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