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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

io = STDIN
n=io.gets.to_i
s=io.gets.chomp.split(//).chunk_while{|a,b|a==b}.to_a
size=s.size
def calc(ss,ch) # chにするために必要な数
    ss.select{|ar|ar[0]!=ch}.inject(0){|s,ar|s+ar.size}
end
mid=(0...(size-1)).map do |i|
  calc(s[0..i],".")+calc(s[(i+1)..-1],"#")
end
puts [calc(s,"."),mid,calc(s,"#")].flatten.min