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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let rec sum10 n acc =
  let m = n / 10 in
  if m = 0 then n + acc
  else sum10 m (acc + (n mod 10))


let solve n =
  Array.init 100 (fun i -> sum10 (n * (i + 1)) 0)
  |> Array.fold_left min n

let () = Scanf.scanf "%d" solve |> Printf.printf "%d"