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}.

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.

Constraints

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

Sample Input 1

3
1 3 2

Sample Output 1

1 2 0

The answer for K=0 is 1: the tree with edges connecting vertices 1,2 and 1,3. Indeed, P_1 < P_2 and P_1<P_3.
The answer for K=1 is 2: the tree with edges connecting vertices 1,2 and 2,3, and another with edges connecting vertices 1,3 and 2,3. Indeed, in the tree with edges connecting vertices 1,2 and 2,3, we have P_1 < P_2, P_2>P_3.

Sample Input 2

10
3 1 4 10 8 6 9 2 7 5

Sample Output 2

294448 2989776 12112684 25422152 30002820 20184912 7484084 1397576 108908 2640

见题面 Input 部分

见题面 Output 部分