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 = "# https://zxi.mytechroad.com/blog/searching/leetcode-943-find-the-shortest-superstring/\n# 将每个单词看作是一个节点, 两两之间有一条带有权重的有向路径, 权重表示为\n# g[i][j]: the cost of appending word[j] after word[i]\n# 如将 gcta 放在 catg 后面的 cost 为 3 因为它们有公共子串 g, 所以总长度只需要再增加 3\n# 问题转化为了在一个有向图里, 从任意点出发找到经过所有点各一次的最短路径\n# dp[s][i]: min cost to visit nodes of s and ends with i (s is a binary string)\n# dp[14][2] is the min cost of visit nodes 1, 2, 3 and ends with 2 (14 = 2^1 + 2^2 + 2^3)\n# 初始化 dp[2^i][i] = len(A[i]), visit A[i] cost len(A[i])\n# dp[s][i] = min(dp[s - 2^i][j] + g[j][i]), 找到所有的没有经过节点 i 的状态, 然后将 i 接在 j 后面\n# 结果是 min(dp[2^n - 1][*]), 遍历完了所有的点 (2^n - 1) 的最小 cost\n# 用 parent[2^i][i] 数组存储节点 i 的父节点, 以便回溯得到最终的字符串\n# O(n^2 * 2^n) time complexity, O(n * 2^n) space complexity\nclass Solution:\n    def shortestSuperstring(self, A: List[str]) -> str:\n        \n        def dist(s1, s2):\n            ans = 0\n            for k in range(min(len(s1), len(s2))):\n                if s1[len(s1) - k:] == s2[:k]:\n                    ans = len(s2) - k\n            return ans\n        \n        \n        n = len(A)\n        g = [[0] * n for _ in range(n)]\n        for i in range(n):\n            for j in range(i + 1, n):\n                g[i][j] = dist(A[i], A[j])\n                g[j][i] = dist(A[j], A[i])\n        \n        parent = [[-1] * n for _ in range(1 << n)]\n        dp = [[float('inf')] * n for _ in range(1 << n)]\n        for i in range(n):\n            dp[1 << i][i] = len(A[i])  # 初始化每个节点是第一个点的情况\n\n        for s in range(1, 1 << n):\n            for i in range(n):\n                if not (s & (1 << i)):  # 以点 i 作为结尾则状态 s 必须已经访问过 i, 所以 s 的第 i 位是 1\n                    continue\n                prev = s - (1 << i)  # 找到上一个状态\n                for j in range(n):  # 对于所有点, 尝试让它们作为上一个点\n                    if dp[prev][j] + g[j][i] < dp[s][i]:\n                        dp[s][i] = dp[prev][j] + g[j][i]\n                        parent[s][i] = j\n\n        end = dp[-1].index(min(dp[-1]))  # 找到遍历完所有点后的最小 cost 的最终节点\n        s = (1 << n) - 1  # 最终的状态\n        res = ''\n        while s:\n            prev = parent[s][end]\n            if prev < 0:  # 初始化 parent 为 -1, 小于 0 说明这个节点没有父节点\n                res = A[end] + res\n            else:\n                res = A[end][len(A[end]) - g[prev][end]:] + res\n            s &= ~ (1 << end)  # 上一个状态\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: 8950