Problem Statement

You are given a binary tree with N vertices. The vertices are numbered 1 to N, with vertex 1 being the root. The $i-th edge (1\leq i \leq N-1) connects vertex i+1$ and vertex P_i\ $(\leq i)$ bidirectionally.
There are one basket and M balls on this tree. The balls are numbered 1 to M, and each ball j has a designated start vertex S_j and goal vertex T_j. Initially, the basket is empty and placed at vertex 1, and the balls are placed at their respective start vertices.
You can perform the following operation any number of times in any order.

• Let v be the current vertex where the basket is placed. Do one of the following:
• Choose one edge connected to vertex v, and move the basket along that edge to the adjacent vertex. The balls inside the basket move together with it.
• Choose a ball with the start vertex v that is still placed at v, and put it into the basket. This operation can only be performed if the basket contains fewer than K balls (that is, the basket cannot contain K+1 or more balls).
• Choose a ball with the goal vertex v from the basket and take it out, placing it at vertex v.

A sequence of operations is called a good operation sequence if and only if the basket is eventually empty and placed at vertex 1, and the balls are eventually placed at their respective goal vertices.
Since it is tiring to move the basket many times, the basket's movement path should traverse each edge exactly twice before returning to vertex 1. Find the number, modulo 998244353, of those paths such that a good operation sequence exists following that path.

Input

The input is given from Standard Input in the following format:
N M K
$P_1 P_2 \dots P_{N-1}$
S_1 T_1
S_2 T_2
$\vdots$
S_M T_M

Output

Print the number, modulo 998244353, of paths traversing every edge exactly twice before returning to vertex 1 such that a good operation sequence exists following that path.

Constraints

• $2\leq N \leq 10^4$
• $1\leq M \leq 2\times 10^5$
• $1\leq K \leq 10^3$
• $1\leq P_i \leq i$
• For every v\ $(1\leq v \leq N),$ there are at most two i's such that P_i=v.
• $1\leq S_j, T_j \leq N$
• $S_j \neq T_j$
• All input values are integers.

Sample Input 1

5 2 1
1 1 3 3
2 4
5 3

Sample Output 1

1

The given graph is shown in the figure below. The circles and squares written next to the vertices represent the start and goal vertices of the balls, respectively.

Among the paths where every edge is traversed exactly twice before returning to vertex 1, there is only one path such that a good operation sequence exists following that path, which is shown below:

Here, you can construct the following good operation sequence:

• Move the basket to vertex 2.
• Put ball 1 into the basket.
• Move the basket to vertex 1.
• Move the basket to vertex 3.
• Move the basket to vertex 4.
• Take ball 1 out of the basket and place it at vertex 4.
• Move the basket to vertex 3.
• Move the basket to vertex 5.
• Put ball 2 into the basket.
• Move the basket to vertex 3.
• Take ball 2 out of the basket and place it at vertex 3.
• Move the basket to vertex 1.

Sample Input 2

5 2 2
1 1 3 3
2 4
5 3

Sample Output 2

2

The value of K has increased by 1 from Sample Input 1. This allows you to construct a good operation sequence for the following path, in addition to the one illustrated above.

Sample Input 3

15 4 2
1 2 1 4 2 3 4 7 3 7 5 9 11 8
14 12
5 4
13 15
5 12

Sample Output 3

8

见题面 Input 部分

见题面 Output 部分