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>
#include <vector>
#include <algorithm>

using namespace std;

int main(){
	const int N = 1299709 + 1;
	vector<int> primes;
	vector<bool> sieve(N, false);
	sieve[0] = sieve[1] = true;
	for(int i = 2; i < N; ++i){
		if(sieve[i]){ continue; }
		primes.push_back(i);
		for(int j = i + i; j < N; j += i){ sieve[j] = true; }
	}
	while(true){
		int k;
		cin >> k;
		if(k == 0){ break; }
		if(k < 2 || !sieve[k]){
			cout << 0 << endl;
		}else{
			vector<int>::iterator it =
				lower_bound(primes.begin(), primes.end(), k);
			int upper = *it;
			int lower = *--it;
			cout << upper - lower << endl;
		}
	}
	return 0;
}