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[1500000];

void setPrime() {
	isPrime[0] = isPrime[1] = false;
	for (int i = 2; i < 1500000; i++) { isPrime[i] = true; }
	for (int i = 2; i < 1500000; i++) {
		if (isPrime[i]) {
			for (int j = i * 2; j < 1500000; j += i) {
				isPrime[j] = false;
			}
		}
	}
}

int main() {
	setPrime();
	int n;
	while (cin >> n) {
		if (!n) break;
		if (isPrime[n]) { cout << 0 << endl; continue; }
		
		int l, r;
		for (l = n - 1; !isPrime[l]; l--);
		for (r = n + 1; !isPrime[r]; r++);
		cout << r - l << endl;
	}
	return 0;
}