With one die of 6 sides we will have six different possible results:```  1, 2, 3, 4, 5, 6``` .

With 2 dice of six sides, we will have 36 different possible results:
``` 
(1,1),(1,2),(2,1),(1,3),(3,1),(1,4),(4,1),(1,5),
(5,1), (1,6),(6,1),(2,2),(2,3),(3,2),(2,4),(4,2),
(2,5),(5,2)(2,6),(6,2),(3,3),(3,4),(4,3),(3,5),(5,3),
(3,6),(6,3),(4,4),(4,5),(5,4),(4,6),(6,4),(5,5),
(5,6),(6,5),(6,6)
``` 
So, with 2 dice of 6 sides we get 36 different events.
``` 
([6,6] ---> 36)
``` 
But with 2 different dice we can get for this case, the same number of events.
One die of ```4 sides```  and another of ```9 sides```  will produce the exact amount of events.
``` 
([4,9] ---> 36)
``` 
We say that the dice set ```[4,9]``` is equivalent to ```[6,6]``` because both produce the same number of events.

Also we may have an amount of three dice producing the same amount of events. It will be for:
``` 
[4,3,3] ---> 36
``` 
(One die of 4 sides and two dice of 3 sides each)

Perhaps you may think that the following set is equivalent: ```[6,3,2]``` but unfortunately dice have a **minimum of three sides** (well, really a 
tetrahedron with one empty side)

The task for this kata is to get the amount of equivalent dice sets, having **2 dice at least**,for a given set.

For example, for the previous case: [6,6] we will have 3 equivalent sets that are: ``` [4, 3, 3], [12, 3], [9, 4]``` .

You may assume that dice are available from 3 and above for any value up to an icosahedral die (20 sides).
``` 
[5,6,4] ---> 5 (they are [10, 4, 3], [8, 5, 3], [20, 6], [15, 8], [12, 10])
``` 
For the cases we cannot get any equivalent set the result will be `0`.
For example for the set `[3,3]` we will not have equivalent dice.

Range of inputs for Random Tests:
``` 
3 <= sides <= 15
2 <= dices <= 7
``` 
See examples in the corresponding box.

Enjoy it!!

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from functools import reduce\ndef get_factors(m):\n    li, j = [], 2\n    while j * j <= m:\n        if m % j:\n            j += 1\n            continue\n        m //= j\n        li.append(j)\n    return li+([m] if m>1 else [])\n\ndef divide(arr, cache):\n    store = []\n    for i in range(len(arr)):\n        for j in range(i + 1, len(arr)):\n            m = arr[:i] + arr[i + 1:j] + [arr[i] * arr[j]] + arr[j + 1:]\n            tp = tuple(sorted(m))\n            if m != arr and len(m)>1 and tp not in cache:\n                cache.add(tp)\n                store.extend([tp] + divide(m,cache))\n    return store\n\ndef eq_dice(arr):\n    m, arr = reduce(lambda x, y: x * y, arr), tuple(sorted(arr))\n    return sum(1 for i in set(divide(get_factors(m),set())) if i!=arr and all(2<k<21 for k in i))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'eq_dice'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 9124