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<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<climits>
#include<iomanip>
#include<cstdio>
#include<vector>
#include<queue>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
using namespace std;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef stack<int> SI;
typedef queue<int> QI;
typedef list<int> LI;
typedef pair<int,int> PII;
typedef long long LL;

#define d(x)  cout<<#x<<" = "<<(x)<<endl;
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define EMP empty()
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define REACH(i,c) for(typeof((c).rbegin()) i=(c).rbegin(); i!=(c).rend(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c,n) sort(c,c+n)
#define VSORT(c) sort((c).begin(),(c).end())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)
#define DFOR(i,b,a) for(int i=(b)-1;i>=(a);--i)
#define DREP(i,n) DFOR(i,n,0)
#define INF 1000000000
#define PI  acos(-1.0)
////////////////////////////////////////////////
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)
class Vector
{
public:
	double x,y;
	Vector(double x=0,double y=0):x(x),y(y){}
	
	Vector operator + (Vector p){return Vector(x+p.x,y+p.y);}
	Vector operator - (Vector p){return Vector(x-p.x,y-p.y);}
	Vector operator * (double a){return Vector(x*a,y*a);}
	Vector operator / (double a){return Vector(x/a,y/a);}
	
	double abs(){return sqrt(norm());}
	double norm(){return x*x+y*y;}
	
	bool operator <  (const Vector &p)const{return x!=p.x?x<p.x:y<p.y;}
	bool operator == (const Vector &p)const{return fabs(x-p.x)<EPS && fabs(y-p.y<EPS);}
};

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-b.x*a.y;}

int ccw(Vector p0,Vector p1,Vector p2)
{
	Vector a=p1-p0;
	Vector b=p2-p0;
	if(cross(a,b)>EPS)return 1;//???????¨???????
	if(cross(a,b)<-EPS)return -1;//????¨???????
	if(dot(a,b)<-EPS)return 2;//p0?????????
	if(a.norm()<b.norm())return -2;//p1????\\
	return 0;//?????????
}

bool intersect(Vector p0,Vector p1,Vector p2,Vector p3)
{
	return (ccw(p0,p1,p2)*ccw(p0,p1,p3)<=0&&ccw(p2,p3,p0)*ccw(p2,p3,p1)<=0);
}

int main()
{
	int n;cin>>n;
	Vector p[4];
	cout<<fixed<<setprecision(10);
	REP(i,n)
	{
		REP(j,4)cin>>p[j].x>>p[j].y;
		if(intersect(p[0],p[1],p[2],p[3])){cout<<0<<endl;continue;}
		double a,b,c,d;
		if(dot(p[1]-p[0],p[2]-p[0])>0&&dot(p[0]-p[1],p[2]-p[1])>0)
		{
			a=abs(cross(p[1]-p[0],p[2]-p[0]))/(p[1]-p[0]).abs();
		}
		else
		{
			a=min((p[2]-p[0]).abs(),(p[2]-p[1]).abs());
		}
		
		if(dot(p[1]-p[0],p[3]-p[0])>0&&dot(p[0]-p[1],p[3]-p[1])>0)
		{
			b=abs(cross(p[1]-p[0],p[3]-p[0]))/(p[1]-p[0]).abs();
		}
		else
		{
			b=min((p[3]-p[0]).abs(),(p[3]-p[1]).abs());
		}
		
		if(dot(p[3]-p[2],p[0]-p[2])>0&&dot(p[2]-p[3],p[0]-p[3])>0)
		{
			c=abs(cross(p[3]-p[2],p[0]-p[2]))/(p[3]-p[2]).abs();
		}
		else
		{
			c=min((p[0]-p[2]).abs(),(p[0]-p[3]).abs());
		}
		
		if(dot(p[3]-p[2],p[1]-p[2])>0&&dot(p[2]-p[3],p[1]-p[3])>0)
		{
			d=abs(cross(p[3]-p[2],p[1]-p[2]))/(p[3]-p[2]).abs();
		}
		else
		{
			d=min((p[1]-p[2]).abs(),(p[1]-p[3]).abs());
		}
		
		cout<<min(min(a,b),min(c,d))<<endl;
	}
	return 0;
}