#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];
pii rows[MX][MX],cols[MX][MX];
vector<pair<ll,int> > row_map,col_map;
vector<pair<ll,ll> > quer_row,quer_col;
bitset<MX*MX*6> b1,b2;
vi gg[MX][MX];
void check_rectangle(int x1,int y1,int x2,int y2,int q){
quer_row.pb({(y1-1)*MX*MX+(y2+1)*MX+x1,q*MX+x2});
quer_col.pb({(x1-1)*MX*MX+(x2+1)*MX+y1,q*MX+y2});
}
ll count_rectangles(vector<vi> a){
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(rows[j][gr[i][j]].F == i+1){
rows[j][gr[i][j]].F--;
}
else{
rows[j][gr[i][j]] = {i,i};
}
row_map.pb({val,rows[j][gr[i][j]].S});
}
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(rows[gl[i][j]][j].F == i+1){
rows[gl[i][j]][j].F--;
}
else{
rows[gl[i][j]][j] = {i,i};
}
row_map.pb({val,rows[gl[i][j]][j].S});
}
}
}
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(cols[i][gd[i][j]].F == j+1){
cols[i][gd[i][j]].F--;
}
else{
cols[i][gd[i][j]] = {j,j};
}
col_map.pb({val,cols[i][gd[i][j]].S});
}
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(cols[gu[i][j]][i].F == j+1){
cols[gu[i][j]][i].F--;
}
else{
cols[gu[i][j]][i] = {j,j};
}
col_map.pb({val,cols[gu[i][j]][i].S});
}
}
}
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){
gg[i][j].pb((gd[i-1][j]-1)*MX+gr[i][j-1]-1);
}
// topright
if(gl[i][j+1] != -1 and gd[i-1][j] != -1){
gg[i][(gl[i][j+1]+1)].pb((gd[i-1][j]-1)*MX+j);
}
// bottomleft
if(gr[i][j-1] != -1 and gu[i+1][j] != -1){
gg[(gu[i+1][j]+1)][j].pb((i)*MX+gr[i][j-1]-1);
}
// bottomright
if(gl[i][j+1] != -1 and gu[i+1][j] != -1){
gg[(gu[i+1][j]+1)][(gl[i][j+1]+1)].pb((i)*MX+j);
}
// clockwise
if(gr[i][j-1] != -1 and gd[i-1][gr[i][j-1]-1] != -1){
gg[i][j].pb((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){
gg[i][(gl[i][j+1]+1)].pb((gd[i-1][gl[i][j+1]+1]-1)*MX+j);
}
}
}
ll last = -1;
int q = 0;
FOR(i,1,n-1){
FOR(j,1,m-1){
sort_heap(all(gg[i][j]));
for(auto x:gg[i][j]){
ll val = i*MX*MX*MX+j*MX*MX+x;
if(val == last) continue;
last = val;
check_rectangle(i,j,x/MX,x%MX,q);
q++;
}
}
}
sort(all(quer_col));
sort(all(quer_row));
sort(all(col_map));
sort(all(row_map));
int cur = 0;
for(auto x:col_map){
while(cur < q and quer_col[cur].F < x.F) cur++;
while(cur < q and quer_col[cur].F == x.F){
if(quer_col[cur].S%MX <= x.S) b1[quer_col[cur].S/MX] = 1;
cur++;
}
}
cur = 0;
for(auto x:row_map){
while(cur < q and quer_row[cur].F < x.F) cur++;
while(cur < q and quer_row[cur].F == x.F){
if(quer_row[cur].S%MX <= x.S) b2[quer_row[cur].S/MX] = 1;
cur++;
}
}
REP(i,q){
if(b1[i] and b2[i]) ans++;
}
cout << ((double)clock() / CLOCKS_PER_SEC) << "\n";
return ans;
}
