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.chars
a = Array.new(n){Array.new(2, 0)}
if s[0] == '.'
  a[0][0] = 1
else
  a[0][1] = 1
end
1.upto(n - 1) do |i|
  if s[i] == '.'
    a[i][0] = a[i - 1][0] + 1
    a[i][1] = a[i - 1][1]
  else
    a[i][0] = a[i - 1][0]
    a[i][1] = a[i - 1][1] + 1
  end
end
min = [a[n - 1][0], a[n - 1][1]].min
n.times do |i|
  min = a[n - 1][0] - a[i][0] + a[i][1] if min > a[n - 1][0] - a[i][0] + a[i][1]
end
puts min