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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class B {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] nums = new int[n];
        StringTokenizer st = new StringTokenizer(br.readLine());
        for (int i = 0; i < n; i++)
            nums[i] = Integer.parseInt(st.nextToken());

        int[] freq = new int[33];
        for (int i = 0; i < n; i++) {
            int cnt = 0;
            for (int j = 0; j < 32; j++)
                if (((nums[i] >> j) & 1) == 0)
                    cnt++;
            freq[cnt]++;
        }

        long res = 0;
        for (int i = 0; i < freq.length; i++)
            if (freq[i] > 1) {
                long k = freq[i];
                res += (k * (k - 1)) / 2;
            }
        
        System.out.println(res);
    }
}
