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.*;
import java.io.*;
public class dimaseq{
public static void main(String args[]) throws IOException{
BufferedReader lector = new BufferedReader(new InputStreamReader(System.in));
int tmp = Integer.parseInt(lector.readLine());
int tales[] = new int[50];
String t[] = lector.readLine().split(" ");
for(int n = 0;n<tmp;n++){
int h = Integer.parseInt(t[n]);
int c = 0;
do{
c+=(h&1);
}while((h>>=1)>0);
tales[c]++;
}
long res =0;
for(int n = 0;n<50;n++)
res+=((long)tales[n]*((long)tales[n]-1L))>>1L;
System.out.println(res);
}
}
