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;
	cin >> N;
	string S;
	cin >> S;
	int rB = 0;
	for (int i = 0; i < S.size(); ++i) {
		if (S[i] == '#') {
			rB++;
		}
	}
	int rW = N - rB;
	int lB = 0;
	int lW = 0;
	int ans = rW + lB;
	for (int i = 0; i < S.size(); ++i) {
		if (S[i] == '.') {
			rW--;
			lW++;
		}
		else {
			rB--;
			lB++;
		}
		ans = min(ans, lB + rW);
	}
	cout << ans <<  endl;
}