Given an array A of strings, find any smallest string that contains each string in A as a substring.
We may assume that no string in A is substring of another string in A.
 

Example 1:
Input: ["alex","loves","leetcode"]
Output: "alexlovesleetcode"
Explanation: All permutations of "alex","loves","leetcode" would also be accepted.


Example 2:
Input: ["catg","ctaagt","gcta","ttca","atgcatc"]
Output: "gctaagttcatgcatc"
 


Note:

1 <= A.length <= 12
1 <= A[i].length <= 20

```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 shortestSuperstring(self, A: List[str]) -> str:\n        def save(w1,w2):\n            n = len(w1)\n            for i in range(n):\n                if w1[i:] == w2[:n-i]:\n                    return n-i\n            return 0\n        \n        N = len(A)\n        s = [[0] * N for i in range(N)]\n        for i in range(N):\n            for j in range(N):\n                if i != j:\n                    s[i][j] = save(A[i],A[j])\n        \n        end_state = (1<<N) - 1\n        \n        import functools\n        @functools.lru_cache(None)\n        def DFS(cur_state,cur_pos):\n            if cur_state == end_state:\n                return 0,[cur_pos]\n            cur_save = -100\n            pre_pos = 0\n            for pre_pos in range(N):\n                if pre_pos == 0 :\n                    pre_pos_b = 1\n                else:\n                    pre_pos_b = pre_pos_b << 1\n                if pre_pos_b|cur_state == cur_state:\n                    continue\n                if cur_save < s[pre_pos][cur_pos] + DFS(cur_state|pre_pos_b,pre_pos)[0]:\n                    cur_save = s[pre_pos][cur_pos] + DFS(cur_state|pre_pos_b,pre_pos)[0]\n                    path = DFS(cur_state|pre_pos_b,pre_pos)[1] + [cur_pos]\n            return cur_save,path\n        \n        ss = -1\n        pp = []\n        for last_pos in range(N):\n            if not last_pos:\n                last_pos_b = 1\n            else:\n                last_pos_b = last_pos_b << 1\n            if ss < DFS(last_pos_b,last_pos)[0]:\n                ss,pp = DFS(last_pos_b,last_pos)\n\n        res = A[pp[0]]\n        for i in range(1,N):\n            res += A[pp[i]][s[pp[i-1]][pp[i]]:]\n            \n        return res\n                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'shortestSuperstring'
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: 11978