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,min = 200000;
  string s;
  cin >> n >> s;
  vector<int>w(n+1,0);
  vector<int>b(n+1,0);
  for(int i = 1;i <= n;i++){
    if(s[i-1] == '#') b[i]++;
    if(i != n) b[i+1] = b[i];
  }
  for(int i = n-1;i >= 0;i--){
    if(s[i] == '.') w[i]++;
    if(i != 0) w[i-1] = w[i];
  }
  for(int i = 0;i < n+1;i++){
    if(min > w[i]+b[i]) min = w[i]+b[i];
  }
  cout << min << endl;
}