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.
#! /Library/Frameworks/Python.framework/Versions/2.6/bin/python

n = int(raw_input())

inp = raw_input().split()
a = [int(inp[i]) for i in range(n)]

def f(ai):
	if (ai == 0):
		return 0
	elif (ai % 2 == 0):
		return f(ai/2)
	else:
		return f(ai/2) + 1

fCount = [0 for i in range(32)]

for i in range(n):
	fCount[f(a[i])] += 1

ans = 0

for j in range(32):
	ans += (fCount[j] * (fCount[j] - 1))/2

print ans


