acdeream Matrix Multiplication

D - Matrix Multiplication

Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

SubmitStatus

Problem Description

Let us consider undirected graph G = {V; E} which has N vertices and M edges. Incidence matrix of this graph is N × M matrix A = {a_i,j}, such that a_i,j 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.

Input

The first line of the input file contains two integer numbers — N and M (2 ≤ N ≤ 10 000, 1 ≤ M ≤100 000). Then 2*M 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 Input

4 4
1 2
1 3
2 3
2 4

Sample Output

18

 1 /*
 2 * this code is made by 987690183
 3 * Problem: 1213
 4 * Verdict: Accepted
 5 * Submission Date: 2014-10-14 13:40:27
 6 * Time: 236MS
 7 * Memory: 1716KB
 8 */
 9 #include<iostream>
10 #include<stdio.h>
11 #include<cstring>
12 #include<cstdlib>
13 using namespace std;
14
15 int num[10002];
16 long long get(int n,int m)/**Cn,m**/
17 {
18     long long sum = 1;
19     for(int i=1,j=n;i<=m;i++,j--)
20         sum=sum*j/i;
21     return sum;
22 }
23 int main()
24 {
25     int n,m,x,y;
26     int hxl=  0;
27     while(scanf("%d%d",&n,&m)>0)
28     {
29         memset(num,0,sizeof(num));
30         for(int i=1;i<=m;i++)
31         {
32             scanf("%d%d",&x,&y);
33             num[x]++;
34             num[y]++;
35             hxl = hxl+2;
36         }
37         long long tom = hxl;
38         for(int i=1;i<=10000;i++)
39         if(num[i]>=2)
40         {
41             tom=tom+get(num[i],2)*2;
42         }
43         printf("%lld\n",tom);
44     }
45     return 0;
46 }