Problem:
Score : 800 points

Problem Statement

Takahashi has received an undirected graph with N vertices, numbered 1, 2, ..., N.
The edges in this graph are represented by (u_i, v_i).
There are no self-loops and multiple edges in this graph.

Based on this graph, Takahashi is now constructing a new graph with N^2 vertices, where each vertex is labeled with a pair of integers (a, b) (1 \leq a \leq N, 1 \leq b \leq N).
The edges in this new graph are generated by the following rule:

Span an edge between vertices (a, b) and (a', b') if and only if both of the following two edges exist in the original graph: an edge between vertices a and a', and an edge between vertices b and b'.

How many connected components are there in this new graph?

Constraints

2 \leq N \leq 100,000

0 \leq M \leq 200,000

1 \leq u_i < v_i \leq N

There exists no pair of distinct integers i and j such that u_i = u_j and v_i = v_j.

Input

The input is given from Standard Input in the following format:

N M
u_1 v_1
u_2 v_2
:
u_M v_M

Output

Print the number of the connected components in the graph constructed by Takahashi.

Sample Input 1

3 1
1 2

Sample Output 1

7

The graph constructed by Takahashi is as follows.

Sample Input 2

7 5
1 2
3 4
3 5
4 5
2 6

Sample Output 2

18

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iostream>
#include <map>
#include <memory>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

typedef long long ll;

#define sz size()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define all(c) (c).begin(), (c).end()
#define rep(i,a,b) for(ll i=(a);i<(b);++i)
#define per(i,a,b) for(ll i=(b-1);i>=(a);--i)
#define clr(a, b) memset((a), (b) ,sizeof(a))
#define ctos(c) string(1,c)
#define print(x) cout<<#x<<" = "<<x<<endl;

#define MOD 1000000007

vector<int> uf, usz;
int nc;

void init(int n){
  vector<int> uf_(n);
  vector<int> usz_(n, 1);
  uf = uf_;
  usz = usz_;
  nc = n;

  for(int i = 0; i < uf.size(); i++){
    uf[i] = i;
  }
}

int find(int a){
  return (uf[a] == a) ? a : uf[a] = find(uf[a]);
}

void union_(int a, int b){
  a = find(a);
  b = find(b);

  if(a != b){
    if(usz[a] >= usz[b]){
      swap(a, b);
    }
    uf[a] = b;
    usz[b] += usz[a];
    nc--;
  }
}

int check(int a, int b){
  return (find(a) == find(b)) ? 1 : 0;
}

int get_size(int a){
  return usz[find(a)];
}

ll d[100010];
vector<vector<ll> > vv;
int flag = 0;

ll dfs(ll p, ll index1){
  d[p] = index1;
  rep(i,0,vv[p].sz){
    int index2 = d[vv[p][i]];
    if(abs(index1-index2)%2==0)flag=1;
    if(d[vv[p][i]]!=0)continue;
    dfs(vv[p][i],index1+1);
  }
}


int main() {
  ll n,m;
  cin>>n>>m;
  init(n);
  vector<pair<ll,ll> > v;
  vector<vector<ll> > vv_(n,vector<ll>());
  vv = vv_;
  rep(i,0,m){
    ll a,b;
    cin>>a>>b;
    a--;b--;
    v.pb(mp(a,b));
    union_(a,b);
    vv[a].pb(b);
    vv[b].pb(a);
  }
  clr(d,0);
  ll ans = 0;
  rep(i,0,n){
    if(d[i]!=0)continue;
    flag = 0;
    dfs(i,1);
    if(flag == 1)ans++;
    else ans+=2;
  }
  cout << nc*ans << endl;
  return 0;
}