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 <math.h>
#include <iostream>
using namespace std;

#define EPS (1e-10)
#define equals(a, b) (fabs(a - b) < EPS)

class Point{
public:
    double x, y;

    Point(double x_ = 0, double y_ = 0){
        x = x_;
        y = y_;
    }

    Point operator+ (Point p){
        return Point(x + p.x, y + p.y);
    };

    Point operator- (Point p){
        return Point(x - p.x, y - p.y);
    };

    Point operator* (double k){
        return Point(x * k, y * k);
    }

    Point operator/ (double k){
        return Point(x / k, y / k);
    }

    double norm(){
        return x * x + y * y;
    }

    double abs(){
        return sqrt(norm());
    }

    bool operator == (const Point &p) const{
        return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
    }
};

typedef Point Vector;

class Seg{
public:
    Point p1;
    Point p2;
    Seg(Point p1_, Point p2_){
        p1 = p1_;
        p2 = p2_;
    }
};

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

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

bool isParallel(Vector a, Vector b){
    return equals(cross(a, b), 0.0);
}

bool isOrthogonal(Vector a, Vector b){
    return equals(dot(a, b), 0.0);
}
;
double getCos(Vector a, Vector b){
    return dot(a, b) / (a.abs() * b.abs());
}

double dist(Point p1, Point p2){
    return sqrt(pow((p1.x - p2.x), 2) + pow((p1.y - p2.y), 2));
}

Point project(Seg s, Point p0){
    if(s.p1 == p0){
        return p0;
    }
    if(s.p2 == p0){
        return p0;
    }
    return s.p1 + (s.p2 - s.p1) / (s.p2 - s.p1).abs() * (p0 - s.p1).abs() * getCos(s.p2 - s.p1, p0 - s.p1);
}

Point reflect(Seg s, Point p0){
    Point p = project(s, p0);
    return p0 + (p - p0) * 2;
}


#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

int counterClockwise(Point p0, Point p1, Point p2){
    Vector v1 = p1 - p0;
    Vector v2 = p2 - p0;
    if(cross(v1, v2) > EPS) return COUNTER_CLOCKWISE;
    if(cross(v1, v2) < -EPS) return CLOCKWISE;
    if(dot(v1, v2) < -EPS) return ONLINE_BACK;
    if(v1.norm() < v2.norm()) return ONLINE_FRONT;
    return ON_SEGMENT;
}

bool intersect(Seg s1, Seg s2){
    int t1 = counterClockwise(s1.p1, s1.p2, s2.p1);
    int t2 = counterClockwise(s1.p1, s1.p2, s2.p2);
    int t3 = counterClockwise(s2.p1, s2.p2, s1.p1);
    int t4 = counterClockwise(s2.p1, s2.p2, s1.p2);
    if(t1 * t2 <= 0){
        if(t3 * t4 <= 0){
            return true;
        }
    }
    return false;
}

double getDistanceSP(Seg s, Point p0){
    if(dot(s.p2 - s.p1, p0 - s.p1) < 0.0) return (p0 - s.p1).abs();
    if(dot(s.p1 - s.p2, p0 - s.p2) < 0.0) return (p0 - s.p2).abs();
    return (project(s, p0) -  p0).abs();
}

double getDistance(Seg s1, Seg s2){
    if(intersect(s1, s2)){
        return 0.0;
    }
    return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
                min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

int main(){
    int q;
    scanf("%d", &q);

    for(int i = 0; i < q; i++){
        int xp0, yp0, xp1, yp1, xp2, yp2, xp3, yp3;
        scanf("%d", &xp0);
        scanf("%d", &yp0);
        scanf("%d", &xp1);
        scanf("%d", &yp1);
        scanf("%d", &xp2);
        scanf("%d", &yp2);
        scanf("%d", &xp3);
        scanf("%d", &yp3);

        printf("%.10f\n", getDistance(Seg(Point(xp0, yp0), Point(xp1, yp1)), Seg(Point(xp2, yp2), Point(xp3, yp3))));
    }

}