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.*;
import java.lang.*;
import java.io.*;

public class Main{
	Scanner sc=new Scanner(System.in);

	void run(){
		boolean[] p=new boolean[2000000];
		Arrays.fill(p, true);
		p[0]=p[1]=false;
		for(int i=2; i<p.length; i++){
			if(p[i]){
				for(int j=i*2; j<p.length; j+=i){
					p[j]=false;
				}
			}
		}
		for(;;){
			int m=sc.nextInt();
			if(m==0){
				break;
			}
			int ans=0;
			for(int i=m; i>=0&&!p[i]; i--){
				ans++;
			}
			for(int i=m; i<p.length&&!p[i]; i++){
				ans++;
			}
			println(""+ans);
		}
	}

	void print(String s){
		System.out.print(s);
	}

	void println(String s){
		System.out.println(s);
	}

	public static void main(String[] args){
		new Main().run();
	}
}