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 ll long long
using namespace std;
 
int main() {
int n;	cin>>n;
		string sd;cin>>sd;
		int mi=INT_MAX,f=0;
		int z=0,o=0;
	for(int i=0;i<sd.length();i++)
	{
	if(sd[i]=='.')z++;
	else o++;
	}

	mi=min(mi,min(z,o));
	int one=0,zero=0;
	for(int i=0;i<sd.length();i++)
	{
		if(sd[i]=='#')one++;
		else zero++;
		
		mi=min(mi,one+z-zero);
	}
	cout<<mi<<"\n";
	
	
	
	
	
}