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;
typedef long long ll;
#define f first
#define s second
#define pb push_back
#define ep emplace
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define uniquev(v) sort(all(v)), (v).resize(unique(all(v)) - (v).begin())
#define mem(f,x) memset(f , x , sizeof(f))
#define sz(x) (ll)(x).size()
#define __lcm(a, b) (1ll * ((a) / __gcd((a), (b))) * (b))
#define mxx *max_element
#define mnn *min_element
#define cntbit(x) __builtin_popcountll(x)
#define len(x) (int)(x.length())
const int N = 1e6 + 10;
int p[N], sz[N], cnt, col[N], id[N * 2];
vector <int> ed[N];
int get(int x) {
return p[x] ? get(p[x]) : x;
}
bool same(int a, int b) {
return get(a) == get(b);
}
bool add_edge(int a, int b) {
a = get(a), b = get(b);
if (a == b)
return 0;
cnt--;
if (sz[a] < sz[b]) {
swap(a, b);
}
sz[a] += sz[b];
p[b] = a;
return 1;
}
bool insersect(vector <pair <int, int>> seg) {
sort(all(seg));
set <int> save;
for (auto x : seg) {
auto it = save.lower_bound(x.f);
if (it != save.end() && *it < x.s)
return 1;
save.insert(x.s);
}
return 0;
}
void dfs(int u) {
for (auto x : ed[u]) {
if (col[x] == -1) {
col[x] = 1 ^ col[u];
dfs(x);
}
}
}
ll solve() {
mem(col, -1);
vector <pair <int, int>> seg;
int n;
cin >> n;
for (int i = 1; i <= n; i++) {
sz[i] = 1;
}
cnt = n;
for (int i = 1; i <= n; i++) {
int a, b;
cin >> a >> b;
seg.pb({a, b});
}
sort(all(seg));
set <int> save;
for (int i = 0; i < n; i++) {
id[seg[i].f] = id[seg[i].s] = i + 1;
auto it = save.lower_bound(seg[i].f);
auto pr = save.lower_bound(seg[i].s);
while (it != save.end() && *it < seg[i].s) {
if (add_edge(i + 1, id[*it])) {
ed[i + 1].pb(id[*it]);
ed[id[*it]].pb(i + 1);
}
if (same(id[*it], id[*prev(pr)]))
break;
it = next(it);
}
save.insert(seg[i].s);
}
for (int i = 1; i <= n; i++) {
if (col[i] == -1) {
col[i] = 0;
dfs(i);
}
}
vector <pair <int, int>> A, B;
for (int i = 1; i <= n; i++) {
if (col[i] == 0) {
A.pb(seg[i - 1]);
} else {
B.pb(seg[i - 1]);
}
}
if (insersect(A) || insersect(B))
return 0;
ll ans = 1, mod = 1e9 + 7;
for (int i = 1; i <= cnt; i++) {
ans = (ans + ans) % mod;
}
return ans;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t = 1;
//cin >> t;
while (t--) {
cout << solve() << '\n';
}
return 0;
}
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