#943601 (C++23) No.2602 Real Collider

• 問題: No.2602 Real Collider
• ユーザー: hitonanode
• 提出日時: 2024-01-12 22:40:44
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 80 ms / 2,000 ms
• コード長: 17,238 bytes
• コンパイル時間: 2,196 ms
• コンパイル使用メモリ: 185,552 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-09-27 23:24:27
• 合計ジャッジ時間: 7,475 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	80 ms; 5,376 KB
testcase_11	AC	31 ms; 5,376 KB
testcase_12	AC	41 ms; 5,376 KB
testcase_13	AC	20 ms; 5,376 KB
testcase_14	AC	45 ms; 5,376 KB
testcase_15	AC	22 ms; 5,376 KB
testcase_16	AC	35 ms; 5,376 KB
testcase_17	AC	40 ms; 5,376 KB
testcase_18	AC	29 ms; 5,376 KB
testcase_19	AC	34 ms; 5,376 KB
testcase_20	AC	48 ms; 5,376 KB
testcase_21	AC	27 ms; 5,376 KB
testcase_22	AC	34 ms; 5,376 KB
testcase_23	AC	23 ms; 5,376 KB
testcase_24	AC	32 ms; 5,376 KB
testcase_25	AC	33 ms; 5,376 KB
testcase_26	AC	23 ms; 5,376 KB
testcase_27	AC	38 ms; 5,376 KB
testcase_28	AC	40 ms; 5,376 KB
testcase_29	AC	32 ms; 5,376 KB
testcase_30	AC	36 ms; 5,376 KB
testcase_31	AC	38 ms; 5,376 KB
testcase_32	AC	32 ms; 5,376 KB
testcase_33	AC	37 ms; 5,376 KB
testcase_34	AC	37 ms; 5,376 KB
testcase_35	AC	24 ms; 5,376 KB
testcase_36	AC	23 ms; 5,376 KB
testcase_37	AC	41 ms; 5,376 KB
testcase_38	AC	42 ms; 5,376 KB
testcase_39	AC	40 ms; 5,376 KB
testcase_40	AC	20 ms; 5,376 KB
testcase_41	AC	45 ms; 5,376 KB
testcase_42	AC	35 ms; 5,376 KB
testcase_43	AC	37 ms; 5,376 KB
testcase_44	AC	45 ms; 5,376 KB
testcase_45	AC	29 ms; 5,376 KB
testcase_46	AC	28 ms; 5,376 KB
testcase_47	AC	39 ms; 5,376 KB
testcase_48	AC	30 ms; 5,376 KB
testcase_49	AC	27 ms; 5,376 KB
testcase_50	AC	21 ms; 5,376 KB
testcase_51	AC	21 ms; 5,376 KB
testcase_52	AC	16 ms; 5,376 KB
testcase_53	AC	35 ms; 5,376 KB
testcase_54	AC	30 ms; 5,376 KB
testcase_55	AC	33 ms; 5,376 KB
testcase_56	AC	32 ms; 5,376 KB
testcase_57	AC	29 ms; 5,376 KB
testcase_58	AC	13 ms; 5,376 KB
testcase_59	AC	34 ms; 5,376 KB
testcase_60	AC	30 ms; 5,376 KB
testcase_61	AC	25 ms; 5,376 KB
testcase_62	AC	37 ms; 5,376 KB
testcase_63	AC	43 ms; 5,376 KB
testcase_64	AC	50 ms; 5,376 KB
testcase_65	AC	24 ms; 5,376 KB
testcase_66	AC	40 ms; 5,376 KB
testcase_67	AC	19 ms; 6,940 KB
testcase_68	AC	22 ms; 6,944 KB
testcase_69	AC	16 ms; 6,944 KB
testcase_70	AC	19 ms; 6,940 KB
testcase_71	AC	23 ms; 6,940 KB
testcase_72	AC	36 ms; 6,940 KB
testcase_73	AC	28 ms; 6,944 KB
testcase_74	AC	38 ms; 6,940 KB
testcase_75	AC	38 ms; 6,944 KB
testcase_76	AC	33 ms; 6,944 KB
testcase_77	AC	33 ms; 6,940 KB
testcase_78	AC	42 ms; 6,940 KB
testcase_79	AC	38 ms; 6,940 KB
testcase_80	AC	42 ms; 6,944 KB

ソースコード

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

#include <algorithm>
#include <cassert>
#include <cmath>
#include <complex>
#include <iostream>
#include <tuple>
#include <utility>
#include <vector>

template <typename T_P> struct Point2d {
    static T_P EPS;
    static void set_eps(T_P e) { EPS = e; }
    T_P x, y;
    Point2d() : x(0), y(0) {}
    Point2d(T_P x, T_P y) : x(x), y(y) {}
    Point2d(const std::pair<T_P, T_P> &p) : x(p.first), y(p.second) {}
    Point2d(const std::complex<T_P> &p) : x(p.real()), y(p.imag()) {}
    std::complex<T_P> to_complex() const noexcept { return {x, y}; }
    Point2d operator+(const Point2d &p) const noexcept { return Point2d(x + p.x, y + p.y); }
    Point2d operator-(const Point2d &p) const noexcept { return Point2d(x - p.x, y - p.y); }
    Point2d operator*(const Point2d &p) const noexcept {
        static_assert(std::is_floating_point<T_P>::value == true);
        return Point2d(x * p.x - y * p.y, x * p.y + y * p.x);
    }
    Point2d operator*(T_P d) const noexcept { return Point2d(x * d, y * d); }
    Point2d operator/(T_P d) const noexcept {
        static_assert(std::is_floating_point<T_P>::value == true);
        return Point2d(x / d, y / d);
    }
    Point2d inv() const {
        static_assert(std::is_floating_point<T_P>::value == true);
        return conj() / norm2();
    }
    Point2d operator/(const Point2d &p) const { return (*this) * p.inv(); }
    bool operator<(const Point2d &r) const noexcept { return x != r.x ? x < r.x : y < r.y; }
    bool operator==(const Point2d &r) const noexcept { return x == r.x and y == r.y; }
    bool operator!=(const Point2d &r) const noexcept { return !((*this) == r); }
    T_P dot(Point2d p) const noexcept { return x * p.x + y * p.y; }
    T_P det(Point2d p) const noexcept { return x * p.y - y * p.x; }
    T_P absdet(Point2d p) const noexcept { return std::abs(det(p)); }
    T_P norm() const noexcept {
        static_assert(std::is_floating_point<T_P>::value == true);
        return std::sqrt(x * x + y * y);
    }
    T_P norm2() const noexcept { return x * x + y * y; }
    T_P arg() const noexcept { return std::atan2(y, x); }
    // rotate point/vector by rad
    Point2d rotate(T_P rad) const noexcept {
        static_assert(std::is_floating_point<T_P>::value == true);
        return Point2d(x * std::cos(rad) - y * std::sin(rad), x * std::sin(rad) + y * std::cos(rad));
    }
    Point2d normalized() const {
        static_assert(std::is_floating_point<T_P>::value == true);
        return (*this) / this->norm();
    }
    Point2d conj() const noexcept { return Point2d(x, -y); }

    template <class IStream> friend IStream &operator>>(IStream &is, Point2d &p) {
        T_P x, y;
        is >> x >> y;
        p = Point2d(x, y);
        return is;
    }
    template <class OStream> friend OStream &operator<<(OStream &os, const Point2d &p) {
        return os << '(' << p.x << ',' << p.y << ')';
    }
};
template <> double Point2d<double>::EPS = 1e-9;
template <> long double Point2d<long double>::EPS = 1e-12;
template <> long long Point2d<long long>::EPS = 0;

template <typename T_P>
int ccw(const Point2d<T_P> &a, const Point2d<T_P> &b, const Point2d<T_P> &c) {
    // a->b->cの曲がり方
    Point2d<T_P> v1 = b - a;
    Point2d<T_P> v2 = c - a;
    if (v1.det(v2) > Point2d<T_P>::EPS) return 1;   // 左折
    if (v1.det(v2) < -Point2d<T_P>::EPS) return -1; // 右折
    if (v1.dot(v2) < -Point2d<T_P>::EPS) return 2;  // c-a-b
    if (v1.norm() < v2.norm()) return -2;           // a-b-c
    return 0;                                       // a-c-b
}

// Convex hull （凸包）
// return: IDs of vertices used for convex hull, counterclockwise
// include_boundary: If true, interior angle pi is allowed
template <typename T_P>
std::vector<int> convex_hull(const std::vector<Point2d<T_P>> &ps, bool include_boundary = false) {
    int n = ps.size();
    if (n <= 1) return std::vector<int>(n, 0);
    std::vector<std::pair<Point2d<T_P>, int>> points(n);
    for (size_t i = 0; i < ps.size(); i++) points[i] = std::make_pair(ps[i], i);
    std::sort(points.begin(), points.end());
    int k = 0;
    std::vector<std::pair<Point2d<T_P>, int>> qs(2 * n);
    auto ccw_check = [&](int c) { return include_boundary ? (c == -1) : (c <= 0); };
    for (int i = 0; i < n; i++) {
        while (k > 1 and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
        qs[k++] = points[i];
    }
    for (int i = n - 2, t = k; i >= 0; i--) {
        while (k > t and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
        qs[k++] = points[i];
    }
    std::vector<int> ret(k - 1);
    for (int i = 0; i < k - 1; i++) ret[i] = qs[i].second;
    return ret;
}

// Solve r1 + t1 * v1 == r2 + t2 * v2
template <typename T_P, typename std::enable_if<std::is_floating_point<T_P>::value>::type * = nullptr>
Point2d<T_P> lines_crosspoint(Point2d<T_P> r1, Point2d<T_P> v1, Point2d<T_P> r2, Point2d<T_P> v2) {
    static_assert(std::is_floating_point<T_P>::value == true);
    assert(v2.det(v1) != 0);
    return r1 + v1 * (v2.det(r2 - r1) / v2.det(v1));
}

// Whether two segments s1t1 & s2t2 intersect or not (endpoints not included)
// Google Code Jam 2013 Round 3 - Rural Planning
// Google Code Jam 2021 Round 3 - Fence Design
template <typename T>
bool intersect_open_segments(Point2d<T> s1, Point2d<T> t1, Point2d<T> s2, Point2d<T> t2) {
    if (s1 == t1 or s2 == t2) return false; // Not segment but point
    int nbad = 0;
    for (int t = 0; t < 2; t++) {
        Point2d<T> v1 = t1 - s1, v2 = t2 - s2;
        T den = v2.det(v1);
        if (den == 0) {
            if (s1.det(v1) == s2.det(v1)) {
                auto L1 = s1.dot(v1), R1 = t1.dot(v1);
                auto L2 = s2.dot(v1), R2 = t2.dot(v1);
                if (L1 > R1) std::swap(L1, R1);
                if (L2 > R2) std::swap(L2, R2);
                if (L1 > L2) std::swap(L1, L2), std::swap(R1, R2);
                return R1 > L2;
            } else {
                return false;
            }
        } else {
            auto num = v2.det(s2 - s1);
            if ((0 < num and num < den) or (den < num and num < 0)) nbad++;
        }
        std::swap(s1, s2);
        std::swap(t1, t2);
    }
    return nbad == 2;
}

// Whether point p is on segment (s, t) (endpoints not included)
// Google Code Jam 2013 Round 3 - Rural Planning
template <typename PointNd> bool is_point_on_open_segment(PointNd s, PointNd t, PointNd p) {
    if (s == t) return false; // not segment but point
    if (p == s or p == t) return false;
    auto v = t - s, w = p - s;
    if (v.absdet(w)) return false;
    auto vv = v.dot(v), vw = v.dot(w);
    return vw > 0 and vw < vv;
}

// Convex cut
// Cut the convex polygon g by line p1->p2 and return the leftward one
template <typename T_P>
std::vector<Point2d<T_P>>
convex_cut(const std::vector<Point2d<T_P>> &g, Point2d<T_P> p1, Point2d<T_P> p2) {
    static_assert(std::is_floating_point<T_P>::value == true);
    assert(p1 != p2);
    std::vector<Point2d<T_P>> ret;
    for (int i = 0; i < (int)g.size(); i++) {
        const Point2d<T_P> &now = g[i], &nxt = g[(i + 1) % g.size()];
        if (ccw(p1, p2, now) != -1) ret.push_back(now);
        if ((ccw(p1, p2, now) == -1) xor (ccw(p1, p2, nxt) == -1)) {
            ret.push_back(lines_crosspoint(now, nxt - now, p1, p2 - p1));
        }
    }
    return ret;
}

// 2円の交点 (ABC157F, SRM 559 Div.1 900)
template <typename T_P>
std::vector<Point2d<T_P>>
IntersectTwoCircles(const Point2d<T_P> &Ca, T_P Ra, const Point2d<T_P> &Cb, T_P Rb) {
    static_assert(std::is_floating_point<T_P>::value == true);
    T_P d = (Ca - Cb).norm();
    if (Ra + Rb < d) return {};
    T_P rc = (d * d + Ra * Ra - Rb * Rb) / (2 * d);
    T_P rs2 = Ra * Ra - rc * rc;
    if (rs2 < 0) return {};
    T_P rs = std::sqrt(rs2);
    Point2d<T_P> diff = (Cb - Ca) / d;
    return {Ca + diff * Point2d<T_P>(rc, rs), Ca + diff * Point2d<T_P>(rc, -rs)};
}

// Solve |x0 + vt| = R (SRM 543 Div.1 1000, GCJ 2016 R3 C)
template <typename PointNd, typename Float>
std::vector<Float> IntersectCircleLine(const PointNd &x0, const PointNd &v, Float R) {
    static_assert(std::is_floating_point<Float>::value == true);
    Float b = Float(x0.dot(v)) / v.norm2();
    Float c = Float(x0.norm2() - Float(R) * R) / v.norm2();
    if (b * b - c < 0) return {};
    Float ret1 = -b + sqrtl(b * b - c) * (b > 0 ? -1 : 1);
    Float ret2 = c / ret1;
    return ret1 < ret2 ? std::vector<Float>{ret1, ret2} : std::vector<Float>{ret2, ret1};
}

// Distance between point p <-> line ab
template <typename PointFloat>
decltype(PointFloat::x)
DistancePointLine(const PointFloat &p, const PointFloat &a, const PointFloat &b) {
    assert(a != b);
    return (b - a).absdet(p - a) / (b - a).norm();
}

// Distance between point p <-> line segment ab
template <typename PointFloat>
decltype(PointFloat::x)
DistancePointSegment(const PointFloat &p, const PointFloat &a, const PointFloat &b) {
    if (a == b) {
        return (p - a).norm();
    } else if ((p - a).dot(b - a) <= 0) {
        return (p - a).norm();
    } else if ((p - b).dot(a - b) <= 0) {
        return (p - b).norm();
    } else {
        return DistancePointLine<PointFloat>(p, a, b);
    }
}

// Area of polygon (might be negative)
template <typename T_P> T_P signed_area_of_polygon(const std::vector<Point2d<T_P>> &poly) {
    static_assert(std::is_floating_point<T_P>::value == true);
    T_P area = 0;
    for (size_t i = 0; i < poly.size(); i++) area += poly[i].det(poly[(i + 1) % poly.size()]);
    return area * 0.5;
}


int main() {
    int Q;
    cin >> Q;

    using Float = long double;
    using Pt = Point2d<Float>;

    vector<Pt> ps(3);
    cin >> ps;

    Pt center(0, 0);
    Float rad2 = -1;

    REP(_, 3) {
        if ((ps.at(1) - ps.at(0)).dot(ps.at(2) - ps.at(0)) <= 0) {
            center = (ps.at(1) + ps.at(2)) * 0.5;
            rad2 = (ps.at(1) - center).norm2();
        }

        rotate(ps.begin(), ps.begin() + 1, ps.end());
    }

    dbg(rad2);

    if (rad2 < 0) {
        Float a2 = (ps.at(1) - ps.at(2)).norm2();
        Float b2 = (ps.at(0) - ps.at(2)).norm2();
        Float c2 = (ps.at(0) - ps.at(1)).norm2();
        Float den = a2 * (b2 + c2 - a2) + b2 * (c2 + a2 - b2) + c2 * (a2 + b2 - c2);
        center = (ps.at(0) * a2 * (b2 + c2 - a2) + ps.at(1) * b2 * (c2 + a2 - b2) + ps.at(2) * c2 * (a2 + b2 - c2)) / den;

        rad2 = (ps.at(0) - center).norm2();
    }

    while (Q--) {
        Pt p;
        cin >> p;

        auto d = (p - center).norm2();
        if (d <= rad2 + 1e-10) {
            puts("Yes");
        } else {
            puts("No");
        }
    }
}