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.Arrays;
import java.util.Scanner;

//Prime Gap
public class Main{

	void run(){
		int N = 1299709;
		boolean[] p = new boolean[N+1];
		Arrays.fill(p, true);
		p[0]=p[1]=true;
		for(int i=2;i<=N;i++)if(p[i])for(int j=i+i;j<=N;j+=i)p[j]=false;
		Scanner sc = new Scanner(System.in);
		for(;;){
			int k = sc.nextInt();
			if(k==0)break;
			int l = k, r = k;
			while(!p[l])l--;
			while(!p[r])r++;
			System.out.println(r-l);
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
}