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;
/*******************??????********************/
const double EPS = 1e-8;
const double INF = 1e12;
typedef complex<double> P;
namespace std {
	bool operator < (const P& a, const P& b) {
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
}
double cross(const P& a, const P& b) {//??????
	return imag(conj(a)*b);
}
double dot(const P& a, const P& b) {//??????
	return real(conj(a)*b);
}

struct L : public vector<P> {//??????
	L(const P &a, const P &b) {
		push_back(a); push_back(b);
	}
};

typedef vector<P> G;
struct C {//???
	P p; double r;
	C(const P &p, double r) : p(p), r(r) { }
};

int ccw(P a, P b, P c) {//??????????????????
	b -= a; c -= a;
  if (cross(b, c) > 0)   return +1;       // counter clockwise
  if (cross(b, c) < 0)   return -1;       // clockwise
  if (dot(b, c) < 0)     return +2;       // c--a--b on line
  if (norm(b) < norm(c)) return -2;       // a--b--c on line
  return 0;
}

bool intersectLL(const L& l,const L& m){
	//non-parallel || sameline
	return abs(cross(l[1]-l[0],m[1]-m[0])) > EPS || abs(cross(l[1]-l[0],m[0]-l[0])) < EPS;
}
bool intersectLS(const L& l,const L& s){
	// s[0] is left of l,s[1] is right of l
	return cross(l[1]-l[0],s[0]-l[0]) * cross(l[1]-l[0],s[1]-l[0]) < EPS;
}
bool intersectSS(const L &s, const L &t) {
	return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
		ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
bool intersectLP(const L& l,const P& p){
	return abs(cross(l[1]-p,l[0]-p)) < EPS;
}
bool intersectSP(const L& s,const P& p){
	return abs(s[0]-p)+abs(s[1]-p) - abs(s[1]-s[0]) < EPS;// triangle inequality
}
// ??´???????????????
bool orthogonalLL(const L &l1, const L &l2){
	return (dot(l1[0]-l1[1], l2[0]-l2[1]) <= EPS && dot(l1[0]-l1[1], l2[0]-l2[1]) >= -EPS);
}
// ??????????????????
bool parallelLL(const L &l1, const L &l2){
	return (cross(l1[0]-l1[1], l2[0]-l2[1]) <= EPS && cross(l1[0]-l1[1], l2[0]-l2[1]) >= -EPS);
}

P projection(const L& l,const P& p){
	double t = dot(p-l[0],l[0]-l[1]) / norm(l[0]-l[1]);
	return l[0] + t*(l[0]-l[1]);
}
P reflection(const L& l,const P& p){
	return p + 2. * (projection(l,p) - p);
}
double distancePP(const P &a, const P &b){
	return abs(a - b);
}
double distanceSP(const L &s, const P &p) {
	const P r = projection(s, p);
	if (intersectSP(s, r)) return abs(r - p);
	return min(abs(s[0] - p), abs(s[1] - p));
}
double distanceLP(const L& l,const P& p){
	return abs(p - projection(l,p));
}
double distanceLL(const L& l,const L& m){
	return intersectLL(l,m) ? 0 : distanceLP(l,m[0]);
}
double distanceLS(const L& l,const L& s){
	if(intersectLS(l,s)) return 0;
	return min(distanceLP(l, s[0]),distanceLP(l, s[1]));
}
double distanceSS(const L &s, const L &t) {
	if (intersectSS(s, t)) return 0;
	return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
		min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
// ??????
P crosspointLL(const L &l, const L &m) {
	double A = cross(l[1] - l[0], m[1] - m[0]);
	double B = cross(l[1] - l[0], l[1] - m[0]);
	if (abs(A) < EPS && abs(B) < EPS) return m[0]; // same line
	if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
	return m[0] + B / A * (m[1] - m[0]);
}

int main(void){
	int q;
	cin >> q;
	for(int i=0;i<q;i++){
		vector<P> p(4);
		int x,y;
		for(int j=0;j<4;j++){
			cin >> x >> y;
			p[j] = P(x,y);
		}
		L l0(p[0],p[1]),l1(p[2],p[3]);
		cout <<fixed << setprecision(20) << distanceSS(l0,l1) << endl;

	}

	return 0;
}