1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
 
#define mp make_pair
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define eb emplace_back
#define st first
#define nd second
#define vt vector
#define VAR(__var)  #__var << ": " << __var << " "
#define PAIR(__var) #__var << ": " << __var.first << ", " << __var.second << " "
#define FOR(__var, __start, __end)  for(int __var=__start; __var<__end; ++__var)
#define FORB(__var, __start, __end) for(int __var=__start; __var>__end; --__var)
#define REP(__var, __cnt) for(int __var=0; __var<(__cnt); ++__var)
#define EACH(__var, __x) for(auto __var : __x)
#define maxi(__x, __y) __x = (__x>__y?__x:__y)
#define mini(__x, __y) __x = (__x<__y?__x:__y)
#define all(__var)     (__var).begin(),(__var).end()
#define rall(__var)    (__var).rbegin(),(__var).rend()
#define sz(__var)      (int)(__var).size()

using namespace std;
 
using namespace __gnu_pbds;
template <typename T>
using ord_set = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;

#ifdef DEBUG
template<typename Stream, typename T1, typename T2>
Stream& operator << (Stream& out, pair<T1, T2> a) {return out << "(" << a.st << ", " << a.nd << ")";}
 
template<typename Stream, typename T>
Stream &operator << (Stream& out, T v) {
	out << "{";
	int i = 0;
	for (auto x : v)
		out << x << ((++ i) != sz(v) ? ", " : "");
	return out << "}";
}
 
template<typename... Args>
void dump(Args... x) {((cerr << x << ", "), ...) << '\n';}
 
#define debug(x...) cerr << "[" #x "]: ", dump(x)
#else
#define debug(...) 0
#endif
 
typedef       long long ll;
typedef     long double ld;
typedef   pair<ll, ll> pll;
typedef pair<int, int> pii;

const bool __test_cases = false;
 
const int INF = 1e9+2137;
const ll mod = 1'000'000'007;
vt<ll> sln;

inline ll add(ll a, ll b) {
	return (a+b)%mod;
}

inline ll mul(ll a, ll b) {
	return (a*b)%mod;
}

ll bin(ll a, ll b) {
	if(b == 0)
		return 1ll;
	if(b&1)
		return mul(bin(a, b-1), a);
	ll x = bin(a, b/2);
	return mul(x, x);
}

inline ll inv(ll a) {
	return bin(a, mod-2);
}

inline ll nck(ll n, ll k) {
	return mul(sln[n], inv(mul(sln[k], sln[n-k])));
}

struct Segment {
	vt<int> t;
	int base;
	Segment(int n) {
		base = 1;
		while(base < n)
			base *= 2;

		t.resize(2*base, -1);
	}

	void upd(int l, int r, int tl, int tr, int v, int x) {
		if(r < tl || tr < l)
			return;

		if(l <= tl && tr <= r) {
			t[v] = x;
			return;
		}

		int tm = tl + (tr-tl)/2;
		upd(l, r, tl, tm, 2*v, x);
		upd(l, r, tm+1, tr, 2*v+1, x);
	}

	void upd(int l, int r, int x) {
		upd(l, r, 0, base-1, 1, x);
	}

	int get(int v) {
		v += base;
		int res = -1;
		while(v > 0) {
			if(t[v] > res)
				res = t[v];
			v/=2;
		}
		return res;
	}
};

void solve() {
	int n;
	cin >> n;

	sln.resize(n+1);
	sln[0] = 1;
	FOR(i, 1, n+1)
		sln[i] = mul(sln[i-1], i);

	vt<vt<int>> g(n);
	vt<int> wch(n, 0), ile(n, 0);
	Segment seg(2*n);
	vt<pii> a;
	FOR(i, 0, n) {
		int l, r;
		cin >> l >> r;
		a.pb({l-1, r-1});
	}
		
	FOR(i, 0, n) {
		auto [l, r] = a[i];
		int res = seg.get(l);

		if(res != -1) {
			g[i].pb(res);
			++wch[res];
		}

		int prev = res;
		res = seg.get(r);
		if(res != -1 && prev != res) {
			g[i].pb(res);
			++wch[res];
		}
		
		seg.upd(l, r, i);
	}
	
	queue<int> q;
	FOR(i, 0, n) {
		if(wch[i] == 0)
			q.push(i);
	}

	const int MAXN = 100'000;
	vector<bitset<MAXN>> kto(n);
	while(!q.empty()) {
		auto v = q.front();
		q.pop();
		for(auto u : g[v]) {
			--wch[u];
			if(wch[u] == 0)
				q.push(u);
			kto[u] |= kto[v];
			kto[u][v] = 1;
		}
	}

	FOR(i, 0, n)
		ile[i] = kto[i].count();
	
	ll res = 0;

	FOR(i, 0, n) {
		res = add(res, mul(nck(n, ile[i]+1), mul(sln[ile[i]], sln[n-ile[i]-1])));
	}

	cout << mul(res, inv(sln[n])) << '\n';
}
 
int32_t main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	
	int t=1;
	if(__test_cases)
		cin >> t;
	while(t--) {
		solve();
	}

	return 0;
}