#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef pair <pi,pi> pipi;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 2501
#define INF (ll)1e9
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
int N,M;
set <pi> hpairs[maxn], vpairs[maxn];
bool intersect(pi x, pi y){
return max(x.f, y.f) <= min(x.s, y.s);
}
struct FW{
int n;
unordered_map <int,int> fw;
FW(){
n = max(N, M);
}
void upd(int p,int v){
p++;
for (int i = p; i <= n; i += i & (-i)) fw[i] += v;
}
int qry(int p){
p++;
int ans = 0;
for (int i = p; i > 0; i -= i & (-i)) ans += fw[i];
return ans;
}
};
struct Group{
set <pi> st, st2;
FW fw;
Group(){
fw = FW();
}
void insert(pi x){
st.insert(x); st2.insert(pi(x.s, x.f)); fw.upd(x.f, 1);
}
int qry(pi x){
auto it = st.upper_bound(pi(x.f, INF));
auto it2 = st2.lower_bound(pi(x.s, -1));
if (it == st.begin() || it2 == st2.end()) return 0;
return fw.qry(min((--it)->f, it2->s));
}
};
struct RangeContainer{
set <pii> st;
vector <Group> grps;
RangeContainer(){
}
void insert(pi x){
int grp = 0;
auto it = st.lower_bound(pii(x, -1));
if (it != st.end() && intersect(x, it->f)){
grp = it->s;
}else if (it != st.begin()){
it--;
if (intersect(x, it->f)) grp = it->s;
}else{
grp = grps.size();
grps.pb(Group());
}
st.insert(pii(x, grp));
grps[grp].insert(x);
}
int qry(pi x){
int grp = 0;
auto it = st.lower_bound(pii(x, -1));
if (it != st.end() && intersect(x, it->f)){
grp = it->s;
}else if (it != st.begin()){
it--;
if (intersect(x, it->f)) grp = it->s;
}else return 0;
return grps[grp].qry(x);
}
};
vector <pii> B[maxn];
vi C[maxn],D[maxn];
long long count_rectangles(std::vector<std::vector<int> > a) {
N = a.size(); M = a[0].size();
FOR(i,0,N-1){
stack <pi> st;
FOR(j,0,M-1){
while (!st.empty() && st.top().f < a[i][j]) st.pop();
if (!st.empty() && j - st.top().s + 1 >= 3) hpairs[i].insert(pi(st.top().s+1, j-1));
st.push(pi(a[i][j], j));
}
while (!st.empty()) st.pop();
DEC(j,M-1,0){
while (!st.empty() && st.top().f < a[i][j]) st.pop();
if (!st.empty() && st.top().s - j + 1 >= 3) hpairs[i].insert(pi(j+1, st.top().s-1));
st.push(pi(a[i][j], j));
}
}
FOR(j,0,M-1){
stack <pi> st;
FOR(i,0,N-1){
while (!st.empty() && st.top().f < a[i][j]) st.pop();
if (!st.empty() && i - st.top().s + 1 >= 3) vpairs[j].insert(pi(st.top().s+1, i-1));
st.push(pi(a[i][j], i));
}
while (!st.empty()) st.pop();
DEC(i,N-1,0){
while (!st.empty() && st.top().f < a[i][j]) st.pop();
if (!st.empty() && st.top().s - i + 1 >= 3) vpairs[j].insert(pi(i+1, st.top().s-1));
st.push(pi(a[i][j], i));
}
}
/*
cout << "HPAIRS: \n";
FOR(i,0,N-1){
cout << "ROW " << i << '\n';
aFOR(j, hpairs[i]) cout << j.f << ' ' << j.s << '\n';
}
cout << "VPAIRS: \n";
FOR(i,0,M-1){
cout << "COL " << i << '\n';
aFOR(j, vpairs[i]) cout << j.f << ' ' << j.s << '\n';
}
*/
vector <pipi> hrects, vrects;
FOR(i,0,N-1){
aFOR(j, hpairs[i]){
int a = i, b = j.f, c = N - 1, d = j.s;
FOR(k,i+1,N-1){
if (hpairs[k].count(j)){
hpairs[k].erase(j);
}else{
c = k - 1;
break;
}
}
hrects.pb(pipi(pi(a,b), pi(c,d)));
}
}
FOR(i,0,M-1){
aFOR(j, vpairs[i]){
int a = j.f, b = i, c = j.s, d = M - 1;
FOR(k,i+1,M-1){
if (vpairs[k].count(j)){
vpairs[k].erase(j);
}else{
d = k - 1;
break;
}
}
vrects.pb(pipi(pi(a,b), pi(c,d)));
}
}
/*
cout << "HRECTS: \n";
aFOR(i, hrects) cout << i.f.f << ' ' << i.f.s << ' ' << i.s.f << ' ' << i.s.s << '\n';
cout << "VRECTS: \n";
aFOR(i, vrects) cout << i.f.f << ' ' << i.f.s << ' ' << i.s.f << ' ' << i.s.s << '\n';
*/
int ans = 0;
aFOR(i, hrects){
if (i.f.s > 0) B[i.f.s-1].pb(pii(pi(i.f.f, i.s.f), -1));
B[i.s.s].pb(pii(pi(i.f.f, i.s.f), 1));
}
FOR(i,0,vrects.size() - 1){
C[vrects[i].s.s].pb(i);
}
FOR(i,0,vrects.size() - 1){
D[vrects[i].f.s].pb(i);
}
RangeContainer cont = RangeContainer(), cont2 = RangeContainer();
FOR(i,0,M-1){
aFOR(j,C[i]){
cont.insert(pi(vrects[j].f.f, vrects[j].s.f));
}
aFOR(j, D[i]){
cont2.insert(pi(vrects[j].f.f, vrects[j].s.f));
}
aFOR(j, B[i]){
if (j.s == 1) ans += cont.qry(j.f);
else ans -= cont2.qry(j.f);
}
}
return ans;
}
