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 = "\n# we can memorize the path while doing dp\n# let dp[used][i] = (string length, actual string) represents the bitmask used ends with ith element.\n\nclass Solution:\n    def shortestSuperstring(self, A: List[str]) -> str:\n        n = len(A)\n        common = {}\n        for i, s1 in enumerate(A):\n            for j in range(i):\n                s2 = A[j]\n                longest1, longest2 = 0, 0\n                for k in range(min(len(s1), len(s2)) + 1):\n                    if s1.endswith(s2[:k]):\n                        longest1 = k\n                    if s2.endswith(s1[: k]):\n                        longest2 = k\n                common[(i, j)] = longest1\n                common[(j, i)] = longest2\n        \n        end = 1 << n\n        dp = [[(float('inf'), '') \n               for i in range(n)] for m in range(end)]\n        le, res = float('inf'), ''\n        for used in range(end):\n            for i, s in enumerate(A):\n                if (used >> i) & 1 != 1:\n                    continue\n                mask = 1 << i\n                if used ^ mask == 0:\n                    dp[used][i] = (len(A[i]), A[i])\n                else:\n                    for j, last in enumerate(A):\n                        if i == j or (used >> j) & 1 != 1:\n                            continue\n                        l, pref = dp[used ^ mask][j]\n                        cand = pref + A[i][common[(j, i)] :]    \n                        if len(cand) < dp[used][i][0]:\n                            dp[used][i] = (len(cand), cand)\n                if used == end - 1 and dp[used][i][0] < le:\n                    le, res = dp[used][i]\n        return res\n\n\n# class Solution:\n    \n#     def addCost(self, from_word, to_word):\n#         n = min(len(from_word), len(to_word))\n#         cost = len(to_word)\n#         for i in range(n):\n#             if from_word[-i-1] == to_word[i]:\n#                 cost -= 1\n#         return cost \n    \n#     def shortestSuperstring(self, A: List[str]) -> str:\n#         # initalize 2D adjacency matrix\n#         n = len(A)\n#         adj_mat = [[0,] * n, ] * n\n#         # travers words list, memo the cost by adj_mat\n#         for i in range(n):\n#             for j in range(n):\n#                 if r != c:\n#                     from_word, to_word = A[i], A[j]\n#                     adj_mat[i][j] = self.addCost(from_word, to_word)\n#         # DP memo, the length of start words as the initial values \n#         # dp = [len(w) for w in A] * n \n#         dp = [0, ] * n\n#         for i, w in enumerate(A):\n#             visited = {w}\n#             dp[i] = len(w)\n#             while len(visited) < n:\n#                 from_w = w\n#                 to_w = min(adj_mat[from_w])\n                \n        \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: 10716