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: Wrong Answer)

(let* ((n (read))
       (arr (read-line))
       (c 0)
       (d 0))
  (defun a-f (x)
    (cond ((= (1- n) x) x)
          ((char= (aref arr x) #\.) (a-f (1+ x)))
          (t (incf c) x)))
  (defun b-f (y)
    (cond ((= 0 y) y)
          ((char= (aref arr y) #\#) (b-f (1- y)))
          (t (incf d) y)))
  (defun f (a b)
    (let* ((p (a-f a))
           (q (b-f b)))
      (cond ((or (= p q) (= (1+ p) q)) (princ (1- (+ c d))))
            ((< q p) (princ (+ c d)))
            (t (f (1+ p) (1- q))))))
  (f 0 (1- n)))