I.cpp

#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; ++i)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; --i)
#define REP(i,a) for(int i=0,_a=(a); i < _a; ++i)

#define DEBUG(X) { cout << #X << " = " << X << endl; }
#define PR(A,n)  { cout << #A << " = "; FOR(_,1,n) cout << A[_] << ' '; cout << endl; }
#define PR0(A,n) { cout << #A << " = "; REP(_,n) cout << A[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))
#define ll long long
#define SZ(x) ((int) (x).size())
using namespace std;

const double EPS = 1e-6;
inline int cmp(double a, double b) {
    return (a < b - EPS) ? -1 : ((a > b + EPS) ? 1 : 0);
}

const int MN = 5011;
struct Point {
    double x, y;
    Point(double x = 0.0, double y = 0.0) : x(x), y(y) {}

    Point operator + (Point a) { return Point(x+a.x, y+a.y); }
    Point operator - (Point a) { return Point(x-a.x, y-a.y); }
    Point operator * (double k) { return Point(x*k, y*k); }
    Point operator / (double k) { return Point(x/k, y/k); }

    double operator * (Point a) { return x*a.x + y*a.y; } // dot product
    double operator % (Point a) { return x*a.y - y*a.x; } // cross product

    int cmp(Point q) const { if (int t = ::cmp(x,q.x)) return t; return ::cmp(y,q.y); }

    #define Comp(x) bool operator x (Point q) const { return cmp(q) x 0; }
    Comp(>) Comp(<) Comp(==) Comp(>=) Comp(<=) Comp(!=)
    #undef Comp

    Point conj() { return Point(x, -y); }
    double norm() { return x*x + y*y; }

    // Note: There are 2 ways for implementing len():
    // 1. sqrt(norm()) --> fast, but inaccurate (produce some values that are of order X^2)
    // 2. hypot(x, y) --> slow, but much more accurate
    double len() { return sqrt(norm()); }

    Point rotate(double alpha) {
        double cosa = cos(alpha), sina = sin(alpha);
        return Point(x * cosa - y * sina, x * sina + y * cosa);
    }
} a[MN];
int n;

struct DSU {
    int lab[MN];
    void init(int n) {
        REP(i,n+1) lab[i] = -1;
    }

    int getRoot(int u) {
        if (lab[u] < 0) return u;
        return lab[u] = getRoot(lab[u]);
    }

    bool merge(int u, int v) {
        u = getRoot(u); v = getRoot(v);
        if (u == v) return false;
        if (lab[u] > lab[v]) swap(u, v);
        lab[u] += lab[v];
        lab[v] = u;
        return true;
    }
} dsu;

struct Circle : Point {
    double r;
    Circle(double x = 0, double y = 0, double r = 0) : Point(x, y), r(r) {}
    Circle(Point p, double r) : Point(p), r(r) {}
    
    bool contains(Point p) { return (*this - p).len() <= r + EPS; }
};
bool areIntersect(Circle u, Circle v) {
    if (cmp((u - v).len(), u.r + v.r) > 0) return false;
    if (cmp((u - v).len() + v.r, u.r) < 0) return false;
    if (cmp((u - v).len() + u.r, v.r) < 0) return false;
    return true;
}
vector<Point> circleIntersect(Circle u, Circle v) {
    vector<Point> res;
    if (!areIntersect(u, v)) return res;
    double d = (u - v).len();
    double alpha = acos((u.r * u.r + d*d - v.r * v.r) / 2.0 / u.r / d);

    Point p1 = (v - u).rotate(alpha);
    Point p2 = (v - u).rotate(-alpha);
    res.push_back(p1 / p1.len() * u.r + u);
    res.push_back(p2 / p2.len() * u.r + u);
    return res;
}

double dist(int i, int j) {
    return sqrt(
            sqr(a[i].x - a[j].x) +
            sqr(a[i].y - a[j].y));
}

int main() {
    ios :: sync_with_stdio(0); cin.tie(0);
    while (cin >> n) {
        FOR(i,1,n) cin >> a[i].x >> a[i].y;
        dsu.init(n+1);

        FOR(i,1,n) FOR(j,i+1,n)
            if (dist(i,j) < 2.0 + EPS) dsu.merge(i, j);

        int res = 0;
        FOR(i,1,n)
            if (dsu.lab[i] < 0) res = max(res, -dsu.lab[i] + 1);

        FOR(i,1,n) {
            int rooti = dsu.getRoot(i);
            FOR(j,i+1,n) {
                int rootj = dsu.getRoot(j);
                if (rooti == rootj) continue;
                
                int sum = -dsu.lab[rooti] - dsu.lab[rootj] + 1;
                set<int> allRoot; allRoot.insert(rooti); allRoot.insert(rootj);

                Circle ci = Circle(a[i].x, a[i].y, 2);
                Circle cj = Circle(a[j].x, a[j].y, 2);
                if (!areIntersect(ci, cj)) continue;

                auto intersections = circleIntersect(ci, cj);
                for(auto p : intersections) {
                    FOR(k,j+1,n) {
                        int rootk = dsu.getRoot(k);
                        if (allRoot.count(rootk)) continue;

                        if ((a[k] - p).len() < 2.0 + EPS) {
                            allRoot.insert(rootk);
                            sum -= dsu.lab[rootk];
                        }
                    }
                }
                res = max(res, sum);
            }
        }

        cout << res << endl;
    }
}