#include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; namespace std { __int128 gcd(__int128 x, __int128 y) { while (y != 0) std::swap(x %= y, y); return x; } } template struct Rational { T num, den; Rational() : num(0), den(1) {} Rational(const T num, const T den = 1) : num(num), den(den) { // assert(den != 0); reduce(); } template Real to_real() const { return static_cast(num) / den; } Rational& operator+=(const Rational& x) { const T g = std::gcd(den, x.den); num = num * (x.den / g) + x.num * (den / g); den *= x.den / g; reduce(); return *this; } Rational& operator-=(const Rational& x) { return *this += -x; } Rational& operator*=(const Rational& x) { const T g1 = std::gcd(num, x.den), g2 = std::gcd(den, x.num); num = (num / g1) * (x.num / g2); den = (den / g2) * (x.den / g1); reduce(); return *this; } Rational& operator/=(const Rational& x) { return *this *= Rational(x.den, x.num); } auto operator<=>(const Rational& x) const { return num * x.den <=> x.num * den; } bool operator==(const Rational& x) const { return num == x.num && den == x.den; } Rational& operator++() { if ((num += den) == 0) den = 1; return *this; } Rational operator++(int) { const Rational res = *this; ++*this; return res; } Rational& operator--() { if ((num -= den) == 0) den = 1; return *this; } Rational operator--(int) { const Rational res = *this; --*this; return res; } Rational operator+() const { return *this; } Rational operator-() const { return Rational(-num, den); } Rational operator+(const Rational& x) const { return Rational(*this) += x; } Rational operator-(const Rational& x) const { return Rational(*this) -= x; } Rational operator*(const Rational& x) const { return Rational(*this) *= x; } Rational operator/(const Rational& x) const { return Rational(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const Rational& x) { if (x.den == 1) return os << x.num; return os << x.num << '/' << x.den; } private: void reduce() { const T g = std::gcd(num, den); num /= g; den /= g; if (den < 0) { num = -num; den = -den; } } }; using rational = Rational<__int128>; using Point = pair; tuple smallest_enclosing_circle( const Point& p1, const Point& p2, const Point& p3) { const auto get_circle = [](const Point& p1, const Point& p2) -> tuple { const auto [p1x, p1y] = p1; const auto [p2x, p2y] = p2; return {rational(p1x + p2x, 2), rational(p1y + p2y, 2), rational((p2x - p1x) * (p2x - p1x) + (p2y - p1y) * (p2y - p1y), 4)}; }; auto [cx, cy, cr] = get_circle(p1, p2); const auto is_in = [&](const Point& p) -> bool { const auto [x, y] = p; return (cx - x) * (cx - x) + (cy - y) * (cy - y) <= cr; }; if (!is_in(p3)) { tie(cx, cy, cr) = get_circle(p1, p3); if (!is_in(p2)) { tie(cx, cy, cr) = get_circle(p2, p3); if (!is_in(p1)) { const int a = (p3.first - p2.first) * (p3.first - p2.first) + (p3.second - p2.second) * (p3.second - p2.second); const int b = (p1.first - p3.first) * (p1.first - p3.first) + (p1.second - p3.second) * (p1.second - p3.second); const int c = (p2.first - p1.first) * (p2.first - p1.first) + (p2.second - p1.second) * (p2.second - p1.second); const int idx = p3.first - p1.first, idy = p3.second - p1.second; const int jdx = p2.first - p1.first, jdy = p2.second - p1.second; const int s = idx * jdy - idy * jdx; cx = rational(__int128{p1.first} * a * (b + c - a) + __int128{p2.first} * b * (c + a - b) + __int128{p3.first} * c * (a + b - c), 4LL * s * s); cy = rational(__int128{p1.second} * a * (b + c - a) + __int128{p2.second} * b * (c + a - b) + __int128{p3.second} * c * (a + b - c), 4LL * s * s); cr = (cx - p1.first) * (cx - p1.first) + (cy - p1.second) * (cy - p1.second); } } } return {cx, cy, cr}; } #include using namespace boost::multiprecision; int main() { int q, xa, ya, xb, yb, xc, yc; cin >> q >> xa >> ya >> xb >> yb >> xc >> yc; const auto [cx, cy, cr] = smallest_enclosing_circle({xa, ya}, {xb, yb}, {xc, yc}); while (q--) { int x, y; cin >> x >> y; const rational dx = cx - x, dy = cy - y; cout << ((int256_t{dx.num} * dx.num * dy.den * dy.den + int256_t{dy.num} * dy.num * dx.den * dx.den) * cr.den <= int256_t{cr.num} * dx.den * dx.den * dy.den * dy.den ? "Yes\n" : "No\n"); } return 0; }