Given an $N$-variable polynomial $\displaystyle s(x _ 0, x _ 1, \dots, x _ {N - 1}) = \sum _ {i = 0} ^ {2 ^ N - 1} b _ i \prod _ {k = 0} ^ {N - 1} x _ k ^ {i _ k} \in \mathbb{F} _ {998244353} \lbrack x _ 0, x _ 1, \dots, x _ {N - 1} \rbrack$.
Here, $i_k$ represents the number in the $2 ^ k$'s place when $i$ is expressed in binary.
Print $c _ 0, c _ 1, \dots, c _ {2 ^ N - 1} ~ (0 \leq c _ i \lt 998244353)$ satisfying

$\sum _ {m = 0} ^ N \frac{s(x _ 0, x _ 1, \dots, x _ {N - 1})^m}{m!} \equiv \sum _ {i = 0} ^ {2 ^ N - 1} c _ i \prod _ {k = 0} ^ {N - 1} x _ k ^ {i _ k} \pmod{(x _ 0 ^ 2, x _ 1 ^ 2, \dots, x _ {N - 1} ^ 2)}$

$N$
$b_0$ $b_1$ $\cdots$ $b_{2^N-1}$

$c_0$ $c_1$ $\cdots$ $c_{2^N-1}$

- $0 \leq N \leq 20$
- $0 \leq b_i \lt 998244353$
- $b_0 = 0$