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 j
{
public static void main(String a[])throws IOException
{
BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
int v=0,u=0,i=0,k=0,n=0;
n=Integer.parseInt(b.readLine());
String s;
int d[]=new int[n];
s=b.readLine();
StringTokenizer c=new StringTokenizer(s);
for(i=0;i<n;i++)
{
d[i]=Integer.parseInt(c.nextToken());
if(d[i]%2==0&&d[i]!=0)
u++;
if(d[i]%2==1&&d[i]!=1)
v++;
if(d[i]==1)
u++;
}
if(u>1)
k+=u*(u-1)/2;
if(v>1)
k+=v*(v-1)/2;
System.out.print(k);
}
}