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

bc = 0
wc = 0

bc_list = []
wc_list = []

S.each_char do |s|
  if s == '#'
    bc += 1
  else
    wc += 1
  end

  bc_list << bc
  wc_list << wc
end

ans = Float::INFINITY

(N + 1).times do |i|
  lwrb = if i == 0
           bc
         elsif i == N
           wc
         else
           bc_list[i - 1] + wc - wc_list[i - 1]
         end

  ans = lwrb if ans > lwrb
end

puts ans