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;
using ll=long long;
 
 
int main(){
  int N;
  string S;
  cin>>N>>S;
 
  int dot=0;
  //累積和
  int dotcount[200010]={0};
  int sharpcount[200010]={0};
  for(int i=0;i<N;i++){
    if(S[i]=='.')  dot++;
    dotcount[i+1]=dot;
    sharpcount[i+1]=i+1-dot;
  }
 
  int ans=10e6+1;
  for(int i=0;i<=N;i++){
    
    ans=min(ans,sharpcount[i]+dotcount[N]-dotcount[i]);
  }
  cout<<ans<<endl;
 
  return 0;
}