问题 G: Matching In Multiplication 问题 G: Matching In Multiplication
时间限制: 6 Sec 内存限制: 128 MB
提交: 6 解决: 1
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In the mathematical discipline of graph theory, a bipartite graph is a graph whose vertices can be divided into two disjoint sets U
and V
(that is, U
and V
are each independent sets) such that every edge connects a vertex in U
to one in V
. Vertex sets U
and V
are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. A matching in a graph is a set of edges without common vertices. A perfect matching is a matching that each vertice is covered by an edge in the set.
Little Q misunderstands the definition of bipartite graph, he thinks the size of U
is equal to the size of V
, and for each vertex p
in U
, there are exactly two edges from p
. Based on such weighted graph, he defines the weight of a perfect matching as the product of all the edges' weight, and the weight of a graph is the sum of all the perfect matchings' weight.
Please write a program to compute the weight of a weighted ''bipartite graph'' made by Little Q. 输入描述
The first line of the input contains an integer T(1≤T≤15), denoting the number of test cases.
In each test case, there is an integer n(1≤n≤300000) in the first line, denoting the size of U. The vertex in U and V are labeled by 1,2,...,n.
For the next n lines, each line contains 4 integers vi,1,wi,1,vi,2,wi,2(1≤vi,j≤n,1≤wi,j≤109), denoting there is an edge between Ui and Vvi,1, weighted wi,1, and there is another edge between Ui and Vvi,2, weighted wi,2.
It is guaranteed that each graph has at least one perfect matchings, and there are at most one edge between every pair of vertex.
输出描述
For each test case, print a single line containing an integer, denoting the weight of the given graph. Since the answer may be very large, please print the answer modulo 998244353.
样例输入
1
2
2 1 1 4
1 4 2 3
样例输出
16
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