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 math

def listfullzero(n):
    list = [0] * n
    return list
n = int(input())
q = raw_input().split(' ');
i = 0;
res = 0
list = listfullzero(35)
while i < n:
    a = int(q[i])
    tmp = 0
    while a > 0:
        if a % 2:
            a = (a - 1) / 2
            tmp += 1
        else:
            a = a / 2
    list[tmp] += 1
    i += 1
i = 0
while i < 35:
    res += list[i] * (list[i] - 1) / 2
    i += 1
print(res)