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 () =
  let n = Scanf.scanf "%d " (fun a -> a) in
  let s = Scanf.scanf "%s " (fun a -> a) in
  let cs = Batteries.String.to_list s in
  let is = List.map (fun x -> if x = 'I' then 1 else -1) cs in

  let rec f last res = function
    | [] -> res
    | hd :: tl -> 
      f (last+hd) ((last+hd)::res) tl
  in
  let max = (f 0 [] (0::is) |> List.sort compare |> List.rev |> List.hd) in
  Printf.printf "%d\n" max