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 <iostream>
#include<vector>
using namespace std;
int main(void){
    int n;
    string s;
    cin >> n;
    cin >> s;
   vector<int> b(n + 1);
   vector<int> w(n + 1);
   for(int i = 1;i <= n;i++){
         if(s[i - 1] == '#')b[i]++;
         else w[i]++;
         b[i] += b[i - 1];
         w[i] += w[i - 1];
   }
   int ans = n;
   for(int i = 0;i <= n;i++){
         ans = min(ans,b[i] + w[n] - w[i]);
   }
   cout << ans << endl;
}