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>

bool isprime[1600000];

void solve(int n) {
  int left = n, right = n;
  for(int i = n; i > 0; --i) {
    if( isprime[i] ) {
      left = i;
      break;
    }
  }
  for(int i = n; i < 1600000; ++i) {
    if( isprime[i] ) {
      right = i;
      break;
    }
  }
  std::cout << right - left << std::endl;
}

int main() {

  for(int i = 0; i < 1600000; ++i) {
    isprime[i] = true;
  }
  isprime[0] = isprime[1] = false;
  for(int i = 2; i < 4000; ++i) {
    if( isprime[i] ) {
      for(int j = i + i; j < 1600000; j+=i) {
        isprime[j] = false;
      }
    }
  }

  for(;;) {
    int n;
    std::cin >> n;
    if( n == 0 ) break;

    solve(n);
  }

  return 0;
}
  