D. Many Perfect Squarestime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given a set a_1, a_2, \ldots, a_n of distinct positive integers.We define the squareness of an integer x as the number of perfect squares among the numbers a_1 + x, a_2 + x, \ldots, a_n + x.Find the maximum squareness among all integers x between 0 and 10^{18}, inclusive.Perfect squares are integers of the form t^2, where t is a non-negative integer. The smallest perfect squares are 0, 1, 4, 9, 16, \ldots.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 50). The description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 50) — the size of the set.The second line contains n distinct integers a_1, a_2, \ldots, a_n in increasing order (1 \le a_1 < a_2 < \ldots < a_n \le 10^9) — the set itself.It is guaranteed that the sum of n over all test cases does not exceed 50.OutputFor each test case, print a single integer — the largest possible number of perfect squares among a_1 + x, a_2 + x, \ldots, a_n + x, for some 0 \le x \le 10^{18}.ExampleInput
451 2 3 4 551 6 13 22 97110052 5 10 17 26Output
2
5
1
2
NoteIn the first test case, for x = 0 the set contains two perfect squares: 1 and 4. It is impossible to obtain more than two perfect squares.In the second test case, for x = 3 the set looks like 4, 9, 16, 25, 100, that is, all its elements are perfect squares.
451 2 3 4 551 6 13 22 97110052 5 10 17 26
2 5 1 2 
['brute force', 'math', 'number theory', '*1800']