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:
///
// File:  cgl_2_d.cpp
// Author: ymiyamoto
//
// Created on Mon Oct 23 00:28:22 2017
//
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>

using namespace std;
#define EPS 1e-10
#define equals(x, y) (fabs(x - y) < EPS)

struct vector_t {
  double x;
  double y;

  vector_t(double a, double b) : x(a), y(b)
  {
  }

  double norm2()
  {
    return x * x + y * y;
  }

  double norm()
  {
    return sqrt(norm2());
  }

  double dot(vector_t a)
  {
    return x * a.x + y * a.y;
  }

  double cross(vector_t a)
  {
    return x * a.y - y * a.x;
  }

  vector_t operator*(double a)
  {
    return vector_t(a * x, a * y);
  }
};

struct point_t {
  double x;
  double y;

  point_t operator+(const point_t a)
  {
    return point_t({x + a.x, y + a.y});
  }

  void print()
  {
    cout << fixed << setprecision(10) << x << " " << y << endl;
  }

  point_t operator+(const vector_t vec)
  {
    return point_t({x + vec.x, y + vec.y});
  }

  vector_t operator-(const point_t p)
  {
    return vector_t({x - p.x, y - p.y});
  }

  point_t project(point_t p1, point_t p2)
  {
    vector_t vec1(x - p1.x, y - p1.y);
    vector_t vec2(p2.x - x, p2.y - y);
    return point_t({x, y}) + vec1 * (vec1.dot(vec2) / vec1.norm2());
  }

  point_t reflect(point_t p1, point_t p2)
  {
    point_t proj = project(p1, p2);
    return p2 + (proj - p2) * 2.0;
  }
};

enum pos_t {
  CCLOCKWISE = -1,
  CLOCKWISE = 1,
  ONLINE_BACK = 2,
  ONLINE_FRONT = -2,
  ON_SEGMENT = 0,
};

pos_t ccw(point_t p0, point_t p1, point_t p2)
{
  if ((p1 - p0).cross(p2 - p0) > EPS) {
    return CCLOCKWISE;
  } else if ((p1 - p0).cross(p2 - p0) < -EPS) {
    return CLOCKWISE;
  } else if ((p1 - p0).dot(p2 - p0) < -EPS) {
    return ONLINE_BACK;
  } else {
    if ((p1 - p0).norm2() < (p2 - p0).norm2()) {
      return ONLINE_FRONT;
    } else {
      return ON_SEGMENT;
    }
  }
}

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

struct segment_t {
  point_t a;
  point_t b;

  double distance(point_t p0)
  {
    if ((b - a).dot(p0 - a) < 0.0) {
      return (p0 - a).norm();
    } else if ((a - b).dot(p0 - b) < 0.0) {
      return (p0 - b).norm();
    } else {
      return fabs((b - a).cross(p0 - a) / (b - a).norm());
    }
  }
};

int32_t main()
{
  uint32_t q;
  cin >> q;

  for (uint32_t i = 0; i < q; i++) {
    double x, y;
    cin >> x >> y;
    point_t p0({x, y});
    cin >> x >> y;
    point_t p1({x, y});
    cin >> x >> y;
    point_t p2({x, y});
    cin >> x >> y;
    point_t p3({x, y});
    if (intersection(p0, p1, p2, p3)) {
      cout << fixed << setprecision(10) << 0.0 << endl;
    } else {
      segment_t seg1({p0, p1});
      segment_t seg2({p2, p3});
      double dist = min(seg2.distance(p0), min(seg2.distance(p1), min(seg1.distance(p2), seg1.distance(p3))));
      cout << fixed << setprecision(10) << dist << endl;
    }
  }

  return 0;
}