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;

bool erat[2000000];
set<int> primes; 
int main(){
	for(int i = 0; i < 2000000; i++){
		erat[i] = true;
	}
	for(int i = 2; i < 2000000; i++){
		if(erat[i]){
			primes.insert(i);
			for(int j = i + i; j < 2000000; j += i){
				erat[j] = false;
			}
		}
	}
	int N;
	while(cin >> N, N){
		if(primes.count(N)){
			cout << 0 << endl;
		}else{
			auto it = primes.lower_bound(N);
			cout << (*it - *(--it)) << endl;
		}
	}
}