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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10000000)
def check_and_back_or_go_to(li, ind, N, counter):
    back = True
    # print('see {} {} and {} counter{}'.format(ind, li[ind - 1], li[ind], counter))
    if ind == 0:
        return counter
    elif ind + 1 == N:
        back = False
    # access
    if li[ind - 1] == '#' and li[ind] == '.':
        li[ind] = '#'
        if back:
            c=check_and_back_or_go_to(li, ind + 1, N, counter + 1)
            return c
        c=check_and_back_or_go_to(li, ind - 1, N, counter + 1)
        return c
    else:
        c=check_and_back_or_go_to(li, ind - 1, N, counter)
        return c


N = int(input())
S = list(input())
r = range(N)
count = check_and_back_or_go_to(S, len(S) - 1, N, 0)
print(min([count,N-count]))