Given a string s, return the maximum number of unique substrings that the given string can be split into.
You can split string s into any list of non-empty substrings, where the concatenation of the substrings forms the original string. However, you must split the substrings such that all of them are unique.
A substring is a contiguous sequence of characters within a string.
 
Example 1:
Input: s = "ababccc"
Output: 5
Explanation: One way to split maximally is ['a', 'b', 'ab', 'c', 'cc']. Splitting like ['a', 'b', 'a', 'b', 'c', 'cc'] is not valid as you have 'a' and 'b' multiple times.

Example 2:
Input: s = "aba"
Output: 2
Explanation: One way to split maximally is ['a', 'ba'].

Example 3:
Input: s = "aa"
Output: 1
Explanation: It is impossible to split the string any further.

 
Constraints:


1 <= s.length <= 16


s contains only lower case English letters.

```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 Solution:\n    def maxUniqueSplit(self, s: str) -> int:\n        # dp = [[\\"\\"] for _ in range(len(s))]\n        # dp[0] = [s[0]]\n        # for i in range(1, len(s)):\n        #     maxnum_ = 1\n        #     for j in range(i):\n        #         if s[j+1:i] not in dp[j]:\n        #             maxnum = len(dp[j]) + 1\n        #             if maxnum > maxnum_:\n        #                 maxnum_ = maxnum\n        #                 dp[i] = dp[j].copy() \n        #                 dp[i].append(s[j+1:i])\n        # print(dp)\n        # return len(dp[len(s)-1])\n#         return len(self.maxUniqueSplit_(s, len(s)-1)[-1])\n    \n#     @lru_cache\n#     def maxUniqueSplit_(self, s, i):\n#         if i == 0:\n#             return [[s[i]]]\n#         else:\n#             max_ = 0\n#             toreturn = []\n#             for j in range(i):\n#                 maxUniqueSplit_j = self.maxUniqueSplit_(s, j)\n#                 for uniquesplit_j in maxUniqueSplit_j:\n#                     if s[j+1:i+1] not in uniquesplit_j:\n#                         if len(uniquesplit_j) + 1 > max_:\n#                             toreturn = [uniquesplit_j + [s[j+1:i+1]]]\n#                             max_ = len(uniquesplit_j) + 1\n#                         elif len(uniquesplit_j) + 1 == max_:\n#                             toreturn.append(uniquesplit_j + [s[j+1:i+1]])\n#                     if j == i - 1 and len(toreturn) == 0:\n#                         toreturn = [uniquesplit_j]\n#             print(toreturn, i)\n#             return toreturn\n        if len(s) == 1:\n            return 1\n        def splitter(str):\n            for i in range(1, len(str)):\n                start = str[0:i]\n                end = str[i:]\n                yield (start, end)\n                for split in splitter(end):\n                    result = [start]\n                    result.extend(split)\n                    yield result\n        \n        maxnum = 0\n        for split in splitter(s):\n            if len(set(split)) == len(split):\n                maxnum = max(len(split), maxnum)\n        if maxnum == 0:\n            return self.maxUniqueSplit(s[:len(s)-1])\n        else:\n            return maxnum\n                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxUniqueSplit'
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: 11888