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
//一番近い素数までの合計距離

import java.util.*;
public class Main{
    static Scanner kbd = new Scanner(System.in);
    public static void main(String[] args){
	boolean[] PrimeN = new boolean[1299710];//問題中の最大素数まで
	putN(PrimeN);

	while(kbd.hasNext()){
	    int n = kbd.nextInt();
	    if(n!=0){
		solve(n, PrimeN);
	    }
	}
    }

    static void solve(int n, boolean[] PrimeN){
	if(PrimeN[n]) System.out.println("0");
	else{
	    int fn = n+1;
	    int bn = n-1;
	    while(!PrimeN[fn]) fn++;
	    while(!PrimeN[bn]) bn--;
	    System.out.println(fn-bn);
	}
    }

    static void putN(boolean[] p){
	Arrays.fill(p, true);
	p[0] = false;
	p[1] = false;
	for(int i=2; i<p.length; i++){
	    if(p[i]){
		for(int j=i+i; j<p.length; j+=i){
		    p[j] = false;
		}
	    }
	    //System.out.println(i+" "+p[i]);
	}
    }
}