This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/** Created by: Humberto Yusta
Codeforces User: humbertoyusta
Country: Cuba */
#include<bits/stdc++.h>
using namespace std;
/// Pragmas
#pragma GCC optimize("Ofast","unroll-loops","omit-frame-pointer","inline","03") // Optimization flags
//#pragma GCC option("arch=native","tune=native","no-zero=upper") // Enable AVX
//#pragma GCC target("avx2") // Enable AVX
//#pragma comment(linker, "/STACK:1024000000,1024000000") // Increase stack limit
//#pragma GCC target("sse,sse2,sse,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") // I don't know what it is
/// Macros:
#define int long long
#define f first
#define s second
#define db(x) cerr << #x << ": " << (x) << '\n';
#define pb push_back
#define lb lower_bound
#define up upper_bound
#define all(x) x.begin() , x.end()
#define rall(x) x.rbegin() , x.rend()
#define enl '\n'
typedef pair<int,int> ii;
typedef long double ld;
typedef unsigned long long ull;
/// Constraints:
const int maxn = 200010;
const int mod = 1000000007;
const int mod2 = 998244353;
const ld eps = 1e-9;
const int inf = ((1ll<<31ll)-1ll);
const int INF = 1ll * mod * mod;
const ld pi = acos(-1);
/// Prime Numbers:
// 2, 173, 179, 181, 197, 311, 331, 737, 1009, 2011, 2027, 3079, 4001, 10037, 10079, 20011, 20089;
// 100003, 100019, 100043, 200003, 200017, 1000003, 1000033, 1000037, 1000081;
// 2000003, 2000029, 2000039, 1000000007, 1000000021, 2000000099;
/// Functions:
#define lg2(x) 31 - __builtin_clz(x)
#define lgx(x,b) ( log(x) / log(b) )
/// Red-Black Tree Template ---------------------------------
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree < long long , null_type , less<long long> , rb_tree_tag , tree_order_statistics_node_update > ordered_set;
/// Quick Pow------------------------------------------------
int qpow(int b,int e){
if( !e ) return 1;
if( e & 1 ) return qpow(b,e-1) * b % mod;
int pwur = qpow(b,e>>1);
return pwur * pwur % mod;
}
int modinv(int x){ return qpow(x,mod-2); }
bool isprime(int x){
for(int i=2; i*i<=x; i++)
if( x % i == 0 )
return false;
return true;
}
/// My Code -------------------------------------------------
int n, res;
map<int,set<ii>> mp, imp;
vector<pair<int,ii>> g[maxn];
priority_queue<pair<ii,ii>> q;
void bfs(){
while( !q.empty() ){
ii nod = q.top().f;
int dir = q.top().s.f;
int lwbound = q.top().s.s;
q.pop();
if( dir == 3 || dir == 1 ){
while( !mp[nod.f+nod.s].empty() ){
ii nwn = *prev(mp[nod.f+nod.s].end());
//db(nwn.f - nod.f)
if( nwn.f - nod.f < lwbound ) break;
q.push({nwn,{dir%4+1,nwn.f - nod.f}});//db("4")db(nwn.f)db(nwn.s)
mp[nwn.f+nwn.s].erase(nwn);
imp[nwn.f-nwn.s].erase(nwn);
}
}
if( dir == 4 || dir == 2 ){
while( !imp[nod.f-nod.s].empty() ){
ii nwn = *imp[nod.f-nod.s].begin();
//db(nod.f - nwn.f)
if( nod.f - nwn.f < lwbound ) break;
q.push({nwn,{dir%4+1,nod.f - nwn.f}});//db("3")db(nwn.f)db(nwn.s)
mp[nwn.f+nwn.s].erase(nwn);
imp[nwn.f-nwn.s].erase(nwn);
}
}
if( dir == 3 || dir == 1 ){
while( !mp[nod.f+nod.s].empty() ){
ii nwn = *mp[nod.f+nod.s].begin();
//db(nod.f - nwn.f)
if( nod.f - nwn.f < lwbound ) break;
q.push({nwn,{dir%4+1,nod.f - nwn.f}});//db("2")db(nwn.f)db(nwn.s)
mp[nwn.f+nwn.s].erase(nwn);
imp[nwn.f-nwn.s].erase(nwn);
}
}
if( dir == 4 || dir == 2 ){
while( !imp[nod.f-nod.s].empty() ){
ii nwn = *prev(imp[nod.f-nod.s].end());
//db(nwn.f - nod.f)
if( nwn.f - nod.f < lwbound ) break;
q.push({nwn,{dir%4+1,nwn.f - nod.f}});//db("1")db(nwn.f)db(nwn.s)
mp[nwn.f+nwn.s].erase(nwn);
imp[nwn.f-nwn.s].erase(nwn);
}
}
res ++;
}
}
int solve(vector<ii> &vx,int init_dir){
mp.clear();
imp.clear();
int cnt = 0;
for(auto i : vx){
int u = i.f;
int v = i.s;
cnt ++;
mp[u+v].insert({u,v});
imp[u-v].insert({u,v});
}
res = 0;
mp[vx[0].f+vx[0].s].erase({vx[0].f,vx[0].s});
imp[vx[0].f-vx[0].s].erase({vx[0].f,vx[0].s});
while( !q.empty() ) q.pop();
q.push({ { vx[0].f , vx[0].s } , { init_dir , 0 } });
bfs();
//db(res)
return res;
}
int32_t main(){
ios_base::sync_with_stdio(0); cin.tie(0);
cout.setf(ios::fixed); cout.precision(10);
srand(time(NULL));
//freopen("sample-01-in.txt","r",stdin);
//freopen("a.in","w",stdout);
cin >> n;
vector<ii> vx;
for(int i=1; i<=n; i++){
int u, v;
cin >> u >> v;
vx.pb({u,v});
}
int ans = 0;
for(int i=1; i<=4; i++){
ans = max( ans , solve( vx , i ) );
}
cout << ans << '\n';
return 0;
}
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