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.math.BigInteger;
import java.util.*;
public class Sequence {

	
	public static void main(String[] args) throws NumberFormatException, IOException {
		int[] dp = new int[100];
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int cur, cnt;
		for(int i = 0; i < n; i++) {
			cnt = 0;
			cur = Integer.parseInt(st.nextToken());
			while(cur != 0) {
				while( cur % 2 == 0 ) cur /= 2;
				cur--;
				cnt++;
			}
			dp[cnt]++;
		}
		BigInteger ans = new BigInteger("0");
		for(int i = 0; i < 100; i++) {
			if(dp[i] == 0) continue;
			BigInteger aux = new BigInteger(dp[i]+"");
			ans = ans.add(aux.multiply(aux.subtract(BigInteger.ONE)).divide(BigInteger.ONE.add(BigInteger.ONE)));
		}
		System.out.println(ans);
		
	}
	
	
}
