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 <bits/stdc++.h>

using namespace std;

int N;
bool isPrime[1299710];

void primes() {
	fill(isPrime, isPrime + 1299710, 1);
	for (int i = 2; i < 1299710; i++) {
		if (isPrime[i]) {
			for (int j = 2 * i; j < 1299710; j += i) isPrime[j] = false;
		}
	}
}

void solve() {
	int l = N, r = N;
	while (!isPrime[l]) { l--; }
	while (!isPrime[r]) { r++; }
	cout << r - l << endl;
}

int main() {
	primes();
	
	while (1) {
		cin >> N; if (N == 0) break;
		solve();
	}
	
	return 0;
}