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
// 2017-02-21
#include <iostream>
using namespace std;
#define N 1299709

int main() {
	static bool a[N + 1] = {true, true};
	static int b[N + 1], c[N + 1];
	{
		int t = 2;
		for (int i = 2; i <= N; i++) {
			if (a[i]) {
				b[i] = t;
			} else {
				c[t] = i - t;
				t = i;
				for (int j = 2 * i; j <= N; j += i) {
					a[j] = true;
				}
			}
		}
	}
	int n;
	while (cin >> n, n) {
		if (a[n]) {
			cout << c[b[n]] << endl;
		} else {
			cout << 0 << endl;
		}
	}
	return 0;
}