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 <iostream>
#include <math.h>
#include <algorithm>
#include <string>
using namespace std;

int main() {
	char S[1000000 * 2 + 1] = {};
	int N, ans = 0,count;
	bool flag = false;
	cin >> N >> S;
	for (int i = 0; i < N; i++)
	{
		if (!flag&&S[i] == '#')
		{
			flag = true;
		}
		if (S[i] == '#')
		{
			count++;
		}
		if (flag&&S[i] == '.')
		{
			ans++;
		}
		ans = min(ans, count);
	}
	cout << ans;
	return 0;
}