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 <complex>
#include <cmath>
#include <algorithm>

using Real = long double;

const Real EPS = 1e-10;

// 宇宙船演算子
inline Real compare(Real a, Real b) {
    if (std::abs(a - b) < EPS) return 0;
    return a - b > 0 ? 1 : -1;
}

template <class T>
inline T sq(T x) { return x * x; }


using Point = std::complex<Real>;
using Segment = std::pair<Point, Point>;

inline Real dist(Point a, Point b) {
    return std::abs(a - b);
}

inline Real length(Segment s) {
    return dist(s.first, s.second);
}

// inner product
inline Real dot(Point x, Point y) {
    return std::real(std::conj(x) * (y));
}

// outer product
inline Real cross(Point x, Point y) {
    return std::imag(std::conj(x) * (y));
}

// lに対するxの正射影
Point proj(Segment s, Point p) {
    Real ratio = dot(s.second - s.first, p - s.first) / sq(length(s));
    return s.first + (s.second - s.first) * ratio;
}

// lを軸としてxに対称な点
Point refl(Segment s, Point p) {
    Point t = proj(s, p);
    return t + (t - p);
}

// lに対するpの位置
// counter clockwise -> 1, clockwise   -> -1
// online front      -> 2, online back -> -2
// on segment        -> 0
int side(Segment s, Point p) {
    Real c = cross(s.second - s.first, p - s.first);
    if (compare(c, 0) != 0) return compare(c, 0);

    Real d = dot(s.second - s.first, p - s.first);
    if (compare(d, 0) < 0) return -2;

    return (compare(length(Segment(s.first, p)), length(s)) > 0 ? 2 : 0);
}

inline bool isorthogonal(Segment s1, Segment s2) {
    return compare(dot(s1.second - s1.first, s2.second - s2.first), 0) == 0;
}

inline bool isparallel(Segment s1, Segment s2) {
    return compare(cross(s1.second - s1.first, s2.second - s2.first), 0) == 0;
}

inline bool intersect(Segment s1, Segment s2) {
    return (side(s1, s2.first) * side(s1, s2.second) <= 0) &&
           (side(s2, s1.first) * side(s2, s1.second) <= 0);
}

Point intersection(Segment s1, Segment s2) {
    Real c1 = cross(s2.second - s2.first, s1.second - s1.first);
    Real c2 = cross(s2.second - s2.first, s1.first - s2.first);
    return s1.first + (s1.second - s1.first) * (-c2 / c1);
}

Real dist(Segment s, Point p) {
    Point t = proj(s, p);
    if (side(s, t) == 0) return dist(p, t);
    return std::min(dist(p, s.first), dist(p, s.second));
}

Real dist(Segment s1, Segment s2) {
    if (intersect(s1, s2)) return 0;
    return std::min({dist(s1, s2.first),
                     dist(s1, s2.second),
                     dist(s2, s1.first),
                     dist(s2, s1.second)});
}


#include <iostream>
#include <iomanip>

using namespace std;

int main() {
    cout << fixed << setprecision(10);

    int Q;
    cin >> Q;

    for (int q = 0; q < Q; ++q) {
        Segment s[2];
        for (int i = 0; i < 2; ++i) {
            Point p[2];
            for (int j = 0; j < 2; ++j) {
                Real x, y;
                cin >> x >> y;
                p[j] = Point(x, y);
            }
            s[i] = Segment(p[0], p[1]);
        }

        cout << dist(s[0], s[1]) << endl;
    }
    return 0;
}