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 <bits/stdc++.h>
using namespace std;

typedef long double ld;

const ld EPS = 1e-9;
const ld INF = 1e10;
const ld PI = M_PI;

struct Point{
  ld x, y;
  Point(ld x, ld y):x(x), y(y){}
  Point(){}
};

Point operator+(const Point &a, const Point &b){
  return Point(a.x + b.x, a.y + b.y);
}
Point operator-(const Point &a, const Point &b){
  return Point(a.x - b.x, a.y - b.y);
}
Point operator*(const Point &a, const ld b){
  return Point(a.x * b, a.y * b);
}
Point operator*(const Point &a, const Point &b){
  return Point(a.x*b.x-a.y*b.y, a.x*b.y+a.y*b.x);
}
Point operator/(const Point &a, const ld b){
  return Point(a.x / b, a.y / b);
}

ld cross(const Point &a, const Point &b){
  return a.x*b.y - a.y*b.x;
}

ld dot(const Point &a, const Point &b){
  return a.x*b.x + a.y*b.y;
}

ld norm(const Point &a){
  return dot(a, a);
}

struct Line:vector<Point>{
  Line(Point a = Point(0, 0), Point b = Point(0, 0)){
    this->push_back(a);
    this->push_back(b);
  }
};

int ccw(Point a, Point b, Point c){
  b = b - a;
  c = c - a;
  if(cross(b, c) > EPS) return +1; // 反時計周り
  if(cross(b, c) < -EPS) return -1; // 時計周り
  if(dot(b, c) < 0) return +2; // c -- a -- b がこの順番に一直線上
  if(norm(b) < norm(c)) return -2; // a -- b -- c がこの順番に一直線上
  return 0; // a -- c -- b が一直線上
}

ld abs(const Point &a){
  return sqrt(norm(a));
}

Point projection(const Line &l, const Point &p){
  ld t = dot(p-l[0], l[1]-l[0]) / norm(l[0] - l[1]);
  return l[0] + (l[1] - l[0]) * t;
}

bool is_intersect_SS(const Line &s, const Line &t){
  return ccw(s[0], s[1], t[0]) * ccw(s[0], s[1], t[1]) <= 0 &&
    ccw(t[0], t[1], s[0]) * ccw(t[0], t[1], s[1]) <= 0;
}

bool is_intersect_SP(const Line &l, const Point &p){
  return ccw(l[0], l[1], p) == 0;
}

ld distance_SP(const Line &s, const Point &p){
  const Point r = projection(s, p);
  if(is_intersect_SP(s, r)) return abs(r - p);
  return min(abs(s[0] - p), abs(s[1] - p));
}

ld distance_SS(const Line &s, const Line &t){
  if(is_intersect_SS(s, t)) return 0;
  return min(min(distance_SP(s, t[0]), distance_SP(s, t[1])),
	     min(distance_SP(t, s[0]), distance_SP(t, s[1])));
}

int main(){  
  int q;
  cin >> q;
  while(q--){
    Point p0, p1;
    Line l1, l2;
    cin >> p0.x >> p0.y >> p1.x >> p1.y;
    l1 = Line(p0, p1);
    
    cin >> p0.x >> p0.y >> p1.x >> p1.y;
    l2 = Line(p0, p1);
    
    ld ans = distance_SS(l1, l2);
    printf("%.10Lf\n", ans);
    //printf("%.10Lf %.10Lf\n", ans.x, ans.y);
  }
  
  return 0;
}