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;

  vector<int> cnt_B(N + 1, 0);
  for (int i = 0; i < N; i++) {
    cnt_B[i + 1] = cnt_B[i];
    if (S[i] == '#') cnt_B[i + 1]++;
  }

  int ans = N, cnt = 0;
  for (int i = 0; i < N + 1; i++) {
    int left_B = cnt_B[i];
    int right_W = (N - i) - (cnt_B[N] - cnt_B[i]);
    ans = min(ans, left_B + right_W);
  }

  cout << ans << endl;
}