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 <cstdio>
#include <cstring>
using namespace std;

#define MAX 10000001

bool p[MAX];

int main(){
  memset(p, 1, sizeof(p));
  p[0] = p[1] = 0;
  for(int i = 0 ; i < MAX ; i++){
    if(p[i]){
      for(int j = 2 * i ; j < MAX ; j += i){
	p[j] = 0;
      }
    }
  }

  int n;
  while(cin >> n, n){
    int next, prev;
    if(p[n] == 1) cout << 0 << endl;

    else{
      for(int i = n ; ; i++){
	if(p[i] == 1){
	  next = i;
	  break;
	}
      }
      for(int i = n ; ; i--){
	if(p[i] == 1){
	  prev = i;
	  break;
	}
      }
      cout << next - prev << endl;
    }
  }
  return 0;
}
   