1776: Complete the Permutations
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
ZS the Coder is given two permutations p and q of {1,2,...,n}, but some of their elements are replaced with 0. The distance between two permutations p and q is defined as the minimum number of moves required to turn p into q. A move consists of swapping exactly 2 elements of p.
ZS the Coder wants to determine the number of ways to replace the zeros with positive integers from the set {1,2,...,n} such that p and q are permutations of {1,2,...,n} and the distance between p and q is exactly k.
ZS the Coder wants to find the answer for all 0≤k≤n-1. Can you help him?
The first line of the input contains a single integer n (1≤n≤250)− the number of elements in the permutations.
The second line contains n integers, p1,p2,...,pn (0≤pi≤n)− the permutation p. It is guaranteed that there is at least one way to replace zeros such that p is a permutation of {1,2,...,n}.
The third line contains n integers, q1,q2,...,qn (0≤qi≤n)− the permutation q. It is guaranteed that there is at least one way to replace zeros such that q is a permutation of {1,2,...,n}.
Print n integers, i-th of them should denote the answer for k=i-1. Since the answer may be quite large, and ZS the Coder loves weird primes, print them modulo 998244353=223·7·17+1, which is a prime.
3
1 0 0
0 2 0
1 2 1
4
1 0 0 3
0 0 0 4
0 2 6 4
6
1 3 2 5 4 6
6 4 5 1 0 0
0 0 0 0 1 1
4
1 2 3 4
2 3 4 1
0 0 0 1
In the first sample case, there is the only way to replace zeros so that it takes 0 swaps to convert p into q, namely p=(1,2,3),q=(1,2,3).
There are two ways to replace zeros so that it takes 1 swap to turn p into q. One of these ways is p=(1,2,3),q=(3,2,1), then swapping 1 and 3 from p transform it into q. The other way is p=(1,3,2),q=(1,2,3). Swapping 2 and 3 works in this case.
Finally, there is one way to replace zeros so that it takes 2 swaps to turn p into q, namely p=(1,3,2),q=(3,2,1). Then, we can transform p into q like following: 
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