#include <bits/stdc++.h>
#include "rect.h"
#define all(x) x.begin(),x.end()
#define PB push_back
#define sz(x) ((int)x.size())
#define pii pair<int,int>
#define MP make_pair
#define ft first
#define sd second
using namespace std;
typedef long long ll;
const int N = 2510;
const int oo = 2e9;
const int PW = 13;
vector<int> lst[N][N];
vector<int> qr[N];
stack<int> stk;
int n, m, kol = 0, mx, my, Mx, My, up[N][N], down[N][N], spar[2][N][N][PW], po[N];
int fen[N];
ll ans = 0, big = 0;
int get(int tp, int i, int l, int r){
int len = r - l + 1;
int pw = po[len];
if (tp == 1)
return min(spar[tp][i][l][pw], spar[tp][i][r - (1 << pw) + 1][pw]);
else return max(spar[tp][i][l][pw], spar[tp][i][r - (1 << pw) + 1][pw]);
}
void upd(int x, int vl){
for (; x < n; x = (x | (x + 1)))
fen[x] += vl;
}
int sum(int x){
int res = 0;
for (; x >= 0; x = (x & (x + 1)) - 1)
res += fen[x];
return res;
}
long long count_rectangles(std::vector<std::vector<int> > a) {
n = sz(a);
m = sz(a[0]);
if (n < 3 || m < 3) return 0;
for (int i = 1; i < n - 1; i++){
while (sz(stk)) stk.pop();
stk.push(0);
bool was = 0;
for (int j = 1; j < m; j++){
while (sz(stk) > 0 && a[i][stk.top()] <= a[i][j]) {
if (a[i][stk.top()] == a[i][j]){
if (!was){
was = 1;
lst[stk.top() + 1][j - 1].PB(i);
}
} else lst[stk.top() + 1][j - 1].PB(i);
stk.pop();
}
if (sz(stk) && !was)
lst[stk.top() + 1][j - 1].PB(i);
stk.push(j);
}
}
for (int j = 0; j < m; j++){
while (sz(stk)) stk.pop();
stk.push(-1);
for (int i = 0; i < n; i++){
while (sz(stk) > 1 && a[stk.top()][j] < a[i][j])
stk.pop();
up[i][j] = stk.top();
stk.push(i);
}
while (sz(stk)) stk.pop();
stk.push(n);
for (int i = n - 1; i >= 0; i--){
while (sz(stk) > 1 && a[stk.top()][j] < a[i][j])
stk.pop();
down[i][j] = stk.top();
stk.push(i);
}
}
po[0] = -1;
for (int i = 1; i <= max(n, m); i++)
po[i] = po[i >> 1] + 1;
for (int i = 1; i < n - 1; i++){
for (int j = 0; j < m; j++){
spar[0][i][j][0] = up[i + 1][j];
spar[1][i][j][0] = down[i - 1][j];
}
for (int pw = 1; pw < PW; pw++)
for (int j = 0; j + (1 << pw) - 1 < m; j++){
spar[0][i][j][pw] = max(spar[0][i][j][pw - 1], spar[0][i][j + (1 << (pw - 1))][pw - 1]);
spar[1][i][j][pw] = min(spar[1][i][j][pw - 1], spar[1][i][j + (1 << (pw - 1))][pw - 1]);
}
}
for (int c1 = 1; c1 < m - 1; c1++)
for (int c2 = c1; c2 < m - 1; c2++){
for (int it = 0; it < sz(lst[c1][c2]); ){
int r1 = lst[c1][c2][it];
int j = it + 1;
while (j < sz(lst[c1][c2]) && lst[c1][c2][j] - 1 == lst[c1][c2][j - 1])
j++;
int i = lst[c1][c2][j - 1] + 1;
for (int r2 = r1; r2 < i; r2++){
int bd = min(n - 1, get(1, r2, c1, c2));
qr[r2].PB(-bd);
}
for (int r2 = r1; r2 < i; r2++)
qr[max(get(0, r2, c1, c2), r1 - 1)].PB(r2);
for (int r2 = r1 - 1; r2 < i; r2++) {
if (sz(qr[r2])) {
for (int cr : qr[r2])
if (cr < 0)
ans += sum(-cr - 1) - sum(r2 - 1);
else upd(cr, 1);
qr[r2].clear();
}
}
for (int r2 = r1; r2 < i; r2++)
upd(r2, -1);
it = j;
}
}
return ans;
}
