#include<iostream>
#include<vector>
#include<algorithm>
#include<tuple>
#include<queue>
#include<set>
#include<cstring>
#include "soccer.h"
using namespace std;
const int MAX_N=2e3+3;
int n;
int a[MAX_N][MAX_N];
int p[MAX_N][MAX_N];
int lastok[2][MAX_N][MAX_N];//0 : back | 1 : forward
set<int>block[MAX_N];
bool allempty(int x1,int y1,int x2,int y2)
{
if(y1<0)return 0;
if(y2>=n)return 0;
int x11=min(x1,x2),x22=max(x1,x2);
int y11=min(y1,y2),y22=max(y1,y2);
x1=x11+1;y1=y11+1;x2=x22+1;y2=y22+1;
if(p[x2][y2]-p[x1-1][y2]-p[x2][y1-1]+p[x1-1][y1-1]==(x2-x1+1)*(y2-y1+1))return 1;
return 0;
}
int tree[2][2][MAX_N][4*MAX_N];
int lazy[2][2][MAX_N][4*MAX_N];
void push_lazy(int topbottom,int dir,int node,int l,int r,int row)
{
tree[topbottom][dir][row][node]=max(tree[topbottom][dir][row][node],lazy[topbottom][dir][row][node]);
if(l!=r)
{
lazy[topbottom][dir][row][2*node]=max(lazy[topbottom][dir][row][2*node],lazy[topbottom][dir][row][node]);
lazy[topbottom][dir][row][2*node+1]=max(lazy[topbottom][dir][row][2*node+1],lazy[topbottom][dir][row][node]);
}
lazy[topbottom][dir][row][node]=0;
}
void update(int topbottom,int dir,int node,int l,int r,int row,int ql,int qr,int val)
{
push_lazy(topbottom,dir,node,l,r,row);
if(r<ql or l>qr)return;
if(ql<=l && r<=qr)
{
lazy[topbottom][dir][row][node]=max(lazy[topbottom][dir][row][node],val);
push_lazy(topbottom,dir,node,l,r,row);
return;
}
int mid=(l+r)/2;
update(topbottom,dir,2*node,l,mid,row,ql,qr,val);
update(topbottom,dir,2*node+1,mid+1,r,row,ql,qr,val);
tree[topbottom][dir][row][node]=max(tree[topbottom][dir][row][2*node],tree[topbottom][dir][row][2*node+1]);
}
int query(int topbottom,int dir,int node,int l,int r,int row,int idx)
{
push_lazy(topbottom,dir,node,l,r,row);
if(r<idx or l>idx)return -1;
if(l==r)
{
return tree[topbottom][dir][row][node];
}
int mid=(l+r)/2;
return max(query(topbottom,dir,2*node,l,mid,row,idx),query(topbottom,dir,2*node+1,mid+1,r,row,idx));
}
void rowupdate(int topbottom,int row,int leftborder,int rightborder,int cur)
{
auto it=block[row].lower_bound(leftborder-1);
int first=(*(it));
if(first>rightborder+1)return;
auto it2=block[row].upper_bound(rightborder);
int last=(*(it2));
if(last>rightborder+1)
{
it2--;
}
last=(*(it2));
if(leftborder<=last-1)update(topbottom,1,1,0,n-1,row,leftborder,last-1,cur);
if(first+1<=rightborder)update(topbottom,0,1,0,n-1,row,first+1,rightborder,cur);
}
vector<tuple<pair<int,int>,int,int,bool>>states[MAX_N];
int solve()
{
int ans=1;
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(a[i][j])continue;
int l=j,r=lastok[1][i][j];
states[r-l+1].push_back({{l,r},i,j,1});
l=lastok[0][i][j];r=j;
if(lastok[1][i][l]==r)continue;
states[r-l+1].push_back({{l,r},i,j,0});
}
}
for(int len=1;len<=n;len++)sort(states[len].rbegin(),states[len].rend());
for(int len=n;len>=1;len--)
{
for(int id=0;id<states[len].size();id++)
{
int row,col,dir;
pair<int,int>borders;
tie(borders,row,col,dir)=states[len][id];
int leftborder=borders.first,rightborder=borders.second;
int l=0,r=row-1;
int rowtop=row;
while(l<=r)
{
int mid=(l+r)/2;
if(allempty(mid,leftborder-1,row-1,rightborder) && allempty(mid,leftborder,row-1,rightborder+1))
{
rowtop=mid;
r=mid-1;
}
else l=mid+1;
}
int other=-1;
if(dir==1)
{
if(leftborder-1>=0 && a[row][leftborder-1]==0)other=query(0,dir,1,0,n-1,row,col-1);
}
else
{
if(rightborder+1<n && a[row][rightborder]==0)other=query(0,dir,1,0,n-1,row,rightborder+1);
}
int cur=len+max(1+other,query(0,dir,1,0,n-1,row,col));
//cout<<row<<" "<<leftborder<<" "<<rightborder<<" "<<rowtop<<" "<<len+query(0,dir,1,0,n-1,row,col)+(row-rowtop)*len<<" "<<len+query(1,dir,1,0,n-1,row,col)<<"\n";
ans=max(ans,cur+(row-rowtop)*len);
if(rowtop-1>=0)
{
rowupdate(0,rowtop-1,leftborder,rightborder,cur+(row-rowtop)*len);
}
}
///minimum at the top
reverse(states[len].begin(),states[len].end());
for(int id=0;id<states[len].size();id++)
{
int row,col,dir;
pair<int,int>borders;
tie(borders,row,col,dir)=states[len][id];
int leftborder=borders.first,rightborder=borders.second;
int l=row+1,r=n-1;
int rowbottom=row;
while(l<=r)
{
int mid=(l+r)/2;
if(allempty(row+1,leftborder-1,mid,rightborder) && allempty(row+1,leftborder,mid,rightborder+1))
{
rowbottom=mid;
l=mid+1;
}
else r=mid-1;
}
int other=-1;
if(dir==1)
{
if(leftborder-1>=0 && a[row][leftborder-1]==0)other=query(1,dir,1,0,n-1,row,col-1);
}
else
{
if(rightborder+1<n && a[row][rightborder]==0)other=query(1,dir,1,0,n-1,row,rightborder+1);
}
int cur=len+max(other+1,query(1,dir,1,0,n-1,row,col));
//cout<<row<<" "<<leftborder<<" "<<rightborder<<" "<<rowbottom<<" "<<pre[id]<<" "<<len+query(1,dir,1,0,n-1,row,col)+(rowbottom-row)*len<<"\n";
ans=max(ans,cur+(rowbottom-row)*len);
if(rowbottom+1<n)
{
rowupdate(1,rowbottom+1,leftborder,rightborder,cur+(rowbottom-row)*len);
}
}
///minimum at the bottom
}
return ans;
}
vector<pair<int,int>>intervals;
int b[MAX_N][MAX_N];
bool inside(int i,int j)
{
if(intervals[j].first<=intervals[i].first && intervals[j].second>=intervals[i].second)return 1;
return 0;
}
bool check()
{
intervals.clear();
int hasprev=0,haslast=0;
for(int i=0;i<n;i++)
{
int f=-1,s=-2;
for(int j=0;j<n;j++)
{
if(b[i][j]==0)
{
if(f==-1)f=j;
s=j;
}
}
for(int j=f;j<=s;j++)
{
if(b[i][j])return 0;
}
int hasnow=(f!=-1 ? 1 : 0);
if(hasnow)
{
intervals.push_back({f,s});
if(haslast==0 && hasprev)return 0;
}
haslast=hasnow;
hasprev=max(hasprev,hasnow);
}
for(int i=1;i<intervals.size();i++)
{
if(inside(i-1,i))continue;
for(int j=i;j<intervals.size();j++)
{
if(inside(j,j-1))
{
continue;
}
return 0;
}
break;
}
for(int i=0;i<intervals.size();i++)intervals[i].second*=-1;
sort(intervals.begin(),intervals.end());
for(int i=0;i<intervals.size();i++)intervals[i].second*=-1;
for(int i=1;i<intervals.size();i++)
{
if(inside(i,i-1))continue;
return 0;
}
return 1;
}
int shit()
{
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
b[i][j]=1;
}
}
vector<pair<int,int>>cells;
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(a[i][j]==0)cells.push_back({i,j});
}
}
int sz=cells.size();
vector<pair<int,int>>masks;
for(int mask=1;mask<(1<<sz);mask++)
{
masks.push_back({__builtin_popcount(mask),mask});
}
sort(masks.rbegin(),masks.rend());
for(auto [cnt,mask]:masks)
{
for(int i=0;i<sz;i++)
{
if(((1<<i)&(mask))==0)continue;
int x=cells[i].first,y=cells[i].second;
b[x][y]=0;
}
bool ok=check();
for(int i=0;i<sz;i++)
{
if(((1<<i)&(mask))==0)continue;
int x=cells[i].first,y=cells[i].second;
b[x][y]=1;
}
if(ok)return cnt;
}
return 1;
}
void reset()
{
memset(tree,0,sizeof(tree));
memset(lazy,0,sizeof(lazy));
memset(a,0,sizeof(a));
memset(b,0,sizeof(b));
memset(p,0,sizeof(p));
memset(lastok,0,sizeof(lastok));
for(int i=0;i<n;i++)
{
block[i].clear();
}
for(int i=1;i<=n;i++)
{
states[i].clear();
}
}
int biggest_stadium(int N, std::vector<std::vector<int>> F)
{
n=N;
reset();
for(int i=0;i<n;i++)
{
block[i].insert(-1);
block[i].insert(n);
for(int j=0;j<n;j++)
{
a[i][j]=F[i][j];
if(a[i][j])block[i].insert(j);
}
}
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
{
p[i][j]=(a[i-1][j-1]==0)+p[i-1][j]+p[i][j-1]-p[i-1][j-1];
}
}
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(a[i][j])continue;
if(j==0 or a[i][j-1])
{
lastok[0][i][j]=j;
continue;
}
lastok[0][i][j]=lastok[0][i][j-1];
}
for(int j=n-1;j>=0;j--)
{
if(a[i][j])continue;
if(j==n-1 or a[i][j+1])
{
lastok[1][i][j]=j;
continue;
}
lastok[1][i][j]=lastok[1][i][j+1];
}
}
/*int x=solve(),y=shit();
if(x!=y)
{
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
cout<<a[i][j]<<" ";
}
cout<<"\n";
}
cout<<"\n";
cout<<"Correct : "<<y<<"\n";
cout<<"My idea : "<<x<<"\n";
return 1;
}
return 0;*/
return solve();
}
