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() {
	cin.tie(0)->sync_with_stdio(false);

	int n; cin >> n;
	string s; cin >> s;

	int mini = n;
	int cntB = 0;
	int cntW = 0;
	REP(i, n) {
		if (s[i] == '.')
			cntW++;
	}
	mini = min(mini, cntB + cntW);
	REP(i, n) {
		if (s[i] == '#')
			cntB++;
		else
			cntW--;
		mini = min(mini, cntB + cntW);
	}
	cout << mini << '\n';
	return 0;
}