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

EPS = 1e-10

def equals(a, b):
    return abs(a - b) < EPS


class Point:
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    def __add__(self, p):
        return Point(self.x + p.x, self.y + p.y)

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

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

    def __rmul__(self, a):
        return self * a

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

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

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

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

    def __eq__(self, p):
        return equals(self.x, p.x) and equals(self.y, p.y)


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


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


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


def ccw(p0, p1, p2):
    COUNTER_CLOCKWISE = 1
    CLOCKWISE = -1
    ONLINE_BACK = 2
    ONLINE_FRONT = -2
    ON_SEGMENT = 0
    a = p1 - p0
    b = p2 - p0
    if cross(a, b) > EPS:
        return COUNTER_CLOCKWISE
    if cross(a, b) < -EPS:
        return CLOCKWISE
    if dot(a, b) < -EPS:
        return ONLINE_BACK
    if a.norm() < b.norm():
        return ONLINE_FRONT
    return ON_SEGMENT


def intersect(s1, s2):
    p1 = s1.p1
    p2 = s1.p2
    p3 = s2.p1
    p4 = s2.p2
    return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 and
            ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0)


def getDistanceLP(l, p):
    v = l.p2 - l.p1
    return abs(cross(v, p - l.p1) / v.abs())


def getDistanceSP(s, p):
    if dot(s.p2 - s.p1, p - s.p1) < 0:
        v = p - s.p1
        return v.abs()
    if dot(s.p1 - s.p2, p - s.p2) < 0:
        v = p - s.p2
        return v.abs()
    return getDistanceLP(s, p)


def getDistance(s1, s2):
    if intersect(s1, s2):
        return 0
    return min(
        getDistanceSP(s1, s2.p1),
        getDistanceSP(s1, s2.p2),
        getDistanceSP(s2, s1.p1),
        getDistanceSP(s2, s1.p2)
    )


if __name__ == '__main__':
    q = int(input())
    ans = []
    for i in range(q):
        x0, y0, x1, y1, x2, y2, x3, y3 = [int(v) for v in input().split()]
        s1 = Segment(Point(x0, y0), Point(x1, y1))
        s2 = Segment(Point(x2, y2), Point(x3, y3))
        ans.append(getDistance(s1, s2))

    for v in ans:
        print('{0:.10f}'.format(v))