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, p 1 , p 2 , ..., p n ( 0 ≤ p i ≤ 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, q 1 , q 2 , ..., q n ( 0 ≤ q i ≤ 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 = 2 23 ·7·17 + 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: .