196. Matrix Multiplication
time limit per test: 0.25
sec.
memory limit per test: 65536
KB
input: standard
output: standard
Let us consider an undirected graph G = <V, E> which has N vertices and M edges. Incidence matrix of this graph is an N × M matrix A = {a_{ij}}, such that a_{ij} is 1 if ith vertex is one of the ends of jth edge and 0 in the other case. Your task is to find the sum of all elements of the matrix A^{T}A where A^{T} is A transposed, i.e. an M × N matrix obtained from A by turning its columns to rows and vice versa.
Input
The first line of the input file contains two integer numbers — N and M (2 le N le 10,000, 1 le M le 100,000). 2M integer numbers follow, forming M pairs, each pair describes one edge of the graph. All edges are different and there are no loops (i.e. edge ends are distinct).
Output
Output the only number — the sum requested.
Sample test(s)
Input
4 4
1 2
1 3
2 3
2 4
Output
18
Author:  Andrew Stankevich, Georgiy Korneev

Resource:  Petrozavodsk Winter Trainings 2003

Date:  20030206

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