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;
typedef long long ll;
ll cnt[2][214514];
int main(){
	ll n;
	string s;
	cin>>n>>s;
	if(s[0]=='#')cnt[0][0]++;
	else cnt[1][0]++;
	for(int i=1;i<n;i++){
		cnt[0][i]=cnt[0][i-1];
		cnt[1][i]=cnt[1][i-1];
		if(s[i]=='#')cnt[0][i]++;
		else cnt[1][i]++;
	}
	ll ans=cnt[1][n-1];
	for(int i=0;i<n;i++){
			ans=min(ans,cnt[0][i]+cnt[1][n-1]-cnt[1][i]);
	}
	cout<<ans;
	return 0;
}