Problem Statement

You are given $N$ sets $A_1,$ $A_2,$ $\dots,$ $A_N$.
The set $A_i$ $(1 \le i \le N)$ has $k_i$ elements, and the set $A_i$ is $\{C_{i,1},$ $C_{i,2},$ $\dots,$ $C_{i,k_i}\}$.
Among the $2^N-1$ ways to choose $1$ or more of the $N$ sets, how many ways are there such that the intersection (common part) of all the chosen sets is the empty set?
Since the answer can be very large, output it modulo $998244353$.

Input

$N$
$k_1$ $C_{1,1}$ $\dots$ $C_{1,k_1}$
$k_2$ $C_{2,1}$ $\dots$ $C_{2,k_2}$
$\vdots$
$k_N$ $C_{N,1}$ $\dots$ $C_{N,k_N}$

• $1 \le N \le 500$
  
• $0 \le k_i \le 12$
  
• $1 \le C_{ij} \le 12$
  
• $C_{i,1},$ $C_{i,2},$ $\dots,$ $C_{i,k_i}$ are pairwise distinct
  
• All inputs are integers

Output

Output, modulo $998244353$, the number of ways among the $2^N-1$ ways to choose such that the intersection of all the chosen sets is the empty set. Print a newline at the end.

Sample

3
2 1 2
2 1 3 
2 2 3

1

4
0
0
0
0

15

32
5 1 2 3 4 5
4 1 2 3 4
4 1 2 3 5
4 1 2 4 5 
4 1 3 4 5
4 2 3 4 5
3 1 2 3
3 1 2 4
3 1 2 5
3 1 3 4
3 1 3 5
3 1 4 5
3 2 3 4
3 2 3 5
3 2 4 5
3 3 4 5
2 1 2 
2 1 3
2 1 4
2 1 5
2 2 3
2 2 4
2 2 5
2 3 4
2 3 5
2 4 5
1 1 
1 2
1 3
1 4
1 5
0

301664622