#include "rect.h"
#include <bits/stdc++.h>
#define int long long
using namespace std;
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 len > other.len;
return fst < other.fst;
}
};
vector<goodPair> pairsLig[MAXN], pairsCol[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, (int)1e18}) -
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, (int)1e18}) -
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;
}
}
long long count_rectangles(vector<vector<signed>> a) {
height = a;
nbLig = a.size(), nbCol = a[0].size();
precompute();
int sol = 0;
for (int iLig = 0; iLig < nbLig; ++iLig)
for (auto [fstLig, sndLig, lenLig] : pairsLig[iLig]) {
int id = lower_bound(pairsCol[fstLig].begin(), pairsCol[fstLig].end(),
goodPair{iLig, 0, (int)1e18}) -
pairsCol[fstLig].begin();
for (; id < (int)pairsCol[fstLig].size() and
pairsCol[fstLig][id].fst == iLig and
pairsCol[fstLig][id].len >= sndLig - fstLig + 1;
++id) {
auto [fstCol, sndCol, lenCol] = pairsCol[fstLig][id];
if (lenLig >= sndCol - fstCol + 1)
sol++;
}
}
return sol;
}
