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: Time Limit Exceeded)

#include<iostream>
#include<string>
#include<vector>
#include<math.h>
#include<cmath>
#include<stack>
//#include<stdlib.h>
using namespace std;
int main() {
	int n, p = -1, f = 0, t = 0, x = 0; string s;
	cin >> n >> s;
	vector<bool>u(n);
	for (int a = 0; a < n; a++)
	{
		if (s[a] == '.') {
			u[a] = true;
			if (p != -1) {
				t++; f += x; x = 0;
			}
		}
		else { u[a] = false; if (p == -1) { p = a; } x++; }

	}
	int p2 = -1, f2 = 0, t2 = 0, x2 = 0;
	for (int a = n-1; a > -1; a++)
	{
		if (u[a]) {
			if (p2 == -1) { p2 = a; }x2++;
		}
		else {	if (p2 != -1) {
			f2++; t2 += x2; x2 = 0;
		}
		}

	}

	cout << ((f2 > t) ? t : f2);
	return 0;
}