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 <vector>
#include <cmath>
using namespace std;

int main()
{
	vector<bool> numbers(1300000, true);
	vector<int> primes;

	numbers[0] = false;
	numbers[1] = false;

	for (int i = 2; i <= sqrt(1300000); i++) {
		for (int j = i + i; j < 1300000; j += i) {
			numbers[j] = false;
		}
	}

	for (int i = 2; i < 1300000; i++) {
		if (numbers[i] == true) {
			primes.push_back(i);
		}
	}

	while (true) {
		int n;
		cin >> n;

		if (n == 0) {
			break;
		}

		for (int i = 0; i < primes.size(); i++) {
			if (n == primes[i]) {
				cout << 0 << endl;
				break;
			}
			else if (n > primes[i] && n < primes[i + 1]) {
				cout << primes[i + 1] - primes[i] << endl;
				break;
			}
		}
	}

	return 0;
}