#include "rect.h"
#include <iostream>
#include <cassert>
using namespace std;
using ll = long long;
const int INF = 1e9 + 177013;
struct cell {
short l;
short r;
short u;
short d;
cell operator+(cell a) {
cell ans;
ans.l = min(l, a.l);
ans.u = min(u, a.u);
ans.r = max(r, a.r);
ans.d = max(d, a.d);
return ans;
}
};
vector<vector<cell>> cl;
ll count_rectangles(vector<vector<int>> a) {
int n = a.size();
int m = a[0].size();
cl.assign(n, vector<cell>(m));
for (int i = 0; i < n; ++i) {
vector<pair<int, int>> stck = {{INF, -1}};
for (int j = 0; j < m; ++j) {
while (stck.back().first <= a[i][j])
stck.pop_back();
cl[i][j].l = stck.back().second;
stck.push_back({a[i][j], j});
}
}
for (int i = 0; i < n; ++i) {
vector<pair<int, int>> stck = {{INF, m}};
for (int j = m - 1; j >= 0; --j) {
while (stck.back().first <= a[i][j])
stck.pop_back();
cl[i][j].r = stck.back().second;
stck.push_back({a[i][j], j});
}
}
for (int j = 0; j < m; ++j) {
vector<pair<int, int>> stck = {{INF, -1}};
for (int i = 0; i < n; ++i) {
while (stck.back().first <= a[i][j])
stck.pop_back();
cl[i][j].u = stck.back().second;
stck.push_back({a[i][j], i});
}
}
for (int j = 0; j < m; ++j) {
vector<pair<int, int>> stck = {{INF, n}};
for (int i = n - 1; i >= 0; --i) {
while (stck.back().first <= a[i][j])
stck.pop_back();
cl[i][j].d = stck.back().second;
stck.push_back({a[i][j], i});
}
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
assert(cl[i][j].u == -1 || a[cl[i][j].u][j] > a[i][j]);
assert(cl[i][j].l == -1 || a[i][cl[i][j].l] > a[i][j]);
assert(cl[i][j].d == n || a[cl[i][j].d][j] > a[i][j]);
assert(cl[i][j].r == m || a[i][cl[i][j].r] > a[i][j]);
}
}
vector<vector<cell>> colmn(n, vector<cell>(m));
ll ans = 0;
for (int i = n - 2; i > 0; --i) {
for (int j = m - 2; j > 0; --j) {
colmn[i][j] = cl[i][j];
for (int u = i; u < n - 1; ++u) {
cell board = cl[i][j];
for (int v = j; v < m - 1; ++v) {
if (u > i)
colmn[u][v] = colmn[u][v] + cl[i][v];
board = board + colmn[u][v];
if (board.u < i - 1 || board.l < j - 1 || board.d > u + 1)
break;
if (board.r <= v + 1) {
++ans;
}
}
}
}
}
return ans;
}
