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.split("")
bw = []
i = cnt = 0
jud = s[0]
s.each do |c|
  if jud == c
    cnt += 1
  else
    bw[i] = cnt
    jud = c
    i += 1
    cnt = 1
  end
end
bw[i] = cnt

min = 999999999999
bsums = Array.new(i+2)
wsums = Array.new(i+2)
bsums[0] = 0
wsums[0] = 0
i = 1
le = 0
le = 1 if s[0] == "."
bw.each do |k|
  if i % 2 == le
    bsums[i] = bsums[i-1] + k
    wsums[i] = wsums[i-1]
  else
    wsums[i] = wsums[i-1] + k
    bsums[i] = bsums[i-1]
  end
  i += 1
end
for j in 0..(i-1)
  ch = bsums[j] + (wsums[i-1] - wsums[j])
  min = ch if min > ch
end
puts min