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(void){
  int N;
  string S;
  cin >> N >> S;
  
  int ls = 0, rd = 0;
  for (char c: S) {
    if (c == '.') { rd++; }
  }
  int ans = rd;
  for (char c: S) {
    if (c == '#' ) {
      ls++;
    } else {
      rd--;
    }
    if (ls+rd < ans) { ans = ls+rd; }
  }
  
  cout << ans;
}