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.to_i
s = gets.chomp

def num_change(s, n)
  return 0 if s.chars.uniq.size == 1

  hl = hash_left(s)

  min_num_change = n
  hl.each_with_index do |nn, i|
    min_num_change = [min_num_change, nn + i].min
  end

  ss = repl(s)

  hl = hash_left(s)

  min_num_change = n
  hl.each_with_index do |nn, i|
    min_num_change = [min_num_change, nn + i].min
  end

  min_num_change
end

def hash_left(s)
  a = []
  num_hashes = 0
  s.chars.each do |c|
    if c == '#'
      num_hashes += 1
    else
      a << num_hashes
    end
  end
  a.reverse
end

def repl(s)
  ss = s.chars.map{ |c| c == '.' ? '#' : '.'}.join
  ss.reverse
end