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 _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long lint;
typedef pair<int,int> P;
const int    INF=(int)1e9;
const int    MOD=(int)1e9+7;
const double EPS=(double)1e-10;
const int    dx[]={-1,0,0,1};
const int    dy[]={0,-1,1,0};
struct Accelerate_Cin{
    Accelerate_Cin(){
        cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);
    };
};

//幾何学テンプレート

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

//点
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);}

  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 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;
  }
};

//ベクトル
typedef Point Vector;

//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;
}

//線分
struct Segment{Point p1,p2;};

//直線
typedef Segment Line;

//円
class Circle{
public:
  Point c;   //中心
  double r;  //半径
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

//多角形
typedef vector<Point> Polygon;

//距離を求める。


//3点の位置関係を調べる。
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;
  if(cross(a,b)<-EPS)  return CLOCKWISE;
  if(dot(a,b)<-EPS)    return ONLINE_BACK;
  if(a.norm()<b.norm())return ONLINE_FRONT;

  return ON_SEGMENT;
}

//二つの線分の交差判定をする。
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 getDistance(Point a, Point b){
  return (a-b).abs();
}

//点と直線の距離
double getDistanceLP(Line l, Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/(l.p2-l.p1).abs());
}

//点と線分の距離
double getDistanceSP(Segment s,Point p){
  if(dot(s.p2-s.p1,p-s.p1)<0.0) return (p-s.p1).abs();
  if(dot(s.p1-s.p2,p-s.p2)<0.0) return (p-s.p2).abs();
  return getDistanceLP(s,p);
}

//線分と線分の距離
double getDistance(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
             min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}


signed main(){
  int q;cin>>q;
  for(int i=0;i<q;i++){
    double x0,y0,x1,y1,x2,y2,x3,y3;cin>>x0>>y0>>x1>>y1>>x2>>y2>>x3>>y3;
    Segment s1={Point{x0,y0},Point{x1,y1}},s2={Point{x2,y2},Point{x3,y3}};
    cout<<fixed<<setprecision(15)<<getDistance(s1,s2)<<endl;
  }

  return 0;
}