Problem Statement

You are given a simple connected undirected graph with N vertices and M edges (a simple graph contains no self-loop and no multi-edges).
For $i = 1, 2, \ldots, M$, the i-th edge connects vertex u_i and vertex v_i bidirectionally.
Determine whether there is a way to paint each vertex black or white to satisfy both of the following conditions, and show one such way if it exists.

• At least one vertex is painted black.
• For every $i = 1, 2, \ldots, K$, the following holds:
• the minimum distance between vertex p_i and a vertex painted black is exactly d_i.

Here, the distance between vertex u and vertex v is the minimum number of edges in a path connecting u and v.

Input

The input is given from Standard Input in the following format:
N M
u_1 v_1
u_2 v_2
$\vdots$
u_M v_M
K
p_1 d_1
p_2 d_2
$\vdots$
p_K d_K

Output

If there is no way to paint each vertex black or white to satisfy the conditions, print No.
Otherwise, print Yes in the first line, and a string S representing a coloring of the vertices in the second line, as shown below.
Here, S is a string of length N such that, for each $i = 1, 2, \ldots, N$, the i-th character of S is 1 if vertex i is painted black and 0 if white.
Yes
S

If multiple solutions exist, you may print any of them.

Constraints

• $1 \leq N \leq 2000$
• $N-1 \leq M \leq \min\lbrace N(N-1)/2, 2000 \rbrace$
• $1 \leq u_i, v_i \leq N$
• $0 \leq K \leq N$
• $1 \leq p_1 \lt p_2 \lt \cdots \lt p_K \leq N$
• $0 \leq d_i \leq N$
• The given graph is simple and connected.
• All values in the input are integers.

Sample Input 1

5 5
1 2
2 3
3 1
3 4
4 5
2
1 0
5 2

Sample Output 1

Yes
10100

One way to satisfy the conditions is to paint vertices 1, 3 black and vertices 2, 4, 5 white.
Indeed, for each i = 1, 2, 3, 4, 5, let A_i denote the minimum distance between vertex i and a vertex painted black, and we have (A_1, A_2, A_3, A_4, A_5) = (0, 1, 0, 1, 2), where A_1 = 0, A_5 = 2.

Sample Input 2

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

Sample Output 2

No

There is no way to satisfy the conditions by painting each vertex black or white, so you should print No.

Sample Input 3

1 0
0

Sample Output 3

Yes
1

见题面 Input 部分

见题面 Output 部分