Random Forest Rank

3000ms

524288K

Description:

Let's define rank of undirected graph as rank of its adjacency matrix in $$$\mathbb{R}^{n \times n}$$$.

Given a tree. Each edge of this tree will be deleted with probability $$$1/2$$$, all these deletions are independent. Let $$$E$$$ be the expected rank of resulting forest. Find $$$E \cdot 2^{n-1}$$$ modulo $$$998244353$$$ (it is easy to show that $$$E \cdot 2^{n-1}$$$ is an integer).

Input:

First line of input contains $$$n$$$ ($$$1 \le n \le 5 \cdot 10^{5}$$$) — number of vertices.

Next $$$n-1$$$ lines contains two integers $$$u$$$ $$$v$$$ ($$$1 \le u, \,\, v \le n; \,\, u \ne v$$$) — indices of vertices connected by edge.

It is guaranteed that given graph is a tree.

Output:

Print one integer — answer to the problem.

Sample Input:

3
1 2
2 3

Sample Output:

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Informação

Provedor Codeforces

Código CF1067E