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: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        char[] s = br.readLine().toCharArray();
        int startPoint = 0;
        int endPoint = n;
        int halfPoint = n;
        int minCount = n;
        int first = 0;
        int latter = 0;
        int full = 0;
        int count1 = 0;
        for(int i = 0;i < n - 1;i++){
            if(s[i] == '#' && s[i] != s[i+1]) count1++;
        }
        while(true) {
            first = 0;
            latter = 0;
            full = 0;
            for(int i = startPoint; i < halfPoint; i++) {
                if(s[i] == '#') first++;
            }
            for(int i = halfPoint; i < endPoint; i++) {
                if(s[i] == '.') latter++;
            }
            for(int i = 0; i < halfPoint; i++){
                if(s[i] == '#') full++;
            }
            for (int i = halfPoint; i < n; i++) {
                if(s[i] == '.') full++;
            }
            if(minCount > full) minCount = full;
            if(startPoint == halfPoint) break;
            if(first >= latter) {
                endPoint = halfPoint;
                halfPoint = (startPoint + endPoint) / 2;
            } else {
                startPoint = halfPoint;
                halfPoint = (startPoint + endPoint) / 2;
            }
        }
        if(minCount > count1) minCount = count1;
        System.out.println(minCount);
    }
}