#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define pb push_back
#define REP(i,n) for(int i = 0; i < n; i++)
#define FOR(i,a,b) for(int i = a; i < b; i++)
#define FORD(i,a,b) for(int i = a; i >= b; i --)
#define pii pair<int,int>
#define F first
#define S second
#define all(v) v.begin(),v.end()
const int MX = 2505;
int n,m;
vector<vi> A;
int gl[MX][MX],gr[MX][MX],gu[MX][MX],gd[MX][MX];
vi rows[MX][MX];
vi cols[MX][MX];
ll count_rectangles(vector<vi> a) {
n = a.size();
m = a[0].size();
A = a;
if(n <= 2 or m <= 2) return 0;
ll ans = 0;
REP(i,n){
stack<int> st;
REP(j,m){
gl[i][j] = gr[i][j] = gu[i][j] = gd[i][j] = -1;
}
REP(j,m){
while(st.size() and a[i][st.top()] <= a[i][j]){
gr[i][st.top()] = j;
st.pop();
}
st.push(j);
}
while(!st.empty()) st.pop();
FORD(j,m-1,0){
while(st.size() and a[i][st.top()] <= a[i][j]){
gl[i][st.top()] = j;
st.pop();
}
st.push(j);
}
set<pii> s;
REP(j,m){
if(gr[i][j] != -1 and gr[i][j] != j+1) s.insert({j,gr[i][j]});
if(gl[i][j] != -1 and gl[i][j] != j-1) s.insert({gl[i][j],j});
}
for(auto x:s){
// cout << "row: " << i << " -> " << x.F << " " << x.S << "\n";
rows[x.F][x.S].pb(i);
}
}
REP(j,m){
stack<int> st;
REP(i,n){
while(st.size() and a[st.top()][j] <= a[i][j]){
gd[st.top()][j] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()) st.pop();
FORD(i,n-1,0){
while(st.size() and a[st.top()][j] <= a[i][j]){
gu[st.top()][j] = i;
st.pop();
}
st.push(i);
}
set<pii> s;
REP(i,n){
if(gd[i][j] != -1 and gd[i][j] != i+1) s.insert({i,gd[i][j]});
if(gu[i][j] != -1 and gu[i][j] != i-1) s.insert({gu[i][j],i});
}
for(auto x:s){
cols[x.F][x.S].pb(j);
// cout << "col: " << j << " -> " << x.F << " " << x.S << "\n";
}
}
FOR(c1,1,n-1){
FOR(c2,c1,n-1){
FOR(r1,1,m-1){
FOR(r2,r1,m-1){
bool flag = true;
FOR(i,c1,c2+1){
flag &= binary_search(all(rows[r1-1][r2+1]),i);
}
FOR(i,r1,r2+1){
flag &= binary_search(all(cols[c1-1][c2+1]),i);
}
if(flag){
ans++;
// cout << c1 << " " << c2 << " " << r1 << " " << r2 << "\n";
}
}
}
}
}
return ans;
}
