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 C___Stones
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var S = Console.ReadLine();
            var S_rev = string.Join("", S.Reverse());

            int[] w_arr = new int[N + 1], b_arr = new int[N + 1];
            int cost = 0, min = int.MaxValue;

            for (int i = 0; i <= N; i++)
            {
                if (i == 0)
                {
                    w_arr[i] = 0;
                    b_arr[i] = 0;
                    continue;
                }

                w_arr[i] = S[i - 1] == '#' ? w_arr[i - 1] + 1 : w_arr[i - 1];
                b_arr[i] = S_rev[i - 1] == '.' ? b_arr[i - 1] + 1 : b_arr[i - 1];
            }

            for (int i = 0; i <= N; i++)
            {
                cost = w_arr[i] + b_arr[N - i];
                min = Math.Min(min, cost);
            }

            Console.WriteLine(min);
        }
    }
}