Problem: For given two segments s1 and s2, print the distance between them.

s1 is formed by end points p0 and p1, and s2 is formed by end points p2 and p3.

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xpi, ypi ≤ 10000
* p0 ≠ p1 and p2 ≠ p3.

Input

The entire input looks like:


q (the number of queries)
1st query
2nd query
...
qth query


Each query consists of integer coordinates of end points of s1 and s2 in the following format:


xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3


Output

For each query, print the distance. The output values should be in a decimal fraction with an error less than 0.00000001.

Example

Input

3
0 0 1 0 0 1 1 1
0 0 1 0 2 1 1 2
-1 0 1 0 0 1 0 -1


Output

1.0000000000
1.4142135624
0.0000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
const int COUNTER_CLOCKWISE = 1;
const int CLOCKWISE = -1;
const int ONLINE_BACK = 2;
const int ONLINE_FRONT = -2;
const int ON_SEGMENT = 0;

class Point
{
public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}

  Point operator+(Point p)
  {
    return Point(x + p.x, y + p.y);
  }
  Point operator-(Point p)
  {
    return Point(x - p.x, y - p.y);
  }
  Point operator*(double a)
  {
    return Point(a * x, a * y);
  }
  Point operator/(double a)
  {
    return Point(x / a, y / a);
  }

  double abs()
  {
    return sqrt(norm());
  }
  double norm()
  {
    return x * x + y * y;
  }

  bool operator<(const Point &p) const
  {
    return x != p.x ? x < p.x : y < p.y;
  }
  bool operator==(const Point &p) const
  {
    return equals(x, p.x) && equals(y, p.y);
  }

  void print()
  {
    printf("%.10f %.10f\n", x, y);
  }
};

typedef Point Vector;

double dot(Vector a, Vector b)
{
  return a.x * b.x + a.y * b.y;
}
double cross(Vector a, Vector b)
{
  return a.x * b.y - a.y * b.x;
}

struct Segment
{
  Point p1, p2;
};

typedef Segment Line;

class Circle
{
public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0) : c(c), r(r) {}
};

typedef vector<Point> Polygon;

Point projection(Line l, Point p)
{
  return l.p1 + (l.p2 - l.p1) * (dot(p - l.p1, l.p2 - l.p1) / (l.p2 - l.p1).norm());
}

Point reflection(Line l, Point p)
{
  Point x = projection(l, p);
  return p + (x - p) * 2;
}

int ccw(Point p0, Point p1, Point p2)
{
  Vector a = p1 - p0, b = p2 - p0;
  if (cross(a, b) > EPS)
  {
    return COUNTER_CLOCKWISE;
  }
  if (cross(a, b) < -EPS)
  {
    return CLOCKWISE;
  }
  if (dot(a, b) < -EPS)
  {
    return ONLINE_BACK;
  }
  if (a.norm() < b.norm())
  {
    return ONLINE_FRONT;
  }
  return ON_SEGMENT;
}

bool is_parallel(Line l1, Line l2)
{
  Vector a = l1.p2 - l1.p1, b = l2.p2 - l2.p1;
  return equals(cross(a, b), 0);
}

bool is_orthogonal(Line l1, Line l2)
{
  Vector a = l1.p2 - l1.p1, b = l2.p2 - l2.p1;
  return equals(dot(a, b), 0);
}

bool intersect(Segment s1, Segment s2)
{
  Point p0 = s1.p1, p1 = s1.p2, p2 = s2.p1, p3 = s2.p2;
  return (ccw(p0, p1, p2) * ccw(p0, p1, p3) <= 0) && (ccw(p2, p3, p0) * ccw(p2, p3, p1) <= 0);
}

Point intersection(Segment s1, Segment s2)
{
  Point p0 = s1.p1, p1 = s1.p2, p2 = s2.p1, p3 = s2.p2;
  double a0 = fabs(cross(p2 - p0, p3 - p0)), a1 = fabs(cross(p2 - p1, p3 - p1));
  return (p0 * a1 + p1 * a0) / (a0 + a1);
}

double distance(Segment s, Point p)
{
  Point p0 = s.p1, p1 = s.p2;
  if (dot(p1 - p0, p - p0) < -EPS)
  {
    return (p0 - p).abs();
  }
  if (dot(p0 - p1, p - p1) < -EPS)
  {
    return (p1 - p).abs();
  }
  return fabs(cross(p1 - p0, p - p0)) / (p1 - p0).abs();
}

double distance(Segment s1, Segment s2)
{
  if (intersect(s1, s2))
  {
    return 0;
  }
  double res = distance(s1, s2.p1);
  res = min(res, distance(s1, s2.p2));
  res = min(res, distance(s2, s1.p1));
  res = min(res, distance(s2, s1.p2));
  return res;
}

int main()
{
  int q;
  cin >> q;
  vector<bool> ans;
  rep(i, q)
  {
    double x0, y0, x1, y1, x2, y2, x3, y3;
    cin >> x0 >> y0 >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
    Segment s1 = {Point{x0, y0}, Point{x1, y1}}, s2 = {Point{x2, y2}, Point{x3, y3}};
    printf("%.10f\n", distance(s1, s2));
  }
}