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 n,b[200005],w[200005],minf=1145141,p,pp;
string s;
int main(){
    cin>>n>>s;
    for(int i=0;i<n;i++){
        if(s[i]=='#')p++;
        b[i]=p;
    }
    for(int i=n-1;i>=0;i--){
        if(s[i]=='.')pp++;
        w[i]=pp;
    }
    for(int i=0;i<n;i++) if(minf>(b[i]+w[i]-1))minf=b[i]+w[i]-1;
    cout<<minf<<endl;
}