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

int main() {
	int n;
	string s;
	cin >> n >> s;

	vector<int>sumw(n + 1), sumb(n + 1);
	sumw[0] = 0;
	sumb[0] = 0;
	for (int i = 0; i < n; i++) {
		if (s[i] == '.') {
			sumw[i + 1] = sumw[i] + 1;
			sumb[i + 1] = sumb[i];
		}
		else {
			sumw[i + 1] = sumw[i];
			sumb[i + 1] = sumb[i] + 1;
		}
	}

	int ans = 10000000;
	for (int i = 0; i <= n; i++) {
		ans = min(ans, sumb[i] + sumw[n] - sumw[i]);
	}
	cout << ans << endl;


	return 0;
}