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<vector>
#include<string>
#include<algorithm>

using namespace std;
typedef long long ll;

int main(){
    int n;
    string s;
    cin >> n >> s;
    int tmp1=0, tmp2=0;
    vector<int> a(n+1, 0), b(n, 0);
    for (int i = 0; i < n; i++)
    {
        if(s[i]=='#') tmp1++;
        a[i+1] = tmp1;
        
        int j = n-1-i;
        if(s[j]=='.') tmp2++;
        b[j]=tmp2;
    }
    int ans=n;
    for (int i = 0; i < n+1; i++)
    {  
        ans = min(a[i]+b[i], ans);
    }
    cout << ans << endl;
    

}