import java.util.BitSet;

public class Mod3AlgoTest
{
  public static void main(String[] args)
  {
    int maxNum = 65535;


    int nbits = 32 - Integer.numberOfLeadingZeros(maxNum);
    System.out.println("Number of bits: " + nbits);
    boolean allCorrect = true;
    for (int i = 0; i <= maxNum; i++) {
      int j = collapse(i, nbits);
      boolean correct = (i % 3) == (j % 3);
      allCorrect &= correct;
    }
    System.out.println("All correct? " + allCorrect);
  }

  public static int collapse(int nbr, int nbits) {
    BitSet bset = BitSet.valueOf(new long[] {nbr});
    int accu = 0;
    for (int i = 0; i < nbits; i++) {
      if (bset.get(i)) {
        accu += 1 + (i & 1);
      }
    }
    return accu;
  }
}