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>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repr(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define FORR(i, m, n) for (int i = (m); i >= (n); --i)
#define equals(a, b) (fabs((a) - (b)) < EPS)
using namespace std;
typedef long long ll;
const ll mod = 1000000007;
const ll mod2 = 998244353;
const int INF = 1000000005;
const long double EPS = 1e-10;

class Point {
  public:
  long double x, y;

  Point(long double x = 0, long 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 * (long double k) {
    return Point(x * k, y * k);
  }

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

  bool operator < (const Point &p) const {
    return x != p.x ? x < p.x : y < p.y;
  }

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

long double norm(Point p) {
  return p.x * p.x + p.y * p.y;
}

long double abs(Point p) {
  return sqrt(norm(p));
}

long double dot(Point p1, Point p2) {
  return p1.x * p2.x + p1.y * p2.y;
}

long double cross(Point p1, Point p2) {
  return p1.x * p2.y - p1.y * p2.x;
}

int ccw(Point p0, Point p1, Point p2) {
  Point v1 = p1 - p0, v2 = p2 - p0;
  if (cross(v1, v2) > 0) return 1;
  else if (cross(v1, v2) < 0) return -1;
  else if (dot(v1, v2) < 0) return 2;
  else if (norm(v1) < norm(v2)) return -2;
  else 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);
}

long double getDistanceLP(Point p1, Point p2, Point p3) {
  return fabs(cross(p2-p1, p3-p1) / abs(p2-p1));
}

long double getDistanceSP(Point p1, Point p2, Point p3) {
  if (dot(p2-p1, p3-p1) < 0) return abs(p3-p1);
  else if (dot(p1-p2, p3-p2) < 0) return abs(p3-p2);
  else return getDistanceLP(p1, p2, p3);
}

long double getDistanceTS(Point p1, Point p2, Point p3, Point p4) {
  if (intersect(p1, p2, p3, p4)) return 0;
  long double ans = INF;
  ans = min(ans, getDistanceSP(p1, p2, p3));
  ans = min(ans, getDistanceSP(p1, p2, p4));
  ans = min(ans, getDistanceSP(p3, p4, p1));
  ans = min(ans, getDistanceSP(p3, p4, p2));
  return ans;
}

int main() {
  int q;
  cin >> q;
  Point p0, p1, p2, p3;
  rep(i, q) {
    cin >> p0.x >> p0.y >> p1.x >> p1.y >> p2.x >> p2.y >> p3.x >> p3.y;
    cout << setprecision(15) << getDistanceTS(p0, p1, p2, p3) << endl;
  }

  
  return 0;
}