// #pragma GCC optimize("unroll-loops", "omit-frame-pointer", "inline")
// #pragma GCC option("arch=native", "tune=native", "no-zero-upper")
// #pragma GCC
// target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("tree-vectorize","openmp","predictive-commoning")
// #pragma GCC option("D_GLIBCXX_PARALLEL","openmp")

// #pragma GCC optimize("O3")
// #pragma GCC target("avx2")

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<ll> vll;
// #define int long long
#define pb push_back
#define mp make_pair
#define eps 1e-9
#define INF 2000000000              // 2e9
#define LLINF 2000000000000000000ll // 2e18 (llmax:9e18)
#define fi first
#define sec second
#define all(x) (x).begin(), (x).end()
#define sq(x) ((x) * (x))
#define dmp(x) cerr << #x << ": " << x << endl;

template <class T>
void chmin(T &a, const T &b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T &a, const T &b) {
  if (a < b) a = b;
}

template <class T>
using MaxHeap = priority_queue<T>;
template <class T>
using MinHeap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
vector<T> vect(int len, T elem) {
  return vector<T>(len, elem);
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.fi << ',' << p.sec;
  return os;
}
template <class T, class U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.fi >> p.sec;
  return is;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i];
    if (i + 1 < vec.size()) os << ' ';
  }
  return os;
}
template <class T>
istream &operator>>(istream &is, vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) is >> vec[i];
  return is;
}
void fastio() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
}

#define endl "\n"

#include <atcoder/convolution>
#include <atcoder/modint>

template <int MOD> // if inv is needed, this shold be prime.
struct ModInt {
  ll val;
  ModInt() : val(0ll) {}
  ModInt(const ll &v) : val(((v % MOD) + MOD) % MOD) {}
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return !(*this == x); }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return !(*this < x); }
  bool operator<=(const ModInt &x) const { return !(*this > x); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt inv() const { return this->pow(MOD - 2); }
  ModInt &operator+=(const ModInt &x) {
    if ((val += x.val) >= MOD) val -= MOD;
    return *this;
  }
  ModInt &operator-=(const ModInt &x) {
    if ((val += MOD - x.val) >= MOD) val -= MOD;
    return *this;
  }
  ModInt &operator*=(const ModInt &x) {
    (val *= x.val) %= MOD;
    return *this;
  }
  ModInt &operator/=(const ModInt &x) { return *this *= x.inv(); };
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend istream &operator>>(istream &i, ModInt &x) {
    ll v;
    i >> v;
    x = v;
    return i;
  }
  friend ostream &operator<<(ostream &o, const ModInt &x) {
    o << x.val;
    return o;
  }
  ModInt pow(ll x) const {
    auto res = ModInt(1ll);
    auto b = *this;
    while (x) {
      if (x & 1) res *= b;
      x >>= 1;
      b *= b;
    }
    return res;
  }
};

template <int MOD>
ModInt<MOD> pow(ModInt<MOD> a, ll x) {
  ModInt<MOD> res = ModInt<MOD>(1ll);
  while (x) {
    if (x & 1) res *= a;
    x >>= 1;
    a *= a;
  }
  return res;
}

// constexpr int MOD = 1e9 + 7;
constexpr int MOD = 998244353;
using mint = ModInt<MOD>;

vector<mint> inv, fac, facinv;
// notice: 0C0 = 1
mint nCr(int n, int r) {
  assert(!(n < r));
  assert(!(n < 0 || r < 0));
  return fac[n] * facinv[r] * facinv[n - r];
}

void init(int SIZE) {
  fac.resize(SIZE + 1);
  inv.resize(SIZE + 1);
  facinv.resize(SIZE + 1);
  fac[0] = inv[1] = facinv[0] = mint(1ll);
  for (int i = 1; i <= SIZE; i++) fac[i] = fac[i - 1] * mint(i);
  for (int i = 2; i <= SIZE; i++)
    inv[i] = mint(0ll) - mint(MOD / i) * inv[MOD % i];
  for (int i = 1; i <= SIZE; i++) facinv[i] = facinv[i - 1] * inv[i];
  return;
}

mint func(int n, int k) {
  return fac[n] * facinv[n - 2 * k] / pow(mint(2ll), k) * facinv[k];
}

void solve() {
  int N;
  cin >> N;
  vector<int> h(2 * N);
  cin >> h;
  vector<int> cnt(100100, 0);
  for (int i = 0; i < 2 * N; i++) { cnt[h[i]]++; }

  vector<mint> A(N + 1, mint(1));
  for (int i = 1; i <= N; i++) { A[i] = nCr(2 * i, 2) * A[i - 1] / mint(i); }
  // dmp(A);

  vector<int> cs;
  for (int i = 0; i < 100100; i++) {
    if (cnt[i] < 2) continue;
    cs.push_back(cnt[i]);
  }
  sort(all(cs));
  // dmp(cs);

  // vector<ll> ans(1, 1ll);
  vector<vector<ll>> b(cs.size());
  MinHeap<pair<int, int>> H;
  for (int i = 0; i < cs.size(); i++) {
    int c = cs[i];
    for (int j = 0; 2 * j <= c; j++) b[i].push_back(func(c, j).val);
    // dmp(b[i]);
    H.push(make_pair((int)b[i].size(), i));
    // dmp(b);
    // ans = atcoder::convolution<998244353>(ans, b);
    // dmp(ans);
  }
  while (H.size() > 1) {
    auto p = H.top();
    H.pop();
    auto q = H.top();
    H.pop();
    // dmp(p);
    // dmp(q);
    // dmp(b[p.second]);
    // dmp(b[q.second]);
    b[p.second] = atcoder::convolution<998244353>(b[p.second], b[q.second]);
    // dmp(b[p.second]);
    H.push(make_pair((int)b[p.second].size(), p.second));
  }
  assert(H.size() <= 1);
  vector<ll> ans;
  if (H.size() == 1)
    ans = b[H.top().second];
  else
    ans = vector<ll>(1, 1ll);
  // dmp(ans);
  mint answer(0);
  for (int i = 0; i < ans.size(); i++) {
    if (i % 2 == 0)
      answer += mint(ans[i]) * A[N - i];
    else
      answer -= mint(ans[i]) * A[N - i];
  }
  cout << answer << endl;
  return;
}

signed main() {
  fastio();
  init(200100);
  solve();
  // int t; cin >> t; while(t--)solve();

  // int t; cin >> t;
  // for(int i=1;i<=t;i++){
  //   cout << "Case #" << i << ": ";
  //   solve();
  // }
  return 0;
}


Measured memory_bytes: 15760