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!

chs = s.chars

# 左の黒の数
memo = []
memo[0] = 0

# 右の白の数
memo2 = []
memo2[n - 1] = 0 

(n - 1).times do |i|
  memo[i + 1] = memo[i] + ((chs[i] == "#") ? 1 : 0)
end

(n - 1).downto(1) do |i|
  memo2[i - 1] = memo2[i] + ((chs[i] == ".") ? 1 : 0)
end

puts n.times.map {|i|
  memo[i] + memo2[i]
}.min