#830000 (C++23) No.2173 Nightcord

• 問題: No.2173 Nightcord
• ユーザー: hitonanode
• 提出日時: 2023-01-03 08:19:17
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2,420 ms / 2,525 ms
• コード長: 20,601 bytes
• コンパイル時間: 3,008 ms
• コンパイル使用メモリ: 219,292 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-11-27 01:43:58
• 合計ジャッジ時間: 53,875 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

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	1 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	1,847 ms; 5,248 KB
testcase_04	AC	5 ms; 5,248 KB
testcase_05	AC	1,244 ms; 5,248 KB
testcase_06	AC	167 ms; 5,248 KB
testcase_07	AC	334 ms; 5,248 KB
testcase_08	AC	1,948 ms; 5,248 KB
testcase_09	AC	1,035 ms; 5,248 KB
testcase_10	AC	599 ms; 5,248 KB
testcase_11	AC	39 ms; 5,248 KB
testcase_12	AC	1,237 ms; 5,248 KB
testcase_13	AC	81 ms; 5,248 KB
testcase_14	AC	1,686 ms; 5,248 KB
testcase_15	AC	1,261 ms; 5,248 KB
testcase_16	AC	2,420 ms; 5,248 KB
testcase_17	AC	176 ms; 5,248 KB
testcase_18	AC	684 ms; 5,248 KB
testcase_19	AC	7 ms; 5,248 KB
testcase_20	AC	726 ms; 5,248 KB
testcase_21	AC	1,010 ms; 5,248 KB
testcase_22	AC	1,239 ms; 5,248 KB
testcase_23	AC	1,119 ms; 5,248 KB
testcase_24	AC	1,854 ms; 5,248 KB
testcase_25	AC	1,545 ms; 5,248 KB
testcase_26	AC	1,903 ms; 5,248 KB
testcase_27	AC	12 ms; 5,248 KB
testcase_28	AC	1,721 ms; 5,248 KB
testcase_29	AC	230 ms; 5,248 KB
testcase_30	AC	2,059 ms; 5,248 KB
testcase_31	AC	399 ms; 5,248 KB
testcase_32	AC	214 ms; 5,248 KB
testcase_33	AC	1,747 ms; 5,248 KB
testcase_34	AC	2,268 ms; 5,248 KB
testcase_35	AC	1,085 ms; 5,248 KB
testcase_36	AC	1,384 ms; 5,248 KB
testcase_37	AC	1,872 ms; 5,248 KB
testcase_38	AC	1,425 ms; 5,248 KB
testcase_39	AC	186 ms; 5,248 KB
testcase_40	AC	2,238 ms; 5,248 KB
testcase_41	AC	1,447 ms; 5,248 KB
testcase_42	AC	1,596 ms; 5,248 KB
testcase_43	AC	106 ms; 5,248 KB
testcase_44	AC	4 ms; 5,248 KB
testcase_45	AC	381 ms; 5,248 KB
testcase_46	AC	1,391 ms; 5,248 KB
testcase_47	AC	524 ms; 5,248 KB
testcase_48	AC	417 ms; 5,248 KB
testcase_49	AC	10 ms; 5,248 KB
testcase_50	AC	109 ms; 5,248 KB
testcase_51	AC	573 ms; 5,248 KB
testcase_52	AC	6 ms; 5,248 KB
testcase_53	AC	575 ms; 5,248 KB
testcase_54	AC	943 ms; 5,248 KB
testcase_55	AC	174 ms; 5,248 KB
testcase_56	AC	392 ms; 5,248 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 <numeric>
#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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
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.norm2() < v2.norm2()) 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;
}

using Pt = Point2d<lint>;

void Yes() {
    puts("Yes");
    exit(0);
}


// Point on grid, sortable by its argument
struct Point {
    constexpr static double eps = 1e-2;
    long long X, Y;
    double theta;
    Point() = default;
    Point(long long x, long long y) : X(x), Y(y), theta(std::atan2(y, x)) {}
    bool operator<(const Point &r) const {
        double b = theta - r.theta;
        return std::abs(b) > eps ? (b < 0) : (X * r.Y > r.X * Y);
    }
    bool operator==(const Point &r) const {
        return std::abs(theta - r.theta) < eps and X * r.Y == r.X * Y;
    }
    bool operator!=(const Point &r) const { return !(*this == r); }
    void rotate_pi() {
        theta += M_PI;
        X *= -1;
        Y *= -1;
    }
};

// Key class must be comparable
// Example: [(2, 3), (1, 5), (2, 2), (2, 3), (1, 4)] -> [(1, [5, 4]), (2, [3, 2, 3])]
// Verified: https://atcoder.jp/contests/abc259/tasks/abc259_h
template <class Key, class Value>
std::vector<std::pair<Key, std::vector<Value>>> groupby(std::vector<std::pair<Key, Value>> xs) {
    using KV = std::pair<Key, Value>;
    std::stable_sort(
        xs.begin(), xs.end(), [&](const KV &l, const KV &r) { return l.first < r.first; });

    std::vector<std::pair<Key, std::vector<Value>>> ret;
    for (const auto &x : xs) {
        if (ret.empty() or ret.back().first != x.first) {
            ret.emplace_back(x.first, std::vector<Value>());
        }
        ret.back().second.push_back(x.second);
    }
    return ret;
}

int main() {
    int N, K;
    cin >> N >> K;
    vector<vector<Pt>> vs(2);
    vector<vector<Point2d<double>>> vfs;
    REP(i, N) {
        int x, y, c;
        cin >> x >> y >> c;
        vs.at(c - 1).emplace_back(x, y);
    }

    REP(_, 2) {
        for (const Pt &p : vs.front()) {
            vector<pair<Point, pair<bool, lint>>> as;
            for (const Pt &q : vs.front()) {
                if (p == q) continue;
                auto dx = q - p;
                as.emplace_back(Point(dx.x, dx.y), make_pair(false, dx.norm2()));
            }
            for (const Pt &q : vs.back()) {
                auto dx = q - p;
                as.emplace_back(Point(dx.x, dx.y), make_pair(true, dx.norm2()));
            }

            for (const auto &[key, vals] : groupby(as)) {
                lint min1 = ((1LL << 62) - 1) * 2 , max0 = -1;
                for (auto [flg, norm2] : vals) {
                    if (flg) {
                        chmin(min1, norm2);
                    } else {
                        chmax(max0, norm2);
                    }
                }
                if (min1 < max0) Yes();
            }
        }
        swap(vs.front(), vs.back());
    }

    for (auto &v : vs) {
        vector<Pt> w;
        vector<Point2d<double>> wf;
        for (int i : convex_hull(v)) {
            w.push_back(v.at(i));
            wf.push_back(Point2d<double>(v.at(i).x, v.at(i).y));
        }
        v = w;
        vfs.push_back(wf);
    }
    dbg(vs);

    if (K > 3 and vs.front().size() and vs.back().size()) {
        REP(_, 2) {
            for (const auto &p : vs.back()) {
                auto flast = vs.front().back();
                bool good = true;
                for (const auto &f : vs.front()) {
                    int c = ccw(p, flast, f);
                    if (c != 1) good = false;
                    flast = f;
                }
                if (good) Yes();
                // double rot = 0;
                // REP(i, vfs.front().size()) {
                //     rot += ((vfs.front().at((i + 1) % vfs.front().size()) - pf) / (vfs.front().at(i) - pf)).arg();
                // }
                // if (abs(rot) < 0.1) Yes();
            }

            Pt flast = vs.front().back();
            for (const auto &f : vs.front()) {
                Pt blast = vs.back().back();
                for (const auto &b : vs.back()) {
                    if (intersect_open_segments(flast, f, blast, b)) Yes();
                    blast = b;
                }
                flast = f;
            }

            swap(vs.front(), vs.back());
            swap(vfs.front(), vfs.back());
        }
    }

    puts("No");
}