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: Time Limit Exceeded)

#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll ans=0;
ll sum(ll x){
    ll ret=0;
    while(x>0){
        ret+=x%10;
        x/=10;
    }
    return ret;
}
int main()
{
    int k;
    cin>>k;
    ans=sum(k);
    for(ll i=2;i<=100000000;i++)
        ans=min(ans,sum(i*k));
    cout<<ans;
    return 0;
}