#include "rect.h"
#include <vector>
#include <iostream>
#include <algorithm>
#define int long long
using namespace std;
struct fenw
{
int n;
vector<int> table;
int query(int k)
{
int res = 0;
for (; k; k -= (k & (-k))) res += table[k];
return res;
}
void update(int k, int v)
{
k++;
for (; k <= n; k += (k & (-k))) table[k] += v;
}
fenw(int in) : n(in), table(vector<int>(n + 1)) {}
};
struct bord
{
int a, b;
int st, en;
bool operator<(const bord& ot)
const {
if (a != ot.a) return a < ot.a;
if (b != ot.b) return b < ot.b;
if (st != ot.st) return st < ot.st;
return en < ot.en;
}
};
vector<bord> compress(vector<bord> ip)
{
vector<bord> res;
sort(ip.begin(), ip.end());
for (auto gp : ip)
{
if (res.empty() || res.back().a != gp.a || res.back().b != gp.b || res.back().en + 1 != gp.st) res.push_back(gp);
else res.back().en = gp.en;
}
return res;
}
int count(vector<pair<int,int>> a, vector<pair<int,int>> b)
{
sort(a.begin(), a.end());
sort(b.begin(), b.end());
auto b2 = b;
for (auto &p : b2) swap(p.first, p.second);
sort(b2.begin(), b2.end());
for (auto &p : b2) swap(p.first, p.second);
fenw f(b.size());
int res = 0;
int s = 0;
for (int i = 0; i < (int)a.size(); i++)
{
while (s < (int)b2.size() && b2[s].second <= a[i].first)
{
int id = lower_bound(b.begin(), b.end(), b2[i]) - b.begin();
f.update(id, 1);
s++;
}
int lb = lower_bound(b.begin(), b.end(), make_pair(a[i].second, -1000ll)) - b.begin();
res += f.query(b.size()) - f.query(lb);
}
return res;
}
int count_rectangles(vector<vector<signed>> ip)
{
int r = ip.size();
int c = ip[0].size();
vector<bord> hor;
vector<bord> ver;
for (int y = 0; y < r; y++)
{
vector<pair<int,int>> st;
for (int x = 0; x < c; x++)
{
int sts = st.size();
for (int i = sts - 1; i >= 0; i--)
{
if (st[i].first + 1 < x) hor.push_back(bord{st[i].first, x, y, y});
if (st[i].second >= ip[y][x]) break;
}
while (!st.empty() && st.back().second <= ip[y][x]) st.pop_back();
st.emplace_back(x, ip[y][x]);
}
}
for (int x = 0; x < c; x++)
{
vector<pair<int,int>> st;
for (int y = 0; y < r; y++)
{
int sts = st.size();
for (int i = sts - 1; i >= 0; i--)
{
if (st[i].first + 1 < y) ver.push_back(bord{st[i].first, y, x, x});
if (st[i].second >= ip[y][x]) break;
}
while (!st.empty() && st.back().second <= ip[y][x]) st.pop_back();
st.emplace_back(y, ip[y][x]);
}
}
hor = compress(hor);
ver = compress(ver);
vector<vector<vector<int>>> lw(r, vector<vector<int>>(c));
vector<vector<vector<int>>> rg(r, vector<vector<int>>(c));
for (int i = 0; i < (int)hor.size(); i++)
{
for (int j = hor[i].st; j <= hor[i].en; j++)
{
rg[j][hor[i].b - 1].push_back(i);
}
}
for (int i = 0; i < (int)ver.size(); i++)
{
for (int j = ver[i].st; j <= ver[i].en; j++)
{
lw[ver[i].b - 1][j].push_back(i);
}
}
int res = 0;
for (int i = 0; i < r; i++)
{
for (int j = 0; j < c; j++)
{
vector<pair<int,int>> nhor;
vector<pair<int,int>> nver;
for (auto k : lw[i][j]) nver.emplace_back(j - ver[k].st + 1, ver[k].b - ver[k].a - 1);
for (auto k : rg[i][j]) nhor.emplace_back(i - hor[k].st + 1, hor[k].b - hor[k].a - 1);
res += count(nhor, nver);
}
}
return res;
}
