#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
struct range {
int l, r, mx;
// bool operator == (const range &b) const {
// return (l==b.l && r==b.r);
// }
};
bool cmp0(range a, range b) {return a.r > b.r;}
bool cmp1(range a, range b) {return a.mx > b.mx;}
const int maxn = 2505, INF = 1e9;
int n, m;
vector<vector<int>> a;
vector<pair<int,int>> pos[2][maxn][maxn];
vector<range> start[2][maxn][maxn];
int fen[maxn];
void update(int id, int val) {
while (id<maxn) {
fen[id] += val;
id += (id & -id);
}
}
int qry(int id) {
int val = 0;
while (id >= 1) {
val += fen[id];
id -= (id & -id);
}
return val;
}
long long count_rectangles(vector<vector<int32_t>> A) {
n = A.size(), m = A[0].size();
a.resize(n);
for (int i=0;i<n;i++) {
a[i].resize(m);
for (int j=0;j<m;j++) a[i][j] = A[i][j];
}
for (int i=0;i<n;i++) {
vector<pair<int,int>> cur;
for (int j=0;j<m;j++) cur.push_back({a[i][j], j});
sort(cur.rbegin(), cur.rend());
set<int> s; s.insert(-1); s.insert(INF);
vector<int> temp;
for (int j=0;j<m;j++) {
auto [val, id] = cur[j];
if (j>0 && val!=cur[j-1].first) {
for (int x:temp) s.insert(x);
temp.clear();
}
auto it = s.upper_bound(id);
int l = *prev(it), r = *it;
if (l!=-1 && r!=INF) {
l++, r--;
if (pos[0][l][r].size()==0 || pos[0][l][r].back().first!=i) {
pos[0][l][r].push_back({i, -1});
start[0][i][l].push_back({l, r, -1});
}
}
temp.push_back(id);
}
}
for (int j=0;j<m;j++) {
vector<pair<int,int>> cur;
for (int i=0;i<n;i++) cur.push_back({a[i][j], i});
sort(cur.rbegin(), cur.rend());
set<int> s; s.insert(-1); s.insert(INF);
vector<int> temp;
for (int i=0;i<n;i++) {
auto [val, id] = cur[i];
if (i>0 && val!=cur[i-1].first) {
for (int x:temp) s.insert(x);
temp.clear();
}
auto it = s.upper_bound(id);
int l = *prev(it), r = *it;
if (l!=-1 && r!=INF) {
l++, r--;
if (pos[1][l][r].size()==0 || pos[1][l][r].back().first!=j) {
pos[1][l][r].push_back({j, -1});
start[1][l][j].push_back({l, r, -1});
}
}
temp.push_back(id);
}
}
for (int I=0;I<=1;I++) {
int nn = m;
if (I==1) nn = n;
for (int l=0;l<nn;l++) for (int r=l;r<nn;r++) {
sort(pos[I][l][r].begin(), pos[I][l][r].end());
// pos[I][l][r].erase(unique(pos[I][l][r].begin(), pos[I][l][r].end()), pos[I][l][r].end());
int sz = pos[I][l][r].size();
// if (I==1 && sz>0) cout << l << " " << r << " " << sz << endl;
for (int i=sz-1;i>=0;i--) {
if (i==sz-1 || pos[I][l][r][i+1].first!=pos[I][l][r][i].first+1) pos[I][l][r][i].second = pos[I][l][r][i].first;
else pos[I][l][r][i].second = pos[I][l][r][i+1].second;
// if (I==1) cout << pos[I][l][r][i].first << " " << pos[I][l][r][i].second << endl;
}
}
}
for (int I=0;I<=1;I++) {
for (int i=0;i<n;i++) for (int j=0;j<m;j++) {
// cout << "test " << I << " " << i << " " << j << endl;
for (auto &[l, r, mx]:start[I][i][j]) {
// cout << l << " " << r << " " << mx << endl;
int id = i;
if (I==1) id = j;
mx = (*lower_bound(pos[I][l][r].begin(), pos[I][l][r].end(), make_pair(id, -INF))).second;
}
}
}
int ans = 0;
for (int i=0;i<n;i++) for (int j=0;j<m;j++) {
sort(start[0][i][j].begin(), start[0][i][j].end(), cmp0);
// start[0][i][j].erase(unique(start[0][i][j].begin(), start[0][i][j].end()), start[0][i][j].end());
sort(start[1][i][j].begin(), start[1][i][j].end(), cmp1);
// start[1][i][j].erase(unique(start[1][i][j].begin(), start[1][i][j].end()), start[1][i][j].end());
int pt = -1;
vector<int> LOG;
for (auto [l, r, mx]:start[0][i][j]) {
while (pt+1 < start[1][i][j].size() && start[1][i][j][pt+1].mx >= r) {
pt++;
// if (i==1 && j==2) cout << start[1][i][j][pt].l << " " << start[1][i][j][pt].r << endl;
update(start[1][i][j][pt].r, 1);
LOG.push_back(start[1][i][j][pt].r);
}
// if (qry(mx) > 0) {
// cout << "ANS " << qry(mx) << endl;
// cout << i << " " << j << endl;
// cout << l << " " << r << endl;
// }
ans += qry(mx);
}
for (int x:LOG) update(x, -1);
}
return ans;
}
