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 main(){
  int N;
  string S;
  cin >> N >> S;
  int w = 0, b = 0;
  for (int i = 0; i < N; i++) {
    if (S.at(i) == '#') {
      b++;
    }
    else {
      w++; 
    }
  }
  int answer = min(N - b, N - w), B = b, W = w;
  for (int i = 0; i < N - 1; i++) {
    if (S.at(i) == '#') {
      b--;
    }
    else{
      w--; 
    }
    answer = min(answer, B - b + w);
  }
  cout << answer << endl;
}