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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        String S = scan.next();
        char[] data = S.toCharArray();
        int[] sum = new int[N+1];
        Arrays.fill(sum, 0);
        int answer = Integer.MAX_VALUE;
        for (int i = 0; i < N; i++) {
            if (data[i] == '#') {
                sum[i+1] += sum[i] + 1;
                continue;
            }
            sum[i+1] += sum[i];
        }
        for (int i = 0; i <= N; i++) {
            answer = Math.min(sub(N, sum, i), answer);
        }
        System.out.println(answer);
    }
    public static int sub(int N, int[] sum, int from) {
        int blackcount_before_from = sum[from];
        int whitecount_before_from = from - sum[from];
        int whitecount_after_from = N - sum[N] - whitecount_before_from;
        return blackcount_before_from + whitecount_after_from;
    }
}