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;
  string s;
  cin >> n >> s;
  int wcnt=0;
  for(int i=0;i<n;++i){
    if(s[i]=='.') wcnt++;
  }
  int min=n,lb=0,rw=wcnt;
  for(int i=0;i<n;++i){
    if(min>lb+rw) min = lb+rw;
    if(s[i]=='#') lb++;
    else if(s[i]=='.') rw--;
  }
  if(min>lb+rw) min = lb+rw;
  cout << min << endl;
  
  return 0;
}