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 B {

	HashMap<Integer, Integer> hm;

	void run() throws IOException {
		hm = new HashMap<Integer, Integer>();
		HashMap<Integer, Integer> hs = new HashMap<Integer, Integer>();
		hm.put(0, 0);
		int n = ni();
		int[] a = na(n);

		for (int i = 0; i < n; i++) {
			int q = f(a[i]);
			int m = 0;
			if (hs.containsKey(q))
				m = hs.remove(q);
			hs.put(q, ++m);
		}

		long ans = 0;
		Collection<Integer> w = hs.values();
		for (Integer h : w) {
			long lh = h;
			ans += (lh * (lh - 1) / 2);
		}
		pw.println(ans);
	}

	int f(int x) {
		if (x == 0)
			return 0;
		int q;
		if (hm.containsKey(x / 2)) {
			q = hm.get(x / 2) + (x % 2);
		} else {
			q = f(x / 2) + (x % 2);
			hm.put(x, q);
		}
		return q;
	}

	int[] na(int a_len) throws IOException {
		int[] _a = new int[a_len];
		for (int i = 0; i < a_len; i++)
			_a[i] = ni();
		return _a;
	}

	int[][] nm(int a_len, int a_hei) throws IOException {
		int[][] _a = new int[a_len][a_hei];
		for (int i = 0; i < a_len; i++)
			for (int j = 0; j < a_hei; j++)
				_a[i][j] = ni();
		return _a;
	}

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

	int ni() throws IOException {
		return Integer.parseInt(next());
	}

	String nl() throws IOException {
		return br.readLine();
	}

	void tr(String debug) {
		if (!OJ)
			pw.println(" " + debug);
	}

	static PrintWriter pw;
	static BufferedReader br;
	static StringTokenizer st;
	static boolean OJ;

	public static void main(String[] args) throws IOException {
		long timeout = System.currentTimeMillis();
		OJ = System.getProperty("ONLINE_JUDGE") != null;
		pw = new PrintWriter(System.out);
		br = new BufferedReader(OJ ? new InputStreamReader(System.in) : new FileReader(new File("B.txt")));

		while (br.ready())
			new B().run();
		if (!OJ) {
			pw.println();
			pw.println(System.currentTimeMillis() - timeout);
		}
		br.close();
		pw.close();
	}

}
