#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()
#define SZ(v) (int)v.size()
const ll MX = 2505;
ll ans = 0;
int n,m;
int gl[MX][MX],gr[MX][MX],gu[MX][MX],gd[MX][MX];
unordered_map<ll,int> row_map,col_map;
void check_rectangle(int x1,int y1,int x2,int y2){
ll val1 = (y1-1)*MX*MX+(y2+1)*MX+x1;
if(row_map.find(val1) == row_map.end()) return;
if(row_map[val1] < x2) return;
ll val2 = (x1-1)*MX*MX+(x2+1)*MX+y1;
if(col_map.find(val2) == col_map.end()) return;
if(col_map[val2] < y2) return;
// cout << x1 << " " << y1 << " " << x2 << " " << y2 << "\n";
ans++;
}
ll count_rectangles(vector<vi> a) {
row_map.max_load_factor(0.25);
col_map.max_load_factor(0.25);
row_map.reserve(1048576);
col_map.reserve(1048576);
n = a.size();
m = a[0].size();
if(n <= 2 or m <= 2) return 0;
FORD(i,n-1,0){
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);
}
REP(j,m){
if(gr[i][j] != -1 and gr[i][j] != j+1){
ll val = j*MX*MX+gr[i][j]*MX+i;
if(row_map.find(val+1) != row_map.end()){
row_map[val] = row_map[val+1];
}
else row_map[val] = i;
}
if(gl[i][j] != -1 and gl[i][j] != j-1 and gr[i][gl[i][j]] != j){
ll val = gl[i][j]*MX*MX+j*MX+i;
if(row_map.find(val+1) != row_map.end()){
row_map[val] = row_map[val+1];
}
else row_map[val] = i;
}
}
}
FORD(j,m-1,0){
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);
}
REP(i,n){
if(gd[i][j] != -1 and gd[i][j] != i+1){
ll val = i*MX*MX+gd[i][j]*MX+j;
if(col_map.find(val+1) != col_map.end()){
col_map[val] = col_map[val+1];
}
else col_map[val] = j;
}
if(gu[i][j] != -1 and gu[i][j] != i-1 and gd[gu[i][j]][j] != i){
ll val = gu[i][j]*MX*MX+i*MX+j;
if(col_map.find(val+1) != col_map.end()){
col_map[val] = col_map[val+1];
}
else col_map[val] = j;
}
}
}
vector<ll> bruh;
FOR(i,1,n-1){
FOR(j,1,m-1){
// topleft
if(gr[i][j-1] != -1 and gd[i-1][j] != -1){
bruh.pb((i)*MX*MX*MX+(j)*MX*MX+(gd[i-1][j]-1)*MX+gr[i][j-1]-1);
}
// topright
if(gl[i][j+1] != -1 and gd[i-1][j] != -1){
bruh.pb((i)*MX*MX*MX+(gl[i][j+1]+1)*MX*MX+(gd[i-1][j]-1)*MX+j);
}
// bottomleft
if(gr[i][j-1] != -1 and gu[i+1][j] != -1){
bruh.pb((gu[i+1][j]+1)*MX*MX*MX+(j)*MX*MX+(i)*MX+gr[i][j-1]-1);
}
// bottomright
if(gl[i][j+1] != -1 and gu[i+1][j] != -1){
bruh.pb((gu[i+1][j]+1)*MX*MX*MX+(gl[i][j+1]+1)*MX*MX+(i)*MX+j);
}
// clockwise
if(gr[i][j-1] != -1 and gd[i-1][gr[i][j-1]-1] != -1){
bruh.pb((i)*MX*MX*MX+(j)*MX*MX+(gd[i-1][gr[i][j-1]-1]-1)*MX+gr[i][j-1]-1);
}
// anti-clockwise
if(gl[i][j+1] != -1 and gd[i-1][gl[i][j+1]+1] != -1){
bruh.pb((i)*MX*MX*MX+(gl[i][j+1]+1)*MX*MX+(gd[i-1][gl[i][j+1]+1]-1)*MX+j);
}
}
}
sort(all(bruh));
REP(i,SZ(bruh)){
if(i == 0 or bruh[i] != bruh[i-1]){
// if((n <= 700 and m <= 700) or n <= 3)
check_rectangle(bruh[i]/(MX*MX*MX),(bruh[i]/(MX*MX))%MX,(bruh[i]/MX)%MX,bruh[i]%MX);
}
}
return ans;
}
