#include <bits/stdc++.h>
#define ll long long
#define ls p << 1
#define rs p << 1 | 1
#define rep(i, a, b) for(int i = (int)a; i <= (int)b; i ++)
#define per(i, a, b) for(int i = (int)a; i >= (int)b; i --)\

void solve() {
    double a, b, c, d;
    std :: cin >> a >> b >> c >> d;
    double x1 = (a + c) / 2, y1 = (b + d) / 2;
    double r1 = sqrt((a - c) * (a - c) + (b - d) * (b - d));
    std :: cin >> a >> b >> c >> d;
    double x2 = (a + c) / 2, y2 = (b + d) / 2;
    double r2 = sqrt((a - c) * (a - c) + (b - d) * (b - d));

    std :: cout << std :: fixed << std :: setprecision(15) << fabs(x1 - x2) + fabs(y1 - y2) - sqrt(0.5) * r2 << "\n";
}

int main() {
    std :: ios :: sync_with_stdio(false);
    std :: cin.tie(0);
    int T;
    std :: cin >> T;
    while(T --) solve();
    return 0;
}