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, a, b) for (int i = a; i < (int)(b); ++i)
#define rrep(i, a, b) for (int i = b - 1; i >= (int)(a); --i)

using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vd = vector<double>;
using vvi = vector<vi>;

constexpr int MOD = 1000000007;

// Data structures.
struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point(const Point& p) : x(p.x), y(p.y) {}

    Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }
    Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }
    Point operator*(double k) const { return Point(k * x, k * y); }
    Point operator/(double k) const { 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) < 1e-10 && fabs(y - p.y) < 1e-10; }

    static double norm(const Point& p) { return sqrt(p.x * p.x + p.y * p.y); }
    static double dot(const Point& p1, const Point& p2) { return p1.x * p2.x + p1.y * p2.y; }
    static double cross(const Point& p1, const Point& p2) { return p1.x * p2.y - p1.y * p2.x; }
};

struct Segment {
    Point s, t;
};

int ccw(const Point& p1, const Point& p2, const Point& p) {
    double cr = Point::cross(p2 - p1, p - p1);
    if (cr > 0) return 1;
    if (cr < 0) return -1;
    // p, p1, p2.
    if (Point::dot(p2 - p1, p - p1) < 0) { return 2; }
    // p1, p2, p.
    if (Point::dot(p - p2, p1 - p2) < 0) { return -2; }
    // p is in [p1, p2].
    return 0;
}

bool intersect(const Segment& s1, const Segment& s2) {
    bool ok1 = ccw(s1.s, s1.t, s2.s) * ccw(s1.s, s1.t, s2.t) <= 0;
    bool ok2 = ccw(s2.s, s2.t, s1.s) * ccw(s2.s, s2.t, s1.t) <= 0;
    return ok1 && ok2;
}

double distance(const Segment& s, const Point& p) {
    if (Point::dot(s.t - s.s, p - s.s) < 0) { return Point::norm(p - s.s); }
    if (Point::dot(s.s - s.t, p - s.t) < 0) { return Point::norm(p - s.t); }
    return abs(Point::cross(s.t - s.s, p - s.s)) / Point::norm(s.t - s.s);
}

double distance(const Segment& s1, const Segment& s2) {
    if (intersect(s1, s2)) { return 0; }
    double ans = DBL_MAX;
    ans = min(ans, distance(s1, s2.s));
    ans = min(ans, distance(s1, s2.t));
    ans = min(ans, distance(s2, s1.s));
    ans = min(ans, distance(s2, s1.t));
    return ans;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int q;
    cin >> q;

    rep(i, 0, q) {
        Segment s1, s2;
        cin >> s1.s.x >> s1.s.y >> s1.t.x >> s1.t.y;
        cin >> s2.s.x >> s2.s.y >> s2.t.x >> s2.t.y;
        printf("%.10f\n", distance(s1, s2));
    }

    return 0;
}