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,white=0;
  cin>>n;
  char a[n];
  for(int i=0;i<n;i++){
    char c;
    cin>>c;
    a[i]=c;
    if(c=='.')white++;
  }
  int b[n+1];
  b[0]=white;
  for(int i=0;i<n;i++){
    if(a[i]=='.')b[i+1]=b[i]-1;
    else b[i+1]=b[i]+1;
  }
  sort(b,b+n+1);
  cout<<b[0]<<endl;
}