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

stack = []
if (s[0] == '#') 
    stack.push(0)
end

tar = s[0]
cnt = 0
min = 0

for i in 1..n do
    if (s[i-1]==tar)
        cnt += 1
    else
        if (tar == ".") 
            min += cnt
        end
        tar = s[i-1]
        stack.push(cnt)
        cnt = 1
    end
end

stack.push(cnt)
if (s[n-1] == '.')
    stack.push(0)
    min += cnt
end
min -= stack[0]

# p stack
# p min
now = min
1.step(stack.size-3,2) do |i|
    now += stack[i]
    now -= stack[i+1]
    # p now
    if (min > now)
        min = now
    end
end

p min