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 <cmath>
#include <cstdint>
#include <iostream>

using namespace std;

bool is_prime(uint32_t n) {
  for (uint32_t i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}

uint32_t above_prime(uint32_t n) {
  for (uint32_t i = n;; i++) {
    if (is_prime(i)) {
      return i;
    }
  }
}

uint32_t below_prime(uint32_t n) {
  for (uint32_t i = n;; i--) {
    if (is_prime(i) || i == 1) {
      return i;
    }
  }
}

int32_t main() {
  while (true) {
    uint32_t n;
    cin >> n;
    if (n == 0) break;

    uint32_t above = above_prime(n);
    uint32_t below = below_prime(n);

    cout << above - below << endl;
  }

  return 0;
}