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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
//using System.Text;
//using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        //黒から白に変わるポイントを消すための対処法は次の二通り。

        //最初に黒から白に変わるポイント以降を全部黒にする
        //最後に黒から白に変わるポイント以前を全部白にする

        int N = int.Parse(Console.ReadLine());
        string S = Console.ReadLine();

        if (S == "#" || S == ".")
        {
            Console.WriteLine(0);
            return;
        }
        

        //それより左に何個黒があるかを知る配列。
        int[] arr1 = new int[N + 1];
        //それより左に何個白があるかを知る配列
        int[] arr2 = new int[N + 1];

        int siroNum = 0;
        int kuroNum = 0;
        for (int i = 0; i < N; i++)
        {
            char c = S[i];
            if (c == '#') kuroNum++;
            else if (c == '.') siroNum++;

            arr1[i + 1] = kuroNum;
            arr2[i + 1] = siroNum;
        }

        int ans = int.MaxValue;
        for (int i = 0; i < N + 1; i++)
        {
            //境界前を全部白にして境界後を全部黒にすると仮定するとどれだけ
            int n1 = arr1[i];
            int n2 = arr2[N] - arr2[i];
            ans = Math.Min(ans, n1 + n2);
        }
        

        Console.WriteLine(ans);
    }
}