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;
struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
#define P(x) cout << (x) << "\n"
#define p(x) cout << (x)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define vv(type, c, m, n, i) vector<vector<type>> c(m, vector<type>(n, i));
#define rep(i,a,n) for(int i=(a), i##_len=(n); i<i##_len; ++i)
#define rrep(i,a,n) for(int i=(a), i##_len=(n); i>i##_len; --i)
#define len(x) ((int)(x).size())
#define mp make_pair
#define eb emplace_back
#define fi first
#define se second
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<long long> vll;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef complex<double> Point;
typedef Point Vector;
typedef pair<Point, Point> Segment;
typedef Segment Line;
constexpr double EPS = (1e-9L);
double dot(const Point& p1, const Point& p2) { return (conj(p1) * p2).real(); }
double cross(const Point& p1, const Point& p2) { return (conj(p1) * p2).imag(); }
constexpr bool eq(double a) { return abs(a) < EPS; }
Point project(Segment s, Point p) {
	Vector base = s.fi - s.se;
	double r = dot(p - s.fi, base) / norm(base);
	return s.fi + base * r;
}
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }
int ccw(const Point& p1, const Point& p2, const Point& p3) {
	Point a = p2 - p1, b = p3 - p1;
	if (cross(a, b) > EPS) return 1;
	if (cross(a, b) < -EPS) return -1;
	if (dot(a, b) < -EPS) return 2;
	if (norm(a) < norm(b)) return -2;
	return 0;
}
bool intersect(Point &p1, Point &p2, Point &p3, Point &p4) {
	return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
			ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment &s1, Segment &s2) {
	return intersect(s1.fi, s1.se, s2.fi, s2.se);
}
double getDistance(Point &a, Point &b) { return abs(a - b); }
double getDistanceLP(Line &l, Point &p) {
	return abs(cross(l.se - l.fi, p - l.fi) / abs(l.se - l.fi));
}
double getDistanceSP(Segment &s, Point &p) {
	if(dot(s.se - s.fi, p - s.fi) < 0.0) return abs(p - s.fi);
	if(dot(s.fi - s.se, p - s.se) < 0.0) return abs(p - s.se);
	return getDistanceLP(s, p);
}
double getDistance(Segment s1, Segment s2) {
	if(intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.fi), getDistanceSP(s1, s2.se)),
				min(getDistanceSP(s2, s1.fi), getDistanceSP(s2, s1.se)));
}
int main() {
	cout << setprecision(10) << fixed;
	int q; cin >> q;
	Segment s1, s2;
	double x1, y1, x2, y2, x3, y3, x4, y4;
	rep(i, 0, q) {
		cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> x4 >> y4;
		s1 = mp(Point(x1, y1), Point(x2, y2));
		s2 = mp(Point(x3, y3), Point(x4, y4));
		P(getDistance(s1, s2));
	}
	return 0;
}