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>
#define MAX_N 1000000
#define xx first
#define yy second
using namespace std;
typedef long long lint;
const lint MOD = (lint)(1e9) + 7;
void modd(lint &a)
{
if(a < 0)
a += MOD;
if(a >= MOD)
a -= MOD;
}
vector <int> g[MAX_N + 1];
void baga(int a, int b)
{
g[a].push_back(b);
}
int n;
pair <int, int> v[MAX_N + 1];
lint rez;
int comps;
int comp[MAX_N + 1];
int cul[MAX_N + 1];
int dim[MAX_N + 1];
void readFile()
{
//ifstream fin("04-01.txt");
cin >> n;
comps = n;
for(int i = 1; i <= n; i ++)
{
cin >> v[i].xx >> v[i].yy;
comp[i] = i;
cul[i] = 1;
dim[i] = 1;
}
}
set<pair <int, int>> s;
int OP;
int viz[MAX_N + 1];
int CR;
set <pair <int, int>> first[MAX_N + 1][2];
void dfs(int a, int c)
{
cul[a] = c;
viz[a] = OP;
first[CR][c - 1].insert({v[a].yy, a});
for(auto u : g[a])
{
if(viz[u] != OP)
{
dfs(u, 3 - c);
}
}
}
int TOT;
void delFirst(int c, int x)
{
first[c][x].erase(*first[c][x].begin());
}
pair <int, int> getFirst(int c, int x)
{
return *first[c][x].begin();
}
void uneste(int a, int b, int x, int y)
{
OP ++;
if(dim[a] < dim[b])
{
swap(a, b);
swap(x, y);
}
CR = a;
dim[a] += dim[b];
comp[b] = a;
TOT += dim[b];
if(first[b][0].size() > 0)
s.erase(getFirst(b, 0));
if(first[b][1].size() > 0)
s.erase(getFirst(b, 1));
first[b][0].clear();
first[b][1].clear();
if(first[a][0].size() > 0)
s.erase(getFirst(a, 0));
if(first[a][1].size() > 0)
s.erase(getFirst(a, 1));
dfs(y, 3 - cul[x]);
if(first[a][0].size() > 0)
s.insert(getFirst(a, 0));
if(first[a][1].size() > 0)
s.insert(getFirst(a, 1));
}
int getComp(int a)
{
return (comp[a] = (comp[a] == a ? a : getComp(comp[a])));
}
void add(int a, int b)
{
int ca = getComp(a);
int cb = getComp(b);
if(ca == cb)
{
if(cul[a] == cul[b])
{
cout << "0\n";
exit(0);
}
return;
}
comps --;
uneste(ca, cb, a, b);
baga(a, b);
baga(b, a);
}
int tmp[MAX_N + 1];
void getEdges()
{
int CATE = 0;
for(int i = 1; i <= n; i ++)
{
while(s.size() > 0)
{
set <pair<int, int>> :: iterator it = s.begin();
if((*it).xx > v[i].xx)
break;
int c = getComp((*it).yy);
int x = cul[(*it).yy] - 1;
s.erase(it);
delFirst(c, x);
if(first[c][x].size() > 0)
s.insert(getFirst(c, x));
}
int k = 0;
if(s.size() > 0)
{
set <pair<int, int>> :: iterator it = s.begin();
while(it != s.end() && (*it).xx < v[i].yy)
{
CATE ++;
tmp[++ k] = (*it).yy;
it ++;
}
}
if(k == 0)
{
first[i][0].insert({v[i].yy, i});
s.insert({v[i].yy, i});
}
else
{
for(int x = 1; x <= k; x ++)
add(tmp[x], i);
}
}
}
void getRez()
{
rez = 1;
for(int i = 1; i <= comps; i ++)
{
rez += rez;
modd(rez);
}
}
void solve()
{
sort(v + 1, v + n + 1);
getEdges();
getRez();
}
void printFile()
{
cout << rez << "\n";
}
int main()
{
readFile();
solve();
printFile();
return 0;
}
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