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 Scala (2.11.7) (judge verdict: Accepted)

object Main {

  def main(args: Array[String]): Unit = {
    def find(l: List[Char]): Int = {
      def min(a: Int, b: Int): Int =
        if (a < b) a else b
      @annotation.tailrec
      def go(l: List[Char], lBlack: Int, rWhite: Int, minN: Int): Int =
        l match {
          case Nil => minN
          case '#' :: t => go(t, lBlack + 1, rWhite,     min(minN, lBlack + rWhite + 1))
          case '.' :: t => go(t, lBlack,     rWhite - 1, min(minN, lBlack + rWhite - 1))
        }
      val rWhite = l.count(_ == '.')
      go(l, 0, rWhite, rWhite)
    }
    scala.io.StdIn.readLine()
    println(find(scala.io.StdIn.readLine().toList))
  }

}