#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int lg[2501];
int SL[2500][2500][12];
int SR[2500][2500][12];
int SU[2500][2500][12];
int SD[2500][2500][12];
int SLQ(int y, int l, int r) {
if (l == r) {
return -1;
}
int k = lg[r - l];
return max(SL[y][l][k], SL[y][r - (1 << k)][k]);
}
int SRQ(int y, int l, int r) {
if (l == r) {
return 2500;
}
int k = lg[r - l];
return min(SR[y][l][k], SR[y][r - (1 << k)][k]);
}
int SUQ(int x, int l, int r) {
if (l == r) {
return -1;
}
int k = lg[r - l];
return max(SU[x][l][k], SU[x][r - (1 << k)][k]);
};
int SDQ(int x, int l, int r) {
if (l == r) {
return 2500;
}
int k = lg[r - l];
return min(SD[x][l][k], SD[x][r - (1 << k)][k]);
};
ll count_rectangles(vector<vector<int>> a) {
for (int i = 2; i <= 2500; i++) {
lg[i] = lg[i / 2] + 1;
}
int n = a.size();
int m = a[0].size();
bool subtask6 = 1;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (a[i][j] > 1) {
subtask6 = 0;
}
}
}
vector<int> stk;
int L[n][m], R[n][m], U[n][m], D[n][m];
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
while (!stk.empty() && a[i][stk.back()] < a[i][j]) {
stk.pop_back();
}
L[i][j] = stk.empty() ? -1 : stk.back();
stk.push_back(j);
}
stk.clear();
for (int j = m - 1; j >= 0; j--) {
while (!stk.empty() && a[i][stk.back()] < a[i][j]) {
stk.pop_back();
}
R[i][j] = stk.empty() ? m : stk.back();
stk.push_back(j);
}
stk.clear();
}
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
while (!stk.empty() && a[stk.back()][j] < a[i][j]) {
stk.pop_back();
}
U[i][j] = stk.empty() ? -1 : stk.back();
stk.push_back(i);
}
stk.clear();
for (int i = n - 1; i >= 0; i--) {
while (!stk.empty() && a[stk.back()][j] < a[i][j]) {
stk.pop_back();
}
D[i][j] = stk.empty() ? n : stk.back();
stk.push_back(i);
}
stk.clear();
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
SU[i][j][0] = U[i][j];
SD[i][j][0] = D[i][j];
}
for (int j = 0; j < lg[m]; j++) {
for (int k = 0; k + (2 << j) <= m; k++) {
SU[i][k][j + 1] = max(SU[i][k][j], SU[i][k + (1 << j)][j]);
SD[i][k][j + 1] = min(SD[i][k][j], SD[i][k + (1 << j)][j]);
}
}
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
SL[i][j][0] = L[j][i];
SR[i][j][0] = R[j][i];
}
for (int j = 0; j < lg[n]; j++) {
for (int k = 0; k + (2 << j) <= n; k++) {
SL[i][k][j + 1] = max(SL[i][k][j], SL[i][k + (1 << j)][j]);
SR[i][k][j + 1] = min(SR[i][k][j], SR[i][k + (1 << j)][j]);
}
}
}
auto check = [&](int x1, int y1, int x2, int y2) -> int {
if (x1 > x2 || y1 > y2) {
return 0;
}
if (SDQ(x1 - 1, y1, y2 + 1) <= x2) {
return 0;
}
if (SUQ(x2 + 1, y1, y2 + 1) >= x1) {
return 0;
}
if (SRQ(y1 - 1, x1, x2 + 1) <= y2) {
return 0;
}
if (SLQ(y2 + 1, x1, x2 + 1) >= y1) {
return 0;
}
return 1;
};
int ans = 0;
if (subtask6) {
for (int i = 1; i < n - 1; i++) {
for (int j = 1; j < m - 1; j++) {
if (a[i][j] == 0 && a[i - 1][j] == 1 && a[i][j - 1] == 1) {
if (D[i - 1][j] != n && R[i][j - 1] != m) {
ans += check(i, j, D[i - 1][j] - 1, R[i][j - 1] - 1);
}
}
}
}
return ans;
}
vector<int> T[n][m];
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (U[i][j] != -1) {
T[U[i][j]][j].push_back(i);
}
}
}
for (int i = 1; i < n - 1; i++) {
for (int j = 1; j < m - 1; j++) {
int y = R[i][j - 1] - 1;
if (y != m - 1) {
int x = D[i - 1][j] - 1;
if (x != n - 1) {
ans += check(i, j, x, y);
}
for (int k : T[i - 1][j]) {
if (a[i - 1][j] != a[k][j]) {
ans += check(i, j, k - 1, y);
}
}
}
y = L[i][j + 1] + 1;
if (y != 0 && a[i][j + 1] != a[i][y - 1]) {
int x = D[i - 1][j] - 1;
if (x != n - 1) {
ans += check(i, y, x, j);
}
for (int k : T[i - 1][j]) {
if (a[i - 1][j] != a[k][j]) {
ans += check(i, y, k - 1, j);
}
}
}
}
}
return ans;
}
