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 PYTHON3):

Solution:
from sys import stdin
import math

EPS = 1e-10

class Vector:
    def __init__(self, x=None, y=None):
        self.x = x
        self.y = y

    def __add__(self, other):
        return Vector(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Vector(self.x - other.x, self.y - other.y)

    def __mul__(self, k):
        return Vector(self.x * k, self.y * k)

    def __gt__(self, other):
        return self.x > other.x and self.y > other.yb

    def __lt__(self, other):
        return self.x < other.x and self.y < other.yb

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    # usually cross operation return Vector but it returns scalor
    def cross(self, other):
        return self.x * other.y - self.y * other.x

    def norm(self):
        return self.x * self.x + self.y * self.y

    def abs(self):
        return math.sqrt(self.norm())

class Point(Vector):
    def __init__(self, *args, **kargs):
        return super().__init__(*args, **kargs)

class Segment:
    def __init__(self, p1=Point(0, 0), p2=Point(1, 1)):
        self.p1 = p1
        self.p2 = p2

def ccw(p0, p1, p2):
    a = p1 - p0
    b = p2 - p0
    if a.cross(b) > EPS:
        return 1
    elif a.cross(b) < -EPS:
        return -1
    elif a.dot(b) < -EPS:
        return 2
    elif a.norm() < b.norm():
        return -2
    else:
        return 0

def intersect(*args, **kwargs):
    # input two segments
    if len(args) == 2:
        s1, s2 = args
        return (ccw(s1.p1, s1.p2, s2.p1) * ccw(s1.p1, s1.p2, s2.p2) <= 0 and
                    ccw(s2.p1, s2.p2, s1.p1) * ccw(s2.p1, s2.p2, s1.p2) <= 0)
    # input four points
    elif len(args) == 4:
        p0, p1, p2, p3 = args
        return (ccw(p0, p1, p2) * ccw(p0, p1, p3) <= 0 and
                    ccw(p2, p3, p0) * ccw(p2, p3, p1) <= 0)
    else:
        raise ArgsError

def get_distance_lp(l, p):
    v1 = l.p1 - l.p2
    v2 = p - l.p1
    return abs(v1.cross(v2))/v1.abs()

def get_distance_sp(s, p):
    v1 = s.p2 - s.p1
    v2 = p - s.p1
    v3 = s.p1 - s.p2
    v4 = p - s.p2
    if v1.dot(v2) < 0:
        return v2.abs()
    elif v3.dot(v4) < 0:
        return v4.abs()
    else:
        return get_distance_lp(s, p)

def get_distance(*args, **kwargs):
    # input two points with the startpoint (0, 0)
    if len(args) == 2:
        p1, p2 = args
        v = p1 - p2
        return v.abs()
    # input two segments
    elif len(kwargs) == 2:
        s1 = kwargs['s1']
        s2 = kwargs['s2']
        if intersect(s1, s2):
            return 0.0
        else:
            return min(min(get_distance_sp(s1, s2.p1), get_distance_sp(s1, s2.p2)),
                        min(get_distance_sp(s2, s1.p1), get_distance_sp(s2, s1.p2)))
    else:
        raise ArgsError

def read_and_print_results(n):
    for _ in range(n):
        line = stdin.readline().strip().split()
        p0 = Vector(int(line[0]), int(line[1]))
        p1 = Vector(int(line[2]), int(line[3]))
        p2 = Vector(int(line[4]), int(line[5]))
        p3 = Vector(int(line[6]), int(line[7]))
        s1 = Segment(p0, p1)
        s2 = Segment(p2, p3)
        d = get_distance(s1=s1, s2=s2)
        print("{0:0.10f}".format(d))

n = int(input())
read_and_print_results(n)