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.Array
import Data.List

foldl_trace::(b->a->b)->b->[a]->[b]
foldl_trace f seed []     = []
foldl_trace f seed (x:xs) = (f seed x):(foldl_trace f (f seed x) xs)


sum_trace::[Int]->[Int]
sum_trace ls = 0:(foldl_trace (+) 0 ls)

still_n::[Int]->Array Int Int
still_n ls = listArray (0,length ls) (sum_trace ls)

solver::String->Int
solver dat = let n = length dat in
             let ar = still_n (map (\ c -> if c == '#' then 1 else 0) dat) in
             minimum [ar!(k-1) + (n - (k-1) - (ar!n) + ar!(k-1)) |k<-[1..(n+1)]]

main::IO()
main=do
  _<-getLine
  print.solver=<<getLine