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 <stdio.h>
#include <algorithm>

const int N = 200005;

char a[N];

int main() {
  int n;
  scanf("%d %s", &n, a);
  int w = 0;
  for (int i = 0; i < n; i++) {
    w += (a[i] == '.');
  }
  int b = 0;
  int ans = (1 << 30);
  for (int i = 0; i < n; i++) {
    ans = std::min(ans, b + w);
    if (a[i] == '#') {
      b++;
    }
    if (a[i] == '.') {
      w--;
    }
  }
  printf("%d\n", std::min(ans, b + w));
  return 0;
}