This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
const int maxn = 2e6 + 6;
const int mod = 1e9 + 7;
int n, s[maxn], t[maxn];
vector<int> g[maxn], w[maxn];
void add_edge(int u, int v, int col) {
	w[u].emplace_back(col);
	w[v].emplace_back(col);
	g[u].emplace_back(v);
	g[v].emplace_back(u);
}
struct info {
	int x, id;
	info () {}
	info (int _x, int _id) {
		x = _x, id = _id;
	}
	bool operator < (const info &that) const {
		return x < that.x;
	}
};
vector<info> ft[maxn];
int ptr[maxn];
void insert(int i, info j, int u = 1, int l = 1, int r = 2 * n) {
	ft[u].emplace_back(j);
	if(l == r) return;
	int m = l + r >> 1;
	if(i <= m) insert(i, j, u << 1, l, m);
	else insert(i, j, u << 1 | 1, m + 1, r);
}
void update(int i, int j, int k, int id, int u = 1, int l = 1, int r = 2 * n) {
	if(r < i or l > j or i > j) return;
	if(i <= l and r <= j) {
		while(ptr[u] < ft[u].size() and ft[u][ptr[u]].x <= k) ptr[u]++;
		if(ptr[u] and ft[u].size()) add_edge(id, ft[u][0].id, 1);
		return;
	} int m = l + r >> 1;
	update(i, j, k, id, u << 1, l, m);
	update(i, j, k, id, u << 1 | 1, m + 1, r);
}
void build(int u = 1, int l = 1, int r = 2 * n) {
	for(int i = 1; i < ptr[u]; i++) {
		add_edge(ft[u][i - 1].id, ft[u][i].id, 0);
	} if(l == r) return;
	int m = l + r >> 1;
	build(u << 1, l, m);
	build(u << 1 | 1, m + 1, r);
}
int vis[maxn];
int col[maxn];
void dfs(int u) {
	vis[u] = 1;
	for(int i = 0; i < g[u].size(); i++) {
		int v = g[u][i], c = w[u][i];
		if(!vis[v]) {
			col[v] = col[u] ^ c;
			dfs(v);
		}
	}
}
bool valid() {
	vector<int> id(2 * n + 5), op(2 * n + 5);
	for(int i = 1; i <= n; i++) {
		id[s[i]] = i, op[s[i]] = +1;
		id[t[i]] = i, op[t[i]] = -1;
	}
	vector<int> A, B;
	for(int i = 1; i <= (2 * n); i++) {
		if(op[i] == +1) {
			col[id[i]] ? A.push_back(id[i]) : B.push_back(id[i]);
		} else {
			vector<int> &w0t = col[id[i]] ? A : B;
			if(w0t.empty() or w0t.back() != id[i]) {
				return false;
			} else {
				w0t.pop_back();
			}
		}
	} return true;
}
int main(int argc, char const *argv[])
{
	// freopen("in", "r", stdin);
	scanf("%d", &n);
	vector<ii> tmp;
	for(int i = 1; i <= n; i++) {
		scanf("%d %d", &s[i], &t[i]);
		tmp.emplace_back(s[i], t[i]);
	}
	sort(tmp.begin(), tmp.end());
	for(int i = 0; i < n; i++) {
		s[i + 1] = tmp[i].first;
		t[i + 1] = tmp[i].second;
	}
	for(int i = 1; i <= n; i++) {
		insert(t[i], info(s[i], i));
	}
	for(int i = 1; i <= n; i++) {
		update(s[i] + 1, t[i] - 1, s[i] - 1, i);
	}
	build();
	int ans = 1;
	for(int i = 1; i <= n; i++) {
		if(!vis[i]) {
			ans <<= 1;
			if(ans >= mod) {
				ans -= mod;
			}
			dfs(i);
		}
	}
	if(valid()) {
		printf("%d\n", ans);
	} else {
		puts("0");
	}
	return 0;
}
Compilation message (stderr)
port_facility.cpp: In function 'void insert(int, info, int, int, int)':
port_facility.cpp:34:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  int m = l + r >> 1;
          ~~^~~
port_facility.cpp: In function 'void update(int, int, int, int, int, int, int)':
port_facility.cpp:42:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(ptr[u] < ft[u].size() and ft[u][ptr[u]].x <= k) ptr[u]++;
         ~~~~~~~^~~~~~~~~~~~~~
port_facility.cpp:45:14: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  } int m = l + r >> 1;
            ~~^~~
port_facility.cpp: In function 'void build(int, int, int)':
port_facility.cpp:54:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  int m = l + r >> 1;
          ~~^~~
port_facility.cpp: In function 'void dfs(int)':
port_facility.cpp:64:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i = 0; i < g[u].size(); i++) {
                 ~~^~~~~~~~~~~~~
port_facility.cpp: In function 'int main(int, const char**)':
port_facility.cpp:97:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &n);
  ~~~~~^~~~~~~~~~
port_facility.cpp:100:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d", &s[i], &t[i]);
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