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 <iostream>
#include <algorithm>
using namespace std;
int main() {
  long int N, cnt = 0, m = 0;
  long int lb = 0, lw = 0, rb = 0, rw = 0;
  string S;
  cin >> N >> S;
  //wb
  for(int i = 0; i < N; ++i)
    if(S[i] == '.') ++rw;
    else ++rb;
  m = min(rw, rb);
  for(int j = 0; j < N + 1; ++j) {
    if(S[j] == '.') {--rw; ++lw;}
    else {--rb; ++lb;}
    m = min(m, lb + rw);
  }
  cout << m << endl;
  return 0;
}