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)

n = gets.chomp.to_i
s = gets.chomp

def fill_right_black(idx, str)
  len = str.length - idx
  cnt = str[idx..-1].split("").count(".")
  str[idx..-1] = "#" * len
  [cnt, str]
end

def fill_left_white(idx, str)
  cnt = str[0..idx].split("").count("#")
  str[0..idx] = "." * idx
  [cnt, str]
end

score1 = score2 = 0

str = s.dup
first_i = str.rindex("#.")
i = first_i
while i
  cnt, str = fill_right_black(i + 1, str)
  score1 += cnt
  i = str.rindex("#.", i)
end
score2, str = fill_left_white(first_i, s) if first_i
puts [score1, score2].min