1. **Abridged problem statement**

- You are given `n` points (oases) in the plane, all distinct, and not all collinear.
- A caravan travels from oasis `s` to oasis `t` at constant speed along a polyline going through oases.
- Among all routes from `s` to `t`, the caravan chooses one that minimizes the **maximum length of any segment** of the route (equivalently, minimizes the maximum time spent outside oases).
- You are given `q` queries `(s_i, t_i)`.  
  For each, output that minimal possible value of the longest segment on an optimal path from `s_i` to `t_i`, with absolute/relative error ≤ 1e-9.

---

2. **Detailed editorial**

### 2.1 Reformulation

- You have `n` points in the plane.
- You can move along straight segments connecting oases; you may choose any sequence of intermediate oases.
- For a path `s = v0, v1, ..., vk = t`, define its **bottleneck** as `max length(vi, v{i+1})`.
- Among all `s-t` paths, you want the minimum possible bottleneck. Call this value `ans(s, t)`.

If we define an undirected, complete graph on the oases with edge weights equal to Euclidean distances, the problem is:

> For each pair `(s, t)`, find the minimum possible maximum-edge-weight over all paths from `s` to `t` in this graph.

This is the classic **minimax path** or **minimum bottleneck path** problem.

### 2.2 MST minimax property

A key graph-theoretical fact:

> In a connected weighted undirected graph, for any two nodes `u, v`, if you take **any minimum spanning tree (MST)** of the graph, then the **unique path in the MST** from `u` to `v` has:
> 
> - maximum edge weight equal to the minimum possible maximum edge weight over all `u-v` paths in the original graph.

So `ans(s, t)` = maximum edge on the unique `s-t` path in the Euclidean MST.

Thus we need:

1. The Euclidean MST on `n` points.
2. For each query `(s, t)`, the maximum edge on the `s-t` path in this MST.

However, the input size can be large (up to around `10^5` points; original problem constraints are large) and the graph is **complete** (`O(n^2)` edges), which is too big.

We need a way to:
- Avoid enumerating all `n^2` edges, but
- Still build the MST correctly.

### 2.3 Euclidean MST via Delaunay/Voronoi

For points in the plane, the Euclidean MST is a subgraph of the **Delaunay triangulation** of the points.

- Delaunay triangulation edges have the property that for each edge, there exists an empty circumcircle touching the two endpoints and containing no other point inside.
- The Euclidean MST uses only Delaunay edges. Thus if we compute all Delaunay edges, we can run Kruskal on only these edges instead of on all `n^2` pairs.

The dual of the Voronoi diagram is the Delaunay triangulation:

- Given a Voronoi diagram of the sites (oases), connect two sites whose Voronoi cells share an edge. Those edges form the Delaunay triangulation.

So the strategy:

1. Compute the Voronoi diagram (Fortune’s sweep-line algorithm).
2. From it, obtain all Delaunay edges: every pair `(i, j)` of sites that are neighbors in the Voronoi diagram.
3. Run MST (Kruskal) using these edges.
4. Answer minimax path queries on the MST.

The provided solution implements step 1 via a custom `VoronoiDiagram` class using a sweep-line method; it returns all neighboring site pairs (`edges`).

### 2.4 Avoiding LCA / Heavy Preprocessing: Parallel Binary Search

We want, for each query `(s, t)`, the maximum edge weight on the path between them in the MST.

A natural approach is to build the MST, root it, and do LCA with binary lifting while maintaining maximum-edge-on-path. That would be `O((n + q) log n)` and works fine.

But the provided solution instead does:

- **Parallel binary search on the edge index during Kruskal-like DSU sweeps**.

Procedure:

1. Let `E` be the list of Delaunay edges between oases, sorted in nondecreasing order of squared Euclidean length.
2. Each query `i` will ultimately correspond to some index `pos_i` in this sorted `E` where `s_i` and `t_i` first become connected if we union edges from `0` upward.

Interpretation:

- If you process edges `E[0..k]`, DSU tells you which vertices are connected using edges of length ≤ `weight(E[k])`.
- For query `(s, t)`, if `s` and `t` are connected at step `k`, then `ans(s, t) ≤ length(E[k])`.
- The smallest `k` for which they are connected is exactly the maximum edge weight on their MST path, in terms of index.

So we want minimal `k` such that `s` and `t` are in the same DSU component when using edges `0..k`.

We can binary search this index for each query, but doing `q` independent binary searches `O(q log |E|)` and rebuild DSU each time (`O(|E|)` per binary search) would be too big: `O(q |E| log |E|)`.

Instead, we do **parallel binary search**:

- Maintain `low[i]` and `high[i]` (over edge indices) for each query `i`, the search range for the minimal connecting edge index.
- Repeatedly:
  - Build DSU from scratch, then scan edges `E[0..]` once.
  - For each edge index `e`, apply union; then process all queries whose current mid candidate equals `e`.
  - If, at index `e`, `s` and `t` are connected, we know the answer index is ≤ `e`, so `high[i] = e - 1`.
  - Otherwise `low[i] = e + 1`.
- Each iteration cuts the range roughly in half for each unresolved query.
- After `O(log |E|)` sweeps, all `low[i] > high[i]`, meaning we have determined the boundary index `pos_i = high[i] + 1`.

Total cost:

- About `O((|E| + q) log |E|)` DSU operations, which is feasible since `|E|` is linear in `n` for Delaunay triangulation.

Edge case: when `s_i == t_i`, answer is 0.0 regardless of the MST edges. The code handles this specially.

### 2.5 Geometry implementation details

The solution uses:

- `struct Point` with:
  - Coordinates `x, y` as `long double` (`coord_t`).
  - Basic vector operations, dot product `*`, cross product `^`, norm, rotate, etc.
  - Functions like `ccw`, `line_line_intersection`, `circumcenter`, etc.

`VoronoiDiagram`:

- Implements a beach-line based algorithm (Fortune's algorithm).
- Keeps a **beach line** as a `multiset<Arc>` ordered by the y-coordinate of the locus of each arc at the current sweep line `x`.
- Cloning the full correctness of Voronoi is complex, but the key:
  - It computes which sites are neighbors in the Voronoi diagram.
  - For each such neighbor pair `(i, j)`, it records an edge `(i, j)` in `edges`.

These edges are exactly the edges of the corresponding Delaunay triangulation up to some boundary issues, but good enough for MST.

Before computing the Voronoi diagram, the points are rotated by 1 radian about the origin to avoid degeneracies like aligned points leading to numeric instability.

After building the Voronoi diagram and extracted edges, the code:

1. Sorts `edges` by squared Euclidean distance.
2. Parallel-binary-searches over these sorted edges to answer queries.

Finally, to print answers:

- For each query `i`:
  - If `s == t`, print `0.0`.
  - Else, the smallest connecting index is `pos_i = high[i] + 1`.
  - Let that edge be `(u, v) = edges[pos_i]`.
  - Print Euclidean distance `|u - v|` with 10 decimal places.

Remember: Although we reason in terms of MST, the code *never explicitly builds the MST tree structure*; it only relies on the order of edges and connectivity in DSU to deduce the bottleneck edge needed for each pair.

---

3. **Provided C++ solution with detailed comments**

```cpp
#include <bits/stdc++.h>

using namespace std;

// Overload << for pair, for debugging / convenience (not central to the logic)
template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1, T2>& x) {
    return out << x.first << ' ' << x.second;
}

// Overload >> for pair, read two elements
template<typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& x) {
    return in >> x.first >> x.second;
}

// Overload >> for vector: read all elements
template<typename T>
istream& operator>>(istream& in, vector<T>& a) {
    for (auto& x: a) {
        in >> x;
    }
    return in;
};

// Overload << for vector: print all elements separated by spaces
template<typename T>
ostream& operator<<(ostream& out, const vector<T>& a) {
    for (auto x: a) {
        out << x << ' ';
    }
    return out;
};

// Use long double for geometric coordinates for more precision
using coord_t = long double;

// 2D point / vector type with many geometric utilities
struct Point {
    static constexpr coord_t eps = 1e-12; // epsilon for floating comparisons

    coord_t x, y;

    Point(coord_t x = 0, coord_t y = 0) : x(x), y(y) {}

    // Basic vector arithmetic
    Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }
    Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }
    Point operator*(coord_t c) const { return Point(x * c, y * c); }
    Point operator/(coord_t c) const { return Point(x / c, y / c); }

    // Dot product
    coord_t operator*(const Point& p) const { return x * p.x + y * p.y; }
    // Cross product (scalar 2D)
    coord_t operator^(const Point& p) const { return x * p.y - y * p.x; }

    // Comparison operators mainly for sorting/ordering
    bool operator==(const Point& p) const { return x == p.x && y == p.y; }
    bool operator!=(const Point& p) const { return x != p.x || y != p.y; }
    bool operator<(const Point& p) const {
        // Sort by x, then y
        return x != p.x ? x < p.x : y < p.y;
    }
    bool operator>(const Point& p) const {
        return x != p.x ? x > p.x : y > p.y;
    }
    bool operator<=(const Point& p) const {
        return x != p.x ? x < p.x : y <= p.y;
    }
    bool operator>=(const Point& p) const {
        return x != p.x ? x > p.x : y >= p.y;
    }

    // Squared norm of vector
    coord_t norm2() const { return x * x + y * y; }
    // Euclidean norm
    coord_t norm() const { return sqrt(norm2()); }
    // Polar angle
    coord_t angle() const { return atan2(y, x); }

    // Rotate by angle a (radians) around origin
    Point rotate(coord_t a) const {
        return Point(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
    }

    // Perpendicular vector (-y, x)
    Point perp() const { return Point(-y, x); }
    // Unit vector in same direction
    Point unit() const { return *this / norm(); }
    // Outward normal unit vector
    Point normal() const { return perp().unit(); }

    // Project point p onto this vector considered as direction from origin
    Point project(const Point& p) const {
        return *this * (*this * p) / norm2();
    }

    // Reflect point p across the line defined by this vector from origin
    Point reflect(const Point& p) const {
        return *this * 2 * (*this * p) / norm2() - p;
    }

    // I/O operators
    friend ostream& operator<<(ostream& os, const Point& p) {
        return os << p.x << ' ' << p.y;
    }
    friend istream& operator>>(istream& is, Point& p) {
        return is >> p.x >> p.y;
    }

    // ccw test: orientation of (a, b, c)
    // returns:
    //  0 if collinear
    //  1 if counter-clockwise
    // -1 if clockwise
    friend int ccw(const Point& a, const Point& b, const Point& c) {
        coord_t v = (b - a) ^ (c - a);
        if (-eps <= v && v <= eps) {
            return 0;
        } else if (v > 0) {
            return 1;
        } else {
            return -1;
        }
    }

    // Check if point p lies on segment ab (with eps tolerance)
    friend bool point_on_segment(
        const Point& a, const Point& b, const Point& p
    ) {
        return ccw(a, b, p) == 0 &&
               p.x >= min(a.x, b.x) - eps &&
               p.x <= max(a.x, b.x) + eps &&
               p.y >= min(a.y, b.y) - eps &&
               p.y <= max(a.y, b.y) + eps;
    }

    // Check if point p is inside or on triangle abc
    friend bool point_in_triangle(
        const Point& a, const Point& b, const Point& c, const Point& p
    ) {
        int d1 = ccw(a, b, p);
        int d2 = ccw(b, c, p);
        int d3 = ccw(c, a, p);
        // On same side (or on edges) wrt all triangle edges
        return (d1 >= 0 && d2 >= 0 && d3 >= 0) ||
               (d1 <= 0 && d2 <= 0 && d3 <= 0);
    }

    // Intersection of lines (a1,b1) and (a2,b2), assuming not parallel
    friend Point line_line_intersection(
        const Point& a1, const Point& b1, const Point& a2, const Point& b2
    ) {
        return a1 +
               (b1 - a1) * ((a2 - a1) ^ (b2 - a2)) / ((b1 - a1) ^ (b2 - a2));
    }

    // Check if 2D vectors a and b are collinear
    friend bool collinear(const Point& a, const Point& b) {
        return abs(a ^ b) < eps;
    }

    // Circumcenter of triangle abc
    friend Point circumcenter(const Point& a, const Point& b, const Point& c) {
        Point mid_ab = (a + b) / 2.0;          // midpoint of ab
        Point mid_ac = (a + c) / 2.0;          // midpoint of ac
        Point perp_ab = (b - a).perp();        // perpendicular direction to ab
        Point perp_ac = (c - a).perp();        // perpendicular direction to ac
        // Intersection of perpendicular bisectors => circumcenter
        return line_line_intersection(
            mid_ab, mid_ab + perp_ab, mid_ac, mid_ac + perp_ac
        );
    }
};

// Fortune-style Voronoi diagram (sweep line) to get Delaunay edges
class VoronoiDiagram {
  private:
    static constexpr coord_t INF = 1e100;   // large number representing infinity
    static inline coord_t sweep_x;          // current x position of sweep line

    // An "arc" on the beach line
    struct Arc {
        mutable Point p, q;  // arc corresponds to site p; q is right breakpoint
        mutable int id = 0;  // event id (negative for circle event)
        mutable int i;       // index of site in vertices array (-1 = fake arc)

        Arc(const Point& p, const Point& q, int i) : p(p), q(q), i(i) {}

        // Compute y-coordinate at given x of this arc's locus
        coord_t get_y(coord_t x) const {
            if (q.y == INF) {
                // Infinite arc, treat y as +INF
                return INF;
            }
            // Slightly shift x to avoid numeric issues
            x += Point::eps;

            // Midpoint of chord (p, q)
            Point mid = (p + q) / 2.0;
            // Direction perpendicular to segment pq
            Point dir = (p - mid).perp();

            // D = (x - p.x)*(x - q.x) appears in formula for intersection
            coord_t D = (x - p.x) * (x - q.x);
            if (D < 0) {
                // No real intersection => arc not present at this x, treat as -INF
                return -INF;
            }

            if (abs(dir.y) < Point::eps) {
                // degenerate: horizontal directive; choose ±INF by side
                return (x < mid.x) ? -INF : INF;
            }

            // Derived formula for y on the beach line at x
            return mid.y +
                   ((mid.x - x) * dir.x + sqrtl(D) * dir.norm()) / dir.y;
        }

        // For multiset ordering: compare y-coordinates at current sweep_x
        bool operator<(const coord_t& y) const { return get_y(sweep_x) < y; }

        bool operator<(const Arc& o) const {
            return get_y(sweep_x) < o.get_y(sweep_x);
        }
    };

    using Beach = multiset<Arc, less<>>;  // beach line as ordered set of arcs

    // Circle event on the sweep line
    struct Event {
        coord_t x;         // x-coordinate where event happens
        int id;            // id>=0: site event, id<0: circle event
        Beach::iterator it;// beach line iterator for circle event

        Event(coord_t x, int id, Beach::iterator it) : x(x), id(id), it(it) {}

        // priority_queue in C++ is max-heap, so invert comparison
        bool operator<(const Event& e) const { return x > e.x; }
    };

    Beach beach_line;                       // current beach line
    vector<pair<Point,int>> vertices;       // (point, original index)
    priority_queue<Event> event_queue;      // events
    vector<pair<int,int>> edges;            // Delaunay edges (indices into pnts)
    vector<bool> valid;                     // circle events validity
    int n;                                  // number of sites
    int next_vertex_id;                     // for negative ids of circle events

    // Try to schedule or update a circle event for beach arc "it"
    void update_vertex_event(Beach::iterator it) {
        if (it->i == -1) {
            // Fake arc (bounding one), don't schedule circle events
            return;
        }

        // Invalidate any previous circle event for this arc
        valid[-it->id] = false;

        auto prev_it = prev(it);
        // If the three sites (prev_it->p, it->p, it->q) are collinear, no circle
        if (collinear(it->q - it->p, prev_it->p - it->p)) {
            return;
        }

        // Assign new negative id for this event
        it->id = --next_vertex_id;
        valid.push_back(true);

        // Compute circumcenter of the three sites
        Point center = circumcenter(it->p, it->q, prev_it->p);
        // The x of circle event: center.x + radius (where sweep line hits)
        coord_t event_x = center.x + (center - it->p).norm();

        // Check that circle event is valid relative to neighbors
        bool valid_event =
            event_x > sweep_x - Point::eps &&
            prev_it->get_y(event_x) + Point::eps > it->get_y(event_x);
        if (valid_event) {
            event_queue.push(Event(event_x, it->id, it));
        }
    }

    // Add an edge between site indices i and j (if both real)
    void add_edge(int i, int j) {
        if (i == -1 || j == -1) {
            // -1 indicates bounding arcs; ignore them
            return;
        }
        // Translate from local vertex index to global original index
        edges.push_back({vertices[i].second, vertices[j].second});
    }

    // Process a site event: new site with index i
    void add_point(int i) {
        Point p = vertices[i].first;

        // Find arc under point p by y-coordinate at sweep_x
        auto split_it = beach_line.lower_bound(p.y);
        // Insert new arc for current site: arc (p, split_it->p)
        auto new_it = beach_line.insert(split_it, Arc(p, split_it->p, i));
        // Insert left part of split arc: arc (split_it->p, p)
        auto prev_it =
            beach_line.insert(new_it, Arc(split_it->p, p, split_it->i));

        // The old arc is now split into 2 arcs; connect new site i to old site
        add_edge(i, split_it->i);

        // Recompute circle events for affected arcs
        update_vertex_event(prev_it);
        update_vertex_event(new_it);
        update_vertex_event(split_it);
    }

    // Process a circle event: remove arc "it" from beach line
    void remove_arc(Beach::iterator it) {
        auto prev_it = prev(it);
        auto next_it = next(it);

        // Remove middle arc
        beach_line.erase(it);
        // Merge breakpoints: prev's right endpoint becomes next's site
        prev_it->q = next_it->p;

        // Delaunay edge between the two sites
        add_edge(prev_it->i, next_it->i);

        // Update circle events for neighbors
        update_vertex_event(prev_it);
        update_vertex_event(next_it);
    }

  public:
    // Construct Voronoi generator from given points
    // fix_coordinates=true rotates points to avoid degeneracies
    VoronoiDiagram(const vector<Point>& points, bool fix_coordinates = true) {
        n = points.size();
        vertices.resize(n);

        // Store points along with their original indices
        for (int i = 0; i < n; i++) {
            vertices[i] = {points[i], i};
        }

        if (fix_coordinates && n > 0) {
            // Rotate around origin by 1.0 radians to avoid degenerate cases
            for (int i = 0; i < n; i++) {
                vertices[i].first = vertices[i].first.rotate(1.0);
            }
        }

        // Sort points by x, then y (due to operator< implementation)
        sort(vertices.begin(), vertices.end());
    }

    // Compute Voronoi diagram and return list of Delaunay edges (site index pairs)
    vector<pair<int, int>> compute(coord_t X = 1e9) {
        edges.clear();
        beach_line.clear();
        event_queue = priority_queue<Event>();

        // Extend bounding box: we add two infinite arcs spanning big range
        X *= 3;
        // Left infinite arc
        beach_line.insert(Arc(Point(-X, -X), Point(-X, X), -1));
        // Right infinite arc
        beach_line.insert(Arc(Point(-X, X), Point(INF, INF), -1));

        // Create site events for each point (x-coordinate is the event key)
        for (int i = 0; i < n; i++) {
            event_queue.push(Event(vertices[i].first.x, i, beach_line.end()));
        }

        next_vertex_id = 0;    // negative ids will start from -1
        valid.assign(1, false);// valid[0] dummy; real circle events at indices >=1

        // Process events in increasing x (priority_queue uses reversed order)
        while (!event_queue.empty()) {
            Event e = event_queue.top();
            event_queue.pop();
            sweep_x = e.x;  // current sweep line x

            if (e.id >= 0) {
                // Site event: insert new site
                add_point(e.id);
            } else if (valid[-e.id]) {
                // Circle event: remove corresponding arc if still valid
                remove_arc(e.it);
            }
        }

        // Edges now contain all Delaunay edges (by original indices)
        return edges;
    }

    // Access already-computed edges
    const vector<pair<int, int>>& get_edges() const { return edges; }
};

// Disjoint Set Union / Union-Find structure for Kruskal & connectivity queries
class DSU {
  public:
    int n;              // number of elements
    vector<int> par;    // parent array
    vector<int> sz;     // size array (for union by size)

    DSU(int _n = 0) { init(_n); }

    // Initialize DSU for [0.._n]
    void init(int _n) {
        n = _n;
        par.assign(n + 1, 0);
        sz.assign(n + 1, 0);
        for (int i = 0; i <= n; i++) {
            par[i] = i;
            sz[i] = 1;
        }
    }

    // Find with path compression
    int root(int u) { return par[u] = ((u == par[u]) ? u : root(par[u])); }

    // Check if two nodes are in the same component
    bool connected(int x, int y) { return root(x) == root(y); }

    // Union by size. Returns new root.
    int unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) {
            return x;
        }
        if (sz[x] > sz[y]) {
            swap(x, y);
        }
        par[x] = y;
        sz[y] += sz[x];
        return y;
    }

    // Extract components (not used in this solution)
    vector<vector<int>> components() {
        vector<vector<int>> comp(n + 1);
        for (int i = 0; i <= n; i++) {
            comp[root(i)].push_back(i);
        }
        return comp;
    }
};

// Global variables: number of points and queries, list of points and queries
int n, q;
vector<Point> pnts;                 // list of oases
vector<pair<int, int>> queries;     // queries (0-based indices)

// Read input
void read() {
    cin >> n;
    pnts.resize(n);
    for (auto& p: pnts) {
        cin >> p.x >> p.y;
    }

    cin >> q;
    queries.resize(q);
    for (auto& query: queries) {
        cin >> query;
        // convert to 0-based indices
        query.first--;
        query.second--;
    }
}

void solve() {
    // We need the Euclidean MST; then ans(s,t) is
    // the maximum edge on the unique path between s and t in the MST.
    // Instead of building MST + LCA, we do parallel binary search over
    // edge indices sorted by weight, using DSU connectivity.

    // Build Voronoi diagram (actually returns Delaunay graph edges)
    auto voronoi = VoronoiDiagram(pnts);
    auto edges = voronoi.compute();

    // Sort edges by squared distance between endpoints
    sort(
        edges.begin(), edges.end(),
        [&](pair<int, int> edge1, pair<int, int> edge2) {
            return (pnts[edge1.first] - pnts[edge1.second]).norm2() <
                   (pnts[edge2.first] - pnts[edge2.second]).norm2();
        }
    );

    int m = (int)edges.size();

    // For each query, maintain search range [low[i], high[i]] of edge index
    vector<int> low(q, 0), high(q, m - 1);

    while (true) {
        bool has_queries = false;

        // queries_at_pos[e] will store all queries whose current mid == e
        vector<vector<int>> queries_at_pos(m);

        // Assign queries to positions based on their current mid
        for (int i = 0; i < q; i++) {
            if (low[i] <= high[i]) {
                has_queries = true;
                int mid = (low[i] + high[i]) / 2;
                queries_at_pos[mid].push_back(i);
            }
        }

        // If no active queries remain, we're done
        if (!has_queries) {
            break;
        }

        // DSU over n nodes (0 .. n-1)
        DSU dsu(n);

        // Sweep through edges from smallest to largest
        for (int i = 0; i < m; i++) {
            // Add this edge to DSU
            dsu.unite(edges[i].first, edges[i].second);

            // Process all queries assigned to this edge index
            for (int query: queries_at_pos[i]) {
                // Check if endpoints are connected if we use edges [0..i]
                if (dsu.connected(queries[query].first, queries[query].second)) {
                    // They connect at or before i, so answer index <= i
                    high[query] = i - 1;
                } else {
                    // They are still disconnected, answer index > i
                    low[query] = i + 1;
                }
            }
        }
    }

    // Now for each query, low[i] == high[i] + 1, and that is the
    // smallest index where s and t are connected.
    for (int i = 0; i < q; i++) {
        if (queries[i].first == queries[i].second) {
            // s == t; no travel, answer 0
            cout << setprecision(10) << fixed << 0.0 << endl;
        } else {
            // Smallest connecting edge index is high[i] + 1
            auto edge = edges[high[i] + 1];
            // Distance between its endpoints (actual Euclidean distance)
            cout << setprecision(10) << fixed
                 << (pnts[edge.first] - pnts[edge.second]).norm() << endl;
        }
    }
}

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

    int T = 1;
    // Problem has a single test case; code is structured to support multiple.
    // cin >> T;
    for (int test = 1; test <= T; test++) {
        read();
        // cout << "Case #" << test << ": ";
        solve();
    }

    return 0;
}
```

---

4. **Python solution with detailed comments**

Below is a Python implementation that follows the same high-level idea, but it does **not implement a full Voronoi diagram** (too long/complex in Python here). Instead, it uses a Delaunay triangulation from `scipy.spatial` if available. If not allowed in your environment, you would need to port a triangulation algorithm; conceptually it’s the same after you get triangulation edges.

If external libraries are not allowed in the judge, you must re-implement Delaunay/Voronoi in Python, which is quite lengthy. Here, I’ll assume we can use `scipy`.

```python
import sys
import math
from collections import defaultdict

# NOTE: This version uses scipy.spatial.Delaunay to obtain the Delaunay
# triangulation and extract edges, then does the same parallel binary search
# on these edges. On an online judge without scipy this would not run.

try:
    from scipy.spatial import Delaunay
except ImportError:
    Delaunay = None  # placeholder, see note above


def read_ints():
    return list(map(int, sys.stdin.readline().split()))


class DSU:
    """Disjoint Set Union / Union-Find with path compression and union by size."""
    def __init__(self, n):
        self.par = list(range(n))  # parent array
        self.sz = [1] * n          # size array

    def root(self, x):
        """Find the representative (root) of x with path compression."""
        if self.par[x] != x:
            self.par[x] = self.root(self.par[x])
        return self.par[x]

    def unite(self, a, b):
        """Union the sets containing a and b."""
        a = self.root(a)
        b = self.root(b)
        if a == b:
            return a
        # union by size
        if self.sz[a] > self.sz[b]:
            a, b = b, a
        self.par[a] = b
        self.sz[b] += self.sz[a]
        return b

    def connected(self, a, b):
        """Check if a and b are in the same component."""
        return self.root(a) == self.root(b)


def main():
    data = sys.stdin.read().strip().split()
    it = iter(data)

    n = int(next(it))
    points = []
    for _ in range(n):
        x = float(next(it))
        y = float(next(it))
        points.append((x, y))

    q = int(next(it))
    queries = []
    for _ in range(q):
        s = int(next(it)) - 1  # to 0-based
        t = int(next(it)) - 1
        queries.append((s, t))

    # Handle small / degenerate cases quickly
    if n <= 1:
        # Only one or zero oases; answer is always 0
        out = []
        for s, t in queries:
            out.append("0.0000000000")
        sys.stdout.write("\n".join(out))
        return

    if Delaunay is None:
        raise RuntimeError("Delaunay triangulation (scipy) not available.")

    # Build Delaunay triangulation: this is a triangulation of the convex hull
    # That gives us all edges used by the Euclidean MST.
    coords = points  # list of (x, y)
    tri = Delaunay(coords)

    # Extract edges from Delaunay triangles.
    # Each simplex is a triangle [i, j, k]; all edges (i,j), (j,k), (k,i) are present.
    edge_set = set()
    for simplex in tri.simplices:
        i, j, k = simplex
        if i > j:
            i, j = j, i
        if j > k:
            j, k = k, j
        if i > j:
            i, j = j, i
        # Add the three undirected edges (i,j), (j,k), (i,k)
        edge_set.add((i, j))
        edge_set.add(tuple(sorted((j, k))))
        edge_set.add(tuple(sorted((i, k))))

    edges = list(edge_set)

    # Sort edges by squared Euclidean distance
    def sqdist(e):
        u, v = e
        dx = coords[u][0] - coords[v][0]
        dy = coords[u][1] - coords[v][1]
        return dx * dx + dy * dy

    edges.sort(key=sqdist)
    m = len(edges)

    # Prepare parallel binary search ranges
    low = [0] * q
    high = [m - 1] * q

    # Precompute which queries have s == t (answer = 0)
    same_node = [queries[i][0] == queries[i][1] for i in range(q)]

    # If s == t, we don't need to binary search at all, but we keep the structure;
    # we will just ignore them at the end.
    while True:
        has_queries = False
        queries_at_pos = [[] for _ in range(m)]

        # Assign each active query an edge index = current mid
        for i in range(q):
            if same_node[i]:
                # This query's answer is 0, no need to refine
                continue
            if low[i] <= high[i]:
                has_queries = True
                mid = (low[i] + high[i]) // 2
                queries_at_pos[mid].append(i)

        if not has_queries:
            break

        # DSU on [0..n-1]
        dsu = DSU(n)

        # Sweep edges from smallest to largest
        for ei in range(m):
            u, v = edges[ei]
            dsu.unite(u, v)

            # Process queries that are checking this mid index
            for qi in queries_at_pos[ei]:
                s, t = queries[qi]
                if dsu.connected(s, t):
                    # If s and t are connected with edges [0..ei], answer index <= ei
                    high[qi] = ei - 1
                else:
                    # Still disconnected, answer index > ei
                    low[qi] = ei + 1

    # Now low[i] == high[i] + 1 for non-degenerate queries.
    # The first index where s and t become connected is pos = high[i] + 1.
    out_lines = []
    for i in range(q):
        if same_node[i]:
            # s == t
            out_lines.append(f"{0.0:.10f}")
        else:
            pos = high[i] + 1
            u, v = edges[pos]
            dx = coords[u][0] - coords[v][0]
            dy = coords[u][1] - coords[v][1]
            dist = math.hypot(dx, dy)
            out_lines.append(f"{dist:.10f}")

    sys.stdout.write("\n".join(out_lines))


if __name__ == "__main__":
    main()
```

**Important note:**  
If you need a pure-standard-library Python solution for a judge, you must implement (or port) a Delaunay triangulation or Voronoi-based method like the C++ code does. The rest of the approach (sorting edges, DSU, parallel binary search) stays essentially the same.

---

5. **Compressed editorial**

- The caravan chooses routes that minimize its maximum time outside oases, i.e., minimize the maximum segment length along the path.
- Model all oases as vertices of a complete Euclidean graph (weight = distance). For a path, define its bottleneck as the max edge weight.
- For any two nodes `s, t`, the minimal possible bottleneck over all `s-t` paths is exactly the maximum edge on the **unique** `s-t` path in a **minimum spanning tree** (MST) of the graph (minimax/MST property).
- The Euclidean MST is a subgraph of the **Delaunay triangulation**. So if we compute the Delaunay triangulation (via Voronoi diagram), we only need to consider those edges for MST, not all `O(n^2)` pairs.
- The code uses a custom Voronoi implementation (`VoronoiDiagram`) to get all pairs of points whose Voronoi cells share an edge, which are exactly Delaunay edges.
- These edges are sorted by squared length. Instead of explicitly building the MST tree and running LCA, the solution uses **parallel binary search** over the edge list:
  - For each query, we binary search the smallest edge index `k` such that `s` and `t` become connected if we union edges `0..k` in that order.
  - Each binary search step is done for all queries simultaneously in `O(|E| + q)` time by:
    - Resetting DSU.
    - Sweeping edges in increasing index, uniting endpoints.
    - At each index `i`, answering connectivity for all queries whose current mid = `i` and narrowing their [low, high] range.
  - Complexity: `O((|E| + q) log |E|)` DSU operations.
- Finally, for query `i`, the minimal bottleneck distance is the length of `edges[pos_i]`, where `pos_i = high[i] + 1` after the search. If `s_i == t_i`, answer is `0.0`.