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 a[1299710]={};
  a[2]=1;
  int fl;
  for(int i=3;i<1299710;i++){
    fl=0;
    for(int j=2;j*j<=i;j++){
      if(i%j==0){
	fl=1;
	break;
      }
    }
    if(fl==0){
      a[i]=1;
    }
  }
  int n,h,t;
  while(1){
    cin >> n;
    if(n==0)break;
    for(int i=n;i>=0;i--){
      if(a[i]==1){
	h=i;
	break;
      }
    }
    for(int i=n;i<=1299709;i++){
      if(a[i]==1){
	t=i;
	break;
      }
    }
    cout << t-h<< endl;
  }
  return 0;
}