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

int main(){
  int n;
  string s;
  cin >> n >> s;

  s += '#';
  vector<int> h(n+1,0);
  for(int i=0;i<n+1;i++){
    for(int j=0;j<i;j++) if(s.at(j) == '#') ++h.at(i);
    for(int k=i;k<n+1;k++) if(s.at(k) == '.') ++h.at(i);
  }

  int m=h.at(0);
  for(int i=1;i<n+1;i++) m=min(m,h.at(i));

  cout << m << endl;
}