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 main(void)
{
	int n;
	int min,max;
	int check;

	int i;

	while(1){
		cin >> n;
		if (n==0) break;

		min=n;
		
		while(1){

			check=0;
			for(i=2;i*i<=min;i++){
				if(min%i==0){
					check=1;
					break;
				}
			}
			if(check==0) break;
			else min--;

		}
		max=n;
		while(1){

			check=0;
			for(i=2;i*i<=max;i++){
				if(max%i==0){
					check=1;
					break;
				}
			}
			if(check==0) break;
			else max++;
		}

		cout << max-min << endl;
	}

	return 0;
}