// In the name of Allah
#include <bits/stdc++.h>
#include "rect.h"
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef complex<ld> cld;
#define all(x) (x).begin(),(x).end()
#define len(x) ((ll) (x).size())
#define F first
#define S second
#define pb push_back
#define sep ' '
#define endl '\n'
#define Mp make_pair
#define kill(x) cout << x << '\n', exit(0)
#define set_dec(x) cout << fixed << setprecision(x);
#define file_io(x,y) freopen(x, "r", stdin); freopen(y, "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 2500 + 4;
int n, m;
int A[maxn][maxn], L[maxn], R[maxn];
vector<int> A1[maxn][maxn], A2[maxn][maxn];
vector<int> val1[maxn][maxn], val2[maxn][maxn];
vector<pii> lsx; int t[maxn];
void addx(int i, int x) {
for (++i; i < maxn; i += (i & -i)) t[i] += x;
}
int getx(int i) {
int res = 0;
for (++i; i > 0; i -= (i & -i)) res += t[i];
return res;
}
int G1(int i, int j, int x) {
if (i < 0 || i >= n || j < 0 || j >= m) return -1;
int R = lower_bound(all(A1[i][j]), x) - A1[i][j].begin();
if (R < len(A1[i][j]) && A1[i][j][R] == x) return R;
else return -1;
}
int G2(int i, int j, int x) {
if (i < 0 || i >= n || j < 0 || j >= m) return -1;
int R = lower_bound(all(A2[i][j]), x) - A2[i][j].begin();
if (R < len(A2[i][j]) && A2[i][j][R] == x) return R;
else return -1;
}
ll count_rectangles(vector<vector<int>> a) {
n = len(a); m = len(a[0]);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) A[i][j] = a[i][j];
}
if (n < 3 || m < 3) return 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
for (L[j] = j - 1; L[j] != -1 && A[i][j] > A[i][L[j]]; L[j] = L[L[j]]);
if (L[j] != -1 && (j - L[j]) >= 2) A1[i][L[j]].pb(j);
}
for (int j = m - 1; j >= 0; j--) {
for (R[j] = j + 1; R[j] != m && A[i][j] > A[i][R[j]]; R[j] = R[R[j]]);
if (R[j] != m && (R[j] - j) >= 2 && A[i][j] != A[i][R[j]]) A1[i][j].pb(R[j]);
}
}
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
for (L[i] = i - 1; L[i] != -1 && A[i][j] > A[L[i]][j]; L[i] = L[L[i]]);
if (L[i] != -1 && (i - L[i]) >= 2) A2[L[i]][j].pb(i);
}
for (int i = n - 1; i >= 0; i--) {
for (R[i] = i + 1; R[i] != n && A[i][j] > A[R[i]][j]; R[i] = R[R[i]]);
if (R[i] != n && (R[i] - i) >= 2 && A[i][j] != A[R[i]][j]) A2[i][j].pb(R[i]);
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
sort(all(A1[i][j])); sort(all(A2[i][j]));
val1[i][j].resize(len(A1[i][j])); val2[i][j].resize(len(A2[i][j]));
}
}
for (int i = n - 1; i >= 0; i--) {
for (int j = 0; j < m; j++) {
for (int R = 0; R < len(A1[i][j]); R++) {
int x = G1(i + 1, j, A1[i][j][R]);
if (x != -1) val1[i][j][R] = val1[i + 1][j][x];
else val1[i][j][R] = i;
}
}
}
for (int j = m - 1; j >= 0; j--) {
for (int i = 0; i < n; i++) {
for (int R = 0; R < len(A2[i][j]); R++) {
int x = G2(i, j + 1, A2[i][j][R]);
if (x != -1) val2[i][j][R] = val2[i][j + 1][x];
else val2[i][j][R] = j;
}
}
}
ll ans = 0;
for (int i = 1; i < n; i++) {
for (int j = 1; j < m; j++) {
lsx.clear();
for (int R2 = 0; R2 < len(A2[i - 1][j]); R2++) {
lsx.pb(Mp(val2[i - 1][j][R2], A2[i - 1][j][R2] - 1));
}
sort(all(lsx));
int R2 = len(lsx) - 1;
for (int R1 = len(A1[i][j - 1]) - 1; R1 >= 0; R1--) {
while (R2 >= 0 && lsx[R2].F >= A1[i][j - 1][R1] - 1) {
addx(lsx[R2].S, 1); R2--;
}
ans += getx(val1[i][j - 1][R1]);
}
while (R2 + 1 < len(lsx)) {
addx(lsx[R2 + 1].S, -1); R2++;
}
}
}
return ans;
}
