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>
using namespace std;

#define EPS 1e-10

class point {
public:
	double x, y;
	point() {}
	point( double x_, double y_ ) : 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 *( int a ) { return point( x * a, y * a ); }
};

class segment {
public:
	point p1, p2;
	segment() {}
};

double dot( point a, point b ) { return a.x * b.x + a.y * b.y; }
double cross( point a, point b ) { return a.x * b.y - a.y * b.x; }
double norm( point a ) { return a.x * a.x + a.y * a.y; }

double distance( segment s, point p )
{
	if( dot( s.p2 - s.p1, p - s.p1 ) < 0 ) return sqrt( norm( p - s.p1 ) );
	if( dot( s.p1 - s.p2, p - s.p2 ) < 0 ) return sqrt( norm( p - s.p2 ) );;
	return fabs( cross( s.p2 - s.p1, p - s.p1 ) / sqrt( norm( s.p2 - s.p1 ) ) );
}

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

bool intersect( segment s1, segment s2 )
{
	return ccw( s1.p1, s1.p2, s2.p1 ) * ccw( s1.p1, s1.p2, s2.p2 ) <= 0 &&
			ccw( s2.p1, s2.p2, s1.p1 ) * ccw( s2.p1, s2.p2, s1.p2 ) <= 0;
}

double distance( segment s1, segment s2 )
{
	if( intersect( s1, s2 ) ) return 0;
	return min( { distance( s1, s2.p1 ), distance( s1, s2.p2 ),
					distance( s2, s1.p1 ), distance( s2, s1.p2 ) } );
}

int main()
{
	int q;
	cin >> q;
	for( int i = 0; i < q; i++ ) {
		segment s1, s2;
		cin >> s1.p1.x >> s1.p1.y >> s1.p2.x >> s1.p2.y >> s2.p1.x >> s2.p1.y >> s2.p2.x >> s2.p2.y;
		cout << fixed << setprecision(10) << distance( s1, s2 ) << endl;
	}
}