#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
bool inside(vector<int> &v, int e) {
return find(v.begin(), v.end(), e) != v.end();
}
long long count_rectangles(std::vector<std::vector<int> > a) {
int n = a.size();
int m = a[0].size();
vector<vector<int>> row(n*m), col(n*m);
//row edges
for (int i = 0; i < n; i++) {
vector<pair<int,int>> b(m);
for (int j = 0; j < m; j++) b[j] = make_pair(a[i][j], j);
sort(b.begin(), b.end());
set<int> s;
for (int k = b.size()-1; k >= 0; k--) {
int j = b[k].second;
auto it = s.lower_bound(j);
if (it != s.end()) {
if (abs(*it - j) > 1) row[i*m + j + 1].push_back(*it - 1);
//if (i == 1 && j == 1) cout << "!! " << *it << "\n";
//cout << i << " " << j << " " << i << " " << *it << "\n";
}
s.insert(j);
}
for (int j = 0; j < m; j++) b[j] = make_pair(a[i][j], -j);
sort(b.begin(), b.end());
s.clear();
for (int k = b.size()-1; k >= 0; k--) {
int j = -b[k].second;
auto it = s.lower_bound(j);
if (it != s.begin()) {
--it;
if (abs(*it - j) > 1) row[i*m + j - 1].push_back(*it + 1);
// if (i == 1 && j == 1) cout << "!! " << *it << "\n";
// cout << i << " " << j << " " << i << " " << *it << "\n";
}
s.insert(j);
}
}
//col edges
for (int i = 0; i < m; i++) {
vector<pair<int,int>> b(n);
for (int j = 0; j < n; j++) b[j] = make_pair(a[j][i], j);
sort(b.begin(), b.end());
set<int> s;
for (int k = b.size()-1; k >= 0; k--) {
int j = b[k].second;
auto it = s.lower_bound(j);
if (it != s.end()) {
if (abs(*it - j) > 1) col[(j+1)*m + i].push_back(*it-1);
//cout << j << " " << i << " " << *it << " " << i << "\n";
}
s.insert(j);
}
for (int j = 0; j < n; j++) b[j] = make_pair(a[j][i], -j);
sort(b.begin(), b.end());
s.clear();
for (int k = b.size()-1; k >= 0; k--) {
int j = -b[k].second;
auto it = s.upper_bound(j);
if (it != s.begin()) {
--it;
if (abs(*it - j) > 1) col[(j-1)*m + i].push_back(*it+1);
//cout << j << " " << i << " " << *it << " " << i << "\n";
}
s.insert(j);
}
}
int cnt = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
for (auto B: row[i*m + j]) {
for (auto C: col[i*m + j]) {
//if (abs(C-i) <= 1 || abs(B-j) <= 1) continue;
if (a[C][B] < a[i][j] || (a[C][B] == a[i][j] && (make_pair(C,B) < make_pair(i,j)))) continue;
// if (j > B) swap(j,B);
// if (i > C) swap(i,C);
bool works = true;
for (int y = min(j,B); y <= max(j,B); y++) {
if (!inside(col[i*m + y], C) && !inside(col[C*m + y] , i)) {
works = false;
break;
}
}
for (int x = min(i,C); x <= max(i,C); x++) {
if (!inside(row[x*m + j] , B) && !inside(row[x*m + B] , j)) {
works = false;
break;
}
}
// bool BD = inside(col[i*m + B], C) || inside(col[C*m + B] , i);
// bool CD = inside(row[C*m + j] , B) || inside(row[C*m + B] , j);
if (works) {
//for (int )
//cout << i << " " << j << " " << C << " " << B << "\n";
cnt++;
}
}
}
}
}
return cnt;
}
