#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
#define eb emplace_back
#define pb push_back
#define sz(x) int(x.size())
#define all(x) (x).begin(), (x).end()
template<class T> struct BIT {
vector<T> bit;
int n;
void init(int n_) {
n = n_;
bit.resize(n);
}
T sum(int r) {
T ret = 0;
for (; r >= 0; r = (r & (r + 1)) - 1) ret += bit[r];
return ret;
}
T sum(int l, int r) {
return sum(r) - sum(l - 1);
}
void add(int idx, T delta) {
for (; idx < n; idx = idx | (idx + 1)) bit[idx] += delta;
}
};
struct seg {
short t;
short l, r;
short x, y;
seg(short t_, short l_, short r_, short x_, short y_) {
t = t_, l = l_, r = r_, x = x_, y = y_;
}
};
long long count_rectangles(std::vector<std::vector<int> > a) {
int n = (int) a.size();
int m = (int) a[0].size();
vector<vector<pair<short, short>>> rows(n);
vector<vector<pair<short, short>>> cols(m);
for (int i = 0; i < n; i++) {
vector<int> stk;
for (int j = 0; j < m; j++) {
while (sz(stk) && a[i][stk.back()] < a[i][j]) {
if (stk.back() + 2 <= j)
rows[i].emplace_back(stk.back(), j);
stk.pop_back();
}
if (sz(stk) && stk.back() + 2 <= j)
rows[i].emplace_back(stk.back(), j);
stk.push_back(j);
while (sz(stk) >= 2 && a[i][stk[sz(stk) - 1]] == a[i][stk[sz(stk) - 2]]) {
swap(stk[sz(stk) - 1], stk[sz(stk) - 2]);
stk.pop_back();
}
}
}
for (int j = 0; j < m; j++) {
vector<int> stk;
for (int i = 0; i < n; i++) {
while (sz(stk) && a[stk.back()][j] < a[i][j]) {
if (stk.back() + 2 <= i)
cols[j].emplace_back(stk.back(), i);
stk.pop_back();
}
if (sz(stk) && stk.back() + 2 <= i)
cols[j].emplace_back(stk.back(), i);
stk.push_back(i);
while (sz(stk) >= 2 && a[stk[sz(stk) - 1]][j] == a[stk[sz(stk) - 2]][j]) {
swap(stk[sz(stk) - 1], stk[sz(stk) - 2]);
stk.pop_back();
}
}
}
vector<vector<vector<seg>>> vert_corner(n + 5, vector<vector<seg>>(m + 5));
vector<vector<pair<short, short>>> vert(m, vector<pair<short, short>>(m, {(short) -1, (short) -1}));
vector<seg> tot;
for (int i = 0; i < n; i++) {
for (auto bar : rows[i]) {
if (vert[bar.first][bar.second] == make_pair((short) -1, (short) -1)) {
vert[bar.first][bar.second] = {i, i};
} else {
if (vert[bar.first][bar.second].second + 1 == i) {
vert[bar.first][bar.second].second++;
} else {
int lo = vert[bar.first][bar.second].first;
int hi = vert[bar.first][bar.second].second;
for (int z = lo - 1; z <= hi + 1; z++)
vert_corner[z + 1][bar.first + 1].emplace_back(1, bar.first + 1, bar.second + 1, lo, hi + 2);
vert[bar.first][bar.second] = {i, i};
}
}
}
if (i == n - 1) {
for (int x = 0; x < m; x++) {
for (int y = 0; y < m; y++) {
if (vert[x][y] == make_pair((short) -1, (short) -1)) continue;
int lo = vert[x][y].first;
int hi = vert[x][y].second;
for (int z = lo - 1; z <= hi + 1; z ++)
vert_corner[z + 1][x + 1].emplace_back(1, x + 1, y + 1, lo, hi + 2);
}
}
}
}
vector<vector<vector<seg>>> hori_corner(n + 5, vector<vector<seg>>(m + 5));
vector<vector<pair<short, short>>> hori(n, vector<pair<short, short>>(n, {(short) -1, (short) -1}));
for (int j = 0; j < m; j++) {
for (auto bar : cols[j]) {
if (hori[bar.first][bar.second] == make_pair((short) -1, (short) -1)) {
hori[bar.first][bar.second] = {j, j};
} else {
if (hori[bar.first][bar.second].second + 1 == j) {
hori[bar.first][bar.second].second++;
} else {
int lo = hori[bar.first][bar.second].first;
int hi = hori[bar.first][bar.second].second;
for (int z = lo - 1; z <= hi + 1; z++)
hori_corner[bar.first + 1][z + 1].emplace_back(0, bar.first + 1, bar.second + 1, lo, hi + 2);
hori[bar.first][bar.second] = {j, j};
}
}
}
if (j == m - 1) {
for (int x = 0; x < n; x++) {
for (int y = 0; y < n; y++) {
if (hori[x][y] == make_pair((short) -1, (short) -1)) continue;
int lo = hori[x][y].first;
int hi = hori[x][y].second;
for (int z = lo - 1; z <= hi + 1; z++)
hori_corner[x + 1][z + 1].emplace_back(0, x + 1, y + 1, lo, hi + 2);
}
}
}
}
long long ans = 0;
BIT<long long> B;
B.init(n + 5);
for (int i = 0; i < n + 5; i++) {
for (int j = 0; j < m + 5; j++) {
vector<array<int, 3>> segs;
for (auto s : hori_corner[i][j]) {
B.add(s.r, 1);
segs.push_back({s.y, 1, s.r});
}
for (auto s : vert_corner[i][j])
segs.push_back({s.r, 0, s.y});
sort(segs.begin(), segs.end());
for (auto s : segs) {
if (s[1] == 1) {
B.add(s[2], -1);
} else {
ans += B.sum(0, s[2]);
}
}
}
}
return ans;
}
