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 int2arr(self,x,n):\n        arr = []\n        x1 = x\n        for i in range(n):\n            arr.append(x1 % 2)\n            x1 = x1 // 2\n        return arr\n        \n    def arr2int(self,arr):\n        x=0\n        for i in range(len(arr)):\n            x+=arr[i]*2**i\n        return x\n    \n    \n    \n    def shortestSuperstring(self, A: List[str]) -> str:\n        n = len(A)\n        overlap={}\n        for i in range(n):\n            for j in range(n):\n                short = min(len(A[i]),len(A[j]))\n                for k in range(short,-1,-1):\n                    if A[i][(len(A[i])-k):(len(A[i]))]==A[j][0:k]:\n                        break\n                overlap[(i,j)]=k\n        #print(self.int2arr(7,5))\n        #print(self.arr2int([1, 1, 1, 0, 0]))\n        state_order = []\n        for i in range(0,n+2):\n            state_order.append([])\n        for i in range(0,2**(n)):\n            arr = self.int2arr(i,n)\n            #print(i,arr,sum(arr))\n            state_order[sum(arr)].append(i)\n        #print(state_order)\n        \n        m={}\n        conn={}\n        for i in range(n):\n            x = 2**i\n            m[x,i]=len(A[i])\n            conn[x,i]=A[i]\n        for l in range(2,n+1):\n            for x in state_order[l]:\n                arr = self.int2arr(x,n)\n                for end in range(n):\n                    if arr[end]==1:\n                        m[x,end]=100000\n                        x_prev = x-2**end\n                        arr_prev = self.int2arr(x_prev,n)\n                        for prev in range(n):\n                            if arr_prev[prev]==1 and m[x_prev,prev]+len(A[end])-overlap[prev,end]< m[x,end]:\n                                m[x,end] = m[x_prev,prev]+len(A[end])-overlap[prev,end]\n                                conn[x,end]=conn[x_prev,prev]+A[end][overlap[prev,end]:len(A[end])]\n                         \n        ans = 100000\n        for i in range(n):\n            if m[2**n-1,i]<ans:\n                ans = m[2**n-1,i]\n                ans_str = conn[2**n-1,i]\n        \n        return ans_str\n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n            \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \n        \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: 11702