#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define db double
#define ldb long double
#define max(A,B) (A>B? A:B)
#define min(A,B) (A<B? A:B)
#define yes cout<<"Yes\n"
#define no cout<<"No\n"
#define pir(X) pair<X,X>
#define mpr(A,B) make_pair(A,B)
#define fr first
#define sc second
using namespace std;

void slv(){
    int x1,x2,y1,y2,x3,y3,x4,y4;
    cin>>x1>>y1>>x2>>y2;
    cin>>x3>>y3>>x4>>y4;
    db ans=(abs(x1+x2-x3-x4)+abs(y1+y2-y3-y4))/2.0;
    db r=0.5*sqrt((x4-x3)*(x4-x3)+(y3-y4)*(y3-y4));
    // cout<<ans<<' '<<r<<'\n';
    cout<<fixed<<setprecision(12)<<ans-sqrt(2)*r<<'\n';
}

void fst_IO(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
}

int main(){
    fst_IO();
    int T;
    cin>>T;
    while(T--){
        slv();
    }
    return 0;
}

/*

1
0 0 2 1
5 2 4 5
*/