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)

def cin; gets.split.map(&:to_i) end
def cout(*x); puts x.join(" ") end

# exit if $0 != __FILE__

n = gets.to_i
s = gets.chop.chars

ws = s.reverse.inject([0]) {|m,c| m << ((c=='.') ? m.last+1 : m.last)}
bs = s.inject([0]) {|m,c| m << ((c=='#') ? m.last+1 : m.last)}
ws << ws.last
bs << bs.last

#p ws
#p bs

min = 10**18
[*(0..n)].each do |i|
  x = bs[i] + ws[n-i]
  #p x
  min = [min,x].min
end

puts min