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>
using namespace std;
 
int main() {
  int n;
  string s;
  cin >> n >> s;
 
  int white = 0;
  for (int i = 0; i < n; i++)
    if (s[i] == '.')
      white++;

  int w = 0; 
  int minChange = white;
  for (int i = 0; i < n; i++) {
    if (s[i] == '.')
      w++;
    int change = (white - w) + i + 1 - w;
    minChange = min(minChange, change);
  }
 
  cout << minChange << endl;
  return 0;
}