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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;
import static java.lang.Math.*;
import static java.lang.Integer.*;
import static java.lang.Long.*;
import static java.lang.String.*;
import static java.lang.Character.*;

@SuppressWarnings("unused")
public class round167B {

	static BufferedReader br = new BufferedReader(new InputStreamReader(
			System.in));
	static StringTokenizer st = new StringTokenizer("");

	static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}

	static String next() throws Exception {
		while (true) {
			if (st.hasMoreTokens()) {
				return st.nextToken();
			}
			String s = br.readLine();
			if (s == null) {
				return null;
			}
			st = new StringTokenizer(s);
		}
	}
	
	public static boolean allZero(int [] seq){
		for(int i = 0 ; i < seq.length ; ++i)
			if(seq[i] != 0)
				return false;
		return true;
	}

	public static void main(String[] args) throws Exception {
		PrintWriter out = new PrintWriter(System.out);
		int n = nextInt();
		int[] seq = new int[n];
		for (int i = 0; i < n; ++i)
			seq[i] = nextInt();
		if(allZero(seq)){
			System.out.println((n * (n - 1)) / 2);
			return;
		}
		Arrays.sort(seq);
		HashMap<Integer, Integer> count = new HashMap<Integer, Integer>();
		long ans = 0;
		for (int i = 0; i < n; ++i) {			
			int d1 = seq[i] % 2 == 0 ? seq[i] / 2 : seq[i] / 2 + 1;			
			if (count.containsKey(d1)){
				/*System.out.println("I   " + i);
				System.out.println(d1 + "  " + count.get(d1));*/
				ans += count.get(d1);
				//System.out.println("Answer  " + ans);
			}
			Integer pres = count.get(seq[i]);
			if (pres == null)
				count.put(seq[i], (count.containsKey(d1) ? count.get(d1) : 0) + 1);
			else
				count.put(seq[i], pres + 1);
		}
		out.println(ans);
		out.flush();
	}
}
