import java.io.*;
import java.util.*;

/** 
 * Mersenne Twister and MersenneTwisterFast:
 * <P>
 * <b>MersenneTwisterFast</b> is a drop-in subclass replacement
 * for java.util.Random.  It is properly synchronized and
 * can be used in a multithreaded environment.  
 *
 * <p><b>MersenneTwisterFast</b> is not a subclass of java.util.Random.  It has
 * the same public methods as Random does, however, and it is
 * algorithmically identical to MersenneTwister.  MersenneTwisterFast
 * has hard-code inlined all of its methods directly, and made all of them
 * final (well, the ones of consequence anyway).  Further, these
 * methods are <i>not</i> synchronized, so the same MersenneTwisterFast
 * instance cannot be shared by multiple threads.  But all this helps
 * MersenneTwisterFast achieve over twice the speed of MersenneTwister.
 *
 * <p><b>About the Mersenne Twister. </b>
 * This is a Java version of the C-program for MT19937: Integer version.
 * next(32) generates one pseudorandom unsigned integer (32bit)

 * which is uniformly distributed among 0 to 2^32-1  for each
 * call.  next(int bits) >>>'s by (32-bits) to get a value ranging
 * between 0 and 2^bits-1 long inclusive; hope that's correct.
 * setSeed(seed) set initial values to the working area
 * of 624 words. For setSeed(seed), seed is any 32-bit integer 
 * <b>except for 0</b>.
 *
 * <p>Orignally Coded by Takuji Nishimura, considering the suggestions by
 * Topher Cooper and Marc Rieffel in July-Aug. 1997.
 * More information can be found 
 * <A HREF="http://www.math.keio.ac.jp/matumoto/emt.html">
 * here. </a>

 * <P>
 * Translated to Java by Michael Lecuyer January 30, 1999
 * Copyright (C) 1999 Michael Lecuyer
 * <P>
 * This library is free software; you can redistribute it and or

 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later
 * version.
 * This library is distributed in the hope that it will be useful,

 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU Library General Public License for more details.
 * You should have received a copy of the GNU Library General
 * Public License along with this library; if not, write to the
 * Free Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
 * 02111-1307  USA
 * <P>
 * Makoto Matsumoto and Takuji Nishimura, the original authors
 * ask "When you use this, send an email to: matumoto@math.keio.ac.jp
 * with an appropriate reference to your work"  You might also point
 * out this was a translation.
 * <P>
 * <b>Reference. </b>
 * M. Matsumoto and T. Nishimura,
 * "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform
 * Pseudo-Random Number Generator",
 * <i>ACM Transactions on Modeling and Computer Simulation,</i>
 * Vol. 8, No. 1, January 1998, pp 3--30.
 *
 * <p><b>About this version. </b>  This is a modification of the 
 * <a href="http://www.theorem.com/java/index.htm#Mersenne">original
 * code</a> made to conform to proper java.util.Random format by 
 * <a href="http://www.cs.umd.edu/users/seanl/">Sean Luke,</a>
 * August 7, 1999.
 *
 * <p><b>Bug Fixes. </b>This implementation implements the bug fixes made
 * in Java 1.2's version of Random, which means it can be used with
 * earlier versions of Java.  See 
 * <a href="http://www.javasoft.com/products/jdk/1.2/docs/api/java/util/Random.html">
 * the JDK 1.2 java.util.Random documentation</a> for further documentation
 * on the random-number generation contracts made.  Additionally, there's
 * an undocumented bug in the JDK java.util.Random.nextBytes() method,
 * which this code fixes.
 *
 * <p><b>Important Note. </b> Just like java.util.Random, this
 * generator accepts a long seed but doesn't use all of it.  java.util.Random
 * uses 48 bits.  The Mersenne Twister instead uses 32 bits (int size).
 * So it's best if your seed does not exceed the int range.
 */



public class MersenneTwisterFast implements Serializable
    {
    // Period parameters
    private static final int N = 624;
    private static final int M = 397;
    private static final int MATRIX_A = 0x9908b0df;   //    private static final * constant vector a
    private static final int UPPER_MASK = 0x80000000; // most significant w-r bits
    private static final int LOWER_MASK = 0x7fffffff; // least significant r bits


    // Tempering parameters
    private static final int TEMPERING_MASK_B = 0x9d2c5680;
    private static final int TEMPERING_MASK_C = 0xefc60000;
    
    // #define TEMPERING_SHIFT_U(y)  (y >>> 11)
    // #define TEMPERING_SHIFT_S(y)  (y << 7)
    // #define TEMPERING_SHIFT_T(y)  (y << 15)
    // #define TEMPERING_SHIFT_L(y)  (y >>> 18)
    
    private int mt[]; // the array for the state vector
    private int mti; // mti==N+1 means mt[N] is not initialized
    private int mag01[];
    
    // a good initial seed (of int size, though stored in a long)
    private static final long GOOD_SEED = 4357;

    private double nextNextGaussian;
    private boolean haveNextNextGaussian;


    /**
     * Constructor using the default seed.

     */
    public MersenneTwisterFast()
        {
        setSeed(GOOD_SEED);
        }
    
    /**
     * Constructor using a given seed.  Though you pass this seed in
     * as a long, it's best to make sure it's actually an integer.
     *
     * @param seed generator starting number, often the time of day.
     */
    public MersenneTwisterFast(long seed)
        {
        setSeed(seed);
        }
    
    /**
     * Initalize the pseudo random number generator.
     * The Mersenne Twister only uses an integer for its seed;
     * It's best that you don't pass in a long that's bigger
     * than an int.
     *
     * @param seed from constructor
     *
     */
    public final void setSeed(long seed)
        {
        haveNextNextGaussian = false;

        mt = new int[N];
        
        // setting initial seeds to mt[N] using
        // the generator Line 25 of Table 1 in
        // [KNUTH 1981, The Art of Computer Programming
        //    Vol. 2 (2nd Ed.), pp102]

        // the 0xffffffff is commented out because in Java
        // ints are always 32 bits; hence i & 0xffffffff == i

        mt[0]= ((int)seed); // & 0xffffffff;

        for (mti = 1; mti < N; mti++)
            mt[mti] = (69069 * mt[mti-1]); //& 0xffffffff;

        // mag01[x] = x * MATRIX_A  for x=0,1
        mag01 = new int[2];
        mag01[0] = 0x0;
        mag01[1] = MATRIX_A;
        }
    
    public final int nextInt()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
            }

  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return y;
        }



    public final short nextShort()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];


            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return (short)(y >>> 16);
        }



    public final char nextChar()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time

            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return (char)(y >>> 16);
        }


    public final boolean nextBoolean()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }

            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);

                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return (boolean)((y >>> 31) != 0);
        }


    public final byte nextByte()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return (byte)(y >>> 24);
        }


    public final void nextBytes(byte[] bytes)
        {
        int y;
        
        for (int x=0;x<bytes.length;x++)
            {
            if (mti >= N)   // generate N words at one time
                {
                int kk;
                
                for (kk = 0; kk < N - M; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                for (; kk < N-1; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];
                
                mti = 0;
                }
            
            y = mt[mti++];
            y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

            bytes[x] = (byte)(y >>> 24);
            }
        }


    public final long nextLong()
        {
        int y;
        int z;

        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];


            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        if (mti >= N)   // generate N words at one time

            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
            z = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (z >>> 1) ^ mag01[z & 0x1];
            
            mti = 0;
            }
        
        z = mt[mti++];
        z ^= z >>> 11;                          // TEMPERING_SHIFT_U(z)
        z ^= (z << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(z)
        z ^= (z << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(z)
        z ^= (z >>> 18);                        // TEMPERING_SHIFT_L(z)
        
        return (((long)y) << 32) + (long)z;
        }


    public final double nextDouble()
        {
        int y;
        int z;

        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {

                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
            z = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);

            mt[N-1] = mt[M-1] ^ (z >>> 1) ^ mag01[z & 0x1];
            
            mti = 0;
            }
        
        z = mt[mti++];
        z ^= z >>> 11;                          // TEMPERING_SHIFT_U(z)
        z ^= (z << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(z)
        z ^= (z << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(z)
        z ^= (z >>> 18);                        // TEMPERING_SHIFT_L(z)
        
        /* derived from nextDouble documentation in jdk 1.2 docs, see top */
        return ((((long)(y >>> 6)) << 27) + (z >>> 5)) / (double)(1L << 53);
        }





    public final double nextGaussian()
        {
        if (haveNextNextGaussian)
            {
            haveNextNextGaussian = false;
            return nextNextGaussian;
            } 
        else 
            {
            double v1, v2, s;
            do 
                { 
                int y;
                int z;
                int a;
                int b;
                    
                    if (mti >= N)   // generate N words at one time
                        {
                        int kk;
                        
                        for (kk = 0; kk < N - M; kk++)

                            {
                            y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                            mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                            }
                        for (; kk < N-1; kk++)
                            {
                            y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                            mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                            }
                        y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);

                        mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];
                        
                        mti = 0;
                        }
                
                y = mt[mti++];
                y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
                y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
                y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
                y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)
                
                if (mti >= N)   // generate N words at one time
                    {
                    int kk;
                    
                    for (kk = 0; kk < N - M; kk++)
                        {
                        z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+M] ^ (z >>> 1) ^ mag01[z & 0x1];
                        }
                    for (; kk < N-1; kk++)
                        {
                        z = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+(M-N)] ^ (z >>> 1) ^ mag01[z & 0x1];
                        }
                    z = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N-1] = mt[M-1] ^ (z >>> 1) ^ mag01[z & 0x1];
                    
                    mti = 0;
                    }
                
                z = mt[mti++];
                z ^= z >>> 11;                          // TEMPERING_SHIFT_U(z)
                z ^= (z << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(z)
                z ^= (z << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(z)
                z ^= (z >>> 18);                        // TEMPERING_SHIFT_L(z)
                
                if (mti >= N)   // generate N words at one time
                    {
                    int kk;
                    
                    for (kk = 0; kk < N - M; kk++)
                        {
                        a = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+M] ^ (a >>> 1) ^ mag01[a & 0x1];
                        }
                    for (; kk < N-1; kk++)
                        {

                        a = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+(M-N)] ^ (a >>> 1) ^ mag01[a & 0x1];
                        }
                    a = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N-1] = mt[M-1] ^ (a >>> 1) ^ mag01[a & 0x1];
                    
                    mti = 0;
                    }
                
                a = mt[mti++];
                a ^= a >>> 11;                          // TEMPERING_SHIFT_U(a)
                a ^= (a << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(a)
                a ^= (a << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(a)
                a ^= (a >>> 18);                        // TEMPERING_SHIFT_L(a)
                
                if (mti >= N)   // generate N words at one time
                    {
                    int kk;
                    
                    for (kk = 0; kk < N - M; kk++)
                        {
                        b = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+M] ^ (b >>> 1) ^ mag01[b & 0x1];
                        }
                    for (; kk < N-1; kk++)
                        {
                        b = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                        mt[kk] = mt[kk+(M-N)] ^ (b >>> 1) ^ mag01[b & 0x1];
                        }
                    b = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N-1] = mt[M-1] ^ (b >>> 1) ^ mag01[b & 0x1];
                    
                    mti = 0;
                    }
                
                b = mt[mti++];
                b ^= b >>> 11;                          // TEMPERING_SHIFT_U(b)
                b ^= (b << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(b)
                b ^= (b << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(b)
                b ^= (b >>> 18);                        // TEMPERING_SHIFT_L(b)
                
                /* derived from nextDouble documentation in jdk 1.2 docs, see top */
                v1 = 2 *
                    (((((long)(y >>> 6)) << 27) + (z >>> 5)) / (double)(1L << 53))
                    - 1;
                v2 = 2 * (((((long)(a >>> 6)) << 27) + (b >>> 5)) / (double)(1L << 53))
                    - 1;
                s = v1 * v1 + v2 * v2;
                } while (s >= 1);
            double multiplier = Math.sqrt(-2 * Math.log(s)/s);
            nextNextGaussian = v2 * multiplier;
            haveNextNextGaussian = true;
            return v1 * multiplier;
            }
        }
    
    
    

    








    public final float nextFloat()
        {
        int y;
        
        if (mti >= N)   // generate N words at one time
            {
            int kk;
            
            for (kk = 0; kk < N - M; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            for (; kk < N-1; kk++)
                {
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;

            }
  
        y = mt[mti++];
        y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)

        return (y >>> 8) / ((float)(1 << 24));
        }



    /** Returns an integer drawn uniformly from 0 to n-1.  Suffice it to say,
        n must be > 0, or an IllegalArgumentException is raised. */
    public int nextInt(int n)
        {
        if (n<=0)
            throw new IllegalArgumentException("n must be positive");
        
        if ((n & -n) == n)  // i.e., n is a power of 2
            {
            int y;
        
            if (mti >= N)   // generate N words at one time
                {
                int kk;
                
                for (kk = 0; kk < N - M; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                for (; kk < N-1; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];
                
                mti = 0;
                }
            
            y = mt[mti++];
            y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)
            
            return (int)((n * (long) (y >>> 1) ) >> 31);
            }
        
        int bits, val;
        do 
            {
            int y;
            
            if (mti >= N)   // generate N words at one time
                {
                int kk;
                
                for (kk = 0; kk < N - M; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+M] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                for (; kk < N-1; kk++)
                    {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
                    mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N-1] = mt[M-1] ^ (y >>> 1) ^ mag01[y & 0x1];
                
                mti = 0;
                }
            
            y = mt[mti++];
            y ^= y >>> 11;                          // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B;       // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C;      // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18);                        // TEMPERING_SHIFT_L(y)
        
            bits = (y >>> 1);
            val = bits % n;
            } while(bits - val + (n-1) < 0);
        return val;
        }
    








    /**
     * Tests the code.
     */
    public static void main(String args[])
        { 
        int j;

        MersenneTwisterFast r;

        // UNCOMMENT THIS TO TEST FOR PROPER GAUSSIAN STATE INITIALIZATION
        
        /*
        System.out.println("If the gaussian state is properly initialized when setSeed() is called,\nthen #1 != #2, but #1 == #3\nIt's known that java 1.0.2 doesn't do gaussian initialization right,\nso setSeed() may result in one last gaussian drawn from the *previous* seed.");
        r = new MersenneTwisterFast(1);
        r.nextGaussian();  // loads the later gaussian into the state
        System.out.println("1:  " + r.nextGaussian());
        r = new MersenneTwisterFast(1);
        r.nextGaussian(); // loads the later gaussian into the state
        r.setSeed(1);     // should reset the gaussian state
        System.out.println("2:  " + r.nextGaussian());
        System.out.println("3:  " + r.nextGaussian());
        */

        
        // UNCOMMENT THIS TO TEST FOR CORRECTNESS
        // COMPARE WITH http://www.math.keio.ac.jp/~nisimura/random/int/mt19937int.out
        
        /*
        r = new MersenneTwisterFast(4357);
        System.out.println("Output of MersenneTwisterFast.java");
        for (j=0;j<1000;j++)
            {
            // first, convert the int from signed to "unsigned"
            long l = (long)r.nextInt();

            if (l < 0 ) l += 4294967296L;  // max int value
            String s = String.valueOf(l);

            while(s.length() < 10) s = " " + s;  // buffer
            System.out.print(s + " ");
            if (j%8==7) System.out.println();       
            }
        */


        // UNCOMMENT THIS TO TEST FOR SPEED

        /*
        r = new MersenneTwisterFast();
        System.out.println("\nTime to test grabbing 10000000 ints");
        long ms = System.currentTimeMillis();
        int xx=0;
        for (j = 0; j < 10000000; j++)
            xx += r.nextInt();
        System.out.println("Mersenne Twister: " + (System.currentTimeMillis()-ms + "          Ignore this: " + xx));

        Random rr = new Random(1);
        xx = 0;
        ms = System.currentTimeMillis();
        for (j = 0; j < 10000000; j++)
            xx += rr.nextInt();
        System.out.println("java.util.Random: " + (System.currentTimeMillis()-ms + "          Ignore this: " + xx));
        */

        
        // UNCOMMENT THIS TO DO TEST DIFFERENT TYPE OUTPUTS
        // THIS CAN BE USED TO COMPARE THE DIFFERENCE BETWEEN

        // MersenneTwisterFast.java AND MersenneTwister.java

        /*
        System.out.println("\nGrab the first 1000 booleans");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextBoolean() + " ");
            if (j%8==7) System.out.println();
            }
        if (!(j%8==7)) System.out.println();

        byte[] bytes = new byte[1000];
        System.out.println("\nGrab the first 1000 bytes using nextBytes");
        r = new MersenneTwisterFast();
        r.nextBytes(bytes);
        for (j = 0; j < 1000; j++)
            {
            System.out.print(bytes[j] + " ");
            if (j%16==15) System.out.println();
            }
        if (!(j%16==15)) System.out.println();
        
        byte b;
        System.out.println("\nGrab the first 1000 bytes -- must be same as nextBytes");
        r = new MersenneTwisterFast();

        for (j = 0; j < 1000; j++)
            {
            System.out.print((b = r.nextByte()) + " ");
            if (b!=bytes[j]) System.out.print("BAD ");
            if (j%16==15) System.out.println();
            }
        if (!(j%16==15)) System.out.println();

        System.out.println("\nGrab the first 1000 shorts");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextShort() + " ");
            if (j%8==7) System.out.println();
            }
        if (!(j%8==7)) System.out.println();

        System.out.println("\nGrab the first 1000 ints");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextInt() + " ");
            if (j%4==3) System.out.println();
            }
        if (!(j%4==3)) System.out.println();

        System.out.println("\nGrab the first 1000 ints of different sizes");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextInt(j+1) + " ");
            if (j%4==3) System.out.println();
            }
        if (!(j%4==3)) System.out.println();

        System.out.println("\nGrab the first 1000 longs");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextLong() + " ");
            if (j%3==2) System.out.println();
            }
        if (!(j%3==2)) System.out.println();

        System.out.println("\nGrab the first 1000 floats");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextFloat() + " ");
            if (j%4==3) System.out.println();
            }
        if (!(j%4==3)) System.out.println();

        System.out.println("\nGrab the first 1000 doubles");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextDouble() + " ");
            if (j%3==2) System.out.println();
            }
        if (!(j%3==2)) System.out.println();

        System.out.println("\nGrab the first 1000 gaussian doubles");
        r = new MersenneTwisterFast();
        for (j = 0; j < 1000; j++)
            {
            System.out.print(r.nextGaussian() + " ");
            if (j%3==2) System.out.println();
            }
        if (!(j%3==2)) System.out.println();
        */
        }

    }