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 = '# cook your dish here\n# cook your dish here\nhm={}\ndef gcd(a,b):\n    if b>a:\n        a,b=b,a\n    if b==0:\n        return a\n    else:\n        return gcd(b,a%b)\ndef gcd_list(l,n):\n    gcd1=l[0]\n    for i in range (1,n):\n        gcd1=gcd(gcd1,l[i])\n    return gcd1\n        \nfor _ in range (int(input())):\n    n=int(input())\n    x=[int(n) for n in input().split()]\n    l2=[]\n    l=list(set(x))\n    n=len(l)\n    if n>2:\n        hm={}\n        temp=[]\n        max1=max(l[0],l[1]) \n        max2=min(l[0],l[1]) \n        for i in range(2,len(l)): \n            if l[i]>max1: \n                max2=max1\n                max1=l[i] \n            else: \n                if l[i]>max2: \n                    max2=l[i] \n        m1=max1\n        m2=max2\n        l.remove(m1)\n        l.remove(m2)\n        gcd_1=l[0]\n        for i in range (1,n-2):\n            gcd_1=gcd(gcd_1,l[i])\n        s1=gcd(gcd_1,m2)+m1\n        s2=gcd(gcd_1,m1)+m2\n        print(max(s1,s2))\n    else:\n        if n==1:\n            print(l[0]*2)\n        else:\n            print(sum(l))\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)

```

Measured memory_bytes: 13995