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;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
const ll mod=1e9+7;
struct segtree{
ll n;
vector<ll>d;
segtree(ll n){
d.resize(4*n);
build(1,1,n);
}
void build(ll node,ll l,ll r){
if(l==r){
d[node]=0;
return;
}
ll mid=(l+r)/2;
build(node*2,l,mid);
build(node*2+1,mid+1,r);
d[node]=d[node*2]+d[node*2+1];
}
ll query(ll node,ll l,ll r,ll L,ll R){
if(l > R || r < L || L > R){
return 0ll;
}
if(L <= l && r <= R){
return d[node];
}
ll mid=(l+r)/2;
return query(node*2,l,mid,L,R)+query(node*2+1,mid+1,r,L,R);
}
void update(ll node,ll l,ll r,ll k,ll val){
if(l>k || r<k)return;
if(l==r){
d[node]=val;
return;
}
ll mid=(l+r)/2;
update(node*2,l,mid,k,val);
update(node*2+1,mid+1,r,k,val);
d[node]=d[node*2]+d[node*2+1];
}
};
struct dsu{
vector<ll>p,sz;
dsu(ll n){
p.resize(n+1);
iota(all(p),0);
sz.resize(n+1);
fill(all(sz),1);
}
ll find(ll x){
if(p[x]==x){
return x;
}
return p[x]=find(p[x]);
}
bool same(ll x,ll y){
x=find(x);
y=find(y);
if(x==y){
return true;
}
else{
return false;
}
}
void merge(ll x,ll y){
x=find(x);
y=find(y);
if(x!=y){
if(sz[x]<sz[y]){
swap(x,y);
}
sz[x]+=sz[y];
p[y]=x;
}
}
};
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
ll n;
cin>>n;
vector<ll>a(n+1),b(n+1);
vector<ll>event(2*n+1);
vector<array<ll,3>>d;
for(ll i=1;i<=n;i++){
cin>>a[i]>>b[i];
d.pb({a[i],b[i],i});
event[a[i]]=i;
event[b[i]]=i;
}
dsu ds(n);
sort(all(d));
for(ll i=1;i<n;i++){
if(d[i][0]<d[i-1][1]&&d[i-1][1]<d[i][1]){
ds.merge(d[i-1][2],d[i][2]);
}
}
vector<vector<ll>>v(n+1);
for(ll i=1;i<=n;i++){
ll j=ds.find(i);
v[j].pb(i);
}
vector<pair<ll,ll>>seg(n+1);
for(ll i=1;i<=n;i++){
if(v[i].empty()) continue;
ll l=2*n,r=1;
for(ll j:v[i]){
l=min(l,a[j]);
r=max(r,b[j]);
}
seg[i].ff=l;
seg[i].ss=r;
}
vector<ll>l(n+1),r(n+1);
for(ll i=1;i<=n;i++){
ll j=ds.find(i);
l[i]=seg[j].ff;
r[i]=seg[j].ss;
}
vector<ll>col(n+1,-1);
segtree sg0(2*n),sg1(2*n);
ll ans=1;
for(ll i=1;i<=2*n;i++){
ll j=event[i];
if(a[j]==i){
vector<ll>cnt(2,0);
cnt[0]=sg0.query(1,1,2*n,l[j],r[j]);
cnt[1]=sg1.query(1,1,2*n,l[j],r[j]);
if(cnt[0]+cnt[1]==0){
ans=ans*2%mod;
col[j]=0;
}
else if(cnt[0]>0&&cnt[1]>0){
cout<<0;
return 0;
}
else if(cnt[0]==0){
col[j]=0;
}
else{
col[j]=1;
}
if(col[j]==0){
sg0.update(1,1,2*n,b[j],1);
sg0.update(1,1,2*n,a[j],1);
}
else{
sg1.update(1,1,2*n,b[j],1);
sg1.update(1,1,2*n,a[j],1);
}
}
else{
if(col[j]==0){
sg0.update(1,1,2*n,b[j],0);
sg0.update(1,1,2*n,a[j],0);
}
else{
sg1.update(1,1,2*n,b[j],0);
sg1.update(1,1,2*n,a[j],0);
}
}
}
cout<<ans;
}
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