write a go solution for Description:
Pak Chanek has a tree called the key tree. This tree consists of N vertices and N-1 edges. The edges of the tree are numbered from 1 to N-1 with edge i connecting vertices U_i and V_i. Initially, each edge of the key tree does not have a weight.

Formally, a path with length k in a graph is a sequence [v_1,e_1,v_2,e_2,v_3,e_3,ldots,v_k,e_k,v_k+1] such that:

- For each i, v_i is a vertex and e_i is an edge.
- For each i, e_i connects vertices v_i and v_i+1.

A circuit is a path that starts and ends on the same vertex.

A path in a graph is said to be simple if and only if the path does not use the same edge more than once. Note that a simple path can use the same vertex more than once.

The cost of a simple path in a weighted graph is defined as the maximum weight of all edges it traverses.

Count the number of distinct undirected weighted graphs that satisfy the following conditions:

- The graph has N vertices and 2N-2 edges.
- For each pair of different vertices (x,y), there exists a simple circuit that goes through vertices x and y in the graph.
- The weight of each edge in the graph is an integer between 1 and 2N-2 inclusive. Each edge has distinct weights.
- The graph is formed in a way such that there is a way to assign a weight W_i to each edge i in the key tree that satisfies the following conditions:   For each pair of edges (i,j), if i<j, then W_i<W_j.  For each pair of different vertex indices (x,y), the cost of the only simple path from vertex x to y in the key tree is equal to the minimum cost of a simple circuit that goes through vertices x and y in the graph.
- Note that the graph is allowed to have multi-edges, but is not allowed to have self-loops.

Print the answer modulo 998,244,353.

Two graphs are considered distinct if and only if there exists a triple (a,b,c) such that there exists an edge that connects vertices a and b with weight c in one graph, but not in the other.

Input Format:
The first line contains a single integer N (2<=N<=10^5) — the number of vertices in the key tree.

The i-th of the next N-1 lines contains two integers U_i and V_i (1<=U_i,V_i<=N) — an edge connecting vertices U_i and V_i. The graph in the input is a tree.

Output Format:
An integer representing the number of distinct undirected weighted graphs that satisfy the conditions of the problem modulo 998,244,353.

Note:
The following is an example of a graph that satisfies.

The following is an assignment of edge weights in the key tree that corresponds to the graph above.

As an example, consider a pair of vertex indices (1,4).

- The circuit in the graph for this pair of vertices is 3xarrow22xarrow44xarrow62xarrow11xarrow53 with a cost of 6.
- The path in the key tree for this pair of vertices is 1xarrow53xarrow64 with a cost of 6.. Output only the code with no comments, explanation, or additional text.