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 <algorithm>
#include <vector>
#include <string>
#define int long long
using namespace std;
int n, b[234567], w[234567];
string s;
signed main() {
	cin >> n >> s;
	for (int i = 1; i <= n; i++) {
		if (s[i - 1] == '#')b[i]++; else w[i]++;
		b[i + 1] += b[i]; w[i + 1] += w[i];
	}
	int ans = n + 1;
	for (int i = 0; i <= n; i++) ans = min(ans, b[i] + w[n] - w[i]);
	cout << ans << endl;
}