Problem p02539 (C++) — buggy submission, verdict: Time Limit Exceeded

// warm heart, wagging tail,and a smile just for you!
//                                                                     ███████████
//                                                                   ███╬╬╬╬╬╬╬╬╬╬███
//                                                                ███╬╬╬╬╬████╬╬╬╬╬╬███
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//                                            ██╬╬╬╬╬████╬╬████╬╬╬╬╬██
//                                      █████████╬╬╬╬╬████████████╬╬╬╬╬██╬╬╬╬╬╬███╬╬╬╬╬██
//                               ████████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬██╬╬╬╬╬╬╬██
//                             ████╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬╬╬╬╬╬██
//                           ███╬╬╬█╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬███╬╬╬╬╬╬╬█████
//                         ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬████████╬╬╬╬╬██
//                       ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬╬╬╬╬███
//                     ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬██
//                 ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬████
//     █████████████╬╬╬╬╬╬╬╬██╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬██████
//   ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬██████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████╬╬╬╬╬╬╬███████████╬╬╬╬╬╬╬╬██╬╬╬██╬╬╬██
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬█╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬██
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬▓▓▓▓▓▓╬╬╬████╬╬████╬╬╬╬╬╬╬▓▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬███
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████▓▓▓▓▓▓▓╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬█████
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████████
//   ███╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██
//       ██████████████
//       ████╬╬╬╬╬╬███████████████████████████╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████
//                         ███████                           █████
//                         ███████████████████
//
#include "bits/stdc++.h"
using namespace std;
#define INF (1 << 30)
#define LINF (1LL << 60)
#define fs first
#define sc second
#define int long long
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR2(i, a, b) for (int i = (a); i <= (b); ++i)
#define RFOR(i, a, b) for (int i = (b - 1); i >= (a); --i)
#define RFOR2(i, a, b) for (int i = (b); i >= (a); --i)
#define REP(i, n) FOR(i, 0, (n))
#define REP2(i, n) FOR2(i, 0, (n))
#define RREP(i, n) RFOR(i, 0, (n))
#define RREP2(i, n) RFOR2(i, 0, (n))
#define ITR(itr, mp) for (auto itr = (mp).begin(); itr != (mp).end(); ++itr)
#define RITR(itr, mp) for (auto itr = (mp).rbegin(); itr != (mp).rend(); ++itr)
#define range(i, a, b) ((a) <= (i) && (i) < (b))
#define range2(i, a, b) ((a) <= (i) && (i) <= (b))
#define debug(x) cout << #x << " = " << (x) << endl
#define SP << " " <<
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
#define MSB(x) (63 - __builtin_clzll(x))
#define pcnt(x) (__builtin_popcountll(x))
#define parity(i, j) (i & (1LL << j))
typedef pair<int, int> P;
typedef tuple<int, int, int> T;

vector<int> MODS = {1000000007, 998244353}; // 実行時に決まる
template <int IND = 0> struct Fp {
  long long val;

  int MOD = MODS[IND];
  constexpr Fp(long long v = 0) noexcept : val(v % MODS[IND]) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<IND> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<IND> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<IND> modpow(const Fp<IND> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};
using mint = Fp<1>; // MODを変える場合は値を変更
typedef vector<mint> vec;
typedef vector<vector<mint>> mat;
vec fact, inv;
void init(int n) {
  fact.assign(n + 1, 1);
  inv.assign(n + 1, 1);
  REP(i, n) fact[i + 1] = fact[i] * (i + 1), inv[i + 1] /= fact[i + 1];
}

mint cmb(int n, int r) {
  if (n < r || r < 0)
    return 0;
  return fact[n] * inv[r] * inv[n - r];
}

constexpr int bmds(int x) {
  if (x == 0)
    return 1012924417;
  if (x == 1)
    return 924844033;
  if (x == 2)
    return 998244353;
  if (x == 3)
    return 897581057;
  if (x == 4)
    return 645922817;
}
constexpr int brts(int x) {
  if (x == 0)
    return 5;
  if (x == 1)
    return 5;
  if (x == 2)
    return 3;
  if (x == 3)
    return 3;
  if (x == 4)
    return 3;
}

template <int X> struct NTT {
  static constexpr int md = bmds(X);
  static constexpr int rt = brts(X);

  inline int add(int a, int b) {
    a += b;
    if (a >= md)
      a -= md;
    return a;
  }

  inline int mul(int a, int b) { return 1LL * a * b % md; }

  inline int pow(int a, int b) {
    int res = 1;
    while (b) {
      if (b & 1)
        res = mul(res, a);
      a = mul(a, a);
      b >>= 1;
    }
    return res;
  }

  inline int inv(int x) { return pow(x, md - 2); }

  vector<vector<int>> rts, rrts;

  void ensure_base(int n) {
    if ((int)rts.size() >= n)
      return;
    rts.resize(n);
    rrts.resize(n);
    for (int i = 1; i < n; i <<= 1) {
      if (!rts[i].empty())
        continue;
      int w = pow(rt, (md - 1) / (i << 1));
      int rw = inv(w);
      rts[i].resize(i);
      rrts[i].resize(i);
      rts[i][0] = 1;
      rrts[i][0] = 1;
      for (int k = 1; k < i; k++) {
        rts[i][k] = mul(rts[i][k - 1], w);
        rrts[i][k] = mul(rrts[i][k - 1], rw);
      }
    }
  }

  void ntt(vector<int> &a, bool f, int n = -1) {
    if (n == -1)
      n = a.size();
    assert((n & (n - 1)) == 0);

    for (int i = 0, j = 1; j + 1 < n; j++) {
      for (int k = n >> 1; k > (i ^= k); k >>= 1)
        ;
      if (i > j)
        swap(a[i], a[j]);
    }

    for (int i = 1; i < n; i <<= 1) {
      for (int j = 0; j < n; j += i * 2) {
        for (int k = 0; k < i; k++) {
          int z = mul(a[i + j + k], f ? rrts[i][k] : rts[i][k]);
          a[i + j + k] = add(a[j + k], md - z);
          a[j + k] = add(a[j + k], z);
        }
      }
    }

    if (f) {
      int tmp = inv(n);
      for (int i = 0; i < n; i++)
        a[i] = mul(a[i], tmp);
    }
  }

  vector<int> multiply(vector<int> &a, vector<int> &b) {
    int need = a.size() + b.size() - 1;
    int sz = 1;
    while (sz < need)
      sz <<= 1;
    ensure_base(sz);

    vector<int> f(sz), g(sz);
    for (int i = 0; i < (int)a.size(); i++)
      f[i] = a[i];
    for (int i = 0; i < (int)b.size(); i++)
      g[i] = b[i];
    ntt(f, 0);
    ntt(g, 0);
    for (int i = 0; i < sz; i++)
      f[i] = mul(f[i], g[i]);
    ntt(f, 1);

    f.resize(need);
    return f;
  }
};

void solve() {
  int N;
  cin >> N;

  init(N * 2);

  vector<int> a(100000, 0), id = a;
  REP(_, N * 2) {
    int x;
    cin >> x;
    a[x - 1]++;
  }

  NTT<2> ntt;
  queue<vector<int>> que;
  REP(i, 100000) {
    if (!a[i])
      continue;
    int M = a[i] / 2;
    vector<int> c(M + 1);
    mint tmp = 1;
    REP2(j, M) {
      c[j] = (tmp * cmb(a[i], 2 * j)).val;
      tmp *= j * 2 + 1;
    }
    que.push(c);
  }

  while (que.size() > 1) {
    vector<int> b = que.front();
    que.pop();
    vector<int> c = que.front();
    que.pop();
    que.push(ntt.multiply(b, c));
  }

  vec fact2(2 * N + 1, 1);
  REP(i, 2 * N) {
    fact2[i + 1] = fact2[i];
    if ((i + 1) % 2)
      fact2[i + 1] *= i + 1;
  }

  mint ans = 0;
  vector<int> b = que.front();
  REP(i, b.size()) {
    if (i % 2)
      ans -= fact2[(N - i) * 2] * b[i];
    else
      ans += fact2[(N - i) * 2] * b[i];
  }

  cout << ans << endl;
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int T = 1;
  // cin >> T;

  while (T--)
    solve();

  return 0;
}

Error: TLE

Fixed submission:

// warm heart, wagging tail,and a smile just for you!
//                                                                     ███████████
//                                                                   ███╬╬╬╬╬╬╬╬╬╬███
//                                                                ███╬╬╬╬╬████╬╬╬╬╬╬███
//                                            ███████████
//                                            ██╬╬╬╬╬████╬╬████╬╬╬╬╬██
//                                      █████████╬╬╬╬╬████████████╬╬╬╬╬██╬╬╬╬╬╬███╬╬╬╬╬██
//                               ████████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬██╬╬╬╬╬╬╬██
//                             ████╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬╬╬╬╬╬██
//                           ███╬╬╬█╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬███╬╬╬╬╬╬╬█████
//                         ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬████████╬╬╬╬╬██
//                       ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬╬╬╬╬███
//                     ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬██
//                 ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬████
//     █████████████╬╬╬╬╬╬╬╬██╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬██████
//   ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬██████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████╬╬╬╬╬╬╬███████████╬╬╬╬╬╬╬╬██╬╬╬██╬╬╬██
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬█╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬██
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬▓▓▓▓▓▓╬╬╬████╬╬████╬╬╬╬╬╬╬▓▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬███
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████▓▓▓▓▓▓▓╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬█████
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████████
//   ███╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██
//       ██████████████
//       ████╬╬╬╬╬╬███████████████████████████╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████
//                         ███████                           █████
//                         ███████████████████
//
#include "bits/stdc++.h"
using namespace std;
#define INF (1 << 30)
#define LINF (1LL << 60)
#define fs first
#define sc second
#define int long long
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR2(i, a, b) for (int i = (a); i <= (b); ++i)
#define RFOR(i, a, b) for (int i = (b - 1); i >= (a); --i)
#define RFOR2(i, a, b) for (int i = (b); i >= (a); --i)
#define REP(i, n) FOR(i, 0, (n))
#define REP2(i, n) FOR2(i, 0, (n))
#define RREP(i, n) RFOR(i, 0, (n))
#define RREP2(i, n) RFOR2(i, 0, (n))
#define ITR(itr, mp) for (auto itr = (mp).begin(); itr != (mp).end(); ++itr)
#define RITR(itr, mp) for (auto itr = (mp).rbegin(); itr != (mp).rend(); ++itr)
#define range(i, a, b) ((a) <= (i) && (i) < (b))
#define range2(i, a, b) ((a) <= (i) && (i) <= (b))
#define debug(x) cout << #x << " = " << (x) << endl
#define SP << " " <<
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
#define MSB(x) (63 - __builtin_clzll(x))
#define pcnt(x) (__builtin_popcountll(x))
#define parity(i, j) (i & (1LL << j))
typedef pair<int, int> P;
typedef tuple<int, int, int> T;

vector<int> MODS = {1000000007, 998244353}; // 実行時に決まる
template <int IND = 0> struct Fp {
  long long val;

  int MOD = MODS[IND];
  constexpr Fp(long long v = 0) noexcept : val(v % MODS[IND]) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<IND> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<IND> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<IND> modpow(const Fp<IND> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};
using mint = Fp<1>; // MODを変える場合は値を変更
typedef vector<mint> vec;
typedef vector<vector<mint>> mat;
vec fact, inv;
void init(int n) {
  fact.assign(n + 1, 1);
  inv.assign(n + 1, 1);
  REP(i, n) fact[i + 1] = fact[i] * (i + 1), inv[i + 1] /= fact[i + 1];
}

mint cmb(int n, int r) {
  if (n < r || r < 0)
    return 0;
  return fact[n] * inv[r] * inv[n - r];
}

constexpr int bmds(int x) {
  if (x == 0)
    return 1012924417;
  if (x == 1)
    return 924844033;
  if (x == 2)
    return 998244353;
  if (x == 3)
    return 897581057;
  if (x == 4)
    return 645922817;
}
constexpr int brts(int x) {
  if (x == 0)
    return 5;
  if (x == 1)
    return 5;
  if (x == 2)
    return 3;
  if (x == 3)
    return 3;
  if (x == 4)
    return 3;
}

template <int X> struct NTT {
  static constexpr int md = bmds(X);
  static constexpr int rt = brts(X);

  inline int add(int a, int b) {
    a += b;
    if (a >= md)
      a -= md;
    return a;
  }

  inline int mul(int a, int b) { return 1LL * a * b % md; }

  inline int pow(int a, int b) {
    int res = 1;
    while (b) {
      if (b & 1)
        res = mul(res, a);
      a = mul(a, a);
      b >>= 1;
    }
    return res;
  }

  inline int inv(int x) { return pow(x, md - 2); }

  vector<vector<int>> rts, rrts;

  void ensure_base(int n) {
    if ((int)rts.size() >= n)
      return;
    rts.resize(n);
    rrts.resize(n);
    for (int i = 1; i < n; i <<= 1) {
      if (!rts[i].empty())
        continue;
      int w = pow(rt, (md - 1) / (i << 1));
      int rw = inv(w);
      rts[i].resize(i);
      rrts[i].resize(i);
      rts[i][0] = 1;
      rrts[i][0] = 1;
      for (int k = 1; k < i; k++) {
        rts[i][k] = mul(rts[i][k - 1], w);
        rrts[i][k] = mul(rrts[i][k - 1], rw);
      }
    }
  }

  void ntt(vector<int> &a, bool f, int n = -1) {
    if (n == -1)
      n = a.size();
    assert((n & (n - 1)) == 0);

    for (int i = 0, j = 1; j + 1 < n; j++) {
      for (int k = n >> 1; k > (i ^= k); k >>= 1)
        ;
      if (i > j)
        swap(a[i], a[j]);
    }

    for (int i = 1; i < n; i <<= 1) {
      for (int j = 0; j < n; j += i * 2) {
        for (int k = 0; k < i; k++) {
          int z = mul(a[i + j + k], f ? rrts[i][k] : rts[i][k]);
          a[i + j + k] = add(a[j + k], md - z);
          a[j + k] = add(a[j + k], z);
        }
      }
    }

    if (f) {
      int tmp = inv(n);
      for (int i = 0; i < n; i++)
        a[i] = mul(a[i], tmp);
    }
  }

  vector<int> multiply(vector<int> &a, vector<int> &b) {
    int need = a.size() + b.size() - 1;
    int sz = 1;
    while (sz < need)
      sz <<= 1;
    ensure_base(sz);

    vector<int> f(sz), g(sz);
    for (int i = 0; i < (int)a.size(); i++)
      f[i] = a[i];
    for (int i = 0; i < (int)b.size(); i++)
      g[i] = b[i];
    ntt(f, 0);
    ntt(g, 0);
    for (int i = 0; i < sz; i++)
      f[i] = mul(f[i], g[i]);
    ntt(f, 1);

    f.resize(need);
    return f;
  }
};

void solve() {
  int N;
  cin >> N;

  init(N * 2);

  vector<int> a(100000, 0), id = a;
  REP(_, N * 2) {
    int x;
    cin >> x;
    a[x - 1]++;
  }

  REP(i, 100000) id[i] = i;

  auto comp = [&](int i, int j) { return a[i] < a[j]; };
  sort(id.begin(), id.end(), comp);

  NTT<2> ntt;
  vector<int> b = {1};
  REP(x, 100000) {
    int i = id[x];
    int M = a[i] / 2;
    if (!a[i])
      continue;
    vector<int> c(M + 1);
    mint tmp = 1;
    REP2(j, M) {
      c[j] = (tmp * cmb(a[i], 2 * j)).val;
      tmp *= j * 2 + 1;
    }
    b = ntt.multiply(b, c);
  }

  vec fact2(2 * N + 1, 1);
  REP(i, 2 * N) {
    fact2[i + 1] = fact2[i];
    if ((i + 1) % 2)
      fact2[i + 1] *= i + 1;
  }

  mint ans = 0;
  REP(i, b.size()) {
    if (i % 2)
      ans -= fact2[(N - i) * 2] * b[i];
    else
      ans += fact2[(N - i) * 2] * b[i];
  }

  cout << ans << endl;
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int T = 1;
  // cin >> T;

  while (T--)
    solve();

  return 0;
}