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 <map>

using namespace std;


bool is_prime[1299709 + 1];

int main(){
  
  
  for(int i = 0; i <= 1299709; ++i){
    is_prime[i] = true;
  }

  for(int i = 2; i * i <= 1299709; ++i){
    if(is_prime[i]){
      for(int j = 0; i * (j + 2) <= 1299709; ++j){
        is_prime[i * (j+2)] = false;
      }
    }
  }

  while(1){
    int k;
    cin >> k;
    if(k == 0) return 0;
    
    if(is_prime[k] == true){
      cout << "0\n";
    }else{
      int left = k, right = k;
      while(is_prime[left] == false){
        left--;
      }
      while(is_prime[right] == false){
        right++;
      }
      cout << right - left << "\n";
    }
  }
    
}
