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.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner std = new Scanner(System.in);
        int n = std.nextInt();
        String s = std.next();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            char c = s.charAt(i);
            if (c == '#') {
                a[i] = 1;
            } else {
                a[i] = 0;
            }
        }

        long[] dp = new long[n+1];
        for (int i = 0; i < n; i++) {
            dp[i+1] += dp[i] + a[i];
        }

        long min = Long.MAX_VALUE;
        for (int i = 0; i <= n; i++) {
            long left = dp[i];
            long right = (n - i) - (dp[n] - dp[i]);
            min = Math.min(left + right, min);
        }

        System.out.println(min);
    }
}