/**
____ ____ ____ ____ ____
||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];
vector <pair <short int, short int>> DProw[NM_MAX][NM_MAX];
vector <pair <short int, short int>> DPcol[NM_MAX][NM_MAX];
int bins (vector <pair <short int, short int>> &v, int key) {
if (v.empty() == true) {
return 0;
}
int l = 0, r = (int) v.size() - 1;
while (l < r) {
int mid = (l + r) / 2;
if (v[mid].first < key) {
l = mid + 1;
} else {
r = mid;
}
}
if (v[l].first == key) {
return v[l].second;
} else {
return 0;
}
}
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].push_back({i2, 1});
}
if (j1 != -1 && j2 != -1) {
DPcol[i][j1].push_back({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 = 0; j < m; j++) {
sort(DProw[i][j].begin(), DProw[i][j].end());
if (j > 0) {
for (pair <short int, short int> &t : DProw[i][j]) {
t.second = bins(DProw[i][j - 1], t.first) + 1;
}
}
}
}
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
sort(DPcol[i][j].begin(), DPcol[i][j].end());
if (i > 0) {
for (pair <short int, short int> &t : DPcol[i][j]) {
t.second = bins(DPcol[i - 1][j], t.first) + 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 (bins(DProw[i1][j2 - 1], i2) >= j2 - j1 - 1
&& bins(DPcol[i2 - 1][j1], j2) >= i2 - i1 - 1) {
answer++;
}
}
return answer;
}
