Neighbour Ordering

题目描述

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 <_{v} w $ if $ u $ comes after $ w $ in $ v $ 's neighbor list. A neighbour ordering is said to be good if, for each simple cycle $ v_1, v_2, \ldots, v_c $ of the graph, one of the following is satisfied: - $ v_1 <_{v_2} v_3, v_2 <_{v_3} v_4, \ldots, v_{c-2} <_{v_{c-1}} v_c, v_{c-1} <_{v_c} v_1, v_c <_{v_1} v_2 $ . - $ v_1 >_{v_2} v_3, v_2 >_{v_3} v_4, \ldots, v_{c-2} >_{v_{c-1}} v_c, v_{c-1} >_{v_c} v_1, v_c >_{v_1} v_2 $ . Given a graph $ G $ , determine whether there exists a good neighbour ordering for it and construct one if it does.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

3
5 6
0 1
0 2
1 2
2 3
3 4
4 1
2 1
0 1
6 10
0 1
2 0
0 3
0 4
1 2
1 4
2 3
2 5
3 5
4 5

输出样例 #1

YES
1 2 
4 2 0 
0 1 3 
2 4 
3 1 
YES
1 
0 
NO