//Zory-2020
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
// typedef __int128 ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define FR first
#define SE second
#define MP make_pair
#define PB push_back
#define vc vector
#define db double
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bin(x) (1ll<<(x))
#define fo(i,l,r) for(int i=(l),I=(r);i<=I;i++)
#define fd(i,r,l) for(int i=(r),I=(l);i>=I;i--)
#define mem(x,val) memset(x,val,sizeof x)
#define Swap(a,b,n) for(int I=0;I<=n;I++) swap(a[I],b[I])
#define PC __builtin_popcountll
#ifdef DEBUG
	#define debug(A,args...) fprintf(stderr,A,##args)
#else
	#define debug(A,args...) printf("")
#endif
#define deb debug("line %d\n",__LINE__)
namespace mine
{
	ll qread()
	{
		ll ans=0,f=1;char c=getchar();
		while(c<'0' or c>'9') {if(c=='-')f=-1;c=getchar();}
		while('0'<=c and c<='9') ans=ans*10+c-'0',c=getchar();
		return ans*f;
	}
	void write(ll num){if(num<0) putchar('-'),num=-num;if(num>=10) write(num/10);putchar('0'+num%10);}
	void write1(ll num){write(num);putchar(' ');}
	void write2(ll num){write(num);putchar('\n');}
	template<typename T>inline bool chmax(T&a,const T&b){return a<b?a=b,1:0;}
	template<typename T>inline bool chmin(T&a,const T&b){return a>b?a=b,1:0;}
	ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
	bool IN(ll x,ll l,ll r){return l<=x and x<=r;}
	void GG(){puts("0");exit(0);}

	const db eps=1e-8;
	const int INF=0x3f3f3f3f;
	const int MOD=1e9+7;
	int mm(const int x){return x>=MOD?x-MOD:x;}
	template<typename T> void add(T &x,const int &y){x=(x+y>=MOD?x+y-MOD:x+y);}
	ll qpower(ll x,ll e,int mod=MOD){ll ans=1;while(e){if(e&1)ans=ans*x%mod;x=x*x%mod;e>>=1;}return ans;}
	ll invm(ll x){return qpower(x,MOD-2);}
	const int MM=5e6+10;
	ll fac[MM],facinv[MM],Inv[MM];ll Comb(int n,int m){return n<0 or n<m?0:fac[n]*facinv[m]%MOD*facinv[n-m]%MOD;}
	void PRE()
	{
		fac[0]=1;fo(i,1,MM-1) fac[i]=fac[i-1]*i%MOD;
		facinv[MM-1]=invm(fac[MM-1]);fd(i,MM-1,1) facinv[i-1]=facinv[i]*i%MOD;
		Inv[1]=1;fo(i,2,MM-1) Inv[i]=(MOD-MOD/i)*Inv[MOD%i]%MOD;
	}

	const int N=1e6+10;
	//------------------FIXED------------------
	vc<int> to[N];
	bool vis[N];stack<int> sta;vc<int> cir,pt;
	void findcir(int x,int fa)
	{
		vis[x]=1;sta.push(x);pt.PB(x);
		for(auto y:to[x]) if(y!=fa)
		{
			if(!vis[y]) findcir(y,x);
			else if(!sz(cir)) { while(sta.top()!=y) cir.PB(sta.top()),sta.pop();cir.PB(y); }
		}if(!sz(cir)) sta.pop();
	}
	ll ret;int siz[N];
	void dfs(int x,int fa){
		vis[x]=1,siz[x]=1;
		for(auto y:to[x]) if(y!=fa)
		{
			if(!vis[y]) dfs(y,x);
			if(y<fa) siz[x]+=siz[y];
		}ret=ret*Inv[siz[x]]%MOD;
	}
	int solve(int rt)
	{
		while(sz(sta)) sta.pop();pt.clear(),cir.clear();findcir(rt,0);if(!sz(cir)) GG();
		int mx=0;fo(t,1,sz(cir)-1) if(cir[t]>cir[mx]) mx=t;rt=cir[mx];//这样rt一定不需要贡献给其他人
		for(auto x:pt) vis[x]=0;ret=1,dfs(rt,cir[(mx+1)%sz(cir)]);int ans=ret;//不可能有二元环
		for(auto x:pt) vis[x]=0;ret=1,dfs(rt,cir[(mx+sz(cir)-1)%sz(cir)]);return mm(ans+ret);
	}
	void main()
	{
		PRE();
		int n=qread();fo(i,1,n+n){ int x=qread(),y=n+qread();to[x].PB(y),to[y].PB(x); }
		ll ans=1;fo(i,1,n+n) if(!vis[i]) ans=ans*solve(i)%MOD;write(ans*fac[n+n]%MOD);
	}
};//变量重名！
signed main()
{
	#ifdef DEBUG
	//freopen("a.in","r",stdin);
	freopen("z.txt","r",stdin);
	//freopen("a.out","w",stdout);
	#endif
	srand(time(0));
	mine::main();
	debug("\n------------------------------------------\nTime: %.2lf s\n",1.0*clock()/CLOCKS_PER_SEC);
}

Measured memory_bytes: 156336