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
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1276

#include <iostream>
#include <cmath>
using namespace std;

bool isPrime(int num){
  if(num<=3) return true;

  for(int i=2;i<=(int)sqrt(num);i++){
    if(num%i==0) return false;
  }

  return true;
}

int main(){
  int k;
  while(cin>>k&&k){
    if(isPrime(k)){
      cout << 0 << endl;
      continue;
    }

    int min_prime, max_prime;
    for(int i=k-1;i>=0;i--){
      if(isPrime(i)){
        min_prime = i;
        break;
      }
    }

    for(int i=k+1;i<=1299709;i++){
      if(isPrime(i)){
        max_prime = i;
        break;
      }
    }

    cout << max_prime - min_prime << endl;
  }

  return 0;
}