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 main()
{
	int n;
	string s;
	cin >> n >> s;
	vector<int> a(n + 1), b(n + 1);
	for(int i = 0; i < n; i++){
		if(s[i] == '#') a[i + 1]++;
		if(s[n - i - 1] == '.') b[n - i - 1]++;
		a[i + 1] += a[i];
		b[n - i - 1] += b[n - i];
	}
	int ans = 100100100;
	for(int i = 0; i < n; i++){
		ans = min(ans, a[i] + b[i + 1]);
	}
	cout << ans << endl;
	return 0;
}