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 <bits/stdc++.h>
using namespace std;

const int MAX_N = 1500000;

vector<int> prime;
bool is_prime[MAX_N+1];

void siege(int n) {
    for (int i = 0; i <= n; i++) is_prime[i] = true;
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i <= n; i++) {
        if (is_prime[i]) {
            prime.push_back(i);
            for (int j = 2*i; j <= n; j += i) is_prime[j] = false;
        }
    }
}

int main(void) {

    siege(MAX_N);
    int N;
    while (cin >> N, N) {
        if (is_prime[N]) {
            cout << 0 << endl;
        } else {
            int idx = lower_bound(prime.begin(), prime.end(), N) - prime.begin();
            cout << prime[idx]-prime[idx-1] << endl;
        }
    }

    return 0;
}