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)

main :: IO ()                                                                                                                                         
main = do                                                                                                                                             
  _ <- getLine                                                                                                                                        
  s <- getLine                                                                                                                                        
  let w = length . filter (=='.') $ s                                                                                                                 
  print $ minimum $ map (uncurry (+)) $ solve 0 w s                                                                                                   
                                                                                                                                                      
solve :: Int -> Int -> String -> [(Int,Int)]                                                                                                          
solve a b [] = [(a,b)]                                                                                                                                
solve a b (x:xs)                                                                                                                                      
  | x == '.' = (a,b) : solve a (b-1) xs                                                                                                               
  | x == '#' = (a,b) : solve (a+1) b xs