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.

Input

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.

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.

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.