Problem p03321 (C++)

Buggy submission (status: Runtime Error):
#include "bits/stdc++.h"
using namespace std;
using ll = long long;
using dd = double;
using pll = pair<ll, ll>;
using tll = tuple<ll, ll, ll>;
using vll = vector<ll>;
using vdd = vector<dd>;
using vpll = vector<pll>;
using vtll = vector<tll>;
using vvll = vector<vll>;
using vvdd = vector<vdd>;
using vvpll = vector<vpll>;
using vvtll = vector<vtll>;
using vvvll = vector<vvll>;
using vvvdd = vector<vvdd>;
using vvvpll = vector<vvpll>;
using vvvtll = vector<vvtll>;
using vvvvll = vector<vvvll>;
using vvvvdd = vector<vvvdd>;
using vvvvpll = vector<vvvpll>;
using vvvvtll = vector<vvvtll>;

constexpr ll INF = 1LL << 60;
constexpr dd EPS = 1e-11;

// cin,cout高速化のおまじない＋桁数指定
struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
  }
} fast;

#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define EACH(e, v) for (auto &&e : v)

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline T MaxE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmax(m, v[i]);
  return m;
} // v[S]～v[E]の最大値
template <class T> inline T MinE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmin(m, v[i]);
  return m;
} // v[S]～v[E]の最小値
template <class T> inline T MaxE(vector<T> &v, ll N) {
  return MaxE(v, 0, N - 1);
} // 先頭N個中の最大値
template <class T> inline T MinE(vector<T> &v, ll N) {
  return MinE(v, 0, N - 1);
}
template <class T> inline T MaxE(vector<T> &v) { return MaxE(v, (ll)v.size()); }
template <class T> inline T MinE(vector<T> &v) { return MinE(v, (ll)v.size()); }
template <class T> inline ll MaxI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] > v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MinI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] < v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MaxI(vector<T> &v, ll N) {
  return MaxI(v, 0, N - 1);
}
template <class T> inline ll MinI(vector<T> &v, ll N) {
  return MinI(v, 0, N - 1);
}
template <class T> inline ll MaxI(vector<T> &v) {
  return MaxI(v, (ll)v.size());
}
template <class T> inline ll MinI(vector<T> &v) {
  return MinI(v, (ll)v.size());
}
template <class T> inline T Sum(vector<T> &v, ll S, ll E) {
  T s = v[S];
  REPS(i, S + 1, E) s += v[i];
  return s;
}
template <class T> inline T Sum(vector<T> &v, ll N) { return Sum(v, 0, N - 1); }
template <class T> inline T Sum(vector<T> &v) { return Sum(v, v.size()); }
template <class T> inline T POW(T a, ll n) {
  T r = 1;
  for (; n > 0; n >>= 1, a *= a) {
    if (n & 1)
      r *= a;
  }
  return r;
}
inline ll POW(int a, ll n) { return POW((ll)a, n); }
inline ll MSB(ll a) {
  for (ll o = 63, x = -1;;) {
    ll m = (o + x) / 2;
    if (a < (1LL << m))
      o = m;
    else
      x = m;
    if (o - x == 1)
      return x;
  }
}
inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; }
ll Gcd(ll a, ll b) { return (b == 0) ? a : Gcd(b, a % b); }
ll Lcm(ll a, ll b) { return a * b / Gcd(a, b); }
inline vll Mask2Idx(ll m) {
  vll v;
  for (ll i = 0; m; m >>= 1, i++)
    if (m & 1)
      v.push_back(i);
  return move(v);
}
inline ll BitNum(ll m) {
  for (ll c = 0;; m >>= 1) {
    c += m & 1;
    if (!m)
      return c;
  }
}
inline ll Bit(ll s, ll i) { return (s >> i) & 1; }       // sの第ibit i=0-63
inline ll BitOn(ll s, ll i) { return s | (1LL << i); }   // sの第ibitON i=0-63
inline ll BitOff(ll s, ll i) { return s & ~(1LL << i); } // sの第ibitOFF i=0-63
template <class T>
inline ll UnderNumOf(vector<T> &v, T x) { // sort済vのx以下の個数を得る
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
template <class T, class Pr>
inline ll UnderNumOf(vector<T> &v, T x, Pr pred) { // x以下個数
  return upper_bound(v.begin(), v.end(), x, pred) - v.begin();
}
template <class T>
inline ll OverNumOf(vector<T> &v, T x) { // sort済vのx以上の個数を得る
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x) - v.begin());
}
template <class T, class Pr>
inline ll OverNumOf(vector<T> &v, T x, Pr pred) { // x以上の個数
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x, pred) - v.begin());
}

template <class T = ll> inline vector<T> cinv(ll N) {
  vector<T> v(N);
  REP(i, N) cin >> v[i];
  return move(v);
}
template <class T = ll, class S = ll> inline vector<pair<T, S>> cinv2(ll N) {
  vector<pair<T, S>> v(N);
  REP(i, N) { cin >> v[i].first >> v[i].second; }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll>
inline vector<tuple<T, S, R>> cinv3(ll N) {
  vector<tuple<T, S, R>> v(N);
  REP(i, N) { cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]); }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll, class Q = ll>
inline vector<tuple<T, S, R, Q>> cinv4(ll N) {
  vector<tuple<T, S, R, Q>> v(N);
  REP(i, N) {
    cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]) >> get<3>(v[i]);
  }
  return move(v);
}
template <class T = ll> inline vector<vector<T>> cinvv(ll N, ll M) {
  vector<vector<T>> vv(N);
  REP(i, N) vv[i] = cinv(M);
  return move(vv);
}
template <class T> inline void coutv(vector<T> &v, char deli = ' ') {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? '\n' : deli); }
}
template <class T> void bye(T a) {
  cout << a << '\n';
  exit(0);
}

#if defined(_DEBUG)
template <class T> void Dump(vector<T> &v) {
  REP(i, (ll)v.size()) { cerr << ((i == 0) ? "[" : " ") << setw(5) << v[i]; }
  cerr << "]";
}
void Dump(vll &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(4);
    if (v[i] == INF)
      cerr << "INF";
    else if (v[i] == -INF)
      cerr << "-INF";
    else
      cerr << v[i];
  }
  cerr << "]";
}
template <class T> void Dump(vector<vector<T>> &v) {
  ll N = (ll)v.size();
  string d[2][2] = {{" ", "["}, {"\n", "]\n"}};
  REP(i, N) {
    cerr << d[0][i == 0];
    Dump(v[i]);
    cerr << d[1][i == N - 1];
  }
}
template <class T> void Dump(vector<vector<vector<T>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  <", "[ <"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ---<", "[ ---<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">---\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ======<", "[ ======<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">======\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
#else
template <class T> void Dump(vector<T> &v) {}
template <class T> void Dump(vector<vector<T>> &v) {}
template <class T> void Dump(vector<vector<vector<T>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {}
#endif

struct mll {
  static ll MOD;
  ll val;
  mll(ll v = 0) : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  mll operator-() const { return -val; }
  mll operator+(const mll &b) const { return val + b.val; }
  mll operator-(const mll &b) const { return val - b.val; }
  mll operator*(const mll &b) const { return val * b.val; }
  mll operator/(const mll &b) const { return mll(*this) /= b; }
  mll operator+(ll b) const { return *this + mll(b); }
  mll operator-(ll b) const { return *this - mll(b); }
  mll operator*(ll b) const { return *this * mll(b); }
  friend mll operator+(ll a, const mll &b) { return b + a; }
  friend mll operator-(ll a, const mll &b) { return -b + a; }
  friend mll operator*(ll a, const mll &b) { return b * a; }
  friend mll operator/(ll a, const mll &b) { return mll(a) / b; }
  mll &operator+=(const mll &b) {
    val = (val + b.val) % MOD;
    return *this;
  }
  mll &operator-=(const mll &b) {
    val = (val + MOD - b.val) % MOD;
    return *this;
  }
  mll &operator*=(const mll &b) {
    val = (val * b.val) % MOD;
    return *this;
  }
  mll &operator/=(const mll &b) {
    ll c = b.val, d = MOD, u = 1, v = 0;
    while (d) {
      ll t = c / d;
      c -= t * d;
      swap(c, d);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  mll &operator+=(ll b) { return *this += mll(b); }
  mll &operator-=(ll b) { return *this -= mll(b); }
  mll &operator*=(ll b) { return *this *= mll(b); }
  mll &operator/=(ll b) { return *this /= mll(b); }
  bool operator==(const mll &b) { return val == b.val; }
  bool operator!=(const mll &b) { return val != b.val; }
  bool operator==(ll b) { return *this == mll(b); }
  bool operator!=(ll b) { return *this != mll(b); }
  friend bool operator==(ll a, const mll &b) { return mll(a) == b.val; }
  friend bool operator!=(ll a, const mll &b) { return mll(a) != b.val; }
  friend ostream &operator<<(ostream &os, const mll &a) { return os << a.val; }
  friend istream &operator>>(istream &is, mll &a) { return is >> a.val; }
  static mll Combination(ll a, ll b) {
    chmin(b, a - b);
    if (b < 0)
      return mll(0);
    mll c = 1;
    REP(i, b) c *= a - i;
    REP(i, b) c /= i + 1;
    return c;
  }
};
ll mll::MOD = 1000000007LL; // 998244353LL;//1000000007LL;
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
using vvvvvmll = std::vector<vvvvmll>;

vll done;
vvll to;

void dfs(ll v, ll &diff) {
  EACH(u, to[v]) {
    if (done[u] == 0) {
      done[u] = -done[v];
      diff += done[u];
      dfs(u, diff);
    } else if (done[u] == done[v]) {
      bye(-1);
    } else {
    }
  }
}

void solve() {
  ll N, M;
  cin >> N >> M;
  vector<pair<ll, ll>> AB = cinv2<ll, ll>(M);

  vvll gy(N, vll(N));
  EACH(e, AB) {
    ll a;
    ll b;
    tie(a, b) = e;
    a--;
    b--;
    gy[a][b] = 1;
    gy[b][a] = 1;
  }

  to.resize(N);
  REP(i, N) REP(j, N) {
    if (i == j)
      continue;
    if (gy[i][j] == 1)
      continue;
    to[i].push_back(j);
  }

  done.resize(N);
  vll df;

  REP(v, N) {
    if (done[v] != 0)
      continue;
    done[v] = 1;
    ll diff = 1;
    dfs(v, diff);
    df.push_back(abs(diff));
  }

  ll dfN = (ll)df.size();

  vvll dp(dfN, vll(N));
  auto Dp = [&](ll i, ll d) -> ll & { return dp[i][abs(d)]; };

  dp[0][df[0]] = 1;
  REPS(i, 1, dfN - 1) {
    REP(d, N) {
      if (Dp(i - 1, d) == 0)
        continue;
      Dp(i, d + df[i]) = 1;
      Dp(i, d - df[i]) = 1;
    }
  }

  ll sa;
  REP(d, N) {
    if (Dp(dfN - 1, d) == 1) {
      sa = d;
      break;
    }
  }
  ll x = (N - sa) / 2;
  ll y = N - x;
  ll ans = x * (x - 1) / 2 + y * (y - 1) / 2;
  cout << ans << '\n';
}

int main() {
  solve();
  return 0;
}


Fixed submission:
#include "bits/stdc++.h"
using namespace std;
using ll = long long;
using dd = double;
using pll = pair<ll, ll>;
using tll = tuple<ll, ll, ll>;
using vll = vector<ll>;
using vdd = vector<dd>;
using vpll = vector<pll>;
using vtll = vector<tll>;
using vvll = vector<vll>;
using vvdd = vector<vdd>;
using vvpll = vector<vpll>;
using vvtll = vector<vtll>;
using vvvll = vector<vvll>;
using vvvdd = vector<vvdd>;
using vvvpll = vector<vvpll>;
using vvvtll = vector<vvtll>;
using vvvvll = vector<vvvll>;
using vvvvdd = vector<vvvdd>;
using vvvvpll = vector<vvvpll>;
using vvvvtll = vector<vvvtll>;

constexpr ll INF = 1LL << 60;
constexpr dd EPS = 1e-11;

// cin,cout高速化のおまじない＋桁数指定
struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
  }
} fast;

#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define EACH(e, v) for (auto &&e : v)

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline T MaxE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmax(m, v[i]);
  return m;
} // v[S]～v[E]の最大値
template <class T> inline T MinE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmin(m, v[i]);
  return m;
} // v[S]～v[E]の最小値
template <class T> inline T MaxE(vector<T> &v, ll N) {
  return MaxE(v, 0, N - 1);
} // 先頭N個中の最大値
template <class T> inline T MinE(vector<T> &v, ll N) {
  return MinE(v, 0, N - 1);
}
template <class T> inline T MaxE(vector<T> &v) { return MaxE(v, (ll)v.size()); }
template <class T> inline T MinE(vector<T> &v) { return MinE(v, (ll)v.size()); }
template <class T> inline ll MaxI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] > v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MinI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] < v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MaxI(vector<T> &v, ll N) {
  return MaxI(v, 0, N - 1);
}
template <class T> inline ll MinI(vector<T> &v, ll N) {
  return MinI(v, 0, N - 1);
}
template <class T> inline ll MaxI(vector<T> &v) {
  return MaxI(v, (ll)v.size());
}
template <class T> inline ll MinI(vector<T> &v) {
  return MinI(v, (ll)v.size());
}
template <class T> inline T Sum(vector<T> &v, ll S, ll E) {
  T s = v[S];
  REPS(i, S + 1, E) s += v[i];
  return s;
}
template <class T> inline T Sum(vector<T> &v, ll N) { return Sum(v, 0, N - 1); }
template <class T> inline T Sum(vector<T> &v) { return Sum(v, v.size()); }
template <class T> inline T POW(T a, ll n) {
  T r = 1;
  for (; n > 0; n >>= 1, a *= a) {
    if (n & 1)
      r *= a;
  }
  return r;
}
inline ll POW(int a, ll n) { return POW((ll)a, n); }
inline ll MSB(ll a) {
  for (ll o = 63, x = -1;;) {
    ll m = (o + x) / 2;
    if (a < (1LL << m))
      o = m;
    else
      x = m;
    if (o - x == 1)
      return x;
  }
}
inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; }
ll Gcd(ll a, ll b) { return (b == 0) ? a : Gcd(b, a % b); }
ll Lcm(ll a, ll b) { return a * b / Gcd(a, b); }
inline vll Mask2Idx(ll m) {
  vll v;
  for (ll i = 0; m; m >>= 1, i++)
    if (m & 1)
      v.push_back(i);
  return move(v);
}
inline ll BitNum(ll m) {
  for (ll c = 0;; m >>= 1) {
    c += m & 1;
    if (!m)
      return c;
  }
}
inline ll Bit(ll s, ll i) { return (s >> i) & 1; }       // sの第ibit i=0-63
inline ll BitOn(ll s, ll i) { return s | (1LL << i); }   // sの第ibitON i=0-63
inline ll BitOff(ll s, ll i) { return s & ~(1LL << i); } // sの第ibitOFF i=0-63
template <class T>
inline ll UnderNumOf(vector<T> &v, T x) { // sort済vのx以下の個数を得る
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
template <class T, class Pr>
inline ll UnderNumOf(vector<T> &v, T x, Pr pred) { // x以下個数
  return upper_bound(v.begin(), v.end(), x, pred) - v.begin();
}
template <class T>
inline ll OverNumOf(vector<T> &v, T x) { // sort済vのx以上の個数を得る
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x) - v.begin());
}
template <class T, class Pr>
inline ll OverNumOf(vector<T> &v, T x, Pr pred) { // x以上の個数
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x, pred) - v.begin());
}

template <class T = ll> inline vector<T> cinv(ll N) {
  vector<T> v(N);
  REP(i, N) cin >> v[i];
  return move(v);
}
template <class T = ll, class S = ll> inline vector<pair<T, S>> cinv2(ll N) {
  vector<pair<T, S>> v(N);
  REP(i, N) { cin >> v[i].first >> v[i].second; }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll>
inline vector<tuple<T, S, R>> cinv3(ll N) {
  vector<tuple<T, S, R>> v(N);
  REP(i, N) { cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]); }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll, class Q = ll>
inline vector<tuple<T, S, R, Q>> cinv4(ll N) {
  vector<tuple<T, S, R, Q>> v(N);
  REP(i, N) {
    cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]) >> get<3>(v[i]);
  }
  return move(v);
}
template <class T = ll> inline vector<vector<T>> cinvv(ll N, ll M) {
  vector<vector<T>> vv(N);
  REP(i, N) vv[i] = cinv(M);
  return move(vv);
}
template <class T> inline void coutv(vector<T> &v, char deli = ' ') {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? '\n' : deli); }
}
template <class T> void bye(T a) {
  cout << a << '\n';
  exit(0);
}

#if defined(_DEBUG)
template <class T> void Dump(vector<T> &v) {
  REP(i, (ll)v.size()) { cerr << ((i == 0) ? "[" : " ") << setw(5) << v[i]; }
  cerr << "]";
}
void Dump(vll &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(4);
    if (v[i] == INF)
      cerr << "INF";
    else if (v[i] == -INF)
      cerr << "-INF";
    else
      cerr << v[i];
  }
  cerr << "]";
}
template <class T> void Dump(vector<vector<T>> &v) {
  ll N = (ll)v.size();
  string d[2][2] = {{" ", "["}, {"\n", "]\n"}};
  REP(i, N) {
    cerr << d[0][i == 0];
    Dump(v[i]);
    cerr << d[1][i == N - 1];
  }
}
template <class T> void Dump(vector<vector<vector<T>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  <", "[ <"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ---<", "[ ---<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">---\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ======<", "[ ======<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">======\n";
    Dump(v[i]);
  }
  cerr << "]\n";
}
#else
template <class T> void Dump(vector<T> &v) {}
template <class T> void Dump(vector<vector<T>> &v) {}
template <class T> void Dump(vector<vector<vector<T>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {}
#endif

struct mll {
  static ll MOD;
  ll val;
  mll(ll v = 0) : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  mll operator-() const { return -val; }
  mll operator+(const mll &b) const { return val + b.val; }
  mll operator-(const mll &b) const { return val - b.val; }
  mll operator*(const mll &b) const { return val * b.val; }
  mll operator/(const mll &b) const { return mll(*this) /= b; }
  mll operator+(ll b) const { return *this + mll(b); }
  mll operator-(ll b) const { return *this - mll(b); }
  mll operator*(ll b) const { return *this * mll(b); }
  friend mll operator+(ll a, const mll &b) { return b + a; }
  friend mll operator-(ll a, const mll &b) { return -b + a; }
  friend mll operator*(ll a, const mll &b) { return b * a; }
  friend mll operator/(ll a, const mll &b) { return mll(a) / b; }
  mll &operator+=(const mll &b) {
    val = (val + b.val) % MOD;
    return *this;
  }
  mll &operator-=(const mll &b) {
    val = (val + MOD - b.val) % MOD;
    return *this;
  }
  mll &operator*=(const mll &b) {
    val = (val * b.val) % MOD;
    return *this;
  }
  mll &operator/=(const mll &b) {
    ll c = b.val, d = MOD, u = 1, v = 0;
    while (d) {
      ll t = c / d;
      c -= t * d;
      swap(c, d);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  mll &operator+=(ll b) { return *this += mll(b); }
  mll &operator-=(ll b) { return *this -= mll(b); }
  mll &operator*=(ll b) { return *this *= mll(b); }
  mll &operator/=(ll b) { return *this /= mll(b); }
  bool operator==(const mll &b) { return val == b.val; }
  bool operator!=(const mll &b) { return val != b.val; }
  bool operator==(ll b) { return *this == mll(b); }
  bool operator!=(ll b) { return *this != mll(b); }
  friend bool operator==(ll a, const mll &b) { return mll(a) == b.val; }
  friend bool operator!=(ll a, const mll &b) { return mll(a) != b.val; }
  friend ostream &operator<<(ostream &os, const mll &a) { return os << a.val; }
  friend istream &operator>>(istream &is, mll &a) { return is >> a.val; }
  static mll Combination(ll a, ll b) {
    chmin(b, a - b);
    if (b < 0)
      return mll(0);
    mll c = 1;
    REP(i, b) c *= a - i;
    REP(i, b) c /= i + 1;
    return c;
  }
};
ll mll::MOD = 1000000007LL; // 998244353LL;//1000000007LL;
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
using vvvvvmll = std::vector<vvvvmll>;

vll done;
vvll to;

void dfs(ll v, ll &diff) {
  EACH(u, to[v]) {
    if (done[u] == 0) {
      done[u] = -done[v];
      diff += done[u];
      dfs(u, diff);
    } else if (done[u] == done[v]) {
      bye(-1);
    } else {
    }
  }
}

void solve() {
  ll N, M;
  cin >> N >> M;
  vector<pair<ll, ll>> AB = cinv2<ll, ll>(M);

  vvll gy(N, vll(N));
  EACH(e, AB) {
    ll a;
    ll b;
    tie(a, b) = e;
    a--;
    b--;
    gy[a][b] = 1;
    gy[b][a] = 1;
  }

  to.resize(N);
  REP(i, N) REP(j, N) {
    if (i == j)
      continue;
    if (gy[i][j] == 1)
      continue;
    to[i].push_back(j);
  }

  done.resize(N);
  vll df;

  REP(v, N) {
    if (done[v] != 0)
      continue;
    done[v] = 1;
    ll diff = 1;
    dfs(v, diff);
    df.push_back(abs(diff));
  }

  ll dfN = (ll)df.size();

  vvll dp(dfN, vll(N));
  auto Dp = [&](ll i, ll d) -> ll & {
    static ll dmy = 0;
    d = abs(d);
    if (d >= N)
      return dmy;
    return dp[i][d];
  };

  dp[0][df[0]] = 1;
  REPS(i, 1, dfN - 1) {
    REP(d, N) {
      if (Dp(i - 1, d) == 0)
        continue;
      Dp(i, d + df[i]) = 1;
      Dp(i, d - df[i]) = 1;
    }
  }

  ll sa;
  REP(d, N) {
    if (Dp(dfN - 1, d) == 1) {
      sa = d;
      break;
    }
  }
  ll x = (N - sa) / 2;
  ll y = N - x;
  ll ans = x * (x - 1) / 2 + y * (y - 1) / 2;
  cout << ans << '\n';
}

int main() {
  solve();
  return 0;
}