// Slower C++ solution:
#include<bits/stdc++.h>

#define il inline

#define stt static

#define rg register

#define ll long long

#define db double

#define pii pair<int,int>

#define mp make_pair

#define fst first

#define snd second

#define pb push_back

#define y1 substitute_of_y1

#define DEBUG(x) cerr<<#x" = "<<x<<endl;

using namespace std;



template<typename T> il T rd(){

	T nmb=0;int sgn=0;char chr=getchar();

	while(!isdigit(chr)){if(chr=='-')sgn=1;chr=getchar();}

	while(isdigit(chr)){nmb=(nmb<<3)+(nmb<<1)+chr-'0';chr=getchar();}

	return sgn?-nmb:nmb;

}

template<typename T> void wt(T nmb){

	if(nmb>9)wt(nmb/10);

	putchar(nmb%10+'0');

}

template<typename T> il void cmax(T &x,T y){x=x>y?x:y;}

template<typename T> il void cmin(T &x,T y){x=x<y?x:y;}

inline void proc_status(){

	ifstream t ("/proc/self/status");

	cerr<<string(istreambuf_iterator<char>(t),istreambuf_iterator<char>())<<endl;

	/*freopen("/proc/self/status","r",stdin);

	char ch[100];

	while(scanf("%s",ch)!=EOF)cerr<<ch<<endl;*/

}



const int L=2e5+10;

const int P=1e9+7;



il int pwr(int x,int y){

	int z=1;

	for(;y;y>>=1,x=(ll)x*x%P)

		if(y&1)z=(ll)z*x%P;

	return z;

}

int fac[L],inv[L];

il void getfac(int n){

	fac[0]=1;

	for(int i=1;i<=n;++i)

		fac[i]=(ll)fac[i-1]*i%P;

	inv[n]=pwr(fac[n],P-2);

	for(int i=n;i;--i)

		inv[i-1]=(ll)inv[i]*i%P;

}

il int C(int n,int m){

	if(n<0||m<0||n<m)return 0;

	return (ll)fac[n]*inv[m]%P*inv[n-m]%P;

}



int F[L];

int get(int x){return x==F[x]?x:F[x]=get(F[x]);}



int To[L<<1],Fs[L],Nx[L<<1],W[L<<1],E;

il void Add(int x,int y,int z){

	To[++E]=y;

	Nx[E]=Fs[x];

	Fs[x]=E;

	W[E]=z;

}



vector<int>vec[L];



int to[L<<1],fs[L],nx[L<<1],w[L<<1],e;

il void add(int x,int y,int z){

	to[++e]=y;

	nx[e]=fs[x];

	fs[x]=e;

	w[e]=z;

}



int st[L],top;

int in[L];



int stx[L],wgt[L],tp;

int num[L],val[L],cnt;

int vis[L];

int Flg;

void findcir(int x,int f){

	stx[++tp]=x,vis[x]=1;

	for(int i=fs[x];i;i=nx[i]){

		int k=to[i];

		if(k==f)continue;

		wgt[tp]=w[i];

		if(!Flg&&vis[k]){

			Flg=1;

			int lb=tp;

			while(stx[lb]!=k)--lb;

			for(int t=lb;t<=tp;++t)

				num[t-lb+1]=stx[t],val[t-lb+1]=wgt[t];

			cnt=tp-lb+1;

		}

		else if(!vis[k])findcir(k,x);

	}

	--tp,vis[x]=0;

}



int Fa[L];

int Vis[L],Wgt[L];

int res;

int ans[L],siz[L];

void dfs(int x,int f){

	siz[x]=ans[x]=1;

	for(int i=fs[x];i;i=nx[i]){

		int k=to[i];

		if(k==f||Vis[k])continue;

		Vis[k]=1,Wgt[k]=w[i];

		if(w[i]<Wgt[x])Fa[k]=x;

		else Fa[k]=0;

		dfs(k,x);

		if(Fa[k]){

			ans[x]=(ll)ans[x]*ans[k]%P*C(siz[x]+siz[k]-1,siz[k])%P;

			siz[x]+=siz[k];

		}

	}

}



il int Pre(int x){return x==1?cnt:x-1;}

il int Nxt(int x){return x==cnt?1:x+1;}



int main(){

	int n=rd<int>();

	int lim=n<<1;

	for(int i=1;i<=lim;++i)F[i]=i;

	for(int i=1;i<=lim;++i){

		int x=rd<int>(),y=rd<int>();

		Add(x,y+n,x+y),Add(y+n,x,x+y);

		F[get(x)]=get(y+n);

	}

	for(int i=1;i<=lim;++i)

		vec[get(i)].pb(i);

	getfac(lim);

	int Ans=1,Sum=0;

	for(int T=1;T<=lim;++T){

		if(vec[T].empty())continue;

		top=0;

		int cnta=(int)vec[T].size(),cntb=0;

		for(int t=vec[T].size()-1;~t;--t){

			int x=vec[T][t];

			st[++top]=x;

			for(int i=Fs[x];i;i=Nx[i]){

				int k=To[i];

				if(get(k)==get(x)){

					++cntb;

					add(x,k,W[i]),++in[k];//反向边在枚举到k时加

				}

			}

		}

		cntb>>=1;

		if(cnta^cntb)return puts("0"),0;





		tp=0,Flg=0;

		findcir(st[1],0);





		int Res=0,Siz=0;

		res=1;

		for(int i=1;i<=cnt;++i)

			Vis[num[i]]=1,Wgt[num[i]]=val[i];

		for(int i=1;i<=cnt;++i)

			dfs(num[i],0);

		for(int i=1;i<=cnt;++i){

			int nxt=Nxt(i);

			if(Wgt[num[i]]<Wgt[num[nxt]])Fa[num[i]]=num[nxt];

			else Fa[num[i]]=0;

		}

		for(int i=1;i<=cnt;++i){

			if(Fa[num[i]])continue;

			for(int k=Nxt(i);Fa[num[k]];k=Nxt(k)){

				int nxt=Nxt(k);

				ans[num[nxt]]=(ll)ans[num[nxt]]*ans[num[k]]%P*C(siz[num[nxt]]+siz[num[k]]-1,siz[num[k]])%P;

				siz[num[nxt]]+=siz[num[k]];

			}

		}

		Siz=0;

		for(int i=1;i<=top;++i){

			if(Fa[st[i]])continue;

			res=(ll)res*ans[st[i]]%P*C(Siz+siz[st[i]],siz[st[i]])%P;

			Siz+=siz[st[i]];

		}

		for(int i=1;i<=top;++i)

			Vis[st[i]]=Wgt[st[i]]=0;

		(Res+=res)%=P;



		res=1;

		for(int i=1;i<=cnt;++i)

			Vis[num[i]]=1,Wgt[num[i]]=i==1?val[cnt]:val[i-1];

		for(int i=1;i<=cnt;++i)

			dfs(num[i],0);

		for(int i=1;i<=cnt;++i){

			int nxt=Pre(i);

			if(Wgt[num[i]]<Wgt[num[nxt]])Fa[num[i]]=num[nxt];

			else Fa[num[i]]=0;

		}

		for(int i=1;i<=cnt;++i){

			if(Fa[num[i]])continue;

			for(int k=Pre(i);Fa[num[k]];k=Pre(k)){

				int nxt=Pre(k);

				ans[num[nxt]]=(ll)ans[num[nxt]]*ans[num[k]]%P*C(siz[num[nxt]]+siz[num[k]]-1,siz[num[k]])%P;

				siz[num[nxt]]+=siz[num[k]];

			}

		}

		Siz=0;

		for(int i=1;i<=top;++i){

			if(Fa[st[i]])continue;

			res=(ll)res*ans[st[i]]%P*C(Siz+siz[st[i]],siz[st[i]])%P;

			Siz+=siz[st[i]];

		}

		for(int i=1;i<=top;++i)

			Vis[st[i]]=Wgt[st[i]]=0;

		(Res+=res)%=P;



		Ans=(ll)Ans*Res%P*C(Sum+cnta,cnta)%P;

		Sum+=cnta;





		for(int i=1;i<=top;++i)

			fs[st[i]]=in[st[i]]=vis[st[i]]=0;//

		e=0;

	}

	printf("%d\n",Ans);

	return 0;

}

// Faster C++ solution for the same problem (measured speedup: 6.47745223282507x):
#include <bits/stdc++.h>



char buf[1 << 20], *p1, *p2;

#define getchar() ((p1 == p2) && (p2 = (p1 = buf) + fread(buf, 1, 1 << 20, stdin), p1 == p2) ? EOF : *p1++)



template<typename T>

void read(T &x) 

{

	x = 0;

	int f = 1; char c = getchar();

	while (!isdigit(c)) { if (c == '-') f = -1; c = getchar(); }

	while (isdigit(c)) { x = x * 10 + c - 48; c = getchar(); }

	x *= f;

}



const int Mod = 1e9 + 7;



inline int add(int a, int b) { return a + b >= Mod ? a + b - Mod : a + b; }

inline int sub(int a, int b) { return a - b < 0 ? a - b + Mod : a - b; }

inline int mul(int a, int b) { return 1LL * a * b % Mod; }

inline void updateA(int &a, int b) { a = add(a, b); }

inline void updateM(int &a, int b) { a = mul(a, b); }



const int MAXN = 2e5 + 9;



int fac[MAXN], inv[MAXN], ifac[MAXN];



void Call(int n) 

{

	fac[0] = 1; for (int i = 1; i <= n; ++i) fac[i] = mul(fac[i - 1], i);

	inv[1] = 1; for (int i = 2; i <= n; ++i) inv[i] = mul(sub(Mod, Mod / i), inv[Mod % i]);

	ifac[0] = 1; for (int i = 1; i <= n; ++i) ifac[i] = mul(ifac[i - 1], inv[i]);

}



int n;



struct Edge { int ver, nxt; } e[MAXN << 2];

int head[MAXN], tot = 0, Head[MAXN];



inline void Add(int x, int y) { e[++tot].ver = y, e[tot].nxt = head[x], head[x] = tot; }

inline void Add_(int x, int y) { e[++tot].ver = y, e[tot].nxt = Head[x], Head[x] = tot; }



int ans = 0;



std::vector<int> G;

bool vis[MAXN];

int edge = 0, s, t;

void GetLoop(int x, int Fa) 

{

	G.push_back(x);

	vis[x] = true;

	for (int i = head[x]; i; ++edge, i = e[i].nxt)

	{

		int y = e[i].ver;

		if (!vis[y]) GetLoop(y, x);

		else if (y != Fa)

			s = x, t = y;

	}

}



int pr[MAXN];

void GetPr(int x) 

{

	for (int i = head[x]; i; i = e[i].nxt) 

	{

		int y = e[i].ver;

		if (y == pr[x] || y == s) continue;

		pr[y] = x;

		GetPr(y);

	}

}



int deg[MAXN];

void Build()

{

	for (auto x : G)

		for (int i = head[x]; i; i = e[i].nxt) 	

		{

			int y = e[i].ver;

			if (y < pr[x]) Add_(x, y), ++deg[y];

			// 令每个点认领它的入边

			// 按照限制关系建边 

		}

}



int sz[MAXN];

void Dfs(int x) 

{

	sz[x] = 1;

	for (int i = Head[x]; i; i = e[i].nxt)

	{

		int y = e[i].ver;

		if (y == pr[x]) continue;

		Dfs(y);

		sz[x] += sz[y];

	}

}



int Calc() 

{

	for (auto i : G)

		Head[i] = deg[i] = 0;

	

	int res = fac[G.size()];

	

	pr[s] = t;

	GetPr(s);

	Build();



	for (auto i : G)

		if (!deg[i])

			Dfs(i);

	for (auto i : G) 

		updateM(res, inv[sz[i]]);

		

	return res;

}



int main() 

{

	read(n);

	for (int i = 1; i <= n << 1; ++i)

	{

		int x, y;

		read(x), read(y);

		Add(x, y + n), Add(y + n, x); 

	}



	n <<= 1; 

	Call(n);



	ans = fac[n];



	for (int i = 1; i <= n; ++i) 

		if (!vis[i])

		{

			GetLoop(i, 0);

			if (G.size() << 1 != edge) { ans = 0; break; } // 是否是基环树 

			updateM(ans, ifac[G.size()]);

			int res = 0;

			updateA(res, Calc());

			std::swap(s, t); // 换个方向 

			updateA(res, Calc());

			updateM(ans, res);

	

			G.clear();

			edge = 0;

		}



	printf("%d\n", ans);	



	return 0;

}