#include <stdio.h>
#include <math.h>
typedef double R;
#define lc 1000

R pi = 3.14159265358979323846;
typedef struct{R x; R y; R z;} v;
R sq(R x){return x*x;}
v sp(R s, v vv){return (v){s*vv.x, s*vv.y, s*vv.z};}
void pv(v x){printf("%9.3f %9.3f %9.3f\n", x.x, x.y, x.z);} // ...
R det(v x, v y, v z){return
   x.x * (y.y * z.z - y.z * z.y)
 + x.y * (y.z * z.x - y.x * z.z)
 + x.z * (y.x * z.y - y.y * z.x);}
v vd(v * a, v * b){return (v){a->x - b->x, a->y - b->y, a->z - b->z};}
v va(v a, v b){return (v){a.x + b.x, a.y + b.y, a.z + b.z};}
void dcir(v * ans, v c, v r1, v r2){
R da = 2.*pi/lc;
{int k=lc; while(k--) {
   ans[k] = va(c, va(sp(cos(da*k), r1), sp(sin(da*k), r2)));}}
   ans[lc] = ans[0];}
v l1[lc+1], l2[lc+1]; // places on the respective curves.
int main(){
  dcir(l1, (v){0,   0, 0}, (v){1, 0, 0}, (v){0, 1, 0});
  dcir(l2, (v){1,   0, 0}, (v){1, 0, 0}, (v){0, 0, 1});

// printf("det=%e\n", det((v){0,2,0}, (v){0,0,1}, (v){1,0,0}));
{R s = 0, rm = 1000.;
{int j=lc; while(j--) {int k=lc; while(k--) {
   v r = 0?vd(l1+j, l2+k):
       sp(0.5, va(vd(l1+j, l2+k), vd(l1+j+1, l2+k+1)));
   R v2 = sq(r.x) + sq(r.y)+ sq(r.z);
   s += det(vd(l1+j+1, l1+j), vd(l2+k+1, l2+k), r)/(sqrt(v2)*v2);
   // printf("(%d %d) %e\n", j, k, det(vd(l1+j+1, l1+j), vd(l2+k+1, l2+k), r)); // ......
  // if(!j&&k==1) {pv(vd(l1+j+1, l1+j)); pv(vd(l2+k+1, l2+k)); pv(r);}
   if(v2<rm) rm=v2;}}}
printf("s = %11.7f, 4π = %11.7f, rm=%e\n", s, 4.*pi, sqrt(rm));}
// printf("l1[0]-l1[1]\n"); pv(*l1); pv(*(l1+1)); // ..... 
// printf("l2[1]-l2[2]\n"); pv(*(l2+1));  pv(*(l2+2)); // ..... 
return 0;}
// s = -12.5663522, 4π =  12.5663706, rm=1.000000e+00