結果
| 問題 | No.96 圏外です。 |
| ユーザー |
 gyouzasushi
|
| 提出日時 | 2022-08-30 23:48:27 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 24,464 bytes |
| コンパイル時間 | 4,509 ms |
| コンパイル使用メモリ | 253,152 KB |
| 実行使用メモリ | 15,488 KB |
| 最終ジャッジ日時 | 2024-11-07 17:07:44 |
| 合計ジャッジ時間 | 29,454 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 3 ms
5,248 KB |
| testcase_01 | AC | 3 ms
5,248 KB |
| testcase_02 | AC | 3 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 128 ms
5,248 KB |
| testcase_05 | AC | 224 ms
5,504 KB |
| testcase_06 | AC | 363 ms
6,016 KB |
| testcase_07 | AC | 554 ms
6,072 KB |
| testcase_08 | AC | 789 ms
6,704 KB |
| testcase_09 | AC | 1,088 ms
7,424 KB |
| testcase_10 | AC | 1,540 ms
7,680 KB |
| testcase_11 | AC | 2,003 ms
9,088 KB |
| testcase_12 | AC | 2,466 ms
11,008 KB |
| testcase_13 | AC | 3,568 ms
10,368 KB |
| testcase_14 | AC | 4,325 ms
12,416 KB |
| testcase_15 | TLE | - |
| testcase_16 | TLE | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
ソースコード
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
using namespace std;
using ll = long long;
const int INF = 1e9;
const ll LINF = 1e18;
template <class T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
if (b < a) {
a = b;
return 1;
}
return 0;
}
template <class T>
vector<T> make_vec(size_t a) {
return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (int i = 0; i < int(v.size()); i++) {
is >> v[i];
}
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < int(v.size()); i++) {
os << v[i];
if (i < int(v.size()) - 1) os << ' ';
}
return os;
}
#pragma region UnionFind
#include <vector>
struct UnionFind {
int n;
std::vector<int> data;
UnionFind(int _n) : n(_n), data(_n, -1) {
}
int root(int x) {
return (data[x] < 0) ? x : data[x] = root(data[x]);
}
bool unite(int x, int y) {
x = root(x);
y = root(y);
if (x != y) {
if (data[y] < data[x]) std::swap(x, y);
data[x] += data[y];
data[y] = x;
}
return x != y;
}
bool find(int x, int y) {
return root(x) == root(y);
}
int size(int x) {
return -data[root(x)];
}
std::vector<std::vector<int>> groups() {
std::vector<int> root_buf(n), group_size(n);
for (int i = 0; i < n; i++) {
root_buf[i] = root(i);
group_size[root_buf[i]]++;
}
std::vector<std::vector<int>> ret(n);
for (int i = 0; i < n; i++) {
ret[i].reserve(group_size[i]);
}
for (int i = 0; i < n; i++) {
ret[root_buf[i]].push_back(i);
}
ret.erase(std::remove_if(
ret.begin(), ret.end(),
[&](const std::vector<int> &v) { return v.empty(); }),
ret.end());
return ret;
}
};
#pragma endregion
#pragma region geometry
namespace geometry {
using coordinate_t = double;
const coordinate_t PI = std::acos(-1);
const coordinate_t EPS = 1e-9;
int sgn(coordinate_t a) {
return (a < -EPS) ? -1 : (a > EPS) ? 1 : 0;
};
struct Point {
coordinate_t x, y;
Point() {
}
Point(coordinate_t _x, coordinate_t _y) : x(_x), y(_y) {
}
Point operator+(const Point &rhs) const {
Point res(*this);
return res += rhs;
}
Point operator-(const Point &rhs) const {
Point res(*this);
return res -= rhs;
}
Point operator*(const coordinate_t &rhs) const {
Point res(*this);
return res *= rhs;
}
Point operator/(const coordinate_t &rhs) const {
Point res(*this);
return res /= rhs;
}
inline bool operator<(const Point &b) {
if (sgn(x - b.x)) return sgn(x - b.x) < 0;
return sgn(y - b.y) < 0;
}
Point operator+=(const Point &rhs) {
x += rhs.x, y += rhs.y;
return *this;
}
Point operator-=(const Point &rhs) {
x -= rhs.x, y -= rhs.y;
return *this;
}
Point operator*=(const coordinate_t &rhs) {
x *= rhs, y *= rhs;
return *this;
}
Point operator/=(const coordinate_t &rhs) {
x /= rhs, y /= rhs;
return *this;
}
coordinate_t abs() const {
return std::sqrt(x * x + y * y);
}
coordinate_t arg() const {
return std::atan2(y, x);
}
Point normal() const {
return Point(-y, x);
}
Point unit() const {
return *this / abs();
}
};
inline bool operator<(const Point &a, const Point &b) {
if (sgn(a.x - b.x)) return sgn(a.x - b.x) < 0;
return sgn(a.y - b.y) < 0;
}
inline bool operator==(const Point &a, const Point &b) {
return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;
}
inline bool operator>(const Point &a, const Point &b) {
if (sgn(a.x - b.x)) return sgn(a.x - b.x) > 0;
return sgn(a.y - b.y) > 0;
}
std::istream &operator>>(std::istream &is, Point &p) {
coordinate_t x, y;
is >> x >> y;
p = {x, y};
return is;
}
std::ostream &operator<<(std::ostream &os, const Point &p) {
return os << p.x << ' ' << p.y;
}
Point rotate(const Point &p, const coordinate_t &theta) {
Point ret;
ret.x = p.x * cos(theta) - p.y * sin(theta);
ret.y = p.x * sin(theta) + p.y * cos(theta);
return ret;
}
coordinate_t dot(const Point &a, const Point &b) {
return a.x * b.x + a.y * b.y;
}
coordinate_t det(const Point &a, const Point &b) {
return a.x * b.y - a.y * b.x;
}
const int COUNTER_CLOCKWISE = 1;
const int CLOCKWISE = -1;
const int ONLINE_BACK = -2;
const int ONLINE_FRONT = 2;
const int ON_SEGMENT = 0;
int ccw(Point a, Point b, Point c) {
if (sgn(det(b - a, c - a)) > 0) {
return COUNTER_CLOCKWISE; // counter clockwise
}
if (sgn(det(b - a, c - a)) < 0) {
return CLOCKWISE; // clockwise
}
if (sgn(dot(b - a, c - a)) < 0) {
return ONLINE_BACK; // c - a - b
}
if (sgn(dot(a - b, c - b)) < 0) {
return ONLINE_FRONT; // a - b - c
}
return ON_SEGMENT; // a - c - b
}
struct Segment {
Point a, b;
Segment() {
}
Segment(Point _a, Point _b) : a(_a), b(_b) {
}
};
std::istream &operator>>(std::istream &is, Segment &s) {
Point a, b;
is >> a >> b;
s = {a, b};
return is;
};
struct Line {
Point a, b;
Line() {
}
Line(Point _a, Point _b) : a(_a), b(_b) {
}
Line(const Segment &s) : a(s.a), b(s.b) {
}
Line vertical_bisector() {
Point c = (a + b) / 2;
Point v = (a - b).normal();
return {c + v, c - v};
}
Point projection(const Point &p) const {
return a +
(b - a) * (dot(b - a, p - a) / ((b - a).abs() * (b - a).abs()));
}
Point reflection(const Point &p) const {
return projection(p) * 2 - p;
}
};
std::istream &operator>>(std::istream &is, Line &l) {
Point a, b;
is >> a >> b;
l = {a, b};
return is;
};
struct Polygon : std::vector<Point> {
Polygon(int n = 0) : std::vector<Point>(n) {
}
coordinate_t area() const {
coordinate_t ret = 0;
for (int i = 0; i < (int)size(); i++) {
ret += det((*this)[i], (*this)[(i + 1) % (int)size()]);
}
ret /= 2.0;
ret = std::fabs(ret);
return ret;
}
bool is_convex() const {
for (int i = 0; i < (int)size(); i++) {
if (ccw((*this)[i], (*this)[(i + 1) % (int)size()],
(*this)[(i + 2) % (int)size()]) == CLOCKWISE) {
return false;
}
}
return true;
}
coordinate_t diameter() const {
assert(is_convex());
coordinate_t ret = 0;
int r = 0;
for (int l = 0; l < (int)size(); l++) {
while (sgn(((*this)[l] - (*this)[r]).abs() -
((*this)[l] - (*this)[(r + 1) % (int)size()]).abs()) <
0) {
r++;
if (r == (int)size()) r = 0;
}
ret = std::max(ret, ((*this)[l] - (*this)[r]).abs());
}
return ret;
}
int contain(const Point &p) const {
bool is_in = false;
for (int i = 0; i < (int)size(); i++) {
int ccw_ = ccw((*this)[i], (*this)[(i + 1) % (int)size()], p);
if (ccw_ == ON_SEGMENT) {
return 1; // p is on a segment of polygon
}
Point a = (*this)[i] - p, b = (*this)[(i + 1) % (int)size()] - p;
if (b < a) std::swap(a, b);
if (sgn(a.x) <= 0 && sgn(b.x) > 0 && sgn(det(a, b)) < 0)
is_in ^= true;
}
return is_in ? 2 /* polygon contains p */ : 0;
}
};
struct Circle {
Point c;
coordinate_t r;
Circle() {
}
Circle(Point _c, coordinate_t _r) : c(_c), r(_r) {
assert(sgn(r) >= 0);
}
coordinate_t area() const {
return r * r * PI;
}
int contain(const Point &p) const {
return sgn((c - p).abs() - r) > 0 ? 0
: sgn((c - p).abs() - r) == 0 ? 1
: 2;
}
};
bool intersect(const Segment &s1, const Segment &s2);
bool intersect(const Line &l1, const Line &l2);
bool intersect(const Segment &s, const Line &l);
bool intersect(const Segment &s, const Circle &c);
bool intersect(const Line &s, const Circle &c);
Point cross_point(const Segment &s1, const Segment &s2);
Point cross_point(const Line &l1, const Line &l2);
Point cross_point(const Segment &s, const Line &l);
std::vector<Point> cross_points(const Segment &s, const Circle &c);
std::vector<Point> cross_points(const Line &l, const Circle &c);
coordinate_t dist(const Point &p1, const Point &p2) {
return (p1 - p2).abs();
}
coordinate_t dist(const Segment &s, const Point &p) {
if (sgn(dot(s.b - s.a, p - s.a)) < 0) {
return (p - s.a).abs();
}
if (sgn(dot(s.a - s.b, p - s.b)) < 0) {
return (p - s.b).abs();
}
return std::fabs(det(p - s.a, s.b - s.a)) / (s.b - s.a).abs();
}
coordinate_t dist(const Point &p, const Segment &s) {
return dist(s, p);
}
coordinate_t dist(const Segment &s1, const Segment &s2) {
if (intersect(s1, s2)) return 0;
return std::min(
{dist(s1, s2.a), dist(s1, s2.b), dist(s2, s1.a), dist(s2, s1.b)});
}
coordinate_t dist(const Line &l, const Point &p) {
return std::fabs(det(p - l.a, l.b - l.a)) / (l.b - l.a).abs();
}
coordinate_t dist(const Point &p, const Line &l) {
return dist(l, p);
}
coordinate_t dist(const Line &l1, const Line &l2) {
if (intersect(l1, l2)) return 0;
return dist(l1.a, l2);
}
coordinate_t dist(const Segment &s, const Line &l) {
if (intersect(s, l)) return 0;
return std::min(dist(s.a, l), dist(s.b, l));
}
coordinate_t dist(const Line &l, const Segment &s) {
return dist(s, l);
}
bool intersect(const Segment &s1, const Segment &s2) {
return sgn(ccw(s1.a, s1.b, s2.a) * ccw(s1.a, s1.b, s2.b)) <= 0 &&
sgn(ccw(s2.a, s2.b, s1.a) * ccw(s2.a, s2.b, s1.b)) <= 0;
}
bool intersect(const Line &l1, const Line &l2) {
return sgn(det(l1.b - l1.a, l2.b - l2.a)) != 0;
}
bool intersect(const Segment &s, const Line &l) {
return ccw(l.a, l.b, s.a) * ccw(l.a, l.b, s.b) == -1;
}
bool intersect(const Line &l, const Segment &s) {
return intersect(s, l);
}
bool intersect(const Segment &s, const Circle &c) {
if (sgn(dist(s, c.c) - c.r) > 0) return false;
return !(sgn((c.c - s.a).abs() - c.r) < 0 &&
sgn((c.c - s.b).abs() - c.r) < 0);
}
bool intersect(const Circle &c, const Segment &s) {
return intersect(s, c);
}
bool intersect(const Line &l, const Circle &c) {
return sgn(dist(l, c.c) - c.r) <= 0;
}
bool intersect(const Circle &c, const Line &l) {
return intersect(l, c);
}
bool intersect(Circle c1, Circle c2) {
return sgn((c1.c - c2.c).abs() - (c1.r + c2.r)) <= 0 &&
sgn((c1.c - c2.c).abs() - std::fabs(c1.r - c2.r)) >= 0;
}
Point cross_point(const Segment &s1, const Segment &s2) {
assert(intersect(s1, s2));
return cross_point(Line(s1), Line(s2));
}
Point cross_point(const Segment &s, const Line &l) {
assert(intersect(s, l));
return s.a + (s.b - s.a) *
(det(l.a - s.a, l.b - l.a) / det(s.b - s.a, l.b - l.a));
}
Point cross_point(const Line &l, const Segment &s) {
return cross_point(s, l);
}
Point cross_point(const Line &l1, const Line &l2) {
assert(intersect(l1, l2));
return l1.a + (l1.b - l1.a) * (det(l2.a - l1.a, l2.b - l2.a) /
det(l1.b - l1.a, l2.b - l2.a));
}
std::vector<Point> cross_points(const Segment &s, const Circle &c) {
if (!intersect(s, c)) return {};
std::vector<Point> ret = cross_points(Line(s), c);
ret.erase(std::remove_if(ret.begin(), ret.end(),
[&](Point p) {
return !(p == s.a) && !(p == s.b) &&
(p < s.a) == (p < s.b);
}),
ret.end());
return ret;
}
std::vector<Point> cross_points(const Circle &c, const Segment &s) {
return cross_points(s, c);
}
std::vector<Point> cross_points(const Line &l, const Circle &c) {
if (!intersect(l, c)) return {};
Point p = l.projection(c.c);
Point v = (l.b - l.a) *
std::sqrt(c.r * c.r - (p - c.c).abs() * (p - c.c).abs()) /
(l.b - l.a).abs();
v = std::max(v, v * -1);
return {p - v, p + v};
}
std::vector<Point> cross_points(const Circle &c, const Line &l) {
return cross_points(l, c);
}
std::vector<Point> cross_points(Circle c1, Circle c2) {
if (!intersect(c1, c2)) return {};
coordinate_t d = (c1.c - c2.c).abs();
coordinate_t d1 = (d + (c1.r * c1.r - c2.r * c2.r) / d) / 2;
coordinate_t h = std::sqrt(c1.r * c1.r - d1 * d1);
Point v = (c2.c - c1.c).normal();
v *= h / v.abs();
std::vector<Point> ret = {c1.c + (c2.c - c1.c) * (d1 / d) + v,
c1.c + (c2.c - c1.c) * (d1 / d) - v};
if (ret[0] > ret[1]) std::swap(ret[0], ret[1]);
return ret;
}
// 三角形の内接円
Circle incircle_of_triangle(const Point &pa, const Point &pb, const Point &pc) {
coordinate_t a = (pb - pc).abs(), b = (pc - pa).abs(), c = (pa - pb).abs();
Point p = (pa * a + pb * b + pc * c) / (a + b + c);
coordinate_t r = dist(Line(pa, pb), p);
return Circle(p, r);
}
// 三角形の内接円
Circle incircle_of_triangle(const Polygon &poly) {
assert((int)poly.size() == 3);
const Point &pa = poly[0], &pb = poly[1], &pc = poly[2];
return incircle_of_triangle(pa, pb, pc);
}
// 三角形の外接円
Circle circumscribed_circle_of_triangle(const Point &pa, const Point &pb,
const Point &pc) {
Line l1 = Line(pa, pb).vertical_bisector();
Line l2 = Line(pa, pc).vertical_bisector();
Point p = cross_point(l1, l2);
coordinate_t r = (pa - p).abs();
return Circle(p, r);
}
// 三角形の外接円
Circle circumscribed_circle_of_triangle(const Polygon &poly) {
assert((int)poly.size() == 3);
const Point &pa = poly[0], &pb = poly[1], &pc = poly[2];
return circumscribed_circle_of_triangle(pa, pb, pc);
}
// 凸包
Polygon convex_hull(std::vector<Point> ps) {
int n = int(ps.size());
std::sort(ps.begin(), ps.end());
Polygon ret(2 * n);
int k = 0;
for (int i = 0; i < n; ret[k++] = ps[i++]) {
while (k >= 2 &&
sgn(det(ret[k - 1] - ret[k - 2], ps[i] - ret[k - 2])) < 0) {
k--;
}
}
for (int i = n - 2, t = k + 1; i >= 0; ret[k++] = ps[i--]) {
while (k >= t &&
sgn(det(ret[k - 1] - ret[k - 2], ps[i] - ret[k - 2])) < 0) {
k--;
}
}
ret.resize(k - 1);
return ret;
}
// 最小包含円
Circle smallest_enclosing_circle(std::vector<Point> ps) {
assert((int)ps.size() >= 2);
std::random_device seed_gen;
std::mt19937_64 rnd(seed_gen());
std::shuffle(ps.begin(), ps.end(), rnd);
Circle ret((ps[0] + ps[1]) / 2, (ps[0] - ps[1]).abs() / 2);
for (int i = 2; i < (int)ps.size(); i++) {
if (ret.contain(ps[i])) continue;
ret = Circle((ps[0] + ps[i]) / 2, (ps[0] - ps[i]).abs() / 2);
for (int j = 1; j < i; j++) {
if (ret.contain(ps[j])) continue;
ret = Circle((ps[i] + ps[j]) / 2, (ps[i] - ps[j]).abs() / 2);
for (int k = 0; k < j; k++) {
if (ret.contain(ps[k])) continue;
ret = circumscribed_circle_of_triangle(ps[i], ps[j], ps[k]);
}
}
}
return ret;
}
// 円cと多角形pの共通部分の面積を返す。
coordinate_t area_of_intersection(Circle c, Polygon p) {
auto signed_area_of_triangle = [](Point a, Point b) -> coordinate_t {
return det(a, b);
};
auto signed_area_of_sector = [&c](Point a, Point b) -> coordinate_t {
return c.r * c.r * (rotate(b, -a.arg()).arg());
};
auto is_in_circle = [&c](Point a) -> bool {
return sgn(a.abs() - c.r) < 0;
};
coordinate_t ret = 0;
for (int i = 0; i < int(p.size()); i++) p[i] -= c.c;
for (int i = 0; i < int(p.size()); i++) {
const Point &a = p[i], &b = p[(i + 1) % int(p.size())];
if (!intersect(Segment(a, b), c)) {
ret += is_in_circle(a) ? signed_area_of_triangle(a, b)
: signed_area_of_sector(a, b);
} else {
std::vector<Point> ps = cross_points(Segment(a, b), c);
Point s = ps[0], t = ps[1 % int(ps.size())];
if ((a < b) != (s < t)) std::swap(s, t);
ret += is_in_circle(a) ? signed_area_of_triangle(a, s)
: signed_area_of_sector(a, s);
ret += signed_area_of_triangle(s, t);
ret += is_in_circle(b) ? signed_area_of_triangle(t, b)
: signed_area_of_sector(t, b);
}
}
ret = std::fabs(ret);
ret /= 2;
return ret;
}
// 円cと多角形pの共通部分の面積を返す。
coordinate_t area_of_intersection(Polygon p, Circle c) {
return area_of_intersection(c, p);
}
// 円c1と円c2の共通部分の面積を返す。
coordinate_t area_of_intersection(const Circle &c1, const Circle &c2) {
if (sgn(c1.r + c2.r - (c1.c - c2.c).abs()) <= 0) {
return 0;
}
if (sgn(std::fabs(c1.r - c2.r) - (c1.c - c2.c).abs()) >= 0) {
return std::min(c1.area(), c2.area());
}
auto unsigned_area_of_triangle = [](Circle c1, Circle c2,
Point p) -> coordinate_t {
return std::fabs(det(c2.c - c1.c, p - c1.c));
};
auto unsigned_area_of_sector = [](Circle c1, Circle c2,
Point p) -> coordinate_t {
return std::fabs(c1.r * c1.r *
rotate(c2.c - c1.c, -(p - c1.c).arg()).arg());
};
Point p = cross_points(c1, c2)[0];
coordinate_t ret = 0;
ret += unsigned_area_of_sector(c1, c2, p);
ret += unsigned_area_of_sector(c2, c1, p);
ret -= unsigned_area_of_triangle(c1, c2, p);
return ret;
}
// 凸多角形polyを直線lで切断したときに、その左側にできる凸多角形。
Polygon convex_cut_left(const Polygon &poly, const Line &l) {
assert(poly.is_convex());
Polygon ret;
for (int i = 0; i < (int)poly.size(); i++) {
if (ccw(l.a, l.b, poly[i]) != CLOCKWISE) {
ret.push_back(poly[i]);
}
Segment s(poly[i], poly[(i + 1) % (int)poly.size()]);
if (intersect(s, l)) {
ret.push_back(cross_point(s, l));
}
}
return ret;
}
// 凸多角形polyを直線lで切断したときに、その右側にできる凸多角形。
Polygon convex_cut_right(const Polygon &poly, const Line &l) {
assert(poly.is_convex());
Polygon ret;
for (int i = 0; i < (int)poly.size(); i++) {
if (ccw(l.a, l.b, poly[i]) != COUNTER_CLOCKWISE) {
ret.push_back(poly[i]);
}
Segment s(poly[i], poly[(i + 1) % (int)poly.size()]);
if (intersect(s, l)) {
ret.push_back(cross_point(s, l));
}
}
return ret;
}
// 点pを通る円cの接線。接点を返す。
std::vector<Point> tangent_points(const Circle &c, const Point &p) {
assert(sgn((p - c.c).abs() - c.r) >= 0);
coordinate_t r = std::sqrt((c.c - p).abs() * (c.c - p).abs() - c.r * c.r);
return cross_points(c, Circle(p, r));
}
// 円c1と円c2の共通接線の本数。
int count_common_tangent(const Circle &c1, const Circle &c2) {
if (sgn((c1.c - c2.c).abs() - (c1.r + c2.r)) > 0) {
return 4; // do not cross
}
if (sgn((c1.c - c2.c).abs() - (c1.r + c2.r)) == 0) {
return 3; // circumscribed
}
if (sgn((c1.c - c2.c).abs() - std::fabs(c1.r - c2.r)) > 0) {
return 2; // intersects
}
if (sgn((c1.c - c2.c).abs() - std::fabs(c1.r - c2.r)) == 0) {
return 1; // inscribed
}
return 0;
}
// 円c1と円c2の共通接線。円c1における接点を返す。
std::vector<Point> common_tangents(const Circle &c1, const Circle &c2) {
std::vector<Point> ret, ret1, ret2;
if (sgn((c1.c - c2.c).abs() - std::fabs(c1.r - c2.r)) >= 0) {
coordinate_t d = (c1.c - c2.c).abs();
coordinate_t r =
std::sqrt(d * d - (c1.r - c2.r) * (c1.r - c2.r) + c2.r * c2.r);
ret1 = cross_points(c1, Circle(c2.c, r));
}
if (sgn((c1.c - c2.c).abs() - (c1.r + c2.r)) >= 0) {
Point p = c1.c + (c2.c - c1.c) * c1.r / (c1.r + c2.r);
ret2 = tangent_points(c1, p);
}
std::merge(ret1.begin(), ret1.end(), ret2.begin(), ret2.end(),
std::back_inserter(ret));
ret.erase(std::unique(ret.begin(), ret.end()), ret.end());
return ret;
}
// (距離, 点のペア) を返す
std::pair<coordinate_t, std::pair<Point, Point>> closest_pair(
std::vector<Point> ps) {
std::sort(ps.begin(), ps.end(),
[](Point a, Point b) { return sgn(a.x - b.x) < 0; });
std::vector<Point> memo(ps.size());
auto dfs = [&](auto dfs, int l,
int r) -> std::pair<coordinate_t, std::pair<Point, Point>> {
if (r - l < 2) return {1e18, {Point(), Point()}};
int m = (r + l) / 2;
coordinate_t x = ps[m].x;
auto l_res = dfs(dfs, l, m), r_res = dfs(dfs, m, r);
auto [d, p] = (l_res.first < r_res.first ? l_res : r_res);
std::inplace_merge(ps.begin() + l, ps.begin() + m, ps.begin() + r,
[](Point a, Point b) { return sgn(a.y - b.y) < 0; });
int cur = 0;
for (int i = l; i < r; i++) {
if (std::fabs(ps[i].x - x) >= d) continue;
for (int j = cur - 1; j >= 0; j--) {
if (ps[i].y - memo[j].y >= d) break;
coordinate_t new_d = (ps[i] - memo[j]).abs();
if (new_d < d) {
d = new_d;
p = {ps[i], memo[j]};
}
}
memo[cur++] = ps[i];
}
return {d, p};
};
return dfs(dfs, 0, (int)ps.size());
}
// (距離, 点のペア) を返す
std::pair<coordinate_t, std::pair<Point, Point>> farthest_pair(
std::vector<Point> ps) {
ps = convex_hull(ps);
std::pair<coordinate_t, std::pair<Point, Point>> ret = {
0, std::make_pair(ps[0], ps[0])};
int r = 0;
for (int l = 0; l < (int)ps.size(); l++) {
while (sgn((ps[l] - ps[r]).abs() -
(ps[l] - ps[(r + 1) % (int)ps.size()]).abs()) < 0) {
r++;
if (r == (int)ps.size()) r = 0;
}
if (sgn(ret.first - (ps[l] - ps[r]).abs()) < 0) {
ret.first = (ps[l] - ps[r]).abs();
ret.second = {ps[l], ps[r]};
}
}
return ret;
}
} // namespace geometry
#pragma endregion
int main() {
int n;
cin >> n;
if (n == 0) {
cout << 1 << '\n';
return 0;
}
vector<int> x(n), y(n);
const int offset = 11000;
vector<unordered_map<int, int>> st(22000);
rep(i, n) {
cin >> x[i] >> y[i];
st[x[i] + offset][y[i]] = i;
}
UnionFind uf(n);
rep(i, n) {
for (int ny = y[i] - 100; ny <= y[i] + 100; ny++) {
for (int nx = x[i] - 100; nx <= x[i] + 100; nx++) {
if ((x[i] - nx) * (x[i] - nx) + (y[i] - ny) * (y[i] - ny) <=
100 &&
st[nx + offset].count(ny)) {
int j = st[nx + offset][ny];
uf.unite(i, j);
}
}
}
}
double ans = 2;
for (auto &v : uf.groups()) {
vector<geometry::Point> ps;
for (int i : v) ps.emplace_back(x[i], y[i]);
chmax(ans, geometry::farthest_pair(ps).first + 2);
}
cout << fixed << setprecision(20);
cout << ans << '\n';
}