Distance

题号：NC255137
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 512 M，其他语言1024 M
64bit IO Format: %lld

题目描述

For the two multisets $A$ and $B$ , In an operation, we can choose one between the following two operations:

1. Update an element $a_i$ in the multiset $A$ , to $a_i=a_i+1$

2. Update an element $b_i$ in the multiset $B$ , to $b_i=b_i+1$

We define $C(A,B)$ as the minimum number of operations to make the multisets $A$ and $B$ identical,meaning that both multisets have the same elements, If there is no way to transform multisets $A$ and $B$ into the same multiset, then $C(A,B)=0$ .

Now you have two multisets $S$ and $T$ , and calc the value of $\sum\limits_{A\subseteq S}\sum\limits_{B\subseteq T}C(A,B)$ modulo $998244353$ .

Note: Subsets in the multiset are allowed to duplicate values, that is, the number of solutions selected from each of the two sets $S$ and $T$ is $(2^{|S|}-1)(2^{|T|}-1)$ .

输入描述:

The first line contains a positive integer ,representing the size of the multiset  and the multiset  .

The second line contains a line of  positive integers , representing the multiset .

The third line contains a line of  positive integers , representing the multiset .

The input sequence is not guaranteed to be ordered.

输出描述:

Output a line with a integer representing the answer, modulo .

示例1

输入

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2
1 2
1 1

输出

复制

说明

A={2} B={1} C(A,B)=1
A={2} B={1} C(A,B)=1
A={1 2} B={1 1} C(A,B)=1

示例2

输入

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3
1 2 2
1 1 3

输出

复制