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 <iostream>
#include <complex>
#include <utility>
#include <algorithm>
using namespace std;

typedef complex<double> Point, Vector;
typedef pair<Point, Point> Segment, Line;

#define X real()
#define Y imag()
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

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;
}

double norm(Vector a){
    return a.X * a.X + a.Y * a.Y;
}

double abs(Vector a){
    return sqrt(norm(a));
}

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(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.first, s1.second, s2.first, s2.second);
}

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

double getDistanceSP(Segment s, Point p){
    if(dot(s.second - s.first, p - s.first) < 0.0) return abs(p - s.first);
    if(dot(s.first - s.second, p - s.second) < 0.0) return abs(p - s.second);
    return getDistanceLP(s, p);
}

double getDistanceSS(Segment s1, Segment s2){
    if(intersect(s1, s2)) return 0.0;
    return min({getDistanceSP(s1, s2.first), getDistanceSP(s1, s2.second), getDistanceSP(s2, s1.first), getDistanceSP(s2, s1.second)});
}

int main(){
    int q; cin>>q;
    while(q--){
        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)};
        Segment s2 = {Point(x2, y2), Point(x3, y3)};
        
        printf("%.10f\n", getDistanceSS(s1, s2));
    }
}