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>
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;

bool is_prime[2000000];
int prime[2000000];
int main() {
	memset(is_prime, 1, sizeof(is_prime));
	is_prime[0] = is_prime[1] = false;
	int p = 0;
	for (int i = 2; i < 2000000; i++) {
		if (is_prime[i]) {
			prime[p++] = i;
			for (int j = i * 2; j < 2000000; j += i)is_prime[j] = false;
		}
	}
	int n;
	while (scanf("%d", &n), n) {
		if (is_prime[n]) {
			puts("0");
			continue;
		}
		int*a = lower_bound(prime, prime + p, n);
		if (a == prime)puts("0");
		else printf("%d\n", *a - *(a - 1));
	}
}