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 < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n); i >= 0; i--)
#define REP(i, m, n) for (int i = (int)(m); i <= (int)(n); i++)
#define REPR(i, m, n) for (int i = (int)(m); i >= (int)(n); i--)
#define all(v) v.begin(), v.end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const long long INF = (1LL<<30);

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

struct Point{
  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(x*a, y*a); }
  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 fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
  }
};

typedef Point Vector;

struct Segment{
  Point p1, p2;
};

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(Segment s, Point p){
  Vector a = s.p2 - s.p1;
  Vector b = p - s.p1;
  return s.p1 + a * (dot(a, b)/a.norm());
}

Point reflect(Segment s, Point p){
  return p + (project(s, p) - p)*2;
}

static const int Counter_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

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

double getDistance(Point a, Point b){
  Point tmp = a-b;
  return tmp.abs();
}

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

double getDistanceSP(Segment s, Point p){
  Vector a = s.p2 - s.p1;
  Vector b = p - s.p1;
  double n = dot(a, b) / a.norm();
  if(0.0 <= n && n <= 1.0) return getDistanceLP(s, p);
  else return min(getDistance(s.p1, p), getDistance(s.p2, p));
}

double getDistanceSS(Segment s1, Segment s2){
  if(intersect(s1.p1, s1.p2, s2.p1, s2.p2)) return 0.0;
  double res = INF;
  chmin(res, getDistanceSP(s1, s2.p1));
  chmin(res, getDistanceSP(s1, s2.p2));
  chmin(res, getDistanceSP(s2, s1.p1));
  chmin(res, getDistanceSP(s2, s1.p2));
  return res;
}

int main(){
  int q;
  cin >> q;

  rep(i, q){
    double x1, y1, x2, y2;
    double x3, y3, x4, y4;
    cin >> x1 >> y1 >> x2 >> y2;
    cin >> x3 >> y3 >> x4 >> y4;
    Point p1 = Point(x1, y1);
    Point p2 = Point(x2, y2);
    Point p3 = Point(x3, y3);
    Point p4 = Point(x4, y4);
    Segment s1 = {p1, p2};
    Segment s2 = {p3, p4};
    cout << fixed << setprecision(10);
    cout << getDistanceSS(s1, s2) << endl;
  }

  return 0;

}