#include<bits/stdc++.h>
using namespace std;
#define int long long
#define lb long double
const int Max = 2*(int)1e3;
int mid[Max][Max],a[Max];
void solve() {
    lb x1,x2,x3,x4,x5,x6,x7,x8;
    lb a,b,c,d,r=0;
    cin>>x1>>x2>>x3>>x4>>x5>>x6>>x7>>x8;
    a=(x1+x3)/(lb)2.0,b=(x2+x4)/(lb)2.0,c=(x5+x7)/(lb)2.0,d=(x6+x8)/(lb)2.0;
    r=(x8-x6)*(x8-x6)+(x5-x7)*(x5-x7);
    r=sqrtl(2*r)/2;
    lb ans=fabs(c-a)+fabs(b-d)-r;
    cout<<fixed<<setprecision(12)<<ans<<"\n";
}
 signed main() {
#ifdef ACM_LOCAL
    freopen("data.in","r",stdin);
    freopen("data.out","w",stdout);
#endif
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t=1;
    cin>>t;
    while(t--) {
        solve();
    }
}