Given a weighted undirected simple graph with n vertices and mmm positive-weighted edges. Sum up the weight of the minimum spanning forest for each of its spanning subgraph, and print the value modulo 998244353 as answer.
A minimum spanning forest of a weighted undirected graph G with vertex set V and edge set E is defined as follows:
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It's a subset of E (not necessarily non-empty or different from E), denoted as S.
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Any pair of vertices (u,v) which can reach each other in G can still reach each other only using edges in S.
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S is the subset with minumum weight among all subsets satisfying the above two conditions. The weight of S is the sum of weight of all edges in it.
A
spanning subgraph of
G is a graph with vertex set
V and edge set a subset of
E (not necessarily non-empty or different from
E).