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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defparameter n (read))
(defparameter s (coerce (read-line) 'list))

(defun f (lst acc# acc)
  (declare (optimize (speed 3) (debug 0) (safety 0)))
  (cond ((or (endp lst)
             (endp (cdr lst)))
         acc)
        ((and (char= #\. (first lst))
              (char= #\# (second lst)))
         (f (cdr lst) acc# (cons acc# acc)))
        ((char= #\# (car lst))
         (f (cdr lst) (1+ acc#) acc))
        (t (f (cdr lst) acc# acc))))
(defun g (lst acc. acc)
  (declare (optimize (speed 3) (debug 0) (safety 0)))
  (cond ((or (endp lst)
             (endp (cdr lst)))
         acc)
        ((and (char= #\# (first lst))
              (char= #\. (second lst)))
         (g (cdr lst) acc. (cons acc. acc)))
        ((char= #\. (car lst))
         (g (cdr lst) (1+ acc.) acc))
        (t (g (cdr lst) acc. acc))))

(format t "~a" (reduce #'min (cons (count #\# s)
                                   (cons (count #\. s)
                                         (mapcar #'+
                                                 (f s 0 '())
                                                 (nreverse (g (reverse s) 0 '())))))))