#include "rect.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 2147483647;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
ll count_rectangles(vector<vector<int>> A){
int n = A.size();
int m = A[0].size();
vector<vector<int>> L(n, vector<int>(m, -1));
vector<vector<int>> R(n, vector<int>(m, -1));
vector<vector<int>> U(n, vector<int>(m, -1));
vector<vector<int>> D(n, vector<int>(m, -1));
for(int i = 0; i < n; i++){
vector<int> v;
for(int j = 0; j < m; j++){
while(!v.empty() && A[i][v.back()] < A[i][j]){
R[i][v.back()] = j;
v.pob;
}
if(v.empty() || A[i][v.back()] == A[i][j]){
v.eb(j);
continue;
}
L[i][j] = v.back();
v.eb(j);
}
}
for(int i = 0; i < m; i++){
vector<int> v;
for(int j = 0; j < n; j++){
while(!v.empty() && A[v.back()][i] < A[j][i]){
D[v.back()][i] = j;
v.pob;
}
if(v.empty() || A[v.back()][i] == A[j][i]){
v.eb(j);
continue;
}
U[j][i] = v.back();
v.eb(j);
}
}
vector<vector<vector<pii>>> row(n, vector<vector<pii>>(m));
vector<vector<vector<pii>>> col(n, vector<vector<pii>>(m));
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
if(L[i][j] == -1 || R[i][j] == -1 || U[i][j] == -1 || D[i][j] == -1) continue;
row[i][L[i][j] + 1].eb(mp(R[i][j] - 1, j));
col[U[i][j] + 1][j].eb(mp(D[i][j] - 1, i));
}
}
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
lsort(row[i][j]);
lsort(col[i][j]);
}
}
auto getrow = [&](int i, int l, int r){
//cerr << "getrow " << i << " " << l << " " << r << " : ";
//printv(row[i][l], cerr);
auto it = lower_bound(iter(row[i][l]), mp(r, 0));
if(it == row[i][l].end() || it->F != r) return -1;
return it->S;
};
auto getcol = [&](int i, int l, int r){
auto it = lower_bound(iter(col[l][i]), mp(r, 0));
if(it == col[l][i].end() || it->F != r) return -1;
return it->S;
};
vector<vector<int>> rc(n, vector<int>(m, -1));
vector<vector<int>> cc(n, vector<int>(m, -1));
for(int i = n - 1; i >= 0; i--){
for(int j = m - 1; j >= 0; j--){
if(L[i][j] == -1 || R[i][j] == -1 || U[i][j] == -1 || D[i][j] == -1) continue;
int id = i == n - 1 ? -1 : getrow(i + 1, L[i][j] + 1, R[i][j] - 1);
if(id == -1) rc[i][j] = i;
else rc[i][j] = rc[i + 1][id];
}
}
for(int j = m - 1; j >= 0; j--){
for(int i = n - 1; i >= 0; i--){
if(L[i][j] == -1 || R[i][j] == -1 || U[i][j] == -1 || D[i][j] == -1) continue;
int id = j == m - 1 ? -1 : getcol(j + 1, U[i][j] + 1, D[i][j] - 1);
if(id == -1) cc[i][j] = j;
else cc[i][j] = cc[id][j + 1];
}
}
vector<pair<pii, pii>> ans;
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
if(L[i][j] == -1 || R[i][j] == -1 || U[i][j] == -1 || D[i][j] == -1) continue;
/*//cerr << "test " << i << " " << j << " " << L[i][j] << " " << R[i][j] << " " << U[i][j] << " " << D[i][j] << "\n";
int idr = getrow(U[i][j] + 1, L[i][j] + 1, R[i][j] - 1);
int idc = getcol(L[i][j] + 1, U[i][j] + 1, D[i][j] - 1);
//cerr << idr << " " << idc << "\n";
if(idr == -1 || idc == -1) continue;
if(rc[U[i][j] + 1][idr] < D[i][j] - 1) continue;
if(cc[idc][L[i][j] + 1] < R[i][j] - 1) continue;*/
bool ok = true;
//cerr << "test " << i << " " << j << "\n";
for(int x = U[i][j] + 1; x < D[i][j]; x++){
int mx = -1, mxp = -1;
for(int y = L[i][j] + 1; y < R[i][j]; y++){
if(A[x][y] > mx) mx = A[x][y], mxp = y;
}
if(L[x][mxp] != L[i][j] || R[x][mxp] != R[i][j]) ok = false;
else{
//cerr << "owo " << x << " " << mxp << "\n";
assert(getrow(x, L[i][j] + 1, R[i][j] - 1) != -1);
}
}
for(int y = L[i][j] + 1; y < R[i][j]; y++){
int mx = -1, mxp = -1;
for(int x = U[i][j] + 1; x < D[i][j]; x++){
if(A[x][y] > mx) mx = A[x][y], mxp = x;
}
if(U[mxp][y] != U[i][j] || D[mxp][y] != D[i][j]) ok = false;
else assert(getcol(y, U[i][j] + 1, D[i][j] - 1) != -1);
}
if(!ok) continue;
ans.eb(mp(mp(L[i][j] + 1, R[i][j] - 1), mp(U[i][j] + 1, D[i][j] - 1)));
}
}
lsort(ans);
uni(ans);
return ans.size();
}
