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)

WHITE = '.'
BLACK = '#'

TOGGLE = {
    WHITE => BLACK,
    BLACK => WHITE
}

def finish?(str)
  str.match(/\A[#{WHITE}]*[#{BLACK}]*\z/)
end

def toggle(str, index)
  tmp = str.dup
  tmp[index] = TOGGLE[str[index]]
  tmp
end

def solve(str, t)
  queue = [[S, 0]]

  while !queue.empty?
    st, ti = queue.shift

    if finish? st
      return ti
    end

    N.times do |i|
      queue.push [toggle(st, i), ti + 1]
    end
  end
end

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

puts solve(S, 0)