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,black= 0,sum,white=0,minv=200005;//blackは黒に、whiteは白にぬりかえるもの
	int j;
	cin >> n;
	string s;
	cin >> s;
	for (int i = 0; i < n; ++i) {
		if (s[i] == '.')++white;
	}
	for (int i = 0; i <= n; ++i) {
		if (i) {
			if (s[i-1] == '#') ++black;
			else --white;
		}
		sum = white + black;
		minv = min(sum, minv);
	}
	cout << minv << endl;
	return 0;
}