import java.util.*;
//
// State is 
// - a BitSet state S
// - integer represetation iS
// - a counter for how often  we have encountered that state
// - number of possible elements in set S (number of bits)
//
// given a collection of states we might access states using the BitSet as a key
//

public class State {

    BitSet S;
    int iS; 
    int counter;
    int n;

    public State(BitSet b,int n){
	this.n = n;
	S = b;    
	iS = toInt(b);
	counter = 1;
    }
    //
    // create a new state, 1st time we have seen it
    //

    public State(int v,int n){	 
	this.n = n;
	S = toBitSet(v);    
	iS = v;
	counter = 1;
    }
    //
    // create a new state, from an integer
    //
    
    public void inc(){counter++;}
    //
    // when we visit an exisiting state increment its counter
    //

    public String toString(){return counter +" "+ S +" "+ iS;}

    private int toInt(BitSet b){
	int result = 0;
	for (int i=n-1;i>=0;i--){
	    result = result*2;
	    if (b.get(i)) result++;
	}
	return result;
    }
    //
    // convert a BitSet to an integer
    //

    private BitSet toBitSet(int v){
	BitSet b = new BitSet(n);
	for (int i=0;i<n;i++,v=v/2) b.set(i,v%2==1);
	return b;
    }
    //
    // convert intger v into a BitSet
    //
}