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;

const int max_p = 1300000;
bool prime[max_p + 1];

void initial_prime()
{
    for (int i = 0; i < max_p; i++)
        prime[i] = true;
    prime[0] = prime[1] = false;

    for (int i = 2; i * i < max_p; i++)
        if (prime[i])
            for (int j = 2 * i; j <= max_p; j += i)
                prime[j] = false;
}

int main()
{
    int k;
    
    initial_prime();

    while (cin >> k, k) {
        int l, r;
        int ans = 0;

        l = r = k;
        while (!prime[l--])
            ans++;
        while (!prime[r++])
            ans++;
        cout << ans << endl;
    }

    return 0;
}