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 <bits/stdc++.h>

long long sumDigits(long long n) {
	long long result = 0;
	while(n != 0) {
		result += n % 10;
		n /= 10;
	}
	return result;
}

int main(void) {
	using namespace std;
	long long K;
	cin >> K;
	const long long INF = 100000;
	long long result = INF;
	for(long long i = 1; i < 10; ++i) {
		long long t = sumDigits(i * K);
		if(t < result) {
			result = t;
		}
	}
	cout << result << '\n';
	return 0;
}