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 \(A\), \(B\), and \(C\) (\(1\le A\le B\le C\)). These
integers are supposed to be secret, so she will not directly reveal them to her
sister Bessie. Instead, she tells Bessie \(N\) (\(4\le N\le 7\)) distinct
integers \(x_1,x_2,\ldots,x_N\) (\(1\le x_i\le 10^9\)), claiming that each \(x_i\) is
one of \(A\), \(B\), \(C\), \(A+B\), \(B+C\), \(C+A\), or \(A+B+C\). 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).

Each input file will contain \(T\) (\(1\le T\le 100\)) test cases that should be
solved independently.

Problem credits: Benjamin Qi

SCORING

• In test cases 1-4, all \(x_i\) are at most \(50\).
• Test cases 5-6 satisfy \(N=7\).
• Test cases 7-15 satisfy no additional constraints.

Problem credits: Benjamin Qi

The first input line contains \(T\).

Each test case starts with \(N\), the number of integers Elsie gives to Bessie.

The second line of each test case contains \(N\) distinct integers
\(x_1,x_2,\ldots,x_N\).

For each test case, output the number of triples \((A,B,C)\) that are consistent
with the numbers Elsie presented.

riseoj 작성

출처 올림피아드 > USACO > 2020-2021 > US Open > Silver