Problem Statement

We have a grid with 2 rows and N columns. Let (i,j) denote the square at the i-th row from the top and j-th column from the left. (i,j) has a postive integer x_{i,j} written on it.
Two squares are said to be adjacent when they share a side.
A path from square X to Y is $a sequence (P_1, \ldots, P_n)$ of distinct squares such that P_1 = X, P_n = Y, and P_i and P_{i+1} are adjacent for every $1\leq i \leq n-1.$ Additionally, the weight of that path is the sum of integers written on $P_1, \ldots, P_n$.
For two squares X and Y, let f(X, Y) denote the minimum weight of a path from X to Y. Find the sum of f(X, Y) over all pairs of squares (X,Y), modulo 998244353.

Input

The input is given from Standard Input in the following format:
N
$x_{1,1} \ldots x_{1,N}$
$x_{2,1} \ldots x_{2,N}$

Output

Print the sum of f(X, Y) over all pairs of squares (X,Y), modulo 998244353.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq x_{i,j} \leq 10^9$

Sample Input 1

1
3
5

Sample Output 1

24

You should find the sum of the following four values.

• For X = (1,1), Y = (1,1): f(X, Y) = 3.
• For X = (1,1), Y = (2,1): f(X, Y) = 8.
• For X = (2,1), Y = (1,1): f(X, Y) = 8.
• For X = (2,1), Y = (2,1): f(X, Y) = 5.

Sample Input 2

2
1 2
3 4

Sample Output 2

76

Sample Input 3

5
1 1000000000 1 1 1
1 1 1 1000000000 1

Sample Output 3

66714886

见题面 Input 部分

见题面 Output 部分