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:
# -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D&lang=jp

"""
import sys
from sys import stdin
input = stdin.readline


class Point(object):
    epsilon = 1e-10

    def __init__(self, x=0.0, y=0.0):
        if isinstance(x, tuple):
            self.x = x[0]
            self.y = x[1]
        else:
            self.x = x
            self.y = y

    # ????????????
    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)

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

    def __mul__(self, other):
        return Point(other * self.x, other * self.y)

    def __truediv__(self, other):
        return Point(other / self.x, other / self.y)

    def __lt__(self, other):
        if self.x == other.x:
            return self.y < other.y
        else:
            return self.x < other.x

    def __eq__(self, other):
        from math import fabs
        if fabs(self.x - other.x) < Point.epsilon and fabs(self.y - other.y) < Point.epsilon:
            return True
        else:
            return False

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

    def __abs__(self):
        from math import sqrt
        return sqrt(self.norm())

    def ccw(self, p0, p1):
        # ??????2???(p0, p1)?????????????????????????????????????????¢????????????
        a = Vector(p1 - p0)
        b = Vector(self - p0)
        if Vector.cross(a, b) > Point.epsilon:
            return 1 # 'COUNTER_CLOCKWISE'
        elif Vector.cross(a, b) < -Point.epsilon:
            return -1 # 'CLOCKWISE'
        elif Vector.dot(a, b) < -Point.epsilon:
            return 2 # 'ONLINE_BACK'
        elif a.norm() < b.norm():
            return -2 # 'ONLINE_FRONT'
        else:
            return 0 # 'ON_SEGMENT'

    def project(self, s):
        # ??????(Point)????????????s??????????????????????????????????????§?¨?(?°???±)????±???????
        base = Vector(s.p2 - s.p1)
        a = Vector(self - s.p1)
        r = Vector.dot(a, base)
        r /= base.norm()
        return s.p1 + base * r

    def reflect(self, s):
        # ??????s???????§°?????¨?????????????????¨???????§°??????????????§?¨?(????°?)????±???????
        proj = self.project(s)
        return self + (proj - self)*2

    def distance(self, s):
        # ????????¨??????s????????¢????¨??????????
        if Vector.dot(s.p2-s.p1, self-s.p1) < 0.0:
            return abs(self - s.p1)
        if Vector.dot(s.p1-s.p2, self-s.p2) < 0.0:
            return abs(self - s.p2)
        return abs(Vector.cross(s.p2-s.p1, self-s.p1) / abs(s.p2-s.p1))


class Vector(Point):
    def __init__(self, x=0.0, y=0.0):
        if isinstance(x, tuple):
            self.x = x[0]
            self.y = x[1]
        elif isinstance(x, Point):
            self.x = x.x
            self.y = x.y
        else:
            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, other):
        return Vector(other * self.x, other * self.y)

    def __truediv__(self, other):
        return Vector(other / self.x, other / self.y)

    @classmethod
    def dot(cls, a, b):
        return a.x * b.x + a.y * b.y

    @classmethod
    def cross(cls, a, b):
        return a.x * b.y - a.y * b.x

    @classmethod
    def is_orthogonal(cls, a, b):
        return Vector.dot(a, b) == 0.0

    @classmethod
    def is_parallel(cls, a, b):
        return Vector.cross(a, b) == 0.0


class Segment(object):
    def __init__(self, p1=Point(), p2=Point()):
        if isinstance(p1, Point):
            self.p1 = p1
            self.p2 = p2
        elif isinstance(p1, tuple):
            self.p1 = Point(p1[0], p1[1])
            self.p2 = Point(p2[0], p2[1])

    def intersect(self, s):
        # ????????¨??????????????????????????????????????????????????????
        ans1 = s.p1.ccw(self.p1, self.p2) * s.p2.ccw(self.p1, self.p2)
        ans2 = self.p1.ccw(s.p1, s.p2) * self.p2.ccw(s.p1, s.p2)
        return ans1 <= 0 and ans2 <= 0

    def cross_point(self, s):
        # ????????¨??????????????????????????????????????§?¨?????±???????
        base = s.p2 - s.p1
        d1 = abs(Vector.cross(base, self.p1-s.p1))
        d2 = abs(Vector.cross(base, self.p2-s.p1))
        t = d1 / (d1 + d2)
        return self.p1 + (self.p2 - self.p1) * t

    def distance(self, s):
        # ????????¨?????????????????????????????¢????±???????
        if self.intersect(s):
            return 0.0
        d1 = s.p1.distance(self)
        d2 = s.p2.distance(self)
        d3 = self.p1.distance(s)
        d4 = self.p2.distance(s)
        return min(d1, d2, d3, d4)


    @classmethod
    def is_orthogonal(cls, s1, s2):
        a = Vector(s1.p2 - s1.p1)
        b = Vector(s2.p2 - s2.p1)
        return Vector.is_orthogonal(a, b)

    @classmethod
    def is_parallel(cls, s1, s2):
        a = Vector(s1.p2 - s1.p1)
        b = Vector(s2.p2 - s2.p1)
        return Vector.is_parallel(a, b)


class Line(Segment):
    pass


class Cirle(object):
    def __init__(self, c=Point(), r=0.0):
        self.c = c
        self.r = r


def main(args):
    q = int(input())
    for _ in range(q):
        x_p0, y_p0, x_p1, y_p1, x_p2, y_p2, x_p3, y_p3 = map(int, input().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)
        s1 = Segment(p0, p1)
        s2 = Segment(p2, p3)
        result = s1.distance(s2)
        print('{:.10f}'.format(result))

if __name__ == '__main__':
    main(sys.argv[1:])