Do You Know Your ABCs?#11235
Farmer John's cows have been holding a daily online gathering on the "mooZ" video meeting platform. For fun, they have invented a simple number game to play during the meeting to keep themselves entertained.
Elsie has three positive integers A, B, C~(1 \le A \le B \le C). These integers are supposed to be secret, so she will not directly reveal them to her sister Bessie. Instead, she tells Bessie distinct integers x_1, x_2, .., x_n~(1 \le x_i \le 10^9), claiming that each x_i is one of A, B, C, A + B, B + C, C + A, A + B + C. However, Elsie may be lying; the integers x_i might not correspond to any valid triple (A, B, C).
Bessie asked you to determine the number of triples (A, B, C) that are consistent with the numbers Elsie presented (possibly zero).
The first line contains the number of test cases t~(1 \le t \le 100).
Each test case starts with n~(4 \le n \le 7), the number of integers Elsie gives to Bessie.
The second line of each test case contains distinct integers x_1, x_2, .., x_n.
For each test case, output the number of triples (A, B, C) that are consistent with the numbers Elsie presented.
For x = \{4, 5, 7, 9\}, the five possible triples are as follows: (2, 2, 5), (2, 3, 4), (2, 4, 5), (3, 4, 5), (4, 5, 7).
Example 1