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 <cstdio>
#include <algorithm>

int w[200001];
int b[200001];

int main()
{
  int n;
  char s[200001];
  scanf("%d%s", &n, s);
  for (int i = 0; i < n; ++i)
  {
    w[i + 1] = w[i] + (s[i] == '.' ? 1 : 0);
    b[i + 1] = b[i] + (s[i] == '#' ? 1 : 0);
  }
  int ans = 1e8;
  for (int i = 0; i <= n; ++i)
  {
    ans = std::min(ans, b[i] + w[n] - w[i]);
  }
  printf("%d\n", ans);
  return 0;
}