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;
#define MOD 1000000007

int main() {
  
  int N;
  string S;

  cin >> N >> S;
  int b = 0,w = 0;
  for(int i = 0;i < N;i++) {
    if(S.at(i) == '.') w++;
  }
  S = 'a' + S + 'a';

  int ans = 10000000;
  for(int i = 0;i < S.size();i++) {
    int sum;
    if(S.at(i) == '#') b++;
    else if(S.at(i) == '.') w--;
    sum = b+w;
    ans = min(ans,sum);
  }
  
  cout << ans << endl;


}