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<vector>
#include<algorithm>
#include<utility>
#include<numeric>
#include<iostream>
#include<array>
#include<string>
#include<sstream>
#include<stack>
#include<queue>
#include<list>
#include<functional>
#define _USE_MATH_DEFINES

#include<math.h>
#include<map>

#define INF 200000000

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, int> pli;

struct OwnVector2
{
	double x, y;
	OwnVector2(double x,double y):x(x),y(y){}
	OwnVector2() :OwnVector2(0, 0) {}
	OwnVector2 operator+(const OwnVector2& v)const
	{
		return OwnVector2(x + v.x, y + v.y);
	}
	OwnVector2 operator-(const OwnVector2& v)const
	{
		return OwnVector2(x - v.x, y - v.y);
	}
	OwnVector2 operator*(const double v)const
	{
		return OwnVector2(x*v, y*v);
	}
	bool operator==(const OwnVector2& v)const
	{
		return abs(x - v.x) <= 0.0000000000001&&abs(y - v.y) <= 0.00000000000001;
	}
	bool operator!=(const OwnVector2& v)const
	{
		return abs(x - v.x) > 0.0000000000001||abs(y - v.y) > 0.00000000000001;
	}

	double dot(const OwnVector2& v)const
	{
		return x*v.x + y*v.y;
	}
	double cross(const OwnVector2& v)const
	{
		return x*v.y - y*v.x;
	}
	double length()const
	{
		return sqrt(x*x + y*y);
	}
	double length2()const
	{
		return x*x + y*y;
	}
};

double CalcMinDistancePointVSSegment(OwnVector2 p1, OwnVector2 p2, OwnVector2 p3)
{
	OwnVector2 p12, p13, p21, p23;
	p12 = p2 - p1; p13 = p3 - p1; p21 = p1 - p2; p23 = p3 - p2;

	if(p12.dot(p13)<0.0)
	{
		return p13.length();
	}

	if (p21.dot(p23) < 0.0)
	{
		return p23.length();
	}

	return abs(p12.cross(p13)) / p12.length();
}

OwnVector2 CalcCrossPoint(OwnVector2 p1, OwnVector2 p2, OwnVector2 p3, OwnVector2 p4)
{
	OwnVector2 p12, p13, p14, p34, p31, p32;
	p12 = p2 - p1; p13 = p3 - p1; p14 = p4 - p1; p34 = p4 - p3; p31 = p1 - p3; p32 = p2 - p3;

	double d, u, v;

	d = p12.cross(p34);

	if (abs(d) <= 0.0000000000001)
	{
		return OwnVector2(INF, INF);
	}

	u = p13.cross(p34) / d;
	v = p13.cross(p12) / d;

	if (u<0.0 || u>1.0)
	{
		return OwnVector2(INF, INF);
	}
	if (v<0.0 || v>1.0)
	{
		return OwnVector2(INF, INF);
	}

	return p1 + p12*u;
}

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);

	int q;
	cin >> q;

	for (int i = 0; i < q; i++)
	{
		double x0, x1, x2, x3, y0, y1, y2, y3;
		cin >> x0 >> y0 >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;

		OwnVector2 p0(x0, y0), p1(x1, y1), p2(x2, y2), p3(x3, y3);

		OwnVector2 crossPoint = CalcCrossPoint(p0, p1, p2, p3);
		if (crossPoint != OwnVector2(INF, INF))
		{
			printf("%.10lf\n", 0.0);
		}
		else
		{
			double d0, d1, d2, d3;
			d0 = CalcMinDistancePointVSSegment(p0, p1, p2);
			d1 = CalcMinDistancePointVSSegment(p0, p1, p3);
			d2 = CalcMinDistancePointVSSegment(p2, p3, p0);
			d3 = CalcMinDistancePointVSSegment(p2, p3, p1);
			printf("%.10lf\n", min(d0, min(d1, min(d2, d3))));
		}
	}

	return 0;
}