#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
template <class T> class Fenwick {
public:
int lim;
vector<T> bit;
Fenwick(int n) : lim(n + 1), bit(lim) {}
void upd(int pos, T val) {
for (pos++; pos < lim; pos += pos & -pos)
bit[pos] += val;
}
T sum(int r) { // < r
T ret = 0;
for (; r; r -= r & -r)
ret += bit[r];
return ret;
}
T sum(int l, int r) { // [l, r)
return sum(r) - sum(l);
}
};
const int MAXN = 2500;
int nbLig, nbCol;
struct goodPair {
int fst, snd, len;
goodPair(int l, int r) : fst(l), snd(r), len(1) {}
goodPair(int l, int r, int le) : fst(l), snd(r), len(le) {}
bool operator<(goodPair other) const {
if (fst == other.fst)
return snd < other.snd;
return fst < other.fst;
}
};
vector<goodPair> pairsLig[MAXN], pairsCol[MAXN];
vector<pair<int, int>> columns[MAXN][MAXN], lines[MAXN][MAXN];
vector<vector<signed>> height;
void precompute() {
for (int iLig = 1; iLig < nbLig - 1; ++iLig) {
vector<int> good;
for (int iCol = 0; iCol < nbCol; ++iCol) {
while (!good.empty() and height[iLig][good.back()] < height[iLig][iCol]) {
if (good.back() + 1 < iCol)
pairsLig[iLig].emplace_back(good.back() + 1, iCol - 1);
good.pop_back();
}
if (!good.empty()) {
if (good.back() + 1 < iCol)
pairsLig[iLig].emplace_back(good.back() + 1, iCol - 1);
if (height[iLig][good.back()] == height[iLig][iCol])
good.pop_back();
}
good.push_back(iCol);
}
sort(pairsLig[iLig].begin(), pairsLig[iLig].end());
}
for (int iCol = 1; iCol < nbCol - 1; ++iCol) {
vector<int> good;
for (int iLig = 0; iLig < nbLig; ++iLig) {
while (!good.empty() and height[good.back()][iCol] < height[iLig][iCol]) {
if (good.back() + 1 < iLig)
pairsCol[iCol].emplace_back(good.back() + 1, iLig - 1);
good.pop_back();
}
if (!good.empty()) {
if (good.back() + 1 < iLig)
pairsCol[iCol].emplace_back(good.back() + 1, iLig - 1);
if (height[good.back()][iCol] == height[iLig][iCol])
good.pop_back();
}
good.push_back(iLig);
}
sort(pairsCol[iCol].begin(), pairsCol[iCol].end());
}
for (int iLig = nbLig - 2; iLig >= 0; --iLig)
for (auto &[fst, snd, len] : pairsLig[iLig]) {
int id = lower_bound(pairsLig[iLig + 1].begin(), pairsLig[iLig + 1].end(),
goodPair{fst, snd, 0}) -
pairsLig[iLig + 1].begin();
if (id < (int)pairsLig[iLig + 1].size() and
pairsLig[iLig + 1][id].fst == fst and
pairsLig[iLig + 1][id].snd == snd)
len = 1 + pairsLig[iLig + 1][id].len;
}
for (int iCol = nbCol - 2; iCol >= 0; --iCol)
for (auto &[fst, snd, len] : pairsCol[iCol]) {
int id = lower_bound(pairsCol[iCol + 1].begin(), pairsCol[iCol + 1].end(),
goodPair{fst, snd, 0}) -
pairsCol[iCol + 1].begin();
if (id < (int)pairsCol[iCol + 1].size() and
pairsCol[iCol + 1][id].fst == fst and
pairsCol[iCol + 1][id].snd == snd)
len = 1 + pairsCol[iCol + 1][id].len;
}
for (int iLig = 0; iLig < nbLig; ++iLig)
for (auto [fst, snd, len] : pairsLig[iLig])
lines[iLig][fst].emplace_back(snd - fst + 1, len);
for (int iCol = 0; iCol < nbCol; ++iCol)
for (auto [fst, snd, len] : pairsCol[iCol])
columns[fst][iCol].emplace_back(snd - fst + 1, len);
}
long long count_rectangles(vector<vector<signed>> a) {
height = a;
nbLig = a.size(), nbCol = a[0].size();
precompute();
int sol = 0;
Fenwick<int> fen(MAXN + 1);
for (int iLig = 0; iLig < nbLig; ++iLig)
for (int iCol = 0; iCol < nbCol; ++iCol) {
sort(columns[iLig][iCol].begin(), columns[iLig][iCol].end(),
[](pair<int, int> lft, pair<int, int> rgt) {
return lft.second < rgt.second;
});
sort(lines[iLig][iCol].begin(), lines[iLig][iCol].end());
int curCol = (int)columns[iLig][iCol].size() - 1;
for (int idLig = (int)lines[iLig][iCol].size() - 1; idLig >= 0; --idLig) {
while (curCol >= 0 and columns[iLig][iCol][curCol].second >=
lines[iLig][iCol][idLig].first)
fen.upd(columns[iLig][iCol][curCol--].first, 1);
sol += fen.sum(1 + lines[iLig][iCol][idLig].second);
}
while (curCol + 1 < (int)columns[iLig][iCol].size()) {
fen.upd(columns[iLig][iCol][++curCol].first, -1);
}
/*for (auto [a, b] : lines[iLig][iCol])
for (auto [c, d] : columns[iLig][iCol])
sol += a <= d and c <= b;*/
}
return sol;
}
