Dima got into number sequences. Now he's got sequence a1, a2, ..., an, consisting of n positive integers. Also, Dima has got a function f(x), which can be defined with the following recurrence:

  * f(0) = 0; 
  * f(2·x) = f(x); 
  * f(2·x + 1) = f(x) + 1. 



Dima wonders, how many pairs of indexes (i, j) (1 ≤ i < j ≤ n) are there, such that f(ai) = f(aj). Help him, count the number of such pairs. 

Input

The first line contains integer n (1 ≤ n ≤ 105). The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

The numbers in the lines are separated by single spaces.

Output

In a single line print the answer to the problem.

Please, don't use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3
1 2 4


Output

3


Input

3
5 3 1


Output

1

Note

In the first sample any pair (i, j) will do, so the answer is 3.

In the second sample only pair (1, 2) will do.

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class B167 {

    public void solve() {
        Scanner sc = new Scanner(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int i = 0, j = 0, k = 0;
        int ans = 0, sum = 0, count = 0;
        int n = sc.nextInt();
        long a[] = new long[n];

        for (i = 0; i < n; ++i) {
            a[i] = sc.nextLong();
        }
        
        for(i=0;i<n;++i){
            for(j=i+1;j<n;++j){
                if( f(a[i],a[j])){
                   // System.out.println(a[i]+"  "+a[j]);
                    count++;
                }
            }
        }
        System.out.println(count);

    }

    public static boolean f(long num1,long num2) {
        
        if(num1==1 && num2%2==0 || num1%2==0 && num2==1 || num1%2==0 && num2%2==0){
            //System.out.println("kjkj");
            return true;
        } else if((num1%2==1 && num2%2==1) && (num1!=num2 && num1!=1) && num2!=1){
            return true;
        }else{
            return false;
        }
        
    }

    public static void main(String[] args) {
        new B167().solve();

    }
}
