#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<int16_t>> U, D, L, R, t, ans;
vector<vector<bool>> ansb;
vector<int16_t> dsu, sz, rtx;
inline void init(){ iota(all(dsu), 0); fill(all(sz), 1); iota(all(rtx), 0); }
int16_t root(int i){ return dsu[i] == i? i: dsu[i] = root(dsu[i]); }
inline void join(int16_t i, int16_t j){ i = root(i), j = root(j); int16_t u = j; if(sz[i] > sz[j])swap(i, j); dsu[i] = j; rtx[j] = u; }
struct node;
vector<node> nodes;
struct node{
int L, R;
int16_t l, r;
vector<vector<pair<int16_t, pair<int16_t, int16_t>>>> queries;
void init(int16_t ix, int16_t ll, int16_t rr, int16_t m){
queries.resize(m);
l = ll, r = rr;
if(l != r)L = ix*2, R = ix*2+1, nodes[L].init(L, l, l+r>>1, m), nodes[R].init(R, (l+r>>1)+1, r, m);
}
void add(int16_t ll, int16_t rr, int16_t l2, int16_t r2, int16_t x, int16_t y){
if(ll > r || rr < l)return;
if(ll <= l && r <= rr)queries[r2].pb({l2, {x, y}});
else nodes[L].add(ll, rr, l2, r2, x, y), nodes[R].add(ll, rr, l2, r2, x, y);
}
inline void answer(int l, const bool c){
::init(); tmp.resize(0);
for(int i = 0; i < t[l].size(); i++){
while(tmp.size() && (c?t[l][i] < tmp.back().ff:t[l][i]>tmp.back().ff))join(tmp.back().ss, i), tmp.pop_back();
tmp.pb({t[l][i], i});
for(auto p: queries[i]) //
if(ans[p.ss.ff][p.ss.ss] == -2 || (c?t[l][root(p.ff)]<ans[p.ss.ff][p.ss.ss]:t[l][root(p.ff)]>ans[p.ss.ff][p.ss.ss]))
ans[p.ss.ff][p.ss.ss] = t[l][rtx[root(p.ff)]];
}
}
void process(const bool c){
//cout << "process" << l << " " << r << endl;
if(l != r){
nodes[L].process(c), nodes[R].process(c);
for(int i = 0; i < t[l].size(); i++)
t[l][i] = (c?t[l][i]<t[(l+r>>1)+1][i]:t[l][i]>t[(l+r>>1)+1][i])?t[l][i]:t[(l+r>>1)+1][i];
}
answer(l, c);
//cout << "end_process" << l << " " << r << endl;
}
};
vector<tuple<int16_t, int16_t, int16_t, int16_t>> st;
long long count_rectangles(vector<vector<int>> a) {
int n = a.size(), m = a[0].size();
ans.resize(n); for(auto& i: ans)i.resize(m);
ansb.resize(n); for(auto& i: ansb)i.resize(m, 1);
dsu.resize(m); rtx.resize(m); sz.resize(m, 1);
U = D = L = R = ans;
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});
}
}
nodes.resize(4*m+10);
nodes[1].init(1, 0, n-1, m);
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))
nodes[1].add(U[i][j]+1, D[i][j]-1, L[i][j]+1, R[i][j]-1, i, j);
for(auto& i: ans)fill(all(i), -2); t = U, nodes[1].process(1); for(int i = 1; i <= n-2; i++) for(int j = 1; j <= m-2; j++) if(ans[i][j] != U[i][j])ansb[i][j] = false;
for(auto& i: ans)fill(all(i), -2); t = L, nodes[1].process(1); for(int i = 1; i <= n-2; i++) for(int j = 1; j <= m-2; j++) if(ans[i][j] != L[i][j])ansb[i][j] = false;
for(auto& i: ans)fill(all(i), -2); t = D, nodes[1].process(0); for(int i = 1; i <= n-2; i++) for(int j = 1; j <= m-2; j++) if(ans[i][j] != D[i][j])ansb[i][j] = false;
for(auto& i: ans)fill(all(i), -2); t = R, nodes[1].process(0); for(int i = 1; i <= n-2; i++) for(int j = 1; j <= m-2; j++) if(ans[i][j] != R[i][j])ansb[i][j] = false;
//cout << "hi" << endl;
//u.init(n, m), d.init(n, m), l.init(n, m), r.init(n, m);
for(int i = 1; i <= n-2; i++)
for(int j = 1; j <= m-2; j++)
if(ansb[i][j])
st.pb({U[i][j], L[i][j], D[i][j], R[i][j]});
sort(all(st));
return unique(all(st))-st.begin();
}
