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 <iostream>
#include <algorithm>
#include <iomanip>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = uint32_t;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

using real = double;
real EPS = 1e-10;
struct Point {
    real x, y;
    Point& operator+=(const Point a) { x += a.x; y += a.y;  return *this; }
    Point& operator-=(const Point a) { x -= a.x; y -= a.y;  return *this; }
    Point& operator*=(const real k) { x *= k; y *= k;  return *this; }
    Point& operator/=(const real k) { x /= k; y /= k;  return *this; }
    Point operator+(const Point a) const {return Point(*this) += a; }
    Point operator-(const Point a) const {return Point(*this) -= a; }
    Point operator*(const real k) const {return Point(*this) *= k; }
    Point operator/(const real k) const {return Point(*this) /= k; }
    bool operator<(const Point &a) const { return (x != a.x ? x < a.x : y < a.y); }
    explicit Point(real a = 0, real b = 0) : x(a), y(b) {};
};

istream& operator>> (istream& s, Point& P){
    s >> P.x >> P.y;
    return s;
}

inline real dot(Point a, Point b){ return a.x*b.x + a.y*b.y; }
inline real cross(Point a, Point b){ return a.x*b.y - a.y*b.x; }
inline real abs(Point a){ return sqrt(dot(a, a)); }

static constexpr int COUNTER_CLOCKWISE = 1;
static constexpr int CLOCKWISE = -1;
static constexpr int ONLINE_BACK = 2;
static constexpr int ONLINE_FRONT = -2;
static constexpr int ON_SEGMENT = 0;

int ccw(Point a, Point b, Point c){
    b -= a; c -= a;
    if(cross(b, c) > EPS) return COUNTER_CLOCKWISE;
    if(cross(b, c) < -EPS) return CLOCKWISE;
    if(dot(b, c) < 0) return ONLINE_BACK;
    if(abs(b) < abs(c)) return ONLINE_FRONT;
    return ON_SEGMENT;
}
struct Segment {
    Point a, b;
    Segment(Point x, Point y) : a(x), b(y) {};
};

bool intersect(Segment s, Segment t){
    return (ccw(s.a, s.b, t.a)*ccw(s.a, s.b, t.b) <= 0 &&
            ccw(t.a, t.b, s.a)*ccw(t.a, t.b, s.b) <= 0);
}

double distance(Segment s, Point c){
    if(dot(s.b-s.a, c-s.a) < EPS) return abs(c-s.a);
    if(dot(s.a-s.b, c-s.b) < EPS) return abs(c-s.b);
    return abs(cross(s.b-s.a, c-s.a)) / abs(s.a-s.b);
}

double distance(Segment s, Segment t){
    if(intersect(s, t)) return 0.0;
    return min({distance(s, t.a), distance(s, t.b),
                distance(t, s.a), distance(t, s.b)});
}



Point crossPoint(Segment s, Segment t){
    real d1 = abs(cross(s.b-s.a, t.b-t.a));
    real d2 = abs(cross(s.b-s.a, s.b-t.a));
    if(d1 < EPS && d2 < EPS) return t.a;
    return t.a+(t.b-t.a)*d2/d1;
}

Point project(Segment s, Point p){
    Point Q = s.b-s.a;
    return s.a + Q*(dot(p-s.a, Q) / dot(Q, Q));
}

Point refrect(Segment s, Point p){
    Point Q = project(s, p);
    return Q*2-p;
}

bool isOrthogonal(Segment s, Segment t){
    return fabs(dot(s.b-s.a, t.b-t.a)) < EPS;
}

bool isparallel(Segment s, Segment t){
    return fabs(cross(s.b-s.a, t.b-t.a)) < EPS;
}


int main() {
    int q;
    cin >> q;
    for (int i = 0; i < q; ++i) {
        Point a, b, c, d;
        cin >> a >> b >> c >> d;
        Segment s(a, b), t(c, d);
        auto ans = distance(s, t);
        printf("%.10f\n", ans);
    }
    return 0;
}