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: Wrong Answer)

s = gets.to_i
n = gets.chomp.split("")
bw = Array.new(s).map{Array.new(2,0)}
bw2 = Array.new(4,0)
count = -1
check = 2
ans = 10**6
for i in 1..s
  if n[-i] == "#" && check == 0
    bw[count][1] += 1
    bw2[0] += 1
  elsif n[-i] == "#" && (check == 1 || check == 2)
    count += 1
    bw[count][0] = 0
    bw[count][1] = 1
    check = 0
    bw2[0] += 1
  elsif n[-i] == "." && (check == 0 || check == 2)
    count += 1
    bw[count][0] = 1
    bw[count][1] = 1
    check = 1
    bw2[1] += 1
  else
    bw[count][1] += 1
    bw2[1] += 1
  end
end
for i in 0..bw.length-1
  if bw[i][0] == 0
    bw2[0] -= bw[i][0]
    bw2[2] += bw[i][0]
  else
    bw2[1] -= bw[i][1]
    bw2[3] += bw[i][1]
  end
  if ans > [bw2[0],bw2[1]].min + bw2[3]
    ans = [bw2[0],bw2[1]].min + bw2[3]
    if bw2[2] == 0
      ans = [bw2[0],bw2[1]].min
    end
  end
end
puts ans