## Task

You are given three non negative integers `a`, `b` and `n`, and making an infinite sequence just like fibonacci sequence, use the following rules:

- step 1: use `ab` as the initial sequence.
- step 2: calculate the sum of the last two digits of the sequence, and append it to the end of sequence.
- repeat step 2 until you have enough digits

Your task is to complete the function which returns the `n`th digit (0-based) of the sequence.

### Notes:

- `0 <= a, b <= 9`, `0 <= n <= 10^10`
- `16` fixed testcases
- `100` random testcases, testing for correctness of solution
- `100` random testcases, testing for performance of code
- All inputs are valid.
- Pay attention to code performance.


## Examples

For `a = 7, b = 8 and n = 9` the output should be `5`, because the sequence is:
```
78 -> 7815 -> 78156 -> 7815611 -> 78156112 -> 781561123 -> 7815611235 -> ...
``` 

and the 9th digit of the sequence is `5`.

---

For `a = 0, b = 0 and n = 100000000` the output should be `0`, because all the digits in this sequence are `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 = 'L = [\n("", "0"),\n("0", "1123581347"),\n("0224610", "1123581347"),\n("03369156", "1123581347"),\n("0448", "1235813471"),\n("05510", "1123581347"),\n("066", "1235813471"),\n("077", "1459"),\n("088167", "1347112358"),\n("099189178156", "1123581347"),\n("10", "1123581347"),\n("", "1123581347"),\n("", "1235813471"),\n("", "1347112358"),\n("", "1459"),\n("156", "1123581347"),\n("167", "1347112358"),\n("178156", "1123581347"),\n("189178156", "1123581347"),\n("1910", "1123581347"),\n("20224610", "1123581347"),\n("2", "1347112358"),\n("224610", "1123581347"),\n("", "2358134711"),\n("24610", "1123581347"),\n("257", "1235813471"),\n("268", "1459"),\n("279167", "1347112358"),\n("2810", "1123581347"),\n("29", "1123581347"),\n("303369156", "1123581347"),\n("3", "1459"),\n("3257", "1235813471"),\n("3369156", "1123581347"),\n("", "3471123581"),\n("", "3581347112"),\n("369156", "1123581347"),\n("3710", "1123581347"),\n("38", "1123581347"),\n("39", "1235813471"),\n("40448", "1235813471"),\n("4156", "1123581347"),\n("4268", "1459"),\n("43710", "1123581347"),\n("448", "1235813471"),\n("", "4591"),\n("4610", "1123581347"),\n("", "4711235813"),\n("48", "1235813471"),\n("49", "1347112358"),\n("505510", "1123581347"),\n("5167", "1347112358"),\n("5279167", "1347112358"),\n("538", "1123581347"),\n("549", "1347112358"),\n("5510", "1123581347"),\n("56", "1123581347"),\n("57", "1235813471"),\n("", "5813471123"),\n("", "5914"),\n("6066", "1235813471"),\n("6178156", "1123581347"),\n("62810", "1123581347"),\n("639", "1235813471"),\n("6410", "1123581347"),\n("65", "1123581347"),\n("66", "1235813471"),\n("67", "1347112358"),\n("68", "1459"),\n("69156", "1123581347"),\n("7077", "1459"),\n("7189178156", "1123581347"),\n("729", "1123581347"),\n("7310", "1123581347"),\n("74", "1123581347"),\n("75", "1235813471"),\n("76", "1347112358"),\n("77", "1459"),\n("78156", "1123581347"),\n("79167", "1347112358"),\n("8088167", "1347112358"),\n("81910", "1123581347"),\n("8210", "1123581347"),\n("83", "1123581347"),\n("84", "1235813471"),\n("85", "1347112358"),\n("86", "1459"),\n("87156", "1123581347"),\n("88167", "1347112358"),\n("89178156", "1123581347"),\n("9099189178156", "1123581347"),\n("9110", "1123581347"),\n("92", "1123581347"),\n("93", "1235813471"),\n("94", "1347112358"),\n("95", "1459"),\n("96156", "1123581347"),\n("97167", "1347112358"),\n("98178156", "1123581347"),\n("99189178156", "1123581347")\n]\n\n# I couldn\'t get my hand on a working pattern so fuck it\n# At least it\'s fast\ndef find(a, b, n):\n    start, loop = L[10*a+b]\n    if n < len(start): return int(start[n])\n    return int(loop[(n-len(start))%len(loop)])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find'
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: 5556