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Alexander has recently achieved ridiculously high rating on Chessforces competition website. Alexander's coach challenged him with a difficult problem so that Alexander could truly prove his mettle.
Consider an $n \times n$ chessboard. A bishop is a chess piece that attacks all positions sharing a diagonal with it. A non-attacking configuration is an arrangement of several bishops on the chessboard such that no two bishops occupy the same position, and no bishop attacks any other.
Alexander has to count the number of non-attacking bishop configurations with exactly $k$ bishops for each $k$ from $1$ to $2n - 1$. Since the answers can be large, each number has to be computed modulo a completely random number $998\,244\,353$.
The first line contains a single integer $n$ ($1 \leq n \leq 10^5$).
Print $2n - 1$ integers. The $k$-th of these integers should be the number (modulo $998\,244\,353$) of non-attacking configurations of exactly $k$ bishops on an $n \times n$ chessboard.
4 4 0
9 26 26 8 0
100 4380 110960 1809464 20014112 154215760 837543200 214861037 625796024 941559921 770927213 837612209 756883449 146369278 295974400 17275136 246784 1024 0