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.chomp.to_i
s = gets.chomp

left_b = Array.new(n, 0)
right_w = Array.new(n, 0)

left_b[0] = 1 if s[0] == '#'
for i in 1..(n-1)
  if s[i] == '#'
  	left_b[i] = left_b[i-1] + 1
  else
    left_b[i] = left_b[i-1]
  end
end

right_w[n-1] = 1 if s[n-1] == '.'
for i in 1..(n-1)
  if s[n-1-i] == '.'
  	right_w[n-1-i] = right_w[n-i] + 1
  else
    right_w[n-1-i] = right_w[n-i]
  end
end

sum = Array.new(n+1, 0)
sum[0] = right_w[0]
sum[n] = left_b[n-1]
for i in 0..n-2
  sum[i+1] = left_b[i] + right_w[i+1]
end
puts sum.min