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<bits/stdc++.h>
#define  __  ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);

using namespace std;

int main()
{
    __;

    int n,white=0,ans=0;

    string s;

	cin >> n >> s;

	for (int i = 0; i < s.size(); i++) {
		if (s[i] == '.') white++;
	}

	 ans = white;

	for (int i = 0; i < s.size(); i++) {

		if (s[i] == '#') white++;

		else white--;

		if (ans > white) ans = white;
	}

	cout<<ans;

    return 0;
}