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 <algorithm>
#include <vector>

using namespace std;

int main() {
	vector<bool> isprime(1300000, true);
	isprime[0] = isprime[1] = false;
	vector<int> prime;
	for (long long i = 2; i < 1300000; ++i) {
		if (isprime[i]) {
			prime.push_back(i);
			for (long long j = i * i; j < 1300000; j += i) isprime[j] = false;
		}
	}
	int k;
	while (cin >> k, k) {
		auto it = lower_bound(prime.begin(), prime.end(), k);
		if (*it == k) cout << 0;
		else cout << *it - *(it - 1);
		cout << endl;
	}

	return 0;
}
