A. Cherry
greedy
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 \(f(1, 2) = f(1, 3) = f(2, 3) = 6\).