#include <bits/stdc++.h>
//#include <chrono>
//#pragma GCC optimize("Ofast")
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()
#define fi first
#define se second

using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;

ll N,M,H,W,Q,K,A,B;
string S;
typedef pair<ll, ll> P;
const ll INF = (1LL<<58);

template <unsigned long long mod > class modint{
public:
    ll x;
    constexpr modint(){x = 0;}
    constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){}
    constexpr modint set_raw(ll _x){
        //_x in [0, mod)
        x = _x;
        return *this;
    }
    constexpr modint operator-(){
        return x == 0 ? 0 : mod - x;
    }
    constexpr modint& operator+=(const modint& a){
        if((x += a.x) >= mod) x -= mod;
        return *this;
    }
    constexpr modint operator+(const modint& a) const{
        return modint(*this) += a;
    }
    constexpr modint& operator-=(const modint& a){
        if((x -= a.x) < 0) x += mod;
        return *this;
    }
    constexpr modint operator-(const modint& a) const{
        return modint(*this) -= a;
    }
    constexpr modint& operator*=(const modint& a){
        (x *= a.x)%=mod;
        return *this;
    }
    constexpr modint operator*(const modint& a) const{
        return modint(*this) *= a;
    }
    constexpr modint pow(unsigned long long pw) const{
        modint res(1), comp(*this);
        while(pw){
            if(pw&1) res *= comp;
            comp *= comp;
            pw >>= 1;
        }
        return res;
    }
    //以下、modが素数のときのみ
    constexpr modint inv() const{
        return modint(*this).pow(mod - 2);
    }
    constexpr modint& operator/=(const modint &a){
        (x *= a.inv().x)%=mod;
        return *this;
    }
    constexpr modint operator/(const modint &a) const{
        return modint(*this) /= a;
    }
};
#define mod1 998244353
using mint = modint<mod1>;

ostream& operator<<(ostream& os, const mint& a){
    os << a.x;
    return os;
}
using vm = vector<mint>;

class NTT{
    const int root;

    void make_root_pow(int n, vm &root_pow){
        root_pow.resize(n + 1);
        mint new_root = mint(root).pow((mod1 - 1) / n);
        root_pow[0].x = 1;
        rep(i,n){
            root_pow[i + 1] = root_pow[i] * new_root;
        }
    }
    static void make_bit_reverse(int n, vector<int> &v){
        v.resize(n);
        iota(ALL(v), 0);
        for(int i = 1; (1<<i) <= n; ++i){
            int l = 1<<(i - 1), r = 1<<i;
            int plus = n >> i;
            for(int j = l; j < r; ++j){
                int temp = v[j - l] + plus;
                if(j < temp) swap(v[j], v[temp]);
            }
        }
    }
    static void dft(int n, vm &f, bool inv, vm &root_pow, vector<int> &id){
        vm g(n);
        rep(i,n) g[i] = f[id[i]];
        swap(f, g);
        for(int l = n / 2, len = 1; l >= 1; l /= 2, len *= 2){
            for(int i = 0; i < n; i += len * 2){
                rep(j, len){
                    mint z_f = (inv ? root_pow[n - l * j] : root_pow[l * j]) * f[i + len + j];
                    g[i + j] = f[i + j] + z_f;
                    g[i + len + j] = f[i + j] - z_f;
                }
            }
            swap(f, g);
        }
        if(inv) {
            mint n_inv = mint(n).inv();
            rep(i, n) f[i] *= n_inv;
        }
    }
public:
    NTT(int _x = 3) : root(_x){}
    vm convolution(vm &a, vm &b, int size_a = INT_MAX, int size_b = INT_MAX){
        if(size_a > (int)a.size()) size_a = (int)a.size();
        if(size_b > (int)b.size()) size_b = (int)b.size();
        int sz = size_a + size_b - 1, n = 1;
        while(sz > n) n *= 2;
        vm g(n), h(n), root_pow, gh(n);
        vector<int> id;
        copy(a.begin(), a.begin() + size_a, g.begin());
        copy(b.begin(), b.begin() + size_b, h.begin());
        make_root_pow(n, root_pow);
        make_bit_reverse(n, id);
        dft(n, g, false, root_pow, id);
        dft(n, h, false, root_pow, id);
        rep(i, n) gh[i] = g[i] * h[i];
        dft(n, gh, true, root_pow, id);
        gh.resize(sz);
        return gh;
    }
};

vm polynomial_product(vector<vm> &polys){
    //time complexity : O(N log^2 N) (N : sum of polys[i].size())
    if(polys.empty()){
        vm BLA(0);
        return BLA;
    }
    struct _cmp{
        int sz, id;
        _cmp(int _sz, int _id) : sz(_sz), id(_id){}
        bool operator > (const _cmp &b){ return sz > b.sz;}
    };
    vector<vm> poly_copy(polys);
    priority_queue<_cmp, vector<_cmp>, greater<> > pque;
    rep(i, (int)poly_copy.size()) pque.emplace((int)poly_copy[i].size(), i);
    NTT ntt;
    while(pque.size() > 1){
        _cmp c = pque.top(); pque.pop();
        _cmp d = pque.top(); pque.pop();
        poly_copy[c.id] = ntt.convolution(poly_copy[c.id], poly_copy[d.id]);
        poly_copy[d.id].clear();
        pque.emplace(c.sz + d.sz - 1, c.id);
    }
    return poly_copy[pque.top().id];
}

const ll MAX_N = ll(4e+5) + 10;
vm fact(MAX_N, mint(1)), fact_inv(MAX_N, mint(1)), n_inv(MAX_N, mint(1)), two_inv(MAX_N, mint(1));
void makefact(){
    two_inv[1] = (mod1 + 1) / 2;
    mint tmp;
    reps(i,2,MAX_N) {
        fact[i] = fact[i-1] * tmp.set_raw(i);
        two_inv[i] = two_inv[i-1] * two_inv[1];
    }
    fact_inv[MAX_N - 1] = fact[MAX_N - 1].inv();
    Rreps(i, MAX_N - 1, 1){
        fact_inv[i] = fact_inv[i + 1] * tmp.set_raw(i + 1);
        n_inv[i + 1] = fact[i] * fact_inv[i + 1];
    }
}
mint nCm(ll n, ll m){
    return fact[n] * fact_inv[n-m] * fact_inv[m];
}
mint nCm_inv(ll n, ll m){
    return fact[n-m] * fact[m] * fact_inv[n];
}

int main() {
    makefact();
    cin>>N;
    vec h(N * 2), num(100000, 0);
    rep(i, N * 2){
        cin>>h[i];
        --h[i];
        ++num[h[i]];
    }

    vector<vm> polys(0);
    rep(i, 100000){
        int k = 1;
        vm temp(1, 1);
        while(num[i] >= k * 2){
            temp.push_back(fact[num[i]] * fact_inv[k] * fact_inv[num[i] - k * 2] * two_inv[k]);
            ++k;
        }
        if(temp.size() != 1) polys.push_back(temp);
    }
    mint res = fact[N * 2] * two_inv[N] * fact_inv[N];

    vm polv = polynomial_product(polys);
    reps(k, 1, (int)polv.size()){
        if(k > N) break;
        res += mint(k&1 ? -1 : 1) * polv[k] * fact[(N - k) * 2] * two_inv[N - k] * fact_inv[N - k];
    }
    cout<<res<<endl;
}


Measured memory_bytes: 29456