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;
using ll = long long;

inline bool isprime(ll n)
{
    for (ll i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

int main()
{
    while (true) {
        ll n;
        cin >> n;
        if (n == 0) {
            break;
        }
        ll inf = n;
        for (;; inf--) {
            if (isprime(inf)) {
                break;
            }
        }
        ll sup = n;
        for (;; sup++) {
            if (isprime(sup)) {
                break;
            }
        }
        cout << sup - inf << endl;
    }

    return 0;
}