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 = 'class Solution1:\n    def splitArraySameAverage(self, A: List[int]) -> bool:\n        \n        N = len(A)\n        \n        if N <= 1:\n            return False\n        \n        max_sum = sum(A)\n        #print(max_sum)\n        sums = [0] * (max_sum+1)\n        for i in range(N):\n            num = A[i]\n            for s in range(max_sum, num-1, -1):\n                if sums[s-num]:\n                    sums[s] |= sums[s-num] << 1\n            sums[num] |= 1\n            #print(sums)\n        #print(sums)\n        for l in range(1, N):\n            if (max_sum * l) % N == 0:\n                s = int((max_sum * l) / N)\n                if (sums[s] >> (l-1)) & 1:\n                    return True\n        return False\n\nimport math\nclass Solution2:\n    def splitArraySameAverage(self, A: List[int]) -> bool:\n        A.sort(reverse=True)\n        N = len(A)\n        if N <= 1:\n            return False\n        max_size = math.ceil(N / 2)\n        \n        max_sum = sum(A)\n        target_mean = max_sum / N\n        #print(target_mean)\n        ans = False\n        \n        def choose(max_n, curr_n, curr_sum, next_id):\n            nonlocal target_mean\n            nonlocal ans\n            nonlocal N\n            #print(max_n, curr_n, curr_sum, next_id)\n            if ans:\n                return\n            if curr_n > max_n:\n                return\n            if curr_n:\n                curr_mean = curr_sum / curr_n\n                if curr_mean < target_mean:\n                    return\n                if curr_mean == target_mean:\n                    ans = True\n                    return\n            if next_id == N -1:\n                return\n            for i in range(next_id, N):\n                choose(max_n, curr_n + 1, curr_sum + A[i], i+1)\n        \n        choose(max_size, 0, 0, 0)\n        \n        return ans\n    \nclass Solution(object):\n    def splitArraySameAverage(self, A):\n        from fractions import Fraction\n        N = len(A)\n        S = sum(A)\n        A = [z - Fraction(S, N) for z in A]\n\n        if N == 1: return False\n\n        #Want zero subset sum\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)'
_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: 15501