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)

BLACK = '#'

N = gets.chomp.to_i
S = gets.chomp

# 黒の数の累積和
black_cumulative = [0]

N.times do |i|
  black_cumulative[i + 1] =
      if S[i] == BLACK
        black_cumulative[i] + 1
      else
        black_cumulative[i]
      end
end

# 白の数の累積和
white_cumulative = black_cumulative.map.with_index do |blacks, i|
  i - blacks
end

costs =
  (N + 1).times.map do |i|
    change_blacks = black_cumulative[i]
    change_whites = white_cumulative.last - white_cumulative[i]
    change_blacks + change_whites
  end

puts costs.min