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 = 'def gcd(a,b):\n    if b==0:\n        return a\n    else:\n        return gcd(b,a%b)\n\n\nt=int(input())\nfor _ in range(t):\n    n=int(input())\n    l=list(map(int,input().split()))\n    l=list(set(l))\n    n=len(l)\n    if(len(l)==1):\n        print(l[0]*2)\n    p=[0 for x in range(n)]\n    s=[0 for x in range(n)]\n    ans1=0\n    p[0]=l[0]\n    for i in range(1,n):\n        p[i]=gcd(l[i],p[i-1])\n    s[n-1]=l[n-1]\n    for i in range(n-2,-1,-1):\n        s[i]=gcd(l[i],s[i+1])\n    #print(p)\n    #print(s)\n    for i in range(n):\n        if(i==0):\n            ans=s[i+1]+l[0]\n        elif(i==n-1):\n            ans=p[n-2]+l[n-1]\n        else:\n            ans=gcd(p[i-1],s[i+1])+l[i]\n        #print(ans)\n        ans1=max(ans1,ans)\n    print(ans1)\n    '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13835