#include #include #include #include using namespace std; const long long INF = 1LL << 60; using Pt = pair; #define x first #define y second long long cross(const Pt &a, const Pt &b, const Pt &o = Pt(0, 0)) { return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x); } template vector convex_hull(It lo, It hi) { int k = 0; if (hi - lo <= 1) { return vector(lo, hi); } vector res(2 * distance(lo, hi)); sort(lo, hi); for (It it = lo; it != hi; ++it) { while (k >= 2 && cross(res[k - 1], *it, res[k - 2]) >= 0) { k--; } res[k++] = *it; } int t = k + 1; for (It it = hi - 2; it != lo - 1; --it) { while (k >= t && cross(res[k - 1], *it, res[k - 2]) >= 0) { k--; } res[k++] = *it; } res.resize(k - 1); return res; } int N; long long K, D; long long solve() { cin >> N >> K >> D; vector P(N); for (int i = 0; i < N; i++) { cin >> P[i].x >> P[i].y; } auto hull = convex_hull(P.begin(), P.end()); int V = hull.size(); // Find start/end. int start = -1, dest = -1; for (int i = 0; i < V; i++) { if (hull[i] == P[0]) { start = i; } else if (hull[i] == P[N - 1]) { dest = i; } } // Dijkstra in O(V^2) time / O(V) space. vector vis(V); vector dist(V, INF); dist[start] = 0; while (true) { int u = -1; long long mindist = INF; for (int i = 0; i < V; i++) { if (!vis[i] && mindist > dist[i]) { u = i; mindist = dist[i]; } } if (mindist == INF || u == dest) { break; } vis[u] = true; for (int v = 0; v < V; v++) { long long d = (hull[u].x - hull[v].x) * (hull[u].x - hull[v].x) + (hull[u].y - hull[v].y) * (hull[u].y - hull[v].y); if (!vis[v] && d <= D*D && dist[v] > dist[u] + max(K, d)) { dist[v] = dist[u] + max(K, d); } } } return dist[dest] < INF ? dist[dest] : -1; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }