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 JAVA):

Solution:

import java.util.*;
import java.math.BigDecimal;

class Main{
	public static void main(String[] args){
		Scanner stdIn = new Scanner(System.in);
		int q = stdIn.nextInt();
		for(int i=0;i<q;i++){
			double x0 = stdIn.nextDouble();
			double y0 = stdIn.nextDouble();
			double x1 = stdIn.nextDouble();
			double y1 = stdIn.nextDouble();
			double x2 = stdIn.nextDouble();
			double y2 = stdIn.nextDouble();
			double x3 = stdIn.nextDouble();
			double y3 = stdIn.nextDouble();
			Point p0 = new Point(x0,y0);
			Point p1 = new Point(x1,y1);
			Point p2 = new Point(x2,y2);
			Point p3 = new Point(x3,y3);
			double d = p0.getDistance(p1,p2,p3);
			System.out.println(d);
		}

	}	
}

class Vector{
	public final double EPS = Math.pow(10,-8);
	public double x,y;
	final int cutoff = 9;

	Vector( double x1 , double y1 , double x2 , double y2 ){
		this.x = x2 - x1;
		this.y = y2 - y1;
	}

	double dot( Vector a ){	
		return rounding(this.x * a.x + this.y * a.y);
	}
	double cross( Vector a ){	
		return rounding(this.x * a.y - this.y * a.x);
	}

	void add( Vector a ){
		this.x = rounding(this.x + a.x);
		this.y = rounding(this.y + a.y);
	}
	void sub( Vector a ){
		this.x = rounding(this.x - a.x);
		this.y = rounding(this.y - a.y);
	}
	void mul( double z ){
		this.x = rounding(this.x * z);
		this.y = rounding(this.y * z);
	}
	void div( double z ){
		this.x = rounding(this.x / z);
		this.y = rounding(this.y / z);
	}

	double abs(){
		return Math.sqrt(norm());
	}
	double norm(){
		return rounding(this.x * this.x + this.y * this.y);
	}

	void projection( Vector a ){
		if(judge(a.norm())){
			this.x = 0;
			this.y = 0;
		}
		else{
			double cos = dot(a)/(abs() * a.abs());
			double frac = a.abs() * cos/abs();
			mul(frac);
		}
	}
	Vector reflection( Vector a ){
		projection(a);
		return new Vector(a.x,a.y,this.x,this.y);
	}

	boolean judgeisOrthogonal( Vector a ){	
		return judge(dot(a)) ? true : false;
	}  
	boolean judgeisParallel( Vector a ){	
		return judge(cross(a)) ? true : false;
	}

	boolean judge( double a ){		
		return Math.abs(a)<EPS ? true : false;
	}
	double rounding(double a){
		BigDecimal bi = new BigDecimal(String.valueOf(a));
		return bi.setScale(cutoff,BigDecimal.ROUND_HALF_UP).doubleValue();
	}
} 


class Point{

	public double x,y;
	final double EPS = Math.pow(10,-8);
	final int cutoff = 9;

	Point(double x,double y){
		this.x = x;
		this.y = y;
	}

	double abs(){
		Point a = new Point(0,0);	
		return Math.sqrt(norm(a));	
	}
	double abs( Point a ){
		return Math.sqrt(norm(a));
	}
	double norm( Point a ){	
		return rounding((this.x - a.x) * (this.x - a.x) + (this.y - a.y) * (this.y - a.y));
	}

	void add( Point a ){
		this.x = rounding(this.x + a.x);
		this.y = rounding(this.y + a.y);
	}
	void sub( Point a ){
		this.x = rounding(this.x - a.x);
		this.y = rounding(this.y - a.y);
	}
	void mul( double z){
		this.x = rounding(this.x * z);
		this.y = rounding(this.x * z);
	}
	void div( double z){
		this.x = rounding(this.x / z);
		this.y = rounding(this.x / z);
	}

	Point getCrossPoint( Point a , Point b , Point c ){
		Point d = new Point(this.x,this.y);
		Vector s1 = new Vector(d.x,d.y,a.x,a.y);
		Vector s2 = new Vector(b.x,b.y,c.x,c.y);
		s2.mul(-10000);
		Point b2 = new Point(s2.x+b.x,s2.y+b.y);
		s2.mul(-1);
		Point c2 = new Point(s2.x+c.x,s2.y+c.y);
		double t1 = getDistanceSP(b2,c2);
		double t2 = a.getDistanceSP(b2,c2);
		s1.mul(t1/(t1+t2));
		Vector s3 = new Vector(b.x,b.y,d.x,d.y);
		s3.add(s1);
		return new Point(b.x+s3.x,b.y+s3.y);
	}

	double getDistance( Point a , Point b , Point c ){
		if(intersect(a,b,c)){
			return 0.0;
		}
		Point d = new Point(this.x,this.y);
		double x = Math.min(getDistanceSP(b,c),a.getDistanceSP(b,c));
		double y = Math.min(b.getDistanceSP(a,d),c.getDistanceSP(a,d));
		return Math.min(x,y);
	}
	double getDistanceSP( Point a , Point b ){
		Vector s = new Vector( a.x , a.y , b.x , b.y);
		Vector sa = new Vector( a.x , a.y , this.x , this.y );
		Vector sb = new Vector( b.x , b.y , this.x , this.y );
		if(s.dot(sa)<0.00){
			return abs(a);
		}
		s.mul(-1);
		if(s.dot(sb)<0.00){
			return abs(b);
		}
		return Math.abs(s.cross(sb)/s.abs());
	}

	int CCW( Point a , Point b ){
		Vector sa = new Vector( this.x , this.y , a.x , a.y );
		Vector sb = new Vector( this.x , this.y , b.x , b.y );
		if(sa.cross(sb) > EPS){
			return -1;
		}
		else if(sa.cross(sb) < -EPS){
			return 1;
		}
		else if(sa.dot(sb) < -EPS){
			return -2;
		}
		else if(sa.norm() < sb.norm()){
			return 2;
		}
		else{
			return 0;
		}
	}
	boolean intersect( Point a , Point b , Point c ){
		Point d = new Point(this.x,this.y);
		if(CCW(a,b)*CCW(a,c) <= 0 && b.CCW(c,a)*b.CCW(c,d) <= 0){
			return true;
		}
		else{
			return false;
		}
	}

	int contains( Point[] query ){
		boolean flag1 = false;
		boolean flag2 = false;
		Point p1 = new Point(this.x+1,this.y);
		for(int i=0;i<query.length;i++){
			if(CCW(query[i],p1) == 2 || CCW(query[i],p1) == 0){
				flag1 = true;
			}
		}
		Point p2 = new Point(Integer.MAX_VALUE/2,this.y);
		final int l = query.length;
		for(int i=0;i<l;i++){
			if(intersect(p2,query[i%l],query[(i+1)%l])){
				flag2 = true;
			}
		}

		if(flag1){
			return 2;
		}
		else if(flag2){
			return 1;
		}
		return 0;
	}

	void temp( Point a ){
		Point temp = new Point(0,0);
		temp.x = this.x;
		temp.y = this.y;
		this.x = a.x;
		this.y = a.y;
		a.x = temp.x;
		a.y = temp.y;
	}
	void sort( Point[] query ){
		for(int i=0;i<query.length;i++){
			for(int j=0;j<query.length-1-i;j++){
				if(query[j].x > query[j+1].x){
					query[j].temp(query[j+1]);
				}
				else if(query[j].x == query[j+1].x && query[j].y > query[j+1].y){
					query[j].temp(query[j+1]);
				}
			}
		}
	}
	ArrayList<Point> andrewScan( Point[] query ){
		ArrayList<Point> list = new ArrayList<Point>();
		if(query.length<4){
			for(int i=0;i<query.length;i++){
				list.add(query[i]);
			}
		}
		else{
			sort(query);
			ArrayList<Point> list1 = new ArrayList<Point>();
			ArrayList<Point> list2 = new ArrayList<Point>();
			list1.add(query[0]);
			list1.add(query[1]);
			int next = 2;
			while(next<query.length-1){
				if(list1.size()<2){
					list1.add(query[next]);
					next++;
				}
				else{
					Point p1 = list1.get(list1.size()-2);
					Point p2 = list1.get(list1.size()-1);
					if(p1.CCW(p2,query[next])!=-1){
						list1.add(query[next]);
						next++;
					}
					else{
						list1.remove(list1.size()-1);
					}
				}
			}
			Point p1 = list1.get(list1.size()-2);
			Point p2 = list1.get(list1.size()-1);
			if(p1.CCW(p2,query[query.length-1])!=-1){
				list1.add(query[query.length-1]);
			}
			else{
				list1.remove(list1.size()-1);
				list1.add(query[query.length-1]);
			}
			list2.add(query[query.length-1]);
			list2.add(query[query.length-2]);
			next = query.length-3;
			while(next>0){
				if(list2.size()<2){
					list2.add(query[next]);
					next--;
				}
				else{
					Point a = list2.get(list2.size()-2);
					Point b = list2.get(list2.size()-1);
					if(a.CCW(b,query[next])!=-1){
						list2.add(query[next]);
						next--;
					}
					else{
						list2.remove(list2.size()-1);
					}
				}
			}
			p1 = list2.get(list2.size()-2);
			p2 = list2.get(list2.size()-1);
			if(p1.CCW(p2,query[0])>=0){
				list2.add(query[0]);
			}
			else{
				list2.remove(list2.size()-1);
				list2.add(query[0]);
			}
			for(int i=0;i<list1.size();i++){
				list.add(list1.get(i));
			}
			for(int i=1;i<list2.size()-1;i++){
				list.add(list2.get(i));
			}
		}
		return list;
	}

	Point polarCos(double cos_a){
		double sin_a = Math.sqrt(1-Math.pow(cos_a,2));
		double x = cos_a*this.x - sin_a*this.y;
		double y = sin_a*this.x + cos_a*this.y;
		return new Point(x,y); 
	}
	Point polarSin(double sin_a){
		double cos_a = Math.sqrt(1-Math.pow(sin_a,2));
		double x = cos_a*this.x - sin_a*this.y;
		double y = sin_a*this.x + cos_a*this.y;
		return new Point(x,y); 
	}

	boolean judge( Point a ){	
		if( Math.abs( this.x - a.x ) < EPS && Math.abs( this.y - a.y ) < EPS){
			return true;
		}
		else{
			return false;
		}
	}
	double rounding(double a){
		BigDecimal bi = new BigDecimal(String.valueOf(a));
		return bi.setScale(cutoff,BigDecimal.ROUND_HALF_UP).doubleValue();
	}
}