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<algorithm>
#include<string>
#include<map>
#include<vector>
using namespace std;
using ll=long long;

int main(){
	int n,ans,count=0;
	string s;

	cin>>n>>s;
	
	//ある点を境に右は黒色、左は白色にする;
	//一端全部#にした時を考える;
	for(int i=0;i<n;i++)
		if(s[i]=='.')count++;
	ans=count;
	for(int i=0;i<n;i++){
		if(s[i]=='.')count--;
		else count++;
		ans=min(ans,count);
	}
	cout<<ans;
}