Migrated from Lutece 2962 Redcrown's math problem II

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Description

You are given five integer sequences $A=(A_1,...,A_n),B=(B_1,...,B_n),C=(C_1,...,C_n),D=(D_1,...,D_n),E=(E_1,...,E_n)$ of length $n$.

Find the following value modulo 998244353.

$\sum^n_{i=1} \sum^n_{j=1} \sum^n_{k=1} \sum^n_{l=1} \sum^n_{m=1} \operatorname{med}(A_i,B_j,C_k,D_l,E_m)$

Here, $\operatorname{med}(a,b,c,d,e)$ represents the median of $a,b,c,d,e$.

Input

Input consist of $6$ lines.

The first line contains one integer number $n$ indicate the length of five integer sequences.

Each line of the following five lines contains $n$ integer numbers, indicate a sequence.

Output

Print the answer.

Samples

1
1
2
3
4
5

3

3
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2

486

Constraints

It's guaranteed that $1 \le n \le 10^5$ , $0 \le A_i,B_i,C_i,D_i,E_i \le 10^9$

Resources

2023暑期前集训第一次队内赛