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<cstdio>
#include<cstring>

char prime[1300000];

int main(void) {
    memset(prime, 1, sizeof(prime));

    prime[0] = prime[1] = 0;
    for(int i=0; i<1300000; i++) {
        if(!prime[i]) continue;
        for(int j=2; i*j<1300000; j++) {
            prime[i*j] = 0;
        }
    }

    while(true) {
        int n,lb,ub;
        scanf("%d", &n);
        if(!n) break;

        lb = ub = n;
        while(!prime[ub++]);
        while(!prime[lb--]);
        printf("%d\n",ub-lb-2);
    }
    return 0;
}