Ho ho! So you think you know integers, do you? Well then, young wizard, tell us what the Nth digit of the [Champernowne constant](https://en.wikipedia.org/wiki/Champernowne_constant) is!

The constant proceeds like this: `0.12345678910111213141516...`

I hope you see the pattern!

Conjure a function that will accept an integer, `n`, and return the (one-indexed) `n`th digit of Champernowne's constant. Can you get it to run in _constant_ time?

For example:

`n = 1` should return `0` (the very first digit)

`n = 2` should return `1` (we ignore the period character since it's not a digit!)

`n = 20` should return `4` (that's the `4` in the number `14`, 20th in sequence)

For any invalid values, such as `0` and below, or non-integers, return... `NaN`!

I hope (for your sake) that you've been practicing your mathemagical spells, because a naïve solution will _not_ be fast enough to compete in this championship!

Invoke with _precision_, and be wary of rounding errors in the realms of enormity!

May the best integer win!

```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 = "DIGIT_CNTS = [1] + [(10**i - 10**(i-1)) * i for i in range(1, 20)]\n\ndef champernowneDigit(n):\n    if not isinstance(n, int) or n is True or n <= 0:\n        return float('nan')\n    n -= 1\n    for digits, cnt in enumerate(DIGIT_CNTS):\n        if n < cnt:\n            break\n        n -= cnt\n    start = int(10 ** (digits-1))\n    q, r = divmod(n, digits) if digits > 1 else (n, 0)\n    return int(str(start + q)[r])"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'champernowneDigit'
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: 5640