Vasya and Maximum Matching

Description:

Input:

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.

Output:

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 $$$998244353$$$.

Sample Input:

4
1 2
1 3
1 4

Sample Output:

4

Sample Input:

4
1 2
2 3
3 4

Sample Output:

6

Sample Input:

1

Sample Output:

1

Note:

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.