#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(x) (x).begin(),(x).end()
//#pragma GCC optimize ("-O3")
using namespace std; using namespace atcoder;
void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); }
typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60;
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
//---------------------------------------------------------------------------------------------------
template<int MOD> struct ModInt {
    static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
    ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    int get() const { return (int)x; }
    ModInt& operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
    ModInt& operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
    ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
    ModInt& operator/=(ModInt that) { return *this *= that.inverse(); }
    ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
    ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
    ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
    ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
    ModInt inverse() const {
        long long a = x, b = MOD, u = 1, v = 0;
        while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
        return ModInt(u);
    }
    bool operator==(ModInt that) const { return x == that.x; }
    bool operator!=(ModInt that) const { return x != that.x; }
    ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; };
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
    ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r;
}
template<typename T, int FAC_MAX> struct Comb {
    vector<T> fac, ifac;
    Comb() {
        fac.resize(FAC_MAX, 1); ifac.resize(FAC_MAX, 1); rep(i, 1, FAC_MAX)fac[i] = fac[i - 1] * i;
        ifac[FAC_MAX - 1] = T(1) / fac[FAC_MAX - 1]; rrep(i, FAC_MAX - 2, 1)ifac[i] = ifac[i + 1] * T(i + 1);
    }
    T aPb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b]; }
    T aCb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b] * ifac[b]; }
    // nHk = (n+k-1)Ck : n is separator (k balls to n boxs)
    T nHk(int n, int k) {
        if (n == 0 && k == 0) return T(1); if (n <= 0 || k < 0) return 0;
        return aCb(n + k - 1, k);
    }
    T pairCombination(int n) { if (n % 2 == 1)return T(0); return fac[n] * ifac[n / 2] / (T(2) ^ (n / 2)); }
    // combination of paris for n
};
typedef ModInt<998244353> mint;
/*---------------------------------------------------------------------------------------------------
　　　　　　　　　　　 ∧＿∧
　　　　　 ∧＿∧ 　（´<_｀ ）　 Welcome to My Coding Space!
　　　　 （ ´_ゝ`）　/　 ⌒i     @hamayanhamayan0
　　　　／　　　＼　 　  |　|
　　　 /　　 /￣￣￣￣/　　|
　 ＿_(__ﾆつ/　    ＿/ .| .|＿＿＿＿
　 　　　＼/＿＿＿＿/　（u　⊃
---------------------------------------------------------------------------------------------------*/














int N, cnt[101010];
Comb<mint, 201010> com;
//---------------------------------------------------------------------------------------------------
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
vector<int> allConvolution(vector<vector<int>> vs) {
    min_priority_queue<pair<int, int>> que;
    int n = vs.size();

    rep(i, 0, n) que.push({ vs[i].size(), i });
    while (2 <= que.size()) {
        int i1 = que.top().second; que.pop();
        int i2 = que.top().second; que.pop();
        vs[i1] = convolution(vs[i1], vs[i2]);
        que.push({ vs[i1].size(), i1 });
    }

    return vs[que.top().second];
}
//---------------------------------------------------------------------------------------------------
void _main() {
	cin >> N;
    rep(i, 0, N * 2) {
        int h; cin >> h;
        cnt[h]++;
    }

    vector<vector<int>> vs;
    rep(h, 1, 101010) {
        vector<int> cmb;
        rep(pr, 0, cnt[h] / 2 + 1) cmb.push_back((com.aCb(cnt[h], pr*2) * com.pairCombination(pr * 2)).get());
        vs.push_back(cmb);
    }
    sort(all(vs));

    vs.push_back({ 1 });
    auto dp = allConvolution(vs);

    mint ans = 0;
    int n = dp.size();
    rep(i, 0, n) {
        mint cmb = mint(dp[i]) * com.pairCombination(N * 2 - i * 2);
        if (i % 2 == 0) ans += cmb;
        else ans -= cmb;
    }

    cout << ans << endl;
}







Measured memory_bytes: 19988