public class PQ
{
	static final boolean DEBUG=false;
	
	private InterestingPoint [] a;
	private int N;
	private InterestingPoint last=null;


	public PQ(int max)
	{
		a=new InterestingPoint[max+1];
		N=0;
	}

	public void insert(InterestingPoint v)
	{
		if(DEBUG) System.out.println("PQ: Inserting "+v+" at " +(N+1));
		a[++N]=v;
		upheap(N);
	}

	public void upheap(int k)
	{
		if(DEBUG) System.out.println("PQ: upheap");
		InterestingPoint v;
		v=a[k];
		while(k!=1 && a[k/2].ge(v) )
		{
			a[k]=a[k/2];
			k=k/2;
		}
		if(DEBUG) System.out.println("PQ: element "+v+" ended up at "+k);
		a[k]=v;
	}

	public void downheap(int k)
	{

		if(DEBUG) System.out.println("PQ: downheap");
		int j;
		InterestingPoint v=a[k];
		while(k<=N/2)
		{
			j=k+k;
			if(j<N && a[j].g(a[j+1]) ) j++;
			if( v.le(a[j]) ) break;
			a[k] = a[j]; // swap the j element up
			k=j;
		}
		a[k] = v;
	}

	public InterestingPoint remove()
	{
		if(N==0) return null;
		
		InterestingPoint v=a[1];

		a[1] = a[N--];

		downheap(1);
		if(DEBUG) System.out.println("PQ: remove returning "+v);
		if(last!=null && v.X()==last.X() && v.Y()==last.Y())return remove();
		last=v;
		return v;
	}

	public String toString()
	{
		StringBuffer s=new StringBuffer("PQ->");

		for(int i=1;i<=N;i++)
		{
			s.append(a[i]+"->");
		}
		return s.toString();
	}
} // PQ