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;
using ll = long long;
const ll INF = 1e16;
const ll mod = 1000000007;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

template<class T> inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template<class T> inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
int ctoi(char c) {
  if (c >= '0' && c <= '9') {
    return c - '0';
  }
  return 0;
}
ll factorial(ll n) {
  if (n == 1) {
    return 1;
  }
  ll ans = factorial(n-1);
  return ans*n;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a%b);
}
ll lcm(ll a, ll b) {
  return (a/gcd(a, b))*b;
}
bool is_prime(ll n) {
  for (ll i = 2; i*i <= n; i++) {
    if (n%i == 0) return false;
  }
  return n != 1;
}
ll mod_pow(ll x, ll n, ll mod) {
  if (n == 0) return 1;
  ll res = mod_pow(x*x%mod, n/2, mod);
  if (n & 1) res = res * x % mod;
  return res;
}

#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 a) { return Point(a * x, a * y); }
  Point operator / (double a) { return Point(x / a, y / a); }
  double norm() { return x*x + y*y; }
  double abs() { return pow(norm(), 0.5); }
  bool operator < (const Point &p) const {
    return x != p.x ? x < p.x : y < p.y;
  }
};
typedef Point Vector;
struct Segment {
  Point p1, p2;
};
typedef Segment Line;
double dot(Vector a, Vector b) {
  return a.x * b.x + a.y * b.y;
}
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p-s.p1, base) / base.norm();
  return s.p1 + base * r;
}
Point reflect(Segment s, Point p) {
  return p + (project(s, p) - p) * 2.0;
}
double cross(Point a, Point b) {
  return a.x*b.y - a.y*b.x;
}
ll ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0, b = p2 - p0;
  if (cross(a, b) > EPS) return 1;
  if (cross(a, b) < -EPS) return -1;
  if (dot(a, b) < -EPS) return 2;
  if (a.norm() < b.norm()) return -2;
  return 0;
}
bool intersect(Point p1, Point p2, Point p3, Point p4) {
  return ccw(p1, p2, p3)*ccw(p1, p2, p4)<=0 && ccw(p3, p4, p1)*ccw(p3, p4, p2)<=0;
}
bool intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
double getDistanceLP(Line l, Point p) {
  return abs(cross(l.p2-l.p1, p-l.p1) / (l.p2-l.p1).abs());
}
double getDistanceSP(Segment s, Point p) {
  if (dot(s.p2-s.p1, p-s.p1) < 0.0) return (p - s.p1).abs();
  if (dot(s.p1-s.p2, p-s.p2) < 0.0) return (p - s.p2).abs();
  return getDistanceLP(s, p);
}
double getDistance(Segment s1, Segment 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() {
  ll n;
  cin >> n;
  cout << fixed << setprecision(10);
  rep(i, n) {
    Point p1, p2, p3, p4;
    cin >> p1.x >> p1.y >> p2.x >> p2.y >> p3.x >> p3.y >> p4.x >> p4.y;
    Segment s1, s2;
    s1.p1 = p1; s1.p2 = p2; s2.p1 = p3; s2.p2 = p4;
    cout << getDistance(s1, s2) << endl;
  }
}