Problem: Problem

In this problem, a straight line passing through a certain point X and a certain point Y in the three-dimensional space is written as a straight line XY.

A cone and a point P inside the cone are given in three-dimensional space. Let point Q be the intersection of a straight line passing through point P and perpendicular to the bottom of the cone and the bottom of the cone. At this time, the center of the bottom surface of the cone is O, and the intersection of the straight line OQ and the circumference of the bottom surface of the cone is point A and point B from the side closer to point Q (however, point O and point Q are the same point). In the case of, let points A and B be the intersections of any straight line passing through point O and the circumference of the bottom of the cone.) Also, in a plane that includes the bottom surface of the cone, let points C and D be the intersections of the straight line that passes through point O and intersects the straight line AB perpendicularly with the circumference of the bottom surface of the cone (however, points C and D). Can be replaced).


The figure below is a view of the bottom surface of the cone as seen from the direction of the apex of the cone.

View of the bottom of the cone as seen from the apex of the cone


Let the intersection of the straight line AP and the cone of the straight line BP (in the case of the straight line AP, the intersection that is not the point A. The same applies to the straight line BP) be the point A'and the point B', and pass through the points A'and B'. Cut the cone at the plane S parallel to the straight line CD. At this time, output the volume of the figure including the vertices after cutting and the volume of the other figure separated by blanks.

Input

X coordinate y coordinate z coordinate of the apex of the cone
X coordinate y coordinate z coordinate of the center of the base of the cone Radius of the base of the cone
X coordinate y coordinate z coordinate of point P

Each value on each row is given separated by spaces.

Constraint

All input values ​​are integers, the absolute value of which is less than or equal to 1000.
The height of the cone and the radius of its base are greater than or equal to 1, and the distance between point P and the cone is greater than or equal to 10-5.

Output

Output the volume of the figure including the vertices after cutting and the volume of the other figure separated by blanks.
However, it must not contain an error greater than 10-5.

Sample Input 1


0 0 10
0 0 0 4
0 0 1


Sample Output 1


91.769438 75.782170


Sample Input 2


0 0 10
0 0 0 4
1 1 1


Sample Output 2


84.050413 83.501195


Sample Input 3


0 0 0
8 9 10 5
1 1 1


Sample Output 3


0.071663 409.709196






Example

Input

0 0 10
0 0 0 4
0 0 1


Output

91.769438 75.782170

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const double PI = acos(-1);
const double PIH = PI / 2;

/* typedef */

template <typename T>
struct Pt {
  T x, y;

  Pt() {}
  Pt(T _x, T _y) : x(_x), y(_y) {}
  Pt(const Pt& pt) : x(pt.x), y(pt.y) {}

  Pt operator+(const Pt pt) const { return Pt(x + pt.x, y + pt.y); }
  Pt operator-() const { return Pt(-x, -y); }
  Pt operator-(const Pt pt) const { return Pt(x - pt.x, y - pt.y); }
  Pt operator*(T t) const { return Pt(x * t, y * t); }
  Pt operator/(T t) const { return Pt(x / t, y / t); }
  T dot(Pt v) { return x * v.x + y * v.y; }
  T cross(Pt v) { return x * v.y - y * v.x; }
  Pt mid(const Pt pt) { return Pt((x + pt.x) / 2, (y + pt.y) / 2); }
  T d2() { return x * x + y * y; }
  double d() { return sqrt(d2()); }

  Pt rot(double th) {
    double c = cos(th), s = sin(th);
    return Pt(c * x - s * y, s * x + c * y);
  }
  
  void print(string format) {
    printf(("(" + format + ", " + format + ")\n").c_str(), x, y);
  }
};

template <typename T>
struct Pt3D {
  T x, y, z;

  Pt3D() {}
  Pt3D(T _x, T _y, T _z) { x = _x; y = _y; z = _z; }

  bool operator==(const Pt3D<T>& pt) {
    return x == pt.x && y == pt.y && z == pt.z;
  }

  bool operator<(const Pt3D<T>& pt) const {
    return x < pt.x || (x == pt.x && (y < pt.y || (y == pt.y && z < pt.z)));
  }
  
  Pt3D<T> operator+(const Pt3D<T>& pt) {
    return Pt3D<T>(x + pt.x, y + pt.y, z + pt.z);
  }

  Pt3D<T> operator-(const Pt3D<T>& pt) {
    return Pt3D<T>(x - pt.x, y - pt.y, z - pt.z);
  }
  
  Pt3D<T> operator-() { return Pt3D<T>(-x, -y, -z); }
  Pt3D<T> operator*(const T& t) { return Pt3D<T>(x * t, y * t, z * t); }
  Pt3D<T> operator/(const T& t) { return Pt3D<T>(x / t, y / t, z / t); }

  T dot(const Pt3D<T>& v) { return x * v.x + y * v.y + z * v.z; }

  Pt3D<T> cross(const Pt3D<T>& v) {
    return Pt3D<T>(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x);
  }

  T d2() { return x * x + y * y + z * z; }
  double d() { return sqrt(d2()); }
  Pt3D<T> normalize() { return *this / d(); }

  void print(string format) {
    printf(("(" + format + ", " + format + ", " + format + ")\n").c_str(),
	   x, y, z);
  }
};

typedef Pt<double> pt;
typedef Pt3D<double> pt3d;

/* global variables */

pt3d t, b, p;
double r;

/* subroutines */

pt3d rot_x(const pt3d pt, double th) {
  double c = cos(th), s = sin(th);
  return pt3d(pt.x, c * pt.y - s * pt.z, s * pt.y + c * pt.z);
}

pt3d rot_y(const pt3d pt, double th) {
  double c = cos(th), s = sin(th);
  return pt3d(s * pt.z + c * pt.x, pt.y, c * pt.z - s * pt.x);
}

pt3d rot_z(const pt3d pt, double th) {
  double c = cos(th), s = sin(th);
  return pt3d(c * pt.x - s * pt.y, s * pt.x + c * pt.y, pt.z);
}

bool cross_lines(const pt& a0, const pt& a1, const pt& b0, const pt& b1,
                 pt& ret) {
  pt da = a1 - a0;
  pt db = b1 - b0;

  double op01 = da.cross(db);
  if (op01 == 0.0) return false; /* need to handle parallel?? */

  pt v = b0 - a0;
  double op0 = v.cross(da);
  double op1 = v.cross(db);

  double t0 = op1 / op01;
  double t1 = op0 / op01;

  ret = db * t1 + b0;
  return true;
}

/* main */

int main() {
  cin >> t.x >> t.y >> t.z;
  cin >> b.x >> b.y >> b.z >> r;
  cin >> p.x >> p.y >> p.z;

  t = t - b;
  p = p - b;

  double th0 = atan2(t.y, t.x);
  t = rot_z(t, -th0);
  p = rot_z(p, -th0);
  //t.print("%.6lf");
  
  double th1 = atan2(t.x, t.z);
  t = rot_y(t, -th1);
  p = rot_y(p, -th1);
  //t.print("%.6lf");
  
  double th2 = atan2(p.y, p.x);
  p = rot_z(p, PIH - th2);
  //p.print("%.6lf");
  
  double v = PI * r * r * t.z / 3;
  //printf("%.6lf\n", v);

  pt pp(p.y, p.z), aa(r, 0.0), bb(-r, 0.0), tt(0.0, t.z);
  pt aad, bbd;
  
  cross_lines(aa, pp, bb, tt, aad);
  cross_lines(bb, pp, aa, tt, bbd);
  //aad.print("%.6lf");
  //bbd.print("%.6lf");

  pt mo = aad.mid(bbd);
  //mo.print("%.6lf");

  pt dabd = aad - bbd;
  double ry = dabd.d() / 2;

  double mr = r * (t.z - mo.y) / t.z;
  double rx = sqrt(mr * mr - mo.x * mo.x);
  //printf("rx=%.6lf, ry=%.6lf\n", rx, ry);

  pt oo(0.0, 0.0), dtt;
  cross_lines(aad, bbd, oo, tt, dtt);
  //dtt.print("%.6lf");

  double th3 = atan2(abs(dabd.y), abs(dabd.x));
  double h = (tt.y - dtt.y) * cos(th3);
  //printf("tt.y=%.6lf, dtt.y=%.6lf, cos=%.6lf, h=%.6lf\n",
  //tt.y, dtt.y, cos(th3), h);

  double v0 = PI * rx * ry * h / 3;
  printf("%.6lf %.6lf\n", v0, v - v0);
  
  return 0;
}