LA 4973

// LA4973 Ardenia
// Rujia Liu
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;

struct Point3 {
int x, y, z;
Point3(int x=0, int y=0, int z=0):x(x),y(y),z(z) { }
};

typedef Point3 Vector3;

Vector3 operator + (const Vector3& A, const Vector3& B) { return Vector3(A.x+B.x, A.y+B.y, A.z+B.z); }
Vector3 operator - (const Point3& A, const Point3& B) { return Vector3(A.x-B.x, A.y-B.y, A.z-B.z); }
Vector3 operator * (const Vector3& A, int p) { return Vector3(A.x*p, A.y*p, A.z*p); }

bool operator == (const Point3& a, const Point3& b) {
return a.x==b.x && a.y==b.y && a.z==b.z;
}

Point3 read_point3() {
Point3 p;
scanf("%d%d%d", &p.x, &p.y, &p.z);
return p;
}

int Dot(const Vector3& A, const Vector3& B) { return A.x*B.x + A.y*B.y + A.z*B.z; }
int Length2(const Vector3& A) { return Dot(A, A); }
Vector3 Cross(const Vector3& A, const Vector3& B) { return Vector3(A.y*B.z - A.z*B.y, A.z*B.x - A.x*B.z, A.x*B.y - A.y*B.x); }

typedef long long LL;

LL gcd(LL a, LL b) { return b ? gcd(b, a%b) : a; }
LL lcm(LL a, LL b) { return a / gcd(a,b) * b; }

struct Rat {
LL a, b;
Rat(LL a=0):a(a),b(1) { }
Rat(LL x, LL y):a(x),b(y) {
if(b < 0) a = -a, b = -b;
LL d = gcd(a, b); if(d < 0) d = -d;
a /= d; b /= d;
}
};

Rat operator + (const Rat& A, const Rat& B) {
LL x = lcm(A.b, B.b);
return Rat(A.a*(x/A.b)+B.a*(x/B.b), x);
}

Rat operator - (const Rat& A, const Rat& B) { return A + Rat(-B.a, B.b); }
Rat operator * (const Rat& A, const Rat& B) { return Rat(A.a*B.a, A.b*B.b); }

void updatemin(Rat& A, const Rat& B) {
if(A.a*B.b > B.a*A.b) A.a = B.a, A.b = B.b;
}

// 点P到线段AB的距离的平方
Rat Rat_Distance2ToSegment(const Point3& P, const Point3& A, const Point3& B) {
if(A == B) return Length2(P-A);
Vector3 v1 = B - A, v2 = P - A, v3 = P - B;
if(Dot(v1, v2) < 0) return Length2(v2);
else if(Dot(v1, v3) > 0) return Length2(v3);
else return Rat(Length2(Cross(v1, v2)), Length2(v1));
}

// 求异面直线p1+su和p2+tv的公垂线对应的s。如果平行/重合，返回false
bool Rat_LineDistance3D(const Point3& p1, const Vector3& u, const Point3& p2, const Vector3& v, Rat& s) {
LL b = (LL)Dot(u,u)*Dot(v,v) - (LL)Dot(u,v)*Dot(u,v);
if(b == 0) return false;
LL a = (LL)Dot(u,v)*Dot(v,p1-p2) - (LL)Dot(v,v)*Dot(u,p1-p2);
s = Rat(a, b);
return true;
}

void Rat_GetPointOnLine(const Point3& A, const Point3& B, const Rat& t, Rat& x, Rat& y, Rat& z) {
x = Rat(A.x) + Rat(B.x-A.x) * t;
y = Rat(A.y) + Rat(B.y-A.y) * t;
z = Rat(A.z) + Rat(B.z-A.z) * t;
}

Rat Rat_Distance2(const Rat& x1, const Rat& y1, const Rat& z1, const Rat& x2, const Rat& y2, const Rat& z2) {
return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)+(z1-z2)*(z1-z2);
}

int main() {
int T;
scanf("%d", &T);
LL maxx = 0;
while(T--) {
Point3 A = read_point3();
Point3 B = read_point3();
Point3 C = read_point3();
Point3 D = read_point3();
Rat s, t;
bool ok = false;
Rat ans = Rat(1000000000);
if(Rat_LineDistance3D(A, B-A, C, D-C, s))
if(s.a > 0 && s.a < s.b && Rat_LineDistance3D(C, D-C, A, B-A, t))
if(t.a > 0 && t.a < t.b) {
ok = true; // 异面直线/相交直线
Rat x1, y1, z1, x2, y2, z2;
Rat_GetPointOnLine(A, B, s, x1, y1, z1);
Rat_GetPointOnLine(C, D, t, x2, y2, z2);
ans = Rat_Distance2(x1, y1, z1, x2, y2, z2);
}
if(!ok) { // 平行直线/重合直线
updatemin(ans, Rat_Distance2ToSegment(A, C, D));
updatemin(ans, Rat_Distance2ToSegment(B, C, D));
updatemin(ans, Rat_Distance2ToSegment(C, A, B));
updatemin(ans, Rat_Distance2ToSegment(D, A, B));
}
printf("%lld %lld\n", ans.a, ans.b);
}
return 0;
}