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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <algorithm>

const int N = 200005;
char a[N];

int main() {
  int n;
  scanf("%d", &n);
  scanf("%s", a);
  int ans = 0;
  for (int i = 1; i < n; ) {
    if (a[i] == '.' && a[i - 1] == '#') {
      int j = i - 1, k = i;
      int change_left = 0;
      int change_right = 0;
      while (j >= 0 && a[j] == '#') {
        j--;
        change_left++;
      }
      while (k < n && a[k] == '.') {
        k++;
        change_right++;
      }
      if (change_right < change_left) {
        for (int w = i; w < k; w++) {
          a[w] = '#';
        }
      }
      i = k;
      ans += std::min(change_left, change_right);
    } else {
      i++;
    }
  }
  printf("%d\n", ans);
  return 0;
}