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(){
	const int maxP = 1299710;
	bool pr[maxP+1];
	for(int i=2;i<=maxP;i++) pr[i] = true;
	for(int i=2;i<=maxP;i++){
		if(!pr[i]) continue;
		for(int j=2*i;j<=maxP;j+=i)
			pr[j] = false;
	}
	int p;
	while(cin >> p, p){
		int L = p, R = p;
		while(!pr[L]) L--;
		while(!pr[R]) R++;
		printf("%d\n", R-L);
	}
}