E. Centroid Probabilitiestime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider every tree (connected undirected acyclic graph) with n vertices (n is odd, vertices numbered from 1 to n), and for each 2 \le i \le n the i-th vertex is adjacent to exactly one vertex with a smaller index.For each i (1 \le i \le n) calculate the number of trees for which the i-th vertex will be the centroid. The answer can be huge, output it modulo 998\,244\,353.A vertex is called a centroid if its removal splits the tree into subtrees with at most (n-1)/2 vertices each.InputThe first line contains an odd integer n (3 \le n < 2 \cdot 10^5, n is odd) — the number of the vertices in the tree.OutputPrint n integers in a single line, the i-th integer is the answer for the i-th vertex (modulo 998\,244\,353).ExamplesInput
3
Output
1 1 0 
Input
5
Output
10 10 4 0 0 
Input
7
Output
276 276 132 36 0 0 0 
NoteExample 1: there are two possible trees: with edges (1-2), and (1-3) — here the centroid is 1; and with edges (1-2), and (2-3) — here the centroid is 2. So the answer is 1, 1, 0.Example 2: there are 24 possible trees, for example with edges (1-2), (2-3), (3-4), and (4-5). Here the centroid is 3.
3

1 1 0  
['combinatorics', 'dp', 'fft', 'math', '*3000']