/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<< (os, a); } return os; } template void print_tuple(tuple &a) { operator<< <0, true>(std::cout, a); } void pprint() { std::cout << endl; } template void pprint(Head &&head, Tail &&...tail) { std::cout << head; if (sizeof...(Tail) > 0) std::cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((std::cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr); std::cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) std::cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; #include /* #region RealGeometry */ // ここから幾何テンプレート using P = complex; // 2次元平面上の点 using G = vector

; const ld pi = acos(-1); ld cross(const P &a, const P &b) { return a.real() * b.imag() - a.imag() * b.real(); } ld dot(const P &a, const P &b) { return a.real() * b.real() + a.imag() * b.imag(); } /* #region CCW */ /* CCW -- BEHIND -- [a -- ON -- b] --- FRONT -- CW */ // CCW (Counter Clock Wise) 結果列挙体 enum CCW_RESULT { CCW = +1, // 反時計回り CW = -1, // 時計回り BEHIND = +2, // 広報 FRONT = -2, // 前方 ON = 0 // 2点間 }; // ベクトル A→B を基準に,点 C がどの方向にあるか(反時計回りかどうか)を調べる. // 反時計回り ― 延長線上 ― 時計回り,で 1, 0, -1 を返す. CCW_RESULT ccw(P a, P b, P c) { b -= a; c -= a; if (cross(b, c) > EPS) return CCW; // counter clockwise if (cross(b, c) < -EPS) return CW; // clockwise if (dot(b, c) < 0) return BEHIND; // c--a--b on line if (norm(b) < norm(c)) return FRONT; // a--b--c on line return ON; } /* #endregion */ bool operator<(const P &a, const P &b) { // return abs(real(a) - real(b)) > EPS ? real(a) < real(b) : imag(a) < imag(b); } // 2次元平面上の直線を表す構造体 struct L : public vector

{ void regist(const P &a, const P &b) { begin()[0] = a; begin()[1] = b; } L(const P &a = P(), const P &b = P()) : vector

(2) { regist(a, b); } // Ax + By + C = 0 L(ld A, ld B, ld C) : vector

(2) { if (abs(A) < EPS && abs(B) < EPS) abort(); else if (abs(A) < EPS) regist(P(0, -C / B), P(1, -C / B)); else if (abs(B) < EPS) regist(P(-C / A, 0), P(-C / A, 1)); else regist(P(0, -C / B), P(-C / A, 0)); } }; /* #endregion */ /* #region MinBall */ // 2次元平面上の円を表す構造体 struct Circle { P p; // 中心 ld r; // 半径 Circle(const P &p = 0, ld r = 0) : p(p), r(r) {} }; // 2次元平面上の円を表す構造体,ただし半径は2乗で保持する struct Circle2 { P p; // 中心 ld r2; // 半径の2乗 Circle2(const P &p = 0, ld r2 = 0) : p(p), r2(r2) {} ld r() { return sqrt(r2); } // 半径を返す }; // 最小包含円 Circle2 min_ball(vc

&points, const int seed = 1333) { const int n = ISIZE(points); // 点の個数 assert(n >= 1); if (n == 1) { return Circle2(points[0], ld(0)); } mt19937 mt(seed); shuffle(ALL(points), mt); // シャッフルすることで平均計算量 O(n) に近づける // std::random_shuffle(left, right); // simple but deprecated // 3頂点を円周に持つ最小の円を求める auto make_circle_3 = [](const P &a, const P &b, const P &c) -> Circle2 { ld A = std::norm(b - c), B = std::norm(c - a), C = std::norm(a - b), S = cross(b - a, c - a); P p = (A * (B + C - A) * a + B * (C + A - B) * b + C * (A + B - C) * c) / (4 * S * S); ld r2 = std::norm(p - a); return Circle2(p, r2); }; // 2頂点を円周に持つ最小の円を求める auto make_circle_2 = [](const P &a, const P &b) -> Circle2 { P c = (a + b) / (ld)2; ld r2 = std::norm(a - c); return Circle2(c, r2); }; // ある点が,ある円の内部または周上にあるときに true を返す // 最終的には,「入るかどうか」ではなく「円の半径の数値」が欲しいので,EPS を足すという仕様でよい auto in_circle = [](const P &a, const Circle2 &c) -> bool { return std::norm(a - c.p) <= c.r2 + EPS; }; // 初期円 Circle2 c = make_circle_2(points[0], points[1]); // MiniDisc for (int i = 2; i < n; ++i) { if (in_circle(points[i], c)) continue; // 点 i は円の内部に入っているので,c は更新しない // MiniDiscWithPoint c = make_circle_2(points[0], points[i]); for (int j = 1; j < i; ++j) { if (in_circle(points[j], c)) continue; // MiniDiscWith2Points c = make_circle_2(points[i], points[j]); for (int k = 0; k < j; ++k) { if (in_circle(points[k], c)) continue; c = make_circle_3(points[i], points[j], points[k]); } } // この時点で,円 c は点 0, 1, ..., i を含む最小の円になっている } return c; } /* #endregion */ // Problem void solve() { VAR(ll, q); VAR(ll, xa, ya, xb, yb, xc, yc); vll x(q), y(q); REP(i, 0, q) cin >> x[i], y[i]; vc

points = {P(xa, ya), P(xb, yb), P(xc, yc)}; Circle2 c = min_ball(points); REP(i, 0, q) { // 中心からの距離 P rv = P(x[i], y[i]) - c.p; ld r2 = rv.real() * rv.real() + rv.imag() * rv.imag(); Yn(r2 <= c.r2 + EPS); } } // entry point int main() { solve(); return 0; }