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: Time Limit Exceeded)

using System;
using System.Threading.Tasks;
class program{
  static void Main(string[] args){
    program p = new program();
    p.Run();
  }
  void Run(){
	int n = int.Parse(Console.ReadLine());
    string s = Console.ReadLine();
    int m=n;
    int[] l=new int[n+1];
    int[] r=new int[n+1];
    
    Parallel.For(0,n+1,(i,state)=>{
      l[i]=lookup(s.Substring(0,i),"#");
      r[i]=lookup(s.Substring(i,n-i),".");
      if(l[i]+r[i]<m){
        m=l[i]+r[i];
      }
      if(m==0){
        state.Stop();
      }
    });
    Console.WriteLine(m.ToString());
    
  }
  
  int lookup(string s,string c){
    return s.Length - s.Replace(c,"").Length;
  }
}