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\ndef gh(a,b):\n    if len(a) and len(b):\n        x=a[0]\n        y=b[0]\n        for i in a[1:]:\n            x=gcd(x,i)\n        for i in b[1:]:\n            y=gcd(y,i)\n        return x+y\n    return 0\ndef abc(l):\n    s=2**len(l)\n    i=0\n    d="{0:0"+str(len(l))+"b}"\n    ans=0\n    while i<s:\n        x=d.format(i)\n        a=[]\n        b=[]\n        for j in range(len(l)):\n            if x[j]==\'1\':\n                a.append(l[j])\n            else:\n                b.append(l[j])\n        ans=max(ans,gh(a,b))\n        i+=1\n    return ans\n                \nimport random    \nfor _ in range(int(input())):\n    n=int(input())\n    l=list(map(int,input().split()))\n    #\n    d={}\n    for i in l:\n        try:\n            d[i]+=1\n        except:\n            d[i]=1\n    x=list(d.keys())\n    x.sort()\n    if len(x)==1:\n        print(2*l[0])\n    else:\n        ans=x[-1]\n        c=x[0]\n        for i in range(len(x)-1):\n            c=gcd(c,x[i])\n        vy=ans+c\n        ans=x[-2]\n        c=0\n        for i in range(len(x)-2):\n            c=gcd(c,x[i])\n        c=gcd(c,x[-1])\n        vx=ans+c\n        print(max(vx,vy))\n            \n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13841