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<iostream>
#include<algorithm>
using namespace std;

bool isprime(int a) {
	for (int i = 2;i*i <= a;i++) {
		if (a%i == 0)return false;
	}
	return a != 1;
}

int main() {
	int n;
	while (cin >> n, n) {
		int ans;
		int sp, bp;
		if (isprime(n))ans = 0;
		else {
			for (int i = n;i > 0;i--) {
				if (isprime(i)) {
					sp = i;
					break;
				}
			}
			for (int i = n;i < 1300000;i++) {
				if (isprime(i)) {
					bp = i;
					break;
				}
			}
			ans = bp - sp;
		}
		cout << ans << endl;
	}
	return 0;
}