Problem Statement

There is a rooted tree with N vertices numbered 1 to N. Vertex 1 is the root, and the parent of vertex $i (2\leq i\leq N)$ is P_i.
You are given a non-negative integer r and a sequence of $non-negative integers A = (A_1, \ldots, A_N).$ You can perform the following operation on the sequence any number of times, possibly zero.

• Choose an i such that $i\geq 2$ and $A_i \geq 1. Replace A_i$ with A_i - 1 and A_{P_i} with A_{P_i}+r.

Find the number, modulo 998244353, of possible final states of the sequence A.

Input

The input is given from Standard Input in the following format:
N
$P_2 \ldots P_N$
r
$A_1 \ldots A_N$

Output

Print the number, modulo 998244353, of possible final states of the sequence A.

Constraints

• $2\leq N\leq 300$
• $1\leq P_i \leq i - 1 (2\leq i\leq N)$
• $0\leq r \leq 10^9$
• $0\leq A_i \leq 10^9$

Sample Input 1

3
1 1
2
1 1 1

Sample Output 1

4

The four possible final states of A are (1,1,1), (3,0,1), (3,1,0), and (5,0,0).

Sample Input 2

3
1 2
1
1 1 1

Sample Output 2

5

The five possible final states of A are (1,1,1), (1,2,0), (2,0,1), (2,1,0), and (3,0,0).

Sample Input 3

3
1 2
2
1 1 1

Sample Output 3

6

The six possible final states of A are (1,1,1), (1,3,0), (3,0,1), (3,2,0), (5,1,0), and (7,0,0).

Sample Input 4

5
1 1 3 3
2
0 1 0 1 2

Sample Output 4

48

Sample Input 5

5
1 1 3 3
123456789
1 2 3 4 5

Sample Output 5

87782255

见题面 Input 部分

见题面 Output 部分