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 <cmath>
#include <cstdio>
#include <complex>
#include <algorithm>
using namespace std;
// ------ Defines ------ //
#define Point complex<long double>
#define px real()
#define py imag()
// ------ Classes ------ //
class Segment {
public:
	Point p1, p2;
	Segment(Point p1_, Point p2_) : p1(p1_), p2(p2_) {};
	Segment(long double p1x, long double p1y, long double p2x, long double p2y) : p1(Point(p1x, p1y)), p2(Point(p2x, p2y)) {};
	friend bool operator==(const Segment& s1, const Segment& s2) { return (s1.p1 == s2.p1 && s1.p2 == s2.p2) || (s1.p1 == s2.p2 && s1.p2 == s2.p1); }
	friend bool operator!=(const Segment& s1, const Segment& s2) { return !(s1 == s2); }
};
class Line {
public:
	Point p1, p2;
	Line(Point p1_, Point p2_) : p1(p1_), p2(p2_) {};
	Line(long double p1x, long double p1y, long double p2x, long double p2y) : p1(Point(p1x, p1y)), p2(Point(p2x, p2y)) {};
	friend bool operator==(const Line& s1, const Line& s2) { return (s1.p1 == s2.p1 && s1.p2 == s2.p2) || (s1.p1 == s2.p2 && s1.p2 == s2.p1); }
	friend bool operator!=(const Line& s1, const Line& s2) { return !(s1 == s2); }
};
// ------ Functions ------ //
long double dot(const Point& a, const Point& b) { return a.px * b.px + a.py * b.py; }
long double crs(const Point& a, const Point& b) { return a.px * b.py - a.py * b.px; }
int ccw(Point p0, Point p1, Point p2) {
	Point a = p1 - p0, b = p2 - p0;
	if (crs(a, b) > 1e-10) return 1;
	if (crs(a, b) < -1e-10) return -1;
	if (dot(a, b) < -1e-10) return 2;
	if (norm(a) < norm(b)) return -2;
	return 0;
}
bool its(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 its(Segment s1, Segment s2) {
	return its(s1.p1, s1.p2, s2.p1, s2.p2);
}
long double dst(const Line& a, const Point& b) {
	return abs(crs(a.p2 - a.p1, b - a.p1) / abs(a.p2 - a.p1));
}
long double dst(const Segment& a, const Point& b) {
	if (dot(a.p2 - a.p1, b - a.p1) < 0.0) return abs(b - a.p1);
	if (dot(a.p1 - a.p2, b - a.p2) < 0.0) return abs(b - a.p2);
	return abs(crs(a.p2 - a.p1, b - a.p1) / abs(a.p2 - a.p1));
}
long double dst(const Segment& a, const Segment& b) {
	if (its(a, b)) return 0;
	return min({ dst(a, b.p1), dst(a, b.p2), dst(b, a.p1), dst(b, a.p2) });
}
int q, px1, py1, px2, py2, qx1, qy1, qx2, qy2;
int main() {
	scanf("%d", &q);
	for (int i = 0; i < q; i++) {
		scanf("%d%d%d%d%d%d%d%d", &px1, &py1, &px2, &py2, &qx1, &qy1, &qx2, &qy2);
		printf("%.9Lf\n", dst(Segment(px1, py1, px2, py2), Segment(qx1, qy1, qx2, qy2)));
	}
	return 0;
}