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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>

using namespace std;

int main(){
    int N;
    string S;
    cin >> N >> S;

    int tmp[N+1];
    int black = 0;
    int white = 0;
    int cnt = 0;

    tmp[0] = 0;
    for(int i = 0; i < N; i++){
        if( S[i] == '.' ) ++cnt;
        tmp[i+1] = cnt;
    }

    int ans = 2000000;
    for(int i = 0; i < N+1; i++){
        black = tmp[N] - tmp[i];
        white = i - tmp[i];

        ans = min( ans, black+white);
    }

    cout << ans << endl;
        
    return 0;
}