Problem p02539 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define ALL(obj) (obj).begin(), (obj).end()
template <class T>
using priority_queue_reverse = priority_queue<T, vector<T>, greater<T>>;

constexpr long long MOD = 1'000'000'000LL + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433L;

template <class T> vector<T> multivector(size_t N, T init) {
  return vector<T>(N, init);
}
template <class... T> auto multivector(size_t N, T... t) {
  return vector<decltype(multivector(t...))>(N, multivector(t...));
}
template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const multiset<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max(a, b); }
template <class T> void chmin(T &a, const T b) { a = min(a, b); }
vector<string> split(const string &str, const char delemiter) {
  vector<string> res;
  stringstream ss(str);
  string buffer;
  while (getline(ss, buffer, delemiter))
    res.push_back(buffer);
  return res;
}
int msb(int x) { return x ? 31 - __builtin_clz(x) : -1; }
void YN(bool flg) { cout << (flg ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << (flg ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << (flg ? "yes" : "no") << endl; }

/*
 * @title ModInt
 * @docs md/util/ModInt.md
 */
template <long long mod> class ModInt {
public:
  long long x;
  constexpr ModInt() : x(0) {}
  constexpr ModInt(long long y)
      : x(y >= 0 ? (y % mod) : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator+=(const long long y) {
    ModInt p(y);
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator+=(const int y) {
    ModInt p(y);
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const long long y) {
    ModInt p(y);
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const int y) {
    ModInt p(y);
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator*=(const long long y) {
    ModInt p(y);
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator*=(const int y) {
    ModInt p(y);
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator^=(const ModInt &p) {
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator^=(const long long y) {
    ModInt p(y);
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator^=(const int y) {
    ModInt p(y);
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inv();
    return *this;
  }
  ModInt &operator/=(const long long y) {
    ModInt p(y);
    *this *= p.inv();
    return *this;
  }
  ModInt &operator/=(const int y) {
    ModInt p(y);
    *this *= p.inv();
    return *this;
  }
  ModInt operator=(const int y) {
    ModInt p(y);
    *this = p;
    return *this;
  }
  ModInt operator=(const long long y) {
    ModInt p(y);
    *this = p;
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator++() {
    x++;
    if (x >= mod)
      x -= mod;
    return *this;
  }
  ModInt operator--() {
    x--;
    if (x < 0)
      x += mod;
    return *this;
  }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inv() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(long long n) const {
    ModInt ret(1), mul(x);
    for (; n > 0; mul *= mul, n >>= 1)
      if (n & 1)
        ret *= mul;
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    long long t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
};
using modint = ModInt<MOD2>;

/*
 * @title FormalPowerSeries - 形式的冪級数
 * @docs md/math/FormalPowerSeries.md
 */
template <int mod> struct FormalPowerSeries : public vector<ModInt<mod>> {
  inline static constexpr int prime1 = 1004535809;
  inline static constexpr int prime2 = 998244353;
  inline static constexpr int prime3 = 985661441;
  inline static constexpr int inv21 = 332747959; // ModInt<mod2>(mod1).inv().x;
  inline static constexpr int inv31 = 766625513; // ModInt<mod3>(mod1).inv().x;
  inline static constexpr int inv32 = 657107549; // ModInt<mod3>(mod2).inv().x;
  inline static constexpr int prime12 = (1002772198720536577LL) % mod;
  inline static constexpr array<int, 26> pow2 = {
      1,       2,       4,       8,        16,      32,     64,
      128,     256,     512,     1024,     2048,    4096,   8192,
      16384,   32768,   65536,   131072,   262144,  524288, 1048576,
      2097152, 4194304, 8388608, 16777216, 33554432};
  using vector<ModInt<mod>>::vector;
  using Mint = ModInt<mod>;
  using Mint1 = ModInt<prime1>;
  using Mint2 = ModInt<prime2>;
  using Mint3 = ModInt<prime3>;
  using Fps = FormalPowerSeries<mod>;
  Fps even(void) const {
    Fps ret;
    for (int i = 0; i < this->size(); i += 2)
      ret.push_back((*this)[i]);
    return ret;
  }
  Fps odd(void) const {
    Fps ret;
    for (int i = 1; i < this->size(); i += 2)
      ret.push_back((*this)[i]);
    return ret;
  }
  Fps minus_x(void) const {
    Fps ret(this->size());
    for (int i = 0; i < ret.size(); ++i)
      ret[i] = (*this)[i] * (i & 1 ? -1 : 1);
    return ret;
  }
  inline Mint garner(const Mint1 &b1, const Mint2 &b2, const Mint3 &b3) {
    Mint2 t2 = (b2 - b1.x) * inv21;
    Mint3 t3 = ((b3 - b1.x) * inv31 - t2.x) * inv32;
    return Mint(prime12 * t3.x + b1.x + prime1 * t2.x);
  }
  template <int prime> inline void ntt(vector<ModInt<prime>> &f) {
    const int N = f.size(), M = N >> 1;
    const int log2N = __builtin_ctz(N);
    ModInt<prime> h(3);
    vector<ModInt<prime>> g(N), base(log2N);
    for (int i = 0; i < log2N; ++i)
      base[i] = h.pow((prime - 1) / pow2[i + 1]);
    for (int n = 0; n < log2N; ++n) {
      const int &p = pow2[log2N - n - 1];
      ModInt<prime> w = 1;
      for (int i = 0, k = 0; i < M; i += p, k = i << 1, w *= base[n]) {
        for (int j = 0; j < p; ++j) {
          ModInt<prime> l = f[k | j], r = w * f[k | j | p];
          g[i | j] = l + r;
          g[i | j | M] = l - r;
        }
      }
      swap(f, g);
    }
  }
  template <int prime = mod>
  inline vector<ModInt<prime>> convolution_friendrymod(const vector<Mint> &a,
                                                       const vector<Mint> &b) {
    if (min(a.size(), b.size()) <= 60) {
      vector<ModInt<prime>> f(a.size() + b.size() - 1);
      for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < b.size(); j++)
          f[i + j] += a[i].x * b[j].x;
      return f;
    }
    int N, M = a.size() + b.size() - 1;
    for (N = 1; N < M; N *= 2)
      ;
    ModInt<prime> inverse(N);
    inverse = inverse.inv();
    vector<ModInt<prime>> g(N, 0), h(N, 0);
    for (int i = 0; i < a.size(); ++i)
      g[i] = a[i].x;
    for (int i = 0; i < b.size(); ++i)
      h[i] = b[i].x;
    ntt<prime>(g);
    ntt<prime>(h);
    for (int i = 0; i < N; ++i)
      g[i] *= h[i] * inverse;
    reverse(g.begin() + 1, g.end());
    ntt<prime>(g);
    return g;
  }
  inline vector<Mint> convolution_arbitrarymod(const vector<Mint> &g,
                                               const vector<Mint> &h) {
    auto f1 = convolution_friendrymod<prime1>(g, h);
    auto f2 = convolution_friendrymod<prime2>(g, h);
    auto f3 = convolution_friendrymod<prime3>(g, h);
    vector<Mint> f(f1.size());
    for (int i = 0; i < f1.size(); ++i)
      f[i] = garner(f1[i], f2[i], f3[i]);
    return f;
  }
  inline vector<ModInt<998244353>>
  convolution(const vector<ModInt<998244353>> &g,
              const vector<ModInt<998244353>> &h) {
    return convolution_friendrymod<998244353>(g, h);
  }
  inline vector<ModInt<1000000007>>
  convolution(const vector<ModInt<1000000007>> &g,
              const vector<ModInt<1000000007>> &h) {
    return convolution_arbitrarymod(g, h);
  }
  static inline Mint nth_term_impl(long long n, Fps numerator,
                                   Fps denominator) {
    while (n) {
      numerator *= denominator.minus_x();
      numerator = ((n & 1) ? numerator.odd() : numerator.even());
      denominator *= denominator.minus_x();
      denominator = denominator.even();
      n >>= 1;
    }
    return numerator[0];
  }

public:
  // a0 + a_1*x^1 + a_2*x^2 + ... + a_(n-1)*x^(n-1)
  inline static Mint nth_term(long long n, const Fps &numerator,
                              const Fps &denominator) {
    return nth_term_impl(n, numerator, denominator);
  }
  FormalPowerSeries(vector<Mint> v) {
    *this = FormalPowerSeries(v.size());
    for (int i = 0; i < v.size(); ++i)
      (*this)[i] = v[i];
  }
  Fps operator*(const Fps &r) const { return Fps(*this) *= r; }
  Fps &operator*=(const Fps &r) { return *this = convolution(*this, r); }
  Fps operator*(const int r) const { return Fps(*this) *= r; }
  Fps &operator*=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator*(const long long int r) const { return Fps(*this) *= r; }
  Fps &operator*=(const long long int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator*(const Mint r) const { return Fps(*this) *= r; }
  Fps &operator*=(const Mint r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator/(const int r) const { return Fps(*this) /= r; }
  Fps &operator/=(const int r) { return (*this) *= Mint(r).inv(); }
  Fps operator+(const Fps &r) const { return Fps(*this) += r; }
  Fps &operator+=(const Fps &r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < r.size(); i++)
      (*this)[i] += r[i];
    return *this;
  }
  Fps operator+(const int r) const { return Fps(*this) += r; }
  Fps &operator+=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] += r;
    return *this;
  }
  Fps operator-(void) const { return Fps(*this) *= (-1); }
  Fps operator-(const Fps &r) const { return Fps(*this) -= r; }
  Fps &operator-=(const Fps &r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < r.size(); i++)
      (*this)[i] -= r[i];
    return *this;
  }
  Fps operator-(const int r) const { return Fps(*this) -= r; }
  Fps &operator-=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] -= r;
    return *this;
  }
  Fps prefix(size_t n) const {
    return Fps(this->begin(), this->begin() + min(n, this->size()));
  }
  Fps pow(long long k, size_t n) const {
    Fps ret(n, 0);
    for (size_t i = 0; i < min(n, this->size()) && i * k < n; ++i) {
      if ((*this)[i].x == 0)
        continue;
      Mint t0 = (*this)[i], t0_inv = t0.inv();
      Fps tmp(n - i);
      for (int j = i; j < min(n, this->size()); ++j)
        tmp[j - i] = (*this)[j] * t0_inv;
      tmp = (tmp.log(n) * k).exp(n) * (t0.pow(k));
      for (int j = 0; j + i * k < n; ++j)
        ret[j + i * k] = tmp[j];
      break;
    }
    return ret;
  }
  Fps pow(long long k) const { return pow(k, this->size()); }
  Fps inv(size_t n) const {
    Fps ret({Mint(1) / (*this)[0]});
    for (size_t i = 1; i < n; i <<= 1)
      ret = (ret * 2 - ret * (ret * (this->prefix(i << 1))).prefix(i << 1))
                .prefix(i << 1);
    return ret.prefix(n);
  }
  Fps inv(void) const { return inv(this->size()); }
  Fps diff(void) const {
    Fps ret(max(0, int(this->size()) - 1));
    for (int i = 0; i < ret.size(); ++i)
      ret[i] = (*this)[i + 1] * (i + 1);
    return ret;
  }
  Fps intg(void) const {
    Fps ret(this->size() + 1);
    for (int i = 1; i < ret.size(); ++i)
      ret[i] = (*this)[i - 1] / i;
    return ret;
  }
  Fps log(size_t n) const {
    return (this->diff() * this->inv(n)).intg().prefix(n);
  }
  Fps log(void) const { return log(this->size()); }
  Fps exp(size_t n) const {
    Fps ret(1, 1);
    for (size_t i = 1; i < n; i <<= 1)
      ret = (ret * (this->prefix(i << 1) + Fps(1, 1) - ret.log(i << 1)))
                .prefix(i << 1);
    return ret.prefix(n);
  }
  Fps exp(void) const { return exp(this->size()); }
  friend ostream &operator<<(ostream &os, const Fps &fps) {
    os << "{" << fps[0];
    for (int i = 1; i < fps.size(); ++i)
      os << ", " << fps[i];
    return os << "}";
  }
};

using fps = FormalPowerSeries<MOD2>;

/*
 * @title CombinationMod - mod上の二項係数・階乗
 * @docs md/math/CombinationMod.md
 */
template <long long mod> class CombinationMod {
  vector<long long> fac, finv, inv;

public:
  CombinationMod(int N) : fac(N + 1), finv(N + 1), inv(N + 1) {
    fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
    for (int i = 2; i <= N; ++i) {
      fac[i] = fac[i - 1] * i % mod;
      inv[i] = mod - inv[mod % i] * (mod / i) % mod;
      finv[i] = finv[i - 1] * inv[i] % mod;
    }
  }
  inline long long binom(int n, int k) {
    return ((n < 0 || k < 0 || n < k)
                ? 0
                : fac[n] * (finv[k] * finv[n - k] % mod) % mod);
  }
  inline long long factorial(int n) { return fac[n]; }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;

  int M = 100000;
  vector<int> cnt(M + 1, 0);
  for (int i = 0; i < 2 * N; ++i) {
    int h;
    cin >> h;
    cnt[h]++;
  }

  vector<modint> fact_odd(2 * N, 0);
  fact_odd[1] = 1;
  for (int i = 3; i < 2 * N; i += 2)
    fact_odd[i] = fact_odd[i - 2] * i;

  CombinationMod<MOD2> CM(2 * N);

  vector<fps> vf;
  priority_queue_reverse<pair<int, int>> pq;
  for (int i = 1; i <= M; ++i) {
    if (!cnt[i])
      continue;
    int n = cnt[i];
    int m = n / 2;
    fps f(m + 1, 0);
    f[0] = 1;
    for (int j = 1; j <= m; ++j) {
      // n人から2j人選ぶ-> n_C_2j
      // 2j人からjペア作る-> (2j-1)*(2j-3)*...*3*1;
      f[j] = fact_odd[2 * j - 1] * CM.binom(n, 2 * j);
    }
    vf.push_back(f);
    pq.push({f.size(), vf.size() - 1});
  }
  while (pq.size() >= 2) {
    auto l = pq.top().second;
    pq.pop();
    auto r = pq.top().second;
    pq.pop();
    auto f = vf[l] * vf[r];
    vf.push_back(f);
    pq.push({f.size(), vf.size() - 1});
  }
  modint ans = 0;
  {
    auto c = pq.top().second;
    pq.pop();
    auto f = vf[c];
    int m = min(int(f.size()), N + 1);
    for (int i = 0; i < m; ++i)
      f[i] *= (i == N ? 1 : fact_odd[2 * (N - i) - 1]);
    for (int i = 0; i < m; ++i)
      ans += f[i] * (1 - 2 * (i % 2));
  }
  cout << ans << endl;
  return 0;
}


Error: 0

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define ALL(obj) (obj).begin(), (obj).end()
template <class T>
using priority_queue_reverse = priority_queue<T, vector<T>, greater<T>>;

constexpr long long MOD = 1'000'000'000LL + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433L;

template <class T> vector<T> multivector(size_t N, T init) {
  return vector<T>(N, init);
}
template <class... T> auto multivector(size_t N, T... t) {
  return vector<decltype(multivector(t...))>(N, multivector(t...));
}
template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const multiset<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max(a, b); }
template <class T> void chmin(T &a, const T b) { a = min(a, b); }
vector<string> split(const string &str, const char delemiter) {
  vector<string> res;
  stringstream ss(str);
  string buffer;
  while (getline(ss, buffer, delemiter))
    res.push_back(buffer);
  return res;
}
int msb(int x) { return x ? 31 - __builtin_clz(x) : -1; }
void YN(bool flg) { cout << (flg ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << (flg ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << (flg ? "yes" : "no") << endl; }

/*
 * @title ModInt
 * @docs md/util/ModInt.md
 */
template <long long mod> class ModInt {
public:
  long long x;
  constexpr ModInt() : x(0) {}
  constexpr ModInt(long long y)
      : x(y >= 0 ? (y % mod) : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator+=(const long long y) {
    ModInt p(y);
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator+=(const int y) {
    ModInt p(y);
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const long long y) {
    ModInt p(y);
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const int y) {
    ModInt p(y);
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator*=(const long long y) {
    ModInt p(y);
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator*=(const int y) {
    ModInt p(y);
    x = (x * p.x % mod);
    return *this;
  }
  ModInt &operator^=(const ModInt &p) {
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator^=(const long long y) {
    ModInt p(y);
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator^=(const int y) {
    ModInt p(y);
    x = (x ^ p.x) % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inv();
    return *this;
  }
  ModInt &operator/=(const long long y) {
    ModInt p(y);
    *this *= p.inv();
    return *this;
  }
  ModInt &operator/=(const int y) {
    ModInt p(y);
    *this *= p.inv();
    return *this;
  }
  ModInt operator=(const int y) {
    ModInt p(y);
    *this = p;
    return *this;
  }
  ModInt operator=(const long long y) {
    ModInt p(y);
    *this = p;
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator++() {
    x++;
    if (x >= mod)
      x -= mod;
    return *this;
  }
  ModInt operator--() {
    x--;
    if (x < 0)
      x += mod;
    return *this;
  }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inv() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(long long n) const {
    ModInt ret(1), mul(x);
    for (; n > 0; mul *= mul, n >>= 1)
      if (n & 1)
        ret *= mul;
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    long long t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
};
using modint = ModInt<MOD2>;

/*
 * @title FormalPowerSeries - 形式的冪級数
 * @docs md/math/FormalPowerSeries.md
 */
template <int mod> struct FormalPowerSeries : public vector<ModInt<mod>> {
  inline static constexpr int prime1 = 1004535809;
  inline static constexpr int prime2 = 998244353;
  inline static constexpr int prime3 = 985661441;
  inline static constexpr int inv21 = 332747959; // ModInt<mod2>(mod1).inv().x;
  inline static constexpr int inv31 = 766625513; // ModInt<mod3>(mod1).inv().x;
  inline static constexpr int inv32 = 657107549; // ModInt<mod3>(mod2).inv().x;
  inline static constexpr int prime12 = (1002772198720536577LL) % mod;
  inline static constexpr array<int, 26> pow2 = {
      1,       2,       4,       8,        16,      32,     64,
      128,     256,     512,     1024,     2048,    4096,   8192,
      16384,   32768,   65536,   131072,   262144,  524288, 1048576,
      2097152, 4194304, 8388608, 16777216, 33554432};
  using vector<ModInt<mod>>::vector;
  using Mint = ModInt<mod>;
  using Mint1 = ModInt<prime1>;
  using Mint2 = ModInt<prime2>;
  using Mint3 = ModInt<prime3>;
  using Fps = FormalPowerSeries<mod>;
  Fps even(void) const {
    Fps ret;
    for (int i = 0; i < this->size(); i += 2)
      ret.push_back((*this)[i]);
    return ret;
  }
  Fps odd(void) const {
    Fps ret;
    for (int i = 1; i < this->size(); i += 2)
      ret.push_back((*this)[i]);
    return ret;
  }
  Fps minus_x(void) const {
    Fps ret(this->size());
    for (int i = 0; i < ret.size(); ++i)
      ret[i] = (*this)[i] * (i & 1 ? -1 : 1);
    return ret;
  }
  inline Mint garner(const Mint1 &b1, const Mint2 &b2, const Mint3 &b3) {
    Mint2 t2 = (b2 - b1.x) * inv21;
    Mint3 t3 = ((b3 - b1.x) * inv31 - t2.x) * inv32;
    return Mint(prime12 * t3.x + b1.x + prime1 * t2.x);
  }
  template <int prime> inline void ntt(vector<ModInt<prime>> &f) {
    const int N = f.size(), M = N >> 1;
    const int log2N = __builtin_ctz(N);
    ModInt<prime> h(3);
    vector<ModInt<prime>> g(N), base(log2N);
    for (int i = 0; i < log2N; ++i)
      base[i] = h.pow((prime - 1) / pow2[i + 1]);
    for (int n = 0; n < log2N; ++n) {
      const int &p = pow2[log2N - n - 1];
      ModInt<prime> w = 1;
      for (int i = 0, k = 0; i < M; i += p, k = i << 1, w *= base[n]) {
        for (int j = 0; j < p; ++j) {
          ModInt<prime> l = f[k | j], r = w * f[k | j | p];
          g[i | j] = l + r;
          g[i | j | M] = l - r;
        }
      }
      swap(f, g);
    }
  }
  template <int prime = mod>
  inline vector<ModInt<prime>> convolution_friendrymod(const vector<Mint> &a,
                                                       const vector<Mint> &b) {
    if (min(a.size(), b.size()) <= 60) {
      vector<ModInt<prime>> f(a.size() + b.size() - 1);
      for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < b.size(); j++)
          f[i + j] += a[i].x * b[j].x;
      return f;
    }
    int N, M = a.size() + b.size() - 1;
    for (N = 1; N < M; N *= 2)
      ;
    ModInt<prime> inverse(N);
    inverse = inverse.inv();
    vector<ModInt<prime>> g(N, 0), h(N, 0);
    for (int i = 0; i < a.size(); ++i)
      g[i] = a[i].x;
    for (int i = 0; i < b.size(); ++i)
      h[i] = b[i].x;
    ntt<prime>(g);
    ntt<prime>(h);
    for (int i = 0; i < N; ++i)
      g[i] *= h[i] * inverse;
    reverse(g.begin() + 1, g.end());
    ntt<prime>(g);
    return g;
  }
  inline vector<Mint> convolution_arbitrarymod(const vector<Mint> &g,
                                               const vector<Mint> &h) {
    auto f1 = convolution_friendrymod<prime1>(g, h);
    auto f2 = convolution_friendrymod<prime2>(g, h);
    auto f3 = convolution_friendrymod<prime3>(g, h);
    vector<Mint> f(f1.size());
    for (int i = 0; i < f1.size(); ++i)
      f[i] = garner(f1[i], f2[i], f3[i]);
    return f;
  }
  inline vector<ModInt<998244353>>
  convolution(const vector<ModInt<998244353>> &g,
              const vector<ModInt<998244353>> &h) {
    return convolution_friendrymod<998244353>(g, h);
  }
  inline vector<ModInt<1000000007>>
  convolution(const vector<ModInt<1000000007>> &g,
              const vector<ModInt<1000000007>> &h) {
    return convolution_arbitrarymod(g, h);
  }
  static inline Mint nth_term_impl(long long n, Fps numerator,
                                   Fps denominator) {
    while (n) {
      numerator *= denominator.minus_x();
      numerator = ((n & 1) ? numerator.odd() : numerator.even());
      denominator *= denominator.minus_x();
      denominator = denominator.even();
      n >>= 1;
    }
    return numerator[0];
  }

public:
  // a0 + a_1*x^1 + a_2*x^2 + ... + a_(n-1)*x^(n-1)
  inline static Mint nth_term(long long n, const Fps &numerator,
                              const Fps &denominator) {
    return nth_term_impl(n, numerator, denominator);
  }
  FormalPowerSeries(vector<Mint> v) {
    *this = FormalPowerSeries(v.size());
    for (int i = 0; i < v.size(); ++i)
      (*this)[i] = v[i];
  }
  Fps operator*(const Fps &r) const { return Fps(*this) *= r; }
  Fps &operator*=(const Fps &r) { return *this = convolution(*this, r); }
  Fps operator*(const int r) const { return Fps(*this) *= r; }
  Fps &operator*=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator*(const long long int r) const { return Fps(*this) *= r; }
  Fps &operator*=(const long long int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator*(const Mint r) const { return Fps(*this) *= r; }
  Fps &operator*=(const Mint r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] *= r;
    return *this;
  }
  Fps operator/(const int r) const { return Fps(*this) /= r; }
  Fps &operator/=(const int r) { return (*this) *= Mint(r).inv(); }
  Fps operator+(const Fps &r) const { return Fps(*this) += r; }
  Fps &operator+=(const Fps &r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < r.size(); i++)
      (*this)[i] += r[i];
    return *this;
  }
  Fps operator+(const int r) const { return Fps(*this) += r; }
  Fps &operator+=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] += r;
    return *this;
  }
  Fps operator-(void) const { return Fps(*this) *= (-1); }
  Fps operator-(const Fps &r) const { return Fps(*this) -= r; }
  Fps &operator-=(const Fps &r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < r.size(); i++)
      (*this)[i] -= r[i];
    return *this;
  }
  Fps operator-(const int r) const { return Fps(*this) -= r; }
  Fps &operator-=(const int r) {
    for (int i = 0; i < this->size(); ++i)
      (*this)[i] -= r;
    return *this;
  }
  Fps prefix(size_t n) const {
    return Fps(this->begin(), this->begin() + min(n, this->size()));
  }
  Fps pow(long long k, size_t n) const {
    Fps ret(n, 0);
    for (size_t i = 0; i < min(n, this->size()) && i * k < n; ++i) {
      if ((*this)[i].x == 0)
        continue;
      Mint t0 = (*this)[i], t0_inv = t0.inv();
      Fps tmp(n - i);
      for (int j = i; j < min(n, this->size()); ++j)
        tmp[j - i] = (*this)[j] * t0_inv;
      tmp = (tmp.log(n) * k).exp(n) * (t0.pow(k));
      for (int j = 0; j + i * k < n; ++j)
        ret[j + i * k] = tmp[j];
      break;
    }
    return ret;
  }
  Fps pow(long long k) const { return pow(k, this->size()); }
  Fps inv(size_t n) const {
    Fps ret({Mint(1) / (*this)[0]});
    for (size_t i = 1; i < n; i <<= 1)
      ret = (ret * 2 - ret * (ret * (this->prefix(i << 1))).prefix(i << 1))
                .prefix(i << 1);
    return ret.prefix(n);
  }
  Fps inv(void) const { return inv(this->size()); }
  Fps diff(void) const {
    Fps ret(max(0, int(this->size()) - 1));
    for (int i = 0; i < ret.size(); ++i)
      ret[i] = (*this)[i + 1] * (i + 1);
    return ret;
  }
  Fps intg(void) const {
    Fps ret(this->size() + 1);
    for (int i = 1; i < ret.size(); ++i)
      ret[i] = (*this)[i - 1] / i;
    return ret;
  }
  Fps log(size_t n) const {
    return (this->diff() * this->inv(n)).intg().prefix(n);
  }
  Fps log(void) const { return log(this->size()); }
  Fps exp(size_t n) const {
    Fps ret(1, 1);
    for (size_t i = 1; i < n; i <<= 1)
      ret = (ret * (this->prefix(i << 1) + Fps(1, 1) - ret.log(i << 1)))
                .prefix(i << 1);
    return ret.prefix(n);
  }
  Fps exp(void) const { return exp(this->size()); }
  friend ostream &operator<<(ostream &os, const Fps &fps) {
    os << "{" << fps[0];
    for (int i = 1; i < fps.size(); ++i)
      os << ", " << fps[i];
    return os << "}";
  }
};

using fps = FormalPowerSeries<MOD2>;

/*
 * @title CombinationMod - mod上の二項係数・階乗
 * @docs md/math/CombinationMod.md
 */
template <long long mod> class CombinationMod {
  vector<long long> fac, finv, inv;

public:
  CombinationMod(int N) : fac(N + 1), finv(N + 1), inv(N + 1) {
    fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
    for (int i = 2; i <= N; ++i) {
      fac[i] = fac[i - 1] * i % mod;
      inv[i] = mod - inv[mod % i] * (mod / i) % mod;
      finv[i] = finv[i - 1] * inv[i] % mod;
    }
  }
  inline long long binom(int n, int k) {
    return ((n < 0 || k < 0 || n < k)
                ? 0
                : fac[n] * (finv[k] * finv[n - k] % mod) % mod);
  }
  inline long long factorial(int n) { return fac[n]; }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;

  int M = 100000;
  vector<int> cnt(M + 1, 0);
  for (int i = 0; i < 2 * N; ++i) {
    int h;
    cin >> h;
    cnt[h]++;
  }

  vector<modint> fact_odd(2 * N, 0);
  fact_odd[1] = 1;
  for (int i = 3; i < 2 * N; i += 2)
    fact_odd[i] = fact_odd[i - 2] * i;

  CombinationMod<MOD2> CM(2 * N);

  vector<fps> vf;
  priority_queue_reverse<pair<int, int>> pq;
  for (int i = 1; i <= M; ++i) {
    if (!cnt[i])
      continue;
    int n = cnt[i];
    int m = n / 2;
    fps f(m + 1, 0);
    f[0] = 1;
    for (int j = 1; j <= m; ++j) {
      // n人から2j人選ぶ-> n_C_2j
      // 2j人からjペア作る-> (2j-1)*(2j-3)*...*3*1;
      f[j] = fact_odd[2 * j - 1] * CM.binom(n, 2 * j);
    }
    vf.push_back(f);
    pq.push({f.size(), vf.size() - 1});
  }
  while (pq.size() >= 2) {
    auto l = pq.top().second;
    pq.pop();
    auto r = pq.top().second;
    pq.pop();
    auto f = vf[l] * vf[r];
    vf.push_back(f);
    pq.push({f.size(), vf.size() - 1});
  }
  modint ans = 0;
  {
    auto c = pq.top().second;
    pq.pop();
    auto f = vf[c];
    for (int i = 0; i < f.size(); ++i)
      f[i] *= fact_odd[2 * (N - i) - 1];
    for (int i = 0; i < f.size(); ++i)
      ans += f[i] * (1 - 2 * (i % 2));
  }
  cout << ans << endl;
  return 0;
}