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 <vector>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <cassert>
using namespace std;

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

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	vector<int> ps;
	for(int i = 2; i <= 1500000; i++) {
		if(isPrime(i)) ps.push_back(i);
	}

	int n;
	while(cin >> n, n) {
		for(int i = 0; i < ps.size(); i++) {
			if(ps[i] <= n && n < ps[i + 1]) {
				if(ps[i] == n) {
					cout << 0 << endl;
				}
				else {
					cout << ps[i + 1] - ps[i] << endl;
				}
				break;
			}
		}
	}
}