Organizing a Music Festival

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1\le n,\,m\le 100$$$) — the number of singers and the number of friends correspondingly.

The $$$i$$$-th of the next $$$m$$$ lines contains the integer $$$q_i$$$ ($$$1\le q_i\le n$$$) — the number of favorite singers of the $$$i$$$-th friend – followed by the $$$q_i$$$ integers $$$s_{i,1}, \, s_{i, 2}, \, \dots, \,s_{i, q_i}$$$ ($$$1\le s_{i,1}<s_{i,2}<\cdots<s_{i,q_i}\le n$$$) — the indexes of his favorite singers.

Output:

Print the number of valid orderings of the singers modulo $$$998\,244\,353$$$.

Sample Input:

3 1
2 1 3

Sample Output:

4

Sample Input:

5 5
2 1 2
2 2 3
2 3 4
2 4 5
2 1 5

Sample Output:

0

Sample Input:

100 1
1 50

Sample Output:

35305197

Sample Input:

5 1
5 1 2 3 4 5

Sample Output:

120

Sample Input:

2 5
1 2
1 2
1 2
1 1
1 1

Sample Output:

2

Sample Input:

11 4
5 4 5 7 9 11
2 2 10
2 9 11
7 1 2 3 5 8 10 11

Sample Output:

384

Note:

Explanation of the first sample: There are $$$3$$$ singers and only $$$1$$$ friend. The friend likes the two singers $$$1$$$ and $$$3$$$. Thus, the $$$4$$$ valid orderings are:

• 1 3 2
• 2 1 3
• 2 3 1
• 3 1 2

Explanation of the second sample: There are $$$5$$$ singers and $$$5$$$ friends. One can show that no ordering is valid.

Explanation of the third sample: There are $$$100$$$ singers and only $$$1$$$ friend. The friend likes only singer $$$50$$$, hence all the $$$100!$$$ possible orderings are valid.

Explanation of the fourth sample: There are $$$5$$$ singers and only $$$1$$$ friend. The friend likes all the singers, hence all the $$$5!=120$$$ possible orderings are valid.