Problem: 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.

Examples

Input

3
#.#


Output

1


Input

3
.#


Output

1


Input

5
.##.


Output

2


Input

9
.........


Output

0

Solution (in CPP):

Solution:
#include <iostream>
#include <string>
using namespace std;

int main() {

	int N;
	string S; // .->白 #->黒

	cin >> N;
	cin >> S;

	int w = 0, b = 0, ans = 0;
	for (char c : S) {
		if (c == '.') {
			w++;
		}
	}
	ans = w;
	for (char c : S) {
		if (c == '#') {
			b++;
		}
		else {
			w--;
		}
		if (b + w < ans) {
			ans = b + w;
		}
	}
	cout << ans << endl;
}