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>
#include <math.h>
using namespace std;
#define MAX 1299709

int isPrime(int a){
  int i;
  if (a==2) return 1;
  if (a%2==0) return 0;
  for (i=3;i<=sqrt(a);i+=2){
    if (a%i==0) return 0;
  }
  return 1;
}

int main(){
  int n,a,b;
  cin >> n;
  while (n!=0){
    a=0;
    b=0;
    if (isPrime(n)) cout << 0 << endl;
    else{
      for (int i=1;;i++){
	if (a==0) if (isPrime(n-i))a=n-i;
	if (b==0) if (isPrime(n+i))b=n+i;
	if (a!=0&&b!=0) break;
      }
      cout << b-a << endl;
    }
    cin >> n;
  }
  return 0;
}