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 <vector>
using namespace std;
int main()
{
	int n;
	int r=0;
	char s;
	cin >> n;
	vector<int> vec(n+1);
	for(int i=1;i<=n;i++){
		cin >> s;
		if(s=='#'){
			vec[i]=vec[i-1];
		}else{
			vec[i]=vec[i-1]+1;
		}
	}
	r= 0 - 2*(vec[0]);
	for(int i=1;i<=n;i++){
		if(r>i-(2*vec[i])){
			r=i-(2*vec[i]);
		}
	}
	cout << r+vec[n];
	return 0;
}