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


i = 0
min = 10000000000

def get_num(i, j, a)
  if i == 0
    l = 0
  else
    l = a[i - 1]
  end
  num = a[j] - l
  return num
end


b_a = Array.new(n, 0)
w_a = Array.new(n, 0)

s.each_char.with_index do |c, i|
  if c == '#'
    b_a[i] = b_a[i - 1] + 1
  else
    b_a[i] = b_a[i - 1]
  end
end

s.each_char.with_index do |c, i|
  if c == '.'
    w_a[i] = w_a[i - 1] + 1
  else
    w_a[i] = w_a[i - 1]
  end
end

s.each_char.each_cons(2) do |c1, c2|
  i = i + 1
  if c1 == '#' && c2 == '.'
    #l_w = s[0..i - 1].count('.')
    #l_b = s[0..i - 1].count('#')
    #r_w = s[i..-1].count('.')
    #r_b = s[i..-1].count('#')
    l_w = get_num(0, i - 1, w_a)
    l_b = get_num(0, i - 1, b_a)
    r_w = get_num(i, -1, w_a)
    r_b = get_num(i, -1, b_a)
    co = [l_b + r_w, l_b + r_b, l_w + r_w].min
    if co < min
      min = co
    end
  end
end

if min == 10000000000
  puts 0
else
  puts min
end