Dima and Sequence

2000ms

262144K

Description:

Dima got into number sequences. Now he's got sequence a₁, a₂, ..., 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.

Input:

The first line contains integer n (1 ≤ n ≤ 10⁵). The second line contains n positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 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.

Sample Input:

3
1 2 4

Sample Output:

Sample Input:

3
5 3 1

Sample Output:

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.

Informação

Provedor Codeforces

Código CF272B