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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
int f(long long a){
  int s=0;
  for(;a;a/=10)s+=a%10;
  return s;
}
int main(){
  int min=1e9,n,i;
  scanf("%d",&n);
  for(i=1;i<100000010;i++){
    if(min>f(1LL*i*n))min=f(1LL*i*n);
  }
  printf("%d\n",min);
  return 0;
}