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 \le k \le n-1. Can you help him?

The first line of the input contains a single integer n (1 \le n \le 250)- the number of elements in the permutations.

The second line contains n integers, p1,p2,...,pn (0 \le pi \le 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 \le qi \le 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 \cdot 7 \cdot 17+1, which is a prime.

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: .