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

#white[i]:左端から数えてi個の石のうち，白い石が何個あるか
#ただし，white[0] = 0
white = Array.new(n+1, 0)
#black[i]: 黒について同様の定義
black = Array.new(n+1, 0)

for i in 0..n-1 do
  if s[i] == "."
    white[i+1] = white[i] + 1
    black[i+1] = black[i]
  else
    white[i+1] = white[i]
    black[i+1] = black[i] + 1
  end
end

min = 10**9

for i in 0..n do
  tmp = (black[i] - black[0]) + (white[n] - white[i])
  min = tmp if tmp < min
end

puts min