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<cmath>
using namespace std;

int main(void){
  int n;
  string s;
  cin >> n >> s;
  int n_b = 0;
  int n_all_b = 0;
  for( int i=0; i<n; ++i){
    if( s[i] == '#') n_all_b++;
  }
  int  ans = n - n_all_b;
  for( int i=0; i<n; ++i){
    if( s[i] == '#') n_b++;
    ans = min(n_b + ( (n - (i+1)) - (n_all_b - n_b) ), ans);
  }
  cout << ans << endl;
  return 0;
}