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 = 'def next_num(n):\n\n    \'\'\'\n    I work on input number converting it to string throughout the code.\n    We check if number is polydivisible, if not we find where in the number \n    first problem occurs and then substitute proper part into the initial \n    number and check over again.\n    \'\'\'\n    number=str(n+1)\n\n                                                    # Inner funtion checking for polydivisibility.\n                                                    # It returns place where polydivisibility test fails at first or \n                                                    # 0 if number is polydivisible\n    def isNumPoly(number):\n        for i in range(1,len(number)+1):\n            if not (int(number[0:i]))%(i)==0:\n                return i\n        return 0\n                                                    # Upper bound is the number greater than biggest polydivisible number that\n                                                    # won\'t be reached if searching for existing polydivisible number\n    while (int(number)<3610000000000000000000000):\n                                                      # Checking for place where something went wrong in:\n        where = isNumPoly(number)\n                                                      # If 0 return number as polydivisible\n        if where==0:\n            return int(number)\n                                                      # If not replace failing piece of the number with nicely divisible one\n        badPiece=number[0:where]\n        replacement = str(int(badPiece)+(where-int(badPiece)%where))\n                                                      # Create new number with working first part and 0\'s for the rest, \n                                                      # not to skip over any number along the way\n        number = replacement + "0"*len(number[where:]) \n    return None'
_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: 5770