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;
	vector<int> w(n,0),b(n,0);
	rep(i,n-1){
		b[i+1]=b[i];
		if (s[i]=='#')
			b[i+1]++;
	}
	for (int i=n;i>=1;--i){
		w[i-1]=w[i];
		if (s[i]=='.')
			w[i-1]++;
	}
	int ans=10000000;
	rep(i,n){
		ans = min(ans,(b[i]+w[i]));
	}
	cout <<ans <<endl;
}