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 = '# import math\n\n# class Solution(object):\n#     def maxUniqueSplit(self, s):\n#         \\"\\"\\"\n#         :type s: str\n#         :rtype: int\n#         \\"\\"\\"\n#         account = 0\n#         solutions = set()\n#         account = self.findSolutions(s, solutions)\n#         print(\\"finished\\")\n#         print(solutions)\n#         print(account)\n        \n#         # if substring are the same than the solution is not right\n#         # if one solution has more substring than another adopt this one\n#         # could use divide and conqure to go done a string\n        \n#     def findSolutions(self, s, solutions):\n#         strLen = len(s)\n#         if strLen != 1:\n#             halfPoint = math.ceil(strLen / 2) # use floor so that the left side is always smaller string\n#             leftSubStr = s[:halfPoint]\n#             rightSubStr = s[halfPoint:]\n#             print(\\"strlength is: {} mid point : {} left string: {} right string: {} \\".format(strLen, halfPoint, leftSubStr, rightSubStr))\n#             # only keep spliting when the substring is unique in solutions\n#             if leftSubStr not in solutions:\n#                 # remove previous solution if it is in it\n#                 solutions.add(leftSubStr)\n#                 return self.findSolutions(leftSubStr, solutions) + 1\n#                 solutions.remove(leftSubStr)\n\n#             if rightSubStr not in solutions:\n#                 solutions.add(rightSubStr)\n#                 return account + self.findSolutions(rightSubStr, solutions) + 1\n#                 solutions.remove(rightSubStr)\n\n#         else:\n#             print(s)\n#             return 1\n        \nclass Solution:\n    book = set()\n    def maxUniqueSplit(self, s):\n        result = 0\n        for i in range(1, len(s)+1): #go through all the length of sub strings from left to right\n            curr = s[:i]\n            if curr not in self.book:\n                self.book.add(curr) # add a type of sub string if it is not in it\n                result = max(result, 1 + self.maxUniqueSplit(s[i:]))\n                self.book.remove(curr)\n        return result'
_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: 7835