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<cmath>
using namespace std;
int X, Y, A, i, j;
int main() {
	while (true) {
		cin >> A; if (A == 0) { break; }
		for (i = A; i >= 2; i--) { for (j = 2; j <= sqrt(i); j++) { if (i%j == 0) { goto E; } }X = i; goto F; E:; }
	F:; for (i = A; i < 99999999; i++) { for (j = 2; j <= sqrt(i); j++) { if (i%j == 0) { goto G; } }Y = i; goto H; G:; }
	H:; cout << Y - X << endl;
	}
}