// correct/BM_bigRec_N2log.cpp
#include "soccer.h"
#include <algorithm>
#include <set>
#include <vector>
#include <iostream>
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 upLeft[MAXN][MAXN];
int upRight[MAXN][MAXN];
int down[MAXN][MAXN];
int downLeft[MAXN][MAXN];
int downRight[MAXN][MAXN];
int sum[MAXN][MAXN];
int nxt[2][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;
down[i][j] = N - 1;
downLeft[i][j] = N - 1;
downRight[i][j] = N - 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];
}
for (int i = 0; i < N; i++)
{
nxt[0][i][N - 1] = nxt[1][i][N - 1] = N;
for (int j = N - 2; j >= 0; j--)
{
int nxt_elem = F[i][j + 1];
nxt[nxt_elem][i][j] = j + 1;
nxt[1 - nxt_elem][i][j] = nxt[1 - nxt_elem][i][j + 1];
}
}
bMost[0] = -1;
bMost[N - 1] = -1;
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 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 = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
up[i][j] = up[i - 1][j];
if (F[i][j] == 1)
{
up[i][j] = i;
}
else
{
upLeft[i][j] = max(upLeft[i][j - 1], up[i][j]);
}
}
for (int j = N - 2; j > 0; j--)
{
if (F[i][j] == 0)
{
upRight[i][j] = max(upRight[i][j + 1], up[i][j]);
}
}
}
for (int i = N - 2; i > 0; i--)
{
for (int j = 1; j < N - 1; j++)
{
down[i][j] = down[i + 1][j];
if (F[i][j] == 1)
{
down[i][j] = i;
}
else
{
downLeft[i][j] = min(downLeft[i][j - 1], down[i][j]);
}
}
for (int j = N - 2; j > 0; j--)
{
if (F[i][j] == 0)
{
downRight[i][j] = min(downRight[i][j + 1], down[i][j]);
}
}
}
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 upMax = 0, downMin = 0;
int x = h1 - 1;
while (x < h2)
{
int xx = nxt[0][v1 - 1][x];
int yy = (xx == N ? N : nxt[1][v1 - 1][xx] - 1);
x = yy;
int b = min(h2 + 1, yy + 1);
int a = max(h1 - 1, xx - 1);
// std::cerr<<v1<<" "<<v2<<" "<<h1<<" "<<h2<<" "<<a<<" "<<b<<"\n";
if (a + 1 < b)
{
if (a == h1 - 1)
{
upMax = upRight[v1 - 1][a + 1], downMin = downRight[v1 - 1][a + 1];
}
else
{
upMax = upLeft[v1 - 1][b - 1], downMin = downLeft[v1 - 1][b - 1];
}
int val1 = (b - a - 1) * N + (a + 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 * (b - a - 1));
}
}
x = h1 - 1;
while (x < h2)
{
int xx = nxt[0][v2 + 1][x];
int yy = (xx == N ? N : nxt[1][v2 + 1][xx] - 1);
x = yy;
int b = min(h2 + 1, yy + 1);
int a = max(h1 - 1, xx - 1);
// std::cerr<<v1<<" "<<v2<<" "<<h1<<" "<<h2<<" "<<a<<" "<<b<<"\n";
if (a + 1 < b)
{
if (a == h1 - 1)
{
upMax = upRight[v2 + 1][a + 1], downMin = downRight[v2 + 1][a + 1];
}
else
{
upMax = upLeft[v2 + 1][b - 1], downMin = downLeft[v2 + 1][b - 1];
}
int val1 = (b - a - 1) * N + (a + 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 * (b - a - 1));
}
}
// std::cerr<<v1<<" "<<v2<<" "<<h1<<" "<<h2<<" "<<maxi<<"!!\n";
ans[mId].second = maxi;
}
maxi = 0;
for (int i = 0; i < where; i++)
maxi = max(maxi, ans[i].second);
return maxi;
}
