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

 /*
 * this code is made by 987690183
 * Problem: 1213
 * Verdict: Accepted
 * Submission Date: 2014-10-14 13:40:27
 * Time: 236MS
 * Memory: 1716KB
 */
 #include<iostream>
 #include<stdio.h>
 #include<cstring>
 #include<cstdlib>
 using namespace std;

 int num[];
 long long get(int n,int m)/**Cn,m**/
 {
     long long sum = ;
     for(int i=,j=n;i<=m;i++,j--)
         sum=sum*j/i;
     return sum;
 }
 int main()
 {
     int n,m,x,y;
     int hxl=  ;
     while(scanf("%d%d",&n,&m)>)
     {
         memset(num,,sizeof(num));
         for(int i=;i<=m;i++)
         {
             scanf("%d%d",&x,&y);
             num[x]++;
             num[y]++;
             hxl = hxl+;
         }
         long long tom = hxl;
         for(int i=;i<=;i++)
         if(num[i]>=)
         {
             tom=tom+get(num[i],)*;
         }
         printf("%lld\n",tom);
     }
     return ;
 }