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.
/**
 * Created with IntelliJ IDEA.
 * User: yuantian
 * Date: 3/8/13
 * Time: 12:35 AM
 * To change this template use File | Settings | File Templates.
 */

import java.util.*;

public class DimaAndSequence {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        int[] a = new int[n];
        for(int i = 0; i < n; i++)
            a[i] = in.nextInt();

        long[] count = new long[40];
        for(int i : a) {
            int x = i;
            int c = 1;
            while(x > 1) {
                if((x%2) == 1) {
                    c++;
                    x--;
                }
                x >>= 1;
            }
            count[c]++;
        }

        long ret = 0;
        for(long i : count) {
            if(i > 1)
                ret += i*(i-1)/2;
        }
        System.out.println(ret);
    }
}
