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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdlib>
#include <string>
#include <vector>
#include <map>
#include <algorithm>
#include <functional>
using namespace std;

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

    int black = 0;
    int white = 0;
    int ba[n+1];
    int wa[n+1];
    int m = 1 << 30;
    for(int i = 0; i < n; i++){
        if(s[i] == '#'){
            black++;
        }
        ba[i] = black;
    }
    ba[n] = black;
    for(int i = n-1; i >= 0; i--){
        if(s[i] == '.'){
            white++;
        }
        wa[i] = white;
    }
    wa[n] = 0;
    for(int i = 1; i <= n; i++){
        cerr << m << endl;
        cerr << "(" << ba[i-1] << " " << wa[i] << ")" << endl;
        m = min(ba[i-1]+wa[i], m);
    }

    cout << m << endl;
    
    return 0;
}