#include <bits/stdc++.h>
#define int ll
using namespace std;
#define ll long long
#define y1 zck_is_king
#define pii pair<ll, ll>
#define ull unsigned ll
#define f first
#define s second
#define ALL(x) x.begin(),x.end()
#define SZ(x) (int)x.size()
#define SQ(x) (x)*(x)
#define MN(a,b) a = min(a,(__typeof__(a))(b))
#define MX(a,b) a = max(a,(__typeof__(a))(b))
#define pb push_back
#define REP(i,n) for (int i = 0; i<n; ++i)
#define RREP(i,n) for (int i = n-1; i>=0; --i)
#define REP1(i,n) for (int i = 1; i<=n; ++i)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#ifdef BALBIT
#define IOS()
#define bug(...) fprintf(stderr,"#%d (%s) = ",__LINE__,#__VA_ARGS__),_do(__VA_ARGS__);
template<typename T> void _do(T &&x){cerr<<x<<endl;}
template<typename T, typename ...S> void _do(T &&x, S &&...y){cerr<<x<<", ";_do(y...);}
#else
#define IOS() ios_base::sync_with_stdio(0);cin.tie(0);
#define endl '\n'
#define bug(...)
#endif
const int iinf = 1e9+10;
const ll inf = 0x3f3f3f3f3f3f3f3f;
const ll mod = 1e9+7 ;
void GG(){cout<<"0\n"; exit(0);}
ll mpow(ll a, ll n, ll mo = mod){ // a^n % mod
ll re=1;
while (n>0){
if (n&1) re = re*a %mo;
a = a*a %mo;
n>>=1;
}
return re;
}
ll inv (ll b, ll mo = mod){
if (b==1) return b;
return (mo-mo/b) * inv(mo%b,mo) % mo;
}
const int maxn = 1e5+5;
int n;
struct pt{
int x,y;
void in(){
cin>>x>>y;
x*=2; y*=2;
}
int dist(pt &o) {
return abs(o.x-x) + abs(o.y-y);
}
pt operator - (pt &o) {
return {x - o.x, y - o.y};
}
};
pt P[maxn];
ll dst[maxn];
int dir[maxn];
bool done[maxn];
pii D4[4] = {{1,0}, {0,1}, {-1,0}, {0,-1}};
pii Dia4[4] = {{1,1},{-1,1},{-1,-1},{1,-1}};
inline int diagof(pii & p) {
return find(Dia4, Dia4+4, p) - Dia4;
}
inline int F4(int x) {
return x<0?x+4:(x>=4?x-4:x);
}
inline pt unrot(pt p, int d) {
if (d == 0) return p;
if (d == 1) return {p.y, -p.x};
if (d == 2) return {-p.x, -p.y};
if (d == 3) return {-p.y, p.x};
}
map<int, set<pair<int, int> > > MP[4][2];
map<int, set<pair<int, int> > > SMP[4]; // map for straight movements
//map<int, set<pair<int, int> > > DONE[4][2];
ll closest[maxn][3];
int run(int idir){
bug(idir);
dir[0] = idir;
memset(done, 0, sizeof done);
REP(i,4) REP(j,2) {
MP[i][j].clear();
// DONE[i][j].clear();
}
REP(i,4) SMP[i].clear();
REP1(i,n-1) {
int x = P[i].x, y = P[i].y;
if (x == y || x == -y) {
assert(x && y);
pii tmp = {x/abs(x), y/abs(x)};
int at = diagof(tmp);
if (at == idir) {
dir[i] = F4(idir-1);
}else if (at == F4(idir-1)) {
dir[i] = F4(idir+1);
}else{
dir[i] = idir;
}
}else{
dir[i] = (y<x?vector<int>{1,2}:vector<int>{0,3})[y>-x];
}
bug(i, dir[i]);
}
REP(i,n) {
// build the maps
{
int nd = F4(dir[i] + 1);
pt at = unrot(P[i], nd);
MP[nd][0][at.x - at.y].insert({at.x, i});
}
{
int nd = F4(dir[i] - 1);
pt at = unrot(P[i], nd);
MP[nd][1][at.x + at.y].insert({at.x, i});
}
{
pt at = unrot(P[i], dir[i]);
SMP[dir[i]][at.y].insert({at.x, i});
}
}
priority_queue<pii, vector<pii>, greater<pii> > pq;
pq.push({0,0});
memset(dst, 0x3f, sizeof dst);
memset(closest, 0x3f, sizeof closest);
dst[0] = 0;
auto UPD = [&](int u, int d, int branch) {
MN(closest[u][branch], d);
if (dst[u] > d) {
dst[u] = d;
pq.push({dst[u], u});
}
};
while (!pq.empty()) {
int v = pq.top().s; ll w = pq.top().f; pq.pop();
if (done[v] || dst[v] != w) continue;
done[v] = 1;
int dr = dir[v];
pt R = unrot(P[v], dr);
auto gt0 = MP[dr][0][R.x-R.y].lower_bound({R.x + w,-1});
if (gt0 != MP[dr][0][R.x-R.y].end()) {
UPD(gt0->s, gt0->f - R.x, 1);
}
auto gt1 = MP[dr][1][R.x+R.y].lower_bound({R.x + w,-1});
if (gt1 != MP[dr][1][R.x+R.y].end()) {
UPD(gt1->s, gt1->f - R.x, 0);
}
{
int dr2 = F4(dr + 2);
pt R2 = unrot(R, 2);
auto gts = SMP[dr2][R2.y].lower_bound({R2.x - w*2, 10000000});
if (gts != SMP[dr2][R2.y].begin()) {
--gts;
UPD(gts->s, (R2.x - gts->f)/2, 2);
}
}
{
int nd = F4(dir[v] + 1);
pt at = unrot(P[v], nd);
auto clo1 = MP[nd][0][at.x - at.y].lower_bound({at.x+1, -1});
// from my perspective, it is the 1-branch
if (clo1 != MP[nd][0][at.x - at.y].end()) {
UPD(clo1->s, closest[v][1] + (clo1->f) - at.x, 1);
}
MP[nd][0][at.x - at.y].erase({at.x, v});
}
{
int nd = F4(dir[v] - 1);
pt at = unrot(P[v], nd);
auto clo0 = MP[nd][1][at.x + at.y].lower_bound({at.x+1, -1});
// from my perspective, it is the 0-branch
if (clo0 != MP[nd][1][at.x + at.y].end()) {
UPD(clo0->s, closest[v][0] + (clo0->f) - at.x, 0);
}
MP[nd][1][at.x + at.y].erase({at.x, v});
}
{
auto gt = SMP[dr][R.y].lower_bound({R.x, -1});
if (gt != SMP[dr][R.y].begin()) {
--gt;
UPD(gt->s, closest[v][2] + (R.x - gt->f) / 2, 2);
}
SMP[dr][R.y].erase({R.x, v});
}
}
int re = 0;
REP(i,n) {
if (dst[i] != inf) {
bug(i, dst[i]);
++re;
}
}
return re;
}
signed main(){
IOS();
cin>>n;
REP(i,n) {
P[i].in();
if (i) {
P[i].x -= P[0].x; P[i].y -= P[0].y;
}
}
P[0] = {0,0};
int re = 0;
REP(idir, 4) {
MX(re, run(idir));
}
cout<<re<<endl;
}
