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;

bool prime_check(int n, int k = 2)
{
	if (n < k * k) { return true; }

	if (n % k == 0) { return false; }

	return prime_check(n, k + 1);
}

int main()
{
	int n;

	while (true)
	{
		cin >> n;

		if (n == 0) { break; }

		int l = n;
		int r = n;

		while (prime_check(l) == false)
		{
			l--;
		}

		while(prime_check(r) == false)
		{
			r++;
		}

		cout << r - l << endl;
	}

	return 0;
}