Problem Statement

You are given a permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$.

For each $K=0,1,\ldots,N-1$, find the number, modulo $998244353$, of trees with $N$ vertices numbered $1$ to $N$ that satisfy the following condition.

• Among the pairs of vertices $(u_i,v_i)\ (u_i < v_i)$ that are directly connected by an edge in the tree, exactly $K$ pairs satisfy $P_{u_i}>P_{v_i}$.

Constraints

• $2\leq N\leq 500$
• $P$ is a permutation of $(1,2,\ldots,N)$.

Input

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

N
P_1 P_2 \ldots P_N

Output

For each $K=0,1,\ldots,N-1$, print the number, modulo $998244353$, of trees that satisfy the condition, with spaces in between.