#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<string.h>

#ifdef LOCAL
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define NDEBUG
#define eprintf(...) do {} while (0)
#endif
#include<cassert>

using namespace std;

typedef long long LL;
typedef vector<int> VI;

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define EACH(i,c) for(__typeof((c).begin()) i=(c).begin(),i##_end=(c).end();i!=i##_end;++i)

template<class T> inline void amin(T &x, const T &y) { if (y<x) x=y; }
template<class T> inline void amax(T &x, const T &y) { if (x<y) x=y; }
template<class Iter> void rprintf(const char *fmt, Iter begin, Iter end) {
    for (bool sp=0; begin!=end; ++begin) { if (sp) putchar(' '); else sp = true; printf(fmt, *begin); }
    putchar('\n');
}
template<unsigned MOD> struct ModInt {
    static const unsigned static_MOD = MOD;
    unsigned x;
    void undef() { x = (unsigned)-1; }
    bool isnan() const { return x == (unsigned)-1; }
    inline int geti() const { return (int)x; }
    ModInt() { x = 0; }
    ModInt(const ModInt &y) { x = y.x; }
    ModInt(int y) { if (y<0 || (int)MOD<=y) y %= (int)MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt(long long y) { if (y<0 || MOD<=y) y %= MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned long long y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt &operator+=(const ModInt y) { if ((x += y.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(const ModInt y) { if ((x -= y.x) & (1u<<31)) x += MOD; return *this; }
    ModInt &operator*=(const ModInt y) { x = (unsigned long long)x * y.x % MOD; return *this; }
    ModInt &operator/=(const ModInt y) { x = (unsigned long long)x * y.inv().x % MOD; return *this; }
    ModInt operator-() const { return (x ? MOD-x: 0); }

    ModInt inv() const {
	unsigned a = MOD, b = x; int u = 0, v = 1;
	while (b) {
	    int t = a / b;
	    a -= t * b; swap(a, b);
	    u -= t * v; swap(u, v);
	}
	if (u < 0) u += MOD;
	return ModInt(u);
    }
    ModInt pow(long long y) const {
	ModInt b = *this, r = 1;
	if (y < 0) { b = b.inv(); y = -y; }
	for (; y; y>>=1) {
	    if (y&1) r *= b;
	    b *= b;
	}
	return r;
    }
    friend ModInt operator+(ModInt x, const ModInt y) { return x += y; }
    friend ModInt operator-(ModInt x, const ModInt y) { return x -= y; }
    friend ModInt operator*(ModInt x, const ModInt y) { return x *= y; }
    friend ModInt operator/(ModInt x, const ModInt y) { return x *= y.inv(); }
    friend bool operator<(const ModInt x, const ModInt y) { return x.x < y.x; }
    friend bool operator==(const ModInt x, const ModInt y) { return x.x == y.x; }
    friend bool operator!=(const ModInt x, const ModInt y) { return x.x != y.x; }
};

const LL MOD = 1000000007;
typedef ModInt<MOD> Mint;
const int MAX = 300000;
Mint inv[MAX+1], fact[MAX+1], fact_inv[MAX+1];

void init() {
    inv[1] = 1;
    for (int i=2; i<=MAX; i++) inv[i] = inv[MOD%i] * (MOD-MOD/i);

    fact[0] = fact_inv[0] = 1;
    for (int i=1; i<=MAX; i++) {
	fact[i] = fact[i-1] * i;
	fact_inv[i] = fact_inv[i-1] * inv[i];
    }
}

Mint nCk(int n, int k) {
    return fact[n] * fact_inv[k] * fact_inv[n-k];
}


int N;
VI G[200011];
int par[200011];
bool use[200011];
int target[200011];
VI H[200011];
int indeg[200011];

int sz[200011];
Mint dp[200011];

void MAIN() {
    init();
    scanf("%d", &N);
    REP (i, N*2) {
	int x, y;
	scanf("%d%d", &x, &y);
	x--; y--;
	G[x].push_back(y+N);
	G[y+N].push_back(x);
    }
    N += N;

    memset(par, -1, sizeof par);
    Mint ans = 1;
    int size = 0;
    REP (s, N) if (!use[s]) {
	par[s] = s;
	VI ord;
	ord.push_back(s);
	use[s] = true;
	vector<pair<int, int> > cut;
	for (int i=0; i<(int)ord.size(); i++) {
	    int v = ord[i];
	    EACH (e, G[v]) if (*e != par[v]) {
		if (!use[*e]) {
		    par[*e] = v;
		    ord.push_back(*e);
		    use[*e] = true;
		} else {
		    cut.emplace_back(min(v, *e), max(v, *e));
		}
	    }
	}

	if (cut.size() != 2 || cut[0] != cut[1]) {
	    ans = 0;
	    goto END;
	}


	EACH (e, ord) {
	    par[*e] = -1;
	    use[*e] = false;
	}
	int root = cut[0].first;
	cut.clear();
	ord.clear();
	ord.push_back(root);

	use[root] = true;

	for (int i=0; i<(int)ord.size(); i++) {
	    int v = ord[i];
	    EACH (e, G[v]) if (*e != par[v]) {
		if (!use[*e]) {
		    par[*e] = v;
		    ord.push_back(*e);
		    use[*e] = true;
		} else {
		    cut.emplace_back(min(v, *e), max(v, *e));
		}
	    }
	}

	Mint ans_1 = 0;
	EACH (e, ord) target[*e] = par[*e];
	int a = cut[0].first, b = cut[0].second;
	REP (t, 2) {
	    target[a] = b;
	    {
		int v = a;
		while (v != root) {
		    target[par[v]] = v;
		    v = par[v];
		}
		v = b;
		while (v != root) {
		    target[v] = par[v];
		    v = par[v];
		}
	    }

	    EACH (e, ord) {
		H[*e].clear();
		indeg[*e] = 0;
	    }
	    EACH (e, ord) EACH (f, G[*e]) if (*f < target[*e]) {
		H[*e].push_back(*f);
		indeg[*f]++;
	    }

	    Mint ans_inner = 1;
	    int size_inner = 0;
	    EACH (e, ord) if (indeg[*e] == 0) {
		VI ord2;
		ord2.push_back(*e);
		for (int i=0; i<(int)ord2.size(); i++) {
		    int v = ord2[i];
		    EACH (f, H[v]) {
			ord2.push_back(*f);
		    }
		}
		for (int i=ord2.size(); i--;) {
		    int v = ord2[i];
		    sz[v] = 0;
		    dp[v] = 1;
		    EACH (f, H[v]) {
			dp[v] = dp[v] * dp[*f] * nCk(sz[v] + sz[*f], sz[v]);
			sz[v] += sz[*f];
		    }
		    sz[v]++;
		}

		ans_inner = ans_inner * dp[*e] * nCk(size_inner + sz[*e], size_inner);
		size_inner += sz[*e];
	    }

	    ans_1 += ans_inner;
	    swap(a, b);
	}

	ans = ans * ans_1 * nCk(size + (int)ord.size(), size);
	size += ord.size();
    }

END:
    printf("%d\n", ans.geti());
}

int main() {
    int TC = 1;
//    scanf("%d", &TC);
    REP (tc, TC) MAIN();
    return 0;
}



Measured memory_bytes: 27128