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: Runtime Error)

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

a = []
(0...n).each do |i|
  a << i if s[i] == '#'
end

if a.empty?
  puts 0

else
  w = []
  w[0] = a[0] == 0 ? 0 : s[0, a[0] - 1].count('#')
  (1...a.length).each do |i|
    w[i] = w[i - 1] + s[a[i - 1], a[i] - a[i - 1]].count('#')
  end

  b = []
  b[a.length - 1] = s[a[-1], n - a[-1]].count('.')
  (a.length - 2).downto(0).each do |i|
    b[i] = b[i + 1] + s[a[i], a[i + 1] - a[i]].count('.')
  end

  counts = []
  (0...a.length).each do |i|
    counts[i] = w[i] + b[i]
  end
  counts << a.counts('#')

  puts counts.min
end