Most of this problem is by the original author of [the harder kata](https://www.codewars.com/kata/556206664efbe6376700005c), I just made it simpler.

I read a book recently, titled "Things to Make and Do in the Fourth Dimension" by comedian and mathematician Matt Parker ( [Youtube](https://www.youtube.com/user/standupmaths) ), and in the first chapter of the book Matt talks about problems he likes to solve in his head to take his mind off the fact that he is in his dentist's chair, we've all been there!

The problem he talks about relates to polydivisible numbers, and I thought a kata should be written on the subject as it's quite interesting. (Well it's interesting to me, so there!)

### Polydivisib... huh what?

So what are they?

A polydivisible number is divisible in an unusual way. The first digit is cleanly divisible by `1`, the first two digits are cleanly divisible by `2`, the first three by `3`, and so on.

### Examples

Let's take the number `1232` as an example.
```
1     / 1 = 1     // Works
12    / 2 = 6     // Works
123   / 3 = 41    // Works
1232  / 4 = 308   // Works
```
`1232` is a polydivisible number.


However, let's take the number `123220` and see what happens.
```
 1      /1 = 1    // Works
 12     /2 = 6    // Works
 123    /3 = 41   // Works
 1232   /4 = 308  // Works
 12322  /5 = 2464.4         // Doesn't work
 123220 /6 = 220536.333...  // Doesn't work
```
`123220` is not polydivisible.

### Your job: check if a number is polydivisible or not.

Return `true` if it is, and `false` if it isn't.

Note: All inputs will be valid numbers between `0` and `2^53-1 (9,007,199,254,740,991)` (inclusive).   
Note: All single digit numbers (including `0`) are trivially polydivisible.
Note: Except for `0`, no numbers will start with `0`.

```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 polydivisible(n):\n    s = str(n)\n    return all(not int(s[:i])%i for i in range(2,len(s)+1))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'polydivisible'
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: 5747