/***************** NEW ******************/
VI tree[N],g[N];//edge list representation of graph
int U[M],V[M],vis[N],arr[N],T,cmpno,dsu[N];
bool isbridge[M]; // if i'th edge is a bridge edge or not
int adj(int u,int e){
  return U[e]^V[e]^u;
}
int f(int x){
  return dsu[x]=(dsu[x]==x?x:f(dsu[x]));
}
void merge(int a,int b){
  a=f(a);b=f(b);
  dsu[a]=b;
}
int dfs0(int u,int edge){ //mark bridges
  vis[u]=1;arr[u]=T++;
  int dbe = arr[u];
  for(auto e : g[u]){
    int w = adj(u,e);
    if(!vis[w])dbe = min(dbe,dfs0(w,e));
    else if(e!=edge)dbe = min(dbe,arr[w]);
  }
  if(dbe == arr[u] && edge!=-1)isbridge[edge]=true;
  else if(edge!=-1)merge(U[edge],V[edge]);
  return dbe;
}
void buildBridgeTree(int n){
  for(int i=1;i<=n;i++)dsu[i]=i;
  for(int i=1;i<=n;i++)if(!vis[i])dfs0(i,-1);
  for(int i=1;i<=m;i++)
    if(f(U[i])!=f(V[i]))
      tree[f(U[i])].PB(f(V[i])),
        tree[(f(V[i])].PB(U[i]);
}