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.*;
import java.util.*;

public class CCC implements Runnable {
	BufferedReader br;
	StringTokenizer in;
	PrintWriter out;

	public static int f(int x) {
		int s = 1;
		while (x != 1) {
			if ((x % 2) == 1)
				s++;
			x /= 2;
		}
		return s;
	}

	public void solve() throws IOException {
		int n = nextInt();
		int[] a = new int[n];
		int[] b = new int[10000];
		Arrays.fill(b, 0);

		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
			b[f(a[i])]++;
		}
		long sum = 0;
		for (int i = 0; i < b.length; i++) {
			long x;
			if (b[i] <= 1)
				x = 0;
			else
				x = (long) (((long) b[i] * (long) (b[i] - 1)) / (long) 2);
			sum += x;
		}
		System.out.print(sum);
	}

	public String nextToken() throws IOException {
		while ((in == null) || (!in.hasMoreTokens()))
			in = new StringTokenizer(br.readLine());
		return in.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			out.close();
		} catch (IOException e) {
		}
	}

	public static void main(String[] args) {
		new Thread(new CCC()).start();
	}
}
