#pragma GCC optimize("Ofast")
#ifndef EVAL
#include "grader.cpp"
#endif
#include "rect.h"
#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define F first
#define S second
using namespace std;
struct BIT
{
int bit[2500], N;
void init(int n)
{
N = n;
for (int i = 1; i <= N; i++)
bit[i] = 0;
}
void modify(int pos, int val)
{
for (int i = pos + 1; i <= N; i += (i & -i))
bit[i] += val;
}
int query(int pos)
{
int ans = 0;
for (int i = pos + 1; i; i -= (i & -i))
ans += bit[i];
return ans;
}
} bit[2500];
int N, M;
pii table[2500][2500];
vector<pii> ver[2500], hor[2500];
vector<tuple<int, int, int, int>> event[2500];
ll ans;
void add_query(int l, int r, pii range)
{
if (range == pii(-1, -1))
return;
// fprintf(stderr, "query i = %d time %d range (%d, %d)\n", l, r, range.F, range.S);
for (int i = range.F - 1; i <= range.S + 1; i++)
event[l].emplace_back(make_tuple(r, 0, i, range.S + 1));
}
void add_modify(pii range, int u, int d)
{
if (range == pii(-1, -1))
return;
// fprintf(stderr, "modify time range (%d, %d), up %d down %d\n", range.F, range.S, u, d);
for (int i = range.F - 1; i <= range.S + 1; i++)
event[i].emplace_back(make_tuple(range.S + 1, 1, u, d));
}
ll count_rectangles(vector<vector<int>> a)
{
N = a.size(), M = a[0].size();
if (N <= 2 || M <= 2)
return 0;
for (int i = 1; i + 1 < N; i++)
{
vector<pii> mono;
for (int j = 0; j < M; j++)
{
bool eq = 0;
while (!mono.empty() && mono.back().F <= a[i][j])
{
if(mono.back().F == a[i][j])
eq = 1;
if (j - mono.back().S >= 2)
ver[i].emplace_back(pii(mono.back().S, j));
mono.pop_back();
}
if (!mono.empty() && !eq)
if (j - mono.back().S >= 2)
ver[i].emplace_back(pii(mono.back().S, j));
mono.emplace_back(pii(a[i][j], j));
}
}
for (int i = 0; i < M; i++)
for (int j = 0; j < M; j++)
table[i][j] = pii(-1, -1);
for (int i = 1; i + 1 < N; i++)
for (auto [x, y] : ver[i])
if (table[x][y].S == i - 1)
table[x][y].S++;
else
{
add_query(x, y, table[x][y]);
table[x][y] = pii(i, i);
}
for (int i = 0; i < M; i++)
for (int j = 0; j < M; j++)
add_query(i, j, table[i][j]);
for (int i = 1; i + 1 < M; i++)
{
vector<pii> mono;
for (int j = 0; j < N; j++)
{
bool eq = 0;
while (!mono.empty() && mono.back().F <= a[j][i])
{
if(mono.back().F == a[j][i])
eq = 1;
if (j - mono.back().S >= 2)
hor[i].emplace_back(pii(mono.back().S, j));
mono.pop_back();
}
if (!mono.empty() && !eq)
if (j - mono.back().S >= 2)
hor[i].emplace_back(pii(mono.back().S, j));
mono.emplace_back(pii(a[j][i], j));
}
}
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
table[i][j] = pii(-1, -1);
for (int i = 1; i + 1 < M; i++)
for (auto [x, y] : hor[i])
if (table[x][y].S == i - 1)
table[x][y].S++;
else
{
add_modify(table[x][y], x, y);
table[x][y] = pii(i, i);
}
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
add_modify(table[i][j], i, j);
for (int i = 0; i < N; i++)
bit[i].init(N);
for (int i = 0; i < M; i++)
{
sort(event[i].begin(), event[i].end(), greater<>());
for (auto [_, t, l, r] : event[i])
{
if (t == 1)
bit[l].modify(r, 1);
else
ans += bit[l].query(r);
}
for (auto [_, t, l, r] : event[i])
if (t == 1)
bit[l].modify(r, -1);
}
return ans;
}
