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 <cmath>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <ostream>
#include <vector>

const double kEpsilon = 1e-10;
inline bool equals(double a, double b)
{
    return fabs(a - b) < kEpsilon;
}

class Point
{
  public:
    double x, y;

    Point() = default;
    Point(double x, double y) : 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 k)
    {
        return Point(x * k, y * k);
    }

    double SquaredNorm()
    {
        return x * x + y * y;
    }
    double abs()
    {
        return sqrt(this->SquaredNorm());
    }

    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) < kEpsilon && fabs(y - p.y) < kEpsilon;
    }

    double dot(const Point &p) const
    {
        return x * p.x + y * p.y;
    }
    double cross(const Point &p) const
    {
        return x * p.y - y * p.x;
    }
};

double dot(const Point &p1, const Point &p2)
{
    return p1.x * p2.x + p1.y * p2.y;
}
double cross(const Point &p1, const Point &p2)
{
    return p1.x * p2.y - p1.y * p2.x;
}

using Vector = Point;

struct Segment
{
    Point p1, p2;

    Segment() = default;
    Segment(Point p1, Point p2) : p1(p1), p2(p2)
    {
    }
};

struct Line
{
    Point p1, p2;

    Line() = default;
    Line(Point &p1, Point &p2) : p1(p1), p2(p2)
    {
    }
    Line(Segment &s) : p1(s.p1), p2(s.p2)
    {
    }
};

int ccw(Point &p0, Point &p1, Point &p2)
{
    auto a = p1 - p0;
    auto b = p2 - p0;

    auto cross_z = a.cross(b);

    if (cross_z > 0.0)
        return 1;
    else if (cross_z < 0.0)
        return -1;
    else
    {
        auto dot_prod = a.dot(b);
        if (dot_prod < 0.0)
            return 100;
        else if (b.abs() > a.abs())
            return -100;
        else
        {
            return 0;
        }
    }
}

bool intersection(Segment &s1, Segment &s2)
{
    return ccw(s1.p1, s1.p2, s2.p1) * ccw(s1.p1, s1.p2, s2.p2) <= 0.0 &&
           ccw(s2.p1, s2.p2, s1.p1) * ccw(s2.p1, s2.p2, s1.p2) <= 0.0;
}

double distance(Point &a, Point &b)
{
    return (a - b).abs();
}

double distance(Point &p, Line &l)
{
    auto q = l.p1 - l.p2;
    auto r = p - l.p2;
    return fabs(r.cross(q)) / q.abs();
}

double distance(Point &p, Segment &s)
{
    auto q1 = s.p2 - s.p1;
    auto q2 = p - s.p1;
    auto r1 = s.p1 - s.p2;
    auto r2 = p - s.p2;
    if (q1.dot(q2) >= 0.0 && r1.dot(r2) >= 0.0)
    {
        Line l(s);
        return distance(p, l);
    }
    else
    {
        return std::min(distance(p, s.p1), distance(p, s.p2));
    }
}

double distance(Segment &s1, Segment &s2)
{
    if (intersection(s1, s2))
        return 0.0;
    return std::min(std::min(distance(s1.p1, s2), distance(s1.p2, s2)),
                    std::min(distance(s2.p1, s1), distance(s2.p2, s1)));
}

int main()
{
    Segment s1, s2;
    int q;
    std::cin >> q;

    for (size_t i = 0; i < q; ++i)
    {
        std::cin >> s1.p1.x >> s1.p1.y;
        std::cin >> s1.p2.x >> s1.p2.y;
        std::cin >> s2.p1.x >> s2.p1.y;
        std::cin >> s2.p2.x >> s2.p2.y;

        std::cout << std::setprecision(20);
        std::cout << distance(s1, s2) << std::endl;
    }
}