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: Wrong Answer)

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

cnt = 0
white_zone = 0
if n % 2 == 0
  white_zone = n/2 - 1
else
  white_zone = n/2
end

flag = true
(white_zone+1).upto(n-1).each do |i|
  #puts "black_zone: i=#{i}, flag=#{flag}"
  next if s[i] == '.' && flag
  flag = false
  if s[i] == '.'
    cnt += 1
  end
end

flag = true
first_flag = true
white_zone.downto(0).each do |i|
  #puts "white_zone: i=#{i}, flag=#{flag}"
  if first_flag
    first_flag = false
    if s[i+1] == '#' && s[i] == '#'
      next
    elsif s[i+1] == '#' && s[i] == '.'
      flag = false
      next
    elsif s[i+1] == '.' && s[i] == '#'
      flag = false
      cnt += 1
      next
    elsif s[i+1] == '.' && s[i] == '.'
      flag = false
      next
    end
  end

  next if s[i] == '#' && flag
  flag = false
  if s[i] == '#'
    cnt += 1
  end
end

puts cnt