#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define ss short
#define ll long long
struct range {
ss r, mx;
};
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 = 2505, lg = 12;
int n, m;
vector<vector<vector<pair<ss,ss>>>> pos[2];
vector<vector<vector<range>>> start[2];
ss 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;
}
pair<int,int> st[maxn][lg];
int qry1(int l, int r) {
int lg = log2(r-l+1);
pair<int,int> lhs = st[l][lg], rhs = st[r-(1<<lg)+1][lg];
if (rhs.first > lhs.first) return rhs.second;
else return lhs.second;
}
int nn, II, ii;
void dfs(int l, int r) {
if (l>r) return;
int mid = qry1(l, r);
// if (II==0 && ii==1) cout << l << " " << r << " " << mid << endl;
if (l>=1 && r<=nn-1 && st[mid][0].first < st[l-1][0].first && st[mid][0].first < st[r+1][0].first) {
// if (II==1) cout << ii << " " << l << " " << r << endl;
pos[II][l][r-l].push_back({(ss)ii, -1});
if (II==0) start[II][ii][l].push_back({(ss)r, -1});
else start[II][l][ii].push_back({(ss)r, -1});
}
dfs(l, mid-1); dfs(mid+1, r);
}
long long count_rectangles(vector<vector<int32_t>> a) {
n = a.size(), m = a[0].size();
pos[0].resize(m);
for (int i=0;i<m;i++) pos[0][i].resize(m - i);
pos[1].resize(n);
for (int i=0;i<n;i++) pos[1][i].resize(n - i);
start[0].resize(n); start[1].resize(n);
for (int i=0;i<n;i++) start[0][i].resize(m), start[1][i].resize(m);
nn = m, II = 0;
for (int i=0;i<n;i++) {
ii = i;
for (int j=m-1;j>=0;j--) {
st[j][0] = {a[i][j], j};
for (int k=1;k<lg;k++) {
if (j+(1<<k)-1 < m) {
st[j][k] = st[j][k-1];
pair<int,int> nxt = st[j + (1 << (k-1))][k-1];
if (nxt.first > st[j][k].first) st[j][k] = nxt;
} else break;
}
}
dfs(0, m-1);
}
nn = n, II = 1;
for (int j=0;j<m;j++) {
ii = j;
for (int i=n-1;i>=0;i--) {
st[i][0] = {a[i][j], i};
for (int k=1;k<lg;k++) {
if (i+(1<<k)-1 < n) {
st[i][k] = st[i][k-1];
pair<int,int> nxt = st[i + (1 << (k-1))][k-1];
if (nxt.first > st[i][k].first) st[i][k] = nxt;
} else break;
}
}
dfs(0, n-1);
}
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-l].begin(), pos[I][l][r-l].end());
int sz = pos[I][l][r-l].size();
for (int i=sz-1;i>=0;i--) {
if (i==sz-1 || pos[I][l][r-l][i+1].first!=pos[I][l][r-l][i].first+1) pos[I][l][r-l][i].second = pos[I][l][r-l][i].first;
else pos[I][l][r-l][i].second = pos[I][l][r-l][i+1].second;
}
}
}
for (int I=0;I<=1;I++) {
for (int i=0;i<n;i++) for (int j=0;j<m;j++) {
for (auto &[r, mx]:start[I][i][j]) {
ss x = j, y = i;
if (I==1) x = i, y = j;
mx = (*lower_bound(pos[I][x][r-x].begin(), pos[I][x][r-x].end(), make_pair(y, (ss)-1))).second;
}
}
}
ll ans = 0;
vector<int> LOG;
for (int i=1;i<n-1;i++) for (int j=1;j<m-1;j++) {
sort(start[0][i][j].begin(), start[0][i][j].end(), cmp0);
sort(start[1][i][j].begin(), start[1][i][j].end(), cmp1);
int pt = -1;
LOG.clear();
for (auto [r, mx]:start[0][i][j]) {
while (pt+1 < start[1][i][j].size() && start[1][i][j][pt+1].mx >= r) {
pt++;
update(start[1][i][j][pt].r, 1);
LOG.push_back(start[1][i][j][pt].r);
}
ans += qry(mx);
}
for (int x:LOG) update(x, -1);
}
return ans;
}
