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:
import math
from typing import Union


class Point(object):
    __slots__ = ['x', 'y']

    def __init__(self, x, y):
        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: Union[int, float]):
        return Point(self.x * other, self.y * other)

    def norm(self):
        return pow(self.x, 2) + pow(self.y, 2)

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

    def __repr__(self):
        return f"({self.x},{self.y})"


class Vector(Point):
    __slots__ = ['x', 'y', 'pt1', 'pt2']

    def __init__(self, pt1: Point, pt2: Point):
        super().__init__(pt2.x - pt1.x, pt2.y - pt1.y)
        self.pt1 = pt1
        self.pt2 = pt2

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

    def cross(self, other):
        return self.x * other.y - self.y * other.x

    def __repr__(self):
        return f"{self.pt1},{self.pt2}"


class Segment(Vector):
    __slots__ = ['x', 'y', 'pt1', 'pt2']

    def __init__(self, pt1: Point, pt2: Point):
        super().__init__(pt1, pt2)

    def projection(self, pt: Point)-> Point:
        t = self.dot(Vector(self.pt1, pt)) / self.norm()
        return self.pt1 + self * t

    def reflection(self, pt: Point) -> Point:
        return self.projection(pt) * 2 - pt

    def is_intersected_with(self, other) -> bool:
        if (self.point_geometry(other.pt1) * self.point_geometry(other.pt2)) <= 0\
                and other.point_geometry(self.pt1) * other.point_geometry(self.pt2) <= 0:
            return True
        else:
            return False

    def point_geometry(self, pt: Point) -> int:
        """
        [-2:"Online Back", -1:"Counter Clockwise", 0:"On Segment", 1:"Clockwise",  2:"Online Front"]
        """
        vec_pt1_to_pt = Vector(self.pt1, pt)
        cross = self.cross(vec_pt1_to_pt)
        if cross > 0:
            return -1   # counter clockwise
        elif cross < 0:
            return 1    # clockwise
        else:           # cross == 0
            dot = self.dot(vec_pt1_to_pt)
            if dot < 0:
                return -2    # online back
            else:       # dot > 0
                if self.abs() < vec_pt1_to_pt.abs():
                    return 2    # online front
                else:
                    return 0    # on segment

    def cross_point(self, other) -> Point:
        d1 = abs(self.cross(Vector(self.pt1, other.pt1)))       # / self.abs()
        d2 = abs(self.cross(Vector(self.pt1, other.pt2)))       # / self.abs()
        t = d1 / (d1 + d2)
        return other.pt1 + other * t

    def distance_to_point(self, pt: Point) -> Union[int, float]:
        vec_pt1_to_pt = Vector(self.pt1, pt)
        if self.dot(vec_pt1_to_pt) <= 0:
            return vec_pt1_to_pt.abs()
        vec_pt2_to_pt = Vector(self.pt2, pt)
        if Vector.dot(self * -1, vec_pt2_to_pt) <= 0:
            return vec_pt2_to_pt.abs()
        return (self.projection(pt) - pt).abs()

    def segment_distance(self, other) -> Union[int, float]:
        if self.is_intersected_with(other):
            return 0.0
        else:
            return min(
                self.distance_to_point(other.pt1),
                self.distance_to_point(other.pt2),
                other.distance_to_point(self.pt1),
                other.distance_to_point(self.pt2)
            )

    def __repr__(self):
        return f"{self.pt1},{self.pt2}"


def main():
    num_query = int(input())
    for i in range(num_query):
        p0_x, p0_y, p1_x, p1_y, p2_x, p2_y, p3_x, p3_y = map(int, input().split())
        seg_1 = Segment(Point(p0_x, p0_y), Point(p1_x, p1_y))
        seg_2 = Segment(Point(p2_x, p2_y), Point(p3_x, p3_y))

        print(f'{seg_1.segment_distance(seg_2):.10f}')
    return


main()