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 <algorithm>
#include <cstdio>
const int MAXN = 2e5+5;
char S[MAXN];
int N;

bool is_white(char c) { return (c == '.'); }

int main() {
  scanf(" %d%s", &N, S);
  int cnt = std::count_if(S, S+N, is_white);
  int ret = cnt;
  for (int i = 0; i < N; ++i) {
    if (is_white(S[i])) {
      --cnt;
    } else {
      ++cnt;
    }
    ret = std::min(cnt, ret);
  }
  printf("%d\n", ret);
  return 0;
}