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>
using namespace std;
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

class Point {
public:
	double x, y;
	Point(double x = 0.0, double y = 0.0) :
			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 k) {
		return Point(x * k, y * k);
	}
	Point operator /(double k) {
		return Point(x / k, y / k);
	}

	double norm() {
		return x * x + y * y;
	}
	double abs() {
		return sqrt(norm());
	}

	bool operator <(Point p) {
		return x != p.x ? x < p.x : y < p.y;
	}
	bool operator ==(Point p) {
		return equals(x, p.x) && equals(y, p.y);
	}
};
typedef Point Vector;

class Segment {
public:
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point()) :
			p1(p1), p2(p2) {
	}
};
typedef Segment Line;

double dot(Vector v1, Vector v2) {
	return v1.x * v2.x + v1.y * v2.y;
}
double cross(Vector v1, Vector v2) {
	return v1.x * v2.y - v1.y * v2.x;
}
bool isOrthogonal(Vector v1, Vector v2) {
	return equals(dot(v1, v2), 0.0);
}
bool isOrthogonal(Segment s1, Segment s2) {
	return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool isOrthogonal(Point l1, Point l2, Point m1, Point m2) {
	return isOrthogonal(l2 - l1, m2 - m1);
}
bool isParallel(Vector v1, Vector v2) {
	return equals(cross(v1, v2), 0.0);
}
bool isParallel(Segment s1, Segment s2) {
	return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool isParallel(Point l1, Point l2, Point m1, Point m2) {
	return isParallel(l1 - l2, m1 - m2);
}

enum PositionSP {
	COUNTER_CLOCKWISE = -1,
	CLOCKWISE = 1,
	ONLINE_BACK = 2,
	ONLINE_FRONT = -2,
	ON_SEGMENT = 0
};
PositionSP ccw(Point p1, Point p2, Point p) {
	Vector a = p2 - p1, b = p - p1;
	if (cross(a, b) > EPS)
		return COUNTER_CLOCKWISE;
	else if (cross(a, b) < -EPS)
		return CLOCKWISE;
	else if (dot(a, b) < -EPS)
		return ONLINE_BACK;
	else if (a.norm() < b.norm())
		return ONLINE_FRONT;
	else
		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 distancePP(Point p1, Point p2) {
	return (p1 - p2).abs();
}
double distanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / distancePP(l.p2, l.p1));
}
double distanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0)
		return distancePP(s.p1, p);
	else if (dot(s.p1 - s.p2, p - s.p2) < 0.0)
		return distancePP(s.p2, p);
	else
		return distanceLP(s, p);
}
double distanceSS(Segment s1, Segment s2) {
	if (intersect(s1, s2))
		return 0.0;
	else {
		return min(min(distanceSP(s1, s2.p1), distanceSP(s1, s2.p2)),
				min(distanceSP(s2, s1.p1), distanceSP(s2, s1.p2)));
	}
}

int main() {
	int q;
	cin >> q;
	for (int i = 0; i < q; i++) {
		Segment s1, s2;
		cin >> s1.p1.x >> s1.p1.y;
		cin >> s1.p2.x >> s1.p2.y;
		cin >> s2.p1.x >> s2.p1.y;
		cin >> s2.p2.x >> s2.p2.y;
		cout << fixed << setprecision(10) << distanceSS(s1, s2) << endl;
	}
	return 0;
}