A. Divide and Multiplytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output  William has array of n numbers a_1, a_2, \dots, a_n. He can perform the following sequence of operations any number of times:   Pick any two items from array a_i and a_j, where a_i must be a multiple of 2  a_i = \frac{a_i}{2}  a_j = a_j \cdot 2 Help William find the maximal sum of array elements, which he can get by performing the sequence of operations described above.InputEach 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.OutputFor each test case output the maximal sum of array elements after performing an optimal sequence of operations.ExampleInput
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
Output
50
46
10
26
35184372088846
NoteIn the first example test case the optimal sequence would be:   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].  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].  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.
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

50 46 10 26 35184372088846 
['greedy', 'implementation', 'math', 'number theory', '*900']