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 n;
string s;
vector<int> v, w;
int ans;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> n >> s;
	for(auto i:s){
		v.push_back(i=='.'?1:0);
		w.push_back(i=='#'?1:0);
	}
	for(int i=n-2; i>=0; --i) v[i] += v[i+1];
	for(int i=1; i<n; ++i) w[i] += w[i-1];
	ans = min(v[0], w[n-1]);
	for(int i=0; i<n-1; ++i) ans = min(ans, w[i]+v[i+1]);
	cout << ans << "\n";
}