#include #include #include #include #include #include #include #include #include #include #include static const int MOD = 1000000007; using ll = long long; using u32 = uint32_t; using namespace std; template constexpr T INF = ::numeric_limits::max() / 32 * 15 + 208; using real = double; static constexpr real EPS = 1e-10; struct Point { real x, y; Point& operator+=(const Point a) { x += a.x; y += a.y; return *this; } Point& operator-=(const Point a) { x -= a.x; y -= a.y; return *this; } Point& operator*=(const real k) { x *= k; y *= k; return *this; } Point& operator/=(const real k) { x /= k; y /= k; return *this; } Point operator+(const Point a) const {return Point(*this) += a; } Point operator-(const Point a) const {return Point(*this) -= a; } Point operator*(const real k) const {return Point(*this) *= k; } Point operator/(const real k) const {return Point(*this) /= k; } bool operator<(const Point &a) const { return (x != a.x ? x < a.x : y < a.y); } explicit Point(real a = 0, real b = 0) : x(a), y(b) {}; }; bool sorty(Point a, Point b){ return (a.y != b.y ? a.y < b.y : a.x < b.x); } istream& operator>> (istream& s, Point& P){ s >> P.x >> P.y; return s; } inline real dot(Point a, Point b){ return a.x*b.x + a.y*b.y; } inline real cross(Point a, Point b){ return a.x*b.y - a.y*b.x; } inline real abs(Point a){ return sqrt(dot(a, a)); } real angle(Point A, Point B){ return acos(dot(A, B)/abs(A)/abs(B)); } static constexpr int COUNTER_CLOCKWISE = 1; static constexpr int CLOCKWISE = -1; static constexpr int ONLINE_BACK = 2; static constexpr int ONLINE_FRONT = -2; static constexpr int ON_SEGMENT = 0; int ccw(Point a, Point b, Point c){ b -= a; c -= a; if(cross(b, c) > EPS) return COUNTER_CLOCKWISE; if(cross(b, c) < -EPS) return CLOCKWISE; if(dot(b, c) < 0) return ONLINE_BACK; if(abs(b) < abs(c)) return ONLINE_FRONT; return ON_SEGMENT; } struct Segment { Point a, b; Segment(Point x, Point y) : a(x), b(y) {}; }; struct Line { Point a, b; Line(Point x, Point y) : a(x), b(y) {}; }; struct Circle{ Point c; real r; Circle(Point c, real r): c(c), r(r) {}; }; using Polygon = vector; bool intersect(Segment s, Segment t){ return (ccw(s.a, s.b, t.a)*ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a)*ccw(t.a, t.b, s.b) <= 0); } Point polar(double r, double t){ return Point(r*cos(t), r*sin(t)); } double arg(Point p){ return atan2(p.y, p.x); } static constexpr int CONTAIN = 0; static constexpr int INSCRIBE = 1; static constexpr int INTERSECT = 2; static constexpr int CIRCUMSCRIBED = 3; static constexpr int SEPARATE = 4; int intersect(Circle c1, Circle c2){ if(c1.r < c2.r) swap(c1, c2); real d = abs(c1.c-c2.c); real r = c1.r + c2.r; if(fabs(d-r) < EPS) return CIRCUMSCRIBED; if(d > r) return SEPARATE; if(fabs(d+c2.r-c1.r) < EPS) return INSCRIBE; if(d+c2.r < c1.r) return CONTAIN; return INTERSECT; } real distance(Line l, Point c){ return abs(cross(l.b-l.a, c-l.a)/abs(l.b-l.a)); } real distance(Segment s, Point c){ if(dot(s.b-s.a, c-s.a) < EPS) return abs(c-s.a); if(dot(s.a-s.b, c-s.b) < EPS) return abs(c-s.b); return abs(cross(s.b-s.a, c-s.a)) / abs(s.a-s.b); } real distance(Segment s, Segment t){ if(intersect(s, t)) return 0.0; return min({distance(s, t.a), distance(s, t.b), distance(t, s.a), distance(t, s.b)}); } Point project(Line l, Point p){ Point Q = l.b-l.a; return l.a + Q*(dot(p-l.a, Q) / dot(Q, Q)); } Point project(Segment s, Point p){ Point Q = s.b-s.a; return s.a + Q*(dot(p-s.a, Q) / dot(Q, Q)); } Point refrect(Segment s, Point p){ Point Q = project(s, p); return Q*2-p; } bool isOrthogonal(Segment s, Segment t){ return fabs(dot(s.b-s.a, t.b-t.a)) < EPS; } bool isparallel(Segment s, Segment t){ return fabs(cross(s.b-s.a, t.b-t.a)) < EPS; } Point crossPoint(Segment s, Segment t){ real d1 = cross(s.b-s.a, t.b-t.a); real d2 = cross(s.b-s.a, s.b-t.a); if(fabs(d1) < EPS && fabs(d2) < EPS) return t.a; return t.a+(t.b-t.a)*d2/d1; } Point crossPoint(Line s, Line t){ real d1 = cross(s.b-s.a, t.b-t.a); real d2 = cross(s.b-s.a, s.b-t.a); if(fabs(d1) < EPS && fabs(d2) < EPS) return t.a; return t.a+(t.b-t.a)*d2/d1; } Polygon crossPoint(Circle c, Line l){ Point p = project(l, c.c), q = (l.b-l.a)/abs(l.b-l.a); if(abs(distance(l, c.c)-c.r) < EPS){ return {p}; } double k = sqrt(c.r*c.r-dot(p-c.c, p-c.c)); return {p-q*k, p+q*k}; } Polygon crossPoint(Circle c, Segment s){ auto tmp = crossPoint(c, Line(s.a, s.b)); Polygon ret; for (auto &&i : tmp) { if(distance(s, i) < EPS) ret.emplace_back(i); } return ret; } Polygon crossPoint(Circle c1, Circle c2){ double d = abs(c1.c-c2.c); double a = acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d)); double t = arg(c2.c-c1.c); return {c1.c+polar(c1.r, t+a), c1.c+polar(c1.r, t-a)}; } Polygon tangent(Circle c1, Point p){ Circle c2 = Circle(p, sqrt(dot(c1.c-p, c1.c-p)-c1.r*c1.r)); return crossPoint(c1, c2); } vector tangent(Circle c1, Circle c2){ vector ret; if(c1.r < c2.r) swap(c1, c2); double k = dot(c1.c-c2.c, c1.c-c2.c); if(abs(k) < EPS) return {}; Point u = (c2.c-c1.c)/sqrt(k); Point v(-u.y, u.x); for (auto &&i : {-1, 1}) { double h = (c1.r+i*c2.r)/sqrt(k); if(abs(h*h-1) < EPS){ ret.emplace_back(c1.c+u*c1.r, c1.c+(u+v)*c1.r); }else if(h*h < 1){ Point u2 = u*h, v2 = v*sqrt(1-h*h); ret.emplace_back(c1.c+(u2+v2)*c1.r, c2.c-(u2+v2)*c2.r*i); ret.emplace_back(c1.c+(u2-v2)*c1.r, c2.c-(u2-v2)*c2.r*i); } } return ret; } real area(Polygon v){ if(v.size() < 3) return 0.0; real ans = 0.0; for (int i = 0; i < v.size(); ++i) { ans += cross(v[i], v[(i+1)%v.size()]); } return ans/2; } real area(Circle c, Polygon &v){ int n = v.size(); real ans = 0.0; Polygon u; for (int i = 0; i < n; ++i) { u.emplace_back(v[i]); auto q = crossPoint(c, Segment(v[i], v[(i+1)%n])); for (auto &&j : q) { u.emplace_back(j); } } for (int i = 0; i < u.size(); ++i) { Point A = u[i]-c.c, B = u[(i+1)%u.size()]-c.c; if(abs(A) >= c.r+EPS || abs(B) >= c.r+EPS){ Point C = polar(1, arg(B)-arg(A)); ans += c.r*c.r*arg(C)/2; }else { ans += cross(A, B)/2; } } return ans; } Polygon convex_hull(Polygon v){ int n = v.size(); sort(v.begin(),v.end(), sorty); int k = 0; Polygon ret(n*2); for (int i = 0; i < n; ++i) { while(k > 1 && cross(ret[k-1]-ret[k-2], v[i]-ret[k-1]) < 0) k--; ret[k++] = v[i]; } for(int i = n-2, t=k; i >= 0; i--){ while(k > t && cross(ret[k-1]-ret[k-2], v[i]-ret[k-1]) < 0) k--; ret[k++] = v[i]; } ret.resize(k-1); return ret; } bool isconvex(Polygon v){ int n = v.size(); for (int i = 0; i < n; ++i) { if(ccw(v[(i+n-1)%n], v[i], v[(i+1)%n]) < 0) return false; } return true; } int contains(Polygon v, Point p){ int n = v.size(); bool x = false; static constexpr int IN = 2; static constexpr int ON = 1; static constexpr int OUT = 0; for (int i = 0; i < n; ++i) { Point a = v[i]-p, b = v[(i+1)%n]-p; if(fabs(cross(a, b)) < EPS && dot(a, b) < EPS) return ON; if(a.y > b.y) swap(a, b); if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x; } return (x?IN:OUT); } real diameter(Polygon v){ int n = v.size(); if(n == 2) return abs(v[0]-v[1]); int i = 0, j = 0; for (int k = 0; k < n; ++k) { if(v[i] < v[k]) i = k; if(!(v[j] < v[k])) j = k; } real ret = 0; int si = i, sj = j; while(i != sj || j != si){ ret = max(ret, abs(v[i]-v[j])); if(cross(v[(i+1)%n]-v[i], v[(j+1)%n]-v[j]) < 0.0) i = (i+1)%n; else j = (j+1)%n; } return ret; } Polygon convexCut(Polygon v, Line l){ Polygon q; int n = v.size(); for (int i = 0; i < n; ++i) { Point a = v[i], b = v[(i+1)%n]; if(ccw(l.a, l.b, a) != -1) q.push_back(a); if(ccw(l.a, l.b, a)*ccw(l.a, l.b, b) < 0){ q.push_back(crossPoint(Line(a, b), l)); } } return q; } real closest_pair(Polygon &v, int l = 0, int r = -1){ if(!(~r)){ r = v.size(); sort(v.begin(),v.end()); } if(r - l < 2) { return abs(v.front()-v.back()); } int mid = (l+r)/2; real p = v[mid].x; real d = min(closest_pair(v, l, mid), closest_pair(v, mid, r)); inplace_merge(v.begin()+l, v.begin()+mid, v.begin()+r, sorty); Polygon u; for (int i = l; i < r; ++i) { if(fabs(v[i].x-p) >= d) continue; for (int j = 0; j < u.size(); ++j) { real dy = v[i].y-next(u.rbegin(), j)->y; if(dy >= d) break; d = min(d, abs(v[i]-*next(u.rbegin(), j))); } u.emplace_back(v[i]); } return d; } int main() { Polygon v(5); for (auto &&i : v) { cin >> i; } puts(convex_hull(v).size() == 5 && isconvex(convex_hull(v)) ? "YES" : "NO"); return 0; }