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 <cstdio>
#include <algorithm>
const int maxn = 2e5+10;
char s[maxn+10];
int n, ans, p[maxn];
int main() {
	scanf("%d%s", &n, s+1);
	for (int i = 1; i <= n; ++i) {
		p[i] = p[i-1]+(s[i]=='#');
	}
	ans = 1e9;
	//.(i)#(n-i)
	for (int i = 0; i <= n; ++i) {
		ans = std::min(ans, p[i]+(n-i-(p[n]-p[i])));
	}
	printf("%d\n", ans);
}