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;
#include<cmath>
bool isprime(int n) {
	if (n == 2)return true;
	if (n % 2 == 0)return false;
	for (int i = 3; i <= sqrt(n); i += 2) if (n%i == 0)return false;
	return true;
}
int main() {
	int n;
	while (cin >> n, n) {
		if (isprime(n))cout << "0\n";
		else {
			int r, l;
			for (r = n - 1; !isprime(r); r--);
			for (l = n + 1; !isprime(l); l++);
			cout << l - r << endl;
		}
	}
}