A14396. 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 $f(1, 2) = f(1, 3) = f(2, 3) = 6$ .