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 isPrime(int n)
{
	for (int i = 2; i * i <= n; i++)
	{
		if (n % i == 0)return false;
	}

	return true;
}

int main()
{
	int k;
	while (cin >> k && k != 0)
	{
		int min = k;
		int max = k;
		int length = 0;
		while (true)
		{
			bool primeMin = isPrime(min);
			bool primeMax = isPrime(max);

			if (primeMin && primeMax)break;
			if (!primeMin)
			{
				min--;
				length++;
			}

			if (!primeMax)
			{
				max++;
				length++;
			}
		}

		cout << length << endl;
	}
	return 0;
}