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>
#include <cmath>
#include <vector>
using namespace std;
const double EPS = 1e-10;
const int COUNTER_CLOCKWISE = 1, CLOCKWISE = -1, ONLINE_BACK = 2, ONLINE_FRONT = -2, ON_SEGMENT = 0;
bool equals(double a, double b) {
	return fabs(a - b) < EPS;
}
struct Point {
	double x, y;
	Point(double x = 0, double y = 0) :x(x), y(y) {}
	Point operator + (Point rhs) {
		return Point(x + rhs.x, y + rhs.y);
	}
	Point operator - (Point rhs) {
		return Point(x - rhs.x, y - rhs.y);
	}
	Point operator * (double k) {
		return Point(k * x, k * y);
	}
	bool operator < (const Point& rhs) const {
		return x != rhs.x ? x < rhs.x : y < rhs.y;
	}
	bool operator == (const Point& rhs) const {
		return equals(x, rhs.x) && equals(y, rhs.y);
	}
	double norm() {
		return x * x + y * y;
	}
	double abs() {
		return sqrt(norm());
	}
};
typedef Point Vector;
struct Segment {
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point()) :p1(p1), p2(p2) {}
};
typedef Segment Line;
struct Circle {
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0) :c(c), r(r) {}
};
typedef vector<Point> Polygon;
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);
}
bool isOrthogonal(Segment a, Segment b) {
	return isOrthogonal(Vector(a.p2.x - a.p1.x, a.p2.y - a.p1.y), Vector(b.p2.x - b.p1.x, b.p2.y - b.p1.y));
}
bool isParallel(Vector a, Vector b) {
	return equals(cross(a, b), 0);
}
bool isParallel(Segment a, Segment b) {
	return isParallel(Vector(a.p2.x - a.p1.x, a.p2.y - a.p1.y), Vector(b.p2.x - b.p1.x, b.p2.y - b.p1.y));
}
Point project(Point p, Segment s) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / base.norm();
	return s.p1 + (base * r);
}
Point reflect(Point p, Segment s) {
	return p + (project(p, s) - p) * 2;
}
int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0, b = p2 - p0;
	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;
	return ON_SEGMENT;
}
bool intersect(Segment s1, Segment s2) {
	return (ccw(s1.p1, s1.p2, s2.p1) * ccw(s1.p1, s1.p2, s2.p2) <= 0 && ccw(s2.p1, s2.p2, s1.p1) * ccw(s2.p1, s2.p2, s1.p2) <= 0); 
}
double getDistance(Point a, Point b) {
	return (b - a).abs();
}
double getDistancePL(Point p, Line l) {
	return fabs(cross(l.p2 - l.p1, p - l.p1)) / (l.p2 - l.p1).abs();
}
double getDistancePS(Point p, Segment s) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0) return (p - s.p1).abs();
	else if (dot(s.p1 - s.p2, p - s.p2) < 0) return (p - s.p2).abs();
	else return getDistancePL(p, s);
}
double getDistance(Segment s1, Segment s2) {
	if (intersect(s1, s2)) return 0;
	return min(min(getDistancePS(s2.p1, s1), getDistancePS(s2.p2, s1)), min(getDistancePS(s1.p1, s2), getDistancePS(s1.p2, s2)));
}
int main() {
    int q;
    scanf("%d", &q);
    while (q--) {
    	double x0, y0, x1, y1;
    	scanf("%lf%lf%lf%lf", &x0, &y0, &x1, &y1);
    	Segment s1 = Segment(Point(x0, y0), Point(x1, y1));
    	scanf("%lf%lf%lf%lf", &x0, &y0, &x1, &y1);
    	Segment s2 = Segment(Point(x0, y0), Point(x1, y1));
    	printf("%.010lf\n", getDistance(s1, s2));
	}
	return 0;
}