Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

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

long long n, r = 1e16;

int main() {
    scanf("%lld", &n);

    for (int i = 1; i <= 1000000; i++) {
        long long k = n*i, s = 0;
        while (k) {
            s += k % 10;
            k /= 10;
        }
        r = min(s, r);
    }

    printf("%lld", r);

    return 0;
}