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
s=gets.chomp
j=c=b=w=0
i=0
i+=1 while i<n and s[i]=='.'
i+=1 while i<n and s[i]=='#'
if i==n
  puts 0
  exit
end
0.upto(n-2){|i| 
  if s[i].eql?("#")
    b+=1
  else
    w+=1
  end
  if b*1.0/(i+1) <= c*1.0/(j+1)
    j=i
    c=b
  end
}
puts c+s[(j+1)..-1].count('.')