Given an unrooted tree with $n$ nodes, we wish to build bus routes between some pairs of nodes such that any two nodes can be reached using at most two bus routes.

Formally, consider all $\frac{n(n-1)}{2}$ simple paths between distinct endpoints in the tree. A subset $S$ of these paths is called "good" if and only if:

• Consider a new graph $G$. For any pair of nodes $u, v$, we add an undirected edge with weight 1 between $u$ and $v$ if and only if there exists a path $P \in S$ such that both $u$ and $v$ are on $P$.
• The distance between any two nodes in $G$ is at most 2.

You need to find the number of good subsets $S$. Since the answer can be very large, output the result modulo 998244353.

Input

The first line contains a positive integer $n$, representing the number of nodes.

The next $n-1$ lines each contain two positive integers $u, v$, representing a tree edge $(u, v)$.

Output

Output a single integer representing the number of good subsets modulo 998244353.

Examples

Input 1

3
1 2
2 3

Output 1

5

Note

For the first example, all valid subsets are $\{(1, 3)\}$, $\{(1, 3), (1, 2)\}$, $\{(1, 3), (2, 3)\}$, $\{(1, 3), (1, 2), (2, 3)\}$, and $\{(1, 2), (2, 3)\}$.

Input 2

6
1 2
2 3
2 4
3 5
3 6

Output 2

27296

Constraints

For all data, $1 \le n \le 3000$.

The details are as follows:

Special Property A: The tree is guaranteed to be a chain.