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
public class Main{
  public void run(java.io.InputStream in, java.io.PrintStream out){
    java.util.Scanner sc = new java.util.Scanner(in);
    int n, i, j;

    for(;;){
      n = sc.nextInt();
      if(n == 0)break;
      for(i = n;;i--)if(isprime(i))break;
      for(j = n;;j++)if(isprime(j))break;
      out.println(j - i);
    }

    sc.close();
  }
  public static void main(String[] args){
    (new Main()).run(System.in, System.out);
  }
  private static boolean isprime(int p){
    int i;
    if(p == 1)return false;
    for(i = 2;i * i <= p;i++)if(p % i == 0)return false;
    return true;
  }
}