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 <vector>

using namespace std;

int main() {
  int N, ans{200000};
  string S;
  cin >> N >> S;
  vector<int> l(N+1), r(N+1);
  for (int i = 0; i != N; ++i) {
    l[i+1] = l[i] + (S[i] == '#');
    r[N-i-1] = r[N-i] + (S[N-i-1] == '.');
  }
  for (int i = 0; i <= N; ++i) ans = min(ans, l[i] + r[i]);
  cout << ans << endl;
}