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 const MAX=1299709;
int prime[MAX+1]={0};//0::prime 1::NOTprime;

void hurui(){
  prime[1]=1;
  for(int i=1;i*i<=MAX;i++){
    for(int j=2;j<=MAX/i;j++){
      if(prime[i]==0)prime[i*j]=1;
    }
  }
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
    
  hurui();
  int n;
  //for(int i=1;i<=30;i++) cout << prime[i] << endl;
  while(cin >> n,n){
    int res=0;
    if(prime[n]==0){
      cout << res << endl;
    }
    else{
      int mae=n,ato=n+1;
      while(prime[mae]==1){
        res++;
        mae--;
      }
      while(prime[ato]==1){
        res++;
        ato++;
      }
      cout << res+1 << endl;
    }
  }
}