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,ans=200001,w[200005]={};
	int b[200005]={};
	string s;
	cin>>n>>s;
	for(int i=0;i<n;i++){
		if(s[i]=='#'){
			b[i]++;
		}
		else{
			w[i]++;
		}
		b[i]+=b[i-1];
		w[i]+=w[i-1];
	}

	for(int i=0;i<n;i++){
		ans=min(ans,b[i-1]+w[n-1]-w[i]);
	}
	cout<<ans<<endl;
  return(0);
}