#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
using namespace std;
using mii = map<int, int>;
using vi = vector<int>;
using pii = pair<int, int>;
#define sz(x) int(x.size())
const int dr = 0;
const int dt = 1;
const int dl = 2;
const int dd = 3;
const int INF = 2'000'000'001;
int* X;
int* Y;
struct person
{
int i;
int x;
int y;
person(int I)
{
i = I, x = X[I], y = Y[I];
}
person(int X, int Y)
{
x = X, y = Y, i = -1;
}
};
bool operator < (person A, person B)
{
if(A.x != B.x) return A.x < B.x;
else return A.y < B.y;
}
struct event
{
int t;
int i;
int p;
};
bool operator < (event A, event B)
{
return vi{A.t, A.i, A.p} < vi{B.t, B.i, B.p};
}
const int mx = 100'000;
vi L_label(mx), T_label(mx), TL_label(mx), TR_label(mx);
mii L_map, T_map, TL_map, TR_map;
set<person> L_set[mx][4], T_set[mx][4], TL_set[mx][4], TR_set[mx][4];
vi dir;
vi visit;
set<event> tbv;
vi inftime;
void activate(event z);
void reload(int i);
void activate(event z)
{
int t = z.t, i = z.i, p = z.p;
cerr << "activate " << t << ' ' << i << ' ' << p << "\n";
L_set[L_label[i]][dir[i]].erase(person(i));
T_set[T_label[i]][dir[i]].erase(person(i));
TL_set[TL_label[i]][dir[i]].erase(person(i));
TR_set[TR_label[i]][dir[i]].erase(person(i));
reload(p);
reload(i);
}
void add_event(int i, int p)
{
cerr << "add event " << i << ' ' << p << '\n';
int t;
if(X[i] == X[p]) t = abs(Y[i] - Y[p])/2;
else if(Y[i] == Y[p]) t = abs(X[i] - X[p])/2;
else t = abs(X[i] - X[p]);
if(inftime[i] == -1 || inftime[i] > t)
{
inftime[i] = t;
visit[i] = 1;
tbv.insert({t, i, p});
}
}
void reload(int p)
{
cerr << "\n\n";
cerr << "reload " << p << '\n';
// cerr << "reload " << p << "\n";
if(dir[p] == dt)
{
cerr << "entered \n";
// cerr << "hi\n";
// auto it = T_set[T_label[p]][dd].lower_bound(person(p));
// if(it != T_set[T_label[p]][dd].begin())
// {
// it--;
// int i = it->i;
// add_event(it->i, i);
// T_set[T_label[p]][dd].erase(it);
// }
set<person>& z = TL_set[TL_label[p]][dr];
auto it = z.lower_bound(person(X[p] - inftime[p], INF));
cerr << "z = ";
for(person xv : z) cerr << xv.x << ' ' << xv.y << " | ";
cerr << "\n";
if(it != z.begin())
{
it--;
add_event(it->i, p);
// cerr << "# " << it->i << '\n';
}
set<person>& z2 = TR_set[TR_label[p]][dl];
it = z2.lower_bound(person(X[p] + inftime[p], -INF));
cerr << "z2 = ";
for(person xv : z2) cerr << xv.x << ' ' << xv.y << " | ";
cerr << "\n";
// cerr << "coords = " << X[0]-Y[0] << ' ' << X[1]-Y[1] << ' ' << X[2]-Y[2] << '\n';
// cerr << "z = ";
// for(person q : z) cerr << q.i << " / ";
// cerr << '\n';
if(it != z2.end())
{
add_event(it->i, p);
// cerr << "#\n";
}
}
else if(dir[p] == dd)
{
set<person>& z = TL_set[TL_label[p]][dr];
auto it = z.lower_bound(person(X[p] + inftime[p], -INF));
if(it != z.end())
{
add_event(it->i, p);
}
set<person>& z2 = TR_set[TR_label[p]][dl];
it = z2.lower_bound(person(X[p] - inftime[p], +INF));
if(it != z2.begin())
{
it--;
add_event(it->i, p);
}
}
else if(dir[p] == dl)
{
set<person>& z = TL_set[TL_label[p]][dd];
auto it = z.lower_bound(person(X[p] - inftime[p], +INF));
if(it != z.begin())
{
it--;
add_event(it->i, p);
}
set<person>& z2 = TR_set[TR_label[p]][dt];
it = z2.lower_bound(person(X[p] - inftime[p], +INF));
if(it != z2.begin())
{
it--;
add_event(it->i, p);
}
}
else if(dir[p] == dr)
{
set<person>& z = TL_set[TL_label[p]][dt];
auto it = z.lower_bound(person(X[p] + inftime[p], -INF));
if(it != z.end())
{
add_event(it->i, p);
}
set<person>& z2 = TR_set[TR_label[p]][dd];
it = z2.lower_bound(person(X[p] + inftime[p], -INF));
if(it != z2.end())
{
add_event(it->i, p);
}
}
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int N;
cin >> N;
X = new int[N];
Y = new int[N];
for(int i = 0; i < N; i++)
{
cin >> X[i] >> Y[i];
X[i] *= 2;
Y[i] *= 2;
}
int res = 1;
for(int i = N-1; i >= 0; i--)
{
X[i] -= X[0];
Y[i] -= Y[0];
}
// cerr << X[0] << ' ' << X[1] << ' ' << X[2] << '\n';
// cerr << Y[0] << ' ' << Y[1] << ' ' << Y[2] << '\n';
for(int t = 0; t < 4; t++)
{
cerr << "\n\n\n\n\n\n t = " << t << '\n';
// if(t == 1)
// {
L_map.clear();
T_map.clear();
TL_map.clear();
TR_map.clear();
for(int i = 0; i < N; i++)
{
L_map[X[i]] = 0;
T_map[Y[i]] = 0;
TL_map[X[i]+Y[i]] = 0;
TR_map[X[i]-Y[i]] = 0;
}
for(mii* mp : {&L_map, &T_map, &TL_map, &TR_map})
{
mii& m = *mp;
int ct = -1;
for(auto& z : m)
{
z.second = ++ct;
}
}
for(int i = 0; i < N; i++)
{
L_label[i] = L_map[X[i]];
T_label[i] = T_map[Y[i]];
TL_label[i] = TL_map[X[i] + Y[i]];
TR_label[i] = TR_map[X[i] - Y[i]];
}
//0 = right, 1 = top, 2 = left, 3 = down
dir = vi(N);
dir[0] = dt;
for(int i = 1; i < N; i++)
{
if(Y[i] > 0 && X[i]+Y[i] > 0 && Y[i]-X[i] > 0)
dir[i] = dd;
else if(Y[i] < 0 && X[i]+Y[i] <= 0 && Y[i]-X[i] <= 0)
dir[i] = dt;
else if(X[i] < 0)
dir[i] = dr;
else if(X[i] > 0)
dir[i] = dl;
}
// cerr << dir[0] << ' ' << dir[1] << ' ' << dir[2] << '\n';
visit = vi(N, 0);
inftime = vi(N, -1);
for(int i = 0; i < N; i++)
{
for(int d = 0; d < 4; d++)
{
L_set[i][d].clear();
T_set[i][d].clear();
TL_set[i][d].clear();
TR_set[i][d].clear();
}
}
for(int i = 0; i < N; i++)
{
L_set[L_label[i]][dir[i]].insert(person(i));
T_set[T_label[i]][dir[i]].insert(person(i));
TL_set[TL_label[i]][dir[i]].insert(person(i));
TR_set[TR_label[i]][dir[i]].insert(person(i));
}
tbv.insert({0, 0, 0});
visit[0] = 1;
inftime[0] = 0;
while(!tbv.empty())
{
event x = *tbv.begin();
tbv.erase(x);
activate(x);
}
int curr = 0;
for(int i = 0; i < N; i++) curr += visit[i];
res = max(res, curr);
// }
for(int i = 0; i < N; i++)
{
int newX = -Y[i], newY = X[i];
X[i] = newX;
Y[i] = newY;
}
}
cout << res << '\n';
}
