#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
double dis(double a1,double b1,double a2,double b2)
{
    return (a1-a2)*(a1-a2)+(b1-b2)*(b1-b2);
}
double manh(double a1,double b1,double a2,double b2)
{
    if(a1<a2) swap(a1,a2);
    if(b1<b2) swap(b1,b2);
    return a1-a2+b1-b2;
}
void solve()
{
    double a1,a2,a3,a4,b1,b2,b3,b4;
    cin>>a1>>b1>>a2>>b2;
    cin>>a3>>b3>>a4>>b4;
    double x=manh(1.0*(a1+a2)/2.0,1.0*(b1+b2)/2.0,1.0*(a3+a4)/2.0,1.0*(b3+b4)/2.0);
    // cout<<x<<endl;
    printf("%.10lf\n",x-sqrt(dis(a3, b3,a4,b4)/2));
    //cout<<<<endl;
}
signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int T;
    cin>>T;
    while(T--)
    {
        solve();
    }
    return 0;
}