#include #define For(i, a, b) for(int (i)=(int)(a); (i)<(int)(b); ++(i)) #define rFor(i, a, b) for(int (i)=(int)(a)-1; (i)>=(int)(b); --(i)) #define rep(i, n) For((i), 0, (n)) #define rrep(i, n) rFor((i), (n), 0) #define fi first #define se second using namespace std; typedef long long lint; typedef unsigned long long ulint; typedef pair pii; typedef pair pll; template bool chmax(T &a, const T &b){if(a bool chmin(T &a, const T &b){if(a>b){a=b; return true;} return false;} template T div_floor(T a, T b){ if(b < 0) a *= -1, b *= -1; return a>=0 ? a/b : (a+1)/b-1; } template T div_ceil(T a, T b){ if(b < 0) a *= -1, b *= -1; return a>0 ? (a-1)/b+1 : a/b; } constexpr lint mod = 1e9+7; constexpr lint INF = mod * mod; constexpr int MAX = 200010; constexpr double eps=1e-9; constexpr double PI=3.14159265358979323846264338327950; inline int sgn(double x){ if(x<-eps) return -1; if(x>eps) return 1; return 0; } inline bool EQ(double x, double y){ return sgn(x-y)==0; } inline bool GE(double x, double y){ return sgn(x-y)==1; } inline bool LE(double x, double y){ return sgn(x-y)==-1; } inline bool GEQ(double x, double y){ return sgn(x-y)>=0; } inline bool LEQ(double x, double y){ return sgn(x-y)<=0; } struct Point{ double x, y; Point(double x=0, double y=0): x(x), y(y){} Point operator+(const Point &p){ return {x+p.x, y+p.y}; } Point operator-(const Point &p){ return {x-p.x, y-p.y}; } Point operator*(const double k){ return {k*x, k*y}; } Point operator/(const double k){ return {x/k, y/k}; } double operator*(const Point &p){ return x*p.x+y*p.y; } double operator^(const Point &p){ return x*p.y-y*p.x; } bool operator==(const Point &p){ return EQ(x, p.x) && EQ(y, p.y); } bool operator<(const Point &p) const{ if(EQ(x, p.x)) return LE(y, p.y); return LE(x, p.x); } }; using Vec=Point; using Polygon=vector; double norm(Point p){ return p.x*p.x+p.y*p.y; } double abs(Point p){ return sqrt(norm(p)); } double arg(Point p){ return atan2(p.y, p.x); } Point rot(Point p, double t){ return {p.x*cos(t)-p.y*sin(t), p.x*sin(t)+p.y*cos(t)}; } Point proj(Point a, Vec v, Point p){ double t=v*(p-a)/norm(v); return a+v*t; } Point refl(Point a, Vec v, Point p){ return proj(a, v, p)*2-p; } constexpr int CCW_COUNTER_CLOCKWISE=1; //反時計回り constexpr int CCW_CLOCKWISE=-1; //時計回り constexpr int CCW_ONLINE_BACK=-2; //一直線, C->A->B constexpr int CCW_ONLINE_FRONT=2; //一直線, A->B->C constexpr int CCW_ON_SEGMENT=0; //一直線, A->C->B inline int ccw(Point a, Point b, Point c){ Vec v=b-a, w=c-a; if(GE(v^w, 0)) return CCW_COUNTER_CLOCKWISE; if(LE(v^w, 0)) return CCW_CLOCKWISE; if(LE(v*w, 0)) return CCW_ONLINE_BACK; if(LE((a-b)*(c-b), 0)) return CCW_ONLINE_FRONT; return CCW_ON_SEGMENT; } bool isParallel(Vec v, Vec w){ return EQ(v^w, 0); } bool isOrthogonal(Vec v, Vec w){ return EQ(v*w, 0); } bool intersectSS(Point a, Point b, Point c, Point d){ return ccw(a, b, c)*ccw(a, b, d)<=0 && ccw(c, d, a)*ccw(c, d, b)<=0; } Point getCrossPointLL(Point a, Vec v, Point b, Vec w){ double t=((b-a)^w)/(v^w); return a+v*t; } double getDistanceLP(Point a, Vec v, Point p){ return abs(v^(p-a)/abs(v)); } double getDistanceSP(Point a, Point b, Point p){ if(LE((b-a)*(p-a), 0)) return abs(p-a); if(LE((a-b)*(p-b), 0)) return abs(p-b); return getDistanceLP(a, b-a, p); } double getDistanceLL(Point a, Vec v, Point b, Vec w){ if(isParallel(v, w)) return getDistanceLP(a, v, b); return 0; } double getDistanceLS(Point a, Vec v, Point c, Point d){ Point b=a+v; if(ccw(a, b, c)*ccw(a, b, d)<=0) return 0; return min(getDistanceLP(a, v, c), getDistanceLP(a, v, d)); } double getDistanceSS(Point a, Point b, Point c, Point d){ if(intersectSS(a, b, c, d)) return 0; return min({getDistanceSP(a, b, c), getDistanceSP(a, b, d), getDistanceSP(c, d, a), getDistanceSP(c, d, b)}); } double getAreaP(Polygon &p){ double ret=0; rep(i, (int)p.size()) ret+=p[i]^p[(i+1)%p.size()]/2; return abs(ret); } bool isConvex(Polygon &p){ int n=p.size(); bool flag1=false, flag2=false; rep(i, n){ int tmp=ccw(p[(i+n-1)%n], p[i], p[(i+1)%n]); if(tmp==CCW_COUNTER_CLOCKWISE){ if(flag2) return false; flag1=true; } else if(tmp==CCW_CLOCKWISE){ if(flag1) return false; flag2=true; } } return true; } Polygon convex_hull(Polygon p){ int n=p.size(); sort(p.begin(), p.end()); Polygon ch(2*n); int k=0; rep(i, n){ while(k>1 && LE((ch[k-1]-ch[k-2])^(p[i]-ch[k-1]), 0)) --k; ch[k++]=p[i]; } for(int i=n-2, t=k; i>=0; --i){ while(k>t && LE((ch[k-1]-ch[k-2])^(p[i]-ch[k-1]), 0)) --k; ch[k++]=p[i]; } ch.resize(k-1); return ch; } int intersectCC(Point c1, double r1, Point c2, double r2){ if(r1=3) return 0; if(flag<=1){ double r=min(r1, r2); return PI*r*r; } double d=abs(c1-c2); double ret=0; rep(i, 2) { double x=(d*d+r1*r1-r2*r2)/(2*d); double t=acos(x/r1)*2; ret+=(t-sin(t))*r1*r1/2; swap(c1, c2); swap(r1, r2); } return ret; } Polygon Tangent(Point c, double r, Point p){ Polygon ps; double d=abs(p-c); double t=acos(r/d); ps.push_back(c+rot(p-c, t)*r/d); ps.push_back(c+rot(p-c, -t)*r/d); return ps; } Polygon getCommonTangent(Point c1, double r1, Point c2, double r2){ Polygon ps; int flag=intersectCC(c1, r1,c2, r2); if(flag>=2){ double d=abs(c2-c1); double t=acos(abs(r1-r2)/d); if(LE(r1, r2)) t=PI-t; ps.push_back(c1+rot(c2-c1, t)*r1/d); ps.push_back(c1+rot(c2-c1, -t)*r1/d); } if(flag==4){ double d=abs(c2-c1); double L=d*r1/(r1+r2); double t=acos(r1/L); ps.push_back(c1+rot(c2-c1, t)*r1/d); ps.push_back(c1+rot(c2-c1, -t)*r1/d); } if(flag==3 || flag==1){ Polygon tg=getCrossPointCC(c1, r1, c2, r2); ps.push_back(tg[0]); } return ps; } Point getO(Point a, Point b, Point c){ Point M=(a+b)/2, N=(a+c)/2; Vec v={-(b-a).y, (b-a).x}, w={-(c-a).y, (c-a).x}; return getCrossPointLL(M, v, N, w); } Point getI(Point a, Point b, Point c){ double A=abs(b-c), B=abs(c-a), C=abs(a-b); return (a*A+b*B+c*C)/(A+B+C); } Point getH(Point a, Point b, Point c){ Vec v={-(c-b).y, (c-b).x}, w={-(c-a).y, (c-a).x}; return getCrossPointLL(a, v, b, w); } pair MinimumBoundingCircle(Polygon &p){ Point C; double r; if(p.size()==1) C=p[0], r=0; else if(p.size()==2) C=(p[0]+p[1])/2, r=abs(p[0]-C); else{ r=INF; Polygon ch=convex_hull(p); int K=ch.size(); auto check=[&](Point tc, double tr){ rep(i, K){ if(GE(abs(ch[i]-tc), tr)) return false; } return true; }; rep(i, K)For(j, i+1, K){ Point tc=(ch[i]+ch[j])/2; double tr=abs(ch[i]-tc); if(check(tc, tr) && chmin(r, tr)) C=tc; For(k, j+1, K){ int ccw_flag=ccw(ch[i], ch[j], ch[k]); if(ccw_flag!=CCW_COUNTER_CLOCKWISE && ccw_flag!=CCW_CLOCKWISE) continue; tc=getO(ch[i], ch[j], ch[k]); tr=abs(ch[i]-tc); if(check(tc, tr) && chmin(r, tr)) C=tc; } } } return {C, r}; } int main(){ int n; scanf("%d", &n); Polygon p(n); rep(i, n) scanf("%lf%lf", &p[i].x, &p[i].y); int ans = 0; rep(i, n)For(j, i+1, n){ int tmp = 0; rep(k, n) tmp += (proj(p[i], p[j]-p[i], p[k]) == p[k]); chmax(ans, tmp); } printf("%d\n", ans); }