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 <cstdio>
#include <vector>
#include <algorithm>
#include <set>

int main() {
  int N = 1299709;
  std::vector<int> s(N+1);
  for (int i=2; i*i<=N; ++i) {
    if (s[i]) continue;
    for (int j=i*i; j<=N; j+=i) {
      s[j] = i;
    }
  }

  std::set<int> p;
  for (int i=2; i<=N; ++i)
    if (s[i] == 0) p.insert(i);

  while (true) {
    int n;
    scanf("%d", &n);
    if (n == 0) break;

    if (p.count(n)) {
      puts("0");
      continue;
    }

    auto it = p.lower_bound(n);
    int ub = *it;
    int lb = *--it;
    printf("%d\n", ub-lb);
  }
}

