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<cstdio>
#include<cmath>

using namespace std;


const int CCW_COUNTER_CLOCKWISE = 1;
const int CCW_CLOCKWISE = -1;
const int CCW_ONLINE_BACK = 2;
const int CCW_ONLINE_FRONT = -2;
const int CCW_ON_SEGMENT = 0;


const double EPS = 1e-10;
inline bool equals(double x, double y) {
  return fabs(x-y) < EPS;
}


struct Point {
  Point(int _x, int _y) : x(_x), y(_y) {}

  double x, y;

  Point operator+(const Point& other) const {
    return Point(x+other.x, y+other.y);
  }

  Point operator-(const Point& other) const {
    return Point(x-other.x, y-other.y);
  }

  Point operator*(double k) const {
    return Point(x*k, y*k);
  }
};


typedef Point Vector;


struct Segment {
  Segment(Point _p1, Point _p2) : p1(_p1), p2(_p2) {}
  Point p1, p2;
};


typedef Segment Line;


double norm(Vector v) {
  return v.x*v.x + v.y*v.y;
}

double abs(Vector v) {
  return sqrt(norm(v));
}

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;
}

int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0;
  Vector b = p2 - p0;
  if (cross(a, b) > EPS) return CCW_COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS) return CCW_CLOCKWISE;
  if (dot(a, b) < -EPS) return CCW_ONLINE_BACK;
  if (norm(a) < norm(b)) return CCW_ONLINE_FRONT;
  return CCW_ON_SEGMENT;
}

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

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

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

double getDistanceSS(Segment s1, Segment s2) {
  if (intersect(s1.p1, s1.p2, s2.p1, s2.p2)) return 0.0; 
  return fmin(fmin(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
              fmin(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}


void solve(int n) {
  for (int i = 0; i < n; ++i) {
    int x0, y0, x1, y1, x2, y2, x3, y3;
    scanf("%d %d %d %d %d %d %d %d", &x0, &y0, &x1, &y1, &x2, &y2, &x3, &y3);
    Point p0(x0, y0), p1(x1, y1), p2(x2, y2), p3(x3, y3);
    Segment s1(p0, p1), s2(p2, p3);
    printf("%.10lf\n", getDistanceSS(s1, s2));
  }
}

int main() {
  
  int n;
  scanf("%d", &n);

  solve(n);
  return 0;
}