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<algorithm>
#include<vector>
#include<math.h>
#include<map>
#include<string>
using namespace std;

int main() {
	int N, C[200005];
	string S;
	cin >> N >> S;

	C[0] = 0;

	for (int i = 0; i < N; i++) {
		C[i + 1] = C[i];
		if (S.at(i) == '.') C[i + 1]++;
	}

	int ans = 2000000;
	for (int i = 0; i <= N; i++) {
		int cnt = i - C[i] + C[N] - C[i];
		ans = min(ans, cnt);
	}

	cout << ans << endl;
	return 0;
}