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;

int main() {

	int n = 1299709 + 1;
	bool prime[n+1];
  memset(prime, true, sizeof(prime));
 
  for (int p=2; p*p<=n; p++)
  {
      if (prime[p] == true)
      {
          for (int i=p*2; i<=n; i += p)
              prime[i] = false;
      }
  }

  int N;
	while (cin >> N && N != 0) {
		int ans = 0;
		if (N < 2 && N > 1299709) {
			ans = 0;
			cout << ans << '\n';
			continue;
		}

		int l = N, r = N;
		while(!prime[l] || !prime[r]) {
			if (!prime[l])
				l--;
			if (!prime[r])
				r++;
		}
		ans = r-l;
		cout << ans << '\n';
	}

	return 0;
}