#include <stdio.h>#include <string.h>#include <stdlib.h>#include <math.h>#define pi acos(-1.)#define le 12const double eps = 1e-8;typedef struct{ double x,y,r;}re;re p[le];int N,k,vis[le];double ans;double max(double a,double b){ return a > b ? a : b;}int in_circle(re a,re b){ double x = (a.x - b.x); double y = (a.y - b.y); double dist = x * x + y * y; return (dist < a.r * a.r + eps && sqrt(dist) > a.r - b.r + eps);}double dis(re a,re b){ return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));}int intersect(re a,re b){ return dis(a,b) < a.r + b.r - eps;}double ***_area(double r,double r2,double d){ double h = (r + r2 + d) / 2; return sqrt(h * (h - r) * (h - r2) * (h - d));}double in_area(re a,re b){ double d = dis(a,b); double s = ***_area(a.r,b.r,d); double angle = acos((a.r * a.r + d * d - b.r * b.r) / (2 * a.r * d)); double angle2 = acos((b.r * b.r + d * d - a.r * a.r) / (2 * b.r * d)); return angle * a.r * a.r + angle2 * b.r * b.r - 2 * s;}double area(re a,re b){ return pi * b.r * b.r - in_area(a,b);}void input(){ int i; for(i = 0;i <= N;i++) scanf("%lf%lf%lf",&p[i].x,&p[i].y,&p[i].r);}void available(){ int i; k = 1; for(i = 1;i <= N;i++) if(in_circle(p[0],p[i])) p[k++] = p[i];}void dfs(int ind,double sum){ int i; for(i = 1;i < k;i++) if(vis[i] && intersect(p[ind],p[i])) return ; vis[ind] = 1; sum += area(p[0],p[ind]); ans = max(ans,sum); for(i = 1;i < k;i++) if(!vis[i]) dfs(i,sum); vis[ind] = 0;}void enmue(){ int i; double sum; ans = pi * p[0].r * p[0].r; for(i = 1;i < k;i++){ memset(vis,0,sizeof(vis)); sum = pi * p[0].r * p[0].r; dfs(i,sum); }}void deal(){ available(); enmue(); printf("%.4lfn",ans);}int main(void){ while(scanf("%d",&N) == 1){ input(); deal(); } return 0;}
