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: Time Limit Exceeded)

main = do
    n <- readLn
    s <- getLine
    print $ naive n s

naive :: Int -> String -> Int
naive n s = minimum (map (diff s) (lists n))
    where
        diff :: Eq a => [a] -> [a] -> Int
        diff ls ms = length [1 | (x,y)<-zip ls ms, x/=y]
        lists n = [replicate l '.' ++ replicate (n-l) '#' | l<-[0..n]]