#include "bits/stdc++.h"
using namespace std;
using     ll=long long;
using    vll=vector<   ll>;
using   vvll=vector<  vll>;
using  vvvll=vector< vvll>;
using vvvvll=vector<vvvll>;
using     dd=double;
using    vdd=vector<   dd>;
using   vvdd=vector<  vdd>;
using pll=pair<ll,ll>; using tll=tuple<ll,ll,ll>; using qll=tuple<ll,ll,ll,ll>;

constexpr ll INF = 1LL << 60;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define rep(i, S, E)  for (ll i = (S); i <= (E); i++)
#define dep(i, E, S)  for (ll i = (E); i >= (S); i--)
#define each(e, v) for (auto&& e : v)
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> inline T MaxE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; }
template<class T> inline T MinE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; }
template<class T> inline T MaxE(vector<T> &v) { return MaxE(v,0,(ll)v.size()-1); }
template<class T> inline T MinE(vector<T> &v) { return MinE(v,0,(ll)v.size()-1); }
template<class T> inline T Sum(vector<T> &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; }
template<class T> inline T Sum(vector<T> &v) { return Sum(v,0,v.size()-1); }
template<class T> inline ll sz(T &v){ return (ll)v.size(); }
inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; }
inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); }

//vector用テンプレート
template<class T> inline vector<T>& operator+=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]+=b[i];  return a; }
template<class T> inline vector<T>& operator-=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]-=b[i];  return a; }
template<class T> inline vector<T>& operator*=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]*=b[i];  return a; }
template<class T> inline vector<T>& operator/=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]/=b[i];  return a; }
template<class T> inline vector<T>& operator%=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]%=b[i];  return a; }
template<class T,class S> inline vector<T>& operator+=(vector<T> &a,S b){ for (T &e: a) e+=b;  return a; }
template<class T,class S> inline vector<T>& operator-=(vector<T> &a,S b){ for (T &e: a) e-=b;  return a; }
template<class T,class S> inline vector<T>& operator*=(vector<T> &a,S b){ for (T &e: a) e*=b;  return a; }
template<class T,class S> inline vector<T>& operator/=(vector<T> &a,S b){ for (T &e: a) e/=b;  return a; }
template<class T,class S> inline vector<T>& operator%=(vector<T> &a,S b){ for (T &e: a) e%=b;  return a; }
template<class T,class S> inline vector<T> operator+(const vector<T> &a,S b){ vector<T> c=a; return c+=b; }
template<class T,class S> inline vector<T> operator-(const vector<T> &a,S b){ vector<T> c=a; return c-=b; }
template<class T,class S> inline vector<T> operator*(const vector<T> &a,S b){ vector<T> c=a; return c*=b; }
template<class T,class S> inline vector<T> operator/(const vector<T> &a,S b){ vector<T> c=a; return c/=b; }
template<class T,class S> inline vector<T> operator%(const vector<T> &a,S b){ vector<T> c=a; return c%=b; }
template<class T,class S> inline vector<T> operator-(S b,const vector<T> &a){ vector<T> c=-a; return c+=b; }
template<class T> inline vector<T> operator-(const vector<T> &a){ vector<T> c=a; return c*=(-1); }
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i];  return os; }

//pair用テンプレート
using  vpll=vector< pll>;
using vvpll=vector<vpll>;
template<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }
template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }
template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }
template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }
template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }
template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }
template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }
template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }

template<ll MOD> struct mll_{
	ll val;
	mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; }
	mll_ operator - () const { return -val; }
	mll_ operator + (const mll_ &b) const { return val + b.val; }
	mll_ operator - (const mll_ &b) const { return val - b.val; }
	mll_ operator * (const mll_ &b) const { return val * b.val; }
	mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; }
	mll_ operator + (ll b) const { return *this + mll_(b); }
	mll_ operator - (ll b) const { return *this - mll_(b); }
	mll_ operator * (ll b) const { return *this * mll_(b); }
	friend mll_ operator + (ll a,const mll_ &b) { return b + a; }
	friend mll_ operator - (ll a,const mll_ &b) { return -b + a; }
	friend mll_ operator * (ll a,const mll_ &b) { return b * a; }
	friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; }
	mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; }
	mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; }
	mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; }
	mll_ &operator /= (const mll_ &b) {
		ll c=b.val,d=MOD,u=1,v=0;
		while (d){
			ll t = c / d;
			c -= t * d; swap(c,d);
			u -= t * v; swap(u,v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	mll_ &operator += (ll b) { return *this += mll_(b); }
	mll_ &operator -= (ll b) { return *this -= mll_(b); }
	mll_ &operator *= (ll b) { return *this *= mll_(b); }
	mll_ &operator /= (ll b) { return *this /= mll_(b); }
	bool operator == (const mll_ &b) const { return val == b.val; }
	bool operator != (const mll_ &b) const { return val != b.val; }
	bool operator == (ll b) const { return *this == mll_(b); }
	bool operator != (ll b) const { return *this != mll_(b); }
	friend bool operator == (ll a,const mll_ &b) { return mll_(a) == b.val; }
	friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; }
	friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; }
	friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; }
	static mll_ Combination(ll a,ll b){
		chmin(b,a-b);
		if (b<0) return mll_(0);
		mll_ c = 1;
		rep(i,0,b-1) c *= a-i;
		rep(i,0,b-1) c /= i+1;
		return c;
	}
};
using mll = mll_<998244353LL>;
using vmll    = std::vector<mll>;
using vvmll   = std::vector<vmll>;
using vvvmll  = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;

#if 1
#include <atcoder/all>
using namespace atcoder;
#endif


struct Combination{
	vmll f,g;
	Combination(){}
	Combination(ll maxN): f(maxN+1,1),g(maxN+1){ InitSub(maxN); }
	void init(ll maxN){ f.resize(maxN+1,1); g.resize(maxN+1); InitSub(maxN); }
	mll operator () (ll n,ll r){ return (n<0||r<0||n<r) ? mll(0) : f[n]*g[n-r]*g[r]; }//nCr
	mll P(ll n,ll r){ return (n<0 || r<0 || n<r) ? mll(0) : f[n]*g[n-r]; } //nPr
	mll H(ll n,ll r){ return operator()(n+r-1,r); }//nHr
	mll inv(ll n) { return f[n-1] * g[n]; } //1/n
	mll fact(ll n) { return f[n]; } //n!
	mll finv(ll n) { return g[n]; } //1/n!
	void InitSub(ll maxN){
		rep(i,1,maxN){ f[i] = f[i-1] * i; }
		g[maxN] = 1 / f[maxN];
		dep(i,maxN,1){ g[i-1] = g[i] * i; }
	}
};
/*
Combination cmb(n); //nCrまで計算可能
mll v1 = cmb(100,5); //100 C 5
mll v2 = cmb(85,86); //85 C 86 →0になる
mll v3 = cmb.P(10,5); //10 P 5
mll v4 = cmb.H(10,5); //10 H 5 初期化時のnに10+5-1以上をset要
mll v5 = cmb.inv(7);  // 7の逆数
mll v6 = cmb.finv(7); // 7!の逆数
mll v7 = cmb.fact(7); // 7!
cmb.init(n); //後で初期化する場合
*/

template<class T> inline T POW(T a,ll n){ T r=1; for (; n>0; n>>=1,a*=a){ if (n&1)r*=a; } return r; }
inline ll POW(int a,ll n){ return POW((ll)a,n); }


void solve()
{
	ll n;  cin >> n;
	vector<ll> h(n*2);  rep(i,0,n*2-1){ ll h_; cin>>h_; h[i]=h_; }

	map<ll,ll> cnt;
	each(e,h)cnt[e]++;

	Combination cmb(2*n+10);
	vmll twoinv(2*n+10); //twoinv[i]:2^-i
	twoinv[0]=1;
	twoinv[1]=mll(1)/mll(2);
	rep(i,2,2*n+10-1) twoinv[i]=twoinv[i-1]*twoinv[1];

	auto func=[&](ll N){
		if (N==0) return mll(1);
		return cmb.fact(2*N-1)*twoinv[N-1]*cmb.finv(N-1);
	};

	multimap<ll,vll> mp;
	each(e,cnt){
		ll nm=e.second;
		if (nm<=1)continue;
		auto it=mp.insert(pair<ll,vll>(nm/2,vll()));
		vll &v=it->second;
		rep(k,0,nm/2){
			mll tmp=cmb.P(nm,2*k)*cmb.finv(k)*twoinv[k];
			v.push_back(tmp.val);
		}
	}
	if (mp.empty()){
		cout << func(n) << '\n'; return;
	}

	while (sz(mp)>1){
		auto it=mp.begin();
		vll &v1=it->second;
		it++;
		vll &v2=it->second;

		vll vret=convolution(v1,v2);

		mp.erase(mp.begin());
		mp.erase(mp.begin());
		mp.emplace(move(sz(vret)),move(vret));
	}

	auto it=mp.begin();
	vll &v=it->second;


	mll ans=func(n);
	rep(k,1,sz(v)-1){
		ans += POW(mll(-1),k) * v[k] * func(n-k);
	}
	cout << ans << '\n';
}



int main(){
#if 1
	solve();
#else
	ll t;  cin >> t;
	rep(i, 0, t-1){
		solve();
	}
#endif
	return 0;
}


Measured memory_bytes: 12780