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;
    cin >> n;
    string s;
    cin >> s;
    int lb = 0;
    int rw = count(s.begin(), s.end(), '.');
    int ans = numeric_limits<int>::max();
    for (int i = 0; i <= n; i++) {
        ans = min(ans, lb + rw);
        if (i < n) {
            lb += s[i] == '#';
            rw -= s[i] == '.';
        }
    }
    cout << ans << '\n';
}