Solve the programming task below in a Python markdown code block.
You are given an array A of length N. 

The *interesting value* of a subarray is defined as the product of the maximum and minimum elements of the subarray.

Find the minimum and maximum *interesting value* over all subarrays for the given array.

Note: A subarray is obtained by deletion of several (possibly zero) elements from the beginning of the array and several (possibly zero) elements from the end of the array.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- The first line of each test case contains an integer N - the length of the array A.
- The second line of each test case contains N space-separated integers A_{1},A_{2},\ldots,A_{N}.

------ Output Format ------ 

For each test case, output two space-separated integers on a new line the minimum and maximum *interesting value* over all subarrays for the given array.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$-10^{9} ≤ A_{i} ≤ 10^{9}$
- The sum of $N$ over all test cases won't exceed $3 \cdot 10^{5}$.

----- Sample Input 1 ------ 
2
2
2 2
3
5 0 9

----- Sample Output 1 ------ 
4 4
0 81
----- explanation 1 ------ 
Test case $1$: The minimum *interesting value* possible is $4$. A subarray with *interesting value* equal to $4$ is $[2,2]$. Here, both minimum and maximum elements of the subarray are $2$. It can be proven that no subarray of the array has *interesting value* less than $4$.  
The maximum *interesting value* possible is $4$. A subarray with *interesting value* equal to $4$ is $[2,2]$. Here, both minimum and maximum elements of the subarray are $2$. It can be proven that no subarray of the array has *interesting value* greater than $4$.

Test case $2$: The minimum *interesting value* possible is $0$. A subarray with *interesting value* equal to $0$ is $[5, 0, 9]$. Here, minimum element is $0$ and maximum element is $9$. It can be proven that no subarray of the array has *interesting value* less than $0$.  
The maximum *interesting value* possible is $81$. A subarray with *interesting value* equal to $81$ is $[9]$. Here, both minimum and maximum elements of the subarray are $9$. It can be proven that no subarray of the array has *interesting value* more than $81$.