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 EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < (EPS))

#define COUNTER_CLOCKWISE (1)
#define CLOCKWISE (-1)
#define ONLINE_BACK (2)
#define ONLINE_FRONT (-2)
#define ON_SEGMENT (0)

struct Point 
{
  double x, y;
  
  Point() {}
  
  Point(double x, double y) : x(x), y(y) {}
  
  void input() { scanf("%lf %lf", &x, &y); }
  void output() { printf("%.10f %.10f\n", x, y); }
  double abs() { return (sqrt(norm())); }
  double norm() { return (x * x + y * y); }
  
  Point operator + (Point d) { return (Point(x + d.x, y + d.y)); }
  Point operator - (Point d) { return (Point(x - d.x, y - d.y)); }
  Point operator - () { return (Point(-x, -y)); }
  Point operator * (double a) { return (Point(x * a, y * a)); }
  Point operator / (double a) { return (Point(x / a, y / a)); }
  
};

struct Segment
{
  Point p1, p2;
  
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}

  void input() { p1.input(); p2.input(); }
  
};

typedef Point Vector;
typedef vector < Point > Polygon;
typedef Segment Line;

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);
}

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

Point reflect(Line l, Point p)
{
  return (-p + project(l, p) * 2.0);
}


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 intersect(Point p1, Point p2, Point p3, Point p4)
{
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2)
{
  return (intersect(s1.p1, s1.p2, s2.p1, s2.p2));
}

double getDistanceLP(Line l, Point p)
{
  return (abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs()));
}

double getDistanceSP(Segment s, Point p)
{
  if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return ((p - s.p1).abs());
  if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return ((p - s.p2).abs());
  return (getDistanceLP(s, p));
}

double getDistance(Segment s1, Segment s2)
{
  double ans;

  if(intersect(s1, s2)) {
    ans = 0.0;
  } else {
    ans = min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2));
    ans = min(ans, min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)));
  }

  return (ans);
}


int main()
{
  int n;
  
  cin >> n;
  for(int i = 0; i < n; i++) {
    Segment s1, s2;
    s1.input(); s2.input();
    printf("%.10f\n", getDistance(s1, s2));
  }

  return (0);
}