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<algorithm>
#include<cmath>
#include<iomanip>
using namespace std;

static const int COUNTER_CLOCKWISE = 1; //??????????????¨??????
static const int CLOCKWISE = -1;
static const int ON_SEGMENT = 0;
static const int ONLINE_FRONT = 2;
static const int ONLINE_BACK = -2;
const double EPS = 1e-10;

bool equals(double a, double b) {
	return fabs(a - b) < EPS;
}

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);
	}
	Point operator * (double k) {
		return Point(k * x, k * y);
	}
	Point operator / (double k) {
		return Point(x / k, y / k);
	}

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

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

typedef Point Vector;

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;
}

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

	Point project(Point p) {
		Vector a = Vector(p.x - p1.x, p.y - p1.y);
		Vector b = Vector(p2.x - p1.x, p2.y - p1.y);
		return p1 + p2 * (dot(a, b) / b.norm());
	}

	Point refrect(Point p) {
		Point pro = project(p);
		return pro * 2 - p;
	}

	double distance(Point p) {
		Vector a = Vector((p - p1).x, (p - p1).y);
		Vector b = Vector((p2 - p1).x, (p2 - p1).y);
		Vector c = Vector((p - p2).x, (p - p2).y);
		Vector d = Vector((p1 - p2).x, (p1 - p2).y);
		if (dot(a, b) < 0) return (p - p1).abs();
		else if (dot(c, d) < 0) return (p - p2).abs();
		else return fabs(cross(a, b)) / b.abs();
	}
};

int check(Vector v0, Vector v1) { 
	double c = cross(v0, v1);
	if (equals(c, 0)) {
		if (dot(v0, v1) < 0) return ONLINE_BACK;
		else if (v1.norm() > v0.norm()) return ONLINE_FRONT;
		else return ON_SEGMENT;
	} else if (c > 0) {
		return COUNTER_CLOCKWISE;
	} else {
		return CLOCKWISE;
	}
}

int intersect(Segment s1, Segment s2) { 
	Point p1 = s1.p1, p2 = s1.p2, p3 = s2.p1, p4 = s2.p2;
	Vector v0 = Vector((p2 - p1).x, (p2 - p1).y);
	Vector v1 = Vector((p3 - p1).x, (p3 - p1).y);
	Vector v2 = Vector((p4 - p1).x, (p4 - p1).y);
	Vector v3 = Vector((p4 - p3).x, (p4 - p3).y);
	Vector v4 = Vector((p1 - p3).x, (p1 - p3).y);
	Vector v5 = Vector((p2 - p3).x, (p2 - p3).y);
	if (check(v0, v1) * check(v0, v2) <= 0 && check(v3, v4) * check(v3, v5) <= 0) return 1;
	return 0;
}

double sDistance(Segment s1, Segment s2) {
	Point p1 = s1.p1, p2 = s1.p2, p3 = s2.p1, p4 = s2.p2;
	if (intersect(s1, s2)) return 0;
	double d1 = s1.distance(p3);
	double d2 = s1.distance(p4);
	double d3 = s2.distance(p1);
	double d4 = s2.distance(p2);
	return min(min(d1, d2), min(d3, d4));
}

int main() {
	int q;
	cin >> q;
	int x0, y0, x1, y1, x2, y2, x3, y3;
	for (int i = 0; i < q; i++) {
		cin >> x0 >> y0 >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
		Segment s1 = Segment(Point(x0, y0), Point(x1, y1));
		Segment s2 = Segment(Point(x2, y2), Point(x3, y3));
		cout << fixed << setprecision(10) << sDistance(s1, s2) << endl;
	}
	return 0;
}