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

class Point{
    public:
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
    Point operator+(const Point &p){
        return Point(x+p.x,y+p.y);
    }
    Point operator-(const Point &p){
        return Point(x-p.x,y-p.y);
    }
    Point operator*(const double &a){
        return Point(a*x,a*y);
    }
    Point operator/(const 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){
        return x!=p.x?x<p.x:y<p.y;
    }
    bool operator==(const Point &p){
        return fabs(x-p.x)<EPS&&fabs(y-p.y)<EPS;
    }
};
typedef Point Vector;
struct Segment{
    Point p1,p2;
    Segment(){}
    Segment(Point p1,Point p2):p1(p1),p2(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;
}

bool isOrthogonal(Segment s1,Segment s2){
    return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

bool isParallel(Segment s1,Segment s2){
    return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

Point project(Segment s,Point p){
    Vector base=s.p2-s.p1;
    double r=dot(p-s.p1,base)/base.norm();
    return s.p1+base*r;   
}

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

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

double getDistanceSP(Segment s,Point p){
    if(dot(s.p2-s.p1,p-s.p1)<0){
        return (p-s.p1).abs();
    }
    if(dot(s.p1-s.p2,p-s.p2)<0){
        return (p-s.p2).abs();
    }
    return getDistanceLP(s,p);
}

int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return 1;
    if(cross(a,b)<-EPS) return -1;
    if(dot(a,b)<-EPS) return 2;
    if(a.norm()<b.norm()) return -2;
    return 0;
}

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);
}

double getDistance(Segment s1,Segment s2){
    if(intersect(s1,s2)) return 0;
    return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
        min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

Point getCrossPoint(Segment s1,Segment s2){
    Vector base=s2.p2-s2.p1;
    double d1=abs(cross(base,s1.p1-s2.p1));
    double d2=abs(cross(base,s1.p2-s2.p1));
    double t=d1/(d1+d2);
    return s1.p1+(s1.p2-s1.p1)*t;
}

int main(){
    int q;
    cin>>q;
    int a,b,c,d,e,f,g,h;
    Point p1,p2,p3,p4;
    for(int i=0;i<q;i++){
        cin>>a>>b>>c>>d>>e>>f>>g>>h;
        p1=Point(a,b);
        p2=Point(c,d);
        p3=Point(e,f);
        p4=Point(g,h);
        Segment s1(p1,p2),s2(p3,p4);
        printf("%.10lf\n",getDistance(s1,s2));
    }
}