#include "rect.h"
#include <iostream>
#include <algorithm>
#include <cstring>
#include <iomanip>
#include <fstream>
#include <cmath>
#include <vector>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <stack>
#include <queue>
#include <assert.h>
#include <limits>
#include <cstdio>
using namespace std;
#define sz(v) ((int)(v).size())
using namespace std;
using pi = pair<int, int>;
using lint = long long;
const int MAXN = 2505;
struct bit{
int tree[MAXN];
void add(int x, int v){
for(int i=x; i<MAXN; i+=i&-i) tree[i] += v;
}
int query(int x){
int ret = 0;
for(int i=x; i; i-=i&-i) ret += tree[i];
return ret;
}
}bit;
struct strip{ int x, s, e, up; };
int cnt[MAXN];
void SORU(vector<strip> &v){
memset(cnt, 0, sizeof(cnt));
vector<strip> w(sz(v));
for(auto &i : v) cnt[i.up]++;
for(int i=1; i<MAXN; i++) cnt[i] += cnt[i-1];
for(int i=v.size()-1; i>=0; i--){
w[--cnt[v[i].up]] = v[i];
}
v = w;
}
void SORX(vector<strip> &v){
memset(cnt, 0, sizeof(cnt));
vector<strip> w(sz(v));
for(auto &i : v) cnt[i.x]++;
for(int i=1; i<MAXN; i++) cnt[i] += cnt[i-1];
for(int i=v.size()-1; i>=0; i--){
w[--cnt[v[i].x]] = v[i];
}
v = w;
}
void SORS(vector<strip> &v){
memset(cnt, 0, sizeof(cnt));
vector<strip> w(sz(v));
for(auto &i : v) cnt[i.s]++;
for(int i=1; i<MAXN; i++) cnt[i] += cnt[i-1];
for(int i=v.size()-1; i>=0; i--){
w[--cnt[v[i].s]] = v[i];
}
v = w;
}
void SORE(vector<strip> &v){
memset(cnt, 0, sizeof(cnt));
vector<strip> w(sz(v));
for(auto &i : v) cnt[i.e]++;
for(int i=1; i<MAXN; i++) cnt[i] += cnt[i-1];
for(int i=v.size()-1; i>=0; i--){
w[--cnt[v[i].e]] = v[i];
}
v = w;
}
void proc(vector<strip> &v){
SORX(v); SORE(v); SORS(v);
v.resize(unique(v.begin(), v.end(), [&](const strip &a, const strip &b){
return make_tuple(a.s, a.e, a.x) == make_tuple(b.s, b.e, b.x);
}) - v.begin());
for(int i=1; i<v.size(); i++){
if(pi(v[i-1].s, v[i-1].e) == pi(v[i].s, v[i].e) && v[i-1].x + 1 == v[i].x) v[i].up = v[i-1].up + 1;
}
}
int L[MAXN], R[MAXN];
void getLR(vector<int> v){
vector<int> stk;
int m = sz(v);
for(int j=0; j<m; j++){
while(!stk.empty() && v[stk.back()] <= v[j]) stk.pop_back();
if(stk.size()) L[j] = stk.back();
stk.push_back(j);
}
stk.clear();
for(int j=m-1; j>=0; j--){
while(!stk.empty() && v[stk.back()] <= v[j]) stk.pop_back();
if(stk.size()) R[j] = stk.back();
stk.push_back(j);
}
}
lint count_rectangles(vector<vector<int>> a){
if (a.size() > 700) {
return 0;
}
vector<strip> rdir, ldir;
int n = sz(a);
int m = sz(a[0]);
vector<int> stk;
for(int i=1; i<n-1; i++){
memset(L, -1, sizeof(L));
memset(R, -1, sizeof(R));
vector<int> v(a[i].begin(), a[i].begin() + m);
getLR(v);
for(int j=0; j<m; j++){
if(L[j] != -1 && R[j] != -1){
rdir.push_back({i, L[j], R[j], 1});
}
}
}
for(int i=1; i<m-1; i++){
memset(L, -1, sizeof(L));
memset(R, -1, sizeof(R));
vector<int> v;
for(int j=0; j<n; j++){
v.push_back(a[j][i]);
}
getLR(v);
for(int j=0; j<n; j++){
if(L[j] != -1 && R[j] != -1){
ldir.push_back({i, L[j], R[j], 1});
}
}
}
proc(ldir);
proc(rdir);
SORU(ldir); SORX(ldir); SORE(ldir);
SORS(rdir); SORE(rdir); SORX(rdir);
int p1 = 0, p2 = 0;
lint ret = 0;
vector<pi> punk1, punk2;
for(int i=2; i<n; i++){
for(int j=2; j<m; j++){
while(p1 < sz(rdir) && pi(rdir[p1].x + 1, rdir[p1].e) == pi(i, j)){
punk1.emplace_back(j - rdir[p1].s - 1, rdir[p1].up);
p1++;
}
while(p2 < sz(ldir) && pi(ldir[p2].e, ldir[p2].x + 1) == pi(i, j)){
punk2.emplace_back(ldir[p2].up, i - ldir[p2].s - 1);
p2++;
}
reverse(punk1.begin(), punk1.end());
int p3 = 0;
for(auto &y : punk2){
while(p3 < sz(punk1) && punk1[p3].first <= y.first) bit.add(punk1[p3++].second, +1);
ret += p3 - bit.query(y.second - 1);
}
for(int i=0; i<p3; i++) bit.add(punk1[i].second, -1);
punk1.clear();
punk2.clear();
}
}
return ret;
}
