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;

int main(){
	char est[1300000];
	for(int i = 2; i < 1300000; i++){
		est[i] = '1';
	}
	for(int i = 2; i * i <= 1300000; i++){
		for(int k = 2; k * i < 1300000; k++){
			est[i*k] = '0';
		}
	}
	int n;
	while(cin >> n){
		if(n == 0) break;
		int i = n, j = n;
		while(est[i] == '0') i--;
		while(est[j] == '0') j++;
		cout << j - i << endl;
	}
	return 0;
}