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;
  string S;

  cin >> N;
  cin >> S;

  int b = 0;
  for(int i=0;i<N;i++)
    if( S[i] == '.') b++;

  vector<int> c;
  c.push_back(b);
  for(int i=0;i<N;i++){
    if(S[i] == '#'){
      c.push_back(c[i]+1);
    }else{
      c.push_back(c[i]-1);
    }
  }

  int min=N;
  for(int n:c)
    if(min>n) min=n;

  cout << min;

  return 0;
}