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 <string>

using namespace std;
int main(){
  int n; cin >> n;
  string s; cin >> s;
  
  int now_white = 0;
  for (int i=0; i<n; i++) if (s.at(i) == '.') now_white++;
  int now_white_right=now_white, nbl=0, min_change=now_white;
  for (int i=0; i<n; i++) {
    if (s.at(i) == '.') now_white_right--;
    else nbl++;
    min_change = min(now_white_right+nbl, min_change);
  }
  cout << min_change << endl;
}