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>
using namespace std;

int min_change(int N,string S){
    int kuro=0,shiro=0;

    for(int i=0;i<N;i++){
        if(S[i]=='.') shiro++;
    }
    int m=shiro;
    for(int i=0;i<N;i++){
        if(S[i]=='#') kuro++;
        if(S[i]=='.') shiro--;
        m = min(m,(kuro+shiro));
    }

    return m;
}

int main(){
    int N;
    string S;
    cin >> N >> S;
    cout << min_change(N,S) << endl;
    return 0;
}