Sloth

题意翻译

给出一棵$n$个节点的树，你选择删掉一条边，再加上一条边（也要保证为树），问最后树上的节点能够两两完美匹配的加删边方案数？ 翻译By Dark_sky

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.

输入输出格式

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.

输出格式

Output a single integer — the answer to the problem.

输入输出样例

输入样例 #1

4
1 2
2 3
3 4

输出样例 #1

8

输入样例 #2

5
1 2
2 3
3 4
3 5

输出样例 #2

0

输入样例 #3

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

输出样例 #3

22

说明

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 $ .