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

dot_from_back=[0]
old=0
S.reverse.each_char do |c|
    if c=="."
        old+=1
    end
    dot_from_back << old
end
dot_from_back << old
dot_from_for=dot_from_back.reverse

sharp_from_for=[0]
old=0
S.each_char do |c|
    if c=="#"
        old+=1
    end
    sharp_from_for << old
end

sharp_from_for << old


min=Float::INFINITY
(S.length+1).times do |i|
    temp=sharp_from_for[i]+dot_from_for[i+1]
    min=temp if temp<min
end


puts min