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 equal(a,b) (fabs(a-b) < EPS)

struct Point{
  double x,y;

  Point(){}
  Point(double x,double y) : x(x),y(y) {}

  Point operator + (const Point &p)const{ return Point(x+p.x,y+p.y); }
  Point operator - (const Point &p)const{ return Point(x-p.x,y-p.y); }
  Point operator * (const double &k)const{ return Point(x*k,y*k); }
  Point operator / (const double &k)const{ return Point(x/k,y/k); }
};

double cross(const Point &a,const Point &b){ return a.x*b.y - b.x*a.y; }
double dot(const Point &a,const Point &b){ return a.x*b.x+a.y*b.y; }
double norm(const Point &p){ return dot(p,p); }
double abs(const Point &p){ return sqrt(norm(p)); }

istream &operator >> (istream &is,Point &p){ 
  return is >> p.x >> p.y;
}

typedef Point Vector;

#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
typedef Point Vector;

int ccw(Point p0,Point p1,Point p2){
  Vector a = p1 - p0;
  Vector 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(norm(a) < norm(b)){ return ONLINE_FRONT; }
  return ON_SEGMENT;
}

struct Segment{
  Point s,t;
  Segment(){}
  Segment(Point s,Point t) : s(s),t(t) {}
};

Point projection(Segment s,Point p){
  Vector b = s.t-s.s;
  double t = dot(p-s.s,b)/norm(b);
  return s.s+b*t;
}

bool isIntersectSP(const Segment &s,const Point &p){
  return equal(ccw(s.s,s.t,p),0);
}

bool isIntersectSS(const Segment &a,const Segment &b){
  Point s[2] = {a.s,a.t}, t[2] = {b.s,b.t};
  return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0
    && ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}

double distanceSP(const Segment &s,const Point &p){
  Point r = projection(s,p);
  if(isIntersectSP(s,r)){ return abs(r-p); }
  return min(abs(s.s-p),abs(s.t-p));
}

double distanceSS(const Segment &a,const Segment &b){
  if(isIntersectSS(a,b)){ return 0; }
  return min(min(distanceSP(a,b.s),distanceSP(a,b.t)),
             min(distanceSP(b,a.s),distanceSP(b,a.t)));
}

int main(){
  int Q;
  Segment s1,s2;
  cin >> Q;
  while(Q--){
    cin >> s1.s >> s1.t >> s2.s >> s2.t;
    printf("%.10f\n",distanceSS(s1,s2));
  }
  return 0;
}