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 "rect.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
//#pragma GCC target("avx2")
//#pragma GCC optimization("unroll-loops")
//#pragma GCC optimize("O2")
//#pragma GCC optimize("O3")
#define FOR(i,a) for (int i=0;i<(a);++i)
#define FORD(i,a) for (int i=(a)-1;i>=0;i--)
#define FORT(i,a,b) for (int i=(a);i<=(b);++i)
#define FORTD(i,b,a) for (int i=(b);i>=(a);--i)
#define trav(i,v) for (auto i : v)
#define all(v) v.begin(),v.end()
#define ad push_back
#define fr first
#define sc second
#define mpr(a,b) make_pair(a,b)
#define pir pair<int,int>
#define make_unique(v) v.erase(unique(all(v)),v.end())
const int N=2506;
vector<int> ver[N][N],bn[N][N];
int en[N][N], sk[N][N];
long long count_rectangles(vector<vector<int> > a) {
int n=a.size();
int m=a[0].size();
FORT(j,1,m-2){
stack<pir> s;
s.push({INT_MAX,-1});
int qan=0;
FOR(i,n){
while(s.top().fr<=a[i][j]){
if (s.top().sc==i-1){
s.pop();
continue;
}
ver[i-1][j].ad(s.top().sc+1);
bn[i-1][s.top().sc+1].ad(j);
qan++;
s.pop();
}
s.push({a[i][j],i});
}
while(s.size()!=1)s.pop();
assert(s.top().fr==INT_MAX);
FORD(i,n){
while(s.top().fr<a[i][j]){
if (s.top().sc==i+1){
s.pop();
continue;
}
ver[s.top().sc-1][j].ad(i+1);
bn[s.top().sc-1][i+1].ad(j);
qan++;
s.pop();
}
s.push({a[i][j],i});
}
/*
if (a[0][j]>a[1][j] && a[2][j]>a[1][j]);
else assert(qan==0);*/
}
ll ans=0;
FORT(i,1,n-2){
stack<pir> s;
s.push({INT_MAX,-1});
FOR(j,m){
while(s.top().fr<=a[i][j]){
//cout<<i<<" hey "<<s.top().fr<<" "<<s.top().sc<<" "<<a[i][j]<<endl;
if (s.top().sc==j-1){
s.pop();
continue;
}
int l=s.top().sc+1,r=j-1;
//cout<<i<<" "<<l<<" "<<r<<" "<<sk[l][r]<<" "<<en[l][r]<<endl;
if (en[l][r]!=i-1){
sk[l][r]=i;
}
en[l][r]=i;
trav(to,ver[i][l]){
if (to<sk[l][r])continue;
if (upper_bound(all(bn[i][to]),r)-lower_bound(all(bn[i][to]),l)==r-l+1)ans++;
}
s.pop();
}
s.push({a[i][j],j});
}
while(s.size()!=1)s.pop();
FORD(j,m){
while(s.top().fr<a[i][j]){
//cout<<i<<" "<<s.top().fr<<" "<<s.top().sc<<" "<<a[i][j]<<endl;
if (s.top().sc==j+1){
s.pop();
continue;
}
int l=j+1,r=s.top().sc-1;
//cout<<"hey "<<i<<" "<<l<<" "<<r<<" "<<sk[l][r]<<" "<<en[l][r]<<endl;
if (en[l][r]!=i-1){
sk[l][r]=i;
}
en[l][r]=i;
trav(to,ver[i][r]){
if (to<sk[l][r])continue;
if (upper_bound(all(bn[i][to]),r)-lower_bound(all(bn[i][to]),l)==r-l+1)ans++;
}
s.pop();
}
s.push({a[i][j],j});
}
}
return ans;
}
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