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:
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.
3
1 2 4
3
3
5 3 1
1
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.
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