我觉得wordpress就是傻逼，又丑又难用，也可能是我太菜了，这并不影响我现阶段觉得wordpress是傻逼。主要是插件一直下不上。。
历史遗留问题。大概还是省赛排位的时候，当时我才刚碰计算几何。。。施展不出来。。。
现在有教练模式准备补一补。然后看了别人的代码。。发现求了个圆切线，，然后没了。
？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？
？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？？
这不是傻逼题吗为什么我当时不会？
题目的意思应该是不存在两棵树相切的情况。所以枚举切线就行了。
好嘛博客园md竟然不能实时预览，wtmd。。。。
#include <bits/stdc++.h>
#define mp make_pair
#define fi first
#define se second
#define pb push_back
using namespace std;
typedef double db;
const db eps=1e-6;
const db pi=acos(-1);
int sign(db k){
if (k>eps) return 1; else if (k<-eps) return -1; return 0;
}
int cmp(db k1,db k2){return sign(k1-k2);}
int inmid(db k1,db k2,db k3){return sign(k1-k3)*sign(k2-k3)<=0;}// k3 在 [k1,k2] 内
struct point{
db x,y;
point operator + (const point &k1) const{return (point){k1.x+x,k1.y+y};}
point operator - (const point &k1) const{return (point){x-k1.x,y-k1.y};}
point operator * (db k1) const{return (point){x*k1,y*k1};}
point operator / (db k1) const{return (point){x/k1,y/k1};}
int operator == (const point &k1) const{return cmp(x,k1.x)==0&&cmp(y,k1.y)==0;}
// 逆时针旋转
point turn(db k1){return (point){x*cos(k1)-y*sin(k1),x*sin(k1)+y*cos(k1)};}
point turn90(){return (point){-y,x};}
bool operator < (const point k1) const{
int a=cmp(x,k1.x);
if (a==-1) return 1; else if (a==1) return 0; else return cmp(y,k1.y)==-1;
}
db abs(){return sqrt(x*x+y*y);}
db abs2(){return x*x+y*y;}
db dis(point k1){return ((*this)-k1).abs();}
point unit(){db w=abs(); return (point){x/w,y/w};}
void scan(){double k1,k2; scanf("%lf%lf",&k1,&k2); x=k1; y=k2;}
void print(){printf("%.11lf %.11lf
",x,y);}
db getw(){return atan2(y,x);}
point getdel(){if (sign(x)==-1||(sign(x)==0&&sign(y)==-1)) return (*this)*(-1); else return (*this);}
int getP() const{return sign(y)==1||(sign(y)==0&&sign(x)==-1);}
};
int inmid(point k1,point k2,point k3){return inmid(k1.x,k2.x,k3.x)&&inmid(k1.y,k2.y,k3.y);}
db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y;}
db rad(point k1,point k2){return atan2(cross(k1,k2),dot(k1,k2));}
// -pi -> pi
int compareangle (point k1,point k2){//极角排序+
return k1.getP()<k2.getP()||(k1.getP()==k2.getP()&&sign(cross(k1,k2))>0);
}
point proj(point k1,point k2,point q){ // q 到直线 k1,k2 的投影
point k=k2-k1; return k1+k*(dot(q-k1,k)/k.abs2());
}
point reflect(point k1,point k2,point q){return proj(k1,k2,q)*2-q;}
int clockwise(point k1,point k2,point k3){// k1 k2 k3 逆时针 1 顺时针 -1 否则 0
return sign(cross(k2-k1,k3-k1));
}
int checkLL(point k1,point k2,point k3,point k4){// 求直线 (L) 线段 (S)k1,k2 和 k3,k4 的交点
return cmp(cross(k3-k1,k4-k1),cross(k3-k2,k4-k2))!=0;
}
point getLL(point k1,point k2,point k3,point k4){
db w1=cross(k1-k3,k4-k3),w2=cross(k4-k3,k2-k3); return (k1*w2+k2*w1)/(w1+w2);
}
int intersect(db l1,db r1,db l2,db r2){
if (l1>r1) swap(l1,r1); if (l2>r2) swap(l2,r2); return cmp(r1,l2)!=-1&&cmp(r2,l1)!=-1;
}
int checkSS(point k1,point k2,point k3,point k4){
return intersect(k1.x,k2.x,k3.x,k4.x)&&intersect(k1.y,k2.y,k3.y,k4.y)&&
sign(cross(k3-k1,k4-k1))*sign(cross(k3-k2,k4-k2))<=0&&
sign(cross(k1-k3,k2-k3))*sign(cross(k1-k4,k2-k4))<=0;
}
db disSP(point k1,point k2,point q){
point k3=proj(k1,k2,q);
if (inmid(k1,k2,k3)) return q.dis(k3); else return min(q.dis(k1),q.dis(k2));
}
db disSS(point k1,point k2,point k3,point k4){
if (checkSS(k1,k2,k3,k4)) return 0;
else return min(min(disSP(k1,k2,k3),disSP(k1,k2,k4)),min(disSP(k3,k4,k1),disSP(k3,k4,k2)));
}
int onS(point k1,point k2,point q){return inmid(k1,k2,q)&&sign(cross(k1-q,k2-k1))==0;}
struct circle{
point o; db r;
void scan(){o.scan(); scanf("%lf",&r);}
int inside(point k){return cmp(r,o.dis(k));}
};
struct line{
// p[0]->p[1]
point p[2];
line(point k1,point k2){p[0]=k1; p[1]=k2;}
point& operator [] (int k){return p[k];}
int include(point k){return sign(cross(p[1]-p[0],k-p[0]))>0;}
point dir(){return p[1]-p[0];}
line push(){ // 向外 ( 左手边 ) 平移 eps
const db eps = 1e-6;
point delta=(p[1]-p[0]).turn90().unit()*eps;
return {p[0]-delta,p[1]-delta};
}
};
point getLL(line k1,line k2){return getLL(k1[0],k1[1],k2[0],k2[1]);}
int parallel(line k1,line k2){return sign(cross(k1.dir(),k2.dir()))==0;}
int sameDir(line k1,line k2){return parallel(k1,k2)&&sign(dot(k1.dir(),k2.dir()))==1;}
int operator < (line k1,line k2){
if (sameDir(k1,k2)) return k2.include(k1[0]);
return compareangle(k1.dir(),k2.dir());
}
int checkpos(line k1,line k2,line k3){return k3.include(getLL(k1,k2));}
vector<line> getHL(vector<line> &L){ // 求半平面交 , 半平面是逆时针方向 , 输出按照逆时针
sort(L.begin(),L.end()); deque<line> q;
for (int i=0;i<(int)L.size();i++){
if (i&&sameDir(L[i],L[i-1])) continue;
while (q.size()>1&&!checkpos(q[q.size()-2],q[q.size()-1],L[i])) q.pop_back();
while (q.size()>1&&!checkpos(q[1],q[0],L[i])) q.pop_front();
q.push_back(L[i]);
}
while (q.size()>2&&!checkpos(q[q.size()-2],q[q.size()-1],q[0])) q.pop_back();
while (q.size()>2&&!checkpos(q[1],q[0],q[q.size()-1])) q.pop_front();
vector<line>ans; for (int i=0;i<q.size();i++) ans.push_back(q[i]);
return ans;
}
db closepoint(vector<point>&A,int l,int r){ // 最近点对 , 先要按照 x 坐标排序
if (r-l<=5){
db ans=1e20;
for (int i=l;i<=r;i++) for (int j=i+1;j<=r;j++) ans=min(ans,A[i].dis(A[j]));
return ans;
}
int mid=l+r>>1; db ans=min(closepoint(A,l,mid),closepoint(A,mid+1,r));
vector<point>B; for (int i=l;i<=r;i++) if (abs(A[i].x-A[mid].x)<=ans) B.push_back(A[i]);
sort(B.begin(),B.end(),[](point k1,point k2){return k1.y<k2.y;});
for (int i=0;i<B.size();i++) for (int j=i+1;j<B.size()&&B[j].y-B[i].y<ans;j++) ans=min(ans,B[i].dis(B[j]));
return ans;
}
int checkposCC(circle k1,circle k2){// 返回两个圆的公切线数量
if (cmp(k1.r,k2.r)==-1) swap(k1,k2);
db dis=k1.o.dis(k2.o); int w1=cmp(dis,k1.r+k2.r),w2=cmp(dis,k1.r-k2.r);
if (w1>0) return 4; else if (w1==0) return 3; else if (w2>0) return 2;
else if (w2==0) return 1; else return 0;
}
vector<point> getCL(circle k1,point k2,point k3){ // 沿着 k2->k3 方向给出 , 相切给出两个
point k=proj(k2,k3,k1.o); db d=k1.r*k1.r-(k-k1.o).abs2();
if (sign(d)==-1) return {};
point del=(k3-k2).unit()*sqrt(max((db)0.0,d)); return {k-del,k+del};
}
vector<point> getCC(circle k1,circle k2){// 沿圆 k1 逆时针给出 , 相切给出两个
int pd=checkposCC(k1,k2); if (pd==0||pd==4) return {};
db a=(k2.o-k1.o).abs2(),cosA=(k1.r*k1.r+a-k2.r*k2.r)/(2*k1.r*sqrt(max(a,(db)0.0)));
db b=k1.r*cosA,c=sqrt(max((db)0.0,k1.r*k1.r-b*b));
point k=(k2.o-k1.o).unit(),m=k1.o+k*b,del=k.turn90()*c;
return {m-del,m+del};
}
vector<point> TangentCP(circle k1,point k2){// 沿圆 k1 逆时针给出
db a=(k2-k1.o).abs(),b=k1.r*k1.r/a,c=sqrt(max((db)0.0,k1.r*k1.r-b*b));
point k=(k2-k1.o).unit(),m=k1.o+k*b,del=k.turn90()*c;
return {m-del,m+del};
}
vector<line> TangentoutCC(circle k1,circle k2){
int pd=checkposCC(k1,k2); if (pd==0) return {};
if (pd==1){point k=getCC(k1,k2)[0]; return {(line){k,k}};}
if (cmp(k1.r,k2.r)==0){
point del=(k2.o-k1.o).unit().turn90().getdel();
return {(line){k1.o-del*k1.r,k2.o-del*k2.r},(line){k1.o+del*k1.r,k2.o+del*k2.r}};
} else {
point p=(k2.o*k1.r-k1.o*k2.r)/(k1.r-k2.r);
vector<point>A=TangentCP(k1,p),B=TangentCP(k2,p);
vector<line>ans; for (int i=0;i<A.size();i++) ans.push_back((line){A[i],B[i]});
return ans;
}
}
vector<line> TangentinCC(circle k1,circle k2){
int pd=checkposCC(k1,k2); if (pd<=2) return {};
if (pd==3){point k=getCC(k1,k2)[0]; return {(line){k,k}};}
point p=(k2.o*k1.r+k1.o*k2.r)/(k1.r+k2.r);
vector<point>A=TangentCP(k1,p),B=TangentCP(k2,p);
vector<line>ans; for (int i=0;i<A.size();i++) ans.push_back((line){A[i],B[i]});
return ans;
}
vector<line> TangentCC(circle k1,circle k2){
int flag=0; if (k1.r<k2.r) swap(k1,k2),flag=1;
vector<line>A=TangentoutCC(k1,k2),B=TangentinCC(k1,k2);
for (line k:B) A.push_back(k);
if (flag) for (line &k:A) swap(k[0],k[1]);
return A;
}
db getarea(circle k1,point k2,point k3){
// 圆 k1 与三角形 k2 k3 k1.o 的有向面积交
point k=k1.o; k1.o=k1.o-k; k2=k2-k; k3=k3-k;
int pd1=k1.inside(k2),pd2=k1.inside(k3);
vector<point>A=getCL(k1,k2,k3);
if (pd1>=0){
if (pd2>=0) return cross(k2,k3)/2;
return k1.r*k1.r*rad(A[1],k3)/2+cross(k2,A[1])/2;
} else if (pd2>=0){
return k1.r*k1.r*rad(k2,A[0])/2+cross(A[0],k3)/2;
}else{
int pd=cmp(k1.r,disSP(k2,k3,k1.o));
if (pd<=0) return k1.r*k1.r*rad(k2,k3)/2;
return cross(A[0],A[1])/2+k1.r*k1.r*(rad(k2,A[0])+rad(A[1],k3))/2;
}
}
circle getcircle(point k1,point k2,point k3){
db a1=k2.x-k1.x,b1=k2.y-k1.y,c1=(a1*a1+b1*b1)/2;
db a2=k3.x-k1.x,b2=k3.y-k1.y,c2=(a2*a2+b2*b2)/2;
db d=a1*b2-a2*b1;
point o=(point){k1.x+(c1*b2-c2*b1)/d,k1.y+(a1*c2-a2*c1)/d};
return (circle){o,k1.dis(o)};
}
circle c[520];
vector<line> v,g;
vector<point> p ;
int n;
bool check(point x,point y){
for(int i=1;i<=n-2;i++)if(cmp(c[i].r,disSP(x,y,c[i].o))>0)return false;
return true;
}
bool can(line a){
p = getCL(c[n-1],a[0],a[1]);
if(p.empty())return false;
point x = p[0];
p = getCL(c[n],a[0],a[1]);
if(p.empty())return false;
point y = p[0];
return check(x,y);
}
int main(){
freopen("garden.in", "r", stdin);
freopen("garden.out", "w", stdout);
scanf("%d",&n);
n+=2;
for(int i=1;i<=n;i++){
scanf("%lf%lf%lf",&c[i].o.x,&c[i].o.y,&c[i].r);
}
for(int i=1;i<n;i++){
for(int j=i+1;j<=n;j++){
g=TangentCC(c[i],c[j]);
for(auto x:g)v.push_back(x);
}
}
bool f=0;
for(auto x:v){
if(can(x)){
f=1;
break;
}
}
if(f)printf("YES
");
else printf("NO
");
}