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 = '# from functools import lru_cache\n# class Solution:\n#     def splitArraySameAverage(self, A: List[int]) -> bool:\n#         # A.sort(reverse=True)\n#         n, total = len(A), sum(A)\n#         avag = total/n\n#         # epsilon = 0.000001\n#         # print(avag)\n#         @lru_cache(None)\n#         def dfs(idx, sums, sz):\n#             if 0 < sz <= n//2 and total*sz%n == 0 and sums == total*sz//n:\n#                 return True\n#             if idx == n or sz > n//2 or sums > total/2:\n#                 return False\n            \n#             return dfs(idx+1, sums+A[idx], sz+1) or dfs(idx+1, sums, sz)\n#             # print(idx,sums,sz,res)\n#         return dfs(0,0,0)\n\nfrom functools import lru_cache\nclass Solution:\n    def splitArraySameAverage(self, A: List[int]) -> bool:\n        n, total = len(A), sum(A)\n        @lru_cache(None)\n        def dfs(idx, target, sz):\n            if sz < 0 or target < 0 or idx+sz > n:\n                return False\n            if idx == n:\n                return target == 0\n            \n            \n            return dfs(idx+1, target-A[idx], sz-1) or dfs(idx+1, target, sz)\n            # print(idx,sums,sz,res)\n        return any(dfs(0,total*k//n,k) for k in range(1,n//2+1) if total*k%n == 0)'
_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: 16536