#include #include #include #include #include #include using namespace std; #define EPS (1e-10) #define equals(a, b) (fabs((a) - (b)) < EPS) struct Point; typedef Point Vector; typedef vector Polygon; struct Circle; struct Segment; typedef Segment Line; double norm(Point a); double abs(Point a); double dot(Vector a, Vector b); double cross(Vector a, Vector b); double getDistance(Point a, Point b); double getDistanceLP(Line l, Point p); double getDistanceSP(Segment s, Point p); double getDistance(Segment s1, Segment s2); bool isOrthogonal(Vector a, Vector b); bool isOrthogonal(Point a1, Point a2, Point b1, Point b2); bool isOrthogonal(Segment s1, Segment s2); bool isParallel(Vector a, Vector b); bool isParallel(Point a1, Point a2, Point b1, Point b2); bool isParallel(Segment s1, Segment s2); int ccw(Point p0, Point p1, Point p2); bool intersect(Point p1, Point p2, Point p3, Point p4); bool intersect(Segment s1, Segment s2); bool intersect(Circle c, Line l); // 誤差の検証をしていない bool intersect(Circle c1, Circle c2); // 誤差の検証をしていない Point project(Segment s, Point p); Point reflect(Segment s, Point p); Point getCrossPoint(Segment s1, Segment s2); pair getCrossPoints(Circle c, Line l); pair getCrossPoints(Circle c1, Circle c2); // 誤差の検証をしていない pair getContactPoints(Circle c, Point p); // 接点 点は円の外部 double area(Polygon g); // convexでなくてもよい. absを消せば符号付き面積 bool isConvex(Polygon g); // O(n^2) 線形時間アルゴリズムが存在するらしい int contains(Polygon g, Point p); double arg(Vector p); // 偏角 Vector polar(double a, double r); // 極座標系->ベクトル Polygon andrewScan(Polygon g); // 凸包の辺上の点も含めたければ!=CLOCKWISEを==COUNTER_CLOCKWISEに double convexDiameter(Polygon g); // gはconvex struct Point{ double x, y; Point(double x = 0, double y = 0) : x(x), y(y) {} Point operator + (Point p){ return Point(x+p.x, y+p.y); } Point operator - (Point p){ return Point(x-p.x, y-p.y); } Point operator * (double a){ return Point(a*x, a*y); } Point operator / (double a){ return Point(x/a, y/a); } double abs() { return sqrt(norm()); } double norm() { return x*x + y*y; } bool operator < (const Point &p) const{ return x != p.x ? x < p.x : y < p.y; } bool operator == (const Point &p) const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; } }; typedef Point Vector; typedef vector Polygon; struct Circle{ Point c; double r; Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {} }; struct Segment{ Point p1, p2; Segment(Point p1, Point p2) : p1(p1), p2(p2) {} }; typedef Segment Line; double norm(Point a){ return a.x * a.x + a.y * a.y; } double abs(Point a){ return sqrt(norm(a)); } double dot(Vector a, Vector b){ return a.x * b.x + a.y * b.y; } double cross(Vector a, Vector b){ return a.x * b.y - a.y * b.x; } double getDistance(Point a, Point b){ return abs(a - b); } double getDistanceLP(Line l, Point p){ return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1)); } double getDistanceSP(Segment s, Point p){ if(dot(s.p2-s.p1, p-s.p1) < 0.0) return abs(p-s.p1); if(dot(s.p1-s.p2, p-s.p2) < 0.0) return abs(p-s.p2); return getDistanceLP(s, p); } double getDistance(Segment s1, Segment s2){ if(intersect(s1, s2)) return 0.0; return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2), getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)}); } bool isOrthogonal(Vector a, Vector b){ return equals(dot(a, b), 0.0); } bool isOrthogonal(Point a1, Point a2, Point b1, Point b2){ return isOrthogonal(a1-a2, b1-b2); } bool isOrthogonal(Segment s1, Segment s2){ return equals(dot(s1.p2-s1.p1, s2.p2-s2.p1), 0.0); } bool isParallel(Vector a, Vector b){ return equals(cross(a, b), 0.0); } bool isParallel(Point a1, Point a2, Point b1, Point b2){ return isParallel(a1-a2, b1-b2); } bool isParallel(Segment s1, Segment s2){ return equals(cross(s1.p2-s1.p1, s2.p2-s2.p1), 0.0); } static const int COUNTER_CLOCKWISE = 1; static const int CLOCKWISE = -1; static const int ONLINE_BACK = 2; // p2->p0->p1 static const int ONLINE_FRONT = -2; // p0->p1->p2 static const int ON_SEGMENT = 0; // p0->p2->p1 int ccw(Point p0, Point p1, Point p2){ Vector a = p1 - p0; Vector b = p2 - p0; if(cross(a, b) > EPS) return COUNTER_CLOCKWISE; if(cross(a, b) < -EPS) return CLOCKWISE; if(dot(a, b) < -EPS) return ONLINE_BACK; if(norm(a) < norm(b)) return ONLINE_FRONT; return ON_SEGMENT; } bool intersect(Point p1, Point p2, Point p3, Point p4){ return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0); } bool intersect(Segment s1, Segment s2){ return intersect(s1.p1, s1.p2, s2.p1, s2.p2); } bool intersect(Circle c, Line l){ return getDistanceLP(l, c.c) < c.r+EPS; } bool intersect(Circle c1, Circle c2){ return abs(c1.r-c2.r) <= getDistance(c1.c, c2.c) && getDistance(c1.c, c2.c) < c1.r+c2.r+EPS; } Point project(Segment s, Point p){ Vector base = s.p2 - s.p1; double r = dot(p - s.p1, base) / norm(base); return s.p1 + base * r; } Point reflect(Segment s, Point p){ return p + (project(s, p) - p) * 2.0; } Point getCrossPoint(Segment s1, Segment s2){ Vector base = s2.p2 - s2.p1; double d1 = abs(cross(base, s1.p1-s2.p1)); double d2 = abs(cross(base, s1.p2-s2.p1)); double t = d1 / (d1 + d2); return s1.p1 + (s1.p2 - s1.p1) * t; } pair getCrossPoints(Circle c, Line l){ assert(intersect(c, l)); Vector pr = project(l, c.c); Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1); double base = sqrt(c.r * c.r - norm(pr - c.c)); return make_pair(pr + e*base, pr - e*base); } pair getCrossPoints(Circle c1, Circle c2){ assert(intersect(c1, 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 make_pair(c1.c + polar(c1.r, t+a), c1.c + polar(c1.r, t-a)); } pair getContactPoints(Circle c, Point p){ assert(c.r < getDistance(c.c, p)); double d = getDistance(c.c, p); return getCrossPoints(c, Circle(p, sqrt(d*d-c.r*c.r))); } double area(Polygon g){ if(g.size() < 3) return 0; int n = g.size(); Point o(0.0, 0.0); double s = 0.0; for(int i = 0; i < n; i++) s += cross(g[i]-o, g[(i+1)%n]-o); return abs(s) / 2.0; } bool isConvex(Polygon g){ bool ret = true; int n = g.size(); for(int i = 0; i < n; i++){ for(int j = i+1; j < n; j++){ if(cross(g[i]-g[(i+n-1)%n], g[j]-g[(i+n-1)%n]) < -EPS || cross(g[(i+1)%n]-g[i], g[j]-g[i]) < -EPS){ ret = false; } } } return ret; } static const int IN = 2; static const int ON = 1; static const int OUT = 0; int contains(Polygon g, Point p){ int n = g.size(); bool x = false; for(int i = 0; i < n; i++){ Point a = g[i] - p, b = g[(i+1)%n] - p; if(abs(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; } double arg(Vector p){ return atan2(p.y, p.x); } Vector polar(double a, double r){ return Point(a * cos(r), a * sin(r)); } Polygon andrewScan(Polygon g){ Polygon u, l; if(g.size() < 3) return g; sort(g.begin(), g.end()); u.push_back(g[0]); u.push_back(g[1]); l.push_back(g[g.size()-1]); l.push_back(g[g.size()-2]); // upper for(int i = 2; i < g.size(); i++){ for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], g[i]) != CLOCKWISE; n--){ u.pop_back(); } u.push_back(g[i]); } // lower for(int i = g.size()-3; i >= 0; i--){ for(int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], g[i]) != CLOCKWISE; n--){ l.pop_back(); } l.push_back(g[i]); } reverse(l.begin(), l.end()); for(int i = u.size()-2; i >= 1; i--) l.push_back(u[i]); return l; } double convexDiameter(Polygon g){ double d = 0.0; int n = g.size(); int is = 0, js = 0; for(int i = 1; i < n; i++){ if(g[i].y > g[is].y) is = i; if(g[i].y < g[js].y) js = i; } d = getDistance(g[is], g[js]); int i = is, j = js, maxi = is, maxj = js; do{ if(cross(g[(i+1)%n]-g[i], g[(j+1)%n]-g[j]) >= 0.0) j = (j+1)%n; else i = (i+1)%n; if(getDistance(g[i], g[j]) > d){ d = getDistance(g[i], g[j]); maxi = i, maxj = j; } }while(i != is || j != js); return d; // farthest pair is (maxi, maxj). } // 無理にsegmentを使わなければもっと簡潔に書ける // 外積を使えば交差判定を1回で済ませることが出来る int main(){ int n; cin >> n; vector v; for(int i = 0; i < n; i++){ int a, b, c, d; cin >> a >> b >> c >> d; v.push_back(Segment(Point(a,b), Point(c,d))); } int ans = 0; for(int i = 0; i < n; i++){ for(int j = 0; j < 2; j++){ for(int k = 0; k < n; k++){ for(int l = 0; l < 2; l++){ if(i==k && j==l) continue; Point a = j==0 ? v[i].p1 : v[i].p2; Point b = l==0 ? v[k].p1 : v[k].p2; Vector diff = b-a; b = b + diff*200; a = a - diff*200; int tmp = 0; for(int m = 0; m < n; m++){ if(equals(abs(dot(b-a, v[m].p1-v[m].p2)), 1.0)){ tmp++; }else if(intersect(a, b, v[m].p1, v[m].p2)){ tmp++; } } ans = max(ans, tmp); } } } } cout << ans << endl; return 0; }