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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <stdio.h>
#include <bits/stdc++.h>
#include <queue>
#include <math.h>
#include <bitset>
#define INF 100000000000
#define N 1000000007
#define ll long long
using namespace std;

int main(){
    ll n; cin>>n;
    char data[n];
    for(ll i=0; i<n; i++) cin>>data[i];
    
    if(n==1){
        cout<<"0"<<endl;
        return 0;
    }
    
    bool point=true;
    for(ll i=1; i<n; i++) if(data[i]!=data[i-1]) point=false; 
    if(point){
        cout<<"0"<<endl;
        return 0;
    }
    
    ll black[n];
    ll white[n];
    ll min=INF;
    
    if(data[0]=='#') black[0]=1;
    else black[0]=0;
    
    if(data[n-1]=='.') white[n-1]=1;
    else white[n-1]=0;
    
    for(ll i=1; i<n; i++){
        if(data[i]=='#') black[i]=black[i-1]+1;
        else black[i]=black[i-1];
    }
    
    for(ll i=n-2; i>=0; i--){
        if(data[i]=='.') white[i]=white[i+1]+1;
        else white[i]=white[i+1];
    }
    
    for(ll i=0; i<n; i++){
        if(min>black[i]+white[n-1-i]) min=black[i]+white[n-1-i];
    }
    
    cout<<min<<endl;
}