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:
class Point:
    def __init__(self, x , y):
        self.x = x
        self.y = y
    def __sub__(self, p):
        x_sub = self.x - p.x
        y_sub = self.y - p.y
        return Point(x_sub, y_sub)

class Vector:
    def __init__(self, p):
        self.x = p.x
        self.y = p.y
        self.norm = (p.x ** 2 + p.y ** 2) ** 0.5

def cross(v1, v2):
    return v1.x * v2.y - v1.y * v2.x

def dot(v1, v2):
    return v1.x * v2.x + v1.y * v2.y

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

def intersect(p1, p2, p3, p4):
    if (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0) and \
       (ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0):
        return True
    else:
        return False

def getDistanceSP(sp1, sp2, p):
    a = Vector(sp2 - sp1)
    b = Vector(p - sp1)
    if dot(a, b) < 0:
        return b.norm
    c = Vector(sp1 - sp2)
    d = Vector(p - sp2)
    if dot(c, d) < 0:
        return d.norm
    return abs(cross(a, b) / a.norm)

def getDistance(p1, p2, p3, p4):
    if intersect(p1, p2, p3, p4):
        print("0.00000000")
    else:
        d = min(getDistanceSP(p1, p2, p3), getDistanceSP(p1, p2, p4),
                getDistanceSP(p3, p4, p1), getDistanceSP(p3, p4, p2))
        print("{0:.10f}".format(d))


import sys

file_input = sys.stdin

sq = file_input.readline()

for line in file_input:
    x_p0, y_p0, x_p1, y_p1, x_p2, y_p2, x_p3, y_p3 = map(int, line.split())
    p0 = Point(x_p0, y_p0)
    p1 = Point(x_p1, y_p1)
    p2 = Point(x_p2, y_p2)
    p3 = Point(x_p3, y_p3)
    getDistance(p0, p1, p2, p3)