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 sys # sys.exit() quit()
readln = lambda: map(int, raw_input().split())
#sys.stdin = open('input.txt','r'); sys.stdout = open('output.txt','w')
# graph: G = [[] for _ in xrange(NMAX)]
# v=[];[v.append(raw_input().split()) for i in xrange(n)]
# print x, #no endl

n=int(raw_input())
a=readln()
nr=0
H={}
cache={}
def f(x):
    if x in cache:
        return cache[x]
    if x == 0:
        return 0
    if x%2:
        cache[x]=f((x-1)/2)+1
        return cache[x]
    cache[x]=f(x/2)
    return cache[x]
for i in xrange(n):
    t = f(a[i])
#    print t
    if t in H:
        H[t]=H[t]+1
    else:
        H[t]=1
        
for x in H:
    #print H[x]
    nr+=H[x]*(H[x]-1)/2
print nr