#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
typedef pair<int,int> pt;
typedef pair<int,int> range;
class HiddenSquares {
public:
int count(vector <int> x1, vector <int> y1, vector <int> x2, vector <int> y2)
{
vector< pair<int, range> > xseg, yseg;
for(int i=0; i<x1.size(); ++i)
{
xseg.push_back( make_pair(x1[i], range(y1[i], y2[i])) );
xseg.push_back( make_pair(x2[i], range(y1[i], y2[i])) );
yseg.push_back( make_pair(y1[i], range(x1[i], x2[i])) );
yseg.push_back( make_pair(y2[i], range(x1[i], x2[i])) );
}
// copy and
map<int, vector<range> > xray;
for(int i=0; i<xseg.size(); ++i)
{
set<int> p;
p.insert(xseg[i].second.first);
p.insert(xseg[i].second.second);
for(int j=0; j<yseg.size(); ++j)
if( xseg[i].second.first<=yseg[j].first && yseg[j].first<=xseg[i].second.second
&& yseg[j].second.first<=xseg[i].first && xseg[i].first<=yseg[j].second.second )
p.insert( yseg[j].first );
int py = xseg[i].second.first;
for(set<int>::iterator y=p.begin(); ++y!=p.end(); py=*y)
xray[xseg[i].first].push_back( range(py,*y) );
}
// paset!
map<int, vector<range> > yray;
for(int i=0; i<yseg.size(); ++i)
{
set<int> p;
p.insert(yseg[i].second.first);
p.insert(yseg[i].second.second);
for(int j=0; j<xseg.size(); ++j)
if( yseg[i].second.first<=xseg[j].first && xseg[j].first<=yseg[i].second.second
&& xseg[j].second.first<=yseg[i].first && yseg[i].first<=xseg[j].second.second )
p.insert( xseg[j].first );
int px = yseg[i].second.first;
for(set<int>::iterator x=p.begin(); ++x!=p.end(); px=*x)
yray[yseg[i].first].push_back( range(px,*x) );
}
// copy and
map< pt, set<pt> > xconn;
for(map<int, vector< pt > >::iterator it=xray.begin(); it!=xray.end(); ++it)
{
int x = it->first;
vector<range>& r = it->second;
vector< pair<int,bool> > es;
for(int i=0; i!=r.size(); ++i)
es.push_back( make_pair(r[i].first,false) ),
es.push_back( make_pair(r[i].second,true) );
sort(es.begin(), es.end());
vector<int> cur;
int nest = 0;
for(int i=0; i!=es.size(); ++i)
{
cur.push_back( es[i].first );
es[i].second ? --nest : ++nest;
if( nest == 0 )
{
for(int j=0; j<cur.size(); ++j)
for(int k=j+1; k<cur.size(); ++k)
if( cur[j] < cur[k] )
xconn[pt(x,cur[j])].insert( pt(x,cur[k]) );
cur.clear();
}
}
}
// paste!
map< pt, set<pt> > yconn;
for(map<int, vector< pt > >::iterator it=yray.begin(); it!=yray.end(); ++it)
{
int y = it->first;
vector<range>& r = it->second;
vector< pair<int,bool> > es;
for(int i=0; i!=r.size(); ++i)
es.push_back( make_pair(r[i].first,false) ),
es.push_back( make_pair(r[i].second,true) );
sort(es.begin(), es.end());
vector<int> cur;
int nest = 0;
for(int i=0; i!=es.size(); ++i)
{
cur.push_back( es[i].first );
es[i].second ? --nest : ++nest;
if( nest == 0 )
{
for(int j=0; j<cur.size(); ++j)
for(int k=j+1; k<cur.size(); ++k)
if( cur[j] < cur[k] )
yconn[pt(cur[j],y)].insert( pt(cur[k],y) );
cur.clear();
}
}
}
// count squares
int cnt = 0;
for(map< pt, set<pt> >::iterator it=xconn.begin(); it!=xconn.end(); ++it)
{
pt p = it->first;
set<pt>& c = it->second;
for(set<pt>::iterator jt=c.begin(); jt!=c.end(); ++jt)
{
pt q = *jt;
int w = q.second-p.second;
pt p1(p.first+w,p.second);
pt q1(q.first+w,q.second);
if( yconn[p].count(p1) && yconn[q].count(q1) && xconn[p1].count(q1) )
++cnt;
}
}
return cnt;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time;string timer() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const int &Expected, const int &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
int x1_[] = {0,1,0};
vector <int> x1(x1_, x1_+sizeof(x1_)/sizeof(*x1_));
int y1_[] = {0,0,1};
vector <int> y1(y1_, y1_+sizeof(y1_)/sizeof(*y1_));
int x2_[] = {3,2,3};
vector <int> x2(x2_, x2_+sizeof(x2_)/sizeof(*x2_));
int y2_[] = {3,3,2};
vector <int> y2(y2_, y2_+sizeof(y2_)/sizeof(*y2_));
int RetVal = 14;
return verify_case(RetVal, HiddenSquares().count(x1, y1, x2, y2)); }
int Test_(Case_<1>) {
int x1_[] = {0,2};
vector <int> x1(x1_, x1_+sizeof(x1_)/sizeof(*x1_));
int y1_[] = {0,0};
vector <int> y1(y1_, y1_+sizeof(y1_)/sizeof(*y1_));
int x2_[] = {2,4};
vector <int> x2(x2_, x2_+sizeof(x2_)/sizeof(*x2_));
int y2_[] = {4,4};
vector <int> y2(y2_, y2_+sizeof(y2_)/sizeof(*y2_));
int RetVal = 1;
return verify_case(RetVal, HiddenSquares().count(x1, y1, x2, y2)); }
int Test_(Case_<2>) {
int x1_[] = {0,0,3};
vector <int> x1(x1_, x1_+sizeof(x1_)/sizeof(*x1_));
int y1_[] = {0,3,0};
vector <int> y1(y1_, y1_+sizeof(y1_)/sizeof(*y1_));
int x2_[] = {1,4,4};
vector <int> x2(x2_, x2_+sizeof(x2_)/sizeof(*x2_));
int y2_[] = {3,4,3};
vector <int> y2(y2_, y2_+sizeof(y2_)/sizeof(*y2_));
int RetVal = 0;
return verify_case(RetVal, HiddenSquares().count(x1, y1, x2, y2)); }
int Test_(Case_<3>) {
int x1_[] = {453453463,453453500,453453495,453453512,453453478,453453489,
453453466,453453500,453453498,453453510,453453472,453453512,
453453519,453453514,453453521,453453518,453453523,453453517,
453453466,453453525,453453496,453453495,453453463,453453461,
453453460,453453522,453453471,453453468,453453479,453453517,
453453485,453453518,453453499,453453464,453453494};
vector <int> x1(x1_, x1_+sizeof(x1_)/sizeof(*x1_));
int y1_[] = {364646438,364646402,364646449,364646438,364646415,364646401,
364646446,364646416,364646456,364646414,364646463,364646407,
364646436,364646450,364646421,364646411,364646414,364646419,
364646445,364646427,364646405,364646442,364646418,364646464,
364646457,364646463,364646432,364646426,364646444,364646431,
364646450,364646418,364646434,364646458,364646402};
vector <int> y1(y1_, y1_+sizeof(y1_)/sizeof(*y1_));
int x2_[] = {453453488,453453510,453453525,453453523,453453493,453453500,
453453470,453453511,453453499,453453521,453453518,453453524,
453453523,453453523,453453524,453453523,453453525,453453519,
453453473,453453526,453453511,453453517,453453470,453453464,
453453511,453453524,453453516,453453516,453453492,453453524,
453453513,453453522,453453520,453453505,453453512};
vector <int> x2(x2_, x2_+sizeof(x2_)/sizeof(*x2_));
int y2_[] = {364646460,364646454,364646462,364646466,364646464,364646455,
364646457,364646461,364646457,364646450,364646466,364646453,
364646441,364646451,364646460,364646461,364646446,364646464,
364646447,364646460,364646454,364646450,364646444,364646466,
364646458,364646466,364646455,364646442,364646462,364646435,
364646464,364646444,364646455,364646459,364646430};
vector <int> y2(y2_, y2_+sizeof(y2_)/sizeof(*y2_));
int RetVal = 124;
return verify_case(RetVal, HiddenSquares().count(x1, y1, x2, y2)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE