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;
const int c = 300000;
int main(){
   int n,b[c]={},w[c]={},ans=c;
   string s;
   cin >> n >> s;
   for(int i=0;i<n;i++){
       int flag = 0,flag1=0;
       if(s[i]=='#') flag++;
       b[i+1] = b[i] + flag;
       if(s[n-i-1]=='.') flag1++;
       w[i+1] = w[i] + flag1;
   }
   reverse(w,w+n+1);
   for(int i=0;i<=n;i++) ans = min(ans,b[i]+w[i]);
   cout << ans << endl;
}