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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <list>
#define pie 3.141592653589793
#define si(a) scanf("%d",&a)
#define ss(a) scanf("%s",a)
#define sl(a) scanf("%lld",&a)
#define pi(a) printf("%d",a)
#define pl(a) printf("%lld",a)
#define ps(a) printf("%s",a)
#define ll long long
using namespace std;

ll solve(ll n){
  ll ans=0;
  while(n){
    ans+=n%10;
    n/=10;
  }
  return ans;
}


int main()
{
  ll n;
  sl(n);
  ll ans = 1e11;
  for(ll i=1;i<10;i++){
    ll temp = solve(n*i);
    if(temp<ans)
      ans=temp;
  }
  printf("%lld\n",ans);
  return 0;
}