#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #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) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; struct Vec { using etype = int; // type of elements using ptype = int; // type of product results etype x = 0, y = 0; constexpr Vec operator-() const { return {-x, -y}; } friend constexpr Vec operator+(const Vec& a, const Vec& b) { return {a.x + b.x, a.y + b.y}; } friend constexpr Vec operator-(const Vec& a, const Vec& b) { return {a.x - b.x, a.y - b.y}; } friend constexpr ptype operator*(const Vec& a, const Vec& b) { return (ptype)a.x * b.y - (ptype)a.y * b.x; } template >* = nullptr> friend constexpr Vec operator*(T c, const Vec& a) { return {c * a.x, c * a.y}; } template >* = nullptr> friend constexpr Vec operator*(const Vec& a, T c) { return c * a; } template >* = nullptr> friend constexpr Vec operator/(const Vec& a, T c) { return {a.x / c, a.y / c}; } Vec& operator+=(const Vec& a) { x += a.x; y += a.y; return *this; } Vec& operator-=(const Vec& a) { x -= a.x; y -= a.y; return *this; } template >* = nullptr> Vec& operator*=(T c) { x *= c; y *= c; return *this; } friend constexpr bool operator==(const Vec& a, const Vec& b) { return a.x == b.x && a.y == b.y; } friend constexpr bool operator!=(const Vec& a, const Vec& b) { return !(a == b); } constexpr int quadrant() const { return y > 0 ? (x > 0 ? 0 : 1) : y < 0 ? (x < 0 ? 2 : 3) : (x > 0 ? 0 : x < 0 ? 2 : -1); } friend constexpr bool operator<(const Vec& a, const Vec& b) { int qa = a.quadrant(), qb = b.quadrant(); if (qa != qb) return qa < qb; ptype p1 = (ptype)a.x * b.y, p2 = (ptype)a.y * b.x; return p1 > p2 || (p1 == p2 && (a.x != 0 ? abs(a.x) < abs(b.x) : abs(a.y) < abs(b.y))); } friend constexpr bool operator>(const Vec& a, const Vec& b) { return b < a; } friend constexpr bool operator<=(const Vec& a, const Vec& b) { return !(b < a); } friend constexpr bool operator>=(const Vec& a, const Vec& b) { return !(a < b); } constexpr int ccw(const Vec& u, const Vec& v) const { ptype p = (u - *this) * (v - *this); return p > 0 ? 1 : p < 0 ? -1 : 0; } static constexpr bool intersects(const Vec& a, const Vec& b, const Vec& c, const Vec& d) { return a.ccw(b, c) * a.ccw(b, d) <= 0 && c.ccw(d, a) * c.ccw(d, b) <= 0; } constexpr bool parallel_to(const Vec& a) const { return (ptype)x * a.y == (ptype)y * a.x; } constexpr ptype dot(const Vec& a) const { return (ptype)x * a.x + (ptype)y * a.y; } constexpr ptype norm2() const { return (ptype)x * x + (ptype)y * y; } constexpr bool is_zero() const { return x == 0 && y == 0; } constexpr Vec normalize() const { if (x == 0) return Vec{0, (y == 0 ? 0 : 1)}; etype g = gcd(x, y); return *this / (x > 0 ? g : -g); } constexpr Vec rot90() const { return {-y, x}; } // exclusive constexpr bool in_between(const Vec& a, const Vec& b) const { Vec x = a - *this, y = b - *this; return x.parallel_to(y) && x.dot(y) < 0; } friend std::ostream& operator<< (std::ostream& os, const Vec& t) { return os << t.x << ' ' << t.y; } friend std::istream& operator>> (std::istream& os, Vec& t) { return os >> t.x >> t.y; } }; } int main() { ios::sync_with_stdio(false); cin.tie(0); int q; cin >> q; Vec a, b, c; cin >> a >> b >> c; a *= 2, b *= 2, c *= 2; rep(_, 3) { Vec o = (a + b) / 2; ll r2 = (a - o).norm2(); if ((c - o).norm2() > r2) { swap(a, b); swap(b, c); continue; } rep(_, q) { Vec v; cin >> v; v *= 2; bool ans = (v - o).norm2() <= r2; cout << (ans ? "Yes\n" : "No\n"); } return 0; } auto cs = [](Vec a, Vec b, Vec c) { int p = b.norm2() + c.norm2() - a.norm2(); ll p2 = (ll)p * p; ll q2 = (ll)b.norm2() * c.norm2(); return pair(p2, q2); }; rep(_, q) { Vec v; cin >> v; v *= 2; bool ans = false; auto [pa, qa] = cs(b - a, a - c, b - c); auto [px, qx] = cs(b - a, a - v, b - v); auto ca = __int128(pa) * qx; auto cx = __int128(px) * qa; // cout << a << endl; // cout << b << endl; // cout << c << endl; // cout << pa << ' ' << qa << ' ' << px << ' ' << qx << endl; // exit(0); if (((b - a) * (c - a) >= 0) == ((b - a) * (v - a) >= 0)) { ans = cx <= ca; } else { ans = cx <= -ca; } cout << (ans ? "Yes\n" : "No\n"); } }