#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define UP 0
#define LEFT 1
#define DOWN 2
#define RIGHT 3
struct SparseTable {
static const int LG = 13;
int n;
vector<array<int, LG>> st;
SparseTable() {}
SparseTable(vector<int> v) : n(v.size()) {
st.resize(n);
for (int i = 0; i < n; ++i) st[i][0] = v[i];
for (int j = 1; j < LG; ++j) {
for (int i = 0; i + (1 << j) <= n; ++i) {
st[i][j] = max(st[i][j-1], st[i + (1 << (j-1))][j-1]);
}
}
}
int query(int l, int r) {
// [l, r)
int lg = 31 - __builtin_clz(r - l);
return max(st[l][lg], st[r - (1 << lg)][lg]);
}
};
vector<int> next_geq_val(vector<int> v) {
int n = v.size();
stack<pair<int, int>> st;
st.push({1e9, n});
vector<int> ans(n);
for (int i = n-1; i >= 0; --i) {
while (st.top().first < v[i]) st.pop();
ans[i] = st.top().second;
st.push({v[i], i});
}
return ans;
}
vector<int> prev_geq_val(vector<int> v) {
int n = v.size();
reverse(v.begin(), v.end());
auto r = next_geq_val(v);
reverse(r.begin(), r.end());
for (int& i : r) {
i = n - 1 - i;
}
return r;
}
LL count_rectangles(vector<vector<int>> a) {
int n = a.size();
int m = a[0].size();
vector<vector<array<int, 4>>> ext(n, vector<array<int, 4>>(m));
// LEFT & RIGHT
for (int i = 0; i < n; ++i) {
auto v = a[i];
auto nxt = next_geq_val(v);
auto prv = prev_geq_val(v);
for (int j = 0; j < m; ++j) {
ext[i][j][LEFT] = prv[j];
ext[i][j][RIGHT] = nxt[j];
}
}
// UP & DOWN
for (int j = 0; j < m; ++j) {
vector<int> v(n);
for (int i = 0; i < n; ++i) v[i] = a[i][j];
auto nxt = next_geq_val(v);
auto prv = prev_geq_val(v);
for (int i = 0; i < n; ++i) {
ext[i][j][UP] = prv[i];
ext[i][j][DOWN] = nxt[i];
}
}
vector<SparseTable> strow(n);
vector<SparseTable> stcol(m);
for (int i = 0; i < n; ++i) {
vector<int> v(m);
for (int j = 0; j < m; ++j) {
v[j] = ext[i][j][UP];
}
strow[i] = SparseTable(v);
}
for (int j = 0; j < m; ++j) {
vector<int> v(n);
for (int i = 0; i < n; ++i) {
v[i] = ext[i][j][LEFT];
}
stcol[j] = SparseTable(v);
}
LL ans = 0;
for (int r = 0; r < n; ++r) for (int c = 0; c < m; ++c) {
int rwall = m-1;
for (int rr = r+2; rr < n; ++rr) {
rwall = min(rwall, ext[rr-1][c][RIGHT]);
int dwall = n-1;
for (int cc = c+2; cc <= rwall; ++cc) {
dwall = min(dwall, ext[r][cc-1][DOWN]);
if (rr > dwall) break;
bool works = true;
// orizzontali
works &= (strow[rr].query(c+1, cc) <= r);
/*
for (int j = c+1; works && j < cc; ++j) {
// works &= (ext[r][j][DOWN] >= rr);
works &= (ext[rr][j][UP] <= r);
}
*/
// verticali
works &= (stcol[cc].query(r+1, rr) <= c);
/*
for (int i = r+1; works && i < rr; ++i) {
// works &= (ext[i][c][RIGHT] >= cc);
works &= (ext[i][cc][LEFT] <= c);
}
*/
ans += works;
}
}
}
return ans;
}
