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    # https://www.youtube.com/watch?v=u_Wc4jwrp3Q\n    # time: O(n^2 * 2 ^ n), space(n * 2 ^ n)\n    def shortestSuperstring(self, A: List[str]) -> str:\n        # add string t in the end of string s. cost = # of chars can't be merged.\n        def mergecost(s, t):\n            c = len(t)\n            for i in range(1, min(len(s), len(t))):\n                if s[len(s) - i:] == t[0:i]:\n                    c = len(t) - i\n            return c\n        \n        n = len(A)\n        cost = [[0 for _ in range(n)] for _ in range(n)]\n        for i in range(n):\n            for j in range(i + 1, n):\n                cost[i][j] = mergecost(A[i], A[j])\n                cost[j][i] = mergecost(A[j], A[i])\n        dp = [[float('inf') for _ in range(n)] for _ in range(1 << n)]\n        parent = [[-1 for _ in range(n)] for _ in range(1 << n)]\n        \n        for i in range(n):\n            dp[1 << i][i] = len(A[i])\n        \n        for s in range(1, 1 << n):\n            for i in range(n):\n                # s doesn't contain index i.\n                if not (s & (1 << i)):\n                    continue\n                # connect i to prev set.\n                prev = s - (1 << i)\n                for j in range(n):\n                    if dp[s][i] > dp[prev][j] + cost[j][i]:\n                        dp[s][i] = dp[prev][j] + cost[j][i]\n                        parent[s][i] = j\n        minCost, end = float('inf'), 0\n        for i in range(n):\n            if dp[-1][i] < minCost:\n                minCost = dp[-1][i]\n                end = i\n        # the state that all nodes are visited.\n        s = (1 << n) - 1\n        res = ''\n        while s:\n            prev = parent[s][end]\n            if prev < 0:\n                return A[end] + res\n            res = A[end][len(A[end]) - cost[prev][end]:] + res\n            s &= ~(1 << end)\n            end = prev\n        return res\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: 10054