#include<bits/stdc++.h>
#define MAXN 200007
using namespace std;
long long n,m,a[MAXN],b[MAXN],k;
vector< pair<int,int> > v[MAXN];
vector<int> tree[MAXN];
long long sz[MAXN],sum[MAXN],szcomp[MAXN],ans;
bool li[MAXN],bridge[MAXN];
int dp[MAXN],low[MAXN];
long long comp[MAXN],where[MAXN];
void bcc(int x,int p,int dep,int edge){
li[x]=true; dp[x]=low[x]=dep;
for(int i=0;i<v[x].size();i++){
if(!li[v[x][i].first]){
bcc(v[x][i].first,x,dep+1,v[x][i].second);
low[x]=min(low[x],low[v[x][i].first]);
}else if(v[x][i].first!=p){
low[x]=min(low[x],dp[v[x][i].first]);
}
}
if(p!=0 and low[x]==dp[x]){
bridge[edge]=true;
}
}
void mark(int x){
comp[k]++;
where[x]=k;
li[x]=true;
for(int i=0;i<v[x].size();i++){
if(li[v[x][i].first] or bridge[v[x][i].second])continue;
mark(v[x][i].first);
}
}
void dfs(int x,int p){
sz[x]=comp[x];
for(int i=0;i<tree[x].size();i++){
if(tree[x][i]==p or sz[tree[x][i]]!=0)continue;
dfs(tree[x][i],x);
sum[x]+=sz[tree[x][i]]*(sz[tree[x][i]]-1);
sz[x]+=sz[tree[x][i]];
}
}
void dfs2(int x,int p,int s){
szcomp[x]=s;
for(int i=0;i<tree[x].size();i++){
if(tree[x][i]==p or szcomp[tree[x][i]]!=0)continue;
dfs2(tree[x][i],x,s);
}
sum[x]+=(s-sz[x])*(s-sz[x]-1);
}
bool check(int x,int y,int z,bool s){
if(x==y)s=true;
if(x==z and s)return true;
for(int i=0;i<v[x].size();i++){
if(!li[v[x][i].first]){
li[v[x][i].first]=true;
if(check(v[x][i].first,y,z,s))return true;
li[v[x][i].first]=false;
}
}
return false;
}
void brute(){
int res=0;
for(int i=1;i<=n;i++){
for(int f=1;f<=n;f++){
for(int t=1;t<=n;t++){
if(i==f or f==t or i==t)continue;
for(int z=1;z<=n;z++)li[z]=false;
li[i]=true;
if(check(i,f,t,false))res++;
}
}
}
cout<<res<<"\n";
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin>>n>>m;
for(int i=1;i<=m;i++){
cin>>a[i]>>b[i];
v[a[i]].push_back({b[i],i});
v[b[i]].push_back({a[i],i});
}
for(int i=1;i<=n;i++){
if(!li[i])bcc(i,0,0,0);
}
for(int i=1;i<=n;i++)li[i]=false;
for(int i=1;i<=n;i++){
if(!li[i]){
k++; mark(i);
}
}
for(int i=1;i<=m;i++){
if(where[a[i]]==where[b[i]])continue;
tree[where[a[i]]].push_back(where[b[i]]);
tree[where[b[i]]].push_back(where[a[i]]);
}
for(int i=1;i<=k;i++){
if(sz[i]==0){
dfs(i,0);
dfs2(i,0,sz[i]);
}
}
for(int i=1;i<=k;i++){
ans+=(long long) comp[i]*((szcomp[i]-1)*(szcomp[i]-2)-sum[i]);
ans-=(long long) 2*(comp[i]-1)*(szcomp[i]-comp[i]);
}
for(int i=1;i<=n;i++){
long long res=0,sq=0;
for(int f=0;f<v[i].size();f++){
if(where[i]==where[v[i][f].first])continue;
if(sz[where[i]]>sz[where[v[i][f].first]]){
res+=sz[where[v[i][f].first]];
sq+=(sz[where[v[i][f].first]]-1)*sz[where[v[i][f].first]];
}else{
res+=(szcomp[where[i]]-sz[where[i]]);
sq+=(szcomp[where[i]]-sz[where[i]])*(szcomp[where[i]]-sz[where[i]]-1);
}
}
res=res*(res-1);
res-=sq;
ans-=(long long) (comp[where[i]]-1)*res;
}
cout<<ans<<"\n";
brute();
return 0;
}
/**
19 24
1 2
2 3
3 4
4 1
5 6
6 7
7 5
8 9
9 10
10 8
11 12
12 13
13 11
14 15
15 16
16 14
17 18
18 19
17 19
7 8
4 5
7 11
13 17
12 14
*/
Compilation message
count_triplets.cpp: In function 'void bcc(int, int, int, int)':
count_triplets.cpp:20:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
20 | for(int i=0;i<v[x].size();i++){
| ~^~~~~~~~~~~~
count_triplets.cpp: In function 'void mark(int)':
count_triplets.cpp:39:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
39 | for(int i=0;i<v[x].size();i++){
| ~^~~~~~~~~~~~
count_triplets.cpp: In function 'void dfs(int, int)':
count_triplets.cpp:48:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
48 | for(int i=0;i<tree[x].size();i++){
| ~^~~~~~~~~~~~~~~
count_triplets.cpp: In function 'void dfs2(int, int, int)':
count_triplets.cpp:60:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
60 | for(int i=0;i<tree[x].size();i++){
| ~^~~~~~~~~~~~~~~
count_triplets.cpp: In function 'bool check(int, int, int, bool)':
count_triplets.cpp:73:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
73 | for(int i=0;i<v[x].size();i++){
| ~^~~~~~~~~~~~
count_triplets.cpp: In function 'int main()':
count_triplets.cpp:148:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
148 | for(int f=0;f<v[i].size();f++){
| ~^~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
4 ms |
9816 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
4 ms |
9816 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1065 ms |
23980 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1045 ms |
9816 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1051 ms |
23120 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1063 ms |
9820 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1076 ms |
23116 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
4 ms |
9816 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
4 ms |
9816 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
