#include <bits/stdc++.h>
using namespace std;
#define double long double
const int N = 1e6 + 9;
const int mod = 1e9 + 7;
#define inf 2e18

void solve()
{
    int x11, x12, y11, y12, x21, x22, y21, y22;
    cin >> x11 >> y11 >> x12 >> y12;
    cin >> x21 >> y21 >> x22 >> y22;

    double a = (x11 + x12) * 1.0 / 2, b = (y11 + y12) * 1.0 / 2;
    double c = (x21 + x22) * 1.0 / 2, d = (y21 + y22) * 1.0 / 2;

    double res = fabs(a - c) + fabs(b - d);

    double s = sqrt((x22 - x21) * (x22 - x21) + (y21 - y22) * (y21 - y22)) * 1.0 / 2 * sqrt(2.000);

    cout << fixed << setprecision(20) << res - s << '\n';
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    int _ = 1;
    cin >> _;
    while (_--)
        solve();
    return 0;
}