In an infinite array with two rows, the numbers in the top row are denoted

`. . . , A[−2], A[−1], A[0], A[1], A[2], . . .`

and the numbers in the bottom row are denoted

`. . . , B[−2], B[−1], B[0], B[1], B[2], . . .`

For each integer `k`, the entry `A[k]` is directly above
the entry `B[k]` in the array, as shown:


...|A[-2]|A[-1]|A[0]|A[1]|A[2]|...
...|B[-2]|B[-1]|B[0]|B[1]|B[2]|...



For each integer `k`, `A[k]` is the average of the entry to its left, the entry to its right,
and the entry below it; similarly, each entry `B[k]` is the average of the entry to its
left, the entry to its right, and the entry above it.


Given `A[0], A[1], A[2] and A[3]`, determine the value of `A[n]`. (Where range of n is -1000 Inputs and Outputs in BigInt!** 

Adapted from 2018 Euclid Mathematics Contest.
https://www.cemc.uwaterloo.ca/contests/past_contests/2018/2018EuclidContest.pdf

```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 find_a(array, n):\n    if n in [0,1,2,3]:\n        return array[n]\n    b1 = 3*array[1] - array[0] - array[2]\n    b2 = 3*array[2] - array[1] - array[3]\n    if n > 3:\n        ak = array[3]\n        bk = 3*b2 - b1 - array[2]\n        ap = array[2]\n        bp = b2\n        i = 3\n        while i < n:\n            ak, ap = 3 * ak - bk - ap, ak\n            bk, bp = 3 * bk - ap - bp, bk\n            i += 1\n        return ak\n    else:\n        ak = array[0]\n        bk = 3 * b1 - b2 - array[1]\n        ap = array[1]\n        bp = b1\n        i = 0\n        while i > n:\n            ak, ap = 3 * ak - bk - ap, ak\n            bk, bp = 3 * bk - ap - bp, bk\n            i -= 1\n        return ak'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find_a'
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: 5742