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  _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <math.h>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <math.h>
#include <iostream>
#include <random>
#include<map>
#include <iomanip>
#include <time.h>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
#include <cassert>
#include<fstream>
#include <unordered_map>
#include <cstdlib>
using namespace std;
#define Ma_PI 3.141592653589793
#define eps 0.00000001
#define LONG_INF 3000000000000000000
#define GOLD 1.61803398874989484820458
#define MAX_MOD 1000000007
#define MOD 998244353
#define REP(i,n) for(long long i = 0;i < n;++i)    
#define seg_size 524288
#include <complex>
typedef complex<double> P;
double dot(P a, P b) {
	return (a.real() * b.real() + a.imag() * b.imag());
}
double cross(P a, P b) {
	return (a.real() * b.imag() - a.imag() * b.real());
}
int ccw(P a, P b,P c) {
	P e = b - a;
	P f = c - a;
	if (cross(e, f) > eps) {
		return 1;
	}
	if (cross(e, f) < -eps) {
		return -1;
	}
	if (dot(e, f) < -eps) return 2;
	if (abs(e) < abs(f)) return -2;
	return 0;
}
bool intersect(P a, P b, P c, P d) {
	if (ccw(a, b, c) * ccw(a, b, d) <= 0) {
		if (ccw(c, d, a) * ccw(c, d, b) <= 0){
			return 1;
		}
	}
	return 0;
}
double getDistanceLP(P a, P b, P c) {
	return abs(cross(b - a, c - a) / abs(b - a));
}
double getDistanceSP(P a, P b, P c) {
	if (dot(b - a, c - a) < 0.0) return abs(c - a);
	if (dot(a - b, c - b) < 0.0) return abs(c - b);
	return getDistanceLP(a, b, c);
}
double getDistance(P a, P b, P c, P d) {
	if (intersect(a, b, c, d)) return 0.0;
	return min({ getDistanceSP(a, b, c), getDistanceSP(a, b, d), getDistanceSP(c, d, a), getDistanceSP(c, d, b) });
}
int main() {
	int query;
	cin >> query;
	REP(i, query) {
		double a, b, c, d, e, f, g, h;
		cin >> a >> b >> c >> d >> e >> f >> g >> h;
		cout << fixed << setprecision(10) << getDistance(P(a, b), P(c, d), P(e, f), P(g, h)) << endl;
	}
	return 0;
}