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:
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; ++i)
using namespace std;

const double EPS = 1e-10;
double add(double a, double b) {
    if(abs(a+b) < EPS*(abs(a)+abs(b))) return 0;
    return a+b;
}
struct Vector {
    double x, y;
    Vector() {}
    Vector(double x, double y):x(x), y(y) {}
    Vector operator+(Vector v) {return Vector(add(x, v.x), add(y, v.y));}
    Vector operator-(Vector v) {return Vector(add(x, -v.x), add(y, -v.y));}
    Vector operator*(double d) {return Vector(x*d, y*d);}
    Vector operator/(double d) {return Vector(x/d, y/d);}
    double dot(Vector v) {return add(x*v.x, y*v.y);}
    double cross(Vector v) {return add(x*v.y, -y*v.x);}
};
istream &operator>>(istream &is, Vector &v) {return is >> v.x >> v.y;}
ostream &operator<<(ostream &os, const Vector &v) {return os << v.x << ' ' << v.y;}
double sqdist(Vector &v, const Vector &u) {return (v-u).dot(v-u);}
//線分v2-v1上にあるか
bool on_seg(Vector &v1,Vector &v2, const Vector &p) {
    return (v1-p).cross(v2-p) == 0 && (v1-p).dot(v2-p) <= 0;
}
//v1-v2とu1-u2の交点
Vector intersection(Vector &v1,Vector &v2,Vector &u1,Vector &u2) {
    assert((v1-v2).cross(u1-u2)); //2直線が平行だとだめ
    return v1 + (v2-v1)*((u2-u1).cross(u1-v1)/(u2-u1).cross(v2-v1));
}
//p2-p1へのQの投影
Vector projection(Vector &p1,Vector &p2,Vector &Q) {
    return p1+(p2-p1)*(Q-p1).dot(p2-p1)/sqdist(p1, p2);
}
//p1-p2を軸としたQの線対称移動
Vector reflection(Vector &p1,Vector &p2,Vector &Q) {
    return projection(p1, p2, Q)*2-Q;
}
bool cmp_x(const Vector &v, const Vector &u) {
    if(v.x != u.x) return v.x < u.x;
    return v.y < u.y;
}
//頂点数nの頂点集合vv
vector<Vector> convex_hull(vector<Vector> &vv, int n) {
    sort(vv.begin(), vv.end(), cmp_x);
    int k = 0;
    vector<Vector> res(n*2);
    for(int i = 0; i < n; i++) {
        while(k > 1 && (res[k-1]-res[k-2]).cross(vv[i]-res[k-1]) <= 0) k--;
        res[k++] = vv[i];
    }
    for(int i = n-2, t = k; i >= 0; i--) {
        while(k > t && (res[k-1]-res[k-2]).cross(vv[i]-res[k-1]) <= 0) k--;
        res[k++] = vv[i];
    }
    res.resize(k-1);
    return res;
}
//点と線の距離
double distpl(Vector &p0, Vector &p1, Vector &Q) {
    Vector pp = projection(p0, p1, Q);
    return sqrt(sqdist(pp, Q));
}
//線分と線分の距離
double distss(Vector &p0, Vector &p1, Vector &p2, Vector &p3) {
    if((p0-p1).cross(p2-p3) != 0) {
        Vector p = intersection(p0, p1, p2, p3);
        if(on_seg(p0, p1, p) and on_seg(p2, p3, p)) {
            return 0.0;
        }
    }
    double res = min({sqdist(p0, p2), sqdist(p0, p3), sqdist(p1, p2), sqdist(p1, p3)});
    Vector pp0, pp1, pp2, pp3;
    pp2 = projection(p0, p1, p2);
    pp3 = projection(p0, p1, p3);
    pp0 = projection(p2, p3, p0);
    pp1 = projection(p2, p3, p1);
    if(on_seg(p0, p1, pp2)) res = min(res, sqdist(pp2, p2));
    if(on_seg(p0, p1, pp3)) res = min(res, sqdist(pp3, p3));
    if(on_seg(p2, p3, pp0)) res = min(res, sqdist(pp0, p0));
    if(on_seg(p2, p3, pp1)) res = min(res, sqdist(pp1, p1));
    res = sqrt(res);
    return res;
}

signed main() {
    cout << fixed << setprecision(13);
    Vector p0, p1, p2, p3;
    int q;
    cin >> q;
    while(q--) {
        cin >> p0 >> p1 >> p2 >> p3;
        cout << distss(p0, p1, p2, p3) << endl;
    }

}