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 i;
int main() {
	int N, ans = 0;
	string S;
	cin >> N >> S;

	for (i = 0; i < N; i++) {
		if (S[i] == '.') {
			ans++;
		}
	}
	vector<int> v(N + 1);
	v[0] = ans;
	for (i = 1; i < N+1; i++) {
		if (S[i-1] == '#') {
			v[i] = v[i - 1] + 1;
		}
		else {
			v[i] = v[i - 1] - 1;
		}
	}
  	sort(v.begin(),v.end());
	cout << v[0] << endl;
}