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 <iostream>
#include <vector>
#include <cstring>
using namespace std;

int main(){
  bool compnum[1299710];
  memset(compnum, false, sizeof(compnum));
  for (int i = 2; i*i <= 1299709; i++) {
    for (int j = i+i; j <= 1299709; j+=i) {
      compnum[j] = true;
    }
  }
  while (true) {
    int x;
    cin >> x;
    if (x == 0) break;
    int l, r;
    l = r = x;
    while (l > 2 && compnum[l]) l--;
    while (r < 1299709 && compnum[r]) r++;
    cout << r-l << endl;
  }
}