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.util.Arrays;
import java.util.Scanner;


public class Program {

	static int f(int k){
		if(k==0) return 0;
		if(k%2==1){
			return f((k-1)/1)+1;
		}
		else{
			return f(k/2);
		}
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] nums = new int[n];
		
		int max = -1;
		int readNum;
		for(int i=0; i<n; ++i){
			readNum = sc.nextInt();   // save numbers in line here
			nums[i] = readNum;
			max = Math.max(max,readNum);
		}
		
		
		int[] resArr = new int[n];
		

		// save the results f[a_i] in resArr2
		for(int i=0; i<n; ++i){
			resArr[i] = f(nums[i]);
		}
		
		Arrays.sort(resArr);
		
				
//		// TEST - print result array
//		System.out.println("sorted resArr2:");
//		for(int i=0; i<n; ++i){
//			System.out.print(resArr2[i] + " ");
//		}
//		System.out.println();
//		//
		
		
		int pairs=0;
		int occ=1;   
		for(int i=0; i<n-1; ++i){
			if(resArr[i]==resArr[i+1]){
				occ++;
			}
			else{
				pairs += ((occ-1)*occ)/2;
				occ = 1;
			}
		}
		pairs += ((occ-1)*occ)/2;
		
		
		System.out.println(pairs);
		
		
	}
		
}
