#include <bits/stdc++.h>
#include "rect.h"
//~ #include "grader.cpp"
using namespace std;
#define ll long long
const int N = 2501;
const int INF = (int)1e9;
struct segment{
vector <int> tree;
int n;
void build(vector <int> &a, int b){
n = a.size();
tree.resize(2 * n, -INF);
for(int i = 0 ; i < n ; i++){
if(a[i] != -1) tree[i + n] = a[i] * b;
}
for(int i = n - 1 ; i > 0 ; i--){
tree[i] = max(tree[i << 1], tree[i << 1 | 1]);
}
}
int query(int l, int r){
r++;
int ret = -INF;
for(l += n, r += n ; l < r ; l >>= 1, r >>= 1){
if(l & 1) ret = max(ret, tree[l++]);
if(r & 1) ret = max(ret, tree[--r]);
}
return ret;
}
};
int n, m, vis[N * N];
vector <vector <int> > a;
vector <vector <int> > us, rs, ds, ls, ue, re, de, le;
vector <segment> ue_tree, re_tree, de_tree, le_tree;
vector <int> v[N * N];
vector <int> calc(vector <int> &a, int b, int c){
//~ b = 0 for >
//~ b = 1 for >=
//~ c = 0 for forward
//~ c = 1 for backward
int n = a.size();
vector <int> inds;
for(int i = 0 ; i < n ; i++){
if(c == 0) inds.push_back(i);
else inds.push_back(n - i - 1);
}
vector <int> ret(n);
vector <int> cur;
for(auto &i : inds){
while(cur.size() && a[i] >= a[cur.back()] + b){
cur.pop_back();
}
if(cur.size() == 0) ret[i] = -1;
else ret[i] = cur.back();
cur.push_back(i);
}
return ret;
}
void add(int r1, int c1, int r2, int c2){
if(r1 == -1 || c1 == -1 || r2 == -1 || c2 == -1) return;
v[r1 * m + c1].push_back(r2 * m + c2);
}
bool check(int r1, int c1, int r2, int c2){
int v = -de_tree[r1].query(c1 + 1, c2 - 1);
if(v < r2) return 0;
v = ue_tree[r2].query(c1 + 1, c2 - 1);
if(v > r1) return 0;
v = -re_tree[c1].query(r1 + 1, r2 - 1);
if(v < c2) return 0;
v = le_tree[c2].query(r1 + 1, r2 - 1);
if(v > c1) return 0;
return 1;
}
long long count_rectangles(std::vector<std::vector<int> > A) {
a = A;
n = a.size();
m = a[0].size();
us.resize(n, vector <int>(m));
ue.resize(n, vector <int>(m));
ds.resize(n, vector <int>(m));
de.resize(n, vector <int>(m));
ls.resize(n, vector <int>(m));
le.resize(n, vector <int>(m));
rs.resize(n, vector <int>(m));
re.resize(n, vector <int>(m));
ue_tree.resize(n);
de_tree.resize(n);
le_tree.resize(m);
re_tree.resize(m);
for(int i = 0 ; i < n ; i++){
vector <int> cur = a[i];
ls[i] = calc(cur, 0, 0);
le[i] = calc(cur, 1, 0);
rs[i] = calc(cur, 0, 1);
re[i] = calc(cur, 1, 1);
}
for(int j = 0 ; j < m ; j++){
vector <int> cur(n);
for(int i = 0 ; i < n ; i++){
cur[i] = a[i][j];
}
vector <int> g;
g = calc(cur, 0, 0);
for(int i = 0 ; i < n ; i++){
us[i][j] = g[i];
}
g = calc(cur, 1, 0);
for(int i = 0 ; i < n ; i++){
ue[i][j] = g[i];
}
g = calc(cur, 0, 1);
for(int i = 0 ; i < n ; i++){
ds[i][j] = g[i];
}
g = calc(cur, 1, 1);
for(int i = 0 ; i < n ; i++){
de[i][j] = g[i];
}
}
for(int i = 0 ; i < n ; i++){
ue_tree[i].build(ue[i], 1);
de_tree[i].build(de[i], -1);
}
for(int j = 0 ; j < m ; j++){
vector <int> cur(n);
for(int i = 0 ; i < n ; i++){
cur[i] = le[i][j];
}
le_tree[j].build(cur, 1);
cur.assign(n, 0);
for(int i = 0 ; i < n ; i++){
cur[i] = re[i][j];
}
re_tree[j].build(cur, -1);
}
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < m ; j++){
add(us[i][j], ls[i][j], ds[i][j], rs[i][j]);
}
}
int ret = 0;
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < m ; j++){
for(auto &k : v[i * m + j]){
if(vis[k]) continue;
vis[k] = 1;
ret += check(i, j, k / m, k % m);
}
for(auto &k : v[i * m + j]){
vis[k] = 0;
}
}
}
return ret;
}
