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() {
  long long N, white, ans; cin >> N;
  vector<long long> V(N);
  char c;
  cin >> c; if (c=='.') V[0]=1;
  for (long long i=1; i<N; i++) {
    cin >> c;
    if (c=='.') V[i]= V[i-1]+1;
    else V[i]= V[i-1];
  }
  white = V[N-1];
  ans = white;
  for (long long i=0; i<N; i++) {
    ans = min(ans, i+1-V[i]+ white-V[i]);
  }
  cout << ans << "\n";
}