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;

const int MAX_N = 1e+7;
bool is_p[MAX_N+1] = {false,false};

void sieve(){
	for(int i = 2 ; i <= MAX_N ; i++ )
		is_p[i] = true;
	for(int i = 2 ; i*i <= MAX_N ; i++ ){
		if( is_p[i] ){
			for(int j = i+i ; j <= MAX_N ; j += i ){
				is_p[j] = false;
			}
		}
	}
}

int main(){
	sieve();
	int k;
	while( cin >> k , k ){
		int a, b;
		for(int i=k ; 2 <= i ; i-- ){
			if( is_p[i] ){
				a = i;
				break;
			}
		}
		for(int i=k ; true ; i++ ){
			if( is_p[i] ){
				b = i;
				break;
			}
		}
		cout << b - a << endl;
	}
}