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 is_prime(int n){
  for (int i = 2; i * i <= n; i++){
    if (n % i == 0){
      return false;
    }
  }
  return true;
}
int main(){
  while (1){
    int n;
    cin >> n;
    if (n == 0){
      break;
    }
    if (is_prime(n)){
      cout << 0 << endl;
    } else {
      int L = n;
      while (!is_prime(L)){
        L--;
      }
      int R = n;
      while (!is_prime(R)){
        R++;
      }
      cout << R - L << endl;
    }
  }
}
