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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static int allBlack;
        static int allWhite;

        static void Main(string[] args)
        {
            //[summary]C - Stones
            int n = int.Parse(Console.ReadLine());
            string s = Console.ReadLine();

            //全部を黒(または白)に統一するケース
            allBlack = s.Count(x => x == '.');
            allWhite = n - allBlack;

            //最初は白で、途中から全部黒になるケース
            //(白の個数を左から1コずつ増やしていく)
            var halfways = CountHalfways(s, n).ToList();

            var counts = new List<int>(halfways);
            counts.Add(allBlack);
            counts.Add(allWhite);

            Console.WriteLine(counts.Min());
        }

        static IEnumerable<int> CountHalfways(string s, int n)
        {
            string defS = GetDefaultS(n);
            int changed = 0;

            for(int i = 0; i < n; i++)
            {
                if (s[i] != defS[i])
                {
                    changed++;
                }
            }

            for (int i = 0; i < s.Length - 1; i++)
            {
                if (s[i] == '.')
                {
                    changed--;
                }


                yield return changed;
            }
        }

        static string GetDefaultS(int n)
        {
            return "." + new string('#', n - 1);
        }
    }
}