~~~if-not:java
You have to code a function **getAllPrimeFactors** wich take an integer as parameter and return an array containing its prime decomposition by ascending factors, if a factors appears multiple time in the decomposition it should appear as many time in the array. 

exemple: `getAllPrimeFactors(100)` returns `[2,2,5,5]` in this order. 

This decomposition may not be the most practical. 

You should also write **getUniquePrimeFactorsWithCount**, a function which will return an array containing two arrays: one with prime numbers appearing in the decomposition and the other containing their respective power. 

exemple: `getUniquePrimeFactorsWithCount(100)` returns `[[2,5],[2,2]]`

You should also write **getUniquePrimeFactorsWithProducts** an array containing the prime factors to their respective powers. 

exemple: `getUniquePrimeFactorsWithProducts(100)` returns `[4,25]`
~~~
~~~if:java
You have to code a function **getAllPrimeFactors** wich take an integer as parameter and return an array containing its prime decomposition by ascending factors, if a factors appears multiple time in the decomposition it should appear as many time in the array. 

exemple: `getAllPrimeFactors(100)` returns `[2,2,5,5]` in this order. 

This decomposition may not be the most practical. 

You should also write **getUniquePrimeFactorsWithCount**, a function which will return an array containing two arrays: one with prime numbers appearing in the decomposition and the other containing their respective power. 

exemple: `getUniquePrimeFactorsWithCount(100)` returns `[[2,5],[2,2]]`

You should also write **getPrimeFactorPotencies** an array containing the prime factors to their respective powers. 

exemple: `getPrimeFactorPotencies(100)` returns `[4,25]`
~~~

Errors, if:

* `n` is not a number
* `n` not an integer 
* `n` is negative or 0 

The three functions should respectively return `[]`,  `[[],[]]` and `[]`. 

Edge cases: 

* if `n=0`, the function should respectively return `[]`, `[[],[]]` and  `[]`.
* if `n=1`, the function should respectively return `[1]`, `[[1],[1]]`, `[1]`.
* if `n=2`, the function should respectively return `[2]`, `[[2],[1]]`, `[2]`.

The result for `n=2` is normal. The result for `n=1` is arbitrary and has been chosen to return a usefull result. The result for `n=0` is also arbitrary 
but can not be chosen to be both usefull and intuitive. (`[[0],[0]]` would be meaningfull but wont work for general use of decomposition, `[[0],[1]]` would work but is not intuitive.)

```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 = 'def getAllPrimeFactors(n):\n  if type(n) is not int or n < 1:\n      return []\n  elif n < 3:\n      return [n]\n  factors = []\n  while n > 1:\n      for i in range(2, n+1):\n          if is_prime(i) and not n % i:\n              factors.append(i)\n              n = int(n/i)\n              break\n  return factors\n\ndef getUniquePrimeFactorsWithCount(n):\n  f = getAllPrimeFactors(n)\n  factors = list(set(f))\n  powers = [f.count(factor) for factor in factors]\n  return [factors, powers]\n\ndef getUniquePrimeFactorsWithProducts(n):\n  cf = getUniquePrimeFactorsWithCount(n)\n  return [factor**count for factor, count in zip(cf[0], cf[1])]\n  \ndef is_prime(n):\n    for i in range(2, n):\n        if not n % i:\n            return False\n    return True\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'getAllPrimeFactors'
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: 5710