#include "rect.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template<class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U>
void ckmin(T &a, U b)
{
if (a > b) a = b;
}
template<class T, class U>
void ckmax(T &a, U b)
{
if (a < b) a = b;
}
#define y1 qkx
#define y2 wsm
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define SZ(x) ((int) (x).size())
#define ALL(x) (x).begin(), (x).end()
#define INF 1000000007
#define MAXN 2513
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
int N, M;
vector<pair<short, short> > ev[MAXN][MAXN], eh[MAXN][MAXN];
int fen[MAXN];
ll ans;
void update(int idx, int v)
{
for (int e = idx + 1; e <= max(N, M); e += e & (-e)) fen[e] += v;
}
int query(int idx)
{
int res = 0;
for (int e = idx + 1; e; e -= e & (-e)) res += fen[e];
return res;
}
bool cmp(pair<short, short> a, pair<short, short> b)
{
return (a.se < b.se);
}
ll count_rectangles(vector<vi> a)
{
N = SZ(a); M = SZ(a[0]);
FOR(i, 0, N)
{
vpi cand; cand.PB({INF, M + 1});
FORD(j, M, 0)
{
while(cand.back().fi < a[i][j]) cand.pop_back();
short idx = cand.back().se;
if (idx < M && idx != j + 1)
{
eh[i][j + 1].PB({idx - 1, i});
}
cand.PB({a[i][j], j});
}
cand.clear(); cand.PB({INF, -2});
FOR(j, 0, M)
{
while(cand.back().fi < a[i][j]) cand.pop_back();
short idx = cand.back().se;
if (idx >= 0 & idx != j - 1)
{
eh[i][idx + 1].PB({j - 1, i});
}
cand.PB({a[i][j], j});
}
}
FOR(i, 0, M)
{
vpi cand; cand.PB({INF, N + 1});
FORD(j, N, 0)
{
while(cand.back().fi < a[j][i]) cand.pop_back();
short idx = cand.back().se;
if (idx < N && idx != j + 1)
{
ev[j + 1][i].PB({idx - 1, i});
}
cand.PB({a[j][i], j});
}
cand.clear(); cand.PB({INF, -2});
FOR(j, 0, N)
{
while(cand.back().fi < a[j][i]) cand.pop_back();
short idx = cand.back().se;
if (idx >= 0 && idx != j - 1)
{
ev[idx + 1][i].PB({j - 1, i});
}
cand.PB({a[j][i], j});
}
}
FOR(i, 0, N)
{
FOR(j, 0, M)
{
sort(ALL(ev[i][j])); ev[i][j].erase(unique(ALL(ev[i][j])), ev[i][j].end());
sort(ALL(eh[i][j])); eh[i][j].erase(unique(ALL(eh[i][j])), eh[i][j].end());
}
}
FOR(i, 0, N)
{
FORD(j, M, 0)
{
int idx = 0;
FOR(k, 0, SZ(ev[i][j]))
{
int x = ev[i][j][k].fi;
while(idx < SZ(ev[i][j + 1]) && ev[i][j + 1][idx].fi < x) idx++;
if (idx >= SZ(ev[i][j + 1]) || ev[i][j + 1][idx].fi != x) continue;
ev[i][j][k].se = ev[i][j + 1][idx].se;
}
}
}
FOR(i, 0, M)
{
FORD(j, N, 0)
{
int idx = 0;
FOR(k, 0, SZ(eh[j][i]))
{
int y = eh[j][i][k].fi;
while(idx < SZ(eh[j + 1][i]) && eh[j + 1][i][idx].fi < y) idx++;
if (idx >= SZ(eh[j + 1][i]) || eh[j + 1][i][idx].fi != y) continue;
eh[j][i][k].se = eh[j + 1][i][idx].se;
}
}
}
//log factor here too.
FOR(i, 1, N - 1)
{
FOR(j, 1, M - 1)
{
sort(ALL(eh[i][j]), cmp);
for (auto p : eh[i][j])
{
update(p.fi, 1);
}
int iter = 0;
FOR(k, 0, SZ(ev[i][j]))
{
while(iter < SZ(eh[i][j]) && eh[i][j][iter].se < ev[i][j][k].fi)
{
update(eh[i][j][iter].fi, -1);
iter++;
}
ans += query(ev[i][j][k].se);
}
while(iter < SZ(eh[i][j]))
{
update(eh[i][j][iter].fi, -1);
iter++;
}
}
}
return ans;
}
