#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;
int n, m;
vector <vector <int> > a;
set <pair <pair <int, int>, pair <int, int> > > vis;
vector <vector <int> > us, rs, ds, ls, ue, re, de, le;
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;
}
bool check(int r1, int c1, int r2, int c2){
if(r1 == -1 || c1 == -1 || r2 == -1 || c2 == -1) return 0;
if(vis.count(make_pair(make_pair(r1, c1), make_pair(r2, c2)))) return 0;
vis.insert(make_pair(make_pair(r1, c1), make_pair(r2, c2)));
int v = INF;
for(int c = c1 + 1 ; c < c2 ; c++){
if(de[r1][c] != -1) v = min(v, de[r1][c]);
}
if(v < r2) return 0;
v = -INF;
for(int c = c1 + 1 ; c < c2 ; c++){
if(ue[r2][c] != -1) v = max(v, ue[r2][c]);
}
if(v > r1) return 0;
v = INF;
for(int r = r1 + 1 ; r < r2 ; r++){
if(re[r][c1] != -1) v = min(v, re[r][c1]);
}
if(v < c2) return 0;
v = -INF;
for(int r = r1 + 1 ; r < r2 ; r++){
if(le[r][c2] != -1) v = max(v, le[r][c2]);
}
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));
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];
}
}
int ret = 0;
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < m ; j++){
ret += check(us[i][j], ls[i][j], ds[i][j], rs[i][j]);
}
}
return ret;
}
