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.util.Scanner;

public class Main {

    public static void main(String[] args) {
    // write your code here
        Scanner scan = new Scanner(System.in);
        long count = scan.nextInt();
        long[] fResultCount = new long[50];
        for (int i=0;i<count;i++){
            fResultCount[f(scan.nextInt())]++;
        }
        long pairCount = 0;
        for (int i=0;i<50;i++){
            pairCount+=(fResultCount[i]*(fResultCount[i]-1))/2;
        }
        System.out.print(pairCount);
    }

    public static int f(int num){
        if (num==0){
            return 0;
        }
        if (num % 2 == 0){
            return (f(num/2));
        }
        return (f(num/2)+1);
    }
}
