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: Accepted)

N = gets.to_i
S = gets.chomp.chars.take(N)

s = S.drop_while { |ch| ch == '.' }.reverse
  .drop_while { |ch| ch == '#' }.reverse

list = []
white_count = 0
black_count = 0
s.each.with_index do |ch, i|
  if ch == '#'
    if white_count > 0
      list.push([black_count, white_count])
      black_count = 1
      white_count = 0
    else
      black_count += 1
    end
  else
    white_count += 1
    list.push([black_count, white_count]) if i == s.size - 1
  end
end
dp = Array.new(list.size + 10)
dp[0] = { 'white' => 0, 'black' => 0}
list.each.with_index do |(black_count, white_count), i|
  dp[i + 1] = {}
  dp[i + 1]['white'] = dp[i]['white'] + black_count
  dp[i + 1]['black'] = [
    dp[i]['white'] + white_count,
    dp[i]['black'] + white_count,
  ].min
end
ans = [dp[list.size]['white'], dp[list.size]['black']].min
puts ans