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
{
static int nooibn(int n)
{
int i=2,count=1,rem;
while(true)
{
if(n/i==0)
return count;
rem=n%i;
n=n/i;
if(rem==1)
count++;
}
}
public static void main(String aa[])throws IOException
{
BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
int sum=0,p=0,i=0,m=0;
String s;
m=Integer.parseInt(b.readLine());
int d[]=new int[50];
for(i=0;i<50;i++)
d[i]=0;
s=b.readLine();
StringTokenizer z=new StringTokenizer(s);
for(i=0;i<m;i++)
{
p=Integer.parseInt(z.nextToken());
//System.out.print(nooibn(p));
d[nooibn(p)-1]++;
}
for(i=0;i<50;i++)
sum+=d[i]*(d[i]-1)/2;
System.out.print(sum);
}
}