Graph Coloring

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 5000$$$; $$$0 \le m \le 10^5$$$) — the number of vertices and edges in the graph.

The second line contains three integers $$$n_1$$$, $$$n_2$$$ and $$$n_3$$$ ($$$0 \le n_1, n_2, n_3 \le n$$$) — the number of labels 1, 2 and 3, respectively. It's guaranteed that $$$n_1 + n_2 + n_3 = n$$$.

Next $$$m$$$ lines contan description of edges: the $$$i$$$-th line contains two integers $$$u_i$$$, $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$; $$$u_i \neq v_i$$$) — the vertices the $$$i$$$-th edge connects. It's guaranteed that the graph doesn't contain self-loops or multiple edges.

Output:

If valid labeling exists then print "YES" (without quotes) in the first line. In the second line print string of length $$$n$$$ consisting of 1, 2 and 3. The $$$i$$$-th letter should be equal to the label of the $$$i$$$-th vertex.

If there is no valid labeling, print "NO" (without quotes).

Sample Input:

6 3
2 2 2
3 1
5 4
2 5

Sample Output:

YES
112323

Sample Input:

5 9
0 2 3
1 2
1 3
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output:

NO