You are given an undirected graph without self-loops or multiple edges which consists of $$$n$$$ vertices and $$$m$$$ edges. Also you are given three integers $$$n_1$$$, $$$n_2$$$ and $$$n_3$$$.
Can you label each vertex with one of three numbers 1, 2 or 3 in such way, that:
If there are multiple valid labelings, print any of them.
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.
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).
6 3 2 2 2 3 1 5 4 2 5
YES 112323
5 9 0 2 3 1 2 1 3 1 5 2 3 2 4 2 5 3 4 3 5 4 5
NO
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