CF1656I Neighbour Ordering

Given an undirected graph $ G $ , we say that a neighbour ordering is an ordered list of all the neighbours of a vertex for each of the vertices of $ G $ . Consider a given neighbour ordering of $ G $ and three vertices $ u $ , $ v $ and $ w $ , such that $ v $ is a neighbor of $ u $ and $ w $ . We write $ u

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains two integers $ n $ and $ m $ ( $ 2 \leq n \leq 3 \cdot 10^5 $ , $ 1 \leq m \leq 3 \cdot 10^5 $ ), the number of vertices and the number of edges of the graph. The next $ m $ lines each contain two integers $ u, v $ ( $ 0 \leq u, v < n $ ), denoting that there is an edge connecting vertices $ u $ and $ v $ . It is guaranteed that the graph is connected and there are no loops or multiple edges between the same vertices. The sum of $ n $ and the sum of $ m $ for all test cases are at most $ 3 \cdot 10^5 $ .

For each test case, output one line with YES if there is a good neighbour ordering, otherwise output one line with NO. You can print each letter in any case (upper or lower). If the answer is YES, additionally output $ n $ lines describing a good neighbour ordering. In the $ i $ -th line, output the neighbours of vertex $ i $ in order. If there are multiple good neigbour orderings, print any.