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B - Products of Min-Max /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

ただし、答えは非常に大きくなる場合があるので、 998244353 で割った余りを答えてください。

### 制約

• 入力は全て整数
• 1 \leq N \leq 2 \times 10^5
• 0 \leq A_i \leq 998244352

### 入力

N
A_1 A_2 \cdots A_N


### 入力例 1

3
2 4 3


### 出力例 1

63


B として、以下の 7 つが考えられます。

• 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

### 入力例 2

1
10


### 出力例 2

100


### 入力例 3

7
853983 14095 543053 143209 4324 524361 45154


### 出力例 3

206521341


Score : 400 points

### 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


### 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