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 <stdio.h>
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <iostream>
#include <queue>
#include <stack>
#include <string>
#include <vector>
typedef long long int          ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;

struct Point {
    double x, y;
};

typedef Point Vector;

struct Segment {
    void set(double x1, double y1, double x2, double y2) {
        p1.x = x1;
        p1.y = y1;
        p2.x = x2;
        p2.y = y2;
    }
    Point p1, p2;
};

typedef Segment Line;

int func(double x1, double y1, double x2, double y2, double xp, double yp) {
    double naiseki, norm1, norm2, gaiseki;
    norm1   = sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
    norm2   = sqrt((xp - x1) * (xp - x1) + (yp - y1) * (yp - y1));
    naiseki = (xp - x1) * (x2 - x1) + (yp - y1) * (y2 - y1);
    gaiseki = (x2 - x1) * (yp - y1) - (xp - x1) * (y2 - y1);
    if (gaiseki > EPS) {
        return 1;
    } else if (gaiseki < -EPS) {
        return -1;
    }
    if (naiseki < -EPS) {
        return 2;
    }

    if (norm1 < norm2) {
        return -2;
    }
    return 0;
}

double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }

Point calc_minus(Point a, Point b) {
    Point ret;

    ret.x = a.x - b.x;
    ret.y = a.y - b.y;

    return ret;
}

double calc_len(Vector a) { return sqrt(a.x * a.x + a.y * a.y); }

double getDistanceLP(Line l, Point p) {
    return fabs(cross(calc_minus(l.p2, l.p1), calc_minus(p, l.p1)) /
                calc_len(calc_minus(l.p2, l.p1)));
}

double getDistanceSP(Segment s, Point p) {
    if (dot(calc_minus(s.p2, s.p1), calc_minus(p, s.p1)) < 0.0)
        return calc_len(calc_minus(p, s.p1));
    if (dot(calc_minus(s.p1, s.p2), calc_minus(p, s.p2)) < 0.0)
        return calc_len(calc_minus(p, s.p2));
    return getDistanceLP(s, p);
}

double getDistance(Segment s1, Segment s2) {
    return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
               min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

int main() {
    double x1, x2, x3, x4, y1, y2, y3, y4;
    int    q;
    scanf("%d", &q);

    for (int i = 0; i < q; i++) {
        scanf("%lf %lf %lf %lf %lf %lf %lf %lf", &x1, &y1, &x2, &y2, &x3, &y3,
              &x4, &y4);

        if (func(x1, y1, x2, y2, x3, y3) * func(x1, y1, x2, y2, x4, y4) <= 0 &&
            func(x3, y3, x4, y4, x1, y1) * func(x3, y3, x4, y4, x2, y2) <= 0) {
            printf("0.0000000000\n");
            continue;
        }

        Segment s1, s2;
        s1.set(x1, y1, x2, y2);
        s2.set(x3, y3, x4, y4);

        printf("%.10lf\n", getDistance(s1, s2));
    }

    return 0;
}