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 = "INF = 1 << 60\nclass Solution:\n    def shortestSuperstring(self, A: List[str]) -> str:\n        n = len(A)\n        \n        # calculate overlap\n        overlap = [[0] * n for _ in range(n)]\n        for i, j in product(range(n), repeat = 2):\n            l = min(len(A[i]), len(A[j]))\n            overlap[i][j] = max(k for k in range(l + 1) if A[i][len(A[i]) - k:] == A[j][:k])\n        \n        # TSP\n        dp = [[INF] * n for _ in range(1 << n)]\n        prev = [[(None, None)] * n for _ in range(1 << n)]\n        \n        for i, S in enumerate(A):\n            dp[1 << i][i] = len(S)\n        \n        for U, i in product(range(1 << n), range(n)):\n            if not U >> i & 1:\n                continue\n            for ni in range(n):\n                if U >> ni & 1:\n                    continue\n                if dp[U | 1 << ni][ni] > dp[U][i] + len(A[ni]) -  overlap[i][ni]:\n                    dp[U | 1 << ni][ni] = dp[U][i] + len(A[ni]) -  overlap[i][ni]\n                    prev[U | 1 << ni][ni] = (U, i)\n        \n        U, i = (1 << n) - 1, min(range(n), key = lambda i : dp[-1][i])\n        res = []\n        while U is not None:\n            res.append(A[i])\n            U, i = prev[U][i]\n        res.reverse()\n        \n        ans = ''\n        for S in res:\n            l = min(len(ans), len(S))\n            k = max(k for k in range(l + 1) if ans[len(ans) - k:] == S[:k])\n            ans += S[k:]\n        return ans"
_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: 10793