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>
#include <algorithm>

using namespace std;


int main(){

	int N;
	int a = 0;
	int b = 0;
	int bl = 0;
	int wh = 0;
	int MIN = 0;


	string S;
	cin >> N >> S;

	for (int i = 0; i < N; i++){
		if (S[i] == '.') wh++;
	}
	MIN = wh + bl;
	for (int i = 0; i < N; i++){
		
		if (S[i] == '.'){
			bl--;
		}
		else wh++;
		if (MIN > wh + bl)	MIN = wh + bl;
	}
	cout << MIN << endl;


	return 0;
}