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.
def main():
    from collections import defaultdict
    
    def f(x):
        if x < L:
            return prec[x]
        return f(x // 2) + x % 2
    
    n = int(input())
    
    a = [int(i) for i in input().split()]
    
    L = 10**5
    prec = [0]
    for i in range(1, L):
        if i % 2 == 1:
            prec.append(prec[i - 1] + 1)
        else:
            prec.append(prec[i // 2])
    
    d = defaultdict(int)
    
    for i in a:
        d[f(i)] += 1
    
    result = 0
    for i in d.values():
        result += i * (i - 1) // 2
    
    print(result)

main()
