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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List

main :: IO ()
main = do
  n <- readLn
  s <- getLine
  let
    bn = length $ filter (== '#') s
    (c, _, _) = foldl' go (bn, 0, 0) s
    go (ans, cbn, i) '#' = (min ans (cbn + ((n - i) - (bn - cbn))),     cbn + 1, i + 1)
    go (ans, cbn, i) '.' = (min ans (cbn + ((n - i) - (bn - cbn)) + 1), cbn + 0, i + 1)
  print c