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>
#include <complex>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define loop(i, x, n) for (int i = (x); i < (n); i++)
#define all(v) (v).begin(), (v).end()
#define EQ(a, b) (abs((a) - (b)) < EPS)
#define int long long
#define INF 1e9
#define MOD 1e9 + 7
using namespace std;

template<typename T> void cmin(T &a, T b) { a = min(a, b); }
template<typename T> void cmax(T &a, T b) { a = max(a, b); }

using P = complex<double>;
const double PI = acos(-1);
const double EPS = 1e-9;
// P p(a,b)=a+bi -> 点p(a,b)
namespace std {
  bool operator<(const P &a, const P &b) { return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b); }
  bool operator==(const P &a, const P &b) { return a.real() == b.real() && a.imag() == b.imag(); }
} // namespace std

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a);
    push_back(b);
  }
};
//内積
double dot(P a, P b) { return real(conj(a) * b); }
//外戚
double cross(P a, P b) { return imag(conj(a) * b); }

//点pから直線aに推薦を下ろした足
P projection(L a, P p) {
  double t = dot(p - a[0], a[0] - a[1]) / norm(a[0] - a[1]);
  return a[0] + t * (a[0] - a[1]);
}

//点の位置関係
int ccw(P a, P b, P c) {
  b -= a;
  c -= a;
  if (cross(b, c) > 0) return +1; // counter clockwise
  if (cross(b, c) < 0) return -1; // clockwise
  if (dot(b, c) < 0) return +2; // c--a--b on line
  if (norm(b) < norm(c)) return -2; // a--b--c on line
  return 0;
}

bool intersectSS(const L &s, const L &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 intersectSP(const L &s, const P &p) { // triangle inequality
  return abs(s[0] - p) + abs(s[1] - p) - abs(s[1] - s[0]) < EPS;
}
double distanceSP(const L &s, const P &p) {
  const P r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s[0] - p), abs(s[1] - p));
}

double distanceSS(const L &s, const L &t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])), min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
signed main() {
  int q;
  cin >> q;
  while (q--) {
    int a, b, c, d, e, f, g, h;
    cin >> a >> b >> c >> d >> e >> f >> g >> h;
    L l(P(a, b), P(c, d)), m(P(e, f), P(g, h));
    double ans = distanceSS(l, m);
    printf("%.10lf\n", ans);
  }
  return 0;
}