#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;

class UnionFindTree{
  struct base_node{
    int parent;
    int rank;
    int size;
  };
  
  vector<base_node> node;
 public:
  UnionFindTree(int n){
    node.resize(n);
    for(int i=0; i<n; i++){
      node[i].parent=i;
      node[i].rank=0;
      node[i].size=1;
    }
  }

  int find(int x){  //return root node of x
    if(node[x].parent == x) return x;
    else{
      return node[x].parent = find(node[x].parent);
    }
  }
  
  bool same(int x, int y){
    return find(x) == find(y);
  }

  int size(int at){
    return node[find(at)].size;
  }

  void unite(int x, int y){
    x = find(node[x].parent);
    y = find(node[y].parent);

    if(x==y) return;

    if(node[x].rank < node[y].rank){
      node[x].parent = y;
      node[y].size += node[x].size;
    }else if(node[x].rank > node[y].rank){
      node[y].parent = x;
      node[x].size += node[y].size;
    }else{
      node[x].rank++;
      unite(x,y);
    }
  }
};


int main(){
  long long n,m;
  cin >> n,m;

  vector<pair<int,int>> e(m);
  cin >> e;

  vector<vector<int>> G(n);
  for(auto p : e){
    int a,b;
    tie(a,b) = p;
    a--; b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  for(auto& v : G){
    sort(v.begin(), v.end());
  }

  if(false){
    UnionFindTree uft(n*n);
    for(int a=0; a<n; a++){
      for(int b=0; b<n; b++){
        for(auto u : G[a]){
          for(auto v : G[b]){
            uft.unite( a*n + b, u*n + v );
          }
        }
      }
    }
  
    set<int> cmp;
    for(int a=0; a<n; a++){
      for(int b=0; b<n; b++){
        cmp.insert( uft.find(a*n + b) );
      }
    }
    eprintln("ans = " , cmp.size() );
    println(cmp.size());
  }

  vector<int> visit(n, 0);
  vector<int> color(n, -1);

  function<bool(int,int,int)> dfs = [&](int pos, int last, int c){
    visit[pos] = true;
    color[pos] = c;
    for(auto nx : G[pos]){
      if(nx == last) continue;
      if( visit[nx] ){
        if( color[nx] == color[pos] ){
          return false;
        }else{
          continue;
        }
      }
      bool tmp = dfs(nx, pos, c^1);
      if(tmp == false) return false;
    }
    return true;
  };

  UnionFindTree uft(n);
  for(int i=0; i<n; i++){
    for(auto nx : G[i]){
      uft.unite( i,nx );
    }
  }

  vector<vector<long long>> type_cnt(3);
  for(int i=0; i<n; i++){
    if(visit[ uft.find(i) ]) continue;
    bool no_loop = dfs(i, -1, 0);
    visit[uft.find(i)] = true;
    long long cnt = uft.size(i);
    if(cnt == 1){
      type_cnt[0].push_back( cnt );
    }else if(no_loop){
      type_cnt[1].push_back( cnt );
    }else{
      type_cnt[2].push_back( cnt );
    }
  }

  vector<long long> sums(3);
  for(int t=0; t<3; t++){
    sums[t] = accumulate(type_cnt[t].begin(), type_cnt[t].end(), 0ll);
  }

  long long ans = 0;

  for(int t=0; t<3; t++){
    for(long long x : type_cnt[t]){
      for(int u=0; u<3; u++){
        if(sums[u] == 0)continue;
        if(t==0){ //one
          ans += sums[u];
        }else if(t==1){ //no_loop;
          if( u==0 ){
            ans += x*type_cnt[0].size();
          }else if(u==1){
            ans += 2ll*type_cnt[1].size();
          }else{
            ans += 1ll*type_cnt[2].size();
          }
        }else{ //loop
          if( u==0 ){
            ans += x*type_cnt[0].size();
          }else{
            ans += 1ll*type_cnt[u].size();
          }
        }
      }
    }
  }

  println(ans);

  return 0;
}


Measured memory_bytes: 10368