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;

#define N 11451419

int ans[N+1];
bool is_composite[N+1];
vector<int> primes;

int main() {
  is_composite[1] = true;
  for (int i=2; i<=N; i++) {
    if (!is_composite[i]) {
      primes.push_back(i);
      for (int j=i+i; j<=N; j+=i) {
        is_composite[j] = true;
      }
    }
  }

  int n = primes.size();
  for (int i=0; i<n-1; i++) {
    int a = primes[i];
    int b = primes[i+1];
    for (int j=a+1; j<b; j++) ans[j] = b-a;
  }

  while (1) {
    int k;
    scanf("%d", &k);
    if (k == 0) return 0;
    printf("%d\n", ans[k]);
  }
}