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>
#define rep(i,n) for(int i = 0; i < n; i++)
#define pb push_back
using namespace std;
typedef long long ll;

int main() {
  int n;
  string s;
  cin>>n>>s;
  
  vector<int> a(n+1),b(n+1);
  rep(i,n){
    if(s[i]=='.'){
      a[i+1]=a[i]+1;
      b[i+1]=b[i];
    }else{
      a[i+1]=a[i];
      b[i+1]=b[i]+1;
    }
  }
  int ans = n+1;
  rep(i,n+1){
    ans = min(ans,a[n]-a[i]+b[i]);
  }
  cout << ans << endl;
}