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: Wrong Answer)

#include <iostream>
#include <algorithm>
using namespace std;

int main()
{
    int N;
    char S[2*100000 + 10];
    cin >> N >> S;
    //白の数
    int w = 0;
    //黒の数
    int b = 0;
    //左白、右黒の最小値
    int min_h;
    //全部黒の最小値
    int min_b;
    //全部白の最小値
    int min_w;
    //min_bとmin_wを求める
    for(int i = 0; i < N; i++){
        if(S[i] == '.') w++;
    }
    b = N - w;
    min_b = w;
    min_w = b;
    
    //min_hを求める
    int dp[2*100000 + 10];//dp[i - 1]はi番目より左を白、右を黒にしたときの最小値(i番目は白)
    if(S[0] == '.') dp[0] = w - 1;//最初のところ以外の白を黒に
    else dp[0] = 1 + w;//最初の黒と残りの白
    for(int i = 1; i < N; i++){
        if(S[i] == '.'){
            dp[i] = dp[i - 1] - 1;
        }
        else{
            dp[i] = dp[i - 1] + 1;
        }
    }
    for(int i = 1; i < N; i++) min_h = min(dp[i],dp[i - 1]);
    
    cout << min(min_h,min(min_b,min_w));
    //lavel:
    return 0;
    
}