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277,
        12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379,
        12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473,
        12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541,
        12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619,
        12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713,
        12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821,
        12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917,
        12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001,
        13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099,
        13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
        13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291,
        13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397,
        13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477,
        13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597,
        13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691,
        13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759,
        13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873,
        13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933,
        13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057,
        14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173,
        14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303,
        14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407,
        14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489,
        14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563,
        14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669,
        14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753,
        14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831,
        14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929,
        14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053,
        15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137,
        15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233,
        15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307,
        15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383,
        15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473,
        15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583,
        15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667,
        15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761,
        15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859,
        15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937,
        15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063,
        16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139,
        16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249,
        16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363,
        16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453,
        16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567,
        16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661,
        16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763,
        16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889,
        16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981,
        16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053,
        17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183,
        17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293,
        17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383,
        17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467,
        17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551,
        17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657,
        17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749,
        17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863,
        17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957,
        17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047,
        18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131,
        18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223,
        18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307,
        18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401,
        18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493,
        18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593,
        18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731,
        18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859,
        18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979,
        19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081,
        19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211,
        19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301,
        19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417,
        19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469,
        19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553,
        19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687,
        19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763,
        19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867,
        19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973,
        19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051,
        20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143,
        20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233,
        20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347,
        20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431,
        20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543,
        20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663,
        20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753,
        20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879,
        20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963,
        20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059,
        21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157,
        21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247,
        21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377,
        21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481,
        21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557,
        21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613,
        21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737,
        21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821,
        21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929,
        21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031,
        22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109,
        22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189,
        22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291,
        22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409,
        22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531,
        22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637,
        22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717,
        22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807,
        22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921,
        22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021,
        23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081,
        23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197,
        23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297,
        23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417,
        23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549,
        23557, 23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623,
        23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719,
        23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813,
        23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893,
        23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993,
        24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077,
        24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137,
        24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247,
        24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391,
        24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499,
        24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623,
        24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749,
        24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851,
        24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967,
        24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073,
        25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169,
        25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261,
        25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367,
        25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463,
        25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589,
        25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673,
        25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771,
        25793, 25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889,
        25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981,
        25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099,
        26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183,
        26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267,
        26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387,
        26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479,
        26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597,
        26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699,
        26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777,
        26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879,
        26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959,
        26981, 26987, 26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067,
        27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191,
        27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283,
        27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409, 27427, 27431,
        27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539,
        27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673,
        27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751,
        27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817,
        27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941,
        27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027,
        28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111,
        28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277,
        28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387,
        28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477,
        28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571,
        28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631,
        28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711,
        28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813,
        28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921,
        28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027,
        29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147,
        29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231,
        29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339,
        29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429,
        29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567,
        29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663,
        29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789,
        29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881,
        29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029,
        30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119,
        30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211,
        30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319,
        30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449,
        30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553,
        30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671,
        30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773,
        30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859,
        30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971,
        30977, 30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079,
        31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177,
        31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249,
        31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333,
        31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481,
        31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573,
        31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687,
        31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793,
        31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957,
        31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057,
        32059, 32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141,
        32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237,
        32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327,
        32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411,
        32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503,
        32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587,
        32603, 32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707,
        32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801,
        32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917,
        32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999,
        33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091,
        33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199,
        33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329,
        33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409,
        33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521,
        33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599,
        33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679,
        33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773,
        33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871,
        33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997,
        34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141,
        34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253,
        34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319,
        34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429,
        34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513,
        34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613,
        34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721,
        34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841,
        34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939,
        34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069,
        35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149,
        35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279,
        35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381,
        35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491,
        35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573,
        35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747,
        35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839,
        35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951,
        35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017,
        36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137,
        36151, 36161, 36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263,
        36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353,
        36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479,
        36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571,
        36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677,
        36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767,
        36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857,
        36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931,
        36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039,
        37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171,
        37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277,
        37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369,
        37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493,
        37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567,
        37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649,
        37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799,
        37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897,
        37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011,
        38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167,
        38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261,
        38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333,
        38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461,
        38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611,
        38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707,
        38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791,
        38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903,
        38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019,
        39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113,
        39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209,
        39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313,
        39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397,
        39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511,
        39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631,
        39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749,
        39761, 39769, 39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841,
        39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937,
        39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039,
        40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153,
        40163, 40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253,
        40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427,
        40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519,
        40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627,
        40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763,
        40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849,
        40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949,
        40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057,
        41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177,
        41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233,
        41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357,
        41381, 41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479,
        41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593,
        41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641, 41647, 41651,
        41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771,
        41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887,
        41893, 41897, 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959,
        41969, 41981, 41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061,
        42071, 42073, 42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179,
        42181, 42187, 42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257,
        42281, 42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359,
        42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443,
        42451, 42457, 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509,
        42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649,
        42667, 42677, 42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727,
        42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829,
        42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937,
        42943, 42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037,
        43049, 43051, 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159,
        43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291,
        43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427,
        43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573,
        43577, 43579, 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649,
        43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777,
        43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891,
        43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, 43991,
        43997, 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087,
        44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179,
        44189, 44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269,
        44273, 44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389,
        44417, 44449, 44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531,
        44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623,
        44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711,
        44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819,
        44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927,
        44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053,
        45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161,
        45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289,
        45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377,
        45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503,
        45523, 45533, 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613,
        45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737,
        45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833,
        45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959,
        45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091,
        46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183,
        46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301,
        46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439,
        46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511,
        46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633,
        46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723,
        46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819,
        46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933,
        46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093,
        47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189,
        47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303,
        47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407,
        47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513,
        47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609,
        47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711,
        47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807,
        47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917,
        47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023,
        48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157,
        48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271,
        48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397,
        48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487,
        48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589,
        48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679,
        48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799,
        48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883,
        48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019,
        49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117,
        49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201,
        49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331,
        49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417,
        49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529,
        49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633,
        49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741,
        49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831,
        49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939,
        49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051,
        50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129,
        50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261,
        50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359,
        50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461,
        50497, 50503, 50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587,
        50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723,
        50741, 50753, 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849,
        50857, 50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957,
        50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061,
        51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197,
        51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287,
        51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413,
        51419, 51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479,
        51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577,
        51581, 51593, 51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673,
        51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769, 51787,
        51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871,
        51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977,
        51991, 52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103,
        52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201,
        52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313,
        52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457,
        52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567,
        52571, 52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691,
        52697, 52709, 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783,
        52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883, 52889, 52901,
        52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999,
        53003, 53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101,
        53113, 53117, 53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197,
        53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309,
        53323, 53327, 53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419,
        53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, 53569,
        53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639,
        53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773,
        53777, 53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881,
        53887, 53891, 53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959,
        53987, 53993, 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091,
        54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217,
        54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347,
        54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421,
        54437, 54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521,
        54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617,
        54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721,
        54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851,
        54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973,
        54979, 54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073,
        55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207,
        55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291, 55313, 55331,
        55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439,
        55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541, 55547, 55579,
        55589, 55603, 55609, 55619, 55621, 55631, 55633, 55639, 55661, 55663,
        55667, 55673, 55681, 55691, 55697, 55711, 55717, 55721, 55733, 55763,
        55787, 55793, 55799, 55807, 55813, 55817, 55819, 55823, 55829, 55837,
        55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931,
        55933, 55949, 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053,
        56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149, 56167,
        56171, 56179, 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267,
        56269, 56299, 56311, 56333, 56359, 56369, 56377, 56383, 56393, 56401,
        56417, 56431, 56437, 56443, 56453, 56467, 56473, 56477, 56479, 56489,
        56501, 56503, 56509, 56519, 56527, 56531, 56533, 56543, 56569, 56591,
        56597, 56599, 56611, 56629, 56633, 56659, 56663, 56671, 56681, 56687,
        56701, 56711, 56713, 56731, 56737, 56747, 56767, 56773, 56779, 56783,
        56807, 56809, 56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893,
        56897, 56909, 56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963,
        56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073, 57077,
        57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149, 57163, 57173,
        57179, 57191, 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269,
        57271, 57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373,
        57383, 57389, 57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503,
        57527, 57529, 57557, 57559, 57571, 57587, 57593, 57601, 57637, 57641,
        57649, 57653, 57667, 57679, 57689, 57697, 57709, 57713, 57719, 57727,
        57731, 57737, 57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809,
        57829, 57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923,
        57943, 57947, 57973, 57977, 57991, 58013, 58027, 58031, 58043, 58049,
        58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129, 58147, 58151,
        58153, 58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, 58229,
        58231, 58237, 58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367,
        58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441,
        58451, 58453, 58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573,
        58579, 58601, 58603, 58613, 58631, 58657, 58661, 58679, 58687, 58693,
        58699, 58711, 58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789,
        58831, 58889, 58897, 58901, 58907, 58909, 58913, 58921, 58937, 58943,
        58963, 58967, 58979, 58991, 58997, 59009, 59011, 59021, 59023, 59029,
        59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107, 59113, 59119,
        59123, 59141, 59149, 59159, 59167, 59183, 59197, 59207, 59209, 59219,
        59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333, 59341, 59351,
        59357, 59359, 59369, 59377, 59387, 59393, 59399, 59407, 59417, 59419,
        59441, 59443, 59447, 59453, 59467, 59471, 59473, 59497, 59509, 59513,
        59539, 59557, 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629,
        59651, 59659, 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729,
        59743, 59747, 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863,
        59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999, 60013,
        60017, 60029, 60037, 60041, 60077, 60083, 60089, 60091, 60101, 60103,
        60107, 60127, 60133, 60139, 60149, 60161, 60167, 60169, 60209, 60217,
        60223, 60251, 60257, 60259, 60271, 60289, 60293, 60317, 60331, 60337,
        60343, 60353, 60373, 60383, 60397, 60413, 60427, 60443, 60449, 60457,
        60493, 60497, 60509, 60521, 60527, 60539, 60589, 60601, 60607, 60611,
        60617, 60623, 60631, 60637, 60647, 60649, 60659, 60661, 60679, 60689,
        60703, 60719, 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779,
        60793, 60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913,
        60917, 60919, 60923, 60937, 60943, 60953, 60961, 61001, 61007, 61027,
        61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151,
        61153, 61169, 61211, 61223, 61231, 61253, 61261, 61283, 61291, 61297,
        61331, 61333, 61339, 61343, 61357, 61363, 61379, 61381, 61403, 61409,
        61417, 61441, 61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511,
        61519, 61543, 61547, 61553, 61559, 61561, 61583, 61603, 61609, 61613,
        61627, 61631, 61637, 61643, 61651, 61657, 61667, 61673, 61681, 61687,
        61703, 61717, 61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837,
        61843, 61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967,
        61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047, 62053,
        62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143,
        62171, 62189, 62191, 62201, 62207, 62213, 62219, 62233, 62273, 62297,
        62299, 62303, 62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417,
        62423, 62459, 62467, 62473, 62477, 62483, 62497, 62501, 62507, 62533,
        62539, 62549, 62563, 62581, 62591, 62597, 62603, 62617, 62627, 62633,
        62639, 62653, 62659, 62683, 62687, 62701, 62723, 62731, 62743, 62753,
        62761, 62773, 62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873,
        62897, 62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983,
        62987, 62989, 63029, 63031, 63059, 63067, 63073, 63079, 63097, 63103,
        63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211, 63241, 63247,
        63277, 63281, 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353,
        63361, 63367, 63377, 63389, 63391, 63397, 63409, 63419, 63421, 63439,
        63443, 63463, 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533,
        63541, 63559, 63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617,
        63629, 63647, 63649, 63659, 63667, 63671, 63689, 63691, 63697, 63703,
        63709, 63719, 63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799,
        63803, 63809, 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907,
        63913, 63929, 63949, 63977, 63997, 64007, 64013, 64019, 64033, 64037,
        64063, 64067, 64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171,
        64187, 64189, 64217, 64223, 64231, 64237, 64271, 64279, 64283, 64301,
        64303, 64319, 64327, 64333, 64373, 64381, 64399, 64403, 64433, 64439,
        64451, 64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579,
        64591, 64601, 64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667,
        64679, 64693, 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811,
        64817, 64849, 64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921,
        64927, 64937, 64951, 64969, 64997, 65003, 65011, 65027, 65029, 65033,
        65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123, 65129,
        65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203, 65213, 65239,
        65257, 65267, 65269, 65287, 65293, 65309, 65323, 65327, 65353, 65357,
        65371, 65381, 65393, 65407, 65413, 65419, 65423, 65437, 65447, 65449,
        65479, 65497, 65519, 65521, 65537
    ];
}

interface iPKCS
{
    static string encodeKey(BigInt modulus, BigInt exponent);
    static Nullable!RSAKeyInfo decodeKey(string key);
}

class SimpleFormat : iPKCS
{
    static string encodeKey(BigInt modulus, BigInt exponent)
    {
        ubyte[] m_bytes = BigIntHelper.bigIntToUByteArray(modulus);
        ubyte[] e_bytes = BigIntHelper.bigIntToUByteArray(exponent);

        ubyte[] buffer = new ubyte[4];

        buffer.write!int(cast(int) m_bytes.length, 0);
        buffer ~= m_bytes;
        buffer ~= e_bytes;

        return Base64.encode(buffer);
    }

    static Nullable!RSAKeyInfo decodeKey(string key)
    {
        ubyte[] buffer = Base64.decode(key);
        int m_len = buffer.peek!int(0);
        ubyte[] modulus_bytes = buffer[4 .. 4 + m_len];
        ubyte[] exponent_bytes = buffer[4 + m_len .. $];

        return Nullable!RSAKeyInfo(RSAKeyInfo(BigIntHelper.bigIntFromUByteArray(modulus_bytes),
                modulus_bytes, BigIntHelper.bigIntFromUByteArray(exponent_bytes), exponent_bytes));
    }
}

class PKCS1 : iPKCS
{
    static string encodeKey(BigInt modulus, BigInt exponent)
    {
        return string.init;
    }

    static Nullable!RSAKeyInfo decodeKey(string key)
    {
        return Nullable!RSAKeyInfo();
    }
}

class PKCS8 : iPKCS
{
    static string encodeKey(BigInt modulus, BigInt exponent)
    {
        return string.init;
    }

    static Nullable!RSAKeyInfo decodeKey(string key)
    {
        return Nullable!RSAKeyInfo();
    }
}

unittest
{
    import std.stdio;

    import crypto.rsa;

    RSAKeyPair keyPair = RSA.generateKeyPair(1024);
    writeln(keyPair.privateKey);
    writeln(keyPair.publicKey);

    string data = `
And the workload proves (POW) reusable workload proof (RPOW) 2. hash function
The hash function (Hash Function), also known as a hash function, gives an input x, which calculates the corresponding output H (x). The main features of a hash function are:
The input x can be a string of any length
The output, that is, the length of H (x) is fixed

The procedure for calculating H (x) is efficient (for string X of length n), the time complexity of H (x) should be O (n)
For bitcoin, the hash function used by such cryptographic systems, it needs to have the following properties:
	`;

    ubyte[] sb = cast(ubyte[]) data;
    ubyte[] db = RSA.encrypt(keyPair.privateKey, sb);
    sb = RSA.decrypt(keyPair.publicKey, db);
    writeln(cast(string) sb);
}

unittest
{
    import std.stdio;

    import std.bigint;
    import crypto.rsa;

    RSAKeyPair keyPair = RSA.generateKeyPair(1024);
    writeln(keyPair.privateKey);
    writeln(keyPair.publicKey);

    RSAKeyInfo pri_key = RSA.decodeKey(keyPair.privateKey);
    RSAKeyInfo pub_key = RSA.decodeKey(keyPair.publicKey);

    string data = `
And the workload proves (POW) reusable workload proof (RPOW) 2. hash function
The hash function (Hash Function), also known as a hash function, gives an input x, which calculates the corresponding output H (x). The main features of a hash function are:
The input x can be a string of any length
The output, that is, the length of H (x) is fixed

The procedure for calculating H (x) is efficient (for string X of length n), the time complexity of H (x) should be O (n)
For bitcoin, the hash function used by such cryptographic systems, it needs to have the following properties:
	`;

    ubyte[] sb = cast(ubyte[]) data;
    ubyte[] db = RSA.encrypt(pri_key, sb);
    sb = RSA.decrypt(pub_key, db);
    writeln(cast(string) sb);
}