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>
using namespace std;
int main(void){
    // Your code here!
    int N;
    cin >> N;
    char S[N];
    cin >> S;
    
    /* a . b # */
    long long a[N];
    long long b[N];
    
    if(S[0] == '.'){
        a[0] = 1;
        b[0] = 0;
    } else{
        a[0] = 0;
        b[0] = 1;
    }
    
    for(int i = 1; i < N; i++){
        if(S[i]=='.'){
            a[i] = a[i-1] + 1;
            b[i] = b[i-1];
        } else{
            a[i] = a[i-1];
            b[i] = b[i-1] + 1;
        }
    }
    
    long long ans = 10000000;
    for(int i = 0; i < N; i++){
        ans = min(ans, b[i] + a[N-1] - a[i]);
    }
    
    ans = min(ans, a[N-1]);
    cout << ans << endl;
   
}