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;

constexpr int lim = 2e6;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  vector<bool> prime(lim + 1, true);
  prime[0] = prime[1] = false;
  for (int p = 2; p * p <= lim; ++p) {
    if (prime[p]) {
      for (int i = 2 * p; i <= lim; i += p) {
        prime[i] = false;
      }
    }
  }
  int n;
  while (cin >> n, n) {
    if (prime[n]) {
      cout << "0\n";
    } else {
      int l = n, r = n;
      while (not prime[l - 1]) {
        --l;
      }
      while (not prime[r + 1]) {
        ++r;
      }
      cout << r - l + 2 << '\n';
    }
  }
}

