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>

#define MAX 1299710

bool is_prime[MAX];

int main(int argc,char* argv[]){
  
  for(int i = 2; i < MAX; i++){
    is_prime[i] = true;
  }
  is_prime[0] = is_prime[1] = false;

  for(int i = 2; i <= 1140; i++){
    if(is_prime[i]){
      for(int j = 2*i; j < MAX; j += i){
	is_prime[j] = false;
      } 
    }
  }

  while(true){
    int n;

    std::cin >> n;

    if(n == 0){
      break;
    }

    int low = 0, high = 0;

    for(low = n; low >= 0; low--){
      if(is_prime[low]){
	break;
      }
    }

    for(high = n; high < MAX; high++){
      if(is_prime[high]){
	break;
      }
    }
    
    std::cout << (high - low) << std::endl;
  }

  return 0;
  
}