Given a graph, try to find an optimal coloring. Available colors are black and white only. The coloring of the graph is called optimal if a maximum of nodes is black. The coloring is restricted by the rule that no two connected nodes are black.
The input file contains M graphs. The number M is given on the first line. The first line of each graph contains N and K, the number of nodes and the number of edges, respectively.( 1 <= N <= 30 ). The following K lines contain the edges given by a pair of node numbers, which are separated by a space. The nodes are indexd from 1 to N.
The output should consist of 2M lines, two lines for each graph found in the input file. The first line of should contain the maximum number of nodes that can be colored black in the graph. The second line should contain one possible optimal coloring. It is given by the sorted list of black nodes, separated by spaces.