A11416. Sloth
编程题
普及/提高-
知识点
题目描述
Sloth is bad, mkay? So we decided to prepare a problem to punish lazy guys.
You are given a tree, you should count the number of ways to remove an edge from it and then add an edge to it such that the final graph is a tree and has a perfect matching. Two ways of this operation are considered different if their removed edges or their added edges aren't the same. The removed edge and the added edge can be equal.
A perfect matching is a subset of edges such that each vertex is an endpoint of exactly one of these edges.
You are given a tree, you should count the number of ways to remove an edge from it and then add an edge to it such that the final graph is a tree and has a perfect matching. Two ways of this operation are considered different if their removed edges or their added edges aren't the same. The removed edge and the added edge can be equal.
A perfect matching is a subset of edges such that each vertex is an endpoint of exactly one of these edges.
输入格式
The first line contains $n$ ( $2<=n<=5·10^{5}$ ) — the number of vertices.
Each of the next $n-1$ lines contains two integers $a$ and $b$ ( $1<=a,b<=n$ ) — the endpoints of one edge. It's guaranteed that the graph is a tree.
Each of the next $n-1$ lines contains two integers $a$ and $b$ ( $1<=a,b<=n$ ) — the endpoints of one edge. It's guaranteed that the graph is a tree.
输出格式
Output a single integer — the answer to the problem.
输入输出样例
输入 #1
4 1 2 2 3 3 4
输出 #1
8
输入 #2
5 1 2 2 3 3 4 3 5
输出 #2
0
输入 #3
8 1 2 2 3 3 4 1 5 5 6 6 7 1 8
输出 #3
22
说明/提示
In first sample, there are $8$ ways:
- edge between $2$ and $3$ turns to edge between $1$ and $3$ ,
- edge between $2$ and $3$ turns to edge between $1$ and $4$ ,
- edge between $2$ and $3$ turns to edge between $2$ and $3$ ,
- edge between $2$ and $3$ turns to edge between $2$ and $4$ ,
- edge between $1$ and $2$ turns to edge between $1$ and $2$ ,
- edge between $1$ and $2$ turns to edge between $1$ and $4$ ,
- edge between $3$ and $4$ turns to edge between $1$ and $4$ ,
- edge between $3$ and $4$ turns to edge between $3$ and $4$ .
- edge between $2$ and $3$ turns to edge between $1$ and $3$ ,
- edge between $2$ and $3$ turns to edge between $1$ and $4$ ,
- edge between $2$ and $3$ turns to edge between $2$ and $3$ ,
- edge between $2$ and $3$ turns to edge between $2$ and $4$ ,
- edge between $1$ and $2$ turns to edge between $1$ and $2$ ,
- edge between $1$ and $2$ turns to edge between $1$ and $4$ ,
- edge between $3$ and $4$ turns to edge between $1$ and $4$ ,
- edge between $3$ and $4$ turns to edge between $3$ and $4$ .