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<iomanip>
#include<algorithm>
#include<cmath>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n) for(int i=0;i<(n);i++)
#define PII pair<int,int>
#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)const { return Point(x + p.x, y + p.y); };
	Point operator -(const Point &p)const { return Point(x - p.x, y - p.y); };
	Point operator *(const double a)const { return Point(x*a, y*a); };
	Point operator /(const double a)const { return Point(x / a, y / a); };
	double norm()const { return x*x + y*y; };
	double length()const { return sqrt(norm()); };
	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; };
	bool operator ==(const Point &p)const
	{
		return fabs(x - p.x)<EPS &&fabs(y - p.y)<EPS;
	}
	friend ostream& operator <<(ostream& os, const Point &p);
	int CCW(Point p1, Point p2)
	{
		Point p0(x, y);
		Point V1 = p1 - p0;
		Point V2 = p2 - p0;
		if (V1.cross(V2) > 0.0)return -1;
		else if (V1.cross(V2) < 0.0)return 1;
		else if (V1.dot(V2) < 0.0)return -2;
		else if (V1.norm() < V2.norm())return 2;
		return 0;
	}
};
typedef Point Vector;

ostream& operator <<(ostream& os, const Point &p)
{
	return os << "(" << p.x << "," << p.y << ")";
}

class Segment
{
public:
	Point p1, p2;
	Segment(double x1, double y1, double x2, double y2)
	{
		p1.x = x1;
		p1.y = y1;
		p2.x = x2;
		p2.y = y2;
	}
	double GetLength()
	{
		Point temp = p2 - p1;
		return temp.length();
	}
	double GetDistanceSeg(double X, double Y)
	{
		Point p(X, Y);
		Point a = p2 - p1;
		Point b = p - p1;
		Point c = p1 - p2;
		Point d = p - p2;
		if (a.dot(b) < 0.0)return b.length();
		if (c.dot(d) < 0.0)return d.length();
		return GetDistanceLine(X, Y);
	}
	double GetDistanceLine(double X, double Y)
	{
		Point t(X, Y);
		Point a = p2 - p1;
		Point b = t - p1;
		return abs(a.cross(b) / a.length());
	}
	bool IsIntersect(Segment &s)
	{
		int s1, s2;
		s1 = p1.CCW(p2, s.p1)*p1.CCW(p2, s.p2);
		s2 = s.p1.CCW(s.p2, p1)*s.p1.CCW(s.p2, p2);
		return s1 <= 0 && s2 <= 0;
	}
	bool IsOrthogonal(const Segment &s)
	{
		Vector t1 = p2 - p1;
		Vector t2 = s.p2 - s.p1;
		return equals(0.0, t1.dot(t2));
	}
	bool IsParallel(const Segment &s)
	{
		Vector t1 = p2 - p1;
		Vector t2 = s.p2 - s.p1;
		return equals(0.0, t1.cross(t2));
	}
	Point GetProjection(double X, double Y)const
	{
		Vector V = p2 - p1;
		Point P(X, Y);
		Point ret = V*(V.dot(P - p1) / V.norm());
		return ret + p1;
	}
	Point GetReflect(double X, double Y)
	{
		Point t(X, Y);
		Point Pro = GetProjection(X, Y);
		Vector dV = Pro - t;
		return t + dV*2.0;
	}
};
typedef Segment Line;

class Circle
{
public:
	Point c;
	double r;
	Circle(Point C = Point(), double R = 0)
	{
		c = C;
		r = R;
	}
};

int main()
{
	int q;
	cin >> q;
	REP(i, q)
	{
		int x0, y0, x1, y1, x2, y2, x3, y3;
		cin >> x0 >> y0 >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
		Segment s1(x0, y0, x1, y1), s2(x2, y2, x3, y3);
		double ans;
		if (s1.IsIntersect(s2))ans = 0;
		else {ans = min({ s2.GetDistanceSeg(x0, y0), s2.GetDistanceSeg(x1, y1),s1.GetDistanceSeg(x2, y2), s1.GetDistanceSeg(x3, y3) });}
		cout << fixed << setprecision(10) << ans << endl;
	}
	return 0;
}