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 CPP):

Solution:
#include<iostream>
using namespace std;
#include<cstdio>
#include<cmath>

struct Point{ double x, y; };

Point set_p(double a, double b)
{
    Point p;
    p.x = a; p.y = b;
    return p;
}

struct Vector{ double vx, vy; };

Vector set_v(const Point &p1, const Point &p2)
{
    Vector v;
    v.vx = p2.x - p1.x;
    v.vy = p2.y - p1.y;
    return v;
}

double dot(const Vector &v1, const Vector &v2)
{
    return (v1.vx * v2.vx) + (v1.vy * v2.vy);
}

double cross(const Vector &v1, const Vector &v2)
{
    return (v1.vx * v2.vy) - (v1.vy * v2.vx);
}

double cross0(const Point &P0, const Point &P1)
{
	return (P0.x * P1.y) - (P1.x * P0.y);
}

double onenorm(const Vector &v)
{
    return abs(v.vx) + abs(v.vy);
}

double norm(const Vector &v)
{
	return sqrt(v.vx * v.vx + v.vy * v.vy);
}

int ccw(const Point &P0, const Point &P1, const Point &P2)
{
    Vector V1 = set_v(P0, P1);
    Vector V2 = set_v(P0, P2);
    double c = cross(V1, V2);
    if(c > 0){ return 1; }else if(c < 0){ return -1; }
    if(dot(V1, V2) < 0){ return -2; }
    if(onenorm(V1) < onenorm(V2)){ return 2; }
    return 0;
}

int intersect(const Point &P0, const Point &P1, const Point &P2, const Point &P3)
{
    if(ccw(P0, P1, P2) * ccw(P0, P1, P3) <= 0 && ccw(P2, P3, P0) * ccw(P2, P3, P1) <= 0){
        return 1;
    }else{
        return 0;
    }
}

double dist_seg(const Point &P0, const Point &P1, const Point &P2) // Segment P0P1 & Point P2.
{
    Vector V01 = set_v(P0, P1), V12 = set_v(P1, P2), V02 = set_v(P0, P2);
    if(dot(V01, V12) > 0) return norm(V12);
    if(dot(V01, V02) < 0) return norm(V02);
    double c_sum;
    c_sum = cross0(P0, P1) + cross0(P1, P2) + cross0(P2, P0);
    if(c_sum < 0) c_sum *= -1.0;
    return c_sum / norm(V01);
}

int main()
{
    int q;
    double x0, y0, x1, y1, x2, y2, x3, y3, dist;
    Point P0, P1, P2, P3;
    scanf("%d", &q);

    for(int i = 0; i < q; i++){
        scanf("%lf %lf %lf %lf %lf %lf %lf %lf", &x0, &y0, &x1, &y1, &x2, &y2, &x3, &y3);
        P0 = set_p(x0, y0), P1 = set_p(x1, y1), P2 = set_p(x2, y2), P3 = set_p(x3, y3);
        if(intersect(P0, P1, P2, P3)){
            printf("0\n");
        }else{
            dist = min(min(dist_seg(P0, P1, P2), dist_seg(P0, P1, P3)), min(dist_seg(P2, P3, P0), dist_seg(P2, P3, P1)));
            printf("%.13f\n", dist);
        }
    }
    return 0;
}