Given a formal power series $F(x) = \displaystyle \sum_{i=0}^{n-1} f_ix^i$, satisfying $f_0 = 0$ and $f_1 \ne 0$. You need to find $G(x)$ such that $F(G(x)) \equiv x \pmod{x^n}$, and return the coefficients of $G$ modulo $998\,244\,353$.
Input
The first line contains an integer $N$.
The next line contains $N$ integers $f_0, f_1, \cdots, f_{n-1}$. It is guaranteed that $f_0 = 0$, $f_1 \ne 0$, and $0 \leq f_i < 998\,244\,353$ for each $i$.
Output
Output one line containing $N$ integers $g_0, g_1, \cdots, g_{n-1}$.
Examples
Input 1
6
0 9 0 2 2 8Output 1
0 443664157 0 842292446 315420128 301682335Subtasks
For all data, we have $1 \leq N \leq 200\,000$.
| Subtask | $N \leq $ |
|---|---|
| $1$ | $10$ |
| $2$ | $1\,000$ |
| $3$ | $3\,000$ |
| $4$ | $5\,000$ |
| $5$ | $10\,000$ |
| $6$ | $25\,000$ |
| $7$ | $50\,000$ |
| $8$ | $100\,000$ |
| $9$ | $150\,000$ |
| $10$ | $200\,000$ |