bombs

#include <bits/stdc++.h>

using namespace std;

//#define double long double

const int M = 1010;
const double eps = 1e-7;

struct Point {
    double x, y;

    Point(): x(0), y(0) {}
    Point(double x, double y): x(x), y(y) {}

    Point operator + (const Point &to) const {
        return Point(x + to.x, y + to.y);
    }
    Point operator - (const Point &to) const {
        return Point(x - to.x, y - to.y);
    }

    Point operator * (const double c) const {
        return Point(x * c, y * c);
    }
    Point operator / (const double c) const {
        return Point(x / c, y / c);
    }

    bool operator == (const Point &to) const {
        return fabs(x - to.x) + fabs(y - to.y) <= eps;
    }

    double sqlen() const {
        return x * x + y * y;
    }
    double len() const {
        return sqrt(sqlen());
    }

    Point norm() const {
        return Point(x / len(), y / len());
    }
    Point perp() const {
        return Point(-y, x);
    }

    double ang() {
        if (x >= 0 && y >= 0)
            return y;
        if (x < 0 && y >= 0)
            return 1 - x;
        if (x < 0 && y < 0)
            return 2 - y;
        if (x >= 0 && y < 0)
            return 3 + x;
    }
};

const Point zero;

int n;
Point p[M];
double r;

void read() {
    cin >> n;
    for (int i = 0; i < n; ++i)
        cin >> p[i].x >> p[i].y;
    cin >> r;
}

int run(Point pivot) {
    for (int i = 0; i < n; ++i)
        p[i] = p[i] - pivot;

    int bon = 0, tot = 0, ans = 0;
    vector<pair<double, int>> segments;

    for (int i = 0; i < n; ++i)
        if (p[i] == zero) {
            ++bon;
        } else {
            Point d = p[i] / 2.0;
            Point perp = d.perp().norm();
            if (d.sqlen() > r * r)
                continue;
            double len = sqrt(r * r - d.sqlen());
            Point from = d - (perp * len);
            Point to = d + (perp * len);

            assert(fabs(from.len() - r) <= eps);
            assert(fabs(to.len() - r) <= eps);

            double fromAng = from.norm().ang() - eps;
            double toAng = to.norm().ang() + eps;

            if (fromAng > toAng)
                ++tot;

            segments.emplace_back(toAng, -1);
            segments.emplace_back(fromAng, 1);
        }

    sort(segments.begin(), segments.end());
    for (int i = 0; i < (int) segments.size(); ++i) {
        pair<double, int> x = segments[i];
        ans = max(ans, tot);
        tot += x.second;
        assert(tot >= 0);
    }
    ans = max(ans, tot);

    return ans + bon;
}

void kill() {
    int ans = 0;
    for (int i = 0; i < n; ++i)
        ans = max(ans, run(p[i]));
    cout << ans << "\n";
}

int main() {
#ifndef LOCAL
    freopen("bombing.in", "r", stdin);
    freopen("bombing.out", "w", stdout);
#endif
    read();
    kill();
    return 0;
}