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, last = 0, min = 0;
  char white = '.', black = '#';
  string s;
  cin >> n >> s;

  for (int i = 0; i < s.size(); i++) if (s.at(i) == white) last++;
  min = last;
  for (int i = 1; i <= s.size(); i++) {
    s.at(i - 1) == black ? last++ : last--;
    if (min > last) min = last;
  }
  cout << min << endl;
}