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>
using namespace std;
int qzh[200005],hzh[200005];
int main(int argc, char** argv) {
	int n,ans=1e9;
	cin >> n;
	for(int i=1;i<=n;i++)
	{
		char x;
		cin >> x;
		if(x=='#') ++qzh[i];
		else ++hzh[i];
	}
	for(int i=1;i<=n;i++) qzh[i]+=qzh[i-1];
	for(int i=n;i>=1;i--) hzh[i]+=hzh[i+1];
	for(int i=0;i<=n;i++) ans=min(ans,qzh[i]+hzh[i+1]);
	cout << ans;
	return 0;
}