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)

#ifdef _DEBUG
#include "MyLib.h"
#else
#define main_D main
#include "bits/stdc++.h" 
#include <regex>
#define _USE_MATH_DEFINES
#include <math.h>
#define FOR(i,s,e) for (int i = int(s); i < int(e); ++i)
#define REP(i,e) FOR(i,0,e)
#define INF (INT_MAX/2)
#define EPS (1.0e-8)
#define LINF (LLONG_MAX/2)
const int MGN = 8;
const int ARY_SZ_MAX = 10000000;
using namespace std;
using ll = long long; using ull = unsigned long long;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vl = vector<ll>; using vvl = vector<vl>;
using vd = vector<double>; using vs = vector<string>;
using pii = pair<int, int>; using pll = pair<ll, ll>;
// functions
ll digit_sum(ll n) {
    if (n < 10) return n;
    else return n%10 + digit_sum(n/10);
}
#endif


int main_D() {
    cin.tie(0);
    ios::sync_with_stdio(false);


    ll K; cin >> K;
    ll ans = LINF;
    FOR(i,1,1000000) {
        ans = min(ans, digit_sum(K*i));
    }

    cout << ans << endl;


    return 0;
}