The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.



Input

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

Example

Input

10
11
27
2
492170
0


Output

4
0
6
0
114
import java.util.*;

class Main{
	static Scanner s=new Scanner(System.in);
	public static void main(String[] $){
		int n;
		PrimeIterator p=new PrimeIterator(1300000);
		while(true) {
			n=s.nextInt();
			if(n==0)return;
			System.out.println(
					p.bitset.nextSetBit(n)
					-p.bitset.previousSetBit(n));
		}
	}
}

class PrimeIterator implements Iterable<Integer>,PrimitiveIterator.OfInt{
	BitSet		bitset;
	private int	currentvalue,limit;

	public PrimeIterator(int limit){
		currentvalue=0;
		bitset=new BitSet(limit+1);
		this.limit=limit;
		construct();
	}
	/** Atkin's sieve */
	private final void construct(){
		int sqLim=(int)Math.sqrt(limit+0.5);
		{
			int n;
			for(int z=1;z<=5;z+=4){
				for(int y=z;y<=sqLim;y+=6){
					int ysq=y*y;
					for(int x=1;x<=sqLim&&(n=4*x*x+ysq)<=limit;++x)
						bitset.flip(n);
					for(int x=y+1;x<=sqLim&&(n=3*x*x-ysq)<=limit;x+=2)
						bitset.flip(n);
				}
			}
			for(int z=2;z<=4;z+=2){
				for(int y=z;y<=sqLim;y+=6){
					int ysq=y*y;
					for(int x=1;x<=sqLim&&(n=3*x*x+ysq)<=limit;x+=2)
						bitset.flip(n);
					for(int x=y+1;x<=sqLim&&(n=3*x*x-ysq)<=limit;x+=2)
						bitset.flip(n);
				}
			}
			for(int y=3;y<=sqLim;y+=6){
				int ysq=y*y;
				for(int z=1;z<=2;++z)
					for(int x=z;x<=sqLim&&(n=4*x*x+ysq)<=limit;x+=3)
						bitset.flip(n);
			}
		}
		{
			//remove square
			for(int n=5;n<=sqLim&&n!=-1;n=bitset.nextSetBit(n+1)){
				int nsq=n*n;
				for(int k=nsq;k<=limit;k+=nsq)
					bitset.clear(k);
			}
		}
		bitset.set(2);
		bitset.set(3);
	}

	@Override
	public boolean hasNext(){
		int r=getNextValue();
		return 0<=r&&r<=limit;
	}
	private int getNextValue(){
		return bitset.nextSetBit(currentvalue+1);
	}
	@Override
	public int nextInt(){
		int r=getNextValue();
		if(r<0||limit<r) throw new NoSuchElementException();
		return currentvalue=r;
	}
	@Override
	public OfInt iterator(){
		return this;
	}
	public BitSet getClonedBitSet(){
		return (BitSet)bitset.clone();
	}
}
