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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;

#define M 1299709

bool tbl[M + 1];

int main(){
	vector<int> p;
	p.reserve(100005);

	for(int i = 2; i * i <= M; ++i){
		if( !tbl[i] ){
			for(int j = i * i; j <= M; j += i){
				tbl[j] = true;
			}
		}
	}

	for(int i = 2; i <= M; ++i){
		if( !tbl[i] ){	p.push_back(i);	}
	}
	
	int k;
	while( scanf("%d", &k), k != 0 ){
		printf("%d\n", *lower_bound(p.begin(), p.end(), k) - *(upper_bound(p.begin(), p.end(), k) - 1));
	}
}