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


class Vector2():
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, v):
        return Vector2(self.x+v.x, self.y+v.y)

    def __sub__(self, v):
        return Vector2(self.x-v.x, self.y-v.y)

    def __mul__(self, v):
        return Vector2(self.x*v, self.y*v)

    def __truediv__(self, v):
        return Vector2(self.x/v, self.y/v)

    def __abs__(self):
        return math.sqrt(float(self.x*self.x+self.y*self.y))

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

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

    def norm(self):
        d = abs(self)
        return Vector2(self.x/d, self.y/d)


def distanceLP(v1, v2, p):
    '''
    v1 -> v2の直線とpとの距離
    '''
    return abs((v2-v1).cross(p-v1))/abs(v2-v1)


def distanceSP(v1, v2, p):
    '''
    v1 -> v2の線分とpとの距離
    '''
    if (v2-v1).dot(p-v1) < 0.0:
        return abs(p-v1)
    if (v1-v2).dot(p-v2) < 0.0:
        return abs(p-v2)
    return distanceLP(v1, v2, p)


def intersect(p1, p2, p3, p4):
    '''
    p1p2とp3p4の交差判定
    '''
    t1 = (p1.x-p2.x)*(p3.y-p1.y)+(p1.y-p2.y)*(p1.x-p3.x)
    t2 = (p1.x-p2.x)*(p4.y-p1.y)+(p1.y-p2.y)*(p1.x-p4.x)
    t3 = (p3.x-p4.x)*(p1.y-p3.y)+(p3.y-p4.y)*(p3.x-p1.x)
    t4 = (p3.x-p4.x)*(p2.y-p3.y)+(p3.y-p4.y)*(p3.x-p2.x)
    return (t1*t2) < 0.0 and (t3*t4) < 0.0


def distance(a1, a2, b1, b2):
    '''
    線分a1a2とb1b2の距離
    '''
    if intersect(a1, a2, b1, b2):
        return 0.0
    return min([
        min([distanceSP(a1, a2, b1), distanceSP(a1, a2, b2)]),
        min([distanceSP(b1, b2, a1), distanceSP(b1, b2, a2)])
    ])


q = int(input())
for i in range(q):
    x0, y0, x1, y1, x2, y2, x3, y3 = map(int, input().split())
    p0 = Vector2(x0, y0)
    p1 = Vector2(x1, y1)
    p2 = Vector2(x2, y2)
    p3 = Vector2(x3, y3)
    s1 = p1-p0
    s2 = p3-p2
    print(f"{distance(p0, p1, p2, p3):.10f}")