In a given integer array A, we must move every element of A to either list B or list C. (B and C initially start empty.)
Return true if and only if after such a move, it is possible that the average value of B is equal to the average value of C, and B and C are both non-empty.
Example :
Input: 
[1,2,3,4,5,6,7,8]
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have the average of 4.5.

Note:

The length of A will be in the range [1, 30].
A[i] will be in the range of [0, 10000].

```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 = "#\n# @lc app=leetcode id=805 lang=python3\n#\n# [805] Split Array With Same Average\n#\n# https://leetcode.com/problems/split-array-with-same-average/description/\n#\n# algorithms\n# Hard (24.71%)\n# Likes:    244\n# Dislikes: 49\n# Total Accepted:    10.3K\n# Total Submissions: 41.6K\n# Testcase Example:  '[1,2,3,4,5,6,7,8]'\n#\n# In a given integer array A, we must move every element of A to either list B\n# or list C. (B and C initially start empty.)\n# \n# Return true if and only if after such a move, it is possible that the average\n# value of B is equal to the average value of C, and B and C are both\n# non-empty.\n# \n# \n# Example :\n# Input: \n# [1,2,3,4,5,6,7,8]\n# Output: true\n# Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of\n# them have the average of 4.5.\n# \n# \n# Note:\n# \n# \n# The length of A will be in the range\xa0[1, 30].\n# A[i] will be in the range of [0, 10000].\n# \n# \n# \n# \n#\nfrom fractions import Fraction\n\nclass Solution:\n    def splitArraySameAverage(self, A: List[int]) -> bool:\n        # Time  complexity: O(2^(N/2))\n        # Space complexity: O(2^(N/2))\n        N, S = len(A), sum(A)\n        A = [z - Fraction(S, N) for z in A]\n\n        if N == 1: return False\n\n        left = {A[0]}\n        for i in range(1, N//2):\n            left = {z + A[i] for z in left} | left | {A[i]}\n        if 0 in left: return True\n\n        right = {A[-1]}\n        for i in range(N//2, N-1):\n            right = {z + A[i] for z in right} | right | {A[i]}\n        if 0 in right: return True\n\n        sleft = sum(A[i] for i in range(N//2))\n        sright = sum(A[i] for i in range(N//2, N))\n\n        return any(-ha in right and (ha, -ha) != (sleft, sright) for ha in left)\n\n        \n\n\n        \n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'splitArraySameAverage'
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: 15383