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{

    void solve(){
        Scanner sc = new Scanner(System.in);

        int max = 1500000;
        int[] p = new int[max];
        for(int i=2; i<p.length; i++) p[i] = 1;
        for(int i=2; i<Math.sqrt(max)+1; i++){
            for(int j=i*2; j<max; j+=i) p[j] = 0;
        }

        while(true){
            int n = sc.nextInt();
            if(n==0) break;

            int idx1 = n, idx2 = n;
            while(p[idx1]!=1) idx1--;
            while(p[idx2]!=1) idx2++;
            System.out.println(idx2 - idx1);
        }
    }

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