#include "bits/stdc++.h"
using namespace std;
struct Point {
int x, y;
Point(int x, int y): x(x), y(y) {}
};
bool operator<(const Point &a, const Point &b) {
return a.x < b.x || (a.x == b.x && a.y < b.y);
}
int biggest_stadium(int N, vector<vector<int>> F) {
int num_trees = 0;
for (auto i: F) for (int j: i) num_trees += j;
if (num_trees == 0) {
return N*N;
}
if (num_trees == 1) {
int x, y;
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)
if (F[i][j] == 1) {
x = i, y = j;
break;
}
return N*N - min(x + 1, N - x) * min(y + 1, N - y);
}
for (int i = 0; i < N; i++) {
F[i].insert(F[i].begin(), 1);
F[i].push_back(1);
}
F.insert(F.begin(), vector<int>(N + 2, 1));
F.push_back(vector<int>(N + 2, 1));
N += 2;
if (N <= 10) {
vector<vector<set<Point>>> quads[4];
for (auto &q: quads) q.resize(N, vector<set<Point>>(N, set<Point>()));
// index, dx, dy, starting x, starting y, x increment, y increment
int m = N - 1;
int quad_dirs[4][7] = {
{0, -1, -1, 0, 0, 1, 1},
{1, -1, 1, 0, m, 1, -1},
{2, 1, 1, m, m, -1, -1},
{3, 1, -1, m, 0, -1, 1}
};
for (auto [idx, dx, dy, sx, sy, ix, iy]: quad_dirs) {
for (int i = sx; i < N && i >= 0; i += ix) for (int j = sy; j < N && j >= 0; j += iy) {
if (F[i][j] == 1) continue;
int a[2] = {i + dx, j};
int b[2] = {i, j + dy};
if (F[a[0]][a[1]] == 0)
for (auto p: quads[idx][a[0]][a[1]]) if (p.y == j) quads[idx][i][j].insert(p);
if (F[b[0]][b[1]] == 0)
for (auto p: quads[idx][b[0]][b[1]]) if (p.x == i) quads[idx][i][j].insert(p);
quads[idx][i][j].insert(Point(i, j));
}
}
vector<vector<set<Point>>> lines = vector<vector<set<Point>>>(N, vector<set<Point>>(N, set<Point>()));
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
for (int k = 0; k < 4; k++)
for (auto p: quads[k][i][j]) lines[i][j].insert(p);
for (auto [idx, dx, dy, sx, sy, ix, iy]: quad_dirs) {
for (int i = sx; i < N && i >= 0; i += ix) for (int j = sy; j < N && j >= 0; j += iy) {
if (F[i][j] == 1) continue;
int a[2] = {i + dx, j};
int b[2] = {i, j + dy};
if (F[a[0]][a[1]] == 1 || F[b[0]][b[1]] == 1) continue;
set<Point> temp;
set_intersection(quads[idx][a[0]][a[1]].begin(), quads[idx][a[0]][a[1]].end(),
quads[idx][b[0]][b[1]].begin(), quads[idx][b[0]][b[1]].end(),
inserter(temp, temp.begin()));
for (auto p: temp) quads[idx][i][j].insert(p);
}
}
int max_area = 0;
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
if (F[i][j] == 1) continue;
auto print_union = [&](set<Point> &a, set<Point> &b, set<Point> &c) {
// return;
set<Point> t;
for (auto p: a) t.insert(p);
for (auto p: b) t.insert(p);
for (auto p: c) t.insert(p);
for (int x = 0; x < N; x++) {
for (int y = 0; y < N; y++) {
if (x == i && y == j) cerr << "X ";
else cerr << (t.count(Point(x, y)) ? 'x' : (F[x][y] ? '-': ' ')) << " ";
}
cerr << endl;
}
cerr << endl;
};
auto union_size = [&](set<Point> &a, set<Point> &b, set<Point> &c) {
set<Point> t;
for (auto p: a) t.insert(p);
for (auto p: b) t.insert(p);
for (auto p: c) t.insert(p);
vector<pair<int, int>> rows = vector<pair<int, int>>(N, {N, 0});
int max_row_len = 0;
for (auto p: t) {
rows[p.x].first = min(rows[p.x].first , p.y);
rows[p.x].second = max(rows[p.x].second, p.y);
max_row_len = max(max_row_len, rows[p.x].second - rows[p.x].first);
}
int max_row_beg = N, max_row_end = 0;
for (int i = 0; i < N; i++) {
if (rows[i].first == 0 && rows[i].second == N) continue;
if (rows[i].second - rows[i].first == max_row_len) {
max_row_beg = min(max_row_beg, i);
max_row_end = max(max_row_end, i);
}
}
int max_ext_len = 0;
int best_i = 0;
for (int i = max_row_beg; i <= max_row_end; i++) {
// try to see if it's extendable
set<Point> l_ext;
for (auto p: quads[0][i][rows[i].first - 1]) if (p.x >= max_row_beg) l_ext.insert(p);
for (auto p: quads[3][i][rows[i].first - 1]) if (p.x <= max_row_end) l_ext.insert(p);
set<Point> r_ext;
for (auto p: quads[1][i][rows[i].second + 1]) if (p.x >= max_row_beg) r_ext.insert(p);
for (auto p: quads[2][i][rows[i].second + 1]) if (p.x <= max_row_end) r_ext.insert(p);
if (r_ext.size() + l_ext.size() > max_ext_len) {
// set<Point> s;
// for (auto p: r_ext) s.insert(p);
// for (auto p: l_ext) s.insert(p);
deque<Point> vec_r = deque<Point>(r_ext.begin(), r_ext.end());
deque<Point> vec_l = deque<Point>(l_ext.begin(), l_ext.end());
sort(vec_r.begin(), vec_r.end());
sort(vec_l.begin(), vec_l.end(), [](Point a, Point b) {
return a.x > b.x || (a.x == b.x && a.y > b.y);
});
while (vec_r.size() && vec_l.size()) {
Point r = vec_r.back();
Point l = vec_l.back();
if (r_ext.count(Point(l.x, r.y)) && l_ext.count(Point(r.x, l.y))) {
break;
} else {
if (rows[max_row_beg].first - r.y > l.y - rows[max_row_beg].second) {
vec_l.pop_back();
} else {
vec_r.pop_back();
}
}
}
sort(vec_r.begin(), vec_r.end(), [](Point a, Point b) {
return a.x > b.x;
});
sort(vec_l.begin(), vec_l.end(), [](Point a, Point b) {
return a.x < b.x;
});
while (vec_r.size() && vec_l.size()) {
Point r = vec_r.back();
Point l = vec_l.back();
if (r_ext.count(Point(l.x, r.y)) && l_ext.count(Point(r.x, l.y))) {
break;
} else {
if (rows[max_row_beg].first - r.y > l.y - rows[max_row_beg].second) {
vec_l.pop_back();
} else {
vec_r.pop_back();
}
}
}
if (vec_r.size() + vec_l.size() > max_ext_len) {
max_ext_len = vec_r.size() + vec_l.size();
best_i = i;
}
}
}
int size = t.size() + max_ext_len;
// if (size == 6) {
// cerr << "ext" << endl;
// cerr << max_row_beg << " " << max_row_end << endl;
// set<Point> e = set<Point>();
// int i = best_i;
// print_union(quads[0][i][rows[i].first - 1], e, e);
// print_union(quads[3][i][rows[i].first - 1], e, e);
// print_union(quads[1][i][rows[i].second + 1], e, e);
// print_union(quads[2][i][rows[i].second + 1], e, e);
// print_union(max_ext, max_ext, max_ext);
// print_union(t, t, t);
// print_union(t, max_ext, max_ext);
// }
return size;
};
auto extreme = [&](set<Point> &t) {
int minx = N, maxx = 0, miny = N, maxy = 0;
for (auto p: t) {
minx = min(minx, p.x);
maxx = max(maxx, p.x);
miny = min(miny, p.y);
maxy = max(maxy, p.y);
}
vector<Point> res;
for (auto p: t) {
if (p.x == minx || p.x == maxx || p.y == miny || p.y == maxy) res.push_back(p);
}
return res;
};
for (int k = 0; k < 4; k++) {
int a = k, b = (k + 1) % 4, c = (k + 2) % 4;
vector<Point> a_extreme = extreme(quads[a][i][j]);
vector<Point> c_extreme = extreme(quads[c][i][j]);
bool possible = true;
for (auto ap: a_extreme) for (auto cp: c_extreme) {
if (ap.x == cp.x && ap.y == cp.y) continue;
if (!(
quads[b][i][j].count(Point(ap.x, cp.y)) ||
quads[b][i][j].count(Point(cp.x, ap.y))
)) {
possible = false;
break;
}
}
if (possible) {
int area = union_size(quads[a][i][j], quads[b][i][j], quads[c][i][j]);
if (area > max_area) {
max_area = area;
print_union(quads[a][i][j], quads[b][i][j], quads[c][i][j]);
// for (auto p: a_extreme) cerr << p.x << " " << p.y << endl;
// cerr << endl;
// for (auto p: c_extreme) cerr << p.x << " " << p.y << endl;
// cerr << endl;
set<Point> t;
print_union(quads[a][i][j], t, t);
print_union(t, quads[b][i][j], t);
print_union(t, t, quads[c][i][j]);
}
}
}
for (int k = 0; k < 4; k++) {
int area = union_size(quads[k][i][j], quads[(k + 1) % 4][i][j], lines[i][j]);
if (area > max_area) {
max_area = area;
print_union(quads[k][i][j], quads[(k + 1) % 4][i][j], lines[i][j]);
}
}
}
return max_area;
}
// for (auto row: F) {
// bool beg = false, end = false;
// for (int i: row) {
// if (i == 0 && !beg) beg = true;
// if (i == 1 && beg) end = true;
// if (i == 0 && end) return 0;
// }
// }
bool beg, end;
for (int i = 0; i < N; i++) {
beg = false, end = false;
for (int j = 0; j < N; j++) {
if (F[j][i] == 0 && !beg) beg = true;
if (F[j][i] == 1 && beg) end = true;
if (F[j][i] == 0 && end) return 0;
}
beg = false, end = false;
for (int j = 0; j < N; j++) {
if (F[i][j] == 0 && !beg) beg = true;
if (F[i][j] == 1 && beg) end = true;
if (F[i][j] == 0 && end) return 0;
}
}
auto valid = [&](int n) {
return n >= 0 && n < N;
};
int dirs[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
vector<vector<bool>> seen(N, vector<bool>(N, false));
queue<tuple<int, int, bool>> q;
bool f1 = false, f0 = false;
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
if (!f1 && F[i][j] == 1)
q.push({i, j, 1}), f1 = 1, seen[i][j] = true;
if (!f0 && F[i][j] == 0)
q.push({i, j, 0}), f0 = 1, seen[i][j] = true;
}
while (!q.empty()) {
auto [x, y, t] = q.front();
q.pop();
for (auto [dx, dy]: dirs) {
int nx = x + dx, ny = y + dy;
if (valid(nx) && valid(ny) && !seen[nx][ny] && F[nx][ny] == t) {
q.push({nx, ny, t});
seen[nx][ny] = true;
}
}
}
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)
if (!seen[i][j]) return 0; // islands!!!
// most extreme zeros
// Point minx = {N, N}, maxx = {0, 0}, miny = {N, N}, maxy = {0, 0};
// for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
// if (F[i][j] == 0) {
// if (i < minx.x) minx = {i, j};
// if (i > maxx.x) maxx = {i, j};
// if (j < miny.y) miny = {i, j};
// if (j > maxy.y) maxy = {i, j};
// }
// }
// Point points[4] = {minx, maxx, miny, maxy};
vector<Point> points;
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
if (F[i][j] == 0) {
int corners[4][2][2] = {
{{ 1, 0}, {0, 1}},
{{ 1, 0}, {0, -1}},
{{-1, 0}, {0, 1}},
{{-1, 0}, {0, -1}}
};
for (auto [a, b]: corners) {
int ax = i + a[0], ay = j + a[1];
int bx = i + b[0], by = j + b[1];
if (F[ax][ay] + F[bx][by] == 2) {
points.push_back(Point(i, j));
break;
}
}
}
}
for (int i = 0; i < points.size(); i++) for (int j = i + 1; j < points.size(); j++) {
if (F[points[i].x][points[j].y] + F[points[j].x][points[i].y] == 2) {
return 0; // 3 or more kicks
}
}
int zeros = 0;
for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
if (F[i][j] == 0) zeros++;
}
return zeros;
}
