196. Matrix Multiplication

time limit per test: 0.25 sec / memory limit per test: 65536 KB

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 i-th vertex is one of the ends of j-th edge and 0 in the other case. Your task is to find the sum of all elements of the matrix \(A^TA\) 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.

Example(s)

Sample Input	Sample Output
4 4 1 2 1 3 2 3 2 4	18