#include "rect.h"
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#pragma GCC target("popcnt")
using namespace std;
using ll = long long;
using ull = unsigned long long;
using lld = long double;
using ii = pair<int,int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
using vii = vector<ii>;
using vpll = vector<pll>;
using vlld = vector<lld>;
#define all(x) x.begin(),x.end()
#define lsb(x) x&(-x)
#define gcd(a,b) __gcd(a,b)
#define sz(x) (int)x.size()
#define pb push_back
#define fi first
#define se second
#define fls cout.flush()
#define fore(i, l, r) for (auto i = l; i < r; i++)
#define fo(i, n) fore (i, 0, n)
#define forex(i, r, l) for (auto i = r-1; i >= l; i--)
#define ffo(i, n) forex (i, n, 0)
bool cmin(ll &a, ll b) { if (b < a) { a=b; return 1; } return 0; }
bool cmax(ll &a, ll b) { if (b > a) { a=b; return 1; } return 0; }
const ll INF = 1e18;
const int N = 2505;
struct Fenwick {
vll ft;
ll n;
Fenwick () { }
Fenwick (ll n): n(n+2), ft (n+4, 0) { }
void update (ll i, ll v) {
i++;
for (; i <= n; i += lsb(i))
ft[i] += v;
}
ll query (ll i) {
i++;
ll r = 0;
for (; i > 0; i -= lsb(i))
r += ft[i];
return r;
}
void update (ll l, ll r, ll v) { update(l, +v); update(r+1, -v); }
ll query (ll l, ll r) { if (l>r) return 0ll; return query(r) - query(l-1); }
};
vector<array<int, 3>> updates[N][N], qrys[N][N];
ll count_rectangles(vector<vector<int> > a) {
ll n = a.size(), m = a[0].size(), ans = 0;
vector<vll> down(n, vll(m)), up(n, vll(m));
fo (j, m) {
stack<ll> stk;
stk.push(-1);
fo (i, n) {
while (stk.top() != -1 && a[stk.top()][j] < a[i][j]) stk.pop();
up[i][j] = stk.top();
stk.push(i);
}
while (stk.size()) stk.pop();
stk.push(n);
ffo (i, n) {
while (stk.top() != n && a[stk.top()][j] < a[i][j]) stk.pop();
down[i][j] = stk.top();
stk.push(i);
}
}
forex (i, n-1, 1) {
vll L(m), R(m);
stack<ll> stk;
stk.push(-1);
fo (j, m) {
while (stk.top() != -1 && a[i][stk.top()] <= a[i][j]) stk.pop();
L[j] = stk.top() + 1;
stk.push(j);
}
while (stk.size()) stk.pop();
stk.push(m);
ffo (j, m) {
while (stk.top() != m && a[i][stk.top()] < a[i][j]) stk.pop();
R[j] = stk.top() - 1;
stk.push(j);
}
fo (j, m) {
if (L[j] < 1 || m-2 < R[j] || a[i][R[j]+1] == a[i][j]) continue;
ll mx;
if (updates[L[j]][R[j]].empty() || updates[L[j]][R[j]].back()[0] > i+1) {
mx = 0;
fore (j2, L[j], R[j]+1)
mx = max(mx, up[i+1][j2]);
updates[L[j]][R[j]].pb(array<int, 3>{int(mx+1), -1, int(i+1)});
updates[L[j]][R[j]].pb(array<int, 3>{int(i+1), +1, int(i+1)});
}
mx = 0;
fore (j2, L[j], R[j]+1)
mx = max(mx, up[i][j2]);
updates[L[j]][R[j]].pb(array<int, 3>{int(mx+1), -1, int(i)});
updates[L[j]][R[j]].pb(array<int, 3>{int(i), +1, int(i)});
ll k = n-1;
fore (j2, L[j], R[j]+1) k = min(k, down[i-1][j2]);
qrys[L[j]][R[j]].pb(array<int, 3>{int(i+1), int(k), -1});
}
}
Fenwick ft(n+1);
fo (l, m) {
fo (r, m) {
if (qrys[l][r].empty()) continue;
sort(all(updates[l][r]));
int ls = n+5;
for (auto [lb, rb, _]: qrys[l][r]) {
while (updates[l][r].size() && updates[l][r].back()[0] >= lb) {
ft.update(updates[l][r].back()[2], updates[l][r].back()[1]);
updates[l][r].pop_back();
}
int i = lb-1;
if (i+1 != ls ) ls = i;
ans += ft.query(lb, min(rb, ls+1));
}
while (updates[l][r].size()) {
ft.update(updates[l][r].back()[2], updates[l][r].back()[1]);
updates[l][r].pop_back();
}
}
}
return ans;
}
