Problem Statement

You are given a sequence $(A_1, A_2, \ldots , A_N)$. Let us define a sequence $(F_0, F_1, \ldots , F_N)$ by the following formulae.

• $F_0 = 1$
• $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j$ $(1 \leq n \leq N)$

Find $F_1, \ldots , F_N$ modulo $998244353$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i < 998244353$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print $F_1, \ldots , F_N$ modulo $998244353$ in this order, with spaces in between.