Problem:
Score : 200 points

Problem Statement

You have an integer variable x.
Initially, x=0.

Some person gave you a string S of length N, and using the string you performed the following operation N times.
In the i-th operation, you incremented the value of x by 1 if S_i=I, and decremented the value of x by 1 if S_i=D.

Find the maximum value taken by x during the operations (including before the first operation, and after the last operation).

Constraints

1≤N≤100

|S|=N

No characters except I and D occur in S.

Input

The input is given from Standard Input in the following format:

N
S

Output

Print the maximum value taken by x during the operations.

Sample Input 1

5
IIDID

Sample Output 1

2

After each operation, the value of x becomes 1, 2, 1, 2 and 1, respectively. Thus, the output should be 2, the maximum value.

Sample Input 2

7
DDIDDII

Sample Output 2

0

The initial value x=0 is the maximum value taken by x, thus the output should be 0.

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let (|>) x f = f x ;;
let n = Scanf.scanf "%d\n" (fun n -> n) ;;
let s = Scanf.scanf "%s\n" (fun s -> s) ;;

let string_to_list str =
  let id_to_int c =
    if c = 'I' then 1
    else -1
  in
  let rec loop idx arr=
    if idx = -1 then arr
    else loop (idx-1) ((id_to_int (String.get str idx))::arr)
  in
  loop (n-1) []
;;

let solve arr =
  let rec sim ma v arr = 
    match arr with
    | [] -> ma
    | h::t ->
      let w = v + h in
      let new_max = max ma w in
      sim new_max w t
  in
  sim 0 0 arr
;;

let () =
  s
  |> string_to_list
  |> solve
  |> Printf.printf "%d\n"