This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define int long long
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define rng(i,x,n) for(int i=x;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define vec(...) vector<__VA_ARGS__>
#define _3wX6R40 ios::sync_with_stdio(0),cin.tie(0)
typedef long long ll;
using pii=pair<int,int>;
using vi=vector<int>;
void print(){cout<<'\n';}
template<class h,class...t>
void print(const h&v,const t&...u){cout<<v<<' ',print(u...);}
// e
const int di[]={1,-1,0,0};
const int dj[]={0,0,1,-1};
signed main(){
_3wX6R40;
int n;
cin>>n;
vec(pii) a(n);
rep(i,n){
cin>>a[i].fi>>a[i].se;
a[i].fi*=2;
a[i].se*=2;
}
const int inf=1e9;
using T=pair<int,pii>;
int res=0;
rep(sdir,4){
// {
// int sdir=0;
priority_queue<T,vec(T),greater<T>> pq;
vec(vi) dp(n,vi(4,inf));
dp[0][sdir]=0;
pq.push({0,{0,sdir}});
while(sz(pq)){
auto top=pq.top();
pq.pop();
auto [i,dir]=top.se;
int cosu=top.fi;
if(dp[i][dir]!=cosu) continue;
rep(j,n){
if(i==j) continue;
// 0 ->
// 1 <-
// 2 ^
// 3 v
rep(ndir,4){
if(dir==ndir) continue;
int t=(pii)minmax(dir,ndir)==(pii){2,3}?1:(pii)minmax(dir,ndir)==(pii){0,1}?2:0;
pii p=a[i],q=a[j];
if(t==1){
if(dir!=2) swap(p,q);
if(p.se>q.se or p.fi!=q.fi) continue;
int _t=q.se-p.se;
if(cosu>_t) continue;
if(dp[j][ndir]>_t){
dp[j][ndir]=_t;
pq.push({_t,{j,ndir}});
}
}else if(t==2){
if(dir!=0) swap(p,q);
if(p.fi>q.fi or p.se!=q.se) continue;
int _t=q.fi-p.fi;
if(cosu>_t) continue;
if(dp[j][ndir]>_t){
dp[j][ndir]=_t;
pq.push({_t,{j,ndir}});
}
}else{
if(abs(p.fi-q.fi)!=abs(p.se-q.se)) continue;
int _t=abs(p.fi-q.fi);
int x=p.fi+di[dir]*_t,y=p.se+dj[dir]*_t;
int nx=q.fi+di[ndir]*_t,ny=q.se+dj[ndir]*_t;
// print("ndir = ",ndir,", ",x,y,nx,ny,"...",p.fi,p.se,q.fi,q.se);
if(nx!=x or ny!=y) continue;
if(cosu>_t) continue;
if(dp[j][ndir]>_t){
dp[j][ndir]=_t;
pq.push({_t,{j,ndir}});
}
}
}
}
}
int now=0;
rep(i,n){
rep(dir,4){
now+=(dp[i][dir]<inf);
}
}
res=max(res,now);
}
print(res);
//
return 0;
}
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