Divide and Multiply

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). Description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ $$$(1 \le n \le 15)$$$, the number of elements in William's array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ $$$(1 \le a_i < 16)$$$, the contents of William's array.

Output:

For each test case output the maximal sum of array elements after performing an optimal sequence of operations.

Sample Input:

5
3
6 4 2
5
1 2 3 4 5
1
10
3
2 3 4
15
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

Sample Output:

50
46
10
26
35184372088846

Note:

In the first example test case the optimal sequence would be:

1. Pick $$$i = 2$$$ and $$$j = 1$$$. After performing a sequence of operations $$$a_2 = \frac{4}{2} = 2$$$ and $$$a_1 = 6 \cdot 2 = 12$$$, making the array look as: [12, 2, 2].
2. Pick $$$i = 2$$$ and $$$j = 1$$$. After performing a sequence of operations $$$a_2 = \frac{2}{2} = 1$$$ and $$$a_1 = 12 \cdot 2 = 24$$$, making the array look as: [24, 1, 2].
3. Pick $$$i = 3$$$ and $$$j = 1$$$. After performing a sequence of operations $$$a_3 = \frac{2}{2} = 1$$$ and $$$a_1 = 24 \cdot 2 = 48$$$, making the array look as: [48, 1, 1].

The final answer $$$48 + 1 + 1 = 50$$$.

In the third example test case there is no way to change the sum of elements, so the answer is $$$10$$$.