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>
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
using namespace std;
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(x * a, y * a);}
    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 equals(x, p.x) && equals(y, p.y);
    }
};typedef Point Vector;

struct Segment {
    Point p1, p2;
    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(Vector a, Vector b){
    return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2){
    return isOrthogonal(a1 - a2, b1 - b2);
}

bool isParallel(Vector a, Vector b){
    return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2){
    return isParallel(a1 - a2, b1 - b2);
}
double get_distance(Point a, Point b){
    return (a-b).abs();
}
double get_distance(Line l, Point p){
    return abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs());
}
double get_distanceSP(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 get_distance(s, p);
}
int ccw(Point p0, Point p1, Point p2){
    Vector a = p1 - p0, 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 p0, Point p1, Point p2, Point p3){
    if (ccw(p0, p1, p2) == 0 || ccw(p0, p1, p3) == 0 || 
        ccw(p2, p3, p0) == 0 || ccw(p2, p3, p1) == 0)
        return true;
    if (ccw(p0, p1, p2) * ccw(p0, p1, p3) == -1 && ccw(p2, p3, p0) * ccw(p2, p3, p1) == -1)
        return true;
    return false;
}
double get_distanceSS(Segment s1, Segment s2){
    if (intersect(s1.p1, s1.p2, s2.p1, s2.p2)) return 0.0;
    return min(min(get_distanceSP(s1, s2.p1), get_distanceSP(s1, s2.p2)),
    min(get_distanceSP(s2, s1.p1), get_distanceSP(s2, s1.p2)));
}

#include<iostream>
#include<iomanip>
int main(){
    int q, dots[8];
    std::cin >> q;
    for (int i = 0; i < q; i++)
    {
        for (int i = 0; i < 8; i++)
            std::cin >> dots[i];
        Point a1 = Point(dots[0], dots[1]);
        Point a2 = Point(dots[2], dots[3]);
        Point b1 = Point(dots[4], dots[5]);
        Point b2 = Point(dots[6], dots[7]);
        Segment s = Segment(a1, a2), t = Segment(b1, b2);
        cout << fixed << setprecision(10) << get_distanceSS(s, t) << endl;
    }   
}