#include<bits/stdc++.h>
using namespace std;
using ll = long long ;
using d = double;
constexpr ll inf = 0x3f3f3f3f3f3f3f3f;
int main () {
    cin.tie(nullptr)->sync_with_stdio(false);
    cout.tie(nullptr)->sync_with_stdio(false);
                                                                                                         
    int tt = 1;
    cin >> tt;
    while (tt--) {
        int a, b, c, d;
        cin >> a >> b >> c >> d;
        double x11 = a, y11 = b, x12 = c, y12 = d;
        double c1x = (x11 + x12) / 2.0;
        double c1y = (y11 + y12) / 2.0;
        double r1 = sqrt( (c1x - x11) * (c1x - x11) + (c1y - y11) * (c1y - y11) );

        cin >> a >> b >> c >> d;
        double x21 = a, y21 = b, x22 = c, y22 = d;
        double c2x = (x21 + x22) / 2.0;
        double c2y = (y21 + y22) / 2.0;
        double r2 = sqrt( (c2x - x21) * (c2x - x21) + (c2y - y21) * (c2y - y21) );

        double px = c2x, py = c2y;
        if (c1x < c2x) {
            // cout << "!!!\n";
            px -= r2 * sqrt(2) / 2.0;
        } else {
            px += r2 * sqrt(2) / 2.0;
        }
        if (c1y < c2y) {
            // cout << "!!!\n";
            py -= r2 * sqrt(2) / 2.0;
        } else {
            py += r2 * sqrt(2) / 2.0;
        }
        double ans = abs(px - c1x) + abs(py - c1y);
        cout << fixed << setprecision(10) << ans << "\n";
    }
    // d a = 7.0 / 2.0 - sqrt(5) / 2.0;
    // d b = 3.0 - sqrt(5) / 2.0;
    // cout << a + b << "\n";

}
/*
C1 (1 , 1 / 2)  r = sqrt(5) / 2
C2 (9 / 2 , 7 / 2)  r = sqrt(10) / 2

*/