CF1554A Cherry

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 $ .

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 $ .

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

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 $ .