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;
  
  vector<int> res(N + 1);
  
  int left = 0;
  int right = count(S.begin(), S.end(), '.');
  res.at(0) = left + right;
  
  for(int i = 0; i < N; i++){
    if(S.at(i) == '#')
      left++;
    else
      right--;
    
    res.at(i + 1) = left + right;
  }
  
  cout << *min_element(res.begin(), res.end()) << endl;
}