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;

bool so(int n){
  int cnt=0;
  for(int i=2;i*i<=n;i++){
    if(n%i==0){
      cnt++;
      break;
    }
  }
  if(cnt==0)return true;
  else return false;
}

int main(){
  int n;
  while(cin>>n,n){
    int cnt=0;
    if(!so(n)){
      for(int i=n+1;;i++){
        if(so(i))break;
        else cnt++;
      }
      for(int i=n-1;;i--){
        if(so(i))break;
        else cnt++;
      }
      cnt+=2;
    }
    cout<<cnt<<endl;
  }
  return 0;
}