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<bits/stdc++.h>
using namespace std;

int isPrime(int x){
  int i;
  if(x < 2)return 0;
  else if(x==2)return 1;
  if(x%2 == 0)return 0;
  for(i=3 ; i*i <= x ; i+=2){
    if(x%i == 0)return 0;
  }
  return 1;
}

int main(){
  
  int k;
  int i,j;

  while(1){
    cin >>k;
    if(k==0)break;
    
    if(isPrime(k)){
      cout <<"0"<<endl;
    }else{
      for(i=k+1 ; isPrime(i) != 1 ; i++);
      for(j=k-1 ; isPrime(j) != 1 ; j--);
      cout <<i-j<<endl;
    }
  }

  return 0;
}