This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// n <= 2000
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9+7;
const int mn = 2e6+7;
int n;
vector<pair<int,int>> t;
bool dwu = 1;
vector<pair<int,int>> d[mn*2]; //{L, ind przedzialu}
pair<int,int> pier[mn*2];
int start[mn*2];
int rep[mn], waga[mn];
int odw[mn];
vector<int> G[mn];
bool krawedz(pair<int,int> a, pair<int,int> b){
return (a.first < b.first && b.first < a.second) ^ (a.first < b.second && b.second < a.second);
}
int findd(int a){
if (rep[a] == a) return a;
return rep[a] = findd(rep[a]);
}
void unionn(int x, int y){
int a = findd(x);
int b = findd(y);
if (a == b) return;
if (waga[a] < waga[b]) swap(a,b);
rep[b] = a;
waga[a] += waga[b];
G[x].push_back(y);
G[y].push_back(x);
}
void mergenode(int poz, pair<int,int> x){
if (pier[poz] == make_pair(-1, -1)) return;
// pair<int,int> naj = d[poz].front();
if (pier[poz] < x) unionn(x.second, pier[poz].second);
while (start[poz] < (int)d[poz].size() && d[poz][start[poz]] < x){
// cout<<"xd "<<x.second<<" "<<(*d[poz].begin()).second<<"\n";
unionn(x.second, (d[poz][start[poz]]).second);
// d[poz].erase(d[poz].begin());
start[poz]++;
}
// d[poz].push_front(naj);
}
void update(int ind, pair<int,int> x){
ind += mn;
if (pier[ind] == make_pair(-1,-1)) pier[ind] = x;
else d[ind].push_back(x);
while (ind /= 2){
if (pier[ind] == make_pair(-1,-1)) pier[ind] = x;
else d[ind].push_back(x);
}
}
void mergee(int l, int r, pair<int,int> x){
for (l += mn, r += mn+1; l < r; l /= 2, r /= 2){
if (l&1) mergenode(l++, x);
if (r&1) mergenode(--r, x);
}
}
void dfs(int v, int kt){
// cout<<v<<" ";
// teraz.push_back(v);
odw[v] = kt;
for (auto i : G[v]){
if (!odw[i]){
if (kt == 1) dfs(i, 2);
else dfs(i, 1);
}
}
}
int main(){
ios_base::sync_with_stdio(0); cout.tie(0); cout.tie(0);
for (int i = 0; i < 2*mn; i++){
pier[i] = {-1, -1};
}
cin>>n;
for (int i = 0; i < n; i++){
int a,b;
cin>>a>>b;
t.push_back({a,b});
rep[i] = i;
waga[i] = 1;
}
sort(t.begin(), t.end());
for (int i = 0; i < n; i++){
int L = t[i].first;
int R = t[i].second;
mergee(L, R, {L, i});
update(R, {L, i});
}
int ile = 0;
for (int i = 0; i < n; i++){
if (!odw[i]){
dfs(i, 1);
ile++;
// cout<<"\n";
// cout<<"\n";
}
}
t.push_back({3*n, 3*n});
rep[n] = n;
vector<pair<int,int>> st1 = {{2*n+1, n}}, st2 = {{2*n+1, n}};
for (int i = 0; i < n; i++){
int L = t[i].first;
int R = t[i].second;
int poz = i;
// cout<<L<<" "<<R<<" "<<poz<<"\n";
while (st1.back().first < L) st1.pop_back();
while (st2.back().first < L) st2.pop_back();
int poz1 = st1.back().second;
// int R1 = st1.back().first;
int poz2 = st2.back().second;
// int R2 = st2.back().first;
if ((findd(poz) == findd(poz1) && odw[poz] == odw[poz1]) || (findd(poz) == findd(poz2) && odw[poz] != odw[poz2])){
if (krawedz(t[poz], t[poz1])){
dwu = 0;
break;
}
st1.push_back({R, poz});
// cout<<'a';
}
else if ((findd(poz) == findd(poz1) && odw[poz] != odw[poz1]) || (findd(poz) == findd(poz2) && odw[poz] == odw[poz2])){
if (krawedz(t[poz], t[poz2])){
dwu = 0;
break;
}
st2.push_back({R, poz});
// cout<<'b';
}
else if (findd(poz) != findd(poz1) && findd(poz) != findd(poz2)){
st1.push_back({R, poz});
// cout<<'c';
}
else{
assert(0);
}
}
int w = 1;
if (!dwu) w = 0;
for (int i = 0; i < ile; i++) w = (w*2)%mod;
cout<<w<<"\n";
}
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