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;

#define MAX 1299709

int main(){

	int hurui[MAX + 1] = { 0 };
	int n,cnt;

	hurui[0] = 1, hurui[1] = 1;
	for (int i = 0; i <= MAX; i++){
		if (hurui[i] == 0){
			for (int j = i * 2; j <= MAX; j += i){
				hurui[j] = 1;
			}
		}
	}

	while (1){
		cin >> n;
		if (n == 0) break;

		if (hurui[n] == 0){
			cout << "0" << endl;
			continue;
		}

		while (hurui[n] == 1) n--;

		cnt = 1;
		n++;
		while (hurui[n] == 1) n++, cnt++;

		cout << cnt << endl;
	}
	return 0;
}