#include "rect.h"
#include <bits/stdc++.h>
#define sz(v) ((int)(v).size())
using namespace std;
using pi = pair<int, int>;
using lint = long long;
struct strip{ int x, s, e, up; };
void proc(vector<strip> &v){
sort(v.begin(), v.end(), [&](const strip &a, const strip &b){
return make_tuple(a.s, a.e, a.x) < make_tuple(b.s, b.e, b.x);
});
for(int i=0; i<v.size(); i++){
v[i].up = 1;
if(i > 0 && pi(v[i-1].s, v[i-1].e) == pi(v[i].s, v[i].e) && v[i-1].x + 1 == v[i].x) v[i].up = v[i-1].up + 1;
}
}
lint count_rectangles(vector<vector<int>> a){
vector<strip> rdir, ldir;
int n = sz(a);
int m = sz(a[0]);
for(int i=1; i<n-1; i++){
vector<int> L(m, -1), R(m, -1);
vector<int> stk;
for(int j=0; j<m; j++){
while(!stk.empty() && a[i][stk.back()] <= a[i][j]) stk.pop_back();
if(stk.size()) L[j] = stk.back();
stk.push_back(j);
}
stk.clear();
for(int j=m-1; j>=0; j--){
while(!stk.empty() && a[i][stk.back()] <= a[i][j]) stk.pop_back();
if(stk.size()) R[j] = stk.back();
stk.push_back(j);
}
stk.clear();
for(int j=0; j<m; j++){
if(L[j] != -1 && R[j] >= 2){
rdir.push_back({i, L[j], R[j]});
}
}
}
for(int i=1; i<m-1; i++){
vector<int> L(n, -1), R(n, -1);
vector<int> stk;
for(int j=0; j<n; j++){
while(!stk.empty() && a[stk.back()][i] <= a[j][i]) stk.pop_back();
if(stk.size()) L[j] = stk.back();
stk.push_back(j);
}
stk.clear();
for(int j=n-1; j>=0; j--){
while(!stk.empty() && a[stk.back()][i] <= a[j][i]) stk.pop_back();
if(stk.size()) R[j] = stk.back();
stk.push_back(j);
}
stk.clear();
for(int j=0; j<n; j++){
if(L[j] != -1 && R[j] >= 2){
ldir.push_back({i, L[j], R[j]});
}
}
}
proc(ldir);
proc(rdir);
sort(ldir.begin(), ldir.end(), [&](const strip &a, const strip &b){
return pi(a.e, a.x) < pi(b.e, b.x);
});
sort(rdir.begin(), rdir.end(), [&](const strip &a, const strip &b){
return pi(a.x, a.e) < pi(b.x, b.e);
});
int p1 = 0, p2 = 0;
lint ret = 0;
for(int i=2; i<n; i++){
for(int j=2; j<m; j++){
vector<pi> punk1, punk2;
while(p1 < sz(rdir) && pi(rdir[p1].x + 1, rdir[p1].e) == pi(i, j)){
punk1.emplace_back(j - rdir[p1].s - 1, rdir[p1].up);
p1++;
}
while(p2 < sz(ldir) && pi(ldir[p2].e, ldir[p2].x + 1) == pi(i, j)){
punk2.emplace_back(i - ldir[p2].s - 1, ldir[p2].up);
p2++;
}
for(auto &x : punk1){
for(auto &y : punk2){
if(x.first <= y.second && y.first <= x.second) ret++;
}
}
}
}
return ret;
}
