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: Runtime Error)

n = gets.chomp.to_i
s = gets.chomp

#puts "now s = #{s}"


count_1=0
count_2=0
flag = -1

kuro=[]
shiro=[]
#kuroの処理(先頭から)
s.length.times do |i|
  if s[i]=="#" then
    count_1+=1 
    if flag==-1 then
      flag = i
    end
  end
  kuro << count_1
end
flag2 = -1

#shiroの処理(末尾から)
s.length.times do|i_kari|
  i = (s.length-1)-i_kari
  if s[i]=="." then
    count_2 += 1
    if flag2==-1 then
      flag2 = i
    end
  end
  shiro.unshift(count_2)
end
#puts "kuro = #{kuro}"
#puts "shiro = #{shiro}"

min = 2*(10**5)
(s.length-1).times do|i|
  #puts "kuro[#{i}] = #{kuro[i]}"
  #puts "shiro[#{i}] = #{shiro[i]}"
  if min>(kuro[i] + shiro[i+1]) then
    min = (kuro[i] + shiro[i+1])
  end
end

if  (s[flag,(s.length-1)].include?(".")==0) || (s[0,flag2].include?("#")==0) || kuro[0] == kuro[kuro.length-1] || shiro[0] == shiro[shiro.length-1] then
  min = 0
end
puts min