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        # 20*2**12 = 4092*20 = 80000\n        N = len(A)\n        cost = [\n            [0]*N for _ in range(N)\n        ]\n        for i in range(N):\n            for j in range(N):\n                # cost of adding A[j] to A[i]\n                cost[i][j] = math.inf\n                for k in range(len(A[i])):\n                    if A[j].startswith(A[i][k:]):\n                        cost[i][j] = k+len(A[j])-len(A[i])\n                        break\n                if cost[i][j] == math.inf:\n                    cost[i][j] = len(A[j])\n                    \n        dp = [[math.inf for _ in range(1<<N)] for i in range(N)]\n        for i in range(N):\n            dp[i][1<<i] = len(A[i])\n        backtrack = [\n            [None]*(1<<N) for _ in range(N)\n        ]\n        for i in range(N):\n            backtrack[i][1<<i] = (i, 0)\n            \n        for i in range(1<<N):\n            for j in range(N):\n                if i&(1<<j):\n                    for k in range(N):\n                        if i&(1<<k) and i!=k:\n                            if dp[j][i] > dp[k][i^(1<<j)]+cost[k][j]:\n                                dp[j][i] = dp[k][i^(1<<j)]+cost[k][j]\n                                backtrack[j][i] = (k, i^(1<<j))\n        min_cost = math.inf\n        min_index = -1\n        for i in range(N):\n            if min_cost > dp[i][(1<<N)-1]:\n                min_cost = dp[i][(1<<N)-1]\n                min_index = i\n        mask = (1<<N)-1\n        order = []\n        while mask:\n            order.append(min_index)\n            min_index, mask = backtrack[min_index][mask]\n        order.reverse()\n        \n        answer = []\n        last_i = -1\n        for i in order:\n            if len(answer) == 0:\n                answer.append(A[i])\n            else:\n                answer.append(A[i][-cost[last_i][i]:])\n            last_i = i\n        return ''.join(answer)"
_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: 9089