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>
#include<fstream>
using namespace std;
#define sz(a) (int)a.size()
#define ALL(v) v.begin(), v.end()
#define ALLR(v) v.rbegin(), v.rend()
#define ll long long
#define pb push_back
#define forr(i, a, b) for(int i = a; i < b; i++)
#define dorr(i, a, b) for(int i = a; i >= b; i--)
#define ld long double
#define vt vector
#include<fstream>
#define fi first
#define se second
#define pll pair<ll, ll>
#define pii pair<int, int>
#define mpp make_pair
const ld PI = 3.14159265359, prec = 1e-9;;
//using u128 = __uint128_t;
//const int x[4] = {1, 0, -1, 0};
//const int y[4] = {0, -1, 0, 1};
const ll mod = 1e9 + 7, pr = 31;
const int mxn = 1e6 + 5, mxq = 1e5 + 5, sq = 500, mxv = 5e4 + 1;
//const int base = (1 <<18);
const ll inf = 1e9 + 5, neg = -69420, inf2 = 1e14;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
// have fun!
//JOIIIIIIIIIIIIIII
int n;
pii p[mxn + 1];
int c[mxn + 1];
int st[4 * mxn + 1], st2[4 * mxn + 1];
void upd(int nd, int l, int r, int id, int v){
if(l == r){
st[nd] = v; return;
}
int mid = (l + r) >> 1;
if(id <= mid)upd(nd << 1, l, mid, id, v);
else upd(nd << 1 | 1, mid + 1, r, id, v);
int cand1 = st[nd << 1], cand2 = st[nd << 1 | 1];
st[nd] = ((p[cand1].se > p[cand2].se) ? cand1: cand2);
}
void upd2(int nd, int l, int r, int id, int v){
if(l == r){
st2[nd] = v; return;
}
int mid = (l + r) >> 1;
if(id <= mid)upd2(nd << 1, l, mid, id, v);
else upd2(nd << 1 | 1, mid + 1, r, id, v);
int cand1 = st2[nd << 1], cand2 = st2[nd << 1 | 1];
st[nd] = ((p[cand1].fi < p[cand2].fi) ? cand1: cand2);
}
int get(int nd, int l, int r, int ql, int qr){
if(ql > r || qr < l)return(0);
if(ql <= l && qr >= r)return(st[nd]);
int mid = (l + r) >> 1;
int cand1 = get(nd << 1, l, mid, ql, qr), cand2 = get(nd << 1 | 1, mid + 1, r, ql, qr);
return((p[cand1].se > p[cand2].se) ? cand1 : cand2);
}
int get2(int nd, int l, int r, int ql, int qr){
if(ql > r || qr < l)return(0);
if(ql <= l && qr >= r)return(st2[nd]);
int mid = (l + r) >> 1;
int cand1 = get2(nd << 1, l, mid, ql, qr), cand2 = get2(nd << 1 | 1, mid + 1, r, ql, qr);
return((p[cand1].fi < p[cand2].fi) ? cand1 : cand2);
}
void dfs(int s){
upd(1, 1, 2 * n, p[s].fi, 0); upd2(1, 1, 2 * n, p[s].se, 0);
while(1){
int v = get(1, 1, 2 * n, p[s].fi, p[s].se);
if(p[v].se > p[s].se){
c[v] = c[s] ^ 1;
dfs(v);
}else{
break;
}
}
while(1){
int v = get2(1, 1, 2 * n, p[s].fi, p[s].se);
if(p[v].fi < p[s].fi){
c[v] = c[s] ^ 1; dfs(v);
}else{
break;
}
}
}
void solve(){
cin >> n;
p[0].fi = inf; p[0].se = 0;
for(int i = 1; i <= n; i++)cin >> p[i].fi >> p[i].se;
sort(p + 1, p + n + 1);
for(int i = 1; i <= n; i++){
upd(1, 1, 2 * n, p[i].fi, i); upd2(1, 1, 2 * n, p[i].se, i);
}
int cnt = 0;
for(int i = 1; i <= n; i++)c[i] = -1;
for(int i = 1; i <= n; i++){
if(c[i] == -1){
c[i] = 0; dfs(i); ++cnt;
}
}
set<int>s1, s2;
for(int i = 1; i <= n; i++){
if(c[i] == 0){
auto it = s1.lower_bound(p[i].fi);
if(it == s1.end() || (*it) > p[i].se){
s1.insert(p[i].se);
}else{
cout << 0; return;
}
}else{
auto it = s2.lower_bound(p[i].fi);
if(it == s2.end() || (*it) > p[i].se){
s2.insert(p[i].se);
}else{
cout << 0; return;
}
}
}
int ans = 1;
for(int i = 0; i < cnt; i++)ans = (ans * 2) % mod;
cout << ans;
}
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//freopen("DATA.inp", "r", stdin);
//freopen("DATA.out", "w", stdout);
int tt; tt = 1;
while(tt--){
solve();
}
return(0);
}
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