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 p[1300000];

void prime() {
  fill(p, p+1300000, true);
  p[0] = false;
  p[1] = false;
  for(int i = 2; i < 1300000; i++) {
    if(p[i]) {
      for(int j = 2; i*j < 1300000; j++) {
	p[i*j] = false;
      }
    }
  }
}

int main() {
  int n;
  prime();
  while(cin >> n, n) {
    int ans = 0;
    for(int i = n; !p[i]; i--) ans++;
    for(int i = n; !p[i]; i++) ans++;
    cout << ans << endl;
  }
}