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;

const int MOD = (int)1e9+7;

int main(){
	int N;
	string S;
	cin >> N >> S;

	int w=0;
	int b=0;
	for(int i=0;i<N;i++){
		if(S.at(i)=='.')	w++;
		else	b++;
	}
	int now_w=0;
	int now_b=0;
	int ans=1e9;
	if(w==0 || b==0)	ans=0;
	ans=min(ans,w);
	for(int i=0;i<N;i++){
		if(S.at(i)=='.')	now_w++;
		else	now_b++;
		int x=(w-now_w)+now_b;
		ans=min(ans,x);
	}
	cout << ans << endl;

	return 0;
}