#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;
#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);
struct Sparse {
vector<vector<int>> table;
int size, LOGN;
Sparse(vector<int> &data, int n) {
size = n;
LOGN = log2(size) + 1;
table = vector<vector<int>>(size, vector<int>(LOGN, 0));
build(data);
}
// handle merge here
int merge(int left, int right) {
return max(left, right);
}
void build(vector<int> &data) {
for (int i = 0; i < size; i++) {
table[i][0] = data[i];
}
for (int j = 1; j < LOGN; j++) {
for (int i = 0; i + (1 << j) - 1 < size; i++) {
table[i][j] = merge(table[i][j-1], table[i+(1 << (j-1))][j-1]);
}
}
}
int query(int l, int r) {
int sz = r - l + 1;
int j = log2(sz);
return merge(table[l][j], table[r-(1<<(j))+1][j]);
}
};
// giving up and turning in a brute force
ll count_rectangles(vector<vector<int>> a) {
ll n = a.size(), m = a[0].size();
ll ans = 0, curr;
vector<Sparse> rows, cols;
REP(i, 0, n) {
rows.push_back(Sparse(a[i], m));
}
REP(i, 0, m) {
vector<int> col(n);
REP(j, 0, n) {
col[j] = a[j][i];
}
cols.push_back(Sparse(col, n));
}
auto in = [&](int x, int y) -> bool {
return (0 < x and x < n-1 and 0 < y and y < m-1);
};
map<pair<pair<int, int>, pair<int, int>>, bool> vis;
auto checkRect = [&](int x, int y, int xx, int yy) -> int {
if (!in(x,y) or !in(xx, yy)) return 0;
if (x > xx) swap(x, xx);
if (y > yy) swap(y, yy);
if (vis[{{x, y}, {xx, yy}}]) return 0;
vis[{{x, y}, {xx, yy}}] = true;
int cap;
REP(i, x, xx+1) {
cap = min(a[i][y-1], a[i][yy+1]);
if (rows[i].query(y, yy) >= cap) {
return 0;
}
}
REP(i, y, yy+1) {
cap = min(a[x-1][i], a[xx+1][i]);
if (cols[i].query(x, xx) >= cap) {
return 0;
}
}
return 1;
};
REP(i, 0, n*m) {
int x = i / m, y = i % m;
REP(j, i, n*m) {
int xx = j / m, yy = j % m;
ans += checkRect(x, y, xx, yy);
}
}
return ans;
}
