#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MAXN = 1e5 + 5;
const int INF = 1e18;
const bool LINES = 0;
int n;
int x[MAXN], y[MAXN], d1[MAXN], d2[MAXN];
unordered_map<int, set<pair<int,int>>> of_d1, of_d2, of_x[2], of_y[2];
void baga(int id)
{
of_d1[d1[id]].insert({x[id], id});
of_d2[d2[id]].insert({x[id], id});
//of_x[x[id] % 2][x[id]].insert({y[id] / 2, id});
//of_y[y[id] % 2][y[id]].insert({x[id] / 2, id});
}
void scoate(int id)
{
of_d1[d1[id]].erase({x[id], id});
of_d2[d2[id]].insert({x[id], id});
of_x[x[id] % 2][x[id]].erase({y[id] / 2, id});
of_y[y[id] % 2][y[id]].erase({x[id] / 2, id});
}
int dist[MAXN];
priority_queue<pair<int, pair<int,int>>> pq;//{-dist, {nod, dir}}
vector<int> aux;
int myd;
void add_to_pq(int nod, int dir, int t)
{
if(dist[nod] <= t)
return;
//assert(t >= myd);
if(t < myd)
return;
aux.push_back(nod);
dist[nod] = t;
pq.push({-dist[nod], {nod, dir}});
}
int solve(int root_dir)
{
for(int i=1;i<=n;i++)
{
dist[i] = INF;
baga(i);
}
while(!pq.empty())
pq.pop();
add_to_pq(1, root_dir, 0);
scoate(1);
while(!pq.empty())
{
int cdist = -pq.top().first, nod = pq.top().second.first, dir = pq.top().second.second;
pq.pop();
//assert(cdist == dist[nod]);
if(cdist != dist[nod])
continue;
myd = dist[nod];
//add equal x and y cases-------------------------------------------------------------
aux.clear();
int ct;
if(dir == 0)
{
//cv - x[nod] > dist[nod] => cv > dist[nod] + x[nod]
auto it1 = of_d1[d1[nod]].lower_bound({dist[nod] + x[nod], INF});
while(it1 != of_d1[d1[nod]].end())
{
ct = (*it1).first - x[nod];
add_to_pq((*it1).second, 3, ct);
it1 = of_d1[d1[nod]].erase(it1);
}
auto it2 = of_d2[d2[nod]].lower_bound({dist[nod] + x[nod], INF});
while(it2 != of_d2[d2[nod]].end())
{
ct = (*it2).first - x[nod];
add_to_pq((*it2).second, 2, ct);
it2 = of_d2[d2[nod]].erase(it2);
}
if(LINES)
{
auto it3 = of_y[y[nod] % 2][y[nod]].lower_bound({x[nod] / 2 + dist[nod], INF});
while(it3 != of_y[y[nod] % 2][y[nod]].end())
{
ct = (*it3).first - x[nod] / 2;
add_to_pq((*it3).second, 1, ct);
it3 = of_y[y[nod] % 2][y[nod]].erase(it3);
}
}
}
else if(dir == 1)
{
auto it1 = of_d1[d1[nod]].lower_bound({x[nod] - dist[nod], 0});
while(it1 != of_d1[d1[nod]].begin())
{
it1--;
ct = x[nod] - (*it1).first;
add_to_pq((*it1).second, 2, ct);
it1 = of_d1[d1[nod]].erase(it1);
}
auto it2 = of_d2[d2[nod]].lower_bound({x[nod] - dist[nod], 0});
while(it2 != of_d2[d2[nod]].begin())
{
it2--;
ct = x[nod] - (*it2).first;
add_to_pq((*it2).second, 3, ct);
it2 = of_d2[d2[nod]].erase(it2);
}
if(LINES)
{
auto it3 = of_y[y[nod] % 2][y[nod]].lower_bound({x[nod] / 2 - dist[nod], 0});
while(it3 != of_y[y[nod] % 2][y[nod]].begin())
{
it3--;
ct = x[nod] / 2 - (*it3).first;
add_to_pq((*it3).second, 0, ct);
it3 = of_y[y[nod] % 2][y[nod]].erase(it3);
}
}
}
else if(dir == 2)
{
auto it1 = of_d1[d1[nod]].lower_bound({dist[nod] + x[nod], INF});
while(it1 != of_d1[d1[nod]].end())
{
ct = (*it1).first - x[nod];
add_to_pq((*it1).second, 1, ct);
it1 = of_d1[d1[nod]].erase(it1);
}
auto it2 = of_d2[d2[nod]].lower_bound({x[nod] - dist[nod], 0});
while(it2 != of_d2[d2[nod]].begin())
{
it2--;
ct = x[nod] - (*it2).first;
add_to_pq((*it2).second, 0, ct);
it2 = of_d2[d2[nod]].erase(it2);
}
if(LINES)
{
auto it3 = of_x[x[nod] % 2][x[nod]].lower_bound({y[nod] / 2 + dist[nod], INF});
while(it3 != of_x[x[nod] % 2][x[nod]].end())
{
ct = (*it3).first - y[nod] / 2;
add_to_pq((*it3).second, 3, ct);
it3 = of_x[x[nod] % 2][x[nod]].erase(it3);
}
}
}
else
{
assert(dir == 3);
auto it1 = of_d1[d1[nod]].lower_bound({x[nod] - dist[nod], 0});
while(it1 != of_d1[d1[nod]].begin())
{
it1--;
ct = x[nod] - (*it1).first;
add_to_pq((*it1).second, 0, ct);
it1 = of_d1[d1[nod]].erase(it1);
}
auto it2 = of_d2[d2[nod]].lower_bound({dist[nod] + x[nod], INF});
while(it2 != of_d2[d2[nod]].end())
{
ct = (*it2).first - x[nod];
add_to_pq((*it2).second, 1, ct);
it2 = of_d2[d2[nod]].erase(it2);
}
if(LINES)
{
auto it3 = of_x[x[nod] % 2][x[nod]].lower_bound({y[nod] / 2 - dist[nod], 0});
while(it3 != of_x[x[nod] % 2][x[nod]].begin())
{
it3--;
ct = y[nod] / 2 - (*it3).first;
add_to_pq((*it3).second, 2, ct);
it3 = of_x[x[nod] % 2][x[nod]].erase(it3);
}
}
}
for(int v:aux)
scoate(v);
}
int cnt = 0;
for(int i=1;i<=n;i++)
if(dist[i] < INF)
cnt++;
return cnt;
}
signed main()
{
ios_base::sync_with_stdio(0);cin.tie(0);
cin>>n;
for(int i=1;i<=n;i++)
{
cin>>x[i]>>y[i];
x[i] = x[i] * 2;
y[i] = y[i] * 2;
d1[i] = x[i] + y[i];
d2[i] = x[i] - y[i];
}
int mxm = 0;
for(int dir=0;dir<4;dir++)
mxm = max(mxm, solve(dir));
cout<<mxm;
return 0;
}
