#include<bits/stdc++.h>

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef double lf;
typedef long double llf;
typedef std::pair<int,int> pii;

#define xx first
#define yy second

template<typename T> inline T max(T a,T b){return a>b?a:b;}
template<typename T> inline T min(T a,T b){return a<b?a:b;}
template<typename T> inline T abs(T a){return a>0?a:-a;}
template<typename T> inline bool repr(T &a,T b){return a<b?a=b,1:0;}
template<typename T> inline bool repl(T &a,T b){return a>b?a=b,1:0;}
template<typename T> inline T gcd(T a,T b){T t;if(a<b){while(a){t=a;a=b%a;b=t;}return b;}else{while(b){t=b;b=a%b;a=t;}return a;}}
template<typename T> inline T sqr(T x){return x*x;}
#define mp(a,b) std::make_pair(a,b)
#define pb push_back
#define I inline
#define mset(a,b) memset(a,b,sizeof(a))
#define mcpy(a,b) memcpy(a,b,sizeof(a))

#define fo0(i,n) for(int i=0,i##end=n;i<i##end;i++)
#define fo1(i,n) for(int i=1,i##end=n;i<=i##end;i++)
#define fo(i,a,b) for(int i=a,i##end=b;i<=i##end;i++)
#define fd0(i,n) for(int i=(n)-1;~i;i--)
#define fd1(i,n) for(int i=n;i;i--)
#define fd(i,a,b) for(int i=a,i##end=b;i>=i##end;i--)
#define foe(i,x)for(__typeof((x).end())i=(x).begin();i!=(x).end();++i)

struct Cg{I char operator()(){return getchar();}};
struct Cp{I void operator()(char x){putchar(x);}};
#define OP operator
#define RT return *this;
#define RX x=0;char t=P();while((t<'0'||t>'9')&&t!='-')t=P();bool f=0;\
if(t=='-')t=P(),f=1;x=t-'0';for(t=P();t>='0'&&t<='9';t=P())x=x*10+t-'0'
#define RL if(t=='.'){lf u=0.1;for(t=P();t>='0'&&t<='9';t=P(),u*=0.1)x+=u*(t-'0');}if(f)x=-x
#define RU x=0;char t=P();while(t<'0'||t>'9')t=P();x=t-'0';for(t=P();t>='0'&&t<='9';t=P())x=x*10+t-'0'
#define TR *this,x;return x;
I bool IS(char x){return x==10||x==13||x==' ';}template<typename T>struct Fr{T P;I Fr&OP,(int&x)
{RX;if(f)x=-x;RT}I OP int(){int x;TR}I Fr&OP,(ll &x){RX;if(f)x=-x;RT}I OP ll(){ll x;TR}I Fr&OP,(char&x)
{for(x=P();IS(x);x=P());RT}I OP char(){char x;TR}I Fr&OP,(char*x){char t=P();for(;IS(t);t=P());if(~t){for(;!IS
(t)&&~t;t=P())*x++=t;}*x++=0;RT}I Fr&OP,(lf&x){RX;RL;RT}I OP lf(){lf x;TR}I Fr&OP,(llf&x){RX;RL;RT}I OP llf()
{llf x;TR}I Fr&OP,(uint&x){RU;RT}I OP uint(){uint x;TR}I Fr&OP,(ull&x){RU;RT}I OP ull(){ull x;TR}};Fr<Cg>in;
#define WI(S) if(x){if(x<0)P('-'),x=-x;char s[S],c=0;while(x)s[c++]=x%10+'0',x/=10;while(c--)P(s[c]);}else P('0')
#define WL if(y){lf t=0.5;for(int i=y;i--;)t*=0.1;if(x>=0)x+=t;else x-=t,P('-');*this,(ll)(abs(x));P('.');if(x<0)\
x=-x;while(y--){x*=10;x-=floor(x*0.1)*10;P(((int)x)%10+'0');}}else if(x>=0)*this,(ll)(x+0.5);else *this,(ll)(x-0.5);
#define WU(S) if(x){char s[S],c=0;while(x)s[c++]=x%10+'0',x/=10;while(c--)P(s[c]);}else P('0')
template<typename T>struct Fw{T P;I Fw&OP,(int x){WI(10);RT}I Fw&OP()(int x){WI(10);RT}I Fw&OP,(uint x){WU(10);RT}
I Fw&OP()(uint x){WU(10);RT}I Fw&OP,(ll x){WI(19);RT}I Fw&OP()(ll x){WI(19);RT}I Fw&OP,(ull x){WU(20);RT}I Fw&OP()
(ull x){WU(20);RT}I Fw&OP,(char x){P(x);RT}I Fw&OP()(char x){P(x);RT}I Fw&OP,(const char*x){while(*x)P(*x++);RT}
I Fw&OP()(const char*x){while(*x)P(*x++);RT}I Fw&OP()(lf x,int y){WL;RT}I Fw&OP()(llf x,int y){WL;RT}};Fw<Cp>out;

const int N=200007,P=1000000007;

inline int pow(int a,int b)
{
	int r=1;
	for(;b;b>>=1,a=(ll)a*a%P)
		if(b&1)r=(ll)r*a%P;
	return r;
}

std::vector<int>p[N],pv[N],ux,uy,ps[N];
int n,uf[N],fa[N],fac[N],fin[N],f[N],sz[N],ec[N];
bool vis[N],vv[N],flag;

inline int find(int x)
{
	return x==fa[x]?x:fa[x]=find(fa[x]);
}

inline void dfs(int x)
{
	foe(i,p[x])if(*i!=fa[x])fa[*i]=x,dfs(*i);
}

inline void dfs2(int x)
{
	if(vv[x]){flag=1;return;}vv[x]=1;
	sz[x]=1,f[x]=1;
	foe(i,pv[x])if(*i<fa[x])
	{
		dfs2(*i);
		f[x]=(ll)f[x]*fin[sz[*i]]%P*f[*i]%P;
		sz[x]+=sz[*i];
	}
	f[x]=(ll)f[x]*fac[sz[x]-1]%P;
}

inline int solve(int ux,int uy,std::vector<int>&li)
{
	//out,"solve:",ux,' ',uy,' ',li.size(),'\n';
	fa[ux]=uy;
	dfs(ux);
	foe(i,li)vis[*i]=0;
	foe(i,li)foe(j,pv[*i])if(*j<fa[*i])vis[*j]=1;
	//foe(i,li)foe(j,pv[*i])if(*j<fa[*i])out,"tree:",*i,' ',*j,'\n';
	int res=fac[li.size()];
	foe(i,li)vv[*i]=0;flag=0;
	foe(i,li)if(!vis[*i])dfs2(*i),res=(ll)res*fin[sz[*i]]%P*f[*i]%P;
	foe(i,li)if(!vv[*i])return 0;
	if(flag)return 0;
	//foe(i,li)out,'(',f[*i],',',sz[*i],')',' ';out,'\n';
	//out,ux,' ',uy,' ',res,'\n';
	return res;
}

int main()
{
	fac[0]=1;
	fo1(i,N-1)fac[i]=(ll)fac[i-1]*i%P;
	fin[N-1]=pow(fac[N-1],P-2);
	fd1(i,N-1)fin[i-1]=(ll)fin[i]*i%P;
	in,n;n*=2;
	fo1(i,n)fa[i]=i;
	fo1(i,n)
	{
		int x,y;
		in,x,y;y+=n/2;
		//out,"e:",x,' ',y,'\n';
		//if(find(x)==find(y))out,"u:",x,' ',y,'\n';
		if(find(x)==find(y))ux.pb(x),uy.pb(y);
		else fa[find(x)]=find(y),p[x].pb(y),p[y].pb(x);
		pv[x].pb(y),pv[y].pb(x);
	}
	fo1(i,n)ps[find(i)].pb(i);
	fo1(i,n)ec[find(i)]+=pv[i].size();
	fo1(i,n)if(find(i)==i&&ps[i].size()*2!=ec[i])return puts("0"),0;
	fo1(i,n)std::sort(pv[i].begin(),pv[i].end());
	int ans=fac[n];
	fo0(i,ux.size())
	{
		int ro=find(ux[i]);
		ans=(ll)ans*fin[ps[ro].size()]%P*(solve(ux[i],uy[i],ps[ro])+solve(uy[i],ux[i],ps[ro]))%P;
	}
	out,ans,'\n';
}

Measured memory_bytes: 34548