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>
#define pb push_back

using namespace std;

typedef pair<int, int> P;
typedef long long int LL;

int main() {
    vector<bool> v(1300000, false);

    for (int i = 2; i < 1200; i++) {
        for (int j = 2; j * i <= 1300000; j++) {
            v[j * i] = true;
        }
    }

    int k;
    while (cin >> k, k) {
        int a = -1, b = -1;
        for (int i = 1; true; i++) {
            if (!v[k]) break;
            if (a != -1 && b != -1) break;

            if (k - i > 0 && !v[k - i] && a == -1) a = k - i;
            if (k + i < 1300000 && !v[k + i] && b == -1) b = k + i;
        }
        cout << b - a << endl;
    }

    return 0;
}