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
// Prime Gap
// English only

#include <iostream>

using namespace std;

const int Size = 1299710;

int main() {
  int k;
  bool prime[Size];
  fill(prime, prime+Size, true);
  prime[0]=prime[1]=false;
  for(int i=2; i<Size; i++) {
    if(prime[i]) { // iが素数であれば
      for(int j=2; i*j<Size; j++) {
	prime[i*j] = false;
      }
    }
  }

  while(1) {
    cin>>k;
    if(k==0) {
      break;
    }

    int l=k, r=k;
    while(!prime[l]) {
      l--;
    }
    while(!prime[r]) {
      r++;
    }
    cout<<r-l<<endl;
  }
}