1183_F. Topforces Strikes Back
One important contest will take place on the most famous programming platform (Topforces) very soon!

The authors have a pool of n problems and should choose at most three of them into this contest. The prettiness of the i-th problem is a_i. The authors have to compose the most pretty contest (in other words, the cumulative prettinesses of chosen problems should be maximum possible).

But there is one important thing in the contest preparation: because of some superstitions of authors, the prettinesses of problems cannot divide each other. In other words, if the prettinesses of chosen problems are x, y, z, then x should be divisible by neither y, nor z, y should be divisible by neither x, nor z and z should be divisible by neither x, nor y. If the prettinesses of chosen problems are x and y then neither x should be divisible by y nor y should be divisible by x. Any contest composed from one problem is considered good.

Your task is to find out the maximum possible total prettiness of the contest composed of at most three problems from the given pool.

You have to answer q independent queries.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

The first line of the query contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of problems.

The second line of the query contains n integers a_1, a_2, ..., a_n (2 ≤ a_i ≤ 2 ⋅ 10^5), where a_i is the prettiness of the i-th problem.

It is guaranteed that the sum of n over all queries does not exceed 2 ⋅ 10^5.

Output

For each query print one integer — the maximum possible cumulative prettiness of the contest composed of at most three problems from the given pool of problems in the query.

Example

Input


3
4
5 6 15 30
4
10 6 30 15
3
3 4 6


Output


30
31
10
```python
from sys import stdin
from itertools import tee

def input():
    return stdin.readline()

def remove_divisors(x, xs):
    return [y for y in xs if y%xs != 0]


q = int(input())
for _ in range(q):
    n = int(input())
    aas = list(set(map(int,input().split())))
    aas.sort(reverse=True)
    # if len(aas) > 2 and aas[1]*2 > aas[0] and aas[2]*2 > aas[0]:
    #     print(sum(aas[0:3]))
    #     continue
    ulim2 = list(map(sum, zip(aas[:-1], aas[1:])))  + [0]
    ulim3 = list(map(sum, zip(aas[:-2], ulim2[1:]))) + [0,0]

    it1 = iter(zip(aas, ulim3, ulim2))

    answer = 0
    try:
        while True:
            a, u3, _ = next(it1)
            if u3 < answer:
                break
            it1, it2 = tee(it1)

            def f1(i):
                b, _, _ = i
                return a%b != 0

            it2 = filter(f1, it2)
            tsum = 0
            try:
                while True:
                    b, _, u2 = next(it2)
                    if u2 < tsum:
                        break
                    it2, it3 = tee(it2)

                    def f2(i):
                        c, _, _ = i
                        return b%c != 0

                    it3 = filter (f2 , it3)
                    c,_,_ = next(it3, (0,0,0))
                    tsum = max(tsum, b+c)
            except StopIteration:
                pass
            answer = max(answer, a + tsum)
    except StopIteration:
        pass
    print(answer)

```