#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2.5e3 + 20;
int a[maxn][maxn];
vector<pair<int, int>> cand_left[maxn][maxn];
vector<pair<int, int>> cand_up[maxn][maxn];
int n, m;
void add_left(int row, int lt, int rt, bool ins) {
if (lt > rt) {
return;
}
if (!ins) {
cand_left[row][lt].emplace_back(rt - lt + 1, -1);
}
else {
int len = rt - lt + 1;
vector<pair<int, int>> &cur = cand_left[row][lt];
int pt = (int)cur.size() - 1;
while (pt >= 0 && cur[pt].first > len) {
pt--;
}
cur.insert(cur.begin() + pt + 1, make_pair(len, -1));
}
}
void find_left(int row) {
vector<int> q;
for (int i = 1; i <= m; i++) {
while (!q.empty() && a[row][i] > a[row][q.back()]) {
q.pop_back();
}
if (!q.empty() && a[row][i] < a[row][q.back()]) {
add_left(row, q.back() + 1, i - 1, false);
}
q.push_back(i);
}
q.clear();
for (int i = m; i >= 1; i--) {
while (!q.empty() && a[row][i] > a[row][q.back()]) {
q.pop_back();
}
if (!q.empty()) {
add_left(row, i + 1, q.back() - 1, true);
}
q.push_back(i);
}
}
void add_up(int col, int lt, int rt, bool ins) {
if (lt > rt) {
return;
}
if (!ins) {
cand_up[lt][col].emplace_back(rt - lt + 1, -1);
}
else {
int len = rt - lt + 1;
vector<pair<int, int>> &cur = cand_up[lt][col];
int pt = (int)cur.size() - 1;
while (pt >= 0 && cur[pt].first > len) {
pt--;
}
cur.insert(cur.begin() + pt + 1, make_pair(len, -1));
}
}
void find_up(int col) {
vector<int> q;
for (int i = 1; i <= n; i++) {
while (!q.empty() && a[i][col] > a[q.back()][col]) {
q.pop_back();
}
if (!q.empty() && a[i][col] < a[q.back()][col]) {
add_up(col, q.back() + 1, i - 1, false);
}
q.push_back(i);
}
q.clear();
for (int i = n; i >= 1; i--) {
while (!q.empty() && a[i][col] > a[q.back()][col]) {
q.pop_back();
}
if (!q.empty()) {
add_up(col, i + 1, q.back() - 1, true);
}
q.push_back(i);
}
}
long long count_rectangles(vector<vector<int>> _a) {
n = _a.size();
m = _a[0].size();
if (n < 3 || m < 3) {
return 0;
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
a[i][j] = _a[i - 1][j - 1];
}
}
for (int i = 1; i <= n; i++) {
find_left(i);
}
for (int i = 1; i <= m; i++) {
find_up(i);
}
for (int i = n; i >= 1; i--) {
for (int j = 1; j <= m; j++) {
int pt = 0;
vector<pair<int, int>> &cur = cand_left[i][j];
vector<pair<int, int>> &nxt = cand_left[i + 1][j];
for (int k = 0; k < (int)cur.size(); k++) {
while (pt < (int)nxt.size() && nxt[pt].first < cur[k].first) {
pt++;
}
if (pt < (int)nxt.size() && nxt[pt].first == cur[k].first) {
cur[k].second = nxt[pt].second + 1;
}
else {
cur[k].second = 1;
}
}
}
}
for (int i = 1; i <= n; i++) {
for (int j = m; j >= 1; j--) {
int pt = 0;
vector<pair<int, int>> &cur = cand_up[i][j];
vector<pair<int, int>> &nxt = cand_up[i][j + 1];
for (int k = 0; k < (int)cur.size(); k++) {
while (pt < (int)nxt.size() && nxt[pt].first < cur[k].first) {
pt++;
}
if (pt < (int)nxt.size() && nxt[pt].first == cur[k].first) {
cur[k].second = nxt[pt].second + 1;
}
else {
cur[k].second = 1;
}
}
}
}
int res = 0;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
for (auto p1: cand_left[i][j]) {
for (auto p2: cand_up[i][j]) {
if (p1.second >= p2.first && p2.second >= p1.first) {
res++;
}
}
}
}
}
return res;
}
