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)

n = gets.to_i
ss = gets.chomp.chars

b = Array.new(n, 0)
c = Array.new(n, 0)
n.times do |i|
  if ss[i] == '#'
    b[i] = 1
  else
    c[i] = 1
  end
end
b = b.inject([0]) { |i, j| i << i.last + j }
c = c.inject([0]) { |i, j| i << i.last + j }.reverse
z = []
(n+1).times do |i|
  z.push(b[i] + c[i])
end

puts z.min