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:
//#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"

using namespace std;


int main() {
	int n;
	string s;
	cin >> n >> s ;
	int i = 0;
	int ans = 0;
	int ans1 = 0;
	int ans2 = 0;
	while (i < n && s.at(i) == '.') i++;
	while (i < n) {
		if (s.at(i) == '.') {
			ans1 += 1;
			if (ans1 > ans2) {
				ans += ans2;
				ans1 = 0;
				ans2 = 0;
			}
		}
		else {
			ans2 += 1;
		}
		i++;
	}
	cout << ans+min(ans1,ans2) << endl;
}