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.Linq;

namespace AtCoder2
{
    class Program
    {
        static void Main(string[] args)
        {
            checked
            {
                Console.ReadLine();
                var s = Console.ReadLine();

                var white = s.Select(c => c == '.' ? 1 : 0).ToList();

                {
                    var sum = 0;
                    for (int n = white.Count - 1; n >= 0; n--)
                    {
                        sum += white[n];
                        white[n] = sum;
                    }
                }

                var black = s.Select(c => c == '#' ? 1 : 0).ToList();

                {
                    var sum = 0;
                    for (int n = 0; n < black.Count; n++)
                    {
                        sum += black[n];
                        black[n] = sum;
                    }
                }

                white.RemoveAt(0);
                white.Add(0);
                black.RemoveAt(black.Count - 1);
                black.Insert(0, 0);

                var res = white.Zip(black, (w, b) => w + b).Min();

                Console.WriteLine(res);
            }
        }
    }
}