#include<bits/stdc++.h>
#include "rect.h"
using namespace std;
using ll = long long;
struct SegTree {
static const int N = (1 << 12);
vector<bool> t;
SegTree() {
t.assign(2 * N, false);
}
void insert(int pos) {
for(t[pos += N] = true; pos > 1; pos >>= 1)
t[pos >> 1] = true;
}
int right(int x, int l = 0, int r = N - 1, int v = 1) {
if(r < x || !t[v]) return -1;
if(l == r) return l;
int mid = (l + r) / 2;
int res = right(x, l, mid, 2 * v);
if(res == -1) res = right(x, mid + 1, r, 2 * v + 1);
return res;
}
int left(int x, int l = 0, int r = N - 1, int v = 1) {
if(l > x || !t[v]) return -1;
if(l == r) return l;
int mid = (l + r) / 2;
int res = left(x, mid + 1, r, 2 * v + 1);
if(res == -1) res = left(x, l, mid, 2 * v);
return res;
}
};
struct FenwickTree {
vector<int> bit; // binary indexed tree
int n;
FenwickTree(int n) {
this->n = n;
bit.assign(n, 0);
}
FenwickTree(vector<int> const &a) : FenwickTree(a.size()) {
for (size_t i = 0; i < a.size(); i++)
add(i, a[i]);
}
int sum(int r) {
int ret = 0;
for (; r >= 0; r = (r & (r + 1)) - 1)
ret += bit[r];
return ret;
}
int sum(int l, int r) {
return sum(r) - sum(l - 1);
}
void add(int idx, int delta) {
for (; idx < n; idx = idx | (idx + 1))
bit[idx] += delta;
}
};
// O(nlogn)
SegTree sg;
vector<pair<int, int>> get_segments(vector<int> a) {
int n = (int)a.size();
vector<pair<int, int>> b;
vector<pair<int, int>> res;
for(int i = 0; i < n; i++) {
b.push_back({a[i], i});
}
sort(b.rbegin(), b.rend());
int l = 0;
while(l < n) {
int r = l;
while(r < n && b[r].first == b[l].first) ++r;
for(int i = l; i < r; i++)
sg.insert(b[i].second);
for(int i = l; i < r; i++) {
int pos = b[i].second;
int rb = sg.right(pos + 1), lb = sg.left(pos - 1);
if(rb != -1 && rb - pos > 1)
res.push_back({pos + 1, rb - 1});
if(lb != -1 && pos - lb > 1 && (i == r - 1 || b[i + 1].second != lb))
res.push_back({lb + 1, pos - 1});
}
l = r;
}
sg = SegTree();
return res;
}
const int N = 2505;
struct segment {
int l, d;
};
vector<segment> h[N][N], g[N][N];
ll count_rectangles(vector<vector<int>> a) {
int n = (int)a.size(), m = (int)a[0].size();
if(n < 3 || m < 3) return 0;
for(int i = 0; i < n; i++) {
vector<pair<int, int>> s = get_segments(a[i]);
for(auto [l, r] : s)
g[i][r].push_back({l, 0});
}
for(int i = 0; i < m; i++) {
vector<int> b;
for(int j = 0; j < n; j++)
b.push_back(a[j][i]);
vector<pair<int, int>> s = get_segments(b);
for(auto [l, r] : s)
h[r][i].push_back({l, 0});
}
for(int i = 0; i < n; i++) {
int cnt[n] = {};
bool us[n] = {};
for(int j = 0; j < m; j++) {
if(!j) {
for(auto c : h[i][j])
cnt[c.l]++;
} else {
for(auto c : h[i][j])
us[c.l] = 1;
for(auto c : h[i][j - 1])
if(!us[c.l]) cnt[c.l] = 0;
for(auto c : h[i][j]) {
cnt[c.l]++;
us[c.l] = 0;
}
}
for(auto &c : h[i][j]) {
c.d = cnt[c.l];
}
}
}
for(int i = 0; i < m; i++) {
int cnt[m] = {};
bool us[m] = {};
for(int j = 0; j < n; j++) {
if(!j) {
for(auto c : g[j][i])
cnt[c.l]++;
} else {
for(auto c : g[j][i])
us[c.l] = 1;
for(auto c : g[j - 1][i])
if(!us[c.l])
cnt[c.l] = 0;
for(auto c : g[j][i]) {
cnt[c.l]++;
us[c.l] = 0;
}
}
for(auto &c : g[j][i])
c.d = cnt[c.l];
}
}
ll ans = 0;
FenwickTree st(n);
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
sort(h[i][j].begin(), h[i][j].end(), [](segment x, segment y) {return x.d > y.d;});
int h_l = 0;
for(segment cur : g[i][j]) {
while(h_l < (int)h[i][j].size() && j - h[i][j][h_l].d < cur.l) {
st.add(h[i][j][h_l++].l, +1);
}
ans += st.sum(i - cur.d + 1, i);
}
while(h_l > 0)
st.add(h[i][j][--h_l].l, -1);
}
}
return ans;
}
