E. Graph Coloringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:   Each vertex should be labeled by exactly one number 1, 2 or 3;  The total number of vertices with label 1 should be equal to n_1;  The total number of vertices with label 2 should be equal to n_2;  The total number of vertices with label 3 should be equal to n_3;  |col_u - col_v| = 1 for each edge (u, v), where col_x is the label of vertex x. If there are multiple valid labelings, print any of them.InputThe 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.OutputIf 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).ExamplesInput
6 3
2 2 2
3 1
5 4
2 5
Output
YES
112323
Input
5 9
0 2 3
1 2
1 3
1 5
2 3
2 4
2 5
3 4
3 5
4 5
Output
NO

6 3
2 2 2
3 1
5 4
2 5

YES 112323 
['dfs and similar', 'dp', 'graphs', '*2100']