# Your Task
You have a cuboid with dimensions x,y,z ∈ ℕ. A subcuboid of this cuboid has dimensions length, width, height ∈ ℕ where 1≤length≤x, 1≤width≤y, 1≤height≤z. If two subcuboids have the same length, width, and height, but they are at different positions within the cuboid, they are distinct. Find the total number of subcuboids for the given cuboid.
# Examples
See sample tests and the image below
### 27 subcuboids for a 2×2×2 cuboid
![subcuboids(2,2,2)](https://i.imgur.com/3CnboOW.jpg)

```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 = "# This was a really fun kata!\n# I merely guessed the pattern.\n# I reasoned out answers between (1,1,1) and (2,2,2),\n# interpolated some educated guesses between the test cases,\n# and noticed (if my guesses were right):\n# (n, n, n) -> nth triangular number cubed (n*(n+1)/2) ** 3\n#\n# I struggled for a while to figure out\n# what's going on when x and y and z aren't all the same ?\n# \n# And then I thought, could it be this simple?\n# The xth cubic number times the yth cubic number times the zth cubic number?\n# \n# And I ran the sample tests and the answer was yeah lol\n\n# But I failed on my first solution attempt\n# Because I forgot to use integer division instead of float division ;(\n\ndef subcuboids(x,y,z):\n    return (x * (x+1) // 2) * (y * (y+1) // 2) * (z * (z+1) // 2)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'subcuboids'
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: 5396