/**
____ ____ ____ ____ ____
||a |||t |||o |||d |||o ||
||__|||__|||__|||__|||__||
|/__\|/__\|/__\|/__\|/__\|
**/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int NM_MAX = 2500;
short int L[NM_MAX][NM_MAX];
short int R[NM_MAX][NM_MAX];
short int U[NM_MAX][NM_MAX];
short int D[NM_MAX][NM_MAX];
map <short int, short int> DProw[NM_MAX][NM_MAX];
map <short int, short int> DPcol[NM_MAX][NM_MAX];
vector <pair <pair <short int, short int>, pair <short int, short int>>> cand;
ll count_rectangles (vector <vector <int>> h) {
int n = (int) h.size();
int m = (int) h[0].size();
for (int i = 0; i < n; i++) {
vector <int> st;
for (int j = 0; j < m; j++) {
while (st.empty() == false && h[i][st.back()] <= h[i][j]) {
st.pop_back();
}
L[i][j] = (st.empty() == false ? st.back() : -1);
st.push_back(j);
}
st.clear();
for (int j = m - 1; j >= 0; j--) {
while (st.empty() == false && h[i][st.back()] <= h[i][j]) {
st.pop_back();
}
R[i][j] = (st.empty() == false ? st.back() : -1);
st.push_back(j);
}
}
for (int j = 0; j < m; j++) {
vector <int> st;
for (int i = 0; i < n; i++) {
while (st.empty() == false && h[st.back()][j] <= h[i][j]) {
st.pop_back();
}
U[i][j] = (st.empty() == false ? st.back() : -1);
st.push_back(i);
}
st.clear();
for (int i = n - 1; i >= 0; i--) {
while (st.empty() == false && h[st.back()][j] <= h[i][j]) {
st.pop_back();
}
D[i][j] = (st.empty() == false ? st.back() : -1);
st.push_back(i);
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
int i1 = U[i][j], i2 = D[i][j];
int j1 = L[i][j], j2 = R[i][j];
if (i1 != -1 && i2 != -1) {
DProw[i1][j][i2] = 1;
}
if (j1 != -1 && j2 != -1) {
DPcol[i][j1][j2] = 1;
}
if (i1 != -1 && j1 != -1 && i2 != -1 && j2 != -1) {
cand.push_back({{i1, j1}, {i2, j2}});
}
}
}
sort(cand.begin(), cand.end());
cand.resize(unique(cand.begin(), cand.end()) - cand.begin());
for (int i = 0; i < n; i++) {
for (int j = 1; j < m; j++) {
for (pair <int, int> _ : DProw[i][j]) {
int i2 = _.first;
if (DProw[i][j - 1].count(i2) > 0) {
DProw[i][j][i2] = DProw[i][j - 1][i2] + 1;
}
}
}
}
for (int j = 0; j < m; j++) {
for (int i = 1; i < n; i++) {
for (pair <int, int> _ : DPcol[i][j]) {
int j2 = _.first;
if (DPcol[i - 1][j].count(j2) > 0) {
DPcol[i][j][j2] = DPcol[i - 1][j][j2] + 1;
}
}
}
}
int answer = 0;
for (pair <pair <int, int>, pair <int, int>> c : cand) {
int i1, j1; tie(i1, j1) = c.first;
int i2, j2; tie(i2, j2) = c.second;
if (DProw[i1][j2 - 1][i2] >= j2 - j1 - 1
&& DPcol[i2 - 1][j1][j2] >= i2 - i1 - 1) {
answer++;
}
}
return answer;
}
