New Year and Social Network

题意翻译

给定两棵大小为 $n(n\le 2.5\times 10^5)$ 的树$T_1,T_2$。 若你删去$T_1$上的一条边 $i$ 后，可以选择$T_2$上的一条边 $j$ 连接上来而形成树，则称 $(i,j)$ 是匹配的。 对于树 $T_1$ 的一条边，你需要为其标记一个数字/不标记，你标记的数字不能相同，你标记的数字 $x$ 与此边所构成的二元组 $(i,x)$ 是匹配的时候，你才能以数字 $x$ 标记其。 求你最多能标记多少条边。

题目描述

Donghyun's new social network service (SNS) contains $ n $ users numbered $ 1, 2, \ldots, n $ . Internally, their network is a tree graph, so there are $ n-1 $ direct connections between each user. Each user can reach every other users by using some sequence of direct connections. From now on, we will denote this primary network as $ T_1 $ . To prevent a possible server breakdown, Donghyun created a backup network $ T_2 $ , which also connects the same $ n $ users via a tree graph. If a system breaks down, exactly one edge $ e \in T_1 $ becomes unusable. In this case, Donghyun will protect the edge $ e $ by picking another edge $ f \in T_2 $ , and add it to the existing network. This new edge should make the network be connected again. Donghyun wants to assign a replacement edge $ f \in T_2 $ for as many edges $ e \in T_1 $ as possible. However, since the backup network $ T_2 $ is fragile, $ f \in T_2 $ can be assigned as the replacement edge for at most one edge in $ T_1 $ . With this restriction, Donghyun wants to protect as many edges in $ T_1 $ as possible. Formally, let $ E(T) $ be an edge set of the tree $ T $ . We consider a bipartite graph with two parts $ E(T_1) $ and $ E(T_2) $ . For $ e \in E(T_1), f \in E(T_2) $ , there is an edge connecting $ \{e, f\} $ if and only if graph $ T_1 - \{e\} + \{f\} $ is a tree. You should find a maximum matching in this bipartite graph.

输入输出格式

输入格式

The first line contains an integer $ n $ ( $ 2 \le n \le 250\,000 $ ), the number of users. In the next $ n-1 $ lines, two integers $ a_i $ , $ b_i $ ( $ 1 \le a_i, b_i \le n $ ) are given. Those two numbers denote the indices of the vertices connected by the corresponding edge in $ T_1 $ . In the next $ n-1 $ lines, two integers $ c_i $ , $ d_i $ ( $ 1 \le c_i, d_i \le n $ ) are given. Those two numbers denote the indices of the vertices connected by the corresponding edge in $ T_2 $ . It is guaranteed that both edge sets form a tree of size $ n $ .

输出格式

In the first line, print the number $ m $ ( $ 0 \leq m < n $ ), the maximum number of edges that can be protected. In the next $ m $ lines, print four integers $ a_i, b_i, c_i, d_i $ . Those four numbers denote that the edge $ (a_i, b_i) $ in $ T_1 $ is will be replaced with an edge $ (c_i, d_i) $ in $ T_2 $ . All printed edges should belong to their respective network, and they should link to distinct edges in their respective network. If one removes an edge $ (a_i, b_i) $ from $ T_1 $ and adds edge $ (c_i, d_i) $ from $ T_2 $ , the network should remain connected. The order of printing the edges or the order of vertices in each edge does not matter. If there are several solutions, you can print any.

输入输出样例

输入样例 #1

4
1 2
2 3
4 3
1 3
2 4
1 4

输出样例 #1

3
3 2 4 2
2 1 1 3
4 3 1 4

输入样例 #2

5
1 2
2 4
3 4
4 5
1 2
1 3
1 4
1 5

输出样例 #2

4
2 1 1 2
3 4 1 3
4 2 1 4
5 4 1 5

输入样例 #3

9
7 9
2 8
2 1
7 5
4 7
2 4
9 6
3 9
1 8
4 8
2 9
9 5
7 6
1 3
4 6
5 3

输出样例 #3

8
4 2 9 2
9 7 6 7
5 7 5 9
6 9 4 6
8 2 8 4
3 9 3 5
2 1 1 8
7 4 1 3