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;

const int N = int(3e5);
int pref[N];

int main(){
	int n;

	scanf("%d", &n);

	for(int i = 1 ; i <= n ; i++){
		char c;

		scanf("\n%c", &c);

		pref[i] = (c == '#');
		
		pref[i] += pref[i - 1];
	}

	int best = 1e9;

	for(int i = 0 ; i <= n ; i++){
		int twhite = pref[i];
		int tblack = (n - i) - (pref[n] - pref[i]);
		
		best = min(best, twhite + tblack);
	}

	printf("%d\n", best);

	return 0;
}