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 <algorithm>
#include <cstdlib>
#include <iostream>
#include <vector>
using namespace std;

vector<int> sieve(int n) {
	vector<int> res(1, 2);
	vector<bool> prime(n, true);
	for(int i = 3; i < n; i += 2) {
		if(prime[i]) {
			res.push_back(i);
			for(int j = i * 3; j < n; j += i * 2)
				prime[j] = false;
		}
	}

	return res;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	const int MAX = 1299709;
	vector<int> primes = sieve(MAX + 1);
	for(int k; cin >> k, k;) {
		int idx = lower_bound(primes.begin(), primes.end(), k) - primes.begin();
		if(primes[idx] == k)
			cout << 0 << endl;
		else
			cout << primes[idx] - primes[idx - 1] << endl;
	}

	return EXIT_SUCCESS;
}