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 isPrime(int x) {
	if (x == 2) return true;
	for (int i=2; i*i <= x; ++i) if (x % i == 0) return false;
	return true;
}

int main() {
	int k;
	while (cin >> k, k != 0) {
		if (isPrime(k)) puts("0");
		else {
			int ans = 1, x = k-1;
			while (!isPrime(x)) {
				++ans;
				--x;
			}
			
			x = k+1;
			while (!isPrime(x)) {
				++ans;
				++x;
			}
			
			cout << ans + 1 << endl;
		}
	}
}
