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.
n = int(input())
lis=list(map(int,input().split()))
ans=[0]*(n)
for i in range(n):
    k=lis[i]
    c=0
    while k>0:
        if k%2!=0:
            c+=1
        k=k//2    
    ans[i]=c   
ans.sort()
c=1
fin=0
#print(ans)
for i in range(1,n):
    if ans[i-1]==ans[i]:
        c+=1
    else:
        fin+=((c*(c-1))//2)
        c=1    
fin+=((c*(c-1))//2)
print(fin)            


