// correct/BM_bigRec_N3log.cpp
#include "soccer.h"
#include <algorithm>
#include <set>
#include <vector>
using namespace std;
const int MAXN = 3202;
int N, maxi, where;
int F[MAXN][MAXN];
int bMost[MAXN];
int id[MAXN];
set<int> block;
pair<pair<int, int>, int> ans[MAXN * MAXN];
int up[MAXN][MAXN];
int down[MAXN][MAXN];
int sum[MAXN][MAXN];
bool small(int x, int y)
{
return bMost[x] > bMost[y];
}
int biggest_stadium(int NN, std::vector<std::vector<int>> FF)
{
N = NN;
N += 2;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
F[i][j] = 1;
id[i] = i;
}
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
F[i][j] = FF[i - 1][j - 1];
}
bMost[0] = -1;
bMost[N - 1] = -1;
for (int j = 0; j < N; j++)
down[N - 1][j] = N - 1;
for (int i = 1; i < N - 1; i++)
{
for (int j = 0; j < N; j++)
{
up[i][j] = up[i - 1][j];
down[N - 1 - i][j] = down[N - i][j];
if (F[i][j] == 1)
up[i][j] = i;
if (F[N - 1 - i][j] == 1)
down[N - 1 - i][j] = N - 1 - i;
}
}
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
sum[i][j] = F[i][j];
if (j != 0)
sum[i][j] += sum[i][j - 1];
}
}
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
if (F[i][j] == 1)
bMost[j] = i;
}
std::sort(id + 1, id + N - 1, small);
block.clear();
block.insert(0);
block.insert(N - 1);
for (int j = 1; j < N - 1; j++)
{
int pos = id[j];
if (bMost[pos] != i)
{
auto it = block.lower_bound(pos);
int b = (*it);
it--;
int a = (*it);
int v = i - bMost[pos], h = b - a - 1;
if (bMost[a] != bMost[pos] && bMost[b] != bMost[pos] && sum[i + 1][b - 1] - sum[i + 1][a] >= 1)
{
ans[where++] = {{h * N + (a + 1), v * N + (bMost[pos] + 1)}, v * h};
}
}
block.insert(pos);
}
}
sort(ans, ans + where);
for (int mId = 0; mId < where; mId++)
{
auto i = ans[mId];
maxi = i.second;
int h1 = i.first.first % N, h2 = i.first.first % N + i.first.first / N - 1;
int v1 = i.first.second % N, v2 = i.first.second % N + i.first.second / N - 1;
int last = h1 - 1, upMax = 0, downMin = N - 1;
for (int j = h1; j <= h2 + 1; j++)
{
if (j == h2 + 1 || F[v1 - 1][j] == 1)
{
if (last + 1 < j)
{
int val1 = (j - last - 1) * N + (last + 1), val2 = (downMin - upMax - 1) * N + (upMax + 1);
int l = 0, r = mId - 1;
while (l != r)
{
int half = (l + r) / 2;
if (ans[half].first.first < val1 || (ans[half].first.first == val1 && ans[half].first.second < val2))
{
l = half + 1;
}
else
{
r = half;
}
}
const auto &k = ans[l];
if (k.first.first != val1 || k.first.second != val2)
continue;
maxi = max(maxi, i.second + k.second - i.first.second / N * (j - last - 1));
}
last = j;
upMax = 0, downMin = N - 1;
}
else
{
upMax = max(upMax, up[v1][j]);
downMin = min(downMin, down[v1][j]);
}
}
last = h1 - 1, upMax = 0, downMin = N - 1;
for (int j = h1; j <= h2 + 1; j++)
{
if (j == h2 + 1 || F[v2 + 1][j] == 1)
{
if (last + 1 < j)
{
int val1 = (j - last - 1) * N + (last + 1), val2 = (downMin - upMax - 1) * N + (upMax + 1);
int l = 0, r = mId - 1;
while (l != r)
{
int half = (l + r) / 2;
if (ans[half].first.first < val1 || (ans[half].first.first == val1 && ans[half].first.second < val2))
{
l = half + 1;
}
else
{
r = half;
}
}
const auto &k = ans[l];
if (k.first.first != val1 || k.first.second != val2)
continue;
maxi = max(maxi, i.second + k.second - i.first.second / N * (j - last - 1));
}
last = j;
upMax = 0, downMin = N - 1;
}
else
{
upMax = max(upMax, up[v1][j]);
downMin = min(downMin, down[v1][j]);
}
}
ans[mId].second = maxi;
}
maxi = 0;
for (int i = 0; i < where; i++)
maxi = max(maxi, ans[i].second);
return maxi;
}
