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 <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for(int i=(a);i<(n);i++)
#define per(i,a,n) for(int i=(n)-1;i>=(a);i--)
#define MP make_pair

typedef double db;

const db EPS = 1e-8;

inline int sign(db a) {
	return a < -EPS ? -1 : a > EPS;
}

inline int cmp(db a, db b){
	return sign(a-b);
}

struct P {
	db x, y;
	P() {
	}
	P(db _x, db _y) :
			x(_x), y(_y) {
	}
	P operator+(P p) {
		return P(x + p.x, y + p.y);
	}
	P operator-(P p)  {
		return P(x - p.x, y - p.y);
	}
	P operator*(db d) {
		return P(x * d, y * d);
	}
	P operator/(db d) {
		return P(x / d, y / d);
	}
	bool operator<(P p) const {
		int c = sign(x - p.x);
		if (c)
			return c == -1;
		return sign(y - p.y) == -1;
	}
	db dot(P p) {
		return x * p.x + y * p.y;
	}
	db det(P p) {
		return x * p.y - y * p.x;
	}
	db distTo(P p) { return (*this-p).abs(); }

	db alpha() {
		return atan2(y, x);
	}
	void read() {
		cin>>x>>y;
	}
	db abs() {
		return sqrt(abs2());
	}
	db abs2() {
		return x * x + y * y;
	}
	P rot90(){
		return P(-y,x);
	}
};

#define cross(p1,p2,p3) ((p2.x-p1.x)*(p3.y-p1.y)-(p3.x-p1.x)*(p2.y-p1.y))
#define crossOp(p1,p2,p3) sign(cross(p1,p2,p3))

P isLL(P p1, P p2, P q1, P q2) {
	db a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
	return (p1 * a2 + p2 * a1) / (a1 + a2);
}

bool intersect(db l1,db r1,db l2,db r2){
	if(l1>r1) swap(l1,r1); if(l2>r2) swap(l2,r2); 
	return !( cmp(r1,l2) == -1 || cmp(r2,l1) == -1 );
}

bool isSS(P p1, P p2, P q1, P q2){
    return intersect(p1.x,p2.x,q1.x,q2.x) && intersect(p1.y,p2.y,q1.y,q2.y) && 
    crossOp(p1,p2,q1) * crossOp(p1,p2,q2) <= 0 && crossOp(q1,q2,p1)
            * crossOp(q1,q2,p2) <= 0;
}

bool isMiddle(db a, db m, db b) {
    return sign(a - m) == 0 || sign(b - m) == 0 || (a < m != b < m);
}
 
bool isMiddle(P a, P m, P b) {
    return isMiddle(a.x, m.x, b.x) && isMiddle(a.y, m.y, b.y);
}

bool onSegment(P p1, P p2, P q){
	return crossOp(p1,p2,q) == 0 && isMiddle(p1, q, p2);
}

P proj(P p1, P p2, P q) {
    P dir = p2 - p1;
    return p1 + dir * (dir.dot(q - p1) / dir.abs2());
}

P reflect(P p1, P p2, P q){
	return proj(p1,p2,q) * 2 - q;
}

db nearest(P p1,P p2,P q){
	P h = proj(p1,p2,q);
	if(isMiddle(p1,h,p2))
		return q.distTo(h);
	return min(p1.distTo(q),p2.distTo(q));
}

db disSS(P p1, P p2, P q1, P q2){
	if(isSS(p1,p2,q1,q2)) return 0;
	return min(min(nearest(p1,p2,q1),nearest(p1,p2,q2)), min(nearest(q1,q2,p1),nearest(q1,q2,p2)) );
}

db getrad(P p1,P p2){
	return atan2l(p1.det(p2),p1.dot(p2));
}

db incircle(P p1, P p2, P p3){
	db A = p1.distTo(p2);
	db B = p2.distTo(p3);
	db C = p3.distTo(p1);
	return sqrtl(A*B*C/(A+B+C));
}

int main(){
	int n;cin>>n;
	rep(i,0,n){
		P p1,p2,q1,q2;
		p1.read(),p2.read(),q1.read(),q2.read();
		printf("%0.10f\n", disSS(p1,p2,q1,q2));
	}

	return 0;
}