#943940 (C++23) No.2602 Real Collider

提出ソース
結果

問題	No.2602 Real Collider
ユーザー	👑 bo9chan
提出日時	2024-01-13 08:20:27
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	698 ms / 2,000 ms
コード長	35,407 bytes
コンパイル時間	5,348 ms
コンパイル使用メモリ	408,464 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-09-28 01:13:36
合計ジャッジ時間	24,957 ms
ジャッジサーバーID （参考情報）	judge3 / judge2
このコードへのチャレンジ
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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	2 ms 6,812 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	698 ms 6,940 KB
testcase_11	AC	214 ms 6,940 KB
testcase_12	AC	192 ms 6,940 KB
testcase_13	AC	93 ms 6,944 KB
testcase_14	AC	207 ms 6,944 KB
testcase_15	AC	177 ms 6,944 KB
testcase_16	AC	259 ms 6,944 KB
testcase_17	AC	283 ms 6,940 KB
testcase_18	AC	135 ms 6,944 KB
testcase_19	AC	166 ms 6,940 KB
testcase_20	AC	318 ms 6,944 KB
testcase_21	AC	132 ms 6,940 KB
testcase_22	AC	157 ms 6,944 KB
testcase_23	AC	103 ms 6,940 KB
testcase_24	AC	150 ms 6,948 KB
testcase_25	AC	156 ms 6,940 KB
testcase_26	AC	153 ms 6,940 KB
testcase_27	AC	178 ms 6,944 KB
testcase_28	AC	245 ms 6,944 KB
testcase_29	AC	158 ms 6,940 KB
testcase_30	AC	174 ms 6,944 KB
testcase_31	AC	335 ms 6,940 KB
testcase_32	AC	234 ms 6,944 KB
testcase_33	AC	330 ms 6,940 KB
testcase_34	AC	250 ms 6,940 KB
testcase_35	AC	211 ms 6,940 KB
testcase_36	AC	146 ms 6,940 KB
testcase_37	AC	356 ms 6,944 KB
testcase_38	AC	277 ms 6,940 KB
testcase_39	AC	361 ms 6,944 KB
testcase_40	AC	131 ms 6,940 KB
testcase_41	AC	321 ms 6,940 KB
testcase_42	AC	238 ms 6,940 KB
testcase_43	AC	237 ms 6,940 KB
testcase_44	AC	339 ms 6,940 KB
testcase_45	AC	195 ms 6,940 KB
testcase_46	AC	237 ms 6,940 KB
testcase_47	AC	310 ms 6,940 KB
testcase_48	AC	213 ms 6,940 KB
testcase_49	AC	246 ms 6,940 KB
testcase_50	AC	139 ms 6,940 KB
testcase_51	AC	160 ms 6,944 KB
testcase_52	AC	103 ms 6,944 KB
testcase_53	AC	336 ms 6,944 KB
testcase_54	AC	201 ms 6,940 KB
testcase_55	AC	227 ms 6,944 KB
testcase_56	AC	223 ms 6,944 KB
testcase_57	AC	202 ms 6,940 KB
testcase_58	AC	74 ms 6,940 KB
testcase_59	AC	311 ms 6,940 KB
testcase_60	AC	206 ms 6,944 KB
testcase_61	AC	163 ms 6,940 KB
testcase_62	AC	253 ms 6,940 KB
testcase_63	AC	284 ms 6,944 KB
testcase_64	AC	429 ms 6,940 KB
testcase_65	AC	172 ms 6,944 KB
testcase_66	AC	290 ms 6,940 KB
testcase_67	AC	129 ms 6,940 KB
testcase_68	AC	157 ms 6,940 KB
testcase_69	AC	102 ms 6,944 KB
testcase_70	AC	125 ms 6,944 KB
testcase_71	AC	220 ms 6,940 KB
testcase_72	AC	246 ms 6,940 KB
testcase_73	AC	211 ms 6,944 KB
testcase_74	AC	335 ms 6,944 KB
testcase_75	AC	272 ms 6,940 KB
testcase_76	AC	314 ms 6,940 KB
testcase_77	AC	243 ms 6,940 KB
testcase_78	AC	400 ms 6,944 KB
testcase_79	AC	255 ms 6,944 KB
testcase_80	AC	296 ms 6,944 KB
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ソースコード

raw source code
#ifdef __LOCAL
#include <mytemplate.hpp>  // プリコンパイル済みヘッダ ~/local/include/mytemplate.hpp.gch
#else
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream> 
#include <iterator>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#endif
#pragma GCC target "no-avx"  // gcc12.2のバグ回避用。少し実行速度が落ちる
using namespace std;
#include <boost/multiprecision/cpp_int.hpp>
using bint = boost::multiprecision::cpp_int;
using int128 = __int128_t;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vvd = vector<vd>;
using vc = vector<char>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
#define REP1(i, n) REP3(i, 0, n, 1)
#define REP2(i, s, n) REP3(i, s, n, 1)
#define REP3(i, s, n, d) for(ll i = (ll)(s); i < (ll)(n); i += (d))
#define REP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define rep(...) REP_OVERLOAD(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)
#define DEP1(i, n) DEP3(i, n, -1, 1)
#define DEP2(i, n, s) DEP3(i, n, s, 1)
#define DEP3(i, n, s, d) for(ll i = (ll)(n); (ll)(s) < i; i -= (d))
#define DEP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define dep(...) DEP_OVERLOAD(__VA_ARGS__, DEP3, DEP2, DEP1)(__VA_ARGS__)
#define fore(e, a) for (auto&& e: (a))
#define len(a) (ll)(a).size()
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define th third
/*********    C O N S T A N T    **********/
constexpr ll INF = LONG_LONG_MAX / 2 - 10000LL;  // 4,611,686,018,427,377,903  ~= 4.6e+18, 19桁
const double PI = acos(-1);
/*********       P A I R       **********/
template<class T, class U> inline pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U> b);
template<class T, class U> inline pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U> b);
template<class T, class U> inline pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U> b);
template<class T, class U> inline pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U> b);
template<class T, class U> inline pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U> b);
template<class T, class U, class V> inline pair<T, U>& operator+=(pair<T, U>& a, const V b);
template<class T, class U, class V> inline pair<T, U>& operator-=(pair<T, U>& a, const V b);
template<class T, class U, class V> inline pair<T, U>& operator*=(pair<T, U>& a, const V b);
template<class T, class U, class V> inline pair<T, U>& operator/=(pair<T, U>& a, const V b);
template<class T, class U, class V> inline pair<T, U>& operator%=(pair<T, U>& a, const V b);
template<class T, class U, class V> inline pair<T, U> operator+(pair<T, U> a, const V& b);
template<class T, class U, class V> inline pair<T, U> operator-(pair<T, U> a, const V& b);
template<class T, class U, class V> inline pair<T, U> operator*(pair<T, U> a, const V& b);
template<class T, class U, class V> inline pair<T, U> operator/(pair<T, U> a, const V& b);
template<class T, class U, class V> inline pair<T, U> operator%(pair<T, U> a, const V& b);
template<class T, class U> inline pair<T, U> operator+(pair<T, U> a);
template<class T, class U> inline pair<T, U> operator-(pair<T, U> a);
template<class T, class U> istream& operator >>(istream& stream, pair<T, U>& a);
template<class T, class U> ostream& operator <<(ostream &stream, const pair<T, U>& a);
/*********       V E C T O R      **********/
template<class T> inline vector<T>& operator+=(vector<T>& a, const vector<T> b);
template<class T> inline vector<T>& operator-=(vector<T>& a, const vector<T> b);
template<class T> inline vector<T>& operator*=(vector<T>& a, const vector<T> b);
template<class T> inline vector<T>& operator/=(vector<T>& a, const vector<T> b);
template<class T> inline vector<T>& operator%=(vector<T>& a, const vector<T> b);
template<class T, class U> inline vector<T>& operator+=(vector<T>& a, const U b);
template<class T, class U> inline vector<T>& operator-=(vector<T>& a, const U b);
template<class T, class U> inline vector<T>& operator*=(vector<T>& a, const U b);
template<class T, class U> inline vector<T>& operator/=(vector<T>& a, const U b);
template<class T, class U> inline vector<T>& operator%=(vector<T>& a, const U b);
template<class T, class U> inline vector<T> operator+(vector<T> a, const U& b);
template<class T, class U> inline vector<T> operator-(vector<T> a, const U& b);
template<class T, class U> inline vector<T> operator*(vector<T> a, const U& b);
template<class T, class U> inline vector<T> operator/(vector<T> a, const U& b);
template<class T, class U> inline vector<T> operator%(vector<T> a, const U& b);
template<class T> inline vector<T> operator+(vector<T> a);
template<class T> inline vector<T> operator-(vector<T> a);
template<class T> istream& operator >>(istream& stream, vector<T>& a);
template<class T> ostream& operator <<(ostream& stream, const vector<T>& v);
template<class T> ostream& operator <<(ostream& stream, const vector<vector<T>>& vv);
template<class T> inline T Sum(const vector<T>& v) {return reduce(all(v));}  // v.size() == 0 のとき T() を返す
template<class T> inline T Max(const vector<T>& v) {assert(v.size()); return *max_element(all(v));}
template<class T> inline T Min(const vector<T>& v) {assert(v.size()); return *min_element(all(v));}
template<class T> inline ll Argmax(const vector<T>& v) {assert(v.size()); return max_element(all(v)) - v.begin();}
template<class T> inline ll Argmin(const vector<T>& v) {assert(v.size()); return min_element(all(v)) - v.begin();}
template<class T, class U> inline bool Contains(const vector<T>& v, const U& a) {return find(all(v), a) != v.end();}
template<class T> inline void Unique(vector<T>& v) {sort(all(v)); v.erase(unique(all(v)), v.end());}  // ソートされたユニーク値のvectorに書き換える, O(NlogN).
template<class T, class U> vector<T> make_vector(int n, U v) { return vector<T>(n, v); }
template <class T, class... Args> auto make_vector(int n, Args... args) {auto val = make_vector<T>(args...); return make_vector<decltype(val)>(n, move(val));}
/*********        S E T        **********/
template<class T> istream& operator >>(istream& stream, set<T>& st);
template<class T> ostream& operator <<(ostream& stream, const set<T>& st);
template<class T> inline T Max(const set<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const set<T>& st) {assert(st.size()); return *st.begin();}
/*********   M U L T I S E T   **********/
template<class T> istream& operator >>(istream& stream, multiset<T>& st);
template<class T> ostream& operator <<(ostream& stream, const multiset<T>& st);
template<class T> inline T Max(const multiset<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const multiset<T>& st) {assert(st.size()); return *st.begin();}
template<class T> inline bool EraseOne(multiset<T>& st, T x) {auto it=st.find(x); if (it!=st.end()) {st.erase(it); return true;} else return false;}  // 要素xを1つ削除. 消せたらtrueを返す.
/*********     S T R I N G     **********/
inline string ToUpper(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t; }
inline string ToLower(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t; }
inline char ToUpper(const char& c) {string s{c}, t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t[0]; }
inline char ToLower(const char& c) {string s{c}, t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t[0]; }
/*********       T R I O       **********/
template<class T1, class T2, class T3> struct trio {
    T1 first; T2 second; T3 third;
    // コンストラクタ・代入演算子
    trio() {first=T1(); second=T2(); third=T3();}
    trio(const T1& x) : first(x), second(x), third(x) {}
    trio(const T1& x, const T2& y, const T3& z) : first(x), second(y), third(z) {}
    trio(const trio& t) {first=t.first; second=t.second; third=t.third;}  // コピーコンストラクタ
    trio& operator =(const trio& t) {first=t.first; second=t.second; third=t.third; return *this;}
    // 比較演算子
    auto operator <=>(const trio&) const = default;
    // 単項演算子（+ -）
    trio operator +() const { return *this; }
    trio operator -() const { return (-1) * (*this); }
    // 複合代入演算子
    trio& operator +=(const trio& t) {first += t.first; second += t.second; third += t.third; return *this;}
    trio& operator -=(const trio& t) {first -= t.first; second -= t.second; third -= t.third; return *this;}
    trio& operator *=(const trio& t) {first *= t.first; second *= t.second; third *= t.third; return *this;}
    trio& operator /=(const trio& t) {first /= t.first; second /= t.second; third /= t.third; return *this;}
    trio& operator %=(const trio& t) {first %= t.first; second %= t.second; third %= t.third; return *this;}
    // 算術演算子
    friend trio operator +(const trio& lhs, const trio& rhs) {return trio(lhs) += rhs;}
    friend trio operator -(const trio& lhs, const trio& rhs) {return trio(lhs) -= rhs;}
    friend trio operator *(const trio& lhs, const trio& rhs) {return trio(lhs) *= rhs;}
    friend trio operator /(const trio& lhs, const trio& rhs) {return trio(lhs) /= rhs;}
    friend trio operator %(const trio& lhs, const trio& rhs) {return trio(lhs) %= rhs;}
    // 入出力
    template<class U1, class U2, class U3> friend istream& operator >>(istream&, trio<U1, U2, U3>&);
    template<class U1, class U2, class U3> friend ostream& operator <<(ostream&, const trio<U1, U2, U3>&);
    operator tuple<T1&, T2&, T3&>() {return tie(first, second, third);}
};
using tll = trio<ll, ll, ll>;
/*********     R A N D O M     **********/
struct Random {
    mt19937_64 rnd;
    Random() {
        random_device seed_gen;
        rnd.seed(seed_gen());
    }
    ll randint(ll a, ll b) {  // [a, b]
        uniform_int_distribution<ll> dist(a, b);
        return dist(rnd);
    }
    double randreal(double a, double b) {
        uniform_real_distribution<double> dist(a, b);
        return dist(rnd);
    }
    char randchar(char a, char b) {  // [a, b]
        uniform_int_distribution<ll> dist(a, b);
        return dist(rnd);
    }
};
/*********       P R I N T       **********/
template<class T> inline void print(const T& e);
template<class H, class... T> inline void print(const H& h, const T&... t);
template<class... T> inline void End(const T&... t);
/*********       D E B U G       **********/
#ifdef __LOCAL
#define debug(...) if(DEBUG) do{cout << '[' << #__VA_ARGS__ << "] ";debug_(__VA_ARGS__);}while(0)
#else
#define debug(...)
#endif
void dbg_(const long long& e);
template<class T> void dbg_(const T& e);
template<class T, class U> void dbg_(const pair<T, U>& p);
template<class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t);
template<class T> void debug_(const T& e);
template<class T> void debug_(const vector<T>& v);
template<class T> void debug_(const vector<vector<T>>& vv);
template<class T, class U> void debug_(const map<T, U>& mp);
template<class T, class U> void debug_(const vector<map<T, U>>& vm);
template<class T> void debug_(const set<T>& st);
template<class T> void debug_(const multiset<T>& st);
template<class T> void debug_(const vector<set<T>>& vs);
template<class T> void debug_(const vector<multiset<T>>& vs);
template<class H, class... T> void debug_(const H& h, const T&... t);
/*********       O T H E R S       **********/
template<class T, class U> inline bool chmin(T& a, U b) {if (a > b) {a = b; return true;} return false;}  // bは値渡し!
template<class T, class U> inline bool chmax(T& a, U b) {if (a < b) {a = b; return true;} return false;}
template<class T, class U> inline auto Mod(const T& a, const U& m) {return (a % m + m) % m;}  // 負もOK
template<class T, class U> inline auto Ceil(const T& x, const U& y) {return x < 0 ? x/y : (x + y - 1) / y;}  // 負もOK
template<class T, class U> inline auto Floor(const T& x, const U& y) {return -(Ceil(-x, y)); }  // 負もOK
inline ll Isqrt(ll n) {assert(n >= 0); ll x = round(sqrt(n)); while(x * x > n) --x; return x;}
inline ll Comb(ll n, ll r) {if (r < 0 || n < r) return 0; r = min(r, n - r); ll ret = 1; rep(i, r) {ret *= n - i; ret /= i + 1;} return ret;}  // n=60, r=30までOK
template<class T> inline T Pow(T x, ll n) {assert(n >= 0); T ret = 1; while(1) {if (n % 2) ret *= x; n /= 2; if(!n) return ret; x = x * x;}}  // べき乗 mintもOK
template<class T> inline T Aseries(T a, T d, ll n) {assert(n >= 0); return a * n + n * (n - 1) / 2 * d;}  // 等差級数 mintもOK
template<class T> inline T Gseries(T a, T r, ll n) {assert(n >= 0); if (r == 1) return a * n; else return a * (1 - Pow(r, n)) / (1 - r);}  // 等比級数 mintもOK
template<class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
inline bool Bit(ll b, int i) {assert(0 <= i && i < 64); return (b >> i) & 1;}
inline ll Popcount(ll b) {return __builtin_popcountll(b);}
inline ll Mask(ll n) {assert(0 <= n && n < 63); return (1LL << n) - 1LL;}  // [0, n)のbitが立った64bit整数を返す。
inline ll Mask(ll n, ll m) {assert(n >= m); return Mask(n) ^ Mask(m);}  // [m, n)のbitが立った64bit整数を返す。
inline void PrintYesNo(bool b) {b ? print("Yes") : print("No");}
/*********       M  O  D       **********/
// #include <atcoder/modint>  // https://atcoder.github.io/ac-library/production/document_ja/
// using namespace atcoder;
// using mint = modint998244353;     // modint1000000007;
// istream& operator >>(istream& stream, mint& e) {ll n; stream >> n; e = n; return stream; }
// ostream& operator <<(ostream& stream, const mint& e) { stream << e.val(); return stream; }
// using vm = vector<mint>;
// using vvm = vector<vm>;
/***************************************/
constexpr bool DEBUG = false;

/**************　デ　カ　ル　ト　座　標　構　造　体　**************/
template<class T> struct Point {
    T x, y;
    // コンストラクタ・代入演算子
    Point() { x = T(); y = T(); }
    Point(const T& x_) : x(x_), y(x_) { }
    Point(const T& x_, const T& y_) : x(x_), y(y_) { }
    Point(const pair<T, T> p) : x(p.first), y(p.second) {}
    Point (const Point& p) { x = p.x; y = p.y; }  // コピーコンストラクタ
    Point& operator =(const Point& p) { x = p.x; y = p.y; return *this; }

    // // 比較演算子（Pairと同じ）
    bool operator <(const Point& other) const {
        if (x < other.x) return true;
        else if (x == other.x && y < other.y) return true;
        else return false;
    }

    // 単項演算子（+ -）
    Point operator +() const { return *this; }
    Point operator -() const { return Point(-x, -y); }

    // 複合代入演算子
    Point& operator +=(const Point& p) { x += p.x; y += p.y; return *this; }
    Point& operator -=(const Point& p) { x -= p.x; y -= p.y; return *this; }
    Point& operator *=(const Point& p) { x *= p.x; y *= p.y; return *this; }
    Point& operator /=(const Point& p) { x /= p.x; y /= p.y; return *this; }
    Point& operator %=(const Point& p) { x %= p.x; y %= p.y; return *this; }

    // 算術演算子（+ - * /）
    friend Point operator +(const Point& lhs, const Point& rhs) { return Point(lhs) += rhs; }
    friend Point operator -(const Point& lhs, const Point& rhs) { return Point(lhs) -= rhs; }
    friend Point operator *(const Point& lhs, const Point& rhs) { return Point(lhs) *= rhs; }
    friend Point operator /(const Point& lhs, const Point& rhs) { return Point(lhs) /= rhs; }
    friend Point operator %(const Point& lhs, const Point& rhs) { return Point(lhs) %= rhs; }

    // // 二乗 (x^2, y^2)
    Point sq() const { return Point(x * x, y * y); }
    // 絶対値 (|x|, |y|)
    Point abs() const { return Point(std::abs(x), std::abs(y)); }
    // 大きさの二乗 x^2 + y^2
    T mag2() const { return x * x + y * y; }

    // // 入出力、型変換
    friend istream& operator >>(istream &stream, Point<T>& p) {return stream >> p.x >> p.y; }
    friend ostream& operator <<(ostream &stream, const Point<T>& p) {return stream << p.x << ' ' << p.y; }
    template<class U> operator pair<U, U>() const { pair<U, U> p{x, y}; return p; } 
};

// 内積 x1x2 + y1y2
template<class T> T Dot(const Point<T>& p1, const Point<T>& p2) { return p1.x * p2.x + p1.y * p2.y; }
// クロス積 x1y2 - x2y1
template<class T> T Cross(const Point<T>& p1, const Point<T>& p2) { return p1.x * p2.y - p2.x * p1.y; }
// 距離の二乗 (x2-x1)^2 + (y2-y1)^2
template<class T> T Dist2(const Point<T>& p1, const Point<T>& p2) { return (p2 - p1).mag2(); }

// p1ベクトルに対するp2ベクトルのなす角[0, 2π)
template<class T> T Angle(const Point<T>& p1, const Point<T>& p2) {
    T cos = Dot(p1, p2) / sqrt(p1.mag2() * p2.mag2());
    T theta = acos(cos);
    if (Cross(p1, p2) >= 0) return theta;
    else return 2 * acos((T)(-1)) - theta;
}
// pベクトルの偏角 [0, 2π)
template<class T> T Angle(const Point<T>& p) {
    return Angle(Point<T>(1, 0), p);
}
// pベクトルを theta [rad]回転
template<class T> Point<T> Rotate(const Point<T>& p, T theta) {
    T x = cos(theta) * p.x - sin(theta) * p.y;
    T y = sin(theta) * p.x + cos(theta) * p.y;
    return Point<T>(x, y);
}
// rad -> deg
template<class T> T Degrees(T rad) { return rad / acos((T)(-1)) * 180; }
// deg -> rad
template<class T> T Radians(T deg) { return acos((T)(-1)) * deg / 180; }

// ベクトルpに対してqのなす角θが 0° < θ < 90° を満たすか
template<class T> bool Acute(const Point<T>& p, const Point<T>& q) {return (Dot(p, q) > 0) && (Cross(p, q) > 0);}

// ベクトルpに対してqのなす角θが θ = 90° を満たすか
template<class T> bool Deg90(const Point<T>& p, const Point<T>& q) {return (Dot(p, q) == 0) && (Cross(p, q) > 0);}

// ベクトルのなす角のうち小さい方（2: 0°, 1: 鋭角, 0: 直角, -1:, 鈍角, -2: 180°）
template<class T> ll TypeOfAngle(const Point<T>& p1, const Point<T>& p2) {
    if (Dot(p1, p2) > T(0)) return Cross(p1, p2) == T(0) ? 2 : 1;
    else if (Dot(p1, p2) == T(0)) return 0;
    else return Cross(p1, p2) == T(0) ? -2 : -1;
}

// 偏角による比較関数. 原点(0, 0)は不可. Arg(p1) < Arg(p2)ならtrue.
template<class T> bool CompareByArg(const Point<T>& p1, const Point<T>& p2) {
    assert((p1.x != 0 || p1.y != 0) && (p2.x != 0 || p2.y != 0));
    if (Cross(p1, p2) == 0 && Dot(p1, p2) > 0) {
        // なす角が0°のとき、ソート結果を一意にするためベクトルの大きさで比較する
        return p1.mag2() < p2.mag2();
    } else {
        auto& [x1, y1] = p1;
        auto& [x2, y2] = p2;
        if (y1 == 0 && y2 == 0) return x1 > 0 && x2 < 0;  // p1が0°, p2が180°でtrue
        else if (y1 >= 0 && y2 < 0) return true;          // p1 <= 180° < p2
        else if (y1 < 0 && y2 >= 0) return false;         // p2 <= 180° < p1
        else return x1 * y2 > x2 * y1;                    // p1, p2 <= 180° or 180° < p1, p2
    }
}

// 凸多角形かどうか
template<class T> bool IsConvex(const vector<Point<T>>& vec) {
    ll n = vec.size();
    for(ll i = 0; i < n; i++) {
        ll j = (i + 1) % n;
        ll k = (i - 1 + n) % n;
        if (Cross(vec[j] - vec[i], vec[k] - vec[i]) <= 0) return false;
    }
    return true;
}


// 分数構造体
// 利用可能演算子：+ - * / == != < > <= >=
// 利用可能関数：sq(), inv(), abs(), val()
// Examples:
// Rational<ll> r(-6, 20);             // -6/20 = -3/10
// Rational<ll> s(4, 30);              //  4/30 =  2/15
// cout << ((r + s) * 2 / 3) << endl;  //  (-3/10 + 2/15) * 2 / 3 = -1/9
// cout << s.val() << endl;            //  2/15 = 0.1333333333
template<class T> struct Rational {
    private:
        T num, den;  // 分子, 分母
    public:
        T get_num() { return num; }
        T get_den() { return den; }

        // コンストラクタ
        Rational() { num = 0; den = 1; }
        Rational(const T& num_) { num = num_; den = 1; }
        Rational(const Rational& r) {num = r.num; den = r.den; }  // コピーコンストラクタ
        Rational(const T& num_, const T& den_) {
            assert(num_ != 0 || den_ != 0);
            if (num_ == 0) {
                num = 0;
                den = 1;
            }
            else {
                // 分母 > 0にする & 約分する
                T sign = den_ < 0 ? -1 : 1;
                T g = gcd(num_, den_);
                num = sign * num_ / g;
                den = sign * den_ / g;
            }
        }

        // 代入演算子
        Rational& operator =(const Rational& other) {
            num = other.num;
            den = other.den;
            return *this;
        }

        // 比較演算子（== != < > <= >=）
        bool operator <(const Rational& other) const {
            T num2 = other.num;
            T den2 = other.den;
            if (*this == other) {
                // 両辺が（+/-infも含めて）同一のとき
                return false;
            }
            else if ((num == -1 && den == 0) || (other.num == 1 && other.den == 0)) {
                // 左辺が-inf か、右辺が+inf
                return true;
            }
            else if ((num == 1 && den == 0) || (other.num == -1 && other.den == 0)) {
                // 左辺が+infか、右辺が-inf
                return false;
            }
            else {
                return num * den2 < num2 * den;
            }
        }
        bool operator ==(const Rational& other) const { return (num == other.num) && (den == other.den); }
        bool operator !=(const Rational& other) const { return !(*this == other); }
        bool operator >(const Rational& other) const { return !(*this < other) && (*this != other); }
        bool operator <=(const Rational& other) const { return !(*this > other); }
        bool operator >=(const Rational& other) const { return !(*this < other); }

        // 単項演算子（+ -）
        Rational operator +() const { return *this; }
        Rational operator -() const { return Rational(-num, den); }

        // 算術演算子（+ - * /）
        Rational operator +(const Rational& other) const {
            T num2 = other.num;
            T den2 = other.den;
            // （マイナス）無限大との和の返り値は（マイナス）無限大
            // ただし無限大とマイナス無限大の和は未定義
            if (den == 0) {
                return Rational(num, 0);
            }
            else if (den2 == 0) {
                return Rational(num2, 0);
            }
            T num_ans = num * den2 + num2 * den;
            T den_ans = den * den2;
            return Rational(num_ans, den_ans);
        }
        Rational operator -(const Rational& other) const { return *this + (-other); }
        Rational operator *(const Rational& other) const { return Rational(num * other.num, den * other.den); }  // ゼロ * infはエラー
        Rational operator /(const Rational& other) const { return *this * other.inv(); }

        // 二乗、絶対値、逆数
        Rational sq() const { return Rational(num * num, den * den); }
        Rational abs() const { if (num < 0) return Rational(-num, den); else return *this; }
        Rational inv() const { return Rational(den, num); }

        // double型に変換
        double val() const { return (double)num / (double)den; }

        // 入出力。参考：https://stackoverflow.com/questions/4039817/friend-declaration-declares-a-non-template-function
        template<class U> friend istream& operator >>(istream&, Rational<U>&);        // 入力時はインスタンスを生成 & 変更するのでconstをつけない
        template<class U> friend ostream& operator <<(ostream&, const Rational<U>&);  // 出力時は変更しないのでconstをつける

        // 整数型との演算
        template<class U> Rational operator +(const U& x) const { return *this + Rational<T>((T)x); }
        template<class U> Rational operator -(const U& x) const { return *this - Rational<T>((T)x); }
        template<class U> Rational operator *(const U& x) const { return *this * Rational<T>((T)x); }
        template<class U> Rational operator /(const U& x) const { return *this / Rational<T>((T)x); }
};
template<class T> istream& operator >>(istream &stream, Rational<T>& r) { stream >> r.num; return stream; }
template<class T> ostream& operator <<(ostream &stream, const Rational<T>& r) { stream << r.num << '/' << r.den; return stream; }
template<class T, class U> Rational<T> operator +(const U& x, const Rational<T>& r) { return Rational<T>((T)x) + r; }
template<class T, class U> Rational<T> operator -(const U& x, const Rational<T>& r) { return Rational<T>((T)x) - r; }
template<class T, class U> Rational<T> operator *(const U& x, const Rational<T>& r) { return Rational<T>((T)x) * r; }
template<class T, class U> Rational<T> operator /(const U& x, const Rational<T>& r) { return Rational<T>((T)x) / r; }

using R = Rational<bint>;
// using R = long double;

int main() {
    cin.tie(nullptr); cout << fixed << setprecision(10);

    ll Q;
    cin >> Q;
    vector<Point<R>> P(3);
    cin >> P;

    Point<R> C;  // 最小円の中心
    R r2;        // 最小円の半径の二乗
    rep(i, 3) {
        ll i1 = (i + 1) % 3;
        ll i2 = (i + 2) % 3;
        auto p = P[i];
        auto p1 = P[i1];
        auto p2 = P[i2];
        auto dx1 = p1.x - p.x;
        auto dy1 = p1.y - p.y;
        auto dx2 = p2.x - p.x;
        auto dy2 = p2.y - p.y;
        Point<R> dp1 = {dx1, dy1};
        Point<R> dp2 = {dx2, dy2};
        if (TypeOfAngle(dp1, dp2) <= 0) {
            // 直角三角形 or 鈍角三角形 or 直線
            C.x = (p1.x + p2.x) / 2;
            C.y = (p1.y + p2.y) / 2;
            r2 = (p1.x - C.x).sq() + (p1.y - C.y).sq();
            break;
        }
        debug(i);
        if (i == 2) {
            vector<R> X(2), Y(2);
            vector<R> A(2);
            ll cnt = 0;
            rep(i1, 3) {
                if (cnt == 2) break;
                ll i2 = (i1 + 1) % 3;
                auto [x1, y1] = P[i1];
                auto [x2, y2] = P[i2];
                if (y1 == y2) continue;

                A[cnt] = -(x2 - x1) / (y2 - y1);
                X[cnt] = (x1 + x2) / 2;
                Y[cnt] = (y1 + y2) / 2;
                cnt++;
            }
            assert(cnt == 2);
            assert(A[0] != A[1]);
            R cx = (-Y[0] + Y[1] + A[0] * X[0] - A[1] * X[1]) / (A[0] - A[1]);
            R cy = A[0] * (cx - X[0]) + Y[0];
            C = {cx, cy};
            r2 = (C.x - P[0].x).sq() + (C.y - P[0].y).sq();
        }
    }
    debug("chk");

    rep(q, Q) {
        Point<R> pt;
        cin >> pt;
        R d2 = (C.x - pt.x).sq() + (C.y - pt.y).sq();
        if (d2 <= r2) print("Yes");
        else print("No");
    }
}





/*********       P A I R       **********/
template<class T, class U> inline pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U> b) {a.fi += b.fi; a.se += b.se; return a;}
template<class T, class U> inline pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U> b) {a.fi -= b.fi; a.se -= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U> b) {a.fi *= b.fi; a.se *= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U> b) {a.fi /= b.fi; a.se /= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U> b) {a.fi %= b.fi; a.se %= b.se; return a;}
template<class T, class U, class V> inline pair<T, U>& operator+=(pair<T, U>& a, const V b) {a.fi += b; a.se += b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator-=(pair<T, U>& a, const V b) {a.fi -= b; a.se -= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator*=(pair<T, U>& a, const V b) {a.fi *= b; a.se *= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator/=(pair<T, U>& a, const V b) {a.fi /= b; a.se /= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator%=(pair<T, U>& a, const V b) {a.fi %= b; a.se %= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator+(pair<T, U> a, const V& b) {a += b; return a;}
template<class T, class U, class V> inline pair<T, U> operator-(pair<T, U> a, const V& b) {a -= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator*(pair<T, U> a, const V& b) {a *= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator/(pair<T, U> a, const V& b) {a /= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator%(pair<T, U> a, const V& b) {a %= b; return a;}
template<class T, class U> inline pair<T, U> operator+(pair<T, U> a) {return a;}
template<class T, class U> inline pair<T, U> operator-(pair<T, U> a) {return a * (-1);}
template<class T, class U> istream& operator >>(istream& stream, pair<T, U>& a) {stream >> a.fi >> a.se; return stream;}
template<class T, class U> ostream& operator <<(ostream &stream, const pair<T, U>& a) { stream << a.fi << " " << a.se; return stream; }
/*********       V E C T O R      **********/
template<class T> inline vector<T>& operator+=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] += b[i]; return a;}
template<class T> inline vector<T>& operator-=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] -= b[i]; return a;}
template<class T> inline vector<T>& operator*=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] *= b[i]; return a;}
template<class T> inline vector<T>& operator/=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] /= b[i]; return a;}
template<class T> inline vector<T>& operator%=(vector<T>& a, const vector<T> b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] %= b[i]; return a;}
template<class T, class U> inline vector<T>& operator+=(vector<T>& a, const U b) {fore(e, a) e += b; return a;}
template<class T, class U> inline vector<T>& operator-=(vector<T>& a, const U b) {fore(e, a) e -= b; return a;}
template<class T, class U> inline vector<T>& operator*=(vector<T>& a, const U b) {fore(e, a) e *= b; return a;}
template<class T, class U> inline vector<T>& operator/=(vector<T>& a, const U b) {fore(e, a) e /= b; return a;}
template<class T, class U> inline vector<T>& operator%=(vector<T>& a, const U b) {fore(e, a) e %= b; return a;}
template<class T, class U> inline vector<T> operator+(vector<T> a, const U& b) {a += b; return a;}
template<class T, class U> inline vector<T> operator-(vector<T> a, const U& b) {a -= b; return a;}
template<class T, class U> inline vector<T> operator*(vector<T> a, const U& b) {a *= b; return a;}
template<class T, class U> inline vector<T> operator/(vector<T> a, const U& b) {a /= b; return a;}
template<class T, class U> inline vector<T> operator%(vector<T> a, const U& b) {a %= b; return a;}
template<class T> inline vector<T> operator+(vector<T> a) {return a;}
template<class T> inline vector<T> operator-(vector<T> a) {return a * (-1);}
template<class T> istream& operator >>(istream& stream, vector<T>& a) {fore(e, a) stream >> e; return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<T>& v) {if(v.size()){stream << v[0]; rep(i, 1, v.size()) cout << " " << v[i];} return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<vector<T>>& vv) {if(vv.size()){stream << vv[0]; rep(i, 1, vv.size()) cout << '\n' << vv[i];} return stream;}
/*********        S E T        **********/
template<class T> istream& operator >>(istream& stream, set<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const set<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
/*********   M U L T I S E T   **********/
template<class T> istream& operator >>(istream& stream, multiset<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const multiset<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
/*********       P R I N T       **********/
template<class T> inline void print(const T& e) {cout << e << '\n';}
template<class H, class... T> inline void print(const H& h, const T&... t) {cout << h << ' '; print(t...);}
template<class... T> inline void End(const T&... t) {print(t...); exit(0);}
/*********       D E B U G       **********/
void dbg_(const long long& e) {if (e == INF) cout << "INF"; else if (e == -INF) cout << "-INF"; else cout << e;}
template<class T> void dbg_(const T& e) {cout << e;}
template<class T, class U> void dbg_(const pair<T, U>& p) {cout << '('; dbg_(p.first); cout << ' '; dbg_(p.second); cout << ')';}
template<class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t) {cout << '('; dbg_(t.first); cout << ' '; dbg_(t.second); cout << ' '; dbg_(t.third); cout << ')';}
template<class T> void debug_(const T& e) {dbg_(e); cout << '\n';}
template<class T> void debug_(const vector<T>& v) {if (v.size()){auto it=v.begin(); dbg_(*it++); for(; it!=v.end(); ++it){cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<vector<T>>& vv) {cout << '\n'; ll cnt=0; for(auto&& v : vv){cout << cnt++ << ": "; debug_(v);}}
template<class T, class U> void debug_(const map<T, U>& mp) {if (mp.size()) {auto it = mp.begin(); dbg_(*it++); for(; it != mp.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T, class U> void debug_(const vector<map<T, U>>& vm){cout << '\n'; ll cnt=0; for(auto&& mp : vm){cout << cnt++ << ": "; debug_(mp);}}
template<class T> void debug_(const set<T>& st) {if(st.size()){auto it=st.begin(); dbg_(*it++); for(; it!=st.end(); ++it) {cout << ' '; dbg_(*it);}}cout << '\n';}
template<class T> void debug_(const multiset<T>& st) {if(st.size()) {auto it=st.begin(); dbg_(*it++); for(; it != st.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<set<T>>& vs) {cout << '\n'; ll cnt=0; for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class T> void debug_(const vector<multiset<T>>& vs) {cout << '\n'; ll cnt=0;for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class H, class... T> void debug_(const H& h, const T&... t) {dbg_(h); cout << ", "; debug_(t...);}
/*********       T R I O       **********/
template<class T1, class T2, class T3> istream& operator >>(istream &stream, trio<T1, T2, T3>& t) {return stream >> t.first >> t.second >> t.third;}
template<class T1, class T2, class T3> ostream& operator <<(ostream &stream, const trio<T1, T2, T3>& t) {return stream << t.first << " " << t.second << " " << t.third;}
yukicoder

結果

テストケース

ソースコード
