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>
using namespace std;

int main(){
  int data[1400000],i,j;
  for(i = 2; i*i < 1400000; i++){
    if(data[i]==0){
      for(j = i*2; j < 1400000; j+=i){
	data[j]=1;
      }
    }
  }
  data[0]=1;
  data[1]=2;
  int n,down,up;
  while(1){
    cin >> n;
    if(n==0)break;
  
    for(i = n; i >=2; i--){
      if(data[i]==0){
	down = i;
	break;
      }
    }
    
    for(i = n; i < 1400000; i++){
      if(data[i]==0){
	up = i;
	break;
      }
    }
    
    if(data[n]==0)cout << "0" << endl;
    else cout << up - down << endl;
  }
  return 0;
}