#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class K,class V> using ht = gp_hash_table<
K,
null_type,
hash<K>,
equal_to<K>,
direct_mask_range_hashing<>,
linear_probe_fn<>,
hash_standard_resize_policy<
hash_exponential_size_policy<>,
hash_load_check_resize_trigger<>,
true
>
>;
typedef long long ll;
typedef pair<int, int> pi;
typedef vector<int> vi;
typedef vector<pi> vpi;
const int MOD = 1000000007;
#define ins insert
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define all(x) begin(x), end(x)
#define bk back()
const int mx = 2505;
int n, m;
ht<int, null_type> ints2[mx];
vector<pair<int, pi>> queries[mx];
vector<pair<int, pi>> updates[mx];
vpi res;
vi R;
vi cur;
vpi getInts(const vi &a){
// cout << "Q: ";
// for(auto u: a) cout << u << " ";
// cout << "\n";
res.clear();
R = vi(sz(a), -1);
cur.clear();
for(int i = sz(a)-1; i >= 0; i--){
while(sz(cur)){
if(a[cur.bk] <= a[i]){
cur.pop_back();
}
else break;
}
if(sz(cur)) R[i] = cur.bk;
cur.pb(i);
}
cur.clear();
for(int i = 0; i < sz(a); i++){
while(sz(cur)){
if(a[cur.bk] <= a[i]){
cur.pop_back();
}
else break;
}
int L = -1;
if(sz(cur)) L = cur.bk;
cur.pb(i);
if(R[i] != -1 && L != -1){
res.pb(mp(L+1, R[i]-1));
}
}
// vpi vals;
// for(int i = 0; i < sz(a); i++){
// vals.pb(mp(a[i], i));
// }
// sort(vals.rbegin(), vals.rend());
// set<int> poses;
// for(int i = 0; i < sz(vals); i++){
// auto it1 = poses.lb(vals[i].s);
// if(sz(poses) >= 2 && it1 != poses.end() && it1 != poses.begin()){
// int p1 = *(prev(it1));
// int p2 = *it1;
// if(vals[i].f < min(a[p1], a[p2])){
// res.pb(mp(p1+1, p2-1));
// }
// }
// poses.ins(vals[i].s);
// }
// for(int i = 0; i < sz(vals); i++){
// pair<pi, pi> b = *(prev(rang.lb(mp(mp(vals[i].s, MOD), mp(0, 0)))));
// //cout << i << "\n";
// assert(b.f.f <= vals[i].s && vals[i].s <= b.f.s);
// rang.erase(b);
// //if vals[i] is the max in range & if not on boundary
// if(vals[i].f < min(b.s.f, b.s.s) && 1 <= b.f.f && b.f.s <= sz(a)-2){
// res.pb(b.f);
// }
// //only divide if range added
// if(b.f.f <= vals[i].s-1){
// rang.ins(mp(mp(b.f.f, vals[i].s-1), mp(b.s.f, vals[i].f)));
// }
// if(vals[i].s+1 <= b.f.s){
// rang.ins(mp(mp(vals[i].s+1, b.f.s), mp(vals[i].f, b.s.s)));
// }
// }
// cout << "R: ";
// for(auto u: res) cout << "(" << u.f << " " << u.s << "), ";
// cout << "\n";
return res;
}
int val[mx];
vi curin;
void upd(int a, int v){
if(v == 1) curin.pb(a);
for(; a < mx; a+=a&-a) val[a]+=v;
}
int sum(int a){
int res = 0;
for(; a > 0; a-=a&-a) res+=val[a];
return res;
}
int query(int a, int b){
return sum(b)-sum(a-1);
}
void clearBIT(){
for(auto u: curin){
upd(u, -1);
}
curin.clear();
}
ll count_rectangles(vector<vi> a){
// clock_t c = clock();
// cout << fixed << setprecision(5);
// cout << double(clock()-c)/CLOCKS_PER_SEC << "\n";
n = sz(a);
m = sz(a[0]);
// double r1 = 0;
// double r2 = 0;
for(int i = 1; i+1 < n; i++){
vi nums;
for(int j = 0; j < m; j++){
nums.pb(a[i][j]);
}
// clock_t d = clock();
vpi a = getInts(nums);
// r1+=double(clock()-d)/CLOCKS_PER_SEC;
// d = clock();
for(auto u: a){
ints2[i].ins(mx*u.f+u.s);
}
// r2+=double(clock()-d)/CLOCKS_PER_SEC;
// d = clock();
}
// cout << "r1: " << r1 << "\n";
// cout << "r2: " << r2 << "\n";
// cout << double(clock()-c)/CLOCKS_PER_SEC << "\n";
ht<int, null_type> vals;
for(int i = 1; i+1 < n; i++){
vals = ints2[i];
for(auto x: vals){
int j = x/mx;
int u = x % mx;
for(int K = i; K+1 < n; K++){
if(ints2[K+1].find(mx*j+u) == ints2[K+1].end()){
for(int k = i; k <= K; k++){
queries[k].pb(mp(j, mp(K, u)));
//cout << "Q: " << k << " " << j << " " << K << " " << u << "\n";
ints2[k].erase(mx*j+u);
}
break;
}
}
}
}
// cout << double(clock()-c)/CLOCKS_PER_SEC << "\n";
for(int i = 0; i < mx; i++){
ints2[i].clear();
}
for(int j = 1; j+1 < m; j++){
//cout << "j: " << j << "\n";
vi nums;
for(int i = 0; i < n; i++){
nums.pb(a[i][j]);
}
vpi a = getInts(nums);
// cout << "a: " << "\n";
// for(auto u: a){
// cout << u.f << " " << u.s << "\n";
// }
for(auto u: a){
ints2[j].ins(mx*u.f+u.s);
//ints[u.f][j].ins(u.s);
}
}
for(int j = 1; j+1 < m; j++){
vals = ints2[j];
for(auto x: vals){
int i = x/mx;
int u = x % mx;
for(int K = j; K+1 < m; K++){
if(ints2[K+1].find(mx*i+u) == ints2[K+1].end()){
for(int k = j; k <= K; k++){
updates[i].pb(mp(k, mp(u, K)));
//cout << "U: " << i << " " << k << " " << u << " " << K << "\n";
//cout << i << " " << j << " " << k << "\n";
ints2[k].erase(mx*i+u);
}
break;
}
}
}
}
// cout << double(clock()-c)/CLOCKS_PER_SEC << "\n";
ll ans = 0;
for(int i = 1; i+1 < n; i++){
sort(all(queries[i]));
sort(all(updates[i]));
int updind = 0;
int lasty = -1;
for(auto u: queries[i]){
if(u.f != lasty) clearBIT();
while(updind < sz(updates[i])){
if(updates[i][updind].f < u.f){
updind++;
continue;
}
if(updates[i][updind].f > u.f){
break;
}
if(updates[i][updind].s.f <= u.s.f){
upd(updates[i][updind].s.s, 1);
updind++;
continue;
}
else break;
}
ans+=query(u.s.s, 2504);
lasty = u.f;
}
// for(int j = 1; j+1 < m; j++){
// sort(all(queries[i][j]));
// sort(all(updates[i][j]));
// int updind = 0;
// for(auto u: queries[i][j]){
// while(updind < sz(updates[i][j])){
// if(updates[i][j][updind].f <= u.f){
// upd(updates[i][j][updind].s, 1);
// updind++;
// }
// else break;
// }
// //if(query(u.s, 2504) > 0) cout << i << " " << j << "\n";
// ans+=query(u.s, 2504); //number of things >=
// }
// clearBIT();
// }
}
// cout << double(clock()-c)/CLOCKS_PER_SEC << "\n";
return ans;
}
