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<string>
#include<algorithm>

using namespace std;

int main() {
    int n;
    string s;
    cin >> n;
    cin >> s;

    int res=0;

    int cnt=0;
    for(int i=0; i<s.size();i++) {
        if (s[i] == '.') cnt++;
    }

    res = cnt;

    for(int i=0; i<s.size();i++) {
        if(s[i] == '.') cnt--; 
        else cnt++;
        res = min(res, cnt);
    }

    cout <<res<<endl;
}