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 <algorithm>
#include <iostream>
#include <vector>
#include <numeric>
using namespace std;

vector<int> prime_table(int n) {
    vector<int> is_prime(n + 1);
    if (n) iota(is_prime.begin() + 2, is_prime.end(), 2);
    for (int i = 2; i * i <= n; i++) if (is_prime[i]) {
        for (int j = i + i; j <= n; j += i) is_prime[j] = 0;
    }
    return is_prime;
}

int main() {
    auto is_prime = prime_table(2e6);
    int n;
    while (cin >> n, n) {
        int prv = n, nxt = n;
        while (!is_prime[prv]) prv--;
        while (!is_prime[nxt]) nxt++;
        cout << nxt - prv << endl;
    }
    return 0;
}

