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 <string>
#include <vector>
#include <cstring>
using namespace std;

const int MX = 1500000;
bool sieve[MX];

int main() {
    memset(sieve, false, sizeof sieve);
    sieve[0] = sieve[1] = true;
    for (int i=2; i*i<MX; ++i) {
        if ( ! sieve[i]) {
            for (int j=i*i; j<MX; j+=i) {
                sieve[j] = true;
            }
        }
    }
    int n;
    while (cin >> n, n) {
        int l, h;
        for (int i=n; ; ++i) {
            if ( ! sieve[i]) {
                h = i; break;
            }
        }
        for (int i=n; ; --i) {
            if ( ! sieve[i]) {
                l = i; break;
            }
        }
        cout << h-l << endl;
    }
    return 0;
}