201161: [AtCoder]ARC116 B - Products of Min-Max

Problem Statement

Given is a sequence $A$ of $N$ integers. There are $2^N - 1$ non-empty subsequences $B$ of $A$. Find the sum of $\max\left(B\right) \times \min\left(B\right)$ over all of them.

Since the answer can be enormous, report it modulo $998244353$.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 998244352$

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

Sample Input 1

3
2 4 3

Sample Output 1

63

There are $7$ subsequences $B$, as follows:

• $B = \left(2\right)$ : $\max\left(B\right) \times \min\left(B\right) = 4$
• $B = \left(4\right)$ : $\max\left(B\right) \times \min\left(B\right) = 16$
• $B = \left(3\right)$ : $\max\left(B\right) \times \min\left(B\right) = 9$
• $B = \left(2, 4\right)$ : $\max\left(B\right) \times \min\left(B\right) = 8$
• $B = \left(2, 3\right)$ : $\max\left(B\right) \times \min\left(B\right) = 6$
• $B = \left(4, 3\right)$ : $\max\left(B\right) \times \min\left(B\right) = 12$
• $B = \left(2, 4, 3\right)$ : $\max\left(B\right) \times \min\left(B\right) = 8$

The answer is the sum of them: $63$.

Sample Input 2

1
10

Sample Output 2

100

Sample Input 3

7
853983 14095 543053 143209 4324 524361 45154

Sample Output 3

206521341