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, p = 0;
	int a[200000];
	string s;

	cin >> n >> s;

	for (int i = 0; i < n; i++) {
		if (s[i] == '.')
			p++;

		a[i] = p;
	}

	int m = p;

	for (int i = 0; i < n; i++)
		m = min(p + i + 1 - a[i] * 2, m);	

	cout << m << endl;

	return 0;
}