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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int main(){ int N; cin >> N; 
 string S; cin >> S;
  vector<int> B(N+1,0); vector<int> W(N+1,0);
  //'.'が白、'#'が黒を表す 
  //左端からの黒の個数をB,右端からの白の個数をWに保存する
  
  for(int i = 0; i < N; i++){
    if(S[i] == '#'){ B[i+1] = B[i]+1;}
    else{ B[i+1] = B[i];}
                 }
  for(int j = N-1; j >= 0; j--){
    if(S[j] == '.'){ W[j] = W[j+1] + 1;}
    else{ W[j] = W[j+1];}
  }
                 
 int ans = 1e9;
 for(int i = 0; i <= N; i++){ ans = min( ans, B[i]+W[i]);}
 cout << ans << endl; return 0;}