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>
#include <vector>
#include <cstring>

using namespace std;

inline int nextInt() { int d; cin >> d; return d; }

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

int main() {
  while (true) {
    int p = nextInt();
    if (p == 0) {
      break;
    }
    int u, d;
    for (u = p; ; u++) {
      if (isPrime(u)) {
        break;
      }
    }
    for (d = p; ; d--) {
      if (isPrime(d)) {
        break;
      }
    }
    cout << u - d << endl;
  }

  return 0;
}