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>
#define REP(i,n) for(int i=0;i<(n);++i)
using namespace std;

int main(){
	int n;
	string s;
	cin>>n>>s;
	
	int wsum=0;
	REP(i,n){
		if(s[i]=='.') wsum++;
	}
	
	int bsum=0;
	int ans=wsum;//全部Bのとき.
	REP(i,n){//i番目はW.
		if(s[i]=='#'){
			bsum++;
			ans=min(ans,wsum+bsum);
		}else{
			wsum--;
			ans=min(ans,wsum+bsum);
		}
	}
	
	cout<<ans<<endl;
}//解説参考.