Problem Statement

You are given integer sequences of length N: $A=(A_1,A_2,\cdots,A_N), B=(B_1,B_2,\cdots,B_N), X=(X_1,X_2,\cdots,X_N)$, and $Y=(Y_1,Y_2,\cdots,Y_N). Here, A$ and B satisfy the following properties:

• A_1=1.
• B_1=2.
• $(A_1,A_2,\cdots,A_N,B_1,B_2,\cdots,B_N)$ is a permutation of $(1,2,\cdots,2N)$.

Define the integers $d_{i,j} (1 \leq i,j \leq N)$ as follows:

• d_{1,1}=0.
• If $(i,j) \neq (1,1)$ and A_i<B_j, then d_{i,j}=d_{i,j-1}+X_i.
• If $(i,j) \neq (1,1)$ and A_i>B_j, then d_{i,j}=d_{i-1,j}+Y_j.

Find $\sum_{1 \leq i \leq N}\sum_{1 \leq j \leq N}d_{i,j}, modulo 998244353$.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$
$B_1 B_2 \cdots B_N$
$X_1 X_2 \cdots X_N$
$Y_1 Y_2 \cdots Y_N$

Output

Print the answer.

Constraints

• $2 \leq N \leq 250000$
• A_1=1
• B_1=2
• $(A_1,A_2,\cdots,A_N,B_1,B_2,\cdots,B_N)$ is a permutation of $(1,2,\cdots,2N)$.
• $1 \leq X_i \leq 10^9$
• $1 \leq Y_i \leq 10^9$
• All input values are integers.

Sample Input 1

2
1 4
2 3
2 2
1 3

Sample Output 1

8

The values of d_{i,j} are as follows:

• d_{1,1}=0
• d_{1,2}=d_{1,1}+X_1=0+2=2
• d_{2,1}=d_{1,1}+Y_1=0+1=1
• d_{2,2}=d_{1,2}+Y_2=2+3=5

Thus, the answer is 0+2+1+5=8.

Sample Input 2

3
1 3 5
2 6 4
1 10 100
1000 10000 100000

Sample Output 2

108153

Sample Input 3

3
1 6 5
2 4 3
1 10 100
1000 10000 100000

Sample Output 3

333009

Sample Input 4

10
1 17 4 7 16 18 9 3 12 6
2 19 20 14 5 11 13 8 15 10
744280520 249168130 239276621 320064892 910500852 164832983 245532751 198319687 715892722 967824729
769431650 80707350 459924868 257261830 777045524 583882654 950300099 438099970 322288793 532405020

Sample Output 4

746075419

见题面 Input 部分

见题面 Output 部分