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 <cmath>
#include <algorithm>
#include <iomanip>
#define ESP (1e-10)
using namespace std;

typedef struct Point {
	double x; 
	double y;

	Point() { }

	Point(double x, double y) :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);
	}
};

typedef Point Vector;

 struct Line {
	Point p1, p2;
	Line() {}
	Line(const Point& a,const Point& b) : p1(a),p2(b) { }
};

 typedef Line Segment;

double abs(Point p1, Point p2) {
	double norm = (p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y);
	return sqrt(norm);
}

double product(Vector v1, Vector v2) {
	return v1.x*v2.x + v1.y*v2.y;
}

double cross(Vector p1, Vector p2) {
	return p1.x*p2.y - p1.y*p2.x;
}

int ccw(Point p0, Point p1, Point p2) {
	Vector v0 = p1 - p0;
	Vector v1 = p2 - p0;
	if (cross(v0, v1) > ESP) return 1;   //p0,p1,p2??????????¨???????
	if (cross(v0, v1) < -ESP) return -1;   //p0,p1,p2???????¨???????
	if (product(v0, v1) < -ESP) return 2;  //p2,p0,p1????????§????????´??????
	if (abs(p0, p1) < abs(p0, p2)) return -2;  //p0,p1,p2????????§????????´??????
	return 0;   //p2?????????(p0,p1)???
}

bool intersect(Point p0, Point p1, Point p2, Point p3) {
	return (ccw(p0, p1, p2)*ccw(p0, p1, p3) <= 0&&ccw(p2,p3,p0)*ccw(p2,p3,p1)<=0);
	//?????????????????????????????¶
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

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

double DistanceSP(Segment s, Point p) {
	if (product(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p, s.p1);
	if (product(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p, s.p2);
	return DistanceLP(s, p);
}

double DistanceSS(Segment s1, Segment s2) {
	if (intersect(s1, s2)) return 0.0;
	return min(min(DistanceSP(s1, s2.p1), DistanceSP(s1,s2.p2)), min(DistanceSP(s2, s1.p1), DistanceSP(s2, s1.p2)));
}

int main() {
	Segment s0,s1;
	int q; 
	cin >> q;
	for (int i = 0;i < q;i++) {
		cin >> s0.p1.x; cin >> s0.p1.y;
		cin >> s0.p2.x; cin >> s0.p2.y;
		cin >> s1.p1.x; cin >> s1.p1.y;
		cin >> s1.p2.x; cin >> s1.p2.y;
		cout <<setprecision(20)<< DistanceSS(s0, s1) << endl;
	}
}