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: Accepted)

#include<bits/stdc++.h>
using namespace std;

int main()
{
	int n;
	string s;
	cin >> n >> s;
	vector<int> a(n + 1), b(n + 1);
	for(int i = 0; i < n; i++){
		if(s[i] == '#') a[i + 1]++;
		if(s[n - i - 1] == '.') b[n - i - 1]++;
		a[i + 1] += a[i];
		b[n - i - 1] += b[n - i];
	}
	int ans = 100100100;
	for(int i = 0; i < n; i++){
		ans = min(ans, a[i] + b[i + 1]);
	}
	cout << ans << endl;
	return 0;
}