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
#include <bits/stdc++.h>

using namespace std;

bool p[2000001];
int pr[2000001];

int main()
{
    p[0] = p[1] = 1;
    for (int i = 4; i <= 2000000; i += 2) p[i] = 1;
    
    
    int ind = 0;
    pr[ind++] = 2;
    for (int i = 3; i * i <= 2000000; i += 2){
        if (!p[i]){
            for (int j = 3 * i; j <= 2000000; j += 2 * i) p[j] = 1;
        }
    }
    for (int i = 3; i <= 2000000; i++) if (!p[i]) pr[ind++] = i;
    
    int n;
    while (scanf("%d", &n) && n){
        if (binary_search(pr, pr + 100000, n) == 1) printf("0\n");
        else printf("%d\n", *upper_bound(pr, pr + 100000, n) - *(lower_bound(pr, pr + 100000, n) - 1));
    }
    
    return (0);
}