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 <bits/stdc++.h>
using namespace std;

#define MAX 1299809

int main(){

	  vector<int> pri;
	  bool is_p[MAX]={};
	  for(int i=2; i<MAX; i++) is_p[i] = true;
	  for(int i=2; i<MAX; i++){
			if( is_p[i] ) {
				  pri.push_back(i);
				  for(int j=2; i*j<MAX; j++)
						is_p[i*j] = false;
			}
	  }
	  int n;
	  while(cin >> n,n){
			
			int index = lower_bound(pri.begin(), pri.end(), n) - pri.begin();
			if( n == pri[index])
				  cout << 0 << endl;
			else
				  cout << pri[index] - pri[index-1]  << endl;
			
	  }
			
}