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:
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(v) v.begin(), v.end()
typedef long long ll;

#include <bits/stdc++.h>
using namespace std;

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

// cout<<fixed<<setprecision(15)
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;

//点またはベクトル
class Point{
  public:
  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(a*x,a*y);}
  Point operator/(double a){return Point(x/a,y/a);}
  
  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;
//ベクトルの二乗和と絶対値
double norm(Point p){return p.x*p.x+p.y*p.y;}
double abs(Point p){return sqrt(norm(p));}
//線分または直線
struct Segment{Point p1,p2;};
typedef Segment Line;
//円
class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(), double r=0.0): c(c), r(r) {}
};
//多角形
typedef vector<Point> Polygon;
//内積
double dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
//外積
double cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
//直交判定
bool isOrthgonal(Vector a,Vector b){return equals(dot(a,b), 0.0);}
//平行判定
bool isParallel(Vector a,Vector b){return equals(cross(a,b), 0.0);}
//射影
Point project(Segment s,Point p){
  Vector base=s.p2-s.p1;
  double r=dot(p-s.p1,base)/norm(base);
  return s.p1+base*r;
}
//反射
Point reflect(Segment s,Point p){return p+(project(s,p)-p)*2.0;}
//反時計周りCounter-Clockwise
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;
}
//線分の交差判定
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);
}
bool intersect(Segment s1,Segment s2){return intersect(s1.p1,s1.p2,s2.p1,s2.p2);}
//点と点の距離
double getDisPP(Point a,Point b){return abs(a-b);}
//直線と点の距離
double getDisLP(Line l,Point p){return abs(cross(l.p2-l.p1,p-l.p1))/abs(l.p2-l.p1);}
//線分と点の距離
double getDisSP(Segment s,Point p){
  if(dot(s.p2-s.p1,p-s.p1)<0.0) return abs(p-s.p1);
  if(dot(s.p1-s.p2,p-s.p2)<0.0) return abs(p-s.p2);
  return getDisLP(s,p);
}
//線分と線分の距離
double getDisSS(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDisSP(s1,s2.p1),getDisSP(s1,s2.p2)),
             min(getDisSP(s2,s1.p1),getDisSP(s2,s1.p2)));
}

int main(){
  Point p0,p1,p2,p3;
  int q;
  cin>>q;
  
  Segment s1,s2;
  rep(i,q){
    cin>>p0.x>>p0.y>>p1.x>>p1.y>>p2.x>>p2.y>>p3.x>>p3.y;
    s1.p1=p0,s1.p2=p1,s2.p1=p2,s2.p2=p3;
    cout<<fixed<<setprecision(15)<<getDisSS(s1,s2)<<endl;
  }
    
  return 0;
}