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;
int isPrime[2000001];
int main(){

  fill(isPrime,isPrime + 2000001,1); 
  isPrime[0]=isPrime[1]=0;
  for(int i = 2 ; i*i < 2000001 ; i++ ){
    if(isPrime[i])for(int j = i*2 ; j < 2000001 ; j+=i )isPrime[j] = 0;
  }
  int n;
  while(cin >> n,n){
    int cnt = 0;
    int p,q;
    for(int i = n ; ; i++){
      if(isPrime[i] == 1){
	p = i;
	break;
      }
    }
    int f = 1;
    for(int i = n ; ; i--){
      if(i < 0){
	f = 0;
	break;
      }
      if(isPrime[i] == 1){
	q = i;
	break;
      }
    }
    if(f == 0)cout << 0 << endl;
    else cout << p-q << endl;
  }
  return 0;
}