This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc282/tasks/abc282_d
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// 2色塗り分けの verify
#include <iostream>
#include <vector>
#include "src/DataStructure/UnionFind.hpp"
#include "src/Graph/Graph.hpp"
#include "src/Graph/BipartiteGraph.hpp"
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
int N, M;
cin >> N >> M;
Graph g(N, M);
for (int i= 0; i < M; ++i) cin >> g[i], --g[i];
UnionFind uf(N);
for (auto [u, v]: g) uf.unite(u, v);
auto col= paint_two_colors(g);
if (col.empty()) return cout << 0 << '\n', 0;
vector cnt(2, vector(N, 0));
for (int v= N; v--;) ++cnt[col[v]][uf.leader(v)];
long long ans= 0;
for (int s= 2; s--;)
for (int v= N; v--;) ans+= (long long)cnt[s][v] * (N - cnt[s][v]);
ans/= 2, ans-= M;
cout << ans << '\n';
return 0;
}
#line 1 "test/atcoder/abc282_d.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc282/tasks/abc282_d
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// 2色塗り分けの verify
#include <iostream>
#include <vector>
#line 3 "src/DataStructure/UnionFind.hpp"
#include <algorithm>
class UnionFind {
std::vector<int> par;
public:
UnionFind(int n): par(n, -1) {}
int leader(int u) { return par[u] < 0 ? u : par[u]= leader(par[u]); }
bool unite(int u, int v) {
if ((u= leader(u)) == (v= leader(v))) return false;
if (par[u] > par[v]) std::swap(u, v);
return par[u]+= par[v], par[v]= u, true;
}
bool connected(int u, int v) { return leader(u) == leader(v); }
int size(int u) { return -par[leader(u)]; }
};
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
template <class T> struct name { \
using Iterator= typename std::vector<T>::IT; \
Iterator bg, ed; \
Iterator begin() const { return bg; } \
Iterator end() const { return ed; } \
size_t size() const { return std::distance(bg, ed); } \
CT &operator[](int i) const { return bg[i]; } \
}
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
std::vector<T> dat;
std::vector<int> p;
size_t size() const { return p.size() - 1; }
ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
os << '[';
for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
using std::pair<int, int>::pair;
Edge &operator--() { return --first, --second, *this; }
int to(int v) const { return first ^ second ^ v; }
friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
size_t n;
Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
size_t vertex_size() const { return n; }
size_t edge_size() const { return size(); }
size_t add_vertex() { return n++; }
size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
for (auto [u, v]: *this) a; \
for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
for (int i= size(); i--;) { \
auto [u, v]= (*this)[i]; \
b; \
}
#define _ADJ(a, b) \
vector<int> p(n + 1), c(size() << !dir); \
if (!dir) { \
_ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
} else if (dir > 0) { \
_ADJ_FOR(++p[u], c[--p[u]]= a) \
} else { \
_ADJ_FOR(++p[v], c[--p[v]]= b) \
} \
return {c, p}
CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 2 "src/Graph/BipartiteGraph.hpp"
#include <cassert>
#include <tuple>
#line 6 "src/Graph/BipartiteGraph.hpp"
// [0, L) is left, [L, n) is right
struct BipartiteGraph: Graph {
size_t L;
BipartiteGraph() {}
BipartiteGraph(size_t L, size_t R, size_t m= 0): Graph(L + R, m), L(L) {}
size_t left_size() const { return L; }
size_t right_size() const { return this->n - L; }
};
std::vector<int> paint_two_colors(const CSRArray<int> &adj) {
const int n= adj.size();
std::vector<int> col(n, -1);
for (int s= n; s--;)
if (col[s] == -1) {
std::vector<int> q= {s};
for (int i= col[s]= 0, v; i < (int)q.size(); ++i)
for (int u: adj[v= q[i]])
if (int c= col[v]; col[u] == c) return {};
else if (col[u] == -1) col[u]= c ^ 1, q.push_back(u);
}
return col;
}
std::vector<int> paint_two_colors(const Graph &g) { return paint_two_colors(g.adjacency_vertex(0)); }
// { BipartiteGraph , original to new, new to original }
// {{},{},{}} if not bipartite
std::tuple<BipartiteGraph, std::vector<int>, std::vector<int>> graph_to_bipartite(const Graph &g, std::vector<int> color= {}) {
if (color.empty()) color= paint_two_colors(g);
if (color.empty()) return {};
const int n= g.vertex_size(), m= g.edge_size();
std::vector<int> a(n), b(n);
int l= 0, r= n;
for (int i= n; i--;) b[a[i]= color[i] ? --r : l++]= i;
BipartiteGraph bg(l, n - l, m);
for (int i= m; i--;) {
auto [u, v]= g[i];
bg[i]= std::minmax(a[u], a[v]);
}
return {bg, a, b};
}
namespace _bg_internal {
std::vector<int> _bm(int L, const CSRArray<int> &adj, std::vector<int> &m) {
std::vector<int> a, p, q(L);
for (bool u= true; u;) {
u= false, a.assign(L, -1), p.assign(L, -1);
int t= 0;
for (int l= L; l--;)
if (m[l] == -1) q[t++]= a[l]= p[l]= l;
for (int i= 0; i < t; ++i)
if (int l= q[i], x; m[a[l]] == -1)
for (int r: adj[l]) {
if (x= m[r]; x == -1) {
for (u= true; r != -1; l= p[l]) m[r]= l, std::swap(m[l], r);
break;
}
if (p[x] == -1) a[q[t++]= x]= a[p[x]= l];
}
}
return a;
}
}
template <bool lexical= false> std::pair<std::vector<int>, std::vector<int>> bipartite_matching(const BipartiteGraph &bg, std::vector<int> partner= {}) {
const int L= bg.left_size(), M= bg.edge_size();
if (partner.empty()) partner.assign(bg.vertex_size(), -1);
assert(partner.size() == bg.vertex_size());
{
CSRArray<int> adj{std::vector<int>(M), std::vector<int>(L + 1)};
for (auto [l, r]: bg) ++adj.p[l];
for (int i= 0; i < L; ++i) adj.p[i + 1]+= adj.p[i];
for (auto [l, r]: bg) adj.dat[--adj.p[l]]= r;
if constexpr (lexical) {
for (int l= L; l--;) std::sort(adj[l].begin(), adj[l].end());
_bg_internal::_bm(L, adj, partner);
std::vector<char> a(L, 1);
for (int l= 0; l < L; ++l)
if (int r= partner[l], v= l; r != -1) {
std::vector<int> p(L, partner[v]= partner[r]= -1), c(adj.p.begin(), adj.p.begin() + L);
for (p[v]= -2;;) {
if (c[v] == adj.p[v + 1]) v= p[v];
else if (int u= partner[r= adj.dat[c[v]++]]; u == -1) {
for (; r != -1; v= p[v]) partner[r]= v, std::swap(partner[v], r);
break;
} else if (a[u] && p[u] == -1) p[u]= v, v= u;
}
a[l]= 0;
}
} else _bg_internal::_bm(L, adj, partner);
}
std::vector<int> c;
std::vector<char> p(L);
for (int i= 0; i < M; ++i)
if (auto [l, r]= bg[i]; partner[l] == r && !p[l]) c.push_back(i), p[l]= 1;
return {c, partner};
}
#line 12 "test/atcoder/abc282_d.test.cpp"
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
int N, M;
cin >> N >> M;
Graph g(N, M);
for (int i= 0; i < M; ++i) cin >> g[i], --g[i];
UnionFind uf(N);
for (auto [u, v]: g) uf.unite(u, v);
auto col= paint_two_colors(g);
if (col.empty()) return cout << 0 << '\n', 0;
vector cnt(2, vector(N, 0));
for (int v= N; v--;) ++cnt[col[v]][uf.leader(v)];
long long ans= 0;
for (int s= 2; s--;)
for (int v= N; v--;) ans+= (long long)cnt[s][v] * (N - cnt[s][v]);
ans/= 2, ans-= M;
cout << ans << '\n';
return 0;
}