#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[2505], 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++)
{
set<int> st;
vector<int> o;
for (int j = 0; j < M; j++)
o.emplace_back(j);
sort(o.begin(), o.end(), [&](int j, int k)
{ return pii(a[i][j], -j) > pii(a[i][k], -k); });
for (int j = 0; j < M; j++)
{
auto iter = st.insert(o[j]).F;
if (iter != st.begin())
if (*prev(iter) + 2 <= *iter)
ver[i].emplace_back(pii(*prev(iter), *iter));
if (next(iter) != st.end() && !(j + 1 < M && a[i][o[j]] == a[i][o[j + 1]] && o[j + 1] < *next(iter)))
if (*iter + 2 <= *next(iter))
ver[i].emplace_back(pii(*iter, *next(iter)));
}
}
// for (int i = 1; i + 1 < N; i++)
// for (auto [x, y] : ver[i])
// cout << i << ' ' << x << ' ' << y << '\n';
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++)
{
set<int> st;
vector<int> o;
for (int j = 0; j < N; j++)
o.emplace_back(j);
sort(o.begin(), o.end(), [&](int j, int k)
{ return pii(a[j][i], -j) > pii(a[k][i], -k); });
for (int j = 0; j < N; j++)
{
auto iter = st.insert(o[j]).F;
if (iter != st.begin())
if (*prev(iter) + 2 <= *iter)
hor[i].emplace_back(pii(*prev(iter), *iter));
if (next(iter) != st.end() && !(j + 1 < N && a[o[j]][i] == a[o[j + 1]][i] && o[j + 1] < *next(iter)))
if (*iter + 2 <= *next(iter))
hor[i].emplace_back(pii(*iter, *next(iter)));
}
}
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;
}
