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;
  cin >> N;
  int b[N + 1], w[N + 1];
  string S;
  cin >> S;
  b[0] = 0;
  w[0] = 0;
  for (int i = 1; i < N + 1; i++) {
    b[i] = b[i - 1];
    w[i] = w[i - 1];
    if (S[i - 1] == '#')
      b[i]++;
    else
      w[i]++;
  }
  int ans = INT32_MAX;
  for (int i = 0; i < N + 1; i++) {
    ans = min(b[i] + w[N] - w[i], ans);
  }
  cout << ans;
  return 0;
}