#include <bits/stdc++.h>
using namespace std;
#define int long long
struct thing {
int u, t;
bool operator < (const thing &b) const {
return t > b.t;
}
};
const int maxn = 1e5 + 5, INF = 1e16;
int n;
pair<int,int> a[maxn];
pair<int,int> tran[4] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
int dir[maxn];
bool vis[maxn];
int meet(int u, int v) {
auto [ux, uy] = a[u];
auto [vx, vy] = a[v];
auto [udx, udy] = tran[dir[u]];
auto [vdx, vdy] = tran[dir[v]];
if (dir[v] == (dir[u]+1)%4 || dir[v] == (dir[u] + 3)%4) {
// cout << u << " " << v << " " << (vx - ux) * (udx + vdx) << " " << (vy - uy) * (udy + vdy) << endl;
if ((vx - ux) * (udx - vdx) == (vy - uy) * (udy - vdy)) {
int t = (vx - ux) * (udx - vdx);
// cout << u << " " << v << " " << t << endl;
if (t >= 0) return t;
}
} else if (dir[v] == (dir[u]+2)%4) {
int vt = - ux * udx - vx * vdx - uy * udy - vy * vdy;
if (vt == abs(ux - vx) + abs(uy - vy)) return vt / 2;
}
return -1;
}
int solve() {
dir[0] = 1;
auto [x0, y0] = a[0];
for (int i=1;i<n;i++) {
auto [x, y] = a[i];
if (abs(x - x0) == abs(y - y0)) {
if (x < x0) dir[i] = 1;
else if (y < y0) dir[i] = 0;
else if (y > y0) dir[i] = 2;
} else {
pair<int,int> mx = {-INF, -INF};
for (int j=0;j<4;j++) {
auto [dx, dy] = tran[j];
mx = max(make_pair((x0 - x) * dx + (y0 - y) * dy, j), mx);
}
dir[i] = mx.second;
}
}
for (int i=0;i<n;i++) vis[i] = false;
priority_queue<thing> pq;
pq.push({0, 0});
while (pq.size()) {
auto [u, t] = pq.top();
pq.pop();
if (vis[u]) continue;
vis[u] = true;
auto [ux, uy] = a[u];
for (int v=0;v<n;v++) if (!vis[v]) {
auto [vx, vy] = a[v];
int vt = meet(u, v);
if (vt != -1 && vt >= t) pq.push({v, vt});
}
}
int ret = 0;
for (int i=0;i<n;i++) ret += vis[i];
return ret;
}
signed main() {
ios::sync_with_stdio(0); cin.tie(0);
cin >> n;
for (int i=0;i<n;i++) {
int x, y;
cin >> x >> y;
a[i] = {x * 2, y * 2};
}
int ans = 0;
for (int ii=0;ii<4;ii++) {
ans = max(solve(), ans);
for (int i=1;i<n;i++) {
int newx = a[0].first + (a[i].second - a[0].second);
int newy = a[0].second - (a[i].first - a[0].first);
a[i] = {newx, newy};
}
}
cout << ans << "\n";
}
