CF1033E Hidden Bipartite Graph

**这是一道交互题。** 给定一个连通图（不包括自环和重边），你可以询问一个点集 $s$，系统会返回在 $s$ 中有两个端点的边的数量。你最多可以询问 $20000$ 次。 你需要判断这个图是不是一个二分图。

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In the first case, Alice learns that there are $ 4 $ edges in the whole graph. Over the course of the next three queries, she learns that vertex $ 1 $ has two neighbors: $ 3 $ and $ 4 $ . She then learns that while vertex $ 2 $ is adjacent to $ 4 $ , the vertex $ 3 $ isn't adjacent to $ 4 $ . There is only one option for the remaining edge, and that is $ (2, 3) $ . This means that the graph is a cycle on four vertices, with $ (1, 2) $ being one partition and $ (3, 4) $ being the second. Here, it would be also valid to output "3 4" on the second line. In the second case, we also have a graph on four vertices and four edges. In the second query, Alice learns that there are three edges among vertices $ (1, 2, 4) $ . The only way this could possibly happen is that those form a triangle. As the triangle is not bipartite, Alice can report it as a proof. Notice that she does not learn where the fourth edge is, but she is able to answer Bob correctly anyway.