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>
using namespace std;
using ar = array<int,3>;
const int mxN = (int)3e3+10;
const int X[] = {-1,1,0,0};
const int Y[] = {0,0,-1,1};
int n, d[mxN], x[mxN], y[mxN], sick[mxN];
priority_queue<ar,vector<ar>,greater<ar>> pq;
int main(){
cin >> n; sick[0]=1; int ans = 1;
for(int i = 0; i < n; i++)
cin >> x[i] >> y[i];
for(int i = n-1; i >= 0; i--)
x[i]-=x[0], y[i]-=y[0];
for(int t = 0; t < 4; t++){
fill(sick+1,sick+n,0);
for(int i = 0; i < n; i++){
if(abs(x[i])==abs(y[i])) d[i]=(x[i]>=0?0:y[i]<0?3:2);
else if(abs(x[i])>abs(y[i])) d[i]=(x[i]>0?0:1);
else d[i]=(y[i]>0?2:3);
}
for(int i = 0; i < n; i++){
for(int j = 0; j < n; j++){
if(d[i]/2==0 and d[j]/2==1){
int t1=(x[j]-x[i])/X[d[i]];
int t2=(y[i]-y[j])/Y[d[j]];
if(t1==t2) pq.push({2*t1,i,j});
}
if(d[i]==1 and d[j]==0)
if(y[i]==y[j] and x[i]<x[j])
pq.push({x[j]-x[i],i,j});
if(d[i]==3 and d[j]==2)
if(x[i]==x[j] and y[i]<y[j])
pq.push({y[j]-y[i],i,j});
}
}
while(!empty(pq)){
auto [t,i,j] = pq.top(); pq.pop();
sick[i]=sick[j]=sick[i]|sick[j];
}
ans = max(ans, accumulate(sick,sick+n,0));
for(int i = 0; i < n; i++)swap(x[i],y[i]),x[i]*=-1;
}
cout << ans << "\n";
}
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