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(){
  int N;cin>>N;
  string S;cin>>S;
  vector<int>A(N+1);
  vector<int>B(N+1);
  for(int i=0;i<N;i++){
    if(i!=0)A[i+1]+=A[i];
    if(S.at(i)=='#')A[i+1]++;
  }
  for(int i=N-1;i>=0;i--){
    if(i!=N-1)B[i]+=B[i+1];
    if(S.at(i)=='.')B[i]++;
  }
  int ans=10000000;
  for(int i=0;i<=N;i++){
    ans=min(ans,A[i]+B[i]);
  }
  cout<<ans<<endl;
}