#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
#define all(x) x.begin(),x.end()
#define HAS(a,b) (lower_bound(all(a),b)!=upper_bound(all(a),b))
vector<int>pos[2501][2501],pos2[2501][2501],stb[2501][20];
vector<int> operator & (const vector<int>&a,const vector<int>&b){
vector<int>c;
if(a.size()<b.size()){
for(auto i:a)
if(HAS(b,i))
c.push_back(i);
} else for(auto i:b)
if(HAS(a,i))
c.push_back(i);
return c;
}
vector<array<int,4>> ops;
int CC;
vector<int>res;
int calc(int r1,int r2,int beg){
for(int i=20;i--;)
if(HAS(stb[beg][i],r2))
beg+=1<<i;
return beg-1;
}
int cnt(int l,int r,int col){
int x=31-__builtin_clz(r-l+1);
vector<int>k=stb[l][x]&stb[r-(1<<x)+1][x];
return upper_bound(k.begin(),k.end(),res[CC++])-k.begin();
}
long long count_rectangles(std::vector<std::vector<int> > a) {
int n=a.size(),m=a[0].size();
int ans=0;
for(int i=1;i<n-1;i++){
stack<int>stk;
stk.push(m-1);
for(int j=m-1;j--;){
while(stk.size()&&a[i][j]>a[i][stk.top()])
pos[i][j+1].push_back(stk.top()-1),stk.pop();
if(stk.size()){
pos[i][j+1].push_back(stk.top()-1);
if(a[i][stk.top()]==a[i][j])
stk.pop();
}
stk.push(j);
if(pos[i][j+1].size())
pos[i][j+1].erase(pos[i][j+1].begin());
}
}
for(int j=1;j<m-1;j++){
stack<int>stk;
stk.push(n-1);
for(int i=n-1;i--;){
while(stk.size()&&a[i][j]>a[stk.top()][j])
pos2[i+1][j].push_back(stk.top()-1),stk.pop();
if(stk.size()){
pos2[i+1][j].push_back(stk.top()-1);
if(a[stk.top()][j]==a[i][j])
stk.pop();
}
stk.push(i);
if(pos2[i+1][j].size())
pos2[i+1][j].erase(pos2[i+1][j].begin());
}
}
for(int j=1;j<m-1;j++)
for(int i=1;i<n-1;i++)
for(auto x:pos2[i][j])
ops.push_back({i,x,j,CC++});
res.resize(CC);
CC=0;
sort(ops.begin(),ops.end());
int currr=0;
for(auto[r1,r2,col,id]:ops){
if(r1-currr) {
currr=r1;
for(int i=1;i<m-1;i++)
stb[i][0]=pos2[r1][i];
for(int j=1;j<20;j++) for(int i=1;i+(1<<j)<m;i++)
stb[i][j]=stb[i][j-1]&stb[i+(1<<j-1)][j-1];
}
res[id]=calc(r1,r2,col);
}
ops.clear();
for(int col=1;col<m-1;col++){
for(int i=1;i<n-1;i++)
stb[i][0]=pos[i][col];
for(int j=1;j<20;j++) for(int i=1;i+(1<<j)<n;i++)
stb[i][j]=stb[i][j-1]&stb[i+(1<<j-1)][j-1];
for(int row1=1;row1<n-1;row1++)
for(auto row2:pos2[row1][col])
ans+=cnt(row1,row2,col);
}
return ans;
}
