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.to_i
ary = gets.chomp.split("")

return puts 0 unless ary.include?('#')

sary = []
tmp = 0
n.times do |i|
  tmp += 1 if ary[i] == '#'
  sary << tmp
end

m = 9999999
(n + 1).times do |i|
  if i == 0
    t = n - sary[-1]
  elsif i == n
    t = sary[-1]
  else
    t = sary[i - 1] + (n - i) - (sary[-1] - sary[i - 1])
  end
  m = [m, t].min
end

puts m