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 <cmath>

#define N 1299710

using namespace std;

int main(){
	bool prime[N];
	for (int i = 0; i < N; i++) prime[i] = 1;
	prime[1] = 0;
	for (int i = 1; i < sqrt(N); i++) {
		if (!prime[i]) continue;
		else {
			for (int j = 2; i * j < N; j++) prime[i * j] = 0;	
		}
	}

	int k;
	while (cin >> k, k) {
		if (prime[k]) {
			cout << "0" << endl;	
		} else {
			int a, b;
			for (a = k; !prime[a]; a--);
			for (b = k; !prime[b]; b++);
			cout << b - a << endl;
		}	
	}
	return 0;
}