310090: CF1781D. Many Perfect Squares
Memory Limit:512 MB
Time Limit:4 S
Judge Style:Text Compare
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Description
Many Perfect Squares
题意翻译
有 $n$ 个数 $(1 \le n \le 50)$ 。 它们分别是 $a_1,a_2,...,a_n$ 。你需要选择一个数 $x$ ,使得 $x$ 在 $0$ 至 $10^{18}$ 之内,并且 $a_1 + x,a_2 + x,a_3 + x ... a_n +x$ 中有尽可能多的完全平方数。询问当 $x$ 最优时,有多少个数是完全平方数。题目描述
You 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 $ .输入输出格式
输入格式
Each 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 $ .
输出格式
For 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} $ .
输入输出样例
输入样例 #1
4
5
1 2 3 4 5
5
1 6 13 22 97
1
100
5
2 5 10 17 26
输出样例 #1
2
5
1
2