Given a non-negative number, return the next bigger polydivisible number, or an empty value like `null` or `Nothing`.

A number is polydivisible if its first digit is cleanly divisible by `1`, its first two digits by `2`, its first three by `3`, and so on. There are finitely many polydivisible numbers.

```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 = '# solution building polydivisible numbers ground up\n# using sets over lists and removing multiple type conversions helped speed\ndef next_num(n):\n    mpl = 25 #maximum length of polydivisible number\n    lpn = 3608528850368400786036725 #largest polydivisible number\n    if n >= lpn: return None\n    nl = len(str(n))\n    \n    extend = {}\n    for i in range(1, mpl+2):\n        if i % 10 == 0: extend[i] = {"0"}\n        elif i % 5 == 0: extend[i] = {"0","5"}\n        elif i % 2 == 0: extend[i] = {"0","2","4","6","8"}\n        else: extend[i] = {"0","1","2","3","4","5","6","7","8","9"}\n    \n    d = {1: {"1","2","3","4","5","6","7","8","9"}} #dictionary of all polydivisible numbers, excluding 0\n    for l in range(2,2+nl):\n        d[l] = {p+i for i in extend[l] for p in d[l-1] if int(p+i)%(l) == 0}\n    d[1].add("0")\n    \n    if n >= max(map(int,d[nl])):\n        return min(map(int,d[nl+1]))\n    else:\n        for i in sorted(map(int,d[nl])):\n            if i > n: return i'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'next_num'
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: 26385