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:
// C++ 14
#include <math.h>
#include <iostream>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>

#define ll long long
#define Int ll
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

#define EPS 0.000000001
#define fequals(a,b) (fabs((a) - (b)) < EPS)

class Vector2 {
public:
  double x, y;
  
  Vector2(double x = 0, double y = 0): x(x), y(y) {}
  
  Vector2 operator + (const Vector2 v) const { return Vector2(x + v.x, y + v.y); }
  Vector2 operator - (const Vector2 v) const { return Vector2(x - v.x, y - v.y); }
  Vector2 operator * (const double k) const { return Vector2(x * k, y * k); }
  Vector2 operator / (const double k) const { return Vector2(x / k, y / k); }
  
  double length() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  double dot (Vector2 const v) { return x * v.x + y * v.y; }
  double cross (Vector2 const v) { return x * v.y - y * v.x; }
  
  bool parallel(Vector2 &other) {
    return fequals(fabs(dot(other)), length() * other.length());
  }
  
  bool orthogonal(Vector2 &other) {
    return fequals(0, dot(other));
  }
  
  bool operator < (const Vector2 &v) {
    return x != v.x ? x < v.x : y < v.y;
  }
  
  bool operator == (const Vector2 &v) {
    return fabs(x - v.x) < EPS && fabs(y - v.y) < EPS;
  }
};

ostream & operator << (ostream & out, Vector2 const & v) { 
  out<< "Vector2(" << v.x << ", " << v.y << ')';
  return out;
}

istream & operator >> (istream & in, Vector2 & v) { 
  double x, y;
  in >> x;
  in >> y;
  v.x = x;
  v.y = y;
  return in;
}

double p2Seg(Vector2 start_, Vector2 end_, Vector2 p) {
  if ((p - start_).dot(end_ - start_) < 0.0) return (p - start_).length();
  if ((p - end_).dot(start_ - end_) < 0.0) return (p - end_).length();
  return abs((end_ - start_).cross(p - start_)) / (end_ - start_).length();
}


double distance(Vector2 p1, Vector2 p2, Vector2 p3, Vector2 p4) {
  double t3 = (p1.x - p2.x) * (p3.y - p1.y) + (p1.y - p2.y) * (p1.x - p3.x);
  double t4 = (p1.x - p2.x) * (p4.y - p1.y) + (p1.y - p2.y) * (p1.x - p4.x);
  double t1 = (p3.x - p4.x) * (p1.y - p3.y) + (p3.y - p4.y) * (p3.x - p1.x);
  double t2 = (p3.x - p4.x) * (p2.y - p3.y) + (p3.y - p4.y) * (p3.x - p2.x);
  if (t3 * t4 < 0 && t1 * t2 < 0) return 0.0;
  double min_ = -1;
  min_ = min<double>(p2Seg(p1, p2, p3), p2Seg(p1, p2, p4));
  min_ = min<double>(min_, p2Seg(p3, p4, p1));
  min_ = min<double>(min_, p2Seg(p3, p4, p2));
  return min_;
}

#define MAX_N 1001
Int N;
Vector2 p1, p2, p3, p4;

void input() {
  cin >> N;
  while (cin >> p1 >> p2 >> p3 >> p4) {
    cout << distance(p1, p2, p3, p4) << endl;
  }
}

int main() {
  cout.precision(15);
  input();
}