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>
const int MAX = 1299709;
using namespace std;

bool isPrime[MAX+5];
int seqPrime[MAX+5];
int ITR = 0;

void  eratos() {
	// 初期化
	for(int i=0;i<=MAX;i++) {
		isPrime[i] = true;
	}
	for(int i=2;i<=MAX;i++) {
		if(isPrime[i]) {
			seqPrime[ITR++] = i;
			for(int j=2*i;j<=MAX;j+=i) {
				isPrime[j] = false;
			}
		}
	}
}

int main()
{
	eratos();
	int k;
	while(1) {
		cin >> k;
		if(k==0) break;
		auto now = upper_bound(seqPrime, seqPrime+ITR, k);
		auto before = now-1;
		if(*before == k) cout << 0 << endl;
		else cout << (*now-*before) << endl;
	}
}
