Given a list of integers, output the number of permutations of the integers, with indistinguishable permutations counted once. If there are `n` integers, and each group of indistinguishable numbers has length `n_i`, this is `n! / (n_1! * n_2! * ...)`

Rules
-----

* Input will be some form of list as arguments to a function or the program with 1 to 12 non-negative integers.
* Output will be printing or returning the number of permutations as described above.
* No standard loopholes or built-in functions (generating permutations, combinations, etc.). Factorials are allowed.

Test Cases
----------

**Inputs:**

```
1, 3000, 2, 2, 8
1, 1, 1
2, 4, 3, 2, 3, 4, 4, 4, 4, 4, 1, 1

```

**Outputs:**

```
60
1
83160

```