Problem:
Score : 200 points

Problem Statement

Takahashi has two positive integers A and B.

It is known that A plus B equals N.
Find the minimum possible value of "the sum of the digits of A" plus "the sum of the digits of B" (in base 10).

Constraints

2 ≤ N ≤ 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum possible value of "the sum of the digits of A" plus "the sum of the digits of B".

Sample Input 1

15

Sample Output 1

6

When A=2 and B=13, the sums of their digits are 2 and 4, which minimizes the value in question.

Sample Input 2

100000

Sample Output 2

10

Solution in OCaml (4.02.3) (judge verdict: Runtime Error)

let rec fact n =
  if n = 0 then 1 else n * fact (n - 1)
;;
let bi_c  n k =
  fact n / ((fact k) * (fact (n - k)))
;;

let rec rgb a b n k x sum  =
  if x <= 0 then sum
  else
    let y = (k - a * x) / b in
    if a * x + b * y = k && 0 <= y && y <= n then
      rgb a b n k (x - 1) (sum +  (bi_c n x) * (bi_c n y))
    else
      rgb a b n k (x - 1) (sum)
  
let () =
  let n, a, b, k = Scanf.scanf "%d %d %d %d"
                     (fun n a b k -> n, a, b, k) in
  (rgb a b n k n 0) mod 998244353 
|> print_int