#include "rect.h"
#include <stack>
#include <algorithm>
using namespace std;
enum {
TOP = 0,
BOTTOM = 1,
LEFT = 2,
RIGHT = 3,
};
struct Case {
int next[4] = {-1, -1, -1, -1};
bool hasrect() {
return next[0] != -1 && next[1] != -1 && next[2] != -1 && next[3] != -1;
}
};
struct Rect1d {
int a, b, w = 1;
bool operator<(const Rect1d& other) const {
return a == other.a ? b < other.b : a < other.a;
}
bool operator==(const Rect1d& other) const {
return a == other.a && b == other.b;
}
};
struct Rectangle {
int r1, c1, r2, c2;
bool operator<(const Rectangle& other) const {
if (r1 != other.r1)
return r1 < other.r1;
if (c1 != other.c1)
return c1 < other.c1;
if (r2 != other.r2)
return r2 < other.r2;
if (c2 != other.c2)
return c2 < other.c2;
return false;
}
bool operator==(const Rectangle& other) const {
return r1 == other.r1 && c1 == other.c1 && r2 == other.r2 && c2 == other.c2;
}
};
long long count_rectangles(vector<vector<int>> A) {
const int R = A.size(), C = A[0].size();
vector<vector<Case>> cases(R, vector<Case>(C));
stack<int> dec_seq;
for (int r = 0; r < R; r++) {
for (int c = 0; c < C; c++) {
while (!dec_seq.empty() && A[r][dec_seq.top()] < A[r][c]) {
dec_seq.pop();
}
if (!dec_seq.empty() && A[r][dec_seq.top()] > A[r][c]) cases[r][c].next[LEFT] = dec_seq.top();
dec_seq.push(c);
}
while (!dec_seq.empty()) dec_seq.pop();
for (int c = C-1; c >= 0; c--) {
while (!dec_seq.empty() && A[r][dec_seq.top()] <= A[r][c]) {
dec_seq.pop();
}
if (!dec_seq.empty()) cases[r][c].next[RIGHT] = dec_seq.top();
dec_seq.push(c);
}
while (!dec_seq.empty()) dec_seq.pop();
}
for (int c = 0; c < C; c++) {
for (int r = 0; r < R; r++) {
while (!dec_seq.empty() && A[dec_seq.top()][c] < A[r][c]) {
dec_seq.pop();
}
if (!dec_seq.empty() && A[dec_seq.top()][c] > A[r][c]) cases[r][c].next[TOP] = dec_seq.top();
dec_seq.push(r);
}
while (!dec_seq.empty()) dec_seq.pop();
for (int r = R-1; r >= 0; r--) {
while (!dec_seq.empty() && A[dec_seq.top()][c] <= A[r][c]) {
dec_seq.pop();
}
if (!dec_seq.empty()) cases[r][c].next[BOTTOM] = dec_seq.top();
dec_seq.push(r);
}
while (!dec_seq.empty()) dec_seq.pop();
}
vector<Rectangle> rects;
for (int r = 0; r < R; r++) {
for (int c = 0; c < C; c++) {
if (cases[r][c].hasrect()) {
rects.push_back({cases[r][c].next[TOP]+1, cases[r][c].next[LEFT]+1, cases[r][c].next[BOTTOM]-1, cases[r][c].next[RIGHT]-1});
}
}
}
sort(rects.begin(), rects.end());
rects.resize(unique(rects.begin(), rects.end()) - rects.begin());
vector<vector<Rect1d>> rect1ds[2];
rect1ds[0].resize(R);
rect1ds[1].resize(C);
for (int r = 0; r < R; r++) {
for (int c = 0; c < C; c++) {
if (cases[r][c].next[LEFT] != -1 && cases[r][c].next[RIGHT] != -1) {
Rect1d newr = {cases[r][c].next[LEFT]+1, cases[r][c].next[RIGHT]-1};
if (r > 0) {
auto it = lower_bound(rect1ds[0][r-1].begin(), rect1ds[0][r-1].end(), newr);
if (it != rect1ds[0][r-1].end() && *it == newr) {
newr.w = 1+it->w;
}
}
rect1ds[0][r].push_back(newr);
}
}
sort(rect1ds[0][r].begin(), rect1ds[0][r].end());
}
for (int c = 0; c < C; c++) {
for (int r = 0; r < R; r++) {
if (cases[r][c].next[TOP] != -1 && cases[r][c].next[BOTTOM] != -1) {
Rect1d newr = {cases[r][c].next[TOP]+1, cases[r][c].next[BOTTOM]-1};
if (c > 0) {
auto it = lower_bound(rect1ds[1][c-1].begin(), rect1ds[1][c-1].end(), newr);
if (it != rect1ds[1][c-1].end() && *it == newr) {
newr.w = 1+it->w;
}
}
rect1ds[1][c].push_back(newr);
}
}
sort(rect1ds[1][c].begin(), rect1ds[1][c].end());
}
int ans = 0;
for (auto& r : rects) {
auto& v = rect1ds[0][r.r2];
auto it = lower_bound(v.begin(), v.end(), Rect1d{r.c1, r.c2});
if (it != v.end() && *it == Rect1d{r.c1, r.c2} && it->w >= r.r2-r.r1+1) {
auto& v = rect1ds[1][r.c2];
auto it = lower_bound(v.begin(), v.end(), Rect1d{r.r1, r.r2});
if (it != v.end() && *it == Rect1d{r.r1, r.r2} && it->w >= r.c2-r.c1+1) {
ans++;
}
}
}
return ans;
}
