#include<bits/stdc++.h>
using ll = long long;
const int mod = 998244353;
#define pdd std::pair<double, double> 
#define db double
#define x first
#define y second

pdd operator- (const pdd a, const pdd b) {
    return {a.x - b.x, a.y - b.y};
}

db dis(pdd a, pdd b) {
    pdd c = a - b;
    return sqrt(c.x * c.x + c.y * c.y);
}

void solve() {
    db x1l, y1l, x1r, y1r;
    db x2l, y2l, x2r, y2r;
    std::cin >> x1l >> y1l >> x1r >> y1r >> x2l >> y2l >> x2r >> y2r;
    pdd o1 = {(x1l + x1r) / 2, (y1l + y1r) / 2};
    pdd o2 = {(x2l + x2r) / 2, (y2l + y2r) / 2};
    
    db r1 = dis({x1l, y1l}, {x1r, y1r}) / 2;
    db r2 = dis({x2l, y2l}, {x2r, y2r}) / 2;
    db T = sqrt(2);
    std::cout << std::fixed << std::setprecision(15);
    if (o1.x > o2.x && o1.y > o2.y) {
        std::cout << o1.x + o1.y - (o2.x + o2.y + T * r2) << "\n";
    } 
    else if (o1.x < o2.x && o1.y < o2.y) {
        std::cout << o2.x + o2.y - T * r2 - (o1.x + o1.y) << "\n";
    }
    else if (o1.x < o2.x && o1.y > o2.y) {
        std::cout << (o1.y - o1.x) - (o2.y - o2.x + T * r2) << "\n";
    }
    else {
        std::cout << o2.y - o2.x - T * r2 - (o1.y - o1.x) << "\n";
    }
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int t = 1;
    std::cin >> t;

    while (t--) {
        solve();
    }
    return 0;
}