#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define all(x) (x).begin(), (x).end()
typedef int64_t lld;
typedef pair<int, int> pii;
/*
#include<bits/extc++.h>
using namespace __gnu_pbds;
template<typename T, typename comp = greater<T>>
using OST = tree<T, null_type, comp, rb_tree_tag, tree_order_statistics_node_update>;
*/
template<typename T1, typename T2>
ostream& operator<<(ostream& out, pair<T1, T2> p){
return out << "(" << p.ff << ", " << p.ss << ")";
}
vector<pii> tmp;
vector<vector<int>> U, D, L, R;
template<typename Cmp>
struct node{
node *L, *R;
int l, r, mid, s;
int cmp(int a, int b){ return Cmp()(a, b)?a:b; }
vector<int16_t> data;
node(int ll, int rr, int st, const vector<vector<int>>& v) : l(ll), r(rr), mid((l+r)/2), s(st) {
data.resize(s*4);
if(l != r){
L = new node(l, mid, s, v), R = new node(mid+1, r, s, v);
for(int i = 0; i < data.size(); i++)data.at(i) = cmp(L->data.at(i), R->data.at(i));
}
else build_data(1, 0, s, v.at(l));
}
void build_data(int i, int ll, int rr, const vector<int>& v){
if(data.size() <= i)data.resize(i+1);
if(ll == rr)data[i] = v[ll];
else build_data(i<<1, ll, (ll+rr)>>1, v), build_data((i<<1)+1, ((ll+rr)>>1)+1, rr, v), data[i] = cmp(data[i<<1], data[(i<<1)+1]);
}
int query_data(int i, int ll, int rr, int ql, int qr){
//cout << ll << " " << rr << " " << ql << " " << qr << endl;
assert(ql <= rr && qr >= ll);
if(ql <= ll && qr >= rr)return data[i];
if(qr <= ((ll+rr)>>1))return query_data(i<<1, ll, (ll+rr)>>1, ql, qr);
if(ql > ((ll+rr)>>1))return query_data((i<<1)+1, ((ll+rr)>>1)+1, rr, ql, qr);
return cmp(query_data(i<<1, ll, (ll+rr)>>1, ql, qr), query_data((i<<1)+1, ((ll+rr)>>1)+1, rr, ql, qr));
}
int query(int l1, int r1, int l2, int r2){
assert(l1 <= r && r1 >= l);
if(l1 <= l && r1 >= r)return query_data(1, 0, s, l2, r2);
if(l1 > mid)return R->query(l1, r1, l2, r2);
if(r1 <= mid)return L->query(l1, r1, l2, r2);
return cmp(L->query(l1, r1, l2, r2), R->query(l1, r1, l2, r2));
}
};
node<greater<int>> *d, *r;
node<less<int>> *u, *l;
set<tuple<int, int, int, int>> st;
long long count_rectangles(vector<vector<int>> a) {
int n = a.size(), m = a[0].size();
U = D = L = R = a;
for(int i = 1; i < n; i++){
tmp.resize(0); tmp.pb({INT_MAX, -1});
for(int j = 0; j < m; j++){
while(tmp.back().ff <= a[i][j])tmp.pop_back();
L[i][j] = tmp.back().ss;
tmp.pb({a[i][j], j});
}
tmp.resize(0); tmp.pb({INT_MAX, m});
for(int j = m-1; j > 0; j--){
while(tmp.back().ff <= a[i][j])tmp.pop_back();
R[i][j] = tmp.back().ss;
tmp.pb({a[i][j], j});
}
}
for(int j = 1; j < m; j++){
tmp.resize(0); tmp.pb({INT_MAX, -1});
for(int i = 0; i < n; i++){
while(tmp.back().ff <= a[i][j])tmp.pop_back();
U[i][j] = tmp.back().ss;
tmp.pb({a[i][j], i});
}
tmp.resize(0); tmp.pb({INT_MAX, n});
for(int i = n-1; i > 0; i--){
while(tmp.back().ff <= a[i][j])tmp.pop_back();
D[i][j] = tmp.back().ss;
tmp.pb({a[i][j], i});
}
}
u = new node<less<int>>(0, n-1, m-1, U), l = new node<less<int>>(0, n-1, m-1, L);
d = new node<greater<int>>(0, n-1, m-1, D), r = new node<greater<int>>(0, n-1, m-1, R);
for(int i = 1; i <= n-2; i++)
for(int j = 1; j <= m-2; j++){
if(U[i][j] < 0 || D[i][j] >= n || L[i][j] < 0 || R[i][j] >= m)goto next;
//cout << i << " " << j << " " << U[i][j] << D[i][j] << L[i][j] << R[i][j] << " " << u->query(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1) << endl;
if(u->query(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1) != U[i][j])goto next;
if(l->query(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1) != L[i][j])goto next;
if(d->query(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1) != D[i][j])goto next;
if(r->query(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1) != R[i][j])goto next;
st.insert({U[i][j], L[i][j], D[i][j], R[i][j]});
next:;
}
return st.size();
}
