You are given a certain integer, ```n, n > 0```. You have to search the partition or partitions, of n, with maximum product value.

Let'see the case for ```n = 8```.
```
Partition                 Product
[8]                          8
[7, 1]                       7
[6, 2]                      12
[6, 1, 1]                    6
[5, 3]                      15
[5, 2, 1]                   10
[5, 1, 1, 1]                 5
[4, 4]                      16
[4, 3, 1]                   12
[4, 2, 2]                   16
[4, 2, 1, 1]                 8
[4, 1, 1, 1, 1]              4
[3, 3, 2]                   18   <---- partition with maximum product value
[3, 3, 1, 1]                 9
[3, 2, 2, 1]                12
[3, 2, 1, 1, 1]              6
[3, 1, 1, 1, 1, 1]           3
[2, 2, 2, 2]                16
[2, 2, 2, 1, 1]              8
[2, 2, 1, 1, 1, 1]           4
[2, 1, 1, 1, 1, 1, 1]        2
[1, 1, 1, 1, 1, 1, 1, 1]     1
```
So our needed function will work in that way for Python and Ruby:
```
find_part_max_prod(8) == [[3, 3, 2], 18]
```
For javascript
```
findPartMaxProd(8) --> [[3, 3, 2], 18]
```
If there are more than one partition with maximum product value, the function should output the patitions in a length sorted way.
Python and Ruby
```
find_part_max_prod(10) == [[4, 3, 3], [3, 3, 2, 2], 36]
```
Javascript
```
findPartMaxProd(10) --> [[4, 3, 3], [3, 3, 2, 2], 36]
```
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 = "def partitions(n, s=float('inf')):\n    if not n: yield []; return\n    for i in range(min(n, s), 0, -1):\n        for p in partitions(n - i, i):\n            yield [i] + p\n\nfrom collections import defaultdict\nfrom functools import reduce\nfrom operator import mul\ndef find_part_max_prod(n):\n    products = defaultdict(list)\n    for p in partitions(n):\n        products[reduce(mul, p)].append(p)\n    m = max(products)\n    return products[m] + [m]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find_part_max_prod'
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: 14262