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 <stack>
using namespace std;

int main(){
    int N;
    cin >> N;

    string S;
    cin >> S;

    stack<char> s;
    int ans = 0;
    for(int i = 0; i < N; ++i){
        if(S[i] == '#'){
            s.emplace(S[i]);
        }else{
            if(!s.empty()){
                s.pop();
                ++ans;
            }
        }
    }

    cout << ans << endl;
}