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
#include <bits/stdc++.h>
using namespace std;

#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define REP(i, n) for(int i = 0; i < (n); ++i)

template<class T> int size(T && a) {
	return (int)(a.size());
}
ostream& operator << (ostream &os, string str) {
    for(char c : str) os << c;
    return os;
}
template <class A, class B> ostream& operator << (ostream &os, const pair<A, B> &p) {
	return os << '(' << p.first << "," << p.second << ')';
}
template <class T> auto operator << (ostream &os, T &&x) -> decltype(x.begin(), os) {
	os << '{';
	for(auto it = x.begin(); it != x.end(); ++it)
		os << *it << (it == prev(x.end()) ? "" : " ");
	return os << '}';
}
template <class T> ostream& operator << (ostream &os, vector<vector<T>> vec) {
    for(auto x : vec)
    	os << "\n  " << x;
    return os;
}
void dump() {}
template <class T, class... Args> void dump(T &&x, Args... args) {
    cerr << x << "; ";
    dump(args...);
}
#ifdef DEBUG
# define debug(x...) cerr << "[" #x "]: ", dump(x), cerr << '\n'
#else 
# define debug(...) 0
#endif

//--------------------------------------------------

constexpr int MOD = int(1e9) + 7;

int add(int a, int b) {
	if (a + b >= MOD)
		return a + b - MOD;
	return a + b;
}

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

int fast_pow(int a, int p) {
	if (p == 0) return 1;
	if (p % 2 == 1) return mul(fast_pow(a, p - 1), a);

	int ret = fast_pow(a, p / 2);
	return mul(ret, ret);
}

int divide(int a, int b) {
	return mul(a, fast_pow(b, MOD - 2));
}

struct BinomCoeff {
	vector<int> fac, rev;
	BinomCoeff(int n) {
		fac = rev = vector<int>(n + 1, 1);
		FOR(i, 1, n) fac[i] = mul(fac[i - 1], i);
		rev[n] = divide(1, fac[n]);
		for(int i = n; i >= 1; i--)
			rev[i - 1] = mul(rev[i], i);
	}

	int operator()(int n, int k) {
		return mul(fac[n], mul(rev[n - k], rev[k]));
	}
};

const int MAX_N = int(5e5);

struct SegmentTree {
	vector<int> T;
	int size = 1;

	SegmentTree(int n) {
		while (size < n) size *= 2;
		T.resize(2 * size, -1);
	}

	void add(int l, int r, int value) {
		l += size;
		r += size;

		T[l] = T[r] = value;

		while (l / 2 != r / 2) {
			if (l % 2 == 0) T[l + 1] = value;
			if (r % 2 == 1) T[r - 1] = value;
			l /= 2, r /= 2;
		}

		debug(T);
	}

	int get(int p) {
		p += size;
		int ret = T[p];

		while (p /= 2) {
			ret = max(ret, T[p]);
		}

		return ret;
	}
};

using graph_t = vector<array<int, 2>>;

graph_t get_dag(const vector<pair<int, int>> &segments) {
	int n = ssize(segments);
	graph_t graph(n, {-1, -1});

	SegmentTree tree(2 * n);

	REP (i, n) {
		auto [l, r] = segments[i];

		graph[i][0] = tree.get(l);
		graph[i][1] = tree.get(r);

		tree.add(l, r, i);
	}

	return graph;
}

vector<int> get_before_cnt(const graph_t &graph) {
	int n = ssize(graph);

	vector<bitset<MAX_N>> before(n);
	vector<int> answer(n);

	for (int u = n - 1; u >= 0; --u) {
		answer[u] = before[u].count();

		before[u][u] = 1;
		for (int v : graph[u]) if (v != -1)
			before[v] |= before[u];
	}

	return answer;
}


int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	int n;
	cin >> n;

	vector<pair<int, int>> segments(n);
	REP (i, n) {
		int l, r;
		cin >> l >> r;
		--l, --r;

		segments[i] = pair(l, r);
	}

	graph_t dag = get_dag(segments);
	debug(dag);

	vector<int> before_cnt = get_before_cnt(dag);
	debug(before_cnt);

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

	BinomCoeff C(n + 1);
	int answer = 0;
	REP (u, n) {
		int c = before_cnt[u];
		int res = mul(mul(fac[n - c - 1], fac[c]), C(n, c + 1));
		answer = add(answer, res);
	}

	cout << divide(answer, fac[n]) << '\n';
}