#include "rect.h"
#include <bits/stdc++.h>
#define IO_OP ios::sync_with_stdio(0), cin.tie(0)
#define F first
#define S second
#define V vector
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(), (v).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef V<int> vi;
#ifdef CHEISSMART
void dbg() { cerr << "]" << endl; }
template<class H, class ...T> void dbg(H h, T... t) {
cerr << to_string(h);
if(sizeof...(t)) cerr << ", ";
dbg(t...);
}
#define debug(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ <<"]: [", dbg(__VA_ARGS__);
#else
#define debug(...)
#endif
const int INF = 1e9 + 7, N = 3000;
int bit[N];
void add(int pos, int val) {
for(; pos < N; pos += pos & -pos)
bit[pos] += val;
}
int qry(int pos) {
int res = 0;
for(; pos; pos -= pos & -pos)
res += bit[pos];
return res;
}
ll count_rectangles(V<vi> a) {
int n = SZ(a), m = SZ(a[0]);
V<V<V<pair<short, short>>>> ver(n, V<V<pair<short, short>>>(m));
V<V<V<pair<short, short>>>> hor(n, V<V<pair<short, short>>>(m));
auto add_hor = [&] (int i, int j, int jj) {
if(jj == j + 1) return;
hor[i][j].EB(jj, i);
};
auto add_ver = [&] (int i, int j, int ii) {
if(ii == i + 1) return;
ver[i][j].EB(ii, j);
};
for(int i = 0; i < n; i++) {
vi stk;
for(int j = m - 1; j >= 0; j--) {
while(SZ(stk) && a[i][stk.back()] < a[i][j]) {
add_hor(i, j, stk.back());
stk.pop_back();
}
if(SZ(stk))
add_hor(i, j, stk.back());
if(SZ(stk) && a[i][stk.back()] == a[i][j])
stk.pop_back();
stk.PB(j);
}
}
for(int j = 0; j < m; j++) {
vi stk;
for(int i = n - 1; i >= 0; i--) {
while(SZ(stk) && a[stk.back()][j] < a[i][j]) {
add_ver(i, j, stk.back());
stk.pop_back();
}
if(SZ(stk))
add_ver(i, j, stk.back());
if(SZ(stk) && a[stk.back()][j] == a[i][j])
stk.pop_back();
stk.PB(i);
}
}
for(int i = n - 2; i >= 0; i--) {
for(int j = 0; j < m; j++) {
map<short, short> mp;
for(auto[he, be]:hor[i + 1][j])
mp[he] = be;
V<pair<short, short>> todo;
for(auto[jj, ii]:hor[i][j]) {
if(mp.count(jj))
todo.EB(jj, mp[jj]);
else
todo.EB(jj, ii);
}
hor[i][j] = todo;
}
}
for(int j = m - 2; j >= 0; j--) {
for(int i = 0; i < n; i++) {
map<short, short> mp;
for(auto[he, be]:ver[i][j + 1])
mp[he] = be;
V<pair<short, short>> todo;
for(auto[ii, jj]:ver[i][j])
if(mp.count(ii))
todo.EB(ii, mp[ii]);
else
todo.EB(ii, jj);
ver[i][j] = todo;
}
}
ll ans = 0;
for(int i = 1; i < n - 1; i++) {
for(int j = 1; j < m - 1; j++) {
V<pi> aux;
for(auto[d, right]:ver[i - 1][j])
aux.EB(right, d);
V<pi> tt;
for(auto[r, down]:hor[i][j - 1])
tt.EB(r, down);
if(aux.empty() || tt.empty()) continue;
sort(ALL(aux));
sort(ALL(tt), greater<pi>());
vi undo;
for(auto[r, down]:tt) {
while(SZ(aux) && aux.back().F >= r - 1) {
int d = aux.back().S;
add(d, 1);
undo.PB(d);
aux.pop_back();
}
ans += qry(down + 1);
}
for(int d:undo)
add(d, -1);
}
}
return ans;
}
