Chef has a sequence of positive integers $A_1, A_2, \ldots, A_N$. He wants to split this sequence into two non-empty (not necessarily contiguous) subsequences $B$ and $C$ such that $\mathrm{GCD}\,(B) + \mathrm{GCD}\,(C)$ is maximum possible. Help him find this maximum value.
Note: The greatest common divisor (GCD) of a sequence of positive integers is the largest positive integer that divides each element of this sequence. For example, the GCD of the sequence $(8, 12)$ is $4$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer — the maximum value of $\mathrm{GCD}\,(B) + \mathrm{GCD}\,(C)$.

-----Constraints-----
- $1 \le T \le 10$
- $2 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (20 points): $2 \le N \le 20$
Subtask #2 (80 points): original constraints

-----Example Input-----
1              
4                    
4 4 7 6                    

-----Example Output-----
9

-----Explanation-----
Example case 1: For example, the sequence $A$ can be divided into subsequences $B = (4, 4, 6)$ and $C = (7)$.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import math\r\n\r\ndef __starting_point():\r\n    for _ in range(int(input())):\r\n        n=int(input())\r\n        a=list(set(map(int, input().split())))\r\n        n=len(a)\r\n        flag=0\r\n        if n==1:\r\n            print(a[0]*2)\r\n        else:\r\n            Lgcd=[0]\r\n            Rgcd=[0]\r\n            for i in range(n):\r\n                gcd=math.gcd(Lgcd[i],a[i])\r\n                Lgcd.append(gcd)\r\n            a=a[::-1]\r\n            for i in range(n):\r\n                gcd=math.gcd(Rgcd[i],a[i])\r\n                Rgcd.append(gcd)\r\n            Rgcd=Rgcd[::-1]\r\n          \r\n            a=a[::-1]\r\n            ans=[]\r\n            for i in range(n):\r\n                gcd=a[i] + math.gcd(Lgcd[i],Rgcd[i+1])\r\n                ans.append(gcd)\r\n           # print(ans)\r\n            print(max(ans))\r\n            \r\n            \r\n                \r\n            \r\n                \r\n\r\n\r\n\r\n\r\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14159