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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  string S;
  cin >> N >> S;
  vector<int>count(N-1);
  vector<int>black(N,0);
  vector<int>white(N,0);
  int A = 0;
  int B = 0;
  
  for (int i = 0; i < N; i++){
    if (S.at(i) == '#'){
      A++;
    }
    else {
      B++;
    }
    black.at(i) = A;
    white.at(i) = B;
  }
  
  int sumb = black.at(N-1);
  int sumw = white.at(N-1);
  
  int ans = sumb;
  for (int i = 0; i < N-1; i++){
    if (ans > black.at(i) + sumw - white.at(i)){
      ans = black.at(i) + sumw - white.at(i);
    }
  }
  cout << ans << endl;
}