B'An array a_1, ... ,a_n of length n is initially all blank. There are n updates where one entry of a is updated to some number, such that a becomes a permutation of 1,2, ... ,n after all the updates. After each update, find the number of ways (modulo 998 ,244 ,353 ) to fill in the remaining blank entries of a so that a becomes a permutation of 1,2, ... ,n and all cycle lengths in a are multiples of 3 . A permutation of 1,2, ... ,n is an array of length n consisting of n distinct integers from 1 to n in arbitrary order. A cycle in a permutation a is a sequence of pairwise distinct integers (i_1, ... ,i_k) such that i_2 = a_{i_1},i_3 = a_{i_2}, ... ,i_k = a_{i_{k-1}},i_1 = a_{i_k} . The length of this cycle is the number k , which is a multiple of 3 if and only if k equiv 0 pmod 3 . The first line contains a single integer n ( 3 <= n <= 3 cdot 10^5 , n equiv 0 pmod 3 ). The i -th of the next n lines contains two integers x_i and y_i , representing that the i -th update changes a_{x_i} to y_i . It is guaranteed that x_1, ... ,x_n and y_1, ... ,y_n are permutations of 1,2, ... ,n , i.e. a becomes a permutation of 1,2, ... ,n after all the updates. Output n lines: the number of ways (modulo 998 ,244 ,353 ) after the first 1,2, ... ,n updates. In the first sample, for example, after the 3 rd update the 3 ways to complete the permutation a = [4, _,2,5, _, _] are as follows: In the second sample, the first update creates a cycle of length 1 , so there are no ways to make all cycle lengths a multiple of 3 . '...