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 $n$ 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 $(A, B, C)$. This is too hard for Bessie to wrap her head around, so it is up to you to determine the number of triples $(A, B, C)$ that are consistent with the numbers Elsie presented (possibly zero). \InputFile 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 $n$ distinct integers $x_1, x_2, .., x_n$. \OutputFile For each test case, output the number of triples $(A, B, C)$ that are consistent with the numbers Elsie presented. \Examples For $x = \{4, 5, 7, 9\}$, the five possible triples are as follows: $(2, 2, 5), (2, 3, 4), (2, 4, 5), (3, 4, 5), (4, 5, 7)$.