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

int main ()
{
    vector<bool> num(2222222, true);
    num[0] = num[1] = false;
    vector<int> prim;
    for (int i = 2; i <= 2222222; i++) {
        for (int j = 2; num[i] && j * i <= 2222222; j++) {
            num[i * j] = false;
        }
        if (num[i]) prim.push_back(i);
    }
    int n;
    while (cin >> n, n) {
        auto i = lower_bound(prim.begin(), prim.end(), n) - prim.begin();

        int res = 0;
        if (n < prim[i]) res = prim[i] - prim[i-1];
        if (n > prim[i]) res = prim[i+1] - prim[i];

        cout << res << endl;
    }

    return 0;
}