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;

#define Rep(i,a,b)  for (int i=(a);i<(b);i++)
#define rep(i,n)    for (int i=0;i<(n);i++)
#define all(x)      (x).begin(), (x).end()

#define ll long long

int main()
{
	int n;
	string s;
	cin >> n;
	cin >> s;
	int w = count(all(s), '.');
	int b = w;
	rep (i, n) {
		if (s[i] == '#')
			w++;
		else
			w--;
		if (b > w)
			b = w;
	}
	cout << b << endl;
}