#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> void chmax(T& x, U y){if(x<y) x=y;}
template<class T,class U> void chmin(T& x, U y){if(y<x) x=y;}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	ll extgcd(ll a,ll b,ll &x,ll &y) const{
		ll p[]={a,1,0},q[]={b,0,1};
		while(*q){
			ll t=*p/ *q;
			rep(i,3) swap(p[i]-=t*q[i],q[i]);
		}
		if(p[0]<0) rep(i,3) p[i]=-p[i];
		x=p[1],y=p[2];
		return p[0];
	}
	ModInt inv() const {
		ll x,y;
		extgcd(v,mod,x,y);
		return make(normS(x+mod));
	}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<1000000007>;
V<mint> fact,ifact;
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}
void InitFact(int N){
	fact.resize(N);
	ifact.resize(N);
	fact[0] = 1;
	rep1(i,N-1) fact[i] = fact[i-1] * i;
	ifact[N-1] = fact[N-1].inv();
	for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
}

bool dfsc(int v, int p, const vector<vector<int>>& G, vector<int>& vis, vector<int>& cyc, bool& done){
	if(vis[v]==1){
		cyc.pb(v);
		return 1;
	}
	if(vis[v]==2) return 0;

	vis[v] = 1;
	for(int u:G[v]) if(u != p){
		if(dfsc(u,v,G,vis,cyc,done)){
			if(v==cyc[0]) done=1;
			if(!done) cyc.pb(v);
			return 1;
		}
	}
	vis[v] = 2;
	return 0;
}

vector<int> getcycle(const vector<vector<int>>& G, V<int>& vis, int r){
	int N = G.size();
	bool done = 0;
	vector<int> cyc;
	assert(dfsc(r,-1,G,vis,cyc,done));
	return cyc;
}
struct UnionFind{
	vector<int> par,rank;
	UnionFind(int N){
		par.assign(N,0);
		rank.assign(N,0);
		rep(i,N) par[i]=i;
	}
	int find(int x){
		if(par[x]==x) return x;
		return par[x]=find(par[x]);
	}
	bool same(int x,int y){
		return find(x)==find(y);
	}
	void unite(int x,int y){
		x=find(x),y=find(y);
		if(x==y) return;
		if(rank[x]<rank[y]) swap(x,y);

		//x becomes root
		par[y]=x;
		if(rank[x]==rank[y]) rank[x]++;
	}
};

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	InitFact(500000);

	int N; cin >> N;
	VV<int> G(N+N);
	UnionFind UF(N+N);
	rep(i,N+N){
		int x,y; cin >> x >> y; x--,y--;
		G[x].pb(y+N);
		G[y+N].pb(x);
		UF.unite(x,y+N);
	}
	VV<int> r2vs(N+N);
	rep(i,N+N) r2vs[UF.find(i)].pb(i);
	V<int> vis(N+N);
	V<bool> incycle(N+N);
	mint ans = 1;
	int sn = 0;
	rep(r,N+N) if(r2vs[r].size()){
		auto vs = r2vs[r];
		int n = si(vs), m = 0;
		for(int v: vs){
			for(int u: G[v]) if(v<u) m++;
		}
		if(n != m){
			cout << 0 << endl;
			return 0;
		}
		ans *= Choose(sn+n,n);
		sn += n;
		auto c = getcycle(G,vis,r);
		int K = si(c);
		for(int v: c) incycle[v] = true;
		mint f = 0;
		rep(dir,2){
			map<int,int> to;
			rep(i,K) to[c[i]] = c[(i+1)%K];
			function<void(int,int)> dfs = [&](int v,int p){
				for(int u: G[v]) if(u != p && !incycle[u]){
					to[u] = v;
					dfs(u,v);
				}
			};
			rep(i,K) dfs(c[i],-1);
			dump(to);
			map<int,V<int>> T;
			map<int,int> sz;
			for(int a: vs){
				int b = to[a], c = to[b];
				if(a < c){
					T[b].pb(a);
				}
			}
			map<int,bool> done;
			map<int,bool> notroot;
			mint tmp = 1;
			function<void(int)> dfssz = [&](int v){
				if(done[v]) return;
				done[v] = true;
				sz[v] = 0;
				for(int u: T[v]){
					notroot[u] = true;
					dfssz(u);
					tmp *= Choose(sz[v]+sz[u],sz[u]);
					sz[v] += sz[u];
				}
				sz[v]++;
			};
			for(int v: vs){
				dfssz(v);
			}
			dump(c);
			dump(T);
			dump(sz);
			dump(done);
			dump(notroot);
			int s = 0;
			for(int v: vs) if(!notroot[v]){
				tmp *= Choose(s+sz[v],sz[v]);
				s += sz[v];
			}
			show(s);
			f += tmp;
			reverse(all(c));
		}
		ans *= f;
	}
	cout << ans << endl;
}


Measured memory_bytes: 83960