G. Count Votingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere are n people that will participate in voting. Each person has exactly one vote.i-th person has a team t_i (1 \leq t_i \leq n) where t_i = t_j means i, j are in the same team. By the rules each person should vote for the person from the different team. Note that it automatically means that each person can't vote for himself.Each person knows the number of votes c_i he wants to get. How many possible votings exists, such that each person will get the desired number of votes? Due to this number can be big, find it by modulo 998\,244\,353.InputThe first line contains a single integer n (1 \leq n \leq 200) — the number of people.The second line contains n integers c_1, c_2, \ldots, c_n (0 \leq c_i \leq n) — desired number of votes. It is guaranteed, that \sum\limits_{i=1}^{n} c_i = n.The third line contains n integers t_1, t_2, \ldots, t_n (1 \leq t_i \leq n) — team numbers.OutputPrint a single integer — the number of possible votings by modulo 998\,244\,353.ExamplesInput
3
1 1 1
1 2 3
Output
2
Input
5
2 0 1 0 2
1 2 3 4 5
Output
10
Input
5
1 2 2 0 0
3 5 4 3 4
Output
5
NoteIn the first test there are two possible votings: (2, 3, 1), (3, 1, 2).In the third test there are five possible votings: (3, 3, 2, 2, 1), (2, 3, 2, 3, 1), (3, 3, 1, 2, 2), (3, 1, 2, 3, 2), (2, 3, 1, 3, 2).
3
1 1 1
1 2 3

2 
['combinatorics', 'dp', 'math', '*2600']