Problem Statement

There is a simple undirected graph with N vertices and M edges, where vertices are numbered from 1 to N, and edges are numbered from 1 to M. Edge i connects vertex a_i and vertex b_i.
K security guards numbered from 1 to K are on some vertices. Guard i is on vertex p_i and has a stamina of h_i. All p_i are distinct.
A vertex v is said to be guarded when the following condition is satisfied:

• there is at least one guard i such that the distance between vertex v and vertex p_i is at most h_i.

Here, the distance between vertex u and vertex v is the minimum number of edges in the path connecting vertices u and v.
List all guarded vertices in ascending order.

Input

The input is given from Standard Input in the following format:
N M K
a_1 b_1
a_2 b_2
$\vdots$
a_M b_M
p_1 h_1
p_2 h_2
$\vdots$
p_K h_K

Output

Print the answer in the following format. Here,

• G is the number of guarded vertices,
• and $v_1, v_2, \dots, v_G$ are the vertex numbers of the guarded vertices in ascending order.

G
$v_1 v_2 \dots v_G$

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq \min \left(\frac{N(N-1)}{2}, 2 \times 10^5 \right)$
• $1 \leq K \leq N$
• $1 \leq a_i, b_i \leq N$
• The given graph is simple.
• $1 \leq p_i \leq N$
• All p_i are distinct.
• $1 \leq h_i \leq N$
• All input values are integers.

Sample Input 1

5 5 2
1 2
2 3
2 4
3 5
1 5
1 1
5 2

Sample Output 1

4
1 2 3 5

The guarded vertices are 1, 2, 3, 5.
These vertices are guarded because of the following reasons.

• The distance between vertex 1 and vertex p_1 = 1 is 0, which is not greater than h_1 = 1. Thus, vertex 1 is guarded.
• The distance between vertex 2 and vertex p_1 = 1 is 1, which is not greater than h_1 = 1. Thus, vertex 2 is guarded.
• The distance between vertex 3 and vertex p_2 = 5 is 1, which is not greater than h_2 = 2. Thus, vertex 3 is guarded.
• The distance between vertex 5 and vertex p_1 = 1 is 1, which is not greater than h_1 = 1. Thus, vertex 5 is guarded.

Sample Input 2

3 0 1
2 3

Sample Output 2

1
2

The given graph may have no edges.

Sample Input 3

10 10 2
2 1
5 1
6 1
2 4
2 5
2 10
8 5
8 6
9 6
7 9
3 4
8 2

Sample Output 3

7
1 2 3 5 6 8 9

见题面 Input 部分

见题面 Output 部分