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

int main(){
  int n,sum;
  while(1){
    cin>>n;
    if(n==0)break;
    sum=0;
    for(int i=n;;i++){
      if(pri(i)==1)break;
      else sum++;
    }
    for(int i=n;i>=1;i--){
      if(pri(i)==1)break;
      else sum++;
    }
    cout<<sum<<endl;
  }
  return 0;
}