Cherry

题意翻译

给定长度为 $n$ 的序列 $a_1, a_2, \dots, a_n$，求： $$ \max_{1 \le l < r \le n}\left(\max_{i=l}^r a_i \times \min_{i=l}^r a_i\right) $$ 数据范围 $n \le 10^5$。

题目描述

You are given $ n $ integers $ a_1, a_2, \ldots, a_n $ . Find the maximum value of $ max(a_l, a_{l + 1}, \ldots, a_r) \cdot min(a_l, a_{l + 1}, \ldots, a_r) $ over all pairs $ (l, r) $ of integers for which $ 1 \le l < r \le n $ .

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10\,000 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ). The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^6 $ ). It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 3 \cdot 10^5 $ .

输出格式

For each test case, print a single integer — the maximum possible value of the product from the statement.

输入输出样例

输入样例 #1

4
3
2 4 3
4
3 2 3 1
2
69 69
6
719313 273225 402638 473783 804745 323328

输出样例 #1

12
6
4761
381274500335

说明

Let $ f(l, r) = max(a_l, a_{l + 1}, \ldots, a_r) \cdot min(a_l, a_{l + 1}, \ldots, a_r) $ . In the first test case, - $ f(1, 2) = max(a_1, a_2) \cdot min(a_1, a_2) = max(2, 4) \cdot min(2, 4) = 4 \cdot 2 = 8 $ . - $ f(1, 3) = max(a_1, a_2, a_3) \cdot min(a_1, a_2, a_3) = max(2, 4, 3) \cdot min(2, 4, 3) = 4 \cdot 2 = 8 $ . - $ f(2, 3) = max(a_2, a_3) \cdot min(a_2, a_3) = max(4, 3) \cdot min(4, 3) = 4 \cdot 3 = 12 $ . So the maximum is $ f(2, 3) = 12 $ . In the second test case, the maximum is $ f(1, 2) = f(1, 3) = f(2, 3) = 6 $ .