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>
#include<vector>
#include<algorithm>
#include<cmath>
#include<stdio.h>
#include<queue>
#include <climits>
#include <map>
const int mod = 1e9 + 7;
const long long INF = 1LL << 60;
using namespace std;
typedef long long ll;

int main()
{
    int n;
    cin >> n;
    string s;
    cin >> s;
    int b[n+1],w[n+1];
    for(int i = 0; i < n+1; i++){
        b[i] = 0;
        w[i] = 0;
    }
    for(int i = 1; i < n+1; i++){
        if(s[i-1] == '#'){
            b[i] = b[i-1] + 1;
        }else{
            b[i] = b[i-1];
        }
    }
    for(int i = n-1; i >= 0; i--){
        if(s[i] == '.'){
            w[i] = w[i+1] + 1;
        }else{
            w[i] = w[i+1];
        }
    }
    int ans = mod;
    for(int i = 0; i <= n; i++){
        int tmp = b[i] + w[i];
        ans = min(ans,tmp);
    }
    cout << ans;
}