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 n,ans=1e6,cnt=0,b[200001];
string s;
int main() {
  cin >> n >> s;
  for(int i=0 ;i<n ;i++){
    if(s[i] == '#' ){
      cnt++;
    }
    b[i+1] = cnt;
  }
  for(int i=0 ;i<=n ;i++){
    ans = min(ans,n-i-b[n]+2*b[i]);
  }
  cout << ans << endl;
}