A8956. Dima and Sequence

Dima got into number sequences. Now he's got sequence $a_{1},a_{2},...,a_{n}$ , 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 $f(a_{i})=f(a_{j})$ . Help him, count the number of such pairs.

The first line contains integer $n$ $(1<=n<=10^{5})$ . The second line contains $n$ positive integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{9})$ .

The numbers in the lines are separated by single spaces.

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.

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.