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<string>
#define SIZE 1299710
using namespace std;

int main() {
	bool *hantei;
	hantei = new bool[SIZE] {};
	hantei[0] = hantei[1] = true;
	for (int a = 2; a < SIZE; a++) {
		if (!hantei[a]) {
			for (int b = a * 2; b < SIZE; b += a)hantei[b] = true;
		}
	}
	int c;
	while (cin >> c, c) {
		if (c == 1 || !hantei[c]) { cout << 0 << endl; continue; }
		int d = 1;
		for (int e = c + 1;; e++) {
			if (!hantei[e])break;
			d++;
		}
		for (int f = c - 1;; f--) {
			if (!hantei[f])break;
			d++;
		}
		cout << d+1<< endl;
	}
}