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>
using namespace std;

int main() {
	int n;
	string s;
	cin >> n >> s;
	s += 'Y';
	vector<int> wh(n + 1,0),bl(n+1,0);
	int co = 0;
	for (int i = 1;i < n + 1;i++) {
		if (s[i-1] == '#')
			co++;
		wh[i] = co;
	}
	co = 0;
	for (int i= n-1;i >= 0;i--) {
		if (s[i] == '.')
			co++;
		bl[i] = co;
	}
	int ans = 200000;
	for (int i = 0;i < n + 1;i++) {
		ans = min(ans, wh[i] + bl[i]);
	}
	cout << ans << endl;
}