Problem:
Score : 300 points

Problem Statement

There are N stones arranged in a row. Every stone is painted white or black.
A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is ., and the stone is black if the character is #.

Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.
Find the minimum number of stones that needs to be recolored.

Constraints

1 \leq N \leq 2\times 10^5

S is a string of length N consisting of . and #.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the minimum number of stones that needs to be recolored.

Sample Input 1

3
#.#

Sample Output 1

1

It is enough to change the color of the first stone to white.

Sample Input 2

5
#.##.

Sample Output 2

2

Sample Input 3

9
.........

Sample Output 3

0

Solution in OCaml (4.02.3) (judge verdict: Wrong Answer)

open Printf open Scanf
open Array

let print_array f a = Array.iter (fun v -> printf "%s " @@ f v) a; print_newline ()

let () = scanf " %d %s" @@ fun n s ->
  let a = init n (fun i -> s.[i]) in
  let res = ref 0 in
  let rec lp i black =
    let rec lp2 i =
      if i<n && a.(i) = '.' then lp2 (i+1)
      else i
    in
    if i=n then ()
    else if a.(i-1) = '#' && black > 0
      && a.(i) = '.' then (
      let j = lp2 @@ i+1 in
      let white = j - i in
      if black >= white then (
        res := !res + white;
        lp j (black + white);
      ) else (
        res := !res + black;
        lp j 0;
      );
    ) else lp (i+1) (black + if a.(i) = '#' then 1 else 0)
  in
  lp 1 (if a.(0) = '#' then 1 else 0);
  print_int !res;