CF1781D.Many Perfect Squares
普及/提高-
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题目描述
You are given a set a1,a2,…,an of distinct positive integers.
We define the squareness of an integer x as the number of perfect squares among the numbers a1+x,a2+x,…,an+x .
Find the maximum squareness among all integers x between 0 and 1018 , inclusive.
Perfect squares are integers of the form t2 , where t is a non-negative integer. The smallest perfect squares are 0,1,4,9,16,… .
输入格式
Each test contains multiple test cases. The first line contains the number of test cases t ( 1≤t≤50 ). The description of the test cases follows.
The first line of each test case contains a single integer n ( 1≤n≤50 ) — the size of the set.
The second line contains n distinct integers a1,a2,…,an in increasing order ( 1≤a1<a2<…<an≤109 ) — the set itself.
It is guaranteed that the sum of n over all test cases does not exceed 50 .
输出格式
For each test case, print a single integer — the largest possible number of perfect squares among a1+x,a2+x,…,an+x , for some 0≤x≤1018 .
输入输出样例
输入#1
4 5 1 2 3 4 5 5 1 6 13 22 97 1 100 5 2 5 10 17 26
输出#1
2 5 1 2
说明/提示
In 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.