#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
void debug_out() {cerr<<endl;}
template <typename Head, typename... Tail>
void debug_out(Head _H, Tail... _T) {cerr<<" "<<to_string(_H);debug_out(_T...);}
#define debug(...) cerr<<"["<<#__VA_ARGS__<<"]:",debug_out(__VA_ARGS__)
const int MAXN = 2505;
const int inf=1000000500ll;
const long long oo =1000000000000000500ll;
const int MOD = (int)1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef pair<int,int> pi;
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
int n,m;
long long ans;
struct fenw {
int fw[MAXN];
void update(int x, int nval){
for(;x<MAXN;x+=x&-x)fw[x]+=nval;
}
int point(int x){
int res=0;
for(;x;x-=x&-x)res+=fw[x];
return res;
}
}fw;
vector<int> vxi[MAXN][MAXN];
vector<int> vyi[MAXN][MAXN];
vector<pi> H[MAXN][MAXN];
vector<pi> V[MAXN][MAXN];
struct hash_pair {
static uint64_t splitmix64(uint64_t x) {
x ^= 0x9e3779b97f4a7c15;
x ^= 0x9effb97adfde7c15;
return x ^ (x >> 31);
}
size_t operator()(pair<uint64_t,uint64_t> x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x.first + FIXED_RANDOM)^(splitmix64(x.second + FIXED_RANDOM) >> 1);
}
};
long long count_rectangles(std::vector<std::vector<int> > A) {
n=A.size();
m=A[0].size();
for(int i=1;i<=n;i++){
vector<pi> E;
for(int j=1;j<=m;j++){
E.push_back({A[i-1][j-1],j});
}
sort(E.begin(),E.end(),greater<pi>());
set<int> s;
vector<int> lazy;
int pre=-1;
unordered_set<pi,hash_pair> st;
for(auto x:E){
if(x.first!=pre){
for(auto y:lazy){
s.insert(y);
}
lazy.clear();
}
//debug(x.first,x.second);
auto it=s.lower_bound(x.second);
if(it == s.begin() || it==s.end());
else {
int L=*prev(it);
int R=*it;
st.insert({L+1,R-1});
}
lazy.push_back(x.second);
pre=x.first;
}
for(auto x:st){
int L=x.first;
int R=x.second;
vyi[L][R].push_back(i);
}
}
for(int i=1;i<=m;i++){
vector<pi> E;
for(int j=1;j<=n;j++){
E.push_back({A[j-1][i-1],j});
}
sort(E.begin(),E.end(),greater<pi>());
set<int> s;
vector<int> lazy;
int pre=-1;
unordered_set<pi,hash_pair> st;
for(auto x:E){
if(x.first!=pre){
for(auto y:lazy){
s.insert(y);
}
lazy.clear();
}
//debug(x.first,x.second);
auto it=s.lower_bound(x.second);
if(it == s.begin() || it==s.end());
else {
int L=*prev(it);
int R=*it;
//vxi[L][R].push_back(i);
st.insert({L+1,R-1});
}
lazy.push_back(x.second);
pre=x.first;
}
for(auto x:st){
int L=x.first;
int R=x.second;
vxi[L][R].push_back(i);
}
}
//debug(clock());
for(int i=1;i<=n;i++){
for(int j=i;j<=n;j++){
int st=0;
for(int k=0;k<(int)vxi[i][j].size();k++){
//debug(i,j,k,vxi[i][j][k]);
int col=vxi[i][j][k];
V[j][col].push_back({i,vxi[i][j][st]});
if(k==((int)vxi[i][j].size()-1) || vxi[i][j][k]+1!=vxi[i][j][k+1]){
st=k+1;
} else{
}
}
}
}
for(int i=1;i<=m;i++){
for(int j=i;j<=m;j++){
int st=0;
for(int k=0;k<(int)vyi[i][j].size();k++){
int row=vyi[i][j][k];
H[row][j].push_back({vyi[i][j][st],i});
if(k==((int)vyi[i][j].size()-1) || vyi[i][j][k]+1!=vyi[i][j][k+1]){
st=k+1;
} else{
}
}
}
}
for(int i=2;i<=n-1;i++){
for(int j=2;j<=m-1;j++){
// try this guy as the bottom right corner
sort(H[i][j].begin(),H[i][j].end(),[](pi x, pi y) { return x.second>y.second; });
sort(V[i][j].begin(),V[i][j].end(),[](pi x, pi y) { return x.second>y.second; });
int idx=0;
for(int k=0;k<(int)V[i][j].size();k++){
while(idx<(int)H[i][j].size() && H[i][j][idx].second >= V[i][j][k].second) {
fw.update(H[i][j][idx].first,1);
++idx;
}
ans+=fw.point(V[i][j][k].first);
}
for(int k=0;k<idx;k++){
fw.update(H[i][j][k].first,-1);
}
}
}
return ans;
}
