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>
#include<vector>
#include<algorithm>
using namespace std;
int main(){
  int n;
  string s;
  cin >> n >> s;
  int cntb=0,cntw=0;
  vector<int> b(n+2,0),w(n+2,0);
  for(int i=0;i<n;i++){
    if(s[i]=='#') cntb++;
    if(s[n-1-i]=='.') cntw++;
    b[i+1]=cntb;
    w[n-i]=cntw;
  }
  int ans=b[0]+w[1];
  for(int i=1;i<n+2;i++){
    ans=min(ans,b[i-1]+w[i]);
  }
  cout << ans << endl;
}