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 $998244353$.

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.

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.