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;

bool check(int x){
	if(x == 2)return true;
	if(x < 2 || x%2 == 0)return false;
	for(int i = 3;i <= sqrt(x);i+=2){
		if(x%i == 0)return false;
	}
	return true;
}

int main(){
	int n,a,b;
	while(1){
		cin >> n;
		if(n == 0)break;
		if(check(n)){
			cout << 0 <<endl;
			continue;
		}
		for(int i = n + 1;i <= 1299709;i++){
			if(check(i)){
				a = i;
				break;
			}
		}
		for(int i = n - 1;i >= 3;i--){
			if(check(i)){
				b = i;
				break;
			}
		}
		cout << a - b <<endl;
	}
	return 0;
}