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 <bits/stdc++.h>
using namespace std;

int main() {
	vector<bool>x( 2000000, 1 );
	vector<long long int>prime;
	x[0] = x[1] = 0;
	for( size_t i = 0; i < 2000000; i++ ) {
		if( x[i] ) {
			prime.emplace_back( i );
			long long int j = 2;
			while( i*j < 2000000 ) {
				x[i*j] = 0;
				j++;
			}
		}
	}
	long long int N, M;
	while( cin >> N, N ) {
		if( find( prime.begin(), prime.end(), N ) != prime.end() ) {
			cout << 0 << endl;
		} else {
			auto now = upper_bound( prime.begin(), prime.end(), N ) - prime.begin();
			cout << prime[now] - prime[now - 1] << endl;
		}
	}
}