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>

int main()
{
    int n;
    std::string s;
    std::cin >> n >> s;
    s += '#';
    int w = 0;
    for(int i = 0; i <= n; i++){
        if(s[i] == '.')w++;
    }
    
    int rw = w, lb = 0, min = INT_MAX;

    for(int i = 0; i <= n; i++){
        min = std::min(min,rw + lb);
            if(s[i] == '#')lb++;
            else rw--;
    }
    std::cout << min << std::endl;
}