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: Wrong Answer)

f s n
 |null s=n
 |head s=='.' = f (tail s) n+1
 |otherwise=n+1
g s n
 |null s=n
 |head s=='#' = g (tail s) n+1
 |otherwise=n+1
main=do
 l<-readLn :: IO Int
 s<-getLine
 let sr=f s 0
     srr=g (reverse s) 0
     sp=take (l-sr)$reverse s
     sl=length$filter(=='.')sp
     sq=take (l-srr) s
     sd=length$filter(=='#')sq
     ss=length$filter(=='.')s
     sa=length$filter(=='#')s
 print$min sd sl