Products of Min-Max

AtCoder

IDarc116_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3
2 4 3

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: $63$.

Input #2

1
10

Output #2

Input #3

7
853983 14095 543053 143209 4324 524361 45154

Output #3

206521341

API Response (JSON)

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