1 #include<algorithm>
2 #include<iostream>
3 #include<cstdlib>
4 #include<cstring>
5 #include<cstdio>
6 #include<string>
7 #include<cmath>
8 #include<ctime>
9 #include<queue>
10 #include<stack>
11 #include<map>
12 #include<set>
13 #define rre(i,r,l) for(int i=(r);i>=(l);i--)
14 #define re(i,l,r) for(int i=(l);i<=(r);i++)
15 #define Clear(a,b) memset(a,b,sizeof(a))
16 #define inout(x) printf("%d",(x))
17 #define douin(x) scanf("%lf",&x)
18 #define strin(x) scanf("%s",(x))
19 #define LLin(x) scanf("%lld",&x)
20 #define op operator
21 #define CSC main
22 typedef unsigned long long ULL;
23 typedef const int cint;
24 typedef long long LL;
25 using namespace std;
26 void inin(int &ret)
27 {
28 ret=0;int f=0;char ch=getchar();
29 while(ch<'0'||ch>'9'){if(ch=='-')f=1;ch=getchar();}
30 while(ch>='0'&&ch<='9')ret*=10,ret+=ch-'0',ch=getchar();
31 ret=f?-ret:ret;
32 }
33 const double eps=1e-8;
34 const double pi=acos(-1);
35 const double inf=2147483647;
36 double f(const long double &a){return a*a;}
37 inline int dcmp(const long double &a){return abs(a)<eps?0:a<0?-1:1;}
38 struct xl
39 {
40 double x,y;
41 xl(double x=0.,double y=0.):x(x),y(y){}
42 void in(){douin(x),douin(y);}
43 bool op == (const xl &rhs)const {return !dcmp(x-rhs.x)&&!dcmp(y-rhs.y);}
44 bool op < (const xl &rhs)const {return !dcmp(x-rhs.x)?y<rhs.y:x<rhs.x;}
45 xl op + (const xl &rhs)const {return xl(x+rhs.x,y+rhs.y);}
46 xl op - (const xl &rhs)const {return xl(x-rhs.x,y-rhs.y);}
47 xl op * (const double &rhs)const {return xl(x*rhs,y*rhs);}
48 xl op / (const double &rhs)const {return xl(x/rhs,y/rhs);}
49 xl rotate(const double &rad)const {return xl(x*cos(rad)-y*sin(rad),x*sin(rad)+y*cos(rad));}
50 double len()const {return sqrt(f(x)+f(y));}
51 double angle()const {return atan2(y,x);}
52 };
53 double D_(const xl &a,const xl &b){return a.x*b.x+a.y*b.y;}
54 double X_(const xl &a,const xl &b){return a.x*b.y-a.y*b.x;}
55 double dis(const xl &a,const xl &b){return sqrt(f(a.x-b.x)+f(a.y-b.y));}
56 double dis2(const xl &a,const xl &b){return f(a.x-b.x)+f(a.y-b.y);}
57 double angle(const xl &a,const xl &b){return acos(D_(a,b)/a.len()/b.len());}
58 struct LINE
59 {
60 xl u,v;double rad;
61 LINE(xl u=xl(0.,0.),xl v=xl(0.,0.)):u(u),v(v){}
62 void js(){rad=(v-u).angle();}
63 bool op < (const LINE &rhs)const {return rad<rhs.rad;}
64 double k()const {return !dcmp(u.x-v.x)?inf:(v.y-u.y)/(v.x-u.x);}
65 double len()const {return (v-u).len();}
66 };
67 xl getjd(const LINE &a,const LINE &b)
68 {
69 xl u=a.u-b.u,v1=a.v-a.u,v2=b.v-b.u;
70 long double t=X_(v2,u)/X_(v1,v2);
71 return a.u+v1*t;
72 }
73 bool pdxj(const LINE &a,const LINE &b)
74 {
75 if(!dcmp(X_(a.u,b.v-b.u)-X_(a.v,b.v-b.u)))return 0;
76 return 1;
77 }
78 double distoline(const xl &a,const LINE &l)
79 {
80 return abs(X_(a-l.u,l.v-l.u))/l.len();
81 }
82 double distoseg(const xl &a,const LINE &l)
83 {
84 xl v1=a-l.u,v2=a-l.v,u=l.v-l.u;
85 int t1=dcmp(X_(v1,u)),t2=dcmp(X_(v2,u));
86 if(t1>0&&t2>0)return v2.len();
87 if(t1<0&&t2<0)return v1.len();
88 return distoline(a,l);
89 }
90 xl getpoty(const xl &a,const LINE &l)
91 {
92 xl v=l.v-l.u;
93 return l.u+v*D_(a-l.u,v)/D_(v,v);
94 }
95 bool pdxjseg(const LINE &a,const LINE &b)
96 {
97 xl u1=a.u-b.u,u2=a.v-b.u,u=a.v-a.u;
98 xl v1=b.u-a.u,v2=b.v-a.u,v=b.v-b.u;
99 int t1=dcmp(X_(u1,v)),t2=dcmp(X_(u2,v));
100 int t3=dcmp(X_(v1,u)),t4=dcmp(X_(v2,v));
101 return t1*t2<=0&&t3*t4<=0;
102 }
103 bool onseg(const xl &a,const LINE &l)
104 {
105 return !dcmp(D_(a-l.u,a-l.v))&&dcmp(X_(a-l.u,a-l.v))<=0;
106 }
107 struct cir
108 {
109 xl c;double r;
110 cir(xl c=xl(0.,0.),double r=0):c(c),r(r){}
111 bool op < (const cir &rhs)const {return c==rhs.c?r<rhs.r:c<rhs.c;}
112 xl point (const double &rad)const {return c+xl(r*cos(rad),r*sin(rad));}
113 };
114 int getjd(const LINE &l,const cir &c,xl &ans1,xl &ans2)
115 {
116 double d=distoline(c.c,l);
117 if(dcmp(d-c.r)>0)return 0;
118 if(!dcmp(d-c.r))return ans1=getpoty(c.c,l),1;
119 xl temp=getpoty(c.c,l);
120 xl v=c.c-temp;swap(v.x,v.y);
121 double len=sqrt(f(c.r)-f(v.len()));
122 v=v*len/v.len();
123 ans1=temp+v,ans2=temp-v;
124 return 2;
125 }
126 int getjd(const cir &a,const cir &b,xl &ans1,xl &ans2)
127 {
128 double d=(b.c-a.c).len();
129 if(!dcmp(d))if(!dcmp(b.r-a.r))return inf;else return 0;else ;
130 if(dcmp(a.r+b.r-d)<0||dcmp(fabs(a.r-b.r)-d)>0)return 0;
131 double rad=(b.c-a.c).angle();
132 double da=acos((f(a.r)+f(d)-f(b.r))/(2*a.r*d));
133 ans1=a.point(rad-da);
134 xl ans3=a.point(rad+da);
135 if(ans1==ans3)return 1;
136 ans2=ans3;return 2;
137 }
138 int gettangents(cir &A,cir &B,LINE *ans)
139 {
140 if(A.c==B.c)if(!dcmp(A.r-B.r))return inf;
141 else return 0;else ;
142 if(A.r<B.r)swap(A,B);
143 double dd=f(A.c.x-B.c.x)+f(A.c.y-B.c.y);
144 double rdiff=A.r-B.r,rsum=A.r+B.r;
145 if(dcmp(dd-f(rdiff))<0)return 0;
146 xl u=B.c-A.c;
147 double base=atan2(B.c.y-A.c.y,B.c.x-A.c.x);
148 if(!dcmp(dd-f(rdiff)))
149 {
150 xl p=A.point(base);
151 ans[1]=LINE(p,p+u.rotate(pi/2));return 1;
152 }
153 double rad=acos((A.r-B.r)/sqrt(dd));
154 ans[1]=LINE(A.point(base+rad),B.point(base+rad));
155 ans[2]=LINE(A.point(base-rad),B.point(base-rad));
156 if(dcmp(dd-f(rsum))<0)return 2;
157 if(!dcmp(dd-f(rsum)))
158 {
159 xl p=A.point(base);
160 ans[3]=LINE(p,p+u.rotate(pi/2));
161 return 3;
162 }
163 rad=acos((A.r+B.r)/sqrt(dd));
164 ans[3]=LINE(A.point(base+rad),B.point(base+rad+pi));
165 ans[4]=LINE(A.point(base-rad),B.point(base-rad+pi));
166 return 4;
167 }
168 cir outoftriangle(const xl &A,const xl &B,const xl &C)
169 {
170 double bx=B.x-A.x,by=B.y-A.y;
171 double cx=C.x-A.x,cy=C.y-A.y;
172 double area=2*(bx*cy-by*cx);
173 double x=(cy*(f(bx)+f(by))-by*(f(cx)+f(cy)))/area+A.x;
174 double y=(bx*(f(cx)+f(cy))-cx*(f(bx)+f(by)))/area+A.y;
175 return cir(xl(x,y),(A-xl(x,y)).len());
176 }
177 cir inoftriangle(const xl &A,const xl &B,const xl &C)
178 {
179 double a=(B-C).len(),b=(C-A).len(),c=(A-B).len();
180 xl cc=(A*a+B*b+C*c)/(a+b+c);
181 return cir(cc,distoline(cc,LINE(A,B)));
182 }
183 struct pol
184 {
185 xl a[100010];int n;
186 void in(){inin(n);re(i,0,n-1)a[i].in();}
187 void Sort(){sort(a,a+n);}
188 xl& op [] (int x){return a[x];}
189 };
190 int pdinpol(const xl &p,pol &a)
191 {
192 int sum=0,n=a.n;
193 re(i,0,n)
194 {
195 if(onseg(p,LINE(a[i],a[(i+1)%n])))return -1;
196 int k=dcmp(X_(a[(i+1)%n]-a[i],p-a[i]));
197 int d1=dcmp(a[i].y-p.y);
198 int d2=dcmp(a[(i+1)%n].y-p.y);
199 if(k>0&&d1<=0&&d2>0)sum++;
200 if(k<0&&d2<=0&&d1>0)sum--;
201 }
202 if(sum!=0)return 1;
203 return 0;
204 }
205 void hull(pol &p,pol &ch)
206 {
207 int n=p.n,m=0;
208 p.Sort();
209 re(i,0,n-1)
210 {
211 while(m>1&&dcmp(X_(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<0)m--;
212 ch[m++]=p[i];
213 }
214 int k=m;
215 rre(i,n-1,0)
216 {
217 while(m>k&&dcmp(X_(ch[m-1]-ch[m-2],p[i]-ch[m-2]))<0)m--;
218 ch[m++]=p[i];
219 }
220 if(n>1)m--;
221 ch.n=m;
222 }
223 double lenofpol(pol &p)
224 {
225 double ret=0;
226 re(i,0,p.n-1)ret+=(p[(i+1)%p.n]-p[i]).len();
227 return ret;
228 }
229 double areaofpol(pol &p)
230 {
231 double ret=0;int n=p.n;
232 re(i,1,n-2)ret+=X_(p[i]-p[0],p[i+1]-p[0]);
233 return ret/2;
234 }
235 double diameterofhull(pol &p)
236 {
237 int n=p.n;double ret=0.;
238 if(n<=1)return 0.;
239 if(n==2)return dis2(p[0],p[1]);
240 int r=1;
241 re(l,0,n-1)while(1)
242 {
243 double d=X_(p[l+1]-p[l],p[r+1]-p[r]);
244 if(dcmp(d)<=0)
245 {
246 ret=max(ret,dis2(p[l],p[r]));
247 if(!dcmp(d))ret=max(ret,dis2(p[l],p[r+1]));
248 break;
249 }
250 r++,r%=n;
251 }
252 return ret;
253 }
254 bool onleft(const xl &a,const LINE &l){return X_(l.v-l.u,a-l.u)>0;}
255 bool halfplanej(LINE *l,int n,pol &ch)
256 {
257 re(i,0,n-1)l[i].js();
258 sort(l,l+n);
259 int ll=0,rr=0;
260 xl p[n];
261 LINE q[n];q[0]=l[0];
262 re(i,1,n-1)
263 {
264 while(ll<rr&&!onleft(p[rr-1],l[i]))rr--;
265 while(ll<rr&&!onleft(p[ll],l[i]))ll++;
266 q[++rr]=l[i];
267 if(!dcmp(X_(q[rr].v-q[rr].u,q[rr-1].v-q[rr-1].u)))
268 {
269 rr--;
270 if(onleft(l[i].u,q[rr]))q[rr]=l[i];
271 }
272 if(ll<rr)p[rr-1]=getjd(q[rr-1],q[rr]);
273 }
274 while(ll<rr&&!onleft(p[rr-1],q[ll]))rr--;
275 if(rr-ll<=1)return 0;
276 p[rr]=getjd(q[rr],q[ll]);
277 re(i,ll,rr)ch[ch.n++]=p[i];
278 ch[ch.n]=ch[0];return 1;
279 }
280 int main()
281 {
282 return 0;
283 }
