Vasya and Maximum Matching

题意翻译

给你一棵n个节点的树，可以删除任意条边，使得删除玩之后的图仅有一种最大匹配的方法。问有多少种删边方法。1<=n<=3*10^5

题目描述

Vasya has got a tree consisting of $ n $ vertices. He wants to delete some (possibly zero) edges in this tree such that the maximum matching in the resulting graph is unique. He asks you to calculate the number of ways to choose a set of edges to remove. A matching in the graph is a subset of its edges such that there is no vertex incident to two (or more) edges from the subset. A maximum matching is a matching such that the number of edges in the subset is maximum possible among all matchings in this graph. Since the answer may be large, output it modulo $ 998244353 $ .

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 1 \le n \le 3 \cdot 10^5 $ ) — the number of vertices in the tree. Each of the next $ n − 1 $ lines contains two integers $ u $ and $ v $ ( $ 1 \le u, v \le n, u \neq v $ ) denoting an edge between vertex $ u $ and vertex $ v $ . It is guaranteed that these edges form a tree.

输出格式

Print one integer — the number of ways to delete some (possibly empty) subset of edges so that the maximum matching in the resulting graph is unique. Print the answer modulo $ 998244353 $ .

输入输出样例

输入样例 #1

4
1 2
1 3
1 4

输出样例 #1

4

输入样例 #2

4
1 2
2 3
3 4

输出样例 #2

6

输入样例 #3

1

输出样例 #3

1

说明

Possible ways to delete edges in the first example: - delete $ (1, 2) $ and $ (1, 3) $ . - delete $ (1, 2) $ and $ (1, 4) $ . - delete $ (1, 3) $ and $ (1, 4) $ . - delete all edges. Possible ways to delete edges in the second example: - delete no edges. - delete $ (1, 2) $ and $ (2, 3) $ . - delete $ (1, 2) $ and $ (3, 4) $ . - delete $ (2, 3) $ and $ (3, 4) $ . - delete $ (2, 3) $ . - delete all edges.

题意翻译

给你一棵n个节点的树，可以删除任意条边，使得删除玩之后的图仅有一种最大匹配的方法。问有多少种删边方法。1<=n<=3*10^5