1 //一些点一些圆，过圆不能连线，相邻点不能连线，问最多连几条线
2 //计算几何模板+区间dp
3 //关键是判断圆和线段是否相交
4 #include <cstdio>
5 #include <cmath>
6 #include <algorithm>
7 #define N 500
8 #define ll long long
9 #define sqr(x) ((x)*(x))
10 using namespace std;
11 bool ok[N][N];
12 ll n,m,r,f[N][N];
13 struct poi
14 {
15 ll x,y;
16 poi(ll X,ll Y)
17 {
18 x=X;y=Y;
19 }
20 poi()
21 {
22 }
23 } p[N],q[N];
24 ll cro(poi a,poi b)
25 {
26 return (a.x*b.y-a.y*b.x);
27 }
28 ll dot(poi a,poi b)
29 {
30 return a.x*b.x+a.y*b.y;
31 }
32 poi tr(poi a,poi b)
33 {
34 return poi(a.x-b.x,a.y-b.y);
35 }
36 double dis(poi a,poi b)
37 {
38 return sqrt((double)(sqr(a.x-b.x)+sqr(a.y-b.y)));
39 }
40 bool cmp(poi a,poi b)
41 {
42 return (a.x<b.x)||(a.x==b.x && a.y<b.y);
43 }
44 bool cmp2(poi a,poi b)
45 {
46 return cro(tr(a,p[1]),tr(b,p[1]))>0;
47 }
48 bool check(poi a,poi b)
49 {
50 double C=dis(a,b);
51 for(int i=1;i<=m;i++)
52 {
53 double A=dis(q[i],a);
54 double B=dis(q[i],b);
55 double COSA=(B*B+C*C-A*A)/(2*B*C);
56 double COSB=(A*A+C*C-B*B)/(2*A*C);
57 if(COSA<1e-10||COSB<1e-10){
58 if(A<1.0*r+1e-10||B<1.0*r+1e-10)return 0;
59 else continue;
60 }
61 double SINA=sqrt(1-COSA*COSA);
62 double H=B*SINA;
63 if(H<1.0*r+1e-10)return 0;
64 }
65 return 1;
66 }
67 int main()
68 {
69 scanf("%d%d%d",&n,&m,&r);
70 for(int i=1;i<=n;i++)
71 scanf("%d%d",&p[i].x,&p[i].y);
72 sort(p+1,p+1+n,cmp);
73 sort(p+2,p+1+n,cmp2);
74 for(int i=1;i<=m;i++)
75 scanf("%d%d",&q[i].x,&q[i].y);
76 for(int i=1;i<=n;i++)
77 for(int j=i+2;j<=n;j++)
78 if(i!=1 || j!=n)
79 ok[i][j]=check(p[i],p[j]);
80 for(int len=2;len<=n;len++)
81 for(int start=1;start<=n;start++){
82 ll end=start+len;
83 for(int k=start+1;k<min(end,n);k++)
84 f[start][end]=max(f[start][end],f[start][k]+f[k][end]);
85 f[start][end]+=ok[start][end];
86 }
87 printf("%d\n",f[1][n]);
88 }
