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:

//be naame khodaa
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef complex<ld> PT;
typedef pair<PT, PT> LS;
#define F first
#define S second
#define X real()
#define Y imag()

inline int in(){int x, y; y = scanf("%d", &x); return x; }

const int N = -1;
const ld EPS = 1e-12;

const int LEFT = 0, RIGHT = 1, BACK = 2, FRONT = 3, ON = 4;

inline bool Geq(ld a, ld b){ return a + EPS > b; }
inline bool Grt(ld a, ld b){ return a > b + EPS; }
inline bool Leq(ld a, ld b){ return a < b + EPS; }
inline bool Lss(ld a, ld b){ return a + EPS < b; }
inline bool Equ(ld a, ld b){ return Geq(a, b) && Geq(b, a); }

istream& operator>> (istream& is, complex<ld>& p){
	ld val;
	is >> val;
	p.real(val);
	is >> val;
	p.imag(val);
	return is;
}

ld dot(PT a, PT b){ return real(conj(a)*b); }
ld cross(PT a, PT b){ return imag(conj(a)*b); }
ld sqlen(PT a){ return dot(a, a); }
ld len(PT a){ return sqrt(sqlen(a)); }

PT proj(PT a, PT b, PT c){
	b -= a, c -= a;
	return a + b*real(c/b);
}

PT reflect(PT a, PT b, PT c){
	b -= a, c -= a;
	return a + conj(c/b)*b;
}

PT rotate(PT a, PT b, ld theta){
	return (b-a)*polar<ld>(1, theta) + a;
}

int relpos(PT a, PT b, PT c){
	b -= a, c -= a;
	c /= b;
	if (Grt(c.imag(), 0)) return RIGHT;
	if (Lss(c.imag(), 0)) return LEFT;
	if (Lss(c.real(), 0)) return BACK;
	if (Grt(c.real(), 1)) return FRONT;
	return ON;
}

int side(PT a, PT b, PT c){
	b -= a, c -= a;
	ld cr = (c/b).Y;
	return Grt(cr, 0) ? 1 : (Lss(cr, 0) ? -1 : 0);
}

//If LineSegments Intersect
bool intersect(PT a, PT b, PT c, PT d){
	int as = side(c, d, a), bs = side(c, d, b), cs = side(a, b, c), ds = side(a, b, d);
	if (as && as == bs || cs && cs == ds) return false;
	else if (as || bs || cs || ds) return true;
	for (int j = 0; j < 2; j++, swap(a, c), swap(b, d)){
		ld mx = min(a.X, b.X), Mx = max(a.X, b.X), my = min(a.Y, b.Y), My = max(a.Y, b.Y);
		for (int k = 0; k < 2; k++, swap(c, d))
			if (Geq(c.X, mx) && Leq(c.X, Mx) && Geq(c.Y, my) && Leq(c.Y, My))
				return true;
	}
	return false;
}

//LineSegments Intersection (intersect is true)
PT intersection(PT a, PT b, PT c, PT d){
	ld c1 = cross(b-a, c-a), c2 = cross(b-a, d-a);
	return (c1*d - c2*c)/(c1-c2);
}

ld distLSP(PT a, PT b, PT c){
	int pos = relpos(a, b, proj(a, b, c));
	if (pos == BACK) return len(c-a);
	if (pos == FRONT) return len(c-b);
	b -= a, c -= a;
	return abs(imag(c/b))*len(b);
}

ld distLS(PT a, PT b, PT c, PT d){
	if (intersect(a, b, c, d)) return 0;
	return min(min(distLSP(a, b, c), distLSP(a, b, d)), min(distLSP(c, d, a), distLSP(c, d, b)));
}

int main(){	
	cout << setprecision(10) << fixed;
	for (int i = in(); i; i--){
		PT a, b, c, d;
		cin >> a >> b >> c >> d;
		cout << distLS(a, b, c, d) << '\n';;
	}
	return 0;
}