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
// AOJ 1276

#include <iostream>

using namespace std;

bool prime[2000000];
void makeprime()
{
	fill(prime, prime + 2000000, true);
	prime[0] = prime[1] = false;
	for (int i = 4; i < 2000000; i+=2) prime[i] = false;
	for (int i = 3; i*i <= 2000000; i += 2){
		if (prime[i]){
			for (int j = i*2; j < 2000000; j += i){
				prime[j] = false;
			}
		}
	}

	return;
}

int main(void)
{
	makeprime();

	int k;
	while (cin >> k, k){
		int a = 0, b = 0;
		for (int i = k; i < 2000000; i++){
			if (prime[i]){
				a = i;
				break;
			}
		}
		for (int i = k; 0 <= i; i--){
			if (prime[i]){
				b = i;
				break;
			}
		}
		cout << a - b << endl;

	}

	return 0;
}