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 <cstdio>           // printf(), scanf()
#include <cmath>            // fabs(), sqrt()
#include <algorithm>        // min()

using namespace std;
#define equals(a, b) (fabs((a) - (b)) < EPS)

static const double EPS = 1e-10;
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;

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); }
};

struct Segment
{
	Point p1, p2;
};

typedef Point Vector;
typedef Segment Line;

double
norm(Vector a)
{
	return a.x * a.x + a.y * a.y;
}

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

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;
}

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;
}

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

double
getDistanceSP(Segment s, Point p)
{
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
		return abs(p - s.p1);

	if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
		return abs(p - s.p2);

	return getDistanceLP(s, p);
}

double
getDistance(Segment s1, Segment s2)
{
	if (intersect(s1, s2))
		return 0.0;

	return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

int
main(int argc, char** argv)
{
	int n;

	scanf("%d", &n);
	while (n--)
	{
		int s1x, s1y, s2x, s2y;
		int t1x, t1y, t2x, t2y;
		Segment s1, s2;

		scanf("%d %d %d %d %d %d %d %d", &s1x, &s1y, &s2x, &s2y, &t1x, &t1y, &t2x, &t2y);
		s1.p1.x = s1x, s1.p1.y = s1y;
		s1.p2.x = s2x, s1.p2.y = s2y;
		s2.p1.x = t1x, s2.p1.y = t1y;
		s2.p2.x = t2x, s2.p2.y = t2y;
		printf("%.10f\n", getDistance(s1, s2));
	}

	return 0;
}