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;
	vector<int> B(N+1, 0);
	vector<int> W(N+1, 0);

	int black = 0, white = 0;
	for (int i = 0; i < N; i++) {
        if (S[i] == '#') {
			black++;
		}
		B[i + 1] = black;
		if (S[N - i - 1] == '.') {
			white++;
		}
		W[N - i - 1] = white;
	}

	int ans = 10e8;
	for (int i = 0; i <= N; i++) {
		ans = min(ans, B[i] + W[i]);
	}
	cout << ans << endl;	
}