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<string>
using namespace std;
int main()
{
  int n,b,c,i,t,res;
  string s;
  cin >> n;
  cin >> s;
  c=0;
  for(i=1;i<=n;i++)
    if(s.substr(i-1,1)=="#") c++;
  res=n-c;
  b=0;
  for(i=1;i<=n;i++){
    if(s.substr(i-1,1)=="#") b++;
    t=n-i-c+2*b;
    if(t<res) res=t;
  }
  cout << res << endl;
  return 0;
}