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 = "from math import gcd\r\n\r\n__author__ = 'Prateek'\r\n\r\n\r\ndef test():\r\n    n = int(input())\r\n    a = list(map(int, input().split()))\r\n    a = list(set(a))\r\n    n = len(a)\r\n    if len(a) == 1:\r\n        print(2 * a[0])\r\n        return\r\n    g1 = [0 for i in range(n)]\r\n    g2 = [0 for i in range(n)]\r\n    g1[0] = a[0]\r\n    g2[n - 1] = a[n - 1]\r\n    for i in range(1, n):\r\n        g1[i] = gcd(g1[i - 1], a[i])\r\n    for i in range(n - 2, -1, -1):\r\n        g2[i] = gcd(g2[i + 1], a[i])\r\n    ans = 0\r\n    for i in range(n):\r\n        if i == 0:\r\n            ans = max(ans, g2[i + 1] + a[i])\r\n        elif i == n - 1:\r\n            ans = max(ans, g1[i - 1] + a[i])\r\n        else:\r\n            ans = max(ans, gcd(g1[i - 1], g2[i + 1]) + a[i])\r\n    print(ans)\r\n\r\n\r\nif __author__ == 'Prateek':\r\n    t = int(input())\r\n    for _ in range(t):\r\n        test()\r\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12983