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[(1 << 21) + 10];
vector<int> prime;

void sieve(int n) {
  fill(is_prime, is_prime + n, true);
  for (int i = 2; i <= n; i++) {
    if (!is_prime[i]) continue;
    prime.push_back(i);
    for (int j = 2 * i; j <= n; j += i) {
      is_prime[j] = false;
    }
  }
}

int main(void) {
  sieve(1 << 21);
  
  int n;
  while (cin >> n, n) {
    auto p = upper_bound(prime.begin(), prime.end(), n);
    cout << (is_prime[n] ? 0 : *p - *(p - 1)) << endl;
  }

  return 0;
}
