Solve the programming task below in a Python markdown code block.
Let f be a function, such that, for an array A of size M, f(A) is defined as

f(A) = \sum_{i=1}^{M}\sum_{j=1, j \ne i}^{j=M} (A_{i}\cdot A_{j})

You are given an array C of size N. In one operation on the array, you can:
Choose an index i (1≤ i ≤ |C|)
Select two positive integers X and Y such that X+Y = C_{i}
Remove the element C_{i} from the array C
Insert the elements X and Y to the array C

Find the maximum value of f(C) that can be obtained using any (possibly zero) number of given operations. Since this value can be huge, output the answer modulo 998244353.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two lines of input.
- The first line of each test case contains an integer N, denoting the size of the array.
- The next line contains N space-separated integers C_{1}, C_{2}, \ldots, C_{N}, the elements of the array C.

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

For each test case, output on a new line, the maximum value of f(C) that can be obtained using any (possibly zero) number of given operations. Since this value can be huge, output the answer modulo 998244353.

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

$1 ≤ T ≤ 10^{3}$
$1 ≤ N ≤ 2\cdot 10^{5}$
$1 ≤ C_{i} ≤ 10^{9}$
- The sum of $N$ over all test cases won't exceed $2\cdot 10^{5}$.

----- Sample Input 1 ------ 
2
2
1 2
2
1 3

----- Sample Output 1 ------ 
6
12

----- explanation 1 ------ 
Test case $1$: Using one operation, we choose $i = 2$, set $X = 1$ and $Y = 1$, remove $2$ from the array, and insert $X$ and $Y$. Thus, the final array is $C = [1, 1, 1]$.  
Here, $f(C) = (A_{1}\cdot A_{2}) + (A_{1}\cdot A_{3}) + (A_{2}\cdot A_{1}) + (A_{2}\cdot A_{3}) + (A_{3}\cdot A_{1}) + (A_{3}\cdot A_{2}) = 1+1+1+1+1+1 = 6$. 

Test case $2$:
- Operation $1$: We choose $i = 2$, set $X = 1$ and $Y = 2$, remove $3$ from the array, and insert $X$ and $Y$. Thus, the final array is $C = [1, 1, 2]$.  
- Operation $2$: We choose $i = 3$, set $X = 1$ and $Y = 1$, remove $3$ from the array, and insert $X$ and $Y$. Thus, the final array is $C = [1, 1, 1, 1]$. 

Here, $f(C) = 12$.