Given an array of strings arr. String s is a concatenation of a sub-sequence of arr which have unique characters.
Return the maximum possible length of s.
 
Example 1:
Input: arr = ["un","iq","ue"]
Output: 4
Explanation: All possible concatenations are "","un","iq","ue","uniq" and "ique".
Maximum length is 4.

Example 2:
Input: arr = ["cha","r","act","ers"]
Output: 6
Explanation: Possible solutions are "chaers" and "acters".

Example 3:
Input: arr = ["abcdefghijklmnopqrstuvwxyz"]
Output: 26

 
Constraints:

1 <= arr.length <= 16
1 <= arr[i].length <= 26
arr[i] 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 = '#https://wentao-shao.gitbook.io/leetcode/graph-search/1239.maximum-length-of-a-concatenated-string-with-unique-characters\n\nclass Solution:\n    def maxLength1(self, arr: List[str]) -> int:\n        \n        def dfs(start, seen):\n            nonlocal res\n            if start==len(arr):\n                res = max(res, sum(len(arr[i]) for i in seen) )\n            else:\n                is_end = True\n                for i in graph[start]:\n                    if all(len(arr[j].intersection(arr[i]))==0 for j in seen):\n                        is_end = False\n                        seen.append(i)\n                        dfs(i, seen)\n                        seen.pop()\n                if is_end:\n                    res = max(res, sum(len(arr[i]) for i in seen) )\n        \n        arr = [item for item in arr if len(item)==len(set(item))]\n        arr = list(map(set, arr))\n        graph = collections.defaultdict(list)\n        for i in range(len(arr)):\n            for j in range(i+1, len(arr)):\n                if len(arr[i].intersection(arr[j]))==0:\n                    graph[i].append(j)\n            \n        res = 0\n        for i in range(len(arr)):\n            dfs(i, [i])\n        return res\n            \n    def maxLength(self, arr: List[str]) -> int:\n        \n        def dfs(seen):\n            nonlocal res\n            is_end = True\n            for i in graph[seen[-1]]:\n                if all(len(arr[j].intersection(arr[i]))==0 for j in seen):\n                    is_end = False\n                    seen.append(i)\n                    dfs(seen)\n                    seen.pop()\n            if is_end:\n                res = max(res, sum(len(arr[i]) for i in seen) )\n        \n        arr = [item for item in arr if len(item)==len(set(item))]\n        arr = list(map(set, arr))\n        graph = collections.defaultdict(list)\n        for i in range(len(arr)):\n            for j in range(i+1, len(arr)):\n                if len(arr[i].intersection(arr[j]))==0:\n                    graph[i].append(j)\n            \n        res = 0\n        for i in range(len(arr)):\n            dfs([i])\n        return res\n            \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxLength'
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: 6472